Properties

Label 588.4.k.d.521.8
Level $588$
Weight $4$
Character 588.521
Analytic conductor $34.693$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 588.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(34.6931230834\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 2 x^{14} - 94 x^{12} - 128 x^{10} + 2719 x^{8} - 10368 x^{6} - 616734 x^{4} + 1062882 x^{2} + 43046721\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{16}\cdot 3^{12} \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 521.8
Root \(-0.00599769 + 2.99999i\) of defining polynomial
Character \(\chi\) \(=\) 588.521
Dual form 588.4.k.d.509.8

$q$-expansion

\(f(q)\) \(=\) \(q+(5.19614 + 0.0103883i) q^{3} +(-8.45479 - 14.6441i) q^{5} +(26.9998 + 0.107958i) q^{9} +O(q^{10})\) \(q+(5.19614 + 0.0103883i) q^{3} +(-8.45479 - 14.6441i) q^{5} +(26.9998 + 0.107958i) q^{9} +(45.7714 + 26.4261i) q^{11} -49.8375i q^{13} +(-43.7802 - 76.1808i) q^{15} +(-0.687566 + 1.19090i) q^{17} +(-62.9115 + 36.3220i) q^{19} +(166.990 - 96.4117i) q^{23} +(-80.4669 + 139.373i) q^{25} +(140.294 + 0.841448i) q^{27} -34.2666i q^{29} +(-81.2050 - 46.8837i) q^{31} +(237.560 + 137.789i) q^{33} +(-150.121 - 260.017i) q^{37} +(0.517727 - 258.963i) q^{39} -88.2653 q^{41} +136.747 q^{43} +(-226.697 - 396.301i) q^{45} +(-283.337 - 490.755i) q^{47} +(-3.58506 + 6.18094i) q^{51} +(-395.847 - 228.542i) q^{53} -893.710i q^{55} +(-327.274 + 188.081i) q^{57} +(126.542 - 219.178i) q^{59} +(-215.803 + 124.594i) q^{61} +(-729.827 + 421.366i) q^{65} +(54.3074 - 94.0632i) q^{67} +(868.705 - 499.234i) q^{69} -21.4904i q^{71} +(-310.185 - 179.085i) q^{73} +(-419.565 + 723.365i) q^{75} +(597.582 + 1035.04i) q^{79} +(728.977 + 5.82970i) q^{81} +834.327 q^{83} +23.2529 q^{85} +(0.355972 - 178.054i) q^{87} +(-114.929 - 199.063i) q^{89} +(-421.466 - 244.458i) q^{93} +(1063.81 + 614.189i) q^{95} -1140.39i q^{97} +(1232.97 + 718.441i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 12 q^{9} + O(q^{10}) \) \( 16 q + 12 q^{9} - 120 q^{15} - 320 q^{25} - 80 q^{37} + 732 q^{39} + 640 q^{43} - 552 q^{51} - 1560 q^{57} - 1840 q^{67} + 3176 q^{79} + 3456 q^{81} + 1920 q^{85} - 3960 q^{93} + 1152 q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(197\) \(295\) \(493\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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
\(3\) 5.19614 + 0.0103883i 0.999998 + 0.00199923i
\(4\) 0 0
\(5\) −8.45479 14.6441i −0.756219 1.30981i −0.944766 0.327746i \(-0.893711\pi\)
0.188546 0.982064i \(-0.439622\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 26.9998 + 0.107958i 0.999992 + 0.00399845i
\(10\) 0 0
\(11\) 45.7714 + 26.4261i 1.25460 + 0.724344i 0.972020 0.234900i \(-0.0754763\pi\)
0.282580 + 0.959244i \(0.408810\pi\)
\(12\) 0 0
\(13\) 49.8375i 1.06326i −0.846975 0.531632i \(-0.821579\pi\)
0.846975 0.531632i \(-0.178421\pi\)
\(14\) 0 0
\(15\) −43.7802 76.1808i −0.753599 1.31132i
\(16\) 0 0
\(17\) −0.687566 + 1.19090i −0.00980937 + 0.0169903i −0.870888 0.491481i \(-0.836456\pi\)
0.861079 + 0.508471i \(0.169789\pi\)
\(18\) 0 0
\(19\) −62.9115 + 36.3220i −0.759626 + 0.438570i −0.829161 0.559009i \(-0.811182\pi\)
0.0695358 + 0.997579i \(0.477848\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 166.990 96.4117i 1.51390 0.874053i 0.514037 0.857768i \(-0.328149\pi\)
0.999867 0.0162856i \(-0.00518411\pi\)
\(24\) 0 0
\(25\) −80.4669 + 139.373i −0.643735 + 1.11498i
\(26\) 0 0
\(27\) 140.294 + 0.841448i 0.999982 + 0.00599766i
\(28\) 0 0
\(29\) 34.2666i 0.219419i −0.993964 0.109709i \(-0.965008\pi\)
0.993964 0.109709i \(-0.0349920\pi\)
\(30\) 0 0
\(31\) −81.2050 46.8837i −0.470479 0.271631i 0.245961 0.969280i \(-0.420896\pi\)
−0.716440 + 0.697649i \(0.754230\pi\)
\(32\) 0 0
\(33\) 237.560 + 137.789i 1.25315 + 0.726850i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −150.121 260.017i −0.667018 1.15531i −0.978734 0.205134i \(-0.934237\pi\)
0.311715 0.950176i \(-0.399096\pi\)
\(38\) 0 0
\(39\) 0.517727 258.963i 0.00212571 1.06326i
\(40\) 0 0
\(41\) −88.2653 −0.336213 −0.168106 0.985769i \(-0.553765\pi\)
−0.168106 + 0.985769i \(0.553765\pi\)
\(42\) 0 0
