Properties

Label 117.4.g.e.55.4
Level $117$
Weight $4$
Character 117.55
Analytic conductor $6.903$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 117.g (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.90322347067\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \( x^{8} - 2x^{7} + 29x^{6} + 2x^{5} + 595x^{4} - 288x^{3} + 2526x^{2} + 1872x + 6084 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4}\cdot 3 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 55.4
Root \(2.66520 + 4.61626i\) of defining polynomial
Character \(\chi\) \(=\) 117.55
Dual form 117.4.g.e.100.4

$q$-expansion

\(f(q)\) \(=\) \(q+(2.66520 + 4.61626i) q^{2} +(-10.2065 + 17.6783i) q^{4} +16.4131 q^{5} +(-4.83984 + 8.38285i) q^{7} -66.1667 q^{8} +O(q^{10})\) \(q+(2.66520 + 4.61626i) q^{2} +(-10.2065 + 17.6783i) q^{4} +16.4131 q^{5} +(-4.83984 + 8.38285i) q^{7} -66.1667 q^{8} +(43.7441 + 75.7670i) q^{10} +(13.7941 + 23.8921i) q^{11} +(-37.3033 - 28.3807i) q^{13} -51.5965 q^{14} +(-94.6948 - 164.016i) q^{16} +(53.9641 - 93.4685i) q^{17} +(1.12362 - 1.94616i) q^{19} +(-167.521 + 290.155i) q^{20} +(-73.5279 + 127.354i) q^{22} +(20.9045 + 36.2077i) q^{23} +144.390 q^{25} +(31.5919 - 247.842i) q^{26} +(-98.7961 - 171.120i) q^{28} +(30.8106 + 53.3656i) q^{29} +191.932 q^{31} +(240.094 - 415.855i) q^{32} +575.300 q^{34} +(-79.4368 + 137.589i) q^{35} +(-49.2118 - 85.2373i) q^{37} +11.9786 q^{38} -1086.00 q^{40} +(-15.3726 - 26.6261i) q^{41} +(-119.163 + 206.396i) q^{43} -563.160 q^{44} +(-111.429 + 193.001i) q^{46} +511.482 q^{47} +(124.652 + 215.903i) q^{49} +(384.826 + 666.539i) q^{50} +(882.459 - 369.788i) q^{52} -492.825 q^{53} +(226.404 + 392.142i) q^{55} +(320.236 - 554.665i) q^{56} +(-164.233 + 284.460i) q^{58} +(242.089 - 419.311i) q^{59} +(222.011 - 384.534i) q^{61} +(511.536 + 886.007i) q^{62} +1044.47 q^{64} +(-612.262 - 465.815i) q^{65} +(-95.0568 - 164.643i) q^{67} +(1101.57 + 1907.98i) q^{68} -846.858 q^{70} +(242.392 - 419.836i) q^{71} -957.780 q^{73} +(262.318 - 454.348i) q^{74} +(22.9365 + 39.7271i) q^{76} -267.045 q^{77} -375.216 q^{79} +(-1554.23 - 2692.01i) q^{80} +(81.9421 - 141.928i) q^{82} +715.765 q^{83} +(885.717 - 1534.11i) q^{85} -1270.37 q^{86} +(-912.708 - 1580.86i) q^{88} +(-519.076 - 899.066i) q^{89} +(418.453 - 175.350i) q^{91} -853.451 q^{92} +(1363.20 + 2361.13i) q^{94} +(18.4420 - 31.9425i) q^{95} +(-32.7818 + 56.7797i) q^{97} +(-664.443 + 1150.85i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{2} - 22 q^{4} + 12 q^{5} + 14 q^{7} - 108 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{2} - 22 q^{4} + 12 q^{5} + 14 q^{7} - 108 q^{8} + 62 q^{10} + 40 q^{11} - 60 q^{13} - 80 q^{14} - 122 q^{16} + 98 q^{17} - 124 q^{19} - 466 q^{20} - 220 q^{22} + 104 q^{23} - 116 q^{25} - 14 q^{26} + 144 q^{28} + 194 q^{29} + 52 q^{31} + 654 q^{32} + 2124 q^{34} + 88 q^{35} - 102 q^{37} - 664 q^{38} - 1996 q^{40} - 1054 q^{41} - 450 q^{43} + 88 q^{44} + 172 q^{46} + 192 q^{47} - 1070 q^{49} + 996 q^{50} + 2280 q^{52} - 524 q^{53} - 204 q^{55} + 2164 q^{56} - 722 q^{58} + 308 q^{59} + 928 q^{61} + 2780 q^{62} + 2052 q^{64} - 2346 q^{65} + 1134 q^{67} + 1786 q^{68} - 4648 q^{70} + 1064 q^{71} + 1904 q^{73} + 1158 q^{74} + 1708 q^{76} - 5016 q^{77} - 1492 q^{79} - 2922 q^{80} - 1734 q^{82} + 808 q^{83} + 1394 q^{85} - 6336 q^{86} - 3060 q^{88} + 1620 q^{89} + 3278 q^{91} - 664 q^{92} + 772 q^{94} + 2204 q^{95} - 2166 q^{97} - 1906 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(92\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.66520 + 4.61626i 0.942289 + 1.63209i 0.761090 + 0.648647i \(0.224665\pi\)
0.181199 + 0.983446i \(0.442002\pi\)
\(3\) 0 0
\(4\) −10.2065 + 17.6783i −1.27582 + 2.20978i
\(5\) 16.4131 1.46803 0.734016 0.679132i \(-0.237644\pi\)
0.734016 + 0.679132i \(0.237644\pi\)
\(6\) 0 0
\(7\) −4.83984 + 8.38285i −0.261327 + 0.452631i −0.966595 0.256309i \(-0.917493\pi\)
0.705268 + 0.708941i \(0.250827\pi\)
\(8\) −66.1667 −2.92418
\(9\) 0 0
\(10\) 43.7441 + 75.7670i 1.38331 + 2.39596i
\(11\) 13.7941 + 23.8921i 0.378098 + 0.654884i 0.990785 0.135441i \(-0.0432451\pi\)
−0.612688 + 0.790325i \(0.709912\pi\)
\(12\) 0 0
\(13\) −37.3033 28.3807i −0.795852 0.605491i
\(14\) −51.5965 −0.984982
\(15\) 0 0
\(16\) −94.6948 164.016i −1.47961 2.56275i
\(17\) 53.9641 93.4685i 0.769895 1.33350i −0.167725 0.985834i \(-0.553642\pi\)
0.937619 0.347663i \(-0.113025\pi\)
\(18\) 0 0
\(19\) 1.12362 1.94616i 0.0135671 0.0234989i −0.859162 0.511703i \(-0.829015\pi\)
0.872729 + 0.488205i \(0.162348\pi\)
\(20\) −167.521 + 290.155i −1.87294 + 3.24403i
\(21\) 0 0
\(22\) −73.5279 + 127.354i −0.712554 + 1.23418i
\(23\) 20.9045 + 36.2077i 0.189517 + 0.328253i 0.945089 0.326812i \(-0.105974\pi\)
−0.755572 + 0.655065i \(0.772641\pi\)
