Properties

Label 99.3.l.a.71.1
Level $99$
Weight $3$
Character 99.71
Analytic conductor $2.698$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 99.l (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.69755461717\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 71.1
Character \(\chi\) \(=\) 99.71
Dual form 99.3.l.a.53.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.44320 + 1.11876i) q^{2} +(7.36792 - 5.35311i) q^{4} +(-0.157113 - 0.0510491i) q^{5} +(-8.33195 + 6.05352i) q^{7} +(-10.8683 + 14.9589i) q^{8} +O(q^{10})\) \(q+(-3.44320 + 1.11876i) q^{2} +(7.36792 - 5.35311i) q^{4} +(-0.157113 - 0.0510491i) q^{5} +(-8.33195 + 6.05352i) q^{7} +(-10.8683 + 14.9589i) q^{8} +0.598083 q^{10} +(3.56713 - 10.4056i) q^{11} +(-6.29016 - 19.3591i) q^{13} +(21.9161 - 30.1649i) q^{14} +(9.42903 - 29.0196i) q^{16} +(-21.8883 - 7.11194i) q^{17} +(3.34849 + 2.43282i) q^{19} +(-1.43087 + 0.464917i) q^{20} +(-0.641003 + 39.8192i) q^{22} -13.5095i q^{23} +(-20.2033 - 14.6786i) q^{25} +(43.3165 + 59.6201i) q^{26} +(-28.9840 + 89.2036i) q^{28} +(2.36082 + 3.24939i) q^{29} +(-6.33587 - 19.4998i) q^{31} +36.5080i q^{32} +83.3223 q^{34} +(1.61808 - 0.525747i) q^{35} +(-35.2682 + 25.6238i) q^{37} +(-14.2513 - 4.63052i) q^{38} +(2.47119 - 1.79542i) q^{40} +(-30.6080 + 42.1283i) q^{41} +62.5698 q^{43} +(-29.4197 - 95.7625i) q^{44} +(15.1139 + 46.5159i) q^{46} +(-22.7504 + 31.3132i) q^{47} +(17.6345 - 54.2734i) q^{49} +(85.9860 + 27.9385i) q^{50} +(-149.977 - 108.965i) q^{52} +(33.6465 - 10.9324i) q^{53} +(-1.09164 + 1.45275i) q^{55} -190.428i q^{56} +(-11.7641 - 8.54709i) q^{58} +(11.5725 + 15.9281i) q^{59} +(-1.98522 + 6.10989i) q^{61} +(43.6314 + 60.0534i) q^{62} +(-3.12770 - 9.62606i) q^{64} +3.36267i q^{65} -3.98708 q^{67} +(-199.342 + 64.7702i) q^{68} +(-4.98319 + 3.62050i) q^{70} +(-52.0905 - 16.9252i) q^{71} +(18.4526 - 13.4066i) q^{73} +(92.7684 - 127.685i) q^{74} +37.6946 q^{76} +(33.2690 + 108.292i) q^{77} +(-17.6623 - 54.3588i) q^{79} +(-2.96284 + 4.07801i) q^{80} +(58.2578 - 179.299i) q^{82} +(54.0258 + 17.5540i) q^{83} +(3.07587 + 2.23475i) q^{85} +(-215.440 + 70.0008i) q^{86} +(116.887 + 166.451i) q^{88} -28.1602i q^{89} +(169.600 + 123.222i) q^{91} +(-72.3178 - 99.5369i) q^{92} +(43.3020 - 133.270i) q^{94} +(-0.401898 - 0.553165i) q^{95} +(25.6275 + 78.8733i) q^{97} +206.603i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{4} - 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 16 q^{4} - 16 q^{7} + 48 q^{10} + 8 q^{13} + 96 q^{16} - 40 q^{19} - 60 q^{22} - 188 q^{25} - 348 q^{28} - 164 q^{31} + 296 q^{34} - 36 q^{37} + 48 q^{40} + 544 q^{43} + 296 q^{46} + 196 q^{49} - 640 q^{52} - 440 q^{55} - 208 q^{58} - 432 q^{61} - 328 q^{64} + 48 q^{67} + 112 q^{70} + 712 q^{73} + 2104 q^{76} + 432 q^{79} + 676 q^{82} - 68 q^{85} - 176 q^{88} + 64 q^{91} - 1360 q^{94} + 132 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.44320 + 1.11876i −1.72160 + 0.559382i −0.992194 0.124701i \(-0.960203\pi\)
−0.729405 + 0.684082i \(0.760203\pi\)
\(3\) 0 0
\(4\) 7.36792 5.35311i 1.84198 1.33828i
\(5\) −0.157113 0.0510491i −0.0314226 0.0102098i 0.293264 0.956032i \(-0.405259\pi\)
−0.324686 + 0.945822i \(0.605259\pi\)
\(6\) 0 0
\(7\) −8.33195 + 6.05352i −1.19028 + 0.864788i −0.993294 0.115619i \(-0.963115\pi\)
−0.196985 + 0.980407i \(0.563115\pi\)
\(8\) −10.8683 + 14.9589i −1.35854 + 1.86987i
\(9\) 0 0
\(10\) 0.598083 0.0598083
\(11\) 3.56713 10.4056i 0.324285 0.945959i
\(12\) 0 0
\(13\) −6.29016 19.3591i −0.483858 1.48916i −0.833628 0.552327i \(-0.813740\pi\)
0.349769 0.936836i \(-0.386260\pi\)
\(14\) 21.9161 30.1649i 1.56544 2.15464i
\(15\) 0 0
\(16\) 9.42903 29.0196i 0.589314 1.81372i
\(17\) −21.8883 7.11194i −1.28755 0.418349i −0.416315 0.909221i \(-0.636679\pi\)
−0.871232 + 0.490871i \(0.836679\pi\)
\(18\) 0 0
\(19\) 3.34849 + 2.43282i 0.176237 + 0.128043i 0.672406 0.740182i \(-0.265261\pi\)
−0.496170 + 0.868225i \(0.665261\pi\)
\(20\) −1.43087 + 0.464917i −0.0715433 + 0.0232458i
\(21\) 0 0
\(22\) −0.641003 + 39.8192i −0.0291365 + 1.80996i
\(23\) 13.5095i 0.587369i −0.955902 0.293685i \(-0.905118\pi\)
0.955902 0.293685i \(-0.0948816\pi\)
\(24\) 0 0
\(25\) −20.2033 14.6786i −0.808134 0.587144i
\(26\) 43.3165 + 59.6201i 1.66602 + 2.29308i
\(27\) 0 0
\(28\) −28.9840 + 89.2036i −1.03514 + 3.18584i
\(29\) 2.36082 + 3.24939i 0.0814075 + 0.112048i 0.847779 0.530350i \(-0.177940\pi\)
−0.766371 + 0.642398i \(0.777940\pi\)
\(30\) 0 0
\(31\) −6.33587 19.4998i −0.204383 0.629026i −0.999738 0.0228826i \(-0.992716\pi\)
0.795355 0.606144i \(-0.207284\pi\)
\(32\) 36.5080i 1.14088i
\(33\) 0 0
\(34\) 83.3223 2.45066
\(35\) 1.61808 0.525747i 0.0462309 0.0150213i
\(36\) 0 0
\(37\) −35.2682 + 25.6238i −0.953195 + 0.692536i −0.951560 0.307462i \(-0.900520\pi\)
−0.00163432 + 0.999999i \(0.500520\pi\)
\(38\) −14.2513 4.63052i −0.375034 0.121856i
\(39\) 0 0
