Properties

Label 60.7.c.a.31.20
Level $60$
Weight $7$
Character 60.31
Analytic conductor $13.803$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 60.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.8032450172\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 31.20
Character \(\chi\) \(=\) 60.31
Dual form 60.7.c.a.31.19

$q$-expansion

\(f(q)\) \(=\) \(q+(5.40467 + 5.89827i) q^{2} -15.5885i q^{3} +(-5.57916 + 63.7564i) q^{4} -55.9017 q^{5} +(91.9449 - 84.2504i) q^{6} +125.427i q^{7} +(-406.206 + 311.674i) q^{8} -243.000 q^{9} +O(q^{10})\) \(q+(5.40467 + 5.89827i) q^{2} -15.5885i q^{3} +(-5.57916 + 63.7564i) q^{4} -55.9017 q^{5} +(91.9449 - 84.2504i) q^{6} +125.427i q^{7} +(-406.206 + 311.674i) q^{8} -243.000 q^{9} +(-302.130 - 329.723i) q^{10} +685.839i q^{11} +(993.863 + 86.9705i) q^{12} -3316.77 q^{13} +(-739.803 + 677.892i) q^{14} +871.421i q^{15} +(-4033.75 - 711.414i) q^{16} -3071.82 q^{17} +(-1313.33 - 1433.28i) q^{18} +6082.98i q^{19} +(311.884 - 3564.09i) q^{20} +1955.22 q^{21} +(-4045.26 + 3706.73i) q^{22} +6974.95i q^{23} +(4858.52 + 6332.12i) q^{24} +3125.00 q^{25} +(-17926.0 - 19563.2i) q^{26} +3788.00i q^{27} +(-7996.78 - 699.778i) q^{28} -13736.6 q^{29} +(-5139.88 + 4709.74i) q^{30} -37542.0i q^{31} +(-17604.9 - 27637.1i) q^{32} +10691.2 q^{33} +(-16602.2 - 18118.4i) q^{34} -7011.59i q^{35} +(1355.74 - 15492.8i) q^{36} +64357.4 q^{37} +(-35879.0 + 32876.5i) q^{38} +51703.3i q^{39} +(22707.6 - 17423.1i) q^{40} +2744.47 q^{41} +(10567.3 + 11532.4i) q^{42} +100421. i q^{43} +(-43726.6 - 3826.40i) q^{44} +13584.1 q^{45} +(-41140.2 + 37697.3i) q^{46} +72930.9i q^{47} +(-11089.8 + 62879.9i) q^{48} +101917. q^{49} +(16889.6 + 18432.1i) q^{50} +47884.9i q^{51} +(18504.8 - 211465. i) q^{52} +99684.3 q^{53} +(-22342.6 + 20472.9i) q^{54} -38339.6i q^{55} +(-39092.5 - 50949.2i) q^{56} +94824.2 q^{57} +(-74241.8 - 81022.2i) q^{58} +237946. i q^{59} +(-55558.6 - 4861.80i) q^{60} +274238. q^{61} +(221433. - 202902. i) q^{62} -30478.8i q^{63} +(67862.0 - 253208. i) q^{64} +185413. q^{65} +(57782.2 + 63059.4i) q^{66} -444734. i q^{67} +(17138.2 - 195848. i) q^{68} +108729. q^{69} +(41356.3 - 37895.3i) q^{70} +324805. i q^{71} +(98708.0 - 75736.9i) q^{72} -689523. q^{73} +(347830. + 379597. i) q^{74} -48713.9i q^{75} +(-387829. - 33937.9i) q^{76} -86022.8 q^{77} +(-304960. + 279439. i) q^{78} -147732. i q^{79} +(225493. + 39769.2i) q^{80} +59049.0 q^{81} +(14832.9 + 16187.6i) q^{82} +355588. i q^{83} +(-10908.5 + 124657. i) q^{84} +171720. q^{85} +(-592309. + 542741. i) q^{86} +214133. i q^{87} +(-213758. - 278592. i) q^{88} +24831.9 q^{89} +(73417.6 + 80122.8i) q^{90} -416013. i q^{91} +(-444698. - 38914.4i) q^{92} -585221. q^{93} +(-430166. + 394167. i) q^{94} -340049. i q^{95} +(-430819. + 274434. i) q^{96} -938268. q^{97} +(550828. + 601134. i) q^{98} -166659. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 20q^{2} - 246q^{4} + 162q^{6} - 340q^{8} - 5832q^{9} + O(q^{10}) \) \( 24q + 20q^{2} - 246q^{4} + 162q^{6} - 340q^{8} - 5832q^{9} - 750q^{10} + 5040q^{13} - 2596q^{14} + 4194q^{16} - 4860q^{18} + 7000q^{20} + 19440q^{21} + 45780q^{22} + 24786q^{24} + 75000q^{25} + 75852q^{26} + 54300q^{28} + 132800q^{29} - 10700q^{32} - 173484q^{34} + 59778q^{36} - 69840q^{37} + 215800q^{38} - 14250q^{40} - 70448q^{41} - 189540q^{42} - 395668q^{44} - 158760q^{46} + 252720q^{48} - 642984q^{49} + 62500q^{50} - 210240q^{52} - 644320q^{53} - 39366q^{54} - 917708q^{56} + 408240q^{57} - 1345020q^{58} + 222750q^{60} - 222864q^{61} + 1948520q^{62} + 935922q^{64} + 266000q^{65} - 640548q^{66} + 572680q^{68} - 541728q^{69} + 220500q^{70} + 82620q^{72} + 771120q^{73} - 589164q^{74} - 191544q^{76} + 1383840q^{77} - 693360q^{78} - 946000q^{80} + 1417176q^{81} + 2672520q^{82} + 1256796q^{84} - 372000q^{85} + 1781528q^{86} + 956940q^{88} - 1566224q^{89} + 182250q^{90} - 3040560q^{92} + 1496880q^{93} - 3788352q^{94} - 413262q^{96} - 1666800q^{97} - 2709660q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(41\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.40467 + 5.89827i 0.675583 + 0.737284i
\(3\) 15.5885i 0.577350i
\(4\) −5.57916 + 63.7564i −0.0871743 + 0.996193i
\(5\) −55.9017 −0.447214
\(6\) 91.9449 84.2504i 0.425671 0.390048i
\(7\) 125.427i 0.365677i 0.983143 + 0.182838i \(0.0585285\pi\)
−0.983143 + 0.182838i \(0.941471\pi\)
\(8\) −406.206 + 311.674i −0.793370 + 0.608739i
\(9\) −243.000 −0.333333
\(10\) −302.130 329.723i −0.302130 0.329723i
\(11\) 685.839i 0.515281i 0.966241 + 0.257640i \(0.0829450\pi\)
−0.966241 + 0.257640i \(0.917055\pi\)
\(12\) 993.863 + 86.9705i 0.575152 + 0.0503301i
\(13\) −3316.77 −1.50968 −0.754840 0.655909i \(-0.772286\pi\)
−0.754840 + 0.655909i \(0.772286\pi\)
\(14\) −739.803 + 677.892i −0.269608 + 0.247045i
\(15\) 871.421i 0.258199i
\(16\) −4033.75 711.414i −0.984801 0.173685i
\(17\) −3071.82 −0.625243 −0.312621 0.949878i \(-0.601207\pi\)
−0.312621 + 0.949878i \(0.601207\pi\)
\(18\) −1313.33 1433.28i −0.225194 0.245761i
\(19\) 6082.98i 0.886861i 0.896309 + 0.443430i \(0.146239\pi\)
−0.896309 + 0.443430i \(0.853761\pi\)
\(20\) 311.884 3564.09i 0.0389856 0.445511i
\(21\) 1955.22 0.211124
\(22\) −4045.26 + 3706.73i −0.379908 + 0.348115i
\(23\) 6974.95i 0.573268i 0.958040 + 0.286634i \(0.0925364\pi\)
−0.958040 + 0.286634i \(0.907464\pi\)
\(24\) 4858.52 + 6332.12i 0.351456 + 0.458053i
\(25\) 3125.00 0.200000
\(26\) −17926.0 19563.2i −1.01991 1.11306i
\(27\) 3788.00i 0.192450i
\(28\) −7996.78 699.778i −0.364285 0.0318776i
\(29\) −13736.6 −0.563230 −0.281615 0.959528i \(-0.590870\pi\)
