Properties

Label 60.7.c.a.31.8
Level $60$
Weight $7$
Character 60.31
Analytic conductor $13.803$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 31.8
Character \(\chi\) \(=\) 60.31
Dual form 60.7.c.a.31.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.08457 + 7.38143i) q^{2} -15.5885i q^{3} +(-44.9709 - 45.5370i) q^{4} +55.9017 q^{5} +(115.065 + 48.0836i) q^{6} +200.003i q^{7} +(474.844 - 191.487i) q^{8} -243.000 q^{9} +O(q^{10})\) \(q+(-3.08457 + 7.38143i) q^{2} -15.5885i q^{3} +(-44.9709 - 45.5370i) q^{4} +55.9017 q^{5} +(115.065 + 48.0836i) q^{6} +200.003i q^{7} +(474.844 - 191.487i) q^{8} -243.000 q^{9} +(-172.433 + 412.634i) q^{10} -76.4809i q^{11} +(-709.852 + 701.027i) q^{12} -2210.14 q^{13} +(-1476.31 - 616.922i) q^{14} -871.421i q^{15} +(-51.2371 + 4095.68i) q^{16} -7764.25 q^{17} +(749.550 - 1793.69i) q^{18} -3205.95i q^{19} +(-2513.95 - 2545.60i) q^{20} +3117.74 q^{21} +(564.538 + 235.911i) q^{22} -12464.7i q^{23} +(-2984.99 - 7402.08i) q^{24} +3125.00 q^{25} +(6817.33 - 16314.0i) q^{26} +3788.00i q^{27} +(9107.53 - 8994.31i) q^{28} -36699.1 q^{29} +(6432.33 + 2687.96i) q^{30} -13711.2i q^{31} +(-30073.9 - 13011.6i) q^{32} -1192.22 q^{33} +(23949.3 - 57311.2i) q^{34} +11180.5i q^{35} +(10927.9 + 11065.5i) q^{36} -44039.1 q^{37} +(23664.5 + 9888.97i) q^{38} +34452.7i q^{39} +(26544.6 - 10704.5i) q^{40} -75533.6 q^{41} +(-9616.87 + 23013.3i) q^{42} +22258.6i q^{43} +(-3482.71 + 3439.42i) q^{44} -13584.1 q^{45} +(92007.5 + 38448.3i) q^{46} +176111. i q^{47} +(63845.3 + 798.708i) q^{48} +77647.8 q^{49} +(-9639.27 + 23067.0i) q^{50} +121033. i q^{51} +(99392.1 + 100643. i) q^{52} -75090.0 q^{53} +(-27960.8 - 11684.3i) q^{54} -4275.41i q^{55} +(38298.0 + 94970.1i) q^{56} -49975.8 q^{57} +(113201. - 270891. i) q^{58} -176642. i q^{59} +(-39681.9 + 39188.6i) q^{60} -32696.9 q^{61} +(101208. + 42293.2i) q^{62} -48600.7i q^{63} +(188809. - 181853. i) q^{64} -123551. q^{65} +(3677.48 - 8800.28i) q^{66} +309523. i q^{67} +(349165. + 353560. i) q^{68} -194306. q^{69} +(-82528.0 - 34487.0i) q^{70} -377693. i q^{71} +(-115387. + 46531.4i) q^{72} +423700. q^{73} +(135841. - 325071. i) q^{74} -48713.9i q^{75} +(-145989. + 144174. i) q^{76} +15296.4 q^{77} +(-254310. - 106272. i) q^{78} -643249. i q^{79} +(-2864.24 + 228955. i) q^{80} +59049.0 q^{81} +(232988. - 557546. i) q^{82} +824425. i q^{83} +(-140207. - 141972. i) q^{84} -434035. q^{85} +(-164300. - 68658.0i) q^{86} +572082. i q^{87} +(-14645.1 - 36316.5i) q^{88} -539925. q^{89} +(41901.1 - 100270. i) q^{90} -442035. i q^{91} +(-567607. + 560550. i) q^{92} -213737. q^{93} +(-1.29995e6 - 543227. i) q^{94} -179218. i q^{95} +(-202831. + 468806. i) q^{96} +1.03950e6 q^{97} +(-239510. + 573152. i) q^{98} +18584.9i 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.08457 + 7.38143i −0.385571 + 0.922678i
\(3\) 15.5885i 0.577350i
\(4\) −44.9709 45.5370i −0.702670 0.711516i
\(5\) 55.9017 0.447214
\(6\) 115.065 + 48.0836i 0.532709 + 0.222609i
\(7\) 200.003i 0.583099i 0.956556 + 0.291549i \(0.0941708\pi\)
−0.956556 + 0.291549i \(0.905829\pi\)
\(8\) 474.844 191.487i 0.927429 0.373999i
\(9\) −243.000 −0.333333
\(10\) −172.433 + 412.634i −0.172433 + 0.412634i
\(11\) 76.4809i 0.0574613i −0.999587 0.0287306i \(-0.990853\pi\)
0.999587 0.0287306i \(-0.00914650\pi\)
\(12\) −709.852 + 701.027i −0.410794 + 0.405687i
\(13\) −2210.14 −1.00598 −0.502991 0.864292i \(-0.667767\pi\)
−0.502991 + 0.864292i \(0.667767\pi\)
\(14\) −1476.31 616.922i −0.538013 0.224826i
\(15\) 871.421i 0.258199i
\(16\) −51.2371 + 4095.68i −0.0125091 + 0.999922i
\(17\) −7764.25 −1.58035 −0.790174 0.612883i \(-0.790010\pi\)
−0.790174 + 0.612883i \(0.790010\pi\)
\(18\) 749.550 1793.69i 0.128524 0.307559i
\(19\) 3205.95i 0.467408i −0.972308 0.233704i \(-0.924915\pi\)
0.972308 0.233704i \(-0.0750846\pi\)
\(20\) −2513.95 2545.60i −0.314244 0.318199i
\(21\) 3117.74 0.336652
\(22\) 564.538 + 235.911i 0.0530182 + 0.0221554i
\(23\) 12464.7i 1.02447i −0.858845 0.512235i \(-0.828818\pi\)
0.858845 0.512235i \(-0.171182\pi\)
\(24\) −2984.99 7402.08i −0.215928 0.535451i
\(25\) 3125.00 0.200000
\(26\) 6817.33 16314.0i 0.387877 0.928198i
\(27\) 3788.00i 0.192450i
\(28\) 9107.53 8994.31i 0.414884 0.409726i
\(29\) −36699.1 −1.50474 −0.752369 0.658742i \(-0.771089\pi\)
−0.752369 + 0.658742i \(0.771089\pi\)
\(30\) 6432.33 + 2687.96i 0.238234 + 0.0995540i
\(31\) 13711.2i 0.460247i −0.973161 0.230124i \(-0.926087\pi\)
0.973161 0.230124i \(-0.0739130\pi\)
\(32\) −30073.9 13011.6i −0.917783 0.397083i
\(33\) −1192.22 −0.0331753
\(34\) 23949.3 57311.2i 0.609336 1.45815i
\(35\) 11180.5i 0.260770i
\(36\) 10927.9 + 11065.5i 0.234223 + 0.237172i
\(37\) −44039.1 −0.869427 −0.434713 0.900569i \(-0.643150\pi\)
−0.434713 + 0.900569i \(0.643150\pi\)
\(38\) 23664.5 + 9888.97i 0.431267 + 0.180219i
\(39\) 34452.7i 0.580804i
\(40\) 26544.6 10704.5i 0.414759 0.167257i
\(41\) −75533.6 −1.09594 −0.547972 0.836497i \(-0.684600\pi\)
−0.547972 + 0.836497i \(0.684600\pi\)
\(42\) −9616.87 + 23013.3i −0.129803 + 0.310622i
\(43\) 22258.6i 0.279957i 0.990155 + 0.139979i \(0.0447034\pi\)
−0.990155 + 0.139979i \(0.955297\pi\)
\(44\) −3482.71 + 3439.42i −0.0408846 + 0.0403763i
\(45\) −13584.1 −0.149071
\(46\) 92007.5 + 38448.3i 0.945257 + 0.395006i
\(47\) 176111.i 1.69627i 0.529783 + 0.848133i \(0.322273\pi\)
−0.529783 + 0.848133i \(0.677727\pi\)
\(48\) 63845.3 + 798.708i 0.577305 + 0.00722211i
