Properties

Label 177.3.c.a.58.19
Level $177$
Weight $3$
Character 177.58
Analytic conductor $4.823$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.82290067918\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \(x^{20} + 60 x^{18} + 1522 x^{16} + 21286 x^{14} + 179593 x^{12} + 941588 x^{10} + 3057025 x^{8} + 5962230 x^{6} + 6517782 x^{4} + 3428244 x^{2} + 570861\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{7}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.19
Root \(3.38526i\) of defining polynomial
Character \(\chi\) \(=\) 177.58
Dual form 177.3.c.a.58.2

$q$-expansion

\(f(q)\) \(=\) \(q+3.38526i q^{2} +1.73205 q^{3} -7.45997 q^{4} +9.27487 q^{5} +5.86344i q^{6} -9.96030 q^{7} -11.7129i q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+3.38526i q^{2} +1.73205 q^{3} -7.45997 q^{4} +9.27487 q^{5} +5.86344i q^{6} -9.96030 q^{7} -11.7129i q^{8} +3.00000 q^{9} +31.3978i q^{10} +20.5213i q^{11} -12.9211 q^{12} +4.19899i q^{13} -33.7182i q^{14} +16.0645 q^{15} +9.81130 q^{16} +0.362285 q^{17} +10.1558i q^{18} +11.7217 q^{19} -69.1903 q^{20} -17.2518 q^{21} -69.4698 q^{22} -21.5797i q^{23} -20.2873i q^{24} +61.0232 q^{25} -14.2147 q^{26} +5.19615 q^{27} +74.3036 q^{28} +18.1338 q^{29} +54.3826i q^{30} -42.6196i q^{31} -13.6378i q^{32} +35.5439i q^{33} +1.22643i q^{34} -92.3805 q^{35} -22.3799 q^{36} -46.4991i q^{37} +39.6809i q^{38} +7.27287i q^{39} -108.636i q^{40} +16.1117 q^{41} -58.4016i q^{42} +30.4120i q^{43} -153.088i q^{44} +27.8246 q^{45} +73.0530 q^{46} -5.06360i q^{47} +16.9937 q^{48} +50.2077 q^{49} +206.579i q^{50} +0.627496 q^{51} -31.3244i q^{52} +36.6918 q^{53} +17.5903i q^{54} +190.332i q^{55} +116.664i q^{56} +20.3025 q^{57} +61.3875i q^{58} +(-52.1348 - 27.6217i) q^{59} -119.841 q^{60} -32.0930i q^{61} +144.279 q^{62} -29.8809 q^{63} +85.4127 q^{64} +38.9451i q^{65} -120.325 q^{66} +81.4723i q^{67} -2.70263 q^{68} -37.3772i q^{69} -312.732i q^{70} +9.92600 q^{71} -35.1387i q^{72} +43.0824i q^{73} +157.412 q^{74} +105.695 q^{75} -87.4433 q^{76} -204.398i q^{77} -24.6205 q^{78} -104.049 q^{79} +90.9985 q^{80} +9.00000 q^{81} +54.5422i q^{82} -118.124i q^{83} +128.698 q^{84} +3.36014 q^{85} -102.953 q^{86} +31.4086 q^{87} +240.364 q^{88} +48.1069i q^{89} +94.1935i q^{90} -41.8233i q^{91} +160.984i q^{92} -73.8194i q^{93} +17.1416 q^{94} +108.717 q^{95} -23.6214i q^{96} -125.543i q^{97} +169.966i q^{98} +61.5638i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 40q^{4} - 8q^{7} + 60q^{9} + O(q^{10}) \) \( 20q - 40q^{4} - 8q^{7} + 60q^{9} - 24q^{12} + 24q^{15} - 8q^{16} + 16q^{17} - 60q^{19} - 164q^{20} + 40q^{22} + 100q^{25} - 156q^{26} + 200q^{28} - 60q^{29} - 32q^{35} - 120q^{36} + 28q^{41} + 180q^{46} - 96q^{48} + 284q^{49} - 24q^{51} - 8q^{53} + 24q^{57} - 152q^{59} - 72q^{60} - 8q^{62} - 24q^{63} + 204q^{64} - 120q^{66} + 384q^{68} + 92q^{71} + 104q^{74} + 240q^{75} + 120q^{76} - 468q^{78} - 420q^{79} + 376q^{80} + 180q^{81} + 168q^{84} - 348q^{85} + 232q^{86} + 144q^{87} - 212q^{88} + 152q^{94} + 788q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.38526i 1.69263i 0.532684 + 0.846315i \(0.321184\pi\)
−0.532684 + 0.846315i \(0.678816\pi\)
\(3\) 1.73205 0.577350
\(4\) −7.45997 −1.86499
\(5\) 9.27487 1.85497 0.927487 0.373855i \(-0.121964\pi\)
0.927487 + 0.373855i \(0.121964\pi\)
\(6\) 5.86344i 0.977240i
\(7\) −9.96030 −1.42290 −0.711450 0.702736i \(-0.751961\pi\)
−0.711450 + 0.702736i \(0.751961\pi\)
\(8\) 11.7129i 1.46411i
\(9\) 3.00000 0.333333
\(10\) 31.3978i 3.13978i
\(11\) 20.5213i 1.86557i 0.360434 + 0.932785i \(0.382629\pi\)
−0.360434 + 0.932785i \(0.617371\pi\)
\(12\) −12.9211 −1.07675
\(13\) 4.19899i 0.323000i 0.986873 + 0.161500i \(0.0516331\pi\)
−0.986873 + 0.161500i \(0.948367\pi\)
\(14\) 33.7182i 2.40844i
\(15\) 16.0645 1.07097
\(16\) 9.81130 0.613206
\(17\) 0.362285 0.0213109 0.0106554 0.999943i \(-0.496608\pi\)
0.0106554 + 0.999943i \(0.496608\pi\)
\(18\) 10.1558i 0.564210i
\(19\) 11.7217 0.616930 0.308465 0.951236i \(-0.400185\pi\)
0.308465 + 0.951236i \(0.400185\pi\)
\(20\) −69.1903 −3.45951
\(21\) −17.2518 −0.821512
\(22\) −69.4698 −3.15772
\(23\) 21.5797i 0.938249i −0.883132 0.469125i \(-0.844569\pi\)
0.883132 0.469125i \(-0.155431\pi\)
\(24\) 20.2873i 0.845306i
\(25\) 61.0232 2.44093
\(26\) −14.2147 −0.546718
