Properties

Label 637.2.c.f.246.4
Level $637$
Weight $2$
Character 637.246
Analytic conductor $5.086$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \(x^{8} + 11 x^{6} + 36 x^{4} + 31 x^{2} + 3\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 246.4
Root \(-0.332375i\) of defining polynomial
Character \(\chi\) \(=\) 637.246
Dual form 637.2.c.f.246.5

$q$-expansion

\(f(q)\) \(=\) \(q-0.332375i q^{2} +1.45984 q^{3} +1.88953 q^{4} -1.44562i q^{5} -0.485214i q^{6} -1.29278i q^{8} -0.868875 q^{9} +O(q^{10})\) \(q-0.332375i q^{2} +1.45984 q^{3} +1.88953 q^{4} -1.44562i q^{5} -0.485214i q^{6} -1.29278i q^{8} -0.868875 q^{9} -0.480489 q^{10} -5.95516i q^{11} +2.75840 q^{12} +(1.88953 + 3.07078i) q^{13} -2.11037i q^{15} +3.34936 q^{16} -4.32871 q^{17} +0.288793i q^{18} -1.95753i q^{19} -2.73154i q^{20} -1.97935 q^{22} +0.540163 q^{23} -1.88725i q^{24} +2.91018 q^{25} +(1.02065 - 0.628032i) q^{26} -5.64793 q^{27} +7.15857 q^{29} -0.701436 q^{30} +6.10800i q^{31} -3.69881i q^{32} -8.69356i q^{33} +1.43876i q^{34} -1.64176 q^{36} +8.02881i q^{37} -0.650636 q^{38} +(2.75840 + 4.48284i) q^{39} -1.86887 q^{40} +7.55362i q^{41} -4.24839 q^{43} -11.2524i q^{44} +1.25606i q^{45} -0.179537i q^{46} +6.26084i q^{47} +4.88953 q^{48} -0.967272i q^{50} -6.31922 q^{51} +(3.57031 + 5.80232i) q^{52} -2.77905 q^{53} +1.87723i q^{54} -8.60891 q^{55} -2.85768i q^{57} -2.37933i q^{58} -0.851152i q^{59} -3.98760i q^{60} +6.77905 q^{61} +2.03015 q^{62} +5.46933 q^{64} +(4.43919 - 2.73154i) q^{65} -2.88953 q^{66} +0.987106i q^{67} -8.17922 q^{68} +0.788550 q^{69} -3.76223i q^{71} +1.12327i q^{72} -9.13519i q^{73} +2.66858 q^{74} +4.24839 q^{75} -3.69881i q^{76} +(1.48999 - 0.916825i) q^{78} -0.131125 q^{79} -4.84191i q^{80} -5.63843 q^{81} +2.51064 q^{82} -2.66812i q^{83} +6.25768i q^{85} +1.41206i q^{86} +10.4503 q^{87} -7.69873 q^{88} +9.71739i q^{89} +0.417485 q^{90} +1.02065 q^{92} +8.91668i q^{93} +2.08095 q^{94} -2.82985 q^{95} -5.39966i q^{96} -6.58319i q^{97} +5.17429i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{3} - 6q^{4} + 12q^{9} + O(q^{10}) \) \( 8q + 4q^{3} - 6q^{4} + 12q^{9} + 6q^{10} - 18q^{12} - 6q^{13} - 2q^{16} - 8q^{17} - 18q^{22} + 12q^{23} + 6q^{26} + 16q^{27} - 8q^{29} - 38q^{30} - 28q^{36} - 34q^{38} - 18q^{39} + 4q^{40} + 8q^{43} + 18q^{48} - 16q^{51} + 42q^{52} + 20q^{53} + 12q^{55} + 12q^{61} + 22q^{62} + 44q^{64} + 30q^{65} - 2q^{66} + 2q^{68} - 28q^{69} - 42q^{74} - 8q^{75} + 10q^{78} - 20q^{79} + 24q^{81} + 16q^{82} + 68q^{87} - 4q^{88} - 108q^{90} + 6q^{92} + 26q^{94} + 16q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.332375i 0.235025i −0.993071 0.117512i \(-0.962508\pi\)
0.993071 0.117512i \(-0.0374920\pi\)
\(3\) 1.45984 0.842837 0.421419 0.906866i \(-0.361532\pi\)
0.421419 + 0.906866i \(0.361532\pi\)
\(4\) 1.88953 0.944763
\(5\) 1.44562i 0.646502i −0.946313 0.323251i \(-0.895224\pi\)
0.946313 0.323251i \(-0.104776\pi\)
\(6\) 0.485214i 0.198088i
\(7\) 0 0
\(8\) 1.29278i 0.457068i
\(9\) −0.868875 −0.289625
\(10\) −0.480489 −0.151944
\(11\) 5.95516i 1.79555i −0.440456 0.897774i \(-0.645183\pi\)
0.440456 0.897774i \(-0.354817\pi\)
\(12\) 2.75840 0.796282
\(13\) 1.88953 + 3.07078i 0.524060 + 0.851681i
\(14\) 0 0
\(15\) 2.11037i 0.544896i
\(16\) 3.34936 0.837341
\(17\) −4.32871 −1.04987 −0.524933 0.851143i \(-0.675910\pi\)
−0.524933 + 0.851143i \(0.675910\pi\)
\(18\) 0.288793i 0.0680691i
\(19\) 1.95753i 0.449089i −0.974464 0.224545i \(-0.927911\pi\)
0.974464 0.224545i \(-0.0720894\pi\)
\(20\) 2.73154i 0.610791i
\(21\) 0 0
\(22\) −1.97935 −0.421998
\(23\) 0.540163 0.112632 0.0563158 0.998413i \(-0.482065\pi\)
0.0563158 + 0.998413i \(0.482065\pi\)
\(24\) 1.88725i 0.385234i
\(25\) 2.91018 0.582036
\(26\) 1.02065 0.628032i 0.200166 0.123167i
\(27\) −5.64793 −1.08694
\(28\) 0 0
\(29\) 7.15857 1.32931 0.664656 0.747149i \(-0.268578\pi\)
0.664656 + 0.747149i \(0.268578\pi\)
\(30\) −0.701436 −0.128064
\(31\) 6.10800i 1.09703i 0.836141 + 0.548514i \(0.184806\pi\)
−0.836141 + 0.548514i \(0.815194\pi\)
\(32\) 3.69881i 0.653864i
\(33\) 8.69356i 1.51336i
\(34\) 1.43876i 0.246745i
\(35\) 0 0
\(36\) −1.64176 −0.273627
\(37\) 8.02881i 1.31993i 0.751297 + 0.659964i \(0.229429\pi\)
