Properties

Label 2667.2.a.j.1.6
Level $2667$
Weight $2$
Character 2667.1
Self dual yes
Analytic conductor $21.296$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2667 = 3 \cdot 7 \cdot 127 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2667.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(21.2961022191\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: 7.7.118870813.1
Defining polynomial: \(x^{7} - 9 x^{5} - 3 x^{4} + 20 x^{3} + 7 x^{2} - 13 x - 4\)
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 \(2.69855\) of defining polynomial
Character \(\chi\) \(=\) 2667.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.840819 q^{2} +1.00000 q^{3} -1.29302 q^{4} +2.74724 q^{5} +0.840819 q^{6} +1.00000 q^{7} -2.76884 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.840819 q^{2} +1.00000 q^{3} -1.29302 q^{4} +2.74724 q^{5} +0.840819 q^{6} +1.00000 q^{7} -2.76884 q^{8} +1.00000 q^{9} +2.30993 q^{10} -5.62069 q^{11} -1.29302 q^{12} -3.65275 q^{13} +0.840819 q^{14} +2.74724 q^{15} +0.257957 q^{16} -5.86462 q^{17} +0.840819 q^{18} -2.05868 q^{19} -3.55225 q^{20} +1.00000 q^{21} -4.72598 q^{22} +2.78500 q^{23} -2.76884 q^{24} +2.54733 q^{25} -3.07130 q^{26} +1.00000 q^{27} -1.29302 q^{28} -4.83208 q^{29} +2.30993 q^{30} -6.87419 q^{31} +5.75457 q^{32} -5.62069 q^{33} -4.93108 q^{34} +2.74724 q^{35} -1.29302 q^{36} -8.71097 q^{37} -1.73097 q^{38} -3.65275 q^{39} -7.60666 q^{40} -4.09940 q^{41} +0.840819 q^{42} -2.48024 q^{43} +7.26768 q^{44} +2.74724 q^{45} +2.34168 q^{46} +12.6576 q^{47} +0.257957 q^{48} +1.00000 q^{49} +2.14185 q^{50} -5.86462 q^{51} +4.72310 q^{52} +4.92291 q^{53} +0.840819 q^{54} -15.4414 q^{55} -2.76884 q^{56} -2.05868 q^{57} -4.06291 q^{58} -9.41559 q^{59} -3.55225 q^{60} +4.96498 q^{61} -5.77995 q^{62} +1.00000 q^{63} +4.32264 q^{64} -10.0350 q^{65} -4.72598 q^{66} +4.57422 q^{67} +7.58309 q^{68} +2.78500 q^{69} +2.30993 q^{70} +2.13466 q^{71} -2.76884 q^{72} +9.59565 q^{73} -7.32435 q^{74} +2.54733 q^{75} +2.66192 q^{76} -5.62069 q^{77} -3.07130 q^{78} -10.0298 q^{79} +0.708669 q^{80} +1.00000 q^{81} -3.44685 q^{82} -5.06691 q^{83} -1.29302 q^{84} -16.1115 q^{85} -2.08543 q^{86} -4.83208 q^{87} +15.5628 q^{88} +2.73622 q^{89} +2.30993 q^{90} -3.65275 q^{91} -3.60107 q^{92} -6.87419 q^{93} +10.6428 q^{94} -5.65568 q^{95} +5.75457 q^{96} +14.0813 q^{97} +0.840819 q^{98} -5.62069 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 2q^{2} + 7q^{3} + 4q^{4} - 8q^{5} - 2q^{6} + 7q^{7} - 9q^{8} + 7q^{9} + O(q^{10}) \) \( 7q - 2q^{2} + 7q^{3} + 4q^{4} - 8q^{5} - 2q^{6} + 7q^{7} - 9q^{8} + 7q^{9} - 3q^{11} + 4q^{12} - 23q^{13} - 2q^{14} - 8q^{15} + 2q^{16} + 3q^{17} - 2q^{18} - 9q^{19} - 9q^{20} + 7q^{21} - 19q^{22} + 12q^{23} - 9q^{24} + 3q^{25} + 18q^{26} + 7q^{27} + 4q^{28} - 9q^{29} - 33q^{31} + 10q^{32} - 3q^{33} - 2q^{34} - 8q^{35} + 4q^{36} - 33q^{37} - 3q^{38} - 23q^{39} - 9q^{40} - 3q^{41} - 2q^{42} - 9q^{43} + 2q^{44} - 8q^{45} - 32q^{46} + 11q^{47} + 2q^{48} + 7q^{49} + 29q^{50} + 3q^{51} - 21q^{52} + q^{53} - 2q^{54} - 16q^{55} - 9q^{56} - 9q^{57} - 5q^{58} - 30q^{59} - 9q^{60} - 19q^{61} + 3q^{62} + 7q^{63} - 21q^{64} + 14q^{65} - 19q^{66} - 30q^{67} + 24q^{68} + 12q^{69} + 8q^{71} - 9q^{72} - 20q^{73} - 9q^{74} + 3q^{75} - 42q^{76} - 3q^{77} + 18q^{78} + 8q^{79} + 12q^{80} + 7q^{81} + 10q^{82} - 34q^{83} + 4q^{84} - 28q^{85} + 24q^{86} - 9q^{87} - q^{88} - 12q^{89} - 23q^{91} + 60q^{92} - 33q^{93} - 3q^{94} + 12q^{95} + 10q^{96} + 7q^{97} - 2q^{98} - 3q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.840819 0.594549 0.297274 0.954792i \(-0.403922\pi\)
0.297274 + 0.954792i \(0.403922\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.29302 −0.646512
\(5\) 2.74724 1.22860 0.614302 0.789071i \(-0.289438\pi\)
0.614302 + 0.789071i \(0.289438\pi\)
\(6\) 0.840819 0.343263
\(7\) 1.00000 0.377964
\(8\) −2.76884 −0.978932
\(9\) 1.00000 0.333333
\(10\) 2.30993 0.730465
\(11\) −5.62069 −1.69470 −0.847351 0.531034i \(-0.821804\pi\)
−0.847351 + 0.531034i \(0.821804\pi\)
\(12\) −1.29302 −0.373264
\(13\) −3.65275 −1.01309 −0.506546 0.862213i \(-0.669078\pi\)
−0.506546 + 0.862213i \(0.669078\pi\)
\(14\) 0.840819 0.224718
\(15\) 2.74724 0.709335
\(16\) 0.257957 0.0644892
\(17\) −5.86462 −1.42238 −0.711189 0.703000i \(-0.751843\pi\)
−0.711189 + 0.703000i \(0.751843\pi\)
\(18\) 0.840819 0.198183
\(19\) −2.05868 −0.472293 −0.236146 0.971718i \(-0.575884\pi\)
−0.236146 + 0.971718i \(0.575884\pi\)
\(20\) −3.55225 −0.794307
\(21\) 1.00000 0.218218
\(22\) −4.72598 −1.00758
\(23\) 2.78500 0.580713 0.290356 0.956919i \(-0.406226\pi\)
0.290356 + 0.956919i \(0.406226\pi\)
\(24\) −2.76884 −0.565186
\(25\) 2.54733 0.509467
\(26\) −3.07130 −0.602332
\(27\) 1.00000 0.192450
\(28\) −1.29302 −0.244358
\(29\) −4.83208 −0.897295 −0.448648 0.893709i \(-0.648094\pi\)
−0.448648 + 0.893709i \(0.648094\pi\)
\(30\) 2.30993 0.421734
\(31\) −6.87419 −1.23464 −0.617321 0.786712i \(-0.711782\pi\)
−0.617321 + 0.786712i \(0.711782\pi\)
\(32\) 5.75457 1.01727
\(33\) −5.62069 −0.978436
\(34\) −4.93108 −0.845674
\(35\) 2.74724 0.464369
\(36\) −1.29302 −0.215504
\(37\) −8.71097 −1.43207 −0.716037 0.698062i \(-0.754046\pi\)
−0.716037 + 0.698062i \(0.754046\pi\)
\(38\) −1.73097 −0.280801
\(39\) −3.65275 −0.584909
\(40\) −7.60666 −1.20272
