LMFDB - Embedded newform 62.6.d.b.47.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,6,Mod(33,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, 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("62.33"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	62.d (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,24] 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:	$9.94379682840$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			47.1
Character	$\chi$	$=$	62.47
Dual form			62.6.d.b.33.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.23607 - 2.35114i) q^{2} +(-21.7909 - 15.8320i) q^{3} +(4.94427 - 15.2169i) q^{4} -35.9579 q^{5} -107.740 q^{6} +(17.1597 - 52.8123i) q^{7} +(-19.7771 - 60.8676i) q^{8} +(149.100 + 458.882i) q^{9} +(-116.362 + 84.5421i) q^{10} +(-55.4932 + 170.791i) q^{11} +(-348.655 + 253.312i) q^{12} +(2.25748 + 1.64016i) q^{13} +(-68.6390 - 211.249i) q^{14} +(783.555 + 569.286i) q^{15} +(-207.108 - 150.473i) q^{16} +(514.865 + 1584.59i) q^{17} +(1561.39 + 1134.42i) q^{18} +(-651.898 + 473.631i) q^{19} +(-177.786 + 547.168i) q^{20} +(-1210.05 + 879.154i) q^{21} +(221.973 + 683.162i) q^{22} +(-875.134 - 2693.39i) q^{23} +(-532.697 + 1639.47i) q^{24} -1832.03 q^{25} +11.1616 q^{26} +(1993.42 - 6135.12i) q^{27} +(-718.797 - 522.236i) q^{28} +(202.188 - 146.898i) q^{29} +3874.11 q^{30} +(-5225.09 - 1152.21i) q^{31} -1024.00 q^{32} +(3913.21 - 2843.11i) q^{33} +(5391.74 + 3917.33i) q^{34} +(-617.028 + 1899.02i) q^{35} +7719.95 q^{36} -12107.4 q^{37} +(-996.011 + 3065.41i) q^{38} +(-23.2256 - 71.4811i) q^{39} +(711.142 + 2188.67i) q^{40} +(-6462.24 + 4695.09i) q^{41} +(-1848.79 + 5690.00i) q^{42} +(2533.26 - 1840.52i) q^{43} +(2324.53 + 1688.87i) q^{44} +(-5361.31 - 16500.4i) q^{45} +(-9164.53 - 6658.42i) q^{46} +(14431.1 + 10484.8i) q^{47} +(2130.79 + 6557.89i) q^{48} +(11102.5 + 8066.42i) q^{49} +(-5928.58 + 4307.36i) q^{50} +(13867.9 - 42681.0i) q^{51} +(36.1197 - 26.2425i) q^{52} +(-6214.61 - 19126.6i) q^{53} +(-7973.69 - 24540.5i) q^{54} +(1995.42 - 6141.27i) q^{55} -3553.93 q^{56} +21704.0 q^{57} +(308.915 - 950.743i) q^{58} +(-17901.6 - 13006.3i) q^{59} +(12536.9 - 9108.58i) q^{60} -54767.6 q^{61} +(-19617.7 + 8556.30i) q^{62} +26793.1 q^{63} +(-3313.73 + 2407.57i) q^{64} +(-81.1743 - 58.9766i) q^{65} +(5978.85 - 18401.0i) q^{66} +58730.1 q^{67} +26658.2 q^{68} +(-23571.8 + 72546.5i) q^{69} +(2468.11 + 7596.07i) q^{70} +(-9183.34 - 28263.4i) q^{71} +(24982.3 - 18150.7i) q^{72} +(-25365.8 + 78068.0i) q^{73} +(-39180.4 + 28466.2i) q^{74} +(39921.6 + 29004.7i) q^{75} +(3984.04 + 12261.6i) q^{76} +(8067.59 + 5861.44i) q^{77} +(-243.222 - 176.711i) q^{78} +(8451.28 + 26010.4i) q^{79} +(7447.18 + 5410.69i) q^{80} +(-45715.4 + 33214.2i) q^{81} +(-9873.43 + 30387.3i) q^{82} +(-29931.0 + 21746.2i) q^{83} +(7395.17 + 22760.0i) q^{84} +(-18513.5 - 56978.6i) q^{85} +(3870.48 - 11912.1i) q^{86} -6731.54 q^{87} +11493.1 q^{88} +(-30638.1 + 94294.5i) q^{89} +(-56144.3 - 40791.3i) q^{90} +(125.358 - 91.0781i) q^{91} -45311.9 q^{92} +(95617.7 + 107831. i) q^{93} +71351.5 q^{94} +(23440.9 - 17030.8i) q^{95} +(22313.9 + 16212.0i) q^{96} +(25684.2 - 79047.8i) q^{97} +54893.6 q^{98} -86646.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{2} - 2 q^{3} - 96 q^{4} - 4 q^{5} + 8 q^{6} - 246 q^{7} + 384 q^{8} - 572 q^{9} + 596 q^{10} - 62 q^{11} - 32 q^{12} - 935 q^{13} + 984 q^{14} + 3343 q^{15} - 1536 q^{16} - 311 q^{17} + 428 q^{18}+ \cdots - 347058 q^{99}+O(q^{100}) $ 24 * q + 24 * q^2 - 2 * q^3 - 96 * q^4 - 4 * q^5 + 8 * q^6 - 246 * q^7 + 384 * q^8 - 572 * q^9 + 596 * q^10 - 62 * q^11 - 32 * q^12 - 935 * q^13 + 984 * q^14 + 3343 * q^15 - 1536 * q^16 - 311 * q^17 + 428 * q^18 - 4094 * q^19 + 2416 * q^20 + 149 * q^21 + 248 * q^22 + 2719 * q^23 - 192 * q^24 - 484 * q^25 + 5320 * q^26 - 2303 * q^27 + 4704 * q^28 + 13353 * q^29 + 10408 * q^30 - 7117 * q^31 - 24576 * q^32 - 1904 * q^33 + 844 * q^34 + 5436 * q^35 + 21728 * q^36 - 55872 * q^37 - 25404 * q^38 + 19008 * q^39 - 9664 * q^40 - 9557 * q^41 + 49004 * q^42 - 3760 * q^43 + 10928 * q^44 - 2407 * q^45 - 16256 * q^46 + 44908 * q^47 + 768 * q^48 - 62986 * q^49 + 23676 * q^50 + 24658 * q^51 - 14960 * q^52 - 41007 * q^53 + 9212 * q^54 - 74553 * q^55 + 6144 * q^56 - 2368 * q^57 + 41068 * q^58 - 31734 * q^59 + 53488 * q^60 - 192700 * q^61 + 18348 * q^62 + 393066 * q^63 - 24576 * q^64 - 96202 * q^65 - 108464 * q^66 + 122022 * q^67 + 16704 * q^68 + 125538 * q^69 - 21744 * q^70 - 106651 * q^71 + 6848 * q^72 + 41543 * q^73 - 190012 * q^74 + 22898 * q^75 + 101616 * q^76 - 230254 * q^77 + 100148 * q^78 + 224694 * q^79 - 38144 * q^80 + 108929 * q^81 + 68828 * q^82 - 80770 * q^83 - 196016 * q^84 - 339465 * q^85 - 81160 * q^86 - 314616 * q^87 + 79488 * q^88 + 258277 * q^89 + 80848 * q^90 + 448172 * q^91 - 217056 * q^92 + 539557 * q^93 + 41888 * q^94 + 295692 * q^95 + 2048 * q^96 + 100250 * q^97 - 284736 * q^98 - 347058 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	3.23607	−	2.35114i	0.572061	−	0.415627i
$2$	3.23607	−	2.35114i	0.572061	−	0.415627i
$3$	−21.7909	−	15.8320i	−1.39789	−	1.01562i	−0.994947	−	0.100398i	$-0.967988\pi$
$3$	−21.7909	−	15.8320i	−1.39789	−	1.01562i	−0.402940	−	0.915226i	$-0.632012\pi$
$4$	4.94427	−	15.2169i	0.154508	−	0.475528i
$5$	−35.9579			−0.643234			−0.321617	−	0.946870i	$-0.604226\pi$
$5$	−35.9579			−0.643234			−0.321617	+	0.946870i	$0.604226\pi$
$6$	−107.740			−1.22180
$7$	17.1597	−	52.8123i	0.132363	−	0.407371i	−0.862808	−	0.505532i	$-0.831296\pi$
$7$	17.1597	−	52.8123i	0.132363	−	0.407371i	0.995170	+	0.0981616i	$0.0312962\pi$
$8$	−19.7771	−	60.8676i	−0.109254	−	0.336249i
$9$	149.100	+	458.882i	0.613579	+	1.88840i
$10$	−116.362	+	84.5421i	−0.367969	+	0.267345i
$11$	−55.4932	+	170.791i	−0.138280	+	0.425581i	−0.996086	−	0.0883925i	$-0.971827\pi$
$11$	−55.4932	+	170.791i	−0.138280	+	0.425581i	0.857806	+	0.513973i	$0.171827\pi$
$12$	−348.655	+	253.312i	−0.698944	+	0.507812i
$13$	2.25748	+	1.64016i	0.00370481	+	0.00269170i	0.589636	−	0.807669i	$-0.299271\pi$
$13$	2.25748	+	1.64016i	0.00370481	+	0.00269170i	−0.585931	+	0.810361i	$0.699271\pi$
$14$	−68.6390	−	211.249i	−0.0935946	−	0.288054i
$15$	783.555	+	569.286i	0.899169	+	0.653285i
$16$	−207.108	−	150.473i	−0.202254	−	0.146946i
$17$	514.865	+	1584.59i	0.432087	+	1.32983i	0.896043	+	0.443968i	$0.146430\pi$
$17$	514.865	+	1584.59i	0.432087	+	1.32983i	−0.463956	+	0.885858i	$0.653570\pi$
$18$	1561.39	+	1134.42i	1.13588	+	0.825262i
$19$	−651.898	+	473.631i	−0.414281	+	0.300993i	−0.775333	−	0.631553i	$-0.782418\pi$
$19$	−651.898	+	473.631i	−0.414281	+	0.300993i	0.361051	+	0.932546i	$0.382418\pi$
$20$	−177.786	+	547.168i	−0.0993851	+	0.305876i
$21$	−1210.05	+	879.154i	−0.598764	+	0.435027i
$22$	221.973	+	683.162i	0.0977785	+	0.300931i
$23$	−875.134	−	2693.39i	−0.344949	−	1.06164i	−0.961611	−	0.274416i	$-0.911515\pi$
$23$	−875.134	−	2693.39i	−0.344949	−	1.06164i	0.616662	−	0.787228i	$-0.288485\pi$
$24$	−532.697	+	1639.47i	−0.188778	+	0.581000i
$25$	−1832.03			−0.586250
$26$	11.1616			0.00323813
$27$	1993.42	−	6135.12i	0.526247	−	1.61962i
$28$	−718.797	−	522.236i	−0.173265	−	0.125884i
$29$	202.188	−	146.898i	0.0446436	−	0.0324355i	−0.565240	−	0.824927i	$-0.691216\pi$
$29$	202.188	−	146.898i	0.0446436	−	0.0324355i	0.609883	+	0.792491i	$0.291216\pi$
$30$	3874.11			0.785903
$31$	−5225.09	−	1152.21i	−0.976539	−	0.215341i
$31$	−5225.09	−	1152.21i	−0.976539	−	0.215341i
$32$	−1024.00			−0.176777
$33$	3913.21	−	2843.11i	0.625530	−	0.454474i
$34$	5391.74	+	3917.33i	0.799892	+	0.581156i
$35$	−617.028	+	1899.02i	−0.0851402	+	0.262035i
$36$	7719.95			0.992791
$37$	−12107.4			−1.45394			−0.726970	−	0.686669i	$-0.759072\pi$
$37$	−12107.4			−1.45394			−0.726970	+	0.686669i	$0.759072\pi$
$38$	−996.011	+	3065.41i	−0.111894	+	0.344373i
$39$	−23.2256	−	71.4811i	−0.00244515	−	0.00752540i
$40$	711.142	+	2188.67i	0.0702759	+	0.216287i
$41$	−6462.24	+	4695.09i	−0.600376	+	0.436199i	−0.846012	−	0.533163i	$-0.821003\pi$
$41$	−6462.24	+	4695.09i	−0.600376	+	0.436199i	0.245636	+	0.969362i	$0.421003\pi$
$42$	−1848.79	+	5690.00i	−0.161721	+	0.497725i
$43$	2533.26	−	1840.52i	0.208934	−	0.151799i	−0.478397	−	0.878144i	$-0.658782\pi$
$43$	2533.26	−	1840.52i	0.208934	−	0.151799i	0.687331	+	0.726344i	$0.258782\pi$
$44$	2324.53	+	1688.87i	0.181010	+	0.131512i
$45$	−5361.31	−	16500.4i	−0.394675	−	1.21468i
$46$	−9164.53	−	6658.42i	−0.638580	−	0.463956i
$47$	14431.1	+	10484.8i	0.952919	+	0.692336i	0.951495	−	0.307663i	$-0.0995470\pi$
$47$	14431.1	+	10484.8i	0.952919	+	0.692336i	0.00142327	+	0.999999i	$0.499547\pi$
$48$	2130.79	+	6557.89i	0.133486	+	0.410829i
$49$	11102.5	+	8066.42i	0.660586	+	0.479944i
$50$	−5928.58	+	4307.36i	−0.335371	+	0.243661i
$51$	13867.9	−	42681.0i	0.746596	−	2.29779i
$52$	36.1197	−	26.2425i	0.00185241	−	0.00134585i
$53$	−6214.61	−	19126.6i	−0.303896	−	0.935294i	−0.980087	−	0.198568i	$-0.936371\pi$
$53$	−6214.61	−	19126.6i	−0.303896	−	0.935294i	0.676192	−	0.736726i	$-0.263629\pi$
$54$	−7973.69	−	24540.5i	−0.372113	−	1.14525i
$55$	1995.42	−	6141.27i	0.0889462	−	0.273748i
$56$	−3553.93			−0.151439
$57$	21704.0			0.884815
$58$	308.915	−	950.743i	0.0120578	−	0.0371102i
$59$	−17901.6	−	13006.3i	−0.669517	−	0.486433i	0.200346	−	0.979725i	$-0.435793\pi$
$59$	−17901.6	−	13006.3i	−0.669517	−	0.486433i	−0.869863	+	0.493293i	$0.835793\pi$
$60$	12536.9	−	9108.58i	0.449584	−	0.326642i
