Properties

Label 60.7.c.a.31.15
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 31.15
Character \(\chi\) \(=\) 60.31
Dual form 60.7.c.a.31.16

$q$-expansion

\(f(q)\) \(=\) \(q+(3.43879 - 7.22321i) q^{2} +15.5885i q^{3} +(-40.3494 - 49.6782i) q^{4} +55.9017 q^{5} +(112.599 + 53.6055i) q^{6} +472.024i q^{7} +(-497.589 + 120.619i) q^{8} -243.000 q^{9} +O(q^{10})\) \(q+(3.43879 - 7.22321i) q^{2} +15.5885i q^{3} +(-40.3494 - 49.6782i) q^{4} +55.9017 q^{5} +(112.599 + 53.6055i) q^{6} +472.024i q^{7} +(-497.589 + 120.619i) q^{8} -243.000 q^{9} +(192.234 - 403.790i) q^{10} +939.392i q^{11} +(774.407 - 628.985i) q^{12} +22.5854 q^{13} +(3409.52 + 1623.19i) q^{14} +871.421i q^{15} +(-839.847 + 4008.97i) q^{16} +6247.86 q^{17} +(-835.626 + 1755.24i) q^{18} +11163.0i q^{19} +(-2255.60 - 2777.10i) q^{20} -7358.12 q^{21} +(6785.42 + 3230.37i) q^{22} -1168.18i q^{23} +(-1880.27 - 7756.65i) q^{24} +3125.00 q^{25} +(77.6664 - 163.139i) q^{26} -3788.00i q^{27} +(23449.3 - 19045.9i) q^{28} +25619.9 q^{29} +(6294.46 + 2996.64i) q^{30} +4304.29i q^{31} +(26069.6 + 19852.4i) q^{32} -14643.7 q^{33} +(21485.1 - 45129.6i) q^{34} +26386.9i q^{35} +(9804.91 + 12071.8i) q^{36} -50696.3 q^{37} +(80632.6 + 38387.2i) q^{38} +352.071i q^{39} +(-27816.1 + 6742.82i) q^{40} -113093. q^{41} +(-25303.0 + 53149.2i) q^{42} -113727. i q^{43} +(46667.3 - 37903.9i) q^{44} -13584.1 q^{45} +(-8438.03 - 4017.14i) q^{46} +184245. i q^{47} +(-62493.7 - 13091.9i) q^{48} -105157. q^{49} +(10746.2 - 22572.5i) q^{50} +97394.5i q^{51} +(-911.307 - 1122.00i) q^{52} -133403. q^{53} +(-27361.5 - 13026.1i) q^{54} +52513.6i q^{55} +(-56935.1 - 234874. i) q^{56} -174014. q^{57} +(88101.5 - 185058. i) q^{58} -55214.8i q^{59} +(43290.6 - 35161.3i) q^{60} +204814. q^{61} +(31090.8 + 14801.5i) q^{62} -114702. i q^{63} +(233046. - 120038. i) q^{64} +1262.56 q^{65} +(-50356.5 + 105774. i) q^{66} -244236. i q^{67} +(-252098. - 310383. i) q^{68} +18210.2 q^{69} +(190598. + 90739.1i) q^{70} -14227.6i q^{71} +(120914. - 29310.5i) q^{72} -278492. q^{73} +(-174334. + 366190. i) q^{74} +48713.9i q^{75} +(554557. - 450420. i) q^{76} -443415. q^{77} +(2543.08 + 1210.70i) q^{78} -358976. i q^{79} +(-46948.9 + 224108. i) q^{80} +59049.0 q^{81} +(-388902. + 816892. i) q^{82} +820615. i q^{83} +(296896. + 365538. i) q^{84} +349266. q^{85} +(-821472. - 391083. i) q^{86} +399375. i q^{87} +(-113309. - 467431. i) q^{88} +1.00519e6 q^{89} +(-46712.9 + 98120.9i) q^{90} +10660.8i q^{91} +(-58033.3 + 47135.6i) q^{92} -67097.2 q^{93} +(1.33084e6 + 633579. i) q^{94} +624030. i q^{95} +(-309469. + 406385. i) q^{96} +1.44195e6 q^{97} +(-361614. + 759572. i) q^{98} -228272. 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.43879 7.22321i 0.429849 0.902901i
\(3\) 15.5885i 0.577350i
\(4\) −40.3494 49.6782i −0.630460 0.776222i
\(5\) 55.9017 0.447214
\(6\) 112.599 + 53.6055i 0.521290 + 0.248173i
\(7\) 472.024i 1.37616i 0.725634 + 0.688081i \(0.241547\pi\)
−0.725634 + 0.688081i \(0.758453\pi\)
\(8\) −497.589 + 120.619i −0.971854 + 0.235585i
\(9\) −243.000 −0.333333
\(10\) 192.234 403.790i 0.192234 0.403790i
\(11\) 939.392i 0.705779i 0.935665 + 0.352890i \(0.114801\pi\)
−0.935665 + 0.352890i \(0.885199\pi\)
\(12\) 774.407 628.985i 0.448152 0.363996i
\(13\) 22.5854 0.0102801 0.00514005 0.999987i \(-0.498364\pi\)
0.00514005 + 0.999987i \(0.498364\pi\)
\(14\) 3409.52 + 1623.19i 1.24254 + 0.591542i
\(15\) 871.421i 0.258199i
\(16\) −839.847 + 4008.97i −0.205041 + 0.978753i
\(17\) 6247.86 1.27170 0.635850 0.771813i \(-0.280650\pi\)
0.635850 + 0.771813i \(0.280650\pi\)
\(18\) −835.626 + 1755.24i −0.143283 + 0.300967i
\(19\) 11163.0i 1.62750i 0.581219 + 0.813748i \(0.302576\pi\)
−0.581219 + 0.813748i \(0.697424\pi\)
\(20\) −2255.60 2777.10i −0.281950 0.347137i
\(21\) −7358.12 −0.794527
\(22\) 6785.42 + 3230.37i 0.637248 + 0.303378i
\(23\) 1168.18i 0.0960125i −0.998847 0.0480062i \(-0.984713\pi\)
0.998847 0.0480062i \(-0.0152867\pi\)
\(24\) −1880.27 7756.65i −0.136015 0.561100i
\(25\) 3125.00 0.200000
\(26\) 77.6664 163.139i 0.00441889 0.00928191i
\(27\) 3788.00i 0.192450i
\(28\) 23449.3 19045.9i 1.06821 0.867615i
\(29\) 25619.9 1.05047 0.525235 0.850957i \(-0.323977\pi\)
0.525235 + 0.850957i \(0.323977\pi\)
\(30\) 6294.46 + 2996.64i 0.233128 + 0.110987i
\(31\) 4304.29i 0.144483i 0.997387 + 0.0722414i \(0.0230152\pi\)
−0.997387 + 0.0722414i \(0.976985\pi\)
\(32\) 26069.6 + 19852.4i 0.795581 + 0.605848i
\(33\) −14643.7 −0.407482
\(34\) 21485.1 45129.6i 0.546639 1.14822i
\(35\) 26386.9i 0.615438i
\(36\) 9804.91 + 12071.8i 0.210153 + 0.258741i
\(37\) −50696.3 −1.00086 −0.500428 0.865778i \(-0.666824\pi\)
−0.500428 + 0.865778i \(0.666824\pi\)
\(38\) 80632.6 + 38387.2i 1.46947 + 0.699577i
\(39\) 352.071i 0.00593522i
\(40\) −27816.1 + 6742.82i −0.434626 + 0.105357i
\(41\) −113093. −1.64090 −0.820452 0.571715i \(-0.806278\pi\)
−0.820452 + 0.571715i \(0.806278\pi\)
\(42\) −25303.0 + 53149.2i −0.341527 + 0.717380i
\(43\) 113727.i 1.43040i −0.698920 0.715200i \(-0.746336\pi\)
0.698920 0.715200i \(-0.253664\pi\)
\(44\) 46667.3 37903.9i 0.547841 0.444965i
\(45\) −13584.1 −0.149071
\(46\) −8438.03 4017.14i −0.0866898 0.0412709i
\(47\) 184245.i 1.77460i 0.461190 + 0.887301i \(0.347422\pi\)
−0.461190 + 0.887301i \(0.652578\pi\)
\(48\) −62493.7 13091.9i −0.565084 0.118380i
\(49\) −105157. −0.893822
\(50\) 10746.2 22572.5i 0.0859698 0.180580i