\(41\) −4.09940 −0.640219 −0.320109 0.947381i \(-0.603720\pi\)
−0.320109 + 0.947381i \(0.603720\pi\)
\(42\) 0.840819 0.129741
\(43\) −2.48024 −0.378233 −0.189116 0.981955i \(-0.560562\pi\)
−0.189116 + 0.981955i \(0.560562\pi\)
\(44\) 7.26768 1.09564
\(45\) 2.74724 0.409535
\(46\) 2.34168 0.345262
\(47\) 12.6576 1.84630 0.923152 0.384434i \(-0.125603\pi\)
0.923152 + 0.384434i \(0.125603\pi\)
\(48\) 0.257957 0.0372328
\(49\) 1.00000 0.142857
\(50\) 2.14185 0.302903
\(51\) −5.86462 −0.821211
\(52\) 4.72310 0.654975
\(53\) 4.92291 0.676214 0.338107 0.941108i \(-0.390213\pi\)
0.338107 + 0.941108i \(0.390213\pi\)
\(54\) 0.840819 0.114421
\(55\) −15.4414 −2.08212
\(56\) −2.76884 −0.370001
\(57\) −2.05868 −0.272678
\(58\) −4.06291 −0.533486
\(59\) −9.41559 −1.22581 −0.612903 0.790158i \(-0.709998\pi\)
−0.612903 + 0.790158i \(0.709998\pi\)
\(60\) −3.55225 −0.458593
\(61\) 4.96498 0.635701 0.317850 0.948141i \(-0.397039\pi\)
0.317850 + 0.948141i \(0.397039\pi\)
\(62\) −5.77995 −0.734055
\(63\) 1.00000 0.125988
\(64\) 4.32264 0.540330
\(65\) −10.0350 −1.24469
\(66\) −4.72598 −0.581728
\(67\) 4.57422 0.558829 0.279415 0.960171i \(-0.409860\pi\)
0.279415 + 0.960171i \(0.409860\pi\)
\(68\) 7.58309 0.919585
\(69\) 2.78500 0.335275
\(70\) 2.30993 0.276090
\(71\) 2.13466 0.253338 0.126669 0.991945i \(-0.459571\pi\)
0.126669 + 0.991945i \(0.459571\pi\)
\(72\) −2.76884 −0.326311
\(73\) 9.59565 1.12309 0.561543 0.827448i \(-0.310208\pi\)
0.561543 + 0.827448i \(0.310208\pi\)
\(74\) −7.32435 −0.851438
\(75\) 2.54733 0.294141
\(76\) 2.66192 0.305343
\(77\) −5.62069 −0.640537
\(78\) −3.07130 −0.347757
\(79\) −10.0298 −1.12844 −0.564220 0.825624i \(-0.690823\pi\)
−0.564220 + 0.825624i \(0.690823\pi\)
\(80\) 0.708669 0.0792316
\(81\) 1.00000 0.111111
\(82\) −3.44685 −0.380641
\(83\) −5.06691 −0.556166 −0.278083 0.960557i \(-0.589699\pi\)
−0.278083 + 0.960557i \(0.589699\pi\)
\(84\) −1.29302 −0.141080
\(85\) −16.1115 −1.74754
\(86\) −2.08543 −0.224878
\(87\) −4.83208 −0.518054
\(88\) 15.5628 1.65900
\(89\) 2.73622 0.290039 0.145019 0.989429i \(-0.453676\pi\)
0.145019 + 0.989429i \(0.453676\pi\)
\(90\) 2.30993 0.243488
\(91\) −3.65275 −0.382913
\(92\) −3.60107 −0.375437
\(93\) −6.87419 −0.712821
\(94\) 10.6428 1.09772
\(95\) −5.65568 −0.580260
\(96\) 5.75457 0.587323
\(97\) 14.0813 1.42974 0.714872 0.699255i \(-0.246485\pi\)
0.714872 + 0.699255i \(0.246485\pi\)
\(98\) 0.840819 0.0849355
\(99\) −5.62069 −0.564900
\(100\) −3.29376 −0.329376
\(101\) −2.91727 −0.290279 −0.145139 0.989411i \(-0.546363\pi\)
−0.145139 + 0.989411i \(0.546363\pi\)
\(102\) −4.93108 −0.488250
\(103\) 17.2096 1.69571 0.847855 0.530228i \(-0.177894\pi\)
0.847855 + 0.530228i \(0.177894\pi\)
\(104\) 10.1139 0.991747
\(105\) 2.74724 0.268103
\(106\) 4.13928 0.402042
\(107\) 3.25655 0.314823 0.157411 0.987533i \(-0.449685\pi\)
0.157411 + 0.987533i \(0.449685\pi\)
\(108\) −1.29302 −0.124421
\(109\) 9.69847 0.928945 0.464472 0.885588i \(-0.346244\pi\)
0.464472 + 0.885588i \(0.346244\pi\)
\(110\) −12.9834 −1.23792
\(111\) −8.71097 −0.826808
\(112\) 0.257957 0.0243746
\(113\) 1.89566 0.178329 0.0891645 0.996017i \(-0.471580\pi\)
0.0891645 + 0.996017i \(0.471580\pi\)
\(114\) −1.73097 −0.162121
\(115\) 7.65107 0.713466
\(116\) 6.24800 0.580112
\(117\) −3.65275 −0.337697
\(118\) −7.91681 −0.728801
\(119\) −5.86462 −0.537609
\(120\) −7.60666 −0.694390
\(121\) 20.5921 1.87201
\(122\) 4.17465 0.377955
\(123\) −4.09940 −0.369631
\(124\) 8.88849 0.798210
\(125\) −6.73807 −0.602671
\(126\) 0.840819 0.0749061
\(127\) −1.00000 −0.0887357
\(128\) −7.87458 −0.696021
\(129\) −2.48024 −0.218373
\(130\) −8.43761 −0.740028
\(131\) 5.84500 0.510680 0.255340 0.966851i \(-0.417813\pi\)
0.255340 + 0.966851i \(0.417813\pi\)
\(132\) 7.26768 0.632571
\(133\) −2.05868 −0.178510
\(134\) 3.84609 0.332251
\(135\) 2.74724 0.236445
\(136\) 16.2382 1.39241
\(137\) −10.6774 −0.912233 −0.456117 0.889920i \(-0.650760\pi\)
−0.456117 + 0.889920i \(0.650760\pi\)
\(138\) 2.34168 0.199337
\(139\) −21.7313 −1.84323 −0.921613 0.388111i \(-0.873128\pi\)
−0.921613 + 0.388111i \(0.873128\pi\)
\(140\) −3.55225 −0.300220
\(141\) 12.6576 1.06596
\(142\) 1.79486 0.150622
\(143\) 20.5310 1.71689
\(144\) 0.257957 0.0214964
\(145\) −13.2749 −1.10242
\(146\) 8.06821 0.667729
\(147\) 1.00000 0.0824786
\(148\) 11.2635 0.925853
\(149\) −16.2091 −1.32790 −0.663952 0.747775i \(-0.731122\pi\)
−0.663952 + 0.747775i \(0.731122\pi\)
\(150\) 2.14185 0.174881
\(151\) −22.1101 −1.79929 −0.899646 0.436621i \(-0.856175\pi\)
−0.899646 + 0.436621i \(0.856175\pi\)
\(152\) 5.70014 0.462342
\(153\) −5.86462 −0.474126
\(154\) −4.72598 −0.380830
\(155\) −18.8851 −1.51688
\(156\) 4.72310 0.378150
\(157\) 23.2986 1.85943 0.929714 0.368282i \(-0.120054\pi\)
0.929714 + 0.368282i \(0.120054\pi\)
\(158\) −8.43325 −0.670913
\(159\) 4.92291 0.390412
\(160\) 15.8092 1.24983
\(161\) 2.78500 0.219489
\(162\) 0.840819 0.0660610
\(163\) −21.5951 −1.69146 −0.845731 0.533609i \(-0.820835\pi\)
−0.845731 + 0.533609i \(0.820835\pi\)
\(164\) 5.30062 0.413909
\(165\) −15.4414 −1.20211
\(166\) −4.26036 −0.330668
\(167\) −3.26635 −0.252758 −0.126379 0.991982i \(-0.540336\pi\)
−0.126379 + 0.991982i \(0.540336\pi\)
\(168\) −2.76884 −0.213620
\(169\) 0.342604 0.0263542
