Properties

Label 731.2.a.c.1.4
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 1.4
Root \(-1.30704\)
Character \(\chi\) = 731.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.291653 q^{2} -0.858197 q^{3} -1.91494 q^{4} +3.99528 q^{5} -0.250296 q^{6} -2.74049 q^{7} -1.14180 q^{8} -2.26350 q^{9} +O(q^{10})\) \(q+0.291653 q^{2} -0.858197 q^{3} -1.91494 q^{4} +3.99528 q^{5} -0.250296 q^{6} -2.74049 q^{7} -1.14180 q^{8} -2.26350 q^{9} +1.16523 q^{10} +3.05674 q^{11} +1.64339 q^{12} -5.80993 q^{13} -0.799273 q^{14} -3.42873 q^{15} +3.49687 q^{16} -1.00000 q^{17} -0.660156 q^{18} -3.69042 q^{19} -7.65071 q^{20} +2.35188 q^{21} +0.891508 q^{22} -2.72155 q^{23} +0.979892 q^{24} +10.9622 q^{25} -1.69448 q^{26} +4.51712 q^{27} +5.24788 q^{28} -10.1277 q^{29} -1.00000 q^{30} +3.83106 q^{31} +3.30348 q^{32} -2.62329 q^{33} -0.291653 q^{34} -10.9490 q^{35} +4.33446 q^{36} -9.47073 q^{37} -1.07632 q^{38} +4.98607 q^{39} -4.56182 q^{40} -10.0824 q^{41} +0.685933 q^{42} -1.00000 q^{43} -5.85347 q^{44} -9.04330 q^{45} -0.793748 q^{46} +7.25723 q^{47} -3.00100 q^{48} +0.510306 q^{49} +3.19717 q^{50} +0.858197 q^{51} +11.1257 q^{52} -0.0256123 q^{53} +1.31743 q^{54} +12.2125 q^{55} +3.12911 q^{56} +3.16711 q^{57} -2.95377 q^{58} -4.19905 q^{59} +6.56581 q^{60} -6.73795 q^{61} +1.11734 q^{62} +6.20310 q^{63} -6.03026 q^{64} -23.2123 q^{65} -0.765089 q^{66} +11.5581 q^{67} +1.91494 q^{68} +2.33563 q^{69} -3.19332 q^{70} -8.72587 q^{71} +2.58447 q^{72} +3.33134 q^{73} -2.76217 q^{74} -9.40775 q^{75} +7.06693 q^{76} -8.37698 q^{77} +1.45420 q^{78} -6.10660 q^{79} +13.9709 q^{80} +2.91392 q^{81} -2.94057 q^{82} -8.98937 q^{83} -4.50371 q^{84} -3.99528 q^{85} -0.291653 q^{86} +8.69156 q^{87} -3.49020 q^{88} -0.838307 q^{89} -2.63751 q^{90} +15.9221 q^{91} +5.21160 q^{92} -3.28780 q^{93} +2.11659 q^{94} -14.7442 q^{95} -2.83503 q^{96} +17.2844 q^{97} +0.148832 q^{98} -6.91893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - q^{2} - 3q^{3} + 5q^{4} + 3q^{5} - 7q^{6} - 7q^{7} - 9q^{8} - 3q^{9} + O(q^{10}) \) \( 6q - q^{2} - 3q^{3} + 5q^{4} + 3q^{5} - 7q^{6} - 7q^{7} - 9q^{8} - 3q^{9} - 4q^{10} + 4q^{11} + 11q^{12} - 10q^{13} - 7q^{14} + q^{15} - q^{16} - 6q^{17} + q^{18} - 20q^{19} + q^{20} - 8q^{21} + 2q^{22} - 3q^{23} - 9q^{24} - 7q^{25} - 3q^{26} - 6q^{27} - 11q^{28} - 15q^{29} - 6q^{30} + 12q^{31} + q^{32} - 2q^{33} + q^{34} - 9q^{35} - 16q^{36} - 14q^{37} + 27q^{38} + 5q^{39} - 7q^{40} - 2q^{41} + 19q^{42} - 6q^{43} - 12q^{44} - 18q^{45} + 14q^{46} - 11q^{47} - 6q^{48} + 3q^{49} + 7q^{50} + 3q^{51} - 5q^{52} + 3q^{53} + 25q^{54} + 6q^{55} + 22q^{56} + 11q^{57} - 21q^{58} + 2q^{59} - q^{60} - 20q^{61} + 3q^{62} + 23q^{63} - 39q^{64} - 34q^{65} + 7q^{66} - 2q^{67} - 5q^{68} - 17q^{69} - q^{70} + q^{71} + 21q^{72} + 13q^{73} + 28q^{74} - 5q^{75} - 29q^{76} - 11q^{77} - 26q^{79} + 12q^{80} + 2q^{81} - 9q^{82} + 10q^{83} - 3q^{84} - 3q^{85} + q^{86} + 12q^{87} - 6q^{88} - 15q^{89} + 15q^{90} + 8q^{91} - 9q^{92} - 11q^{93} - 33q^{94} - 21q^{95} + 25q^{96} - 22q^{97} - 3q^{98} - 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.291653 0.206230 0.103115 0.994669i \(-0.467119\pi\)
0.103115 + 0.994669i \(0.467119\pi\)
\(3\) −0.858197 −0.495480 −0.247740 0.968827i \(-0.579688\pi\)
−0.247740 + 0.968827i \(0.579688\pi\)
\(4\) −1.91494 −0.957469
\(5\) 3.99528 1.78674 0.893371 0.449320i \(-0.148334\pi\)
0.893371 + 0.449320i \(0.148334\pi\)
\(6\) −0.250296 −0.102183
\(7\) −2.74049 −1.03581 −0.517905 0.855438i \(-0.673288\pi\)
−0.517905 + 0.855438i \(0.673288\pi\)
\(8\) −1.14180 −0.403688
\(9\) −2.26350 −0.754500
\(10\) 1.16523 0.368479
\(11\) 3.05674 0.921642 0.460821 0.887493i \(-0.347555\pi\)
0.460821 + 0.887493i \(0.347555\pi\)
\(12\) 1.64339 0.474407
\(13\) −5.80993 −1.61139 −0.805693 0.592333i \(-0.798207\pi\)
−0.805693 + 0.592333i \(0.798207\pi\)
\(14\) −0.799273 −0.213615
\(15\) −3.42873 −0.885295
\(16\) 3.49687 0.874217
\(17\) −1.00000 −0.242536
\(18\) −0.660156 −0.155600
\(19\) −3.69042 −0.846641 −0.423320 0.905980i \(-0.639135\pi\)
−0.423320 + 0.905980i \(0.639135\pi\)
\(20\) −7.65071 −1.71075
\(21\) 2.35188 0.513223
\(22\) 0.891508 0.190070
\(23\) −2.72155 −0.567482 −0.283741 0.958901i \(-0.591576\pi\)
−0.283741 + 0.958901i \(0.591576\pi\)
\(24\) 0.979892 0.200020
\(25\) 10.9622 2.19245
\(26\) −1.69448 −0.332316
\(27\) 4.51712 0.869320
\(28\) 5.24788 0.991756
\(29\) −10.1277 −1.88067 −0.940334 0.340254i \(-0.889487\pi\)
−0.940334 + 0.340254i \(0.889487\pi\)
\(30\) −1.00000 −0.182574
\(31\) 3.83106 0.688079 0.344039 0.938955i \(-0.388205\pi\)
0.344039 + 0.938955i \(0.388205\pi\)
\(32\) 3.30348 0.583978
\(33\) −2.62329 −0.456655
\(34\) −0.291653 −0.0500181
\(35\) −10.9490 −1.85072
\(36\) 4.33446 0.722410
\(37\) −9.47073 −1.55698 −0.778489 0.627658i \(-0.784014\pi\)
−0.778489 + 0.627658i \(0.784014\pi\)
\(38\) −1.07632 −0.174602
\(39\) 4.98607 0.798410
\(40\) −4.56182 −0.721287
\(41\) −10.0824 −1.57461 −0.787305 0.616564i \(-0.788524\pi\)
−0.787305 + 0.616564i \(0.788524\pi\)
\(42\) 0.685933 0.105842
\(43\) −1.00000 −0.152499
\(44\) −5.85347 −0.882444
\(45\) −9.04330 −1.34810
\(46\) −0.793748 −0.117032
\(47\) 7.25723 1.05858 0.529288 0.848442i \(-0.322459\pi\)
0.529288 + 0.848442i \(0.322459\pi\)