−0.281615 + 0.959528i \(0.590870\pi\)
\(30\) −5139.88 + 4709.74i −0.190366 + 0.174435i
\(31\) 37542.0i 1.26018i −0.776523 0.630089i \(-0.783018\pi\)
0.776523 0.630089i \(-0.216982\pi\)
\(32\) −17604.9 27637.1i −0.537260 0.843417i
\(33\) 10691.2 0.297498
\(34\) −16602.2 18118.4i −0.422404 0.460981i
\(35\) 7011.59i 0.163536i
\(36\) 1355.74 15492.8i 0.0290581 0.332064i
\(37\) 64357.4 1.27055 0.635277 0.772284i \(-0.280886\pi\)
0.635277 + 0.772284i \(0.280886\pi\)
\(38\) −35879.0 + 32876.5i −0.653868 + 0.599148i
\(39\) 51703.3i 0.871614i
\(40\) 22707.6 17423.1i 0.354806 0.272236i
\(41\) 2744.47 0.0398205 0.0199103 0.999802i \(-0.493662\pi\)
0.0199103 + 0.999802i \(0.493662\pi\)
\(42\) 10567.3 + 11532.4i 0.142632 + 0.155658i
\(43\) 100421.i 1.26304i 0.775358 + 0.631522i \(0.217569\pi\)
−0.775358 + 0.631522i \(0.782431\pi\)
\(44\) −43726.6 3826.40i −0.513319 0.0449193i
\(45\) 13584.1 0.149071
\(46\) −41140.2 + 37697.3i −0.422661 + 0.387290i
\(47\) 72930.9i 0.702455i 0.936290 + 0.351227i \(0.114236\pi\)
−0.936290 + 0.351227i \(0.885764\pi\)
\(48\) −11089.8 + 62879.9i −0.100277 + 0.568575i
\(49\) 101917. 0.866280
\(50\) 16889.6 + 18432.1i 0.135117 + 0.147457i
\(51\) 47884.9i 0.360984i
\(52\) 18504.8 211465.i 0.131605 1.50393i
\(53\) 99684.3 0.669575 0.334787 0.942294i \(-0.391335\pi\)
0.334787 + 0.942294i \(0.391335\pi\)
\(54\) −22342.6 + 20472.9i −0.141890 + 0.130016i
\(55\) 38339.6i 0.230441i
\(56\) −39092.5 50949.2i −0.222602 0.290117i
\(57\) 94824.2 0.512029
\(58\) −74241.8 81022.2i −0.380509 0.415260i
\(59\) 237946.i 1.15857i 0.815126 + 0.579284i \(0.196668\pi\)
−0.815126 + 0.579284i \(0.803332\pi\)
\(60\) −55558.6 4861.80i −0.257216 0.0225083i
\(61\) 274238. 1.20820 0.604099 0.796909i \(-0.293533\pi\)
0.604099 + 0.796909i \(0.293533\pi\)
\(62\) 221433. 202902.i 0.929108 0.851355i
\(63\) 30478.8i 0.121892i
\(64\) 67862.0 253208.i 0.258873 0.965911i
\(65\) 185413. 0.675150
\(66\) 57782.2 + 63059.4i 0.200984 + 0.219340i
\(67\) 444734.i 1.47869i −0.673329 0.739343i \(-0.735136\pi\)
0.673329 0.739343i \(-0.264864\pi\)
\(68\) 17138.2 195848.i 0.0545051 0.622863i
\(69\) 108729. 0.330977
\(70\) 41356.3 37895.3i 0.120572 0.110482i
\(71\) 324805.i 0.907502i 0.891128 + 0.453751i \(0.149914\pi\)
−0.891128 + 0.453751i \(0.850086\pi\)
\(72\) 98708.0 75736.9i 0.264457 0.202913i
\(73\) −689523. −1.77247 −0.886237 0.463231i \(-0.846690\pi\)
−0.886237 + 0.463231i \(0.846690\pi\)
\(74\) 347830. + 379597.i 0.858365 + 0.936759i
\(75\) 48713.9i 0.115470i
\(76\) −387829. 33937.9i −0.883485 0.0773115i
\(77\) −86022.8 −0.188426
\(78\) −304960. + 279439.i −0.642627 + 0.588848i
\(79\) 147732.i 0.299636i −0.988714 0.149818i \(-0.952131\pi\)
0.988714 0.149818i \(-0.0478687\pi\)
\(80\) 225493. + 39769.2i 0.440417 + 0.0776743i
\(81\) 59049.0 0.111111
\(82\) 14832.9 + 16187.6i 0.0269021 + 0.0293590i
\(83\) 355588.i 0.621889i 0.950428 + 0.310944i \(0.100645\pi\)
−0.950428 + 0.310944i \(0.899355\pi\)
\(84\) −10908.5 + 124657.i −0.0184046 + 0.210320i
\(85\) 171720. 0.279617
\(86\) −592309. + 542741.i −0.931221 + 0.853291i
\(87\) 214133.i 0.325181i
\(88\) −213758. 278592.i −0.313672 0.408809i
\(89\) 24831.9 0.0352241 0.0176121 0.999845i \(-0.494394\pi\)
0.0176121 + 0.999845i \(0.494394\pi\)
\(90\) 73417.6 + 80122.8i 0.100710 + 0.109908i
\(91\) 416013.i 0.552055i
\(92\) −444698. 38914.4i −0.571086 0.0499743i
\(93\) −585221. −0.727564
\(94\) −430166. + 394167.i −0.517908 + 0.474567i
\(95\) 340049.i 0.396616i
\(96\) −430819. + 274434.i −0.486947 + 0.310187i
\(97\) −938268. −1.02804 −0.514022 0.857777i \(-0.671845\pi\)
−0.514022 + 0.857777i \(0.671845\pi\)
\(98\) 550828. + 601134.i 0.585245 + 0.638694i
\(99\) 166659.i 0.171760i
\(100\) −17434.9 + 199239.i −0.0174349 + 0.199239i
\(101\) −1.57672e6 −1.53035 −0.765175 0.643822i \(-0.777348\pi\)
−0.765175 + 0.643822i \(0.777348\pi\)
\(102\) −282438. + 258802.i −0.266148 + 0.243875i
\(103\) 1.87489e6i 1.71579i −0.513825 0.857895i \(-0.671772\pi\)
0.513825 0.857895i \(-0.328228\pi\)
\(104\) 1.34729e6 1.03375e6i 1.19774 0.919002i
\(105\) −109300. −0.0944174
\(106\) 538760. + 587965.i 0.452354 + 0.493667i
\(107\) 1.81947e6i 1.48523i 0.669719 + 0.742615i \(0.266415\pi\)
−0.669719 + 0.742615i \(0.733585\pi\)
\(108\) −241509. 21133.8i −0.191717 0.0167767i
\(109\) 1.10563e6 0.853747 0.426873 0.904311i \(-0.359615\pi\)
0.426873 + 0.904311i \(0.359615\pi\)
\(110\) 226137. 207213.i 0.169900 0.155682i
\(111\) 1.00323e6i 0.733555i
\(112\) 89230.6 505941.i 0.0635126 0.360119i
\(113\) −2.60750e6 −1.80713 −0.903563 0.428454i \(-0.859058\pi\)
−0.903563 + 0.428454i \(0.859058\pi\)
\(114\) 512493. + 559299.i 0.345918 + 0.377511i
\(115\) 389912.i 0.256373i
\(116\) 76638.7 875796.i 0.0490992 0.561086i
\(117\) 805975. 0.503227
\(118\) −1.40347e6 + 1.28602e6i −0.854193 + 0.782709i
\(119\) 385290.i 0.228637i
\(120\) −271600. 353976.i −0.157176 0.204847i
\(121\) 1.30119e6 0.734486
\(122\) 1.48216e6 + 1.61753e6i 0.816238 + 0.890784i
\(123\) 42782.0i 0.0229904i
\(124\) 2.39354e6 + 209452.i 1.25538 + 0.109855i
\(125\) −174693. −0.0894427
\(126\) 179772. 164728.i 0.0898692 0.0823484i
\(127\) 113916.i 0.0556127i −0.999613 0.0278064i \(-0.991148\pi\)
0.999613 0.0278064i \(-0.00885218\pi\)
\(128\) 1.86026e6 968235.i 0.887041 0.461691i
\(129\) 1.56540e6 0.729218
\(130\) 1.00210e6 + 1.09362e6i 0.456120 + 0.497777i
\(131\) 305614.i 0.135944i −0.997687 0.0679720i \(-0.978347\pi\)
0.997687 0.0679720i \(-0.0216528\pi\)
\(132\) −59647.7 + 681630.i −0.0259342 + 0.296365i
\(133\) −762971. −0.324305
\(134\) 2.62316e6 2.40364e6i 1.09021 0.998976i
