Properties

Label 60.7.c.a.31.3
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 31.3
Character \(\chi\) \(=\) 60.31
Dual form 60.7.c.a.31.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-6.61106 - 4.50487i) q^{2} +15.5885i q^{3} +(23.4123 + 59.5639i) q^{4} -55.9017 q^{5} +(70.2239 - 103.056i) q^{6} -489.339i q^{7} +(113.547 - 499.250i) q^{8} -243.000 q^{9} +O(q^{10})\) \(q+(-6.61106 - 4.50487i) q^{2} +15.5885i q^{3} +(23.4123 + 59.5639i) q^{4} -55.9017 q^{5} +(70.2239 - 103.056i) q^{6} -489.339i q^{7} +(113.547 - 499.250i) q^{8} -243.000 q^{9} +(369.570 + 251.830i) q^{10} +1671.97i q^{11} +(-928.510 + 364.962i) q^{12} -528.612 q^{13} +(-2204.41 + 3235.05i) q^{14} -871.421i q^{15} +(-2999.73 + 2789.06i) q^{16} +8236.70 q^{17} +(1606.49 + 1094.68i) q^{18} -3892.37i q^{19} +(-1308.79 - 3329.73i) q^{20} +7628.03 q^{21} +(7532.02 - 11053.5i) q^{22} +23107.8i q^{23} +(7782.54 + 1770.03i) q^{24} +3125.00 q^{25} +(3494.69 + 2381.33i) q^{26} -3788.00i q^{27} +(29146.9 - 11456.6i) q^{28} +43960.2 q^{29} +(-3925.64 + 5761.02i) q^{30} +18298.7i q^{31} +(32395.7 - 4925.29i) q^{32} -26063.5 q^{33} +(-54453.3 - 37105.2i) q^{34} +27354.9i q^{35} +(-5689.20 - 14474.0i) q^{36} +76080.2 q^{37} +(-17534.6 + 25732.7i) q^{38} -8240.25i q^{39} +(-6347.49 + 27908.9i) q^{40} -77333.8 q^{41} +(-50429.4 - 34363.3i) q^{42} +45051.5i q^{43} +(-99589.3 + 39144.8i) q^{44} +13584.1 q^{45} +(104098. - 152767. i) q^{46} +79645.0i q^{47} +(-43477.2 - 46761.1i) q^{48} -121803. q^{49} +(-20659.6 - 14077.7i) q^{50} +128397. i q^{51} +(-12376.0 - 31486.2i) q^{52} +46149.0 q^{53} +(-17064.4 + 25042.7i) q^{54} -93466.2i q^{55} +(-244302. - 55563.1i) q^{56} +60676.0 q^{57} +(-290623. - 198035. i) q^{58} +122143. i q^{59} +(51905.3 - 20402.0i) q^{60} +173832. q^{61} +(82433.2 - 120974. i) q^{62} +118909. i q^{63} +(-236358. - 113377. i) q^{64} +29550.3 q^{65} +(172307. + 117413. i) q^{66} -354754. i q^{67} +(192840. + 490610. i) q^{68} -360215. q^{69} +(123230. - 180845. i) q^{70} -37307.9i q^{71} +(-27592.0 + 121318. i) q^{72} +366139. q^{73} +(-502971. - 342731. i) q^{74} +48713.9i q^{75} +(231845. - 91129.4i) q^{76} +818161. q^{77} +(-37121.2 + 54476.8i) q^{78} +110073. i q^{79} +(167690. - 155913. i) q^{80} +59049.0 q^{81} +(511259. + 348379. i) q^{82} -353049. i q^{83} +(178590. + 454356. i) q^{84} -460445. q^{85} +(202951. - 297838. i) q^{86} +685271. i q^{87} +(834733. + 189848. i) q^{88} -965332. q^{89} +(-89805.4 - 61194.6i) q^{90} +258670. i q^{91} +(-1.37639e6 + 541008. i) q^{92} -285248. q^{93} +(358790. - 526538. i) q^{94} +217590. i q^{95} +(76777.6 + 504999. i) q^{96} -368862. q^{97} +(805249. + 548707. i) q^{98} -406290. 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −6.61106 4.50487i −0.826383 0.563109i
\(3\) 15.5885i 0.577350i
\(4\) 23.4123 + 59.5639i 0.365818 + 0.930687i
\(5\) −55.9017 −0.447214
\(6\) 70.2239 103.056i 0.325111 0.477112i
\(7\) 489.339i 1.42664i −0.700837 0.713321i \(-0.747190\pi\)
0.700837 0.713321i \(-0.252810\pi\)
\(8\) 113.547 499.250i 0.221772 0.975099i
\(9\) −243.000 −0.333333
\(10\) 369.570 + 251.830i 0.369570 + 0.251830i
\(11\) 1671.97i 1.25618i 0.778141 + 0.628089i \(0.216163\pi\)
−0.778141 + 0.628089i \(0.783837\pi\)
\(12\) −928.510 + 364.962i −0.537332 + 0.211205i
\(13\) −528.612 −0.240606 −0.120303 0.992737i \(-0.538387\pi\)
−0.120303 + 0.992737i \(0.538387\pi\)
\(14\) −2204.41 + 3235.05i −0.803355 + 1.17895i
\(15\) 871.421i 0.258199i
\(16\) −2999.73 + 2789.06i −0.732355 + 0.680923i
\(17\) 8236.70 1.67651 0.838255 0.545278i \(-0.183576\pi\)
0.838255 + 0.545278i \(0.183576\pi\)
\(18\) 1606.49 + 1094.68i 0.275461 + 0.187703i
\(19\) 3892.37i 0.567483i −0.958901 0.283742i \(-0.908424\pi\)
0.958901 0.283742i \(-0.0915758\pi\)
\(20\) −1308.79 3329.73i −0.163599 0.416216i
\(21\) 7628.03 0.823673
\(22\) 7532.02 11053.5i 0.707365 1.03808i
\(23\) 23107.8i 1.89922i 0.313432 + 0.949611i \(0.398521\pi\)
−0.313432 + 0.949611i \(0.601479\pi\)
\(24\) 7782.54 + 1770.03i 0.562973 + 0.128040i
\(25\) 3125.00 0.200000
\(26\) 3494.69 + 2381.33i 0.198833 + 0.135488i
\(27\) 3788.00i 0.192450i
\(28\) 29146.9 11456.6i 1.32776 0.521891i
\(29\) 43960.2 1.80246 0.901229 0.433343i \(-0.142666\pi\)
0.901229 + 0.433343i \(0.142666\pi\)
\(30\) −3925.64 + 5761.02i −0.145394 + 0.213371i
\(31\) 18298.7i 0.614236i 0.951672 + 0.307118i \(0.0993646\pi\)
−0.951672 + 0.307118i \(0.900635\pi\)
\(32\) 32395.7 4925.29i 0.988639 0.150308i
\(33\) −26063.5 −0.725255
\(34\) −54453.3 37105.2i −1.38544 0.944058i
\(35\) 27354.9i 0.638014i
\(36\) −5689.20 14474.0i −0.121939 0.310229i
\(37\) 76080.2 1.50199 0.750994 0.660309i \(-0.229575\pi\)
0.750994 + 0.660309i \(0.229575\pi\)
\(38\) −17534.6 + 25732.7i −0.319555 + 0.468958i
\(39\) 8240.25i 0.138914i
\(40\) −6347.49 + 27908.9i −0.0991795 + 0.436077i
\(41\) −77333.8 −1.12206 −0.561032 0.827794i \(-0.689596\pi\)
−0.561032 + 0.827794i \(0.689596\pi\)
\(42\) −50429.4 34363.3i −0.680669 0.463817i
\(43\) 45051.5i 0.566636i 0.959026 + 0.283318i \(0.0914352\pi\)
−0.959026 + 0.283318i \(0.908565\pi\)
\(44\) −99589.3 + 39144.8i −1.16911 + 0.459532i
\(45\) 13584.1 0.149071
\(46\) 104098. 152767.i 1.06947 1.56948i
\(47\) 79645.0i 0.767123i 0.923515 + 0.383562i \(0.125303\pi\)
−0.923515 + 0.383562i \(0.874697\pi\)
\(48\) −43477.2 46761.1i −0.393131 0.422825i
\(49\) −121803. −1.03531
\(50\) −20659.6 14077.7i −0.165277 0.112622i
