Properties

Label 483.3.f.a.22.19
Level $483$
Weight $3$
Character 483.22
Analytic conductor $13.161$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 483.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.1607967686\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 22.19
Character \(\chi\) \(=\) 483.22
Dual form 483.3.f.a.22.20

$q$-expansion

\(f(q)\) \(=\) \(q-0.876983 q^{2} +1.73205 q^{3} -3.23090 q^{4} +8.50705i q^{5} -1.51898 q^{6} +2.64575i q^{7} +6.34138 q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-0.876983 q^{2} +1.73205 q^{3} -3.23090 q^{4} +8.50705i q^{5} -1.51898 q^{6} +2.64575i q^{7} +6.34138 q^{8} +3.00000 q^{9} -7.46053i q^{10} -12.5240i q^{11} -5.59608 q^{12} +23.0788 q^{13} -2.32028i q^{14} +14.7346i q^{15} +7.36233 q^{16} +13.0806i q^{17} -2.63095 q^{18} +23.2463i q^{19} -27.4854i q^{20} +4.58258i q^{21} +10.9834i q^{22} +(-19.0867 + 12.8334i) q^{23} +10.9836 q^{24} -47.3698 q^{25} -20.2397 q^{26} +5.19615 q^{27} -8.54816i q^{28} -13.6391 q^{29} -12.9220i q^{30} -23.6204 q^{31} -31.8221 q^{32} -21.6923i q^{33} -11.4714i q^{34} -22.5075 q^{35} -9.69270 q^{36} +38.3359i q^{37} -20.3866i q^{38} +39.9737 q^{39} +53.9464i q^{40} -27.0412 q^{41} -4.01884i q^{42} -5.04663i q^{43} +40.4639i q^{44} +25.5211i q^{45} +(16.7387 - 11.2547i) q^{46} -21.8114 q^{47} +12.7519 q^{48} -7.00000 q^{49} +41.5425 q^{50} +22.6562i q^{51} -74.5654 q^{52} +55.7900i q^{53} -4.55694 q^{54} +106.543 q^{55} +16.7777i q^{56} +40.2637i q^{57} +11.9613 q^{58} +50.7804 q^{59} -47.6061i q^{60} -68.5432i q^{61} +20.7146 q^{62} +7.93725i q^{63} -1.54183 q^{64} +196.333i q^{65} +19.0238i q^{66} -34.3720i q^{67} -42.2620i q^{68} +(-33.0592 + 22.2281i) q^{69} +19.7387 q^{70} -103.295 q^{71} +19.0241 q^{72} +128.233 q^{73} -33.6199i q^{74} -82.0470 q^{75} -75.1064i q^{76} +33.1355 q^{77} -35.0562 q^{78} -130.267i q^{79} +62.6316i q^{80} +9.00000 q^{81} +23.7147 q^{82} +39.2795i q^{83} -14.8058i q^{84} -111.277 q^{85} +4.42581i q^{86} -23.6237 q^{87} -79.4196i q^{88} +5.35404i q^{89} -22.3816i q^{90} +61.0608i q^{91} +(61.6674 - 41.4635i) q^{92} -40.9117 q^{93} +19.1282 q^{94} -197.757 q^{95} -55.1176 q^{96} +142.335i q^{97} +6.13888 q^{98} -37.5721i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 4q^{2} + 116q^{4} - 24q^{6} - 4q^{8} + 144q^{9} + O(q^{10}) \) \( 48q + 4q^{2} + 116q^{4} - 24q^{6} - 4q^{8} + 144q^{9} + 16q^{13} + 324q^{16} + 12q^{18} - 4q^{23} - 24q^{24} - 176q^{25} + 136q^{26} - 128q^{29} - 8q^{31} - 252q^{32} - 56q^{35} + 348q^{36} + 96q^{39} - 24q^{41} - 148q^{46} - 408q^{47} - 96q^{48} - 336q^{49} + 236q^{50} - 32q^{52} - 72q^{54} - 24q^{55} - 56q^{58} + 136q^{59} + 184q^{62} + 716q^{64} - 48q^{69} - 112q^{70} + 48q^{71} - 12q^{72} - 224q^{73} - 48q^{75} + 224q^{77} - 96q^{78} + 432q^{81} + 640q^{82} - 424q^{85} + 312q^{87} + 1060q^{92} + 192q^{93} + 216q^{94} + 624q^{95} + 48q^{96} - 28q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(346\) \(442\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.876983 −0.438491 −0.219246 0.975670i \(-0.570360\pi\)
−0.219246 + 0.975670i \(0.570360\pi\)
\(3\) 1.73205 0.577350
\(4\) −3.23090 −0.807725
\(5\) 8.50705i 1.70141i 0.525644 + 0.850705i \(0.323824\pi\)
−0.525644 + 0.850705i \(0.676176\pi\)
\(6\) −1.51898 −0.253163
\(7\) 2.64575i 0.377964i
\(8\) 6.34138 0.792672
\(9\) 3.00000 0.333333
\(10\) 7.46053i 0.746053i
\(11\) 12.5240i 1.13855i −0.822148 0.569275i \(-0.807224\pi\)
0.822148 0.569275i \(-0.192776\pi\)
\(12\) −5.59608 −0.466340
\(13\) 23.0788 1.77529 0.887647 0.460525i \(-0.152339\pi\)
0.887647 + 0.460525i \(0.152339\pi\)
\(14\) 2.32028i 0.165734i
\(15\) 14.7346i 0.982309i
\(16\) 7.36233 0.460145
\(17\) 13.0806i 0.769445i 0.923032 + 0.384723i \(0.125703\pi\)
−0.923032 + 0.384723i \(0.874297\pi\)
\(18\) −2.63095 −0.146164
\(19\) 23.2463i 1.22349i 0.791056 + 0.611744i \(0.209532\pi\)
−0.791056 + 0.611744i \(0.790468\pi\)
\(20\) 27.4854i 1.37427i
\(21\) 4.58258i 0.218218i
\(22\) 10.9834i 0.499244i
\(23\) −19.0867 + 12.8334i −0.829858 + 0.557974i
\(24\) 10.9836 0.457649
\(25\) −47.3698 −1.89479
\(26\) −20.2397 −0.778451
\(27\) 5.19615 0.192450
\(28\) 8.54816i 0.305291i
\(29\) −13.6391 −0.470315 −0.235158 0.971957i \(-0.575561\pi\)
−0.235158 + 0.971957i \(0.575561\pi\)
\(30\) 12.9220i 0.430734i
\(31\) −23.6204 −0.761947 −0.380973 0.924586i \(-0.624411\pi\)
