Properties

Label 6014.2.a.i.1.11
Level $6014$
Weight $2$
Character 6014.1
Self dual yes
Analytic conductor $48.022$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6014,2,Mod(1,6014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6014, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6014.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6014 = 2 \cdot 31 \cdot 97 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6014.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(48.0220317756\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) \(=\) 6014.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -0.492368 q^{3} +1.00000 q^{4} -0.547220 q^{5} -0.492368 q^{6} +4.87929 q^{7} +1.00000 q^{8} -2.75757 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -0.492368 q^{3} +1.00000 q^{4} -0.547220 q^{5} -0.492368 q^{6} +4.87929 q^{7} +1.00000 q^{8} -2.75757 q^{9} -0.547220 q^{10} -1.69298 q^{11} -0.492368 q^{12} -3.38537 q^{13} +4.87929 q^{14} +0.269434 q^{15} +1.00000 q^{16} -3.46765 q^{17} -2.75757 q^{18} -3.29297 q^{19} -0.547220 q^{20} -2.40241 q^{21} -1.69298 q^{22} +6.12734 q^{23} -0.492368 q^{24} -4.70055 q^{25} -3.38537 q^{26} +2.83485 q^{27} +4.87929 q^{28} +3.87968 q^{29} +0.269434 q^{30} -1.00000 q^{31} +1.00000 q^{32} +0.833572 q^{33} -3.46765 q^{34} -2.67005 q^{35} -2.75757 q^{36} +3.70114 q^{37} -3.29297 q^{38} +1.66685 q^{39} -0.547220 q^{40} +4.48593 q^{41} -2.40241 q^{42} +5.13533 q^{43} -1.69298 q^{44} +1.50900 q^{45} +6.12734 q^{46} +1.82777 q^{47} -0.492368 q^{48} +16.8075 q^{49} -4.70055 q^{50} +1.70736 q^{51} -3.38537 q^{52} +12.1557 q^{53} +2.83485 q^{54} +0.926435 q^{55} +4.87929 q^{56} +1.62135 q^{57} +3.87968 q^{58} +2.18113 q^{59} +0.269434 q^{60} +9.59850 q^{61} -1.00000 q^{62} -13.4550 q^{63} +1.00000 q^{64} +1.85254 q^{65} +0.833572 q^{66} +13.3781 q^{67} -3.46765 q^{68} -3.01691 q^{69} -2.67005 q^{70} +6.24843 q^{71} -2.75757 q^{72} +6.47204 q^{73} +3.70114 q^{74} +2.31440 q^{75} -3.29297 q^{76} -8.26056 q^{77} +1.66685 q^{78} -4.26535 q^{79} -0.547220 q^{80} +6.87693 q^{81} +4.48593 q^{82} -3.67643 q^{83} -2.40241 q^{84} +1.89757 q^{85} +5.13533 q^{86} -1.91023 q^{87} -1.69298 q^{88} +14.3678 q^{89} +1.50900 q^{90} -16.5182 q^{91} +6.12734 q^{92} +0.492368 q^{93} +1.82777 q^{94} +1.80198 q^{95} -0.492368 q^{96} -1.00000 q^{97} +16.8075 q^{98} +4.66853 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9} + 10 q^{10} + 12 q^{11} + 12 q^{12} + 20 q^{13} + 13 q^{14} + 19 q^{15} + 28 q^{16} - 4 q^{17} + 38 q^{18} + 35 q^{19} + 10 q^{20} + 30 q^{21} + 12 q^{22} + 20 q^{23} + 12 q^{24} + 46 q^{25} + 20 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 19 q^{30} - 28 q^{31} + 28 q^{32} + 12 q^{33} - 4 q^{34} + 36 q^{35} + 38 q^{36} + 11 q^{37} + 35 q^{38} - 4 q^{39} + 10 q^{40} - 5 q^{41} + 30 q^{42} + 43 q^{43} + 12 q^{44} + 11 q^{45} + 20 q^{46} + 18 q^{47} + 12 q^{48} + 99 q^{49} + 46 q^{50} - 43 q^{51} + 20 q^{52} + 11 q^{53} + 39 q^{54} + 66 q^{55} + 13 q^{56} - 15 q^{57} + 5 q^{58} + 34 q^{59} + 19 q^{60} + 66 q^{61} - 28 q^{62} + 65 q^{63} + 28 q^{64} - 16 q^{65} + 12 q^{66} + 5 q^{67} - 4 q^{68} - 33 q^{69} + 36 q^{70} + 25 q^{71} + 38 q^{72} - 9 q^{73} + 11 q^{74} + 92 q^{75} + 35 q^{76} + 4 q^{77} - 4 q^{78} + 15 q^{79} + 10 q^{80} - 5 q^{82} - 12 q^{83} + 30 q^{84} + 88 q^{85} + 43 q^{86} + 31 q^{87} + 12 q^{88} + 8 q^{89} + 11 q^{90} + 34 q^{91} + 20 q^{92} - 12 q^{93} + 18 q^{94} + 32 q^{95} + 12 q^{96} - 28 q^{97} + 99 q^{98} + 51 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −0.492368 −0.284269 −0.142135 0.989847i \(-0.545397\pi\)