\(48\) −3.00100 −0.433157
\(49\) 0.510306 0.0729009
\(50\) 3.19717 0.452148
\(51\) 0.858197 0.120172
\(52\) 11.1257 1.54285
\(53\) −0.0256123 −0.00351813 −0.00175906 0.999998i \(-0.500560\pi\)
−0.00175906 + 0.999998i \(0.500560\pi\)
\(54\) 1.31743 0.179280
\(55\) 12.2125 1.64674
\(56\) 3.12911 0.418144
\(57\) 3.16711 0.419493
\(58\) −2.95377 −0.387850
\(59\) −4.19905 −0.546670 −0.273335 0.961919i \(-0.588127\pi\)
−0.273335 + 0.961919i \(0.588127\pi\)
\(60\) 6.56581 0.847643
\(61\) −6.73795 −0.862706 −0.431353 0.902183i \(-0.641964\pi\)
−0.431353 + 0.902183i \(0.641964\pi\)
\(62\) 1.11734 0.141902
\(63\) 6.20310 0.781518
\(64\) −6.03026 −0.753783
\(65\) −23.2123 −2.87913
\(66\) −0.765089 −0.0941759
\(67\) 11.5581 1.41205 0.706024 0.708188i \(-0.250487\pi\)
0.706024 + 0.708188i \(0.250487\pi\)
\(68\) 1.91494 0.232220
\(69\) 2.33563 0.281176
\(70\) −3.19332 −0.381674
\(71\) −8.72587 −1.03557 −0.517785 0.855511i \(-0.673243\pi\)
−0.517785 + 0.855511i \(0.673243\pi\)
\(72\) 2.58447 0.304583
\(73\) 3.33134 0.389904 0.194952 0.980813i \(-0.437545\pi\)
0.194952 + 0.980813i \(0.437545\pi\)
\(74\) −2.76217 −0.321095
\(75\) −9.40775 −1.08631
\(76\) 7.06693 0.810632
\(77\) −8.37698 −0.954646
\(78\) 1.45420 0.164656
\(79\) −6.10660 −0.687046 −0.343523 0.939144i \(-0.611620\pi\)
−0.343523 + 0.939144i \(0.611620\pi\)
\(80\) 13.9709 1.56200
\(81\) 2.91392 0.323769
\(82\) −2.94057 −0.324732
\(83\) −8.98937 −0.986712 −0.493356 0.869828i \(-0.664230\pi\)
−0.493356 + 0.869828i \(0.664230\pi\)
\(84\) −4.50371 −0.491395
\(85\) −3.99528 −0.433349
\(86\) −0.291653 −0.0314497
\(87\) 8.69156 0.931833
\(88\) −3.49020 −0.372056
\(89\) −0.838307 −0.0888604 −0.0444302 0.999012i \(-0.514147\pi\)
−0.0444302 + 0.999012i \(0.514147\pi\)
\(90\) −2.63751 −0.278018
\(91\) 15.9221 1.66909
\(92\) 5.21160 0.543347
\(93\) −3.28780 −0.340929
\(94\) 2.11659 0.218310
\(95\) −14.7442 −1.51273
\(96\) −2.83503 −0.289349
\(97\) 17.2844 1.75497 0.877483 0.479607i \(-0.159221\pi\)
0.877483 + 0.479607i \(0.159221\pi\)
\(98\) 0.148832 0.0150343
\(99\) −6.91893 −0.695379
\(100\) −20.9920 −2.09920
\(101\) −5.66451 −0.563640 −0.281820 0.959467i \(-0.590938\pi\)
−0.281820 + 0.959467i \(0.590938\pi\)
\(102\) 0.250296 0.0247830
\(103\) 7.12119 0.701672 0.350836 0.936437i \(-0.385898\pi\)
0.350836 + 0.936437i \(0.385898\pi\)
\(104\) 6.63380 0.650498
\(105\) 9.39642 0.916997
\(106\) −0.00746991 −0.000725542 0
\(107\) 19.2706 1.86296 0.931481 0.363790i \(-0.118517\pi\)
0.931481 + 0.363790i \(0.118517\pi\)
\(108\) −8.65000 −0.832347
\(109\) −3.88034 −0.371669 −0.185835 0.982581i \(-0.559499\pi\)
−0.185835 + 0.982581i \(0.559499\pi\)
\(110\) 3.56182 0.339606
\(111\) 8.12775 0.771452
\(112\) −9.58314 −0.905522
\(113\) 16.4216 1.54481 0.772407 0.635128i \(-0.219053\pi\)
0.772407 + 0.635128i \(0.219053\pi\)
\(114\) 0.923696 0.0865120
\(115\) −10.8733 −1.01394
\(116\) 19.3939 1.80068
\(117\) 13.1508 1.21579
\(118\) −1.22467 −0.112740
\(119\) 2.74049 0.251221
\(120\) 3.91494 0.357383
\(121\) −1.65633 −0.150575
\(122\) −1.96514 −0.177916
\(123\) 8.65270 0.780188
\(124\) −7.33624 −0.658814
\(125\) 23.8208 2.13059
\(126\) 1.80915 0.161172
\(127\) −9.00730 −0.799268 −0.399634 0.916675i \(-0.630863\pi\)
−0.399634 + 0.916675i \(0.630863\pi\)
\(128\) −8.36570 −0.739430
\(129\) 0.858197 0.0755600
\(130\) −6.76993 −0.593762
\(131\) 17.6371 1.54096 0.770480 0.637464i \(-0.220017\pi\)
0.770480 + 0.637464i \(0.220017\pi\)
\(132\) 5.02343 0.437234
\(133\) 10.1136 0.876958
\(134\) 3.37096 0.291206
\(135\) 18.0471 1.55325
\(136\) 1.14180 0.0979088
\(137\) −14.7349 −1.25889 −0.629445 0.777045i \(-0.716718\pi\)
−0.629445 + 0.777045i \(0.716718\pi\)
\(138\) 0.681192 0.0579869
\(139\) 9.48346 0.804376 0.402188 0.915557i \(-0.368250\pi\)
0.402188 + 0.915557i \(0.368250\pi\)
\(140\) 20.9667 1.77201
\(141\) −6.22813 −0.524503
\(142\) −2.54493 −0.213565
\(143\) −17.7595 −1.48512
\(144\) −7.91515 −0.659596
\(145\) −40.4630 −3.36027
\(146\) 0.971595 0.0804098
\(147\) −0.437943 −0.0361210
\(148\) 18.1359 1.49076
\(149\) 19.5571 1.60218 0.801091 0.598543i \(-0.204253\pi\)
0.801091 + 0.598543i \(0.204253\pi\)
\(150\) −2.74380 −0.224030
\(151\) 2.35499 0.191647 0.0958233 0.995398i \(-0.469452\pi\)
0.0958233 + 0.995398i \(0.469452\pi\)
\(152\) 4.21373 0.341779
\(153\) 2.26350 0.182993
\(154\) −2.44317 −0.196876
\(155\) 15.3061 1.22942
\(156\) −9.54801 −0.764453
\(157\) 8.30078 0.662475 0.331237 0.943547i \(-0.392534\pi\)
0.331237 + 0.943547i \(0.392534\pi\)
\(158\) −1.78101 −0.141689
\(159\) 0.0219804 0.00174316
\(160\) 13.1983 1.04342
\(161\) 7.45839 0.587804
\(162\) 0.849854 0.0667708
\(163\) 16.9278 1.32588 0.662942 0.748670i \(-0.269307\pi\)
0.662942 + 0.748670i \(0.269307\pi\)
\(164\) 19.3072 1.50764
\(165\) −10.4808 −0.815925
\(166\) −2.62178 −0.203489
\(167\) −3.65977 −0.283202 −0.141601 0.989924i \(-0.545225\pi\)
−0.141601 + 0.989924i \(0.545225\pi\)
\(168\) −2.68539 −0.207182
\(169\) 20.7553 1.59656
\(170\) −1.16523 −0.0893694
\(171\) 8.35326 0.638790
\(172\) 1.91494 0.146013
\(173\) −8.91665 −0.677920 −0.338960 0.940801i \(-0.610075\pi\)
−0.338960 + 0.940801i \(0.610075\pi\)
\(174\) 2.53492 0.192172
\(175\) −30.0419 −2.27096
\(176\) 10.6890 0.805715
\(177\) 3.60361 0.270864
