LMFDB - Embedded newform 82.6.d.a.57.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [82,6,Mod(37,82)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(82, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("82.37"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 82 = 2 \cdot 41 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	82.d (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [36,-36] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$13.1514732247$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			57.2
Character	$\chi$	$=$	82.57
Dual form			82.6.d.a.59.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.23607 - 3.80423i) q^{2} -20.9318 q^{3} +(-12.9443 - 9.40456i) q^{4} +(-49.5992 - 36.0360i) q^{5} +(-25.8731 + 79.6292i) q^{6} +(-63.1646 - 194.401i) q^{7} +(-51.7771 + 37.6183i) q^{8} +195.140 q^{9} +(-198.397 + 144.144i) q^{10} +(147.244 - 106.979i) q^{11} +(270.947 + 196.854i) q^{12} +(-278.423 + 856.897i) q^{13} -817.620 q^{14} +(1038.20 + 754.297i) q^{15} +(79.1084 + 243.470i) q^{16} +(614.221 - 446.257i) q^{17} +(241.206 - 742.355i) q^{18} +(133.991 + 412.382i) q^{19} +(303.124 + 932.919i) q^{20} +(1322.15 + 4069.15i) q^{21} +(-224.968 - 692.381i) q^{22} +(-178.040 + 547.949i) q^{23} +(1083.79 - 787.417i) q^{24} +(195.816 + 602.661i) q^{25} +(2915.68 + 2118.37i) q^{26} +1001.80 q^{27} +(-1010.63 + 3110.41i) q^{28} +(-4395.40 - 3193.45i) q^{29} +(4152.80 - 3017.19i) q^{30} +(3788.83 - 2752.74i) q^{31} +1024.00 q^{32} +(-3082.07 + 2239.26i) q^{33} +(-938.446 - 2888.24i) q^{34} +(-3872.50 + 11918.3i) q^{35} +(-2525.94 - 1835.20i) q^{36} +(3000.76 + 2180.18i) q^{37} +1734.42 q^{38} +(5827.88 - 17936.4i) q^{39} +3923.71 q^{40} +(-7125.45 - 8067.47i) q^{41} +17114.2 q^{42} +(-400.047 + 1231.22i) q^{43} -2912.05 q^{44} +(-9678.77 - 7032.04i) q^{45} +(1864.45 + 1354.61i) q^{46} +(-6942.41 + 21366.5i) q^{47} +(-1655.88 - 5096.27i) q^{48} +(-20204.7 + 14679.6i) q^{49} +2534.70 q^{50} +(-12856.7 + 9340.96i) q^{51} +(11662.7 - 8473.46i) q^{52} +(3815.39 + 2772.04i) q^{53} +(1238.30 - 3811.09i) q^{54} -11158.3 q^{55} +(10583.5 + 7689.36i) q^{56} +(-2804.67 - 8631.90i) q^{57} +(-17581.6 + 12773.8i) q^{58} +(-13373.7 + 41159.9i) q^{59} +(-6344.92 - 19527.6i) q^{60} +(-5273.90 - 16231.4i) q^{61} +(-5788.81 - 17816.1i) q^{62} +(-12325.9 - 37935.2i) q^{63} +(1265.73 - 3895.53i) q^{64} +(44688.6 - 32468.2i) q^{65} +(4708.99 + 14492.8i) q^{66} +(-2062.80 - 1498.71i) q^{67} -12147.5 q^{68} +(3726.69 - 11469.6i) q^{69} +(40553.3 + 29463.7i) q^{70} +(61739.7 - 44856.5i) q^{71} +(-10103.8 + 7340.81i) q^{72} -54905.3 q^{73} +(12003.0 - 8720.71i) q^{74} +(-4098.79 - 12614.8i) q^{75} +(2143.86 - 6598.12i) q^{76} +(-30097.3 - 21867.0i) q^{77} +(-61030.4 - 44341.2i) q^{78} -74201.2 q^{79} +(4849.98 - 14926.7i) q^{80} -68388.5 q^{81} +(-39498.0 + 17134.9i) q^{82} +76561.3 q^{83} +(21154.4 - 65106.4i) q^{84} -46546.2 q^{85} +(4189.34 + 3043.74i) q^{86} +(92003.6 + 66844.5i) q^{87} +(-3599.49 + 11078.1i) q^{88} +(-9214.97 - 28360.8i) q^{89} +(-38715.1 + 28128.2i) q^{90} +184168. q^{91} +(7457.82 - 5418.42i) q^{92} +(-79306.9 + 57619.8i) q^{93} +(72701.8 + 52821.0i) q^{94} +(8214.74 - 25282.4i) q^{95} -21434.1 q^{96} +(113033. + 82123.0i) q^{97} +(30870.0 + 95008.1i) q^{98} +(28733.1 - 20875.8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{2} + 20 q^{3} - 144 q^{4} - 98 q^{5} - 20 q^{6} + 120 q^{7} - 576 q^{8} + 2876 q^{9} - 392 q^{10} - 436 q^{11} - 80 q^{12} - 617 q^{13} + 280 q^{14} + 789 q^{15} - 2304 q^{16} + 1359 q^{17}+ \cdots + 261106 q^{99}+O(q^{100}) $ 36 * q - 36 * q^2 + 20 * q^3 - 144 * q^4 - 98 * q^5 - 20 * q^6 + 120 * q^7 - 576 * q^8 + 2876 * q^9 - 392 * q^10 - 436 * q^11 - 80 * q^12 - 617 * q^13 + 280 * q^14 + 789 * q^15 - 2304 * q^16 + 1359 * q^17 - 4976 * q^18 + 4876 * q^19 + 352 * q^20 - 13529 * q^21 + 2476 * q^22 + 819 * q^23 - 320 * q^24 - 10487 * q^25 - 2088 * q^26 + 1592 * q^27 + 1920 * q^28 + 5249 * q^29 + 3156 * q^30 - 2992 * q^31 + 36864 * q^32 - 5676 * q^33 + 4136 * q^34 + 21607 * q^35 - 3104 * q^36 - 11508 * q^37 + 10664 * q^38 + 8144 * q^39 + 9728 * q^40 - 44187 * q^41 + 97464 * q^42 - 88677 * q^43 - 5856 * q^44 - 45045 * q^45 - 6864 * q^46 - 56670 * q^47 - 1280 * q^48 - 59417 * q^49 + 88352 * q^50 - 26259 * q^51 - 8352 * q^52 + 21963 * q^53 + 29968 * q^54 + 128202 * q^55 - 9920 * q^56 + 16428 * q^57 + 20996 * q^58 - 77668 * q^59 - 7856 * q^60 - 168787 * q^61 - 34428 * q^62 + 247961 * q^63 - 36864 * q^64 - 74533 * q^65 + 48036 * q^66 - 40269 * q^67 - 76576 * q^68 + 242095 * q^69 - 20492 * q^70 - 44665 * q^71 - 12416 * q^72 - 76360 * q^73 - 46032 * q^74 - 154234 * q^75 + 78016 * q^76 - 8441 * q^77 - 71044 * q^78 + 230228 * q^79 + 5632 * q^80 + 184156 * q^81 + 36752 * q^82 + 673200 * q^83 - 216464 * q^84 - 130180 * q^85 + 194192 * q^86 - 398341 * q^87 + 39616 * q^88 - 409131 * q^89 - 180180 * q^90 + 355046 * q^91 - 27456 * q^92 - 51949 * q^93 + 234960 * q^94 - 588753 * q^95 + 20480 * q^96 + 138500 * q^97 - 43248 * q^98 + 261106 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	1.23607	−	3.80423i	0.218508	−	0.672499i
$2$	1.23607	−	3.80423i	0.218508	−	0.672499i
$3$	−20.9318			−1.34277			−0.671387	−	0.741107i	$-0.734301\pi$
$3$	−20.9318			−1.34277			−0.671387	+	0.741107i	$0.734301\pi$
$4$	−12.9443	−	9.40456i	−0.404508	−	0.293893i
$5$	−49.5992	−	36.0360i	−0.887258	−	0.644631i	0.0479035	−	0.998852i	$-0.484746\pi$
$5$	−49.5992	−	36.0360i	−0.887258	−	0.644631i	−0.935162	+	0.354221i	$0.884746\pi$
$6$	−25.8731	+	79.6292i	−0.293407	+	0.903014i
$7$	−63.1646	−	194.401i	−0.487224	−	1.49952i	−0.828734	−	0.559643i	$-0.810938\pi$
$7$	−63.1646	−	194.401i	−0.487224	−	1.49952i	0.341510	−	0.939878i	$-0.389062\pi$
$8$	−51.7771	+	37.6183i	−0.286031	+	0.207813i
$9$	195.140			0.803043
$10$	−198.397	+	144.144i	−0.627386	+	0.455823i
$11$	147.244	−	106.979i	0.366906	−	0.266573i	−0.389021	−	0.921229i	$-0.627187\pi$
$11$	147.244	−	106.979i	0.366906	−	0.266573i	0.755927	+	0.654656i	$0.227187\pi$
$12$	270.947	+	196.854i	0.543164	+	0.394632i
$13$	−278.423	+	856.897i	−0.456926	+	1.40627i	0.411932	+	0.911214i	$0.364854\pi$
$13$	−278.423	+	856.897i	−0.456926	+	1.40627i	−0.868859	+	0.495060i	$0.835146\pi$
$14$	−817.620			−1.11489
$15$	1038.20	+	754.297i	1.19139	+	0.865594i
$16$	79.1084	+	243.470i	0.0772542	+	0.237764i
$17$	614.221	−	446.257i	0.515469	−	0.374510i	−0.299426	−	0.954120i	$-0.596795\pi$
$17$	614.221	−	446.257i	0.515469	−	0.374510i	0.814894	+	0.579610i	$0.196795\pi$
$18$	241.206	−	742.355i	0.175471	−	0.540045i
$19$	133.991	+	412.382i	0.0851515	+	0.262069i	0.984562	−	0.175035i	$-0.0560040\pi$
$19$	133.991	+	412.382i	0.0851515	+	0.262069i	−0.899411	+	0.437105i	$0.856004\pi$
$20$	303.124	+	932.919i	0.169451	+	0.521517i
$21$	1322.15	+	4069.15i	0.654232	+	2.01352i
$22$	−224.968	−	692.381i	−0.0990979	−	0.304992i
$23$	−178.040	+	547.949i	−0.0701774	+	0.215984i	−0.979994	−	0.199027i	$-0.936222\pi$
$23$	−178.040	+	547.949i	−0.0701774	+	0.215984i	0.909817	+	0.415010i	$0.136222\pi$
$24$	1083.79	−	787.417i	0.384075	−	0.279047i
$25$	195.816	+	602.661i	0.0626613	+	0.192852i
$26$	2915.68	+	2118.37i	0.845875	+	0.614565i
$27$	1001.80			0.264468
$28$	−1010.63	+	3110.41i	−0.243612	+	0.749761i
$29$	−4395.40	−	3193.45i	−0.970518	−	0.705123i	−0.0149487	−	0.999888i	$-0.504758\pi$
$29$	−4395.40	−	3193.45i	−0.970518	−	0.705123i	−0.955570	+	0.294765i	$0.904758\pi$
$30$	4152.80	−	3017.19i	0.842438	−	0.612067i
$31$	3788.83	−	2752.74i	0.708109	−	0.514472i	−0.174454	−	0.984665i	$-0.555816\pi$
$31$	3788.83	−	2752.74i	0.708109	−	0.514472i	0.882563	+	0.470194i	$0.155816\pi$
$32$	1024.00			0.176777
$33$	−3082.07	+	2239.26i	−0.492672	+	0.357947i
$34$	−938.446	−	2888.24i	−0.139223	−	0.428485i
$35$	−3872.50	+	11918.3i	−0.534344	+	1.64454i
$36$	−2525.94	−	1835.20i	−0.324838	−	0.236009i
$37$	3000.76	+	2180.18i	0.360352	+	0.261811i	0.753199	−	0.657793i	$-0.228510\pi$
$37$	3000.76	+	2180.18i	0.360352	+	0.261811i	−0.392847	+	0.919604i	$0.628510\pi$
$38$	1734.42			0.194848
$39$	5827.88	−	17936.4i	0.613549	−	1.88831i
$40$	3923.71			0.387746
$41$	−7125.45	−	8067.47i	−0.661992	−	0.749511i
$41$	−7125.45	−	8067.47i	−0.661992	−	0.749511i
$42$	17114.2			1.49704
$43$	−400.047	+	1231.22i	−0.0329944	+	0.101546i	−0.966197	−	0.257803i	$-0.917001\pi$
$43$	−400.047	+	1231.22i	−0.0329944	+	0.101546i	0.933203	+	0.359349i	$0.117001\pi$
$44$	−2912.05			−0.226760
$45$	−9678.77	−	7032.04i	−0.712507	−	0.517667i
$46$	1864.45	+	1354.61i	0.129914	+	0.0943883i
$47$	−6942.41	+	21366.5i	−0.458422	+	1.41088i	0.408648	+	0.912692i	$0.366000\pi$
$47$	−6942.41	+	21366.5i	−0.458422	+	1.41088i	−0.867070	+	0.498186i	$0.834000\pi$
$48$	−1655.88	−	5096.27i	−0.103735	−	0.319264i
$49$	−20204.7	+	14679.6i	−1.20216	+	0.873420i
$50$	2534.70			0.143384
$51$	−12856.7	+	9340.96i	−0.692158	+	0.502882i
$52$	11662.7	−	8473.46i	0.598124	−	0.434563i
$53$	3815.39	+	2772.04i	0.186573	+	0.135553i	0.677151	−	0.735844i	$-0.263214\pi$
$53$	3815.39	+	2772.04i	0.186573	+	0.135553i	−0.490578	+	0.871397i	$0.663214\pi$
$54$	1238.30	−	3811.09i	0.0577885	−	0.177855i
$55$	−11158.3			−0.497381
$56$	10583.5	+	7689.36i	0.450982	+	0.327657i
$57$	−2804.67	−	8631.90i	−0.114339	−	0.351900i
$58$	−17581.6	+	12773.8i	−0.686260	+	0.498597i
$59$	−13373.7	+	41159.9i	−0.500173	+	1.53937i	0.308565	+	0.951203i	$0.400151\pi$
$59$	−13373.7	+	41159.9i	−0.500173	+	1.53937i	−0.808737	+	0.588170i	$0.799849\pi$
