Properties

Label 60.7.c.a.31.1
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 31.1
Character \(\chi\) \(=\) 60.31
Dual form 60.7.c.a.31.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-7.80071 - 1.77450i) q^{2} -15.5885i q^{3} +(57.7023 + 27.6847i) q^{4} +55.9017 q^{5} +(-27.6617 + 121.601i) q^{6} +264.480i q^{7} +(-400.993 - 318.353i) q^{8} -243.000 q^{9} +O(q^{10})\) \(q+(-7.80071 - 1.77450i) q^{2} -15.5885i q^{3} +(57.7023 + 27.6847i) q^{4} +55.9017 q^{5} +(-27.6617 + 121.601i) q^{6} +264.480i q^{7} +(-400.993 - 318.353i) q^{8} -243.000 q^{9} +(-436.073 - 99.1975i) q^{10} -29.4629i q^{11} +(431.562 - 899.490i) q^{12} -2759.92 q^{13} +(469.319 - 2063.13i) q^{14} -871.421i q^{15} +(2563.11 + 3194.95i) q^{16} +1562.12 q^{17} +(1895.57 + 431.203i) q^{18} +7299.42i q^{19} +(3225.66 + 1547.62i) q^{20} +4122.83 q^{21} +(-52.2820 + 229.832i) q^{22} +16832.0i q^{23} +(-4962.64 + 6250.86i) q^{24} +3125.00 q^{25} +(21529.4 + 4897.48i) q^{26} +3788.00i q^{27} +(-7322.05 + 15261.1i) q^{28} +36225.1 q^{29} +(-1546.34 + 6797.71i) q^{30} +45432.8i q^{31} +(-14324.7 - 29471.1i) q^{32} -459.282 q^{33} +(-12185.6 - 2771.97i) q^{34} +14784.9i q^{35} +(-14021.7 - 6727.39i) q^{36} -40535.5 q^{37} +(12952.8 - 56940.7i) q^{38} +43023.0i q^{39} +(-22416.2 - 17796.5i) q^{40} +54626.1 q^{41} +(-32161.1 - 7315.97i) q^{42} +53952.0i q^{43} +(815.673 - 1700.08i) q^{44} -13584.1 q^{45} +(29868.3 - 131301. i) q^{46} -112919. i q^{47} +(49804.3 - 39955.0i) q^{48} +47699.4 q^{49} +(-24377.2 - 5545.31i) q^{50} -24351.0i q^{51} +(-159254. - 76407.7i) q^{52} -78155.8 q^{53} +(6721.79 - 29549.1i) q^{54} -1647.03i q^{55} +(84198.1 - 106055. i) q^{56} +113787. q^{57} +(-282582. - 64281.5i) q^{58} +267725. i q^{59} +(24125.1 - 50283.0i) q^{60} -353443. q^{61} +(80620.4 - 354408. i) q^{62} -64268.6i q^{63} +(59446.3 + 255315. i) q^{64} -154284. q^{65} +(3582.73 + 814.995i) q^{66} +203409. i q^{67} +(90137.6 + 43246.7i) q^{68} +262385. q^{69} +(26235.8 - 115333. i) q^{70} -51657.2i q^{71} +(97441.2 + 77359.9i) q^{72} +221763. q^{73} +(316206. + 71930.2i) q^{74} -48713.9i q^{75} +(-202083. + 421193. i) q^{76} +7792.35 q^{77} +(76344.2 - 335610. i) q^{78} +540997. i q^{79} +(143282. + 178603. i) q^{80} +59049.0 q^{81} +(-426123. - 96934.0i) q^{82} +264246. i q^{83} +(237897. + 114140. i) q^{84} +87324.9 q^{85} +(95737.8 - 420864. i) q^{86} -564694. i q^{87} +(-9379.62 + 11814.4i) q^{88} +314597. q^{89} +(105966. + 24105.0i) q^{90} -729945. i q^{91} +(-465989. + 971244. i) q^{92} +708227. q^{93} +(-200374. + 880846. i) q^{94} +408050. i q^{95} +(-459409. + 223300. i) q^{96} -155146. q^{97} +(-372089. - 84642.5i) q^{98} +7159.49i 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −7.80071 1.77450i −0.975089 0.221812i
\(3\) 15.5885i 0.577350i
\(4\) 57.7023 + 27.6847i 0.901599 + 0.432574i
\(5\) 55.9017 0.447214
\(6\) −27.6617 + 121.601i −0.128063 + 0.562968i
\(7\) 264.480i 0.771079i 0.922691 + 0.385539i \(0.125985\pi\)
−0.922691 + 0.385539i \(0.874015\pi\)
\(8\) −400.993 318.353i −0.783189 0.621784i
\(9\) −243.000 −0.333333
\(10\) −436.073 99.1975i −0.436073 0.0991975i
\(11\) 29.4629i 0.0221359i −0.999939 0.0110680i \(-0.996477\pi\)
0.999939 0.0110680i \(-0.00352312\pi\)
\(12\) 431.562 899.490i 0.249747 0.520538i
\(13\) −2759.92 −1.25622 −0.628112 0.778123i \(-0.716172\pi\)
−0.628112 + 0.778123i \(0.716172\pi\)
\(14\) 469.319 2063.13i 0.171035 0.751870i
\(15\) 871.421i 0.258199i
\(16\) 2563.11 + 3194.95i 0.625760 + 0.780016i
\(17\) 1562.12 0.317955 0.158978 0.987282i \(-0.449180\pi\)
0.158978 + 0.987282i \(0.449180\pi\)
\(18\) 1895.57 + 431.203i 0.325030 + 0.0739375i
\(19\) 7299.42i 1.06421i 0.846678 + 0.532105i \(0.178599\pi\)
−0.846678 + 0.532105i \(0.821401\pi\)
\(20\) 3225.66 + 1547.62i 0.403207 + 0.193453i
\(21\) 4122.83 0.445182
\(22\) −52.2820 + 229.832i −0.00491003 + 0.0215845i
\(23\) 16832.0i 1.38341i 0.722179 + 0.691706i \(0.243141\pi\)
−0.722179 + 0.691706i \(0.756859\pi\)
\(24\) −4962.64 + 6250.86i −0.358987 + 0.452174i
\(25\) 3125.00 0.200000
\(26\) 21529.4 + 4897.48i 1.22493 + 0.278646i
\(27\) 3788.00i 0.192450i
\(28\) −7322.05 + 15261.1i −0.333548 + 0.695203i
\(29\) 36225.1 1.48531 0.742653 0.669676i \(-0.233567\pi\)
0.742653 + 0.669676i \(0.233567\pi\)
\(30\) −1546.34 + 6797.71i −0.0572717 + 0.251767i
\(31\) 45432.8i 1.52505i 0.646959 + 0.762525i \(0.276041\pi\)
−0.646959 + 0.762525i \(0.723959\pi\)
\(32\) −14324.7 29471.1i −0.437154 0.899386i
\(33\) −459.282 −0.0127802
\(34\) −12185.6 2771.97i −0.310035 0.0705265i
\(35\) 14784.9i 0.344837i
\(36\) −14021.7 6727.39i −0.300533 0.144191i
\(37\) −40535.5 −0.800258 −0.400129 0.916459i \(-0.631035\pi\)
−0.400129 + 0.916459i \(0.631035\pi\)
\(38\) 12952.8 56940.7i 0.236055 1.03770i
\(39\) 43023.0i 0.725281i
\(40\) −22416.2 17796.5i −0.350253 0.278070i
\(41\) 54626.1 0.792590 0.396295 0.918123i \(-0.370296\pi\)
0.396295 + 0.918123i \(0.370296\pi\)
\(42\) −32161.1 7315.97i −0.434093 0.0987470i
\(43\) 53952.0i 0.678582i 0.940681 + 0.339291i \(0.110187\pi\)
−0.940681 + 0.339291i \(0.889813\pi\)
\(44\) 815.673 1700.08i 0.00957543 0.0199577i
\(45\) −13584.1 −0.149071
\(46\) 29868.3 131301.i 0.306858 1.34895i
\(47\) 112919.i 1.08761i −0.839213 0.543803i \(-0.816984\pi\)
0.839213 0.543803i \(-0.183016\pi\)
\(48\) 49804.3 39955.0i 0.450342 0.361283i
\(49\) 47699.4 0.405438
\(50\) −24377.2 5545.31i −0.195018 0.0443625i