−0.751297 + 0.659964i \(0.770571\pi\)
\(38\) −0.650636 −0.105547
\(39\) 2.75840 + 4.48284i 0.441698 + 0.717829i
\(40\) −1.86887 −0.295495
\(41\) 7.55362i 1.17968i 0.807521 + 0.589839i \(0.200809\pi\)
−0.807521 + 0.589839i \(0.799191\pi\)
\(42\) 0 0
\(43\) −4.24839 −0.647873 −0.323936 0.946079i \(-0.605006\pi\)
−0.323936 + 0.946079i \(0.605006\pi\)
\(44\) 11.2524i 1.69637i
\(45\) 1.25606i 0.187243i
\(46\) 0.179537i 0.0264713i
\(47\) 6.26084i 0.913237i 0.889663 + 0.456618i \(0.150940\pi\)
−0.889663 + 0.456618i \(0.849060\pi\)
\(48\) 4.88953 0.705742
\(49\) 0 0
\(50\) 0.967272i 0.136793i
\(51\) −6.31922 −0.884867
\(52\) 3.57031 + 5.80232i 0.495113 + 0.804637i
\(53\) −2.77905 −0.381732 −0.190866 0.981616i \(-0.561130\pi\)
−0.190866 + 0.981616i \(0.561130\pi\)
\(54\) 1.87723i 0.255459i
\(55\) −8.60891 −1.16082
\(56\) 0 0
\(57\) 2.85768i 0.378509i
\(58\) 2.37933i 0.312421i
\(59\) 0.851152i 0.110811i −0.998464 0.0554053i \(-0.982355\pi\)
0.998464 0.0554053i \(-0.0176451\pi\)
\(60\) 3.98760i 0.514798i
\(61\) 6.77905 0.867969 0.433984 0.900920i \(-0.357107\pi\)
0.433984 + 0.900920i \(0.357107\pi\)
\(62\) 2.03015 0.257829
\(63\) 0 0
\(64\) 5.46933 0.683667
\(65\) 4.43919 2.73154i 0.550613 0.338806i
\(66\) −2.88953 −0.355676
\(67\) 0.987106i 0.120594i 0.998180 + 0.0602971i \(0.0192048\pi\)
−0.998180 + 0.0602971i \(0.980795\pi\)
\(68\) −8.17922 −0.991876
\(69\) 0.788550 0.0949302
\(70\) 0 0
\(71\) 3.76223i 0.446494i −0.974762 0.223247i \(-0.928334\pi\)
0.974762 0.223247i \(-0.0716657\pi\)
\(72\) 1.12327i 0.132378i
\(73\) 9.13519i 1.06919i −0.845107 0.534597i \(-0.820463\pi\)
0.845107 0.534597i \(-0.179537\pi\)
\(74\) 2.66858 0.310216
\(75\) 4.24839 0.490561
\(76\) 3.69881i 0.424283i
\(77\) 0 0
\(78\) 1.48999 0.916825i 0.168708 0.103810i
\(79\) −0.131125 −0.0147527 −0.00737636 0.999973i \(-0.502348\pi\)
−0.00737636 + 0.999973i \(0.502348\pi\)
\(80\) 4.84191i 0.541342i
\(81\) −5.63843 −0.626492
\(82\) 2.51064 0.277253
\(83\) 2.66812i 0.292865i −0.989221 0.146432i \(-0.953221\pi\)
0.989221 0.146432i \(-0.0467791\pi\)
\(84\) 0 0
\(85\) 6.25768i 0.678741i
\(86\) 1.41206i 0.152266i
\(87\) 10.4503 1.12039
\(88\) −7.69873 −0.820687
\(89\) 9.71739i 1.03004i 0.857178 + 0.515021i \(0.172216\pi\)
−0.857178 + 0.515021i \(0.827784\pi\)
\(90\) 0.417485 0.0440068
\(91\) 0 0
\(92\) 1.02065 0.106410
\(93\) 8.91668i 0.924617i
\(94\) 2.08095 0.214633
\(95\) −2.82985 −0.290337
\(96\) 5.39966i 0.551101i
\(97\) 6.58319i 0.668422i −0.942498 0.334211i \(-0.891530\pi\)
0.942498 0.334211i \(-0.108470\pi\)
\(98\) 0 0
\(99\) 5.17429i 0.520036i
\(100\) 5.49886 0.549886
\(101\) 0.0708289 0.00704774 0.00352387 0.999994i \(-0.498878\pi\)
0.00352387 + 0.999994i \(0.498878\pi\)
\(102\) 2.10035i 0.207966i
\(103\) −6.33821 −0.624522 −0.312261 0.949996i \(-0.601086\pi\)
−0.312261 + 0.949996i \(0.601086\pi\)
\(104\) 3.96985 2.44275i 0.389276 0.239531i
\(105\) 0 0
\(106\) 0.923689i 0.0897166i
\(107\) 7.74953 0.749175 0.374588 0.927192i \(-0.377784\pi\)
0.374588 + 0.927192i \(0.377784\pi\)
\(108\) −10.6719 −1.02691
\(109\) 0.0335623i 0.00321468i 0.999999 + 0.00160734i \(0.000511633\pi\)
−0.999999 + 0.00160734i \(0.999488\pi\)
\(110\) 2.86139i 0.272823i
\(111\) 11.7208i 1.11249i
\(112\) 0 0
\(113\) −9.19987 −0.865451 −0.432725 0.901526i \(-0.642448\pi\)
−0.432725 + 0.901526i \(0.642448\pi\)
\(114\) −0.949823 −0.0889591
\(115\) 0.780871i 0.0728166i
\(116\) 13.5263 1.25589
\(117\) −1.64176 2.66812i −0.151781 0.246668i
\(118\) −0.282902 −0.0260432
\(119\) 0 0
\(120\) −2.72825 −0.249054
\(121\) −24.4639 −2.22399
\(122\) 2.25319i 0.203994i
\(123\) 11.0271i 0.994276i
\(124\) 11.5412i 1.03643i
\(125\) 11.4351i 1.02279i
\(126\) 0 0
\(127\) −14.3952 −1.27737 −0.638683 0.769470i \(-0.720520\pi\)
−0.638683 + 0.769470i \(0.720520\pi\)
\(128\) 9.21550i 0.814542i
\(129\) −6.20195 −0.546052
\(130\) −0.907897 1.47548i −0.0796278 0.129408i
\(131\) −9.46828 −0.827248 −0.413624 0.910448i \(-0.635737\pi\)
−0.413624 + 0.910448i \(0.635737\pi\)
\(132\) 16.4267i 1.42976i
\(133\) 0 0
\(134\) 0.328090 0.0283426
\(135\) 8.16477i 0.702711i
\(136\) 5.59609i 0.479860i
\(137\) 16.6063i 1.41877i 0.704822 + 0.709384i \(0.251027\pi\)