\(40\) 2.47119 1.79542i 0.0617797 0.0448856i
\(41\) −30.6080 + 42.1283i −0.746536 + 1.02752i 0.251679 + 0.967811i \(0.419017\pi\)
−0.998216 + 0.0597086i \(0.980983\pi\)
\(42\) 0 0
\(43\) 62.5698 1.45511 0.727556 0.686048i \(-0.240656\pi\)
0.727556 + 0.686048i \(0.240656\pi\)
\(44\) −29.4197 95.7625i −0.668629 2.17642i
\(45\) 0 0
\(46\) 15.1139 + 46.5159i 0.328564 + 1.01121i
\(47\) −22.7504 + 31.3132i −0.484050 + 0.666238i −0.979277 0.202526i \(-0.935085\pi\)
0.495227 + 0.868764i \(0.335085\pi\)
\(48\) 0 0
\(49\) 17.6345 54.2734i 0.359888 1.10762i
\(50\) 85.9860 + 27.9385i 1.71972 + 0.558771i
\(51\) 0 0
\(52\) −149.977 108.965i −2.88417 2.09547i
\(53\) 33.6465 10.9324i 0.634840 0.206272i 0.0261220 0.999659i \(-0.491684\pi\)
0.608718 + 0.793387i \(0.291684\pi\)
\(54\) 0 0
\(55\) −1.09164 + 1.45275i −0.0198479 + 0.0264136i
\(56\) 190.428i 3.40051i
\(57\) 0 0
\(58\) −11.7641 8.54709i −0.202829 0.147364i
\(59\) 11.5725 + 15.9281i 0.196143 + 0.269968i 0.895748 0.444562i \(-0.146641\pi\)
−0.699605 + 0.714530i \(0.746641\pi\)
\(60\) 0 0
\(61\) −1.98522 + 6.10989i −0.0325446 + 0.100162i −0.966009 0.258507i \(-0.916769\pi\)
0.933465 + 0.358669i \(0.116769\pi\)
\(62\) 43.6314 + 60.0534i 0.703731 + 0.968603i
\(63\) 0 0
\(64\) −3.12770 9.62606i −0.0488703 0.150407i
\(65\) 3.36267i 0.0517334i
\(66\) 0 0
\(67\) −3.98708 −0.0595087 −0.0297543 0.999557i \(-0.509472\pi\)
−0.0297543 + 0.999557i \(0.509472\pi\)
\(68\) −199.342 + 64.7702i −2.93150 + 0.952503i
\(69\) 0 0
\(70\) −4.98319 + 3.62050i −0.0711885 + 0.0517215i
\(71\) −52.0905 16.9252i −0.733670 0.238384i −0.0817299 0.996655i \(-0.526044\pi\)
−0.651940 + 0.758271i \(0.726044\pi\)
\(72\) 0 0
\(73\) 18.4526 13.4066i 0.252776 0.183652i −0.454180 0.890910i \(-0.650068\pi\)
0.706956 + 0.707257i \(0.250068\pi\)
\(74\) 92.7684 127.685i 1.25363 1.72547i
\(75\) 0 0
\(76\) 37.6946 0.495981
\(77\) 33.2690 + 108.292i 0.432065 + 1.40639i
\(78\) 0 0
\(79\) −17.6623 54.3588i −0.223573 0.688086i −0.998433 0.0559542i \(-0.982180\pi\)
0.774861 0.632132i \(-0.217820\pi\)
\(80\) −2.96284 + 4.07801i −0.0370356 + 0.0509751i
\(81\) 0 0
\(82\) 58.2578 179.299i 0.710461 2.18658i
\(83\) 54.0258 + 17.5540i 0.650913 + 0.211494i 0.615817 0.787890i \(-0.288826\pi\)
0.0350962 + 0.999384i \(0.488826\pi\)
\(84\) 0 0
\(85\) 3.07587 + 2.23475i 0.0361868 + 0.0262912i
\(86\) −215.440 + 70.0008i −2.50512 + 0.813963i
\(87\) 0 0
\(88\) 116.887 + 166.451i 1.32826 + 1.89149i
\(89\) 28.1602i 0.316407i −0.987407 0.158203i \(-0.949430\pi\)
0.987407 0.158203i \(-0.0505701\pi\)
\(90\) 0 0
\(91\) 169.600 + 123.222i 1.86374 + 1.35408i
\(92\) −72.3178 99.5369i −0.786063 1.08192i
\(93\) 0 0
\(94\) 43.3020 133.270i 0.460659 1.41776i
\(95\) −0.401898 0.553165i −0.00423051 0.00582279i
\(96\) 0 0
\(97\) 25.6275 + 78.8733i 0.264201 + 0.813127i 0.991876 + 0.127205i \(0.0406007\pi\)
−0.727676 + 0.685922i \(0.759399\pi\)
\(98\) 206.603i 2.10819i
\(99\) 0 0
\(100\) −227.433 −2.27433
\(101\) −145.555 + 47.2938i −1.44114 + 0.468255i −0.922253 0.386587i \(-0.873654\pi\)
−0.518888 + 0.854842i \(0.673654\pi\)
\(102\) 0 0
\(103\) −85.0431 + 61.7875i −0.825662 + 0.599878i −0.918329 0.395819i \(-0.870461\pi\)
0.0926670 + 0.995697i \(0.470461\pi\)
\(104\) 357.955 + 116.307i 3.44187 + 1.11833i
\(105\) 0 0
\(106\) −103.621 + 75.2850i −0.977555 + 0.710235i
\(107\) 66.2803 91.2270i 0.619442 0.852588i −0.377870 0.925858i \(-0.623344\pi\)
0.997312 + 0.0732701i \(0.0233435\pi\)
\(108\) 0 0
\(109\) −96.1530 −0.882137 −0.441069 0.897473i \(-0.645400\pi\)
−0.441069 + 0.897473i \(0.645400\pi\)
\(110\) 2.13344 6.22338i 0.0193949 0.0565762i
\(111\) 0 0
\(112\) 97.1082 + 298.868i 0.867038 + 2.66847i
\(113\) 61.1891 84.2196i 0.541497 0.745306i −0.447331 0.894368i \(-0.647625\pi\)
0.988828 + 0.149062i \(0.0476254\pi\)
\(114\) 0 0
\(115\) −0.689647 + 2.12252i −0.00599693 + 0.0184567i
\(116\) 34.7886 + 11.3035i 0.299902 + 0.0974441i
\(117\) 0 0
\(118\) −57.6661 41.8969i −0.488696 0.355058i
\(119\) 225.424 73.2448i 1.89432 0.615503i
\(120\) 0 0
\(121\) −95.5511 74.2360i −0.789679 0.613521i
\(122\) 23.2585i 0.190644i
\(123\) 0 0
\(124\) −151.067 109.756i −1.21828 0.885133i
\(125\) 4.85240 + 6.67876i 0.0388192 + 0.0534301i
\(126\) 0 0
\(127\) −2.49011 + 7.66378i −0.0196072 + 0.0603447i −0.960381 0.278689i \(-0.910100\pi\)
0.940774 + 0.339034i \(0.110100\pi\)
\(128\) −64.2969 88.4971i −0.502320 0.691384i
\(129\) 0 0
\(130\) −3.76203 11.5784i −0.0289387 0.0890642i
\(131\) 240.588i 1.83655i −0.395947 0.918273i \(-0.629584\pi\)
0.395947 0.918273i \(-0.370416\pi\)
\(132\) 0 0
\(133\) −42.6266 −0.320501
\(134\) 13.7283 4.46060i 0.102450 0.0332881i
\(135\) 0 0
\(136\) 344.275 250.131i 2.53144 1.83920i
\(137\) 17.9446 + 5.83054i 0.130982 + 0.0425587i 0.373775 0.927520i \(-0.378063\pi\)
−0.242792 + 0.970078i \(0.578063\pi\)
\(138\) 0 0
\(139\) 27.0837 19.6775i 0.194847 0.141565i −0.486084 0.873912i \(-0.661575\pi\)
