Properties

Label 731.2.a.c.1.2
Level 731
Weight 2
Character 731.1
Self dual yes
Analytic conductor 5.837
Analytic rank 1
Dimension 6
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(5.83706438776\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: 6.6.2460365.1
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.05953\)
Character \(\chi\) = 731.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.24167 q^{2} +0.297851 q^{3} +3.02506 q^{4} +1.49772 q^{5} -0.667683 q^{6} +2.00334 q^{7} -2.29785 q^{8} -2.91128 q^{9} +O(q^{10})\) \(q-2.24167 q^{2} +0.297851 q^{3} +3.02506 q^{4} +1.49772 q^{5} -0.667683 q^{6} +2.00334 q^{7} -2.29785 q^{8} -2.91128 q^{9} -3.35738 q^{10} -0.727213 q^{11} +0.901019 q^{12} -6.17068 q^{13} -4.49083 q^{14} +0.446097 q^{15} -0.899115 q^{16} -1.00000 q^{17} +6.52613 q^{18} -3.49578 q^{19} +4.53069 q^{20} +0.596699 q^{21} +1.63017 q^{22} -5.48527 q^{23} -0.684418 q^{24} -2.75684 q^{25} +13.8326 q^{26} -1.76068 q^{27} +6.06025 q^{28} +7.44532 q^{29} -1.00000 q^{30} -4.37940 q^{31} +6.61122 q^{32} -0.216601 q^{33} +2.24167 q^{34} +3.00044 q^{35} -8.80682 q^{36} +4.71286 q^{37} +7.83637 q^{38} -1.83794 q^{39} -3.44153 q^{40} -7.24643 q^{41} -1.33760 q^{42} -1.00000 q^{43} -2.19987 q^{44} -4.36028 q^{45} +12.2961 q^{46} -0.886945 q^{47} -0.267802 q^{48} -2.98661 q^{49} +6.17992 q^{50} -0.297851 q^{51} -18.6667 q^{52} +6.71670 q^{53} +3.94686 q^{54} -1.08916 q^{55} -4.60339 q^{56} -1.04122 q^{57} -16.6899 q^{58} +7.08700 q^{59} +1.34947 q^{60} +1.56709 q^{61} +9.81714 q^{62} -5.83231 q^{63} -13.0219 q^{64} -9.24194 q^{65} +0.485548 q^{66} -9.37603 q^{67} -3.02506 q^{68} -1.63379 q^{69} -6.72599 q^{70} -1.41342 q^{71} +6.68970 q^{72} -2.66641 q^{73} -10.5647 q^{74} -0.821129 q^{75} -10.5750 q^{76} -1.45686 q^{77} +4.12006 q^{78} -12.5560 q^{79} -1.34662 q^{80} +8.20943 q^{81} +16.2441 q^{82} -2.32470 q^{83} +1.80505 q^{84} -1.49772 q^{85} +2.24167 q^{86} +2.21760 q^{87} +1.67103 q^{88} -6.18893 q^{89} +9.77429 q^{90} -12.3620 q^{91} -16.5933 q^{92} -1.30441 q^{93} +1.98823 q^{94} -5.23569 q^{95} +1.96916 q^{96} -1.30314 q^{97} +6.69498 q^{98} +2.11712 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - q^{2} - 3q^{3} + 5q^{4} + 3q^{5} - 7q^{6} - 7q^{7} - 9q^{8} - 3q^{9} + O(q^{10}) \) \( 6q - q^{2} - 3q^{3} + 5q^{4} + 3q^{5} - 7q^{6} - 7q^{7} - 9q^{8} - 3q^{9} - 4q^{10} + 4q^{11} + 11q^{12} - 10q^{13} - 7q^{14} + q^{15} - q^{16} - 6q^{17} + q^{18} - 20q^{19} + q^{20} - 8q^{21} + 2q^{22} - 3q^{23} - 9q^{24} - 7q^{25} - 3q^{26} - 6q^{27} - 11q^{28} - 15q^{29} - 6q^{30} + 12q^{31} + q^{32} - 2q^{33} + q^{34} - 9q^{35} - 16q^{36} - 14q^{37} + 27q^{38} + 5q^{39} - 7q^{40} - 2q^{41} + 19q^{42} - 6q^{43} - 12q^{44} - 18q^{45} + 14q^{46} - 11q^{47} - 6q^{48} + 3q^{49} + 7q^{50} + 3q^{51} - 5q^{52} + 3q^{53} + 25q^{54} + 6q^{55} + 22q^{56} + 11q^{57} - 21q^{58} + 2q^{59} - q^{60} - 20q^{61} + 3q^{62} + 23q^{63} - 39q^{64} - 34q^{65} + 7q^{66} - 2q^{67} - 5q^{68} - 17q^{69} - q^{70} + q^{71} + 21q^{72} + 13q^{73} + 28q^{74} - 5q^{75} - 29q^{76} - 11q^{77} - 26q^{79} + 12q^{80} + 2q^{81} - 9q^{82} + 10q^{83} - 3q^{84} - 3q^{85} + q^{86} + 12q^{87} - 6q^{88} - 15q^{89} + 15q^{90} + 8q^{91} - 9q^{92} - 11q^{93} - 33q^{94} - 21q^{95} + 25q^{96} - 22q^{97} - 3q^{98} - 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.24167 −1.58510 −0.792548 0.609809i \(-0.791246\pi\)
−0.792548 + 0.609809i \(0.791246\pi\)
\(3\) 0.297851 0.171964 0.0859822 0.996297i \(-0.472597\pi\)
0.0859822 + 0.996297i \(0.472597\pi\)
\(4\) 3.02506 1.51253
\(5\) 1.49772 0.669800 0.334900 0.942254i \(-0.391298\pi\)
0.334900 + 0.942254i \(0.391298\pi\)
\(6\) −0.667683 −0.272580
\(7\) 2.00334 0.757193 0.378597 0.925562i \(-0.376407\pi\)
0.378597 + 0.925562i \(0.376407\pi\)
\(8\) −2.29785 −0.812413
\(9\) −2.91128 −0.970428
\(10\) −3.35738 −1.06170
\(11\) −0.727213 −0.219263 −0.109631 0.993972i \(-0.534967\pi\)
−0.109631 + 0.993972i \(0.534967\pi\)
\(12\) 0.901019 0.260102
\(13\) −6.17068 −1.71144 −0.855720 0.517440i \(-0.826885\pi\)
−0.855720 + 0.517440i \(0.826885\pi\)
\(14\) −4.49083 −1.20022
\(15\) 0.446097 0.115182
\(16\) −0.899115 −0.224779
\(17\) −1.00000 −0.242536
\(18\) 6.52613 1.53822
\(19\) −3.49578 −0.801987 −0.400994 0.916081i \(-0.631335\pi\)
−0.400994 + 0.916081i \(0.631335\pi\)
\(20\) 4.53069 1.01309
\(21\) 0.596699 0.130210
\(22\) 1.63017 0.347553
\(23\) −5.48527 −1.14376 −0.571879 0.820338i \(-0.693785\pi\)
−0.571879 + 0.820338i \(0.693785\pi\)
\(24\) −0.684418 −0.139706
\(25\) −2.75684 −0.551368
\(26\) 13.8326 2.71280
\(27\) −1.76068 −0.338844
\(28\) 6.06025 1.14528
\(29\) 7.44532 1.38256 0.691281 0.722586i \(-0.257047\pi\)
0.691281 + 0.722586i \(0.257047\pi\)
\(30\) −1.00000 −0.182574
\(31\) −4.37940 −0.786563 −0.393282 0.919418i \(-0.628660\pi\)
−0.393282 + 0.919418i \(0.628660\pi\)
\(32\) 6.61122 1.16871
\(33\) −0.216601 −0.0377054
\(34\) 2.24167 0.384442
\(35\) 3.00044 0.507168
\(36\) −8.80682 −1.46780
\(37\) 4.71286 0.774789 0.387395 0.921914i \(-0.373375\pi\)
0.387395 + 0.921914i \(0.373375\pi\)
\(38\) 7.83637 1.27123
\(39\) −1.83794 −0.294307
\(40\) −3.44153 −0.544154
\(41\) −7.24643 −1.13170 −0.565851 0.824508i \(-0.691452\pi\)
−0.565851 + 0.824508i \(0.691452\pi\)
\(42\) −1.33760 −0.206396
