Properties

Label 230.3.d.a.91.12
Level $230$
Weight $3$
Character 230.91
Analytic conductor $6.267$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 230.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.26704608029\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \( x^{16} + 78x^{14} + 2165x^{12} + 28310x^{10} + 184804x^{8} + 569634x^{6} + 696037x^{4} + 285578x^{2} + 529 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 91.12
Root \(3.68124i\) of defining polynomial
Character \(\chi\) \(=\) 230.91
Dual form 230.3.d.a.91.11

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421 q^{2} -3.36596 q^{3} +2.00000 q^{4} +2.23607i q^{5} -4.76019 q^{6} +1.16919i q^{7} +2.82843 q^{8} +2.32968 q^{9} +O(q^{10})\) \(q+1.41421 q^{2} -3.36596 q^{3} +2.00000 q^{4} +2.23607i q^{5} -4.76019 q^{6} +1.16919i q^{7} +2.82843 q^{8} +2.32968 q^{9} +3.16228i q^{10} +10.6148i q^{11} -6.73192 q^{12} -15.0913 q^{13} +1.65348i q^{14} -7.52651i q^{15} +4.00000 q^{16} +20.0887i q^{17} +3.29467 q^{18} +22.5221i q^{19} +4.47214i q^{20} -3.93543i q^{21} +15.0116i q^{22} +(-20.9683 + 9.45142i) q^{23} -9.52037 q^{24} -5.00000 q^{25} -21.3424 q^{26} +22.4520 q^{27} +2.33837i q^{28} +32.5993 q^{29} -10.6441i q^{30} -27.0975 q^{31} +5.65685 q^{32} -35.7289i q^{33} +28.4097i q^{34} -2.61438 q^{35} +4.65936 q^{36} -53.0568i q^{37} +31.8510i q^{38} +50.7968 q^{39} +6.32456i q^{40} +9.43720 q^{41} -5.56554i q^{42} +36.4382i q^{43} +21.2296i q^{44} +5.20933i q^{45} +(-29.6537 + 13.3663i) q^{46} -49.1365 q^{47} -13.4638 q^{48} +47.6330 q^{49} -7.07107 q^{50} -67.6176i q^{51} -30.1827 q^{52} -104.253i q^{53} +31.7520 q^{54} -23.7354 q^{55} +3.30696i q^{56} -75.8083i q^{57} +46.1023 q^{58} +53.5457 q^{59} -15.0530i q^{60} -23.5166i q^{61} -38.3217 q^{62} +2.72383i q^{63} +8.00000 q^{64} -33.7453i q^{65} -50.5284i q^{66} +59.4754i q^{67} +40.1773i q^{68} +(70.5785 - 31.8131i) q^{69} -3.69729 q^{70} +55.2130 q^{71} +6.58933 q^{72} -8.77305 q^{73} -75.0337i q^{74} +16.8298 q^{75} +45.0441i q^{76} -12.4107 q^{77} +71.8376 q^{78} +57.0848i q^{79} +8.94427i q^{80} -96.5397 q^{81} +13.3462 q^{82} -55.1788i q^{83} -7.87086i q^{84} -44.9196 q^{85} +51.5314i q^{86} -109.728 q^{87} +30.0232i q^{88} +139.825i q^{89} +7.36710i q^{90} -17.6446i q^{91} +(-41.9366 + 18.9028i) q^{92} +91.2091 q^{93} -69.4894 q^{94} -50.3608 q^{95} -19.0407 q^{96} -19.8635i q^{97} +67.3632 q^{98} +24.7291i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9} + 24 q^{13} + 64 q^{16} - 32 q^{18} + 4 q^{23} - 16 q^{24} - 80 q^{25} + 96 q^{26} - 96 q^{27} - 108 q^{29} - 116 q^{31} + 60 q^{35} + 128 q^{36} + 248 q^{39} - 156 q^{41} - 124 q^{46} - 128 q^{47} - 28 q^{49} + 48 q^{52} + 224 q^{54} + 160 q^{58} + 204 q^{59} + 64 q^{62} + 128 q^{64} - 268 q^{69} - 120 q^{70} + 236 q^{71} - 64 q^{72} - 112 q^{73} - 936 q^{77} - 432 q^{78} - 136 q^{81} - 64 q^{82} + 60 q^{85} - 152 q^{87} + 8 q^{92} + 856 q^{93} - 216 q^{94} - 160 q^{95} - 32 q^{96} + 256 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421 0.707107
\(3\) −3.36596 −1.12199 −0.560993 0.827820i \(-0.689581\pi\)
−0.560993 + 0.827820i \(0.689581\pi\)
\(4\) 2.00000 0.500000
\(5\) 2.23607i 0.447214i
\(6\) −4.76019 −0.793364
\(7\) 1.16919i 0.167026i 0.996507 + 0.0835132i \(0.0266141\pi\)
−0.996507 + 0.0835132i \(0.973386\pi\)
\(8\) 2.82843 0.353553
\(9\) 2.32968 0.258853
\(10\) 3.16228i 0.316228i
\(11\) 10.6148i 0.964981i 0.875901 + 0.482490i \(0.160268\pi\)
−0.875901 + 0.482490i \(0.839732\pi\)
\(12\) −6.73192 −0.560993
\(13\) −15.0913 −1.16087 −0.580436 0.814306i \(-0.697118\pi\)
−0.580436 + 0.814306i \(0.697118\pi\)
\(14\) 1.65348i 0.118106i
\(15\) 7.52651i 0.501768i
\(16\) 4.00000 0.250000
\(17\) 20.0887i 1.18169i 0.806787 + 0.590843i \(0.201205\pi\)
−0.806787 + 0.590843i \(0.798795\pi\)
\(18\) 3.29467 0.183037
\(19\) 22.5221i 1.18537i 0.805434 + 0.592686i \(0.201932\pi\)
−0.805434 + 0.592686i \(0.798068\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 3.93543i 0.187401i
\(22\) 15.0116i 0.682344i
\(23\) −20.9683 + 9.45142i −0.911666 + 0.410931i
\(24\) −9.52037 −0.396682
\(25\) −5.00000 −0.200000
\(26\) −21.3424 −0.820860
\(27\) 22.4520 0.831556
\(28\) 2.33837i 0.0835132i
\(29\) 32.5993 1.12411 0.562056 0.827099i \(-0.310010\pi\)
0.562056 + 0.827099i \(0.310010\pi\)
\(30\) 10.6441i 0.354803i
\(31\) −27.0975 −0.874113 −0.437056 0.899434i \(-0.643979\pi\)
