Properties

Label 1441.2.a.e.1.7
Level $1441$
Weight $2$
Character 1441.1
Self dual yes
Analytic conductor $11.506$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1441 = 11 \cdot 131 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1441.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(11.5064429313\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) \(=\) 1441.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.13972 q^{2} +3.40925 q^{3} -0.701031 q^{4} -0.104086 q^{5} -3.88560 q^{6} +1.00506 q^{7} +3.07843 q^{8} +8.62297 q^{9} +O(q^{10})\) \(q-1.13972 q^{2} +3.40925 q^{3} -0.701031 q^{4} -0.104086 q^{5} -3.88560 q^{6} +1.00506 q^{7} +3.07843 q^{8} +8.62297 q^{9} +0.118629 q^{10} +1.00000 q^{11} -2.38999 q^{12} +1.47074 q^{13} -1.14549 q^{14} -0.354854 q^{15} -2.10649 q^{16} -0.523035 q^{17} -9.82779 q^{18} +4.88589 q^{19} +0.0729673 q^{20} +3.42651 q^{21} -1.13972 q^{22} -3.18640 q^{23} +10.4951 q^{24} -4.98917 q^{25} -1.67623 q^{26} +19.1701 q^{27} -0.704580 q^{28} +4.16319 q^{29} +0.404435 q^{30} -7.69918 q^{31} -3.75604 q^{32} +3.40925 q^{33} +0.596115 q^{34} -0.104612 q^{35} -6.04497 q^{36} +4.51585 q^{37} -5.56856 q^{38} +5.01410 q^{39} -0.320420 q^{40} -4.28457 q^{41} -3.90527 q^{42} -7.09033 q^{43} -0.701031 q^{44} -0.897527 q^{45} +3.63161 q^{46} +7.07039 q^{47} -7.18155 q^{48} -5.98985 q^{49} +5.68627 q^{50} -1.78315 q^{51} -1.03103 q^{52} -4.44226 q^{53} -21.8486 q^{54} -0.104086 q^{55} +3.09401 q^{56} +16.6572 q^{57} -4.74488 q^{58} +3.97795 q^{59} +0.248763 q^{60} +14.0507 q^{61} +8.77494 q^{62} +8.66662 q^{63} +8.49383 q^{64} -0.153082 q^{65} -3.88560 q^{66} -12.2458 q^{67} +0.366664 q^{68} -10.8632 q^{69} +0.119229 q^{70} +11.2219 q^{71} +26.5452 q^{72} +7.92036 q^{73} -5.14682 q^{74} -17.0093 q^{75} -3.42516 q^{76} +1.00506 q^{77} -5.71469 q^{78} +12.9966 q^{79} +0.219256 q^{80} +39.4866 q^{81} +4.88322 q^{82} +1.05831 q^{83} -2.40209 q^{84} +0.0544404 q^{85} +8.08101 q^{86} +14.1933 q^{87} +3.07843 q^{88} -9.63567 q^{89} +1.02293 q^{90} +1.47818 q^{91} +2.23376 q^{92} -26.2484 q^{93} -8.05829 q^{94} -0.508551 q^{95} -12.8053 q^{96} -3.03765 q^{97} +6.82677 q^{98} +8.62297 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9} + O(q^{10}) \) \( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9} + 14 q^{10} + 28 q^{11} - 6 q^{12} + 3 q^{13} - q^{14} + 19 q^{15} + 29 q^{16} + 9 q^{17} - 2 q^{18} + 20 q^{19} + 6 q^{20} + 6 q^{21} + 7 q^{22} + 24 q^{23} + 20 q^{24} + 23 q^{25} + 10 q^{26} - 20 q^{27} - 3 q^{28} + 43 q^{29} + 11 q^{30} + 3 q^{31} + 44 q^{32} - 2 q^{33} - 28 q^{34} + 32 q^{35} + 24 q^{36} - 4 q^{37} + 24 q^{38} + 37 q^{39} + 22 q^{40} + 32 q^{41} - 27 q^{42} + 25 q^{43} + 27 q^{44} - 36 q^{45} + 10 q^{46} + 19 q^{47} + 42 q^{48} + 17 q^{49} + q^{50} + 39 q^{51} - 19 q^{52} + 5 q^{53} + 6 q^{54} + 3 q^{55} + 8 q^{56} + 2 q^{57} + 21 q^{58} + 44 q^{59} + 65 q^{60} + 28 q^{61} + 60 q^{62} - 8 q^{63} + 5 q^{64} + 33 q^{65} - q^{66} + 7 q^{67} + 13 q^{68} - 22 q^{69} + 9 q^{70} + 117 q^{71} - 17 q^{72} + 7 q^{73} + 41 q^{74} - 40 q^{75} + 34 q^{76} + 7 q^{77} - 97 q^{78} + 48 q^{79} + 41 q^{80} + 40 q^{81} + 2 q^{82} + 22 q^{83} + 27 q^{84} + 30 q^{85} + 24 q^{86} + 37 q^{87} + 21 q^{88} - 6 q^{89} + 4 q^{90} - 33 q^{91} + 18 q^{92} + 5 q^{93} - 43 q^{94} + 64 q^{95} + 55 q^{96} - 50 q^{97} + 97 q^{98} + 28 q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.13972 −0.805906 −0.402953 0.915221i \(-0.632016\pi\)
−0.402953 + 0.915221i \(0.632016\pi\)
\(3\) 3.40925 1.96833 0.984165 0.177255i \(-0.0567219\pi\)
0.984165 + 0.177255i \(0.0567219\pi\)
\(4\) −0.701031 −0.350516
\(5\) −0.104086 −0.0465485 −0.0232742 0.999729i \(-0.507409\pi\)
−0.0232742 + 0.999729i \(0.507409\pi\)
\(6\) −3.88560 −1.58629
\(7\) 1.00506 0.379878 0.189939 0.981796i \(-0.439171\pi\)
0.189939 + 0.981796i \(0.439171\pi\)
\(8\) 3.07843 1.08839
\(9\) 8.62297 2.87432
\(10\) 0.118629 0.0375137
\(11\) 1.00000 0.301511
\(12\) −2.38999 −0.689930
\(13\) 1.47074 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(14\) −1.14549 −0.306146
\(15\) −0.354854 −0.0916228
\(16\) −2.10649 −0.526623
\(17\) −0.523035 −0.126855 −0.0634273 0.997986i \(-0.520203\pi\)
−0.0634273 + 0.997986i \(0.520203\pi\)
\(18\) −9.82779 −2.31643
\(19\) 4.88589 1.12090 0.560450 0.828188i \(-0.310628\pi\)
0.560450 + 0.828188i \(0.310628\pi\)
\(20\) 0.0729673 0.0163160
\(21\) 3.42651 0.747725
\(22\) −1.13972 −0.242990
\(23\) −3.18640 −0.664409 −0.332205 0.943207i \(-0.607792\pi\)
−0.332205 + 0.943207i \(0.607792\pi\)
\(24\) 10.4951 2.14231
\(25\) −4.98917 −0.997833
\(26\) −1.67623 −0.328736
\(27\) 19.1701 3.68928
\(28\) −0.704580 −0.133153
\(29\) 4.16319 0.773084 0.386542 0.922272i \(-0.373669\pi\)
0.386542 + 0.922272i \(0.373669\pi\)
\(30\) 0.404435 0.0738393
\(31\) −7.69918 −1.38281 −0.691407 0.722466i \(-0.743009\pi\)
−0.691407 + 0.722466i \(0.743009\pi\)
\(32\) −3.75604 −0.663980
\(33\) 3.40925 0.593474
\(34\) 0.596115 0.102233
\(35\) −0.104612 −0.0176827
\(36\) −6.04497 −1.00749
\(37\) 4.51585 0.742402 0.371201 0.928553i \(-0.378946\pi\)
0.371201 + 0.928553i \(0.378946\pi\)
\(38\) −5.56856 −0.903340
\(39\) 5.01410 0.802899
\(40\) −0.320420 −0.0506628
\(41\) −4.28457 −0.669137 −0.334569 0.942371i \(-0.608591\pi\)
−0.334569 + 0.942371i \(0.608591\pi\)
