Properties

Label 403.2.c.b.311.12
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 311.12
Character \(\chi\) = 403.311
Dual form 403.2.c.b.311.21

$q$-expansion

\(f(q)\) \(=\) \(q-1.01245i q^{2} -1.05136 q^{3} +0.974950 q^{4} -3.24438i q^{5} +1.06445i q^{6} -1.79572i q^{7} -3.01198i q^{8} -1.89463 q^{9} +O(q^{10})\) \(q-1.01245i q^{2} -1.05136 q^{3} +0.974950 q^{4} -3.24438i q^{5} +1.06445i q^{6} -1.79572i q^{7} -3.01198i q^{8} -1.89463 q^{9} -3.28477 q^{10} +6.09683i q^{11} -1.02503 q^{12} +(-1.47046 - 3.29207i) q^{13} -1.81807 q^{14} +3.41103i q^{15} -1.09957 q^{16} +4.79598 q^{17} +1.91821i q^{18} -1.84875i q^{19} -3.16311i q^{20} +1.88796i q^{21} +6.17272 q^{22} -7.94273 q^{23} +3.16669i q^{24} -5.52601 q^{25} +(-3.33305 + 1.48876i) q^{26} +5.14604 q^{27} -1.75074i q^{28} -2.23287 q^{29} +3.45349 q^{30} +1.00000i q^{31} -4.91070i q^{32} -6.40999i q^{33} -4.85568i q^{34} -5.82601 q^{35} -1.84717 q^{36} -8.64644i q^{37} -1.87176 q^{38} +(1.54599 + 3.46117i) q^{39} -9.77201 q^{40} -0.0498113i q^{41} +1.91146 q^{42} +4.76573 q^{43} +5.94410i q^{44} +6.14691i q^{45} +8.04159i q^{46} +4.00376i q^{47} +1.15605 q^{48} +3.77538 q^{49} +5.59480i q^{50} -5.04233 q^{51} +(-1.43362 - 3.20961i) q^{52} +0.588394 q^{53} -5.21010i q^{54} +19.7804 q^{55} -5.40868 q^{56} +1.94371i q^{57} +2.26066i q^{58} -3.49014i q^{59} +3.32558i q^{60} +12.1590 q^{61} +1.01245 q^{62} +3.40223i q^{63} -7.17097 q^{64} +(-10.6807 + 4.77073i) q^{65} -6.48978 q^{66} +1.72095i q^{67} +4.67585 q^{68} +8.35070 q^{69} +5.89852i q^{70} -10.3643i q^{71} +5.70659i q^{72} -2.28292i q^{73} -8.75406 q^{74} +5.80985 q^{75} -1.80244i q^{76} +10.9482 q^{77} +(3.50425 - 1.56523i) q^{78} +16.1812 q^{79} +3.56743i q^{80} +0.273525 q^{81} -0.0504314 q^{82} +10.2561i q^{83} +1.84067i q^{84} -15.5600i q^{85} -4.82505i q^{86} +2.34756 q^{87} +18.3635 q^{88} +7.99914i q^{89} +6.22342 q^{90} +(-5.91165 + 2.64053i) q^{91} -7.74376 q^{92} -1.05136i q^{93} +4.05360 q^{94} -5.99805 q^{95} +5.16294i q^{96} -10.1745i q^{97} -3.82238i q^{98} -11.5512i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + O(q^{10}) \) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + 4q^{10} - 16q^{12} + 10q^{13} - 16q^{14} + 28q^{16} - 8q^{17} - 16q^{22} - 8q^{23} + 4q^{25} + 18q^{26} + 20q^{27} - 16q^{29} + 40q^{30} - 4q^{35} - 44q^{36} + 12q^{38} + 4q^{39} + 28q^{40} + 28q^{42} - 32q^{43} - 64q^{49} - 64q^{52} - 12q^{53} + 44q^{55} + 8q^{56} + 16q^{61} + 8q^{62} - 76q^{64} - 66q^{65} - 68q^{66} + 64q^{68} + 20q^{69} + 16q^{74} - 32q^{77} - 20q^{78} + 64q^{79} - 16q^{81} + 12q^{82} - 72q^{87} + 80q^{88} + 68q^{90} + 22q^{91} + 28q^{92} + 88q^{94} + 4q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.01245i 0.715908i −0.933739 0.357954i \(-0.883474\pi\)
0.933739 0.357954i \(-0.116526\pi\)
\(3\) −1.05136 −0.607006 −0.303503 0.952831i \(-0.598156\pi\)
−0.303503 + 0.952831i \(0.598156\pi\)
\(4\) 0.974950 0.487475
\(5\) 3.24438i 1.45093i −0.688258 0.725466i \(-0.741624\pi\)
0.688258 0.725466i \(-0.258376\pi\)
\(6\) 1.06445i 0.434561i
\(7\) 1.79572i 0.678719i −0.940657 0.339360i \(-0.889790\pi\)
0.940657 0.339360i \(-0.110210\pi\)
\(8\) 3.01198i 1.06490i
\(9\) −1.89463 −0.631544
\(10\) −3.28477 −1.03873
\(11\) 6.09683i 1.83826i 0.393951 + 0.919131i \(0.371108\pi\)
−0.393951 + 0.919131i \(0.628892\pi\)
\(12\) −1.02503 −0.295900
\(13\) −1.47046 3.29207i −0.407832 0.913057i
\(14\) −1.81807 −0.485901
\(15\) 3.41103i 0.880724i
\(16\) −1.09957 −0.274893
\(17\) 4.79598 1.16320 0.581598 0.813476i \(-0.302428\pi\)
0.581598 + 0.813476i \(0.302428\pi\)
\(18\) 1.91821i 0.452128i
\(19\) 1.84875i 0.424133i −0.977255 0.212066i \(-0.931981\pi\)
0.977255 0.212066i \(-0.0680193\pi\)
\(20\) 3.16311i 0.707293i
\(21\) 1.88796i 0.411986i
\(22\) 6.17272 1.31603
\(23\) −7.94273 −1.65617 −0.828086 0.560600i \(-0.810570\pi\)
−0.828086 + 0.560600i \(0.810570\pi\)
\(24\) 3.16669i 0.646398i
\(25\) −5.52601 −1.10520
\(26\) −3.33305 + 1.48876i −0.653665 + 0.291970i
\(27\) 5.14604 0.990357
\(28\) 1.75074i 0.330859i
\(29\) −2.23287 −0.414633 −0.207317 0.978274i \(-0.566473\pi\)
−0.207317 + 0.978274i \(0.566473\pi\)
\(30\) 3.45349 0.630518
\(31\) 1.00000i 0.179605i
\(32\) 4.91070i 0.868098i
\(33\) 6.40999i 1.11584i
\(34\) 4.85568i 0.832742i
\(35\) −5.82601 −0.984775
\(36\) −1.84717 −0.307862
\(37\) 8.64644i 1.42147i −0.703462 0.710733i \(-0.748364\pi\)
