Properties

Label 403.2.c.b.311.10
Level 403
Weight 2
Character 403.311
Analytic conductor 3.218
Analytic rank 0
Dimension 32
CM No

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Newspace parameters

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

Newform invariants

Self dual: No
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(32\)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 311.10
Character \(\chi\) = 403.311
Dual form 403.2.c.b.311.23

$q$-expansion

\(f(q)\) \(=\) \(q-1.44015i q^{2} -2.79139 q^{3} -0.0740342 q^{4} +2.61757i q^{5} +4.02002i q^{6} -4.99660i q^{7} -2.77368i q^{8} +4.79185 q^{9} +O(q^{10})\) \(q-1.44015i q^{2} -2.79139 q^{3} -0.0740342 q^{4} +2.61757i q^{5} +4.02002i q^{6} -4.99660i q^{7} -2.77368i q^{8} +4.79185 q^{9} +3.76969 q^{10} -0.0546038i q^{11} +0.206658 q^{12} +(-1.72882 + 3.16404i) q^{13} -7.19586 q^{14} -7.30664i q^{15} -4.14259 q^{16} -5.08006 q^{17} -6.90098i q^{18} -1.17518i q^{19} -0.193789i q^{20} +13.9475i q^{21} -0.0786376 q^{22} -7.81207 q^{23} +7.74242i q^{24} -1.85165 q^{25} +(4.55670 + 2.48976i) q^{26} -5.00174 q^{27} +0.369920i q^{28} -7.02474 q^{29} -10.5227 q^{30} -1.00000i q^{31} +0.418588i q^{32} +0.152420i q^{33} +7.31605i q^{34} +13.0789 q^{35} -0.354761 q^{36} -6.75099i q^{37} -1.69243 q^{38} +(4.82581 - 8.83208i) q^{39} +7.26030 q^{40} +1.55918i q^{41} +20.0864 q^{42} -3.02644 q^{43} +0.00404255i q^{44} +12.5430i q^{45} +11.2506i q^{46} -0.191499i q^{47} +11.5636 q^{48} -17.9661 q^{49} +2.66666i q^{50} +14.1804 q^{51} +(0.127992 - 0.234248i) q^{52} +8.59226 q^{53} +7.20326i q^{54} +0.142929 q^{55} -13.8590 q^{56} +3.28038i q^{57} +10.1167i q^{58} +2.91407i q^{59} +0.540942i q^{60} +5.96368 q^{61} -1.44015 q^{62} -23.9430i q^{63} -7.68234 q^{64} +(-8.28210 - 4.52530i) q^{65} +0.219508 q^{66} -1.50321i q^{67} +0.376098 q^{68} +21.8065 q^{69} -18.8357i q^{70} -1.44037i q^{71} -13.2911i q^{72} -13.9550i q^{73} -9.72244 q^{74} +5.16869 q^{75} +0.0870034i q^{76} -0.272833 q^{77} +(-12.7195 - 6.94989i) q^{78} +1.10819 q^{79} -10.8435i q^{80} -0.413740 q^{81} +2.24545 q^{82} -1.74923i q^{83} -1.03259i q^{84} -13.2974i q^{85} +4.35854i q^{86} +19.6088 q^{87} -0.151453 q^{88} -2.35995i q^{89} +18.0638 q^{90} +(15.8095 + 8.63823i) q^{91} +0.578360 q^{92} +2.79139i q^{93} -0.275787 q^{94} +3.07611 q^{95} -1.16844i q^{96} +12.1357i q^{97} +25.8738i q^{98} -0.261653i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + O(q^{10}) \) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + 4q^{10} - 16q^{12} + 10q^{13} - 16q^{14} + 28q^{16} - 8q^{17} - 16q^{22} - 8q^{23} + 4q^{25} + 18q^{26} + 20q^{27} - 16q^{29} + 40q^{30} - 4q^{35} - 44q^{36} + 12q^{38} + 4q^{39} + 28q^{40} + 28q^{42} - 32q^{43} - 64q^{49} - 64q^{52} - 12q^{53} + 44q^{55} + 8q^{56} + 16q^{61} + 8q^{62} - 76q^{64} - 66q^{65} - 68q^{66} + 64q^{68} + 20q^{69} + 16q^{74} - 32q^{77} - 20q^{78} + 64q^{79} - 16q^{81} + 12q^{82} - 72q^{87} + 80q^{88} + 68q^{90} + 22q^{91} + 28q^{92} + 88q^{94} + 4q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.44015i 1.01834i −0.860666 0.509170i \(-0.829952\pi\)
0.860666 0.509170i \(-0.170048\pi\)
\(3\) −2.79139 −1.61161 −0.805804 0.592182i \(-0.798267\pi\)
−0.805804 + 0.592182i \(0.798267\pi\)
\(4\) −0.0740342 −0.0370171
\(5\) 2.61757i 1.17061i 0.810813 + 0.585306i \(0.199025\pi\)
−0.810813 + 0.585306i \(0.800975\pi\)
\(6\) 4.02002i 1.64117i
\(7\) 4.99660i 1.88854i −0.329173 0.944269i \(-0.606770\pi\)
0.329173 0.944269i \(-0.393230\pi\)
\(8\) 2.77368i 0.980644i
\(9\) 4.79185 1.59728
\(10\) 3.76969 1.19208
\(11\) 0.0546038i 0.0164637i −0.999966 0.00823183i \(-0.997380\pi\)
0.999966 0.00823183i \(-0.00262030\pi\)
\(12\) 0.206658 0.0596571
\(13\) −1.72882 + 3.16404i −0.479489 + 0.877548i
\(14\) −7.19586 −1.92318
\(15\) 7.30664i 1.88657i
\(16\) −4.14259 −1.03565
\(17\) −5.08006 −1.23209 −0.616047 0.787709i \(-0.711267\pi\)
−0.616047 + 0.787709i \(0.711267\pi\)
\(18\) 6.90098i 1.62658i
\(19\) 1.17518i 0.269604i −0.990873 0.134802i \(-0.956960\pi\)
0.990873 0.134802i \(-0.0430399\pi\)
\(20\) 0.193789i 0.0433326i
\(21\) 13.9475i 3.04359i
\(22\) −0.0786376 −0.0167656
\(23\) −7.81207 −1.62893 −0.814464 0.580213i \(-0.802969\pi\)
−0.814464 + 0.580213i \(0.802969\pi\)
\(24\) 7.74242i 1.58041i
\(25\) −1.85165 −0.370331
\(26\) 4.55670 + 2.48976i 0.893643 + 0.488283i
\(27\) −5.00174 −0.962586
\(28\) 0.369920i 0.0699082i