0.680931 + 0.732347i \(0.261575\pi\)
\(140\) 9.10752 12.5354i 0.0650537 0.0895388i
\(141\) 0 0
\(142\) 198.293 1.39643
\(143\) −223.880 3.60399i −1.56560 0.0252027i
\(144\) 0 0
\(145\) −0.205037 0.631038i −0.00141405 0.00435199i
\(146\) −48.5373 + 66.8058i −0.332447 + 0.457574i
\(147\) 0 0
\(148\) −122.686 + 377.589i −0.828960 + 2.55128i
\(149\) −98.3588 31.9587i −0.660126 0.214488i −0.0402525 0.999190i \(-0.512816\pi\)
−0.619874 + 0.784701i \(0.712816\pi\)
\(150\) 0 0
\(151\) 231.688 + 168.331i 1.53435 + 1.11477i 0.953755 + 0.300585i \(0.0971818\pi\)
0.580600 + 0.814189i \(0.302818\pi\)
\(152\) −72.7848 + 23.6492i −0.478848 + 0.155587i
\(153\) 0 0
\(154\) −235.705 335.652i −1.53055 2.17956i
\(155\) 3.38711i 0.0218523i
\(156\) 0 0
\(157\) −211.399 153.591i −1.34649 0.978285i −0.999178 0.0405362i \(-0.987093\pi\)
−0.347315 0.937748i \(-0.612907\pi\)
\(158\) 121.629 + 167.408i 0.769806 + 1.05955i
\(159\) 0 0
\(160\) 1.86370 5.73588i 0.0116481 0.0358492i
\(161\) 81.7800 + 112.560i 0.507950 + 0.699133i
\(162\) 0 0
\(163\) 59.4847 + 183.075i 0.364937 + 1.12316i 0.950021 + 0.312187i \(0.101062\pi\)
−0.585084 + 0.810973i \(0.698938\pi\)
\(164\) 474.246i 2.89174i
\(165\) 0 0
\(166\) −205.660 −1.23892
\(167\) 200.857 65.2624i 1.20274 0.390793i 0.361970 0.932190i \(-0.382104\pi\)
0.840767 + 0.541397i \(0.182104\pi\)
\(168\) 0 0
\(169\) −198.485 + 144.208i −1.17447 + 0.853303i
\(170\) −13.0910 4.25353i −0.0770059 0.0250207i
\(171\) 0 0
\(172\) 461.009 334.943i 2.68029 1.94734i
\(173\) −60.9963 + 83.9542i −0.352580 + 0.485284i −0.948063 0.318084i \(-0.896961\pi\)
0.595483 + 0.803368i \(0.296961\pi\)
\(174\) 0 0
\(175\) 257.190 1.46966
\(176\) −268.330 201.631i −1.52460 1.14563i
\(177\) 0 0
\(178\) 31.5046 + 96.9611i 0.176992 + 0.544725i
\(179\) −6.49962 + 8.94596i −0.0363107 + 0.0499774i −0.826786 0.562516i \(-0.809833\pi\)
0.790476 + 0.612494i \(0.209833\pi\)
\(180\) 0 0
\(181\) 38.4345 118.289i 0.212345 0.653532i −0.786986 0.616971i \(-0.788360\pi\)
0.999331 0.0365609i \(-0.0116403\pi\)
\(182\) −721.822 234.534i −3.96606 1.28865i
\(183\) 0 0
\(184\) 202.088 + 146.825i 1.09830 + 0.797963i
\(185\) 6.84916 2.22543i 0.0370225 0.0120293i
\(186\) 0 0
\(187\) −152.082 + 202.391i −0.813274 + 1.08230i
\(188\) 352.498i 1.87499i
\(189\) 0 0
\(190\) 2.00268 + 1.45503i 0.0105404 + 0.00765805i
\(191\) 104.367 + 143.649i 0.546425 + 0.752090i 0.989522 0.144384i \(-0.0461201\pi\)
−0.443097 + 0.896474i \(0.646120\pi\)
\(192\) 0 0
\(193\) 75.1934 231.421i 0.389603 1.19907i −0.543483 0.839420i \(-0.682895\pi\)
0.933086 0.359654i \(-0.117105\pi\)
\(194\) −176.481 242.905i −0.909696 1.25209i
\(195\) 0 0
\(196\) −160.602 494.282i −0.819397 2.52184i
\(197\) 215.588i 1.09435i −0.837017 0.547177i \(-0.815702\pi\)
0.837017 0.547177i \(-0.184298\pi\)
\(198\) 0 0
\(199\) −44.0830 −0.221523 −0.110761 0.993847i \(-0.535329\pi\)
−0.110761 + 0.993847i \(0.535329\pi\)
\(200\) 439.152 142.689i 2.19576 0.713446i
\(201\) 0 0
\(202\) 448.265 325.684i 2.21913 1.61230i
\(203\) −39.3404 12.7825i −0.193795 0.0629679i
\(204\) 0 0
\(205\) 6.95952 5.05639i 0.0339489 0.0246653i
\(206\) 223.695 307.890i 1.08590 1.49461i
\(207\) 0 0
\(208\) −621.103 −2.98607
\(209\) 37.2594 26.1647i 0.178275 0.125190i
\(210\) 0 0
\(211\) −81.6747 251.369i −0.387084 1.19132i −0.934957 0.354761i \(-0.884562\pi\)
0.547873 0.836562i \(-0.315438\pi\)
\(212\) 189.382 260.663i 0.893313 1.22954i
\(213\) 0 0
\(214\) −126.155 + 388.264i −0.589508 + 1.81432i
\(215\) −9.83052 3.19413i −0.0457234 0.0148564i
\(216\) 0 0
\(217\) 170.833 + 124.117i 0.787247 + 0.571969i
\(218\) 331.074 107.572i 1.51869 0.493451i
\(219\) 0 0
\(220\) −0.266377 + 16.5474i −0.00121081 + 0.0752153i
\(221\) 468.473i 2.11979i
\(222\) 0 0
\(223\) −11.7428 8.53162i −0.0526581 0.0382584i 0.561145 0.827718i \(-0.310361\pi\)
−0.613803 + 0.789459i \(0.710361\pi\)
\(224\) −221.002 304.183i −0.986616 1.35796i
\(225\) 0 0
\(226\) −116.465 + 358.441i −0.515330 + 1.58602i
\(227\) 72.0137 + 99.1183i 0.317241 + 0.436645i 0.937622 0.347656i \(-0.113022\pi\)
−0.620381 + 0.784300i \(0.713022\pi\)
\(228\) 0 0
\(229\) 1.20322 + 3.70313i 0.00525423 + 0.0161709i 0.953649 0.300920i \(-0.0972938\pi\)
−0.948395 + 0.317091i \(0.897294\pi\)
\(230\) 8.07980i 0.0351295i
\(231\) 0 0
\(232\) −74.2654 −0.320110
\(233\) −347.865 + 113.028i −1.49298 + 0.485100i −0.937963 0.346736i \(-0.887290\pi\)
−0.555022 + 0.831836i \(0.687290\pi\)
\(234\) 0 0
\(235\) 5.17288 3.75832i 0.0220123 0.0159928i
\(236\) 170.530 + 55.4085i 0.722585 + 0.234782i
\(237\) 0 0
\(238\) −694.237 + 504.393i −2.91696 + 2.11930i
\(239\) −86.5794 + 119.166i −0.362257 + 0.498604i −0.950776 0.309880i \(-0.899711\pi\)
0.588519 + 0.808483i \(0.299711\pi\)
\(240\) 0 0
\(241\) 278.601 1.15602 0.578010 0.816029i \(-0.303829\pi\)
0.578010 + 0.816029i \(0.303829\pi\)
\(242\) 412.054 + 148.710i 1.70270 + 0.614505i
\(243\) 0 0
