Properties

Label 429.2.b.b.298.1
Level $429$
Weight $2$
Character 429.298
Analytic conductor $3.426$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} + \cdots)\)
Defining polynomial: \(x^{14} + 23 x^{12} + 201 x^{10} + 835 x^{8} + 1695 x^{6} + 1565 x^{4} + 511 x^{2} + 49\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 298.1
Root \(-2.73878i\) of defining polynomial
Character \(\chi\) \(=\) 429.298
Dual form 429.2.b.b.298.14

$q$-expansion

\(f(q)\) \(=\) \(q-2.73878i q^{2} +1.00000 q^{3} -5.50093 q^{4} +2.84154i q^{5} -2.73878i q^{6} +3.93129i q^{7} +9.58828i q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.73878i q^{2} +1.00000 q^{3} -5.50093 q^{4} +2.84154i q^{5} -2.73878i q^{6} +3.93129i q^{7} +9.58828i q^{8} +1.00000 q^{9} +7.78236 q^{10} +1.00000i q^{11} -5.50093 q^{12} +(1.78444 - 3.13301i) q^{13} +10.7670 q^{14} +2.84154i q^{15} +15.2584 q^{16} -3.81818 q^{17} -2.73878i q^{18} +2.94082i q^{19} -15.6311i q^{20} +3.93129i q^{21} +2.73878 q^{22} +1.89484 q^{23} +9.58828i q^{24} -3.07435 q^{25} +(-8.58064 - 4.88720i) q^{26} +1.00000 q^{27} -21.6258i q^{28} -2.09928 q^{29} +7.78236 q^{30} +6.16032i q^{31} -22.6127i q^{32} +1.00000i q^{33} +10.4572i q^{34} -11.1709 q^{35} -5.50093 q^{36} +8.34404i q^{37} +8.05426 q^{38} +(1.78444 - 3.13301i) q^{39} -27.2455 q^{40} -6.35787i q^{41} +10.7670 q^{42} +11.7275 q^{43} -5.50093i q^{44} +2.84154i q^{45} -5.18956i q^{46} +5.31137i q^{47} +15.2584 q^{48} -8.45506 q^{49} +8.41997i q^{50} -3.81818 q^{51} +(-9.81609 + 17.2345i) q^{52} -2.37985 q^{53} -2.73878i q^{54} -2.84154 q^{55} -37.6943 q^{56} +2.94082i q^{57} +5.74947i q^{58} -5.38624i q^{59} -15.6311i q^{60} -2.34857 q^{61} +16.8718 q^{62} +3.93129i q^{63} -31.4147 q^{64} +(8.90258 + 5.07056i) q^{65} +2.73878 q^{66} -10.4731i q^{67} +21.0035 q^{68} +1.89484 q^{69} +30.5947i q^{70} -10.0939i q^{71} +9.58828i q^{72} -15.1079i q^{73} +22.8525 q^{74} -3.07435 q^{75} -16.1772i q^{76} -3.93129 q^{77} +(-8.58064 - 4.88720i) q^{78} +1.57120 q^{79} +43.3572i q^{80} +1.00000 q^{81} -17.4128 q^{82} -10.6736i q^{83} -21.6258i q^{84} -10.8495i q^{85} -32.1190i q^{86} -2.09928 q^{87} -9.58828 q^{88} +3.23647i q^{89} +7.78236 q^{90} +(12.3168 + 7.01516i) q^{91} -10.4234 q^{92} +6.16032i q^{93} +14.5467 q^{94} -8.35645 q^{95} -22.6127i q^{96} +17.7914i q^{97} +23.1566i q^{98} +1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 14q^{3} - 18q^{4} + 14q^{9} + O(q^{10}) \) \( 14q + 14q^{3} - 18q^{4} + 14q^{9} - 18q^{12} + 16q^{14} + 34q^{16} + 4q^{17} + 6q^{22} - 8q^{23} - 26q^{25} - 6q^{26} + 14q^{27} - 24q^{29} - 8q^{35} - 18q^{36} - 32q^{38} - 20q^{40} + 16q^{42} + 32q^{43} + 34q^{48} - 46q^{49} + 4q^{51} + 4q^{52} + 20q^{53} + 12q^{55} - 32q^{56} - 20q^{61} + 72q^{62} - 58q^{64} + 12q^{65} + 6q^{66} - 20q^{68} - 8q^{69} - 26q^{75} - 12q^{77} - 6q^{78} + 12q^{79} + 14q^{81} + 20q^{82} - 24q^{87} - 30q^{88} + 16q^{91} - 24q^{92} + 64q^{94} - 36q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.73878i 1.93661i −0.249768 0.968306i \(-0.580354\pi\)
0.249768 0.968306i \(-0.419646\pi\)
\(3\) 1.00000 0.577350
\(4\) −5.50093 −2.75046
\(5\) 2.84154i 1.27078i 0.772193 + 0.635388i \(0.219160\pi\)
−0.772193 + 0.635388i \(0.780840\pi\)
\(6\) 2.73878i 1.11810i
\(7\) 3.93129i 1.48589i 0.669353 + 0.742944i \(0.266571\pi\)
−0.669353 + 0.742944i \(0.733429\pi\)
\(8\) 9.58828i 3.38997i
\(9\) 1.00000 0.333333
\(10\) 7.78236 2.46100
\(11\) 1.00000i 0.301511i
\(12\) −5.50093 −1.58798
\(13\) 1.78444 3.13301i 0.494915 0.868941i
\(14\) 10.7670 2.87759
\(15\) 2.84154i 0.733682i
\(16\) 15.2584 3.81459
\(17\) −3.81818 −0.926044 −0.463022 0.886347i \(-0.653235\pi\)
−0.463022 + 0.886347i \(0.653235\pi\)
\(18\) 2.73878i 0.645537i
\(19\) 2.94082i 0.674670i 0.941385 + 0.337335i \(0.109526\pi\)
−0.941385 + 0.337335i \(0.890474\pi\)
\(20\) 15.6311i 3.49522i
\(21\) 3.93129i 0.857878i
\(22\) 2.73878 0.583910
\(23\) 1.89484 0.395102 0.197551 0.980293i \(-0.436701\pi\)
0.197551 + 0.980293i \(0.436701\pi\)
\(24\) 9.58828i 1.95720i
\(25\) −3.07435 −0.614869
\(26\) −8.58064 4.88720i −1.68280 0.958459i
\(27\) 1.00000 0.192450
\(28\) 21.6258i 4.08688i
\(29\) −2.09928 −0.389826 −0.194913 0.980821i \(-0.562443\pi\)
−0.194913 + 0.980821i \(0.562443\pi\)
\(30\) 7.78236 1.42086
\(31\) 6.16032i 1.10643i 0.833040 + 0.553213i \(0.186598\pi\)
−0.833040 + 0.553213i \(0.813402\pi\)
\(32\) 22.6127i 3.99741i