\(27\) 5.19615 0.192450
\(28\) 74.3036 2.65370
\(29\) 18.1338 0.625303 0.312651 0.949868i \(-0.398783\pi\)
0.312651 + 0.949868i \(0.398783\pi\)
\(30\) 54.3826i 1.81275i
\(31\) 42.6196i 1.37483i −0.726266 0.687414i \(-0.758746\pi\)
0.726266 0.687414i \(-0.241254\pi\)
\(32\) 13.6378i 0.426182i
\(33\) 35.5439i 1.07709i
\(34\) 1.22643i 0.0360714i
\(35\) −92.3805 −2.63944
\(36\) −22.3799 −0.621664
\(37\) 46.4991i 1.25673i −0.777917 0.628367i \(-0.783724\pi\)
0.777917 0.628367i \(-0.216276\pi\)
\(38\) 39.6809i 1.04423i
\(39\) 7.27287i 0.186484i
\(40\) 108.636i 2.71589i
\(41\) 16.1117 0.392968 0.196484 0.980507i \(-0.437048\pi\)
0.196484 + 0.980507i \(0.437048\pi\)
\(42\) 58.4016i 1.39052i
\(43\) 30.4120i 0.707257i 0.935386 + 0.353628i \(0.115052\pi\)
−0.935386 + 0.353628i \(0.884948\pi\)
\(44\) 153.088i 3.47927i
\(45\) 27.8246 0.618325
\(46\) 73.0530 1.58811
\(47\) 5.06360i 0.107736i −0.998548 0.0538681i \(-0.982845\pi\)
0.998548 0.0538681i \(-0.0171551\pi\)
\(48\) 16.9937 0.354035
\(49\) 50.2077 1.02465
\(50\) 206.579i 4.13159i
\(51\) 0.627496 0.0123038
\(52\) 31.3244i 0.602392i
\(53\) 36.6918 0.692299 0.346149 0.938179i \(-0.387489\pi\)
0.346149 + 0.938179i \(0.387489\pi\)
\(54\) 17.5903i 0.325747i
\(55\) 190.332i 3.46058i
\(56\) 116.664i 2.08329i
\(57\) 20.3025 0.356185
\(58\) 61.3875i 1.05841i
\(59\) −52.1348 27.6217i −0.883641 0.468164i
\(60\) −119.841 −1.99735
\(61\) 32.0930i 0.526115i −0.964780 0.263058i \(-0.915269\pi\)
0.964780 0.263058i \(-0.0847309\pi\)
\(62\) 144.279 2.32707
\(63\) −29.8809 −0.474300
\(64\) 85.4127 1.33457
\(65\) 38.9451i 0.599156i
\(66\) −120.325 −1.82311
\(67\) 81.4723i 1.21600i 0.793936 + 0.608002i \(0.208029\pi\)
−0.793936 + 0.608002i \(0.791971\pi\)
\(68\) −2.70263 −0.0397446
\(69\) 37.3772i 0.541699i
\(70\) 312.732i 4.46760i
\(71\) 9.92600 0.139803 0.0699014 0.997554i \(-0.477732\pi\)
0.0699014 + 0.997554i \(0.477732\pi\)
\(72\) 35.1387i 0.488038i
\(73\) 43.0824i 0.590170i 0.955471 + 0.295085i \(0.0953480\pi\)
−0.955471 + 0.295085i \(0.904652\pi\)
\(74\) 157.412 2.12718
\(75\) 105.695 1.40927
\(76\) −87.4433 −1.15057
\(77\) 204.398i 2.65452i
\(78\) −24.6205 −0.315648
\(79\) −104.049 −1.31708 −0.658541 0.752545i \(-0.728826\pi\)
−0.658541 + 0.752545i \(0.728826\pi\)
\(80\) 90.9985 1.13748
\(81\) 9.00000 0.111111
\(82\) 54.5422i 0.665149i
\(83\) 118.124i 1.42318i −0.702597 0.711588i \(-0.747977\pi\)
0.702597 0.711588i \(-0.252023\pi\)
\(84\) 128.698 1.53211
\(85\) 3.36014 0.0395311
\(86\) −102.953 −1.19712
\(87\) 31.4086 0.361019
\(88\) 240.364 2.73140
\(89\) 48.1069i 0.540527i 0.962786 + 0.270264i \(0.0871108\pi\)
−0.962786 + 0.270264i \(0.912889\pi\)
\(90\) 94.1935i 1.04659i
\(91\) 41.8233i 0.459596i
\(92\) 160.984i 1.74983i
\(93\) 73.8194i 0.793757i
\(94\) 17.1416 0.182358
\(95\) 108.717 1.14439
\(96\) 23.6214i 0.246056i
\(97\) 125.543i 1.29426i −0.762379 0.647130i \(-0.775969\pi\)
0.762379 0.647130i \(-0.224031\pi\)
\(98\) 169.966i 1.73435i
\(99\) 61.5638i 0.621856i
\(100\) −455.232 −4.55232
\(101\) 34.1908i 0.338523i −0.985571 0.169261i \(-0.945862\pi\)
0.985571 0.169261i \(-0.0541382\pi\)
\(102\) 2.12424i 0.0208258i
\(103\) 119.958i 1.16464i −0.812959 0.582321i \(-0.802145\pi\)
0.812959 0.582321i \(-0.197855\pi\)
\(104\) 49.1824 0.472908
\(105\) −160.008 −1.52388
\(106\) 124.211i 1.17180i
\(107\) 39.8153 0.372106 0.186053 0.982540i \(-0.440430\pi\)
0.186053 + 0.982540i \(0.440430\pi\)
\(108\) −38.7632 −0.358918
\(109\) 168.447i 1.54538i 0.634781 + 0.772692i \(0.281090\pi\)
−0.634781 + 0.772692i \(0.718910\pi\)
\(110\) −644.323 −5.85748
\(111\) 80.5389i 0.725575i
\(112\) −97.7235 −0.872532
\(113\) 23.4960i 0.207929i 0.994581 + 0.103965i \(0.0331529\pi\)
−0.994581 + 0.103965i \(0.966847\pi\)
\(114\) 68.7293i 0.602888i
\(115\) 200.149i 1.74043i
\(116\) −135.278 −1.16619
\(117\) 12.5970i 0.107667i
\(118\) 93.5065 176.490i 0.792428 1.49568i
\(119\) −3.60847 −0.0303233
\(120\) 188.162i 1.56802i
\(121\) −300.122 −2.48035
\(122\) 108.643 0.890518
\(123\) 27.9062 0.226880
\(124\) 317.941i 2.56404i
\(125\) 334.111 2.67289
\(126\) 101.155i 0.802814i
\(127\) −40.6699 −0.320236 −0.160118 0.987098i \(-0.551187\pi\)
−0.160118 + 0.987098i \(0.551187\pi\)
\(128\) 234.593i 1.83276i
\(129\) 52.6752i 0.408335i
\(130\) −131.839 −1.01415
