Properties

Label 105.3.h.a.76.6
Level 105
Weight 3
Character 105.76
Analytic conductor 2.861
Analytic rank 0
Dimension 12
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 76.6
Root \(-1.01714 - 1.76174i\) of \(x^{12} - 2 x^{11} + 21 x^{10} - 26 x^{9} + 295 x^{8} - 372 x^{7} + 1704 x^{6} - 1074 x^{5} + 5613 x^{4} - 5472 x^{3} + 4950 x^{2} - 1638 x + 441\)
Character \(\chi\) \(=\) 105.76
Dual form 105.3.h.a.76.5

$q$-expansion

\(f(q)\) \(=\) \(q-1.71214 q^{2} +1.73205i q^{3} -1.06857 q^{4} -2.23607i q^{5} -2.96552i q^{6} +(-3.33344 - 6.15534i) q^{7} +8.67811 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q-1.71214 q^{2} +1.73205i q^{3} -1.06857 q^{4} -2.23607i q^{5} -2.96552i q^{6} +(-3.33344 - 6.15534i) q^{7} +8.67811 q^{8} -3.00000 q^{9} +3.82847i q^{10} +17.0001 q^{11} -1.85082i q^{12} -16.3319i q^{13} +(5.70733 + 10.5388i) q^{14} +3.87298 q^{15} -10.5839 q^{16} -13.4266i q^{17} +5.13643 q^{18} -13.7499i q^{19} +2.38940i q^{20} +(10.6614 - 5.77369i) q^{21} -29.1066 q^{22} -16.6179 q^{23} +15.0309i q^{24} -5.00000 q^{25} +27.9626i q^{26} -5.19615i q^{27} +(3.56202 + 6.57741i) q^{28} +32.1793 q^{29} -6.63110 q^{30} +6.74366i q^{31} -16.5913 q^{32} +29.4450i q^{33} +22.9883i q^{34} +(-13.7637 + 7.45380i) q^{35} +3.20571 q^{36} -69.2141 q^{37} +23.5418i q^{38} +28.2878 q^{39} -19.4048i q^{40} +39.7391i q^{41} +(-18.2538 + 9.88538i) q^{42} +43.2210 q^{43} -18.1658 q^{44} +6.70820i q^{45} +28.4522 q^{46} -40.1384i q^{47} -18.3318i q^{48} +(-26.7763 + 41.0369i) q^{49} +8.56071 q^{50} +23.2556 q^{51} +17.4518i q^{52} +22.5002 q^{53} +8.89655i q^{54} -38.0134i q^{55} +(-28.9280 - 53.4167i) q^{56} +23.8155 q^{57} -55.0956 q^{58} -81.6005i q^{59} -4.13855 q^{60} -14.9859i q^{61} -11.5461i q^{62} +(10.0003 + 18.4660i) q^{63} +70.7422 q^{64} -36.5193 q^{65} -50.4141i q^{66} +72.0872 q^{67} +14.3473i q^{68} -28.7831i q^{69} +(23.5655 - 12.7620i) q^{70} -25.7338 q^{71} -26.0343 q^{72} -75.0647i q^{73} +118.504 q^{74} -8.66025i q^{75} +14.6927i q^{76} +(-56.6689 - 104.641i) q^{77} -48.4327 q^{78} +80.0480 q^{79} +23.6663i q^{80} +9.00000 q^{81} -68.0389i q^{82} +102.112i q^{83} +(-11.3924 + 6.16959i) q^{84} -30.0228 q^{85} -74.0005 q^{86} +55.7362i q^{87} +147.529 q^{88} +128.381i q^{89} -11.4854i q^{90} +(-100.529 + 54.4416i) q^{91} +17.7574 q^{92} -11.6804 q^{93} +68.7227i q^{94} -30.7457 q^{95} -28.7371i q^{96} +159.448i q^{97} +(45.8449 - 70.2610i) q^{98} -51.0003 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{2} + 44q^{4} - 8q^{7} + 4q^{8} - 36q^{9} + O(q^{10}) \) \( 12q - 4q^{2} + 44q^{4} - 8q^{7} + 4q^{8} - 36q^{9} - 16q^{11} - 40q^{14} + 92q^{16} + 12q^{18} + 36q^{21} - 88q^{22} - 64q^{23} - 60q^{25} + 88q^{28} + 104q^{29} - 228q^{32} + 60q^{35} - 132q^{36} + 32q^{37} - 24q^{39} - 60q^{42} + 152q^{43} + 192q^{44} + 200q^{46} + 60q^{49} + 20q^{50} + 24q^{51} + 176q^{53} - 368q^{56} - 240q^{57} - 400q^{58} + 24q^{63} - 20q^{64} - 240q^{65} + 168q^{67} - 60q^{70} + 32q^{71} - 12q^{72} + 184q^{74} + 8q^{77} + 456q^{78} + 120q^{79} + 108q^{81} + 108q^{84} + 120q^{85} + 400q^{86} - 536q^{88} + 24q^{91} + 192q^{92} + 48q^{93} + 884q^{98} + 48q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.71214 −0.856071 −0.428035 0.903762i \(-0.640794\pi\)
−0.428035 + 0.903762i \(0.640794\pi\)
\(3\) 1.73205i 0.577350i
\(4\) −1.06857 −0.267143
\(5\) 2.23607i 0.447214i
\(6\) 2.96552i 0.494253i
\(7\) −3.33344 6.15534i −0.476206 0.879334i
\(8\) 8.67811 1.08476
\(9\) −3.00000 −0.333333
\(10\) 3.82847i 0.382847i
\(11\) 17.0001 1.54546 0.772732 0.634732i \(-0.218890\pi\)
0.772732 + 0.634732i \(0.218890\pi\)
\(12\) 1.85082i 0.154235i
\(13\) 16.3319i 1.25630i −0.778091 0.628152i \(-0.783812\pi\)
0.778091 0.628152i \(-0.216188\pi\)
\(14\) 5.70733 + 10.5388i 0.407666 + 0.752772i
\(15\) 3.87298 0.258199
\(16\) −10.5839 −0.661492
\(17\) 13.4266i 0.789801i −0.918724 0.394900i \(-0.870779\pi\)
0.918724 0.394900i \(-0.129221\pi\)
\(18\) 5.13643 0.285357
\(19\) 13.7499i 0.723679i −0.932240 0.361839i \(-0.882149\pi\)
0.932240 0.361839i \(-0.117851\pi\)
\(20\) 2.38940i 0.119470i
\(21\) 10.6614 5.77369i 0.507684 0.274938i
\(22\) −29.1066 −1.32303
\(23\) −16.6179 −0.722518 −0.361259 0.932466i \(-0.617653\pi\)
−0.361259 + 0.932466i \(0.617653\pi\)
\(24\) 15.0309i 0.626289i
\(25\) −5.00000 −0.200000
\(26\) 27.9626i 1.07548i
\(27\) 5.19615i 0.192450i
\(28\) 3.56202 + 6.57741i 0.127215 + 0.234907i
\(29\) 32.1793 1.10963 0.554816 0.831973i \(-0.312789\pi\)
0.554816 + 0.831973i \(0.312789\pi\)
\(30\) −6.63110 −0.221037
\(31\) 6.74366i 0.217538i 0.994067 + 0.108769i \(0.0346908\pi\)