\(51\) 97394.5i 0.734216i
\(52\) −911.307 1122.00i −0.00648119 0.00797964i
\(53\) −133403. −0.896063 −0.448032 0.894018i \(-0.647875\pi\)
−0.448032 + 0.894018i \(0.647875\pi\)
\(54\) −27361.5 13026.1i −0.173763 0.0827245i
\(55\) 52513.6i 0.315634i
\(56\) −56935.1 234874.i −0.324202 1.33743i
\(57\) −174014. −0.939635
\(58\) 88101.5 185058.i 0.451543 0.948470i
\(59\) 55214.8i 0.268844i −0.990924 0.134422i \(-0.957082\pi\)
0.990924 0.134422i \(-0.0429177\pi\)
\(60\) 43290.6 35161.3i 0.200420 0.162784i
\(61\) 204814. 0.902341 0.451170 0.892438i \(-0.351007\pi\)
0.451170 + 0.892438i \(0.351007\pi\)
\(62\) 31090.8 + 14801.5i 0.130454 + 0.0621058i
\(63\) 114702.i 0.458721i
\(64\) 233046. 120038.i 0.889000 0.457907i
\(65\) 1262.56 0.00459740
\(66\) −50356.5 + 105774.i −0.175156 + 0.367916i
\(67\) 244236.i 0.812056i −0.913861 0.406028i \(-0.866914\pi\)
0.913861 0.406028i \(-0.133086\pi\)
\(68\) −252098. 310383.i −0.801756 0.987121i
\(69\) 18210.2 0.0554328
\(70\) 190598. + 90739.1i 0.555680 + 0.264546i
\(71\) 14227.6i 0.0397518i −0.999802 0.0198759i \(-0.993673\pi\)
0.999802 0.0198759i \(-0.00632711\pi\)
\(72\) 120914. 29310.5i 0.323951 0.0785282i
\(73\) −278492. −0.715885 −0.357943 0.933744i \(-0.616522\pi\)
−0.357943 + 0.933744i \(0.616522\pi\)
\(74\) −174334. + 366190.i −0.430216 + 0.903673i
\(75\) 48713.9i 0.115470i
\(76\) 554557. 450420.i 1.26330 1.02607i
\(77\) −443415. −0.971266
\(78\) 2543.08 + 1210.70i 0.00535891 + 0.00255125i
\(79\) 358976.i 0.728088i −0.931382 0.364044i \(-0.881396\pi\)
0.931382 0.364044i \(-0.118604\pi\)
\(80\) −46948.9 + 224108.i −0.0916971 + 0.437712i
\(81\) 59049.0 0.111111
\(82\) −388902. + 816892.i −0.705341 + 1.48157i
\(83\) 820615.i 1.43518i 0.696468 + 0.717588i \(0.254754\pi\)
−0.696468 + 0.717588i \(0.745246\pi\)
\(84\) 296896. + 365538.i 0.500918 + 0.616730i
\(85\) 349266. 0.568722
\(86\) −821472. 391083.i −1.29151 0.614856i
\(87\) 399375.i 0.606489i
\(88\) −113309. 467431.i −0.166271 0.685914i
\(89\) 1.00519e6 1.42587 0.712935 0.701230i \(-0.247365\pi\)
0.712935 + 0.701230i \(0.247365\pi\)
\(90\) −46712.9 + 98120.9i −0.0640781 + 0.134597i
\(91\) 10660.8i 0.0141471i
\(92\) −58033.3 + 47135.6i −0.0745270 + 0.0605320i
\(93\) −67097.2 −0.0834172
\(94\) 1.33084e6 + 633579.i 1.60229 + 0.762811i
\(95\) 624030.i 0.727838i
\(96\) −309469. + 406385.i −0.349786 + 0.459329i
\(97\) 1.44195e6 1.57992 0.789962 0.613156i \(-0.210100\pi\)
0.789962 + 0.613156i \(0.210100\pi\)
\(98\) −361614. + 759572.i −0.384208 + 0.807032i
\(99\) 228272.i 0.235260i
\(100\) −126092. 155244.i −0.126092 0.155244i
\(101\) 778264. 0.755375 0.377688 0.925933i \(-0.376719\pi\)
0.377688 + 0.925933i \(0.376719\pi\)
\(102\) 703501. + 334919.i 0.662925 + 0.315602i
\(103\) 1.15772e6i 1.05948i −0.848161 0.529739i \(-0.822290\pi\)
0.848161 0.529739i \(-0.177710\pi\)
\(104\) −11238.2 + 2724.23i −0.00999076 + 0.00242183i
\(105\) −411331. −0.355323
\(106\) −458746. + 963599.i −0.385172 + 0.809056i
\(107\) 1.02649e6i 0.837925i −0.908004 0.418962i \(-0.862394\pi\)
0.908004 0.418962i \(-0.137606\pi\)
\(108\) −188181. + 152843.i −0.149384 + 0.121332i
\(109\) 769438. 0.594147 0.297074 0.954855i \(-0.403989\pi\)
0.297074 + 0.954855i \(0.403989\pi\)
\(110\) 379317. + 180583.i 0.284986 + 0.135675i
\(111\) 790277.i 0.577844i
\(112\) −1.89233e6 396428.i −1.34692 0.282169i
\(113\) −337398. −0.233834 −0.116917 0.993142i \(-0.537301\pi\)
−0.116917 + 0.993142i \(0.537301\pi\)
\(114\) −598397. + 1.25694e6i −0.403901 + 0.848397i
\(115\) 65303.5i 0.0429381i
\(116\) −1.03375e6 1.27275e6i −0.662279 0.815398i
\(117\) −5488.25 −0.00342670
\(118\) −398828. 189872.i −0.242739 0.115562i
\(119\) 2.94914e6i 1.75007i
\(120\) −105110. 433610.i −0.0608277 0.250932i
\(121\) 889104. 0.501876
\(122\) 704313. 1.47942e6i 0.387870 0.814724i
\(123\) 1.76294e6i 0.947376i
\(124\) 213829. 173676.i 0.112151 0.0910906i
\(125\) 174693. 0.0894427
\(126\) −828514. 394435.i −0.414179 0.197181i
\(127\) 3.10443e6i 1.51555i −0.652515 0.757776i \(-0.726286\pi\)
0.652515 0.757776i \(-0.273714\pi\)
\(128\) −65660.6 2.09612e6i −0.0313094 0.999510i
\(129\) 1.77283e6 0.825842
\(130\) 4341.68 9119.74i 0.00197619 0.00415100i
\(131\) 70316.0i 0.0312781i 0.999878 + 0.0156390i \(0.00497826\pi\)
−0.999878 + 0.0156390i \(0.995022\pi\)
\(132\) 590864. + 727471.i 0.256901 + 0.316296i
\(133\) −5.26919e6 −2.23970
\(134\) −1.76417e6 839878.i −0.733206 0.349061i
\(135\) 211755.i 0.0860663i
\(136\) −3.10887e6 + 753613.i −1.23591 + 0.299593i
\(137\) 3.75318e6 1.45961 0.729807 0.683654i \(-0.239610\pi\)
0.729807 + 0.683654i \(0.239610\pi\)
\(138\) 62621.0 131536.i 0.0238277 0.0500504i
\(139\) 4.22525e6i 1.57329i 0.617406 + 0.786645i \(0.288184\pi\)
−0.617406 + 0.786645i \(0.711816\pi\)
\(140\) 1.31085e6 1.06470e6i 0.477717 0.388009i
\(141\) −2.87209e6 −1.02457
\(142\) −102769. 48925.7i −0.0358919 0.0170873i
\(143\) 21216.5i 0.00725548i
\(144\) 204083. 974181.i 0.0683470 0.326251i
\(145\) 1.43220e6 0.469784
\(146\) −957674. + 2.01160e6i −0.307722 + 0.646373i
\(147\) 1.63924e6i 0.516048i
\(148\) 2.04557e6 + 2.51850e6i 0.630999 + 0.776886i
\(149\) 3.77574e6 1.14141 0.570707 0.821154i \(-0.306669\pi\)
0.570707 + 0.821154i \(0.306669\pi\)
\(150\) 351871. + 167517.i 0.104258 + 0.0496347i
\(151\) 3.33342e6i 0.968186i −0.875017 0.484093i \(-0.839150\pi\)
0.875017 0.484093i \(-0.160850\pi\)
\(152\) −1.34647e6 5.55458e6i −0.383413 1.58169i