\(24\) 0 0
\(25\) 144.390 1.15512
\(26\) 31.5919 247.842i 0.238296 1.86945i
\(27\) 0 0
\(28\) −98.7961 171.120i −0.666811 1.15495i
\(29\) 30.8106 + 53.3656i 0.197289 + 0.341715i 0.947649 0.319315i \(-0.103453\pi\)
−0.750359 + 0.661030i \(0.770119\pi\)
\(30\) 0 0
\(31\) 191.932 1.11200 0.556000 0.831182i \(-0.312335\pi\)
0.556000 + 0.831182i \(0.312335\pi\)
\(32\) 240.094 415.855i 1.32634 2.29729i
\(33\) 0 0
\(34\) 575.300 2.90185
\(35\) −79.4368 + 137.589i −0.383636 + 0.664477i
\(36\) 0 0
\(37\) −49.2118 85.2373i −0.218659 0.378728i 0.735740 0.677265i \(-0.236835\pi\)
−0.954398 + 0.298537i \(0.903501\pi\)
\(38\) 11.9786 0.0511366
\(39\) 0 0
\(40\) −1086.00 −4.29279
\(41\) −15.3726 26.6261i −0.0585561 0.101422i 0.835261 0.549853i \(-0.185316\pi\)
−0.893817 + 0.448431i \(0.851983\pi\)
\(42\) 0 0
\(43\) −119.163 + 206.396i −0.422608 + 0.731978i −0.996194 0.0871672i \(-0.972219\pi\)
0.573586 + 0.819145i \(0.305552\pi\)
\(44\) −563.160 −1.92953
\(45\) 0 0
\(46\) −111.429 + 193.001i −0.357160 + 0.618618i
\(47\) 511.482 1.58739 0.793695 0.608316i \(-0.208155\pi\)
0.793695 + 0.608316i \(0.208155\pi\)
\(48\) 0 0
\(49\) 124.652 + 215.903i 0.363416 + 0.629456i
\(50\) 384.826 + 666.539i 1.08845 + 1.88526i
\(51\) 0 0
\(52\) 882.459 369.788i 2.35337 0.986162i
\(53\) −492.825 −1.27726 −0.638630 0.769514i \(-0.720498\pi\)
−0.638630 + 0.769514i \(0.720498\pi\)
\(54\) 0 0
\(55\) 226.404 + 392.142i 0.555059 + 0.961390i
\(56\) 320.236 554.665i 0.764167 1.32358i
\(57\) 0 0
\(58\) −164.233 + 284.460i −0.371807 + 0.643989i
\(59\) 242.089 419.311i 0.534192 0.925248i −0.465010 0.885306i \(-0.653949\pi\)
0.999202 0.0399427i \(-0.0127175\pi\)
\(60\) 0 0
\(61\) 222.011 384.534i 0.465993 0.807123i −0.533253 0.845956i \(-0.679031\pi\)
0.999246 + 0.0388329i \(0.0123640\pi\)
\(62\) 511.536 + 886.007i 1.04783 + 1.81489i
\(63\) 0 0
\(64\) 1044.47 2.03998
\(65\) −612.262 465.815i −1.16834 0.888880i
\(66\) 0 0
\(67\) −95.0568 164.643i −0.173329 0.300215i 0.766253 0.642539i \(-0.222119\pi\)
−0.939582 + 0.342325i \(0.888786\pi\)
\(68\) 1101.57 + 1907.98i 1.96449 + 3.40260i
\(69\) 0 0
\(70\) −846.858 −1.44598
\(71\) 242.392 419.836i 0.405164 0.701765i −0.589176 0.808005i \(-0.700548\pi\)
0.994341 + 0.106239i \(0.0338810\pi\)
\(72\) 0 0
\(73\) −957.780 −1.53561 −0.767806 0.640683i \(-0.778651\pi\)
−0.767806 + 0.640683i \(0.778651\pi\)
\(74\) 262.318 454.348i 0.412079 0.713742i
\(75\) 0 0
\(76\) 22.9365 + 39.7271i 0.0346183 + 0.0599607i
\(77\) −267.045 −0.395228
\(78\) 0 0
\(79\) −375.216 −0.534368 −0.267184 0.963646i \(-0.586093\pi\)
−0.267184 + 0.963646i \(0.586093\pi\)
\(80\) −1554.23 2692.01i −2.17211 3.76220i
\(81\) 0 0
\(82\) 81.9421 141.928i 0.110354 0.191138i
\(83\) 715.765 0.946571 0.473286 0.880909i \(-0.343068\pi\)
0.473286 + 0.880909i \(0.343068\pi\)
\(84\) 0 0
\(85\) 885.717 1534.11i 1.13023 1.95762i
\(86\) −1270.37 −1.59288
\(87\) 0 0
\(88\) −912.708 1580.86i −1.10563 1.91500i
\(89\) −519.076 899.066i −0.618224 1.07080i −0.989810 0.142397i \(-0.954519\pi\)
0.371585 0.928399i \(-0.378814\pi\)
\(90\) 0 0
\(91\) 418.453 175.350i 0.482042 0.201996i
\(92\) −853.451 −0.967157
\(93\) 0 0
\(94\) 1363.20 + 2361.13i 1.49578 + 2.59077i
\(95\) 18.4420 31.9425i 0.0199169 0.0344972i
\(96\) 0 0
\(97\) −32.7818 + 56.7797i −0.0343143 + 0.0594341i −0.882673 0.469989i \(-0.844258\pi\)
0.848358 + 0.529423i \(0.177591\pi\)
\(98\) −664.443 + 1150.85i −0.684887 + 1.18626i
\(99\) 0 0
\(100\) −1473.72 + 2552.56i −1.47372 + 2.55256i
\(101\) 265.899 + 460.551i 0.261960 + 0.453728i 0.966763 0.255676i \(-0.0822979\pi\)
−0.704803 + 0.709403i \(0.748965\pi\)
\(102\) 0 0
\(103\) −735.984 −0.704064 −0.352032 0.935988i \(-0.614509\pi\)
−0.352032 + 0.935988i \(0.614509\pi\)
\(104\) 2468.23 + 1877.86i 2.32721 + 1.77057i
\(105\) 0 0
\(106\) −1313.48 2275.01i −1.20355 2.08461i
\(107\) −391.632 678.327i −0.353837 0.612863i 0.633081 0.774085i \(-0.281790\pi\)
−0.986918 + 0.161222i \(0.948456\pi\)
\(108\) 0 0
\(109\) −532.339 −0.467788 −0.233894 0.972262i \(-0.575147\pi\)
−0.233894 + 0.972262i \(0.575147\pi\)
\(110\) −1206.82 + 2090.27i −1.04605 + 1.81182i
\(111\) 0 0
\(112\) 1833.23 1.54664
\(113\) −90.2946 + 156.395i −0.0751699 + 0.130198i −0.901160 0.433486i \(-0.857283\pi\)
0.825990 + 0.563684i \(0.190617\pi\)
\(114\) 0 0
\(115\) 343.107 + 594.280i 0.278217 + 0.481886i
\(116\) −1257.88 −1.00682
\(117\) 0 0
\(118\) 2580.86 2.01346
\(119\) 522.355 + 904.746i 0.402389 + 0.696957i
\(120\) 0 0
\(121\) 284.947 493.542i 0.214085 0.370805i
\(122\) 2366.81 1.75640
\(123\) 0 0
\(124\) −1958.96 + 3393.02i −1.41871 + 2.45728i
\(125\) 318.242 0.227716
\(126\) 0 0
\(127\) −715.817 1239.83i −0.500146 0.866278i −1.00000 0.000168331i \(-0.999946\pi\)
