Properties

Label 241.2.a.a.1.6
Level $241$
Weight $2$
Character 241.1
Self dual yes
Analytic conductor $1.924$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 241.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(1.92439468871\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: 7.7.31056073.1
Defining polynomial: \(x^{7} - 3 x^{6} - 3 x^{5} + 11 x^{4} + x^{3} - 9 x^{2} + 1\)
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 1.6
Root \(1.48734\) of defining polynomial
Character \(\chi\) \(=\) 241.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.487343 q^{2} -0.815004 q^{3} -1.76250 q^{4} +0.961999 q^{5} -0.397187 q^{6} -4.61392 q^{7} -1.83363 q^{8} -2.33577 q^{9} +O(q^{10})\) \(q+0.487343 q^{2} -0.815004 q^{3} -1.76250 q^{4} +0.961999 q^{5} -0.397187 q^{6} -4.61392 q^{7} -1.83363 q^{8} -2.33577 q^{9} +0.468824 q^{10} +1.93974 q^{11} +1.43644 q^{12} -3.85571 q^{13} -2.24856 q^{14} -0.784033 q^{15} +2.63139 q^{16} +5.40289 q^{17} -1.13832 q^{18} -4.17145 q^{19} -1.69552 q^{20} +3.76036 q^{21} +0.945321 q^{22} -1.42545 q^{23} +1.49441 q^{24} -4.07456 q^{25} -1.87905 q^{26} +4.34867 q^{27} +8.13202 q^{28} -4.85744 q^{29} -0.382093 q^{30} -7.24699 q^{31} +4.94964 q^{32} -1.58090 q^{33} +2.63306 q^{34} -4.43859 q^{35} +4.11678 q^{36} +7.12597 q^{37} -2.03293 q^{38} +3.14242 q^{39} -1.76395 q^{40} +9.18955 q^{41} +1.83259 q^{42} +2.93624 q^{43} -3.41879 q^{44} -2.24701 q^{45} -0.694685 q^{46} +2.48170 q^{47} -2.14459 q^{48} +14.2883 q^{49} -1.98571 q^{50} -4.40338 q^{51} +6.79568 q^{52} +5.64997 q^{53} +2.11930 q^{54} +1.86603 q^{55} +8.46022 q^{56} +3.39975 q^{57} -2.36724 q^{58} -11.9783 q^{59} +1.38186 q^{60} -13.9214 q^{61} -3.53177 q^{62} +10.7771 q^{63} -2.85060 q^{64} -3.70919 q^{65} -0.770440 q^{66} -7.30682 q^{67} -9.52258 q^{68} +1.16175 q^{69} -2.16312 q^{70} -14.8844 q^{71} +4.28293 q^{72} +0.240264 q^{73} +3.47279 q^{74} +3.32078 q^{75} +7.35217 q^{76} -8.94983 q^{77} +1.53144 q^{78} -3.15128 q^{79} +2.53139 q^{80} +3.46313 q^{81} +4.47847 q^{82} -2.46821 q^{83} -6.62763 q^{84} +5.19758 q^{85} +1.43096 q^{86} +3.95883 q^{87} -3.55677 q^{88} +5.55181 q^{89} -1.09506 q^{90} +17.7900 q^{91} +2.51235 q^{92} +5.90632 q^{93} +1.20944 q^{94} -4.01293 q^{95} -4.03398 q^{96} +5.27964 q^{97} +6.96330 q^{98} -4.53079 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 4q^{2} - 3q^{3} + 2q^{4} - 8q^{5} - 5q^{6} - 7q^{7} - 6q^{8} - 2q^{9} + O(q^{10}) \) \( 7q - 4q^{2} - 3q^{3} + 2q^{4} - 8q^{5} - 5q^{6} - 7q^{7} - 6q^{8} - 2q^{9} + 3q^{10} - 18q^{11} + q^{12} - q^{13} - 6q^{14} - 11q^{15} + 4q^{16} - 2q^{17} + 8q^{18} - 6q^{19} - 8q^{20} - 2q^{21} + 10q^{22} - 22q^{23} - 3q^{24} + 5q^{25} + 8q^{26} + 3q^{27} + 9q^{28} - 16q^{29} + 29q^{30} - 18q^{31} - 6q^{32} + 4q^{33} + 11q^{34} + 7q^{35} - 7q^{36} + 8q^{37} + 16q^{38} - 9q^{39} + 14q^{40} - 15q^{41} + 19q^{42} + 14q^{43} - 4q^{44} + 3q^{45} + 11q^{46} - 10q^{47} + 31q^{48} + 6q^{49} - 4q^{50} + 13q^{51} + 27q^{52} + 15q^{53} + 16q^{54} + 29q^{55} + 13q^{56} + 14q^{57} + 17q^{58} - 18q^{59} + 15q^{60} + 4q^{61} + 13q^{62} - 16q^{63} + 2q^{64} - 7q^{65} + 16q^{66} + 18q^{67} - 15q^{68} + 26q^{69} + 8q^{70} - 50q^{71} + 30q^{72} + 10q^{74} + 16q^{75} - 20q^{76} + 17q^{77} - 32q^{78} - 15q^{79} - 11q^{80} - 9q^{81} + 45q^{82} - 24q^{83} + 6q^{84} - 2q^{85} - 23q^{86} + 12q^{87} + 8q^{88} - 13q^{89} - 39q^{90} - 12q^{91} - 10q^{92} + 14q^{93} - 32q^{94} - 41q^{95} - 15q^{96} + q^{97} + 9q^{98} - 20q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.487343 0.344604 0.172302 0.985044i \(-0.444880\pi\)
0.172302 + 0.985044i \(0.444880\pi\)
\(3\) −0.815004 −0.470543 −0.235271 0.971930i \(-0.575598\pi\)
−0.235271 + 0.971930i \(0.575598\pi\)
\(4\) −1.76250 −0.881248
\(5\) 0.961999 0.430219 0.215110 0.976590i \(-0.430989\pi\)
0.215110 + 0.976590i \(0.430989\pi\)
\(6\) −0.397187 −0.162151
\(7\) −4.61392 −1.74390 −0.871950 0.489596i \(-0.837144\pi\)
−0.871950 + 0.489596i \(0.837144\pi\)
\(8\) −1.83363 −0.648285
\(9\) −2.33577 −0.778590
\(10\) 0.468824 0.148255
\(11\) 1.93974 0.584855 0.292427 0.956288i \(-0.405537\pi\)
0.292427 + 0.956288i \(0.405537\pi\)
\(12\) 1.43644 0.414665
\(13\) −3.85571 −1.06938 −0.534691 0.845048i \(-0.679572\pi\)
−0.534691 + 0.845048i \(0.679572\pi\)
\(14\) −2.24856 −0.600954
\(15\) −0.784033 −0.202436
\(16\) 2.63139 0.657847
\(17\) 5.40289 1.31039 0.655197 0.755458i \(-0.272586\pi\)
0.655197 + 0.755458i \(0.272586\pi\)
\(18\) −1.13832 −0.268305
\(19\) −4.17145 −0.956997 −0.478498 0.878088i \(-0.658819\pi\)
−0.478498 + 0.878088i \(0.658819\pi\)
\(20\) −1.69552 −0.379130
\(21\) 3.76036 0.820579
\(22\) 0.945321 0.201543
\(23\) −1.42545 −0.297227 −0.148614 0.988895i \(-0.547481\pi\)
−0.148614 + 0.988895i \(0.547481\pi\)
\(24\) 1.49441 0.305046
\(25\) −4.07456 −0.814911
\(26\) −1.87905 −0.368513
\(27\) 4.34867 0.836902
\(28\) 8.13202 1.53681
\(29\) −4.85744 −0.902003 −0.451002 0.892523i \(-0.648933\pi\)
−0.451002 + 0.892523i \(0.648933\pi\)
\(30\) −0.382093 −0.0697604
\(31\) −7.24699 −1.30160 −0.650799 0.759250i \(-0.725566\pi\)
−0.650799 + 0.759250i \(0.725566\pi\)
\(32\) 4.94964 0.874982
\(33\) −1.58090 −0.275199
\(34\) 2.63306 0.451567
\(35\) −4.43859 −0.750259
\(36\) 4.11678 0.686131
\(37\) 7.12597 1.17150 0.585751 0.810491i \(-0.300800\pi\)
0.585751 + 0.810491i \(0.300800\pi\)