−0.437056 + 0.899434i \(0.643979\pi\)
\(32\) 5.65685 0.176777
\(33\) 35.7289i 1.08270i
\(34\) 28.4097i 0.835578i
\(35\) −2.61438 −0.0746965
\(36\) 4.65936 0.129427
\(37\) 53.0568i 1.43397i −0.697089 0.716984i \(-0.745522\pi\)
0.697089 0.716984i \(-0.254478\pi\)
\(38\) 31.8510i 0.838184i
\(39\) 50.7968 1.30248
\(40\) 6.32456i 0.158114i
\(41\) 9.43720 0.230176 0.115088 0.993355i \(-0.463285\pi\)
0.115088 + 0.993355i \(0.463285\pi\)
\(42\) 5.56554i 0.132513i
\(43\) 36.4382i 0.847400i 0.905802 + 0.423700i \(0.139269\pi\)
−0.905802 + 0.423700i \(0.860731\pi\)
\(44\) 21.2296i 0.482490i
\(45\) 5.20933i 0.115763i
\(46\) −29.6537 + 13.3663i −0.644645 + 0.290572i
\(47\) −49.1365 −1.04546 −0.522728 0.852499i \(-0.675086\pi\)
−0.522728 + 0.852499i \(0.675086\pi\)
\(48\) −13.4638 −0.280497
\(49\) 47.6330 0.972102
\(50\) −7.07107 −0.141421
\(51\) 67.6176i 1.32584i
\(52\) −30.1827 −0.580436
\(53\) 104.253i 1.96703i −0.180815 0.983517i \(-0.557874\pi\)
0.180815 0.983517i \(-0.442126\pi\)
\(54\) 31.7520 0.587999
\(55\) −23.7354 −0.431552
\(56\) 3.30696i 0.0590528i
\(57\) 75.8083i 1.32997i
\(58\) 46.1023 0.794868
\(59\) 53.5457 0.907554 0.453777 0.891115i \(-0.350076\pi\)
0.453777 + 0.891115i \(0.350076\pi\)
\(60\) 15.0530i 0.250884i
\(61\) 23.5166i 0.385518i −0.981246 0.192759i \(-0.938257\pi\)
0.981246 0.192759i \(-0.0617435\pi\)
\(62\) −38.3217 −0.618091
\(63\) 2.72383i 0.0432354i
\(64\) 8.00000 0.125000
\(65\) 33.7453i 0.519158i
\(66\) 50.5284i 0.765581i
\(67\) 59.4754i 0.887692i 0.896103 + 0.443846i \(0.146386\pi\)
−0.896103 + 0.443846i \(0.853614\pi\)
\(68\) 40.1773i 0.590843i
\(69\) 70.5785 31.8131i 1.02288 0.461060i
\(70\) −3.69729 −0.0528184
\(71\) 55.2130 0.777648 0.388824 0.921312i \(-0.372881\pi\)
0.388824 + 0.921312i \(0.372881\pi\)
\(72\) 6.58933 0.0915185
\(73\) −8.77305 −0.120179 −0.0600894 0.998193i \(-0.519139\pi\)
−0.0600894 + 0.998193i \(0.519139\pi\)
\(74\) 75.0337i 1.01397i
\(75\) 16.8298 0.224397
\(76\) 45.0441i 0.592686i
\(77\) −12.4107 −0.161177
\(78\) 71.8376 0.920994
\(79\) 57.0848i 0.722592i 0.932451 + 0.361296i \(0.117666\pi\)
−0.932451 + 0.361296i \(0.882334\pi\)
\(80\) 8.94427i 0.111803i
\(81\) −96.5397 −1.19185
\(82\) 13.3462 0.162759
\(83\) 55.1788i 0.664805i −0.943138 0.332403i \(-0.892141\pi\)
0.943138 0.332403i \(-0.107859\pi\)
\(84\) 7.87086i 0.0937007i
\(85\) −44.9196 −0.528466
\(86\) 51.5314i 0.599203i
\(87\) −109.728 −1.26124
\(88\) 30.0232i 0.341172i
\(89\) 139.825i 1.57107i 0.618815 + 0.785536i \(0.287613\pi\)
−0.618815 + 0.785536i \(0.712387\pi\)
\(90\) 7.36710i 0.0818567i
\(91\) 17.6446i 0.193896i
\(92\) −41.9366 + 18.9028i −0.455833 + 0.205466i
\(93\) 91.2091 0.980743
\(94\) −69.4894 −0.739249
\(95\) −50.3608 −0.530114
\(96\) −19.0407 −0.198341
\(97\) 19.8635i 0.204778i −0.994744 0.102389i \(-0.967351\pi\)
0.994744 0.102389i \(-0.0326487\pi\)
\(98\) 67.3632 0.687380
\(99\) 24.7291i 0.249789i
\(100\) −10.0000 −0.100000
\(101\) 86.5639 0.857068 0.428534 0.903526i \(-0.359030\pi\)
0.428534 + 0.903526i \(0.359030\pi\)
\(102\) 95.6258i 0.937507i
\(103\) 144.118i 1.39920i 0.714535 + 0.699600i \(0.246639\pi\)
−0.714535 + 0.699600i \(0.753361\pi\)
\(104\) −42.6847 −0.410430
\(105\) 8.79989 0.0838085
\(106\) 147.436i 1.39090i
\(107\) 10.4544i 0.0977050i −0.998806 0.0488525i \(-0.984444\pi\)
0.998806 0.0488525i \(-0.0155564\pi\)
\(108\) 44.9040 0.415778
\(109\) 69.1221i 0.634148i −0.948401 0.317074i \(-0.897300\pi\)
0.948401 0.317074i \(-0.102700\pi\)
\(110\) −33.5669 −0.305154
\(111\) 178.587i 1.60889i
\(112\) 4.67674i 0.0417566i
\(113\) 137.264i 1.21473i 0.794423 + 0.607364i \(0.207773\pi\)
−0.794423 + 0.607364i \(0.792227\pi\)
\(114\) 107.209i 0.940431i
\(115\) −21.1340 46.8866i −0.183774 0.407710i
\(116\) 65.1985 0.562056
\(117\) −35.1580 −0.300496
\(118\) 75.7250 0.641738
\(119\) −23.4874 −0.197373
\(120\) 21.2882i 0.177402i
\(121\) 8.32629 0.0688123
\(122\) 33.2575i 0.272602i
\(123\) −31.7652 −0.258254
\(124\) −54.1950 −0.437056
\(125\) 11.1803i 0.0894427i
\(126\) 3.85208i 0.0305720i
\(127\) 57.9697 0.456455 0.228227 0.973608i \(-0.426707\pi\)
0.228227 + 0.973608i \(0.426707\pi\)
\(128\) 11.3137 0.0883883
\(129\) 122.650i 0.950772i
\(130\) 47.7230i 0.367100i
\(131\) −95.0810 −0.725809 −0.362905 0.931826i \(-0.618215\pi\)
−0.362905 + 0.931826i \(0.618215\pi\)
\(132\) 71.4579i 0.541348i