$61$	−54767.6			−1.88451			−0.942257	−	0.334890i	$-0.891301\pi$
$61$	−54767.6			−1.88451			−0.942257	+	0.334890i	$0.891301\pi$
$62$	−19617.7	+	8556.30i	−0.648142	+	0.282688i
$63$	26793.1			0.850494
$64$	−3313.73	+	2407.57i	−0.101127	+	0.0734732i
$65$	−81.1743	−	58.9766i	−0.00238306	−	0.00173140i
$66$	5978.85	−	18401.0i	0.168950	−	0.519974i
$67$	58730.1			1.59836			0.799179	−	0.601094i	$-0.205268\pi$
$67$	58730.1			1.59836			0.799179	+	0.601094i	$0.205268\pi$
$68$	26658.2			0.699131
$69$	−23571.8	+	72546.5i	−0.596032	+	1.83440i
$70$	2468.11	+	7596.07i	0.0602032	+	0.185286i
$71$	−9183.34	−	28263.4i	−0.216200	−	0.665394i	−0.999066	−	0.0432045i	$-0.986243\pi$
$71$	−9183.34	−	28263.4i	−0.216200	−	0.665394i	0.782867	−	0.622190i	$-0.213757\pi$
$72$	24982.3	−	18150.7i	0.567938	−	0.412631i
$73$	−25365.8	+	78068.0i	−0.557112	+	1.71461i	0.133189	+	0.991091i	$0.457478\pi$
$73$	−25365.8	+	78068.0i	−0.557112	+	1.71461i	−0.690301	+	0.723523i	$0.742522\pi$
$74$	−39180.4	+	28466.2i	−0.831743	+	0.604297i
$75$	39921.6	+	29004.7i	0.819511	+	0.595410i
$76$	3984.04	+	12261.6i	0.0791207	+	0.243509i
$77$	8067.59	+	5861.44i	0.155066	+	0.112662i
$78$	−243.222	−	176.711i	−0.00452653	−	0.00328872i
$79$	8451.28	+	26010.4i	0.152354	+	0.468898i	0.997883	−	0.0650314i	$-0.0207148\pi$
$79$	8451.28	+	26010.4i	0.152354	+	0.468898i	−0.845529	+	0.533930i	$0.820715\pi$
$80$	7447.18	+	5410.69i	0.130097	+	0.0945209i
$81$	−45715.4	+	33214.2i	−0.774194	+	0.562485i
$82$	−9873.43	+	30387.3i	−0.162156	+	0.499065i
$83$	−29931.0	+	21746.2i	−0.476899	+	0.346488i	−0.800124	−	0.599835i	$-0.795233\pi$
$83$	−29931.0	+	21746.2i	−0.476899	+	0.346488i	0.323225	+	0.946322i	$0.395233\pi$
$84$	7395.17	+	22760.0i	0.114354	+	0.351944i
$85$	−18513.5	−	56978.6i	−0.277933	−	0.855390i
$86$	3870.48	−	11912.1i	0.0564311	−	0.173677i
$87$	−6731.54			−0.0953490
$88$	11493.1			0.158209
$89$	−30638.1	+	94294.5i	−0.410003	+	1.26186i	0.506641	+	0.862157i	$0.330887\pi$
$89$	−30638.1	+	94294.5i	−0.410003	+	1.26186i	−0.916644	+	0.399704i	$0.869113\pi$
$90$	−56144.3	−	40791.3i	−0.730634	−	0.530837i
$91$	125.358	−	91.0781i	0.00158690	−	0.00115295i
$92$	−45311.9			−0.558140
$93$	95617.7	+	107831.i	1.14639	+	1.29282i
$94$	71351.5			0.832881
$95$	23440.9	−	17030.8i	0.266480	−	0.193609i
$96$	22313.9	+	16212.0i	0.247114	+	0.179539i
$97$	25684.2	−	79047.8i	0.277164	−	0.853023i	−0.711475	−	0.702712i	$-0.751972\pi$
$97$	25684.2	−	79047.8i	0.277164	−	0.853023i	0.988639	−	0.150311i	$-0.0480276\pi$
$98$	54893.6			0.577373
$99$	−86646.7			−0.888513
$100$	−9058.06	+	27877.8i	−0.0905806	+	0.278778i
$101$	−57942.2	−	178328.i	−0.565186	−	1.73946i	−0.667398	−	0.744701i	$-0.732592\pi$
$101$	−57942.2	−	178328.i	−0.565186	−	1.73946i	0.102212	−	0.994763i	$-0.467408\pi$
$102$	−55471.6	−	170724.i	−0.527923	−	1.62478i
$103$	−83563.6	+	60712.5i	−0.776112	+	0.563878i	−0.903809	−	0.427935i	$-0.859241\pi$
$103$	−83563.6	+	60712.5i	−0.776112	+	0.563878i	0.127698	+	0.991813i	$0.459241\pi$
$104$	55.1861	−	169.845i	0.000500318	−	0.00153982i
$105$	43510.9	−	31612.5i	0.385145	−	0.279824i
$106$	−65080.3	−	47283.6i	−0.562580	−	0.408739i
$107$	−3294.70	−	10140.0i	−0.0278199	−	0.0856210i	0.936183	−	0.351514i	$-0.114333\pi$
$107$	−3294.70	−	10140.0i	−0.0278199	−	0.0856210i	−0.964002	+	0.265893i	$0.914333\pi$
$108$	−83501.6	−	60667.4i	−0.688867	−	0.500491i
$109$	−61346.4	−	44570.7i	−0.494564	−	0.359322i	0.312373	−	0.949960i	$-0.398876\pi$
$109$	−61346.4	−	44570.7i	−0.494564	−	0.359322i	−0.806937	+	0.590638i	$0.798876\pi$
$110$	−7981.68	−	24565.1i	−0.0628945	−	0.193569i
$111$	263831.	+	191685.i	2.03244	+	1.47666i
$112$	−11500.7	+	8355.78i	−0.0866325	+	0.0629422i
$113$	57820.9	−	177954.i	0.425979	−	1.31103i	−0.476074	−	0.879405i	$-0.657941\pi$
$113$	57820.9	−	177954.i	0.425979	−	1.31103i	0.902053	−	0.431625i	$-0.142059\pi$
$114$	70235.6	−	51029.1i	0.506168	−	0.367753i
$115$	31468.0	+	96848.5i	0.221883	+	0.682886i
$116$	−1235.66	−	3802.97i	−0.00852617	−	0.0262409i
$117$	−416.048	+	1280.46i	−0.00280982	+	0.00864775i
$118$	−88510.3			−0.585179
$119$	92520.8			0.598924
$120$	19154.6	−	58951.9i	0.121429	−	0.373719i
$121$	104203.	+	75708.0i	0.647019	+	0.470087i
$122$	−177232.	+	128766.i	−1.07806	+	0.783255i
$123$	215151.			1.28227
$124$	−43367.3	+	73812.9i	−0.253284	+	0.431100i
$125$	178244.			1.02033
$126$	86704.2	−	62994.3i	0.486535	−	0.353488i
$127$	−149837.	−	108863.i	−0.824347	−	0.598923i	0.0936075	−	0.995609i	$-0.470160\pi$
$127$	−149837.	−	108863.i	−0.824347	−	0.598923i	−0.917954	+	0.396686i	$0.870160\pi$
$128$	−5062.93	+	15582.1i	−0.0273135	+	0.0840623i
$129$	−84341.3			−0.446237
$130$	−401.348			−0.00208287
$131$	45613.3	−	140383.i	0.232227	−	0.714722i	−0.765250	−	0.643733i	$-0.777385\pi$
$131$	45613.3	−	140383.i	0.232227	−	0.714722i	0.997477	−	0.0709886i	$-0.0226154\pi$
$132$	−23915.4	−	73604.0i	−0.119466	−	0.367677i
$133$	13827.1	+	42555.6i	0.0677803	+	0.208606i
$134$	190055.	−	138083.i	0.914358	−	0.664320i
$135$	−71679.3	+	220606.i	−0.338500	+	1.04180i
$136$	86267.8	−	62677.2i	0.399946	−	0.290578i
$137$	−115156.	−	83665.6i	−0.524185	−	0.380843i	0.293993	−	0.955808i	$-0.405016\pi$
$137$	−115156.	−	83665.6i	−0.524185	−	0.380843i	−0.818178	+	0.574965i	$0.805016\pi$
$138$	94287.1	+	290186.i	0.421458	+	1.29712i
$139$	−314855.	−	228756.i	−1.38221	−	1.00423i	−0.996670	−	0.0815429i	$-0.974015\pi$
$139$	−314855.	−	228756.i	−1.38221	−	1.00423i	−0.385540	−	0.922691i	$-0.625985\pi$
$140$	25846.4	+	18778.5i	0.111450	+	0.0809732i
$141$	−148471.	−	456948.i	−0.628920	−	1.93562i
$142$	−96169.2	−	69871.0i	−0.400235	−	0.290788i
$143$	−405.399	+	294.539i	−0.00165784	+	0.00120449i
$144$	38169.5	−	117474.i	0.153395	−	0.472100i
$145$	−7270.24	+	5282.14i	−0.0287163	+	0.0208636i
$146$	101463.	+	312272.i	0.393937	+	1.21241i
$147$	−114225.	−	351549.i	−0.435982	−	1.34182i
$148$	−59862.3	+	184237.i	−0.224646	+	0.691390i
$149$	−16287.1			−0.0601004			−0.0300502	−	0.999548i	$-0.509567\pi$
$149$	−16287.1			−0.0601004			−0.0300502	+	0.999548i	$0.509567\pi$
$150$	197383.			0.716279
$151$	15660.0	−	48196.7i	0.0558921	−	0.172018i	−0.919213	−	0.393760i	$-0.871174\pi$
$151$	15660.0	−	48196.7i	0.0558921	−	0.172018i	0.975105	+	0.221742i	$0.0711741\pi$
$152$	41721.5	+	30312.4i	0.146471	+	0.106417i
$153$	−650374.	+	472524.i	−2.24613	+	1.63191i
$154$	39888.3			0.135533
$155$	187883.	+	41430.9i	0.628143	+	0.138515i
$156$	−1202.55			−0.00395634
$157$	16630.6	−	12082.8i	0.0538466	−	0.0391219i	−0.560536	−	0.828130i	$-0.689405\pi$
$157$	16630.6	−	12082.8i	0.0538466	−	0.0391219i	0.614383	+	0.789008i	$0.289405\pi$
$158$	88502.9	+	64301.1i	0.282043	+	0.204916i
$159$	−167391.	+	515176.i	−0.525096	+	1.61608i
$160$	36820.9			0.113709
$161$	−157261.			−0.478141
$162$	−69846.9	+	214967.i	−0.209103	+	0.643551i
$163$	−12457.7	−	38340.9i	−0.0367256	−	0.113030i	0.931013	−	0.364986i	$-0.118926\pi$
$163$	−12457.7	−	38340.9i	−0.0367256	−	0.113030i	−0.967739	+	0.251956i	$0.918926\pi$
$164$	39493.7	+	121549.i	0.114662	+	0.352892i
$165$	−140711.	+	102232.i	−0.402362	+	0.292333i
$166$	−45730.6	+	140744.i	−0.128806	+	0.396424i
$167$	476763.	−	346389.i	1.32285	−	0.961109i	0.322961	−	0.946412i	$-0.395322\pi$
$167$	476763.	−	346389.i	1.32285	−	0.961109i	0.999892	−	0.0146967i	$-0.00467827\pi$
$168$	77443.3	+	56265.8i	0.211695	+	0.153805i
$169$	−114733.	−	353113.i	−0.309011	−	0.951037i
$170$	−193875.	−	140859.i	−0.514518	−	0.373819i
$171$	−314538.	−	228526.i	−0.822590	−	0.597647i
$172$	−15481.9	−	47648.4i	−0.0399028	−	0.122808i
$173$	432287.	+	314075.i	1.09814	+	0.797844i	0.980755	−	0.195243i	$-0.0625495\pi$
$173$	432287.	+	314075.i	1.09814	+	0.797844i	0.117383	+	0.993087i	$0.462550\pi$
$174$	−21783.7	+	15826.8i	−0.0545455	+	0.0396296i
$175$	−31437.2	+	96753.7i	−0.0775976	+	0.238821i
$176$	37192.5	−	27021.9i	0.0905052	−	0.0657559i
$177$	184176.	+	566837.i	0.441876	+	1.35996i
$178$	122553.	+	377178.i	0.289916	+	0.892270i
$179$	135344.	−	416544.i	0.315722	−	0.971692i	−0.659734	−	0.751499i	$-0.729331\pi$
$179$	135344.	−	416544.i	0.315722	−	0.971692i	0.975456	−	0.220193i	$-0.0706689\pi$
$180$	−277593.			−0.638597
$181$	−335864.			−0.762021			−0.381010	−	0.924571i	$-0.624424\pi$
$181$	−335864.			−0.762021			−0.381010	+	0.924571i	$0.624424\pi$
$182$	191.530	−	589.470i	0.000428607	−	0.00131912i
$183$	1.19344e6	+	867082.i	2.63434	+	1.91396i
$184$	−146632.	+	106535.i	−0.319290	+	0.231978i
$185$	435356.			0.935224
$186$	562952.	+	124139.i	1.19313	+	0.263103i
$187$	−299205.			−0.625698
$188$	230898.	−	167757.i	0.476459	−	0.346168i
$189$	−289803.	−	210554.i	−0.590131	−	0.428755i
$190$	35814.5	−	110226.i	0.0719738	−	0.221513i
$191$	419759.			0.832563			0.416281	−	0.909236i	$-0.363333\pi$
$191$	419759.			0.832563			0.416281	+	0.909236i	$0.363333\pi$
$192$	110326.			0.215985
$193$	−138534.	+	426363.i	−0.267709	+	0.823922i	0.723348	+	0.690483i	$0.242602\pi$
$193$	−138534.	+	426363.i	−0.267709	+	0.823922i	−0.991057	+	0.133439i	$0.957398\pi$
$194$	−102737.	−	316191.i	−0.195985	−	0.603178i
$195$	835.144	+	2570.31i	0.00157280	+	0.00484059i
$196$	177640.	−	129063.i	0.330293	−	0.239972i
$197$	−170168.	+	523725.i	−0.312402	+	0.961474i	0.664409	+	0.747369i	$0.268683\pi$
$197$	−170168.	+	523725.i	−0.312402	+	0.961474i	−0.976811	+	0.214105i	$0.931317\pi$
$198$	−280394.	+	203719.i	−0.508284	+	0.369290i
$199$	73912.3	+	53700.4i	0.132307	+	0.0961269i	0.651971	−	0.758244i	$-0.273943\pi$
$199$	73912.3	+	53700.4i	0.132307	+	0.0961269i	−0.519663	+	0.854371i	$0.673943\pi$
