Properties

Label 690.3.f.a.229.20
Level $690$
Weight $3$
Character 690.229
Analytic conductor $18.801$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 229.20
Character \(\chi\) \(=\) 690.229
Dual form 690.3.f.a.229.18

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421i q^{2} -1.73205i q^{3} -2.00000 q^{4} +(1.15789 + 4.86408i) q^{5} +2.44949 q^{6} -1.79343 q^{7} -2.82843i q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+1.41421i q^{2} -1.73205i q^{3} -2.00000 q^{4} +(1.15789 + 4.86408i) q^{5} +2.44949 q^{6} -1.79343 q^{7} -2.82843i q^{8} -3.00000 q^{9} +(-6.87885 + 1.63751i) q^{10} -0.382184i q^{11} +3.46410i q^{12} -24.0468i q^{13} -2.53629i q^{14} +(8.42483 - 2.00553i) q^{15} +4.00000 q^{16} +22.1605 q^{17} -4.24264i q^{18} -17.6049i q^{19} +(-2.31579 - 9.72816i) q^{20} +3.10631i q^{21} +0.540489 q^{22} +(-1.50786 + 22.9505i) q^{23} -4.89898 q^{24} +(-22.3186 + 11.2642i) q^{25} +34.0074 q^{26} +5.19615i q^{27} +3.58685 q^{28} -1.79697 q^{29} +(2.83625 + 11.9145i) q^{30} +40.3465 q^{31} +5.65685i q^{32} -0.661961 q^{33} +31.3397i q^{34} +(-2.07660 - 8.72337i) q^{35} +6.00000 q^{36} +42.7110 q^{37} +24.8971 q^{38} -41.6503 q^{39} +(13.7577 - 3.27502i) q^{40} +1.26689 q^{41} -4.39298 q^{42} +16.5675 q^{43} +0.764367i q^{44} +(-3.47368 - 14.5922i) q^{45} +(-32.4569 - 2.13244i) q^{46} -5.75045i q^{47} -6.92820i q^{48} -45.7836 q^{49} +(-15.9300 - 31.5632i) q^{50} -38.3831i q^{51} +48.0937i q^{52} +81.4797 q^{53} -7.34847 q^{54} +(1.85897 - 0.442528i) q^{55} +5.07258i q^{56} -30.4925 q^{57} -2.54131i q^{58} +18.0948 q^{59} +(-16.8497 + 4.01106i) q^{60} -33.1411i q^{61} +57.0586i q^{62} +5.38028 q^{63} -8.00000 q^{64} +(116.966 - 27.8437i) q^{65} -0.936155i q^{66} +116.835 q^{67} -44.3210 q^{68} +(39.7515 + 2.61169i) q^{69} +(12.3367 - 2.93676i) q^{70} +28.3516 q^{71} +8.48528i q^{72} -112.311i q^{73} +60.4025i q^{74} +(19.5101 + 38.6569i) q^{75} +35.2098i q^{76} +0.685419i q^{77} -58.9025i q^{78} +62.0766i q^{79} +(4.63158 + 19.4563i) q^{80} +9.00000 q^{81} +1.79165i q^{82} +148.140 q^{83} -6.21261i q^{84} +(25.6595 + 107.790i) q^{85} +23.4300i q^{86} +3.11245i q^{87} -1.08098 q^{88} -102.736i q^{89} +(20.6365 - 4.91253i) q^{90} +43.1262i q^{91} +(3.01572 - 45.9010i) q^{92} -69.8822i q^{93} +8.13236 q^{94} +(85.6316 - 20.3846i) q^{95} +9.79796 q^{96} -150.611 q^{97} -64.7478i q^{98} +1.14655i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 96q^{4} - 144q^{9} + O(q^{10}) \) \( 48q - 96q^{4} - 144q^{9} + 192q^{16} + 96q^{25} + 64q^{26} - 152q^{29} - 8q^{31} + 56q^{35} + 288q^{36} - 48q^{39} + 40q^{41} - 160q^{46} + 424q^{49} + 96q^{50} + 32q^{55} + 360q^{59} - 384q^{64} + 192q^{69} - 496q^{70} - 152q^{71} + 144q^{75} + 432q^{81} - 136q^{85} + 256q^{94} + 496q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) 1.73205i 0.577350i
\(4\) −2.00000 −0.500000
\(5\) 1.15789 + 4.86408i 0.231579 + 0.972816i
\(6\) 2.44949 0.408248
\(7\) −1.79343 −0.256204 −0.128102 0.991761i \(-0.540888\pi\)
−0.128102 + 0.991761i \(0.540888\pi\)
\(8\) 2.82843i 0.353553i
\(9\) −3.00000 −0.333333
\(10\) −6.87885 + 1.63751i −0.687885 + 0.163751i
\(11\) 0.382184i 0.0347440i −0.999849 0.0173720i \(-0.994470\pi\)
0.999849 0.0173720i \(-0.00552995\pi\)
\(12\) 3.46410i 0.288675i
\(13\) 24.0468i 1.84976i −0.380264 0.924878i \(-0.624167\pi\)
0.380264 0.924878i \(-0.375833\pi\)
\(14\) 2.53629i 0.181164i
\(15\) 8.42483 2.00553i 0.561656 0.133702i
\(16\) 4.00000 0.250000
\(17\) 22.1605 1.30356 0.651779 0.758409i \(-0.274023\pi\)
0.651779 + 0.758409i \(0.274023\pi\)
\(18\) 4.24264i 0.235702i
\(19\) 17.6049i 0.926573i −0.886209 0.463286i \(-0.846670\pi\)
0.886209 0.463286i \(-0.153330\pi\)
\(20\) −2.31579 9.72816i −0.115789 0.486408i
\(21\) 3.10631i 0.147919i
\(22\) 0.540489 0.0245677
\(23\) −1.50786 + 22.9505i −0.0655591 + 0.997849i
\(24\) −4.89898 −0.204124
\(25\) −22.3186 + 11.2642i −0.892742 + 0.450567i
\(26\) 34.0074 1.30798
\(27\) 5.19615i 0.192450i
\(28\) 3.58685 0.128102
\(29\) −1.79697 −0.0619646 −0.0309823 0.999520i \(-0.509864\pi\)
−0.0309823 + 0.999520i \(0.509864\pi\)
\(30\) 2.83625 + 11.9145i 0.0945417 + 0.397151i
\(31\) 40.3465 1.30150 0.650750 0.759292i \(-0.274455\pi\)
0.650750 + 0.759292i \(0.274455\pi\)
\(32\) 5.65685i 0.176777i
\(33\) −0.661961 −0.0200594
\(34\) 31.3397i 0.921755i
\(35\) −2.07660 8.72337i −0.0593314 0.249239i
\(36\) 6.00000 0.166667
\(37\) 42.7110 1.15435 0.577175 0.816620i \(-0.304155\pi\)
0.577175 + 0.816620i \(0.304155\pi\)
\(38\) 24.8971 0.655186
\(39\) −41.6503 −1.06796
\(40\) 13.7577 3.27502i 0.343942 0.0818755i
\(41\) 1.26689 0.0308998 0.0154499 0.999881i \(-0.495082\pi\)
0.0154499 + 0.999881i \(0.495082\pi\)
\(42\) −4.39298 −0.104595
\(43\) 16.5675 0.385291 0.192646 0.981268i \(-0.438293\pi\)
