Properties

Label 403.2.c.b.311.8
Level 403
Weight 2
Character 403.311
Analytic conductor 3.218
Analytic rank 0
Dimension 32
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 403.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(32\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 311.8
Character \(\chi\) = 403.311
Dual form 403.2.c.b.311.25

$q$-expansion

\(f(q)\) \(=\) \(q-1.48947i q^{2} +2.99747 q^{3} -0.218531 q^{4} +0.692562i q^{5} -4.46466i q^{6} +1.15260i q^{7} -2.65345i q^{8} +5.98485 q^{9} +O(q^{10})\) \(q-1.48947i q^{2} +2.99747 q^{3} -0.218531 q^{4} +0.692562i q^{5} -4.46466i q^{6} +1.15260i q^{7} -2.65345i q^{8} +5.98485 q^{9} +1.03155 q^{10} +2.69554i q^{11} -0.655040 q^{12} +(-3.22749 + 1.60727i) q^{13} +1.71676 q^{14} +2.07594i q^{15} -4.38931 q^{16} -4.04263 q^{17} -8.91428i q^{18} -5.06961i q^{19} -0.151346i q^{20} +3.45488i q^{21} +4.01494 q^{22} -1.01940 q^{23} -7.95365i q^{24} +4.52036 q^{25} +(2.39399 + 4.80726i) q^{26} +8.94703 q^{27} -0.251878i q^{28} -8.56509 q^{29} +3.09205 q^{30} +1.00000i q^{31} +1.23085i q^{32} +8.07982i q^{33} +6.02139i q^{34} -0.798246 q^{35} -1.30787 q^{36} +5.88104i q^{37} -7.55104 q^{38} +(-9.67431 + 4.81776i) q^{39} +1.83768 q^{40} -11.8895i q^{41} +5.14596 q^{42} -3.63935 q^{43} -0.589058i q^{44} +4.14488i q^{45} +1.51836i q^{46} -0.848777i q^{47} -13.1568 q^{48} +5.67152 q^{49} -6.73295i q^{50} -12.1177 q^{51} +(0.705305 - 0.351239i) q^{52} +1.67652 q^{53} -13.3264i q^{54} -1.86683 q^{55} +3.05836 q^{56} -15.1960i q^{57} +12.7575i q^{58} +1.68042i q^{59} -0.453656i q^{60} +2.00772 q^{61} +1.48947 q^{62} +6.89813i q^{63} -6.94529 q^{64} +(-1.11314 - 2.23524i) q^{65} +12.0347 q^{66} -8.32497i q^{67} +0.883439 q^{68} -3.05562 q^{69} +1.18897i q^{70} -5.15229i q^{71} -15.8805i q^{72} +14.8210i q^{73} +8.75965 q^{74} +13.5497 q^{75} +1.10786i q^{76} -3.10687 q^{77} +(7.17593 + 14.4096i) q^{78} +0.873238 q^{79} -3.03987i q^{80} +8.86392 q^{81} -17.7091 q^{82} +10.8692i q^{83} -0.754998i q^{84} -2.79977i q^{85} +5.42072i q^{86} -25.6736 q^{87} +7.15249 q^{88} -3.90690i q^{89} +6.17370 q^{90} +(-1.85254 - 3.71999i) q^{91} +0.222769 q^{92} +2.99747i q^{93} -1.26423 q^{94} +3.51102 q^{95} +3.68945i q^{96} +10.3729i q^{97} -8.44757i q^{98} +16.1324i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + O(q^{10}) \) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + 4q^{10} - 16q^{12} + 10q^{13} - 16q^{14} + 28q^{16} - 8q^{17} - 16q^{22} - 8q^{23} + 4q^{25} + 18q^{26} + 20q^{27} - 16q^{29} + 40q^{30} - 4q^{35} - 44q^{36} + 12q^{38} + 4q^{39} + 28q^{40} + 28q^{42} - 32q^{43} - 64q^{49} - 64q^{52} - 12q^{53} + 44q^{55} + 8q^{56} + 16q^{61} + 8q^{62} - 76q^{64} - 66q^{65} - 68q^{66} + 64q^{68} + 20q^{69} + 16q^{74} - 32q^{77} - 20q^{78} + 64q^{79} - 16q^{81} + 12q^{82} - 72q^{87} + 80q^{88} + 68q^{90} + 22q^{91} + 28q^{92} + 88q^{94} + 4q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.48947i 1.05322i −0.850108 0.526608i \(-0.823463\pi\)
0.850108 0.526608i \(-0.176537\pi\)
\(3\) 2.99747 1.73059 0.865296 0.501261i \(-0.167130\pi\)
0.865296 + 0.501261i \(0.167130\pi\)
\(4\) −0.218531 −0.109265
\(5\) 0.692562i 0.309723i 0.987936 + 0.154862i \(0.0494932\pi\)
−0.987936 + 0.154862i \(0.950507\pi\)
\(6\) 4.46466i 1.82269i
\(7\) 1.15260i 0.435641i 0.975989 + 0.217821i \(0.0698947\pi\)
−0.975989 + 0.217821i \(0.930105\pi\)
\(8\) 2.65345i 0.938137i
\(9\) 5.98485 1.99495
\(10\) 1.03155 0.326206
\(11\) 2.69554i 0.812736i 0.913709 + 0.406368i \(0.133205\pi\)
−0.913709 + 0.406368i \(0.866795\pi\)
\(12\) −0.655040 −0.189094
\(13\) −3.22749 + 1.60727i −0.895144 + 0.445777i
\(14\) 1.71676 0.458824
\(15\) 2.07594i 0.536005i
\(16\) −4.38931 −1.09733
\(17\) −4.04263 −0.980482 −0.490241 0.871587i \(-0.663091\pi\)
−0.490241 + 0.871587i \(0.663091\pi\)
\(18\) 8.91428i 2.10112i
\(19\) 5.06961i 1.16305i −0.813530 0.581524i \(-0.802457\pi\)
0.813530 0.581524i \(-0.197543\pi\)
\(20\) 0.151346i 0.0338420i
\(21\) 3.45488i 0.753917i
\(22\) 4.01494 0.855987
\(23\) −1.01940 −0.212559 −0.106279 0.994336i \(-0.533894\pi\)
−0.106279 + 0.994336i \(0.533894\pi\)
\(24\) 7.95365i 1.62353i
\(25\) 4.52036 0.904071
\(26\) 2.39399 + 4.80726i 0.469500 + 0.942780i
\(27\) 8.94703 1.72186
\(28\) 0.251878i 0.0476005i
\(29\) −8.56509 −1.59050 −0.795249 0.606283i \(-0.792660\pi\)
−0.795249 + 0.606283i \(0.792660\pi\)
\(30\) 3.09205 0.564529
\(31\) 1.00000i 0.179605i