\(133\) −26.3325 −0.197988
\(134\) 84.1109i 0.627693i
\(135\) 50.2042i 0.371883i
\(136\) 56.8193i 0.417789i
\(137\) 198.711i 1.45045i −0.688514 0.725223i \(-0.741737\pi\)
0.688514 0.725223i \(-0.258263\pi\)
\(138\) 99.8131 44.9905i 0.723283 0.326018i
\(139\) −0.129480 −0.000931508 −0.000465754 1.00000i \(-0.500148\pi\)
−0.000465754 1.00000i \(0.500148\pi\)
\(140\) −5.22876 −0.0373483
\(141\) 165.391 1.17299
\(142\) 78.0830 0.549880
\(143\) 160.191i 1.12022i
\(144\) 9.31873 0.0647134
\(145\) 72.8942i 0.502718i
\(146\) −12.4070 −0.0849792
\(147\) −160.331 −1.09069
\(148\) 106.114i 0.716984i
\(149\) 63.8745i 0.428688i −0.976758 0.214344i \(-0.931239\pi\)
0.976758 0.214344i \(-0.0687613\pi\)
\(150\) 23.8009 0.158673
\(151\) −35.2673 −0.233558 −0.116779 0.993158i \(-0.537257\pi\)
−0.116779 + 0.993158i \(0.537257\pi\)
\(152\) 63.7020i 0.419092i
\(153\) 46.8002i 0.305884i
\(154\) −17.5513 −0.113970
\(155\) 60.5919i 0.390915i
\(156\) 101.594 0.651241
\(157\) 289.136i 1.84163i 0.390002 + 0.920814i \(0.372474\pi\)
−0.390002 + 0.920814i \(0.627526\pi\)
\(158\) 80.7300i 0.510950i
\(159\) 350.911i 2.20699i
\(160\) 12.6491i 0.0790569i
\(161\) −11.0505 24.5159i −0.0686364 0.152272i
\(162\) −136.528 −0.842764
\(163\) −46.2536 −0.283764 −0.141882 0.989884i \(-0.545315\pi\)
−0.141882 + 0.989884i \(0.545315\pi\)
\(164\) 18.8744 0.115088
\(165\) 79.8923 0.484196
\(166\) 78.0346i 0.470088i
\(167\) −90.8735 −0.544153 −0.272076 0.962276i \(-0.587710\pi\)
−0.272076 + 0.962276i \(0.587710\pi\)
\(168\) 11.1311i 0.0662564i
\(169\) 58.7484 0.347624
\(170\) −63.5259 −0.373682
\(171\) 52.4692i 0.306837i
\(172\) 72.8764i 0.423700i
\(173\) −90.7893 −0.524794 −0.262397 0.964960i \(-0.584513\pi\)
−0.262397 + 0.964960i \(0.584513\pi\)
\(174\) −155.179 −0.891831
\(175\) 5.84593i 0.0334053i
\(176\) 42.4591i 0.241245i
\(177\) −180.233 −1.01826
\(178\) 197.743i 1.11092i
\(179\) 301.636 1.68511 0.842557 0.538607i \(-0.181049\pi\)
0.842557 + 0.538607i \(0.181049\pi\)
\(180\) 10.4187i 0.0578814i
\(181\) 248.547i 1.37319i 0.727040 + 0.686595i \(0.240895\pi\)
−0.727040 + 0.686595i \(0.759105\pi\)
\(182\) 24.9532i 0.137105i
\(183\) 79.1558i 0.432546i
\(184\) −59.3074 + 26.7327i −0.322323 + 0.145286i
\(185\) 118.639 0.641290
\(186\) 128.989 0.693490
\(187\) −213.237 −1.14030
\(188\) −98.2729 −0.522728
\(189\) 26.2506i 0.138892i
\(190\) −71.2210 −0.374847
\(191\) 146.382i 0.766397i 0.923666 + 0.383199i \(0.125178\pi\)
−0.923666 + 0.383199i \(0.874822\pi\)
\(192\) −26.9277 −0.140248
\(193\) −120.648 −0.625120 −0.312560 0.949898i \(-0.601187\pi\)
−0.312560 + 0.949898i \(0.601187\pi\)
\(194\) 28.0912i 0.144800i
\(195\) 113.585i 0.582488i
\(196\) 95.2660 0.486051
\(197\) 31.6502 0.160661 0.0803305 0.996768i \(-0.474402\pi\)
0.0803305 + 0.996768i \(0.474402\pi\)
\(198\) 34.9722i 0.176627i
\(199\) 37.4496i 0.188189i 0.995563 + 0.0940944i \(0.0299955\pi\)
−0.995563 + 0.0940944i \(0.970004\pi\)
\(200\) −14.1421 −0.0707107
\(201\) 200.192i 0.995979i
\(202\) 122.420 0.606039
\(203\) 38.1146i 0.187757i
\(204\) 135.235i 0.662918i
\(205\) 21.1022i 0.102938i
\(206\) 203.813i 0.989384i
\(207\) −48.8495 + 22.0188i −0.235988 + 0.106371i
\(208\) −60.3653 −0.290218
\(209\) −239.067 −1.14386
\(210\) 12.4449 0.0592615
\(211\) −43.6572 −0.206906 −0.103453 0.994634i \(-0.532989\pi\)
−0.103453 + 0.994634i \(0.532989\pi\)
\(212\) 208.506i 0.983517i
\(213\) −185.845 −0.872510
\(214\) 14.7848i 0.0690879i
\(215\) −81.4783 −0.378969
\(216\) 63.5039 0.294000
\(217\) 31.6820i 0.146000i
\(218\) 97.7535i 0.448410i
\(219\) 29.5297 0.134839
\(220\) −47.4708 −0.215776
\(221\) 303.165i 1.37179i
\(222\) 252.560i 1.13766i
\(223\) 348.623 1.56333 0.781666 0.623697i \(-0.214370\pi\)
0.781666 + 0.623697i \(0.214370\pi\)
\(224\) 6.61391i 0.0295264i
\(225\) −11.6484 −0.0517707
\(226\) 194.121i 0.858943i
\(227\) 175.793i 0.774421i 0.921991 + 0.387210i \(0.126561\pi\)
−0.921991 + 0.387210i \(0.873439\pi\)
\(228\) 151.617i 0.664985i
\(229\) 1.44148i 0.00629466i 0.999995 + 0.00314733i \(0.00100183\pi\)
−0.999995 + 0.00314733i \(0.998998\pi\)
\(230\) −29.8880 66.3077i −0.129948 0.288294i
\(231\) 41.7738 0.180839
\(232\) 92.2047 0.397434
\(233\) −113.416 −0.486763 −0.243381 0.969931i \(-0.578257\pi\)
−0.243381 + 0.969931i \(0.578257\pi\)
\(234\) −49.7209 −0.212483
\(235\) 109.872i 0.467542i
\(236\) 107.091 0.453777
