LMFDB - Embedded newform 62.6.d.a.35.5

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			35.5
Character	$\chi$	$=$	62.35
Dual form			62.6.d.a.39.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.23607 + 3.80423i) q^{2} +(6.17234 - 18.9965i) q^{3} +(-12.9443 + 9.40456i) q^{4} -50.2806 q^{5} +79.8964 q^{6} +(-60.1640 + 43.7117i) q^{7} +(-51.7771 - 37.6183i) q^{8} +(-126.178 - 91.6738i) q^{9} +(-62.1502 - 191.279i) q^{10} +(-415.284 + 301.722i) q^{11} +(98.7574 + 303.944i) q^{12} +(-197.521 + 607.907i) q^{13} +(-240.656 - 174.847i) q^{14} +(-310.349 + 955.155i) q^{15} +(79.1084 - 243.470i) q^{16} +(-334.250 - 242.847i) q^{17} +(192.783 - 593.325i) q^{18} +(-20.2858 - 62.4334i) q^{19} +(650.846 - 472.867i) q^{20} +(459.017 + 1412.71i) q^{21} +(-1661.14 - 1206.89i) q^{22} +(-2021.37 - 1468.61i) q^{23} +(-1034.20 + 751.391i) q^{24} -596.861 q^{25} -2556.76 q^{26} +(1406.44 - 1021.84i) q^{27} +(367.690 - 1131.63i) q^{28} +(-1282.64 - 3947.57i) q^{29} -4017.24 q^{30} +(-2775.01 - 4574.76i) q^{31} +1024.00 q^{32} +(3168.38 + 9751.28i) q^{33} +(510.689 - 1571.74i) q^{34} +(3025.08 - 2197.85i) q^{35} +2495.44 q^{36} +4915.05 q^{37} +(212.436 - 154.344i) q^{38} +(10328.9 + 7504.41i) q^{39} +(2603.38 + 1891.47i) q^{40} +(6006.12 + 18484.9i) q^{41} +(-4806.89 + 3492.41i) q^{42} +(1869.63 + 5754.14i) q^{43} +(2537.99 - 7811.14i) q^{44} +(6344.31 + 4609.41i) q^{45} +(3088.38 - 9505.05i) q^{46} +(3126.38 - 9622.00i) q^{47} +(-4136.80 - 3005.56i) q^{48} +(-3484.65 + 10724.7i) q^{49} +(-737.761 - 2270.60i) q^{50} +(-6676.34 + 4850.65i) q^{51} +(-3160.33 - 9726.51i) q^{52} +(-10512.2 - 7637.55i) q^{53} +(5625.75 + 4087.34i) q^{54} +(20880.7 - 15170.8i) q^{55} +4759.48 q^{56} -1311.23 q^{57} +(13432.0 - 9758.93i) q^{58} +(5563.72 - 17123.4i) q^{59} +(-4965.58 - 15282.5i) q^{60} -9974.67 q^{61} +(13973.3 - 16211.5i) q^{62} +11598.6 q^{63} +(1265.73 + 3895.53i) q^{64} +(9931.47 - 30565.9i) q^{65} +(-33179.7 + 24106.5i) q^{66} +1885.74 q^{67} +6610.49 q^{68} +(-40375.1 + 29334.2i) q^{69} +(12100.3 + 8791.41i) q^{70} +(-18542.3 - 13471.8i) q^{71} +(3084.53 + 9493.20i) q^{72} +(-56325.4 + 40922.8i) q^{73} +(6075.33 + 18697.9i) q^{74} +(-3684.03 + 11338.3i) q^{75} +(849.745 + 617.376i) q^{76} +(11796.4 - 36305.6i) q^{77} +(-15781.2 + 48569.6i) q^{78} +(24258.9 + 17625.2i) q^{79} +(-3977.62 + 12241.8i) q^{80} +(-22441.9 - 69069.0i) q^{81} +(-62896.9 + 45697.2i) q^{82} +(21180.4 + 65186.7i) q^{83} +(-19227.6 - 13969.6i) q^{84} +(16806.3 + 12210.5i) q^{85} +(-19579.1 + 14225.0i) q^{86} -82906.9 q^{87} +32852.5 q^{88} +(84823.4 - 61627.8i) q^{89} +(-9693.24 + 29832.7i) q^{90} +(-14689.0 - 45208.1i) q^{91} +39976.8 q^{92} +(-104033. + 24478.6i) q^{93} +40468.7 q^{94} +(1019.98 + 3139.19i) q^{95} +(6320.47 - 19452.4i) q^{96} +(-4237.42 + 3078.66i) q^{97} -45106.3 q^{98} +80059.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - 20 q^{3} - 96 q^{4} + 120 q^{5} + 280 q^{6} - 180 q^{7} - 384 q^{8} - 200 q^{9} - 100 q^{10} + 354 q^{11} - 320 q^{12} + 39 q^{13} - 720 q^{14} + 535 q^{15} - 1536 q^{16} - 1027 q^{17}+ \cdots + 339042 q^{99}+O(q^{100}) $ 24 * q - 24 * q^2 - 20 * q^3 - 96 * q^4 + 120 * q^5 + 280 * q^6 - 180 * q^7 - 384 * q^8 - 200 * q^9 - 100 * q^10 + 354 * q^11 - 320 * q^12 + 39 * q^13 - 720 * q^14 + 535 * q^15 - 1536 * q^16 - 1027 * q^17 - 1420 * q^18 + 334 * q^19 - 560 * q^20 - 1867 * q^21 + 1416 * q^22 - 1051 * q^23 - 960 * q^24 + 4812 * q^25 + 12536 * q^26 - 5135 * q^27 + 4000 * q^28 - 1143 * q^29 + 9080 * q^30 - 8583 * q^31 + 24576 * q^32 - 24628 * q^33 - 8108 * q^34 - 7496 * q^35 + 17760 * q^36 - 25204 * q^37 - 2844 * q^38 - 20114 * q^39 - 2240 * q^40 + 19615 * q^41 + 3212 * q^42 + 22358 * q^43 - 20496 * q^44 + 6725 * q^45 - 5264 * q^46 + 4766 * q^47 - 3840 * q^48 - 12058 * q^49 + 4628 * q^50 + 6844 * q^51 + 624 * q^52 - 7393 * q^53 - 20540 * q^54 + 11861 * q^55 - 8960 * q^56 + 176704 * q^57 + 4268 * q^58 - 21070 * q^59 + 8560 * q^60 + 76556 * q^61 - 49652 * q^62 + 105854 * q^63 - 24576 * q^64 - 107146 * q^65 + 57968 * q^66 - 150906 * q^67 + 97728 * q^68 - 212560 * q^69 - 29984 * q^70 + 27475 * q^71 - 22720 * q^72 + 49671 * q^73 + 90124 * q^74 - 156002 * q^75 - 11376 * q^76 + 253908 * q^77 - 9036 * q^78 - 7162 * q^79 - 6400 * q^80 + 38329 * q^81 - 92940 * q^82 - 246088 * q^83 + 12848 * q^84 - 104879 * q^85 - 149088 * q^86 - 247668 * q^87 + 118656 * q^88 + 159253 * q^89 - 167880 * q^90 - 68566 * q^91 + 75744 * q^92 + 260391 * q^93 + 18784 * q^94 + 222814 * q^95 - 20480 * q^96 + 190 * q^97 - 144032 * q^98 + 339042 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	1.23607	+	3.80423i	0.218508	+	0.672499i
$2$	1.23607	+	3.80423i	0.218508	+	0.672499i
$3$	6.17234	−	18.9965i	0.395956	−	1.21863i	−0.532259	−	0.846581i	$-0.678657\pi$
$3$	6.17234	−	18.9965i	0.395956	−	1.21863i	0.928215	−	0.372045i	$-0.121343\pi$
$4$	−12.9443	+	9.40456i	−0.404508	+	0.293893i
$5$	−50.2806			−0.899447			−0.449723	−	0.893168i	$-0.648477\pi$
$5$	−50.2806			−0.899447			−0.449723	+	0.893168i	$0.648477\pi$
$6$	79.8964			0.906044
$7$	−60.1640	+	43.7117i	−0.464079	+	0.337173i	−0.795129	−	0.606440i	$-0.792597\pi$
$7$	−60.1640	+	43.7117i	−0.464079	+	0.337173i	0.331050	+	0.943613i	$0.392597\pi$
$8$	−51.7771	−	37.6183i	−0.286031	−	0.207813i
$9$	−126.178	−	91.6738i	−0.519251	−	0.377258i
$10$	−62.1502	−	191.279i	−0.196536	−	0.604877i
$11$	−415.284	+	301.722i	−1.03482	+	0.751839i	−0.969267	−	0.246010i	$-0.920880\pi$
$11$	−415.284	+	301.722i	−1.03482	+	0.751839i	−0.0655506	+	0.997849i	$0.520880\pi$
$12$	98.7574	+	303.944i	0.197978	+	0.609313i
$13$	−197.521	+	607.907i	−0.324156	+	0.997651i	0.647663	+	0.761927i	$0.275746\pi$
$13$	−197.521	+	607.907i	−0.324156	+	0.997651i	−0.971820	+	0.235725i	$0.924254\pi$
$14$	−240.656	−	174.847i	−0.328153	−	0.238417i
$15$	−310.349	+	955.155i	−0.356141	+	1.09609i
$16$	79.1084	−	243.470i	0.0772542	−	0.237764i
$17$	−334.250	−	242.847i	−0.280511	−	0.203803i	0.438630	−	0.898668i	$-0.355464\pi$
$17$	−334.250	−	242.847i	−0.280511	−	0.203803i	−0.719140	+	0.694865i	$0.755464\pi$
$18$	192.783	−	593.325i	0.140245	−	0.431630i
$19$	−20.2858	−	62.4334i	−0.0128917	−	0.0396765i	0.944404	−	0.328788i	$-0.106640\pi$
$19$	−20.2858	−	62.4334i	−0.0128917	−	0.0396765i	−0.957295	+	0.289112i	$0.906640\pi$
$20$	650.846	−	472.867i	0.363834	−	0.264341i
$21$	459.017	+	1412.71i	0.227133	+	0.699044i
$22$	−1661.14	−	1206.89i	−0.731727	−	0.531631i
$23$	−2021.37	−	1468.61i	−0.796758	−	0.578878i	0.113204	−	0.993572i	$-0.463889\pi$
$23$	−2021.37	−	1468.61i	−0.796758	−	0.578878i	−0.909961	+	0.414694i	$0.863889\pi$
$24$	−1034.20	+	751.391i	−0.366502	+	0.266280i
$25$	−596.861			−0.190996
$26$	−2556.76			−0.741750
$27$	1406.44	−	1021.84i	0.371288	−	0.269756i
$28$	367.690	−	1131.63i	0.0886312	−	0.272779i
$29$	−1282.64	−	3947.57i	−0.283212	−	0.871636i	−0.986929	−	0.161156i	$-0.948478\pi$
$29$	−1282.64	−	3947.57i	−0.283212	−	0.871636i	0.703717	−	0.710480i	$-0.251522\pi$
$30$	−4017.24			−0.814938
$31$	−2775.01	−	4574.76i	−0.518634	−	0.854996i
$31$	−2775.01	−	4574.76i	−0.518634	−	0.854996i
$32$	1024.00			0.176777
$33$	3168.38	+	9751.28i	0.506469	+	1.55875i
$34$	510.689	−	1571.74i	0.0757633	−	0.233175i
$35$	3025.08	−	2197.85i	0.417414	−	0.303269i
$36$	2495.44			0.320915
$37$	4915.05			0.590233			0.295116	−	0.955461i	$-0.404642\pi$
$37$	4915.05			0.590233			0.295116	+	0.955461i	$0.404642\pi$
$38$	212.436	−	154.344i	0.0238654	−	0.0173393i
$39$	10328.9	+	7504.41i	1.08741	+	0.790051i
$40$	2603.38	+	1891.47i	0.257269	+	0.186917i
$41$	6006.12	+	18484.9i	0.558000	+	1.71735i	0.687887	+	0.725818i	$0.258539\pi$
$41$	6006.12	+	18484.9i	0.558000	+	1.71735i	−0.129887	+	0.991529i	$0.541461\pi$
$42$	−4806.89	+	3492.41i	−0.420476	+	0.305494i
$43$	1869.63	+	5754.14i	0.154200	+	0.474580i	0.998079	−	0.0619542i	$-0.0197333\pi$
$43$	1869.63	+	5754.14i	0.154200	+	0.474580i	−0.843879	+	0.536534i	$0.819733\pi$
$44$	2537.99	−	7811.14i	0.197633	−	0.608251i
$45$	6344.31	+	4609.41i	0.467039	+	0.339324i
$46$	3088.38	−	9505.05i	0.215197	−	0.662308i
$47$	3126.38	−	9622.00i	0.206441	−	0.635361i	−0.793210	−	0.608949i	$-0.791592\pi$
$47$	3126.38	−	9622.00i	0.206441	−	0.635361i	0.999651	−	0.0264128i	$-0.00840844\pi$
$48$	−4136.80	−	3005.56i	−0.259156	−	0.188288i
$49$	−3484.65	+	10724.7i	−0.207333	+	0.638107i
$50$	−737.761	−	2270.60i	−0.0417341	−	0.128444i
$51$	−6676.34	+	4850.65i	−0.359429	+	0.261141i
$52$	−3160.33	−	9726.51i	−0.162078	−	0.498826i
$53$	−10512.2	−	7637.55i	−0.514048	−	0.373477i	0.300309	−	0.953842i	$-0.402910\pi$
$53$	−10512.2	−	7637.55i	−0.514048	−	0.373477i	−0.814357	+	0.580364i	$0.802910\pi$
$54$	5625.75	+	4087.34i	0.262540	+	0.190747i
$55$	20880.7	−	15170.8i	0.930763	−	0.676239i
$56$	4759.48			0.202810
$57$	−1311.23			−0.0534553
$58$	13432.0	−	9758.93i	0.524290	−	0.380919i
$59$	5563.72	−	17123.4i	0.208082	−	0.640412i	−0.791490	−	0.611182i	$-0.790694\pi$
$59$	5563.72	−	17123.4i	0.208082	−	0.640412i	0.999573	−	0.0292299i	$-0.00930550\pi$
$60$	−4965.58	−	15282.5i	−0.178070	−	0.548045i
$61$	−9974.67			−0.343221			−0.171611	−	0.985165i	$-0.554897\pi$
$61$	−9974.67			−0.343221			−0.171611	+	0.985165i	$0.554897\pi$
$62$	13973.3	−	16211.5i	0.461658	−	0.535604i
$63$	11598.6			0.368175
$64$	1265.73	+	3895.53i	0.0386271	+	0.118882i
$65$	9931.47	−	30565.9i	0.291561	−	0.897334i
$66$	−33179.7	+	24106.5i	−0.937590	+	0.681199i