\(178\) −0.244495 −0.0183257
\(179\) −1.72001 −0.128559 −0.0642796 0.997932i \(-0.520475\pi\)
−0.0642796 + 0.997932i \(0.520475\pi\)
\(180\) 17.3174 1.29076
\(181\) −18.1564 −1.34956 −0.674779 0.738020i \(-0.735761\pi\)
−0.674779 + 0.738020i \(0.735761\pi\)
\(182\) 4.64372 0.344216
\(183\) 5.78249 0.427454
\(184\) 3.10748 0.229086
\(185\) −37.8382 −2.78192
\(186\) −0.958897 −0.0703098
\(187\) −3.05674 −0.223531
\(188\) −13.8972 −1.01355
\(189\) −12.3791 −0.900449
\(190\) −4.30020 −0.311970
\(191\) −3.06795 −0.221989 −0.110994 0.993821i \(-0.535404\pi\)
−0.110994 + 0.993821i \(0.535404\pi\)
\(192\) 5.17515 0.373484
\(193\) 11.9306 0.858785 0.429393 0.903118i \(-0.358728\pi\)
0.429393 + 0.903118i \(0.358728\pi\)
\(194\) 5.04105 0.361926
\(195\) 19.9207 1.42655
\(196\) −0.977206 −0.0698004
\(197\) −1.46807 −0.104596 −0.0522980 0.998632i \(-0.516655\pi\)
−0.0522980 + 0.998632i \(0.516655\pi\)
\(198\) −2.01793 −0.143408
\(199\) −23.7362 −1.68261 −0.841306 0.540559i \(-0.818213\pi\)
−0.841306 + 0.540559i \(0.818213\pi\)
\(200\) −12.5167 −0.885065
\(201\) −9.91913 −0.699641
\(202\) −1.65207 −0.116239
\(203\) 27.7549 1.94801
\(204\) −1.64339 −0.115061
\(205\) −40.2821 −2.81342
\(206\) 2.07692 0.144706
\(207\) 6.16022 0.428165
\(208\) −20.3166 −1.40870
\(209\) −11.2807 −0.780300
\(210\) 2.74049 0.189112
\(211\) −16.7405 −1.15246 −0.576230 0.817287i \(-0.695477\pi\)
−0.576230 + 0.817287i \(0.695477\pi\)
\(212\) 0.0490461 0.00336850
\(213\) 7.48851 0.513105
\(214\) 5.62034 0.384198
\(215\) −3.99528 −0.272476
\(216\) −5.15766 −0.350934
\(217\) −10.4990 −0.712718
\(218\) −1.13171 −0.0766493
\(219\) −2.85895 −0.193190
\(220\) −23.3862 −1.57670
\(221\) 5.80993 0.390818
\(222\) 2.37048 0.159096
\(223\) 19.7499 1.32255 0.661275 0.750143i \(-0.270016\pi\)
0.661275 + 0.750143i \(0.270016\pi\)
\(224\) −9.05316 −0.604890
\(225\) −24.8130 −1.65420
\(226\) 4.78941 0.318587
\(227\) −18.2590 −1.21189 −0.605945 0.795506i \(-0.707205\pi\)
−0.605945 + 0.795506i \(0.707205\pi\)
\(228\) −6.06481 −0.401652
\(229\) −8.84328 −0.584381 −0.292190 0.956360i \(-0.594384\pi\)
−0.292190 + 0.956360i \(0.594384\pi\)
\(230\) −3.17124 −0.209106
\(231\) 7.18910 0.473008
\(232\) 11.5638 0.759204
\(233\) 0.229827 0.0150565 0.00752823 0.999972i \(-0.497604\pi\)
0.00752823 + 0.999972i \(0.497604\pi\)
\(234\) 3.83546 0.250732
\(235\) 28.9946 1.89140
\(236\) 8.04092 0.523419
\(237\) 5.24067 0.340418
\(238\) 0.799273 0.0518092
\(239\) −11.0420 −0.714244 −0.357122 0.934058i \(-0.616242\pi\)
−0.357122 + 0.934058i \(0.616242\pi\)
\(240\) −11.9898 −0.773940
\(241\) −17.5678 −1.13164 −0.565821 0.824528i \(-0.691441\pi\)
−0.565821 + 0.824528i \(0.691441\pi\)
\(242\) −0.483073 −0.0310531
\(243\) −16.0521 −1.02974
\(244\) 12.9028 0.826015
\(245\) 2.03882 0.130255
\(246\) 2.52359 0.160898
\(247\) 21.4411 1.36426
\(248\) −4.37432 −0.277769
\(249\) 7.71465 0.488896
\(250\) 6.94740 0.439392
\(251\) −6.11065 −0.385701 −0.192851 0.981228i \(-0.561773\pi\)
−0.192851 + 0.981228i \(0.561773\pi\)
\(252\) −11.8786 −0.748279
\(253\) −8.31908 −0.523016
\(254\) −2.62700 −0.164833
\(255\) 3.42873 0.214716
\(256\) 9.62065 0.601290
\(257\) −9.41028 −0.586997 −0.293499 0.955959i \(-0.594820\pi\)
−0.293499 + 0.955959i \(0.594820\pi\)
\(258\) 0.250296 0.0155827
\(259\) 25.9545 1.61273
\(260\) 44.4501 2.75668
\(261\) 22.9240 1.41896
\(262\) 5.14391 0.317792
\(263\) −10.9976 −0.678143 −0.339072 0.940761i \(-0.610113\pi\)
−0.339072 + 0.940761i \(0.610113\pi\)
\(264\) 2.99528 0.184347
\(265\) −0.102328 −0.00628598
\(266\) 2.94965 0.180855
\(267\) 0.719432 0.0440285
\(268\) −22.1331 −1.35199
\(269\) 22.1408 1.34995 0.674975 0.737841i \(-0.264155\pi\)
0.674975 + 0.737841i \(0.264155\pi\)
\(270\) 5.26350 0.320326
\(271\) 10.4406 0.634221 0.317110 0.948389i \(-0.397287\pi\)
0.317110 + 0.948389i \(0.397287\pi\)
\(272\) −3.49687 −0.212029
\(273\) −13.6643 −0.827000
\(274\) −4.29749 −0.259621
\(275\) 33.5087 2.02065
\(276\) −4.47258 −0.269218
\(277\) 7.12840 0.428304 0.214152 0.976800i \(-0.431301\pi\)
0.214152 + 0.976800i \(0.431301\pi\)
\(278\) 2.76588 0.165886
\(279\) −8.67160 −0.519155
\(280\) 12.5016 0.747116
\(281\) 14.8324 0.884827 0.442414 0.896811i \(-0.354122\pi\)
0.442414 + 0.896811i \(0.354122\pi\)
\(282\) −1.81645 −0.108168
\(283\) −6.63105 −0.394175 −0.197088 0.980386i \(-0.563148\pi\)
−0.197088 + 0.980386i \(0.563148\pi\)
\(284\) 16.7095 0.991527
\(285\) 12.6535 0.749527
\(286\) −5.17960 −0.306276
\(287\) 27.6308 1.63100
\(288\) −7.47742 −0.440611
\(289\) 1.00000 0.0588235
\(290\) −11.8011 −0.692987
\(291\) −14.8334 −0.869551
\(292\) −6.37931 −0.373321
\(293\) −20.1059 −1.17460 −0.587301 0.809369i \(-0.699809\pi\)
−0.587301 + 0.809369i \(0.699809\pi\)
\(294\) −0.127727 −0.00744922
\(295\) −16.7764 −0.976758
\(296\) 10.8137 0.628534
\(297\) 13.8077 0.801202
\(298\) 5.70389 0.330418
\(299\) 15.8120 0.914433
\(300\) 18.0153 1.04011
\(301\) 2.74049 0.157959
\(302\) 0.686840 0.0395232
\(303\) 4.86126 0.279272
\(304\) −12.9049 −0.740147
\(305\) −26.9200 −1.54143
\(306\) 0.660156 0.0377386
\(307\) −8.05642 −0.459804 −0.229902 0.973214i \(-0.573841\pi\)
−0.229902 + 0.973214i \(0.573841\pi\)
\(308\) 16.0414 0.914044
\(309\) −6.11138 −0.347664
\(310\) 4.46408 0.253543