−0.994067 + 0.108769i \(0.965309\pi\)
\(32\) −16.5913 −0.518480
\(33\) 29.4450i 0.892274i
\(34\) 22.9883i 0.676125i
\(35\) −13.7637 + 7.45380i −0.393250 + 0.212966i
\(36\) 3.20571 0.0890475
\(37\) −69.2141 −1.87065 −0.935325 0.353789i \(-0.884893\pi\)
−0.935325 + 0.353789i \(0.884893\pi\)
\(38\) 23.5418i 0.619520i
\(39\) 28.2878 0.725327
\(40\) 19.4048i 0.485121i
\(41\) 39.7391i 0.969246i 0.874723 + 0.484623i \(0.161043\pi\)
−0.874723 + 0.484623i \(0.838957\pi\)
\(42\) −18.2538 + 9.88538i −0.434613 + 0.235366i
\(43\) 43.2210 1.00514 0.502570 0.864537i \(-0.332388\pi\)
0.502570 + 0.864537i \(0.332388\pi\)
\(44\) −18.1658 −0.412859
\(45\) 6.70820i 0.149071i
\(46\) 28.4522 0.618526
\(47\) 40.1384i 0.854009i −0.904249 0.427005i \(-0.859569\pi\)
0.904249 0.427005i \(-0.140431\pi\)
\(48\) 18.3318i 0.381913i
\(49\) −26.7763 + 41.0369i −0.546456 + 0.837488i
\(50\) 8.56071 0.171214
\(51\) 23.2556 0.455992
\(52\) 17.4518i 0.335612i
\(53\) 22.5002 0.424533 0.212266 0.977212i \(-0.431916\pi\)
0.212266 + 0.977212i \(0.431916\pi\)
\(54\) 8.89655i 0.164751i
\(55\) 38.0134i 0.691153i
\(56\) −28.9280 53.4167i −0.516571 0.953869i
\(57\) 23.8155 0.417816
\(58\) −55.0956 −0.949924
\(59\) 81.6005i 1.38306i −0.722348 0.691529i \(-0.756937\pi\)
0.722348 0.691529i \(-0.243063\pi\)
\(60\) −4.13855 −0.0689759
\(61\) 14.9859i 0.245671i −0.992427 0.122836i \(-0.960801\pi\)
0.992427 0.122836i \(-0.0391988\pi\)
\(62\) 11.5461i 0.186228i
\(63\) 10.0003 + 18.4660i 0.158735 + 0.293111i
\(64\) 70.7422 1.10535
\(65\) −36.5193 −0.561836
\(66\) 50.4141i 0.763850i
\(67\) 72.0872 1.07593 0.537964 0.842968i \(-0.319194\pi\)
0.537964 + 0.842968i \(0.319194\pi\)
\(68\) 14.3473i 0.210989i
\(69\) 28.7831i 0.417146i
\(70\) 23.5655 12.7620i 0.336650 0.182314i
\(71\) −25.7338 −0.362448 −0.181224 0.983442i \(-0.558006\pi\)
−0.181224 + 0.983442i \(0.558006\pi\)
\(72\) −26.0343 −0.361588
\(73\) 75.0647i 1.02828i −0.857705 0.514142i \(-0.828110\pi\)
0.857705 0.514142i \(-0.171890\pi\)
\(74\) 118.504 1.60141
\(75\) 8.66025i 0.115470i
\(76\) 14.6927i 0.193325i
\(77\) −56.6689 104.641i −0.735959 1.35898i
\(78\) −48.4327 −0.620931
\(79\) 80.0480 1.01327 0.506633 0.862162i \(-0.330890\pi\)
0.506633 + 0.862162i \(0.330890\pi\)
\(80\) 23.6663i 0.295828i
\(81\) 9.00000 0.111111
\(82\) 68.0389i 0.829743i
\(83\) 102.112i 1.23027i 0.788421 + 0.615135i \(0.210899\pi\)
−0.788421 + 0.615135i \(0.789101\pi\)
\(84\) −11.3924 + 6.16959i −0.135624 + 0.0734476i
\(85\) −30.0228 −0.353210
\(86\) −74.0005 −0.860471
\(87\) 55.7362i 0.640646i
\(88\) 147.529 1.67646
\(89\) 128.381i 1.44248i 0.692683 + 0.721242i \(0.256429\pi\)
−0.692683 + 0.721242i \(0.743571\pi\)
\(90\) 11.4854i 0.127616i
\(91\) −100.529 + 54.4416i −1.10471 + 0.598259i
\(92\) 17.7574 0.193015
\(93\) −11.6804 −0.125595
\(94\) 68.7227i 0.731092i
\(95\) −30.7457 −0.323639
\(96\) 28.7371i 0.299344i
\(97\) 159.448i 1.64379i 0.569636 + 0.821897i \(0.307084\pi\)
−0.569636 + 0.821897i \(0.692916\pi\)
\(98\) 45.8449 70.2610i 0.467805 0.716949i
\(99\) −51.0003 −0.515155
\(100\) 5.34285 0.0534285
\(101\) 24.1380i 0.238990i 0.992835 + 0.119495i \(0.0381276\pi\)
−0.992835 + 0.119495i \(0.961872\pi\)
\(102\) −39.8168 −0.390361
\(103\) 87.3469i 0.848028i −0.905656 0.424014i \(-0.860621\pi\)
0.905656 0.424014i \(-0.139379\pi\)
\(104\) 141.730i 1.36279i
\(105\) −12.9104 23.8395i −0.122956 0.227043i
\(106\) −38.5236 −0.363430
\(107\) 168.359 1.57344 0.786722 0.617307i \(-0.211776\pi\)
0.786722 + 0.617307i \(0.211776\pi\)
\(108\) 5.55245i 0.0514116i
\(109\) −155.570 −1.42725 −0.713624 0.700529i \(-0.752947\pi\)
−0.713624 + 0.700529i \(0.752947\pi\)
\(110\) 65.0843i 0.591676i
\(111\) 119.882i 1.08002i
\(112\) 35.2807 + 65.1473i 0.315007 + 0.581672i
\(113\) −20.9965 −0.185810 −0.0929050 0.995675i \(-0.529615\pi\)
−0.0929050 + 0.995675i \(0.529615\pi\)
\(114\) −40.7756 −0.357680
\(115\) 37.1588i 0.323120i
\(116\) −34.3859 −0.296430
\(117\) 48.9958i 0.418768i
\(118\) 139.712i 1.18400i
\(119\) −82.6453 + 44.7568i −0.694498 + 0.376108i
\(120\) 33.6102 0.280085
\(121\) 168.004 1.38846
\(122\) 25.6581i 0.210312i
\(123\) −68.8301 −0.559594
\(124\) 7.20608i 0.0581135i
\(125\) 11.1803i 0.0894427i
\(126\) −17.1220 31.6164i −0.135889 0.250924i
\(127\) −59.8712 −0.471427 −0.235713 0.971823i \(-0.575743\pi\)
−0.235713 + 0.971823i \(0.575743\pi\)
\(128\) −54.7554 −0.427776
\(129\) 74.8609i 0.580317i
\(130\) 62.5263 0.480971
\(131\) 166.868i 1.27380i 0.770947 + 0.636899i \(0.219783\pi\)
−0.770947 + 0.636899i \(0.780217\pi\)
\(132\) 31.4641i 0.238364i