\(38\) −2.03293 −0.329785
\(39\) 3.14242 0.503190
\(40\) −1.76395 −0.278905
\(41\) 9.18955 1.43517 0.717583 0.696473i \(-0.245248\pi\)
0.717583 + 0.696473i \(0.245248\pi\)
\(42\) 1.83259 0.282775
\(43\) 2.93624 0.447772 0.223886 0.974615i \(-0.428126\pi\)
0.223886 + 0.974615i \(0.428126\pi\)
\(44\) −3.41879 −0.515402
\(45\) −2.24701 −0.334964
\(46\) −0.694685 −0.102426
\(47\) 2.48170 0.361994 0.180997 0.983484i \(-0.442068\pi\)
0.180997 + 0.983484i \(0.442068\pi\)
\(48\) −2.14459 −0.309545
\(49\) 14.2883 2.04118
\(50\) −1.98571 −0.280822
\(51\) −4.40338 −0.616596
\(52\) 6.79568 0.942391
\(53\) 5.64997 0.776083 0.388041 0.921642i \(-0.373152\pi\)
0.388041 + 0.921642i \(0.373152\pi\)
\(54\) 2.11930 0.288400
\(55\) 1.86603 0.251616
\(56\) 8.46022 1.13054
\(57\) 3.39975 0.450308
\(58\) −2.36724 −0.310834
\(59\) −11.9783 −1.55944 −0.779718 0.626131i \(-0.784638\pi\)
−0.779718 + 0.626131i \(0.784638\pi\)
\(60\) 1.38186 0.178397
\(61\) −13.9214 −1.78245 −0.891223 0.453565i \(-0.850152\pi\)
−0.891223 + 0.453565i \(0.850152\pi\)
\(62\) −3.53177 −0.448535
\(63\) 10.7771 1.35778
\(64\) −2.85060 −0.356325
\(65\) −3.70919 −0.460069
\(66\) −0.770440 −0.0948346
\(67\) −7.30682 −0.892670 −0.446335 0.894866i \(-0.647271\pi\)
−0.446335 + 0.894866i \(0.647271\pi\)
\(68\) −9.52258 −1.15478
\(69\) 1.16175 0.139858
\(70\) −2.16312 −0.258542
\(71\) −14.8844 −1.76645 −0.883226 0.468948i \(-0.844633\pi\)
−0.883226 + 0.468948i \(0.844633\pi\)
\(72\) 4.28293 0.504748
\(73\) 0.240264 0.0281208 0.0140604 0.999901i \(-0.495524\pi\)
0.0140604 + 0.999901i \(0.495524\pi\)
\(74\) 3.47279 0.403704
\(75\) 3.32078 0.383450
\(76\) 7.35217 0.843352
\(77\) −8.94983 −1.01993
\(78\) 1.53144 0.173401
\(79\) −3.15128 −0.354546 −0.177273 0.984162i \(-0.556728\pi\)
−0.177273 + 0.984162i \(0.556728\pi\)
\(80\) 2.53139 0.283018
\(81\) 3.46313 0.384792
\(82\) 4.47847 0.494564
\(83\) −2.46821 −0.270922 −0.135461 0.990783i \(-0.543251\pi\)
−0.135461 + 0.990783i \(0.543251\pi\)
\(84\) −6.62763 −0.723134
\(85\) 5.19758 0.563757
\(86\) 1.43096 0.154304
\(87\) 3.95883 0.424431
\(88\) −3.55677 −0.379153
\(89\) 5.55181 0.588491 0.294246 0.955730i \(-0.404932\pi\)
0.294246 + 0.955730i \(0.404932\pi\)
\(90\) −1.09506 −0.115430
\(91\) 17.7900 1.86489
\(92\) 2.51235 0.261931
\(93\) 5.90632 0.612457
\(94\) 1.20944 0.124744
\(95\) −4.01293 −0.411718
\(96\) −4.03398 −0.411716
\(97\) 5.27964 0.536067 0.268033 0.963410i \(-0.413626\pi\)
0.268033 + 0.963410i \(0.413626\pi\)
\(98\) 6.96330 0.703400
\(99\) −4.53079 −0.455362
\(100\) 7.18139 0.718139
\(101\) −12.4239 −1.23623 −0.618113 0.786089i \(-0.712103\pi\)
−0.618113 + 0.786089i \(0.712103\pi\)
\(102\) −2.14596 −0.212481
\(103\) −9.80533 −0.966148 −0.483074 0.875580i \(-0.660480\pi\)
−0.483074 + 0.875580i \(0.660480\pi\)
\(104\) 7.06994 0.693264
\(105\) 3.61747 0.353029
\(106\) 2.75347 0.267441
\(107\) −9.15031 −0.884593 −0.442297 0.896869i \(-0.645836\pi\)
−0.442297 + 0.896869i \(0.645836\pi\)
\(108\) −7.66452 −0.737519
\(109\) 3.24534 0.310847 0.155424 0.987848i \(-0.450326\pi\)
0.155424 + 0.987848i \(0.450326\pi\)
\(110\) 0.909398 0.0867077
\(111\) −5.80769 −0.551241
\(112\) −12.1410 −1.14722
\(113\) −0.842874 −0.0792909 −0.0396455 0.999214i \(-0.512623\pi\)
−0.0396455 + 0.999214i \(0.512623\pi\)
\(114\) 1.65684 0.155178
\(115\) −1.37128 −0.127873
\(116\) 8.56121 0.794889
\(117\) 9.00605 0.832610
\(118\) −5.83752 −0.537387
\(119\) −24.9285 −2.28520
\(120\) 1.43762 0.131237
\(121\) −7.23740 −0.657945
\(122\) −6.78448 −0.614238
\(123\) −7.48952 −0.675307
\(124\) 12.7728 1.14703
\(125\) −8.72972 −0.780810
\(126\) 5.25213 0.467897
\(127\) 11.3416 1.00641 0.503203 0.864168i \(-0.332155\pi\)
0.503203 + 0.864168i \(0.332155\pi\)
\(128\) −11.2885 −0.997773
\(129\) −2.39305 −0.210696
\(130\) −1.80765 −0.158541
\(131\) 14.1261 1.23421 0.617103 0.786882i \(-0.288306\pi\)
0.617103 + 0.786882i \(0.288306\pi\)
\(132\) 2.78633 0.242519
\(133\) 19.2468 1.66891
\(134\) −3.56093 −0.307617
\(135\) 4.18342 0.360051
\(136\) −9.90689 −0.849509
\(137\) −12.9555 −1.10686 −0.553430 0.832896i \(-0.686681\pi\)
−0.553430 + 0.832896i \(0.686681\pi\)
\(138\) 0.566170 0.0481956
\(139\) 8.23606 0.698574 0.349287 0.937016i \(-0.386424\pi\)
0.349287 + 0.937016i \(0.386424\pi\)
\(140\) 7.82300 0.661164
\(141\) −2.02260 −0.170333
\(142\) −7.25380 −0.608726
\(143\) −7.47909 −0.625433
\(144\) −6.14631 −0.512193
\(145\) −4.67285 −0.388059
\(146\) 0.117091 0.00969054
\(147\) −11.6450 −0.960464
\(148\) −12.5595 −1.03238
\(149\) 4.48606 0.367513 0.183756 0.982972i \(-0.441174\pi\)
0.183756 + 0.982972i \(0.441174\pi\)
\(150\) 1.61836 0.132138
\(151\) 0.0933624 0.00759773 0.00379886 0.999993i \(-0.498791\pi\)
0.00379886 + 0.999993i \(0.498791\pi\)
\(152\) 7.64889 0.620407
\(153\) −12.6199 −1.02026
\(154\) −4.36164 −0.351471
\(155\) −6.97160 −0.559972
\(156\) −5.53850 −0.443435
\(157\) −10.1337 −0.808760 −0.404380 0.914591i \(-0.632513\pi\)
−0.404380 + 0.914591i \(0.632513\pi\)
\(158\) −1.53575 −0.122178
\(159\) −4.60474 −0.365180
\(160\) 4.76155 0.376434
\(161\) 6.57693 0.518334
\(162\) 1.68773 0.132601
\(163\) 7.49804 0.587292 0.293646 0.955914i \(-0.405131\pi\)
0.293646 + 0.955914i \(0.405131\pi\)
\(164\) −16.1965 −1.26474
\(165\) −1.52082 −0.118396
\(166\) −1.20287 −0.0933606
