Properties

Label 224.3.n.a.17.9
Level 224
Weight 3
Character 224.17
Analytic conductor 6.104
Analytic rank 0
Dimension 28
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 224.n (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.10355792167\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 17.9
Character \(\chi\) \(=\) 224.17
Dual form 224.3.n.a.145.9

$q$-expansion

\(f(q)\) \(=\) \(q+(0.455431 - 0.788830i) q^{3} +(3.17251 + 5.49495i) q^{5} +(-3.79106 + 5.88455i) q^{7} +(4.08516 + 7.07571i) q^{9} +O(q^{10})\) \(q+(0.455431 - 0.788830i) q^{3} +(3.17251 + 5.49495i) q^{5} +(-3.79106 + 5.88455i) q^{7} +(4.08516 + 7.07571i) q^{9} +(-11.4442 - 6.60732i) q^{11} -19.4243 q^{13} +5.77945 q^{15} +(13.7930 + 7.96338i) q^{17} +(8.22725 + 14.2500i) q^{19} +(2.91534 + 5.67051i) q^{21} +(11.9607 + 20.7166i) q^{23} +(-7.62967 + 13.2150i) q^{25} +15.6398 q^{27} -16.6618i q^{29} +(11.1360 + 6.42939i) q^{31} +(-10.4241 + 6.01837i) q^{33} +(-44.3625 - 2.16288i) q^{35} +(41.1844 - 23.7778i) q^{37} +(-8.84646 + 15.3225i) q^{39} +6.49499i q^{41} +33.2928i q^{43} +(-25.9205 + 44.8956i) q^{45} +(18.9713 - 10.9531i) q^{47} +(-20.2558 - 44.6173i) q^{49} +(12.5635 - 7.25355i) q^{51} +(-32.2028 - 18.5923i) q^{53} -83.8473i q^{55} +14.9878 q^{57} +(27.3428 - 47.3591i) q^{59} +(-5.12340 - 8.87399i) q^{61} +(-57.1245 - 2.78508i) q^{63} +(-61.6240 - 106.736i) q^{65} +(14.8386 + 8.56706i) q^{67} +21.7892 q^{69} -32.0568 q^{71} +(92.8082 + 53.5828i) q^{73} +(6.94958 + 12.0370i) q^{75} +(82.2668 - 42.2953i) q^{77} +(-29.1542 - 50.4965i) q^{79} +(-29.6436 + 51.3443i) q^{81} +36.3441 q^{83} +101.056i q^{85} +(-13.1433 - 7.58829i) q^{87} +(0.929882 - 0.536867i) q^{89} +(73.6388 - 114.303i) q^{91} +(10.1434 - 5.85629i) q^{93} +(-52.2021 + 90.4167i) q^{95} -169.517i q^{97} -107.968i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{7} - 32q^{9} + O(q^{10}) \) \( 28q + 4q^{7} - 32q^{9} - 28q^{15} - 6q^{17} - 30q^{23} - 32q^{25} + 6q^{31} - 6q^{33} + 20q^{39} + 294q^{47} - 20q^{49} + 124q^{57} - 432q^{63} - 52q^{65} + 136q^{71} + 234q^{73} + 162q^{79} - 18q^{81} - 48q^{87} - 150q^{89} - 290q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.455431 0.788830i 0.151810 0.262943i −0.780083 0.625677i \(-0.784823\pi\)
0.931893 + 0.362733i \(0.118156\pi\)
\(4\) 0 0
\(5\) 3.17251 + 5.49495i 0.634503 + 1.09899i 0.986620 + 0.163035i \(0.0521283\pi\)
−0.352118 + 0.935956i \(0.614538\pi\)
\(6\) 0 0
\(7\) −3.79106 + 5.88455i −0.541579 + 0.840650i
\(8\) 0 0
\(9\) 4.08516 + 7.07571i 0.453907 + 0.786190i
\(10\) 0 0
\(11\) −11.4442 6.60732i −1.04038 0.600666i −0.120442 0.992720i \(-0.538431\pi\)
−0.919942 + 0.392054i \(0.871764\pi\)
\(12\) 0 0
\(13\) −19.4243 −1.49418 −0.747090 0.664723i \(-0.768550\pi\)
−0.747090 + 0.664723i \(0.768550\pi\)
\(14\) 0 0
\(15\) 5.77945 0.385296
\(16\) 0 0
\(17\) 13.7930 + 7.96338i 0.811352 + 0.468434i 0.847425 0.530915i \(-0.178152\pi\)
−0.0360732 + 0.999349i \(0.511485\pi\)
\(18\) 0 0
\(19\) 8.22725 + 14.2500i 0.433013 + 0.750001i 0.997131 0.0756934i \(-0.0241170\pi\)
−0.564118 + 0.825694i \(0.690784\pi\)
\(20\) 0 0
\(21\) 2.91534 + 5.67051i 0.138826 + 0.270024i
\(22\) 0 0
\(23\) 11.9607 + 20.7166i 0.520032 + 0.900721i 0.999729 + 0.0232870i \(0.00741316\pi\)
−0.479697 + 0.877434i \(0.659254\pi\)
\(24\) 0 0
\(25\) −7.62967 + 13.2150i −0.305187 + 0.528599i
\(26\) 0 0
\(27\) 15.6398 0.579252
\(28\) 0 0
\(29\) 16.6618i 0.574544i −0.957849 0.287272i \(-0.907252\pi\)
0.957849 0.287272i \(-0.0927483\pi\)
\(30\) 0 0
\(31\) 11.1360 + 6.42939i 0.359227 + 0.207400i 0.668741 0.743495i \(-0.266833\pi\)
−0.309515 + 0.950895i \(0.600167\pi\)
\(32\) 0 0
\(33\) −10.4241 + 6.01837i −0.315882 + 0.182375i
\(34\) 0 0
\(35\) −44.3625 2.16288i −1.26750 0.0617964i
\(36\) 0 0
\(37\) 41.1844 23.7778i 1.11309 0.642644i 0.173463 0.984840i \(-0.444504\pi\)
0.939628 + 0.342196i \(0.111171\pi\)
\(38\) 0 0
\(39\) −8.84646 + 15.3225i −0.226832 + 0.392885i
\(40\) 0 0
\(41\) 6.49499i 0.158415i 0.996858 + 0.0792073i \(0.0252389\pi\)
−0.996858 + 0.0792073i \(0.974761\pi\)
\(42\) 0 0
\(43\) 33.2928i 0.774252i 0.922027 + 0.387126i \(0.126532\pi\)
−0.922027 + 0.387126i \(0.873468\pi\)
\(44\) 0 0