\(311\) −26.0287 −1.47595 −0.737975 0.674828i \(-0.764218\pi\)
−0.737975 + 0.674828i \(0.764218\pi\)
\(312\) −5.69311 −0.322309
\(313\) 15.0857 0.852692 0.426346 0.904560i \(-0.359801\pi\)
0.426346 + 0.904560i \(0.359801\pi\)
\(314\) 2.42095 0.136622
\(315\) 24.7831 1.39637
\(316\) 11.6938 0.657826
\(317\) −15.4286 −0.866559 −0.433279 0.901260i \(-0.642644\pi\)
−0.433279 + 0.901260i \(0.642644\pi\)
\(318\) 0.00641066 0.000359492 0
\(319\) −30.9578 −1.73330
\(320\) −24.0926 −1.34682
\(321\) −16.5380 −0.923061
\(322\) 2.17526 0.121223
\(323\) 3.69042 0.205340
\(324\) −5.57998 −0.309999
\(325\) −63.6899 −3.53288
\(326\) 4.93703 0.273437
\(327\) 3.33010 0.184155
\(328\) 11.5121 0.635652
\(329\) −19.8884 −1.09648
\(330\) −3.05674 −0.168268
\(331\) 0.688160 0.0378247 0.0189123 0.999821i \(-0.493980\pi\)
0.0189123 + 0.999821i \(0.493980\pi\)
\(332\) 17.2141 0.944746
\(333\) 21.4370 1.17474
\(334\) −1.06738 −0.0584046
\(335\) 46.1778 2.52296
\(336\) 8.22422 0.448668
\(337\) −31.6565 −1.72444 −0.862221 0.506532i \(-0.830927\pi\)
−0.862221 + 0.506532i \(0.830927\pi\)
\(338\) 6.05335 0.329259
\(339\) −14.0930 −0.765424
\(340\) 7.65071 0.414918
\(341\) 11.7106 0.634162
\(342\) 2.43625 0.131737
\(343\) 17.7850 0.960298
\(344\) 1.14180 0.0615619
\(345\) 9.33147 0.502389
\(346\) −2.60057 −0.139807
\(347\) −14.0369 −0.753543 −0.376771 0.926306i \(-0.622966\pi\)
−0.376771 + 0.926306i \(0.622966\pi\)
\(348\) −16.6438 −0.892202
\(349\) −1.09785 −0.0587666 −0.0293833 0.999568i \(-0.509354\pi\)
−0.0293833 + 0.999568i \(0.509354\pi\)
\(350\) −8.76182 −0.468339
\(351\) −26.2441 −1.40081
\(352\) 10.0979 0.538219
\(353\) −4.70964 −0.250669 −0.125334 0.992115i \(-0.540000\pi\)
−0.125334 + 0.992115i \(0.540000\pi\)
\(354\) 1.05100 0.0558602
\(355\) −34.8623 −1.85030
\(356\) 1.60531 0.0850811
\(357\) −2.35188 −0.124475
\(358\) −0.501645 −0.0265128
\(359\) 12.9863 0.685391 0.342696 0.939446i \(-0.388660\pi\)
0.342696 + 0.939446i \(0.388660\pi\)
\(360\) 10.3257 0.544211
\(361\) −5.38080 −0.283200
\(362\) −5.29538 −0.278319
\(363\) 1.42146 0.0746071
\(364\) −30.4898 −1.59810
\(365\) 13.3096 0.696658
\(366\) 1.68648 0.0881537
\(367\) −4.48210 −0.233964 −0.116982 0.993134i \(-0.537322\pi\)
−0.116982 + 0.993134i \(0.537322\pi\)
\(368\) −9.51690 −0.496103
\(369\) 22.8216 1.18804
\(370\) −11.0356 −0.573714
\(371\) 0.0701905 0.00364411
\(372\) 6.29594 0.326429
\(373\) −7.86900 −0.407441 −0.203721 0.979029i \(-0.565303\pi\)
−0.203721 + 0.979029i \(0.565303\pi\)
\(374\) −0.891508 −0.0460988
\(375\) −20.4429 −1.05567
\(376\) −8.28633 −0.427335
\(377\) 58.8413 3.03048
\(378\) −3.61041 −0.185699
\(379\) 17.3002 0.888654 0.444327 0.895865i \(-0.353443\pi\)
0.444327 + 0.895865i \(0.353443\pi\)
\(380\) 28.2343 1.44839
\(381\) 7.73003 0.396022
\(382\) −0.894776 −0.0457807
\(383\) −5.67171 −0.289811 −0.144906 0.989445i \(-0.546288\pi\)
−0.144906 + 0.989445i \(0.546288\pi\)
\(384\) 7.17942 0.366373
\(385\) −33.4684 −1.70571
\(386\) 3.47960 0.177107
\(387\) 2.26350 0.115060
\(388\) −33.0986 −1.68033
\(389\) 17.1355 0.868805 0.434402 0.900719i \(-0.356960\pi\)
0.434402 + 0.900719i \(0.356960\pi\)
\(390\) 5.80993 0.294197
\(391\) 2.72155 0.137635
\(392\) −0.582670 −0.0294293
\(393\) −15.1361 −0.763515
\(394\) −0.428168 −0.0215708
\(395\) −24.3976 −1.22757
\(396\) 13.2493 0.665804
\(397\) 21.3267 1.07035 0.535177 0.844740i \(-0.320245\pi\)
0.535177 + 0.844740i \(0.320245\pi\)
\(398\) −6.92272 −0.347005
\(399\) −8.67944 −0.434515
\(400\) 38.3335 1.91667
\(401\) −32.6052 −1.62823 −0.814114 0.580705i \(-0.802777\pi\)
−0.814114 + 0.580705i \(0.802777\pi\)
\(402\) −2.89294 −0.144287
\(403\) −22.2582 −1.10876
\(404\) 10.8472 0.539668
\(405\) 11.6419 0.578492
\(406\) 8.09480 0.401738
\(407\) −28.9496 −1.43498
\(408\) −0.979892 −0.0485119
\(409\) −10.5782 −0.523056 −0.261528 0.965196i \(-0.584226\pi\)
−0.261528 + 0.965196i \(0.584226\pi\)
\(410\) −11.7484 −0.580211
\(411\) 12.6455 0.623755
\(412\) −13.6366 −0.671829
\(413\) 11.5075 0.566246
\(414\) 1.79665 0.0883004
\(415\) −35.9150 −1.76300
\(416\) −19.1930 −0.941014
\(417\) −8.13867 −0.398552
\(418\) −3.29004 −0.160921
\(419\) −17.3706 −0.848608 −0.424304 0.905520i \(-0.639481\pi\)
−0.424304 + 0.905520i \(0.639481\pi\)
\(420\) −17.9936 −0.877996
\(421\) −4.46786 −0.217750 −0.108875 0.994055i \(-0.534725\pi\)
−0.108875 + 0.994055i \(0.534725\pi\)
\(422\) −4.88240 −0.237672
\(423\) −16.4267 −0.798695
\(424\) 0.0292443 0.00142023
\(425\) −10.9622 −0.531746
\(426\) 2.18405 0.105817
\(427\) 18.4653 0.893599
\(428\) −36.9021 −1.78373
\(429\) 15.2411 0.735848
\(430\) −1.16523 −0.0561926
\(431\) 10.0244 0.482860 0.241430 0.970418i \(-0.422384\pi\)
0.241430 + 0.970418i \(0.422384\pi\)
\(432\) 15.7958 0.759974
\(433\) −9.06344 −0.435561 −0.217781 0.975998i \(-0.569882\pi\)
−0.217781 + 0.975998i \(0.569882\pi\)
\(434\) −3.06206 −0.146984
\(435\) 34.7252 1.66495
\(436\) 7.43062 0.355862
\(437\) 10.0437 0.480454
\(438\) −0.833820 −0.0398415
\(439\) 29.4502 1.40558 0.702791 0.711397i \(-0.251937\pi\)
0.702791 + 0.711397i \(0.251937\pi\)
\(440\) −13.9443 −0.664769
\(441\) −1.15508 −0.0550037
\(442\) 1.69448 0.0805984
\(443\) 9.04833 0.429899 0.214950 0.976625i \(-0.431041\pi\)
0.214950 + 0.976625i \(0.431041\pi\)