\(43\) 136.747 0.484971 0.242485 0.970155i \(-0.422037\pi\)
0.242485 + 0.970155i \(0.422037\pi\)
\(44\) 0 0
\(45\) −226.697 396.301i −0.750976 1.31282i
\(46\) 0 0
\(47\) −283.337 490.755i −0.879341 1.52306i −0.852066 0.523435i \(-0.824650\pi\)
−0.0272750 0.999628i \(-0.508683\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −3.58506 + 6.18094i −0.00984332 + 0.0169707i
\(52\) 0 0
\(53\) −395.847 228.542i −1.02592 0.592315i −0.110107 0.993920i \(-0.535119\pi\)
−0.915813 + 0.401605i \(0.868453\pi\)
\(54\) 0 0
\(55\) 893.710i 2.19105i
\(56\) 0 0
\(57\) −327.274 + 188.081i −0.760501 + 0.437050i
\(58\) 0 0
\(59\) 126.542 219.178i 0.279227 0.483636i −0.691966 0.721930i \(-0.743255\pi\)
0.971193 + 0.238295i \(0.0765884\pi\)
\(60\) 0 0
\(61\) −215.803 + 124.594i −0.452963 + 0.261518i −0.709081 0.705127i \(-0.750890\pi\)
0.256118 + 0.966646i \(0.417556\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −729.827 + 421.366i −1.39268 + 0.804061i
\(66\) 0 0
\(67\) 54.3074 94.0632i 0.0990255 0.171517i −0.812256 0.583301i \(-0.801761\pi\)
0.911282 + 0.411784i \(0.135094\pi\)
\(68\) 0 0
\(69\) 868.705 499.234i 1.51565 0.871025i
\(70\) 0 0
\(71\) 21.4904i 0.0359218i −0.999839 0.0179609i \(-0.994283\pi\)
0.999839 0.0179609i \(-0.00571743\pi\)
\(72\) 0 0
\(73\) −310.185 179.085i −0.497321 0.287128i 0.230286 0.973123i \(-0.426034\pi\)
−0.727607 + 0.685995i \(0.759367\pi\)
\(74\) 0 0
\(75\) −419.565 + 723.365i −0.645963 + 1.11369i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 597.582 + 1035.04i 0.851053 + 1.47407i 0.880259 + 0.474494i \(0.157369\pi\)
−0.0292056 + 0.999573i \(0.509298\pi\)
\(80\) 0 0
\(81\) 728.977 + 5.82970i 0.999968 + 0.00799684i
\(82\) 0 0
\(83\) 834.327 1.10336 0.551682 0.834054i \(-0.313986\pi\)
0.551682 + 0.834054i \(0.313986\pi\)
\(84\) 0 0
\(85\) 23.2529 0.0296721
\(86\) 0 0
\(87\) 0.355972 178.054i 0.000438669 0.219418i
\(88\) 0 0
\(89\) −114.929 199.063i −0.136882 0.237086i 0.789433 0.613837i \(-0.210375\pi\)
−0.926315 + 0.376751i \(0.877041\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −421.466 244.458i −0.469935 0.272571i
\(94\) 0 0
\(95\) 1063.81 + 614.189i 1.14889 + 0.663310i
\(96\) 0 0
\(97\) 1140.39i 1.19370i −0.802352 0.596851i \(-0.796418\pi\)
0.802352 0.596851i \(-0.203582\pi\)
\(98\) 0 0
\(99\) 1232.97 + 718.441i 1.25169 + 0.729354i
\(100\) 0 0
\(101\) 79.2514 137.267i 0.0780773 0.135234i −0.824343 0.566091i \(-0.808455\pi\)
0.902420 + 0.430857i \(0.141789\pi\)
\(102\) 0 0
\(103\) 215.773 124.576i 0.206415 0.119174i −0.393229 0.919440i \(-0.628642\pi\)
0.599644 + 0.800267i \(0.295309\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 810.305 467.830i 0.732104 0.422681i −0.0870872 0.996201i \(-0.527756\pi\)
0.819192 + 0.573520i \(0.194423\pi\)
\(108\) 0 0
\(109\) −772.055 + 1337.24i −0.678435 + 1.17508i 0.297017 + 0.954872i \(0.404008\pi\)
−0.975452 + 0.220212i \(0.929325\pi\)
\(110\) 0 0
\(111\) −777.347 1352.64i −0.664707 1.15664i
\(112\) 0 0
\(113\) 214.314i 0.178415i 0.996013 + 0.0892077i \(0.0284335\pi\)
−0.996013 + 0.0892077i \(0.971566\pi\)
\(114\) 0 0
\(115\) −2823.73 1630.28i −2.28969 1.32195i
\(116\) 0 0
\(117\) 5.38037 1345.60i 0.00425141 1.06326i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 731.181 + 1266.44i 0.549347 + 0.951497i
\(122\) 0 0
\(123\) −458.639 0.916927i −0.336212 0.000672167i
\(124\) 0 0
\(125\) 607.627 0.434782
\(126\) 0 0
\(127\) 43.2529 0.0302211 0.0151105 0.999886i \(-0.495190\pi\)
0.0151105 + 0.999886i \(0.495190\pi\)
\(128\) 0 0
\(129\) 710.557 + 1.42057i 0.484970 + 0.000969568i
\(130\) 0 0
\(131\) 641.264 + 1110.70i 0.427691 + 0.740783i 0.996668 0.0815711i \(-0.0259938\pi\)
−0.568976 + 0.822354i \(0.692660\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −1173.83 2061.59i −0.748350 1.31432i
\(136\) 0 0
\(137\) −544.226 314.209i −0.339389 0.195947i 0.320613 0.947210i \(-0.396111\pi\)
−0.660002 + 0.751264i \(0.729445\pi\)
\(138\) 0 0
\(139\) 1295.74i 0.790671i 0.918537 + 0.395336i \(0.129372\pi\)
−0.918537 + 0.395336i \(0.870628\pi\)
\(140\) 0 0
\(141\) −1467.16 2552.98i −0.876294 1.52482i
\(142\) 0 0
\(143\) 1317.01 2281.13i 0.770169 1.33397i