$60$	−6344.92	−	19527.6i	−0.227535	−	0.700280i
$61$	−5273.90	−	16231.4i	−0.181471	−	0.558511i	0.818399	−	0.574651i	$-0.194862\pi$
$61$	−5273.90	−	16231.4i	−0.181471	−	0.558511i	−0.999870	+	0.0161403i	$0.994862\pi$
$62$	−5788.81	−	17816.1i	−0.191254	−	0.588619i
$63$	−12325.9	−	37935.2i	−0.391262	−	1.20418i
$64$	1265.73	−	3895.53i	0.0386271	−	0.118882i
$65$	44688.6	−	32468.2i	1.31194	−	0.953180i
$66$	4708.99	+	14492.8i	0.133066	+	0.409535i
$67$	−2062.80	−	1498.71i	−0.0561397	−	0.0407879i	0.559362	−	0.828924i	$-0.311046\pi$
$67$	−2062.80	−	1498.71i	−0.0561397	−	0.0407879i	−0.615501	+	0.788136i	$0.711046\pi$
$68$	−12147.5			−0.318577
$69$	3726.69	−	11469.6i	0.0942324	−	0.290017i
$70$	40553.3	+	29463.7i	0.989194	+	0.718691i
$71$	61739.7	−	44856.5i	1.45351	−	1.05604i	0.468516	−	0.883455i	$-0.344789\pi$
$71$	61739.7	−	44856.5i	1.45351	−	1.05604i	0.984995	−	0.172583i	$-0.0552113\pi$
$72$	−10103.8	+	7340.81i	−0.229695	+	0.166883i
$73$	−54905.3			−1.20589			−0.602944	−	0.797784i	$-0.706006\pi$
$73$	−54905.3			−1.20589			−0.602944	+	0.797784i	$0.706006\pi$
$74$	12003.0	−	8720.71i	0.254807	−	0.185128i
$75$	−4098.79	−	12614.8i	−0.0841399	−	0.258956i
$76$	2143.86	−	6598.12i	0.0425757	−	0.131035i
$77$	−30097.3	−	21867.0i	−0.578497	−	0.420303i
$78$	−61030.4	−	44341.2i	−1.13582	−	0.825222i
$79$	−74201.2			−1.33765			−0.668826	−	0.743419i	$-0.733203\pi$
$79$	−74201.2			−1.33765			−0.668826	+	0.743419i	$0.733203\pi$
$80$	4849.98	−	14926.7i	0.0847256	−	0.260759i
$81$	−68388.5			−1.15816
$82$	−39498.0	+	17134.9i	−0.648695	+	0.281415i
$83$	76561.3			1.21987			0.609936	−	0.792451i	$-0.291195\pi$
$83$	76561.3			1.21987			0.609936	+	0.792451i	$0.291195\pi$
$84$	21154.4	−	65106.4i	0.327116	−	1.00676i
$85$	−46546.2			−0.698774
$86$	4189.34	+	3043.74i	0.0610801	+	0.0443773i
$87$	92003.6	+	66844.5i	1.30319	+	0.946821i
$88$	−3599.49	+	11078.1i	−0.0495490	+	0.152496i
$89$	−9214.97	−	28360.8i	−0.123316	−	0.379527i	0.870275	−	0.492567i	$-0.163941\pi$
$89$	−9214.97	−	28360.8i	−0.123316	−	0.379527i	−0.993590	+	0.113040i	$0.963941\pi$
$90$	−38715.1	+	28128.2i	−0.503818	+	0.366046i
$91$	184168.			2.33136
$92$	7457.82	−	5418.42i	0.0918633	−	0.0667426i
$93$	−79306.9	+	57619.8i	−0.950831	+	0.690819i
$94$	72701.8	+	52821.0i	0.848644	+	0.616576i
$95$	8214.74	−	25282.4i	0.0933866	−	0.287414i
$96$	−21434.1			−0.237371
$97$	113033.	+	82123.0i	1.21976	+	0.886208i	0.996080	−	0.0884550i	$-0.0281929\pi$
$97$	113033.	+	82123.0i	1.21976	+	0.886208i	0.223680	+	0.974663i	$0.428193\pi$
$98$	30870.0	+	95008.1i	0.324692	+	0.999299i
$99$	28733.1	−	20875.8i	0.294641	−	0.214070i
$100$	3133.06	−	9642.58i	0.0313306	−	0.0964258i
$101$	26962.2	+	82981.1i	0.262998	+	0.809424i	0.992148	+	0.125070i	$0.0399155\pi$
$101$	26962.2	+	82981.1i	0.262998	+	0.809424i	−0.729150	+	0.684354i	$0.760084\pi$
$102$	19643.3	+	60456.0i	0.186945	+	0.575359i
$103$	45361.7	+	139609.i	0.421305	+	1.29664i	0.906488	+	0.422231i	$0.138753\pi$
$103$	45361.7	+	139609.i	0.421305	+	1.29664i	−0.485183	+	0.874413i	$0.661247\pi$
$104$	−17819.0	−	54841.4i	−0.161548	−	0.497193i
$105$	81058.3	−	249472.i	0.717504	−	2.20825i
$106$	15261.5	−	11088.2i	0.131927	−	0.0958506i
$107$	61453.2	+	189134.i	0.518902	+	1.59702i	0.776069	+	0.630648i	$0.217211\pi$
$107$	61453.2	+	189134.i	0.518902	+	1.59702i	−0.257167	+	0.966367i	$0.582789\pi$
$108$	−12967.6	−	9421.54i	−0.106980	−	0.0777253i
$109$	−219996.			−1.77357			−0.886786	−	0.462181i	$-0.847067\pi$
$109$	−219996.			−1.77357			−0.886786	+	0.462181i	$0.847067\pi$
$110$	−13792.4	+	42448.5i	−0.108682	+	0.334488i
$111$	−62811.2	−	45635.0i	−0.483871	−	0.351553i
$112$	42334.0	−	30757.4i	0.318892	−	0.231689i
$113$	32043.0	−	23280.6i	0.236068	−	0.171514i	−0.463462	−	0.886117i	$-0.653393\pi$
$113$	32043.0	−	23280.6i	0.236068	−	0.171514i	0.699530	+	0.714603i	$0.253393\pi$
$114$	−36304.5			−0.261636
$115$	28576.5	−	20762.1i	0.201495	−	0.146395i
$116$	26862.3	+	82673.7i	0.185353	+	0.570456i
$117$	−54331.3	+	167214.i	−0.366932	+	1.12930i
$118$	140051.	+	101753.i	0.925935	+	0.672731i
$119$	−125550.	−	91217.2i	−0.812734	−	0.590486i
$120$	−82130.3			−0.520656
$121$	−39531.3	+	121665.i	−0.245458	+	0.755442i
$122$	−68266.8			−0.415250
$123$	149148.	+	168867.i	0.888906	+	1.00642i
$124$	−74931.9			−0.437636
$125$	−47198.7	+	145263.i	−0.270181	+	0.831532i
$126$	−159550.			−0.895303
$127$	−90700.4	−	65897.7i	−0.498999	−	0.362544i	0.309635	−	0.950855i	$-0.399793\pi$
$127$	−90700.4	−	65897.7i	−0.498999	−	0.362544i	−0.808635	+	0.588311i	$0.799793\pi$
$128$	−13254.9	−	9630.27i	−0.0715077	−	0.0519534i
$129$	8373.69	−	25771.6i	0.0443040	−	0.136354i
$130$	−68278.2	−	210139.i	−0.354343	−	1.09055i
$131$	244871.	−	177909.i	1.24669	−	0.905773i	0.248665	−	0.968590i	$-0.420008\pi$
$131$	244871.	−	177909.i	1.24669	−	0.905773i	0.998025	+	0.0628162i	$0.0200082\pi$
$132$	60954.4			0.304488
$133$	71703.9	−	52095.9i	0.351491	−	0.255373i
$134$	−8251.20	+	5994.85i	−0.0396968	+	0.0288414i
$135$	−49688.8	−	36101.0i	−0.234652	−	0.170484i
$136$	−15015.1	+	46211.8i	−0.0696116	+	0.214243i
$137$	18621.3			0.0847636			0.0423818	−	0.999101i	$-0.486505\pi$
$137$	18621.3			0.0847636			0.0423818	+	0.999101i	$0.486505\pi$
$138$	−39026.4	−	28354.3i	−0.174446	−	0.126742i
$139$	−78720.4	−	242276.i	−0.345581	−	1.06359i	−0.961272	−	0.275602i	$-0.911123\pi$
$139$	−78720.4	−	242276.i	−0.345581	−	1.06359i	0.615691	−	0.787988i	$-0.288877\pi$
$140$	162213.	−	117855.i	0.699465	−	0.508191i
$141$	145317.	−	447240.i	0.615557	−	1.89449i
$142$	−94329.8	−	290317.i	−0.392580	−	1.20824i
$143$	50673.8	+	155958.i	0.207226	+	0.637775i
$144$	15437.2	+	47510.7i	0.0620385	+	0.190935i
$145$	102930.	+	316785.i	0.406556	+	1.25125i
$146$	−67866.7	+	208872.i	−0.263496	+	0.810958i
$147$	422920.	−	307269.i	1.61423	−	1.17281i
$148$	−18339.0	−	56441.6i	−0.0688210	−	0.211809i
$149$	−117353.	−	85261.8i	−0.433040	−	0.314622i	0.349824	−	0.936816i	$-0.386242\pi$
$149$	−117353.	−	85261.8i	−0.433040	−	0.314622i	−0.782863	+	0.622194i	$0.786242\pi$
$150$	−53055.8			−0.192533
$151$	64308.5	−	197921.i	0.229523	−	0.706399i	−0.768278	−	0.640116i	$-0.778886\pi$
$151$	64308.5	−	197921.i	0.229523	−	0.706399i	0.997801	−	0.0662826i	$-0.0211139\pi$
$152$	−22450.8	−	16311.4i	−0.0788175	−	0.0572642i
$153$	119859.	−	87082.5i	0.413944	−	0.300748i
$154$	−120389.	+	87467.9i	−0.409059	+	0.297199i
$155$	−287121.			−0.959920
$156$	−244121.	+	177365.i	−0.803146	+	0.583520i
$157$	68626.3	+	211210.i	0.222199	+	0.683857i	0.998564	+	0.0535736i	$0.0170612\pi$
$157$	68626.3	+	211210.i	0.222199	+	0.683857i	−0.776365	+	0.630283i	$0.782939\pi$
$158$	−91717.7	+	282278.i	−0.292288	+	0.899569i
$159$	−79862.8	−	58023.7i	−0.250525	−	0.182017i
$160$	−50789.6	−	36900.8i	−0.156847	−	0.113956i
$161$	117768.			0.358064
$162$	−84532.8	+	260165.i	−0.253068	+	0.778864i
$163$	−583779.			−1.72099			−0.860497	−	0.509455i	$-0.829847\pi$
$163$	−583779.			−1.72099			−0.860497	+	0.509455i	$0.829847\pi$
$164$	16362.8	+	171439.i	0.0475058	+	0.497738i
$165$	233562.			0.667871
$166$	94635.0	−	291257.i	0.266552	−	0.820362i
$167$	−117547.			−0.326151			−0.163076	−	0.986614i	$-0.552141\pi$
$167$	−117547.			−0.326151			−0.163076	+	0.986614i	$0.552141\pi$
$168$	−221531.	−	160952.i	−0.605567	−	0.439970i
$169$	−356371.	−	258918.i	−0.959810	−	0.697342i
$170$	−57534.3	+	177072.i	−0.152688	+	0.469925i
$171$	26147.0	+	80472.1i	0.0683803	+	0.210453i
$172$	16757.4	−	12174.9i	0.0431902	−	0.0313795i
$173$	246849.			0.627070			0.313535	−	0.949577i	$-0.398487\pi$
$173$	246849.			0.627070			0.313535	+	0.949577i	$0.398487\pi$
$174$	368015.	−	267378.i	0.921493	−	0.669504i
$175$	104789.	−	76133.7i	0.258655	−	0.187924i
$176$	37694.4	+	27386.6i	0.0917265	+	0.0666432i
$177$	279934.	−	861549.i	0.671619	−	2.06703i
$178$	−119281.			−0.282177
$179$	529068.	+	384391.i	1.23418	+	0.896686i	0.997197	−	0.0748273i	$-0.0238406\pi$
$179$	529068.	+	384391.i	1.23418	+	0.896686i	0.236986	+	0.971513i	$0.423841\pi$
$180$	59151.4	+	182049.i	0.136077	+	0.418801i
$181$	−594911.	+	432228.i	−1.34976	+	0.980655i	−0.350733	+	0.936476i	$0.614067\pi$
$181$	−594911.	+	432228.i	−1.34976	+	0.980655i	−0.999024	+	0.0441798i	$0.985933\pi$
$182$	227644.	−	700616.i	0.509422	−	1.56784i
$183$	110392.	+	339752.i	0.243675	+	0.749954i
$184$	−11394.5	−	35068.8i	−0.0248114	−	0.0763618i
$185$	−70270.5	−	216270.i	−0.150954	−	0.464588i
$186$	121170.	+	372923.i	0.256811	+	0.790382i
$187$	42700.0	−	131417.i	0.0892944	−	0.274820i
$188$	290807.	−	211284.i	0.600082	−	0.435985i
$189$	−63278.6	−	194751.i	−0.128855	−	0.396576i
$190$	−86025.8	−	62501.4i	−0.172880	−	0.125605i
$191$	−582943.			−1.15623			−0.578113	−	0.815957i	$-0.696211\pi$
$191$	−582943.			−1.15623			−0.578113	+	0.815957i	$0.696211\pi$
$192$	−26494.1	+	81540.3i	−0.0518675	+	0.159632i
$193$	−774965.	−	563045.i	−1.49758	−	1.08805i	−0.971334	−	0.237717i	$-0.923601\pi$
$193$	−774965.	−	563045.i	−1.49758	−	1.08805i	−0.526241	−	0.850335i	$-0.676399\pi$
$194$	452130.	−	328492.i	0.862501	−	0.626643i
$195$	−935413.	+	679617.i	−1.76164	+	1.27991i
$196$	399590.			0.742975
$197$	482377.	−	350467.i	0.885566	−	0.643401i	−0.0491522	−	0.998791i	$-0.515652\pi$
$197$	482377.	−	350467.i	0.885566	−	0.643401i	0.934718	+	0.355390i	$0.115652\pi$
$198$	−43900.2	−	135111.i	−0.0795799	−	0.244922i
$199$	−204714.	+	630045.i	−0.366450	+	1.12782i	0.582618	+	0.812746i	$0.302028\pi$