\(444\) −15.5641 −0.738641
\(445\) −3.34927 −0.158771
\(446\) 5.76011 0.272749
\(447\) −16.7839 −0.793849
\(448\) 16.5259 0.780776
\(449\) 14.7810 0.697557 0.348779 0.937205i \(-0.386597\pi\)
0.348779 + 0.937205i \(0.386597\pi\)
\(450\) −7.23678 −0.341145
\(451\) −30.8194 −1.45123
\(452\) −31.4463 −1.47911
\(453\) −2.02105 −0.0949570
\(454\) −5.32528 −0.249928
\(455\) 63.6131 2.98223
\(456\) −3.61621 −0.169345
\(457\) 3.87054 0.181056 0.0905281 0.995894i \(-0.471144\pi\)
0.0905281 + 0.995894i \(0.471144\pi\)
\(458\) −2.57917 −0.120517
\(459\) −4.51712 −0.210841
\(460\) 20.8218 0.970821
\(461\) 15.4345 0.718854 0.359427 0.933173i \(-0.382972\pi\)
0.359427 + 0.933173i \(0.382972\pi\)
\(462\) 2.09672 0.0975483
\(463\) −17.0689 −0.793260 −0.396630 0.917979i \(-0.629820\pi\)
−0.396630 + 0.917979i \(0.629820\pi\)
\(464\) −35.4152 −1.64411
\(465\) −13.1357 −0.609153
\(466\) 0.0670297 0.00310509
\(467\) −34.5188 −1.59734 −0.798670 0.601770i \(-0.794462\pi\)
−0.798670 + 0.601770i \(0.794462\pi\)
\(468\) −25.1829 −1.16408
\(469\) −31.6749 −1.46261
\(470\) 8.45637 0.390063
\(471\) −7.12370 −0.328243
\(472\) 4.79449 0.220684
\(473\) −3.05674 −0.140549
\(474\) 1.52846 0.0702043
\(475\) −40.4552 −1.85621
\(476\) −5.24788 −0.240536
\(477\) 0.0579735 0.00265442
\(478\) −3.22042 −0.147298
\(479\) −6.40545 −0.292673 −0.146336 0.989235i \(-0.546748\pi\)
−0.146336 + 0.989235i \(0.546748\pi\)
\(480\) −11.3267 −0.516993
\(481\) 55.0243 2.50889
\(482\) −5.12371 −0.233378
\(483\) −6.40077 −0.291245
\(484\) 3.17177 0.144171
\(485\) 69.0560 3.13567
\(486\) −4.68163 −0.212363
\(487\) −28.4585 −1.28958 −0.644788 0.764361i \(-0.723054\pi\)
−0.644788 + 0.764361i \(0.723054\pi\)
\(488\) 7.69342 0.348265
\(489\) −14.5273 −0.656949
\(490\) 0.594627 0.0268625
\(491\) 25.9394 1.17063 0.585314 0.810807i \(-0.300971\pi\)
0.585314 + 0.810807i \(0.300971\pi\)
\(492\) −16.5694 −0.747006
\(493\) 10.1277 0.456129
\(494\) 6.25336 0.281352
\(495\) −27.6430 −1.24246
\(496\) 13.3967 0.601530
\(497\) 23.9132 1.07265
\(498\) 2.25000 0.100825
\(499\) −36.4020 −1.62958 −0.814790 0.579757i \(-0.803148\pi\)
−0.814790 + 0.579757i \(0.803148\pi\)
\(500\) −45.6153 −2.03998
\(501\) 3.14080 0.140321
\(502\) −1.78219 −0.0795430
\(503\) 38.9182 1.73528 0.867638 0.497197i \(-0.165637\pi\)
0.867638 + 0.497197i \(0.165637\pi\)
\(504\) −7.08272 −0.315490
\(505\) −22.6313 −1.00708
\(506\) −2.42628 −0.107861
\(507\) −17.8122 −0.791066
\(508\) 17.2484 0.765275
\(509\) −22.3222 −0.989415 −0.494708 0.869060i \(-0.664725\pi\)
−0.494708 + 0.869060i \(0.664725\pi\)
\(510\) 1.00000 0.0442807
\(511\) −9.12952 −0.403866
\(512\) 19.5373 0.863434
\(513\) −16.6701 −0.736001
\(514\) −2.74454 −0.121056
\(515\) 28.4511 1.25371
\(516\) −1.64339 −0.0723464
\(517\) 22.1835 0.975629
\(518\) 7.56970 0.332593
\(519\) 7.65224 0.335896
\(520\) 26.5039 1.16227
\(521\) −9.08470 −0.398008 −0.199004 0.979999i \(-0.563771\pi\)
−0.199004 + 0.979999i \(0.563771\pi\)
\(522\) 6.68586 0.292632
\(523\) −10.0141 −0.437888 −0.218944 0.975737i \(-0.570261\pi\)
−0.218944 + 0.975737i \(0.570261\pi\)
\(524\) −33.7740 −1.47542
\(525\) 25.7819 1.12521
\(526\) −3.20749 −0.139853
\(527\) −3.83106 −0.166884
\(528\) −9.17328 −0.399216
\(529\) −15.5932 −0.677964
\(530\) −0.0298444 −0.00129636
\(531\) 9.50454 0.412462
\(532\) −19.3669 −0.839660
\(533\) 58.5782 2.53730
\(534\) 0.209825 0.00908000
\(535\) 76.9915 3.32863
\(536\) −13.1971 −0.570027
\(537\) 1.47610 0.0636986
\(538\) 6.45743 0.278400
\(539\) 1.55988 0.0671886
\(540\) −34.5591 −1.48719
\(541\) 17.4916 0.752024 0.376012 0.926615i \(-0.377295\pi\)
0.376012 + 0.926615i \(0.377295\pi\)
\(542\) 3.04503 0.130795
\(543\) 15.5818 0.668679
\(544\) −3.30348 −0.141635
\(545\) −15.5030 −0.664077
\(546\) −3.98523 −0.170552
\(547\) 9.21314 0.393926 0.196963 0.980411i \(-0.436892\pi\)
0.196963 + 0.980411i \(0.436892\pi\)
\(548\) 28.2165 1.20535
\(549\) 15.2513 0.650912
\(550\) 9.77292 0.416719
\(551\) 37.3755 1.59225
\(552\) −2.66682 −0.113508
\(553\) 16.7351 0.711649
\(554\) 2.07902 0.0883290
\(555\) 32.4726 1.37839
\(556\) −18.1602 −0.770166
\(557\) −8.45542 −0.358268 −0.179134 0.983825i \(-0.557329\pi\)
−0.179134 + 0.983825i \(0.557329\pi\)
\(558\) −2.52910 −0.107065
\(559\) 5.80993 0.245734
\(560\) −38.2873 −1.61793
\(561\) 2.62329 0.110755
\(562\) 4.32592 0.182478
\(563\) −29.1351 −1.22790 −0.613949 0.789346i \(-0.710420\pi\)
−0.613949 + 0.789346i \(0.710420\pi\)
\(564\) 11.9265 0.502196
\(565\) 65.6088 2.76018
\(566\) −1.93397 −0.0812907
\(567\) −7.98558 −0.335363
\(568\) 9.96323 0.418048
\(569\) −13.0424 −0.546767 −0.273383 0.961905i \(-0.588143\pi\)
−0.273383 + 0.961905i \(0.588143\pi\)
\(570\) 3.69042 0.154575
\(571\) 1.70766 0.0714633 0.0357317 0.999361i \(-0.488624\pi\)
0.0357317 + 0.999361i \(0.488624\pi\)
\(572\) 34.0083 1.42196
\(573\) 2.63290 0.109991
\(574\) 8.05861 0.336360
\(575\) −29.8343 −1.24417
\(576\) 13.6495 0.568729
\(577\) 34.3329 1.42930 0.714648 0.699484i \(-0.246587\pi\)
0.714648 + 0.699484i \(0.246587\pi\)
\(578\) 0.291653 0.0121312
\(579\) −10.2388 −0.425511
\(580\) 77.4841 3.21735
\(581\) 24.6353 1.02205
\(582\) −4.32621 −0.179327
\(583\) −0.0782903 −0.00324245
\(584\) −3.80374 −0.157400
\(585\) 52.5410 2.17230