0.499854 0.866110i \(-0.333387\pi\)
\(128\) 862.972 + 1494.71i 0.595912 + 1.03215i
\(129\) 0 0
\(130\) 518.521 4067.85i 0.349825 2.74441i
\(131\) −2067.32 −1.37880 −0.689400 0.724381i \(-0.742126\pi\)
−0.689400 + 0.724381i \(0.742126\pi\)
\(132\) 0 0
\(133\) 10.8762 + 18.8382i 0.00709090 + 0.0122818i
\(134\) 506.690 877.613i 0.326652 0.565778i
\(135\) 0 0
\(136\) −3570.62 + 6184.50i −2.25131 + 3.89939i
\(137\) −193.756 + 335.595i −0.120830 + 0.209283i −0.920095 0.391695i \(-0.871889\pi\)
0.799265 + 0.600978i \(0.205222\pi\)
\(138\) 0 0
\(139\) −376.284 + 651.743i −0.229611 + 0.397699i −0.957693 0.287792i \(-0.907079\pi\)
0.728082 + 0.685491i \(0.240412\pi\)
\(140\) −1621.55 2808.61i −0.978900 1.69550i
\(141\) 0 0
\(142\) 2584.09 1.52713
\(143\) 163.508 1282.74i 0.0956171 0.750126i
\(144\) 0 0
\(145\) 505.698 + 875.894i 0.289627 + 0.501649i
\(146\) −2552.67 4421.36i −1.44699 2.50626i
\(147\) 0 0
\(148\) 2009.13 1.11587
\(149\) −1318.36 + 2283.47i −0.724862 + 1.25550i 0.234169 + 0.972196i \(0.424763\pi\)
−0.959031 + 0.283301i \(0.908570\pi\)
\(150\) 0 0
\(151\) −3332.42 −1.79595 −0.897975 0.440046i \(-0.854962\pi\)
−0.897975 + 0.440046i \(0.854962\pi\)
\(152\) −74.3459 + 128.771i −0.0396727 + 0.0687151i
\(153\) 0 0
\(154\) −711.727 1232.75i −0.372419 0.645049i
\(155\) 3150.20 1.63245
\(156\) 0 0
\(157\) −1625.26 −0.826179 −0.413089 0.910690i \(-0.635550\pi\)
−0.413089 + 0.910690i \(0.635550\pi\)
\(158\) −1000.02 1732.09i −0.503529 0.872138i
\(159\) 0 0
\(160\) 3940.68 6825.46i 1.94711 3.37250i
\(161\) −404.698 −0.198104
\(162\) 0 0
\(163\) 917.683 1589.47i 0.440972 0.763786i −0.556790 0.830653i \(-0.687967\pi\)
0.997762 + 0.0668673i \(0.0213004\pi\)
\(164\) 627.605 0.298828
\(165\) 0 0
\(166\) 1907.65 + 3304.15i 0.891944 + 1.54489i
\(167\) 972.498 + 1684.42i 0.450624 + 0.780503i 0.998425 0.0561052i \(-0.0178682\pi\)
−0.547801 + 0.836609i \(0.684535\pi\)
\(168\) 0 0
\(169\) 586.072 + 2117.39i 0.266760 + 0.963763i
\(170\) 9442.44 4.26001
\(171\) 0 0
\(172\) −2432.48 4213.18i −1.07834 1.86774i
\(173\) 1265.81 2192.45i 0.556289 0.963522i −0.441512 0.897255i \(-0.645558\pi\)
0.997802 0.0662666i \(-0.0211088\pi\)
\(174\) 0 0
\(175\) −698.823 + 1210.40i −0.301863 + 0.522842i
\(176\) 2612.46 4524.90i 1.11887 1.93794i
\(177\) 0 0
\(178\) 2766.88 4792.38i 1.16509 2.01800i
\(179\) 2131.51 + 3691.88i 0.890035 + 1.54159i 0.839831 + 0.542847i \(0.182654\pi\)
0.0502037 + 0.998739i \(0.484013\pi\)
\(180\) 0 0
\(181\) 3944.61 1.61989 0.809946 0.586504i \(-0.199496\pi\)
0.809946 + 0.586504i \(0.199496\pi\)
\(182\) 1924.72 + 1464.35i 0.783900 + 0.596398i
\(183\) 0 0
\(184\) −1383.18 2395.74i −0.554182 0.959871i
\(185\) −807.717 1399.01i −0.320998 0.555984i
\(186\) 0 0
\(187\) 2977.54 1.16438
\(188\) −5220.46 + 9042.11i −2.02522 + 3.50779i
\(189\) 0 0
\(190\) 196.606 0.0750701
\(191\) −107.054 + 185.424i −0.0405559 + 0.0702449i −0.885591 0.464466i \(-0.846246\pi\)
0.845035 + 0.534711i \(0.179580\pi\)
\(192\) 0 0
\(193\) 603.593 + 1045.45i 0.225117 + 0.389914i 0.956355 0.292209i \(-0.0943902\pi\)
−0.731238 + 0.682123i \(0.761057\pi\)
\(194\) −349.480 −0.129336
\(195\) 0 0
\(196\) −5089.06 −1.85461
\(197\) −463.816 803.352i −0.167744 0.290541i 0.769883 0.638186i \(-0.220315\pi\)
−0.937626 + 0.347645i \(0.886981\pi\)
\(198\) 0 0
\(199\) −239.476 + 414.784i −0.0853064 + 0.147755i −0.905522 0.424300i \(-0.860520\pi\)
0.820215 + 0.572055i \(0.193854\pi\)
\(200\) −9553.77 −3.37777
\(201\) 0 0
\(202\) −1417.35 + 2454.92i −0.493684 + 0.855086i
\(203\) −596.474 −0.206228
\(204\) 0 0
\(205\) −252.312 437.017i −0.0859621 0.148891i
\(206\) −1961.54 3397.49i −0.663432 1.14910i
\(207\) 0 0
\(208\) −1122.46 + 8805.85i −0.374178 + 2.93546i
\(209\) 61.9970 0.0205188
\(210\) 0 0
\(211\) 725.477 + 1256.56i 0.236701 + 0.409978i 0.959766 0.280802i \(-0.0906005\pi\)
−0.723065 + 0.690780i \(0.757267\pi\)
\(212\) 5030.04 8712.29i 1.62955 2.82246i
\(213\) 0 0
\(214\) 2087.55 3615.75i 0.666833 1.15499i
\(215\) −1955.83 + 3387.59i −0.620402 + 1.07457i
\(216\) 0 0
\(217\) −928.920 + 1608.94i −0.290595 + 0.503326i
\(218\) −1418.79 2457.41i −0.440791 0.763473i
\(219\) 0 0
\(220\) −9243.19 −2.83262
\(221\) −4665.74 + 1955.15i −1.42014 + 0.595101i
\(222\) 0 0
\(223\) 1029.89 + 1783.83i 0.309268 + 0.535668i 0.978202 0.207654i \(-0.0665827\pi\)
−0.668935 + 0.743321i \(0.733249\pi\)
\(224\) 2324.03 + 4025.34i 0.693218 + 1.20069i
\(225\) 0 0
\(226\) −962.612 −0.283327
\(227\) 2241.23 3881.93i 0.655311 1.13503i −0.326504 0.945196i \(-0.605871\pi\)
0.981816 0.189837i \(-0.0607959\pi\)
\(228\) 0 0
\(229\) −1630.39 −0.470477 −0.235239 0.971938i \(-0.575587\pi\)
−0.235239 + 0.971938i \(0.575587\pi\)
\(230\) −1828.90 + 3167.74i −0.524321 + 0.908151i
\(231\) 0 0
