Properties

Label 588.4.i.b.361.1
Level $588$
Weight $4$
Character 588.361
Analytic conductor $34.693$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 588.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(34.6931230834\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 588.361
Dual form 588.4.i.b.373.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 + 2.59808i) q^{3} +(2.00000 + 3.46410i) q^{5} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(-1.50000 + 2.59808i) q^{3} +(2.00000 + 3.46410i) q^{5} +(-4.50000 - 7.79423i) q^{9} +(10.0000 - 17.3205i) q^{11} +4.00000 q^{13} -12.0000 q^{15} +(12.0000 - 20.7846i) q^{17} +(22.0000 + 38.1051i) q^{19} +(-36.0000 - 62.3538i) q^{23} +(54.5000 - 94.3968i) q^{25} +27.0000 q^{27} -38.0000 q^{29} +(92.0000 - 159.349i) q^{31} +(30.0000 + 51.9615i) q^{33} +(15.0000 + 25.9808i) q^{37} +(-6.00000 + 10.3923i) q^{39} +216.000 q^{41} -164.000 q^{43} +(18.0000 - 31.1769i) q^{45} +(260.000 + 450.333i) q^{47} +(36.0000 + 62.3538i) q^{51} +(73.0000 - 126.440i) q^{53} +80.0000 q^{55} -132.000 q^{57} +(230.000 - 398.372i) q^{59} +(314.000 + 543.864i) q^{61} +(8.00000 + 13.8564i) q^{65} +(-278.000 + 481.510i) q^{67} +216.000 q^{69} +592.000 q^{71} +(512.000 - 886.810i) q^{73} +(163.500 + 283.190i) q^{75} +(52.0000 + 90.0666i) q^{79} +(-40.5000 + 70.1481i) q^{81} +324.000 q^{83} +96.0000 q^{85} +(57.0000 - 98.7269i) q^{87} +(448.000 + 775.959i) q^{89} +(276.000 + 478.046i) q^{93} +(-88.0000 + 152.420i) q^{95} +920.000 q^{97} -180.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 3q^{3} + 4q^{5} - 9q^{9} + O(q^{10}) \) \( 2q - 3q^{3} + 4q^{5} - 9q^{9} + 20q^{11} + 8q^{13} - 24q^{15} + 24q^{17} + 44q^{19} - 72q^{23} + 109q^{25} + 54q^{27} - 76q^{29} + 184q^{31} + 60q^{33} + 30q^{37} - 12q^{39} + 432q^{41} - 328q^{43} + 36q^{45} + 520q^{47} + 72q^{51} + 146q^{53} + 160q^{55} - 264q^{57} + 460q^{59} + 628q^{61} + 16q^{65} - 556q^{67} + 432q^{69} + 1184q^{71} + 1024q^{73} + 327q^{75} + 104q^{79} - 81q^{81} + 648q^{83} + 192q^{85} + 114q^{87} + 896q^{89} + 552q^{93} - 176q^{95} + 1840q^{97} - 360q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(493\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.50000 + 2.59808i −0.288675 + 0.500000i
\(4\) 0 0
\(5\) 2.00000 + 3.46410i 0.178885 + 0.309839i 0.941499 0.337016i \(-0.109418\pi\)
−0.762614 + 0.646854i \(0.776084\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) 0 0
\(11\) 10.0000 17.3205i 0.274101 0.474757i −0.695807 0.718229i \(-0.744953\pi\)
0.969908 + 0.243472i \(0.0782863\pi\)
\(12\) 0 0
\(13\) 4.00000 0.0853385 0.0426692 0.999089i \(-0.486414\pi\)
0.0426692 + 0.999089i \(0.486414\pi\)
\(14\) 0 0
\(15\) −12.0000 −0.206559
\(16\) 0 0
\(17\) 12.0000 20.7846i 0.171202 0.296530i −0.767639 0.640883i \(-0.778568\pi\)
0.938840 + 0.344353i \(0.111902\pi\)
\(18\) 0 0
\(19\) 22.0000 + 38.1051i 0.265639 + 0.460101i 0.967731 0.251986i \(-0.0810837\pi\)
−0.702092 + 0.712087i \(0.747750\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −36.0000 62.3538i −0.326370 0.565290i 0.655418 0.755266i \(-0.272492\pi\)
−0.981789 + 0.189976i \(0.939159\pi\)
\(24\) 0 0
\(25\) 54.5000 94.3968i 0.436000 0.755174i
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) −38.0000 −0.243325 −0.121662 0.992572i \(-0.538823\pi\)
−0.121662 + 0.992572i \(0.538823\pi\)
\(30\) 0 0
\(31\) 92.0000 159.349i 0.533022 0.923222i −0.466234 0.884661i \(-0.654390\pi\)
0.999256 0.0385601i \(-0.0122771\pi\)
\(32\) 0 0
\(33\) 30.0000 + 51.9615i 0.158252 + 0.274101i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 15.0000 + 25.9808i 0.0666482 + 0.115438i 0.897424 0.441169i \(-0.145436\pi\)
−0.830776 + 0.556607i \(0.812103\pi\)
\(38\) 0 0
\(39\) −6.00000 + 10.3923i −0.0246351 + 0.0426692i
\(40\) 0 0
\(41\) 216.000 0.822769 0.411385 0.911462i \(-0.365045\pi\)
0.411385 + 0.911462i \(0.365045\pi\)
\(42\) 0 0
\(43\) −164.000 −0.581622 −0.290811 0.956780i \(-0.593925\pi\)
−0.290811 + 0.956780i \(0.593925\pi\)
\(44\) 0 0