\(51\) 128397.i 0.967934i
\(52\) −12376.0 31486.2i −0.0880181 0.223929i
\(53\) 46149.0 0.309980 0.154990 0.987916i \(-0.450465\pi\)
0.154990 + 0.987916i \(0.450465\pi\)
\(54\) −17064.4 + 25042.7i −0.108370 + 0.159037i
\(55\) 93466.2i 0.561780i
\(56\) −244302. 55563.1i −1.39112 0.316390i
\(57\) 60676.0 0.327637
\(58\) −290623. 198035.i −1.48952 1.01498i
\(59\) 122143.i 0.594718i 0.954766 + 0.297359i \(0.0961058\pi\)
−0.954766 + 0.297359i \(0.903894\pi\)
\(60\) 51905.3 20402.0i 0.240302 0.0944537i
\(61\) 173832. 0.765843 0.382922 0.923781i \(-0.374918\pi\)
0.382922 + 0.923781i \(0.374918\pi\)
\(62\) 82433.2 120974.i 0.345881 0.507594i
\(63\) 118909.i 0.475548i
\(64\) −236358. 113377.i −0.901634 0.432499i
\(65\) 29550.3 0.107602
\(66\) 172307. + 117413.i 0.599338 + 0.408397i
\(67\) 354754.i 1.17951i −0.807581 0.589757i \(-0.799224\pi\)
0.807581 0.589757i \(-0.200776\pi\)
\(68\) 192840. + 490610.i 0.613297 + 1.56031i
\(69\) −360215. −1.09652
\(70\) 123230. 180845.i 0.359271 0.527244i
\(71\) 37307.9i 0.104238i −0.998641 0.0521189i \(-0.983403\pi\)
0.998641 0.0521189i \(-0.0165975\pi\)
\(72\) −27592.0 + 121318.i −0.0739240 + 0.325033i
\(73\) 366139. 0.941190 0.470595 0.882349i \(-0.344039\pi\)
0.470595 + 0.882349i \(0.344039\pi\)
\(74\) −502971. 342731.i −1.24122 0.845782i
\(75\) 48713.9i 0.115470i
\(76\) 231845. 91129.4i 0.528149 0.207595i
\(77\) 818161. 1.79212
\(78\) −37121.2 + 54476.8i −0.0782238 + 0.114796i
\(79\) 110073.i 0.223253i 0.993750 + 0.111627i \(0.0356061\pi\)
−0.993750 + 0.111627i \(0.964394\pi\)
\(80\) 167690. 155913.i 0.327519 0.304518i
\(81\) 59049.0 0.111111
\(82\) 511259. + 348379.i 0.927255 + 0.631844i
\(83\) 353049.i 0.617449i −0.951151 0.308725i \(-0.900098\pi\)
0.951151 0.308725i \(-0.0999021\pi\)
\(84\) 178590. + 454356.i 0.301314 + 0.766581i
\(85\) −460445. −0.749759
\(86\) 202951. 297838.i 0.319078 0.468258i
\(87\) 685271.i 1.04065i
\(88\) 834733. + 189848.i 1.22490 + 0.278585i
\(89\) −965332. −1.36933 −0.684663 0.728860i \(-0.740050\pi\)
−0.684663 + 0.728860i \(0.740050\pi\)
\(90\) −89805.4 61194.6i −0.123190 0.0839433i
\(91\) 258670.i 0.343259i
\(92\) −1.37639e6 + 541008.i −1.76758 + 0.694768i
\(93\) −285248. −0.354629
\(94\) 358790. 526538.i 0.431974 0.633938i
\(95\) 217590.i 0.253786i
\(96\) 76777.6 + 504999.i 0.0867803 + 0.570791i
\(97\) −368862. −0.404155 −0.202078 0.979370i \(-0.564769\pi\)
−0.202078 + 0.979370i \(0.564769\pi\)
\(98\) 805249. + 548707.i 0.855562 + 0.582992i
\(99\) 406290.i 0.418726i
\(100\) 73163.5 + 186137.i 0.0731635 + 0.186137i
\(101\) 270425. 0.262472 0.131236 0.991351i \(-0.458105\pi\)
0.131236 + 0.991351i \(0.458105\pi\)
\(102\) 578413. 848844.i 0.545052 0.799884i
\(103\) 528514.i 0.483666i −0.970318 0.241833i \(-0.922251\pi\)
0.970318 0.241833i \(-0.0777485\pi\)
\(104\) −60022.5 + 263910.i −0.0533598 + 0.234615i
\(105\) −426420. −0.368358
\(106\) −305094. 207895.i −0.256163 0.174553i
\(107\) 1.09673e6i 0.895255i −0.894220 0.447628i \(-0.852269\pi\)
0.894220 0.447628i \(-0.147731\pi\)
\(108\) 225628. 88685.8i 0.179111 0.0704016i
\(109\) 33665.5 0.0259959 0.0129980 0.999916i \(-0.495863\pi\)
0.0129980 + 0.999916i \(0.495863\pi\)
\(110\) −421053. + 617911.i −0.316343 + 0.464245i
\(111\) 1.18597e6i 0.867173i
\(112\) 1.36479e6 + 1.46788e6i 0.971434 + 1.04481i
\(113\) 2.26998e6 1.57321 0.786607 0.617455i \(-0.211836\pi\)
0.786607 + 0.617455i \(0.211836\pi\)
\(114\) −401133. 273337.i −0.270753 0.184495i
\(115\) 1.29177e6i 0.849357i
\(116\) 1.02921e6 + 2.61844e6i 0.659371 + 1.67752i
\(117\) 128453. 0.0802022
\(118\) 550236. 807492.i 0.334891 0.491465i
\(119\) 4.03053e6i 2.39178i
\(120\) −435057. 98947.5i −0.251769 0.0572613i
\(121\) −1.02393e6 −0.577984
\(122\) −1.14921e6 783090.i −0.632880 0.431253i
\(123\) 1.20552e6i 0.647824i
\(124\) −1.08994e6 + 428415.i −0.571661 + 0.224698i
\(125\) −174693. −0.0894427
\(126\) 535671. 786117.i 0.267785 0.392984i
\(127\) 753363.i 0.367784i 0.982946 + 0.183892i \(0.0588697\pi\)
−0.982946 + 0.183892i \(0.941130\pi\)
\(128\) 1.05183e6 + 1.81430e6i 0.501551 + 0.865128i
\(129\) −702284. −0.327147
\(130\) −195359. 133120.i −0.0889209 0.0605919i
\(131\) 1.18839e6i 0.528623i 0.964437 + 0.264311i \(0.0851447\pi\)
−0.964437 + 0.264311i \(0.914855\pi\)
\(132\) −610207. 1.55244e6i −0.265311 0.674985i
\(133\) −1.90469e6 −0.809596
\(134\) −1.59812e6 + 2.34530e6i −0.664194 + 0.974730i
\(135\) 211755.i 0.0860663i
\(136\) 935255. 4.11218e6i 0.371803 1.63476i
\(137\) −2.07235e6 −0.805938 −0.402969 0.915214i \(-0.632022\pi\)
−0.402969 + 0.915214i \(0.632022\pi\)
\(138\) 2.38141e6 + 1.62272e6i 0.906142 + 0.617457i
\(139\) 2.53703e6i 0.944673i 0.881418 + 0.472336i \(0.156589\pi\)
−0.881418 + 0.472336i \(0.843411\pi\)
\(140\) −1.62936e6 + 640441.i −0.593791 + 0.233397i
\(141\) −1.24154e6 −0.442899
\(142\) −168067. + 246645.i −0.0586972 + 0.0861404i
\(143\) 883826.i 0.302245i
\(144\) 728933. 677742.i 0.244118 0.226974i
\(145\) −2.45745e6 −0.806084
\(146\) −2.42057e6 1.64941e6i −0.777783 0.529992i
\(147\) 1.89872e6i 0.597736i
\(148\) 1.78121e6 + 4.53163e6i 0.549453 + 1.39788i
\(149\) 2.04152e6 0.617156 0.308578 0.951199i \(-0.400147\pi\)
0.308578 + 0.951199i \(0.400147\pi\)
\(150\) 219450. 322051.i 0.0650222 0.0954225i
\(151\) 1.03197e6i 0.299735i −0.988706 0.149868i \(-0.952115\pi\)
0.988706 0.149868i \(-0.0478848\pi\)
\(152\) −1.94327e6 441968.i −0.553352 0.125852i
\(153\) −2.00152e6 −0.558837