\(49\) 77647.8 0.659996
\(50\) −9639.27 + 23067.0i −0.0771142 + 0.184536i
\(51\) 121033.i 0.912414i
\(52\) 99392.1 + 100643.i 0.706873 + 0.715772i
\(53\) −75090.0 −0.504376 −0.252188 0.967678i \(-0.581150\pi\)
−0.252188 + 0.967678i \(0.581150\pi\)
\(54\) −27960.8 11684.3i −0.177570 0.0742031i
\(55\) 4275.41i 0.0256975i
\(56\) 38298.0 + 94970.1i 0.218078 + 0.540783i
\(57\) −49975.8 −0.269858
\(58\) 113201. 270891.i 0.580183 1.38839i
\(59\) 176642.i 0.860080i −0.902810 0.430040i \(-0.858499\pi\)
0.902810 0.430040i \(-0.141501\pi\)
\(60\) −39681.9 + 39188.6i −0.183713 + 0.181429i
\(61\) −32696.9 −0.144051 −0.0720255 0.997403i \(-0.522946\pi\)
−0.0720255 + 0.997403i \(0.522946\pi\)
\(62\) 101208. + 42293.2i 0.424660 + 0.177458i
\(63\) 48600.7i 0.194366i
\(64\) 188809. 181853.i 0.720250 0.693715i
\(65\) −123551. −0.449889
\(66\) 3677.48 8800.28i 0.0127914 0.0306101i
\(67\) 309523.i 1.02913i 0.857453 + 0.514563i \(0.172046\pi\)
−0.857453 + 0.514563i \(0.827954\pi\)
\(68\) 349165. + 353560.i 1.11046 + 1.12444i
\(69\) −194306. −0.591478
\(70\) −82528.0 34487.0i −0.240607 0.100545i
\(71\) 377693.i 1.05527i −0.849471 0.527635i \(-0.823079\pi\)
0.849471 0.527635i \(-0.176921\pi\)
\(72\) −115387. + 46531.4i −0.309143 + 0.124666i
\(73\) 423700. 1.08915 0.544577 0.838711i \(-0.316690\pi\)
0.544577 + 0.838711i \(0.316690\pi\)
\(74\) 135841. 325071.i 0.335226 0.802201i
\(75\) 48713.9i 0.115470i
\(76\) −145989. + 144174.i −0.332568 + 0.328434i
\(77\) 15296.4 0.0335056
\(78\) −254310. 106272.i −0.535895 0.223941i
\(79\) 643249.i 1.30466i −0.757934 0.652331i \(-0.773791\pi\)
0.757934 0.652331i \(-0.226209\pi\)
\(80\) −2864.24 + 228955.i −0.00559422 + 0.447179i
\(81\) 59049.0 0.111111
\(82\) 232988. 557546.i 0.422564 1.01120i
\(83\) 824425.i 1.44184i 0.693019 + 0.720919i \(0.256280\pi\)
−0.693019 + 0.720919i \(0.743720\pi\)
\(84\) −140207. 141972.i −0.236556 0.239533i
\(85\) −434035. −0.706753
\(86\) −164300. 68658.0i −0.258310 0.107943i
\(87\) 572082.i 0.868761i
\(88\) −14645.1 36316.5i −0.0214904 0.0532912i
\(89\) −539925. −0.765885 −0.382942 0.923772i \(-0.625089\pi\)
−0.382942 + 0.923772i \(0.625089\pi\)
\(90\) 41901.1 100270.i 0.0574775 0.137545i
\(91\) 442035.i 0.586587i
\(92\) −567607. + 560550.i −0.728927 + 0.719865i
\(93\) −213737. −0.265724
\(94\) −1.29995e6 543227.i −1.56511 0.654031i
\(95\) 179218.i 0.209031i
\(96\) −202831. + 468806.i −0.229256 + 0.529882i
\(97\) 1.03950e6 1.13896 0.569481 0.822005i \(-0.307144\pi\)
0.569481 + 0.822005i \(0.307144\pi\)
\(98\) −239510. + 573152.i −0.254475 + 0.608964i
\(99\) 18584.9i 0.0191538i
\(100\) −140534. 142303.i −0.140534 0.142303i
\(101\) 1.03704e6 1.00654 0.503269 0.864130i \(-0.332130\pi\)
0.503269 + 0.864130i \(0.332130\pi\)
\(102\) −893393. 373333.i −0.841864 0.351800i
\(103\) 147507.i 0.134989i 0.997720 + 0.0674947i \(0.0215006\pi\)
−0.997720 + 0.0674947i \(0.978499\pi\)
\(104\) −1.04947e6 + 423214.i −0.932977 + 0.376236i
\(105\) 174287. 0.150555
\(106\) 231620. 554271.i 0.194473 0.465377i
\(107\) 2.37593e6i 1.93947i −0.244159 0.969735i \(-0.578512\pi\)
0.244159 0.969735i \(-0.421488\pi\)
\(108\) 172494. 170350.i 0.136931 0.135229i
\(109\) 220507. 0.170272 0.0851361 0.996369i \(-0.472867\pi\)
0.0851361 + 0.996369i \(0.472867\pi\)
\(110\) 31558.7 + 13187.8i 0.0237105 + 0.00990819i
\(111\) 686501.i 0.501964i
\(112\) −819148. 10247.6i −0.583053 0.00729402i
\(113\) −6962.21 −0.00482516 −0.00241258 0.999997i \(-0.500768\pi\)
−0.00241258 + 0.999997i \(0.500768\pi\)
\(114\) 154154. 368893.i 0.104049 0.248992i
\(115\) 696800.i 0.458157i
\(116\) 1.65039e6 + 1.67116e6i 1.05733 + 1.07064i
\(117\) 537065. 0.335327
\(118\) 1.30387e6 + 544865.i 0.793577 + 0.331622i
\(119\) 1.55287e6i 0.921499i
\(120\) −166866. 413789.i −0.0965661 0.239461i
\(121\) 1.76571e6 0.996698
\(122\) 100856. 241349.i 0.0555419 0.132913i
\(123\) 1.17745e6i 0.632744i
\(124\) −624368. + 616606.i −0.327473 + 0.323402i
\(125\) 174693. 0.0894427
\(126\) 358742. + 149912.i 0.179338 + 0.0749420i
\(127\) 1.62503e6i 0.793324i 0.917965 + 0.396662i \(0.129832\pi\)
−0.917965 + 0.396662i \(0.870168\pi\)
\(128\) 759941. + 1.95462e6i 0.362368 + 0.932035i
\(129\) 346977. 0.161633
\(130\) 381100. 911980.i 0.173464 0.415103i
\(131\) 2.19004e6i 0.974178i −0.873352 0.487089i \(-0.838059\pi\)
0.873352 0.487089i \(-0.161941\pi\)
\(132\) 53615.2 + 54290.1i 0.0233113 + 0.0236047i
\(133\) 641199. 0.272545
\(134\) −2.28472e6 954744.i −0.949552 0.396801i
\(135\) 211755.i 0.0860663i
\(136\) −3.68680e6 + 1.48676e6i −1.46566 + 0.591048i
\(137\) 645148. 0.250898 0.125449 0.992100i \(-0.459963\pi\)
0.125449 + 0.992100i \(0.459963\pi\)
\(138\) 599350. 1.43426e6i 0.228057 0.545744i
\(139\) 1.82992e6i 0.681376i 0.940176 + 0.340688i \(0.110660\pi\)
−0.940176 + 0.340688i \(0.889340\pi\)
\(140\) 509127. 502797.i 0.185542 0.183235i
\(141\) 2.74531e6 0.979340
\(142\) 2.78791e6 + 1.16502e6i 0.973675 + 0.406881i
\(143\) 169034.i 0.0578050i
\(144\) 12450.6 995250.i 0.00416969 0.333307i
\(145\) −2.05154e6 −0.672939
\(146\) −1.30693e6 + 3.12751e6i −0.419946 + 1.00494i
\(147\) 1.21041e6i 0.381049i
\(148\) 1.98048e6 + 2.00541e6i 0.610920 + 0.618611i
\(149\) −5.15717e6 −1.55902 −0.779511 0.626388i \(-0.784532\pi\)
−0.779511 + 0.626388i \(0.784532\pi\)
\(150\) 359578. + 150261.i 0.106542 + 0.0445219i
\(151\) 4.15675e6i 1.20732i 0.797241 + 0.603662i \(0.206292\pi\)
−0.797241 + 0.603662i \(0.793708\pi\)