−0.142135 + 0.989847i \(0.545397\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.547220 −0.244724 −0.122362 0.992486i \(-0.539047\pi\)
−0.122362 + 0.992486i \(0.539047\pi\)
\(6\) −0.492368 −0.201009
\(7\) 4.87929 1.84420 0.922099 0.386953i \(-0.126472\pi\)
0.922099 + 0.386953i \(0.126472\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.75757 −0.919191
\(10\) −0.547220 −0.173046
\(11\) −1.69298 −0.510454 −0.255227 0.966881i \(-0.582150\pi\)
−0.255227 + 0.966881i \(0.582150\pi\)
\(12\) −0.492368 −0.142135
\(13\) −3.38537 −0.938932 −0.469466 0.882951i \(-0.655553\pi\)
−0.469466 + 0.882951i \(0.655553\pi\)
\(14\) 4.87929 1.30405
\(15\) 0.269434 0.0695676
\(16\) 1.00000 0.250000
\(17\) −3.46765 −0.841030 −0.420515 0.907286i \(-0.638151\pi\)
−0.420515 + 0.907286i \(0.638151\pi\)
\(18\) −2.75757 −0.649966
\(19\) −3.29297 −0.755459 −0.377729 0.925916i \(-0.623295\pi\)
−0.377729 + 0.925916i \(0.623295\pi\)
\(20\) −0.547220 −0.122362
\(21\) −2.40241 −0.524249
\(22\) −1.69298 −0.360945
\(23\) 6.12734 1.27764 0.638819 0.769357i \(-0.279423\pi\)
0.638819 + 0.769357i \(0.279423\pi\)
\(24\) −0.492368 −0.100504
\(25\) −4.70055 −0.940110
\(26\) −3.38537 −0.663925
\(27\) 2.83485 0.545567
\(28\) 4.87929 0.922099
\(29\) 3.87968 0.720438 0.360219 0.932868i \(-0.382702\pi\)
0.360219 + 0.932868i \(0.382702\pi\)
\(30\) 0.269434 0.0491917
\(31\) −1.00000 −0.179605
\(32\) 1.00000 0.176777
\(33\) 0.833572 0.145106
\(34\) −3.46765 −0.594698
\(35\) −2.67005 −0.451320
\(36\) −2.75757 −0.459596
\(37\) 3.70114 0.608463 0.304231 0.952598i \(-0.401600\pi\)
0.304231 + 0.952598i \(0.401600\pi\)
\(38\) −3.29297 −0.534190
\(39\) 1.66685 0.266909
\(40\) −0.547220 −0.0865231
\(41\) 4.48593 0.700584 0.350292 0.936640i \(-0.386082\pi\)
0.350292 + 0.936640i \(0.386082\pi\)
\(42\) −2.40241 −0.370700
\(43\) 5.13533 0.783130 0.391565 0.920150i \(-0.371934\pi\)
0.391565 + 0.920150i \(0.371934\pi\)
\(44\) −1.69298 −0.255227
\(45\) 1.50900 0.224948
\(46\) 6.12734 0.903427
\(47\) 1.82777 0.266607 0.133303 0.991075i \(-0.457441\pi\)
0.133303 + 0.991075i \(0.457441\pi\)
\(48\) −0.492368 −0.0710673
\(49\) 16.8075 2.40107
\(50\) −4.70055 −0.664758
\(51\) 1.70736 0.239079
\(52\) −3.38537 −0.469466
\(53\) 12.1557 1.66971 0.834857 0.550468i \(-0.185551\pi\)
0.834857 + 0.550468i \(0.185551\pi\)
\(54\) 2.83485 0.385774
\(55\) 0.926435 0.124920
\(56\) 4.87929 0.652023
\(57\) 1.62135 0.214754
\(58\) 3.87968 0.509426
\(59\) 2.18113 0.283959 0.141980 0.989870i \(-0.454653\pi\)
0.141980 + 0.989870i \(0.454653\pi\)
\(60\) 0.269434 0.0347838
\(61\) 9.59850 1.22896 0.614481 0.788931i \(-0.289365\pi\)
0.614481 + 0.788931i \(0.289365\pi\)
\(62\) −1.00000 −0.127000
\(63\) −13.4550 −1.69517
\(64\) 1.00000 0.125000
\(65\) 1.85254 0.229779
\(66\) 0.833572 0.102606
\(67\) 13.3781 1.63440 0.817198 0.576356i \(-0.195526\pi\)
0.817198 + 0.576356i \(0.195526\pi\)
\(68\) −3.46765 −0.420515