$199$	−204714.	+	630045.i	−0.366450	+	1.12782i	−0.949068	+	0.315071i	$0.897972\pi$
$200$	−32809.9	−	23837.8i	−0.0580002	−	0.0421396i
$201$	43178.1	+	31370.7i	0.0753829	+	0.0547689i
$202$	349006.			0.601803
$203$	−343174.	+	1.05618e6i	−0.584487	+	1.79887i
$204$	254269.			0.427777
$205$	62698.0	+	656913.i	0.104200	+	1.09175i
$206$	587175.			0.964050
$207$	−34742.6	+	106927.i	−0.0563555	+	0.173444i
$208$	−230655.			−0.369661
$209$	63845.5	+	46386.5i	0.101103	+	0.0734557i
$210$	−848853.	−	616728.i	−1.32826	−	0.965040i
$211$	72004.5	−	221607.i	0.111341	−	0.342671i	−0.879826	−	0.475297i	$-0.842341\pi$
$211$	72004.5	−	221607.i	0.111341	−	0.342671i	0.991166	+	0.132625i	$0.0423407\pi$
$212$	−23317.6	−	71764.1i	−0.0356323	−	0.109665i
$213$	−1.29232e6	+	938926.i	−1.95174	+	1.41802i
$214$	795467.			1.18737
$215$	64210.1	−	46651.4i	0.0947343	−	0.0688285i
$216$	−51870.5	+	37686.2i	−0.0756461	+	0.0549601i
$217$	−774455.	−	562674.i	−1.11647	−	0.811162i
$218$	−271930.	+	836915.i	−0.387540	+	1.19272i
$219$	1.14927e6			1.61924
$220$	144435.	+	104939.i	0.201195	+	0.146177i
$221$	211384.	+	650572.i	0.291132	+	0.896014i
$222$	−251245.	+	182540.i	−0.342148	+	0.248585i
$223$	381993.	−	1.17565e6i	0.514391	−	1.58313i	−0.269996	−	0.962861i	$-0.587022\pi$
$223$	381993.	−	1.17565e6i	0.514391	−	1.58313i	0.784387	−	0.620271i	$-0.212978\pi$
$224$	−64680.5	−	199066.i	−0.0861298	−	0.265080i
$225$	38211.5	+	117603.i	0.0503197	+	0.154868i
$226$	−48957.4	−	150675.i	−0.0637598	−	0.196233i
$227$	−208223.	−	640846.i	−0.268204	−	0.825447i	−0.990938	−	0.134320i	$-0.957115\pi$
$227$	−208223.	−	640846.i	−0.268204	−	0.825447i	0.722734	−	0.691126i	$-0.242885\pi$
$228$	−44874.8	+	138110.i	−0.0571696	+	0.175950i
$229$	−255966.	+	185970.i	−0.322547	+	0.234344i	−0.737262	−	0.675607i	$-0.763881\pi$
$229$	−255966.	+	185970.i	−0.322547	+	0.234344i	0.414715	+	0.909952i	$0.363881\pi$
$230$	−43661.0	−	134375.i	−0.0544220	−	0.167494i
$231$	629991.	+	457715.i	0.776791	+	0.564372i
$232$	347713.			0.424132
$233$	−290914.	+	895342.i	−0.351055	+	1.08044i	0.607207	+	0.794544i	$0.292290\pi$
$233$	−290914.	+	895342.i	−0.351055	+	1.08044i	−0.958262	+	0.285892i	$0.907710\pi$
$234$	568964.	+	413377.i	0.679275	+	0.493522i
$235$	1.11430e6	−	809588.i	1.31623	−	0.956300i
$236$	560203.	−	407011.i	0.654735	−	0.475693i
$237$	1.55316e6			1.79616
$238$	−502199.	+	364869.i	−0.574690	+	0.417536i
$239$	213711.	+	657736.i	0.242010	+	0.744830i	0.996114	+	0.0880748i	$0.0280714\pi$
$239$	213711.	+	657736.i	0.242010	+	0.744830i	−0.754104	+	0.656755i	$0.771929\pi$
$240$	−101519.	+	312442.i	−0.113767	+	0.350140i
$241$	−760978.	−	552883.i	−0.843975	−	0.613183i	0.0795035	−	0.996835i	$-0.474667\pi$
$241$	−760978.	−	552883.i	−0.843975	−	0.613183i	−0.923478	+	0.383651i	$0.874667\pi$
$242$	413977.	+	300772.i	0.454399	+	0.330140i
$243$	1.18805e6			1.29069
$244$	−84382.4	+	259702.i	−0.0907355	+	0.279255i
$245$	1.53113e6			1.62966
$246$	826764.	−	358664.i	0.871052	−	0.377876i
$247$	−390675.			−0.407449
$248$	−92621.0	+	285058.i	−0.0956269	+	0.294309i
$249$	−1.60257e6			−1.63801
$250$	494271.	+	359109.i	0.500167	+	0.363393i
$251$	1.16248e6	+	844589.i	1.16466	+	0.846177i	0.990360	−	0.138515i	$-0.0442330\pi$
$251$	1.16248e6	+	844589.i	1.16466	+	0.846177i	0.174302	+	0.984692i	$0.444233\pi$
$252$	−197215.	+	606964.i	−0.195631	+	0.602090i
$253$	32403.8	+	99728.5i	0.0318269	+	0.0979531i
$254$	−362802.	+	263591.i	−0.352846	+	0.256358i
$255$	974295.			0.938296
$256$	−53019.7	+	38521.1i	−0.0505636	+	0.0367366i
$257$	−1.18511e6	+	861034.i	−1.11925	+	0.813182i	−0.984095	−	0.177643i	$-0.943153\pi$
$257$	−1.18511e6	+	861034.i	−1.11925	+	0.813182i	−0.135153	+	0.990825i	$0.543153\pi$
$258$	−87690.4	−	63710.8i	−0.0820168	−	0.0595887i
$259$	234286.	−	721059.i	0.217019	−	0.667915i
$260$	−883811.			−0.810823
$261$	−857717.	−	623168.i	−0.779368	−	0.566244i
$262$	−374129.	−	1.15145e6i	−0.336719	−	1.03632i
$263$	195318.	−	141907.i	0.174122	−	0.126507i	−0.497311	−	0.867572i	$-0.665679\pi$
$263$	195318.	−	141907.i	0.174122	−	0.126507i	0.671433	+	0.741065i	$0.265679\pi$
$264$	75343.8	−	231884.i	0.0665331	−	0.204768i
$265$	−89347.1	−	274982.i	−0.0781566	−	0.240541i
$266$	−109554.	−	337172.i	−0.0949344	−	0.292178i
$267$	192886.	+	593641.i	0.165585	+	0.509619i
$268$	12606.7	+	38799.5i	0.0107217	+	0.0329981i
$269$	138206.	−	425355.i	0.116452	−	0.358402i	−0.875795	−	0.482683i	$-0.839662\pi$
$269$	138206.	−	425355.i	0.116452	−	0.358402i	0.992247	+	0.124281i	$0.0396623\pi$
$270$	−198755.	+	144404.i	−0.165924	+	0.120551i
$271$	−409555.	−	1.26048e6i	−0.338758	−	1.04259i	−0.964841	−	0.262833i	$-0.915343\pi$
$271$	−409555.	−	1.26048e6i	−0.338758	−	1.04259i	0.626084	−	0.779756i	$-0.284657\pi$
$272$	157240.	+	114242.i	0.128867	+	0.0936274i
$273$	−3.85496e6			−3.13050
$274$	23017.2	−	70839.8i	0.0185215	−	0.0570034i
$275$	93304.6	+	67789.8i	0.0743998	+	0.0540546i
$276$	−156105.	+	113417.i	−0.123352	+	0.0896203i
$277$	890983.	−	647337.i	0.697702	−	0.506910i	−0.181481	−	0.983394i	$-0.558089\pi$
$277$	890983.	−	647337.i	0.697702	−	0.506910i	0.879183	+	0.476484i	$0.158089\pi$
$278$	−1.01898e6			−0.790775
$279$	739350.	−	537169.i	0.568643	−	0.413143i
$280$	−247840.	−	762773.i	−0.188919	−	0.581433i
$281$	533043.	−	1.64054e6i	0.402713	−	1.23942i	−0.520076	−	0.854120i	$-0.674096\pi$
$281$	533043.	−	1.64054e6i	0.402713	−	1.23942i	0.922789	−	0.385305i	$-0.125904\pi$
$282$	−1.52178e6	−	1.10564e6i	−1.13954	−	0.827923i
$283$	1.75048e6	+	1.27180e6i	1.29925	+	0.943957i	0.999948	−	0.0102029i	$-0.00324774\pi$
$283$	1.75048e6	+	1.27180e6i	1.29925	+	0.943957i	0.299297	+	0.954160i	$0.403248\pi$
$284$	−1.22103e6			−0.898319
$285$	−171949.	+	529205.i	−0.125397	+	0.385933i
$286$	655935.			0.474183
$287$	−1.11825e6	+	1.89477e6i	−0.801369	+	1.35785i
$288$	199823.			0.141959
$289$	−260639.	+	802163.i	−0.183567	+	0.564960i
$290$	1.33235e6			0.930301
$291$	−2.36597e6	−	1.71898e6i	−1.63786	−	1.18998i
$292$	710709.	+	516360.i	0.487792	+	0.354402i
$293$	−425419.	+	1.30930e6i	−0.289499	+	0.890988i	0.695514	+	0.718512i	$0.255177\pi$
$293$	−425419.	+	1.30930e6i	−0.289499	+	0.890988i	−0.985014	+	0.172476i	$0.944823\pi$
$294$	−646164.	−	1.98869e6i	−0.435988	−	1.34183i
$295$	2.14656e6	−	1.55957e6i	1.43611	−	1.04339i
$296$	−237385.			−0.157479
$297$	147509.	−	107172.i	0.0970350	−	0.0705001i
$298$	−469411.	+	341047.i	−0.306205	+	0.222471i
$299$	−419966.	−	305123.i	−0.271666	−	0.197377i
$300$	−65580.6	+	201836.i	−0.0420700	+	0.129478i
$301$	264618.			0.168346
$302$	−673448.	−	489288.i	−0.424900	−	0.308708i
$303$	−564367.	−	1.73694e6i	−0.353147	−	1.08687i
$304$	−89803.1	+	65245.8i	−0.0557324	+	0.0404919i
$305$	−323333.	+	995115.i	−0.199021	+	0.612525i
$306$	−183128.	−	563610.i	−0.111802	−	0.344092i
$307$	387323.	+	1.19206e6i	0.234546	+	0.721858i	0.997181	+	0.0750294i	$0.0239051\pi$
$307$	387323.	+	1.19206e6i	0.234546	+	0.721858i	−0.762635	+	0.646829i	$0.776095\pi$
$308$	183938.	+	566104.i	0.110483	+	0.340032i
$309$	−949502.	−	2.92227e6i	−0.565718	−	1.74110i
$310$	−354901.	+	1.09227e6i	−0.209750	+	0.645545i
$311$	−896811.	+	651571.i	−0.525775	+	0.381998i	−0.818775	−	0.574115i	$-0.805346\pi$
$311$	−896811.	+	651571.i	−0.525775	+	0.381998i	0.293000	+	0.956112i	$0.405346\pi$
$312$	372984.	+	1.14793e6i	0.216922	+	0.667618i
$313$	−131746.	−	95719.3i	−0.0760112	−	0.0552253i	0.549131	−	0.835736i	$-0.314959\pi$
$313$	−131746.	−	95719.3i	−0.0760112	−	0.0552253i	−0.625142	+	0.780511i	$0.714959\pi$
$314$	888317.			0.508445
$315$	−755677.	+	2.32574e6i	−0.429101	+	1.32064i
$316$	960480.	+	697830.i	0.541091	+	0.393126i
$317$	−43613.8	+	31687.3i	−0.0243767	+	0.0177107i	−0.599907	−	0.800070i	$-0.704796\pi$
$317$	−43613.8	+	31687.3i	−0.0243767	+	0.0177107i	0.575530	+	0.817781i	$0.304796\pi$
$318$	−319451.	+	232095.i	−0.177148	+	0.128706i
$319$	−988826.			−0.544056
$320$	−203158.	+	147603.i	−0.110907	+	0.0805789i
$321$	−1.28633e6	−	3.95890e6i	−0.696768	−	2.14443i
$322$	145569.	−	448014.i	0.0782399	−	0.240798i
$323$	266329.	+	193499.i	0.142040	+	0.103198i
$324$	885239.	+	643164.i	0.468487	+	0.340376i
$325$	−570938.			−0.299834
$326$	−721590.	+	2.22083e6i	−0.376051	+	1.15737i
$327$	4.60491e6			2.38151
$328$	672419.	+	149663.i	0.345109	+	0.0768122i
$329$	4.59218e6			2.33900
$330$	288699.	−	888523.i	0.145935	−	0.449142i
$331$	−211775.			−0.106244			−0.0531221	−	0.998588i	$-0.516917\pi$
$331$	−211775.			−0.106244			−0.0531221	+	0.998588i	$0.516917\pi$
$332$	−991031.	−	720026.i	−0.493449	−	0.358511i
$333$	585566.	+	425439.i	0.289378	+	0.210245i
$334$	−145296.	+	447174.i	−0.0712667	+	0.219336i
$335$	48305.8	+	148670.i	0.0235173	+	0.0723788i
$336$	−886125.	+	643808.i	−0.428200	+	0.311106i
$337$	−329782.			−0.158180			−0.0790901	−	0.996867i	$-0.525201\pi$
$337$	−329782.			−0.158180			−0.0790901	+	0.996867i	$0.525201\pi$
$338$	−1.42548e6	+	1.03567e6i	−0.678688	+	0.493096i
$339$	−670718.	+	487305.i	−0.316986	+	0.230304i
$340$	602507.	+	437747.i	0.282660	+	0.205365i
$341$	263395.	−	810648.i	0.122665	−	0.377525i
$342$	338454.			0.156471
$343$	1.35061e6	+	981278.i	0.619863	+	0.450357i
$344$	−25603.0	−	78797.9i	−0.0116653	−	0.0359020i
$345$	−598157.	+	434587.i	−0.270563	+	0.196575i
$346$	305122.	−	939069.i	0.137020	−	0.421704i
$347$	−411624.	−	1.26685e6i	−0.183517	−	0.564809i	0.816402	−	0.577484i	$-0.195965\pi$
$347$	−411624.	−	1.26685e6i	−0.183517	−	0.564809i	−0.999920	+	0.0126750i	$0.995965\pi$
$348$	−562276.	−	1.73051e6i	−0.248887	−	0.765994i