\(232\) −2038.64 3531.02i −0.576910 0.999237i
\(233\) 1903.69 0.535258 0.267629 0.963522i \(-0.413760\pi\)
0.267629 + 0.963522i \(0.413760\pi\)
\(234\) 0 0
\(235\) 8395.00 2.33034
\(236\) 4941.79 + 8559.44i 1.36306 + 2.36090i
\(237\) 0 0
\(238\) −2784.36 + 4822.65i −0.758333 + 1.31347i
\(239\) −3763.79 −1.01866 −0.509328 0.860572i \(-0.670106\pi\)
−0.509328 + 0.860572i \(0.670106\pi\)
\(240\) 0 0
\(241\) 1807.37 3130.46i 0.483083 0.836724i −0.516728 0.856149i \(-0.672850\pi\)
0.999811 + 0.0194250i \(0.00618357\pi\)
\(242\) 3037.75 0.806918
\(243\) 0 0
\(244\) 4531.92 + 7849.52i 1.18904 + 2.05948i
\(245\) 2045.92 + 3543.64i 0.533507 + 0.924061i
\(246\) 0 0
\(247\) −97.1479 + 40.7092i −0.0250258 + 0.0104869i
\(248\) −12699.5 −3.25169
\(249\) 0 0
\(250\) 848.178 + 1469.09i 0.214574 + 0.371653i
\(251\) −2864.88 + 4962.12i −0.720438 + 1.24783i 0.240387 + 0.970677i \(0.422726\pi\)
−0.960824 + 0.277158i \(0.910608\pi\)
\(252\) 0 0
\(253\) −576.717 + 998.903i −0.143312 + 0.248223i
\(254\) 3815.59 6608.79i 0.942564 1.63257i
\(255\) 0 0
\(256\) −422.095 + 731.091i −0.103051 + 0.178489i
\(257\) −2762.89 4785.47i −0.670602 1.16152i −0.977734 0.209849i \(-0.932703\pi\)
0.307132 0.951667i \(-0.400631\pi\)
\(258\) 0 0
\(259\) 952.709 0.228565
\(260\) 14483.9 6069.37i 3.45482 1.44772i
\(261\) 0 0
\(262\) −5509.82 9543.28i −1.29923 2.25033i
\(263\) 2611.60 + 4523.43i 0.612313 + 1.06056i 0.990850 + 0.134971i \(0.0430941\pi\)
−0.378536 + 0.925586i \(0.623573\pi\)
\(264\) 0 0
\(265\) −8088.78 −1.87506
\(266\) −57.9747 + 100.415i −0.0133634 + 0.0231460i
\(267\) 0 0
\(268\) 3880.81 0.884545
\(269\) 3601.94 6238.75i 0.816410 1.41406i −0.0919010 0.995768i \(-0.529294\pi\)
0.908311 0.418295i \(-0.137372\pi\)
\(270\) 0 0
\(271\) 4288.84 + 7428.49i 0.961360 + 1.66512i 0.719091 + 0.694916i \(0.244558\pi\)
0.242269 + 0.970209i \(0.422108\pi\)
\(272\) −20440.5 −4.55656
\(273\) 0 0
\(274\) −2065.59 −0.455427
\(275\) 1991.72 + 3449.76i 0.436747 + 0.756467i
\(276\) 0 0
\(277\) −3584.60 + 6208.70i −0.777536 + 1.34673i 0.155822 + 0.987785i \(0.450197\pi\)
−0.933358 + 0.358947i \(0.883136\pi\)
\(278\) −4011.48 −0.865442
\(279\) 0 0
\(280\) 5256.06 9103.77i 1.12182 1.94305i
\(281\) −849.157 −0.180272 −0.0901360 0.995929i \(-0.528730\pi\)
−0.0901360 + 0.995929i \(0.528730\pi\)
\(282\) 0 0
\(283\) −557.686 965.941i −0.117141 0.202895i 0.801492 0.598005i \(-0.204040\pi\)
−0.918634 + 0.395110i \(0.870706\pi\)
\(284\) 4947.97 + 8570.14i 1.03383 + 1.79065i
\(285\) 0 0
\(286\) 6357.23 2663.95i 1.31437 0.550779i
\(287\) 297.604 0.0612091
\(288\) 0 0
\(289\) −3367.75 5833.11i −0.685476 1.18728i
\(290\) −2695.57 + 4668.86i −0.545825 + 0.945396i
\(291\) 0 0
\(292\) 9775.62 16931.9i 1.95916 3.39337i
\(293\) −931.764 + 1613.86i −0.185782 + 0.321784i −0.943840 0.330403i \(-0.892815\pi\)
0.758058 + 0.652188i \(0.226149\pi\)
\(294\) 0 0
\(295\) 3973.43 6882.19i 0.784211 1.35829i
\(296\) 3256.18 + 5639.87i 0.639397 + 1.10747i
\(297\) 0 0
\(298\) −14054.8 −2.73212
\(299\) 247.792 1943.95i 0.0479269 0.375992i
\(300\) 0 0
\(301\) −1153.46 1997.85i −0.220878 0.382571i
\(302\) −8881.55 15383.3i −1.69230 2.93116i
\(303\) 0 0
\(304\) −425.602 −0.0802959
\(305\) 3643.88 6311.39i 0.684092 1.18488i
\(306\) 0 0
\(307\) −6387.50 −1.18747 −0.593736 0.804660i \(-0.702348\pi\)
−0.593736 + 0.804660i \(0.702348\pi\)
\(308\) 2725.60 4720.89i 0.504239 0.873368i
\(309\) 0 0
\(310\) 8395.89 + 14542.1i 1.53824 + 2.66431i
\(311\) 3492.59 0.636806 0.318403 0.947955i \(-0.396853\pi\)
0.318403 + 0.947955i \(0.396853\pi\)
\(312\) 0 0
\(313\) −5912.01 −1.06762 −0.533812 0.845603i \(-0.679241\pi\)
−0.533812 + 0.845603i \(0.679241\pi\)
\(314\) −4331.64 7502.63i −0.778499 1.34840i
\(315\) 0 0
\(316\) 3829.66 6633.16i 0.681756 1.18084i
\(317\) 1677.54 0.297224 0.148612 0.988896i \(-0.452519\pi\)
0.148612 + 0.988896i \(0.452519\pi\)
\(318\) 0 0
\(319\) −850.009 + 1472.26i −0.149189 + 0.258403i
\(320\) 17143.0 2.99476
\(321\) 0 0
\(322\) −1078.60 1868.19i −0.186671 0.323323i
\(323\) −121.270 210.045i −0.0208905 0.0361834i
\(324\) 0 0
\(325\) −5386.21 4097.88i −0.919301 0.699413i
\(326\) 9783.22 1.66209
\(327\) 0 0
\(328\) 1017.15 + 1761.76i 0.171228 + 0.296576i
\(329\) −2475.49 + 4287.68i −0.414828 + 0.718503i
\(330\) 0 0
\(331\) −1005.15 + 1740.98i −0.166913 + 0.289102i −0.937333 0.348435i \(-0.886713\pi\)
0.770420 + 0.637537i \(0.220047\pi\)
\(332\) −7305.49 + 12653.5i −1.20765 + 2.09172i
\(333\) 0 0
\(334\) −5183.80 + 8978.60i −0.849236 + 1.47092i
\(335\) −1560.18 2702.30i −0.254452 0.440724i
\(336\) 0 0
\(337\) 7139.24 1.15400 0.577002 0.816743i \(-0.304222\pi\)
0.577002 + 0.816743i \(0.304222\pi\)
\(338\) −8212.40 + 8348.71i −1.32159 + 1.34352i
\(339\) 0 0
\(340\) 18080.2 + 31315.9i 2.88394 + 4.99512i