−0.380973 + 0.924586i \(0.624411\pi\)
\(32\) −31.8221 −0.994442
\(33\) 21.6923i 0.657342i
\(34\) 11.4714i 0.337395i
\(35\) −22.5075 −0.643072
\(36\) −9.69270 −0.269242
\(37\) 38.3359i 1.03610i 0.855349 + 0.518052i \(0.173343\pi\)
−0.855349 + 0.518052i \(0.826657\pi\)
\(38\) 20.3866i 0.536489i
\(39\) 39.9737 1.02497
\(40\) 53.9464i 1.34866i
\(41\) −27.0412 −0.659542 −0.329771 0.944061i \(-0.606972\pi\)
−0.329771 + 0.944061i \(0.606972\pi\)
\(42\) 4.01884i 0.0956867i
\(43\) 5.04663i 0.117363i −0.998277 0.0586817i \(-0.981310\pi\)
0.998277 0.0586817i \(-0.0186897\pi\)
\(44\) 40.4639i 0.919635i
\(45\) 25.5211i 0.567136i
\(46\) 16.7387 11.2547i 0.363886 0.244667i
\(47\) −21.8114 −0.464071 −0.232036 0.972707i \(-0.574539\pi\)
−0.232036 + 0.972707i \(0.574539\pi\)
\(48\) 12.7519 0.265665
\(49\) −7.00000 −0.142857
\(50\) 41.5425 0.830851
\(51\) 22.6562i 0.444239i
\(52\) −74.5654 −1.43395
\(53\) 55.7900i 1.05264i 0.850286 + 0.526321i \(0.176429\pi\)
−0.850286 + 0.526321i \(0.823571\pi\)
\(54\) −4.55694 −0.0843877
\(55\) 106.543 1.93714
\(56\) 16.7777i 0.299602i
\(57\) 40.2637i 0.706381i
\(58\) 11.9613 0.206229
\(59\) 50.7804 0.860685 0.430342 0.902666i \(-0.358393\pi\)
0.430342 + 0.902666i \(0.358393\pi\)
\(60\) 47.6061i 0.793436i
\(61\) 68.5432i 1.12366i −0.827253 0.561830i \(-0.810098\pi\)
0.827253 0.561830i \(-0.189902\pi\)
\(62\) 20.7146 0.334107
\(63\) 7.93725i 0.125988i
\(64\) −1.54183 −0.0240911
\(65\) 196.333i 3.02050i
\(66\) 19.0238i 0.288239i
\(67\) 34.3720i 0.513015i −0.966542 0.256508i \(-0.917428\pi\)
0.966542 0.256508i \(-0.0825719\pi\)
\(68\) 42.2620i 0.621500i
\(69\) −33.0592 + 22.2281i −0.479119 + 0.322146i
\(70\) 19.7387 0.281982
\(71\) −103.295 −1.45486 −0.727431 0.686181i \(-0.759286\pi\)
−0.727431 + 0.686181i \(0.759286\pi\)
\(72\) 19.0241 0.264224
\(73\) 128.233 1.75662 0.878308 0.478096i \(-0.158673\pi\)
0.878308 + 0.478096i \(0.158673\pi\)
\(74\) 33.6199i 0.454323i
\(75\) −82.0470 −1.09396
\(76\) 75.1064i 0.988242i
\(77\) 33.1355 0.430331
\(78\) −35.0562 −0.449439
\(79\) 130.267i 1.64894i −0.565903 0.824472i \(-0.691472\pi\)
0.565903 0.824472i \(-0.308528\pi\)
\(80\) 62.6316i 0.782896i
\(81\) 9.00000 0.111111
\(82\) 23.7147 0.289204
\(83\) 39.2795i 0.473247i 0.971601 + 0.236624i \(0.0760409\pi\)
−0.971601 + 0.236624i \(0.923959\pi\)
\(84\) 14.8058i 0.176260i
\(85\) −111.277 −1.30914
\(86\) 4.42581i 0.0514629i
\(87\) −23.6237 −0.271537
\(88\) 79.4196i 0.902496i
\(89\) 5.35404i 0.0601578i 0.999548 + 0.0300789i \(0.00957586\pi\)
−0.999548 + 0.0300789i \(0.990424\pi\)
\(90\) 22.3816i 0.248684i
\(91\) 61.0608i 0.670998i
\(92\) 61.6674 41.4635i 0.670298 0.450690i
\(93\) −40.9117 −0.439910
\(94\) 19.1282 0.203491
\(95\) −197.757 −2.08165
\(96\) −55.1176 −0.574141
\(97\) 142.335i 1.46737i 0.679487 + 0.733687i \(0.262202\pi\)
−0.679487 + 0.733687i \(0.737798\pi\)
\(98\) 6.13888 0.0626416
\(99\) 37.5721i 0.379516i
\(100\) 153.047 1.53047
\(101\) 83.7772 0.829477 0.414738 0.909941i \(-0.363873\pi\)
0.414738 + 0.909941i \(0.363873\pi\)
\(102\) 19.8691i 0.194795i
\(103\) 45.4480i 0.441243i 0.975360 + 0.220621i \(0.0708085\pi\)
−0.975360 + 0.220621i \(0.929192\pi\)
\(104\) 146.351 1.40723
\(105\) −38.9842 −0.371278
\(106\) 48.9269i 0.461574i
\(107\) 93.2200i 0.871215i 0.900137 + 0.435607i \(0.143466\pi\)
−0.900137 + 0.435607i \(0.856534\pi\)
\(108\) −16.7883 −0.155447
\(109\) 121.762i 1.11708i −0.829476 0.558542i \(-0.811361\pi\)
0.829476 0.558542i \(-0.188639\pi\)
\(110\) −93.4360 −0.849418
\(111\) 66.3997i 0.598195i
\(112\) 19.4789i 0.173919i
\(113\) 139.100i 1.23098i 0.788146 + 0.615488i \(0.211041\pi\)
−0.788146 + 0.615488i \(0.788959\pi\)
\(114\) 35.3106i 0.309742i
\(115\) −109.174 162.372i −0.949342 1.41193i
\(116\) 44.0667 0.379886
\(117\) 69.2365 0.591765
\(118\) −44.5336 −0.377403
\(119\) −34.6079 −0.290823
\(120\) 93.4379i 0.778649i
\(121\) −35.8516 −0.296294
\(122\) 60.1113i 0.492715i
\(123\) −46.8368 −0.380787
\(124\) 76.3150 0.615444
\(125\) 190.301i 1.52241i
\(126\) 6.96084i 0.0552447i
\(127\) −202.970 −1.59819 −0.799096 0.601204i \(-0.794688\pi\)
−0.799096 + 0.601204i \(0.794688\pi\)
\(128\) 128.641 1.00501
\(129\) 8.74102i 0.0677598i
\(130\) 172.180i 1.32446i
\(131\) −28.7014 −0.219095 −0.109547 0.993982i \(-0.534940\pi\)
−0.109547 + 0.993982i \(0.534940\pi\)
\(132\) 70.0856i 0.530951i
\(133\) −61.5039 −0.462435