\(135\) 211755.i 0.0860663i
\(136\) 1.24779e6 957407.i 0.496049 0.380610i
\(137\) −1.92315e6 −0.747913 −0.373957 0.927446i \(-0.621999\pi\)
−0.373957 + 0.927446i \(0.621999\pi\)
\(138\) 587643. + 641311.i 0.223602 + 0.244024i
\(139\) 1.07520e6i 0.400353i −0.979760 0.200177i \(-0.935848\pi\)
0.979760 0.200177i \(-0.0641516\pi\)
\(140\) 447034. + 39118.8i 0.162913 + 0.0142561i
\(141\) 1.13688e6 0.405562
\(142\) −1.91579e6 + 1.75546e6i −0.669086 + 0.613093i
\(143\) 2.27477e6i 0.777909i
\(144\) 980200. + 172873.i 0.328267 + 0.0578950i
\(145\) 767900. 0.251884
\(146\) −3.72664e6 4.06699e6i −1.19745 1.30682i
\(147\) 1.58873e6i 0.500147i
\(148\) −359060. + 4.10319e6i −0.110760 + 1.26572i
\(149\) 3.38454e6 1.02315 0.511577 0.859238i \(-0.329062\pi\)
0.511577 + 0.859238i \(0.329062\pi\)
\(150\) 287328. 263283.i 0.0851342 0.0780096i
\(151\) 6.23793e6i 1.81180i 0.423494 + 0.905899i \(0.360803\pi\)
−0.423494 + 0.905899i \(0.639197\pi\)
\(152\) −1.89591e6 2.47094e6i −0.539867 0.703609i
\(153\) 746452. 0.208414
\(154\) −464925. 507386.i −0.127298 0.138924i
\(155\) 2.09866e6i 0.563569i
\(156\) −3.29641e6 288461.i −0.868296 0.0759824i
\(157\) −249290. −0.0644179 −0.0322090 0.999481i \(-0.510254\pi\)
−0.0322090 + 0.999481i \(0.510254\pi\)
\(158\) 871364. 798443.i 0.220916 0.202429i
\(159\) 1.55392e6i 0.386579i
\(160\) 984146. + 1.54496e6i 0.240270 + 0.377187i
\(161\) −874849. −0.209631
\(162\) 319140. + 348287.i 0.0750648 + 0.0819204i
\(163\) 1.98756e6i 0.458942i 0.973316 + 0.229471i \(0.0736996\pi\)
−0.973316 + 0.229471i \(0.926300\pi\)
\(164\) −15311.8 + 174977.i −0.00347133 + 0.0396689i
\(165\) −597654. −0.133045
\(166\) −2.09735e6 + 1.92183e6i −0.458509 + 0.420138i
\(167\) 4.42965e6i 0.951086i 0.879693 + 0.475543i \(0.157748\pi\)
−0.879693 + 0.475543i \(0.842252\pi\)
\(168\) −794220. + 609391.i −0.167499 + 0.128519i
\(169\) 6.17414e6 1.27913
\(170\) 928089. + 1.01285e6i 0.188905 + 0.206157i
\(171\) 1.47816e6i 0.295620i
\(172\) −6.40246e6 560263.i −1.25823 0.110105i
\(173\) −7.51606e6 −1.45162 −0.725808 0.687897i \(-0.758534\pi\)
−0.725808 + 0.687897i \(0.758534\pi\)
\(174\) −1.26301e6 + 1.15732e6i −0.239751 + 0.219687i
\(175\) 391960.i 0.0731354i
\(176\) 487915. 2.76650e6i 0.0894965 0.507449i
\(177\) 3.70920e6 0.668899
\(178\) 134208. + 146465.i 0.0237968 + 0.0259702i
\(179\) 2.01873e6i 0.351980i 0.984392 + 0.175990i \(0.0563127\pi\)
−0.984392 + 0.175990i \(0.943687\pi\)
\(180\) −75787.9 + 866074.i −0.0129952 + 0.148504i
\(181\) 6.78948e6 1.14499 0.572493 0.819909i \(-0.305976\pi\)
0.572493 + 0.819909i \(0.305976\pi\)
\(182\) 2.45376e6 2.24841e6i 0.407021 0.372959i
\(183\) 4.27495e6i 0.697553i
\(184\) −2.17391e6 2.83327e6i −0.348971 0.454814i
\(185\) −3.59769e6 −0.568209
\(186\) −3.16293e6 3.45179e6i −0.491530 0.536421i
\(187\) 2.10677e6i 0.322176i
\(188\) −4.64981e6 406893.i −0.699780 0.0612360i
\(189\) −475118. −0.0703746
\(190\) 2.00570e6 1.83785e6i 0.292419 0.267947i
\(191\) 9.09426e6i 1.30517i 0.757715 + 0.652585i \(0.226316\pi\)
−0.757715 + 0.652585i \(0.773684\pi\)
\(192\) −3.94712e6 1.05786e6i −0.557669 0.149460i
\(193\) −7.91992e6 −1.10166 −0.550831 0.834616i \(-0.685689\pi\)
−0.550831 + 0.834616i \(0.685689\pi\)
\(194\) −5.07103e6 5.53416e6i −0.694530 0.757960i
\(195\) 2.89030e6i 0.389798i
\(196\) −568611. + 6.49786e6i −0.0755174 + 0.862982i
\(197\) 1.10853e7 1.44994 0.724969 0.688781i \(-0.241854\pi\)
0.724969 + 0.688781i \(0.241854\pi\)
\(198\) 982999. 900735.i 0.126636 0.116038i
\(199\) 55779.8i 0.00707812i 0.999994 + 0.00353906i \(0.00112652\pi\)
−0.999994 + 0.00353906i \(0.998873\pi\)
\(200\) −1.26939e6 + 973983.i −0.158674 + 0.121748i
\(201\) −6.93272e6 −0.853720
\(202\) −8.52165e6 9.29993e6i −1.03388 1.12830i
\(203\) 1.72294e6i 0.205960i
\(204\) −3.05297e6 267157.i −0.359610 0.0314686i
\(205\) −153421. −0.0178083
\(206\) 1.10586e7 1.01332e7i 1.26502 1.15916i
\(207\) 1.69491e6i 0.191089i
\(208\) 1.33790e7 + 2.35959e6i 1.48674 + 0.262209i
\(209\) −4.17194e6 −0.456982
\(210\) −590730. 644680.i −0.0637868 0.0696124i
\(211\) 1.32243e7i 1.40775i 0.710322 + 0.703877i \(0.248549\pi\)
−0.710322 + 0.703877i \(0.751451\pi\)
\(212\) −556154. + 6.35551e6i −0.0583697 + 0.667026i
\(213\) 5.06321e6 0.523947
\(214\) −1.07317e7 + 9.83363e6i −1.09504 + 1.00340i
\(215\) 5.61369e6i 0.564850i
\(216\) −1.18062e6 1.53870e6i −0.117152 0.152684i
\(217\) 4.70878e6 0.460818
\(218\) 5.97554e6 + 6.52128e6i 0.576777 + 0.629453i
\(219\) 1.07486e7i 1.02334i
\(220\) 2.44439e6 + 213902.i 0.229563 + 0.0200885i
\(221\) 1.01885e7 0.943917
\(222\) 5.91733e6 5.42213e6i 0.540838 0.495577i
\(223\) 9.36634e6i 0.844609i −0.906454 0.422304i \(-0.861221\pi\)
0.906454 0.422304i \(-0.138779\pi\)
\(224\) 3.46644e6 2.20814e6i 0.308418 0.196464i
\(225\) −759375. −0.0666667
\(226\) −1.40927e7 1.53797e7i −1.22086 1.33237i
\(227\) 1.58575e7i 1.35568i 0.735211 + 0.677838i \(0.237083\pi\)
−0.735211 + 0.677838i \(0.762917\pi\)
\(228\) −529039. + 6.04565e6i −0.0446358 + 0.510080i
\(229\) −1.61507e7 −1.34489 −0.672443 0.740149i \(-0.734755\pi\)
−0.672443 + 0.740149i \(0.734755\pi\)
\(230\) 2.29980e6 2.10734e6i 0.189020 0.173202i
\(231\) 1.34096e6i 0.108788i
\(232\) 5.57989e6 4.28135e6i 0.446850 0.342860i
\(233\) −4.22772e6 −0.334224 −0.167112 0.985938i \(-0.553444\pi\)
−0.167112 + 0.985938i \(0.553444\pi\)
\(234\) 4.35602e6 + 4.75385e6i 0.339972 + 0.371021i
\(235\) 4.07696e6i 0.314147i
\(236\) −1.51705e7 1.32754e6i −1.15416 0.100997i
\(237\) −2.30292e6 −0.172995
\(238\) 2.27254e6 2.08236e6i 0.168570 0.154463i
\(239\) 3.67362e6i 0.269092i −0.990907 0.134546i \(-0.957042\pi\)