\(45\) 18.0000 31.1769i 0.0596285 0.103280i
\(46\) 0 0
\(47\) 260.000 + 450.333i 0.806913 + 1.39761i 0.914992 + 0.403472i \(0.132197\pi\)
−0.108079 + 0.994142i \(0.534470\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 36.0000 + 62.3538i 0.0988433 + 0.171202i
\(52\) 0 0
\(53\) 73.0000 126.440i 0.189195 0.327695i −0.755787 0.654817i \(-0.772746\pi\)
0.944982 + 0.327122i \(0.106079\pi\)
\(54\) 0 0
\(55\) 80.0000 0.196131
\(56\) 0 0
\(57\) −132.000 −0.306734
\(58\) 0 0
\(59\) 230.000 398.372i 0.507516 0.879044i −0.492446 0.870343i \(-0.663897\pi\)
0.999962 0.00870069i \(-0.00276955\pi\)
\(60\) 0 0
\(61\) 314.000 + 543.864i 0.659075 + 1.14155i 0.980855 + 0.194737i \(0.0623854\pi\)
−0.321780 + 0.946814i \(0.604281\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 8.00000 + 13.8564i 0.0152658 + 0.0264412i
\(66\) 0 0
\(67\) −278.000 + 481.510i −0.506912 + 0.877997i 0.493056 + 0.869998i \(0.335880\pi\)
−0.999968 + 0.00799979i \(0.997454\pi\)
\(68\) 0 0
\(69\) 216.000 0.376860
\(70\) 0 0
\(71\) 592.000 0.989542 0.494771 0.869023i \(-0.335252\pi\)
0.494771 + 0.869023i \(0.335252\pi\)
\(72\) 0 0
\(73\) 512.000 886.810i 0.820891 1.42183i −0.0841280 0.996455i \(-0.526810\pi\)
0.905019 0.425371i \(-0.139856\pi\)
\(74\) 0 0
\(75\) 163.500 + 283.190i 0.251725 + 0.436000i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 52.0000 + 90.0666i 0.0740564 + 0.128269i 0.900676 0.434492i \(-0.143072\pi\)
−0.826619 + 0.562762i \(0.809739\pi\)
\(80\) 0 0
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 324.000 0.428477 0.214239 0.976781i \(-0.431273\pi\)
0.214239 + 0.976781i \(0.431273\pi\)
\(84\) 0 0
\(85\) 96.0000 0.122502
\(86\) 0 0
\(87\) 57.0000 98.7269i 0.0702419 0.121662i
\(88\) 0 0
\(89\) 448.000 + 775.959i 0.533572 + 0.924174i 0.999231 + 0.0392095i \(0.0124840\pi\)
−0.465659 + 0.884964i \(0.654183\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 276.000 + 478.046i 0.307741 + 0.533022i
\(94\) 0 0
\(95\) −88.0000 + 152.420i −0.0950380 + 0.164611i
\(96\) 0 0
\(97\) 920.000 0.963009 0.481504 0.876444i \(-0.340091\pi\)
0.481504 + 0.876444i \(0.340091\pi\)
\(98\) 0 0
\(99\) −180.000 −0.182734
\(100\) 0 0
\(101\) 554.000 959.556i 0.545793 0.945341i −0.452764 0.891630i \(-0.649562\pi\)
0.998557 0.0537102i \(-0.0171047\pi\)
\(102\) 0 0
\(103\) 724.000 + 1254.00i 0.692600 + 1.19962i 0.970983 + 0.239149i \(0.0768684\pi\)
−0.278383 + 0.960470i \(0.589798\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −658.000 1139.69i −0.594498 1.02970i −0.993618 0.112802i \(-0.964018\pi\)
0.399120 0.916899i \(-0.369316\pi\)
\(108\) 0 0
\(109\) 43.0000 74.4782i 0.0377858 0.0654469i −0.846514 0.532366i \(-0.821303\pi\)
0.884300 + 0.466919i \(0.154636\pi\)
\(110\) 0 0
\(111\) −90.0000 −0.0769588
\(112\) 0 0
\(113\) 1778.00 1.48018 0.740089 0.672509i \(-0.234783\pi\)
0.740089 + 0.672509i \(0.234783\pi\)
\(114\) 0 0
\(115\) 144.000 249.415i 0.116766 0.202244i
\(116\) 0 0
\(117\) −18.0000 31.1769i −0.0142231 0.0246351i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 465.500 + 806.270i 0.349737 + 0.605762i
\(122\) 0 0
\(123\) −324.000 + 561.184i −0.237513 + 0.411385i
\(124\) 0 0
\(125\) 936.000 0.669747
\(126\) 0 0
\(127\) −928.000 −0.648399 −0.324200 0.945989i \(-0.605095\pi\)
−0.324200 + 0.945989i \(0.605095\pi\)
\(128\) 0 0
\(129\) 246.000 426.084i 0.167900 0.290811i
\(130\) 0 0
\(131\) 702.000 + 1215.90i 0.468199 + 0.810944i 0.999339 0.0363397i \(-0.0115698\pi\)
−0.531141 + 0.847284i \(0.678236\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 54.0000 + 93.5307i 0.0344265 + 0.0596285i
\(136\) 0 0
\(137\) 685.000 1186.45i 0.427179 0.739895i −0.569442 0.822031i \(-0.692841\pi\)
0.996621 + 0.0821359i \(0.0261741\pi\)
\(138\) 0 0
\(139\) −516.000 −0.314867 −0.157434 0.987530i \(-0.550322\pi\)
−0.157434 + 0.987530i \(0.550322\pi\)
\(140\) 0 0
\(141\) −1560.00 −0.931743
\(142\) 0 0
\(143\) 40.0000 69.2820i 0.0233914 0.0405151i
\(144\) 0 0
\(145\) −76.0000 131.636i −0.0435273 0.0753915i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −695.000 1203.78i −0.382125 0.661860i 0.609241 0.792985i \(-0.291474\pi\)
