LMFDB - Embedded newform 82.6.d.b.59.7

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			59.7
Character	$\chi$	$=$	82.59
Dual form			82.6.d.b.57.7

$q$-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} +13.2777 q^{3} +(-12.9443 + 9.40456i) q^{4} +(-68.5323 + 49.7916i) q^{5} +(-16.4122 - 50.5116i) q^{6} +(50.6057 - 155.748i) q^{7} +(51.7771 + 37.6183i) q^{8} -66.7014 q^{9} +(274.129 + 199.166i) q^{10} +(579.683 + 421.165i) q^{11} +(-171.871 + 124.871i) q^{12} +(198.810 + 611.874i) q^{13} -655.054 q^{14} +(-909.954 + 661.120i) q^{15} +(79.1084 - 243.470i) q^{16} +(542.175 + 393.913i) q^{17} +(82.4475 + 253.747i) q^{18} +(-470.251 + 1447.28i) q^{19} +(418.832 - 1289.03i) q^{20} +(671.930 - 2067.99i) q^{21} +(885.677 - 2725.83i) q^{22} +(1342.23 + 4130.96i) q^{23} +(687.483 + 499.486i) q^{24} +(1251.79 - 3852.61i) q^{25} +(2081.96 - 1512.64i) q^{26} -4112.14 q^{27} +(809.691 + 2491.97i) q^{28} +(-290.273 + 210.895i) q^{29} +(3639.82 + 2644.48i) q^{30} +(3070.49 + 2230.84i) q^{31} -1024.00 q^{32} +(7696.89 + 5592.12i) q^{33} +(828.370 - 2549.46i) q^{34} +(4286.84 + 13193.5i) q^{35} +(863.402 - 627.298i) q^{36} +(3819.44 - 2774.99i) q^{37} +6087.06 q^{38} +(2639.75 + 8124.31i) q^{39} -5421.47 q^{40} +(-8244.37 - 6920.01i) q^{41} -8697.64 q^{42} +(-4692.13 - 14440.9i) q^{43} -11464.4 q^{44} +(4571.20 - 3321.17i) q^{45} +(14056.0 - 10212.3i) q^{46} +(-57.8927 - 178.175i) q^{47} +(1050.38 - 3232.74i) q^{48} +(-8099.46 - 5884.60i) q^{49} -16203.5 q^{50} +(7198.86 + 5230.28i) q^{51} +(-8327.86 - 6050.54i) q^{52} +(3508.79 - 2549.29i) q^{53} +(5082.88 + 15643.5i) q^{54} -60697.5 q^{55} +(8479.20 - 6160.50i) q^{56} +(-6243.87 + 19216.7i) q^{57} +(1161.09 + 843.582i) q^{58} +(-1913.27 - 5888.43i) q^{59} +(5561.14 - 17115.4i) q^{60} +(-3187.05 + 9808.73i) q^{61} +(4691.30 - 14438.3i) q^{62} +(-3375.47 + 10388.6i) q^{63} +(1265.73 + 3895.53i) q^{64} +(-44091.1 - 32034.0i) q^{65} +(11759.8 - 36192.9i) q^{66} +(-43306.1 + 31463.7i) q^{67} -10722.6 q^{68} +(17821.8 + 54849.9i) q^{69} +(44892.3 - 32616.2i) q^{70} +(40176.1 + 29189.6i) q^{71} +(-3453.61 - 2509.19i) q^{72} -88300.4 q^{73} +(-15277.8 - 11100.0i) q^{74} +(16620.9 - 51154.0i) q^{75} +(-7524.02 - 23156.5i) q^{76} +(94931.0 - 68971.4i) q^{77} +(27643.8 - 20084.4i) q^{78} +67994.9 q^{79} +(6701.31 + 20624.5i) q^{80} -38391.5 q^{81} +(-16134.7 + 39917.0i) q^{82} +84673.1 q^{83} +(10750.9 + 33087.8i) q^{84} -56770.1 q^{85} +(-49136.6 + 35699.8i) q^{86} +(-3854.17 + 2800.22i) q^{87} +(14170.8 + 43613.4i) q^{88} +(-18886.0 + 58125.2i) q^{89} +(-18284.8 - 13284.7i) q^{90} +105359. q^{91} +(-56224.1 - 40849.2i) q^{92} +(40769.2 + 29620.6i) q^{93} +(-606.260 + 440.474i) q^{94} +(-39835.2 - 122600. i) q^{95} -13596.4 q^{96} +(35023.8 - 25446.3i) q^{97} +(-12374.9 + 38086.0i) q^{98} +(-38665.7 - 28092.3i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 36 q^{2} + 2 q^{3} - 144 q^{4} + 26 q^{5} + 112 q^{6} - 120 q^{7} + 576 q^{8} + 4006 q^{9} - 104 q^{10} + 747 q^{11} + 432 q^{12} + 907 q^{13} + 280 q^{14} - 4149 q^{15} - 2304 q^{16} - 3177 q^{17}+ \cdots + 276325 q^{99}+O(q^{100}) $ 36 * q + 36 * q^2 + 2 * q^3 - 144 * q^4 + 26 * q^5 + 112 * q^6 - 120 * q^7 + 576 * q^8 + 4006 * q^9 - 104 * q^10 + 747 * q^11 + 432 * q^12 + 907 * q^13 + 280 * q^14 - 4149 * q^15 - 2304 * q^16 - 3177 * q^17 + 3696 * q^18 + 1557 * q^19 - 624 * q^20 - 4785 * q^21 + 2252 * q^22 + 1809 * q^23 - 1728 * q^24 - 6323 * q^25 + 10132 * q^26 + 8828 * q^27 - 1920 * q^28 + 1179 * q^29 + 16596 * q^30 - 2190 * q^31 - 36864 * q^32 + 19669 * q^33 - 4572 * q^34 - 69 * q^35 - 17264 * q^36 + 47551 * q^37 - 6128 * q^38 + 62888 * q^39 - 1664 * q^40 + 41071 * q^41 - 16600 * q^42 + 46110 * q^43 - 5888 * q^44 + 51325 * q^45 + 144 * q^46 - 65162 * q^47 - 7168 * q^48 - 83129 * q^49 - 151288 * q^50 + 98677 * q^51 - 40528 * q^52 - 122095 * q^53 + 41748 * q^54 - 161798 * q^55 - 9920 * q^56 - 11800 * q^57 - 4716 * q^58 + 17054 * q^59 + 72656 * q^60 + 86317 * q^61 - 30540 * q^62 - 166377 * q^63 - 36864 * q^64 + 32896 * q^65 + 66064 * q^66 + 95554 * q^67 + 65088 * q^68 + 132527 * q^69 + 23156 * q^70 + 158283 * q^71 + 69056 * q^72 - 239776 * q^73 - 190204 * q^74 - 357133 * q^75 + 24912 * q^76 + 253599 * q^77 + 242748 * q^78 + 98380 * q^79 - 9984 * q^80 + 1044 * q^81 - 84824 * q^82 - 24346 * q^83 - 76560 * q^84 + 376378 * q^85 + 98560 * q^86 + 12625 * q^87 + 36032 * q^88 + 260385 * q^89 - 205300 * q^90 - 726414 * q^91 - 576 * q^92 - 100227 * q^93 - 189392 * q^94 - 257337 * q^95 - 2048 * q^96 + 109321 * q^97 - 145824 * q^98 + 276325 * q^99

Character values

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

$n$	$47$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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
$3$	13.2777			0.851768			0.425884	−	0.904778i	$-0.359963\pi$
$3$	13.2777			0.851768			0.425884	+	0.904778i	$0.359963\pi$
$4$	−12.9443	+	9.40456i	−0.404508	+	0.293893i
$5$	−68.5323	+	49.7916i	−1.22594	+	0.890699i	−0.996579	−	0.0826419i	$-0.973664\pi$
$5$	−68.5323	+	49.7916i	−1.22594	+	0.890699i	−0.229363	+	0.973341i	$0.573664\pi$
$6$	−16.4122	−	50.5116i	−0.186118	−	0.572813i
$7$	50.6057	−	155.748i	0.390350	−	1.20137i	−0.542174	−	0.840266i	$-0.682399\pi$
$7$	50.6057	−	155.748i	0.390350	−	1.20137i	0.932524	−	0.361108i	$-0.117601\pi$
$8$	51.7771	+	37.6183i	0.286031	+	0.207813i
$9$	−66.7014			−0.274492
$10$	274.129	+	199.166i	0.866872	+	0.629819i
$11$	579.683	+	421.165i	1.44447	+	1.04947i	0.987084	+	0.160203i	$0.0512149\pi$
$11$	579.683	+	421.165i	1.44447	+	1.04947i	0.457388	+	0.889267i	$0.348785\pi$
$12$	−171.871	+	124.871i	−0.344547	+	0.250328i
$13$	198.810	+	611.874i	0.326272	+	1.00416i	0.970863	+	0.239634i	$0.0770276\pi$
$13$	198.810	+	611.874i	0.326272	+	1.00416i	−0.644591	+	0.764527i	$0.722972\pi$
$14$	−655.054			−0.893217
$15$	−909.954	+	661.120i	−1.04422	+	0.758669i
$16$	79.1084	−	243.470i	0.0772542	−	0.237764i
$17$	542.175	+	393.913i	0.455006	+	0.330581i	0.791569	−	0.611080i	$-0.209264\pi$
$17$	542.175	+	393.913i	0.455006	+	0.330581i	−0.336563	+	0.941661i	$0.609264\pi$
$18$	82.4475	+	253.747i	0.0599786	+	0.184595i
$19$	−470.251	+	1447.28i	−0.298845	+	0.919750i	0.683058	+	0.730364i	$0.260650\pi$
$19$	−470.251	+	1447.28i	−0.298845	+	0.919750i	−0.981903	+	0.189386i	$0.939350\pi$
$20$	418.832	−	1289.03i	0.234134	−	0.720591i
$21$	671.930	−	2067.99i	0.332488	−	1.02329i
$22$	885.677	−	2725.83i	0.390139	−	1.20072i
$23$	1342.23	+	4130.96i	0.529063	+	1.62829i	0.756138	+	0.654412i	$0.227084\pi$
$23$	1342.23	+	4130.96i	0.529063	+	1.62829i	−0.227074	+	0.973877i	$0.572916\pi$
$24$	687.483	+	499.486i	0.243632	+	0.177009i
$25$	1251.79	−	3852.61i	0.400572	−	1.23283i
$26$	2081.96	−	1512.64i	0.604004	−	0.438835i
$27$	−4112.14			−1.08557
$28$	809.691	+	2491.97i	0.195175	+	0.600687i
$29$	−290.273	+	210.895i	−0.0640931	+	0.0465664i	−0.619370	−	0.785099i	$-0.712612\pi$
$29$	−290.273	+	210.895i	−0.0640931	+	0.0465664i	0.555277	+	0.831665i	$0.312612\pi$
$30$	3639.82	+	2644.48i	0.738374	+	0.536460i
$31$	3070.49	+	2230.84i	0.573858	+	0.416932i	0.836504	−	0.547960i	$-0.184595\pi$
$31$	3070.49	+	2230.84i	0.573858	+	0.416932i	−0.262647	+	0.964892i	$0.584595\pi$
$32$	−1024.00			−0.176777
$33$	7696.89	+	5592.12i	1.23035	+	0.893905i
$34$	828.370	−	2549.46i	0.122893	−	0.378226i
$35$	4286.84	+	13193.5i	0.591516	+	1.82050i
$36$	863.402	−	627.298i	0.111034	−	0.0806710i
$37$	3819.44	−	2774.99i	0.458665	−	0.333240i	−0.334342	−	0.942452i	$-0.608514\pi$
$37$	3819.44	−	2774.99i	0.458665	−	0.333240i	0.793007	+	0.609212i	$0.208514\pi$
$38$	6087.06			0.683830
$39$	2639.75	+	8124.31i	0.277908	+	0.855313i
$40$	−5421.47			−0.535756
$41$	−8244.37	−	6920.01i	−0.765945	−	0.642906i
$41$	−8244.37	−	6920.01i	−0.765945	−	0.642906i
$42$	−8697.64			−0.760814
$43$	−4692.13	−	14440.9i	−0.386989	−	1.19103i	−0.935027	−	0.354577i	$-0.884625\pi$
$43$	−4692.13	−	14440.9i	−0.386989	−	1.19103i	0.548038	−	0.836454i	$-0.315375\pi$
$44$	−11464.4			−0.892733
$45$	4571.20	−	3321.17i	0.336511	−	0.244489i
$46$	14056.0	−	10212.3i	0.979418	−	0.711589i
$47$	−57.8927	−	178.175i	−0.00382278	−	0.0117653i	0.949127	−	0.314894i	$-0.101969\pi$
$47$	−57.8927	−	178.175i	−0.00382278	−	0.0117653i	−0.952950	+	0.303128i	$0.901969\pi$
$48$	1050.38	−	3232.74i	0.0658027	−	0.202520i
$49$	−8099.46	−	5884.60i	−0.481910	−	0.350128i
$50$	−16203.5			−0.916608
$51$	7198.86	+	5230.28i	0.387560	+	0.281579i
$52$	−8327.86	−	6050.54i	−0.427095	−	0.310303i
$53$	3508.79	−	2549.29i	0.171581	−	0.124661i	−0.498681	−	0.866786i	$-0.666182\pi$
$53$	3508.79	−	2549.29i	0.171581	−	0.124661i	0.670261	+	0.742125i	$0.266182\pi$
$54$	5082.88	+	15643.5i	0.237206	+	0.730045i
$55$	−60697.5			−2.70560
$56$	8479.20	−	6160.50i	0.361314	−	0.262510i
$57$	−6243.87	+	19216.7i	−0.254546	+	0.783413i
$58$	1161.09	+	843.582i	0.0453207	+	0.0329274i
$59$	−1913.27	−	5888.43i	−0.0715559	−	0.220226i	0.908883	−	0.417052i	$-0.136937\pi$
$59$	−1913.27	−	5888.43i	−0.0715559	−	0.220226i	−0.980439	+	0.196826i	$0.936937\pi$
$60$	5561.14	−	17115.4i	0.199428	−	0.613776i
$61$	−3187.05	+	9808.73i	−0.109664	+	0.337511i	−0.990797	−	0.135358i	$-0.956782\pi$
$61$	−3187.05	+	9808.73i	−0.109664	+	0.337511i	0.881133	+	0.472869i	$0.156782\pi$
$62$	4691.30	−	14438.3i	0.154994	−	0.477021i
$63$	−3375.47	+	10388.6i	−0.107148	+	0.329767i
$64$	1265.73	+	3895.53i	0.0386271	+	0.118882i