\(45\) −25.9205 + 44.8956i −0.576010 + 0.997679i
\(46\) 0 0
\(47\) 18.9713 10.9531i 0.403645 0.233045i −0.284411 0.958703i \(-0.591798\pi\)
0.688056 + 0.725658i \(0.258465\pi\)
\(48\) 0 0
\(49\) −20.2558 44.6173i −0.413383 0.910557i
\(50\) 0 0
\(51\) 12.5635 7.25355i 0.246343 0.142226i
\(52\) 0 0
\(53\) −32.2028 18.5923i −0.607601 0.350798i 0.164425 0.986390i \(-0.447423\pi\)
−0.772026 + 0.635591i \(0.780756\pi\)
\(54\) 0 0
\(55\) 83.8473i 1.52450i
\(56\) 0 0
\(57\) 14.9878 0.262944
\(58\) 0 0
\(59\) 27.3428 47.3591i 0.463437 0.802696i −0.535693 0.844413i \(-0.679949\pi\)
0.999129 + 0.0417169i \(0.0132827\pi\)
\(60\) 0 0
\(61\) −5.12340 8.87399i −0.0839902 0.145475i 0.820970 0.570971i \(-0.193433\pi\)
−0.904960 + 0.425496i \(0.860100\pi\)
\(62\) 0 0
\(63\) −57.1245 2.78508i −0.906737 0.0442076i
\(64\) 0 0
\(65\) −61.6240 106.736i −0.948061 1.64209i
\(66\) 0 0
\(67\) 14.8386 + 8.56706i 0.221471 + 0.127867i 0.606631 0.794983i \(-0.292520\pi\)
−0.385160 + 0.922850i \(0.625854\pi\)
\(68\) 0 0
\(69\) 21.7892 0.315785
\(70\) 0 0
\(71\) −32.0568 −0.451505 −0.225752 0.974185i \(-0.572484\pi\)
−0.225752 + 0.974185i \(0.572484\pi\)
\(72\) 0 0
\(73\) 92.8082 + 53.5828i 1.27135 + 0.734011i 0.975241 0.221144i \(-0.0709792\pi\)
0.296104 + 0.955156i \(0.404313\pi\)
\(74\) 0 0
\(75\) 6.94958 + 12.0370i 0.0926611 + 0.160494i
\(76\) 0 0
\(77\) 82.2668 42.2953i 1.06840 0.549290i
\(78\) 0 0
\(79\) −29.1542 50.4965i −0.369040 0.639196i 0.620376 0.784305i \(-0.286980\pi\)
−0.989416 + 0.145109i \(0.953647\pi\)
\(80\) 0 0
\(81\) −29.6436 + 51.3443i −0.365971 + 0.633880i
\(82\) 0 0
\(83\) 36.3441 0.437880 0.218940 0.975738i \(-0.429740\pi\)
0.218940 + 0.975738i \(0.429740\pi\)
\(84\) 0 0
\(85\) 101.056i 1.18889i
\(86\) 0 0
\(87\) −13.1433 7.58829i −0.151072 0.0872217i
\(88\) 0 0
\(89\) 0.929882 0.536867i 0.0104481 0.00603222i −0.494767 0.869026i \(-0.664747\pi\)
0.505215 + 0.862994i \(0.331413\pi\)
\(90\) 0 0
\(91\) 73.6388 114.303i 0.809217 1.25608i
\(92\) 0 0
\(93\) 10.1434 5.85629i 0.109069 0.0629709i
\(94\) 0 0
\(95\) −52.2021 + 90.4167i −0.549496 + 0.951755i
\(96\) 0 0
\(97\) 169.517i 1.74760i −0.486286 0.873799i \(-0.661649\pi\)
0.486286 0.873799i \(-0.338351\pi\)
\(98\) 0 0
\(99\) 107.968i 1.09059i
\(100\) 0 0
\(101\) −14.0630 + 24.3579i −0.139238 + 0.241167i −0.927208 0.374546i \(-0.877799\pi\)
0.787971 + 0.615713i \(0.211132\pi\)
\(102\) 0 0
\(103\) 144.029 83.1551i 1.39834 0.807331i 0.404120 0.914706i \(-0.367578\pi\)
0.994219 + 0.107374i \(0.0342444\pi\)
\(104\) 0 0
\(105\) −21.9102 + 34.0094i −0.208669 + 0.323899i
\(106\) 0 0
\(107\) −171.112 + 98.7918i −1.59918 + 0.923288i −0.607536 + 0.794292i \(0.707842\pi\)
−0.991645 + 0.128996i \(0.958825\pi\)
\(108\) 0 0
\(109\) 9.97643 + 5.75990i 0.0915269 + 0.0528431i 0.545065 0.838394i \(-0.316505\pi\)
−0.453538 + 0.891237i \(0.649838\pi\)
\(110\) 0 0
\(111\) 43.3167i 0.390240i
\(112\) 0 0
\(113\) −14.7908 −0.130892 −0.0654460 0.997856i \(-0.520847\pi\)
−0.0654460 + 0.997856i \(0.520847\pi\)
\(114\) 0 0
\(115\) −75.8911 + 131.447i −0.659923 + 1.14302i
\(116\) 0 0
\(117\) −79.3516 137.441i −0.678219 1.17471i
\(118\) 0 0
\(119\) −99.1509 + 50.9758i −0.833201 + 0.428368i
\(120\) 0 0
\(121\) 26.8135 + 46.4423i 0.221599 + 0.383821i
\(122\) 0 0
\(123\) 5.12345 + 2.95802i 0.0416541 + 0.0240490i
\(124\) 0 0
\(125\) 61.8047 0.494438
\(126\) 0 0
\(127\) 70.2656 0.553272 0.276636 0.960975i \(-0.410780\pi\)
0.276636 + 0.960975i \(0.410780\pi\)
\(128\) 0 0
\(129\) 26.2624 + 15.1626i 0.203584 + 0.117540i
\(130\) 0 0
\(131\) 71.0646 + 123.088i 0.542478 + 0.939600i 0.998761 + 0.0497649i \(0.0158472\pi\)
−0.456283 + 0.889835i \(0.650819\pi\)
\(132\) 0 0
\(133\) −115.045 5.60897i −0.864999 0.0421727i
\(134\) 0 0
\(135\) 49.6175 + 85.9400i 0.367537 + 0.636593i
\(136\) 0 0
\(137\) −126.537 + 219.168i −0.923626 + 1.59977i −0.129870 + 0.991531i \(0.541456\pi\)
−0.793756 + 0.608236i \(0.791877\pi\)
\(138\) 0 0
\(139\) 49.1909 0.353892 0.176946 0.984221i \(-0.443378\pi\)
0.176946 + 0.984221i \(0.443378\pi\)
\(140\) 0 0
\(141\) 19.9535i 0.141514i
\(142\) 0 0
\(143\) 222.296 + 128.343i 1.55452 + 0.897503i
\(144\) 0 0
\(145\) 91.5556 52.8597i 0.631418 0.364549i