0.192646 + 0.981268i \(0.438293\pi\)
\(44\) 0.764367i 0.0173720i
\(45\) −3.47368 14.5922i −0.0771930 0.324272i
\(46\) −32.4569 2.13244i −0.705586 0.0463573i
\(47\) 5.75045i 0.122350i −0.998127 0.0611750i \(-0.980515\pi\)
0.998127 0.0611750i \(-0.0194848\pi\)
\(48\) 6.92820i 0.144338i
\(49\) −45.7836 −0.934360
\(50\) −15.9300 31.5632i −0.318599 0.631264i
\(51\) 38.3831i 0.752610i
\(52\) 48.0937i 0.924878i
\(53\) 81.4797 1.53735 0.768677 0.639637i \(-0.220915\pi\)
0.768677 + 0.639637i \(0.220915\pi\)
\(54\) −7.34847 −0.136083
\(55\) 1.85897 0.442528i 0.0337995 0.00804597i
\(56\) 5.07258i 0.0905818i
\(57\) −30.4925 −0.534957
\(58\) 2.54131i 0.0438156i
\(59\) 18.0948 0.306691 0.153346 0.988173i \(-0.450995\pi\)
0.153346 + 0.988173i \(0.450995\pi\)
\(60\) −16.8497 + 4.01106i −0.280828 + 0.0668511i
\(61\) 33.1411i 0.543296i −0.962397 0.271648i \(-0.912431\pi\)
0.962397 0.271648i \(-0.0875687\pi\)
\(62\) 57.0586i 0.920300i
\(63\) 5.38028 0.0854013
\(64\) −8.00000 −0.125000
\(65\) 116.966 27.8437i 1.79947 0.428365i
\(66\) 0.936155i 0.0141842i
\(67\) 116.835 1.74381 0.871904 0.489677i \(-0.162885\pi\)
0.871904 + 0.489677i \(0.162885\pi\)
\(68\) −44.3210 −0.651779
\(69\) 39.7515 + 2.61169i 0.576108 + 0.0378506i
\(70\) 12.3367 2.93676i 0.176239 0.0419537i
\(71\) 28.3516 0.399318 0.199659 0.979865i \(-0.436017\pi\)
0.199659 + 0.979865i \(0.436017\pi\)
\(72\) 8.48528i 0.117851i
\(73\) 112.311i 1.53850i −0.638948 0.769250i \(-0.720630\pi\)
0.638948 0.769250i \(-0.279370\pi\)
\(74\) 60.4025i 0.816249i
\(75\) 19.5101 + 38.6569i 0.260135 + 0.515425i
\(76\) 35.2098i 0.463286i
\(77\) 0.685419i 0.00890154i
\(78\) 58.9025i 0.755160i
\(79\) 62.0766i 0.785780i 0.919585 + 0.392890i \(0.128525\pi\)
−0.919585 + 0.392890i \(0.871475\pi\)
\(80\) 4.63158 + 19.4563i 0.0578947 + 0.243204i
\(81\) 9.00000 0.111111
\(82\) 1.79165i 0.0218494i
\(83\) 148.140 1.78481 0.892407 0.451231i \(-0.149015\pi\)
0.892407 + 0.451231i \(0.149015\pi\)
\(84\) 6.21261i 0.0739597i
\(85\) 25.6595 + 107.790i 0.301877 + 1.26812i
\(86\) 23.4300i 0.272442i
\(87\) 3.11245i 0.0357753i
\(88\) −1.08098 −0.0122838
\(89\) 102.736i 1.15434i −0.816623 0.577171i \(-0.804157\pi\)
0.816623 0.577171i \(-0.195843\pi\)
\(90\) 20.6365 4.91253i 0.229295 0.0545837i
\(91\) 43.1262i 0.473915i
\(92\) 3.01572 45.9010i 0.0327796 0.498924i
\(93\) 69.8822i 0.751422i
\(94\) 8.13236 0.0865145
\(95\) 85.6316 20.3846i 0.901385 0.214575i
\(96\) 9.79796 0.102062
\(97\) −150.611 −1.55269 −0.776343 0.630310i \(-0.782928\pi\)
−0.776343 + 0.630310i \(0.782928\pi\)
\(98\) 64.7478i 0.660692i
\(99\) 1.14655i 0.0115813i
\(100\) 44.6371 22.5284i 0.446371 0.225284i
\(101\) −105.835 −1.04787 −0.523937 0.851757i \(-0.675537\pi\)
−0.523937 + 0.851757i \(0.675537\pi\)
\(102\) 54.2819 0.532175
\(103\) −110.093 −1.06886 −0.534432 0.845211i \(-0.679474\pi\)
−0.534432 + 0.845211i \(0.679474\pi\)
\(104\) −68.0147 −0.653988
\(105\) −15.1093 + 3.59678i −0.143898 + 0.0342550i
\(106\) 115.230i 1.08707i
\(107\) 145.434 1.35920 0.679599 0.733584i \(-0.262154\pi\)
0.679599 + 0.733584i \(0.262154\pi\)
\(108\) 10.3923i 0.0962250i
\(109\) 108.845i 0.998578i 0.866435 + 0.499289i \(0.166405\pi\)
−0.866435 + 0.499289i \(0.833595\pi\)
\(110\) 0.625830 + 2.62898i 0.00568936 + 0.0238998i
\(111\) 73.9776i 0.666465i
\(112\) −7.17371 −0.0640510
\(113\) −56.0495 −0.496013 −0.248007 0.968758i \(-0.579775\pi\)
−0.248007 + 0.968758i \(0.579775\pi\)
\(114\) 43.1230i 0.378272i
\(115\) −113.379 + 19.2399i −0.985905 + 0.167304i
\(116\) 3.59395 0.0309823
\(117\) 72.1405i 0.616585i
\(118\) 25.5899i 0.216863i
\(119\) −39.7432 −0.333977
\(120\) −5.67250 23.8290i −0.0472709 0.198575i
\(121\) 120.854 0.998793
\(122\) 46.8686 0.384169
\(123\) 2.19432i 0.0178400i
\(124\) −80.6930 −0.650750
\(125\) −80.6325 95.5165i −0.645060 0.764132i
\(126\) 7.60887i 0.0603878i
\(127\) 67.2083i 0.529199i −0.964358 0.264599i \(-0.914760\pi\)
0.964358 0.264599i \(-0.0852397\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) 28.6958i 0.222448i
\(130\) 39.3769 + 165.415i 0.302899 + 1.27242i
\(131\) −144.689 −1.10450 −0.552249 0.833679i \(-0.686230\pi\)
−0.552249 + 0.833679i \(0.686230\pi\)
\(132\) 1.32392 0.0100297
\(133\) 31.5731i 0.237392i
\(134\) 165.230i 1.23306i
\(135\) −25.2745 + 6.01660i −0.187219 + 0.0445674i
\(136\) 62.6793i 0.460877i
\(137\) −66.2233 −0.483381 −0.241691 0.970353i \(-0.577702\pi\)
−0.241691 + 0.970353i \(0.577702\pi\)
\(138\) −3.69349 + 56.2171i −0.0267644 + 0.407370i
\(139\) 58.2706 0.419213 0.209606 0.977786i \(-0.432782\pi\)
0.209606 + 0.977786i \(0.432782\pi\)
\(140\) 4.15320 + 17.4467i 0.0296657 + 0.124620i
\(141\) −9.96007 −0.0706388
\(142\) 40.0952i 0.282360i
\(143\) −9.19030 −0.0642679
\(144\) −12.0000 −0.0833333