0.703462 0.710733i \(-0.251636\pi\)
\(38\) −1.87176 −0.303640
\(39\) 1.54599 + 3.46117i 0.247556 + 0.554231i
\(40\) −9.77201 −1.54509
\(41\) 0.0498113i 0.00777923i −0.999992 0.00388961i \(-0.998762\pi\)
0.999992 0.00388961i \(-0.00123811\pi\)
\(42\) 1.91146 0.294945
\(43\) 4.76573 0.726767 0.363384 0.931640i \(-0.381621\pi\)
0.363384 + 0.931640i \(0.381621\pi\)
\(44\) 5.94410i 0.896107i
\(45\) 6.14691i 0.916327i
\(46\) 8.04159i 1.18567i
\(47\) 4.00376i 0.584008i 0.956417 + 0.292004i \(0.0943221\pi\)
−0.956417 + 0.292004i \(0.905678\pi\)
\(48\) 1.15605 0.166862
\(49\) 3.77538 0.539341
\(50\) 5.59480i 0.791224i
\(51\) −5.04233 −0.706067
\(52\) −1.43362 3.20961i −0.198808 0.445093i
\(53\) 0.588394 0.0808221 0.0404111 0.999183i \(-0.487133\pi\)
0.0404111 + 0.999183i \(0.487133\pi\)
\(54\) 5.21010i 0.709005i
\(55\) 19.7804 2.66719
\(56\) −5.40868 −0.722765
\(57\) 1.94371i 0.257451i
\(58\) 2.26066i 0.296840i
\(59\) 3.49014i 0.454377i −0.973851 0.227189i \(-0.927047\pi\)
0.973851 0.227189i \(-0.0729534\pi\)
\(60\) 3.32558i 0.429331i
\(61\) 12.1590 1.55680 0.778400 0.627769i \(-0.216032\pi\)
0.778400 + 0.627769i \(0.216032\pi\)
\(62\) 1.01245 0.128581
\(63\) 3.40223i 0.428641i
\(64\) −7.17097 −0.896371
\(65\) −10.6807 + 4.77073i −1.32478 + 0.591736i
\(66\) −6.48978 −0.798836
\(67\) 1.72095i 0.210247i 0.994459 + 0.105124i \(0.0335238\pi\)
−0.994459 + 0.105124i \(0.966476\pi\)
\(68\) 4.67585 0.567029
\(69\) 8.35070 1.00531
\(70\) 5.89852i 0.705009i
\(71\) 10.3643i 1.23002i −0.788519 0.615011i \(-0.789152\pi\)
0.788519 0.615011i \(-0.210848\pi\)
\(72\) 5.70659i 0.672529i
\(73\) 2.28292i 0.267196i −0.991036 0.133598i \(-0.957347\pi\)
0.991036 0.133598i \(-0.0426531\pi\)
\(74\) −8.75406 −1.01764
\(75\) 5.80985 0.670864
\(76\) 1.80244i 0.206754i
\(77\) 10.9482 1.24766
\(78\) 3.50425 1.56523i 0.396779 0.177228i
\(79\) 16.1812 1.82053 0.910265 0.414027i \(-0.135878\pi\)
0.910265 + 0.414027i \(0.135878\pi\)
\(80\) 3.56743i 0.398851i
\(81\) 0.273525 0.0303917
\(82\) −0.0504314 −0.00556921
\(83\) 10.2561i 1.12575i 0.826541 + 0.562877i \(0.190306\pi\)
−0.826541 + 0.562877i \(0.809694\pi\)
\(84\) 1.84067i 0.200833i
\(85\) 15.5600i 1.68772i
\(86\) 4.82505i 0.520299i
\(87\) 2.34756 0.251685
\(88\) 18.3635 1.95756
\(89\) 7.99914i 0.847907i 0.905684 + 0.423953i \(0.139358\pi\)
−0.905684 + 0.423953i \(0.860642\pi\)
\(90\) 6.22342 0.656006
\(91\) −5.91165 + 2.64053i −0.619709 + 0.276803i
\(92\) −7.74376 −0.807343
\(93\) 1.05136i 0.109021i
\(94\) 4.05360 0.418097
\(95\) −5.99805 −0.615387
\(96\) 5.16294i 0.526940i
\(97\) 10.1745i 1.03307i −0.856268 0.516533i \(-0.827223\pi\)
0.856268 0.516533i \(-0.172777\pi\)
\(98\) 3.82238i 0.386118i
\(99\) 11.5512i 1.16094i
\(100\) −5.38759 −0.538759
\(101\) −10.3806 −1.03291 −0.516454 0.856315i \(-0.672748\pi\)
−0.516454 + 0.856315i \(0.672748\pi\)
\(102\) 5.10509i 0.505479i
\(103\) 7.56287 0.745191 0.372596 0.927994i \(-0.378468\pi\)
0.372596 + 0.927994i \(0.378468\pi\)
\(104\) −9.91566 + 4.42899i −0.972311 + 0.434299i
\(105\) 6.12526 0.597764
\(106\) 0.595718i 0.0578612i
\(107\) 9.88355 0.955478 0.477739 0.878502i \(-0.341456\pi\)
0.477739 + 0.878502i \(0.341456\pi\)
\(108\) 5.01714 0.482774
\(109\) 5.97227i 0.572040i 0.958224 + 0.286020i \(0.0923323\pi\)
−0.958224 + 0.286020i \(0.907668\pi\)
\(110\) 20.0266i 1.90947i
\(111\) 9.09056i 0.862838i
\(112\) 1.97452i 0.186575i
\(113\) 5.83695 0.549094 0.274547 0.961574i \(-0.411472\pi\)
0.274547 + 0.961574i \(0.411472\pi\)
\(114\) 1.96791 0.184311
\(115\) 25.7692i 2.40299i
\(116\) −2.17694 −0.202123
\(117\) 2.78598 + 6.23727i 0.257564 + 0.576636i
\(118\) −3.53358 −0.325292
\(119\) 8.61225i 0.789484i
\(120\) 10.2740 0.937879
\(121\) −26.1713 −2.37921
\(122\) 12.3103i 1.11453i
\(123\) 0.0523699i 0.00472204i
\(124\) 0.974950i 0.0875531i
\(125\) 1.70658i 0.152641i
\(126\) 3.44458 0.306868
\(127\) 1.76344 0.156480 0.0782399 0.996935i \(-0.475070\pi\)
0.0782399 + 0.996935i \(0.475070\pi\)
\(128\) 2.56118i 0.226378i
\(129\) −5.01052 −0.441152
\(130\) 4.83011 + 10.8137i 0.423629 + 0.948423i
\(131\) 15.7996 1.38042 0.690209 0.723610i \(-0.257518\pi\)
0.690209 + 0.723610i \(0.257518\pi\)
\(132\) 6.24942i 0.543942i
\(133\) −3.31984 −0.287867
\(134\) 1.74237 0.150518
\(135\) 16.6957i 1.43694i
\(136\) 14.4454i 1.23868i
\(137\) 14.0263i 1.19835i 0.800619 + 0.599174i \(0.204504\pi\)