\(131\) 121.173i 0.924988i 0.886622 + 0.462494i \(0.153045\pi\)
−0.886622 + 0.462494i \(0.846955\pi\)
\(132\) 265.156i 2.00876i
\(133\) −116.751 −0.877830
\(134\) −275.805 −2.05824
\(135\) 48.1936 0.356990
\(136\) 4.24341i 0.0312015i
\(137\) −198.510 −1.44898 −0.724489 0.689286i \(-0.757924\pi\)
−0.724489 + 0.689286i \(0.757924\pi\)
\(138\) 126.531 0.916895
\(139\) 228.034 1.64053 0.820267 0.571981i \(-0.193825\pi\)
0.820267 + 0.571981i \(0.193825\pi\)
\(140\) 689.156 4.92254
\(141\) 8.77042i 0.0622016i
\(142\) 33.6021i 0.236634i
\(143\) −86.1687 −0.602578
\(144\) 29.4339 0.204402
\(145\) 168.188 1.15992
\(146\) −145.845 −0.998940
\(147\) 86.9622 0.591580
\(148\) 346.882i 2.34380i
\(149\) 95.3536i 0.639957i −0.947425 0.319979i \(-0.896324\pi\)
0.947425 0.319979i \(-0.103676\pi\)
\(150\) 357.806i 2.38537i
\(151\) 262.692i 1.73968i 0.493333 + 0.869841i \(0.335779\pi\)
−0.493333 + 0.869841i \(0.664221\pi\)
\(152\) 137.295i 0.903255i
\(153\) 1.08685 0.00710362
\(154\) 691.940 4.49312
\(155\) 395.292i 2.55027i
\(156\) 54.2554i 0.347791i
\(157\) 23.3960i 0.149019i −0.997220 0.0745096i \(-0.976261\pi\)
0.997220 0.0745096i \(-0.0237392\pi\)
\(158\) 352.234i 2.22933i
\(159\) 63.5521 0.399699
\(160\) 126.489i 0.790556i
\(161\) 214.941i 1.33504i
\(162\) 30.4673i 0.188070i
\(163\) −29.9339 −0.183644 −0.0918218 0.995775i \(-0.529269\pi\)
−0.0918218 + 0.995775i \(0.529269\pi\)
\(164\) −120.193 −0.732882
\(165\) 329.665i 1.99797i
\(166\) 399.879 2.40891
\(167\) −140.361 −0.840485 −0.420242 0.907412i \(-0.638055\pi\)
−0.420242 + 0.907412i \(0.638055\pi\)
\(168\) 202.068i 1.20279i
\(169\) 151.368 0.895671
\(170\) 11.3750i 0.0669115i
\(171\) 35.1650 0.205643
\(172\) 226.873i 1.31903i
\(173\) 122.872i 0.710245i −0.934820 0.355123i \(-0.884439\pi\)
0.934820 0.355123i \(-0.115561\pi\)
\(174\) 106.326i 0.611071i
\(175\) −607.810 −3.47320
\(176\) 201.340i 1.14398i
\(177\) −90.3002 47.8422i −0.510171 0.270295i
\(178\) −162.854 −0.914912
\(179\) 13.1743i 0.0735996i −0.999323 0.0367998i \(-0.988284\pi\)
0.999323 0.0367998i \(-0.0117164\pi\)
\(180\) −207.571 −1.15317
\(181\) −194.551 −1.07487 −0.537433 0.843307i \(-0.680606\pi\)
−0.537433 + 0.843307i \(0.680606\pi\)
\(182\) 141.583 0.777926
\(183\) 55.5867i 0.303753i
\(184\) −252.761 −1.37370
\(185\) 431.274i 2.33121i
\(186\) 249.898 1.34354
\(187\) 7.43454i 0.0397569i
\(188\) 37.7743i 0.200927i
\(189\) −51.7553 −0.273837
\(190\) 368.035i 1.93703i
\(191\) 299.916i 1.57024i 0.619342 + 0.785121i \(0.287399\pi\)
−0.619342 + 0.785121i \(0.712601\pi\)
\(192\) 147.939 0.770517
\(193\) −27.4449 −0.142202 −0.0711008 0.997469i \(-0.522651\pi\)
−0.0711008 + 0.997469i \(0.522651\pi\)
\(194\) 424.996 2.19070
\(195\) 67.4549i 0.345923i
\(196\) −374.548 −1.91096
\(197\) 82.5430 0.419000 0.209500 0.977809i \(-0.432816\pi\)
0.209500 + 0.977809i \(0.432816\pi\)
\(198\) −208.409 −1.05257
\(199\) −41.4291 −0.208186 −0.104093 0.994568i \(-0.533194\pi\)
−0.104093 + 0.994568i \(0.533194\pi\)
\(200\) 714.759i 3.57379i
\(201\) 141.114i 0.702060i
\(202\) 115.745 0.572994
\(203\) −180.618 −0.889744
\(204\) −4.68110 −0.0229466
\(205\) 149.434 0.728945
\(206\) 406.089 1.97131
\(207\) 64.7392i 0.312750i
\(208\) 41.1976i 0.198065i
\(209\) 240.543i 1.15093i
\(210\) 541.668i 2.57937i
\(211\) 241.695i 1.14547i 0.819740 + 0.572736i \(0.194118\pi\)
−0.819740 + 0.572736i \(0.805882\pi\)
\(212\) −273.720 −1.29113
\(213\) 17.1923 0.0807152
\(214\) 134.785i 0.629837i
\(215\) 282.068i 1.31194i
\(216\) 60.8620i 0.281769i
\(217\) 424.505i 1.95624i
\(218\) −570.236 −2.61576
\(219\) 74.6210i 0.340735i
\(220\) 1419.87i 6.45396i
\(221\) 1.52123i 0.00688340i
\(222\) 272.645 1.22813
\(223\) 200.733 0.900148 0.450074 0.892991i \(-0.351398\pi\)
0.450074 + 0.892991i \(0.351398\pi\)
\(224\) 135.837i 0.606414i
\(225\) 183.070 0.813643
\(226\) −79.5400 −0.351947
\(227\) 221.780i 0.977002i −0.872563 0.488501i \(-0.837544\pi\)
0.872563 0.488501i \(-0.162456\pi\)
\(228\) −151.456 −0.664282
\(229\) 169.854i 0.741720i −0.928689 0.370860i \(-0.879063\pi\)
0.928689 0.370860i \(-0.120937\pi\)
\(230\) 677.557 2.94590
\(231\) 354.028i 1.53259i
\(232\) 212.399i 0.915514i
\(233\) 56.1420i 0.240953i −0.992716 0.120476i \(-0.961558\pi\)
0.992716 0.120476i \(-0.0384422\pi\)
\(234\) −42.6440 −0.182239
\(235\) 46.9643i 0.199848i