$200$	36232.2	+	111511.i	0.0640501	+	0.197126i
$201$	−1.27978e6	−	929816.i	−2.23432	−	1.62333i
$202$	−606778.	−	440850.i	−1.04629	−	0.760173i
$203$	−4288.52	−	13198.7i	−0.00730411	−	0.0224797i
$204$	−580907.	−	422053.i	−0.977307	−	0.710055i
$205$	232369.	−	168826.i	0.386183	−	0.280578i
$206$	−127674.	+	392940.i	−0.209621	+	0.645146i
$207$	1.10546e6	−	803166.i	1.79316	−	1.30281i
$208$	−220.744	−	679.381i	−0.000353778	−	0.00108882i
$209$	−44715.9	−	137621.i	−0.0708102	−	0.217931i
$210$	66478.7	−	204600.i	0.104024	−	0.320154i
$211$	−874046.			−1.35154			−0.675769	−	0.737113i	$-0.736188\pi$
$211$	−874046.			−1.35154			−0.675769	+	0.737113i	$0.736188\pi$
$212$	−321774.			−0.491713
$213$	−247354.	+	761277.i	−0.373568	+	1.14972i
$214$	−34502.5	−	25067.6i	−0.0515011	−	0.0374177i
$215$	−91090.7	+	66181.3i	−0.134393	+	0.0976425i
$216$	−412854.			−0.602092
$217$	−150512.	+	256177.i	−0.216981	+	0.369310i
$218$	−303313.			−0.432265
$219$	1.78872e6	−	1.29958e6i	2.52018	−	1.83102i
$220$	−83585.2	−	60728.2i	−0.116432	−	0.0845929i
$221$	−1436.68	+	4421.65i	−0.00197870	+	0.00608981i
$222$	1.30445e6			1.77642
$223$	−580551.			−0.781769			−0.390885	−	0.920440i	$-0.627831\pi$
$223$	−580551.			−0.781769			−0.390885	+	0.920440i	$0.627831\pi$
$224$	−17571.6	+	54079.8i	−0.0233986	+	0.0720136i
$225$	−273155.	−	840685.i	−0.359710	−	1.10707i
$226$	−231284.	−	711818.i	−0.301213	−	0.927038i
$227$	5423.17	−	3940.16i	0.00698535	−	0.00507516i	−0.584287	−	0.811547i	$-0.698626\pi$
$227$	5423.17	−	3940.16i	0.00698535	−	0.00507516i	0.591272	+	0.806472i	$0.298626\pi$
$228$	107310.	−	330267.i	0.136711	−	0.420754i
$229$	−234175.	+	170138.i	−0.295088	+	0.214394i	−0.725472	−	0.688252i	$-0.758378\pi$
$229$	−234175.	+	170138.i	−0.295088	+	0.214394i	0.430384	+	0.902646i	$0.358378\pi$
$230$	329537.	+	239423.i	0.410757	+	0.298432i
$231$	−83001.5	−	255452.i	−0.102343	−	0.314978i
$232$	−12940.0	−	9401.46i	−0.0157839	−	0.0114677i
$233$	316816.	+	230180.i	0.382311	+	0.277766i	0.762298	−	0.647227i	$-0.224071\pi$
$233$	316816.	+	230180.i	0.382311	+	0.277766i	−0.379986	+	0.924992i	$0.624071\pi$
$234$	1664.19	+	5121.86i	0.00198684	+	0.00611488i
$235$	−518913.	−	377012.i	−0.612950	−	0.445334i
$236$	−286425.	+	208100.i	−0.334759	+	0.243216i
$237$	227635.	−	700590.i	0.263250	−	0.810202i
$238$	299404.	−	217529.i	0.342622	−	0.248929i
$239$	407886.	+	1.25534e6i	0.461896	+	1.42157i	0.862845	+	0.505468i	$0.168680\pi$
$239$	407886.	+	1.25534e6i	0.461896	+	1.42157i	−0.400950	+	0.916100i	$0.631320\pi$
$240$	−76618.6	−	235808.i	−0.0858630	−	0.264259i
$241$	−513222.	+	1.57953e6i	−0.569197	+	1.75181i	0.0859441	+	0.996300i	$0.472609\pi$
$241$	−513222.	+	1.57953e6i	−0.569197	+	1.75181i	−0.655141	+	0.755507i	$0.727391\pi$
$242$	515208.			0.565515
$243$	−45530.5			−0.0494637
$244$	−270786.	+	833394.i	−0.291173	+	0.896140i
$245$	−399221.	−	290051.i	−0.424912	−	0.308716i
$246$	696243.	−	505850.i	0.733539	−	0.532947i
$247$	−2248.48			−0.00234502
$248$	33205.0	+	340826.i	0.0342826	+	0.351887i
$249$	996511.			1.01855
$250$	576811.	−	419078.i	0.583691	−	0.424077i
$251$	−427968.	−	310937.i	−0.428773	−	0.311522i	0.352385	−	0.935855i	$-0.385371\pi$
$251$	−427968.	−	310937.i	−0.428773	−	0.311522i	−0.781158	+	0.624333i	$0.785371\pi$
$252$	132472.	−	407708.i	0.131409	−	0.404434i
$253$	508569.			0.499515
$254$	−740835.			−0.720506
$255$	−498661.	+	1.53472e6i	−0.480236	+	1.47801i
$256$	20251.7	+	62328.4i	0.0193136	+	0.0594410i
$257$	145084.	+	446523.i	0.137021	+	0.421707i	0.995899	−	0.0904733i	$-0.0288380\pi$
$257$	145084.	+	446523.i	0.137021	+	0.421707i	−0.858878	+	0.512180i	$0.828838\pi$
$258$	−272934.	+	198298.i	−0.255275	+	0.185468i
$259$	−207760.	+	639419.i	−0.192447	+	0.592292i
$260$	−1298.79	+	943.626i	−0.00119153	+	0.000865698i
$261$	97554.8	+	70877.7i	0.0886436	+	0.0644033i
$262$	−182453.	−	561533.i	−0.164209	−	0.505385i
$263$	−155080.	−	112672.i	−0.138250	−	0.100445i	0.516511	−	0.856281i	$-0.327231\pi$
$263$	−155080.	−	112672.i	−0.138250	−	0.100445i	−0.654761	+	0.755836i	$0.727231\pi$
$264$	−250445.	−	181959.i	−0.221158	−	0.160681i
$265$	223464.	+	687752.i	0.195476	+	0.601613i
$266$	144800.	+	105203.i	0.125477	+	0.0911643i
$267$	2.16051e6	−	1.56970e6i	1.85472	−	1.34753i
$268$	290378.	−	893691.i	0.246960	−	0.760064i
$269$	110022.	−	79935.8i	0.0927043	−	0.0673536i	−0.540468	−	0.841365i	$-0.681753\pi$
$269$	110022.	−	79935.8i	0.0927043	−	0.0673536i	0.633172	+	0.774011i	$0.281753\pi$
$270$	286717.	+	882424.i	0.239356	+	0.736662i
$271$	−294633.	−	906786.i	−0.243701	−	0.750035i	−0.995847	−	0.0910390i	$-0.970981\pi$
$271$	−294633.	−	906786.i	−0.243701	−	0.750035i	0.752146	−	0.658996i	$-0.229019\pi$
$272$	131805.	−	405655.i	0.108022	−	0.332457i
$273$	−4173.62			−0.00338927
$274$	−569362.			−0.458154
$275$	101665.	−	312894.i	0.0810664	−	0.249497i
$276$	987388.	+	717379.i	0.780216	+	0.566860i
$277$	−84401.5	+	61321.3i	−0.0660923	+	0.0480188i	−0.620341	−	0.784332i	$-0.713006\pi$
$277$	−84401.5	+	61321.3i	−0.0660923	+	0.0480188i	0.554249	+	0.832351i	$0.313006\pi$
$278$	−1.55673e6			−1.20810
$279$	−250332.	−	2.56949e6i	−0.192534	−	1.97623i
$280$	127792.			0.0974109
$281$	1.01466e6	−	737194.i	0.766575	−	0.556949i	−0.134345	−	0.990935i	$-0.542893\pi$
$281$	1.01466e6	−	737194.i	0.766575	−	0.556949i	0.900920	+	0.433985i	$0.142893\pi$
$282$	−1.55481e6	−	1.12964e6i	−1.16427	−	0.845895i
$283$	−560750.	+	1.72581e6i	−0.416201	+	1.28093i	0.494972	+	0.868909i	$0.335178\pi$
$283$	−560750.	+	1.72581e6i	−0.416201	+	1.28093i	−0.911172	+	0.412025i	$0.864822\pi$
$284$	−475487.			−0.349818
$285$	−780429.			−0.569143
$286$	−619.394	+	1906.30i	−0.000447767	+	0.00137808i
$287$	137068.	+	421852.i	0.0982272	+	0.302312i
$288$	−152678.	−	469895.i	−0.108466	−	0.333825i
$289$	−1.09716e6	+	797130.i	−0.772723	+	0.561416i
$290$	−11107.9	+	34186.7i	−0.00775601	+	0.0238705i
$291$	−1.81117e6	+	1.31589e6i	−1.25380	+	0.910936i
$292$	1.06254e6	+	771979.i	0.729269	+	0.529845i
$293$	−579874.	−	1.78467e6i	−0.394607	−	1.21447i	−0.929267	−	0.369408i	$-0.879560\pi$
$293$	−579874.	−	1.78467e6i	−0.394607	−	1.21447i	0.534660	−	0.845067i	$-0.320440\pi$
$294$	−1.19618e6	−	869077.i	−0.807103	−	0.586395i
$295$	643703.	+	467678.i	0.430656	+	0.312890i
$296$	239449.	+	736948.i	0.158849	+	0.488886i
$297$	937200.	+	680916.i	0.616511	+	0.447922i
$298$	−52706.1	+	38293.2i	−0.0343811	+	0.0249793i
$299$	2441.98	−	7515.64i	0.00157966	−	0.00486170i
$300$	638746.	−	464076.i	0.409756	−	0.297705i
$301$	−53732.0	−	165370.i	−0.0341835	−	0.105206i
$302$	−62640.2	−	192787.i	−0.0395217	−	0.121635i
$303$	−1.56068e6	+	4.80326e6i	−0.976576	+	3.00559i
$304$	206282.			0.128020
$305$	1.96933e6			1.21218
$306$	−993682.	+	3.05824e6i	−0.606658	+	1.86710i
$307$	−493698.	−	358692.i	−0.298961	−	0.217208i	0.428184	−	0.903691i	$-0.359153\pi$
$307$	−493698.	−	358692.i	−0.298961	−	0.217208i	−0.727146	+	0.686483i	$0.759153\pi$
$308$	129081.	−	93783.1i	0.0775330	−	0.0563310i
$309$	2.78213e6			1.65761
$310$	705413.	−	307667.i	0.416907	−	0.181834i
$311$	−305691.			−0.179218			−0.0896091	−	0.995977i	$-0.528562\pi$
$311$	−305691.			−0.179218			−0.0896091	+	0.995977i	$0.528562\pi$
$312$	−3891.55	+	2827.37i	−0.00226327	+	0.00164436i
$313$	2.19801e6	+	1.59695e6i	1.26815	+	0.921363i	0.999127	−	0.0417714i	$-0.0133001\pi$
$313$	2.19801e6	+	1.59695e6i	1.26815	+	0.921363i	0.269020	+	0.963134i	$0.413300\pi$
$314$	25409.3	−	78201.7i	0.0145435	−	0.0447602i
$315$	−963422.			−0.547067
$316$	437582.			0.246514
$317$	−663617.	+	2.04240e6i	−0.370910	+	1.14155i	0.575286	+	0.817952i	$0.304891\pi$
$317$	−663617.	+	2.04240e6i	−0.370910	+	1.14155i	−0.946196	+	0.323593i	$0.895109\pi$
$318$	669563.	+	2.06070e6i	0.371299	+	1.14274i
$319$	13868.7	+	42683.6i	0.00763062	+	0.0234846i
$320$	119155.	−	86571.1i	0.0650484	−	0.0472604i
$321$	−88742.9	+	273122.i	−0.0480696	+	0.147943i
$322$	−508907.	+	369743.i	−0.273526	+	0.198728i
$323$	−1.08615e6	−	789135.i	−0.579274	−	0.420867i
$324$	279387.	+	859866.i	0.147858	+	0.455060i
$325$	−4135.78	−	3004.82i	−0.00217195	−	0.00157801i
$326$	−130459.	−	94783.9i	−0.0679876	−	0.0493959i
$327$	631148.	+	1.94247e6i	0.326409	+	1.00458i
$328$	413583.	+	300486.i	0.212265	+	0.154220i
$329$	801362.	−	582224.i	0.408168	−	0.296552i
$330$	−214987.	+	661661.i	−0.108674	+	0.334465i
$331$	210487.	−	152928.i	0.105598	−	0.0767215i	−0.533733	−	0.845653i	$-0.679211\pi$
$331$	210487.	−	152928.i	0.105598	−	0.0767215i	0.639331	+	0.768931i	$0.279211\pi$
$332$	182922.	+	562977.i	0.0910797	+	0.280314i
$333$	−1.80521e6	−	5.55586e6i	−0.892107	−	2.74562i
$334$	728429.	−	2.24188e6i	0.357290	−	1.09963i
$335$	−2.11181e6			−1.02812
$336$	382901.			0.185028
$337$	880683.	−	2.71046e6i	0.422420	−	1.30008i	−0.483023	−	0.875608i	$-0.660461\pi$
$337$	880683.	−	2.71046e6i	0.422420	−	1.30008i	0.905443	−	0.424468i	$-0.139539\pi$
$338$	−1.20150e6	−	872944.i	−0.572049	−	0.415618i
$339$	−4.07735e6	+	2.96237e6i	−1.92699	+	1.40004i
$340$	−958573.			−0.449705
$341$	486743.	−	828456.i	0.226680	−	0.385819i
$342$	−1.55516e6			−0.718970
$343$	1.37157e6	−	996506.i	0.629482	−	0.457345i
$344$	−162129.	−	117793.i	−0.0738693	−	0.0536692i
$345$	847592.	−	2.60862e6i	0.383388	−	1.17995i
$346$	2.13734e6			0.959808
$347$	380998.			0.169863			0.0849315	−	0.996387i	$-0.472933\pi$
$347$	380998.			0.169863			0.0849315	+	0.996387i	$0.472933\pi$
$348$	−33282.6	+	102433.i	−0.0147322	+	0.0453412i