−0.991366 + 0.131125i \(0.958141\pi\)
\(150\) 0 0
\(151\) −68.0000 + 117.779i −0.0366474 + 0.0634752i −0.883767 0.467927i \(-0.845001\pi\)
0.847120 + 0.531402i \(0.178335\pi\)
\(152\) 0 0
\(153\) −216.000 −0.114134
\(154\) 0 0
\(155\) 736.000 0.381400
\(156\) 0 0
\(157\) −74.0000 + 128.172i −0.0376168 + 0.0651543i −0.884221 0.467069i \(-0.845310\pi\)
0.846604 + 0.532223i \(0.178643\pi\)
\(158\) 0 0
\(159\) 219.000 + 379.319i 0.109232 + 0.189195i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 606.000 + 1049.62i 0.291200 + 0.504373i 0.974094 0.226145i \(-0.0726122\pi\)
−0.682894 + 0.730518i \(0.739279\pi\)
\(164\) 0 0
\(165\) −120.000 + 207.846i −0.0566181 + 0.0980654i
\(166\) 0 0
\(167\) −1976.00 −0.915614 −0.457807 0.889052i \(-0.651365\pi\)
−0.457807 + 0.889052i \(0.651365\pi\)
\(168\) 0 0
\(169\) −2181.00 −0.992717
\(170\) 0 0
\(171\) 198.000 342.946i 0.0885464 0.153367i
\(172\) 0 0
\(173\) −1346.00 2331.34i −0.591529 1.02456i −0.994027 0.109137i \(-0.965191\pi\)
0.402498 0.915421i \(-0.368142\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 690.000 + 1195.12i 0.293015 + 0.507516i
\(178\) 0 0
\(179\) 1290.00 2234.35i 0.538654 0.932977i −0.460322 0.887752i \(-0.652266\pi\)
0.998977 0.0452249i \(-0.0144004\pi\)
\(180\) 0 0
\(181\) 2036.00 0.836103 0.418052 0.908423i \(-0.362713\pi\)
0.418052 + 0.908423i \(0.362713\pi\)
\(182\) 0 0
\(183\) −1884.00 −0.761034
\(184\) 0 0
\(185\) −60.0000 + 103.923i −0.0238448 + 0.0413004i
\(186\) 0 0
\(187\) −240.000 415.692i −0.0938531 0.162558i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1980.00 3429.46i −0.750093 1.29920i −0.947777 0.318933i \(-0.896675\pi\)
0.197684 0.980266i \(-0.436658\pi\)
\(192\) 0 0
\(193\) −1.00000 + 1.73205i −0.000372962 + 0.000645988i −0.866212 0.499677i \(-0.833452\pi\)
0.865839 + 0.500323i \(0.166785\pi\)
\(194\) 0 0
\(195\) −48.0000 −0.0176274
\(196\) 0 0
\(197\) 3774.00 1.36491 0.682453 0.730930i \(-0.260913\pi\)
0.682453 + 0.730930i \(0.260913\pi\)
\(198\) 0 0
\(199\) −1780.00 + 3083.05i −0.634075 + 1.09825i 0.352636 + 0.935761i \(0.385285\pi\)
−0.986710 + 0.162489i \(0.948048\pi\)
\(200\) 0 0
\(201\) −834.000 1444.53i −0.292666 0.506912i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 432.000 + 748.246i 0.147181 + 0.254926i
\(206\) 0 0
\(207\) −324.000 + 561.184i −0.108790 + 0.188430i
\(208\) 0 0
\(209\) 880.000 0.291248
\(210\) 0 0
\(211\) −2692.00 −0.878317 −0.439159 0.898410i \(-0.644723\pi\)
−0.439159 + 0.898410i \(0.644723\pi\)
\(212\) 0 0
\(213\) −888.000 + 1538.06i −0.285656 + 0.494771i
\(214\) 0 0
\(215\) −328.000 568.113i −0.104044 0.180209i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 1536.00 + 2660.43i 0.473942 + 0.820891i
\(220\) 0 0
\(221\) 48.0000 83.1384i 0.0146101 0.0253054i
\(222\) 0 0
\(223\) −4528.00 −1.35972 −0.679859 0.733342i \(-0.737959\pi\)
−0.679859 + 0.733342i \(0.737959\pi\)
\(224\) 0 0
\(225\) −981.000 −0.290667
\(226\) 0 0
\(227\) −1826.00 + 3162.72i −0.533903 + 0.924746i 0.465313 + 0.885146i \(0.345942\pi\)
−0.999216 + 0.0396002i \(0.987392\pi\)
\(228\) 0 0
\(229\) −2402.00 4160.39i −0.693138 1.20055i −0.970804 0.239873i \(-0.922894\pi\)
0.277666 0.960678i \(-0.410439\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1379.00 2388.50i −0.387731 0.671570i 0.604413 0.796671i \(-0.293408\pi\)
−0.992144 + 0.125102i \(0.960074\pi\)
\(234\) 0 0
\(235\) −1040.00 + 1801.33i −0.288690 + 0.500026i
\(236\) 0 0
\(237\) −312.000 −0.0855130
\(238\) 0 0
\(239\) 6528.00 1.76678 0.883392 0.468635i \(-0.155254\pi\)
0.883392 + 0.468635i \(0.155254\pi\)
\(240\) 0 0
\(241\) −28.0000 + 48.4974i −0.00748398 + 0.0129626i −0.869743 0.493505i \(-0.835716\pi\)
0.862259 + 0.506467i \(0.169049\pi\)
\(242\) 0 0
\(243\) −121.500 210.444i −0.0320750 0.0555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 88.0000 + 152.420i 0.0226693 + 0.0392643i
\(248\) 0 0
\(249\) −486.000 + 841.777i −0.123691 + 0.214239i