\(152\) −613899. 1.52233e6i −0.174810 0.433488i
\(153\) 1.88671e6 0.526782
\(154\) −47182.8 + 112909.i −0.0129188 + 0.0309149i
\(155\) 766480.i 0.205829i
\(156\) 1.56887e6 1.54937e6i 0.413251 0.408114i
\(157\) 2.10057e6 0.542798 0.271399 0.962467i \(-0.412514\pi\)
0.271399 + 0.962467i \(0.412514\pi\)
\(158\) 4.74810e6 + 1.98415e6i 1.20378 + 0.503040i
\(159\) 1.17054e6i 0.291202i
\(160\) −1.68118e6 727371.i −0.410445 0.177581i
\(161\) 2.49298e6 0.597368
\(162\) −182141. + 435866.i −0.0428412 + 0.102520i
\(163\) 7.38999e6i 1.70640i 0.521583 + 0.853200i \(0.325342\pi\)
−0.521583 + 0.853200i \(0.674658\pi\)
\(164\) 3.39681e6 + 3.43957e6i 0.770088 + 0.779782i
\(165\) −66647.1 −0.0148364
\(166\) −6.08543e6 2.54299e6i −1.33035 0.555931i
\(167\) 5.20318e6i 1.11717i −0.829447 0.558585i \(-0.811344\pi\)
0.829447 0.558585i \(-0.188656\pi\)
\(168\) 1.48044e6 597007.i 0.312221 0.125908i
\(169\) 57919.0 0.0119994
\(170\) 1.33881e6 3.20379e6i 0.272503 0.652105i
\(171\) 779046.i 0.155803i
\(172\) 1.01359e6 1.00099e6i 0.199194 0.196718i
\(173\) −7.71907e6 −1.49083 −0.745413 0.666603i \(-0.767747\pi\)
−0.745413 + 0.666603i \(0.767747\pi\)
\(174\) −4.22278e6 1.76462e6i −0.801587 0.334969i
\(175\) 625009.i 0.116620i
\(176\) 313241. + 3918.66i 0.0574568 + 0.000718787i
\(177\) −2.75358e6 −0.496567
\(178\) 1.66543e6 3.98542e6i 0.295303 0.706665i
\(179\) 5.62557e6i 0.980860i −0.871481 0.490430i \(-0.836840\pi\)
0.871481 0.490430i \(-0.163160\pi\)
\(180\) 610890. + 618580.i 0.104748 + 0.106066i
\(181\) −8.06911e6 −1.36079 −0.680393 0.732848i \(-0.738191\pi\)
−0.680393 + 0.732848i \(0.738191\pi\)
\(182\) 3.26285e6 + 1.36349e6i 0.541231 + 0.226171i
\(183\) 509694.i 0.0831679i
\(184\) −2.38684e6 5.91880e6i −0.383151 0.950124i
\(185\) −2.46186e6 −0.388819
\(186\) 659285. 1.57768e6i 0.102455 0.245178i
\(187\) 593817.i 0.0908087i
\(188\) 8.01959e6 7.91989e6i 1.20692 1.19192i
\(189\) −757610. −0.112217
\(190\) 1.32288e6 + 552810.i 0.192868 + 0.0805963i
\(191\) 4.37551e6i 0.627955i 0.949430 + 0.313978i \(0.101662\pi\)
−0.949430 + 0.313978i \(0.898338\pi\)
\(192\) −2.83481e6 2.94324e6i −0.400516 0.415836i
\(193\) −1.27283e7 −1.77052 −0.885259 0.465099i \(-0.846019\pi\)
−0.885259 + 0.465099i \(0.846019\pi\)
\(194\) −3.20640e6 + 7.67299e6i −0.439150 + 1.05089i
\(195\) 1.92596e6i 0.259743i
\(196\) −3.49189e6 3.53585e6i −0.463759 0.469597i
\(197\) 1.95623e6 0.255872 0.127936 0.991782i \(-0.459165\pi\)
0.127936 + 0.991782i \(0.459165\pi\)
\(198\) −137183. 57326.3i −0.0176727 0.00738513i
\(199\) 4.27520e6i 0.542497i −0.962509 0.271248i \(-0.912564\pi\)
0.962509 0.271248i \(-0.0874365\pi\)
\(200\) 1.48389e6 598398.i 0.185486 0.0747998i
\(201\) 4.82498e6 0.594166
\(202\) −3.19881e6 + 7.65482e6i −0.388092 + 0.928711i
\(203\) 7.33992e6i 0.877411i
\(204\) 5.51146e6 5.44295e6i 0.649197 0.641126i
\(205\) −4.22246e6 −0.490121
\(206\) −1.08881e6 454994.i −0.124552 0.0520480i
\(207\) 3.02893e6i 0.341490i
\(208\) 113241. 9.05203e6i 0.0125839 1.00590i
\(209\) −245194. −0.0268578
\(210\) −537599. + 1.28648e6i −0.0580498 + 0.138914i
\(211\) 1.28034e7i 1.36294i −0.731846 0.681470i \(-0.761341\pi\)
0.731846 0.681470i \(-0.238659\pi\)
\(212\) 3.37686e6 + 3.41937e6i 0.354410 + 0.358871i
\(213\) −5.88765e6 −0.609260
\(214\) 1.75378e7 + 7.32873e6i 1.78951 + 0.747803i
\(215\) 1.24429e6i 0.125201i
\(216\) 725353. + 1.79871e6i 0.0719761 + 0.178484i
\(217\) 2.74228e6 0.268369
\(218\) −680170. + 1.62766e6i −0.0656520 + 0.157106i
\(219\) 6.60482e6i 0.628824i
\(220\) −194690. + 192269.i −0.0182841 + 0.0180568i
\(221\) 1.71601e7 1.58980
\(222\) −5.06736e6 2.11756e6i −0.463151 0.193543i
\(223\) 1.08749e7i 0.980643i 0.871542 + 0.490321i \(0.163121\pi\)
−0.871542 + 0.490321i \(0.836879\pi\)
\(224\) 2.60236e6 6.01487e6i 0.231538 0.535158i
\(225\) −759375. −0.0666667
\(226\) 21475.4 51391.0i 0.00186044 0.00445207i
\(227\) 2.18048e6i 0.186412i −0.995647 0.0932059i \(-0.970289\pi\)
0.995647 0.0932059i \(-0.0297115\pi\)
\(228\) 2.24746e6 + 2.27575e6i 0.189621 + 0.192008i
\(229\) 4.73117e6 0.393969 0.196985 0.980407i \(-0.436885\pi\)
0.196985 + 0.980407i \(0.436885\pi\)
\(230\) 5.14338e6 + 2.14933e6i 0.422732 + 0.176652i
\(231\) 238447.i 0.0193445i
\(232\) −1.74263e7 + 7.02741e6i −1.39554 + 0.562770i
\(233\) −1.55698e7 −1.23088 −0.615440 0.788183i \(-0.711022\pi\)
−0.615440 + 0.788183i \(0.711022\pi\)
\(234\) −1.65661e6 + 3.96430e6i −0.129292 + 0.309399i
\(235\) 9.84493e6i 0.758593i
\(236\) −8.04376e6 + 7.94377e6i −0.611960 + 0.604353i
\(237\) −1.00273e7 −0.753247
\(238\) 1.14624e7 + 4.78994e6i 0.850247 + 0.355303i
\(239\) 2.29769e7i 1.68306i 0.540214 + 0.841528i \(0.318343\pi\)
−0.540214 + 0.841528i \(0.681657\pi\)
\(240\) 3.56906e6 + 44649.1i 0.258179 + 0.00322983i
\(241\) 2.43938e7 1.74272 0.871362 0.490642i \(-0.163238\pi\)
0.871362 + 0.490642i \(0.163238\pi\)
\(242\) −5.44646e6 + 1.30335e7i −0.384298 + 0.919632i
\(243\) 920483.i 0.0641500i
\(244\) 1.47041e6 + 1.48892e6i 0.101220 + 0.102495i
\(245\) 4.34065e6 0.295159
\(246\) −8.69127e6 3.63193e6i −0.583819 0.243968i
\(247\) 7.08561e6i 0.470204i
\(248\) −2.62553e6 6.51069e6i −0.172132 0.426846i
\(249\) 1.28515e7 0.832446
\(250\) −538852. + 1.28948e6i −0.0344865 + 0.0825268i
\(251\) 7.13591e6i 0.451261i −0.974213 0.225631i \(-0.927556\pi\)
0.974213 0.225631i \(-0.0724442\pi\)
\(252\) −2.21313e6 + 2.18562e6i −0.138295 + 0.136575i
\(253\) −953315. −0.0588674