$65$	−44091.1	−	32034.0i	−1.29440	−	0.940434i
$66$	11759.8	−	36192.9i	0.332307	−	1.02274i
$67$	−43306.1	+	31463.7i	−1.17859	+	0.856294i	−0.992012	−	0.126146i	$-0.959739\pi$
$67$	−43306.1	+	31463.7i	−1.17859	+	0.856294i	−0.186577	+	0.982440i	$0.559739\pi$
$68$	−10722.6			−0.281209
$69$	17821.8	+	54849.9i	0.450639	+	1.38692i
$70$	44892.3	−	32616.2i	1.09503	−	0.795588i
$71$	40176.1	+	29189.6i	0.945849	+	0.687199i	0.949821	−	0.312793i	$-0.101265\pi$
$71$	40176.1	+	29189.6i	0.945849	+	0.687199i	−0.00397269	+	0.999992i	$0.501265\pi$
$72$	−3453.61	−	2509.19i	−0.0785130	−	0.0570430i
$73$	−88300.4			−1.93935			−0.969674	−	0.244403i	$-0.921408\pi$
$73$	−88300.4			−1.93935			−0.969674	+	0.244403i	$0.921408\pi$
$74$	−15277.8	−	11100.0i	−0.324325	−	0.235636i
$75$	16620.9	−	51154.0i	0.341195	−	1.05009i
$76$	−7524.02	−	23156.5i	−0.149422	−	0.459875i
$77$	94931.0	−	68971.4i	1.82466	−	1.32569i
$78$	27643.8	−	20084.4i	0.514471	−	0.373785i
$79$	67994.9			1.22577			0.612885	−	0.790172i	$-0.290009\pi$
$79$	67994.9			1.22577			0.612885	+	0.790172i	$0.290009\pi$
$80$	6701.31	+	20624.5i	0.117067	+	0.360295i
$81$	−38391.5			−0.650163
$82$	−16134.7	+	39917.0i	−0.264988	+	0.655577i
$83$	84673.1			1.34912			0.674559	−	0.738221i	$-0.264334\pi$
$83$	84673.1			1.34912			0.674559	+	0.738221i	$0.264334\pi$
$84$	10750.9	+	33087.8i	0.166244	+	0.511646i
$85$	−56770.1			−0.852260
$86$	−49136.6	+	35699.8i	−0.716406	+	0.520499i
$87$	−3854.17	+	2800.22i	−0.0545924	+	0.0396637i
$88$	14170.8	+	43613.4i	0.195069	+	0.600361i
$89$	−18886.0	+	58125.2i	−0.252735	+	0.777839i	0.741532	+	0.670917i	$0.234099\pi$
$89$	−18886.0	+	58125.2i	−0.252735	+	0.777839i	−0.994267	+	0.106922i	$0.965901\pi$
$90$	−18284.8	−	13284.7i	−0.237949	−	0.172880i
$91$	105359.			1.33373
$92$	−56224.1	−	40849.2i	−0.692553	−	0.503169i
$93$	40769.2	+	29620.6i	0.488793	+	0.355129i
$94$	−606.260	+	440.474i	−0.00707684	+	0.00514163i
$95$	−39835.2	−	122600.i	−0.452854	−	1.39374i
$96$	−13596.4			−0.150573
$97$	35023.8	−	25446.3i	0.377950	−	0.274596i	−0.382550	−	0.923935i	$-0.624954\pi$
$97$	35023.8	−	25446.3i	0.377950	−	0.274596i	0.760500	+	0.649338i	$0.224954\pi$
$98$	−12374.9	+	38086.0i	−0.130159	+	0.400590i
$99$	−38665.7	−	28092.3i	−0.396495	−	0.288071i
$100$	20028.6	+	61641.7i	0.200286	+	0.616417i
$101$	31709.5	−	97591.9i	0.309305	−	0.951942i	−0.668731	−	0.743504i	$-0.733162\pi$
$101$	31709.5	−	97591.9i	0.309305	−	0.951942i	0.978036	−	0.208437i	$-0.0668377\pi$
$102$	10998.9	−	33851.1i	0.104676	−	0.322160i
$103$	−58903.4	+	181286.i	−0.547075	+	1.68372i	0.168929	+	0.985628i	$0.445969\pi$
$103$	−58903.4	+	181286.i	−0.547075	+	1.68372i	−0.716004	+	0.698096i	$0.754031\pi$
$104$	−12723.8	+	39159.9i	−0.115355	+	0.355025i
$105$	56919.5	+	175180.i	0.503835	+	1.55064i
$106$	−14035.2	−	10197.2i	−0.121326	−	0.0881484i
$107$	33325.5	−	102565.i	0.281395	−	0.866046i	−0.706060	−	0.708152i	$-0.749529\pi$
$107$	33325.5	−	102565.i	0.281395	−	0.866046i	0.987456	−	0.157895i	$-0.0504706\pi$
$108$	53228.6	−	38672.9i	0.439123	−	0.319041i
$109$	59062.4			0.476151			0.238076	−	0.971247i	$-0.423483\pi$
$109$	59062.4			0.476151			0.238076	+	0.971247i	$0.423483\pi$
$110$	75026.2	+	230907.i	0.591196	+	1.81951i
$111$	50713.6	−	36845.6i	0.390676	−	0.283843i
$112$	−33916.8	−	24642.0i	−0.255488	−	0.185623i
$113$	41800.4	+	30369.8i	0.307953	+	0.223741i	0.731018	−	0.682359i	$-0.239046\pi$
$113$	41800.4	+	30369.8i	0.307953	+	0.223741i	−0.423065	+	0.906099i	$0.639046\pi$
$114$	80822.4			0.582465
$115$	−297673.	−	216272.i	−2.09892	−	1.52495i
$116$	1773.99	−	5459.78i	0.0122407	−	0.0376730i
$117$	−13260.9	−	40812.9i	−0.0895589	−	0.275634i
$118$	−20036.0	+	14557.0i	−0.132466	+	0.0962425i
$119$	88788.5	−	64508.6i	0.574764	−	0.417590i
$120$	−71984.9			−0.456340
$121$	108886.	+	335116.i	0.676094	+	2.08080i
$122$	41254.1			0.250938
$123$	−109467.	−	91882.2i	−0.652407	−	0.547607i
$124$	−60725.4			−0.354663
$125$	24236.6	+	74592.4i	0.138738	+	0.426992i
$126$	43693.0			0.245181
$127$	−143517.	+	104271.i	−0.789575	+	0.573660i	−0.907837	−	0.419323i	$-0.862268\pi$
$127$	−143517.	+	104271.i	−0.789575	+	0.573660i	0.118262	+	0.992982i	$0.462268\pi$
$128$	13254.9	−	9630.27i	0.0715077	−	0.0519534i
$129$	−62300.9	−	191742.i	−0.329625	−	1.01448i
$130$	−67365.2	+	207329.i	−0.349605	+	1.07597i
$131$	155813.	+	113204.i	0.793276	+	0.576349i	0.908934	−	0.416940i	$-0.136898\pi$
$131$	155813.	+	113204.i	0.793276	+	0.576349i	−0.115658	+	0.993289i	$0.536898\pi$
$132$	−152222.			−0.760401
$133$	201615.	+	146482.i	0.988310	+	0.718049i
$134$	173224.	+	125855.i	0.833388	+	0.605492i
$135$	281814.	−	204750.i	1.33085	−	0.966917i
$136$	13253.9	+	40791.4i	0.0614465	+	0.189113i
$137$	−95946.2			−0.436744			−0.218372	−	0.975866i	$-0.570075\pi$
$137$	−95946.2			−0.436744			−0.218372	+	0.975866i	$0.570075\pi$
$138$	186632.	−	135596.i	0.834237	−	0.606108i
$139$	123037.	−	378670.i	0.540133	−	1.66236i	−0.192157	−	0.981364i	$-0.561548\pi$
$139$	123037.	−	378670.i	0.540133	−	1.66236i	0.732290	−	0.680993i	$-0.238452\pi$
$140$	−179569.	−	130465.i	−0.774305	−	0.562565i
$141$	−768.684	−	2365.77i	−0.00325612	−	0.0100213i
$142$	61383.6	−	188919.i	0.255465	−	0.786240i
$143$	−142453.	+	438425.i	−0.582547	+	1.79290i
$144$	−5276.64	+	16239.8i	−0.0212056	+	0.0652642i
$145$	9392.22	−	28906.3i	0.0370978	−	0.114175i
$146$	109145.	+	335915.i	0.423763	+	1.30421i
$147$	−107543.	−	78134.3i	−0.410475	−	0.298228i
$148$	−23342.4	+	71840.4i	−0.0875972	+	0.269597i
$149$	119926.	−	87131.1i	0.442534	−	0.321520i	−0.344107	−	0.938930i	$-0.611818\pi$
$149$	119926.	−	87131.1i	0.442534	−	0.321520i	0.786641	+	0.617411i	$0.211818\pi$
$150$	−215146.			−0.780737
$151$	−108587.	−	334197.i	−0.387558	−	1.19278i	−0.934608	−	0.355681i	$-0.884249\pi$
$151$	−108587.	−	334197.i	−0.387558	−	1.19278i	0.547050	−	0.837100i	$-0.315751\pi$
$152$	−78792.5	+	57246.1i	−0.276615	+	0.200973i
$153$	−36163.9	−	26274.6i	−0.124895	−	0.0907418i
$154$	−379724.	−	275886.i	−1.29023	−	0.937405i
$155$	−321505.			−1.07488
$156$	−110575.	−	80337.6i	−0.363786	−	0.264306i
$157$	79406.5	−	244388.i	0.257103	−	0.791281i	−0.736305	−	0.676649i	$-0.763431\pi$
$157$	79406.5	−	244388.i	0.257103	−	0.791281i	0.993408	−	0.114631i	$-0.0365687\pi$
$158$	−84046.4	−	258668.i	−0.267841	−	0.824328i
$159$	46588.9	−	33848.8i	0.146147	−	0.106182i
$160$	70177.0	−	50986.6i	0.216718	−	0.157455i
$161$	711315.			2.16271
$162$	47454.5	+	146050.i	0.142066	+	0.437234i
$163$	−369893.			−1.09045			−0.545226	−	0.838289i	$-0.683556\pi$
$163$	−369893.			−1.09045			−0.545226	+	0.838289i	$0.683556\pi$
$164$	171797.	+	12039.9i	0.498777	+	0.0349552i
$165$	−805926.			−2.30454
$166$	−104662.	−	322115.i	−0.294793	−	0.907280i
$167$	257676.			0.714961			0.357480	−	0.933921i	$-0.383636\pi$
$167$	257676.			0.714961			0.357480	+	0.933921i	$0.383636\pi$
$168$	112585.	−	81797.5i	0.307756	−	0.223598i
$169$	−34482.1	+	25052.7i	−0.0928704	+	0.0674743i
$170$	70171.6	+	215966.i	0.186226	+	0.573143i
$171$	31366.4	−	96535.9i	0.0820304	−	0.252464i
$172$	196546.	+	142799.i	0.506575	+	0.368049i
$173$	−587655.			−1.49282			−0.746409	−	0.665487i	$-0.768224\pi$
$173$	−587655.			−1.49282			−0.746409	+	0.665487i	$0.768224\pi$
$174$	15416.7	+	11200.9i	0.0386027	+	0.0280465i
$175$	−536690.	−	389928.i	−1.32473	−	0.962475i
$176$	148399.	−	107818.i	0.361118	−	0.262368i
$177$	−25403.9	−	78185.1i	−0.0609490	−	0.187582i
$178$	244466.			0.578320
$179$	517642.	−	376089.i	1.20753	−	0.877320i	0.212523	−	0.977156i	$-0.431832\pi$
$179$	517642.	−	376089.i	1.20753	−	0.877320i	0.995004	+	0.0998366i	$0.0318320\pi$
$180$	−27936.7	+	85980.3i	−0.0642678	+	0.197796i
$181$	−34971.7	−	25408.4i	−0.0793452	−	0.0576477i	0.547405	−	0.836868i	$-0.315616\pi$
$181$	−34971.7	−	25408.4i	−0.0793452	−	0.0576477i	−0.626751	+	0.779220i	$0.715616\pi$
$182$	−130231.	−	400811.i	−0.291432	−	0.896934i
$183$	−42316.9	+	130238.i	−0.0934083	+	0.287481i
$184$	−85902.8	+	264382.i	−0.187052	+	0.575687i
$185$	−123584.	+	380352.i	−0.265481	+	0.817065i
$186$	62289.9	−	191708.i	0.132019	−	0.406311i
$187$	148388.	+	456690.i	0.310308	+	0.955031i
$188$	2425.04	+	1761.90i	0.00500408	+	0.00363568i
$189$	−208098.	+	640459.i	−0.423753	+	1.30418i
$190$	−417160.	+	303084.i	−0.838336	+	0.609087i
$191$	208894.			0.414327			0.207163	−	0.978306i	$-0.433577\pi$
$191$	208894.			0.414327			0.207163	+	0.978306i	$0.433577\pi$
$192$	16806.1	+	51723.8i	0.0329013	+	0.101260i
$193$	63714.2	−	46291.1i	0.123124	−	0.0894549i	−0.524519	−	0.851399i	$-0.675755\pi$
$193$	63714.2	−	46291.1i	0.123124	−	0.0894549i	0.647643	+	0.761944i	$0.275755\pi$
$194$	−140095.	−	101785.i	−0.267251	−	0.194169i
$195$	−585430.	−	425340.i	−1.10253	−	0.801032i
$196$	160184.			0.297837
$197$	863782.	+	627574.i	1.58576	+	1.15212i	0.909688	+	0.415291i	$0.136320\pi$
$197$	863782.	+	627574.i	1.58576	+	1.15212i	0.676075	+	0.736833i	$0.263680\pi$
$198$	−59076.0	+	181817.i	−0.107090	+	0.329588i
$199$	251032.	+	772597.i	0.449362	+	1.38299i	0.877629	+	0.479341i	$0.159124\pi$
$199$	251032.	+	772597.i	0.449362	+	1.38299i	−0.428267	+	0.903652i	$0.640876\pi$
$200$	209742.	−	152387.i	0.370776	−	0.269384i
$201$	−575007.	+	417767.i	−1.00388	+	0.729364i
$202$	−410457.			−0.707765
$203$	18157.2	+	55882.0i	0.0309249	+	0.0951770i
$204$	−142373.			−0.239525
$205$	909564.	+	63744.0i	1.51164	+	0.105939i
$206$	762461.			1.25184