−0.704822 + 0.709384i \(0.748973\pi\)
\(138\) 0.262094i 0.0223110i
\(139\) 18.4778 1.56726 0.783632 0.621225i \(-0.213365\pi\)
0.783632 + 0.621225i \(0.213365\pi\)
\(140\) 0 0
\(141\) 9.13980i 0.769710i
\(142\) −1.25047 −0.104937
\(143\) 18.2870 11.2524i 1.52923 0.940976i
\(144\) −2.91018 −0.242515
\(145\) 10.3486i 0.859402i
\(146\) −3.03631 −0.251287
\(147\) 0 0
\(148\) 15.1707i 1.24702i
\(149\) 3.08080i 0.252389i 0.992006 + 0.126195i \(0.0402763\pi\)
−0.992006 + 0.126195i \(0.959724\pi\)
\(150\) 1.41206i 0.115294i
\(151\) 2.54885i 0.207422i 0.994607 + 0.103711i \(0.0330717\pi\)
−0.994607 + 0.103711i \(0.966928\pi\)
\(152\) −2.53067 −0.205264
\(153\) 3.76111 0.304068
\(154\) 0 0
\(155\) 8.82985 0.709231
\(156\) 5.21207 + 8.47044i 0.417300 + 0.678178i
\(157\) −9.40904 −0.750923 −0.375461 0.926838i \(-0.622516\pi\)
−0.375461 + 0.926838i \(0.622516\pi\)
\(158\) 0.0435828i 0.00346726i
\(159\) −4.05697 −0.321738
\(160\) −5.34708 −0.422724
\(161\) 0 0
\(162\) 1.87408i 0.147241i
\(163\) 0.695157i 0.0544489i 0.999629 + 0.0272244i \(0.00866688\pi\)
−0.999629 + 0.0272244i \(0.991333\pi\)
\(164\) 14.2728i 1.11452i
\(165\) −12.5676 −0.978387
\(166\) −0.886819 −0.0688305
\(167\) 13.9840i 1.08211i 0.840986 + 0.541056i \(0.181975\pi\)
−0.840986 + 0.541056i \(0.818025\pi\)
\(168\) 0 0
\(169\) −5.85938 + 11.6046i −0.450721 + 0.892665i
\(170\) 2.07990 0.159521
\(171\) 1.70085i 0.130067i
\(172\) −8.02744 −0.612087
\(173\) 5.43648 0.413328 0.206664 0.978412i \(-0.433739\pi\)
0.206664 + 0.978412i \(0.433739\pi\)
\(174\) 3.47344i 0.263321i
\(175\) 0 0
\(176\) 19.9460i 1.50349i
\(177\) 1.24254i 0.0933953i
\(178\) 3.22982 0.242085
\(179\) −5.35824 −0.400493 −0.200247 0.979745i \(-0.564174\pi\)
−0.200247 + 0.979745i \(0.564174\pi\)
\(180\) 2.37337i 0.176900i
\(181\) −7.54016 −0.560456 −0.280228 0.959933i \(-0.590410\pi\)
−0.280228 + 0.959933i \(0.590410\pi\)
\(182\) 0 0
\(183\) 9.89632 0.731557
\(184\) 0.698313i 0.0514803i
\(185\) 11.6066 0.853336
\(186\) 2.96369 0.217308
\(187\) 25.7782i 1.88509i
\(188\) 11.8300i 0.862793i
\(189\) 0 0
\(190\) 0.940574i 0.0682364i
\(191\) 13.5463 0.980178 0.490089 0.871672i \(-0.336964\pi\)
0.490089 + 0.871672i \(0.336964\pi\)
\(192\) 7.98434 0.576220
\(193\) 18.5562i 1.33571i 0.744293 + 0.667853i \(0.232787\pi\)
−0.744293 + 0.667853i \(0.767213\pi\)
\(194\) −2.18809 −0.157096
\(195\) 6.48049 3.98760i 0.464077 0.285558i
\(196\) 0 0
\(197\) 2.66812i 0.190096i 0.995473 + 0.0950480i \(0.0303004\pi\)
−0.995473 + 0.0950480i \(0.969700\pi\)
\(198\) 1.71981 0.122221
\(199\) −20.1999 −1.43193 −0.715965 0.698136i \(-0.754013\pi\)
−0.715965 + 0.698136i \(0.754013\pi\)
\(200\) 3.76223i 0.266030i
\(201\) 1.44101i 0.101641i
\(202\) 0.0235418i 0.00165639i
\(203\) 0 0
\(204\) −11.9403 −0.835990
\(205\) 10.9197 0.762663
\(206\) 2.10666i 0.146778i
\(207\) −0.469334 −0.0326210
\(208\) 6.32871 + 10.2852i 0.438817 + 0.713148i
\(209\) −11.6574 −0.806361
\(210\) 0 0
\(211\) 13.1268 0.903683 0.451842 0.892098i \(-0.350767\pi\)
0.451842 + 0.892098i \(0.350767\pi\)
\(212\) −5.25109 −0.360647
\(213\) 5.49224i 0.376322i
\(214\) 2.57575i 0.176075i
\(215\) 6.14156i 0.418851i
\(216\) 7.30155i 0.496807i
\(217\) 0 0
\(218\) 0.0111553 0.000755530
\(219\) 13.3359i 0.901157i
\(220\) −16.2668 −1.09670
\(221\) −8.17922 13.2925i −0.550194 0.894152i
\(222\) 3.89569 0.261462
\(223\) 2.22334i 0.148886i 0.997225 + 0.0744428i \(0.0237178\pi\)
−0.997225 + 0.0744428i \(0.976282\pi\)
\(224\) 0 0
\(225\) −2.52858 −0.168572
\(226\) 3.05781i 0.203402i
\(227\) 27.1045i 1.79899i −0.436931 0.899495i \(-0.643935\pi\)
0.436931 0.899495i \(-0.356065\pi\)
\(228\) 5.39966i 0.357601i
\(229\) 18.9887i 1.25481i −0.778693 0.627406i \(-0.784117\pi\)
0.778693 0.627406i \(-0.215883\pi\)
\(230\) −0.259542 −0.0171137
\(231\) 0 0
\(232\) 9.25447i 0.607586i
\(233\) −21.7400 −1.42424 −0.712118 0.702059i \(-0.752264\pi\)
−0.712118 + 0.702059i \(0.752264\pi\)
\(234\) −0.886819 + 0.545681i −0.0579731 + 0.0356723i
\(235\) 9.05080 0.590409
\(236\) 1.60827i 0.104690i
\(237\) −0.191421 −0.0124342
\(238\) 0 0
\(239\) 19.9695i 1.29172i −0.763455 0.645861i \(-0.776499\pi\)
0.763455 0.645861i \(-0.223501\pi\)
\(240\) 7.06841i 0.456264i