\(236\) 388.925 + 206.057i 1.64799 + 0.873123i
\(237\) −180.219 −0.760417
\(238\) 12.2156i 0.0513260i
\(239\) −282.703 −1.18286 −0.591429 0.806357i \(-0.701436\pi\)
−0.591429 + 0.806357i \(0.701436\pi\)
\(240\) 157.614 0.656725
\(241\) 90.4885 0.375471 0.187736 0.982220i \(-0.439885\pi\)
0.187736 + 0.982220i \(0.439885\pi\)
\(242\) 1015.99i 4.19831i
\(243\) 15.5885 0.0641500
\(244\) 239.413i 0.981201i
\(245\) 465.669 1.90069
\(246\) 94.4698i 0.384024i
\(247\) 49.2192i 0.199268i
\(248\) −499.200 −2.01290
\(249\) 204.596i 0.821671i
\(250\) 1131.05i 4.52420i
\(251\) 90.8848 0.362091 0.181045 0.983475i \(-0.442052\pi\)
0.181045 + 0.983475i \(0.442052\pi\)
\(252\) 222.911 0.884567
\(253\) 442.843 1.75037
\(254\) 137.678i 0.542040i
\(255\) 5.81994 0.0228233
\(256\) −452.507 −1.76760
\(257\) −75.3044 −0.293013 −0.146507 0.989210i \(-0.546803\pi\)
−0.146507 + 0.989210i \(0.546803\pi\)
\(258\) −178.319 −0.691160
\(259\) 463.146i 1.78821i
\(260\) 290.530i 1.11742i
\(261\) 54.4013 0.208434
\(262\) −410.203 −1.56566
\(263\) 366.374 1.39306 0.696528 0.717530i \(-0.254727\pi\)
0.696528 + 0.717530i \(0.254727\pi\)
\(264\) 416.322 1.57698
\(265\) 340.312 1.28420
\(266\) 395.234i 1.48584i
\(267\) 83.3236i 0.312073i
\(268\) 607.781i 2.26784i
\(269\) 0.373353i 0.00138793i 1.00000 0.000693966i \(0.000220896\pi\)
−1.00000 0.000693966i \(0.999779\pi\)
\(270\) 163.148i 0.604252i
\(271\) −375.056 −1.38397 −0.691986 0.721911i \(-0.743264\pi\)
−0.691986 + 0.721911i \(0.743264\pi\)
\(272\) 3.55449 0.0130680
\(273\) 72.4400i 0.265348i
\(274\) 672.008i 2.45258i
\(275\) 1252.27i 4.55372i
\(276\) 278.833i 1.01026i
\(277\) 87.9624 0.317554 0.158777 0.987314i \(-0.449245\pi\)
0.158777 + 0.987314i \(0.449245\pi\)
\(278\) 771.955i 2.77682i
\(279\) 127.859i 0.458276i
\(280\) 1082.04i 3.86444i
\(281\) −358.335 −1.27521 −0.637607 0.770362i \(-0.720076\pi\)
−0.637607 + 0.770362i \(0.720076\pi\)
\(282\) 29.6901 0.105284
\(283\) 372.886i 1.31762i −0.752311 0.658808i \(-0.771061\pi\)
0.752311 0.658808i \(-0.228939\pi\)
\(284\) −74.0477 −0.260731
\(285\) 188.303 0.660713
\(286\) 291.703i 1.01994i
\(287\) −160.477 −0.559154
\(288\) 40.9135i 0.142061i
\(289\) −288.869 −0.999546
\(290\) 569.361i 1.96332i
\(291\) 217.447i 0.747242i
\(292\) 321.394i 1.10066i
\(293\) −82.4199 −0.281297 −0.140648 0.990060i \(-0.544919\pi\)
−0.140648 + 0.990060i \(0.544919\pi\)
\(294\) 294.390i 1.00132i
\(295\) −483.544 256.188i −1.63913 0.868432i
\(296\) −544.640 −1.84000
\(297\) 106.632i 0.359029i
\(298\) 322.797 1.08321
\(299\) 90.6132 0.303054
\(300\) −788.484 −2.62828
\(301\) 302.913i 1.00636i
\(302\) −889.280 −2.94464
\(303\) 59.2202i 0.195446i
\(304\) 115.005 0.378305
\(305\) 297.659i 0.975930i
\(306\) 3.67928i 0.0120238i
\(307\) −469.709 −1.53000 −0.764999 0.644032i \(-0.777260\pi\)
−0.764999 + 0.644032i \(0.777260\pi\)
\(308\) 1524.80i 4.95066i
\(309\) 207.774i 0.672406i
\(310\) 1338.16 4.31666
\(311\) 53.4334 0.171812 0.0859058 0.996303i \(-0.472622\pi\)
0.0859058 + 0.996303i \(0.472622\pi\)
\(312\) 85.1864 0.273033
\(313\) 8.38179i 0.0267789i 0.999910 + 0.0133894i \(0.00426212\pi\)
−0.999910 + 0.0133894i \(0.995738\pi\)
\(314\) 79.2016 0.252234
\(315\) −277.142 −0.879815
\(316\) 776.206 2.45635
\(317\) −400.493 −1.26338 −0.631692 0.775219i \(-0.717639\pi\)
−0.631692 + 0.775219i \(0.717639\pi\)
\(318\) 215.140i 0.676542i
\(319\) 372.128i 1.16655i
\(320\) 792.192 2.47560
\(321\) 68.9622 0.214836
\(322\) −727.630 −2.25972
\(323\) 4.24658 0.0131473
\(324\) −67.1398 −0.207221
\(325\) 256.236i 0.788419i
\(326\) 101.334i 0.310840i
\(327\) 291.759i 0.892228i
\(328\) 188.714i 0.575349i
\(329\) 50.4350i 0.153298i
\(330\) −1116.00 −3.38182
\(331\) −29.6370 −0.0895377 −0.0447688 0.998997i \(-0.514255\pi\)
−0.0447688 + 0.998997i \(0.514255\pi\)
\(332\) 881.198i 2.65421i
\(333\) 139.497i 0.418911i
\(334\) 475.158i 1.42263i
\(335\) 755.645i 2.25566i
\(336\) −169.262 −0.503756
\(337\) 112.535i 0.333932i 0.985963 + 0.166966i \(0.0533971\pi\)
−0.985963 + 0.166966i \(0.946603\pi\)
\(338\) 512.421i 1.51604i
\(339\) 40.6963i 0.120048i
\(340\) −25.0666 −0.0737253
\(341\) 874.609 2.56484
\(342\) 119.043i 0.348078i
\(343\) −12.0286 −0.0350687
\(344\) 356.213 1.03550
\(345\) 346.669i 1.00484i
\(346\) 415.955 1.20218
\(347\) 388.058i 1.11832i −0.829059 0.559161i \(-0.811123\pi\)