\(42\) −3.90527 −0.602596
\(43\) −7.09033 −1.08127 −0.540633 0.841259i \(-0.681815\pi\)
−0.540633 + 0.841259i \(0.681815\pi\)
\(44\) −0.701031 −0.105684
\(45\) −0.897527 −0.133795
\(46\) 3.63161 0.535451
\(47\) 7.07039 1.03132 0.515662 0.856792i \(-0.327546\pi\)
0.515662 + 0.856792i \(0.327546\pi\)
\(48\) −7.18155 −1.03657
\(49\) −5.98985 −0.855693
\(50\) 5.68627 0.804160
\(51\) −1.78315 −0.249692
\(52\) −1.03103 −0.142978
\(53\) −4.44226 −0.610191 −0.305095 0.952322i \(-0.598688\pi\)
−0.305095 + 0.952322i \(0.598688\pi\)
\(54\) −21.8486 −2.97322
\(55\) −0.104086 −0.0140349
\(56\) 3.09401 0.413455
\(57\) 16.6572 2.20630
\(58\) −4.74488 −0.623033
\(59\) 3.97795 0.517885 0.258943 0.965893i \(-0.416626\pi\)
0.258943 + 0.965893i \(0.416626\pi\)
\(60\) 0.248763 0.0321152
\(61\) 14.0507 1.79900 0.899502 0.436916i \(-0.143929\pi\)
0.899502 + 0.436916i \(0.143929\pi\)
\(62\) 8.77494 1.11442
\(63\) 8.66662 1.09189
\(64\) 8.49383 1.06173
\(65\) −0.153082 −0.0189875
\(66\) −3.88560 −0.478284
\(67\) −12.2458 −1.49607 −0.748033 0.663662i \(-0.769002\pi\)
−0.748033 + 0.663662i \(0.769002\pi\)
\(68\) 0.366664 0.0444645
\(69\) −10.8632 −1.30778
\(70\) 0.119229 0.0142506
\(71\) 11.2219 1.33180 0.665898 0.746043i \(-0.268049\pi\)
0.665898 + 0.746043i \(0.268049\pi\)
\(72\) 26.5452 3.12838
\(73\) 7.92036 0.927008 0.463504 0.886095i \(-0.346592\pi\)
0.463504 + 0.886095i \(0.346592\pi\)
\(74\) −5.14682 −0.598306
\(75\) −17.0093 −1.96406
\(76\) −3.42516 −0.392893
\(77\) 1.00506 0.114537
\(78\) −5.71469 −0.647061
\(79\) 12.9966 1.46223 0.731117 0.682252i \(-0.238999\pi\)
0.731117 + 0.682252i \(0.238999\pi\)
\(80\) 0.219256 0.0245135
\(81\) 39.4866 4.38740
\(82\) 4.88322 0.539262
\(83\) 1.05831 0.116164 0.0580822 0.998312i \(-0.481501\pi\)
0.0580822 + 0.998312i \(0.481501\pi\)
\(84\) −2.40209 −0.262089
\(85\) 0.0544404 0.00590489
\(86\) 8.08101 0.871398
\(87\) 14.1933 1.52168
\(88\) 3.07843 0.328161
\(89\) −9.63567 −1.02138 −0.510690 0.859765i \(-0.670610\pi\)
−0.510690 + 0.859765i \(0.670610\pi\)
\(90\) 1.02293 0.107826
\(91\) 1.47818 0.154955
\(92\) 2.23376 0.232886
\(93\) −26.2484 −2.72183
\(94\) −8.05829 −0.831149
\(95\) −0.508551 −0.0521762
\(96\) −12.8053 −1.30693
\(97\) −3.03765 −0.308426 −0.154213 0.988038i \(-0.549284\pi\)
−0.154213 + 0.988038i \(0.549284\pi\)
\(98\) 6.82677 0.689608
\(99\) 8.62297 0.866641
\(100\) 3.49756 0.349756
\(101\) 12.8550 1.27912 0.639560 0.768742i \(-0.279117\pi\)
0.639560 + 0.768742i \(0.279117\pi\)
\(102\) 2.03230 0.201228
\(103\) −1.44393 −0.142275 −0.0711376 0.997467i \(-0.522663\pi\)
−0.0711376 + 0.997467i \(0.522663\pi\)
\(104\) 4.52755 0.443963
\(105\) −0.356650 −0.0348055
\(106\) 5.06294 0.491757
\(107\) −1.13652 −0.109872 −0.0549359 0.998490i \(-0.517495\pi\)
−0.0549359 + 0.998490i \(0.517495\pi\)
\(108\) −13.4388 −1.29315
\(109\) −11.3071 −1.08302 −0.541510 0.840695i \(-0.682147\pi\)
−0.541510 + 0.840695i \(0.682147\pi\)
\(110\) 0.118629 0.0113108
\(111\) 15.3957 1.46129
\(112\) −2.11716 −0.200052
\(113\) −12.7882 −1.20301 −0.601507 0.798868i \(-0.705433\pi\)
−0.601507 + 0.798868i \(0.705433\pi\)
\(114\) −18.9846 −1.77807
\(115\) 0.331658 0.0309273
\(116\) −2.91852 −0.270978
\(117\) 12.6821 1.17246
\(118\) −4.53377 −0.417367
\(119\) −0.525682 −0.0481892
\(120\) −1.09239 −0.0997212
\(121\) 1.00000 0.0909091
\(122\) −16.0139 −1.44983
\(123\) −14.6072 −1.31708
\(124\) 5.39737 0.484698
\(125\) 1.03973 0.0929961
\(126\) −9.87754 −0.879961
\(127\) −8.52712 −0.756659 −0.378330 0.925671i \(-0.623501\pi\)
−0.378330 + 0.925671i \(0.623501\pi\)
\(128\) −2.16854 −0.191673
\(129\) −24.1727 −2.12829
\(130\) 0.174472 0.0153022
\(131\) −1.00000 −0.0873704
\(132\) −2.38999 −0.208022
\(133\) 4.91062 0.425805
\(134\) 13.9569 1.20569
\(135\) −1.99533 −0.171731
\(136\) −1.61012 −0.138067
\(137\) −19.4991 −1.66592 −0.832959 0.553334i \(-0.813355\pi\)
−0.832959 + 0.553334i \(0.813355\pi\)
\(138\) 12.3810 1.05394
\(139\) −4.36910 −0.370583 −0.185291 0.982684i \(-0.559323\pi\)
−0.185291 + 0.982684i \(0.559323\pi\)
\(140\) 0.0733366 0.00619808
\(141\) 24.1047 2.02998
\(142\) −12.7899 −1.07330
\(143\) 1.47074 0.122989
\(144\) −18.1642 −1.51368
\(145\) −0.433328 −0.0359859
\(146\) −9.02702 −0.747081
\(147\) −20.4209 −1.68429
\(148\) −3.16575 −0.260223
\(149\) 5.11776 0.419264 0.209632 0.977780i \(-0.432773\pi\)
0.209632 + 0.977780i \(0.432773\pi\)
\(150\) 19.3859 1.58285
\(151\) −3.61329 −0.294045 −0.147023 0.989133i \(-0.546969\pi\)
−0.147023 + 0.989133i \(0.546969\pi\)
\(152\) 15.0409 1.21997
\(153\) −4.51011 −0.364621
\(154\) −1.14549 −0.0923064
\(155\) 0.801374 0.0643679
\(156\) −3.51504 −0.281429
\(157\) 14.0393 1.12046 0.560228 0.828339i \(-0.310714\pi\)
0.560228 + 0.828339i \(0.310714\pi\)
\(158\) −14.8125 −1.17842
\(159\) −15.1448 −1.20106
\(160\) 0.390949 0.0309073
\(161\) −3.20253 −0.252394
\(162\) −45.0038 −3.53584
\(163\) −12.4299 −0.973586 −0.486793 0.873517i \(-0.661833\pi\)
−0.486793 + 0.873517i \(0.661833\pi\)
\(164\) 3.00362 0.234543
\(165\) −0.354854 −0.0276253
\(166\) −1.20618 −0.0936175
\(167\) 17.1141 1.32433 0.662165 0.749358i \(-0.269638\pi\)
0.662165 + 0.749358i \(0.269638\pi\)
\(168\) 10.5482 0.813815
\(169\) −10.8369 −0.833611
\(170\) −0.0620470 −0.00475878
\(171\) 42.1309 3.22183
\(172\) 4.97054 0.379000