$349$	−96757.1	−	297788.i	−0.0425226	−	0.130871i	0.927541	−	0.373720i	$-0.121918\pi$
$349$	−96757.1	−	297788.i	−0.0425226	−	0.130871i	−0.970064	+	0.242849i	$0.921918\pi$
$350$	125749.	+	387015.i	0.0548698	+	0.168872i
$351$	14562.7	−	10580.4i	0.00630919	−	0.00458390i
$352$	56825.1	−	174890.i	0.0244446	−	0.0752328i
$353$	2.84859e6	−	2.06962e6i	1.21673	−	0.884005i	0.220905	−	0.975295i	$-0.429099\pi$
$353$	2.84859e6	−	2.06962e6i	1.21673	−	0.884005i	0.995824	+	0.0912901i	$0.0290990\pi$
$354$	1.92872e6	+	1.40130e6i	0.818015	+	0.594323i
$355$	330214.	+	1.01629e6i	0.139067	+	0.428004i
$356$	1.28339e6	+	932435.i	0.536701	+	0.389936i
$357$	−2.01611e6	−	1.46479e6i	−0.837229	−	0.608282i
$358$	−541374.	−	1.66618e6i	−0.223249	−	0.687090i
$359$	−740619.	−	538091.i	−0.303290	−	0.220353i	0.425722	−	0.904854i	$-0.360020\pi$
$359$	−740619.	−	538091.i	−0.303290	−	0.220353i	−0.729012	+	0.684501i	$0.760020\pi$
$360$	−898310.	+	652660.i	−0.365317	+	0.265418i
$361$	−564513.	+	1.73739e6i	−0.227985	+	0.701665i
$362$	−1.08688e6	+	789663.i	−0.435923	+	0.316716i
$363$	−1.07207e6	−	3.29949e6i	−0.427028	−	1.31426i
$364$	−766.122	−	2357.88i	−0.000303071	−	0.000932756i
$365$	912102.	−	2.80716e6i	0.358353	−	1.10290i
$366$	5.90068e6			2.30250
$367$	−1.77940e6			−0.689616			−0.344808	−	0.938673i	$-0.612056\pi$
$367$	−1.77940e6			−0.689616			−0.344808	+	0.938673i	$0.612056\pi$
$368$	−224034.	+	689507.i	−0.0862373	+	0.265411i
$369$	−3.11801e6	−	2.26537e6i	−1.19210	−	0.866109i
$370$	1.40884e6	−	1.02358e6i	0.535005	−	0.388704i
$371$	−1.11676e6			−0.421236
$372$	2.11362e6	−	921858.i	0.791898	−	0.345387i
$373$	770598.			0.286785			0.143392	−	0.989666i	$-0.454199\pi$
$373$	770598.			0.286785			0.143392	+	0.989666i	$0.454199\pi$
$374$	−968247.	+	703473.i	−0.357937	+	0.260057i
$375$	−3.88411e6	−	2.82197e6i	−1.42631	−	1.03627i
$376$	352781.	−	1.08575e6i	0.128687	−	0.396059i
$377$	697.371			0.000252703
$378$	−1.43287e6			−0.515794
$379$	1.31797e6	−	4.05628e6i	0.471310	−	1.45054i	−0.379561	−	0.925167i	$-0.623925\pi$
$379$	1.31797e6	−	4.05628e6i	0.471310	−	1.45054i	0.850871	−	0.525375i	$-0.176075\pi$
$380$	−143258.	−	440902.i	−0.0508931	−	0.156633i
$381$	1.54156e6	+	4.74445e6i	0.544063	+	1.67445i
$382$	1.35837e6	−	986913.i	0.476277	−	0.346035i
$383$	602640.	−	1.85474e6i	0.209924	−	0.646078i	−0.789552	−	0.613684i	$-0.789687\pi$
$383$	602640.	−	1.85474e6i	0.209924	−	0.646078i	0.999475	−	0.0323941i	$-0.0103132\pi$
$384$	357022.	−	259392.i	0.123557	−	0.0897694i
$385$	−290093.	−	210765.i	−0.0997438	−	0.0724681i
$386$	554135.	+	1.70545e6i	0.189299	+	0.582601i
$387$	1.22229e6	+	888046.i	0.414856	+	0.301410i
$388$	−1.07587e6	−	781668.i	−0.362812	−	0.263599i
$389$	−180565.	−	555721.i	−0.0605005	−	0.186201i	0.916238	−	0.400633i	$-0.131210\pi$
$389$	−180565.	−	555721.i	−0.0605005	−	0.186201i	−0.976739	+	0.214432i	$0.931210\pi$
$390$	8745.74	+	6354.15i	0.00291162	+	0.00211542i
$391$	3.81734e6	−	2.77346e6i	1.26276	−	0.917445i
$392$	271409.	−	835311.i	0.0892091	−	0.274557i
$393$	−3.21651e6	+	2.33693e6i	−1.05052	+	0.763245i
$394$	680674.	+	2.09490e6i	0.220901	+	0.679865i
$395$	−303890.	−	935277.i	−0.0979995	−	0.301611i
$396$	−428405.	+	1.31849e6i	−0.137283	+	0.422513i
$397$	5.66329e6			1.80340			0.901701	−	0.432360i	$-0.142319\pi$
$397$	5.66329e6			1.80340			0.901701	+	0.432360i	$0.142319\pi$
$398$	365443.			0.115641
$399$	372435.	−	1.14624e6i	0.117116	−	0.360447i
$400$	379429.	+	275671.i	0.118572	+	0.0861472i
$401$	−5.07420e6	+	3.68662e6i	−1.57582	+	1.14490i	−0.654521	+	0.756044i	$0.727129\pi$
$401$	−5.07420e6	+	3.68662e6i	−1.57582	+	1.14490i	−0.921299	+	0.388856i	$0.872871\pi$
$402$	−6.32759e6			−1.95287
$403$	−9905.75	−	11171.1i	−0.00303826	−	0.00342635i
$404$	−3.00008e6			−0.914490
$405$	1.64383e6	−	1.19431e6i	0.497988	−	0.361809i
$406$	−44910.0	−	32629.0i	−0.0135216	−	0.00982401i
$407$	671878.	−	2.06783e6i	0.201050	−	0.618769i
$408$	−2.87216e6			−0.854197
$409$	5.64831e6			1.66959			0.834796	−	0.550559i	$-0.185585\pi$
$409$	5.64831e6			1.66959			0.834796	+	0.550559i	$0.185585\pi$
$410$	355028.	−	1.09266e6i	0.104304	−	0.321016i
$411$	1.18475e6	+	3.64630e6i	0.345958	+	1.06475i
$412$	510695.	+	1.57176e6i	0.148224	+	0.456187i
$413$	−994077.	+	722239.i	−0.286777	+	0.208356i
$414$	1.68900e6	−	5.19820e6i	0.484315	−	1.49057i
$415$	1.07626e6	−	781947.i	0.306758	−	0.222873i
$416$	−2311.66	−	1679.52i	−0.000654925	−	0.000475831i
$417$	3.23932e6	+	9.96959e6i	0.912249	+	2.80761i
$418$	−468271.	−	340219.i	−0.131086	−	0.0952395i
$419$	2.86518e6	+	2.08167e6i	0.797291	+	0.579266i	0.910118	−	0.414349i	$-0.135991\pi$
$419$	2.86518e6	+	2.08167e6i	0.797291	+	0.579266i	−0.112827	+	0.993615i	$0.535991\pi$
$420$	−265915.	−	818402.i	−0.0735562	−	0.226383i
$421$	3.51645e6	+	2.55485e6i	0.966940	+	0.702523i	0.954752	−	0.297403i	$-0.0961205\pi$
$421$	3.51645e6	+	2.55485e6i	0.966940	+	0.702523i	0.0121876	+	0.999926i	$0.496120\pi$
$422$	−2.82847e6	+	2.05501e6i	−0.773163	+	0.561736i
$423$	−2.65962e6	+	8.18547e6i	−0.722717	+	2.22430i
$424$	−1.04128e6	+	756537.i	−0.281290	+	0.204369i
$425$	−943248.	−	2.90302e6i	−0.253311	−	0.779611i
$426$	989415.	+	3.04511e6i	0.264152	+	0.812977i
$427$	−939799.	+	2.89240e6i	−0.249439	+	0.767696i
$428$	−170590.			−0.0450136
$429$	13497.2			0.00354078
$430$	−139174.	+	428334.i	−0.0362984	+	0.111715i
$431$	−2.85626e6	−	2.07520e6i	−0.740636	−	0.538104i	0.152274	−	0.988338i	$-0.451340\pi$
$431$	−2.85626e6	−	2.07520e6i	−0.740636	−	0.538104i	−0.892910	+	0.450235i	$0.851340\pi$
$432$	−1.33603e6	+	970679.i	−0.344433	+	0.250246i
$433$	−4.99234e6			−1.27963			−0.639815	−	0.768529i	$-0.720989\pi$
$433$	−4.99234e6			−1.27963			−0.639815	+	0.768529i	$0.720989\pi$
$434$	115242.	+	1.18288e6i	0.0293689	+	0.301451i
$435$	242052.			0.0613318
$436$	−981542.	+	713132.i	−0.247282	+	0.179661i
$437$	1.84617e6	+	1.34132e6i	0.462454	+	0.335992i
$438$	2.73292e6	−	8.41106e6i	0.680678	−	2.09491i
$439$	−6.15479e6			−1.52423			−0.762117	−	0.647439i	$-0.775840\pi$
$439$	−6.15479e6			−1.52423			−0.762117	+	0.647439i	$0.775840\pi$
$440$	−413268.			−0.101765
$441$	−2.04616e6	+	6.29742e6i	−0.501005	+	1.54194i
$442$	5746.72	+	17686.6i	0.00139915	+	0.00430614i
$443$	2.18807e6	+	6.73418e6i	0.529726	+	1.63033i	0.754776	+	0.655983i	$0.227746\pi$
$443$	2.18807e6	+	6.73418e6i	0.529726	+	1.63033i	−0.225050	+	0.974347i	$0.572254\pi$
$444$	4.22130e6	−	3.06695e6i	1.01622	−	0.738329i
$445$	1.10168e6	−	3.39063e6i	0.263728	−	0.811672i
$446$	−1.87870e6	+	1.36496e6i	−0.447220	+	0.324924i
$447$	354910.	+	257857.i	0.0840136	+	0.0610395i
$448$	70286.3	+	216319.i	0.0165453	+	0.0509213i
$449$	−3.61107e6	−	2.62360e6i	−0.845318	−	0.614160i	0.0785328	−	0.996912i	$-0.474976\pi$
$449$	−3.61107e6	−	2.62360e6i	−0.845318	−	0.614160i	−0.923851	+	0.382752i	$0.874976\pi$
$450$	−2.86052e6	−	2.07829e6i	−0.665907	−	0.483809i
$451$	−443267.	−	1.36424e6i	−0.102618	−	0.315826i
$452$	−2.42203e6	−	1.75971e6i	−0.557614	−	0.405131i
$453$	−1.10430e6	+	802319.i	−0.252837	+	0.183697i
$454$	8285.86	−	25501.3i	0.00188668	−	0.00580660i
$455$	−4507.62	+	3274.98i	−0.00102075	+	0.000741617i
$456$	−429242.	−	1.32107e6i	−0.0966696	−	0.297518i
$457$	991029.	+	3.05007e6i	0.221971	+	0.683156i	0.998585	+	0.0531794i	$0.0169355\pi$
$457$	991029.	+	3.05007e6i	0.221971	+	0.683156i	−0.776614	+	0.629977i	$0.783064\pi$
$458$	−357787.	+	1.10116e6i	−0.0797005	+	0.245293i
$459$	1.07480e7			2.38120
$460$	1.62932e6			0.359014
$461$	1.01874e6	−	3.13535e6i	0.223259	−	0.687122i	−0.775204	−	0.631711i	$-0.782353\pi$
$461$	1.01874e6	−	3.13535e6i	0.223259	−	0.687122i	0.998464	−	0.0554112i	$-0.0176470\pi$
$462$	−869203.	−	631513.i	−0.189459	−	0.137650i
$463$	−1.26883e6	+	921861.i	−0.275076	+	0.199854i	−0.716767	−	0.697313i	$-0.754379\pi$
$463$	−1.26883e6	+	921861.i	−0.275076	+	0.199854i	0.441691	+	0.897167i	$0.354379\pi$
$464$	−63978.9			−0.0137956
$465$	−3.43821e6	−	3.87739e6i	−0.737395	−	0.831586i
$466$	1.56642e6			0.334152
$467$	−2.81480e6	+	2.04507e6i	−0.597250	+	0.433927i	−0.844902	−	0.534922i	$-0.820341\pi$
$467$	−2.81480e6	+	2.04507e6i	−0.597250	+	0.433927i	0.247652	+	0.968849i	$0.420341\pi$
$468$	17427.7	+	12661.9i	0.00367811	+	0.00267230i
$469$	1.00779e6	−	3.10167e6i	0.211563	−	0.651124i
$470$	−2.56565e6			−0.535738
$471$	−553691.			−0.115005
$472$	−437619.	+	1.34685e6i	−0.0904152	+	0.278269i
$473$	173765.	+	534794.i	0.0357116	+	0.109909i
$474$	−910542.	−	2.80236e6i	−0.186146	−	0.572899i
$475$	1.19430e6	−	867707.i	0.242872	−	0.176457i
$476$	457448.	−	1.40788e6i	0.0925389	−	0.284805i
$477$	7.85025e6	−	5.70354e6i	1.57975	−	1.14775i
$478$	4.27144e6	+	3.10338e6i	0.855075	+	0.621248i
$479$	−899518.	−	2.76843e6i	−0.179131	−	0.551309i	0.820667	−	0.571407i	$-0.193602\pi$
$479$	−899518.	−	2.76843e6i	−0.179131	−	0.551309i	−0.999798	+	0.0200980i	$0.993602\pi$
$480$	−802360.	−	582949.i	−0.158952	−	0.115485i
$481$	−27332.3	−	19858.0i	−0.00538658	−	0.00391358i
$482$	2.05289e6	+	6.31813e6i	0.402483	+	1.23871i
$483$	3.42686e6	+	2.48976e6i	0.668387	+	0.485612i
$484$	1.66725e6	−	1.21133e6i	0.323510	−	0.235043i
$485$	−923550.	+	2.84239e6i	−0.178281	+	0.548694i
$486$	−147340.	+	107049.i	−0.0282963	+	0.0205585i
$487$	−2.60572e6	−	8.01959e6i	−0.497859	−	1.53225i	−0.812454	−	0.583025i	$-0.801869\pi$
$487$	−2.60572e6	−	8.01959e6i	−0.497859	−	1.53225i	0.314595	−	0.949226i	$-0.398131\pi$
$488$	1.08314e6	+	3.33358e6i	0.205891	+	0.633667i
$489$	−335549.	+	1.03271e6i	−0.0634576	+	0.195303i
$490$	−1.97386e6			−0.371386