\(134\) 30.1437i 0.224953i
\(135\) 44.2039i 0.327436i
\(136\) 82.9488i 0.609918i
\(137\) 156.835i 1.14478i 0.819982 + 0.572389i \(0.193983\pi\)
−0.819982 + 0.572389i \(0.806017\pi\)
\(138\) 28.9924 19.4937i 0.210090 0.141258i
\(139\) 159.986 1.15098 0.575488 0.817810i \(-0.304812\pi\)
0.575488 + 0.817810i \(0.304812\pi\)
\(140\) 72.7196 0.519426
\(141\) −37.7784 −0.267932
\(142\) 90.5881 0.637944
\(143\) 289.040i 2.02126i
\(144\) 22.0870 0.153382
\(145\) 116.029i 0.800199i
\(146\) −112.458 −0.770261
\(147\) −12.1244 −0.0824786
\(148\) 123.859i 0.836888i
\(149\) 248.689i 1.66905i −0.550970 0.834525i \(-0.685742\pi\)
0.550970 0.834525i \(-0.314258\pi\)
\(150\) 71.9538 0.479692
\(151\) 127.529 0.844560 0.422280 0.906465i \(-0.361230\pi\)
0.422280 + 0.906465i \(0.361230\pi\)
\(152\) 147.413i 0.969825i
\(153\) 39.2417i 0.256482i
\(154\) −29.0593 −0.188696
\(155\) 200.939i 1.29638i
\(156\) −129.151 −0.827891
\(157\) 30.5819i 0.194789i −0.995246 0.0973946i \(-0.968949\pi\)
0.995246 0.0973946i \(-0.0310509\pi\)
\(158\) 114.242i 0.723048i
\(159\) 96.6311i 0.607743i
\(160\) 270.712i 1.69195i
\(161\) −33.9540 50.4988i −0.210894 0.313657i
\(162\) −7.89285 −0.0487213
\(163\) 272.859 1.67398 0.836990 0.547218i \(-0.184313\pi\)
0.836990 + 0.547218i \(0.184313\pi\)
\(164\) 87.3676 0.532729
\(165\) 184.537 1.11841
\(166\) 34.4475i 0.207515i
\(167\) −87.5074 −0.523996 −0.261998 0.965068i \(-0.584381\pi\)
−0.261998 + 0.965068i \(0.584381\pi\)
\(168\) 29.0598i 0.172975i
\(169\) 363.632 2.15167
\(170\) 97.5880 0.574047
\(171\) 69.7388i 0.407829i
\(172\) 16.3052i 0.0947974i
\(173\) 255.005 1.47402 0.737008 0.675884i \(-0.236238\pi\)
0.737008 + 0.675884i \(0.236238\pi\)
\(174\) 20.7176 0.119067
\(175\) 125.329i 0.716165i
\(176\) 92.2061i 0.523898i
\(177\) 87.9543 0.496917
\(178\) 4.69541i 0.0263787i
\(179\) −341.018 −1.90513 −0.952564 0.304337i \(-0.901565\pi\)
−0.952564 + 0.304337i \(0.901565\pi\)
\(180\) 82.4563i 0.458090i
\(181\) 292.617i 1.61667i 0.588725 + 0.808334i \(0.299630\pi\)
−0.588725 + 0.808334i \(0.700370\pi\)
\(182\) 53.5493i 0.294227i
\(183\) 118.720i 0.648745i
\(184\) −121.036 + 81.3814i −0.657806 + 0.442290i
\(185\) −326.125 −1.76284
\(186\) 35.8788 0.192897
\(187\) 163.822 0.876051
\(188\) 70.4703 0.374842
\(189\) 13.7477i 0.0727393i
\(190\) 173.430 0.912787
\(191\) 115.651i 0.605504i 0.953069 + 0.302752i \(0.0979054\pi\)
−0.953069 + 0.302752i \(0.902095\pi\)
\(192\) −2.67053 −0.0139090
\(193\) −134.250 −0.695598 −0.347799 0.937569i \(-0.613071\pi\)
−0.347799 + 0.937569i \(0.613071\pi\)
\(194\) 124.826i 0.643431i
\(195\) 340.058i 1.74389i
\(196\) 22.6163 0.115389
\(197\) 186.004 0.944182 0.472091 0.881550i \(-0.343499\pi\)
0.472091 + 0.881550i \(0.343499\pi\)
\(198\) 32.9501i 0.166415i
\(199\) 51.5488i 0.259039i 0.991577 + 0.129520i \(0.0413435\pi\)
−0.991577 + 0.129520i \(0.958656\pi\)
\(200\) −300.390 −1.50195
\(201\) 59.5341i 0.296190i
\(202\) −73.4711 −0.363719
\(203\) 36.0858i 0.177763i
\(204\) 73.2000i 0.358823i
\(205\) 230.041i 1.12215i
\(206\) 39.8571i 0.193481i
\(207\) −57.2602 + 38.5002i −0.276619 + 0.185991i
\(208\) 169.914 0.816893
\(209\) 291.137 1.39300
\(210\) 34.1885 0.162802
\(211\) 348.367 1.65103 0.825513 0.564382i \(-0.190886\pi\)
0.825513 + 0.564382i \(0.190886\pi\)
\(212\) 180.252i 0.850245i
\(213\) −178.912 −0.839964
\(214\) 81.7523i 0.382020i
\(215\) 42.9319 0.199683
\(216\) 32.9508 0.152550
\(217\) 62.4936i 0.287989i
\(218\) 106.783i 0.489832i
\(219\) 222.106 1.01418
\(220\) −344.229 −1.56468
\(221\) 301.884i 1.36599i
\(222\) 58.2314i 0.262303i
\(223\) −238.570 −1.06982 −0.534911 0.844909i \(-0.679655\pi\)
−0.534911 + 0.844909i \(0.679655\pi\)
\(224\) 84.1935i 0.375864i
\(225\) −142.109 −0.631598
\(226\) 121.989i 0.539773i
\(227\) 119.769i 0.527615i −0.964575 0.263807i \(-0.915022\pi\)
0.964575 0.263807i \(-0.0849783\pi\)
\(228\) 130.088i 0.570562i
\(229\) 224.050i 0.978382i −0.872177 0.489191i \(-0.837292\pi\)
0.872177 0.489191i \(-0.162708\pi\)
\(230\) 95.7440 + 142.397i 0.416278 + 0.619119i
\(231\) 57.3924 0.248452
\(232\) −86.4910 −0.372806
\(233\) 352.648 1.51351 0.756756 0.653697i \(-0.226783\pi\)
0.756756 + 0.653697i \(0.226783\pi\)
\(234\) −60.7192 −0.259484
\(235\) 185.550i 0.789575i
\(236\) −164.066 −0.695197
\(237\) 225.628i 0.952018i
\(238\) 30.3506 0.127523
\(239\) −365.595 −1.52969 −0.764844 0.644216i \(-0.777184\pi\)