\(237\) 192.145i 0.810738i
\(238\) −33.2162 −0.139564
\(239\) 367.260 1.53665 0.768326 0.640059i \(-0.221090\pi\)
0.768326 + 0.640059i \(0.221090\pi\)
\(240\) 30.1061i 0.125442i
\(241\) 220.365i 0.914378i 0.889370 + 0.457189i \(0.151144\pi\)
−0.889370 + 0.457189i \(0.848856\pi\)
\(242\) 11.7752 0.0486577
\(243\) 122.881 0.505681
\(244\) 47.0332i 0.192759i
\(245\) 106.511i 0.434737i
\(246\) −44.9228 −0.182613
\(247\) 339.888i 1.37606i
\(248\) −76.6433 −0.309046
\(249\) 185.730i 0.745902i
\(250\) 15.8114i 0.0632456i
\(251\) 440.210i 1.75382i −0.480650 0.876912i \(-0.659599\pi\)
0.480650 0.876912i \(-0.340401\pi\)
\(252\) 5.44766i 0.0216177i
\(253\) −100.325 222.574i −0.396541 0.879740i
\(254\) 81.9816 0.322762
\(255\) 151.198 0.592932
\(256\) 16.0000 0.0625000
\(257\) 491.519 1.91252 0.956262 0.292512i \(-0.0944913\pi\)
0.956262 + 0.292512i \(0.0944913\pi\)
\(258\) 173.453i 0.672297i
\(259\) 62.0333 0.239511
\(260\) 67.4905i 0.259579i
\(261\) 75.9459 0.290980
\(262\) −134.465 −0.513225
\(263\) 267.833i 1.01838i −0.860655 0.509189i \(-0.829946\pi\)
0.860655 0.509189i \(-0.170054\pi\)
\(264\) 101.057i 0.382791i
\(265\) 233.116 0.879684
\(266\) −37.2397 −0.139999
\(267\) 470.647i 1.76272i
\(268\) 118.951i 0.443846i
\(269\) 95.6985 0.355756 0.177878 0.984053i \(-0.443077\pi\)
0.177878 + 0.984053i \(0.443077\pi\)
\(270\) 70.9995i 0.262961i
\(271\) −452.255 −1.66884 −0.834419 0.551131i \(-0.814197\pi\)
−0.834419 + 0.551131i \(0.814197\pi\)
\(272\) 80.3547i 0.295422i
\(273\) 59.3909i 0.217549i
\(274\) 281.020i 1.02562i
\(275\) 53.0739i 0.192996i
\(276\) 141.157 63.6262i 0.511439 0.230530i
\(277\) −87.4783 −0.315806 −0.157903 0.987455i \(-0.550473\pi\)
−0.157903 + 0.987455i \(0.550473\pi\)
\(278\) −0.183112 −0.000658676
\(279\) −63.1285 −0.226267
\(280\) −7.39458 −0.0264092
\(281\) 232.157i 0.826183i −0.910690 0.413091i \(-0.864449\pi\)
0.910690 0.413091i \(-0.135551\pi\)
\(282\) 233.899 0.829428
\(283\) 239.367i 0.845820i 0.906172 + 0.422910i \(0.138991\pi\)
−0.906172 + 0.422910i \(0.861009\pi\)
\(284\) 110.426 0.388824
\(285\) 169.513 0.594781
\(286\) 226.545i 0.792114i
\(287\) 11.0338i 0.0384454i
\(288\) 13.1787 0.0457593
\(289\) −114.554 −0.396382
\(290\) 103.088i 0.355476i
\(291\) 66.8597i 0.229758i
\(292\) −17.5461 −0.0600894
\(293\) 581.830i 1.98577i −0.119092 0.992883i \(-0.537998\pi\)
0.119092 0.992883i \(-0.462002\pi\)
\(294\) −226.742 −0.771231
\(295\) 119.732i 0.405871i
\(296\) 150.067i 0.506984i
\(297\) 238.323i 0.802436i
\(298\) 90.3322i 0.303128i
\(299\) 316.440 142.635i 1.05833 0.477039i
\(300\) 33.6596 0.112199
\(301\) −42.6030 −0.141538
\(302\) −49.8755 −0.165151
\(303\) −291.370 −0.961619
\(304\) 90.0882i 0.296343i
\(305\) 52.5847 0.172409
\(306\) 66.1855i 0.216292i
\(307\) 110.134 0.358742 0.179371 0.983782i \(-0.442594\pi\)
0.179371 + 0.983782i \(0.442594\pi\)
\(308\) −24.8213 −0.0805887
\(309\) 485.094i 1.56988i
\(310\) 85.6898i 0.276419i
\(311\) −298.100 −0.958520 −0.479260 0.877673i \(-0.659095\pi\)
−0.479260 + 0.877673i \(0.659095\pi\)
\(312\) 143.675 0.460497
\(313\) 109.474i 0.349758i −0.984590 0.174879i \(-0.944047\pi\)
0.984590 0.174879i \(-0.0559534\pi\)
\(314\) 408.900i 1.30223i
\(315\) −6.09067 −0.0193355
\(316\) 114.170i 0.361296i
\(317\) 474.434 1.49664 0.748318 0.663340i \(-0.230862\pi\)
0.748318 + 0.663340i \(0.230862\pi\)
\(318\) 496.263i 1.56057i
\(319\) 346.034i 1.08475i
\(320\) 17.8885i 0.0559017i
\(321\) 35.1892i 0.109624i
\(322\) −15.6277 34.6707i −0.0485333 0.107673i
\(323\) −452.438 −1.40074
\(324\) −193.079 −0.595924
\(325\) 75.4567 0.232174
\(326\) −65.4124 −0.200652
\(327\) 232.662i 0.711506i
\(328\) 26.6924 0.0813794
\(329\) 57.4496i 0.174619i
\(330\) 112.985 0.342378
\(331\) 255.367 0.771503 0.385751 0.922603i \(-0.373942\pi\)
0.385751 + 0.922603i \(0.373942\pi\)
\(332\) 110.358i 0.332403i
\(333\) 123.606i 0.371188i
\(334\) −128.515 −0.384774
\(335\) −132.991 −0.396988
\(336\) 15.7417i 0.0468504i
\(337\) 458.486i 1.36049i 0.732983 + 0.680247i \(0.238127\pi\)
−0.732983 + 0.680247i \(0.761873\pi\)
\(338\) 83.0828 0.245807
\(339\) 462.026i 1.36291i
\(340\) −89.8392 −0.264233
\(341\) 287.634i 0.843502i
\(342\) 74.2027i 0.216967i
\(343\) 112.982i 0.329393i
\(344\) 103.063i 0.299601i
\(345\) 71.1363 + 157.818i 0.206192 + 0.457445i
\(346\) −128.395 −0.371085
\(347\) 510.676 1.47169 0.735845 0.677151i \(-0.236785\pi\)