$491$	−4.57271e6			−0.855993			−0.427996	−	0.903780i	$-0.640780\pi$
$491$	−4.57271e6			−0.855993			−0.427996	+	0.903780i	$0.640780\pi$
$492$	1.06376e6	−	3.27393e6i	0.198122	−	0.609757i
$493$	336872.	+	244752.i	0.0624235	+	0.0453533i
$494$	−7276.23	+	5286.49i	−0.00134150	+	0.000974653i
$495$	3.11563e6			0.571522
$496$	908784.	+	1.02487e6i	0.165866	+	0.187052i
$497$	−1.65024e6			−0.299679
$498$	3.22478e6	−	2.34294e6i	0.582675	−	0.423338i
$499$	1.51204e6	+	1.09856e6i	0.271838	+	0.197502i	0.715350	−	0.698767i	$-0.246267\pi$
$499$	1.51204e6	+	1.09856e6i	0.271838	+	0.197502i	−0.443511	+	0.896269i	$0.646267\pi$
$500$	881288.	−	2.71233e6i	0.157650	−	0.485196i
$501$	−1.58731e7			−2.82533
$502$	−2.11599e6			−0.374761
$503$	1.03836e6	−	3.19575e6i	0.182990	−	0.563187i	−0.816917	−	0.576755i	$-0.804319\pi$
$503$	1.03836e6	−	3.19575e6i	0.182990	−	0.563187i	0.999908	+	0.0135678i	$0.00431889\pi$
$504$	−529889.	−	1.63083e6i	−0.0929199	−	0.285978i
$505$	2.08348e6	+	6.41229e6i	0.363547	+	1.11888i
$506$	1.64576e6	−	1.19572e6i	0.285753	−	0.207612i
$507$	−3.09035e6	+	9.51112e6i	−0.533934	+	1.64328i
$508$	−2.39739e6	+	1.74181e6i	−0.412173	+	0.299461i
$509$	7.81324e6	+	5.67665e6i	1.33671	+	0.971176i	0.999558	+	0.0297248i	$0.00946310\pi$
$509$	7.81324e6	+	5.67665e6i	1.33671	+	0.971176i	0.337150	+	0.941451i	$0.390537\pi$
$510$	1.99464e6	+	6.13888e6i	0.339578	+	1.04511i
$511$	3.68768e6	+	2.67926e6i	0.624742	+	0.453902i
$512$	212079.	+	154084.i	0.0357538	+	0.0259767i
$513$	1.60628e6	+	4.94362e6i	0.269481	+	0.829377i
$514$	1.51934e6	+	1.10386e6i	0.253657	+	0.184293i
$515$	3.00477e6	−	2.18309e6i	0.499222	−	0.362706i
$516$	−417006.	+	1.28341e6i	−0.0689474	+	0.212198i
$517$	−2.59154e6	+	1.88286e6i	−0.426414	+	0.309808i
$518$	831039.	+	2.55768e6i	0.136081	+	0.418814i
$519$	−4.44748e6	−	1.36880e7i	−0.724763	−	2.23059i
$520$	−1984.37	+	6107.27i	−0.000321822	+	0.000990465i
$521$	7.70263e6			1.24321			0.621605	−	0.783331i	$-0.286481\pi$
$521$	7.70263e6			1.24321			0.621605	+	0.783331i	$0.286481\pi$
$522$	482337.			0.0774773
$523$	−1.46092e6	+	4.49625e6i	−0.233546	+	0.718780i	0.763765	+	0.645494i	$0.223349\pi$
$523$	−1.46092e6	+	4.49625e6i	−0.233546	+	0.718780i	−0.997311	+	0.0732860i	$0.976651\pi$
$524$	−1.91067e6	−	1.38819e6i	−0.303989	−	0.220861i
$525$	2.21685e6	−	1.61064e6i	0.351025	−	0.255035i
$526$	−766757.			−0.120835
$527$	−864438.	−	8.87286e6i	−0.135584	−	1.39167i
$528$	−1.23827e6			−0.193299
$529$	−1.28136e6	+	930964.i	−0.199082	+	0.144642i
$530$	2.34015e6	+	1.70022e6i	0.361871	+	0.262915i
$531$	3.29922e6	−	1.01539e7i	0.507779	−	1.56278i
$532$	715929.			0.109671
$533$	−22289.1			−0.00339840
$534$	3.30096e6	−	1.01593e7i	0.500942	−	1.54174i
$535$	118470.	+	364614.i	0.0178947	+	0.0550744i
$536$	−1.16151e6	−	3.57476e6i	−0.174627	−	0.537446i
$537$	−9.54400e6	+	6.93412e6i	−1.42822	+	1.03766i
$538$	168099.	−	517356.i	0.0250386	−	0.0770608i
$539$	−1.99378e6	+	1.44857e6i	−0.295601	+	0.214766i
$540$	3.00254e6	+	2.18147e6i	0.443103	+	0.321933i
$541$	−3.09556e6	−	9.52717e6i	−0.454723	−	1.39949i	−0.871461	−	0.490466i	$-0.836827\pi$
$541$	−3.09556e6	−	9.52717e6i	−0.454723	−	1.39949i	0.416738	−	0.909027i	$-0.363173\pi$
$542$	−3.08543e6	−	2.24170e6i	−0.451147	−	0.327778i
$543$	7.31878e6	+	5.31740e6i	1.06522	+	0.773927i
$544$	−527222.	−	1.62262e6i	−0.0763829	−	0.235082i
$545$	2.20589e6	+	1.60267e6i	0.318121	+	0.231128i
$546$	−13506.1	+	9812.77i	−0.00193887	+	0.00140867i
$547$	−479093.	+	1.47450e6i	−0.0684624	+	0.210706i	−0.979434	−	0.201762i	$-0.935333\pi$
$547$	−479093.	+	1.47450e6i	−0.0684624	+	0.210706i	0.910972	+	0.412468i	$0.135333\pi$
$548$	−1.84249e6	+	1.33865e6i	−0.262092	+	0.190421i
$549$	−8.16584e6	−	2.51319e7i	−1.15630	−	3.55872i
$550$	−406661.	−	1.25157e6i	−0.0573226	−	0.176421i
$551$	−62230.2	+	191525.i	−0.00873217	+	0.0268748i
$552$	4.88191e6			0.681934
$553$	1.51869e6			0.211181
$554$	−128954.	+	396880.i	−0.0178509	+	0.0549394i
$555$	−9.48681e6	−	6.89257e6i	−1.30734	−	0.949836i
$556$	−5.03768e6	+	3.66009e6i	−0.691105	+	0.502117i
$557$	4.76238e6			0.650409			0.325204	−	0.945644i	$-0.394567\pi$
$557$	4.76238e6			0.650409			0.325204	+	0.945644i	$0.394567\pi$
$558$	−6.85133e6	−	7.72648e6i	−0.931514	−	1.05050i
$559$	8737.54			0.00118266
$560$	413542.	−	300456.i	0.0557250	−	0.0404866i
$561$	6.51994e6	+	4.73702e6i	0.874655	+	0.635474i
$562$	1.55026e6	−	4.77122e6i	0.207045	−	0.637218i
$563$	−1.11230e6			−0.147894			−0.0739468	−	0.997262i	$-0.523559\pi$
$563$	−1.11230e6			−0.147894			−0.0739468	+	0.997262i	$0.523559\pi$
$564$	−7.68742e6			−1.01761
$565$	−2.07912e6	+	6.39886e6i	−0.274005	+	0.843299i
$566$	2.24300e6	+	6.90324e6i	0.294298	+	0.905757i
$567$	969651.	+	2.98428e6i	0.126665	+	0.389836i
$568$	−1.53871e6	+	1.11794e6i	−0.200118	+	0.145394i
$569$	2.14460e6	−	6.60040e6i	0.277693	−	0.854653i	−0.710801	−	0.703393i	$-0.751667\pi$
$569$	2.14460e6	−	6.60040e6i	0.277693	−	0.854653i	0.988494	−	0.151259i	$-0.0483328\pi$
$570$	−2.52552e6	+	1.83490e6i	−0.325585	+	0.236551i
$571$	2.05447e6	+	1.49266e6i	0.263700	+	0.191589i	0.711777	−	0.702406i	$-0.247891\pi$
$571$	2.05447e6	+	1.49266e6i	0.263700	+	0.191589i	−0.448077	+	0.893995i	$0.647891\pi$
$572$	2477.58	+	7625.19i	0.000316619	+	0.000974453i
$573$	−9.14694e6	−	6.64564e6i	−1.16383	−	0.845571i
$574$	1.43540e6	+	1.04288e6i	0.181841	+	0.132115i
$575$	1.60327e6	+	4.93437e6i	0.202226	+	0.622389i
$576$	−1.59887e6	−	1.16164e6i	−0.200796	−	0.145887i
$577$	−1.25567e6	+	912299.i	−0.157013	+	0.114077i	−0.663518	−	0.748160i	$-0.730937\pi$
$577$	−1.25567e6	+	912299.i	−0.157013	+	0.114077i	0.506505	+	0.862237i	$0.330937\pi$
$578$	−1.67630e6	+	5.15914e6i	−0.208705	+	0.642329i
$579$	9.76896e6	−	7.09757e6i	1.21102	−	0.879859i
$580$	44431.7	+	136747.i	0.00548433	+	0.0168790i
$581$	634856.	+	1.95388e6i	0.0780252	+	0.240137i
$582$	−2.76722e6	+	8.51663e6i	−0.338638	+	1.04222i
$583$	3.61151e6			0.440066
$584$	5.25348e6			0.637404
$585$	14960.2	−	46042.8i	0.00180737	−	0.00556253i
$586$	−6.07252e6	−	4.41194e6i	−0.730508	−	0.530745i
$587$	7.19298e6	−	5.22601e6i	0.861616	−	0.626001i	−0.0667080	−	0.997773i	$-0.521250\pi$
$587$	7.19298e6	−	5.22601e6i	0.861616	−	0.626001i	0.928324	+	0.371772i	$0.121250\pi$
$588$	−5.91425e6			−0.705434
$589$	3.95195e6	−	1.72365e6i	0.469378	−	0.204720i
$590$	3.18264e6			0.376407
$591$	1.19997e7	−	8.71833e6i	1.41320	−	1.02675i
$592$	2.50754e6	+	1.82184e6i	0.294066	+	0.213651i
$593$	−4.90581e6	+	1.50985e7i	−0.572894	+	1.76319i	0.0703488	+	0.997522i	$0.477589\pi$
$593$	−4.90581e6	+	1.50985e7i	−0.572894	+	1.76319i	−0.643242	+	0.765663i	$0.722411\pi$
$594$	4.63377e6			0.538851
$595$	−3.32685e6			−0.385249
$596$	−80527.7	+	247839.i	−0.00928602	+	0.0285794i
$597$	−760430.	−	2.34036e6i	−0.0873219	−	0.268749i
$598$	−9767.91	−	30062.5i	−0.00111699	−	0.00343774i
$599$	−1.21639e7	+	8.83761e6i	−1.38518	+	1.00639i	−0.388808	+	0.921319i	$0.627113\pi$
$599$	−1.21639e7	+	8.83761e6i	−1.38518	+	1.00639i	−0.996375	+	0.0850750i	$0.972887\pi$
$600$	975917.	−	3.00356e6i	0.110671	−	0.340611i
$601$	4.57867e6	−	3.32660e6i	0.517075	−	0.375677i	−0.298426	−	0.954433i	$-0.596462\pi$
$601$	4.57867e6	−	3.32660e6i	0.517075	−	0.375677i	0.815501	+	0.578756i	$0.196462\pi$
$602$	−562689.	−	408818.i	−0.0632816	−	0.0459768i
$603$	8.75664e6	+	2.69502e7i	0.980718	+	3.01834i
$604$	−655977.	−	476595.i	−0.0731638	−	0.0531566i
$605$	−3.74692e6	−	2.72230e6i	−0.416185	−	0.302376i
$606$	6.24270e6	+	1.92131e7i	0.690543	+	2.12527i
$607$	−1.40310e7	−	1.01941e7i	−1.54567	−	1.12300i	−0.946648	−	0.322269i	$-0.895554\pi$
$607$	−1.40310e7	−	1.01941e7i	−1.54567	−	1.12300i	−0.599027	−	0.800729i	$-0.704446\pi$
$608$	667543.	−	484999.i	0.0732353	−	0.0532086i
$609$	−115511.	+	355508.i	−0.0126207	+	0.0388424i
$610$	6.37288e6	−	4.63017e6i	0.693444	−	0.503816i
$611$	15381.3	+	47338.7i	0.00166682	+	0.00512995i
$612$	3.97473e6	+	1.22330e7i	0.428972	+	1.32024i
$613$	1.32374e6	−	4.07405e6i	0.142282	−	0.437900i	−0.854369	−	0.519667i	$-0.826056\pi$
$613$	1.32374e6	−	4.07405e6i	0.142282	−	0.437900i	0.996652	+	0.0817663i	$0.0260561\pi$
$614$	−2.44097e6			−0.261302
$615$	−7.73637e6			−0.824802
$616$	197219.	−	606977.i	0.0209410	−	0.0644496i
$617$	241963.	+	175796.i	0.0255880	+	0.0185908i	0.600506	−	0.799620i	$-0.294966\pi$
$617$	241963.	+	175796.i	0.0255880	+	0.0185908i	−0.574918	+	0.818211i	$0.694966\pi$
$618$	9.00316e6	−	6.54118e6i	0.948252	−	0.688945i
$619$	−7.79405e6			−0.817592			−0.408796	−	0.912626i	$-0.634051\pi$
$619$	−7.79405e6			−0.817592			−0.408796	+	0.912626i	$0.634051\pi$
$620$	1.55940e6	−	2.65415e6i	0.162921	−	0.277298i
$621$	−1.82688e7			−1.90099
$622$	−989238.	+	718724.i	−0.102524	+	0.0744879i
$623$	4.45416e6	+	3.23614e6i	0.459776	+	0.334047i
$624$	−5945.76	+	18299.2i	−0.000611288	+	0.00188135i
$625$	−684194.			−0.0700614
$626$	1.08676e7			1.10840
$627$	−1.20442e6	+	3.70684e6i	−0.122352	+	0.376560i
$628$	−101637.	−	312807.i	−0.0102838	−	0.0316503i
$629$	−6.23367e6	−	1.91853e7i	−0.628228	−	1.93349i
$630$	−3.11770e6	+	2.26514e6i	−0.312956	+	0.227376i
$631$	−4.57131e6	+	1.40691e7i	−0.457054	+	1.40667i	0.411652	+	0.911341i	$0.364952\pi$
$631$	−4.57131e6	+	1.40691e7i	−0.457054	+	1.40667i	−0.868707	+	0.495327i	$0.835048\pi$
$632$	1.41605e6	−	1.02882e6i	0.141021	−	0.102458i
$633$	1.90463e7	+	1.38379e7i	1.88930	+	1.37266i
$634$	2.65447e6	+	8.16961e6i	0.262273	+	0.807194i
$635$	5.38782e6	+	3.91448e6i	0.530248	+	0.385248i
$636$	7.01176e6	+	5.09434e6i	0.687360	+	0.499396i
