Properties

Label 1110.2.h.f.961.5
Level $1110$
Weight $2$
Character 1110.961
Analytic conductor $8.863$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.279290944.1
Defining polynomial: \(x^{6} + 26 x^{4} + 169 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{37}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 961.5
Root \(0.309984i\) of defining polynomial
Character \(\chi\) \(=\) 1110.961
Dual form 1110.2.h.f.961.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} +1.00000i q^{5} +1.00000i q^{6} -1.30998 q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} +1.00000i q^{5} +1.00000i q^{6} -1.30998 q^{7} -1.00000i q^{8} +1.00000 q^{9} -1.00000 q^{10} +0.690016 q^{11} -1.00000 q^{12} -2.69002i q^{13} -1.30998i q^{14} +1.00000i q^{15} +1.00000 q^{16} +6.90391i q^{17} +1.00000i q^{18} +2.69002i q^{19} -1.00000i q^{20} -1.30998 q^{21} +0.690016i q^{22} +8.90391i q^{23} -1.00000i q^{24} -1.00000 q^{25} +2.69002 q^{26} +1.00000 q^{27} +1.30998 q^{28} -2.00000i q^{29} -1.00000 q^{30} +9.59393i q^{31} +1.00000i q^{32} +0.690016 q^{33} -6.90391 q^{34} -1.30998i q^{35} -1.00000 q^{36} +(4.10695 + 4.48698i) q^{37} -2.69002 q^{38} -2.69002i q^{39} +1.00000 q^{40} -2.00000 q^{41} -1.30998i q^{42} -8.21389i q^{43} -0.690016 q^{44} +1.00000i q^{45} -8.90391 q^{46} -4.61997 q^{47} +1.00000 q^{48} -5.28394 q^{49} -1.00000i q^{50} +6.90391i q^{51} +2.69002i q^{52} +0.690016 q^{53} +1.00000i q^{54} +0.690016i q^{55} +1.30998i q^{56} +2.69002i q^{57} +2.00000 q^{58} -6.21389i q^{59} -1.00000i q^{60} -2.00000i q^{61} -9.59393 q^{62} -1.30998 q^{63} -1.00000 q^{64} +2.69002 q^{65} +0.690016i q^{66} -1.23993 q^{67} -6.90391i q^{68} +8.90391i q^{69} +1.30998 q^{70} +13.8078 q^{71} -1.00000i q^{72} -12.2839 q^{73} +(-4.48698 + 4.10695i) q^{74} -1.00000 q^{75} -2.69002i q^{76} -0.903910 q^{77} +2.69002 q^{78} -1.59393i q^{79} +1.00000i q^{80} +1.00000 q^{81} -2.00000i q^{82} +10.2839 q^{83} +1.30998 q^{84} -6.90391 q^{85} +8.21389 q^{86} -2.00000i q^{87} -0.690016i q^{88} +5.92995i q^{89} -1.00000 q^{90} +3.52388i q^{91} -8.90391i q^{92} +9.59393i q^{93} -4.61997i q^{94} -2.69002 q^{95} +1.00000i q^{96} +3.38003i q^{97} -5.28394i q^{98} +0.690016 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 6q^{3} - 6q^{4} - 6q^{7} + 6q^{9} + O(q^{10}) \) \( 6q + 6q^{3} - 6q^{4} - 6q^{7} + 6q^{9} - 6q^{10} + 6q^{11} - 6q^{12} + 6q^{16} - 6q^{21} - 6q^{25} + 18q^{26} + 6q^{27} + 6q^{28} - 6q^{30} + 6q^{33} + 10q^{34} - 6q^{36} - 2q^{37} - 18q^{38} + 6q^{40} - 12q^{41} - 6q^{44} - 2q^{46} - 24q^{47} + 6q^{48} + 16q^{49} + 6q^{53} + 12q^{58} - 8q^{62} - 6q^{63} - 6q^{64} + 18q^{65} + 6q^{70} - 20q^{71} - 26q^{73} - 4q^{74} - 6q^{75} + 46q^{77} + 18q^{78} + 6q^{81} + 14q^{83} + 6q^{84} + 10q^{85} - 4q^{86} - 6q^{90} - 18q^{95} + 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.00000 0.577350
\(4\) −1.00000 −0.500000
\(5\) 1.00000i 0.447214i
\(6\) 1.00000i 0.408248i
\(7\) −1.30998 −0.495127 −0.247564 0.968872i \(-0.579630\pi\)
−0.247564 + 0.968872i \(0.579630\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) 0.690016 0.208048 0.104024 0.994575i \(-0.466828\pi\)
0.104024 + 0.994575i \(0.466828\pi\)
\(12\) −1.00000 −0.288675
\(13\) 2.69002i 0.746076i −0.927816 0.373038i \(-0.878316\pi\)
0.927816 0.373038i \(-0.121684\pi\)
\(14\) 1.30998i 0.350108i
\(15\) 1.00000i 0.258199i
\(16\) 1.00000 0.250000
\(17\) 6.90391i 1.67444i 0.546863 + 0.837222i \(0.315822\pi\)
−0.546863 + 0.837222i \(0.684178\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 2.69002i 0.617132i 0.951203 + 0.308566i \(0.0998491\pi\)
−0.951203 + 0.308566i \(0.900151\pi\)
\(20\) 1.00000i 0.223607i
\(21\) −1.30998 −0.285862
\(22\) 0.690016i 0.147112i
\(23\) 8.90391i 1.85659i 0.371840 + 0.928297i \(0.378727\pi\)
−0.371840 + 0.928297i \(0.621273\pi\)
\(24\) 1.00000i 0.204124i
\(25\) −1.00000 −0.200000
\(26\) 2.69002 0.527556
\(27\) 1.00000 0.192450
\(28\) 1.30998 0.247564
\(29\) 2.00000i 0.371391i −0.982607 0.185695i \(-0.940546\pi\)
0.982607 0.185695i \(-0.0594537\pi\)
\(30\) −1.00000 −0.182574
\(31\) 9.59393i 1.72312i 0.507656 + 0.861560i \(0.330512\pi\)
−0.507656 + 0.861560i \(0.669488\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0.690016 0.120116
\(34\) −6.90391 −1.18401
\(35\) 1.30998i 0.221428i
\(36\) −1.00000 −0.166667