\(167\) 17.7922 1.37680 0.688399 0.725332i \(-0.258314\pi\)
0.688399 + 0.725332i \(0.258314\pi\)
\(168\) −6.89511 −0.531969
\(169\) 1.86650 0.143577
\(170\) 2.53301 0.194273
\(171\) 9.74355 0.745108
\(172\) −5.17511 −0.394599
\(173\) 18.4927 1.40597 0.702987 0.711203i \(-0.251849\pi\)
0.702987 + 0.711203i \(0.251849\pi\)
\(174\) 1.92931 0.146260
\(175\) 18.7997 1.42112
\(176\) 5.10421 0.384745
\(177\) 9.76232 0.733781
\(178\) 2.70564 0.202796
\(179\) −17.3387 −1.29595 −0.647977 0.761660i \(-0.724385\pi\)
−0.647977 + 0.761660i \(0.724385\pi\)
\(180\) 3.96034 0.295187
\(181\) 17.7124 1.31655 0.658275 0.752778i \(-0.271287\pi\)
0.658275 + 0.752778i \(0.271287\pi\)
\(182\) 8.66981 0.642649
\(183\) 11.3460 0.838717
\(184\) 2.61375 0.192688
\(185\) 6.85518 0.504003
\(186\) 2.87841 0.211055
\(187\) 10.4802 0.766390
\(188\) −4.37400 −0.319006
\(189\) −20.0644 −1.45947
\(190\) −1.95568 −0.141880
\(191\) 13.2440 0.958303 0.479151 0.877732i \(-0.340944\pi\)
0.479151 + 0.877732i \(0.340944\pi\)
\(192\) 2.32325 0.167666
\(193\) −25.5030 −1.83574 −0.917872 0.396877i \(-0.870094\pi\)
−0.917872 + 0.396877i \(0.870094\pi\)
\(194\) 2.57300 0.184731
\(195\) 3.02300 0.216482
\(196\) −25.1831 −1.79879
\(197\) −15.0303 −1.07087 −0.535433 0.844578i \(-0.679851\pi\)
−0.535433 + 0.844578i \(0.679851\pi\)
\(198\) −2.20805 −0.156919
\(199\) −19.3801 −1.37382 −0.686911 0.726742i \(-0.741034\pi\)
−0.686911 + 0.726742i \(0.741034\pi\)
\(200\) 7.47122 0.528295
\(201\) 5.95508 0.420039
\(202\) −6.05472 −0.426008
\(203\) 22.4118 1.57300
\(204\) 7.76094 0.543374
\(205\) 8.84034 0.617436
\(206\) −4.77856 −0.332938
\(207\) 3.32953 0.231418
\(208\) −10.1459 −0.703489
\(209\) −8.09154 −0.559704
\(210\) 1.76295 0.121655
\(211\) 27.9383 1.92335 0.961675 0.274192i \(-0.0884105\pi\)
0.961675 + 0.274192i \(0.0884105\pi\)
\(212\) −9.95805 −0.683922
\(213\) 12.1308 0.831191
\(214\) −4.45934 −0.304834
\(215\) 2.82466 0.192640
\(216\) −7.97384 −0.542551
\(217\) 33.4370 2.26985
\(218\) 1.58160 0.107119
\(219\) −0.195816 −0.0132320
\(220\) −3.28887 −0.221736
\(221\) −20.8320 −1.40131
\(222\) −2.83034 −0.189960
\(223\) −0.387500 −0.0259489 −0.0129745 0.999916i \(-0.504130\pi\)
−0.0129745 + 0.999916i \(0.504130\pi\)
\(224\) −22.8373 −1.52588
\(225\) 9.51722 0.634482
\(226\) −0.410769 −0.0273240
\(227\) 10.2778 0.682161 0.341081 0.940034i \(-0.389207\pi\)
0.341081 + 0.940034i \(0.389207\pi\)
\(228\) −5.99204 −0.396833
\(229\) −10.5346 −0.696147 −0.348074 0.937467i \(-0.613164\pi\)
−0.348074 + 0.937467i \(0.613164\pi\)
\(230\) −0.668286 −0.0440655
\(231\) 7.29414 0.479919
\(232\) 8.90673 0.584755
\(233\) 25.6725 1.68186 0.840932 0.541141i \(-0.182007\pi\)
0.840932 + 0.541141i \(0.182007\pi\)
\(234\) 4.38904 0.286920
\(235\) 2.38740 0.155737
\(236\) 21.1116 1.37425
\(237\) 2.56830 0.166829
\(238\) −12.1488 −0.787487
\(239\) −25.1312 −1.62560 −0.812801 0.582542i \(-0.802058\pi\)
−0.812801 + 0.582542i \(0.802058\pi\)
\(240\) −2.06309 −0.133172
\(241\) −1.00000 −0.0644157
\(242\) −3.52710 −0.226730
\(243\) −15.8685 −1.01796
\(244\) 24.5363 1.57078
\(245\) 13.7453 0.878157
\(246\) −3.64997 −0.232713
\(247\) 16.0839 1.02339
\(248\) 13.2883 0.843806
\(249\) 2.01160 0.127480
\(250\) −4.25437 −0.269070
\(251\) 2.52238 0.159211 0.0796055 0.996826i \(-0.474634\pi\)
0.0796055 + 0.996826i \(0.474634\pi\)
\(252\) −18.9945 −1.19654
\(253\) −2.76501 −0.173835
\(254\) 5.52726 0.346811
\(255\) −4.23605 −0.265272
\(256\) 0.199817 0.0124886
\(257\) 3.92348 0.244740 0.122370 0.992485i \(-0.460951\pi\)
0.122370 + 0.992485i \(0.460951\pi\)
\(258\) −1.16623 −0.0726066
\(259\) −32.8787 −2.04298
\(260\) 6.53744 0.405435
\(261\) 11.3458 0.702290
\(262\) 6.88428 0.425312
\(263\) 6.24984 0.385382 0.192691 0.981260i \(-0.438279\pi\)
0.192691 + 0.981260i \(0.438279\pi\)
\(264\) 2.89878 0.178407
\(265\) 5.43527 0.333886
\(266\) 9.37978 0.575111
\(267\) −4.52475 −0.276910
\(268\) 12.8782 0.786664
\(269\) 20.4943 1.24956 0.624780 0.780801i \(-0.285189\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(270\) 2.03876 0.124075
\(271\) 15.3179 0.930499 0.465249 0.885180i \(-0.345965\pi\)
0.465249 + 0.885180i \(0.345965\pi\)
\(272\) 14.2171 0.862039
\(273\) −14.4989 −0.877512
\(274\) −6.31376 −0.381428
\(275\) −7.90359 −0.476605
\(276\) −2.04758 −0.123250
\(277\) 3.26388 0.196108 0.0980539 0.995181i \(-0.468738\pi\)
0.0980539 + 0.995181i \(0.468738\pi\)
\(278\) 4.01379 0.240731
\(279\) 16.9273 1.01341
\(280\) 8.13872 0.486382
\(281\) −12.4791 −0.744442 −0.372221 0.928144i \(-0.621404\pi\)
−0.372221 + 0.928144i \(0.621404\pi\)
\(282\) −0.985700 −0.0586976
\(283\) −15.8115 −0.939899 −0.469949 0.882693i \(-0.655728\pi\)
−0.469949 + 0.882693i \(0.655728\pi\)
\(284\) 26.2337 1.55668
\(285\) 3.27056 0.193731
\(286\) −3.64488 −0.215526
\(287\) −42.3999 −2.50279
\(288\) −11.5612 −0.681252
\(289\) 12.1913 0.717133
\(290\) −2.27728 −0.133727
\(291\) −4.30293 −0.252242
\(292\) −0.423465 −0.0247814
\(293\) 18.7147 1.09333 0.546663 0.837353i \(-0.315898\pi\)
0.546663 + 0.837353i \(0.315898\pi\)
\(294\) −5.67512 −0.330979
\(295\) −11.5231 −0.670899
\(296\) −13.0664 −0.759467
\(297\) 8.43530 0.489466
\(298\) 2.18625 0.126646
\(299\) 5.49613 0.317849
\(300\) −5.85286 −0.337915
\(301\) −13.5476 −0.780870
\(302\) 0.0454995 0.00261820
\(303\) 10.1255 0.581697
\(304\) −10.9767 −0.629557
