Properties

Label 224.3.n.a.17.10
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 17.10
Character \(\chi\) \(=\) 224.17
Dual form 224.3.n.a.145.10

$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

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

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
\(3\) 1.16781 2.02271i 0.389271 0.674238i −0.603080 0.797680i \(-0.706060\pi\)
0.992352 + 0.123443i \(0.0393935\pi\)
\(4\) 0 0
\(5\) 1.55055 + 2.68563i 0.310110 + 0.537126i 0.978386 0.206787i \(-0.0663009\pi\)
−0.668276 + 0.743913i \(0.732968\pi\)
\(6\) 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 \(-0.401791\pi\)
−0.673301 + 0.739368i \(0.735124\pi\)
\(12\) 0 0
\(13\) 6.88097 0.529305 0.264653 0.964344i \(-0.414743\pi\)
0.264653 + 0.964344i \(0.414743\pi\)
\(14\) 0 0
\(15\) 7.24301 0.482868
\(16\) 0 0
\(17\) 14.7184 + 8.49765i 0.865786 + 0.499862i 0.865946 0.500138i \(-0.166717\pi\)
−0.000159428 1.00000i \(0.500051\pi\)
\(18\) 0 0
\(19\) −13.1099 22.7070i −0.689994 1.19510i −0.971839 0.235645i \(-0.924280\pi\)
0.281845 0.959460i \(1.59095\pi\)
\(20\) 0 0
\(21\) 5.59297 15.3630i 0.266332 0.731571i
\(22\) 0 0
\(23\) 12.9403 + 22.4132i 0.562620 + 0.974486i 0.997267 + 0.0738851i \(0.0235398\pi\)
−0.434647 + 0.900601i \(0.643127\pi\)
\(24\) 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 0.221077 0.975256i \(-0.429043\pi\)
−0.734058 + 0.679087i \(0.762376\pi\)
\(32\) 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 \(-0.902131\pi\)
−0.214455 + 0.976734i \(0.568797\pi\)
\(38\) 0 0
\(39\) 8.03569 13.9182i 0.206043 0.356878i
\(40\) 0 0
\(41\) 10.7844i 0.263035i 0.991314 + 0.131517i \(0.0419849\pi\)
−0.991314 + 0.131517i \(0.958015\pi\)
\(42\) 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 −0.620719 0.784033i \(-0.713159\pi\)
0.368633 + 0.929575i \(0.379826\pi\)
\(48\) 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 \(-0.354290\pi\)
−0.555893 + 0.831254i \(0.687624\pi\)
\(54\) 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 −0.0722059 + 0.997390i \(0.523004\pi\)
−0.827662 + 0.561227i \(0.810329\pi\)
\(60\) 0 0
\(61\) 46.7304 + 80.9395i 0.766073 + 1.32688i 0.939678 + 0.342062i \(0.111125\pi\)
−0.173605 + 0.984815i \(0.555542\pi\)
\(62\) 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 \(-0.565283\pi\)
−0.949705 + 0.313147i \(0.898617\pi\)
\(68\) 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 −0.981985 0.188961i \(-0.939488\pi\)
−0.654637 0.755943i \(-0.727179\pi\)
\(74\) 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 0.821581 0.570091i \(-0.193092\pi\)
−0.904504 + 0.426465i \(0.859759\pi\)
\(80\) 0 0
\(81\) 18.2653 31.6364i 0.225497 0.390573i
\(82\) 0 0
\(83\) 2.15689 0.0259867 0.0129933 0.999916i \(-0.495864\pi\)
0.0129933 + 0.999916i \(0.495864\pi\)
\(84\) 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 −0.904319 0.426857i \(-0.859621\pi\)
−0.0824908 + 0.996592i \(0.526288\pi\)
\(90\) 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 \(0.151581\pi\)
−0.888740 + 0.458412i \(0.848419\pi\)
\(98\) 0 0
\(99\) 16.6432i 0.168114i
\(100\) 0 0
\(101\) 10.4239 18.0546i 0.103206 0.178759i −0.809798 0.586709i \(-0.800423\pi\)
0.913004 + 0.407951i \(0.133756\pi\)
\(102\) 0 0
\(103\) −2.97469 + 1.71744i −0.0288805 + 0.0166741i −0.514371 0.857568i \(-0.671974\pi\)
0.485490 + 0.874242i \(0.338641\pi\)
\(104\) 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 \(-0.564515\pi\)
0.747652 + 0.664091i \(0.231181\pi\)
\(108\) 0 0
\(109\) −116.961 67.5273i −1.07303 0.619516i −0.144025 0.989574i \(-0.546005\pi\)
−0.929009 + 0.370058i \(0.879338\pi\)
\(110\) 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 0.979835 + 0.199807i \(0.0640316\pi\)
−0.316879 + 0.948466i \(0.602635\pi\)
\(132\) 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 −0.691755 0.722133i \(-0.743162\pi\)