\(254\) −1.19951e7 5.01252e6i −0.731983 0.305883i
\(255\) 6.76593e6i 0.408044i
\(256\) −1.67720e7 419702.i −0.999687 0.0250162i
\(257\) 4.16162e6 0.245168 0.122584 0.992458i \(-0.460882\pi\)
0.122584 + 0.992458i \(0.460882\pi\)
\(258\) −1.07027e6 + 2.56118e6i −0.0623211 + 0.149136i
\(259\) 8.80794e6i 0.506962i
\(260\) 5.55619e6 + 5.62613e6i 0.316123 + 0.320103i
\(261\) 8.91787e6 0.501579
\(262\) 1.61656e7 + 6.75533e6i 0.898853 + 0.375615i
\(263\) 1.42161e7i 0.781474i 0.920502 + 0.390737i \(0.127780\pi\)
−0.920502 + 0.390737i \(0.872220\pi\)
\(264\) −566118. + 228295.i −0.0307677 + 0.0124075i
\(265\) −4.19766e6 −0.225564
\(266\) −1.97782e6 + 4.73297e6i −0.105085 + 0.251471i
\(267\) 8.41660e6i 0.442184i
\(268\) 1.40947e7 1.39195e7i 0.732239 0.723136i
\(269\) 2.27308e7 1.16777 0.583887 0.811835i \(-0.301531\pi\)
0.583887 + 0.811835i \(0.301531\pi\)
\(270\) −1.56306e6 653174.i −0.0794115 0.0331847i
\(271\) 1.88317e7i 0.946196i −0.881010 0.473098i \(-0.843136\pi\)
0.881010 0.473098i \(-0.156864\pi\)
\(272\) 397818. 3.17999e7i 0.0197687 1.58022i
\(273\) −6.89064e6 −0.338666
\(274\) −1.99000e6 + 4.76211e6i −0.0967391 + 0.231498i
\(275\) 239003.i 0.0114923i
\(276\) 8.73811e6 + 8.84811e6i 0.415614 + 0.420846i
\(277\) 3.49012e7 1.64211 0.821053 0.570852i \(-0.193387\pi\)
0.821053 + 0.570852i \(0.193387\pi\)
\(278\) −1.35074e7 5.64450e6i −0.628691 0.262719i
\(279\) 3.33183e6i 0.153416i
\(280\) 2.14093e6 + 5.30899e6i 0.0975276 + 0.241845i
\(281\) −2.31838e6 −0.104488 −0.0522440 0.998634i \(-0.516637\pi\)
−0.0522440 + 0.998634i \(0.516637\pi\)
\(282\) −8.46808e6 + 2.02643e7i −0.377605 + 0.903615i
\(283\) 4.22387e7i 1.86359i −0.362982 0.931796i \(-0.618241\pi\)
0.362982 0.931796i \(-0.381759\pi\)
\(284\) −1.71990e7 + 1.69852e7i −0.750841 + 0.741507i
\(285\) −2.79373e6 −0.120684
\(286\) −1.24771e6 521396.i −0.0533354 0.0222879i
\(287\) 1.51069e7i 0.639044i
\(288\) 7.30796e6 + 3.16182e6i 0.305928 + 0.132361i
\(289\) 3.61460e7 1.49750
\(290\) 6.32811e6 1.51433e7i 0.259466 0.620906i
\(291\) 1.62042e7i 0.657580i
\(292\) −1.90542e7 1.92940e7i −0.765316 0.774950i
\(293\) −3.90188e7 −1.55121 −0.775606 0.631217i \(-0.782556\pi\)
−0.775606 + 0.631217i \(0.782556\pi\)
\(294\) 8.93455e6 + 3.73359e6i 0.351585 + 0.146921i
\(295\) 9.87461e6i 0.384639i
\(296\) −2.09117e7 + 8.43293e6i −0.806332 + 0.325165i
\(297\) 289709. 0.0110584
\(298\) 1.59076e7 3.80672e7i 0.601113 1.43848i
\(299\) 2.75488e7i 1.03060i
\(300\) −2.21829e6 + 2.19071e6i −0.0821588 + 0.0811374i
\(301\) −4.45178e6 −0.163243
\(302\) −3.06828e7 1.28218e7i −1.11397 0.465509i
\(303\) 1.61658e7i 0.581125i
\(304\) 1.31305e7 + 164264.i 0.467371 + 0.00584684i
\(305\) −1.82781e6 −0.0644216
\(306\) −5.81969e6 + 1.39266e7i −0.203112 + 0.486051i
\(307\) 1.55131e7i 0.536146i −0.963399 0.268073i \(-0.913613\pi\)
0.963399 0.268073i \(-0.0863868\pi\)
\(308\) −687893. 696553.i −0.0235434 0.0238398i
\(309\) 2.29940e6 0.0779362
\(310\) 5.65772e6 + 2.36426e6i 0.189914 + 0.0793616i
\(311\) 7.03395e6i 0.233840i −0.993141 0.116920i \(-0.962698\pi\)
0.993141 0.116920i \(-0.0373021\pi\)
\(312\) 6.59726e6 + 1.63597e7i 0.217220 + 0.538654i
\(313\) −2.40261e7 −0.783519 −0.391759 0.920068i \(-0.628133\pi\)
−0.391759 + 0.920068i \(0.628133\pi\)
\(314\) −6.47935e6 + 1.55052e7i −0.209287 + 0.500828i
\(315\) 2.71686e6i 0.0869232i
\(316\) −2.92916e7 + 2.89275e7i −0.928287 + 0.916747i
\(317\) 5.56316e7 1.74640 0.873200 0.487362i \(-0.162041\pi\)
0.873200 + 0.487362i \(0.162041\pi\)
\(318\) −8.64023e6 3.61060e6i −0.268685 0.112279i
\(319\) 2.80678e6i 0.0864641i
\(320\) 1.05548e7 1.01659e7i 0.322105 0.310239i
\(321\) −3.70372e7 −1.11975
\(322\) −7.68977e6 + 1.84018e7i −0.230328 + 0.551178i
\(323\) 2.48918e7i 0.738667i
\(324\) −2.65549e6 2.68891e6i −0.0780745 0.0790573i
\(325\) −6.90669e6 −0.201196
\(326\) −5.45487e7 2.27949e7i −1.57446 0.657938i
\(327\) 3.43737e6i 0.0983067i
\(328\) −3.58666e7 + 1.44637e7i −1.01641 + 0.409882i
\(329\) −3.52228e7 −0.989091
\(330\) 205577. 491951.i 0.00572050 0.0136893i
\(331\) 5.14649e6i 0.141915i −0.997479 0.0709573i \(-0.977395\pi\)
0.997479 0.0709573i \(-0.0226054\pi\)
\(332\) 3.75418e7 3.70751e7i 1.02589 1.01314i
\(333\) 1.07015e7 0.289809
\(334\) 3.84069e7 + 1.60496e7i 1.03079 + 0.430749i
\(335\) 1.73029e7i 0.460239i
\(336\) −159744. + 1.27693e7i −0.00421121 + 0.336626i
\(337\) −6.46645e7 −1.68957 −0.844784 0.535107i \(-0.820271\pi\)
−0.844784 + 0.535107i \(0.820271\pi\)
\(338\) −178655. + 427525.i −0.00462663 + 0.0110716i
\(339\) 108530.i 0.00278581i
\(340\) 1.95189e7 + 1.97646e7i 0.496614 + 0.502866i
\(341\) −1.04865e6 −0.0264464
\(342\) −5.75047e6 2.40302e6i −0.143756 0.0600729i
\(343\) 3.90599e7i 0.967942i
\(344\) 4.26223e6 + 1.05693e7i 0.104704 + 0.259641i
\(345\) −1.08620e7 −0.264517
\(346\) 2.38100e7 5.69777e7i 0.574819 1.37555i
\(347\) 1.93865e7i 0.463994i −0.972717 0.231997i \(-0.925474\pi\)
0.972717 0.231997i \(-0.0745259\pi\)
\(348\) 2.60509e7 2.57270e7i 0.618137 0.610452i
\(349\) −2.55563e7 −0.601205 −0.300602 0.953750i \(-0.597188\pi\)
−0.300602 + 0.953750i \(0.597188\pi\)
\(350\) −4.61346e6 1.92788e6i −0.107603 0.0449652i
\(351\) 8.37201e6i 0.193601i
\(352\) −995139. + 2.30008e6i −0.0228169 + 0.0527370i
\(353\) −4.60766e6 −0.104751 −0.0523753 0.998627i \(-0.516679\pi\)
−0.0523753 + 0.998627i \(0.516679\pi\)
\(354\) 8.49361e6 2.03254e7i 0.191462 0.458172i
\(355\) 2.11137e7i 0.471931i
\(356\) 2.42809e7 + 2.45866e7i 0.538164 + 0.544939i