\(33\) 1.00000i 0.174078i
\(34\) 10.4572i 1.79339i
\(35\) −11.1709 −1.88823
\(36\) −5.50093 −0.916821
\(37\) 8.34404i 1.37175i 0.727719 + 0.685876i \(0.240581\pi\)
−0.727719 + 0.685876i \(0.759419\pi\)
\(38\) 8.05426 1.30657
\(39\) 1.78444 3.13301i 0.285740 0.501683i
\(40\) −27.2455 −4.30789
\(41\) 6.35787i 0.992933i −0.868056 0.496466i \(-0.834631\pi\)
0.868056 0.496466i \(-0.165369\pi\)
\(42\) 10.7670 1.66138
\(43\) 11.7275 1.78842 0.894212 0.447643i \(-0.147736\pi\)
0.894212 + 0.447643i \(0.147736\pi\)
\(44\) 5.50093i 0.829296i
\(45\) 2.84154i 0.423592i
\(46\) 5.18956i 0.765159i
\(47\) 5.31137i 0.774743i 0.921924 + 0.387371i \(0.126617\pi\)
−0.921924 + 0.387371i \(0.873383\pi\)
\(48\) 15.2584 2.20235
\(49\) −8.45506 −1.20787
\(50\) 8.41997i 1.19076i
\(51\) −3.81818 −0.534652
\(52\) −9.81609 + 17.2345i −1.36125 + 2.38999i
\(53\) −2.37985 −0.326898 −0.163449 0.986552i \(-0.552262\pi\)
−0.163449 + 0.986552i \(0.552262\pi\)
\(54\) 2.73878i 0.372701i
\(55\) −2.84154 −0.383153
\(56\) −37.6943 −5.03712
\(57\) 2.94082i 0.389521i
\(58\) 5.74947i 0.754942i
\(59\) 5.38624i 0.701229i −0.936520 0.350615i \(-0.885973\pi\)
0.936520 0.350615i \(-0.114027\pi\)
\(60\) 15.6311i 2.01797i
\(61\) −2.34857 −0.300703 −0.150352 0.988633i \(-0.548041\pi\)
−0.150352 + 0.988633i \(0.548041\pi\)
\(62\) 16.8718 2.14272
\(63\) 3.93129i 0.495296i
\(64\) −31.4147 −3.92684
\(65\) 8.90258 + 5.07056i 1.10423 + 0.628926i
\(66\) 2.73878 0.337121
\(67\) 10.4731i 1.27949i −0.768588 0.639744i \(-0.779040\pi\)
0.768588 0.639744i \(-0.220960\pi\)
\(68\) 21.0035 2.54705
\(69\) 1.89484 0.228112
\(70\) 30.5947i 3.65677i
\(71\) 10.0939i 1.19793i −0.800776 0.598964i \(-0.795579\pi\)
0.800776 0.598964i \(-0.204421\pi\)
\(72\) 9.58828i 1.12999i
\(73\) 15.1079i 1.76824i −0.467260 0.884120i \(-0.654759\pi\)
0.467260 0.884120i \(-0.345241\pi\)
\(74\) 22.8525 2.65655
\(75\) −3.07435 −0.354995
\(76\) 16.1772i 1.85566i
\(77\) −3.93129 −0.448012
\(78\) −8.58064 4.88720i −0.971566 0.553366i
\(79\) 1.57120 0.176774 0.0883872 0.996086i \(-0.471829\pi\)
0.0883872 + 0.996086i \(0.471829\pi\)
\(80\) 43.3572i 4.84748i
\(81\) 1.00000 0.111111
\(82\) −17.4128 −1.92293
\(83\) 10.6736i 1.17157i −0.810465 0.585787i \(-0.800785\pi\)
0.810465 0.585787i \(-0.199215\pi\)
\(84\) 21.6258i 2.35956i
\(85\) 10.8495i 1.17679i
\(86\) 32.1190i 3.46348i
\(87\) −2.09928 −0.225066
\(88\) −9.58828 −1.02211
\(89\) 3.23647i 0.343065i 0.985178 + 0.171533i \(0.0548719\pi\)
−0.985178 + 0.171533i \(0.945128\pi\)
\(90\) 7.78236 0.820333
\(91\) 12.3168 + 7.01516i 1.29115 + 0.735389i
\(92\) −10.4234 −1.08671
\(93\) 6.16032i 0.638795i
\(94\) 14.5467 1.50038
\(95\) −8.35645 −0.857354
\(96\) 22.6127i 2.30790i
\(97\) 17.7914i 1.80645i 0.429172 + 0.903223i \(0.358805\pi\)
−0.429172 + 0.903223i \(0.641195\pi\)
\(98\) 23.1566i 2.33917i
\(99\) 1.00000i 0.100504i
\(100\) 16.9118 1.69118
\(101\) 12.1229 1.20627 0.603136 0.797638i \(-0.293917\pi\)
0.603136 + 0.797638i \(0.293917\pi\)
\(102\) 10.4572i 1.03541i
\(103\) 3.40983 0.335981 0.167990 0.985789i \(-0.446272\pi\)
0.167990 + 0.985789i \(0.446272\pi\)
\(104\) 30.0402 + 17.1097i 2.94568 + 1.67775i
\(105\) −11.1709 −1.09017
\(106\) 6.51790i 0.633075i
\(107\) −12.2352 −1.18282 −0.591411 0.806370i \(-0.701429\pi\)
−0.591411 + 0.806370i \(0.701429\pi\)
\(108\) −5.50093 −0.529327
\(109\) 8.72763i 0.835956i 0.908457 + 0.417978i \(0.137261\pi\)
−0.908457 + 0.417978i \(0.862739\pi\)
\(110\) 7.78236i 0.742019i
\(111\) 8.34404i 0.791981i
\(112\) 59.9850i 5.66805i
\(113\) 0.0155525 0.00146305 0.000731527 1.00000i \(-0.499767\pi\)
0.000731527 1.00000i \(0.499767\pi\)
\(114\) 8.05426 0.754351
\(115\) 5.38427i 0.502086i
\(116\) 11.5480 1.07220
\(117\) 1.78444 3.13301i 0.164972 0.289647i
\(118\) −14.7517 −1.35801
\(119\) 15.0104i 1.37600i
\(120\) −27.2455 −2.48716
\(121\) −1.00000 −0.0909091
\(122\) 6.43222i 0.582346i
\(123\) 6.35787i 0.573270i
\(124\) 33.8875i 3.04318i
\(125\) 5.47182i 0.489414i
\(126\) 10.7670 0.959196
\(127\) 5.91514 0.524883 0.262442 0.964948i \(-0.415472\pi\)
0.262442 + 0.964948i \(0.415472\pi\)
\(128\) 40.8125i 3.60735i
\(129\) 11.7275 1.03255
\(130\) 13.8872 24.3822i 1.21799 2.13846i
\(131\) −1.32191 −0.115496 −0.0577481 0.998331i \(-0.518392\pi\)
−0.0577481 + 0.998331i \(0.518392\pi\)
\(132\) 5.50093i 0.478794i
\(133\) −11.5612 −1.00248
\(134\) −28.6835 −2.47787
\(135\) 2.84154i 0.244561i
\(136\) 36.6097i 3.13926i
