Properties

Label 224.3.n.a.17.6
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 17.6
Character \(\chi\) \(=\) 224.17
Dual form 224.3.n.a.145.6

$q$-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 −0.931893 0.362733i \(-0.881844\pi\)
0.780083 + 0.625677i \(0.215177\pi\)
\(4\) 0 0
\(5\) −3.17251 5.49495i −0.634503 1.09899i −0.986620 0.163035i \(-0.947872\pi\)
0.352118 0.935956i \(1.61454\pi\)
\(6\) 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 0.919942 0.392054i \(-0.128236\pi\)
0.120442 + 0.992720i \(0.461569\pi\)
\(12\) 0 0
\(13\) 19.4243 1.49418 0.747090 0.664723i \(-0.231450\pi\)
0.747090 + 0.664723i \(0.231450\pi\)
\(14\) 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 0.564118 0.825694i \(-0.309216\pi\)
−0.997131 + 0.0756934i \(0.975883\pi\)
\(20\) 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 \(0.0927483\pi\)
−0.957849 + 0.287272i \(0.907252\pi\)
\(30\) 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 −0.939628 0.342196i \(-0.888829\pi\)
−0.173463 + 0.984840i \(0.555496\pi\)
\(38\) 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 \(-0.873468\pi\)
0.922027 0.387126i \(-0.126532\pi\)
\(44\) 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 0.772026 0.635591i \(-0.219244\pi\)
−0.164425 + 0.986390i \(0.552577\pi\)
\(54\) 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 −0.999129 0.0417169i \(-0.986717\pi\)
0.535693 + 0.844413i \(0.320051\pi\)
\(60\) 0 0
\(61\) 5.12340 + 8.87399i 0.0839902 + 0.145475i 0.904960 0.425496i \(-0.139900\pi\)
−0.820970 + 0.570971i \(0.806567\pi\)
\(62\) 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 0.385160 0.922850i \(-0.374146\pi\)
−0.606631 + 0.794983i \(0.707480\pi\)
\(68\) 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 \(-0.570260\pi\)
−0.218940 + 0.975738i \(0.570260\pi\)
\(84\) 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 −0.787971 0.615713i \(-0.788868\pi\)
0.927208 + 0.374546i \(0.122201\pi\)
\(102\) 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 \(-0.292158\pi\)
0.991645 0.128996i \(-0.0411753\pi\)
\(108\) 0 0
\(109\) −9.97643 5.75990i −0.0915269 0.0528431i 0.453538 0.891237i \(-0.350162\pi\)
−0.545065 + 0.838394i \(0.683495\pi\)
\(110\) 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 \(-0.984153\pi\)
0.456283 0.889835i \(1.65082\pi\)
\(132\) 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 \(-0.556622\pi\)
−0.176946 + 0.984221i \(0.556622\pi\)
\(140\) 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 −0.373915 0.927463i \(-0.621985\pi\)
0.616249 + 0.787551i \(0.288652\pi\)
\(150\) 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 −0.817685 0.575666i \(-0.804743\pi\)
0.907384 + 0.420303i \(0.138076\pi\)
\(158\) 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 −0.978306 0.207165i \(-0.933576\pi\)
−0.309743 + 0.950820i \(0.600243\pi\)
\(164\) 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 0.591275 0.806470i \(-0.298625\pi\)
−0.994061 + 0.108824i \(0.965292\pi\)
\(174\) 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 0.995522 0.0945354i \(-0.0301365\pi\)
0.415891 + 0.909415i \(0.363470\pi\)
\(180\) 0 0
\(181\) −166.844 −0.921791 −0.460895 0.887455i \(-0.652472\pi\)
−0.460895 + 0.887455i \(0.652472\pi\)
\(182\) 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 \(0.00169294\pi\)
−0.999986 + 0.00531851i \(0.998307\pi\)
\(198\) 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 \(0.00540717\pi\)
−0.999856 + 0.0169863i \(0.994593\pi\)
\(212\) 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 \(0.400943\pi\)
−0.977527 + 0.210809i \(0.932390\pi\)
\(228\) 0 0
\(229\) −207.344 359.130i −0.905433 1.56826i −0.820335 0.571883i \(-0.806213\pi\)
−0.0850971 0.996373i \(1.47288\pi\)
\(230\) 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 \(-0.556296\pi\)
−0.175937 + 0.984401i \(0.556296\pi\)
\(252\) 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 −0.914479 0.404632i \(-0.867399\pi\)
0.807662 + 0.589646i \(0.200733\pi\)
\(270\) 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 −0.173834 0.984775i \(-0.555616\pi\)
−0.939757 + 0.341842i \(0.888949\pi\)
\(278\) 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 \(-0.571351\pi\)
0.955501 0.294989i \(-0.0953161\pi\)
\(284\) 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 \(-0.282085\pi\)
0.632362 + 0.774673i \(0.282085\pi\)
\(294\) 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 \(-0.584092\pi\)
−0.261120 + 0.965306i \(0.584092\pi\)
\(308\) 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 −0.159580 0.987185i \(-0.551014\pi\)
0.775137 + 0.631793i \(0.217681\pi\)
\(318\) 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 −0.472677 0.881236i \(-0.656712\pi\)
0.526834 + 0.849968i \(0.323379\pi\)