\(145\) −2.08071 8.74063i −0.0143497 0.0602802i
\(146\) 158.831 1.08788
\(147\) 79.2996i 0.539453i
\(148\) −85.4220 −0.577175
\(149\) 178.281i 1.19652i −0.801303 0.598259i \(-0.795860\pi\)
0.801303 0.598259i \(-0.204140\pi\)
\(150\) −54.6691 + 27.5915i −0.364461 + 0.183943i
\(151\) 216.913 1.43651 0.718257 0.695778i \(-0.244940\pi\)
0.718257 + 0.695778i \(0.244940\pi\)
\(152\) −49.7941 −0.327593
\(153\) −66.4815 −0.434519
\(154\) −0.969328 −0.00629434
\(155\) 46.7170 + 196.249i 0.301400 + 1.26612i
\(156\) 83.3007 0.533979
\(157\) −132.164 −0.841810 −0.420905 0.907105i \(-0.638287\pi\)
−0.420905 + 0.907105i \(0.638287\pi\)
\(158\) −87.7896 −0.555631
\(159\) 141.127i 0.887592i
\(160\) −27.5154 + 6.55004i −0.171971 + 0.0409378i
\(161\) 2.70424 41.1601i 0.0167965 0.255653i
\(162\) 12.7279i 0.0785674i
\(163\) 98.3005i 0.603070i 0.953455 + 0.301535i \(0.0974991\pi\)
−0.953455 + 0.301535i \(0.902501\pi\)
\(164\) −2.53378 −0.0154499
\(165\) −0.766482 3.21983i −0.00464534 0.0195141i
\(166\) 209.501i 1.26205i
\(167\) 69.3323i 0.415164i 0.978218 + 0.207582i \(0.0665593\pi\)
−0.978218 + 0.207582i \(0.933441\pi\)
\(168\) 8.78596 0.0522974
\(169\) −409.250 −2.42160
\(170\) −152.439 + 36.2880i −0.896698 + 0.213459i
\(171\) 52.8146i 0.308858i
\(172\) −33.1350 −0.192646
\(173\) 337.945i 1.95344i −0.214522 0.976719i \(-0.568819\pi\)
0.214522 0.976719i \(-0.431181\pi\)
\(174\) −4.40167 −0.0252970
\(175\) 40.0267 20.2015i 0.228724 0.115437i
\(176\) 1.52873i 0.00868599i
\(177\) 31.3411i 0.177068i
\(178\) 145.291 0.816243
\(179\) −135.350 −0.756146 −0.378073 0.925776i \(-0.623413\pi\)
−0.378073 + 0.925776i \(0.623413\pi\)
\(180\) 6.94737 + 29.1845i 0.0385965 + 0.162136i
\(181\) 275.222i 1.52057i 0.649592 + 0.760283i \(0.274940\pi\)
−0.649592 + 0.760283i \(0.725060\pi\)
\(182\) −60.9897 −0.335108
\(183\) −57.4020 −0.313672
\(184\) 64.9139 + 4.26487i 0.352793 + 0.0231787i
\(185\) 49.4548 + 207.750i 0.267323 + 1.12297i
\(186\) 98.8284 0.531335
\(187\) 8.46938i 0.0452908i
\(188\) 11.5009i 0.0611750i
\(189\) 9.31892i 0.0493065i
\(190\) 28.8282 + 121.101i 0.151727 + 0.637375i
\(191\) 43.3590i 0.227010i −0.993537 0.113505i \(-0.963792\pi\)
0.993537 0.113505i \(-0.0362079\pi\)
\(192\) 13.8564i 0.0721688i
\(193\) 41.4539i 0.214787i 0.994217 + 0.107394i \(0.0342505\pi\)
−0.994217 + 0.107394i \(0.965749\pi\)
\(194\) 212.996i 1.09792i
\(195\) −48.2267 202.591i −0.247316 1.03893i
\(196\) 91.5672 0.467180
\(197\) 208.208i 1.05689i 0.848966 + 0.528447i \(0.177226\pi\)
−0.848966 + 0.528447i \(0.822774\pi\)
\(198\) −1.62147 −0.00818923
\(199\) 270.493i 1.35926i 0.733554 + 0.679631i \(0.237860\pi\)
−0.733554 + 0.679631i \(0.762140\pi\)
\(200\) 31.8599 + 63.1264i 0.159300 + 0.315632i
\(201\) 202.364i 1.00679i
\(202\) 149.674i 0.740959i
\(203\) 3.22274 0.0158756
\(204\) 76.7662i 0.376305i
\(205\) 1.46693 + 6.16226i 0.00715574 + 0.0300598i
\(206\) 155.695i 0.755801i
\(207\) 4.52358 68.8516i 0.0218530 0.332616i
\(208\) 96.1873i 0.462439i
\(209\) −6.72830 −0.0321928
\(210\) −5.08661 21.3678i −0.0242220 0.101752i
\(211\) 20.2818 0.0961222 0.0480611 0.998844i \(-0.484696\pi\)
0.0480611 + 0.998844i \(0.484696\pi\)
\(212\) −162.959 −0.768677
\(213\) 49.1063i 0.230546i
\(214\) 205.675i 0.961098i
\(215\) 19.1834 + 80.5857i 0.0892253 + 0.374817i
\(216\) 14.6969 0.0680414
\(217\) −72.3585 −0.333449
\(218\) −153.930 −0.706102
\(219\) −194.528 −0.888254
\(220\) −3.71794 + 0.885057i −0.0168997 + 0.00402299i
\(221\) 532.890i 2.41126i
\(222\) 104.620 0.471262
\(223\) 195.211i 0.875386i −0.899124 0.437693i \(-0.855796\pi\)
0.899124 0.437693i \(-0.144204\pi\)
\(224\) 10.1452i 0.0452909i
\(225\) 66.9557 33.7926i 0.297581 0.150189i
\(226\) 79.2660i 0.350734i
\(227\) 89.0856 0.392448 0.196224 0.980559i \(-0.437132\pi\)
0.196224 + 0.980559i \(0.437132\pi\)
\(228\) 60.9851 0.267479
\(229\) 240.109i 1.04851i −0.851561 0.524255i \(-0.824344\pi\)
0.851561 0.524255i \(-0.175656\pi\)
\(230\) −27.2094 160.342i −0.118302 0.697140i
\(231\) 1.18718 0.00513931
\(232\) 5.08261i 0.0219078i
\(233\) 366.956i 1.57492i −0.616367 0.787459i \(-0.711396\pi\)
0.616367 0.787459i \(-0.288604\pi\)
\(234\) −102.022 −0.435992
\(235\) 27.9706 6.65841i 0.119024 0.0283337i
\(236\) −36.1895 −0.153346
\(237\) 107.520 0.453670
\(238\) 56.2054i 0.236157i
\(239\) 312.460 1.30737 0.653683 0.756769i \(-0.273223\pi\)
0.653683 + 0.756769i \(0.273223\pi\)
\(240\) 33.6993 8.02213i 0.140414 0.0334255i
\(241\) 187.089i 0.776302i −0.921596 0.388151i \(-0.873114\pi\)
0.921596 0.388151i \(-0.126886\pi\)
\(242\) 170.913i 0.706253i
\(243\) 15.5885i 0.0641500i
\(244\) 66.2822i 0.271648i
\(245\) −53.0126 222.695i −0.216378 0.908960i
\(246\) 3.10324 0.0126148
\(247\) −423.342 −1.71393
\(248\) 114.117i 0.460150i
