Properties

Label 224.3.n.a.145.5
Level 224
Weight 3
Character 224.145
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 145.5
Character \(\chi\) \(=\) 224.145
Dual form 224.3.n.a.17.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.16781 - 2.02271i) q^{3} +(-1.55055 + 2.68563i) q^{5} +(6.89374 + 1.21502i) q^{7} +(1.77242 - 3.06992i) q^{9} +O(q^{10})\) \(q+(-1.16781 - 2.02271i) q^{3} +(-1.55055 + 2.68563i) q^{5} +(6.89374 + 1.21502i) q^{7} +(1.77242 - 3.06992i) q^{9} +(4.06604 - 2.34753i) q^{11} -6.88097 q^{13} +7.24301 q^{15} +(14.7184 - 8.49765i) q^{17} +(13.1099 - 22.7070i) q^{19} +(-5.59297 - 15.3630i) q^{21} +(12.9403 - 22.4132i) q^{23} +(7.69160 + 13.3222i) q^{25} -29.3001 q^{27} -42.2701i q^{29} +(-15.9024 + 9.18126i) q^{31} +(-9.49676 - 5.48296i) q^{33} +(-13.9522 + 16.6301i) q^{35} +(43.1997 + 24.9413i) q^{37} +(8.03569 + 13.9182i) q^{39} -10.7844i q^{41} +24.1791i q^{43} +(5.49645 + 9.52013i) q^{45} +(-11.8480 - 6.84046i) q^{47} +(46.0474 + 16.7521i) q^{49} +(-34.3766 - 19.8474i) q^{51} +(6.03948 - 3.48690i) q^{53} +14.5598i q^{55} -61.2396 q^{57} +(53.0922 + 91.9584i) q^{59} +(-46.7304 + 80.9395i) q^{61} +(15.9486 - 19.0097i) q^{63} +(10.6693 - 18.4797i) q^{65} +(77.2753 - 44.6149i) q^{67} -60.4473 q^{69} -81.7898 q^{71} +(-119.473 + 68.9780i) q^{73} +(17.9647 - 31.1158i) q^{75} +(30.8826 - 11.2429i) q^{77} +(-6.55090 + 11.3465i) q^{79} +(18.2653 + 31.6364i) q^{81} -2.15689 q^{83} +52.7041i q^{85} +(-85.5003 + 49.3636i) q^{87} +(-87.8261 - 50.7064i) q^{89} +(-47.4356 - 8.36055i) q^{91} +(37.1421 + 21.4440i) q^{93} +(40.6550 + 70.4166i) q^{95} -88.9318i q^{97} -16.6432i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{7} - 32q^{9} + O(q^{10}) \) \( 28q + 4q^{7} - 32q^{9} - 28q^{15} - 6q^{17} - 30q^{23} - 32q^{25} + 6q^{31} - 6q^{33} + 20q^{39} + 294q^{47} - 20q^{49} + 124q^{57} - 432q^{63} - 52q^{65} + 136q^{71} + 234q^{73} + 162q^{79} - 18q^{81} - 48q^{87} - 150q^{89} - 290q^{95} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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
\(3\) −1.16781 2.02271i −0.389271 0.674238i 0.603080 0.797680i \(-0.293940\pi\)
−0.992352 + 0.123443i \(0.960607\pi\)
\(4\) 0 0
\(5\) −1.55055 + 2.68563i −0.310110 + 0.537126i −0.978386 0.206787i \(-0.933699\pi\)
0.668276 + 0.743913i \(0.267032\pi\)
\(6\) 0 0
\(7\) 6.89374 + 1.21502i 0.984821 + 0.173575i
\(8\) 0 0
\(9\) 1.77242 3.06992i 0.196936 0.341102i
\(10\) 0 0
\(11\) 4.06604 2.34753i 0.369640 0.213412i −0.303661 0.952780i \(-0.598209\pi\)
0.673301 + 0.739368i \(0.264876\pi\)
\(12\) 0 0
\(13\) −6.88097 −0.529305 −0.264653 0.964344i \(-0.585257\pi\)
−0.264653 + 0.964344i \(0.585257\pi\)
\(14\) 0 0
\(15\) 7.24301 0.482868
\(16\) 0 0
\(17\) 14.7184 8.49765i 0.865786 0.499862i −0.000159428 1.00000i \(-0.500051\pi\)
0.865946 + 0.500138i \(0.166717\pi\)
\(18\) 0 0
\(19\) 13.1099 22.7070i 0.689994 1.19510i −0.281845 0.959460i \(-0.590947\pi\)
0.971839 0.235645i \(-0.0757201\pi\)
\(20\) 0 0
\(21\) −5.59297 15.3630i −0.266332 0.731571i
\(22\) 0 0
\(23\) 12.9403 22.4132i 0.562620 0.974486i −0.434647 0.900601i \(-0.643127\pi\)
0.997267 0.0738851i \(-0.0235398\pi\)
\(24\) 0 0
\(25\) 7.69160 + 13.3222i 0.307664 + 0.532889i
\(26\) 0 0
\(27\) −29.3001 −1.08519
\(28\) 0 0
\(29\) 42.2701i 1.45759i −0.684732 0.728795i \(-0.740081\pi\)
0.684732 0.728795i \(-0.259919\pi\)
\(30\) 0 0
\(31\) −15.9024 + 9.18126i −0.512981 + 0.296170i −0.734058 0.679087i \(-0.762376\pi\)
0.221077 + 0.975256i \(0.429043\pi\)
\(32\) 0 0
\(33\) −9.49676 5.48296i −0.287781 0.166150i
\(34\) 0 0
\(35\) −13.9522 + 16.6301i −0.398634 + 0.475145i
\(36\) 0 0
\(37\) 43.1997 + 24.9413i 1.16756 + 0.674090i 0.953104 0.302644i \(-0.0978692\pi\)
0.214455 + 0.976734i \(0.431203\pi\)
\(38\) 0 0
\(39\) 8.03569 + 13.9182i 0.206043 + 0.356878i
\(40\) 0 0
\(41\) 10.7844i 0.263035i −0.991314 0.131517i \(-0.958015\pi\)
0.991314 0.131517i \(-0.0419849\pi\)
\(42\) 0 0
\(43\) 24.1791i 0.562304i 0.959663 + 0.281152i \(0.0907165\pi\)
−0.959663 + 0.281152i \(0.909284\pi\)
\(44\) 0 0
\(45\) 5.49645 + 9.52013i 0.122143 + 0.211558i
\(46\) 0 0
\(47\) −11.8480 6.84046i −0.252086 0.145542i 0.368633 0.929575i \(-0.379826\pi\)