\(305\) −13.3923 −0.766843
\(306\) −6.15023 −0.351585
\(307\) 5.23477 0.298764 0.149382 0.988780i \(-0.452272\pi\)
0.149382 + 0.988780i \(0.452272\pi\)
\(308\) 15.7740 0.898809
\(309\) 7.99138 0.454614
\(310\) −3.39756 −0.192969
\(311\) −26.6878 −1.51332 −0.756662 0.653806i \(-0.773171\pi\)
−0.756662 + 0.653806i \(0.773171\pi\)
\(312\) −5.76202 −0.326210
\(313\) 6.24141 0.352786 0.176393 0.984320i \(-0.443557\pi\)
0.176393 + 0.984320i \(0.443557\pi\)
\(314\) −4.93861 −0.278702
\(315\) 10.3675 0.584144
\(316\) 5.55412 0.312443
\(317\) 6.89526 0.387276 0.193638 0.981073i \(-0.437971\pi\)
0.193638 + 0.981073i \(0.437971\pi\)
\(318\) −2.24409 −0.125842
\(319\) −9.42218 −0.527541
\(320\) −2.74227 −0.153298
\(321\) 7.45753 0.416239
\(322\) 3.20522 0.178620
\(323\) −22.5379 −1.25404
\(324\) −6.10375 −0.339097
\(325\) 15.7103 0.871451
\(326\) 3.65412 0.202383
\(327\) −2.64497 −0.146267
\(328\) −16.8502 −0.930397
\(329\) −11.4504 −0.631281
\(330\) −0.741163 −0.0407997
\(331\) −13.5697 −0.745860 −0.372930 0.927859i \(-0.621647\pi\)
−0.372930 + 0.927859i \(0.621647\pi\)
\(332\) 4.35022 0.238749
\(333\) −16.6446 −0.912119
\(334\) 8.67089 0.474450
\(335\) −7.02916 −0.384044
\(336\) 9.89497 0.539815
\(337\) −20.2288 −1.10193 −0.550966 0.834528i \(-0.685740\pi\)
−0.550966 + 0.834528i \(0.685740\pi\)
\(338\) 0.909627 0.0494772
\(339\) 0.686946 0.0373098
\(340\) −9.16072 −0.496810
\(341\) −14.0573 −0.761245
\(342\) 4.74845 0.256767
\(343\) −33.6276 −1.81572
\(344\) −5.38397 −0.290284
\(345\) 1.11760 0.0601696
\(346\) 9.01229 0.484504
\(347\) 1.52458 0.0818437 0.0409219 0.999162i \(-0.486971\pi\)
0.0409219 + 0.999162i \(0.486971\pi\)
\(348\) −6.97742 −0.374029
\(349\) 16.5585 0.886358 0.443179 0.896433i \(-0.353851\pi\)
0.443179 + 0.896433i \(0.353851\pi\)
\(350\) 9.16191 0.489724
\(351\) −16.7672 −0.894968
\(352\) 9.60104 0.511737
\(353\) 34.6802 1.84584 0.922920 0.384992i \(-0.125796\pi\)
0.922920 + 0.384992i \(0.125796\pi\)
\(354\) 4.75760 0.252864
\(355\) −14.3188 −0.759961
\(356\) −9.78505 −0.518607
\(357\) 20.3168 1.07528
\(358\) −8.44989 −0.446590
\(359\) 18.1341 0.957084 0.478542 0.878065i \(-0.341165\pi\)
0.478542 + 0.878065i \(0.341165\pi\)
\(360\) 4.12018 0.217152
\(361\) −1.59899 −0.0841573
\(362\) 8.63200 0.453688
\(363\) 5.89850 0.309591
\(364\) −31.3547 −1.64343
\(365\) 0.231134 0.0120981
\(366\) 5.52937 0.289025
\(367\) −10.9879 −0.573566 −0.286783 0.957996i \(-0.592586\pi\)
−0.286783 + 0.957996i \(0.592586\pi\)
\(368\) −3.75092 −0.195530
\(369\) −21.4647 −1.11741
\(370\) 3.34082 0.173681
\(371\) −26.0685 −1.35341
\(372\) −10.4099 −0.539727
\(373\) 5.23646 0.271134 0.135567 0.990768i \(-0.456714\pi\)
0.135567 + 0.990768i \(0.456714\pi\)
\(374\) 5.10747 0.264101
\(375\) 7.11475 0.367404
\(376\) −4.55052 −0.234675
\(377\) 18.7289 0.964586
\(378\) −9.77827 −0.502940
\(379\) 8.07101 0.414580 0.207290 0.978280i \(-0.433536\pi\)
0.207290 + 0.978280i \(0.433536\pi\)
\(380\) 7.07278 0.362826
\(381\) −9.24346 −0.473557
\(382\) 6.45438 0.330235
\(383\) 2.46503 0.125957 0.0629785 0.998015i \(-0.479940\pi\)
0.0629785 + 0.998015i \(0.479940\pi\)
\(384\) 9.20017 0.469494
\(385\) −8.60973 −0.438792
\(386\) −12.4287 −0.632604
\(387\) −6.85838 −0.348631
\(388\) −9.30535 −0.472408
\(389\) −28.7159 −1.45595 −0.727977 0.685601i \(-0.759539\pi\)
−0.727977 + 0.685601i \(0.759539\pi\)
\(390\) 1.47324 0.0746004
\(391\) −7.70157 −0.389485
\(392\) −26.1994 −1.32327
\(393\) −11.5128 −0.580746
\(394\) −7.32492 −0.369024
\(395\) −3.03153 −0.152533
\(396\) 7.98550 0.401287
\(397\) 12.0605 0.605301 0.302651 0.953102i \(-0.402129\pi\)
0.302651 + 0.953102i \(0.402129\pi\)
\(398\) −9.44478 −0.473424
\(399\) −15.6862 −0.785291
\(400\) −10.7217 −0.536087
\(401\) −31.7082 −1.58343 −0.791716 0.610890i \(-0.790812\pi\)
−0.791716 + 0.610890i \(0.790812\pi\)
\(402\) 2.90217 0.144747
\(403\) 27.9423 1.39190
\(404\) 21.8971 1.08942
\(405\) 3.33152 0.165545
\(406\) 10.9223 0.542063
\(407\) 13.8225 0.685158
\(408\) 8.07415 0.399730
\(409\) −14.1893 −0.701617 −0.350809 0.936447i \(-0.614093\pi\)
−0.350809 + 0.936447i \(0.614093\pi\)
\(410\) 4.30828 0.212771
\(411\) 10.5587 0.520825
\(412\) 17.2819 0.851416
\(413\) 55.2668 2.71950
\(414\) 1.62262 0.0797476
\(415\) −2.37442 −0.116556
\(416\) −19.0844 −0.935689
\(417\) −6.71242 −0.328709
\(418\) −3.94336 −0.192876
\(419\) 31.1014 1.51941 0.759703 0.650271i \(-0.225345\pi\)
0.759703 + 0.650271i \(0.225345\pi\)
\(420\) −6.37578 −0.311106
\(421\) −27.4415 −1.33742 −0.668709 0.743524i \(-0.733153\pi\)
−0.668709 + 0.743524i \(0.733153\pi\)
\(422\) 13.6155 0.662794
\(423\) −5.79669 −0.281845
\(424\) −10.3599 −0.503123
\(425\) −22.0144 −1.06786
\(426\) 5.91188 0.286431
\(427\) 64.2321 3.10841
\(428\) 16.1274 0.779546
\(429\) 6.09548 0.294293
\(430\) 1.37658 0.0663846
\(431\) −14.1005 −0.679199 −0.339599 0.940570i \(-0.610291\pi\)
−0.339599 + 0.940570i \(0.610291\pi\)
\(432\) 11.4430 0.550553
\(433\) −17.7403 −0.852546 −0.426273 0.904595i \(-0.640174\pi\)
−0.426273 + 0.904595i \(0.640174\pi\)
\(434\) 16.2953 0.782200
\(435\) 3.80839 0.182598
\(436\) −5.71991 −0.273934
\(437\) 5.94621 0.284446
\(438\) −0.0954297 −0.00455981
\(439\) −2.52447 −0.120486 −0.0602431 0.998184i \(-0.519188\pi\)
−0.0602431 + 0.998184i \(0.519188\pi\)
\(440\) −3.42161 −0.163119