0.990907 0.134546i \(-0.0429575\pi\)
\(240\) 619941. 3.51509e6i 0.0448453 0.254275i
\(241\) 2.03391e7 1.45305 0.726526 0.687139i \(-0.241134\pi\)
0.726526 + 0.687139i \(0.241134\pi\)
\(242\) 7.03248e6 + 7.67475e6i 0.496206 + 0.541524i
\(243\) 920483.i 0.0641500i
\(244\) −1.53002e6 + 1.74844e7i −0.105324 + 1.20360i
\(245\) −5.69733e6 −0.387412
\(246\) 252340. 231223.i 0.0169504 0.0155319i
\(247\) 2.01758e7i 1.33888i
\(248\) 1.17009e7 + 1.52498e7i 0.767120 + 0.999788i
\(249\) 5.54307e6 0.359048
\(250\) −944156. 1.03039e6i −0.0604260 0.0659447i
\(251\) 69668.3i 0.00440569i 0.999998 + 0.00220285i \(0.000701188\pi\)
−0.999998 + 0.00220285i \(0.999299\pi\)
\(252\) 1.94322e6 + 170046.i 0.121428 + 0.0106259i
\(253\) −4.78369e6 −0.295394
\(254\) 671908. 615679.i 0.0410023 0.0375710i
\(255\) 2.67685e6i 0.161437i
\(256\) 1.57650e7 + 5.73932e6i 0.939667 + 0.342090i
\(257\) 1.05098e7 0.619151 0.309575 0.950875i \(-0.399813\pi\)
0.309575 + 0.950875i \(0.399813\pi\)
\(258\) 8.46049e6 + 9.23318e6i 0.492648 + 0.537641i
\(259\) 8.07216e6i 0.464612i
\(260\) −1.03445e6 + 1.18213e7i −0.0588557 + 0.672579i
\(261\) 3.33800e6 0.187743
\(262\) 1.80260e6 1.65174e6i 0.100229 0.0918415i
\(263\) 3.25978e7i 1.79193i −0.444124 0.895965i \(-0.646485\pi\)
0.444124 0.895965i \(-0.353515\pi\)
\(264\) −4.34281e6 + 3.33216e6i −0.236026 + 0.181098i
\(265\) −5.57252e6 −0.299443
\(266\) −4.12360e6 4.50021e6i −0.219095 0.239104i
\(267\) 387091.i 0.0203367i
\(268\) 2.83546e7 + 2.48124e6i 1.47306 + 0.128903i
\(269\) −1.89694e7 −0.974534 −0.487267 0.873253i \(-0.662006\pi\)
−0.487267 + 0.873253i \(0.662006\pi\)
\(270\) 1.24899e6 1.14447e6i 0.0634553 0.0581450i
\(271\) 1.42827e7i 0.717634i −0.933408 0.358817i \(-0.883180\pi\)
0.933408 0.358817i \(-0.116820\pi\)
\(272\) 1.23909e7 + 2.18533e6i 0.615740 + 0.108595i
\(273\) −6.48500e6 −0.318729
\(274\) −1.03940e7 1.13432e7i −0.505278 0.551424i
\(275\) 2.14325e6i 0.103056i
\(276\) −606615. + 6.93215e6i −0.0288527 + 0.329716i
\(277\) −120847. −0.00568586 −0.00284293 0.999996i \(-0.500905\pi\)
−0.00284293 + 0.999996i \(0.500905\pi\)
\(278\) 6.34180e6 5.81108e6i 0.295174 0.270472i
\(279\) 9.12269e6i 0.420059i
\(280\) 2.18533e6 + 2.84815e6i 0.0995506 + 0.129744i
\(281\) 2.02777e7 0.913901 0.456951 0.889492i \(-0.348942\pi\)
0.456951 + 0.889492i \(0.348942\pi\)
\(282\) 6.14446e6 + 6.70563e6i 0.273991 + 0.299014i
\(283\) 2.06847e7i 0.912618i −0.889821 0.456309i \(-0.849171\pi\)
0.889821 0.456309i \(-0.150829\pi\)
\(284\) −2.07084e7 1.81214e6i −0.904047 0.0791109i
\(285\) −5.30084e6 −0.228986
\(286\) 1.34172e7 1.22944e7i 0.573540 0.525543i
\(287\) 344231.i 0.0145614i
\(288\) 4.27800e6 + 6.71581e6i 0.179087 + 0.281139i
\(289\) −1.47015e7 −0.609071
\(290\) 4.15024e6 + 4.52928e6i 0.170169 + 0.185710i
\(291\) 1.46262e7i 0.593542i
\(292\) 3.84696e6 4.39615e7i 0.154514 1.76573i
\(293\) −1.71395e6 −0.0681390 −0.0340695 0.999419i \(-0.510847\pi\)
−0.0340695 + 0.999419i \(0.510847\pi\)
\(294\) 9.37075e6 8.58655e6i 0.368750 0.337891i
\(295\) 1.33016e7i 0.518127i
\(296\) −2.61423e7 + 2.00585e7i −1.00802 + 0.773436i
\(297\) −2.59795e6 −0.0991658
\(298\) 1.82923e7 + 1.99629e7i 0.691225 + 0.754354i
\(299\) 2.31343e7i 0.865452i
\(300\) 3.10582e6 + 271783.i 0.115030 + 0.0100660i
\(301\) −1.25955e7 −0.461866
\(302\) −3.67930e7 + 3.37139e7i −1.33581 + 1.22402i
\(303\) 2.45786e7i 0.883548i
\(304\) 4.32751e6 2.45372e7i 0.154034 0.873382i
\(305\) −1.53304e7 −0.540322
\(306\) 4.03432e6 + 4.40277e6i 0.140801 + 0.153660i
\(307\) 2.97507e7i 1.02821i 0.857727 + 0.514105i \(0.171876\pi\)
−0.857727 + 0.514105i \(0.828124\pi\)
\(308\) 479935. 5.48450e6i 0.0164259 0.187709i
\(309\) −2.92266e7 −0.990612
\(310\) −1.23785e7 + 1.13426e7i −0.415510 + 0.380738i
\(311\) 2.32545e7i 0.773084i −0.922272 0.386542i \(-0.873669\pi\)
0.922272 0.386542i \(-0.126331\pi\)
\(312\) −1.61146e7 2.10022e7i −0.530586 0.691513i
\(313\) −2.24367e7 −0.731688 −0.365844 0.930676i \(-0.619220\pi\)
−0.365844 + 0.930676i \(0.619220\pi\)
\(314\) −1.34733e6 1.47038e6i −0.0435197 0.0474943i
\(315\) 1.70382e6i 0.0545119i
\(316\) 9.41886e6 + 824221.i 0.298495 + 0.0261205i
\(317\) −1.50965e7 −0.473914 −0.236957 0.971520i \(-0.576150\pi\)
−0.236957 + 0.971520i \(0.576150\pi\)
\(318\) 9.16546e6 8.39844e6i 0.285019 0.261166i
\(319\) 9.42110e6i 0.290222i
\(320\) −3.79360e6 + 1.41547e7i −0.115772 + 0.431969i
\(321\) 2.83627e7 0.857498
\(322\) −4.72827e6 5.16009e6i −0.141623 0.154557i
\(323\) 1.86858e7i 0.554503i
\(324\) −329444. + 3.76475e6i −0.00968604 + 0.110688i
\(325\) −1.03649e7 −0.301936
\(326\) −1.17232e7 + 1.07421e7i −0.338370 + 0.310053i
\(327\) 1.72350e7i 0.492911i
\(328\) −1.11482e6 + 855381.i −0.0315924 + 0.0242403i
\(329\) −9.14752e6 −0.256871
\(330\) −3.23012e6 3.52513e6i −0.0898829 0.0980919i
\(331\) 5.09403e7i 1.40468i 0.711842 + 0.702340i \(0.247861\pi\)
−0.711842 + 0.702340i \(0.752139\pi\)
\(332\) −2.26710e7 1.98388e6i −0.619521 0.0542128i
\(333\) −1.56388e7 −0.423518
\(334\) −2.61272e7 + 2.39408e7i −0.701220 + 0.642538i
\(335\) 2.48614e7i 0.661289i
\(336\) −7.88685e6 1.39097e6i −0.207915 0.0366690i
\(337\) −3.39896e7 −0.888090 −0.444045 0.896005i \(-0.646457\pi\)
−0.444045 + 0.896005i \(0.646457\pi\)
\(338\) 3.33692e7 + 3.64167e7i 0.864162 + 0.943085i
\(339\) 4.06469e7i 1.04335i
\(340\) −958052. + 1.09482e7i −0.0243754 + 0.278553i
\(341\) 2.57477e7 0.649345
\(342\) 8.71861e6 7.98898e6i 0.217956 0.199716i
\(343\) 2.75396e7i 0.682456i
\(344\) −3.12986e7 4.07915e7i −0.768864 1.00206i
\(345\) −6.07812e6 −0.148017
\(346\) −4.06218e7 4.43317e7i −0.980687 1.07025i