−0.620719 + 0.784033i \(0.713159\pi\)
\(48\) 0 0
\(49\) 46.0474 + 16.7521i 0.939743 + 0.341880i
\(50\) 0 0
\(51\) −34.3766 19.8474i −0.674052 0.389164i
\(52\) 0 0
\(53\) 6.03948 3.48690i 0.113952 0.0657905i −0.441940 0.897044i \(-0.645710\pi\)
0.555893 + 0.831254i \(0.312376\pi\)
\(54\) 0 0
\(55\) 14.5598i 0.264724i
\(56\) 0 0
\(57\) −61.2396 −1.07438
\(58\) 0 0
\(59\) 53.0922 + 91.9584i 0.899868 + 1.55862i 0.827662 + 0.561227i \(0.189671\pi\)
0.0722059 + 0.997390i \(0.476996\pi\)
\(60\) 0 0
\(61\) −46.7304 + 80.9395i −0.766073 + 1.32688i 0.173605 + 0.984815i \(0.444458\pi\)
−0.939678 + 0.342062i \(0.888875\pi\)
\(62\) 0 0
\(63\) 15.9486 19.0097i 0.253153 0.301742i
\(64\) 0 0
\(65\) 10.6693 18.4797i 0.164143 0.284304i
\(66\) 0 0
\(67\) 77.2753 44.6149i 1.15336 0.665894i 0.203659 0.979042i \(-0.434717\pi\)
0.949705 + 0.313147i \(0.101383\pi\)
\(68\) 0 0
\(69\) −60.4473 −0.876047
\(70\) 0 0
\(71\) −81.7898 −1.15197 −0.575984 0.817461i \(-0.695381\pi\)
−0.575984 + 0.817461i \(0.695381\pi\)
\(72\) 0 0
\(73\) −119.473 + 68.9780i −1.63662 + 0.944904i −0.654637 + 0.755943i \(0.727179\pi\)
−0.981985 + 0.188961i \(0.939488\pi\)
\(74\) 0 0
\(75\) 17.9647 31.1158i 0.239529 0.414877i
\(76\) 0 0
\(77\) 30.8826 11.2429i 0.401072 0.146012i
\(78\) 0 0
\(79\) −6.55090 + 11.3465i −0.0829228 + 0.143627i −0.904504 0.426465i \(-0.859759\pi\)
0.821581 + 0.570091i \(0.193092\pi\)
\(80\) 0 0
\(81\) 18.2653 + 31.6364i 0.225497 + 0.390573i
\(82\) 0 0
\(83\) −2.15689 −0.0259867 −0.0129933 0.999916i \(-0.504136\pi\)
−0.0129933 + 0.999916i \(0.504136\pi\)
\(84\) 0 0
\(85\) 52.7041i 0.620048i
\(86\) 0 0
\(87\) −85.5003 + 49.3636i −0.982762 + 0.567398i
\(88\) 0 0
\(89\) −87.8261 50.7064i −0.986810 0.569735i −0.0824908 0.996592i \(-0.526288\pi\)
−0.904319 + 0.426857i \(0.859621\pi\)
\(90\) 0 0
\(91\) −47.4356 8.36055i −0.521271 0.0918742i
\(92\) 0 0
\(93\) 37.1421 + 21.4440i 0.399378 + 0.230581i
\(94\) 0 0
\(95\) 40.6550 + 70.4166i 0.427948 + 0.741227i
\(96\) 0 0
\(97\) 88.9318i 0.916823i −0.888740 0.458412i \(-0.848419\pi\)
0.888740 0.458412i \(-0.151581\pi\)
\(98\) 0 0
\(99\) 16.6432i 0.168114i
\(100\) 0 0
\(101\) −10.4239 18.0546i −0.103206 0.178759i 0.809798 0.586709i \(-0.199577\pi\)
−0.913004 + 0.407951i \(0.866244\pi\)
\(102\) 0 0
\(103\) −2.97469 1.71744i −0.0288805 0.0166741i 0.485490 0.874242i \(-0.338641\pi\)
−0.514371 + 0.857568i \(0.671974\pi\)
\(104\) 0 0
\(105\) 49.9315 + 8.80044i 0.475538 + 0.0838137i
\(106\) 0 0
\(107\) −58.4603 33.7521i −0.546358 0.315440i 0.201294 0.979531i \(-0.435485\pi\)
−0.747652 + 0.664091i \(0.768819\pi\)
\(108\) 0 0
\(109\) 116.961 67.5273i 1.07303 0.619516i 0.144025 0.989574i \(-0.453995\pi\)
0.929009 + 0.370058i \(0.120662\pi\)
\(110\) 0 0
\(111\) 116.507i 1.04962i
\(112\) 0 0
\(113\) 136.328 1.20645 0.603223 0.797573i \(-0.293883\pi\)
0.603223 + 0.797573i \(0.293883\pi\)
\(114\) 0 0
\(115\) 40.1290 + 69.5055i 0.348948 + 0.604395i
\(116\) 0 0
\(117\) −12.1960 + 21.1240i −0.104239 + 0.180547i
\(118\) 0 0
\(119\) 111.790 40.6975i 0.939408 0.341996i
\(120\) 0 0
\(121\) −49.4782 + 85.6988i −0.408911 + 0.708254i
\(122\) 0 0
\(123\) −21.8138 + 12.5942i −0.177348 + 0.102392i
\(124\) 0 0
\(125\) −125.232 −1.00186
\(126\) 0 0
\(127\) 6.39702 0.0503702 0.0251851 0.999683i \(-0.491982\pi\)
0.0251851 + 0.999683i \(0.491982\pi\)
\(128\) 0 0
\(129\) 48.9073 28.2366i 0.379126 0.218889i
\(130\) 0 0
\(131\) −86.8472 + 150.424i −0.662956 + 1.14827i 0.316879 + 0.948466i \(0.397365\pi\)
−0.979835 + 0.199807i \(0.935968\pi\)
\(132\) 0 0
\(133\) 117.966 140.607i 0.886960 1.05720i
\(134\) 0 0
\(135\) 45.4312 78.6892i 0.336528 0.582883i
\(136\) 0 0
\(137\) 38.2926 + 66.3247i 0.279508 + 0.484122i 0.971262 0.238011i \(-0.0764954\pi\)
−0.691755 + 0.722133i \(0.743162\pi\)
\(138\) 0 0
\(139\) 72.4724 0.521384 0.260692 0.965422i \(-0.416049\pi\)
0.260692 + 0.965422i \(0.416049\pi\)
\(140\) 0 0
\(141\) 31.9535i 0.226621i
\(142\) 0 0
\(143\) −27.9783 + 16.1533i −0.195653 + 0.112960i
\(144\) 0 0
\(145\) 113.522 + 65.5419i 0.782909 + 0.452013i
\(146\) 0 0
\(147\) −19.8901 112.704i −0.135307 0.766695i
\(148\) 0 0