\(154\) −5.40891e6 3.68571e6i −1.48098 1.00916i
\(155\) 1.02293e6i 0.274694i
\(156\) 490822. 192923.i 0.129286 0.0508173i
\(157\) −1.65351e6 −0.427275 −0.213637 0.976913i \(-0.568531\pi\)
−0.213637 + 0.976913i \(0.568531\pi\)
\(158\) 495862. 727696.i 0.125716 0.184493i
\(159\) 719391.i 0.178967i
\(160\) −1.81098e6 + 275332.i −0.442133 + 0.0672197i
\(161\) 1.13075e7 2.70951
\(162\) −390377. 266008.i −0.0918203 0.0625676i
\(163\) 3.72806e6i 0.860836i 0.902630 + 0.430418i \(0.141634\pi\)
−0.902630 + 0.430418i \(0.858366\pi\)
\(164\) −1.81056e6 4.60631e6i −0.410471 1.04429i
\(165\) 1.45699e6 0.324344
\(166\) −1.59044e6 + 2.33403e6i −0.347691 + 0.510249i
\(167\) 5.98513e6i 1.28506i 0.766259 + 0.642531i \(0.222116\pi\)
−0.766259 + 0.642531i \(0.777884\pi\)
\(168\) 866143. 3.80830e6i 0.182668 0.803162i
\(169\) −4.54738e6 −0.942109
\(170\) 3.04403e6 + 2.07425e6i 0.619588 + 0.422195i
\(171\) 945845.i 0.189161i
\(172\) −2.68345e6 + 1.05476e6i −0.527360 + 0.207285i
\(173\) 1.24240e6 0.239950 0.119975 0.992777i \(-0.461718\pi\)
0.119975 + 0.992777i \(0.461718\pi\)
\(174\) 3.08706e6 4.53037e6i 0.585999 0.859975i
\(175\) 1.52918e6i 0.285329i
\(176\) −4.66324e6 5.01546e6i −0.855361 0.919968i
\(177\) −1.90401e6 −0.343361
\(178\) 6.38187e6 + 4.34869e6i 1.13159 + 0.771079i
\(179\) 4.24325e6i 0.739842i −0.929063 0.369921i \(-0.879385\pi\)
0.929063 0.369921i \(-0.120615\pi\)
\(180\) 318036. + 809123.i 0.0545329 + 0.138739i
\(181\) 7.51866e6 1.26796 0.633979 0.773350i \(-0.281421\pi\)
0.633979 + 0.773350i \(0.281421\pi\)
\(182\) 1.16528e6 1.71009e6i 0.193292 0.283664i
\(183\) 2.70977e6i 0.442160i
\(184\) 1.15366e7 + 2.62383e6i 1.85193 + 0.421194i
\(185\) −4.25301e6 −0.671709
\(186\) 1.88580e6 + 1.28501e6i 0.293059 + 0.199695i
\(187\) 1.37715e7i 2.10600i
\(188\) −4.74397e6 + 1.86468e6i −0.713951 + 0.280627i
\(189\) −1.85361e6 −0.274558
\(190\) 980214. 1.43850e6i 0.142909 0.209725i
\(191\) 6.32700e6i 0.908025i 0.890995 + 0.454013i \(0.150008\pi\)
−0.890995 + 0.454013i \(0.849992\pi\)
\(192\) 1.76737e6 3.68446e6i 0.249704 0.520559i
\(193\) 3.86775e6 0.538005 0.269002 0.963140i \(-0.413306\pi\)
0.269002 + 0.963140i \(0.413306\pi\)
\(194\) 2.43857e6 + 1.66167e6i 0.333987 + 0.227583i
\(195\) 460644.i 0.0621243i
\(196\) −2.85170e6 7.25508e6i −0.378735 0.963549i
\(197\) 1.29512e7 1.69399 0.846996 0.531600i \(-0.178409\pi\)
0.846996 + 0.531600i \(0.178409\pi\)
\(198\) −1.83028e6 + 2.68601e6i −0.235788 + 0.346028i
\(199\) 1.47597e7i 1.87291i 0.350783 + 0.936457i \(0.385915\pi\)
−0.350783 + 0.936457i \(0.614085\pi\)
\(200\) 354835. 1.56016e6i 0.0443544 0.195020i
\(201\) 5.53007e6 0.680992
\(202\) −1.78780e6 1.21823e6i −0.216902 0.147800i
\(203\) 2.15114e7i 2.57146i
\(204\) −7.64786e6 + 3.00608e6i −0.900843 + 0.354087i
\(205\) 4.32309e6 0.501803
\(206\) −2.38089e6 + 3.49404e6i −0.272356 + 0.399693i
\(207\) 5.61520e6i 0.633074i
\(208\) 1.58569e6 1.47433e6i 0.176209 0.163834i
\(209\) 6.50793e6 0.712860
\(210\) 2.81909e6 + 1.92097e6i 0.304404 + 0.207425i
\(211\) 4.46144e6i 0.474928i 0.971396 + 0.237464i \(0.0763161\pi\)
−0.971396 + 0.237464i \(0.923684\pi\)
\(212\) 1.08045e6 + 2.74881e6i 0.113396 + 0.288495i
\(213\) 581572. 0.0601818
\(214\) −4.94061e6 + 7.25053e6i −0.504126 + 0.739824i
\(215\) 2.51846e6i 0.253407i
\(216\) −1.89116e6 430117.i −0.187658 0.0426801i
\(217\) 8.95425e6 0.876295
\(218\) −222565. 151659.i −0.0214826 0.0146385i
\(219\) 5.70754e6i 0.543396i
\(220\) 5.56721e6 2.18826e6i 0.522841 0.205509i
\(221\) −4.35402e6 −0.403379
\(222\) 5.34265e6 7.84054e6i 0.488312 0.716617i
\(223\) 1.76802e7i 1.59431i −0.603777 0.797153i \(-0.706338\pi\)
0.603777 0.797153i \(-0.293662\pi\)
\(224\) −2.41013e6 1.58525e7i −0.214436 1.41044i
\(225\) −759375. −0.0666667
\(226\) −1.50070e7 1.02260e7i −1.30008 0.885890i
\(227\) 5.13872e6i 0.439316i −0.975577 0.219658i \(-0.929506\pi\)
0.975577 0.219658i \(-0.0704942\pi\)
\(228\) 1.42057e6 + 3.61410e6i 0.119855 + 0.304927i
\(229\) −1.04734e7 −0.872133 −0.436067 0.899914i \(-0.643629\pi\)
−0.436067 + 0.899914i \(0.643629\pi\)
\(230\) −5.81924e6 + 8.53995e6i −0.478280 + 0.701895i
\(231\) 1.27539e7i 1.03468i
\(232\) 4.99156e6 2.19471e7i 0.399735 1.75757i
\(233\) −2.36952e7 −1.87324 −0.936619 0.350351i \(-0.886062\pi\)
−0.936619 + 0.350351i \(0.886062\pi\)
\(234\) −849210. 578663.i −0.0662777 0.0451625i
\(235\) 4.45229e6i 0.343068i
\(236\) −7.27529e6 + 2.85964e6i −0.553496 + 0.217558i
\(237\) −1.71586e6 −0.128895
\(238\) −1.81570e7 + 2.66461e7i −1.34683 + 1.97653i
\(239\) 1.12351e7i 0.822971i 0.911416 + 0.411486i \(0.134990\pi\)
−0.911416 + 0.411486i \(0.865010\pi\)
\(240\) 2.43045e6 + 2.61402e6i 0.175814 + 0.189093i
\(241\) −1.18227e7 −0.844632 −0.422316 0.906449i \(-0.638783\pi\)
−0.422316 + 0.906449i \(0.638783\pi\)
\(242\) 6.76929e6 + 4.61269e6i 0.477636 + 0.325468i
\(243\) 920483.i 0.0641500i
\(244\) 4.06981e6 + 1.03541e7i 0.280159 + 0.712760i
\(245\) 6.80900e6 0.463005
\(246\) −5.43069e6 + 7.96974e6i −0.364795 + 0.535351i
\(247\) 2.05755e6i 0.136540i
\(248\) 9.13563e6 + 2.07777e6i 0.598940 + 0.136220i
\(249\) 5.50349e6 0.356484
\(250\) 1.15491e6 + 786968.i 0.0739139 + 0.0503660i
\(251\) 1.35403e7i 0.856263i 0.903716 + 0.428132i \(0.140828\pi\)
−0.903716 + 0.428132i \(0.859172\pi\)
\(252\) −7.08270e6 + 2.78394e6i −0.442586 + 0.173964i
\(253\) −3.86357e7 −2.38576
\(254\) 3.39380e6 4.98053e6i 0.207103 0.303931i