\(347\) 7.60373e7i 1.81986i 0.414761 + 0.909931i \(0.363865\pi\)
−0.414761 + 0.909931i \(0.636135\pi\)
\(348\) −1.36523e7 1.19468e6i −0.323943 0.0283474i
\(349\) 3.85106e7 0.905949 0.452975 0.891523i \(-0.350363\pi\)
0.452975 + 0.891523i \(0.350363\pi\)
\(350\) −2.31189e6 + 2.11841e6i −0.0539215 + 0.0494091i
\(351\) 1.25639e7i 0.290538i
\(352\) 1.89546e7 1.20742e7i 0.434596 0.276840i
\(353\) 7.10717e7 1.61574 0.807872 0.589358i \(-0.200619\pi\)
0.807872 + 0.589358i \(0.200619\pi\)
\(354\) 2.00470e7 + 2.18779e7i 0.451897 + 0.493169i
\(355\) 1.81572e7i 0.405847i
\(356\) −138541. + 1.58319e6i −0.00307064 + 0.0350900i
\(357\) −6.00607e6 −0.132004
\(358\) −1.19070e7 + 1.09105e7i −0.259509 + 0.237792i
\(359\) 7.94912e7i 1.71805i −0.511934 0.859025i \(-0.671071\pi\)
0.511934 0.859025i \(-0.328929\pi\)
\(360\) −5.51794e6 + 4.23382e6i −0.118269 + 0.0907455i
\(361\) 1.00433e7 0.213478
\(362\) 3.66949e7 + 4.00462e7i 0.773534 + 0.844180i
\(363\) 2.02835e7i 0.424055i
\(364\) 2.65235e7 + 2.32100e6i 0.549954 + 0.0481251i
\(365\) 3.85455e7 0.792675
\(366\) 2.52148e7 2.31047e7i 0.514295 0.471255i
\(367\) 4.00489e6i 0.0810200i −0.999179 0.0405100i \(-0.987102\pi\)
0.999179 0.0405100i \(-0.0128983\pi\)
\(368\) 4.96208e6 2.81352e7i 0.0995680 0.564555i
\(369\) −666906. −0.0132735
\(370\) −1.94443e7 2.12201e7i −0.383873 0.418931i
\(371\) 1.25031e7i 0.244848i
\(372\) 3.26504e6 3.73116e7i 0.0634249 0.724794i
\(373\) 3.28411e6 0.0632836 0.0316418 0.999499i \(-0.489926\pi\)
0.0316418 + 0.999499i \(0.489926\pi\)
\(374\) 1.24263e7 1.13864e7i 0.237535 0.217656i
\(375\) 2.72319e6i 0.0516398i
\(376\) −2.27307e7 2.96250e7i −0.427612 0.557307i
\(377\) 4.55612e7 0.850297
\(378\) −2.56785e6 2.80237e6i −0.0475439 0.0518860i
\(379\) 3.03692e7i 0.557848i 0.960313 + 0.278924i \(0.0899778\pi\)
−0.960313 + 0.278924i \(0.910022\pi\)
\(380\) 2.16803e7 + 1.89719e6i 0.395106 + 0.0345748i
\(381\) −1.77578e6 −0.0321080
\(382\) −5.36404e7 + 4.91514e7i −0.962281 + 0.881752i
\(383\) 8.62249e7i 1.53475i −0.641201 0.767373i \(-0.721563\pi\)
0.641201 0.767373i \(-0.278437\pi\)
\(384\) −1.50933e7 2.89986e7i −0.266557 0.512133i
\(385\) 4.80882e6 0.0842668
\(386\) −4.28045e7 4.67138e7i −0.744265 0.812238i
\(387\) 2.44022e7i 0.421014i
\(388\) 5.23475e6 5.98206e7i 0.0896191 1.02413i
\(389\) 9.20364e7 1.56355 0.781773 0.623563i \(-0.214315\pi\)
0.781773 + 0.623563i \(0.214315\pi\)
\(390\) 1.70478e7 1.56211e7i 0.287392 0.263341i
\(391\) 2.14258e7i 0.358432i
\(392\) −4.13993e7 + 3.17649e7i −0.687281 + 0.527339i
\(393\) −4.76406e6 −0.0784873
\(394\) 5.99125e7 + 6.53842e7i 0.979554 + 1.06902i
\(395\) 8.25847e6i 0.134001i
\(396\) 1.06256e7 + 929816.i 0.171106 + 0.0149731i
\(397\) 8.16043e7 1.30419 0.652096 0.758136i \(-0.273890\pi\)
0.652096 + 0.758136i \(0.273890\pi\)
\(398\) −329004. + 301471.i −0.00521858 + 0.00478186i
\(399\) 1.18935e7i 0.187237i
\(400\) −1.26055e7 2.22317e6i −0.196960 0.0347370i
\(401\) 4.00404e7 0.620962 0.310481 0.950580i \(-0.399510\pi\)
0.310481 + 0.950580i \(0.399510\pi\)
\(402\) −3.74690e7 4.08910e7i −0.576759 0.629434i
\(403\) 1.24518e8i 1.90247i
\(404\) 8.79678e6 1.00526e8i 0.133407 1.52452i
\(405\) −3.30094e6 −0.0496904
\(406\) 1.01624e7 9.31194e6i 0.151851 0.139143i
\(407\) 4.41388e7i 0.654692i
\(408\) −1.49245e7 1.94511e7i −0.219745 0.286394i
\(409\) 1.10874e8 1.62054 0.810272 0.586054i \(-0.199319\pi\)
0.810272 + 0.586054i \(0.199319\pi\)
\(410\) −829187. 904915.i −0.0120310 0.0131297i
\(411\) 2.99789e7i 0.431808i
\(412\) 1.19536e8 + 1.04603e7i 1.70926 + 0.149573i
\(413\) −2.98448e7 −0.423662
\(414\) 9.99706e6 9.16044e6i 0.140887 0.129097i
\(415\) 1.98780e7i 0.278117i
\(416\) 5.83915e7 + 9.16658e7i 0.811091 + 1.27329i
\(417\) −1.67606e7 −0.231144
\(418\) −2.25480e7 2.46072e7i −0.308730 0.336926i
\(419\) 6.94644e7i 0.944322i 0.881512 + 0.472161i \(0.156526\pi\)
−0.881512 + 0.472161i \(0.843474\pi\)
\(420\) 609802. 6.96856e6i 0.00823077 0.0940579i
\(421\) −7.39798e7 −0.991441 −0.495721 0.868482i \(-0.665096\pi\)
−0.495721 + 0.868482i \(0.665096\pi\)
\(422\) −7.80008e7 + 7.14732e7i −1.03791 + 0.951055i
\(423\) 1.77222e7i 0.234152i
\(424\) −4.04923e7 + 3.10691e7i −0.531221 + 0.407596i
\(425\) −9.59943e6 −0.125049
\(426\) 2.73650e7 + 2.98642e7i 0.353970 + 0.386297i
\(427\) 3.43969e7i 0.441810i
\(428\) −1.16003e8 1.01511e7i −1.47958 0.129474i
\(429\) −3.54601e7 −0.449126
\(430\) 3.31111e7 3.03401e7i 0.416455 0.381603i
\(431\) 2.84179e7i 0.354945i −0.984126 0.177472i \(-0.943208\pi\)
0.984126 0.177472i \(-0.0567920\pi\)
\(432\) 2.69483e6 1.52798e7i 0.0334257 0.189525i
\(433\) −1.07801e8 −1.32788 −0.663938 0.747787i \(-0.731116\pi\)
−0.663938 + 0.747787i \(0.731116\pi\)
\(434\) 2.54494e7 + 2.77737e7i 0.311321 + 0.339754i
\(435\) 1.19704e7i 0.145425i
\(436\) −6.16847e6 + 7.04907e7i −0.0744248 + 0.850497i
\(437\) −4.24285e7 −0.508409
\(438\) −6.33981e7 + 5.80926e7i −0.754491 + 0.691351i
\(439\) 2.74240e7i 0.324144i 0.986779 + 0.162072i \(0.0518177\pi\)
−0.986779 + 0.162072i \(0.948182\pi\)
\(440\) 1.19495e7 + 1.55737e7i 0.140278 + 0.182825i
\(441\) −2.47658e7 −0.288760
\(442\) 5.50655e7 + 6.00946e7i 0.637694 + 0.695934i
\(443\) 1.05313e6i 0.0121135i −0.999982 0.00605677i \(-0.998072\pi\)
0.999982 0.00605677i \(-0.00192794\pi\)
\(444\) 6.39624e7 + 5.59719e6i 0.730762 + 0.0639471i
\(445\) −1.38815e6 −0.0157527
\(446\) 5.52452e7 5.06220e7i 0.622716 0.570604i
\(447\) 5.27597e7i 0.590718i
\(448\) 3.17592e7 + 8.51175e6i 0.353212 + 0.0946639i
\(449\) −1.37073e8 −1.51431 −0.757153 0.653237i \(-0.773411\pi\)
−0.757153 + 0.653237i \(0.773411\pi\)
\(450\) −4.10417e6 4.47900e6i −0.0450389 0.0491522i