\(153\) −1.51823e6 −0.423900
\(154\) −1.52481e6 + 3.20288e6i −0.417498 + 0.876957i
\(155\) 240617.i 0.0646147i
\(156\) 17490.3 14205.9i 0.00460705 0.00374192i
\(157\) −7.25721e6 −1.87530 −0.937650 0.347580i \(-0.887003\pi\)
−0.937650 + 0.347580i \(0.887003\pi\)
\(158\) −2.59296e6 1.23444e6i −0.657392 0.312968i
\(159\) 2.07955e6i 0.517342i
\(160\) 1.45733e6 + 1.10978e6i 0.355794 + 0.270943i
\(161\) 551410. 0.132129
\(162\) 203057. 426523.i 0.0477610 0.100322i
\(163\) 2.00685e6i 0.463396i 0.972788 + 0.231698i \(0.0744281\pi\)
−0.972788 + 0.231698i \(0.925572\pi\)
\(164\) 4.56323e6 + 5.61824e6i 1.03452 + 1.27371i
\(165\) −818606. −0.182231
\(166\) 5.92747e6 + 2.82192e6i 1.29582 + 0.616909i
\(167\) 3.95037e6i 0.848182i 0.905620 + 0.424091i \(0.139406\pi\)
−0.905620 + 0.424091i \(0.860594\pi\)
\(168\) 3.66132e6 887531.i 0.772165 0.187178i
\(169\) −4.82630e6 −0.999894
\(170\) 1.20105e6 2.52282e6i 0.244464 0.513499i
\(171\) 2.71261e6i 0.542498i
\(172\) −5.64974e6 + 4.58881e6i −1.11031 + 0.901810i
\(173\) −4.23383e6 −0.817703 −0.408851 0.912601i \(-0.634071\pi\)
−0.408851 + 0.912601i \(0.634071\pi\)
\(174\) 2.88477e6 + 1.37337e6i 0.547599 + 0.260699i
\(175\) 1.47507e6i 0.275232i
\(176\) −3.76600e6 788946.i −0.690784 0.144714i
\(177\) 860714. 0.155217
\(178\) 3.45665e6 7.26072e6i 0.612909 1.28742i
\(179\) 5.09011e6i 0.887499i 0.896151 + 0.443750i \(0.146352\pi\)
−0.896151 + 0.443750i \(0.853648\pi\)
\(180\) 548111. + 674834.i 0.0939834 + 0.115712i
\(181\) 7.69100e6 1.29702 0.648510 0.761206i \(-0.275392\pi\)
0.648510 + 0.761206i \(0.275392\pi\)
\(182\) 77005.4 + 36660.4i 0.0127734 + 0.00608111i
\(183\) 3.19274e6i 0.520967i
\(184\) 140906. + 581276.i 0.0226191 + 0.0933101i
\(185\) −2.83401e6 −0.447596
\(186\) −230733. + 484657.i −0.0358568 + 0.0753174i
\(187\) 5.86919e6i 0.897539i
\(188\) 9.15294e6 7.43416e6i 1.37749 1.11882i
\(189\) 1.78802e6 0.264842
\(190\) 4.50750e6 + 2.14591e6i 0.657165 + 0.312860i
\(191\) 472014.i 0.0677415i −0.999426 0.0338708i \(-0.989217\pi\)
0.999426 0.0338708i \(-0.0107835\pi\)
\(192\) 1.87120e6 + 3.63283e6i 0.264373 + 0.513264i
\(193\) −5.76885e6 −0.802449 −0.401225 0.915980i \(-0.631415\pi\)
−0.401225 + 0.915980i \(0.631415\pi\)
\(194\) 4.95858e6 1.04155e7i 0.679129 1.42651i
\(195\) 19681.4i 0.00265431i
\(196\) 4.24303e6 + 5.22402e6i 0.563519 + 0.693804i
\(197\) 1.01304e7 1.32504 0.662521 0.749043i \(-0.269486\pi\)
0.662521 + 0.749043i \(0.269486\pi\)
\(198\) −1.64886e6 784981.i −0.212416 0.101126i
\(199\) 8.69529e6i 1.10338i −0.834050 0.551690i \(-0.813983\pi\)
0.834050 0.551690i \(-0.186017\pi\)
\(200\) −1.55497e6 + 376935.i −0.194371 + 0.0471169i
\(201\) 3.80727e6 0.468841
\(202\) 2.67629e6 5.62156e6i 0.324697 0.682029i
\(203\) 1.20932e7i 1.44562i
\(204\) 4.83839e6 3.92981e6i 0.569915 0.462894i
\(205\) −6.32208e6 −0.733835
\(206\) −8.36246e6 3.98116e6i −0.956604 0.455416i
\(207\) 283869.i 0.0320042i
\(208\) −18968.3 + 90544.2i −0.00210784 + 0.0100617i
\(209\) −1.04864e7 −1.14865
\(210\) −1.41448e6 + 2.97113e6i −0.152735 + 0.320822i
\(211\) 2.10959e6i 0.224570i 0.993676 + 0.112285i \(0.0358169\pi\)
−0.993676 + 0.112285i \(0.964183\pi\)
\(212\) 5.38274e6 + 6.62723e6i 0.564932 + 0.695544i
\(213\) 221786. 0.0229507
\(214\) −7.41458e6 3.52990e6i −0.756563 0.360181i
\(215\) 6.35752e6i 0.639694i
\(216\) 456905. + 1.88487e6i 0.0453383 + 0.187033i
\(217\) −2.03172e6 −0.198832
\(218\) 2.64594e6 5.55781e6i 0.255394 0.536456i
\(219\) 4.34125e6i 0.413317i
\(220\) 2.60878e6 2.11889e6i 0.245002 0.198995i
\(221\) 141110. 0.0130732
\(222\) −5.70834e6 2.71760e6i −0.521736 0.248386i
\(223\) 5.11069e6i 0.460855i 0.973089 + 0.230428i \(0.0740125\pi\)
−0.973089 + 0.230428i \(0.925987\pi\)
\(224\) −9.37081e6 + 1.23055e7i −0.833744 + 1.09485i
\(225\) −759375. −0.0666667
\(226\) −1.16024e6 + 2.43709e6i −0.100513 + 0.211129i
\(227\) 2.13819e6i 0.182797i −0.995814 0.0913983i \(-0.970866\pi\)
0.995814 0.0913983i \(-0.0291336\pi\)
\(228\) 7.02136e6 + 8.64469e6i 0.592402 + 0.729365i
\(229\) 1.43797e7 1.19741 0.598706 0.800969i \(-0.295682\pi\)
0.598706 + 0.800969i \(0.295682\pi\)
\(230\) −471700. 224565.i −0.0387688 0.0184569i
\(231\) 6.91216e6i 0.560761i
\(232\) −1.27482e7 + 3.09025e6i −1.02090 + 0.247474i
\(233\) −2.16907e7 −1.71477 −0.857385 0.514676i \(-0.827912\pi\)
−0.857385 + 0.514676i \(0.827912\pi\)
\(234\) −18872.9 + 39642.7i −0.00147296 + 0.00309397i
\(235\) 1.02996e7i 0.793626i
\(236\) −2.74297e6 + 2.22789e6i −0.208682 + 0.169495i
\(237\) 5.59588e6 0.420362
\(238\) 2.13022e7 + 1.01415e7i 1.58014 + 0.752264i
\(239\) 4.39731e6i 0.322102i −0.986946 0.161051i \(-0.948512\pi\)
0.986946 0.161051i \(-0.0514883\pi\)
\(240\) −3.49351e6 731861.i −0.252713 0.0529413i
\(241\) 1.72165e7 1.22997 0.614985 0.788539i \(-0.289162\pi\)
0.614985 + 0.788539i \(0.289162\pi\)
\(242\) 3.05744e6 6.42218e6i 0.215731 0.453144i
\(243\) 920483.i 0.0641500i
\(244\) −8.26414e6 1.01748e7i −0.568890 0.700417i
\(245\) −5.87847e6 −0.399729
\(246\) −1.27341e7 6.06239e6i −0.855387 0.407229i
\(247\) 252120.i 0.0167308i
\(248\) −519180. 2.14177e6i −0.0340379 0.140416i
\(249\) −1.27921e7 −0.828600
\(250\) 600732. 1.26184e6i 0.0384469 0.0807579i
\(251\) 4.94767e6i 0.312881i −0.987687 0.156441i \(-0.949998\pi\)
0.987687 0.156441i \(-0.0500020\pi\)
\(252\) −5.69818e6 + 4.62815e6i −0.356069 + 0.289205i
\(253\) 1.09738e6 0.0677636
\(254\) −2.24239e7 1.06755e7i −1.36839 0.651458i