0.735845 + 0.677151i \(0.236785\pi\)
\(348\) −219.456 −0.630620
\(349\) −591.870 −1.69590 −0.847951 0.530075i \(-0.822164\pi\)
−0.847951 + 0.530075i \(0.822164\pi\)
\(350\) 8.26739i 0.0236211i
\(351\) −338.831 −0.965330
\(352\) 60.0463i 0.170586i
\(353\) 168.334 0.476866 0.238433 0.971159i \(-0.423366\pi\)
0.238433 + 0.971159i \(0.423366\pi\)
\(354\) −254.887 −0.720021
\(355\) 123.460i 0.347775i
\(356\) 279.651i 0.785536i
\(357\) 79.0575 0.221450
\(358\) 426.577 1.19156
\(359\) 37.5719i 0.104657i 0.998630 + 0.0523285i \(0.0166643\pi\)
−0.998630 + 0.0523285i \(0.983336\pi\)
\(360\) 14.7342i 0.0409283i
\(361\) −146.243 −0.405105
\(362\) 351.499i 0.970992i
\(363\) −28.0260 −0.0772065
\(364\) 35.2891i 0.0969482i
\(365\) 19.6171i 0.0537456i
\(366\) 111.943i 0.305856i
\(367\) 427.036i 1.16359i 0.813337 + 0.581793i \(0.197649\pi\)
−0.813337 + 0.581793i \(0.802351\pi\)
\(368\) −83.8733 + 37.8057i −0.227917 + 0.102733i
\(369\) 21.9857 0.0595818
\(370\) 167.780 0.453461
\(371\) 121.891 0.328547
\(372\) 182.418 0.490371
\(373\) 369.980i 0.991904i 0.868350 + 0.495952i \(0.165181\pi\)
−0.868350 + 0.495952i \(0.834819\pi\)
\(374\) −301.563 −0.806317
\(375\) 37.6326i 0.100354i
\(376\) −138.979 −0.369625
\(377\) −491.966 −1.30495
\(378\) 37.1239i 0.0982114i
\(379\) 78.8009i 0.207918i 0.994582 + 0.103959i \(0.0331511\pi\)
−0.994582 + 0.103959i \(0.966849\pi\)
\(380\) −100.722 −0.265057
\(381\) −195.124 −0.512136
\(382\) 207.015i 0.541925i
\(383\) 254.083i 0.663403i 0.943384 + 0.331702i \(0.107623\pi\)
−0.943384 + 0.331702i \(0.892377\pi\)
\(384\) −38.0815 −0.0991705
\(385\) 27.7511i 0.0720807i
\(386\) −170.622 −0.442027
\(387\) 84.8894i 0.219353i
\(388\) 39.7270i 0.102389i
\(389\) 322.363i 0.828698i −0.910118 0.414349i \(-0.864009\pi\)
0.910118 0.414349i \(-0.135991\pi\)
\(390\) 160.634i 0.411881i
\(391\) −189.866 421.226i −0.485592 1.07730i
\(392\) 134.726 0.343690
\(393\) 320.039 0.814348
\(394\) 44.7602 0.113605
\(395\) −127.645 −0.323153
\(396\) 49.4581i 0.124894i
\(397\) 715.832 1.80310 0.901552 0.432671i \(-0.142429\pi\)
0.901552 + 0.432671i \(0.142429\pi\)
\(398\) 52.9617i 0.133070i
\(399\) 88.6340 0.222140
\(400\) −20.0000 −0.0500000
\(401\) 441.435i 1.10083i 0.834890 + 0.550417i \(0.185531\pi\)
−0.834890 + 0.550417i \(0.814469\pi\)
\(402\) 283.114i 0.704263i
\(403\) 408.937 1.01473
\(404\) 173.128 0.428534
\(405\) 215.869i 0.533011i
\(406\) 53.9022i 0.132764i
\(407\) 563.187 1.38375
\(408\) 191.252i 0.468754i
\(409\) −608.727 −1.48833 −0.744164 0.667996i \(-0.767152\pi\)
−0.744164 + 0.667996i \(0.767152\pi\)
\(410\) 29.8430i 0.0727879i
\(411\) 668.853i 1.62738i
\(412\) 288.235i 0.699600i
\(413\) 62.6048i 0.151586i
\(414\) −69.0836 + 31.1393i −0.166869 + 0.0752157i
\(415\) 123.384 0.297310
\(416\) −85.3695 −0.205215
\(417\) 0.435823 0.00104514
\(418\) −338.091 −0.808831
\(419\) 287.454i 0.686047i −0.939327 0.343023i \(-0.888549\pi\)
0.939327 0.343023i \(-0.111451\pi\)
\(420\) 17.5998 0.0419042
\(421\) 130.848i 0.310803i −0.987851 0.155402i \(-0.950333\pi\)
0.987851 0.155402i \(-0.0496672\pi\)
\(422\) −61.7406 −0.146305
\(423\) −114.472 −0.270620
\(424\) 294.871i 0.695452i
\(425\) 100.443i 0.236337i
\(426\) −262.824 −0.616958
\(427\) 27.4952 0.0643917
\(428\) 20.9089i 0.0488525i
\(429\) 539.197i 1.25687i
\(430\) −115.228 −0.267972
\(431\) 239.816i 0.556417i −0.960521 0.278209i \(-0.910259\pi\)
0.960521 0.278209i \(-0.0897406\pi\)
\(432\) 89.8081 0.207889
\(433\) 305.542i 0.705640i −0.935691 0.352820i \(-0.885223\pi\)
0.935691 0.352820i \(-0.114777\pi\)
\(434\) 44.8051i 0.103238i
\(435\) 245.359i 0.564043i
\(436\) 138.244i 0.317074i
\(437\) −212.865 472.250i −0.487106 1.08066i
\(438\) 41.7613 0.0953455
\(439\) −579.018 −1.31895 −0.659474 0.751727i \(-0.729221\pi\)
−0.659474 + 0.751727i \(0.729221\pi\)
\(440\) −67.1338 −0.152577
\(441\) 110.970 0.251632
\(442\) 428.740i 0.969999i
\(443\) −606.274 −1.36856 −0.684282 0.729217i \(-0.739884\pi\)
−0.684282 + 0.729217i \(0.739884\pi\)
\(444\) 357.174i 0.804446i
\(445\) −312.659 −0.702605
\(446\) 493.028 1.10544
\(447\) 214.999i 0.480982i
\(448\) 9.35348i 0.0208783i
\(449\) −202.580 −0.451181 −0.225590 0.974222i \(-0.572431\pi\)
−0.225590 + 0.974222i \(0.572431\pi\)
\(450\) −16.4733 −0.0366074
\(451\) 100.174i 0.222115i
\(452\) 274.529i 0.607364i
\(453\) 118.708 0.262049