\(451\) 1.88226e6i 0.0205187i
\(452\) 1.45476e7 1.66245e8i 0.157535 1.80025i
\(453\) 9.72397e7 1.04604
\(454\) −9.35315e7 + 8.57042e7i −0.999518 + 0.915872i
\(455\) 2.32558e7i 0.246887i
\(456\) −3.85181e7 + 2.95543e7i −0.406229 + 0.311692i
\(457\) −1.02848e7 −0.107757 −0.0538786 0.998547i \(-0.517158\pi\)
−0.0538786 + 0.998547i \(0.517158\pi\)
\(458\) −8.72893e7 9.52613e7i −0.908583 0.991563i
\(459\) 1.16360e7i 0.120328i
\(460\) 2.48594e7 + 2.17538e6i 0.255397 + 0.0223492i
\(461\) −1.70299e8 −1.73824 −0.869119 0.494603i \(-0.835314\pi\)
−0.869119 + 0.494603i \(0.835314\pi\)
\(462\) −7.90936e6 + 7.24746e6i −0.0802076 + 0.0734954i
\(463\) 8.24512e7i 0.830719i 0.909657 + 0.415360i \(0.136344\pi\)
−0.909657 + 0.415360i \(0.863656\pi\)
\(464\) 5.54100e7 + 9.77241e6i 0.554670 + 0.0978246i
\(465\) 3.27149e7 0.325376
\(466\) −2.28494e7 2.49362e7i −0.225796 0.246418i
\(467\) 1.65279e8i 1.62281i −0.584487 0.811403i \(-0.698704\pi\)
0.584487 0.811403i \(-0.301296\pi\)
\(468\) −4.49666e6 + 5.13860e7i −0.0438685 + 0.501311i
\(469\) 5.57817e7 0.540721
\(470\) 2.40470e7 2.20346e7i 0.231616 0.212233i
\(471\) 3.88605e6i 0.0371917i
\(472\) −7.41615e7 9.66548e7i −0.705266 0.919173i
\(473\) −6.88725e7 −0.650822
\(474\) −1.24465e7 1.35832e7i −0.116872 0.127546i
\(475\) 1.90093e7i 0.177372i
\(476\) 2.45647e7 + 2.14959e6i 0.227766 + 0.0199313i
\(477\) −2.42233e7 −0.223192
\(478\) 2.16680e7 1.98547e7i 0.198397 0.181794i
\(479\) 1.47850e8i 1.34529i −0.739965 0.672645i \(-0.765158\pi\)
0.739965 0.672645i \(-0.234842\pi\)
\(480\) 2.40835e7 1.53413e7i 0.217769 0.138720i
\(481\) −2.13458e8 −1.91813
\(482\) 1.09926e8 + 1.19966e8i 0.981657 + 1.07131i
\(483\) 1.36375e7i 0.121030i
\(484\) −7.25952e6 + 8.29589e7i −0.0640283 + 0.731690i
\(485\) 5.24508e7 0.459755
\(486\) 5.42926e6 4.97490e6i 0.0472968 0.0433387i
\(487\) 2.20767e8i 1.91138i −0.294379 0.955689i \(-0.595113\pi\)
0.294379 0.955689i \(-0.404887\pi\)
\(488\) −1.11397e8 + 8.54730e7i −0.958548 + 0.735477i
\(489\) 3.09830e7 0.264970
\(490\) −3.07922e7 3.36044e7i −0.261729 0.285633i
\(491\) 3.00650e7i 0.253990i 0.991903 + 0.126995i \(0.0405333\pi\)
−0.991903 + 0.126995i \(0.959467\pi\)
\(492\) 2.72763e6 + 238688.i 0.0229029 + 0.00200417i
\(493\) 4.21964e7 0.352155
\(494\) 1.19002e8 1.09044e8i 0.987132 0.904522i
\(495\) 9.31651e6i 0.0768135i
\(496\) −2.67079e7 + 1.51435e8i −0.218874 + 1.24102i
\(497\) −4.07394e7 −0.331853
\(498\) 2.99584e7 + 3.26945e7i 0.242567 + 0.264720i
\(499\) 7.22660e7i 0.581611i −0.956782 0.290805i \(-0.906077\pi\)
0.956782 0.290805i \(-0.0939233\pi\)
\(500\) 974639. 1.11378e7i 0.00779711 0.0891022i
\(501\) 6.90514e7 0.549110
\(502\) −410922. + 376534.i −0.00324824 + 0.00297641i
\(503\) 5.97200e7i 0.469262i 0.972084 + 0.234631i \(0.0753882\pi\)
−0.972084 + 0.234631i \(0.924612\pi\)
\(504\) 9.49947e6 + 1.23807e7i 0.0742006 + 0.0967058i
\(505\) 8.81414e7 0.684393
\(506\) −2.58543e7 2.82155e7i −0.199563 0.217789i
\(507\) 9.62453e7i 0.738509i
\(508\) 7.26288e6 + 635556.i 0.0554010 + 0.00484800i
\(509\) −4.00798e7 −0.303929 −0.151964 0.988386i \(-0.548560\pi\)
−0.151964 + 0.988386i \(0.548560\pi\)
\(510\) 1.57888e7 1.44675e7i 0.119025 0.109064i
\(511\) 8.64849e7i 0.648153i
\(512\) 5.13525e7 + 1.24005e8i 0.382606 + 0.923912i
\(513\) −2.30423e7 −0.170676
\(514\) 5.68021e7 + 6.19898e7i 0.418288 + 0.456490i
\(515\) 1.04810e8i 0.767325i
\(516\) −8.73364e6 + 9.98045e7i −0.0635691 + 0.726442i
\(517\) −5.00189e7 −0.361961
\(518\) −4.76118e7 + 4.36274e7i −0.342551 + 0.313884i
\(519\) 1.17164e8i 0.838091i
\(520\) −7.53158e7 + 5.77885e7i −0.535644 + 0.410990i
\(521\) 1.91011e7 0.135066 0.0675328 0.997717i \(-0.478487\pi\)
0.0675328 + 0.997717i \(0.478487\pi\)
\(522\) 1.80408e7 + 1.96884e7i 0.126836 + 0.138420i
\(523\) 3.75454e7i 0.262453i 0.991352 + 0.131226i \(0.0418915\pi\)
−0.991352 + 0.131226i \(0.958108\pi\)
\(524\) 1.94849e7 + 1.70507e6i 0.135426 + 0.0118508i
\(525\) 6.11005e6 0.0422247
\(526\) 1.92271e8 1.76180e8i 1.32116 1.21060i
\(527\) 1.15322e8i 0.787917i
\(528\) −4.31255e7 7.60584e6i −0.292976 0.0516708i
\(529\) 9.93859e7 0.671364
\(530\) −3.01176e7 3.28682e7i −0.202299 0.220774i
\(531\) 5.78208e7i 0.386189i
\(532\) 4.25674e6 4.86442e7i 0.0282710 0.323070i
\(533\) −9.10277e6 −0.0601162
\(534\) 2.28317e6 2.09210e6i 0.0149939 0.0137391i
\(535\) 1.01711e8i 0.664215i
\(536\) 1.38612e8 + 1.80653e8i 0.900134 + 1.17315i
\(537\) 3.14688e7 0.203216
\(538\) −1.02523e8 1.11887e8i −0.658379 0.718508i
\(539\) 6.98986e7i 0.446378i
\(540\) 1.35008e7 + 1.18142e6i 0.0857386 + 0.00750277i
\(541\) −8.06882e7 −0.509587 −0.254793 0.966996i \(-0.582007\pi\)
−0.254793 + 0.966996i \(0.582007\pi\)
\(542\) 8.42433e7 7.71933e7i 0.529100 0.484822i
\(543\) 1.05837e8i 0.661059i
\(544\) 5.40792e7 + 8.48961e7i 0.335918 + 0.527340i
\(545\) −6.18064e7 −0.381807
\(546\) −3.50493e7 3.82503e7i −0.215328 0.234994i
\(547\) 1.82861e7i 0.111727i −0.998438 0.0558635i \(-0.982209\pi\)
0.998438 0.0558635i \(-0.0177912\pi\)
\(548\) 1.07296e7 1.22613e8i 0.0651988 0.745066i
\(549\) −6.66398e7 −0.402733
\(550\) −1.26414e7 + 1.15835e7i −0.0759816 + 0.0696230i
\(551\) 8.35595e7i 0.499506i
\(552\) −4.41662e7 + 3.38880e7i −0.262587 + 0.201478i
\(553\) 1.85296e7 0.109570
\(554\) −653137. 712787.i −0.00384127 0.00419209i
\(555\) 5.60824e7i 0.328056i
\(556\) 6.85506e7 + 5.99869e6i 0.398829 + 0.0349005i
\(557\) −4.93908e7 −0.285812 −0.142906 0.989736i \(-0.545645\pi\)
−0.142906 + 0.989736i \(0.545645\pi\)
\(558\) −5.38081e7 + 4.93051e7i −0.309703 + 0.283785i
\(559\) 3.33072e8i 1.90679i
\(560\) −4.98814e6 + 2.82830e7i −0.0284037 + 0.161050i