\(43\) −1.00000 −0.152499
\(44\) −2.19987 −0.331642
\(45\) −4.36028 −0.649992
\(46\) 12.2961 1.81297
\(47\) −0.886945 −0.129374 −0.0646871 0.997906i \(-0.520605\pi\)
−0.0646871 + 0.997906i \(0.520605\pi\)
\(48\) −0.267802 −0.0386539
\(49\) −2.98661 −0.426659
\(50\) 6.17992 0.873972
\(51\) −0.297851 −0.0417075
\(52\) −18.6667 −2.58861
\(53\) 6.71670 0.922610 0.461305 0.887242i \(-0.347381\pi\)
0.461305 + 0.887242i \(0.347381\pi\)
\(54\) 3.94686 0.537100
\(55\) −1.08916 −0.146862
\(56\) −4.60339 −0.615154
\(57\) −1.04122 −0.137913
\(58\) −16.6899 −2.19149
\(59\) 7.08700 0.922649 0.461324 0.887232i \(-0.347374\pi\)
0.461324 + 0.887232i \(0.347374\pi\)
\(60\) 1.34947 0.174216
\(61\) 1.56709 0.200646 0.100323 0.994955i \(-0.468012\pi\)
0.100323 + 0.994955i \(0.468012\pi\)
\(62\) 9.81714 1.24678
\(63\) −5.83231 −0.734802
\(64\) −13.0219 −1.62774
\(65\) −9.24194 −1.14632
\(66\) 0.485548 0.0597668
\(67\) −9.37603 −1.14546 −0.572732 0.819743i \(-0.694116\pi\)
−0.572732 + 0.819743i \(0.694116\pi\)
\(68\) −3.02506 −0.366843
\(69\) −1.63379 −0.196686
\(70\) −6.72599 −0.803910
\(71\) −1.41342 −0.167742 −0.0838710 0.996477i \(-0.526728\pi\)
−0.0838710 + 0.996477i \(0.526728\pi\)
\(72\) 6.68970 0.788389
\(73\) −2.66641 −0.312079 −0.156040 0.987751i \(-0.549873\pi\)
−0.156040 + 0.987751i \(0.549873\pi\)
\(74\) −10.5647 −1.22812
\(75\) −0.821129 −0.0948158
\(76\) −10.5750 −1.21303
\(77\) −1.45686 −0.166024
\(78\) 4.12006 0.466505
\(79\) −12.5560 −1.41266 −0.706329 0.707884i \(-0.749650\pi\)
−0.706329 + 0.707884i \(0.749650\pi\)
\(80\) −1.34662 −0.150557
\(81\) 8.20943 0.912159
\(82\) 16.2441 1.79386
\(83\) −2.32470 −0.255169 −0.127585 0.991828i \(-0.540722\pi\)
−0.127585 + 0.991828i \(0.540722\pi\)
\(84\) 1.80505 0.196947
\(85\) −1.49772 −0.162450
\(86\) 2.24167 0.241725
\(87\) 2.21760 0.237751
\(88\) 1.67103 0.178132
\(89\) −6.18893 −0.656026 −0.328013 0.944673i \(-0.606379\pi\)
−0.328013 + 0.944673i \(0.606379\pi\)
\(90\) 9.77429 1.03030
\(91\) −12.3620 −1.29589
\(92\) −16.5933 −1.72997
\(93\) −1.30441 −0.135261
\(94\) 1.98823 0.205071
\(95\) −5.23569 −0.537171
\(96\) 1.96916 0.200976
\(97\) −1.30314 −0.132314 −0.0661569 0.997809i \(-0.521074\pi\)
−0.0661569 + 0.997809i \(0.521074\pi\)
\(98\) 6.69498 0.676295
\(99\) 2.11712 0.212779
\(100\) −8.33963 −0.833963
\(101\) 10.7298 1.06766 0.533829 0.845592i \(-0.320752\pi\)
0.533829 + 0.845592i \(0.320752\pi\)
\(102\) 0.667683 0.0661104
\(103\) 15.2711 1.50470 0.752352 0.658762i \(-0.228919\pi\)
0.752352 + 0.658762i \(0.228919\pi\)
\(104\) 14.1793 1.39040
\(105\) 0.893686 0.0872148
\(106\) −15.0566 −1.46243
\(107\) 4.07665 0.394104 0.197052 0.980393i \(-0.436863\pi\)
0.197052 + 0.980393i \(0.436863\pi\)
\(108\) −5.32618 −0.512512
\(109\) −16.6080 −1.59075 −0.795377 0.606115i \(-0.792727\pi\)
−0.795377 + 0.606115i \(0.792727\pi\)
\(110\) 2.44153 0.232791
\(111\) 1.40373 0.133236
\(112\) −1.80124 −0.170201
\(113\) 0.707317 0.0665388 0.0332694 0.999446i \(-0.489408\pi\)
0.0332694 + 0.999446i \(0.489408\pi\)
\(114\) 2.33407 0.218606
\(115\) −8.21538 −0.766088
\(116\) 22.5226 2.09117
\(117\) 17.9646 1.66083
\(118\) −15.8867 −1.46249
\(119\) −2.00334 −0.183646
\(120\) −1.02506 −0.0935751
\(121\) −10.4712 −0.951924
\(122\) −3.51290 −0.318043
\(123\) −2.15836 −0.194612
\(124\) −13.2480 −1.18970
\(125\) −11.6176 −1.03911
\(126\) 13.0741 1.16473
\(127\) −5.07059 −0.449942 −0.224971 0.974365i \(-0.572229\pi\)
−0.224971 + 0.974365i \(0.572229\pi\)
\(128\) 15.9683 1.41141
\(129\) −0.297851 −0.0262243
\(130\) 20.7173 1.81703
\(131\) −14.4292 −1.26069 −0.630343 0.776317i \(-0.717086\pi\)
−0.630343 + 0.776317i \(0.717086\pi\)
\(132\) −0.655233 −0.0570307
\(133\) −7.00325 −0.607259
\(134\) 21.0179 1.81567
\(135\) −2.63701 −0.226957
\(136\) 2.29785 0.197039
\(137\) 7.65845 0.654305 0.327153 0.944972i \(-0.393911\pi\)
0.327153 + 0.944972i \(0.393911\pi\)
\(138\) 3.66242 0.311766
\(139\) 14.7934 1.25476 0.627379 0.778714i \(-0.284128\pi\)
0.627379 + 0.778714i \(0.284128\pi\)
\(140\) 9.07654 0.767107
\(141\) −0.264178 −0.0222478
\(142\) 3.16841 0.265887
\(143\) 4.48740 0.375255
\(144\) 2.61758 0.218132
\(145\) 11.1510 0.926039
\(146\) 5.97719 0.494676
\(147\) −0.889565 −0.0733701
\(148\) 14.2567 1.17189
\(149\) −17.0097 −1.39349 −0.696745 0.717319i \(-0.745369\pi\)
−0.696745 + 0.717319i \(0.745369\pi\)
\(150\) 1.84070 0.150292
\(151\) 8.03936 0.654234 0.327117 0.944984i \(-0.393923\pi\)
0.327117 + 0.944984i \(0.393923\pi\)
\(152\) 8.03278 0.651545
\(153\) 2.91128 0.235363
\(154\) 3.26579 0.263165
\(155\) −6.55910 −0.526840
\(156\) −5.55990 −0.445148
\(157\) 14.2495 1.13724 0.568619 0.822601i \(-0.307478\pi\)
0.568619 + 0.822601i \(0.307478\pi\)
\(158\) 28.1463 2.23920
\(159\) 2.00058 0.158656
\(160\) 9.90174 0.782801
\(161\) −10.9889 −0.866045
\(162\) −18.4028 −1.44586
\(163\) 15.0956 1.18238 0.591190 0.806532i \(-0.298658\pi\)
0.591190 + 0.806532i \(0.298658\pi\)
\(164\) −21.9209 −1.71174
\(165\) −0.324407 −0.0252551
\(166\) 5.21121 0.404468
\(167\) 23.6026 1.82642 0.913210 0.407489i \(-0.133595\pi\)
0.913210 + 0.407489i \(0.133595\pi\)
\(168\) −1.37112 −0.105785
\(169\) 25.0773 1.92902
\(170\) 3.35738 0.257499
\(171\) 10.1772 0.778271
\(172\) −3.02506 −0.230659
\(173\) −1.57566 −0.119795 −0.0598977 0.998205i \(-0.519077\pi\)