−0.800619 + 0.599174i \(0.795496\pi\)
\(138\) 8.45465i 0.719707i
\(139\) −8.87486 −0.752756 −0.376378 0.926466i \(-0.622831\pi\)
−0.376378 + 0.926466i \(0.622831\pi\)
\(140\) −5.68007 −0.480053
\(141\) 4.20941i 0.354497i
\(142\) −10.4934 −0.880583
\(143\) 20.0712 8.96513i 1.67844 0.749702i
\(144\) 2.08328 0.173607
\(145\) 7.24428i 0.601605i
\(146\) −2.31134 −0.191288
\(147\) −3.96931 −0.327383
\(148\) 8.42985i 0.692929i
\(149\) 0.896489i 0.0734432i −0.999326 0.0367216i \(-0.988309\pi\)
0.999326 0.0367216i \(-0.0116915\pi\)
\(150\) 5.88217i 0.480277i
\(151\) 0.221338i 0.0180122i −0.999959 0.00900611i \(-0.997133\pi\)
0.999959 0.00900611i \(-0.00286677\pi\)
\(152\) −5.56840 −0.451657
\(153\) −9.08662 −0.734610
\(154\) 11.0845i 0.893213i
\(155\) 3.24438 0.260595
\(156\) 1.50726 + 3.37447i 0.120678 + 0.270174i
\(157\) 8.52165 0.680102 0.340051 0.940407i \(-0.389556\pi\)
0.340051 + 0.940407i \(0.389556\pi\)
\(158\) 16.3826i 1.30333i
\(159\) −0.618617 −0.0490595
\(160\) −15.9322 −1.25955
\(161\) 14.2629i 1.12408i
\(162\) 0.276930i 0.0217576i
\(163\) 0.474988i 0.0372039i 0.999827 + 0.0186019i \(0.00592153\pi\)
−0.999827 + 0.0186019i \(0.994078\pi\)
\(164\) 0.0485636i 0.00379218i
\(165\) −20.7965 −1.61900
\(166\) 10.3838 0.805937
\(167\) 5.99300i 0.463752i 0.972745 + 0.231876i \(0.0744864\pi\)
−0.972745 + 0.231876i \(0.925514\pi\)
\(168\) 5.68650 0.438723
\(169\) −8.67550 + 9.68172i −0.667346 + 0.744748i
\(170\) −15.7537 −1.20825
\(171\) 3.50270i 0.267858i
\(172\) 4.64635 0.354281
\(173\) 0.0189761 0.00144272 0.000721362 1.00000i \(-0.499770\pi\)
0.000721362 1.00000i \(0.499770\pi\)
\(174\) 2.37678i 0.180183i
\(175\) 9.92318i 0.750122i
\(176\) 6.70390i 0.505325i
\(177\) 3.66941i 0.275810i
\(178\) 8.09870 0.607024
\(179\) 5.66716 0.423583 0.211792 0.977315i \(-0.432070\pi\)
0.211792 + 0.977315i \(0.432070\pi\)
\(180\) 5.99293i 0.446687i
\(181\) −15.5416 −1.15520 −0.577598 0.816322i \(-0.696010\pi\)
−0.577598 + 0.816322i \(0.696010\pi\)
\(182\) 2.67340 + 5.98523i 0.198166 + 0.443655i
\(183\) −12.7835 −0.944986
\(184\) 23.9233i 1.76365i
\(185\) −28.0523 −2.06245
\(186\) −1.06445 −0.0780494
\(187\) 29.2403i 2.13826i
\(188\) 3.90347i 0.284690i
\(189\) 9.24086i 0.672174i
\(190\) 6.07271i 0.440561i
\(191\) −7.38826 −0.534596 −0.267298 0.963614i \(-0.586131\pi\)
−0.267298 + 0.963614i \(0.586131\pi\)
\(192\) 7.53931 0.544103
\(193\) 4.22194i 0.303902i 0.988388 + 0.151951i \(0.0485556\pi\)
−0.988388 + 0.151951i \(0.951444\pi\)
\(194\) −10.3012 −0.739580
\(195\) 11.2294 5.01578i 0.804151 0.359187i
\(196\) 3.68081 0.262915
\(197\) 7.13939i 0.508660i −0.967117 0.254330i \(-0.918145\pi\)
0.967117 0.254330i \(-0.0818550\pi\)
\(198\) −11.6950 −0.831129
\(199\) −17.5333 −1.24290 −0.621452 0.783453i \(-0.713457\pi\)
−0.621452 + 0.783453i \(0.713457\pi\)
\(200\) 16.6442i 1.17693i
\(201\) 1.80934i 0.127621i
\(202\) 10.5098i 0.739467i
\(203\) 4.00961i 0.281420i
\(204\) −4.91602 −0.344190
\(205\) −0.161607 −0.0112871
\(206\) 7.65701i 0.533489i
\(207\) 15.0485 1.04595
\(208\) 1.61687 + 3.61987i 0.112110 + 0.250993i
\(209\) 11.2715 0.779667
\(210\) 6.20150i 0.427944i
\(211\) 12.5199 0.861905 0.430952 0.902375i \(-0.358178\pi\)
0.430952 + 0.902375i \(0.358178\pi\)
\(212\) 0.573655 0.0393988
\(213\) 10.8967i 0.746630i
\(214\) 10.0066i 0.684035i
\(215\) 15.4619i 1.05449i
\(216\) 15.4998i 1.05463i
\(217\) 1.79572 0.121902
\(218\) 6.04661 0.409528
\(219\) 2.40019i 0.162190i
\(220\) 19.2849 1.30019
\(221\) −7.05230 15.7887i −0.474389 1.06206i
\(222\) 9.20371 0.617713
\(223\) 13.4782i 0.902565i −0.892381 0.451282i \(-0.850967\pi\)
0.892381 0.451282i \(-0.149033\pi\)
\(224\) −8.81826 −0.589195
\(225\) 10.4698 0.697984
\(226\) 5.90961i 0.393101i
\(227\) 21.7487i 1.44351i 0.692149 + 0.721755i \(0.256664\pi\)
−0.692149 + 0.721755i \(0.743336\pi\)
\(228\) 1.89502i 0.125501i
\(229\) 4.82129i 0.318600i −0.987230 0.159300i \(-0.949076\pi\)
0.987230 0.159300i \(-0.0509237\pi\)
\(230\) 26.0900 1.72032
\(231\) −11.5106 −0.757339
\(232\) 6.72536i 0.441541i
\(233\) −29.1203 −1.90774 −0.953868 0.300227i \(-0.902938\pi\)
−0.953868 + 0.300227i \(0.902938\pi\)
\(234\) 6.31491 2.82066i 0.412818 0.184392i
\(235\) 12.9897 0.847356
\(236\) 3.40271i 0.221498i
\(237\) −17.0124 −1.10507
\(238\) −8.71945 −0.565198
\(239\) 27.1826i 1.75829i −0.476552 0.879147i \(-0.658113\pi\)
0.476552 0.879147i \(-0.341887\pi\)