\(146\) 0 0
\(147\) −44.4206 4.34174i −0.302181 0.0295356i
\(148\) 0 0
\(149\) −36.1077 + 20.8468i −0.242334 + 0.139911i −0.616249 0.787551i \(-0.711348\pi\)
0.373915 + 0.927463i \(0.378015\pi\)
\(150\) 0 0
\(151\) −48.8145 + 84.5492i −0.323275 + 0.559928i −0.981162 0.193188i \(-0.938117\pi\)
0.657887 + 0.753117i \(0.271450\pi\)
\(152\) 0 0
\(153\) 130.127i 0.850503i
\(154\) 0 0
\(155\) 81.5892i 0.526382i
\(156\) 0 0
\(157\) −14.0827 + 24.3919i −0.0896986 + 0.155363i −0.907384 0.420303i \(-0.861924\pi\)
0.817685 + 0.575666i \(0.195257\pi\)
\(158\) 0 0
\(159\) −29.3324 + 16.9350i −0.184480 + 0.106510i
\(160\) 0 0
\(161\) −167.251 8.15428i −1.03883 0.0506477i
\(162\) 0 0
\(163\) 209.952 121.216i 1.28805 0.743655i 0.309743 0.950820i \(-0.399757\pi\)
0.978306 + 0.207165i \(0.0664237\pi\)
\(164\) 0 0
\(165\) −66.1413 38.1867i −0.400856 0.231434i
\(166\) 0 0
\(167\) 60.1108i 0.359945i 0.983672 + 0.179972i \(0.0576008\pi\)
−0.983672 + 0.179972i \(0.942399\pi\)
\(168\) 0 0
\(169\) 208.305 1.23257
\(170\) 0 0
\(171\) −67.2193 + 116.427i −0.393096 + 0.680861i
\(172\) 0 0
\(173\) 69.6820 + 120.693i 0.402786 + 0.697646i 0.994061 0.108824i \(-0.0347085\pi\)
−0.591275 + 0.806470i \(0.701375\pi\)
\(174\) 0 0
\(175\) −48.8397 94.9959i −0.279084 0.542834i
\(176\) 0 0
\(177\) −24.9055 43.1376i −0.140709 0.243715i
\(178\) 0 0
\(179\) −252.643 145.863i −1.41141 0.814879i −0.415891 0.909415i \(-0.636530\pi\)
−0.995522 + 0.0945354i \(0.969863\pi\)
\(180\) 0 0
\(181\) 166.844 0.921791 0.460895 0.887455i \(-0.347528\pi\)
0.460895 + 0.887455i \(0.347528\pi\)
\(182\) 0 0
\(183\) −9.33343 −0.0510024
\(184\) 0 0
\(185\) 261.316 + 150.871i 1.41252 + 0.815518i
\(186\) 0 0
\(187\) −105.233 182.269i −0.562745 0.974703i
\(188\) 0 0
\(189\) −59.2914 + 92.0332i −0.313711 + 0.486948i
\(190\) 0 0
\(191\) −65.6781 113.758i −0.343864 0.595590i 0.641283 0.767305i \(-0.278403\pi\)
−0.985147 + 0.171715i \(0.945069\pi\)
\(192\) 0 0
\(193\) 40.7196 70.5284i 0.210982 0.365432i −0.741040 0.671461i \(-0.765667\pi\)
0.952022 + 0.306029i \(0.0990004\pi\)
\(194\) 0 0
\(195\) −112.262 −0.575702
\(196\) 0 0
\(197\) 2.09549i 0.0106370i −0.999986 0.00531851i \(-0.998307\pi\)
0.999986 0.00531851i \(-0.00169294\pi\)
\(198\) 0 0
\(199\) 109.937 + 63.4721i 0.552447 + 0.318955i 0.750108 0.661315i \(-0.230001\pi\)
−0.197662 + 0.980270i \(0.563335\pi\)
\(200\) 0 0
\(201\) 13.5159 7.80341i 0.0672433 0.0388230i
\(202\) 0 0
\(203\) 98.0469 + 63.1657i 0.482990 + 0.311161i
\(204\) 0 0
\(205\) −35.6897 + 20.6055i −0.174096 + 0.100514i
\(206\) 0 0
\(207\) −97.7231 + 169.261i −0.472092 + 0.817687i
\(208\) 0 0
\(209\) 217.440i 1.04038i
\(210\) 0 0
\(211\) 7.16822i 0.0339726i −0.999856 0.0169863i \(-0.994593\pi\)
0.999856 0.0169863i \(-0.00540717\pi\)
\(212\) 0 0
\(213\) −14.5997 + 25.2874i −0.0685432 + 0.118720i
\(214\) 0 0
\(215\) −182.943 + 105.622i −0.850896 + 0.491265i
\(216\) 0 0
\(217\) −80.0513 + 41.1563i −0.368900 + 0.189660i
\(218\) 0 0
\(219\) 84.5355 48.8066i 0.386007 0.222861i
\(220\) 0 0
\(221\) −267.920 154.683i −1.21231 0.699925i
\(222\) 0 0
\(223\) 279.720i 1.25435i −0.778878 0.627175i \(-0.784211\pi\)
0.778878 0.627175i \(-0.215789\pi\)
\(224\) 0 0
\(225\) −124.674 −0.554106
\(226\) 0 0
\(227\) 152.392 263.950i 0.671330 1.16278i −0.306198 0.951968i \(-0.599057\pi\)
0.977527 0.210809i \(-0.0676098\pi\)
\(228\) 0 0
\(229\) 207.344 + 359.130i 0.905433 + 1.56826i 0.820335 + 0.571883i \(0.193787\pi\)
0.0850971 + 0.996373i \(0.472880\pi\)
\(230\) 0 0
\(231\) 4.10305 84.1572i 0.0177621 0.364317i
\(232\) 0 0
\(233\) 82.4628 + 142.830i 0.353918 + 0.613004i 0.986932 0.161136i \(-0.0515159\pi\)
−0.633014 + 0.774140i \(0.718183\pi\)
\(234\) 0 0
\(235\) 120.373 + 69.4976i 0.512227 + 0.295735i
\(236\) 0 0
\(237\) −53.1109 −0.224097
\(238\) 0 0
\(239\) 19.1182 0.0799926 0.0399963 0.999200i \(-0.487265\pi\)
0.0399963 + 0.999200i \(0.487265\pi\)
\(240\) 0 0
\(241\) −303.376 175.154i −1.25882 0.726780i −0.285975 0.958237i \(-0.592317\pi\)
−0.972845 + 0.231457i \(0.925651\pi\)
\(242\) 0 0
\(243\) 97.3804 + 168.668i 0.400743 + 0.694106i
\(244\) 0 0
\(245\) 180.908 252.854i 0.738401 1.03206i
\(246\) 0 0
\(247\) −159.809 276.797i −0.647000 1.12064i