\(561\) −3.28413e7 −0.186008
\(562\) 1.09594e8 + 1.19603e8i 0.617417 + 0.673805i
\(563\) 3.24854e8i 1.82038i 0.414186 + 0.910192i \(0.364066\pi\)
−0.414186 + 0.910192i \(0.635934\pi\)
\(564\) −6.34284e6 + 7.24834e7i −0.0353546 + 0.404018i
\(565\) 1.45764e8 0.808172
\(566\) 1.22004e8 1.11794e8i 0.672858 0.616550i
\(567\) 7.40635e6i 0.0406308i
\(568\) −1.01233e8 1.31938e8i −0.552432 0.719985i
\(569\) 1.91757e7 0.104091 0.0520457 0.998645i \(-0.483426\pi\)
0.0520457 + 0.998645i \(0.483426\pi\)
\(570\) −2.86493e7 3.12658e7i −0.154699 0.168828i
\(571\) 1.60446e8i 0.861825i −0.902394 0.430913i \(-0.858192\pi\)
0.902394 0.430913i \(-0.141808\pi\)
\(572\) 1.45031e8 + 1.26913e7i 0.774948 + 0.0678137i
\(573\) 1.41766e8 0.753541
\(574\) −2.03037e6 + 1.86045e6i −0.0107359 + 0.00983747i
\(575\) 2.17967e7i 0.114654i
\(576\) −1.64905e7 + 6.15295e7i −0.0862911 + 0.321970i
\(577\) −2.87271e6 −0.0149543 −0.00747713 0.999972i \(-0.502380\pi\)
−0.00747713 + 0.999972i \(0.502380\pi\)
\(578\) −7.94567e7 8.67134e7i −0.411478 0.449058i
\(579\) 1.23459e8i 0.636045i
\(580\) −4.28424e6 + 4.89585e7i −0.0219578 + 0.250925i
\(581\) −4.46004e7 −0.227410
\(582\) −8.62690e7 + 7.90495e7i −0.437609 + 0.400987i
\(583\) 6.83674e7i 0.345019i
\(584\) 2.80088e8 2.14907e8i 1.40623 1.07897i
\(585\) −4.50553e7 −0.225050
\(586\) −9.26333e6 1.01093e7i −0.0460335 0.0502377i
\(587\) 3.45048e8i 1.70595i 0.521954 + 0.852974i \(0.325203\pi\)
−0.521954 + 0.852974i \(0.674797\pi\)
\(588\) 1.01292e8 + 8.86377e6i 0.498243 + 0.0436000i
\(589\) 2.28367e8 1.11760
\(590\) 7.84562e7 7.18905e7i 0.382007 0.350038i
\(591\) 1.72803e8i 0.837122i
\(592\) −2.59601e8 4.57847e7i −1.25124 0.220676i
\(593\) 2.63257e8 1.26246 0.631228 0.775598i \(-0.282551\pi\)
0.631228 + 0.775598i \(0.282551\pi\)
\(594\) −1.40411e7 1.53234e7i −0.0669948 0.0731134i
\(595\) 2.15383e7i 0.102250i
\(596\) −1.88829e7 + 2.15786e8i −0.0891927 + 1.01926i
\(597\) 869521. 0.00408655
\(598\) 1.36452e8 1.25033e8i 0.638083 0.584685i
\(599\) 3.84709e8i 1.78999i 0.446072 + 0.894997i \(0.352822\pi\)
−0.446072 + 0.894997i \(0.647178\pi\)
\(600\) 1.51829e7 + 1.97879e7i 0.0702911 + 0.0916105i
\(601\) −3.33173e7 −0.153478 −0.0767390 0.997051i \(-0.524451\pi\)
−0.0767390 + 0.997051i \(0.524451\pi\)
\(602\) −6.80745e7 7.42916e7i −0.312029 0.340526i
\(603\) 1.08070e8i 0.492895i
\(604\) −3.97708e8 3.48024e7i −1.80490 0.157942i
\(605\) −7.27385e7 −0.328472
\(606\) −1.44971e8 + 1.32839e8i −0.651425 + 0.596910i
\(607\) 2.17537e8i 0.972672i 0.873772 + 0.486336i \(0.161667\pi\)
−0.873772 + 0.486336i \(0.838333\pi\)
\(608\) 1.68116e8 1.07090e8i 0.747993 0.476475i
\(609\) −2.68581e7 −0.118911
\(610\) −8.28555e7 9.04226e7i −0.365033 0.398371i
\(611\) 2.41895e8i 1.06048i
\(612\) −4.16457e6 + 4.75910e7i −0.0181684 + 0.207621i
\(613\) 2.89945e8 1.25874 0.629368 0.777108i \(-0.283314\pi\)
0.629368 + 0.777108i \(0.283314\pi\)
\(614\) −1.75477e8 + 1.60792e8i −0.758082 + 0.694641i
\(615\) 2.39159e6i 0.0102816i
\(616\) 3.49430e7 2.68111e7i 0.149492 0.114702i
\(617\) 3.03530e6 0.0129225 0.00646124 0.999979i \(-0.497943\pi\)
0.00646124 + 0.999979i \(0.497943\pi\)
\(618\) −1.57960e8 1.72387e8i −0.669241 0.730362i
\(619\) 3.35021e8i 1.41254i −0.707944 0.706268i \(-0.750377\pi\)
0.707944 0.706268i \(-0.249623\pi\)
\(620\) −1.33803e8 1.17087e7i −0.561423 0.0491287i
\(621\) −2.64211e7 −0.110326
\(622\) 1.37161e8 1.25683e8i 0.569982 0.522282i
\(623\) 3.11460e6i 0.0128806i
\(624\) 3.67824e7 2.08558e8i 0.151386 0.858367i
\(625\) 9.76562e6 0.0400000
\(626\) −1.21263e8 1.32338e8i −0.494316 0.539461i
\(627\) 6.50341e7i 0.263839i
\(628\) 1.39083e6 1.58939e7i 0.00561559 0.0641727i
\(629\) −1.97694e8 −0.794405
\(630\) −1.00496e7 + 9.20856e6i −0.0401907 + 0.0368273i
\(631\) 2.24962e8i 0.895408i 0.894182 + 0.447704i \(0.147758\pi\)
−0.894182 + 0.447704i \(0.852242\pi\)
\(632\) 4.60443e7 + 6.00096e7i 0.182400 + 0.237722i
\(633\) 2.06147e8 0.812767
\(634\) −8.15918e7 8.90435e7i −0.320169 0.349409i
\(635\) 6.36811e6i 0.0248708i
\(636\) 9.90726e7 + 8.66959e6i 0.385108 + 0.0336998i
\(637\) −3.38035e8 −1.30781
\(638\) 5.55682e7 5.09179e7i 0.213976 0.196069i
\(639\) 7.89276e7i 0.302501i
\(640\) −1.03992e8 + 5.41260e7i −0.396697 + 0.206474i
\(641\) 1.37727e8 0.522931 0.261466 0.965213i \(-0.415794\pi\)
0.261466 + 0.965213i \(0.415794\pi\)
\(642\) 1.53291e8 + 1.67291e8i 0.579311 + 0.632219i
\(643\) 2.19532e8i 0.825781i 0.910781 + 0.412890i \(0.135481\pi\)
−0.910781 + 0.412890i \(0.864519\pi\)
\(644\) 4.88092e6 5.57772e7i 0.0182744 0.208833i
\(645\) −8.75088e7 −0.326116
\(646\) 1.10214e8 1.00991e8i 0.408826 0.374613i
\(647\) 2.78194e8i 1.02715i −0.858043 0.513577i \(-0.828320\pi\)
0.858043 0.513577i \(-0.171680\pi\)
\(648\) −2.39860e7 + 1.84041e7i −0.0881523 + 0.0676377i
\(649\) −1.63192e8 −0.596988
\(650\) −5.60188e7 6.11350e7i −0.203983 0.222613i
\(651\) 7.34026e7i 0.266053i
\(652\) −1.26720e8 1.10889e7i −0.457195 0.0400080i
\(653\) 3.99925e8 1.43628 0.718140 0.695898i \(-0.244994\pi\)
0.718140 + 0.695898i \(0.244994\pi\)
\(654\) 1.01657e8 9.31495e7i 0.363415 0.333002i
\(655\) 1.70844e7i 0.0607960i
\(656\) −1.10705e7 1.95245e6i −0.0392153 0.00691622i
\(657\) 1.67554e8 0.590825
\(658\) −4.94393e7 5.39546e7i −0.173538 0.189387i
\(659\) 2.98899e8i 1.04440i 0.852822 + 0.522202i \(0.174889\pi\)
−0.852822 + 0.522202i \(0.825111\pi\)
\(660\) 3.33441e6 3.81043e7i 0.0115981 0.132538i
\(661\) 3.58267e8 1.24052 0.620258 0.784397i \(-0.287028\pi\)
0.620258 + 0.784397i \(0.287028\pi\)
\(662\) −3.00459e8 + 2.75315e8i −1.03565 + 0.948978i
\(663\) 1.58823e8i 0.544971i