\(51\) 24351.0i 0.183572i
\(52\) −159254. 76407.7i −1.13261 0.543410i
\(53\) −78155.8 −0.524969 −0.262484 0.964936i \(-0.584542\pi\)
−0.262484 + 0.964936i \(0.584542\pi\)
\(54\) 6721.79 29549.1i 0.0426878 0.187656i
\(55\) 1647.03i 0.00989949i
\(56\) 84198.1 106055.i 0.479444 0.603900i
\(57\) 113787. 0.614422
\(58\) −282582. 64281.5i −1.44831 0.329459i
\(59\) 267725.i 1.30357i 0.758406 + 0.651783i \(0.225979\pi\)
−0.758406 + 0.651783i \(0.774021\pi\)
\(60\) 24125.1 50283.0i 0.111690 0.232792i
\(61\) −353443. −1.55715 −0.778575 0.627552i \(-0.784057\pi\)
−0.778575 + 0.627552i \(0.784057\pi\)
\(62\) 80620.4 354408.i 0.338275 1.48706i
\(63\) 64268.6i 0.257026i
\(64\) 59446.3 + 255315.i 0.226770 + 0.973948i
\(65\) −154284. −0.561800
\(66\) 3582.73 + 814.995i 0.0124618 + 0.00283480i
\(67\) 203409.i 0.676310i 0.941090 + 0.338155i \(0.109803\pi\)
−0.941090 + 0.338155i \(0.890197\pi\)
\(68\) 90137.6 + 43246.7i 0.286668 + 0.137539i
\(69\) 262385. 0.798713
\(70\) 26235.8 115333.i 0.0764891 0.336247i
\(71\) 51657.2i 0.144330i −0.997393 0.0721649i \(-0.977009\pi\)
0.997393 0.0721649i \(-0.0229908\pi\)
\(72\) 97441.2 + 77359.9i 0.261063 + 0.207261i
\(73\) 221763. 0.570059 0.285030 0.958519i \(-0.407997\pi\)
0.285030 + 0.958519i \(0.407997\pi\)
\(74\) 316206. + 71930.2i 0.780323 + 0.177507i
\(75\) 48713.9i 0.115470i
\(76\) −202083. + 421193.i −0.460350 + 0.959491i
\(77\) 7792.35 0.0170685
\(78\) 76344.2 335610.i 0.160876 0.707214i
\(79\) 540997.i 1.09727i 0.836062 + 0.548635i \(0.184852\pi\)
−0.836062 + 0.548635i \(0.815148\pi\)
\(80\) 143282. + 178603.i 0.279848 + 0.348834i
\(81\) 59049.0 0.111111
\(82\) −426123. 96934.0i −0.772846 0.175806i
\(83\) 264246.i 0.462141i 0.972937 + 0.231070i \(0.0742228\pi\)
−0.972937 + 0.231070i \(0.925777\pi\)
\(84\) 237897. + 114140.i 0.401376 + 0.192574i
\(85\) 87324.9 0.142194
\(86\) 95737.8 420864.i 0.150518 0.661678i
\(87\) 564694.i 0.857542i
\(88\) −9379.62 + 11814.4i −0.0137638 + 0.0173366i
\(89\) 314597. 0.446257 0.223128 0.974789i \(-0.428373\pi\)
0.223128 + 0.974789i \(0.428373\pi\)
\(90\) 105966. + 24105.0i 0.145358 + 0.0330658i
\(91\) 729945.i 0.968647i
\(92\) −465989. + 971244.i −0.598428 + 1.24728i
\(93\) 708227. 0.880488
\(94\) −200374. + 880846.i −0.241245 + 1.06051i
\(95\) 408050.i 0.475930i
\(96\) −459409. + 223300.i −0.519261 + 0.252391i
\(97\) −155146. −0.169990 −0.0849952 0.996381i \(-0.527087\pi\)
−0.0849952 + 0.996381i \(0.527087\pi\)
\(98\) −372089. 84642.5i −0.395338 0.0899312i
\(99\) 7159.49i 0.00737865i
\(100\) 180320. + 86514.8i 0.180320 + 0.0865148i
\(101\) −1.55143e6 −1.50580 −0.752902 0.658133i \(-0.771347\pi\)
−0.752902 + 0.658133i \(0.771347\pi\)
\(102\) −43210.8 + 189955.i −0.0407185 + 0.178999i
\(103\) 1.69380e6i 1.55007i −0.631920 0.775033i \(-0.717733\pi\)
0.631920 0.775033i \(-0.282267\pi\)
\(104\) 1.10671e6 + 878631.i 0.983861 + 0.781100i
\(105\) 230473. 0.199092
\(106\) 609671. + 138687.i 0.511892 + 0.116445i
\(107\) 1.31304e6i 1.07183i −0.844271 0.535916i \(-0.819966\pi\)
0.844271 0.535916i \(-0.180034\pi\)
\(108\) −104870. + 218576.i −0.0832489 + 0.173513i
\(109\) −150713. −0.116378 −0.0581889 0.998306i \(-0.518533\pi\)
−0.0581889 + 0.998306i \(0.518533\pi\)
\(110\) −2922.65 + 12848.0i −0.00219583 + 0.00965289i
\(111\) 631885.i 0.462029i
\(112\) −844999. + 677892.i −0.601454 + 0.482510i
\(113\) −1.70784e6 −1.18362 −0.591811 0.806077i \(-0.701587\pi\)
−0.591811 + 0.806077i \(0.701587\pi\)
\(114\) −887618. 201914.i −0.599117 0.136287i
\(115\) 940936.i 0.618681i
\(116\) 2.09027e6 + 1.00288e6i 1.33915 + 0.642505i
\(117\) 670662. 0.418741
\(118\) 475078. 2.08845e6i 0.289147 1.27109i
\(119\) 413148.i 0.245169i
\(120\) −277420. + 349434.i −0.160544 + 0.202218i
\(121\) 1.77069e6 0.999510
\(122\) 2.75711e6 + 627185.i 1.51836 + 0.345395i
\(123\) 851536.i 0.457602i
\(124\) −1.25779e6 + 2.62158e6i −0.659697 + 1.37498i
\(125\) 174693. 0.0894427
\(126\) −114045. + 501341.i −0.0570116 + 0.250623i
\(127\) 471582.i 0.230222i 0.993353 + 0.115111i \(0.0367223\pi\)
−0.993353 + 0.115111i \(0.963278\pi\)
\(128\) −10667.6 2.09712e6i −0.00508672 0.999987i
\(129\) 841029. 0.391779
\(130\) 1.20353e6 + 273778.i 0.547806 + 0.124614i
\(131\) 3.66693e6i 1.63113i −0.578666 0.815565i \(-0.696426\pi\)
0.578666 0.815565i \(-0.303574\pi\)
\(132\) −26501.6 12715.1i −0.0115226 0.00552838i
\(133\) −1.93055e6 −0.820590
\(134\) 360949. 1.58674e6i 0.150014 0.659463i
\(135\) 211755.i 0.0860663i
\(136\) −626397. 497305.i −0.249019 0.197700i
\(137\) −1.97967e6 −0.769893 −0.384947 0.922939i \(-0.625780\pi\)
−0.384947 + 0.922939i \(0.625780\pi\)
\(138\) −2.04679e6 465601.i −0.778817 0.177165i
\(139\) 1.30893e6i 0.487383i −0.969853 0.243692i \(-0.921642\pi\)
0.969853 0.243692i \(-0.0783585\pi\)
\(140\) −409315. + 853122.i −0.149167 + 0.310904i
\(141\) −1.76023e6 −0.627930
\(142\) −91665.7 + 402963.i −0.0320141 + 0.140734i
\(143\) 81315.5i 0.0278077i
\(144\) −622836. 776372.i −0.208587 0.260005i
\(145\) 2.02505e6 0.664249
\(146\) −1.72991e6 393518.i −0.555859 0.126446i
\(147\) 743559.i 0.234080i
\(148\) −2.33899e6 1.12221e6i −0.721511 0.346171i
\(149\) −1.19790e6 −0.362126 −0.181063 0.983471i \(-0.557954\pi\)
−0.181063 + 0.983471i \(0.557954\pi\)
\(150\) −86442.8 + 380003.i −0.0256127 + 0.112594i
\(151\) 5.97408e6i 1.73516i −0.497296 0.867581i \(-0.665674\pi\)
0.497296 0.867581i \(-0.334326\pi\)
\(152\) 2.32380e6 2.92701e6i 0.661709 0.833478i