\(357\) −2.42069e7 −0.532027
\(358\) 4.15247e7 + 1.73524e7i 0.905018 + 0.378191i
\(359\) 8.33832e7i 1.80217i 0.433646 + 0.901083i \(0.357227\pi\)
−0.433646 + 0.901083i \(0.642773\pi\)
\(360\) −6.45033e6 + 2.60119e6i −0.138253 + 0.0557525i
\(361\) 3.67678e7 0.781530
\(362\) 2.48897e7 5.95615e7i 0.524679 1.25557i
\(363\) 2.75247e7i 0.575444i
\(364\) −2.01289e7 + 1.98787e7i −0.417366 + 0.412177i
\(365\) 2.36855e7 0.487085
\(366\) −3.76227e6 1.57218e6i −0.0767372 0.0320671i
\(367\) 2.81067e7i 0.568606i 0.958734 + 0.284303i \(0.0917622\pi\)
−0.958734 + 0.284303i \(0.908238\pi\)
\(368\) 5.10516e7 + 638657.i 1.02439 + 0.0128152i
\(369\) 1.83547e7 0.365315
\(370\) 7.59377e6 1.81720e7i 0.149917 0.358755i
\(371\) 1.50182e7i 0.294101i
\(372\) 9.61193e6 + 9.73293e6i 0.186716 + 0.189067i
\(373\) −3.04923e7 −0.587576 −0.293788 0.955871i \(-0.594916\pi\)
−0.293788 + 0.955871i \(0.594916\pi\)
\(374\) −4.38321e6 1.83167e6i −0.0837872 0.0350132i
\(375\) 2.72319e6i 0.0516398i
\(376\) 3.37231e7 + 8.36254e7i 0.634402 + 1.57317i
\(377\) 8.11101e7 1.51374
\(378\) 2.33690e6 5.59224e6i 0.0432678 0.103541i
\(379\) 8.15538e7i 1.49805i −0.662541 0.749026i \(-0.730522\pi\)
0.662541 0.749026i \(-0.269478\pi\)
\(380\) −8.16105e6 + 8.05960e6i −0.148729 + 0.146880i
\(381\) 2.53317e7 0.458026
\(382\) −3.22975e7 1.34966e7i −0.579400 0.242121i
\(383\) 9.61974e7i 1.71225i 0.516769 + 0.856125i \(0.327135\pi\)
−0.516769 + 0.856125i \(0.672865\pi\)
\(384\) 3.04695e7 1.18463e7i 0.538111 0.209213i
\(385\) 855095. 0.0149842
\(386\) 3.92614e7 9.39534e7i 0.682660 1.63362i
\(387\) 5.40883e6i 0.0933191i
\(388\) −4.67472e7 4.73357e7i −0.800314 0.810389i
\(389\) −3.31294e7 −0.562814 −0.281407 0.959589i \(-0.590801\pi\)
−0.281407 + 0.959589i \(0.590801\pi\)
\(390\) −1.42164e7 5.94077e6i −0.239660 0.100149i
\(391\) 9.67793e7i 1.61902i
\(392\) 3.68706e7 1.48686e7i 0.612099 0.246838i
\(393\) −3.41393e7 −0.562442
\(394\) −6.03413e6 + 1.44398e7i −0.0986566 + 0.236087i
\(395\) 3.59587e7i 0.583463i
\(396\) 846299. 835778.i 0.0136282 0.0134588i
\(397\) −8.50731e7 −1.35963 −0.679815 0.733384i \(-0.737940\pi\)
−0.679815 + 0.733384i \(0.737940\pi\)
\(398\) 3.15571e7 + 1.31871e7i 0.500550 + 0.209171i
\(399\) 9.99531e6i 0.157354i
\(400\) −160116. + 1.27990e7i −0.00250181 + 0.199984i
\(401\) 1.16975e7 0.181409 0.0907047 0.995878i \(-0.471088\pi\)
0.0907047 + 0.995878i \(0.471088\pi\)
\(402\) −1.48830e7 + 3.56153e7i −0.229093 + 0.548224i
\(403\) 3.03037e7i 0.463000i
\(404\) −4.66365e7 4.72236e7i −0.707265 0.716168i
\(405\) 3.30094e6 0.0496904
\(406\) 5.41791e7 + 2.26405e7i 0.809568 + 0.338304i
\(407\) 3.36815e6i 0.0499583i
\(408\) 2.31762e7 + 5.74716e7i 0.341242 + 0.846199i
\(409\) −6.19837e7 −0.905958 −0.452979 0.891521i \(-0.649639\pi\)
−0.452979 + 0.891521i \(0.649639\pi\)
\(410\) 1.30244e7 3.11677e7i 0.188976 0.452224i
\(411\) 1.00569e7i 0.144856i
\(412\) 6.71701e6 6.63351e6i 0.0960471 0.0948531i
\(413\) 3.53290e7 0.501512
\(414\) −2.23578e7 9.34294e6i −0.315086 0.131669i
\(415\) 4.60867e7i 0.644810i
\(416\) 6.64676e7 + 2.87575e7i 0.923273 + 0.399458i
\(417\) 2.85256e7 0.393393
\(418\) 756317. 1.80988e6i 0.0103556 0.0247811i
\(419\) 4.21622e7i 0.573167i 0.958055 + 0.286584i \(0.0925197\pi\)
−0.958055 + 0.286584i \(0.907480\pi\)
\(420\) −7.83783e6 7.93650e6i −0.105791 0.107123i
\(421\) 1.11714e7 0.149714 0.0748568 0.997194i \(-0.476150\pi\)
0.0748568 + 0.997194i \(0.476150\pi\)
\(422\) 9.45071e7 + 3.94928e7i 1.25756 + 0.525510i
\(423\) 4.27951e7i 0.565422i
\(424\) −3.56560e7 + 1.43788e7i −0.467773 + 0.188636i
\(425\) −2.42633e7 −0.316069
\(426\) 1.81608e7 4.34592e7i 0.234913 0.562151i
\(427\) 6.53947e6i 0.0839960i
\(428\) −1.08193e8 + 1.06848e8i −1.37996 + 1.36281i
\(429\) 2.63497e6 0.0333737
\(430\) −9.18465e6 3.83810e6i −0.115520 0.0482737i
\(431\) 4.14547e7i 0.517776i 0.965907 + 0.258888i \(0.0833561\pi\)
−0.965907 + 0.258888i \(0.916644\pi\)
\(432\) −1.55144e7 194086.i −0.192435 0.00240737i
\(433\) 1.02877e8 1.26722 0.633612 0.773651i \(-0.281571\pi\)
0.633612 + 0.773651i \(0.281571\pi\)
\(434\) −8.45876e6 + 2.02420e7i −0.103475 + 0.247619i
\(435\) 3.19803e7i 0.388522i
\(436\) −9.91642e6 1.00412e7i −0.119645 0.121151i
\(437\) −3.99613e7 −0.478846
\(438\) 4.87530e7 + 2.03730e7i 0.580202 + 0.242456i
\(439\) 1.17242e8i 1.38576i −0.721052 0.692881i \(-0.756341\pi\)
0.721052 0.692881i \(-0.243659\pi\)
\(440\) −818688. 2.03015e6i −0.00961082 0.0238326i
\(441\) −1.88684e7 −0.219999
\(442\) −5.29314e7 + 1.26666e8i −0.612981 + 1.46687i
\(443\) 1.14320e8i 1.31495i −0.753475 0.657477i \(-0.771624\pi\)
0.753475 0.657477i \(-0.228376\pi\)
\(444\) 3.12612e7 3.08726e7i 0.357155 0.352715i
\(445\) −3.01827e7 −0.342514
\(446\) −8.02723e7 3.35444e7i −0.904818 0.378107i
\(447\) 8.03923e7i 0.900102i
\(448\) 3.63712e7 + 3.77624e7i 0.404504 + 0.419977i
\(449\) 7.55165e6 0.0834262 0.0417131 0.999130i \(-0.486718\pi\)
0.0417131 + 0.999130i \(0.486718\pi\)
\(450\) 2.34234e6 5.60527e6i 0.0257047 0.0615119i
\(451\) 5.77688e6i 0.0629743i
\(452\) 313097. + 317038.i 0.00339049 + 0.00343318i
\(453\) 6.47974e7 0.697048
\(454\) 1.60950e7 + 6.72582e6i 0.171998 + 0.0718750i
\(455\) 2.47105e7i 0.262330i
\(456\) −2.37307e7 + 9.56974e6i −0.250274 + 0.100927i
\(457\) −7.56188e7 −0.792285 −0.396142 0.918189i \(-0.629651\pi\)
−0.396142 + 0.918189i \(0.629651\pi\)
\(458\) −1.45936e7 + 3.49228e7i −0.151903 + 0.363507i
\(459\) 2.94109e7i 0.304138i