−0.0598977 + 0.998205i \(0.519077\pi\)
\(174\) −4.97111 −0.376859
\(175\) −5.52291 −0.417492
\(176\) 0.653848 0.0492857
\(177\) 2.11087 0.158663
\(178\) 13.8735 1.03986
\(179\) 11.0005 0.822214 0.411107 0.911587i \(-0.365142\pi\)
0.411107 + 0.911587i \(0.365142\pi\)
\(180\) −13.1901 −0.983134
\(181\) −19.3879 −1.44109 −0.720547 0.693406i \(-0.756109\pi\)
−0.720547 + 0.693406i \(0.756109\pi\)
\(182\) 27.7115 2.05411
\(183\) 0.466761 0.0345040
\(184\) 12.6043 0.929203
\(185\) 7.05853 0.518954
\(186\) 2.92405 0.214402
\(187\) 0.727213 0.0531791
\(188\) −2.68307 −0.195683
\(189\) −3.52726 −0.256570
\(190\) 11.7367 0.851468
\(191\) −4.98078 −0.360397 −0.180198 0.983630i \(-0.557674\pi\)
−0.180198 + 0.983630i \(0.557674\pi\)
\(192\) −3.87859 −0.279913
\(193\) −18.1741 −1.30820 −0.654099 0.756409i \(-0.726952\pi\)
−0.654099 + 0.756409i \(0.726952\pi\)
\(194\) 2.92121 0.209730
\(195\) −2.75272 −0.197126
\(196\) −9.03469 −0.645335
\(197\) −7.61125 −0.542279 −0.271140 0.962540i \(-0.587400\pi\)
−0.271140 + 0.962540i \(0.587400\pi\)
\(198\) −4.74588 −0.337275
\(199\) 21.5662 1.52879 0.764395 0.644748i \(-0.223038\pi\)
0.764395 + 0.644748i \(0.223038\pi\)
\(200\) 6.33481 0.447939
\(201\) −2.79266 −0.196979
\(202\) −24.0527 −1.69234
\(203\) 14.9155 1.04687
\(204\) −0.901019 −0.0630839
\(205\) −10.8531 −0.758013
\(206\) −34.2326 −2.38510
\(207\) 15.9692 1.10993
\(208\) 5.54815 0.384695
\(209\) 2.54218 0.175846
\(210\) −2.00334 −0.138244
\(211\) −11.1285 −0.766119 −0.383059 0.923724i \(-0.625130\pi\)
−0.383059 + 0.923724i \(0.625130\pi\)
\(212\) 20.3184 1.39548
\(213\) −0.420989 −0.0288457
\(214\) −9.13848 −0.624693
\(215\) −1.49772 −0.102143
\(216\) 4.04579 0.275281
\(217\) −8.77344 −0.595580
\(218\) 37.2295 2.52150
\(219\) −0.794192 −0.0536665
\(220\) −3.29478 −0.222134
\(221\) 6.17068 0.415085
\(222\) −3.14669 −0.211192
\(223\) 3.13480 0.209922 0.104961 0.994476i \(-0.466528\pi\)
0.104961 + 0.994476i \(0.466528\pi\)
\(224\) 13.2445 0.884939
\(225\) 8.02595 0.535064
\(226\) −1.58557 −0.105470
\(227\) 14.3716 0.953876 0.476938 0.878937i \(-0.341747\pi\)
0.476938 + 0.878937i \(0.341747\pi\)
\(228\) −3.14976 −0.208598
\(229\) 1.00576 0.0664625 0.0332312 0.999448i \(-0.489420\pi\)
0.0332312 + 0.999448i \(0.489420\pi\)
\(230\) 18.4161 1.21432
\(231\) −0.433927 −0.0285503
\(232\) −17.1082 −1.12321
\(233\) −5.64195 −0.369617 −0.184808 0.982775i \(-0.559166\pi\)
−0.184808 + 0.982775i \(0.559166\pi\)
\(234\) −40.2706 −2.63257
\(235\) −1.32839 −0.0866548
\(236\) 21.4386 1.39554
\(237\) −3.73981 −0.242927
\(238\) 4.49083 0.291097
\(239\) 19.3056 1.24878 0.624388 0.781114i \(-0.285348\pi\)
0.624388 + 0.781114i \(0.285348\pi\)
\(240\) −0.401092 −0.0258904
\(241\) −13.9659 −0.899620 −0.449810 0.893124i \(-0.648508\pi\)
−0.449810 + 0.893124i \(0.648508\pi\)
\(242\) 23.4728 1.50889
\(243\) 7.72724 0.495703
\(244\) 4.74056 0.303483
\(245\) −4.47310 −0.285776
\(246\) 4.83831 0.308480
\(247\) 21.5714 1.37255
\(248\) 10.0632 0.639014
\(249\) −0.692416 −0.0438801
\(250\) 26.0427 1.64708
\(251\) −30.7373 −1.94012 −0.970061 0.242860i \(-0.921915\pi\)
−0.970061 + 0.242860i \(0.921915\pi\)
\(252\) −17.6431 −1.11141
\(253\) 3.98896 0.250784
\(254\) 11.3666 0.713202
\(255\) −0.446097 −0.0279357
\(256\) −9.75183 −0.609490
\(257\) −18.9680 −1.18319 −0.591594 0.806236i \(-0.701501\pi\)
−0.591594 + 0.806236i \(0.701501\pi\)
\(258\) 0.667683 0.0415681
\(259\) 9.44148 0.586665
\(260\) −27.9575 −1.73385
\(261\) −21.6754 −1.34168
\(262\) 32.3454 1.99831
\(263\) 25.0318 1.54353 0.771765 0.635908i \(-0.219374\pi\)
0.771765 + 0.635908i \(0.219374\pi\)
\(264\) 0.497717 0.0306324
\(265\) 10.0597 0.617964
\(266\) 15.6990 0.962565
\(267\) −1.84338 −0.112813
\(268\) −28.3631 −1.73255
\(269\) −9.15348 −0.558097 −0.279049 0.960277i \(-0.590019\pi\)
−0.279049 + 0.960277i \(0.590019\pi\)
\(270\) 5.91128 0.359749
\(271\) −16.5153 −1.00323 −0.501617 0.865090i \(-0.667261\pi\)
−0.501617 + 0.865090i \(0.667261\pi\)
\(272\) 0.899115 0.0545168
\(273\) −3.68204 −0.222847
\(274\) −17.1677 −1.03714
\(275\) 2.00481 0.120895
\(276\) −4.94233 −0.297493
\(277\) −21.5368 −1.29402 −0.647009 0.762482i \(-0.723981\pi\)
−0.647009 + 0.762482i \(0.723981\pi\)
\(278\) −33.1618 −1.98891
\(279\) 12.7497 0.763303
\(280\) −6.89457 −0.412030
\(281\) −31.2575 −1.86467 −0.932334 0.361598i \(-0.882231\pi\)
−0.932334 + 0.361598i \(0.882231\pi\)
\(282\) 0.592198 0.0352649
\(283\) −32.4786 −1.93066 −0.965328 0.261042i \(-0.915934\pi\)
−0.965328 + 0.261042i \(0.915934\pi\)
\(284\) −4.27568 −0.253715
\(285\) −1.55946 −0.0923743
\(286\) −10.0593 −0.594816
\(287\) −14.5171 −0.856917
\(288\) −19.2471 −1.13415
\(289\) 1.00000 0.0588235
\(290\) −24.9968 −1.46786
\(291\) −0.388142 −0.0227533
\(292\) −8.06605 −0.472030
\(293\) 5.03841 0.294347 0.147174 0.989111i \(-0.452982\pi\)
0.147174 + 0.989111i \(0.452982\pi\)
\(294\) 1.99411 0.116299
\(295\) 10.6143 0.617990
\(296\) −10.8294 −0.629449
\(297\) 1.28039 0.0742959
\(298\) 38.1301 2.20882
\(299\) 33.8478 1.95747
\(300\) −2.48397 −0.143412
\(301\) −2.00334 −0.115471
\(302\) −18.0216 −1.03702
\(303\) 3.19589 0.183599
\(304\) 3.14311 0.180270
\(305\) 2.34706 0.134393
\(306\) −6.52613 −0.373074