\(32\) 1.23085i 0.217586i
\(33\) 8.07982i 1.40652i
\(34\) 6.02139i 1.03266i
\(35\) −0.798246 −0.134928
\(36\) −1.30787 −0.217979
\(37\) 5.88104i 0.966837i 0.875389 + 0.483418i \(0.160605\pi\)
−0.875389 + 0.483418i \(0.839395\pi\)
\(38\) −7.55104 −1.22494
\(39\) −9.67431 + 4.81776i −1.54913 + 0.771459i
\(40\) 1.83768 0.290563
\(41\) 11.8895i 1.85683i −0.371551 0.928413i \(-0.621174\pi\)
0.371551 0.928413i \(-0.378826\pi\)
\(42\) 5.14596 0.794038
\(43\) −3.63935 −0.554996 −0.277498 0.960726i \(-0.589505\pi\)
−0.277498 + 0.960726i \(0.589505\pi\)
\(44\) 0.589058i 0.0888039i
\(45\) 4.14488i 0.617883i
\(46\) 1.51836i 0.223871i
\(47\) 0.848777i 0.123807i −0.998082 0.0619034i \(-0.980283\pi\)
0.998082 0.0619034i \(-0.0197171\pi\)
\(48\) −13.1568 −1.89903
\(49\) 5.67152 0.810217
\(50\) 6.73295i 0.952183i
\(51\) −12.1177 −1.69681
\(52\) 0.705305 0.351239i 0.0978082 0.0487080i
\(53\) 1.67652 0.230287 0.115144 0.993349i \(-0.463267\pi\)
0.115144 + 0.993349i \(0.463267\pi\)
\(54\) 13.3264i 1.81349i
\(55\) −1.86683 −0.251723
\(56\) 3.05836 0.408691
\(57\) 15.1960i 2.01276i
\(58\) 12.7575i 1.67514i
\(59\) 1.68042i 0.218772i 0.993999 + 0.109386i \(0.0348885\pi\)
−0.993999 + 0.109386i \(0.965111\pi\)
\(60\) 0.453656i 0.0585668i
\(61\) 2.00772 0.257062 0.128531 0.991705i \(-0.458974\pi\)
0.128531 + 0.991705i \(0.458974\pi\)
\(62\) 1.48947 0.189163
\(63\) 6.89813i 0.869083i
\(64\) −6.94529 −0.868161
\(65\) −1.11314 2.23524i −0.138068 0.277247i
\(66\) 12.0347 1.48137
\(67\) 8.32497i 1.01706i −0.861045 0.508529i \(-0.830190\pi\)
0.861045 0.508529i \(-0.169810\pi\)
\(68\) 0.883439 0.107133
\(69\) −3.05562 −0.367853
\(70\) 1.18897i 0.142109i
\(71\) 5.15229i 0.611465i −0.952117 0.305732i \(-0.901099\pi\)
0.952117 0.305732i \(-0.0989013\pi\)
\(72\) 15.8805i 1.87154i
\(73\) 14.8210i 1.73466i 0.497730 + 0.867332i \(0.334167\pi\)
−0.497730 + 0.867332i \(0.665833\pi\)
\(74\) 8.75965 1.01829
\(75\) 13.5497 1.56458
\(76\) 1.10786i 0.127081i
\(77\) −3.10687 −0.354061
\(78\) 7.17593 + 14.4096i 0.812514 + 1.63157i
\(79\) 0.873238 0.0982470 0.0491235 0.998793i \(-0.484357\pi\)
0.0491235 + 0.998793i \(0.484357\pi\)
\(80\) 3.03987i 0.339868i
\(81\) 8.86392 0.984880
\(82\) −17.7091 −1.95564
\(83\) 10.8692i 1.19305i 0.802596 + 0.596523i \(0.203452\pi\)
−0.802596 + 0.596523i \(0.796548\pi\)
\(84\) 0.754998i 0.0823770i
\(85\) 2.79977i 0.303678i
\(86\) 5.42072i 0.584531i
\(87\) −25.6736 −2.75250
\(88\) 7.15249 0.762457
\(89\) 3.90690i 0.414131i −0.978327 0.207065i \(-0.933609\pi\)
0.978327 0.207065i \(-0.0663913\pi\)
\(90\) 6.17370 0.650765
\(91\) −1.85254 3.71999i −0.194199 0.389961i
\(92\) 0.222769 0.0232253
\(93\) 2.99747i 0.310824i
\(94\) −1.26423 −0.130395
\(95\) 3.51102 0.360223
\(96\) 3.68945i 0.376553i
\(97\) 10.3729i 1.05321i 0.850110 + 0.526606i \(0.176536\pi\)
−0.850110 + 0.526606i \(0.823464\pi\)
\(98\) 8.44757i 0.853334i
\(99\) 16.1324i 1.62137i
\(100\) −0.987837 −0.0987837
\(101\) −1.55946 −0.155172 −0.0775862 0.996986i \(-0.524721\pi\)
−0.0775862 + 0.996986i \(0.524721\pi\)
\(102\) 18.0490i 1.78711i
\(103\) 18.4902 1.82189 0.910947 0.412523i \(-0.135352\pi\)
0.910947 + 0.412523i \(0.135352\pi\)
\(104\) 4.26482 + 8.56398i 0.418200 + 0.839767i
\(105\) −2.39272 −0.233506
\(106\) 2.49713i 0.242543i
\(107\) 15.4750 1.49602 0.748010 0.663687i \(-0.231009\pi\)
0.748010 + 0.663687i \(0.231009\pi\)
\(108\) −1.95520 −0.188139
\(109\) 11.0776i 1.06104i 0.847673 + 0.530518i \(0.178003\pi\)
−0.847673 + 0.530518i \(0.821997\pi\)
\(110\) 2.78059i 0.265119i
\(111\) 17.6283i 1.67320i
\(112\) 5.05910i 0.478040i
\(113\) 1.83667 0.172780 0.0863898 0.996261i \(-0.472467\pi\)
0.0863898 + 0.996261i \(0.472467\pi\)
\(114\) −22.6341 −2.11987
\(115\) 0.705996i 0.0658344i
\(116\) 1.87174 0.173786
\(117\) −19.3160 + 9.61930i −1.78577 + 0.889304i
\(118\) 2.50294 0.230415
\(119\) 4.65953i 0.427138i
\(120\) 5.50840 0.502846
\(121\) 3.73406 0.339460
\(122\) 2.99045i 0.270743i
\(123\) 35.6384i 3.21341i
\(124\) 0.218531i 0.0196246i
\(125\) 6.59344i 0.589735i
\(126\) 10.2746 0.915333
\(127\) 14.4471 1.28198 0.640988 0.767551i \(-0.278525\pi\)
0.640988 + 0.767551i \(0.278525\pi\)
\(128\) 12.8065i 1.13195i
\(129\) −10.9089 −0.960472
\(130\) −3.32932 + 1.65799i −0.292001 + 0.145415i
\(131\) −6.01302 −0.525360 −0.262680 0.964883i \(-0.584606\pi\)
−0.262680 + 0.964883i \(0.584606\pi\)
\(132\) 1.76569i 0.153683i