\(170\) −13.5469 −1.03900
\(171\) −2.05868 −0.157431
\(172\) 3.20701 0.244532
\(173\) 9.97561 0.758431 0.379216 0.925308i \(-0.376194\pi\)
0.379216 + 0.925308i \(0.376194\pi\)
\(174\) −4.06291 −0.308008
\(175\) 2.54733 0.192560
\(176\) −1.44989 −0.109290
\(177\) −9.41559 −0.707719
\(178\) 2.30066 0.172442
\(179\) 21.3721 1.59743 0.798714 0.601711i \(-0.205514\pi\)
0.798714 + 0.601711i \(0.205514\pi\)
\(180\) −3.55225 −0.264769
\(181\) −23.7938 −1.76858 −0.884288 0.466942i \(-0.845356\pi\)
−0.884288 + 0.466942i \(0.845356\pi\)
\(182\) −3.07130 −0.227660
\(183\) 4.96498 0.367022
\(184\) −7.71121 −0.568478
\(185\) −23.9311 −1.75945
\(186\) −5.77995 −0.423807
\(187\) 32.9632 2.41051
\(188\) −16.3666 −1.19366
\(189\) 1.00000 0.0727393
\(190\) −4.75540 −0.344993
\(191\) 17.1115 1.23814 0.619072 0.785335i \(-0.287509\pi\)
0.619072 + 0.785335i \(0.287509\pi\)
\(192\) 4.32264 0.311959
\(193\) −21.1983 −1.52589 −0.762945 0.646464i \(-0.776247\pi\)
−0.762945 + 0.646464i \(0.776247\pi\)
\(194\) 11.8399 0.850053
\(195\) −10.0350 −0.718621
\(196\) −1.29302 −0.0923588
\(197\) 9.64407 0.687111 0.343556 0.939132i \(-0.388369\pi\)
0.343556 + 0.939132i \(0.388369\pi\)
\(198\) −4.72598 −0.335861
\(199\) −8.11930 −0.575562 −0.287781 0.957696i \(-0.592918\pi\)
−0.287781 + 0.957696i \(0.592918\pi\)
\(200\) −7.05315 −0.498733
\(201\) 4.57422 0.322640
\(202\) −2.45289 −0.172585
\(203\) −4.83208 −0.339146
\(204\) 7.58309 0.530922
\(205\) −11.2620 −0.786575
\(206\) 14.4701 1.00818
\(207\) 2.78500 0.193571
\(208\) −0.942252 −0.0653334
\(209\) 11.5712 0.800395
\(210\) 2.30993 0.159400
\(211\) −10.1539 −0.699023 −0.349511 0.936932i \(-0.613652\pi\)
−0.349511 + 0.936932i \(0.613652\pi\)
\(212\) −6.36544 −0.437180
\(213\) 2.13466 0.146264
\(214\) 2.73817 0.187178
\(215\) −6.81382 −0.464698
\(216\) −2.76884 −0.188395
\(217\) −6.87419 −0.466651
\(218\) 8.15466 0.552303
\(219\) 9.59565 0.648414
\(220\) 19.9661 1.34611
\(221\) 21.4220 1.44100
\(222\) −7.32435 −0.491578
\(223\) 22.3276 1.49517 0.747583 0.664168i \(-0.231214\pi\)
0.747583 + 0.664168i \(0.231214\pi\)
\(224\) 5.75457 0.384493
\(225\) 2.54733 0.169822
\(226\) 1.59391 0.106025
\(227\) −23.3340 −1.54873 −0.774365 0.632739i \(-0.781931\pi\)
−0.774365 + 0.632739i \(0.781931\pi\)
\(228\) 2.66192 0.176290
\(229\) −8.57841 −0.566877 −0.283439 0.958990i \(-0.591475\pi\)
−0.283439 + 0.958990i \(0.591475\pi\)
\(230\) 6.43316 0.424190
\(231\) −5.62069 −0.369814
\(232\) 13.3793 0.878391
\(233\) 14.6183 0.957677 0.478839 0.877903i \(-0.341058\pi\)
0.478839 + 0.877903i \(0.341058\pi\)
\(234\) −3.07130 −0.200777
\(235\) 34.7736 2.26838
\(236\) 12.1746 0.792498
\(237\) −10.0298 −0.651505
\(238\) −4.93108 −0.319635
\(239\) 5.05219 0.326799 0.163399 0.986560i \(-0.447754\pi\)
0.163399 + 0.986560i \(0.447754\pi\)
\(240\) 0.708669 0.0457444
\(241\) −15.9324 −1.02629 −0.513147 0.858301i \(-0.671520\pi\)
−0.513147 + 0.858301i \(0.671520\pi\)
\(242\) 17.3143 1.11300
\(243\) 1.00000 0.0641500
\(244\) −6.41984 −0.410988
\(245\) 2.74724 0.175515
\(246\) −3.44685 −0.219763
\(247\) 7.51983 0.478475
\(248\) 19.0335 1.20863
\(249\) −5.06691 −0.321103
\(250\) −5.66549 −0.358317
\(251\) −11.8771 −0.749678 −0.374839 0.927090i \(-0.622302\pi\)
−0.374839 + 0.927090i \(0.622302\pi\)
\(252\) −1.29302 −0.0814528
\(253\) −15.6536 −0.984134
\(254\) −0.840819 −0.0527577
\(255\) −16.1115 −1.00894
\(256\) −15.2664 −0.954148
\(257\) −19.3728 −1.20844 −0.604221 0.796817i \(-0.706516\pi\)
−0.604221 + 0.796817i \(0.706516\pi\)
\(258\) −2.08543 −0.129833
\(259\) −8.71097 −0.541273
\(260\) 12.9755 0.804705
\(261\) −4.83208 −0.299098
\(262\) 4.91459 0.303624
\(263\) −25.0402 −1.54405 −0.772024 0.635594i \(-0.780755\pi\)
−0.772024 + 0.635594i \(0.780755\pi\)
\(264\) 15.5628 0.957822
\(265\) 13.5244 0.830799
\(266\) −1.73097 −0.106133
\(267\) 2.73622 0.167454
\(268\) −5.91457 −0.361290
\(269\) −20.8253 −1.26974 −0.634870 0.772619i \(-0.718946\pi\)
−0.634870 + 0.772619i \(0.718946\pi\)
\(270\) 2.30993 0.140578
\(271\) 14.7479 0.895871 0.447936 0.894066i \(-0.352159\pi\)
0.447936 + 0.894066i \(0.352159\pi\)
\(272\) −1.51282 −0.0917280
\(273\) −3.65275 −0.221075
\(274\) −8.97778 −0.542367
\(275\) −14.3178 −0.863394
\(276\) −3.60107 −0.216759
\(277\) −12.6554 −0.760389 −0.380195 0.924907i \(-0.624143\pi\)
−0.380195 + 0.924907i \(0.624143\pi\)
\(278\) −18.2721 −1.09589
\(279\) −6.87419 −0.411547
\(280\) −7.60666 −0.454585
\(281\) −30.2858 −1.80670 −0.903350 0.428903i \(-0.858900\pi\)
−0.903350 + 0.428903i \(0.858900\pi\)
\(282\) 10.6428 0.633768
\(283\) −0.554307 −0.0329501 −0.0164751 0.999864i \(-0.505244\pi\)
−0.0164751 + 0.999864i \(0.505244\pi\)
\(284\) −2.76017 −0.163786
\(285\) −5.65568 −0.335013
\(286\) 17.2628 1.02077
\(287\) −4.09940 −0.241980
\(288\) 5.75457 0.339091
\(289\) 17.3937 1.02316
\(290\) −11.1618 −0.655443
\(291\) 14.0813 0.825463
\(292\) −12.4074 −0.726088
\(293\) 10.7329 0.627023 0.313512 0.949584i \(-0.398495\pi\)
0.313512 + 0.949584i \(0.398495\pi\)
\(294\) 0.840819 0.0490376
\(295\) −25.8669 −1.50603
\(296\) 24.1192 1.40190
\(297\) −5.62069 −0.326145
\(298\) −13.6289 −0.789504
\(299\) −10.1729 −0.588315
\(300\) −3.29376 −0.190165
\(301\) −2.48024 −0.142959
\(302\) −18.5906 −1.06977
\(303\) −2.91727 −0.167593
\(304\) −0.531049 −0.0304578