\(241\) 3.23048i 0.208094i 0.994572 + 0.104047i \(0.0331792\pi\)
−0.994572 + 0.104047i \(0.966821\pi\)
\(242\) 8.13120i 0.522694i
\(243\) 8.71259 0.558913
\(244\) 12.8092 0.820025
\(245\) 0 0
\(246\) 3.66512 0.233680
\(247\) 6.01116 3.69881i 0.382481 0.235350i
\(248\) 7.89632 0.501417
\(249\) 3.89503i 0.246837i
\(250\) −3.80075 −0.240381
\(251\) −12.4916 −0.788466 −0.394233 0.919011i \(-0.628990\pi\)
−0.394233 + 0.919011i \(0.628990\pi\)
\(252\) 0 0
\(253\) 3.21675i 0.202236i
\(254\) 4.78460i 0.300213i
\(255\) 9.13519i 0.572068i
\(256\) 7.87566 0.492229
\(257\) −5.82757 −0.363514 −0.181757 0.983343i \(-0.558178\pi\)
−0.181757 + 0.983343i \(0.558178\pi\)
\(258\) 2.06138i 0.128336i
\(259\) 0 0
\(260\) 8.38796 5.16132i 0.520199 0.320091i
\(261\) −6.21990 −0.385002
\(262\) 3.14702i 0.194424i
\(263\) 17.5147 1.08000 0.540002 0.841664i \(-0.318424\pi\)
0.540002 + 0.841664i \(0.318424\pi\)
\(264\) −11.2389 −0.691706
\(265\) 4.01746i 0.246791i
\(266\) 0 0
\(267\) 14.1858i 0.868157i
\(268\) 1.86516i 0.113933i
\(269\) 22.3287 1.36141 0.680703 0.732560i \(-0.261675\pi\)
0.680703 + 0.732560i \(0.261675\pi\)
\(270\) 2.71377 0.165155
\(271\) 26.3695i 1.60183i −0.598777 0.800916i \(-0.704346\pi\)
0.598777 0.800916i \(-0.295654\pi\)
\(272\) −14.4984 −0.879097
\(273\) 0 0
\(274\) 5.51951 0.333446
\(275\) 17.3306i 1.04507i
\(276\) 1.48999 0.0896866
\(277\) 9.37618 0.563360 0.281680 0.959508i \(-0.409108\pi\)
0.281680 + 0.959508i \(0.409108\pi\)
\(278\) 6.14156i 0.368346i
\(279\) 5.30709i 0.317727i
\(280\) 0 0
\(281\) 17.7754i 1.06039i −0.847876 0.530195i \(-0.822119\pi\)
0.847876 0.530195i \(-0.177881\pi\)
\(282\) 3.03785 0.180901
\(283\) 9.60662 0.571055 0.285527 0.958371i \(-0.407831\pi\)
0.285527 + 0.958371i \(0.407831\pi\)
\(284\) 7.10883i 0.421832i
\(285\) −4.13113 −0.244707
\(286\) −3.74003 6.07814i −0.221153 0.359408i
\(287\) 0 0
\(288\) 3.21380i 0.189375i
\(289\) 1.73775 0.102221
\(290\) −3.43961 −0.201981
\(291\) 9.61039i 0.563371i
\(292\) 17.2612i 1.01013i
\(293\) 11.6338i 0.679654i −0.940488 0.339827i \(-0.889631\pi\)
0.940488 0.339827i \(-0.110369\pi\)
\(294\) 0 0
\(295\) −1.23044 −0.0716392
\(296\) 10.3795 0.603297
\(297\) 33.6343i 1.95166i
\(298\) 1.02398 0.0593177
\(299\) 1.02065 + 1.65872i 0.0590258 + 0.0959263i
\(300\) 8.02744 0.463464
\(301\) 0 0
\(302\) 0.847174 0.0487494
\(303\) 0.103399 0.00594010
\(304\) 6.55649i 0.376041i
\(305\) 9.79995i 0.561143i
\(306\) 1.25010i 0.0714635i
\(307\) 13.8280i 0.789204i 0.918852 + 0.394602i \(0.129118\pi\)
−0.918852 + 0.394602i \(0.870882\pi\)
\(308\) 0 0
\(309\) −9.25275 −0.526371
\(310\) 2.93483i 0.166687i
\(311\) −30.7144 −1.74165 −0.870827 0.491590i \(-0.836416\pi\)
−0.870827 + 0.491590i \(0.836416\pi\)
\(312\) 5.79534 3.56601i 0.328096 0.201886i
\(313\) 11.0867 0.626657 0.313328 0.949645i \(-0.398556\pi\)
0.313328 + 0.949645i \(0.398556\pi\)
\(314\) 3.12733i 0.176486i
\(315\) 0 0
\(316\) −0.247764 −0.0139378
\(317\) 23.8834i 1.34142i 0.741718 + 0.670712i \(0.234011\pi\)
−0.741718 + 0.670712i \(0.765989\pi\)
\(318\) 1.34844i 0.0756165i
\(319\) 42.6304i 2.38684i
\(320\) 7.90659i 0.441992i
\(321\) 11.3130 0.631433
\(322\) 0 0
\(323\) 8.47360i 0.471484i
\(324\) −10.6540 −0.591887
\(325\) 5.49886 + 8.93652i 0.305022 + 0.495709i
\(326\) 0.231053 0.0127968
\(327\) 0.0489954i 0.00270945i
\(328\) 9.76519 0.539192
\(329\) 0 0
\(330\) 4.17716i 0.229945i
\(331\) 18.3240i 1.00718i 0.863943 + 0.503589i \(0.167987\pi\)
−0.863943 + 0.503589i \(0.832013\pi\)
\(332\) 5.04149i 0.276688i
\(333\) 6.97603i 0.382284i
\(334\) 4.64793 0.254323
\(335\) 1.42698 0.0779643
\(336\) 0 0
\(337\) 7.21762 0.393169 0.196584 0.980487i \(-0.437015\pi\)
0.196584 + 0.980487i \(0.437015\pi\)
\(338\) 3.85710 + 1.94751i 0.209798 + 0.105931i
\(339\) −13.4303 −0.729434
\(340\) 11.8241i 0.641249i
\(341\) 36.3741 1.96977
\(342\) 0.565321 0.0305691
\(343\) 0 0
\(344\) 5.49224i 0.296122i
\(345\) 1.13994i 0.0613725i
\(346\) 1.80695i 0.0971423i
\(347\) −21.0782 −1.13154 −0.565770 0.824563i \(-0.691421\pi\)
−0.565770 + 0.824563i \(0.691421\pi\)
\(348\) 19.7462 1.05851
\(349\) 30.7629i 1.64670i −0.567534 0.823350i \(-0.692102\pi\)
0.567534 0.823350i \(-0.307898\pi\)
\(350\) 0 0