\(133\) −84.6352 + 45.8345i −0.636355 + 0.344620i
\(134\) −123.423 −0.921071
\(135\) −11.6190 −0.0860663
\(136\) 116.518i 0.856747i
\(137\) 126.139 0.920726 0.460363 0.887731i \(-0.347719\pi\)
0.460363 + 0.887731i \(0.347719\pi\)
\(138\) 49.2807i 0.357106i
\(139\) 211.650i 1.52266i −0.648365 0.761330i \(-0.724547\pi\)
0.648365 0.761330i \(-0.275453\pi\)
\(140\) 14.7075 7.96491i 0.105054 0.0568922i
\(141\) 69.5218 0.493062
\(142\) 44.0599 0.310281
\(143\) 277.645i 1.94157i
\(144\) 31.7516 0.220497
\(145\) 71.9552i 0.496243i
\(146\) 128.521i 0.880284i
\(147\) −71.0780 46.3780i −0.483524 0.315496i
\(148\) 73.9601 0.499730
\(149\) −64.1825 −0.430755 −0.215377 0.976531i \(-0.569098\pi\)
−0.215377 + 0.976531i \(0.569098\pi\)
\(150\) 14.8276i 0.0988506i
\(151\) 110.915 0.734538 0.367269 0.930115i \(-0.380293\pi\)
0.367269 + 0.930115i \(0.380293\pi\)
\(152\) 119.323i 0.785021i
\(153\) 40.2798i 0.263267i
\(154\) 97.0252 + 179.161i 0.630033 + 1.16338i
\(155\) 15.0793 0.0972858
\(156\) −30.2275 −0.193766
\(157\) 290.451i 1.85001i 0.379956 + 0.925004i \(0.375939\pi\)
−0.379956 + 0.925004i \(0.624061\pi\)
\(158\) −137.053 −0.867427
\(159\) 38.9716i 0.245104i
\(160\) 37.0994i 0.231871i
\(161\) 55.3948 + 102.289i 0.344067 + 0.635334i
\(162\) −15.4093 −0.0951190
\(163\) −53.8559 −0.330404 −0.165202 0.986260i \(-0.552828\pi\)
−0.165202 + 0.986260i \(0.552828\pi\)
\(164\) 42.4640i 0.258927i
\(165\) 65.8411 0.399037
\(166\) 174.831i 1.05320i
\(167\) 41.7927i 0.250255i −0.992141 0.125128i \(-0.960066\pi\)
0.992141 0.125128i \(-0.0399341\pi\)
\(168\) 92.5204 50.1047i 0.550717 0.298242i
\(169\) −97.7324 −0.578298
\(170\) 51.4033 0.302372
\(171\) 41.2497i 0.241226i
\(172\) −46.1847 −0.268515
\(173\) 130.344i 0.753434i 0.926328 + 0.376717i \(0.122947\pi\)
−0.926328 + 0.376717i \(0.877053\pi\)
\(174\) 95.4283i 0.548439i
\(175\) 16.6672 + 30.7767i 0.0952412 + 0.175867i
\(176\) −179.927 −1.02231
\(177\) 141.336 0.798509
\(178\) 219.807i 1.23487i
\(179\) 44.9934 0.251360 0.125680 0.992071i \(-0.459889\pi\)
0.125680 + 0.992071i \(0.459889\pi\)
\(180\) 7.16819i 0.0398233i
\(181\) 17.8944i 0.0988640i −0.998777 0.0494320i \(-0.984259\pi\)
0.998777 0.0494320i \(-0.0157411\pi\)
\(182\) 172.119 93.2117i 0.945710 0.512152i
\(183\) 25.9564 0.141838
\(184\) −144.212 −0.783761
\(185\) 154.767i 0.836581i
\(186\) 19.9985 0.107519
\(187\) 228.254i 1.22061i
\(188\) 42.8907i 0.228142i
\(189\) −31.9841 + 17.3211i −0.169228 + 0.0916459i
\(190\) 52.6410 0.277058
\(191\) 178.314 0.933583 0.466791 0.884367i \(-0.345410\pi\)
0.466791 + 0.884367i \(0.345410\pi\)
\(192\) 122.529i 0.638173i
\(193\) −336.283 −1.74240 −0.871200 0.490928i \(-0.836658\pi\)
−0.871200 + 0.490928i \(0.836658\pi\)
\(194\) 272.998i 1.40720i
\(195\) 63.2534i 0.324376i
\(196\) 28.6124 43.8508i 0.145982 0.223729i
\(197\) 49.2082 0.249788 0.124894 0.992170i \(-0.460141\pi\)
0.124894 + 0.992170i \(0.460141\pi\)
\(198\) 87.3198 0.441009
\(199\) 171.789i 0.863262i −0.902050 0.431631i \(-0.857938\pi\)
0.902050 0.431631i \(-0.142062\pi\)
\(200\) −43.3906 −0.216953
\(201\) 124.859i 0.621187i
\(202\) 41.3277i 0.204592i
\(203\) −107.268 198.075i −0.528414 0.975737i
\(204\) −24.8502 −0.121815
\(205\) 88.8593 0.433460
\(206\) 149.550i 0.725972i
\(207\) 49.8537 0.240839
\(208\) 172.855i 0.831035i
\(209\) 233.750i 1.11842i
\(210\) 22.1044 + 40.8166i 0.105259 + 0.194365i
\(211\) −5.09458 −0.0241449 −0.0120725 0.999927i \(-0.503843\pi\)
−0.0120725 + 0.999927i \(0.503843\pi\)
\(212\) −24.0431 −0.113411
\(213\) 44.5722i 0.209259i
\(214\) −288.254 −1.34698
\(215\) 96.6451i 0.449512i
\(216\) 45.0928i 0.208763i
\(217\) 41.5095 22.4796i 0.191288 0.103593i
\(218\) 266.358 1.22183
\(219\) 130.016 0.593680
\(220\) 40.6200i 0.184636i
\(221\) −219.283 −0.992229
\(222\) 205.256i 0.924574i
\(223\) 310.066i 1.39043i 0.718802 + 0.695215i \(0.244691\pi\)
−0.718802 + 0.695215i \(0.755309\pi\)
\(224\) 55.3063 + 102.125i 0.246903 + 0.455917i
\(225\) 15.0000 0.0666667
\(226\) 35.9490 0.159067
\(227\) 108.558i 0.478228i 0.970991 + 0.239114i \(0.0768570\pi\)
−0.970991 + 0.239114i \(0.923143\pi\)
\(228\) −25.4486 −0.111616
\(229\) 236.483i 1.03268i −0.856384 0.516339i \(-0.827294\pi\)
0.856384 0.516339i \(-0.172706\pi\)
\(230\) 63.6211i 0.276613i
\(231\) 181.244 98.1534i 0.784607 0.424906i
\(232\) 279.256 1.20369
\(233\) 151.290 0.649312 0.324656 0.945832i \(-0.394751\pi\)
0.324656 + 0.945832i \(0.394751\pi\)
\(234\) 83.8878i 0.358495i
\(235\) −89.7523 −0.381925
\(236\) 87.1958i 0.369474i
\(237\) 138.647i 0.585009i