\(173\) 8.33709 0.633857 0.316929 0.948449i \(-0.397348\pi\)
0.316929 + 0.948449i \(0.397348\pi\)
\(174\) −16.1765 −1.22633
\(175\) −5.01442 −0.379055
\(176\) −2.10649 −0.158783
\(177\) 13.5618 1.01937
\(178\) 10.9820 0.823135
\(179\) 7.07537 0.528838 0.264419 0.964408i \(-0.414820\pi\)
0.264419 + 0.964408i \(0.414820\pi\)
\(180\) 0.629194 0.0468974
\(181\) 13.6052 1.01127 0.505634 0.862748i \(-0.331259\pi\)
0.505634 + 0.862748i \(0.331259\pi\)
\(182\) −1.68472 −0.124880
\(183\) 47.9022 3.54103
\(184\) −9.80909 −0.723136
\(185\) −0.470035 −0.0345577
\(186\) 29.9159 2.19354
\(187\) −0.523035 −0.0382481
\(188\) −4.95657 −0.361495
\(189\) 19.2671 1.40148
\(190\) 0.579607 0.0420491
\(191\) −24.4823 −1.77148 −0.885740 0.464182i \(-0.846348\pi\)
−0.885740 + 0.464182i \(0.846348\pi\)
\(192\) 28.9576 2.08983
\(193\) −23.2283 −1.67201 −0.836005 0.548722i \(-0.815114\pi\)
−0.836005 + 0.548722i \(0.815114\pi\)
\(194\) 3.46208 0.248563
\(195\) −0.521896 −0.0373737
\(196\) 4.19907 0.299934
\(197\) −9.28048 −0.661206 −0.330603 0.943770i \(-0.607252\pi\)
−0.330603 + 0.943770i \(0.607252\pi\)
\(198\) −9.82779 −0.698431
\(199\) −0.503697 −0.0357061 −0.0178531 0.999841i \(-0.505683\pi\)
−0.0178531 + 0.999841i \(0.505683\pi\)
\(200\) −15.3588 −1.08603
\(201\) −41.7491 −2.94475
\(202\) −14.6511 −1.03085
\(203\) 4.18426 0.293678
\(204\) 1.25005 0.0875208
\(205\) 0.445962 0.0311473
\(206\) 1.64569 0.114660
\(207\) −27.4762 −1.90973
\(208\) −3.09809 −0.214814
\(209\) 4.88589 0.337964
\(210\) 0.406482 0.0280499
\(211\) −9.79724 −0.674470 −0.337235 0.941421i \(-0.609492\pi\)
−0.337235 + 0.941421i \(0.609492\pi\)
\(212\) 3.11416 0.213882
\(213\) 38.2583 2.62141
\(214\) 1.29532 0.0885464
\(215\) 0.738001 0.0503313
\(216\) 59.0137 4.01537
\(217\) −7.73816 −0.525300
\(218\) 12.8869 0.872812
\(219\) 27.0025 1.82466
\(220\) 0.0729673 0.00491945
\(221\) −0.769246 −0.0517451
\(222\) −17.5468 −1.17766
\(223\) −7.42764 −0.497392 −0.248696 0.968582i \(-0.580002\pi\)
−0.248696 + 0.968582i \(0.580002\pi\)
\(224\) −3.77505 −0.252231
\(225\) −43.0214 −2.86809
\(226\) 14.5750 0.969515
\(227\) 21.0243 1.39543 0.697716 0.716374i \(-0.254200\pi\)
0.697716 + 0.716374i \(0.254200\pi\)
\(228\) −11.6772 −0.773343
\(229\) −11.6483 −0.769741 −0.384870 0.922971i \(-0.625754\pi\)
−0.384870 + 0.922971i \(0.625754\pi\)
\(230\) −0.377998 −0.0249245
\(231\) 3.42651 0.225447
\(232\) 12.8161 0.841416
\(233\) −1.58868 −0.104078 −0.0520390 0.998645i \(-0.516572\pi\)
−0.0520390 + 0.998645i \(0.516572\pi\)
\(234\) −14.4541 −0.944893
\(235\) −0.735926 −0.0480065
\(236\) −2.78867 −0.181527
\(237\) 44.3087 2.87816
\(238\) 0.599132 0.0388360
\(239\) 20.8034 1.34566 0.672830 0.739797i \(-0.265079\pi\)
0.672830 + 0.739797i \(0.265079\pi\)
\(240\) 0.747496 0.0482507
\(241\) −7.99233 −0.514831 −0.257416 0.966301i \(-0.582871\pi\)
−0.257416 + 0.966301i \(0.582871\pi\)
\(242\) −1.13972 −0.0732642
\(243\) 77.1095 4.94658
\(244\) −9.84996 −0.630579
\(245\) 0.623457 0.0398312
\(246\) 16.6481 1.06144
\(247\) 7.18585 0.457225
\(248\) −23.7014 −1.50504
\(249\) 3.60803 0.228650
\(250\) −1.18500 −0.0749461
\(251\) 8.35603 0.527428 0.263714 0.964601i \(-0.415053\pi\)
0.263714 + 0.964601i \(0.415053\pi\)
\(252\) −6.07557 −0.382725
\(253\) −3.18640 −0.200327
\(254\) 9.71855 0.609796
\(255\) 0.185601 0.0116228
\(256\) −14.5161 −0.907258
\(257\) 9.46958 0.590696 0.295348 0.955390i \(-0.404564\pi\)
0.295348 + 0.955390i \(0.404564\pi\)
\(258\) 27.5502 1.71520
\(259\) 4.53871 0.282022
\(260\) 0.107316 0.00665543
\(261\) 35.8990 2.22209
\(262\) 1.13972 0.0704123
\(263\) 5.47287 0.337471 0.168736 0.985661i \(-0.446032\pi\)
0.168736 + 0.985661i \(0.446032\pi\)
\(264\) 10.4951 0.645930
\(265\) 0.462375 0.0284035
\(266\) −5.59675 −0.343159
\(267\) −32.8504 −2.01041
\(268\) 8.58471 0.524395
\(269\) 3.78140 0.230556 0.115278 0.993333i \(-0.463224\pi\)
0.115278 + 0.993333i \(0.463224\pi\)
\(270\) 2.27412 0.138399
\(271\) −31.1040 −1.88943 −0.944716 0.327891i \(-0.893662\pi\)
−0.944716 + 0.327891i \(0.893662\pi\)
\(272\) 1.10177 0.0668045
\(273\) 5.03948 0.305003
\(274\) 22.2235 1.34257
\(275\) −4.98917 −0.300858
\(276\) 7.61545 0.458396
\(277\) −1.24461 −0.0747812 −0.0373906 0.999301i \(-0.511905\pi\)
−0.0373906 + 0.999301i \(0.511905\pi\)
\(278\) 4.97957 0.298655
\(279\) −66.3898 −3.97465
\(280\) −0.322042 −0.0192457
\(281\) −5.99503 −0.357633 −0.178817 0.983882i \(-0.557227\pi\)
−0.178817 + 0.983882i \(0.557227\pi\)
\(282\) −27.4727 −1.63598
\(283\) −0.258842 −0.0153866 −0.00769328 0.999970i \(-0.502449\pi\)
−0.00769328 + 0.999970i \(0.502449\pi\)
\(284\) −7.86691 −0.466815
\(285\) −1.73378 −0.102700
\(286\) −1.67623 −0.0991176
\(287\) −4.30626 −0.254190
\(288\) −32.3882 −1.90849
\(289\) −16.7264 −0.983908
\(290\) 0.493874 0.0290013
\(291\) −10.3561 −0.607084
\(292\) −5.55242 −0.324931
\(293\) 18.1873 1.06251 0.531256 0.847211i \(-0.321720\pi\)
0.531256 + 0.847211i \(0.321720\pi\)
\(294\) 23.2741 1.35738
\(295\) −0.414048 −0.0241068
\(296\) 13.9017 0.808022
\(297\) 19.1701 1.11236
\(298\) −5.83283 −0.337887
\(299\) −4.68635 −0.271018
\(300\) 11.9241 0.688436
\(301\) −7.12622 −0.410749
\(302\) 4.11815 0.236973
\(303\) 43.8258 2.51773
\(304\) −10.2921 −0.590292
\(305\) −1.46247 −0.0837410
\(306\) 5.14028 0.293850