0.829059 0.559161i \(-0.188877\pi\)
\(348\) −234.308 −0.673297
\(349\) 542.368i 1.55406i −0.629462 0.777031i \(-0.716725\pi\)
0.629462 0.777031i \(-0.283275\pi\)
\(350\) 2057.59i 5.87884i
\(351\) 21.8186i 0.0621613i
\(352\) 279.865 0.795072
\(353\) 102.916i 0.291546i 0.989318 + 0.145773i \(0.0465669\pi\)
−0.989318 + 0.145773i \(0.953433\pi\)
\(354\) 161.958 305.690i 0.457509 0.863530i
\(355\) 92.0624 0.259331
\(356\) 358.876i 1.00808i
\(357\) −6.25005 −0.0175071
\(358\) 44.5985 0.124577
\(359\) 281.215 0.783328 0.391664 0.920108i \(-0.371899\pi\)
0.391664 + 0.920108i \(0.371899\pi\)
\(360\) 325.907i 0.905297i
\(361\) −223.603 −0.619398
\(362\) 658.604i 1.81935i
\(363\) −519.827 −1.43203
\(364\) 312.000i 0.857144i
\(365\) 399.584i 1.09475i
\(366\) 188.175 0.514141
\(367\) 22.4570i 0.0611907i −0.999532 0.0305953i \(-0.990260\pi\)
0.999532 0.0305953i \(-0.00974032\pi\)
\(368\) 211.725i 0.575340i
\(369\) 48.3350 0.130989
\(370\) 1459.97 3.94587
\(371\) −365.462 −0.985072
\(372\) 550.691i 1.48035i
\(373\) 70.8071 0.189831 0.0949157 0.995485i \(-0.469742\pi\)
0.0949157 + 0.995485i \(0.469742\pi\)
\(374\) −25.1678 −0.0672937
\(375\) 578.697 1.54319
\(376\) −59.3095 −0.157738
\(377\) 76.1436i 0.201973i
\(378\) 175.205i 0.463505i
\(379\) −249.514 −0.658349 −0.329174 0.944269i \(-0.606770\pi\)
−0.329174 + 0.944269i \(0.606770\pi\)
\(380\) −811.025 −2.13428
\(381\) −70.4424 −0.184888
\(382\) −1015.29 −2.65784
\(383\) −674.681 −1.76157 −0.880785 0.473516i \(-0.842985\pi\)
−0.880785 + 0.473516i \(0.842985\pi\)
\(384\) 406.327i 1.05814i
\(385\) 1895.77i 4.92407i
\(386\) 92.9081i 0.240694i
\(387\) 91.2361i 0.235752i
\(388\) 936.549i 2.41379i
\(389\) 493.759 1.26930 0.634651 0.772799i \(-0.281144\pi\)
0.634651 + 0.772799i \(0.281144\pi\)
\(390\) −228.352 −0.585519
\(391\) 7.81801i 0.0199949i
\(392\) 588.077i 1.50020i
\(393\) 209.879i 0.534042i
\(394\) 279.429i 0.709212i
\(395\) −965.045 −2.44315
\(396\) 459.264i 1.15976i
\(397\) 648.987i 1.63473i 0.576122 + 0.817364i \(0.304565\pi\)
−0.576122 + 0.817364i \(0.695435\pi\)
\(398\) 140.248i 0.352382i
\(399\) −202.219 −0.506815
\(400\) 598.717 1.49679
\(401\) 59.8224i 0.149183i −0.997214 0.0745915i \(-0.976235\pi\)
0.997214 0.0745915i \(-0.0237653\pi\)
\(402\) −477.708 −1.18833
\(403\) 178.960 0.444069
\(404\) 255.063i 0.631343i
\(405\) 83.4738 0.206108
\(406\) 611.438i 1.50601i
\(407\) 954.221 2.34452
\(408\) 7.34979i 0.0180142i
\(409\) 279.180i 0.682591i 0.939956 + 0.341296i \(0.110866\pi\)
−0.939956 + 0.341296i \(0.889134\pi\)
\(410\) 505.872i 1.23383i
\(411\) −343.830 −0.836568
\(412\) 894.884i 2.17205i
\(413\) 519.279 + 275.120i 1.25733 + 0.666151i
\(414\) 219.159 0.529369
\(415\) 1095.58i 2.63995i
\(416\) 57.2651 0.137657
\(417\) 394.967 0.947163
\(418\) −814.302 −1.94809
\(419\) 442.679i 1.05651i −0.849085 0.528256i \(-0.822846\pi\)
0.849085 0.528256i \(-0.177154\pi\)
\(420\) 1193.65 2.84203
\(421\) 73.7045i 0.175070i −0.996161 0.0875350i \(-0.972101\pi\)
0.996161 0.0875350i \(-0.0278990\pi\)
\(422\) −818.198 −1.93886
\(423\) 15.1908i 0.0359121i
\(424\) 429.768i 1.01360i
\(425\) 22.1078 0.0520183
\(426\) 58.2005i 0.136621i
\(427\) 319.656i 0.748609i
\(428\) −297.021 −0.693975
\(429\) −149.249 −0.347899
\(430\) −954.872 −2.22063
\(431\) 25.3259i 0.0587607i −0.999568 0.0293804i \(-0.990647\pi\)
0.999568 0.0293804i \(-0.00935340\pi\)
\(432\) 50.9810 0.118012
\(433\) 374.398 0.864659 0.432330 0.901716i \(-0.357692\pi\)
0.432330 + 0.901716i \(0.357692\pi\)
\(434\) −1437.06 −3.31119
\(435\) 291.311 0.669680
\(436\) 1256.61i 2.88213i
\(437\) 252.950i 0.578834i
\(438\) −252.611 −0.576738
\(439\) −282.618 −0.643776 −0.321888 0.946778i \(-0.604318\pi\)
−0.321888 + 0.946778i \(0.604318\pi\)
\(440\) 2229.34 5.06668
\(441\) 150.623 0.341549
\(442\) −5.14976 −0.0116510
\(443\) 543.714i 1.22735i −0.789560 0.613673i \(-0.789691\pi\)
0.789560 0.613673i \(-0.210309\pi\)
\(444\) 600.818i 1.35319i
\(445\) 446.185i 1.00266i
\(446\) 679.533i 1.52362i
\(447\) 165.157i 0.369479i
\(448\) −850.737 −1.89897
\(449\) 369.058 0.821955 0.410977 0.911646i \(-0.365188\pi\)
0.410977 + 0.911646i \(0.365188\pi\)
\(450\) 619.738i 1.37720i
\(451\) 330.632i 0.733109i
\(452\) 175.279i 0.387786i
\(453\) 454.996i 1.00441i
\(454\) 750.781 1.65370