\(238\) 141.500 76.6300i 0.594540 0.321975i
\(239\) 48.2956 0.202074 0.101037 0.994883i \(-0.467784\pi\)
0.101037 + 0.994883i \(0.467784\pi\)
\(240\) −40.9912 −0.170797
\(241\) 230.735i 0.957406i −0.877977 0.478703i \(-0.841107\pi\)
0.877977 0.478703i \(-0.158893\pi\)
\(242\) −287.646 −1.18862
\(243\) 15.5885i 0.0641500i
\(244\) 16.0135i 0.0656292i
\(245\) 91.7613 + 59.8737i 0.374536 + 0.244382i
\(246\) 117.847 0.479053
\(247\) −224.563 −0.909160
\(248\) 58.5223i 0.235977i
\(249\) −176.864 −0.710297
\(250\) 19.1423i 0.0765693i
\(251\) 86.6812i 0.345343i 0.984979 + 0.172672i \(0.0552399\pi\)
−0.984979 + 0.172672i \(0.944760\pi\)
\(252\) −10.6861 19.7322i −0.0424050 0.0783025i
\(253\) −282.506 −1.11663
\(254\) 102.508 0.403575
\(255\) 52.0010i 0.203926i
\(256\) −189.220 −0.739141
\(257\) 141.110i 0.549065i 0.961578 + 0.274532i \(0.0885231\pi\)
−0.961578 + 0.274532i \(0.911477\pi\)
\(258\) 128.173i 0.496793i
\(259\) 230.721 + 426.036i 0.890815 + 1.64493i
\(260\) 39.0235 0.150090
\(261\) −96.5380 −0.369877
\(262\) 285.701i 1.09046i
\(263\) 38.0901 0.144829 0.0724147 0.997375i \(-0.476930\pi\)
0.0724147 + 0.997375i \(0.476930\pi\)
\(264\) 255.527i 0.967907i
\(265\) 50.3121i 0.189857i
\(266\) 144.908 78.4752i 0.544765 0.295019i
\(267\) −222.363 −0.832819
\(268\) −77.0302 −0.287426
\(269\) 454.220i 1.68855i 0.535909 + 0.844275i \(0.319969\pi\)
−0.535909 + 0.844275i \(0.680031\pi\)
\(270\) 19.8933 0.0736789
\(271\) 78.7098i 0.290442i −0.989399 0.145221i \(-0.953611\pi\)
0.989399 0.145221i \(-0.0463893\pi\)
\(272\) 142.106i 0.522447i
\(273\) −94.2956 174.121i −0.345405 0.637805i
\(274\) −215.969 −0.788207
\(275\) −85.0005 −0.309093
\(276\) 30.7567i 0.111437i
\(277\) −85.3396 −0.308085 −0.154043 0.988064i \(-0.549229\pi\)
−0.154043 + 0.988064i \(0.549229\pi\)
\(278\) 362.374i 1.30350i
\(279\) 20.2310i 0.0725125i
\(280\) −119.443 + 64.6849i −0.426583 + 0.231018i
\(281\) 167.376 0.595643 0.297821 0.954622i \(-0.403740\pi\)
0.297821 + 0.954622i \(0.403740\pi\)
\(282\) −119.031 −0.422096
\(283\) 149.591i 0.528588i 0.964442 + 0.264294i \(0.0851390\pi\)
−0.964442 + 0.264294i \(0.914861\pi\)
\(284\) 27.4984 0.0968252
\(285\) 53.2531i 0.186853i
\(286\) 475.367i 1.66212i
\(287\) 244.607 132.468i 0.852291 0.461561i
\(288\) 49.7740 0.172827
\(289\) 108.726 0.376215
\(290\) 123.197i 0.424819i
\(291\) −276.172 −0.949045
\(292\) 80.2119i 0.274698i
\(293\) 145.805i 0.497627i −0.968551 0.248813i \(-0.919959\pi\)
0.968551 0.248813i \(-0.0800406\pi\)
\(294\) 121.696 + 79.4056i 0.413931 + 0.270087i
\(295\) −182.464 −0.618523
\(296\) −600.648 −2.02921
\(297\) 88.3351i 0.297425i
\(298\) 109.889 0.368757
\(299\) 271.403i 0.907701i
\(300\) 9.25409i 0.0308470i
\(301\) −144.075 266.040i −0.478653 0.883853i
\(302\) −189.903 −0.628817
\(303\) −41.8082 −0.137981
\(304\) 145.527i 0.478708i
\(305\) −33.5096 −0.109868
\(306\) 68.9648i 0.225375i
\(307\) 205.594i 0.669686i 0.942274 + 0.334843i \(0.108683\pi\)
−0.942274 + 0.334843i \(0.891317\pi\)
\(308\) 60.5547 + 111.817i 0.196606 + 0.363041i
\(309\) 151.289 0.489609
\(310\) −25.8179 −0.0832835
\(311\) 424.383i 1.36458i −0.731084 0.682288i \(-0.760985\pi\)
0.731084 0.682288i \(-0.239015\pi\)
\(312\) 245.484 0.786809
\(313\) 363.503i 1.16135i −0.814135 0.580676i \(-0.802788\pi\)
0.814135 0.580676i \(-0.197212\pi\)
\(314\) 497.294i 1.58374i
\(315\) 41.2912 22.3614i 0.131083 0.0709886i
\(316\) −85.5369 −0.270686
\(317\) 441.407 1.39245 0.696226 0.717822i \(-0.254861\pi\)
0.696226 + 0.717822i \(0.254861\pi\)
\(318\) 66.7248i 0.209827i
\(319\) 547.052 1.71490
\(320\) 158.184i 0.494326i
\(321\) 291.606i 0.908429i
\(322\) −94.8438 175.133i −0.294546 0.543891i
\(323\) −184.615 −0.571562
\(324\) −9.61713 −0.0296825
\(325\) 81.6597i 0.251261i
\(326\) 92.2089 0.282849
\(327\) 269.455i 0.824022i
\(328\) 344.860i 1.05140i
\(329\) −247.066 + 133.799i −0.750959 + 0.406684i
\(330\) −112.729 −0.341604
\(331\) 509.327 1.53875 0.769376 0.638796i \(-0.220567\pi\)
0.769376 + 0.638796i \(0.220567\pi\)
\(332\) 109.114i 0.328658i
\(333\) 207.642 0.623550
\(334\) 71.5550i 0.214236i
\(335\) 161.192i 0.481170i
\(336\) −112.838 + 61.1080i −0.335829 + 0.181869i
\(337\) 442.557 1.31323 0.656613 0.754228i \(-0.271988\pi\)
0.656613 + 0.754228i \(0.271988\pi\)
\(338\) 167.332 0.495064
\(339\) 36.3671i 0.107277i
\(340\) 32.0815 0.0943573
\(341\) 114.643i 0.336197i
\(342\) 70.6253i 0.206507i
\(343\) 341.853 + 28.0231i 0.996657 + 0.0816999i
\(344\) 375.077 1.09034
\(345\) −64.3609 −0.186553
\(346\) 223.167i 0.644993i
\(347\) −493.763 −1.42295 −0.711475 0.702712i \(-0.751972\pi\)
