Properties

Label 1050.3.e.e.701.9
Level $1050$
Weight $3$
Character 1050.701
Analytic conductor $28.610$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 701.9
Character \(\chi\) \(=\) 1050.701
Dual form 1050.3.e.e.701.11

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421i q^{2} +(-2.46556 + 1.70910i) q^{3} -2.00000 q^{4} +(2.41703 + 3.48683i) q^{6} -2.64575 q^{7} +2.82843i q^{8} +(3.15796 - 8.42777i) q^{9} +O(q^{10})\) \(q-1.41421i q^{2} +(-2.46556 + 1.70910i) q^{3} -2.00000 q^{4} +(2.41703 + 3.48683i) q^{6} -2.64575 q^{7} +2.82843i q^{8} +(3.15796 - 8.42777i) q^{9} -2.66621i q^{11} +(4.93112 - 3.41820i) q^{12} +5.56242 q^{13} +3.74166i q^{14} +4.00000 q^{16} +18.5525i q^{17} +(-11.9187 - 4.46603i) q^{18} -0.634999 q^{19} +(6.52326 - 4.52185i) q^{21} -3.77058 q^{22} -15.6144i q^{23} +(-4.83406 - 6.97365i) q^{24} -7.86645i q^{26} +(6.61774 + 26.1764i) q^{27} +5.29150 q^{28} -43.3517i q^{29} +13.5411 q^{31} -5.65685i q^{32} +(4.55681 + 6.57369i) q^{33} +26.2372 q^{34} +(-6.31593 + 16.8555i) q^{36} -35.0014 q^{37} +0.898024i q^{38} +(-13.7145 + 9.50672i) q^{39} -15.6116i q^{41} +(-6.39486 - 9.22528i) q^{42} +64.4699 q^{43} +5.33241i q^{44} -22.0820 q^{46} +52.5576i q^{47} +(-9.86224 + 6.83639i) q^{48} +7.00000 q^{49} +(-31.7081 - 45.7423i) q^{51} -11.1248 q^{52} +51.6056i q^{53} +(37.0191 - 9.35890i) q^{54} -7.48331i q^{56} +(1.56563 - 1.08528i) q^{57} -61.3086 q^{58} +32.9384i q^{59} -104.197 q^{61} -19.1501i q^{62} +(-8.35519 + 22.2978i) q^{63} -8.00000 q^{64} +(9.29660 - 6.44430i) q^{66} -113.588 q^{67} -37.1050i q^{68} +(26.6865 + 38.4981i) q^{69} +36.8746i q^{71} +(23.8373 + 8.93207i) q^{72} -144.926 q^{73} +49.4995i q^{74} +1.27000 q^{76} +7.05412i q^{77} +(13.4445 + 19.3952i) q^{78} -57.9487 q^{79} +(-61.0545 - 53.2292i) q^{81} -22.0781 q^{82} +45.0936i q^{83} +(-13.0465 + 9.04370i) q^{84} -91.1742i q^{86} +(74.0924 + 106.886i) q^{87} +7.54117 q^{88} -80.9733i q^{89} -14.7168 q^{91} +31.2287i q^{92} +(-33.3865 + 23.1432i) q^{93} +74.3277 q^{94} +(9.66812 + 13.9473i) q^{96} -96.2255 q^{97} -9.89949i q^{98} +(-22.4702 - 8.41978i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 48 q^{4} - 44 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 48 q^{4} - 44 q^{9} + 96 q^{16} + 80 q^{19} - 28 q^{21} + 224 q^{31} - 128 q^{34} + 88 q^{36} + 92 q^{39} - 144 q^{46} + 168 q^{49} - 284 q^{51} + 144 q^{54} - 192 q^{64} + 224 q^{66} + 152 q^{69} - 160 q^{76} + 72 q^{79} - 212 q^{81} + 56 q^{84} + 168 q^{91} + 128 q^{94} + 876 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) −2.46556 + 1.70910i −0.821853 + 0.569700i
\(4\) −2.00000 −0.500000
\(5\) 0 0
\(6\) 2.41703 + 3.48683i 0.402838 + 0.581138i
\(7\) −2.64575 −0.377964
\(8\) 2.82843i 0.353553i
\(9\) 3.15796 8.42777i 0.350885 0.936419i
\(10\) 0 0
\(11\) 2.66621i 0.242382i −0.992629 0.121191i \(-0.961329\pi\)
0.992629 0.121191i \(-0.0386714\pi\)
\(12\) 4.93112 3.41820i 0.410927 0.284850i
\(13\) 5.56242 0.427878 0.213939 0.976847i \(-0.431371\pi\)
0.213939 + 0.976847i \(0.431371\pi\)
\(14\) 3.74166i 0.267261i
\(15\) 0 0
\(16\) 4.00000 0.250000
\(17\) 18.5525i 1.09132i 0.838005 + 0.545662i \(0.183722\pi\)
−0.838005 + 0.545662i \(0.816278\pi\)
\(18\) −11.9187 4.46603i −0.662148 0.248113i
\(19\) −0.634999 −0.0334210 −0.0167105 0.999860i \(-0.505319\pi\)
−0.0167105 + 0.999860i \(0.505319\pi\)
\(20\) 0 0
\(21\) 6.52326 4.52185i 0.310631 0.215326i
\(22\) −3.77058 −0.171390
\(23\) 15.6144i 0.678885i −0.940627 0.339442i \(-0.889762\pi\)
0.940627 0.339442i \(-0.110238\pi\)
\(24\) −4.83406 6.97365i −0.201419 0.290569i
\(25\) 0 0
\(26\) 7.86645i 0.302556i
\(27\) 6.61774 + 26.1764i 0.245101 + 0.969497i
\(28\) 5.29150 0.188982
\(29\) 43.3517i 1.49489i −0.664325 0.747444i \(-0.731281\pi\)
0.664325 0.747444i \(-0.268719\pi\)
\(30\) 0 0
\(31\) 13.5411 0.436811 0.218406 0.975858i \(-0.429914\pi\)
0.218406 + 0.975858i \(0.429914\pi\)
\(32\) 5.65685i 0.176777i
\(33\) 4.55681 + 6.57369i 0.138085 + 0.199203i
\(34\) 26.2372 0.771683
\(35\) 0 0
\(36\) −6.31593 + 16.8555i −0.175442 + 0.468209i
\(37\) −35.0014 −0.945984 −0.472992 0.881067i \(-0.656826\pi\)
−0.472992 + 0.881067i \(0.656826\pi\)
\(38\) 0.898024i 0.0236322i
\(39\) −13.7145 + 9.50672i −0.351653 + 0.243762i
\(40\) 0 0
\(41\) 15.6116i 0.380770i −0.981710 0.190385i \(-0.939026\pi\)
0.981710 0.190385i \(-0.0609736\pi\)
\(42\) −6.39486 9.22528i −0.152259 0.219649i
\(43\) 64.4699 1.49930 0.749650 0.661835i \(-0.230222\pi\)
0.749650 + 0.661835i \(0.230222\pi\)