\(454\) 248.609i 0.547598i
\(455\) 39.4545 0.0867131
\(456\) 214.418i 0.470215i
\(457\) 373.760i 0.817857i 0.912567 + 0.408928i \(0.134097\pi\)
−0.912567 + 0.408928i \(0.865903\pi\)
\(458\) 2.03856i 0.00445100i
\(459\) 451.031i 0.982639i
\(460\) −42.2681 93.7732i −0.0918871 0.203855i
\(461\) 709.377 1.53878 0.769390 0.638780i \(-0.220561\pi\)
0.769390 + 0.638780i \(0.220561\pi\)
\(462\) 59.0770 0.127872
\(463\) 266.488 0.575569 0.287785 0.957695i \(-0.407081\pi\)
0.287785 + 0.957695i \(0.407081\pi\)
\(464\) 130.397 0.281028
\(465\) 203.950i 0.438602i
\(466\) −160.394 −0.344193
\(467\) 686.135i 1.46924i 0.678479 + 0.734620i \(0.262639\pi\)
−0.678479 + 0.734620i \(0.737361\pi\)
\(468\) −70.3160 −0.150248
\(469\) −69.5378 −0.148268
\(470\) 155.383i 0.330602i
\(471\) 973.219i 2.06628i
\(472\) 151.450 0.320869
\(473\) −386.784 −0.817725
\(474\) 271.734i 0.573279i
\(475\) 112.610i 0.237074i
\(476\) −46.9747 −0.0986864
\(477\) 242.876i 0.509174i
\(478\) 519.384 1.08658
\(479\) 176.517i 0.368511i −0.982878 0.184256i \(-0.941013\pi\)
0.982878 0.184256i \(-0.0589874\pi\)
\(480\) 42.5764i 0.0887008i
\(481\) 800.698i 1.66465i
\(482\) 311.643i 0.646563i
\(483\) 37.1954 + 82.5194i 0.0770091 + 0.170848i
\(484\) 16.6526 0.0344062
\(485\) 44.4161 0.0915796
\(486\) 173.779 0.357571
\(487\) 524.802 1.07762 0.538811 0.842427i \(-0.318874\pi\)
0.538811 + 0.842427i \(0.318874\pi\)
\(488\) 66.5149i 0.136301i
\(489\) 155.688 0.318380
\(490\) 150.629i 0.307406i
\(491\) −551.047 −1.12229 −0.561147 0.827716i \(-0.689640\pi\)
−0.561147 + 0.827716i \(0.689640\pi\)
\(492\) −63.5304 −0.129127
\(493\) 654.876i 1.32835i
\(494\) 480.674i 0.973024i
\(495\) −55.2959 −0.111709
\(496\) −108.390 −0.218528
\(497\) 64.5542i 0.129888i
\(498\) 262.661i 0.527433i
\(499\) −736.739 −1.47643 −0.738216 0.674565i \(-0.764331\pi\)
−0.738216 + 0.674565i \(0.764331\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) 305.876 0.610532
\(502\) 622.551i 1.24014i
\(503\) 699.308i 1.39027i 0.718877 + 0.695137i \(0.244656\pi\)
−0.718877 + 0.695137i \(0.755344\pi\)
\(504\) 7.70415i 0.0152860i
\(505\) 193.563i 0.383292i
\(506\) −141.881 314.768i −0.280397 0.622070i
\(507\) −197.745 −0.390029
\(508\) 115.939 0.228227
\(509\) −316.428 −0.621666 −0.310833 0.950464i \(-0.600608\pi\)
−0.310833 + 0.950464i \(0.600608\pi\)
\(510\) 213.826 0.419266
\(511\) 10.2573i 0.0200730i
\(512\) 22.6274 0.0441942
\(513\) 505.666i 0.985703i
\(514\) 695.112 1.35236
\(515\) −322.257 −0.625741
\(516\) 245.299i 0.475386i
\(517\) 521.573i 1.00885i
\(518\) 87.7283 0.169360
\(519\) 305.593 0.588811
\(520\) 95.4460i 0.183550i
\(521\) 798.875i 1.53335i 0.642035 + 0.766675i \(0.278090\pi\)
−0.642035 + 0.766675i \(0.721910\pi\)
\(522\) 107.404 0.205754
\(523\) 819.091i 1.56614i −0.621934 0.783070i \(-0.713653\pi\)
0.621934 0.783070i \(-0.286347\pi\)
\(524\) −190.162 −0.362905
\(525\) 19.6772i 0.0374803i
\(526\) 378.773i 0.720101i
\(527\) 544.353i 1.03293i
\(528\) 142.916i 0.270674i
\(529\) 350.341 396.361i 0.662271 0.749265i
\(530\) 329.676 0.622031
\(531\) 124.744 0.234924
\(532\) −52.6649 −0.0989942
\(533\) −142.420 −0.267204
\(534\) 665.595i 1.24643i
\(535\) 23.3768 0.0436950
\(536\) 168.222i 0.313847i
\(537\) −1015.29 −1.89068
\(538\) 135.338 0.251558
\(539\) 505.614i 0.938060i
\(540\) 100.408i 0.185942i
\(541\) 289.616 0.535335 0.267668 0.963511i \(-0.413747\pi\)
0.267668 + 0.963511i \(0.413747\pi\)
\(542\) −639.585 −1.18005
\(543\) 836.600i 1.54070i
\(544\) 113.639i 0.208895i
\(545\) 154.562 0.283600
\(546\) 83.9914i 0.153830i
\(547\) 996.117 1.82106 0.910528 0.413448i \(-0.135676\pi\)
0.910528 + 0.413448i \(0.135676\pi\)
\(548\) 397.422i 0.725223i
\(549\) 54.7861i 0.0997926i
\(550\) 75.0579i 0.136469i
\(551\) 734.202i 1.33249i
\(552\) 199.626 89.9811i 0.361642 0.163009i
\(553\) −66.7427 −0.120692
\(554\) −123.713 −0.223309
\(555\) −399.333 −0.719519
\(556\) −0.258959 −0.000465754
\(557\) 937.756i 1.68358i 0.539802 + 0.841792i \(0.318499\pi\)
−0.539802 + 0.841792i \(0.681501\pi\)
\(558\) −89.2772 −0.159995
\(559\) 549.901i 0.983723i
\(560\) −10.4575 −0.0186741
\(561\) 717.747 1.27941
\(562\) 328.320i 0.584200i
\(563\) 785.252i 1.39476i −0.716700 0.697382i \(-0.754348\pi\)
0.716700 0.697382i \(-0.245652\pi\)
\(564\) 330.783 0.586494
\(565\) −306.932 −0.543243
\(566\) 338.516i 0.598085i
\(567\) 112.873i 0.199070i