−0.764844 + 0.644216i \(0.777184\pi\)
\(240\) 108.481i 0.452005i
\(241\) 91.4962i 0.379652i −0.981818 0.189826i \(-0.939208\pi\)
0.981818 0.189826i \(-0.0607924\pi\)
\(242\) 31.4412 0.129922
\(243\) 15.5885 0.0641500
\(244\) 221.456i 0.907608i
\(245\) 59.5493i 0.243058i
\(246\) 41.0751 0.166972
\(247\) 536.496i 2.17205i
\(248\) −149.786 −0.603974
\(249\) 68.0342i 0.273230i
\(250\) 166.891i 0.667563i
\(251\) 219.581i 0.874826i −0.899261 0.437413i \(-0.855895\pi\)
0.899261 0.437413i \(-0.144105\pi\)
\(252\) 25.6445i 0.101764i
\(253\) 160.726 + 239.043i 0.635281 + 0.944834i
\(254\) 178.001 0.700793
\(255\) −192.737 −0.755833
\(256\) −106.648 −0.416595
\(257\) −358.124 −1.39348 −0.696740 0.717324i \(-0.745367\pi\)
−0.696740 + 0.717324i \(0.745367\pi\)
\(258\) 7.66572i 0.0297121i
\(259\) −101.427 −0.391611
\(260\) 634.331i 2.43973i
\(261\) −40.9174 −0.156772
\(262\) 25.1706 0.0960711
\(263\) 12.2132i 0.0464378i −0.999730 0.0232189i \(-0.992609\pi\)
0.999730 0.0232189i \(-0.00739148\pi\)
\(264\) 137.559i 0.521056i
\(265\) −474.608 −1.79097
\(266\) 53.9378 0.202774
\(267\) 9.27348i 0.0347321i
\(268\) 111.053i 0.414376i
\(269\) 76.6918 0.285100 0.142550 0.989788i \(-0.454470\pi\)
0.142550 + 0.989788i \(0.454470\pi\)
\(270\) 38.7661i 0.143578i
\(271\) 182.371 0.672955 0.336477 0.941692i \(-0.390764\pi\)
0.336477 + 0.941692i \(0.390764\pi\)
\(272\) 96.3034i 0.354057i
\(273\) 105.760i 0.387401i
\(274\) 137.541i 0.501975i
\(275\) 593.262i 2.15731i
\(276\) 106.811 71.8168i 0.386996 0.260206i
\(277\) −267.169 −0.964510 −0.482255 0.876031i \(-0.660182\pi\)
−0.482255 + 0.876031i \(0.660182\pi\)
\(278\) −140.305 −0.504693
\(279\) −70.8611 −0.253982
\(280\) −142.729 −0.509745
\(281\) 307.421i 1.09402i −0.837125 0.547012i \(-0.815765\pi\)
0.837125 0.547012i \(-0.184235\pi\)
\(282\) 33.1310 0.117486
\(283\) 135.101i 0.477389i −0.971095 0.238694i \(-0.923281\pi\)
0.971095 0.238694i \(-0.0767194\pi\)
\(284\) 333.736 1.17513
\(285\) −342.525 −1.20184
\(286\) 253.483i 0.886305i
\(287\) 71.5444i 0.249284i
\(288\) −95.4664 −0.331481
\(289\) 117.899 0.407954
\(290\) 101.755i 0.350880i
\(291\) 246.532i 0.847189i
\(292\) −414.308 −1.41886
\(293\) 430.595i 1.46961i 0.678280 + 0.734803i \(0.262726\pi\)
−0.678280 + 0.734803i \(0.737274\pi\)
\(294\) 10.6329 0.0361662
\(295\) 431.991i 1.46438i
\(296\) 243.102i 0.821291i
\(297\) 65.0768i 0.219114i
\(298\) 218.096i 0.731864i
\(299\) −440.499 + 296.180i −1.47324 + 0.990568i
\(300\) 265.086 0.883619
\(301\) 13.3521 0.0443592
\(302\) −111.840 −0.370333
\(303\) 145.106 0.478899
\(304\) 171.147i 0.562982i
\(305\) 583.101 1.91181
\(306\) 34.4143i 0.112465i
\(307\) 197.821 0.644368 0.322184 0.946677i \(-0.395583\pi\)
0.322184 + 0.946677i \(0.395583\pi\)
\(308\) −107.057 −0.347589
\(309\) 78.7182i 0.254752i
\(310\) 176.220i 0.568453i
\(311\) 113.735 0.365707 0.182853 0.983140i \(-0.441467\pi\)
0.182853 + 0.983140i \(0.441467\pi\)
\(312\) 253.488 0.812462
\(313\) 360.036i 1.15027i 0.818057 + 0.575137i \(0.195051\pi\)
−0.818057 + 0.575137i \(0.804949\pi\)
\(314\) 26.8198i 0.0854134i
\(315\) −67.5226 −0.214357
\(316\) 420.878i 1.33189i
\(317\) 379.702 1.19780 0.598899 0.800824i \(-0.295605\pi\)
0.598899 + 0.800824i \(0.295605\pi\)
\(318\) 84.7438i 0.266490i
\(319\) 170.817i 0.535477i
\(320\) 13.1164i 0.0409888i
\(321\) 161.462i 0.502996i
\(322\) 29.7771 + 44.2866i 0.0924754 + 0.137536i
\(323\) −304.074 −0.941407
\(324\) −29.0781 −0.0897473
\(325\) −1093.24 −3.36381
\(326\) −239.292 −0.734026
\(327\) 210.898i 0.644949i
\(328\) −171.479 −0.522801
\(329\) 57.7074i 0.175402i
\(330\) −161.836 −0.490412
\(331\) 406.011 1.22662 0.613309 0.789843i \(-0.289838\pi\)
0.613309 + 0.789843i \(0.289838\pi\)
\(332\) 126.908i 0.382254i
\(333\) 115.008i 0.345368i
\(334\) 76.7425 0.229768
\(335\) 292.405 0.872849
\(336\) 33.7384i 0.100412i
\(337\) 471.913i 1.40034i 0.713978 + 0.700168i \(0.246892\pi\)
−0.713978 + 0.700168i \(0.753108\pi\)
\(338\) −318.899 −0.943488
\(339\) 240.929i 0.710705i
\(340\) 359.525 1.05743
\(341\) 295.822i 0.867514i
\(342\) 61.1597i 0.178830i
\(343\) 18.5203i 0.0539949i
\(344\) 32.0026i 0.0930307i
\(345\) −189.096 281.236i −0.548103 0.815177i
\(346\) −223.635 −0.646343
\(347\) 372.428 1.07328 0.536639 0.843812i \(-0.319694\pi\)
0.536639 + 0.843812i \(0.319694\pi\)
\(348\) 76.3258 0.219327