−0.711475 + 0.702712i \(0.751972\pi\)
\(348\) 59.5581i 0.171144i
\(349\) 324.460i 0.929686i −0.885393 0.464843i \(-0.846111\pi\)
0.885393 0.464843i \(-0.153889\pi\)
\(350\) −28.5366 52.6940i −0.0815332 0.150554i
\(351\) −84.8633 −0.241776
\(352\) −282.055 −0.801292
\(353\) 529.424i 1.49979i −0.661559 0.749893i \(-0.730105\pi\)
0.661559 0.749893i \(-0.269895\pi\)
\(354\) −241.988 −0.683581
\(355\) 57.5425i 0.162092i
\(356\) 137.184i 0.385349i
\(357\) −77.5211 143.146i −0.217146 0.400969i
\(358\) −77.0351 −0.215182
\(359\) 64.2261 0.178903 0.0894514 0.995991i \(-0.471489\pi\)
0.0894514 + 0.995991i \(0.471489\pi\)
\(360\) 58.2145i 0.161707i
\(361\) 171.940 0.476289
\(362\) 30.6377i 0.0846346i
\(363\) 290.991i 0.801627i
\(364\) 107.422 58.1747i 0.295115 0.159821i
\(365\) −167.850 −0.459863
\(366\) −44.4411 −0.121424
\(367\) 10.8172i 0.0294747i 0.999891 + 0.0147373i \(0.00469121\pi\)
−0.999891 + 0.0147373i \(0.995309\pi\)
\(368\) 175.882 0.477940
\(369\) 119.217i 0.323082i
\(370\) 264.984i 0.716172i
\(371\) −75.0033 138.497i −0.202165 0.373306i
\(372\) 12.4813 0.0335519
\(373\) 532.850 1.42855 0.714276 0.699864i \(-0.246756\pi\)
0.714276 + 0.699864i \(0.246756\pi\)
\(374\) 390.803i 1.04493i
\(375\) −19.3649 −0.0516398
\(376\) 348.326i 0.926398i
\(377\) 525.551i 1.39403i
\(378\) 54.7613 29.6561i 0.144871 0.0784554i
\(379\) 516.003 1.36149 0.680743 0.732523i \(-0.261657\pi\)
0.680743 + 0.732523i \(0.261657\pi\)
\(380\) 32.8539 0.0864578
\(381\) 103.700i 0.272178i
\(382\) −305.299 −0.799213
\(383\) 415.069i 1.08373i −0.840465 0.541866i \(-0.817718\pi\)
0.840465 0.541866i \(-0.182282\pi\)
\(384\) 94.8391i 0.246977i
\(385\) −233.985 + 126.715i −0.607754 + 0.329131i
\(386\) 575.765 1.49162
\(387\) −129.663 −0.335046
\(388\) 170.381i 0.439127i
\(389\) 54.8032 0.140882 0.0704411 0.997516i \(-0.477559\pi\)
0.0704411 + 0.997516i \(0.477559\pi\)
\(390\) 108.299i 0.277689i
\(391\) 223.122i 0.570645i
\(392\) −232.368 + 356.123i −0.592775 + 0.908477i
\(393\) −289.023 −0.735428
\(394\) −84.2514 −0.213836
\(395\) 178.993i 0.453146i
\(396\) 54.4974 0.137620
\(397\) 19.9434i 0.0502352i −0.999685 0.0251176i \(-0.992004\pi\)
0.999685 0.0251176i \(-0.00799602\pi\)
\(398\) 294.127i 0.739013i
\(399\) −79.3877 146.593i −0.198967 0.367400i
\(400\) 52.9194 0.132298
\(401\) −239.505 −0.597269 −0.298634 0.954368i \(-0.596531\pi\)
−0.298634 + 0.954368i \(0.596531\pi\)
\(402\) 213.776i 0.531781i
\(403\) 110.137 0.273293
\(404\) 25.7931i 0.0638444i
\(405\) 20.1246i 0.0496904i
\(406\) 183.658 + 339.132i 0.452359 + 0.835300i
\(407\) −1176.65 −2.89102
\(408\) 201.814 0.494643
\(409\) 663.541i 1.62235i 0.584804 + 0.811175i \(0.301171\pi\)
−0.584804 + 0.811175i \(0.698829\pi\)
\(410\) −152.140 −0.371072
\(411\) 218.480i 0.531581i
\(412\) 93.3363i 0.226544i
\(413\) −502.278 + 272.010i −1.21617 + 0.658621i
\(414\) −85.3566 −0.206175
\(415\) 228.330 0.550194
\(416\) 270.969i 0.651368i
\(417\) 366.588 0.879108
\(418\) 400.213i 0.957447i
\(419\) 110.648i 0.264077i −0.991245 0.132039i \(-0.957848\pi\)
0.991245 0.132039i \(-0.0421523\pi\)
\(420\) 13.7956 + 25.4742i 0.0328467 + 0.0606528i
\(421\) −521.325 −1.23830 −0.619151 0.785272i \(-0.712523\pi\)
−0.619151 + 0.785272i \(0.712523\pi\)
\(422\) 8.72264 0.0206698
\(423\) 120.415i 0.284670i
\(424\) 195.260 0.460518
\(425\) 67.1330i 0.157960i
\(426\) 76.3140i 0.179141i
\(427\) −92.2435 + 49.9548i −0.216027 + 0.116990i
\(428\) −179.903 −0.420334
\(429\) 480.895 1.12097
\(430\) 165.470i 0.384814i
\(431\) 573.019 1.32951 0.664755 0.747062i \(-0.268536\pi\)
0.664755 + 0.747062i \(0.268536\pi\)
\(432\) 54.9954i 0.127304i
\(433\) 429.740i 0.992472i 0.868188 + 0.496236i \(0.165285\pi\)
−0.868188 + 0.496236i \(0.834715\pi\)
\(434\) −71.0702 + 38.4883i −0.163756 + 0.0886827i
\(435\) 124.630 0.286506
\(436\) 166.237 0.381279
\(437\) 228.495i 0.522871i
\(438\) −222.606 −0.508232
\(439\) 83.0494i 0.189179i −0.995516 0.0945893i \(-0.969846\pi\)
0.995516 0.0945893i \(-0.0301538\pi\)
\(440\) 329.884i 0.749737i
\(441\) 80.3290 123.111i 0.182152 0.279163i
\(442\) 375.443 0.849419
\(443\) −410.010 −0.925530 −0.462765 0.886481i \(-0.653143\pi\)
−0.462765 + 0.886481i \(0.653143\pi\)
\(444\) 128.103i 0.288520i
\(445\) 287.069 0.645099
\(446\) 530.876i 1.19031i
\(447\) 111.167i 0.248696i
\(448\) −235.815 435.442i −0.526373 0.971969i
\(449\) −205.948 −0.458682 −0.229341 0.973346i \(-0.573657\pi\)
−0.229341 + 0.973346i \(0.573657\pi\)
\(450\) −25.6821 −0.0570714
\(451\) 675.569i 1.49793i
\(452\) 22.4363 0.0496378
\(453\) 192.111i 0.424086i