\(37\) 4.10695 + 4.48698i 0.675178 + 0.737655i
\(38\) −2.69002 −0.436378
\(39\) 2.69002i 0.430747i
\(40\) 1.00000 0.158114
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 1.30998i 0.202135i
\(43\) 8.21389i 1.25261i −0.779579 0.626304i \(-0.784567\pi\)
0.779579 0.626304i \(-0.215433\pi\)
\(44\) −0.690016 −0.104024
\(45\) 1.00000i 0.149071i
\(46\) −8.90391 −1.31281
\(47\) −4.61997 −0.673891 −0.336946 0.941524i \(-0.609394\pi\)
−0.336946 + 0.941524i \(0.609394\pi\)
\(48\) 1.00000 0.144338
\(49\) −5.28394 −0.754849
\(50\) 1.00000i 0.141421i
\(51\) 6.90391i 0.966741i
\(52\) 2.69002i 0.373038i
\(53\) 0.690016 0.0947810 0.0473905 0.998876i \(-0.484909\pi\)
0.0473905 + 0.998876i \(0.484909\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 0.690016i 0.0930418i
\(56\) 1.30998i 0.175054i
\(57\) 2.69002i 0.356301i
\(58\) 2.00000 0.262613
\(59\) 6.21389i 0.808980i −0.914542 0.404490i \(-0.867449\pi\)
0.914542 0.404490i \(-0.132551\pi\)
\(60\) 1.00000i 0.129099i
\(61\) 2.00000i 0.256074i −0.991769 0.128037i \(-0.959132\pi\)
0.991769 0.128037i \(-0.0408676\pi\)
\(62\) −9.59393 −1.21843
\(63\) −1.30998 −0.165042
\(64\) −1.00000 −0.125000
\(65\) 2.69002 0.333655
\(66\) 0.690016i 0.0849352i
\(67\) −1.23993 −0.151482 −0.0757410 0.997128i \(-0.524132\pi\)
−0.0757410 + 0.997128i \(0.524132\pi\)
\(68\) 6.90391i 0.837222i
\(69\) 8.90391i 1.07190i
\(70\) 1.30998 0.156573
\(71\) 13.8078 1.63869 0.819343 0.573303i \(-0.194338\pi\)
0.819343 + 0.573303i \(0.194338\pi\)
\(72\) 1.00000i 0.117851i
\(73\) −12.2839 −1.43773 −0.718863 0.695151i \(-0.755337\pi\)
−0.718863 + 0.695151i \(0.755337\pi\)
\(74\) −4.48698 + 4.10695i −0.521601 + 0.477423i
\(75\) −1.00000 −0.115470
\(76\) 2.69002i 0.308566i
\(77\) −0.903910 −0.103010
\(78\) 2.69002 0.304584
\(79\) 1.59393i 0.179331i −0.995972 0.0896654i \(-0.971420\pi\)
0.995972 0.0896654i \(-0.0285798\pi\)
\(80\) 1.00000i 0.111803i
\(81\) 1.00000 0.111111
\(82\) 2.00000i 0.220863i
\(83\) 10.2839 1.12881 0.564405 0.825498i \(-0.309106\pi\)
0.564405 + 0.825498i \(0.309106\pi\)
\(84\) 1.30998 0.142931
\(85\) −6.90391 −0.748834
\(86\) 8.21389 0.885727
\(87\) 2.00000i 0.214423i
\(88\) 0.690016i 0.0735560i
\(89\) 5.92995i 0.628574i 0.949328 + 0.314287i \(0.101765\pi\)
−0.949328 + 0.314287i \(0.898235\pi\)
\(90\) −1.00000 −0.105409
\(91\) 3.52388i 0.369403i
\(92\) 8.90391i 0.928297i
\(93\) 9.59393i 0.994844i
\(94\) 4.61997i 0.476513i
\(95\) −2.69002 −0.275990
\(96\) 1.00000i 0.102062i
\(97\) 3.38003i 0.343190i 0.985168 + 0.171595i \(0.0548921\pi\)
−0.985168 + 0.171595i \(0.945108\pi\)
\(98\) 5.28394i 0.533759i
\(99\) 0.690016 0.0693493
\(100\) 1.00000 0.100000
\(101\) 8.97396 0.892942 0.446471 0.894798i \(-0.352681\pi\)
0.446471 + 0.894798i \(0.352681\pi\)
\(102\) −6.90391 −0.683589
\(103\) 19.1879i 1.89064i 0.326151 + 0.945318i \(0.394248\pi\)
−0.326151 + 0.945318i \(0.605752\pi\)
\(104\) −2.69002 −0.263778
\(105\) 1.30998i 0.127841i
\(106\) 0.690016i 0.0670203i
\(107\) 18.1438 1.75403 0.877016 0.480461i \(-0.159531\pi\)
0.877016 + 0.480461i \(0.159531\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 17.5239i 1.67848i −0.543759 0.839242i \(-0.682999\pi\)
0.543759 0.839242i \(-0.317001\pi\)
\(110\) −0.690016 −0.0657905
\(111\) 4.10695 + 4.48698i 0.389814 + 0.425885i
\(112\) −1.30998 −0.123782
\(113\) 2.00000i 0.188144i 0.995565 + 0.0940721i \(0.0299884\pi\)
−0.995565 + 0.0940721i \(0.970012\pi\)
\(114\) −2.69002 −0.251943
\(115\) −8.90391 −0.830294
\(116\) 2.00000i 0.185695i
\(117\) 2.69002i 0.248692i
\(118\) 6.21389 0.572035
\(119\) 9.04401i 0.829063i
\(120\) 1.00000 0.0912871
\(121\) −10.5239 −0.956716
\(122\) 2.00000 0.181071
\(123\) −2.00000 −0.180334
\(124\) 9.59393i 0.861560i
\(125\) 1.00000i 0.0894427i
\(126\) 1.30998i 0.116703i
\(127\) −10.6900 −0.948586 −0.474293 0.880367i \(-0.657296\pi\)
−0.474293 + 0.880367i \(0.657296\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 8.21389i 0.723193i
\(130\) 2.69002i 0.235930i
\(131\) 8.97396i 0.784058i −0.919953 0.392029i \(-0.871773\pi\)
0.919953 0.392029i \(-0.128227\pi\)
\(132\) −0.690016 −0.0600582
\(133\) 3.52388i 0.305559i
\(134\) 1.23993i 0.107114i
\(135\) 1.00000i 0.0860663i
\(136\) 6.90391 0.592005
\(137\) −11.5939 −0.990536 −0.495268 0.868740i \(-0.664930\pi\)
−0.495268 + 0.868740i \(0.664930\pi\)
\(138\) −8.90391 −0.757951