\(341\) 2647.53 + 4585.65i 0.420444 + 0.728231i
\(342\) 0 0
\(343\) −5733.31 −0.902536
\(344\) 7884.60 13656.5i 1.23578 2.14044i
\(345\) 0 0
\(346\) 13494.6 2.09674
\(347\) 0.569949 0.987181i 8.81743e−5 0.000152722i −0.865981 0.500076i \(-0.833305\pi\)
0.866069 + 0.499924i \(0.166639\pi\)
\(348\) 0 0
\(349\) −6099.55 10564.7i −0.935535 1.62039i −0.773678 0.633579i \(-0.781585\pi\)
−0.161857 0.986814i \(-0.551748\pi\)
\(350\) −7450.00 −1.13777
\(351\) 0 0
\(352\) 13247.5 2.00595
\(353\) −5446.15 9433.01i −0.821160 1.42229i −0.904819 0.425796i \(-0.859994\pi\)
0.0836595 0.996494i \(-0.473339\pi\)
\(354\) 0 0
\(355\) 3978.41 6890.80i 0.594794 1.03021i
\(356\) 21191.9 3.15497
\(357\) 0 0
\(358\) −11361.8 + 19679.2i −1.67734 + 2.90524i
\(359\) 3525.78 0.518339 0.259169 0.965832i \(-0.416551\pi\)
0.259169 + 0.965832i \(0.416551\pi\)
\(360\) 0 0
\(361\) 3426.97 + 5935.69i 0.499632 + 0.865388i
\(362\) 10513.2 + 18209.3i 1.52641 + 2.64382i
\(363\) 0 0
\(364\) −1171.08 + 9187.24i −0.168630 + 1.32292i
\(365\) −15720.1 −2.25433
\(366\) 0 0
\(367\) −1191.88 2064.39i −0.169525 0.293625i 0.768728 0.639576i \(-0.220890\pi\)
−0.938253 + 0.345950i \(0.887557\pi\)
\(368\) 3959.09 6857.35i 0.560821 0.971370i
\(369\) 0 0
\(370\) 4305.45 7457.26i 0.604945 1.04780i
\(371\) 2385.20 4131.28i 0.333782 0.578128i
\(372\) 0 0
\(373\) 6641.10 11502.7i 0.921885 1.59675i 0.125390 0.992108i \(-0.459982\pi\)
0.796495 0.604645i \(-0.206685\pi\)
\(374\) 7935.73 + 13745.1i 1.09718 + 1.90038i
\(375\) 0 0
\(376\) −33843.1 −4.64181
\(377\) 365.214 2865.14i 0.0498925 0.391412i
\(378\) 0 0
\(379\) 2218.36 + 3842.32i 0.300659 + 0.520756i 0.976285 0.216488i \(-0.0694601\pi\)
−0.675627 + 0.737244i \(0.736127\pi\)
\(380\) 376.458 + 652.045i 0.0508208 + 0.0880242i
\(381\) 0 0
\(382\) −1141.28 −0.152862
\(383\) −405.206 + 701.838i −0.0540602 + 0.0936351i −0.891789 0.452451i \(-0.850550\pi\)
0.837729 + 0.546086i \(0.183883\pi\)
\(384\) 0 0
\(385\) −4383.03 −0.580207
\(386\) −3217.39 + 5572.68i −0.424251 + 0.734824i
\(387\) 0 0
\(388\) −669.177 1159.05i −0.0875576 0.151654i
\(389\) −3463.79 −0.451469 −0.225734 0.974189i \(-0.572478\pi\)
−0.225734 + 0.974189i \(0.572478\pi\)
\(390\) 0 0
\(391\) 4512.37 0.583633
\(392\) −8247.80 14285.6i −1.06270 1.84064i
\(393\) 0 0
\(394\) 2472.32 4282.18i 0.316126 0.547546i
\(395\) −6158.45 −0.784469
\(396\) 0 0
\(397\) −212.703 + 368.412i −0.0268898 + 0.0465745i −0.879157 0.476532i \(-0.841894\pi\)
0.852267 + 0.523106i \(0.175227\pi\)
\(398\) −2553.00 −0.321533
\(399\) 0 0
\(400\) −13672.9 23682.2i −1.70912 2.96028i
\(401\) −593.424 1027.84i −0.0739007 0.128000i 0.826707 0.562633i \(-0.190211\pi\)
−0.900608 + 0.434633i \(0.856878\pi\)
\(402\) 0 0
\(403\) −7159.70 5447.16i −0.884987 0.673306i
\(404\) −10855.6 −1.33685
\(405\) 0 0
\(406\) −1589.72 2753.48i −0.194327 0.336583i
\(407\) 1357.66 2351.54i 0.165349 0.286392i
\(408\) 0 0
\(409\) −4003.71 + 6934.63i −0.484036 + 0.838375i −0.999832 0.0183369i \(-0.994163\pi\)
0.515796 + 0.856711i \(0.327496\pi\)
\(410\) 1344.92 2329.47i 0.162002 0.280596i
\(411\) 0 0
\(412\) 7511.85 13010.9i 0.898258 1.55583i
\(413\) 2343.35 + 4058.80i 0.279198 + 0.483585i
\(414\) 0 0
\(415\) 11747.9 1.38960
\(416\) −20758.5 + 8698.72i −2.44656 + 1.02522i
\(417\) 0 0
\(418\) 165.234 + 286.194i 0.0193346 + 0.0334885i
\(419\) 3416.23 + 5917.08i 0.398314 + 0.689901i 0.993518 0.113674i \(-0.0362620\pi\)
−0.595204 + 0.803575i \(0.702929\pi\)
\(420\) 0 0
\(421\) 10739.6 1.24326 0.621632 0.783309i \(-0.286470\pi\)
0.621632 + 0.783309i \(0.286470\pi\)
\(422\) −3867.08 + 6697.98i −0.446082 + 0.772636i
\(423\) 0 0
\(424\) 32608.6 3.73494
\(425\) 7791.85 13495.9i 0.889318 1.54034i
\(426\) 0 0
\(427\) 2148.99 + 3722.16i 0.243553 + 0.421846i
\(428\) 15988.9 1.80573
\(429\) 0 0
\(430\) −20850.7 −2.33839
\(431\) 2607.22 + 4515.84i 0.291382 + 0.504688i 0.974137 0.225959i \(-0.0725517\pi\)
−0.682755 + 0.730647i \(0.739218\pi\)
\(432\) 0 0
\(433\) −4321.12 + 7484.40i −0.479584 + 0.830664i −0.999726 0.0234161i \(-0.992546\pi\)
0.520142 + 0.854080i \(0.325879\pi\)
\(434\) −9903.02 −1.09530
\(435\) 0 0
\(436\) 5433.34 9410.83i 0.596812 1.03371i
\(437\) 93.9545 0.0102848
\(438\) 0 0
\(439\) 6513.12 + 11281.1i 0.708097 + 1.22646i 0.965562 + 0.260172i \(0.0837793\pi\)
−0.257466 + 0.966287i \(0.582887\pi\)
\(440\) −14980.4 25946.8i −1.62309 2.81128i
\(441\) 0 0
\(442\) −21460.6 16327.4i −2.30945 1.75705i
\(443\) 11533.0 1.23690 0.618450 0.785824i \(-0.287761\pi\)
0.618450 + 0.785824i \(0.287761\pi\)
\(444\) 0 0
\(445\) −8519.64 14756.5i −0.907573 1.57196i
\(446\) −5489.74 + 9508.50i −0.582840 + 1.00951i
\(447\) 0 0
\(448\) −5055.08 + 8755.65i −0.533103 + 0.923361i
\(449\) 4941.37 8558.71i 0.519372 0.899578i −0.480375 0.877063i \(-0.659499\pi\)