\(586\) −5.86396 −0.242238
\(587\) 9.88207 0.407877 0.203938 0.978984i \(-0.434626\pi\)
0.203938 + 0.978984i \(0.434626\pi\)
\(588\) 0.838634 0.0345847
\(589\) −14.1382 −0.582555
\(590\) −4.89288 −0.201437
\(591\) 1.25990 0.0518252
\(592\) −33.1179 −1.36114
\(593\) 10.8310 0.444774 0.222387 0.974958i \(-0.428615\pi\)
0.222387 + 0.974958i \(0.428615\pi\)
\(594\) 4.02704 0.165232
\(595\) 10.9490 0.448866
\(596\) −37.4507 −1.53404
\(597\) 20.3703 0.833701
\(598\) 4.61162 0.188583
\(599\) 14.7511 0.602715 0.301358 0.953511i \(-0.402560\pi\)
0.301358 + 0.953511i \(0.402560\pi\)
\(600\) 10.7418 0.438532
\(601\) 11.1801 0.456047 0.228023 0.973656i \(-0.426774\pi\)
0.228023 + 0.973656i \(0.426774\pi\)
\(602\) 0.799273 0.0325759
\(603\) −26.1618 −1.06539
\(604\) −4.50966 −0.183496
\(605\) −6.61749 −0.269039
\(606\) 1.41780 0.0575943
\(607\) −44.3193 −1.79887 −0.899433 0.437059i \(-0.856020\pi\)
−0.899433 + 0.437059i \(0.856020\pi\)
\(608\) −12.1912 −0.494419
\(609\) −23.8192 −0.965201
\(610\) −7.85129 −0.317889
\(611\) −42.1640 −1.70577
\(612\) −4.33446 −0.175210
\(613\) −11.9423 −0.482344 −0.241172 0.970482i \(-0.577532\pi\)
−0.241172 + 0.970482i \(0.577532\pi\)
\(614\) −2.34968 −0.0948253
\(615\) 34.5699 1.39399
\(616\) 9.56487 0.385379
\(617\) 20.8460 0.839230 0.419615 0.907702i \(-0.362165\pi\)
0.419615 + 0.907702i \(0.362165\pi\)
\(618\) −1.78240 −0.0716987
\(619\) −44.3104 −1.78098 −0.890492 0.454999i \(-0.849640\pi\)
−0.890492 + 0.454999i \(0.849640\pi\)
\(620\) −29.3103 −1.17713
\(621\) −12.2936 −0.493324
\(622\) −7.59134 −0.304385
\(623\) 2.29738 0.0920424
\(624\) 17.4356 0.697983
\(625\) 40.3594 1.61438
\(626\) 4.39978 0.175851
\(627\) 9.68103 0.386623
\(628\) −15.8955 −0.634299
\(629\) 9.47073 0.377623
\(630\) 7.22807 0.287973
\(631\) 11.4916 0.457473 0.228736 0.973488i \(-0.426541\pi\)
0.228736 + 0.973488i \(0.426541\pi\)
\(632\) 6.97254 0.277353
\(633\) 14.3666 0.571021
\(634\) −4.49981 −0.178710
\(635\) −35.9866 −1.42809
\(636\) −0.0420912 −0.00166902
\(637\) −2.96485 −0.117472
\(638\) −9.02893 −0.357459
\(639\) 19.7510 0.781337
\(640\) −33.4233 −1.32117
\(641\) −11.5475 −0.456100 −0.228050 0.973649i \(-0.573235\pi\)
−0.228050 + 0.973649i \(0.573235\pi\)
\(642\) −4.82335 −0.190363
\(643\) 26.3988 1.04107 0.520533 0.853842i \(-0.325733\pi\)
0.520533 + 0.853842i \(0.325733\pi\)
\(644\) −14.2824 −0.562804
\(645\) 3.42873 0.135006
\(646\) 1.07632 0.0423473
\(647\) 33.2667 1.30785 0.653924 0.756561i \(-0.273122\pi\)
0.653924 + 0.756561i \(0.273122\pi\)
\(648\) −3.32713 −0.130702
\(649\) −12.8354 −0.503834
\(650\) −18.5753 −0.728585
\(651\) 9.01020 0.353138
\(652\) −32.4156 −1.26949
\(653\) −11.1145 −0.434945 −0.217472 0.976067i \(-0.569781\pi\)
−0.217472 + 0.976067i \(0.569781\pi\)
\(654\) 0.971232 0.0379782
\(655\) 70.4651 2.75330
\(656\) −35.2569 −1.37655
\(657\) −7.54049 −0.294182
\(658\) −5.80051 −0.226127
\(659\) −32.1156 −1.25104 −0.625522 0.780206i \(-0.715114\pi\)
−0.625522 + 0.780206i \(0.715114\pi\)
\(660\) 20.0700 0.781223
\(661\) −7.71808 −0.300199 −0.150099 0.988671i \(-0.547959\pi\)
−0.150099 + 0.988671i \(0.547959\pi\)
\(662\) 0.200704 0.00780057
\(663\) −4.98607 −0.193643
\(664\) 10.2641 0.398324
\(665\) 40.4065 1.56690
\(666\) 6.25216 0.242266
\(667\) 27.5631 1.06725
\(668\) 7.00824 0.271157
\(669\) −16.9493 −0.655297
\(670\) 13.4679 0.520310
\(671\) −20.5962 −0.795107
\(672\) 7.76939 0.299711
\(673\) 23.9188 0.922003 0.461002 0.887399i \(-0.347490\pi\)
0.461002 + 0.887399i \(0.347490\pi\)
\(674\) −9.23272 −0.355631
\(675\) 49.5177 1.90594
\(676\) −39.7452 −1.52866
\(677\) 13.7725 0.529321 0.264661 0.964342i \(-0.414740\pi\)
0.264661 + 0.964342i \(0.414740\pi\)
\(678\) −4.11025 −0.157853
\(679\) −47.3678 −1.81781
\(680\) 4.56182 0.174938
\(681\) 15.6698 0.600467
\(682\) 3.41542 0.130783
\(683\) 10.7891 0.412835 0.206418 0.978464i \(-0.433819\pi\)
0.206418 + 0.978464i \(0.433819\pi\)
\(684\) −15.9960 −0.611622
\(685\) −58.8701 −2.24931
\(686\) 5.18704 0.198042
\(687\) 7.58928 0.289549
\(688\) −3.49687 −0.133317
\(689\) 0.148806 0.00566906
\(690\) 2.72155 0.103608
\(691\) 4.14875 0.157826 0.0789130 0.996882i \(-0.474855\pi\)
0.0789130 + 0.996882i \(0.474855\pi\)
\(692\) 17.0748 0.649088
\(693\) 18.9613 0.720280
\(694\) −4.09392 −0.155403
\(695\) 37.8890 1.43721
\(696\) −9.92405 −0.376170
\(697\) 10.0824 0.381899
\(698\) −0.320192 −0.0121194
\(699\) −0.197237 −0.00746018
\(700\) 57.5285 2.17437
\(701\) 9.71741 0.367021 0.183511 0.983018i \(-0.441254\pi\)
0.183511 + 0.983018i \(0.441254\pi\)
\(702\) −7.65418 −0.288889
\(703\) 34.9510 1.31820
\(704\) −18.4330 −0.694718
\(705\) −24.8831 −0.937152
\(706\) −1.37358 −0.0516954
\(707\) 15.5236 0.583824
\(708\) −6.90069 −0.259344
\(709\) −35.0387 −1.31591 −0.657953 0.753059i \(-0.728578\pi\)
−0.657953 + 0.753059i \(0.728578\pi\)
\(710\) −10.1677 −0.381586
\(711\) 13.8223 0.518376
\(712\) 0.957182 0.0358719
\(713\) −10.4264 −0.390472
\(714\) −0.685933 −0.0256704
\(715\) −70.9540 −2.65353
\(716\) 3.29371 0.123092
\(717\) 9.47617 0.353894
\(718\) 3.78750 0.141348
\(719\) 27.6154 1.02988 0.514940 0.857226i \(-0.327814\pi\)
0.514940 + 0.857226i \(0.327814\pi\)
\(720\) −31.6232 −1.17853
\(721\) −19.5156 −0.726798
\(722\) −1.56933 −0.0584042