\(307\) −22.3425 −1.27515 −0.637577 0.770387i \(-0.720063\pi\)
−0.637577 + 0.770387i \(0.720063\pi\)
\(308\) −4.40709 −0.251117
\(309\) 4.54851 0.258755
\(310\) 14.7033 0.835092
\(311\) 6.41103 0.363536 0.181768 0.983341i \(-0.441818\pi\)
0.181768 + 0.983341i \(0.441818\pi\)
\(312\) 4.22332 0.239099
\(313\) 30.7262 1.73675 0.868373 0.495911i \(-0.165166\pi\)
0.868373 + 0.495911i \(0.165166\pi\)
\(314\) −31.9427 −1.80263
\(315\) −8.73515 −0.492170
\(316\) −37.9826 −2.13669
\(317\) −7.33901 −0.412200 −0.206100 0.978531i \(-0.566077\pi\)
−0.206100 + 0.978531i \(0.566077\pi\)
\(318\) −4.48462 −0.251485
\(319\) −5.41433 −0.303145
\(320\) −19.5031 −1.09026
\(321\) 1.21423 0.0677719
\(322\) 24.6334 1.37277
\(323\) 3.49578 0.194510
\(324\) 24.8341 1.37967
\(325\) 17.0116 0.943634
\(326\) −33.8393 −1.87419
\(327\) −4.94670 −0.273553
\(328\) 16.6512 0.919409
\(329\) −1.77686 −0.0979613
\(330\) 0.727213 0.0400318
\(331\) 5.71279 0.314004 0.157002 0.987598i \(-0.449817\pi\)
0.157002 + 0.987598i \(0.449817\pi\)
\(332\) −7.03238 −0.385952
\(333\) −13.7205 −0.751877
\(334\) −52.9090 −2.89505
\(335\) −14.0426 −0.767231
\(336\) −0.536501 −0.0292685
\(337\) 7.38566 0.402322 0.201161 0.979558i \(-0.435529\pi\)
0.201161 + 0.979558i \(0.435529\pi\)
\(338\) −56.2149 −3.05769
\(339\) 0.210675 0.0114423
\(340\) −4.53069 −0.245711
\(341\) 3.18476 0.172464
\(342\) −22.8139 −1.23363
\(343\) −20.0066 −1.08026
\(344\) 2.29785 0.123892
\(345\) −2.44696 −0.131740
\(346\) 3.53211 0.189887
\(347\) 27.4257 1.47229 0.736145 0.676824i \(-0.236644\pi\)
0.736145 + 0.676824i \(0.236644\pi\)
\(348\) 6.70837 0.359607
\(349\) 25.4762 1.36371 0.681854 0.731488i \(-0.261174\pi\)
0.681854 + 0.731488i \(0.261174\pi\)
\(350\) 12.3805 0.661766
\(351\) 10.8646 0.579910
\(352\) −4.80776 −0.256255
\(353\) 26.9024 1.43187 0.715936 0.698165i \(-0.246000\pi\)
0.715936 + 0.698165i \(0.246000\pi\)
\(354\) −4.73187 −0.251496
\(355\) −2.11690 −0.112354
\(356\) −18.7219 −0.992260
\(357\) −0.596699 −0.0315806
\(358\) −24.6594 −1.30329
\(359\) −4.85198 −0.256078 −0.128039 0.991769i \(-0.540868\pi\)
−0.128039 + 0.991769i \(0.540868\pi\)
\(360\) 10.0193 0.528062
\(361\) −6.77952 −0.356817
\(362\) 43.4613 2.28427
\(363\) −3.11885 −0.163697
\(364\) −37.3959 −1.96008
\(365\) −3.99352 −0.209031
\(366\) −1.04632 −0.0546921
\(367\) 21.8899 1.14264 0.571321 0.820727i \(-0.306431\pi\)
0.571321 + 0.820727i \(0.306431\pi\)
\(368\) 4.93189 0.257092
\(369\) 21.0964 1.09824
\(370\) −15.8229 −0.822592
\(371\) 13.4559 0.698594
\(372\) −3.94592 −0.204586
\(373\) −21.4999 −1.11322 −0.556611 0.830774i \(-0.687898\pi\)
−0.556611 + 0.830774i \(0.687898\pi\)
\(374\) −1.63017 −0.0842940
\(375\) −3.46030 −0.178689
\(376\) 2.03807 0.105105
\(377\) −45.9427 −2.36617
\(378\) 7.90693 0.406688
\(379\) −11.3882 −0.584973 −0.292486 0.956270i \(-0.594483\pi\)
−0.292486 + 0.956270i \(0.594483\pi\)
\(380\) −15.8383 −0.812488
\(381\) −1.51028 −0.0773740
\(382\) 11.1653 0.571264
\(383\) 6.94715 0.354983 0.177491 0.984122i \(-0.443202\pi\)
0.177491 + 0.984122i \(0.443202\pi\)
\(384\) 4.75618 0.242713
\(385\) −2.18196 −0.111203
\(386\) 40.7402 2.07362
\(387\) 2.91128 0.147989
\(388\) −3.94208 −0.200129
\(389\) −19.7153 −0.999606 −0.499803 0.866139i \(-0.666594\pi\)
−0.499803 + 0.866139i \(0.666594\pi\)
\(390\) 6.17068 0.312465
\(391\) 5.48527 0.277402
\(392\) 6.86278 0.346623
\(393\) −4.29775 −0.216793
\(394\) 17.0619 0.859565
\(395\) −18.8053 −0.946197
\(396\) 6.40444 0.321835
\(397\) 37.2137 1.86770 0.933852 0.357659i \(-0.116425\pi\)
0.933852 + 0.357659i \(0.116425\pi\)
\(398\) −48.3443 −2.42328
\(399\) −2.08593 −0.104427
\(400\) 2.47872 0.123936
\(401\) −16.9944 −0.848660 −0.424330 0.905508i \(-0.639490\pi\)
−0.424330 + 0.905508i \(0.639490\pi\)
\(402\) 6.26021 0.312231
\(403\) 27.0239 1.34615
\(404\) 32.4584 1.61487
\(405\) 12.2954 0.610964
\(406\) −33.4357 −1.65938
\(407\) −3.42725 −0.169883
\(408\) 0.684418 0.0338837
\(409\) 14.1474 0.699543 0.349771 0.936835i \(-0.386259\pi\)
0.349771 + 0.936835i \(0.386259\pi\)
\(410\) 24.3290 1.20152
\(411\) 2.28108 0.112517
\(412\) 46.1960 2.27591
\(413\) 14.1977 0.698623
\(414\) −35.7975 −1.75935
\(415\) −3.48175 −0.170912
\(416\) −40.7957 −2.00017
\(417\) 4.40623 0.215774
\(418\) −5.69871 −0.278733
\(419\) −5.20461 −0.254262 −0.127131 0.991886i \(-0.540577\pi\)
−0.127131 + 0.991886i \(0.540577\pi\)
\(420\) 2.70346 0.131915
\(421\) −6.46690 −0.315177 −0.157589 0.987505i \(-0.550372\pi\)
−0.157589 + 0.987505i \(0.550372\pi\)
\(422\) 24.9464 1.21437
\(423\) 2.58215 0.125548
\(424\) −15.4340 −0.749540
\(425\) 2.75684 0.133726
\(426\) 0.943716 0.0457232
\(427\) 3.13943 0.151928
\(428\) 12.3321 0.596095
\(429\) 1.33658 0.0645306
\(430\) 3.35738 0.161907
\(431\) 8.69335 0.418744 0.209372 0.977836i \(-0.432858\pi\)
0.209372 + 0.977836i \(0.432858\pi\)
\(432\) 1.58306 0.0761648
\(433\) 22.8774 1.09942 0.549709 0.835356i \(-0.314739\pi\)
0.549709 + 0.835356i \(0.314739\pi\)
\(434\) 19.6671 0.944052
\(435\) 3.32133 0.159246
\(436\) −50.2401 −2.40607
\(437\) 19.1753 0.917279
\(438\) 1.78031 0.0850667
\(439\) −14.9697 −0.714464 −0.357232 0.934016i \(-0.616280\pi\)
−0.357232 + 0.934016i \(0.616280\pi\)
\(440\) 2.50273 0.119313
\(441\) 8.69487 0.414041
\(442\) −13.8326 −0.657950