\(351\) −10.6719 17.3435i −0.569624 0.925730i
\(352\) −22.0270 −1.17404
\(353\) 6.12173i 0.325827i −0.986640 0.162913i \(-0.947911\pi\)
0.986640 0.162913i \(-0.0520891\pi\)
\(354\) −0.412991 −0.0219502
\(355\) −5.43876 −0.288659
\(356\) 18.3613i 0.973145i
\(357\) 0 0
\(358\) 1.78095i 0.0941259i
\(359\) 19.4287i 1.02541i −0.858566 0.512703i \(-0.828644\pi\)
0.858566 0.512703i \(-0.171356\pi\)
\(360\) 1.62382 0.0855827
\(361\) 15.1681 0.798319
\(362\) 2.50616i 0.131721i
\(363\) −35.7133 −1.87446
\(364\) 0 0
\(365\) −13.2060 −0.691235
\(366\) 3.28929i 0.171934i
\(367\) −5.40467 −0.282122 −0.141061 0.990001i \(-0.545051\pi\)
−0.141061 + 0.990001i \(0.545051\pi\)
\(368\) 1.80920 0.0943111
\(369\) 6.56315i 0.341664i
\(370\) 3.85776i 0.200555i
\(371\) 0 0
\(372\) 16.8483i 0.873544i
\(373\) 16.2507 0.841428 0.420714 0.907193i \(-0.361780\pi\)
0.420714 + 0.907193i \(0.361780\pi\)
\(374\) 8.56803 0.443042
\(375\) 16.6934i 0.862045i
\(376\) 8.09390 0.417411
\(377\) 13.5263 + 21.9824i 0.696640 + 1.13215i
\(378\) 0 0
\(379\) 25.1730i 1.29305i −0.762893 0.646525i \(-0.776222\pi\)
0.762893 0.646525i \(-0.223778\pi\)
\(380\) −5.34708 −0.274300
\(381\) −21.0146 −1.07661
\(382\) 4.50247i 0.230366i
\(383\) 3.81438i 0.194906i −0.995240 0.0974529i \(-0.968930\pi\)
0.995240 0.0974529i \(-0.0310695\pi\)
\(384\) 13.4531i 0.686527i
\(385\) 0 0
\(386\) 6.16764 0.313924
\(387\) 3.69132 0.187640
\(388\) 12.4391i 0.631500i
\(389\) 2.87096 0.145563 0.0727817 0.997348i \(-0.476812\pi\)
0.0727817 + 0.997348i \(0.476812\pi\)
\(390\) −1.32538 2.15396i −0.0671133 0.109070i
\(391\) −2.33821 −0.118248
\(392\) 0 0
\(393\) −13.8222 −0.697236
\(394\) 0.886819 0.0446773
\(395\) 0.189557i 0.00953766i
\(396\) 9.77696i 0.491310i
\(397\) 19.1184i 0.959524i −0.877399 0.479762i \(-0.840723\pi\)
0.877399 0.479762i \(-0.159277\pi\)
\(398\) 6.71394i 0.336539i
\(399\) 0 0
\(400\) 9.74725 0.487362
\(401\) 2.99824i 0.149725i 0.997194 + 0.0748625i \(0.0238518\pi\)
−0.997194 + 0.0748625i \(0.976148\pi\)
\(402\) 0.478958 0.0238882
\(403\) −18.7563 + 11.5412i −0.934319 + 0.574909i
\(404\) 0.133833 0.00665844
\(405\) 8.15104i 0.405028i
\(406\) 0 0
\(407\) 47.8129 2.37000
\(408\) 8.16937i 0.404444i
\(409\) 34.0805i 1.68517i 0.538560 + 0.842587i \(0.318969\pi\)
−0.538560 + 0.842587i \(0.681031\pi\)
\(410\) 3.62943i 0.179245i
\(411\) 24.2424i 1.19579i
\(412\) −11.9762 −0.590026
\(413\) 0 0
\(414\) 0.155995i 0.00766674i
\(415\) −3.85710 −0.189337
\(416\) 11.3582 6.98900i 0.556883 0.342664i
\(417\) 26.9746 1.32095
\(418\) 3.87464i 0.189515i
\(419\) 34.7759 1.69891 0.849457 0.527657i \(-0.176929\pi\)
0.849457 + 0.527657i \(0.176929\pi\)
\(420\) 0 0
\(421\) 24.1400i 1.17651i 0.808674 + 0.588257i \(0.200186\pi\)
−0.808674 + 0.588257i \(0.799814\pi\)
\(422\) 4.36301i 0.212388i
\(423\) 5.43988i 0.264496i
\(424\) 3.59271i 0.174478i
\(425\) −12.5973 −0.611060
\(426\) −1.82549 −0.0884451
\(427\) 0 0
\(428\) 14.6429 0.707793
\(429\) 26.6960 16.4267i 1.28890 0.793089i
\(430\) 2.04130 0.0984404
\(431\) 4.76477i 0.229511i 0.993394 + 0.114755i \(0.0366084\pi\)
−0.993394 + 0.114755i \(0.963392\pi\)
\(432\) −18.9170 −0.910143
\(433\) −22.0231 −1.05836 −0.529181 0.848509i \(-0.677501\pi\)
−0.529181 + 0.848509i \(0.677501\pi\)
\(434\) 0 0
\(435\) 15.1072i 0.724337i
\(436\) 0.0634168i 0.00303711i
\(437\) 1.05739i 0.0505817i
\(438\) −4.43252 −0.211794
\(439\) −3.43240 −0.163819 −0.0819097 0.996640i \(-0.526102\pi\)
−0.0819097 + 0.996640i \(0.526102\pi\)
\(440\) 11.1294i 0.530576i
\(441\) 0 0
\(442\) −4.41811 + 2.71857i −0.210148 + 0.129309i
\(443\) −8.70594 −0.413632 −0.206816 0.978380i \(-0.566310\pi\)
−0.206816 + 0.978380i \(0.566310\pi\)
\(444\) 22.1467i 1.05104i
\(445\) 14.0477 0.665923
\(446\) 0.738982 0.0349918
\(447\) 4.49747i 0.212723i
\(448\) 0 0
\(449\) 17.6120i 0.831159i −0.909557 0.415580i \(-0.863579\pi\)
0.909557 0.415580i \(-0.136421\pi\)
\(450\) 0.840438i 0.0396186i
\(451\) 44.9830 2.11817
\(452\) −17.3834 −0.817646
\(453\) 3.72090i 0.174823i
\(454\) −9.00887 −0.422807
\(455\) 0 0
\(456\) −3.69436 −0.173004
\(457\) 9.07268i 0.424402i −0.977226 0.212201i \(-0.931937\pi\)
0.977226 0.212201i \(-0.0680631\pi\)
\(458\) −6.31139 −0.294912
\(459\) 24.4483 1.14115