$637$	11833.4	+	36419.6i	0.00115548	+	0.00355620i
$638$	145235.	+	105520.i	0.0141260	+	0.0102632i
$639$	1.16003e7	−	8.42813e6i	1.12388	−	0.816543i
$640$	182052.	−	560300.i	0.0175690	−	0.0540718i
$641$	3.00649e6	−	2.18434e6i	0.289011	−	0.209979i	−0.433827	−	0.900996i	$-0.642837\pi$
$641$	3.00649e6	−	2.18434e6i	0.289011	−	0.209979i	0.722838	+	0.691017i	$0.242837\pi$
$642$	354971.	+	1.09249e6i	0.0339904	+	0.104612i
$643$	−1.26146e6	−	3.88238e6i	−0.120323	−	0.370315i	0.872697	−	0.488262i	$-0.162369\pi$
$643$	−1.26146e6	−	3.88238e6i	−0.120323	−	0.370315i	−0.993020	+	0.117947i	$0.962369\pi$
$644$	−777541.	+	2.39302e6i	−0.0738769	+	0.227370i
$645$	3.03273e6			0.287035
$646$	−5.37023e6			−0.506304
$647$	−1.53707e6	+	4.73062e6i	−0.144355	+	0.444280i	−0.996928	−	0.0783293i	$-0.975041\pi$
$647$	−1.53707e6	+	4.73062e6i	−0.144355	+	0.444280i	0.852572	+	0.522610i	$0.175041\pi$
$648$	2.92578e6	+	2.12571e6i	0.273719	+	0.198868i
$649$	3.21476e6	−	2.33566e6i	0.299597	−	0.217670i
$650$	−20448.4			−0.00189835
$651$	7.33559e6	−	3.19943e6i	0.678395	−	0.295883i
$652$	−645024.			−0.0594233
$653$	8.59236e6	−	6.24271e6i	0.788550	−	0.572915i	−0.118982	−	0.992896i	$-0.537963\pi$
$653$	8.59236e6	−	6.24271e6i	0.788550	−	0.572915i	0.907533	+	0.419981i	$0.137963\pi$
$654$	6.60947e6	+	4.80206e6i	0.604258	+	0.439019i
$655$	−1.64016e6	+	5.04789e6i	−0.149376	+	0.459734i
$656$	2.04487e6			0.185526
$657$	−3.96060e7			−3.57971
$658$	1.22437e6	−	3.76823e6i	0.110242	−	0.339291i
$659$	3.10375e6	+	9.55236e6i	0.278402	+	0.856835i	0.988299	+	0.152529i	$0.0487417\pi$
$659$	3.10375e6	+	9.55236e6i	0.278402	+	0.856835i	−0.709897	+	0.704306i	$0.751258\pi$
$660$	859947.	+	2.64665e6i	0.0768443	+	0.236503i
$661$	−3.08829e6	+	2.24378e6i	−0.274925	+	0.199745i	−0.716701	−	0.697381i	$-0.754349\pi$
$661$	−3.08829e6	+	2.24378e6i	−0.274925	+	0.199745i	0.441776	+	0.897126i	$0.354349\pi$
$662$	321596.	−	989771.i	0.0285211	−	0.0877788i
$663$	101310.	−	73606.2i	0.00895096	−	0.00650325i
$664$	1.91559e6	+	1.39176e6i	0.168609	+	0.122502i
$665$	−497195.	−	1.53021e6i	−0.0435986	−	0.134183i
$666$	−1.89044e7	−	1.37348e7i	−1.65149	−	1.19988i
$667$	−572594.	−	416014.i	−0.0498347	−	0.0362071i
$668$	−2.91372e6	−	8.96750e6i	−0.252642	−	0.777553i
$669$	1.26507e7	+	9.19130e6i	1.09283	+	0.793984i
$670$	−6.83396e6	+	4.96516e6i	−0.588147	+	0.427314i
$671$	3.03923e6	−	9.35380e6i	0.260590	−	0.802013i
$672$	1.23909e6	−	900253.i	0.105847	−	0.0769027i
$673$	−2.25202e6	−	6.93101e6i	−0.191662	−	0.589874i	−0.999999	−	0.00115472i	$-0.999632\pi$
$673$	−2.25202e6	−	6.93101e6i	−0.191662	−	0.589874i	0.808338	−	0.588719i	$-0.200368\pi$
$674$	−3.52273e6	−	1.08418e7i	−0.298696	−	0.919292i
$675$	−3.65201e6	+	1.12397e7i	−0.308512	+	0.949504i
$676$	−5.94056e6			−0.499990
$677$	−1.46951e7			−1.23225			−0.616126	−	0.787648i	$-0.711299\pi$
$677$	−1.46951e7			−1.23225			−0.616126	+	0.787648i	$0.711299\pi$
$678$	−6.22963e6	+	1.91728e7i	−0.520461	+	1.60181i
$679$	−3.73396e6	−	2.71288e6i	−0.310810	−	0.225817i
$680$	−3.10201e6	+	2.25374e6i	−0.257259	+	0.186910i
$681$	−180557.			−0.0149192
$682$	−372684.	−	3.82534e6i	−0.0306817	−	0.314927i
$683$	−1.70528e7			−1.39876			−0.699381	−	0.714750i	$-0.746541\pi$
$683$	−1.70528e7			−1.39876			−0.699381	+	0.714750i	$0.746541\pi$
$684$	−5.03261e6	+	3.65641e6i	−0.411295	+	0.298823i
$685$	4.14076e6	+	3.00844e6i	0.337174	+	0.244971i
$686$	2.09558e6	−	6.44952e6i	0.170017	−	0.523259i
$687$	7.79651e6			0.630244
$688$	−801609.			−0.0645641
$689$	17341.3	−	53370.9i	0.00139166	−	0.00428309i
$690$	−3.39037e6	−	1.04345e7i	−0.271096	−	0.834349i
$691$	−3.00383e6	−	9.24485e6i	−0.239321	−	0.736554i	−0.996519	−	0.0833687i	$-0.973432\pi$
$691$	−3.00383e6	−	9.24485e6i	−0.239321	−	0.736554i	0.757198	−	0.653186i	$-0.226568\pi$
$692$	6.91659e6	−	5.02520e6i	0.549069	−	0.398922i
$693$	−1.48683e6	+	4.57601e6i	−0.117606	+	0.361954i
$694$	1.23293e6	−	895779.i	0.0971720	−	0.0705996i
$695$	1.13215e7	+	8.22557e6i	0.889085	+	0.645958i
$696$	133130.	+	409733.i	0.0104173	+	0.0320610i
$697$	−1.07670e7	−	7.82267e6i	−0.839484	−	0.609921i
$698$	−1.01325e6	−	736172.i	−0.0787190	−	0.0571927i
$699$	−3.25949e6	−	1.00317e7i	−0.252323	−	0.776570i
$700$	1.31686e6	+	956753.i	0.101577	+	0.0737997i
$701$	1.26865e7	−	9.21726e6i	0.975093	−	0.708446i	0.0184862	−	0.999829i	$-0.494115\pi$
$701$	1.26865e7	−	9.21726e6i	0.975093	−	0.708446i	0.956607	+	0.291383i	$0.0941153\pi$
$702$	22249.8	−	68477.9i	0.00170405	−	0.00524454i
$703$	7.89278e6	−	5.73444e6i	0.602340	−	0.437626i
$704$	−227300.	−	699558.i	−0.0172850	−	0.0531976i
$705$	5.33872e6	+	1.64309e7i	0.404543	+	1.24505i
$706$	4.35226e6	−	1.33949e7i	0.328627	−	1.01141i
$707$	−1.04122e7			−0.783416
$708$	9.53612e6			0.714971
$709$	−3.40913e6	+	1.04922e7i	−0.254700	+	0.783885i	0.739189	+	0.673498i	$0.235209\pi$
$709$	−3.40913e6	+	1.04922e7i	−0.254700	+	0.783885i	−0.993889	+	0.110387i	$0.964791\pi$
$710$	3.45804e6	+	2.51241e6i	0.257445	+	0.187045i
$711$	−1.06756e7	+	7.75627e6i	−0.791987	+	0.575412i
$712$	6.34542e6			0.469094
$713$	1.46932e6	+	1.50815e7i	0.108241	+	1.11102i
$714$	−9.96821e6			−0.731765
$715$	14577.3	−	10591.0i	0.00106638	−	0.000774769i
$716$	−5.66934e6	−	4.11902e6i	−0.413285	−	0.300269i
$717$	1.09864e7	−	3.38127e7i	0.798102	−	2.45631i
$718$	−3.66182e6			−0.265086
$719$	7.48780e6			0.540172			0.270086	−	0.962836i	$-0.412948\pi$
$719$	7.48780e6			0.540172			0.270086	+	0.962836i	$0.412948\pi$
$720$	−1.37249e6	+	4.22410e6i	−0.0986687	+	0.303671i
$721$	1.77244e6	+	5.45499e6i	0.126979	+	0.390801i
$722$	2.25805e6	+	6.94957e6i	0.161210	+	0.496152i
$723$	3.61908e7	−	2.62941e7i	2.57485	−	1.87074i
$724$	−1.66060e6	+	5.11081e6i	−0.117739	+	0.362362i
$725$	−370414.	+	269121.i	−0.0261723	+	0.0190153i
$726$	−1.12269e7	−	8.15679e6i	−0.790527	−	0.574351i
$727$	4.26543e6	+	1.31276e7i	0.299314	+	0.921193i	0.981738	+	0.190237i	$0.0609256\pi$
$727$	4.26543e6	+	1.31276e7i	0.299314	+	0.921193i	−0.682425	+	0.730956i	$0.739074\pi$
$728$	−8022.93	−	5829.00i	−0.000561054	−	0.000407630i
$729$	1.21010e7	+	8.79188e6i	0.843338	+	0.612721i
$730$	−3.64841e6	−	1.12286e7i	−0.253394	−	0.779867i
$731$	4.22076e6	+	3.06656e6i	0.292144	+	0.212255i
$732$	1.90950e7	−	1.38733e7i	1.31717	−	0.956980i
$733$	−8.21707e6	+	2.52895e7i	−0.564881	+	1.73852i	0.103424	+	0.994637i	$0.467020\pi$
$733$	−8.21707e6	+	2.52895e7i	−0.564881	+	1.73852i	−0.668305	+	0.743887i	$0.732980\pi$
$734$	−5.75824e6	+	4.18361e6i	−0.394503	+	0.286623i
$735$	4.10730e6	+	1.26410e7i	0.280439	+	0.863101i
$736$	896138.	+	2.75803e6i	0.0609790	+	0.187674i
$737$	−3.25912e6	+	1.00305e7i	−0.221020	+	0.680230i
$738$	−1.54163e7			−1.04193
$739$	−1.09231e6			−0.0735757			−0.0367879	−	0.999323i	$-0.511713\pi$
$739$	−1.09231e6			−0.0735757			−0.0367879	+	0.999323i	$0.511713\pi$
$740$	2.15252e6	−	6.62478e6i	0.144500	−	0.444725i
$741$	48996.4	+	35598.0i	0.00327807	+	0.00238166i
$742$	−3.61391e6	+	2.62566e6i	−0.240973	+	0.175077i
$743$	2.53984e7			1.68785			0.843926	−	0.536459i	$-0.180239\pi$
$743$	2.53984e7			1.68785			0.843926	+	0.536459i	$0.180239\pi$
$744$	4.67240e6	−	7.95261e6i	0.309462	−	0.526717i
$745$	585649.			0.0386586
$746$	2.49371e6	−	1.81179e6i	0.164058	−	0.119195i
$747$	−1.44416e7	−	1.04925e7i	−0.946923	−	0.687980i
$748$	−1.47935e6	+	4.55297e6i	−0.0966756	+	0.297537i
$749$	−592055.			−0.0385618
$750$	−1.92041e7			−1.24664
$751$	7.39978e6	−	2.27742e7i	0.478761	−	1.47348i	−0.362056	−	0.932156i	$-0.617925\pi$
$751$	7.39978e6	−	2.27742e7i	0.478761	−	1.47348i	0.840817	−	0.541319i	$-0.182075\pi$
$752$	−1.41112e6	−	4.34299e6i	−0.0909956	−	0.280056i
$753$	4.40305e6	+	1.35512e7i	0.282987	+	0.870944i
$754$	2256.74	−	1639.62i	0.000144562	−	0.000105030i
$755$	−563102.	+	1.73305e6i	−0.0359517	+	0.110648i
$756$	−4.63685e6	+	3.36887e6i	−0.295066	+	0.214378i
$757$	−4.01790e6	−	2.91918e6i	−0.254835	−	0.185149i	0.453032	−	0.891494i	$-0.350342\pi$
$757$	−4.01790e6	−	2.91918e6i	−0.254835	−	0.185149i	−0.707867	+	0.706346i	$0.750342\pi$
$758$	−5.27187e6	−	1.62251e7i	−0.333266	−	1.02569i
$759$	−1.10822e7	−	8.05168e6i	−0.698266	−	0.507320i
$760$	−1.50022e6	−	1.08997e6i	−0.0942149	−	0.0684511i
$761$	−2.50636e6	−	7.71377e6i	−0.156885	−	0.482842i	0.841462	−	0.540316i	$-0.181695\pi$
$761$	−2.50636e6	−	7.71377e6i	−0.156885	−	0.482842i	−0.998347	+	0.0574741i	$0.981695\pi$
$762$	1.61435e7	+	1.17289e7i	1.00719	+	0.731763i
$763$	−3.40657e6	+	2.47502e6i	−0.211839	+	0.153910i
$764$	2.07540e6	−	6.38744e6i	0.128638	−	0.395907i
$765$	2.33861e7	−	1.69910e7i	1.44479	−	1.04970i
$766$	−2.41056e6	−	7.41894e6i	−0.148438	−	0.456846i
$767$	−19080.2	−	58722.9i	−0.00117110	−	0.00360428i
$768$	545481.	−	1.67882e6i	0.0333716	−	0.102707i
$769$	−1.88101e7			−1.14703			−0.573516	−	0.819194i	$-0.694421\pi$
$769$	−1.88101e7			−1.14703			−0.573516	+	0.819194i	$0.694421\pi$
$770$	−1.43430e6			−0.0871793
$771$	3.90784e6	−	1.20271e7i	0.236756	−	0.728661i
$772$	5.80298e6	+	4.21611e6i	0.350435	+	0.254606i
$773$	−1.08598e7	+	7.89013e6i	−0.653694	+	0.474936i	−0.864528	−	0.502585i	$-0.832382\pi$
$773$	−1.08598e7	+	7.89013e6i	−0.653694	+	0.474936i	0.210834	+	0.977522i	$0.432382\pi$
$774$	6.04333e6			0.362597
$775$	9.57253e6	+	2.11088e6i	0.572496	+	0.126244i
$776$	−5.31941e6			−0.317110
$777$	1.46506e7	−	1.06443e7i	0.870567	−	0.632504i
$778$	−1.89090e6	−	1.37382e6i	−0.112000	−	0.0813730i
$779$	1.98898e6	−	6.12144e6i	0.117432	−	0.361418i
$780$	43241.3			0.00254485
$781$	5.33674e6			0.313075