0.999747 0.0225149i \(-0.00716731\pi\)
\(450\) 0 0
\(451\) 424.102 734.566i 0.0442798 0.0766949i
\(452\) −1843.19 3192.50i −0.191806 0.332218i
\(453\) 0 0
\(454\) 23893.3 2.46997
\(455\) 6868.11 2878.04i 0.707653 0.296537i
\(456\) 0 0
\(457\) 7814.04 + 13534.3i 0.799836 + 1.38536i 0.919722 + 0.392569i \(0.128414\pi\)
−0.119886 + 0.992788i \(0.538253\pi\)
\(458\) −4345.31 7526.31i −0.443326 0.767863i
\(459\) 0 0
\(460\) −14007.8 −1.41982
\(461\) −3873.73 + 6709.50i −0.391361 + 0.677858i −0.992629 0.121190i \(-0.961329\pi\)
0.601268 + 0.799047i \(0.294662\pi\)
\(462\) 0 0
\(463\) −333.422 −0.0334675 −0.0167337 0.999860i \(-0.505327\pi\)
−0.0167337 + 0.999860i \(0.505327\pi\)
\(464\) 5835.21 10106.9i 0.583821 1.01121i
\(465\) 0 0
\(466\) 5073.71 + 8787.93i 0.504368 + 0.873590i
\(467\) −8198.33 −0.812363 −0.406182 0.913792i \(-0.633140\pi\)
−0.406182 + 0.913792i \(0.633140\pi\)
\(468\) 0 0
\(469\) 1840.24 0.181182
\(470\) 22374.3 + 38753.5i 2.19585 + 3.80333i
\(471\) 0 0
\(472\) −16018.2 + 27744.4i −1.56208 + 2.70559i
\(473\) −6574.96 −0.639148
\(474\) 0 0
\(475\) 162.238 281.005i 0.0156716 0.0271440i
\(476\) −21325.8 −2.05350
\(477\) 0 0
\(478\) −10031.2 17374.6i −0.959870 1.66254i
\(479\) −3217.94 5573.64i −0.306955 0.531662i 0.670740 0.741693i \(-0.265977\pi\)
−0.977695 + 0.210031i \(0.932643\pi\)
\(480\) 0 0
\(481\) −583.332 + 4576.30i −0.0552966 + 0.433807i
\(482\) 19268.0 1.82082
\(483\) 0 0
\(484\) 5816.64 + 10074.7i 0.546266 + 0.946160i
\(485\) −538.050 + 931.931i −0.0503745 + 0.0872511i
\(486\) 0 0
\(487\) −4047.69 + 7010.80i −0.376629 + 0.652340i −0.990569 0.137012i \(-0.956250\pi\)
0.613941 + 0.789352i \(0.289583\pi\)
\(488\) −14689.7 + 25443.3i −1.36265 + 2.36017i
\(489\) 0 0
\(490\) −10905.6 + 18889.0i −1.00544 + 1.74147i
\(491\) 2558.23 + 4430.99i 0.235135 + 0.407266i 0.959312 0.282348i \(-0.0911134\pi\)
−0.724177 + 0.689614i \(0.757780\pi\)
\(492\) 0 0
\(493\) 6650.67 0.607568
\(494\) −446.842 339.962i −0.0406971 0.0309628i
\(495\) 0 0
\(496\) −18175.0 31479.9i −1.64532 2.84978i
\(497\) 2346.28 + 4063.88i 0.211761 + 0.366780i
\(498\) 0 0
\(499\) −18050.7 −1.61936 −0.809682 0.586870i \(-0.800360\pi\)
−0.809682 + 0.586870i \(0.800360\pi\)
\(500\) −3248.15 + 5625.97i −0.290524 + 0.503202i
\(501\) 0 0
\(502\) −30541.9 −2.71544
\(503\) 5265.53 9120.16i 0.466756 0.808445i −0.532523 0.846416i \(-0.678756\pi\)
0.999279 + 0.0379705i \(0.0120893\pi\)
\(504\) 0 0
\(505\) 4364.22 + 7559.06i 0.384565 + 0.666087i
\(506\) −6148.25 −0.540165
\(507\) 0 0
\(508\) 29224.1 2.55238
\(509\) −981.654 1700.27i −0.0854834 0.148062i 0.820114 0.572201i \(-0.193910\pi\)
−0.905597 + 0.424139i \(0.860577\pi\)
\(510\) 0 0
\(511\) 4635.50 8028.93i 0.401297 0.695066i
\(512\) 9307.69 0.803409
\(513\) 0 0
\(514\) 14727.3 25508.5i 1.26380 2.18897i
\(515\) −12079.8 −1.03359
\(516\) 0 0
\(517\) 7055.43 + 12220.4i 0.600188 + 1.03956i
\(518\) 2539.16 + 4397.95i 0.215375 + 0.373040i
\(519\) 0 0
\(520\) 40511.4 + 30821.4i 3.41642 + 2.59925i
\(521\) 7044.93 0.592407 0.296203 0.955125i \(-0.404279\pi\)
0.296203 + 0.955125i \(0.404279\pi\)
\(522\) 0 0
\(523\) 1606.65 + 2782.79i 0.134328 + 0.232664i 0.925341 0.379137i \(-0.123779\pi\)
−0.791012 + 0.611800i \(0.790446\pi\)
\(524\) 21100.2 36546.6i 1.75910 3.04685i
\(525\) 0 0
\(526\) −13920.9 + 24111.7i −1.15395 + 1.99870i
\(527\) 10357.4 17939.6i 0.856123 1.48285i
\(528\) 0 0
\(529\) 5209.50 9023.13i 0.428167 0.741606i
\(530\) −21558.2 37339.9i −1.76685 3.06027i
\(531\) 0 0
\(532\) −444.036 −0.0361868
\(533\) −182.219 + 1429.53i −0.0148082 + 0.116172i
\(534\) 0 0
\(535\) −6427.90 11133.4i −0.519443 0.899702i
\(536\) 6289.59 + 10893.9i 0.506845 + 0.877882i
\(537\) 0 0
\(538\) 38399.5 3.07718
\(539\) −3438.92 + 5956.38i −0.274814 + 0.475991i
\(540\) 0 0
\(541\) 11251.4 0.894150 0.447075 0.894497i \(-0.352466\pi\)
0.447075 + 0.894497i \(0.352466\pi\)
\(542\) −22861.2 + 39596.8i −1.81176 + 3.13806i
\(543\) 0 0
\(544\) −25912.9 44882.4i −2.04229 3.53735i
\(545\) −8737.33 −0.686727
\(546\) 0 0
\(547\) 1533.54 0.119871 0.0599353 0.998202i \(-0.480911\pi\)
0.0599353 + 0.998202i \(0.480911\pi\)
\(548\) −3955.16 6850.53i −0.308314 0.534015i
\(549\) 0 0
\(550\) −10616.7 + 18388.6i −0.823083 + 1.42562i
\(551\) 138.477 0.0107066
\(552\) 0 0
\(553\) 1815.98 3145.38i 0.139645 0.241872i
\(554\) −38214.6 −2.93066
\(555\) 0 0
\(556\) −7681.12 13304.1i −0.585885 1.01478i
\(557\) 8422.84 + 14588.8i 0.640731 + 1.10978i 0.985270 + 0.171006i \(0.0547019\pi\)
−0.344539 + 0.938772i \(0.611965\pi\)
\(558\) 0 0
\(559\) 10302.8 4317.33i 0.779540 0.326661i
\(560\) 30089.0 2.27052
\(561\) 0 0
\(562\) −2263.17 3919.92i −0.169868 0.294221i
\(563\) −10410.0 + 18030.7i −0.779273 + 1.34974i 0.153089 + 0.988212i \(0.451078\pi\)