\(460\) −3.17302e7 + 3.13357e7i −0.325986 + 0.321933i
\(461\) −1.40082e8 −1.42981 −0.714905 0.699222i \(-0.753530\pi\)
−0.714905 + 0.699222i \(0.753530\pi\)
\(462\) 1.76008e6 + 735507.i 0.0178487 + 0.00745866i
\(463\) 8.24447e7i 0.830653i 0.909672 + 0.415327i \(0.136333\pi\)
−0.909672 + 0.415327i \(0.863667\pi\)
\(464\) 1.88035e6 1.50308e8i 0.0188229 1.50462i
\(465\) −1.19482e7 −0.118835
\(466\) 4.80262e7 1.14928e8i 0.474592 1.13571i
\(467\) 1.71631e8i 1.68518i −0.538556 0.842589i \(-0.681030\pi\)
0.538556 0.842589i \(-0.318970\pi\)
\(468\) −2.41523e7 2.44563e7i −0.235624 0.238591i
\(469\) −6.19055e7 −0.600082
\(470\) −7.26696e7 3.03673e7i −0.699937 0.292491i
\(471\) 3.27447e7i 0.313385i
\(472\) −3.38248e7 8.38775e7i −0.321669 0.797663i
\(473\) 1.70236e6 0.0160867
\(474\) 3.09298e7 7.40155e7i 0.290430 0.695005i
\(475\) 1.00186e7i 0.0934816i
\(476\) −7.07131e7 + 6.98340e7i −0.655661 + 0.647510i
\(477\) 1.82469e7 0.168125
\(478\) −1.69603e8 7.08739e7i −1.55292 0.648937i
\(479\) 1.12033e8i 1.01939i −0.860355 0.509694i \(-0.829758\pi\)
0.860355 0.509694i \(-0.170242\pi\)
\(480\) −1.13386e7 + 2.62070e7i −0.102526 + 0.236971i
\(481\) 9.73326e7 0.874627
\(482\) −7.52443e7 + 1.80061e8i −0.671943 + 1.60797i
\(483\) 3.88618e7i 0.344890i
\(484\) −7.94056e7 8.04052e7i −0.700350 0.709166i
\(485\) 5.81098e7 0.509359
\(486\) 6.79448e6 + 2.83929e6i 0.0591898 + 0.0247344i
\(487\) 1.66667e8i 1.44299i 0.692419 + 0.721496i \(0.256545\pi\)
−0.692419 + 0.721496i \(0.743455\pi\)
\(488\) −1.55259e7 + 6.26104e6i −0.133597 + 0.0538749i
\(489\) 1.15199e8 0.985191
\(490\) −1.33890e7 + 3.20402e7i −0.113805 + 0.272337i
\(491\) 1.44837e7i 0.122358i 0.998127 + 0.0611792i \(0.0194861\pi\)
−0.998127 + 0.0611792i \(0.980514\pi\)
\(492\) 5.36176e7 5.29511e7i 0.450207 0.444610i
\(493\) 2.84940e8 2.37801
\(494\) −5.23019e7 2.18560e7i −0.433847 0.181297i
\(495\) 1.03893e6i 0.00856582i
\(496\) 5.61568e7 + 702524.i 0.460211 + 0.00575726i
\(497\) 7.55396e7 0.615327
\(498\) −3.96413e7 + 9.48625e7i −0.320967 + 0.768080i
\(499\) 1.82797e8i 1.47118i −0.677425 0.735592i \(-0.736904\pi\)
0.677425 0.735592i \(-0.263096\pi\)
\(500\) −7.85609e6 7.95499e6i −0.0628487 0.0636399i
\(501\) −8.11096e7 −0.644999
\(502\) 5.26732e7 + 2.20112e7i 0.416369 + 0.173993i
\(503\) 1.85820e8i 1.46012i −0.683382 0.730061i \(-0.739491\pi\)
0.683382 0.730061i \(-0.260509\pi\)
\(504\) −9.30642e6 2.30777e7i −0.0726928 0.180261i
\(505\) 5.79722e7 0.450138
\(506\) 2.94056e6 7.03682e6i 0.0226975 0.0543156i
\(507\) 902867.i 0.00692788i
\(508\) 7.39991e7 7.30792e7i 0.564463 0.557446i
\(509\) −4.52912e7 −0.343447 −0.171724 0.985145i \(-0.554934\pi\)
−0.171724 + 0.985145i \(0.554934\pi\)
\(510\) −4.99422e7 2.08700e7i −0.376493 0.157330i
\(511\) 8.47412e7i 0.635085i
\(512\) 5.48322e7 1.22506e8i 0.408532 0.912744i
\(513\) 1.21441e7 0.0899527
\(514\) −1.28368e7 + 3.07187e7i −0.0945296 + 0.226211i
\(515\) 8.24587e6i 0.0603691i
\(516\) −1.56039e7 1.58003e7i −0.113575 0.115005i
\(517\) 1.34692e7 0.0974696
\(518\) 6.50152e7 + 2.71687e7i 0.467762 + 0.195470i
\(519\) 1.20328e8i 0.860728i
\(520\) −5.86673e7 + 2.36584e7i −0.417240 + 0.168258i
\(521\) 1.08623e7 0.0768086 0.0384043 0.999262i \(-0.487773\pi\)
0.0384043 + 0.999262i \(0.487773\pi\)
\(522\) −2.75078e7 + 6.58266e7i −0.193394 + 0.462796i
\(523\) 8.35512e7i 0.584047i 0.956411 + 0.292023i \(0.0943285\pi\)
−0.956411 + 0.292023i \(0.905671\pi\)
\(524\) −9.97279e7 + 9.84881e7i −0.693143 + 0.684526i
\(525\) 9.74293e6 0.0673305
\(526\) −1.04935e8 4.38507e7i −0.721049 0.301314i
\(527\) 1.06457e8i 0.727350i
\(528\) 61085.9 4.88295e6i 0.000414992 0.0331727i
\(529\) −7.33375e6 −0.0495403
\(530\) 1.29480e7 3.09847e7i 0.0869708 0.208123i
\(531\) 4.29241e7i 0.286693i
\(532\) −2.88353e7 2.91983e7i −0.191509 0.193920i
\(533\) 1.66940e8 1.10250
\(534\) −6.21265e7 2.59616e7i −0.407993 0.170493i
\(535\) 1.32819e8i 0.867358i
\(536\) 5.92697e7 + 1.46975e8i 0.384892 + 0.954441i
\(537\) −8.76939e7 −0.566300
\(538\) −7.01148e7 + 1.67786e8i −0.450259 + 1.07748i
\(539\) 5.93858e6i 0.0379242i
\(540\) 9.64270e6 9.52283e6i 0.0612375 0.0604762i
\(541\) −6.89690e7 −0.435574 −0.217787 0.975996i \(-0.569884\pi\)
−0.217787 + 0.975996i \(0.569884\pi\)
\(542\) 1.39005e8 + 5.80876e7i 0.873034 + 0.364826i
\(543\) 1.25785e8i 0.785650i
\(544\) 2.33501e8 + 1.01025e8i 1.45042 + 0.627528i
\(545\) 1.23267e7 0.0761480
\(546\) 2.12546e7 5.08628e7i 0.130580 0.312480i
\(547\) 1.06248e8i 0.649170i −0.945857 0.324585i \(-0.894775\pi\)
0.945857 0.324585i \(-0.105225\pi\)
\(548\) −2.90129e7 2.93781e7i −0.176299 0.178518i
\(549\) 7.94534e6 0.0480170
\(550\) 1.76418e6 + 737220.i 0.0106036 + 0.00443108i
\(551\) 1.17655e8i 0.703326i
\(552\) −9.22650e7 + 3.72072e7i −0.548554 + 0.221212i
\(553\) 1.28652e8 0.760747
\(554\) −1.07655e8 + 2.57621e8i −0.633148 + 1.51513i
\(555\) 3.83766e7i 0.224485i
\(556\) 8.33289e7 8.22930e7i 0.484810 0.478783i
\(557\) −1.14599e8 −0.663154 −0.331577 0.943428i \(-0.607581\pi\)
−0.331577 + 0.943428i \(0.607581\pi\)
\(558\) −2.45936e7 1.02772e7i −0.141553 0.0591526i
\(559\) 4.91946e7i 0.281632i
\(560\) −4.57918e7 572857.i −0.260749 0.00326199i
\(561\) 9.25669e6 0.0524284
\(562\) 7.15121e6 1.71130e7i 0.0402875 0.0964088i
\(563\) 1.15455e8i 0.646975i −0.946232 0.323488i \(-0.895145\pi\)
0.946232 0.323488i \(-0.104855\pi\)
\(564\) −1.23459e8 1.25013e8i −0.688153 0.696816i
\(565\) −389199. −0.00215788