\(460\) 1.47548i 0.0687944i
\(461\) 6.58319i 0.306610i 0.988179 + 0.153305i \(0.0489917\pi\)
−0.988179 + 0.153305i \(0.951008\pi\)
\(462\) 0 0
\(463\) 3.47344i 0.161424i −0.996737 0.0807121i \(-0.974281\pi\)
0.996737 0.0807121i \(-0.0257194\pi\)
\(464\) 23.9766 1.11309
\(465\) 12.8901 0.597766
\(466\) 7.22585i 0.334731i
\(467\) −29.7854 −1.37830 −0.689152 0.724617i \(-0.742017\pi\)
−0.689152 + 0.724617i \(0.742017\pi\)
\(468\) −3.10215 5.04149i −0.143397 0.233043i
\(469\) 0 0
\(470\) 3.00826i 0.138761i
\(471\) −13.7357 −0.632906
\(472\) −1.10035 −0.0506479
\(473\) 25.2998i 1.16329i
\(474\) 0.0636237i 0.00292233i
\(475\) 5.69677i 0.261386i
\(476\) 0 0
\(477\) 2.41465 0.110559
\(478\) −6.63738 −0.303587
\(479\) 35.1855i 1.60767i −0.594855 0.803833i \(-0.702791\pi\)
0.594855 0.803833i \(-0.297209\pi\)
\(480\) −7.80587 −0.356288
\(481\) −24.6547 + 15.1707i −1.12416 + 0.691722i
\(482\) 1.07373 0.0489072
\(483\) 0 0
\(484\) −46.2252 −2.10115
\(485\) −9.51680 −0.432136
\(486\) 2.89585i 0.131358i
\(487\) 1.80154i 0.0816355i −0.999167 0.0408178i \(-0.987004\pi\)
0.999167 0.0408178i \(-0.0129963\pi\)
\(488\) 8.76384i 0.396721i
\(489\) 1.01482i 0.0458916i
\(490\) 0 0
\(491\) 8.19322 0.369755 0.184877 0.982762i \(-0.440811\pi\)
0.184877 + 0.982762i \(0.440811\pi\)
\(492\) 20.8359i 0.939356i
\(493\) −30.9874 −1.39560
\(494\) −1.22939 1.99796i −0.0553131 0.0898925i
\(495\) 7.48006 0.336204
\(496\) 20.4579i 0.918587i
\(497\) 0 0
\(498\) −1.29461 −0.0580129
\(499\) 36.5164i 1.63470i −0.576141 0.817350i \(-0.695442\pi\)
0.576141 0.817350i \(-0.304558\pi\)
\(500\) 21.6070i 0.966293i
\(501\) 20.4143i 0.912045i
\(502\) 4.15192i 0.185309i
\(503\) −3.02972 −0.135089 −0.0675443 0.997716i \(-0.521516\pi\)
−0.0675443 + 0.997716i \(0.521516\pi\)
\(504\) 0 0
\(505\) 0.102392i 0.00455637i
\(506\) −1.06917 −0.0475304
\(507\) −8.55374 + 16.9409i −0.379885 + 0.752371i
\(508\) −27.2001 −1.20681
\(509\) 29.3447i 1.30068i 0.759642 + 0.650341i \(0.225374\pi\)
−0.759642 + 0.650341i \(0.774626\pi\)
\(510\) 3.03631 0.134450
\(511\) 0 0
\(512\) 21.0487i 0.930229i
\(513\) 11.0560i 0.488135i
\(514\) 1.93694i 0.0854348i
\(515\) 9.16265i 0.403755i
\(516\) −11.7188 −0.515890
\(517\) 37.2843 1.63976
\(518\) 0 0
\(519\) 7.93637 0.348368
\(520\) −3.53129 5.73890i −0.154857 0.251668i
\(521\) −29.6838 −1.30047 −0.650236 0.759732i \(-0.725330\pi\)
−0.650236 + 0.759732i \(0.725330\pi\)
\(522\) 2.06734i 0.0904851i
\(523\) 20.5727 0.899583 0.449791 0.893134i \(-0.351498\pi\)
0.449791 + 0.893134i \(0.351498\pi\)
\(524\) −17.8906 −0.781553
\(525\) 0 0
\(526\) 5.82146i 0.253828i
\(527\) 26.4398i 1.15173i
\(528\) 29.1179i 1.26719i
\(529\) −22.7082 −0.987314
\(530\) 1.33530 0.0580019
\(531\) 0.739544i 0.0320935i
\(532\) 0 0
\(533\) −23.1955 + 14.2728i −1.00471 + 0.618222i
\(534\) 4.71501 0.204039
\(535\) 11.2029i 0.484343i
\(536\) 1.27611 0.0551197
\(537\) −7.82216 −0.337551
\(538\) 7.42151i 0.319964i
\(539\) 0 0
\(540\) 15.4275i 0.663896i
\(541\) 34.0668i 1.46465i 0.680957 + 0.732324i \(0.261564\pi\)
−0.680957 + 0.732324i \(0.738436\pi\)
\(542\) −8.76457 −0.376470
\(543\) −11.0074 −0.472373
\(544\) 16.0111i 0.686470i
\(545\) 0.0485183 0.00207830
\(546\) 0 0
\(547\) −0.850931 −0.0363832 −0.0181916 0.999835i \(-0.505791\pi\)
−0.0181916 + 0.999835i \(0.505791\pi\)
\(548\) 31.3780i 1.34040i
\(549\) −5.89015 −0.251385
\(550\) −5.76026 −0.245618
\(551\) 14.0131i 0.596980i
\(552\) 1.01942i 0.0433895i
\(553\) 0 0
\(554\) 3.11641i 0.132404i
\(555\) 16.9438 0.719224
\(556\) 34.9143 1.48069
\(557\) 17.7281i 0.751162i −0.926789 0.375581i \(-0.877443\pi\)
0.926789 0.375581i \(-0.122557\pi\)
\(558\) −1.76394 −0.0746737
\(559\) −8.02744 13.0459i −0.339525 0.551781i
\(560\) 0 0
\(561\) 37.6319i 1.58882i
\(562\) −5.90809 −0.249218
\(563\) 24.1806 1.01909 0.509545 0.860444i \(-0.329814\pi\)
0.509545 + 0.860444i \(0.329814\pi\)
\(564\) 17.2699i 0.727194i
\(565\) 13.2995i 0.559515i
\(566\) 3.19301i 0.134212i
\(567\) 0 0
\(568\) −4.86375 −0.204078
\(569\) 42.7749 1.79322 0.896608 0.442825i \(-0.146024\pi\)
0.896608 + 0.442825i \(0.146024\pi\)
\(570\) 1.37308i 0.0575122i
\(571\) −7.36280 −0.308124 −0.154062 0.988061i \(-0.549235\pi\)