\(349\) 33.8607 0.0970222 0.0485111 0.998823i \(-0.484552\pi\)
0.0485111 + 0.998823i \(0.484552\pi\)
\(350\) 109.911i 0.314032i
\(351\) 119.921 0.341655
\(352\) 398.542i 1.13222i
\(353\) 128.147 0.363023 0.181512 0.983389i \(-0.441901\pi\)
0.181512 + 0.983389i \(0.441901\pi\)
\(354\) −77.1344 −0.217894
\(355\) 878.736i 2.47531i
\(356\) 17.2984i 0.0485910i
\(357\) −59.9427 −0.167907
\(358\) 299.067 0.835383
\(359\) 495.508i 1.38025i −0.723692 0.690123i \(-0.757556\pi\)
0.723692 0.690123i \(-0.242444\pi\)
\(360\) 161.839i 0.449553i
\(361\) −179.389 −0.496923
\(362\) 256.620i 0.708895i
\(363\) −62.0967 −0.171065
\(364\) 197.281i 0.541982i
\(365\) 1090.88i 2.98872i
\(366\) 104.116i 0.284469i
\(367\) 551.754i 1.50342i −0.659495 0.751709i \(-0.729230\pi\)
0.659495 0.751709i \(-0.270770\pi\)
\(368\) −140.523 + 94.4837i −0.381855 + 0.256749i
\(369\) −81.1237 −0.219847
\(370\) 286.006 0.772989
\(371\) −147.606 −0.397861
\(372\) 132.182 0.355327
\(373\) 351.979i 0.943643i −0.881694 0.471821i \(-0.843597\pi\)
0.881694 0.471821i \(-0.156403\pi\)
\(374\) −143.669 −0.384141
\(375\) 329.611i 0.878963i
\(376\) −138.314 −0.367856
\(377\) −314.775 −0.834948
\(378\) 12.0565i 0.0318956i
\(379\) 42.9132i 0.113227i −0.998396 0.0566137i \(-0.981970\pi\)
0.998396 0.0566137i \(-0.0180303\pi\)
\(380\) 638.934 1.68140
\(381\) −351.555 −0.922716
\(382\) 101.424i 0.265508i
\(383\) 57.1916i 0.149325i 0.997209 + 0.0746626i \(0.0237880\pi\)
−0.997209 + 0.0746626i \(0.976212\pi\)
\(384\) 222.812 0.580240
\(385\) 281.885i 0.732169i
\(386\) 117.735 0.305014
\(387\) 15.1399i 0.0391211i
\(388\) 459.871i 1.18524i
\(389\) 360.807i 0.927524i −0.885960 0.463762i \(-0.846499\pi\)
0.885960 0.463762i \(-0.153501\pi\)
\(390\) 298.225i 0.764680i
\(391\) −167.868 249.665i −0.429330 0.638530i
\(392\) −44.3896 −0.113239
\(393\) −49.7123 −0.126494
\(394\) −163.122 −0.414016
\(395\) 1108.18 2.80553
\(396\) 121.392i 0.306545i
\(397\) 130.989 0.329948 0.164974 0.986298i \(-0.447246\pi\)
0.164974 + 0.986298i \(0.447246\pi\)
\(398\) 45.2074i 0.113587i
\(399\) −106.528 −0.266987
\(400\) −348.752 −0.871880
\(401\) 439.104i 1.09502i 0.836799 + 0.547511i \(0.184425\pi\)
−0.836799 + 0.547511i \(0.815575\pi\)
\(402\) 52.2104i 0.129877i
\(403\) −545.130 −1.35268
\(404\) −270.676 −0.669989
\(405\) 76.5634i 0.189045i
\(406\) 31.6466i 0.0779473i
\(407\) 480.120 1.17966
\(408\) 143.672i 0.352136i
\(409\) 349.213 0.853822 0.426911 0.904294i \(-0.359602\pi\)
0.426911 + 0.904294i \(0.359602\pi\)
\(410\) 201.742i 0.492054i
\(411\) 271.645i 0.660938i
\(412\) 146.838i 0.356403i
\(413\) 134.352i 0.325308i
\(414\) 50.2162 33.7640i 0.121295 0.0815556i
\(415\) −334.153 −0.805188
\(416\) −734.417 −1.76543
\(417\) 277.103 0.664516
\(418\) −255.322 −0.610819
\(419\) 286.780i 0.684438i 0.939620 + 0.342219i \(0.111178\pi\)
−0.939620 + 0.342219i \(0.888822\pi\)
\(420\) 125.954 0.299891
\(421\) 242.493i 0.575993i −0.957631 0.287997i \(-0.907011\pi\)
0.957631 0.287997i \(-0.0929892\pi\)
\(422\) −305.512 −0.723961
\(423\) −65.4341 −0.154690
\(424\) 353.785i 0.834400i
\(425\) 619.624i 1.45794i
\(426\) 156.903 0.368317
\(427\) 181.348 0.424703
\(428\) 301.185i 0.703702i
\(429\) 500.632i 1.16697i
\(430\) −37.6505 −0.0875594
\(431\) 332.399i 0.771227i −0.922660 0.385614i \(-0.873990\pi\)
0.922660 0.385614i \(-0.126010\pi\)
\(432\) 38.2558 0.0885550
\(433\) 478.058i 1.10406i −0.833824 0.552030i \(-0.813854\pi\)
0.833824 0.552030i \(-0.186146\pi\)
\(434\) 54.8058i 0.126281i
\(435\) 200.968i 0.461995i
\(436\) 393.401i 0.902297i
\(437\) −298.329 443.696i −0.682675 1.01532i
\(438\) −194.783 −0.444710
\(439\) −63.2723 −0.144128 −0.0720641 0.997400i \(-0.522959\pi\)
−0.0720641 + 0.997400i \(0.522959\pi\)
\(440\) 675.627 1.53551
\(441\) −21.0000 −0.0476190
\(442\) 264.747i 0.598975i
\(443\) 228.582 0.515987 0.257993 0.966147i \(-0.416939\pi\)
0.257993 + 0.966147i \(0.416939\pi\)
\(444\) 214.531i 0.483177i
\(445\) −45.5471 −0.102353
\(446\) 209.222 0.469108
\(447\) 430.741i 0.963627i
\(448\) 4.07930i 0.00910558i
\(449\) −100.730 −0.224343 −0.112171 0.993689i \(-0.535781\pi\)
−0.112171 + 0.993689i \(0.535781\pi\)
\(450\) 124.628 0.276950
\(451\) 338.666i 0.750921i
\(452\) 449.419i 0.994291i
\(453\) 220.886 0.487607
\(454\) 105.035i 0.231354i
\(455\) −519.447 −1.14164
\(456\) 255.327i 0.559929i