\(244\) 18.0799 + 55.6442i 0.0740980 + 0.228050i
\(245\) −5.54121 + 7.62683i −0.0226172 + 0.0311299i
\(246\) 0 0
\(247\) 26.0348 80.1267i 0.105404 0.324400i
\(248\) 360.556 + 117.152i 1.45386 + 0.472387i
\(249\) 0 0
\(250\) −24.1797 17.5676i −0.0967190 0.0702705i
\(251\) −45.9565 + 14.9322i −0.183094 + 0.0594907i −0.399129 0.916895i \(-0.630687\pi\)
0.216035 + 0.976386i \(0.430687\pi\)
\(252\) 0 0
\(253\) −140.574 48.1902i −0.555628 0.190475i
\(254\) 29.1737i 0.114857i
\(255\) 0 0
\(256\) 353.148 + 256.577i 1.37948 + 1.00225i
\(257\) −117.102 161.176i −0.455648 0.627146i 0.517951 0.855410i \(-0.326695\pi\)
−0.973599 + 0.228265i \(0.926695\pi\)
\(258\) 0 0
\(259\) 138.739 426.993i 0.535670 1.64862i
\(260\) 18.0007 + 24.7759i 0.0692336 + 0.0952919i
\(261\) 0 0
\(262\) 269.161 + 828.391i 1.02733 + 3.16180i
\(263\) 69.3106i 0.263538i 0.991280 + 0.131769i \(0.0420658\pi\)
−0.991280 + 0.131769i \(0.957934\pi\)
\(264\) 0 0
\(265\) −5.84439 −0.0220543
\(266\) 146.772 47.6891i 0.551774 0.179282i
\(267\) 0 0
\(268\) −29.3765 + 21.3433i −0.109614 + 0.0796391i
\(269\) 175.083 + 56.8880i 0.650868 + 0.211480i 0.615797 0.787905i \(-0.288834\pi\)
0.0350710 + 0.999385i \(0.488834\pi\)
\(270\) 0 0
\(271\) 70.9627 51.5574i 0.261855 0.190249i −0.449109 0.893477i \(-0.648259\pi\)
0.710964 + 0.703228i \(0.248259\pi\)
\(272\) −412.771 + 568.130i −1.51754 + 2.08871i
\(273\) 0 0
\(274\) −68.3096 −0.249305
\(275\) −224.807 + 157.867i −0.817480 + 0.574060i
\(276\) 0 0
\(277\) −77.0171 237.034i −0.278040 0.855719i −0.988399 0.151880i \(-0.951467\pi\)
0.710359 0.703840i \(-0.248533\pi\)
\(278\) −71.2402 + 98.0537i −0.256260 + 0.352711i
\(279\) 0 0
\(280\) −9.72119 + 29.9188i −0.0347185 + 0.106853i
\(281\) −16.0221 5.20589i −0.0570181 0.0185263i 0.280369 0.959892i \(-0.409543\pi\)
−0.337387 + 0.941366i \(0.609543\pi\)
\(282\) 0 0
\(283\) −38.5194 27.9860i −0.136111 0.0988904i 0.517646 0.855595i \(-0.326808\pi\)
−0.653757 + 0.756704i \(0.726808\pi\)
\(284\) −474.402 + 154.142i −1.67043 + 0.542755i
\(285\) 0 0
\(286\) 774.896 238.060i 2.70943 0.832376i
\(287\) 536.297i 1.86863i
\(288\) 0 0
\(289\) 194.712 + 141.466i 0.673744 + 0.489503i
\(290\) 1.41196 + 1.94340i 0.00486884 + 0.00670139i
\(291\) 0 0
\(292\) 64.1905 197.558i 0.219830 0.676568i
\(293\) 249.870 + 343.916i 0.852797 + 1.17377i 0.983239 + 0.182319i \(0.0583604\pi\)
−0.130442 + 0.991456i \(0.541640\pi\)
\(294\) 0 0
\(295\) −1.00507 3.09328i −0.00340701 0.0104857i
\(296\) 806.062i 2.72318i
\(297\) 0 0
\(298\) 374.423 1.25645
\(299\) −261.532 + 84.9769i −0.874689 + 0.284204i
\(300\) 0 0
\(301\) −521.329 + 378.767i −1.73199 + 1.25836i
\(302\) −986.069 320.393i −3.26513 1.06090i
\(303\) 0 0
\(304\) 102.173 74.2327i 0.336094 0.244187i
\(305\) 0.623808 0.858598i 0.00204527 0.00281507i
\(306\) 0 0
\(307\) −463.469 −1.50967 −0.754836 0.655914i \(-0.772284\pi\)
−0.754836 + 0.655914i \(0.772284\pi\)
\(308\) 824.823 + 619.796i 2.67800 + 2.01233i
\(309\) 0 0
\(310\) −3.78938 11.6625i −0.0122238 0.0376210i
\(311\) −84.1378 + 115.806i −0.270539 + 0.372366i −0.922572 0.385826i \(-0.873917\pi\)
0.652032 + 0.758191i \(0.273917\pi\)
\(312\) 0 0
\(313\) 73.4669 226.108i 0.234719 0.722390i −0.762440 0.647059i \(-0.775999\pi\)
0.997159 0.0753307i \(-0.0240012\pi\)
\(314\) 899.722 + 292.337i 2.86536 + 0.931011i
\(315\) 0 0
\(316\) −421.123 305.964i −1.33267 0.968239i
\(317\) 298.545 97.0032i 0.941783 0.306004i 0.202411 0.979301i \(-0.435122\pi\)
0.739372 + 0.673297i \(0.235122\pi\)
\(318\) 0 0
\(319\) 42.2330 12.9746i 0.132392 0.0406728i
\(320\) 1.67204i 0.00522514i
\(321\) 0 0
\(322\) −407.513 296.076i −1.26557 0.919490i
\(323\) −55.9907 77.0646i −0.173346 0.238590i
\(324\) 0 0
\(325\) −157.082 + 483.450i −0.483330 + 1.48754i
\(326\) −409.635 563.814i −1.25655 1.72949i
\(327\) 0 0
\(328\) −297.537 915.725i −0.907126 2.79185i
\(329\) 398.620i 1.21161i
\(330\) 0 0
\(331\) −52.4920 −0.158586 −0.0792931 0.996851i \(-0.525266\pi\)
−0.0792931 + 0.996851i \(0.525266\pi\)
\(332\) 492.026 159.869i 1.48201 0.481533i
\(333\) 0 0
\(334\) −618.578 + 449.423i −1.85203 + 1.34558i
\(335\) 0.626422 + 0.203537i 0.00186992 + 0.000607572i
\(336\) 0 0
\(337\) 399.526 290.273i 1.18554 0.861343i 0.192751 0.981248i \(-0.438259\pi\)
0.992785 + 0.119905i \(0.0382589\pi\)
\(338\) 522.090 718.596i 1.54465 2.12602i
\(339\) 0 0
\(340\) 34.6257 0.101840
\(341\) −225.507 3.63018i −0.661312 0.0106457i
\(342\) 0 0
\(343\) 25.6717 + 79.0092i 0.0748445 + 0.230348i
\(344\) −680.027 + 935.978i −1.97682 + 2.72086i
\(345\) 0 0
\(346\) 116.098 357.311i 0.335542 1.03269i
\(347\) 429.602 + 139.586i 1.23805 + 0.402266i 0.853623 0.520891i \(-0.174400\pi\)
0.384424 + 0.923157i \(0.374400\pi\)
\(348\) 0 0
\(349\) −143.320 104.128i −0.410659 0.298362i 0.363209 0.931708i \(-0.381681\pi\)
−0.773869 + 0.633346i \(0.781681\pi\)
\(350\) −885.558 + 287.735i −2.53016 + 0.822100i