−0.154062 + 0.988061i \(0.549235\pi\)
\(572\) 34.5537 21.2618i 1.44476 0.888999i
\(573\) 19.7754 0.826131
\(574\) 0 0
\(575\) 1.57197 0.0655557
\(576\) −4.75217 −0.198007
\(577\) 8.19393i 0.341118i 0.985347 + 0.170559i \(0.0545573\pi\)
−0.985347 + 0.170559i \(0.945443\pi\)
\(578\) 0.577585i 0.0240244i
\(579\) 27.0891i 1.12578i
\(580\) 19.5539i 0.811932i
\(581\) 0 0
\(582\) −3.19426 −0.132406
\(583\) 16.5497i 0.685419i
\(584\) −11.8098 −0.488694
\(585\) −3.85710 + 2.37337i −0.159471 + 0.0981266i
\(586\) −3.86679 −0.159736
\(587\) 39.1141i 1.61441i −0.590271 0.807205i \(-0.700979\pi\)
0.590271 0.807205i \(-0.299021\pi\)
\(588\) 0 0
\(589\) 11.9566 0.492664
\(590\) 0.408969i 0.0168370i
\(591\) 3.89503i 0.160220i
\(592\) 26.8914i 1.10523i
\(593\) 1.21338i 0.0498276i −0.999690 0.0249138i \(-0.992069\pi\)
0.999690 0.0249138i \(-0.00793113\pi\)
\(594\) 11.1792 0.458689
\(595\) 0 0
\(596\) 5.82125i 0.238448i
\(597\) −29.4885 −1.20688
\(598\) 0.551318 0.339240i 0.0225451 0.0138725i
\(599\) 32.6638 1.33461 0.667303 0.744786i \(-0.267449\pi\)
0.667303 + 0.744786i \(0.267449\pi\)
\(600\) 5.49224i 0.224220i
\(601\) 2.50114 0.102024 0.0510118 0.998698i \(-0.483755\pi\)
0.0510118 + 0.998698i \(0.483755\pi\)
\(602\) 0 0
\(603\) 0.857671i 0.0349271i
\(604\) 4.81611i 0.195965i
\(605\) 35.3656i 1.43781i
\(606\) 0.0343672i 0.00139607i
\(607\) 12.6456 0.513271 0.256635 0.966508i \(-0.417386\pi\)
0.256635 + 0.966508i \(0.417386\pi\)
\(608\) −7.24055 −0.293643
\(609\) 0 0
\(610\) −3.25726 −0.131883
\(611\) −19.2256 + 11.8300i −0.777787 + 0.478591i
\(612\) 7.10672 0.287272
\(613\) 20.0280i 0.808923i −0.914555 0.404462i \(-0.867459\pi\)
0.914555 0.404462i \(-0.132541\pi\)
\(614\) 4.59608 0.185483
\(615\) 15.9409 0.642801
\(616\) 0 0
\(617\) 45.2926i 1.82341i 0.410846 + 0.911705i \(0.365233\pi\)
−0.410846 + 0.911705i \(0.634767\pi\)
\(618\) 3.07539i 0.123710i
\(619\) 4.43315i 0.178183i −0.996023 0.0890917i \(-0.971604\pi\)
0.996023 0.0890917i \(-0.0283964\pi\)
\(620\) 16.6842 0.670055
\(621\) −3.05080 −0.122424
\(622\) 10.2087i 0.409332i
\(623\) 0 0
\(624\) 9.23889 + 15.0147i 0.369852 + 0.601067i
\(625\) −1.97997 −0.0791988
\(626\) 3.68494i 0.147280i
\(627\) −17.0179 −0.679631
\(628\) −17.7786 −0.709444
\(629\) 34.7544i 1.38575i
\(630\) 0 0
\(631\) 19.7358i 0.785672i 0.919609 + 0.392836i \(0.128506\pi\)
−0.919609 + 0.392836i \(0.871494\pi\)
\(632\) 0.169516i 0.00674300i
\(633\) 19.1629 0.761658
\(634\) 7.93824 0.315268
\(635\) 20.8100i 0.825819i
\(636\) −7.66574 −0.303967
\(637\) 0 0
\(638\) −14.1693 −0.560968
\(639\) 3.26891i 0.129316i
\(640\) −13.3221 −0.526603
\(641\) −39.6425 −1.56579 −0.782893 0.622157i \(-0.786257\pi\)
−0.782893 + 0.622157i \(0.786257\pi\)
\(642\) 3.76018i 0.148402i
\(643\) 20.8300i 0.821453i 0.911759 + 0.410727i \(0.134725\pi\)
−0.911759 + 0.410727i \(0.865275\pi\)
\(644\) 0 0
\(645\) 8.96568i 0.353023i
\(646\) 2.81642 0.110810
\(647\) 15.7441 0.618965 0.309482 0.950905i \(-0.399844\pi\)
0.309482 + 0.950905i \(0.399844\pi\)
\(648\) 7.28927i 0.286350i
\(649\) −5.06874 −0.198966
\(650\) 2.97028 1.82769i 0.116504 0.0716877i
\(651\) 0 0
\(652\) 1.31352i 0.0514413i
\(653\) −27.0264 −1.05762 −0.528812 0.848739i \(-0.677362\pi\)
−0.528812 + 0.848739i \(0.677362\pi\)
\(654\) 0.0162849 0.000636789
\(655\) 13.6876i 0.534817i
\(656\) 25.2998i 0.987792i
\(657\) 7.93734i 0.309665i
\(658\) 0 0
\(659\) −6.79491 −0.264692 −0.132346 0.991204i \(-0.542251\pi\)
−0.132346 + 0.991204i \(0.542251\pi\)
\(660\) −23.7468 −0.924344
\(661\) 7.20526i 0.280252i −0.990134 0.140126i \(-0.955249\pi\)
0.990134 0.140126i \(-0.0447508\pi\)
\(662\) 6.09044 0.236712
\(663\) −11.9403 19.4049i −0.463724 0.753625i
\(664\) −3.44930 −0.133859
\(665\) 0 0
\(666\) −2.31866 −0.0898463
\(667\) 3.86679 0.149723
\(668\) 26.4231i 1.02234i
\(669\) 3.24571i 0.125486i
\(670\) 0.474293i 0.0183236i
\(671\) 40.3703i 1.55848i
\(672\) 0 0
\(673\) −8.32130 −0.320763 −0.160381 0.987055i \(-0.551272\pi\)
−0.160381 + 0.987055i \(0.551272\pi\)
\(674\) 2.39896i 0.0924044i
\(675\) −16.4365 −0.632640
\(676\) −11.0715 + 21.9273i −0.425825 + 0.843357i
\(677\) −29.9956 −1.15283 −0.576413 0.817159i \(-0.695548\pi\)
−0.576413 + 0.817159i \(0.695548\pi\)