\(332\) 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 −0.160083 0.987104i \(-0.551176\pi\)
−0.934898 + 0.354916i \(0.884509\pi\)
\(348\) 0 0
\(349\) −435.121 −1.24677 −0.623383 0.781917i \(-0.714242\pi\)
−0.623383 + 0.781917i \(0.714242\pi\)
\(350\) 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 0.368579 0.929597i \(-0.379845\pi\)
0.989344 + 0.145600i \(0.0465112\pi\)
\(374\) 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 \(-0.945915\pi\)
0.985599 0.169098i \(-0.0540853\pi\)
\(380\) 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 0.721175 0.692753i \(-0.243602\pi\)
−0.239354 + 0.970932i \(0.576936\pi\)
\(390\) 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 \(0.176774\pi\)
0.0317493 + 0.999496i \(0.489892\pi\)
\(398\) 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 \(-0.118195\pi\)
0.931849 + 0.362846i \(0.118195\pi\)
\(420\) 0 0
\(421\) 114.961i 0.273068i −0.990635 0.136534i \(-0.956404\pi\)
0.990635 0.136534i \(-0.0435962\pi\)
\(422\) 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 0.00235617 0.999997i \(-0.499250\pi\)
0.867201 + 0.497958i \(0.165917\pi\)
\(444\) 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 \(-0.555069\pi\)
−0.172141 + 0.985072i \(0.555069\pi\)
\(462\) 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 0.531551 0.847026i \(-0.321609\pi\)
−0.999322 + 0.0368236i \(0.988276\pi\)
\(468\) 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 \(0.267786\pi\)
−0.666514 + 0.745492i \(0.732214\pi\)
\(492\) 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 −0.476648 0.879094i \(-0.658148\pi\)
0.522994 + 0.852337i \(0.324815\pi\)
\(500\) 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 0.923833 0.382796i \(-0.125039\pi\)
−0.793428 + 0.608665i \(0.791705\pi\)
\(510\) 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 0.631231 0.775595i \(-0.282550\pi\)
−0.987300 + 0.158865i \(0.949217\pi\)
\(524\) 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 −0.443198 0.896424i \(-0.646156\pi\)
0.554727 + 0.832032i \(0.312823\pi\)
\(542\) 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 \(0.140212\pi\)
−0.904543 + 0.426383i \(0.859788\pi\)
\(548\) 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 0.602866 0.797842i \(-0.294025\pi\)
−0.389518 + 0.921019i \(0.627358\pi\)
\(558\) 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 −0.931301 0.364250i \(-0.881325\pi\)
0.781100 + 0.624406i \(0.214659\pi\)
\(564\) 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 0.987494 0.157655i \(-0.0503935\pi\)
0.357213 + 0.934023i \(0.383727\pi\)
\(572\) 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 \(-0.448017\pi\)
0.162584 + 0.986695i \(0.448017\pi\)
\(588\) 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 0.297898 0.954598i \(-0.403714\pi\)
−0.677757 + 0.735286i \(0.737048\pi\)
\(614\) 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 \(0.463217\pi\)
−0.917900 + 0.396812i \(0.870116\pi\)
\(620\) 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 \(-0.793229\pi\)
−0.796331 + 0.604861i \(0.793229\pi\)
\(644\) 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 −0.481154 0.876636i \(-0.659782\pi\)
0.518612 + 0.855010i \(0.326449\pi\)
\(654\) 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 \(-0.968021\pi\)
0.994958 0.100295i \(-0.0319785\pi\)
\(660\) 0 0
\(661\) −346.924 + 600.889i −0.524847 + 0.909061i 0.474735 + 0.880129i \(0.342544\pi\)
−0.999581 + 0.0289321i \(0.990789\pi\)
\(662\) 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 0.952152 0.305626i \(-0.0988657\pi\)
−0.740756 + 0.671775i \(0.765532\pi\)
\(678\) 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 0.756288 0.654239i \(-0.227011\pi\)
−0.188443 + 0.982084i \(0.560344\pi\)
\(684\) 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 \(0.0978417\pi\)
−0.214539 + 0.976715i \(0.568825\pi\)
\(692\) 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 \(0.384696\pi\)
−0.354369 + 0.935106i \(0.615304\pi\)
\(702\) 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 −0.134410 0.990926i \(-0.542914\pi\)
0.790962 + 0.611865i \(0.209581\pi\)
\(710\) 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 0.887872 0.460091i \(-0.152183\pi\)
−0.842386 + 0.538874i \(0.818850\pi\)
\(734\) 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 −0.159665 0.987171i \(-0.551042\pi\)
−0.934748 + 0.355311i \(0.884375\pi\)
\(740\) 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 \(-0.955874\pi\)
0.990407 0.138182i \(-0.0441259\pi\)
\(758\) 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 −0.565754 0.824574i \(-0.691415\pi\)
0.996979 + 0.0776701i \(0.0247481\pi\)
\(774\) 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 \(-0.634659\pi\)
0.994948 0.100387i