\(255\) 7.17763e6i 0.432873i
\(256\) 1.21950e6 1.67328e7i 0.0726876 0.997355i
\(257\) −2.13424e7 −1.25731 −0.628657 0.777682i \(-0.716395\pi\)
−0.628657 + 0.777682i \(0.716395\pi\)
\(258\) 4.64284e6 + 3.16370e6i 0.270349 + 0.184219i
\(259\) 3.72290e7i 2.14280i
\(260\) 691842. + 1.76013e6i 0.0393629 + 0.100144i
\(261\) −1.06823e7 −0.600819
\(262\) 5.35355e6 7.85654e6i 0.297672 0.436845i
\(263\) 3.34374e6i 0.183808i −0.995768 0.0919042i \(-0.970705\pi\)
0.995768 0.0919042i \(-0.0292954\pi\)
\(264\) −2.95944e6 + 1.30122e7i −0.160841 + 0.707195i
\(265\) −2.57980e6 −0.138627
\(266\) 1.25920e7 + 8.58036e6i 0.669036 + 0.455890i
\(267\) 1.50480e7i 0.790580i
\(268\) 2.11305e7 8.30562e6i 1.09776 0.431487i
\(269\) 1.17373e7 0.602991 0.301496 0.953468i \(-0.402514\pi\)
0.301496 + 0.953468i \(0.402514\pi\)
\(270\) 953930. 1.39993e6i 0.0484647 0.0711237i
\(271\) 7.60965e6i 0.382346i −0.981556 0.191173i \(-0.938771\pi\)
0.981556 0.191173i \(-0.0612292\pi\)
\(272\) −2.47078e7 + 2.29727e7i −1.22780 + 1.14157i
\(273\) −4.03227e6 −0.198181
\(274\) 1.37005e7 + 9.33567e6i 0.666014 + 0.453831i
\(275\) 5.22492e6i 0.251236i
\(276\) −8.43348e6 2.14558e7i −0.401125 1.02051i
\(277\) 3.37880e7 1.58973 0.794864 0.606788i \(-0.207542\pi\)
0.794864 + 0.606788i \(0.207542\pi\)
\(278\) 1.14290e7 1.67725e7i 0.531953 0.780662i
\(279\) 4.44658e6i 0.204745i
\(280\) 1.36569e7 + 3.10607e6i 0.622127 + 0.141494i
\(281\) 3.45425e6 0.155681 0.0778404 0.996966i \(-0.475198\pi\)
0.0778404 + 0.996966i \(0.475198\pi\)
\(282\) 8.20792e6 + 5.59299e6i 0.366004 + 0.249400i
\(283\) 3.62562e7i 1.59964i −0.600238 0.799822i \(-0.704927\pi\)
0.600238 0.799822i \(-0.295073\pi\)
\(284\) 2.22220e6 873464.i 0.0970128 0.0381320i
\(285\) −3.39189e6 −0.146524
\(286\) −3.98152e6 + 5.84303e6i −0.170197 + 0.249770i
\(287\) 3.78424e7i 1.60079i
\(288\) −7.87216e6 + 1.19685e6i −0.329546 + 0.0501026i
\(289\) 4.37056e7 1.81069
\(290\) 1.62463e7 + 1.10705e7i 0.666134 + 0.453913i
\(291\) 5.74998e6i 0.233339i
\(292\) 8.57216e6 + 2.18087e7i 0.344304 + 0.875953i
\(293\) −3.73544e7 −1.48504 −0.742521 0.669823i \(-0.766370\pi\)
−0.742521 + 0.669823i \(0.766370\pi\)
\(294\) −8.55350e6 + 1.25526e7i −0.336590 + 0.493959i
\(295\) 6.82798e6i 0.265966i
\(296\) 8.63870e6 3.79831e7i 0.333099 1.46459i
\(297\) 6.33343e6 0.241752
\(298\) −1.34966e7 9.19678e6i −0.510007 0.347526i
\(299\) 1.22151e7i 0.456965i
\(300\) −2.90159e6 + 1.14051e6i −0.107466 + 0.0422410i
\(301\) 2.20454e7 0.808387
\(302\) −4.64891e6 + 6.82245e6i −0.168784 + 0.247696i
\(303\) 4.21551e6i 0.151538i
\(304\) 1.08560e7 + 1.16760e7i 0.386412 + 0.415599i
\(305\) −9.71750e6 −0.342496
\(306\) 1.32322e7 + 9.01657e6i 0.461813 + 0.314686i
\(307\) 3.42634e7i 1.18417i −0.805874 0.592087i \(-0.798304\pi\)
0.805874 0.592087i \(-0.201696\pi\)
\(308\) 1.91551e7 + 4.87329e7i 0.655588 + 1.66790i
\(309\) 8.23872e6 0.279244
\(310\) −4.60816e6 + 6.76264e6i −0.154683 + 0.227003i
\(311\) 2.53880e7i 0.844008i 0.906594 + 0.422004i \(0.138673\pi\)
−0.906594 + 0.422004i \(0.861327\pi\)
\(312\) −4.11395e6 935659.i −0.135455 0.0308073i
\(313\) 1.21539e7 0.396354 0.198177 0.980166i \(-0.436498\pi\)
0.198177 + 0.980166i \(0.436498\pi\)
\(314\) 1.09314e7 + 7.44883e6i 0.353093 + 0.240602i
\(315\) 6.64723e6i 0.212671i
\(316\) −6.55635e6 + 2.57705e6i −0.207779 + 0.0816699i
\(317\) −3.66896e7 −1.15177 −0.575884 0.817532i \(-0.695342\pi\)
−0.575884 + 0.817532i \(0.695342\pi\)
\(318\) 3.24076e6 4.75594e6i 0.100778 0.147896i
\(319\) 7.35002e7i 2.26421i
\(320\) 1.32128e7 + 6.33797e6i 0.403223 + 0.193420i
\(321\) 1.70963e7 0.516876
\(322\) −7.47549e7 5.09390e7i −2.23909 1.52575i
\(323\) 3.20603e7i 0.951392i
\(324\) 1.38247e6 + 3.51719e6i 0.0406464 + 0.103410i
\(325\) −1.65191e6 −0.0481213
\(326\) 1.67944e7 2.46465e7i 0.484744 0.711380i
\(327\) 524793.i 0.0150088i
\(328\) −8.78105e6 + 3.86090e7i −0.248843 + 1.09412i
\(329\) 3.89734e7 1.09441
\(330\) −9.63227e6 6.56356e6i −0.268032 0.182641i
\(331\) 1.02423e7i 0.282432i −0.989979 0.141216i \(-0.954899\pi\)
0.989979 0.141216i \(-0.0451012\pi\)
\(332\) 2.10290e7 8.26571e6i 0.574652 0.225874i
\(333\) −1.84875e7 −0.500662
\(334\) 2.69622e7 3.95681e7i 0.723630 1.06195i
\(335\) 1.98314e7i 0.527494i
\(336\) −2.28820e7 + 2.12750e7i −0.603221 + 0.560858i
\(337\) −1.49174e7 −0.389766 −0.194883 0.980826i \(-0.562433\pi\)
−0.194883 + 0.980826i \(0.562433\pi\)
\(338\) 3.00630e7 + 2.04853e7i 0.778542 + 0.530509i
\(339\) 3.53856e7i 0.908295i
\(340\) −1.07801e7 2.74259e7i −0.274275 0.697790i
\(341\) −3.05949e7 −0.771589
\(342\) 4.26091e6 6.25304e6i 0.106518 0.156319i
\(343\) 2.03280e6i 0.0503746i
\(344\) 2.24920e7 + 5.11548e6i 0.552526 + 0.125664i
\(345\) 2.01366e7 0.490377
\(346\) −8.21355e6 5.59683e6i −0.198291 0.135118i
\(347\) 6.50530e7i 1.55697i 0.627666 + 0.778483i \(0.284010\pi\)
−0.627666 + 0.778483i \(0.715990\pi\)
\(348\) −4.08174e7 + 1.60438e7i −0.968519 + 0.380688i
\(349\) −4.79094e7 −1.12705 −0.563527 0.826098i \(-0.690556\pi\)
−0.563527 + 0.826098i \(0.690556\pi\)
\(350\) −6.88877e6 + 1.01095e7i −0.160671 + 0.235791i
\(351\) 2.00238e6i 0.0463047i
\(352\) 8.23495e6 + 5.41648e7i 0.188813 + 1.24191i
\(353\) 2.86619e7 0.651599 0.325800 0.945439i \(-0.394367\pi\)
0.325800 + 0.945439i \(0.394367\pi\)
\(354\) 1.25876e7 + 8.57733e6i 0.283747 + 0.193349i
\(355\) 2.08557e6i 0.0466166i
\(356\) −2.26007e7 5.74990e7i −0.500923 1.27441i
\(357\) 6.28298e7 1.38090