$349$	334336.	+	1.02898e6i	0.146933	+	0.452213i	0.997255	−	0.0740503i	$-0.0235925\pi$
$349$	334336.	+	1.02898e6i	0.146933	+	0.452213i	−0.850322	+	0.526264i	$0.823593\pi$
$350$	−160103.	−	492747.i	−0.0698603	−	0.215008i
$351$	−278925.	+	858443.i	−0.120843	+	0.371915i
$352$	150777.	−	109546.i	0.0648604	−	0.0471239i
$353$	13245.3	+	40764.8i	0.00565751	+	0.0174120i	0.953845	−	0.300298i	$-0.0970861\pi$
$353$	13245.3	+	40764.8i	0.00565751	+	0.0174120i	−0.948188	+	0.317710i	$0.897086\pi$
$354$	−2.93151e6	−	2.12987e6i	−1.24332	−	0.903326i
$355$	−4.67869e6			−1.97039
$356$	−147440.	+	453772.i	−0.0616579	+	0.189764i
$357$	2.62798e6	+	1.90934e6i	1.09132	+	0.792889i
$358$	2.11627e6	−	1.53756e6i	0.872699	−	0.634053i
$359$	873956.	−	634966.i	0.357893	−	0.260024i	−0.394280	−	0.918990i	$-0.629006\pi$
$359$	873956.	−	634966.i	0.357893	−	0.260024i	0.752173	+	0.658966i	$0.229006\pi$
$360$	765672.			0.311377
$361$	1.85110e6	−	1.34490e6i	0.747587	−	0.543154i
$362$	908943.	+	2.79744e6i	0.364557	+	1.12199i
$363$	827460.	−	2.54666e6i	0.329595	−	1.01439i
$364$	−2.38392e6	−	1.73202e6i	−0.943056	−	0.685171i
$365$	2.72326e6	+	1.97856e6i	1.06993	+	0.777353i
$366$	1.42895e6			0.557588
$367$	−830133.	+	2.55489e6i	−0.321723	+	0.990162i	0.651175	+	0.758928i	$0.274276\pi$
$367$	−830133.	+	2.55489e6i	−0.321723	+	0.990162i	−0.972898	+	0.231234i	$0.925724\pi$
$368$	−147494.			−0.0567747
$369$	−1.39046e6	−	1.57428e6i	−0.531608	−	0.601890i
$370$	−909600.			−0.345419
$371$	297889.	−	916808.i	0.112362	−	0.345815i
$372$	1.56846e6			0.587646
$373$	−3.33120e6	−	2.42026e6i	−1.23974	−	0.900721i	−0.242155	−	0.970238i	$-0.577854\pi$
$373$	−3.33120e6	−	2.42026e6i	−1.23974	−	0.900721i	−0.997581	+	0.0695170i	$0.977854\pi$
$374$	−447160.	−	324881.i	−0.165304	−	0.120101i
$375$	987953.	−	3.04061e6i	0.362792	−	1.11656i
$376$	−444314.	−	1.36746e6i	−0.162077	−	0.498821i
$377$	3.96023e6	−	2.87728e6i	1.43505	−	1.04263i
$378$	−819095.			−0.294853
$379$	−755960.	+	549237.i	−0.270334	+	0.196409i	−0.714690	−	0.699441i	$-0.753432\pi$
$379$	−755960.	+	549237.i	−0.270334	+	0.196409i	0.444356	+	0.895850i	$0.353432\pi$
$380$	−344103.	+	250006.i	−0.122245	+	0.0888159i
$381$	1.89852e6	+	1.37936e6i	0.670044	+	0.486815i
$382$	−720558.	+	2.21765e6i	−0.252645	+	0.777561i
$383$	−4.88348e6			−1.70111			−0.850555	−	0.525886i	$-0.823734\pi$
$383$	−4.88348e6			−1.70111			−0.850555	+	0.525886i	$0.823734\pi$
$384$	277449.	+	201579.i	0.0960187	+	0.0697617i
$385$	704807.	+	2.16917e6i	0.242336	+	0.745834i
$386$	−3.09986e6	+	2.25218e6i	−1.05895	+	0.769369i
$387$	−78064.9	+	240259.i	−0.0264959	+	0.0815460i
$388$	−690794.	−	2.12605e6i	−0.232953	−	0.716957i
$389$	−927634.	−	2.85496e6i	−0.310816	−	0.956592i	−0.977443	−	0.211201i	$-0.932263\pi$
$389$	−927634.	−	2.85496e6i	−0.310816	−	0.956592i	0.666627	−	0.745391i	$-0.267737\pi$
$390$	1.42918e6	+	4.39858e6i	0.475802	+	1.46437i
$391$	135171.	+	416013.i	0.0447138	+	0.137615i
$392$	493920.	−	1.52013e6i	0.162346	−	0.499650i
$393$	−5.12558e6	+	3.72395e6i	−1.67402	+	1.21625i
$394$	−737006.	−	2.26827e6i	−0.239183	−	0.736130i
$395$	3.68032e6	+	2.67391e6i	1.18684	+	0.862292i
$396$	−568256.			−0.182098
$397$	−1.08225e6	+	3.33083e6i	−0.344629	+	1.06066i	0.617153	+	0.786843i	$0.288286\pi$
$397$	−1.08225e6	+	3.33083e6i	−0.344629	+	1.06066i	−0.961782	+	0.273816i	$0.911714\pi$
$398$	2.14379e6	+	1.55756e6i	0.678384	+	0.492874i
$399$	−1.50089e6	+	1.09046e6i	−0.471973	+	0.342908i
$400$	−131239.	+	95351.0i	−0.0410123	+	0.0297972i
$401$	2.10473e6			0.653635			0.326818	−	0.945087i	$-0.394024\pi$
$401$	2.10473e6			0.653635			0.326818	+	0.945087i	$0.394024\pi$
$402$	172712.	−	125483.i	0.0533038	−	0.0387275i
$403$	1.30392e6	+	4.01306e6i	0.399935	+	1.23087i
$404$	431395.	−	1.32770e6i	0.131499	−	0.404712i
$405$	3.39202e6	+	2.46444e6i	1.02759	+	0.746589i
$406$	3.59377e6	+	2.61103e6i	1.08202	+	0.786133i
$407$	675075.			0.202007
$408$	314293.	−	967296.i	0.0934727	−	0.287680i
$409$	4.63698e6			1.37065			0.685326	−	0.728237i	$-0.259660\pi$
$409$	4.63698e6			1.37065			0.685326	+	0.728237i	$0.259660\pi$
$410$	2.57654e6	+	573472.i	0.756969	+	0.168482i
$411$	−389778.			−0.113818
$412$	725788.	−	2.23375e6i	0.210653	−	0.648322i
$413$	8.84625e6			2.55202
$414$	363829.	+	264337.i	0.104327	+	0.0757979i
$415$	−3.79738e6	−	2.75896e6i	−1.08234	−	0.786367i
$416$	−285105.	+	877462.i	−0.0807739	+	0.248597i
$417$	1.64776e6	+	5.07128e6i	0.464038	+	1.42816i
$418$	255382.	−	185546.i	0.0714907	−	0.0519410i
$419$	2.71320e6			0.754999			0.377499	−	0.926010i	$-0.376784\pi$
$419$	2.71320e6			0.754999			0.377499	+	0.926010i	$0.376784\pi$
$420$	−3.39541e6	+	2.46691e6i	−0.939224	+	0.682386i
$421$	−3.40599e6	+	2.47460e6i	−0.936566	+	0.680455i	−0.947592	−	0.319484i	$-0.896490\pi$
$421$	−3.40599e6	+	2.47460e6i	−0.936566	+	0.680455i	0.0110257	+	0.999939i	$0.496490\pi$
$422$	−754041.	−	547843.i	−0.206117	−	0.149753i
$423$	−1.35474e6	+	4.16946e6i	−0.368133	+	1.13300i
$424$	−301829.			−0.0815354
$425$	389216.	+	282782.i	0.104525	+	0.0759416i
$426$	1.97449e6	+	6.07686e6i	0.527146	+	1.62239i
$427$	−2.82227e6	+	2.05050e6i	−0.749081	+	0.544239i
$428$	983251.	−	3.02614e6i	0.259451	−	0.798508i
$429$	−1.06069e6	−	3.26448e6i	−0.278257	−	0.856388i
$430$	−98104.3	−	301934.i	−0.0255869	−	0.0787483i
$431$	−847995.	−	2.60986e6i	−0.219887	−	0.676744i	−0.998770	−	0.0495745i	$-0.984213\pi$
$431$	−847995.	−	2.60986e6i	−0.219887	−	0.676744i	0.778883	−	0.627169i	$-0.215787\pi$
$432$	79251.1	+	243910.i	0.0204313	+	0.0628811i
$433$	1.22911e6	−	3.78282e6i	0.315045	−	0.969608i	−0.660691	−	0.750658i	$-0.729737\pi$
$433$	1.22911e6	−	3.78282e6i	0.315045	−	0.969608i	0.975736	−	0.218950i	$-0.0702632\pi$
$434$	−3.09782e6	+	2.25070e6i	−0.789463	+	0.573578i
$435$	−2.15450e6	−	6.63088e6i	−0.545914	−	1.68015i
$436$	2.84769e6	+	2.06897e6i	0.717425	+	0.521240i
$437$	−249820.			−0.0625784
$438$	1.42057e6	−	4.37207e6i	0.353816	−	1.08893i
$439$	−4.56038e6	−	3.31331e6i	−1.12938	−	0.820541i	−0.143774	−	0.989611i	$-0.545924\pi$
$439$	−4.56038e6	−	3.31331e6i	−1.12938	−	0.820541i	−0.985604	+	0.169070i	$0.945924\pi$
$440$	577742.	−	419754.i	0.142266	−	0.103363i
$441$	−3.94273e6	+	2.86456e6i	−0.965386	+	0.701394i
$442$	2.73621e6			0.666183
$443$	−778301.	+	565468.i	−0.188425	+	0.136899i	−0.677998	−	0.735063i	$-0.737152\pi$
$443$	−778301.	+	565468.i	−0.188425	+	0.136899i	0.489574	+	0.871962i	$0.337152\pi$
$444$	383868.	+	1.18142e6i	0.0924111	+	0.284412i
$445$	−564952.	+	1.73874e6i	−0.135242	+	0.416232i
$446$	−4.00028e6	−	2.90638e6i	−0.952256	−	0.691854i
$447$	2.45640e6	+	1.78468e6i	0.581475	+	0.422466i
$448$	−837243.			−0.197086
$449$	568413.	−	1.74939e6i	0.133060	−	0.409517i	−0.862223	−	0.506529i	$-0.830928\pi$
$449$	568413.	−	1.74939e6i	0.133060	−	0.409517i	0.995283	+	0.0970117i	$0.0309284\pi$
$450$	494620.			0.115144
$451$	−1.91223e6	−	425612.i	−0.442688	−	0.0985308i
$452$	−633718.			−0.145898
$453$	−1.34609e6	+	4.14285e6i	−0.308198	+	0.948535i
$454$	−2.69530e6			−0.613716
$455$	−9.13458e6	−	6.63666e6i	−2.06852	−	1.50287i
$456$	469935.	+	341428.i	0.105834	+	0.0768930i
$457$	−591896.	+	1.82167e6i	−0.132573	+	0.408018i	−0.995205	−	0.0978149i	$-0.968815\pi$
$457$	−591896.	+	1.82167e6i	−0.132573	+	0.408018i	0.862632	+	0.505833i	$0.168815\pi$
$458$	391081.	+	1.20362e6i	0.0871170	+	0.268118i
$459$	615329.	−	447063.i	0.136325	−	0.0990460i
$460$	−565160.			−0.124531
$461$	−3.82536e6	+	2.77929e6i	−0.838339	+	0.609089i	−0.921906	−	0.387413i	$-0.873369\pi$
$461$	−3.82536e6	+	2.77929e6i	−0.838339	+	0.609089i	0.0835669	+	0.996502i	$0.473369\pi$
$462$	2.51996e6	−	1.83086e6i	0.549274	−	0.399071i
$463$	−2.89917e6	−	2.10637e6i	−0.628522	−	0.456648i	0.227366	−	0.973809i	$-0.426989\pi$
$463$	−2.89917e6	−	2.10637e6i	−0.628522	−	0.456648i	−0.855888	+	0.517161i	$0.826989\pi$
$464$	429797.	−	1.32278e6i	0.0926763	−	0.285228i
$465$	6.00995e6			1.28896
$466$	3.04649e6	+	2.21341e6i	0.649883	+	0.472168i
$467$	461554.	+	1.42052e6i	0.0979333	+	0.301408i	0.988007	−	0.154409i	$-0.0493473\pi$
$467$	461554.	+	1.42052e6i	0.0979333	+	0.301408i	−0.890074	+	0.455817i	$0.849347\pi$
$468$	2.27586e6	−	1.65351e6i	0.480320	−	0.348973i
$469$	−161055.	+	495675.i	−0.0338097	+	0.104055i
$470$	−1.70250e6	−	5.23976e6i	−0.355503	−	1.09412i
$471$	−1.43647e6	−	4.42100e6i	−0.298363	−	0.918265i
$472$	−855914.	−	2.63423e6i	−0.176838	−	0.544251i
$473$	72809.8	+	224085.i	0.0149636	+	0.0460533i
$474$	1.91981e6	−	5.90858e6i	0.392476	−	1.20792i
$475$	−222289.	+	161503.i	−0.0452048	+	0.0328432i
$476$	767292.	+	2.36148e6i	0.155218	+	0.477713i
$477$	744533.	+	540935.i	0.149826	+	0.108855i
$478$	2.76634e6			0.553778
$479$	1.48519e6	−	4.57094e6i	0.295762	−	0.910263i	−0.687202	−	0.726466i	$-0.741161\pi$
$479$	1.48519e6	−	4.57094e6i	0.295762	−	0.910263i	0.982964	−	0.183797i	$-0.0588388\pi$
$480$	1.06312e6	+	772400.i	0.210610	+	0.153017i
$481$	−2.70367e6	+	1.96433e6i	−0.532832	+	0.387125i
$482$	−3.04391e6	+	2.21153e6i	−0.596780	+	0.433586i
$483$	−2.46508e6			−0.480799
$484$	1.65591e6	−	1.20309e6i	0.321309	−	0.233444i
$485$	−2.64695e6	−	8.14648e6i	−0.510965	−	1.57259i
$486$	1.46852e6	−	4.51963e6i	0.282025	−	0.867984i
$487$	3.94489e6	+	2.86613e6i	0.753724	+	0.547613i	0.896979	−	0.442073i	$-0.145757\pi$
$487$	3.94489e6	+	2.86613e6i	0.753724	+	0.547613i	−0.143255	+	0.989686i	$0.545757\pi$
$488$	883664.	+	642020.i	0.167972	+	0.122039i
$489$	1.22195e7			2.31091
