Properties

Label 483.3.f.a.22.42
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 22.42
Character \(\chi\) \(=\) 483.22
Dual form 483.3.f.a.22.41

$q$-expansion

\(f(q)\) \(=\) \(q+3.29742 q^{2} +1.73205 q^{3} +6.87299 q^{4} -7.57309i q^{5} +5.71130 q^{6} +2.64575i q^{7} +9.47346 q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+3.29742 q^{2} +1.73205 q^{3} +6.87299 q^{4} -7.57309i q^{5} +5.71130 q^{6} +2.64575i q^{7} +9.47346 q^{8} +3.00000 q^{9} -24.9717i q^{10} -5.86948i q^{11} +11.9044 q^{12} +8.02426 q^{13} +8.72416i q^{14} -13.1170i q^{15} +3.74602 q^{16} +15.4704i q^{17} +9.89226 q^{18} +2.95882i q^{19} -52.0498i q^{20} +4.58258i q^{21} -19.3541i q^{22} +(15.3879 - 17.0942i) q^{23} +16.4085 q^{24} -32.3517 q^{25} +26.4594 q^{26} +5.19615 q^{27} +18.1842i q^{28} -45.9869 q^{29} -43.2522i q^{30} +57.0921 q^{31} -25.5416 q^{32} -10.1662i q^{33} +51.0126i q^{34} +20.0365 q^{35} +20.6190 q^{36} +39.0150i q^{37} +9.75646i q^{38} +13.8984 q^{39} -71.7434i q^{40} +19.9091 q^{41} +15.1107i q^{42} +65.5584i q^{43} -40.3409i q^{44} -22.7193i q^{45} +(50.7406 - 56.3667i) q^{46} -82.3550 q^{47} +6.48830 q^{48} -7.00000 q^{49} -106.677 q^{50} +26.7956i q^{51} +55.1506 q^{52} -26.9049i q^{53} +17.1339 q^{54} -44.4501 q^{55} +25.0644i q^{56} +5.12482i q^{57} -151.638 q^{58} +44.4998 q^{59} -90.1529i q^{60} +93.3172i q^{61} +188.257 q^{62} +7.93725i q^{63} -99.2055 q^{64} -60.7685i q^{65} -33.5224i q^{66} -3.33186i q^{67} +106.328i q^{68} +(26.6527 - 29.6080i) q^{69} +66.0689 q^{70} -62.7363 q^{71} +28.4204 q^{72} +49.4431 q^{73} +128.649i q^{74} -56.0349 q^{75} +20.3359i q^{76} +15.5292 q^{77} +45.8290 q^{78} +3.58601i q^{79} -28.3690i q^{80} +9.00000 q^{81} +65.6487 q^{82} +122.355i q^{83} +31.4960i q^{84} +117.159 q^{85} +216.174i q^{86} -79.6517 q^{87} -55.6042i q^{88} +27.0685i q^{89} -74.9150i q^{90} +21.2302i q^{91} +(105.761 - 117.488i) q^{92} +98.8864 q^{93} -271.559 q^{94} +22.4074 q^{95} -44.2394 q^{96} +44.3649i q^{97} -23.0820 q^{98} -17.6084i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 4q^{2} + 116q^{4} - 24q^{6} - 4q^{8} + 144q^{9} + O(q^{10}) \) \( 48q + 4q^{2} + 116q^{4} - 24q^{6} - 4q^{8} + 144q^{9} + 16q^{13} + 324q^{16} + 12q^{18} - 4q^{23} - 24q^{24} - 176q^{25} + 136q^{26} - 128q^{29} - 8q^{31} - 252q^{32} - 56q^{35} + 348q^{36} + 96q^{39} - 24q^{41} - 148q^{46} - 408q^{47} - 96q^{48} - 336q^{49} + 236q^{50} - 32q^{52} - 72q^{54} - 24q^{55} - 56q^{58} + 136q^{59} + 184q^{62} + 716q^{64} - 48q^{69} - 112q^{70} + 48q^{71} - 12q^{72} - 224q^{73} - 48q^{75} + 224q^{77} - 96q^{78} + 432q^{81} + 640q^{82} - 424q^{85} + 312q^{87} + 1060q^{92} + 192q^{93} + 216q^{94} + 624q^{95} + 48q^{96} - 28q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.29742 1.64871 0.824355 0.566073i \(-0.191538\pi\)
0.824355 + 0.566073i \(0.191538\pi\)
\(3\) 1.73205 0.577350
\(4\) 6.87299 1.71825
\(5\) 7.57309i 1.51462i −0.653056 0.757309i \(-0.726514\pi\)
0.653056 0.757309i \(-0.273486\pi\)
\(6\) 5.71130 0.951884
\(7\) 2.64575i 0.377964i
\(8\) 9.47346 1.18418
\(9\) 3.00000 0.333333
\(10\) 24.9717i 2.49717i
\(11\) 5.86948i 0.533589i −0.963753 0.266795i \(-0.914035\pi\)
0.963753 0.266795i \(-0.0859645\pi\)
\(12\) 11.9044 0.992030
\(13\) 8.02426 0.617251 0.308625 0.951184i \(-0.400131\pi\)
0.308625 + 0.951184i \(0.400131\pi\)
\(14\) 8.72416i 0.623154i
\(15\) 13.1170i 0.874466i
\(16\) 3.74602 0.234126
\(17\) 15.4704i 0.910026i 0.890485 + 0.455013i \(0.150365\pi\)
−0.890485 + 0.455013i \(0.849635\pi\)
\(18\) 9.89226 0.549570
\(19\) 2.95882i 0.155727i 0.996964 + 0.0778636i \(0.0248099\pi\)
−0.996964 + 0.0778636i \(0.975190\pi\)
\(20\) 52.0498i 2.60249i
\(21\) 4.58258i 0.218218i
\(22\) 19.3541i 0.879734i
\(23\) 15.3879 17.0942i 0.669041 0.743225i
\(24\) 16.4085 0.683688
\(25\) −32.3517 −1.29407
\(26\) 26.4594 1.01767
\(27\) 5.19615 0.192450
\(28\) 18.1842i 0.649436i
\(29\) −45.9869 −1.58576 −0.792878 0.609380i \(-0.791418\pi\)
−0.792878 + 0.609380i \(0.791418\pi\)
\(30\) 43.2522i 1.44174i
\(31\) 57.0921 1.84168 0.920840 0.389941i \(-0.127505\pi\)
0.920840 + 0.389941i \(0.127505\pi\)
\(32\) −25.5416 −0.798175
\(33\) 10.1662i 0.308068i
\(34\) 51.0126i 1.50037i
\(35\) 20.0365 0.572472
\(36\) 20.6190 0.572749
\(37\) 39.0150i 1.05446i 0.849723 + 0.527229i \(0.176769\pi\)