\(248\) 0 0
\(249\) 16.5522 28.6693i 0.0664748 0.115138i
\(250\) 0 0
\(251\) 88.3204 0.351874 0.175937 0.984401i \(-0.443704\pi\)
0.175937 + 0.984401i \(0.443704\pi\)
\(252\) 0 0
\(253\) 316.114i 1.24946i
\(254\) 0 0
\(255\) 79.7158 + 46.0240i 0.312611 + 0.180486i
\(256\) 0 0
\(257\) 74.5499 43.0414i 0.290077 0.167476i −0.347899 0.937532i \(-0.613105\pi\)
0.637977 + 0.770056i \(0.279772\pi\)
\(258\) 0 0
\(259\) −16.2106 + 332.495i −0.0625893 + 1.28376i
\(260\) 0 0
\(261\) 117.894 68.0661i 0.451701 0.260789i
\(262\) 0 0
\(263\) 159.605 276.444i 0.606863 1.05112i −0.384891 0.922962i \(-0.625761\pi\)
0.991754 0.128156i \(-0.0409057\pi\)
\(264\) 0 0
\(265\) 235.937i 0.890330i
\(266\) 0 0
\(267\) 0.978025i 0.00366302i
\(268\) 0 0
\(269\) 28.7340 49.7687i 0.106818 0.185014i −0.807662 0.589646i \(-0.799267\pi\)
0.914479 + 0.404632i \(0.132601\pi\)
\(270\) 0 0
\(271\) −26.7398 + 15.4382i −0.0986709 + 0.0569677i −0.548523 0.836135i \(-0.684810\pi\)
0.449853 + 0.893103i \(0.351477\pi\)
\(272\) 0 0
\(273\) −56.6286 110.146i −0.207431 0.403465i
\(274\) 0 0
\(275\) 174.631 100.823i 0.635023 0.366631i
\(276\) 0 0
\(277\) 308.465 + 178.092i 1.11359 + 0.642933i 0.939757 0.341842i \(-0.111051\pi\)
0.173834 + 0.984775i \(0.444384\pi\)
\(278\) 0 0
\(279\) 105.060i 0.376561i
\(280\) 0 0
\(281\) −294.160 −1.04683 −0.523416 0.852077i \(-0.675343\pi\)
−0.523416 + 0.852077i \(0.675343\pi\)
\(282\) 0 0
\(283\) −207.501 + 359.402i −0.733219 + 1.26997i 0.222282 + 0.974982i \(0.428649\pi\)
−0.955501 + 0.294989i \(0.904684\pi\)
\(284\) 0 0
\(285\) 47.5490 + 82.3572i 0.166838 + 0.288973i
\(286\) 0 0
\(287\) −38.2201 24.6229i −0.133171 0.0857940i
\(288\) 0 0
\(289\) −17.6691 30.6037i −0.0611386 0.105895i
\(290\) 0 0
\(291\) −133.720 77.2034i −0.459520 0.265304i
\(292\) 0 0
\(293\) −370.564 −1.26472 −0.632362 0.774673i \(-0.717915\pi\)
−0.632362 + 0.774673i \(0.717915\pi\)
\(294\) 0 0
\(295\) 346.981 1.17621
\(296\) 0 0
\(297\) −178.986 103.337i −0.602645 0.347937i
\(298\) 0 0
\(299\) −232.329 402.406i −0.777021 1.34584i
\(300\) 0 0
\(301\) −195.913 126.215i −0.650875 0.419319i
\(302\) 0 0
\(303\) 12.8095 + 22.1867i 0.0422755 + 0.0732233i
\(304\) 0 0
\(305\) 32.5081 56.3057i 0.106584 0.184609i
\(306\) 0 0
\(307\) 160.327 0.522239 0.261120 0.965306i \(-0.415908\pi\)
0.261120 + 0.965306i \(0.415908\pi\)
\(308\) 0 0
\(309\) 151.486i 0.490245i
\(310\) 0 0
\(311\) −409.490 236.419i −1.31669 0.760191i −0.333495 0.942752i \(-0.608228\pi\)
−0.983195 + 0.182561i \(0.941561\pi\)
\(312\) 0 0
\(313\) 200.063 115.506i 0.639179 0.369030i −0.145119 0.989414i \(-0.546357\pi\)
0.784298 + 0.620384i \(0.213023\pi\)
\(314\) 0 0
\(315\) −165.924 322.732i −0.526743 1.02455i
\(316\) 0 0
\(317\) −195.132 + 112.659i −0.615557 + 0.355392i −0.775137 0.631793i \(-0.782319\pi\)
0.159580 + 0.987185i \(0.448986\pi\)
\(318\) 0 0
\(319\) −110.090 + 190.681i −0.345109 + 0.597746i
\(320\) 0 0
\(321\) 179.972i 0.560659i
\(322\) 0 0
\(323\) 262.067i 0.811353i
\(324\) 0 0
\(325\) 148.201 256.692i 0.456004 0.789822i
\(326\) 0 0
\(327\) 9.08716 5.24648i 0.0277895 0.0160443i
\(328\) 0 0
\(329\) −7.46732 + 153.161i −0.0226970 + 0.465536i
\(330\) 0 0
\(331\) −17.9257 + 10.3494i −0.0541561 + 0.0312671i −0.526834 0.849968i \(-0.676621\pi\)
0.472677 + 0.881236i \(0.343288\pi\)
\(332\) 0 0
\(333\) 336.490 + 194.273i 1.01048 + 0.583401i
\(334\) 0 0
\(335\) 108.716i 0.324527i
\(336\) 0 0
\(337\) 34.9645 0.103752 0.0518762 0.998654i \(-0.483480\pi\)
0.0518762 + 0.998654i \(0.483480\pi\)
\(338\) 0 0
\(339\) −6.73619 + 11.6674i −0.0198708 + 0.0344172i
\(340\) 0 0
\(341\) −84.9621 147.159i −0.249156 0.431550i
\(342\) 0 0
\(343\) 339.343 + 49.9505i 0.989339 + 0.145628i
\(344\) 0 0
\(345\) 69.1264 + 119.730i 0.200366 + 0.347045i
\(346\) 0 0
\(347\) 379.958 + 219.369i 1.09498 + 0.632188i 0.934898 0.354916i \(-0.115491\pi\)
0.160083 + 0.987104i \(0.448824\pi\)
\(348\) 0 0
\(349\) 435.121 1.24677 0.623383 0.781917i \(-0.285758\pi\)
0.623383 + 0.781917i \(0.285758\pi\)
\(350\) 0 0
\(351\) −303.793 −0.865507
\(352\) 0 0
\(353\) 243.447 + 140.554i 0.689653 + 0.398171i 0.803482 0.595329i \(-0.202978\pi\)
−0.113829 + 0.993500i \(0.536312\pi\)