\(305\) 13.6400 0.781024
\(306\) −4.93108 −0.281891
\(307\) 5.96740 0.340577 0.170289 0.985394i \(-0.445530\pi\)
0.170289 + 0.985394i \(0.445530\pi\)
\(308\) 7.26768 0.414115
\(309\) 17.2096 0.979019
\(310\) −15.8789 −0.901862
\(311\) 26.7130 1.51475 0.757377 0.652978i \(-0.226481\pi\)
0.757377 + 0.652978i \(0.226481\pi\)
\(312\) 10.1139 0.572585
\(313\) −25.9107 −1.46456 −0.732279 0.681005i \(-0.761543\pi\)
−0.732279 + 0.681005i \(0.761543\pi\)
\(314\) 19.5899 1.10552
\(315\) 2.74724 0.154790
\(316\) 12.9688 0.729550
\(317\) −6.29184 −0.353385 −0.176693 0.984266i \(-0.556540\pi\)
−0.176693 + 0.984266i \(0.556540\pi\)
\(318\) 4.13928 0.232119
\(319\) 27.1596 1.52065
\(320\) 11.8753 0.663851
\(321\) 3.25655 0.181763
\(322\) 2.34168 0.130497
\(323\) 12.0733 0.671779
\(324\) −1.29302 −0.0718346
\(325\) −9.30478 −0.516136
\(326\) −18.1576 −1.00566
\(327\) 9.69847 0.536327
\(328\) 11.3506 0.626731
\(329\) 12.6576 0.697838
\(330\) −12.9834 −0.714713
\(331\) 6.26075 0.344122 0.172061 0.985086i \(-0.444957\pi\)
0.172061 + 0.985086i \(0.444957\pi\)
\(332\) 6.55164 0.359568
\(333\) −8.71097 −0.477358
\(334\) −2.74641 −0.150277
\(335\) 12.5665 0.686580
\(336\) 0.257957 0.0140727
\(337\) 10.6291 0.579003 0.289502 0.957178i \(-0.406510\pi\)
0.289502 + 0.957178i \(0.406510\pi\)
\(338\) 0.288068 0.0156688
\(339\) 1.89566 0.102958
\(340\) 20.8326 1.12980
\(341\) 38.6377 2.09235
\(342\) −1.73097 −0.0936003
\(343\) 1.00000 0.0539949
\(344\) 6.86738 0.370264
\(345\) 7.65107 0.411920
\(346\) 8.38768 0.450925
\(347\) 24.2445 1.30151 0.650757 0.759286i \(-0.274452\pi\)
0.650757 + 0.759286i \(0.274452\pi\)
\(348\) 6.24800 0.334928
\(349\) 19.2656 1.03127 0.515633 0.856810i \(-0.327557\pi\)
0.515633 + 0.856810i \(0.327557\pi\)
\(350\) 2.14185 0.114487
\(351\) −3.65275 −0.194970
\(352\) −32.3446 −1.72397
\(353\) 2.47593 0.131780 0.0658902 0.997827i \(-0.479011\pi\)
0.0658902 + 0.997827i \(0.479011\pi\)
\(354\) −7.91681 −0.420774
\(355\) 5.86443 0.311251
\(356\) −3.53800 −0.187513
\(357\) −5.86462 −0.310389
\(358\) 17.9701 0.949749
\(359\) 31.8474 1.68084 0.840422 0.541933i \(-0.182307\pi\)
0.840422 + 0.541933i \(0.182307\pi\)
\(360\) −7.60666 −0.400906
\(361\) −14.7619 −0.776940
\(362\) −20.0062 −1.05150
\(363\) 20.5921 1.08081
\(364\) 4.72310 0.247557
\(365\) 26.3616 1.37983
\(366\) 4.17465 0.218213
\(367\) 9.45164 0.493372 0.246686 0.969095i \(-0.420658\pi\)
0.246686 + 0.969095i \(0.420658\pi\)
\(368\) 0.718409 0.0374497
\(369\) −4.09940 −0.213406
\(370\) −20.1217 −1.04608
\(371\) 4.92291 0.255585
\(372\) 8.88849 0.460847
\(373\) −8.74070 −0.452576 −0.226288 0.974060i \(-0.572659\pi\)
−0.226288 + 0.974060i \(0.572659\pi\)
\(374\) 27.7161 1.43316
\(375\) −6.73807 −0.347952
\(376\) −35.0469 −1.80741
\(377\) 17.6504 0.909042
\(378\) 0.840819 0.0432471
\(379\) −15.3774 −0.789882 −0.394941 0.918707i \(-0.629235\pi\)
−0.394941 + 0.918707i \(0.629235\pi\)
\(380\) 7.31292 0.375145
\(381\) −1.00000 −0.0512316
\(382\) 14.3877 0.736137
\(383\) 19.4375 0.993210 0.496605 0.867977i \(-0.334580\pi\)
0.496605 + 0.867977i \(0.334580\pi\)
\(384\) −7.87458 −0.401848
\(385\) −15.4414 −0.786966
\(386\) −17.8240 −0.907216
\(387\) −2.48024 −0.126078
\(388\) −18.2075 −0.924347
\(389\) 20.2992 1.02921 0.514604 0.857428i \(-0.327939\pi\)
0.514604 + 0.857428i \(0.327939\pi\)
\(390\) −8.43761 −0.427255
\(391\) −16.3330 −0.825993
\(392\) −2.76884 −0.139847
\(393\) 5.84500 0.294841
\(394\) 8.10891 0.408521
\(395\) −27.5543 −1.38641
\(396\) 7.26768 0.365215
\(397\) −5.04735 −0.253319 −0.126660 0.991946i \(-0.540426\pi\)
−0.126660 + 0.991946i \(0.540426\pi\)
\(398\) −6.82686 −0.342200
\(399\) −2.05868 −0.103063
\(400\) 0.657102 0.0328551
\(401\) 0.828202 0.0413584 0.0206792 0.999786i \(-0.493417\pi\)
0.0206792 + 0.999786i \(0.493417\pi\)
\(402\) 3.84609 0.191825
\(403\) 25.1097 1.25080
\(404\) 3.77209 0.187669
\(405\) 2.74724 0.136512
\(406\) −4.06291 −0.201639
\(407\) 48.9616 2.42694
\(408\) 16.2382 0.803909
\(409\) 7.63539 0.377546 0.188773 0.982021i \(-0.439549\pi\)
0.188773 + 0.982021i \(0.439549\pi\)
\(410\) −9.46934 −0.467657
\(411\) −10.6774 −0.526678
\(412\) −22.2524 −1.09630
\(413\) −9.41559 −0.463311
\(414\) 2.34168 0.115087
\(415\) −13.9200 −0.683308
\(416\) −21.0200 −1.03059
\(417\) −21.7313 −1.06419
\(418\) 9.72926 0.475874
\(419\) −0.606948 −0.0296514 −0.0148257 0.999890i \(-0.504719\pi\)
−0.0148257 + 0.999890i \(0.504719\pi\)
\(420\) −3.55225 −0.173332
\(421\) 12.2074 0.594951 0.297476 0.954729i \(-0.403855\pi\)
0.297476 + 0.954729i \(0.403855\pi\)
\(422\) −8.53759 −0.415603
\(423\) 12.6576 0.615435
\(424\) −13.6307 −0.661967
\(425\) −14.9391 −0.724655
\(426\) 1.79486 0.0869614
\(427\) 4.96498 0.240272
\(428\) −4.21080 −0.203537
\(429\) 20.5310 0.991245
\(430\) −5.72919 −0.276286
\(431\) 27.6025 1.32957 0.664783 0.747037i \(-0.268524\pi\)
0.664783 + 0.747037i \(0.268524\pi\)
\(432\) 0.257957 0.0124109
\(433\) −21.0747 −1.01278 −0.506392 0.862304i \(-0.669021\pi\)
−0.506392 + 0.862304i \(0.669021\pi\)
\(434\) −5.77995 −0.277447
\(435\) −13.2749 −0.636483
\(436\) −12.5403 −0.600574
\(437\) −5.73341 −0.274266
\(438\) 8.06821 0.385514
\(439\) −11.8630 −0.566189 −0.283094 0.959092i \(-0.591361\pi\)
−0.283094 + 0.959092i \(0.591361\pi\)
\(440\) 42.7547 2.03825
\(441\) 1.00000 0.0476190