−0.849723 + 0.527229i \(0.823231\pi\)
\(38\) 9.75646i 0.256749i
\(39\) 13.8984 0.356370
\(40\) 71.7434i 1.79358i
\(41\) 19.9091 0.485588 0.242794 0.970078i \(-0.421936\pi\)
0.242794 + 0.970078i \(0.421936\pi\)
\(42\) 15.1107i 0.359778i
\(43\) 65.5584i 1.52461i 0.647216 + 0.762307i \(0.275933\pi\)
−0.647216 + 0.762307i \(0.724067\pi\)
\(44\) 40.3409i 0.916838i
\(45\) 22.7193i 0.504873i
\(46\) 50.7406 56.3667i 1.10306 1.22536i
\(47\) −82.3550 −1.75223 −0.876117 0.482099i \(-0.839874\pi\)
−0.876117 + 0.482099i \(0.839874\pi\)
\(48\) 6.48830 0.135173
\(49\) −7.00000 −0.142857
\(50\) −106.677 −2.13355
\(51\) 26.7956i 0.525404i
\(52\) 55.1506 1.06059
\(53\) 26.9049i 0.507640i −0.967251 0.253820i \(-0.918313\pi\)
0.967251 0.253820i \(-0.0816871\pi\)
\(54\) 17.1339 0.317295
\(55\) −44.4501 −0.808184
\(56\) 25.0644i 0.447579i
\(57\) 5.12482i 0.0899091i
\(58\) −151.638 −2.61445
\(59\) 44.4998 0.754234 0.377117 0.926166i \(-0.376916\pi\)
0.377117 + 0.926166i \(0.376916\pi\)
\(60\) 90.1529i 1.50255i
\(61\) 93.3172i 1.52979i 0.644155 + 0.764895i \(0.277209\pi\)
−0.644155 + 0.764895i \(0.722791\pi\)
\(62\) 188.257 3.03640
\(63\) 7.93725i 0.125988i
\(64\) −99.2055 −1.55009
\(65\) 60.7685i 0.934899i
\(66\) 33.5224i 0.507915i
\(67\) 3.33186i 0.0497292i −0.999691 0.0248646i \(-0.992085\pi\)
0.999691 0.0248646i \(-0.00791547\pi\)
\(68\) 106.328i 1.56365i
\(69\) 26.6527 29.6080i 0.386271 0.429101i
\(70\) 66.0689 0.943841
\(71\) −62.7363 −0.883610 −0.441805 0.897111i \(-0.645662\pi\)
−0.441805 + 0.897111i \(0.645662\pi\)
\(72\) 28.4204 0.394727
\(73\) 49.4431 0.677303 0.338651 0.940912i \(-0.390029\pi\)
0.338651 + 0.940912i \(0.390029\pi\)
\(74\) 128.649i 1.73850i
\(75\) −56.0349 −0.747132
\(76\) 20.3359i 0.267578i
\(77\) 15.5292 0.201678
\(78\) 45.8290 0.587551
\(79\) 3.58601i 0.0453925i 0.999742 + 0.0226963i \(0.00722507\pi\)
−0.999742 + 0.0226963i \(0.992775\pi\)
\(80\) 28.3690i 0.354612i
\(81\) 9.00000 0.111111
\(82\) 65.6487 0.800594
\(83\) 122.355i 1.47415i 0.675810 + 0.737075i \(0.263794\pi\)
−0.675810 + 0.737075i \(0.736206\pi\)
\(84\) 31.4960i 0.374952i
\(85\) 117.159 1.37834
\(86\) 216.174i 2.51365i
\(87\) −79.6517 −0.915537
\(88\) 55.6042i 0.631866i
\(89\) 27.0685i 0.304141i 0.988370 + 0.152070i \(0.0485941\pi\)
−0.988370 + 0.152070i \(0.951406\pi\)
\(90\) 74.9150i 0.832389i
\(91\) 21.2302i 0.233299i
\(92\) 105.761 117.488i 1.14958 1.27704i
\(93\) 98.8864 1.06329
\(94\) −271.559 −2.88893
\(95\) 22.4074 0.235867
\(96\) −44.2394 −0.460827
\(97\) 44.3649i 0.457370i 0.973500 + 0.228685i \(0.0734426\pi\)
−0.973500 + 0.228685i \(0.926557\pi\)
\(98\) −23.0820 −0.235530
\(99\) 17.6084i 0.177863i
\(100\) −222.353 −2.22353
\(101\) −24.6852 −0.244408 −0.122204 0.992505i \(-0.538996\pi\)
−0.122204 + 0.992505i \(0.538996\pi\)
\(102\) 88.3564i 0.866239i
\(103\) 116.855i 1.13451i −0.823542 0.567256i \(-0.808005\pi\)
0.823542 0.567256i \(-0.191995\pi\)
\(104\) 76.0174 0.730937
\(105\) 34.7043 0.330517
\(106\) 88.7169i 0.836951i
\(107\) 131.508i 1.22905i −0.788898 0.614524i \(-0.789348\pi\)
0.788898 0.614524i \(-0.210652\pi\)
\(108\) 35.7131 0.330677
\(109\) 142.937i 1.31135i −0.755045 0.655673i \(-0.772385\pi\)
0.755045 0.655673i \(-0.227615\pi\)
\(110\) −146.571 −1.33246
\(111\) 67.5759i 0.608792i
\(112\) 9.91104i 0.0884914i
\(113\) 67.5371i 0.597673i −0.954304 0.298837i \(-0.903401\pi\)
0.954304 0.298837i \(-0.0965986\pi\)
\(114\) 16.8987i 0.148234i
\(115\) −129.456 116.534i −1.12570 1.01334i
\(116\) −316.068 −2.72472
\(117\) 24.0728 0.205750
\(118\) 146.735 1.24351
\(119\) −40.9309 −0.343958
\(120\) 124.263i 1.03553i
\(121\) 86.5492 0.715283
\(122\) 307.706i 2.52218i
\(123\) 34.4836 0.280354
\(124\) 392.393 3.16446
\(125\) 55.6755i 0.445404i
\(126\) 26.1725i 0.207718i
\(127\) −158.007 −1.24415 −0.622073 0.782959i \(-0.713710\pi\)
−0.622073 + 0.782959i \(0.713710\pi\)
\(128\) −224.956 −1.75747
\(129\) 113.550i 0.880236i
\(130\) 200.379i 1.54138i
\(131\) −86.9617 −0.663830 −0.331915 0.943309i \(-0.607695\pi\)
−0.331915 + 0.943309i \(0.607695\pi\)
\(132\) 69.8724i 0.529337i
\(133\) −7.82829 −0.0588593
\(134\) 10.9865i 0.0819891i
\(135\) 39.3509i 0.291489i
\(136\) 146.559i 1.07764i
\(137\) 69.3020i 0.505854i −0.967485 0.252927i \(-0.918607\pi\)
0.967485 0.252927i \(-0.0813933\pi\)
\(138\) 87.8852 97.6300i 0.636849 0.707464i