\(457\) 15.9353i 0.0348695i 0.999848 + 0.0174347i \(0.00554993\pi\)
−0.999848 + 0.0174347i \(0.994450\pi\)
\(458\) 196.488i 0.429012i
\(459\) 67.9686i 0.148080i
\(460\) 352.732 + 524.607i 0.766808 + 1.14045i
\(461\) 166.928 0.362100 0.181050 0.983474i \(-0.442050\pi\)
0.181050 + 0.983474i \(0.442050\pi\)
\(462\) −50.3321 −0.108944
\(463\) 540.984 1.16843 0.584216 0.811598i \(-0.301402\pi\)
0.584216 + 0.811598i \(0.301402\pi\)
\(464\) −100.416 −0.216413
\(465\) 348.037i 0.748467i
\(466\) −309.267 −0.663662
\(467\) 177.590i 0.380279i −0.981757 0.190139i \(-0.939106\pi\)
0.981757 0.190139i \(-0.0608940\pi\)
\(468\) −223.696 −0.477983
\(469\) 90.9399 0.193902
\(470\) 162.724i 0.346222i
\(471\) 52.9694i 0.112462i
\(472\) 322.018 0.682241
\(473\) −63.2042 −0.133624
\(474\) 197.872i 0.417452i
\(475\) 1101.17i 2.31826i
\(476\) 111.815 0.234905
\(477\) 167.370i 0.350881i
\(478\) 320.621 0.670755
\(479\) 67.8651i 0.141681i 0.997488 + 0.0708404i \(0.0225681\pi\)
−0.997488 + 0.0708404i \(0.977432\pi\)
\(480\) 468.888i 0.976849i
\(481\) 884.746i 1.83939i
\(482\) 80.2406i 0.166474i
\(483\) −58.8100 87.4664i −0.121760 0.181090i
\(484\) 115.833 0.239324
\(485\) −1210.85 −2.49660
\(486\) −13.6708 −0.0281292
\(487\) −406.664 −0.835039 −0.417520 0.908668i \(-0.637100\pi\)
−0.417520 + 0.908668i \(0.637100\pi\)
\(488\) 434.659i 0.890694i
\(489\) 472.605 0.966473
\(490\) 52.2237i 0.106579i
\(491\) −23.5446 −0.0479524 −0.0239762 0.999713i \(-0.507633\pi\)
−0.0239762 + 0.999713i \(0.507633\pi\)
\(492\) 151.325 0.307571
\(493\) 178.408i 0.361882i
\(494\) 470.498i 0.952425i
\(495\) 319.628 0.645713
\(496\) −173.901 −0.350606
\(497\) 273.293i 0.549886i
\(498\) 59.6648i 0.119809i
\(499\) 485.859 0.973665 0.486832 0.873495i \(-0.338152\pi\)
0.486832 + 0.873495i \(0.338152\pi\)
\(500\) 614.844i 1.22969i
\(501\) −151.567 −0.302529
\(502\) 192.569i 0.383604i
\(503\) 19.6069i 0.0389799i −0.999810 0.0194900i \(-0.993796\pi\)
0.999810 0.0194900i \(-0.00620424\pi\)
\(504\) 50.3331i 0.0998673i
\(505\) 712.696i 1.41128i
\(506\) −140.954 209.637i −0.278565 0.414302i
\(507\) 629.829 1.24227
\(508\) 655.777 1.29090
\(509\) −271.092 −0.532597 −0.266299 0.963891i \(-0.585801\pi\)
−0.266299 + 0.963891i \(0.585801\pi\)
\(510\) 169.027 0.331426
\(511\) 339.272i 0.663938i
\(512\) −421.034 −0.822332
\(513\) 120.791i 0.235460i
\(514\) 314.069 0.611029
\(515\) −386.628 −0.750734
\(516\) 28.2414i 0.0547313i
\(517\) 273.166i 0.528368i
\(518\) 88.9499 0.171718
\(519\) 441.681 0.851023
\(520\) 1245.02i 2.39427i
\(521\) 262.852i 0.504514i 0.967660 + 0.252257i \(0.0811729\pi\)
−0.967660 + 0.252257i \(0.918827\pi\)
\(522\) 35.8839 0.0687431
\(523\) 699.055i 1.33662i 0.743881 + 0.668312i \(0.232983\pi\)
−0.743881 + 0.668312i \(0.767017\pi\)
\(524\) 92.7314 0.176968
\(525\) 217.076i 0.413478i
\(526\) 10.7107i 0.0203626i
\(527\) 308.968i 0.586276i
\(528\) 159.706i 0.302473i
\(529\) 199.608 489.896i 0.377330 0.926079i
\(530\) 416.223 0.785327
\(531\) 152.341 0.286895
\(532\) 198.713 0.373520
\(533\) −624.080 −1.17088
\(534\) 8.13268i 0.0152297i
\(535\) −793.027 −1.48229
\(536\) 217.966i 0.406653i
\(537\) −590.661 −1.09993
\(538\) −67.2574 −0.125014
\(539\) 87.6683i 0.162650i
\(540\) 142.818i 0.264479i
\(541\) −128.516 −0.237553 −0.118777 0.992921i \(-0.537897\pi\)
−0.118777 + 0.992921i \(0.537897\pi\)
\(542\) −159.936 −0.295085
\(543\) 506.827i 0.933383i
\(544\) 416.252i 0.765168i
\(545\) 1035.84 1.90062
\(546\) 92.7501i 0.169872i
\(547\) 827.377 1.51257 0.756286 0.654241i \(-0.227012\pi\)
0.756286 + 0.654241i \(0.227012\pi\)
\(548\) 506.717i 0.924666i
\(549\) 205.630i 0.374553i
\(550\) 520.280i 0.945964i
\(551\) 317.059i 0.575425i
\(552\) −209.641 + 140.957i −0.379784 + 0.255356i
\(553\) 344.653 0.623242
\(554\) 234.303 0.422929
\(555\) −564.865 −1.01777
\(556\) −516.898 −0.929672
\(557\) 9.93497i 0.0178366i 0.999960 + 0.00891828i \(0.00283882\pi\)
−0.999960 + 0.00891828i \(0.997161\pi\)
\(558\) 62.1439 0.111369
\(559\) 116.470i 0.208355i
\(560\) −165.708 −0.295907
\(561\) 283.747 0.505788
\(562\) 269.603i 0.479720i
\(563\) 30.4387i 0.0540651i 0.999635 + 0.0270326i \(0.00860578\pi\)
−0.999635 + 0.0270326i \(0.991394\pi\)
\(564\) 122.058 0.216415
\(565\) −1183.33 −2.09439
\(566\) 118.481i 0.209331i
\(567\) 23.8118i 0.0419961i
\(568\) −655.033 −1.15323
\(569\) 575.238i 1.01096i 0.862837 + 0.505481i \(0.168685\pi\)