\(249\) 256.585i 1.03046i
\(250\) 135.081 114.032i 0.540323 0.456126i
\(251\) 100.664i 0.401051i 0.979688 + 0.200525i \(0.0642649\pi\)
−0.979688 + 0.200525i \(0.935735\pi\)
\(252\) −10.7606 −0.0427006
\(253\) 8.77131 + 0.576279i 0.0346692 + 0.00227778i
\(254\) 95.0468 0.374200
\(255\) 186.698 44.4436i 0.732151 0.174289i
\(256\) 16.0000 0.0625000
\(257\) 43.1857i 0.168038i −0.996464 0.0840188i \(-0.973224\pi\)
0.996464 0.0840188i \(-0.0267756\pi\)
\(258\) 40.5820 0.157294
\(259\) −76.5990 −0.295749
\(260\) −233.931 + 55.6874i −0.899736 + 0.214182i
\(261\) 5.39092 0.0206549
\(262\) 204.621i 0.780998i
\(263\) −149.557 −0.568657 −0.284329 0.958727i \(-0.591771\pi\)
−0.284329 + 0.958727i \(0.591771\pi\)
\(264\) 1.87231i 0.00709208i
\(265\) 94.3450 + 396.324i 0.356019 + 1.49556i
\(266\) −44.6511 −0.167861
\(267\) −177.945 −0.666459
\(268\) −233.670 −0.871904
\(269\) 7.50830 0.0279119 0.0139560 0.999903i \(-0.495558\pi\)
0.0139560 + 0.999903i \(0.495558\pi\)
\(270\) −8.50875 35.7435i −0.0315139 0.132384i
\(271\) −333.946 −1.23227 −0.616136 0.787640i \(-0.711303\pi\)
−0.616136 + 0.787640i \(0.711303\pi\)
\(272\) 88.6420 0.325890
\(273\) 74.6968 0.273615
\(274\) 93.6538i 0.341802i
\(275\) 4.30499 + 8.52979i 0.0156545 + 0.0310174i
\(276\) −79.5029 5.22338i −0.288054 0.0189253i
\(277\) 17.8761i 0.0645347i −0.999479 0.0322674i \(-0.989727\pi\)
0.999479 0.0322674i \(-0.0102728\pi\)
\(278\) 82.4070i 0.296428i
\(279\) −121.040 −0.433833
\(280\) −24.6734 + 5.87351i −0.0881194 + 0.0209768i
\(281\) 375.566i 1.33654i 0.743921 + 0.668268i \(0.232964\pi\)
−0.743921 + 0.668268i \(0.767036\pi\)
\(282\) 14.0857i 0.0499492i
\(283\) −401.091 −1.41728 −0.708642 0.705568i \(-0.750692\pi\)
−0.708642 + 0.705568i \(0.750692\pi\)
\(284\) −56.7031 −0.199659
\(285\) −35.3072 148.318i −0.123885 0.520415i
\(286\) 12.9971i 0.0454442i
\(287\) −2.27208 −0.00791664
\(288\) 16.9706i 0.0589256i
\(289\) 202.087 0.699264
\(290\) 12.3611 2.94256i 0.0426245 0.0101468i
\(291\) 260.865i 0.896444i
\(292\) 224.621i 0.769250i
\(293\) −79.9606 −0.272903 −0.136452 0.990647i \(-0.543570\pi\)
−0.136452 + 0.990647i \(0.543570\pi\)
\(294\) −112.147 −0.381451
\(295\) 20.9518 + 88.0144i 0.0710232 + 0.298354i
\(296\) 120.805i 0.408125i
\(297\) 1.98588 0.00668648
\(298\) 252.127 0.846065
\(299\) 551.887 + 36.2593i 1.84578 + 0.121268i
\(300\) −39.0203 77.3138i −0.130068 0.257713i
\(301\) −29.7126 −0.0987131
\(302\) 306.762i 1.01577i
\(303\) 183.312i 0.604991i
\(304\) 70.4195i 0.231643i
\(305\) 161.201 38.3739i 0.528527 0.125816i
\(306\) 94.0190i 0.307252i
\(307\) 245.949i 0.801137i −0.916267 0.400568i \(-0.868813\pi\)
0.916267 0.400568i \(-0.131187\pi\)
\(308\) 1.37084i 0.00445077i
\(309\) 190.687i 0.617109i
\(310\) −277.538 + 66.0678i −0.895282 + 0.213122i
\(311\) −426.643 −1.37184 −0.685921 0.727676i \(-0.740601\pi\)
−0.685921 + 0.727676i \(0.740601\pi\)
\(312\) 117.805i 0.377580i
\(313\) −330.486 −1.05587 −0.527933 0.849286i \(-0.677033\pi\)
−0.527933 + 0.849286i \(0.677033\pi\)
\(314\) 186.908i 0.595250i
\(315\) 6.22980 + 26.1701i 0.0197771 + 0.0830798i
\(316\) 124.153i 0.392890i
\(317\) 45.8757i 0.144718i −0.997379 0.0723591i \(-0.976947\pi\)
0.997379 0.0723591i \(-0.0230528\pi\)
\(318\) 199.584 0.627622
\(319\) 0.686774i 0.00215290i
\(320\) −9.26316 38.9126i −0.0289474 0.121602i
\(321\) 251.899i 0.784733i
\(322\) 58.2092 + 3.82437i 0.180774 + 0.0118769i
\(323\) 390.133i 1.20784i
\(324\) −18.0000 −0.0555556
\(325\) 270.868 + 536.691i 0.833440 + 1.65136i
\(326\) −139.018 −0.426435
\(327\) 188.525 0.576530
\(328\) 3.58331i 0.0109247i
\(329\) 10.3130i 0.0313465i
\(330\) 4.55353 1.08397i 0.0137986 0.00328475i
\(331\) −528.078 −1.59540 −0.797701 0.603053i \(-0.793951\pi\)
−0.797701 + 0.603053i \(0.793951\pi\)
\(332\) −296.279 −0.892407
\(333\) −128.133 −0.384784
\(334\) −98.0507 −0.293565
\(335\) 135.283 + 568.295i 0.403829 + 1.69640i
\(336\) 12.4252i 0.0369798i
\(337\) 478.649 1.42032 0.710162 0.704039i \(-0.248622\pi\)
0.710162 + 0.704039i \(0.248622\pi\)
\(338\) 578.767i 1.71233i
\(339\) 97.0806i 0.286373i
\(340\) −51.3190 215.581i −0.150938 0.634061i
\(341\) 15.4198i 0.0452193i
\(342\) −74.6912 −0.218395
\(343\) 169.988 0.495590
\(344\) 46.8600i 0.136221i
\(345\) 33.3245 + 196.378i 0.0965929 + 0.569213i
\(346\) 477.926 1.38129
\(347\) 45.8278i 0.132069i 0.997817 + 0.0660344i \(0.0210347\pi\)
−0.997817 + 0.0660344i \(0.978965\pi\)
\(348\) 6.22490i 0.0178877i
\(349\) 38.0051 0.108897 0.0544486 0.998517i \(-0.482660\pi\)
0.0544486 + 0.998517i \(0.482660\pi\)
\(350\) 28.5692 + 56.6063i 0.0816264 + 0.161732i
\(351\) 124.951 0.355986
\(352\) 2.16196 0.00614192
\(353\) 332.010i 0.940540i 0.882523 + 0.470270i \(0.155843\pi\)
−0.882523 + 0.470270i \(0.844157\pi\)