\(566\) 3.11782e8 + 1.30288e8i 1.71950 + 0.718547i
\(567\) 1.18100e7i 0.0647888i
\(568\) −7.23234e7 1.79345e8i −0.394670 0.978688i
\(569\) −2.08398e8 −1.13125 −0.565624 0.824663i \(-0.691365\pi\)
−0.565624 + 0.824663i \(0.691365\pi\)
\(570\) 8.61746e6 2.06217e7i 0.0465323 0.111353i
\(571\) 1.99293e8i 1.07049i 0.844696 + 0.535246i \(0.179781\pi\)
−0.844696 + 0.535246i \(0.820219\pi\)
\(572\) 7.69729e6 7.60160e6i 0.0411291 0.0406178i
\(573\) 6.82074e7 0.362550
\(574\) 1.11511e8 + 4.65984e7i 0.589632 + 0.246397i
\(575\) 3.89523e7i 0.204894i
\(576\) −4.58806e7 + 4.41903e7i −0.240083 + 0.231238i
\(577\) 2.29061e8 1.19240 0.596201 0.802835i \(-0.296676\pi\)
0.596201 + 0.802835i \(0.296676\pi\)
\(578\) −1.11495e8 + 2.66809e8i −0.577391 + 1.38171i
\(579\) 1.98415e8i 1.02221i
\(580\) 9.22596e7 + 9.34210e7i 0.472854 + 0.478807i
\(581\) −1.64887e8 −0.840735
\(582\) 1.19610e8 + 4.99829e7i 0.606734 + 0.253544i
\(583\) 5.74295e6i 0.0289821i
\(584\) 2.01191e8 8.11331e7i 1.01011 0.407343i
\(585\) 3.00228e7 0.149963
\(586\) 1.20356e8 2.88015e8i 0.598103 1.43127i
\(587\) 1.44645e8i 0.715137i 0.933887 + 0.357569i \(0.116394\pi\)
−0.933887 + 0.357569i \(0.883606\pi\)
\(588\) −5.51184e7 + 5.44332e7i −0.271122 + 0.267752i
\(589\) −4.39575e7 −0.215123
\(590\) 7.28887e7 + 3.04589e7i 0.354898 + 0.148306i
\(591\) 3.04947e7i 0.147728i
\(592\) 2.25644e6 1.80370e8i 0.0108757 0.869359i
\(593\) 7.73515e7 0.370941 0.185471 0.982650i \(-0.440619\pi\)
0.185471 + 0.982650i \(0.440619\pi\)
\(594\) −893628. + 2.13847e6i −0.00426381 + 0.0102034i
\(595\) 8.68082e7i 0.412107i
\(596\) 2.31922e8 + 2.34842e8i 1.09548 + 1.10927i
\(597\) −6.66438e7 −0.313211
\(598\) −2.03350e8 8.49762e7i −0.950911 0.397369i
\(599\) 2.61293e8i 1.21576i 0.794029 + 0.607880i \(0.207980\pi\)
−0.794029 + 0.607880i \(0.792020\pi\)
\(600\) −9.32810e6 2.31315e7i −0.0431857 0.107090i
\(601\) −1.90411e8 −0.877141 −0.438570 0.898697i \(-0.644515\pi\)
−0.438570 + 0.898697i \(0.644515\pi\)
\(602\) 1.37318e7 3.28605e7i 0.0629417 0.150621i
\(603\) 7.52141e7i 0.343042i
\(604\) 1.89286e8 1.86933e8i 0.859029 0.848350i
\(605\) 9.87063e7 0.445737
\(606\) 1.19327e8 + 4.98645e7i 0.536192 + 0.224065i
\(607\) 8.66310e7i 0.387354i −0.981065 0.193677i \(-0.937959\pi\)
0.981065 0.193677i \(-0.0620413\pi\)
\(608\) −4.17145e7 + 9.64155e7i −0.185599 + 0.428979i
\(609\) −1.14418e8 −0.506573
\(610\) 5.63800e6 1.34918e7i 0.0248391 0.0594404i
\(611\) 3.89231e8i 1.70641i
\(612\) −8.48471e7 8.59152e7i −0.370154 0.374814i
\(613\) −3.14018e7 −0.136324 −0.0681620 0.997674i \(-0.521713\pi\)
−0.0681620 + 0.997674i \(0.521713\pi\)
\(614\) 1.14509e8 + 4.78511e7i 0.494690 + 0.206722i
\(615\) 6.58216e7i 0.282972i
\(616\) 7.26340e6 2.92907e6i 0.0310741 0.0125311i
\(617\) −2.78014e8 −1.18362 −0.591808 0.806079i \(-0.701585\pi\)
−0.591808 + 0.806079i \(0.701585\pi\)
\(618\) −7.09266e6 + 1.69729e7i −0.0300499 + 0.0719100i
\(619\) 6.69159e7i 0.282135i −0.990000 0.141068i \(-0.954947\pi\)
0.990000 0.141068i \(-0.0450535\pi\)
\(620\) −3.49032e7 + 3.44693e7i −0.146450 + 0.144630i
\(621\) 4.72164e7 0.197159
\(622\) 5.19206e7 + 2.16967e7i 0.215759 + 0.0901618i
\(623\) 1.07987e8i 0.446586i
\(624\) −1.41107e8 1.76526e6i −0.580758 0.00726531i
\(625\) 9.76562e6 0.0400000
\(626\) 7.41100e7 1.77347e8i 0.302102 0.722936i
\(627\) 3.82220e6i 0.0155064i
\(628\) −9.44646e7 9.56537e7i −0.381408 0.386210i
\(629\) 3.41930e8 1.37400
\(630\) 2.00543e7 + 8.38034e6i 0.0802022 + 0.0335151i
\(631\) 5.44695e7i 0.216803i −0.994107 0.108401i \(-0.965427\pi\)
0.994107 0.108401i \(-0.0345732\pi\)
\(632\) −1.23174e8 3.05443e8i −0.487942 1.20998i
\(633\) −1.99585e8 −0.786894
\(634\) −1.71599e8 + 4.10640e8i −0.673361 + 1.61136i
\(635\) 9.08421e7i 0.354786i
\(636\) 5.33028e7 5.26401e7i 0.207195 0.204619i
\(637\) −1.71613e8 −0.663944
\(638\) −2.07180e7 8.65769e6i −0.0797786 0.0333380i
\(639\) 9.17793e7i 0.351757i
\(640\) 4.24820e7 + 1.09267e8i 0.162056 + 0.416819i
\(641\) −2.54657e8 −0.966899 −0.483450 0.875372i \(-0.660616\pi\)
−0.483450 + 0.875372i \(0.660616\pi\)
\(642\) 1.14244e8 2.73387e8i 0.431744 1.03317i
\(643\) 2.69874e8i 1.01514i 0.861610 + 0.507572i \(0.169457\pi\)
−0.861610 + 0.507572i \(0.830543\pi\)
\(644\) −1.12112e8 1.13523e8i −0.419753 0.425036i
\(645\) 1.93966e7 0.0722847
\(646\) −1.83737e8 7.67804e7i −0.681552 0.284808i
\(647\) 4.58078e8i 1.69132i −0.533719 0.845662i \(-0.679206\pi\)
0.533719 0.845662i \(-0.320794\pi\)
\(648\) 2.80390e7 1.13071e7i 0.103048 0.0415554i
\(649\) −1.35098e7 −0.0494213
\(650\) 2.13042e7 5.09812e7i 0.0775755 0.185640i
\(651\) 4.27480e7i 0.154943i
\(652\) 3.36518e8 3.32335e8i 1.21413 1.19904i
\(653\) −2.94949e8 −1.05927 −0.529636 0.848225i \(-0.677671\pi\)
−0.529636 + 0.848225i \(0.677671\pi\)
\(654\) 2.53727e7 + 1.06028e7i 0.0907054 + 0.0379042i
\(655\) 1.22427e8i 0.435666i
\(656\) 3.87012e6 3.09361e8i 0.0137092 1.09586i
\(657\) −1.02959e8 −0.363051
\(658\) 1.08647e8 2.59994e8i 0.381365 0.912613i
\(659\) 2.78956e8i 0.974720i 0.873201 + 0.487360i \(0.162040\pi\)
−0.873201 + 0.487360i \(0.837960\pi\)
\(660\) 2.99718e6 + 3.03491e6i 0.0104251 + 0.0105564i
\(661\) −3.82952e8 −1.32599 −0.662995 0.748624i \(-0.730715\pi\)
−0.662995 + 0.748624i \(0.730715\pi\)
\(662\) 3.79884e7 + 1.58747e7i 0.130942 + 0.0547182i
\(663\) 2.67499e8i 0.917872i
\(664\) 1.57867e8 + 3.91473e8i 0.539246 + 1.33720i
\(665\) 3.58441e7 0.121886
\(666\) −3.30095e7 + 7.89923e7i −0.111742 + 0.267400i