\(44\) 5.33241i 0.121191i
\(45\) 0 0
\(46\) −22.0820 −0.480044
\(47\) 52.5576i 1.11825i 0.829084 + 0.559124i \(0.188862\pi\)
−0.829084 + 0.559124i \(0.811138\pi\)
\(48\) −9.86224 + 6.83639i −0.205463 + 0.142425i
\(49\) 7.00000 0.142857
\(50\) 0 0
\(51\) −31.7081 45.7423i −0.621727 0.896908i
\(52\) −11.1248 −0.213939
\(53\) 51.6056i 0.973691i 0.873488 + 0.486846i \(0.161853\pi\)
−0.873488 + 0.486846i \(0.838147\pi\)
\(54\) 37.0191 9.35890i 0.685538 0.173313i
\(55\) 0 0
\(56\) 7.48331i 0.133631i
\(57\) 1.56563 1.08528i 0.0274672 0.0190399i
\(58\) −61.3086 −1.05705
\(59\) 32.9384i 0.558277i 0.960251 + 0.279139i \(0.0900489\pi\)
−0.960251 + 0.279139i \(0.909951\pi\)
\(60\) 0 0
\(61\) −104.197 −1.70815 −0.854077 0.520147i \(-0.825877\pi\)
−0.854077 + 0.520147i \(0.825877\pi\)
\(62\) 19.1501i 0.308872i
\(63\) −8.35519 + 22.2978i −0.132622 + 0.353933i
\(64\) −8.00000 −0.125000
\(65\) 0 0
\(66\) 9.29660 6.44430i 0.140858 0.0976409i
\(67\) −113.588 −1.69535 −0.847673 0.530519i \(-0.821997\pi\)
−0.847673 + 0.530519i \(0.821997\pi\)
\(68\) 37.1050i 0.545662i
\(69\) 26.6865 + 38.4981i 0.386760 + 0.557944i
\(70\) 0 0
\(71\) 36.8746i 0.519361i 0.965695 + 0.259680i \(0.0836172\pi\)
−0.965695 + 0.259680i \(0.916383\pi\)
\(72\) 23.8373 + 8.93207i 0.331074 + 0.124057i
\(73\) −144.926 −1.98529 −0.992645 0.121058i \(-0.961371\pi\)
−0.992645 + 0.121058i \(0.961371\pi\)
\(74\) 49.4995i 0.668912i
\(75\) 0 0
\(76\) 1.27000 0.0167105
\(77\) 7.05412i 0.0916119i
\(78\) 13.4445 + 19.3952i 0.172366 + 0.248656i
\(79\) −57.9487 −0.733528 −0.366764 0.930314i \(-0.619534\pi\)
−0.366764 + 0.930314i \(0.619534\pi\)
\(80\) 0 0
\(81\) −61.0545 53.2292i −0.753760 0.657150i
\(82\) −22.0781 −0.269245
\(83\) 45.0936i 0.543296i 0.962397 + 0.271648i \(0.0875686\pi\)
−0.962397 + 0.271648i \(0.912431\pi\)
\(84\) −13.0465 + 9.04370i −0.155316 + 0.107663i
\(85\) 0 0
\(86\) 91.1742i 1.06016i
\(87\) 74.0924 + 106.886i 0.851637 + 1.22858i
\(88\) 7.54117 0.0856951
\(89\) 80.9733i 0.909813i −0.890539 0.454906i \(-0.849673\pi\)
0.890539 0.454906i \(-0.150327\pi\)
\(90\) 0 0
\(91\) −14.7168 −0.161723
\(92\) 31.2287i 0.339442i
\(93\) −33.3865 + 23.1432i −0.358995 + 0.248851i
\(94\) 74.3277 0.790720
\(95\) 0 0
\(96\) 9.66812 + 13.9473i 0.100710 + 0.145284i
\(97\) −96.2255 −0.992016 −0.496008 0.868318i \(-0.665201\pi\)
−0.496008 + 0.868318i \(0.665201\pi\)
\(98\) 9.89949i 0.101015i
\(99\) −22.4702 8.41978i −0.226971 0.0850483i
\(100\) 0 0
\(101\) 91.9696i 0.910590i 0.890341 + 0.455295i \(0.150466\pi\)
−0.890341 + 0.455295i \(0.849534\pi\)
\(102\) −64.6894 + 44.8420i −0.634210 + 0.439627i
\(103\) 30.6043 0.297129 0.148565 0.988903i \(-0.452535\pi\)
0.148565 + 0.988903i \(0.452535\pi\)
\(104\) 15.7329i 0.151278i
\(105\) 0 0
\(106\) 72.9814 0.688504
\(107\) 190.645i 1.78173i 0.454270 + 0.890864i \(0.349900\pi\)
−0.454270 + 0.890864i \(0.650100\pi\)
\(108\) −13.2355 52.3529i −0.122551 0.484749i
\(109\) −73.9965 −0.678867 −0.339433 0.940630i \(-0.610235\pi\)
−0.339433 + 0.940630i \(0.610235\pi\)
\(110\) 0 0
\(111\) 86.2980 59.8208i 0.777460 0.538927i
\(112\) −10.5830 −0.0944911
\(113\) 128.861i 1.14037i 0.821518 + 0.570183i \(0.193128\pi\)
−0.821518 + 0.570183i \(0.806872\pi\)
\(114\) −1.53481 2.21413i −0.0134633 0.0194222i
\(115\) 0 0
\(116\) 86.7035i 0.747444i
\(117\) 17.5659 46.8788i 0.150136 0.400673i
\(118\) 46.5819 0.394762
\(119\) 49.0853i 0.412482i
\(120\) 0 0
\(121\) 113.891 0.941251
\(122\) 147.357i 1.20785i
\(123\) 26.6817 + 38.4912i 0.216924 + 0.312937i
\(124\) −27.0823 −0.218406
\(125\) 0 0
\(126\) 31.5338 + 11.8160i 0.250268 + 0.0937779i
\(127\) −95.8035 −0.754358 −0.377179 0.926140i \(-0.623106\pi\)
−0.377179 + 0.926140i \(0.623106\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) −158.954 + 110.185i −1.23220 + 0.854150i
\(130\) 0 0
\(131\) 148.465i 1.13332i 0.823952 + 0.566660i \(0.191765\pi\)
−0.823952 + 0.566660i \(0.808235\pi\)
\(132\) −9.11361 13.1474i −0.0690425 0.0996013i
\(133\) 1.68005 0.0126320
\(134\) 160.638i 1.19879i
\(135\) 0 0
\(136\) −52.4744 −0.385842
\(137\) 115.295i 0.841572i −0.907160 0.420786i \(-0.861754\pi\)
0.907160 0.420786i \(-0.138246\pi\)
\(138\) 54.4445 37.7404i 0.394526 0.273481i
\(139\) −95.1005 −0.684176 −0.342088 0.939668i \(-0.611134\pi\)
−0.342088 + 0.939668i \(0.611134\pi\)
\(140\) 0 0
\(141\) −89.8262 129.584i −0.637065 0.919035i
\(142\) 52.1486 0.367244
\(143\) 14.8305i 0.103710i
\(144\) 12.6319 33.7111i 0.0877212 0.234105i
\(145\) 0 0