\(354\) 44.3230 0.125206
\(355\) 32.8281 + 137.904i 0.0924736 + 0.388463i
\(356\) 205.473i 0.577171i
\(357\) 68.8373i 0.192822i
\(358\) 191.414i 0.534676i
\(359\) 384.549i 1.07117i −0.844482 0.535584i \(-0.820091\pi\)
0.844482 0.535584i \(-0.179909\pi\)
\(360\) −41.2731 + 9.82506i −0.114647 + 0.0272918i
\(361\) 51.0681 0.141463
\(362\) −389.223 −1.07520
\(363\) 209.325i 0.576653i
\(364\) 86.2525i 0.236957i
\(365\) 546.287 130.044i 1.49668 0.356284i
\(366\) 81.1787i 0.221800i
\(367\) 158.946 0.433096 0.216548 0.976272i \(-0.430520\pi\)
0.216548 + 0.976272i \(0.430520\pi\)
\(368\) −6.03144 + 91.8021i −0.0163898 + 0.249462i
\(369\) −3.80067 −0.0102999
\(370\) −293.802 + 69.9397i −0.794061 + 0.189026i
\(371\) −146.128 −0.393876
\(372\) 139.764i 0.375711i
\(373\) 353.352 0.947324 0.473662 0.880707i \(-0.342932\pi\)
0.473662 + 0.880707i \(0.342932\pi\)
\(374\) 11.9775 0.0320254
\(375\) −165.439 + 139.660i −0.441172 + 0.372425i
\(376\) −16.2647 −0.0432573
\(377\) 43.2115i 0.114619i
\(378\) 13.1789 0.0348649
\(379\) 494.663i 1.30518i 0.757712 + 0.652589i \(0.226317\pi\)
−0.757712 + 0.652589i \(0.773683\pi\)
\(380\) −171.263 + 40.7692i −0.450692 + 0.107287i
\(381\) −116.408 −0.305533
\(382\) 61.3189 0.160521
\(383\) 329.711 0.860864 0.430432 0.902623i \(-0.358361\pi\)
0.430432 + 0.902623i \(0.358361\pi\)
\(384\) −19.5959 −0.0510310
\(385\) −3.33393 + 0.793642i −0.00865956 + 0.00206141i
\(386\) −58.6247 −0.151878
\(387\) −49.7025 −0.128430
\(388\) 301.221 0.776343
\(389\) 318.459i 0.818660i 0.912386 + 0.409330i \(0.134238\pi\)
−0.912386 + 0.409330i \(0.865762\pi\)
\(390\) 286.506 68.2028i 0.734632 0.174879i
\(391\) −33.4149 + 508.595i −0.0854601 + 1.30075i
\(392\) 129.496i 0.330346i
\(393\) 250.609i 0.637682i
\(394\) −294.451 −0.747337
\(395\) −301.946 + 71.8782i −0.764420 + 0.181970i
\(396\) 2.29310i 0.00579066i
\(397\) 68.2935i 0.172024i −0.996294 0.0860119i \(-0.972588\pi\)
0.996294 0.0860119i \(-0.0274123\pi\)
\(398\) −382.535 −0.961143
\(399\) 54.6862 0.137058
\(400\) −89.2742 + 45.0567i −0.223186 + 0.112642i
\(401\) 486.040i 1.21207i 0.795438 + 0.606035i \(0.207241\pi\)
−0.795438 + 0.606035i \(0.792759\pi\)
\(402\) 286.186 0.711906
\(403\) 970.206i 2.40746i
\(404\) 211.671 0.523937
\(405\) 10.4211 + 43.7767i 0.0257310 + 0.108091i
\(406\) 4.55765i 0.0112257i
\(407\) 16.3234i 0.0401067i
\(408\) −108.564 −0.266088
\(409\) −124.021 −0.303230 −0.151615 0.988440i \(-0.548447\pi\)
−0.151615 + 0.988440i \(0.548447\pi\)
\(410\) −8.71475 + 2.07455i −0.0212555 + 0.00505987i
\(411\) 114.702i 0.279080i
\(412\) 220.186 0.534432
\(413\) −32.4517 −0.0785754
\(414\) 97.3708 + 6.39731i 0.235195 + 0.0154524i
\(415\) 171.530 + 720.563i 0.413325 + 1.73630i
\(416\) 136.029 0.326994
\(417\) 100.928i 0.242033i
\(418\) 9.51525i 0.0227638i
\(419\) 628.400i 1.49976i 0.661573 + 0.749881i \(0.269889\pi\)
−0.661573 + 0.749881i \(0.730111\pi\)
\(420\) 30.2187 7.19355i 0.0719492 0.0171275i
\(421\) 258.480i 0.613966i 0.951715 + 0.306983i \(0.0993195\pi\)
−0.951715 + 0.306983i \(0.900681\pi\)
\(422\) 28.6828i 0.0679687i
\(423\) 17.2513i 0.0407833i
\(424\) 230.460i 0.543537i
\(425\) −494.590 + 249.620i −1.16374 + 0.587341i
\(426\) 69.4468 0.163021
\(427\) 59.4361i 0.139195i
\(428\) −290.868 −0.679599
\(429\) 15.9181i 0.0371051i
\(430\) −113.965 + 27.1295i −0.265036 + 0.0630918i
\(431\) 360.875i 0.837298i 0.908148 + 0.418649i \(0.137496\pi\)
−0.908148 + 0.418649i \(0.862504\pi\)
\(432\) 20.7846i 0.0481125i
\(433\) 527.704 1.21872 0.609358 0.792896i \(-0.291427\pi\)
0.609358 + 0.792896i \(0.291427\pi\)
\(434\) 102.330i 0.235784i
\(435\) −15.1392 + 3.60389i −0.0348028 + 0.00828481i
\(436\) 217.690i 0.499289i
\(437\) 404.041 + 26.5457i 0.924579 + 0.0607453i
\(438\) 275.103i 0.628090i
\(439\) 678.504 1.54557 0.772784 0.634669i \(-0.218864\pi\)
0.772784 + 0.634669i \(0.218864\pi\)
\(440\) −1.25166 5.25797i −0.00284468 0.0119499i
\(441\) 137.351 0.311453
\(442\) 753.620 1.70502
\(443\) 296.200i 0.668624i −0.942462 0.334312i \(-0.891496\pi\)
0.942462 0.334312i \(-0.108504\pi\)
\(444\) 147.955i 0.333232i
\(445\) 499.718 118.958i 1.12296 0.267321i
\(446\) 276.070 0.618991
\(447\) −308.792 −0.690810
\(448\) 14.3474 0.0320255
\(449\) 535.630 1.19294 0.596470 0.802635i \(-0.296569\pi\)
0.596470 + 0.802635i \(0.296569\pi\)
\(450\) 47.7899 + 94.6896i 0.106200 + 0.210421i
\(451\) 0.484185i 0.00107358i
\(452\) 112.099 0.248007
\(453\) 375.705i 0.829371i
\(454\) 125.986i 0.277502i
\(455\) −209.770 + 49.9356i −0.461032 + 0.109749i
\(456\) 86.2460i 0.189136i
\(457\) −198.709 −0.434813 −0.217406 0.976081i \(-0.569760\pi\)
−0.217406 + 0.976081i \(0.569760\pi\)
\(458\) 339.565 0.741409
\(459\) 115.149i 0.250870i
\(460\) 226.758 38.4799i 0.492953 0.0836519i