\(678\) 4.46391i 0.171435i
\(679\) 0 0
\(680\) 8.08982 0.310231
\(681\) 39.5682i 1.51626i
\(682\) 12.0899i 0.462944i
\(683\) 36.0839i 1.38071i 0.723469 + 0.690356i \(0.242546\pi\)
−0.723469 + 0.690356i \(0.757454\pi\)
\(684\) 3.21380i 0.122883i
\(685\) 24.0064 0.917236
\(686\) 0 0
\(687\) 27.7205i 1.05760i
\(688\) −14.2294 −0.542491
\(689\) −5.25109 8.53386i −0.200051 0.325114i
\(690\) −0.378889 −0.0144241
\(691\) 25.7677i 0.980248i −0.871653 0.490124i \(-0.836951\pi\)
0.871653 0.490124i \(-0.163049\pi\)
\(692\) 10.2724 0.390497
\(693\) 0 0
\(694\) 7.00589i 0.265940i
\(695\) 26.7119i 1.01324i
\(696\) 13.5100i 0.512096i
\(697\) 32.6974i 1.23850i
\(698\) −10.2248 −0.387016
\(699\) −31.7369 −1.20040
\(700\) 0 0
\(701\) −41.7872 −1.57828 −0.789141 0.614213i \(-0.789474\pi\)
−0.789141 + 0.614213i \(0.789474\pi\)
\(702\) −5.76457 + 3.54708i −0.217570 + 0.133876i
\(703\) 15.7167 0.592765
\(704\) 32.5708i 1.22756i
\(705\) 13.2127 0.497619
\(706\) −2.03471 −0.0765774
\(707\) 0 0
\(708\) 2.34782i 0.0882364i
\(709\) 0.343847i 0.0129135i −0.999979 0.00645673i \(-0.997945\pi\)
0.999979 0.00645673i \(-0.00205525\pi\)
\(710\) 1.80771i 0.0678421i
\(711\) 0.113931 0.00427276
\(712\) 12.5625 0.470799
\(713\) 3.29931i 0.123560i
\(714\) 0 0
\(715\) −16.2668 26.4361i −0.608342 0.988652i
\(716\) −10.1245 −0.378372
\(717\) 29.1523i 1.08871i
\(718\) −6.45761 −0.240996
\(719\) −8.78010 −0.327443 −0.163721 0.986507i \(-0.552350\pi\)
−0.163721 + 0.986507i \(0.552350\pi\)
\(720\) 4.20702i 0.156786i
\(721\) 0 0
\(722\) 5.04149i 0.187625i
\(723\) 4.71598i 0.175389i
\(724\) −14.2473 −0.529498
\(725\) 20.8327 0.773707
\(726\) 11.8702i 0.440546i
\(727\) 17.3658 0.644064 0.322032 0.946729i \(-0.395634\pi\)
0.322032 + 0.946729i \(0.395634\pi\)
\(728\) 0 0
\(729\) 29.6343 1.09757
\(730\) 4.38936i 0.162458i
\(731\) 18.3900 0.680180
\(732\) 18.6994 0.691148
\(733\) 9.05895i 0.334600i −0.985906 0.167300i \(-0.946495\pi\)
0.985906 0.167300i \(-0.0535048\pi\)
\(734\) 1.79638i 0.0663056i
\(735\) 0 0
\(736\) 1.99796i 0.0736458i
\(737\) 5.87837 0.216533
\(738\) −2.18143 −0.0802995
\(739\) 7.07843i 0.260384i 0.991489 + 0.130192i \(0.0415594\pi\)
−0.991489 + 0.130192i \(0.958441\pi\)
\(740\) 21.9310 0.806201
\(741\) 8.77531 5.39966i 0.322369 0.198362i
\(742\) 0 0
\(743\) 14.6779i 0.538479i −0.963073 0.269240i \(-0.913228\pi\)
0.963073 0.269240i \(-0.0867724\pi\)
\(744\) 11.5273 0.422613
\(745\) 4.45367 0.163170
\(746\) 5.40132i 0.197756i
\(747\) 2.31827i 0.0848209i
\(748\) 48.7085i 1.78096i
\(749\) 0 0
\(750\) −5.54848 −0.202602
\(751\) 31.7113 1.15716 0.578580 0.815626i \(-0.303607\pi\)
0.578580 + 0.815626i \(0.303607\pi\)
\(752\) 20.9698i 0.764691i
\(753\) −18.2358 −0.664548
\(754\) 7.30640 4.49581i 0.266083 0.163728i
\(755\) 3.68467 0.134099
\(756\) 0 0
\(757\) 15.5317 0.564510 0.282255 0.959339i \(-0.408918\pi\)
0.282255 + 0.959339i \(0.408918\pi\)
\(758\) −8.36688 −0.303899
\(759\) 4.69594i 0.170452i
\(760\) 3.65839i 0.132704i
\(761\) 0.250369i 0.00907587i −0.999990 0.00453794i \(-0.998556\pi\)
0.999990 0.00453794i \(-0.00144447\pi\)
\(762\) 6.98474i 0.253030i
\(763\) 0 0
\(764\) 25.5961 0.926036
\(765\) 5.43714i 0.196580i
\(766\) −1.26781 −0.0458077
\(767\) 2.61370 1.60827i 0.0943752 0.0580714i
\(768\) 11.4972 0.414869
\(769\) 24.0146i 0.865988i −0.901397 0.432994i \(-0.857457\pi\)
0.901397 0.432994i \(-0.142543\pi\)
\(770\) 0 0
\(771\) −8.50731 −0.306383
\(772\) 35.0625i 1.26193i
\(773\) 30.5062i 1.09723i 0.836074 + 0.548616i \(0.184845\pi\)
−0.836074 + 0.548616i \(0.815155\pi\)
\(774\) 1.22690i 0.0441001i
\(775\) 17.7754i 0.638510i
\(776\) −8.51064 −0.305514
\(777\) 0 0
\(778\) 0.954237i 0.0342110i
\(779\) 14.7865 0.529780
\(780\) 12.2451 7.53469i 0.438443 0.269785i
\(781\) −22.4047 −0.801702
\(782\) 0.777163i 0.0277913i
\(783\) −40.4311 −1.44489
\(784\) 0 0
\(785\) 13.6019i 0.485473i
\(786\) 4.59414i 0.163868i
\(787\) 19.8492i 0.707548i −0.935331 0.353774i \(-0.884898\pi\)
0.935331 0.353774i \(-0.115102\pi\)
\(788\) 5.04149i 0.179596i
\(789\) 25.5686 0.910268
\(790\) 0.0630042 0.00224159
\(791\) 0 0
\(792\) 6.68923 0.237691
\(793\) 12.8092 + 20.8170i 0.454868 + 0.739233i
\(794\) −6.35448 −0.225512
\(795\)