\(133\) 5.84322 0.506671
\(134\) −12.3998 −1.07118
\(135\) 6.19637i 0.533299i
\(136\) 10.7269i 0.919826i
\(137\) 16.9039i 1.44420i −0.691791 0.722098i \(-0.743178\pi\)
0.691791 0.722098i \(-0.256822\pi\)
\(138\) 4.55126i 0.387429i
\(139\) −0.0379050 −0.00321506 −0.00160753 0.999999i \(-0.500512\pi\)
−0.00160753 + 0.999999i \(0.500512\pi\)
\(140\) 0.174441 0.0147430
\(141\) 2.54419i 0.214259i
\(142\) −7.67421 −0.644005
\(143\) −4.33247 8.69982i −0.362299 0.727516i
\(144\) −26.2694 −2.18911
\(145\) 5.93186i 0.492614i
\(146\) 22.0754 1.82698
\(147\) 17.0002 1.40216
\(148\) 1.28519i 0.105642i
\(149\) 16.6078i 1.36056i 0.732952 + 0.680281i \(0.238142\pi\)
−0.732952 + 0.680281i \(0.761858\pi\)
\(150\) 20.1819i 1.64784i
\(151\) 3.90890i 0.318102i 0.987270 + 0.159051i \(0.0508434\pi\)
−0.987270 + 0.159051i \(0.949157\pi\)
\(152\) −13.4519 −1.09110
\(153\) −24.1945 −1.95601
\(154\) 4.62761i 0.372903i
\(155\) −0.692562 −0.0556279
\(156\) 2.11413 1.05283i 0.169266 0.0842937i
\(157\) 4.63903 0.370235 0.185117 0.982716i \(-0.440733\pi\)
0.185117 + 0.982716i \(0.440733\pi\)
\(158\) 1.30066i 0.103475i
\(159\) 5.02532 0.398534
\(160\) −0.852441 −0.0673914
\(161\) 1.17495i 0.0925994i
\(162\) 13.2026i 1.03729i
\(163\) 14.1214i 1.10607i 0.833158 + 0.553035i \(0.186531\pi\)
−0.833158 + 0.553035i \(0.813469\pi\)
\(164\) 2.59822i 0.202887i
\(165\) −5.59578 −0.435631
\(166\) 16.1893 1.25654
\(167\) 10.5161i 0.813759i −0.913482 0.406879i \(-0.866617\pi\)
0.913482 0.406879i \(-0.133383\pi\)
\(168\) 9.16736 0.707277
\(169\) 7.83335 10.3749i 0.602565 0.798070i
\(170\) −4.17019 −0.319839
\(171\) 30.3409i 2.32022i
\(172\) 0.795310 0.0606418
\(173\) 20.5134 1.55960 0.779801 0.626028i \(-0.215320\pi\)
0.779801 + 0.626028i \(0.215320\pi\)
\(174\) 38.2402i 2.89898i
\(175\) 5.21015i 0.393851i
\(176\) 11.8316i 0.891837i
\(177\) 5.03702i 0.378606i
\(178\) −5.81923 −0.436170
\(179\) −10.7116 −0.800620 −0.400310 0.916380i \(-0.631098\pi\)
−0.400310 + 0.916380i \(0.631098\pi\)
\(180\) 0.905785i 0.0675132i
\(181\) −23.9491 −1.78012 −0.890061 0.455842i \(-0.849338\pi\)
−0.890061 + 0.455842i \(0.849338\pi\)
\(182\) −5.54083 + 2.75931i −0.410714 + 0.204534i
\(183\) 6.01810 0.444871
\(184\) 2.70492i 0.199409i
\(185\) −4.07299 −0.299452
\(186\) 4.46466 0.327365
\(187\) 10.8971i 0.796873i
\(188\) 0.185484i 0.0135278i
\(189\) 10.3123i 0.750111i
\(190\) 5.22957i 0.379393i
\(191\) −3.30915 −0.239442 −0.119721 0.992808i \(-0.538200\pi\)
−0.119721 + 0.992808i \(0.538200\pi\)
\(192\) −20.8183 −1.50243
\(193\) 9.66509i 0.695709i −0.937549 0.347854i \(-0.886910\pi\)
0.937549 0.347854i \(-0.113090\pi\)
\(194\) 15.4502 1.10926
\(195\) −3.33660 6.70006i −0.238939 0.479801i
\(196\) −1.23940 −0.0885286
\(197\) 26.5454i 1.89128i −0.325212 0.945641i \(-0.605436\pi\)
0.325212 0.945641i \(-0.394564\pi\)
\(198\) 24.0288 1.70765
\(199\) −6.60253 −0.468041 −0.234021 0.972232i \(-0.575188\pi\)
−0.234021 + 0.972232i \(0.575188\pi\)
\(200\) 11.9945i 0.848143i
\(201\) 24.9539i 1.76011i
\(202\) 2.32278i 0.163430i
\(203\) 9.87211i 0.692886i
\(204\) 2.64808 0.185403
\(205\) 8.23421 0.575102
\(206\) 27.5407i 1.91885i
\(207\) −6.10094 −0.424045
\(208\) 14.1664 7.05481i 0.982265 0.489163i
\(209\) 13.6653 0.945250
\(210\) 3.56390i 0.245932i
\(211\) −18.1733 −1.25110 −0.625551 0.780183i \(-0.715126\pi\)
−0.625551 + 0.780183i \(0.715126\pi\)
\(212\) −0.366371 −0.0251624
\(213\) 15.4439i 1.05820i
\(214\) 23.0495i 1.57563i
\(215\) 2.52048i 0.171895i
\(216\) 23.7405i 1.61534i
\(217\) −1.15260 −0.0782434
\(218\) 16.4997 1.11750
\(219\) 44.4255i 3.00200i
\(220\) 0.407960 0.0275046
\(221\) 13.0475 6.49761i 0.877672 0.437076i
\(222\) 26.2568 1.76224
\(223\) 3.90568i 0.261544i −0.991412 0.130772i \(-0.958254\pi\)
0.991412 0.130772i \(-0.0417456\pi\)
\(224\) −1.41868 −0.0947894
\(225\) 27.0537 1.80358
\(226\) 2.73568i 0.181974i
\(227\) 16.9202i 1.12303i −0.827466 0.561515i \(-0.810219\pi\)
0.827466 0.561515i \(-0.189781\pi\)
\(228\) 3.32080i 0.219925i
\(229\) 11.5304i 0.761949i −0.924585 0.380975i \(-0.875589\pi\)
0.924585 0.380975i \(-0.124411\pi\)
\(230\) −1.05156 −0.0693379
\(231\) −9.31278 −0.612736
\(232\) 22.7271i 1.49210i
\(233\) 0.108649 0.00711784 0.00355892 0.999994i \(-0.498867\pi\)
0.00355892 + 0.999994i \(0.498867\pi\)
\(234\) 14.3277 + 28.7707i 0.936630 + 1.88080i
\(235\) 0.587831 0.0383459
\(236\) 0.367224i 0.0239042i
\(237\) 2.61751 0.170026