\(255\) 5.44452e6i 0.328352i
\(256\) −1.53665e7 6.73385e6i −0.915916 0.401369i
\(257\) 2.51861e7 1.48375 0.741876 0.670537i \(-0.233936\pi\)
0.741876 + 0.670537i \(0.233936\pi\)
\(258\) 6.09638e6 1.28055e7i 0.354987 0.745653i
\(259\) 2.39299e7i 1.37734i
\(260\) −50943.6 62721.8i −0.00289848 0.00356860i
\(261\) −6.22564e6 −0.350157
\(262\) 507907. + 241802.i 0.0282410 + 0.0134448i
\(263\) 4.00969e6i 0.220416i −0.993909 0.110208i \(-0.964848\pi\)
0.993909 0.110208i \(-0.0351518\pi\)
\(264\) 7.28653e6 1.76631e6i 0.396013 0.0959964i
\(265\) −7.45747e6 −0.400732
\(266\) −1.81197e7 + 3.80605e7i −0.962731 + 2.02222i
\(267\) 1.56694e7i 0.823226i
\(268\) −1.21332e7 + 9.85480e6i −0.630336 + 0.511969i
\(269\) 777261. 0.0399310 0.0199655 0.999801i \(-0.493644\pi\)
0.0199655 + 0.999801i \(0.493644\pi\)
\(270\) −1.52955e6 728183.i −0.0777093 0.0369955i
\(271\) 3.29929e7i 1.65773i −0.559450 0.828864i \(-0.688988\pi\)
0.559450 0.828864i \(-0.311012\pi\)
\(272\) −5.24725e6 + 2.50475e7i −0.260750 + 1.24468i
\(273\) −166186. −0.00816782
\(274\) 1.29064e7 2.71100e7i 0.627413 1.31789i
\(275\) 2.93560e6i 0.141156i
\(276\) −734771. 904649.i −0.0349482 0.0430282i
\(277\) −2.00830e7 −0.944906 −0.472453 0.881356i \(-0.656631\pi\)
−0.472453 + 0.881356i \(0.656631\pi\)
\(278\) 3.05199e7 + 1.45298e7i 1.42052 + 0.676277i
\(279\) 1.04594e6i 0.0481609i
\(280\) −3.18277e6 1.31298e7i −0.144988 0.598116i
\(281\) 3.59969e7 1.62235 0.811177 0.584800i \(-0.198827\pi\)
0.811177 + 0.584800i \(0.198827\pi\)
\(282\) −9.87651e6 + 2.07457e7i −0.440409 + 0.925082i
\(283\) 8.24433e6i 0.363744i −0.983322 0.181872i \(-0.941784\pi\)
0.983322 0.181872i \(-0.0582157\pi\)
\(284\) −706801. + 574075.i −0.0308562 + 0.0250619i
\(285\) −9.72767e6 −0.420217
\(286\) 153251. + 72959.2i 0.00655098 + 0.00311876i
\(287\) 5.33824e7i 2.25815i
\(288\) −6.33491e6 4.82414e6i −0.265194 0.201949i
\(289\) 1.48982e7 0.617221
\(290\) 4.92502e6 1.03451e7i 0.201936 0.424169i
\(291\) 2.24778e7i 0.912169i
\(292\) 1.12370e7 + 1.38350e7i 0.451337 + 0.555686i
\(293\) 1.01669e7 0.404191 0.202096 0.979366i \(-0.435225\pi\)
0.202096 + 0.979366i \(0.435225\pi\)
\(294\) −1.18406e7 5.63700e6i −0.465940 0.221823i
\(295\) 3.08660e6i 0.120230i
\(296\) 2.52259e7 6.11495e6i 0.972685 0.235786i
\(297\) 3.55841e6 0.135827
\(298\) 1.29840e7 2.72729e7i 0.490635 1.03058i
\(299\) 26383.9i 0.000987018i
\(300\) 2.42002e6 1.96558e6i 0.0896304 0.0727992i
\(301\) 5.36817e7 1.96846
\(302\) −2.40780e7 1.14629e7i −0.874176 0.416174i
\(303\) 1.21319e7i 0.436116i
\(304\) −4.47521e7 9.37521e6i −1.59292 0.333703i
\(305\) 1.14495e7 0.403539
\(306\) −5.22088e6 + 1.09665e7i −0.182213 + 0.382740i
\(307\) 1.30424e7i 0.450756i 0.974271 + 0.225378i \(0.0723617\pi\)
−0.974271 + 0.225378i \(0.927638\pi\)
\(308\) 1.78915e7 + 2.20281e7i 0.612344 + 0.753918i
\(309\) 1.80471e7 0.611690
\(310\) 1.73803e6 + 827432.i 0.0583406 + 0.0277745i
\(311\) 1.78289e7i 0.592712i 0.955077 + 0.296356i \(0.0957716\pi\)
−0.955077 + 0.296356i \(0.904228\pi\)
\(312\) −42466.6 175187.i −0.00139825 0.00576817i
\(313\) 992789. 0.0323761 0.0161880 0.999869i \(-0.494847\pi\)
0.0161880 + 0.999869i \(0.494847\pi\)
\(314\) −2.49560e7 + 5.24203e7i −0.806096 + 1.69321i
\(315\) 6.41202e6i 0.205146i
\(316\) −1.78333e7 + 1.44845e7i −0.565158 + 0.459030i
\(317\) −4.91937e6 −0.154430 −0.0772150 0.997014i \(-0.524603\pi\)
−0.0772150 + 0.997014i \(0.524603\pi\)
\(318\) −1.50210e7 7.15114e6i −0.467109 0.222379i
\(319\) 2.40671e7i 0.741400i
\(320\) 1.30277e7 6.71031e6i 0.397573 0.204782i
\(321\) 1.60015e7 0.483776
\(322\) 1.89619e6 3.98295e6i 0.0567954 0.119299i
\(323\) 6.97448e7i 2.06969i
\(324\) −2.38259e6 2.93345e6i −0.0700511 0.0862469i
\(325\) 70579.3 0.00205602
\(326\) 1.44959e7 + 6.90114e6i 0.418400 + 0.199190i
\(327\) 1.19944e7i 0.343031i
\(328\) 5.62737e7 1.36412e7i 1.59472 0.386572i
\(329\) −8.69678e7 −2.44214
\(330\) −2.81502e6 + 5.91296e6i −0.0783320 + 0.164537i
\(331\) 5.36048e7i 1.47815i 0.673620 + 0.739077i \(0.264738\pi\)
−0.673620 + 0.739077i \(0.735262\pi\)
\(332\) 4.07667e7 3.31114e7i 1.11402 0.904821i
\(333\) 1.23192e7 0.333618
\(334\) 2.85344e7 + 1.35845e7i 0.765824 + 0.364590i
\(335\) 1.36532e7i 0.363162i
\(336\) 6.17970e6 2.94985e7i 0.162911 0.777646i
\(337\) 6.45496e7 1.68657 0.843284 0.537468i \(-0.180619\pi\)
0.843284 + 0.537468i \(0.180619\pi\)
\(338\) −1.65966e7 + 3.48614e7i −0.429803 + 0.902805i
\(339\) 5.25951e6i 0.135004i
\(340\) −1.40927e7 1.73509e7i −0.358556 0.441454i
\(341\) −4.04341e6 −0.101973
\(342\) −1.95937e7 9.32809e6i −0.489822 0.233192i
\(343\) 5.89641e6i 0.146119i
\(344\) 1.37176e7 + 5.65892e7i 0.336980 + 1.39014i
\(345\) 1.01798e6 0.0247903
\(346\) −1.45593e7 + 3.05819e7i −0.351489 + 0.738305i
\(347\) 4.82937e7i 1.15585i −0.816089 0.577926i \(-0.803862\pi\)
0.816089 0.577926i \(-0.196138\pi\)
\(348\) 1.98402e7 1.61145e7i 0.470770 0.382367i
\(349\) −3.08221e7 −0.725081 −0.362541 0.931968i \(-0.618091\pi\)
−0.362541 + 0.931968i \(0.618091\pi\)
\(350\) 1.06548e7 + 5.07247e6i 0.248508 + 0.118308i
\(351\) 85553.3i 0.00197841i
\(352\) −1.86492e7 + 2.44896e7i −0.427595 + 0.561504i
\(353\) −6.23969e7 −1.41853 −0.709266 0.704941i \(-0.750974\pi\)
−0.709266 + 0.704941i \(0.750974\pi\)
\(354\) 2.95981e6 6.21711e6i 0.0667198 0.140145i
\(355\) 795347.i 0.0177775i
\(356\) −4.05590e7 4.99362e7i −0.898954 1.10679i
\(357\) −4.59725e7 −1.01040
\(358\) 3.67669e7 + 1.75038e7i 0.801324 + 0.381491i