\(69\) −3.01691 −0.363193
\(70\) −2.67005 −0.319132
\(71\) 6.24843 0.741552 0.370776 0.928722i \(-0.379092\pi\)
0.370776 + 0.928722i \(0.379092\pi\)
\(72\) −2.75757 −0.324983
\(73\) 6.47204 0.757496 0.378748 0.925500i \(-0.376355\pi\)
0.378748 + 0.925500i \(0.376355\pi\)
\(74\) 3.70114 0.430248
\(75\) 2.31440 0.267244
\(76\) −3.29297 −0.377729
\(77\) −8.26056 −0.941378
\(78\) 1.66685 0.188733
\(79\) −4.26535 −0.479889 −0.239945 0.970787i \(-0.577129\pi\)
−0.239945 + 0.970787i \(0.577129\pi\)
\(80\) −0.547220 −0.0611811
\(81\) 6.87693 0.764103
\(82\) 4.48593 0.495388
\(83\) −3.67643 −0.403541 −0.201770 0.979433i \(-0.564670\pi\)
−0.201770 + 0.979433i \(0.564670\pi\)
\(84\) −2.40241 −0.262124
\(85\) 1.89757 0.205820
\(86\) 5.13533 0.553757
\(87\) −1.91023 −0.204798
\(88\) −1.69298 −0.180473
\(89\) 14.3678 1.52298 0.761490 0.648177i \(-0.224468\pi\)
0.761490 + 0.648177i \(0.224468\pi\)
\(90\) 1.50900 0.159063
\(91\) −16.5182 −1.73158
\(92\) 6.12734 0.638819
\(93\) 0.492368 0.0510562
\(94\) 1.82777 0.188520
\(95\) 1.80198 0.184879
\(96\) −0.492368 −0.0502521
\(97\) −1.00000 −0.101535
\(98\) 16.8075 1.69781
\(99\) 4.66853 0.469205
\(100\) −4.70055 −0.470055
\(101\) 1.89529 0.188589 0.0942944 0.995544i \(-0.469941\pi\)
0.0942944 + 0.995544i \(0.469941\pi\)
\(102\) 1.70736 0.169054
\(103\) 11.1729 1.10090 0.550448 0.834869i \(-0.314457\pi\)
0.550448 + 0.834869i \(0.314457\pi\)
\(104\) −3.38537 −0.331962
\(105\) 1.31465 0.128296
\(106\) 12.1557 1.18067
\(107\) −12.0847 −1.16828 −0.584138 0.811655i \(-0.698567\pi\)
−0.584138 + 0.811655i \(0.698567\pi\)
\(108\) 2.83485 0.272783
\(109\) −10.3866 −0.994854 −0.497427 0.867506i \(-0.665722\pi\)
−0.497427 + 0.867506i \(0.665722\pi\)
\(110\) 0.926435 0.0883321
\(111\) −1.82232 −0.172967
\(112\) 4.87929 0.461050
\(113\) −12.4005 −1.16654 −0.583269 0.812279i \(-0.698227\pi\)
−0.583269 + 0.812279i \(0.698227\pi\)
\(114\) 1.62135 0.151854
\(115\) −3.35300 −0.312669
\(116\) 3.87968 0.360219
\(117\) 9.33540 0.863058
\(118\) 2.18113 0.200790
\(119\) −16.9197 −1.55103
\(120\) 0.269434 0.0245958
\(121\) −8.13381 −0.739437
\(122\) 9.59850 0.869008
\(123\) −2.20873 −0.199154
\(124\) −1.00000 −0.0898027
\(125\) 5.30834 0.474792
\(126\) −13.4550 −1.19867
\(127\) 10.7595 0.954752 0.477376 0.878699i \(-0.341588\pi\)
0.477376 + 0.878699i \(0.341588\pi\)
\(128\) 1.00000 0.0883883
\(129\) −2.52847 −0.222620
\(130\) 1.85254 0.162479
\(131\) 2.16298 0.188981 0.0944904 0.995526i \(-0.469878\pi\)
0.0944904 + 0.995526i \(0.469878\pi\)
\(132\) 0.833572 0.0725531
\(133\) −16.0674 −1.39322
\(134\) 13.3781 1.15569
\(135\) −1.55129 −0.133513
\(136\) −3.46765 −0.297349
\(137\) −21.6698 −1.85138 −0.925688 0.378287i \(-0.876513\pi\)
−0.925688 + 0.378287i \(0.876513\pi\)
\(138\) −3.01691 −0.256816
\(139\) 14.8221 1.25719 0.628596 0.777732i \(-0.283630\pi\)
0.628596 + 0.777732i \(0.283630\pi\)
\(140\) −2.67005 −0.225660
\(141\) −0.899934 −0.0757881
\(142\) 6.24843 0.524356
\(143\) 5.73137 0.479281
\(144\) −2.75757 −0.229798
\(145\) −2.12304 −0.176309
\(146\) 6.47204 0.535630
\(147\) −8.27548 −0.682550
\(148\) 3.70114 0.304231
\(149\) 4.82747 0.395482 0.197741 0.980254i \(-0.436640\pi\)
0.197741 + 0.980254i \(0.436640\pi\)
\(150\) 2.31440 0.188970