\(358\) −1.91153e7 + 2.80524e7i −0.416611 + 0.611393i
\(359\) 6.83927e7i 1.47818i −0.673609 0.739088i \(-0.735257\pi\)
0.673609 0.739088i \(-0.264743\pi\)
\(360\) 1.54244e6 6.78187e6i 0.0330598 0.145359i
\(361\) 3.18954e7 0.677963
\(362\) −4.97063e7 3.38706e7i −1.04782 0.713998i
\(363\) 1.59616e7i 0.333699i
\(364\) −1.54074e7 + 6.05608e6i −0.319467 + 0.125570i
\(365\) −2.04678e7 −0.420913
\(366\) 1.22072e7 1.79145e7i 0.248984 0.365393i
\(367\) 4.76260e7i 0.963488i −0.876312 0.481744i \(-0.840004\pi\)
0.876312 0.481744i \(-0.159996\pi\)
\(368\) −6.44491e7 6.93171e7i −1.29322 1.39090i
\(369\) 1.87921e7 0.374022
\(370\) 2.81169e7 + 1.91593e7i 0.555089 + 0.378245i
\(371\) 2.25825e7i 0.442231i
\(372\) −6.67833e6 1.69905e7i −0.129730 0.330048i
\(373\) 8.65965e7 1.66868 0.834341 0.551248i \(-0.185848\pi\)
0.834341 + 0.551248i \(0.185848\pi\)
\(374\) 6.20390e7 9.10445e7i 1.18590 1.74036i
\(375\) 2.72319e6i 0.0516398i
\(376\) 3.97628e7 + 9.04348e6i 0.748021 + 0.170127i
\(377\) −2.32379e7 −0.433683
\(378\) 1.22543e7 + 8.35028e6i 0.226890 + 0.154606i
\(379\) 3.25539e7i 0.597979i 0.954256 + 0.298989i \(0.0966495\pi\)
−0.954256 + 0.298989i \(0.903350\pi\)
\(380\) −1.29605e7 + 5.09429e6i −0.236195 + 0.0928395i
\(381\) −1.17438e7 −0.212340
\(382\) 2.85023e7 4.18282e7i 0.511317 0.750376i
\(383\) 5.20471e7i 0.926404i 0.886253 + 0.463202i \(0.153300\pi\)
−0.886253 + 0.463202i \(0.846700\pi\)
\(384\) −2.82822e7 + 1.63964e7i −0.499482 + 0.289571i
\(385\) −4.57366e7 −0.801460
\(386\) −2.55699e7 1.74237e7i −0.444598 0.302955i
\(387\) 1.09475e7i 0.188879i
\(388\) −8.63591e6 2.19709e7i −0.147847 0.376142i
\(389\) −3.96590e7 −0.673741 −0.336871 0.941551i \(-0.609368\pi\)
−0.336871 + 0.941551i \(0.609368\pi\)
\(390\) 2.07514e6 3.04535e6i 0.0349827 0.0513385i
\(391\) 1.90332e8i 3.18406i
\(392\) −1.38304e7 + 6.08103e7i −0.229603 + 1.00953i
\(393\) −1.85252e7 −0.305201
\(394\) −8.56212e7 5.83434e7i −1.39989 0.953901i
\(395\) 6.15324e6i 0.0998419i
\(396\) 2.42002e7 9.51218e6i 0.389703 0.153177i
\(397\) −3.49965e7 −0.559310 −0.279655 0.960101i \(-0.590220\pi\)
−0.279655 + 0.960101i \(0.590220\pi\)
\(398\) 6.64904e7 9.75772e7i 1.05465 1.54774i
\(399\) 2.96911e7i 0.467420i
\(400\) −9.37414e6 + 8.71581e6i −0.146471 + 0.136185i
\(401\) −3.61187e7 −0.560143 −0.280072 0.959979i \(-0.590358\pi\)
−0.280072 + 0.959979i \(0.590358\pi\)
\(402\) −3.65596e7 2.49122e7i −0.562761 0.383473i
\(403\) 9.67291e6i 0.147789i
\(404\) 6.33128e6 + 1.61076e7i 0.0960168 + 0.244279i
\(405\) −3.30094e6 −0.0496904
\(406\) −9.69060e7 + 1.42213e8i −1.44801 + 2.12501i
\(407\) 1.27204e8i 1.88676i
\(408\) 6.41025e7 + 1.45792e7i 0.943831 + 0.214661i
\(409\) −1.44295e7 −0.210903 −0.105451 0.994424i \(-0.533629\pi\)
−0.105451 + 0.994424i \(0.533629\pi\)
\(410\) −2.85802e7 1.94750e7i −0.414681 0.282569i
\(411\) 3.23048e7i 0.465309i
\(412\) 3.14804e7 1.23738e7i 0.450141 0.176933i
\(413\) 5.97691e7 0.848450
\(414\) −2.52957e7 + 3.71225e7i −0.356489 + 0.523161i
\(415\) 1.97361e7i 0.276132i
\(416\) −1.71248e7 + 2.60357e6i −0.237873 + 0.0361650i
\(417\) −3.95484e7 −0.545407
\(418\) −4.30244e7 2.93174e7i −0.589095 0.401418i
\(419\) 6.90024e7i 0.938041i −0.883187 0.469021i \(-0.844607\pi\)
0.883187 0.469021i \(-0.155393\pi\)
\(420\) −9.98348e6 2.53993e7i −0.134752 0.342825i
\(421\) 6.10435e7 0.818075 0.409037 0.912518i \(-0.365865\pi\)
0.409037 + 0.912518i \(0.365865\pi\)
\(422\) 2.00982e7 2.94949e7i 0.267436 0.392472i
\(423\) 1.93537e7i 0.255708i
\(424\) 5.24009e6 2.30399e7i 0.0687450 0.302261i
\(425\) 2.57397e7 0.335302
\(426\) −3.84481e6 2.61991e6i −0.0497332 0.0338889i
\(427\) 8.50626e7i 1.09258i
\(428\) 6.53253e7 2.56769e7i 0.833202 0.327500i
\(429\) 1.37775e7 0.174501
\(430\) −1.13453e7 + 1.66497e7i −0.142696 + 0.209411i
\(431\) 1.07830e8i 1.34682i −0.739270 0.673409i \(-0.764829\pi\)
0.739270 0.673409i \(-0.235171\pi\)
\(432\) 1.05649e7 + 1.13629e7i 0.131044 + 0.140942i
\(433\) −9.10528e7 −1.12158 −0.560789 0.827958i \(-0.689502\pi\)
−0.560789 + 0.827958i \(0.689502\pi\)
\(434\) −5.91971e7 4.03377e7i −0.724155 0.493449i
\(435\) 3.83078e7i 0.465393i
\(436\) 788187. + 2.00525e6i 0.00950977 + 0.0241941i
\(437\) 8.99441e7 1.07778
\(438\) 2.57117e7 3.77329e7i 0.305991 0.449053i
\(439\) 7.88744e7i 0.932272i 0.884713 + 0.466136i \(0.154354\pi\)
−0.884713 + 0.466136i \(0.845646\pi\)
\(440\) −4.66630e7 1.06128e7i −0.547791 0.124587i
\(441\) 2.95982e7 0.345103
\(442\) 2.87847e7 + 1.96143e7i 0.333346 + 0.227146i
\(443\) 6.25122e7i 0.719041i 0.933137 + 0.359520i \(0.117060\pi\)
−0.933137 + 0.359520i \(0.882940\pi\)
\(444\) −7.06412e7 + 2.77664e7i −0.807066 + 0.317227i
\(445\) 5.39637e7 0.612381
\(446\) −7.96468e7 + 1.16885e8i −0.897768 + 1.31751i
\(447\) 3.18241e7i 0.356315i
\(448\) −5.54798e7 + 1.15659e8i −0.617022 + 1.28631i
\(449\) −1.83745e7 −0.202990 −0.101495 0.994836i \(-0.532363\pi\)
−0.101495 + 0.994836i \(0.532363\pi\)
\(450\) 5.02028e6 + 3.42088e6i 0.0550922 + 0.0375406i
\(451\) 1.29300e8i 1.40951i
\(452\) 5.31456e7 + 1.35209e8i 0.575509 + 1.46417i
\(453\) 1.60869e7 0.173052
\(454\) −2.31492e7 + 3.39724e7i −0.247383 + 0.363043i
\(455\) 1.44601e7i 0.153510i
\(456\) 6.88960e6 3.02925e7i 0.0726607 0.319478i
\(457\) 3.53983e7 0.370880 0.185440 0.982656i \(-0.440629\pi\)
0.185440 + 0.982656i \(0.440629\pi\)
\(458\) 6.92406e7 + 4.71815e7i 0.720716 + 0.491106i
\(459\) 3.12006e7i 0.322645i
\(460\) 7.69427e7 3.02433e7i 0.790486 0.310710i