−0.932361 + 0.361528i \(0.882255\pi\)
\(564\) 0 0
\(565\) −1482.01 + 2566.92i −0.110352 + 0.191135i
\(566\) 2972.69 5148.84i 0.220762 0.382371i
\(567\) 0 0
\(568\) −16038.3 + 27779.1i −1.18477 + 2.05209i
\(569\) 11818.3 + 20469.9i 0.870735 + 1.50816i 0.861237 + 0.508203i \(0.169690\pi\)
0.00949803 + 0.999955i \(0.496977\pi\)
\(570\) 0 0
\(571\) −26955.1 −1.97554 −0.987771 0.155913i \(-0.950168\pi\)
−0.987771 + 0.155913i \(0.950168\pi\)
\(572\) 21007.7 + 15982.9i 1.53562 + 1.16832i
\(573\) 0 0
\(574\) 793.173 + 1373.82i 0.0576767 + 0.0998989i
\(575\) 3018.39 + 5228.01i 0.218914 + 0.379170i
\(576\) 0 0
\(577\) 23499.8 1.69551 0.847755 0.530388i \(-0.177954\pi\)
0.847755 + 0.530388i \(0.177954\pi\)
\(578\) 17951.4 31092.8i 1.29183 2.23752i
\(579\) 0 0
\(580\) −20645.7 −1.47805
\(581\) −3464.19 + 6000.15i −0.247365 + 0.428448i
\(582\) 0 0
\(583\) −6798.07 11774.6i −0.482929 0.836457i
\(584\) 63373.1 4.49040
\(585\) 0 0
\(586\) −9933.33 −0.700243
\(587\) 2318.75 + 4016.19i 0.163041 + 0.282395i 0.935958 0.352112i \(-0.114536\pi\)
−0.772917 + 0.634507i \(0.781203\pi\)
\(588\) 0 0
\(589\) 215.658 373.530i 0.0150866 0.0261308i
\(590\) 42359.9 2.95582
\(591\) 0 0
\(592\) −9320.20 + 16143.1i −0.647057 + 1.12074i
\(593\) −12633.5 −0.874869 −0.437434 0.899250i \(-0.644113\pi\)
−0.437434 + 0.899250i \(0.644113\pi\)
\(594\) 0 0
\(595\) 8573.47 + 14849.7i 0.590719 + 1.02316i
\(596\) −26911.8 46612.7i −1.84958 3.20357i
\(597\) 0 0
\(598\) 9634.18 4037.14i 0.658814 0.276072i
\(599\) 18757.1 1.27946 0.639730 0.768600i \(-0.279046\pi\)
0.639730 + 0.768600i \(0.279046\pi\)
\(600\) 0 0
\(601\) 1816.49 + 3146.25i 0.123288 + 0.213541i 0.921062 0.389415i \(-0.127323\pi\)
−0.797774 + 0.602956i \(0.793989\pi\)
\(602\) 6148.38 10649.3i 0.416261 0.720986i
\(603\) 0 0
\(604\) 34012.5 58911.4i 2.29131 3.96866i
\(605\) 4676.85 8100.55i 0.314283 0.544354i
\(606\) 0 0
\(607\) 6349.99 10998.5i 0.424610 0.735445i −0.571774 0.820411i \(-0.693745\pi\)
0.996384 + 0.0849656i \(0.0270781\pi\)
\(608\) −539.546 934.522i −0.0359893 0.0623353i
\(609\) 0 0
\(610\) 38846.6 2.57845
\(611\) −19080.0 14516.2i −1.26333 0.961151i
\(612\) 0 0
\(613\) −10820.1 18740.9i −0.712918 1.23481i −0.963757 0.266781i \(-0.914040\pi\)
0.250839 0.968029i \(-0.419293\pi\)
\(614\) −17023.9 29486.3i −1.11894 1.93806i
\(615\) 0 0
\(616\) 17669.5 1.15572
\(617\) −8270.85 + 14325.5i −0.539663 + 0.934723i 0.459259 + 0.888302i \(0.348115\pi\)
−0.998922 + 0.0464208i \(0.985219\pi\)
\(618\) 0 0
\(619\) −21138.9 −1.37261 −0.686303 0.727316i \(-0.740767\pi\)
−0.686303 + 0.727316i \(0.740767\pi\)
\(620\) −32152.6 + 55690.0i −2.08271 + 3.60736i
\(621\) 0 0
\(622\) 9308.44 + 16122.7i 0.600055 + 1.03933i
\(623\) 10049.0 0.646235
\(624\) 0 0
\(625\) −12825.4 −0.820823
\(626\) −15756.7 27291.3i −1.00601 1.74246i
\(627\) 0 0
\(628\) 16588.3 28731.8i 1.05405 1.82568i
\(629\) −10622.7 −0.673377
\(630\) 0 0
\(631\) −2744.90 + 4754.31i −0.173174 + 0.299946i −0.939528 0.342473i \(-0.888736\pi\)
0.766354 + 0.642419i \(0.222069\pi\)
\(632\) 24826.8 1.56259
\(633\) 0 0
\(634\) 4470.97 + 7743.94i 0.280071 + 0.485097i
\(635\) −11748.8 20349.5i −0.734230 1.27172i
\(636\) 0 0
\(637\) 1477.56 11591.6i 0.0919044 0.720999i
\(638\) −9061.76 −0.562318
\(639\) 0 0
\(640\) 14164.0 + 24532.8i 0.874817 + 1.51523i
\(641\) 2148.52 3721.35i 0.132389 0.229305i −0.792208 0.610251i \(-0.791068\pi\)
0.924597 + 0.380946i \(0.124402\pi\)
\(642\) 0 0
\(643\) −12848.5 + 22254.2i −0.788016 + 1.36488i 0.139164 + 0.990269i \(0.455558\pi\)
−0.927181 + 0.374615i \(0.877775\pi\)
\(644\) 4130.57 7154.35i 0.252744 0.437766i
\(645\) 0 0
\(646\) 646.416 1119.62i 0.0393698 0.0681905i
\(647\) 1087.49 + 1883.59i 0.0660798 + 0.114454i 0.897172 0.441680i \(-0.145617\pi\)
−0.831093 + 0.556134i \(0.812284\pi\)
\(648\) 0 0
\(649\) 13357.6 0.807907
\(650\) 4561.54 35785.7i 0.275259 2.15943i
\(651\) 0 0
\(652\) 18732.7 + 32446.1i 1.12520 + 1.94890i
\(653\) −7727.27 13384.0i −0.463080 0.802078i 0.536032 0.844197i \(-0.319922\pi\)
−0.999113 + 0.0421191i \(0.986589\pi\)
\(654\) 0 0
\(655\) −33931.1 −2.02412
\(656\) −2911.41 + 5042.71i −0.173280 + 0.300129i
\(657\) 0 0
\(658\) −26390.7 −1.56355
\(659\) −1574.39 + 2726.92i −0.0930643 + 0.161192i −0.908799 0.417234i \(-0.863000\pi\)
0.815735 + 0.578426i \(0.196333\pi\)
\(660\) 0 0
\(661\) 1049.85 + 1818.39i 0.0617767 + 0.107000i 0.895260 0.445545i \(-0.146990\pi\)
−0.833483 + 0.552545i \(0.813657\pi\)
\(662\) −10715.7 −0.629122
\(663\) 0 0
\(664\) −47359.8 −2.76795
\(665\) 178.513 + 309.193i 0.0104097 + 0.0180301i
\(666\) 0 0
\(667\) −1288.16 + 2231.16i −0.0747794 + 0.129522i
\(668\) −39703.4 −2.29966
\(669\) 0 0
\(670\) 8316.35 14404.3i 0.479535 0.830580i