\(139\) −6.76007 −0.573381 −0.286691 0.958023i \(-0.592555\pi\)
−0.286691 + 0.958023i \(0.592555\pi\)
\(140\) 1.30998i 0.110714i
\(141\) −4.61997 −0.389071
\(142\) 13.8078i 1.15873i
\(143\) 1.85616i 0.155220i
\(144\) 1.00000 0.0833333
\(145\) 2.00000 0.166091
\(146\) 12.2839i 1.01663i
\(147\) −5.28394 −0.435812
\(148\) −4.10695 4.48698i −0.337589 0.368827i
\(149\) 10.2139 0.836755 0.418377 0.908273i \(-0.362599\pi\)
0.418377 + 0.908273i \(0.362599\pi\)
\(150\) 1.00000i 0.0816497i
\(151\) 22.2839 1.81344 0.906721 0.421731i \(-0.138577\pi\)
0.906721 + 0.421731i \(0.138577\pi\)
\(152\) 2.69002 0.218189
\(153\) 6.90391i 0.558148i
\(154\) 0.903910i 0.0728392i
\(155\) −9.59393 −0.770603
\(156\) 2.69002i 0.215374i
\(157\) 12.2139 0.974775 0.487387 0.873186i \(-0.337950\pi\)
0.487387 + 0.873186i \(0.337950\pi\)
\(158\) 1.59393 0.126806
\(159\) 0.690016 0.0547219
\(160\) −1.00000 −0.0790569
\(161\) 11.6640i 0.919250i
\(162\) 1.00000i 0.0785674i
\(163\) 6.07005i 0.475443i 0.971333 + 0.237721i \(0.0764006\pi\)
−0.971333 + 0.237721i \(0.923599\pi\)
\(164\) 2.00000 0.156174
\(165\) 0.690016i 0.0537177i
\(166\) 10.2839i 0.798189i
\(167\) 8.90391i 0.689005i −0.938785 0.344503i \(-0.888048\pi\)
0.938785 0.344503i \(-0.111952\pi\)
\(168\) 1.30998i 0.101067i
\(169\) 5.76381 0.443370
\(170\) 6.90391i 0.529506i
\(171\) 2.69002i 0.205711i
\(172\) 8.21389i 0.626304i
\(173\) 19.8779 1.51129 0.755643 0.654983i \(-0.227324\pi\)
0.755643 + 0.654983i \(0.227324\pi\)
\(174\) 2.00000 0.151620
\(175\) 1.30998 0.0990254
\(176\) 0.690016 0.0520119
\(177\) 6.21389i 0.467065i
\(178\) −5.92995 −0.444469
\(179\) 19.5939i 1.46452i −0.681026 0.732259i \(-0.738466\pi\)
0.681026 0.732259i \(-0.261534\pi\)
\(180\) 1.00000i 0.0745356i
\(181\) −9.18785 −0.682928 −0.341464 0.939895i \(-0.610923\pi\)
−0.341464 + 0.939895i \(0.610923\pi\)
\(182\) −3.52388 −0.261207
\(183\) 2.00000i 0.147844i
\(184\) 8.90391 0.656405
\(185\) −4.48698 + 4.10695i −0.329889 + 0.301949i
\(186\) −9.59393 −0.703461
\(187\) 4.76381i 0.348364i
\(188\) 4.61997 0.336946
\(189\) −1.30998 −0.0952873
\(190\) 2.69002i 0.195154i
\(191\) 20.9039i 1.51255i 0.654252 + 0.756277i \(0.272984\pi\)
−0.654252 + 0.756277i \(0.727016\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 8.61997i 0.620479i −0.950658 0.310239i \(-0.899591\pi\)
0.950658 0.310239i \(-0.100409\pi\)
\(194\) −3.38003 −0.242672
\(195\) 2.69002 0.192636
\(196\) 5.28394 0.377425
\(197\) −12.6900 −0.904126 −0.452063 0.891986i \(-0.649312\pi\)
−0.452063 + 0.891986i \(0.649312\pi\)
\(198\) 0.690016i 0.0490373i
\(199\) 22.8339i 1.61865i −0.587361 0.809325i \(-0.699833\pi\)
0.587361 0.809325i \(-0.300167\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) −1.23993 −0.0874582
\(202\) 8.97396i 0.631406i
\(203\) 2.61997i 0.183886i
\(204\) 6.90391i 0.483370i
\(205\) 2.00000i 0.139686i
\(206\) −19.1879 −1.33688
\(207\) 8.90391i 0.618865i
\(208\) 2.69002i 0.186519i
\(209\) 1.85616i 0.128393i
\(210\) 1.30998 0.0903975
\(211\) −5.38003 −0.370377 −0.185188 0.982703i \(-0.559290\pi\)
−0.185188 + 0.982703i \(0.559290\pi\)
\(212\) −0.690016 −0.0473905
\(213\) 13.8078 0.946096
\(214\) 18.1438i 1.24029i
\(215\) 8.21389 0.560183
\(216\) 1.00000i 0.0680414i
\(217\) 12.5679i 0.853164i
\(218\) 17.5239 1.18687
\(219\) −12.2839 −0.830072
\(220\) 0.690016i 0.0465209i
\(221\) 18.5716 1.24926
\(222\) −4.48698 + 4.10695i −0.301146 + 0.275640i
\(223\) −0.833861 −0.0558395 −0.0279197 0.999610i \(-0.508888\pi\)
−0.0279197 + 0.999610i \(0.508888\pi\)
\(224\) 1.30998i 0.0875270i
\(225\) −1.00000 −0.0666667
\(226\) −2.00000 −0.133038
\(227\) 15.1879i 1.00805i 0.863688 + 0.504027i \(0.168149\pi\)
−0.863688 + 0.504027i \(0.831851\pi\)
\(228\) 2.69002i 0.178151i
\(229\) −7.80782 −0.515955 −0.257978 0.966151i \(-0.583056\pi\)
−0.257978 + 0.966151i \(0.583056\pi\)
\(230\) 8.90391i 0.587106i
\(231\) −0.903910 −0.0594729
\(232\) −2.00000 −0.131306
\(233\) 3.59393 0.235446 0.117723 0.993046i \(-0.462441\pi\)
0.117723 + 0.993046i \(0.462441\pi\)
\(234\) 2.69002 0.175852
\(235\) 4.61997i 0.301373i
\(236\) 6.21389i 0.404490i
\(237\) 1.59393i 0.103537i
\(238\) 9.04401 0.586236
\(239\) 7.18785i 0.464944i −0.972603 0.232472i \(-0.925319\pi\)
0.972603 0.232472i \(-0.0746813\pi\)
\(240\) 1.00000i 0.0645497i
\(241\) 3.18785i 0.205348i −0.994715 0.102674i \(-0.967260\pi\)
0.994715 0.102674i \(-0.0327398\pi\)