\(139\) 65.8380 0.473655 0.236827 0.971552i \(-0.423892\pi\)
0.236827 + 0.971552i \(0.423892\pi\)
\(140\) 137.711 0.983649
\(141\) −142.643 −1.01165
\(142\) −206.868 −1.45682
\(143\) 47.0982i 0.329358i
\(144\) 11.2381 0.0780421
\(145\) 348.263i 2.40182i
\(146\) 163.035 1.11668
\(147\) −12.1244 −0.0824786
\(148\) 268.149i 1.81182i
\(149\) 68.5623i 0.460150i 0.973173 + 0.230075i \(0.0738971\pi\)
−0.973173 + 0.230075i \(0.926103\pi\)
\(150\) −184.771 −1.23180
\(151\) −99.5097 −0.659005 −0.329502 0.944155i \(-0.606881\pi\)
−0.329502 + 0.944155i \(0.606881\pi\)
\(152\) 28.0302i 0.184409i
\(153\) 46.4113i 0.303342i
\(154\) 51.2063 0.332508
\(155\) 432.364i 2.78944i
\(156\) 95.5237 0.612331
\(157\) 219.442i 1.39772i −0.715259 0.698860i \(-0.753691\pi\)
0.715259 0.698860i \(-0.246309\pi\)
\(158\) 11.8246i 0.0748392i
\(159\) 46.6007i 0.293086i
\(160\) 193.429i 1.20893i
\(161\) 45.2270 + 40.7127i 0.280913 + 0.252874i
\(162\) 29.6768 0.183190
\(163\) −90.8942 −0.557633 −0.278817 0.960344i \(-0.589942\pi\)
−0.278817 + 0.960344i \(0.589942\pi\)
\(164\) 136.835 0.834360
\(165\) −76.9899 −0.466605
\(166\) 403.454i 2.43045i
\(167\) 113.830 0.681617 0.340809 0.940133i \(-0.389299\pi\)
0.340809 + 0.940133i \(0.389299\pi\)
\(168\) 43.4128i 0.258410i
\(169\) −104.611 −0.619002
\(170\) 386.323 2.27249
\(171\) 8.87645i 0.0519091i
\(172\) 450.582i 2.61966i
\(173\) −26.0187 −0.150397 −0.0751986 0.997169i \(-0.523959\pi\)
−0.0751986 + 0.997169i \(0.523959\pi\)
\(174\) −262.645 −1.50946
\(175\) 85.5947i 0.489112i
\(176\) 21.9872i 0.124927i
\(177\) 77.0759 0.435457
\(178\) 89.2564i 0.501440i
\(179\) 266.337 1.48792 0.743958 0.668227i \(-0.232946\pi\)
0.743958 + 0.668227i \(0.232946\pi\)
\(180\) 156.149i 0.867496i
\(181\) 132.464i 0.731844i 0.930645 + 0.365922i \(0.119246\pi\)
−0.930645 + 0.365922i \(0.880754\pi\)
\(182\) 70.0049i 0.384642i
\(183\) 161.630i 0.883225i
\(184\) 145.777 161.941i 0.792267 0.880114i
\(185\) 295.464 1.59710
\(186\) 326.070 1.75306
\(187\) 90.8035 0.485580
\(188\) −566.025 −3.01077
\(189\) 13.7477i 0.0727393i
\(190\) 73.8866 0.388877
\(191\) 18.3189i 0.0959107i −0.998849 0.0479553i \(-0.984729\pi\)
0.998849 0.0479553i \(-0.0152705\pi\)
\(192\) −171.829 −0.894943
\(193\) −15.1110 −0.0782952 −0.0391476 0.999233i \(-0.512464\pi\)
−0.0391476 + 0.999233i \(0.512464\pi\)
\(194\) 146.290i 0.754071i
\(195\) 105.254i 0.539764i
\(196\) −48.1109 −0.245464
\(197\) −130.153 −0.660675 −0.330338 0.943863i \(-0.607163\pi\)
−0.330338 + 0.943863i \(0.607163\pi\)
\(198\) 58.0624i 0.293245i
\(199\) 169.341i 0.850961i −0.904968 0.425480i \(-0.860105\pi\)
0.904968 0.425480i \(-0.139895\pi\)
\(200\) −306.483 −1.53241
\(201\) 5.77095i 0.0287112i
\(202\) −81.3975 −0.402958
\(203\) 121.670i 0.599360i
\(204\) 184.166i 0.902774i
\(205\) 150.774i 0.735481i
\(206\) 385.319i 1.87048i
\(207\) 46.1638 51.2825i 0.223014 0.247742i
\(208\) 30.0590 0.144515
\(209\) 17.3667 0.0830943
\(210\) 114.435 0.544927
\(211\) 75.1735 0.356272 0.178136 0.984006i \(-0.442993\pi\)
0.178136 + 0.984006i \(0.442993\pi\)
\(212\) 184.917i 0.872251i
\(213\) −108.662 −0.510152
\(214\) 433.638i 2.02635i
\(215\) 496.480 2.30921
\(216\) 49.2255 0.227896
\(217\) 151.051i 0.696090i
\(218\) 471.323i 2.16203i
\(219\) 85.6379 0.391041
\(220\) −305.505 −1.38866
\(221\) 124.139i 0.561714i
\(222\) 222.826i 1.00372i
\(223\) −230.770 −1.03484 −0.517422 0.855730i \(-0.673108\pi\)
−0.517422 + 0.855730i \(0.673108\pi\)
\(224\) 67.5768i 0.301682i
\(225\) −97.0552 −0.431357
\(226\) 222.698i 0.985390i
\(227\) 417.077i 1.83734i −0.395023 0.918671i \(-0.629263\pi\)
0.395023 0.918671i \(-0.370737\pi\)
\(228\) 35.2228i 0.154486i
\(229\) 238.384i 1.04098i 0.853869 + 0.520489i \(0.174250\pi\)
−0.853869 + 0.520489i \(0.825750\pi\)
\(230\) −426.870 384.263i −1.85596 1.67071i
\(231\) 26.8973 0.116439
\(232\) −435.655 −1.87782
\(233\) 336.842 1.44567 0.722836 0.691020i \(-0.242838\pi\)
0.722836 + 0.691020i \(0.242838\pi\)
\(234\) 79.3781 0.339223
\(235\) 623.682i 2.65397i
\(236\) 305.847 1.29596
\(237\) 6.21115i 0.0262074i
\(238\) −134.967 −0.567087
\(239\) −247.716 −1.03647 −0.518233 0.855239i \(-0.673410\pi\)
−0.518233 + 0.855239i \(0.673410\pi\)
\(240\) 49.1365i 0.204735i
\(241\) 243.494i 1.01035i −0.863017 0.505175i \(-0.831428\pi\)
0.863017 0.505175i \(-0.168572\pi\)