\(664\) −1.10828e8 1.44442e8i −0.378568 0.493388i
\(665\) 4.26514e7 0.145033
\(666\) −8.45227e7 9.22421e7i −0.286122 0.312253i
\(667\) 9.58122e7i 0.322882i
\(668\) −2.82418e8 2.47137e7i −0.947465 0.0829103i
\(669\) −1.46007e8 −0.487635
\(670\) −1.46639e8 + 1.34368e8i −0.487557 + 0.446755i
\(671\) 1.88083e8i 0.622561i
\(672\) −3.44215e7 5.40365e7i −0.113428 0.178065i
\(673\) −4.43991e8 −1.45656 −0.728281 0.685279i \(-0.759680\pi\)
−0.728281 + 0.685279i \(0.759680\pi\)
\(674\) −1.83703e8 2.00480e8i −0.599979 0.654774i
\(675\) 1.18375e7i 0.0384900i
\(676\) −3.44465e7 + 3.93641e8i −0.111508 + 1.27427i
\(677\) −2.82838e8 −0.911533 −0.455767 0.890099i \(-0.650635\pi\)
−0.455767 + 0.890099i \(0.650635\pi\)
\(678\) −2.39746e8 + 2.19683e8i −0.769241 + 0.704867i
\(679\) 1.17684e8i 0.375932i
\(680\) −6.97536e7 + 5.35207e7i −0.221840 + 0.170214i
\(681\) 2.47193e8 0.782700
\(682\) 1.39158e8 + 1.51867e8i 0.438687 + 0.478752i
\(683\) 5.76518e8i 1.80947i −0.425978 0.904733i \(-0.640070\pi\)
0.425978 0.904733i \(-0.359930\pi\)
\(684\) 9.42423e7 + 8.24691e6i 0.294495 + 0.0257705i
\(685\) 1.07507e8 0.334477
\(686\) −1.62436e8 + 1.48842e8i −0.503163 + 0.461056i
\(687\) 2.51765e8i 0.776470i
\(688\) 7.14407e7 4.05072e8i 0.219372 1.24385i
\(689\) −3.30630e8 −1.01084
\(690\) −3.28502e7 3.58504e7i −0.0999979 0.109131i
\(691\) 2.97209e8i 0.900799i 0.892827 + 0.450399i \(0.148718\pi\)
−0.892827 + 0.450399i \(0.851282\pi\)
\(692\) 4.19333e7 4.79196e8i 0.126544 1.44609i
\(693\) 2.09035e7 0.0628088
\(694\) −4.48488e8 + 4.10956e8i −1.34175 + 1.22947i
\(695\) 6.01053e7i 0.179043i
\(696\) −6.67397e7 8.69819e7i −0.197950 0.257989i
\(697\) −8.43051e6 −0.0248975
\(698\) 2.08137e8 + 2.27146e8i 0.612044 + 0.667942i
\(699\) 6.59036e7i 0.192964i
\(700\) −2.49899e7 2.18681e6i −0.0728570 0.00637553i
\(701\) −4.28723e8 −1.24458 −0.622289 0.782787i \(-0.713797\pi\)
−0.622289 + 0.782787i \(0.713797\pi\)
\(702\) 7.41053e7 6.79037e7i 0.214209 0.196283i
\(703\) 3.91484e8i 1.12680i
\(704\) 1.73660e8 + 4.65424e7i 0.497716 + 0.133392i
\(705\) −6.35536e7 −0.181373
\(706\) 3.84119e8 + 4.19200e8i 1.09157 + 1.19126i
\(707\) 1.97764e8i 0.559614i
\(708\) −2.06942e7 + 2.36485e8i −0.0583109 + 0.666353i
\(709\) −1.53889e8 −0.431785 −0.215893 0.976417i \(-0.569266\pi\)
−0.215893 + 0.976417i \(0.569266\pi\)
\(710\) 1.07096e8 9.81333e7i 0.299225 0.274184i
\(711\) 3.58989e7i 0.0998786i
\(712\) −1.00869e7 + 7.73947e6i −0.0279458 + 0.0214423i
\(713\) 2.61853e8 0.722420
\(714\) −3.24608e7 3.54254e7i −0.0891794 0.0973241i
\(715\) 1.27163e8i 0.347892i
\(716\) −1.28707e8 1.12628e7i −0.350640 0.0306837i
\(717\) −5.72660e7 −0.155360
\(718\) 4.68860e8 4.29623e8i 1.26669 1.16069i
\(719\) 1.95775e7i 0.0526709i −0.999653 0.0263354i \(-0.991616\pi\)
0.999653 0.0263354i \(-0.00838380\pi\)
\(720\) −5.47949e7 9.66392e6i −0.146806 0.0258914i
\(721\) 2.35162e8 0.627425
\(722\) 5.42805e7 + 5.92379e7i 0.144222 + 0.157394i
\(723\) 3.17055e8i 0.838920i
\(724\) −3.78796e7 + 4.32872e8i −0.0998135 + 1.14063i
\(725\) −4.29269e7 −0.112646
\(726\) 1.19637e8 1.09625e8i 0.312649 0.286485i
\(727\) 2.39913e8i 0.624383i 0.950019 + 0.312192i \(0.101063\pi\)
−0.950019 + 0.312192i \(0.898937\pi\)
\(728\) 1.29661e8 + 1.68987e8i 0.336058 + 0.437984i
\(729\) −1.43489e7 −0.0370370
\(730\) 2.08326e8 + 2.27352e8i 0.535518 + 0.584426i
\(731\) 3.08474e8i 0.789709i
\(732\) 2.72555e8 + 2.38506e7i 0.694898 + 0.0608088i
\(733\) 1.15594e8 0.293510 0.146755 0.989173i \(-0.453117\pi\)
0.146755 + 0.989173i \(0.453117\pi\)
\(734\) 2.36219e7 2.16451e7i 0.0597348 0.0547358i
\(735\) 8.88127e7i 0.223673i
\(736\) 1.92767e8 1.22794e8i 0.483504 0.307994i
\(737\) 3.05016e8 0.761939
\(738\) −3.60441e6 3.93359e6i −0.00896736 0.00978634i
\(739\) 1.13904e8i 0.282232i −0.989993 0.141116i \(-0.954931\pi\)
0.989993 0.141116i \(-0.0450690\pi\)
\(740\) 2.00721e7 2.29375e8i 0.0495332 0.566046i
\(741\) −3.14510e8 −0.773001
\(742\) −7.37468e7 + 6.75752e7i −0.180522 + 0.165415i
\(743\) 2.71020e8i 0.660747i 0.943850 + 0.330373i \(0.107175\pi\)
−0.943850 + 0.330373i \(0.892825\pi\)
\(744\) 2.37720e8 1.82398e8i 0.577228 0.442897i
\(745\) −1.89201e8 −0.457568
\(746\) 1.77495e7 + 1.93706e7i 0.0427533 + 0.0466579i
\(747\) 8.64079e7i 0.207296i
\(748\) 1.34320e8 + 1.17540e7i 0.320949 + 0.0280855i
\(749\) −2.28211e8 −0.543114
\(750\) −1.60621e7 + 1.47179e7i −0.0380732 + 0.0348870i
\(751\) 8.80268e7i 0.207824i 0.994587 + 0.103912i \(0.0331360\pi\)
−0.994587 + 0.103912i \(0.966864\pi\)
\(752\) 5.18841e7 2.94185e8i 0.122006 0.691778i
\(753\) 1.08602e6 0.00254363
\(754\) 2.46243e8 + 2.68732e8i 0.574447 + 0.626910i
\(755\) 3.48711e8i 0.810261i
\(756\) 2.65076e6 3.02918e7i 0.00613486 0.0701067i
\(757\) 4.60925e8 1.06253 0.531266 0.847205i \(-0.321716\pi\)
0.531266 + 0.847205i \(0.321716\pi\)
\(758\) −1.79126e8 + 1.64136e8i −0.411293 + 0.376873i
\(759\) 7.45704e7i 0.170546i
\(760\) 1.05985e8 + 1.38130e8i 0.241436 + 0.314664i
\(761\) 1.29119e8 0.292980 0.146490 0.989212i \(-0.453202\pi\)
0.146490 + 0.989212i \(0.453202\pi\)
\(762\) −9.59748e6 1.04740e7i −0.0216916 0.0236727i
\(763\) 1.38676e8i 0.312195i
\(764\) −5.79817e8 5.07383e7i −1.30020 0.113777i
\(765\) −4.17279e7 −0.0932057
\(766\) 5.08578e8 4.66017e8i 1.13154 1.03685i
\(767\) 7.89210e8i 1.74907i
\(768\) 8.94672e7 2.45752e8i 0.197506 0.542517i
\(769\) 3.63552e8 0.799443 0.399722 0.916637i \(-0.369107\pi\)
0.399722 + 0.916637i \(0.369107\pi\)
\(770\) 2.59901e7 + 2.83637e7i 0.0569293 + 0.0621285i
\(771\) 1.63832e8i 0.357467i
\(772\) 4.41865e7 5.04945e8i 0.0960367 1.09747i
\(773\) 2.47148e8 0.535080