\(442\) 18.0120 0.856745
\(443\) 11.0804 0.526446 0.263223 0.964735i \(-0.415214\pi\)
0.263223 + 0.964735i \(0.415214\pi\)
\(444\) 11.2635 0.534541
\(445\) 7.51705 0.356342
\(446\) 18.7735 0.888949
\(447\) −16.2091 −0.766666
\(448\) 4.32264 0.204225
\(449\) 21.1462 0.997949 0.498974 0.866617i \(-0.333710\pi\)
0.498974 + 0.866617i \(0.333710\pi\)
\(450\) 2.14185 0.100968
\(451\) 23.0415 1.08498
\(452\) −2.45114 −0.115292
\(453\) −22.1101 −1.03882
\(454\) −19.6196 −0.920796
\(455\) −10.0350 −0.470448
\(456\) 5.70014 0.266933
\(457\) −0.600191 −0.0280758 −0.0140379 0.999901i \(-0.504469\pi\)
−0.0140379 + 0.999901i \(0.504469\pi\)
\(458\) −7.21289 −0.337036
\(459\) −5.86462 −0.273737
\(460\) −9.89301 −0.461264
\(461\) −31.0470 −1.44600 −0.723001 0.690847i \(-0.757238\pi\)
−0.723001 + 0.690847i \(0.757238\pi\)
\(462\) −4.72598 −0.219873
\(463\) 9.93441 0.461691 0.230846 0.972990i \(-0.425851\pi\)
0.230846 + 0.972990i \(0.425851\pi\)
\(464\) −1.24647 −0.0578658
\(465\) −18.8851 −0.875774
\(466\) 12.2913 0.569386
\(467\) −6.15650 −0.284889 −0.142444 0.989803i \(-0.545496\pi\)
−0.142444 + 0.989803i \(0.545496\pi\)
\(468\) 4.72310 0.218325
\(469\) 4.57422 0.211218
\(470\) 29.2383 1.34866
\(471\) 23.2986 1.07354
\(472\) 26.0702 1.19998
\(473\) 13.9407 0.640992
\(474\) −8.43325 −0.387352
\(475\) −5.24413 −0.240617
\(476\) 7.58309 0.347570
\(477\) 4.92291 0.225405
\(478\) 4.24798 0.194298
\(479\) 15.7671 0.720417 0.360209 0.932872i \(-0.382706\pi\)
0.360209 + 0.932872i \(0.382706\pi\)
\(480\) 15.8092 0.721587
\(481\) 31.8190 1.45082
\(482\) −13.3962 −0.610182
\(483\) 2.78500 0.126722
\(484\) −26.6261 −1.21028
\(485\) 38.6849 1.75659
\(486\) 0.840819 0.0381403
\(487\) −6.30114 −0.285532 −0.142766 0.989756i \(-0.545600\pi\)
−0.142766 + 0.989756i \(0.545600\pi\)
\(488\) −13.7472 −0.622308
\(489\) −21.5951 −0.976566
\(490\) 2.30993 0.104352
\(491\) −2.75670 −0.124408 −0.0622040 0.998063i \(-0.519813\pi\)
−0.0622040 + 0.998063i \(0.519813\pi\)
\(492\) 5.30062 0.238971
\(493\) 28.3383 1.27629
\(494\) 6.32282 0.284477
\(495\) −15.4414 −0.694039
\(496\) −1.77324 −0.0796210
\(497\) 2.13466 0.0957526
\(498\) −4.26036 −0.190911
\(499\) 1.20293 0.0538506 0.0269253 0.999637i \(-0.491428\pi\)
0.0269253 + 0.999637i \(0.491428\pi\)
\(500\) 8.71248 0.389634
\(501\) −3.26635 −0.145930
\(502\) −9.98652 −0.445720
\(503\) 29.0110 1.29354 0.646769 0.762686i \(-0.276120\pi\)
0.646769 + 0.762686i \(0.276120\pi\)
\(504\) −2.76884 −0.123334
\(505\) −8.01443 −0.356637
\(506\) −13.1619 −0.585116
\(507\) 0.342604 0.0152156
\(508\) 1.29302 0.0573686
\(509\) −9.23054 −0.409136 −0.204568 0.978852i \(-0.565579\pi\)
−0.204568 + 0.978852i \(0.565579\pi\)
\(510\) −13.5469 −0.599866
\(511\) 9.59565 0.424487
\(512\) 2.91291 0.128734
\(513\) −2.05868 −0.0908927
\(514\) −16.2890 −0.718478
\(515\) 47.2789 2.08336
\(516\) 3.20701 0.141181
\(517\) −71.1446 −3.12894
\(518\) −7.32435 −0.321813
\(519\) 9.97561 0.437881
\(520\) 27.7853 1.21846
\(521\) −29.3043 −1.28385 −0.641923 0.766769i \(-0.721863\pi\)
−0.641923 + 0.766769i \(0.721863\pi\)
\(522\) −4.06291 −0.177829
\(523\) 5.55943 0.243097 0.121549 0.992585i \(-0.461214\pi\)
0.121549 + 0.992585i \(0.461214\pi\)
\(524\) −7.55772 −0.330161
\(525\) 2.54733 0.111175
\(526\) −21.0543 −0.918012
\(527\) 40.3145 1.75613
\(528\) −1.44989 −0.0630985
\(529\) −15.2438 −0.662773
\(530\) 11.3716 0.493951
\(531\) −9.41559 −0.408602
\(532\) 2.66192 0.115409
\(533\) 14.9741 0.648600
\(534\) 2.30066 0.0995595
\(535\) 8.94654 0.386793
\(536\) −12.6653 −0.547056
\(537\) 21.3721 0.922276
\(538\) −17.5103 −0.754922
\(539\) −5.62069 −0.242100
\(540\) −3.55225 −0.152864
\(541\) −12.1035 −0.520371 −0.260186 0.965559i \(-0.583784\pi\)
−0.260186 + 0.965559i \(0.583784\pi\)
\(542\) 12.4003 0.532639
\(543\) −23.7938 −1.02109
\(544\) −33.7483 −1.44695
\(545\) 26.6440 1.14130
\(546\) −3.07130 −0.131440
\(547\) 27.7176 1.18512 0.592561 0.805526i \(-0.298117\pi\)
0.592561 + 0.805526i \(0.298117\pi\)
\(548\) 13.8062 0.589770
\(549\) 4.96498 0.211900
\(550\) −12.0387 −0.513330
\(551\) 9.94769 0.423786
\(552\) −7.71121 −0.328211
\(553\) −10.0298 −0.426510
\(554\) −10.6409 −0.452088
\(555\) −23.9311 −1.01582
\(556\) 28.0991 1.19167
\(557\) 2.98048 0.126287 0.0631435 0.998004i \(-0.479887\pi\)
0.0631435 + 0.998004i \(0.479887\pi\)
\(558\) −5.77995 −0.244685
\(559\) 9.05970 0.383185
\(560\) 0.708669 0.0299467
\(561\) 32.9632 1.39171
\(562\) −25.4649 −1.07417
\(563\) −36.8092 −1.55132 −0.775662 0.631149i \(-0.782584\pi\)
−0.775662 + 0.631149i \(0.782584\pi\)
\(564\) −16.3666 −0.689159
\(565\) 5.20784 0.219096
\(566\) −0.466072 −0.0195904
\(567\) 1.00000 0.0419961
\(568\) −5.91052 −0.248000
\(569\) −30.9224 −1.29633 −0.648167 0.761499i \(-0.724464\pi\)
−0.648167 + 0.761499i \(0.724464\pi\)
\(570\) −4.75540 −0.199182
\(571\) 13.7621 0.575925 0.287963 0.957642i \(-0.407022\pi\)
0.287963 + 0.957642i \(0.407022\pi\)
\(572\) −26.5470 −1.10999
\(573\) 17.1115 0.714842
\(574\) −3.44685 −0.143869
\(575\) 7.09432 0.295854
\(576\) 4.32264 0.180110
\(577\) 35.2200 1.46623 0.733114 0.680106i \(-0.238066\pi\)
0.733114 + 0.680106i \(0.238066\pi\)
\(578\) 14.6250 0.608320
\(579\) −21.1983 −0.880973
\(580\) 17.1648 0.712728
\(581\) −5.06691 −0.210211
\(582\) 11.8399 0.490778