\(242\) 285.389 1.17929
\(243\) 15.5885 0.0641500
\(244\) 641.368i 2.62856i
\(245\) 53.0117i 0.216374i
\(246\) 113.707 0.462223
\(247\) 23.7423i 0.0961227i
\(248\) 540.859 2.18088
\(249\) 211.924i 0.851101i
\(250\) 183.586i 0.734342i
\(251\) 219.315i 0.873766i −0.899518 0.436883i \(-0.856082\pi\)
0.899518 0.436883i \(-0.143918\pi\)
\(252\) 54.5527i 0.216479i
\(253\) −100.334 90.3192i −0.396577 0.356993i
\(254\) −521.015 −2.05124
\(255\) 202.926 0.795787
\(256\) −344.953 −1.34747
\(257\) 164.767 0.641116 0.320558 0.947229i \(-0.396130\pi\)
0.320558 + 0.947229i \(0.396130\pi\)
\(258\) 374.424i 1.45125i
\(259\) −103.224 −0.398548
\(260\) 417.661i 1.60639i
\(261\) −137.961 −0.528586
\(262\) −286.749 −1.09446
\(263\) 447.220i 1.70046i 0.526413 + 0.850229i \(0.323536\pi\)
−0.526413 + 0.850229i \(0.676464\pi\)
\(264\) 96.3094i 0.364808i
\(265\) −203.753 −0.768881
\(266\) −25.8132 −0.0970420
\(267\) 46.8841i 0.175596i
\(268\) 22.8998i 0.0854471i
\(269\) 248.479 0.923713 0.461857 0.886955i \(-0.347183\pi\)
0.461857 + 0.886955i \(0.347183\pi\)
\(270\) 129.757i 0.480580i
\(271\) 86.7024 0.319935 0.159967 0.987122i \(-0.448861\pi\)
0.159967 + 0.987122i \(0.448861\pi\)
\(272\) 57.9526i 0.213061i
\(273\) 36.7718i 0.134695i
\(274\) 228.518i 0.834007i
\(275\) 189.888i 0.690502i
\(276\) 183.184 203.495i 0.663709 0.737302i
\(277\) 149.706 0.540455 0.270227 0.962797i \(-0.412901\pi\)
0.270227 + 0.962797i \(0.412901\pi\)
\(278\) 217.096 0.780920
\(279\) 171.276 0.613893
\(280\) 189.815 0.677911
\(281\) 128.064i 0.455742i 0.973691 + 0.227871i \(0.0731765\pi\)
−0.973691 + 0.227871i \(0.926824\pi\)
\(282\) −470.354 −1.66792
\(283\) 518.246i 1.83126i 0.402025 + 0.915629i \(0.368306\pi\)
−0.402025 + 0.915629i \(0.631694\pi\)
\(284\) −431.186 −1.51826
\(285\) 38.8107 0.136178
\(286\) 155.303i 0.543016i
\(287\) 52.6746i 0.183535i
\(288\) −76.6248 −0.266058
\(289\) 49.6653 0.171852
\(290\) 1148.37i 3.95990i
\(291\) 76.8423i 0.264063i
\(292\) 339.822 1.16377
\(293\) 500.822i 1.70929i −0.519213 0.854645i \(-0.673775\pi\)
0.519213 0.854645i \(-0.326225\pi\)
\(294\) −39.9791 −0.135983
\(295\) 337.001i 1.14238i
\(296\) 369.607i 1.24867i
\(297\) 30.4987i 0.102689i
\(298\) 226.079i 0.758654i
\(299\) 123.477 137.168i 0.412966 0.458756i
\(300\) −385.127 −1.28376
\(301\) −173.451 −0.576250
\(302\) −328.126 −1.08651
\(303\) −42.7560 −0.141109
\(304\) 11.0838i 0.0364598i
\(305\) 706.700 2.31705
\(306\) 153.038i 0.500123i
\(307\) −386.940 −1.26039 −0.630195 0.776437i \(-0.717025\pi\)
−0.630195 + 0.776437i \(0.717025\pi\)
\(308\) 106.732 0.346532
\(309\) 202.398i 0.655010i
\(310\) 1425.69i 4.59898i
\(311\) 137.261 0.441355 0.220677 0.975347i \(-0.429173\pi\)
0.220677 + 0.975347i \(0.429173\pi\)
\(312\) 131.666 0.422007
\(313\) 237.239i 0.757953i −0.925406 0.378977i \(-0.876276\pi\)
0.925406 0.378977i \(-0.123724\pi\)
\(314\) 723.593i 2.30443i
\(315\) 60.1096 0.190824
\(316\) 24.6466i 0.0779956i
\(317\) 341.309 1.07668 0.538342 0.842726i \(-0.319051\pi\)
0.538342 + 0.842726i \(0.319051\pi\)
\(318\) 153.662i 0.483214i
\(319\) 269.919i 0.846142i
\(320\) 751.293i 2.34779i
\(321\) 227.779i 0.709591i
\(322\) 149.132 + 134.247i 0.463144 + 0.416916i
\(323\) −45.7742 −0.141716
\(324\) 61.8569 0.190916
\(325\) −259.599 −0.798765
\(326\) −299.716 −0.919376
\(327\) 247.574i 0.757106i
\(328\) 188.608 0.575025
\(329\) 217.891i 0.662282i
\(330\) −253.868 −0.769297
\(331\) −628.965 −1.90020 −0.950099 0.311950i \(-0.899018\pi\)
−0.950099 + 0.311950i \(0.899018\pi\)
\(332\) 840.941i 2.53296i
\(333\) 117.045i 0.351486i
\(334\) 375.346 1.12379
\(335\) −25.2325 −0.0753208
\(336\) 17.1664i 0.0510905i
\(337\) 53.9970i 0.160229i 0.996786 + 0.0801143i \(0.0255285\pi\)
−0.996786 + 0.0801143i \(0.974471\pi\)
\(338\) −344.948 −1.02055
\(339\) 116.978i 0.345067i
\(340\) 805.233 2.36833
\(341\) 335.101i 0.982700i
\(342\) 29.2694i 0.0855830i
\(343\) 18.5203i 0.0539949i
\(344\) 621.064i 1.80542i
\(345\) −224.224 201.843i −0.649925 0.585054i
\(346\) −85.7947 −0.247962
\(347\) −479.369 −1.38147 −0.690734 0.723109i \(-0.742712\pi\)
−0.690734 + 0.723109i \(0.742712\pi\)
\(348\) −547.445 −1.57312
\(349\) 610.168 1.74833 0.874166 0.485627i \(-0.161409\pi\)
0.874166 + 0.485627i \(0.161409\pi\)
\(350\) 282.242i 0.806405i
\(351\) 41.6953 0.118790