\(351\) 0 0
\(352\) 379.886 + 130.229i 1.07922 + 0.369969i
\(353\) 590.460i 1.67269i −0.548203 0.836346i \(-0.684688\pi\)
0.548203 0.836346i \(-0.315312\pi\)
\(354\) 0 0
\(355\) 7.32008 + 5.31835i 0.0206199 + 0.0149813i
\(356\) −150.745 207.482i −0.423440 0.582815i
\(357\) 0 0
\(358\) 12.3711 38.0742i 0.0345561 0.106353i
\(359\) −348.052 479.052i −0.969503 1.33441i −0.942297 0.334777i \(-0.891339\pi\)
−0.0272060 0.999630i \(-0.508661\pi\)
\(360\) 0 0
\(361\) −106.261 327.039i −0.294353 0.905925i
\(362\) 450.292i 1.24390i
\(363\) 0 0
\(364\) 1909.22 5.24510
\(365\) −3.58354 + 1.16436i −0.00981793 + 0.00319004i
\(366\) 0 0
\(367\) −183.454 + 133.287i −0.499875 + 0.363181i −0.808969 0.587851i \(-0.799974\pi\)
0.309094 + 0.951031i \(0.399974\pi\)
\(368\) −392.040 127.381i −1.06533 0.346145i
\(369\) 0 0
\(370\) −21.0933 + 15.3252i −0.0570089 + 0.0414194i
\(371\) −214.162 + 294.768i −0.577255 + 0.794523i
\(372\) 0 0
\(373\) −76.5478 −0.205222 −0.102611 0.994722i \(-0.532720\pi\)
−0.102611 + 0.994722i \(0.532720\pi\)
\(374\) 297.222 867.015i 0.794711 2.31822i
\(375\) 0 0
\(376\) −221.154 680.642i −0.588176 1.81022i
\(377\) 48.0553 66.1425i 0.127468 0.175444i
\(378\) 0 0
\(379\) 108.644 334.371i 0.286659 0.882247i −0.699237 0.714890i \(-0.746477\pi\)
0.985896 0.167357i \(-0.0535232\pi\)
\(380\) −5.92230 1.92427i −0.0155850 0.00506388i
\(381\) 0 0
\(382\) −520.066 377.850i −1.36143 0.989137i
\(383\) 544.836 177.028i 1.42255 0.462214i 0.506137 0.862453i \(-0.331073\pi\)
0.916411 + 0.400239i \(0.131073\pi\)
\(384\) 0 0
\(385\) 0.301230 18.7125i 0.000782417 0.0486038i
\(386\) 880.953i 2.28226i
\(387\) 0 0
\(388\) 611.038 + 443.945i 1.57484 + 1.14419i
\(389\) −115.310 158.711i −0.296427 0.407997i 0.634661 0.772791i \(-0.281140\pi\)
−0.931089 + 0.364793i \(0.881140\pi\)
\(390\) 0 0
\(391\) −96.0787 + 295.700i −0.245726 + 0.756266i
\(392\) 620.215 + 853.653i 1.58218 + 2.17769i
\(393\) 0 0
\(394\) 241.192 + 742.311i 0.612161 + 1.88404i
\(395\) 9.44211i 0.0239041i
\(396\) 0 0
\(397\) −105.240 −0.265089 −0.132544 0.991177i \(-0.542315\pi\)
−0.132544 + 0.991177i \(0.542315\pi\)
\(398\) 151.787 49.3184i 0.381373 0.123916i
\(399\) 0 0
\(400\) −616.464 + 447.888i −1.54116 + 1.11972i
\(401\) −466.038 151.425i −1.16219 0.377618i −0.336467 0.941695i \(-0.609232\pi\)
−0.825722 + 0.564077i \(0.809232\pi\)
\(402\) 0 0
\(403\) −337.646 + 245.314i −0.837830 + 0.608719i
\(404\) −819.271 + 1127.63i −2.02790 + 2.79116i
\(405\) 0 0
\(406\) 149.757 0.368861
\(407\) 140.824 + 458.389i 0.346005 + 1.12626i
\(408\) 0 0
\(409\) 164.971 + 507.730i 0.403353 + 1.24139i 0.922263 + 0.386564i \(0.126338\pi\)
−0.518910 + 0.854829i \(0.673662\pi\)
\(410\) −18.3061 + 25.1962i −0.0446490 + 0.0614541i
\(411\) 0 0
\(412\) −295.836 + 910.490i −0.718049 + 2.20993i
\(413\) −192.842 62.6583i −0.466931 0.151715i
\(414\) 0 0
\(415\) −7.59202 5.51593i −0.0182940 0.0132914i
\(416\) 706.763 229.641i 1.69895 0.552022i
\(417\) 0 0
\(418\) −99.0194 + 131.775i −0.236888 + 0.315251i
\(419\) 344.904i 0.823160i 0.911374 + 0.411580i \(0.135023\pi\)
−0.911374 + 0.411580i \(0.864977\pi\)
\(420\) 0 0
\(421\) 326.412 + 237.152i 0.775325 + 0.563307i 0.903572 0.428435i \(-0.140935\pi\)
−0.128247 + 0.991742i \(0.540935\pi\)
\(422\) 562.445 + 774.139i 1.33281 + 1.83445i
\(423\) 0 0
\(424\) −202.143 + 622.132i −0.476753 + 1.46729i
\(425\) 337.824 + 464.974i 0.794879 + 1.09406i
\(426\) 0 0
\(427\) −20.4455 62.9248i −0.0478818 0.147365i
\(428\) 1026.96i 2.39943i
\(429\) 0 0
\(430\) 37.4219 0.0870277
\(431\) 126.197 41.0039i 0.292800 0.0951366i −0.158934 0.987289i \(-0.550806\pi\)
0.451734 + 0.892153i \(0.350806\pi\)
\(432\) 0 0
\(433\) 666.538 484.268i 1.53935 1.11840i 0.588608 0.808419i \(-0.299676\pi\)
0.950742 0.309984i \(-0.100324\pi\)
\(434\) −727.068 236.239i −1.67527 0.544329i
\(435\) 0 0
\(436\) −708.447 + 514.717i −1.62488 + 1.18054i
\(437\) 32.8662 45.2365i 0.0752087 0.103516i
\(438\) 0 0
\(439\) 109.320 0.249021 0.124511 0.992218i \(-0.460264\pi\)
0.124511 + 0.992218i \(0.460264\pi\)
\(440\) −9.86731 32.1186i −0.0224257 0.0729968i
\(441\) 0 0
\(442\) −524.111 1613.05i −1.18577 3.64943i
\(443\) 220.853 303.978i 0.498540 0.686181i −0.483395 0.875403i \(-0.660596\pi\)
0.981934 + 0.189221i \(0.0605963\pi\)
\(444\) 0 0
\(445\) −1.43755 + 4.42433i −0.00323045 + 0.00994231i
\(446\) 49.9775 + 16.2387i 0.112057 + 0.0364096i
\(447\) 0 0
\(448\) 84.3313 + 61.2703i 0.188240 + 0.136764i
\(449\) 358.602 116.517i 0.798668 0.259503i 0.118877 0.992909i \(-0.462070\pi\)
0.679791 + 0.733406i \(0.262070\pi\)
\(450\) 0 0
\(451\) 329.185 + 468.770i 0.729901 + 1.03940i
\(452\) 948.075i 2.09751i
\(453\) 0 0
\(454\) −358.847 260.718i −0.790413 0.574268i
\(455\) −20.3560 28.0176i −0.0447385 0.0615772i
\(456\) 0 0
\(457\) −122.907 + 378.268i −0.268942 + 0.827719i 0.721817 + 0.692084i \(0.243307\pi\)
−0.990759 + 0.135635i \(0.956693\pi\)