\(354\) 0 0
\(355\) −101.701 176.151i −0.286481 0.496200i
\(356\) 0 0
\(357\) −4.94514 + 101.429i −0.0138519 + 0.284115i
\(358\) 0 0
\(359\) 131.965 + 228.570i 0.367590 + 0.636685i 0.989188 0.146652i \(-0.0468497\pi\)
−0.621598 + 0.783336i \(0.713516\pi\)
\(360\) 0 0
\(361\) 45.1247 78.1583i 0.124999 0.216505i
\(362\) 0 0
\(363\) 48.8468 0.134564
\(364\) 0 0
\(365\) 679.969i 1.86293i
\(366\) 0 0
\(367\) 134.181 + 77.4694i 0.365615 + 0.211088i 0.671541 0.740967i \(-0.265633\pi\)
−0.305926 + 0.952055i \(0.598966\pi\)
\(368\) 0 0
\(369\) −45.9567 + 26.5331i −0.124544 + 0.0719055i
\(370\) 0 0
\(371\) 231.490 119.015i 0.623962 0.320794i
\(372\) 0 0
\(373\) −506.505 + 292.431i −1.35792 + 0.783997i −0.989344 0.145600i \(-0.953489\pi\)
−0.368579 + 0.929597i \(0.620155\pi\)
\(374\) 0 0
\(375\) 28.1478 48.7534i 0.0750608 0.130009i
\(376\) 0 0
\(377\) 323.644i 0.858472i
\(378\) 0 0
\(379\) 128.176i 0.338195i 0.985599 + 0.169098i \(0.0540853\pi\)
−0.985599 + 0.169098i \(0.945915\pi\)
\(380\) 0 0
\(381\) 32.0011 55.4276i 0.0839925 0.145479i
\(382\) 0 0
\(383\) 216.437 124.960i 0.565110 0.326266i −0.190084 0.981768i \(-0.560876\pi\)
0.755194 + 0.655502i \(0.227543\pi\)
\(384\) 0 0
\(385\) 493.403 + 317.870i 1.28157 + 0.825636i
\(386\) 0 0
\(387\) −235.571 + 136.007i −0.608709 + 0.351439i
\(388\) 0 0
\(389\) −187.428 108.212i −0.481821 0.278179i 0.239354 0.970932i \(-0.423064\pi\)
−0.721175 + 0.692753i \(0.756398\pi\)
\(390\) 0 0
\(391\) 380.991i 0.974402i
\(392\) 0 0
\(393\) 129.460 0.329415
\(394\) 0 0
\(395\) 184.984 320.401i 0.468314 0.811143i
\(396\) 0 0
\(397\) −349.941 606.116i −0.881463 1.52674i −0.849714 0.527244i \(-0.823226\pi\)
−0.0317493 0.999496i \(1.48989\pi\)
\(398\) 0 0
\(399\) −56.8196 + 88.1964i −0.142405 + 0.221044i
\(400\) 0 0
\(401\) 90.4903 + 156.734i 0.225662 + 0.390858i 0.956518 0.291674i \(-0.0942123\pi\)
−0.730856 + 0.682532i \(0.760879\pi\)
\(402\) 0 0
\(403\) −216.310 124.887i −0.536749 0.309892i
\(404\) 0 0
\(405\) −376.179 −0.928837
\(406\) 0 0
\(407\) −628.431 −1.54406
\(408\) 0 0
\(409\) −310.767 179.421i −0.759821 0.438683i 0.0694104 0.997588i \(-0.477888\pi\)
−0.829232 + 0.558905i \(0.811222\pi\)
\(410\) 0 0
\(411\) 115.258 + 199.632i 0.280432 + 0.485723i
\(412\) 0 0
\(413\) 175.029 + 340.441i 0.423798 + 0.824312i
\(414\) 0 0
\(415\) 115.302 + 199.709i 0.277836 + 0.481226i
\(416\) 0 0
\(417\) 22.4031 38.8033i 0.0537245 0.0930535i
\(418\) 0 0
\(419\) −780.890 −1.86370 −0.931849 0.362846i \(-0.881805\pi\)
−0.931849 + 0.362846i \(0.881805\pi\)
\(420\) 0 0
\(421\) 114.961i 0.273068i 0.990635 + 0.136534i \(0.0435962\pi\)
−0.990635 + 0.136534i \(0.956404\pi\)
\(422\) 0 0
\(423\) 155.002 + 89.4904i 0.366435 + 0.211561i
\(424\) 0 0
\(425\) −210.472 + 121.516i −0.495228 + 0.285920i
\(426\) 0 0
\(427\) 71.6425 + 3.49290i 0.167781 + 0.00818010i
\(428\) 0 0
\(429\) 202.482 116.903i 0.471985 0.272501i
\(430\) 0 0
\(431\) 154.856 268.219i 0.359295 0.622317i −0.628548 0.777771i \(-0.716351\pi\)
0.987843 + 0.155453i \(0.0496838\pi\)
\(432\) 0 0
\(433\) 595.775i 1.37592i 0.725747 + 0.687962i \(0.241494\pi\)
−0.725747 + 0.687962i \(0.758506\pi\)
\(434\) 0 0
\(435\) 96.2958i 0.221370i
\(436\) 0 0
\(437\) −196.808 + 340.881i −0.450361 + 0.780048i
\(438\) 0 0
\(439\) −698.796 + 403.450i −1.59179 + 0.919020i −0.598789 + 0.800907i \(0.704351\pi\)
−0.993000 + 0.118113i \(0.962315\pi\)
\(440\) 0 0
\(441\) 232.951 325.593i 0.528233 0.738306i
\(442\) 0 0
\(443\) −385.214 + 222.403i −0.869557 + 0.502039i −0.867201 0.497958i \(-0.834083\pi\)
−0.00235617 + 0.999997i \(0.500750\pi\)
\(444\) 0 0
\(445\) 5.90012 + 3.40644i 0.0132587 + 0.00765491i
\(446\) 0 0
\(447\) 37.9772i 0.0849601i
\(448\) 0 0
\(449\) 262.420 0.584455 0.292228 0.956349i \(-0.405604\pi\)
0.292228 + 0.956349i \(0.405604\pi\)
\(450\) 0 0
\(451\) 42.9145 74.3302i 0.0951542 0.164812i
\(452\) 0 0
\(453\) 44.4633 + 77.0127i 0.0981530 + 0.170006i
\(454\) 0 0
\(455\) 861.712 + 42.0124i 1.89387 + 0.0923350i
\(456\) 0 0
\(457\) −194.738 337.296i −0.426122 0.738065i 0.570403 0.821365i \(-0.306787\pi\)
−0.996524 + 0.0833004i \(0.973454\pi\)
\(458\) 0 0
\(459\) 215.720 + 124.546i 0.469978 + 0.271342i
\(460\) 0 0