\(240\) 3.75067i 0.242105i
\(241\) 21.6242i 1.39294i −0.717588 0.696468i \(-0.754754\pi\)
0.717588 0.696468i \(-0.245246\pi\)
\(242\) 26.4971i 1.70330i
\(243\) −15.7257 −1.00880
\(244\) 11.8544 0.758901
\(245\) 12.2488i 0.782546i
\(246\) 0.0530218 0.00338054
\(247\) −6.08623 + 2.71851i −0.387257 + 0.172975i
\(248\) 3.01198 0.191261
\(249\) 10.7829i 0.683339i
\(250\) 1.72782 0.109277
\(251\) 23.7774 1.50082 0.750410 0.660973i \(-0.229856\pi\)
0.750410 + 0.660973i \(0.229856\pi\)
\(252\) 3.31701i 0.208952i
\(253\) 48.4254i 3.04448i
\(254\) 1.78539i 0.112025i
\(255\) 16.3592i 1.02446i
\(256\) −16.9350 −1.05844
\(257\) 3.84862 0.240070 0.120035 0.992770i \(-0.461699\pi\)
0.120035 + 0.992770i \(0.461699\pi\)
\(258\) 5.07289i 0.315824i
\(259\) −15.5266 −0.964776
\(260\) −10.4132 + 4.65122i −0.645799 + 0.288457i
\(261\) 4.23046 0.261859
\(262\) 15.9963i 0.988253i
\(263\) −27.4393 −1.69198 −0.845991 0.533198i \(-0.820990\pi\)
−0.845991 + 0.533198i \(0.820990\pi\)
\(264\) −19.3068 −1.18825
\(265\) 1.90897i 0.117267i
\(266\) 3.36117i 0.206086i
\(267\) 8.41001i 0.514684i
\(268\) 1.67784i 0.102490i
\(269\) 4.99431 0.304508 0.152254 0.988341i \(-0.451347\pi\)
0.152254 + 0.988341i \(0.451347\pi\)
\(270\) −16.9035 −1.02872
\(271\) 27.8192i 1.68990i 0.534848 + 0.844948i \(0.320369\pi\)
−0.534848 + 0.844948i \(0.679631\pi\)
\(272\) −5.27353 −0.319754
\(273\) 6.21530 2.77617i 0.376167 0.168021i
\(274\) 14.2009 0.857908
\(275\) 33.6911i 2.03165i
\(276\) 8.14152 0.490062
\(277\) 19.5970 1.17747 0.588734 0.808327i \(-0.299627\pi\)
0.588734 + 0.808327i \(0.299627\pi\)
\(278\) 8.98533i 0.538904i
\(279\) 1.89463i 0.113429i
\(280\) 17.5478i 1.04868i
\(281\) 9.44497i 0.563440i 0.959497 + 0.281720i \(0.0909049\pi\)
−0.959497 + 0.281720i \(0.909095\pi\)
\(282\) −4.26181 −0.253787
\(283\) 11.1656 0.663726 0.331863 0.943328i \(-0.392323\pi\)
0.331863 + 0.943328i \(0.392323\pi\)
\(284\) 10.1047i 0.599605i
\(285\) 6.30614 0.373544
\(286\) −9.07673 20.3210i −0.536718 1.20161i
\(287\) −0.0894473 −0.00527991
\(288\) 9.30397i 0.548242i
\(289\) 6.00145 0.353027
\(290\) 7.33445 0.430694
\(291\) 10.6971i 0.627077i
\(292\) 2.22574i 0.130251i
\(293\) 19.3914i 1.13286i 0.824110 + 0.566429i \(0.191676\pi\)
−0.824110 + 0.566429i \(0.808324\pi\)
\(294\) 4.01871i 0.234376i
\(295\) −11.3233 −0.659270
\(296\) −26.0429 −1.51371
\(297\) 31.3745i 1.82054i
\(298\) −0.907647 −0.0525786
\(299\) 11.6795 + 26.1480i 0.675440 + 1.51218i
\(300\) 5.66432 0.327030
\(301\) 8.55793i 0.493271i
\(302\) −0.224093 −0.0128951
\(303\) 10.9138 0.626981
\(304\) 2.03283i 0.116591i
\(305\) 39.4484i 2.25881i
\(306\) 9.19973i 0.525913i
\(307\) 2.97843i 0.169988i −0.996381 0.0849939i \(-0.972913\pi\)
0.996381 0.0849939i \(-0.0270871\pi\)
\(308\) 10.6740 0.608205
\(309\) −7.95133 −0.452336
\(310\) 3.28477i 0.186562i
\(311\) −15.2149 −0.862756 −0.431378 0.902171i \(-0.641972\pi\)
−0.431378 + 0.902171i \(0.641972\pi\)
\(312\) 10.4250 4.65649i 0.590198 0.263622i
\(313\) −6.83949 −0.386591 −0.193295 0.981141i \(-0.561918\pi\)
−0.193295 + 0.981141i \(0.561918\pi\)
\(314\) 8.62773i 0.486891i
\(315\) 11.0381 0.621929
\(316\) 15.7759 0.887463
\(317\) 17.3492i 0.974431i −0.873282 0.487215i \(-0.838013\pi\)
0.873282 0.487215i \(-0.161987\pi\)
\(318\) 0.626317i 0.0351221i
\(319\) 13.6134i 0.762205i
\(320\) 23.2654i 1.30057i
\(321\) −10.3912 −0.579981
\(322\) 14.4405 0.804735
\(323\) 8.86658i 0.493350i
\(324\) 0.266673 0.0148152
\(325\) 8.12577 + 18.1920i 0.450737 + 1.00911i
\(326\) 0.480900 0.0266346
\(327\) 6.27904i 0.347231i
\(328\) −0.150031 −0.00828407
\(329\) 7.18964 0.396378
\(330\) 21.0553i 1.15906i
\(331\) 5.82160i 0.319984i −0.987118 0.159992i \(-0.948853\pi\)
0.987118 0.159992i \(-0.0511469\pi\)
\(332\) 9.99920i 0.548777i
\(333\) 16.3818i 0.897718i
\(334\) 6.06760 0.332004
\(335\) 5.58341 0.305054
\(336\) 2.07595i 0.113252i
\(337\) −30.6724 −1.67083 −0.835415 0.549620i \(-0.814773\pi\)
−0.835415 + 0.549620i \(0.814773\pi\)
\(338\) 9.80223 + 8.78349i 0.533171 + 0.477759i
\(339\) −6.13677 −0.333303
\(340\) 15.1702i 0.822721i
\(341\) −6.09683 −0.330162
\(342\) 3.54630 0.191762
\(343\) 19.3496i 1.04478i
\(344\) 14.3543i 0.773932i
\(345\) 27.0929i 1.45863i
\(346\) 0.0192123i 0.00103286i
\(347\) −24.5555 −1.31821 −0.659103 0.752053i \(-0.729064\pi\)
−0.659103 + 0.752053i \(0.729064\pi\)
\(348\) 2.28875 0.122690