\(461\) 1.10748e7 0.113040 0.0565199 0.998401i \(-0.482000\pi\)
0.0565199 + 0.998401i \(0.482000\pi\)
\(462\) 5.74545e7 8.43166e7i 0.582637 0.855042i
\(463\) 1.34336e8i 1.35347i 0.736225 + 0.676737i \(0.236606\pi\)
−0.736225 + 0.676737i \(0.763394\pi\)
\(464\) −1.31868e8 + 1.22608e8i −1.32004 + 1.22734i
\(465\) 1.59459e7 0.158595
\(466\) 1.56651e8 + 1.06744e8i 1.54801 + 1.05484i
\(467\) 9.60280e7i 0.942860i −0.881903 0.471430i \(-0.843738\pi\)
0.881903 0.471430i \(-0.156262\pi\)
\(468\) 3.00738e6 + 7.65116e6i 0.0293394 + 0.0746431i
\(469\) −1.73595e8 −1.68274
\(470\) −2.00570e7 + 2.94344e7i −0.193184 + 0.283505i
\(471\) 2.57756e7i 0.246687i
\(472\) 6.09797e7 + 1.38690e7i 0.579909 + 0.131892i
\(473\) −7.53249e7 −0.711796
\(474\) 1.13437e7 + 7.72973e6i 0.106517 + 0.0725820i
\(475\) 1.21636e7i 0.113497i
\(476\) 2.40074e8 9.43642e7i 2.22600 0.874956i
\(477\) −1.12142e7 −0.103327
\(478\) 5.06128e7 7.42762e7i 0.463422 0.680089i
\(479\) 1.53193e7i 0.139390i −0.997568 0.0696951i \(-0.977797\pi\)
0.997568 0.0696951i \(-0.0222026\pi\)
\(480\) −4.29200e6 2.82303e7i −0.0388093 0.255266i
\(481\) −4.02169e7 −0.361388
\(482\) 7.81609e7 + 5.32599e7i 0.697989 + 0.475619i
\(483\) 1.76267e8i 1.56434i
\(484\) −2.39727e7 6.09896e7i −0.211437 0.537922i
\(485\) 2.06200e7 0.180744
\(486\) 4.14665e6 6.08537e6i 0.0361234 0.0530125i
\(487\) 9.26753e7i 0.802375i −0.915996 0.401187i \(-0.868598\pi\)
0.915996 0.401187i \(-0.131402\pi\)
\(488\) 1.97381e7 8.67856e7i 0.169843 0.746773i
\(489\) −5.81148e7 −0.497004
\(490\) −4.50148e7 3.06737e7i −0.382619 0.260722i
\(491\) 4.66588e7i 0.394175i 0.980386 + 0.197088i \(0.0631483\pi\)
−0.980386 + 0.197088i \(0.936852\pi\)
\(492\) 7.18052e7 2.82239e7i 0.602922 0.236986i
\(493\) 3.62087e8 3.02184
\(494\) 9.26901e6 1.36026e7i 0.0768869 0.112834i
\(495\) 2.27123e7i 0.187260i
\(496\) −5.10362e7 5.48911e7i −0.418247 0.449838i
\(497\) −1.82562e7 −0.148710
\(498\) −3.63840e7 2.47925e7i −0.294593 0.200739i
\(499\) 5.88986e7i 0.474027i −0.971506 0.237014i \(-0.923831\pi\)
0.971506 0.237014i \(-0.0761686\pi\)
\(500\) −4.08997e6 1.04054e7i −0.0327197 0.0832431i
\(501\) −9.32990e7 −0.741931
\(502\) 6.09973e7 8.95158e7i 0.482169 0.707601i
\(503\) 9.59290e7i 0.753782i −0.926258 0.376891i \(-0.876993\pi\)
0.926258 0.376891i \(-0.123007\pi\)
\(504\) 5.93655e7 + 1.35018e7i 0.463706 + 0.105463i
\(505\) −1.51172e7 −0.117381
\(506\) 2.55423e8 + 1.74049e8i 1.97155 + 1.34344i
\(507\) 7.08866e7i 0.543927i
\(508\) −4.48733e7 + 1.76380e7i −0.342292 + 0.134542i
\(509\) 4.35652e7 0.330359 0.165179 0.986264i \(-0.447180\pi\)
0.165179 + 0.986264i \(0.447180\pi\)
\(510\) −3.23343e7 + 4.74518e7i −0.243755 + 0.357719i
\(511\) 1.79166e8i 1.34274i
\(512\) −8.34414e7 + 1.05128e8i −0.621687 + 0.783266i
\(513\) −1.47443e7 −0.109212
\(514\) 1.41096e8 + 9.61447e7i 1.03902 + 0.708005i
\(515\) 2.95449e7i 0.216302i
\(516\) −1.64421e7 4.18308e7i −0.119676 0.304472i
\(517\) −1.33164e8 −0.963644
\(518\) −1.67712e8 + 2.46123e8i −1.20663 + 1.77077i
\(519\) 1.93670e7i 0.138535i
\(520\) 3.35536e6 1.47530e7i 0.0238632 0.104923i
\(521\) 1.99431e8 1.41020 0.705099 0.709108i \(-0.250902\pi\)
0.705099 + 0.709108i \(0.250902\pi\)
\(522\) 7.06215e7 + 4.81224e7i 0.496507 + 0.338327i
\(523\) 3.33251e7i 0.232952i −0.993194 0.116476i \(-0.962840\pi\)
0.993194 0.116476i \(-0.0371598\pi\)
\(524\) −7.07853e7 + 2.78230e7i −0.491982 + 0.193380i
\(525\) 2.38376e7 0.164735
\(526\) −1.50631e7 + 2.21057e7i −0.103504 + 0.151896i
\(527\) 1.50721e8i 1.02977i
\(528\) 7.81833e7 7.26926e7i 0.531144 0.493843i
\(529\) −3.85936e8 −2.60704
\(530\) 1.70553e7 + 1.16217e7i 0.114559 + 0.0780623i
\(531\) 2.96807e7i 0.198239i
\(532\) −4.45931e7 1.13451e8i −0.296164 0.753480i
\(533\) 4.08796e7 0.269976
\(534\) −6.77894e7 + 9.94835e7i −0.445183 + 0.653322i
\(535\) 6.13089e7i 0.400370i
\(536\) −1.77111e8 4.02814e7i −1.15014 0.261583i
\(537\) 6.61457e7 0.427148
\(538\) −7.75960e7 5.28749e7i −0.498302 0.339549i
\(539\) 2.03652e8i 1.30053i
\(540\) −1.26130e7 + 4.95769e6i −0.0801007 + 0.0314846i
\(541\) −1.29602e8 −0.818500 −0.409250 0.912422i \(-0.634210\pi\)
−0.409250 + 0.912422i \(0.634210\pi\)
\(542\) −3.42805e7 + 5.03079e7i −0.215302 + 0.315964i
\(543\) 1.17204e8i 0.732056i
\(544\) 2.66834e8 4.05681e7i 1.65746 0.251993i
\(545\) −1.88196e6 −0.0116257
\(546\) 2.66576e7 + 1.81649e7i 0.163773 + 0.111597i
\(547\) 9.98146e7i 0.609862i 0.952374 + 0.304931i \(0.0986335\pi\)
−0.952374 + 0.304931i \(0.901367\pi\)
\(548\) −4.85186e7 1.23437e8i −0.294826 0.750076i
\(549\) −4.22411e7 −0.255281
\(550\) 2.35376e7 3.45423e7i 0.141473 0.207617i
\(551\) 1.71109e8i 1.02286i
\(552\) −4.09015e7 + 1.79838e8i −0.243177 + 1.06921i
\(553\) 5.38627e7 0.318503
\(554\) −2.23374e8 1.52210e8i −1.31372 0.895189i
\(555\) 6.62979e7i 0.387811i
\(556\) −1.51116e8 + 5.93978e7i −0.879194 + 0.345578i
\(557\) −2.67691e8 −1.54906 −0.774529 0.632538i \(-0.782013\pi\)
−0.774529 + 0.632538i \(0.782013\pi\)
\(558\) −2.00313e7 + 2.93966e7i −0.115294 + 0.169198i
\(559\) 2.38148e7i 0.136336i
\(560\) −7.62943e7 8.20571e7i −0.434438 0.467253i
\(561\) −2.14677e8 −1.21590
\(562\) −2.28363e7 1.55610e7i −0.128652 0.0876652i
\(563\) 1.44353e7i 0.0808912i 0.999182 + 0.0404456i \(0.0128777\pi\)
−0.999182 + 0.0404456i \(0.987122\pi\)
\(564\) −2.90674e7 7.39512e7i −0.162020 0.412200i
\(565\) −1.26896e8 −0.703562
\(566\) −1.63329e8 + 2.39692e8i −0.900773 + 1.32192i