\(454\) 185.866i 0.409397i
\(455\) 121.735 + 224.789i 0.267550 + 0.494041i
\(456\) 206.674 0.453232
\(457\) −640.868 −1.40234 −0.701169 0.712995i \(-0.747338\pi\)
−0.701169 + 0.712995i \(0.747338\pi\)
\(458\) 404.893i 0.884046i
\(459\) −69.7667 −0.151997
\(460\) 39.7068i 0.0863190i
\(461\) 166.085i 0.360272i −0.983642 0.180136i \(-0.942346\pi\)
0.983642 0.180136i \(-0.0576538\pi\)
\(462\) −310.316 + 168.052i −0.671679 + 0.363750i
\(463\) −10.4409 −0.0225505 −0.0112753 0.999936i \(-0.503589\pi\)
−0.0112753 + 0.999936i \(0.503589\pi\)
\(464\) −340.582 −0.734013
\(465\) 26.1181i 0.0561680i
\(466\) −259.029 −0.555857
\(467\) 269.736i 0.577592i 0.957391 + 0.288796i \(0.0932550\pi\)
−0.957391 + 0.288796i \(0.906745\pi\)
\(468\) 52.3555i 0.111871i
\(469\) −240.298 443.721i −0.512364 0.946100i
\(470\) 153.669 0.326954
\(471\) −503.077 −1.06810
\(472\) 708.138i 1.50029i
\(473\) 734.761 1.55341
\(474\) 237.384i 0.500809i
\(475\) 68.7495i 0.144736i
\(476\) 88.3123 47.8258i 0.185530 0.100474i
\(477\) −67.5007 −0.141511
\(478\) −82.6889 −0.172989
\(479\) 649.820i 1.35662i 0.734777 + 0.678309i \(0.237287\pi\)
−0.734777 + 0.678309i \(0.762713\pi\)
\(480\) −64.2580 −0.133871
\(481\) 1130.40i 2.35011i
\(482\) 395.051i 0.819608i
\(483\) −177.169 + 95.9467i −0.366810 + 0.198647i
\(484\) −179.524 −0.370917
\(485\) 356.537 0.735127
\(486\) 26.6897i 0.0549170i
\(487\) 597.640 1.22719 0.613593 0.789622i \(-0.289723\pi\)
0.613593 + 0.789622i \(0.289723\pi\)
\(488\) 130.050i 0.266495i
\(489\) 93.2811i 0.190759i
\(490\) −157.108 102.512i −0.320629 0.209209i
\(491\) −107.625 −0.219195 −0.109598 0.993976i \(-0.534956\pi\)
−0.109598 + 0.993976i \(0.534956\pi\)
\(492\) 73.5498 0.149491
\(493\) 432.059i 0.876388i
\(494\) 384.483 0.778306
\(495\) 114.040i 0.230384i
\(496\) 71.3741i 0.143899i
\(497\) 85.7821 + 158.400i 0.172600 + 0.318713i
\(498\) 302.816 0.608065
\(499\) −420.611 −0.842908 −0.421454 0.906850i \(-0.638480\pi\)
−0.421454 + 0.906850i \(0.638480\pi\)
\(500\) 11.9470i 0.0238940i
\(501\) 72.3870 0.144485
\(502\) 148.410i 0.295638i
\(503\) 837.716i 1.66544i 0.553694 + 0.832720i \(0.313218\pi\)
−0.553694 + 0.832720i \(0.686782\pi\)
\(504\) 86.7840 + 160.250i 0.172190 + 0.317956i
\(505\) 53.9742 0.106880
\(506\) 483.691 0.955910
\(507\) 169.278i 0.333881i
\(508\) 63.9766 0.125938
\(509\) 511.304i 1.00453i −0.864715 0.502264i \(-0.832501\pi\)
0.864715 0.502264i \(-0.167499\pi\)
\(510\) 89.0331i 0.174575i
\(511\) −462.049 + 250.224i −0.904205 + 0.489675i
\(512\) 542.993 1.06053
\(513\) −71.4466 −0.139272
\(514\) 241.600i 0.470038i
\(515\) −195.314 −0.379250
\(516\) 79.9942i 0.155027i
\(517\) 682.358i 1.31984i
\(518\) −395.027 729.434i −0.762601 1.40817i
\(519\) −225.762 −0.434995
\(520\) −316.919 −0.609459
\(521\) 958.401i 1.83954i −0.392455 0.919771i \(-0.628374\pi\)
0.392455 0.919771i \(-0.371626\pi\)
\(522\) 165.287 0.316641
\(523\) 152.860i 0.292275i 0.989264 + 0.146138i \(0.0466843\pi\)
−0.989264 + 0.146138i \(0.953316\pi\)
\(524\) 178.310i 0.340286i
\(525\) −53.3068 + 28.8685i −0.101537 + 0.0549875i
\(526\) −65.2157 −0.123984
\(527\) 90.5445 0.171811
\(528\) 311.643i 0.590232i
\(529\) −252.845 −0.477968
\(530\) 86.1414i 0.162531i
\(531\) 244.801i 0.461020i
\(532\) 90.4387 48.9774i 0.169998 0.0920627i
\(533\) 649.017 1.21767
\(534\) 380.716 0.712952
\(535\) 376.461i 0.703666i
\(536\) 625.581 1.16713
\(537\) 77.9309i 0.145123i
\(538\) 777.689i 1.44552i
\(539\) −455.200 + 697.632i −0.844527 + 1.29431i
\(540\) 12.4157 0.0229920
\(541\) −285.016 −0.526832 −0.263416 0.964682i \(-0.584849\pi\)
−0.263416 + 0.964682i \(0.584849\pi\)
\(542\) 134.762i 0.248639i
\(543\) 30.9940 0.0570791
\(544\) 222.766i 0.409495i
\(545\) 347.865i 0.638285i
\(546\) 161.447 + 298.119i 0.295691 + 0.546006i
\(547\) −195.330 −0.357092 −0.178546 0.983932i \(-0.557139\pi\)
−0.178546 + 0.983932i \(0.557139\pi\)
\(548\) −134.789 −0.245965
\(549\) 44.9578i 0.0818904i
\(550\) 145.533 0.264605
\(551\) 442.463i 0.803017i
\(552\) 249.783i 0.452505i
\(553\) −266.835 492.722i −0.482523 0.890999i
\(554\) 146.113 0.263743
\(555\) −268.065 −0.483000
\(556\) 226.163i 0.406767i
\(557\) −27.9390 −0.0501598 −0.0250799 0.999685i \(-0.507984\pi\)
−0.0250799 + 0.999685i \(0.507984\pi\)
\(558\) 34.6383i 0.0620759i
\(559\) 705.883i 1.26276i
\(560\) 145.674 78.8901i 0.260132 0.140875i
\(561\) 395.347 0.704719
\(562\) −286.571 −0.509912
\(563\) 459.585i 0.816314i 0.912912 + 0.408157i \(0.133828\pi\)
−0.912912 + 0.408157i \(0.866172\pi\)
\(564\) −74.2889 −0.131718
\(565\) 46.9497i 0.0830968i