\(153\) −379594. −0.105985
\(154\) −60785.9 13827.5i −0.0166434 0.00378602i
\(155\) 2.53977e6i 0.682023i
\(156\) −1.19108e6 + 2.48252e6i −0.313738 + 0.653912i
\(157\) 2.98776e6 0.772053 0.386026 0.922488i \(-0.373847\pi\)
0.386026 + 0.922488i \(0.373847\pi\)
\(158\) 959998. 4.22016e6i 0.243388 1.06994i
\(159\) 1.21833e6i 0.303091i
\(160\) −800774. 1.64748e6i −0.195501 0.402218i
\(161\) −4.45172e6 −1.06672
\(162\) −460624. 104782.i −0.108343 0.0246458i
\(163\) 5.21249e6i 1.20360i 0.798646 + 0.601801i \(0.205550\pi\)
−0.798646 + 0.601801i \(0.794450\pi\)
\(164\) 3.15205e6 + 1.51231e6i 0.714598 + 0.342854i
\(165\) −25674.6 −0.00571547
\(166\) 468905. 2.06131e6i 0.102509 0.450629i
\(167\) 4.71791e6i 1.01298i 0.862246 + 0.506490i \(0.169057\pi\)
−0.862246 + 0.506490i \(0.830943\pi\)
\(168\) −1.65323e6 1.31252e6i −0.348662 0.276807i
\(169\) 2.79037e6 0.578099
\(170\) −681197. 154958.i −0.138652 0.0315404i
\(171\) 1.77376e6i 0.354737i
\(172\) −1.49365e6 + 3.11315e6i −0.293537 + 0.611808i
\(173\) −898914. −0.173612 −0.0868060 0.996225i \(-0.527666\pi\)
−0.0868060 + 0.996225i \(0.527666\pi\)
\(174\) −1.00205e6 + 4.40502e6i −0.190213 + 0.836180i
\(175\) 826500.i 0.154216i
\(176\) 94132.5 75516.8i 0.0172664 0.0138518i
\(177\) 4.17342e6 0.752614
\(178\) −2.45408e6 558252.i −0.435140 0.0989853i
\(179\) 3.75535e6i 0.654774i 0.944890 + 0.327387i \(0.106168\pi\)
−0.944890 + 0.327387i \(0.893832\pi\)
\(180\) −783835. 376072.i −0.134402 0.0644843i
\(181\) 1.00688e7 1.69802 0.849008 0.528380i \(-0.177200\pi\)
0.849008 + 0.528380i \(0.177200\pi\)
\(182\) −1.29529e6 + 5.69409e6i −0.214858 + 0.944518i
\(183\) 5.50964e6i 0.899021i
\(184\) 5.35852e6 6.74950e6i 0.860183 1.08347i
\(185\) −2.26600e6 −0.357886
\(186\) −5.52467e6 1.25675e6i −0.858554 0.195303i
\(187\) 46024.5i 0.00703824i
\(188\) 3.12612e6 6.51566e6i 0.470470 0.980585i
\(189\) −1.00185e6 −0.148394
\(190\) 724085. 3.18308e6i 0.105567 0.464074i
\(191\) 9.44334e6i 1.35527i 0.735399 + 0.677634i \(0.236995\pi\)
−0.735399 + 0.677634i \(0.763005\pi\)
\(192\) 3.97996e6 926676.i 0.562309 0.130925i
\(193\) 1.09450e7 1.52246 0.761228 0.648485i \(-0.224597\pi\)
0.761228 + 0.648485i \(0.224597\pi\)
\(194\) 1.21025e6 + 275306.i 0.165756 + 0.0377060i
\(195\) 2.40506e6i 0.324356i
\(196\) 2.75236e6 + 1.32054e6i 0.365542 + 0.175382i
\(197\) −1.05084e7 −1.37448 −0.687242 0.726428i \(-0.741179\pi\)
−0.687242 + 0.726428i \(0.741179\pi\)
\(198\) 12704.5 55849.2i 0.00163668 0.00719484i
\(199\) 1.04841e7i 1.33037i 0.746679 + 0.665184i \(0.231647\pi\)
−0.746679 + 0.665184i \(0.768353\pi\)
\(200\) −1.25310e6 994854.i −0.156638 0.124357i
\(201\) 3.17083e6 0.390468
\(202\) 1.21023e7 + 2.75301e6i 1.46829 + 0.334006i
\(203\) 9.58082e6i 1.14529i
\(204\) 674150. 1.40511e6i 0.0794083 0.165508i
\(205\) 3.05369e6 0.354457
\(206\) −3.00565e6 + 1.32128e7i −0.343824 + 1.51145i
\(207\) 4.09017e6i 0.461137i
\(208\) −7.07399e6 8.81781e6i −0.786094 0.979875i
\(209\) 215062. 0.0235573
\(210\) −1.79786e6 408975.i −0.194132 0.0441610i
\(211\) 1.36416e7i 1.45217i −0.687602 0.726087i \(-0.741337\pi\)
0.687602 0.726087i \(-0.258663\pi\)
\(212\) −4.50977e6 2.16372e6i −0.473311 0.227088i
\(213\) −805256. −0.0833288
\(214\) −2.32999e6 + 1.02427e7i −0.237746 + 1.04513i
\(215\) 3.01601e6i 0.303471i
\(216\) 1.20592e6 1.51896e6i 0.119662 0.150725i
\(217\) −1.20161e7 −1.17593
\(218\) 1.17567e6 + 267439.i 0.113479 + 0.0258140i
\(219\) 3.45694e6i 0.329124i
\(220\) 45597.5 95037.3i 0.00428226 0.00892537i
\(221\) −4.31132e6 −0.399423
\(222\) 1.12128e6 4.92916e6i 0.102484 0.450520i
\(223\) 2.02736e7i 1.82817i 0.405523 + 0.914085i \(0.367089\pi\)
−0.405523 + 0.914085i \(0.632911\pi\)
\(224\) 7.79451e6 3.78859e6i 0.693498 0.337080i
\(225\) −759375. −0.0666667
\(226\) 1.33224e7 + 3.03057e6i 1.15414 + 0.262542i
\(227\) 1.36821e7i 1.16970i −0.811140 0.584852i \(-0.801152\pi\)
0.811140 0.584852i \(-0.198848\pi\)
\(228\) 6.56576e6 + 3.15015e6i 0.553962 + 0.265783i
\(229\) −1.72378e7 −1.43541 −0.717705 0.696347i \(-0.754808\pi\)
−0.717705 + 0.696347i \(0.754808\pi\)
\(230\) 1.66969e6 7.33997e6i 0.137231 0.603269i
\(231\) 121471.i 0.00985453i
\(232\) −1.45260e7 1.15324e7i −1.16328 0.923540i
\(233\) 1.24552e7 0.984656 0.492328 0.870410i \(-0.336146\pi\)
0.492328 + 0.870410i \(0.336146\pi\)
\(234\) −5.23164e6 1.19009e6i −0.408310 0.0928820i
\(235\) 6.31234e6i 0.486393i
\(236\) −7.41189e6 + 1.54484e7i −0.563888 + 1.17529i
\(237\) 8.43330e6 0.633509
\(238\) 733131. 3.22285e6i 0.0543814 0.239061i
\(239\) 2.17394e7i 1.59241i −0.605028 0.796204i \(-0.706838\pi\)
0.605028 0.796204i \(-0.293162\pi\)
\(240\) 2.78414e6 2.23355e6i 0.201399 0.161570i
\(241\) −7.91913e6 −0.565752 −0.282876 0.959156i \(-0.591289\pi\)
−0.282876 + 0.959156i \(0.591289\pi\)
\(242\) −1.38127e7 3.14209e6i −0.974612 0.221704i
\(243\) 920483.i 0.0641500i
\(244\) −2.03945e7 9.78498e6i −1.40392 0.673582i
\(245\) 2.66648e6 0.181317
\(246\) −1.51105e6 + 6.64259e6i −0.101502 + 0.446203i
\(247\) 2.01458e7i 1.33689i
\(248\) 1.44637e7 1.82182e7i 0.948252 1.19440i
\(249\) 4.11919e6 0.266817
\(250\) −1.36273e6 309992.i −0.0872146 0.0198395i
\(251\) 2.60051e7i 1.64451i −0.569118 0.822256i \(-0.692715\pi\)
0.569118 0.822256i \(-0.307285\pi\)
\(252\) 1.77926e6 3.70845e6i 0.111183 0.231734i
\(253\) 495919. 0.0306231
\(254\) 836822. 3.67868e6i 0.0510660 0.224487i
\(255\) 1.36126e6i 0.0820957i
\(256\) −3.63813e6 + 1.63780e7i −0.216850 + 0.976205i