\(583\) −27.6702 −1.14598
\(584\) −26.5688 −1.09942
\(585\) −10.0350 −0.414896
\(586\) 9.02443 0.372796
\(587\) 17.1613 0.708322 0.354161 0.935184i \(-0.384766\pi\)
0.354161 + 0.935184i \(0.384766\pi\)
\(588\) −1.29302 −0.0533234
\(589\) 14.1517 0.583112
\(590\) −21.7494 −0.895408
\(591\) 9.64407 0.396704
\(592\) −2.24705 −0.0923533
\(593\) −41.1163 −1.68845 −0.844223 0.535992i \(-0.819938\pi\)
−0.844223 + 0.535992i \(0.819938\pi\)
\(594\) −4.72598 −0.193909
\(595\) −16.1115 −0.660508
\(596\) 20.9588 0.858506
\(597\) −8.11930 −0.332301
\(598\) −8.55358 −0.349782
\(599\) 15.4682 0.632013 0.316007 0.948757i \(-0.397658\pi\)
0.316007 + 0.948757i \(0.397658\pi\)
\(600\) −7.05315 −0.287944
\(601\) −14.5724 −0.594421 −0.297210 0.954812i \(-0.596056\pi\)
−0.297210 + 0.954812i \(0.596056\pi\)
\(602\) −2.08543 −0.0849959
\(603\) 4.57422 0.186276
\(604\) 28.5888 1.16326
\(605\) 56.5716 2.29996
\(606\) −2.45289 −0.0996419
\(607\) 41.7362 1.69402 0.847009 0.531578i \(-0.178401\pi\)
0.847009 + 0.531578i \(0.178401\pi\)
\(608\) −11.8468 −0.480451
\(609\) −4.83208 −0.195806
\(610\) 11.4688 0.464357
\(611\) −46.2352 −1.87048
\(612\) 7.58309 0.306528
\(613\) −43.5236 −1.75790 −0.878951 0.476913i \(-0.841756\pi\)
−0.878951 + 0.476913i \(0.841756\pi\)
\(614\) 5.01750 0.202490
\(615\) −11.2620 −0.454129
\(616\) 15.5628 0.627042
\(617\) 18.8239 0.757823 0.378912 0.925433i \(-0.376298\pi\)
0.378912 + 0.925433i \(0.376298\pi\)
\(618\) 14.4701 0.582075
\(619\) −29.5177 −1.18642 −0.593209 0.805049i \(-0.702139\pi\)
−0.593209 + 0.805049i \(0.702139\pi\)
\(620\) 24.4188 0.980684
\(621\) 2.78500 0.111758
\(622\) 22.4608 0.900595
\(623\) 2.73622 0.109624
\(624\) −0.942252 −0.0377203
\(625\) −31.2478 −1.24991
\(626\) −21.7862 −0.870751
\(627\) 11.5712 0.462108
\(628\) −30.1256 −1.20214
\(629\) 51.0865 2.03695
\(630\) 2.30993 0.0920299
\(631\) −24.2239 −0.964337 −0.482169 0.876078i \(-0.660151\pi\)
−0.482169 + 0.876078i \(0.660151\pi\)
\(632\) 27.7709 1.10467
\(633\) −10.1539 −0.403581
\(634\) −5.29030 −0.210105
\(635\) −2.74724 −0.109021
\(636\) −6.36544 −0.252406
\(637\) −3.65275 −0.144727
\(638\) 22.8363 0.904099
\(639\) 2.13466 0.0844458
\(640\) −21.6334 −0.855134
\(641\) 28.0303 1.10713 0.553564 0.832806i \(-0.313267\pi\)
0.553564 + 0.832806i \(0.313267\pi\)
\(642\) 2.73817 0.108067
\(643\) −42.3142 −1.66871 −0.834354 0.551229i \(-0.814159\pi\)
−0.834354 + 0.551229i \(0.814159\pi\)
\(644\) −3.60107 −0.141902
\(645\) −6.81382 −0.268294
\(646\) 10.1515 0.399405
\(647\) −28.5548 −1.12260 −0.561302 0.827611i \(-0.689699\pi\)
−0.561302 + 0.827611i \(0.689699\pi\)
\(648\) −2.76884 −0.108770
\(649\) 52.9221 2.07737
\(650\) −7.82364 −0.306868
\(651\) −6.87419 −0.269421
\(652\) 27.9230 1.09355
\(653\) −0.00473242 −0.000185194 0 −9.25970e−5 1.00000i \(-0.500029\pi\)
−9.25970e−5 1.00000i \(0.500029\pi\)
\(654\) 8.15466 0.318872
\(655\) 16.0576 0.627423
\(656\) −1.05747 −0.0412872
\(657\) 9.59565 0.374362
\(658\) 10.6428 0.414899
\(659\) 1.08891 0.0424181 0.0212090 0.999775i \(-0.493248\pi\)
0.0212090 + 0.999775i \(0.493248\pi\)
\(660\) 19.9661 0.777178
\(661\) −34.1649 −1.32886 −0.664431 0.747350i \(-0.731326\pi\)
−0.664431 + 0.747350i \(0.731326\pi\)
\(662\) 5.26415 0.204597
\(663\) 21.4220 0.831962
\(664\) 14.0295 0.544449
\(665\) −5.65568 −0.219318
\(666\) −7.32435 −0.283813
\(667\) −13.4574 −0.521071
\(668\) 4.22347 0.163411
\(669\) 22.3276 0.863235
\(670\) 10.5661 0.408205
\(671\) −27.9066 −1.07732
\(672\) 5.75457 0.221987
\(673\) −5.87608 −0.226506 −0.113253 0.993566i \(-0.536127\pi\)
−0.113253 + 0.993566i \(0.536127\pi\)
\(674\) 8.93714 0.344246
\(675\) 2.54733 0.0980469
\(676\) −0.442995 −0.0170383
\(677\) −3.17149 −0.121890 −0.0609452 0.998141i \(-0.519411\pi\)
−0.0609452 + 0.998141i \(0.519411\pi\)
\(678\) 1.59391 0.0612137
\(679\) 14.0813 0.540393
\(680\) 44.6102 1.71072
\(681\) −23.3340 −0.894160
\(682\) 32.4873 1.24400
\(683\) 16.1790 0.619074 0.309537 0.950887i \(-0.399826\pi\)
0.309537 + 0.950887i \(0.399826\pi\)
\(684\) 2.66192 0.101781
\(685\) −29.3334 −1.12077
\(686\) 0.840819 0.0321026
\(687\) −8.57841 −0.327287
\(688\) −0.639794 −0.0243919
\(689\) −17.9822 −0.685067
\(690\) 6.43316 0.244906
\(691\) −20.6251 −0.784617 −0.392309 0.919834i \(-0.628323\pi\)
−0.392309 + 0.919834i \(0.628323\pi\)
\(692\) −12.8987 −0.490335
\(693\) −5.62069 −0.213512
\(694\) 20.3852 0.773813
\(695\) −59.7011 −2.26459
\(696\) 13.3793 0.507139
\(697\) 24.0414 0.910634
\(698\) 16.1989 0.613138
\(699\) 14.6183 0.552915
\(700\) −3.29376 −0.124493
\(701\) −4.12137 −0.155662 −0.0778311 0.996967i \(-0.524799\pi\)
−0.0778311 + 0.996967i \(0.524799\pi\)
\(702\) −3.07130 −0.115919
\(703\) 17.9331 0.676358
\(704\) −24.2962 −0.915697
\(705\) 34.7736 1.30965
\(706\) 2.08181 0.0783498
\(707\) −2.91727 −0.109715
\(708\) 12.1746 0.457549
\(709\) −0.871563 −0.0327322 −0.0163661 0.999866i \(-0.505210\pi\)
−0.0163661 + 0.999866i \(0.505210\pi\)
\(710\) 4.93092 0.185054
\(711\) −10.0298 −0.376147
\(712\) −7.57614 −0.283928
\(713\) −19.1446 −0.716972
\(714\) −4.93108 −0.184541
\(715\) 56.4036 2.10937
\(716\) −27.6347 −1.03276
\(717\) 5.05219 0.188677
\(718\) 26.7779 0.999343
\(719\) −40.4977 −1.51031 −0.755154 0.655547i \(-0.772438\pi\)
−0.755154 + 0.655547i \(0.772438\pi\)
\(720\) 0.708669 0.0264105