\(352\) 149.916i 0.425898i
\(353\) 186.410 0.528073 0.264037 0.964513i \(-0.414946\pi\)
0.264037 + 0.964513i \(0.414946\pi\)
\(354\) 254.152 0.717943
\(355\) 475.108i 1.33833i
\(356\) 186.042i 0.522589i
\(357\) −70.8945 −0.198584
\(358\) 878.225 2.45314
\(359\) 34.4445i 0.0959457i 0.998849 + 0.0479729i \(0.0152761\pi\)
−0.998849 + 0.0479729i \(0.984724\pi\)
\(360\) 215.230i 0.597861i
\(361\) 352.245 0.975749
\(362\) 436.789i 1.20660i
\(363\) 149.908 0.412969
\(364\) 145.915i 0.400865i
\(365\) 374.437i 1.02586i
\(366\) 532.963i 1.45618i
\(367\) 57.4543i 0.156551i 0.996932 + 0.0782757i \(0.0249414\pi\)
−0.996932 + 0.0782757i \(0.975059\pi\)
\(368\) 57.6436 64.0351i 0.156640 0.174009i
\(369\) 59.7273 0.161863
\(370\) 974.269 2.63316
\(371\) 71.1837 0.191870
\(372\) 679.645 1.82700
\(373\) 693.643i 1.85963i −0.368025 0.929816i \(-0.619966\pi\)
0.368025 0.929816i \(-0.380034\pi\)
\(374\) 299.417 0.800581
\(375\) 96.4328i 0.257154i
\(376\) −780.186 −2.07496
\(377\) −369.011 −0.978809
\(378\) 45.3321i 0.119926i
\(379\) 269.440i 0.710924i −0.934691 0.355462i \(-0.884323\pi\)
0.934691 0.355462i \(-0.115677\pi\)
\(380\) 154.006 0.405278
\(381\) −273.676 −0.718309
\(382\) 60.4053i 0.158129i
\(383\) 421.940i 1.10167i −0.834614 0.550836i \(-0.814309\pi\)
0.834614 0.550836i \(-0.185691\pi\)
\(384\) −389.635 −1.01468
\(385\) 117.604i 0.305465i
\(386\) −49.8273 −0.129086
\(387\) 196.675i 0.508205i
\(388\) 304.919i 0.785875i
\(389\) 217.859i 0.560048i −0.959993 0.280024i \(-0.909658\pi\)
0.959993 0.280024i \(-0.0903424\pi\)
\(390\) 347.067i 0.889915i
\(391\) 264.455 + 238.058i 0.676354 + 0.608845i
\(392\) −66.3142 −0.169169
\(393\) −150.622 −0.383262
\(394\) −429.169 −1.08926
\(395\) 27.1572 0.0687524
\(396\) 121.023i 0.305613i
\(397\) −522.340 −1.31572 −0.657859 0.753141i \(-0.728538\pi\)
−0.657859 + 0.753141i \(0.728538\pi\)
\(398\) 558.389i 1.40299i
\(399\) −13.5590 −0.0339825
\(400\) −121.190 −0.302976
\(401\) 647.324i 1.61427i 0.590365 + 0.807137i \(0.298984\pi\)
−0.590365 + 0.807137i \(0.701016\pi\)
\(402\) 19.0293i 0.0473365i
\(403\) 458.121 1.13678
\(404\) −169.661 −0.419953
\(405\) 68.1578i 0.168291i
\(406\) 401.197i 0.988171i
\(407\) 228.998 0.562648
\(408\) 253.847i 0.622174i
\(409\) −66.5915 −0.162815 −0.0814077 0.996681i \(-0.525942\pi\)
−0.0814077 + 0.996681i \(0.525942\pi\)
\(410\) 497.164i 1.21260i
\(411\) 120.035i 0.292055i
\(412\) 803.141i 1.94937i
\(413\) 117.735i 0.285074i
\(414\) 152.222 169.100i 0.367685 0.408455i
\(415\) 926.602 2.23278
\(416\) −204.952 −0.492674
\(417\) 114.035 0.273465
\(418\) 57.2654 0.136998
\(419\) 44.6542i 0.106573i 0.998579 + 0.0532867i \(0.0169697\pi\)
−0.998579 + 0.0532867i \(0.983030\pi\)
\(420\) 238.522 0.567910
\(421\) 569.648i 1.35308i −0.736404 0.676542i \(-0.763478\pi\)
0.736404 0.676542i \(-0.236522\pi\)
\(422\) 247.879 0.587390
\(423\) −247.065 −0.584078
\(424\) 254.883i 0.601138i
\(425\) 500.496i 1.17764i
\(426\) −358.306 −0.841094
\(427\) −246.894 −0.578207
\(428\) 903.854i 2.11181i
\(429\) 81.5765i 0.190155i
\(430\) 1637.10 3.80722
\(431\) 232.773i 0.540078i −0.962849 0.270039i \(-0.912963\pi\)
0.962849 0.270039i \(-0.0870365\pi\)
\(432\) 19.4649 0.0450576
\(433\) 190.916i 0.440915i −0.975397 0.220458i \(-0.929245\pi\)
0.975397 0.220458i \(-0.0707551\pi\)
\(434\) 498.080i 1.14765i
\(435\) 603.210i 1.38669i
\(436\) 982.402i 2.25322i
\(437\) 50.5785 + 45.5301i 0.115740 + 0.104188i
\(438\) 282.384 0.644713
\(439\) 855.700 1.94920 0.974602 0.223944i \(-0.0718934\pi\)
0.974602 + 0.223944i \(0.0718934\pi\)
\(440\) −421.096 −0.957037
\(441\) −21.0000 −0.0476190
\(442\) 409.338i 0.926104i
\(443\) −117.069 −0.264265 −0.132132 0.991232i \(-0.542182\pi\)
−0.132132 + 0.991232i \(0.542182\pi\)
\(444\) 464.448i 1.04606i
\(445\) 204.993 0.460658
\(446\) −760.947 −1.70616
\(447\) 118.753i 0.265668i
\(448\) 262.473i 0.585878i
\(449\) −619.668 −1.38011 −0.690054 0.723758i \(-0.742413\pi\)
−0.690054 + 0.723758i \(0.742413\pi\)
\(450\) −320.032 −0.711182
\(451\) 116.856i 0.259104i
\(452\) 464.182i 1.02695i
\(453\) −172.356 −0.380477
\(454\) 1375.28i 3.02925i
\(455\) 160.778 0.353359
\(456\) 48.5498i 0.106469i
\(457\) 853.352i 1.86729i 0.358198 + 0.933646i \(0.383391\pi\)
−0.358198 + 0.933646i \(0.616609\pi\)
\(458\) 786.052i 1.71627i
\(459\) 80.3868i 0.175135i