$490$	1.89258e6	−	5.82476e6i	0.356094	−	1.09594i
$491$	−7.63902e6			−1.42999			−0.714996	−	0.699128i	$-0.753572\pi$
$491$	−7.63902e6			−1.42999			−0.714996	+	0.699128i	$0.753572\pi$
$492$	−342502.	−	3.58853e6i	−0.0637896	−	0.668350i
$493$	−4.12485e6			−0.764347
$494$	−482901.	+	1.48622e6i	−0.0890310	+	0.274009i
$495$	−2.17742e6			−0.399419
$496$	969939.	+	704702.i	0.177027	+	0.128618i
$497$	−1.26199e7	−	9.16889e6i	−2.29174	−	1.66504i
$498$	−1.98088e6	+	6.09652e6i	−0.357919	+	1.10156i
$499$	−1.99473e6	−	6.13915e6i	−0.358619	−	1.10372i	−0.953881	−	0.300184i	$-0.902952\pi$
$499$	−1.99473e6	−	6.13915e6i	−0.358619	−	1.10372i	0.595262	−	0.803531i	$-0.297048\pi$
$500$	1.97709e6	−	1.43644e6i	0.353672	−	0.256958i
$501$	2.46046e6			0.437948
$502$	4.64991e6	−	3.37836e6i	0.823541	−	0.598338i
$503$	−4.53571e6	+	3.29539e6i	−0.799329	+	0.580747i	−0.910717	−	0.413030i	$-0.864470\pi$
$503$	−4.53571e6	+	3.29539e6i	−0.799329	+	0.580747i	0.111388	+	0.993777i	$0.464470\pi$
$504$	2.06526e6	+	1.50050e6i	0.362158	+	0.263123i
$505$	1.65300e6	−	5.08741e6i	0.288433	−	0.887704i
$506$	419443.			0.0728277
$507$	7.45947e6	+	5.41962e6i	1.28881	+	0.936374i
$508$	554312.	+	1.70600e6i	0.0953004	+	0.293305i
$509$	−4.05648e6	+	2.94721e6i	−0.693993	+	0.504215i	−0.877970	−	0.478715i	$-0.841103\pi$
$509$	−4.05648e6	+	2.94721e6i	−0.693993	+	0.504215i	0.183977	+	0.982930i	$0.441103\pi$
$510$	1.20429e6	−	3.70644e6i	0.205025	−	0.631003i
$511$	3.46807e6	+	1.06736e7i	0.587537	+	1.80825i
$512$	81007.0	+	249314.i	0.0136568	+	0.0420312i
$513$	134233.	+	413127.i	0.0225199	+	0.0693090i
$514$	1.81069e6	+	5.57273e6i	0.302299	+	0.930380i
$515$	2.78104e6	−	8.55916e6i	0.462050	−	1.42204i
$516$	−350762.	+	254843.i	−0.0579947	+	0.0421356i
$517$	1.26354e6	+	3.88878e6i	0.207904	+	0.639862i
$518$	−2.45348e6	−	1.78256e6i	−0.401752	−	0.291890i
$519$	−5.16699e6			−0.842013
$520$	−1.09245e6	+	3.36222e6i	−0.177171	+	0.545277i
$521$	−1.73575e6	−	1.26110e6i	−0.280152	−	0.203542i	0.438832	−	0.898569i	$-0.355392\pi$
$521$	−1.73575e6	−	1.26110e6i	−0.280152	−	0.203542i	−0.718984	+	0.695027i	$0.755392\pi$
$522$	−3.43087e6	+	2.49267e6i	−0.551097	+	0.400395i
$523$	444013.	−	322595.i	0.0709809	−	0.0515707i	−0.551729	−	0.834023i	$-0.686032\pi$
$523$	444013.	−	322595.i	0.0709809	−	0.0515707i	0.622710	+	0.782453i	$0.286032\pi$
$524$	−4.84283e6			−0.770497
$525$	−2.19342e6	+	1.59361e6i	−0.347315	+	0.252339i
$526$	−298419.	−	918440.i	−0.0470287	−	0.144739i
$527$	1.09874e6	−	3.38158e6i	0.172333	−	0.530388i
$528$	−789010.	−	573250.i	−0.123168	−	0.0894868i
$529$	4.93856e6	+	3.58807e6i	0.767293	+	0.557471i
$530$	−1.15653e6			−0.178842
$531$	−2.60973e6	+	8.03192e6i	−0.401660	+	1.23618i
$532$	−1.41809e6			−0.217233
$533$	8.89688e6	−	3.85961e6i	1.35650	−	0.588472i
$534$	2.49677e6			0.378900
$535$	3.76758e6	−	1.15954e7i	0.569086	−	1.75147i
$536$	163185.			0.0245339
$537$	−1.10743e7	−	8.04598e6i	−1.65723	−	1.20405i
$538$	−1.44731e6	−	1.05153e6i	−0.215579	−	0.156628i
$539$	−1.40461e6	+	4.32294e6i	−0.208249	+	0.640926i
$540$	303671.	+	934602.i	0.0448145	+	0.137925i
$541$	−1.56163e6	+	1.13459e6i	−0.229395	+	0.166665i	−0.696546	−	0.717513i	$-0.745281\pi$
$541$	−1.56163e6	+	1.13459e6i	−0.229395	+	0.166665i	0.467151	+	0.884178i	$0.345281\pi$
$542$	−5.30139e6			−0.775160
$543$	1.24525e7	−	9.04730e6i	1.81242	−	1.31680i
$544$	628962.	−	456968.i	0.0911228	−	0.0662046i
$545$	1.09116e7	+	7.92777e6i	1.57362	+	1.14330i
$546$	−4.76499e6	+	1.46651e7i	−0.684038	+	2.10525i
$547$	−3.37247e6			−0.481926			−0.240963	−	0.970534i	$-0.577463\pi$
$547$	−3.37247e6			−0.481926			−0.240963	+	0.970534i	$0.577463\pi$
$548$	−241040.	−	175126.i	−0.0342876	−	0.0249114i
$549$	−1.02915e6	−	3.16739e6i	−0.145729	−	0.448508i
$550$	373219.	−	271159.i	0.0526086	−	0.0382224i
$551$	727976.	−	2.24048e6i	0.102150	−	0.314385i
$552$	238508.	+	734052.i	0.0333162	+	0.102537i
$553$	4.68689e6	+	1.44248e7i	0.651736	+	2.00584i
$554$	−1.36130e6	−	4.18965e6i	−0.188443	−	0.579967i
$555$	1.47089e6	+	4.52692e6i	0.202697	+	0.623836i
$556$	−1.25953e6	+	3.87642e6i	−0.172791	+	0.531795i
$557$	−8.65071e6	+	6.28511e6i	−1.18145	+	0.858370i	−0.992334	−	0.123586i	$-0.960561\pi$
$557$	−8.65071e6	+	6.28511e6i	−1.18145	+	0.858370i	−0.189111	+	0.981956i	$0.560561\pi$
$558$	−1.12963e6	−	3.47663e6i	−0.153585	−	0.472686i
$559$	−943644.	−	685598.i	−0.127726	−	0.0927982i
$560$	−3.20811e6			−0.432293
$561$	−893787.	+	2.75079e6i	−0.119902	+	0.369021i
$562$	−5.58209e6	−	4.05563e6i	−0.745515	−	0.541648i
$563$	−1.23432e6	+	896784.i	−0.164118	+	0.119239i	−0.666813	−	0.745225i	$-0.732342\pi$
$563$	−1.23432e6	+	896784.i	−0.164118	+	0.119239i	0.502695	+	0.864464i	$0.332342\pi$
$564$	−6.08712e6	+	4.42255e6i	−0.805775	+	0.585430i
$565$	−2.42825e6			−0.320016
$566$	7.00192e6	−	5.08719e6i	0.918705	−	0.667478i
$567$	4.31973e6	+	1.32948e7i	0.564286	+	1.73669i
$568$	−1.50928e6	+	4.64508e6i	−0.196290	+	0.604118i
$569$	3.89544e6	+	2.83020e6i	0.504401	+	0.366468i	0.810695	−	0.585468i	$-0.199089\pi$
$569$	3.89544e6	+	2.83020e6i	0.504401	+	0.366468i	−0.306295	+	0.951937i	$0.599089\pi$
$570$	1.80067e6	+	1.30827e6i	0.232139	+	0.168659i
$571$	−2.42216e6			−0.310894			−0.155447	−	0.987844i	$-0.549682\pi$
$571$	−2.42216e6			−0.310894			−0.155447	+	0.987844i	$0.549682\pi$
$572$	810781.	−	2.49533e6i	0.103613	−	0.318887i
$573$	1.22020e7			1.55255
$574$	5.82591e6	+	6.59612e6i	0.738047	+	0.835620i
$575$	−365091.			−0.0460502
$576$	246995.	−	760171.i	0.0310193	−	0.0954675i
$577$	6.38235e6			0.798070			0.399035	−	0.916936i	$-0.369345\pi$
$577$	6.38235e6			0.798070			0.399035	+	0.916936i	$0.369345\pi$
$578$	2.72944e6	+	1.98306e6i	0.339824	+	0.246897i
$579$	1.62214e7	+	1.17855e7i	2.01091	+	1.46101i
$580$	1.64688e6	−	5.06856e6i	0.203278	−	0.625626i
$581$	−4.83596e6	−	1.48836e7i	−0.594351	−	1.82922i
$582$	−9.46390e6	+	6.87592e6i	−1.15814	+	0.841441i
$583$	858341.			0.104590
$584$	2.84284e6	−	2.06544e6i	0.344921	−	0.250600i
$585$	8.72052e6	−	6.33583e6i	1.05354	−	0.765445i
$586$	4.45505e6	+	3.23678e6i	0.535930	+	0.389376i
$587$	516235.	−	1.58881e6i	0.0618375	−	0.190316i	−0.915365	−	0.402624i	$-0.868098\pi$
$587$	516235.	−	1.58881e6i	0.0618375	−	0.190316i	0.977203	+	0.212308i	$0.0680981\pi$
$588$	−8.36413e6			−0.997648
$589$	1.64285e6	+	1.19360e6i	0.195124	+	0.141766i
$590$	−3.27965e6	−	1.00937e7i	−0.387880	−	1.19377i
$591$	−1.00970e7	+	7.33591e6i	−1.18912	+	0.863943i
$592$	−293424.	+	903066.i	−0.0344105	+	0.105905i
$593$	3.79818e6	+	1.16896e7i	0.443546	+	1.36509i	0.884071	+	0.467353i	$0.154792\pi$
$593$	3.79818e6	+	1.16896e7i	0.443546	+	1.36509i	−0.440525	+	0.897740i	$0.645208\pi$
$594$	−225374.	−	693631.i	−0.0262083	−	0.0806607i
$595$	2.94007e6	+	9.04861e6i	0.340460	+	1.04783i
$596$	717196.	+	2.20730e6i	0.0827032	+	0.254534i
$597$	4.28503e6	−	1.31880e7i	0.492060	−	1.51441i
$598$	−1.67986e6	+	1.22049e6i	−0.192097	+	0.139567i
$599$	−887965.	−	2.73288e6i	−0.101118	−	0.311209i	0.887682	−	0.460458i	$-0.152315\pi$
$599$	−887965.	−	2.73288e6i	−0.101118	−	0.311209i	−0.988800	+	0.149248i	$0.952315\pi$
$600$	686769.	+	498967.i	0.0778812	+	0.0565840i
$601$	−5.28522e6			−0.596866			−0.298433	−	0.954431i	$-0.596464\pi$
$601$	−5.28522e6			−0.596866			−0.298433	+	0.954431i	$0.596464\pi$
$602$	327086.	−	1.00667e6i	0.0367850	−	0.113213i
$603$	−402534.	−	292458.i	−0.0450826	−	0.0327544i
$604$	−2.69379e6	+	1.95715e6i	−0.300449	+	0.218289i
$605$	6.34503e6	−	4.60993e6i	0.704766	−	0.512043i
$606$	−7.30532e6			−0.808086
$607$	−9.06928e6	+	6.58922e6i	−0.999082	+	0.725876i	−0.961891	−	0.273432i	$-0.911841\pi$
$607$	−9.06928e6	+	6.58922e6i	−0.999082	+	0.725876i	−0.0371911	+	0.999308i	$0.511841\pi$
$608$	137207.	+	422280.i	0.0150528	+	0.0463277i
$609$	7.18325e6	−	2.21078e7i	0.784834	−	2.41547i
$610$	3.38598e6	+	2.46006e6i	0.368434	+	0.267683i
$611$	−1.63760e7	−	1.18979e7i	−1.77462	−	1.28933i
$612$	−2.37046e6			−0.255831
$613$	−1.31427e6	+	4.04491e6i	−0.141265	+	0.434768i	−0.996512	−	0.0834523i	$-0.973405\pi$
$613$	−1.31427e6	+	4.04491e6i	−0.141265	+	0.434768i	0.855247	+	0.518221i	$0.173405\pi$
$614$	5.01362e6			0.536699
$615$	−1.31238e6	−	1.37504e7i	−0.139918	−	1.46597i
$616$	2.38095e6			0.252812
$617$	−3.33200e6	+	1.02548e7i	−0.352364	+	1.08447i	0.605158	+	0.796106i	$0.293110\pi$
$617$	−3.33200e6	+	1.02548e7i	−0.352364	+	1.08447i	−0.957522	+	0.288360i	$0.906890\pi$
$618$	−1.22906e7			−1.29450
$619$	7.11361e6	+	5.16834e6i	0.746214	+	0.542156i	0.894651	−	0.446766i	$-0.147424\pi$
$619$	7.11361e6	+	5.16834e6i	0.746214	+	0.542156i	−0.148437	+	0.988922i	$0.547424\pi$
$620$	3.71657e6	+	2.70024e6i	0.388296	+	0.282113i
$621$	−178361.	+	548938.i	−0.0185597	+	0.0571209i
$622$	1.37021e6	+	4.21706e6i	0.142007	+	0.437053i
$623$	−4.93129e6	+	3.58279e6i	−0.509027	+	0.369829i
$624$	4.82801e6			0.496372
$625$	9.17774e6	−	6.66802e6i	0.939801	−	0.682805i
$626$	−526985.	+	382877.i	−0.0537480	+	0.0390502i
$627$	−1.33640e6	−	970952.i	−0.135759	−	0.0986345i
$628$	1.09802e6	−	3.37936e6i	0.111099	−	0.341928i
$629$	2.81605e6			0.283801
$630$	7.91356e6	+	5.74953e6i	0.794365	+	0.577140i
$631$	−1.03748e6	−	3.19302e6i	−0.103730	−	0.319248i	0.885700	−	0.464258i	$-0.153679\pi$
$631$	−1.03748e6	−	3.19302e6i	−0.103730	−	0.319248i	−0.989430	+	0.145009i	$0.953679\pi$
$632$	3.84192e6	−	2.79132e6i	0.382609	−	0.277982i
$633$	−1.50718e6	+	4.63863e6i	−0.149505	+	0.460130i
$634$	66636.0	+	205084.i	0.00658393	+	0.0202633i
$635$	2.12399e6	+	6.53695e6i	0.209034	+	0.643341i