\(242\) 10.5239i 0.676500i
\(243\) 1.00000 0.0641500
\(244\) 2.00000i 0.128037i
\(245\) 5.28394i 0.337579i
\(246\) 2.00000i 0.127515i
\(247\) 7.23619 0.460428
\(248\) 9.59393 0.609215
\(249\) 10.2839 0.651718
\(250\) 1.00000 0.0632456
\(251\) 11.5939i 0.731802i −0.930654 0.365901i \(-0.880761\pi\)
0.930654 0.365901i \(-0.119239\pi\)
\(252\) 1.30998 0.0825212
\(253\) 6.14384i 0.386260i
\(254\) 10.6900i 0.670751i
\(255\) −6.90391 −0.432340
\(256\) 1.00000 0.0625000
\(257\) 25.5239i 1.59214i −0.605207 0.796068i \(-0.706910\pi\)
0.605207 0.796068i \(-0.293090\pi\)
\(258\) 8.21389 0.511375
\(259\) −5.38003 5.87787i −0.334299 0.365233i
\(260\) −2.69002 −0.166828
\(261\) 2.00000i 0.123797i
\(262\) 8.97396 0.554413
\(263\) 18.5679 1.14494 0.572472 0.819924i \(-0.305984\pi\)
0.572472 + 0.819924i \(0.305984\pi\)
\(264\) 0.690016i 0.0424676i
\(265\) 0.690016i 0.0423874i
\(266\) 3.52388 0.216063
\(267\) 5.92995i 0.362907i
\(268\) 1.23993 0.0757410
\(269\) −13.3100 −0.811524 −0.405762 0.913979i \(-0.632994\pi\)
−0.405762 + 0.913979i \(0.632994\pi\)
\(270\) −1.00000 −0.0608581
\(271\) 17.9479 1.09026 0.545129 0.838352i \(-0.316481\pi\)
0.545129 + 0.838352i \(0.316481\pi\)
\(272\) 6.90391i 0.418611i
\(273\) 3.52388i 0.213275i
\(274\) 11.5939i 0.700415i
\(275\) −0.690016 −0.0416096
\(276\) 8.90391i 0.535952i
\(277\) 13.7378i 0.825423i 0.910862 + 0.412711i \(0.135418\pi\)
−0.910862 + 0.412711i \(0.864582\pi\)
\(278\) 6.76007i 0.405442i
\(279\) 9.59393i 0.574373i
\(280\) −1.30998 −0.0782865
\(281\) 4.54992i 0.271425i 0.990748 + 0.135713i \(0.0433324\pi\)
−0.990748 + 0.135713i \(0.956668\pi\)
\(282\) 4.61997i 0.275115i
\(283\) 27.7378i 1.64884i 0.565979 + 0.824420i \(0.308498\pi\)
−0.565979 + 0.824420i \(0.691502\pi\)
\(284\) −13.8078 −0.819343
\(285\) −2.69002 −0.159343
\(286\) 1.85616 0.109757
\(287\) 2.61997 0.154652
\(288\) 1.00000i 0.0589256i
\(289\) −30.6640 −1.80376
\(290\) 2.00000i 0.117444i
\(291\) 3.38003i 0.198141i
\(292\) 12.2839 0.718863
\(293\) −3.30998 −0.193371 −0.0966857 0.995315i \(-0.530824\pi\)
−0.0966857 + 0.995315i \(0.530824\pi\)
\(294\) 5.28394i 0.308166i
\(295\) 6.21389 0.361787
\(296\) 4.48698 4.10695i 0.260800 0.238711i
\(297\) 0.690016 0.0400388
\(298\) 10.2139i 0.591675i
\(299\) 23.9517 1.38516
\(300\) 1.00000 0.0577350
\(301\) 10.7601i 0.620200i
\(302\) 22.2839i 1.28230i
\(303\) 8.97396 0.515541
\(304\) 2.69002i 0.154283i
\(305\) 2.00000 0.114520
\(306\) −6.90391 −0.394670
\(307\) 21.9479 1.25263 0.626317 0.779569i \(-0.284562\pi\)
0.626317 + 0.779569i \(0.284562\pi\)
\(308\) 0.903910 0.0515051
\(309\) 19.1879i 1.09156i
\(310\) 9.59393i 0.544898i
\(311\) 18.7601i 1.06379i −0.846812 0.531893i \(-0.821481\pi\)
0.846812 0.531893i \(-0.178519\pi\)
\(312\) −2.69002 −0.152292
\(313\) 21.1879i 1.19761i −0.800896 0.598804i \(-0.795643\pi\)
0.800896 0.598804i \(-0.204357\pi\)
\(314\) 12.2139i 0.689270i
\(315\) 1.30998i 0.0738092i
\(316\) 1.59393i 0.0896654i
\(317\) 23.5418 1.32224 0.661121 0.750279i \(-0.270081\pi\)
0.661121 + 0.750279i \(0.270081\pi\)
\(318\) 0.690016i 0.0386942i
\(319\) 1.38003i 0.0772670i
\(320\) 1.00000i 0.0559017i
\(321\) 18.1438 1.01269
\(322\) 11.6640 0.650008
\(323\) −18.5716 −1.03335
\(324\) −1.00000 −0.0555556
\(325\) 2.69002i 0.149215i
\(326\) −6.07005 −0.336189
\(327\) 17.5239i 0.969073i
\(328\) 2.00000i 0.110432i
\(329\) 6.05208 0.333662
\(330\) −0.690016 −0.0379842
\(331\) 16.4061i 0.901759i −0.892585 0.450880i \(-0.851110\pi\)
0.892585 0.450880i \(-0.148890\pi\)
\(332\) −10.2839 −0.564405
\(333\) 4.10695 + 4.48698i 0.225059 + 0.245885i
\(334\) 8.90391 0.487200
\(335\) 1.23993i 0.0677448i
\(336\) −1.30998 −0.0714655
\(337\) 23.3317 1.27096 0.635479 0.772118i \(-0.280803\pi\)
0.635479 + 0.772118i \(0.280803\pi\)
\(338\) 5.76381i 0.313510i
\(339\) 2.00000i 0.108625i
\(340\) 6.90391 0.374417
\(341\) 6.61997i 0.358491i
\(342\) −2.69002 −0.145459
\(343\) 16.0918 0.868874
\(344\) −8.21389 −0.442863
\(345\) −8.90391 −0.479370
\(346\) 19.8779i 1.06864i
\(347\) 5.38003i 0.288815i 0.989518 + 0.144408i \(0.0461277\pi\)
−0.989518 + 0.144408i \(0.953872\pi\)
\(348\) 2.00000i 0.107211i
\(349\) −29.1879 −1.56239 −0.781195 0.624287i \(-0.785390\pi\)
−0.781195 + 0.624287i \(0.785390\pi\)
\(350\) 1.30998i 0.0700216i
\(351\) 2.69002i 0.143582i
\(352\) 0.690016i 0.0367780i