\(257\) −1.09623e7 −0.645807 −0.322903 0.946432i \(-0.604659\pi\)
−0.322903 + 0.946432i \(0.604659\pi\)
\(258\) −6.56062e6 1.49240e6i −0.382020 0.0869015i
\(259\) 1.07208e7i 0.617062i
\(260\) −8.90257e6 4.27132e6i −0.506518 0.243020i
\(261\) −8.80271e6 −0.495102
\(262\) −6.50696e6 + 2.86047e7i −0.361805 + 1.59050i
\(263\) 1.86567e7i 1.02558i 0.858515 + 0.512788i \(0.171387\pi\)
−0.858515 + 0.512788i \(0.828613\pi\)
\(264\) 184169. + 146214.i 0.0100093 + 0.00794652i
\(265\) −4.36904e6 −0.234773
\(266\) 1.50597e7 + 3.42576e6i 0.800149 + 0.182017i
\(267\) 4.90408e6i 0.257646i
\(268\) −5.63133e6 + 1.17372e7i −0.292554 + 0.609760i
\(269\) 3.29387e7 1.69219 0.846095 0.533033i \(-0.178948\pi\)
0.846095 + 0.533033i \(0.178948\pi\)
\(270\) 375760. 1.65184e6i 0.0190906 0.0839223i
\(271\) 4.83316e6i 0.242842i −0.992601 0.121421i \(-0.961255\pi\)
0.992601 0.121421i \(-0.0387450\pi\)
\(272\) 4.00388e6 + 4.99087e6i 0.198964 + 0.248010i
\(273\) −1.13787e7 −0.559249
\(274\) 1.54428e7 + 3.51292e6i 0.750714 + 0.170772i
\(275\) 92071.7i 0.00442719i
\(276\) 1.51402e7 + 7.26404e6i 0.720119 + 0.345503i
\(277\) −951737. −0.0447793 −0.0223897 0.999749i \(-0.507127\pi\)
−0.0223897 + 0.999749i \(0.507127\pi\)
\(278\) −2.32269e6 + 1.02106e7i −0.108108 + 0.475242i
\(279\) 1.10402e7i 0.508350i
\(280\) 4.70682e6 5.92863e6i 0.214414 0.270072i
\(281\) 1.05420e7 0.475121 0.237560 0.971373i \(-0.423652\pi\)
0.237560 + 0.971373i \(0.423652\pi\)
\(282\) 1.37310e7 + 3.12352e6i 0.612288 + 0.139283i
\(283\) 2.15466e7i 0.950648i 0.879811 + 0.475324i \(0.157669\pi\)
−0.879811 + 0.475324i \(0.842331\pi\)
\(284\) 1.43012e6 2.98074e6i 0.0624333 0.130127i
\(285\) 6.36087e6 0.274778
\(286\) 144294. 634319.i 0.00616809 0.0271150i
\(287\) 1.44475e7i 0.611149i
\(288\) 3.48090e6 + 7.16148e6i 0.145718 + 0.299795i
\(289\) −2.16974e7 −0.898904
\(290\) −1.57968e7 3.59344e6i −0.647702 0.147339i
\(291\) 2.41848e6i 0.0981440i
\(292\) 1.27962e7 + 6.13944e6i 0.513965 + 0.246593i
\(293\) 2.97274e7 1.18183 0.590915 0.806734i \(-0.298767\pi\)
0.590915 + 0.806734i \(0.298767\pi\)
\(294\) −1.31945e6 + 5.80030e6i −0.0519218 + 0.228249i
\(295\) 1.49663e7i 0.582972i
\(296\) 1.62544e7 + 1.29046e7i 0.626753 + 0.497587i
\(297\) 111605. 0.00426006
\(298\) 9.34444e6 + 2.12566e6i 0.353105 + 0.0803241i
\(299\) 4.64550e7i 1.73788i
\(300\) 1.34863e6 2.81091e6i 0.0499493 0.104108i
\(301\) −1.42692e7 −0.523240
\(302\) −1.06010e7 + 4.66021e7i −0.384880 + 1.69194i
\(303\) 2.41844e7i 0.869376i
\(304\) −2.33213e7 + 1.87092e7i −0.830101 + 0.665940i
\(305\) −1.97581e7 −0.696379
\(306\) 2.96110e6 + 673589.i 0.103345 + 0.0235088i
\(307\) 1.66951e7i 0.576999i −0.957480 0.288499i \(-0.906844\pi\)
0.957480 0.288499i \(-0.0931563\pi\)
\(308\) 449637. + 215729.i 0.0153890 + 0.00738341i
\(309\) −2.64037e7 −0.894931
\(310\) 4.50682e6 1.98120e7i 0.151281 0.665033i
\(311\) 2.09869e7i 0.697699i −0.937179 0.348849i \(-0.886572\pi\)
0.937179 0.348849i \(-0.113428\pi\)
\(312\) 1.36965e7 1.72519e7i 0.450968 0.568032i
\(313\) −2.69018e7 −0.877299 −0.438650 0.898658i \(-0.644543\pi\)
−0.438650 + 0.898658i \(0.644543\pi\)
\(314\) −2.33067e7 5.30178e6i −0.752820 0.171251i
\(315\) 3.59273e6i 0.114946i
\(316\) −1.49773e7 + 3.12168e7i −0.474650 + 0.989297i
\(317\) 3.75955e7 1.18021 0.590104 0.807327i \(-0.299087\pi\)
0.590104 + 0.807327i \(0.299087\pi\)
\(318\) 2.16192e6 9.50383e6i 0.0672293 0.295541i
\(319\) 1.06730e6i 0.0328787i
\(320\) 3.32315e6 + 1.42725e7i 0.101414 + 0.435563i
\(321\) −2.04683e7 −0.618823
\(322\) 3.47266e7 + 7.89957e6i 1.04015 + 0.236612i
\(323\) 1.14025e7i 0.338372i
\(324\) 3.40726e6 + 1.63476e6i 0.100178 + 0.0480638i
\(325\) −8.62476e6 −0.251245
\(326\) 9.24957e6 4.06612e7i 0.266974 1.17362i
\(327\) 2.34938e6i 0.0671908i
\(328\) −2.19047e7 1.73904e7i −0.620748 0.492820i
\(329\) 2.98647e7 0.838630
\(330\) 200280. + 45559.6i 0.00557310 + 0.00126776i
\(331\) 9.30712e6i 0.256644i 0.991733 + 0.128322i \(0.0409591\pi\)
−0.991733 + 0.128322i \(0.959041\pi\)
\(332\) −7.31558e6 + 1.52476e7i −0.199910 + 0.416665i
\(333\) 9.85012e6 0.266753
\(334\) 8.37194e6 3.68031e7i 0.224691 0.987745i
\(335\) 1.13709e7i 0.302455i
\(336\) 1.05673e7 + 1.31722e7i 0.278577 + 0.347249i
\(337\) 6.20337e7 1.62083 0.810417 0.585854i \(-0.199241\pi\)
0.810417 + 0.585854i \(0.199241\pi\)
\(338\) −2.17669e7 4.95151e6i −0.563698 0.128229i
\(339\) 2.66226e7i 0.683364i
\(340\) 5.03885e6 + 2.41757e6i 0.128202 + 0.0615094i
\(341\) 1.33858e6 0.0337584
\(342\) −3.14754e6 + 1.38366e7i −0.0786851 + 0.345900i
\(343\) 4.37313e7i 1.08370i
\(344\) 1.71758e7 2.16344e7i 0.421931 0.531458i
\(345\) 1.46677e7 0.357195
\(346\) 7.01217e6 + 1.59512e6i 0.169287 + 0.0385093i
\(347\) 2.00609e7i 0.480132i 0.970757 + 0.240066i \(0.0771692\pi\)
−0.970757 + 0.240066i \(0.922831\pi\)
\(348\) 1.56334e7 3.25841e7i 0.370950 0.773159i
\(349\) −7.17249e7 −1.68731 −0.843653 0.536889i \(-0.819599\pi\)
−0.843653 + 0.536889i \(0.819599\pi\)
\(350\) 1.46662e6 6.44729e6i 0.0342070 0.150374i
\(351\) 1.04546e7i 0.241760i
\(352\) −868305. + 422047.i −0.0199088 + 0.00967682i
\(353\) 1.66396e7 0.378284 0.189142 0.981950i \(-0.439429\pi\)
0.189142 + 0.981950i \(0.439429\pi\)
\(354\) −3.25557e7 7.40573e6i −0.733866 0.166939i
\(355\) 2.88773e6i 0.0645462i
\(356\) 1.81530e7 + 8.70954e6i 0.402344 + 0.193039i
\(357\) 6.44034e6 0.141548
\(358\) 6.66387e6 2.92944e7i 0.145237 0.638463i