\(458\) −8.28584 11.4045i −0.0180914 0.0249006i
\(459\) 0 0
\(460\) 6.28079 + 19.3303i 0.0136539 + 0.0420223i
\(461\) 452.581i 0.981737i 0.871234 + 0.490869i \(0.163320\pi\)
−0.871234 + 0.490869i \(0.836680\pi\)
\(462\) 0 0
\(463\) −125.818 −0.271745 −0.135873 0.990726i \(-0.543384\pi\)
−0.135873 + 0.990726i \(0.543384\pi\)
\(464\) 116.556 37.8714i 0.251198 0.0816193i
\(465\) 0 0
\(466\) 1071.32 778.358i 2.29896 1.67030i
\(467\) 263.442 + 85.5976i 0.564117 + 0.183293i 0.577173 0.816622i \(-0.304156\pi\)
−0.0130560 + 0.999915i \(0.504156\pi\)
\(468\) 0 0
\(469\) 33.2202 24.1359i 0.0708319 0.0514624i
\(470\) −13.6066 + 18.7279i −0.0289502 + 0.0398465i
\(471\) 0 0
\(472\) −364.041 −0.771273
\(473\) 223.195 651.074i 0.471871 1.37648i
\(474\) 0 0
\(475\) −31.9404 98.3023i −0.0672429 0.206952i
\(476\) 1268.82 1746.38i 2.66559 3.66887i
\(477\) 0 0
\(478\) 164.791 507.175i 0.344751 1.06104i
\(479\) −476.471 154.815i −0.994721 0.323204i −0.233967 0.972245i \(-0.575171\pi\)
−0.760754 + 0.649040i \(0.775171\pi\)
\(480\) 0 0
\(481\) 717.898 + 521.583i 1.49251 + 1.08437i
\(482\) −959.279 + 311.689i −1.99020 + 0.646657i
\(483\) 0 0
\(484\) −1101.41 35.4697i −2.27563 0.0732846i
\(485\) 13.7003i 0.0282480i
\(486\) 0 0
\(487\) −558.354 405.668i −1.14652 0.832993i −0.158503 0.987359i \(-0.550667\pi\)
−0.988014 + 0.154366i \(0.950667\pi\)
\(488\) −69.8213 96.1008i −0.143077 0.196928i
\(489\) 0 0
\(490\) 10.5469 32.4600i 0.0215243 0.0662449i
\(491\) 209.152 + 287.873i 0.425971 + 0.586299i 0.967023 0.254690i \(-0.0819736\pi\)
−0.541051 + 0.840990i \(0.681974\pi\)
\(492\) 0 0
\(493\) −28.5648 87.9135i −0.0579408 0.178324i
\(494\) 305.019i 0.617447i
\(495\) 0 0
\(496\) −625.618 −1.26133
\(497\) 536.473 174.311i 1.07942 0.350726i
\(498\) 0 0
\(499\) −117.317 + 85.2357i −0.235104 + 0.170813i −0.699099 0.715025i \(-0.746415\pi\)
0.463995 + 0.885838i \(0.346415\pi\)
\(500\) 71.5042 + 23.2331i 0.143008 + 0.0464663i
\(501\) 0 0
\(502\) 141.532 102.829i 0.281936 0.204838i
\(503\) −510.737 + 702.968i −1.01538 + 1.39755i −0.0999885 + 0.994989i \(0.531881\pi\)
−0.915392 + 0.402563i \(0.868119\pi\)
\(504\) 0 0
\(505\) 25.2829 0.0500651
\(506\) 537.937 + 8.65963i 1.06312 + 0.0171139i
\(507\) 0 0
\(508\) 22.6781 + 69.7959i 0.0446419 + 0.137394i
\(509\) −296.308 + 407.833i −0.582137 + 0.801243i −0.993928 0.110036i \(-0.964904\pi\)
0.411791 + 0.911279i \(0.364904\pi\)
\(510\) 0 0
\(511\) −72.5893 + 223.407i −0.142053 + 0.437195i
\(512\) −1086.87 353.145i −2.12279 0.689737i
\(513\) 0 0
\(514\) 583.522 + 423.954i 1.13526 + 0.824813i
\(515\) 16.5156 5.36623i 0.0320691 0.0104199i
\(516\) 0 0
\(517\) 244.677 + 348.428i 0.473264 + 0.673943i
\(518\) 1625.44i 3.13791i
\(519\) 0 0
\(520\) −50.3020 36.5465i −0.0967346 0.0702818i
\(521\) 152.184 + 209.464i 0.292101 + 0.402042i 0.929695 0.368330i \(-0.120070\pi\)
−0.637594 + 0.770372i \(0.720070\pi\)
\(522\) 0 0
\(523\) 184.539 567.952i 0.352847 1.08595i −0.604401 0.796680i \(-0.706587\pi\)
0.957248 0.289270i \(-0.0934125\pi\)
\(524\) −1287.89 1772.63i −2.45781 3.38288i
\(525\) 0 0
\(526\) −77.5421 238.650i −0.147418 0.453707i
\(527\) 471.878i 0.895404i
\(528\) 0 0
\(529\) 346.493 0.654997
\(530\) 20.1234 6.53849i 0.0379687 0.0123368i
\(531\) 0 0
\(532\) −314.069 + 228.185i −0.590356 + 0.428919i
\(533\) 1008.10 + 327.550i 1.89136 + 0.614541i
\(534\) 0 0
\(535\) −15.0705 + 10.9494i −0.0281692 + 0.0204661i
\(536\) 43.3328 59.6425i 0.0808447 0.111273i
\(537\) 0 0
\(538\) −666.491 −1.23883
\(539\) −501.840 377.097i −0.931058 0.699624i
\(540\) 0 0
\(541\) 74.6911 + 229.876i 0.138061 + 0.424909i 0.996054 0.0887536i \(-0.0282884\pi\)
−0.857992 + 0.513662i \(0.828288\pi\)
\(542\) −186.658 + 256.913i −0.344388 + 0.474009i
\(543\) 0 0
\(544\) 259.643 799.098i 0.477285 1.46893i
\(545\) 15.1069 + 4.90852i 0.0277190 + 0.00900646i
\(546\) 0 0
\(547\) 433.072 + 314.645i 0.791722 + 0.575220i 0.908474 0.417942i \(-0.137248\pi\)
−0.116752 + 0.993161i \(0.537248\pi\)
\(548\) 163.425 53.1002i 0.298222 0.0968981i
\(549\) 0 0
\(550\) 597.440 795.071i 1.08625 1.44558i
\(551\) 16.6240i 0.0301706i
\(552\) 0 0
\(553\) 476.223 + 345.996i 0.861163 + 0.625671i
\(554\) 530.370 + 729.992i 0.957347 + 1.31768i
\(555\) 0 0
\(556\) 94.2150 289.964i 0.169451 0.521518i
\(557\) −22.7200 31.2714i −0.0407900 0.0561426i 0.788135 0.615503i \(-0.211047\pi\)
−0.828925 + 0.559360i \(0.811047\pi\)
\(558\) 0 0
\(559\) −393.574 1211.30i −0.704068 2.16690i
\(560\) 51.9134i 0.0927024i
\(561\) 0 0
\(562\) 60.9914 0.108526
\(563\) −338.625 + 110.026i −0.601465 + 0.195428i −0.593894 0.804543i \(-0.702410\pi\)
−0.00757154 + 0.999971i \(0.502410\pi\)
\(564\) 0 0
\(565\) −13.9129 + 10.1083i −0.0246247 + 0.0178909i
\(566\) 163.940 + 53.2672i 0.289646 + 0.0941117i
\(567\) 0 0
\(568\) 819.319 595.270i 1.44246 1.04801i
\(569\) −58.0232 + 79.8620i −0.101974 + 0.140355i −0.856954 0.515392i \(-0.827646\pi\)