\(151\) −11.1519 −0.907530 −0.453765 0.891121i \(-0.649919\pi\)
−0.453765 + 0.891121i \(0.649919\pi\)
\(152\) −3.29297 −0.267095
\(153\) 9.56231 0.773067
\(154\) −8.26056 −0.665655
\(155\) 0.547220 0.0439538
\(156\) 1.66685 0.133455
\(157\) 23.1586 1.84826 0.924129 0.382080i \(-0.124792\pi\)
0.924129 + 0.382080i \(0.124792\pi\)
\(158\) −4.26535 −0.339333
\(159\) −5.98508 −0.474648
\(160\) −0.547220 −0.0432616
\(161\) 29.8971 2.35622
\(162\) 6.87693 0.540303
\(163\) −5.17824 −0.405591 −0.202796 0.979221i \(-0.565003\pi\)
−0.202796 + 0.979221i \(0.565003\pi\)
\(164\) 4.48593 0.350292
\(165\) −0.456147 −0.0355110
\(166\) −3.67643 −0.285347
\(167\) −4.22756 −0.327138 −0.163569 0.986532i \(-0.552301\pi\)
−0.163569 + 0.986532i \(0.552301\pi\)
\(168\) −2.40241 −0.185350
\(169\) −1.53930 −0.118407
\(170\) 1.89757 0.145537
\(171\) 9.08060 0.694411
\(172\) 5.13533 0.391565
\(173\) 13.8562 1.05347 0.526735 0.850030i \(-0.323416\pi\)
0.526735 + 0.850030i \(0.323416\pi\)
\(174\) −1.91023 −0.144814
\(175\) −22.9354 −1.73375
\(176\) −1.69298 −0.127613
\(177\) −1.07392 −0.0807208
\(178\) 14.3678 1.07691
\(179\) −9.02751 −0.674748 −0.337374 0.941371i \(-0.609539\pi\)
−0.337374 + 0.941371i \(0.609539\pi\)
\(180\) 1.50900 0.112474
\(181\) 6.06735 0.450983 0.225491 0.974245i \(-0.427601\pi\)
0.225491 + 0.974245i \(0.427601\pi\)
\(182\) −16.5182 −1.22441
\(183\) −4.72600 −0.349356
\(184\) 6.12734 0.451713
\(185\) −2.02534 −0.148906
\(186\) 0.492368 0.0361022
\(187\) 5.87068 0.429307
\(188\) 1.82777 0.133303
\(189\) 13.8320 1.00613
\(190\) 1.80198 0.130729
\(191\) −15.5144 −1.12258 −0.561290 0.827619i \(-0.689695\pi\)
−0.561290 + 0.827619i \(0.689695\pi\)
\(192\) −0.492368 −0.0355336
\(193\) 20.3696 1.46624 0.733120 0.680100i \(-0.238064\pi\)
0.733120 + 0.680100i \(0.238064\pi\)
\(194\) −1.00000 −0.0717958
\(195\) −0.912133 −0.0653192
\(196\) 16.8075 1.20053
\(197\) −1.04076 −0.0741509 −0.0370755 0.999312i \(-0.511804\pi\)
−0.0370755 + 0.999312i \(0.511804\pi\)
\(198\) 4.66853 0.331778
\(199\) −13.3436 −0.945903 −0.472951 0.881089i \(-0.656811\pi\)
−0.472951 + 0.881089i \(0.656811\pi\)
\(200\) −4.70055 −0.332379
\(201\) −6.58696 −0.464608
\(202\) 1.89529 0.133352
\(203\) 18.9301 1.32863
\(204\) 1.70736 0.119539
\(205\) −2.45479 −0.171450
\(206\) 11.1729 0.778451
\(207\) −16.8966 −1.17439
\(208\) −3.38537 −0.234733
\(209\) 5.57494 0.385627
\(210\) 1.31465 0.0907193
\(211\) −10.8417 −0.746372 −0.373186 0.927757i \(-0.621735\pi\)
−0.373186 + 0.927757i \(0.621735\pi\)
\(212\) 12.1557 0.834857
\(213\) −3.07653 −0.210800
\(214\) −12.0847 −0.826095
\(215\) −2.81016 −0.191651
\(216\) 2.83485 0.192887
\(217\) −4.87929 −0.331228
\(218\) −10.3866 −0.703468
\(219\) −3.18663 −0.215333
\(220\) 0.926435 0.0624602
\(221\) 11.7393 0.789669
\(222\) −1.82232 −0.122306
\(223\) −9.29209 −0.622244 −0.311122 0.950370i \(-0.600705\pi\)
−0.311122 + 0.950370i \(0.600705\pi\)
\(224\) 4.87929 0.326011
\(225\) 12.9621 0.864141
\(226\) −12.4005 −0.824867
\(227\) −5.03824 −0.334400 −0.167200 0.985923i \(-0.553472\pi\)
−0.167200 + 0.985923i \(0.553472\pi\)
\(228\) 1.62135 0.107377
\(229\) 12.8339 0.848089 0.424044 0.905641i \(-0.360610\pi\)
0.424044 + 0.905641i \(0.360610\pi\)
\(230\) −3.35300 −0.221090
\(231\) 4.06724 0.267605