$207$	−89528.8	−	275541.i	−0.145223	−	0.446952i
$208$	164701.			0.263960
$209$	−882141.	+	640913.i	−1.39692	+	1.01492i
$210$	596069.	−	433069.i	0.932713	−	0.677656i
$211$	−312019.	−	960296.i	−0.482475	−	1.48491i	−0.835605	−	0.549331i	$-0.814882\pi$
$211$	−312019.	−	960296.i	−0.482475	−	1.48491i	0.353129	−	0.935575i	$-0.385118\pi$
$212$	−21443.8	+	65997.4i	−0.0327690	+	0.100853i
$213$	533448.	+	387573.i	0.805644	+	0.585334i
$214$	−431374.			−0.643902
$215$	1.04060e6	+	756038.i	1.53528	+	1.11544i
$216$	−212914.	−	154691.i	−0.310507	−	0.225596i
$217$	502835.	−	365331.i	0.724897	−	0.526668i
$218$	−73005.2	−	224687.i	−0.104043	−	0.320211i
$219$	−1.17243e6			−1.65187
$220$	785684.	−	570833.i	1.09444	−	0.795156i
$221$	−133236.	+	410057.i	−0.183501	+	0.564759i
$222$	−202854.	−	147382.i	−0.276250	−	0.200707i
$223$	−196841.	−	605816.i	−0.265066	−	0.815790i	−0.991678	−	0.128742i	$-0.958906\pi$
$223$	−196841.	−	605816.i	−0.265066	−	0.815790i	0.726612	−	0.687048i	$-0.241094\pi$
$224$	−51820.2	+	159486.i	−0.0690048	+	0.212375i
$225$	−83496.1	+	256975.i	−0.109954	+	0.338403i
$226$	63865.3	−	196557.i	0.0831752	−	0.255987i
$227$	100865.	−	310432.i	0.129920	−	0.399854i	−0.864845	−	0.502039i	$-0.832583\pi$
$227$	100865.	−	310432.i	0.129920	−	0.399854i	0.994765	+	0.102185i	$0.0325834\pi$
$228$	−99902.0	−	307467.i	−0.127273	−	0.391707i
$229$	130375.	+	94723.3i	0.164288	+	0.119363i	0.666892	−	0.745155i	$-0.267624\pi$
$229$	130375.	+	94723.3i	0.164288	+	0.119363i	−0.502603	+	0.864517i	$0.667624\pi$
$230$	−454804.	+	1.39974e6i	−0.566898	+	1.74473i
$231$	1.26047e6	−	915785.i	1.55418	−	1.12918i
$232$	−22963.0			−0.0280097
$233$	−249917.	−	769165.i	−0.301582	−	0.928175i	−0.980931	−	0.194359i	$-0.937737\pi$
$233$	−249917.	−	769165.i	−0.301582	−	0.928175i	0.679348	−	0.733816i	$-0.262263\pi$
$234$	−138870.	+	100895.i	−0.165794	+	0.120456i
$235$	12839.2	+	9328.19i	0.0151658	+	0.0110186i
$236$	80144.0	+	58228.0i	0.0936679	+	0.0680537i
$237$	902820.			1.04407
$238$	−355154.	−	258034.i	−0.406419	−	0.295281i
$239$	−230717.	+	710073.i	−0.261267	+	0.804097i	0.731263	+	0.682095i	$0.238931\pi$
$239$	−230717.	+	710073.i	−0.261267	+	0.804097i	−0.992530	+	0.122001i	$0.961069\pi$
$240$	88978.3	+	273847.i	0.0997140	+	0.306888i
$241$	54255.3	−	39418.8i	0.0601727	−	0.0437180i	−0.557292	−	0.830316i	$-0.688160\pi$
$241$	54255.3	−	39418.8i	0.0601727	−	0.0437180i	0.617465	+	0.786598i	$0.288160\pi$
$242$	1.14027e6	−	828451.i	1.25161	−	0.909345i
$243$	489497.			0.531783
$244$	−50992.8	−	156940.i	−0.0548320	−	0.168756i
$245$	848078.			0.902653
$246$	−214232.	+	530008.i	−0.225708	+	0.558399i
$247$	−979046.			−1.02108
$248$	75060.8	+	231013.i	0.0774968	+	0.238511i
$249$	1.12427e6			1.14914
$250$	253808.	−	184403.i	0.256836	−	0.186602i
$251$	−310779.	+	225794.i	−0.311363	+	0.226219i	−0.732481	−	0.680787i	$-0.761638\pi$
$251$	−310779.	+	225794.i	−0.311363	+	0.226219i	0.421118	+	0.907006i	$0.361638\pi$
$252$	−54007.6	−	166218.i	−0.0535739	−	0.164884i
$253$	−961746.	+	2.95995e6i	−0.944625	+	2.90726i
$254$	574067.	+	417084.i	0.558314	+	0.405639i
$255$	−753778.			−0.725927
$256$	−53019.7	−	38521.1i	−0.0505636	−	0.0367366i
$257$	−713855.	−	518646.i	−0.674182	−	0.489822i	0.197240	−	0.980355i	$-0.436802\pi$
$257$	−713855.	−	518646.i	−0.674182	−	0.489822i	−0.871423	+	0.490533i	$0.836802\pi$
$258$	−652424.	+	474014.i	−0.610212	+	0.443345i
$259$	−238914.	−	735302.i	−0.221306	−	0.681109i
$260$	871993.			0.799981
$261$	19361.6	−	14067.0i	0.0175930	−	0.0127821i
$262$	238060.	−	732675.i	0.214257	−	0.659414i
$263$	137713.	+	100054.i	0.122768	+	0.0891962i	0.647475	−	0.762087i	$-0.275825\pi$
$263$	137713.	+	100054.i	0.122768	+	0.0891962i	−0.524707	+	0.851283i	$0.675825\pi$
$264$	188157.	+	579087.i	0.166154	+	0.511369i
$265$	−113532.	+	349417.i	−0.0993128	+	0.305653i
$266$	308040.	−	948049.i	0.266933	−	0.821536i
$267$	−250764.	+	771772.i	−0.215272	+	0.662538i
$268$	264663.	−	814550.i	0.225090	−	0.692757i
$269$	499300.	+	1.53669e6i	0.420708	+	1.29481i	0.907045	+	0.421034i	$0.138333\pi$
$269$	499300.	+	1.53669e6i	0.420708	+	1.29481i	−0.486337	+	0.873771i	$0.661667\pi$
$270$	−1.12726e6	−	819000.i	−0.941051	−	0.683714i
$271$	−524400.	+	1.61394e6i	−0.433750	+	1.33495i	0.460611	+	0.887602i	$0.347630\pi$
$271$	−524400.	+	1.61394e6i	−0.433750	+	1.33495i	−0.894362	+	0.447344i	$0.852370\pi$
$272$	138797.	−	100842.i	0.113752	−	0.0826453i
$273$	1.39893e6			1.13603
$274$	118596.	+	365001.i	0.0954320	+	0.293709i
$275$	2.34822e6	−	1.70608e6i	1.87244	−	1.36041i
$276$	−746530.	−	542385.i	−0.589894	−	0.428583i
$277$	−548689.	−	398646.i	−0.429662	−	0.312168i	0.351852	−	0.936056i	$-0.385552\pi$
$277$	−548689.	−	398646.i	−0.429662	−	0.312168i	−0.781514	+	0.623888i	$0.785552\pi$
$278$	−1.59263e6			−1.23596
$279$	−204806.	−	148801.i	−0.157519	−	0.114444i
$280$	−274357.	+	844386.i	−0.209133	+	0.643644i
$281$	−242814.	−	747306.i	−0.183446	−	0.564589i	0.816472	−	0.577385i	$-0.195927\pi$
$281$	−242814.	−	747306.i	−0.183446	−	0.564589i	−0.999918	+	0.0127959i	$0.995927\pi$
$282$	−8049.77	+	5848.50i	−0.00602782	+	0.00437947i
$283$	1.48741e6	−	1.08067e6i	1.10399	−	0.802094i	0.122282	−	0.992495i	$-0.460979\pi$
$283$	1.48741e6	−	1.08067e6i	1.10399	−	0.802094i	0.981706	+	0.190401i	$0.0609788\pi$
$284$	−794566.			−0.584567
$285$	−528922.	−	1.62785e6i	−0.385726	−	1.18714i
$286$	1.84395e6			1.33301
$287$	−1.49499e6	+	933854.i	−1.07136	+	0.669228i
$288$	68302.3			0.0485237
$289$	−299974.	−	923224.i	−0.211270	−	0.650223i
$290$	−121575.			−0.0848889
$291$	465037.	−	337869.i	0.321925	−	0.233892i
$292$	1.14298e6	−	830427.i	0.784483	−	0.569960i
$293$	−697599.	−	2.14699e6i	−0.474719	−	1.46104i	−0.846336	−	0.532650i	$-0.821196\pi$
$293$	−697599.	−	2.14699e6i	−0.474719	−	1.46104i	0.371616	−	0.928386i	$-0.378804\pi$
$294$	−164310.	+	505696.i	−0.110866	+	0.341209i
$295$	424315.	+	308283.i	0.283879	+	0.206250i
$296$	302150.			0.200444
$297$	−2.38374e6	−	1.73189e6i	−1.56808	−	1.13927i
$298$	−479703.	−	348525.i	−0.312919	−	0.227349i
$299$	−2.26078e6	+	1.64255e6i	−1.46245	+	1.06253i
$300$	265935.	+	818463.i	0.170597	+	0.525044i
$301$	−2.48659e6			−1.58193
$302$	−1.13714e6	+	826181.i	−0.717459	+	0.521264i
$303$	421031.	−	1.29580e6i	0.263456	−	0.810833i
$304$	315170.	+	228984.i	0.195596	+	0.142109i
$305$	−269977.	−	830903.i	−0.166179	−	0.511447i
$306$	−55253.5	+	170053.i	−0.0337331	+	0.103820i
$307$	318279.	−	979562.i	0.192736	−	0.593179i	−0.807260	−	0.590196i	$-0.799050\pi$
$307$	318279.	−	979562.i	0.192736	−	0.593179i	0.999996	−	0.00298310i	$-0.000949552\pi$
$308$	−580167.	+	1.78557e6i	−0.348478	+	1.07251i
$309$	−782104.	+	2.40707e6i	−0.465981	+	1.43414i
$310$	397402.	+	1.22308e6i	0.234869	+	0.722853i
$311$	−810221.	−	588660.i	−0.475010	−	0.345115i	0.324381	−	0.945927i	$-0.394844\pi$
$311$	−810221.	−	588660.i	−0.475010	−	0.345115i	−0.799391	+	0.600812i	$0.794844\pi$
$312$	−168944.	+	519956.i	−0.0982553	+	0.302399i
$313$	−1.20593e6	+	876157.i	−0.695761	+	0.505500i	−0.878549	−	0.477652i	$-0.841488\pi$
$313$	−1.20593e6	+	876157.i	−0.695761	+	0.505500i	0.182788	+	0.983152i	$0.441488\pi$
$314$	−1.02786e6			−0.588314
$315$	−285938.	−	880027.i	−0.162366	−	0.499712i
$316$	−880145.	+	639463.i	−0.495834	+	0.360245i
$317$	1.70884e6	+	1.24154e6i	0.955109	+	0.693927i	0.952010	−	0.306068i	$-0.0990135\pi$
$317$	1.70884e6	+	1.24154e6i	0.955109	+	0.693927i	0.00309905	+	0.999995i	$0.499014\pi$
$318$	−186356.	−	135395.i	−0.103341	−	0.0750819i
$319$	−257088.			−0.141451
$320$	−280708.	−	203946.i	−0.153243	−	0.111337i
$321$	442487.	−	1.36184e6i	0.239684	−	0.737670i
$322$	−879234.	−	2.70600e6i	−0.472569	−	1.45442i
$323$	−825063.	+	599443.i	−0.440028	+	0.319699i
$324$	496950.	−	361055.i	0.262996	−	0.191078i
$325$	2.60618e6			1.36866
$326$	457213.	+	1.40716e6i	0.238273	+	0.733328i
$327$	784216.			0.405570
$328$	−166550.	−	668437.i	−0.0854793	−	0.343065i
$329$	−30680.2			−0.0156268
$330$	996179.	+	3.06592e6i	0.503561	+	1.54980i
$331$	1.79434e6			0.900191			0.450095	−	0.892981i	$-0.351390\pi$
$331$	1.79434e6			0.900191			0.450095	+	0.892981i	$0.351390\pi$
$332$	−1.09603e6	+	796313.i	−0.545730	+	0.396496i
$333$	−254762.	+	185096.i	−0.125900	+	0.0914715i
$334$	−318505.	−	980256.i	−0.156225	−	0.480810i
$335$	1.40124e6	−	4.31256e6i	0.682180	−	2.09954i
$336$	−450339.	−	327190.i	−0.217616	−	0.158107i
$337$	1.93445e6			0.927860			0.463930	−	0.885872i	$-0.346439\pi$
$337$	1.93445e6			0.927860			0.463930	+	0.885872i	$0.346439\pi$
$338$	137928.	+	100211.i	0.0656693	+	0.0477115i
$339$	555015.	+	403242.i	0.262304	+	0.190575i
$340$	734847.	−	533898.i	0.344746	−	0.250473i
$341$	840362.	+	2.58637e6i	0.391363	+	1.20449i
$342$	−406015.			−0.187706
$343$	900320.	−	654121.i	0.413201	−	0.300208i
$344$	300296.	−	924217.i	0.136821	−	0.421093i
$345$	−3.95243e6	−	2.87161e6i	−1.78779	−	1.29891i
$346$	726381.	+	2.23557e6i	0.326193	+	1.00392i
$347$	−549174.	+	1.69018e6i	−0.244842	+	0.753547i	0.750820	+	0.660507i	$0.229658\pi$
$347$	−549174.	+	1.69018e6i	−0.244842	+	0.753547i	−0.995662	+	0.0930400i	$0.970342\pi$
$348$	23554.6	−	72493.5i	0.0104262	−	0.0320886i
$349$	969464.	−	2.98370e6i	0.426058	−	1.31127i	−0.475920	−	0.879488i	$-0.657885\pi$
$349$	969464.	−	2.98370e6i	0.426058	−	1.31127i	0.901978	−	0.431782i	$-0.142115\pi$
$350$	−819989.	+	2.52367e6i	−0.357798	+	1.10119i
$351$	−817534.	−	2.51611e6i	−0.354191	−	1.09009i