\(460\) −889.749 800.939i −1.93424 1.74117i
\(461\) −13.4727 −0.0292250 −0.0146125 0.999893i \(-0.504651\pi\)
−0.0146125 + 0.999893i \(0.504651\pi\)
\(462\) 88.6918 0.191974
\(463\) 511.888 1.10559 0.552795 0.833317i \(-0.313561\pi\)
0.552795 + 0.833317i \(0.313561\pi\)
\(464\) −172.268 −0.371267
\(465\) 748.876i 1.61049i
\(466\) 1110.71 2.38349
\(467\) 176.944i 0.378895i −0.981891 0.189447i \(-0.939330\pi\)
0.981891 0.189447i \(-0.0606697\pi\)
\(468\) 165.452 0.353530
\(469\) 8.81527 0.0187959
\(470\) 2056.54i 4.37562i
\(471\) 380.085i 0.806974i
\(472\) 421.567 0.893150
\(473\) 384.794 0.813517
\(474\) 20.4808i 0.0432084i
\(475\) 95.7229i 0.201522i
\(476\) −281.318 −0.591004
\(477\) 80.7148i 0.169213i
\(478\) −816.823 −1.70883
\(479\) 526.453i 1.09907i 0.835472 + 0.549534i \(0.185195\pi\)
−0.835472 + 0.549534i \(0.814805\pi\)
\(480\) 335.029i 0.697977i
\(481\) 313.066i 0.650865i
\(482\) 802.904i 1.66578i
\(483\) 78.3354 + 70.5164i 0.162185 + 0.145997i
\(484\) 594.852 1.22903
\(485\) 335.980 0.692741
\(486\) 51.4017 0.105765
\(487\) −737.679 −1.51474 −0.757370 0.652985i \(-0.773516\pi\)
−0.757370 + 0.652985i \(0.773516\pi\)
\(488\) 884.037i 1.81155i
\(489\) −157.433 −0.321950
\(490\) 174.802i 0.356738i
\(491\) 155.714 0.317135 0.158568 0.987348i \(-0.449312\pi\)
0.158568 + 0.987348i \(0.449312\pi\)
\(492\) 237.005 0.481718
\(493\) 711.439i 1.44308i
\(494\) 78.2884i 0.158479i
\(495\) −133.350 −0.269395
\(496\) 213.868 0.431186
\(497\) 165.985i 0.333973i
\(498\) 698.804i 1.40322i
\(499\) −247.861 −0.496714 −0.248357 0.968669i \(-0.579891\pi\)
−0.248357 + 0.968669i \(0.579891\pi\)
\(500\) 382.657i 0.765314i
\(501\) 197.160 0.393532
\(502\) 723.175i 1.44059i
\(503\) 348.300i 0.692445i −0.938153 0.346222i \(-0.887464\pi\)
0.938153 0.346222i \(-0.112536\pi\)
\(504\) 75.1932i 0.149193i
\(505\) 186.943i 0.370185i
\(506\) −330.843 297.821i −0.653841 0.588578i
\(507\) −181.192 −0.357381
\(508\) −1085.98 −2.13775
\(509\) 285.376 0.560659 0.280330 0.959904i \(-0.409556\pi\)
0.280330 + 0.959904i \(0.409556\pi\)
\(510\) 669.131 1.31202
\(511\) 130.814i 0.255996i
\(512\) −237.630 −0.464122
\(513\) 15.3745i 0.0299697i
\(514\) 543.306 1.05701
\(515\) −884.951 −1.71835
\(516\) 780.431i 1.51246i
\(517\) 483.381i 0.934972i
\(518\) −340.373 −0.657090
\(519\) −45.0658 −0.0868319
\(520\) 575.687i 1.10709i
\(521\) 1031.41i 1.97967i 0.142215 + 0.989836i \(0.454578\pi\)
−0.142215 + 0.989836i \(0.545422\pi\)
\(522\) −454.915 −0.871485
\(523\) 432.943i 0.827808i 0.910321 + 0.413904i \(0.135835\pi\)
−0.910321 + 0.413904i \(0.864165\pi\)
\(524\) −597.687 −1.14062
\(525\) 148.254i 0.282389i
\(526\) 1474.67i 2.80356i
\(527\) 883.240i 1.67598i
\(528\) 38.0829i 0.0721267i
\(529\) −55.4221 526.089i −0.104768 0.994497i
\(530\) −671.861 −1.26766
\(531\) 133.499 0.251411
\(532\) −53.8038 −0.101135
\(533\) 159.756 0.299730
\(534\) 154.597i 0.289507i
\(535\) −995.924 −1.86154
\(536\) 31.5642i 0.0588885i
\(537\) 461.309 0.859048
\(538\) 819.340 1.52294
\(539\) 41.0864i 0.0762270i
\(540\) 270.459i 0.500849i
\(541\) −307.455 −0.568310 −0.284155 0.958778i \(-0.591713\pi\)
−0.284155 + 0.958778i \(0.591713\pi\)
\(542\) 285.894 0.527480
\(543\) 229.434i 0.422531i
\(544\) 395.140i 0.726361i
\(545\) −1082.47 −1.98619
\(546\) 121.252i 0.222073i
\(547\) −643.947 −1.17723 −0.588617 0.808412i \(-0.700327\pi\)
−0.588617 + 0.808412i \(0.700327\pi\)
\(548\) 476.312i 0.869183i
\(549\) 279.952i 0.509930i
\(550\) 626.141i 1.13844i
\(551\) 136.067i 0.246945i
\(552\) 252.493 280.490i 0.457415 0.508134i
\(553\) −9.48769 −0.0171568
\(554\) 493.644 0.891054
\(555\) 511.759 0.922088
\(556\) 452.504 0.813856
\(557\) 243.277i 0.436763i 0.975863 + 0.218382i \(0.0700777\pi\)
−0.975863 + 0.218382i \(0.929922\pi\)
\(558\) 564.770 1.01213
\(559\) 526.057i 0.941069i
\(560\) 75.0572 0.134031
\(561\) 157.276 0.280350
\(562\) 422.280i 0.751387i
\(563\) 24.9265i 0.0442744i −0.999755 0.0221372i \(-0.992953\pi\)
0.999755 0.0221372i \(-0.00704707\pi\)
\(564\) −980.384 −1.73827
\(565\) −511.465 −0.905247
\(566\) 1708.87i 3.01921i
\(567\) 23.8118i 0.0419961i
\(568\) −594.330 −1.04635
\(569\) 877.581i 1.54232i 0.636640 + 0.771161i \(0.280324\pi\)
−0.636640 + 0.771161i \(0.719676\pi\)
\(570\) 127.975 0.224518
\(571\) 682.902i 1.19598i 0.801505 + 0.597988i \(0.204033\pi\)