0.754981 + 0.655747i \(0.227646\pi\)
\(570\) 0 0
\(571\) −37.7221 −0.0660633 −0.0330316 0.999454i \(-0.510516\pi\)
−0.0330316 + 0.999454i \(0.510516\pi\)
\(572\) −1668.82 + 1171.90i −2.91752 + 2.04878i
\(573\) 0 0
\(574\) 599.989 + 1846.58i 1.04528 + 3.21703i
\(575\) −198.300 + 272.937i −0.344870 + 0.474673i
\(576\) 0 0
\(577\) −302.325 + 930.462i −0.523961 + 1.61259i 0.242400 + 0.970176i \(0.422065\pi\)
−0.766361 + 0.642410i \(0.777935\pi\)
\(578\) −828.699 269.261i −1.43374 0.465849i
\(579\) 0 0
\(580\) −4.88871 3.55185i −0.00842881 0.00612389i
\(581\) −556.403 + 180.786i −0.957665 + 0.311164i
\(582\) 0 0
\(583\) 6.26380 389.108i 0.0107441 0.667424i
\(584\) 421.739i 0.722156i
\(585\) 0 0
\(586\) −1245.11 904.626i −2.12476 1.54373i
\(587\) −655.577 902.324i −1.11683 1.53718i −0.810957 0.585105i \(-0.801053\pi\)
−0.305868 0.952074i \(-0.598947\pi\)
\(588\) 0 0
\(589\) 26.2240 80.7091i 0.0445229 0.137027i
\(590\) 6.92129 + 9.52634i 0.0117310 + 0.0161463i
\(591\) 0 0
\(592\) 411.048 + 1265.08i 0.694338 + 2.13695i
\(593\) 1006.79i 1.69779i −0.528563 0.848894i \(-0.677269\pi\)
0.528563 0.848894i \(-0.322731\pi\)
\(594\) 0 0
\(595\) −39.1562 −0.0658087
\(596\) −895.778 + 291.056i −1.50298 + 0.488349i
\(597\) 0 0
\(598\) 805.438 585.185i 1.34689 0.978570i
\(599\) 561.257 + 182.364i 0.936991 + 0.304447i 0.737418 0.675436i \(-0.236045\pi\)
0.199572 + 0.979883i \(0.436045\pi\)
\(600\) 0 0
\(601\) 607.440 441.331i 1.01071 0.734327i 0.0463560 0.998925i \(-0.485239\pi\)
0.964359 + 0.264598i \(0.0852391\pi\)
\(602\) 1371.29 1887.42i 2.27789 3.13524i
\(603\) 0 0
\(604\) 2608.15 4.31813
\(605\) 11.2226 + 16.5412i 0.0185498 + 0.0273409i
\(606\) 0 0
\(607\) 54.4372 + 167.540i 0.0896823 + 0.276014i 0.985831 0.167739i \(-0.0536467\pi\)
−0.896149 + 0.443753i \(0.853647\pi\)
\(608\) −88.8175 + 122.247i −0.146081 + 0.201064i
\(609\) 0 0
\(610\) −1.18733 + 3.65422i −0.00194644 + 0.00599052i
\(611\) 749.299 + 243.462i 1.22635 + 0.398465i
\(612\) 0 0
\(613\) −734.937 533.963i −1.19892 0.871065i −0.204741 0.978816i \(-0.565635\pi\)
−0.994178 + 0.107751i \(0.965635\pi\)
\(614\) 1595.82 518.512i 2.59905 0.844483i
\(615\) 0 0
\(616\) −1981.51 679.284i −3.21674 1.10273i
\(617\) 836.440i 1.35566i −0.735220 0.677828i \(-0.762921\pi\)
0.735220 0.677828i \(-0.237079\pi\)
\(618\) 0 0
\(619\) −777.042 564.554i −1.25532 0.912043i −0.256801 0.966464i \(-0.582668\pi\)
−0.998518 + 0.0544217i \(0.982668\pi\)
\(620\) 18.1316 + 24.9560i 0.0292445 + 0.0402516i
\(621\) 0 0
\(622\) 160.144 492.872i 0.257466 0.792399i
\(623\) 170.468 + 234.629i 0.273625 + 0.376612i
\(624\) 0 0
\(625\) 192.503 + 592.464i 0.308005 + 0.947943i
\(626\) 860.727i 1.37496i
\(627\) 0 0
\(628\) −2379.76 −3.78943
\(629\) 954.196 310.037i 1.51700 0.492905i
\(630\) 0 0
\(631\) −186.323 + 135.371i −0.295282 + 0.214535i −0.725555 0.688164i \(-0.758417\pi\)
0.430274 + 0.902698i \(0.358417\pi\)
\(632\) 1005.11 + 326.580i 1.59036 + 0.516740i
\(633\) 0 0
\(634\) −919.427 + 668.003i −1.45020 + 1.05363i
\(635\) 0.782457 1.07696i 0.00123222 0.00169600i
\(636\) 0 0
\(637\) −1161.61 −1.82356
\(638\) −130.901 + 91.9229i −0.205174 + 0.144080i
\(639\) 0 0
\(640\) 5.58418 + 17.1863i 0.00872528 + 0.0268537i
\(641\) −281.497 + 387.447i −0.439152 + 0.604441i −0.970023 0.243011i \(-0.921865\pi\)
0.530871 + 0.847453i \(0.321865\pi\)
\(642\) 0 0
\(643\) −221.374 + 681.320i −0.344284 + 1.05960i 0.617683 + 0.786428i \(0.288072\pi\)
−0.961966 + 0.273169i \(0.911928\pi\)
\(644\) 1205.10 + 391.560i 1.87127 + 0.608012i
\(645\) 0 0
\(646\) 279.004 + 202.708i 0.431895 + 0.313790i
\(647\) −929.344 + 301.962i −1.43639 + 0.466711i −0.920770 0.390106i \(-0.872438\pi\)
−0.515620 + 0.856817i \(0.672438\pi\)
\(648\) 0 0
\(649\) 207.022 63.6001i 0.318985 0.0979971i
\(650\) 1840.35i 2.83131i
\(651\) 0 0
\(652\) 1418.30 + 1030.45i 2.17530 + 1.58045i
\(653\) −524.834 722.372i −0.803728 1.10624i −0.992261 0.124169i \(-0.960373\pi\)
0.188533 0.982067i \(-0.439627\pi\)
\(654\) 0 0
\(655\) −12.2818 + 37.7994i −0.0187508 + 0.0577090i
\(656\) 933.941 + 1285.46i 1.42369 + 1.95954i
\(657\) 0 0
\(658\) 445.961 + 1372.53i 0.677752 + 2.08591i
\(659\) 350.792i 0.532309i 0.963930 + 0.266154i \(0.0857531\pi\)
−0.963930 + 0.266154i \(0.914247\pi\)
\(660\) 0 0
\(661\) −285.033 −0.431215 −0.215607 0.976480i \(-0.569173\pi\)
−0.215607 + 0.976480i \(0.569173\pi\)
\(662\) 180.740 58.7261i 0.273022 0.0887102i
\(663\) 0 0
\(664\) −849.757 + 617.385i −1.27976 + 0.929797i
\(665\) 6.69719 + 2.17605i 0.0100710 + 0.00327225i
\(666\) 0 0
\(667\) 43.8976 31.8935i 0.0658135 0.0478163i
\(668\) 1130.54 1556.06i 1.69243 2.32943i
\(669\) 0 0
\(670\) −2.38460 −0.00355911
\(671\) 56.4952 + 42.4521i 0.0841955 + 0.0632669i
\(672\) 0 0
\(673\) 31.2838 + 96.2816i 0.0464841 + 0.143063i 0.971605 0.236610i \(-0.0760364\pi\)
−0.925121 + 0.379673i \(0.876036\pi\)