\(721\) 17.2096 0.640918
\(722\) −12.4120 −0.461929
\(723\) −15.9324 −0.592531
\(724\) 30.7659 1.14340
\(725\) −12.3089 −0.457142
\(726\) 17.3143 0.642592
\(727\) 20.3846 0.756022 0.378011 0.925801i \(-0.376608\pi\)
0.378011 + 0.925801i \(0.376608\pi\)
\(728\) 10.1139 0.374845
\(729\) 1.00000 0.0370370
\(730\) 22.1653 0.820375
\(731\) 14.5457 0.537991
\(732\) −6.41984 −0.237284
\(733\) −45.0929 −1.66554 −0.832772 0.553617i \(-0.813247\pi\)
−0.832772 + 0.553617i \(0.813247\pi\)
\(734\) 7.94712 0.293334
\(735\) 2.74724 0.101334
\(736\) 16.0265 0.590743
\(737\) −25.7102 −0.947049
\(738\) −3.44685 −0.126880
\(739\) −18.1927 −0.669230 −0.334615 0.942355i \(-0.608606\pi\)
−0.334615 + 0.942355i \(0.608606\pi\)
\(740\) 30.9435 1.13751
\(741\) 7.51983 0.276248
\(742\) 4.13928 0.151958
\(743\) 33.9156 1.24424 0.622122 0.782921i \(-0.286271\pi\)
0.622122 + 0.782921i \(0.286271\pi\)
\(744\) 19.0335 0.697803
\(745\) −44.5304 −1.63147
\(746\) −7.34935 −0.269079
\(747\) −5.06691 −0.185389
\(748\) −42.6222 −1.55842
\(749\) 3.25655 0.118992
\(750\) −5.66549 −0.206875
\(751\) 26.1611 0.954631 0.477316 0.878732i \(-0.341610\pi\)
0.477316 + 0.878732i \(0.341610\pi\)
\(752\) 3.26512 0.119067
\(753\) −11.8771 −0.432827
\(754\) 14.8408 0.540470
\(755\) −60.7417 −2.21062
\(756\) −1.29302 −0.0470268
\(757\) −8.54392 −0.310534 −0.155267 0.987873i \(-0.549624\pi\)
−0.155267 + 0.987873i \(0.549624\pi\)
\(758\) −12.9296 −0.469623
\(759\) −15.6536 −0.568190
\(760\) 15.6596 0.568035
\(761\) 6.45289 0.233917 0.116959 0.993137i \(-0.462686\pi\)
0.116959 + 0.993137i \(0.462686\pi\)
\(762\) −0.840819 −0.0304597
\(763\) 9.69847 0.351108
\(764\) −22.1255 −0.800474
\(765\) −16.1115 −0.582513
\(766\) 16.3434 0.590512
\(767\) 34.3928 1.24185
\(768\) −15.2664 −0.550878
\(769\) −12.6368 −0.455695 −0.227847 0.973697i \(-0.573169\pi\)
−0.227847 + 0.973697i \(0.573169\pi\)
\(770\) −12.9834 −0.467890
\(771\) −19.3728 −0.697694
\(772\) 27.4099 0.986505
\(773\) 1.63697 0.0588776 0.0294388 0.999567i \(-0.490628\pi\)
0.0294388 + 0.999567i \(0.490628\pi\)
\(774\) −2.08543 −0.0749593
\(775\) −17.5109 −0.629009
\(776\) −38.9890 −1.39962
\(777\) −8.71097 −0.312504
\(778\) 17.0679 0.611914
\(779\) 8.43934 0.302371
\(780\) 12.9755 0.464597
\(781\) −11.9983 −0.429331
\(782\) −13.7331 −0.491093
\(783\) −4.83208 −0.172685
\(784\) 0.257957 0.00921274
\(785\) 64.0068 2.28450
\(786\) 4.91459 0.175297
\(787\) 32.4089 1.15525 0.577626 0.816301i \(-0.303979\pi\)
0.577626 + 0.816301i \(0.303979\pi\)
\(788\) −12.4700 −0.444225
\(789\) −25.0402 −0.891456
\(790\) −23.1682 −0.824286
\(791\) 1.89566 0.0674020
\(792\) 15.5628 0.552999
\(793\) −18.1359 −0.644023
\(794\) −4.24391 −0.150611
\(795\) 13.5244 0.479662
\(796\) 10.4985 0.372108
\(797\) 28.3883 1.00557 0.502783 0.864413i \(-0.332310\pi\)
0.502783 + 0.864413i \(0.332310\pi\)
\(798\) −1.73097 −0.0612758
\(799\) −74.2322 −2.62614
\(800\) 14.6588 0.518267
\(801\) 2.73622 0.0966795
\(802\) 0.696368 0.0245896
\(803\) −53.9342 −1.90330
\(804\) −5.91457 −0.208591
\(805\) 7.65107 0.269665
\(806\) 21.1127 0.743664
\(807\) −20.8253 −0.733085
\(808\) 8.07743 0.284163
\(809\) 0.0199237 0.000700480 0 0.000350240 1.00000i \(-0.499889\pi\)
0.000350240 1.00000i \(0.499889\pi\)
\(810\) 2.30993 0.0811628
\(811\) 8.52421 0.299326 0.149663 0.988737i \(-0.452181\pi\)
0.149663 + 0.988737i \(0.452181\pi\)
\(812\) 6.24800 0.219262
\(813\) 14.7479 0.517232
\(814\) 41.1679 1.44293
\(815\) −59.3271 −2.07814
\(816\) −1.51282 −0.0529592
\(817\) 5.10601 0.178637
\(818\) 6.41998 0.224469
\(819\) −3.65275 −0.127638
\(820\) 14.5621 0.508530
\(821\) −21.9384 −0.765655 −0.382828 0.923820i \(-0.625050\pi\)
−0.382828 + 0.923820i \(0.625050\pi\)
\(822\) −8.97778 −0.313136
\(823\) 16.5378 0.576471 0.288236 0.957559i \(-0.406931\pi\)
0.288236 + 0.957559i \(0.406931\pi\)
\(824\) −47.6505 −1.65998
\(825\) −14.3178 −0.498481
\(826\) −7.91681 −0.275461
\(827\) −0.791654 −0.0275285 −0.0137643 0.999905i \(-0.504381\pi\)
−0.0137643 + 0.999905i \(0.504381\pi\)
\(828\) −3.60107 −0.125146
\(829\) −41.5550 −1.44326 −0.721632 0.692277i \(-0.756608\pi\)
−0.721632 + 0.692277i \(0.756608\pi\)
\(830\) −11.7042 −0.406260
\(831\) −12.6554 −0.439011
\(832\) −15.7895 −0.547403
\(833\) −5.86462 −0.203197
\(834\) −18.2721 −0.632711
\(835\) −8.97345 −0.310539
\(836\) −14.9618 −0.517465
\(837\) −6.87419 −0.237607
\(838\) −0.510334 −0.0176292
\(839\) 44.5008 1.53634 0.768169 0.640247i \(-0.221168\pi\)
0.768169 + 0.640247i \(0.221168\pi\)
\(840\) −7.60666 −0.262455
\(841\) −5.65097 −0.194861
\(842\) 10.2642 0.353728
\(843\) −30.2858 −1.04310
\(844\) 13.1292 0.451926
\(845\) 0.941216 0.0323788
\(846\) 10.6428 0.365906
\(847\) 20.5921 0.707554
\(848\) 1.26990 0.0436085
\(849\) −0.554307 −0.0190238
\(850\) −12.5611 −0.430843
\(851\) −24.2600 −0.831623
\(852\) −2.76017 −0.0945617
\(853\) −18.5412 −0.634838 −0.317419 0.948285i \(-0.602816\pi\)
−0.317419 + 0.948285i \(0.602816\pi\)
\(854\) 4.17465 0.142854
\(855\) −5.65568 −0.193420
\(856\) −9.01686 −0.308190
\(857\) 37.2675 1.27304 0.636518 0.771262i \(-0.280374\pi\)
0.636518 + 0.771262i \(0.280374\pi\)
\(858\) 17.2628 0.589344
\(859\) −16.3924 −0.559303 −0.279651 0.960102i \(-0.590219\pi\)
−0.279651 + 0.960102i \(0.590219\pi\)
\(860\) 8.81042 0.300433