\(359\) 2.91649e7i 0.630344i 0.949035 + 0.315172i \(0.102062\pi\)
−0.949035 + 0.315172i \(0.897938\pi\)
\(360\) 5.44713e6 + 4.32455e6i 0.116751 + 0.0926901i
\(361\) −6.23568e6 −0.132545
\(362\) −7.85438e7 1.78671e7i −1.65572 0.376641i
\(363\) 2.76024e7i 0.577067i
\(364\) 2.02083e7 4.21195e7i 0.419012 0.873331i
\(365\) 1.23969e7 0.254938
\(366\) 9.77685e6 4.29791e7i 0.199414 0.876626i
\(367\) 6.15826e7i 1.24583i 0.782288 + 0.622917i \(0.214052\pi\)
−0.782288 + 0.622917i \(0.785948\pi\)
\(368\) −5.37772e7 + 4.31422e7i −1.07908 + 0.865684i
\(369\) −1.32741e7 −0.264197
\(370\) 1.76764e7 + 4.02102e6i 0.348971 + 0.0793836i
\(371\) 2.06706e7i 0.404792i
\(372\) 4.08663e7 + 1.96071e7i 0.793847 + 0.380876i
\(373\) 6.41180e7 1.23553 0.617765 0.786363i \(-0.288038\pi\)
0.617765 + 0.786363i \(0.288038\pi\)
\(374\) −81670.4 + 359024.i −0.00156117 + 0.00686291i
\(375\) 2.72319e6i 0.0516398i
\(376\) −3.59480e7 + 4.52795e7i −0.676256 + 0.851801i
\(377\) −9.99786e7 −1.86588
\(378\) 7.81514e6 + 1.77778e6i 0.144698 + 0.0329157i
\(379\) 4.31205e7i 0.792075i −0.918234 0.396038i \(-0.870385\pi\)
0.918234 0.396038i \(-0.129615\pi\)
\(380\) −1.12968e7 + 2.35454e7i −0.205875 + 0.429097i
\(381\) 7.35124e6 0.132918
\(382\) 1.67572e7 7.36648e7i 0.300615 1.32151i
\(383\) 4.47938e7i 0.797299i 0.917103 + 0.398650i \(0.130521\pi\)
−0.917103 + 0.398650i \(0.869479\pi\)
\(384\) −3.26909e7 + 166292.i −0.577343 + 0.00293682i
\(385\) 435606. 0.00763329
\(386\) −8.53790e7 1.94219e7i −1.48453 0.337699i
\(387\) 1.31103e7i 0.226194i
\(388\) −8.95226e6 4.29516e6i −0.153263 0.0735334i
\(389\) 6.70778e7 1.13954 0.569770 0.821804i \(-0.307032\pi\)
0.569770 + 0.821804i \(0.307032\pi\)
\(390\) 4.26777e6 1.87612e7i 0.0719461 0.316276i
\(391\) 2.62935e7i 0.439863i
\(392\) −1.91271e7 1.51853e7i −0.317534 0.252095i
\(393\) −5.71617e7 −0.941733
\(394\) 8.19734e7 + 1.86472e7i 1.34025 + 0.304878i
\(395\) 3.02426e7i 0.490714i
\(396\) −198209. + 413119.i −0.00319181 + 0.00665258i
\(397\) 3.89648e7 0.622731 0.311366 0.950290i \(-0.399214\pi\)
0.311366 + 0.950290i \(0.399214\pi\)
\(398\) 1.86040e7 8.17835e7i 0.295092 1.29723i
\(399\) 3.00943e7i 0.473768i
\(400\) 8.00972e6 + 9.98420e6i 0.125152 + 0.156003i
\(401\) 9.85306e7 1.52805 0.764026 0.645186i \(-0.223220\pi\)
0.764026 + 0.645186i \(0.223220\pi\)
\(402\) −2.47348e7 5.62664e6i −0.380741 0.0866107i
\(403\) 1.25391e8i 1.91580i
\(404\) −8.95212e7 4.29510e7i −1.35763 0.651372i
\(405\) 3.30094e6 0.0496904
\(406\) 1.70012e7 7.47373e7i 0.254039 1.11676i
\(407\) 1.19429e6i 0.0177145i
\(408\) −7.75221e6 + 9.76456e6i −0.114142 + 0.143771i
\(409\) 2.55058e7 0.372794 0.186397 0.982475i \(-0.440319\pi\)
0.186397 + 0.982475i \(0.440319\pi\)
\(410\) −2.38210e7 5.41877e6i −0.345627 0.0786230i
\(411\) 3.08600e7i 0.444498i
\(412\) 4.68924e7 9.77361e7i 0.670518 1.39754i
\(413\) −7.08079e7 −1.00515
\(414\) −7.25800e6 + 3.19063e7i −0.102286 + 0.449650i
\(415\) 1.47718e7i 0.206676i
\(416\) 3.95350e7 + 8.13380e7i 0.549164 + 1.12983i
\(417\) −2.04041e7 −0.281391
\(418\) −1.67764e6 381628.i −0.0229705 0.00522530i
\(419\) 4.64583e6i 0.0631569i −0.999501 0.0315785i \(-0.989947\pi\)
0.999501 0.0315785i \(-0.0100534\pi\)
\(420\) 1.32988e7 + 6.38059e6i 0.179501 + 0.0861218i
\(421\) −6.21970e7 −0.833534 −0.416767 0.909013i \(-0.636837\pi\)
−0.416767 + 0.909013i \(0.636837\pi\)
\(422\) −2.42071e7 + 1.06414e8i −0.322110 + 1.41600i
\(423\) 2.74392e7i 0.362536i
\(424\) 3.13399e7 + 2.48812e7i 0.411150 + 0.326417i
\(425\) 4.88161e6 0.0635911
\(426\) 6.28157e6 + 1.42893e6i 0.0812530 + 0.0184834i
\(427\) 9.34787e7i 1.20068i
\(428\) 3.63512e7 7.57655e7i 0.463647 0.966363i
\(429\) 1.26758e6 0.0160548
\(430\) 5.35191e6 2.35270e7i 0.0673136 0.295911i
\(431\) 8.54691e7i 1.06752i 0.845635 + 0.533761i \(0.179222\pi\)
−0.845635 + 0.533761i \(0.820778\pi\)
\(432\) −1.21024e7 + 9.70906e6i −0.150114 + 0.120428i
\(433\) 4.86765e7 0.599591 0.299796 0.954003i \(-0.403081\pi\)
0.299796 + 0.954003i \(0.403081\pi\)
\(434\) 9.37338e7 + 2.13225e7i 1.14664 + 0.260837i
\(435\) 3.15674e7i 0.383505i
\(436\) −8.69647e6 4.17244e6i −0.104926 0.0503420i
\(437\) −1.22864e8 −1.47224
\(438\) −6.13434e6 + 2.69666e7i −0.0730038 + 0.320925i
\(439\) 1.38585e8i 1.63804i 0.573768 + 0.819018i \(0.305481\pi\)
−0.573768 + 0.819018i \(0.694519\pi\)
\(440\) −524337. + 660446.i −0.00615534 + 0.00775317i
\(441\) −1.15909e7 −0.135146
\(442\) 3.36314e7 + 7.65043e6i 0.389473 + 0.0885970i
\(443\) 1.24746e8i 1.43488i −0.696619 0.717442i \(-0.745313\pi\)
0.696619 0.717442i \(-0.254687\pi\)
\(444\) −1.74936e7 + 3.64612e7i −0.199862 + 0.416565i
\(445\) 1.75865e7 0.199572
\(446\) 3.59755e7 1.58149e8i 0.405511 1.78263i
\(447\) 1.86733e7i 0.209074i
\(448\) −6.75256e7 + 1.57223e7i −0.750991 + 0.174857i
\(449\) 4.35883e7 0.481539 0.240769 0.970582i \(-0.422600\pi\)
0.240769 + 0.970582i \(0.422600\pi\)
\(450\) 5.92367e6 + 1.34751e6i 0.0650060 + 0.0147875i
\(451\) 1.60944e6i 0.0175447i
\(452\) −9.85465e7 4.72812e7i −1.06715 0.512004i
\(453\) −9.31266e7 −1.00180
\(454\) −2.42789e7 + 1.06730e8i −0.259455 + 1.14057i
\(455\) 4.08051e7i 0.433192i
\(456\) −4.56276e7 3.62244e7i −0.481209 0.382038i
\(457\) 3.43555e7 0.359954 0.179977 0.983671i \(-0.442398\pi\)
0.179977 + 0.983671i \(0.442398\pi\)
\(458\) 1.34467e8 + 3.05885e7i 1.39965 + 0.318392i
\(459\) 5.91728e6i 0.0611906i
\(460\) −2.60496e7 + 5.42942e7i −0.267625 + 0.557802i
\(461\) −6.32112e7 −0.645195 −0.322598 0.946536i \(-0.604556\pi\)