\(568\) 156.166 0.274940
\(569\) 403.851i 0.709755i 0.934913 + 0.354877i \(0.115477\pi\)
−0.934913 + 0.354877i \(0.884523\pi\)
\(570\) 239.727 0.420574
\(571\) 335.474i 0.587519i −0.955879 0.293760i \(-0.905093\pi\)
0.955879 0.293760i \(-0.0949065\pi\)
\(572\) 320.383i 0.560110i
\(573\) 492.715i 0.859887i
\(574\) 15.6042i 0.0271850i
\(575\) 104.842 47.2571i 0.182333 0.0821863i
\(576\) 18.6375 0.0323567
\(577\) −152.703 −0.264649 −0.132325 0.991206i \(-0.542244\pi\)
−0.132325 + 0.991206i \(0.542244\pi\)
\(578\) −162.004 −0.280284
\(579\) 406.097 0.701376
\(580\) 145.788i 0.251359i
\(581\) 64.5143 0.111040
\(582\) 94.5538i 0.162464i
\(583\) 1106.62 1.89815
\(584\) −24.8139 −0.0424896
\(585\) 78.6157i 0.134386i
\(586\) 822.831i 1.40415i
\(587\) 129.262 0.220207 0.110104 0.993920i \(-0.464882\pi\)
0.110104 + 0.993920i \(0.464882\pi\)
\(588\) −320.662 −0.545343
\(589\) 610.291i 1.03615i
\(590\) 169.326i 0.286994i
\(591\) −106.533 −0.180260
\(592\) 212.227i 0.358492i
\(593\) −879.853 −1.48373 −0.741866 0.670548i \(-0.766059\pi\)
−0.741866 + 0.670548i \(0.766059\pi\)
\(594\) 337.040i 0.567408i
\(595\) 52.5194i 0.0882678i
\(596\) 127.749i 0.214344i
\(597\) 126.054i 0.211145i
\(598\) 447.514 201.716i 0.748351 0.337317i
\(599\) −709.708 −1.18482 −0.592411 0.805636i \(-0.701824\pi\)
−0.592411 + 0.805636i \(0.701824\pi\)
\(600\) 47.6019 0.0793364
\(601\) 238.861 0.397439 0.198719 0.980056i \(-0.436322\pi\)
0.198719 + 0.980056i \(0.436322\pi\)
\(602\) −60.2498 −0.100083
\(603\) 138.559i 0.229782i
\(604\) −70.5346 −0.116779
\(605\) 18.6182i 0.0307738i
\(606\) −412.060 −0.679967
\(607\) −1082.53 −1.78341 −0.891703 0.452621i \(-0.850489\pi\)
−0.891703 + 0.452621i \(0.850489\pi\)
\(608\) 127.404i 0.209546i
\(609\) 128.292i 0.210660i
\(610\) 74.3659 0.121911
\(611\) 741.535 1.21364
\(612\) 93.6004i 0.152942i
\(613\) 54.0902i 0.0882384i 0.999026 + 0.0441192i \(0.0140481\pi\)
−0.999026 + 0.0441192i \(0.985952\pi\)
\(614\) 155.753 0.253669
\(615\) 71.0292i 0.115495i
\(616\) −35.1026 −0.0569848
\(617\) 454.342i 0.736373i −0.929752 0.368186i \(-0.879979\pi\)
0.929752 0.368186i \(-0.120021\pi\)
\(618\) 686.027i 1.11008i
\(619\) 153.676i 0.248264i −0.992266 0.124132i \(-0.960385\pi\)
0.992266 0.124132i \(-0.0396147\pi\)
\(620\) 121.184i 0.195458i
\(621\) −470.781 + 212.204i −0.758102 + 0.341713i
\(622\) −421.577 −0.677776
\(623\) −163.482 −0.262411
\(624\) 203.187 0.325621
\(625\) 25.0000 0.0400000
\(626\) 154.820i 0.247316i
\(627\) 804.689 1.28340
\(628\) 578.271i 0.920814i
\(629\) 1065.84 1.69450
\(630\) −8.61350 −0.0136722
\(631\) 1241.15i 1.96696i −0.181027 0.983478i \(-0.557942\pi\)
0.181027 0.983478i \(-0.442058\pi\)
\(632\) 161.460i 0.255475i
\(633\) 146.948 0.232146
\(634\) 670.950 1.05828
\(635\) 129.624i 0.204133i
\(636\) 701.821i 1.10349i
\(637\) −718.846 −1.12849
\(638\) 489.366i 0.767032i
\(639\) 128.629 0.201297
\(640\) 25.2982i 0.0395285i
\(641\) 545.978i 0.851759i 0.904780 + 0.425880i \(0.140035\pi\)
−0.904780 + 0.425880i \(0.859965\pi\)
\(642\) 49.7651i 0.0775157i
\(643\) 539.118i 0.838441i 0.907884 + 0.419221i \(0.137697\pi\)
−0.907884 + 0.419221i \(0.862303\pi\)
\(644\) −22.1009 49.0317i −0.0343182 0.0761362i
\(645\) 274.253 0.425198
\(646\) −639.844 −0.990470
\(647\) 652.715 1.00883 0.504417 0.863460i \(-0.331708\pi\)
0.504417 + 0.863460i \(0.331708\pi\)
\(648\) −273.056 −0.421382
\(649\) 568.376i 0.875772i
\(650\) 106.712 0.164172
\(651\) 106.640i 0.163810i
\(652\) −92.5071 −0.141882
\(653\) 374.815 0.573989 0.286995 0.957932i \(-0.407344\pi\)
0.286995 + 0.957932i \(0.407344\pi\)
\(654\) 329.034i 0.503110i
\(655\) 212.608i 0.324592i
\(656\) 37.7488 0.0575439
\(657\) −20.4384 −0.0311087
\(658\) 81.2460i 0.123474i
\(659\) 440.090i 0.667815i −0.942606 0.333907i \(-0.891633\pi\)
0.942606 0.333907i \(-0.108367\pi\)
\(660\) 159.785 0.242098
\(661\) 72.6725i 0.109943i −0.998488 0.0549716i \(-0.982493\pi\)
0.998488 0.0549716i \(-0.0175068\pi\)
\(662\) 361.144 0.545535
\(663\) 1020.44i 1.53913i
\(664\) 156.069i 0.235044i
\(665\) 58.8812i 0.0885431i
\(666\) 174.805i 0.262469i
\(667\) −683.552 + 308.110i −1.02482 + 0.461933i
\(668\) −181.747 −0.272076
\(669\) −1173.45 −1.75404
\(670\) −188.078 −0.280713
\(671\) 249.623 0.372017
\(672\) 22.2622i 0.0331282i
\(673\) −1052.88 −1.56445 −0.782227 0.622993i \(-0.785916\pi\)
−0.782227 + 0.622993i \(0.785916\pi\)