\(861\) −4.09940 −0.139707
\(862\) 23.2087 0.790491
\(863\) −47.5599 −1.61896 −0.809479 0.587149i \(-0.800250\pi\)
−0.809479 + 0.587149i \(0.800250\pi\)
\(864\) 5.75457 0.195774
\(865\) 27.4054 0.931812
\(866\) −17.7200 −0.602149
\(867\) 17.3937 0.590723
\(868\) 8.88849 0.301695
\(869\) 56.3744 1.91237
\(870\) −11.1618 −0.378420
\(871\) −16.7085 −0.566145
\(872\) −26.8535 −0.909373
\(873\) 14.0813 0.476581
\(874\) −4.82076 −0.163065
\(875\) −6.73807 −0.227788
\(876\) −12.4074 −0.419207
\(877\) −22.3076 −0.753275 −0.376637 0.926361i \(-0.622920\pi\)
−0.376637 + 0.926361i \(0.622920\pi\)
\(878\) −9.97462 −0.336627
\(879\) 10.7329 0.362012
\(880\) −3.98321 −0.134274
\(881\) 20.9990 0.707474 0.353737 0.935345i \(-0.384911\pi\)
0.353737 + 0.935345i \(0.384911\pi\)
\(882\) 0.840819 0.0283118
\(883\) 24.4512 0.822849 0.411425 0.911444i \(-0.365031\pi\)
0.411425 + 0.911444i \(0.365031\pi\)
\(884\) −27.6992 −0.931623
\(885\) −25.8669 −0.869507
\(886\) 9.31662 0.312998
\(887\) 17.1615 0.576227 0.288113 0.957596i \(-0.406972\pi\)
0.288113 + 0.957596i \(0.406972\pi\)
\(888\) 24.1192 0.809389
\(889\) −1.00000 −0.0335389
\(890\) 6.32048 0.211863
\(891\) −5.62069 −0.188300
\(892\) −28.8701 −0.966643
\(893\) −26.0579 −0.871996
\(894\) −13.6289 −0.455820
\(895\) 58.7144 1.96261
\(896\) −7.87458 −0.263071
\(897\) −10.1729 −0.339664
\(898\) 17.7801 0.593329
\(899\) 33.2167 1.10784
\(900\) −3.29376 −0.109792
\(901\) −28.8710 −0.961833
\(902\) 19.3737 0.645073
\(903\) −2.48024 −0.0825372
\(904\) −5.24878 −0.174572
\(905\) −65.3672 −2.17288
\(906\) −18.5906 −0.617630
\(907\) 31.9309 1.06025 0.530124 0.847920i \(-0.322145\pi\)
0.530124 + 0.847920i \(0.322145\pi\)
\(908\) 30.1714 1.00127
\(909\) −2.91727 −0.0967596
\(910\) −8.43761 −0.279704
\(911\) 37.7485 1.25067 0.625333 0.780358i \(-0.284963\pi\)
0.625333 + 0.780358i \(0.284963\pi\)
\(912\) −0.531049 −0.0175848
\(913\) 28.4795 0.942535
\(914\) −0.504652 −0.0166924
\(915\) 13.6400 0.450925
\(916\) 11.0921 0.366493
\(917\) 5.84500 0.193019
\(918\) −4.93108 −0.162750
\(919\) 48.2941 1.59308 0.796538 0.604588i \(-0.206662\pi\)
0.796538 + 0.604588i \(0.206662\pi\)
\(920\) −21.1845 −0.698434
\(921\) 5.96740 0.196632
\(922\) −26.1049 −0.859718
\(923\) −7.79739 −0.256654
\(924\) 7.26768 0.239089
\(925\) −22.1897 −0.729594
\(926\) 8.35304 0.274498
\(927\) 17.2096 0.565237
\(928\) −27.8066 −0.912795
\(929\) 59.7282 1.95962 0.979810 0.199932i \(-0.0640720\pi\)
0.979810 + 0.199932i \(0.0640720\pi\)
\(930\) −15.8789 −0.520690
\(931\) −2.05868 −0.0674704
\(932\) −18.9018 −0.619149
\(933\) 26.7130 0.874543
\(934\) −5.17650 −0.169380
\(935\) 90.5578 2.96156
\(936\) 10.1139 0.330582
\(937\) −27.0530 −0.883782 −0.441891 0.897069i \(-0.645692\pi\)
−0.441891 + 0.897069i \(0.645692\pi\)
\(938\) 3.84609 0.125579
\(939\) −25.9107 −0.845563
\(940\) −44.9630 −1.46653
\(941\) 32.2760 1.05217 0.526084 0.850433i \(-0.323660\pi\)
0.526084 + 0.850433i \(0.323660\pi\)
\(942\) 19.5899 0.638273
\(943\) −11.4168 −0.371783
\(944\) −2.42882 −0.0790512
\(945\) 2.74724 0.0893678
\(946\) 11.7216 0.381101
\(947\) 4.40313 0.143083 0.0715413 0.997438i \(-0.477208\pi\)
0.0715413 + 0.997438i \(0.477208\pi\)
\(948\) 12.9688 0.421206
\(949\) −35.0505 −1.13779
\(950\) −4.40937 −0.143059
\(951\) −6.29184 −0.204027
\(952\) 16.2382 0.526282
\(953\) 17.0635 0.552741 0.276370 0.961051i \(-0.410868\pi\)
0.276370 + 0.961051i \(0.410868\pi\)
\(954\) 4.13928 0.134014
\(955\) 47.0094 1.52119
\(956\) −6.53260 −0.211279
\(957\) 27.1596 0.877946
\(958\) 13.2573 0.428323
\(959\) −10.6774 −0.344792
\(960\) 11.8753 0.383274
\(961\) 16.2545 0.524340
\(962\) 26.7540 0.862584
\(963\) 3.25655 0.104941
\(964\) 20.6009 0.663511
\(965\) −58.2369 −1.87471
\(966\) 2.34168 0.0753423
\(967\) −26.9109 −0.865398 −0.432699 0.901539i \(-0.642439\pi\)
−0.432699 + 0.901539i \(0.642439\pi\)
\(968\) −57.0163 −1.83257
\(969\) 12.0733 0.387852
\(970\) 32.5270 1.04438
\(971\) −28.9843 −0.930151 −0.465076 0.885271i \(-0.653973\pi\)
−0.465076 + 0.885271i \(0.653973\pi\)
\(972\) −1.29302 −0.0414737
\(973\) −21.7313 −0.696674
\(974\) −5.29812 −0.169763
\(975\) −9.30478 −0.297991
\(976\) 1.28075 0.0409958
\(977\) −50.2194 −1.60666 −0.803330 0.595534i \(-0.796941\pi\)
−0.803330 + 0.595534i \(0.796941\pi\)
\(978\) −18.1576 −0.580616
\(979\) −15.3794 −0.491529
\(980\) −3.55225 −0.113472
\(981\) 9.69847 0.309648
\(982\) −2.31788 −0.0739667
\(983\) −1.32859 −0.0423756 −0.0211878 0.999776i \(-0.506745\pi\)
−0.0211878 + 0.999776i \(0.506745\pi\)
\(984\) 11.3506 0.361843
\(985\) 26.4946 0.844187
\(986\) 23.8274 0.758819
\(987\) 12.6576 0.402897
\(988\) −9.72332 −0.309340
\(989\) −6.90747 −0.219645
\(990\) −12.9834 −0.412640
\(991\) −38.1866 −1.21304 −0.606518 0.795070i \(-0.707434\pi\)
−0.606518 + 0.795070i \(0.707434\pi\)
\(992\) −39.5580 −1.25597
\(993\) 6.26075 0.198679
\(994\) 1.79486 0.0569296
\(995\) −22.3057 −0.707138
\(996\) 6.55164 0.207597
\(997\) 34.2759 1.08553 0.542764 0.839885i \(-0.317378\pi\)
0.542764 + 0.839885i \(0.317378\pi\)
\(998\) 1.01145 0.0320168
\(999\) −8.71097 −0.275603
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 2667.2.a.j.1.6 7
3.2 odd 2 8001.2.a.l.1.2 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2667.2.a.j.1.6 7 1.1 even 1 trivial
8001.2.a.l.1.2 7 3.2 odd 2