$352$	−593596.	−	431273.i	−0.255349	−	0.185522i
$353$	444017.	−	1.36654e6i	0.189654	−	0.583695i	−0.810343	−	0.585955i	$-0.800719\pi$
$353$	444017.	−	1.36654e6i	0.189654	−	0.583695i	0.999997	+	0.00225996i	$0.000719367\pi$
$354$	−266033.	+	193284.i	−0.112831	+	0.0819763i
$355$	−4.20676e6			−1.77164
$356$	−302176.	−	930004.i	−0.126368	−	0.388919i
$357$	1.17891e6	−	856529.i	0.489565	−	0.355690i
$358$	−2.07057e6	−	1.50436e6i	−0.853850	−	0.620359i
$359$	1.81772e6	+	1.32065e6i	0.744374	+	0.540820i	0.894078	−	0.447911i	$-0.147832\pi$
$359$	1.81772e6	+	1.32065e6i	0.744374	+	0.540820i	−0.149704	+	0.988731i	$0.547832\pi$
$360$	361620.			0.147061
$361$	129712.	+	94241.4i	0.0523857	+	0.0380604i
$362$	−53432.0	+	164447.i	−0.0214304	+	0.0659560i
$363$	1.44576e6	+	4.44958e6i	0.575875	+	1.77236i
$364$	−1.36380e6	+	990858.i	−0.539507	+	0.391975i
$365$	6.05143e6	−	4.39662e6i	2.37753	−	1.72738i
$366$	547761.			0.213741
$367$	−519372.	−	1.59846e6i	−0.201286	−	0.619494i	−0.999845	−	0.0175785i	$-0.994404\pi$
$367$	−519372.	−	1.59846e6i	−0.201286	−	0.619494i	0.798560	−	0.601916i	$-0.205596\pi$
$368$	1.11195e6			0.428021
$369$	549911.	+	461575.i	0.210245	+	0.176472i
$370$	1.59970e6			0.607485
$371$	−219482.	−	675497.i	−0.0827875	−	0.254794i
$372$	−806297.			−0.302091
$373$	1.17005e6	−	850088.i	0.435443	−	0.316368i	−0.348379	−	0.937354i	$-0.613268\pi$
$373$	1.17005e6	−	850088.i	0.435443	−	0.316368i	0.783821	+	0.620986i	$0.213268\pi$
$374$	1.55393e6	−	1.12900e6i	0.574452	−	0.417364i
$375$	321807.	+	990420.i	0.118173	+	0.363698i
$376$	3705.13	−	11403.2i	0.00135156	−	0.00415966i
$377$	−186751.	−	135682.i	−0.0676719	−	0.0491665i
$378$	2.69367e6			0.969650
$379$	2.26811e6	+	1.64788e6i	0.811086	+	0.589289i	0.914145	−	0.405387i	$-0.132863\pi$
$379$	2.26811e6	+	1.64788e6i	0.811086	+	0.589289i	−0.103059	+	0.994675i	$0.532863\pi$
$380$	1.66864e6	+	1.21234e6i	0.592793	+	0.430690i
$381$	−1.90558e6	+	1.38448e6i	−0.672534	+	0.488625i
$382$	−258208.	−	794681.i	−0.0905338	−	0.278634i
$383$	2.02146e6			0.704155			0.352077	−	0.935971i	$-0.385475\pi$
$383$	2.02146e6			0.704155			0.352077	+	0.935971i	$0.385475\pi$
$384$	175996.	−	127868.i	0.0609079	−	0.0442522i
$385$	−3.07164e6	+	9.45353e6i	−1.05613	+	3.25044i
$386$	−254857.	−	185164.i	−0.0870619	−	0.0632542i
$387$	312972.	+	963228.i	0.106225	+	0.326928i
$388$	−214046.	+	658767.i	−0.0721820	+	0.222153i
$389$	−966617.	+	2.97494e6i	−0.323877	+	0.996791i	0.648068	+	0.761583i	$0.275577\pi$
$389$	−966617.	+	2.97494e6i	−0.323877	+	0.996791i	−0.971945	+	0.235209i	$0.924423\pi$
$390$	−894458.	+	2.75286e6i	−0.297782	+	0.916478i
$391$	−899517.	+	2.76843e6i	−0.297555	+	0.915780i
$392$	−197998.	−	609375.i	−0.0650797	−	0.200295i
$393$	2.06884e6	+	1.50310e6i	0.675687	+	0.490915i
$394$	1.31974e6	−	4.06174e6i	0.428300	−	1.31817i
$395$	−4.65985e6	+	3.38558e6i	−1.50272	+	1.09179i
$396$	764695.			0.245048
$397$	−1.39905e6	−	4.30585e6i	−0.445511	−	1.37114i	−0.881922	−	0.471394i	$-0.843751\pi$
$397$	−1.39905e6	−	4.30585e6i	−0.445511	−	1.37114i	0.436412	−	0.899747i	$-0.356249\pi$
$398$	2.62884e6	−	1.90996e6i	0.831872	−	0.604390i
$399$	2.67699e6	+	1.94495e6i	0.841810	+	0.611611i
$400$	−838969.	−	609547.i	−0.262178	−	0.190483i
$401$	3.54701e6			1.10154			0.550771	−	0.834656i	$-0.314334\pi$
$401$	3.54701e6			1.10154			0.550771	+	0.834656i	$0.314334\pi$
$402$	2.30003e6	+	1.67107e6i	0.709853	+	0.515738i
$403$	−754551.	+	2.32227e6i	−0.231433	+	0.712279i
$404$	507352.	+	1.56147e6i	0.154652	+	0.475971i
$405$	2.63105e6	−	1.91157e6i	0.797062	−	0.579100i
$406$	190144.	−	138148.i	0.0572490	−	0.0415939i
$407$	3.38279e6			1.01225
$408$	175982.	+	541617.i	0.0523381	+	0.161080i
$409$	−5.75917e6			−1.70236			−0.851181	−	0.524873i	$-0.824113\pi$
$409$	−5.75917e6			−1.70236			−0.851181	+	0.524873i	$0.824113\pi$
$410$	−881786.	−	3.53898e6i	−0.259062	−	1.03972i
$411$	−1.27395e6			−0.372004
$412$	−942454.	−	2.90057e6i	−0.273538	−	0.841862i
$413$	−1.01394e6			−0.292506
$414$	−937557.	+	681175.i	−0.268842	+	0.195325i
$415$	−5.80283e6	+	4.21601e6i	−1.65394	+	1.20166i
$416$	−203581.	−	626559.i	−0.0576773	−	0.177512i
$417$	1.63366e6	−	5.02789e6i	0.460068	−	1.41594i
$418$	3.52857e6	+	2.56365e6i	0.987774	+	0.717660i
$419$	160652.			0.0447046			0.0223523	−	0.999750i	$-0.492884\pi$
$419$	160652.			0.0447046			0.0223523	+	0.999750i	$0.492884\pi$
$420$	−2.38428e6	−	1.73228e6i	−0.659528	−	0.479175i
$421$	−715010.	−	519485.i	−0.196611	−	0.142846i	0.485124	−	0.874445i	$-0.338774\pi$
$421$	−715010.	−	519485.i	−0.196611	−	0.142846i	−0.681735	+	0.731599i	$0.738774\pi$
$422$	−3.26751e6	+	2.37398e6i	−0.893172	+	0.648928i
$423$	3861.53	+	11884.6i	0.00104932	+	0.00322948i
$424$	277575.			0.0749835
$425$	2.19628e6	−	1.59569e6i	0.589815	−	0.428526i
$426$	815036.	−	2.50842e6i	0.217597	−	0.669694i
$427$	1.36641e6	+	992756.i	0.362670	+	0.263495i
$428$	533208.	+	1.64104e6i	0.140698	+	0.433023i
$429$	−1.89145e6	+	5.82130e6i	−0.496195	+	1.52713i
$430$	1.58989e6	−	4.89318e6i	0.414664	−	1.27620i
$431$	1.14951e6	−	3.53782e6i	0.298070	−	0.917365i	−0.684103	−	0.729385i	$-0.739806\pi$
$431$	1.14951e6	−	3.53782e6i	0.298070	−	0.917365i	0.982173	−	0.187980i	$-0.0601939\pi$
$432$	−325304.	+	1.00118e6i	−0.0838650	+	0.258110i
$433$	1.57141e6	+	4.83631e6i	0.402782	+	1.23964i	0.922733	+	0.385439i	$0.125950\pi$
$433$	1.57141e6	+	4.83631e6i	0.402782	+	1.23964i	−0.519951	+	0.854196i	$0.674050\pi$
$434$	−2.01134e6	−	1.46132e6i	−0.512579	−	0.372411i
$435$	124708.	−	383810.i	0.0315987	−	0.0972509i
$436$	−764520.	+	555456.i	−0.192607	+	0.139937i
$437$	−6.60986e6			−1.65573
$438$	1.44920e6	+	4.46019e6i	0.360948	+	1.11088i
$439$	3.90833e6	−	2.83956e6i	0.967898	−	0.703219i	0.0129262	−	0.999916i	$-0.495885\pi$
$439$	3.90833e6	−	2.83956e6i	0.967898	−	0.703219i	0.954971	+	0.296698i	$0.0958853\pi$
$440$	−3.14274e6	−	2.28333e6i	−0.773885	−	0.562260i
$441$	540246.	+	392512.i	0.132280	+	0.0961072i
$442$	1.72464e6			0.419896
$443$	−772496.	−	561251.i	−0.187020	−	0.135878i	0.490336	−	0.871534i	$-0.336874\pi$
$443$	−772496.	−	561251.i	−0.187020	−	0.135878i	−0.677355	+	0.735656i	$0.736874\pi$
$444$	−309934.	+	953879.i	−0.0746125	+	0.229634i
$445$	−1.59985e6	−	4.92382e6i	−0.382982	−	1.17870i
$446$	−2.06135e6	+	1.49766e6i	−0.490699	+	0.356513i
$447$	1.59234e6	−	1.15691e6i	0.376936	−	0.273860i
$448$	670775.			0.157900
$449$	286678.	+	882305.i	0.0671088	+	0.206539i	0.978988	−	0.203920i	$-0.0653683\pi$
$449$	286678.	+	882305.i	0.0671088	+	0.206539i	−0.911879	+	0.410460i	$0.865368\pi$
$450$	1.08080e6			0.251601
$451$	−1.86466e6	−	7.48365e6i	−0.431676	−	1.73250i
$452$	−826690.			−0.190325
$453$	−1.44179e6	−	4.43739e6i	−0.330109	−	1.01597i
$454$	−1.30563e6			−0.297290
$455$	−7.22051e6	+	5.24601e6i	−1.63508	+	1.18796i
$456$	−1.04619e6	+	760099.i	−0.235612	+	0.171182i
$457$	392005.	+	1.20647e6i	0.0878012	+	0.270224i	0.985311	−	0.170771i	$-0.0546257\pi$
$457$	392005.	+	1.20647e6i	0.0878012	+	0.270224i	−0.897510	+	0.440995i	$0.854626\pi$
$458$	199196.	−	613062.i	0.0443728	−	0.136565i
$459$	−2.22950e6	−	1.61983e6i	−0.493941	−	0.358869i
$460$	5.88711e6			1.29720
$461$	−1.14149e6	−	829344.i	−0.250162	−	0.181753i	0.455637	−	0.890166i	$-0.349412\pi$
$461$	−1.14149e6	−	829344.i	−0.250162	−	0.181753i	−0.705799	+	0.708413i	$0.749412\pi$
$462$	−5.04188e6	−	3.66314e6i	−1.09897	−	0.798451i
$463$	3.79432e6	−	2.75674e6i	0.822586	−	0.597644i	−0.0948658	−	0.995490i	$-0.530242\pi$
$463$	3.79432e6	−	2.75674e6i	0.822586	−	0.597644i	0.917452	+	0.397846i	$0.130242\pi$
$464$	28383.8	+	87356.4i	0.00612035	+	0.0188365i
$465$	−4.26886e6			−0.915546
$466$	−2.61716e6	+	1.90148e6i	−0.558298	+	0.405627i
$467$	−1.23320e6	+	3.79539e6i	−0.261662	+	0.805313i	0.730782	+	0.682611i	$0.239156\pi$
$467$	−1.23320e6	+	3.79539e6i	−0.261662	+	0.805313i	−0.992444	+	0.122701i	$0.960844\pi$
$468$	555480.	+	403580.i	0.117234	+	0.0851756i
$469$	2.70889e6	+	8.33710e6i	0.568668	+	1.75018i
$470$	19616.5	−	60373.3i	0.00409616	−	0.0126067i
$471$	1.05434e6	−	3.24492e6i	0.218992	−	0.673988i
$472$	122449.	−	376860.i	0.0252988	−	0.0778618i
$473$	3.36204e6	−	1.03473e7i	0.690956	−	2.12654i
$474$	−1.11595e6	−	3.43453e6i	−0.228138	−	0.702136i
$475$	4.98716e6	+	3.62339e6i	1.01419	+	0.736853i
$476$	−542627.	+	1.67003e6i	−0.109770	+	0.337838i
$477$	−234042.	+	170041.i	−0.0470974	+	0.0342183i
$478$	2.98646e6			0.597843
$479$	783230.	+	2.41053e6i	0.155973	+	0.480037i	0.998258	−	0.0589960i	$-0.0187899\pi$
$479$	783230.	+	2.41053e6i	0.155973	+	0.480037i	−0.842285	+	0.539033i	$0.818790\pi$
$480$	931793.	−	676987.i	0.184593	−	0.134115i
$481$	2.45729e6	+	1.78532e6i	0.484276	+	0.351847i
$482$	−217021.	−	157675.i	−0.0425485	−	0.0309133i
$483$	9.44466e6			1.84212
$484$	−4.56106e6	−	3.31381e6i	−0.885019	−	0.643004i
$485$	−1.13325e6	+	3.48778e6i	−0.218762	+	0.673279i
$486$	−605052.	−	1.86216e6i	−0.116199	−	0.357623i
$487$	449004.	−	326220.i	0.0857882	−	0.0623288i	−0.544064	−	0.839043i	$-0.683115\pi$
$487$	449004.	−	326220.i	0.0857882	−	0.0623288i	0.629853	+	0.776715i	$0.283115\pi$
$488$	−534004.	+	387976.i	−0.101507	+	0.0737489i
$489$	−4.91134e6			−0.928813
$490$	−1.04828e6	−	3.22628e6i	−0.197237	−	0.607033i
$491$	−4.16395e6			−0.779474			−0.389737	−	0.920926i	$-0.627434\pi$
$491$	−4.16395e6			−0.779474			−0.389737	+	0.920926i	$0.627434\pi$
$492$	2.28108e6	+	159862.i	0.424842	+	0.0297737i