\(461\) 158.714 0.344283 0.172141 0.985072i \(-0.444931\pi\)
0.172141 + 0.985072i \(0.444931\pi\)
\(462\) 0 0
\(463\) 528.844 1.14221 0.571106 0.820877i \(-0.306515\pi\)
0.571106 + 0.820877i \(0.306515\pi\)
\(464\) 0 0
\(465\) 64.3601 + 37.1583i 0.138409 + 0.0799103i
\(466\) 0 0
\(467\) 218.449 + 378.365i 0.467771 + 0.810203i 0.999322 0.0368236i \(-0.0117240\pi\)
−0.531551 + 0.847026i \(0.678391\pi\)
\(468\) 0 0
\(469\) −106.667 + 54.8401i −0.227435 + 0.116930i
\(470\) 0 0
\(471\) 12.8274 + 22.2177i 0.0272344 + 0.0471713i
\(472\) 0 0
\(473\) 219.977 381.011i 0.465067 0.805519i
\(474\) 0 0
\(475\) −251.085 −0.528600
\(476\) 0 0
\(477\) 303.811i 0.636920i
\(478\) 0 0
\(479\) −472.737 272.935i −0.986925 0.569802i −0.0825716 0.996585i \(-0.526313\pi\)
−0.904354 + 0.426783i \(0.859647\pi\)
\(480\) 0 0
\(481\) −799.980 + 461.869i −1.66316 + 0.960226i
\(482\) 0 0
\(483\) −82.6039 + 128.219i −0.171023 + 0.265464i
\(484\) 0 0
\(485\) 931.488 537.795i 1.92059 1.10886i
\(486\) 0 0
\(487\) 324.115 561.384i 0.665534 1.15274i −0.313606 0.949553i \(-0.601537\pi\)
0.979140 0.203185i \(-0.0651294\pi\)
\(488\) 0 0
\(489\) 220.822i 0.451579i
\(490\) 0 0
\(491\) 732.074i 1.49098i −0.666514 0.745492i \(-0.732214\pi\)
0.666514 0.745492i \(-0.267786\pi\)
\(492\) 0 0
\(493\) 132.684 229.815i 0.269136 0.466157i
\(494\) 0 0
\(495\) 593.279 342.530i 1.19854 0.691980i
\(496\) 0 0
\(497\) 121.529 188.640i 0.244526 0.379557i
\(498\) 0 0
\(499\) −23.1264 + 13.3520i −0.0463454 + 0.0267575i −0.522994 0.852337i \(-0.675185\pi\)
0.476648 + 0.879094i \(0.341852\pi\)
\(500\) 0 0
\(501\) 47.4172 + 27.3763i 0.0946451 + 0.0546434i
\(502\) 0 0
\(503\) 616.414i 1.22548i 0.790286 + 0.612738i \(0.209932\pi\)
−0.790286 + 0.612738i \(0.790068\pi\)
\(504\) 0 0
\(505\) −178.460 −0.353387
\(506\) 0 0
\(507\) 94.8687 164.317i 0.187118 0.324097i
\(508\) 0 0
\(509\) −66.3763 114.967i −0.130405 0.225869i 0.793428 0.608665i \(-0.208295\pi\)
−0.923833 + 0.382796i \(0.874961\pi\)
\(510\) 0 0
\(511\) −667.152 + 342.999i −1.30558 + 0.671230i
\(512\) 0 0
\(513\) 128.673 + 222.868i 0.250824 + 0.434440i
\(514\) 0 0
\(515\) 913.867 + 527.621i 1.77450 + 1.02451i
\(516\) 0 0
\(517\) −289.483 −0.559928
\(518\) 0 0
\(519\) 126.942 0.244589
\(520\) 0 0
\(521\) −585.480 338.027i −1.12376 0.648804i −0.181403 0.983409i \(-0.558064\pi\)
−0.942359 + 0.334605i \(0.891397\pi\)
\(522\) 0 0
\(523\) 186.224 + 322.550i 0.356069 + 0.616730i 0.987300 0.158865i \(-0.0507833\pi\)
−0.631231 + 0.775595i \(0.717450\pi\)
\(524\) 0 0
\(525\) −97.1787 4.73791i −0.185102 0.00902459i
\(526\) 0 0
\(527\) 102.399 + 177.361i 0.194306 + 0.336548i
\(528\) 0 0
\(529\) −21.6179 + 37.4433i −0.0408656 + 0.0707813i
\(530\) 0 0
\(531\) 446.799 0.841429
\(532\) 0 0
\(533\) 126.161i 0.236700i
\(534\) 0 0
\(535\) −1085.71 626.836i −2.02937 1.17166i
\(536\) 0 0
\(537\) −230.123 + 132.862i −0.428534 + 0.247414i
\(538\) 0 0
\(539\) −62.9892 + 644.447i −0.116863 + 1.19563i
\(540\) 0 0
\(541\) −60.3373 + 34.8357i −0.111529 + 0.0643914i −0.554727 0.832032i \(-0.687177\pi\)
0.443198 + 0.896424i \(0.353844\pi\)
\(542\) 0 0
\(543\) 75.9860 131.612i 0.139937 0.242379i
\(544\) 0 0
\(545\) 73.0934i 0.134116i
\(546\) 0 0
\(547\) 466.463i 0.852765i −0.904543 0.426383i \(-0.859788\pi\)
0.904543 0.426383i \(-0.140212\pi\)
\(548\) 0 0
\(549\) 41.8599 72.5034i 0.0762475 0.132065i
\(550\) 0 0
\(551\) 237.430 137.081i 0.430908 0.248785i
\(552\) 0 0
\(553\) 407.674 + 19.8760i 0.737204 + 0.0359421i
\(554\) 0 0
\(555\) 238.023 137.423i 0.428870 0.247608i
\(556\) 0 0
\(557\) −118.835 68.6094i −0.213348 0.123177i 0.389518 0.921019i \(-0.372642\pi\)
−0.602866 + 0.797842i \(0.705975\pi\)
\(558\) 0 0
\(559\) 646.692i 1.15687i
\(560\) 0 0
\(561\) −191.706 −0.341722
\(562\) 0 0
\(563\) 84.5632 146.468i 0.150201 0.260156i −0.781100 0.624406i \(-0.785341\pi\)
0.931301 + 0.364250i \(0.118675\pi\)
\(564\) 0 0
\(565\) −46.9240 81.2747i −0.0830513 0.143849i
\(566\) 0 0
\(567\) −189.757 369.088i −0.334669 0.650949i
\(568\) 0 0
\(569\) −372.466 645.129i −0.654597 1.13379i −0.981995 0.188908i \(-0.939505\pi\)
0.327398 0.944887i \(-0.393828\pi\)
\(570\) 0 0
\(571\) −767.828 443.306i −1.34471 0.776367i −0.357213 0.934023i \(-0.616273\pi\)