\(307\) −1.68926 −0.0964112 −0.0482056 0.998837i \(-0.515350\pi\)
−0.0482056 + 0.998837i \(0.515350\pi\)
\(308\) −0.704580 −0.0401472
\(309\) −4.92273 −0.280044
\(310\) −0.913344 −0.0518745
\(311\) −30.2079 −1.71293 −0.856467 0.516203i \(-0.827345\pi\)
−0.856467 + 0.516203i \(0.827345\pi\)
\(312\) 15.4355 0.873866
\(313\) 8.81226 0.498098 0.249049 0.968491i \(-0.419882\pi\)
0.249049 + 0.968491i \(0.419882\pi\)
\(314\) −16.0009 −0.902982
\(315\) −0.902070 −0.0508259
\(316\) −9.11104 −0.512536
\(317\) 6.14160 0.344947 0.172473 0.985014i \(-0.444824\pi\)
0.172473 + 0.985014i \(0.444824\pi\)
\(318\) 17.2608 0.967939
\(319\) 4.16319 0.233094
\(320\) −0.884085 −0.0494219
\(321\) −3.87469 −0.216264
\(322\) 3.64999 0.203406
\(323\) −2.55549 −0.142191
\(324\) −27.6814 −1.53785
\(325\) −7.33774 −0.407025
\(326\) 14.1667 0.784618
\(327\) −38.5485 −2.13174
\(328\) −13.1897 −0.728281
\(329\) 7.10619 0.391777
\(330\) 0.404435 0.0222634
\(331\) 11.9166 0.654993 0.327497 0.944852i \(-0.393795\pi\)
0.327497 + 0.944852i \(0.393795\pi\)
\(332\) −0.741907 −0.0407174
\(333\) 38.9401 2.13390
\(334\) −19.5053 −1.06729
\(335\) 1.27461 0.0696396
\(336\) −7.21791 −0.393769
\(337\) −28.7112 −1.56400 −0.781998 0.623281i \(-0.785799\pi\)
−0.781998 + 0.623281i \(0.785799\pi\)
\(338\) 12.3511 0.671812
\(339\) −43.5981 −2.36793
\(340\) −0.0381644 −0.00206976
\(341\) −7.69918 −0.416934
\(342\) −48.0175 −2.59649
\(343\) −13.0556 −0.704937
\(344\) −21.8271 −1.17684
\(345\) 1.13070 0.0608750
\(346\) −9.50197 −0.510829
\(347\) −21.5606 −1.15743 −0.578717 0.815529i \(-0.696446\pi\)
−0.578717 + 0.815529i \(0.696446\pi\)
\(348\) −9.94997 −0.533374
\(349\) −17.5173 −0.937677 −0.468839 0.883284i \(-0.655327\pi\)
−0.468839 + 0.883284i \(0.655327\pi\)
\(350\) 5.71505 0.305482
\(351\) 28.1941 1.50489
\(352\) −3.75604 −0.200197
\(353\) 29.3367 1.56143 0.780717 0.624885i \(-0.214854\pi\)
0.780717 + 0.624885i \(0.214854\pi\)
\(354\) −15.4567 −0.821516
\(355\) −1.16804 −0.0619931
\(356\) 6.75491 0.358009
\(357\) −1.79218 −0.0948523
\(358\) −8.06396 −0.426194
\(359\) −12.0516 −0.636059 −0.318030 0.948081i \(-0.603021\pi\)
−0.318030 + 0.948081i \(0.603021\pi\)
\(360\) −2.76297 −0.145621
\(361\) 4.87192 0.256417
\(362\) −15.5062 −0.814987
\(363\) 3.40925 0.178939
\(364\) −1.03625 −0.0543143
\(365\) −0.824395 −0.0431508
\(366\) −54.5953 −2.85374
\(367\) −23.4905 −1.22619 −0.613096 0.790009i \(-0.710076\pi\)
−0.613096 + 0.790009i \(0.710076\pi\)
\(368\) 6.71212 0.349893
\(369\) −36.9457 −1.92332
\(370\) 0.535710 0.0278502
\(371\) −4.46474 −0.231798
\(372\) 18.4010 0.954045
\(373\) −13.5774 −0.703011 −0.351506 0.936186i \(-0.614330\pi\)
−0.351506 + 0.936186i \(0.614330\pi\)
\(374\) 0.596115 0.0308244
\(375\) 3.54469 0.183047
\(376\) 21.7657 1.12248
\(377\) 6.12295 0.315348
\(378\) −21.9592 −1.12946
\(379\) −19.6101 −1.00730 −0.503651 0.863907i \(-0.668010\pi\)
−0.503651 + 0.863907i \(0.668010\pi\)
\(380\) 0.356510 0.0182886
\(381\) −29.0710 −1.48935
\(382\) 27.9031 1.42765
\(383\) −21.9292 −1.12053 −0.560264 0.828314i \(-0.689300\pi\)
−0.560264 + 0.828314i \(0.689300\pi\)
\(384\) −7.39307 −0.377276
\(385\) −0.104612 −0.00533155
\(386\) 26.4738 1.34748
\(387\) −61.1397 −3.10791
\(388\) 2.12949 0.108108
\(389\) −16.0085 −0.811662 −0.405831 0.913948i \(-0.633018\pi\)
−0.405831 + 0.913948i \(0.633018\pi\)
\(390\) 0.594817 0.0301197
\(391\) 1.66660 0.0842834
\(392\) −18.4393 −0.931326
\(393\) −3.40925 −0.171974
\(394\) 10.5772 0.532870
\(395\) −1.35276 −0.0680648
\(396\) −6.04497 −0.303771
\(397\) 28.5338 1.43207 0.716035 0.698065i \(-0.245955\pi\)
0.716035 + 0.698065i \(0.245955\pi\)
\(398\) 0.574075 0.0287758
\(399\) 16.7415 0.838125
\(400\) 10.5096 0.525482
\(401\) 34.5253 1.72411 0.862054 0.506816i \(-0.169178\pi\)
0.862054 + 0.506816i \(0.169178\pi\)
\(402\) 47.5824 2.37319
\(403\) −11.3235 −0.564062
\(404\) −9.01175 −0.448351
\(405\) −4.10999 −0.204227
\(406\) −4.76890 −0.236676
\(407\) 4.51585 0.223843
\(408\) −5.48931 −0.271761
\(409\) 1.88479 0.0931966 0.0465983 0.998914i \(-0.485162\pi\)
0.0465983 + 0.998914i \(0.485162\pi\)
\(410\) −0.508273 −0.0251018
\(411\) −66.4772 −3.27908
\(412\) 1.01224 0.0498697
\(413\) 3.99809 0.196733
\(414\) 31.3152 1.53906
\(415\) −0.110155 −0.00540727
\(416\) −5.52414 −0.270843
\(417\) −14.8954 −0.729429
\(418\) −5.56856 −0.272367
\(419\) −20.8076 −1.01652 −0.508259 0.861204i \(-0.669711\pi\)
−0.508259 + 0.861204i \(0.669711\pi\)
\(420\) 0.250023 0.0121999
\(421\) −11.7864 −0.574434 −0.287217 0.957866i \(-0.592730\pi\)
−0.287217 + 0.957866i \(0.592730\pi\)
\(422\) 11.1661 0.543559
\(423\) 60.9678 2.96435
\(424\) −13.6752 −0.664125
\(425\) 2.60951 0.126580
\(426\) −43.6038 −2.11261
\(427\) 14.1218 0.683402
\(428\) 0.796739 0.0385118
\(429\) 5.01410 0.242083
\(430\) −0.841117 −0.0405623
\(431\) 13.7150 0.660630 0.330315 0.943871i \(-0.392845\pi\)
0.330315 + 0.943871i \(0.392845\pi\)
\(432\) −40.3816 −1.94286
\(433\) −29.7123 −1.42788 −0.713942 0.700205i \(-0.753092\pi\)
−0.713942 + 0.700205i \(0.753092\pi\)
\(434\) 8.81936 0.423343
\(435\) −1.47732 −0.0708321
\(436\) 7.92660 0.379615
\(437\) −15.5684 −0.744736
\(438\) −30.7753 −1.47050
\(439\) −24.5212 −1.17033 −0.585166 0.810914i \(-0.698971\pi\)
−0.585166 + 0.810914i \(0.698971\pi\)
\(440\) −0.320420 −0.0152754