$493$	−240453.			−0.0445567
$494$	1.21017e6	+	3.72451e6i	0.223115	+	0.686676i
$495$	4.04861e6			0.742665
$496$	786047.	−	571096.i	0.143464	−	0.104233i
$497$	6.57938e6	−	4.78020e6i	1.19480	−	0.868070i
$498$	−1.38967e6	−	4.27697e6i	−0.251095	−	0.772792i
$499$	−1.43149e6	+	4.40566e6i	−0.257357	+	0.792063i	0.735999	+	0.676982i	$0.236713\pi$
$499$	−1.43149e6	+	4.40566e6i	−0.257357	+	0.792063i	−0.993356	+	0.115081i	$0.963287\pi$
$500$	−1.01523e6	−	737611.i	−0.181611	−	0.131948i
$501$	3.42135e6			0.608981
$502$	1.24312e6	+	903177.i	0.220167	+	0.159961i
$503$	−4.32311e6	−	3.14092e6i	−0.761861	−	0.553525i	0.137619	−	0.990485i	$-0.456055\pi$
$503$	−4.32311e6	−	3.14092e6i	−0.761861	−	0.553525i	−0.899481	+	0.436961i	$0.856055\pi$
$504$	−565575.	+	410914.i	−0.0991776	+	0.0720567i
$505$	2.68613e6	+	8.26706e6i	0.468704	+	1.44252i
$506$	1.24491e7			2.16153
$507$	−457845.	+	332644.i	−0.0791040	+	0.0574724i
$508$	877096.	−	2.69943e6i	0.150795	−	0.464100i
$509$	−6.38623e6	−	4.63987e6i	−1.09257	−	0.793800i	−0.112740	−	0.993625i	$-0.535963\pi$
$509$	−6.38623e6	−	4.63987e6i	−1.09257	−	0.793800i	−0.979832	+	0.199825i	$0.935963\pi$
$510$	931721.	+	2.86754e6i	0.158621	+	0.488185i
$511$	−4.46851e6	+	1.37526e7i	−0.757025	+	2.32988i
$512$	−81007.0	+	249314.i	−0.0136568	+	0.0420312i
$513$	1.93374e6	−	5.95143e6i	0.324417	−	0.998454i
$514$	−1.09067e6	+	3.35675e6i	−0.182090	+	0.560417i
$515$	−4.98973e6	−	1.53568e7i	−0.829009	−	2.55143i
$516$	2.60969e6	+	1.89605e6i	0.431485	+	0.313492i
$517$	41481.7	−	127668.i	0.00682544	−	0.0210065i
$518$	−2.50194e6	+	1.81777e6i	−0.409688	+	0.297655i
$519$	−7.80273e6			−1.27154
$520$	−1.07784e6	−	3.31726e6i	−0.174802	−	0.537986i
$521$	−6.55700e6	+	4.76394e6i	−1.05830	+	0.768903i	−0.973774	−	0.227518i	$-0.926939\pi$
$521$	−6.55700e6	+	4.76394e6i	−1.05830	+	0.768903i	−0.0845305	+	0.996421i	$0.526939\pi$
$522$	−77446.4	−	56268.1i	−0.0124401	−	0.00903829i
$523$	−3.45800e6	−	2.51238e6i	−0.552803	−	0.401635i	0.276015	−	0.961153i	$-0.410986\pi$
$523$	−3.45800e6	−	2.51238e6i	−0.552803	−	0.401635i	−0.828818	+	0.559518i	$0.810986\pi$
$524$	−3.08152e6			−0.490272
$525$	−7.12603e6	−	5.17736e6i	−1.12836	−	0.819805i
$526$	210407.	−	647565.i	0.0331585	−	0.102051i
$527$	785986.	+	2.41902e6i	0.123279	+	0.379413i
$528$	1.97040e6	−	1.43158e6i	0.307589	−	0.223476i
$529$	−1.00562e7	+	7.30623e6i	−1.56240	+	1.13515i
$530$	1.46959e6			0.227252
$531$	127618.	+	392767.i	0.0196415	+	0.0604503i
$532$	−3.98735e6			−0.610809
$533$	2.59512e6	−	6.42028e6i	0.395675	−	0.978895i
$534$	3.24596e6			0.492594
$535$	2.82302e6	+	8.68836e6i	0.426412	+	1.31236i
$536$	−3.42587e6			−0.515062
$537$	6.87312e6	−	4.99361e6i	1.02853	−	0.747273i
$538$	5.22874e6	−	3.79890e6i	0.778827	−	0.565851i
$539$	−2.21674e6	−	6.82241e6i	−0.328656	−	1.01150i
$540$	−1.72229e6	+	5.30068e6i	−0.254169	+	0.782252i
$541$	−824447.	−	598996.i	−0.121107	−	0.0879895i	0.525583	−	0.850742i	$-0.323847\pi$
$541$	−824447.	−	598996.i	−0.121107	−	0.0879895i	−0.646690	+	0.762753i	$0.723847\pi$
$542$	6.78798e6			0.992527
$543$	−464346.	−	337367.i	−0.0675837	−	0.0491024i
$544$	−555187.	−	403367.i	−0.0804345	−	0.0584391i
$545$	−4.04768e6	+	2.94081e6i	−0.583734	+	0.424108i
$546$	−1.72918e6	−	5.32186e6i	−0.248232	−	0.763980i
$547$	−2.45025e6			−0.350140			−0.175070	−	0.984556i	$-0.556015\pi$
$547$	−2.45025e6			−0.350140			−0.175070	+	0.984556i	$0.556015\pi$
$548$	1.24195e6	−	902332.i	0.176666	−	0.128356i
$549$	212581.	−	654257.i	0.0301019	−	0.0926440i
$550$	−9.39289e6	−	6.82434e6i	−1.32401	−	0.961953i
$551$	−168725.	−	519281.i	−0.0236755	−	0.0728657i
$552$	−1.14060e6	+	3.51039e6i	−0.159325	+	0.490352i
$553$	3.44093e6	−	1.05901e7i	0.478479	−	1.47261i
$554$	−838323.	+	2.58009e6i	−0.116048	+	0.357158i
$555$	−1.64092e6	+	5.05022e6i	−0.226128	+	0.695950i
$556$	1.96860e6	+	6.05873e6i	0.270066	+	0.831179i
$557$	1.01660e7	+	7.38602e6i	1.38839	+	1.00872i	0.996040	+	0.0889077i	$0.0283376\pi$
$557$	1.01660e7	+	7.38602e6i	1.38839	+	1.00872i	0.392349	+	0.919816i	$0.371662\pi$
$558$	−312916.	+	963057.i	−0.0425444	+	0.130938i
$559$	7.90316e6	−	5.74199e6i	1.06972	−	0.777200i
$560$	3.55136e6			0.478547
$561$	1.97025e6	+	6.06381e6i	0.264311	+	0.813465i
$562$	−2.54278e6	+	1.84744e6i	−0.339601	+	0.246734i
$563$	−2.74494e6	−	1.99431e6i	−0.364974	−	0.265169i	0.390150	−	0.920751i	$-0.372423\pi$
$563$	−2.74494e6	−	1.99431e6i	−0.364974	−	0.265169i	−0.755124	+	0.655582i	$0.772423\pi$
$564$	32199.1	+	23394.0i	0.00426232	+	0.00309675i
$565$	−4.37683e6			−0.576818
$566$	−5.94964e6	−	4.32266e6i	−0.780638	−	0.567166i
$567$	−1.94283e6	+	5.97941e6i	−0.253791	+	0.781089i
$568$	982137.	+	3.02271e6i	0.127732	+	0.393120i
$569$	−3.08721e6	+	2.24299e6i	−0.399747	+	0.290433i	−0.769438	−	0.638722i	$-0.779464\pi$
$569$	−3.08721e6	+	2.24299e6i	−0.399747	+	0.290433i	0.369691	+	0.929155i	$0.379464\pi$
$570$	−5.53894e6	+	4.02428e6i	−0.714068	+	0.518801i
$571$	1.06121e7			1.36211			0.681056	−	0.732231i	$-0.261521\pi$
$571$	1.06121e7			1.36211			0.681056	+	0.732231i	$0.261521\pi$
$572$	−2.27925e6	−	7.01480e6i	−0.291274	−	0.896448i
$573$	2.77365e6			0.352910
$574$	5.40051e6	+	4.53298e6i	0.684155	+	0.574255i
$575$	1.75952e7			2.21934
$576$	−84426.3	−	259837.i	−0.0106028	−	0.0326321i
$577$	2.24485e6			0.280703			0.140351	−	0.990102i	$-0.455177\pi$
$577$	2.24485e6			0.280703			0.140351	+	0.990102i	$0.455177\pi$
$578$	−3.14137e6	+	2.28234e6i	−0.391110	+	0.284158i
$579$	845981.	−	614642.i	0.104873	−	0.0761948i
$580$	150276.	+	462501.i	0.0185489	+	0.0570877i
$581$	4.28494e6	−	1.31877e7i	0.526629	−	1.62080i
$582$	−1.86015e6	−	1.35148e6i	−0.227636	−	0.165387i
$583$	3.10766e6			0.378671
$584$	−4.57194e6	−	3.32171e6i	−0.554713	−	0.403023i
$585$	2.94094e6	+	2.13672e6i	0.355301	+	0.258141i
$586$	−7.30535e6	+	5.30765e6i	−0.878815	+	0.638496i
$587$	3.28874e6	+	1.01217e7i	0.393943	+	1.21243i	0.929781	+	0.368112i	$0.119996\pi$
$587$	3.28874e6	+	1.01217e7i	0.393943	+	1.21243i	−0.535838	+	0.844321i	$0.680004\pi$
$588$	2.12688e6			0.253688
$589$	−4.67257e6	+	3.39482e6i	−0.554967	+	0.403207i
$590$	648295.	−	1.99525e6i	0.0766731	−	0.235976i
$591$	1.14691e7	+	8.33277e6i	1.35070	+	0.981343i
$592$	−373478.	−	1.14945e6i	−0.0437986	−	0.134798i
$593$	2.11939e6	−	6.52280e6i	0.247499	−	0.761723i	−0.747716	−	0.664018i	$-0.768850\pi$
$593$	2.11939e6	−	6.52280e6i	0.247499	−	0.761723i	0.995215	−	0.0977053i	$-0.0311503\pi$
$594$	−3.64203e6	+	1.12090e7i	−0.423523	+	1.30347i
$595$	−2.87289e6	+	8.84184e6i	−0.332680	+	1.02388i
$596$	−732921.	+	2.25570e6i	−0.0845165	+	0.260115i
$597$	3.33314e6	+	1.02583e7i	0.382752	+	1.17799i
$598$	9.04312e6	+	6.57021e6i	1.03411	+	0.751323i
$599$	−3.19415e6	+	9.83059e6i	−0.363738	+	1.11947i	0.587030	+	0.809566i	$0.300297\pi$
$599$	−3.19415e6	+	9.83059e6i	−0.363738	+	1.11947i	−0.950768	+	0.309905i	$0.899703\pi$
$600$	2.78491e6	−	2.02335e6i	0.315815	−	0.229453i
$601$	−1.16922e6			−0.132041			−0.0660204	−	0.997818i	$-0.521030\pi$
$601$	−1.16922e6			−0.132041			−0.0660204	+	0.997818i	$0.521030\pi$
$602$	3.07360e6	+	9.45956e6i	0.345665	+	1.06385i
$603$	2.88858e6	−	2.09868e6i	0.323512	−	0.235046i
$604$	4.54856e6	+	3.30473e6i	0.507320	+	0.368590i
$605$	−2.41481e7	−	1.75446e7i	−2.68222	−	1.94875i
$606$	−5.44994e6			−0.602851
$607$	5.81208e6	+	4.22272e6i	0.640265	+	0.465180i	0.859941	−	0.510393i	$-0.170500\pi$
$607$	5.81208e6	+	4.22272e6i	0.640265	+	0.465180i	−0.219676	+	0.975573i	$0.570500\pi$
$608$	481537.	−	1.48202e6i	0.0528288	−	0.162590i
$609$	241086.	+	741987.i	0.0263408	+	0.0810687i
$610$	−2.82723e6	+	2.05411e6i	−0.307636	+	0.223511i
$611$	97511.2	−	70846.1i	0.0105670	−	0.00767737i
$612$	715216.			0.0771896
$613$	−291296.	−	896517.i	−0.0313100	−	0.0963624i	0.934180	−	0.356801i	$-0.116133\pi$
$613$	−291296.	−	896517.i	−0.0313100	−	0.0963624i	−0.965490	+	0.260439i	$0.916133\pi$
$614$	−4.11989e6			−0.441026
$615$	1.20770e7	+	846377.i	1.28757	+	0.0902352i
$616$	7.50983e6			0.797404
$617$	−339957.	−	1.04628e6i	−0.0359510	−	0.110646i	0.931471	−	0.363817i	$-0.118527\pi$
$617$	−339957.	−	1.04628e6i	−0.0359510	−	0.110646i	−0.967422	+	0.253171i	$0.918527\pi$
$618$	1.01238e7			1.06628
$619$	1.38238e6	−	1.00436e6i	0.145011	−	0.105357i	−0.512914	−	0.858440i	$-0.671434\pi$
$619$	1.38238e6	−	1.00436e6i	0.145011	−	0.105357i	0.657926	+	0.753083i	$0.271434\pi$
$620$	4.16165e6	−	3.02362e6i	0.434797	−	0.315898i
$621$	−5.51944e6	−	1.69871e7i	−0.574336	−	1.76762i
$622$	−1.23791e6	+	3.80989e6i	−0.128296	+	0.394854i
$623$	8.09717e6	+	5.88294e6i	0.835820	+	0.607259i
$624$	2.18686e6			0.224832
$625$	4.86626e6	+	3.53555e6i	0.498306	+	0.362040i
$626$	4.82371e6	+	3.50463e6i	0.491977	+	0.357442i
$627$	−1.17128e7	+	8.50988e6i	−1.18985	+	0.864480i
$628$	1.27050e6	+	3.91021e6i	0.128551	+	0.395640i
$629$	3.16391e6			0.318858
$630$	−2.99438e6	+	2.17555e6i	−0.300577	+	0.218382i
$631$	1.00802e6	−	3.10236e6i	0.100785	−	0.310184i	−0.887933	−	0.459972i	$-0.847859\pi$
$631$	1.00802e6	−	3.10236e6i	0.100785	−	0.310184i	0.988718	+	0.149789i	$0.0478593\pi$
$632$	3.52058e6	+	2.55785e6i	0.350608	+	0.254731i
$633$	−4.14291e6	−	1.27506e7i	−0.410957	−	1.26480i
$634$	2.61087e6	−	8.03544e6i	0.257966	−	0.793938i
$635$	4.64371e6	−	1.42919e7i	0.457015	−	1.40655i
$636$	−284726.	+	876296.i	−0.0279116	+	0.0859030i
$637$	1.99038e6	−	6.12577e6i	0.194352	−	0.598153i
$638$	317778.	+	978021.i	0.0309081	+	0.0951254i