\(149\) −211.542 122.134i −1.41974 0.819690i −0.423469 0.905911i \(-0.639188\pi\)
−0.996276 + 0.0862205i \(0.972521\pi\)
\(150\) 0 0
\(151\) 103.109 + 178.590i 0.682841 + 1.18272i 0.974110 + 0.226074i \(0.0725893\pi\)
−0.291269 + 0.956641i \(0.594077\pi\)
\(152\) 0 0
\(153\) 60.2456i 0.393762i
\(154\) 0 0
\(155\) 56.9440i 0.367380i
\(156\) 0 0
\(157\) 37.2714 + 64.5559i 0.237397 + 0.411184i 0.959967 0.280114i \(-0.0903723\pi\)
−0.722569 + 0.691298i \(0.757039\pi\)
\(158\) 0 0
\(159\) −14.1060 8.14409i −0.0887169 0.0512207i
\(160\) 0 0
\(161\) 116.439 138.788i 0.723226 0.862037i
\(162\) 0 0
\(163\) −85.1169 49.1422i −0.522189 0.301486i 0.215641 0.976473i \(-0.430816\pi\)
−0.737830 + 0.674987i \(0.764149\pi\)
\(164\) 0 0
\(165\) 29.4504 17.0032i 0.178487 0.103050i
\(166\) 0 0
\(167\) 252.539i 1.51221i −0.654449 0.756106i \(-0.727099\pi\)
0.654449 0.756106i \(-0.272901\pi\)
\(168\) 0 0
\(169\) −121.652 −0.719836
\(170\) 0 0
\(171\) −46.4724 80.4926i −0.271769 0.470717i
\(172\) 0 0
\(173\) 75.1889 130.231i 0.434618 0.752781i −0.562646 0.826698i \(-0.690217\pi\)
0.997264 + 0.0739171i \(0.0235500\pi\)
\(174\) 0 0
\(175\) 36.8371 + 101.186i 0.210497 + 0.578203i
\(176\) 0 0
\(177\) 124.004 214.781i 0.700586 1.21345i
\(178\) 0 0
\(179\) 89.6246 51.7448i 0.500696 0.289077i −0.228305 0.973590i \(-0.573318\pi\)
0.729001 + 0.684513i \(0.239985\pi\)
\(180\) 0 0
\(181\) 95.1121 0.525481 0.262741 0.964867i \(-0.415374\pi\)
0.262741 + 0.964867i \(0.415374\pi\)
\(182\) 0 0
\(183\) 218.290 1.19284
\(184\) 0 0
\(185\) −133.966 + 77.3455i −0.724143 + 0.418084i
\(186\) 0 0
\(187\) 39.8970 69.1036i 0.213353 0.369538i
\(188\) 0 0
\(189\) −201.987 35.6003i −1.06872 0.188362i
\(190\) 0 0
\(191\) 1.97252 3.41650i 0.0103273 0.0178874i −0.860816 0.508917i \(-0.830046\pi\)
0.871143 + 0.491030i \(0.163379\pi\)
\(192\) 0 0
\(193\) 146.091 + 253.037i 0.756949 + 1.31107i 0.944399 + 0.328800i \(0.106644\pi\)
−0.187450 + 0.982274i \(0.560022\pi\)
\(194\) 0 0
\(195\) −49.8390 −0.255584
\(196\) 0 0
\(197\) 160.503i 0.814735i 0.913264 + 0.407367i \(0.133553\pi\)
−0.913264 + 0.407367i \(0.866447\pi\)
\(198\) 0 0
\(199\) −174.461 + 100.725i −0.876688 + 0.506156i −0.869565 0.493819i \(-0.835601\pi\)
−0.00712311 + 0.999975i \(0.502267\pi\)
\(200\) 0 0
\(201\) −180.486 104.204i −0.897943 0.518427i
\(202\) 0 0
\(203\) 51.3592 291.399i 0.253001 1.43546i
\(204\) 0 0
\(205\) 28.9630 + 16.7218i 0.141283 + 0.0815697i
\(206\) 0 0
\(207\) −45.8711 79.4511i −0.221600 0.383822i
\(208\) 0 0
\(209\) 123.103i 0.589012i
\(210\) 0 0
\(211\) 170.542i 0.808256i 0.914702 + 0.404128i \(0.132425\pi\)
−0.914702 + 0.404128i \(0.867575\pi\)
\(212\) 0 0
\(213\) 95.5152 + 165.437i 0.448428 + 0.776701i
\(214\) 0 0
\(215\) −64.9360 37.4908i −0.302028 0.174376i
\(216\) 0 0
\(217\) −120.783 + 43.9714i −0.556602 + 0.202633i
\(218\) 0 0
\(219\) 279.045 + 161.107i 1.27418 + 0.735648i
\(220\) 0 0
\(221\) −101.277 + 58.4721i −0.458265 + 0.264580i
\(222\) 0 0
\(223\) 143.446i 0.643255i 0.946866 + 0.321628i \(0.104230\pi\)
−0.946866 + 0.321628i \(0.895770\pi\)
\(224\) 0 0
\(225\) 54.5309 0.242360
\(226\) 0 0
\(227\) 11.7597 + 20.3683i 0.0518047 + 0.0897284i 0.890765 0.454464i \(-0.150169\pi\)
−0.838960 + 0.544193i \(0.816836\pi\)
\(228\) 0 0
\(229\) −30.7040 + 53.1809i −0.134079 + 0.232231i −0.925245 0.379370i \(-0.876141\pi\)
0.791167 + 0.611601i \(0.209474\pi\)
\(230\) 0 0
\(231\) −58.8063 49.3369i −0.254573 0.213580i
\(232\) 0 0
\(233\) −52.0991 + 90.2384i −0.223601 + 0.387289i −0.955899 0.293696i \(-0.905115\pi\)
0.732297 + 0.680985i \(0.238448\pi\)
\(234\) 0 0
\(235\) 36.7419 21.2129i 0.156348 0.0902678i
\(236\) 0 0
\(237\) 30.6010 0.129118
\(238\) 0 0
\(239\) −104.695 −0.438056 −0.219028 0.975719i \(-0.570289\pi\)
−0.219028 + 0.975719i \(0.570289\pi\)
\(240\) 0 0
\(241\) −142.650 + 82.3591i −0.591910 + 0.341739i −0.765852 0.643017i \(-0.777683\pi\)
0.173943 + 0.984756i \(0.444349\pi\)
\(242\) 0 0
\(243\) −89.1895 + 154.481i −0.367035 + 0.635723i
\(244\) 0 0
\(245\) −116.389 + 97.6913i −0.475056 + 0.398740i
\(246\) 0 0
\(247\) −90.2087 + 156.246i −0.365217 + 0.632575i
\(248\) 0 0
\(249\) 2.51885 + 4.36278i 0.0101159 + 0.0175212i