\(349\) 27.8390i 1.49019i 0.666959 + 0.745094i \(0.267596\pi\)
−0.666959 + 0.745094i \(0.732404\pi\)
\(350\) 10.0467 0.537018
\(351\) −7.56705 16.9412i −0.403899 0.904252i
\(352\) 29.9397 1.59579
\(353\) 7.01905i 0.373586i 0.982399 + 0.186793i \(0.0598094\pi\)
−0.982399 + 0.186793i \(0.940191\pi\)
\(354\) 3.71508 0.197454
\(355\) −33.6259 −1.78468
\(356\) 7.79876i 0.413333i
\(357\) 9.05462i 0.479221i
\(358\) 5.73770i 0.303247i
\(359\) 15.7950i 0.833628i 0.908992 + 0.416814i \(0.136853\pi\)
−0.908992 + 0.416814i \(0.863147\pi\)
\(360\) 18.5144 0.975793
\(361\) 15.5821 0.820112
\(362\) 15.7350i 0.827014i
\(363\) 27.5156 1.44419
\(364\) −5.76356 + 2.57439i −0.302093 + 0.134935i
\(365\) −7.40667 −0.387683
\(366\) 12.9427i 0.676523i
\(367\) 10.2880 0.537029 0.268515 0.963276i \(-0.413467\pi\)
0.268515 + 0.963276i \(0.413467\pi\)
\(368\) 8.73359 0.455270
\(369\) 0.0943742i 0.00491292i
\(370\) 28.4015i 1.47652i
\(371\) 1.05659i 0.0548555i
\(372\) 1.02503i 0.0531453i
\(373\) 33.4821 1.73364 0.866820 0.498622i \(-0.166160\pi\)
0.866820 + 0.498622i \(0.166160\pi\)
\(374\) 29.6042 1.53080
\(375\) 1.79424i 0.0926541i
\(376\) 12.0592 0.621908
\(377\) 3.28334 + 7.35077i 0.169101 + 0.378584i
\(378\) −9.35589 −0.481215
\(379\) 31.2200i 1.60367i 0.597548 + 0.801833i \(0.296142\pi\)
−0.597548 + 0.801833i \(0.703858\pi\)
\(380\) −5.84781 −0.299986
\(381\) −1.85402 −0.0949841
\(382\) 7.48023i 0.382722i
\(383\) 8.55469i 0.437124i 0.975823 + 0.218562i \(0.0701366\pi\)
−0.975823 + 0.218562i \(0.929863\pi\)
\(384\) 2.69273i 0.137413i
\(385\) 35.5202i 1.81027i
\(386\) 4.27450 0.217566
\(387\) −9.02931 −0.458985
\(388\) 9.91964i 0.503594i
\(389\) 38.2805 1.94090 0.970450 0.241303i \(-0.0775749\pi\)
0.970450 + 0.241303i \(0.0775749\pi\)
\(390\) −5.07821 11.3691i −0.257145 0.575699i
\(391\) −38.0932 −1.92645
\(392\) 11.3714i 0.574342i
\(393\) −16.6112 −0.837922
\(394\) −7.22825 −0.364154
\(395\) 52.4980i 2.64146i
\(396\) 11.2619i 0.565931i
\(397\) 18.1469i 0.910767i 0.890295 + 0.455383i \(0.150498\pi\)
−0.890295 + 0.455383i \(0.849502\pi\)
\(398\) 17.7515i 0.889805i
\(399\) 3.49037 0.174737
\(400\) 6.07624 0.303812
\(401\) 23.7338i 1.18521i 0.805493 + 0.592605i \(0.201900\pi\)
−0.805493 + 0.592605i \(0.798100\pi\)
\(402\) −1.83187 −0.0913651
\(403\) 3.29207 1.47046i 0.163990 0.0732488i
\(404\) −10.1206 −0.503517
\(405\) 0.887419i 0.0440962i
\(406\) 4.05952 0.201471
\(407\) 52.7158 2.61303
\(408\) 15.1874i 0.751888i
\(409\) 29.4641i 1.45691i 0.685096 + 0.728453i \(0.259760\pi\)
−0.685096 + 0.728453i \(0.740240\pi\)
\(410\) 0.163619i 0.00808055i
\(411\) 14.7468i 0.727404i
\(412\) 7.37342 0.363262
\(413\) −6.26731 −0.308394
\(414\) 15.2359i 0.748801i
\(415\) 33.2747 1.63339
\(416\) −16.1664 + 7.22099i −0.792623 + 0.354038i
\(417\) 9.33071 0.456927
\(418\) 11.4118i 0.558170i
\(419\) 24.8096 1.21203 0.606014 0.795454i \(-0.292768\pi\)
0.606014 + 0.795454i \(0.292768\pi\)
\(420\) 5.97182 0.291395
\(421\) 0.191902i 0.00935275i −0.999989 0.00467637i \(-0.998511\pi\)
0.999989 0.00467637i \(-0.00148854\pi\)
\(422\) 12.6757i 0.617045i
\(423\) 7.58565i 0.368827i
\(424\) 1.77223i 0.0860672i
\(425\) −26.5027 −1.28557
\(426\) 11.0323 0.534519
\(427\) 21.8342i 1.05663i
\(428\) 9.63597 0.465772
\(429\) −21.1022 + 9.42563i −1.01882 + 0.455074i
\(430\) −15.6543 −0.754918
\(431\) 15.0633i 0.725574i 0.931872 + 0.362787i \(0.118175\pi\)
−0.931872 + 0.362787i \(0.881825\pi\)
\(432\) −5.65844 −0.272242
\(433\) 12.8565 0.617844 0.308922 0.951087i \(-0.400032\pi\)
0.308922 + 0.951087i \(0.400032\pi\)
\(434\) 1.81807i 0.0872703i
\(435\) 7.61638i 0.365178i
\(436\) 5.82267i 0.278855i
\(437\) 14.6841i 0.702437i
\(438\) 2.43006 0.116113
\(439\) −0.561664 −0.0268068 −0.0134034 0.999910i \(-0.504267\pi\)
−0.0134034 + 0.999910i \(0.504267\pi\)
\(440\) 59.5783i 2.84028i
\(441\) −7.15296 −0.340617
\(442\) −15.9853 + 7.14008i −0.760341 + 0.339619i
\(443\) −10.0558 −0.477765 −0.238883 0.971048i \(-0.576781\pi\)
−0.238883 + 0.971048i \(0.576781\pi\)
\(444\) 8.86284i 0.420612i
\(445\) 25.9522 1.23025
\(446\) −13.6459 −0.646154
\(447\) 0.942537i 0.0445805i
\(448\) 12.8771i 0.608384i
\(449\) 15.4936i 0.731187i 0.930775 + 0.365594i \(0.119134\pi\)
−0.930775 + 0.365594i \(0.880866\pi\)
\(450\) 10.6001i 0.499692i
\(451\) 0.303691 0.0143003
\(452\) 5.69074 0.267670
\(453\) 0.232707i 0.0109335i
\(454\) 22.0194 1.03342