\(353\) 22.4278i 1.19371i 0.802349 + 0.596855i \(0.203583\pi\)
−0.802349 + 0.596855i \(0.796417\pi\)
\(354\) 6.21389 0.330265
\(355\) 13.8078i 0.732843i
\(356\) 5.92995i 0.314287i
\(357\) 9.04401i 0.478660i
\(358\) 19.5939 1.03557
\(359\) 20.5679 1.08553 0.542766 0.839884i \(-0.317377\pi\)
0.542766 + 0.839884i \(0.317377\pi\)
\(360\) 1.00000 0.0527046
\(361\) 11.7638 0.619148
\(362\) 9.18785i 0.482903i
\(363\) −10.5239 −0.552360
\(364\) 3.52388i 0.184701i
\(365\) 12.2839i 0.642971i
\(366\) 2.00000 0.104542
\(367\) 17.8779 0.933217 0.466609 0.884464i \(-0.345476\pi\)
0.466609 + 0.884464i \(0.345476\pi\)
\(368\) 8.90391i 0.464148i
\(369\) −2.00000 −0.104116
\(370\) −4.10695 4.48698i −0.213510 0.233267i
\(371\) −0.903910 −0.0469287
\(372\) 9.59393i 0.497422i
\(373\) −34.5896 −1.79098 −0.895491 0.445080i \(-0.853175\pi\)
−0.895491 + 0.445080i \(0.853175\pi\)
\(374\) −4.76381 −0.246331
\(375\) 1.00000i 0.0516398i
\(376\) 4.61997i 0.238257i
\(377\) −5.38003 −0.277086
\(378\) 1.30998i 0.0673783i
\(379\) 15.8599 0.814668 0.407334 0.913279i \(-0.366458\pi\)
0.407334 + 0.913279i \(0.366458\pi\)
\(380\) 2.69002 0.137995
\(381\) −10.6900 −0.547666
\(382\) −20.9039 −1.06954
\(383\) 26.7117i 1.36491i 0.730930 + 0.682453i \(0.239087\pi\)
−0.730930 + 0.682453i \(0.760913\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 0.903910i 0.0460675i
\(386\) 8.61997 0.438745
\(387\) 8.21389i 0.417536i
\(388\) 3.38003i 0.171595i
\(389\) 4.19218i 0.212552i −0.994337 0.106276i \(-0.966107\pi\)
0.994337 0.106276i \(-0.0338927\pi\)
\(390\) 2.69002i 0.136214i
\(391\) −61.4718 −3.10876
\(392\) 5.28394i 0.266879i
\(393\) 8.97396i 0.452676i
\(394\) 12.6900i 0.639314i
\(395\) 1.59393 0.0801992
\(396\) −0.690016 −0.0346746
\(397\) 5.45383 0.273720 0.136860 0.990590i \(-0.456299\pi\)
0.136860 + 0.990590i \(0.456299\pi\)
\(398\) 22.8339 1.14456
\(399\) 3.52388i 0.176415i
\(400\) −1.00000 −0.0500000
\(401\) 34.4978i 1.72274i −0.507978 0.861370i \(-0.669607\pi\)
0.507978 0.861370i \(-0.330393\pi\)
\(402\) 1.23993i 0.0618423i
\(403\) 25.8078 1.28558
\(404\) −8.97396 −0.446471
\(405\) 1.00000i 0.0496904i
\(406\) −2.61997 −0.130027
\(407\) 2.83386 + 3.09609i 0.140469 + 0.153467i
\(408\) 6.90391 0.341794
\(409\) 30.9077i 1.52829i −0.645047 0.764143i \(-0.723162\pi\)
0.645047 0.764143i \(-0.276838\pi\)
\(410\) 2.00000 0.0987730
\(411\) −11.5939 −0.571886
\(412\) 19.1879i 0.945318i
\(413\) 8.14010i 0.400548i
\(414\) −8.90391 −0.437603
\(415\) 10.2839i 0.504819i
\(416\) 2.69002 0.131889
\(417\) −6.76007 −0.331042
\(418\) −1.85616 −0.0907875
\(419\) −21.6857 −1.05942 −0.529708 0.848180i \(-0.677698\pi\)
−0.529708 + 0.848180i \(0.677698\pi\)
\(420\) 1.30998i 0.0639207i
\(421\) 36.3757i 1.77284i −0.462879 0.886422i \(-0.653183\pi\)
0.462879 0.886422i \(-0.346817\pi\)
\(422\) 5.38003i 0.261896i
\(423\) −4.61997 −0.224630
\(424\) 0.690016i 0.0335102i
\(425\) 6.90391i 0.334889i
\(426\) 13.8078i 0.668991i
\(427\) 2.61997i 0.126789i
\(428\) −18.1438 −0.877016
\(429\) 1.85616i 0.0896160i
\(430\) 8.21389i 0.396109i
\(431\) 4.47612i 0.215607i 0.994172 + 0.107804i \(0.0343818\pi\)
−0.994172 + 0.107804i \(0.965618\pi\)
\(432\) 1.00000 0.0481125
\(433\) −13.5239 −0.649916 −0.324958 0.945728i \(-0.605350\pi\)
−0.324958 + 0.945728i \(0.605350\pi\)
\(434\) 12.5679 0.603278
\(435\) 2.00000 0.0958927
\(436\) 17.5239i 0.839242i
\(437\) −23.9517 −1.14576
\(438\) 12.2839i 0.586950i
\(439\) 1.59393i 0.0760740i −0.999276 0.0380370i \(-0.987890\pi\)
0.999276 0.0380370i \(-0.0121105\pi\)
\(440\) 0.690016 0.0328952
\(441\) −5.28394 −0.251616
\(442\) 18.5716i 0.883362i
\(443\) −36.8556 −1.75106 −0.875531 0.483163i \(-0.839488\pi\)
−0.875531 + 0.483163i \(0.839488\pi\)
\(444\) −4.10695 4.48698i −0.194907 0.212943i
\(445\) −5.92995 −0.281107
\(446\) 0.833861i 0.0394845i
\(447\) 10.2139 0.483101
\(448\) 1.30998 0.0618909
\(449\) 12.0738i 0.569798i −0.958558 0.284899i \(-0.908040\pi\)
0.958558 0.284899i \(-0.0919600\pi\)
\(450\) 1.00000i 0.0471405i
\(451\) −1.38003 −0.0649832
\(452\) 2.00000i 0.0940721i
\(453\) 22.2839 1.04699
\(454\) −15.1879 −0.712801
\(455\) −3.52388 −0.165202
\(456\) 2.69002 0.125972
\(457\) 9.18785i 0.429790i −0.976637 0.214895i \(-0.931059\pi\)
0.976637 0.214895i \(-0.0689409\pi\)
\(458\) 7.80782i 0.364835i
\(459\) 6.90391i 0.322247i
\(460\) 8.90391 0.415147