\(232\) 3.87968 0.254713
\(233\) −20.6255 −1.35122 −0.675611 0.737259i \(-0.736120\pi\)
−0.675611 + 0.737259i \(0.736120\pi\)
\(234\) 9.33540 0.610274
\(235\) −1.00019 −0.0652452
\(236\) 2.18113 0.141980
\(237\) 2.10012 0.136418
\(238\) −16.9197 −1.09674
\(239\) −10.7351 −0.694397 −0.347199 0.937792i \(-0.612867\pi\)
−0.347199 + 0.937792i \(0.612867\pi\)
\(240\) 0.269434 0.0173919
\(241\) −10.0980 −0.650472 −0.325236 0.945633i \(-0.605444\pi\)
−0.325236 + 0.945633i \(0.605444\pi\)
\(242\) −8.13381 −0.522861
\(243\) −11.8905 −0.762778
\(244\) 9.59850 0.614481
\(245\) −9.19740 −0.587600
\(246\) −2.20873 −0.140823
\(247\) 11.1479 0.709324
\(248\) −1.00000 −0.0635001
\(249\) 1.81016 0.114714
\(250\) 5.30834 0.335729
\(251\) −13.4245 −0.847350 −0.423675 0.905814i \(-0.639260\pi\)
−0.423675 + 0.905814i \(0.639260\pi\)
\(252\) −13.4550 −0.847586
\(253\) −10.3735 −0.652175
\(254\) 10.7595 0.675111
\(255\) −0.934304 −0.0585084
\(256\) 1.00000 0.0625000
\(257\) 11.8995 0.742271 0.371136 0.928579i \(-0.378969\pi\)
0.371136 + 0.928579i \(0.378969\pi\)
\(258\) −2.52847 −0.157416
\(259\) 18.0589 1.12213
\(260\) 1.85254 0.114890
\(261\) −10.6985 −0.662220
\(262\) 2.16298 0.133630
\(263\) 18.3943 1.13424 0.567120 0.823635i \(-0.308058\pi\)
0.567120 + 0.823635i \(0.308058\pi\)
\(264\) 0.833572 0.0513028
\(265\) −6.65184 −0.408619
\(266\) −16.0674 −0.985153
\(267\) −7.07423 −0.432936
\(268\) 13.3781 0.817198
\(269\) 27.6715 1.68716 0.843580 0.537004i \(-0.180444\pi\)
0.843580 + 0.537004i \(0.180444\pi\)
\(270\) −1.55129 −0.0944083
\(271\) −31.8892 −1.93713 −0.968565 0.248760i \(-0.919977\pi\)
−0.968565 + 0.248760i \(0.919977\pi\)
\(272\) −3.46765 −0.210257
\(273\) 8.13303 0.492234
\(274\) −21.6698 −1.30912
\(275\) 7.95795 0.479883
\(276\) −3.01691 −0.181597
\(277\) −8.16520 −0.490599 −0.245300 0.969447i \(-0.578886\pi\)
−0.245300 + 0.969447i \(0.578886\pi\)
\(278\) 14.8221 0.888969
\(279\) 2.75757 0.165092
\(280\) −2.67005 −0.159566
\(281\) 22.0398 1.31479 0.657393 0.753548i \(-0.271659\pi\)
0.657393 + 0.753548i \(0.271659\pi\)
\(282\) −0.899934 −0.0535903
\(283\) 22.4232 1.33292 0.666461 0.745540i \(-0.267808\pi\)
0.666461 + 0.745540i \(0.267808\pi\)
\(284\) 6.24843 0.370776
\(285\) −0.887238 −0.0525554
\(286\) 5.73137 0.338903
\(287\) 21.8882 1.29202
\(288\) −2.75757 −0.162492
\(289\) −4.97537 −0.292669
\(290\) −2.12304 −0.124669
\(291\) 0.492368 0.0288631
\(292\) 6.47204 0.378748
\(293\) −4.82842 −0.282079 −0.141040 0.990004i \(-0.545045\pi\)
−0.141040 + 0.990004i \(0.545045\pi\)
\(294\) −8.27548 −0.482636
\(295\) −1.19356 −0.0694917
\(296\) 3.70114 0.215124
\(297\) −4.79935 −0.278487
\(298\) 4.82747 0.279648
\(299\) −20.7433 −1.19961
\(300\) 2.31440 0.133622
\(301\) 25.0568 1.44425
\(302\) −11.1519 −0.641721
\(303\) −0.933183 −0.0536099
\(304\) −3.29297 −0.188865
\(305\) −5.25250 −0.300757
\(306\) 9.56231 0.546641
\(307\) 1.93106 0.110211 0.0551057 0.998481i \(-0.482450\pi\)
0.0551057 + 0.998481i \(0.482450\pi\)
\(308\) −8.26056 −0.470689
\(309\) −5.50117 −0.312951
\(310\) 0.547220 0.0310800
\(311\) 7.45672 0.422832 0.211416 0.977396i \(-0.432193\pi\)
0.211416 + 0.977396i \(0.432193\pi\)
\(312\) 1.66685 0.0943667
\(313\) 25.8462 1.46091 0.730457 0.682958i \(-0.239307\pi\)