\(455\) 8.56690 + 19.1796i 0.401623 + 0.899156i
\(456\) 5.85442 0.274159
\(457\) 22.5213i 1.05350i −0.850020 0.526751i \(-0.823410\pi\)
0.850020 0.526751i \(-0.176590\pi\)
\(458\) −4.88131 −0.228088
\(459\) 24.6803 1.15198
\(460\) 25.1237i 1.17140i
\(461\) 11.9714i 0.557563i −0.960354 0.278782i \(-0.910069\pi\)
0.960354 0.278782i \(-0.0899306\pi\)
\(462\) 11.6538i 0.542186i
\(463\) 42.4947i 1.97489i 0.157950 + 0.987447i \(0.449511\pi\)
−0.157950 + 0.987447i \(0.550489\pi\)
\(464\) 2.45520 0.113980
\(465\) −3.41103 −0.158183
\(466\) 29.4828i 1.36576i
\(467\) 35.2701 1.63211 0.816053 0.577977i \(-0.196158\pi\)
0.816053 + 0.577977i \(0.196158\pi\)
\(468\) 2.71619 + 6.08103i 0.125556 + 0.281096i
\(469\) 3.09034 0.142699
\(470\) 13.1514i 0.606629i
\(471\) −8.95937 −0.412826
\(472\) −10.5122 −0.483864
\(473\) 29.0558i 1.33599i
\(474\) 17.2241i 0.791130i
\(475\) 10.2162i 0.468752i
\(476\) 8.39652i 0.384854i
\(477\) −1.11479 −0.0510427
\(478\) −27.5209 −1.25878
\(479\) 17.0249i 0.777888i −0.921261 0.388944i \(-0.872840\pi\)
0.921261 0.388944i \(-0.127160\pi\)
\(480\) 16.7506 0.764555
\(481\) −28.4647 + 12.7142i −1.29788 + 0.579719i
\(482\) −21.8933 −0.997214
\(483\) 14.9955i 0.682321i
\(484\) −25.5157 −1.15981
\(485\) −33.0100 −1.49891
\(486\) 15.9215i 0.722212i
\(487\) 3.52549i 0.159755i −0.996805 0.0798776i \(-0.974547\pi\)
0.996805 0.0798776i \(-0.0254529\pi\)
\(488\) 36.6226i 1.65783i
\(489\) 0.499385i 0.0225830i
\(490\) −12.4012 −0.560231
\(491\) −29.9606 −1.35210 −0.676051 0.736855i \(-0.736310\pi\)
−0.676051 + 0.736855i \(0.736310\pi\)
\(492\) 0.0510581i 0.00230187i
\(493\) −10.7088 −0.482300
\(494\) 2.75235 + 6.16198i 0.123834 + 0.277241i
\(495\) −37.4766 −1.68445
\(496\) 1.09957i 0.0493722i
\(497\) −18.6115 −0.834839
\(498\) −10.9171 −0.489208
\(499\) 9.74284i 0.436149i 0.975932 + 0.218075i \(0.0699776\pi\)
−0.975932 + 0.218075i \(0.930022\pi\)
\(500\) 1.66383i 0.0744088i
\(501\) 6.30083i 0.281500i
\(502\) 24.0734i 1.07445i
\(503\) 15.7364 0.701651 0.350825 0.936441i \(-0.385901\pi\)
0.350825 + 0.936441i \(0.385901\pi\)
\(504\) 10.2475 0.456458
\(505\) 33.6786i 1.49868i
\(506\) −49.0282 −2.17957
\(507\) 9.12112 10.1790i 0.405083 0.452066i
\(508\) 1.71926 0.0762800
\(509\) 30.5793i 1.35541i 0.735336 + 0.677703i \(0.237024\pi\)
−0.735336 + 0.677703i \(0.762976\pi\)
\(510\) 16.5629 0.733416
\(511\) −4.09950 −0.181351
\(512\) 12.0234i 0.531366i
\(513\) 9.51376i 0.420043i
\(514\) 3.89652i 0.171868i
\(515\) 24.5368i 1.08122i
\(516\) −4.88501 −0.215051
\(517\) −24.4102 −1.07356
\(518\) 15.7199i 0.690691i
\(519\) −0.0199508 −0.000875742
\(520\) 14.3693 + 32.1702i 0.630137 + 1.41076i
\(521\) −36.3668 −1.59326 −0.796628 0.604469i \(-0.793385\pi\)
−0.796628 + 0.604469i \(0.793385\pi\)
\(522\) 4.28312i 0.187467i
\(523\) −12.1385 −0.530780 −0.265390 0.964141i \(-0.585501\pi\)
−0.265390 + 0.964141i \(0.585501\pi\)
\(524\) 15.4038 0.672920
\(525\) 10.4329i 0.455328i
\(526\) 27.7809i 1.21130i
\(527\) 4.79598i 0.208916i
\(528\) 7.04824i 0.306735i
\(529\) 40.0869 1.74291
\(530\) −1.93274 −0.0839527
\(531\) 6.61252i 0.286959i
\(532\) −3.23668 −0.140328
\(533\) −0.163983 + 0.0732455i −0.00710288 + 0.00317262i
\(534\) −8.51469 −0.368467
\(535\) 32.0660i 1.38633i
\(536\) 5.18346 0.223891
\(537\) −5.95825 −0.257118
\(538\) 5.05648i 0.218000i
\(539\) 23.0179i 0.991450i
\(540\) 16.2775i 0.700472i
\(541\) 36.2301i 1.55765i −0.627240 0.778826i \(-0.715816\pi\)
0.627240 0.778826i \(-0.284184\pi\)
\(542\) 28.1655 1.20981
\(543\) 16.3399 0.701210
\(544\) 23.5516i 1.00977i
\(545\) 19.3763 0.829991
\(546\) −2.81072 6.29266i −0.120288 0.269301i
\(547\) −4.85710 −0.207675 −0.103837 0.994594i \(-0.533112\pi\)
−0.103837 + 0.994594i \(0.533112\pi\)
\(548\) 13.6750i 0.584165i
\(549\) −23.0368 −0.983187
\(550\) −34.1105 −1.45448
\(551\) 4.12802i 0.175860i
\(552\) 25.1522i 1.07055i
\(553\) 29.0570i 1.23563i
\(554\) 19.8409i 0.842959i
\(555\) 29.4932 1.25192
\(556\) −8.65254 −0.366950
\(557\) 41.4847i 1.75776i −0.477040 0.878882i \(-0.658290\pi\)
0.477040 0.878882i \(-0.341710\pi\)
\(558\) −1.91821 −0.0812045
\(559\) −7.00781 15.6891i −0.296399 0.663580i
\(560\) 6.40611 0.270708
\(561\) 30.7422i 1.29794i
\(562\) 9.56254 0.403371
\(563\) −5.12904 −0.216163 −0.108082 0.994142i \(-0.534471\pi\)
−0.108082 + 0.994142i \(0.534471\pi\)
\(564\) 4.10397i 0.172808i
\(565\) 18.9373i 0.796698i