\(29\) −7.02474 −1.30446 −0.652231 0.758020i \(-0.726167\pi\)
−0.652231 + 0.758020i \(0.726167\pi\)
\(30\) −10.5227 −1.92117
\(31\) 1.00000i 0.179605i
\(32\) 0.418588i 0.0739966i
\(33\) 0.152420i 0.0265330i
\(34\) 7.31605i 1.25469i
\(35\) 13.0789 2.21075
\(36\) −0.354761 −0.0591268
\(37\) 6.75099i 1.10986i −0.831899 0.554928i \(-0.812746\pi\)
0.831899 0.554928i \(-0.187254\pi\)
\(38\) −1.69243 −0.274549
\(39\) 4.82581 8.83208i 0.772748 1.41426i
\(40\) 7.26030 1.14795
\(41\) 1.55918i 0.243503i 0.992561 + 0.121751i \(0.0388511\pi\)
−0.992561 + 0.121751i \(0.961149\pi\)
\(42\) 20.0864 3.09941
\(43\) −3.02644 −0.461528 −0.230764 0.973010i \(-0.574123\pi\)
−0.230764 + 0.973010i \(0.574123\pi\)
\(44\) 0.00404255i 0.000609437i
\(45\) 12.5430i 1.86980i
\(46\) 11.2506i 1.65880i
\(47\) 0.191499i 0.0279330i −0.999902 0.0139665i \(-0.995554\pi\)
0.999902 0.0139665i \(-0.00444582\pi\)
\(48\) 11.5636 1.66906
\(49\) −17.9661 −2.56658
\(50\) 2.66666i 0.377123i
\(51\) 14.1804 1.98565
\(52\) 0.127992 0.234248i 0.0177493 0.0324843i
\(53\) 8.59226 1.18024 0.590119 0.807317i \(-0.299081\pi\)
0.590119 + 0.807317i \(0.299081\pi\)
\(54\) 7.20326i 0.980240i
\(55\) 0.142929 0.0192725
\(56\) −13.8590 −1.85199
\(57\) 3.28038i 0.434497i
\(58\) 10.1167i 1.32839i
\(59\) 2.91407i 0.379379i 0.981844 + 0.189690i \(0.0607482\pi\)
−0.981844 + 0.189690i \(0.939252\pi\)
\(60\) 0.540942i 0.0698353i
\(61\) 5.96368 0.763571 0.381786 0.924251i \(-0.375309\pi\)
0.381786 + 0.924251i \(0.375309\pi\)
\(62\) −1.44015 −0.182899
\(63\) 23.9430i 3.01653i
\(64\) −7.68234 −0.960293
\(65\) −8.28210 4.52530i −1.02727 0.561295i
\(66\) 0.219508 0.0270196
\(67\) 1.50321i 0.183646i −0.995775 0.0918231i \(-0.970731\pi\)
0.995775 0.0918231i \(-0.0292694\pi\)
\(68\) 0.376098 0.0456086
\(69\) 21.8065 2.62520
\(70\) 18.8357i 2.25129i
\(71\) 1.44037i 0.170940i −0.996341 0.0854701i \(-0.972761\pi\)
0.996341 0.0854701i \(-0.0272392\pi\)
\(72\) 13.2911i 1.56637i
\(73\) 13.9550i 1.63331i −0.577124 0.816656i \(-0.695825\pi\)
0.577124 0.816656i \(-0.304175\pi\)
\(74\) −9.72244 −1.13021
\(75\) 5.16869 0.596829
\(76\) 0.0870034i 0.00997997i
\(77\) −0.272833 −0.0310922
\(78\) −12.7195 6.94989i −1.44020 0.786920i
\(79\) 1.10819 0.124681 0.0623404 0.998055i \(-0.480144\pi\)
0.0623404 + 0.998055i \(0.480144\pi\)
\(80\) 10.8435i 1.21234i
\(81\) −0.413740 −0.0459711
\(82\) 2.24545 0.247969
\(83\) 1.74923i 0.192003i −0.995381 0.0960015i \(-0.969395\pi\)
0.995381 0.0960015i \(-0.0306054\pi\)
\(84\) 1.03259i 0.112665i
\(85\) 13.2974i 1.44230i
\(86\) 4.35854i 0.469993i
\(87\) 19.6088 2.10228
\(88\) −0.151453 −0.0161450
\(89\) 2.35995i 0.250154i −0.992147 0.125077i \(-0.960082\pi\)
0.992147 0.125077i \(-0.0399179\pi\)
\(90\) 18.0638 1.90409
\(91\) 15.8095 + 8.63823i 1.65728 + 0.905533i
\(92\) 0.578360 0.0602982
\(93\) 2.79139i 0.289453i
\(94\) −0.275787 −0.0284453
\(95\) 3.07611 0.315602
\(96\) 1.16844i 0.119254i
\(97\) 12.1357i 1.23220i 0.787670 + 0.616098i \(0.211287\pi\)
−0.787670 + 0.616098i \(0.788713\pi\)
\(98\) 25.8738i 2.61365i
\(99\) 0.261653i 0.0262971i
\(100\) 0.137086 0.0137086
\(101\) 11.6128 1.15552 0.577758 0.816208i \(-0.303928\pi\)
0.577758 + 0.816208i \(0.303928\pi\)
\(102\) 20.4219i 2.02207i
\(103\) −12.7238 −1.25371 −0.626857 0.779134i \(-0.715659\pi\)
−0.626857 + 0.779134i \(0.715659\pi\)
\(104\) 8.77605 + 4.79520i 0.860563 + 0.470208i
\(105\) −36.5084 −3.56286
\(106\) 12.3741i 1.20188i
\(107\) −2.95463 −0.285635 −0.142817 0.989749i \(-0.545616\pi\)
−0.142817 + 0.989749i \(0.545616\pi\)
\(108\) 0.370300 0.0356321
\(109\) 19.9084i 1.90688i −0.301587 0.953439i \(-0.597516\pi\)
0.301587 0.953439i \(-0.402484\pi\)
\(110\) 0.205839i 0.0196260i
\(111\) 18.8446i 1.78865i
\(112\) 20.6989i 1.95586i
\(113\) 0.926163 0.0871261 0.0435630 0.999051i \(-0.486129\pi\)
0.0435630 + 0.999051i \(0.486129\pi\)
\(114\) 4.72424 0.442465
\(115\) 20.4486i 1.90684i
\(116\) 0.520071 0.0482874
\(117\) −8.28425 + 15.1616i −0.765879 + 1.40169i
\(118\) 4.19670 0.386337
\(119\) 25.3830i 2.32686i
\(120\) −20.2663 −1.85005
\(121\) 10.9970 0.999729
\(122\) 8.58860i 0.777575i
\(123\) 4.35227i 0.392431i
\(124\) 0.0740342i 0.00664847i
\(125\) 8.24100i 0.737098i
\(126\) −34.4815 −3.07185
\(127\) 16.3194 1.44812 0.724058 0.689739i \(-0.242275\pi\)
0.724058 + 0.689739i \(0.242275\pi\)
\(128\) 11.9009i 1.05190i
\(129\) 8.44798 0.743803
\(130\) −6.51712 + 11.9275i −0.571589 + 1.04611i
\(131\) 15.1689 1.32532 0.662658 0.748922i \(-0.269428\pi\)