\(674\) 648.398i 0.962014i
\(675\) −112.260 −0.166311
\(676\) 117.497 0.173812
\(677\) 393.587i 0.581369i −0.956819 0.290684i \(-0.906117\pi\)
0.956819 0.290684i \(-0.0938830\pi\)
\(678\) 653.404i 0.963722i
\(679\) 23.2241 0.0342034
\(680\) −127.052 −0.186841
\(681\) 591.714i 0.868889i
\(682\) 406.776i 0.596446i
\(683\) −645.240 −0.944714 −0.472357 0.881407i \(-0.656597\pi\)
−0.472357 + 0.881407i \(0.656597\pi\)
\(684\) 104.938i 0.153419i
\(685\) 444.331 0.648659
\(686\) 159.781i 0.232916i
\(687\) 4.85195i 0.00706252i
\(688\) 145.753i 0.211850i
\(689\) 1573.31i 2.28347i
\(690\) 100.602 + 223.189i 0.145800 + 0.323462i
\(691\) 548.216 0.793366 0.396683 0.917956i \(-0.370161\pi\)
0.396683 + 0.917956i \(0.370161\pi\)
\(692\) −181.579 −0.262397
\(693\) −28.9129 −0.0417213
\(694\) 722.205 1.04064
\(695\) 0.289525i 0.000416583i
\(696\) −310.357 −0.445915
\(697\) 189.581i 0.271995i
\(698\) −837.030 −1.19918
\(699\) 381.753 0.546141
\(700\) 11.6919i 0.0167026i
\(701\) 92.2064i 0.131536i −0.997835 0.0657678i \(-0.979050\pi\)
0.997835 0.0657678i \(-0.0209496\pi\)
\(702\) −479.179 −0.682592
\(703\) 1194.95 1.69978
\(704\) 84.9183i 0.120623i
\(705\) 369.826i 0.524576i
\(706\) 238.060 0.337195
\(707\) 101.209i 0.143153i
\(708\) −360.465 −0.509132
\(709\) 922.612i 1.30129i −0.759384 0.650643i \(-0.774499\pi\)
0.759384 0.650643i \(-0.225501\pi\)
\(710\) 174.599i 0.245914i
\(711\) 132.989i 0.187045i
\(712\) 395.486i 0.555458i
\(713\) 568.189 256.110i 0.796899 0.359201i
\(714\) 111.804 0.156589
\(715\) 358.199 0.500977
\(716\) 603.271 0.842557
\(717\) −1236.18 −1.72410
\(718\) 53.1347i 0.0740037i
\(719\) 606.887 0.844071 0.422035 0.906579i \(-0.361316\pi\)
0.422035 + 0.906579i \(0.361316\pi\)
\(720\) 20.8373i 0.0289407i
\(721\) −168.500 −0.233704
\(722\) −206.819 −0.286452
\(723\) 741.740i 1.02592i
\(724\) 497.095i 0.686595i
\(725\) −162.996 −0.224823
\(726\) −39.6347 −0.0545932
\(727\) 787.544i 1.08328i −0.840611 0.541640i \(-0.817804\pi\)
0.840611 0.541640i \(-0.182196\pi\)
\(728\) 49.9064i 0.0685527i
\(729\) 455.246 0.624481
\(730\) 27.7428i 0.0380038i
\(731\) −731.995 −1.00136
\(732\) 158.312i 0.216273i
\(733\) 415.085i 0.566282i 0.959078 + 0.283141i \(0.0913765\pi\)
−0.959078 + 0.283141i \(0.908624\pi\)
\(734\) 603.921i 0.822780i
\(735\) 358.510i 0.487769i
\(736\) −118.615 + 53.4653i −0.161161 + 0.0726431i
\(737\) −631.319 −0.856606
\(738\) 31.0924 0.0421307
\(739\) 639.964 0.865987 0.432993 0.901397i \(-0.357457\pi\)
0.432993 + 0.901397i \(0.357457\pi\)
\(740\) 237.277 0.320645
\(741\) 1144.05i 1.54393i
\(742\) 172.380 0.232318
\(743\) 743.739i 1.00099i −0.865738 0.500497i \(-0.833151\pi\)
0.865738 0.500497i \(-0.166849\pi\)
\(744\) 257.978 0.346745
\(745\) 142.828 0.191715
\(746\) 523.231i 0.701382i
\(747\) 128.549i 0.172087i
\(748\) −426.474 −0.570152
\(749\) 12.2232 0.0163193
\(750\) 53.2205i 0.0709607i
\(751\) 517.047i 0.688478i −0.938882 0.344239i \(-0.888137\pi\)
0.938882 0.344239i \(-0.111863\pi\)
\(752\) −196.546 −0.261364
\(753\) 1481.73i 1.96777i
\(754\) −695.746 −0.922740
\(755\) 78.8601i 0.104450i
\(756\) 52.5011i 0.0694460i
\(757\) 911.823i 1.20452i −0.798299 0.602261i \(-0.794267\pi\)
0.798299 0.602261i \(-0.205733\pi\)
\(758\) 111.441i 0.147020i
\(759\) 337.689 + 749.176i 0.444914 + 0.987057i
\(760\) −142.442 −0.187424
\(761\) 954.073 1.25371 0.626855 0.779136i \(-0.284342\pi\)
0.626855 + 0.779136i \(0.284342\pi\)
\(762\) −275.947 −0.362135
\(763\) 80.8166 0.105920
\(764\) 292.764i 0.383199i
\(765\) −104.648 −0.136795
\(766\) 359.328i 0.469097i
\(767\) −808.076 −1.05355
\(768\) −53.8553 −0.0701242
\(769\) 276.277i 0.359268i −0.983734 0.179634i \(-0.942509\pi\)
0.983734 0.179634i \(-0.0574913\pi\)
\(770\) 39.2459i 0.0509687i
\(771\) −1654.43 −2.14583
\(772\) −241.296 −0.312560
\(773\) 40.8440i 0.0528383i −0.999651 0.0264192i \(-0.991590\pi\)
0.999651 0.0264192i \(-0.00841046\pi\)
\(774\) 120.052i 0.155106i
\(775\) 135.488 0.174823
\(776\) 56.1824i 0.0724000i
\(777\) −208.801 −0.268728
\(778\) 455.891i 0.585978i
\(779\) 212.545i 0.272843i
\(780\) 227.170i 0.291244i
\(781\) 586.074i 0.750415i
\(782\) −268.512 595.703i −0.343365 0.761768i
\(783\) 731.919 0.934763
\(784\) 190.532 0.243026
\(785\) −646.527 −0.823601
\(786\) 452.603 0.575831
\(787\) 1364.69i 1.73404i −0.498274 0.867019i \(-0.666033\pi\)
0.498274