\(146\) 204.957i 1.40381i
\(147\) −17.2589 + 11.9637i −0.117408 + 0.0813857i
\(148\) 70.0028 0.472992
\(149\) 179.342i 1.20364i −0.798632 0.601820i \(-0.794442\pi\)
0.798632 0.601820i \(-0.205558\pi\)
\(150\) 0 0
\(151\) 45.6621 0.302398 0.151199 0.988503i \(-0.451687\pi\)
0.151199 + 0.988503i \(0.451687\pi\)
\(152\) 1.79605i 0.0118161i
\(153\) 156.356 + 58.5882i 1.02194 + 0.382929i
\(154\) 9.97603 0.0647794
\(155\) 0 0
\(156\) 27.4289 19.0134i 0.175827 0.121881i
\(157\) 223.977 1.42661 0.713303 0.700856i \(-0.247198\pi\)
0.713303 + 0.700856i \(0.247198\pi\)
\(158\) 81.9518i 0.518683i
\(159\) −88.1991 127.237i −0.554711 0.800231i
\(160\) 0 0
\(161\) 41.3117i 0.256594i
\(162\) −75.2774 + 86.3441i −0.464675 + 0.532989i
\(163\) −300.309 −1.84239 −0.921195 0.389102i \(-0.872785\pi\)
−0.921195 + 0.389102i \(0.872785\pi\)
\(164\) 31.2231i 0.190385i
\(165\) 0 0
\(166\) 63.7719 0.384168
\(167\) 125.443i 0.751158i 0.926790 + 0.375579i \(0.122556\pi\)
−0.926790 + 0.375579i \(0.877444\pi\)
\(168\) 12.7897 + 18.4506i 0.0761293 + 0.109825i
\(169\) −138.060 −0.816920
\(170\) 0 0
\(171\) −2.00530 + 5.35163i −0.0117269 + 0.0312961i
\(172\) −128.940 −0.749650
\(173\) 195.635i 1.13084i −0.824804 0.565419i \(-0.808714\pi\)
0.824804 0.565419i \(-0.191286\pi\)
\(174\) 151.160 104.782i 0.868736 0.602198i
\(175\) 0 0
\(176\) 10.6648i 0.0605956i
\(177\) −56.2949 81.2115i −0.318050 0.458822i
\(178\) −114.514 −0.643335
\(179\) 164.110i 0.916815i 0.888742 + 0.458408i \(0.151580\pi\)
−0.888742 + 0.458408i \(0.848420\pi\)
\(180\) 0 0
\(181\) 113.029 0.624468 0.312234 0.950005i \(-0.398923\pi\)
0.312234 + 0.950005i \(0.398923\pi\)
\(182\) 20.8127i 0.114355i
\(183\) 256.905 178.084i 1.40385 0.973135i
\(184\) 44.1641 0.240022
\(185\) 0 0
\(186\) 32.7294 + 47.2156i 0.175964 + 0.253847i
\(187\) 49.4648 0.264518
\(188\) 105.115i 0.559124i
\(189\) −17.5089 69.2563i −0.0926397 0.366436i
\(190\) 0 0
\(191\) 196.398i 1.02826i 0.857711 + 0.514132i \(0.171886\pi\)
−0.857711 + 0.514132i \(0.828114\pi\)
\(192\) 19.7245 13.6728i 0.102732 0.0712124i
\(193\) −282.304 −1.46272 −0.731358 0.681994i \(-0.761113\pi\)
−0.731358 + 0.681994i \(0.761113\pi\)
\(194\) 136.083i 0.701461i
\(195\) 0 0
\(196\) −14.0000 −0.0714286
\(197\) 286.761i 1.45564i −0.685767 0.727821i \(-0.740533\pi\)
0.685767 0.727821i \(-0.259467\pi\)
\(198\) −11.9074 + 31.7776i −0.0601382 + 0.160493i
\(199\) 74.9133 0.376449 0.188224 0.982126i \(-0.439727\pi\)
0.188224 + 0.982126i \(0.439727\pi\)
\(200\) 0 0
\(201\) 280.058 194.133i 1.39333 0.965838i
\(202\) 130.065 0.643884
\(203\) 114.698i 0.565014i
\(204\) 63.4162 + 91.4847i 0.310864 + 0.448454i
\(205\) 0 0
\(206\) 43.2810i 0.210102i
\(207\) −131.594 49.3096i −0.635720 0.238210i
\(208\) 22.2497 0.106970
\(209\) 1.69304i 0.00810066i
\(210\) 0 0
\(211\) −136.746 −0.648083 −0.324042 0.946043i \(-0.605042\pi\)
−0.324042 + 0.946043i \(0.605042\pi\)
\(212\) 103.211i 0.486846i
\(213\) −63.0224 90.9166i −0.295880 0.426838i
\(214\) 269.613 1.25987
\(215\) 0 0
\(216\) −74.0381 + 18.7178i −0.342769 + 0.0866565i
\(217\) −35.8265 −0.165099
\(218\) 104.647i 0.480031i
\(219\) 357.324 247.693i 1.63162 1.13102i
\(220\) 0 0
\(221\) 103.197i 0.466954i
\(222\) −84.5994 122.044i −0.381079 0.549747i
\(223\) 25.8662 0.115992 0.0579959 0.998317i \(-0.481529\pi\)
0.0579959 + 0.998317i \(0.481529\pi\)
\(224\) 14.9666i 0.0668153i
\(225\) 0 0
\(226\) 182.238 0.806361
\(227\) 24.3393i 0.107222i 0.998562 + 0.0536109i \(0.0170730\pi\)
−0.998562 + 0.0536109i \(0.982927\pi\)
\(228\) −3.13126 + 2.17055i −0.0137336 + 0.00951997i
\(229\) 241.018 1.05248 0.526239 0.850336i \(-0.323602\pi\)
0.526239 + 0.850336i \(0.323602\pi\)
\(230\) 0 0
\(231\) −12.0562 17.3923i −0.0521913 0.0752915i
\(232\) 122.617 0.528523
\(233\) 24.9582i 0.107117i −0.998565 0.0535584i \(-0.982944\pi\)
0.998565 0.0535584i \(-0.0170563\pi\)
\(234\) −66.2966 24.8420i −0.283319 0.106162i
\(235\) 0 0
\(236\) 65.8767i 0.279139i
\(237\) 142.876 99.0401i 0.602852 0.417891i
\(238\) −69.4172 −0.291669
\(239\) 240.780i 1.00745i 0.863864 + 0.503725i \(0.168037\pi\)
−0.863864 + 0.503725i \(0.831963\pi\)
\(240\) 0 0
\(241\) −147.382 −0.611543 −0.305771 0.952105i \(-0.598914\pi\)
−0.305771 + 0.952105i \(0.598914\pi\)
\(242\) 161.067i 0.665565i
\(243\) 241.507 + 26.8914i 0.993858 + 0.110664i
\(244\) 208.395 0.854077
\(245\) 0 0
\(246\) 54.4348 37.7336i 0.221280 0.153389i
\(247\) −3.53213 −0.0143001
\(248\) 38.3001i 0.154436i
\(249\) −77.0693 111.181i −0.309515 0.446509i