\(441\) −51.6503 −2.45954
\(442\) 0.876727 0.0417017
\(443\) 21.4778 1.02044 0.510220 0.860044i \(-0.329564\pi\)
0.510220 + 0.860044i \(0.329564\pi\)
\(444\) −10.7928 −0.512206
\(445\) 1.00293 0.0475437
\(446\) 8.46546 0.400851
\(447\) 17.4477 0.825249
\(448\) 8.53682 0.403327
\(449\) 0.818727 0.0386381 0.0193191 0.999813i \(-0.493850\pi\)
0.0193191 + 0.999813i \(0.493850\pi\)
\(450\) 49.0325 2.31141
\(451\) −4.28457 −0.201752
\(452\) 8.96493 0.421675
\(453\) −12.3186 −0.578778
\(454\) −23.9619 −1.12459
\(455\) −0.153857 −0.00721294
\(456\) 51.2780 2.40131
\(457\) 39.1336 1.83059 0.915296 0.402783i \(-0.131957\pi\)
0.915296 + 0.402783i \(0.131957\pi\)
\(458\) 13.2758 0.620339
\(459\) −10.0266 −0.468002
\(460\) −0.232503 −0.0108405
\(461\) 28.8028 1.34148 0.670740 0.741693i \(-0.265977\pi\)
0.670740 + 0.741693i \(0.265977\pi\)
\(462\) −3.90527 −0.181689
\(463\) −22.9216 −1.06526 −0.532630 0.846348i \(-0.678796\pi\)
−0.532630 + 0.846348i \(0.678796\pi\)
\(464\) −8.76972 −0.407124
\(465\) 2.73208 0.126697
\(466\) 1.81066 0.0838770
\(467\) 18.6223 0.861737 0.430868 0.902415i \(-0.358207\pi\)
0.430868 + 0.902415i \(0.358207\pi\)
\(468\) −8.89055 −0.410966
\(469\) −12.3078 −0.568322
\(470\) 0.838752 0.0386887
\(471\) 47.8633 2.20543
\(472\) 12.2458 0.563661
\(473\) −7.09033 −0.326014
\(474\) −50.4996 −2.31952
\(475\) −24.3765 −1.11847
\(476\) 0.368520 0.0168911
\(477\) −38.3054 −1.75389
\(478\) −23.7101 −1.08448
\(479\) 26.0559 1.19053 0.595263 0.803531i \(-0.297048\pi\)
0.595263 + 0.803531i \(0.297048\pi\)
\(480\) 1.33284 0.0608357
\(481\) 6.64163 0.302832
\(482\) 9.10904 0.414905
\(483\) −10.9182 −0.496795
\(484\) −0.701031 −0.0318651
\(485\) 0.316175 0.0143568
\(486\) −87.8835 −3.98647
\(487\) 3.78023 0.171298 0.0856492 0.996325i \(-0.472704\pi\)
0.0856492 + 0.996325i \(0.472704\pi\)
\(488\) 43.2540 1.95802
\(489\) −42.3766 −1.91634
\(490\) −0.710568 −0.0321002
\(491\) −0.00784829 −0.000354188 0 −0.000177094 1.00000i \(-0.500056\pi\)
−0.000177094 1.00000i \(0.500056\pi\)
\(492\) 10.2401 0.461658
\(493\) −2.17749 −0.0980693
\(494\) −8.18988 −0.368480
\(495\) −0.897527 −0.0403408
\(496\) 16.2183 0.728222
\(497\) 11.2787 0.505920
\(498\) −4.11216 −0.184270
\(499\) 26.3236 1.17840 0.589202 0.807986i \(-0.299442\pi\)
0.589202 + 0.807986i \(0.299442\pi\)
\(500\) −0.728882 −0.0325966
\(501\) 58.3462 2.60672
\(502\) −9.52356 −0.425057
\(503\) −40.9573 −1.82620 −0.913098 0.407740i \(-0.866317\pi\)
−0.913098 + 0.407740i \(0.866317\pi\)
\(504\) 26.6796 1.18840
\(505\) −1.33802 −0.0595411
\(506\) 3.63161 0.161445
\(507\) −36.9458 −1.64082
\(508\) 5.97778 0.265221
\(509\) 35.8740 1.59009 0.795043 0.606553i \(-0.207448\pi\)
0.795043 + 0.606553i \(0.207448\pi\)
\(510\) −0.211533 −0.00936686
\(511\) 7.96045 0.352150
\(512\) 20.8814 0.922838
\(513\) 93.6629 4.13532
\(514\) −10.7927 −0.476046
\(515\) 0.150293 0.00662269
\(516\) 16.9458 0.745998
\(517\) 7.07039 0.310956
\(518\) −5.17288 −0.227283
\(519\) 28.4232 1.24764
\(520\) −0.471253 −0.0206658
\(521\) 16.6857 0.731015 0.365507 0.930808i \(-0.380895\pi\)
0.365507 + 0.930808i \(0.380895\pi\)
\(522\) −40.9149 −1.79080
\(523\) −20.9358 −0.915459 −0.457730 0.889091i \(-0.651337\pi\)
−0.457730 + 0.889091i \(0.651337\pi\)
\(524\) 0.701031 0.0306247
\(525\) −17.0954 −0.746105
\(526\) −6.23755 −0.271970
\(527\) 4.02694 0.175416
\(528\) −7.18155 −0.312537
\(529\) −12.8469 −0.558560
\(530\) −0.526979 −0.0228905
\(531\) 34.3018 1.48857
\(532\) −3.44250 −0.149251
\(533\) −6.30147 −0.272947
\(534\) 37.4403 1.62020
\(535\) 0.118296 0.00511437
\(536\) −37.6979 −1.62830
\(537\) 24.1217 1.04093
\(538\) −4.30975 −0.185806
\(539\) −5.98985 −0.258001
\(540\) 1.39879 0.0601943
\(541\) −11.5182 −0.495204 −0.247602 0.968862i \(-0.579643\pi\)
−0.247602 + 0.968862i \(0.579643\pi\)
\(542\) 35.4499 1.52270
\(543\) 46.3836 1.99051
\(544\) 1.96454 0.0842289
\(545\) 1.17690 0.0504129
\(546\) −5.74362 −0.245804
\(547\) −11.6750 −0.499187 −0.249593 0.968351i \(-0.580297\pi\)
−0.249593 + 0.968351i \(0.580297\pi\)
\(548\) 13.6695 0.583931
\(549\) 121.159 5.17092
\(550\) 5.68627 0.242463
\(551\) 20.3409 0.866550
\(552\) −33.4416 −1.42337
\(553\) 13.0624 0.555470
\(554\) 1.41851 0.0602666
\(555\) −1.60247 −0.0680209
\(556\) 3.06288 0.129895
\(557\) 10.0985 0.427888 0.213944 0.976846i \(-0.431369\pi\)
0.213944 + 0.976846i \(0.431369\pi\)
\(558\) 75.6660 3.20320
\(559\) −10.4280 −0.441058
\(560\) 0.220365 0.00931214
\(561\) −1.78315 −0.0752849
\(562\) 6.83267 0.288219
\(563\) 44.3884 1.87075 0.935374 0.353660i \(-0.115063\pi\)
0.935374 + 0.353660i \(0.115063\pi\)
\(564\) −16.8982 −0.711541
\(565\) 1.33107 0.0559984
\(566\) 0.295008 0.0124001
\(567\) 39.6865 1.66668
\(568\) 34.5458 1.44951
\(569\) −40.5732 −1.70092 −0.850459 0.526042i \(-0.823675\pi\)
−0.850459 + 0.526042i \(0.823675\pi\)
\(570\) 1.97602 0.0827665
\(571\) 17.2145 0.720406 0.360203 0.932874i \(-0.382707\pi\)
0.360203 + 0.932874i \(0.382707\pi\)
\(572\) −1.03103 −0.0431096
\(573\) −83.4663 −3.48686
\(574\) 4.90794 0.204854
\(575\) 15.8975 0.662970
\(576\) 73.2420 3.05175
\(577\) 5.55353 0.231196 0.115598 0.993296i \(-0.463122\pi\)
0.115598 + 0.993296i \(0.463122\pi\)
\(578\) 19.0635 0.792937
\(579\) −79.1910 −3.29107
\(580\) 0.303776 0.0126136
\(581\) 1.06366 0.0441282