\(566\) 256.120i 0.452509i
\(567\) −30.0010 55.3980i −0.0529118 0.0977037i
\(568\) −223.321 −0.393170
\(569\) −635.353 −1.11661 −0.558306 0.829635i \(-0.688549\pi\)
−0.558306 + 0.829635i \(0.688549\pi\)
\(570\) 91.1769i 0.159959i
\(571\) 205.282 0.359513 0.179757 0.983711i \(-0.442469\pi\)
0.179757 + 0.983711i \(0.442469\pi\)
\(572\) 296.683i 0.518676i
\(573\) 308.849i 0.539004i
\(574\) −418.803 + 226.804i −0.729621 + 0.395129i
\(575\) 83.0895 0.144504
\(576\) −212.227 −0.368449
\(577\) 185.464i 0.321429i 0.987001 + 0.160714i \(0.0513798\pi\)
−0.987001 + 0.160714i \(0.948620\pi\)
\(578\) −186.155 −0.322067
\(579\) 582.460i 1.00598i
\(580\) 76.8892i 0.132568i
\(581\) 628.537 340.386i 1.08182 0.585862i
\(582\) 472.846 0.812450
\(583\) 382.506 0.656100
\(584\) 651.420i 1.11545i
\(585\) 109.558 0.187279
\(586\) 249.638i 0.426004i
\(587\) 673.958i 1.14814i 0.818806 + 0.574070i \(0.194636\pi\)
−0.818806 + 0.574070i \(0.805364\pi\)
\(588\) 75.9519 + 49.5581i 0.129170 + 0.0842825i
\(589\) 92.7247 0.157427
\(590\) 312.405 0.529499
\(591\) 85.2311i 0.144215i
\(592\) 732.553 1.23742
\(593\) 0.486694i 0.000820731i 1.00000 0.000410366i \(0.000130623\pi\)
−1.00000 0.000410366i \(0.999869\pi\)
\(594\) 151.242i 0.254617i
\(595\) 100.079 + 184.800i 0.168201 + 0.310589i
\(596\) 68.5835 0.115073
\(597\) 297.547 0.498404
\(598\) 464.680i 0.777057i
\(599\) 580.285 0.968756 0.484378 0.874859i \(-0.339046\pi\)
0.484378 + 0.874859i \(0.339046\pi\)
\(600\) 75.1546i 0.125258i
\(601\) 781.851i 1.30092i −0.759542 0.650459i \(-0.774577\pi\)
0.759542 0.650459i \(-0.225423\pi\)
\(602\) 246.676 + 455.498i 0.409761 + 0.756641i
\(603\) −216.262 −0.358643
\(604\) −118.521 −0.196226
\(605\) 375.667i 0.620938i
\(606\) 71.5816 0.118121
\(607\) 907.211i 1.49458i 0.664498 + 0.747290i \(0.268646\pi\)
−0.664498 + 0.747290i \(0.731354\pi\)
\(608\) 228.129i 0.375213i
\(609\) 343.075 185.794i 0.563342 0.305080i
\(610\) 57.3732 0.0940544
\(611\) −655.539 −1.07289
\(612\) 43.0418i 0.0703298i
\(613\) −911.642 −1.48718 −0.743590 0.668636i \(-0.766879\pi\)
−0.743590 + 0.668636i \(0.766879\pi\)
\(614\) 352.006i 0.573299i
\(615\) 153.909i 0.250258i
\(616\) −491.779 908.089i −0.798342 1.47417i
\(617\) 637.918 1.03390 0.516951 0.856015i \(-0.327067\pi\)
0.516951 + 0.856015i \(0.327067\pi\)
\(618\) −259.029 −0.419140
\(619\) 862.604i 1.39354i 0.717292 + 0.696772i \(0.245381\pi\)
−0.717292 + 0.696772i \(0.754619\pi\)
\(620\) −16.1133 −0.0259892
\(621\) 86.3492i 0.139049i
\(622\) 726.604i 1.16817i
\(623\) 790.229 427.951i 1.26843 0.686920i
\(624\) −299.394 −0.479798
\(625\) 25.0000 0.0400000
\(626\) 622.369i 0.994200i
\(627\) 404.866 0.645720
\(628\) 310.368i 0.494216i
\(629\) 929.310i 1.47744i
\(630\) −70.6965 + 38.2859i −0.112217 + 0.0607713i
\(631\) −601.057 −0.952547 −0.476273 0.879297i \(-0.658013\pi\)
−0.476273 + 0.879297i \(0.658013\pi\)
\(632\) 694.665 1.09915
\(633\) 8.82406i 0.0139401i
\(634\) −755.752 −1.19204
\(635\) 133.876i 0.210828i
\(636\) 41.6438i 0.0654777i
\(637\) 670.213 + 437.309i 1.05214 + 0.686514i
\(638\) −936.631 −1.46807
\(639\) 77.2014 0.120816
\(640\) 122.437i 0.191307i
\(641\) −884.432 −1.37977 −0.689885 0.723919i \(-0.742339\pi\)
−0.689885 + 0.723919i \(0.742339\pi\)
\(642\) 499.270i 0.777680i
\(643\) 385.448i 0.599453i −0.954025 0.299726i \(-0.903105\pi\)
0.954025 0.299726i \(-0.0968954\pi\)
\(644\) −59.1933 109.303i −0.0919150 0.169725i
\(645\) 167.394 0.259526
\(646\) 316.086 0.489298
\(647\) 1096.93i 1.69540i −0.530473 0.847702i \(-0.677986\pi\)
0.530473 0.847702i \(-0.322014\pi\)
\(648\) 78.1030 0.120529
\(649\) 1387.22i 2.13747i
\(650\) 139.813i 0.215097i
\(651\) 38.9358 + 71.8966i 0.0598093 + 0.110440i
\(652\) 57.5488 0.0882650
\(653\) −556.888 −0.852814 −0.426407 0.904531i \(-0.640221\pi\)
−0.426407 + 0.904531i \(0.640221\pi\)
\(654\) 461.345i 0.705421i
\(655\) 373.127 0.569660
\(656\) 420.594i 0.641149i
\(657\) 225.194i 0.342761i
\(658\) 423.011 229.083i 0.642874 0.348151i
\(659\) −715.578 −1.08585 −0.542927 0.839780i \(-0.682684\pi\)
−0.542927 + 0.839780i \(0.682684\pi\)
\(660\) −70.3559 −0.106600
\(661\) 280.365i 0.424152i −0.977253 0.212076i \(-0.931978\pi\)
0.977253 0.212076i \(-0.0680225\pi\)
\(662\) −872.040 −1.31728
\(663\) 379.809i 0.572864i
\(664\) 886.143i 1.33455i
\(665\) 102.489 + 189.250i 0.154119 + 0.284587i
\(666\) −355.513 −0.533803
\(667\) −534.753 −0.801729
\(668\) 44.6584i 0.0668539i
\(669\) −537.050 −0.802765
\(670\) 275.983i 0.411915i
\(671\) 254.763i 0.379676i
\(672\) −176.886 + 95.7933i −0.263224 + 0.142550i