\(250\) 0 0
\(251\) 387.525i 1.54393i −0.635668 0.771963i \(-0.719275\pi\)
0.635668 0.771963i \(-0.280725\pi\)
\(252\) 16.7104 44.5956i 0.0663110 0.176966i
\(253\) −41.6311 −0.164550
\(254\) 135.487i 0.533412i
\(255\) 0 0
\(256\) 16.0000 0.0625000
\(257\) 11.2525i 0.0437839i −0.999760 0.0218919i \(-0.993031\pi\)
0.999760 0.0218919i \(-0.00696897\pi\)
\(258\) 155.826 + 224.795i 0.603975 + 0.871300i
\(259\) 92.6050 0.357548
\(260\) 0 0
\(261\) −365.358 136.903i −1.39984 0.524533i
\(262\) 209.961 0.801378
\(263\) 308.658i 1.17361i −0.809730 0.586803i \(-0.800386\pi\)
0.809730 0.586803i \(-0.199614\pi\)
\(264\) −18.5932 + 12.8886i −0.0704288 + 0.0488204i
\(265\) 0 0
\(266\) 2.37595i 0.00893214i
\(267\) 138.391 + 199.644i 0.518320 + 0.747732i
\(268\) 227.176 0.847673
\(269\) 198.926i 0.739503i 0.929131 + 0.369751i \(0.120557\pi\)
−0.929131 + 0.369751i \(0.879443\pi\)
\(270\) 0 0
\(271\) −176.341 −0.650706 −0.325353 0.945593i \(-0.605483\pi\)
−0.325353 + 0.945593i \(0.605483\pi\)
\(272\) 74.2101i 0.272831i
\(273\) 36.2851 25.1524i 0.132912 0.0921334i
\(274\) −163.052 −0.595082
\(275\) 0 0
\(276\) −53.3729 76.9962i −0.193380 0.278972i
\(277\) −433.093 −1.56351 −0.781757 0.623583i \(-0.785676\pi\)
−0.781757 + 0.623583i \(0.785676\pi\)
\(278\) 134.492i 0.483786i
\(279\) 42.7624 114.122i 0.153270 0.409038i
\(280\) 0 0
\(281\) 281.134i 1.00048i 0.865887 + 0.500239i \(0.166754\pi\)
−0.865887 + 0.500239i \(0.833246\pi\)
\(282\) −183.259 + 127.033i −0.649856 + 0.450473i
\(283\) 113.795 0.402101 0.201050 0.979581i \(-0.435565\pi\)
0.201050 + 0.979581i \(0.435565\pi\)
\(284\) 73.7492i 0.259680i
\(285\) 0 0
\(286\) −20.9736 −0.0733341
\(287\) 41.3043i 0.143917i
\(288\) −47.6747 17.8641i −0.165537 0.0620283i
\(289\) −55.1959 −0.190989
\(290\) 0 0
\(291\) 237.250 164.459i 0.815291 0.565151i
\(292\) 289.852 0.992645
\(293\) 355.330i 1.21273i −0.795187 0.606365i \(-0.792627\pi\)
0.795187 0.606365i \(-0.207373\pi\)
\(294\) 16.9192 + 24.4078i 0.0575483 + 0.0830197i
\(295\) 0 0
\(296\) 98.9989i 0.334456i
\(297\) 69.7917 17.6443i 0.234989 0.0594083i
\(298\) −253.628 −0.851102
\(299\) 86.8535i 0.290480i
\(300\) 0 0
\(301\) −170.571 −0.566682
\(302\) 64.5759i 0.213828i
\(303\) −157.185 226.756i −0.518763 0.748371i
\(304\) −2.54000 −0.00835525
\(305\) 0 0
\(306\) 82.8562 221.121i 0.270772 0.722618i
\(307\) 404.490 1.31756 0.658778 0.752337i \(-0.271074\pi\)
0.658778 + 0.752337i \(0.271074\pi\)
\(308\) 14.1082i 0.0458059i
\(309\) −75.4567 + 52.3058i −0.244196 + 0.169274i
\(310\) 0 0
\(311\) 530.330i 1.70524i 0.522530 + 0.852621i \(0.324988\pi\)
−0.522530 + 0.852621i \(0.675012\pi\)
\(312\) −26.8891 38.7904i −0.0861829 0.124328i
\(313\) 561.172 1.79288 0.896440 0.443165i \(-0.146144\pi\)
0.896440 + 0.443165i \(0.146144\pi\)
\(314\) 316.751i 1.00876i
\(315\) 0 0
\(316\) 115.897 0.366764
\(317\) 264.560i 0.834574i −0.908775 0.417287i \(-0.862981\pi\)
0.908775 0.417287i \(-0.137019\pi\)
\(318\) −179.940 + 124.732i −0.565849 + 0.392240i
\(319\) −115.585 −0.362334
\(320\) 0 0
\(321\) −325.831 470.046i −1.01505 1.46432i
\(322\) 58.4236 0.181440
\(323\) 11.7808i 0.0364732i
\(324\) 122.109 + 106.458i 0.376880 + 0.328575i
\(325\) 0 0
\(326\) 424.702i 1.30277i
\(327\) 182.443 126.467i 0.557929 0.386750i
\(328\) 44.1561 0.134622
\(329\) 139.054i 0.422658i
\(330\) 0 0
\(331\) 540.436 1.63274 0.816369 0.577530i \(-0.195984\pi\)
0.816369 + 0.577530i \(0.195984\pi\)
\(332\) 90.1871i 0.271648i
\(333\) −110.533 + 294.984i −0.331931 + 0.885837i
\(334\) 177.404 0.531149
\(335\) 0 0
\(336\) 26.0930 18.0874i 0.0776578 0.0538315i
\(337\) 444.323 1.31847 0.659233 0.751939i \(-0.270881\pi\)
0.659233 + 0.751939i \(0.270881\pi\)
\(338\) 195.246i 0.577650i
\(339\) −220.237 317.715i −0.649666 0.937214i
\(340\) 0 0
\(341\) 36.1035i 0.105875i
\(342\) 7.56834 + 2.83593i 0.0221297 + 0.00829219i
\(343\) −18.5203 −0.0539949
\(344\) 182.348i 0.530082i
\(345\) 0 0
\(346\) −276.670 −0.799624
\(347\) 253.956i 0.731861i −0.930642 0.365931i \(-0.880751\pi\)
0.930642 0.365931i \(-0.119249\pi\)
\(348\) −148.185 213.773i −0.425818 0.614289i
\(349\) −415.627 −1.19091 −0.595454 0.803389i \(-0.703028\pi\)
−0.595454 + 0.803389i \(0.703028\pi\)
\(350\) 0 0
\(351\) 36.8106 + 145.604i 0.104874 + 0.414827i
\(352\) −15.0823 −0.0428475
\(353\) 278.041i 0.787652i 0.919185 + 0.393826i \(0.128849\pi\)
−0.919185 + 0.393826i \(0.871151\pi\)
\(354\) −114.850 + 79.6130i −0.324436 + 0.224895i
\(355\) 0 0