\(250\) 0 0
\(251\) −4900.00 −1.23221 −0.616106 0.787663i \(-0.711291\pi\)
−0.616106 + 0.787663i \(0.711291\pi\)
\(252\) 0 0
\(253\) −1440.00 −0.357834
\(254\) 0 0
\(255\) −144.000 + 249.415i −0.0353633 + 0.0612510i
\(256\) 0 0
\(257\) −3392.00 5875.12i −0.823296 1.42599i −0.903214 0.429190i \(-0.858799\pi\)
0.0799181 0.996801i \(-0.474534\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 171.000 + 296.181i 0.0405542 + 0.0702419i
\(262\) 0 0
\(263\) 2272.00 3935.22i 0.532690 0.922646i −0.466581 0.884478i \(-0.654514\pi\)
0.999271 0.0381681i \(-0.0121522\pi\)
\(264\) 0 0
\(265\) 584.000 0.135377
\(266\) 0 0
\(267\) −2688.00 −0.616116
\(268\) 0 0
\(269\) −2026.00 + 3509.13i −0.459210 + 0.795374i −0.998919 0.0464767i \(-0.985201\pi\)
0.539710 + 0.841851i \(0.318534\pi\)
\(270\) 0 0
\(271\) −1376.00 2383.30i −0.308436 0.534226i 0.669585 0.742736i \(-0.266472\pi\)
−0.978020 + 0.208510i \(0.933139\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1090.00 1887.94i −0.239016 0.413988i
\(276\) 0 0
\(277\) −2183.00 + 3781.07i −0.473515 + 0.820153i −0.999540 0.0303164i \(-0.990348\pi\)
0.526025 + 0.850469i \(0.323682\pi\)
\(278\) 0 0
\(279\) −1656.00 −0.355348
\(280\) 0 0
\(281\) 7734.00 1.64189 0.820946 0.571006i \(-0.193447\pi\)
0.820946 + 0.571006i \(0.193447\pi\)
\(282\) 0 0
\(283\) −2026.00 + 3509.13i −0.425559 + 0.737090i −0.996472 0.0839204i \(-0.973256\pi\)
0.570913 + 0.821010i \(0.306589\pi\)
\(284\) 0 0
\(285\) −264.000 457.261i −0.0548702 0.0950380i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 2168.50 + 3755.95i 0.441380 + 0.764493i
\(290\) 0 0
\(291\) −1380.00 + 2390.23i −0.277997 + 0.481504i
\(292\) 0 0
\(293\) 3420.00 0.681906 0.340953 0.940080i \(-0.389250\pi\)
0.340953 + 0.940080i \(0.389250\pi\)
\(294\) 0 0
\(295\) 1840.00 0.363149
\(296\) 0 0
\(297\) 270.000 467.654i 0.0527508 0.0913671i
\(298\) 0 0
\(299\) −144.000 249.415i −0.0278520 0.0482410i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 1662.00 + 2878.67i 0.315114 + 0.545793i
\(304\) 0 0
\(305\) −1256.00 + 2175.46i −0.235798 + 0.408414i
\(306\) 0 0
\(307\) −7324.00 −1.36157 −0.680786 0.732482i \(-0.738362\pi\)
−0.680786 + 0.732482i \(0.738362\pi\)
\(308\) 0 0
\(309\) −4344.00 −0.799746
\(310\) 0 0
\(311\) −2096.00 + 3630.38i −0.382165 + 0.661929i −0.991371 0.131083i \(-0.958155\pi\)
0.609207 + 0.793012i \(0.291488\pi\)
\(312\) 0 0
\(313\) −3420.00 5923.61i −0.617603 1.06972i −0.989922 0.141615i \(-0.954770\pi\)
0.372318 0.928105i \(-0.378563\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3315.00 5741.75i −0.587347 1.01731i −0.994578 0.103990i \(-0.966839\pi\)
0.407232 0.913325i \(-0.366494\pi\)
\(318\) 0 0
\(319\) −380.000 + 658.179i −0.0666957 + 0.115520i
\(320\) 0 0
\(321\) 3948.00 0.686467
\(322\) 0 0
\(323\) 1056.00 0.181911
\(324\) 0 0
\(325\) 218.000 377.587i 0.0372076 0.0644454i
\(326\) 0 0
\(327\) 129.000 + 223.435i 0.0218156 + 0.0377858i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 3434.00 + 5947.86i 0.570241 + 0.987686i 0.996541 + 0.0831042i \(0.0264834\pi\)
−0.426300 + 0.904582i \(0.640183\pi\)
\(332\) 0 0
\(333\) 135.000 233.827i 0.0222161 0.0384794i
\(334\) 0 0
\(335\) −2224.00 −0.362717
\(336\) 0 0
\(337\) −7378.00 −1.19260 −0.596299 0.802763i \(-0.703363\pi\)
−0.596299 + 0.802763i \(0.703363\pi\)
\(338\) 0 0
\(339\) −2667.00 + 4619.38i −0.427291 + 0.740089i
\(340\) 0 0
\(341\) −1840.00 3186.97i −0.292204 0.506112i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 432.000 + 748.246i 0.0674148 + 0.116766i
\(346\) 0 0
\(347\) 1338.00 2317.48i 0.206996 0.358528i −0.743771 0.668435i \(-0.766965\pi\)
0.950767 + 0.309907i \(0.100298\pi\)
\(348\) 0 0
\(349\) 5124.00 0.785907 0.392953 0.919558i \(-0.371453\pi\)
0.392953 + 0.919558i \(0.371453\pi\)
\(350\) 0 0
\(351\) 108.000 0.0164234
\(352\) 0 0
\(353\) 2280.00 3949.08i 0.343774 0.595434i −0.641356 0.767243i \(-0.721628\pi\)
0.985130 + 0.171809i \(0.0549613\pi\)
\(354\) 0 0