$782$	5.83238e6	−	1.79502e7i	0.341058	−	1.04967i
$783$	−498191.	−	1.53328e6i	−0.0290397	−	0.0893749i
$784$	−1.08564e6	−	3.34124e6i	−0.0630804	−	0.194141i
$785$	−598001.	+	434473.i	−0.0346360	+	0.0251645i
$786$	−4.91438e6	+	1.51249e7i	−0.283735	+	0.873246i
$787$	2.57675e7	−	1.87212e7i	1.48298	−	1.07745i	0.506399	−	0.862299i	$-0.330976\pi$
$787$	2.57675e7	−	1.87212e7i	1.48298	−	1.07745i	0.976581	−	0.215149i	$-0.0690237\pi$
$788$	7.12811e6	+	5.17888e6i	0.408939	+	0.297112i
$789$	1.59550e6	+	4.91045e6i	0.0912442	+	0.280821i
$790$	−3.18238e6	−	2.31213e6i	−0.181419	−	0.131809i
$791$	−8.40598e6	−	6.10730e6i	−0.477691	−	0.347063i
$792$	1.71362e6	+	5.27398e6i	0.0970736	+	0.298762i
$793$	−123637.	−	89827.6i	−0.00698177	−	0.00507255i
$794$	1.83268e7	−	1.33152e7i	1.03166	−	0.749543i
$795$	6.01902e6	−	1.85246e7i	0.337760	−	1.03952i
$796$	1.18260e6	−	859207.i	0.0661537	−	0.0480635i
$797$	6.51807e6	+	2.00605e7i	0.363474	+	1.11866i	0.950931	+	0.309402i	$0.100129\pi$
$797$	6.51807e6	+	2.00605e7i	0.363474	+	1.11866i	−0.587458	+	0.809255i	$0.699871\pi$
$798$	−1.48974e6	−	4.58495e6i	−0.0828139	−	0.254875i
$799$	−9.18409e6	+	2.82657e7i	−0.508943	+	1.56637i
$800$	1.87600e6			0.103635
$801$	−4.78382e7			−2.63447
$802$	−7.75268e6	+	2.38603e7i	−0.425614	+	1.30991i
$803$	−1.19257e7	−	8.66449e6i	−0.652670	−	0.474192i
$804$	−2.04765e7	+	1.48771e7i	−1.11716	+	0.811665i
$805$	5.65477e6			0.307557
$806$	−58320.4	−	12860.5i	−0.00316216	−	0.000697301i
$807$	−3.66303e6			−0.197996
$808$	−9.70845e6	+	7.05360e6i	−0.523145	+	0.380087i
$809$	−1.96707e7	−	1.42916e7i	−1.05669	−	0.767731i	−0.0832175	−	0.996531i	$-0.526520\pi$
$809$	−1.96707e7	−	1.42916e7i	−1.05669	−	0.767731i	−0.973473	+	0.228801i	$0.926520\pi$
$810$	2.51155e6	−	7.72974e6i	0.134502	−	0.413954i
$811$	5.18635e6			0.276892			0.138446	−	0.990370i	$-0.455789\pi$
$811$	5.18635e6			0.276892			0.138446	+	0.990370i	$0.455789\pi$
$812$	−222047.			−0.0118183
$813$	−7.93595e6	+	2.44243e7i	−0.421088	+	1.29597i
$814$	−2.68751e6	−	8.27132e6i	−0.142164	−	0.437536i
$815$	447953.	+	1.37866e6i	0.0236232	+	0.0727047i
$816$	−9.29451e6	+	6.75285e6i	−0.488653	+	0.355027i
$817$	−779698.	+	2.39966e6i	−0.0408669	+	0.125775i
$818$	1.82783e7	−	1.32800e7i	0.955110	−	0.693928i
$819$	60484.9	+	43944.9i	0.00315092	+	0.00228928i
$820$	−1.42011e6	−	4.37065e6i	−0.0737543	−	0.226992i
$821$	−1.78743e7	−	1.29864e7i	−0.925488	−	0.672406i	0.0193962	−	0.999812i	$-0.493826\pi$
$821$	−1.78743e7	−	1.29864e7i	−0.925488	−	0.672406i	−0.944884	+	0.327406i	$0.893826\pi$
$822$	1.24069e7	+	9.01415e6i	0.640448	+	0.465313i
$823$	−4.43763e6	−	1.36576e7i	−0.228376	−	0.702870i	−0.997931	−	0.0642894i	$-0.979522\pi$
$823$	−4.43763e6	−	1.36576e7i	−0.228376	−	0.702870i	0.769555	−	0.638581i	$-0.220478\pi$
$824$	5.34807e6	+	3.88560e6i	0.274397	+	0.199361i
$825$	−7.16912e6	+	5.20867e6i	−0.366717	+	0.266435i
$826$	−1.51881e6	+	4.67443e6i	−0.0774559	+	0.238385i
$827$	−3.66079e6	+	2.65972e6i	−0.186128	+	0.135230i	−0.676947	−	0.736032i	$-0.736697\pi$
$827$	−3.66079e6	+	2.65972e6i	−0.186128	+	0.135230i	0.490819	+	0.871261i	$0.336697\pi$
$828$	−6.75599e6	−	2.07928e7i	−0.342463	−	1.05399i
$829$	−1.18362e6	−	3.64281e6i	−0.0598173	−	0.184099i	0.916683	−	0.399616i	$-0.130856\pi$
$829$	−1.18362e6	−	3.64281e6i	−0.0598173	−	0.184099i	−0.976500	+	0.215517i	$0.930856\pi$
$830$	1.64437e6	−	5.06086e6i	0.0828525	−	0.254994i
$831$	2.81002e6			0.141159
$832$	−11429.5			−0.000572425
$833$	−7.06570e6	+	2.17460e7i	−0.352812	+	1.08584i
$834$	3.39226e7	+	2.46462e7i	1.68878	+	1.22697i
$835$	−1.71434e7	+	1.24554e7i	−0.850904	+	0.618218i
$836$	−2.31526e6			−0.114573
$837$	−1.74847e7	+	2.97597e7i	−0.862672	+	1.46830i
$838$	1.41662e7			0.696858
$839$	−1.01244e7	+	7.35584e6i	−0.496554	+	0.360767i	−0.807699	−	0.589595i	$-0.799287\pi$
$839$	−1.01244e7	+	7.35584e6i	−0.496554	+	0.360767i	0.311145	+	0.950362i	$0.399287\pi$
$840$	−2.78470e6	−	2.02320e6i	−0.136169	−	0.0989329i
$841$	−6.31899e6	+	1.94479e7i	−0.308076	+	0.948160i
$842$	1.73863e7			0.845136
$843$	−3.37816e7			−1.63724
$844$	−4.32152e6	+	1.33003e7i	−0.208824	+	0.642695i
$845$	4.12557e6	+	1.26972e7i	0.198766	+	0.611739i
$846$	1.06385e7	+	3.27419e7i	0.511038	+	1.57281i
$847$	5.78641e6	−	4.20407e6i	0.277141	−	0.201355i
$848$	−1.59094e6	+	4.89641e6i	−0.0759739	+	0.233824i
$849$	3.95423e7	−	2.87292e7i	1.88275	−	1.36790i
$850$	−9.87782e6	−	7.17666e6i	−0.468936	−	0.340702i
$851$	1.05956e7	+	3.26099e7i	0.501535	+	1.54357i
$852$	1.03613e7	+	7.52792e6i	0.489007	+	0.355284i
$853$	−6.78684e6	−	4.93093e6i	−0.319371	−	0.232036i	0.416536	−	0.909119i	$-0.363244\pi$
$853$	−6.78684e6	−	4.93093e6i	−0.319371	−	0.232036i	−0.735907	+	0.677083i	$0.763244\pi$
$854$	3.75919e6	+	1.15696e7i	0.176380	+	0.542843i
$855$	1.13101e7	+	8.21729e6i	0.529118	+	0.384427i
$856$	−552041.	+	401081.i	−0.0257506	+	0.0187089i
$857$	7.05361e6	−	2.17088e7i	0.328064	−	1.00968i	−0.641974	−	0.766727i	$-0.721884\pi$
$857$	7.05361e6	−	2.17088e7i	0.328064	−	1.00968i	0.970038	−	0.242952i	$-0.0781158\pi$
$858$	43677.7	−	31733.7i	0.00202554	−	0.00147164i
$859$	1.01250e7	+	3.11616e7i	0.468180	+	1.44091i	0.854939	+	0.518729i	$0.173595\pi$
$859$	1.01250e7	+	3.11616e7i	0.468180	+	1.44091i	−0.386759	+	0.922181i	$0.626405\pi$
$860$	556697.	+	1.71334e6i	0.0256669	+	0.0789945i
$861$	3.69193e6	−	1.13626e7i	0.169725	−	0.522360i
$862$	−1.41221e7			−0.647340
$863$	2.70314e7			1.23550			0.617748	−	0.786376i	$-0.288045\pi$
$863$	2.70314e7			1.23550			0.617748	+	0.786376i	$0.288045\pi$
$864$	−2.04126e6	+	6.28237e6i	−0.0930283	+	0.286312i
$865$	−1.55441e7	−	1.12935e7i	−0.706360	−	0.513200i
$866$	−1.61555e7	+	1.17377e7i	−0.732026	+	0.531848i
$867$	3.65282e7			1.65037
$868$	3.15405e6	+	3.55693e6i	0.142092	+	0.160242i
$869$	−4.91131e6			−0.220622
$870$	783297.	−	569098.i	0.0350855	−	0.0254911i
$871$	132582.	+	96326.7i	0.00592161	+	0.00430230i
$872$	−1.49966e6	+	4.61549e6i	−0.0667886	+	0.205554i
$873$	4.01031e7			1.78091
$874$	9.12797e6			0.404199
$875$	3.05863e6	−	9.41349e6i	0.135054	−	0.415652i
$876$	−1.09317e7	−	3.36443e7i	−0.481312	−	1.48133i
$877$	−3.31758e6	−	1.02105e7i	−0.145654	−	0.448277i	0.851440	−	0.524451i	$-0.175730\pi$
$877$	−3.31758e6	−	1.02105e7i	−0.145654	−	0.448277i	−0.997095	+	0.0761742i	$0.975730\pi$
$878$	−1.99173e7	+	1.44708e7i	−0.871956	+	0.633513i
$879$	−1.56189e7	+	4.80701e7i	−0.681835	+	2.09847i
$880$	−1.33736e6	+	971651.i	−0.0582160	+	0.0422964i
$881$	5.32445e6	+	3.86844e6i	0.231119	+	0.167918i	0.697317	−	0.716762i	$-0.254377\pi$
$881$	5.32445e6	+	3.86844e6i	0.231119	+	0.167918i	−0.466199	+	0.884680i	$0.654377\pi$
$882$	8.18462e6	+	2.51897e7i	0.354264	+	1.09031i
$883$	−1.13581e7	−	8.25213e6i	−0.490234	−	0.356176i	0.315041	−	0.949078i	$-0.397982\pi$
$883$	−1.13581e7	−	8.25213e6i	−0.490234	−	0.356176i	−0.805274	+	0.592903i	$0.797982\pi$
$884$	60180.5	+	43723.7i	0.00259015	+	0.00188185i
$885$	−6.62260e6	−	2.03823e7i	−0.284230	−	0.874770i
$886$	2.29137e7	+	1.66478e7i	0.980645	+	0.712480i
$887$	−1.77532e7	+	1.28985e7i	−0.757648	+	0.550464i	−0.898188	−	0.439611i	$-0.855116\pi$
$887$	−1.77532e7	+	1.28985e7i	−0.757648	+	0.550464i	0.140540	+	0.990075i	$0.455116\pi$
$888$	6.44957e6	−	1.98497e7i	0.274472	−	0.844739i
$889$	−8.32047e6	+	6.04517e6i	−0.353096	+	0.256540i
$890$	−4.40673e6	−	1.35625e7i	−0.186484	−	0.573939i
$891$	−3.13577e6	−	9.65091e6i	−0.132328	−	0.407262i
$892$	−2.87040e6	+	8.83419e6i	−0.120790	+	0.371753i
$893$	−1.43736e7			−0.603165
$894$	1.75477e6			0.0734306
$895$	−4.86667e6	+	1.49781e7i	−0.203083	+	0.625026i
$896$	736048.	+	534770.i	0.0306292	+	0.0222534i
$897$	−172201.	+	125111.i	−0.00714585	+	0.00519176i
$898$	−1.78541e7			−0.738835
$899$	−1.22571e6	+	534593.i	−0.0505809	+	0.0220609i
$900$	−1.41432e7			−0.582024
$901$	2.71082e7	−	1.96952e7i	1.11247	−	0.808257i
$902$	−4.64195e6	−	3.37258e6i	−0.189970	−	0.138021i
$903$	−1.44727e6	+	4.45425e6i	−0.0590652	+	0.181784i
$904$	−1.19752e7			−0.487373
$905$	1.20770e7			0.490158
$906$	−1.68722e6	+	5.19272e6i	−0.0682889	+	0.210172i
$907$	−6.82038e6	−	2.09910e7i	−0.275290	−	0.847255i	−0.989143	−	0.146959i	$-0.953051\pi$
$907$	−6.82038e6	−	2.09910e7i	−0.275290	−	0.847255i	0.713853	−	0.700296i	$-0.246949\pi$
$908$	−33143.5	−	102005.i	−0.00133408	−	0.00410589i
$909$	7.31921e7	−	5.31772e7i	2.93802	−	2.13460i
$910$	−6887.03	+	21196.1i	−0.000275695	+	0.000848501i
$911$	−3.15133e7	+	2.28958e7i	−1.25805	+	0.914027i	−0.998660	−	0.0517458i	$-0.983521\pi$
$911$	−3.15133e7	+	2.28958e7i	−1.25805	+	0.914027i	−0.259390	+	0.965773i	$0.583521\pi$
$912$	−4.49508e6	−	3.26586e6i	−0.178958	−	0.130020i
$913$	−2.05307e6	−	6.31871e6i	−0.0815131	−	0.250871i
$914$	1.03782e7	+	7.54020e6i	0.410919	+	0.298550i
$915$	−4.29135e7	−	3.11785e7i	−1.69450	−	1.23112i
$916$	1.43115e6	+	4.40463e6i	0.0563568	+	0.173448i
$917$	−6.63124e6	−	4.81788e6i	−0.260418	−	0.189205i
$918$	3.47813e7	−	2.52701e7i	1.36219	−	0.989692i
$919$	3.02652e6	−	9.31467e6i	0.118210	−	0.363813i	−0.874393	−	0.485219i	$-0.838740\pi$
$919$	3.02652e6	−	9.31467e6i	0.118210	−	0.363813i	0.992603	+	0.121405i	$0.0387400\pi$
$920$	5.27259e6	−	3.83076e6i	0.205378	−	0.149216i
$921$	5.07929e6	+	1.56325e7i	0.197312	+	0.607265i
$922$	−4.07495e6	−	1.25414e7i	−0.157868	−	0.485869i
$923$	25625.2	−	78866.4i	0.000990065	−	0.00304711i
$924$	−4.29758e6			−0.165594
$925$	2.21811e7			0.852372
$926$	−1.93860e6	+	5.96641e6i	−0.0742954	+	0.228658i
$927$	−4.03192e7	−	2.92936e7i	−1.54103	−	1.11963i
$928$	−207040.	+	150423.i	−0.00789195	+	0.00573384i