$67$	1885.74			0.0513209			0.0256604	−	0.999671i	$-0.491831\pi$
$67$	1885.74			0.0513209			0.0256604	+	0.999671i	$0.491831\pi$
$68$	6610.49			0.173365
$69$	−40375.1	+	29334.2i	−1.02092	+	0.741739i
$70$	12100.3	+	8791.41i	0.295156	+	0.214444i
$71$	−18542.3	−	13471.8i	−0.436534	−	0.317160i	0.347722	−	0.937598i	$-0.386955\pi$
$71$	−18542.3	−	13471.8i	−0.436534	−	0.317160i	−0.784256	+	0.620437i	$0.786955\pi$
$72$	3084.53	+	9493.20i	0.0701225	+	0.215815i
$73$	−56325.4	+	40922.8i	−1.23708	+	0.898790i	−0.997400	−	0.0720628i	$-0.977042\pi$
$73$	−56325.4	+	40922.8i	−1.23708	+	0.898790i	−0.239678	+	0.970853i	$0.577042\pi$
$74$	6075.33	+	18697.9i	0.128971	+	0.396931i
$75$	−3684.03	+	11338.3i	−0.0756258	+	0.232752i
$76$	849.745	+	617.376i	0.0168754	+	0.0122607i
$77$	11796.4	−	36305.6i	0.226737	−	0.697825i
$78$	−15781.2	+	48569.6i	−0.293700	+	0.903915i
$79$	24258.9	+	17625.2i	0.437325	+	0.317735i	0.784571	−	0.620039i	$-0.212883\pi$
$79$	24258.9	+	17625.2i	0.437325	+	0.317735i	−0.347246	+	0.937774i	$0.612883\pi$
$80$	−3977.62	+	12241.8i	−0.0694861	+	0.213856i
$81$	−22441.9	−	69069.0i	−0.380055	−	1.16969i
$82$	−62896.9	+	45697.2i	−1.03299	+	0.750508i
$83$	21180.4	+	65186.7i	0.337474	+	1.03864i	0.965491	+	0.260437i	$0.0838667\pi$
$83$	21180.4	+	65186.7i	0.337474	+	1.03864i	−0.628017	+	0.778199i	$0.716133\pi$
$84$	−19227.6	−	13969.6i	−0.297321	−	0.216017i
$85$	16806.3	+	12210.5i	0.252304	+	0.183310i
$86$	−19579.1	+	14225.0i	−0.285460	+	0.207399i
$87$	−82906.9			−1.17434
$88$	32852.5			0.452232
$89$	84823.4	−	61627.8i	1.13512	−	0.824711i	0.148685	−	0.988885i	$-0.452496\pi$
$89$	84823.4	−	61627.8i	1.13512	−	0.824711i	0.986431	+	0.164174i	$0.0524958\pi$
$90$	−9693.24	+	29832.7i	−0.126143	+	0.388228i
$91$	−14689.0	−	45208.1i	−0.185947	−	0.572286i
$92$	39976.8			0.492423
$93$	−104033.	+	24478.6i	−1.24728	+	0.293480i
$94$	40468.7			0.472389
$95$	1019.98	+	3139.19i	0.0115954	+	0.0356869i
$96$	6320.47	−	19452.4i	0.0699957	−	0.215425i
$97$	−4237.42	+	3078.66i	−0.0457269	+	0.0332226i	−0.610414	−	0.792083i	$-0.708997\pi$
$97$	−4237.42	+	3078.66i	−0.0457269	+	0.0332226i	0.564687	+	0.825305i	$0.308997\pi$
$98$	−45106.3			−0.474430
$99$	80059.8			0.820968
$100$	7725.94	−	5613.22i	0.0772594	−	0.0561322i
$101$	−157587.	−	114493.i	−1.53715	−	1.11680i	−0.952092	−	0.305813i	$-0.901072\pi$
$101$	−157587.	−	114493.i	−1.53715	−	1.11680i	−0.585058	−	0.810992i	$-0.698928\pi$
$102$	−26705.4	−	19402.6i	−0.254155	−	0.184654i
$103$	17213.9	+	52979.0i	0.159877	+	0.492052i	0.998622	−	0.0524726i	$-0.0167102\pi$
$103$	17213.9	+	52979.0i	0.159877	+	0.492052i	−0.838745	+	0.544524i	$0.816710\pi$
$104$	33095.5	−	24045.3i	0.300044	−	0.217995i
$105$	−23079.7	−	71031.9i	−0.204294	−	0.628753i
$106$	16061.2	−	49431.3i	0.138840	−	0.427304i
$107$	−10317.4	−	7496.01i	−0.0871184	−	0.0632952i	0.543373	−	0.839491i	$-0.317147\pi$
$107$	−10317.4	−	7496.01i	−0.0871184	−	0.0632952i	−0.630492	+	0.776196i	$0.717147\pi$
$108$	−8595.38	+	26453.8i	−0.0709097	+	0.218238i
$109$	−1536.43	+	4728.64i	−0.0123864	+	0.0381215i	−0.957059	−	0.289894i	$-0.906380\pi$
$109$	−1536.43	+	4728.64i	−0.0123864	+	0.0381215i	0.944672	+	0.328016i	$0.106380\pi$
$110$	83523.0	+	60683.0i	0.658149	+	0.478173i
$111$	30337.3	−	93368.7i	0.233706	−	0.719273i
$112$	5883.04	+	18106.1i	0.0443156	+	0.136389i
$113$	−125168.	+	90939.5i	−0.922137	+	0.669972i	−0.944055	−	0.329788i	$-0.893023\pi$
$113$	−125168.	+	90939.5i	−0.922137	+	0.669972i	0.0219177	+	0.999760i	$0.493023\pi$
$114$	−1620.77	−	4988.21i	−0.0116804	−	0.0359486i
$115$	101636.	+	73842.7i	0.716641	+	0.520670i
$116$	53728.1	+	39035.7i	0.370729	+	0.269350i
$117$	80651.9	−	58597.1i	0.544691	−	0.395741i
$118$	72018.3			0.476143
$119$	30725.1			0.198896
$120$	52000.2	−	37780.4i	0.329649	−	0.239504i
$121$	31657.6	−	97432.1i	0.196569	−	0.604977i
$122$	−12329.4	−	37945.9i	−0.0749965	−	0.230816i
$123$	388221.			2.31375
$124$	78944.2	+	33119.2i	0.461069	+	0.193431i
$125$	187137.			1.07124
$126$	14336.7	+	44123.7i	0.0804492	+	0.247597i
$127$	−50503.3	+	155433.i	−0.277850	+	0.855135i	0.710601	+	0.703595i	$0.248423\pi$
$127$	−50503.3	+	155433.i	−0.277850	+	0.855135i	−0.988451	+	0.151540i	$0.951577\pi$
$128$	−13254.9	+	9630.27i	−0.0715077	+	0.0519534i
$129$	120849.			0.639392
$130$	128556.			0.667164
$131$	−221345.	+	160816.i	−1.12691	+	0.818751i	−0.985243	−	0.171163i	$-0.945247\pi$
$131$	−221345.	+	160816.i	−1.12691	+	0.818751i	−0.141671	+	0.989914i	$0.545247\pi$
$132$	−132719.	−	96425.9i	−0.662976	−	0.481680i
$133$	3949.55	+	2869.52i	0.0193606	+	0.0140663i
$134$	2330.90	+	7173.77i	0.0112140	+	0.0345132i
$135$	−70716.5	+	51378.5i	−0.333954	+	0.242632i
$136$	8171.02	+	25147.8i	0.0378816	+	0.116588i
$137$	111053.	−	341787.i	0.505510	−	1.55580i	−0.294402	−	0.955682i	$-0.595120\pi$
$137$	111053.	−	341787.i	0.505510	−	1.55580i	0.799912	−	0.600118i	$-0.204880\pi$
$138$	−161500.	−	117337.i	−0.721897	−	0.524489i
$139$	−119949.	+	369165.i	−0.526574	+	1.62063i	0.234609	+	0.972090i	$0.424619\pi$
$139$	−119949.	+	369165.i	−0.526574	+	1.62063i	−0.761183	+	0.648538i	$0.775381\pi$
$140$	−18487.7	+	56899.2i	−0.0797190	+	0.245350i
$141$	−163487.	−	118780.i	−0.692526	−	0.503150i
$142$	28330.1	−	87191.1i	0.117904	−	0.362870i
$143$	−101391.	−	312051.i	−0.414630	−	1.27610i
$144$	−32301.6	+	23468.5i	−0.129813	+	0.0943146i
$145$	64492.1	+	198486.i	0.254734	+	0.783990i
$146$	−225302.	−	163691.i	−0.874746	−	0.635540i
$147$	182223.	+	132392.i	0.695518	+	0.505324i
$148$	−63621.7	+	46223.9i	−0.238754	+	0.173465i
$149$	−431448.			−1.59207			−0.796036	−	0.605249i	$-0.793074\pi$
$149$	−431448.			−1.59207			−0.796036	+	0.605249i	$0.793074\pi$
$150$	−47687.1			−0.173050
$151$	268412.	−	195013.i	0.957987	−	0.696018i	0.00530447	−	0.999986i	$-0.498312\pi$
$151$	268412.	−	195013.i	0.957987	−	0.696018i	0.952682	+	0.303968i	$0.0983115\pi$
$152$	−1298.29	+	3995.74i	−0.00455789	+	0.0140278i
$153$	19912.4	+	61283.9i	0.0687692	+	0.211650i
$154$	152696.			0.518831
$155$	139529.	+	230022.i	0.466484	+	0.769024i
$156$	−204276.			−0.672058
$157$	83734.2	+	257707.i	0.271115	+	0.834406i	0.990221	+	0.139506i	$0.0445514\pi$
$157$	83734.2	+	257707.i	0.271115	+	0.834406i	−0.719106	+	0.694900i	$0.755449\pi$
$158$	−37064.4	+	114072.i	−0.118117	+	0.363528i
$159$	−209971.	+	152553.i	−0.658669	+	0.478551i
$160$	−51487.3			−0.159001
$161$	185809.			0.564941
$162$	235014.	−	170748.i	0.703569	−	0.511173i
$163$	368575.	+	267785.i	1.08657	+	0.789437i	0.978816	−	0.204741i	$-0.0656352\pi$
$163$	368575.	+	267785.i	1.08657	+	0.789437i	0.107751	+	0.994178i	$0.465635\pi$
$164$	−251587.	−	182789.i	−0.730431	−	0.530689i
$165$	−159308.	−	490300.i	−0.455542	−	1.40201i
$166$	−221804.	+	161150.i	−0.624741	+	0.453901i
$167$	−106460.	−	327649.i	−0.295388	−	0.909112i	−0.983091	−	0.183119i	$-0.941381\pi$
$167$	−106460.	−	327649.i	−0.295388	−	0.909112i	0.687702	−	0.725993i	$-0.258619\pi$
$168$	29377.1	−	90413.4i	0.0803037	−	0.247149i
$169$	−30153.9	−	21908.1i	−0.0812133	−	0.0590049i
$170$	−25677.7	+	79027.9i	−0.0681450	+	0.209729i
$171$	−3163.88	+	9737.41i	−0.00827426	+	0.0254656i
$172$	−78316.2	−	56900.1i	−0.201851	−	0.146653i
$173$	−212738.	+	654739.i	−0.540417	+	1.66323i	0.191226	+	0.981546i	$0.438754\pi$
$173$	−212738.	+	654739.i	−0.540417	+	1.66323i	−0.731644	+	0.681687i	$0.761246\pi$
$174$	−102479.	−	315397.i	−0.256602	−	0.789740i
$175$	35909.6	−	26089.8i	0.0886371	−	0.0643986i
$176$	40607.9	+	124978.i	0.0988163	+	0.304125i
$177$	−290943.	−	211382.i	−0.698031	−	0.507149i
$178$	339294.	+	246511.i	0.802649	+	0.583158i
$179$	−169661.	+	123266.i	−0.395777	+	0.287549i	−0.767819	−	0.640667i	$-0.778658\pi$
$179$	−169661.	+	123266.i	−0.395777	+	0.287549i	0.372042	+	0.928216i	$0.378658\pi$
$180$	−125472.			−0.288646
$181$	−142043.			−0.322273			−0.161136	−	0.986932i	$-0.551516\pi$
$181$	−142043.			−0.322273			−0.161136	+	0.986932i	$0.551516\pi$
$182$	153825.	−	111761.i	0.344230	−	0.250098i
$183$	−61567.0	+	189484.i	−0.135900	+	0.418258i
$184$	49414.1	+	152081.i	0.107598	+	0.331154i
$185$	−247131.			−0.530883
$186$	−221714.	−	365507.i	−0.469905	−	0.774664i
$187$	212081.			0.443504
$188$	50022.1	+	153952.i	0.103221	+	0.317681i
$189$	−39950.7	+	122956.i	−0.0813523	+	0.250377i
$190$	−10681.4	+	7760.50i	−0.0214657	+	0.0155957i
$191$	346724.			0.687702			0.343851	−	0.939024i	$-0.388269\pi$
$191$	346724.			0.687702			0.343851	+	0.939024i	$0.388269\pi$
$192$	81813.9			0.160167
$193$	−125488.	+	91172.4i	−0.242499	+	0.176186i	−0.702396	−	0.711787i	$-0.747886\pi$
$193$	−125488.	+	91172.4i	−0.242499	+	0.176186i	0.459897	+	0.887972i	$0.347886\pi$
$194$	−16949.7	−	12314.7i	−0.0323338	−	0.0234919i
$195$	−519345.	−	377326.i	−0.978069	−	0.710609i
$196$	−55754.4	−	171595.i	−0.103667	−	0.319053i
$197$	−616837.	+	448158.i	−1.13241	+	0.822746i	−0.986044	−	0.166484i	$-0.946759\pi$
$197$	−616837.	+	448158.i	−1.13241	+	0.822746i	−0.146369	+	0.989230i	$0.546759\pi$
$198$	98959.3	+	304565.i	0.179388	+	0.552100i
$199$	170850.	−	525822.i	0.305831	−	0.941252i	−0.673534	−	0.739156i	$-0.735225\pi$
$199$	170850.	−	525822.i	0.305831	−	0.941252i	0.979366	−	0.202096i	$-0.0647753\pi$
$200$	30903.7	+	22452.9i	0.0546306	+	0.0396915i
$201$	11639.4	−	35822.4i	0.0203208	−	0.0625409i
$202$	240771.	−	741017.i	0.415170	−	1.27776i
$203$	249724.	+	181435.i	0.425325	+	0.309016i