0.662658 + 0.748922i \(0.269428\pi\)
\(132\) 0.0112843i 0.000982174i
\(133\) −5.87190 −0.509158
\(134\) −2.16485 −0.187014
\(135\) 13.0924i 1.12681i
\(136\) 14.0905i 1.20825i
\(137\) 11.4877i 0.981463i 0.871311 + 0.490732i \(0.163270\pi\)
−0.871311 + 0.490732i \(0.836730\pi\)
\(138\) 31.4047i 2.67334i
\(139\) −6.64791 −0.563869 −0.281934 0.959434i \(-0.590976\pi\)
−0.281934 + 0.959434i \(0.590976\pi\)
\(140\) −0.968289 −0.0818354
\(141\) 0.534548i 0.0450170i
\(142\) −2.07435 −0.174075
\(143\) 0.172769 + 0.0944001i 0.0144476 + 0.00789413i
\(144\) −19.8506 −1.65422
\(145\) 18.3877i 1.52702i
\(146\) −20.0973 −1.66327
\(147\) 50.1502 4.13632
\(148\) 0.499804i 0.0410836i
\(149\) 1.35792i 0.111245i 0.998452 + 0.0556224i \(0.0177143\pi\)
−0.998452 + 0.0556224i \(0.982286\pi\)
\(150\) 7.44369i 0.607775i
\(151\) 12.4451i 1.01277i −0.862308 0.506384i \(-0.830982\pi\)
0.862308 0.506384i \(-0.169018\pi\)
\(152\) −3.25957 −0.264386
\(153\) −24.3429 −1.96800
\(154\) 0.392921i 0.0316625i
\(155\) 2.61757 0.210248
\(156\) −0.357275 + 0.653876i −0.0286049 + 0.0523520i
\(157\) 15.5894 1.24417 0.622086 0.782949i \(-0.286286\pi\)
0.622086 + 0.782949i \(0.286286\pi\)
\(158\) 1.59596i 0.126968i
\(159\) −23.9843 −1.90208
\(160\) −1.09568 −0.0866213
\(161\) 39.0338i 3.07630i
\(162\) 0.595848i 0.0468143i
\(163\) 2.52440i 0.197726i 0.995101 + 0.0988632i \(0.0315206\pi\)
−0.995101 + 0.0988632i \(0.968479\pi\)
\(164\) 0.115433i 0.00901377i
\(165\) −0.398970 −0.0310598
\(166\) −2.51916 −0.195524
\(167\) 9.92382i 0.767928i −0.923348 0.383964i \(-0.874559\pi\)
0.923348 0.383964i \(-0.125441\pi\)
\(168\) 38.6858 2.98468
\(169\) −7.02236 10.9401i −0.540181 0.841549i
\(170\) −19.1502 −1.46876
\(171\) 5.63127i 0.430634i
\(172\) 0.224060 0.0170844
\(173\) −20.3536 −1.54745 −0.773726 0.633520i \(-0.781609\pi\)
−0.773726 + 0.633520i \(0.781609\pi\)
\(174\) 28.2396i 2.14084i
\(175\) 9.25199i 0.699385i
\(176\) 0.226201i 0.0170505i
\(177\) 8.13429i 0.611411i
\(178\) −3.39869 −0.254742
\(179\) 4.85781 0.363090 0.181545 0.983383i \(-0.441890\pi\)
0.181545 + 0.983383i \(0.441890\pi\)
\(180\) 0.928610i 0.0692145i
\(181\) 6.82673 0.507427 0.253713 0.967279i \(-0.418348\pi\)
0.253713 + 0.967279i \(0.418348\pi\)
\(182\) 12.4404 22.7680i 0.922141 1.68768i
\(183\) −16.6469 −1.23058
\(184\) 21.6682i 1.59740i
\(185\) 17.6712 1.29921
\(186\) 4.02002 0.294762
\(187\) 0.277390i 0.0202848i
\(188\) 0.0141775i 0.00103400i
\(189\) 24.9917i 1.81788i
\(190\) 4.43006i 0.321390i
\(191\) −13.8071 −0.999043 −0.499522 0.866301i \(-0.666491\pi\)
−0.499522 + 0.866301i \(0.666491\pi\)
\(192\) 21.4444 1.54762
\(193\) 8.92165i 0.642194i −0.947046 0.321097i \(-0.895948\pi\)
0.947046 0.321097i \(-0.104052\pi\)
\(194\) 17.4773 1.25479
\(195\) 23.1185 + 12.6319i 1.65555 + 0.904588i
\(196\) 1.33010 0.0950073
\(197\) 8.13765i 0.579783i 0.957059 + 0.289892i \(0.0936193\pi\)
−0.957059 + 0.289892i \(0.906381\pi\)
\(198\) −0.376820 −0.0267794
\(199\) 12.4940 0.885678 0.442839 0.896601i \(-0.353971\pi\)
0.442839 + 0.896601i \(0.353971\pi\)
\(200\) 5.13590i 0.363163i
\(201\) 4.19604i 0.295966i
\(202\) 16.7242i 1.17671i
\(203\) 35.0999i 2.46353i
\(204\) −1.04984 −0.0735032
\(205\) −4.08126 −0.285047
\(206\) 18.3242i 1.27671i
\(207\) −37.4342 −2.60186
\(208\) 7.16179 13.1073i 0.496581 0.908830i
\(209\) −0.0641691 −0.00443867
\(210\) 52.5776i 3.62820i
\(211\) −20.8611 −1.43614 −0.718068 0.695973i \(-0.754973\pi\)
−0.718068 + 0.695973i \(0.754973\pi\)
\(212\) −0.636121 −0.0436890
\(213\) 4.02063i 0.275489i
\(214\) 4.25511i 0.290873i
\(215\) 7.92192i 0.540270i
\(216\) 13.8732i 0.943954i
\(217\) −4.99660 −0.339192
\(218\) −28.6711 −1.94185
\(219\) 38.9539i 2.63226i
\(220\) −0.0105816 −0.000713414
\(221\) 8.78251 16.0735i 0.590775 1.08122i
\(222\) 27.1391 1.82146
\(223\) 18.6577i 1.24941i −0.780859 0.624707i \(-0.785218\pi\)
0.780859 0.624707i \(-0.214782\pi\)
\(224\) 2.09152 0.139746
\(225\) −8.87285 −0.591523
\(226\) 1.33381i 0.0887240i
\(227\) 27.9915i 1.85786i −0.370251 0.928932i \(-0.620728\pi\)
0.370251 0.928932i \(-0.379272\pi\)
\(228\) 0.242860i 0.0160838i
\(229\) 9.20943i 0.608576i 0.952580 + 0.304288i \(0.0984186\pi\)
−0.952580 + 0.304288i \(0.901581\pi\)
\(230\) −29.4491 −1.94181
\(231\) 0.761584 0.0501085
\(232\) 19.4844i 1.27921i
\(233\) 19.5339 1.27971 0.639854 0.768497i \(-0.278995\pi\)
0.639854 + 0.768497i \(0.278995\pi\)
\(234\) 21.8350 + 11.9306i 1.42740 + 0.779925i