\(566\) 11.3046i 0.475167i
\(567\) 0.491175i 0.0206274i
\(568\) −31.2172 −1.30984
\(569\) −20.7637 −0.870458 −0.435229 0.900320i \(-0.643333\pi\)
−0.435229 + 0.900320i \(0.643333\pi\)
\(570\) 6.38464i 0.267423i
\(571\) −29.8037 −1.24725 −0.623623 0.781726i \(-0.714340\pi\)
−0.623623 + 0.781726i \(0.714340\pi\)
\(572\) 19.5684 8.74056i 0.818197 0.365461i
\(573\) 7.76776 0.324503
\(574\) 0.0905607i 0.00377993i
\(575\) 43.8916 1.83041
\(576\) 13.5863 0.566098
\(577\) 31.5439i 1.31319i −0.754243 0.656596i \(-0.771996\pi\)
0.754243 0.656596i \(-0.228004\pi\)
\(578\) 6.07615i 0.252735i
\(579\) 4.43880i 0.184470i
\(580\) 7.06281i 0.293267i
\(581\) 18.4171 0.764071
\(582\) 10.8303 0.448929
\(583\) 3.58734i 0.148572i
\(584\) −6.87612 −0.284536
\(585\) 20.2361 9.03878i 0.836659 0.373707i
\(586\) 19.6328 0.811023
\(587\) 32.0469i 1.32272i 0.750071 + 0.661358i \(0.230019\pi\)
−0.750071 + 0.661358i \(0.769981\pi\)
\(588\) −3.86988 −0.159591
\(589\) 1.84875 0.0761765
\(590\) 11.4643i 0.471977i
\(591\) 7.50610i 0.308760i
\(592\) 9.50737i 0.390751i
\(593\) 30.8314i 1.26609i −0.774114 0.633046i \(-0.781804\pi\)
0.774114 0.633046i \(-0.218196\pi\)
\(594\) 31.7651 1.30334
\(595\) −27.9414 −1.14549
\(596\) 0.874032i 0.0358017i
\(597\) 18.4339 0.754449
\(598\) 26.4735 11.8248i 1.08258 0.483553i
\(599\) −29.6376 −1.21096 −0.605479 0.795861i \(-0.707018\pi\)
−0.605479 + 0.795861i \(0.707018\pi\)
\(600\) 17.4992i 0.714401i
\(601\) 29.7503 1.21354 0.606769 0.794878i \(-0.292465\pi\)
0.606769 + 0.794878i \(0.292465\pi\)
\(602\) −8.66445 −0.353137
\(603\) 3.26056i 0.132780i
\(604\) 0.215793i 0.00878051i
\(605\) 84.9097i 3.45207i
\(606\) 11.0496i 0.448861i
\(607\) −34.1070 −1.38436 −0.692181 0.721724i \(-0.743350\pi\)
−0.692181 + 0.721724i \(0.743350\pi\)
\(608\) −9.07867 −0.368189
\(609\) 4.21556i 0.170823i
\(610\) −39.9394 −1.61710
\(611\) 13.1807 5.88736i 0.533233 0.238177i
\(612\) −8.85900 −0.358104
\(613\) 23.4986i 0.949100i 0.880228 + 0.474550i \(0.157389\pi\)
−0.880228 + 0.474550i \(0.842611\pi\)
\(614\) −3.01550 −0.121696
\(615\) 0.169908 0.00685135
\(616\) 32.9758i 1.32863i
\(617\) 13.5012i 0.543539i 0.962362 + 0.271770i \(0.0876089\pi\)
−0.962362 + 0.271770i \(0.912391\pi\)
\(618\) 8.05031i 0.323831i
\(619\) 15.3528i 0.617080i 0.951211 + 0.308540i \(0.0998404\pi\)
−0.951211 + 0.308540i \(0.900160\pi\)
\(620\) 3.16311 0.127034
\(621\) −40.8736 −1.64020
\(622\) 15.4043i 0.617654i
\(623\) 14.3642 0.575490
\(624\) −1.69992 3.80580i −0.0680515 0.152354i
\(625\) −22.0933 −0.883730
\(626\) 6.92463i 0.276764i
\(627\) −11.8505 −0.473263
\(628\) 8.30819 0.331533
\(629\) 41.4682i 1.65344i
\(630\) 11.1755i 0.445244i
\(631\) 12.9193i 0.514310i 0.966370 + 0.257155i \(0.0827850\pi\)
−0.966370 + 0.257155i \(0.917215\pi\)
\(632\) 48.7375i 1.93867i
\(633\) −13.1630 −0.523181
\(634\) −17.5652 −0.697603
\(635\) 5.72126i 0.227041i
\(636\) −0.603121 −0.0239153
\(637\) −5.55155 12.4288i −0.219960 0.492449i
\(638\) −13.7829 −0.545669
\(639\) 19.6366i 0.776813i
\(640\) −8.30943 −0.328459
\(641\) 37.2265 1.47036 0.735180 0.677872i \(-0.237098\pi\)
0.735180 + 0.677872i \(0.237098\pi\)
\(642\) 10.5206i 0.415213i
\(643\) 24.3497i 0.960259i −0.877198 0.480130i \(-0.840590\pi\)
0.877198 0.480130i \(-0.159410\pi\)
\(644\) 13.9056i 0.547959i
\(645\) 16.2560i 0.640081i
\(646\) −8.97695 −0.353193
\(647\) 24.9639 0.981433 0.490717 0.871319i \(-0.336735\pi\)
0.490717 + 0.871319i \(0.336735\pi\)
\(648\) 0.823852i 0.0323640i
\(649\) 21.2788 0.835264
\(650\) 18.4185 8.22692i 0.722432 0.322686i
\(651\) −1.88796 −0.0739949
\(652\) 0.463089i 0.0181360i
\(653\) −2.17194 −0.0849947 −0.0424974 0.999097i \(-0.513531\pi\)
−0.0424974 + 0.999097i \(0.513531\pi\)
\(654\) −6.35719 −0.248586
\(655\) 51.2600i 2.00289i
\(656\) 0.0547711i 0.00213845i
\(657\) 4.32530i 0.168746i
\(658\) 7.27913i 0.283770i
\(659\) 3.53137 0.137563 0.0687814 0.997632i \(-0.478089\pi\)
0.0687814 + 0.997632i \(0.478089\pi\)
\(660\) −20.2755 −0.789223
\(661\) 0.781774i 0.0304075i 0.999884 + 0.0152037i \(0.00483969\pi\)
−0.999884 + 0.0152037i \(0.995160\pi\)
\(662\) −5.89407 −0.229079
\(663\) 7.41454 + 16.5997i 0.287957 + 0.644680i
\(664\) 30.8912 1.19881
\(665\) 10.7708i 0.417675i
\(666\) 16.5857 0.642684
\(667\) 17.7351 0.686705
\(668\) 5.84288i 0.226068i
\(669\) 14.1705i 0.547862i
\(670\) 5.65291i 0.218391i
\(671\) 74.1313i 2.86181i