\(441\) −33.3741 −1.58924
\(442\) −10.1523 −0.482897
\(443\) −16.8382 −0.800008 −0.400004 0.916513i \(-0.630991\pi\)
−0.400004 + 0.916513i \(0.630991\pi\)
\(444\) 10.2360 0.485780
\(445\) 5.34084 0.253180
\(446\) −0.188846 −0.00894211
\(447\) −3.65616 −0.172930
\(448\) 13.1524 0.621394
\(449\) −30.5688 −1.44263 −0.721314 0.692608i \(-0.756462\pi\)
−0.721314 + 0.692608i \(0.756462\pi\)
\(450\) 4.63816 0.218645
\(451\) 17.8254 0.839364
\(452\) 1.48556 0.0698750
\(453\) −0.0760907 −0.00357505
\(454\) 5.00882 0.235075
\(455\) 17.1139 0.802313
\(456\) −6.23387 −0.291928
\(457\) −32.7043 −1.52984 −0.764922 0.644123i \(-0.777223\pi\)
−0.764922 + 0.644123i \(0.777223\pi\)
\(458\) −5.13398 −0.239895
\(459\) 23.4954 1.09667
\(460\) 2.41688 0.112688
\(461\) 12.3932 0.577210 0.288605 0.957448i \(-0.406809\pi\)
0.288605 + 0.957448i \(0.406809\pi\)
\(462\) 3.55475 0.165382
\(463\) 12.1379 0.564094 0.282047 0.959401i \(-0.408987\pi\)
0.282047 + 0.959401i \(0.408987\pi\)
\(464\) −12.7818 −0.593380
\(465\) 5.68188 0.263491
\(466\) 12.5113 0.579577
\(467\) 5.38203 0.249051 0.124525 0.992216i \(-0.460259\pi\)
0.124525 + 0.992216i \(0.460259\pi\)
\(468\) −15.8731 −0.733736
\(469\) 33.7131 1.55673
\(470\) 1.16348 0.0536675
\(471\) 8.25903 0.380556
\(472\) 21.9637 1.01096
\(473\) 5.69555 0.261882
\(474\) 1.25165 0.0574900
\(475\) 16.9968 0.779868
\(476\) 43.9365 2.01382
\(477\) −13.1970 −0.604250
\(478\) −12.2475 −0.560188
\(479\) −25.3752 −1.15942 −0.579711 0.814822i \(-0.696834\pi\)
−0.579711 + 0.814822i \(0.696834\pi\)
\(480\) −3.88068 −0.177128
\(481\) −27.4757 −1.25278
\(482\) −0.487343 −0.0221979
\(483\) −5.36022 −0.243898
\(484\) 12.7559 0.579813
\(485\) 5.07901 0.230626
\(486\) −7.73339 −0.350794
\(487\) −10.4243 −0.472369 −0.236185 0.971708i \(-0.575897\pi\)
−0.236185 + 0.971708i \(0.575897\pi\)
\(488\) 25.5266 1.15553
\(489\) −6.11093 −0.276346
\(490\) 6.69869 0.302616
\(491\) 34.2858 1.54730 0.773649 0.633614i \(-0.218429\pi\)
0.773649 + 0.633614i \(0.218429\pi\)
\(492\) 13.2002 0.595113
\(493\) −26.2442 −1.18198
\(494\) 7.83839 0.352666
\(495\) −4.35862 −0.195905
\(496\) −19.0696 −0.856252
\(497\) 68.6754 3.08051
\(498\) 0.980341 0.0439301
\(499\) 15.9672 0.714792 0.357396 0.933953i \(-0.383665\pi\)
0.357396 + 0.933953i \(0.383665\pi\)
\(500\) 15.3861 0.688087
\(501\) −14.5007 −0.647842
\(502\) 1.22926 0.0548647
\(503\) −4.53174 −0.202060 −0.101030 0.994883i \(-0.532214\pi\)
−0.101030 + 0.994883i \(0.532214\pi\)
\(504\) −19.7611 −0.880230
\(505\) −11.9518 −0.531849
\(506\) −1.34751 −0.0599041
\(507\) −1.52121 −0.0675591
\(508\) −19.9896 −0.886893
\(509\) −4.08798 −0.181197 −0.0905983 0.995888i \(-0.528878\pi\)
−0.0905983 + 0.995888i \(0.528878\pi\)
\(510\) −2.06441 −0.0914136
\(511\) −1.10856 −0.0490398
\(512\) 22.6744 1.00208
\(513\) −18.1403 −0.800913
\(514\) 1.91208 0.0843384
\(515\) −9.43272 −0.415655
\(516\) 4.21774 0.185675
\(517\) 4.81387 0.211714
\(518\) −16.0232 −0.704019
\(519\) −15.0716 −0.661571
\(520\) 6.80127 0.298256
\(521\) 34.2884 1.50220 0.751102 0.660186i \(-0.229523\pi\)
0.751102 + 0.660186i \(0.229523\pi\)
\(522\) 5.52932 0.242012
\(523\) 33.7724 1.47676 0.738382 0.674382i \(-0.235590\pi\)
0.738382 + 0.674382i \(0.235590\pi\)
\(524\) −24.8973 −1.08764
\(525\) −15.3218 −0.668699
\(526\) 3.04582 0.132804
\(527\) −39.1547 −1.70561
\(528\) −4.15995 −0.181039
\(529\) −20.9681 −0.911656
\(530\) 2.64884 0.115058
\(531\) 27.9784 1.21416
\(532\) −33.9223 −1.47072
\(533\) −35.4322 −1.53474
\(534\) −2.20511 −0.0954243
\(535\) −8.80259 −0.380569
\(536\) 13.3980 0.578705
\(537\) 14.1311 0.609801
\(538\) 9.98777 0.430603
\(539\) 27.7156 1.19380
\(540\) −7.37326 −0.317295
\(541\) −31.0330 −1.33421 −0.667106 0.744963i \(-0.732467\pi\)
−0.667106 + 0.744963i \(0.732467\pi\)
\(542\) 7.46510 0.320653
\(543\) −14.4356 −0.619492
\(544\) 26.7424 1.14657
\(545\) 3.12202 0.133733
\(546\) −7.06593 −0.302394
\(547\) −33.0104 −1.41142 −0.705712 0.708499i \(-0.749373\pi\)
−0.705712 + 0.708499i \(0.749373\pi\)
\(548\) 22.8340 0.975418
\(549\) 32.5171 1.38779
\(550\) −3.85176 −0.164240
\(551\) 20.2626 0.863214
\(552\) −2.13021 −0.0906679
\(553\) 14.5398 0.618293
\(554\) 1.59063 0.0675795
\(555\) −5.58699 −0.237155
\(556\) −14.5160 −0.615617
\(557\) 15.4826 0.656019 0.328010 0.944674i \(-0.393622\pi\)
0.328010 + 0.944674i \(0.393622\pi\)
\(558\) 8.24940 0.349225
\(559\) −11.3213 −0.478840
\(560\) −11.6797 −0.493555
\(561\) −8.54142 −0.360619
\(562\) −6.08161 −0.256537
\(563\) 6.21072 0.261751 0.130875 0.991399i \(-0.458221\pi\)
0.130875 + 0.991399i \(0.458221\pi\)
\(564\) 3.56482 0.150106
\(565\) −0.810845 −0.0341125
\(566\) −7.70565 −0.323893
\(567\) −15.9786 −0.671038
\(568\) 27.2924 1.14516
\(569\) −20.3014 −0.851078 −0.425539 0.904940i \(-0.639916\pi\)
−0.425539 + 0.904940i \(0.639916\pi\)
\(570\) 1.59388 0.0667604
\(571\) −38.5209 −1.61205 −0.806024 0.591882i \(-0.798385\pi\)
−0.806024 + 0.591882i \(0.798385\pi\)
\(572\) 13.1819 0.551161
\(573\) −10.7939 −0.450922
\(574\) −20.6633 −0.862469
\(575\) 5.80809 0.242214
\(576\) 6.65834 0.277431
\(577\) 19.3481 0.805472 0.402736 0.915316i \(-0.368059\pi\)
0.402736 + 0.915316i \(0.368059\pi\)
\(578\) 5.94133 0.247127
\(579\) 20.7850 0.863795
\(580\) 8.23588 0.341976
\(581\) 11.3881 0.472460
\(582\) −2.09700 −0.0869236
\(583\) 10.9595 0.453896