\(137\) 4.82127i 0.411909i 0.978562 + 0.205955i \(0.0660299\pi\)
−0.978562 + 0.205955i \(0.933970\pi\)
\(138\) 5.18956i 0.441765i
\(139\) 17.1877 1.45784 0.728919 0.684600i \(-0.240023\pi\)
0.728919 + 0.684600i \(0.240023\pi\)
\(140\) 61.4504 5.19351
\(141\) 5.31137i 0.447298i
\(142\) −27.6451 −2.31992
\(143\) 3.13301 + 1.78444i 0.261996 + 0.149223i
\(144\) 15.2584 1.27153
\(145\) 5.96518i 0.495382i
\(146\) −41.3771 −3.42439
\(147\) −8.45506 −0.697361
\(148\) 45.8999i 3.77295i
\(149\) 5.31754i 0.435629i 0.975990 + 0.217815i \(0.0698929\pi\)
−0.975990 + 0.217815i \(0.930107\pi\)
\(150\) 8.41997i 0.687487i
\(151\) 6.77573i 0.551401i −0.961244 0.275700i \(-0.911090\pi\)
0.961244 0.275700i \(-0.0889098\pi\)
\(152\) −28.1974 −2.28711
\(153\) −3.81818 −0.308681
\(154\) 10.7670i 0.867626i
\(155\) −17.5048 −1.40602
\(156\) −9.81609 + 17.2345i −0.785916 + 1.37986i
\(157\) 16.2884 1.29995 0.649977 0.759954i \(-0.274779\pi\)
0.649977 + 0.759954i \(0.274779\pi\)
\(158\) 4.30319i 0.342343i
\(159\) −2.37985 −0.188735
\(160\) 64.2550 5.07981
\(161\) 7.44918i 0.587077i
\(162\) 2.73878i 0.215179i
\(163\) 11.4032i 0.893170i 0.894741 + 0.446585i \(0.147360\pi\)
−0.894741 + 0.446585i \(0.852640\pi\)
\(164\) 34.9742i 2.73103i
\(165\) −2.84154 −0.221214
\(166\) −29.2325 −2.26888
\(167\) 14.7302i 1.13985i −0.821695 0.569927i \(-0.806971\pi\)
0.821695 0.569927i \(-0.193029\pi\)
\(168\) −37.6943 −2.90818
\(169\) −6.63153 11.1814i −0.510118 0.860105i
\(170\) −29.7144 −2.27899
\(171\) 2.94082i 0.224890i
\(172\) −64.5121 −4.91900
\(173\) −0.186647 −0.0141905 −0.00709527 0.999975i \(-0.502259\pi\)
−0.00709527 + 0.999975i \(0.502259\pi\)
\(174\) 5.74947i 0.435866i
\(175\) 12.0862i 0.913627i
\(176\) 15.2584i 1.15014i
\(177\) 5.38624i 0.404855i
\(178\) 8.86399 0.664384
\(179\) −10.9555 −0.818856 −0.409428 0.912342i \(-0.634272\pi\)
−0.409428 + 0.912342i \(0.634272\pi\)
\(180\) 15.6311i 1.16507i
\(181\) 8.52034 0.633312 0.316656 0.948540i \(-0.397440\pi\)
0.316656 + 0.948540i \(0.397440\pi\)
\(182\) 19.2130 33.7330i 1.42416 2.50046i
\(183\) −2.34857 −0.173611
\(184\) 18.1683i 1.33938i
\(185\) −23.7099 −1.74319
\(186\) 16.8718 1.23710
\(187\) 3.81818i 0.279213i
\(188\) 29.2175i 2.13090i
\(189\) 3.93129i 0.285959i
\(190\) 22.8865i 1.66036i
\(191\) −11.8003 −0.853840 −0.426920 0.904289i \(-0.640401\pi\)
−0.426920 + 0.904289i \(0.640401\pi\)
\(192\) −31.4147 −2.26716
\(193\) 10.9405i 0.787518i 0.919214 + 0.393759i \(0.128826\pi\)
−0.919214 + 0.393759i \(0.871174\pi\)
\(194\) 48.7268 3.49838
\(195\) 8.90258 + 5.07056i 0.637527 + 0.363111i
\(196\) 46.5107 3.32219
\(197\) 9.43307i 0.672079i −0.941848 0.336039i \(-0.890912\pi\)
0.941848 0.336039i \(-0.109088\pi\)
\(198\) 2.73878 0.194637
\(199\) 15.3198 1.08599 0.542996 0.839735i \(-0.317290\pi\)
0.542996 + 0.839735i \(0.317290\pi\)
\(200\) 29.4777i 2.08439i
\(201\) 10.4731i 0.738713i
\(202\) 33.2020i 2.33608i
\(203\) 8.25288i 0.579238i
\(204\) 21.0035 1.47054
\(205\) 18.0661 1.26179
\(206\) 9.33878i 0.650664i
\(207\) 1.89484 0.131701
\(208\) 27.2277 47.8046i 1.88790 3.31465i
\(209\) −2.94082 −0.203421
\(210\) 30.5947i 2.11124i
\(211\) 2.91243 0.200500 0.100250 0.994962i \(-0.468036\pi\)
0.100250 + 0.994962i \(0.468036\pi\)
\(212\) 13.0914 0.899122
\(213\) 10.0939i 0.691625i
\(214\) 33.5096i 2.29067i
\(215\) 33.3241i 2.27269i
\(216\) 9.58828i 0.652400i
\(217\) −24.2180 −1.64403
\(218\) 23.9031 1.61892
\(219\) 15.1079i 1.02089i
\(220\) 15.6311 1.05385
\(221\) −6.81332 + 11.9624i −0.458313 + 0.804677i
\(222\) 22.8525 1.53376
\(223\) 10.8511i 0.726641i −0.931664 0.363320i \(-0.881643\pi\)
0.931664 0.363320i \(-0.118357\pi\)
\(224\) 88.8973 5.93970
\(225\) −3.07435 −0.204956
\(226\) 0.0425948i 0.00283337i
\(227\) 0.322636i 0.0214141i −0.999943 0.0107070i \(-0.996592\pi\)
0.999943 0.0107070i \(-0.00340822\pi\)
\(228\) 16.1772i 1.07136i
\(229\) 5.94060i 0.392566i −0.980547 0.196283i \(-0.937113\pi\)
0.980547 0.196283i \(-0.0628871\pi\)
\(230\) 14.7463 0.972345
\(231\) −3.93129 −0.258660
\(232\) 20.1285i 1.32150i
\(233\) 12.6202 0.826774 0.413387 0.910555i \(-0.364346\pi\)
0.413387 + 0.910555i \(0.364346\pi\)
\(234\) −8.58064 4.88720i −0.560934 0.319486i
\(235\) −15.0925 −0.984524
\(236\) 29.6293i 1.92871i
\(237\) 1.57120 0.102061
\(238\) −41.1101 −2.66477
\(239\) 20.7706i 1.34354i −0.740762 0.671768i \(-0.765535\pi\)
0.740762 0.671768i \(-0.234465\pi\)