\(144\) 0 0
\(145\) −501.804 + 289.717i −0.287397 + 0.165929i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 24.6445 14.2285i 0.0135501 0.00782313i −0.493210 0.869910i \(-0.664176\pi\)
0.506760 + 0.862087i \(0.330843\pi\)
\(150\) 0 0
\(151\) 118.724 205.636i 0.0639842 0.110824i −0.832259 0.554387i \(-0.812953\pi\)
0.896243 + 0.443564i \(0.146286\pi\)
\(152\) 0 0
\(153\) −18.6927 + 32.0798i −0.00987723 + 0.0169510i
\(154\) 0 0
\(155\) 1585.57i 0.821651i
\(156\) 0 0
\(157\) 2526.01 + 1458.39i 1.28406 + 0.741352i 0.977588 0.210527i \(-0.0675181\pi\)
0.306472 + 0.951880i \(0.400851\pi\)
\(158\) 0 0
\(159\) −2054.50 1191.65i −1.02473 0.594365i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −488.284 845.733i −0.234634 0.406398i 0.724532 0.689241i \(-0.242056\pi\)
−0.959166 + 0.282843i \(0.908723\pi\)
\(164\) 0 0
\(165\) 9.28413 4643.84i 0.00438041 2.19105i
\(166\) 0 0
\(167\) 2802.61 1.29864 0.649318 0.760517i \(-0.275054\pi\)
0.649318 + 0.760517i \(0.275054\pi\)
\(168\) 0 0
\(169\) −286.778 −0.130532
\(170\) 0 0
\(171\) −1702.52 + 973.893i −0.761373 + 0.435529i
\(172\) 0 0
\(173\) 1365.20 + 2364.59i 0.599965 + 1.03917i 0.992826 + 0.119571i \(0.0381520\pi\)
−0.392861 + 0.919598i \(0.628515\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 659.808 1137.56i 0.280193 0.483076i
\(178\) 0 0
\(179\) −1354.53 782.039i −0.565600 0.326549i 0.189790 0.981825i \(-0.439219\pi\)
−0.755390 + 0.655275i \(0.772553\pi\)
\(180\) 0 0
\(181\) 2818.69i 1.15752i −0.815498 0.578761i \(-0.803537\pi\)
0.815498 0.578761i \(-0.196463\pi\)
\(182\) 0 0
\(183\) −1122.64 + 645.165i −0.453484 + 0.260612i
\(184\) 0 0
\(185\) −2538.48 + 4396.77i −1.00882 + 1.74734i
\(186\) 0 0
\(187\) −62.9417 + 36.3394i −0.0246137 + 0.0142107i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −696.633 + 402.202i −0.263909 + 0.152368i −0.626116 0.779730i \(-0.715357\pi\)
0.362207 + 0.932098i \(0.382023\pi\)
\(192\) 0 0
\(193\) −2101.70 + 3640.26i −0.783854 + 1.35768i 0.145827 + 0.989310i \(0.453416\pi\)
−0.929681 + 0.368365i \(0.879918\pi\)
\(194\) 0 0
\(195\) −3796.66 + 2181.89i −1.39428 + 0.801275i
\(196\) 0 0
\(197\) 4885.06i 1.76673i −0.468686 0.883365i \(-0.655272\pi\)
0.468686 0.883365i \(-0.344728\pi\)
\(198\) 0 0
\(199\) 1750.52 + 1010.66i 0.623572 + 0.360019i 0.778258 0.627944i \(-0.216103\pi\)
−0.154687 + 0.987964i \(0.549437\pi\)
\(200\) 0 0
\(201\) 283.166 488.202i 0.0993682 0.171319i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 746.265 + 1292.57i 0.254251 + 0.440375i
\(206\) 0 0
\(207\) 4519.10 2585.07i 1.51739 0.867993i
\(208\) 0 0
\(209\) −3839.40 −1.27070
\(210\) 0 0
\(211\) 214.374 0.0699435 0.0349718 0.999388i \(-0.488866\pi\)
0.0349718 + 0.999388i \(0.488866\pi\)
\(212\) 0 0
\(213\) 0.223249 111.667i 7.18159e−5 0.0359217i
\(214\) 0 0
\(215\) −1156.17 2002.54i −0.366744 0.635220i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −1609.91 933.776i −0.496746 0.288122i
\(220\) 0 0
\(221\) 59.3515 + 34.2666i 0.0180652 + 0.0104300i
\(222\) 0 0
\(223\) 5589.50i 1.67848i 0.543763 + 0.839239i \(0.316999\pi\)
−0.543763 + 0.839239i \(0.683001\pi\)
\(224\) 0 0
\(225\) −2187.64 + 3754.35i −0.648189 + 1.11240i
\(226\) 0 0
\(227\) 1756.33 3042.05i 0.513532 0.889463i −0.486345 0.873767i \(-0.661670\pi\)
0.999877 0.0156961i \(-0.00499644\pi\)
\(228\) 0 0
\(229\) 3494.64 2017.63i 1.00844 0.582222i 0.0977038 0.995216i \(-0.468850\pi\)
0.910734 + 0.412994i \(0.135517\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 4824.61 2785.49i 1.35653 0.783191i 0.367372 0.930074i \(-0.380257\pi\)
0.989154 + 0.146883i \(0.0469241\pi\)
\(234\) 0 0
\(235\) −4791.12 + 8298.46i −1.32995 + 2.30354i
\(236\) 0 0
\(237\) 3094.37 + 5384.43i 0.848104 + 1.47577i
\(238\) 0 0
\(239\) 398.423i 0.107832i 0.998545 + 0.0539160i \(0.0171703\pi\)
−0.998545 + 0.0539160i \(0.982830\pi\)
\(240\) 0 0
\(241\) 4288.39 + 2475.91i 1.14622 + 0.661772i 0.947964 0.318377i \(-0.103138\pi\)
0.198259 + 0.980150i \(0.436471\pi\)
\(242\) 0 0
\(243\) 3787.81 + 37.8648i 0.999950 + 0.00999599i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 1810.20 + 3135.35i 0.466316 + 0.807683i