\(674\) −1050.90 + 1446.44i −1.55920 + 2.14605i
\(675\) 0 0
\(676\) −690.463 + 2125.03i −1.02140 + 3.14353i
\(677\) −379.528 123.316i −0.560603 0.182151i 0.0149896 0.999888i \(-0.495228\pi\)
−0.575592 + 0.817737i \(0.695228\pi\)
\(678\) 0 0
\(679\) −690.988 502.032i −1.01765 0.739370i
\(680\) −66.8590 + 21.7238i −0.0983221 + 0.0319468i
\(681\) 0 0
\(682\) 780.528 239.790i 1.14447 0.351598i
\(683\) 781.537i 1.14427i 0.820159 + 0.572135i \(0.193885\pi\)
−0.820159 + 0.572135i \(0.806115\pi\)
\(684\) 0 0
\(685\) −2.52168 1.83210i −0.00368128 0.00267461i
\(686\) −176.785 243.324i −0.257704 0.354700i
\(687\) 0 0
\(688\) 589.973 1815.75i 0.857519 2.63917i
\(689\) −423.284 582.600i −0.614345 0.845574i
\(690\) 0 0
\(691\) −170.504 524.757i −0.246749 0.759416i −0.995344 0.0963881i \(-0.969271\pi\)
0.748595 0.663028i \(-0.230729\pi\)
\(692\) 945.087i 1.36573i
\(693\) 0 0
\(694\) −1635.37 −2.35644
\(695\) −5.25972 + 1.70899i −0.00756794 + 0.00245897i
\(696\) 0 0
\(697\) 969.571 704.434i 1.39106 1.01067i
\(698\) 609.975 + 198.193i 0.873889 + 0.283944i
\(699\) 0 0
\(700\) 1894.96 1376.77i 2.70708 1.96681i
\(701\) 192.537 265.005i 0.274661 0.378038i −0.649295 0.760536i \(-0.724936\pi\)
0.923956 + 0.382498i \(0.124936\pi\)
\(702\) 0 0
\(703\) −180.434 −0.256662
\(704\) −111.321 1.79204i −0.158127 0.00254551i
\(705\) 0 0
\(706\) 660.585 + 2033.07i 0.935673 + 2.87970i
\(707\) 926.465 1275.17i 1.31042 1.80364i
\(708\) 0 0
\(709\) 321.304 988.873i 0.453179 1.39474i −0.420080 0.907487i \(-0.637998\pi\)
0.873259 0.487256i \(-0.162002\pi\)
\(710\) −31.1544 10.1227i −0.0438795 0.0142573i
\(711\) 0 0
\(712\) 421.246 + 306.053i 0.591638 + 0.429850i
\(713\) −263.433 + 85.5945i −0.369471 + 0.120048i
\(714\) 0 0
\(715\) 34.9905 + 11.9951i 0.0489377 + 0.0167764i
\(716\) 100.706i 0.140651i
\(717\) 0 0
\(718\) 1734.36 + 1260.08i 2.41554 + 1.75499i
\(719\) −534.348 735.467i −0.743182 1.02290i −0.998429 0.0560264i \(-0.982157\pi\)
0.255247 0.966876i \(-0.417843\pi\)
\(720\) 0 0
\(721\) 334.544 1029.62i 0.464000 1.42804i
\(722\) 731.758 + 1007.18i 1.01352 + 1.39498i
\(723\) 0 0
\(724\) −350.033 1077.29i −0.483470 1.48797i
\(725\) 100.302i 0.138348i
\(726\) 0 0
\(727\) −709.728 −0.976242 −0.488121 0.872776i \(-0.662318\pi\)
−0.488121 + 0.872776i \(0.662318\pi\)
\(728\) −3686.53 + 1197.83i −5.06391 + 1.64536i
\(729\) 0 0
\(730\) 11.0362 8.01827i 0.0151181 0.0109839i
\(731\) −1369.55 444.993i −1.87353 0.608745i
\(732\) 0 0
\(733\) −401.167 + 291.465i −0.547294 + 0.397632i −0.826787 0.562515i \(-0.809834\pi\)
0.279493 + 0.960148i \(0.409834\pi\)
\(734\) 482.553 664.177i 0.657428 0.904873i
\(735\) 0 0
\(736\) 493.205 0.670115
\(737\) −14.2225 + 41.4878i −0.0192978 + 0.0562928i
\(738\) 0 0
\(739\) 339.775 + 1045.72i 0.459776 + 1.41505i 0.865435 + 0.501022i \(0.167042\pi\)
−0.405658 + 0.914025i \(0.632958\pi\)
\(740\) 38.5511 53.0611i 0.0520961 0.0717041i
\(741\) 0 0
\(742\) 407.625 1254.54i 0.549360 1.69076i
\(743\) 688.259 + 223.629i 0.926324 + 0.300981i 0.733058 0.680166i \(-0.238092\pi\)
0.193265 + 0.981147i \(0.438092\pi\)
\(744\) 0 0
\(745\) 13.8220 + 10.0423i 0.0185530 + 0.0134795i
\(746\) 263.569 85.6389i 0.353310 0.114797i
\(747\) 0 0
\(748\) −37.1105 + 2305.31i −0.0496130 + 3.08196i
\(749\) 1161.33i 1.55050i
\(750\) 0 0
\(751\) 439.525 + 319.333i 0.585253 + 0.425211i 0.840614 0.541635i \(-0.182194\pi\)
−0.255361 + 0.966846i \(0.582194\pi\)
\(752\) 694.181 + 955.459i 0.923114 + 1.27056i
\(753\) 0 0
\(754\) −91.4663 + 281.504i −0.121308 + 0.373348i
\(755\) −27.8080 38.2744i −0.0368317 0.0506945i
\(756\) 0 0
\(757\) −107.305 330.251i −0.141751 0.436263i 0.854828 0.518911i \(-0.173662\pi\)
−0.996579 + 0.0826476i \(0.973662\pi\)
\(758\) 1272.85i 1.67923i
\(759\) 0 0
\(760\) 12.6427 0.0166351
\(761\) −762.958 + 247.900i −1.00257 + 0.325756i −0.763893 0.645342i \(-0.776715\pi\)
−0.238680 + 0.971098i \(0.576715\pi\)
\(762\) 0 0
\(763\) 801.142 582.064i 1.04999 0.762862i
\(764\) 1537.94 + 499.706i 2.01301 + 0.654066i
\(765\) 0 0
\(766\) −1677.93 + 1219.08i −2.19050 + 1.59149i
\(767\) 235.562 324.223i 0.307121 0.422716i
\(768\) 0 0
\(769\) −1441.35 −1.87432 −0.937158 0.348905i \(-0.886554\pi\)
−0.937158 + 0.348905i \(0.886554\pi\)
\(770\) 19.8976 + 64.7677i 0.0258411 + 0.0841139i
\(771\) 0 0
\(772\) −684.805 2107.61i −0.887053 2.73007i
\(773\) −783.612 + 1078.55i −1.01373 + 1.39528i −0.0972200 + 0.995263i \(0.530995\pi\)
−0.916509 + 0.400015i \(0.869005\pi\)
\(774\) 0 0
\(775\) −158.224 + 486.963i −0.204160 + 0.628340i
\(776\) −1458.39 473.859i −1.87936 0.610643i
\(777\) 0 0
\(778\) 574.596 + 417.469i 0.738556 + 0.536592i
\(779\) −204.981 + 66.6025i −0.263134 + 0.0854974i
\(780\) 0 0
\(781\) −361.931 + 481.656i −0.463419 + 0.616717i
\(782\) 1125.64i 1.43944i
\(783\) 0 0
\(784\) −1408.72 1023.49i −1.79683 1.30547i
\(785\) 25.3729 + 34.9228i 0.0323222 + 0.0444877i
\(786\) 0 0
\(787\) −136.617 + 420.465i </