\(240\) 43.3572i 2.79870i
\(241\) 18.2163i 1.17341i −0.809800 0.586706i \(-0.800424\pi\)
0.809800 0.586706i \(-0.199576\pi\)
\(242\) 2.73878i 0.176056i
\(243\) 1.00000 0.0641500
\(244\) 12.9193 0.827074
\(245\) 24.0254i 1.53492i
\(246\) −17.4128 −1.11020
\(247\) 9.21362 + 5.24772i 0.586249 + 0.333905i
\(248\) −59.0668 −3.75075
\(249\) 10.6736i 0.676409i
\(250\) 14.9861 0.947806
\(251\) 22.6662 1.43068 0.715340 0.698776i \(-0.246272\pi\)
0.715340 + 0.698776i \(0.246272\pi\)
\(252\) 21.6258i 1.36229i
\(253\) 1.89484i 0.119128i
\(254\) 16.2003i 1.01650i
\(255\) 10.8495i 0.679422i
\(256\) 48.9471 3.05920
\(257\) −17.7333 −1.10617 −0.553087 0.833124i \(-0.686550\pi\)
−0.553087 + 0.833124i \(0.686550\pi\)
\(258\) 32.1190i 1.99964i
\(259\) −32.8028 −2.03827
\(260\) −48.9724 27.8928i −3.03714 1.72984i
\(261\) −2.09928 −0.129942
\(262\) 3.62044i 0.223671i
\(263\) 29.5107 1.81971 0.909853 0.414930i \(-0.136194\pi\)
0.909853 + 0.414930i \(0.136194\pi\)
\(264\) −9.58828 −0.590118
\(265\) 6.76245i 0.415414i
\(266\) 31.6637i 1.94142i
\(267\) 3.23647i 0.198069i
\(268\) 57.6116i 3.51919i
\(269\) −9.02091 −0.550015 −0.275007 0.961442i \(-0.588680\pi\)
−0.275007 + 0.961442i \(0.588680\pi\)
\(270\) 7.78236 0.473619
\(271\) 4.58320i 0.278410i 0.990264 + 0.139205i \(0.0444547\pi\)
−0.990264 + 0.139205i \(0.955545\pi\)
\(272\) −58.2591 −3.53248
\(273\) 12.3168 + 7.01516i 0.745446 + 0.424577i
\(274\) 13.2044 0.797708
\(275\) 3.07435i 0.185390i
\(276\) −10.4234 −0.627414
\(277\) −20.9859 −1.26092 −0.630461 0.776221i \(-0.717134\pi\)
−0.630461 + 0.776221i \(0.717134\pi\)
\(278\) 47.0732i 2.82327i
\(279\) 6.16032i 0.368809i
\(280\) 107.110i 6.40104i
\(281\) 10.5360i 0.628524i 0.949336 + 0.314262i \(0.101757\pi\)
−0.949336 + 0.314262i \(0.898243\pi\)
\(282\) 14.5467 0.866242
\(283\) 2.57169 0.152871 0.0764355 0.997075i \(-0.475646\pi\)
0.0764355 + 0.997075i \(0.475646\pi\)
\(284\) 55.5260i 3.29486i
\(285\) −8.35645 −0.494993
\(286\) 4.88720 8.58064i 0.288986 0.507384i
\(287\) 24.9947 1.47539
\(288\) 22.6127i 1.33247i
\(289\) −2.42153 −0.142443
\(290\) −16.3373 −0.959362
\(291\) 17.7914i 1.04295i
\(292\) 83.1072i 4.86348i
\(293\) 5.16162i 0.301545i 0.988568 + 0.150772i \(0.0481761\pi\)
−0.988568 + 0.150772i \(0.951824\pi\)
\(294\) 23.1566i 1.35052i
\(295\) 15.3052 0.891105
\(296\) −80.0050 −4.65019
\(297\) 1.00000i 0.0580259i
\(298\) 14.5636 0.843645
\(299\) 3.38124 5.93656i 0.195542 0.343320i
\(300\) 16.9118 0.976401
\(301\) 46.1042i 2.65740i
\(302\) −18.5572 −1.06785
\(303\) 12.1229 0.696442
\(304\) 44.8720i 2.57359i
\(305\) 6.67355i 0.382126i
\(306\) 10.4572i 0.597796i
\(307\) 30.0561i 1.71539i −0.514156 0.857697i \(-0.671895\pi\)
0.514156 0.857697i \(-0.328105\pi\)
\(308\) 21.6258 1.23224
\(309\) 3.40983 0.193978
\(310\) 47.9418i 2.72291i
\(311\) 21.7462 1.23311 0.616557 0.787310i \(-0.288527\pi\)
0.616557 + 0.787310i \(0.288527\pi\)
\(312\) 30.0402 + 17.1097i 1.70069 + 0.968648i
\(313\) −24.4361 −1.38121 −0.690606 0.723231i \(-0.742656\pi\)
−0.690606 + 0.723231i \(0.742656\pi\)
\(314\) 44.6103i 2.51751i
\(315\) −11.1709 −0.629410
\(316\) −8.64309 −0.486212
\(317\) 21.1040i 1.18532i −0.805454 0.592658i \(-0.798079\pi\)
0.805454 0.592658i \(-0.201921\pi\)
\(318\) 6.51790i 0.365506i
\(319\) 2.09928i 0.117537i
\(320\) 89.2661i 4.99013i
\(321\) −12.2352 −0.682903
\(322\) 20.4017 1.13694
\(323\) 11.2286i 0.624774i
\(324\) −5.50093 −0.305607
\(325\) −5.48600 + 9.63196i −0.304308 + 0.534285i
\(326\) 31.2310 1.72972
\(327\) 8.72763i 0.482639i
\(328\) 60.9611 3.36601
\(329\) −20.8805 −1.15118
\(330\) 7.78236i 0.428405i
\(331\) 0.560518i 0.0308089i −0.999881 0.0154044i \(-0.995096\pi\)
0.999881 0.0154044i \(-0.00490358\pi\)
\(332\) 58.7144i 3.22237i
\(333\) 8.34404i 0.457250i
\(334\) −40.3427 −2.20745
\(335\) 29.7596 1.62594
\(336\) 59.9850i 3.27245i
\(337\) 7.76850 0.423177 0.211589 0.977359i \(-0.432136\pi\)
0.211589 + 0.977359i \(0.432136\pi\)
\(338\) −30.6233 + 18.1623i −1.66569 + 0.987900i
\(339\) 0.0155525 0.000844695
\(340\) 59.6823i 3.23673i
\(341\) −6.16032 −0.333600
\(342\) 8.05426 0.435525
\(343\) 5.72025i 0.308864i
\(344\) 112.446i 6.06270i
\(345\) 5.38427i 0.289879i
\(346\) 0.511186i 0.0274816i
\(347\) −10.1357 −0.544110 −0.272055 0.962282i \(-0.587703\pi\)
−0.272055 + 0.962282i \(0.587703\pi\)
\(348\) 11.5480 0.619037
\(349\) 20.0030i 1.07074i −0.844619 0.535369i \(-0.820173\pi\)