−0.801505 + 0.597988i \(0.795967\pi\)
\(572\) 323.705i 0.565919i
\(573\) 31.7293i 0.0553741i
\(574\) 173.690i 0.302596i
\(575\) −497.827 + 553.027i −0.865786 + 0.961785i
\(576\) −297.617 −0.516696
\(577\) −194.040 −0.336292 −0.168146 0.985762i \(-0.553778\pi\)
−0.168146 + 0.985762i \(0.553778\pi\)
\(578\) 163.768 0.283335
\(579\) −26.1730 −0.0452038
\(580\) 2393.61i 4.12692i
\(581\) −323.720 −0.557177
\(582\) 253.381i 0.435363i
\(583\) −157.918 −0.270871
\(584\) 468.397 0.802049
\(585\) 182.305i 0.311633i
\(586\) 1651.42i 2.81812i
\(587\) −686.812 −1.17004 −0.585018 0.811020i \(-0.698913\pi\)
−0.585018 + 0.811020i \(0.698913\pi\)
\(588\) −83.3306 −0.141719
\(589\) 168.925i 0.286800i
\(590\) 1111.23i 1.88345i
\(591\) −225.432 −0.381441
\(592\) 146.151i 0.246876i
\(593\) 605.769 1.02153 0.510767 0.859719i \(-0.329362\pi\)
0.510767 + 0.859719i \(0.329362\pi\)
\(594\) 100.567i 0.169305i
\(595\) 309.974i 0.520965i
\(596\) 471.228i 0.790651i
\(597\) 293.308i 0.491303i
\(598\) 407.155 452.301i 0.680862 0.756356i
\(599\) −961.119 −1.60454 −0.802270 0.596962i \(-0.796374\pi\)
−0.802270 + 0.596962i \(0.796374\pi\)
\(600\) −530.844 −0.884740
\(601\) −375.280 −0.624427 −0.312213 0.950012i \(-0.601070\pi\)
−0.312213 + 0.950012i \(0.601070\pi\)
\(602\) −571.942 −0.950069
\(603\) 9.99558i 0.0165764i
\(604\) −683.929 −1.13233
\(605\) 655.445i 1.08338i
\(606\) −140.985 −0.232648
\(607\) −462.146 −0.761361 −0.380680 0.924707i \(-0.624310\pi\)
−0.380680 + 0.924707i \(0.624310\pi\)
\(608\) 75.5729i 0.124298i
\(609\) 210.739i 0.346041i
\(610\) 2330.29 3.82014
\(611\) −660.837 −1.08157
\(612\) 318.985i 0.521217i
\(613\) 260.942i 0.425681i −0.977087 0.212840i \(-0.931729\pi\)
0.977087 0.212840i \(-0.0682714\pi\)
\(614\) −1275.90 −2.07802
\(615\) 261.147i 0.424630i
\(616\) 147.115 0.238823
\(617\) 490.693i 0.795289i 0.917540 + 0.397644i \(0.130172\pi\)
−0.917540 + 0.397644i \(0.869828\pi\)
\(618\) 667.392i 1.07992i
\(619\) 366.338i 0.591822i 0.955216 + 0.295911i \(0.0956231\pi\)
−0.955216 + 0.295911i \(0.904377\pi\)
\(620\) 2971.63i 4.79295i
\(621\) 79.9581 88.8240i 0.128757 0.143034i
\(622\) 452.608 0.727666
\(623\) −71.6166 −0.114954
\(624\) 52.0638 0.0834355
\(625\) −387.158 −0.619453
\(626\) 782.278i 1.24965i
\(627\) 30.0800 0.0479745
\(628\) 1508.22i 2.40163i
\(629\) −603.579 −0.959585
\(630\) 198.207 0.314614
\(631\) 545.854i 0.865062i 0.901619 + 0.432531i \(0.142379\pi\)
−0.901619 + 0.432531i \(0.857621\pi\)
\(632\) 33.9719i 0.0537530i
\(633\) 130.204 0.205694
\(634\) 1125.44 1.77514
\(635\) 1196.60i 1.88441i
\(636\) 320.286i 0.503594i
\(637\) −56.1698 −0.0881787
\(638\) 890.038i 1.39504i
\(639\) −188.209 −0.294537
\(640\) 1703.61i 2.66190i
\(641\) 812.170i 1.26704i 0.773728 + 0.633518i \(0.218390\pi\)
−0.773728 + 0.633518i \(0.781610\pi\)
\(642\) 751.083i 1.16991i
\(643\) 859.191i 1.33622i −0.744061 0.668111i \(-0.767103\pi\)
0.744061 0.668111i \(-0.232897\pi\)
\(644\) 310.844 + 279.818i 0.482678 + 0.434500i
\(645\) 859.928 1.33322
\(646\) −150.937 −0.233648
\(647\) 759.541 1.17394 0.586971 0.809608i \(-0.300320\pi\)
0.586971 + 0.809608i \(0.300320\pi\)
\(648\) 85.2611 0.131576
\(649\) 261.191i 0.402451i
\(650\) −856.007 −1.31693
\(651\) 261.629i 0.401887i
\(652\) −624.715 −0.958151
\(653\) 215.811 0.330491 0.165245 0.986252i \(-0.447158\pi\)
0.165245 + 0.986252i \(0.447158\pi\)
\(654\) 816.355i 1.24825i
\(655\) 658.569i 1.00545i
\(656\) 74.5799 0.113689
\(657\) 148.329 0.225768
\(658\) 718.478i 1.09191i
\(659\) 1201.52i 1.82325i −0.411019 0.911627i \(-0.634827\pi\)
0.411019 0.911627i \(-0.365173\pi\)
\(660\) −529.150 −0.801743
\(661\) 386.123i 0.584149i −0.956396 0.292075i \(-0.905654\pi\)
0.956396 0.292075i \(-0.0943456\pi\)
\(662\) −2073.96 −3.13288
\(663\) 215.015i 0.324306i
\(664\) 1159.12i 1.74566i
\(665\) 59.2844i 0.0891495i
\(666\) 385.946i 0.579499i
\(667\) −707.645 + 786.109i −1.06094 + 1.17857i
\(668\) 782.353 1.17119
\(669\) −399.706 −0.597468
\(670\) −83.2021 −0.124182
\(671\) 547.724 0.816280
\(672\) 117.046i 0.174176i
\(673\) 62.5259 0.0929063 0.0464531 0.998920i \(-0.485208\pi\)
0.0464531 + 0.998920i \(0.485208\pi\)
\(674\) 178.051i 0.264170i
\(675\) −168.105 −0.249044
\(676\) −718.992 −1.06360
\(677\) 538.571i 0.795526i 0.917488 + 0.397763i \(0.130213\pi\)