$636$	488078.	+	1.50215e6i	0.0478461	+	0.147255i
$637$	−6.95343e6	−	2.14005e7i	−0.678970	−	2.08965i
$638$	−1.22226e6	+	3.76172e6i	−0.118880	+	0.365877i
$639$	1.20478e7	−	8.75328e6i	1.16723	−	0.848044i
$640$	310399.	+	955309.i	0.0299550	+	0.0921921i
$641$	1.12983e7	+	8.20872e6i	1.08610	+	0.789097i	0.978736	−	0.205123i	$-0.0657593\pi$
$641$	1.12983e7	+	8.20872e6i	1.08610	+	0.789097i	0.107363	+	0.994220i	$0.465759\pi$
$642$	−1.66505e7			−1.59438
$643$	−2.25215e6	+	6.93140e6i	−0.214817	+	0.661140i	0.784349	+	0.620320i	$0.212997\pi$
$643$	−2.25215e6	+	6.93140e6i	−0.214817	+	0.661140i	−0.999167	+	0.0408202i	$0.987003\pi$
$644$	−1.52441e6	−	1.10755e6i	−0.144840	−	0.105232i
$645$	−1.34403e6	+	976497.i	−0.127207	+	0.0924212i
$646$	1.06532e6	−	773997.i	0.100438	−	0.0729723i
$647$	1.20334e7			1.13013			0.565066	−	0.825046i	$-0.308851\pi$
$647$	1.20334e7			1.13013			0.565066	+	0.825046i	$0.308851\pi$
$648$	3.54096e6	−	2.57265e6i	0.331271	−	0.240682i
$649$	2.43405e6	+	7.49122e6i	0.226839	+	0.698138i
$650$	−705718.	+	2.17198e6i	−0.0655161	+	0.201638i
$651$	1.62107e7	+	1.17778e7i	1.49917	+	1.08921i
$652$	7.55659e6	+	5.49019e6i	0.696157	+	0.505787i
$653$	−1.46912e7			−1.34826			−0.674130	−	0.738613i	$-0.735481\pi$
$653$	−1.46912e7			−1.34826			−0.674130	+	0.738613i	$0.735481\pi$
$654$	5.69198e6	−	1.75181e7i	0.520378	−	1.60156i
$655$	−1.85565e7			−1.69003
$656$	1.40051e6	−	2.37304e6i	0.127065	−	0.215301i
$657$	−1.07142e7			−0.968380
$658$	5.67625e6	−	1.74697e7i	0.511089	−	1.57297i
$659$	−174986.			−0.0156961			−0.00784803	−	0.999969i	$-0.502498\pi$
$659$	−174986.			−0.0156961			−0.00784803	+	0.999969i	$0.502498\pi$
$660$	−3.02329e6	−	2.19655e6i	−0.270160	−	0.196282i
$661$	4.96303e6	+	3.60585e6i	0.441818	+	0.321000i	0.786357	−	0.617772i	$-0.211965\pi$
$661$	4.96303e6	+	3.60585e6i	0.441818	+	0.321000i	−0.344539	+	0.938772i	$0.611965\pi$
$662$	−261768.	+	805640.i	−0.0232152	+	0.0714490i
$663$	−4.42464e6	−	1.36176e7i	−0.390925	−	1.20314i
$664$	−3.96412e6	+	2.88010e6i	−0.348921	+	0.253506i
$665$	−5.43379e6			−0.476484
$666$	2.34226e6	−	1.70176e6i	0.204621	−	0.148666i
$667$	2.53240e6	−	1.83990e6i	0.220403	−	0.160132i
$668$	1.52156e6	+	1.10548e6i	0.131931	+	0.0958535i
$669$	−7.99580e6	+	2.46085e7i	−0.690711	+	2.12579i
$670$	625283.			0.0538133
$671$	−2.51296e6	−	1.82577e6i	−0.215467	−	0.156546i
$672$	1.35388e6	+	4.16681e6i	0.115653	+	0.355943i
$673$	−5.65332e6	+	4.10738e6i	−0.481134	+	0.349564i	−0.801765	−	0.597640i	$-0.796105\pi$
$673$	−5.65332e6	+	4.10738e6i	−0.481134	+	0.349564i	0.320630	+	0.947204i	$0.396105\pi$
$674$	−407633.	+	1.25457e6i	−0.0345636	+	0.106376i
$675$	196170.	+	603749.i	0.0165719	+	0.0510031i
$676$	2.17794e6	+	6.70302e6i	0.183307	+	0.564162i
$677$	818703.	+	2.51971e6i	0.0686522	+	0.211290i	0.979497	−	0.201460i	$-0.0645685\pi$
$677$	818703.	+	2.51971e6i	0.0686522	+	0.211290i	−0.910845	+	0.412749i	$0.864568\pi$
$678$	1.02477e6	+	3.15390e6i	0.0856151	+	0.263496i
$679$	8.82510e6	−	2.71609e7i	0.734591	−	2.26084i
$680$	2.41003e6	−	1.75099e6i	0.199871	−	0.145215i
$681$	4.35849e6	+	1.34140e7i	0.360137	+	1.10839i
$682$	−2.75831e6	−	2.00403e6i	−0.227082	−	0.164985i
$683$	1.68710e7			1.38385			0.691927	−	0.721968i	$-0.256762\pi$
$683$	1.68710e7			1.38385			0.691927	+	0.721968i	$0.256762\pi$
$684$	418352.	−	1.28755e6i	0.0341902	−	0.105227i
$685$	−923604.	−	671038.i	−0.0752072	−	0.0546412i
$686$	5.40245e6	−	3.92511e6i	0.438309	−	0.318450i
$687$	5.35782e6	−	3.89268e6i	0.433108	−	0.314671i
$688$	−331412.			−0.0266930
$689$	−3.43764e6	+	2.49759e6i	−0.275875	+	0.200435i
$690$	913903.	+	2.81270e6i	0.0730765	+	0.224906i
$691$	−2.93212e6	+	9.02414e6i	−0.233607	+	0.718970i	0.763696	+	0.645577i	$0.223383\pi$
$691$	−2.93212e6	+	9.02414e6i	−0.233607	+	0.718970i	−0.997303	+	0.0733934i	$0.976617\pi$
$692$	−3.19528e6	−	2.32151e6i	−0.253655	−	0.184291i
$693$	−5.87318e6	−	4.26711e6i	−0.464558	−	0.337521i
$694$	−5.32818e6			−0.419933
$695$	−4.82619e6	+	1.48535e7i	−0.379003	+	1.16645i
$696$	−7.27826e6			−0.569514
$697$	−7.97677e6	−	1.77542e6i	−0.621935	−	0.138427i
$698$	4.32773e6			0.336219
$699$	6.08935e6	−	1.87411e7i	0.471387	−	1.45078i
$700$	−2.07242e6			−0.159857
$701$	−2.47276e6	−	1.79657e6i	−0.190058	−	0.138086i	0.488687	−	0.872459i	$-0.337476\pi$
$701$	−2.47276e6	−	1.79657e6i	−0.190058	−	0.138086i	−0.678745	+	0.734374i	$0.737476\pi$
$702$	2.92094e6	+	2.12219e6i	0.223707	+	0.162533i
$703$	−496992.	+	1.52958e6i	−0.0379281	+	0.116731i
$704$	−230367.	−	708998.i	−0.0175182	−	0.0539155i
$705$	−2.33243e7	+	1.69461e7i	−1.76741	+	1.28410i
$706$	171451.			0.0129458
$707$	1.44285e7	−	1.04829e7i	1.08561	−	0.788741i
$708$	−1.17260e7	+	8.51947e6i	−0.879161	+	0.638748i
$709$	−1.37084e7	−	9.95975e6i	−1.02417	−	0.744103i	−0.0570360	−	0.998372i	$-0.518165\pi$
$709$	−1.37084e7	−	9.95975e6i	−1.02417	−	0.744103i	−0.967133	+	0.254270i	$0.918165\pi$
$710$	−5.78318e6	+	1.77988e7i	−0.430547	+	1.32509i
$711$	−1.44796e7			−1.07419
$712$	1.54401e6	+	1.12179e6i	0.114143	+	0.0829297i
$713$	833803.	+	2.56618e6i	0.0614242	+	0.189044i
$714$	1.05119e7	−	7.63736e6i	0.771679	−	0.560657i
$715$	3.10671e6	−	9.56147e6i	0.227267	−	0.699455i
$716$	−3.23338e6	−	9.95132e6i	−0.235708	−	0.725434i
$717$	−4.47336e6	−	1.37676e7i	−0.324965	−	1.00014i
$718$	−1.33529e6	−	4.10959e6i	−0.0966636	−	0.297500i
$719$	178507.	+	549389.i	0.0128776	+	0.0396331i	0.957289	−	0.289133i	$-0.0933671\pi$
$719$	178507.	+	549389.i	0.0128776	+	0.0396331i	−0.944411	+	0.328766i	$0.893367\pi$
$720$	946422.	−	2.91279e6i	0.0680383	−	0.209401i
$721$	2.42748e7	−	1.76367e7i	1.73907	−	1.26351i
$722$	−2.82823e6	−	8.70440e6i	−0.201916	−	0.621435i
$723$	1.59286e7	+	1.15728e7i	1.13327	+	0.823367i
$724$	1.17656e7			0.834195
$725$	1.06387e6	−	3.27427e6i	0.0751701	−	0.231350i
$726$	−8.66527e6	−	6.29569e6i	−0.610156	−	0.443304i
$727$	−3.13983e6	+	2.28122e6i	−0.220328	+	0.160078i	−0.692475	−	0.721442i	$-0.743479\pi$
$727$	−3.13983e6	+	2.28122e6i	−0.220328	+	0.160078i	0.472146	+	0.881520i	$0.343479\pi$
$728$	−9.53567e6	+	6.92807e6i	−0.666842	+	0.484489i
$729$	−8.24969e6			−0.574935
$730$	1.08930e7	−	7.91426e6i	0.756558	−	0.549671i
$731$	303723.	+	934763.i	0.0210225	+	0.0647006i
$732$	1.76627e6	−	5.43603e6i	0.121837	−	0.374977i
$733$	−2.26519e7	−	1.64576e7i	−1.55720	−	1.13137i	−0.938259	−	0.345934i	$-0.887562\pi$
$733$	−2.26519e7	−	1.64576e7i	−1.55720	−	1.13137i	−0.618941	−	0.785438i	$-0.712438\pi$
$734$	8.69326e6	+	6.31602e6i	0.595583	+	0.432717i
$735$	−3.20493e7			−2.18826
$736$	−182313.	+	561100.i	−0.0124057	+	0.0381809i
$737$	−464064.			−0.0314709
$738$	−7.70763e6	+	3.34370e6i	−0.520931	+	0.225988i
$739$	−4.58479e6			−0.308822			−0.154411	−	0.988007i	$-0.549348\pi$
$739$	−4.58479e6			−0.308822			−0.154411	+	0.988007i	$0.549348\pi$
$740$	−1.12433e6	+	3.46032e6i	−0.0754768	+	0.232294i
$741$	8.17753e6			0.547113
$742$	−3.11953e6	−	2.26647e6i	−0.208008	−	0.151127i
$743$	−7.65066e6	−	5.55853e6i	−0.508425	−	0.369393i	0.303801	−	0.952736i	$-0.401744\pi$
$743$	−7.65066e6	−	5.55853e6i	−0.508425	−	0.369393i	−0.812226	+	0.583343i	$0.801744\pi$
$744$	1.93872e6	−	5.96677e6i	0.128405	−	0.395191i
$745$	2.74812e6	+	8.45784e6i	0.181403	+	0.558301i
$746$	−1.33248e7	+	9.68104e6i	−0.876625	+	0.636906i
$747$	1.49401e7			0.979610
$748$	−1.78864e6	+	1.29952e6i	−0.116888	+	0.0849240i
$749$	3.28860e7	−	2.38931e7i	2.14194	−	1.55621i
$750$	−1.03460e7	−	7.51679e6i	−0.671612	−	0.487955i
$751$	−1.58856e6	+	4.88909e6i	−0.102779	+	0.316321i	−0.989203	−	0.146553i	$-0.953182\pi$
$751$	−1.58856e6	+	4.88909e6i	−0.102779	+	0.316321i	0.886424	+	0.462875i	$0.153182\pi$
$752$	−5.75132e6			−0.370871
$753$	−2.43327e7	−	1.76788e7i	−1.56388	−	1.13622i
$754$	−6.05070e6	−	1.86221e7i	−0.387594	−	1.19289i
$755$	−1.03219e7	+	7.49933e6i	−0.659013	+	0.478801i
$756$	−1.01246e6	+	3.11602e6i	−0.0644277	+	0.198288i
$757$	5.00161e6	+	1.53934e7i	0.317227	+	0.976324i	0.974828	+	0.222958i	$0.0715712\pi$
$757$	5.00161e6	+	1.53934e7i	0.317227	+	0.976324i	−0.657601	+	0.753366i	$0.728429\pi$
$758$	1.15500e6	+	3.55474e6i	0.0730148	+	0.224716i
$759$	−678268.	−	2.08750e6i	−0.0427363	−	0.131529i
$760$	525743.	+	1.61807e6i	0.0330172	+	0.101616i
$761$	−5.40747e6	+	1.66425e7i	−0.338479	+	1.04173i	0.626503	+	0.779419i	$0.284486\pi$
$761$	−5.40747e6	+	1.66425e7i	−0.338479	+	1.04173i	−0.964983	+	0.262314i	$0.915514\pi$
$762$	7.59409e6	−	5.51743e6i	0.473792	−	0.344230i
$763$	1.38960e7	+	4.27674e7i	0.864126	+	2.65951i
$764$	7.54578e6	+	5.48233e6i	0.467703	+	0.339806i
$765$	−9.08300e6			−0.561146
$766$	−6.03631e6	+	1.85779e7i	−0.371706	+	1.14399i
$767$	−3.15462e7	−	2.29197e7i	−1.93624	−	1.40676i
$768$	1.10980e6	−	806315.i	0.0678955	−	0.0493289i
$769$	1.29635e7	−	9.41852e6i	0.790507	−	0.574337i	−0.117607	−	0.993060i	$-0.537522\pi$
$769$	1.29635e7	−	9.41852e6i	0.790507	−	0.574337i	0.908114	+	0.418723i	$0.137522\pi$
$770$	9.12321e6			0.554525
$771$	2.48065e7	−	1.80230e7i	1.50290	−	1.09192i
$772$	4.73616e6	+	1.45764e7i	0.286012	+	0.880253i
$773$	355806.	−	1.09506e6i	0.0214173	−	0.0659157i	−0.939777	−	0.341789i	$-0.888967\pi$
$773$	355806.	−	1.09506e6i	0.0214173	−	0.0659157i	0.961194	+	0.275874i	$0.0889671\pi$
$774$	817507.	+	593953.i	0.0490500	+	0.0356369i
$775$	2.40089e6	+	1.74435e6i	0.143588	+	0.104323i
$776$	−8.94182e6			−0.533055
$777$	−4.90403e6	+	1.50930e7i	−0.291407	+	0.896860i
$778$	−1.20075e7			−0.711222
$779$	2.37214e6	−	4.01938e6i	0.140054	−	0.237310i
$780$	1.84997e7			1.08875