\(235\) 0.501261 0.0326987
\(236\) 0.215741i 0.0140435i
\(237\) −3.09338 −0.200937
\(238\) 36.5554 2.36953
\(239\) 16.9297i 1.09509i −0.836776 0.547546i \(-0.815562\pi\)
0.836776 0.547546i \(-0.184438\pi\)
\(240\) 30.2684i 1.95382i
\(241\) 14.6063i 0.940875i −0.882433 0.470438i \(-0.844096\pi\)
0.882433 0.470438i \(-0.155904\pi\)
\(242\) 15.8374i 1.01806i
\(243\) 16.1601 1.03667
\(244\) −0.441516 −0.0282652
\(245\) 47.0273i 3.00447i
\(246\) −6.26793 −0.399629
\(247\) 3.71832 + 2.03167i 0.236591 + 0.129272i
\(248\) −2.77368 −0.176129
\(249\) 4.88278i 0.309434i
\(250\) 11.8683 0.750616
\(251\) −28.9232 −1.82561 −0.912807 0.408391i \(-0.866090\pi\)
−0.912807 + 0.408391i \(0.866090\pi\)
\(252\) 1.77260i 0.111663i
\(253\) 0.426568i 0.0268181i
\(254\) 23.5025i 1.47468i
\(255\) 37.1182i 2.32443i
\(256\) 1.77442 0.110901
\(257\) −19.4544 −1.21353 −0.606767 0.794880i \(-0.707534\pi\)
−0.606767 + 0.794880i \(0.707534\pi\)
\(258\) 12.1664i 0.757445i
\(259\) −33.7320 −2.09601
\(260\) 0.613159 + 0.335027i 0.0380265 + 0.0207775i
\(261\) −33.6615 −2.08359
\(262\) 21.8456i 1.34962i
\(263\) 20.2310 1.24750 0.623750 0.781624i \(-0.285608\pi\)
0.623750 + 0.781624i \(0.285608\pi\)
\(264\) 0.422765 0.0260194
\(265\) 22.4908i 1.38160i
\(266\) 8.45642i 0.518496i
\(267\) 6.58754i 0.403151i
\(268\) 0.111289i 0.00679805i
\(269\) −8.30420 −0.506316 −0.253158 0.967425i \(-0.581469\pi\)
−0.253158 + 0.967425i \(0.581469\pi\)
\(270\) −18.8550 −1.14748
\(271\) 14.7486i 0.895912i 0.894056 + 0.447956i \(0.147848\pi\)
−0.894056 + 0.447956i \(0.852152\pi\)
\(272\) 21.0446 1.27601
\(273\) −44.1304 24.1127i −2.67089 1.45936i
\(274\) 16.5441 0.999464
\(275\) 0.101107i 0.00609700i
\(276\) −1.61443 −0.0971772
\(277\) −15.4228 −0.926664 −0.463332 0.886185i \(-0.653346\pi\)
−0.463332 + 0.886185i \(0.653346\pi\)
\(278\) 9.57400i 0.574210i
\(279\) 4.79185i 0.286880i
\(280\) 36.2768i 2.16795i
\(281\) 17.2595i 1.02962i −0.857306 0.514808i \(-0.827863\pi\)
0.857306 0.514808i \(-0.172137\pi\)
\(282\) 0.769829 0.0458427
\(283\) 12.2230 0.726583 0.363291 0.931676i \(-0.381653\pi\)
0.363291 + 0.931676i \(0.381653\pi\)
\(284\) 0.106636i 0.00632771i
\(285\) −8.58661 −0.508627
\(286\) 0.135950 0.248813i 0.00803891 0.0147126i
\(287\) 7.79060 0.459865
\(288\) 2.00581i 0.118194i
\(289\) 8.80698 0.518057
\(290\) −26.4811 −1.55502
\(291\) 33.8755i 1.98582i
\(292\) 1.03315i 0.0604605i
\(293\) 11.5516i 0.674850i 0.941352 + 0.337425i \(0.109556\pi\)
−0.941352 + 0.337425i \(0.890444\pi\)
\(294\) 72.2239i 4.21218i
\(295\) −7.62776 −0.444106
\(296\) −18.7251 −1.08837
\(297\) 0.273114i 0.0158477i
\(298\) 1.95560 0.113285
\(299\) 13.5057 24.7177i 0.781053 1.42946i
\(300\) −0.382660 −0.0220929
\(301\) 15.1219i 0.871614i
\(302\) −17.9228 −1.03134
\(303\) −32.4158 −1.86224
\(304\) 4.86828i 0.279215i
\(305\) 15.6103i 0.893845i
\(306\) 35.0574i 2.00410i
\(307\) 22.1226i 1.26260i 0.775537 + 0.631302i \(0.217479\pi\)
−0.775537 + 0.631302i \(0.782521\pi\)
\(308\) 0.0201990 0.00115095
\(309\) 35.5171 2.02050
\(310\) 3.76969i 0.214104i
\(311\) −17.1273 −0.971203 −0.485601 0.874180i \(-0.661399\pi\)
−0.485601 + 0.874180i \(0.661399\pi\)
\(312\) −24.4974 13.3853i −1.38689 0.757791i
\(313\) −28.9822 −1.63817 −0.819086 0.573670i \(-0.805519\pi\)
−0.819086 + 0.573670i \(0.805519\pi\)
\(314\) 22.4511i 1.26699i
\(315\) 62.6723 3.53118
\(316\) −0.0820438 −0.00461532
\(317\) 6.22426i 0.349590i 0.984605 + 0.174795i \(0.0559262\pi\)
−0.984605 + 0.174795i \(0.944074\pi\)
\(318\) 34.5410i 1.93697i
\(319\) 0.383577i 0.0214762i
\(320\) 20.1090i 1.12413i
\(321\) 8.24751 0.460331
\(322\) 56.2146 3.13272
\(323\) 5.96997i 0.332178i
\(324\) 0.0306309 0.00170172
\(325\) 3.20118 5.85872i 0.177569 0.324983i
\(326\) 3.63552 0.201353
\(327\) 55.5720i 3.07314i
\(328\) 4.32467 0.238790
\(329\) −0.956844 −0.0527525
\(330\) 0.574577i 0.0316294i
\(331\) 5.28437i 0.290455i 0.989398 + 0.145228i \(0.0463915\pi\)
−0.989398 + 0.145228i \(0.953609\pi\)
\(332\) 0.129503i 0.00710740i
\(333\) 32.3497i 1.77275i
\(334\) −14.2918 −0.782012
\(335\) 3.93475 0.214978
\(336\) 57.7786i 3.15208i
\(337\) −7.23845 −0.394304 −0.197152 0.980373i \(-0.563169\pi\)
−0.197152 + 0.980373i \(0.563169\pi\)
\(338\) −15.7554 + 10.1133i −0.856983 + 0.550089i
\(339\) −2.58528 −0.140413
\(340\) 0.984462i 0.0533899i
\(341\) −0.0546038 −0.00295696
\(342\) −8.10988 −0.438532
\(343\) 54.7930i 2.95855i
\(344\) 8.39439i 0.452595i