−0.987494 + 0.157655i \(0.949606\pi\)
\(572\) 0 0
\(573\) −119.647 −0.208809
\(574\) 0 0
\(575\) −365.026 −0.634827
\(576\) 0 0
\(577\) −207.900 120.031i −0.360311 0.208026i 0.308906 0.951093i \(-0.400037\pi\)
−0.669217 + 0.743067i \(0.733370\pi\)
\(578\) 0 0
\(579\) −37.0900 64.2417i −0.0640586 0.110953i
\(580\) 0 0
\(581\) −137.782 + 213.868i −0.237147 + 0.368104i
\(582\) 0 0
\(583\) 245.691 + 425.549i 0.421425 + 0.729930i
\(584\) 0 0
\(585\) 503.488 872.067i 0.860663 1.49071i
\(586\) 0 0
\(587\) −190.873 −0.325168 −0.162584 0.986695i \(-0.551983\pi\)
−0.162584 + 0.986695i \(0.551983\pi\)
\(588\) 0 0
\(589\) 211.585i 0.359227i
\(590\) 0 0
\(591\) −1.65299 0.954353i −0.00279693 0.00161481i
\(592\) 0 0
\(593\) 637.548 368.089i 1.07512 0.620723i 0.145547 0.989351i \(-0.453506\pi\)
0.929577 + 0.368629i \(0.120173\pi\)
\(594\) 0 0
\(595\) −594.667 383.108i −0.999441 0.643879i
\(596\) 0 0
\(597\) 100.137 57.8144i 0.167734 0.0968415i
\(598\) 0 0
\(599\) 558.330 967.057i 0.932104 1.61445i 0.152386 0.988321i \(-0.451304\pi\)
0.779718 0.626131i \(-0.215362\pi\)
\(600\) 0 0
\(601\) 183.100i 0.304659i −0.988330 0.152329i \(-0.951323\pi\)
0.988330 0.152329i \(-0.0486774\pi\)
\(602\) 0 0
\(603\) 139.991i 0.232158i
\(604\) 0 0
\(605\) −170.132 + 294.678i −0.281210 + 0.487071i
\(606\) 0 0
\(607\) −394.026 + 227.491i −0.649136 + 0.374779i −0.788125 0.615515i \(-0.788948\pi\)
0.138989 + 0.990294i \(0.455615\pi\)
\(608\) 0 0
\(609\) 94.4807 48.5748i 0.155141 0.0797615i
\(610\) 0 0
\(611\) −368.505 + 212.757i −0.603118 + 0.348211i
\(612\) 0 0
\(613\) 232.853 + 134.438i 0.379859 + 0.219312i 0.677757 0.735286i \(-0.262952\pi\)
−0.297898 + 0.954598i \(0.596286\pi\)
\(614\) 0 0
\(615\) 37.5375i 0.0610366i
\(616\) 0 0
\(617\) −184.934 −0.299731 −0.149866 0.988706i \(-0.547884\pi\)
−0.149866 + 0.988706i \(0.547884\pi\)
\(618\) 0 0
\(619\) 496.809 860.498i 0.802599 1.39014i −0.115301 0.993331i \(-0.536783\pi\)
0.917900 0.396812i \(-0.129884\pi\)
\(620\) 0 0
\(621\) 187.064 + 324.004i 0.301229 + 0.521745i
\(622\) 0 0
\(623\) −0.366012 + 7.50723i −0.000587499 + 0.0120501i
\(624\) 0 0
\(625\) 386.818 + 669.988i 0.618909 + 1.07198i
\(626\) 0 0
\(627\) −171.524 99.0292i −0.273562 0.157941i
\(628\) 0 0
\(629\) 757.408 1.20415
\(630\) 0 0
\(631\) −805.857 −1.27711 −0.638555 0.769576i \(-0.720468\pi\)
−0.638555 + 0.769576i \(0.720468\pi\)
\(632\) 0 0
\(633\) −5.65451 3.26463i −0.00893287 0.00515740i
\(634\) 0 0
\(635\) 222.918 + 386.106i 0.351053 + 0.608041i
\(636\) 0 0
\(637\) 393.455 + 866.662i 0.617669 + 1.36054i
\(638\) 0 0
\(639\) −130.957 226.825i −0.204941 0.354969i
\(640\) 0 0
\(641\) −2.75221 + 4.76696i −0.00429361 + 0.00743676i −0.868164 0.496277i \(-0.834700\pi\)
0.863871 + 0.503714i \(0.168033\pi\)
\(642\) 0 0
\(643\) 1024.08 1.59266 0.796331 0.604861i \(-0.206771\pi\)
0.796331 + 0.604861i \(0.206771\pi\)
\(644\) 0 0
\(645\) 192.414i 0.298317i
\(646\) 0 0
\(647\) −395.404 228.287i −0.611134 0.352839i 0.162275 0.986746i \(-0.448117\pi\)
−0.773409 + 0.633907i \(0.781450\pi\)
\(648\) 0 0
\(649\) −625.834 + 361.325i −0.964304 + 0.556741i
\(650\) 0 0
\(651\) −3.99255 + 81.8908i −0.00613295 + 0.125792i
\(652\) 0 0
\(653\) −24.4603 + 14.1222i −0.0374584 + 0.0216266i −0.518612 0.855010i \(-0.673551\pi\)
0.481154 + 0.876636i \(0.340218\pi\)
\(654\) 0 0
\(655\) −450.907 + 780.994i −0.688407 + 1.19236i
\(656\) 0 0
\(657\) 875.579i 1.33269i
\(658\) 0 0
\(659\) 132.188i 0.200589i 0.994958 + 0.100295i \(0.0319785\pi\)
−0.994958 + 0.100295i \(0.968021\pi\)
\(660\) 0 0
\(661\) 346.924 600.889i 0.524847 0.909061i −0.474735 0.880129i \(-0.657456\pi\)
0.999581 0.0289321i \(-0.00921065\pi\)
\(662\) 0 0
\(663\) −244.038 + 140.895i −0.368082 + 0.212512i
\(664\) 0 0
\(665\) −334.160 649.960i −0.502497 0.977384i
\(666\) 0 0
\(667\) 345.175 199.287i 0.517504 0.298781i
\(668\) 0 0
\(669\) −220.652 127.393i −0.329823 0.190424i
\(670\) 0 0
\(671\) 135.408i 0.201800i
\(672\) 0 0
\(673\) 532.137 0.790694 0.395347 0.918532i \(-0.370624\pi\)
0.395347 + 0.918532i \(0.370624\pi\)
\(674\) 0 0
\(675\) −119.327 + 206.680i −0.176780 + 0.306192i
\(676\) 0 0