−0.917488 + 0.397763i \(0.869787\pi\)
\(678\) 385.725i 0.568915i
\(679\) −117.378 −0.172870
\(680\) 1109.90 1.63221
\(681\) 722.398i 1.06079i
\(682\) 1104.97i 1.62019i
\(683\) 1009.25 1.47767 0.738834 0.673887i \(-0.235377\pi\)
0.738834 + 0.673887i \(0.235377\pi\)
\(684\) 61.0077i 0.0891926i
\(685\) −524.831 −0.766176
\(686\) 61.0691i 0.0890220i
\(687\) 412.893i 0.601008i
\(688\) 245.583i 0.356952i
\(689\) 215.892i 0.313341i
\(690\) −739.361 665.563i −1.07154 0.964584i
\(691\) 9.17135 0.0132726 0.00663629 0.999978i \(-0.497888\pi\)
0.00663629 + 0.999978i \(0.497888\pi\)
\(692\) −178.826 −0.258420
\(693\) 46.5875 0.0672259
\(694\) −1580.68 −2.27764
\(695\) 498.598i 0.717407i
\(696\) −754.577 −1.08416
\(697\) 308.003i 0.441898i
\(698\) 2011.98 2.88249
\(699\) 583.427 0.834659
\(700\) 588.291i 0.840416i
\(701\) 518.407i 0.739525i −0.929126 0.369763i \(-0.879439\pi\)
0.929126 0.369763i \(-0.120561\pi\)
\(702\) 137.487 0.195850
\(703\) −115.438 −0.164208
\(704\) 582.285i 0.827109i
\(705\) 1080.25i 1.53227i
\(706\) 614.672 0.870640
\(707\) 65.3109i 0.0923775i
\(708\) 529.742 0.748223
\(709\) 668.918i 0.943467i −0.881741 0.471734i \(-0.843628\pi\)
0.881741 0.471734i \(-0.156372\pi\)
\(710\) 1566.63i 2.20652i
\(711\) 10.7580i 0.0151308i
\(712\) 256.433i 0.360158i
\(713\) 878.530 975.942i 1.23216 1.36878i
\(714\) −233.769 −0.327408
\(715\) −356.679 −0.498852
\(716\) 1830.53 2.55661
\(717\) −429.056 −0.598404
\(718\) 113.578i 0.158187i
\(719\) −741.327 −1.03105 −0.515526 0.856874i \(-0.672404\pi\)
−0.515526 + 0.856874i \(0.672404\pi\)
\(720\) 85.1069i 0.118204i
\(721\) 309.168 0.428805
\(722\) 1161.50 1.60873
\(723\) 421.745i 0.583326i
\(724\) 910.423i 1.25749i
\(725\) 1487.76 2.05208
\(726\) 494.309 0.680866
\(727\) 678.078i 0.932707i 0.884598 + 0.466354i \(0.154433\pi\)
−0.884598 + 0.466354i \(0.845567\pi\)
\(728\) 201.123i 0.276268i
\(729\) 27.0000 0.0370370
\(730\) 1234.68i 1.69134i
\(731\) −1014.22 −1.38744
\(732\) 1110.88i 1.51760i
\(733\) 227.261i 0.310043i 0.987911 + 0.155021i \(0.0495446\pi\)
−0.987911 + 0.155021i \(0.950455\pi\)
\(734\) 189.451i 0.258108i
\(735\) 91.8189i 0.124924i
\(736\) −393.033 + 436.613i −0.534012 + 0.593224i
\(737\) −19.5563 −0.0265350
\(738\) 196.946 0.266865
\(739\) 381.721 0.516538 0.258269 0.966073i \(-0.416848\pi\)
0.258269 + 0.966073i \(0.416848\pi\)
\(740\) 2030.72 2.74422
\(741\) 41.1229i 0.0554965i
\(742\) 234.723 0.316338
\(743\) 459.108i 0.617911i 0.951076 + 0.308956i \(0.0999795\pi\)
−0.951076 + 0.308956i \(0.900021\pi\)
\(744\) 936.796 1.25913
\(745\) 519.229 0.696951
\(746\) 2287.23i 3.06600i
\(747\) 367.064i 0.491384i
\(748\) 624.091 0.834346
\(749\) 347.938 0.464537
\(750\) 317.979i 0.423973i
\(751\) 788.305i 1.04967i 0.851203 + 0.524837i \(0.175874\pi\)
−0.851203 + 0.524837i \(0.824126\pi\)
\(752\) −308.503 −0.410244
\(753\) 379.865i 0.504469i
\(754\) −1216.79 −1.61377
\(755\) 753.597i 0.998141i
\(756\) 94.4880i 0.124984i
\(757\) 331.974i 0.438539i 0.975664 + 0.219269i \(0.0703674\pi\)
−0.975664 + 0.219269i \(0.929633\pi\)
\(758\) 888.459i 1.17211i
\(759\) −173.783 156.438i −0.228964 0.206110i
\(760\) 212.275 0.279310
\(761\) −942.828 −1.23893 −0.619466 0.785023i \(-0.712651\pi\)
−0.619466 + 0.785023i \(0.712651\pi\)
\(762\) −902.424 −1.18428
\(763\) 378.175 0.495642
\(764\) 125.906i 0.164798i
\(765\) 351.477 0.459448
\(766\) 1391.32i 1.81634i
\(767\) 357.078 0.465551
\(768\) −597.476 −0.777963
\(769\) 12.1026i 0.0157381i 0.999969 + 0.00786906i \(0.00250483\pi\)
−0.999969 + 0.00786906i \(0.997495\pi\)
\(770\) 387.790i 0.503623i
\(771\) 285.384 0.370148
\(772\) −103.858 −0.134531
\(773\) 112.155i 0.145091i 0.997365 + 0.0725454i \(0.0231122\pi\)
−0.997365 + 0.0725454i \(0.976888\pi\)
\(774\) 648.521i 0.837882i
\(775\) −1847.03 −2.38326
\(776\) 420.289i 0.541609i
\(777\) −178.789 −0.230102
\(778\) 718.372i 0.923357i
\(779\) 58.9074i 0.0756193i
\(780\) 723.410i 0.927449i
\(781\) 368.229i 0.471485i
\(782\) 872.018 + 784.979i 1.11511 + 1.00381i
\(783\) −238.955 −0.305179
\(784\) −26.2221 −0.0334466
\(785\) −1661.85 −2.11701
\(786\) −496.664 −0.631889
\(787\) 1226.22i 1.55809i 0.626968 + 0.779045i \(0.284296\pi\)
−0.626968 + 0.779045i \(0.715704\pi\)
\(788\) −894.540 −1.13520
\(789\) 774.608i 0.981760i
\(790\) 89.5487 0.113353
\(791\) 178.686 0.225899