\(443\) 15.2218 0.723210 0.361605 0.932331i \(-0.382229\pi\)
0.361605 + 0.932331i \(0.382229\pi\)
\(444\) 4.24638 0.201524
\(445\) −9.26927 −0.439406
\(446\) −7.02717 −0.332746
\(447\) −5.06636 −0.239631
\(448\) −26.0874 −1.23251
\(449\) 18.6220 0.878828 0.439414 0.898285i \(-0.355186\pi\)
0.439414 + 0.898285i \(0.355186\pi\)
\(450\) −17.9915 −0.848128
\(451\) 5.26970 0.248140
\(452\) 2.13968 0.100642
\(453\) 2.39453 0.112505
\(454\) −32.2163 −1.51199
\(455\) −18.5148 −0.867987
\(456\) 2.39257 0.112043
\(457\) 39.1215 1.83003 0.915013 0.403425i \(-0.132180\pi\)
0.915013 + 0.403425i \(0.132180\pi\)
\(458\) −2.25458 −0.105349
\(459\) 1.76068 0.0821816
\(460\) −24.8521 −1.15873
\(461\) −16.4757 −0.767351 −0.383676 0.923468i \(-0.625342\pi\)
−0.383676 + 0.923468i \(0.625342\pi\)
\(462\) 0.972719 0.0452550
\(463\) 8.93949 0.415454 0.207727 0.978187i \(-0.433394\pi\)
0.207727 + 0.978187i \(0.433394\pi\)
\(464\) −6.69420 −0.310770
\(465\) −1.95364 −0.0905977
\(466\) 12.6474 0.585878
\(467\) −3.30805 −0.153078 −0.0765392 0.997067i \(-0.524387\pi\)
−0.0765392 + 0.997067i \(0.524387\pi\)
\(468\) 54.3441 2.51206
\(469\) −18.7834 −0.867337
\(470\) 2.97781 0.137356
\(471\) 4.24424 0.195564
\(472\) −16.2849 −0.749572
\(473\) 0.727213 0.0334373
\(474\) 8.38340 0.385063
\(475\) 9.63732 0.442190
\(476\) −6.06025 −0.277771
\(477\) −19.5542 −0.895326
\(478\) −43.2767 −1.97943
\(479\) −2.00706 −0.0917049 −0.0458525 0.998948i \(-0.514600\pi\)
−0.0458525 + 0.998948i \(0.514600\pi\)
\(480\) 2.94924 0.134614
\(481\) −29.0816 −1.32600
\(482\) 31.3068 1.42598
\(483\) −3.27305 −0.148929
\(484\) −31.6759 −1.43982
\(485\) −1.95174 −0.0886238
\(486\) −17.3219 −0.785737
\(487\) 6.61849 0.299912 0.149956 0.988693i \(-0.452087\pi\)
0.149956 + 0.988693i \(0.452087\pi\)
\(488\) −3.60095 −0.163007
\(489\) 4.49625 0.203327
\(490\) 10.0272 0.452982
\(491\) 10.0944 0.455552 0.227776 0.973714i \(-0.426855\pi\)
0.227776 + 0.973714i \(0.426855\pi\)
\(492\) −6.52917 −0.294358
\(493\) −7.44532 −0.335320
\(494\) −48.3558 −2.17563
\(495\) 3.17085 0.142519
\(496\) 3.93758 0.176803
\(497\) −2.83157 −0.127013
\(498\) 1.55216 0.0695542
\(499\) −9.68516 −0.433568 −0.216784 0.976220i \(-0.569557\pi\)
−0.216784 + 0.976220i \(0.569557\pi\)
\(500\) −35.1439 −1.57168
\(501\) 7.03005 0.314079
\(502\) 68.9028 3.07528
\(503\) 8.65668 0.385982 0.192991 0.981201i \(-0.438181\pi\)
0.192991 + 0.981201i \(0.438181\pi\)
\(504\) 13.4018 0.596962
\(505\) 16.0703 0.715117
\(506\) −8.94191 −0.397516
\(507\) 7.46931 0.331724
\(508\) −15.3389 −0.680552
\(509\) 27.3411 1.21187 0.605937 0.795512i \(-0.292798\pi\)
0.605937 + 0.795512i \(0.292798\pi\)
\(510\) 1.00000 0.0442807
\(511\) −5.34173 −0.236304
\(512\) −10.0763 −0.445314
\(513\) 6.15496 0.271748
\(514\) 42.5198 1.87547
\(515\) 22.8717 1.00785
\(516\) −0.901019 −0.0396651
\(517\) 0.644998 0.0283670
\(518\) −21.1646 −0.929921
\(519\) −0.469313 −0.0206006
\(520\) 21.2366 0.931286
\(521\) −31.2266 −1.36806 −0.684032 0.729452i \(-0.739775\pi\)
−0.684032 + 0.729452i \(0.739775\pi\)
\(522\) 48.5891 2.12669
\(523\) −16.6387 −0.727560 −0.363780 0.931485i \(-0.618514\pi\)
−0.363780 + 0.931485i \(0.618514\pi\)
\(524\) −43.6493 −1.90683
\(525\) −1.64500 −0.0717939
\(526\) −56.1130 −2.44664
\(527\) 4.37940 0.190770
\(528\) 0.194749 0.00847538
\(529\) 7.08816 0.308181
\(530\) −22.5505 −0.979532
\(531\) −20.6323 −0.895364
\(532\) −21.1853 −0.918499
\(533\) 44.7154 1.93684
\(534\) 4.13224 0.178820
\(535\) 6.10566 0.263971
\(536\) 21.5447 0.930590
\(537\) 3.27650 0.141392
\(538\) 20.5190 0.884638
\(539\) 2.17190 0.0935504
\(540\) −7.97711 −0.343280
\(541\) −1.04118 −0.0447639 −0.0223820 0.999749i \(-0.507125\pi\)
−0.0223820 + 0.999749i \(0.507125\pi\)
\(542\) 37.0218 1.59022
\(543\) −5.77472 −0.247817
\(544\) −6.61122 −0.283454
\(545\) −24.8740 −1.06549
\(546\) 8.25389 0.353234
\(547\) −15.4871 −0.662182 −0.331091 0.943599i \(-0.607417\pi\)
−0.331091 + 0.943599i \(0.607417\pi\)
\(548\) 23.1673 0.989658
\(549\) −4.56226 −0.194712
\(550\) −4.49412 −0.191630
\(551\) −26.0272 −1.10880
\(552\) 3.75421 0.159790
\(553\) −25.1539 −1.06965
\(554\) 48.2782 2.05114
\(555\) 2.10239 0.0892416
\(556\) 44.7509 1.89786
\(557\) 18.8685 0.799484 0.399742 0.916628i \(-0.369100\pi\)
0.399742 + 0.916628i \(0.369100\pi\)
\(558\) −28.5805 −1.20991
\(559\) 6.17068 0.260992
\(560\) −2.69774 −0.114000
\(561\) 0.216601 0.00914491
\(562\) 70.0689 2.95568
\(563\) −7.26623 −0.306235 −0.153118 0.988208i \(-0.548931\pi\)
−0.153118 + 0.988208i \(0.548931\pi\)
\(564\) −0.799154 −0.0336505
\(565\) 1.05936 0.0445676
\(566\) 72.8063 3.06028
\(567\) 16.4463 0.690681
\(568\) 3.24783 0.136276
\(569\) 5.55165 0.232737 0.116369 0.993206i \(-0.462875\pi\)
0.116369 + 0.993206i \(0.462875\pi\)
\(570\) 3.49578 0.146422
\(571\) 8.49637 0.355562 0.177781 0.984070i \(-0.443108\pi\)
0.177781 + 0.984070i \(0.443108\pi\)
\(572\) 13.5747 0.567586
\(573\) −1.48353 −0.0619755
\(574\) 32.5425 1.35830
\(575\) 15.1220 0.630632
\(576\) 37.9105 1.57960
\(577\) 16.1381 0.671838 0.335919 0.941891i \(-0.390953\pi\)
0.335919 + 0.941891i \(0.390953\pi\)
\(578\) −2.24167 −0.0932410
\(579\) −5.41317 −0.224964
\(580\) 33.7325 1.40066
\(581\) −4.65718 −0.193213
\(582\) 0.870084 0.0360662
\(583\) −4.88447 −0.202294