\(250\) 0 0
\(251\) −399.066 −1.58990 −0.794952 0.606672i \(-0.792504\pi\)
−0.794952 + 0.606672i \(0.792504\pi\)
\(252\) 0 0
\(253\) 121.511i 0.480279i
\(254\) 0 0
\(255\) 106.605 61.5486i 0.418060 0.241367i
\(256\) 0 0
\(257\) 2.12341 + 1.22595i 0.00826231 + 0.00477025i 0.504125 0.863630i \(-0.331815\pi\)
−0.495863 + 0.868401i \(0.665148\pi\)
\(258\) 0 0
\(259\) 267.503 + 224.428i 1.03283 + 0.866517i
\(260\) 0 0
\(261\) −129.766 74.9204i −0.497187 0.287051i
\(262\) 0 0
\(263\) 28.7798 + 49.8481i 0.109429 + 0.189536i 0.915539 0.402229i \(-0.131764\pi\)
−0.806110 + 0.591766i \(0.798431\pi\)
\(264\) 0 0
\(265\) 21.6264i 0.0816091i
\(266\) 0 0
\(267\) 236.863i 0.887126i
\(268\) 0 0
\(269\) 120.201 + 208.195i 0.446845 + 0.773958i 0.998179 0.0603267i \(-0.0192143\pi\)
−0.551334 + 0.834285i \(0.685881\pi\)
\(270\) 0 0
\(271\) −116.507 67.2655i −0.429916 0.248212i 0.269395 0.963030i \(-0.413176\pi\)
−0.699311 + 0.714818i \(0.746510\pi\)
\(272\) 0 0
\(273\) 38.4850 + 105.712i 0.140971 + 0.387225i
\(274\) 0 0
\(275\) 62.5487 + 36.1125i 0.227450 + 0.131318i
\(276\) 0 0
\(277\) 95.6097 55.2003i 0.345161 0.199279i −0.317391 0.948295i \(-0.602807\pi\)
0.662552 + 0.749016i \(0.269473\pi\)
\(278\) 0 0
\(279\) 65.0922i 0.233305i
\(280\) 0 0
\(281\) −154.087 −0.548351 −0.274175 0.961680i \(-0.588405\pi\)
−0.274175 + 0.961680i \(0.588405\pi\)
\(282\) 0 0
\(283\) −15.4714 26.7972i −0.0546692 0.0946899i 0.837396 0.546597i \(-0.184077\pi\)
−0.892065 + 0.451907i \(0.850744\pi\)
\(284\) 0 0
\(285\) 94.9551 164.467i 0.333176 0.577077i
\(286\) 0 0
\(287\) 13.1034 74.3451i 0.0456563 0.259042i
\(288\) 0 0
\(289\) −0.0797964 + 0.138211i −0.000276112 + 0.000478240i
\(290\) 0 0
\(291\) −179.884 + 103.856i −0.618157 + 0.356893i
\(292\) 0 0
\(293\) 511.686 1.74637 0.873184 0.487390i \(-0.162051\pi\)
0.873184 + 0.487390i \(0.162051\pi\)
\(294\) 0 0
\(295\) −329.288 −1.11623
\(296\) 0 0
\(297\) −119.135 + 68.7828i −0.401129 + 0.231592i
\(298\) 0 0
\(299\) −89.0415 + 154.224i −0.297798 + 0.515801i
\(300\) 0 0
\(301\) −29.3782 + 166.684i −0.0976018 + 0.553768i
\(302\) 0 0
\(303\) −24.3463 + 42.1689i −0.0803507 + 0.139171i
\(304\) 0 0
\(305\) −144.916 251.001i −0.475133 0.822955i
\(306\) 0 0
\(307\) −51.2670 −0.166993 −0.0834967 0.996508i \(-0.526609\pi\)
−0.0834967 + 0.996508i \(0.526609\pi\)
\(308\) 0 0
\(309\) 8.02259i 0.0259631i
\(310\) 0 0
\(311\) 17.7940 10.2734i 0.0572153 0.0330333i −0.471119 0.882069i \(-0.656150\pi\)
0.528335 + 0.849036i \(0.322817\pi\)
\(312\) 0 0
\(313\) 291.960 + 168.563i 0.932780 + 0.538541i 0.887690 0.460442i \(-0.152309\pi\)
0.0450905 + 0.998983i \(0.485642\pi\)
\(314\) 0 0
\(315\) 26.3239 + 72.3076i 0.0835680 + 0.229548i
\(316\) 0 0
\(317\) 80.7634 + 46.6288i 0.254774 + 0.147094i 0.621948 0.783058i \(-0.286341\pi\)
−0.367174 + 0.930152i \(0.619675\pi\)
\(318\) 0 0
\(319\) −99.2304 171.872i −0.311067 0.538784i
\(320\) 0 0
\(321\) 157.665i 0.491167i
\(322\) 0 0
\(323\) 445.613i 1.37961i
\(324\) 0 0
\(325\) −52.9256 91.6699i −0.162848 0.282061i
\(326\) 0 0
\(327\) −273.177 157.719i −0.835403 0.482320i
\(328\) 0 0
\(329\) −73.3659 61.5520i −0.222997 0.187088i
\(330\) 0 0
\(331\) 64.9939 + 37.5242i 0.196356 + 0.113366i 0.594955 0.803759i \(-0.297170\pi\)
−0.398599 + 0.917125i \(0.630503\pi\)
\(332\) 0 0
\(333\) 153.136 88.4130i 0.459867 0.265505i
\(334\) 0 0
\(335\) 276.711i 0.826002i
\(336\) 0 0
\(337\) −140.105 −0.415743 −0.207872 0.978156i \(-0.566654\pi\)
−0.207872 + 0.978156i \(0.566654\pi\)
\(338\) 0 0
\(339\) −159.206 275.753i −0.469635 0.813431i
\(340\) 0 0
\(341\) −43.1066 + 74.6628i −0.126412 + 0.218952i
\(342\) 0 0
\(343\) 297.085 + 171.434i 0.866137 + 0.499807i
\(344\) 0 0
\(345\) 93.7264 162.339i 0.271671 0.470548i
\(346\) 0 0
\(347\) 64.9715 37.5113i 0.187238 0.108102i −0.403451 0.915001i \(-0.632189\pi\)
0.590689 + 0.806899i \(0.298856\pi\)
\(348\) 0 0
\(349\) −603.618 −1.72956 −0.864782 0.502148i \(-0.832543\pi\)
−0.864782 + 0.502148i \(0.832543\pi\)
\(350\) 0 0
\(351\) 201.613 0.574396
\(352\) 0 0
\(353\) 337.515 194.864i 0.956132 0.552023i 0.0611514 0.998129i \(-0.480523\pi\)
0.894980 + 0.446106i \(0.147189\pi\)
\(354\) 0 0