$639$	−2.67980e6	−	1.94699e6i	−0.259627	−	0.188630i
$640$	−428884.	+	1.31997e6i	−0.0413895	+	0.127384i
$641$	4.36261e6	−	3.16962e6i	0.419374	−	0.304693i	−0.358012	−	0.933717i	$-0.616545\pi$
$641$	4.36261e6	−	3.16962e6i	0.419374	−	0.304693i	0.777386	+	0.629024i	$0.216545\pi$
$642$	−5.72768e6			−0.548455
$643$	−4.85057e6	−	1.49285e7i	−0.462663	−	1.42393i	−0.861898	−	0.507082i	$-0.830724\pi$
$643$	−4.85057e6	−	1.49285e7i	−0.462663	−	1.42393i	0.399234	−	0.916849i	$-0.369276\pi$
$644$	−9.20746e6	+	6.68961e6i	−0.874833	+	0.635603i
$645$	1.38168e7	+	1.00385e7i	1.30770	+	0.950099i
$646$	3.30025e6	+	2.39777e6i	0.311147	+	0.226062i
$647$	−5.60404e6			−0.526309			−0.263154	−	0.964754i	$-0.584763\pi$
$647$	−5.60404e6			−0.526309			−0.263154	+	0.964754i	$0.584763\pi$
$648$	−1.98780e6	−	1.44422e6i	−0.185967	−	0.135113i
$649$	1.37091e6	−	4.21923e6i	0.127761	−	0.393207i
$650$	−3.22141e6	−	9.91449e6i	−0.299063	−	0.920422i
$651$	6.67651e6	−	4.85077e6i	0.617444	−	0.448599i
$652$	4.78799e6	−	3.47868e6i	0.441097	−	0.320476i
$653$	1.14685e7			1.05250			0.526251	−	0.850329i	$-0.323597\pi$
$653$	1.14685e7			1.05250			0.526251	+	0.850329i	$0.323597\pi$
$654$	−969344.	−	2.98333e6i	−0.0886204	−	0.272745i
$655$	−1.63148e7			−1.48586
$656$	−2.33702e6	+	1.45983e6i	−0.212032	+	0.132447i
$657$	5.88977e6			0.532334
$658$	37922.8	+	116714.i	0.00341457	+	0.0105090i
$659$	−1.47645e7			−1.32435			−0.662177	−	0.749348i	$-0.730367\pi$
$659$	−1.47645e7			−1.32435			−0.662177	+	0.749348i	$0.730367\pi$
$660$	1.04321e7	−	7.57938e6i	0.932208	−	0.677289i
$661$	7.91305e6	−	5.74917e6i	0.704434	−	0.511801i	−0.176939	−	0.984222i	$-0.556620\pi$
$661$	7.91305e6	−	5.74917e6i	0.704434	−	0.511801i	0.881373	+	0.472420i	$0.156620\pi$
$662$	−2.21793e6	−	6.82607e6i	−0.196699	−	0.605377i
$663$	−1.76907e6	+	5.44463e6i	−0.156301	+	0.481044i
$664$	4.38412e6	+	3.18525e6i	0.385889	+	0.280365i
$665$	−2.11107e7			−1.85118
$666$	1.01905e6	+	740383.i	0.0890245	+	0.0646801i
$667$	−1.26081e6	−	916035.i	−0.109733	−	0.0797256i
$668$	−3.33542e6	+	2.42333e6i	−0.289208	+	0.210122i
$669$	−2.61361e6	−	8.04387e6i	−0.225775	−	0.694864i
$670$	−1.81380e7			−1.56100
$671$	−5.97857e6	+	4.34369e6i	−0.512615	+	0.372436i
$672$	−688056.	+	2.11762e6i	−0.0587761	+	0.180894i
$673$	9.53158e6	+	6.92510e6i	0.811199	+	0.589370i	0.914178	−	0.405313i	$-0.132837\pi$
$673$	9.53158e6	+	6.92510e6i	0.811199	+	0.589370i	−0.102979	+	0.994684i	$0.532837\pi$
$674$	−2.39111e6	−	7.35908e6i	−0.202745	−	0.623985i
$675$	−5.14753e6	+	1.58425e7i	−0.434850	+	1.33833i
$676$	210736.	−	648579.i	0.0177367	−	0.0545878i
$677$	369844.	−	1.13826e6i	0.0310133	−	0.0954490i	−0.934352	−	0.356352i	$-0.884020\pi$
$677$	369844.	−	1.13826e6i	0.0310133	−	0.0954490i	0.965365	+	0.260903i	$0.0840203\pi$
$678$	847987.	−	2.60984e6i	0.0708460	−	0.218041i
$679$	−2.19081e6	−	6.74263e6i	−0.182360	−	0.561248i
$680$	−2.93939e6	−	2.13559e6i	−0.243772	−	0.177111i
$681$	1.33926e6	−	4.12183e6i	0.110662	−	0.340583i
$682$	8.80038e6	−	6.39385e6i	0.724504	−	0.526383i
$683$	−1.33908e7			−1.09839			−0.549194	−	0.835695i	$-0.685065\pi$
$683$	−1.33908e7			−1.09839			−0.549194	+	0.835695i	$0.685065\pi$
$684$	501863.	+	1.54457e6i	0.0410152	+	0.126232i
$685$	6.57541e6	−	4.77732e6i	0.535422	−	0.389007i
$686$	−3.60128e6	−	2.61648e6i	−0.292178	−	0.212279i
$687$	1.73109e6	+	1.25771e6i	0.139936	+	0.101669i
$688$	−3.88712e6			−0.313081
$689$	2.25743e6	+	1.64012e6i	0.181161	+	0.131621i
$690$	−6.03878e6	+	1.85854e7i	−0.482866	+	1.48611i
$691$	−2.62638e6	−	8.08317e6i	−0.209249	−	0.644001i	−0.999512	−	0.0312340i	$-0.990056\pi$
$691$	−2.62638e6	−	8.08317e6i	−0.209249	−	0.644001i	0.790263	−	0.612767i	$-0.209944\pi$
$692$	7.60677e6	−	5.52664e6i	0.603858	−	0.438728i
$693$	−6.33203e6	+	4.60049e6i	−0.500853	+	0.363891i
$694$	7.10866e6			0.560259
$695$	1.04226e7	+	3.20774e7i	0.818489	+	2.51905i
$696$	−304897.			−0.0238578
$697$	−1.74401e6	−	6.99943e6i	−0.135977	−	0.545733i
$698$	−1.25490e7			−0.974924
$699$	−3.31833e6	−	1.02128e7i	−0.256878	−	0.790589i
$700$	1.06142e7			0.818730
$701$	5.73911e6	−	4.16971e6i	0.441113	−	0.320487i	−0.344964	−	0.938616i	$-0.612109\pi$
$701$	5.73911e6	−	4.16971e6i	0.441113	−	0.320487i	0.786077	+	0.618129i	$0.212109\pi$
$702$	−8.56132e6	+	6.22017e6i	−0.655689	+	0.476386i
$703$	2.22010e6	+	6.83276e6i	0.169427	+	0.521444i
$704$	−906934.	+	2.79125e6i	−0.0689674	+	0.212260i
$705$	170475.	+	123857.i	0.0129178	+	0.00938532i
$706$	−5.74747e6			−0.433975
$707$	−1.35951e7	−	9.87741e6i	−1.02290	−	0.743181i
$708$	1.06413e6	+	773137.i	0.0797833	+	0.0579660i
$709$	−5.05437e6	+	3.67222e6i	−0.377617	+	0.274355i	−0.760362	−	0.649499i	$-0.774979\pi$
$709$	−5.05437e6	+	3.67222e6i	−0.377617	+	0.274355i	0.382745	+	0.923854i	$0.374979\pi$
$710$	5.19984e6	+	1.60034e7i	0.387118	+	1.19143i
$711$	−4.53536e6			−0.336463
$712$	−3.16443e6	+	2.29910e6i	−0.233935	+	0.169964i
$713$	−5.09422e6	+	1.56784e7i	−0.375279	+	1.15499i
$714$	−4.71564e6	−	3.42612e6i	−0.346175	−	0.251511i
$715$	−1.20673e7	−	3.71392e7i	−0.882762	−	2.71686i
$716$	−3.16355e6	+	9.73639e6i	−0.230617	+	0.709766i
$717$	−3.06340e6	+	9.42817e6i	−0.222539	+	0.684904i
$718$	2.77723e6	−	8.54744e6i	0.201049	−	0.618764i
$719$	−252412.	+	776846.i	−0.0182091	+	0.0560419i	−0.959748	−	0.280862i	$-0.909380\pi$
$719$	−252412.	+	776846.i	−0.0182091	+	0.0560419i	0.941539	+	0.336904i	$0.109380\pi$
$720$	−446987.	−	1.37568e6i	−0.0321339	−	0.0988980i
$721$	2.52541e7	+	1.83482e7i	1.80923	+	1.31448i
$722$	198182.	−	609943.i	0.0141489	−	0.0435458i
$723$	720388.	−	523393.i	0.0512532	−	0.0372376i
$724$	691639.			0.0490380
$725$	449138.	+	1.38230e6i	0.0317347	+	0.0976694i
$726$	1.51402e7	−	1.10000e7i	1.06608	−	0.774551i
$727$	−3.79436e6	−	2.75676e6i	−0.266258	−	0.193448i	0.446644	−	0.894712i	$-0.352619\pi$
$727$	−3.79436e6	−	2.75676e6i	−0.266258	−	0.193448i	−0.712901	+	0.701264i	$0.752619\pi$
$728$	5.45520e6	+	3.96343e6i	0.381489	+	0.277168i
$729$	1.58285e7			1.10312
$730$	−2.42057e7	−	1.75865e7i	−1.68117	−	1.22144i
$731$	3.14450e6	−	9.67778e6i	0.217650	−	0.669858i
$732$	−677070.	−	2.08381e6i	−0.0467042	−	0.143741i
$733$	−2.15816e6	+	1.56800e6i	−0.148363	+	0.107792i	−0.659490	−	0.751713i	$-0.729228\pi$
$733$	−2.15816e6	+	1.56800e6i	−0.148363	+	0.107792i	0.511128	+	0.859505i	$0.329228\pi$
$734$	−5.43893e6	+	3.95162e6i	−0.372626	+	0.270729i
$735$	1.12606e7			0.768851
$736$	−1.37444e6	−	4.23011e6i	−0.0935261	−	0.287844i
$737$	−3.83552e7			−2.60109
$738$	1.07621e6	−	2.66252e6i	0.0727370	−	0.179950i
$739$	−1.68584e7			−1.13555			−0.567773	−	0.823185i	$-0.692195\pi$
$739$	−1.68584e7			−1.13555			−0.567773	+	0.823185i	$0.692195\pi$
$740$	−1.97734e6	−	6.08564e6i	−0.132740	−	0.408533i
$741$	−1.29995e7			−0.869725
$742$	−2.29845e6	+	1.66992e6i	−0.153259	+	0.111349i
$743$	2.28349e7	−	1.65906e7i	1.51750	−	1.10253i	0.554786	−	0.831993i	$-0.312800\pi$
$743$	2.28349e7	−	1.65906e7i	1.51750	−	1.10253i	0.962711	−	0.270533i	$-0.0871998\pi$
$744$	996638.	+	3.06734e6i	0.0660093	+	0.203156i
$745$	−3.88038e6	+	1.19426e7i	−0.256144	+	0.788329i
$746$	−4.68018e6	−	3.40035e6i	−0.307904	−	0.223706i
$747$	−5.64781e6			−0.370322
$748$	−6.21574e6	−	4.51600e6i	−0.406199	−	0.295121i
$749$	−1.42879e7	−	1.03808e7i	−0.930603	−	0.676123i
$750$	3.37000e6	−	2.44845e6i	0.218765	−	0.158942i
$751$	−6.82732e6	−	2.10123e7i	−0.441723	−	1.35948i	−0.886037	−	0.463614i	$-0.846553\pi$
$751$	−6.82732e6	−	2.10123e7i	−0.441723	−	1.35948i	0.444314	−	0.895871i	$-0.353447\pi$
$752$	−47960.2			−0.00309269
$753$	−4.12645e6	+	2.99804e6i	−0.265209	+	0.192686i
$754$	−285329.	+	878154.i	−0.0182776	+	0.0562526i
$755$	2.40820e7	+	1.74966e7i	1.53753	+	1.11708i
$756$	−3.32956e6	−	1.02473e7i	−0.211876	−	0.652089i
$757$	1.43501e6	−	4.41650e6i	0.0910154	−	0.280117i	−0.895179	−	0.445706i	$-0.852953\pi$
$757$	1.43501e6	−	4.41650e6i	0.0910154	−	0.280117i	0.986195	+	0.165589i	$0.0529526\pi$
$758$	3.46537e6	−	1.06653e7i	0.219067	−	0.674219i
$759$	−1.27698e7	+	3.93015e7i	−0.804601	+	2.47631i
$760$	2.54945e6	−	7.84641e6i	0.160108	−	0.492762i
$761$	6.34935e6	+	1.95413e7i	0.397437	+	1.22318i	0.927048	+	0.374944i	$0.122338\pi$
$761$	6.34935e6	+	1.95413e7i	0.397437	+	1.22318i	−0.529611	+	0.848241i	$0.677662\pi$
$762$	7.62232e6	+	5.53794e6i	0.475554	+	0.345510i
$763$	2.98890e6	−	9.19887e6i	0.185866	−	0.572036i
$764$	−2.70398e6	+	1.96456e6i	−0.167599	+	0.121768i
$765$	3.78664e6			0.233938
$766$	−2.49866e6	−	7.69009e6i	−0.153863	−	0.473543i
$767$	3.22260e6	−	2.34136e6i	0.197796	−	0.143707i
$768$	−703983.	−	511473.i	−0.0430684	−	0.0312910i
$769$	−5.07712e6	−	3.68874e6i	−0.309600	−	0.224938i	0.422125	−	0.906538i	$-0.361284\pi$
$769$	−5.07712e6	−	3.68874e6i	−0.309600	−	0.224938i	−0.731725	+	0.681600i	$0.761284\pi$
$770$	3.97601e7			2.41669
$771$	−9.47839e6	−	6.88645e6i	−0.574247	−	0.417215i
$772$	−389387.	+	1.19841e6i	−0.0235146	+	0.0723706i
$773$	7.92810e6	+	2.44002e7i	0.477222	+	1.46874i	0.842938	+	0.538011i	$0.180824\pi$
$773$	7.92810e6	+	2.44002e7i	0.477222	+	1.46874i	−0.365716	+	0.930726i	$0.619176\pi$
$774$	3.27748e6	−	2.38123e6i	0.196647	−	0.142873i
$775$	1.24382e7	−	9.03687e6i	0.743880	−	0.540460i
$776$	2.77067e6			0.165170
$777$	−3.17224e6	−	9.76316e6i	−0.188501	−	0.580146i
$778$	1.25121e7			0.741110
$779$	1.38921e7	−	8.67779e6i	0.820211	−	0.512349i
$780$	1.15781e7			0.681398
$781$	1.09958e7	+	3.38415e7i	0.645057	+	1.98528i
$782$	1.16436e7			0.680879