\(248\) 0 0
\(249\) 4335.28 + 8.66724i 1.10336 + 0.00220588i
\(250\) 0 0
\(251\) −4083.93 −1.02699 −0.513496 0.858092i \(-0.671650\pi\)
−0.513496 + 0.858092i \(0.671650\pi\)
\(252\) 0 0
\(253\) 10191.2 2.53246
\(254\) 0 0
\(255\) 120.825 + 0.241558i 0.0296721 + 5.93214e-5i
\(256\) 0 0
\(257\) 1730.25 + 2996.89i 0.419962 + 0.727396i 0.995935 0.0900727i \(-0.0287099\pi\)
−0.575973 + 0.817469i \(0.695377\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 3.69936 925.191i 0.000877336 0.219417i
\(262\) 0 0
\(263\) 2442.98 + 1410.46i 0.572778 + 0.330694i 0.758258 0.651954i \(-0.226051\pi\)
−0.185480 + 0.982648i \(0.559384\pi\)
\(264\) 0 0
\(265\) 7729.11i 1.79168i
\(266\) 0 0
\(267\) −595.121 1035.55i −0.136407 0.237359i
\(268\) 0 0
\(269\) −1405.44 + 2434.29i −0.318554 + 0.551751i −0.980187 0.198077i \(-0.936531\pi\)
0.661633 + 0.749828i \(0.269864\pi\)
\(270\) 0 0
\(271\) −6714.72 + 3876.75i −1.50513 + 0.868988i −0.505148 + 0.863033i \(0.668562\pi\)
−0.999982 + 0.00595501i \(0.998104\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −7366.17 + 4252.86i −1.61526 + 0.932571i
\(276\) 0 0
\(277\) −283.222 + 490.554i −0.0614337 + 0.106406i −0.895106 0.445852i \(-0.852901\pi\)
0.833673 + 0.552259i \(0.186234\pi\)
\(278\) 0 0
\(279\) −2187.46 1274.62i −0.469389 0.273510i
\(280\) 0 0
\(281\) 5958.94i 1.26506i 0.774538 + 0.632528i \(0.217983\pi\)
−0.774538 + 0.632528i \(0.782017\pi\)
\(282\) 0 0
\(283\) −2591.09 1495.97i −0.544256 0.314226i 0.202546 0.979273i \(-0.435078\pi\)
−0.746802 + 0.665047i \(0.768412\pi\)
\(284\) 0 0
\(285\) 5521.31 + 3202.47i 1.14756 + 0.665606i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 2455.55 + 4253.15i 0.499808 + 0.865692i
\(290\) 0 0
\(291\) 11.8467 5925.63i 0.00238648 1.19370i
\(292\) 0 0
\(293\) −5247.58 −1.04630 −0.523151 0.852240i \(-0.675244\pi\)
−0.523151 + 0.852240i \(0.675244\pi\)
\(294\) 0 0
\(295\) −4279.55 −0.844628
\(296\) 0 0
\(297\) 6399.20 + 3745.93i 1.25023 + 0.731855i
\(298\) 0 0
\(299\) −4804.92 8322.36i −0.929350 1.60968i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 413.227 712.438i 0.0783475 0.135077i
\(304\) 0 0
\(305\) 3649.13 + 2106.83i 0.685078 + 0.395530i
\(306\) 0 0
\(307\) 210.991i 0.0392243i −0.999808 0.0196122i \(-0.993757\pi\)
0.999808 0.0196122i \(-0.00624315\pi\)
\(308\) 0 0
\(309\) 1122.48 645.075i 0.206652 0.118761i
\(310\) 0 0
\(311\) −4628.03 + 8015.98i −0.843831 + 1.46156i 0.0428024 + 0.999084i \(0.486371\pi\)
−0.886633 + 0.462474i \(0.846962\pi\)
\(312\) 0 0
\(313\) 7305.05 4217.57i 1.31919 0.761634i 0.335590 0.942008i \(-0.391064\pi\)
0.983598 + 0.180375i \(0.0577310\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −5146.01 + 2971.05i −0.911763 + 0.526406i −0.880998 0.473120i \(-0.843128\pi\)
−0.0307648 + 0.999527i \(0.509794\pi\)
\(318\) 0 0
\(319\) 905.533 1568.43i 0.158935 0.275283i
\(320\) 0 0
\(321\) 4215.32 2422.49i 0.732948 0.421216i
\(322\) 0 0
\(323\) 99.8950i 0.0172084i
\(324\) 0 0
\(325\) 6946.00 + 4010.27i 1.18552 + 0.684461i
\(326\) 0 0
\(327\) −4025.60 + 6940.46i −0.680783 + 1.17373i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 3110.61 + 5387.74i 0.516540 + 0.894673i 0.999816 + 0.0192049i \(0.00611349\pi\)
−0.483276 + 0.875468i \(0.660553\pi\)
\(332\) 0 0
\(333\) −4025.15 7036.60i −0.662394 1.15797i
\(334\) 0 0
\(335\) −1836.63 −0.299540
\(336\) 0 0
\(337\) −7108.23 −1.14899 −0.574496 0.818508i \(-0.694802\pi\)
−0.574496 + 0.818508i \(0.694802\pi\)
\(338\) 0 0
\(339\) −2.22636 + 1113.61i −0.000356694 + 0.178415i
\(340\) 0 0
\(341\) −2477.91 4291.87i −0.393508 0.681577i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −14655.6 8500.51i −2.28704 1.32653i
\(346\) 0 0
\(347\) −9666.81 5581.13i −1.49551 0.863432i −0.495521 0.868596i \(-0.665023\pi\)
−0.999987 + 0.00516366i \(0.998356\pi\)
\(348\) 0 0
\(349\) 2438.46i 0.374006i 0.982359 + 0.187003i \(0.0598773\pi\)
−0.982359 + 0.187003i \(0.940123\pi\)
\(350\) 0 0
\(351\) 41.9357 6991.88i 0.00637710 1.06325i
\(352\) 0 0
\(353\) −451.700 + 782.368i −0.0681064 + 0.117964i −0.898068 0.439857i \(-0.855029\pi\)
0.829961 + 0.557821i \(0.188362\pi\)