\(356\) 161.947i 0.454906i
\(357\) 83.8917 + 121.023i 0.234991 + 0.339000i
\(358\) 232.086 0.648286
\(359\) 81.6150i 0.227340i 0.993519 + 0.113670i \(0.0362606\pi\)
−0.993519 + 0.113670i \(0.963739\pi\)
\(360\) 0 0
\(361\) −360.597 −0.998883
\(362\) 159.847i 0.441565i
\(363\) −280.806 + 194.652i −0.773570 + 0.536230i
\(364\) 29.4335 0.0808614
\(365\) 0 0
\(366\) −251.848 363.318i −0.688110 0.992673i
\(367\) −514.501 −1.40191 −0.700955 0.713206i \(-0.747242\pi\)
−0.700955 + 0.713206i \(0.747242\pi\)
\(368\) 62.4574i 0.169721i
\(369\) −131.571 49.3007i −0.356560 0.133606i
\(370\) 0 0
\(371\) 136.536i 0.368021i
\(372\) 66.7730 46.2863i 0.179497 0.124426i
\(373\) −80.1359 −0.214842 −0.107421 0.994214i \(-0.534259\pi\)
−0.107421 + 0.994214i \(0.534259\pi\)
\(374\) 69.9538i 0.187042i
\(375\) 0 0
\(376\) −148.655 −0.395360
\(377\) 241.140i 0.639630i
\(378\) −97.9432 + 24.7613i −0.259109 + 0.0655061i
\(379\) −706.877 −1.86511 −0.932556 0.361026i \(-0.882427\pi\)
−0.932556 + 0.361026i \(0.882427\pi\)
\(380\) 0 0
\(381\) 236.209 163.738i 0.619972 0.429758i
\(382\) 277.749 0.727092
\(383\) 49.2802i 0.128669i −0.997928 0.0643345i \(-0.979508\pi\)
0.997928 0.0643345i \(-0.0204924\pi\)
\(384\) −19.3362 27.8946i −0.0503548 0.0726422i
\(385\) 0 0
\(386\) 399.238i 1.03430i
\(387\) 203.594 543.337i 0.526081 1.40397i
\(388\) 192.451 0.496008
\(389\) 2.68340i 0.00689821i −0.999994 0.00344911i \(-0.998902\pi\)
0.999994 0.00344911i \(-0.00109789\pi\)
\(390\) 0 0
\(391\) 289.686 0.740884
\(392\) 19.7990i 0.0505076i
\(393\) −253.741 366.049i −0.645652 0.931423i
\(394\) −405.542 −1.02929
\(395\) 0 0
\(396\) 44.9403 + 16.8396i 0.113486 + 0.0425241i
\(397\) −372.015 −0.937065 −0.468532 0.883446i \(-0.655217\pi\)
−0.468532 + 0.883446i \(0.655217\pi\)
\(398\) 105.943i 0.266190i
\(399\) −4.14226 + 2.87137i −0.0103816 + 0.00719642i
\(400\) 0 0
\(401\) 119.122i 0.297062i 0.988908 + 0.148531i \(0.0474545\pi\)
−0.988908 + 0.148531i \(0.952545\pi\)
\(402\) −274.546 396.062i −0.682950 0.985230i
\(403\) 75.3215 0.186902
\(404\) 183.939i 0.455295i
\(405\) 0 0
\(406\) 162.207 0.399525
\(407\) 93.3209i 0.229290i
\(408\) 129.379 89.6840i 0.317105 0.219814i
\(409\) −198.033 −0.484189 −0.242095 0.970253i \(-0.577834\pi\)
−0.242095 + 0.970253i \(0.577834\pi\)
\(410\) 0 0
\(411\) 197.051 + 284.268i 0.479443 + 0.691649i
\(412\) −61.2086 −0.148565
\(413\) 87.1467i 0.211009i
\(414\) −69.7342 + 186.102i −0.168440 + 0.449522i
\(415\) 0 0
\(416\) 31.4658i 0.0756389i
\(417\) 234.476 162.536i 0.562292 0.389775i
\(418\) 2.39432 0.00572803
\(419\) 229.736i 0.548295i −0.961688 0.274148i \(-0.911604\pi\)
0.961688 0.274148i \(-0.0883957\pi\)
\(420\) 0 0
\(421\) −590.500 −1.40261 −0.701306 0.712860i \(-0.747399\pi\)
−0.701306 + 0.712860i \(0.747399\pi\)
\(422\) 193.387i 0.458264i
\(423\) 442.944 + 165.975i 1.04715 + 0.392376i
\(424\) −145.963 −0.344252
\(425\) 0 0
\(426\) −128.575 + 89.1271i −0.301820 + 0.209219i
\(427\) 275.680 0.645622
\(428\) 381.290i 0.890864i
\(429\) 25.3469 + 36.5656i 0.0590836 + 0.0852345i
\(430\) 0 0
\(431\) 414.879i 0.962597i −0.876557 0.481298i \(-0.840165\pi\)
0.876557 0.481298i \(-0.159835\pi\)
\(432\) 26.4710 + 104.706i 0.0612754 + 0.242374i
\(433\) 219.764 0.507538 0.253769 0.967265i \(-0.418330\pi\)
0.253769 + 0.967265i \(0.418330\pi\)
\(434\) 50.6663i 0.116743i
\(435\) 0 0
\(436\) 147.993 0.339433
\(437\) 9.91510i 0.0226890i
\(438\) −350.291 505.333i −0.799751 1.15373i
\(439\) 638.375 1.45416 0.727079 0.686554i \(-0.240877\pi\)
0.727079 + 0.686554i \(0.240877\pi\)
\(440\) 0 0
\(441\) 22.1057 58.9944i 0.0501264 0.133774i
\(442\) 145.942 0.330186
\(443\) 299.160i 0.675305i 0.941271 + 0.337652i \(0.109633\pi\)
−0.941271 + 0.337652i \(0.890367\pi\)
\(444\) −172.596 + 119.642i −0.388730 + 0.269463i
\(445\) 0 0
\(446\) 36.5803i 0.0820185i
\(447\) 306.514 + 442.179i 0.685713 + 0.989216i
\(448\) 21.1660 0.0472456
\(449\) 580.653i 1.29321i 0.762823 + 0.646607i \(0.223813\pi\)
−0.762823 + 0.646607i \(0.776187\pi\)
\(450\) 0 0
\(451\) −41.6236 −0.0922918
\(452\) 257.723i 0.570183i
\(453\) −112.583 + 78.0410i −0.248527 + 0.172276i
\(454\) 34.4210 0.0758172
\(455\) 0 0
\(456\) 3.06962 + 4.42826i 0.00673163 + 0.00971111i
\(457\) −563.314 −1.23264 −0.616318 0.787498i \(-0.711376\pi\)
−0.616318 + 0.787498i \(0.711376\pi\)
\(458\) 340.850i 0.744215i
\(459\) −485.639 + 122.776i −1.05804 + 0.267485i
\(460\) 0 0
\(461\) 138.227i 0.299842i 0.988698 + 0.149921i \(0.0479020\pi\)
−0.988698 + 0.149921i \(0.952098\pi\)