−0.322598 + 0.946536i \(0.604556\pi\)
\(462\) −215550. + 947559.i −0.00218586 + 0.00960905i
\(463\) 7.88603e7i 0.794539i −0.917702 0.397270i \(-0.869958\pi\)
0.917702 0.397270i \(-0.130042\pi\)
\(464\) 9.28491e7 + 1.15737e8i 0.929445 + 1.15856i
\(465\) 3.95911e7 0.393766
\(466\) −9.71598e7 2.21018e7i −0.960128 0.218409i
\(467\) 5.22025e7i 0.512556i 0.966603 + 0.256278i \(0.0824962\pi\)
−0.966603 + 0.256278i \(0.917504\pi\)
\(468\) 3.86987e7 + 1.85671e7i 0.377537 + 0.181137i
\(469\) −5.37976e7 −0.521488
\(470\) −1.12012e7 + 4.92408e7i −0.107888 + 0.474276i
\(471\) 4.65746e7i 0.445745i
\(472\) 8.52312e7 1.07356e8i 0.810536 1.02094i
\(473\) 1.58958e6 0.0150210
\(474\) −6.57858e7 1.49649e7i −0.617728 0.140520i
\(475\) 2.28107e7i 0.212842i
\(476\) −1.14379e7 + 2.38396e7i −0.106054 + 0.221044i
\(477\) 1.89919e7 0.174990
\(478\) −3.85766e7 + 1.69583e8i −0.353216 + 1.55274i
\(479\) 8.50400e7i 0.773778i 0.922126 + 0.386889i \(0.126450\pi\)
−0.922126 + 0.386889i \(0.873550\pi\)
\(480\) −2.56817e7 + 1.24828e7i −0.232221 + 0.112873i
\(481\) 1.11875e8 1.00530
\(482\) 6.17748e7 + 1.40525e7i 0.551659 + 0.125491i
\(483\) 6.93954e7i 0.615871i
\(484\) 1.02173e8 + 4.90211e7i 0.901157 + 0.432362i
\(485\) −8.67290e6 −0.0760220
\(486\) −1.63340e6 + 7.18042e6i −0.0142293 + 0.0625520i
\(487\) 6.20201e6i 0.0536964i −0.999640 0.0268482i \(-0.991453\pi\)
0.999640 0.0268482i \(-0.00854708\pi\)
\(488\) 1.41728e8 + 1.12520e8i 1.21954 + 0.968211i
\(489\) 8.12547e7 0.694900
\(490\) −2.08004e7 4.73166e6i −0.176801 0.0402184i
\(491\) 1.34450e8i 1.13584i −0.823083 0.567921i \(-0.807748\pi\)
0.823083 0.567921i \(-0.192252\pi\)
\(492\) 2.35746e7 4.91356e7i 0.197947 0.412573i
\(493\) 5.65878e7 0.472261
\(494\) −3.57488e7 + 1.57152e8i −0.296538 + 1.30358i
\(495\) 400228.i 0.00329983i
\(496\) −1.45155e8 + 1.16449e8i −1.18956 + 0.954315i
\(497\) 1.36623e7 0.111290
\(498\) −3.21326e7 7.30950e6i −0.260171 0.0591833i
\(499\) 1.21185e8i 0.975321i 0.873033 + 0.487660i \(0.162150\pi\)
−0.873033 + 0.487660i \(0.837850\pi\)
\(500\) 1.00802e7 + 4.83632e6i 0.0806414 + 0.0386906i
\(501\) 7.35450e7 0.584844
\(502\) −4.61460e7 + 2.02858e8i −0.364773 + 1.60355i
\(503\) 2.01030e8i 1.57964i −0.613342 0.789818i \(-0.710175\pi\)
0.613342 0.789818i \(-0.289825\pi\)
\(504\) −2.04601e7 + 2.57712e7i −0.159815 + 0.201300i
\(505\) −8.67277e7 −0.673416
\(506\) −3.86853e6 880009.i −0.0298603 0.00679259i
\(507\) 4.34976e7i 0.333765i
\(508\) −1.30556e7 + 2.72114e7i −0.0995878 + 0.207567i
\(509\) 2.09283e8 1.58701 0.793507 0.608562i \(-0.208253\pi\)
0.793507 + 0.608562i \(0.208253\pi\)
\(510\) −2.41556e6 + 1.06188e7i −0.0182099 + 0.0800507i
\(511\) 5.86518e7i 0.439560i
\(512\) 5.74428e7 1.21304e8i 0.427982 0.903787i
\(513\) −2.76502e7 −0.204807
\(514\) 8.55138e7 + 1.94526e7i 0.629719 + 0.143248i
\(515\) 9.46863e7i 0.693211i
\(516\) 4.85293e7 + 2.32836e7i 0.353228 + 0.169474i
\(517\) −3.32691e6 −0.0240752
\(518\) −1.90241e7 + 8.36300e7i −0.136872 + 0.601690i
\(519\) 1.40127e7i 0.100235i
\(520\) 6.18669e7 + 4.91170e7i 0.439996 + 0.349318i
\(521\) −1.09676e8 −0.775531 −0.387766 0.921758i \(-0.626753\pi\)
−0.387766 + 0.921758i \(0.626753\pi\)
\(522\) 6.86674e7 + 1.56204e7i 0.482769 + 0.109820i
\(523\) 1.53121e8i 1.07036i −0.844738 0.535180i \(-0.820244\pi\)
0.844738 0.535180i \(-0.179756\pi\)
\(524\) 1.01518e8 2.11590e8i 0.705584 1.47062i
\(525\) 1.28839e7 0.0890365
\(526\) 3.31063e7 1.45536e8i 0.227485 1.00003i
\(527\) 7.09712e7i 0.484898i
\(528\) −1.17719e6 1.46738e6i −0.00799733 0.00996875i
\(529\) −1.35280e8 −0.913829
\(530\) 3.40817e7 + 7.75286e6i 0.228925 + 0.0520756i
\(531\) 6.50572e7i 0.434522i
\(532\) −1.11397e8 5.34468e7i −0.739843 0.354966i
\(533\) −1.50764e8 −0.995670
\(534\) −8.70229e6 + 3.82554e7i −0.0571492 + 0.251228i
\(535\) 7.34013e7i 0.479338i
\(536\) 6.47560e7 8.15656e7i 0.420519 0.529679i
\(537\) 5.85401e7 0.378034
\(538\) −2.56945e8 5.84496e7i −1.65004 0.375349i
\(539\) 1.40536e6i 0.00897475i
\(540\) −5.86239e6 + 1.22188e7i −0.0372300 + 0.0775972i
\(541\) 1.17596e8 0.742676 0.371338 0.928498i \(-0.378899\pi\)
0.371338 + 0.928498i \(0.378899\pi\)
\(542\) −8.57643e6 + 3.77021e7i −0.0538653 + 0.236792i
\(543\) 1.56957e8i 0.980350i
\(544\) −2.23768e7 4.60372e7i −0.138996 0.285965i
\(545\) −8.42509e6 −0.0520457
\(546\) 8.87621e7 + 2.01915e7i 0.545318 + 0.124048i
\(547\) 1.63945e8i 1.00170i −0.865535 0.500848i \(-0.833021\pi\)
0.865535 0.500848i \(-0.166979\pi\)
\(548\) −1.14231e8 5.48065e7i −0.694134 0.333036i
\(549\) 8.58867e7 0.519050
\(550\) −163381. + 718225.i −0.000982005 + 0.00431690i
\(551\) 2.64423e8i 1.58068i
\(552\) −1.05214e8 8.35310e7i −0.625543 0.496627i
\(553\) −1.43083e8 −0.846081
\(554\) 7.42423e6 + 1.68886e6i 0.0436639 + 0.00993262i
\(555\) 3.53235e7i 0.206626i
\(556\) 3.62373e7 7.55280e7i 0.210829 0.439424i
\(557\) −2.93846e8 −1.70041 −0.850206 0.526450i \(-0.823523\pi\)
−0.850206 + 0.526450i \(0.823523\pi\)
\(558\) −1.95908e7 + 8.61212e7i −0.112758 + 0.495687i
\(559\) 1.48903e8i 0.852451i
\(560\) −4.72369e7 + 3.78953e7i −0.268978 + 0.215785i
\(561\) −717451. −0.00406353
\(562\) −8.22352e7 1.87068e7i −0.463285 0.105388i
\(563\) 1.32511e8i 0.742554i −0.928522 0.371277i \(-0.878920\pi\)
0.928522 0.371277i \(-0.121080\pi\)
\(564\) −1.01569e8 4.87314e7i −0.566141 0.271626i
\(565\) −9.54713e7 −0.529331
\(566\) 3.82344e7 1.68079e8i 0.210865 0.926967i
\(567\) 1.56173e7i 0.0856754i