\(461\) 6.14010i 0.285973i 0.989725 + 0.142986i \(0.0456705\pi\)
−0.989725 + 0.142986i \(0.954329\pi\)
\(462\) 0.903910i 0.0420537i
\(463\) 1.09984i 0.0511137i −0.999673 0.0255568i \(-0.991864\pi\)
0.999673 0.0255568i \(-0.00813588\pi\)
\(464\) 2.00000i 0.0928477i
\(465\) −9.59393 −0.444908
\(466\) 3.59393i 0.166485i
\(467\) 3.18785i 0.147516i −0.997276 0.0737581i \(-0.976501\pi\)
0.997276 0.0737581i \(-0.0234993\pi\)
\(468\) 2.69002i 0.124346i
\(469\) 1.62429 0.0750029
\(470\) 4.61997 0.213103
\(471\) 12.2139 0.562787
\(472\) −6.21389 −0.286018
\(473\) 5.66772i 0.260602i
\(474\) 1.59393 0.0732115
\(475\) 2.69002i 0.123426i
\(476\) 9.04401i 0.414531i
\(477\) 0.690016 0.0315937
\(478\) 7.18785 0.328765
\(479\) 41.1916i 1.88209i 0.338278 + 0.941046i \(0.390155\pi\)
−0.338278 + 0.941046i \(0.609845\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 12.0700 11.0478i 0.550347 0.503734i
\(482\) 3.18785 0.145203
\(483\) 11.6640i 0.530729i
\(484\) 10.5239 0.478358
\(485\) −3.38003 −0.153479
\(486\) 1.00000i 0.0453609i
\(487\) 24.4278i 1.10693i 0.832873 + 0.553464i \(0.186694\pi\)
−0.832873 + 0.553464i \(0.813306\pi\)
\(488\) −2.00000 −0.0905357
\(489\) 6.07005i 0.274497i
\(490\) 5.28394 0.238704
\(491\) −0.690016 −0.0311400 −0.0155700 0.999879i \(-0.504956\pi\)
−0.0155700 + 0.999879i \(0.504956\pi\)
\(492\) 2.00000 0.0901670
\(493\) 13.8078 0.621873
\(494\) 7.23619i 0.325572i
\(495\) 0.690016i 0.0310139i
\(496\) 9.59393i 0.430780i
\(497\) −18.0880 −0.811358
\(498\) 10.2839i 0.460835i
\(499\) 8.63794i 0.386687i 0.981131 + 0.193344i \(0.0619332\pi\)
−0.981131 + 0.193344i \(0.938067\pi\)
\(500\) 1.00000i 0.0447214i
\(501\) 8.90391i 0.397797i
\(502\) 11.5939 0.517462
\(503\) 30.3757i 1.35439i 0.735806 + 0.677193i \(0.236804\pi\)
−0.735806 + 0.677193i \(0.763196\pi\)
\(504\) 1.30998i 0.0583513i
\(505\) 8.97396i 0.399336i
\(506\) −6.14384 −0.273127
\(507\) 5.76381 0.255980
\(508\) 10.6900 0.474293
\(509\) −36.9256 −1.63670 −0.818350 0.574721i \(-0.805111\pi\)
−0.818350 + 0.574721i \(0.805111\pi\)
\(510\) 6.90391i 0.305710i
\(511\) 16.0918 0.711858
\(512\) 1.00000i 0.0441942i
\(513\) 2.69002i 0.118767i
\(514\) 25.5239 1.12581
\(515\) −19.1879 −0.845518
\(516\) 8.21389i 0.361597i
\(517\) −3.18785 −0.140202
\(518\) 5.87787 5.38003i 0.258259 0.236385i
\(519\) 19.8779 0.872542
\(520\) 2.69002i 0.117965i
\(521\) 10.8121 0.473689 0.236844 0.971548i \(-0.423887\pi\)
0.236844 + 0.971548i \(0.423887\pi\)
\(522\) 2.00000 0.0875376
\(523\) 20.9219i 0.914850i −0.889248 0.457425i \(-0.848772\pi\)
0.889248 0.457425i \(-0.151228\pi\)
\(524\) 8.97396i 0.392029i
\(525\) 1.30998 0.0571724
\(526\) 18.5679i 0.809598i
\(527\) −66.2356 −2.88527
\(528\) 0.690016 0.0300291
\(529\) −56.2796 −2.44694
\(530\) −0.690016 −0.0299724
\(531\) 6.21389i 0.269660i
\(532\) 3.52388i 0.152779i
\(533\) 5.38003i 0.233035i
\(534\) −5.92995 −0.256614
\(535\) 18.1438i 0.784427i
\(536\) 1.23993i 0.0535570i
\(537\) 19.5939i 0.845540i
\(538\) 13.3100i 0.573834i
\(539\) −3.64601 −0.157045
\(540\) 1.00000i 0.0430331i
\(541\) 25.5239i 1.09736i 0.836033 + 0.548679i \(0.184869\pi\)
−0.836033 + 0.548679i \(0.815131\pi\)
\(542\) 17.9479i 0.770929i
\(543\) −9.18785 −0.394289
\(544\) −6.90391 −0.296003
\(545\) 17.5239 0.750640
\(546\) −3.52388 −0.150808
\(547\) 6.49784i 0.277827i 0.990304 + 0.138914i \(0.0443611\pi\)
−0.990304 + 0.138914i \(0.955639\pi\)
\(548\) 11.5939 0.495268
\(549\) 2.00000i 0.0853579i
\(550\) 0.690016i 0.0294224i
\(551\) 5.38003 0.229197
\(552\) 8.90391 0.378976
\(553\) 2.08802i 0.0887915i
\(554\) −13.7378 −0.583662
\(555\) −4.48698 + 4.10695i −0.190462 + 0.174330i
\(556\) 6.76007 0.286691
\(557\) 0.760066i 0.0322050i 0.999870 + 0.0161025i \(0.00512581\pi\)
−0.999870 + 0.0161025i \(0.994874\pi\)
\(558\) −9.59393 −0.406143
\(559\) −22.0955 −0.934540
\(560\) 1.30998i 0.0553569i
\(561\) 4.76381i 0.201128i
\(562\) −4.54992 −0.191927
\(563\) 18.0880i 0.762319i 0.924509 + 0.381160i \(0.124475\pi\)
−0.924509 + 0.381160i \(0.875525\pi\)
\(564\) 4.61997 0.194536
\(565\) −2.00000 −0.0841406
\(566\) −27.7378 −1.16591
\(567\) −1.30998 −0.0550141
\(568\) 13.8078i 0.579363i
\(569\) 2.74210i 0.114955i −0.998347 0.0574774i \(-0.981694\pi\)
0.998347 0.0574774i \(-0.0183057\pi\)
\(570\) 2.69002i 0.112672i
\(571\) −25.2399 −1.05626 −0.528129 0.849164i \(-0.677106\pi\)