−0.862837 + 0.505481i \(0.831315\pi\)
\(570\) 300.389 0.526998
\(571\) 501.266i 0.877875i 0.898518 + 0.438937i \(0.144645\pi\)
−0.898518 + 0.438937i \(0.855355\pi\)
\(572\) 933.860i 1.63262i
\(573\) 200.314i 0.349588i
\(574\) 62.7432i 0.109309i
\(575\) 904.136 607.916i 1.57241 1.05725i
\(576\) −4.62549 −0.00803036
\(577\) 152.556 0.264396 0.132198 0.991223i \(-0.457797\pi\)
0.132198 + 0.991223i \(0.457797\pi\)
\(578\) −103.395 −0.178884
\(579\) −232.529 −0.401604
\(580\) 374.878i 0.646341i
\(581\) −103.924 −0.178871
\(582\) 216.204i 0.371485i
\(583\) 698.716 1.19848
\(584\) 813.173 1.39242
\(585\) 588.998i 1.00683i
\(586\) 377.624i 0.644410i
\(587\) −636.140 −1.08371 −0.541857 0.840471i \(-0.682278\pi\)
−0.541857 + 0.840471i \(0.682278\pi\)
\(588\) 39.1726 0.0666201
\(589\) 549.085i 0.932233i
\(590\) 378.849i 0.642117i
\(591\) 322.168 0.545124
\(592\) 282.241i 0.476759i
\(593\) 396.439 0.668531 0.334266 0.942479i \(-0.391512\pi\)
0.334266 + 0.942479i \(0.391512\pi\)
\(594\) 57.0713i 0.0960796i
\(595\) 294.411i 0.494809i
\(596\) 803.488i 1.34813i
\(597\) 89.2852i 0.149556i
\(598\) 386.310 259.745i 0.646004 0.434355i
\(599\) 654.905 1.09333 0.546665 0.837351i \(-0.315897\pi\)
0.546665 + 0.837351i \(0.315897\pi\)
\(600\) −520.291 −0.867151
\(601\) 232.243 0.386428 0.193214 0.981157i \(-0.438109\pi\)
0.193214 + 0.981157i \(0.438109\pi\)
\(602\) −11.7096 −0.0194511
\(603\) 103.116i 0.171005i
\(604\) −412.032 −0.682173
\(605\) 304.991i 0.504117i
\(606\) −127.256 −0.209993
\(607\) 590.271 0.972439 0.486220 0.873837i \(-0.338375\pi\)
0.486220 + 0.873837i \(0.338375\pi\)
\(608\) 739.746i 1.21669i
\(609\) 62.5024i 0.102631i
\(610\) −511.369 −0.838310
\(611\) −503.380 −0.823863
\(612\) 126.786i 0.207167i
\(613\) 677.917i 1.10590i −0.833214 0.552950i \(-0.813502\pi\)
0.833214 0.552950i \(-0.186498\pi\)
\(614\) −173.486 −0.282550
\(615\) 398.443i 0.647875i
\(616\) 210.125 0.341111
\(617\) 700.862i 1.13592i 0.823057 + 0.567959i \(0.192267\pi\)
−0.823057 + 0.567959i \(0.807733\pi\)
\(618\) 69.0345i 0.111706i
\(619\) 821.711i 1.32748i −0.747963 0.663741i \(-0.768968\pi\)
0.747963 0.663741i \(-0.231032\pi\)
\(620\) 649.215i 1.04712i
\(621\) −99.1776 + 66.6843i −0.159706 + 0.107382i
\(622\) −99.7435 −0.160359
\(623\) −14.1655 −0.0227375
\(624\) 294.299 0.471633
\(625\) 434.655 0.695448
\(626\) 315.745i 0.504385i
\(627\) 504.264 0.804250
\(628\) 98.8071i 0.157336i
\(629\) −501.455 −0.797225
\(630\) 59.2162 0.0939939
\(631\) 473.991i 0.751174i 0.926787 + 0.375587i \(0.122559\pi\)
−0.926787 + 0.375587i \(0.877441\pi\)
\(632\) 826.069i 1.30707i
\(633\) 603.389 0.953221
\(634\) −332.992 −0.525224
\(635\) 1726.68i 2.71918i
\(636\) 312.206i 0.490889i
\(637\) −161.552 −0.253613
\(638\) 149.804i 0.234802i
\(639\) −309.885 −0.484954
\(640\) 1094.35i 1.70993i
\(641\) 865.776i 1.35066i −0.737514 0.675332i \(-0.764000\pi\)
0.737514 0.675332i \(-0.236000\pi\)
\(642\) 141.599i 0.220559i
\(643\) 875.488i 1.36157i −0.732484 0.680784i \(-0.761639\pi\)
0.732484 0.680784i \(-0.238361\pi\)
\(644\) 109.702 + 163.157i 0.170345 + 0.253349i
\(645\) 74.3602 0.115287
\(646\) 266.668 0.412799
\(647\) 421.449 0.651389 0.325694 0.945475i \(-0.394402\pi\)
0.325694 + 0.945475i \(0.394402\pi\)
\(648\) 57.0724 0.0880747
\(649\) 635.976i 0.979932i
\(650\) 958.752 1.47500
\(651\) 108.242i 0.166270i
\(652\) −881.580 −1.35212
\(653\) 292.745 0.448307 0.224154 0.974554i \(-0.428038\pi\)
0.224154 + 0.974554i \(0.428038\pi\)
\(654\) 184.954i 0.282805i
\(655\) 244.164i 0.372770i
\(656\) −199.086 −0.303485
\(657\) 384.699 0.585538
\(658\) 50.6084i 0.0769125i
\(659\) 148.383i 0.225164i 0.993642 + 0.112582i \(0.0359121\pi\)
−0.993642 + 0.112582i \(0.964088\pi\)
\(660\) −596.221 −0.903366
\(661\) 929.771i 1.40661i 0.710887 + 0.703306i \(0.248294\pi\)
−0.710887 + 0.703306i \(0.751706\pi\)
\(662\) −356.064 −0.537861
\(663\) 522.878i 0.788655i
\(664\) 249.086i 0.375130i
\(665\) 523.216i 0.786791i
\(666\) 100.860i 0.151441i
\(667\) 260.327 175.037i 0.390295 0.262424i
\(668\) 282.728 0.423245
\(669\) −413.216 −0.617662
\(670\) −256.434 −0.382737
\(671\) −858.438 −1.27934
\(672\) 145.827i 0.217005i
\(673\) 38.3818 0.0570308 0.0285154 0.999593i \(-0.490922\pi\)
0.0285154 + 0.999593i \(0.490922\pi\)
\(674\) 413.860i 0.614036i
\(675\) −246.141 −0.364653
\(676\) −1174.86 −1.73796