\(461\) −677.481 −1.46959 −0.734795 0.678290i \(-0.762722\pi\)
−0.734795 + 0.678290i \(0.762722\pi\)
\(462\) 1.67893i 0.00363404i
\(463\) 317.422i 0.685576i −0.939413 0.342788i \(-0.888629\pi\)
0.939413 0.342788i \(-0.111371\pi\)
\(464\) −7.18790 −0.0154912
\(465\) 339.913 80.9162i 0.730995 0.174013i
\(466\) 518.954 1.11364
\(467\) −231.177 −0.495025 −0.247512 0.968885i \(-0.579613\pi\)
−0.247512 + 0.968885i \(0.579613\pi\)
\(468\) 144.281i 0.308293i
\(469\) −209.535 −0.446770
\(470\) 9.41642 + 39.5565i 0.0200349 + 0.0841627i
\(471\) 228.915i 0.486019i
\(472\) 51.1797i 0.108432i
\(473\) 6.33183i 0.0133865i
\(474\) 152.056i 0.320793i
\(475\) 198.305 + 392.916i 0.417484 + 0.827191i
\(476\) 79.4865 0.166988
\(477\) −244.439 −0.512451
\(478\) 441.886i 0.924447i
\(479\) 603.191i 1.25927i 0.776891 + 0.629636i \(0.216796\pi\)
−0.776891 + 0.629636i \(0.783204\pi\)
\(480\) 11.3450 + 47.6581i 0.0236354 + 0.0992876i
\(481\) 1027.06i 2.13527i
\(482\) 264.583 0.548928
\(483\) −71.2914 4.68388i −0.147601 0.00969747i
\(484\) −241.708 −0.499396
\(485\) −174.391 732.582i −0.359570 1.51048i
\(486\) 22.0454 0.0453609
\(487\) 432.259i 0.887596i −0.896127 0.443798i \(-0.853631\pi\)
0.896127 0.443798i \(-0.146369\pi\)
\(488\) −93.7371 −0.192084
\(489\) 170.261 0.348183
\(490\) 314.939 74.9712i 0.642732 0.153002i
\(491\) −457.843 −0.932471 −0.466235 0.884661i \(-0.654390\pi\)
−0.466235 + 0.884661i \(0.654390\pi\)
\(492\) 4.38864i 0.00892000i
\(493\) −39.8218 −0.0807745
\(494\) 598.695i 1.21193i
\(495\) −5.57692 + 1.32759i −0.0112665 + 0.00268199i
\(496\) 161.386 0.325375
\(497\) −50.8465 −0.102307
\(498\) 362.866 0.728647
\(499\) 232.828 0.466589 0.233294 0.972406i \(-0.425049\pi\)
0.233294 + 0.972406i \(0.425049\pi\)
\(500\) 161.265 + 191.033i 0.322530 + 0.382066i
\(501\) 120.087 0.239695
\(502\) −142.360 −0.283586
\(503\) 874.235 1.73804 0.869021 0.494775i \(-0.164750\pi\)
0.869021 + 0.494775i \(0.164750\pi\)
\(504\) 15.2177i 0.0301939i
\(505\) −122.546 514.792i −0.242666 1.01939i
\(506\) −0.814982 + 12.4045i −0.00161064 + 0.0245148i
\(507\) 708.842i 1.39811i
\(508\) 134.417i 0.264599i
\(509\) 670.805 1.31789 0.658944 0.752192i \(-0.271003\pi\)
0.658944 + 0.752192i \(0.271003\pi\)
\(510\) 62.8527 + 264.032i 0.123241 + 0.517709i
\(511\) 201.421i 0.394170i
\(512\) 22.6274i 0.0441942i
\(513\) 91.4776 0.178319
\(514\) 61.0738 0.118821
\(515\) −127.476 535.501i −0.247526 1.03981i
\(516\) 57.3916i 0.111224i
\(517\) −2.19773 −0.00425092
\(518\) 108.327i 0.209126i
\(519\) −585.338 −1.12782
\(520\) −78.7539 330.829i −0.151450 0.636210i
\(521\) 251.816i 0.483332i −0.970359 0.241666i \(-0.922306\pi\)
0.970359 0.241666i \(-0.0776939\pi\)
\(522\) 7.62392i 0.0146052i
\(523\) −755.642 −1.44482 −0.722411 0.691464i \(-0.756966\pi\)
−0.722411 + 0.691464i \(0.756966\pi\)
\(524\) 289.378 0.552249
\(525\) −34.9900 69.3283i −0.0666477 0.132054i
\(526\) 211.505i 0.402102i
\(527\) 894.098 1.69658
\(528\) −2.64785 −0.00501486
\(529\) −524.453 69.2123i −0.991404 0.130836i
\(530\) −560.487 + 133.424i −1.05752 + 0.251743i
\(531\) −54.2843 −0.102230
\(532\) 63.1461i 0.118696i
\(533\) 30.4647i 0.0571571i
\(534\) 251.652i 0.471258i
\(535\) 168.398 + 707.404i 0.314762 + 1.32225i
\(536\) 330.460i 0.616529i
\(537\) 234.433i 0.436561i
\(538\) 10.6183i 0.0197367i
\(539\) 17.4977i 0.0324634i
\(540\) 50.5490 12.0332i 0.0936093 0.0222837i
\(541\) −422.567 −0.781085 −0.390543 0.920585i \(-0.627713\pi\)
−0.390543 + 0.920585i \(0.627713\pi\)
\(542\) 472.270i 0.871348i
\(543\) 476.699 0.877899
\(544\) 125.359i 0.230439i
\(545\) −529.431 + 126.031i −0.971433 + 0.231250i
\(546\) 105.637i 0.193475i
\(547\) 962.341i 1.75931i 0.475615 + 0.879653i \(0.342226\pi\)
−0.475615 + 0.879653i \(0.657774\pi\)
\(548\) 132.447 0.241691
\(549\) 99.4232i 0.181099i
\(550\) −12.0629 + 6.08817i −0.0219326 + 0.0110694i
\(551\) 31.6355i 0.0574147i
\(552\) 7.38697 112.434i 0.0133822 0.203685i
\(553\) 111.330i 0.201320i
\(554\) 25.2807 0.0456329
\(555\) 359.833 85.6583i 0.648348 0.154339i
\(556\) −116.541 −0.209606
\(557\) 157.867 0.283424 0.141712 0.989908i \(-0.454739\pi\)
0.141712 + 0.989908i \(0.454739\pi\)
\(558\) 171.176i 0.306767i
\(559\) 398.396i 0.712695i
\(560\) −8.30640 34.8935i −0.0148329 0.0623098i
\(561\) −14.6694 −0.0261486
\(562\) −531.131 −0.945073
\(563\) −417.217 −0.741060 −0.370530 0.928820i \(-0.620824\pi\)
−0.370530 + 0.928820i \(0.620824\pi\)
\(564\) 19.9201 0.0353194
\(565\) −64.8994 272.629i −0.114866 0.482530i
\(566\) 567.229i 1.00217i
\(567\) −16.1408 −0.0284671
\(568\) 80.1903i 0.141180i
\(569\) 93.8235i 0.164892i −0.996596 0.0824460i \(-0.973727\pi\)
0.996596 0.0824460i \(-0.0262732\pi\)
\(570\) 209.754 49.9319i 0.367989 0.0875998i