\(359\) 5.26134e7i 1.13714i −0.822636 0.568569i \(-0.807497\pi\)
0.822636 0.568569i \(-0.192503\pi\)
\(360\) 6.75931e6 1.63851e6i 0.144875 0.0351189i
\(361\) −7.75664e7 −1.64874
\(362\) 2.64477e7 5.55537e7i 0.557523 1.17108i
\(363\) 1.38598e7i 0.289758i
\(364\) 529611. 430158.i 0.0109813 0.00891917i
\(365\) −1.55681e7 −0.320154
\(366\) 2.30618e7 + 1.09792e7i 0.470381 + 0.223937i
\(367\) 2.05775e7i 0.416288i −0.978098 0.208144i \(-0.933258\pi\)
0.978098 0.208144i \(-0.0667423\pi\)
\(368\) 4.68322e6 + 981096.i 0.0939726 + 0.0196865i
\(369\) 2.74815e7 0.546968
\(370\) −9.74557e6 + 2.04706e7i −0.192399 + 0.404135i
\(371\) 6.29695e7i 1.23313i
\(372\) 2.70733e6 + 3.33327e6i 0.0525912 + 0.0647502i
\(373\) −2.72046e7 −0.524222 −0.262111 0.965038i \(-0.584419\pi\)
−0.262111 + 0.965038i \(0.584419\pi\)
\(374\) 4.23944e7 + 2.01829e7i 0.810389 + 0.385806i
\(375\) 2.72319e6i 0.0516398i
\(376\) −2.22234e7 9.16781e7i −0.418069 1.72465i
\(377\) 578635. 0.0107989
\(378\) 6.14864e6 1.29153e7i 0.113842 0.239127i
\(379\) 7.15245e7i 1.31382i 0.753967 + 0.656912i \(0.228138\pi\)
−0.753967 + 0.656912i \(0.771862\pi\)
\(380\) 3.10007e7 2.51793e7i 0.564964 0.458873i
\(381\) 4.83933e7 0.875004
\(382\) −3.40946e6 1.62316e6i −0.0611639 0.0291186i
\(383\) 4.10963e7i 0.731486i −0.930716 0.365743i \(-0.880815\pi\)
0.930716 0.365743i \(-0.119185\pi\)
\(384\) 3.26753e7 1.02355e6i 0.577067 0.0180765i
\(385\) −2.47877e7 −0.434363
\(386\) −1.98379e7 + 4.16696e7i −0.344932 + 0.724532i
\(387\) 2.76356e7i 0.476800i
\(388\) −5.81820e7 7.16337e7i −0.996078 1.22637i
\(389\) −1.73618e7 −0.294948 −0.147474 0.989066i \(-0.547114\pi\)
−0.147474 + 0.989066i \(0.547114\pi\)
\(390\) 142163. + 67680.2i 0.00239658 + 0.00114095i
\(391\) 7.29865e6i 0.122099i
\(392\) 5.23251e7 1.26840e7i 0.868664 0.210571i
\(393\) −1.09612e6 −0.0180584
\(394\) 3.48365e7 7.31743e7i 0.569568 1.19638i
\(395\) 2.00674e7i 0.325611i
\(396\) −1.13402e7 + 9.21065e6i −0.182614 + 0.148322i
\(397\) −1.59499e7 −0.254909 −0.127455 0.991844i \(-0.540681\pi\)
−0.127455 + 0.991844i \(0.540681\pi\)
\(398\) −6.28079e7 2.99013e7i −0.996242 0.474286i
\(399\) 8.21386e7i 1.29309i
\(400\) −2.62452e6 + 1.25280e7i −0.0410082 + 0.195751i
\(401\) −4.96019e7 −0.769245 −0.384623 0.923074i \(-0.625668\pi\)
−0.384623 + 0.923074i \(0.625668\pi\)
\(402\) 1.30924e7 2.75007e7i 0.201531 0.423317i
\(403\) 97214.0i 0.00148530i
\(404\) −3.14025e7 3.86628e7i −0.476234 0.586339i
\(405\) 3.30094e6 0.0496904
\(406\) 8.73517e7 + 4.15860e7i 1.30525 + 0.621397i
\(407\) 4.76237e7i 0.706383i
\(408\) −1.17477e7 4.84625e7i −0.172970 0.713551i
\(409\) 7.38246e7 1.07902 0.539512 0.841978i \(-0.318609\pi\)
0.539512 + 0.841978i \(0.318609\pi\)
\(410\) −2.17403e7 + 4.56657e7i −0.315438 + 0.662580i
\(411\) 5.85063e7i 0.842708i
\(412\) −5.75135e7 + 4.67134e7i −0.822390 + 0.667959i
\(413\) 2.60627e7 0.369972
\(414\) 2.05044e6 + 976165.i 0.0288966 + 0.0137570i
\(415\) 4.58738e7i 0.641830i
\(416\) 588792. + 448374.i 0.00817865 + 0.00622817i
\(417\) −6.58652e7 −0.908339
\(418\) −3.60606e7 + 7.57456e7i −0.493747 + 1.03712i
\(419\) 1.31477e8i 1.78735i 0.448717 + 0.893674i \(0.351881\pi\)
−0.448717 + 0.893674i \(0.648119\pi\)
\(420\) 1.65970e7 + 2.04342e7i 0.224017 + 0.275810i
\(421\) −1.33132e8 −1.78417 −0.892087 0.451863i \(-0.850760\pi\)
−0.892087 + 0.451863i \(0.850760\pi\)
\(422\) 1.52380e7 + 7.25444e6i 0.202764 + 0.0965310i
\(423\) 4.47714e7i 0.591534i
\(424\) 6.63800e7 1.60910e7i 0.870843 0.211099i
\(425\) 1.95246e7 0.254340
\(426\) 762676. 1.60201e6i 0.00986533 0.0207222i
\(427\) 9.66771e7i 1.24177i
\(428\) −5.09944e7 + 4.14184e7i −0.650416 + 0.528278i
\(429\) −330733. −0.00418895
\(430\) −4.59217e7 2.18622e7i −0.577581 0.274972i
\(431\) 4.13997e7i 0.517089i −0.965999 0.258544i \(-0.916757\pi\)
0.965999 0.258544i \(-0.0832428\pi\)
\(432\) 1.51860e7 + 3.18134e6i 0.188361 + 0.0394601i
\(433\) −1.14745e8 −1.41341 −0.706706 0.707507i \(-0.749820\pi\)
−0.706706 + 0.707507i \(0.749820\pi\)
\(434\) −6.98668e6 + 1.46756e7i −0.0854676 + 0.179525i
\(435\) 2.23257e7i 0.271230i
\(436\) −3.10464e7 3.82243e7i −0.374586 0.461190i
\(437\) 1.30404e7 0.156260
\(438\) −3.13578e7 1.49287e7i −0.373184 0.177664i
\(439\) 6.31007e7i 0.745832i 0.927865 + 0.372916i \(0.121642\pi\)
−0.927865 + 0.372916i \(0.878358\pi\)
\(440\) −6.33415e6 2.61302e7i −0.0743585 0.306750i
\(441\) 2.55532e7 0.297941
\(442\) 485249. 1.01927e6i 0.00561950 0.0118038i
\(443\) 3.81520e7i 0.438840i 0.975630 + 0.219420i \(0.0704165\pi\)
−0.975630 + 0.219420i \(0.929584\pi\)
\(444\) −3.92596e7 + 3.18872e7i −0.448535 + 0.364307i
\(445\) 5.61921e7 0.637668
\(446\) 3.69156e7 + 1.75746e7i 0.416107 + 0.198098i
\(447\) 5.88579e7i 0.658996i
\(448\) 5.66606e7 + 1.10003e8i 0.630155 + 1.22341i
\(449\) 1.25616e8 1.38773 0.693867 0.720103i \(-0.255905\pi\)
0.693867 + 0.720103i \(0.255905\pi\)
\(450\) −2.61133e6 + 5.48512e6i −0.0286566 + 0.0601934i
\(451\) 1.06238e8i 1.15812i
\(452\) 1.36138e7 + 1.67613e7i 0.147423 + 0.181507i
\(453\) 5.19628e7 0.558982
\(454\) −1.54446e7 7.35278e6i −0.165047 0.0785749i
\(455\) 595959.i 0.00632677i
\(456\) 8.65874e7 2.09894e7i 0.913188 0.221363i
\(457\) 5.74907e7 0.602350 0.301175 0.953569i \(-0.402621\pi\)
0.301175 + 0.953569i \(0.402621\pi\)
\(458\) 4.94488e7 1.03868e8i 0.514707 1.08114i
\(459\) 2.36669e7i 0.244739i
\(460\) −3.24416e6 + 2.63496e6i −0.0333295 + 0.0270707i