$783$	1.19364e6	−	867231.i	0.0695776	−	0.0505511i
$784$	−2.07346e6	+	1.50646e6i	−0.120478	+	0.0875320i
$785$	6.72656e6	+	2.07022e7i	0.389600	+	1.19907i
$786$	3.16091e6	−	9.72827e6i	0.182497	−	0.561667i
$787$	686422.	+	498715.i	0.0395052	+	0.0287022i	0.607363	−	0.794425i	$-0.292228\pi$
$787$	686422.	+	498715.i	0.0395052	+	0.0287022i	−0.567857	+	0.823127i	$0.692228\pi$
$788$	−1.70831e7			−0.980056
$789$	1.82852e6	+	1.32850e6i	0.104570	+	0.0759744i
$790$	1.86394e7	+	1.35423e7i	1.06259	+	0.772014i
$791$	6.84538e6	−	4.97346e6i	0.389006	−	0.282629i
$792$	−945215.	−	2.90907e6i	−0.0535449	−	0.164794i
$793$	−6.63533e6			−0.374696
$794$	−1.46511e7	+	1.06446e7i	−0.824743	+	0.599211i
$795$	−1.50746e6	+	4.63947e6i	−0.0845915	+	0.260346i
$796$	−1.05154e7	−	7.63985e6i	−0.588222	−	0.427368i
$797$	1.06537e7	+	3.27888e7i	0.594095	+	1.82844i	0.559180	+	0.829046i	$0.311116\pi$
$797$	1.06537e7	+	3.27888e7i	0.594095	+	1.82844i	0.0349155	+	0.999390i	$0.488884\pi$
$798$	4.09007e6	−	1.25880e7i	0.227365	−	0.699758i
$799$	38797.7	−	119407.i	0.00215000	−	0.00661702i
$800$	−1.28183e6	+	3.94507e6i	−0.0708118	+	0.217936i
$801$	1.25973e6	−	3.87704e6i	0.0693737	−	0.213510i
$802$	−4.38434e6	−	1.34936e7i	−0.240696	−	0.740785i
$803$	−5.11863e7	−	3.71890e7i	−2.80133	−	2.03529i
$804$	3.51413e6	−	1.08154e7i	0.191725	−	0.590068i
$805$	−4.87480e7	+	3.54175e7i	−2.65135	+	1.92632i
$806$	9.76712e6			0.529577
$807$	6.62958e6	+	2.04037e7i	0.358345	+	1.10287i
$808$	5.31306e6	−	3.86017e6i	0.286297	−	0.208007i
$809$	−2.42833e7	−	1.76428e7i	−1.30447	−	0.947757i	−0.304486	−	0.952517i	$-0.598485\pi$
$809$	−2.42833e7	−	1.76428e7i	−1.30447	−	0.947757i	−0.999989	+	0.00476017i	$0.998485\pi$
$810$	−1.05242e7	−	7.64629e6i	−0.563608	−	0.409485i
$811$	1.02085e7			0.545018			0.272509	−	0.962153i	$-0.412146\pi$
$811$	1.02085e7			0.545018			0.272509	+	0.962153i	$0.412146\pi$
$812$	−760577.	−	552592.i	−0.0404812	−	0.0294113i
$813$	−6.96286e6	+	2.14295e7i	−0.369455	+	1.13706i
$814$	−4.18136e6	−	1.28689e7i	−0.221186	−	0.680739i
$815$	2.53496e7	−	1.84176e7i	1.33683	−	0.971265i
$816$	1.84291e6	−	1.33895e6i	0.0968899	−	0.0703946i
$817$	2.31065e7			1.21110
$818$	7.11873e6	+	2.19092e7i	0.371980	+	1.14484i
$819$	−7.02762e6			−0.366099
$820$	−1.23731e7	+	7.72893e6i	−0.642606	+	0.401407i
$821$	1.03883e7			0.537881			0.268940	−	0.963157i	$-0.413327\pi$
$821$	1.03883e7			0.537881			0.268940	+	0.963157i	$0.413327\pi$
$822$	1.57469e6	+	4.84639e6i	0.0812859	+	0.250172i
$823$	2.97682e7			1.53198			0.765990	−	0.642853i	$-0.222249\pi$
$823$	2.97682e7			1.53198			0.765990	+	0.642853i	$0.222249\pi$
$824$	−9.86950e6	+	7.17061e6i	−0.506381	+	0.367907i
$825$	3.11791e7	−	2.26530e7i	1.59488	−	1.15875i
$826$	1.25329e6	+	3.85724e6i	0.0639150	+	0.196710i
$827$	9.82551e6	−	3.02398e7i	0.499564	−	1.53750i	−0.310156	−	0.950686i	$-0.600381\pi$
$827$	9.82551e6	−	3.02398e7i	0.499564	−	1.53750i	0.809721	−	0.586816i	$-0.199619\pi$
$828$	3.75023e6	+	2.72470e6i	0.190100	+	0.138116i
$829$	−1.51005e7			−0.763142			−0.381571	−	0.924340i	$-0.624617\pi$
$829$	−1.51005e7			−0.763142			−0.381571	+	0.924340i	$0.624617\pi$
$830$	2.32113e7	+	1.68640e7i	1.16951	+	0.849701i
$831$	−7.28536e6	−	5.29312e6i	−0.365972	−	0.265894i
$832$	−2.13193e6	+	1.54894e6i	−0.106774	+	0.0775758i
$833$	−2.07330e6	−	6.38097e6i	−0.103526	−	0.318621i
$834$	−2.11465e7			−1.05275
$835$	−1.76591e7	+	1.28301e7i	−0.876501	+	0.636815i
$836$	5.39117e6	−	1.65923e7i	0.266789	−	0.821091i
$837$	−1.26263e7	−	9.17354e6i	−0.622963	−	0.452609i
$838$	−198577.	−	611158.i	−0.00976831	−	0.0300638i
$839$	−1.08910e6	+	3.35191e6i	−0.0534150	+	0.164394i	−0.974205	−	0.225663i	$-0.927545\pi$
$839$	−1.08910e6	+	3.35191e6i	−0.0534150	+	0.164394i	0.920790	+	0.390058i	$0.127545\pi$
$840$	−3.64285e6	+	1.12115e7i	−0.178132	+	0.548235i
$841$	−6.29851e6	+	1.93848e7i	−0.307077	+	0.945087i
$842$	−1.09244e6	+	3.36218e6i	−0.0531027	+	0.163433i
$843$	−3.22403e6	−	9.92253e6i	−0.156253	−	0.480899i
$844$	1.30700e7	+	9.49593e6i	0.631568	+	0.458861i
$845$	1.11572e6	−	3.43384e6i	0.0537544	−	0.165439i
$846$	40438.4	−	29380.2i	0.00194253	−	0.00141133i
$847$	5.77039e7			2.76374
$848$	−343101.	−	1.05596e6i	−0.0163845	−	0.0504263i
$849$	1.97494e7	−	1.43488e7i	0.940342	−	0.683198i
$850$	−8.78513e6	−	6.38277e6i	−0.417062	−	0.303013i
$851$	1.65899e7	+	1.20533e7i	0.785274	+	0.570535i
$852$	−1.05500e7			−0.497915
$853$	−4.80793e6	−	3.49317e6i	−0.226248	−	0.164379i	0.468886	−	0.883258i	$-0.344655\pi$
$853$	−4.80793e6	−	3.49317e6i	−0.226248	−	0.164379i	−0.695135	+	0.718879i	$0.744655\pi$
$854$	2.08769e6	−	6.42525e6i	0.0979538	−	0.301471i
$855$	2.65707e6	+	8.17761e6i	0.124305	+	0.382570i
$856$	5.58382e6	−	4.05689e6i	0.260464	−	0.189238i
$857$	1.49487e7	−	1.08609e7i	0.695267	−	0.505141i	−0.183121	−	0.983090i	$-0.558620\pi$
$857$	1.49487e7	−	1.08609e7i	0.695267	−	0.505141i	0.878387	+	0.477950i	$0.158620\pi$
$858$	2.44835e7			1.13542
$859$	1.06067e7	+	3.26440e7i	0.490452	+	1.50946i	0.823926	+	0.566697i	$0.191779\pi$
$859$	1.06067e7	+	3.26440e7i	0.490452	+	1.50946i	−0.333474	+	0.942759i	$0.608221\pi$
$860$	−2.05800e7			−0.948853
$861$	−1.98501e7	+	1.23995e7i	−0.912548	+	0.570027i
$862$	−1.48795e7			−0.682057
$863$	−2.51404e6	−	7.73742e6i	−0.114907	−	0.353647i	0.877021	−	0.480452i	$-0.159527\pi$
$863$	−2.51404e6	−	7.73742e6i	−0.114907	−	0.353647i	−0.991928	+	0.126806i	$0.959527\pi$
$864$	4.21083e6			0.191904
$865$	4.02733e7	−	2.92603e7i	1.83011	−	1.32965i
$866$	1.64560e7	−	1.19560e7i	0.745642	−	0.541741i
$867$	−3.98298e6	−	1.22583e7i	−0.179953	−	0.553839i
$868$	−3.07305e6	+	9.45789e6i	−0.138443	+	0.426084i
$869$	3.94155e7	+	2.86371e7i	1.77059	+	1.28641i
$870$	−1.61425e6			−0.0723056
$871$	−2.78615e7	−	2.02426e7i	−1.24440	−	0.904108i
$872$	3.05808e6	+	2.22183e6i	0.136194	+	0.0989507i
$873$	−2.33614e6	+	1.69730e6i	−0.103744	+	0.0753744i
$874$	8.17024e6	+	2.51454e7i	0.361790	+	1.11347i
$875$	1.28442e7			0.567134
$876$	1.51763e7	−	1.10262e7i	0.668197	−	0.485474i
$877$	4.04918e6	−	1.24621e7i	0.177774	−	0.547132i	−0.821975	−	0.569523i	$-0.807128\pi$
$877$	4.04918e6	−	1.24621e7i	0.177774	−	0.547132i	0.999749	+	0.0223914i	$0.00712799\pi$
$878$	−1.56333e7	−	1.13583e7i	−0.684407	−	0.497251i
$879$	−9.26255e6	−	2.85072e7i	−0.404351	−	1.24446i
$880$	−4.80168e6	+	1.47780e7i	−0.209019	+	0.643295i
$881$	−9.10226e6	+	2.80139e7i	−0.395102	+	1.21600i	0.533780	+	0.845623i	$0.320771\pi$
$881$	−9.10226e6	+	2.80139e7i	−0.395102	+	1.21600i	−0.928882	+	0.370376i	$0.879229\pi$
$882$	825422.	−	2.54039e6i	0.0357277	−	0.109958i
$883$	6.49595e6	−	1.99925e7i	0.280376	−	0.862909i	−0.707370	−	0.706843i	$-0.750119\pi$
$883$	6.49595e6	−	1.99925e7i	0.280376	−	0.862909i	0.987747	−	0.156066i	$-0.0498813\pi$
$884$	−2.13177e6	−	6.56091e6i	−0.0917507	−	0.282380i
$885$	5.63395e6	+	4.09330e6i	0.241799	+	0.175677i
$886$	−1.18027e6	+	3.63249e6i	−0.0505122	+	0.155461i
$887$	−2.96371e7	+	2.15326e7i	−1.26481	+	0.918941i	−0.998983	−	0.0450784i	$-0.985646\pi$
$887$	−2.96371e7	+	2.15326e7i	−1.26481	+	0.918941i	−0.265831	+	0.964020i	$0.585646\pi$
$888$	4.01187e6			0.170732
$889$	8.97727e6	+	2.76292e7i	0.380969	+	1.17250i
$890$	−1.67538e7	+	1.21723e7i	−0.708987	+	0.515109i
$891$	−2.22549e7	−	1.61691e7i	−0.939142	−	0.682327i
$892$	8.24540e6	+	5.99064e6i	0.346976	+	0.252093i
$893$	285094.			0.0119635
$894$	−6.36937e6	−	4.62762e6i	−0.266534	−	0.193648i
$895$	−1.67491e7	+	5.15484e7i	−0.698930	+	2.15109i
$896$	−829124.	−	2.55178e6i	−0.0345024	−	0.106187i
$897$	−3.00181e7	+	2.18094e7i	−1.24567	+	0.905029i
$898$	3.00214e6	−	2.18118e6i	0.124234	−	0.0902611i
$899$	−1.36176e6			−0.0561953
$900$	−1.33594e6	−	4.11159e6i	−0.0549769	−	0.169201i
$901$	2.90658e6			0.119281
$902$	−2.61647e7	+	1.63439e7i	−1.07078	+	0.668866i
$903$	−3.30164e7			−1.34744
$904$	1.02184e6	+	3.14492e6i	0.0415876	+	0.127993i
$905$	3.66182e6			0.148619
$906$	−1.50987e7	+	1.09698e7i	−0.611108	+	0.443996i
$907$	−1.89360e7	+	1.37578e7i	−0.764310	+	0.555304i	−0.900229	−	0.435416i	$-0.856601\pi$
$907$	−1.89360e7	+	1.37578e7i	−0.764310	+	0.555304i	0.135919	+	0.990720i	$0.456601\pi$
$908$	1.61385e6	+	4.96690e6i	0.0649602	+	0.199927i
$909$	−2.11507e6	+	6.50952e6i	−0.0849015	+	0.261300i
$910$	2.88820e7	+	2.09840e7i	1.15618	+	0.840012i
$911$	1.40159e7			0.559531			0.279765	−	0.960068i	$-0.409743\pi$
$911$	1.40159e7			0.559531			0.279765	+	0.960068i	$0.409743\pi$
$912$	4.18475e6	+	3.04040e6i	0.166603	+	0.121044i
$913$	4.90836e7	+	3.56613e7i	1.94876	+	1.41586i
$914$	4.10513e6	−	2.98255e6i	0.162540	−	0.118092i
$915$	−3.58468e6	−	1.10325e7i	−0.141546	−	0.435634i
$916$	−2.57845e6			−0.101536
$917$	2.55164e7	−	1.85388e7i	1.00207	−	0.728044i
$918$	−3.40637e6	+	1.04837e7i	−0.133409	+	0.410591i
$919$	−3.45529e7	−	2.51041e7i	−1.34957	−	0.980520i	−0.999033	−	0.0439712i	$-0.985999\pi$
$919$	−3.45529e7	−	2.51041e7i	−1.34957	−	0.980520i	−0.350537	−	0.936549i	$-0.614001\pi$
$920$	−7.27687e6	−	2.23959e7i	−0.283449	−	0.872367i
$921$	4.22603e6	−	1.30064e7i	0.164166	−	0.505251i
$922$	−1.74405e6	+	5.36763e6i	−0.0675665	+	0.207948i
$923$	−9.87297e6	+	3.03859e7i	−0.381455	+	1.17400i
$924$	−7.70330e6	+	2.37083e7i	−0.296823	+	0.913526i
$925$	−5.90981e6	−	1.81885e7i	−0.227101	−	0.698945i
$926$	−1.51773e7	−	1.10269e7i	−0.581656	−	0.422598i
$927$	3.92894e6	−	1.20920e7i	0.150167	−	0.462168i
$928$	297239.	−	215957.i	0.0113302	−	0.00823185i