0.844619 0.535369i \(-0.179827\pi\)
\(350\) −33.1013 −1.76934
\(351\) 1.78444 3.13301i 0.0952465 0.167228i
\(352\) 22.6127 1.20526
\(353\) 26.7905i 1.42591i 0.701208 + 0.712957i \(0.252645\pi\)
−0.701208 + 0.712957i \(0.747355\pi\)
\(354\) −14.7517 −0.784047
\(355\) 28.6823 1.52230
\(356\) 17.8036i 0.943589i
\(357\) 15.0104i 0.794433i
\(358\) 30.0049i 1.58581i
\(359\) 26.7347i 1.41101i 0.708707 + 0.705503i \(0.249279\pi\)
−0.708707 + 0.705503i \(0.750721\pi\)
\(360\) −27.2455 −1.43596
\(361\) 10.3516 0.544820
\(362\) 23.3354i 1.22648i
\(363\) −1.00000 −0.0524864
\(364\) −67.7537 38.5899i −3.55126 2.02266i
\(365\) 42.9296 2.24704
\(366\) 6.43222i 0.336218i
\(367\) 1.89563 0.0989512 0.0494756 0.998775i \(-0.484245\pi\)
0.0494756 + 0.998775i \(0.484245\pi\)
\(368\) 28.9122 1.50715
\(369\) 6.35787i 0.330978i
\(370\) 64.9363i 3.37588i
\(371\) 9.35590i 0.485734i
\(372\) 33.8875i 1.75698i
\(373\) −36.7517 −1.90293 −0.951464 0.307759i \(-0.900421\pi\)
−0.951464 + 0.307759i \(0.900421\pi\)
\(374\) −10.4572 −0.540726
\(375\) 5.47182i 0.282564i
\(376\) −50.9269 −2.62635
\(377\) −3.74604 + 6.57707i −0.192931 + 0.338736i
\(378\) 10.7670 0.553792
\(379\) 26.1328i 1.34235i 0.741298 + 0.671176i \(0.234211\pi\)
−0.741298 + 0.671176i \(0.765789\pi\)
\(380\) 45.9682 2.35812
\(381\) 5.91514 0.303042
\(382\) 32.3185i 1.65356i
\(383\) 16.9211i 0.864629i −0.901723 0.432315i \(-0.857697\pi\)
0.901723 0.432315i \(-0.142303\pi\)
\(384\) 40.8125i 2.08270i
\(385\) 11.1709i 0.569323i
\(386\) 29.9638 1.52512
\(387\) 11.7275 0.596142
\(388\) 97.8693i 4.96856i
\(389\) 5.05607 0.256353 0.128177 0.991751i \(-0.459088\pi\)
0.128177 + 0.991751i \(0.459088\pi\)
\(390\) 13.8872 24.3822i 0.703204 1.23464i
\(391\) −7.23484 −0.365882
\(392\) 81.0694i 4.09462i
\(393\) −1.32191 −0.0666818
\(394\) −25.8351 −1.30156
\(395\) 4.46464i 0.224640i
\(396\) 5.50093i 0.276432i
\(397\) 15.7731i 0.791631i 0.918330 + 0.395815i \(0.129538\pi\)
−0.918330 + 0.395815i \(0.870462\pi\)
\(398\) 41.9576i 2.10314i
\(399\) −11.5612 −0.578785
\(400\) −46.9095 −2.34547
\(401\) 8.42218i 0.420584i 0.977639 + 0.210292i \(0.0674414\pi\)
−0.977639 + 0.210292i \(0.932559\pi\)
\(402\) −28.6835 −1.43060
\(403\) 19.3003 + 10.9927i 0.961419 + 0.547587i
\(404\) −66.6872 −3.31781
\(405\) 2.84154i 0.141197i
\(406\) −22.6028 −1.12176
\(407\) −8.34404 −0.413599
\(408\) 36.6097i 1.81245i
\(409\) 31.3861i 1.55194i −0.630768 0.775971i \(-0.717260\pi\)
0.630768 0.775971i \(-0.282740\pi\)
\(410\) 49.4792i 2.44361i
\(411\) 4.82127i 0.237816i
\(412\) −18.7572 −0.924102
\(413\) 21.1749 1.04195
\(414\) 5.18956i 0.255053i
\(415\) 30.3293 1.48881
\(416\) −70.8460 40.3512i −3.47351 1.97838i
\(417\) 17.1877 0.841683
\(418\) 8.05426i 0.393947i
\(419\) −6.62928 −0.323861 −0.161931 0.986802i \(-0.551772\pi\)
−0.161931 + 0.986802i \(0.551772\pi\)
\(420\) 61.4504 2.99847
\(421\) 2.61327i 0.127363i 0.997970 + 0.0636816i \(0.0202842\pi\)
−0.997970 + 0.0636816i \(0.979716\pi\)
\(422\) 7.97651i 0.388290i
\(423\) 5.31137i 0.258248i
\(424\) 22.8187i 1.10817i
\(425\) 11.7384 0.569396
\(426\) −27.6451 −1.33941
\(427\) 9.23291i 0.446812i
\(428\) 67.3050 3.25331
\(429\) 3.13301 + 1.78444i 0.151263 + 0.0861537i
\(430\) 91.2675 4.40131
\(431\) 24.8745i 1.19816i 0.800688 + 0.599081i \(0.204467\pi\)
−0.800688 + 0.599081i \(0.795533\pi\)
\(432\) 15.2584 0.734118
\(433\) −6.55556 −0.315040 −0.157520 0.987516i \(-0.550350\pi\)
−0.157520 + 0.987516i \(0.550350\pi\)
\(434\) 66.3278i 3.18384i
\(435\) 5.96518i 0.286009i
\(436\) 48.0101i 2.29927i
\(437\) 5.57239i 0.266563i
\(438\) −41.3771 −1.97707
\(439\) 38.2180 1.82405 0.912023 0.410138i \(-0.134520\pi\)
0.912023 + 0.410138i \(0.134520\pi\)
\(440\) 27.2455i 1.29888i
\(441\) −8.45506 −0.402622
\(442\) 32.7624 + 18.6602i 1.55835 + 0.887575i
\(443\) −12.7407 −0.605330 −0.302665 0.953097i \(-0.597876\pi\)
−0.302665 + 0.953097i \(0.597876\pi\)
\(444\) 45.8999i 2.17831i
\(445\) −9.19656 −0.435959
\(446\) −29.7187 −1.40722
\(447\) 5.31754i 0.251511i
\(448\) 123.500i 5.83484i
\(449\) 25.9513i 1.22472i 0.790581 + 0.612358i \(0.209779\pi\)
−0.790581 + 0.612358i \(0.790221\pi\)
\(450\) 8.41997i 0.396921i
\(451\) 6.35787 0.299381
\(452\) −0.0855531 −0.00402408
\(453\) 6.77573i 0.318351i
\(454\) −0.883629 −0.0414708
\(455\) −19.9339 + 34.9986i −0.934514 + 1.64076i
\(456\) −28.1974 −1.32046
\(457\) 16.0372i 0.750190i −0.926986 0.375095i \(-0.877610\pi\)