\(584\) −0.440555 −0.0182303
\(585\) 8.66381 0.358205
\(586\) 9.12050 0.376764
\(587\) −20.0183 −0.826243 −0.413122 0.910676i \(-0.635562\pi\)
−0.413122 + 0.910676i \(0.635562\pi\)
\(588\) 20.5243 0.846407
\(589\) 30.2305 1.24562
\(590\) −5.61569 −0.231194
\(591\) 12.2498 0.503888
\(592\) 18.7512 0.770668
\(593\) 12.5904 0.517027 0.258513 0.966008i \(-0.416767\pi\)
0.258513 + 0.966008i \(0.416767\pi\)
\(594\) 4.11089 0.168672
\(595\) −23.9812 −0.983135
\(596\) −7.90667 −0.323870
\(597\) 15.7949 0.646441
\(598\) 2.67850 0.109532
\(599\) 24.4282 0.998107 0.499054 0.866571i \(-0.333681\pi\)
0.499054 + 0.866571i \(0.333681\pi\)
\(600\) −6.08907 −0.248585
\(601\) 9.02256 0.368038 0.184019 0.982923i \(-0.441089\pi\)
0.184019 + 0.982923i \(0.441089\pi\)
\(602\) −6.60233 −0.269091
\(603\) 17.0670 0.695024
\(604\) −0.164551 −0.00669548
\(605\) −6.96237 −0.283061
\(606\) 4.93462 0.200455
\(607\) −19.0044 −0.771364 −0.385682 0.922632i \(-0.626034\pi\)
−0.385682 + 0.922632i \(0.626034\pi\)
\(608\) −20.6472 −0.837355
\(609\) −18.2657 −0.740165
\(610\) −6.52666 −0.264257
\(611\) −9.56873 −0.387110
\(612\) 22.2426 0.899102
\(613\) 3.38617 0.136766 0.0683831 0.997659i \(-0.478216\pi\)
0.0683831 + 0.997659i \(0.478216\pi\)
\(614\) 2.55113 0.102955
\(615\) −7.20491 −0.290530
\(616\) 16.4106 0.661204
\(617\) −33.9920 −1.36847 −0.684234 0.729263i \(-0.739863\pi\)
−0.684234 + 0.729263i \(0.739863\pi\)
\(618\) 3.89455 0.156662
\(619\) 29.6477 1.19164 0.595822 0.803117i \(-0.296826\pi\)
0.595822 + 0.803117i \(0.296826\pi\)
\(620\) 12.2874 0.493475
\(621\) −6.19882 −0.248750
\(622\) −13.0061 −0.521497
\(623\) −25.6156 −1.02627
\(624\) 8.26892 0.331022
\(625\) 11.9748 0.478992
\(626\) 3.04171 0.121571
\(627\) 6.59464 0.263364
\(628\) 17.8607 0.712718
\(629\) 38.5008 1.53513
\(630\) 5.05254 0.201298
\(631\) 14.6241 0.582176 0.291088 0.956696i \(-0.405983\pi\)
0.291088 + 0.956696i \(0.405983\pi\)
\(632\) 5.77827 0.229847
\(633\) −22.7698 −0.905018
\(634\) 3.36036 0.133457
\(635\) 10.9106 0.432975
\(636\) 8.11585 0.321814
\(637\) −55.0915 −2.18280
\(638\) −4.59184 −0.181793
\(639\) 34.7665 1.37534
\(640\) −10.8595 −0.429261
\(641\) 4.17547 0.164921 0.0824606 0.996594i \(-0.473722\pi\)
0.0824606 + 0.996594i \(0.473722\pi\)
\(642\) 3.63438 0.143437
\(643\) 23.1928 0.914635 0.457317 0.889304i \(-0.348810\pi\)
0.457317 + 0.889304i \(0.348810\pi\)
\(644\) −11.5918 −0.456781
\(645\) −2.30211 −0.0906455
\(646\) −10.9837 −0.432148
\(647\) −31.0975 −1.22257 −0.611284 0.791411i \(-0.709347\pi\)
−0.611284 + 0.791411i \(0.709347\pi\)
\(648\) −6.35008 −0.249455
\(649\) −23.2347 −0.912043
\(650\) 7.65632 0.300305
\(651\) −27.2513 −1.06806
\(652\) −13.2153 −0.517550
\(653\) −31.5439 −1.23441 −0.617204 0.786803i \(-0.711735\pi\)
−0.617204 + 0.786803i \(0.711735\pi\)
\(654\) −1.28901 −0.0504041
\(655\) 13.5893 0.530979
\(656\) 24.1813 0.944120
\(657\) −0.561202 −0.0218946
\(658\) −5.58027 −0.217542
\(659\) 25.2754 0.984590 0.492295 0.870428i \(-0.336158\pi\)
0.492295 + 0.870428i \(0.336158\pi\)
\(660\) 2.68044 0.104336
\(661\) −21.7628 −0.846476 −0.423238 0.906018i \(-0.639107\pi\)
−0.423238 + 0.906018i \(0.639107\pi\)
\(662\) −6.61312 −0.257026
\(663\) 16.9781 0.659377
\(664\) 4.52578 0.175634
\(665\) 18.5154 0.717995
\(666\) −8.11164 −0.314320
\(667\) 6.92404 0.268100
\(668\) −31.3586 −1.21330
\(669\) 0.315814 0.0122101
\(670\) −3.42561 −0.132343
\(671\) −27.0038 −1.04247
\(672\) 18.6125 0.717991
\(673\) −37.2710 −1.43669 −0.718346 0.695686i \(-0.755101\pi\)
−0.718346 + 0.695686i \(0.755101\pi\)
\(674\) −9.85835 −0.379730
\(675\) −17.7189 −0.682001
\(676\) −3.28970 −0.126527
\(677\) −33.5515 −1.28949 −0.644745 0.764398i \(-0.723036\pi\)
−0.644745 + 0.764398i \(0.723036\pi\)
\(678\) 0.334778 0.0128571
\(679\) −24.3599 −0.934846
\(680\) −9.53043 −0.365475
\(681\) −8.37644 −0.320986
\(682\) −6.85073 −0.262328
\(683\) 8.94737 0.342362 0.171181 0.985240i \(-0.445242\pi\)
0.171181 + 0.985240i \(0.445242\pi\)
\(684\) −17.1730 −0.656625
\(685\) −12.4631 −0.476192
\(686\) −16.3882 −0.625704
\(687\) 8.58575 0.327567
\(688\) 7.72638 0.294566
\(689\) −21.7846 −0.829929
\(690\) 0.544656 0.0207347
\(691\) 7.04969 0.268183 0.134092 0.990969i \(-0.457188\pi\)
0.134092 + 0.990969i \(0.457188\pi\)
\(692\) −32.5933 −1.23901
\(693\) 20.9047 0.794105
\(694\) 0.742994 0.0282036
\(695\) 7.92309 0.300540
\(696\) −7.25902 −0.275152
\(697\) 49.6502 1.88063
\(698\) 8.06969 0.305442
\(699\) −20.9232 −0.791389
\(700\) −33.1344 −1.25236
\(701\) −5.19179 −0.196091 −0.0980456 0.995182i \(-0.531259\pi\)
−0.0980456 + 0.995182i \(0.531259\pi\)
\(702\) −8.17139 −0.308409
\(703\) −29.7256 −1.12112
\(704\) −5.52943 −0.208398
\(705\) −1.94574 −0.0732807
\(706\) 16.9012 0.636083
\(707\) 57.3230 2.15586
\(708\) −17.2061 −0.646643
\(709\) −16.3067 −0.612410 −0.306205 0.951966i \(-0.599059\pi\)
−0.306205 + 0.951966i \(0.599059\pi\)
\(710\) −6.97816 −0.261886
\(711\) 7.36066 0.276046
\(712\) −10.1800 −0.381510
\(713\) 10.3302 0.386870
\(714\) 9.90128 0.370546
\(715\) −7.19488 −0.269073
\(716\) 30.5594 1.14206
\(717\) 20.4820 0.764915
\(718\) 8.83756 0.329815
\(719\) −27.4968 −1.02546 −0.512729 0.858551i \(-0.671365\pi\)
−0.512729 + 0.858551i \(0.671365\pi\)
\(720\) −5.91275 −0.220355
\(721\) 45.2410 1.68486
\(722\) −0.779256 −0.0290009