\(571\) 781.206i 1.36814i 0.729418 + 0.684068i \(0.239791\pi\)
−0.729418 + 0.684068i \(0.760209\pi\)
\(572\) 18.3806 0.0321339
\(573\) −75.1000 −0.131065
\(574\) 3.21320i 0.00559791i
\(575\) −224.866 529.207i −0.391071 0.920361i
\(576\) 24.0000 0.0416667
\(577\) 877.034i 1.51999i −0.649929 0.759995i \(-0.725201\pi\)
0.649929 0.759995i \(-0.274799\pi\)
\(578\) 285.795i 0.494454i
\(579\) 71.8003 0.124007
\(580\) 4.16141 + 17.4813i 0.00717485 + 0.0301401i
\(581\) −265.678 −0.457276
\(582\) −368.919 −0.633882
\(583\) 31.1402i 0.0534138i
\(584\) −317.662 −0.543942
\(585\) −350.897 + 83.5311i −0.599824 + 0.142788i
\(586\) 113.081i 0.192972i
\(587\) 820.156i 1.39720i 0.715513 + 0.698600i \(0.246193\pi\)
−0.715513 + 0.698600i \(0.753807\pi\)
\(588\) 158.599i 0.269726i
\(589\) 710.296i 1.20593i
\(590\) −124.471 + 29.6304i −0.210968 + 0.0502210i
\(591\) 360.627 0.610198
\(592\) 170.844 0.288588
\(593\) 423.705i 0.714510i 0.934007 + 0.357255i \(0.116287\pi\)
−0.934007 + 0.357255i \(0.883713\pi\)
\(594\) 2.80846i 0.00472805i
\(595\) −46.0185 193.314i −0.0773420 0.324898i
\(596\) 356.562i 0.598259i
\(597\) 468.508 0.784770
\(598\) −51.2783 + 780.486i −0.0857497 + 1.30516i
\(599\) 874.974 1.46073 0.730363 0.683060i \(-0.239351\pi\)
0.730363 + 0.683060i \(0.239351\pi\)
\(600\) 109.338 55.1830i 0.182230 0.0919717i
\(601\) −644.991 −1.07320 −0.536598 0.843838i \(-0.680291\pi\)
−0.536598 + 0.843838i \(0.680291\pi\)
\(602\) 42.0200i 0.0698007i
\(603\) −350.505 −0.581269
\(604\) −433.827 −0.718257
\(605\) 139.936 + 587.843i 0.231299 + 0.971642i
\(606\) −259.243 −0.427793
\(607\) 251.491i 0.414318i −0.978307 0.207159i \(-0.933578\pi\)
0.978307 0.207159i \(-0.0664217\pi\)
\(608\) 99.5883 0.163796
\(609\) 5.58195i 0.00916577i
\(610\) 54.2689 + 227.972i 0.0889653 + 0.373725i
\(611\) −138.280 −0.226318
\(612\) 132.963 0.217260
\(613\) 986.481 1.60927 0.804634 0.593771i \(-0.202361\pi\)
0.804634 + 0.593771i \(0.202361\pi\)
\(614\) 347.824 0.566489
\(615\) 10.6733 2.54079i 0.0173550 0.00413137i
\(616\) 1.93866 0.00314717
\(617\) −192.369 −0.311782 −0.155891 0.987774i \(-0.549825\pi\)
−0.155891 + 0.987774i \(0.549825\pi\)
\(618\) −269.672 −0.436362
\(619\) 864.558i 1.39670i −0.715756 0.698351i \(-0.753918\pi\)
0.715756 0.698351i \(-0.246082\pi\)
\(620\) −93.4340 392.497i −0.150700 0.633060i
\(621\) −119.254 7.83507i −0.192036 0.0126169i
\(622\) 603.364i 0.970039i
\(623\) 184.250i 0.295747i
\(624\) −166.601 −0.266989
\(625\) 371.236 502.801i 0.593978 0.804481i
\(626\) 467.377i 0.746609i
\(627\) 11.6538i 0.0185865i
\(628\) 264.328 0.420905
\(629\) 946.496 1.50476
\(630\) −37.0101 + 8.81027i −0.0587463 + 0.0139846i
\(631\) 643.458i 1.01974i −0.860251 0.509871i \(-0.829693\pi\)
0.860251 0.509871i \(-0.170307\pi\)
\(632\) 175.579 0.277815
\(633\) 35.1291i 0.0554962i
\(634\) 64.8780 0.102331
\(635\) 326.906 77.8201i 0.514813 0.122551i
\(636\) 282.254i 0.443796i
\(637\) 1100.95i 1.72834i
\(638\) −0.971245 −0.00152233
\(639\) −85.0547 −0.133106
\(640\) 55.0308 13.1001i 0.0859856 0.0204689i
\(641\) 716.907i 1.11842i 0.829026 + 0.559210i \(0.188895\pi\)
−0.829026 + 0.559210i \(0.811105\pi\)
\(642\) 356.240 0.554890
\(643\) −275.422 −0.428339 −0.214170 0.976796i \(-0.568705\pi\)
−0.214170 + 0.976796i \(0.568705\pi\)
\(644\) −5.40847 + 82.3202i −0.00839825 + 0.127826i
\(645\) 139.579 33.2267i 0.216401 0.0515142i
\(646\) 551.731 0.854073
\(647\) 593.326i 0.917041i 0.888684 + 0.458521i \(0.151620\pi\)
−0.888684 + 0.458521i \(0.848380\pi\)
\(648\) 25.4558i 0.0392837i
\(649\) 6.91553i 0.0106557i
\(650\) −758.995 + 383.065i −1.16768 + 0.589331i
\(651\) 125.329i 0.192517i
\(652\) 196.601i 0.301535i
\(653\) 376.904i 0.577188i 0.957452 + 0.288594i \(0.0931877\pi\)
−0.957452 + 0.288594i \(0.906812\pi\)
\(654\) 266.615i 0.407668i
\(655\) −167.535 703.780i −0.255778 1.07447i
\(656\) 5.06756 0.00772494
\(657\) 336.932i 0.512833i
\(658\) −14.5848 −0.0221654
\(659\) 821.196i 1.24612i 0.782172 + 0.623062i \(0.214112\pi\)
−0.782172 + 0.623062i \(0.785888\pi\)
\(660\) 1.53296 + 6.43967i 0.00232267 + 0.00975707i
\(661\) 1108.77i 1.67741i −0.544587 0.838705i \(-0.683313\pi\)
0.544587 0.838705i \(-0.316687\pi\)
\(662\) 746.816i 1.12812i
\(663\) −922.992 −1.39214
\(664\) 419.002i 0.631027i
\(665\) −153.574 + 36.5583i −0.230938 + 0.0549749i
\(666\) 181.207i 0.272083i
\(667\) 2.70959 41.2415i 0.00406235 0.0618313i
\(668\) 138.665i 0.207582i
\(669\) −338.115 −0.505404
\(670\) −803.691 + 191.319i −1.19954 + 0.285550i
\(671\) −12.6660 −0.0188763
\(672\) −17.5719 −0.0261487
\(673\) 45.4888i 0.0675911i −0.999429 0.0337955i \(-0.989240\pi\)
0.999429 0.0337955i \(-0.0107595\pi\)
\(674\) 676.912i 1.00432i
\(675\) −58.5304 115.971i −0.0867117 0.171808i
\(676\) 818.500 1.21080