0.730457 + 0.682958i \(0.239307\pi\)
\(314\) 23.1586 1.30692
\(315\) 7.36285 0.414850
\(316\) −4.26535 −0.239945
\(317\) −12.3077 −0.691267 −0.345634 0.938370i \(-0.612336\pi\)
−0.345634 + 0.938370i \(0.612336\pi\)
\(318\) −5.98508 −0.335627
\(319\) −6.56823 −0.367750
\(320\) −0.547220 −0.0305905
\(321\) 5.95014 0.332105
\(322\) 29.8971 1.66610
\(323\) 11.4189 0.635363
\(324\) 6.87693 0.382052
\(325\) 15.9131 0.882699
\(326\) −5.17824 −0.286796
\(327\) 5.11402 0.282806
\(328\) 4.48593 0.247694
\(329\) 8.91820 0.491676
\(330\) −0.456147 −0.0251101
\(331\) −5.39932 −0.296774 −0.148387 0.988929i \(-0.547408\pi\)
−0.148387 + 0.988929i \(0.547408\pi\)
\(332\) −3.67643 −0.201770
\(333\) −10.2062 −0.559294
\(334\) −4.22756 −0.231322
\(335\) −7.32078 −0.399977
\(336\) −2.40241 −0.131062
\(337\) −6.99344 −0.380957 −0.190479 0.981691i \(-0.561004\pi\)
−0.190479 + 0.981691i \(0.561004\pi\)
\(338\) −1.53930 −0.0837267
\(339\) 6.10560 0.331611
\(340\) 1.89757 0.102910
\(341\) 1.69298 0.0916802
\(342\) 9.08060 0.491023
\(343\) 47.8536 2.58385
\(344\) 5.13533 0.276878
\(345\) 1.65091 0.0888822
\(346\) 13.8562 0.744915
\(347\) −12.5591 −0.674208 −0.337104 0.941467i \(-0.609447\pi\)
−0.337104 + 0.941467i \(0.609447\pi\)
\(348\) −1.91023 −0.102399
\(349\) 8.37399 0.448250 0.224125 0.974560i \(-0.428048\pi\)
0.224125 + 0.974560i \(0.428048\pi\)
\(350\) −22.9354 −1.22595
\(351\) −9.59700 −0.512250
\(352\) −1.69298 −0.0902363
\(353\) −18.0438 −0.960375 −0.480187 0.877166i \(-0.659431\pi\)
−0.480187 + 0.877166i \(0.659431\pi\)
\(354\) −1.07392 −0.0570783
\(355\) −3.41927 −0.181476
\(356\) 14.3678 0.761490
\(357\) 8.33072 0.440909
\(358\) −9.02751 −0.477119
\(359\) −28.9683 −1.52889 −0.764444 0.644691i \(-0.776986\pi\)
−0.764444 + 0.644691i \(0.776986\pi\)
\(360\) 1.50900 0.0795313
\(361\) −8.15636 −0.429282
\(362\) 6.06735 0.318893
\(363\) 4.00483 0.210199
\(364\) −16.5182 −0.865788
\(365\) −3.54163 −0.185378
\(366\) −4.72600 −0.247032
\(367\) 15.6555 0.817212 0.408606 0.912711i \(-0.366015\pi\)
0.408606 + 0.912711i \(0.366015\pi\)
\(368\) 6.12734 0.319410
\(369\) −12.3703 −0.643971
\(370\) −2.02534 −0.105292
\(371\) 59.3112 3.07928
\(372\) 0.492368 0.0255281
\(373\) −25.0761 −1.29839 −0.649196 0.760621i \(-0.724895\pi\)
−0.649196 + 0.760621i \(0.724895\pi\)
\(374\) 5.87068 0.303566
\(375\) −2.61366 −0.134969
\(376\) 1.82777 0.0942598
\(377\) −13.1341 −0.676442
\(378\) 13.8320 0.711444
\(379\) 22.0357 1.13190 0.565950 0.824439i \(-0.308509\pi\)
0.565950 + 0.824439i \(0.308509\pi\)
\(380\) 1.80198 0.0924396
\(381\) −5.29764 −0.271406
\(382\) −15.5144 −0.793784
\(383\) 25.9200 1.32445 0.662224 0.749306i \(-0.269613\pi\)
0.662224 + 0.749306i \(0.269613\pi\)
\(384\) −0.492368 −0.0251261
\(385\) 4.52035 0.230378
\(386\) 20.3696 1.03679
\(387\) −14.1610 −0.719846
\(388\) −1.00000 −0.0507673
\(389\) −33.8834 −1.71796 −0.858978 0.512012i \(-0.828900\pi\)
−0.858978 + 0.512012i \(0.828900\pi\)
\(390\) −0.912133 −0.0461876
\(391\) −21.2475 −1.07453
\(392\) 16.8075 0.848906
\(393\) −1.06498 −0.0537214
\(394\) −1.04076 −0.0524326
\(395\) 2.33409 0.117441
\(396\) 4.66853 0.234602
\(397\) 1.42616 0.0715771 0.0357886 0.999359i \(-0.488606\pi\)
0.0357886 + 0.999359i \(0.488606\pi\)