\(568\) −1.64452e7 + 2.07142e7i −0.0897419 + 0.113037i
\(569\) −1.92681e8 −1.04593 −0.522964 0.852354i \(-0.675174\pi\)
−0.522964 + 0.852354i \(0.675174\pi\)
\(570\) −4.96193e7 1.12874e7i −0.267933 0.0609492i
\(571\) 7.65822e7i 0.411357i 0.978620 + 0.205679i \(0.0659402\pi\)
−0.978620 + 0.205679i \(0.934060\pi\)
\(572\) −2.25120e6 + 4.69209e6i −0.0120289 + 0.0250714i
\(573\) 1.47207e8 0.782465
\(574\) 2.56371e7 1.12701e8i 0.135560 0.595925i
\(575\) 5.25999e7i 0.276682i
\(576\) −1.44454e7 6.20415e7i −0.0755899 0.324649i
\(577\) 1.71942e8 0.895066 0.447533 0.894268i \(-0.352303\pi\)
0.447533 + 0.894268i \(0.352303\pi\)
\(578\) 1.69255e8 + 3.85020e7i 0.876512 + 0.199388i
\(579\) 1.70616e8i 0.878990i
\(580\) 1.16850e8 + 5.60629e7i 0.598886 + 0.287337i
\(581\) −6.98878e7 −0.356347
\(582\) 4.29159e6 1.88659e7i 0.0217695 0.0956991i
\(583\) 2.30270e6i 0.0116207i
\(584\) −8.89252e7 7.05989e7i −0.446464 0.354454i
\(585\) 3.74911e7 0.187267
\(586\) −2.31895e8 5.27513e7i −1.15239 0.262144i
\(587\) 1.75375e8i 0.867068i 0.901137 + 0.433534i \(0.142734\pi\)
−0.901137 + 0.433534i \(0.857266\pi\)
\(588\) 2.05852e7 4.29051e7i 0.101257 0.211046i
\(589\) −3.31633e8 −1.62297
\(590\) 2.65577e7 1.16748e8i 0.129310 0.568450i
\(591\) 1.63810e8i 0.793559i
\(592\) −1.03897e8 1.29509e8i −0.500769 0.624214i
\(593\) −1.46804e8 −0.704003 −0.352001 0.935999i \(-0.614499\pi\)
−0.352001 + 0.935999i \(0.614499\pi\)
\(594\) −870602. 198044.i −0.00415394 0.000944935i
\(595\) 2.30957e7i 0.109643i
\(596\) −6.91213e7 3.31634e7i −0.326492 0.156646i
\(597\) 1.63431e8 0.768088
\(598\) −8.24343e7 + 3.62382e8i −0.385482 + 1.69458i
\(599\) 1.52954e8i 0.711672i −0.934548 0.355836i \(-0.884196\pi\)
0.934548 0.355836i \(-0.115804\pi\)
\(600\) −1.55082e7 + 1.95339e7i −0.0717974 + 0.0904349i
\(601\) 1.98847e8 0.916003 0.458001 0.888952i \(-0.348565\pi\)
0.458001 + 0.888952i \(0.348565\pi\)
\(602\) 1.11310e8 + 2.53207e7i 0.510206 + 0.116061i
\(603\) 4.94284e7i 0.225437i
\(604\) 1.65391e8 3.44718e8i 0.750586 1.56442i
\(605\) 9.89847e7 0.446994
\(606\) 4.29152e7 1.88656e8i 0.192838 0.847720i
\(607\) 2.62997e8i 1.17594i 0.808883 + 0.587970i \(0.200073\pi\)
−0.808883 + 0.587970i \(0.799927\pi\)
\(608\) 2.15122e8 1.04562e8i 0.957137 0.465224i
\(609\) 1.49350e8 0.661232
\(610\) 1.54127e8 + 3.50607e7i 0.679031 + 0.154465i
\(611\) 3.11647e8i 1.36628i
\(612\) −2.19034e7 1.05090e7i −0.0955561 0.0458464i
\(613\) 3.30925e8 1.43664 0.718321 0.695712i \(-0.244911\pi\)
0.718321 + 0.695712i \(0.244911\pi\)
\(614\) −2.96255e7 + 1.30234e8i −0.127986 + 0.562625i
\(615\) 4.76023e7i 0.204646i
\(616\) −3.12468e6 2.48072e6i −0.0133679 0.0106129i
\(617\) 3.38754e8 1.44221 0.721106 0.692824i \(-0.243634\pi\)
0.721106 + 0.692824i \(0.243634\pi\)
\(618\) 2.05968e8 + 4.68534e7i 0.872638 + 0.198507i
\(619\) 2.66432e8i 1.12335i 0.827358 + 0.561675i \(0.189843\pi\)
−0.827358 + 0.561675i \(0.810157\pi\)
\(620\) −7.03128e7 + 1.46551e8i −0.295025 + 0.614911i
\(621\) −6.37594e7 −0.266238
\(622\) −3.72413e7 + 1.63713e8i −0.154758 + 0.680319i
\(623\) 8.32046e7i 0.344099i
\(624\) −1.37456e8 + 1.10273e8i −0.565731 + 0.453852i
\(625\) 9.76562e6 0.0400000
\(626\) 2.09853e8 + 4.77372e7i 0.855445 + 0.194596i
\(627\) 3.35249e6i 0.0136008i
\(628\) 1.72401e8 + 8.27153e7i 0.696081 + 0.333970i
\(629\) −6.33211e7 −0.254446
\(630\) −6.37529e6 + 2.80258e7i −0.0254964 + 0.112082i
\(631\) 1.51752e8i 0.604013i 0.953306 + 0.302007i \(0.0976565\pi\)
−0.953306 + 0.302007i \(0.902343\pi\)
\(632\) 1.72228e8 2.16936e8i 0.682265 0.859369i
\(633\) −2.12652e8 −0.838413
\(634\) −2.93272e8 6.67133e7i −1.15081 0.261785i
\(635\) 2.63622e7i 0.102958i
\(636\) −3.37291e7 + 7.03004e7i −0.131109 + 0.273266i
\(637\) −1.31647e8 −0.509321
\(638\) −1.89392e6 + 8.32569e6i −0.00729289 + 0.0320596i
\(639\) 1.25527e7i 0.0481099i
\(640\) −596339. 1.17233e8i −0.00227485 0.447208i
\(641\) −1.47284e8 −0.559219 −0.279610 0.960114i \(-0.590205\pi\)
−0.279610 + 0.960114i \(0.590205\pi\)
\(642\) 1.59667e8 + 3.63210e7i 0.603408 + 0.137263i
\(643\) 5.45081e7i 0.205035i 0.994731 + 0.102518i \(0.0326898\pi\)
−0.994731 + 0.102518i \(0.967310\pi\)
\(644\) −2.56874e8 1.23245e8i −0.961753 0.461435i
\(645\) 4.70149e7 0.175209
\(646\) 2.02338e7 8.89479e7i 0.0750550 0.329943i
\(647\) 1.13471e8i 0.418960i 0.977813 + 0.209480i \(0.0671771\pi\)
−0.977813 + 0.209480i \(0.932823\pi\)
\(648\) −2.36782e7 1.87984e7i −0.0870210 0.0690871i
\(649\) 7.88796e6 0.0288556
\(650\) 6.72793e7 + 1.53046e7i 0.244986 + 0.0557292i
\(651\) 1.87312e8i 0.678925i
\(652\) −1.44306e8 + 3.00773e8i −0.520647 + 1.08517i
\(653\) 1.43973e8 0.517060 0.258530 0.966003i \(-0.416762\pi\)
0.258530 + 0.966003i \(0.416762\pi\)
\(654\) 4.16897e6 1.83268e7i 0.0149037 0.0655170i
\(655\) 2.04988e8i 0.729463i
\(656\) 1.40013e8 + 1.74527e8i 0.495971 + 0.618233i
\(657\) −5.38883e7 −0.190020
\(658\) −2.32966e8 5.29949e7i −0.817739 0.186019i
\(659\) 8.17629e7i 0.285693i −0.989745 0.142847i \(-0.954374\pi\)
0.989745 0.142847i \(-0.0456256\pi\)
\(660\) −1.48149e6 710795.i −0.00515306 0.00247236i
\(661\) −1.06717e7 −0.0369512 −0.0184756 0.999829i \(-0.505881\pi\)
−0.0184756 + 0.999829i \(0.505881\pi\)
\(662\) 1.65155e7 7.26022e7i 0.0569268 0.250251i
\(663\) 6.72068e7i 0.230607i
\(664\) 8.41236e7 1.05961e8i 0.287352 0.361944i
\(665\) −1.07921e8 −0.366979
\(666\) −7.68380e7 1.74790e7i −0.260108 0.0591690i
\(667\) 6.09741e8i 2.05479i