$204$	40802.2	−	125576.i	0.0686449	−	0.211267i
$205$	−301991.	−	929433.i	−0.501891	−	1.54466i
$206$	−180267.	+	130971.i	−0.295970	+	0.215034i
$207$	120420.	+	370613.i	0.195331	+	0.601167i
$208$	132382.	+	96181.0i	0.212163	+	0.154146i
$209$	27261.9	+	19806.9i	0.0431709	+	0.0313655i
$210$	241693.	−	175600.i	0.378196	−	0.274775i
$211$	1.19169e6			1.84270			0.921352	−	0.388730i	$-0.127086\pi$
$211$	1.19169e6			1.84270			0.921352	+	0.388730i	$0.127086\pi$
$212$	207900.			0.317699
$213$	−370366.	+	269086.i	−0.559348	+	0.406390i
$214$	15763.6	−	48515.2i	0.0235299	−	0.0724175i
$215$	−94006.3	−	289322.i	−0.138695	−	0.426859i
$216$	−111261.			−0.162259
$217$	366927.	+	153935.i	0.528969	+	0.221916i
$218$	−19887.9			−0.0283432
$219$	429730.	+	1.32257e6i	0.605461	+	1.86342i
$220$	−127612.	+	392749.i	−0.177760	+	0.547089i
$221$	213650.	−	155226.i	0.294253	−	0.213788i
$222$	392695.			0.534777
$223$	1.03409e6			1.39250			0.696252	−	0.717797i	$-0.254850\pi$
$223$	1.03409e6			1.39250			0.696252	+	0.717797i	$0.254850\pi$
$224$	−61608.0	+	44760.8i	−0.0820383	+	0.0596043i
$225$	75310.8	+	54716.5i	0.0991748	+	0.0720547i
$226$	−500670.	−	363758.i	−0.652050	−	0.473742i
$227$	−369961.	−	1.13862e6i	−0.476531	−	1.46661i	−0.843882	−	0.536528i	$-0.819735\pi$
$227$	−369961.	−	1.13862e6i	−0.476531	−	1.46661i	0.367352	−	0.930082i	$-0.380265\pi$
$228$	16972.9	−	12331.5i	0.0216231	−	0.0157101i
$229$	−133663.	−	411374.i	−0.168432	−	0.518380i	0.830841	−	0.556510i	$-0.187860\pi$
$229$	−133663.	−	411374.i	−0.168432	−	0.518380i	−0.999273	+	0.0381301i	$0.987860\pi$
$230$	−155286.	+	477920.i	−0.193558	+	0.595711i
$231$	−616868.	−	448181.i	−0.760610	−	0.552616i
$232$	−82089.2	+	252645.i	−0.100130	+	0.308170i
$233$	−28119.5	+	86543.0i	−0.0339327	+	0.104434i	−0.966588	−	0.256334i	$-0.917485\pi$
$233$	−28119.5	+	86543.0i	−0.0339327	+	0.104434i	0.932656	+	0.360768i	$0.117485\pi$
$234$	322608.	+	234388.i	0.385155	+	0.279831i
$235$	−157196.	+	483800.i	−0.185683	+	0.571474i
$236$	89019.5	+	273974.i	0.104041	+	0.320206i
$237$	484551.	−	352047.i	0.560361	−	0.407126i
$238$	37978.3	+	116885.i	0.0434603	+	0.133757i
$239$	403525.	+	293178.i	0.456957	+	0.331999i	0.792336	−	0.610084i	$-0.208864\pi$
$239$	403525.	+	293178.i	0.456957	+	0.331999i	−0.335379	+	0.942083i	$0.608864\pi$
$240$	208001.	+	151122.i	0.233097	+	0.169355i
$241$	−586701.	+	426263.i	−0.650690	+	0.472754i	−0.863506	−	0.504338i	$-0.831736\pi$
$241$	−586701.	+	426263.i	−0.650690	+	0.472754i	0.212816	+	0.977092i	$0.431736\pi$
$242$	409785.			0.449798
$243$	−1.02814e6			−1.11696
$244$	129115.	−	93807.4i	0.138836	−	0.100870i
$245$	175210.	−	539242.i	0.186485	−	0.573943i
$246$	479867.	+	1.47688e6i	0.505572	+	1.55599i
$247$	41960.6			0.0437622
$248$	−28412.4	+	341259.i	−0.0293345	+	0.352334i
$249$	1.36905e6			1.39933
$250$	231315.	+	711913.i	0.234074	+	0.720405i
$251$	300552.	−	925003.i	0.301117	−	0.926742i	−0.679981	−	0.733230i	$-0.738012\pi$
$251$	300552.	−	925003.i	0.301117	−	0.926742i	0.981098	−	0.193512i	$-0.0619880\pi$
$252$	−150135.	+	109080.i	−0.148930	+	0.108204i
$253$	1.28256e6			1.25972
$254$	−653729.			−0.635789
$255$	335691.	−	243893.i	0.323287	−	0.234882i
$256$	−53019.7	−	38521.1i	−0.0505636	−	0.0367366i
$257$	−813957.	−	591374.i	−0.768721	−	0.558508i	0.132852	−	0.991136i	$-0.457587\pi$
$257$	−813957.	−	591374.i	−0.768721	−	0.558508i	−0.901573	+	0.432627i	$0.857587\pi$
$258$	149377.	+	459735.i	0.139712	+	0.429990i
$259$	−295709.	+	214845.i	−0.273915	+	0.199011i
$260$	158904.	+	489055.i	0.145781	+	0.448667i
$261$	−200047.	+	615682.i	−0.181774	+	0.559442i
$262$	−885378.	−	643265.i	−0.796848	−	0.578944i
$263$	564707.	−	1.73799e6i	0.503423	−	1.54938i	−0.299981	−	0.953945i	$-0.596981\pi$
$263$	564707.	−	1.73799e6i	0.503423	−	1.54938i	0.803405	−	0.595433i	$-0.203019\pi$
$264$	202776.	−	624082.i	0.179064	−	0.551102i
$265$	528559.	+	384021.i	0.462358	+	0.335923i
$266$	−6034.38	+	18571.9i	−0.00522912	+	0.0160936i
$267$	−647154.	−	1.99173e6i	−0.555558	−	1.70983i
$268$	−24409.5	+	17734.5i	−0.0207597	+	0.0150828i
$269$	149204.	+	459202.i	0.125718	+	0.386922i	0.994031	−	0.109095i	$-0.0347954\pi$
$269$	149204.	+	459202.i	0.125718	+	0.386922i	−0.868313	+	0.496017i	$0.834795\pi$
$270$	−282866.	−	205514.i	−0.236141	−	0.171566i
$271$	−1.27427e6	−	925812.i	−1.05399	−	0.765772i	−0.0810269	−	0.996712i	$-0.525820\pi$
$271$	−1.27427e6	−	925812.i	−1.05399	−	0.765772i	−0.972968	+	0.230940i	$0.925820\pi$
$272$	−85568.0	+	62168.8i	−0.0701276	+	0.0509507i
$273$	−949461.			−0.771029
$274$	1.43750e6			1.15673
$275$	247867.	−	180086.i	0.197646	−	0.143598i
$276$	246750.	−	759419.i	0.194978	−	0.600080i
$277$	415031.	+	1.27734e6i	0.324999	+	1.00024i	0.971441	+	0.237280i	$0.0762560\pi$
$277$	415031.	+	1.27734e6i	0.324999	+	1.00024i	−0.646443	+	0.762963i	$0.723744\pi$
$278$	−1.55265e6			−1.20493
$279$	−69239.6	+	831631.i	−0.0532530	+	0.639617i
$280$	−239309.			−0.182417
$281$	236925.	+	729181.i	0.178997	+	0.550896i	0.999793	−	0.0203247i	$-0.00647000\pi$
$281$	236925.	+	729181.i	0.178997	+	0.550896i	−0.820796	+	0.571221i	$0.806470\pi$
$282$	249786.	−	768763.i	0.187045	−	0.575665i
$283$	−1.95306e6	+	1.41898e6i	−1.44961	+	1.05320i	−0.463684	+	0.886001i	$0.653473\pi$
$283$	−1.95306e6	+	1.41898e6i	−1.44961	+	1.05320i	−0.985923	+	0.167200i	$0.946527\pi$
$284$	366713.			0.269793
$285$	65929.3			0.0480802
$286$	1.06178e6	−	771432.i	0.767576	−	0.557676i
$287$	−1.16936e6	−	849590.i	−0.837999	−	0.608842i
$288$	−129206.	−	93873.9i	−0.0917916	−	0.0666905i
$289$	−386011.	−	1.18802e6i	−0.271866	−	0.836719i
$290$	−675370.	+	490685.i	−0.471571	+	0.342616i
$291$	32329.1	+	99498.7i	0.0223800	+	0.0688787i
$292$	344230.	−	1.05943e6i	0.236261	−	0.727136i
$293$	−952251.	−	691851.i	−0.648011	−	0.470807i	0.214582	−	0.976706i	$-0.431161\pi$
$293$	−952251.	−	691851.i	−0.648011	−	0.470807i	−0.862593	+	0.505899i	$0.831161\pi$
$294$	−278411.	+	856862.i	−0.187853	+	0.578152i
$295$	−279747.	+	860973.i	−0.187159	+	0.576016i
$296$	−254487.	−	184895.i	−0.168825	−	0.122658i
$297$	−275761.	+	848705.i	−0.181402	+	0.558298i
$298$	−533299.	−	1.64133e6i	−0.347881	−	1.07067i
$299$	1.29204e6	−	938723.i	0.835793	−	0.607239i
$300$	−58944.5	−	181412.i	−0.0378129	−	0.116376i
$301$	−364008.	−	264467.i	−0.231577	−	0.168250i
$302$	1.07365e6	+	780051.i	0.677399	+	0.492159i
$303$	−3.14765e6	+	2.28690e6i	−1.96961	+	1.43101i
$304$	−16805.5			−0.0104296
$305$	501532.			0.308709
$306$	−208525.	+	151502.i	−0.127308	+	0.0924944i
$307$	−522294.	+	1.60746e6i	−0.316278	+	0.973404i	0.658947	+	0.752189i	$0.271002\pi$
$307$	−522294.	+	1.60746e6i	−0.316278	+	0.973404i	−0.975225	+	0.221215i	$0.928998\pi$
$308$	188742.	+	580890.i	0.113369	+	0.348913i
$309$	1.11267e6			0.662931
$310$	−702587.	+	815124.i	−0.415237	+	0.481747i
$311$	−19234.5			−0.0112767			−0.00563833	−	0.999984i	$-0.501795\pi$
$311$	−19234.5			−0.0112767			−0.00563833	+	0.999984i	$0.501795\pi$
$312$	−252499.	−	777113.i	−0.146850	−	0.451958i
$313$	243475.	−	749339.i	0.140473	−	0.432332i	−0.855928	−	0.517095i	$-0.827013\pi$
$313$	243475.	−	749339.i	0.140473	−	0.432332i	0.996401	+	0.0847630i	$0.0270133\pi$
$314$	−876875.	+	637087.i	−0.501896	+	0.364649i
$315$	−583185.			−0.331154
$316$	−479771.			−0.270282
$317$	−665565.	+	483561.i	−0.372000	+	0.270273i	−0.758040	−	0.652209i	$-0.773843\pi$
$317$	−665565.	+	483561.i	−0.372000	+	0.270273i	0.386040	+	0.922482i	$0.373843\pi$
$318$	−839886.	−	610213.i	−0.465750	−	0.338387i
$319$	1.72373e6	+	1.25236e6i	0.948402	+	0.689054i
$320$	−63641.8	−	195869.i	−0.0347430	−	0.106928i
$321$	−206080.	+	149726.i	−0.111628	+	0.0811027i
$322$	229673.	+	706861.i	0.123444	+	0.379922i
$323$	−8381.22	+	25794.7i	−0.00446993	+	0.0137570i
$324$	940057.	+	682992.i	0.497499	+	0.361454i
$325$	117893.	−	362836.i	0.0619125	−	0.190547i
$326$	−563132.	+	1.73314e6i	−0.293472	+	0.903213i
$327$	80344.3	+	58373.5i	0.0415514	+	0.0301888i
$328$	384391.	−	1.18304e6i	0.197283	−	0.607174i
$329$	232499.	+	715558.i	0.118422	+	0.364464i
$330$	1.66830e6	−	1.21209e6i	0.843312	−	0.612702i
$331$	926080.	+	2.85018e6i	0.464599	+	1.42989i	0.859486	+	0.511160i	$0.170784\pi$
$331$	926080.	+	2.85018e6i	0.464599	+	1.42989i	−0.394887	+	0.918730i	$0.629216\pi$
$332$	−887218.	−	644601.i	−0.441759	−	0.320956i
$333$	−620171.	−	450581.i	−0.306479	−	0.222670i
$334$	1.11486e6	−	809992.i	0.546832	−	0.397297i
$335$	−94816.0			−0.0461604
$336$	380265.			0.183755
$337$	−315702.	+	229371.i	−0.151427	+	0.110018i	−0.660919	−	0.750457i	$-0.729833\pi$
$337$	−315702.	+	229371.i	−0.151427	+	0.110018i	0.509492	+	0.860475i	$0.329833\pi$
$338$	46071.1	−	141792.i	0.0219350	−	0.0675089i
$339$	954957.	+	2.93905e6i	0.451320	+	1.38902i
$340$	−332380.			−0.155933
$341$	2.53273e6	+	1.06255e6i	1.17951	+	0.494836i
$342$	−40954.1			−0.0189335
$343$	−645378.	−	1.98627e6i	−0.296196	−	0.911597i
$344$	119657.	−	368265.i	0.0545181	−	0.167789i
$345$	2.03008e6	−	1.47494e6i	0.918260	−	0.667155i
$346$	−2.75373e6			−1.23661
$347$	1.83267e6			0.817074			0.408537	−	0.912742i	$-0.366039\pi$
$347$	1.83267e6			0.817074			0.408537	+	0.912742i	$0.366039\pi$
$348$	1.07317e6	−	779704.i	0.475029	−	0.345129i
$349$	342927.	+	249151.i	0.150709	+	0.109496i	0.660584	−	0.750752i	$-0.270309\pi$
$349$	342927.	+	249151.i	0.150709	+	0.109496i	−0.509876	+	0.860248i	$0.670309\pi$
$350$	143638.	+	104359.i	0.0626759	+	0.0455367i