\(345\) 57.0800i 3.07308i
\(346\) 29.3122i 1.57583i
\(347\) 33.0880 1.77626 0.888128 0.459597i \(-0.152006\pi\)
0.888128 + 0.459597i \(0.152006\pi\)
\(348\) −1.45172 −0.0778204
\(349\) 6.94086i 0.371536i 0.982594 + 0.185768i \(0.0594772\pi\)
−0.982594 + 0.185768i \(0.940523\pi\)
\(350\) 13.3243 0.712211
\(351\) 8.64711 15.8257i 0.461549 0.844715i
\(352\) 0.0228565 0.00121825
\(353\) 30.0813i 1.60107i 0.599288 + 0.800534i \(0.295450\pi\)
−0.599288 + 0.800534i \(0.704550\pi\)
\(354\) −11.7146 −0.622624
\(355\) 3.77026 0.200105
\(356\) 0.174717i 0.00925999i
\(357\) 70.8539i 3.74999i
\(358\) 6.99598i 0.369749i
\(359\) 3.73997i 0.197388i 0.995118 + 0.0986940i \(0.0314665\pi\)
−0.995118 + 0.0986940i \(0.968534\pi\)
\(360\) 34.7902 1.83361
\(361\) 17.6190 0.927314
\(362\) 9.83152i 0.516733i
\(363\) −30.6969 −1.61117
\(364\) −1.17044 0.639525i −0.0613478 0.0335202i
\(365\) 36.5282 1.91197
\(366\) 23.9741i 1.25315i
\(367\) 4.57778 0.238958 0.119479 0.992837i \(-0.461878\pi\)
0.119479 + 0.992837i \(0.461878\pi\)
\(368\) 32.3622 1.68700
\(369\) 7.47135i 0.388943i
\(370\) 25.4491i 1.32304i
\(371\) 42.9321i 2.22892i
\(372\) 0.206658i 0.0107147i
\(373\) −11.9473 −0.618607 −0.309303 0.950963i \(-0.600096\pi\)
−0.309303 + 0.950963i \(0.600096\pi\)
\(374\) 0.399484 0.0206568
\(375\) 23.0038i 1.18791i
\(376\) −0.531157 −0.0273923
\(377\) 12.1445 22.2266i 0.625475 1.14473i
\(378\) 35.9919 1.85122
\(379\) 0.620093i 0.0318521i −0.999873 0.0159260i \(-0.994930\pi\)
0.999873 0.0159260i \(-0.00506963\pi\)
\(380\) −0.227737 −0.0116827
\(381\) −45.5539 −2.33380
\(382\) 19.8842i 1.01737i
\(383\) 27.8945i 1.42534i −0.701498 0.712671i \(-0.747485\pi\)
0.701498 0.712671i \(-0.252515\pi\)
\(384\) 33.2201i 1.69525i
\(385\) 0.714160i 0.0363969i
\(386\) −12.8485 −0.653972
\(387\) −14.5023 −0.737191
\(388\) 0.898459i 0.0456123i
\(389\) 12.8614 0.652097 0.326048 0.945353i \(-0.394283\pi\)
0.326048 + 0.945353i \(0.394283\pi\)
\(390\) 18.1918 33.2942i 0.921178 1.68592i
\(391\) 39.6858 2.00699
\(392\) 49.8321i 2.51690i
\(393\) −42.3424 −2.13589
\(394\) 11.7194 0.590417
\(395\) 2.90075i 0.145953i
\(396\) 0.0193713i 0.000973443i
\(397\) 24.6396i 1.23663i 0.785931 + 0.618314i \(0.212184\pi\)
−0.785931 + 0.618314i \(0.787816\pi\)
\(398\) 17.9933i 0.901922i
\(399\) 16.3907 0.820564
\(400\) 7.67064 0.383532
\(401\) 20.3020i 1.01383i −0.861995 0.506917i \(-0.830785\pi\)
0.861995 0.506917i \(-0.169215\pi\)
\(402\) 6.04293 0.301394
\(403\) 3.16404 + 1.72882i 0.157612 + 0.0861187i
\(404\) −0.859744 −0.0427739
\(405\) 1.08299i 0.0538143i
\(406\) 50.5491 2.50871
\(407\) −0.368629 −0.0182723
\(408\) 39.3319i 1.94722i
\(409\) 7.67595i 0.379551i 0.981827 + 0.189776i \(0.0607761\pi\)
−0.981827 + 0.189776i \(0.939224\pi\)
\(410\) 5.87762i 0.290275i
\(411\) 32.0667i 1.58174i
\(412\) 0.941997 0.0464089
\(413\) 14.5604 0.716472
\(414\) 53.9110i 2.64958i
\(415\) 4.57873 0.224761
\(416\) −1.32443 0.723664i −0.0649356 0.0354805i
\(417\) 18.5569 0.908736
\(418\) 0.0924132i 0.00452008i
\(419\) −24.4074 −1.19238 −0.596189 0.802844i \(-0.703319\pi\)
−0.596189 + 0.802844i \(0.703319\pi\)
\(420\) 2.70287 0.131887
\(421\) 7.83588i 0.381898i −0.981600 0.190949i \(-0.938844\pi\)
0.981600 0.190949i \(-0.0611564\pi\)
\(422\) 30.0431i 1.46248i
\(423\) 0.917633i 0.0446169i
\(424\) 23.8322i 1.15739i
\(425\) 9.40651 0.456283
\(426\) 5.79031 0.280541
\(427\) 29.7982i 1.44203i
\(428\) 0.218744 0.0105734
\(429\) −0.482265 0.263507i −0.0232840 0.0127223i
\(430\) −11.4088 −0.550179
\(431\) 7.77841i 0.374673i −0.982296 0.187337i \(-0.940015\pi\)
0.982296 0.187337i \(-0.0599855\pi\)
\(432\) 20.7202 0.996899
\(433\) 26.6655 1.28146 0.640732 0.767765i \(-0.278631\pi\)
0.640732 + 0.767765i \(0.278631\pi\)
\(434\) 7.19586i 0.345413i
\(435\) 51.3273i 2.46096i
\(436\) 1.47390i 0.0705871i
\(437\) 9.18057i 0.439166i
\(438\) 56.0995 2.68054
\(439\) 14.4283 0.688626 0.344313 0.938855i \(-0.388112\pi\)
0.344313 + 0.938855i \(0.388112\pi\)
\(440\) 0.396439i 0.0188995i
\(441\) −86.0906 −4.09955
\(442\) −23.1483 12.6481i −1.10105 0.601610i
\(443\) 5.19341 0.246746 0.123373 0.992360i \(-0.460629\pi\)
0.123373 + 0.992360i \(0.460629\pi\)
\(444\) 1.39515i 0.0662108i
\(445\) 6.17733 0.292834
\(446\) −26.8699 −1.27233
\(447\) 3.79047i 0.179283i
\(448\) 38.3856i 1.81355i
\(449\) 14.9729i 0.706615i −0.935507 0.353308i \(-0.885057\pi\)
0.935507 0.353308i \(-0.114943\pi\)
\(450\) 12.7782i 0.602372i