\(398\) −13.3436 −0.668854
\(399\) 7.91106 0.396048
\(400\) −4.70055 −0.235028
\(401\) 17.0063 0.849257 0.424628 0.905368i \(-0.360405\pi\)
0.424628 + 0.905368i \(0.360405\pi\)
\(402\) −6.58696 −0.328528
\(403\) 3.38537 0.168637
\(404\) 1.89529 0.0942944
\(405\) −3.76320 −0.186995
\(406\) 18.9301 0.939483
\(407\) −6.26596 −0.310592
\(408\) 1.70736 0.0845271
\(409\) 11.6724 0.577161 0.288581 0.957456i \(-0.406817\pi\)
0.288581 + 0.957456i \(0.406817\pi\)
\(410\) −2.45479 −0.121233
\(411\) 10.6695 0.526289
\(412\) 11.1729 0.550448
\(413\) 10.6424 0.523677
\(414\) −16.8966 −0.830422
\(415\) 2.01182 0.0987563
\(416\) −3.38537 −0.165981
\(417\) −7.29792 −0.357381
\(418\) 5.57494 0.272679
\(419\) 18.4560 0.901635 0.450818 0.892616i \(-0.351132\pi\)
0.450818 + 0.892616i \(0.351132\pi\)
\(420\) 1.31465 0.0641482
\(421\) −16.7262 −0.815187 −0.407594 0.913163i \(-0.633632\pi\)
−0.407594 + 0.913163i \(0.633632\pi\)
\(422\) −10.8417 −0.527765
\(423\) −5.04020 −0.245063
\(424\) 12.1557 0.590333
\(425\) 16.2999 0.790660
\(426\) −3.07653 −0.149058
\(427\) 46.8339 2.26645
\(428\) −12.0847 −0.584138
\(429\) −2.82195 −0.136245
\(430\) −2.81016 −0.135518
\(431\) −21.6759 −1.04409 −0.522045 0.852918i \(-0.674831\pi\)
−0.522045 + 0.852918i \(0.674831\pi\)
\(432\) 2.83485 0.136392
\(433\) 31.9479 1.53532 0.767659 0.640858i \(-0.221421\pi\)
0.767659 + 0.640858i \(0.221421\pi\)
\(434\) −4.87929 −0.234213
\(435\) 1.04532 0.0501191
\(436\) −10.3866 −0.497427
\(437\) −20.1771 −0.965203
\(438\) −3.18663 −0.152263
\(439\) −39.3101 −1.87617 −0.938085 0.346405i \(-0.887402\pi\)
−0.938085 + 0.346405i \(0.887402\pi\)
\(440\) 0.926435 0.0441661
\(441\) −46.3479 −2.20704
\(442\) 11.7393 0.558381
\(443\) 4.44918 0.211387 0.105694 0.994399i \(-0.466294\pi\)
0.105694 + 0.994399i \(0.466294\pi\)
\(444\) −1.82232 −0.0864836
\(445\) −7.86233 −0.372710
\(446\) −9.29209 −0.439993
\(447\) −2.37689 −0.112423
\(448\) 4.87929 0.230525
\(449\) −22.2100 −1.04815 −0.524077 0.851671i \(-0.675590\pi\)
−0.524077 + 0.851671i \(0.675590\pi\)
\(450\) 12.9621 0.611040
\(451\) −7.59460 −0.357616
\(452\) −12.4005 −0.583269
\(453\) 5.49085 0.257983
\(454\) −5.03824 −0.236456
\(455\) 9.03909 0.423759
\(456\) 1.62135 0.0759268
\(457\) 1.37570 0.0643527 0.0321763 0.999482i \(-0.489756\pi\)
0.0321763 + 0.999482i \(0.489756\pi\)
\(458\) 12.8339 0.599689
\(459\) −9.83027 −0.458838
\(460\) −3.35300 −0.156335
\(461\) 11.1892 0.521132 0.260566 0.965456i \(-0.416091\pi\)
0.260566 + 0.965456i \(0.416091\pi\)
\(462\) 4.06724 0.189225
\(463\) 37.2506 1.73118 0.865591 0.500752i \(-0.166943\pi\)
0.865591 + 0.500752i \(0.166943\pi\)
\(464\) 3.87968 0.180109
\(465\) −0.269434 −0.0124947
\(466\) −20.6255 −0.955458
\(467\) −35.7101 −1.65247 −0.826234 0.563327i \(-0.809521\pi\)
−0.826234 + 0.563327i \(0.809521\pi\)
\(468\) 9.33540 0.431529
\(469\) 65.2757 3.01415
\(470\) −1.00019 −0.0461353
\(471\) −11.4026 −0.525403
\(472\) 2.18113 0.100395
\(473\) −8.69403 −0.399752
\(474\) 2.10012 0.0964618
\(475\) 15.4788 0.710214
\(476\) −16.9197 −0.775513
\(477\) −33.5202 −1.53479
\(478\) −10.7351 −0.491013
\(479\) 3.85971 0.176355 0.0881773 0.996105i \(-0.471896\pi\)
0.0881773 + 0.996105i \(0.471896\pi\)
\(480\) 0.269434 0.0122979
\(481\) −12.5297 −0.571305