\(238\) −6.94024 −0.449869
\(239\) 15.8424i 1.02476i 0.858760 + 0.512378i \(0.171235\pi\)
−0.858760 + 0.512378i \(0.828765\pi\)
\(240\) 9.11193i 0.588172i
\(241\) 4.44336i 0.286222i −0.989707 0.143111i \(-0.954289\pi\)
0.989707 0.143111i \(-0.0457106\pi\)
\(242\) 5.56178i 0.357525i
\(243\) −0.271696 −0.0174293
\(244\) −0.438749 −0.0280880
\(245\) 3.92788i 0.250943i
\(246\) −53.0825 −3.38442
\(247\) 8.14824 + 16.3621i 0.518460 + 1.04109i
\(248\) 2.65345 0.168494
\(249\) 32.5801i 2.06468i
\(250\) 9.82075 0.621119
\(251\) 8.24869 0.520653 0.260326 0.965521i \(-0.416170\pi\)
0.260326 + 0.965521i \(0.416170\pi\)
\(252\) 1.50745i 0.0949606i
\(253\) 2.74783i 0.172754i
\(254\) 21.5186i 1.35020i
\(255\) 8.39225i 0.525543i
\(256\) 5.18440 0.324025
\(257\) −8.29303 −0.517305 −0.258652 0.965970i \(-0.583278\pi\)
−0.258652 + 0.965970i \(0.583278\pi\)
\(258\) 16.2485i 1.01159i
\(259\) −6.77847 −0.421194
\(260\) 0.243255 + 0.488468i 0.0150860 + 0.0302935i
\(261\) −51.2608 −3.17297
\(262\) 8.95624i 0.553318i
\(263\) −19.7412 −1.21729 −0.608646 0.793442i \(-0.708287\pi\)
−0.608646 + 0.793442i \(0.708287\pi\)
\(264\) 21.4394 1.31950
\(265\) 1.16109i 0.0713254i
\(266\) 8.70331i 0.533634i
\(267\) 11.7108i 0.716692i
\(268\) 1.81926i 0.111129i
\(269\) −28.8863 −1.76123 −0.880614 0.473834i \(-0.842870\pi\)
−0.880614 + 0.473834i \(0.842870\pi\)
\(270\) 9.22933 0.561679
\(271\) 0.993095i 0.0603262i 0.999545 + 0.0301631i \(0.00960268\pi\)
−0.999545 + 0.0301631i \(0.990397\pi\)
\(272\) 17.7443 1.07591
\(273\) −5.55294 11.1506i −0.336079 0.674864i
\(274\) −25.1779 −1.52105
\(275\) 12.1848i 0.734772i
\(276\) 0.667746 0.0401936
\(277\) 1.99748 0.120017 0.0600085 0.998198i \(-0.480887\pi\)
0.0600085 + 0.998198i \(0.480887\pi\)
\(278\) 0.0564585i 0.00338616i
\(279\) 5.98485i 0.358304i
\(280\) 2.11811i 0.126581i
\(281\) 9.22146i 0.550106i −0.961429 0.275053i \(-0.911305\pi\)
0.961429 0.275053i \(-0.0886955\pi\)
\(282\) −3.78950 −0.225661
\(283\) −6.66812 −0.396379 −0.198189 0.980164i \(-0.563506\pi\)
−0.198189 + 0.980164i \(0.563506\pi\)
\(284\) 1.12593i 0.0668119i
\(285\) 10.5242 0.623399
\(286\) −12.9582 + 6.45310i −0.766232 + 0.381580i
\(287\) 13.7038 0.808909
\(288\) 7.36647i 0.434073i
\(289\) −0.657150 −0.0386559
\(290\) −8.83535 −0.518829
\(291\) 31.0926i 1.82268i
\(292\) 3.23884i 0.189539i
\(293\) 20.6409i 1.20585i 0.797797 + 0.602926i \(0.205999\pi\)
−0.797797 + 0.602926i \(0.794001\pi\)
\(294\) 25.3214i 1.47677i
\(295\) −1.16380 −0.0677589
\(296\) 15.6050 0.907025
\(297\) 24.1171i 1.39941i
\(298\) 24.7368 1.43297
\(299\) 3.29009 1.63845i 0.190271 0.0947539i
\(300\) −2.96102 −0.170954
\(301\) 4.19471i 0.241779i
\(302\) 5.82220 0.335030
\(303\) −4.67445 −0.268540
\(304\) 22.2520i 1.27624i
\(305\) 1.39047i 0.0796182i
\(306\) 36.0371i 2.06011i
\(307\) 3.05469i 0.174340i 0.996193 + 0.0871702i \(0.0277824\pi\)
−0.996193 + 0.0871702i \(0.972218\pi\)
\(308\) 0.678947 0.0386866
\(309\) 55.4239 3.15296
\(310\) 1.03155i 0.0585883i
\(311\) −22.9204 −1.29969 −0.649847 0.760065i \(-0.725167\pi\)
−0.649847 + 0.760065i \(0.725167\pi\)
\(312\) 12.7837 + 25.6703i 0.723734 + 1.45330i
\(313\) 10.3566 0.585391 0.292695 0.956206i \(-0.405448\pi\)
0.292695 + 0.956206i \(0.405448\pi\)
\(314\) 6.90971i 0.389937i
\(315\) −4.77739 −0.269175
\(316\) −0.190829 −0.0107350
\(317\) 9.04755i 0.508161i −0.967183 0.254080i \(-0.918227\pi\)
0.967183 0.254080i \(-0.0817728\pi\)
\(318\) 7.48508i 0.419742i
\(319\) 23.0876i 1.29265i
\(320\) 4.81005i 0.268890i
\(321\) 46.3858 2.58900
\(322\) −1.75006 −0.0975272
\(323\) 20.4945i 1.14035i
\(324\) −1.93704 −0.107613
\(325\) −14.5894 + 7.26545i −0.809274 + 0.403015i
\(326\) 21.0334 1.16493
\(327\) 33.2047i 1.83622i
\(328\) −31.5482 −1.74196
\(329\) 0.978299 0.0539354
\(330\) 8.33476i 0.458813i
\(331\) 32.1476i 1.76699i −0.468438 0.883496i \(-0.655183\pi\)
0.468438 0.883496i \(-0.344817\pi\)
\(332\) 2.37525i 0.130359i
\(333\) 35.1972i 1.92879i
\(334\) −15.6634 −0.857064
\(335\) 5.76556 0.315006
\(336\) 15.1645i 0.827293i
\(337\) 31.7351 1.72872 0.864361 0.502871i \(-0.167723\pi\)
0.864361 + 0.502871i \(0.167723\pi\)
\(338\) −15.4531 11.6676i −0.840540 0.634632i
\(339\) 5.50538 0.299011
\(340\) 0.611836i 0.0331815i
\(341\) −2.69554 −0.145972
\(342\) −45.1919 −2.44370
\(343\) 14.6052i 0.788605i
\(344\) 9.65684i 0.520662i
\(345\) 2.11620i 0.113933i
\(346\) 30.5541i 1.64260i