\(723\) 0.815004 0.0303103
\(724\) −31.2180 −1.16021
\(725\) 19.7919 0.735053
\(726\) 2.87460 0.106686
\(727\) −15.2319 −0.564919 −0.282460 0.959279i \(-0.591150\pi\)
−0.282460 + 0.959279i \(0.591150\pi\)
\(728\) −32.6201 −1.20898
\(729\) 2.54349 0.0942032
\(730\) 0.112642 0.00416905
\(731\) 15.8642 0.586758
\(732\) −19.9972 −0.739118
\(733\) 6.76475 0.249862 0.124931 0.992165i \(-0.460129\pi\)
0.124931 + 0.992165i \(0.460129\pi\)
\(734\) −5.35490 −0.197653
\(735\) −11.2025 −0.413210
\(736\) −7.05548 −0.260068
\(737\) −14.1734 −0.522082
\(738\) −10.4607 −0.385062
\(739\) 17.9519 0.660372 0.330186 0.943916i \(-0.392889\pi\)
0.330186 + 0.943916i \(0.392889\pi\)
\(740\) −12.0822 −0.444151
\(741\) −13.1084 −0.481551
\(742\) −12.7043 −0.466390
\(743\) −17.2096 −0.631357 −0.315679 0.948866i \(-0.602232\pi\)
−0.315679 + 0.948866i \(0.602232\pi\)
\(744\) −10.8300 −0.397047
\(745\) 4.31559 0.158111
\(746\) 2.55195 0.0934336
\(747\) 5.76518 0.210937
\(748\) −18.4714 −0.675380
\(749\) 42.2188 1.54264
\(750\) 3.46733 0.126609
\(751\) 4.98853 0.182034 0.0910170 0.995849i \(-0.470988\pi\)
0.0910170 + 0.995849i \(0.470988\pi\)
\(752\) 6.53032 0.238136
\(753\) −2.05575 −0.0749156
\(754\) 9.12739 0.332400
\(755\) 0.0898146 0.00326869
\(756\) 35.3635 1.28616
\(757\) −19.5585 −0.710864 −0.355432 0.934702i \(-0.615666\pi\)
−0.355432 + 0.934702i \(0.615666\pi\)
\(758\) 3.93335 0.142866
\(759\) 2.25349 0.0817966
\(760\) 7.35823 0.266911
\(761\) −41.0235 −1.48710 −0.743550 0.668681i \(-0.766859\pi\)
−0.743550 + 0.668681i \(0.766859\pi\)
\(762\) −4.50474 −0.163189
\(763\) −14.9738 −0.542087
\(764\) −23.3425 −0.844503
\(765\) −12.1403 −0.438935
\(766\) 1.20131 0.0434053
\(767\) 46.1847 1.66763
\(768\) −0.162852 −0.00587641
\(769\) 11.7068 0.422159 0.211079 0.977469i \(-0.432302\pi\)
0.211079 + 0.977469i \(0.432302\pi\)
\(770\) −4.19589 −0.151209
\(771\) −3.19765 −0.115161
\(772\) 44.9489 1.61775
\(773\) −6.66278 −0.239643 −0.119822 0.992795i \(-0.538232\pi\)
−0.119822 + 0.992795i \(0.538232\pi\)
\(774\) −3.34238 −0.120140
\(775\) 29.5283 1.06069
\(776\) −9.68090 −0.347524
\(777\) 26.7962 0.961309
\(778\) −13.9945 −0.501727
\(779\) −38.3338 −1.37345
\(780\) −5.32803 −0.190774
\(781\) −28.8719 −1.03312
\(782\) −3.75331 −0.134218
\(783\) −21.1234 −0.754888
\(784\) 37.5980 1.34279
\(785\) −9.74865 −0.347944
\(786\) −5.61071 −0.200127
\(787\) 2.88890 0.102978 0.0514891 0.998674i \(-0.483603\pi\)
0.0514891 + 0.998674i \(0.483603\pi\)
\(788\) 26.4909 0.943698
\(789\) −5.09364 −0.181338
\(790\) −1.47739 −0.0525633
\(791\) 3.88896 0.138275
\(792\) 8.30778 0.295204
\(793\) 53.6767 1.90612
\(794\) 5.87762 0.208589
\(795\) −4.42976 −0.157107
\(796\) 34.1574 1.21068
\(797\) 18.0912 0.640824 0.320412 0.947278i \(-0.396179\pi\)
0.320412 + 0.947278i \(0.396179\pi\)
\(798\) −7.64455 −0.270614
\(799\) 13.4084 0.474355
\(800\) −20.1676 −0.713033
\(801\) −12.9678 −0.458193
\(802\) −15.4528 −0.545656
\(803\) 0.466051 0.0164466
\(804\) −10.4958 −0.370159
\(805\) 6.32700 0.222997
\(806\) 13.6175 0.479655
\(807\) −16.7029 −0.587971
\(808\) 22.7809 0.801428
\(809\) 8.04121 0.282714 0.141357 0.989959i \(-0.454853\pi\)
0.141357 + 0.989959i \(0.454853\pi\)
\(810\) 1.62360 0.0570474
\(811\) 24.5111 0.860701 0.430350 0.902662i \(-0.358390\pi\)
0.430350 + 0.902662i \(0.358390\pi\)
\(812\) −39.5008 −1.38621
\(813\) −12.4842 −0.437839
\(814\) 6.73632 0.236108
\(815\) 7.21311 0.252664
\(816\) −11.5870 −0.405626
\(817\) −12.2484 −0.428517
\(818\) −6.91507 −0.241780
\(819\) −41.5532 −1.45199
\(820\) −15.5811 −0.544115
\(821\) −10.6539 −0.371823 −0.185912 0.982566i \(-0.559524\pi\)
−0.185912 + 0.982566i \(0.559524\pi\)
\(822\) 5.14574 0.179478
\(823\) 25.6473 0.894009 0.447004 0.894532i \(-0.352491\pi\)
0.447004 + 0.894532i \(0.352491\pi\)
\(824\) 17.9793 0.626339
\(825\) 6.44146 0.224263
\(826\) 26.9339 0.937150
\(827\) 18.0150 0.626442 0.313221 0.949680i \(-0.398592\pi\)
0.313221 + 0.949680i \(0.398592\pi\)
\(828\) −5.86828 −0.203937
\(829\) 10.1189 0.351444 0.175722 0.984440i \(-0.443774\pi\)
0.175722 + 0.984440i \(0.443774\pi\)
\(830\) −1.15716 −0.0401655
\(831\) −2.66008 −0.0922771
\(832\) 10.9911 0.381047
\(833\) 77.1981 2.67476
\(834\) −3.27125 −0.113274
\(835\) 17.1160 0.592325
\(836\) 14.2613 0.493238
\(837\) −31.5148 −1.08931
\(838\) 15.1571 0.523593
\(839\) −46.0365 −1.58936 −0.794679 0.607030i \(-0.792361\pi\)
−0.794679 + 0.607030i \(0.792361\pi\)
\(840\) −6.63309 −0.228863
\(841\) −5.40531 −0.186390
\(842\) −13.3734 −0.460879
\(843\) 10.1705 0.350292
\(844\) −49.2411 −1.69495
\(845\) 1.79557 0.0617696
\(846\) −2.82498 −0.0971247
\(847\) 33.3928 1.14739
\(848\) 14.8673 0.510544
\(849\) 12.8865 0.442262
\(850\) −10.7286 −0.367987
\(851\) −10.1577 −0.348202
\(852\) −21.3805 −0.732485
\(853\) −55.0001 −1.88317 −0.941584 0.336780i \(-0.890662\pi\)
−0.941584 + 0.336780i \(0.890662\pi\)
\(854\) 31.3031 1.07117
\(855\) 9.37329 0.320560
\(856\) 16.7783 0.573469
\(857\) −31.5202 −1.07671 −0.538354 0.842719i \(-0.680954\pi\)
−0.538354 + 0.842719i \(0.680954\pi\)
\(858\) 2.97059 0.101414
\(859\) −37.2208 −1.26996 −0.634979 0.772529i \(-0.718991\pi\)
−0.634979 + 0.772529i \(0.718991\pi\)
\(860\) −4.97846 −0.169764
\(861\) 34.5561 1.17767
\(862\) −6.87180 −0.234054
\(863\) 30.3224 1.03218 0.516092 0.856533i \(-0.327386\pi\)