\(461\) 2.77042e7 0.282776 0.141388 0.989954i \(-0.454844\pi\)
0.141388 + 0.989954i \(0.454844\pi\)
\(462\) −4.99279e7 2.37695e7i −0.506311 0.241042i
\(463\) 1.76037e8i 1.77362i −0.462137 0.886809i \(-0.652917\pi\)
0.462137 0.886809i \(-0.347083\pi\)
\(464\) −2.15168e7 + 1.02710e8i −0.215389 + 1.02815i
\(465\) −3.75085e6 −0.0373053
\(466\) −7.45898e7 + 1.56676e8i −0.737092 + 1.54827i
\(467\) 7.46722e7i 0.733176i 0.930383 + 0.366588i \(0.119474\pi\)
−0.930383 + 0.366588i \(0.880526\pi\)
\(468\) 221448. + 272646.i 0.00216040 + 0.00265988i
\(469\) 1.15285e8 1.11752
\(470\) 7.43960e7 + 3.54181e7i 0.716566 + 0.341139i
\(471\) 1.13129e8i 1.08271i
\(472\) 6.65997e6 + 2.74743e7i 0.0633354 + 0.261277i
\(473\) 1.06834e8 1.00955
\(474\) 1.92431e7 4.04202e7i 0.180692 0.379545i
\(475\) 3.48843e7i 0.325499i
\(476\) 1.46508e8 1.18996e8i 1.35844 1.10335i
\(477\) 3.24170e7 0.298688
\(478\) −3.17627e7 1.51214e7i −0.290826 0.138455i
\(479\) 1.32477e7i 0.120541i 0.998182 + 0.0602705i \(0.0191963\pi\)
−0.998182 + 0.0602705i \(0.980804\pi\)
\(480\) −1.72998e7 + 2.27176e7i −0.156429 + 0.205418i
\(481\) −1.14500e6 −0.0102889
\(482\) 5.92040e7 1.24359e8i 0.528701 1.11054i
\(483\) 8.59564e6i 0.0762846i
\(484\) −3.58748e7 4.41691e7i −0.316413 0.389567i
\(485\) 8.06077e7 0.706563
\(486\) 6.64884e6 + 3.16535e6i 0.0579211 + 0.0275748i
\(487\) 4.04387e7i 0.350114i 0.984558 + 0.175057i \(0.0560110\pi\)
−0.984558 + 0.175057i \(0.943989\pi\)
\(488\) −1.01913e8 + 2.47045e7i −0.876943 + 0.212578i
\(489\) −3.12837e7 −0.267542
\(490\) −2.02148e7 + 4.24614e7i −0.171823 + 0.360916i
\(491\) 2.04121e8i 1.72442i 0.506547 + 0.862212i \(0.330922\pi\)
−0.506547 + 0.862212i \(0.669078\pi\)
\(492\) −8.75798e7 + 7.11337e7i −0.735374 + 0.597283i
\(493\) 1.60070e8 1.33588
\(494\) 1.82112e6 + 866989.i 0.0151063 + 0.00719172i
\(495\) 1.27608e7i 0.105211i
\(496\) −1.72558e7 3.61494e6i −0.141413 0.0296249i
\(497\) 6.71576e6 0.0547049
\(498\) −4.39895e7 + 9.24002e7i −0.356173 + 0.748143i
\(499\) 6.92447e7i 0.557294i 0.960394 + 0.278647i \(0.0898860\pi\)
−0.960394 + 0.278647i \(0.910114\pi\)
\(500\) −7.04875e6 8.67842e6i −0.0563900 0.0694274i
\(501\) −6.15802e7 −0.489698
\(502\) −3.57381e7 1.70140e7i −0.282501 0.134492i
\(503\) 1.44266e8i 1.13360i −0.823856 0.566799i \(-0.808182\pi\)
0.823856 0.566799i \(-0.191818\pi\)
\(504\) 1.38352e7 + 5.70743e7i 0.108067 + 0.445809i
\(505\) 4.35063e7 0.337814
\(506\) 3.77367e6 7.92662e6i 0.0291281 0.0611838i
\(507\) 7.52346e7i 0.577289i
\(508\) −1.54222e8 + 1.25262e8i −1.17640 + 0.955494i
\(509\) −7.15475e7 −0.542552 −0.271276 0.962502i \(-0.587446\pi\)
−0.271276 + 0.962502i \(0.587446\pi\)
\(510\) 3.93269e7 + 1.87226e7i 0.296469 + 0.141142i
\(511\) 1.31455e8i 0.985174i
\(512\) −1.01482e8 + 8.78393e7i −0.756102 + 0.654454i
\(513\) 4.22853e7 0.313212
\(514\) 8.66097e7 1.81924e8i 0.637789 1.33968i
\(515\) 6.47186e7i 0.473813i
\(516\) −7.15325e7 8.80708e7i −0.520660 0.641037i
\(517\) −1.73078e8 −1.25248
\(518\) −1.72850e8 8.22898e7i −1.24360 0.592048i
\(519\) 6.59989e7i 0.472101i
\(520\) −628237. + 152289.i −0.00446800 + 0.00108308i
\(521\) 8.19625e7 0.579565 0.289783 0.957093i \(-0.406417\pi\)
0.289783 + 0.957093i \(0.406417\pi\)
\(522\) −2.14087e7 + 4.49691e7i −0.150514 + 0.316157i
\(523\) 2.55778e8i 1.78796i −0.448107 0.893980i \(-0.647902\pi\)
0.448107 0.893980i \(-0.352098\pi\)
\(524\) 3.49317e6 2.83721e6i 0.0242787 0.0197196i
\(525\) −2.29941e7 −0.158905
\(526\) −2.89628e7 1.37885e7i −0.199014 0.0947457i
\(527\) 2.68926e7i 0.183739i
\(528\) 1.22984e7 5.87061e7i 0.0835504 0.398824i
\(529\) 1.46671e8 0.990782
\(530\) −2.56447e7 + 5.38668e7i −0.172254 + 0.361821i
\(531\) 1.34172e7i 0.0896145i
\(532\) 2.12609e8 + 2.61764e8i 1.41204 + 1.73850i
\(533\) −2.55424e6 −0.0168687
\(534\) 1.13183e8 + 5.38839e7i 0.743292 + 0.353863i
\(535\) 5.73827e7i 0.374731i
\(536\) 2.94596e7 + 1.21529e8i 0.191308 + 0.789200i
\(537\) −7.93469e7 −0.512398
\(538\) 2.67284e6 5.61432e6i 0.0171643 0.0360537i
\(539\) 9.87838e7i 0.630841i
\(540\) −1.05196e7 + 8.54421e6i −0.0668065 + 0.0542613i
\(541\) −2.16239e8 −1.36566 −0.682831 0.730577i \(-0.739251\pi\)
−0.682831 + 0.730577i \(0.739251\pi\)
\(542\) −2.38315e8 1.13456e8i −1.49676 0.712573i
\(543\) 1.19891e8i 0.748835i
\(544\) 1.62879e8 + 1.24035e8i 1.01174 + 0.770456i
\(545\) 4.30129e7 0.265711
\(546\) −571479. + 1.20040e6i −0.00351093 + 0.00737473i
\(547\) 1.04526e6i 0.00638648i 0.999995 + 0.00319324i \(0.00101644\pi\)
−0.999995 + 0.00319324i \(0.998984\pi\)
\(548\) −1.51439e8 1.86451e8i −0.920227 1.13298i
\(549\) −4.97699e7 −0.300780
\(550\) 2.12044e7 + 1.00949e7i 0.127450 + 0.0606757i
\(551\) 2.85995e8i 1.70963i
\(552\) −9.06119e6 + 2.19650e6i −0.0538726 + 0.0130591i
\(553\) 1.69445e8 1.00197
\(554\) −6.90611e7 + 1.45063e8i −0.406167 + 0.853157i
\(555\) 4.41778e7i 0.258420i
\(556\) 2.09903e8 1.70487e8i 1.22122 0.991895i
\(557\) 1.12606e8 0.651624 0.325812 0.945435i \(-0.394362\pi\)
0.325812 + 0.945435i \(0.394362\pi\)
\(558\) −7.55505e6 3.59678e6i −0.0434845 0.0207019i
\(559\) 2.56856e6i 0.0147047i
\(560\) −1.05784e8 2.21610e7i −0.602362 0.126190i
\(561\) −9.14916e7 −0.518195
\(562\) 1.23786e8 2.60013e8i 0.697367 1.46483i
\(563\) 1.29568e8i 0.726060i 0.931777 + 0.363030i \(0.118258\pi\)
−0.931777 + 0.363030i \(0.881742\pi\)
\(564\) 1.15887e8 + 1.42680e8i 0.645948 + 0.795291i
\(565\) −1.88611e7 −0.104574
\(566\) −5.95505e7 2.83505e7i −0.328425 0.156355i