$351$	343381.	+	1.05682e6i	0.148767	+	0.457859i
$352$	−425251.	+	308963.i	−0.182932	+	0.132908i
$353$	−510120.	−	1.56999e6i	−0.217889	−	0.670594i	−0.998936	−	0.0461215i	$-0.985314\pi$
$353$	−510120.	−	1.56999e6i	−0.217889	−	0.670594i	0.781047	−	0.624473i	$-0.214686\pi$
$354$	444521.	−	1.36810e6i	0.188532	−	0.580241i
$355$	932318.	+	677369.i	0.392639	+	0.285269i
$356$	−518394.	+	1.59545e6i	−0.216788	+	0.667205i
$357$	189646.	−	583669.i	0.0787539	−	0.242380i
$358$	−678646.	−	493065.i	−0.279857	−	0.203328i
$359$	786040.	−	2.41918e6i	0.321891	−	0.990678i	−0.650934	−	0.759135i	$-0.725622\pi$
$359$	786040.	−	2.41918e6i	0.321891	−	0.990678i	0.972824	−	0.231544i	$-0.0743776\pi$
$360$	−155092.	−	477324.i	−0.0630715	−	0.194114i
$361$	1.99972e6	−	1.45288e6i	0.807609	−	0.586762i
$362$	−175575.	−	540364.i	−0.0704191	−	0.216728i
$363$	−1.65547e6	−	1.20277e6i	−0.659408	−	0.479088i
$364$	615301.	+	447042.i	0.243408	+	0.176846i
$365$	2.83207e6	−	2.05762e6i	1.11269	−	0.808413i
$366$	−796940.			−0.310973
$367$	−2.61867e6			−1.01488			−0.507441	−	0.861687i	$-0.669408\pi$
$367$	−2.61867e6			−1.01488			−0.507441	+	0.861687i	$0.669408\pi$
$368$	−517471.	+	375964.i	−0.199189	+	0.144720i
$369$	936742.	−	2.88300e6i	0.358141	−	1.10224i
$370$	−305471.	−	940144.i	−0.116002	−	0.357018i
$371$	966306.			0.364485
$372$	1.11642e6	−	1.29524e6i	0.418282	−	0.485281i
$373$	−4.84940e6			−1.80475			−0.902373	−	0.430956i	$-0.858177\pi$
$373$	−4.84940e6			−1.80475			−0.902373	+	0.430956i	$0.858177\pi$
$374$	262147.	+	806804.i	0.0969092	+	0.298256i
$375$	1.15508e6	−	3.55496e6i	0.424162	−	1.30544i
$376$	−523838.	+	380590.i	−0.191085	+	0.138832i
$377$	2.65310e6			0.961393
$378$	−517133.			−0.186154
$379$	463691.	−	336891.i	0.165818	−	0.120474i	−0.501782	−	0.864994i	$-0.667322\pi$
$379$	463691.	−	336891.i	0.165818	−	0.120474i	0.667599	+	0.744521i	$0.267322\pi$
$380$	−42725.7	−	31042.0i	−0.0151785	−	0.0110279i
$381$	2.64096e6	+	1.91877e6i	0.932073	+	0.677191i
$382$	428574.	+	1.31902e6i	0.150268	+	0.462478i
$383$	−596590.	+	433448.i	−0.207816	+	0.150987i	−0.686825	−	0.726823i	$-0.740996\pi$
$383$	−596590.	+	433448.i	−0.207816	+	0.150987i	0.479009	+	0.877810i	$0.340996\pi$
$384$	101128.	+	311239.i	0.0349979	+	0.107712i
$385$	−593130.	+	1.82547e6i	−0.203938	+	0.627657i
$386$	−501952.	−	364690.i	−0.171472	−	0.124582i
$387$	291597.	−	897443.i	0.0989704	−	0.304600i
$388$	25896.8	−	79702.1i	0.00873306	−	0.0268776i
$389$	1.62858e6	+	1.18324e6i	0.545678	+	0.396458i	0.826189	−	0.563393i	$-0.190504\pi$
$389$	1.62858e6	+	1.18324e6i	0.545678	+	0.396458i	−0.280512	+	0.959851i	$0.590504\pi$
$390$	793489.	−	2.44211e6i	0.264167	−	0.813024i
$391$	318995.	+	981767.i	0.105522	+	0.324763i
$392$	583868.	−	424205.i	0.191911	−	0.139431i
$393$	1.68873e6	+	5.19738e6i	0.551543	+	1.69748i
$394$	−2.46735e6	−	1.79263e6i	−0.800737	−	0.581769i
$395$	−1.21975e6	−	886203.i	−0.393350	−	0.285786i
$396$	−1.03632e6	+	752927.i	−0.332089	+	0.241277i
$397$	−5.72911e6			−1.82436			−0.912180	−	0.409790i	$-0.865602\pi$
$397$	−5.72911e6			−1.82436			−0.912180	+	0.409790i	$0.865602\pi$
$398$	2.21153e6			0.699817
$399$	78888.8	−	57316.0i	0.0248075	−	0.0180237i
$400$	−47216.7	+	145318.i	−0.0147552	+	0.0454119i
$401$	1.36358e6	+	4.19667e6i	0.423468	+	1.30330i	0.904454	+	0.426571i	$0.140279\pi$
$401$	1.36358e6	+	4.19667e6i	0.423468	+	1.30330i	−0.480987	+	0.876728i	$0.659721\pi$
$402$	150664.			0.0464989
$403$	3.32915e6	−	783339.i	1.02111	−	0.240263i
$404$	3.11661e6			0.950011
$405$	1.12839e6	+	3.47283e6i	0.341839	+	1.05207i
$406$	−381545.	+	1.17427e6i	−0.114876	+	0.353553i
$407$	−2.04114e6	+	1.48298e6i	−0.610783	+	0.443760i
$408$	528155.			0.157076
$409$	1.09316e6			0.323130			0.161565	−	0.986862i	$-0.448346\pi$
$409$	1.09316e6			0.323130			0.161565	+	0.986862i	$0.448346\pi$
$410$	3.16249e6	−	2.29768e6i	0.929116	−	0.675042i
$411$	−5.80729e6	−	4.21924e6i	−1.69578	−	1.23206i
$412$	−721066.	−	523885.i	−0.209282	−	0.152052i
$413$	413756.	+	1.27341e6i	0.119363	+	0.367361i
$414$	−1.26105e6	+	916206.i	−0.361602	+	0.262720i
$415$	−1.06497e6	−	3.27763e6i	−0.303539	−	0.934198i
$416$	−202261.	+	622497.i	−0.0573033	+	0.176361i
$417$	6.27247e6	+	4.55722e6i	1.76644	+	1.28339i
$418$	−41652.5	+	128193.i	−0.0116601	+	0.0358859i
$419$	−597395.	+	1.83859e6i	−0.166237	+	0.511624i	−0.999125	−	0.0418169i	$-0.986685\pi$
$419$	−597395.	+	1.83859e6i	−0.166237	+	0.511624i	0.832889	+	0.553441i	$0.186685\pi$
$420$	966773.	+	702402.i	0.267425	+	0.194295i
$421$	1.19997e6	−	3.69312e6i	0.329962	−	1.01552i	−0.639189	−	0.769050i	$-0.720730\pi$
$421$	1.19997e6	−	3.69312e6i	0.329962	−	1.01552i	0.969151	−	0.246469i	$-0.0792703\pi$
$422$	1.47300e6	+	4.53344e6i	0.402646	+	1.23922i
$423$	−1.27657e6	+	927479.i	−0.346890	+	0.252031i
$424$	256979.	+	790900.i	0.0694198	+	0.213652i
$425$	199501.	+	144946.i	0.0535763	+	0.0389255i
$426$	−1.48146e6	−	1.07635e6i	−0.395518	−	0.287361i
$427$	600116.	−	436010.i	0.159282	−	0.115725i
$428$	204048.			0.0538421
$429$	−6.55369e6			−1.71926
$430$	984447.	−	715242.i	0.256756	−	0.186544i
$431$	−410480.	+	1.26333e6i	−0.106439	+	0.327584i	−0.990065	−	0.140608i	$-0.955094\pi$
$431$	−410480.	+	1.26333e6i	−0.106439	+	0.327584i	0.883627	+	0.468192i	$0.155094\pi$
$432$	−137526.	−	423262.i	−0.0354548	−	0.109119i
$433$	−5.93863e6			−1.52218			−0.761091	−	0.648645i	$-0.775336\pi$
$433$	−5.93863e6			−1.52218			−0.761091	+	0.648645i	$0.775336\pi$
$434$	−132059.	+	1.58615e6i	−0.0336545	+	0.404221i
$435$	4.16861e6			1.05625
$436$	−24582.9	−	75658.2i	−0.00619321	−	0.0190608i
$437$	−50685.2	+	155993.i	−0.0126963	+	0.0390752i
$438$	−4.50020e6	+	3.26958e6i	−1.12085	+	0.814343i
$439$	−2.84611e6			−0.704840			−0.352420	−	0.935842i	$-0.614641\pi$
$439$	−2.84611e6			−0.704840			−0.352420	+	0.935842i	$0.614641\pi$
$440$	−1.65184e6			−0.406759
$441$	1.42286e6	−	1.03377e6i	0.348389	−	0.253120i
$442$	854599.	+	620902.i	0.208069	+	0.151171i
$443$	−3.93999e6	−	2.86257e6i	−0.953861	−	0.693021i	−0.00214440	−	0.999998i	$-0.500683\pi$
$443$	−3.93999e6	−	2.86257e6i	−0.953861	−	0.693021i	−0.951717	+	0.306977i	$0.900683\pi$
$444$	485397.	+	1.49390e6i	0.116853	+	0.359636i
$445$	−4.26497e6	+	3.09868e6i	−1.02098	+	0.741783i
$446$	1.27821e6	+	3.93392e6i	0.304273	+	0.936457i
$447$	−2.66304e6	+	8.19600e6i	−0.630390	+	1.94014i
$448$	−246432.	−	179043.i	−0.0580099	−	0.0421466i
$449$	2.41496e6	−	7.43247e6i	0.565319	−	1.73987i	−0.101683	−	0.994817i	$-0.532423\pi$
$449$	2.41496e6	−	7.43247e6i	0.565319	−	1.73987i	0.667002	−	0.745056i	$-0.267577\pi$
$450$	−115065.	+	354133.i	−0.0267862	+	0.0824394i
$451$	−8.07155e6	−	5.86432e6i	−1.86860	−	1.35761i
$452$	764956.	−	2.35429e6i	0.176113	−	0.542019i
$453$	−2.04783e6	−	6.30257e6i	−0.468866	−	1.44302i
$454$	3.87428e6	−	2.81483e6i	0.882168	−	0.640932i
$455$	738572.	+	2.27309e6i	0.167249	+	0.514741i
$456$	67891.5	+	49326.1i	0.0152899	+	0.0111087i
$457$	132259.	+	96092.1i	0.0296235	+	0.0215227i	0.602498	−	0.798120i	$-0.294172\pi$
$457$	132259.	+	96092.1i	0.0296235	+	0.0215227i	−0.572875	+	0.819643i	$0.694172\pi$
$458$	1.39974e6	−	1.01697e6i	0.311806	−	0.226540i
$459$	−718251.			−0.159127
$460$	−2.01006e6			−0.442909
$461$	−5.22371e6	+	3.79525e6i	−1.14479	+	0.831741i	−0.987780	−	0.155855i	$-0.950187\pi$
$461$	−5.22371e6	+	3.79525e6i	−1.14479	+	0.831741i	−0.157013	+	0.987596i	$0.550187\pi$
$462$	942490.	−	2.90069e6i	0.205434	−	0.632260i
$463$	−2.62069e6	−	8.06564e6i	−0.568149	−	1.74858i	−0.658404	−	0.752665i	$-0.728768\pi$
$463$	−2.62069e6	−	8.06564e6i	−0.568149	−	1.74858i	0.0902545	−	0.995919i	$-0.471232\pi$
$464$	−1.06258e6			−0.229123
$465$	5.23083e6	−	1.23080e6i	1.12186	−	0.263970i
$466$	−363987.			−0.0776463
$467$	−2.59503e6	−	7.98668e6i	−0.550618	−	1.69463i	−0.707244	−	0.706969i	$-0.750062\pi$
$467$	−2.59503e6	−	7.98668e6i	−0.550618	−	1.69463i	0.156626	−	0.987658i	$-0.449938\pi$
$468$	−492901.	+	1.51699e6i	−0.104027	+	0.320161i
$469$	−113454.	+	82428.8i	−0.0238169	+	0.0173040i
$470$	−2.03479e6			−0.424888
$471$	5.41237e6			1.12418
$472$	−932224.	+	677301.i	−0.192604	+	0.139935i
$473$	−2.51258e6	−	1.82550e6i	−0.516377	−	0.375170i
$474$	1.93820e6	+	1.40819e6i	0.396235	+	0.287882i
$475$	12107.8	+	37264.1i	0.00246225	+	0.00757804i
$476$	−397714.	+	288956.i	−0.0804551	+	0.0584540i
$477$	626245.	+	1.92738e6i	0.126023	+	0.387857i
$478$	−616531.	+	1.89749e6i	−0.123420	+	0.379847i
$479$	5.93818e6	+	4.31434e6i	1.18254	+	0.859163i	0.992455	−	0.122606i	$-0.0391251\pi$
$479$	5.93818e6	+	4.31434e6i	1.18254	+	0.859163i	0.190081	+	0.981768i	$0.439125\pi$
$480$	−317797.	+	978079.i	−0.0629574	+	0.193763i
$481$	−970825.	+	2.98789e6i	−0.191328	+	0.588846i
$482$	−2.34680e6	−	1.70505e6i	−0.460107	−	0.334288i
$483$	1.14688e6	−	3.52973e6i	0.223691	−	0.688451i
$484$	506522.	+	1.55891e6i	0.0982844	+	0.302488i
$485$	213060.	−	154797.i	0.0411289	−	0.0298819i
$486$	−1.27086e6	−	3.91129e6i	−0.244065	−	0.751155i
$487$	5.29670e6	+	3.84828e6i	1.01201	+	0.735265i	0.964629	−	0.263612i	$-0.0849140\pi$
$487$	5.29670e6	+	3.84828e6i	1.01201	+	0.735265i	0.0473764	+	0.998877i	$0.484914\pi$
$488$	516459.	+	375230.i	0.0981717	+	0.0713259i
$489$	7.36195e6	−	5.34877e6i	1.39226	−	1.01154i
$490$	2.26797e6			0.426724
$491$	−1.93913e6			−0.362998			−0.181499	−	0.983391i	$-0.558095\pi$
$491$	−1.93913e6			−0.362998			−0.181499	+	0.983391i	$0.558095\pi$
$492$	−5.02523e6	+	3.65105e6i	−0.935930	+	0.679993i