\(723\) 15.0766 0.560706
\(724\) 34.7685 1.29216
\(725\) −111.022 −4.12326
\(726\) 0.414572 0.0153862
\(727\) 14.5140 0.538293 0.269146 0.963099i \(-0.413258\pi\)
0.269146 + 0.963099i \(0.413258\pi\)
\(728\) −18.1799 −0.673792
\(729\) 5.03407 0.186447
\(730\) 3.88179 0.143672
\(731\) 1.00000 0.0369863
\(732\) −11.0731 −0.409274
\(733\) −37.2894 −1.37732 −0.688659 0.725086i \(-0.741800\pi\)
−0.688659 + 0.725086i \(0.741800\pi\)
\(734\) −1.30722 −0.0482503
\(735\) −1.74970 −0.0645388
\(736\) −8.99058 −0.331397
\(737\) 35.3301 1.30140
\(738\) 6.65597 0.245010
\(739\) −19.9962 −0.735571 −0.367785 0.929911i \(-0.619884\pi\)
−0.367785 + 0.929911i \(0.619884\pi\)
\(740\) 72.4578 2.66360
\(741\) −18.4007 −0.675966
\(742\) 0.0204713 0.000751523 0
\(743\) −18.9825 −0.696399 −0.348199 0.937420i \(-0.613207\pi\)
−0.348199 + 0.937420i \(0.613207\pi\)
\(744\) 3.75402 0.137629
\(745\) 78.1361 2.86269
\(746\) −2.29502 −0.0840265
\(747\) 20.3474 0.744473
\(748\) 5.85347 0.214024
\(749\) −52.8110 −1.92967
\(750\) −5.96223 −0.217710
\(751\) −40.6916 −1.48486 −0.742429 0.669925i \(-0.766326\pi\)
−0.742429 + 0.669925i \(0.766326\pi\)
\(752\) 25.3776 0.925425
\(753\) 5.24414 0.191107
\(754\) 17.1612 0.624975
\(755\) 9.40884 0.342423
\(756\) 23.7053 0.862152
\(757\) −25.2060 −0.916128 −0.458064 0.888919i \(-0.651457\pi\)
−0.458064 + 0.888919i \(0.651457\pi\)
\(758\) 5.04567 0.183267
\(759\) 7.13940 0.259144
\(760\) 16.8350 0.610671
\(761\) −26.2909 −0.953043 −0.476521 0.879163i \(-0.658103\pi\)
−0.476521 + 0.879163i \(0.658103\pi\)
\(762\) 2.25449 0.0816714
\(763\) 10.6341 0.384979
\(764\) 5.87493 0.212547
\(765\) 9.04330 0.326961
\(766\) −1.65417 −0.0597677
\(767\) 24.3962 0.880896
\(768\) −8.25641 −0.297927
\(769\) 17.5206 0.631809 0.315905 0.948791i \(-0.397692\pi\)
0.315905 + 0.948791i \(0.397692\pi\)
\(770\) −9.76115 −0.351767
\(771\) 8.07587 0.290845
\(772\) −22.8464 −0.822261
\(773\) −47.6695 −1.71455 −0.857277 0.514855i \(-0.827846\pi\)
−0.857277 + 0.514855i \(0.827846\pi\)
\(774\) 0.660156 0.0237288
\(775\) 41.9970 1.50858
\(776\) −19.7354 −0.708460
\(777\) −22.2740 −0.799077
\(778\) 4.99762 0.179173
\(779\) 37.2084 1.33313
\(780\) −38.1469 −1.36588
\(781\) −26.6727 −0.954426
\(782\) 0.793748 0.0283844
\(783\) −45.7480 −1.63490
\(784\) 1.78447 0.0637312
\(785\) 33.1639 1.18367
\(786\) −4.41449 −0.157460
\(787\) 41.4827 1.47870 0.739349 0.673322i \(-0.235133\pi\)
0.739349 + 0.673322i \(0.235133\pi\)
\(788\) 2.81127 0.100147
\(789\) 9.43813 0.336006
\(790\) −7.11562 −0.253162
\(791\) −45.0033 −1.60013
\(792\) 7.90006 0.280716
\(793\) 39.1471 1.39015
\(794\) 6.21999 0.220739
\(795\) 0.0878179 0.00311458
\(796\) 45.4533 1.61105
\(797\) −29.7609 −1.05419 −0.527093 0.849808i \(-0.676718\pi\)
−0.527093 + 0.849808i \(0.676718\pi\)
\(798\) −2.53138 −0.0896100
\(799\) −7.25723 −0.256742
\(800\) 36.2135 1.28034
\(801\) 1.89751 0.0670451
\(802\) −9.50941 −0.335789
\(803\) 10.1831 0.359352
\(804\) 18.9945 0.669885
\(805\) 29.7983 1.05025
\(806\) −6.49167 −0.228659
\(807\) −19.0012 −0.668873
\(808\) 6.46776 0.227535
\(809\) −45.4805 −1.59901 −0.799504 0.600661i \(-0.794904\pi\)
−0.799504 + 0.600661i \(0.794904\pi\)
\(810\) 3.39540 0.119302
\(811\) 20.1527 0.707659 0.353829 0.935310i \(-0.384879\pi\)
0.353829 + 0.935310i \(0.384879\pi\)
\(812\) −53.1489 −1.86516
\(813\) −8.96008 −0.314244
\(814\) −8.44323 −0.295935
\(815\) 67.6311 2.36901
\(816\) 3.00100 0.105056
\(817\) 3.69042 0.129111
\(818\) −3.08515 −0.107870
\(819\) −36.0396 −1.25933
\(820\) 77.1377 2.69377
\(821\) 12.2357 0.427029 0.213515 0.976940i \(-0.431509\pi\)
0.213515 + 0.976940i \(0.431509\pi\)
\(822\) 3.68809 0.128637
\(823\) 31.1224 1.08486 0.542430 0.840101i \(-0.317505\pi\)
0.542430 + 0.840101i \(0.317505\pi\)
\(824\) −8.13100 −0.283257
\(825\) −28.7571 −1.00119
\(826\) 3.35619 0.116777
\(827\) 45.4529 1.58055 0.790276 0.612750i \(-0.209937\pi\)
0.790276 + 0.612750i \(0.209937\pi\)
\(828\) −11.7965 −0.409955
\(829\) 0.205090 0.00712306 0.00356153 0.999994i \(-0.498866\pi\)
0.00356153 + 0.999994i \(0.498866\pi\)
\(830\) −10.4747 −0.363583
\(831\) −6.11757 −0.212216
\(832\) 35.0354 1.21464
\(833\) −0.510306 −0.0176811
\(834\) −2.37367 −0.0821934
\(835\) −14.6218 −0.506008
\(836\) 21.6018 0.747113
\(837\) 17.3053 0.598160
\(838\) −5.06618 −0.175008
\(839\) −15.1516 −0.523093 −0.261546 0.965191i \(-0.584232\pi\)
−0.261546 + 0.965191i \(0.584232\pi\)
\(840\) −10.7289 −0.370181
\(841\) 73.5704 2.53691
\(842\) −1.30307 −0.0449066
\(843\) −12.7291 −0.438414
\(844\) 32.0570 1.10345
\(845\) 82.9233 2.85265
\(846\) −4.79091 −0.164715
\(847\) 4.53916 0.155967
\(848\) −0.0895629 −0.00307560
\(849\) 5.69075 0.195306
\(850\) −3.19717 −0.109662
\(851\) 25.7751 0.883558
\(852\) −14.3400 −0.491282
\(853\) 11.5839 0.396624 0.198312 0.980139i \(-0.436454\pi\)
0.198312 + 0.980139i \(0.436454\pi\)
\(854\) 5.38546 0.184287
\(855\) 33.3736 1.14135
\(856\) −22.0033 −0.752056
\(857\) −13.1807 −0.450246 −0.225123 0.974330i \(-0.572278\pi\)
−0.225123 + 0.974330i \(0.572278\pi\)
\(858\) 4.44512 0.151754
\(859\) 6.31531 0.215476 0.107738 0.994179i \(-0.465639\pi\)
0.107738 + 0.994179i \(0.465639\pi\)
\(860\) 7.65071 0.260887
\(861\) −23.7127 −0.808126
\(862\) 2.92366 0.0995801