\(455\) 387.905i 0.852539i
\(456\) 237.801i 0.521494i
\(457\) 529.971i 1.15967i 0.814732 + 0.579837i \(0.196884\pi\)
−0.814732 + 0.579837i \(0.803116\pi\)
\(458\) 574.999 1.25546
\(459\) 1.88249 0.00410128
\(460\) 1493.11i 3.24589i
\(461\) −131.591 −0.285448 −0.142724 0.989763i \(-0.545586\pi\)
−0.142724 + 0.989763i \(0.545586\pi\)
\(462\) 1198.48 2.59410
\(463\) 489.009i 1.05618i 0.849190 + 0.528088i \(0.177091\pi\)
−0.849190 + 0.528088i \(0.822909\pi\)
\(464\) 177.916 0.383440
\(465\) 684.665i 1.47240i
\(466\) 190.055 0.407844
\(467\) 58.5903i 0.125461i 0.998031 + 0.0627305i \(0.0199808\pi\)
−0.998031 + 0.0627305i \(0.980019\pi\)
\(468\) 93.9732i 0.200797i
\(469\) 811.488i 1.73025i
\(470\) 158.986 0.338268
\(471\) 40.5231i 0.0860363i
\(472\) −323.530 + 610.650i −0.685445 + 1.29375i
\(473\) −624.094 −1.31944
\(474\) 610.087i 1.28710i
\(475\) 715.294 1.50588
\(476\) 26.9191 0.0565527
\(477\) 110.075 0.230766
\(478\) 957.023i 2.00214i
\(479\) 571.506 1.19312 0.596562 0.802567i \(-0.296533\pi\)
0.596562 + 0.802567i \(0.296533\pi\)
\(480\) 219.085i 0.456428i
\(481\) 195.250 0.405924
\(482\) 306.327i 0.635533i
\(483\) 372.288i 0.770783i
\(484\) 2238.90 4.62583
\(485\) 1164.40i 2.40082i
\(486\) 52.7710i 0.108582i
\(487\) 420.688 0.863836 0.431918 0.901913i \(-0.357837\pi\)
0.431918 + 0.901913i \(0.357837\pi\)
\(488\) −375.902 −0.770292
\(489\) −51.8470 −0.106027
\(490\) 1576.41i 3.21717i
\(491\) 880.226 1.79272 0.896360 0.443326i \(-0.146202\pi\)
0.896360 + 0.443326i \(0.146202\pi\)
\(492\) −208.180 −0.423130
\(493\) 6.56959 0.0133257
\(494\) −166.620 −0.337287
\(495\) 570.996i 1.15353i
\(496\) 418.154i 0.843053i
\(497\) −98.8660 −0.198925
\(498\) 692.610 1.39078
\(499\) −232.423 −0.465778 −0.232889 0.972503i \(-0.574818\pi\)
−0.232889 + 0.972503i \(0.574818\pi\)
\(500\) −2492.46 −4.98491
\(501\) −243.112 −0.485254
\(502\) 307.668i 0.612885i
\(503\) 769.859i 1.53053i −0.643713 0.765267i \(-0.722607\pi\)
0.643713 0.765267i \(-0.277393\pi\)
\(504\) 349.992i 0.694429i
\(505\) 317.115i 0.627951i
\(506\) 1499.14i 2.96273i
\(507\) 262.178 0.517116
\(508\) 303.397 0.597237
\(509\) 237.299i 0.466207i 0.972452 + 0.233103i \(0.0748881\pi\)
−0.972452 + 0.233103i \(0.925112\pi\)
\(510\) 19.7020i 0.0386314i
\(511\) 429.114i 0.839754i
\(512\) 593.480i 1.15914i
\(513\) 60.9076 0.118728
\(514\) 254.925i 0.495963i
\(515\) 1112.60i 2.16038i
\(516\) 392.956i 0.761542i
\(517\) 103.912 0.200989
\(518\) −1567.87 −3.02677
\(519\) 212.821i 0.410060i
\(520\) 456.160 0.877232
\(521\) −28.9394 −0.0555459 −0.0277730 0.999614i \(-0.508842\pi\)
−0.0277730 + 0.999614i \(0.508842\pi\)
\(522\) 184.163i 0.352802i
\(523\) −390.540 −0.746730 −0.373365 0.927684i \(-0.621796\pi\)
−0.373365 + 0.927684i \(0.621796\pi\)
\(524\) 903.951i 1.72510i
\(525\) −1052.76 −2.00525
\(526\) 1240.27i 2.35793i
\(527\) 15.4405i 0.0292988i
\(528\) 348.732i 0.660476i
\(529\) 63.3150 0.119688
\(530\) 1152.04i 2.17367i
\(531\) −156.405 82.8651i −0.294547 0.156055i
\(532\) 870.962 1.63715
\(533\) 67.6528i 0.126928i
\(534\) −282.072 −0.528225
\(535\) 369.282 0.690247
\(536\) 954.276 1.78037
\(537\) 22.8186i 0.0424927i
\(538\) −1.26390 −0.00234925
\(539\) 1030.32i 1.91155i
\(540\) −359.523 −0.665784
\(541\) 639.799i 1.18262i 0.806443 + 0.591311i \(0.201390\pi\)
−0.806443 + 0.591311i \(0.798610\pi\)
\(542\) 1269.66i 2.34255i
\(543\) −336.971 −0.620574
\(544\) 4.94077i 0.00908231i
\(545\) 1562.32i 2.86665i
\(546\) 245.228 0.449136
\(547\) −33.9867 −0.0621329 −0.0310664 0.999517i \(-0.509890\pi\)
−0.0310664 + 0.999517i \(0.509890\pi\)
\(548\) 1480.88 2.70234
\(549\) 96.2791i 0.175372i
\(550\) −4239.27 −7.70776
\(551\) 212.558 0.385768
\(552\) −437.795 −0.793108
\(553\) 1036.36 1.87408
\(554\) 297.776i 0.537501i
\(555\) 746.988i 1.34592i
\(556\) −1701.13 −3.05958
\(557\) −587.282 −1.05437 −0.527183 0.849752i \(-0.676752\pi\)
−0.527183 + 0.849752i \(0.676752\pi\)
\(558\) 432.836 0.775691
\(559\) −127.700 −0.228444
\(560\) −906.373 −1.61852
\(561\) 12.8770i 0.0229537i
\(562\) 1213.06i 2.15846i
\(563\) 416.727i 0.740190i −0.928994 0.370095i \(-0.879325\pi\)
0.928994 0.370095i \(-0.120675\pi\)
\(564\) 65.4271i 0.116005i
\(565\) 217.922i 0.385703i
\(566\) 1262.31 2.23024
\(567\) −89.6427 −0.158100
\(568\) 116.262i 0.204687i