−0.528129 + 0.849164i \(0.677106\pi\)
\(572\) 1.85616i 0.0776098i
\(573\) 20.9039i 0.873273i
\(574\) 2.61997i 0.109355i
\(575\) 8.90391i 0.371319i
\(576\) −1.00000 −0.0416667
\(577\) 38.5679i 1.60560i −0.596247 0.802801i \(-0.703342\pi\)
0.596247 0.802801i \(-0.296658\pi\)
\(578\) 30.6640i 1.27545i
\(579\) 8.61997i 0.358234i
\(580\) −2.00000 −0.0830455
\(581\) −13.4718 −0.558904
\(582\) −3.38003 −0.140107
\(583\) 0.476123 0.0197190
\(584\) 12.2839i 0.508313i
\(585\) 2.69002 0.111218
\(586\) 3.30998i 0.136734i
\(587\) 3.32795i 0.137359i 0.997639 + 0.0686796i \(0.0218786\pi\)
−0.997639 + 0.0686796i \(0.978121\pi\)
\(588\) 5.28394 0.217906
\(589\) −25.8078 −1.06339
\(590\) 6.21389i 0.255822i
\(591\) −12.6900 −0.521998
\(592\) 4.10695 + 4.48698i 0.168794 + 0.184414i
\(593\) −24.5896 −1.00977 −0.504887 0.863185i \(-0.668466\pi\)
−0.504887 + 0.863185i \(0.668466\pi\)
\(594\) 0.690016i 0.0283117i
\(595\) 9.04401 0.370768
\(596\) −10.2139 −0.418377
\(597\) 22.8339i 0.934528i
\(598\) 23.9517i 0.979456i
\(599\) 7.85990 0.321147 0.160573 0.987024i \(-0.448666\pi\)
0.160573 + 0.987024i \(0.448666\pi\)
\(600\) 1.00000i 0.0408248i
\(601\) 0.143844 0.00586754 0.00293377 0.999996i \(-0.499066\pi\)
0.00293377 + 0.999996i \(0.499066\pi\)
\(602\) −10.7601 −0.438548
\(603\) −1.23993 −0.0504940
\(604\) −22.2839 −0.906721
\(605\) 10.5239i 0.427856i
\(606\) 8.97396i 0.364542i
\(607\) 27.1879i 1.10352i 0.834003 + 0.551760i \(0.186044\pi\)
−0.834003 + 0.551760i \(0.813956\pi\)
\(608\) −2.69002 −0.109095
\(609\) 2.61997i 0.106166i
\(610\) 2.00000i 0.0809776i
\(611\) 12.4278i 0.502774i
\(612\) 6.90391i 0.279074i
\(613\) −10.9740 −0.443234 −0.221617 0.975134i \(-0.571133\pi\)
−0.221617 + 0.975134i \(0.571133\pi\)
\(614\) 21.9479i 0.885746i
\(615\) 2.00000i 0.0806478i
\(616\) 0.903910i 0.0364196i
\(617\) 8.97396 0.361278 0.180639 0.983549i \(-0.442183\pi\)
0.180639 + 0.983549i \(0.442183\pi\)
\(618\) −19.1879 −0.771849
\(619\) −1.52013 −0.0610992 −0.0305496 0.999533i \(-0.509726\pi\)
−0.0305496 + 0.999533i \(0.509726\pi\)
\(620\) 9.59393 0.385301
\(621\) 8.90391i 0.357302i
\(622\) 18.7601 0.752210
\(623\) 7.76814i 0.311224i
\(624\) 2.69002i 0.107687i
\(625\) 1.00000 0.0400000
\(626\) 21.1879 0.846837
\(627\) 1.85616i 0.0741277i
\(628\) −12.2139 −0.487387
\(629\) −30.9777 + 28.3540i −1.23516 + 1.13055i
\(630\) 1.30998 0.0521910
\(631\) 12.2139i 0.486227i 0.969998 + 0.243114i \(0.0781688\pi\)
−0.969998 + 0.243114i \(0.921831\pi\)
\(632\) −1.59393 −0.0634030
\(633\) −5.38003 −0.213837
\(634\) 23.5418i 0.934966i
\(635\) 10.6900i 0.424220i
\(636\) −0.690016 −0.0273609
\(637\) 14.2139i 0.563175i
\(638\) 1.38003 0.0546360
\(639\) 13.8078 0.546229
\(640\) 1.00000 0.0395285
\(641\) −1.43211 −0.0565651 −0.0282825 0.999600i \(-0.509004\pi\)
−0.0282825 + 0.999600i \(0.509004\pi\)
\(642\) 18.1438i 0.716080i
\(643\) 10.0700i 0.397124i −0.980088 0.198562i \(-0.936373\pi\)
0.980088 0.198562i \(-0.0636271\pi\)
\(644\) 11.6640i 0.459625i
\(645\) 8.21389 0.323422
\(646\) 18.5716i 0.730691i
\(647\) 6.14384i 0.241539i −0.992681 0.120770i \(-0.961464\pi\)
0.992681 0.120770i \(-0.0385363\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 4.28769i 0.168307i
\(650\) −2.69002 −0.105511
\(651\) 12.5679i 0.492574i
\(652\) 6.07005i 0.237721i
\(653\) 45.1879i 1.76834i 0.467168 + 0.884169i \(0.345274\pi\)
−0.467168 + 0.884169i \(0.654726\pi\)
\(654\) 17.5239 0.685238
\(655\) 8.97396 0.350642
\(656\) −2.00000 −0.0780869
\(657\) −12.2839 −0.479242
\(658\) 6.05208i 0.235935i
\(659\) 19.4017 0.755785 0.377892 0.925850i \(-0.376649\pi\)
0.377892 + 0.925850i \(0.376649\pi\)
\(660\) 0.690016i 0.0268589i
\(661\) 0.424042i 0.0164933i 0.999966 + 0.00824666i \(0.00262502\pi\)
−0.999966 + 0.00824666i \(0.997375\pi\)
\(662\) 16.4061 0.637640
\(663\) 18.5716 0.721262
\(664\) 10.2839i 0.399094i
\(665\) 3.52388 0.136650
\(666\) −4.48698 + 4.10695i −0.173867 + 0.159141i
\(667\) 17.8078 0.689522
\(668\) 8.90391i 0.344503i
\(669\) −0.833861 −0.0322389
\(670\) 1.23993 0.0479028
\(671\) 1.38003i 0.0532756i
\(672\) 1.30998i 0.0505337i
\(673\) 2.76381 0.106537 0.0532686 0.998580i \(-0.483036\pi\)
0.0532686 + 0.998580i \(0.483036\pi\)
\(674\) 23.3317i 0.898703i
\(675\) −1.00000 −0.0384900
\(676\) −5.76381 −0.221685
\(677\) 23.5977 0.906932 0.453466 0.891274i \(-0.350187\pi\)