\(863\) −54.1093 −1.84190 −0.920950 0.389680i \(-0.872586\pi\)
−0.920950 + 0.389680i \(0.872586\pi\)
\(864\) 14.9222 0.507663
\(865\) −35.6245 −1.21127
\(866\) −2.64338 −0.0898257
\(867\) −0.858197 −0.0291459
\(868\) 20.1049 0.682406
\(869\) −18.6663 −0.633211
\(870\) 10.1277 0.343361
\(871\) −67.1518 −2.27535
\(872\) 4.43059 0.150039
\(873\) −39.1233 −1.32412
\(874\) 2.92926 0.0990838
\(875\) −65.2807 −2.20689
\(876\) 5.47471 0.184973
\(877\) −10.1191 −0.341699 −0.170849 0.985297i \(-0.554651\pi\)
−0.170849 + 0.985297i \(0.554651\pi\)
\(878\) 8.58924 0.289873
\(879\) 17.2548 0.581992
\(880\) 42.7056 1.43961
\(881\) 35.1813 1.18529 0.592643 0.805465i \(-0.298084\pi\)
0.592643 + 0.805465i \(0.298084\pi\)
\(882\) −0.336882 −0.0113434
\(883\) 41.6661 1.40218 0.701088 0.713075i \(-0.252698\pi\)
0.701088 + 0.713075i \(0.252698\pi\)
\(884\) −11.1257 −0.374197
\(885\) 14.3974 0.483964
\(886\) 2.63897 0.0886580
\(887\) 5.82622 0.195625 0.0978126 0.995205i \(-0.468815\pi\)
0.0978126 + 0.995205i \(0.468815\pi\)
\(888\) −9.28029 −0.311426
\(889\) 24.6844 0.827890
\(890\) −0.976824 −0.0327432
\(891\) 8.90711 0.298399
\(892\) −37.8198 −1.26630
\(893\) −26.7822 −0.896233
\(894\) −4.89506 −0.163715
\(895\) −6.87190 −0.229702
\(896\) 22.9262 0.765909
\(897\) −13.5698 −0.453083
\(898\) 4.31091 0.143857
\(899\) −38.7998 −1.29405
\(900\) 47.5154 1.58385
\(901\) 0.0256123 0.000853271 0
\(902\) −8.98856 −0.299286
\(903\) −2.35188 −0.0782658
\(904\) −18.7502 −0.623623
\(905\) −72.5400 −2.41131
\(906\) −0.589444 −0.0195830
\(907\) 10.9136 0.362381 0.181191 0.983448i \(-0.442005\pi\)
0.181191 + 0.983448i \(0.442005\pi\)
\(908\) 34.9648 1.16035
\(909\) 12.8216 0.425266
\(910\) 18.5530 0.615025
\(911\) −13.1513 −0.435723 −0.217861 0.975980i \(-0.569908\pi\)
−0.217861 + 0.975980i \(0.569908\pi\)
\(912\) 11.0749 0.366728
\(913\) −27.4782 −0.909395
\(914\) 1.12885 0.0373392
\(915\) 23.1026 0.763750
\(916\) 16.9343 0.559526
\(917\) −48.3344 −1.59614
\(918\) −1.31743 −0.0434817
\(919\) 48.1109 1.58703 0.793517 0.608548i \(-0.208248\pi\)
0.793517 + 0.608548i \(0.208248\pi\)
\(920\) 12.4152 0.409318
\(921\) 6.91399 0.227824
\(922\) 4.50151 0.148249
\(923\) 50.6967 1.66870
\(924\) −13.7667 −0.452891
\(925\) −103.820 −3.41359
\(926\) −4.97820 −0.163594
\(927\) −16.1188 −0.529411
\(928\) −33.4567 −1.09827
\(929\) −25.2216 −0.827495 −0.413748 0.910392i \(-0.635780\pi\)
−0.413748 + 0.910392i \(0.635780\pi\)
\(930\) −3.83106 −0.125625
\(931\) −1.88325 −0.0617209
\(932\) −0.440104 −0.0144161
\(933\) 22.3377 0.731304
\(934\) −10.0675 −0.329419
\(935\) −12.2125 −0.399392
\(936\) −15.0156 −0.490800
\(937\) 21.8619 0.714197 0.357098 0.934067i \(-0.383766\pi\)
0.357098 + 0.934067i \(0.383766\pi\)
\(938\) −9.23808 −0.301634
\(939\) −12.9465 −0.422492
\(940\) −55.5230 −1.81096
\(941\) 55.9850 1.82506 0.912530 0.409010i \(-0.134126\pi\)
0.912530 + 0.409010i \(0.134126\pi\)
\(942\) −2.07765 −0.0676935
\(943\) 27.4398 0.893564
\(944\) −14.6835 −0.477908
\(945\) −49.4580 −1.60887
\(946\) −0.891508 −0.0289854
\(947\) 9.19797 0.298894 0.149447 0.988770i \(-0.452251\pi\)
0.149447 + 0.988770i \(0.452251\pi\)
\(948\) −10.0356 −0.325940
\(949\) −19.3549 −0.628286
\(950\) −11.7989 −0.382807
\(951\) 13.2408 0.429363
\(952\) −3.12911 −0.101415
\(953\) 26.3104 0.852276 0.426138 0.904658i \(-0.359874\pi\)
0.426138 + 0.904658i \(0.359874\pi\)
\(954\) 0.0169081 0.000547421 0
\(955\) −12.2573 −0.396637
\(956\) 21.1447 0.683867
\(957\) 26.5679 0.858817
\(958\) −1.86817 −0.0603578
\(959\) 40.3810 1.30397
\(960\) 20.6762 0.667320
\(961\) −16.3230 −0.526548
\(962\) 16.0480 0.517408
\(963\) −43.6190 −1.40560
\(964\) 33.6413 1.08351
\(965\) 47.6662 1.53443
\(966\) −1.86680 −0.0600634
\(967\) −23.2676 −0.748237 −0.374118 0.927381i \(-0.622055\pi\)
−0.374118 + 0.927381i \(0.622055\pi\)
\(968\) 1.89120 0.0607855
\(969\) −3.16711 −0.101742
\(970\) 20.1404 0.646669
\(971\) −22.6891 −0.728128 −0.364064 0.931374i \(-0.618611\pi\)
−0.364064 + 0.931374i \(0.618611\pi\)
\(972\) 30.7387 0.985945
\(973\) −25.9894 −0.833181
\(974\) −8.30000 −0.265949
\(975\) 54.6584 1.75047
\(976\) −23.5617 −0.754192
\(977\) −33.2179 −1.06273 −0.531367 0.847142i \(-0.678321\pi\)
−0.531367 + 0.847142i \(0.678321\pi\)
\(978\) −4.23694 −0.135483
\(979\) −2.56249 −0.0818975
\(980\) −3.90421 −0.124715
\(981\) 8.78315 0.280424
\(982\) 7.56530 0.241418
\(983\) 4.77329 0.152244 0.0761222 0.997098i \(-0.475746\pi\)
0.0761222 + 0.997098i \(0.475746\pi\)
\(984\) −9.87969 −0.314953
\(985\) −5.86536 −0.186886
\(986\) 2.95377 0.0940674
\(987\) 17.0682 0.543285
\(988\) −41.0584 −1.30624
\(989\) 2.72155 0.0865403
\(990\) −8.06217 −0.256233
\(991\) −18.2124 −0.578537 −0.289268 0.957248i \(-0.593412\pi\)
−0.289268 + 0.957248i \(0.593412\pi\)
\(992\) 12.6558 0.401823
\(993\) −0.590576 −0.0187414
\(994\) 6.97435 0.221213
\(995\) −94.8325 −3.00639
\(996\) −14.7731 −0.468103
\(997\) 19.0963 0.604785 0.302393 0.953183i \(-0.402215\pi\)
0.302393 + 0.953183i \(0.402215\pi\)
\(998\) −10.6168 −0.336068
\(999\) −42.7804 −1.35351
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.1.4 6
3.2 odd 2 6579.2.a.j.1.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
731.2.a.c.1.4 6 1.1 even 1 trivial
6579.2.a.j.1.3 6 3.2 odd 2