0.926986 0.375095i \(-0.122390\pi\)
\(458\) −16.2700 −0.760247
\(459\) −3.81818 −0.178217
\(460\) 29.6185i 1.38097i
\(461\) 3.48566i 0.162343i −0.996700 0.0811716i \(-0.974134\pi\)
0.996700 0.0811716i \(-0.0258662\pi\)
\(462\) 10.7670i 0.500924i
\(463\) 27.0784i 1.25844i −0.777227 0.629220i \(-0.783374\pi\)
0.777227 0.629220i \(-0.216626\pi\)
\(464\) −32.0315 −1.48703
\(465\) −17.5048 −0.811765
\(466\) 34.5639i 1.60114i
\(467\) 15.6899 0.726041 0.363020 0.931781i \(-0.381746\pi\)
0.363020 + 0.931781i \(0.381746\pi\)
\(468\) −9.81609 + 17.2345i −0.453749 + 0.796664i
\(469\) 41.1727 1.90118
\(470\) 41.3350i 1.90664i
\(471\) 16.2884 0.750529
\(472\) 51.6448 2.37715
\(473\) 11.7275i 0.539230i
\(474\) 4.30319i 0.197652i
\(475\) 9.04109i 0.414834i
\(476\) 82.5709i 3.78463i
\(477\) −2.37985 −0.108966
\(478\) −56.8860 −2.60191
\(479\) 33.0061i 1.50809i 0.656825 + 0.754043i \(0.271899\pi\)
−0.656825 + 0.754043i \(0.728101\pi\)
\(480\) 64.2550 2.93283
\(481\) 26.1420 + 14.8895i 1.19197 + 0.678901i
\(482\) −49.8904 −2.27244
\(483\) 7.44918i 0.338949i
\(484\) 5.50093 0.250042
\(485\) −50.5550 −2.29559
\(486\) 2.73878i 0.124234i
\(487\) 18.6684i 0.845945i −0.906142 0.422973i \(-0.860987\pi\)
0.906142 0.422973i \(-0.139013\pi\)
\(488\) 22.5187i 1.01938i
\(489\) 11.4032i 0.515672i
\(490\) −65.8003 −2.97255
\(491\) 6.78238 0.306084 0.153042 0.988220i \(-0.451093\pi\)
0.153042 + 0.988220i \(0.451093\pi\)
\(492\) 34.9742i 1.57676i
\(493\) 8.01542 0.360996
\(494\) 14.3724 25.2341i 0.646643 1.13534i
\(495\) −2.84154 −0.127718
\(496\) 93.9963i 4.22056i
\(497\) 39.6822 1.77999
\(498\) −29.2325 −1.30994
\(499\) 0.212900i 0.00953070i 0.999989 + 0.00476535i \(0.00151686\pi\)
−0.999989 + 0.00476535i \(0.998483\pi\)
\(500\) 30.1001i 1.34612i
\(501\) 14.7302i 0.658095i
\(502\) 62.0779i 2.77067i
\(503\) −10.5282 −0.469430 −0.234715 0.972064i \(-0.575416\pi\)
−0.234715 + 0.972064i \(0.575416\pi\)
\(504\) −37.6943 −1.67904
\(505\) 34.4477i 1.53290i
\(506\) 5.18956 0.230704
\(507\) −6.63153 11.1814i −0.294517 0.496582i
\(508\) −32.5387 −1.44367
\(509\) 26.1335i 1.15835i 0.815204 + 0.579175i \(0.196625\pi\)
−0.815204 + 0.579175i \(0.803375\pi\)
\(510\) −29.7144 −1.31578
\(511\) 59.3934 2.62741
\(512\) 52.4306i 2.31713i
\(513\) 2.94082i 0.129840i
\(514\) 48.5677i 2.14223i
\(515\) 9.68917i 0.426956i
\(516\) −64.5121 −2.83999
\(517\) −5.31137 −0.233594
\(518\) 89.8398i 3.94734i
\(519\) −0.186647 −0.00819291
\(520\) −48.6180 + 85.3604i −2.13204 + 3.74330i
\(521\) 44.5983 1.95389 0.976944 0.213495i \(-0.0684847\pi\)
0.976944 + 0.213495i \(0.0684847\pi\)
\(522\) 5.74947i 0.251647i
\(523\) −35.9788 −1.57324 −0.786622 0.617435i \(-0.788172\pi\)
−0.786622 + 0.617435i \(0.788172\pi\)
\(524\) 7.27176 0.317668
\(525\) 12.0862i 0.527483i
\(526\) 80.8233i 3.52406i
\(527\) 23.5212i 1.02460i
\(528\) 15.2584i 0.664035i
\(529\) −19.4096 −0.843895
\(530\) −18.5209 −0.804495
\(531\) 5.38624i 0.233743i
\(532\) 63.5974 2.75730
\(533\) −19.9193 11.3453i −0.862800 0.491418i
\(534\) 8.86399 0.383583
\(535\) 34.7668i 1.50310i
\(536\) 100.419 4.33743
\(537\) −10.9555 −0.472767
\(538\) 24.7063i 1.06516i
\(539\) 8.45506i 0.364185i
\(540\) 15.6311i 0.672656i
\(541\) 19.2806i 0.828937i 0.910064 + 0.414469i \(0.136033\pi\)
−0.910064 + 0.414469i \(0.863967\pi\)
\(542\) 12.5524 0.539172
\(543\) 8.52034 0.365643
\(544\) 86.3395i 3.70177i
\(545\) −24.7999 −1.06231
\(546\) 19.2130 33.7330i 0.822241 1.44364i
\(547\) −18.3680 −0.785359 −0.392679 0.919675i \(-0.628452\pi\)
−0.392679 + 0.919675i \(0.628452\pi\)
\(548\) 26.5215i 1.13294i
\(549\) −2.34857 −0.100234
\(550\) −8.41997 −0.359029
\(551\) 6.17360i 0.263004i
\(552\) 18.1683i 0.773293i
\(553\) 6.17686i 0.262667i
\(554\) 57.4759i 2.44192i
\(555\) −23.7099 −1.00643
\(556\) −94.5481 −4.00973
\(557\) 20.9920i 0.889459i −0.895665 0.444730i \(-0.853300\pi\)
0.895665 0.444730i \(-0.146700\pi\)
\(558\) 16.8718 0.714239
\(559\) 20.9270 36.7424i 0.885119 1.55404i
\(560\) −170.450 −7.20282
\(561\) 3.81818i 0.161204i
\(562\) 28.8558 1.21721
\(563\) −3.18924 −0.134411 −0.0672053 0.997739i \(-0.521408\pi\)
−0.0672053 + 0.997739i \(0.521408\pi\)
\(564\) 29.2175i 1.23028i
\(565\) 0.0441930i 0.00185921i
\(566\) 7.04329i 0.296052i
\(567\) 3.93129i 0.165099i
\(568\) 96.7834 4.06094
\(569\) −19.0570 −0.798909 −0.399455 0.916753i \(-0.630800\pi\)
−0.399455 + 0.916753i \(0.630800\pi\)
\(570\) 22.8865i 0.958610i