\(355\) 1184.00 + 2050.75i 0.177015 + 0.306598i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1828.00 3166.19i −0.268741 0.465474i 0.699796 0.714343i \(-0.253274\pi\)
−0.968537 + 0.248869i \(0.919941\pi\)
\(360\) 0 0
\(361\) 2461.50 4263.44i 0.358872 0.621584i
\(362\) 0 0
\(363\) −2793.00 −0.403842
\(364\) 0 0
\(365\) 4096.00 0.587382
\(366\) 0 0
\(367\) −808.000 + 1399.50i −0.114924 + 0.199055i −0.917750 0.397160i \(-0.869996\pi\)
0.802825 + 0.596215i \(0.203329\pi\)
\(368\) 0 0
\(369\) −972.000 1683.55i −0.137128 0.237513i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −1367.00 2367.71i −0.189760 0.328674i 0.755410 0.655252i \(-0.227438\pi\)
−0.945170 + 0.326578i \(0.894104\pi\)
\(374\) 0 0
\(375\) −1404.00 + 2431.80i −0.193339 + 0.334874i
\(376\) 0 0
\(377\) −152.000 −0.0207650
\(378\) 0 0
\(379\) −1380.00 −0.187034 −0.0935169 0.995618i \(-0.529811\pi\)
−0.0935169 + 0.995618i \(0.529811\pi\)
\(380\) 0 0
\(381\) 1392.00 2411.01i 0.187177 0.324200i
\(382\) 0 0
\(383\) 3444.00 + 5965.18i 0.459478 + 0.795840i 0.998933 0.0461746i \(-0.0147031\pi\)
−0.539455 + 0.842014i \(0.681370\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 738.000 + 1278.25i 0.0969371 + 0.167900i
\(388\) 0 0
\(389\) 1023.00 1771.89i 0.133337 0.230947i −0.791624 0.611009i \(-0.790764\pi\)
0.924961 + 0.380062i \(0.124097\pi\)
\(390\) 0 0
\(391\) −1728.00 −0.223501
\(392\) 0 0
\(393\) −4212.00 −0.540629
\(394\) 0 0
\(395\) −208.000 + 360.267i −0.0264952 + 0.0458911i
\(396\) 0 0
\(397\) 1558.00 + 2698.54i 0.196962 + 0.341148i 0.947542 0.319632i \(-0.103559\pi\)
−0.750580 + 0.660779i \(0.770226\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1479.00 2561.70i −0.184184 0.319016i 0.759117 0.650954i \(-0.225631\pi\)
−0.943301 + 0.331938i \(0.892298\pi\)
\(402\) 0 0
\(403\) 368.000 637.395i 0.0454873 0.0787863i
\(404\) 0 0
\(405\) −324.000 −0.0397523
\(406\) 0 0
\(407\) 600.000 0.0730735
\(408\) 0 0
\(409\) 3972.00 6879.71i 0.480202 0.831735i −0.519540 0.854446i \(-0.673897\pi\)
0.999742 + 0.0227114i \(0.00722990\pi\)
\(410\) 0 0
\(411\) 2055.00 + 3559.36i 0.246632 + 0.427179i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 648.000 + 1122.37i 0.0766484 + 0.132759i
\(416\) 0 0
\(417\) 774.000 1340.61i 0.0908943 0.157434i
\(418\) 0 0
\(419\) −4084.00 −0.476173 −0.238086 0.971244i \(-0.576520\pi\)
−0.238086 + 0.971244i \(0.576520\pi\)
\(420\) 0 0
\(421\) −6306.00 −0.730013 −0.365007 0.931005i \(-0.618933\pi\)
−0.365007 + 0.931005i \(0.618933\pi\)
\(422\) 0 0
\(423\) 2340.00 4053.00i 0.268971 0.465871i
\(424\) 0 0
\(425\) −1308.00 2265.52i −0.149288 0.258574i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 120.000 + 207.846i 0.0135050 + 0.0233914i
\(430\) 0 0
\(431\) 5912.00 10239.9i 0.660722 1.14440i −0.319705 0.947517i \(-0.603584\pi\)
0.980426 0.196886i \(-0.0630830\pi\)
\(432\) 0 0
\(433\) 4504.00 0.499881 0.249940 0.968261i \(-0.419589\pi\)
0.249940 + 0.968261i \(0.419589\pi\)
\(434\) 0 0
\(435\) 456.000 0.0502610
\(436\) 0 0
\(437\) 1584.00 2743.57i 0.173394 0.300326i
\(438\) 0 0
\(439\) 6528.00 + 11306.8i 0.709714 + 1.22926i 0.964963 + 0.262385i \(0.0845092\pi\)
−0.255249 + 0.966875i \(0.582158\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −66.0000 114.315i −0.00707845 0.0122602i 0.862464 0.506118i \(-0.168920\pi\)
−0.869543 + 0.493857i \(0.835586\pi\)
\(444\) 0 0
\(445\) −1792.00 + 3103.84i −0.190897 + 0.330642i
\(446\) 0 0
\(447\) 4170.00 0.441240
\(448\) 0 0
\(449\) 4866.00 0.511449 0.255725 0.966750i \(-0.417686\pi\)
0.255725 + 0.966750i \(0.417686\pi\)
\(450\) 0 0
\(451\) 2160.00 3741.23i 0.225522 0.390616i
\(452\) 0 0
\(453\) −204.000 353.338i −0.0211584 0.0366474i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −5053.00 8752.05i −0.517220 0.895851i −0.999800 0.0199990i \(-0.993634\pi\)
0.482580 0.875852i \(-0.339700\pi\)
\(458\) 0 0
\(459\) 324.000 561.184i 0.0329478 0.0570672i
\(460\) 0 0
\(461\) 18036.0 1.82217 0.911085 0.412219i \(-0.135246\pi\)
0.911085 + 0.412219i \(0.135246\pi\)
\(462\) 0 0
\(463\) 5288.00 0.530787 0.265393 0.964140i \(-0.414498\pi\)