\(567\) 2.88949e7i 0.158516i
\(568\) −1.86260e7 4.23621e6i −0.101642 0.0231171i
\(569\) 1.61516e8 0.876755 0.438378 0.898791i \(-0.355553\pi\)
0.438378 + 0.898791i \(0.355553\pi\)
\(570\) 2.24240e7 + 1.52800e7i 0.121085 + 0.0825086i
\(571\) 1.12052e8i 0.601882i −0.953643 0.300941i \(-0.902699\pi\)
0.953643 0.300941i \(-0.0973007\pi\)
\(572\) 5.26442e7 2.06924e7i 0.281295 0.110566i
\(573\) −9.86282e7 −0.524249
\(574\) 1.70475e8 2.50179e8i 0.901416 1.32286i
\(575\) 7.22119e7i 0.379844i
\(576\) 5.74350e7 + 2.75506e7i 0.300545 + 0.144166i
\(577\) 3.07042e8 1.59835 0.799173 0.601102i \(-0.205271\pi\)
0.799173 + 0.601102i \(0.205271\pi\)
\(578\) −2.88941e8 1.96888e8i −1.49632 1.01961i
\(579\) 6.02922e7i 0.310617i
\(580\) −5.75346e7 1.46375e8i −0.294880 0.750211i
\(581\) −1.72761e8 −0.880879
\(582\) −2.59029e7 + 3.80135e7i −0.131395 + 0.192828i
\(583\) 7.71598e7i 0.389391i
\(584\) 4.15741e7 1.82795e8i 0.208730 0.917753i
\(585\) −7.18073e6 −0.0358675
\(586\) 2.46952e8 + 1.68276e8i 1.22721 + 0.836239i
\(587\) 3.65313e8i 1.80614i −0.429498 0.903068i \(-0.641309\pi\)
0.429498 0.903068i \(-0.358691\pi\)
\(588\) 1.13095e8 4.44535e7i 0.556305 0.218663i
\(589\) 7.12252e7 0.348568
\(590\) −3.07591e7 + 4.51402e7i −0.149768 + 0.219790i
\(591\) 2.01889e8i 0.978026i
\(592\) −2.28220e8 + 2.12192e8i −1.09999 + 1.02274i
\(593\) 2.24772e8 1.07790 0.538949 0.842338i \(-0.318821\pi\)
0.538949 + 0.842338i \(0.318821\pi\)
\(594\) −4.18707e7 2.85313e7i −0.199779 0.136132i
\(595\) 2.25314e8i 1.06964i
\(596\) 4.77967e7 + 1.21601e8i 0.225766 + 0.574379i
\(597\) −2.30081e8 −1.08133
\(598\) −5.50273e7 + 8.07547e7i −0.257321 + 0.377628i
\(599\) 1.94995e8i 0.907284i 0.891184 + 0.453642i \(0.149875\pi\)
−0.891184 + 0.453642i \(0.850125\pi\)
\(600\) 2.43205e7 + 5.53134e6i 0.112595 + 0.0256080i
\(601\) 6.04496e7 0.278465 0.139232 0.990260i \(-0.455537\pi\)
0.139232 + 0.990260i \(0.455537\pi\)
\(602\) −1.45744e8 9.93118e7i −0.668037 0.455210i
\(603\) 8.62052e7i 0.393171i
\(604\) 6.14684e7 2.41609e7i 0.278960 0.109648i
\(605\) 5.72397e7 0.258482
\(606\) 1.89903e7 2.78690e7i 0.0853324 0.125229i
\(607\) 2.42035e8i 1.08221i −0.840954 0.541107i \(-0.818005\pi\)
0.840954 0.541107i \(-0.181995\pi\)
\(608\) −1.91710e7 1.26096e8i −0.0852972 0.561036i
\(609\) 3.35330e8 1.48464
\(610\) 6.42430e7 + 4.37760e7i 0.283032 + 0.192862i
\(611\) 4.21014e7i 0.184575i
\(612\) −4.68602e7 1.19218e8i −0.204432 0.520102i
\(613\) 1.06610e8 0.462826 0.231413 0.972856i \(-0.425665\pi\)
0.231413 + 0.972856i \(0.425665\pi\)
\(614\) −1.54352e8 + 2.26518e8i −0.666818 + 0.978581i
\(615\) 6.73903e7i 0.289716i
\(616\) 9.29000e7 4.08467e8i 0.397442 1.74749i
\(617\) 1.94002e8 0.825945 0.412972 0.910744i \(-0.364491\pi\)
0.412972 + 0.910744i \(0.364491\pi\)
\(618\) −5.44667e7 3.71144e7i −0.230763 0.157245i
\(619\) 2.34375e8i 0.988188i 0.869409 + 0.494094i \(0.164500\pi\)
−0.869409 + 0.494094i \(0.835500\pi\)
\(620\) 6.09296e7 2.39491e7i 0.255654 0.100488i
\(621\) 8.75323e7 0.365505
\(622\) 1.14369e8 1.67841e8i 0.475268 0.697474i
\(623\) 4.72374e8i 1.95354i
\(624\) 2.29826e7 + 2.47185e7i 0.0945899 + 0.101735i
\(625\) 9.76562e6 0.0400000
\(626\) −8.03504e7 5.47518e7i −0.327540 0.223190i
\(627\) 1.01449e8i 0.411570i
\(628\) −3.87125e7 9.84894e7i −0.156305 0.397659i
\(629\) 6.26649e8 2.51810
\(630\) −2.99449e7 + 4.39453e7i −0.119757 + 0.175748i
\(631\) 9.78994e6i 0.0389665i −0.999810 0.0194833i \(-0.993798\pi\)
0.999810 0.0194833i \(-0.00620211\pi\)
\(632\) 5.49538e7 + 1.24984e7i 0.217694 + 0.0495113i
\(633\) −6.95470e7 −0.274200
\(634\) 2.42557e8 + 1.65282e8i 0.951801 + 0.648570i
\(635\) 4.21143e7i 0.164478i
\(636\) −4.28498e7 + 1.68426e7i −0.166562 + 0.0654694i
\(637\) 6.43867e7 0.249102
\(638\) 3.31109e8 4.85915e8i 1.27500 1.87110i
\(639\) 9.06582e6i 0.0347460i
\(640\) −5.87990e7 1.01423e8i −0.224300 0.386897i
\(641\) −2.62400e8 −0.996297 −0.498149 0.867092i \(-0.665987\pi\)
−0.498149 + 0.867092i \(0.665987\pi\)
\(642\) −1.13025e8 7.70165e7i −0.427138 0.291057i
\(643\) 2.58694e8i 0.973090i −0.873655 0.486545i \(-0.838257\pi\)
0.873655 0.486545i \(-0.161743\pi\)
\(644\) 2.64736e8 + 6.73522e8i 0.991186 + 2.52170i
\(645\) 3.92589e7 0.146305
\(646\) −1.44427e8 + 2.11952e8i −0.535737 + 0.786214i
\(647\) 1.56584e8i 0.578141i −0.957308 0.289070i \(-0.906654\pi\)
0.957308 0.289070i \(-0.0933462\pi\)
\(648\) 6.70486e6 2.94802e7i 0.0246413 0.108344i
\(649\) −2.04219e8 −0.747072
\(650\) 1.09209e7 + 7.44165e6i 0.0397666 + 0.0270975i
\(651\) 1.39583e8i 0.505929i
\(652\) −2.22058e8 + 8.72826e7i −0.801169 + 0.314909i
\(653\) −2.72428e7 −0.0978391 −0.0489195 0.998803i \(-0.515578\pi\)
−0.0489195 + 0.998803i \(0.515578\pi\)
\(654\) 2.36412e6 3.46944e6i 0.00845156 0.0124030i
\(655\) 6.64332e7i 0.236407i
\(656\) 2.31980e8 2.15689e8i 0.821750 0.764040i
\(657\) −8.89718e7 −0.313730
\(658\) −2.57656e8 1.75570e8i −0.904402 0.616272i
\(659\) 2.14808e8i 0.750575i −0.926909 0.375287i \(-0.877544\pi\)
0.926909 0.375287i \(-0.122456\pi\)
\(660\) 3.41116e7 + 8.67843e7i 0.118651 + 0.301862i
\(661\) 1.02802e8 0.355958 0.177979 0.984034i \(-0.443044\pi\)
0.177979 + 0.984034i \(0.443044\pi\)
\(662\) −4.61403e7 + 6.77126e7i −0.159040 + 0.233397i
\(663\) 6.78725e7i 0.232891i
\(664\) −1.76260e8 4.00878e7i −0.602074 0.136933i
\(665\) 1.06475e8 0.362062
\(666\) 1.22222e8 + 8.32837e7i 0.413739 + 0.281927i
\(667\) 1.01582e9i 3.42327i