\(668\) −1.30614e8 + 2.72235e8i −0.438188 + 0.913301i
\(669\) 3.16034e8 1.05549
\(670\) 2.01777e7 8.87013e7i 0.0670883 0.294921i
\(671\) 1.04135e7i 0.0344690i
\(672\) −5.90583e7 1.21504e8i −0.194613 0.400391i
\(673\) 4.04111e8 1.32573 0.662865 0.748739i \(-0.269340\pi\)
0.662865 + 0.748739i \(0.269340\pi\)
\(674\) −4.83908e8 1.10079e8i −1.58046 0.359521i
\(675\) 1.18375e7i 0.0384900i
\(676\) 1.61011e8 + 7.72507e7i 0.521213 + 0.250070i
\(677\) 4.71145e8 1.51841 0.759204 0.650853i \(-0.225589\pi\)
0.759204 + 0.650853i \(0.225589\pi\)
\(678\) 4.72419e7 2.07676e8i 0.151579 0.666341i
\(679\) 4.10329e7i 0.131076i
\(680\) −3.50166e7 2.78002e7i −0.111365 0.0884139i
\(681\) −2.13283e8 −0.675329
\(682\) −1.04419e7 2.37531e6i −0.0329175 0.00748803i
\(683\) 3.10535e8i 0.974649i 0.873221 + 0.487325i \(0.162027\pi\)
−0.873221 + 0.487325i \(0.837973\pi\)
\(684\) 4.91060e7 1.02350e8i 0.153450 0.319830i
\(685\) −1.10667e8 −0.344307
\(686\) 7.76012e7 3.41136e8i 0.240379 1.05671i
\(687\) 2.68711e8i 0.828735i
\(688\) −1.72374e8 + 1.38285e8i −0.529305 + 0.424629i
\(689\) 2.15704e8 0.659479
\(690\) −1.14419e8 2.60279e7i −0.348298 0.0792304i
\(691\) 6.84679e7i 0.207517i −0.994603 0.103758i \(-0.966913\pi\)
0.994603 0.103758i \(-0.0330869\pi\)
\(692\) −5.18694e7 2.48862e7i −0.156528 0.0751000i
\(693\) −1.89354e6 −0.00568952
\(694\) 3.55980e7 1.56489e8i 0.106499 0.468172i
\(695\) 7.31712e7i 0.217964i
\(696\) −1.79772e8 + 2.26438e8i −0.533206 + 0.671617i
\(697\) 8.53322e7 0.252008
\(698\) 5.59505e8 + 1.27276e8i 1.64527 + 0.374265i
\(699\) 1.94158e8i 0.568492i
\(700\) −2.28814e7 + 4.76909e7i −0.0667097 + 0.139041i
\(701\) −1.82766e8 −0.530569 −0.265285 0.964170i \(-0.585466\pi\)
−0.265285 + 0.964170i \(0.585466\pi\)
\(702\) −1.85516e7 + 8.15532e7i −0.0536255 + 0.235738i
\(703\) 2.95885e8i 0.851643i
\(704\) 7.52232e6 1.75146e6i 0.0215593 0.00501976i
\(705\) −9.83997e7 −0.280819
\(706\) −1.29801e8 2.95269e7i −0.368861 0.0839081i
\(707\) 4.10323e8i 1.16109i
\(708\) 2.40816e8 + 1.15540e8i 0.678556 + 0.325561i
\(709\) −4.30437e8 −1.20773 −0.603867 0.797085i \(-0.706374\pi\)
−0.603867 + 0.797085i \(0.706374\pi\)
\(710\) −5.12427e6 + 2.25263e7i −0.0143172 + 0.0629383i
\(711\) 1.31462e8i 0.365757i
\(712\) −1.26151e8 1.00153e8i −0.349503 0.277475i
\(713\) −7.64723e8 −2.10977
\(714\) −5.02393e7 1.14284e7i −0.138022 0.0313971i
\(715\) 4.54567e6i 0.0124360i
\(716\) −1.03966e8 + 2.16692e8i −0.283238 + 0.590343i
\(717\) −3.38884e8 −0.919378
\(718\) 5.17532e7 2.27507e8i 0.139818 0.614642i
\(719\) 3.35482e8i 0.902573i −0.892379 0.451287i \(-0.850965\pi\)
0.892379 0.451287i \(-0.149035\pi\)
\(720\) −3.48176e7 4.34005e7i −0.0932828 0.116278i
\(721\) 4.47976e8 1.19522
\(722\) 4.86428e7 + 1.10652e7i 0.129243 + 0.0294001i
\(723\) 1.23447e8i 0.326637i
\(724\) 5.80993e8 + 2.78752e8i 1.53093 + 0.734517i
\(725\) 1.13204e8 0.297061
\(726\) −4.89804e7 + 2.15318e8i −0.128001 + 0.562692i
\(727\) 3.91654e8i 1.01929i −0.860383 0.509647i \(-0.829776\pi\)
0.860383 0.509647i \(-0.170224\pi\)
\(728\) −2.32380e8 + 2.92702e8i −0.602289 + 0.758634i
\(729\) −1.43489e7 −0.0370370
\(730\) −9.67048e7 2.19983e7i −0.248588 0.0565485i
\(731\) 8.42792e7i 0.215759i
\(732\) −1.52533e8 + 3.17919e8i −0.388893 + 0.810556i
\(733\) 4.73042e8 1.20112 0.600562 0.799578i \(-0.294944\pi\)
0.600562 + 0.799578i \(0.294944\pi\)
\(734\) 1.09278e8 4.80389e8i 0.276341 1.21480i
\(735\) 4.15662e7i 0.104684i
\(736\) 4.96057e8 2.41113e8i 1.24422 0.604765i
\(737\) 5.99303e6 0.0149708
\(738\) 1.03548e8 + 2.35550e7i 0.257615 + 0.0586021i
\(739\) 3.38422e8i 0.838543i −0.907861 0.419272i \(-0.862285\pi\)
0.907861 0.419272i \(-0.137715\pi\)
\(740\) −1.30753e8 6.27336e7i −0.322670 0.154812i
\(741\) −3.14043e8 −0.771852
\(742\) −3.66800e7 + 1.61246e8i −0.0897880 + 0.394709i
\(743\) 3.10086e8i 0.755990i 0.925808 + 0.377995i \(0.123386\pi\)
−0.925808 + 0.377995i \(0.876614\pi\)
\(744\) −2.83994e8 2.25466e8i −0.689588 0.547473i
\(745\) −6.69644e7 −0.161948
\(746\) −5.00166e8 1.13777e8i −1.20475 0.274056i
\(747\) 6.42118e7i 0.154047i
\(748\) 1.27418e6 2.65572e6i 0.00304456 0.00634567i
\(749\) 3.47273e8 0.826467
\(750\) −4.83230e6 + 2.12428e7i −0.0114543 + 0.0503534i
\(751\) 3.62391e8i 0.855575i −0.903879 0.427787i \(-0.859293\pi\)
0.903879 0.427787i \(-0.140707\pi\)
\(752\) 3.60769e8 2.89423e8i 0.848351 0.680580i
\(753\) −4.05379e8 −0.949460
\(754\) 7.79905e8 + 1.77412e8i 1.81940 + 0.413875i
\(755\) 3.33961e8i 0.775988i
\(756\) −5.78090e7 2.77359e7i −0.133792 0.0641914i
\(757\) −6.63275e8 −1.52900 −0.764498 0.644627i \(-0.777013\pi\)
−0.764498 + 0.644627i \(0.777013\pi\)
\(758\) −7.65174e7 + 3.36371e8i −0.175692 + 0.772344i
\(759\) 7.73062e6i 0.0176803i
\(760\) 1.29904e8 1.63625e8i 0.295925 0.372743i
\(761\) 3.91992e8 0.889453 0.444726 0.895666i \(-0.353301\pi\)
0.444726 + 0.895666i \(0.353301\pi\)
\(762\) −5.73449e7 1.30448e7i −0.129607 0.0294830i
\(763\) 3.98605e7i 0.0897364i
\(764\) −2.61436e8 + 5.44902e8i −0.586254 + 1.22191i
\(765\) −2.12199e7 −0.0473980
\(766\) 7.94865e7 3.49423e8i 0.176851 0.777438i
\(767\) 7.38901e8i 1.63757i
\(768\) 2.55308e8 + 5.67129e7i 0.563612 + 0.125198i
\(769\) −8.33190e8 −1.83217 −0.916084 0.400988i \(-0.868667\pi\)
−0.916084 + 0.400988i \(0.868667\pi\)
\(770\) −3.39804e6 772982.i −0.00744314 0.00169316i
\(771\) 1.70885e8i 0.372857i
\(772\) 6.31553e8 + 3.03010e8i 1.37264 + 0.658574i
\(773\) 1.73029e7 0.0374612 0.0187306