\(354\) 0 0
\(355\) −314.709 + 181.697i −0.0470507 + 0.0271647i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 6970.32 4024.32i 1.02473 0.591630i 0.109262 0.994013i \(-0.465151\pi\)
0.915472 + 0.402382i \(0.131818\pi\)
\(360\) 0 0
\(361\) −790.930 + 1369.93i −0.115313 + 0.199727i
\(362\) 0 0
\(363\) 3786.16 + 6588.21i 0.547444 + 0.952593i
\(364\) 0 0
\(365\) 6056.52i 0.868528i
\(366\) 0 0
\(367\) −5858.89 3382.63i −0.833329 0.481122i 0.0216624 0.999765i \(-0.493104\pi\)
−0.854991 + 0.518643i \(0.826437\pi\)
\(368\) 0 0
\(369\) −2383.14 9.52896i −0.336210 0.00134433i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 1599.16 + 2769.82i 0.221987 + 0.384493i 0.955411 0.295278i \(-0.0954124\pi\)
−0.733424 + 0.679771i \(0.762079\pi\)
\(374\) 0 0
\(375\) 3157.31 + 6.31221i 0.434781 + 0.000869229i
\(376\) 0 0
\(377\) −1707.76 −0.233300
\(378\) 0 0
\(379\) 2066.41 0.280065 0.140032 0.990147i \(-0.455279\pi\)
0.140032 + 0.990147i \(0.455279\pi\)
\(380\) 0 0
\(381\) 224.748 + 0.449324i 0.0302210 + 6.04188e-5i
\(382\) 0 0
\(383\) 4848.41 + 8397.69i 0.646846 + 1.12037i 0.983872 + 0.178875i \(0.0572459\pi\)
−0.337025 + 0.941496i \(0.609421\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 3692.14 + 14.7630i 0.484967 + 0.00193913i
\(388\) 0 0
\(389\) 2518.43 + 1454.02i 0.328250 + 0.189515i 0.655064 0.755573i \(-0.272642\pi\)
−0.326814 + 0.945089i \(0.605975\pi\)
\(390\) 0 0
\(391\) 265.158i 0.0342956i
\(392\) 0 0
\(393\) 3320.56 + 5778.03i 0.426209 + 0.741636i
\(394\) 0 0
\(395\) 10104.9 17502.1i 1.28717 2.22944i
\(396\) 0 0
\(397\) 4666.67 2694.30i 0.589958 0.340612i −0.175123 0.984547i \(-0.556032\pi\)
0.765081 + 0.643934i \(0.222699\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 7221.31 4169.22i 0.899289 0.519205i 0.0223196 0.999751i \(-0.492895\pi\)
0.876969 + 0.480546i \(0.159562\pi\)
\(402\) 0 0
\(403\) −2336.57 + 4047.06i −0.288816 + 0.500244i
\(404\) 0 0
\(405\) −6077.97 10724.5i −0.745721 1.31582i
\(406\) 0 0
\(407\) 15868.4i 1.93260i
\(408\) 0 0
\(409\) −3222.91 1860.75i −0.389640 0.224959i 0.292364 0.956307i \(-0.405558\pi\)
−0.682004 + 0.731348i \(0.738891\pi\)
\(410\) 0 0
\(411\) −2824.61 1638.33i −0.338997 0.196625i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −7054.06 12218.0i −0.834386 1.44520i
\(416\) 0 0
\(417\) −13.4605 + 6732.85i −0.00158073 + 0.790670i
\(418\) 0 0
\(419\) 5794.95 0.675661 0.337831 0.941207i \(-0.390307\pi\)
0.337831 + 0.941207i \(0.390307\pi\)
\(420\) 0 0
\(421\) 3025.70 0.350269 0.175135 0.984544i \(-0.443964\pi\)
0.175135 + 0.984544i \(0.443964\pi\)
\(422\) 0 0
\(423\) −7597.07 13280.9i −0.873244 1.52657i
\(424\) 0 0
\(425\) −110.653 191.656i −0.0126293 0.0218746i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 6867.08 11839.4i 0.772834 1.33243i
\(430\) 0 0
\(431\) 1945.53 + 1123.25i 0.217431 + 0.125534i 0.604760 0.796408i \(-0.293269\pi\)
−0.387329 + 0.921942i \(0.626602\pi\)
\(432\) 0 0
\(433\) 5546.43i 0.615576i −0.951455 0.307788i \(-0.900411\pi\)
0.951455 0.307788i \(-0.0995887\pi\)
\(434\) 0 0
\(435\) −2610.46 + 1500.20i −0.287728 + 0.165354i
\(436\) 0 0
\(437\) −7003.72 + 12130.8i −0.766667 + 1.32791i
\(438\) 0 0
\(439\) 0.592611 0.342144i 6.44277e−5 3.71974e-5i −0.499968 0.866044i \(-0.666655\pi\)
0.500032 + 0.866007i \(0.333321\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 8974.71 5181.55i 0.962532 0.555718i 0.0655803 0.997847i \(-0.479110\pi\)
0.896951 + 0.442129i \(0.145777\pi\)
\(444\) 0 0
\(445\) −1943.40 + 3366.08i −0.207025 + 0.358578i
\(446\) 0 0
\(447\) 128.204 73.6775i 0.0135657 0.00779603i
\(448\) 0 0
\(449\) 737.618i 0.0775286i −0.999248 0.0387643i \(-0.987658\pi\)
0.999248 0.0387643i \(-0.0123421\pi\)
\(450\) 0 0
\(451\) −4040.03 2332.51i −0.421812 0.243534i
\(452\) 0 0
\(453\) 619.042 1067.28i 0.0642056 0.110696i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 6091.92 + 10551.5i 0.623562 + 1.08004i 0.988817 + 0.149134i \(0.0476485\pi\)
−0.365255 + 0.930907i \(0.619018\pi\)
\(458\) 0 0
\(459\) −97.4632 + 166.497i −0.00991109 + 0.0169312i
\(460\) 0 0
\(461\) 16111.1 1.62770 0.813848 0.581078i \(-0.197369\pi\)