\(571\) −13.1418 −0.549967 −0.274984 0.961449i \(-0.588672\pi\)
−0.274984 + 0.961449i \(0.588672\pi\)
\(572\) −17.2345 9.81609i −0.720610 0.410431i
\(573\) −11.8003 −0.492965
\(574\) 68.4549i 2.85725i
\(575\) −5.82540 −0.242936
\(576\) −31.4147 −1.30895
\(577\) 6.38825i 0.265946i −0.991120 0.132973i \(-0.957548\pi\)
0.991120 0.132973i \(-0.0424524\pi\)
\(578\) 6.63205i 0.275857i
\(579\) 10.9405i 0.454674i
\(580\) 32.8140i 1.36253i
\(581\) 41.9608 1.74083
\(582\) 48.7268 2.01979
\(583\) 2.37985i 0.0985635i
\(584\) 144.858 5.99428
\(585\) 8.90258 + 5.07056i 0.368076 + 0.209642i
\(586\) 14.1365 0.583975
\(587\) 8.66483i 0.357636i 0.983882 + 0.178818i \(0.0572273\pi\)
−0.983882 + 0.178818i \(0.942773\pi\)
\(588\) 46.5107 1.91807
\(589\) −18.1164 −0.746472
\(590\) 41.9177i 1.72572i
\(591\) 9.43307i 0.388025i
\(592\) 127.316i 5.23267i
\(593\) 5.41552i 0.222389i 0.993799 + 0.111194i \(0.0354676\pi\)
−0.993799 + 0.111194i \(0.964532\pi\)
\(594\) 2.73878 0.112374
\(595\) 42.6525 1.74858
\(596\) 29.2514i 1.19818i
\(597\) 15.3198 0.626997
\(598\) −16.2590 9.26047i −0.664878 0.378689i
\(599\) 17.1821 0.702041 0.351021 0.936368i \(-0.385835\pi\)
0.351021 + 0.936368i \(0.385835\pi\)
\(600\) 29.4777i 1.20342i
\(601\) 4.44618 0.181364 0.0906818 0.995880i \(-0.471095\pi\)
0.0906818 + 0.995880i \(0.471095\pi\)
\(602\) 126.269 5.14635
\(603\) 10.4731i 0.426496i
\(604\) 37.2728i 1.51661i
\(605\) 2.84154i 0.115525i
\(606\) 33.2020i 1.34874i
\(607\) 12.1499 0.493148 0.246574 0.969124i \(-0.420695\pi\)
0.246574 + 0.969124i \(0.420695\pi\)
\(608\) 66.5000 2.69693
\(609\) 8.25288i 0.334423i
\(610\) −18.2774 −0.740031
\(611\) 16.6406 + 9.47783i 0.673206 + 0.383432i
\(612\) 21.0035 0.849017
\(613\) 30.6073i 1.23622i 0.786093 + 0.618108i \(0.212101\pi\)
−0.786093 + 0.618108i \(0.787899\pi\)
\(614\) −82.3172 −3.32205
\(615\) 18.0661 0.728497
\(616\) 37.6943i 1.51875i
\(617\) 15.3414i 0.617622i −0.951123 0.308811i \(-0.900069\pi\)
0.951123 0.308811i \(-0.0999311\pi\)
\(618\) 9.33878i 0.375661i
\(619\) 10.0391i 0.403505i −0.979437 0.201752i \(-0.935336\pi\)
0.979437 0.201752i \(-0.0646636\pi\)
\(620\) 96.2926 3.86720
\(621\) 1.89484 0.0760374
\(622\) 59.5581i 2.38806i
\(623\) −12.7235 −0.509757
\(624\) 27.2277 47.8046i 1.08998 1.91372i
\(625\) −30.9201 −1.23681
\(626\) 66.9253i 2.67487i
\(627\) −2.94082 −0.117445
\(628\) −89.6012 −3.57548
\(629\) 31.8590i 1.27030i
\(630\) 30.5947i 1.21892i
\(631\) 20.8523i 0.830119i 0.909794 + 0.415059i \(0.136239\pi\)
−0.909794 + 0.415059i \(0.863761\pi\)
\(632\) 15.0652i 0.599260i
\(633\) 2.91243 0.115759
\(634\) −57.7991 −2.29550
\(635\) 16.8081i 0.667009i
\(636\) 13.0914 0.519108
\(637\) −15.0876 + 26.4898i −0.597791 + 1.04956i
\(638\) −5.74947 −0.227624
\(639\) 10.0939i 0.399310i
\(640\) −115.970 −4.58413
\(641\) −29.3934 −1.16097 −0.580484 0.814272i \(-0.697137\pi\)
−0.580484 + 0.814272i \(0.697137\pi\)
\(642\) 33.5096i 1.32252i
\(643\) 7.23812i 0.285444i 0.989763 + 0.142722i \(0.0455854\pi\)
−0.989763 + 0.142722i \(0.954415\pi\)
\(644\) 40.9774i 1.61474i
\(645\) 33.3241i 1.31214i
\(646\) −30.7526 −1.20994
\(647\) 25.4069 0.998848 0.499424 0.866358i \(-0.333545\pi\)
0.499424 + 0.866358i \(0.333545\pi\)
\(648\) 9.58828i 0.376663i
\(649\) 5.38624 0.211429
\(650\) 26.3799 + 15.0249i 1.03470 + 0.589327i
\(651\) −24.2180 −0.949178
\(652\) 62.7284i 2.45663i
\(653\) −10.1486 −0.397146 −0.198573 0.980086i \(-0.563631\pi\)
−0.198573 + 0.980086i \(0.563631\pi\)
\(654\) 23.9031 0.934685
\(655\) 3.75627i 0.146770i
\(656\) 97.0107i 3.78763i
\(657\) 15.1079i 0.589413i
\(658\) 57.1873i 2.22939i
\(659\) −18.8648 −0.734869 −0.367434 0.930049i \(-0.619764\pi\)
−0.367434 + 0.930049i \(0.619764\pi\)
\(660\) 15.6311 0.608440
\(661\) 7.39059i 0.287461i −0.989617 0.143730i \(-0.954090\pi\)
0.989617 0.143730i \(-0.0459098\pi\)
\(662\) −1.53514 −0.0596648
\(663\) −6.81332 + 11.9624i −0.264607 + 0.464581i
\(664\) 102.341 3.97160
\(665\) 32.8516i 1.27393i
\(666\) 22.8525 0.885516
\(667\) −3.97780 −0.154021
\(668\) 81.0296i 3.13513i
\(669\) 10.8511i 0.419526i
\(670\) 81.5052i 3.14882i
\(671\) 2.34857i 0.0906655i
\(672\) 88.8973 3.42929
\(673\) 13.8241 0.532879 0.266439 0.963852i \(-0.414153\pi\)
0.266439 + 0.963852i \(0.414153\pi\)
\(674\) 21.2762i 0.819530i
\(675\) −3.07435 −0.118332
\(676\) 36.4796 + 61.5079i 1.40306 + 2.36569i
\(677\) −28.1714 −1.08272 −0.541358 0.840792i \(-0.682090\pi\)