0.453466 + 0.891274i \(0.350187\pi\)
\(678\) −2.00000 −0.0768095
\(679\) 4.42779i 0.169923i
\(680\) 6.90391i 0.264753i
\(681\) 15.1879i 0.582000i
\(682\) −6.61997 −0.253492
\(683\) 17.9479i 0.686758i 0.939197 + 0.343379i \(0.111572\pi\)
−0.939197 + 0.343379i \(0.888428\pi\)
\(684\) 2.69002i 0.102855i
\(685\) 11.5939i 0.442981i
\(686\) 16.0918i 0.614386i
\(687\) −7.80782 −0.297887
\(688\) 8.21389i 0.313152i
\(689\) 1.85616i 0.0707139i
\(690\) 8.90391i 0.338966i
\(691\) 46.2356 1.75889 0.879443 0.476005i \(-0.157915\pi\)
0.879443 + 0.476005i \(0.157915\pi\)
\(692\) −19.8779 −0.755643
\(693\) −0.903910 −0.0343367
\(694\) −5.38003 −0.204223
\(695\) 6.76007i 0.256424i
\(696\) −2.00000 −0.0758098
\(697\) 13.8078i 0.523008i
\(698\) 29.1879i 1.10478i
\(699\) 3.59393 0.135935
\(700\) −1.30998 −0.0495127
\(701\) 0.192180i 0.00725852i −0.999993 0.00362926i \(-0.998845\pi\)
0.999993 0.00362926i \(-0.00115523\pi\)
\(702\) 2.69002 0.101528
\(703\) −12.0700 + 11.0478i −0.455231 + 0.416674i
\(704\) −0.690016 −0.0260060
\(705\) 4.61997i 0.173998i
\(706\) −22.4278 −0.844081
\(707\) −11.7557 −0.442120
\(708\) 6.21389i 0.233532i
\(709\) 3.85616i 0.144821i 0.997375 + 0.0724105i \(0.0230692\pi\)
−0.997375 + 0.0724105i \(0.976931\pi\)
\(710\) −13.8078 −0.518198
\(711\) 1.59393i 0.0597769i
\(712\) 5.92995 0.222234
\(713\) −85.4235 −3.19913
\(714\) 9.04401 0.338464
\(715\) 1.85616 0.0694163
\(716\) 19.5939i 0.732259i
\(717\) 7.18785i 0.268435i
\(718\) 20.5679i 0.767587i
\(719\) 15.6156 0.582365 0.291183 0.956668i \(-0.405951\pi\)
0.291183 + 0.956668i \(0.405951\pi\)
\(720\) 1.00000i 0.0372678i
\(721\) 25.1358i 0.936105i
\(722\) 11.7638i 0.437804i
\(723\) 3.18785i 0.118558i
\(724\) 9.18785 0.341464
\(725\) 2.00000i 0.0742781i
\(726\) 10.5239i 0.390578i
\(727\) 31.0478i 1.15150i −0.817627 0.575749i \(-0.804711\pi\)
0.817627 0.575749i \(-0.195289\pi\)
\(728\) 3.52388 0.130604
\(729\) 1.00000 0.0370370
\(730\) 12.2839 0.454649
\(731\) 56.7080 2.09742
\(732\) 2.00000i 0.0739221i
\(733\) −36.7818 −1.35857 −0.679283 0.733876i \(-0.737709\pi\)
−0.679283 + 0.733876i \(0.737709\pi\)
\(734\) 17.8779i 0.659884i
\(735\) 5.28394i 0.194901i
\(736\) −8.90391 −0.328202
\(737\) −0.855575 −0.0315155
\(738\) 2.00000i 0.0736210i
\(739\) 31.8958 1.17331 0.586654 0.809838i \(-0.300445\pi\)
0.586654 + 0.809838i \(0.300445\pi\)
\(740\) 4.48698 4.10695i 0.164945 0.150974i
\(741\) 7.23619 0.265828
\(742\) 0.903910i 0.0331836i
\(743\) 21.1879 0.777307 0.388653 0.921384i \(-0.372940\pi\)
0.388653 + 0.921384i \(0.372940\pi\)
\(744\) 9.59393 0.351730
\(745\) 10.2139i 0.374208i
\(746\) 34.5896i 1.26642i
\(747\) 10.2839 0.376270
\(748\) 4.76381i 0.174182i
\(749\) −23.7681 −0.868469
\(750\) 1.00000 0.0365148
\(751\) 16.0000 0.583848 0.291924 0.956441i \(-0.405705\pi\)
0.291924 + 0.956441i \(0.405705\pi\)
\(752\) −4.61997 −0.168473
\(753\) 11.5939i 0.422506i
\(754\) 5.38003i 0.195929i
\(755\) 22.2839i 0.810996i
\(756\) 1.30998 0.0476436
\(757\) 24.7780i 0.900573i −0.892884 0.450286i \(-0.851322\pi\)
0.892884 0.450286i \(-0.148678\pi\)
\(758\) 15.8599i 0.576058i
\(759\) 6.14384i 0.223007i
\(760\) 2.69002i 0.0975772i
\(761\) −10.8121 −0.391940 −0.195970 0.980610i \(-0.562786\pi\)
−0.195970 + 0.980610i \(0.562786\pi\)
\(762\) 10.6900i 0.387258i
\(763\) 22.9560i 0.831063i
\(764\) 20.9039i 0.756277i
\(765\) −6.90391 −0.249611
\(766\) −26.7117 −0.965134
\(767\) −16.7155 −0.603561
\(768\) 1.00000 0.0360844
\(769\) 15.0478i 0.542636i −0.962490 0.271318i \(-0.912541\pi\)
0.962490 0.271318i \(-0.0874595\pi\)
\(770\) 0.903910 0.0325747
\(771\) 25.5239i 0.919220i
\(772\) 8.61997i 0.310239i
\(773\) 34.0700 1.22541 0.612707 0.790310i \(-0.290080\pi\)
0.612707 + 0.790310i \(0.290080\pi\)
\(774\) 8.21389 0.295242
\(775\) 9.59393i 0.344624i
\(776\) 3.38003 0.121336
\(777\) −5.38003 5.87787i −0.193008 0.210867i
\(778\) 4.19218 0.150297
\(779\) 5.38003i 0.192760i
\(780\) −2.69002 −0.0963180
\(781\) 9.52762 0.340925
\(782\) 61.4718i 2.19823i
\(783\) 2.00000i 0.0714742i
\(784\) −5.28394 −0.188712
\(785\) 12.2139i 0.435933i
\(786\) 8.97396 0.320091
\(787\) 11.3280 0.403798 0.201899 0.979406i \(-0.435289\pi\)
0.201899 + 0.979406i \(0.435289\pi\)
\(788\) 12.6900 0.452063
\(789\) 18.5679 0.661034
\(790\) 1.59393i 0.0567094i
\(791\) 2.61997i 0.0931553i
\(792\) 0.690016i 0.0245187i
\(793\) −5.38003