\(347\) −1.57708 −0.0846622 −0.0423311 0.999104i \(-0.513478\pi\)
−0.0423311 + 0.999104i \(0.513478\pi\)
\(348\) 5.61048 0.300753
\(349\) 33.0608i 1.76970i −0.465872 0.884852i \(-0.654259\pi\)
0.465872 0.884852i \(-0.345741\pi\)
\(350\) 7.76039 0.414810
\(351\) −28.8764 + 14.3803i −1.54131 + 0.767564i
\(352\) −3.31781 −0.176840
\(353\) 4.70845i 0.250605i 0.992119 + 0.125303i \(0.0399902\pi\)
−0.992119 + 0.125303i \(0.960010\pi\)
\(354\) 7.50251 0.398754
\(355\) 3.56829 0.189385
\(356\) 0.853778i 0.0452502i
\(357\) 13.9668i 0.739202i
\(358\) 15.9546i 0.843226i
\(359\) 27.2147i 1.43634i 0.695868 + 0.718169i \(0.255020\pi\)
−0.695868 + 0.718169i \(0.744980\pi\)
\(360\) 10.9982 0.579659
\(361\) −6.70090 −0.352679
\(362\) 35.6715i 1.87485i
\(363\) 11.1928 0.587467
\(364\) 0.404837 + 0.812933i 0.0212192 + 0.0426093i
\(365\) −10.2644 −0.537266
\(366\) 8.96379i 0.468545i
\(367\) 4.82539 0.251883 0.125942 0.992038i \(-0.459805\pi\)
0.125942 + 0.992038i \(0.459805\pi\)
\(368\) 4.47444 0.233246
\(369\) 71.1568i 3.70428i
\(370\) 6.06660i 0.315388i
\(371\) 1.93235i 0.100323i
\(372\) 0.655040i 0.0339623i
\(373\) 17.5308 0.907710 0.453855 0.891076i \(-0.350048\pi\)
0.453855 + 0.891076i \(0.350048\pi\)
\(374\) −16.2309 −0.839280
\(375\) 19.7637i 1.02059i
\(376\) −2.25219 −0.116148
\(377\) 27.6437 13.7664i 1.42372 0.709008i
\(378\) 15.3599 0.790030
\(379\) 33.9284i 1.74279i 0.490586 + 0.871393i \(0.336783\pi\)
−0.490586 + 0.871393i \(0.663217\pi\)
\(380\) −0.767265 −0.0393599
\(381\) 43.3049 2.21858
\(382\) 4.92889i 0.252184i
\(383\) 6.07830i 0.310587i −0.987868 0.155293i \(-0.950368\pi\)
0.987868 0.155293i \(-0.0496323\pi\)
\(384\) 38.3872i 1.95894i
\(385\) 2.15170i 0.109661i
\(386\) −14.3959 −0.732732
\(387\) −21.7810 −1.10719
\(388\) 2.26680i 0.115080i
\(389\) 15.9014 0.806232 0.403116 0.915149i \(-0.367927\pi\)
0.403116 + 0.915149i \(0.367927\pi\)
\(390\) −9.97956 + 4.96978i −0.505335 + 0.251654i
\(391\) 4.12104 0.208410
\(392\) 15.0491i 0.760094i
\(393\) −18.0239 −0.909185
\(394\) −39.5387 −1.99193
\(395\) 0.604772i 0.0304294i
\(396\) 3.52543i 0.177159i
\(397\) 26.8597i 1.34805i −0.738709 0.674024i \(-0.764564\pi\)
0.738709 0.674024i \(-0.235436\pi\)
\(398\) 9.83430i 0.492949i
\(399\) 17.5149 0.876841
\(400\) −19.8412 −0.992062
\(401\) 29.4467i 1.47050i −0.677797 0.735249i \(-0.737065\pi\)
0.677797 0.735249i \(-0.262935\pi\)
\(402\) −37.1682 −1.85378
\(403\) −1.60727 3.22749i −0.0800640 0.160773i
\(404\) 0.340791 0.0169550
\(405\) 6.13882i 0.305040i
\(406\) −14.7042 −0.729759
\(407\) −15.8526 −0.785783
\(408\) 32.1537i 1.59184i
\(409\) 38.4627i 1.90186i −0.309408 0.950930i \(-0.600131\pi\)
0.309408 0.950930i \(-0.399869\pi\)
\(410\) 12.2646i 0.605707i
\(411\) 50.6690i 2.49932i
\(412\) −4.04068 −0.199070
\(413\) −1.93685 −0.0953062
\(414\) 9.08719i 0.446611i
\(415\) −7.52757 −0.369514
\(416\) −1.97831 3.97256i −0.0969949 0.194771i
\(417\) −0.113619 −0.00556396
\(418\) 20.3541i 0.995554i
\(419\) 6.73204 0.328882 0.164441 0.986387i \(-0.447418\pi\)
0.164441 + 0.986387i \(0.447418\pi\)
\(420\) 0.522883 0.0255141
\(421\) 0.815884i 0.0397637i −0.999802 0.0198819i \(-0.993671\pi\)
0.999802 0.0198819i \(-0.00632901\pi\)
\(422\) 27.0686i 1.31768i
\(423\) 5.07981i 0.246989i
\(424\) 4.44856i 0.216041i
\(425\) −18.2741 −0.886425
\(426\) −23.0032 −1.11451
\(427\) 2.31410i 0.111987i
\(428\) −3.38175 −0.163463
\(429\) −12.9865 26.0775i −0.626993 1.25903i
\(430\) −3.75418 −0.181043
\(431\) 35.7637i 1.72268i 0.508032 + 0.861338i \(0.330373\pi\)
−0.508032 + 0.861338i \(0.669627\pi\)
\(432\) −39.2712 −1.88944
\(433\) −25.8780 −1.24362 −0.621808 0.783170i \(-0.713601\pi\)
−0.621808 + 0.783170i \(0.713601\pi\)
\(434\) 1.71676i 0.0824073i
\(435\) 17.7806i 0.852515i
\(436\) 2.42078i 0.115935i
\(437\) 5.16794i 0.247216i
\(438\) 66.1706 3.16175
\(439\) −24.4490 −1.16689 −0.583444 0.812153i \(-0.698295\pi\)
−0.583444 + 0.812153i \(0.698295\pi\)
\(440\) 4.95354i 0.236151i
\(441\) 33.9432 1.61634
\(442\) −9.67802 19.4340i −0.460336 0.924379i
\(443\) 15.4138 0.732330 0.366165 0.930550i \(-0.380671\pi\)
0.366165 + 0.930550i \(0.380671\pi\)
\(444\) 3.85232i 0.182823i
\(445\) 2.70577 0.128266
\(446\) −5.81741 −0.275462
\(447\) 49.7814i 2.35458i
\(448\) 8.00513i 0.378207i
\(449\) 1.20092i 0.0566750i 0.999598 + 0.0283375i \(0.00902131\pi\)
−0.999598 + 0.0283375i \(0.990979\pi\)
\(450\) 40.2957i 1.89956i
\(451\) 32.0486 1.50911