\(451\) 0.0851371 0.00400895
\(452\) −0.0685677 −0.00322516
\(453\) 34.7391i 1.63218i
\(454\) −40.3120 −1.89194
\(455\) −22.6112 + 41.3824i −1.06003 + 1.94004i
\(456\) 9.09872 0.426087
\(457\) 42.0543i 1.96722i 0.180316 + 0.983609i \(0.442288\pi\)
−0.180316 + 0.983609i \(0.557712\pi\)
\(458\) 13.2630 0.619738
\(459\) 25.4091 1.18600
\(460\) 1.51390i 0.0705858i
\(461\) 9.31370i 0.433782i 0.976196 + 0.216891i \(0.0695917\pi\)
−0.976196 + 0.216891i \(0.930408\pi\)
\(462\) 1.09680i 0.0510275i
\(463\) 10.3203i 0.479625i −0.970819 0.239813i \(-0.922914\pi\)
0.970819 0.239813i \(-0.0770860\pi\)
\(464\) 29.1006 1.35096
\(465\) −7.30664 −0.338838
\(466\) 28.1318i 1.30318i
\(467\) −0.661824 −0.0306255 −0.0153128 0.999883i \(-0.504874\pi\)
−0.0153128 + 0.999883i \(0.504874\pi\)
\(468\) 0.613318 1.12248i 0.0283506 0.0518866i
\(469\) −7.51094 −0.346823
\(470\) 0.721891i 0.0332984i
\(471\) −43.5161 −2.00512
\(472\) 8.08269 0.372036
\(473\) 0.165255i 0.00759844i
\(474\) 4.45493i 0.204622i
\(475\) 2.17602i 0.0998428i
\(476\) 1.87921i 0.0861336i
\(477\) 41.1728 1.88517
\(478\) −24.3813 −1.11518
\(479\) 3.63440i 0.166060i 0.996547 + 0.0830300i \(0.0264597\pi\)
−0.996547 + 0.0830300i \(0.973540\pi\)
\(480\) 3.05847 0.139600
\(481\) 21.3604 + 11.6712i 0.973952 + 0.532163i
\(482\) −21.0353 −0.958131
\(483\) 108.959i 4.95778i
\(484\) −0.814156 −0.0370071
\(485\) −31.7661 −1.44242
\(486\) 23.2730i 1.05569i
\(487\) 31.1232i 1.41033i −0.709045 0.705163i \(-0.750874\pi\)
0.709045 0.705163i \(-0.249126\pi\)
\(488\) 16.5413i 0.748792i
\(489\) 7.04659i 0.318658i
\(490\) −67.7265 −3.05957
\(491\) 17.9607 0.810555 0.405277 0.914194i \(-0.367175\pi\)
0.405277 + 0.914194i \(0.367175\pi\)
\(492\) 0.322217i 0.0145267i
\(493\) 35.6861 1.60722
\(494\) 2.92591 5.35493i 0.131643 0.240930i
\(495\) 0.684894 0.0307837
\(496\) 4.14259i 0.186008i
\(497\) −7.19695 −0.322827
\(498\) 7.03194 0.315109
\(499\) 8.12403i 0.363681i 0.983328 + 0.181841i \(0.0582055\pi\)
−0.983328 + 0.181841i \(0.941794\pi\)
\(500\) 0.610116i 0.0272852i
\(501\) 27.7012i 1.23760i
\(502\) 41.6537i 1.85910i
\(503\) −38.6811 −1.72471 −0.862354 0.506307i \(-0.831010\pi\)
−0.862354 + 0.506307i \(0.831010\pi\)
\(504\) −66.4102 −2.95814
\(505\) 30.3973i 1.35266i
\(506\) 0.614323 0.0273100
\(507\) 19.6021 + 30.5382i 0.870561 + 1.35625i
\(508\) −1.20820 −0.0536051
\(509\) 16.1272i 0.714826i −0.933946 0.357413i \(-0.883659\pi\)
0.933946 0.357413i \(-0.116341\pi\)
\(510\) 53.4558 2.36706
\(511\) −69.7278 −3.08458
\(512\) 21.2464i 0.938967i
\(513\) 5.87794i 0.259517i
\(514\) 28.0173i 1.23579i
\(515\) 33.3054i 1.46761i
\(516\) −0.625439 −0.0275334
\(517\) −0.0104566 −0.000459879
\(518\) 48.5792i 2.13445i
\(519\) 56.8147 2.49389
\(520\) −12.5517 + 22.9719i −0.550431 + 1.00738i
\(521\) 5.58342 0.244614 0.122307 0.992492i \(-0.460971\pi\)
0.122307 + 0.992492i \(0.460971\pi\)
\(522\) 48.4776i 2.12181i
\(523\) −24.8140 −1.08504 −0.542520 0.840043i \(-0.682530\pi\)
−0.542520 + 0.840043i \(0.682530\pi\)
\(524\) −1.12302 −0.0490594
\(525\) 25.8259i 1.12713i
\(526\) 29.1358i 1.27038i
\(527\) 5.08006i 0.221291i
\(528\) 0.631414i 0.0274788i
\(529\) 38.0284 1.65341
\(530\) 32.3901 1.40694
\(531\) 13.9638i 0.605976i
\(532\) 0.434721 0.0188476
\(533\) −4.93331 2.69554i −0.213686 0.116757i
\(534\) 9.48705 0.410545
\(535\) 7.73394i 0.334367i
\(536\) −4.16942 −0.180092
\(537\) −13.5600 −0.585159
\(538\) 11.9593i 0.515602i
\(539\) 0.981014i 0.0422553i
\(540\) 0.969285i 0.0417114i
\(541\) 30.2928i 1.30239i −0.758911 0.651195i \(-0.774268\pi\)
0.758911 0.651195i \(-0.225732\pi\)
\(542\) 21.2402 0.912344
\(543\) −19.0560 −0.817773
\(544\) 2.12645i 0.0911709i
\(545\) 52.1115 2.23221
\(546\) −34.7259 + 63.5544i −1.48613 + 2.71988i
\(547\) −0.782832 −0.0334715 −0.0167357 0.999860i \(-0.505327\pi\)
−0.0167357 + 0.999860i \(0.505327\pi\)
\(548\) 0.850485i 0.0363309i
\(549\) 28.5770 1.21964
\(550\) 0.145610 0.00620882
\(551\) 8.25532i 0.351688i
\(552\) 60.4843i 2.57438i
\(553\) 5.53717i 0.235465i
\(554\) 22.2111i 0.943659i
\(555\) −49.3271 −2.09382
\(556\) 0.492173 0.0208728
\(557\) 12.1105i 0.513140i −0.966526 0.256570i \(-0.917408\pi\)
0.966526 0.256570i \(-0.0825924\pi\)
\(558\) −6.90098 −0.292142
\(559\) 5.23218 9.57580i 0.221298 0.405013i
\(560\) −54.1807 −2.28955
\(561\) 0.774304i 0.0326911i
\(562\) −24.8563 −1.04850
\(563\) 11.9218 0.502446 0.251223 0.967929i \(-0.419167\pi\)