\(584\) 6.12700 0.253537
\(585\) 26.9059 1.11242
\(586\) −11.2944 −0.466569
\(587\) −24.8302 −1.02485 −0.512426 0.858731i \(-0.671253\pi\)
−0.512426 + 0.858731i \(0.671253\pi\)
\(588\) −2.69099 −0.110975
\(589\) 15.3094 0.630813
\(590\) −23.7938 −0.979574
\(591\) −2.26702 −0.0932527
\(592\) −4.23740 −0.174156
\(593\) −31.3845 −1.28881 −0.644404 0.764685i \(-0.722895\pi\)
−0.644404 + 0.764685i \(0.722895\pi\)
\(594\) −2.87021 −0.117766
\(595\) −3.00044 −0.123006
\(596\) −51.4555 −2.10770
\(597\) 6.42353 0.262897
\(598\) −75.8755 −3.10278
\(599\) 30.9965 1.26648 0.633240 0.773955i \(-0.281724\pi\)
0.633240 + 0.773955i \(0.281724\pi\)
\(600\) 1.88683 0.0770296
\(601\) −0.100686 −0.00410707 −0.00205354 0.999998i \(-0.500654\pi\)
−0.00205354 + 0.999998i \(0.500654\pi\)
\(602\) 4.49083 0.183033
\(603\) 27.2963 1.11159
\(604\) 24.3196 0.989550
\(605\) −15.6828 −0.637598
\(606\) −7.16413 −0.291023
\(607\) 9.02357 0.366256 0.183128 0.983089i \(-0.441378\pi\)
0.183128 + 0.983089i \(0.441378\pi\)
\(608\) −23.1114 −0.937290
\(609\) 4.44261 0.180024
\(610\) −5.26133 −0.213025
\(611\) 5.47305 0.221416
\(612\) 8.80682 0.355995
\(613\) −13.6132 −0.549832 −0.274916 0.961468i \(-0.588650\pi\)
−0.274916 + 0.961468i \(0.588650\pi\)
\(614\) 50.0844 2.02124
\(615\) −3.23261 −0.130351
\(616\) 3.34764 0.134880
\(617\) −14.8074 −0.596123 −0.298062 0.954547i \(-0.596340\pi\)
−0.298062 + 0.954547i \(0.596340\pi\)
\(618\) −10.1962 −0.410152
\(619\) 29.3824 1.18098 0.590490 0.807045i \(-0.298935\pi\)
0.590490 + 0.807045i \(0.298935\pi\)
\(620\) −19.8417 −0.796862
\(621\) 9.65782 0.387555
\(622\) −14.3714 −0.576240
\(623\) −12.3986 −0.496738
\(624\) 1.65252 0.0661539
\(625\) −3.61561 −0.144624
\(626\) −68.8778 −2.75291
\(627\) 0.757191 0.0302393
\(628\) 43.1058 1.72011
\(629\) −4.71286 −0.187914
\(630\) 19.5813 0.780137
\(631\) 7.80047 0.310532 0.155266 0.987873i \(-0.450377\pi\)
0.155266 + 0.987873i \(0.450377\pi\)
\(632\) 28.8518 1.14766
\(633\) −3.31464 −0.131745
\(634\) 16.4516 0.653377
\(635\) −7.59431 −0.301371
\(636\) 6.05187 0.239972
\(637\) 18.4294 0.730200
\(638\) 12.1371 0.480513
\(639\) 4.11487 0.162782
\(640\) 23.9160 0.945365
\(641\) −10.4027 −0.410883 −0.205442 0.978669i \(-0.565863\pi\)
−0.205442 + 0.978669i \(0.565863\pi\)
\(642\) −2.72191 −0.107425
\(643\) −6.14305 −0.242258 −0.121129 0.992637i \(-0.538652\pi\)
−0.121129 + 0.992637i \(0.538652\pi\)
\(644\) −33.2421 −1.30992
\(645\) −0.446097 −0.0175650
\(646\) −7.83637 −0.308318
\(647\) −5.93404 −0.233291 −0.116646 0.993174i \(-0.537214\pi\)
−0.116646 + 0.993174i \(0.537214\pi\)
\(648\) −18.8641 −0.741050
\(649\) −5.15376 −0.202303
\(650\) −38.1343 −1.49575
\(651\) −2.61318 −0.102419
\(652\) 45.6652 1.78839
\(653\) 31.0089 1.21347 0.606735 0.794904i \(-0.292479\pi\)
0.606735 + 0.794904i \(0.292479\pi\)
\(654\) 11.0888 0.433608
\(655\) −21.6109 −0.844406
\(656\) 6.51537 0.254382
\(657\) 7.76267 0.302851
\(658\) 3.98312 0.155278
\(659\) 24.2847 0.945999 0.473000 0.881063i \(-0.343171\pi\)
0.473000 + 0.881063i \(0.343171\pi\)
\(660\) −0.981354 −0.0381991
\(661\) 8.41934 0.327474 0.163737 0.986504i \(-0.447645\pi\)
0.163737 + 0.986504i \(0.447645\pi\)
\(662\) −12.8062 −0.497726
\(663\) 1.83794 0.0713799
\(664\) 5.34182 0.207303
\(665\) −10.4889 −0.406742
\(666\) 30.7567 1.19180
\(667\) −40.8396 −1.58131
\(668\) 71.3992 2.76252
\(669\) 0.933703 0.0360991
\(670\) 31.4789 1.21614
\(671\) −1.13961 −0.0439942
\(672\) 3.94490 0.152178
\(673\) −32.8860 −1.26766 −0.633831 0.773472i \(-0.718518\pi\)
−0.633831 + 0.773472i \(0.718518\pi\)
\(674\) −16.5562 −0.637720
\(675\) 4.85393 0.186828
\(676\) 75.8605 2.91771
\(677\) −29.7603 −1.14378 −0.571891 0.820329i \(-0.693790\pi\)
−0.571891 + 0.820329i \(0.693790\pi\)
\(678\) −0.472263 −0.0181372
\(679\) −2.61064 −0.100187
\(680\) 3.44153 0.131977
\(681\) 4.28060 0.164033
\(682\) −7.13916 −0.273372
\(683\) 30.0115 1.14836 0.574180 0.818729i \(-0.305321\pi\)
0.574180 + 0.818729i \(0.305321\pi\)
\(684\) 30.7867 1.17716
\(685\) 11.4702 0.438253
\(686\) 44.8482 1.71231
\(687\) 0.299567 0.0114292
\(688\) 0.899115 0.0342784
\(689\) −41.4466 −1.57899
\(690\) 5.48527 0.208821
\(691\) 14.8505 0.564941 0.282470 0.959276i \(-0.408846\pi\)
0.282470 + 0.959276i \(0.408846\pi\)
\(692\) −4.76648 −0.181194
\(693\) 4.24133 0.161115
\(694\) −61.4793 −2.33372
\(695\) 22.1563 0.840437
\(696\) −5.09571 −0.193152
\(697\) 7.24643 0.274478
\(698\) −57.1091 −2.16161
\(699\) −1.68046 −0.0635609
\(700\) −16.7071 −0.631471
\(701\) −47.4476 −1.79207 −0.896035 0.443984i \(-0.853565\pi\)
−0.896035 + 0.443984i \(0.853565\pi\)
\(702\) −24.3548 −0.919214
\(703\) −16.4751 −0.621371
\(704\) 9.46970 0.356903
\(705\) −0.395663 −0.0149015
\(706\) −60.3063 −2.26966
\(707\) 21.4956 0.808424
\(708\) 6.38552 0.239983
\(709\) 29.2229 1.09749 0.548744 0.835991i \(-0.315106\pi\)
0.548744 + 0.835991i \(0.315106\pi\)
\(710\) 4.74539 0.178091
\(711\) 36.5540 1.37088
\(712\) 14.2212 0.532964
\(713\) 24.0222 0.899637
\(714\) 1.33760 0.0500584
\(715\) 6.72086 0.251346
\(716\) 33.2771 1.24363
\(717\) 5.75020 0.214745
\(718\) 10.8765 0.405908
\(719\) −50.0086 −1.86501 −0.932504 0.361160i \(-0.882381\pi\)
−0.932504 + 0.361160i \(0.882381\pi\)
\(720\) 3.92039 0.146104
\(721\) 30.5932 1.13935