0.265393 + 0.964140i \(0.414498\pi\)
\(464\) 0 0
\(465\) −1104.00 + 1912.18i −0.110101 + 0.190700i
\(466\) 0 0
\(467\) 7582.00 + 13132.4i 0.751291 + 1.30128i 0.947197 + 0.320652i \(0.103902\pi\)
−0.195906 + 0.980623i \(0.562765\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −222.000 384.515i −0.0217181 0.0376168i
\(472\) 0 0
\(473\) −1640.00 + 2840.56i −0.159423 + 0.276129i
\(474\) 0 0
\(475\) 4796.00 0.463275
\(476\) 0 0
\(477\) −1314.00 −0.126130
\(478\) 0 0
\(479\) 3948.00 6838.14i 0.376594 0.652281i −0.613970 0.789329i \(-0.710428\pi\)
0.990564 + 0.137049i \(0.0437617\pi\)
\(480\) 0 0
\(481\) 60.0000 + 103.923i 0.00568766 + 0.00985132i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1840.00 + 3186.97i 0.172268 + 0.298377i
\(486\) 0 0
\(487\) −1460.00 + 2528.79i −0.135850 + 0.235299i −0.925922 0.377715i \(-0.876710\pi\)
0.790072 + 0.613014i \(0.210043\pi\)
\(488\) 0 0
\(489\) −3636.00 −0.336249
\(490\) 0 0
\(491\) −7932.00 −0.729055 −0.364528 0.931193i \(-0.618770\pi\)
−0.364528 + 0.931193i \(0.618770\pi\)
\(492\) 0 0
\(493\) −456.000 + 789.815i −0.0416576 + 0.0721531i
\(494\) 0 0
\(495\) −360.000 623.538i −0.0326885 0.0566181i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 1002.00 + 1735.51i 0.0898911 + 0.155696i 0.907465 0.420128i \(-0.138015\pi\)
−0.817574 + 0.575824i \(0.804681\pi\)
\(500\) 0 0
\(501\) 2964.00 5133.80i 0.264315 0.457807i
\(502\) 0 0
\(503\) −4496.00 −0.398542 −0.199271 0.979944i \(-0.563857\pi\)
−0.199271 + 0.979944i \(0.563857\pi\)
\(504\) 0 0
\(505\) 4432.00 0.390537
\(506\) 0 0
\(507\) 3271.50 5666.40i 0.286573 0.496359i
\(508\) 0 0
\(509\) 6310.00 + 10929.2i 0.549481 + 0.951729i 0.998310 + 0.0581114i \(0.0185079\pi\)
−0.448829 + 0.893618i \(0.648159\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 594.000 + 1028.84i 0.0511223 + 0.0885464i
\(514\) 0 0
\(515\) −2896.00 + 5016.02i −0.247792 + 0.429189i
\(516\) 0 0
\(517\) 10400.0 0.884703
\(518\) 0 0
\(519\) 8076.00 0.683039
\(520\) 0 0
\(521\) 9004.00 15595.4i 0.757145 1.31141i −0.187156 0.982330i \(-0.559927\pi\)
0.944301 0.329083i \(-0.106740\pi\)
\(522\) 0 0
\(523\) 6646.00 + 11511.2i 0.555658 + 0.962428i 0.997852 + 0.0655088i \(0.0208670\pi\)
−0.442194 + 0.896920i \(0.645800\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2208.00 3824.37i −0.182509 0.316114i
\(528\) 0 0
\(529\) 3491.50 6047.46i 0.286965 0.497038i
\(530\) 0 0
\(531\) −4140.00 −0.338344
\(532\) 0 0
\(533\) 864.000 0.0702139
\(534\) 0 0
\(535\) 2632.00 4558.76i 0.212694 0.368397i
\(536\) 0 0
\(537\) 3870.00 + 6703.04i 0.310992 + 0.538654i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 4285.00 + 7421.84i 0.340530 + 0.589815i 0.984531 0.175210i \(-0.0560603\pi\)
−0.644002 + 0.765024i \(0.722727\pi\)
\(542\) 0 0
\(543\) −3054.00 + 5289.68i −0.241362 + 0.418052i
\(544\) 0 0
\(545\) 344.000 0.0270373
\(546\) 0 0
\(547\) −1916.00 −0.149766 −0.0748832 0.997192i \(-0.523858\pi\)
−0.0748832 + 0.997192i \(0.523858\pi\)
\(548\) 0 0
\(549\) 2826.00 4894.78i 0.219692 0.380517i
\(550\) 0 0
\(551\) −836.000 1447.99i −0.0646367 0.111954i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −180.000 311.769i −0.0137668 0.0238448i
\(556\) 0 0
\(557\) −9963.00 + 17256.4i −0.757892 + 1.31271i 0.186032 + 0.982544i \(0.440437\pi\)
−0.943924 + 0.330164i \(0.892896\pi\)
\(558\) 0 0
\(559\) −656.000 −0.0496348
\(560\) 0 0
\(561\) 1440.00 0.108372
\(562\) 0 0
\(563\) 2122.00 3675.41i 0.158848 0.275133i −0.775605 0.631218i \(-0.782555\pi\)
0.934454 + 0.356085i \(0.115889\pi\)
\(564\) 0 0
\(565\) 3556.00 + 6159.17i 0.264782 + 0.458617i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 11397.0 + 19740.2i 0.839696 + 1.45440i 0.890149 + 0.455670i \(0.150600\pi\)
−0.0504527 + 0.998726i \(0.516066\pi\)
\(570\) 0 0
\(571\) −7014.00 + 12148.6i −0.514057 + 0.890374i 0.485810 + 0.874065i \(0.338525\pi\)
−0.999867 + 0.0163089i \(0.994809\pi\)
\(572\) 0 0
\(573\) 11880.0 0.866133
\(574\) 0 0
\(575\) −7848.00 −0.569190
\(576\) 0 0