\(452\) −0.401369 −0.0188788
\(453\) 11.7168i 0.550504i
\(454\) −25.2021 −1.18279
\(455\) 2.57633 1.28300i 0.120780 0.0601479i
\(456\) −40.3219 −1.88824
\(457\) 4.20576i 0.196737i 0.995150 + 0.0983686i \(0.0313624\pi\)
−0.995150 + 0.0983686i \(0.968638\pi\)
\(458\) −17.1742 −0.802498
\(459\) −36.1695 −1.68825
\(460\) 0.154282i 0.00719342i
\(461\) 14.1239i 0.657814i 0.944362 + 0.328907i \(0.106680\pi\)
−0.944362 + 0.328907i \(0.893320\pi\)
\(462\) 13.8711i 0.645344i
\(463\) 21.9558i 1.02037i 0.860064 + 0.510186i \(0.170423\pi\)
−0.860064 + 0.510186i \(0.829577\pi\)
\(464\) 37.5948 1.74530
\(465\) −2.07594 −0.0962693
\(466\) 0.161830i 0.00749663i
\(467\) −0.918022 −0.0424810 −0.0212405 0.999774i \(-0.506762\pi\)
−0.0212405 + 0.999774i \(0.506762\pi\)
\(468\) 4.22115 2.10211i 0.195123 0.0971701i
\(469\) 9.59535 0.443072
\(470\) 0.875559i 0.0403865i
\(471\) 13.9054 0.640726
\(472\) 4.45892 0.205238
\(473\) 9.81002i 0.451065i
\(474\) 3.89871i 0.179074i
\(475\) 22.9164i 1.05148i
\(476\) 1.01825i 0.0466714i
\(477\) 10.0337 0.459412
\(478\) 23.5968 1.07929
\(479\) 4.85495i 0.221828i 0.993830 + 0.110914i \(0.0353778\pi\)
−0.993830 + 0.110914i \(0.964622\pi\)
\(480\) −2.55517 −0.116627
\(481\) −9.45243 18.9810i −0.430994 0.865458i
\(482\) −6.61826 −0.301454
\(483\) 3.52190i 0.160252i
\(484\) −0.816007 −0.0370912
\(485\) −7.18390 −0.326204
\(486\) 0.404684i 0.0183568i
\(487\) 39.7612i 1.80175i 0.434075 + 0.900877i \(0.357075\pi\)
−0.434075 + 0.900877i \(0.642925\pi\)
\(488\) 5.32739i 0.241160i
\(489\) 42.3284i 1.91416i
\(490\) 5.85047 0.264297
\(491\) 6.08825 0.274759 0.137379 0.990519i \(-0.456132\pi\)
0.137379 + 0.990519i \(0.456132\pi\)
\(492\) 7.78809i 0.351114i
\(493\) 34.6255 1.55945
\(494\) 24.3709 12.1366i 1.09650 0.546051i
\(495\) −11.1727 −0.502176
\(496\) 4.38931i 0.197086i
\(497\) 5.93852 0.266379
\(498\) 48.5271 2.17455
\(499\) 26.0135i 1.16453i 0.813001 + 0.582263i \(0.197832\pi\)
−0.813001 + 0.582263i \(0.802168\pi\)
\(500\) 1.44087i 0.0644376i
\(501\) 31.5217i 1.40829i
\(502\) 12.2862i 0.548360i
\(503\) −26.6423 −1.18792 −0.593962 0.804493i \(-0.702437\pi\)
−0.593962 + 0.804493i \(0.702437\pi\)
\(504\) 18.3039 0.815318
\(505\) 1.08003i 0.0480605i
\(506\) −4.09281 −0.181948
\(507\) 23.4803 31.0985i 1.04279 1.38113i
\(508\) −3.15714 −0.140075
\(509\) 33.0607i 1.46539i −0.680558 0.732694i \(-0.738262\pi\)
0.680558 0.732694i \(-0.261738\pi\)
\(510\) −12.5000 −0.553511
\(511\) −17.0826 −0.755691
\(512\) 17.8910i 0.790679i
\(513\) 45.3579i 2.00260i
\(514\) 12.3522i 0.544834i
\(515\) 12.8056i 0.564283i
\(516\) 2.38392 0.104946
\(517\) 2.28791 0.100622
\(518\) 10.0964i 0.443608i
\(519\) 61.4883 2.69904
\(520\) −5.93109 + 2.95365i −0.260095 + 0.129526i
\(521\) 25.8957 1.13451 0.567255 0.823543i \(-0.308006\pi\)
0.567255 + 0.823543i \(0.308006\pi\)
\(522\) 76.3516i 3.34182i
\(523\) −25.9541 −1.13489 −0.567447 0.823410i \(-0.692069\pi\)
−0.567447 + 0.823410i \(0.692069\pi\)
\(524\) 1.31403 0.0574037
\(525\) 15.6173i 0.681595i
\(526\) 29.4039i 1.28207i
\(527\) 4.04263i 0.176100i
\(528\) 35.4648i 1.54341i
\(529\) −21.9608 −0.954819
\(530\) 1.72942 0.0751211
\(531\) 10.0571i 0.436440i
\(532\) −1.27692 −0.0553616
\(533\) 19.1096 + 38.3732i 0.827731 + 1.66213i
\(534\) −17.4430 −0.754832
\(535\) 10.7174i 0.463352i
\(536\) −22.0899 −0.954139
\(537\) −32.1077 −1.38555
\(538\) 43.0254i 1.85496i
\(539\) 15.2878i 0.658493i
\(540\) 1.35410i 0.0582711i
\(541\) 28.6632i 1.23233i −0.787618 0.616164i \(-0.788686\pi\)
0.787618 0.616164i \(-0.211314\pi\)
\(542\) 1.47919 0.0635366
\(543\) −71.7868 −3.08067
\(544\) 4.97588i 0.213339i
\(545\) −7.67189 −0.328628
\(546\) −16.6085 + 8.27096i −0.710778 + 0.353964i
\(547\) 12.0729 0.516198 0.258099 0.966119i \(-0.416904\pi\)
0.258099 + 0.966119i \(0.416904\pi\)
\(548\) 3.69402i 0.157801i
\(549\) 12.0159 0.512827
\(550\) 18.1489 0.773874
\(551\) 43.4216i 1.84982i
\(552\) 8.10793i 0.345096i
\(553\) 1.00649i 0.0428004i
\(554\) 2.97520i 0.126404i
\(555\) −12.2087 −0.518229
\(556\) 0.00828341 0.000351295
\(557\) 2.10575i 0.0892234i −0.999004 0.0446117i \(-0.985795\pi\)
0.999004 0.0446117i \(-0.0142051\pi\)
\(558\) 8.91428 0.377372
\(559\) 11.7460 5.84943i 0.496801 0.247405i
\(560\) 3.50374 0.148060
\(561\) 32.6637i 1.37906i
\(562\) −13.7351 −0.579381
\(563\) 22.0349 0.928662 0.464331 0.885662i \(-0.346295\pi\)
0.464331 + 0.885662i \(0.346295\pi\)