\(462\) −24.5965 + 17.0500i −0.0532391 + 0.0369048i
\(463\) −154.802 −0.334346 −0.167173 0.985928i \(-0.553464\pi\)
−0.167173 + 0.985928i \(0.553464\pi\)
\(464\) 173.407i 0.373722i
\(465\) 0 0
\(466\) −35.2963 −0.0757431
\(467\) 462.873i 0.991162i −0.868562 0.495581i \(-0.834955\pi\)
0.868562 0.495581i \(-0.165045\pi\)
\(468\) −35.1318 + 93.7575i −0.0750680 + 0.200337i
\(469\) 300.526 0.640781
\(470\) 0 0
\(471\) −552.229 + 382.799i −1.17246 + 0.812737i
\(472\) −93.1637 −0.197381
\(473\) 171.890i 0.363404i
\(474\) −140.064 202.057i −0.295493 0.426281i
\(475\) 0 0
\(476\) 98.1707i 0.206241i
\(477\) 434.920 + 162.969i 0.911782 + 0.341653i
\(478\) 340.515 0.712374
\(479\) 836.942i 1.74727i 0.486582 + 0.873635i \(0.338243\pi\)
−0.486582 + 0.873635i \(0.661757\pi\)
\(480\) 0 0
\(481\) −194.692 −0.404766
\(482\) 208.429i 0.432426i
\(483\) −70.6058 101.856i −0.146182 0.210883i
\(484\) −227.783 −0.470625
\(485\) 0 0
\(486\) 38.0302 341.543i 0.0782515 0.702764i
\(487\) 212.042 0.435405 0.217703 0.976015i \(-0.430144\pi\)
0.217703 + 0.976015i \(0.430144\pi\)
\(488\) 294.715i 0.603924i
\(489\) 740.431 513.258i 1.51417 1.04961i
\(490\) 0 0
\(491\) 79.1998i 0.161303i −0.996742 0.0806516i \(-0.974300\pi\)
0.996742 0.0806516i \(-0.0257001\pi\)
\(492\) −53.3634 76.9824i −0.108462 0.156468i
\(493\) 804.284 1.63141
\(494\) 4.99519i 0.0101117i
\(495\) 0 0
\(496\) 54.1646 0.109203
\(497\) 97.5611i 0.196300i
\(498\) −157.233 + 108.992i −0.315730 + 0.218860i
\(499\) 259.432 0.519905 0.259952 0.965621i \(-0.416293\pi\)
0.259952 + 0.965621i \(0.416293\pi\)
\(500\) 0 0
\(501\) −214.395 309.288i −0.427934 0.617341i
\(502\) −548.044 −1.09172
\(503\) 175.890i 0.349683i 0.984597 + 0.174841i \(0.0559412\pi\)
−0.984597 + 0.174841i \(0.944059\pi\)
\(504\) −63.0676 23.6320i −0.125134 0.0468890i
\(505\) 0 0
\(506\) 58.8752i 0.116354i
\(507\) 340.394 235.957i 0.671388 0.465399i
\(508\) 191.607 0.377179
\(509\) 577.094i 1.13378i −0.823794 0.566890i \(-0.808147\pi\)
0.823794 0.566890i \(-0.191853\pi\)
\(510\) 0 0
\(511\) 383.439 0.750369
\(512\) 22.6274i 0.0441942i
\(513\) −4.20226 16.6220i −0.00819154 0.0324016i
\(514\) −15.9134 −0.0309599
\(515\) 0 0
\(516\) 317.909 220.371i 0.616102 0.427075i
\(517\) 140.129 0.271043
\(518\) 130.963i 0.252825i
\(519\) 334.360 + 482.350i 0.644238 + 0.929383i
\(520\) 0 0
\(521\) 198.309i 0.380631i −0.981723 0.190316i \(-0.939049\pi\)
0.981723 0.190316i \(-0.0609512\pi\)
\(522\) −193.610 + 516.695i −0.370901 + 0.989837i
\(523\) −307.722 −0.588378 −0.294189 0.955747i \(-0.595049\pi\)
−0.294189 + 0.955747i \(0.595049\pi\)
\(524\) 296.930i 0.566660i
\(525\) 0 0
\(526\) −436.509 −0.829864
\(527\) 251.222i 0.476703i
\(528\) 18.2272 + 26.2947i 0.0345213 + 0.0498007i
\(529\) 285.192 0.539115
\(530\) 0 0
\(531\) 277.597 + 104.018i 0.522781 + 0.195891i
\(532\) −3.36010 −0.00631598
\(533\) 86.8380i 0.162923i
\(534\) 282.340 195.715i 0.528726 0.366507i
\(535\) 0 0
\(536\) 321.276i 0.599395i
\(537\) −280.480 404.623i −0.522309 0.753487i
\(538\) 281.324 0.522907
\(539\) 18.6634i 0.0346260i
\(540\) 0 0
\(541\) 229.692 0.424569 0.212284 0.977208i \(-0.431910\pi\)
0.212284 + 0.977208i \(0.431910\pi\)
\(542\) 249.384i 0.460118i
\(543\) −278.679 + 193.177i −0.513221 + 0.355759i
\(544\) 104.949 0.192921
\(545\) 0 0
\(546\) −35.5709 51.3148i −0.0651482 0.0939832i
\(547\) −296.031 −0.541191 −0.270596 0.962693i \(-0.587221\pi\)
−0.270596 + 0.962693i \(0.587221\pi\)
\(548\) 230.591i 0.420786i
\(549\) −329.052 + 878.151i −0.599365 + 1.59955i
\(550\) 0 0
\(551\) 27.5283i 0.0499606i
\(552\) −108.889 + 75.4807i −0.197263 + 0.136740i
\(553\) 153.318 0.277247
\(554\) 612.487i 1.10557i
\(555\) 0 0
\(556\) 190.201 0.342088
\(557\) 659.047i 1.18321i 0.806228 + 0.591604i \(0.201505\pi\)
−0.806228 + 0.591604i \(0.798495\pi\)
\(558\) −161.392 60.4752i −0.289234 0.108379i
\(559\) 358.608 0.641518
\(560\) 0 0
\(561\) −121.958 + 84.5403i −0.217395 + 0.150696i
\(562\) 397.584 0.707444
\(563\) 1041.64i 1.85016i 0.379774 + 0.925079i \(0.376002\pi\)
−0.379774 + 0.925079i \(0.623998\pi\)
\(564\) 179.652 + 259.168i 0.318533 + 0.459518i
\(565\) 0 0
\(566\) 160.930i 0.284328i
\(567\) 161.535 + 140.831i 0.284894 + 0.248379i
\(568\) −104.297 −0.183622
\(569\) 143.782i 0.252692i −0.991986 0.126346i \(-0.959675\pi\)
0.991986 0.126346i \(-0.0403250\pi\)
\(570\) 0 0
\(571\) 198.901 0.348337 0.174169 0.984716i \(-0.444276\pi\)
0.174169 + 0.984716i \(0.444276\pi\)
\(572\) 29.6611i 0.0518551i