$493$	−529932.	+	1.63096e6i	−0.0981980	+	0.302222i
$494$	51866.1	+	159628.i	0.00956239	+	0.0294300i
$495$	−4.02545e6			−0.738417
$496$	−1.33335e6	+	313732.i	−0.243354	+	0.0572605i
$497$	1.70445e6			0.309524
$498$	1.69224e6	+	5.20818e6i	0.305766	+	0.941050i
$499$	1.30469e6	−	4.01543e6i	0.234561	−	0.721905i	−0.762618	−	0.646849i	$-0.776086\pi$
$499$	1.30469e6	−	4.01543e6i	0.234561	−	0.721905i	0.997179	−	0.0750562i	$-0.0239136\pi$
$500$	−2.42236e6	+	1.75995e6i	−0.433325	+	0.314829i
$501$	−6.88128e6			−1.22483
$502$	3.89042e6			0.689029
$503$	5.57447e6	−	4.05009e6i	0.982389	−	0.713748i	0.0241481	−	0.999708i	$-0.492313\pi$
$503$	5.57447e6	−	4.05009e6i	0.982389	−	0.713748i	0.958241	+	0.285961i	$0.0923127\pi$
$504$	−600542.	−	436319.i	−0.105309	−	0.0765117i
$505$	7.92355e6	+	5.75680e6i	1.38258	+	1.00451i
$506$	1.58533e6	+	4.87913e6i	0.275259	+	0.847161i
$507$	−602298.	+	437595.i	−0.104062	+	0.0756053i
$508$	−808053.	−	2.48693e6i	−0.138925	−	0.427567i
$509$	−22364.6	+	68831.3i	−0.00382620	+	0.0117758i	−0.952951	−	0.303123i	$-0.901971\pi$
$509$	−22364.6	+	68831.3i	−0.00382620	+	0.0117758i	0.949125	+	0.314899i	$0.101971\pi$
$510$	1.34276e6	+	975574.i	0.228599	+	0.166087i
$511$	1.59996e6	−	4.92416e6i	0.271054	−	0.834219i
$512$	81007.0	−	249314.i	0.0136568	−	0.0420312i
$513$	−92327.5	−	67079.9i	−0.0154895	−	0.0112538i
$514$	1.24362e6	−	3.82746e6i	0.207624	−	0.639002i
$515$	−865526.	−	2.66382e6i	−0.143801	−	0.442574i
$516$	−1.56430e6	+	1.13653e6i	−0.258639	+	0.187913i
$517$	1.60483e6	+	4.93916e6i	0.264060	+	0.812694i
$518$	−1.18284e6	−	859381.i	−0.193687	−	0.140722i
$519$	1.11247e7	+	8.08254e6i	1.81288	+	1.31713i
$520$	−1.66406e6	+	1.20901e6i	−0.269874	+	0.196075i
$521$	4.02248e6			0.649231			0.324615	−	0.945846i	$-0.394765\pi$
$521$	4.02248e6			0.649231			0.324615	+	0.945846i	$0.394765\pi$
$522$	−2.58946e6			−0.415943
$523$	−2.63014e6	+	1.91091e6i	−0.420459	+	0.305482i	−0.777823	−	0.628484i	$-0.783676\pi$
$523$	−2.63014e6	+	1.91091e6i	−0.420459	+	0.305482i	0.357363	+	0.933965i	$0.383676\pi$
$524$	1.35274e6	−	4.16330e6i	0.215221	−	0.662383i
$525$	−273970.	−	843192.i	−0.0433815	−	0.133514i
$526$	7.30972e6			1.15196
$527$	−183418.	+	2.20302e6i	−0.0287684	+	0.345535i
$528$	2.62479e6			0.409742
$529$	−59821.6	−	184112.i	−0.00929435	−	0.0286051i
$530$	−807566.	+	2.48543e6i	−0.124879	+	0.384337i
$531$	−2.27178e6	+	1.65055e6i	−0.349648	+	0.254034i
$532$	−78110.6			−0.0119655
$533$	−1.24234e7			−1.89419
$534$	6.77708e6	−	4.92384e6i	1.02847	−	0.747224i
$535$	518764.	+	376904.i	0.0783584	+	0.0569307i
$536$	−97637.9	−	70938.1i	−0.0146793	−	0.0106652i
$537$	1.29442e6	+	3.98381e6i	0.193704	+	0.596161i
$538$	−1.56248e6	+	1.13521e6i	−0.232734	+	0.169091i
$539$	−1.78874e6	−	5.50518e6i	−0.265201	−	0.816205i
$540$	432181.	−	1.33012e6i	0.0637795	−	0.196293i
$541$	4.83587e6	+	3.51347e6i	0.710365	+	0.516111i	0.883291	−	0.468824i	$-0.155322\pi$
$541$	4.83587e6	+	3.51347e6i	0.710365	+	0.516111i	−0.172926	+	0.984935i	$0.555322\pi$
$542$	1.94691e6	−	5.99198e6i	0.284674	−	0.876137i
$543$	−876737.	+	2.69832e6i	−0.127606	+	0.392730i
$544$	−342272.	−	248675.i	−0.0495877	−	0.0360276i
$545$	77252.5	−	237759.i	0.0111409	−	0.0342883i
$546$	−1.17360e6	−	3.61197e6i	−0.168476	−	0.518516i
$547$	2.30085e6	−	1.67167e6i	0.328791	−	0.238881i	−0.411126	−	0.911578i	$-0.634864\pi$
$547$	2.30085e6	−	1.67167e6i	0.328791	−	0.238881i	0.739918	+	0.672697i	$0.234864\pi$
$548$	1.77685e6	+	5.46859e6i	0.252755	+	0.777900i
$549$	1.25858e6	+	914415.i	0.178218	+	0.129483i
$550$	991469.	+	720344.i	0.139757	+	0.101539i
$551$	−220441.	+	160160.i	−0.0309324	+	0.0224737i
$552$	3.19400e6			0.446157
$553$	−2.22994e6			−0.310085
$554$	−4.34627e6	+	3.15775e6i	−0.601647	+	0.437122i
$555$	−1.52538e6	+	4.69463e6i	−0.210206	+	0.646948i
$556$	−1.91918e6	−	5.90664e6i	−0.263287	−	0.810314i
$557$	−4.60965e6			−0.629549			−0.314775	−	0.949166i	$-0.601929\pi$
$557$	−4.60965e6			−0.629549			−0.314775	+	0.949166i	$0.601929\pi$
$558$	−3.24930e6	+	764549.i	−0.441778	+	0.103949i
$559$	−3.86727e6			−0.523450
$560$	−295803.	−	910387.i	−0.0398595	−	0.122675i
$561$	1.30904e6	−	4.02880e6i	0.175608	−	0.540466i
$562$	−2.48111e6	+	1.80264e6i	−0.331365	+	0.240750i
$563$	1.54106e6			0.204903			0.102452	−	0.994738i	$-0.467331\pi$
$563$	1.54106e6			0.204903			0.102452	+	0.994738i	$0.467331\pi$
$564$	3.23330e6			0.428005
$565$	6.29350e6	−	4.57249e6i	0.829413	−	0.602604i
$566$	−7.81225e6	−	5.67593e6i	−1.02503	−	0.744725i
$567$	4.36932e6	+	3.17450e6i	0.570763	+	0.414684i
$568$	453282.	+	1.39506e6i	0.0589518	+	0.181435i
$569$	4.96302e6	−	3.60585e6i	0.642637	−	0.466903i	−0.218118	−	0.975922i	$-0.569992\pi$
$569$	4.96302e6	−	3.60585e6i	0.642637	−	0.466903i	0.860755	+	0.509019i	$0.169992\pi$
$570$	81493.1	+	250810.i	0.0105059	+	0.0323339i
$571$	−1.46962e6	+	4.52303e6i	−0.188632	+	0.580550i	−0.999992	−	0.00399702i	$-0.998728\pi$
$571$	−1.46962e6	+	4.52303e6i	−0.188632	+	0.580550i	0.811360	+	0.584547i	$0.198728\pi$
$572$	4.24714e6	+	3.08573e6i	0.542758	+	0.394337i
$573$	2.14010e6	−	6.58654e6i	0.272299	−	0.838051i
$574$	1.78662e6	−	5.49866e6i	0.226336	−	0.696590i
$575$	1.20648e6	+	876557.i	0.152177	+	0.110563i
$576$	197410.	−	607565.i	0.0247921	−	0.0763021i
$577$	−3.85469e6	−	1.18635e7i	−0.482004	−	1.48345i	−0.836274	−	0.548312i	$-0.815271\pi$
$577$	−3.85469e6	−	1.18635e7i	−0.482004	−	1.48345i	0.354270	−	0.935143i	$-0.384729\pi$
$578$	4.04236e6	−	2.93695e6i	0.503287	−	0.365660i
$579$	957402.	+	2.94658e6i	0.118686	+	0.365277i
$580$	−2.70148e6	−	1.96274e6i	−0.333451	−	0.242266i
$581$	−4.12372e6	−	2.99606e6i	−0.506815	−	0.368222i
$582$	−338554.	+	245974.i	−0.0414306	+	0.0301011i
$583$	6.66996e6			0.812741
$584$	4.45581e6			0.540623
$585$	−4.05523e6	+	2.94630e6i	−0.489920	+	0.355948i
$586$	1.45491e6	−	4.47775e6i	0.175022	−	0.538661i
$587$	4.15019e6	+	1.27730e7i	0.497134	+	1.53002i	0.813605	+	0.581418i	$0.197502\pi$
$587$	4.15019e6	+	1.27730e7i	0.497134	+	1.53002i	−0.316471	+	0.948602i	$0.602498\pi$
$588$	−3.60383e6			−0.429854
$589$	−229325.	+	266057.i	−0.0272372	+	0.0315999i
$590$	−3.62112e6			−0.428266
$591$	4.70611e6	+	1.44839e7i	0.554235	+	1.70576i
$592$	388821.	−	1.19667e6i	0.0455980	−	0.140336i
$593$	−537126.	+	390245.i	−0.0627248	+	0.0455722i	−0.618706	−	0.785623i	$-0.712343\pi$
$593$	−537126.	+	390245.i	−0.0627248	+	0.0455722i	0.555981	+	0.831195i	$0.312343\pi$
$594$	−3.56953e6			−0.415092
$595$	−1.54488e6			−0.178896
$596$	5.58478e6	−	4.05758e6i	0.644007	−	0.467898i
$597$	−8.93423e6	−	6.49110e6i	−1.02594	−	0.745388i
$598$	5.16817e6	+	3.75489e6i	0.590995	+	0.429383i
$599$	2.83064e6	+	8.71180e6i	0.322342	+	0.992067i	0.972626	+	0.232376i	$0.0746499\pi$
$599$	2.83064e6	+	8.71180e6i	0.322342	+	0.992067i	−0.650284	+	0.759691i	$0.725350\pi$
$600$	617275.	−	448476.i	0.0700004	−	0.0508582i
$601$	490342.	+	1.50912e6i	0.0553749	+	0.170426i	0.974919	−	0.222561i	$-0.0714416\pi$
$601$	490342.	+	1.50912e6i	0.0553749	+	0.170426i	−0.919544	+	0.392987i	$0.871442\pi$
$602$	556155.	−	1.71167e6i	0.0625467	−	0.192499i
$603$	−237939.	−	172873.i	−0.0266484	−	0.0193612i
$604$	−1.64039e6	+	5.04860e6i	−0.182959	+	0.563090i
$605$	−1.59176e6	+	4.89894e6i	−0.176803	+	0.544144i
$606$	−1.25906e7	−	9.14761e6i	−1.39272	−	1.01187i
$607$	1.83792e6	−	5.65655e6i	0.202468	−	0.623132i	−0.797340	−	0.603530i	$-0.793760\pi$
$607$	1.83792e6	−	5.65655e6i	0.202468	−	0.623132i	0.999808	−	0.0196014i	$-0.00623971\pi$
$608$	−20772.7	−	63931.8i	−0.00227895	−	0.00701388i
$609$	4.98802e6	−	3.62401e6i	0.544985	−	0.395955i
$610$	619928.	+	1.90794e6i	0.0674554	+	0.207606i
$611$	5.23176e6	+	3.80109e6i	0.566950	+	0.411913i
$612$	−834099.	−	606009.i	−0.0900201	−	0.0654034i
$613$	−9.10287e6	+	6.61362e6i	−0.978424	+	0.710866i	−0.957356	−	0.288912i	$-0.906707\pi$
$613$	−9.10287e6	+	6.61362e6i	−0.978424	+	0.710866i	−0.0210679	+	0.999778i	$0.506707\pi$
$614$	−6.76072e6			−0.723722
$615$	−1.95200e7			−2.08109
$616$	−1.97654e6	+	1.43604e6i	−0.209871	+	0.152480i
$617$	−2.69678e6	+	8.29983e6i	−0.285189	+	0.877721i	0.701153	+	0.713011i	$0.252669\pi$
$617$	−2.69678e6	+	8.29983e6i	−0.285189	+	0.877721i	−0.986342	+	0.164710i	$0.947331\pi$
$618$	1.37533e6	+	4.23283e6i	0.144856	+	0.445820i
$619$	1.30841e7			1.37251			0.686255	−	0.727361i	$-0.259253\pi$
$619$	1.30841e7			1.37251			0.686255	+	0.727361i	$0.259253\pi$
$620$	−3.96936e6	−	1.66525e6i	−0.414707	−	0.173981i
$621$	−4.34361e6			−0.451983
$622$	−23775.2	−	73172.4i	−0.00246404	−	0.00758353i
$623$	−2.40946e6	+	7.41555e6i	−0.248714	+	0.765462i
$624$	2.64421e6	−	1.92113e6i	0.271853	−	0.197513i
$625$	−7.54419e6			−0.772525
$626$	3.15161e6			0.321437
$627$	544532.	−	395626.i	0.0553165	−	0.0401898i
$628$	−3.50750e6	−	2.54835e6i	−0.354894	−	0.257846i
$629$	−1.64285e6	−	1.19360e6i	−0.165567	−	0.120291i
$630$	−720856.	−	2.21857e6i	−0.0723598	−	0.222700i
$631$	−6.61968e6	+	4.80948e6i	−0.661856	+	0.480867i	−0.867289	−	0.497805i	$-0.834140\pi$
$631$	−6.61968e6	+	4.80948e6i	−0.661856	+	0.480867i	0.205433	+	0.978671i	$0.434140\pi$
$632$	−593030.	−	1.82516e6i	−0.0590587	−	0.181764i
$633$	7.35548e6	−	2.26379e7i	0.729629	−	2.24557i
$634$	−2.66226e6	−	1.93425e6i	−0.263043	−	0.191112i
$635$	2.53934e6	−	7.81528e6i	0.249911	−	0.769148i
$636$	1.28323e6	−	3.94938e6i	0.125795	−	0.387156i
$637$	−5.83130e6	−	4.23669e6i	−0.569399	−	0.413693i
$638$	−2.63362e6	+	8.10546e6i	−0.256155	+	0.788363i