\(577\) 4184.00 7246.90i 0.301876 0.522864i −0.674685 0.738106i \(-0.735721\pi\)
0.976561 + 0.215242i \(0.0690540\pi\)
\(578\) 0 0
\(579\) −3.00000 5.19615i −0.000215329 0.000372962i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −1460.00 2528.79i −0.103717 0.179643i
\(584\) 0 0
\(585\) 72.0000 124.708i 0.00508860 0.00881372i
\(586\) 0 0
\(587\) −52.0000 −0.00365634 −0.00182817 0.999998i \(-0.500582\pi\)
−0.00182817 + 0.999998i \(0.500582\pi\)
\(588\) 0 0
\(589\) 8096.00 0.566366
\(590\) 0 0
\(591\) −5661.00 + 9805.14i −0.394014 + 0.682453i
\(592\) 0 0
\(593\) 2904.00 + 5029.88i 0.201101 + 0.348317i 0.948883 0.315627i \(-0.102215\pi\)
−0.747782 + 0.663944i \(0.768881\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −5340.00 9249.15i −0.366083 0.634075i
\(598\) 0 0
\(599\) 5232.00 9062.09i 0.356884 0.618142i −0.630554 0.776145i \(-0.717172\pi\)
0.987439 + 0.158003i \(0.0505057\pi\)
\(600\) 0 0
\(601\) −1184.00 −0.0803600 −0.0401800 0.999192i \(-0.512793\pi\)
−0.0401800 + 0.999192i \(0.512793\pi\)
\(602\) 0 0
\(603\) 5004.00 0.337941
\(604\) 0 0
\(605\) −1862.00 + 3225.08i −0.125126 + 0.216724i
\(606\) 0 0
\(607\) 6576.00 + 11390.0i 0.439723 + 0.761622i 0.997668 0.0682559i \(-0.0217434\pi\)
−0.557945 + 0.829878i \(0.688410\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1040.00 + 1801.33i 0.0688607 + 0.119270i
\(612\) 0 0
\(613\) 9167.00 15877.7i 0.603999 1.04616i −0.388209 0.921571i \(-0.626906\pi\)
0.992209 0.124586i \(-0.0397604\pi\)
\(614\) 0 0
\(615\) −2592.00 −0.169950
\(616\) 0 0
\(617\) −8122.00 −0.529950 −0.264975 0.964255i \(-0.585364\pi\)
−0.264975 + 0.964255i \(0.585364\pi\)
\(618\) 0 0
\(619\) 2990.00 5178.83i 0.194149 0.336276i −0.752472 0.658624i \(-0.771139\pi\)
0.946621 + 0.322348i \(0.104472\pi\)
\(620\) 0 0
\(621\) −972.000 1683.55i −0.0628100 0.108790i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −4940.50 8557.20i −0.316192 0.547661i
\(626\) 0 0
\(627\) −1320.00 + 2286.31i −0.0840761 + 0.145624i
\(628\) 0 0
\(629\) 720.000 0.0456411
\(630\) 0 0
\(631\) 12528.0 0.790383 0.395192 0.918599i \(-0.370678\pi\)
0.395192 + 0.918599i \(0.370678\pi\)
\(632\) 0 0
\(633\) 4038.00 6994.02i 0.253548 0.439159i
\(634\) 0 0
\(635\) −1856.00 3214.69i −0.115989 0.200899i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −2664.00 4614.18i −0.164924 0.285656i
\(640\) 0 0
\(641\) −10399.0 + 18011.6i −0.640773 + 1.10985i 0.344487 + 0.938791i \(0.388053\pi\)
−0.985260 + 0.171061i \(0.945280\pi\)
\(642\) 0 0
\(643\) 1932.00 0.118492 0.0592462 0.998243i \(-0.481130\pi\)
0.0592462 + 0.998243i \(0.481130\pi\)
\(644\) 0 0
\(645\) 1968.00 0.120139
\(646\) 0 0
\(647\) −4212.00 + 7295.40i −0.255936 + 0.443295i −0.965149 0.261699i \(-0.915717\pi\)
0.709213 + 0.704994i \(0.249050\pi\)
\(648\) 0 0
\(649\) −4600.00 7967.43i −0.278222 0.481894i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 8875.00 + 15372.0i 0.531862 + 0.921211i 0.999308 + 0.0371899i \(0.0118407\pi\)
−0.467447 + 0.884021i \(0.654826\pi\)
\(654\) 0 0
\(655\) −2808.00 + 4863.60i −0.167508 + 0.290132i
\(656\) 0 0
\(657\) −9216.00 −0.547261
\(658\) 0 0
\(659\) −27580.0 −1.63029 −0.815147 0.579254i \(-0.803344\pi\)
−0.815147 + 0.579254i \(0.803344\pi\)
\(660\) 0 0
\(661\) −4646.00 + 8047.11i −0.273386 + 0.473519i −0.969727 0.244193i \(-0.921477\pi\)
0.696340 + 0.717712i \(0.254810\pi\)
\(662\) 0 0
\(663\) 144.000 + 249.415i 0.00843514 + 0.0146101i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 1368.00 + 2369.45i 0.0794141 + 0.137549i
\(668\) 0 0
\(669\) 6792.00 11764.1i 0.392517 0.679859i
\(670\) 0 0
\(671\) 12560.0 0.722613
\(672\) 0 0
\(673\) 11486.0 0.657879 0.328940 0.944351i \(-0.393309\pi\)
0.328940 + 0.944351i \(0.393309\pi\)
\(674\) 0 0
\(675\) 1471.50 2548.71i 0.0839082 0.145333i
\(676\) 0 0
\(677\) 3558.00 + 6162.64i 0.201987 + 0.349851i 0.949168 0.314768i \(-0.101927\pi\)
−0.747182 + 0.664620i \(0.768594\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −5478.00 9488.17i −0.308249 0.533903i
\(682\) 0 0