\(567\) 2.78725e7i 0.152907i
\(568\) 1.71612e6 + 7.07950e6i 0.00936490 + 0.0386329i
\(569\) −9.50189e7 −0.515791 −0.257895 0.966173i \(-0.583029\pi\)
−0.257895 + 0.966173i \(0.583029\pi\)
\(570\) −3.34514e7 + 7.02649e7i −0.180630 + 0.379415i
\(571\) 2.03875e7i 0.109510i 0.998500 + 0.0547552i \(0.0174378\pi\)
−0.998500 + 0.0547552i \(0.982562\pi\)
\(572\) 1.05400e6 856075.i 0.00563186 0.00457429i
\(573\) 7.35797e6 0.0391106
\(574\) −3.85592e8 1.83571e8i −2.03889 0.970663i
\(575\) 3.65058e6i 0.0192025i
\(576\) −5.66302e7 + 2.91692e7i −0.296333 + 0.152636i
\(577\) −1.37188e8 −0.714149 −0.357074 0.934076i \(-0.616226\pi\)
−0.357074 + 0.934076i \(0.616226\pi\)
\(578\) 5.12318e7 1.07613e8i 0.265312 0.557289i
\(579\) 8.99275e7i 0.463294i
\(580\) −5.77883e7 7.11489e7i −0.296180 0.364657i
\(581\) −3.87350e8 −1.97504
\(582\) 1.62362e8 + 7.72966e7i 0.823599 + 0.392095i
\(583\) 1.25318e8i 0.632423i
\(584\) 1.38574e8 3.35914e7i 0.695736 0.168651i
\(585\) −306802. −0.00153247
\(586\) 3.49619e7 7.34378e7i 0.173741 0.364945i
\(587\) 1.85031e8i 0.914808i 0.889259 + 0.457404i \(0.151221\pi\)
−0.889259 + 0.457404i \(0.848779\pi\)
\(588\) −8.14344e7 + 6.61424e7i −0.400568 + 0.325348i
\(589\) −4.80487e7 −0.235145
\(590\) −2.22952e7 1.06142e7i −0.108556 0.0516809i
\(591\) 1.57918e8i 0.765014i
\(592\) 4.25772e7 2.03240e8i 0.205216 0.979590i
\(593\) 1.40041e8 0.671570 0.335785 0.941939i \(-0.390998\pi\)
0.335785 + 0.941939i \(0.390998\pi\)
\(594\) 1.22366e7 2.57031e7i 0.0583852 0.122639i
\(595\) 1.64862e8i 0.782653i
\(596\) −1.52349e8 1.87572e8i −0.719616 0.885990i
\(597\) 1.35546e8 0.637036
\(598\) −190576. 90728.7i −0.000891179 0.000424269i
\(599\) 3.86610e6i 0.0179884i 0.999960 + 0.00899421i \(0.00286298\pi\)
−0.999960 + 0.00899421i \(0.997137\pi\)
\(600\) −5.87584e6 2.42395e7i −0.0272030 0.112220i
\(601\) 1.17489e8 0.541220 0.270610 0.962689i \(-0.412775\pi\)
0.270610 + 0.962689i \(0.412775\pi\)
\(602\) 1.84600e8 3.87754e8i 0.846141 1.77733i
\(603\) 5.93494e7i 0.270685i
\(604\) −1.65598e8 + 1.34501e8i −0.751527 + 0.610402i
\(605\) 4.97024e7 0.224446
\(606\) 8.76315e7 + 4.17192e7i 0.393770 + 0.187464i
\(607\) 3.82398e8i 1.70982i −0.518778 0.854909i \(-0.673613\pi\)
0.518778 0.854909i \(-0.326387\pi\)
\(608\) −2.21612e8 + 2.91015e8i −0.986014 + 1.29480i
\(609\) −1.88514e8 −0.834627
\(610\) 3.93723e7 8.27018e7i 0.173461 0.364356i
\(611\) 4.16123e6i 0.0182431i
\(612\) 6.12597e7 + 7.54230e7i 0.267252 + 0.329040i
\(613\) −91040.9 −0.000395235 −0.000197617 1.00000i \(-0.500063\pi\)
−0.000197617 1.00000i \(0.500063\pi\)
\(614\) 9.42078e7 + 4.48500e7i 0.406988 + 0.193757i
\(615\) 9.85514e7i 0.423680i
\(616\) 2.20639e8 5.34844e7i 0.943929 0.228815i
\(617\) −2.18687e8 −0.931039 −0.465519 0.885038i \(-0.654132\pi\)
−0.465519 + 0.885038i \(0.654132\pi\)
\(618\) 6.20601e7 1.30358e8i 0.262934 0.552296i
\(619\) 1.09965e8i 0.463641i 0.972759 + 0.231820i \(0.0744682\pi\)
−0.972759 + 0.231820i \(0.925532\pi\)
\(620\) 1.19534e7 9.70876e6i 0.0501553 0.0407370i
\(621\) −4.42508e6 −0.0184776
\(622\) 1.28782e8 + 6.13100e7i 0.535161 + 0.254777i
\(623\) 4.74475e8i 1.96223i
\(624\) −1.41144e6 295686.i −0.00580912 0.00121696i
\(625\) 9.76562e6 0.0400000
\(626\) 3.41399e6 7.17112e6i 0.0139168 0.0292324i
\(627\) 1.63467e8i 0.663174i
\(628\) 2.92824e8 + 3.60525e8i 1.18230 + 1.45565i
\(629\) −3.16744e8 −1.27279
\(630\) −4.63154e7 2.20496e7i −0.185227 0.0881818i
\(631\) 6.46615e6i 0.0257370i −0.999917 0.0128685i \(-0.995904\pi\)
0.999917 0.0128685i \(-0.00409628\pi\)
\(632\) 4.32994e7 + 1.78623e8i 0.171526 + 0.707596i
\(633\) −3.28853e7 −0.129655
\(634\) −1.69167e7 + 3.55336e7i −0.0663815 + 0.139435i
\(635\) 1.73543e8i 0.677775i
\(636\) −1.03308e8 + 8.39087e7i −0.401572 + 0.326164i
\(637\) −2.37502e6 −0.00918858
\(638\) 1.73842e8 + 8.27619e7i 0.669410 + 0.318690i
\(639\) 3.45730e6i 0.0132506i
\(640\) −3.67054e6 1.17177e8i −0.0140020 0.446994i
\(641\) 1.74561e7 0.0662785 0.0331393 0.999451i \(-0.489450\pi\)
0.0331393 + 0.999451i \(0.489450\pi\)
\(642\) 5.50257e7 1.15582e8i 0.207951 0.436802i
\(643\) 5.28201e7i 0.198685i −0.995053 0.0993427i \(-0.968326\pi\)
0.995053 0.0993427i \(-0.0316740\pi\)
\(644\) −2.22491e7 2.73931e7i −0.0833019 0.102561i
\(645\) 9.91040e7 0.369328
\(646\) 5.03781e8 + 2.39838e8i 1.86872 + 0.889652i
\(647\) 2.46885e8i 0.911552i −0.890094 0.455776i \(-0.849362\pi\)
0.890094 0.455776i \(-0.150638\pi\)
\(648\) −2.93821e7 + 7.12245e6i −0.107984 + 0.0261761i
\(649\) 5.18683e7 0.189744
\(650\) 242708. 509809.i 0.000883778 0.00185638i
\(651\) 3.16715e7i 0.114796i
\(652\) 9.96967e7 8.09752e7i 0.359698 0.292152i
\(653\) 4.03664e8 1.44971 0.724854 0.688903i \(-0.241907\pi\)
0.724854 + 0.688903i \(0.241907\pi\)
\(654\) 8.66377e7 + 4.12461e7i 0.309723 + 0.147452i
\(655\) 3.93078e6i 0.0139880i
\(656\) 9.49806e7 4.53386e8i 0.336452 1.60604i
\(657\) 6.76734e7 0.238628
\(658\) −2.99064e8 + 6.28186e8i −1.04975 + 2.20501i
\(659\) 1.15030e8i 0.401935i 0.979598 + 0.200968i \(0.0644086\pi\)
−0.979598 + 0.200968i \(0.935591\pi\)
\(660\) 3.30303e7 + 4.06669e7i 0.114890 + 0.141452i
\(661\) −1.28637e8 −0.445410 −0.222705 0.974886i \(-0.571489\pi\)
−0.222705 + 0.974886i \(0.571489\pi\)
\(662\) 3.87199e8 + 1.84336e8i 1.33463 + 0.635383i
\(663\) 2.19969e6i 0.00754782i
\(664\) −9.89820e7 4.08329e8i −0.338105 1.39478i
\(665\) −2.94557e8 −1.00162
\(666\) 4.23632e7 8.89842e7i 0.143405 0.301224i
\(667\) 2.99288e7i 0.100858i