\(672\) 9.27121 0.357645
\(673\) −39.4571 −1.52096 −0.760479 0.649362i \(-0.775036\pi\)
−0.760479 + 0.649362i \(0.775036\pi\)
\(674\) 31.0541i 1.19616i
\(675\) −28.4371 −1.09454
\(676\) −8.45818 + 9.43919i −0.325315 + 0.363046i
\(677\) 44.1582 1.69714 0.848569 0.529085i \(-0.177465\pi\)
0.848569 + 0.529085i \(0.177465\pi\)
\(678\) 6.21315i 0.238615i
\(679\) −18.2706 −0.701161
\(680\) −46.8664 −1.79724
\(681\) 22.8658i 0.876219i
\(682\) 6.17272i 0.236366i
\(683\) 49.3853i 1.88967i −0.327540 0.944837i \(-0.606219\pi\)
0.327540 0.944837i \(-0.393781\pi\)
\(684\) 3.41496i 0.130574i
\(685\) 45.5067 1.73872
\(686\) −19.5904 −0.747967
\(687\) 5.06894i 0.193392i
\(688\) −5.24026 −0.199783
\(689\) −0.865209 1.93704i −0.0329618 0.0737952i
\(690\) −27.4301 −1.04425
\(691\) 12.4149i 0.472284i −0.971719 0.236142i \(-0.924117\pi\)
0.971719 0.236142i \(-0.0758831\pi\)
\(692\) 0.0185007 0.000703292
\(693\) −20.7428 −0.787955
\(694\) 24.8611i 0.943715i
\(695\) 28.7934i 1.09220i
\(696\) 7.07081i 0.268018i
\(697\) 0.238894i 0.00904877i
\(698\) 28.1855 1.06684
\(699\) 30.6161 1.15801
\(700\) 9.67461i 0.365666i
\(701\) 27.1200 1.02431 0.512155 0.858893i \(-0.328847\pi\)
0.512155 + 0.858893i \(0.328847\pi\)
\(702\) −17.1520 + 7.66124i −0.647362 + 0.289155i
\(703\) −15.9851 −0.602890
\(704\) 43.7202i 1.64777i
\(705\) −13.6569 −0.514350
\(706\) 7.10642 0.267454
\(707\) 18.6406i 0.701054i
\(708\) 3.57749i 0.134450i
\(709\) 9.01510i 0.338569i 0.985567 + 0.169285i \(0.0541457\pi\)
−0.985567 + 0.169285i \(0.945854\pi\)
\(710\) 34.0444i 1.27767i
\(711\) −30.6574 −1.14974
\(712\) 24.0932 0.902932
\(713\) 7.94273i 0.297457i
\(714\) 9.16732 0.343078
\(715\) −29.0863 65.1187i −1.08777 2.43530i
\(716\) 5.52520 0.206486
\(717\) 28.5788i 1.06729i
\(718\) 15.9916 0.596801
\(719\) 2.03502 0.0758934 0.0379467 0.999280i \(-0.487918\pi\)
0.0379467 + 0.999280i \(0.487918\pi\)
\(720\) 6.75896i 0.251892i
\(721\) 13.5808i 0.505776i
\(722\) 15.7761i 0.587125i
\(723\) 22.7349i 0.845520i
\(724\) −15.1523 −0.563129
\(725\) 12.3389 0.458254
\(726\) 27.8581i 1.03391i
\(727\) 6.51447 0.241608 0.120804 0.992676i \(-0.461453\pi\)
0.120804 + 0.992676i \(0.461453\pi\)
\(728\) 7.95324 + 17.8058i 0.294767 + 0.659926i
\(729\) 15.7129 0.581959
\(730\) 7.49887i 0.277546i
\(731\) 22.8564 0.845373
\(732\) −12.4633 −0.460657
\(733\) 3.11568i 0.115080i 0.998343 + 0.0575402i \(0.0183257\pi\)
−0.998343 + 0.0575402i \(0.981674\pi\)
\(734\) 10.4161i 0.384464i
\(735\) 12.8779i 0.475010i
\(736\) 39.0044i 1.43772i
\(737\) −10.4923 −0.386490
\(738\) 0.0955489 0.00351720
\(739\) 39.1735i 1.44102i 0.693444 + 0.720510i \(0.256092\pi\)
−0.693444 + 0.720510i \(0.743908\pi\)
\(740\) −27.3496 −1.00539
\(741\) 6.39884 2.85815i 0.235067 0.104997i
\(742\) −1.06974 −0.0392715
\(743\) 30.6791i 1.12551i 0.826625 + 0.562753i \(0.190258\pi\)
−0.826625 + 0.562753i \(0.809742\pi\)
\(744\) −3.16669 −0.116097
\(745\) −2.90855 −0.106561
\(746\) 33.8989i 1.24113i
\(747\) 19.4315i 0.710963i
\(748\) 28.5078i 1.04235i
\(749\) 17.7481i 0.648501i
\(750\) −1.81657 −0.0663318
\(751\) −25.5019 −0.930578 −0.465289 0.885159i \(-0.654050\pi\)
−0.465289 + 0.885159i \(0.654050\pi\)
\(752\) 4.40242i 0.160540i
\(753\) −24.9988 −0.911006
\(754\) 7.44227 3.32421i 0.271031 0.121061i
\(755\) −0.718105 −0.0261345
\(756\) 9.00938i 0.327668i
\(757\) −8.04879 −0.292538 −0.146269 0.989245i \(-0.546727\pi\)
−0.146269 + 0.989245i \(0.546727\pi\)
\(758\) 31.6087 1.14808
\(759\) 50.9128i 1.84802i
\(760\) 18.0660i 0.655324i
\(761\) 52.1296i 1.88970i −0.327508 0.944848i \(-0.606209\pi\)
0.327508 0.944848i \(-0.393791\pi\)
\(762\) 1.87709i 0.0679999i
\(763\) 10.7245 0.388254
\(764\) −7.20319 −0.260602
\(765\) 29.4805i 1.06587i
\(766\) 8.66117 0.312941
\(767\) −11.4898 + 5.13210i −0.414872 + 0.185309i
\(768\) 17.8049 0.642478
\(769\) 3.62057i 0.130561i 0.997867 + 0.0652806i \(0.0207942\pi\)
−0.997867 + 0.0652806i \(0.979206\pi\)
\(770\) −35.9623 −1.29599
\(771\) −4.04630 −0.145724
\(772\) 4.11619i 0.148145i
\(773\) 32.4020i 1.16542i 0.812680 + 0.582710i \(0.198008\pi\)
−0.812680 + 0.582710i \(0.801992\pi\)
\(774\) 9.14170i 0.328592i
\(775\) 5.52601i 0.198500i
\(776\) −30.6454 −1.10011
\(777\) 16.3241 0.585624
\(778\) 38.7570i 1.38951i
\(779\) −0.0920888 −0.00329942
\(780\) 10.9481 4.89013i 0.392004 0.175095i
\(781\) 63.1896 2.26110
\(782\) 38.5673i 1.37917i