0.971262 + 0.238011i \(0.0764954\pi\)
\(138\) 0 0
\(139\) −72.4724 −0.521384 −0.260692 0.965422i \(-0.583951\pi\)
−0.260692 + 0.965422i \(0.583951\pi\)
\(140\) 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 \(-0.360812\pi\)
0.996276 + 0.0862205i \(0.0274790\pi\)
\(150\) 0 0
\(151\) 103.109 178.590i 0.682841 1.18272i −0.291269 0.956641i \(-0.594077\pi\)
0.974110 0.226074i \(-0.0725893\pi\)
\(152\) 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 \(-0.909628\pi\)
0.722569 + 0.691298i \(0.242961\pi\)
\(158\) 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 \(-0.569184\pi\)
0.737830 + 0.674987i \(0.235851\pi\)
\(164\) 0 0
\(165\) −29.4504 17.0032i −0.178487 0.103050i
\(166\) 0 0
\(167\) 252.539i 1.51221i 0.654449 + 0.756106i \(0.272901\pi\)
−0.654449 + 0.756106i \(0.727099\pi\)
\(168\) 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 \(-0.309783\pi\)
−0.997264 + 0.0739171i \(0.976450\pi\)
\(174\) 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 \(-0.426682\pi\)
−0.729001 + 0.684513i \(0.760015\pi\)
\(180\) 0 0
\(181\) −95.1121 −0.525481 −0.262741 0.964867i \(-0.584626\pi\)
−0.262741 + 0.964867i \(0.584626\pi\)
\(182\) 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 0.871143 0.491030i \(-0.163379\pi\)
−0.860816 + 0.508917i \(0.830046\pi\)
\(192\) 0 0
\(193\) 146.091 253.037i 0.756949 1.31107i −0.187450 0.982274i \(-0.560022\pi\)
0.944399 0.328800i \(-0.106644\pi\)
\(194\) 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 −0.00712311 0.999975i \(-0.502267\pi\)
−0.869565 + 0.493819i \(0.835601\pi\)
\(200\) 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 \(-0.895770\pi\)
0.946866 0.321628i \(-0.104230\pi\)
\(224\) 0 0
\(225\) 54.5309 0.242360
\(226\) 0 0
\(227\) −11.7597 + 20.3683i −0.0518047 + 0.0897284i −0.890765 0.454464i \(-0.849831\pi\)
0.838960 + 0.544193i \(0.183164\pi\)
\(228\) 0 0
\(229\) 30.7040 + 53.1809i 0.134079 + 0.232231i 0.925245 0.379370i \(-0.123859\pi\)
−0.791167 + 0.611601i \(0.790526\pi\)
\(230\) 0 0
\(231\) −58.8063 + 49.3369i −0.254573 + 0.213580i
\(232\) 0 0
\(233\) −52.0991 90.2384i −0.223601 0.387289i 0.732297 0.680985i \(-0.238448\pi\)
−0.955899 + 0.293696i \(0.905115\pi\)
\(234\) 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 0.173943 0.984756i \(-0.444349\pi\)
−0.765852 + 0.643017i \(0.777683\pi\)
\(242\) 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 \(-0.207496\pi\)
0.794952 + 0.606672i \(0.207496\pi\)
\(252\) 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 −0.495863 0.868401i \(-0.665148\pi\)
0.504125 + 0.863630i \(0.331815\pi\)
\(258\) 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 −0.806110 0.591766i \(-0.798431\pi\)
0.915539 + 0.402229i \(0.131764\pi\)
\(264\) 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 \(-0.980786\pi\)
0.551334 + 0.834285i \(0.314119\pi\)
\(270\) 0 0
\(271\) −116.507 + 67.2655i −0.429916 + 0.248212i −0.699311 0.714818i \(-0.746510\pi\)
0.269395 + 0.963030i \(0.413176\pi\)
\(272\) 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 \(-0.397193\pi\)
−0.662552 + 0.749016i \(0.730527\pi\)
\(278\) 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 \(-0.815923\pi\)
0.892065 + 0.451907i \(0.149256\pi\)
\(284\) 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 \(-0.837949\pi\)
−0.873184 + 0.487390i \(0.837949\pi\)
\(294\) 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 \(-0.473391\pi\)
0.0834967 + 0.996508i \(0.473391\pi\)
\(308\) 0 0
\(309\) 8.02259i 0.0259631i
\(310\) 0 0
\(311\) 17.7940 + 10.2734i 0.0572153 + 0.0330333i 0.528335 0.849036i \(-0.322817\pi\)
−0.471119 + 0.882069i \(0.656150\pi\)
\(312\) 0 0
\(313\) 291.960 168.563i 0.932780 0.538541i 0.0450905 0.998983i \(-0.485642\pi\)
0.887690 + 0.460442i \(0.152309\pi\)
\(314\) 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 \(-0.713659\pi\)