0.251223 + 0.967929i \(0.419167\pi\)
\(564\) 0.0395748i 0.00166640i
\(565\) 2.42429i 0.101991i
\(566\) 17.6030i 0.739908i
\(567\) 2.06730i 0.0868183i
\(568\) −3.99512 −0.167632
\(569\) −14.4513 −0.605831 −0.302916 0.953017i \(-0.597960\pi\)
−0.302916 + 0.953017i \(0.597960\pi\)
\(570\) 12.3660i 0.517955i
\(571\) −22.3002 −0.933233 −0.466616 0.884460i \(-0.654527\pi\)
−0.466616 + 0.884460i \(0.654527\pi\)
\(572\) −0.0127908 0.00698884i −0.000534810 0.000292218i
\(573\) 38.5408 1.61007
\(574\) 11.2196i 0.468299i
\(575\) 14.4653 0.603243
\(576\) −36.8126 −1.53386
\(577\) 34.1283i 1.42078i −0.703808 0.710390i \(-0.748519\pi\)
0.703808 0.710390i \(-0.251481\pi\)
\(578\) 12.6834i 0.527559i
\(579\) 24.9038i 1.03497i
\(580\) 1.36132i 0.0565258i
\(581\) −8.74022 −0.362605
\(582\) −48.7858 −2.02224
\(583\) 0.469169i 0.0194310i
\(584\) −38.7068 −1.60170
\(585\) −39.6865 21.6846i −1.64084 0.896546i
\(586\) 16.6360 0.687227
\(587\) 17.1675i 0.708579i −0.935136 0.354290i \(-0.884723\pi\)
0.935136 0.354290i \(-0.115277\pi\)
\(588\) −3.71283 −0.153115
\(589\) −1.17518 −0.0484224
\(590\) 10.9851i 0.452251i
\(591\) 22.7153i 0.934384i
\(592\) 27.9666i 1.14942i
\(593\) 23.3023i 0.956909i −0.878112 0.478455i \(-0.841197\pi\)
0.878112 0.478455i \(-0.158803\pi\)
\(594\) 0.393325 0.0161383
\(595\) −66.4418 −2.72385
\(596\) 0.100532i 0.00411796i
\(597\) −34.8757 −1.42737
\(598\) −35.5973 19.4502i −1.45568 0.795378i
\(599\) −12.7509 −0.520986 −0.260493 0.965476i \(-0.583885\pi\)
−0.260493 + 0.965476i \(0.583885\pi\)
\(600\) 14.3363i 0.585277i
\(601\) 21.0313 0.857886 0.428943 0.903332i \(-0.358886\pi\)
0.428943 + 0.903332i \(0.358886\pi\)
\(602\) 21.7779 0.887600
\(603\) 7.20315i 0.293335i
\(604\) 0.921363i 0.0374897i
\(605\) 28.7854i 1.17029i
\(606\) 46.6837i 1.89639i
\(607\) −28.5285 −1.15793 −0.578967 0.815351i \(-0.696544\pi\)
−0.578967 + 0.815351i \(0.696544\pi\)
\(608\) 0.491915 0.0199498
\(609\) 97.9773i 3.97024i
\(610\) 22.4812 0.910238
\(611\) 0.605911 + 0.331067i 0.0245125 + 0.0133935i
\(612\) 1.80220 0.0728498
\(613\) 20.0076i 0.808099i 0.914737 + 0.404050i \(0.132398\pi\)
−0.914737 + 0.404050i \(0.867602\pi\)
\(614\) 31.8599 1.28576
\(615\) 11.3924 0.459385
\(616\) 0.756753i 0.0304904i
\(617\) 5.04682i 0.203177i 0.994826 + 0.101589i \(0.0323926\pi\)
−0.994826 + 0.101589i \(0.967607\pi\)
\(618\) 51.1500i 2.05755i
\(619\) 27.5782i 1.10846i −0.832363 0.554231i \(-0.813013\pi\)
0.832363 0.554231i \(-0.186987\pi\)
\(620\) −0.193789 −0.00778277
\(621\) 39.0740 1.56798
\(622\) 24.6660i 0.989015i
\(623\) −11.7917 −0.472426
\(624\) −19.9913 + 36.5876i −0.800294 + 1.46468i
\(625\) −30.8296 −1.23319
\(626\) 41.7388i 1.66822i
\(627\) 0.179121 0.00715340
\(628\) −1.15415 −0.0460556
\(629\) 34.2954i 1.36745i
\(630\) 90.2576i 3.59595i
\(631\) 46.3626i 1.84566i 0.385202 + 0.922832i \(0.374132\pi\)
−0.385202 + 0.922832i \(0.625868\pi\)
\(632\) 3.07376i 0.122268i
\(633\) 58.2314 2.31449
\(634\) 8.96388 0.356001
\(635\) 42.7172i 1.69518i
\(636\) 1.77566 0.0704095
\(637\) 31.0601 56.8454i 1.23065 2.25230i
\(638\) 0.552409 0.0218701
\(639\) 6.90202i 0.273040i
\(640\) −31.1514 −1.23137
\(641\) 16.3261 0.644843 0.322422 0.946596i \(-0.395503\pi\)
0.322422 + 0.946596i \(0.395503\pi\)
\(642\) 11.8777i 0.468774i
\(643\) 6.80196i 0.268243i −0.990965 0.134122i \(-0.957179\pi\)
0.990965 0.134122i \(-0.0428213\pi\)
\(644\) 2.88984i 0.113876i
\(645\) 22.1131i 0.870704i
\(646\) 8.59766 0.338270
\(647\) −12.7863 −0.502681 −0.251340 0.967899i \(-0.580871\pi\)
−0.251340 + 0.967899i \(0.580871\pi\)
\(648\) 1.14758i 0.0450813i
\(649\) 0.159119 0.00624597
\(650\) −8.43744 4.61018i −0.330944 0.180826i
\(651\) 13.9475 0.546644
\(652\) 0.186892i 0.00731926i
\(653\) 31.3311 1.22608 0.613041 0.790051i \(-0.289946\pi\)
0.613041 + 0.790051i \(0.289946\pi\)
\(654\) 80.0321 3.12950
\(655\) 39.7057i 1.55143i
\(656\) 6.45904i 0.252183i
\(657\) 66.8704i 2.60886i
\(658\) 1.37800i 0.0537200i
\(659\) −18.7431 −0.730127 −0.365064 0.930983i \(-0.618953\pi\)
−0.365064 + 0.930983i \(0.618953\pi\)
\(660\) 0.0295374 0.00114974
\(661\) 13.7249i 0.533836i 0.963719 + 0.266918i \(0.0860053\pi\)
−0.963719 + 0.266918i \(0.913995\pi\)
\(662\) 7.61029 0.295782
\(663\) −24.5154 + 44.8675i −0.952099 + 1.74251i
\(664\) −4.85181 −0.188287
\(665\) 15.3701i 0.596026i
\(666\) −46.5885 −1.80527
\(667\) 54.8778 2.12488
\(668\) 0.734702i 0.0284265i
\(669\) 52.0810i 2.01357i
\(670\) 5.66663i 0.218921i