\(668\) 1.96248e8 1.59395e8i 0.658377 0.534744i
\(669\) −7.96677e7 −0.266075
\(670\) −9.86201e7 4.69506e7i −0.327900 0.156105i
\(671\) 1.92401e8i 0.636853i
\(672\) −1.91823e8 1.46076e8i −0.632111 0.481363i
\(673\) −2.22256e7 −0.0729137 −0.0364568 0.999335i \(-0.511607\pi\)
−0.0364568 + 0.999335i \(0.511607\pi\)
\(674\) 2.21973e8 4.66255e8i 0.724969 1.52280i
\(675\) 1.18375e7i 0.0384900i
\(676\) 1.94738e8 + 2.39762e8i 0.630393 + 0.776140i
\(677\) 1.43051e8 0.461025 0.230512 0.973069i \(-0.425960\pi\)
0.230512 + 0.973069i \(0.425960\pi\)
\(678\) −3.79905e7 1.80864e7i −0.121895 0.0580313i
\(679\) 6.80636e8i 2.17423i
\(680\) −1.73791e8 + 4.21282e7i −0.552714 + 0.133982i
\(681\) 3.33310e7 0.105538
\(682\) −1.39045e7 + 2.92064e7i −0.0438330 + 0.0920715i
\(683\) 1.47199e8i 0.461999i −0.972954 0.231000i \(-0.925800\pi\)
0.972954 0.231000i \(-0.0741996\pi\)
\(684\) −1.34757e8 + 1.09452e8i −0.421099 + 0.342023i
\(685\) 2.09809e8 0.652759
\(686\) 4.25910e7 + 2.02765e7i 0.131931 + 0.0628089i
\(687\) 2.24158e8i 0.691327i
\(688\) 4.55928e8 + 9.55132e7i 1.40001 + 0.293290i
\(689\) −3.01296e6 −0.00921162
\(690\) 3.50062e6 7.35308e6i 0.0106561 0.0223832i
\(691\) 4.86917e8i 1.47578i 0.674922 + 0.737889i \(0.264177\pi\)
−0.674922 + 0.737889i \(0.735823\pi\)
\(692\) 1.70833e8 + 2.10329e8i 0.515529 + 0.634719i
\(693\) 1.07750e8 0.323755
\(694\) −3.48835e8 1.66072e8i −1.04362 0.496842i
\(695\) 2.36199e8i 0.703596i
\(696\) −4.81723e7 1.98725e8i −0.142879 0.589419i
\(697\) −7.06588e8 −2.08674
\(698\) −1.05991e8 + 2.22635e8i −0.311675 + 0.654676i
\(699\) 3.38125e8i 0.990023i
\(700\) 7.32790e7 5.95184e7i 0.213641 0.173523i
\(701\) 3.70660e8 1.07602 0.538012 0.842937i \(-0.319176\pi\)
0.538012 + 0.842937i \(0.319176\pi\)
\(702\) −617969. 294200.i −0.00178630 0.000850416i
\(703\) 5.65922e8i 1.62889i
\(704\) 1.12762e8 + 2.18922e8i 0.323182 + 0.627437i
\(705\) −1.60555e8 −0.458200
\(706\) −2.14570e8 + 4.50706e8i −0.609754 + 1.28079i
\(707\) 3.67359e8i 1.03952i
\(708\) −3.47293e7 4.27587e7i −0.0978580 0.120483i
\(709\) −2.70875e8 −0.760028 −0.380014 0.924981i \(-0.624081\pi\)
−0.380014 + 0.924981i \(0.624081\pi\)
\(710\) −5.74495e6 2.73503e6i −0.0160513 0.00764165i
\(711\) 8.72312e7i 0.242696i
\(712\) −5.00174e8 + 1.21246e8i −1.38574 + 0.335913i
\(713\) 5.02820e6 0.0138722
\(714\) −1.58090e8 + 3.32069e8i −0.434320 + 0.912292i
\(715\) 1.18604e6i 0.00324475i
\(716\) 2.52867e8 2.05383e8i 0.688896 0.559532i
\(717\) 6.85473e7 0.185966
\(718\) −3.80037e8 1.80926e8i −1.02672 0.488797i
\(719\) 6.11851e8i 1.64611i −0.567962 0.823055i \(-0.692268\pi\)
0.567962 0.823055i \(-0.307732\pi\)
\(720\) 1.14086e7 5.44584e7i 0.0305657 0.145904i
\(721\) 5.46471e8 1.45801
\(722\) −2.66735e8 + 5.60278e8i −0.708709 + 1.48865i
\(723\) 2.68379e8i 0.710123i
\(724\) −3.10327e8 3.82075e8i −0.817719 1.00678i
\(725\) 8.00622e7 0.210094
\(726\) 1.00112e8 + 4.76608e7i 0.261623 + 0.124552i
\(727\) 4.50232e8i 1.17175i 0.810403 + 0.585873i \(0.199248\pi\)
−0.810403 + 0.585873i \(0.800752\pi\)
\(728\) −1.28590e6 5.30471e6i −0.00333283 0.0137489i
\(729\) −1.43489e7 −0.0370370
\(730\) −5.35356e7 + 1.12452e8i −0.137618 + 0.289067i
\(731\) 7.10550e8i 1.81904i
\(732\) 1.58609e8 1.28825e8i 0.404386 0.328449i
\(733\) −6.51431e8 −1.65408 −0.827040 0.562143i \(-0.809977\pi\)
−0.827040 + 0.562143i \(0.809977\pi\)
\(734\) −1.48635e8 7.07617e7i −0.375867 0.178941i
\(735\) 9.16362e7i 0.230784i
\(736\) 2.31913e7 3.04541e7i 0.0581689 0.0763857i
\(737\) 2.29434e8 0.573132
\(738\) 9.45033e7 1.98505e8i 0.235114 0.493858i
\(739\) 4.11562e8i 1.01977i −0.860243 0.509885i \(-0.829688\pi\)
0.860243 0.509885i \(-0.170312\pi\)
\(740\) 1.14351e8 + 1.40789e8i 0.282191 + 0.347434i
\(741\) −3.93017e6 −0.00965954
\(742\) −4.54841e8 2.16539e8i −1.11339 0.530059i
\(743\) 1.79409e8i 0.437400i 0.975792 + 0.218700i \(0.0701816\pi\)
−0.975792 + 0.218700i \(0.929818\pi\)
\(744\) 3.33868e7 8.09322e6i 0.0810693 0.0196518i
\(745\) 2.11070e8 0.510456
\(746\) −9.35508e7 + 1.96504e8i −0.225336 + 0.473320i
\(747\) 1.99410e8i 0.478392i
\(748\) 2.91571e8 2.36819e8i 0.696690 0.565862i
\(749\) 4.84529e8 1.15312
\(750\) 1.96702e7 + 9.36449e6i 0.0466256 + 0.0221973i
\(751\) 3.37918e8i 0.797796i −0.916995 0.398898i \(-0.869393\pi\)
0.916995 0.398898i \(-0.130607\pi\)
\(752\) −7.38632e8 1.54737e8i −1.73690 0.363866i
\(753\) 7.71266e7 0.180642
\(754\) 1.98981e6 4.17960e6i 0.00464191 0.00975037i
\(755\) 1.86344e8i 0.432986i
\(756\) −7.21457e7 8.88258e7i −0.166973 0.205577i
\(757\) 4.17269e8 0.961896 0.480948 0.876749i \(-0.340293\pi\)
0.480948 + 0.876749i \(0.340293\pi\)
\(758\) 5.16636e8 + 2.45958e8i 1.18625 + 0.564746i
\(759\) 1.71065e7i 0.0391233i
\(760\) −7.52701e7 3.10511e8i −0.171467 0.707352i
\(761\) −4.73073e8 −1.07343 −0.536715 0.843763i \(-0.680335\pi\)
−0.536715 + 0.843763i \(0.680335\pi\)
\(762\) 1.66414e8 3.49555e8i 0.376119 0.790042i
\(763\) 3.63193e8i 0.817643i
\(764\) −2.34488e7 + 1.90455e7i −0.0525824 + 0.0427083i
\(765\) −8.48717e7 −0.189574
\(766\) −2.96847e8 1.41322e8i −0.660460 0.314429i
\(767\) 1.24705e6i 0.00276374i
\(768\) 1.04970e8 2.39540e8i 0.231730 0.528805i
\(769\) −1.35864e8 −0.298763 −0.149381 0.988780i \(-0.547728\pi\)
−0.149381 + 0.988780i \(0.547728\pi\)
\(770\) −8.52396e7 + 1.79046e8i −0.186711 + 0.392187i
\(771\) 3.92612e8i 0.856645i
\(772\) 2.32770e8 + 2.86586e8i 0.505912 + 0.622879i
\(773\) 8.97765e8 1.94368 0.971839