$781$	4.29208e6	−	1.32097e7i	0.251791	−	0.774933i
$782$	1.74969e6			0.102316
$783$	−4.40334e6	−	3.19921e6i	−0.256671	−	0.186483i
$784$	−5.17240e6	−	3.75797e6i	−0.300540	−	0.218355i
$785$	4.20734e6	−	1.29489e7i	0.243688	−	0.749994i
$786$	7.83119e6	+	2.41019e7i	0.452138	+	1.39154i
$787$	−996235.	+	723807.i	−0.0573357	+	0.0416568i	−0.616084	−	0.787681i	$-0.711282\pi$
$787$	−996235.	+	723807.i	−0.0573357	+	0.0416568i	0.558748	+	0.829337i	$0.311282\pi$
$788$	−9.54001e6			−0.547310
$789$	−4.08835e6	+	2.97036e6i	−0.233806	+	0.169870i
$790$	1.47213e7	−	1.06956e7i	0.839224	−	0.609732i
$791$	−6.54975e6	−	4.75867e6i	−0.372206	−	0.270424i
$792$	−702403.	+	2.16177e6i	−0.0397900	+	0.122461i
$793$	1.53770e7			0.868338
$794$	1.13335e7	+	8.23426e6i	0.637988	+	0.463525i
$795$	1.87019e6	+	5.75587e6i	0.104947	+	0.322993i
$796$	8.57517e6	−	6.23023e6i	0.479690	−	0.348515i
$797$	−861154.	+	2.65036e6i	−0.0480214	+	0.147795i	−0.972192	−	0.234185i	$-0.924758\pi$
$797$	−861154.	+	2.65036e6i	−0.0480214	+	0.147795i	0.924171	+	0.381980i	$0.124758\pi$
$798$	2.29316e6	+	7.05761e6i	0.127475	+	0.392329i
$799$	5.27080e6	+	1.62219e7i	0.292085	+	0.898947i
$800$	200516.	+	617125.i	0.0110770	+	0.0340917i
$801$	−1.79820e6	−	5.53431e6i	−0.0990280	−	0.304777i
$802$	2.60159e6	−	8.00687e6i	0.142825	−	0.439569i
$803$	−8.08445e6	+	5.87370e6i	−0.442447	+	0.321457i
$804$	−263881.	−	812142.i	−0.0143969	−	0.0443090i
$805$	−5.84118e6	−	4.24387e6i	−0.317695	−	0.230819i
$806$	1.68783e7			0.915149
$807$	−2.89290e6	+	8.90343e6i	−0.156369	+	0.481253i
$808$	−4.51763e6	−	3.28225e6i	−0.243435	−	0.176866i
$809$	−2.72855e7	+	1.98241e7i	−1.46575	+	1.06493i	−0.483937	+	0.875103i	$0.660794\pi$
$809$	−2.72855e7	+	1.98241e7i	−1.46575	+	1.06493i	−0.981817	+	0.189830i	$0.939206\pi$
$810$	1.35681e7	−	9.85778e6i	0.726617	−	0.527918i
$811$	−2.92937e7			−1.56395			−0.781973	−	0.623312i	$-0.785787\pi$
$811$	−2.92937e7			−1.56395			−0.781973	+	0.623312i	$0.785787\pi$
$812$	1.43751e7	−	1.04441e7i	0.765103	−	0.555880i
$813$	8.57272e6	+	2.63841e7i	0.454875	+	1.39996i
$814$	834438.	−	2.56814e6i	0.0441401	−	0.135849i
$815$	2.89550e7	+	2.10370e7i	1.52697	+	1.10941i
$816$	−3.29132e6	−	2.39129e6i	−0.173039	−	0.125721i
$817$	−561335.			−0.0294217
$818$	5.73162e6	−	1.76401e7i	0.299498	−	0.921761i
$819$	3.59384e7			1.87219
$820$	5.36640e6	−	9.09291e6i	0.278707	−	0.472246i
$821$	2.15519e7			1.11591			0.557953	−	0.829873i	$-0.311587\pi$
$821$	2.15519e7			1.11591			0.557953	+	0.829873i	$0.311587\pi$
$822$	−481792.	+	1.48280e6i	−0.0248702	+	0.0765427i
$823$	−4.97930e6			−0.256253			−0.128127	−	0.991758i	$-0.540896\pi$
$823$	−4.97930e6			−0.256253			−0.128127	+	0.991758i	$0.540896\pi$
$824$	−7.60055e6	−	5.52212e6i	−0.389966	−	0.283327i
$825$	−1.95303e6	−	1.41896e6i	−0.0999021	−	0.0725831i
$826$	1.09346e7	−	3.36531e7i	0.557637	−	1.71623i
$827$	4.85324e6	+	1.49367e7i	0.246756	+	0.759438i	0.995343	+	0.0964003i	$0.0307329\pi$
$827$	4.85324e6	+	1.49367e7i	0.246756	+	0.759438i	−0.748586	+	0.663037i	$0.769267\pi$
$828$	1.45532e6	−	1.05735e6i	0.0737702	−	0.0535972i
$829$	2.35610e7			1.19071			0.595357	−	0.803461i	$-0.297010\pi$
$829$	2.35610e7			1.19071			0.595357	+	0.803461i	$0.297010\pi$
$830$	−1.51895e7	+	1.10358e7i	−0.765331	+	0.556045i
$831$	−1.86499e7	+	1.35499e7i	−0.936856	+	0.680666i
$832$	2.98566e6	+	2.16921e6i	0.149531	+	0.108641i
$833$	−5.85927e6	+	1.80330e7i	−0.292571	+	0.900441i
$834$	2.13290e7			1.06183
$835$	5.83023e6	+	4.23591e6i	0.289380	+	0.210247i
$836$	−390189.	−	1.20088e6i	−0.0193090	−	0.0594269i
$837$	3.79566e6	−	2.75771e6i	0.187273	−	0.136061i
$838$	3.35370e6	−	1.03216e7i	0.164973	−	0.507736i
$839$	−7.95148e6	−	2.44721e7i	−0.389981	−	1.20024i	−0.932802	−	0.360389i	$-0.882644\pi$
$839$	−7.95148e6	−	2.44721e7i	−0.389981	−	1.20024i	0.542821	−	0.839848i	$-0.317356\pi$
$840$	5.18773e6	+	1.59662e7i	0.253676	+	0.780734i
$841$	2.78317e6	+	8.56572e6i	0.135691	+	0.417613i
$842$	5.20389e6	+	1.60159e7i	0.252958	+	0.778524i
$843$	−1.11575e7	+	3.43394e7i	−0.540753	+	1.66427i
$844$	−3.01617e6	+	2.19137e6i	−0.145747	+	0.105891i
$845$	8.34534e6	+	2.56843e7i	0.402070	+	1.23745i
$846$	1.41870e7	+	1.03075e7i	0.681498	+	0.495137i
$847$	2.61487e7			1.25239
$848$	−373081.	+	1.14823e6i	−0.0178161	+	0.0548324i
$849$	−3.66407e7	−	2.66210e7i	−1.74459	−	1.26752i
$850$	1.55687e6	−	1.13113e6i	0.0739101	−	0.0536988i
$851$	−1.72888e6	+	1.25611e6i	−0.0818354	+	0.0594569i
$852$	2.55584e7			1.20624
$853$	−5.20426e6	+	3.78112e6i	−0.244899	+	0.177929i	−0.703463	−	0.710732i	$-0.748364\pi$
$853$	−5.20426e6	+	3.78112e6i	−0.244899	+	0.177929i	0.458564	+	0.888661i	$0.348364\pi$
$854$	4.31205e6	+	1.32711e7i	0.202320	+	0.622677i
$855$	1.60302e6	−	4.93359e6i	0.0749935	−	0.230806i
$856$	−1.02967e7	−	7.48102e6i	−0.480303	−	0.348961i
$857$	−1.92683e7	−	1.39992e7i	−0.896170	−	0.651106i	0.0413094	−	0.999146i	$-0.486847\pi$
$857$	−1.92683e7	−	1.39992e7i	−0.896170	−	0.651106i	−0.937479	+	0.348041i	$0.886847\pi$
$858$	−1.37299e7			−0.636721
$859$	−1.00358e7	+	3.08870e7i	−0.464054	+	1.42821i	0.396114	+	0.918201i	$0.370358\pi$
$859$	−1.00358e7	+	3.08870e7i	−0.464054	+	1.42821i	−0.860168	+	0.510010i	$0.829642\pi$
$860$	−1.26989e6			−0.0585490
$861$	2.34069e7	−	3.96609e7i	1.07606	−	1.82329i
$862$	−1.09767e7			−0.503156
$863$	3.99590e6	−	1.22981e7i	0.182637	−	0.562098i	−0.817263	−	0.576265i	$-0.804510\pi$
$863$	3.99590e6	−	1.22981e7i	0.182637	−	0.562098i	0.999900	+	0.0141671i	$0.00450969\pi$
$864$	1.02585e6			0.0467518
$865$	−1.22435e7	−	8.89544e6i	−0.556373	−	0.404229i
$866$	−1.28714e7	−	9.35165e6i	−0.583220	−	0.423734i
$867$	5.45563e6	−	1.67907e7i	0.246489	−	0.758615i
$868$	4.73305e6	+	1.45668e7i	0.213227	+	0.656244i
$869$	−1.09256e7	+	7.93795e6i	−0.490792	+	0.356582i
$870$	−2.78885e7			−1.24918
$871$	1.85857e6	−	1.35033e6i	0.0830107	−	0.0603108i
$872$	1.13908e7	−	8.27587e6i	0.507296	−	0.368572i
$873$	2.20571e7	+	1.60254e7i	0.979520	+	0.711663i
$874$	−308795.	+	950374.i	−0.0136739	+	0.0420839i
$875$	3.12204e7			1.37854
$876$	−1.48764e7	−	1.08083e7i	−0.654995	−	0.475881i
$877$	5.36244e6	+	1.65039e7i	0.235431	+	0.724581i	0.997064	+	0.0765730i	$0.0243978\pi$
$877$	5.36244e6	+	1.65039e7i	0.235431	+	0.724581i	−0.761633	+	0.648008i	$0.775602\pi$
$878$	−1.82415e7	+	1.32532e7i	−0.798591	+	0.580210i
$879$	8.90478e6	−	2.74061e7i	0.388733	−	1.19640i
$880$	−882711.	−	2.71671e6i	−0.0384248	−	0.118259i
$881$	−1.05970e6	−	3.26143e6i	−0.0459986	−	0.141569i	0.925419	−	0.378944i	$-0.123713\pi$
$881$	−1.05970e6	−	3.26143e6i	−0.0459986	−	0.141569i	−0.971418	+	0.237375i	$0.923713\pi$
$882$	6.02396e6	+	1.85398e7i	0.260742	+	0.802481i
$883$	−5.31171e6	−	1.63478e7i	−0.229262	−	0.705596i	−0.997831	−	0.0658291i	$-0.979031\pi$
$883$	−5.31171e6	−	1.63478e7i	−0.229262	−	0.705596i	0.768569	−	0.639767i	$-0.220969\pi$
$884$	3.38214e6	−	1.04092e7i	0.145566	−	0.448007i
$885$	−4.49313e7	+	3.26445e7i	−1.92837	+	1.40104i
$886$	1.18914e6	+	3.65979e6i	0.0508918	+	0.156629i
$887$	−1.34955e7	−	9.80507e6i	−0.575945	−	0.418448i	0.261315	−	0.965254i	$-0.415844\pi$
$887$	−1.34955e7	−	9.80507e6i	−0.575945	−	0.418448i	−0.837260	+	0.546805i	$0.815844\pi$
$888$	4.96889e6			0.211459
$889$	−7.08150e6	+	2.17946e7i	−0.300518	+	0.924900i
$890$	5.91625e6	+	4.29841e6i	0.250364	+	0.181900i
$891$	−1.00698e7	+	7.31611e6i	−0.424938	+	0.308735i
$892$	−1.60011e7	+	1.16255e7i	−0.673347	+	0.489215i
$893$	−9.74141e6			−0.408783
$894$	9.82561e6	−	7.13872e6i	0.411165	−	0.298729i
$895$	−1.23895e7	−	3.81310e7i	−0.517007	−	1.59118i
$896$	−1.03489e6	+	3.18506e6i	−0.0430649	+	0.132540i
$897$	8.79063e6	+	6.38677e6i	0.364787	+	0.265033i
$898$	−5.95250e6	−	4.32474e6i	−0.246325	−	0.178965i
$899$	−2.54442e7			−1.05000
$900$	611384.	−	1.88165e6i	0.0251599	−	0.0774341i
$901$	3.58053e6			0.146939
$902$	−3.98276e6	+	6.74845e6i	−0.162993	+	0.276177i
$903$	−5.53893e6			−0.226051
$904$	−783318.	+	2.41081e6i	−0.0318799	+	0.0981163i
$905$	4.50829e7			1.82974
$906$	1.40965e7	+	1.02417e7i	0.570544	+	0.414525i
$907$	−3.63814e7	−	2.64326e7i	−1.46846	−	1.06690i	−0.981058	−	0.193715i	$-0.937946\pi$
$907$	−3.63814e7	−	2.64326e7i	−1.46846	−	1.06690i	−0.487398	−	0.873180i	$-0.662054\pi$
$908$	−3.33158e6	+	1.02535e7i	−0.134102	+	0.412723i
$909$	5.26139e6	+	1.61929e7i	0.211199	+	0.650002i
$910$	−3.65383e7	+	2.65466e7i	−1.46267	+	1.06269i
$911$	2.00906e7			0.802041			0.401020	−	0.916069i	$-0.368656\pi$
$911$	2.00906e7			0.802041			0.401020	+	0.916069i	$0.368656\pi$
$912$	1.87974e6	−	1.36571e6i	0.0748360	−	0.0543715i
$913$	1.12732e7	−	8.19043e6i	0.447578	−	0.325185i
$914$	6.19842e6	+	4.50341e6i	0.245423	+	0.178310i
$915$	6.76793e6	−	2.08295e7i	0.267241	−	0.822483i
$916$	5.06226e6			0.199345
$917$	−5.00528e7	−	3.63655e7i	−1.96564	−	1.42812i
$918$	−940139.	−	2.89345e6i	−0.0368202	−	0.113321i
$919$	3.22503e7	−	2.34312e7i	1.25964	−	0.915179i	0.260896	−	0.965367i	$-0.415982\pi$
$919$	3.22503e7	−	2.34312e7i	1.25964	−	0.915179i	0.998740	+	0.0501884i	$0.0159822\pi$
$920$	−698576.	+	2.15000e6i	−0.0272110	+	0.0837468i
$921$	−8.10737e6	−	2.49519e7i	−0.314942	−	0.969292i
$922$	5.84463e6	+	1.79879e7i	0.226428	+	0.696873i
$923$	2.12477e7	+	6.53936e7i	0.820932	+	2.52657i
$924$	−3.85016e6	−	1.18496e7i	−0.148354	−	0.456586i
$925$	−726310.	+	2.23535e6i	−0.0279105	+	0.0858997i
$926$	−1.15967e7	+	8.42547e6i	−0.444432	+	0.322899i
$927$	8.85187e6	+	2.72433e7i	0.338326	+	1.04126i
$928$	−4.50089e6	−	3.27009e6i	−0.171565	−	0.124649i