0.516092 + 0.856533i \(0.327386\pi\)
\(864\) 21.5244 0.732274
\(865\) 17.7900 0.604877
\(866\) −8.64563 −0.293791
\(867\) −9.93592 −0.337442
\(868\) −58.9327 −2.00031
\(869\) −6.11267 −0.207358
\(870\) 1.85599 0.0629241
\(871\) 28.1730 0.954605
\(872\) −5.95075 −0.201518
\(873\) −12.3320 −0.417376
\(874\) 2.89784 0.0980210
\(875\) 40.2783 1.36165
\(876\) 0.345125 0.0116607
\(877\) 27.0037 0.911849 0.455925 0.890018i \(-0.349309\pi\)
0.455925 + 0.890018i \(0.349309\pi\)
\(878\) −1.23028 −0.0415200
\(879\) −15.2526 −0.514457
\(880\) 4.91025 0.165525
\(881\) −0.565506 −0.0190524 −0.00952619 0.999955i \(-0.503032\pi\)
−0.00952619 + 0.999955i \(0.503032\pi\)
\(882\) −16.2647 −0.547660
\(883\) 23.8838 0.803752 0.401876 0.915694i \(-0.368358\pi\)
0.401876 + 0.915694i \(0.368358\pi\)
\(884\) 36.7163 1.23490
\(885\) 9.39135 0.315687
\(886\) −8.20600 −0.275686
\(887\) −10.1717 −0.341533 −0.170767 0.985311i \(-0.554624\pi\)
−0.170767 + 0.985311i \(0.554624\pi\)
\(888\) 10.6491 0.357362
\(889\) −52.3294 −1.75507
\(890\) 2.60282 0.0872468
\(891\) 6.71757 0.225047
\(892\) 0.682968 0.0228675
\(893\) −10.3523 −0.346427
\(894\) −1.78180 −0.0595924
\(895\) −16.6798 −0.557544
\(896\) 52.0843 1.74001
\(897\) −4.47937 −0.149562
\(898\) −14.8975 −0.497135
\(899\) 35.2018 1.17405
\(900\) −16.7741 −0.559136
\(901\) 30.5262 1.01697
\(902\) 8.68707 0.289248
\(903\) 11.0413 0.367432
\(904\) 1.54552 0.0514031
\(905\) 17.0393 0.566405
\(906\) −0.0370823 −0.00123198
\(907\) −44.1661 −1.46651 −0.733255 0.679954i \(-0.762000\pi\)
−0.733255 + 0.679954i \(0.762000\pi\)
\(908\) −18.1146 −0.601154
\(909\) 29.0194 0.962514
\(910\) 8.34036 0.276480
\(911\) −7.07316 −0.234344 −0.117172 0.993112i \(-0.537383\pi\)
−0.117172 + 0.993112i \(0.537383\pi\)
\(912\) 8.94605 0.296233
\(913\) −4.78770 −0.158450
\(914\) −15.9382 −0.527190
\(915\) 10.9148 0.360832
\(916\) 18.5672 0.613479
\(917\) −65.1769 −2.15233
\(918\) 11.4503 0.377917
\(919\) 23.6016 0.778544 0.389272 0.921123i \(-0.372727\pi\)
0.389272 + 0.921123i \(0.372727\pi\)
\(920\) 2.51442 0.0828981
\(921\) −4.26636 −0.140581
\(922\) 6.03976 0.198909
\(923\) 57.3899 1.88901
\(924\) −12.8559 −0.422928
\(925\) −29.0352 −0.954670
\(926\) 5.91530 0.194389
\(927\) 22.9030 0.752233
\(928\) −24.0426 −0.789236
\(929\) 31.8496 1.04495 0.522475 0.852654i \(-0.325009\pi\)
0.522475 + 0.852654i \(0.325009\pi\)
\(930\) 2.76902 0.0907999
\(931\) −59.6029 −1.95341
\(932\) −45.2478 −1.48214
\(933\) 21.7506 0.712083
\(934\) 2.62290 0.0858238
\(935\) 10.0820 0.329716
\(936\) −16.5137 −0.539768
\(937\) 44.1729 1.44307 0.721533 0.692380i \(-0.243438\pi\)
0.721533 + 0.692380i \(0.243438\pi\)
\(938\) 16.4299 0.536454
\(939\) −5.08677 −0.166001
\(940\) −4.20778 −0.137243
\(941\) −34.5303 −1.12566 −0.562828 0.826574i \(-0.690287\pi\)
−0.562828 + 0.826574i \(0.690287\pi\)
\(942\) 4.02498 0.131141
\(943\) −13.0993 −0.426571
\(944\) −31.5194 −1.02587
\(945\) −19.3020 −0.627893
\(946\) 2.77569 0.0902454
\(947\) −3.46191 −0.112497 −0.0562485 0.998417i \(-0.517914\pi\)
−0.0562485 + 0.998417i \(0.517914\pi\)
\(948\) −4.52662 −0.147018
\(949\) −0.926389 −0.0300719
\(950\) 8.28329 0.268745
\(951\) −5.61966 −0.182230
\(952\) 45.7097 1.48146
\(953\) 60.2596 1.95200 0.976000 0.217771i \(-0.0698785\pi\)
0.976000 + 0.217771i \(0.0698785\pi\)
\(954\) −6.43148 −0.208227
\(955\) 12.7407 0.412280
\(956\) 44.2936 1.43256
\(957\) 7.67911 0.248230
\(958\) −12.3664 −0.399541
\(959\) 59.7755 1.93025
\(960\) 2.23496 0.0721331
\(961\) 21.5188 0.694156
\(962\) −13.3901 −0.431713
\(963\) 21.3730 0.688735
\(964\) 1.76250 0.0567662
\(965\) −24.5338 −0.789772
\(966\) −2.61227 −0.0840483
\(967\) −39.9168 −1.28364 −0.641819 0.766856i \(-0.721820\pi\)
−0.641819 + 0.766856i \(0.721820\pi\)
\(968\) 13.2707 0.426536
\(969\) 18.3685 0.590081
\(970\) 2.47522 0.0794746
\(971\) 43.7104 1.40273 0.701366 0.712801i \(-0.252574\pi\)
0.701366 + 0.712801i \(0.252574\pi\)
\(972\) 27.9681 0.897078
\(973\) −38.0006 −1.21824
\(974\) −5.08020 −0.162780
\(975\) −12.8040 −0.410055
\(976\) −36.6325 −1.17258
\(977\) −0.955388 −0.0305656 −0.0152828 0.999883i \(-0.504865\pi\)
−0.0152828 + 0.999883i \(0.504865\pi\)
\(978\) −2.97812 −0.0952298
\(979\) 10.7691 0.344182
\(980\) −24.2261 −0.773874
\(981\) −7.58037 −0.242023
\(982\) 16.7090 0.533205
\(983\) −48.7488 −1.55485 −0.777423 0.628978i \(-0.783474\pi\)
−0.777423 + 0.628978i \(0.783474\pi\)
\(984\) 13.7330 0.437792
\(985\) −14.4591 −0.460707
\(986\) −12.7899 −0.407315
\(987\) 9.33211 0.297044
\(988\) −28.3478 −0.901865
\(989\) −4.18547 −0.133090
\(990\) −2.12414 −0.0675097
\(991\) 0.488986 0.0155332 0.00776658 0.999970i \(-0.497528\pi\)
0.00776658 + 0.999970i \(0.497528\pi\)
\(992\) −35.8700 −1.13887
\(993\) 11.0594 0.350959
\(994\) 33.4685 1.06156
\(995\) −18.6437 −0.591044
\(996\) −3.54544 −0.112342
\(997\) 39.5339 1.25205 0.626026 0.779802i \(-0.284680\pi\)
0.626026 + 0.779802i \(0.284680\pi\)
\(998\) 7.78153 0.246320
\(999\) 30.9885 0.980432
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 241.2.a.a.1.6 7
3.2 odd 2 2169.2.a.e.1.2 7
4.3 odd 2 3856.2.a.j.1.5 7
5.4 even 2 6025.2.a.f.1.2 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
241.2.a.a.1.6 7 1.1 even 1 trivial
2169.2.a.e.1.2 7 3.2 odd 2
3856.2.a.j.1.5 7 4.3 odd 2
6025.2.a.f.1.2 7 5.4 even 2