0.813848 + 0.581078i \(0.197369\pi\)
\(462\) 0 0
\(463\) 111.903 0.0112324 0.00561619 0.999984i \(-0.498212\pi\)
0.00561619 + 0.999984i \(0.498212\pi\)
\(464\) 0 0
\(465\) −16.4714 + 8238.84i −0.00164267 + 0.821649i
\(466\) 0 0
\(467\) −2468.01 4274.72i −0.244552 0.423577i 0.717453 0.696607i \(-0.245308\pi\)
−0.962006 + 0.273029i \(0.911974\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 13110.3 + 7604.25i 1.28258 + 0.743918i
\(472\) 0 0
\(473\) 6259.11 + 3613.70i 0.608444 + 0.351285i
\(474\) 0 0
\(475\) 11690.9i 1.12929i
\(476\) 0 0
\(477\) −10663.1 6213.33i −1.02354 0.596413i
\(478\) 0 0
\(479\) 2203.81 3817.10i 0.210218 0.364108i −0.741565 0.670881i \(-0.765916\pi\)
0.951783 + 0.306773i \(0.0992493\pi\)
\(480\) 0 0
\(481\) −12958.6 + 7481.64i −1.22840 + 0.709217i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −16700.0 + 9641.76i −1.56352 + 0.902701i
\(486\) 0 0
\(487\) −7376.21 + 12776.0i −0.686341 + 1.18878i 0.286672 + 0.958029i \(0.407451\pi\)
−0.973013 + 0.230749i \(0.925882\pi\)
\(488\) 0 0
\(489\) −2528.41 4399.62i −0.233821 0.406867i
\(490\) 0 0
\(491\) 5995.54i 0.551069i −0.961291 0.275535i \(-0.911145\pi\)
0.961291 0.275535i \(-0.0888549\pi\)
\(492\) 0 0
\(493\) 40.8081 + 23.5605i 0.00372800 + 0.00215236i
\(494\) 0 0
\(495\) 96.4833 24130.0i 0.00876081 2.19103i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −192.202 332.904i −0.0172428 0.0298654i 0.857275 0.514858i \(-0.172155\pi\)
−0.874518 + 0.484993i \(0.838822\pi\)
\(500\) 0 0
\(501\) 14562.7 + 29.1143i 1.29863 + 0.00259627i
\(502\) 0 0
\(503\) 3491.74 0.309521 0.154761 0.987952i \(-0.450539\pi\)
0.154761 + 0.987952i \(0.450539\pi\)
\(504\) 0 0
\(505\) −2680.21 −0.236174
\(506\) 0 0
\(507\) −1490.14 2.97914i −0.130532 0.000260963i
\(508\) 0 0
\(509\) 11168.6 + 19344.5i 0.972571 + 1.68454i 0.687728 + 0.725968i \(0.258608\pi\)
0.284842 + 0.958574i \(0.408059\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −8856.64 + 5042.80i −0.762242 + 0.434006i
\(514\) 0 0
\(515\) −3648.62 2106.53i −0.312189 0.180243i
\(516\) 0 0
\(517\) 29950.1i 2.54778i
\(518\) 0 0
\(519\) 7069.18 + 12300.9i 0.597886 + 1.04037i
\(520\) 0 0
\(521\) 9834.58 17034.0i 0.826988 1.43239i −0.0734020 0.997302i \(-0.523386\pi\)
0.900390 0.435083i \(-0.143281\pi\)
\(522\) 0 0
\(523\) −14136.0 + 8161.42i −1.18188 + 0.682359i −0.956449 0.291900i \(-0.905713\pi\)
−0.225432 + 0.974259i \(0.572379\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 111.668 64.4713i 0.00923020 0.00532906i
\(528\) 0 0
\(529\) 12506.9 21662.6i 1.02794 1.78044i
\(530\) 0 0
\(531\) 3440.28 5904.09i 0.281159 0.482515i
\(532\) 0 0
\(533\) 4398.92i 0.357483i
\(534\) 0 0
\(535\) −13701.9 7910.81i −1.10726 0.639279i
\(536\) 0 0
\(537\) −7030.21 4077.66i −0.564946 0.327679i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −2872.09 4974.61i −0.228246 0.395333i 0.729043 0.684468i \(-0.239966\pi\)
−0.957288 + 0.289135i \(0.906632\pi\)
\(542\) 0 0
\(543\) 29.2814 14646.3i 0.00231415 1.15752i
\(544\) 0 0
\(545\) 26110.2 2.05218
\(546\) 0 0
\(547\) 8889.70 0.694874 0.347437 0.937703i \(-0.387052\pi\)
0.347437 + 0.937703i \(0.387052\pi\)
\(548\) 0 0
\(549\) −5840.08 + 3340.71i −0.454005 + 0.259705i
\(550\) 0 0
\(551\) 1244.63 + 2155.76i 0.0962305 + 0.166676i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −13236.0 + 22819.9i −1.01232 + 1.74531i
\(556\) 0 0
\(557\) −16872.5 9741.36i −1.28350 0.741032i −0.306017 0.952026i \(-0.598997\pi\)
−0.977487 + 0.210994i \(0.932330\pi\)
\(558\) 0 0
\(559\) 6815.14i 0.515652i
\(560\) 0 0
\(561\) −327.432 + 188.171i −0.0246420 + 0.0141615i
\(562\) 0 0
\(563\) −5551.00 + 9614.61i −0.415536 + 0.719729i −0.995485 0.0949240i \(-0.969739\pi\)
0.579949 + 0.814653i \(0.303073\pi\)
\(564\) 0 0
\(565\) 3138.44 1811.98i 0.233690 0.134921i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −2139.17 + 1235.05i −0.157607 + 0.0909947i −0.576729 0.816935i \(-0.695671\pi\)
0.419122 + 0.907930i \(0.362338\pi\)
\(570\) 0 0
\(571\) 1771.80 3068.85i 0.129856 0.224917i −0.793765 0.608225i \(-0.791882\pi\)
0.923621 + 0.383308i \(0.125215\pi\)
\(572\) 0 0
\(573\) −3623.98 + 2082.66i −0.264213 + 0.151840i