\(677\) 849.717i 1.25512i −0.778568 0.627561i \(-0.784053\pi\)
0.778568 0.627561i \(-0.215947\pi\)
\(678\) 211.291i 0.311638i
\(679\) −376.584 −0.554615
\(680\) −705.649 −1.03772
\(681\) 207.445i 0.304618i
\(682\) 259.431i 0.380397i
\(683\) 626.374 0.917092 0.458546 0.888671i \(-0.348370\pi\)
0.458546 + 0.888671i \(0.348370\pi\)
\(684\) 225.319i 0.329414i
\(685\) −1334.20 −1.94774
\(686\) 16.2420i 0.0236763i
\(687\) 388.065i 0.564869i
\(688\) 37.1549i 0.0540042i
\(689\) 1287.57i 1.86875i
\(690\) 165.834 + 246.639i 0.240338 + 0.357448i
\(691\) −839.803 −1.21535 −0.607673 0.794188i \(-0.707897\pi\)
−0.607673 + 0.794188i \(0.707897\pi\)
\(692\) −823.895 −1.19060
\(693\) 99.4065 0.143444
\(694\) −326.613 −0.470624
\(695\) 1361.01i 1.95828i
\(696\) −149.807 −0.215240
\(697\) 353.715i 0.507482i
\(698\) −29.6953 −0.0425434
\(699\) 610.805 0.873827
\(700\) 404.925i 0.578464i
\(701\) 60.0039i 0.0855976i 0.999084 + 0.0427988i \(0.0136274\pi\)
−0.999084 + 0.0427988i \(0.986373\pi\)
\(702\) −105.169 −0.149813
\(703\) −891.166 −1.26766
\(704\) 19.3099i 0.0274289i
\(705\) 321.382i 0.455861i
\(706\) −112.383 −0.159183
\(707\) 221.654i 0.313513i
\(708\) −284.171 −0.401372
\(709\) 513.355i 0.724056i −0.932167 0.362028i \(-0.882085\pi\)
0.932167 0.362028i \(-0.117915\pi\)
\(710\) 770.637i 1.08540i
\(711\) 390.800i 0.549648i
\(712\) 33.9520i 0.0476854i
\(713\) 450.836 303.130i 0.632308 0.425147i
\(714\) 52.5687 0.0736256
\(715\) 2458.88 3.43899
\(716\) 1101.80 1.53882
\(717\) −633.230 −0.883166
\(718\) 434.552i 0.605226i
\(719\) 715.154 0.994651 0.497326 0.867564i \(-0.334315\pi\)
0.497326 + 0.867564i \(0.334315\pi\)
\(720\) 187.895i 0.260965i
\(721\) −120.244 −0.166774
\(722\) 157.321 0.217896
\(723\) 158.476i 0.219192i
\(724\) 945.416i 1.30582i
\(725\) 646.084 0.891150
\(726\) 54.4578 0.0750107
\(727\) 740.130i 1.01806i 0.860749 + 0.509030i \(0.169996\pi\)
−0.860749 + 0.509030i \(0.830004\pi\)
\(728\) 387.210i 0.531881i
\(729\) 27.0000 0.0370370
\(730\) 956.686i 1.31053i
\(731\) 66.0128 0.0903047
\(732\) 383.574i 0.524008i
\(733\) 762.622i 1.04041i 0.854041 + 0.520206i \(0.174145\pi\)
−0.854041 + 0.520206i \(0.825855\pi\)
\(734\) 483.879i 0.659236i
\(735\) 103.142i 0.140330i
\(736\) 607.381 408.386i 0.825246 0.554873i
\(737\) −430.477 −0.584093
\(738\) 71.1441 0.0964012
\(739\) 389.726 0.527369 0.263685 0.964609i \(-0.415062\pi\)
0.263685 + 0.964609i \(0.415062\pi\)
\(740\) 1053.68 1.42389
\(741\) 929.239i 1.25403i
\(742\) 129.448 0.174459
\(743\) 1256.31i 1.69086i −0.534084 0.845432i \(-0.679343\pi\)
0.534084 0.845432i \(-0.320657\pi\)
\(744\) −259.436 −0.348705
\(745\) 2115.60 2.83974
\(746\) 308.679i 0.413779i
\(747\) 117.839i 0.157749i
\(748\) −529.291 −0.707608
\(749\) −246.637 −0.329288
\(750\) 289.063i 0.385418i
\(751\) 1129.63i 1.50417i 0.659066 + 0.752085i \(0.270952\pi\)
−0.659066 + 0.752085i \(0.729048\pi\)
\(752\) −160.582 −0.213540
\(753\) 380.326i 0.505081i
\(754\) 276.053 0.366118
\(755\) 1084.89i 1.43694i
\(756\) 44.4175i 0.0587534i
\(757\) 288.263i 0.380796i −0.981707 0.190398i \(-0.939022\pi\)
0.981707 0.190398i \(-0.0609779\pi\)
\(758\) 37.6341i 0.0496492i
\(759\) 278.386 + 414.035i 0.366780 + 0.545500i
\(760\) −1254.05 −1.65007
\(761\) −550.487 −0.723374 −0.361687 0.932300i \(-0.617799\pi\)
−0.361687 + 0.932300i \(0.617799\pi\)
\(762\) 308.308 0.404603
\(763\) 322.152 0.422218
\(764\) 373.658i 0.489081i
\(765\) −333.831 −0.436380
\(766\) 50.1560i 0.0654778i
\(767\) 1171.95 1.52797
\(768\) −184.720 −0.240521
\(769\) 544.260i 0.707750i −0.935293 0.353875i \(-0.884864\pi\)
0.935293 0.353875i \(-0.115136\pi\)
\(770\) 247.208i 0.321050i
\(771\) −620.289 −0.804526
\(772\) 433.750 0.561852
\(773\) 291.565i 0.377187i 0.982055 + 0.188593i \(0.0603928\pi\)
−0.982055 + 0.188593i \(0.939607\pi\)
\(774\) 13.2774i 0.0171543i
\(775\) 1118.89 1.44373
\(776\) 902.602i 1.16315i
\(777\) −175.677 −0.226096
\(778\) 316.421i 0.406711i
\(779\) 628.608i 0.806942i
\(780\) 1098.69i 1.40858i
\(781\) 1293.67i 1.65643i
\(782\) 147.218 + 218.952i 0.188258 + 0.279990i
\(783\) −70.8711 −0.0905122
\(784\) −51.5363 −0.0657350
\(785\) 260.162 0.331416
\(786\) 43.5968 0.0554667
\(787\) 1263.89i 1.60595i 0.596009 + 0.802977i \(0.296752\pi\)
−0.596009 + 0.802977i \(0.703248\pi\)
\(788\) −600.960 −0.762640
\(789\) 21.1538i 0.0268109i
\(790\) −971.858 −1.23020
\(791\) −368.025 −0.465265