$639$	1.10462e6	+	3.39968e6i	0.107019	+	0.329372i
$640$	666466.	−	484216.i	0.0643173	−	0.0467293i
$641$	−890216.	−	2.73980e6i	−0.0855757	−	0.263375i	0.899108	−	0.437728i	$-0.144217\pi$
$641$	−890216.	−	2.73980e6i	−0.0855757	−	0.263375i	−0.984683	+	0.174353i	$0.944217\pi$
$642$	−824321.	−	598905.i	−0.0789331	−	0.0573482i
$643$	1.19619e7	+	8.69086e6i	1.14097	+	0.828963i	0.987254	−	0.159152i	$-0.0508759\pi$
$643$	1.19619e7	+	8.69086e6i	1.14097	+	0.828963i	0.153716	+	0.988115i	$0.450876\pi$
$644$	−2.40517e6	+	1.74746e6i	−0.228523	+	0.166032i
$645$	−6.07634e6			−0.575099
$646$	−108489.			−0.0102283
$647$	−1.39394e6	+	1.01276e6i	−0.130913	+	0.0951142i	−0.651315	−	0.758808i	$-0.725782\pi$
$647$	−1.39394e6	+	1.01276e6i	−0.130913	+	0.0951142i	0.520401	+	0.853922i	$0.325782\pi$
$648$	−1.43628e6	+	4.42042e6i	−0.134370	+	0.413548i
$649$	2.85597e6	+	8.78976e6i	0.266159	+	0.819154i
$650$	1.52603e6			0.141671
$651$	5.18903e6	−	6.02018e6i	0.479881	−	0.556746i
$652$	−7.28933e6			−0.671535
$653$	2.11144e6	+	6.49833e6i	0.193774	+	0.596374i	0.999989	+	0.00475147i	$0.00151245\pi$
$653$	2.11144e6	+	6.49833e6i	0.193774	+	0.596374i	−0.806215	+	0.591623i	$0.798488\pi$
$654$	−122755.	+	377801.i	−0.0112226	+	0.0345397i
$655$	1.11293e7	−	8.08594e6i	1.01360	−	0.736423i
$656$	4.97567e6			0.451431
$657$	1.08586e7			0.981430
$658$	−2.43476e6	+	1.76896e6i	−0.219226	+	0.159277i
$659$	−1.35612e7	−	9.85281e6i	−1.21643	−	0.883785i	−0.220627	−	0.975358i	$-0.570810\pi$
$659$	−1.35612e7	−	9.85281e6i	−1.21643	−	0.883785i	−0.995798	+	0.0915737i	$0.970810\pi$
$660$	6.67319e6	+	4.84835e6i	0.596312	+	0.433246i
$661$	−3.31865e6	−	1.02137e7i	−0.295432	−	0.909245i	−0.983076	−	0.183198i	$-0.941355\pi$
$661$	−3.31865e6	−	1.02137e7i	−0.295432	−	0.909245i	0.687644	−	0.726048i	$-0.258645\pi$
$662$	−9.69804e6	+	7.04604e6i	−0.860080	+	0.624885i
$663$	−1.63002e6	−	5.01670e6i	−0.144016	−	0.443235i
$664$	1.35555e6	−	4.17195e6i	0.119315	−	0.367214i
$665$	−198586.	−	144281.i	−0.0174138	−	0.0126519i
$666$	947537.	−	2.91622e6i	0.0827772	−	0.254762i
$667$	−3.20475e6	+	9.86321e6i	−0.278920	+	0.858427i
$668$	4.45944e6	+	3.23997e6i	0.386668	+	0.280931i
$669$	6.38276e6	−	1.96441e7i	0.551370	−	1.69694i
$670$	−117199.	−	360701.i	−0.0100864	−	0.0310428i
$671$	4.14232e6	−	3.00957e6i	0.355171	−	0.258047i
$672$	470034.	+	1.44661e6i	0.0401519	+	0.123575i
$673$	8.76652e6	+	6.36925e6i	0.746087	+	0.542064i	0.894611	−	0.446845i	$-0.147452\pi$
$673$	8.76652e6	+	6.36925e6i	0.746087	+	0.542064i	−0.148525	+	0.988909i	$0.547452\pi$
$674$	−1.26281e6	−	917485.i	−0.107075	−	0.0777945i
$675$	−839448.	+	609895.i	−0.0709144	+	0.0515223i
$676$	596357.			0.0501926
$677$	−1.85538e7			−1.55583			−0.777914	−	0.628371i	$-0.783722\pi$
$677$	−1.85538e7			−1.55583			−0.777914	+	0.628371i	$0.783722\pi$
$678$	−1.00004e7	+	7.26574e6i	−0.835497	+	0.607024i
$679$	120366.	−	370450.i	0.0100192	−	0.0308358i
$680$	−410844.	−	1.26445e6i	−0.0340725	−	0.104864i
$681$	−2.39133e7			−1.97593
$682$	−911541.	+	1.09484e7i	−0.0750439	+	0.901345i
$683$	−1.48407e7			−1.21731			−0.608657	−	0.793433i	$-0.708292\pi$
$683$	−1.48407e7			−1.21731			−0.608657	+	0.793433i	$0.708292\pi$
$684$	−50622.0	−	155799.i	−0.00413713	−	0.0127328i
$685$	−5.58382e6	+	1.71852e7i	−0.454679	+	1.39936i
$686$	6.75848e6	−	4.91033e6i	0.548326	−	0.398382i
$687$	−8.63968e6			−0.698403
$688$	1.54887e6			0.124751
$689$	6.71930e6	−	4.88185e6i	0.539232	−	0.391775i
$690$	8.12033e6	+	5.89976e6i	0.649308	+	0.471750i
$691$	1.13714e6	+	826178.i	0.0905978	+	0.0658232i	0.632162	−	0.774836i	$-0.282168\pi$
$691$	1.13714e6	+	826178.i	0.0905978	+	0.0658232i	−0.541564	+	0.840659i	$0.682168\pi$
$692$	−3.40380e6	−	1.04758e7i	−0.270209	−	0.831617i
$693$	−4.81672e6	+	3.49955e6i	−0.380994	+	0.276808i
$694$	2.26531e6	+	6.97190e6i	0.178537	+	0.549481i
$695$	6.03110e6	−	1.85618e7i	0.473625	−	1.45767i
$696$	4.29268e6	+	3.11881e6i	0.335896	+	0.244043i
$697$	2.48146e6	−	7.63715e6i	0.193475	−	0.595456i
$698$	−523946.	+	1.61254e6i	−0.0407050	+	0.125277i
$699$	1.47045e6	+	1.06835e6i	0.113830	+	0.0827025i
$700$	−219460.	+	675428.i	−0.0169282	+	0.0520996i
$701$	555787.	+	1.71054e6i	0.0427183	+	0.131473i	0.970141	−	0.242541i	$-0.0779810\pi$
$701$	555787.	+	1.71054e6i	0.0427183	+	0.131473i	−0.927423	+	0.374015i	$0.877981\pi$
$702$	−3.59593e6	+	2.61259e6i	−0.275403	+	0.200092i
$703$	−99705.9	−	306863.i	−0.00760909	−	0.0234184i
$704$	−1.70100e6	−	1.23585e6i	−0.129352	−	0.0939799i
$705$	8.22024e6	+	5.97235e6i	0.622891	+	0.452556i
$706$	5.34205e6	−	3.88123e6i	0.403363	−	0.293060i
$707$	1.44858e7			1.08992
$708$	5.75400e6			0.431407
$709$	−5.26344e6	+	3.82412e6i	−0.393237	+	0.285703i	−0.766781	−	0.641909i	$-0.778143\pi$
$709$	−5.26344e6	+	3.82412e6i	−0.393237	+	0.285703i	0.373544	+	0.927613i	$0.378143\pi$
$710$	−1.42445e6	+	4.38402e6i	−0.106048	+	0.326382i
$711$	−1.44518e6	−	4.44782e6i	−0.107213	−	0.329969i
$712$	−6.71024e6			−0.496064
$713$	−1.10922e6	+	1.33227e7i	−0.0817133	+	0.981451i
$714$	2.45482e6			0.180208
$715$	5.09802e6	+	1.56901e7i	0.372938	+	1.14778i
$716$	1.03688e6	−	3.19118e6i	0.0755867	−	0.232632i
$717$	8.06005e6	−	5.85597e6i	0.585517	−	0.425403i
$718$	1.01747e7			0.736566
$719$	1.43935e7			1.03835			0.519175	−	0.854668i	$-0.326239\pi$
$719$	1.43935e7			1.03835			0.519175	+	0.854668i	$0.326239\pi$
$720$	1.62414e6	−	1.18001e6i	0.116760	−	0.0848309i
$721$	−3.35146e6	−	2.43498e6i	−0.240102	−	0.174445i
$722$	7.99888e6	+	5.81153e6i	0.571066	+	0.414904i
$723$	4.47619e6	+	1.37763e7i	0.318466	+	0.980137i
$724$	1.83864e6	−	1.33585e6i	0.130362	−	0.0947135i
$725$	765560.	+	2.35615e6i	0.0540922	+	0.166479i
$726$	2.52933e6	−	7.78447e6i	0.178100	−	0.548135i
$727$	−1.45773e6	−	1.05910e6i	−0.102292	−	0.0743194i	0.535464	−	0.844558i	$-0.320137\pi$
$727$	−1.45773e6	−	1.05910e6i	−0.102292	−	0.0743194i	−0.637755	+	0.770239i	$0.720137\pi$
$728$	−940096.	+	2.89332e6i	−0.0657422	+	0.202334i
$729$	−892676.	+	2.74737e6i	−0.0622121	+	0.191469i
$730$	1.13283e7	+	8.23049e6i	0.786788	+	0.571635i
$731$	772450.	−	2.37736e6i	0.0534659	−	0.164551i
$732$	−985072.	−	3.03174e6i	−0.0679501	−	0.209129i
$733$	1.07652e7	−	7.82134e6i	0.740049	−	0.537677i	−0.152678	−	0.988276i	$-0.548790\pi$
$733$	1.07652e7	−	7.82134e6i	0.740049	−	0.537677i	0.892726	+	0.450599i	$0.148790\pi$
$734$	−3.23685e6	−	9.96201e6i	−0.221760	−	0.682506i
$735$	−9.16226e6	−	6.65677e6i	−0.625582	−	0.454512i
$736$	−2.06988e6	−	1.50386e6i	−0.140848	−	0.102332i
$737$	−783117.	+	568968.i	−0.0531077	+	0.0385850i
$738$	1.21254e7			0.819515
$739$	2.41948e7			1.62971			0.814855	−	0.579665i	$-0.196817\pi$
$739$	2.41948e7			1.62971			0.814855	+	0.579665i	$0.196817\pi$
$740$	3.19894e6	−	2.32416e6i	0.214747	−	0.156023i
$741$	258995.	−	797104.i	0.0173279	−	0.0533298i
$742$	1.19442e6	+	3.67605e6i	0.0796430	+	0.245116i
$743$	−1.35693e7			−0.901751			−0.450875	−	0.892587i	$-0.648888\pi$
$743$	−1.35693e7			−0.901751			−0.450875	+	0.892587i	$0.648888\pi$
$744$	6.30736e6	+	2.64610e6i	0.417749	+	0.175257i
$745$	2.16935e7			1.43198
$746$	−5.99419e6	−	1.84482e7i	−0.394351	−	1.21369i
$747$	3.30340e6	−	1.01668e7i	0.216601	−	0.666628i
$748$	−2.74523e6	+	1.99453e6i	−0.179401	+	0.130343i
$749$	948399.			0.0617713
$750$	1.49516e7			0.970588
$751$	−1.22121e7	+	8.87258e6i	−0.790113	+	0.574051i	−0.907997	−	0.418977i	$-0.862389\pi$
$751$	−1.22121e7	+	8.87258e6i	−0.790113	+	0.574051i	0.117884	+	0.993027i	$0.462389\pi$
$752$	−2.09535e6	−	1.52236e6i	−0.135118	−	0.0981687i
$753$	−1.57167e7	−	1.14189e7i	−1.01012	−	0.733897i
$754$	3.27942e6	+	1.00930e7i	0.210072	+	0.646535i
$755$	−1.34959e7	+	9.80536e6i	−0.861658	+	0.626031i
$756$	−639211.	−	1.96729e6i	−0.0406761	−	0.125188i
$757$	5.36919e6	−	1.65247e7i	0.340541	−	1.04808i	−0.623387	−	0.781913i	$-0.714244\pi$
$757$	5.36919e6	−	1.65247e7i	0.340541	−	1.04808i	0.963928	−	0.266163i	$-0.0857560\pi$
$758$	1.85476e6	+	1.34757e6i	0.117251	+	0.0851877i
$759$	7.91636e6	−	2.43641e7i	0.498794	−	1.53513i
$760$	65279.0	−	200908.i	0.00409958	−	0.0126172i
$761$	2.48531e7	+	1.80568e7i	1.55568	+	1.13026i	0.939445	+	0.342699i	$0.111341\pi$
$761$	2.48531e7	+	1.80568e7i	1.55568	+	1.13026i	0.616230	+	0.787566i	$0.288659\pi$
$762$	−4.03503e6	+	1.24186e7i	−0.251744	+	0.774790i
$763$	−114259.	−	351654.i	−0.00710527	−	0.0218678i
$764$	−4.48809e6	+	3.26078e6i	−0.278181	+	0.202110i
$765$	−1.00120e6	−	3.08139e6i	−0.0618542	−	0.190368i
$766$	−2.38636e6	−	1.73379e6i	−0.146948	−	0.106764i
$767$	9.31046e6	+	6.76445e6i	0.571456	+	0.415187i
$768$	−1.05902e6	+	769424.i	−0.0647891	+	0.0470720i
$769$	−8.47787e6			−0.516977			−0.258488	−	0.966014i	$-0.583224\pi$
$769$	−8.47787e6			−0.516977			−0.258488	+	0.966014i	$0.583224\pi$
$770$	−7.67764e6			−0.466660
$771$	−1.62581e7	+	1.18122e7i	−0.984992	+	0.715639i
$772$	766915.	−	2.36032e6i	0.0463131	−	0.142537i
$773$	729116.	+	2.24399e6i	0.0438882	+	0.135074i	0.970600	−	0.240700i	$-0.0773769\pi$
$773$	729116.	+	2.24399e6i	0.0438882	+	0.135074i	−0.926711	+	0.375774i	$0.877377\pi$
$774$	3.77451e6			0.226469
$775$	1.65630e6	+	2.73050e6i	0.0990568	+	0.163301i
$776$	335215.			0.0199834
$777$	2.25609e6	+	6.94353e6i	0.134061	+	0.412599i
$778$	−2.48825e6	+	7.65806e6i	−0.147382	+	0.453597i
$779$	1.03224e6	−	749965.i	0.0609447	−	0.0442789i
$780$	1.02711e7			0.604480
$781$	1.17651e7			0.690186
$782$	−3.34056e6	+	2.42706e6i	−0.195345	+	0.141927i