0.367174 + 0.930152i \(0.380325\pi\)
\(318\) 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 \(-0.702830\pi\)
0.398599 + 0.917125i \(0.369497\pi\)
\(332\) 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 \(-0.367811\pi\)
−0.590689 + 0.806899i \(0.701144\pi\)
\(348\) 0 0
\(349\) 603.618 1.72956 0.864782 0.502148i \(-0.167457\pi\)
0.864782 + 0.502148i \(0.167457\pi\)
\(350\) 0 0
\(351\) 201.613 0.574396
\(352\) 0 0
\(353\) 337.515 + 194.864i 0.956132 + 0.552023i 0.894980 0.446106i \(-0.147189\pi\)
0.0611514 + 0.998129i \(0.480523\pi\)
\(354\) 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 0.946183 0.323633i \(-0.104904\pi\)
−0.753366 + 0.657602i \(0.771571\pi\)
\(360\) 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 0.939852 0.341581i \(-0.110963\pi\)
0.174108 + 0.984727i \(0.444296\pi\)
\(368\) 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 \(-0.651613\pi\)
0.540382 + 0.841420i \(0.318280\pi\)
\(374\) 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 0.281549 0.959547i \(-0.409152\pi\)
0.971766 + 0.235945i \(0.0758184\pi\)
\(384\) 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 \(-0.162550\pi\)
0.0129310 + 0.999916i \(0.495884\pi\)
\(390\) 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 \(-0.117600\pi\)
−0.778988 + 0.627039i \(0.784267\pi\)
\(398\) 0 0
\(399\) −422.170 + 74.4077i −1.05807 + 0.186485i
\(400\) 0 0
\(401\) −124.337 215.358i −0.310067 0.537051i 0.668310 0.743883i \(-0.267018\pi\)
−0.978377 + 0.206832i \(0.933685\pi\)
\(402\) 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 0.996700 0.0811790i \(-0.0258685\pi\)
0.428047 + 0.903757i \(0.359202\pi\)
\(410\) 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 \(-0.568440\pi\)
−0.213359 + 0.976974i \(0.568440\pi\)
\(420\) 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 0.116027 + 0.993246i \(0.462984\pi\)
−0.918190 + 0.396141i \(0.870349\pi\)
\(432\) 0 0
\(433\) 99.8389i 0.230575i −0.993332 0.115287i \(-0.963221\pi\)
0.993332 0.115287i \(-0.0367789\pi\)
\(434\) 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 0.374980 0.927033i \(-0.377649\pi\)
0.990324 + 0.138774i \(0.0443161\pi\)
\(440\) 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 \(-0.568209\pi\)
0.739893 + 0.672724i \(0.234876\pi\)
\(444\) 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 0.991669 0.128811i \(-0.0411160\pi\)
−0.607388 + 0.794405i \(0.707783\pi\)
\(458\) 0 0
\(459\) 431.249 + 248.982i 0.939541 + 0.542444i
\(460\) 0 0
\(461\) −296.940 −0.644122 −0.322061 0.946719i \(-0.604376\pi\)
−0.322061 + 0.946719i \(0.604376\pi\)
\(462\) 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 \(-0.123759\pi\)
−0.790974 + 0.611849i \(0.790426\pi\)
\(468\) 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 0.648511 0.761205i \(-0.275392\pi\)
−0.334967 + 0.942230i \(0.608725\pi\)
\(480\) 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 0.268866 + 0.963178i \(0.413351\pi\)
−0.968569 + 0.248744i \(0.919982\pi\)
\(488\) 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 \(-0.531756\pi\)
0.811919 + 0.583770i \(0.198423\pi\)
\(500\) 0 0
\(501\) 510.815 + 294.919i 1.01959 + 0.588661i
\(502\) 0 0
\(503\) 554.042i 1.10148i −0.834678 0.550738i \(-0.814346\pi\)
0.834678 0.550738i \(-0.185654\pi\)
\(504\) 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 \(-0.180490\pi\)
−0.886915 + 0.461932i \(0.847156\pi\)
\(510\) 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 0.806748 0.590895i \(-0.201225\pi\)
−0.108356 + 0.994112i \(0.534559\pi\)
\(522\) 0 0
\(523\) −137.447 238.065i −0.262805 0.455191i 0.704181 0.710020i \(-0.251314\pi\)
−0.966986 + 0.254829i \(0.917981\pi\)
\(524\) 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 \(-0.839978\pi\)
−0.0208748 + 0.999782i \(0.506645\pi\)
\(542\) 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 \(-0.0979397\pi\)