\(574\) 0 0
\(575\) 31031.8i 2.25064i
\(576\) 0 0
\(577\) 1071.07 + 618.385i 0.0772780 + 0.0446164i 0.538141 0.842855i \(-0.319127\pi\)
−0.460863 + 0.887471i \(0.652460\pi\)
\(578\) 0 0
\(579\) −10958.6 + 18893.5i −0.786567 + 1.35611i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −12079.0 20921.4i −0.858079 1.48624i
\(584\) 0 0
\(585\) −19750.7 + 11298.0i −1.39588 + 0.798486i
\(586\) 0 0
\(587\) −13251.5 −0.931772 −0.465886 0.884845i \(-0.654264\pi\)
−0.465886 + 0.884845i \(0.654264\pi\)
\(588\) 0 0
\(589\) 6811.64 0.476517
\(590\) 0 0
\(591\) 50.7474 25383.4i 0.00353210 1.76673i
\(592\) 0 0
\(593\) −7948.25 13766.8i −0.550414 0.953345i −0.998245 0.0592266i \(-0.981137\pi\)
0.447831 0.894118i \(-0.352197\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 9085.43 + 5269.72i 0.622851 + 0.361265i
\(598\) 0 0
\(599\) 19294.9 + 11139.9i 1.31614 + 0.759873i 0.983105 0.183042i \(-0.0585943\pi\)
0.333034 + 0.942915i \(0.391928\pi\)
\(600\) 0 0
\(601\) 14741.7i 1.00055i 0.865868 + 0.500273i \(0.166767\pi\)
−0.865868 + 0.500273i \(0.833233\pi\)
\(602\) 0 0
\(603\) 1476.44 2533.82i 0.0997105 0.171120i
\(604\) 0 0
\(605\) 12364.0 21415.0i 0.830854 1.43908i
\(606\) 0 0
\(607\) 10850.9 6264.76i 0.725574 0.418911i −0.0912266 0.995830i \(-0.529079\pi\)
0.816801 + 0.576920i \(0.195745\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −24458.0 + 14120.8i −1.61942 + 0.934972i
\(612\) 0 0
\(613\) 763.731 1322.82i 0.0503211 0.0871586i −0.839768 0.542946i \(-0.817309\pi\)
0.890089 + 0.455787i \(0.150642\pi\)
\(614\) 0 0
\(615\) 3864.27 + 6724.12i 0.253370 + 0.440882i
\(616\) 0 0
\(617\) 12982.5i 0.847089i −0.905875 0.423545i \(-0.860786\pi\)
0.905875 0.423545i \(-0.139214\pi\)
\(618\) 0 0
\(619\) −503.141 290.488i −0.0326703 0.0188622i 0.483576 0.875302i \(-0.339338\pi\)
−0.516246 + 0.856440i \(0.672671\pi\)
\(620\) 0 0
\(621\) 23508.7 13385.4i 1.51912 0.864958i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 4921.01 + 8523.44i 0.314945 + 0.545500i
\(626\) 0 0
\(627\) −19950.0 39.8848i −1.27070 0.00254042i
\(628\) 0 0
\(629\) 412.871 0.0261721
\(630\) 0 0
\(631\) −9489.94 −0.598714 −0.299357 0.954141i \(-0.596772\pi\)
−0.299357 + 0.954141i \(0.596772\pi\)
\(632\) 0 0
\(633\) 1113.92 + 2.22698i 0.0699434 + 0.000139833i
\(634\) 0 0
\(635\) −365.694 633.401i −0.0228538 0.0395839i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 2.32007 580.237i 0.000143631 0.0359215i
\(640\) 0 0
\(641\) −14559.8 8406.12i −0.897158 0.517975i −0.0208812 0.999782i \(-0.506647\pi\)
−0.876277 + 0.481807i \(0.839981\pi\)
\(642\) 0 0
\(643\) 7168.19i 0.439636i −0.975541 0.219818i \(-0.929454\pi\)
0.975541 0.219818i \(-0.0705463\pi\)
\(644\) 0 0
\(645\) −5986.81 10417.5i −0.365473 0.635951i
\(646\) 0 0
\(647\) −7911.81 + 13703.7i −0.480750 + 0.832684i −0.999756 0.0220870i \(-0.992969\pi\)
0.519006 + 0.854771i \(0.326302\pi\)
\(648\) 0 0
\(649\) 11584.0 6688.05i 0.700637 0.404513i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 19470.9 11241.6i 1.16686 0.673685i 0.213919 0.976851i \(-0.431377\pi\)
0.952937 + 0.303167i \(0.0980439\pi\)
\(654\) 0 0
\(655\) 10843.5 18781.5i 0.646857 1.12039i
\(656\) 0 0
\(657\) −8355.60 4868.76i −0.496169 0.289115i
\(658\) 0 0
\(659\) 18754.4i 1.10860i 0.832317 + 0.554300i \(0.187014\pi\)
−0.832317 + 0.554300i \(0.812986\pi\)
\(660\) 0 0
\(661\) −5202.33 3003.56i −0.306123 0.176740i 0.339067 0.940762i \(-0.389888\pi\)
−0.645190 + 0.764022i \(0.723222\pi\)
\(662\) 0 0
\(663\) 308.043 + 178.671i 0.0180443 + 0.0104661i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −3303.70 5722.18i −0.191784 0.332179i
\(668\) 0 0
\(669\) −58.0654 + 29043.8i −0.00335566 + 1.67847i
\(670\) 0 0
\(671\) −13170.1 −0.757716
\(672\) 0 0
\(673\) 13481.6 0.772178 0.386089 0.922461i \(-0.373826\pi\)
0.386089 + 0.922461i \(0.373826\pi\)
\(674\) 0 0
\(675\) −11406.3 + 19485.4i −0.650411 + 1.11110i
\(676\) 0 0
\(677\) −1760.98 3050.10i −0.0999702 0.173153i 0.811702 0.584072i \(-0.198541\pi\)
−0.911672 + 0.410918i \(0.865208\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 9157.74 15788.7i 0.515309 0.888434i