\(573\) −335.664 484.232i −0.585801 0.845082i
\(574\) 58.4131 0.101765
\(575\) 0 0
\(576\) −25.2637 + 67.4221i −0.0438606 + 0.117052i
\(577\) −55.7825 −0.0966767 −0.0483384 0.998831i \(-0.515393\pi\)
−0.0483384 + 0.998831i \(0.515393\pi\)
\(578\) 78.0588i 0.135050i
\(579\) 696.037 482.486i 1.20214 0.833308i
\(580\) 0 0
\(581\) 119.306i 0.205347i
\(582\) −232.580 335.522i −0.399622 0.576498i
\(583\) 137.591 0.236005
\(584\) 409.913i 0.701906i
\(585\) 0 0
\(586\) −502.512 −0.857529
\(587\) 679.045i 1.15681i −0.815751 0.578403i \(-0.803676\pi\)
0.815751 0.578403i \(-0.196324\pi\)
\(588\) 34.5178 23.9274i 0.0587038 0.0406928i
\(589\) −8.59862 −0.0145987
\(590\) 0 0
\(591\) 490.104 + 707.027i 0.829278 + 1.19632i
\(592\) −140.006 −0.236496
\(593\) 794.933i 1.34053i 0.742123 + 0.670264i \(0.233819\pi\)
−0.742123 + 0.670264i \(0.766181\pi\)
\(594\) −24.9527 98.7004i −0.0420080 0.166162i
\(595\) 0 0
\(596\) 358.685i 0.601820i
\(597\) −184.703 + 128.034i −0.309386 + 0.214463i
\(598\) −122.829 −0.205400
\(599\) 525.925i 0.878004i 0.898486 + 0.439002i \(0.144668\pi\)
−0.898486 + 0.439002i \(0.855332\pi\)
\(600\) 0 0
\(601\) 169.552 0.282116 0.141058 0.990001i \(-0.454950\pi\)
0.141058 + 0.990001i \(0.454950\pi\)
\(602\) 241.224i 0.400705i
\(603\) −358.707 + 957.295i −0.594871 + 1.58755i
\(604\) −91.3242 −0.151199
\(605\) 0 0
\(606\) −320.682 + 222.293i −0.529178 + 0.366821i
\(607\) −29.1399 −0.0480064 −0.0240032 0.999712i \(-0.507641\pi\)
−0.0240032 + 0.999712i \(0.507641\pi\)
\(608\) 3.59210i 0.00590806i
\(609\) −196.030 282.794i −0.321888 0.464359i
\(610\) 0 0
\(611\) 292.348i 0.478474i
\(612\) −312.713 117.176i −0.510968 0.191465i
\(613\) 167.118 0.272623 0.136311 0.990666i \(-0.456475\pi\)
0.136311 + 0.990666i \(0.456475\pi\)
\(614\) 572.035i 0.931653i
\(615\) 0 0
\(616\) −19.9521 −0.0323897
\(617\) 872.471i 1.41405i 0.707187 + 0.707027i \(0.249964\pi\)
−0.707187 + 0.707027i \(0.750036\pi\)
\(618\) 73.9715 + 106.712i 0.119695 + 0.172673i
\(619\) 852.170 1.37669 0.688344 0.725384i \(-0.258338\pi\)
0.688344 + 0.725384i \(0.258338\pi\)
\(620\) 0 0
\(621\) 408.728 103.332i 0.658177 0.166396i
\(622\) 750.000 1.20579
\(623\) 214.235i 0.343877i
\(624\) −54.8579 + 38.0269i −0.0879133 + 0.0609405i
\(625\) 0 0
\(626\) 793.616i 1.26776i
\(627\) −2.89357 4.17429i −0.00461494 0.00665755i
\(628\) −447.954 −0.713303
\(629\) 649.364i 1.03238i
\(630\) 0 0
\(631\) 550.448 0.872343 0.436171 0.899864i \(-0.356334\pi\)
0.436171 + 0.899864i \(0.356334\pi\)
\(632\) 163.904i 0.259341i
\(633\) 337.154 233.712i 0.532629 0.369213i
\(634\) −374.144 −0.590133
\(635\) 0 0
\(636\) 176.398 + 254.473i 0.277356 + 0.400115i
\(637\) 38.9369 0.0611255
\(638\) 163.461i 0.256209i
\(639\) 310.771 + 116.449i 0.486339 + 0.182236i
\(640\) 0 0
\(641\) 56.3780i 0.0879532i 0.999033 + 0.0439766i \(0.0140027\pi\)
−0.999033 + 0.0439766i \(0.985997\pi\)
\(642\) −664.746 + 460.795i −1.03543 + 0.717749i
\(643\) −934.856 −1.45390 −0.726948 0.686692i \(-0.759062\pi\)
−0.726948 + 0.686692i \(0.759062\pi\)
\(644\) 82.6234i 0.128297i
\(645\) 0 0
\(646\) −16.6606 −0.0257904
\(647\) 523.120i 0.808532i 0.914641 + 0.404266i \(0.132473\pi\)
−0.914641 + 0.404266i \(0.867527\pi\)
\(648\) 150.555 172.688i 0.232338 0.266494i
\(649\) 87.8204 0.135316
\(650\) 0 0
\(651\) 88.3324 61.2310i 0.135687 0.0940569i
\(652\) 600.619 0.921195
\(653\) 629.201i 0.963554i −0.876294 0.481777i \(-0.839992\pi\)
0.876294 0.481777i \(-0.160008\pi\)
\(654\) −178.852 258.013i −0.273474 0.394515i
\(655\) 0 0
\(656\) 62.4462i 0.0951924i
\(657\) −457.672 + 1221.40i −0.696608 + 1.85906i
\(658\) −196.653 −0.298864
\(659\) 1205.86i 1.82983i 0.403644 + 0.914916i \(0.367743\pi\)
−0.403644 + 0.914916i \(0.632257\pi\)
\(660\) 0 0
\(661\) 421.451 0.637596 0.318798 0.947823i \(-0.396721\pi\)
0.318798 + 0.947823i \(0.396721\pi\)
\(662\) 764.292i 1.15452i
\(663\) −176.374 254.438i −0.266024 0.383768i
\(664\) −127.544 −0.192084
\(665\) 0 0
\(666\) 417.170 + 156.317i 0.626381 + 0.234711i
\(667\) −676.909 −1.01486
\(668\) 250.887i 0.375579i
\(669\) −63.7745 + 44.2078i −0.0953281 + 0.0660804i
\(670\) 0 0
\(671\) 277.812i 0.414026i
\(672\) −25.5794 36.9011i −0.0380647 0.0549124i
\(673\) −208.482 −0.309779 −0.154890 0.987932i \(-0.549502\pi\)
−0.154890 + 0.987932i \(0.549502\pi\)
\(674\) 628.368i 0.932297i
\(675\) 0 0
\(676\) 276.119 0.408460
\(677\) 1253.11i 1.85097i 0.378784 + 0.925485i \(0.376342\pi\)
−0.378784 + 0.925485i \(0.623658\pi\)