\(355\) 126.819 219.657i 0.357237 0.618752i
\(356\) 0 0
\(357\) −212.869 178.591i −0.596271 0.500255i
\(358\) 0 0
\(359\) 69.2214 119.895i 0.192817 0.333969i −0.753366 0.657602i \(-0.771571\pi\)
0.946183 + 0.323633i \(0.104904\pi\)
\(360\) 0 0
\(361\) −163.238 282.737i −0.452183 0.783204i
\(362\) 0 0
\(363\) 231.125 0.636709
\(364\) 0 0
\(365\) 427.815i 1.17210i
\(366\) 0 0
\(367\) 408.823 236.034i 1.11396 0.643145i 0.174108 0.984727i \(-0.444296\pi\)
0.939852 + 0.341581i \(0.110963\pi\)
\(368\) 0 0
\(369\) −33.1073 19.1145i −0.0897218 0.0518009i
\(370\) 0 0
\(371\) 45.8713 16.6997i 0.123642 0.0450125i
\(372\) 0 0
\(373\) −30.5419 17.6334i −0.0818818 0.0472745i 0.458500 0.888694i \(-0.348387\pi\)
−0.540382 + 0.841420i \(0.681720\pi\)
\(374\) 0 0
\(375\) 146.248 + 253.309i 0.389995 + 0.675491i
\(376\) 0 0
\(377\) 290.859i 0.771510i
\(378\) 0 0
\(379\) 230.447i 0.608039i −0.952666 0.304019i \(-0.901671\pi\)
0.952666 0.304019i \(-0.0983287\pi\)
\(380\) 0 0
\(381\) −7.47053 12.9393i −0.0196077 0.0339615i
\(382\) 0 0
\(383\) 480.020 + 277.140i 1.25332 + 0.723602i 0.971766 0.235945i \(-0.0758184\pi\)
0.281549 + 0.959547i \(0.409152\pi\)
\(384\) 0 0
\(385\) −17.6906 + 100.372i −0.0459495 + 0.260706i
\(386\) 0 0
\(387\) 74.2278 + 42.8554i 0.191803 + 0.110738i
\(388\) 0 0
\(389\) −344.401 + 198.840i −0.885349 + 0.511157i −0.872418 0.488760i \(-0.837450\pi\)
−0.0129310 + 0.999916i \(0.504116\pi\)
\(390\) 0 0
\(391\) 439.847i 1.12493i
\(392\) 0 0
\(393\) 405.686 1.03228
\(394\) 0 0
\(395\) −20.3150 35.1866i −0.0514304 0.0890800i
\(396\) 0 0
\(397\) −60.9545 + 105.576i −0.153538 + 0.265935i −0.932526 0.361104i \(-0.882400\pi\)
0.778988 + 0.627039i \(0.215733\pi\)
\(398\) 0 0
\(399\) −422.170 74.4077i −1.05807 0.186485i
\(400\) 0 0
\(401\) −124.337 + 215.358i −0.310067 + 0.537051i −0.978377 0.206832i \(-0.933685\pi\)
0.668310 + 0.743883i \(0.267018\pi\)
\(402\) 0 0
\(403\) 109.424 63.1760i 0.271524 0.156764i
\(404\) 0 0
\(405\) −113.285 −0.279716
\(406\) 0 0
\(407\) 234.202 0.575435
\(408\) 0 0
\(409\) 582.721 336.434i 1.42475 0.822578i 0.428047 0.903757i \(-0.359202\pi\)
0.996700 + 0.0811790i \(0.0258685\pi\)
\(410\) 0 0
\(411\) 89.4372 154.910i 0.217609 0.376909i
\(412\) 0 0
\(413\) 254.272 + 698.446i 0.615672 + 1.69115i
\(414\) 0 0
\(415\) 3.34437 5.79262i 0.00805872 0.0139581i
\(416\) 0 0
\(417\) −84.6343 146.591i −0.202960 0.351537i
\(418\) 0 0
\(419\) 178.795 0.426718 0.213359 0.976974i \(-0.431560\pi\)
0.213359 + 0.976974i \(0.431560\pi\)
\(420\) 0 0
\(421\) 212.470i 0.504679i 0.967639 + 0.252340i \(0.0812000\pi\)
−0.967639 + 0.252340i \(0.918800\pi\)
\(422\) 0 0
\(423\) −41.9993 + 24.2483i −0.0992892 + 0.0573247i
\(424\) 0 0
\(425\) 226.415 + 130.721i 0.532742 + 0.307579i
\(426\) 0 0
\(427\) −420.491 + 501.198i −0.984757 + 1.17376i
\(428\) 0 0
\(429\) 65.3470 + 37.7281i 0.152324 + 0.0879442i
\(430\) 0 0
\(431\) −345.732 598.826i −0.802163 1.38939i −0.918190 0.396141i \(-0.870349\pi\)
0.116027 0.993246i \(-0.462984\pi\)
\(432\) 0 0
\(433\) 99.8389i 0.230575i 0.993332 + 0.115287i \(0.0367789\pi\)
−0.993332 + 0.115287i \(0.963221\pi\)
\(434\) 0 0
\(435\) 306.163i 0.703823i
\(436\) 0 0
\(437\) −339.290 587.668i −0.776408 1.34478i
\(438\) 0 0
\(439\) 599.369 + 346.046i 1.36530 + 0.788259i 0.990324 0.138774i \(-0.0443161\pi\)
0.374980 + 0.927033i \(0.377649\pi\)
\(440\) 0 0
\(441\) 133.043 111.670i 0.301685 0.253220i
\(442\) 0 0
\(443\) −233.569 134.851i −0.527244 0.304405i 0.212649 0.977129i \(-0.431791\pi\)
−0.739893 + 0.672724i \(0.765124\pi\)
\(444\) 0 0
\(445\) 272.357 157.246i 0.612039 0.353361i
\(446\) 0 0
\(447\) 570.519i 1.27633i
\(448\) 0 0
\(449\) −76.6510 −0.170715 −0.0853575 0.996350i \(-0.527203\pi\)
−0.0853575 + 0.996350i \(0.527203\pi\)
\(450\) 0 0
\(451\) −25.3168 43.8500i −0.0561348 0.0972283i
\(452\) 0 0
\(453\) 240.824 417.120i 0.531621 0.920795i
\(454\) 0 0
\(455\) 96.0046 114.431i 0.210999 0.251497i
\(456\) 0 0
\(457\) 175.616 304.177i 0.384281 0.665594i −0.607388 0.794405i \(-0.707783\pi\)
0.991669 + 0.128811i \(0.0411160\pi\)
\(458\) 0 0
\(459\) −431.249 + 248.982i −0.939541 + 0.542444i
\(460\) 0 0
\(461\) 296.940 0.644122 0.322061 0.946719i \(-0.395624\pi\)