−0.541358 + 0.840792i \(0.682090\pi\)
\(678\) 0.0425948i 0.00163585i
\(679\) −69.9433 −2.68418
\(680\) 104.028 3.98929
\(681\) 0.322636i 0.0123634i
\(682\) 16.8718i 0.646053i
\(683\) 20.1458i 0.770856i −0.922738 0.385428i \(-0.874054\pi\)
0.922738 0.385428i \(-0.125946\pi\)
\(684\) 16.1772i 0.618552i
\(685\) −13.6998 −0.523444
\(686\) −15.6665 −0.598150
\(687\) 5.94060i 0.226648i
\(688\) 178.942 6.82211
\(689\) −4.24671 + 7.45611i −0.161787 + 0.284055i
\(690\) 14.7463 0.561384
\(691\) 4.60090i 0.175026i 0.996163 + 0.0875132i \(0.0278920\pi\)
−0.996163 + 0.0875132i \(0.972108\pi\)
\(692\) 1.02673 0.0390306
\(693\) −3.93129 −0.149337
\(694\) 27.7593i 1.05373i
\(695\) 48.8394i 1.85258i
\(696\) 20.1285i 0.762968i
\(697\) 24.2755i 0.919499i
\(698\) −54.7839 −2.07360
\(699\) 12.6202 0.477338
\(700\) 66.4851i 2.51290i
\(701\) 2.14477 0.0810067 0.0405033 0.999179i \(-0.487104\pi\)
0.0405033 + 0.999179i \(0.487104\pi\)
\(702\) −8.58064 4.88720i −0.323855 0.184455i
\(703\) −24.5383 −0.925479
\(704\) 31.4147i 1.18399i
\(705\) −15.0925 −0.568415
\(706\) 73.3733 2.76144
\(707\) 47.6586i 1.79239i
\(708\) 29.6293i 1.11354i
\(709\) 18.0751i 0.678826i −0.940637 0.339413i \(-0.889772\pi\)
0.940637 0.339413i \(-0.110228\pi\)
\(710\) 78.5546i 2.94810i
\(711\) 1.57120 0.0589248
\(712\) −31.0322 −1.16298
\(713\) 11.6728i 0.437151i
\(714\) −41.1101 −1.53851
\(715\) −5.07056 + 8.90258i −0.189628 + 0.332938i
\(716\) 60.2657 2.25223
\(717\) 20.7706i 0.775691i
\(718\) 73.2206 2.73257
\(719\) 5.67258 0.211552 0.105776 0.994390i \(-0.466267\pi\)
0.105776 + 0.994390i \(0.466267\pi\)
\(720\) 43.3572i 1.61583i
\(721\) 13.4050i 0.499230i
\(722\) 28.3507i 1.05511i
\(723\) 18.2163i 0.677470i
\(724\) −46.8698 −1.74190
\(725\) 6.45391 0.239692
\(726\) 2.73878i 0.101646i
\(727\) −20.7279 −0.768756 −0.384378 0.923176i \(-0.625584\pi\)
−0.384378 + 0.923176i \(0.625584\pi\)
\(728\) −67.2634 + 118.097i −2.49295 + 4.37696i
\(729\) 1.00000 0.0370370
\(730\) 117.575i 4.35163i
\(731\) −44.7776 −1.65616
\(732\) 12.9193 0.477511
\(733\) 13.8875i 0.512945i −0.966552 0.256473i \(-0.917440\pi\)
0.966552 0.256473i \(-0.0825603\pi\)
\(734\) 5.19172i 0.191630i
\(735\) 24.0254i 0.886189i
\(736\) 42.8476i 1.57938i
\(737\) 10.4731 0.385780
\(738\) −17.4128 −0.640975
\(739\) 2.10062i 0.0772725i −0.999253 0.0386362i \(-0.987699\pi\)
0.999253 0.0386362i \(-0.0123014\pi\)
\(740\) 130.427 4.79457
\(741\) 9.21362 + 5.24772i 0.338471 + 0.192780i
\(742\) −25.6238 −0.940678
\(743\) 39.5255i 1.45005i −0.688722 0.725025i \(-0.741828\pi\)
0.688722 0.725025i \(-0.258172\pi\)
\(744\) −59.0668 −2.16550
\(745\) −15.1100 −0.553587
\(746\) 100.655i 3.68523i
\(747\) 10.6736i 0.390525i
\(748\) 21.0035i 0.767964i
\(749\) 48.1002i 1.75754i
\(750\) 14.9861 0.547216
\(751\) 7.96076 0.290492 0.145246 0.989396i \(-0.453603\pi\)
0.145246 + 0.989396i \(0.453603\pi\)
\(752\) 81.0427i 2.95532i
\(753\) 22.6662 0.826004
\(754\) 18.0132 + 10.2596i 0.656000 + 0.373632i
\(755\) 19.2535 0.700707
\(756\) 21.6258i 0.786521i
\(757\) −21.7720 −0.791316 −0.395658 0.918398i \(-0.629484\pi\)
−0.395658 + 0.918398i \(0.629484\pi\)
\(758\) 71.5721 2.59962
\(759\) 1.89484i 0.0687784i
\(760\) 80.1240i 2.90640i
\(761\) 25.3978i 0.920668i −0.887746 0.460334i \(-0.847730\pi\)
0.887746 0.460334i \(-0.152270\pi\)
\(762\) 16.2003i 0.586874i
\(763\) −34.3109 −1.24214
\(764\) 64.9126 2.34846
\(765\) 10.8495i 0.392264i
\(766\) −46.3433 −1.67445
\(767\) −16.8752 9.61144i −0.609327 0.347049i
\(768\) 48.9471 1.76623
\(769\) 17.5471i 0.632763i 0.948632 + 0.316382i \(0.102468\pi\)
−0.948632 + 0.316382i \(0.897532\pi\)
\(770\) −30.5947 −1.10256
\(771\) −17.7333 −0.638649
\(772\) 60.1832i 2.16604i
\(773\) 16.9181i 0.608503i −0.952592 0.304251i \(-0.901594\pi\)
0.952592 0.304251i \(-0.0984063\pi\)
\(774\) 32.1190i 1.15449i
\(775\) 18.9389i 0.680307i
\(776\) −170.589 −6.12379
\(777\) −32.8028 −1.17680
\(778\) 13.8475i 0.496456i
\(779\) 18.6974 0.669902
\(780\) −48.9724 27.8928i −1.75349 0.998723i
\(781\) 10.0939 0.361189
\(782\) 19.8147i 0.708570i
\(783\) −2.09928 −0.0750221
\(784\) −129.010 −4.60751
\(785\) 46.2841i 1.65195i
\(786\) 3.62044i 0.129137i
\(787\) 27.1659i 0.968361i 0.874968 + 0.484181i \(0.160882\pi\)
−0.874968 + 0.484181i \(0.839118\pi\)
\(788\) 51.8907i 1.84853i
\(789\) 29.5107 1.05061
\(790\) 12.2277 0.435041
\(791\) 0.0611413i 0.00217394i
\(792\) −9.58828 −0.340705