\(667\) 4.57444e8i 1.54156i
\(668\) −2.36937e8 + 2.33992e8i −0.794885 + 0.785003i
\(669\) 1.69523e8 0.566174
\(670\) −1.27720e8 5.33718e7i −0.424652 0.177455i
\(671\) 2.50069e6i 0.00827736i
\(672\) −9.37625e7 4.05667e7i −0.308974 0.133679i
\(673\) −1.79065e8 −0.587443 −0.293722 0.955891i \(-0.594894\pi\)
−0.293722 + 0.955891i \(0.594894\pi\)
\(674\) 1.99462e8 4.77316e8i 0.651449 1.55893i
\(675\) 1.18375e7i 0.0384900i
\(676\) −2.60467e6 2.63746e6i −0.00843164 0.00853778i
\(677\) −2.03295e8 −0.655179 −0.327589 0.944820i \(-0.606236\pi\)
−0.327589 + 0.944820i \(0.606236\pi\)
\(678\) −801106. 334768.i −0.00257040 0.00107413i
\(679\) 2.07903e8i 0.664127i
\(680\) −2.06099e8 + 8.31122e7i −0.655463 + 0.264325i
\(681\) −3.39902e7 −0.107625
\(682\) 3.23462e6 7.74051e6i 0.0101969 0.0244015i
\(683\) 2.12975e8i 0.668446i −0.942494 0.334223i \(-0.891526\pi\)
0.942494 0.334223i \(-0.108474\pi\)
\(684\) 3.54754e7 3.50344e7i 0.110856 0.109478i
\(685\) 3.60649e7 0.112205
\(686\) −2.88318e8 1.20483e8i −0.893099 0.373210i
\(687\) 7.37517e7i 0.227458i
\(688\) −9.11639e7 1.14046e6i −0.279935 0.00350200i
\(689\) 1.65960e8 0.507393
\(690\) 3.35047e7 8.01773e7i 0.101990 0.244064i
\(691\) 3.42495e7i 0.103805i −0.998652 0.0519027i \(-0.983471\pi\)
0.998652 0.0519027i \(-0.0165286\pi\)
\(692\) 3.47134e8 + 3.51503e8i 1.04756 + 1.06075i
\(693\) −3.71703e6 −0.0111685
\(694\) 1.43100e8 + 5.97991e7i 0.428117 + 0.178902i
\(695\) 1.02295e8i 0.304721i
\(696\) 1.09546e8 + 2.71649e8i 0.324916 + 0.805714i
\(697\) 5.86461e8 1.73197
\(698\) 7.88303e7 1.88642e8i 0.231807 0.554719i
\(699\) 2.42710e8i 0.710649i
\(700\) 2.84610e7 2.81072e7i 0.0829768 0.0819452i
\(701\) 1.80432e7 0.0523794 0.0261897 0.999657i \(-0.491663\pi\)
0.0261897 + 0.999657i \(0.491663\pi\)
\(702\) 6.17974e7 + 2.58240e7i 0.178632 + 0.0746470i
\(703\) 1.41187e8i 0.406377i
\(704\) −1.39083e7 1.44403e7i −0.0398617 0.0413865i
\(705\) 1.53467e8 0.437974
\(706\) 1.42126e7 3.40111e7i 0.0403887 0.0966510i
\(707\) 2.07411e8i 0.586911i
\(708\) 1.23831e8 + 1.25390e8i 0.348923 + 0.353316i
\(709\) −3.29774e8 −0.925289 −0.462645 0.886544i \(-0.653099\pi\)
−0.462645 + 0.886544i \(0.653099\pi\)
\(710\) 1.55849e8 + 6.51265e7i 0.435440 + 0.181963i
\(711\) 1.56310e8i 0.434887i
\(712\) −2.56380e8 + 1.03389e8i −0.710304 + 0.286440i
\(713\) −1.70907e8 −0.471510
\(714\) 7.46677e7 1.78681e8i 0.205134 0.490890i
\(715\) 9.44927e6i 0.0258512i
\(716\) −2.56171e8 + 2.52987e8i −0.697897 + 0.689221i
\(717\) 3.58175e8 0.971713
\(718\) −6.15487e8 2.57201e8i −1.66282 0.694863i
\(719\) 4.14856e7i 0.111612i −0.998442 0.0558060i \(-0.982227\pi\)
0.998442 0.0558060i \(-0.0177728\pi\)
\(720\) 696011. 5.56362e7i 0.00186474 0.149060i
\(721\) −2.95018e7 −0.0787122
\(722\) −1.13413e8 + 2.71399e8i −0.301335 + 0.721101i
\(723\) 3.80262e8i 1.00616i
\(724\) 3.62875e8 + 3.67443e8i 0.956184 + 0.968220i
\(725\) −1.14685e8 −0.300948
\(726\) 2.03172e8 + 8.49018e7i 0.530950 + 0.221874i
\(727\) 1.30895e8i 0.340660i −0.985387 0.170330i \(-0.945517\pi\)
0.985387 0.170330i \(-0.0544833\pi\)
\(728\) −8.46441e7 2.09897e8i −0.219383 0.544018i
\(729\) −1.43489e7 −0.0370370
\(730\) −7.30596e7 + 1.74833e8i −0.187806 + 0.449422i
\(731\) 1.72821e8i 0.442430i
\(732\) 2.32099e7 2.29214e7i 0.0591753 0.0584396i
\(733\) 5.25156e8 1.33345 0.666725 0.745304i \(-0.267696\pi\)
0.666725 + 0.745304i \(0.267696\pi\)
\(734\) −2.07467e8 8.66969e7i −0.524640 0.219238i
\(735\) 6.76640e7i 0.170410i
\(736\) −1.62186e8 + 3.74863e8i −0.406799 + 0.940242i
\(737\) 2.36726e7 0.0591348
\(738\) −5.66162e7 + 1.35484e8i −0.140855 + 0.337068i
\(739\) 2.54601e8i 0.630850i −0.948951 0.315425i \(-0.897853\pi\)
0.948951 0.315425i \(-0.102147\pi\)
\(740\) 1.10712e8 + 1.12106e8i 0.273212 + 0.276651i
\(741\) 1.10454e8 0.271472
\(742\) 1.10856e8 + 4.63247e7i 0.271361 + 0.113397i
\(743\) 8.88222e7i 0.216548i −0.994121 0.108274i \(-0.965468\pi\)
0.994121 0.108274i \(-0.0345324\pi\)
\(744\) −1.01492e8 + 4.09279e7i −0.246440 + 0.0993804i
\(745\) −2.88294e8 −0.697216
\(746\) 9.40556e7 2.25077e8i 0.226552 0.542144i
\(747\) 2.00335e8i 0.480613i
\(748\) 2.70406e7 2.67045e7i 0.0646118 0.0638086i
\(749\) 4.75194e8 1.13090
\(750\) 2.01010e7 + 8.39987e6i 0.0476469 + 0.0199108i
\(751\) 8.81576e7i 0.208133i −0.994570 0.104066i \(-0.966815\pi\)
0.994570 0.104066i \(-0.0331854\pi\)
\(752\) −7.21296e8 9.02345e6i −1.69613 0.0212187i
\(753\) −1.11238e8 −0.260536
\(754\) −2.50190e8 + 5.98708e8i −0.583654 + 1.39669i
\(755\) 2.32370e8i 0.539931i
\(756\) 3.40704e7 + 3.44993e7i 0.0788518 + 0.0798445i
\(757\) −2.37075e8 −0.546511 −0.273255 0.961942i \(-0.588100\pi\)
−0.273255 + 0.961942i \(0.588100\pi\)
\(758\) 6.01984e8 + 2.51558e8i 1.38222 + 0.577605i
\(759\) 1.48607e7i 0.0339871i
\(760\) −3.43180e7 8.51006e7i −0.0781774 0.193862i
\(761\) 4.57746e8 1.03865 0.519327 0.854576i \(-0.326183\pi\)
0.519327 + 0.854576i \(0.326183\pi\)
\(762\) −7.81375e7 + 1.86984e8i −0.176602 + 0.422611i
\(763\) 4.41021e7i 0.0992855i
\(764\) 1.99248e8 1.96771e8i 0.446800 0.441245i
\(765\) 1.05470e8 0.235584
\(766\) −7.10074e8 2.96727e8i −1.57986 0.660194i
\(767\) 3.90405e8i 0.865225i
\(768\) −6.54250e6 + 2.61449e8i −0.0144431 + 0.577170i
\(769\) 3.39638e8 0.746857 0.373428 0.927659i \(-0.378182\pi\)
0.373428 + 0.927659i \(0.378182\pi\)
\(770\) −2.63760e6 + 6.31182e6i −0.00577745 + 0.0138256i
\(771\) 6.48733e7i 0.141548i
\(772\) 5.72405e8 + 5.79611e8i 1.24409 + 1.25975i
\(773\) 5.73031e8