$929$	−2.11909e7			−0.805583			−0.402792	−	0.915292i	$-0.631960\pi$
$929$	−2.11909e7			−0.805583			−0.402792	+	0.915292i	$0.631960\pi$
$930$	7.42870e6	−	2.28632e7i	0.281647	−	0.866821i
$931$	−8.76085e6	−	6.36513e6i	−0.331262	−	0.240676i
$932$	1.21860e7	−	8.85362e6i	0.459537	−	0.333873i
$933$	1.87719e7	−	1.36385e7i	0.705997	−	0.512937i
$934$	5.97448e6			0.224096
$935$	−6.85363e6	+	4.97945e6i	−0.256384	+	0.186274i
$936$	−3.47720e6	−	1.07017e7i	−0.129730	−	0.399268i
$937$	1.44539e7	−	4.44847e7i	0.537821	−	1.65524i	−0.199654	−	0.979867i	$-0.563982\pi$
$937$	1.44539e7	−	4.44847e7i	0.537821	−	1.65524i	0.737474	−	0.675375i	$-0.236018\pi$
$938$	1.68659e6	+	1.22538e6i	0.0625895	+	0.0454739i
$939$	2.75768e6	+	2.00357e6i	0.102066	+	0.0741552i
$940$	−2.20376e7			−0.813477
$941$	654372.	−	2.01395e6i	0.0240908	−	0.0741438i	−0.938288	−	0.345854i	$-0.887589\pi$
$941$	654372.	−	2.01395e6i	0.0240908	−	0.0741438i	0.962379	+	0.271710i	$0.0875892\pi$
$942$	−1.85941e7			−0.682727
$943$	5.68918e6	−	2.46806e6i	0.208339	−	0.0903808i
$944$	−1.10792e7			−0.404648
$945$	−3.87949e6	+	1.19398e7i	−0.141317	+	0.434929i
$946$	942469.			0.0342404
$947$	2.07565e7	+	1.50805e7i	0.752107	+	0.546438i	0.896479	−	0.443086i	$-0.146116\pi$
$947$	2.07565e7	+	1.50805e7i	0.752107	+	0.546438i	−0.144372	+	0.989523i	$0.546116\pi$
$948$	−2.01046e7	−	1.46068e7i	−0.726564	−	0.527880i
$949$	1.52869e7	−	4.70482e7i	0.551002	−	1.69581i
$950$	339628.	+	1.04527e6i	0.0122094	+	0.0375766i
$951$	912915.	−	663271.i	0.0327325	−	0.0237815i
$952$	9.93203e6			0.355178
$953$	3.18883e7	−	2.31682e7i	1.13736	−	0.826343i	0.150614	−	0.988593i	$-0.451875\pi$
$953$	3.18883e7	−	2.31682e7i	1.13736	−	0.826343i	0.986750	+	0.162250i	$0.0518750\pi$
$954$	2.97813e6	−	2.16374e6i	0.105943	−	0.0769722i
$955$	2.89135e7	+	2.10069e7i	1.02587	+	0.745339i
$956$	3.41938e6	−	1.05238e7i	0.121005	−	0.372415i
$957$	2.06979e7			0.730544
$958$	−1.55531e7	−	1.13000e7i	−0.547524	−	0.397800i
$959$	−1.17621e6	−	3.62000e6i	−0.0412989	−	0.127105i
$960$	4.25247e6	−	3.08960e6i	0.148923	−	0.108199i
$961$	−2.06929e6	+	6.36861e6i	−0.0722790	+	0.222452i
$962$	4.13083e6	+	1.27134e7i	0.143913	+	0.442919i
$963$	1.19920e7	+	3.69074e7i	0.416701	+	1.28247i
$964$	4.65068e6	+	1.43133e7i	0.161185	+	0.496076i
$965$	1.81478e7	+	5.58532e7i	0.627344	+	1.93077i
$966$	−3.04701e6	+	9.37774e6i	−0.105059	+	0.323337i
$967$	−1.62600e6	+	1.18136e6i	−0.0559183	+	0.0406270i	−0.615393	−	0.788220i	$-0.711003\pi$
$967$	−1.62600e6	+	1.18136e6i	−0.0559183	+	0.0406270i	0.559475	+	0.828847i	$0.311003\pi$
$968$	−2.53000e6	−	7.78654e6i	−0.0867825	−	0.267089i
$969$	−5.57474e6	−	4.05028e6i	−0.190728	−	0.138572i
$970$	−3.42629e7			−1.16921
$971$	1.20881e7	−	3.72034e7i	0.411444	−	1.26629i	−0.503950	−	0.863733i	$-0.668120\pi$
$971$	1.20881e7	−	3.72034e7i	0.411444	−	1.26629i	0.915393	−	0.402561i	$-0.131880\pi$
$972$	−1.53785e7	−	1.11731e7i	−0.522093	−	0.379323i
$973$	−4.21263e7	+	3.06066e7i	−1.42650	+	1.03641i
$974$	1.57796e7	−	1.14645e7i	0.532963	−	0.387221i
$975$	1.19508e7			0.402609
$976$	3.53466e6	−	2.56808e6i	0.118774	−	0.0862946i
$977$	−216728.	−	667020.i	−0.00726404	−	0.0223564i	0.947359	−	0.320174i	$-0.103741\pi$
$977$	−216728.	−	667020.i	−0.00726404	−	0.0223564i	−0.954623	+	0.297817i	$0.903741\pi$
$978$	1.51042e7	−	4.64859e7i	0.504952	−	1.55408i
$979$	−4.39084e6	−	3.19014e6i	−0.146417	−	0.106378i
$980$	−1.98194e7	−	1.43996e7i	−0.659211	−	0.478945i
$981$	−4.29299e7			−1.42425
$982$	−9.44235e6	+	2.90606e7i	−0.312465	+	0.961668i
$983$	1.31308e7			0.433419			0.216710	−	0.976236i	$-0.430467\pi$
$983$	1.31308e7			0.433419			0.216710	+	0.976236i	$0.430467\pi$
$984$	−1.40749e7	−	3.13271e6i	−0.463403	−	0.103141i
$985$	−3.65550e7			−1.20048
$986$	−5.09859e6	+	1.56919e7i	−0.167016	+	0.514022i
$987$	−9.61226e7			−3.14074
$988$	5.05701e6	+	3.67413e6i	0.164817	+	0.119746i
$989$	−603421.	−	438411.i	−0.0196169	−	0.0142525i
$990$	−2.69143e6	+	8.28338e6i	−0.0872762	+	0.268609i
$991$	3.05620e6	+	9.40601e6i	0.0988547	+	0.304243i	0.988239	−	0.152917i	$-0.0488666\pi$
$991$	3.05620e6	+	9.40601e6i	0.0988547	+	0.304243i	−0.889384	+	0.457160i	$0.848867\pi$
$992$	3.87976e6	−	2.81881e6i	0.125177	−	0.0909466i
$993$	4.43283e6			0.142662
$994$	−5.04796e7	+	3.66756e7i	−1.62050	+	1.17736i
$995$	3.28579e7	−	2.38727e7i	1.05216	−	0.764441i
$996$	2.07440e7	+	1.50714e7i	0.662590	+	0.481400i
$997$	−2.78722e6	+	8.57819e6i	−0.0888042	+	0.273311i	−0.985590	−	0.169155i	$-0.945896\pi$
$997$	−2.78722e6	+	8.57819e6i	−0.0888042	+	0.273311i	0.896785	+	0.442466i	$0.145896\pi$
$998$	−2.58204e7			−0.820608
$999$	3.00617e6	+	2.18411e6i	0.0953016	+	0.0692407i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.6.d.a.57.2	✓	36	1.1	even	1	trivial
82.6.d.a.59.2	yes	36	41.18	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 82 = 2 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	82.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.23607 - 3.80423i) q^{2} -20.9318 q^{3} +(-12.9443 - 9.40456i) q^{4} +(-49.5992 - 36.0360i) q^{5} +(-25.8731 + 79.6292i) q^{6} +(-63.1646 - 194.401i) q^{7} +(-51.7771 + 37.6183i) q^{8} +195.140 q^{9} +(-198.397 + 144.144i) q^{10} +(147.244 - 106.979i) q^{11} +(270.947 + 196.854i) q^{12} +(-278.423 + 856.897i) q^{13} -817.620 q^{14} +(1038.20 + 754.297i) q^{15} +(79.1084 + 243.470i) q^{16} +(614.221 - 446.257i) q^{17} +(241.206 - 742.355i) q^{18} +(133.991 + 412.382i) q^{19} +(303.124 + 932.919i) q^{20} +(1322.15 + 4069.15i) q^{21} +(-224.968 - 692.381i) q^{22} +(-178.040 + 547.949i) q^{23} +(1083.79 - 787.417i) q^{24} +(195.816 + 602.661i) q^{25} +(2915.68 + 2118.37i) q^{26} +1001.80 q^{27} +(-1010.63 + 3110.41i) q^{28} +(-4395.40 - 3193.45i) q^{29} +(4152.80 - 3017.19i) q^{30} +(3788.83 - 2752.74i) q^{31} +1024.00 q^{32} +(-3082.07 + 2239.26i) q^{33} +(-938.446 - 2888.24i) q^{34} +(-3872.50 + 11918.3i) q^{35} +(-2525.94 - 1835.20i) q^{36} +(3000.76 + 2180.18i) q^{37} +1734.42 q^{38} +(5827.88 - 17936.4i) q^{39} +3923.71 q^{40} +(-7125.45 - 8067.47i) q^{41} +17114.2 q^{42} +(-400.047 + 1231.22i) q^{43} -2912.05 q^{44} +(-9678.77 - 7032.04i) q^{45} +(1864.45 + 1354.61i) q^{46} +(-6942.41 + 21366.5i) q^{47} +(-1655.88 - 5096.27i) q^{48} +(-20204.7 + 14679.6i) q^{49} +2534.70 q^{50} +(-12856.7 + 9340.96i) q^{51} +(11662.7 - 8473.46i) q^{52} +(3815.39 + 2772.04i) q^{53} +(1238.30 - 3811.09i) q^{54} -11158.3 q^{55} +(10583.5 + 7689.36i) q^{56} +(-2804.67 - 8631.90i) q^{57} +(-17581.6 + 12773.8i) q^{58} +(-13373.7 + 41159.9i) q^{59} +(-6344.92 - 19527.6i) q^{60} +(-5273.90 - 16231.4i) q^{61} +(-5788.81 - 17816.1i) q^{62} +(-12325.9 - 37935.2i) q^{63} +(1265.73 - 3895.53i) q^{64} +(44688.6 - 32468.2i) q^{65} +(4708.99 + 14492.8i) q^{66} +(-2062.80 - 1498.71i) q^{67} -12147.5 q^{68} +(3726.69 - 11469.6i) q^{69} +(40553.3 + 29463.7i) q^{70} +(61739.7 - 44856.5i) q^{71} +(-10103.8 + 7340.81i) q^{72} -54905.3 q^{73} +(12003.0 - 8720.71i) q^{74} +(-4098.79 - 12614.8i) q^{75} +(2143.86 - 6598.12i) q^{76} +(-30097.3 - 21867.0i) q^{77} +(-61030.4 - 44341.2i) q^{78} -74201.2 q^{79} +(4849.98 - 14926.7i) q^{80} -68388.5 q^{81} +(-39498.0 + 17134.9i) q^{82} +76561.3 q^{83} +(21154.4 - 65106.4i) q^{84} -46546.2 q^{85} +(4189.34 + 3043.74i) q^{86} +(92003.6 + 66844.5i) q^{87} +(-3599.49 + 11078.1i) q^{88} +(-9214.97 - 28360.8i) q^{89} +(-38715.1 + 28128.2i) q^{90} +184168. q^{91} +(7457.82 - 5418.42i) q^{92} +(-79306.9 + 57619.8i) q^{93} +(72701.8 + 52821.0i) q^{94} +(8214.74 - 25282.4i) q^{95} -21434.1 q^{96} +(113033. + 82123.0i) q^{97} +(30870.0 + 95008.1i) q^{98} +(28733.1 - 20875.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{2} + 20 q^{3} - 144 q^{4} - 98 q^{5} - 20 q^{6} + 120 q^{7} - 576 q^{8} + 2876 q^{9} - 392 q^{10} - 436 q^{11} - 80 q^{12} - 617 q^{13} + 280 q^{14} + 789 q^{15} - 2304 q^{16} + 1359 q^{17}+ \cdots + 261106 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 20 * q^3 - 144 * q^4 - 98 * q^5 - 20 * q^6 + 120 * q^7 - 576 * q^8 + 2876 * q^9 - 392 * q^10 - 436 * q^11 - 80 * q^12 - 617 * q^13 + 280 * q^14 + 789 * q^15 - 2304 * q^16 + 1359 * q^17 - 4976 * q^18 + 4876 * q^19 + 352 * q^20 - 13529 * q^21 + 2476 * q^22 + 819 * q^23 - 320 * q^24 - 10487 * q^25 - 2088 * q^26 + 1592 * q^27 + 1920 * q^28 + 5249 * q^29 + 3156 * q^30 - 2992 * q^31 + 36864 * q^32 - 5676 * q^33 + 4136 * q^34 + 21607 * q^35 - 3104 * q^36 - 11508 * q^37 + 10664 * q^38 + 8144 * q^39 + 9728 * q^40 - 44187 * q^41 + 97464 * q^42 - 88677 * q^43 - 5856 * q^44 - 45045 * q^45 - 6864 * q^46 - 56670 * q^47 - 1280 * q^48 - 59417 * q^49 + 88352 * q^50 - 26259 * q^51 - 8352 * q^52 + 21963 * q^53 + 29968 * q^54 + 128202 * q^55 - 9920 * q^56 + 16428 * q^57 + 20996 * q^58 - 77668 * q^59 - 7856 * q^60 - 168787 * q^61 - 34428 * q^62 + 247961 * q^63 - 36864 * q^64 - 74533 * q^65 + 48036 * q^66 - 40269 * q^67 - 76576 * q^68 + 242095 * q^69 - 20492 * q^70 - 44665 * q^71 - 12416 * q^72 - 76360 * q^73 - 46032 * q^74 - 154234 * q^75 + 78016 * q^76 - 8441 * q^77 - 71044 * q^78 + 230228 * q^79 + 5632 * q^80 + 184156 * q^81 + 36752 * q^82 + 673200 * q^83 - 216464 * q^84 - 130180 * q^85 + 194192 * q^86 - 398341 * q^87 + 39616 * q^88 - 409131 * q^89 - 180180 * q^90 + 355046 * q^91 - 27456 * q^92 - 51949 * q^93 + 234960 * q^94 - 588753 * q^95 + 20480 * q^96 + 138500 * q^97 - 43248 * q^98 + 261106 * q^99

Introduction

L-functions

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