\(677\) −206.922 −0.305645 −0.152822 0.988254i \(-0.548836\pi\)
−0.152822 + 0.988254i \(0.548836\pi\)
\(678\) −137.293 −0.202497
\(679\) 270.109 0.397804
\(680\) 304.877 72.5761i 0.448349 0.106730i
\(681\) 154.301i 0.226580i
\(682\) 21.8069 0.0319749
\(683\) 437.345i 0.640330i −0.947362 0.320165i \(-0.896262\pi\)
0.947362 0.320165i \(-0.103738\pi\)
\(684\) 105.629i 0.154429i
\(685\) −76.6796 322.115i −0.111941 0.470241i
\(686\) 240.399i 0.350435i
\(687\) −415.881 −0.605358
\(688\) 66.2701 0.0963228
\(689\) 1959.33i 2.84373i
\(690\) −277.721 + 47.1280i −0.402494 + 0.0683015i
\(691\) −552.016 −0.798866 −0.399433 0.916762i \(-0.630793\pi\)
−0.399433 + 0.916762i \(0.630793\pi\)
\(692\) 675.890i 0.976719i
\(693\) 2.05626i 0.00296718i
\(694\) −64.8104 −0.0933867
\(695\) 67.4712 + 283.433i 0.0970809 + 0.407817i
\(696\) 8.80334 0.0126485
\(697\) 28.0749 0.0402797
\(698\) 53.7474i 0.0770020i
\(699\) −635.587 −0.909280
\(700\) −80.0534 + 40.4030i −0.114362 + 0.0577186i
\(701\) 645.651i 0.921042i −0.887649 0.460521i \(-0.847663\pi\)
0.887649 0.460521i \(-0.152337\pi\)
\(702\) 176.707i 0.251720i
\(703\) 751.922i 1.06959i
\(704\) 3.05747i 0.00434300i
\(705\) −11.5327 48.4466i −0.0163585 0.0687186i
\(706\) −469.534 −0.665062
\(707\) 189.808 0.268470
\(708\) 62.6821i 0.0885341i
\(709\) 552.330i 0.779027i 0.921021 + 0.389513i \(0.127357\pi\)
−0.921021 + 0.389513i \(0.872643\pi\)
\(710\) −195.026 + 46.4260i −0.274685 + 0.0653887i
\(711\) 186.230i 0.261927i
\(712\) −290.582 −0.408121
\(713\) −60.8369 + 925.973i −0.0853252 + 1.29870i
\(714\) −97.3506 −0.136345
\(715\) −10.6414 44.7024i −0.0148831 0.0625208i
\(716\) 270.700 0.378073
\(717\) 541.197i 0.754808i
\(718\) 543.835 0.757430
\(719\) 882.221 1.22701 0.613505 0.789691i \(-0.289759\pi\)
0.613505 + 0.789691i \(0.289759\pi\)
\(720\) −13.8947 58.3690i −0.0192982 0.0810680i
\(721\) 197.444 0.273847
\(722\) 72.2213i 0.100029i
\(723\) −324.047 −0.448198
\(724\) 550.445i 0.760283i
\(725\) 40.1059 20.2415i 0.0553185 0.0279192i
\(726\) 296.030 0.407755
\(727\) −574.892 −0.790773 −0.395387 0.918515i \(-0.629389\pi\)
−0.395387 + 0.918515i \(0.629389\pi\)
\(728\) 121.979 0.167554
\(729\) −27.0000 −0.0370370
\(730\) 183.910 + 772.567i 0.251931 + 1.05831i
\(731\) 367.144 0.502249
\(732\) 114.804 0.156836
\(733\) −563.848 −0.769233 −0.384617 0.923076i \(-0.625666\pi\)
−0.384617 + 0.923076i \(0.625666\pi\)
\(734\) 224.784i 0.306245i
\(735\) −385.719 + 91.8205i −0.524788 + 0.124926i
\(736\) −129.828 8.52974i −0.176396 0.0115893i
\(737\) 44.6525i 0.0605868i
\(738\) 5.37496i 0.00728315i
\(739\) 1029.01 1.39244 0.696218 0.717831i \(-0.254865\pi\)
0.696218 + 0.717831i \(0.254865\pi\)
\(740\) −98.9096 415.499i −0.133662 0.561486i
\(741\) 733.249i 0.989540i
\(742\) 206.656i 0.278512i
\(743\) 71.4526 0.0961678 0.0480839 0.998843i \(-0.484689\pi\)
0.0480839 + 0.998843i \(0.484689\pi\)
\(744\) −197.657 −0.265668
\(745\) 867.173 206.431i 1.16399 0.277088i
\(746\) 499.715i 0.669860i
\(747\) −444.419 −0.594938
\(748\) 16.9388i 0.0226454i
\(749\) −260.826 −0.348232
\(750\) −197.508 233.967i −0.263344 0.311956i
\(751\) 579.354i 0.771444i 0.922615 + 0.385722i \(0.126048\pi\)
−0.922615 + 0.385722i \(0.873952\pi\)
\(752\) 23.0018i 0.0305875i
\(753\) 174.355 0.231547
\(754\) −61.1103 −0.0810482
\(755\) 251.163 + 1055.08i 0.332666 + 1.39746i
\(756\) 18.6378i 0.0246532i
\(757\) 1033.03 1.36464 0.682321 0.731052i \(-0.260970\pi\)
0.682321 + 0.731052i \(0.260970\pi\)
\(758\) −699.559 −0.922900
\(759\) 0.998145 15.1924i 0.00131508 0.0200163i
\(760\) −57.6564 242.203i −0.0758636 0.318688i
\(761\) −714.171 −0.938463 −0.469232 0.883075i \(-0.655469\pi\)
−0.469232 + 0.883075i \(0.655469\pi\)
\(762\) 164.626i 0.216045i
\(763\) 195.206i 0.255840i
\(764\) 86.7180i 0.113505i
\(765\) −76.9785 323.371i −0.100626 0.422708i
\(766\) 466.282i 0.608723i
\(767\) 435.122i 0.567304i
\(768\) 27.7128i 0.0360844i
\(769\) 129.899i 0.168919i 0.996427 + 0.0844595i \(0.0269164\pi\)
−0.996427 + 0.0844595i \(0.973084\pi\)
\(770\) −1.12238 4.71489i −0.00145764 0.00612323i
\(771\) −74.7998 −0.0970166
\(772\) 82.9079i 0.107394i
\(773\) 946.778 1.22481 0.612405 0.790544i \(-0.290202\pi\)
0.612405 + 0.790544i \(0.290202\pi\)
\(774\) 70.2900i 0.0908140i
\(775\) −900.476 + 454.471i −1.16190 + 0.586414i
\(776\) 425.991i 0.548958i
\(777\) 132.673i 0.170751i
\(778\) −450.369 −0.578880
\(779\) 22.3035i 0.0286309i
\(780\) 96.4534 + 405.181i 0.123658 + 0.519463i
\(781\) 10.8355i 0.0138739i
\(782\) −719.262 47.2558i −0.919772 0.0604294i
\(783\) 9.33735i 0.0119251i
\(784\) −183.134 −0.233590
\(785\) −153.032 642.857i −0.194945 0.818926i
\(786\) −354.415 −0.450909
\(787\) −1533.79 −1.94890 −0.974450 0.224603i \(-0.927892\pi\)
−0.974450 + 0.224603i \(0.927892\pi\)