\(569\) 429.645i 0.755089i 0.925992 + 0.377544i \(0.123231\pi\)
−0.925992 + 0.377544i \(0.876769\pi\)
\(570\) 637.455i 1.11834i
\(571\) 783.544i 1.37223i 0.727492 + 0.686116i \(0.240686\pi\)
−0.727492 + 0.686116i \(0.759314\pi\)
\(572\) 642.816 1.12380
\(573\) 519.470i 0.906580i
\(574\) 543.257i 0.946440i
\(575\) 1316.87i 2.29020i
\(576\) 256.238 0.444858
\(577\) 14.6938 0.0254659 0.0127330 0.999919i \(-0.495947\pi\)
0.0127330 + 0.999919i \(0.495947\pi\)
\(578\) 977.895i 1.69186i
\(579\) −47.5360 −0.0821001
\(580\) −1254.68 −2.16324
\(581\) 1176.55i 2.02504i
\(582\) 736.115 1.26480
\(583\) 752.963i 1.29153i
\(584\) 504.620 0.864076
\(585\) 116.835i 0.199719i
\(586\) 279.013i 0.476131i
\(587\) 847.153i 1.44319i 0.692315 + 0.721596i \(0.256591\pi\)
−0.692315 + 0.721596i \(0.743409\pi\)
\(588\) −648.736 −1.10329
\(589\) 499.573i 0.848172i
\(590\) 867.261 1636.92i 1.46993 2.77444i
\(591\) 142.969 0.241910
\(592\) 456.217i 0.770637i
\(593\) −669.594 −1.12916 −0.564582 0.825377i \(-0.690963\pi\)
−0.564582 + 0.825377i \(0.690963\pi\)
\(594\) −360.976 −0.607703
\(595\) −33.4681 −0.0562488
\(596\) 711.335i 1.19352i
\(597\) −71.7573 −0.120196
\(598\) 306.749i 0.512958i
\(599\) 666.722 1.11306 0.556529 0.830828i \(-0.312133\pi\)
0.556529 + 0.830828i \(0.312133\pi\)
\(600\) 1238.00i 2.06333i
\(601\) 341.243i 0.567792i −0.958855 0.283896i \(-0.908373\pi\)
0.958855 0.283896i \(-0.0916270\pi\)
\(602\) 1025.44 1.70339
\(603\) 244.417i 0.405335i
\(604\) 1959.67i 3.24449i
\(605\) −2783.59 −4.60098
\(606\) 200.476 0.330818
\(607\) −137.196 −0.226023 −0.113011 0.993594i \(-0.536050\pi\)
−0.113011 + 0.993594i \(0.536050\pi\)
\(608\) 159.858i 0.262924i
\(609\) −312.839 −0.513694
\(610\) 1007.65 1.65189
\(611\) 21.2620 0.0347988
\(612\) −8.10790 −0.0132482
\(613\) 583.317i 0.951577i −0.879560 0.475788i \(-0.842163\pi\)
0.879560 0.475788i \(-0.157837\pi\)
\(614\) 1590.09i 2.58972i
\(615\) 258.827 0.420857
\(616\) −2394.09 −3.88652
\(617\) 775.180 1.25637 0.628185 0.778064i \(-0.283798\pi\)
0.628185 + 0.778064i \(0.283798\pi\)
\(618\) 703.367 1.13813
\(619\) 297.409 0.480467 0.240233 0.970715i \(-0.422776\pi\)
0.240233 + 0.970715i \(0.422776\pi\)
\(620\) 2948.87i 4.75623i
\(621\) 112.132i 0.180566i
\(622\) 180.886i 0.290813i
\(623\) 479.159i 0.769116i
\(624\) 71.3563i 0.114353i
\(625\) 1573.25 2.51721
\(626\) −28.3745 −0.0453267
\(627\) 416.633i 0.664487i
\(628\) 174.534i 0.277920i
\(629\) 16.8459i 0.0267821i
\(630\) 938.196i 1.48920i
\(631\) 172.413 0.273238 0.136619 0.990624i \(-0.456376\pi\)
0.136619 + 0.990624i \(0.456376\pi\)
\(632\) 1218.72i 1.92836i
\(633\) 418.627i 0.661338i
\(634\) 1355.77i 2.13844i
\(635\) −377.208 −0.594029
\(636\) −474.097 −0.745435
\(637\) 210.822i 0.330960i
\(638\) −1259.75 −1.97453
\(639\) 29.7780 0.0466009
\(640\) 2175.82i 3.39972i
\(641\) 219.920 0.343089 0.171544 0.985176i \(-0.445124\pi\)
0.171544 + 0.985176i \(0.445124\pi\)
\(642\) 233.455i 0.363637i
\(643\) −930.457 −1.44706 −0.723528 0.690295i \(-0.757481\pi\)
−0.723528 + 0.690295i \(0.757481\pi\)
\(644\) 1603.45i 2.48983i
\(645\) 488.556i 0.757451i
\(646\) 14.3758i 0.0222535i
\(647\) 748.437 1.15678 0.578390 0.815760i \(-0.303681\pi\)
0.578390 + 0.815760i \(0.303681\pi\)
\(648\) 105.416i 0.162679i
\(649\) 566.832 1069.87i 0.873393 1.64849i
\(650\) −867.426 −1.33450
\(651\) 735.264i 1.12944i
\(652\) 223.306 0.342494
\(653\) −172.727 −0.264514 −0.132257 0.991215i \(-0.542222\pi\)
−0.132257 + 0.991215i \(0.542222\pi\)
\(654\) −987.678 −1.51021
\(655\) 1123.87i 1.71583i
\(656\) 158.077 0.240970
\(657\) 129.247i 0.196723i
\(658\) −170.736 −0.259477
\(659\) 552.763i 0.838790i 0.907804 + 0.419395i \(0.137758\pi\)
−0.907804 + 0.419395i \(0.862242\pi\)
\(660\) 2459.29i 3.72620i
\(661\) 890.466 1.34715 0.673575 0.739119i \(-0.264758\pi\)
0.673575 + 0.739119i \(0.264758\pi\)
\(662\) 100.329i 0.151554i
\(663\) 2.63485i 0.00397413i
\(664\) −1383.57 −2.08369
\(665\) −1082.85 −1.62835
\(666\) 472.235 0.709061
\(667\) 391.322i 0.586690i
\(668\) 1047.09 1.56750
\(669\) 347.680 0.519701
\(670\) −2558.05 −3.81799
\(671\) 658.589 0.981504
\(672\) 235.276i 0.350113i
\(673\) 136.255i 0.202459i −0.994863 0.101230i \(-0.967722\pi\)
0.994863 0.101230i \(-0.0322777\pi\)
\(674\) −380.961 −0.565223
\(675\) 317.086 0.469757
\(676\) −1129.20 −1.67042