$929$	3.66299e7			1.39250			0.696252	−	0.717798i	$-0.254850\pi$
$929$	3.66299e7			1.39250			0.696252	+	0.717798i	$0.254850\pi$
$930$	5.27661e6	+	1.62397e7i	0.200054	+	0.615703i
$931$	1.23255e7	−	8.95498e6i	0.466047	−	0.338603i
$932$	1.04687e7	+	7.60592e6i	0.394776	+	0.286822i
$933$	−1.07579e7	−	7.81608e6i	−0.404598	−	0.293958i
$934$	1.59629e7			0.598747
$935$	−3.29087e7	−	2.39095e7i	−1.23107	−	0.894421i
$936$	848698.	−	2.61202e6i	0.0316638	−	0.0974513i
$937$	−2.50336e6	−	7.70455e6i	−0.0931481	−	0.286681i	0.893618	−	0.448827i	$-0.148158\pi$
$937$	−2.50336e6	−	7.70455e6i	−0.0931481	−	0.286681i	−0.986767	+	0.162147i	$0.948158\pi$
$938$	2.83678e7	−	2.06104e7i	1.05274	−	0.764857i
$939$	−1.60120e7	+	1.16334e7i	−0.592627	+	0.430569i
$940$	−253921.			−0.00937301
$941$	8.36369e6	+	2.57408e7i	0.307910	+	0.947650i	0.978575	+	0.205890i	$0.0660088\pi$
$941$	8.36369e6	+	2.57408e7i	0.307910	+	0.947650i	−0.670665	+	0.741760i	$0.733991\pi$
$942$	−1.36477e7			−0.501107
$943$	1.75205e7	−	4.33454e7i	0.641603	−	1.58732i
$944$	−1.58501e6			−0.0578900
$945$	−1.76281e7	−	5.42536e7i	−0.642133	−	1.97628i
$946$	−4.35192e7			−1.58108
$947$	3.84005e7	−	2.78996e7i	1.39143	−	1.01093i	0.395723	−	0.918370i	$-0.370494\pi$
$947$	3.84005e7	−	2.78996e7i	1.39143	−	1.01093i	0.995707	−	0.0925636i	$-0.0295061\pi$
$948$	−1.16863e7	+	8.49063e6i	−0.422336	+	0.306845i
$949$	−1.75550e7	−	5.40287e7i	−0.632755	−	1.94742i
$950$	7.61971e6	−	2.34510e7i	0.273923	−	0.843050i
$951$	2.26895e7	+	1.64849e7i	0.813531	+	0.591065i
$952$	7.02391e6			0.251181
$953$	−3.76066e7	−	2.73228e7i	−1.34132	−	0.974524i	−0.999394	−	0.0347958i	$-0.988922\pi$
$953$	−3.76066e7	−	2.73228e7i	−1.34132	−	0.974524i	−0.341923	−	0.939728i	$-0.611078\pi$
$954$	936167.	+	680165.i	0.0333029	+	0.0241960i
$955$	−1.43160e7	+	1.04012e7i	−0.507941	+	0.369041i
$956$	−3.69147e6	−	1.13612e7i	−0.130633	−	0.402048i
$957$	−3.41355e6			−0.120483
$958$	8.20209e6	−	5.95917e6i	0.288743	−	0.209784i
$959$	−4.85543e6	+	1.49435e7i	−0.170483	+	0.524692i
$960$	−3.72717e6	−	2.70795e6i	−0.130527	−	0.0948336i
$961$	−4.39563e6	−	1.35283e7i	−0.153537	−	0.472538i
$962$	3.75440e6	−	1.15549e7i	0.130799	−	0.402556i
$963$	−2.22286e6	+	6.84125e6i	−0.0772407	+	0.237722i
$964$	−331579.	+	1.02050e6i	−0.0114920	+	0.0353686i
$965$	−2.06157e6	+	6.34487e6i	−0.0712657	+	0.219333i
$966$	−1.16742e7	−	3.59296e7i	−0.402519	−	1.23883i
$967$	−5.26480e6	−	3.82510e6i	−0.181057	−	0.131546i	0.493565	−	0.869709i	$-0.335693\pi$
$967$	−5.26480e6	−	3.82510e6i	−0.181057	−	0.131546i	−0.674622	+	0.738163i	$0.735693\pi$
$968$	−6.96868e6	+	2.14474e7i	−0.239035	+	0.735675i
$969$	−1.09550e7	+	7.95925e6i	−0.374802	+	0.272310i
$970$	1.46691e7			0.500580
$971$	7.99623e6	+	2.46099e7i	0.272168	+	0.837647i	0.989955	+	0.141384i	$0.0451552\pi$
$971$	7.99623e6	+	2.46099e7i	0.272168	+	0.837647i	−0.717787	+	0.696263i	$0.754845\pi$
$972$	−6.33618e6	+	4.60351e6i	−0.215111	+	0.156287i
$973$	−5.27509e7	−	3.83258e7i	−1.78627	−	1.29780i
$974$	−1.79602e6	−	1.30488e6i	−0.0606614	−	0.0440731i
$975$	3.46042e7			1.16578
$976$	2.13601e6	+	1.55191e6i	0.0717761	+	0.0521484i
$977$	−1.11104e7	+	3.41944e7i	−0.372387	+	1.14609i	0.572838	+	0.819668i	$0.305842\pi$
$977$	−1.11104e7	+	3.41944e7i	−0.372387	+	1.14609i	−0.945225	+	0.326420i	$0.894158\pi$
$978$	6.07075e6	+	1.86839e7i	0.202953	+	0.624625i
$979$	−3.54282e7	+	2.57401e7i	−1.18139	+	0.858328i
$980$	−1.09778e7	+	7.97581e6i	−0.365131	+	0.265283i
$981$	−3.93955e6			−0.130700
$982$	5.14692e6	+	1.58406e7i	0.170321	+	0.524195i
$983$	5.39963e6			0.178230			0.0891149	−	0.996021i	$-0.471596\pi$
$983$	5.39963e6			0.178230			0.0891149	+	0.996021i	$0.471596\pi$
$984$	−2.21141e6	−	8.87534e6i	−0.0728086	−	0.292211i
$985$	−9.04448e7			−2.97025
$986$	297216.	+	914738.i	0.00973600	+	0.0299643i
$987$	−407364.			−0.0133104
$988$	1.26730e7	−	9.20750e6i	0.413036	−	0.300089i
$989$	5.33569e7	−	3.87660e7i	1.73460	−	1.26026i
$990$	−5.00436e6	−	1.54018e7i	−0.162278	−	0.499441i
$991$	1.00311e7	−	3.08724e7i	0.324461	−	0.998589i	−0.647222	−	0.762301i	$-0.724069\pi$
$991$	1.00311e7	−	3.08724e7i	0.324461	−	0.998589i	0.971683	−	0.236287i	$-0.0759306\pi$
$992$	−3.14419e6	−	2.28439e6i	−0.101445	−	0.0737038i
$993$	2.38248e7			0.766754
$994$	−2.63175e7	−	1.91208e7i	−0.844848	−	0.613818i
$995$	−5.56726e7	−	4.04485e7i	−1.78272	−	1.29522i
$996$	−1.45528e7	+	1.05732e7i	−0.464835	+	0.337722i
$997$	1.49466e7	+	4.60010e7i	0.476218	+	1.46565i	0.844309	+	0.535857i	$0.180011\pi$
$997$	1.49466e7	+	4.60010e7i	0.476218	+	1.46565i	−0.368091	+	0.929790i	$0.619989\pi$
$998$	1.85295e7			0.588896
$999$	−1.57061e7	+	1.14111e7i	−0.497914	+	0.361755i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.6.d.b.59.7	yes	36
41.16	even	5	inner	82.6.d.b.57.7	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.6.d.b.57.7	✓	36	41.16	even	5	inner
82.6.d.b.59.7	yes	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.23607 - 3.80423i) q^{2} +13.2777 q^{3} +(-12.9443 + 9.40456i) q^{4} +(-68.5323 + 49.7916i) q^{5} +(-16.4122 - 50.5116i) q^{6} +(50.6057 - 155.748i) q^{7} +(51.7771 + 37.6183i) q^{8} -66.7014 q^{9} +(274.129 + 199.166i) q^{10} +(579.683 + 421.165i) q^{11} +(-171.871 + 124.871i) q^{12} +(198.810 + 611.874i) q^{13} -655.054 q^{14} +(-909.954 + 661.120i) q^{15} +(79.1084 - 243.470i) q^{16} +(542.175 + 393.913i) q^{17} +(82.4475 + 253.747i) q^{18} +(-470.251 + 1447.28i) q^{19} +(418.832 - 1289.03i) q^{20} +(671.930 - 2067.99i) q^{21} +(885.677 - 2725.83i) q^{22} +(1342.23 + 4130.96i) q^{23} +(687.483 + 499.486i) q^{24} +(1251.79 - 3852.61i) q^{25} +(2081.96 - 1512.64i) q^{26} -4112.14 q^{27} +(809.691 + 2491.97i) q^{28} +(-290.273 + 210.895i) q^{29} +(3639.82 + 2644.48i) q^{30} +(3070.49 + 2230.84i) q^{31} -1024.00 q^{32} +(7696.89 + 5592.12i) q^{33} +(828.370 - 2549.46i) q^{34} +(4286.84 + 13193.5i) q^{35} +(863.402 - 627.298i) q^{36} +(3819.44 - 2774.99i) q^{37} +6087.06 q^{38} +(2639.75 + 8124.31i) q^{39} -5421.47 q^{40} +(-8244.37 - 6920.01i) q^{41} -8697.64 q^{42} +(-4692.13 - 14440.9i) q^{43} -11464.4 q^{44} +(4571.20 - 3321.17i) q^{45} +(14056.0 - 10212.3i) q^{46} +(-57.8927 - 178.175i) q^{47} +(1050.38 - 3232.74i) q^{48} +(-8099.46 - 5884.60i) q^{49} -16203.5 q^{50} +(7198.86 + 5230.28i) q^{51} +(-8327.86 - 6050.54i) q^{52} +(3508.79 - 2549.29i) q^{53} +(5082.88 + 15643.5i) q^{54} -60697.5 q^{55} +(8479.20 - 6160.50i) q^{56} +(-6243.87 + 19216.7i) q^{57} +(1161.09 + 843.582i) q^{58} +(-1913.27 - 5888.43i) q^{59} +(5561.14 - 17115.4i) q^{60} +(-3187.05 + 9808.73i) q^{61} +(4691.30 - 14438.3i) q^{62} +(-3375.47 + 10388.6i) q^{63} +(1265.73 + 3895.53i) q^{64} +(-44091.1 - 32034.0i) q^{65} +(11759.8 - 36192.9i) q^{66} +(-43306.1 + 31463.7i) q^{67} -10722.6 q^{68} +(17821.8 + 54849.9i) q^{69} +(44892.3 - 32616.2i) q^{70} +(40176.1 + 29189.6i) q^{71} +(-3453.61 - 2509.19i) q^{72} -88300.4 q^{73} +(-15277.8 - 11100.0i) q^{74} +(16620.9 - 51154.0i) q^{75} +(-7524.02 - 23156.5i) q^{76} +(94931.0 - 68971.4i) q^{77} +(27643.8 - 20084.4i) q^{78} +67994.9 q^{79} +(6701.31 + 20624.5i) q^{80} -38391.5 q^{81} +(-16134.7 + 39917.0i) q^{82} +84673.1 q^{83} +(10750.9 + 33087.8i) q^{84} -56770.1 q^{85} +(-49136.6 + 35699.8i) q^{86} +(-3854.17 + 2800.22i) q^{87} +(14170.8 + 43613.4i) q^{88} +(-18886.0 + 58125.2i) q^{89} +(-18284.8 - 13284.7i) q^{90} +105359. q^{91} +(-56224.1 - 40849.2i) q^{92} +(40769.2 + 29620.6i) q^{93} +(-606.260 + 440.474i) q^{94} +(-39835.2 - 122600. i) q^{95} -13596.4 q^{96} +(35023.8 - 25446.3i) q^{97} +(-12374.9 + 38086.0i) q^{98} +(-38665.7 - 28092.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 36 q^{2} + 2 q^{3} - 144 q^{4} + 26 q^{5} + 112 q^{6} - 120 q^{7} + 576 q^{8} + 4006 q^{9} - 104 q^{10} + 747 q^{11} + 432 q^{12} + 907 q^{13} + 280 q^{14} - 4149 q^{15} - 2304 q^{16} - 3177 q^{17}+ \cdots + 276325 q^{99}+O(q^{100}) \) 36 * q + 36 * q^2 + 2 * q^3 - 144 * q^4 + 26 * q^5 + 112 * q^6 - 120 * q^7 + 576 * q^8 + 4006 * q^9 - 104 * q^10 + 747 * q^11 + 432 * q^12 + 907 * q^13 + 280 * q^14 - 4149 * q^15 - 2304 * q^16 - 3177 * q^17 + 3696 * q^18 + 1557 * q^19 - 624 * q^20 - 4785 * q^21 + 2252 * q^22 + 1809 * q^23 - 1728 * q^24 - 6323 * q^25 + 10132 * q^26 + 8828 * q^27 - 1920 * q^28 + 1179 * q^29 + 16596 * q^30 - 2190 * q^31 - 36864 * q^32 + 19669 * q^33 - 4572 * q^34 - 69 * q^35 - 17264 * q^36 + 47551 * q^37 - 6128 * q^38 + 62888 * q^39 - 1664 * q^40 + 41071 * q^41 - 16600 * q^42 + 46110 * q^43 - 5888 * q^44 + 51325 * q^45 + 144 * q^46 - 65162 * q^47 - 7168 * q^48 - 83129 * q^49 - 151288 * q^50 + 98677 * q^51 - 40528 * q^52 - 122095 * q^53 + 41748 * q^54 - 161798 * q^55 - 9920 * q^56 - 11800 * q^57 - 4716 * q^58 + 17054 * q^59 + 72656 * q^60 + 86317 * q^61 - 30540 * q^62 - 166377 * q^63 - 36864 * q^64 + 32896 * q^65 + 66064 * q^66 + 95554 * q^67 + 65088 * q^68 + 132527 * q^69 + 23156 * q^70 + 158283 * q^71 + 69056 * q^72 - 239776 * q^73 - 190204 * q^74 - 357133 * q^75 + 24912 * q^76 + 253599 * q^77 + 242748 * q^78 + 98380 * q^79 - 9984 * q^80 + 1044 * q^81 - 84824 * q^82 - 24346 * q^83 - 76560 * q^84 + 376378 * q^85 + 98560 * q^86 + 12625 * q^87 + 36032 * q^88 + 260385 * q^89 - 205300 * q^90 - 726414 * q^91 - 576 * q^92 - 100227 * q^93 - 189392 * q^94 - 257337 * q^95 - 2048 * q^96 + 109321 * q^97 - 145824 * q^98 + 276325 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more