\(677\) −143.115 247.883i −0.211396 0.366149i 0.740756 0.671775i \(-0.234468\pi\)
−0.952152 + 0.305626i \(0.901134\pi\)
\(678\) 0 0
\(679\) 997.531 + 642.649i 1.46912 + 0.946464i
\(680\) 0 0
\(681\) −138.808 240.423i −0.203830 0.353043i
\(682\) 0 0
\(683\) −387.838 223.918i −0.567844 0.327845i 0.188443 0.982084i \(-0.439656\pi\)
−0.756288 + 0.654239i \(0.772989\pi\)
\(684\) 0 0
\(685\) −1605.76 −2.34417
\(686\) 0 0
\(687\) 377.724 0.549817
\(688\) 0 0
\(689\) 625.519 + 361.143i 0.907865 + 0.524156i
\(690\) 0 0
\(691\) −510.366 883.980i −0.738591 1.27928i −0.953130 0.302561i \(-0.902158\pi\)
0.214539 0.976715i \(1.56882\pi\)
\(692\) 0 0
\(693\) 635.343 + 409.313i 0.916801 + 0.590639i
\(694\) 0 0
\(695\) 156.059 + 270.302i 0.224545 + 0.388924i
\(696\) 0 0
\(697\) −51.7221 + 89.5854i −0.0742068 + 0.128530i
\(698\) 0 0
\(699\) 150.225 0.214914
\(700\) 0 0
\(701\) 1311.02i 1.87021i −0.354369 0.935106i \(-0.615304\pi\)
0.354369 0.935106i \(-0.384696\pi\)
\(702\) 0 0
\(703\) 677.669 + 391.252i 0.963967 + 0.556546i
\(704\) 0 0
\(705\) 109.644 63.3028i 0.155523 0.0897912i
\(706\) 0 0
\(707\) −90.0213 175.096i −0.127329 0.247661i
\(708\) 0 0
\(709\) −465.495 + 268.754i −0.656552 + 0.379061i −0.790962 0.611865i \(-0.790419\pi\)
0.134410 + 0.990926i \(0.457086\pi\)
\(710\) 0 0
\(711\) 238.199 412.573i 0.335020 0.580271i
\(712\) 0 0
\(713\) 307.601i 0.431417i
\(714\) 0 0
\(715\) 1628.68i 2.27787i
\(716\) 0 0
\(717\) 8.70704 15.0810i 0.0121437 0.0210335i
\(718\) 0 0
\(719\) 233.275 134.681i 0.324443 0.187318i −0.328928 0.944355i \(-0.606687\pi\)
0.653371 + 0.757037i \(0.273354\pi\)
\(720\) 0 0
\(721\) −56.6914 + 1162.79i −0.0786288 + 1.61275i
\(722\) 0 0
\(723\) −276.334 + 159.541i −0.382204 + 0.220666i
\(724\) 0 0
\(725\) 220.185 + 127.124i 0.303703 + 0.175343i
\(726\) 0 0
\(727\) 460.316i 0.633172i 0.948564 + 0.316586i \(0.102537\pi\)
−0.948564 + 0.316586i \(0.897463\pi\)
\(728\) 0 0
\(729\) −356.185 −0.488594
\(730\) 0 0
\(731\) −265.124 + 459.208i −0.362686 + 0.628191i
\(732\) 0 0
\(733\) −33.3410 57.7484i −0.0454857 0.0787836i 0.842386 0.538874i \(-0.181150\pi\)
−0.887872 + 0.460091i \(0.847817\pi\)
\(734\) 0 0
\(735\) −117.067 257.863i −0.159275 0.350834i
\(736\) 0 0
\(737\) −113.211 196.087i −0.153610 0.266061i
\(738\) 0 0
\(739\) 808.772 + 466.944i 1.09441 + 0.631860i 0.934748 0.355311i \(-0.115625\pi\)
0.159665 + 0.987171i \(0.448958\pi\)
\(740\) 0 0
\(741\) −291.128 −0.392885
\(742\) 0 0
\(743\) 1198.23 1.61269 0.806345 0.591446i \(-0.201443\pi\)
0.806345 + 0.591446i \(0.201443\pi\)
\(744\) 0 0
\(745\) −229.104 132.273i −0.307523 0.177548i
\(746\) 0 0
\(747\) 148.471 + 257.160i 0.198757 + 0.344257i
\(748\) 0 0
\(749\) 67.3518 1381.44i 0.0899222 1.84438i
\(750\) 0 0
\(751\) −84.2993 146.011i −0.112249 0.194422i 0.804427 0.594051i \(-0.202472\pi\)
−0.916677 + 0.399629i \(0.869139\pi\)
\(752\) 0 0
\(753\) 40.2239 69.6698i 0.0534182 0.0925230i
\(754\) 0 0
\(755\) −619.458 −0.820474
\(756\) 0 0
\(757\) 209.207i 0.276364i 0.990407 + 0.138182i \(0.0441259\pi\)
−0.990407 + 0.138182i \(0.955874\pi\)
\(758\) 0 0
\(759\) −249.360 143.968i −0.328538 0.189681i
\(760\) 0 0
\(761\) 479.127 276.624i 0.629602 0.363501i −0.150996 0.988534i \(-0.548248\pi\)
0.780598 + 0.625033i \(0.214915\pi\)
\(762\) 0 0
\(763\) −71.7156 + 36.8707i −0.0939916 + 0.0483233i
\(764\) 0 0
\(765\) −715.041 + 412.829i −0.934695 + 0.539646i
\(766\) 0 0
\(767\) −531.115 + 919.919i −0.692458 + 1.19937i
\(768\) 0 0
\(769\) 219.524i 0.285467i 0.989761 + 0.142734i \(0.0455892\pi\)
−0.989761 + 0.142734i \(0.954411\pi\)
\(770\) 0 0
\(771\) 78.4096i 0.101699i
\(772\) 0 0
\(773\) −333.337 + 577.357i −0.431225 + 0.746904i −0.996979 0.0776701i \(-0.975252\pi\)
0.565754 + 0.824574i \(0.308585\pi\)
\(774\) 0 0
\(775\) −169.928 + 98.1082i −0.219262 + 0.126591i
\(776\) 0 0
\(777\) 254.899 + 164.216i 0.328055 + 0.211346i
\(778\) 0 0
\(779\) −92.5538 + 53.4359i −0.118811 + 0.0685956i
\(780\) 0 0
\(781\) 366.866 + 211.810i 0.469738 + 0.271204i
\(782\) 0 0
\(783\) 260.587i 0.332806i
\(784\) 0 0
\(785\) −178.710 −0.227656
\(786\) 0 0
\(787\) −459.932 + 796.626i −0.584412 + 1.01223i 0.410536 + 0.911844i \(0.365341\pi\)
−0.994948 + 0.100387i \(0.967992\pi\)