\(677\) 265.723 0.392501 0.196251 0.980554i \(-0.437123\pi\)
0.196251 + 0.980554i \(0.437123\pi\)
\(678\) −137.767 −0.203197
\(679\) 1250.45i 1.84160i
\(680\) 39.3570i 0.0578780i
\(681\) 384.133i 0.564073i
\(682\) 2960.78i 4.34132i
\(683\) 445.533i 0.652318i −0.945315 0.326159i \(-0.894246\pi\)
0.945315 0.326159i \(-0.105754\pi\)
\(684\) −262.330 −0.383523
\(685\) −1841.16 −2.68782
\(686\) 40.7198i 0.0593583i
\(687\) 294.196i 0.428232i
\(688\) 298.382i 0.433694i
\(689\) 154.069i 0.223612i
\(690\) 1173.56 1.70082
\(691\) 370.939i 0.536815i −0.963306 0.268407i \(-0.913503\pi\)
0.963306 0.268407i \(-0.0864973\pi\)
\(692\) 916.625i 1.32460i
\(693\) 613.194i 0.884840i
\(694\) 1313.68 1.89290
\(695\) 2114.99 3.04315
\(696\) 367.886i 0.528572i
\(697\) 5.83702 0.00837449
\(698\) 1836.05 2.63045
\(699\) 97.2409i 0.139114i
\(700\) 4534.24 6.47749
\(701\) 416.398i 0.594006i 0.954877 + 0.297003i \(0.0959871\pi\)
−0.954877 + 0.297003i \(0.904013\pi\)
\(702\) −73.8616 −0.105216
\(703\) 545.047i 0.775316i
\(704\) 1752.78i 2.48974i
\(705\) 81.3445i 0.115382i
\(706\) −348.397 −0.493480
\(707\) 340.551i 0.481684i
\(708\) 673.637 + 356.901i 0.951465 + 0.504098i
\(709\) −751.459 −1.05989 −0.529943 0.848033i \(-0.677787\pi\)
−0.529943 + 0.848033i \(0.677787\pi\)
\(710\) 311.655i 0.438951i
\(711\) −312.148 −0.439027
\(712\) 563.471 0.791392
\(713\) −919.721 −1.28993
\(714\) 21.1580i 0.0296331i
\(715\) −799.203 −1.11777
\(716\) 98.2801i 0.137263i
\(717\) −489.656 −0.682923
\(718\) 951.985i 1.32588i
\(719\) 869.723i 1.20963i −0.796367 0.604814i \(-0.793247\pi\)
0.796367 0.604814i \(-0.206753\pi\)
\(720\) 272.996 0.379161
\(721\) 1194.82i 1.65717i
\(722\) 756.952i 1.04841i
\(723\) 156.731 0.216778
\(724\) 1451.34 2.00462
\(725\) 1106.58 1.52632
\(726\) 1759.75i 2.42390i
\(727\) 1392.73 1.91572 0.957859 0.287238i \(-0.0927370\pi\)
0.957859 + 0.287238i \(0.0927370\pi\)
\(728\) −489.872 −0.672901
\(729\) 27.0000 0.0370370
\(730\) −1352.70 −1.85301
\(731\) 11.0178i 0.0150723i
\(732\) 414.676i 0.566497i
\(733\) −57.5400 −0.0784993 −0.0392497 0.999229i \(-0.512497\pi\)
−0.0392497 + 0.999229i \(0.512497\pi\)
\(734\) 76.0226 0.103573
\(735\) 806.563 1.09736
\(736\) −294.300 −0.399865
\(737\) −1671.91 −2.26854
\(738\) 163.627i 0.221716i
\(739\) 194.224i 0.262820i 0.991328 + 0.131410i \(0.0419505\pi\)
−0.991328 + 0.131410i \(0.958049\pi\)
\(740\) 3217.29i 4.34769i
\(741\) 85.2502i 0.115047i
\(742\) 1237.18i 1.66736i
\(743\) −365.950 −0.492531 −0.246265 0.969202i \(-0.579203\pi\)
−0.246265 + 0.969202i \(0.579203\pi\)
\(744\) −864.639 −1.16215
\(745\) 884.392i 1.18710i
\(746\) 239.700i 0.321314i
\(747\) 354.371i 0.474392i
\(748\) 55.4615i 0.0741464i
\(749\) −396.573 −0.529470
\(750\) 1959.04i 2.61205i
\(751\) 196.887i 0.262166i 0.991371 + 0.131083i \(0.0418455\pi\)
−0.991371 + 0.131083i \(0.958155\pi\)
\(752\) 49.6805i 0.0660645i
\(753\) 157.417 0.209053
\(754\) −257.766 −0.341865
\(755\) 2436.43i 3.22706i
\(756\) 386.093 0.510705
\(757\) 581.124 0.767667 0.383834 0.923402i \(-0.374604\pi\)
0.383834 + 0.923402i \(0.374604\pi\)
\(758\) 844.670i 1.11434i
\(759\) 767.027 1.01058
\(760\) 1273.39i 1.67551i
\(761\) −1257.55 −1.65249 −0.826246 0.563310i \(-0.809528\pi\)
−0.826246 + 0.563310i \(0.809528\pi\)
\(762\) 238.466i 0.312947i
\(763\) 1677.78i 2.19893i
\(764\) 2237.37i 2.92849i
\(765\) 10.0804 0.0131770
\(766\) 2283.97i 2.98168i
\(767\) 115.983 218.914i 0.151217 0.285416i
\(768\) −783.764 −1.02053
\(769\) 865.286i 1.12521i 0.826726 + 0.562605i \(0.190201\pi\)
−0.826726 + 0.562605i \(0.809799\pi\)
\(770\) 6417.65 8.33462
\(771\) −130.431 −0.169171
\(772\) 204.738 0.265205
\(773\) 1118.01i 1.44633i −0.690675 0.723165i \(-0.742687\pi\)
0.690675 0.723165i \(-0.257313\pi\)
\(774\) −308.858 −0.399041
\(775\) 2600.79i 3.35586i
\(776\) −1470.48 −1.89494
\(777\) 802.192i 1.03242i
\(778\) 1671.50i 2.14846i
\(779\) 188.856 0.242434
\(780\) 503.212i 0.645144i
\(781\) 203.694i 0.260812i
\(782\) 26.4660 0.0338440
\(783\) 94.2259 0.120340
\(784\) 492.602 0.628319
\(785\) 216.995i 0.276427i
\(786\) −710.493 −0.903935
\(787\) −1066.39 −1.35501 −0.677506 0.735517i \(-0.736939\pi\)
−0.677506 + 0.735517i \(0.736939\pi\)
\(788\) −615.769 −0.781432
\(789\) 634.578 0.804281
\(790\) 3266.93i 4.13535i
\(791\) 234.027i 0.295862i
\(792\)