\(564\) 0.555983i 0.0234111i
\(565\) 1.27201i 0.0535139i
\(566\) 9.93199i 0.417473i
\(567\) 10.2165i 0.429054i
\(568\) −13.6714 −0.573638
\(569\) 36.0563 1.51156 0.755780 0.654826i \(-0.227258\pi\)
0.755780 + 0.654826i \(0.227258\pi\)
\(570\) 15.6755i 0.656574i
\(571\) 34.7416 1.45389 0.726945 0.686695i \(-0.240939\pi\)
0.726945 + 0.686695i \(0.240939\pi\)
\(572\) 0.946778 + 1.90118i 0.0395868 + 0.0794923i
\(573\) −9.91909 −0.414376
\(574\) 20.4114i 0.851957i
\(575\) −4.60804 −0.192168
\(576\) −41.5666 −1.73194
\(577\) 11.2505i 0.468364i 0.972193 + 0.234182i \(0.0752411\pi\)
−0.972193 + 0.234182i \(0.924759\pi\)
\(578\) 0.978807i 0.0407130i
\(579\) 28.9709i 1.20399i
\(580\) 1.29629i 0.0538257i
\(581\) −12.5278 −0.519740
\(582\) 46.3116 1.91968
\(583\) 4.51912i 0.187163i
\(584\) 39.3267 1.62735
\(585\) −6.66196 13.3776i −0.275438 0.553094i
\(586\) 30.7440 1.27002
\(587\) 16.1947i 0.668426i −0.942498 0.334213i \(-0.891529\pi\)
0.942498 0.334213i \(-0.108471\pi\)
\(588\) −3.71507 −0.153207
\(589\) 5.06961 0.208889
\(590\) 1.73344i 0.0713648i
\(591\) 79.5692i 3.27304i
\(592\) 25.8137i 1.06094i
\(593\) 23.3449i 0.958660i 0.877635 + 0.479330i \(0.159120\pi\)
−0.877635 + 0.479330i \(0.840880\pi\)
\(594\) 35.9217 1.47389
\(595\) 3.22701 0.132295
\(596\) 3.62931i 0.148662i
\(597\) −19.7909 −0.809989
\(598\) −2.44043 4.90050i −0.0997964 0.200396i
\(599\) −40.5953 −1.65868 −0.829340 0.558744i \(-0.811284\pi\)
−0.829340 + 0.558744i \(0.811284\pi\)
\(600\) 35.9534i 1.46779i
\(601\) −39.5067 −1.61151 −0.805755 0.592249i \(-0.798240\pi\)
−0.805755 + 0.592249i \(0.798240\pi\)
\(602\) −6.24791 −0.254646
\(603\) 49.8237i 2.02898i
\(604\) 0.854214i 0.0347575i
\(605\) 2.58607i 0.105139i
\(606\) 6.96247i 0.282831i
\(607\) 1.07768 0.0437419 0.0218709 0.999761i \(-0.493038\pi\)
0.0218709 + 0.999761i \(0.493038\pi\)
\(608\) 6.23993 0.253063
\(609\) 29.5914i 1.19910i
\(610\) 2.07107 0.0838553
\(611\) 1.36422 + 2.73942i 0.0551903 + 0.110825i
\(612\) 5.28725 0.213724
\(613\) 19.5448i 0.789406i 0.918809 + 0.394703i \(0.129152\pi\)
−0.918809 + 0.394703i \(0.870848\pi\)
\(614\) 4.54988 0.183618
\(615\) 24.6818 0.995267
\(616\) 8.24394i 0.332158i
\(617\) 25.7573i 1.03695i 0.855093 + 0.518474i \(0.173500\pi\)
−0.855093 + 0.518474i \(0.826500\pi\)
\(618\) 82.5525i 3.32075i
\(619\) 23.1573i 0.930770i 0.885108 + 0.465385i \(0.154084\pi\)
−0.885108 + 0.465385i \(0.845916\pi\)
\(620\) 0.151346 0.00607821
\(621\) −9.12057 −0.365996
\(622\) 34.1393i 1.36886i
\(623\) 4.50309 0.180412
\(624\) 42.4635 21.1466i 1.69990 0.846542i
\(625\) 18.0354 0.721417
\(626\) 15.4259i 0.616543i
\(627\) 40.9615 1.63584
\(628\) −1.01377 −0.0404538
\(629\) 23.7749i 0.947966i
\(630\) 7.11579i 0.283500i
\(631\) 42.2030i 1.68008i −0.542528 0.840038i \(-0.682533\pi\)
0.542528 0.840038i \(-0.317467\pi\)
\(632\) 2.31709i 0.0921691i
\(633\) −54.4740 −2.16515
\(634\) −13.4761 −0.535203
\(635\) 10.0055i 0.397058i
\(636\) −1.09819 −0.0435459
\(637\) −18.3048 + 9.11568i −0.725261 + 0.361176i
\(638\) −34.3883 −1.36145
\(639\) 30.8357i 1.21984i
\(640\) −8.86932 −0.350591
\(641\) 35.9647 1.42052 0.710260 0.703939i \(-0.248577\pi\)
0.710260 + 0.703939i \(0.248577\pi\)
\(642\) 69.0904i 2.72678i
\(643\) 11.9104i 0.469701i 0.972032 + 0.234850i \(0.0754600\pi\)
−0.972032 + 0.234850i \(0.924540\pi\)
\(644\) 0.256764i 0.0101179i
\(645\) 7.55507i 0.297481i
\(646\) 30.5261 1.20103
\(647\) 3.70864 0.145802 0.0729009 0.997339i \(-0.476774\pi\)
0.0729009 + 0.997339i \(0.476774\pi\)
\(648\) 23.5200i 0.923952i
\(649\) −4.52965 −0.177804
\(650\) 10.8217 + 21.7305i 0.424462 + 0.852341i
\(651\) −3.45488 −0.135408
\(652\) 3.08595i 0.120855i
\(653\) −13.2111 −0.516991 −0.258496 0.966012i \(-0.583227\pi\)
−0.258496 + 0.966012i \(0.583227\pi\)
\(654\) 49.4575 1.93394
\(655\) 4.16439i 0.162716i
\(656\) 52.1866i 2.03754i
\(657\) 88.7014i 3.46057i
\(658\) 1.45715i 0.0568056i
\(659\) −37.0706 −1.44407 −0.722033 0.691858i \(-0.756792\pi\)
−0.722033 + 0.691858i \(0.756792\pi\)
\(660\) 1.22285 0.0475993
\(661\) 1.86574i 0.0725687i −0.999342 0.0362844i \(-0.988448\pi\)
0.999342 0.0362844i \(-0.0115522\pi\)
\(662\) −47.8830 −1.86103
\(663\) 39.1097 19.4764i 1.51889 0.756401i
\(664\) 28.8408 1.11924
\(665\) 4.04679i 0.156928i
\(666\) 52.4252 2.03144
\(667\) 8.73123 0.338074
\(668\) 2.29809i 0.0889156i
\(669\) 11.7072i 0.452626i
\(670\) 8.58765i 0.331770i