\(582\) 11.8031 0.489253
\(583\) −4.44226 −0.183980
\(584\) 24.3823 1.00894
\(585\) −1.32002 −0.0545763
\(586\) −20.7285 −0.856285
\(587\) −40.3244 −1.66437 −0.832184 0.554500i \(-0.812910\pi\)
−0.832184 + 0.554500i \(0.812910\pi\)
\(588\) 14.3157 0.590369
\(589\) −37.6174 −1.55000
\(590\) 0.471900 0.0194278
\(591\) −31.6394 −1.30147
\(592\) −9.51261 −0.390966
\(593\) −40.6926 −1.67104 −0.835521 0.549458i \(-0.814834\pi\)
−0.835521 + 0.549458i \(0.814834\pi\)
\(594\) −21.8486 −0.896458
\(595\) 0.0547160 0.00224314
\(596\) −3.58771 −0.146958
\(597\) −1.71723 −0.0702815
\(598\) 5.34114 0.218415
\(599\) −27.5848 −1.12708 −0.563541 0.826088i \(-0.690561\pi\)
−0.563541 + 0.826088i \(0.690561\pi\)
\(600\) −52.3619 −2.13767
\(601\) −34.1958 −1.39487 −0.697437 0.716646i \(-0.745676\pi\)
−0.697437 + 0.716646i \(0.745676\pi\)
\(602\) 8.12192 0.331025
\(603\) −105.595 −4.30018
\(604\) 2.53303 0.103067
\(605\) −0.104086 −0.00423168
\(606\) −49.9493 −2.02905
\(607\) 13.0452 0.529486 0.264743 0.964319i \(-0.414713\pi\)
0.264743 + 0.964319i \(0.414713\pi\)
\(608\) −18.3516 −0.744255
\(609\) 14.2652 0.578054
\(610\) 1.66681 0.0674873
\(611\) 10.3987 0.420686
\(612\) 3.16173 0.127805
\(613\) 31.6081 1.27664 0.638320 0.769771i \(-0.279630\pi\)
0.638320 + 0.769771i \(0.279630\pi\)
\(614\) 1.92529 0.0776983
\(615\) 1.52039 0.0613082
\(616\) 3.09401 0.124661
\(617\) 19.3884 0.780549 0.390274 0.920699i \(-0.372380\pi\)
0.390274 + 0.920699i \(0.372380\pi\)
\(618\) 5.61055 0.225689
\(619\) 15.3798 0.618165 0.309083 0.951035i \(-0.399978\pi\)
0.309083 + 0.951035i \(0.399978\pi\)
\(620\) −0.561788 −0.0225620
\(621\) −61.0835 −2.45119
\(622\) 34.4286 1.38046
\(623\) −9.68445 −0.387999
\(624\) −10.5622 −0.422825
\(625\) 24.8376 0.993504
\(626\) −10.0435 −0.401420
\(627\) 16.6572 0.665225
\(628\) −9.84197 −0.392737
\(629\) −2.36195 −0.0941770
\(630\) 1.02811 0.0409609
\(631\) −0.0436089 −0.00173604 −0.000868022 1.00000i \(-0.500276\pi\)
−0.000868022 1.00000i \(0.500276\pi\)
\(632\) 40.0091 1.59148
\(633\) −33.4012 −1.32758
\(634\) −6.99973 −0.277995
\(635\) 0.887550 0.0352213
\(636\) 10.6169 0.420989
\(637\) −8.80949 −0.349045
\(638\) −4.74488 −0.187852
\(639\) 96.7662 3.82801
\(640\) 0.225713 0.00892210
\(641\) −8.14772 −0.321816 −0.160908 0.986969i \(-0.551442\pi\)
−0.160908 + 0.986969i \(0.551442\pi\)
\(642\) 4.41607 0.174288
\(643\) 2.79586 0.110258 0.0551290 0.998479i \(-0.482443\pi\)
0.0551290 + 0.998479i \(0.482443\pi\)
\(644\) 2.24507 0.0884682
\(645\) 2.51603 0.0990686
\(646\) 2.91255 0.114593
\(647\) −33.0032 −1.29749 −0.648744 0.761006i \(-0.724706\pi\)
−0.648744 + 0.761006i \(0.724706\pi\)
\(648\) 121.557 4.77520
\(649\) 3.97795 0.156148
\(650\) 8.36300 0.328024
\(651\) −26.3813 −1.03396
\(652\) 8.71376 0.341257
\(653\) −5.02300 −0.196565 −0.0982826 0.995159i \(-0.531335\pi\)
−0.0982826 + 0.995159i \(0.531335\pi\)
\(654\) 43.9347 1.71798
\(655\) 0.104086 0.00406696
\(656\) 9.02541 0.352383
\(657\) 68.2970 2.66452
\(658\) −8.09908 −0.315735
\(659\) −45.3118 −1.76510 −0.882549 0.470221i \(-0.844174\pi\)
−0.882549 + 0.470221i \(0.844174\pi\)
\(660\) 0.248763 0.00968310
\(661\) 35.9507 1.39832 0.699160 0.714965i \(-0.253557\pi\)
0.699160 + 0.714965i \(0.253557\pi\)
\(662\) −13.5816 −0.527863
\(663\) −2.62255 −0.101851
\(664\) 3.25792 0.126432
\(665\) −0.511125 −0.0198206
\(666\) −44.3809 −1.71972
\(667\) −13.2656 −0.513644
\(668\) −11.9975 −0.464198
\(669\) −25.3227 −0.979031
\(670\) −1.45271 −0.0561230
\(671\) 14.0507 0.542420
\(672\) −12.8701 −0.496474
\(673\) −10.8923 −0.419869 −0.209934 0.977715i \(-0.567325\pi\)
−0.209934 + 0.977715i \(0.567325\pi\)
\(674\) 32.7228 1.26043
\(675\) −95.6427 −3.68129
\(676\) 7.59703 0.292194
\(677\) −23.9805 −0.921646 −0.460823 0.887492i \(-0.652446\pi\)
−0.460823 + 0.887492i \(0.652446\pi\)
\(678\) 49.6898 1.90833
\(679\) −3.05302 −0.117164
\(680\) 0.167591 0.00642681
\(681\) 71.6771 2.74667
\(682\) 8.77494 0.336010
\(683\) 5.82515 0.222893 0.111447 0.993770i \(-0.464452\pi\)
0.111447 + 0.993770i \(0.464452\pi\)
\(684\) −29.5351 −1.12930
\(685\) 2.02957 0.0775460
\(686\) 14.8798 0.568112
\(687\) −39.7119 −1.51510
\(688\) 14.9357 0.569419
\(689\) −6.53339 −0.248902
\(690\) −1.28869 −0.0490595
\(691\) 28.0781 1.06814 0.534070 0.845440i \(-0.320662\pi\)
0.534070 + 0.845440i \(0.320662\pi\)
\(692\) −5.84456 −0.222177
\(693\) 8.66662 0.329218
\(694\) 24.5731 0.932782
\(695\) 0.454761 0.0172501
\(696\) 43.6931 1.65618
\(697\) 2.24098 0.0848831
\(698\) 19.9648 0.755680
\(699\) −5.41620 −0.204860
\(700\) 3.51527 0.132865
\(701\) −32.4425 −1.22534 −0.612668 0.790341i \(-0.709904\pi\)
−0.612668 + 0.790341i \(0.709904\pi\)
\(702\) −32.1335 −1.21280
\(703\) 22.0640 0.832158
\(704\) 8.49383 0.320123
\(705\) −2.50895 −0.0944927
\(706\) −33.4357 −1.25837
\(707\) 12.9201 0.485909
\(708\) −9.50727 −0.357305
\(709\) −19.5920 −0.735795 −0.367897 0.929866i \(-0.619922\pi\)
−0.367897 + 0.929866i \(0.619922\pi\)
\(710\) 1.33124 0.0499606
\(711\) 112.069 4.20293
\(712\) −29.6627 −1.11166
\(713\) 24.5326 0.918754
\(714\) 2.04259 0.0764420
\(715\) −0.153082 −0.00572496
\(716\) −4.96006 −0.185366
\(717\) 70.9239 2.64870
\(718\) 13.7355 0.512604
\(719\) −13.5736 −0.506210 −0.253105 0.967439i \(-0.581452\pi\)
−0.253105 + 0.967439i \(0.581452\pi\)