$783$	−5.83773e6	−	4.24136e6i	−0.340282	−	0.247230i
$784$	2.33547e6	+	1.69682e6i	0.135701	+	0.0985929i
$785$	−4.21020e6	−	1.29577e7i	−0.243853	−	0.750504i
$786$	−1.76846e7	+	1.28486e7i	−1.02103	+	0.741824i
$787$	−7.72142e6	−	2.37641e7i	−0.444386	−	1.36768i	−0.883156	−	0.469079i	$-0.844586\pi$
$787$	−7.72142e6	−	2.37641e7i	−0.444386	−	1.36768i	0.438770	−	0.898599i	$-0.355414\pi$
$788$	3.76977e6	−	1.16022e7i	0.216272	−	0.665616i
$789$	−2.95301e7	−	2.14549e7i	−1.68878	−	1.22697i
$790$	1.86362e6	−	5.73563e6i	0.106240	−	0.326974i
$791$	3.55546e6	−	1.09426e7i	0.202048	−	0.621840i
$792$	−4.14526e6	−	3.01171e6i	−0.234822	−	0.170608i
$793$	1.97021e6	−	6.06367e6i	0.111257	−	0.342415i
$794$	−7.08156e6	−	2.17948e7i	−0.398637	−	1.22688i
$795$	1.05575e7	−	7.67047e6i	0.592438	−	0.430431i
$796$	2.73360e6	+	8.41315e6i	0.152916	+	0.470626i
$797$	3.71490e6	+	2.69903e6i	0.207158	+	0.150509i	0.686527	−	0.727104i	$-0.259134\pi$
$797$	3.71490e6	+	2.69903e6i	0.207158	+	0.150509i	−0.479369	+	0.877613i	$0.659134\pi$
$798$	315555.	+	229264.i	0.0175415	+	0.0127447i
$799$	−3.38167e6	+	2.45692e6i	−0.187397	+	0.136152i
$800$	−611186.			−0.0337636
$801$	−1.63525e7			−0.900540
$802$	−1.42796e7	+	1.03747e7i	−0.783936	+	0.569563i
$803$	1.10438e7	−	3.39892e7i	0.604405	−	1.86017i
$804$	186230.	+	573158.i	0.0101604	+	0.0312705i
$805$	−9.34260e6			−0.508134
$806$	7.09506e6	+	1.16966e7i	0.384697	+	0.634193i
$807$	9.64417e6			0.521292
$808$	3.85234e6	+	1.18563e7i	0.207585	+	0.638881i
$809$	1.05058e6	−	3.23337e6i	0.0564365	−	0.173694i	−0.918865	−	0.394573i	$-0.870893\pi$
$809$	1.05058e6	−	3.23337e6i	0.0564365	−	0.173694i	0.975301	+	0.220879i	$0.0708926\pi$
$810$	−1.18167e7	+	8.58531e6i	−0.632823	+	0.459773i
$811$	−2.08142e6			−0.111124			−0.0555620	−	0.998455i	$-0.517695\pi$
$811$	−2.08142e6			−0.111124			−0.0555620	+	0.998455i	$0.517695\pi$
$812$	−4.93882e6			−0.262865
$813$	−2.54524e7	+	1.84923e7i	−1.35053	+	0.981214i
$814$	−8.16457e6	−	5.93191e6i	−0.431889	−	0.313786i
$815$	−1.85322e7	−	1.34644e7i	−0.977309	−	0.710057i
$816$	652835.	+	2.00922e6i	0.0343224	+	0.105634i
$817$	321324.	−	233455.i	0.0168418	−	0.0122363i
$818$	1.35122e6	+	4.15864e6i	0.0706064	+	0.217304i
$819$	−2.29097e6	+	7.05087e6i	−0.119346	+	0.367310i
$820$	1.26500e7	+	9.19074e6i	0.656984	+	0.477327i
$821$	−1.00246e7	+	3.08527e7i	−0.519052	+	1.59748i	0.256733	+	0.966482i	$0.417354\pi$
$821$	−1.00246e7	+	3.08527e7i	−0.519052	+	1.59748i	−0.775786	+	0.630996i	$0.782646\pi$
$822$	8.87275e6	−	2.73075e7i	0.458014	−	1.40962i
$823$	655692.	+	476388.i	0.0337443	+	0.0245167i	0.604530	−	0.796583i	$-0.293361\pi$
$823$	655692.	+	476388.i	0.0337443	+	0.0245167i	−0.570785	+	0.821099i	$0.693361\pi$
$824$	1.10169e6	−	3.39066e6i	0.0565252	−	0.173967i
$825$	−1.89109e6	−	5.82016e6i	−0.0967333	−	0.297715i
$826$	−4.33291e6	+	3.14804e6i	−0.220968	+	0.160543i
$827$	8.15467e6	+	2.50975e7i	0.414613	+	1.27605i	0.912597	+	0.408861i	$0.134074\pi$
$827$	8.15467e6	+	2.50975e7i	0.414613	+	1.27605i	−0.497984	+	0.867186i	$0.665926\pi$
$828$	−5.04420e6	−	3.66482e6i	−0.255692	−	0.185771i
$829$	2.92531e7	+	2.12536e7i	1.47838	+	1.07410i	0.978075	+	0.208255i	$0.0667785\pi$
$829$	2.92531e7	+	2.12536e7i	1.47838	+	1.07410i	0.500304	+	0.865850i	$0.333222\pi$
$830$	1.11525e7	−	8.10274e6i	0.561921	−	0.408260i
$831$	2.68266e7			1.34761
$832$	−2.61813e6			−0.131124
$833$	3.76919e6	−	2.73848e6i	0.188207	−	0.136740i
$834$	−9.58349e6	+	2.94949e7i	−0.477099	+	1.46836i
$835$	5.35285e6	+	1.64744e7i	0.265686	+	0.817698i
$836$	−539161.			−0.0266811
$837$	−8.57754e6	−	3.59850e6i	−0.423203	−	0.177545i
$838$	−7.73284e6			−0.380390
$839$	−4.12812e6	−	1.27051e7i	−0.202464	−	0.623120i	−0.999808	−	0.0195949i	$-0.993762\pi$
$839$	−4.12812e6	−	1.27051e7i	−0.202464	−	0.623120i	0.797344	−	0.603525i	$-0.206238\pi$
$840$	−1.47710e6	+	4.54604e6i	−0.0722289	+	0.222298i
$841$	2.65573e6	−	1.92950e6i	0.129477	−	0.0940707i
$842$	1.55327e7			0.755034
$843$	1.53143e7			0.742211
$844$	−1.54255e7	+	1.12073e7i	−0.745389	+	0.541557i
$845$	1.51616e6	+	1.10155e6i	0.0730470	+	0.0530718i
$846$	−5.10626e6	−	3.70992e6i	−0.245289	−	0.178213i
$847$	2.35428e6	+	7.24572e6i	0.112758	+	0.347035i
$848$	−2.69112e6	+	1.95521e6i	−0.128512	+	0.0933694i
$849$	1.49008e7	+	4.58598e7i	0.709478	+	2.18355i
$850$	−304810.	+	938110.i	−0.0144705	+	0.0445355i
$851$	−9.93513e6	−	7.21829e6i	−0.470272	−	0.341673i
$852$	2.26347e6	−	6.96626e6i	0.106826	−	0.328776i
$853$	−1.04681e6	+	3.22176e6i	−0.0492603	+	0.151607i	−0.972661	−	0.232230i	$-0.925398\pi$
$853$	−1.04681e6	+	3.22176e6i	−0.0492603	+	0.151607i	0.923401	+	0.383838i	$0.125398\pi$
$854$	2.40047e6	+	1.74404e6i	0.112629	+	0.0818299i
$855$	159082.	−	489603.i	0.00744226	−	0.0229049i
$856$	252217.	+	776244.i	0.0117649	+	0.0362088i
$857$	−7.45476e6	+	5.41620e6i	−0.346722	+	0.251908i	−0.747493	−	0.664270i	$-0.768742\pi$
$857$	−7.45476e6	+	5.41620e6i	−0.346722	+	0.251908i	0.400770	+	0.916179i	$0.368742\pi$
$858$	−8.10081e6	−	2.49317e7i	−0.375673	−	1.15620i
$859$	−1.94573e7	−	1.41366e7i	−0.899705	−	0.653674i	0.0386851	−	0.999251i	$-0.487683\pi$
$859$	−1.94573e7	−	1.41366e7i	−0.899705	−	0.653674i	−0.938390	+	0.345577i	$0.887683\pi$
$860$	3.93779e6	+	2.86097e6i	0.181554	+	0.131907i
$861$	−2.33569e7	+	1.69698e7i	−1.07376	+	0.780133i
$862$	−5.31337e6			−0.243558
$863$	−1.97544e7			−0.902893			−0.451447	−	0.892298i	$-0.649092\pi$
$863$	−1.97544e7			−0.902893			−0.451447	+	0.892298i	$0.649092\pi$
$864$	1.44019e6	−	1.04636e6i	0.0656350	−	0.0476867i
$865$	1.06966e7	−	3.29207e7i	0.486076	−	1.49599i
$866$	−7.34055e6	−	2.25919e7i	−0.332609	−	1.02367i
$867$	−2.49508e7			−1.12729
$868$	−6.19730e6	+	1.45820e6i	−0.279192	+	0.0656930i
$869$	−1.53923e7			−0.691437
$870$	5.15269e6	+	1.58583e7i	0.230800	+	0.710329i
$871$	−372472.	+	1.14635e6i	−0.0166360	+	0.0512003i
$872$	257435.	−	187037.i	0.0114651	−	0.00832985i
$873$	816902.			0.0362773
$874$	−656083.			−0.0290523
$875$	−1.12589e7	+	8.18010e6i	−0.497139	+	0.361192i
$876$	−1.80008e7	−	1.30783e7i	−0.792558	−	0.575827i
$877$	2.45328e7	+	1.78241e7i	1.07708	+	0.782546i	0.977172	−	0.212451i	$-0.0681445\pi$
$877$	2.45328e7	+	1.78241e7i	1.07708	+	0.782546i	0.0999102	+	0.994996i	$0.468144\pi$
$878$	−3.51799e6	−	1.08273e7i	−0.154013	−	0.474004i
$879$	−1.90203e7	+	1.38191e7i	−0.830322	+	0.603264i
$880$	−2.04179e6	−	6.28398e6i	−0.0888800	−	0.273545i
$881$	−6.58217e6	+	2.02578e7i	−0.285713	+	0.879333i	0.700471	+	0.713680i	$0.252973\pi$
$881$	−6.58217e6	+	2.02578e7i	−0.285713	+	0.879333i	−0.986184	+	0.165653i	$0.947027\pi$
$882$	5.69143e6	+	4.13506e6i	0.246348	+	0.178983i
$883$	−1.82648e6	+	5.62132e6i	−0.0788338	+	0.242625i	−0.982705	−	0.185180i	$-0.940713\pi$
$883$	−1.82648e6	+	5.62132e6i	−0.0788338	+	0.242625i	0.903871	+	0.427805i	$0.140713\pi$
$884$	−1.30571e6	+	4.01856e6i	−0.0561974	+	0.172958i
$885$	1.46288e7	+	1.06284e7i	0.627841	+	0.456154i
$886$	6.01976e6	−	1.85269e7i	0.257629	−	0.792901i
$887$	5.15915e6	+	1.58782e7i	0.220176	+	0.677631i	0.998746	+	0.0500730i	$0.0159454\pi$
$887$	5.15915e6	+	1.58782e7i	0.220176	+	0.677631i	−0.778570	+	0.627558i	$0.784055\pi$
$888$	−5.08314e6	+	3.69312e6i	−0.216322	+	0.157167i
$889$	−3.75577e6	−	1.15591e7i	−0.159384	−	0.490534i
$890$	−1.70599e7	−	1.23947e7i	−0.721940	−	0.524520i
$891$	3.01594e7	+	2.19121e7i	1.27271	+	0.924675i
$892$	−1.33856e7	+	9.72517e6i	−0.563280	+	0.409247i
$893$	−664156.			−0.0278703
$894$	−3.44711e7			−1.44249
$895$	8.53068e6	−	6.19790e6i	0.355980	−	0.258635i
$896$	376514.	−	1.15879e6i	0.0156679	−	0.0482209i
$897$	−9.85754e6	−	3.03384e7i	−0.409060	−	1.25896i
$898$	3.12599e7			1.29359
$899$	−1.44998e7	+	1.68224e7i	−0.598362	+	0.694205i
$900$	−1.48943e6			−0.0612934
$901$	1.65894e6	+	5.10570e6i	0.0680800	+	0.209529i
$902$	1.23322e7	−	3.79547e7i	0.504691	−	1.55328i
$903$	−7.27074e6	+	5.28250e6i	−0.296728	+	0.215586i
$904$	9.90180e6			0.402989
$905$	7.14201e6			0.289867
$906$	2.14452e7	−	1.55808e7i	0.867978	−	0.630623i
$907$	1.93467e7	+	1.40562e7i	0.780889	+	0.567349i	0.905246	−	0.424888i	$-0.139687\pi$
$907$	1.93467e7	+	1.40562e7i	0.780889	+	0.567349i	−0.124356	+	0.992238i	$0.539687\pi$
$908$	1.54971e7	+	1.12593e7i	0.623787	+	0.453208i
$909$	9.38795e6	+	2.88931e7i	0.376843	+	1.15980i
$910$	−7.73443e6	+	5.61939e6i	−0.309617	+	0.224950i
$911$	−9.33062e6	−	2.87167e7i	−0.372490	−	1.14641i	−0.945157	−	0.326618i	$-0.894091\pi$
$911$	−9.33062e6	−	2.87167e7i	−0.372490	−	1.14641i	0.572667	−	0.819788i	$-0.305909\pi$
$912$	−103729.	+	319245.i	−0.00412965	+	0.0127098i
$913$	−2.84641e7	−	2.06804e7i	−1.13011	−	0.821074i
$914$	−202074.	+	621921.i	−0.00800103	+	0.0246246i
$915$	3.09563e6	−	9.52736e6i	0.122235	−	0.376201i
$916$	5.59897e6	+	4.06789e6i	0.220480	+	0.160188i
$917$	6.28743e6	−	1.93507e7i	0.246916	−	0.759930i
$918$	−887807.	−	2.73239e6i	−0.0347706	−	0.107013i
$919$	−1.29199e7	+	9.38685e6i	−0.504627	+	0.366633i	−0.810781	−	0.585349i	$-0.800957\pi$
$919$	−1.29199e7	+	9.38685e6i	−0.504627	+	0.366633i	0.306155	+	0.951982i	$0.400957\pi$
$920$	−2.48457e6	−	7.64672e6i	−0.0967791	−	0.297855i
$921$	2.73123e7	+	1.98435e7i	1.06098	+	0.770849i
$922$	−2.08949e7	−	1.51810e7i	−0.809491	−	0.588130i
$923$	1.18521e7	−	8.61103e6i	0.457920	−	0.332699i
$924$	1.21999e7			0.470083
$925$	−2.93360e6			−0.112732
$926$	2.74442e7	−	1.99394e7i	1.05177	−	0.764159i
$927$	2.68476e6	−	8.26286e6i	0.102614	−	0.315814i