\(682\) 0 0
\(683\) 25192.9 + 14545.1i 1.41139 + 0.814866i 0.995519 0.0945581i \(-0.0301438\pi\)
0.415870 + 0.909424i \(0.363477\pi\)
\(684\) 0 0
\(685\) 10626.3i 0.592714i
\(686\) 0 0
\(687\) 18179.6 10447.6i 1.00960 0.580204i
\(688\) 0 0
\(689\) −11390.0 + 19728.0i −0.629788 + 1.09082i
\(690\) 0 0
\(691\) −12510.8 + 7223.09i −0.688758 + 0.397655i −0.803147 0.595781i \(-0.796842\pi\)
0.114389 + 0.993436i \(0.463509\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 18975.0 10955.2i 1.03563 0.597921i
\(696\) 0 0
\(697\) 60.6882 105.115i 0.00329804 0.00571236i
\(698\) 0 0
\(699\) 25098.3 14423.7i 1.35809 0.780477i
\(700\) 0 0
\(701\) 14699.3i 0.791989i −0.918253 0.395994i \(-0.870400\pi\)
0.918253 0.395994i \(-0.129600\pi\)
\(702\) 0 0
\(703\) 18888.6 + 10905.4i 1.01337 + 0.585069i
\(704\) 0 0
\(705\) −24981.5 + 43070.2i −1.33455 + 2.30088i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 2510.97 + 4349.13i 0.133006 + 0.230374i 0.924834 0.380371i \(-0.124204\pi\)
−0.791828 + 0.610745i \(0.790870\pi\)
\(710\) 0 0
\(711\) 16022.8 + 28010.4i 0.845152 + 1.47746i
\(712\) 0 0
\(713\) −18080.6 −0.949680
\(714\) 0 0
\(715\) −44540.3 −2.32967
\(716\) 0 0
\(717\) −4.13894 + 2070.26i −0.000215581 + 0.107832i
\(718\) 0 0
\(719\) 92.1486 + 159.606i 0.00477964 + 0.00827858i 0.868405 0.495855i \(-0.165145\pi\)
−0.863626 + 0.504134i \(0.831812\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 22257.4 + 12909.7i 1.14490 + 0.664063i
\(724\) 0 0
\(725\) 4775.83 + 2757.33i 0.244648 + 0.141248i
\(726\) 0 0
\(727\) 11575.2i 0.590507i 0.955419 + 0.295254i \(0.0954041\pi\)
−0.955419 + 0.295254i \(0.904596\pi\)
\(728\) 0 0
\(729\) 19681.6 + 236.100i 0.999928 + 0.0119951i
\(730\) 0 0
\(731\) −94.0227 + 162.852i −0.00475726 + 0.00823981i
\(732\) 0 0
\(733\) 2996.29 1729.91i 0.150983 0.0871701i −0.422605 0.906314i \(-0.638884\pi\)
0.573588 + 0.819144i \(0.305551\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4971.45 2870.27i 0.248475 0.143457i
\(738\) 0 0
\(739\) 17933.4 31061.6i 0.892681 1.54617i 0.0560320 0.998429i \(-0.482155\pi\)
0.836649 0.547740i \(-0.184512\pi\)
\(740\) 0 0
\(741\) 9373.47 + 16310.5i 0.464700 + 0.808614i
\(742\) 0 0
\(743\) 21120.0i 1.04282i −0.853305 0.521412i \(-0.825406\pi\)
0.853305 0.521412i \(-0.174594\pi\)
\(744\) 0 0
\(745\) −416.729 240.598i −0.0204936 0.0118320i
\(746\) 0 0
\(747\) 22526.6 + 90.0724i 1.10336 + 0.00441175i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −10074.1 17448.9i −0.489493 0.847827i 0.510434 0.859917i \(-0.329485\pi\)
−0.999927 + 0.0120899i \(0.996152\pi\)
\(752\) 0 0
\(753\) −21220.7 42.4251i −1.02699 0.00205319i
\(754\) 0 0
\(755\) −4015.14 −0.193544
\(756\) 0 0
\(757\) −24696.6 −1.18575 −0.592876 0.805293i \(-0.702008\pi\)
−0.592876 + 0.805293i \(0.702008\pi\)
\(758\) 0 0
\(759\) 52954.7 + 105.869i 2.53245 + 0.00506297i
\(760\) 0 0
\(761\) −14444.6 25018.7i −0.688061 1.19176i −0.972464 0.233052i \(-0.925129\pi\)
0.284403 0.958705i \(-0.408205\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 627.823 + 2.51034i 0.0296719 + 0.000118643i
\(766\) 0 0
\(767\) −10923.3 6306.55i −0.514233 0.296892i
\(768\) 0 0
\(769\) 29891.2i 1.40170i 0.713311 + 0.700848i \(0.247195\pi\)
−0.713311 + 0.700848i \(0.752805\pi\)
\(770\) 0 0
\(771\) 8959.52 + 15590.2i 0.418507 + 0.728234i
\(772\) 0 0
\(773\) 2656.64 4601.44i 0.123613 0.214104i −0.797577 0.603217i \(-0.793885\pi\)
0.921190 + 0.389113i \(0.127219\pi\)
\(774\) 0 0
\(775\) 13068.6 7545.18i 0.605728 0.349717i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 5552.90 3205.97i 0.255396 0.147453i
\(780\) 0 0
\(781\) 567.909 983.648i 0.0260197 0.0450674i
\(782\) 0 0
\(783\) 28.8336 4807.38i 0.00131600 0.219415i
\(784\) 0 0
\(785\) 49321.6i 2.24250i
\(786\) 0 0
\(787\) 25168.6 + 14531.1i 1.13998 + 0.658167i 0.946425 0.322923i \(-0.104666\pi\)
0.193553 + 0.981090i \(0.437999\pi\)
\(788\) 0 0
\(789\) 12679.4 + 7354.31i 0.572116 + 0.331838i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 6209.45 + 10755.1i 0.278063 + 0.481619i
\(794\) 0 0
\(795\) −80.2923 + 40161.6i −0.00358198 + 1.79168i
\(796\) 0 0
\(797\) −16751.0