0.322061 + 0.946719i \(0.395624\pi\)
\(462\) 0 0
\(463\) −25.5350 −0.0551513 −0.0275756 0.999620i \(-0.508779\pi\)
−0.0275756 + 0.999620i \(0.508779\pi\)
\(464\) 0 0
\(465\) −115.181 + 66.5000i −0.247702 + 0.143011i
\(466\) 0 0
\(467\) −62.7601 + 108.704i −0.134390 + 0.232770i −0.925364 0.379079i \(-0.876241\pi\)
0.790974 + 0.611849i \(0.209574\pi\)
\(468\) 0 0
\(469\) 586.925 213.673i 1.25144 0.455592i
\(470\) 0 0
\(471\) 87.0521 150.779i 0.184824 0.320125i
\(472\) 0 0
\(473\) 56.7611 + 98.3131i 0.120002 + 0.207850i
\(474\) 0 0
\(475\) 403.344 0.849145
\(476\) 0 0
\(477\) 24.7210i 0.0518259i
\(478\) 0 0
\(479\) 150.188 86.7108i 0.313544 0.181025i −0.334967 0.942230i \(-0.608725\pi\)
0.648511 + 0.761205i \(0.275392\pi\)
\(480\) 0 0
\(481\) −297.256 171.621i −0.617995 0.356800i
\(482\) 0 0
\(483\) −416.708 73.4449i −0.862749 0.152060i
\(484\) 0 0
\(485\) 238.838 + 137.893i 0.492449 + 0.284316i
\(486\) 0 0
\(487\) −340.756 590.206i −0.699704 1.21192i −0.968569 0.248744i \(-0.919982\pi\)
0.268866 0.963178i \(-0.413351\pi\)
\(488\) 0 0
\(489\) 229.556i 0.469440i
\(490\) 0 0
\(491\) 278.104i 0.566404i 0.959060 + 0.283202i \(0.0913966\pi\)
−0.959060 + 0.283202i \(0.908603\pi\)
\(492\) 0 0
\(493\) −359.197 622.147i −0.728594 1.26196i
\(494\) 0 0
\(495\) 44.6976 + 25.8062i 0.0902981 + 0.0521336i
\(496\) 0 0
\(497\) −563.838 99.3766i −1.13448 0.199953i
\(498\) 0 0
\(499\) −355.447 205.217i −0.712319 0.411258i 0.0996002 0.995028i \(-0.468244\pi\)
−0.811919 + 0.583770i \(0.801577\pi\)
\(500\) 0 0
\(501\) −510.815 + 294.919i −1.01959 + 0.588661i
\(502\) 0 0
\(503\) 554.042i 1.10148i 0.834678 + 0.550738i \(0.185654\pi\)
−0.834678 + 0.550738i \(0.814346\pi\)
\(504\) 0 0
\(505\) 64.6508 0.128021
\(506\) 0 0
\(507\) 142.067 + 246.068i 0.280212 + 0.485341i
\(508\) 0 0
\(509\) 22.0971 38.2733i 0.0434127 0.0751931i −0.843503 0.537125i \(-0.819510\pi\)
0.886915 + 0.461932i \(0.152844\pi\)
\(510\) 0 0
\(511\) −907.429 + 330.354i −1.77579 + 0.646485i
\(512\) 0 0
\(513\) −384.121 + 665.317i −0.748773 + 1.29691i
\(514\) 0 0
\(515\) 9.22480 5.32594i 0.0179122 0.0103416i
\(516\) 0 0
\(517\) −64.2327 −0.124241
\(518\) 0 0
\(519\) −351.227 −0.676738
\(520\) 0 0
\(521\) 363.862 210.076i 0.698392 0.403217i −0.108356 0.994112i \(-0.534559\pi\)
0.806748 + 0.590895i \(0.201225\pi\)
\(522\) 0 0
\(523\) 137.447 238.065i 0.262805 0.455191i −0.704181 0.710020i \(-0.748686\pi\)
0.966986 + 0.254829i \(0.0820192\pi\)
\(524\) 0 0
\(525\) 161.651 192.677i 0.307906 0.367003i
\(526\) 0 0
\(527\) −156.038 + 270.266i −0.296088 + 0.512839i
\(528\) 0 0
\(529\) −70.4004 121.937i −0.133082 0.230505i
\(530\) 0 0
\(531\) 376.407 0.708864
\(532\) 0 0
\(533\) 74.2073i 0.139226i
\(534\) 0 0
\(535\) 181.291 104.668i 0.338862 0.195642i
\(536\) 0 0
\(537\) −209.330 120.857i −0.389813 0.225059i
\(538\) 0 0
\(539\) 226.557 39.9828i 0.420328 0.0741797i
\(540\) 0 0
\(541\) 485.358 + 280.221i 0.897149 + 0.517969i 0.876274 0.481813i \(-0.160022\pi\)
0.0208748 + 0.999782i \(0.493355\pi\)
\(542\) 0 0
\(543\) −111.073 192.385i −0.204555 0.354299i
\(544\) 0 0
\(545\) 418.818i 0.768473i
\(546\) 0 0
\(547\) 655.564i 1.19847i 0.800573 + 0.599235i \(0.204529\pi\)
−0.800573 + 0.599235i \(0.795471\pi\)
\(548\) 0 0
\(549\) 165.652 + 286.917i 0.301734 + 0.522618i
\(550\) 0 0
\(551\) −959.826 554.156i −1.74197 1.00573i
\(552\) 0 0
\(553\) −58.9465 + 70.2604i −0.106594 + 0.127053i
\(554\) 0 0
\(555\) 312.896 + 180.650i 0.563776 + 0.325496i
\(556\) 0 0
\(557\) −650.172 + 375.377i −1.16728 + 0.673927i −0.953037 0.302855i \(-0.902060\pi\)
−0.214239 + 0.976781i \(0.568727\pi\)
\(558\) 0 0
\(559\) 166.375i 0.297630i
\(560\) 0 0
\(561\) −186.369 −0.332209
\(562\) 0 0
\(563\) 317.191 + 549.391i 0.563394 + 0.975827i 0.997197 + 0.0748195i \(0.0238381\pi\)
−0.433803 + 0.901008i \(0.642829\pi\)
\(564\) 0 0
\(565\) −211.384 + 366.127i −0.374130 + 0.648013i
\(566\) 0 0
\(567\) 87.4772 + 240.286i 0.154281 + 0.423785i
\(568\) 0 0
\(569\) −196.482 + 340.317i −0.345312 + 0.598097i −0.985410 0.170195i \(-0.945560\pi\)
0.640099 + 0.768293i \(0.278893\pi\)
\(570\) 0 0