$928$	−1.31343e6	−	4.04231e6i	−0.0500652	−	0.154085i
$929$	9.26542e6			0.352230			0.176115	−	0.984370i	$-0.443647\pi$
$929$	9.26542e6			0.352230			0.176115	+	0.984370i	$0.443647\pi$
$930$	1.11479e7	+	1.83779e7i	0.422655	+	0.696769i
$931$	740266.			0.0279907
$932$	−449913.	−	1.38469e6i	−0.0169663	−	0.0522170i
$933$	−118722.	+	365388.i	−0.00446505	+	0.0137420i
$934$	2.71755e7	−	1.97442e7i	1.01932	−	0.740579i
$935$	−1.06636e7			−0.398908
$936$	−6.38024e6			−0.238039
$937$	1.29213e7	−	9.38789e6i	0.480793	−	0.349316i	−0.320840	−	0.947133i	$-0.603965\pi$
$937$	1.29213e7	−	9.38789e6i	0.480793	−	0.349316i	0.801632	+	0.597817i	$0.203965\pi$
$938$	−453814.	−	329715.i	−0.0168411	−	0.0122358i
$939$	−1.27320e7	−	9.25035e6i	−0.471230	−	0.342369i
$940$	−2.51514e6	−	7.74080e6i	−0.0928415	−	0.285737i
$941$	3.83417e7	−	2.78569e7i	1.41155	−	1.02555i	0.418458	−	0.908236i	$-0.362571\pi$
$941$	3.83417e7	−	2.78569e7i	1.41155	−	1.02555i	0.993095	−	0.117317i	$-0.0374293\pi$
$942$	6.69006e6	+	2.05899e7i	0.245642	+	0.756008i
$943$	1.50066e7	−	4.61855e7i	0.549544	−	1.69132i
$944$	−3.72890e6	−	2.70920e6i	−0.136192	−	0.0989490i
$945$	2.00874e6	−	6.18228e6i	0.0731720	−	0.225200i
$946$	3.83888e6	−	1.18149e7i	0.139469	−	0.429240i
$947$	−8.06939e6	−	5.86276e6i	−0.292392	−	0.212435i	0.431912	−	0.901916i	$-0.357839\pi$
$947$	−8.06939e6	−	5.86276e6i	−0.292392	−	0.212435i	−0.724305	+	0.689480i	$0.757839\pi$
$948$	−2.96131e6	+	9.11397e6i	−0.107020	+	0.329372i
$949$	−1.37518e7	−	4.23237e7i	−0.495672	−	1.52552i
$950$	−126795.	+	92121.9i	−0.00455820	+	0.00331172i
$951$	5.07788e6	+	1.56281e7i	0.182067	+	0.560345i
$952$	−1.59086e6	−	1.15582e6i	−0.0568903	−	0.0413332i
$953$	3.14732e7	+	2.28666e7i	1.12256	+	0.815586i	0.984595	−	0.174851i	$-0.0559445\pi$
$953$	3.14732e7	+	2.28666e7i	1.12256	+	0.815586i	0.137963	+	0.990437i	$0.455945\pi$
$954$	−6.55812e6	+	4.76475e6i	−0.233297	+	0.169500i
$955$	−1.74335e7			−0.618551
$956$	−7.98055e6			−0.282415
$957$	3.44300e7	−	2.50148e7i	1.21522	−	0.882912i
$958$	−9.07273e6	+	2.79230e7i	−0.319392	+	0.982988i
$959$	8.25868e6	+	2.54176e7i	0.289977	+	0.892458i
$960$	−4.11365e6			−0.144062
$961$	−1.32277e7	+	2.53901e7i	−0.462038	+	0.886860i
$962$	−1.25666e7			−0.437805
$963$	614639.	+	1.89167e6i	0.0213577	+	0.0657323i
$964$	3.58560e6	−	1.10353e7i	0.124271	−	0.382466i
$965$	6.30962e6	−	4.58420e6i	0.218115	−	0.158469i
$966$	1.48455e7			0.511861
$967$	2.66229e6			0.0915565			0.0457783	−	0.998952i	$-0.485423\pi$
$967$	2.66229e6			0.0915565			0.0457783	+	0.998952i	$0.485423\pi$
$968$	−5.30436e6	+	3.85385e6i	−0.181947	+	0.132192i
$969$	438278.	+	318428.i	0.0149948	+	0.0108943i
$970$	852240.	+	619188.i	0.0290825	+	0.0211297i
$971$	8.95995e6	+	2.75759e7i	0.304970	+	0.938602i	0.979688	+	0.200526i	$0.0642652\pi$
$971$	8.95995e6	+	2.75759e7i	0.304970	+	0.938602i	−0.674718	+	0.738076i	$0.735735\pi$
$972$	1.33086e7	−	9.66925e6i	0.451821	−	0.328267i
$973$	−8.92022e6	−	2.74536e7i	−0.302060	−	0.929646i
$974$	−8.09263e6	+	2.49066e7i	−0.273333	+	0.841233i
$975$	−6.16494e6	−	4.47909e6i	−0.207691	−	0.150896i
$976$	−789080.	+	2.42854e6i	−0.0265153	+	0.0816056i
$977$	−1.61506e7	+	4.97064e7i	−0.541317	+	1.66600i	0.188272	+	0.982117i	$0.439711\pi$
$977$	−1.61506e7	+	4.97064e7i	−0.541317	+	1.66600i	−0.729589	+	0.683885i	$0.760289\pi$
$978$	2.94478e7	+	2.13951e7i	0.984477	+	0.715264i
$979$	−1.66314e7	+	5.11861e7i	−0.554589	+	1.70685i
$980$	2.80337e6	+	8.62788e6i	0.0932427	+	0.286971i
$981$	627356.	−	455801.i	0.0208133	−	0.0151218i
$982$	−2.39690e6	−	7.37690e6i	−0.0793179	−	0.244115i
$983$	−3.55435e7	−	2.58239e7i	−1.17321	−	0.852389i	−0.181822	−	0.983331i	$-0.558200\pi$
$983$	−3.55435e7	−	2.58239e7i	−1.17321	−	0.852389i	−0.991390	+	0.130943i	$0.958200\pi$
$984$	−2.01009e7	−	1.46042e7i	−0.661803	−	0.480828i
$985$	3.10149e7	−	2.25337e7i	1.01855	−	0.740016i
$986$	−6.85958e6			−0.224701
$987$	1.50282e7			0.491036
$988$	−543149.	+	394621.i	−0.0177022	+	0.0128614i
$989$	4.67137e6	−	1.43770e7i	0.151864	−	0.467388i
$990$	−4.97573e6	−	1.53137e7i	−0.161350	−	0.496584i
$991$	−2.10940e7			−0.682299			−0.341149	−	0.940009i	$-0.610816\pi$
$991$	−2.10940e7			−0.682299			−0.341149	+	0.940009i	$0.610816\pi$
$992$	−2.84161e6	−	4.68456e6i	−0.0916824	−	0.151143i
$993$	5.98595e7			1.92646
$994$	2.10682e6	+	6.48413e6i	0.0676335	+	0.208154i
$995$	−8.59043e6	+	2.64386e7i	−0.275079	+	0.846606i
$996$	−1.77214e7	+	1.28753e7i	−0.566043	+	0.411254i
$997$	−7.94504e6			−0.253139			−0.126569	−	0.991958i	$-0.540397\pi$
$997$	−7.94504e6			−0.253139			−0.126569	+	0.991958i	$0.540397\pi$
$998$	1.68883e7			0.536734
$999$	6.91270e6	−	5.02237e6i	0.219146	−	0.159219i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.6.d.a.35.5	✓	24
31.8	even	5	inner	62.6.d.a.39.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.6.d.a.35.5	✓	24	1.1	even	1	trivial
62.6.d.a.39.5	yes	24	31.8	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.23607 + 3.80423i) q^{2} +(6.17234 - 18.9965i) q^{3} +(-12.9443 + 9.40456i) q^{4} -50.2806 q^{5} +79.8964 q^{6} +(-60.1640 + 43.7117i) q^{7} +(-51.7771 - 37.6183i) q^{8} +(-126.178 - 91.6738i) q^{9} +(-62.1502 - 191.279i) q^{10} +(-415.284 + 301.722i) q^{11} +(98.7574 + 303.944i) q^{12} +(-197.521 + 607.907i) q^{13} +(-240.656 - 174.847i) q^{14} +(-310.349 + 955.155i) q^{15} +(79.1084 - 243.470i) q^{16} +(-334.250 - 242.847i) q^{17} +(192.783 - 593.325i) q^{18} +(-20.2858 - 62.4334i) q^{19} +(650.846 - 472.867i) q^{20} +(459.017 + 1412.71i) q^{21} +(-1661.14 - 1206.89i) q^{22} +(-2021.37 - 1468.61i) q^{23} +(-1034.20 + 751.391i) q^{24} -596.861 q^{25} -2556.76 q^{26} +(1406.44 - 1021.84i) q^{27} +(367.690 - 1131.63i) q^{28} +(-1282.64 - 3947.57i) q^{29} -4017.24 q^{30} +(-2775.01 - 4574.76i) q^{31} +1024.00 q^{32} +(3168.38 + 9751.28i) q^{33} +(510.689 - 1571.74i) q^{34} +(3025.08 - 2197.85i) q^{35} +2495.44 q^{36} +4915.05 q^{37} +(212.436 - 154.344i) q^{38} +(10328.9 + 7504.41i) q^{39} +(2603.38 + 1891.47i) q^{40} +(6006.12 + 18484.9i) q^{41} +(-4806.89 + 3492.41i) q^{42} +(1869.63 + 5754.14i) q^{43} +(2537.99 - 7811.14i) q^{44} +(6344.31 + 4609.41i) q^{45} +(3088.38 - 9505.05i) q^{46} +(3126.38 - 9622.00i) q^{47} +(-4136.80 - 3005.56i) q^{48} +(-3484.65 + 10724.7i) q^{49} +(-737.761 - 2270.60i) q^{50} +(-6676.34 + 4850.65i) q^{51} +(-3160.33 - 9726.51i) q^{52} +(-10512.2 - 7637.55i) q^{53} +(5625.75 + 4087.34i) q^{54} +(20880.7 - 15170.8i) q^{55} +4759.48 q^{56} -1311.23 q^{57} +(13432.0 - 9758.93i) q^{58} +(5563.72 - 17123.4i) q^{59} +(-4965.58 - 15282.5i) q^{60} -9974.67 q^{61} +(13973.3 - 16211.5i) q^{62} +11598.6 q^{63} +(1265.73 + 3895.53i) q^{64} +(9931.47 - 30565.9i) q^{65} +(-33179.7 + 24106.5i) q^{66} +1885.74 q^{67} +6610.49 q^{68} +(-40375.1 + 29334.2i) q^{69} +(12100.3 + 8791.41i) q^{70} +(-18542.3 - 13471.8i) q^{71} +(3084.53 + 9493.20i) q^{72} +(-56325.4 + 40922.8i) q^{73} +(6075.33 + 18697.9i) q^{74} +(-3684.03 + 11338.3i) q^{75} +(849.745 + 617.376i) q^{76} +(11796.4 - 36305.6i) q^{77} +(-15781.2 + 48569.6i) q^{78} +(24258.9 + 17625.2i) q^{79} +(-3977.62 + 12241.8i) q^{80} +(-22441.9 - 69069.0i) q^{81} +(-62896.9 + 45697.2i) q^{82} +(21180.4 + 65186.7i) q^{83} +(-19227.6 - 13969.6i) q^{84} +(16806.3 + 12210.5i) q^{85} +(-19579.1 + 14225.0i) q^{86} -82906.9 q^{87} +32852.5 q^{88} +(84823.4 - 61627.8i) q^{89} +(-9693.24 + 29832.7i) q^{90} +(-14689.0 - 45208.1i) q^{91} +39976.8 q^{92} +(-104033. + 24478.6i) q^{93} +40468.7 q^{94} +(1019.98 + 3139.19i) q^{95} +(6320.47 - 19452.4i) q^{96} +(-4237.42 + 3078.66i) q^{97} -45106.3 q^{98} +80059.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - 20 q^{3} - 96 q^{4} + 120 q^{5} + 280 q^{6} - 180 q^{7} - 384 q^{8} - 200 q^{9} - 100 q^{10} + 354 q^{11} - 320 q^{12} + 39 q^{13} - 720 q^{14} + 535 q^{15} - 1536 q^{16} - 1027 q^{17}+ \cdots + 339042 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - 20 * q^3 - 96 * q^4 + 120 * q^5 + 280 * q^6 - 180 * q^7 - 384 * q^8 - 200 * q^9 - 100 * q^10 + 354 * q^11 - 320 * q^12 + 39 * q^13 - 720 * q^14 + 535 * q^15 - 1536 * q^16 - 1027 * q^17 - 1420 * q^18 + 334 * q^19 - 560 * q^20 - 1867 * q^21 + 1416 * q^22 - 1051 * q^23 - 960 * q^24 + 4812 * q^25 + 12536 * q^26 - 5135 * q^27 + 4000 * q^28 - 1143 * q^29 + 9080 * q^30 - 8583 * q^31 + 24576 * q^32 - 24628 * q^33 - 8108 * q^34 - 7496 * q^35 + 17760 * q^36 - 25204 * q^37 - 2844 * q^38 - 20114 * q^39 - 2240 * q^40 + 19615 * q^41 + 3212 * q^42 + 22358 * q^43 - 20496 * q^44 + 6725 * q^45 - 5264 * q^46 + 4766 * q^47 - 3840 * q^48 - 12058 * q^49 + 4628 * q^50 + 6844 * q^51 + 624 * q^52 - 7393 * q^53 - 20540 * q^54 + 11861 * q^55 - 8960 * q^56 + 176704 * q^57 + 4268 * q^58 - 21070 * q^59 + 8560 * q^60 + 76556 * q^61 - 49652 * q^62 + 105854 * q^63 - 24576 * q^64 - 107146 * q^65 + 57968 * q^66 - 150906 * q^67 + 97728 * q^68 - 212560 * q^69 - 29984 * q^70 + 27475 * q^71 - 22720 * q^72 + 49671 * q^73 + 90124 * q^74 - 156002 * q^75 - 11376 * q^76 + 253908 * q^77 - 9036 * q^78 - 7162 * q^79 - 6400 * q^80 + 38329 * q^81 - 92940 * q^82 - 246088 * q^83 + 12848 * q^84 - 104879 * q^85 - 149088 * q^86 - 247668 * q^87 + 118656 * q^88 + 159253 * q^89 - 167880 * q^90 - 68566 * q^91 + 75744 * q^92 + 260391 * q^93 + 18784 * q^94 + 222814 * q^95 - 20480 * q^96 + 190 * q^97 - 144032 * q^98 + 339042 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more