\(671\) 12249.7 0.704763
\(672\) 0 0
\(673\) −15485.4 26821.5i −0.886950 1.53624i −0.843462 0.537189i \(-0.819486\pi\)
−0.0434884 0.999054i \(-0.513847\pi\)
\(674\) 19027.5 + 32956.6i 1.08741 + 1.88344i
\(675\) 0 0
\(676\) −43413.5 11250.5i −2.47004 0.640104i
\(677\) −14640.6 −0.831141 −0.415570 0.909561i \(-0.636418\pi\)
−0.415570 + 0.909561i \(0.636418\pi\)
\(678\) 0 0
\(679\) −317.317 549.610i −0.0179345 0.0310635i
\(680\) −58605.0 + 101507.i −3.30500 + 5.72442i
\(681\) 0 0
\(682\) −14112.4 + 24443.3i −0.792360 + 1.37241i
\(683\) −3342.92 + 5790.10i −0.187281 + 0.324381i −0.944343 0.328963i \(-0.893301\pi\)
0.757062 + 0.653343i \(0.226634\pi\)
\(684\) 0 0
\(685\) −3180.13 + 5508.15i −0.177382 + 0.307235i
\(686\) −15280.4 26466.4i −0.850450 1.47302i
\(687\) 0 0
\(688\) 45136.3 2.50117
\(689\) 18384.0 + 13986.7i 1.01651 + 0.773370i
\(690\) 0 0
\(691\) 15097.0 + 26148.8i 0.831141 + 1.43958i 0.897134 + 0.441758i \(0.145645\pi\)
−0.0659934 + 0.997820i \(0.521022\pi\)
\(692\) 25839.2 + 44754.8i 1.41945 + 2.45856i
\(693\) 0 0
\(694\) 6.07611 0.000332343
\(695\) −6175.98 + 10697.1i −0.337077 + 0.583834i
\(696\) 0 0
\(697\) −3318.28 −0.180328
\(698\) 32513.0 56314.2i 1.76309 3.05376i
\(699\) 0 0
\(700\) −14265.1 24707.9i −0.770245 1.33410i
\(701\) 30300.9 1.63260 0.816298 0.577631i \(-0.196023\pi\)
0.816298 + 0.577631i \(0.196023\pi\)
\(702\) 0 0
\(703\) −221.181 −0.0118663
\(704\) 14407.5 + 24954.6i 0.771313 + 1.33595i
\(705\) 0 0
\(706\) 29030.1 50281.7i 1.54754 2.68042i
\(707\) −5147.64 −0.273829
\(708\) 0 0
\(709\) −13061.6 + 22623.4i −0.691875 + 1.19836i 0.279348 + 0.960190i \(0.409882\pi\)
−0.971223 + 0.238173i \(0.923452\pi\)
\(710\) 42412.9 2.24187
\(711\) 0 0
\(712\) 34345.5 + 59488.2i 1.80780 + 3.13120i
\(713\) 4012.24 + 6949.41i 0.210743 + 0.365017i
\(714\) 0 0
\(715\) 2683.68 21053.7i 0.140369 1.10121i
\(716\) −87021.3 −4.54209
\(717\) 0 0
\(718\) 9396.90 + 16275.9i 0.488425 + 0.845977i
\(719\) 9662.83 16736.5i 0.501200 0.868104i −0.498799 0.866718i \(-0.666225\pi\)
0.999999 0.00138631i \(-0.000441276\pi\)
\(720\) 0 0
\(721\) 3562.05 6169.64i 0.183991 0.318682i
\(722\) −18267.1 + 31639.6i −0.941595 + 1.63089i
\(723\) 0 0
\(724\) −40260.8 + 69733.8i −2.06669 + 3.57961i
\(725\) 4448.73 + 7705.43i 0.227892 + 0.394721i
\(726\) 0 0
\(727\) 26065.8 1.32975 0.664875 0.746954i \(-0.268485\pi\)
0.664875 + 0.746954i \(0.268485\pi\)
\(728\) −27687.7 + 11602.3i −1.40958 + 0.590674i
\(729\) 0 0
\(730\) −41897.2 72568.1i −2.12423 3.67927i
\(731\) 12861.0 + 22275.9i 0.650727 + 1.12709i
\(732\) 0 0
\(733\) 1055.45 0.0531843 0.0265921 0.999646i \(-0.491534\pi\)
0.0265921 + 0.999646i \(0.491534\pi\)
\(734\) 6353.18 11004.0i 0.319482 0.553359i
\(735\) 0 0
\(736\) 20076.2 1.00546
\(737\) 2622.44 4542.21i 0.131070 0.227021i
\(738\) 0 0
\(739\) −4705.20 8149.64i −0.234213 0.405669i 0.724831 0.688927i \(-0.241918\pi\)
−0.959044 + 0.283258i \(0.908585\pi\)
\(740\) 32976.0 1.63814
\(741\) 0 0
\(742\) 25428.1 1.25808
\(743\) −3761.85 6515.72i −0.185746 0.321721i 0.758082 0.652159i \(-0.226137\pi\)
−0.943827 + 0.330439i \(0.892803\pi\)
\(744\) 0 0
\(745\) −21638.4 + 37478.8i −1.06412 + 1.84311i
\(746\) 70799.4 3.47473
\(747\) 0 0
\(748\) −30390.4 + 52637.7i −1.48554 + 2.57303i
\(749\) 7581.76 0.369868
\(750\) 0 0
\(751\) 6492.03 + 11244.5i 0.315443 + 0.546363i 0.979532 0.201291i \(-0.0645136\pi\)
−0.664089 + 0.747654i \(0.731180\pi\)
\(752\) −48434.7 83891.3i −2.34871 4.06809i
\(753\) 0 0
\(754\) 14199.6 5950.24i 0.685833 0.287394i
\(755\) −54695.3 −2.63651
\(756\) 0 0
\(757\) 13967.3 + 24192.1i 0.670609 + 1.16153i 0.977732 + 0.209859i \(0.0673004\pi\)
−0.307123 + 0.951670i \(0.599366\pi\)
\(758\) −11824.7 + 20481.1i −0.566615 + 0.981406i
\(759\) 0 0
\(760\) −1220.25 + 2113.53i −0.0582408 + 0.100876i
\(761\) −7759.63 + 13440.1i −0.369627 + 0.640214i −0.989507 0.144483i \(-0.953848\pi\)
0.619880 + 0.784697i \(0.287181\pi\)
\(762\) 0 0
\(763\) 2576.44 4462.52i 0.122246 0.211735i
\(764\) −2185.31 3785.07i −0.103484 0.179240i
\(765\) 0 0
\(766\) −4319.82 −0.203761
\(767\) −20931.1 + 8771.02i −0.985368 + 0.412912i
\(768\) 0 0
\(769\) −6442.59 11158.9i −0.302114 0.523277i 0.674501 0.738274i \(-0.264359\pi\)
−0.976615 + 0.214997i \(0.931026\pi\)
\(770\) −11681.6 20233.2i −0.546723 0.946952i
\(771\) 0 0
\(772\) −24642.4 −1.14883
\(773\) 2946.02 5102.66i 0.137078 0.237425i −0.789312 0.613993i \(-0.789562\pi\)
0.926389 + 0.376567i \(0.122896\pi\)
\(774\) 0 0
\(775\) 27713.0 1.28449
\(776\) 2169.06 3756.92i 0.100341 0.173796i
\(777\) 0 0
\(778\) −9231.69 15989.8i −0.425414 0.736839i
\(779\) −69.0916 −0.00317775
\(780\) 0 0
\(781\) 13374.3 0.612766
\(782\) 12026.4 + 20830.2i 0.549951 + 0.952542i
\(783\) 0 0
\(784\) 23607.8 40889.8i 1.07543 1.86269i