\(571\) −466.776 + 269.493i −0.817471 + 0.471967i −0.849543 0.527519i \(-0.823122\pi\)
0.0320728 + 0.999486i \(0.489789\pi\)
\(572\) 0 0
\(573\) −9.21414 −0.0160805
\(574\) 0 0
\(575\) 398.125 0.692391
\(576\) 0 0
\(577\) −301.353 + 173.986i −0.522276 + 0.301536i −0.737865 0.674948i \(-0.764166\pi\)
0.215589 + 0.976484i \(0.430833\pi\)
\(578\) 0 0
\(579\) 341.215 591.001i 0.589317 1.02073i
\(580\) 0 0
\(581\) −14.8691 2.62068i −0.0255922 0.00451064i
\(582\) 0 0
\(583\) 16.3712 28.3557i 0.0280809 0.0486376i
\(584\) 0 0
\(585\) −37.8209 65.5077i −0.0646511 0.111979i
\(586\) 0 0
\(587\) 258.936 0.441118 0.220559 0.975374i \(-0.429212\pi\)
0.220559 + 0.975374i \(0.429212\pi\)
\(588\) 0 0
\(589\) 481.461i 0.817421i
\(590\) 0 0
\(591\) 324.651 187.437i 0.549325 0.317153i
\(592\) 0 0
\(593\) 66.6525 + 38.4819i 0.112399 + 0.0648935i 0.555146 0.831753i \(-0.312663\pi\)
−0.442747 + 0.896647i \(0.645996\pi\)
\(594\) 0 0
\(595\) −64.0368 + 363.329i −0.107625 + 0.610636i
\(596\) 0 0
\(597\) 407.476 + 235.256i 0.682539 + 0.394064i
\(598\) 0 0
\(599\) 579.488 + 1003.70i 0.967426 + 1.67563i 0.702951 + 0.711239i \(0.251865\pi\)
0.264475 + 0.964392i \(0.414801\pi\)
\(600\) 0 0
\(601\) 976.895i 1.62545i −0.582648 0.812724i \(-0.697983\pi\)
0.582648 0.812724i \(-0.302017\pi\)
\(602\) 0 0
\(603\) 316.306i 0.524553i
\(604\) 0 0
\(605\) −153.437 265.760i −0.253614 0.439273i
\(606\) 0 0
\(607\) 684.187 + 395.015i 1.12716 + 0.650767i 0.943219 0.332170i \(-0.107781\pi\)
0.183942 + 0.982937i \(0.441114\pi\)
\(608\) 0 0
\(609\) −649.395 + 236.415i −1.06633 + 0.388202i
\(610\) 0 0
\(611\) 81.5259 + 47.0690i 0.133430 + 0.0770360i
\(612\) 0 0
\(613\) −233.690 + 134.921i −0.381223 + 0.220099i −0.678350 0.734739i \(-0.737305\pi\)
0.297127 + 0.954838i \(0.403971\pi\)
\(614\) 0 0
\(615\) 78.1118i 0.127011i
\(616\) 0 0
\(617\) 701.515 1.13698 0.568489 0.822691i \(-0.307528\pi\)
0.568489 + 0.822691i \(0.307528\pi\)
\(618\) 0 0
\(619\) −434.760 753.026i −0.702358 1.21652i −0.967636 0.252349i \(-0.918797\pi\)
0.265278 0.964172i \(1.58546\pi\)
\(620\) 0 0
\(621\) −379.151 + 656.708i −0.610548 + 1.05750i
\(622\) 0 0
\(623\) −543.841 456.268i −0.872939 0.732372i
\(624\) 0 0
\(625\) 1.88880 3.27149i 0.00302208 0.00523439i
\(626\) 0 0
\(627\) −249.003 + 143.762i −0.397134 + 0.229285i
\(628\) 0 0
\(629\) 847.771 1.34781
\(630\) 0 0
\(631\) −100.362 −0.159052 −0.0795258 0.996833i \(-0.525341\pi\)
−0.0795258 + 0.996833i \(0.525341\pi\)
\(632\) 0 0
\(633\) 344.958 199.162i 0.544957 0.314631i
\(634\) 0 0
\(635\) −9.91889 + 17.1800i −0.0156203 + 0.0270552i
\(636\) 0 0
\(637\) −316.851 115.271i −0.497411 0.180959i
\(638\) 0 0
\(639\) −144.966 + 251.088i −0.226863 + 0.392939i
\(640\) 0 0
\(641\) −530.571 918.977i −0.827724 1.43366i −0.899819 0.436263i \(-0.856302\pi\)
0.0720947 0.997398i \(-0.477032\pi\)
\(642\) 0 0
\(643\) 132.853 0.206615 0.103308 0.994649i \(-0.467057\pi\)
0.103308 + 0.994649i \(0.467057\pi\)
\(644\) 0 0
\(645\) 175.129i 0.271518i
\(646\) 0 0
\(647\) −998.259 + 576.345i −1.54290 + 0.890796i −0.544250 + 0.838923i \(0.683186\pi\)
−0.998654 + 0.0518730i \(0.983481\pi\)
\(648\) 0 0
\(649\) 431.750 + 249.271i 0.665255 + 0.384085i
\(650\) 0 0
\(651\) 229.993 + 192.958i 0.353292 + 0.296403i
\(652\) 0 0
\(653\) 25.1758 + 14.5352i 0.0385540 + 0.0222592i 0.519153 0.854681i \(-0.326247\pi\)
−0.480599 + 0.876940i \(0.659581\pi\)
\(654\) 0 0
\(655\) −269.322 466.479i −0.411178 0.712181i
\(656\) 0 0
\(657\) 489.032i 0.744341i
\(658\) 0 0
\(659\) 705.504i 1.07057i 0.844672 + 0.535283i \(0.179795\pi\)
−0.844672 + 0.535283i \(0.820205\pi\)
\(660\) 0 0
\(661\) −63.6678 110.276i −0.0963204 0.166832i 0.813838 0.581091i \(-0.197374\pi\)
−0.910159 + 0.414259i \(0.864041\pi\)
\(662\) 0 0
\(663\) 236.545 + 136.569i 0.356779 + 0.205987i
\(664\) 0 0
\(665\) 194.708 + 534.831i 0.292793 + 0.804257i
\(666\) 0 0
\(667\) −947.407 546.986i −1.42040 0.820069i
\(668\) 0 0
\(669\) 290.150 167.518i 0.433707 0.250401i
\(670\) 0 0
\(671\) 438.805i 0.653956i
\(672\) 0 0
\(673\) −463.380 −0.688528 −0.344264 0.938873i \(-0.611872\pi\)
−0.344264 + 0.938873i \(0.611872\pi\)
\(674\) 0 0
\(675\) −225.364 390.343i −0.333873 0.578285i
\(676\) 0 0