0.214239 + 0.976781i \(0.431273\pi\)
\(558\) 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 0.433803 + 0.901008i \(0.357171\pi\)
−0.997197 + 0.0748195i \(0.976162\pi\)
\(564\) 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 0.640099 0.768293i \(-0.278893\pi\)
−0.985410 + 0.170195i \(0.945560\pi\)
\(570\) 0 0
\(571\) 466.776 + 269.493i 0.817471 + 0.471967i 0.849543 0.527519i \(-0.176878\pi\)
−0.0320728 + 0.999486i \(0.510211\pi\)
\(572\) 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 0.215589 0.976484i \(-0.430833\pi\)
−0.737865 + 0.674948i \(0.764166\pi\)
\(578\) 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 \(-0.570788\pi\)
−0.220559 + 0.975374i \(0.570788\pi\)
\(588\) 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 −0.442747 0.896647i \(-0.645996\pi\)
0.555146 + 0.831753i \(0.312663\pi\)
\(594\) 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 0.264475 0.964392i \(-0.414801\pi\)
0.702951 0.711239i \(-0.251865\pi\)
\(600\) 0 0
\(601\) 976.895i 1.62545i 0.582648 + 0.812724i \(0.302017\pi\)
−0.582648 + 0.812724i \(0.697983\pi\)
\(602\) 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 0.183942 0.982937i \(-0.441114\pi\)
0.943219 + 0.332170i \(0.107781\pi\)
\(608\) 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 \(-0.262695\pi\)
−0.297127 + 0.954838i \(0.596029\pi\)
\(614\) 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 −0.265278 0.964172i \(-0.585464\pi\)
0.967636 0.252349i \(-0.0812029\pi\)
\(620\) 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 0.0720947 + 0.997398i \(0.477032\pi\)
−0.899819 + 0.436263i \(0.856302\pi\)
\(642\) 0 0
\(643\) −132.853 −0.206615 −0.103308 0.994649i \(-0.532943\pi\)
−0.103308 + 0.994649i \(0.532943\pi\)
\(644\) 0 0
\(645\) 175.129i 0.271518i
\(646\) 0 0
\(647\) −998.259 576.345i −1.54290 0.890796i −0.998654 0.0518730i \(-0.983481\pi\)
−0.544250 0.838923i \(-0.683186\pi\)
\(648\) 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 \(-0.673753\pi\)
0.480599 + 0.876940i \(0.340419\pi\)
\(654\) 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 \(-0.802626\pi\)
0.910159 + 0.414259i \(0.135959\pi\)
\(662\) 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 \(-0.0770286\pi\)
−0.692963 + 0.720973i \(0.743695\pi\)
\(678\) 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 \(-0.607662\pi\)
−0.982869 + 0.184308i \(0.940996\pi\)
\(684\) 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 \(-0.249376\pi\)
−0.965416 + 0.260713i \(0.916042\pi\)
\(692\) 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 \(-0.345123\pi\)
0.999314 + 0.0370292i \(0.0117895\pi\)
\(710\) 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 −0.495543 0.868583i \(-0.665031\pi\)
0.504444 + 0.863445i \(0.331698\pi\)
\(720\) 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 \(0.303135\pi\)
−0.579788 + 0.814767i \(0.696865\pi\)
\(728\) 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 −0.985252 0.171108i \(-0.945265\pi\)
0.344442 0.938808i \(1.61193\pi\)
\(734\) 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 \(-0.0538404\pi\)
0.347079 + 0.937836i \(0.387174\pi\)
\(740\) 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 0.921934 0.387346i \(-0.126608\pi\)
−0.796419 + 0.604746i \(0.793275\pi\)
\(752\) 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 −0.295178 0.955442i \(-0.595379\pi\)
0.679848 + 0.733353i \(0.262046\pi\)
\(762\) 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 \(0.128565\pi\)
−0.919535 + 0.393008i \(0.871435\pi\)
\(770\) 0 0
\(771\) 5.72674i 0.00742768i
\(772\) 0 0
\(773\) 390.213 675.869i 0.504804 0.874346i −0.495181 0.868790i \(-0.664898\pi\)
0.999985 0.00555593i \(-0.00176852\pi\)
\(774\) 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 −0.378515 0.925595i \(-0.623565\pi\)
0.990846 0.134994i