\(683\) 3806.00 6592.19i 0.213225 0.369316i −0.739497 0.673160i \(-0.764937\pi\)
0.952722 + 0.303843i \(0.0982700\pi\)
\(684\) 0 0
\(685\) 5480.00 0.305664
\(686\) 0 0
\(687\) 14412.0 0.800367
\(688\) 0 0
\(689\) 292.000 505.759i 0.0161456 0.0279650i
\(690\) 0 0
\(691\) −10786.0 18681.9i −0.593804 1.02850i −0.993714 0.111945i \(-0.964292\pi\)
0.399910 0.916554i \(-0.369041\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1032.00 1787.48i −0.0563252 0.0975581i
\(696\) 0 0
\(697\) 2592.00 4489.48i 0.140859 0.243976i
\(698\) 0 0
\(699\) 8274.00 0.447713
\(700\) 0 0
\(701\) −1702.00 −0.0917028 −0.0458514 0.998948i \(-0.514600\pi\)
−0.0458514 + 0.998948i \(0.514600\pi\)
\(702\) 0 0
\(703\) −660.000 + 1143.15i −0.0354088 + 0.0613298i
\(704\) 0 0
\(705\) −3120.00 5404.00i −0.166675 0.288690i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −3185.00 5516.58i −0.168710 0.292214i 0.769257 0.638940i \(-0.220627\pi\)
−0.937966 + 0.346726i \(0.887293\pi\)
\(710\) 0 0
\(711\) 468.000 810.600i 0.0246855 0.0427565i
\(712\) 0 0
\(713\) −13248.0 −0.695851
\(714\) 0 0
\(715\) 320.000 0.0167375
\(716\) 0 0
\(717\) −9792.00 + 16960.2i −0.510026 + 0.883392i
\(718\) 0 0
\(719\) −4404.00 7627.95i −0.228430 0.395653i 0.728913 0.684607i \(-0.240026\pi\)
−0.957343 + 0.288954i \(0.906693\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −84.0000 145.492i −0.00432088 0.00748398i
\(724\) 0 0
\(725\) −2071.00 + 3587.08i −0.106090 + 0.183753i
\(726\) 0 0
\(727\) −17768.0 −0.906436 −0.453218 0.891400i \(-0.649724\pi\)
−0.453218 + 0.891400i \(0.649724\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) −1968.00 + 3408.68i −0.0995747 + 0.172468i
\(732\) 0 0
\(733\) −2782.00 4818.57i −0.140185 0.242807i 0.787381 0.616466i \(-0.211436\pi\)
−0.927566 + 0.373659i \(0.878103\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 5560.00 + 9630.20i 0.277890 + 0.481320i
\(738\) 0 0
\(739\) 8782.00 15210.9i 0.437146 0.757160i −0.560322 0.828275i \(-0.689323\pi\)
0.997468 + 0.0711154i \(0.0226559\pi\)
\(740\) 0 0
\(741\) −528.000 −0.0261762
\(742\) 0 0
\(743\) −38280.0 −1.89012 −0.945059 0.326901i \(-0.893996\pi\)
−0.945059 + 0.326901i \(0.893996\pi\)
\(744\) 0 0
\(745\) 2780.00 4815.10i 0.136713 0.236794i
\(746\) 0 0
\(747\) −1458.00 2525.33i −0.0714129 0.123691i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −18096.0 31343.2i −0.879271 1.52294i −0.852142 0.523310i \(-0.824697\pi\)
−0.0271284 0.999632i \(-0.508636\pi\)
\(752\) 0 0
\(753\) 7350.00 12730.6i 0.355709 0.616106i
\(754\) 0 0
\(755\) −544.000 −0.0262228
\(756\) 0 0
\(757\) −14.0000 −0.000672178 −0.000336089 1.00000i \(-0.500107\pi\)
−0.000336089 1.00000i \(0.500107\pi\)
\(758\) 0 0
\(759\) 2160.00 3741.23i 0.103298 0.178917i
\(760\) 0 0
\(761\) −13252.0 22953.1i −0.631254 1.09336i −0.987296 0.158894i \(-0.949207\pi\)
0.356041 0.934470i \(-0.384126\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −432.000 748.246i −0.0204170 0.0353633i
\(766\) 0 0
\(767\) 920.000 1593.49i 0.0433107 0.0750163i
\(768\) 0 0
\(769\) −40184.0 −1.88436 −0.942180 0.335109i \(-0.891227\pi\)
−0.942180 + 0.335109i \(0.891227\pi\)
\(770\) 0 0
\(771\) 20352.0 0.950661
\(772\) 0 0
\(773\) −17670.0 + 30605.3i −0.822181 + 1.42406i 0.0818742 + 0.996643i \(0.473909\pi\)
−0.904055 + 0.427416i \(0.859424\pi\)
\(774\) 0 0
\(775\) −10028.0 17369.0i −0.464795 0.805049i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4752.00 + 8230.71i 0.218560 + 0.378557i
\(780\) 0 0
\(781\) 5920.00 10253.7i 0.271235 0.469792i
\(782\) 0 0
\(783\) −1026.00 −0.0468279
\(784\) 0 0
\(785\) −592.000 −0.0269164
\(786\) 0 0
\(787\) −7426.00 + 12862.2i −0.336351 + 0.582577i −0.983743 0.179580i \(-0.942526\pi\)
0.647392 + 0.762157i \(0.275860\pi\)
\(788\) 0 0
\(789\) 6816.00 + 11805.7i 0.307549 + 0.532690i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 1256.00 + 2175.46i 0.0562445 + 0.0974183i
\(794\) 0 0
\(795\) −876.000 + 1517.28i −0.0390799 + 0.0676884i
\(796\) 0 0
\(797\) −19788.0 −0.879457 −0.439728