\(677\) −188.138 + 325.864i −0.277899 + 0.481335i −0.970862 0.239637i \(-0.922971\pi\)
0.692963 + 0.720973i \(0.256305\pi\)
\(678\) 0 0
\(679\) 108.054 613.073i 0.159138 0.902906i
\(680\) 0 0
\(681\) 27.4662 47.5729i 0.0403322 0.0698574i
\(682\) 0 0
\(683\) 897.932 518.421i 1.31469 0.759035i 0.331819 0.943343i \(-0.392338\pi\)
0.982869 + 0.184308i \(0.0590043\pi\)
\(684\) 0 0
\(685\) −237.498 −0.346712
\(686\) 0 0
\(687\) 143.426 0.208772
\(688\) 0 0
\(689\) −41.5575 + 23.9932i −0.0603157 + 0.0348233i
\(690\) 0 0
\(691\) 177.535 307.499i 0.256924 0.445006i −0.708492 0.705719i \(-0.750624\pi\)
0.965416 + 0.260713i \(0.0839575\pi\)
\(692\) 0 0
\(693\) 20.2219 114.734i 0.0291803 0.165562i
\(694\) 0 0
\(695\) −112.372 + 194.634i −0.161686 + 0.280049i
\(696\) 0 0
\(697\) −91.6423 158.729i −0.131481 0.227732i
\(698\) 0 0
\(699\) 243.368 0.348167
\(700\) 0 0
\(701\) 1278.63i 1.82400i −0.410185 0.912002i \(-0.634536\pi\)
0.410185 0.912002i \(-0.365464\pi\)
\(702\) 0 0
\(703\) 1132.69 653.956i 1.61122 0.930236i
\(704\) 0 0
\(705\) −85.8154 49.5455i −0.121724 0.0702774i
\(706\) 0 0
\(707\) −49.9226 137.129i −0.0706118 0.193959i
\(708\) 0 0
\(709\) −1040.03 600.464i −1.46690 0.846917i −0.467589 0.883946i \(-0.654877\pi\)
−0.999314 + 0.0370292i \(0.988211\pi\)
\(710\) 0 0
\(711\) 23.2219 + 40.2215i 0.0326609 + 0.0565704i
\(712\) 0 0
\(713\) 475.231i 0.666524i
\(714\) 0 0
\(715\) 100.186i 0.140120i
\(716\) 0 0
\(717\) 122.265 + 211.769i 0.170523 + 0.295354i
\(718\) 0 0
\(719\) 6.39954 + 3.69478i 0.00890061 + 0.00513877i 0.504444 0.863445i \(-0.331698\pi\)
−0.495543 + 0.868583i \(0.665031\pi\)
\(720\) 0 0
\(721\) −18.4200 15.4539i −0.0255479 0.0214340i
\(722\) 0 0
\(723\) 333.178 + 192.360i 0.460827 + 0.266059i
\(724\) 0 0
\(725\) 563.132 325.125i 0.776734 0.448448i
\(726\) 0 0
\(727\) 1184.67i 1.62953i −0.579788 0.814767i \(-0.696865\pi\)
0.579788 0.814767i \(-0.303135\pi\)
\(728\) 0 0
\(729\) 745.402 1.02250
\(730\) 0 0
\(731\) 205.465 + 355.876i 0.281074 + 0.486835i
\(732\) 0 0
\(733\) 469.714 813.569i 0.640810 1.10992i −0.344442 0.938808i \(-0.611932\pi\)
0.985252 0.171108i \(-0.0547348\pi\)
\(734\) 0 0
\(735\) 333.522 + 121.336i 0.453772 + 0.165083i
\(736\) 0 0
\(737\) 209.470 362.812i 0.284220 0.492283i
\(738\) 0 0
\(739\) −984.945 + 568.658i −1.33281 + 0.769497i −0.985729 0.168339i \(-0.946160\pi\)
−0.347079 + 0.937836i \(0.612826\pi\)
\(740\) 0 0
\(741\) 421.388 0.568675
\(742\) 0 0
\(743\) 455.212 0.612667 0.306333 0.951924i \(-0.400898\pi\)
0.306333 + 0.951924i \(0.400898\pi\)
\(744\) 0 0
\(745\) 656.012 378.749i 0.880554 0.508388i
\(746\) 0 0
\(747\) −3.82292 + 6.62150i −0.00511770 + 0.00886412i
\(748\) 0 0
\(749\) −362.001 303.709i −0.483312 0.405486i
\(750\) 0 0
\(751\) 94.2623 163.267i 0.125516 0.217400i −0.796419 0.604746i \(-0.793275\pi\)
0.921934 + 0.387346i \(0.126608\pi\)
\(752\) 0 0
\(753\) 466.035 + 807.196i 0.618905 + 1.07197i
\(754\) 0 0
\(755\) −639.502 −0.847023
\(756\) 0 0
\(757\) 199.539i 0.263591i −0.991277 0.131796i \(-0.957926\pi\)
0.991277 0.131796i \(-0.0420743\pi\)
\(758\) 0 0
\(759\) −245.781 + 141.902i −0.323822 + 0.186959i
\(760\) 0 0
\(761\) 292.734 + 169.010i 0.384670 + 0.222089i 0.679848 0.733353i \(-0.262046\pi\)
−0.295178 + 0.955442i \(0.595379\pi\)
\(762\) 0 0
\(763\) 888.345 323.406i 1.16428 0.423861i
\(764\) 0 0
\(765\) 161.797 + 93.4138i 0.211500 + 0.122110i
\(766\) 0 0
\(767\) −365.326 632.763i −0.476305 0.824984i
\(768\) 0 0
\(769\) 604.446i 0.786015i −0.919535 0.393008i \(-0.871435\pi\)
0.919535 0.393008i \(-0.128565\pi\)
\(770\) 0 0
\(771\) 5.72674i 0.00742768i
\(772\) 0 0
\(773\) −390.213 675.869i −0.504804 0.874346i −0.999985 0.00555593i \(-0.998231\pi\)
0.495181 0.868790i \(1.66490\pi\)
\(774\) 0 0
\(775\) −244.630 141.237i −0.315651 0.182241i
\(776\) 0 0
\(777\) 141.559 803.172i 0.182187 1.03368i
\(778\) 0 0
\(779\) −244.882 141.383i −0.314354 0.181492i
\(780\) 0 0
\(781\) −332.561 + 192.004i −0.425814 + 0.245844i
\(782\) 0 0
\(783\) 1238.52i 1.58176i
\(784\) 0 0
\(785\) −231.164 −0.294477
\(786\) 0 0
\(787\) −481.905 834.684i −0.612332 1.06059i −0.990846 0.134994i \(-0.956898\pi\)
0.378515 0.925595i