\(722\) 15.1974 0.565589
\(723\) −4.15975 −0.154703
\(724\) −58.6498 −2.17970
\(725\) −20.5256 −0.762301
\(726\) 6.99141 0.259476
\(727\) 23.3036 0.864281 0.432141 0.901806i \(-0.357758\pi\)
0.432141 + 0.901806i \(0.357758\pi\)
\(728\) 28.4060 1.05280
\(729\) −22.3267 −0.826916
\(730\) 8.95214 0.331334
\(731\) 1.00000 0.0369863
\(732\) 1.41198 0.0521883
\(733\) −48.4850 −1.79084 −0.895418 0.445226i \(-0.853123\pi\)
−0.895418 + 0.445226i \(0.853123\pi\)
\(734\) −49.0698 −1.81120
\(735\) −1.33232 −0.0491433
\(736\) −36.2643 −1.33672
\(737\) 6.81837 0.251158
\(738\) −47.2911 −1.74081
\(739\) 19.4837 0.716718 0.358359 0.933584i \(-0.383336\pi\)
0.358359 + 0.933584i \(0.383336\pi\)
\(740\) 21.3525 0.784934
\(741\) 6.42505 0.236030
\(742\) −30.1635 −1.10734
\(743\) −34.6568 −1.27143 −0.635717 0.771923i \(-0.719295\pi\)
−0.635717 + 0.771923i \(0.719295\pi\)
\(744\) 2.99734 0.109888
\(745\) −25.4757 −0.933359
\(746\) 48.1955 1.76456
\(747\) 6.76788 0.247624
\(748\) 2.19987 0.0804351
\(749\) 8.16693 0.298413
\(750\) 7.75684 0.283240
\(751\) 28.0231 1.02258 0.511288 0.859409i \(-0.329169\pi\)
0.511288 + 0.859409i \(0.329169\pi\)
\(752\) 0.797465 0.0290806
\(753\) −9.15515 −0.333632
\(754\) 102.988 3.75061
\(755\) 12.0407 0.438205
\(756\) −10.6702 −0.388070
\(757\) −43.7631 −1.59060 −0.795298 0.606218i \(-0.792686\pi\)
−0.795298 + 0.606218i \(0.792686\pi\)
\(758\) 25.5285 0.927238
\(759\) 1.18812 0.0431259
\(760\) 12.0308 0.436404
\(761\) 39.4736 1.43092 0.715458 0.698656i \(-0.246218\pi\)
0.715458 + 0.698656i \(0.246218\pi\)
\(762\) 3.38554 0.122645
\(763\) −33.2715 −1.20451
\(764\) −15.0672 −0.545112
\(765\) 4.36028 0.157646
\(766\) −15.5732 −0.562682
\(767\) −43.7316 −1.57906
\(768\) −2.90459 −0.104811
\(769\) −0.768704 −0.0277202 −0.0138601 0.999904i \(-0.504412\pi\)
−0.0138601 + 0.999904i \(0.504412\pi\)
\(770\) 4.89123 0.176268
\(771\) −5.64963 −0.203466
\(772\) −54.9777 −1.97869
\(773\) 17.8421 0.641735 0.320868 0.947124i \(-0.396026\pi\)
0.320868 + 0.947124i \(0.396026\pi\)
\(774\) −6.52613 −0.234577
\(775\) 12.0733 0.433686
\(776\) 2.99442 0.107494
\(777\) 2.81216 0.100886
\(778\) 44.1951 1.58447
\(779\) 25.3319 0.907610
\(780\) −8.32716 −0.298160
\(781\) 1.02786 0.0367796
\(782\) −12.2961 −0.439709
\(783\) −13.1089 −0.468472
\(784\) 2.68531 0.0959038
\(785\) 21.3418 0.761721
\(786\) 9.63413 0.343638
\(787\) −42.3067 −1.50807 −0.754036 0.656833i \(-0.771896\pi\)
−0.754036 + 0.656833i \(0.771896\pi\)
\(788\) −23.0245 −0.820215
\(789\) 7.45576 0.265432
\(790\) 42.1552 1.49981
\(791\) 1.41700 0.0503827
\(792\) −4.86484 −0.172864
\(793\) −9.67004 −0.343393
\(794\) −83.4208 −2.96049
\(795\) 2.99630 0.106268
\(796\) 65.2392 2.31234
\(797\) −40.4473 −1.43272 −0.716359 0.697732i \(-0.754193\pi\)
−0.716359 + 0.697732i \(0.754193\pi\)
\(798\) 4.67595 0.165527
\(799\) 0.886945 0.0313779
\(800\) −18.2261 −0.644389
\(801\) 18.0177 0.636626
\(802\) 38.0958 1.34521
\(803\) 1.93905 0.0684274
\(804\) −8.44798 −0.297937
\(805\) −16.4582 −0.580077
\(806\) −60.5785 −2.13379
\(807\) −2.72637 −0.0959729
\(808\) −24.6556 −0.867380
\(809\) −32.9962 −1.16009 −0.580043 0.814586i \(-0.696964\pi\)
−0.580043 + 0.814586i \(0.696964\pi\)
\(810\) −27.5622 −0.968437
\(811\) 10.8857 0.382250 0.191125 0.981566i \(-0.438786\pi\)
0.191125 + 0.981566i \(0.438786\pi\)
\(812\) 45.1205 1.58342
\(813\) −4.91911 −0.172521
\(814\) 7.68275 0.269280
\(815\) 22.6090 0.791958
\(816\) 0.267802 0.00937496
\(817\) 3.49578 0.122302
\(818\) −31.7137 −1.10884
\(819\) 35.9893 1.25757
\(820\) −32.8313 −1.14652
\(821\) 15.2962 0.533840 0.266920 0.963719i \(-0.413994\pi\)
0.266920 + 0.963719i \(0.413994\pi\)
\(822\) −5.11341 −0.178351
\(823\) −39.0366 −1.36073 −0.680365 0.732874i \(-0.738179\pi\)
−0.680365 + 0.732874i \(0.738179\pi\)
\(824\) −35.0906 −1.22244
\(825\) 0.597136 0.0207896
\(826\) −31.8265 −1.10739
\(827\) −35.6204 −1.23864 −0.619321 0.785138i \(-0.712592\pi\)
−0.619321 + 0.785138i \(0.712592\pi\)
\(828\) 48.3078 1.67881
\(829\) 7.02324 0.243927 0.121964 0.992535i \(-0.461081\pi\)
0.121964 + 0.992535i \(0.461081\pi\)
\(830\) 7.80492 0.270913
\(831\) −6.41475 −0.222525
\(832\) 80.3540 2.78578
\(833\) 2.98661 0.103480
\(834\) −9.87729 −0.342022
\(835\) 35.3500 1.22334
\(836\) 7.69025 0.265973
\(837\) 7.71073 0.266522
\(838\) 11.6670 0.403030
\(839\) −20.7784 −0.717350 −0.358675 0.933463i \(-0.616771\pi\)
−0.358675 + 0.933463i \(0.616771\pi\)
\(840\) −2.05356 −0.0708545
\(841\) 26.4328 0.911476
\(842\) 14.4966 0.499586
\(843\) −9.31009 −0.320657
\(844\) −33.6645 −1.15878
\(845\) 37.5587 1.29206
\(846\) −5.78831 −0.199006
\(847\) −20.9773 −0.720790
\(848\) −6.03908 −0.207383
\(849\) −9.67380 −0.332004
\(850\) −6.17992 −0.211969
\(851\) −25.8513 −0.886171
\(852\) −1.27352 −0.0436300
\(853\) −11.8924 −0.407187 −0.203593 0.979056i \(-0.565262\pi\)
−0.203593 + 0.979056i \(0.565262\pi\)
\(854\) −7.03755 −0.240820
\(855\) 15.2426 0.521286
\(856\) −9.36753 −0.320175
\(857\) −4.94434 −0.168895 −0.0844477 0.996428i \(-0.526913\pi\)
−0.0844477 + 0.996428i \(0.526913\pi\)
\(858\) −2.99616 −0.102287
\(859\) 25.4450 0.868173 0.434086 0.900871i \(-0.357071\pi\)
0.434086 + 0.900871i \(0.357071\pi\)
\(860\) −4.53069 −0.154495
\(861\) −4.32393 −0.147359