\(673\) 1067.08 1.58556 0.792781 0.609506i \(-0.208632\pi\)
0.792781 + 0.609506i \(0.208632\pi\)
\(674\) −757.721 −1.12421
\(675\) 25.9808i 0.0384900i
\(676\) 104.434 0.154488
\(677\) 313.071i 0.462439i 0.972902 + 0.231219i \(0.0742715\pi\)
−0.972902 + 0.231219i \(0.925728\pi\)
\(678\) 62.2656i 0.0918371i
\(679\) 981.456 531.511i 1.44544 0.782785i
\(680\) −260.541 −0.383149
\(681\) −188.028 −0.276105
\(682\) 196.285i 0.287808i
\(683\) 505.514 0.740138 0.370069 0.929004i \(-0.379334\pi\)
0.370069 + 0.929004i \(0.379334\pi\)
\(684\) 44.0782i 0.0644418i
\(685\) 282.056i 0.411761i
\(686\) −585.301 47.9795i −0.853209 0.0699409i
\(687\) 409.601 0.596217
\(688\) −457.446 −0.664892
\(689\) 367.473i 0.533342i
\(690\) 110.195 0.159703
\(691\) 276.726i 0.400472i 0.979748 + 0.200236i \(0.0641709\pi\)
−0.979748 + 0.200236i \(0.935829\pi\)
\(692\) 139.282i 0.201274i
\(693\) 170.007 + 313.924i 0.245320 + 0.452993i
\(694\) 845.393 1.21815
\(695\) −473.263 −0.680954
\(696\) 483.685i 0.694950i
\(697\) 533.561 0.765511
\(698\) 555.522i 0.795877i
\(699\) 262.041i 0.374880i
\(700\) −17.8101 32.8870i −0.0254430 0.0469815i
\(701\) 854.178 1.21851 0.609256 0.792973i \(-0.291468\pi\)
0.609256 + 0.792973i \(0.291468\pi\)
\(702\) 145.298 0.206977
\(703\) 951.687i 1.35375i
\(704\) 1202.63 1.70828
\(705\) 155.455i 0.220504i
\(706\) 906.450i 1.28392i
\(707\) 148.577 80.4626i 0.210152 0.113809i
\(708\) −151.028 −0.213316
\(709\) −452.996 −0.638922 −0.319461 0.947599i \(-0.603502\pi\)
−0.319461 + 0.947599i \(0.603502\pi\)
\(710\) 98.5210i 0.138762i
\(711\) −240.144 −0.337755
\(712\) 1114.11i 1.56476i
\(713\) 112.066i 0.157175i
\(714\) 132.727 + 245.086i 0.185892 + 0.343258i
\(715\) −620.833 −0.868297
\(716\) −48.0786 −0.0671489
\(717\) 83.6504i 0.116667i
\(718\) −109.964 −0.153153
\(719\) 840.685i 1.16924i 0.811306 + 0.584621i \(0.198757\pi\)
−0.811306 + 0.584621i \(0.801243\pi\)
\(720\) 70.9988i 0.0986095i
\(721\) −537.650 + 291.166i −0.745700 + 0.403836i
\(722\) −294.386 −0.407737
\(723\) 399.645 0.552759
\(724\) 19.1214i 0.0264108i
\(725\) −160.897 −0.221926
\(726\) 498.217i 0.686250i
\(727\) 1339.58i 1.84262i −0.388829 0.921310i \(-0.627120\pi\)
0.388829 0.921310i \(-0.372880\pi\)
\(728\) −872.398 + 472.450i −1.19835 + 0.648970i
\(729\) −27.0000 −0.0370370
\(730\) 287.383 0.393675
\(731\) 580.311i 0.793860i
\(732\) −27.7363 −0.0378911
\(733\) 536.275i 0.731616i 0.930690 + 0.365808i \(0.119207\pi\)
−0.930690 + 0.365808i \(0.880793\pi\)
\(734\) 18.5206i 0.0252324i
\(735\) −103.704 + 158.935i −0.141094 + 0.216238i
\(736\) 275.713 0.374611
\(737\) 1225.49 1.66281
\(738\) 204.117i 0.276581i
\(739\) −898.552 −1.21590 −0.607951 0.793974i \(-0.708008\pi\)
−0.607951 + 0.793974i \(0.708008\pi\)
\(740\) 165.380i 0.223486i
\(741\) 388.954i 0.524904i
\(742\) 128.416 + 237.126i 0.173068 + 0.319576i
\(743\) 532.720 0.716985 0.358493 0.933533i \(-0.383291\pi\)
0.358493 + 0.933533i \(0.383291\pi\)
\(744\) −101.364 −0.136241
\(745\) 143.516i 0.192639i
\(746\) −912.314 −1.22294
\(747\) 306.337i 0.410090i
\(748\) 243.905i 0.326076i
\(749\) −561.214 1036.30i −0.749284 1.38358i
\(750\) 33.1555 0.0442073
\(751\) 342.085 0.455506 0.227753 0.973719i \(-0.426862\pi\)
0.227753 + 0.973719i \(0.426862\pi\)
\(752\) 424.820i 0.564921i
\(753\) −150.136 −0.199384
\(754\) 899.818i 1.19339i
\(755\) 248.014i 0.328495i
\(756\) 34.1772 18.5088i 0.0452080 0.0244825i
\(757\) 405.961 0.536276 0.268138 0.963381i \(-0.413592\pi\)
0.268138 + 0.963381i \(0.413592\pi\)
\(758\) −883.470 −1.16553
\(759\) 489.315i 0.644684i
\(760\) −266.815 −0.351072
\(761\) 577.340i 0.758660i 0.925261 + 0.379330i \(0.123845\pi\)
−0.925261 + 0.379330i \(0.876155\pi\)
\(762\) 177.549i 0.233004i
\(763\) 518.584 + 957.586i 0.679664 + 1.25503i
\(764\) −190.541 −0.249400
\(765\) 90.0684 0.117737
\(766\) 710.657i 0.927751i
\(767\) −1332.69 −1.73754
\(768\) 327.739i 0.426743i
\(769\) 828.522i 1.07740i −0.842497 0.538701i \(-0.818915\pi\)
0.842497 0.538701i \(-0.181085\pi\)
\(770\) 400.616 216.955i 0.520280 0.281760i
\(771\) −244.409 −0.317003
\(772\) 359.342 0.465469
\(773\) 438.991i 0.567906i −0.958838 0.283953i \(-0.908354\pi\)
0.958838 0.283953i \(-0.0916460\pi\)
\(774\) 222.001 0.286824
\(775\) 33.7183i 0.0435075i
\(776\) 1383.71i 1.78313i
\(777\) −737.916 + 399.621i −0.949699 + 0.514312i
\(778\) −93.8308 −0.120605
\(779\) 546.408 0.701423
\(780\) 67.5906i 0.0866547i
\(781\) −437.477 −0.560150
\(782\) 382.017i 0.488512i
\(783\) 167.209i 0.213549i
\(784\) 283.397 434.330i 0.361476 0.553992i
\(785\) 649.469 0.827349
\(786\) 494.849 0.629579