\(720\) 1.89063 0.0704597
\(721\) −1.45124 −0.0540472
\(722\) −5.55264 −0.206648
\(723\) −27.2478 −1.01336
\(724\) −9.53768 −0.354465
\(725\) −20.7708 −0.771409
\(726\) −3.88560 −0.144208
\(727\) −16.9885 −0.630068 −0.315034 0.949080i \(-0.602016\pi\)
−0.315034 + 0.949080i \(0.602016\pi\)
\(728\) 4.55047 0.168652
\(729\) 144.425 5.34909
\(730\) 0.939582 0.0347755
\(731\) 3.70849 0.137163
\(732\) −33.5810 −1.24119
\(733\) −19.1559 −0.707538 −0.353769 0.935333i \(-0.615100\pi\)
−0.353769 + 0.935333i \(0.615100\pi\)
\(734\) 26.7726 0.988195
\(735\) 2.12552 0.0784010
\(736\) 11.9682 0.441154
\(737\) −12.2458 −0.451081
\(738\) 42.1079 1.55001
\(739\) 35.2345 1.29612 0.648061 0.761589i \(-0.275580\pi\)
0.648061 + 0.761589i \(0.275580\pi\)
\(740\) 0.329509 0.0121130
\(741\) 24.4983 0.899969
\(742\) 5.08857 0.186807
\(743\) 27.6287 1.01360 0.506799 0.862064i \(-0.330828\pi\)
0.506799 + 0.862064i \(0.330828\pi\)
\(744\) −80.8038 −2.96241
\(745\) −0.532685 −0.0195161
\(746\) 15.4745 0.566561
\(747\) 9.12575 0.333894
\(748\) 0.366664 0.0134066
\(749\) −1.14228 −0.0417379
\(750\) −4.03997 −0.147519
\(751\) −38.2670 −1.39638 −0.698191 0.715911i \(-0.746011\pi\)
−0.698191 + 0.715911i \(0.746011\pi\)
\(752\) −14.8937 −0.543119
\(753\) 28.4878 1.03815
\(754\) −6.97846 −0.254141
\(755\) 0.376091 0.0136874
\(756\) −13.5069 −0.491240
\(757\) −9.55929 −0.347438 −0.173719 0.984795i \(-0.555578\pi\)
−0.173719 + 0.984795i \(0.555578\pi\)
\(758\) 22.3501 0.811791
\(759\) −10.8632 −0.394310
\(760\) −1.56554 −0.0567880
\(761\) 24.1317 0.874775 0.437388 0.899273i \(-0.355904\pi\)
0.437388 + 0.899273i \(0.355904\pi\)
\(762\) 33.1329 1.20028
\(763\) −11.3643 −0.411415
\(764\) 17.1629 0.620931
\(765\) 0.469438 0.0169726
\(766\) 24.9932 0.903040
\(767\) 5.85052 0.211250
\(768\) −49.4891 −1.78578
\(769\) 1.54517 0.0557204 0.0278602 0.999612i \(-0.491131\pi\)
0.0278602 + 0.999612i \(0.491131\pi\)
\(770\) 0.119229 0.00429672
\(771\) 32.2841 1.16269
\(772\) 16.2838 0.586065
\(773\) 14.6467 0.526805 0.263403 0.964686i \(-0.415155\pi\)
0.263403 + 0.964686i \(0.415155\pi\)
\(774\) 69.6823 2.50468
\(775\) 38.4125 1.37982
\(776\) −9.35117 −0.335688
\(777\) 15.4736 0.555112
\(778\) 18.2452 0.654123
\(779\) −20.9339 −0.750036
\(780\) 0.365865 0.0131001
\(781\) 11.2219 0.401552
\(782\) −1.89946 −0.0679245
\(783\) 79.8086 2.85213
\(784\) 12.6176 0.450628
\(785\) −1.46129 −0.0521555
\(786\) 3.88560 0.138595
\(787\) −14.1284 −0.503624 −0.251812 0.967776i \(-0.581027\pi\)
−0.251812 + 0.967776i \(0.581027\pi\)
\(788\) 6.50590 0.231763
\(789\) 18.6584 0.664255
\(790\) 1.54177 0.0548538
\(791\) −12.8529 −0.456998
\(792\) 26.5452 0.943242
\(793\) 20.6648 0.733830
\(794\) −32.5206 −1.15411
\(795\) 1.57635 0.0559074
\(796\) 0.353108 0.0125156
\(797\) −9.00312 −0.318907 −0.159453 0.987205i \(-0.550973\pi\)
−0.159453 + 0.987205i \(0.550973\pi\)
\(798\) −19.0807 −0.675450
\(799\) −3.69806 −0.130828
\(800\) 18.7395 0.662541
\(801\) −83.0881 −2.93577
\(802\) −39.3492 −1.38947
\(803\) 7.92036 0.279503
\(804\) 29.2674 1.03218
\(805\) 0.333337 0.0117486
\(806\) 12.9056 0.454581
\(807\) 12.8917 0.453810
\(808\) 39.5731 1.39218
\(809\) −15.5861 −0.547977 −0.273989 0.961733i \(-0.588343\pi\)
−0.273989 + 0.961733i \(0.588343\pi\)
\(810\) 4.68425 0.164588
\(811\) 52.0440 1.82751 0.913756 0.406262i \(-0.133168\pi\)
0.913756 + 0.406262i \(0.133168\pi\)
\(812\) −2.93330 −0.102939
\(813\) −106.041 −3.71902
\(814\) −5.14682 −0.180396
\(815\) 1.29377 0.0453189
\(816\) 3.75620 0.131493
\(817\) −34.6426 −1.21199
\(818\) −2.14813 −0.0751077
\(819\) 12.7463 0.445392
\(820\) −0.312633 −0.0109176
\(821\) 34.8413 1.21597 0.607986 0.793948i \(-0.291978\pi\)
0.607986 + 0.793948i \(0.291978\pi\)
\(822\) 75.7656 2.64263
\(823\) 46.1931 1.61019 0.805094 0.593147i \(-0.202115\pi\)
0.805094 + 0.593147i \(0.202115\pi\)
\(824\) −4.44505 −0.154851
\(825\) −17.0093 −0.592188
\(826\) −4.55672 −0.158548
\(827\) 42.6018 1.48141 0.740705 0.671830i \(-0.234492\pi\)
0.740705 + 0.671830i \(0.234492\pi\)
\(828\) 19.2617 0.669389
\(829\) −0.217175 −0.00754282 −0.00377141 0.999993i \(-0.501200\pi\)
−0.00377141 + 0.999993i \(0.501200\pi\)
\(830\) 0.125546 0.00435775
\(831\) −4.24317 −0.147194
\(832\) 12.4922 0.433088
\(833\) 3.13290 0.108549
\(834\) 16.9766 0.587851
\(835\) −1.78133 −0.0616456
\(836\) −3.42516 −0.118462
\(837\) −147.594 −5.10159
\(838\) 23.7149 0.819218
\(839\) 31.2991 1.08057 0.540283 0.841483i \(-0.318317\pi\)
0.540283 + 0.841483i \(0.318317\pi\)
\(840\) −1.09792 −0.0378819
\(841\) −11.6679 −0.402341
\(842\) 13.4332 0.462940
\(843\) −20.4385 −0.703940
\(844\) 6.86817 0.236412
\(845\) 1.12797 0.0388033
\(846\) −69.4864 −2.38899
\(847\) 1.00506 0.0345343
\(848\) 9.35758 0.321341
\(849\) −0.882457 −0.0302858
\(850\) −2.97412 −0.102011
\(851\) −14.3893 −0.493259
\(852\) −26.8202 −0.918846
\(853\) 6.56028 0.224620 0.112310 0.993673i \(-0.464175\pi\)
0.112310 + 0.993673i \(0.464175\pi\)
\(854\) −16.0949 −0.550758
\(855\) −4.38522 −0.149971
\(856\) −3.49871 −0.119583
\(857\) 26.9210 0.919604 0.459802 0.888021i \(-0.347920\pi\)
0.459802 + 0.888021i \(0.347920\pi\)
\(858\) −5.71469 −0.195096
\(859\) 15.3834 0.524874 0.262437 0.964949i \(-0.415474\pi\)
0.262437 + 0.964949i \(0.415474\pi\)