\(678\) −449.317 + 311.462i −0.662710 + 0.459383i
\(679\) 254.589 0.374947
\(680\) 0 0
\(681\) −41.5983 60.0101i −0.0610842 0.0881205i
\(682\) −51.0580 −0.0748651
\(683\) 982.114i 1.43794i −0.695041 0.718971i \(-0.744614\pi\)
0.695041 0.718971i \(-0.255386\pi\)
\(684\) 4.01061 10.7033i 0.00586346 0.0156480i
\(685\) 0 0
\(686\) 26.1916i 0.0381802i
\(687\) −594.243 + 411.923i −0.864983 + 0.599597i
\(688\) 257.880 0.374825
\(689\) 287.052i 0.416621i
\(690\) 0 0
\(691\) 204.605 0.296099 0.148050 0.988980i \(-0.452700\pi\)
0.148050 + 0.988980i \(0.452700\pi\)
\(692\) 391.270i 0.565419i
\(693\) 59.4504 + 22.2766i 0.0857871 + 0.0321452i
\(694\) −359.148 −0.517504
\(695\) 0 0
\(696\) −302.320 + 209.565i −0.434368 + 0.301099i
\(697\) 289.634 0.415543
\(698\) 587.785i 0.842099i
\(699\) 42.6561 + 61.5360i 0.0610244 + 0.0880343i
\(700\) 0 0
\(701\) 330.503i 0.471473i 0.971817 + 0.235736i \(0.0757502\pi\)
−0.971817 + 0.235736i \(0.924250\pi\)
\(702\) 205.915 52.0581i 0.293327 0.0741568i
\(703\) 22.2259 0.0316157
\(704\) 21.3296i 0.0302978i
\(705\) 0 0
\(706\) 393.210 0.556954
\(707\) 243.329i 0.344171i
\(708\) 112.590 + 162.423i 0.159025 + 0.229411i
\(709\) −265.328 −0.374229 −0.187114 0.982338i \(-0.559914\pi\)
−0.187114 + 0.982338i \(0.559914\pi\)
\(710\) 0 0
\(711\) −183.000 + 488.378i −0.257384 + 0.686889i
\(712\) 229.027 0.321667
\(713\) 211.436i 0.296544i
\(714\) 171.152 118.641i 0.239709 0.166164i
\(715\) 0 0
\(716\) 328.220i 0.458408i
\(717\) −411.517 593.658i −0.573943 0.827975i
\(718\) 115.421 0.160754
\(719\) 994.084i 1.38259i −0.722572 0.691296i \(-0.757040\pi\)
0.722572 0.691296i \(-0.242960\pi\)
\(720\) 0 0
\(721\) −80.9713 −0.112304
\(722\) 509.961i 0.706317i
\(723\) 363.379 251.890i 0.502598 0.348396i
\(724\) −226.057 −0.312234
\(725\) 0 0
\(726\) 275.279 + 397.119i 0.379172 + 0.546996i
\(727\) −1244.89 −1.71236 −0.856182 0.516674i \(-0.827170\pi\)
−0.856182 + 0.516674i \(0.827170\pi\)
\(728\) 41.6253i 0.0571776i
\(729\) −641.411 + 346.458i −0.879851 + 0.475251i
\(730\) 0 0
\(731\) 1196.08i 1.63622i
\(732\) −513.810 + 356.167i −0.701926 + 0.486567i
\(733\) −822.707 −1.12238 −0.561192 0.827686i \(-0.689657\pi\)
−0.561192 + 0.827686i \(0.689657\pi\)
\(734\) 727.614i 0.991300i
\(735\) 0 0
\(736\) −88.3281 −0.120011
\(737\) 302.849i 0.410922i
\(738\) −69.7217 + 186.069i −0.0944739 + 0.252126i
\(739\) 550.154 0.744458 0.372229 0.928141i \(-0.378594\pi\)
0.372229 + 0.928141i \(0.378594\pi\)
\(740\) 0 0
\(741\) 8.70868 6.03676i 0.0117526 0.00814677i
\(742\) −193.091 −0.260230
\(743\) 356.858i 0.480293i −0.970737 0.240147i \(-0.922805\pi\)
0.970737 0.240147i \(-0.0771955\pi\)
\(744\) −65.4587 94.4313i −0.0879821 0.126924i
\(745\) 0 0
\(746\) 113.329i 0.151916i
\(747\) 380.038 + 142.404i 0.508752 + 0.190634i
\(748\) −98.9296 −0.132259
\(749\) 504.399i 0.673430i
\(750\) 0 0
\(751\) 1027.14 1.36770 0.683850 0.729623i \(-0.260304\pi\)
0.683850 + 0.729623i \(0.260304\pi\)
\(752\) 210.231i 0.279562i
\(753\) 662.319 + 955.467i 0.879574 + 1.26888i
\(754\) −341.024 −0.452287
\(755\) 0 0
\(756\) 35.0178 + 138.513i 0.0463198 + 0.183218i
\(757\) −799.336 −1.05593 −0.527963 0.849267i \(-0.677044\pi\)
−0.527963 + 0.849267i \(0.677044\pi\)
\(758\) 999.675i 1.31883i
\(759\) 102.644 71.1516i 0.135236 0.0937439i
\(760\) 0 0
\(761\) 799.993i 1.05124i −0.850720 0.525619i \(-0.823834\pi\)
0.850720 0.525619i \(-0.176166\pi\)
\(762\) −231.560 334.050i −0.303884 0.438386i
\(763\) 195.776 0.256588
\(764\) 392.797i 0.514132i
\(765\) 0 0
\(766\) −69.6927 −0.0909827
\(767\) 183.217i 0.238875i
\(768\) −39.4489 + 27.3456i −0.0513658 + 0.0356062i
\(769\) 1066.44 1.38679 0.693393 0.720560i \(-0.256115\pi\)
0.693393 + 0.720560i \(0.256115\pi\)
\(770\) 0 0
\(771\) 19.2315 + 27.7436i 0.0249436 + 0.0359839i
\(772\) 564.608 0.731358
\(773\) 10.9234i 0.0141311i 0.999975 + 0.00706557i \(0.00224906\pi\)
−0.999975 + 0.00706557i \(0.997751\pi\)
\(774\) −768.395 287.925i −0.992758 0.371996i
\(775\) 0 0
\(776\) 272.167i 0.350731i
\(777\) −228.323 + 158.271i −0.293852 + 0.203695i
\(778\) −3.79491 −0.00487777
\(779\) 9.91332i 0.0127257i
\(780\) 0 0
\(781\) 98.3153 0.125884
\(782\) 409.677i 0.523884i
\(783\) 1134.79 286.891i 1.44929 0.366399i
\(784\) 28.0000 0.0357143
\(785\) 0 0
\(786\) −517.672 + 358.844i −0.658615 + 0.456545i
\(787\) 741.962 0.942772 0.471386 0.881927i \(-0.343754\pi\)
0.471386 + 0.881927i \(0.343754\pi\)
\(788\) 573.523i 0.727821i
\(789\) 527.527 + 761.015i 0.668602 + 0.964531i