\(668\) −3.56498e8 + 1.40126e8i −1.19599 + 0.470099i
\(669\) 2.75607e8 0.920473
\(670\) 8.93376e7 1.31106e8i 0.297037 0.435912i
\(671\) 2.90642e8i 0.962036i
\(672\) 2.47116e8 3.75703e7i 0.814315 0.123804i
\(673\) 2.06604e8 0.677786 0.338893 0.940825i \(-0.389948\pi\)
0.338893 + 0.940825i \(0.389948\pi\)
\(674\) 9.86201e7 + 6.72011e7i 0.322096 + 0.219481i
\(675\) 1.18375e7i 0.0384900i
\(676\) −1.06465e8 2.70860e8i −0.344640 0.876808i
\(677\) −4.17968e7 −0.134703 −0.0673515 0.997729i \(-0.521455\pi\)
−0.0673515 + 0.997729i \(0.521455\pi\)
\(678\) 1.59407e8 2.33936e8i 0.511469 0.750600i
\(679\) 1.80498e8i 0.576585i
\(680\) −5.22823e7 + 2.29878e8i −0.166276 + 0.731088i
\(681\) 8.01047e7 0.253639
\(682\) 2.02265e8 + 1.37826e8i 0.637628 + 0.434489i
\(683\) 3.82961e8i 1.20197i 0.799261 + 0.600983i \(0.205224\pi\)
−0.799261 + 0.600983i \(0.794776\pi\)
\(684\) −5.63383e7 + 2.21444e7i −0.176050 + 0.0691984i
\(685\) 1.15848e8 0.360427
\(686\) 9.15748e6 1.34389e7i 0.0283664 0.0416287i
\(687\) 1.63265e8i 0.503526i
\(688\) −1.25651e8 1.35142e8i −0.385835 0.414979i
\(689\) −2.43949e7 −0.0745833
\(690\) −1.33125e8 9.07129e7i −0.405239 0.276135i
\(691\) 3.85201e8i 1.16749i −0.811937 0.583744i \(-0.801587\pi\)
0.811937 0.583744i \(-0.198413\pi\)
\(692\) 2.90874e7 + 7.40020e7i 0.0877781 + 0.223319i
\(693\) −1.98813e8 −0.597373
\(694\) 2.93055e8 4.30070e8i 0.876740 1.28665i
\(695\) 1.41824e8i 0.422471i
\(696\) 3.42122e8 + 7.78107e7i 1.01474 + 0.230787i
\(697\) −6.36975e8 −1.88115
\(698\) 3.16732e8 + 2.15826e8i 0.931378 + 0.634654i
\(699\) 3.69372e8i 1.08151i
\(700\) 9.10842e7 3.58017e7i 0.265551 0.104378i
\(701\) −4.74929e8 −1.37872 −0.689358 0.724420i \(-0.742107\pi\)
−0.689358 + 0.724420i \(0.742107\pi\)
\(702\) 9.02046e6 1.32379e7i 0.0260746 0.0382654i
\(703\) 2.96132e8i 0.852353i
\(704\) 1.89564e8 3.95184e8i 0.543296 1.13261i
\(705\) 6.94044e7 0.198070
\(706\) −1.89485e8 1.29118e8i −0.538470 0.366921i
\(707\) 1.32329e8i 0.374453i
\(708\) −4.45774e7 1.13411e8i −0.125607 0.319561i
\(709\) 6.32167e8 1.77375 0.886877 0.462006i \(-0.152870\pi\)
0.886877 + 0.462006i \(0.152870\pi\)
\(710\) 9.39524e6 1.37879e7i 0.0262502 0.0385232i
\(711\) 2.67476e7i 0.0744177i
\(712\) −1.09611e8 + 4.81942e8i −0.303678 + 1.33523i
\(713\) −4.22843e8 −1.16657
\(714\) −4.15372e8 2.83040e8i −1.14115 0.777594i
\(715\) 4.94074e7i 0.135168i
\(716\) 2.52744e8 9.93443e7i 0.688561 0.270647i
\(717\) −1.75138e8 −0.475143
\(718\) −3.08100e8 + 4.52148e8i −0.832374 + 1.22154i
\(719\) 6.43480e7i 0.173120i 0.996247 + 0.0865602i \(0.0275875\pi\)
−0.996247 + 0.0865602i \(0.972413\pi\)
\(720\) −4.07486e7 + 3.78869e7i −0.109173 + 0.101506i
\(721\) −2.58622e8 −0.690018
\(722\) −2.10862e8 1.43684e8i −0.560257 0.381767i
\(723\) 1.84298e8i 0.487648i
\(724\) 1.76029e8 + 4.47841e8i 0.463841 + 1.18007i
\(725\) 1.37375e8 0.360492
\(726\) −7.19047e7 + 1.05523e8i −0.187909 + 0.275763i
\(727\) 2.63761e8i 0.686448i −0.939254 0.343224i \(-0.888481\pi\)
0.939254 0.343224i \(-0.111519\pi\)
\(728\) 1.29141e8 + 2.93713e7i 0.334712 + 0.0761254i
\(729\) −1.43489e7 −0.0370370
\(730\) 1.35314e8 + 9.22047e7i 0.347835 + 0.237020i
\(731\) 3.71076e8i 0.949971i
\(732\) −1.61405e8 + 6.34420e7i −0.411512 + 0.161750i
\(733\) −7.94382e7 −0.201705 −0.100853 0.994901i \(-0.532157\pi\)
−0.100853 + 0.994901i \(0.532157\pi\)
\(734\) −2.14549e8 + 3.14859e8i −0.542548 + 0.796210i
\(735\) 1.06142e8i 0.267316i
\(736\) 1.13813e8 + 7.48595e8i 0.285468 + 1.87764i
\(737\) 5.93139e8 1.48168
\(738\) −1.24236e8 8.46560e7i −0.309085 0.210615i
\(739\) 3.58605e8i 0.888552i 0.895890 + 0.444276i \(0.146539\pi\)
−0.895890 + 0.444276i \(0.853461\pi\)
\(740\) −9.95729e7 2.53326e8i −0.245723 0.625151i
\(741\) −3.20741e7 −0.0788315
\(742\) −1.01731e8 + 1.49294e8i −0.249024 + 0.365452i
\(743\) 4.60265e8i 1.12213i −0.827773 0.561063i \(-0.810393\pi\)
0.827773 0.561063i \(-0.189607\pi\)
\(744\) −3.23892e7 + 1.42410e8i −0.0786468 + 0.345798i
\(745\) −1.14124e8 −0.276000
\(746\) −5.72495e8 3.90106e8i −1.37897 0.939650i
\(747\) 8.57910e7i 0.205816i
\(748\) −8.20287e8 + 3.22424e8i −1.96002 + 0.770411i
\(749\) −5.36670e8 −1.27721
\(750\) −1.22676e7 + 1.80032e7i −0.0290788 + 0.0426742i
\(751\) 4.03140e8i 0.951779i −0.879505 0.475889i \(-0.842126\pi\)
0.879505 0.475889i \(-0.157874\pi\)
\(752\) −2.22135e8 2.38913e8i −0.522352 0.561807i
\(753\) −2.11072e8 −0.494364
\(754\) 1.53627e8 + 1.04684e8i 0.358388 + 0.244211i
\(755\) 5.76891e7i 0.134046i
\(756\) −4.33974e7 1.10408e8i −0.100438 0.255527i
\(757\) 3.68817e8 0.850204 0.425102 0.905145i \(-0.360238\pi\)
0.425102 + 0.905145i \(0.360238\pi\)
\(758\) 1.46651e8 2.15216e8i 0.336727 0.494160i
\(759\) 6.02270e8i 1.37742i
\(760\) 1.08632e8 + 2.47068e7i 0.247467 + 0.0562827i
\(761\) 4.74390e8 1.07642 0.538210 0.842811i \(-0.319101\pi\)
0.538210 + 0.842811i \(0.319101\pi\)
\(762\) 7.76388e7 + 5.29042e7i 0.175475 + 0.119571i
\(763\) 1.64738e7i 0.0370869i
\(764\) −3.76861e8 + 1.48130e8i −0.845087 + 0.332172i
\(765\) 1.11888e8 0.249920
\(766\) 2.34465e8 3.44087e8i 0.521666 0.765564i
\(767\) 6.45661e7i 0.143093i
\(768\) 2.60839e8 + 1.90101e7i 0.575823 + 0.0419662i
\(769\) −7.61175e8 −1.67381 −0.836904 0.547349i \(-0.815637\pi\)
−0.836904 + 0.547349i \(0.815637\pi\)
\(770\) 3.02368e8 + 2.06037e8i 0.662312 + 0.451309i
\(771\) 3.32695e8i 0.725911i
\(772\) 9.05530e7 + 2.30378e8i 0.196812 + 0.500714i
\(773\) −4.57650e8 −0.990820 −0.495410