\(860\) −0.517362 −0.0176419
\(861\) −14.6811 −0.500330
\(862\) −15.6313 −0.532405
\(863\) −35.3756 −1.20420 −0.602101 0.798420i \(-0.705669\pi\)
−0.602101 + 0.798420i \(0.705669\pi\)
\(864\) −72.0035 −2.44961
\(865\) −0.867771 −0.0295051
\(866\) 33.8639 1.15074
\(867\) −57.0245 −1.93666
\(868\) 5.42469 0.184126
\(869\) 12.9966 0.440880
\(870\) 1.68374 0.0570840
\(871\) −18.0104 −0.610258
\(872\) −34.8079 −1.17875
\(873\) −26.1935 −0.886516
\(874\) 17.7436 0.600188
\(875\) 1.04499 0.0353272
\(876\) −18.9296 −0.639571
\(877\) −10.1993 −0.344405 −0.172203 0.985062i \(-0.555088\pi\)
−0.172203 + 0.985062i \(0.555088\pi\)
\(878\) 27.9473 0.943177
\(879\) 62.0049 2.09137
\(880\) 0.219256 0.00739110
\(881\) 1.40982 0.0474981 0.0237491 0.999718i \(-0.492440\pi\)
0.0237491 + 0.999718i \(0.492440\pi\)
\(882\) 58.8670 1.98216
\(883\) 29.2312 0.983707 0.491853 0.870678i \(-0.336320\pi\)
0.491853 + 0.870678i \(0.336320\pi\)
\(884\) 0.539265 0.0181375
\(885\) −1.41159 −0.0474501
\(886\) −24.4787 −0.822379
\(887\) 20.9929 0.704874 0.352437 0.935836i \(-0.385353\pi\)
0.352437 + 0.935836i \(0.385353\pi\)
\(888\) 47.3944 1.59045
\(889\) −8.57028 −0.287438
\(890\) −1.14307 −0.0383157
\(891\) 39.4866 1.32285
\(892\) 5.20701 0.174344
\(893\) 34.5452 1.15601
\(894\) −19.8856 −0.665073
\(895\) −0.736444 −0.0246166
\(896\) −2.17951 −0.0728124
\(897\) −15.9769 −0.533453
\(898\) −0.933122 −0.0311387
\(899\) −32.0531 −1.06903
\(900\) 30.1594 1.00531
\(901\) 2.32346 0.0774055
\(902\) 4.88322 0.162594
\(903\) −24.2951 −0.808489
\(904\) −39.3676 −1.30935
\(905\) −1.41611 −0.0470730
\(906\) 14.0398 0.466440
\(907\) 52.9372 1.75775 0.878876 0.477050i \(-0.158294\pi\)
0.878876 + 0.477050i \(0.158294\pi\)
\(908\) −14.7387 −0.489121
\(909\) 110.848 3.67660
\(910\) 0.175355 0.00581295
\(911\) 13.8224 0.457957 0.228978 0.973431i \(-0.426461\pi\)
0.228978 + 0.973431i \(0.426461\pi\)
\(912\) −35.0883 −1.16189
\(913\) 1.05831 0.0350249
\(914\) −44.6014 −1.47528
\(915\) −4.98593 −0.164830
\(916\) 8.16582 0.269806
\(917\) −1.00506 −0.0331901
\(918\) 11.4276 0.377166
\(919\) 52.0476 1.71689 0.858446 0.512904i \(-0.171430\pi\)
0.858446 + 0.512904i \(0.171430\pi\)
\(920\) 1.02098 0.0336609
\(921\) −5.75911 −0.189769
\(922\) −32.8272 −1.08111
\(923\) 16.5045 0.543251
\(924\) −2.40209 −0.0790229
\(925\) −22.5303 −0.740793
\(926\) 26.1243 0.858499
\(927\) −12.4510 −0.408945
\(928\) −15.6371 −0.513312
\(929\) −19.0920 −0.626389 −0.313195 0.949689i \(-0.601399\pi\)
−0.313195 + 0.949689i \(0.601399\pi\)
\(930\) −3.11382 −0.102106
\(931\) −29.2657 −0.959146
\(932\) 1.11371 0.0364809
\(933\) −102.986 −3.37162
\(934\) −21.2243 −0.694479
\(935\) 0.0544404 0.00178039
\(936\) 39.0409 1.27609
\(937\) 2.45217 0.0801087 0.0400544 0.999198i \(-0.487247\pi\)
0.0400544 + 0.999198i \(0.487247\pi\)
\(938\) 14.0275 0.458014
\(939\) 30.0432 0.980422
\(940\) 0.515907 0.0168270
\(941\) 3.38460 0.110335 0.0551674 0.998477i \(-0.482431\pi\)
0.0551674 + 0.998477i \(0.482431\pi\)
\(942\) −54.5509 −1.77737
\(943\) 13.6523 0.444581
\(944\) −8.37953 −0.272730
\(945\) −2.00543 −0.0652366
\(946\) 8.08101 0.262736
\(947\) 20.4572 0.664769 0.332385 0.943144i \(-0.392147\pi\)
0.332385 + 0.943144i \(0.392147\pi\)
\(948\) −31.0618 −1.00884
\(949\) 11.6488 0.378135
\(950\) 27.7825 0.901383
\(951\) 20.9382 0.678969
\(952\) −1.61828 −0.0524486
\(953\) −20.7523 −0.672234 −0.336117 0.941820i \(-0.609114\pi\)
−0.336117 + 0.941820i \(0.609114\pi\)
\(954\) 43.6576 1.41347
\(955\) 2.54826 0.0824597
\(956\) −14.5838 −0.471675
\(957\) 14.1933 0.458805
\(958\) −29.6966 −0.959452
\(959\) −19.5978 −0.632846
\(960\) −3.01406 −0.0972785
\(961\) 28.2774 0.912174
\(962\) −7.56962 −0.244054
\(963\) −9.80020 −0.315807
\(964\) 5.60287 0.180456
\(965\) 2.41773 0.0778295
\(966\) 12.4437 0.400370
\(967\) −39.7338 −1.27775 −0.638877 0.769309i \(-0.720601\pi\)
−0.638877 + 0.769309i \(0.720601\pi\)
\(968\) 3.07843 0.0989444
\(969\) −8.71230 −0.279879
\(970\) −0.360352 −0.0115702
\(971\) 1.99217 0.0639318 0.0319659 0.999489i \(-0.489823\pi\)
0.0319659 + 0.999489i \(0.489823\pi\)
\(972\) −54.0562 −1.73385
\(973\) −4.39122 −0.140776
\(974\) −4.30841 −0.138050
\(975\) −25.0162 −0.801159
\(976\) −29.5976 −0.947397
\(977\) 14.1309 0.452086 0.226043 0.974117i \(-0.427421\pi\)
0.226043 + 0.974117i \(0.427421\pi\)
\(978\) 48.2976 1.54439
\(979\) −9.63567 −0.307957
\(980\) −0.437063 −0.0139615
\(981\) −97.5003 −3.11295
\(982\) 0.00894488 0.000285443 0
\(983\) −4.82055 −0.153752 −0.0768758 0.997041i \(-0.524494\pi\)
−0.0768758 + 0.997041i \(0.524494\pi\)
\(984\) −44.9671 −1.43350
\(985\) 0.965964 0.0307782
\(986\) 2.48174 0.0790346
\(987\) 24.2267 0.771146
\(988\) −5.03751 −0.160264
\(989\) 22.5926 0.718403
\(990\) 1.02293 0.0325109
\(991\) 44.8116 1.42349 0.711744 0.702439i \(-0.247906\pi\)
0.711744 + 0.702439i \(0.247906\pi\)
\(992\) 28.9184 0.918161
\(993\) 40.6265 1.28924
\(994\) −12.8546 −0.407724
\(995\) 0.0524276 0.00166207
\(996\) −2.52934 −0.0801453
\(997\) 30.0396 0.951364 0.475682 0.879617i \(-0.342201\pi\)
0.475682 + 0.879617i \(0.342201\pi\)
\(998\) −30.0016 −0.949683
\(999\) 86.5693 2.73893
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 1441.2.a.e.1.7 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1441.2.a.e.1.7 28 1.1 even 1 trivial