$929$	−2.40300e7			−0.913512			−0.456756	−	0.889592i	$-0.650989\pi$
$929$	−2.40300e7			−0.913512			−0.456756	+	0.889592i	$0.650989\pi$
$930$	−2.02426e7	−	4.46378e6i	−0.767464	−	0.169237i
$931$	−1.10582e7			−0.418128
$932$	5.06906e6	−	3.68288e6i	0.191156	−	0.138883i
$933$	6.66129e6	+	4.83971e6i	0.250527	+	0.182019i
$934$	−4.30064e6	+	1.32360e7i	−0.161312	+	0.496466i
$935$	1.07588e7			0.402470
$936$	86167.0			0.00321478
$937$	2.78929e6	−	8.58456e6i	0.103788	−	0.319425i	−0.885656	−	0.464341i	$-0.846291\pi$
$937$	2.78929e6	−	8.58456e6i	0.103788	−	0.319425i	0.989444	+	0.144916i	$0.0462912\pi$
$938$	−4.03117e6	−	1.24067e7i	−0.149598	−	0.460414i
$939$	−2.26138e7	−	6.95980e7i	−0.836968	−	2.57592i
$940$	−8.30261e6	+	6.03220e6i	−0.306475	+	0.222667i
$941$	−4.60041e6	+	1.41586e7i	−0.169365	+	0.521251i	−0.999331	−	0.0365623i	$-0.988359\pi$
$941$	−4.60041e6	+	1.41586e7i	−0.169365	+	0.521251i	0.829967	+	0.557813i	$0.188359\pi$
$942$	−1.79178e6	+	1.30181e6i	−0.0657897	+	0.0477990i
$943$	1.83010e7	+	1.32965e7i	0.670188	+	0.486920i
$944$	1.75048e6	+	5.38741e6i	0.0639332	+	0.196766i
$945$	1.04207e7	+	7.57109e6i	0.379593	+	0.275790i
$946$	1.81969e6	+	1.32208e6i	0.0661104	+	0.0480320i
$947$	6.22180e6	+	1.91487e7i	0.225445	+	0.693849i	0.998246	+	0.0592006i	$0.0188552\pi$
$947$	6.22180e6	+	1.91487e7i	0.225445	+	0.693849i	−0.772801	+	0.634649i	$0.781145\pi$
$948$	−9.53532e6	−	6.92781e6i	−0.344599	−	0.250366i
$949$	−185307.	+	134633.i	−0.00667923	+	0.00485274i
$950$	1.82472e6	−	5.61592e6i	0.0655976	−	0.201889i
$951$	4.67962e7	−	3.39994e7i	1.67787	−	1.21905i
$952$	−1.82979e6	−	5.63152e6i	−0.0654349	−	0.201388i
$953$	−8.33045e6	−	2.56385e7i	−0.297123	−	0.914451i	−0.982500	−	0.186262i	$-0.940363\pi$
$953$	−8.33045e6	−	2.56385e7i	−0.297123	−	0.914451i	0.685377	−	0.728188i	$-0.259637\pi$
$954$	1.19941e7	−	3.69141e7i	0.426675	−	1.31317i
$955$	−1.50937e7			−0.535533
$956$	2.11191e7			0.747363
$957$	373555.	−	1.14968e6i	0.0131848	−	0.0405787i
$958$	−9.41987e6	−	6.84394e6i	−0.331613	−	0.240931i
$959$	−6.39461e6	+	4.64596e6i	−0.224527	+	0.163128i
$960$	−3.96709e6			−0.138929
$961$	2.59740e7	+	1.20408e7i	0.907257	+	0.420577i
$962$	−135138.			−0.00470804
$963$	4.16184e6	−	3.02375e6i	0.144617	−	0.105070i
$964$	2.14981e7	+	1.56193e7i	0.745088	+	0.541338i
$965$	4.98138e6	−	1.53311e7i	0.172199	−	0.529975i
$966$	1.69433e7			0.584192
$967$	1.05508e7			0.362843			0.181421	−	0.983405i	$-0.441930\pi$
$967$	1.05508e7			0.362843			0.181421	+	0.983405i	$0.441930\pi$
$968$	2.54733e6	−	7.83988e6i	0.0873769	−	0.268919i
$969$	1.11746e7	+	3.43919e7i	0.382317	+	1.17665i
$970$	3.69420e6	+	1.13696e7i	0.126064	+	0.387985i
$971$	1.12030e7	−	8.13944e6i	0.381316	−	0.277043i	−0.380571	−	0.924752i	$-0.624273\pi$
$971$	1.12030e7	−	8.13944e6i	0.381316	−	0.277043i	0.761888	+	0.647709i	$0.224273\pi$
$972$	−225115.	+	692834.i	−0.00764257	+	0.0235214i
$973$	−1.74839e7	+	1.27028e7i	−0.592048	+	0.430148i
$974$	−2.72875e7	−	1.98255e7i	−0.921651	−	0.669618i
$975$	42550.0	+	130955.i	0.00143347	+	0.00441176i
$976$	1.13428e7	+	8.24105e6i	0.381151	+	0.276922i
$977$	−5.50022e6	−	3.99614e6i	−0.184350	−	0.133938i	0.491783	−	0.870718i	$-0.336345\pi$
$977$	−5.50022e6	−	3.99614e6i	−0.184350	−	0.133938i	−0.676133	+	0.736780i	$0.736345\pi$
$978$	1.34220e6	+	4.13086e6i	0.0448713	+	0.138100i
$979$	−1.44044e7	−	1.04654e7i	−0.480329	−	0.348979i
$980$	−6.38754e6	+	4.64082e6i	−0.212456	+	0.154358i
$981$	1.13060e7	−	3.47962e7i	0.375090	−	1.15441i
$982$	−1.47976e7	+	1.07511e7i	−0.489680	+	0.355774i
$983$	−9.44420e6	−	2.90663e7i	−0.311732	−	0.959413i	−0.977079	−	0.212878i	$-0.931716\pi$
$983$	−9.44420e6	−	2.90663e7i	−0.311732	−	0.959413i	0.665347	−	0.746535i	$-0.268284\pi$
$984$	−4.25506e6	−	1.30957e7i	−0.140093	−	0.431163i
$985$	6.11890e6	−	1.88320e7i	0.200948	−	0.618453i
$986$	1.66559e6			0.0545601
$987$	−2.66802e7			−0.871758
$988$	−11117.1	+	34214.9i	−0.000362325	+	0.00111512i
$989$	−7.17418e6	−	5.21235e6i	−0.233229	−	0.169450i
$990$	1.00824e7	−	7.32529e6i	0.326946	−	0.237540i
$991$	−3.07735e6			−0.0995388			−0.0497694	−	0.998761i	$-0.515849\pi$
$991$	−3.07735e6			−0.0995388			−0.0497694	+	0.998761i	$0.515849\pi$
$992$	5.35049e6	+	1.17986e6i	0.172629	+	0.0380672i
$993$	−7.00787e6			−0.225534
$994$	−5.34029e6	+	3.87994e6i	−0.171435	+	0.124555i
$995$	−2.65773e6	−	1.93095e6i	−0.0851046	−	0.0618321i
$996$	4.92702e6	−	1.51638e7i	0.157375	−	0.484351i
$997$	2.21935e7			0.707110			0.353555	−	0.935414i	$-0.384973\pi$
$997$	2.21935e7			0.707110			0.353555	+	0.935414i	$0.384973\pi$
$998$	7.47592e6			0.237596
$999$	−2.41352e7	+	7.42804e7i	−0.765132	+	2.35483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.6.d.b.47.1	yes	24
31.2	even	5	inner	62.6.d.b.33.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.6.d.b.33.1	✓	24	31.2	even	5	inner
62.6.d.b.47.1	yes	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	62.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.23607 - 2.35114i) q^{2} +(-21.7909 - 15.8320i) q^{3} +(4.94427 - 15.2169i) q^{4} -35.9579 q^{5} -107.740 q^{6} +(17.1597 - 52.8123i) q^{7} +(-19.7771 - 60.8676i) q^{8} +(149.100 + 458.882i) q^{9} +(-116.362 + 84.5421i) q^{10} +(-55.4932 + 170.791i) q^{11} +(-348.655 + 253.312i) q^{12} +(2.25748 + 1.64016i) q^{13} +(-68.6390 - 211.249i) q^{14} +(783.555 + 569.286i) q^{15} +(-207.108 - 150.473i) q^{16} +(514.865 + 1584.59i) q^{17} +(1561.39 + 1134.42i) q^{18} +(-651.898 + 473.631i) q^{19} +(-177.786 + 547.168i) q^{20} +(-1210.05 + 879.154i) q^{21} +(221.973 + 683.162i) q^{22} +(-875.134 - 2693.39i) q^{23} +(-532.697 + 1639.47i) q^{24} -1832.03 q^{25} +11.1616 q^{26} +(1993.42 - 6135.12i) q^{27} +(-718.797 - 522.236i) q^{28} +(202.188 - 146.898i) q^{29} +3874.11 q^{30} +(-5225.09 - 1152.21i) q^{31} -1024.00 q^{32} +(3913.21 - 2843.11i) q^{33} +(5391.74 + 3917.33i) q^{34} +(-617.028 + 1899.02i) q^{35} +7719.95 q^{36} -12107.4 q^{37} +(-996.011 + 3065.41i) q^{38} +(-23.2256 - 71.4811i) q^{39} +(711.142 + 2188.67i) q^{40} +(-6462.24 + 4695.09i) q^{41} +(-1848.79 + 5690.00i) q^{42} +(2533.26 - 1840.52i) q^{43} +(2324.53 + 1688.87i) q^{44} +(-5361.31 - 16500.4i) q^{45} +(-9164.53 - 6658.42i) q^{46} +(14431.1 + 10484.8i) q^{47} +(2130.79 + 6557.89i) q^{48} +(11102.5 + 8066.42i) q^{49} +(-5928.58 + 4307.36i) q^{50} +(13867.9 - 42681.0i) q^{51} +(36.1197 - 26.2425i) q^{52} +(-6214.61 - 19126.6i) q^{53} +(-7973.69 - 24540.5i) q^{54} +(1995.42 - 6141.27i) q^{55} -3553.93 q^{56} +21704.0 q^{57} +(308.915 - 950.743i) q^{58} +(-17901.6 - 13006.3i) q^{59} +(12536.9 - 9108.58i) q^{60} -54767.6 q^{61} +(-19617.7 + 8556.30i) q^{62} +26793.1 q^{63} +(-3313.73 + 2407.57i) q^{64} +(-81.1743 - 58.9766i) q^{65} +(5978.85 - 18401.0i) q^{66} +58730.1 q^{67} +26658.2 q^{68} +(-23571.8 + 72546.5i) q^{69} +(2468.11 + 7596.07i) q^{70} +(-9183.34 - 28263.4i) q^{71} +(24982.3 - 18150.7i) q^{72} +(-25365.8 + 78068.0i) q^{73} +(-39180.4 + 28466.2i) q^{74} +(39921.6 + 29004.7i) q^{75} +(3984.04 + 12261.6i) q^{76} +(8067.59 + 5861.44i) q^{77} +(-243.222 - 176.711i) q^{78} +(8451.28 + 26010.4i) q^{79} +(7447.18 + 5410.69i) q^{80} +(-45715.4 + 33214.2i) q^{81} +(-9873.43 + 30387.3i) q^{82} +(-29931.0 + 21746.2i) q^{83} +(7395.17 + 22760.0i) q^{84} +(-18513.5 - 56978.6i) q^{85} +(3870.48 - 11912.1i) q^{86} -6731.54 q^{87} +11493.1 q^{88} +(-30638.1 + 94294.5i) q^{89} +(-56144.3 - 40791.3i) q^{90} +(125.358 - 91.0781i) q^{91} -45311.9 q^{92} +(95617.7 + 107831. i) q^{93} +71351.5 q^{94} +(23440.9 - 17030.8i) q^{95} +(22313.9 + 16212.0i) q^{96} +(25684.2 - 79047.8i) q^{97} +54893.6 q^{98} -86646.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{2} - 2 q^{3} - 96 q^{4} - 4 q^{5} + 8 q^{6} - 246 q^{7} + 384 q^{8} - 572 q^{9} + 596 q^{10} - 62 q^{11} - 32 q^{12} - 935 q^{13} + 984 q^{14} + 3343 q^{15} - 1536 q^{16} - 311 q^{17} + 428 q^{18}+ \cdots - 347058 q^{99}+O(q^{100}) \) 24 * q + 24 * q^2 - 2 * q^3 - 96 * q^4 - 4 * q^5 + 8 * q^6 - 246 * q^7 + 384 * q^8 - 572 * q^9 + 596 * q^10 - 62 * q^11 - 32 * q^12 - 935 * q^13 + 984 * q^14 + 3343 * q^15 - 1536 * q^16 - 311 * q^17 + 428 * q^18 - 4094 * q^19 + 2416 * q^20 + 149 * q^21 + 248 * q^22 + 2719 * q^23 - 192 * q^24 - 484 * q^25 + 5320 * q^26 - 2303 * q^27 + 4704 * q^28 + 13353 * q^29 + 10408 * q^30 - 7117 * q^31 - 24576 * q^32 - 1904 * q^33 + 844 * q^34 + 5436 * q^35 + 21728 * q^36 - 55872 * q^37 - 25404 * q^38 + 19008 * q^39 - 9664 * q^40 - 9557 * q^41 + 49004 * q^42 - 3760 * q^43 + 10928 * q^44 - 2407 * q^45 - 16256 * q^46 + 44908 * q^47 + 768 * q^48 - 62986 * q^49 + 23676 * q^50 + 24658 * q^51 - 14960 * q^52 - 41007 * q^53 + 9212 * q^54 - 74553 * q^55 + 6144 * q^56 - 2368 * q^57 + 41068 * q^58 - 31734 * q^59 + 53488 * q^60 - 192700 * q^61 + 18348 * q^62 + 393066 * q^63 - 24576 * q^64 - 96202 * q^65 - 108464 * q^66 + 122022 * q^67 + 16704 * q^68 + 125538 * q^69 - 21744 * q^70 - 106651 * q^71 + 6848 * q^72 + 41543 * q^73 - 190012 * q^74 + 22898 * q^75 + 101616 * q^76 - 230254 * q^77 + 100148 * q^78 + 224694 * q^79 - 38144 * q^80 + 108929 * q^81 + 68828 * q^82 - 80770 * q^83 - 196016 * q^84 - 339465 * q^85 - 81160 * q^86 - 314616 * q^87 + 79488 * q^88 + 258277 * q^89 + 80848 * q^90 + 448172 * q^91 - 217056 * q^92 + 539557 * q^93 + 41888 * q^94 + 295692 * q^95 + 2048 * q^96 + 100250 * q^97 - 284736 * q^98 - 347058 * q^99

Introduction

L-functions

Modular forms

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