\(671\) 5.41190i 0.208924i
\(672\) −4.25245 −0.164042
\(673\) 38.8121 1.49610 0.748048 0.663645i \(-0.230991\pi\)
0.748048 + 0.663645i \(0.230991\pi\)
\(674\) 47.2686i 1.82072i
\(675\) 40.4438 1.55668
\(676\) −1.71183 + 2.26724i −0.0658395 + 0.0872014i
\(677\) −18.1456 −0.697394 −0.348697 0.937236i \(-0.613376\pi\)
−0.348697 + 0.937236i \(0.613376\pi\)
\(678\) 8.20012i 0.314924i
\(679\) −11.9558 −0.458822
\(680\) −7.42906 −0.284891
\(681\) 50.7178i 1.94351i
\(682\) 4.01494i 0.153740i
\(683\) 23.3612i 0.893891i 0.894561 + 0.446946i \(0.147488\pi\)
−0.894561 + 0.446946i \(0.852512\pi\)
\(684\) 6.63041i 0.253520i
\(685\) 11.7070 0.447301
\(686\) 21.7540 0.830572
\(687\) 34.5620i 1.31862i
\(688\) 15.9742 0.609012
\(689\) −5.41094 + 2.69462i −0.206140 + 0.102657i
\(690\) −3.15203 −0.119996
\(691\) 9.52166i 0.362221i −0.983463 0.181111i \(-0.942031\pi\)
0.983463 0.181111i \(-0.0579692\pi\)
\(692\) −4.48280 −0.170410
\(693\) −18.5942 −0.706335
\(694\) 2.34902i 0.0891676i
\(695\) 0.0262516i 0.000995780i
\(696\) 68.1238i 2.58222i
\(697\) 48.0648i 1.82058i
\(698\) −49.2432 −1.86388
\(699\) 0.325673 0.0123181
\(700\) 1.13858i 0.0430342i
\(701\) 7.92968 0.299500 0.149750 0.988724i \(-0.452153\pi\)
0.149750 + 0.988724i \(0.452153\pi\)
\(702\) 21.4191 + 43.0106i 0.808412 + 1.62333i
\(703\) 29.8145 1.12448
\(704\) 18.7213i 0.705586i
\(705\) 1.76201 0.0663611
\(706\) 7.01310 0.263942
\(707\) 1.79743i 0.0675994i
\(708\) 1.10074i 0.0413685i
\(709\) 0.516551i 0.0193995i −0.999953 0.00969973i \(-0.996912\pi\)
0.999953 0.00969973i \(-0.00308757\pi\)
\(710\) 5.31487i 0.199463i
\(711\) 5.22620 0.195998
\(712\) −10.3668 −0.388511
\(713\) 1.01940i 0.0381767i
\(714\) −20.8032 −0.778540
\(715\) 6.02517 3.00051i 0.225329 0.112213i
\(716\) 2.34081 0.0874800
\(717\) 47.4871i 1.77344i
\(718\) 40.5356 1.51278
\(719\) −25.0988 −0.936026 −0.468013 0.883722i \(-0.655030\pi\)
−0.468013 + 0.883722i \(0.655030\pi\)
\(720\) 18.1932i 0.678019i
\(721\) 21.3118i 0.793692i
\(722\) 9.98081i 0.371447i
\(723\) 13.3188i 0.495333i
\(724\) 5.23361 0.194506
\(725\) −38.7173 −1.43792
\(726\) 16.6713i 0.618730i
\(727\) 24.2348 0.898819 0.449409 0.893326i \(-0.351634\pi\)
0.449409 + 0.893326i \(0.351634\pi\)
\(728\) −9.87082 + 4.91562i −0.365837 + 0.182185i
\(729\) −27.4062 −1.01504
\(730\) 15.2886i 0.565857i
\(731\) 14.7126 0.544163
\(732\) −1.31514 −0.0486089
\(733\) 47.9992i 1.77289i −0.462834 0.886445i \(-0.653167\pi\)
0.462834 0.886445i \(-0.346833\pi\)
\(734\) 7.18729i 0.265288i
\(735\) 11.7737i 0.434280i
\(736\) 1.25473i 0.0462498i
\(737\) 22.4403 0.826599
\(738\) −105.986 −3.90141
\(739\) 13.4514i 0.494817i 0.968911 + 0.247409i \(0.0795790\pi\)
−0.968911 + 0.247409i \(0.920421\pi\)
\(740\) 0.890072 0.0327197
\(741\) 24.4241 + 49.0449i 0.897243 + 1.80171i
\(742\) 2.87818 0.105661
\(743\) 17.9897i 0.659977i −0.943985 0.329989i \(-0.892955\pi\)
0.943985 0.329989i \(-0.107045\pi\)
\(744\) 7.95365 0.291595
\(745\) −11.5019 −0.421397
\(746\) 26.1116i 0.956015i
\(747\) 65.0504i 2.38007i
\(748\) 2.38134i 0.0870706i
\(749\) 17.8364i 0.651728i
\(750\) 29.4375 1.07490
\(751\) 5.17026 0.188666 0.0943328 0.995541i \(-0.469928\pi\)
0.0943328 + 0.995541i \(0.469928\pi\)
\(752\) 3.72554i 0.135857i
\(753\) 24.7252 0.901038
\(754\) −20.5047 41.1746i −0.746739 1.49949i
\(755\) −2.70716 −0.0985235
\(756\) 2.25356i 0.0819612i
\(757\) 16.2563 0.590845 0.295422 0.955367i \(-0.404540\pi\)
0.295422 + 0.955367i \(0.404540\pi\)
\(758\) 50.5355 1.83553
\(759\) 8.23654i 0.298967i
\(760\) 9.31631i 0.337938i
\(761\) 26.5204i 0.961365i 0.876895 + 0.480682i \(0.159611\pi\)
−0.876895 + 0.480682i \(0.840389\pi\)
\(762\) 64.5015i 2.33664i
\(763\) −12.7680 −0.462231
\(764\) 0.723150 0.0261627
\(765\) 16.7562i 0.605823i
\(766\) −9.05347 −0.327115
\(767\) −2.70090 5.42354i −0.0975237 0.195833i
\(768\) 15.5401 0.560755
\(769\) 0.983871i 0.0354793i 0.999843 + 0.0177397i \(0.00564700\pi\)
−0.999843 + 0.0177397i \(0.994353\pi\)
\(770\) −3.20491 −0.115497
\(771\) −24.8581 −0.895244
\(772\) 2.11212i 0.0760168i
\(773\) 27.6879i 0.995866i 0.867215 + 0.497933i \(0.165907\pi\)
−0.867215 + 0.497933i \(0.834093\pi\)
\(774\) 32.4422i 1.16611i
\(775\) 4.52036i 0.162376i
\(776\) 27.5241 0.988056
\(777\) −20.3183 −0.728915
\(778\) 23.6847i 0.849137i
\(779\) −60.2750 −2.15958
\(780\) 0.729149 + 1.46417i 0.0261077 + 0.0524257i
\(781\) 13.8882 0.496960
\(782\) 6.13818i 0.219501i