\(671\) 0.325639i 0.0125712i
\(672\) −5.83824 −0.225215
\(673\) 15.0786 0.581237 0.290619 0.956839i \(-0.406139\pi\)
0.290619 + 0.956839i \(0.406139\pi\)
\(674\) 10.4245i 0.401535i
\(675\) 9.26150 0.356475
\(676\) 0.519895 + 0.809944i 0.0199960 + 0.0311517i
\(677\) −26.8652 −1.03251 −0.516257 0.856434i \(-0.672675\pi\)
−0.516257 + 0.856434i \(0.672675\pi\)
\(678\) 3.72319i 0.142988i
\(679\) 60.6374 2.32705
\(680\) −36.8827 −1.41439
\(681\) 78.1352i 2.99415i
\(682\) 0.0786376i 0.00301119i
\(683\) 10.6702i 0.408285i −0.978941 0.204143i \(-0.934559\pi\)
0.978941 0.204143i \(-0.0654406\pi\)
\(684\) 0.416907i 0.0159408i
\(685\) −30.0699 −1.14891
\(686\) 78.9102 3.01281
\(687\) 25.7071i 0.980787i
\(688\) 12.5373 0.477980
\(689\) −14.8545 + 27.1863i −0.565910 + 1.03571i
\(690\) 82.2038 3.12945
\(691\) 0.654117i 0.0248838i 0.999923 + 0.0124419i \(0.00396048\pi\)
−0.999923 + 0.0124419i \(0.996040\pi\)
\(692\) 1.50686 0.0572822
\(693\) −1.30738 −0.0496631
\(694\) 47.6517i 1.80883i
\(695\) 17.4014i 0.660071i
\(696\) 54.3885i 2.06159i
\(697\) 7.92072i 0.300019i
\(698\) 9.99588 0.378350
\(699\) −54.5267 −2.06239
\(700\) 0.684964i 0.0258892i
\(701\) 20.2045 0.763112 0.381556 0.924346i \(-0.375388\pi\)
0.381556 + 0.924346i \(0.375388\pi\)
\(702\) −22.7914 12.4531i −0.860208 0.470014i
\(703\) −7.93361 −0.299222
\(704\) 0.419485i 0.0158099i
\(705\) −1.39921 −0.0526974
\(706\) 43.3216 1.63043
\(707\) 58.0246i 2.18224i
\(708\) 0.602216i 0.0226327i
\(709\) 48.7025i 1.82906i 0.404518 + 0.914530i \(0.367439\pi\)
−0.404518 + 0.914530i \(0.632561\pi\)
\(710\) 5.42974i 0.203775i
\(711\) 5.31026 0.199150
\(712\) −6.54575 −0.245313
\(713\) 7.81207i 0.292564i
\(714\) −102.040 −3.81876
\(715\) −0.247099 + 0.452234i −0.00924096 + 0.0169126i
\(716\) −0.359644 −0.0134405
\(717\) 47.2574i 1.76486i
\(718\) 5.38612 0.201008
\(719\) 16.7247 0.623725 0.311862 0.950127i \(-0.399047\pi\)
0.311862 + 0.950127i \(0.399047\pi\)
\(720\) 51.9604i 1.93645i
\(721\) 63.5758i 2.36769i
\(722\) 25.3740i 0.944321i
\(723\) 40.7719i 1.51632i
\(724\) −0.505411 −0.0187835
\(725\) 13.0074 0.483083
\(726\) 44.2082i 1.64072i
\(727\) −20.1667 −0.747940 −0.373970 0.927441i \(-0.622004\pi\)
−0.373970 + 0.927441i \(0.622004\pi\)
\(728\) 23.9597 43.8505i 0.888006 1.62521i
\(729\) −43.8680 −1.62474
\(730\) 52.6062i 1.94704i
\(731\) 15.3745 0.568647
\(732\) 1.23244 0.0455524
\(733\) 6.69141i 0.247153i −0.992335 0.123576i \(-0.960564\pi\)
0.992335 0.123576i \(-0.0394364\pi\)
\(734\) 6.59270i 0.243341i
\(735\) 131.272i 4.84203i
\(736\) 3.27004i 0.120535i
\(737\) −0.0820809 −0.00302349
\(738\) 10.7599 0.396076
\(739\) 14.7948i 0.544235i −0.962264 0.272118i \(-0.912276\pi\)
0.962264 0.272118i \(-0.0877240\pi\)
\(740\) −1.30827 −0.0480930
\(741\) −10.3793 5.67118i −0.381292 0.208336i
\(742\) −61.8287 −2.26980
\(743\) 12.2435i 0.449170i −0.974455 0.224585i \(-0.927897\pi\)
0.974455 0.224585i \(-0.0721026\pi\)
\(744\) 7.74242 0.283851
\(745\) −3.55444 −0.130224
\(746\) 17.2059i 0.629952i
\(747\) 8.38205i 0.306683i
\(748\) 0.0205364i 0.000750884i
\(749\) 14.7631i 0.539432i
\(750\) −33.1290 −1.20970
\(751\) 22.4866 0.820548 0.410274 0.911962i \(-0.365433\pi\)
0.410274 + 0.911962i \(0.365433\pi\)
\(752\) 0.793301i 0.0289287i
\(753\) 80.7358 2.94218
\(754\) −32.0096 17.4899i −1.16572 0.636946i
\(755\) 32.5759 1.18556
\(756\) 1.85024i 0.0672927i
\(757\) 3.82393 0.138983 0.0694915 0.997583i \(-0.477862\pi\)
0.0694915 + 0.997583i \(0.477862\pi\)
\(758\) −0.893028 −0.0324362
\(759\) 1.19072i 0.0432203i
\(760\) 8.53214i 0.309493i
\(761\) 33.7254i 1.22254i −0.791420 0.611272i \(-0.790658\pi\)
0.791420 0.611272i \(-0.209342\pi\)
\(762\) 65.6045i 2.37660i
\(763\) −99.4743 −3.60121
\(764\) 1.02219 0.0369817
\(765\) 63.7190i 2.30377i
\(766\) −40.1723 −1.45148
\(767\) −9.22024 5.03790i −0.332923 0.181908i
\(768\) −4.95308 −0.178729
\(769\) 12.5287i 0.451795i 0.974151 + 0.225897i \(0.0725314\pi\)
−0.974151 + 0.225897i \(0.927469\pi\)
\(770\) −1.02850 −0.0370645
\(771\) 54.3048 1.95574
\(772\) 0.660507i 0.0237722i
\(773\) 23.6248i 0.849723i 0.905258 + 0.424862i \(0.139677\pi\)
−0.905258 + 0.424862i \(0.860323\pi\)
\(774\) 20.8854i 0.750711i
\(775\) 1.85165i 0.0665134i
\(776\) 33.6606 1.20835
\(777\) 94.1592 3.37794
\(778\) 18.5223i 0.664056i
\(779\) 1.83231 0.0656494
\(780\) −1.71156 0.935191i −0.0612838 0.0334852i
\(781\) −0.0786495 −0.00281430
\(782\) 57.1535i 2.04380i
\(783\) 35.1359