\(862\) −19.4876 −0.663749
\(863\) −47.4756 −1.61609 −0.808044 0.589122i \(-0.799474\pi\)
−0.808044 + 0.589122i \(0.799474\pi\)
\(864\) −11.6403 −0.396010
\(865\) −2.35990 −0.0802389
\(866\) −51.2835 −1.74268
\(867\) 0.297851 0.0101156
\(868\) −26.5402 −0.900834
\(869\) 9.13087 0.309743
\(870\) −7.44532 −0.252420
\(871\) 57.8565 1.96039
\(872\) 38.1626 1.29235
\(873\) 3.79381 0.128401
\(874\) −42.9846 −1.45398
\(875\) −23.2740 −0.786804
\(876\) −2.40248 −0.0811724
\(877\) −20.3887 −0.688478 −0.344239 0.938882i \(-0.611863\pi\)
−0.344239 + 0.938882i \(0.611863\pi\)
\(878\) 33.5570 1.13250
\(879\) 1.50070 0.0506173
\(880\) 0.979280 0.0330115
\(881\) −10.0601 −0.338933 −0.169467 0.985536i \(-0.554204\pi\)
−0.169467 + 0.985536i \(0.554204\pi\)
\(882\) −19.4910 −0.656296
\(883\) −44.0687 −1.48303 −0.741514 0.670937i \(-0.765892\pi\)
−0.741514 + 0.670937i \(0.765892\pi\)
\(884\) 18.6667 0.627829
\(885\) 3.16149 0.106272
\(886\) −34.1222 −1.14636
\(887\) 29.9883 1.00691 0.503454 0.864022i \(-0.332063\pi\)
0.503454 + 0.864022i \(0.332063\pi\)
\(888\) −3.22556 −0.108243
\(889\) −10.1581 −0.340693
\(890\) 20.7786 0.696501
\(891\) −5.97001 −0.200003
\(892\) 9.48297 0.317513
\(893\) 3.10057 0.103756
\(894\) 11.3571 0.379838
\(895\) 16.4756 0.550719
\(896\) 31.9901 1.06871
\(897\) 10.0816 0.336615
\(898\) −41.7444 −1.39303
\(899\) −32.6060 −1.08747
\(900\) 24.2790 0.809301
\(901\) −6.71670 −0.223766
\(902\) −11.8129 −0.393326
\(903\) −0.596699 −0.0198569
\(904\) −1.62531 −0.0540570
\(905\) −29.0377 −0.965244
\(906\) −5.36774 −0.178331
\(907\) 51.4179 1.70730 0.853651 0.520845i \(-0.174383\pi\)
0.853651 + 0.520845i \(0.174383\pi\)
\(908\) 43.4750 1.44277
\(909\) −31.2376 −1.03609
\(910\) 41.5040 1.37584
\(911\) −52.8464 −1.75088 −0.875440 0.483327i \(-0.839428\pi\)
−0.875440 + 0.483327i \(0.839428\pi\)
\(912\) 0.936178 0.0310000
\(913\) 1.69056 0.0559492
\(914\) −87.6973 −2.90077
\(915\) 0.699076 0.0231107
\(916\) 3.04249 0.100527
\(917\) −28.9067 −0.954582
\(918\) −3.94686 −0.130266
\(919\) 32.5708 1.07441 0.537207 0.843451i \(-0.319480\pi\)
0.537207 + 0.843451i \(0.319480\pi\)
\(920\) 18.8777 0.622380
\(921\) −6.65474 −0.219281
\(922\) 36.9331 1.21633
\(923\) 8.72176 0.287080
\(924\) −1.31266 −0.0431832
\(925\) −12.9926 −0.427194
\(926\) −20.0394 −0.658534
\(927\) −44.4584 −1.46021
\(928\) 49.2226 1.61581
\(929\) 12.9124 0.423643 0.211821 0.977308i \(-0.432060\pi\)
0.211821 + 0.977308i \(0.432060\pi\)
\(930\) 4.37940 0.143606
\(931\) 10.4405 0.342175
\(932\) −17.0673 −0.559057
\(933\) 1.90953 0.0625153
\(934\) 7.41555 0.242644
\(935\) 1.08916 0.0356193
\(936\) −41.2800 −1.34928
\(937\) 8.41379 0.274867 0.137433 0.990511i \(-0.456115\pi\)
0.137433 + 0.990511i \(0.456115\pi\)
\(938\) 42.1061 1.37481
\(939\) 9.15183 0.298659
\(940\) −4.01847 −0.131068
\(941\) −25.6024 −0.834613 −0.417306 0.908766i \(-0.637026\pi\)
−0.417306 + 0.908766i \(0.637026\pi\)
\(942\) −9.51417 −0.309989
\(943\) 39.7486 1.29439
\(944\) −6.37203 −0.207392
\(945\) −5.28283 −0.171851
\(946\) −1.63017 −0.0530013
\(947\) −4.38905 −0.142625 −0.0713125 0.997454i \(-0.522719\pi\)
−0.0713125 + 0.997454i \(0.522719\pi\)
\(948\) −11.3132 −0.367435
\(949\) 16.4535 0.534105
\(950\) −21.6036 −0.700915
\(951\) −2.18593 −0.0708838
\(952\) 4.60339 0.149197
\(953\) −35.5810 −1.15258 −0.576291 0.817245i \(-0.695500\pi\)
−0.576291 + 0.817245i \(0.695500\pi\)
\(954\) 43.8340 1.41918
\(955\) −7.45981 −0.241394
\(956\) 58.4007 1.88881
\(957\) −1.61267 −0.0521301
\(958\) 4.49916 0.145361
\(959\) 15.3425 0.495435
\(960\) −5.80903 −0.187486
\(961\) −11.8209 −0.381319
\(962\) 65.1911 2.10185
\(963\) −11.8683 −0.382450
\(964\) −42.2476 −1.36070
\(965\) −27.2196 −0.876231
\(966\) 7.33709 0.236067
\(967\) −32.6623 −1.05035 −0.525175 0.850995i \(-0.676000\pi\)
−0.525175 + 0.850995i \(0.676000\pi\)
\(968\) 24.0612 0.773355
\(969\) 1.04122 0.0334489
\(970\) 4.37514 0.140477
\(971\) 19.6855 0.631739 0.315870 0.948803i \(-0.397704\pi\)
0.315870 + 0.948803i \(0.397704\pi\)
\(972\) 23.3754 0.749766
\(973\) 29.6362 0.950095
\(974\) −14.8364 −0.475390
\(975\) 5.06692 0.162271
\(976\) −1.40900 −0.0451009
\(977\) −1.71351 −0.0548201 −0.0274101 0.999624i \(-0.508726\pi\)
−0.0274101 + 0.999624i \(0.508726\pi\)
\(978\) −10.0791 −0.322294
\(979\) 4.50067 0.143842
\(980\) −13.5314 −0.432245
\(981\) 48.3505 1.54371
\(982\) −22.6282 −0.722094
\(983\) 45.9288 1.46490 0.732450 0.680820i \(-0.238377\pi\)
0.732450 + 0.680820i \(0.238377\pi\)
\(984\) 4.95958 0.158106
\(985\) −11.3995 −0.363218
\(986\) 16.6899 0.531515
\(987\) −0.529239 −0.0168459
\(988\) 65.2547 2.07603
\(989\) 5.48527 0.174421
\(990\) −7.10799 −0.225907
\(991\) −21.9620 −0.697645 −0.348822 0.937189i \(-0.613418\pi\)
−0.348822 + 0.937189i \(0.613418\pi\)
\(992\) −28.9531 −0.919263
\(993\) 1.70156 0.0539975
\(994\) 6.34743 0.201328
\(995\) 32.3001 1.02398
\(996\) −2.09460 −0.0663700
\(997\) −13.0783 −0.414194 −0.207097 0.978320i \(-0.566402\pi\)
−0.207097 + 0.978320i \(0.566402\pi\)
\(998\) 21.7109 0.687247
\(999\) −8.29785 −0.262532
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 731.2.a.c.1.2 6
3.2 odd 2 6579.2.a.j.1.5 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
731.2.a.c.1.2 6 1.1 even 1 trivial
6579.2.a.j.1.5 6 3.2 odd 2