\(482\) −10.0980 −0.459953
\(483\) −14.7204 −0.669800
\(484\) −8.13381 −0.369718
\(485\) 0.547220 0.0248480
\(486\) −11.8905 −0.539365
\(487\) 37.9468 1.71953 0.859767 0.510687i \(-0.170609\pi\)
0.859767 + 0.510687i \(0.170609\pi\)
\(488\) 9.59850 0.434504
\(489\) 2.54960 0.115297
\(490\) −9.19740 −0.415496
\(491\) 29.7247 1.34146 0.670729 0.741703i \(-0.265981\pi\)
0.670729 + 0.741703i \(0.265981\pi\)
\(492\) −2.20873 −0.0995772
\(493\) −13.4534 −0.605909
\(494\) 11.1479 0.501568
\(495\) −2.55471 −0.114826
\(496\) −1.00000 −0.0449013
\(497\) 30.4879 1.36757
\(498\) 1.81016 0.0811152
\(499\) 21.6164 0.967684 0.483842 0.875155i \(-0.339241\pi\)
0.483842 + 0.875155i \(0.339241\pi\)
\(500\) 5.30834 0.237396
\(501\) 2.08152 0.0929952
\(502\) −13.4245 −0.599167
\(503\) −35.4718 −1.58161 −0.790804 0.612069i \(-0.790338\pi\)
−0.790804 + 0.612069i \(0.790338\pi\)
\(504\) −13.4550 −0.599334
\(505\) −1.03714 −0.0461522
\(506\) −10.3735 −0.461158
\(507\) 0.757901 0.0336596
\(508\) 10.7595 0.477376
\(509\) −37.0953 −1.64422 −0.822110 0.569329i \(-0.807203\pi\)
−0.822110 + 0.569329i \(0.807203\pi\)
\(510\) −0.934304 −0.0413717
\(511\) 31.5790 1.39697
\(512\) 1.00000 0.0441942
\(513\) −9.33506 −0.412153
\(514\) 11.8995 0.524865
\(515\) −6.11402 −0.269416
\(516\) −2.52847 −0.111310
\(517\) −3.09438 −0.136091
\(518\) 18.0589 0.793463
\(519\) −6.82237 −0.299469
\(520\) 1.85254 0.0812393
\(521\) 8.30166 0.363702 0.181851 0.983326i \(-0.441791\pi\)
0.181851 + 0.983326i \(0.441791\pi\)
\(522\) −10.6985 −0.468260
\(523\) 24.6183 1.07648 0.538242 0.842791i \(-0.319089\pi\)
0.538242 + 0.842791i \(0.319089\pi\)
\(524\) 2.16298 0.0944904
\(525\) 11.2926 0.492851
\(526\) 18.3943 0.802029
\(527\) 3.46765 0.151053
\(528\) 0.833572 0.0362766
\(529\) 14.5443 0.632360
\(530\) −6.65184 −0.288938
\(531\) −6.01463 −0.261013
\(532\) −16.0674 −0.696608
\(533\) −15.1865 −0.657801
\(534\) −7.07423 −0.306132
\(535\) 6.61301 0.285905
\(536\) 13.3781 0.577847
\(537\) 4.44486 0.191810
\(538\) 27.6715 1.19300
\(539\) −28.4548 −1.22564
\(540\) −1.55129 −0.0667567
\(541\) 0.373642 0.0160641 0.00803205 0.999968i \(-0.497443\pi\)
0.00803205 + 0.999968i \(0.497443\pi\)
\(542\) −31.8892 −1.36976
\(543\) −2.98737 −0.128200
\(544\) −3.46765 −0.148674
\(545\) 5.68375 0.243465
\(546\) 8.13303 0.348062
\(547\) 7.28654 0.311550 0.155775 0.987793i \(-0.450213\pi\)
0.155775 + 0.987793i \(0.450213\pi\)
\(548\) −21.6698 −0.925688
\(549\) −26.4686 −1.12965
\(550\) 7.95795 0.339328
\(551\) −12.7756 −0.544261
\(552\) −3.01691 −0.128408
\(553\) −20.8119 −0.885011
\(554\) −8.16520 −0.346906
\(555\) 0.997212 0.0423293
\(556\) 14.8221 0.628596
\(557\) 15.4123 0.653041 0.326520 0.945190i \(-0.394124\pi\)
0.326520 + 0.945190i \(0.394124\pi\)
\(558\) 2.75757 0.116737
\(559\) −17.3850 −0.735306
\(560\) −2.67005 −0.112830
\(561\) −2.89054 −0.122039
\(562\) 22.0398 0.929694
\(563\) −7.61341 −0.320867 −0.160434 0.987047i \(-0.551289\pi\)
−0.160434 + 0.987047i \(0.551289\pi\)
\(564\) −0.899934 −0.0378941
\(565\) 6.78579 0.285480
\(566\) 22.4232 0.942518
\(567\) 33.5545 1.40916
\(568\) 6.24843 0.262178
\(569\) 14.1773 0.594345 0.297173 0.954824i \(-0.403956\pi\)
0.297173 + 0.954824i \(0.403956\pi\)
\(570\) −0.887238 −0.0371623
\(571\) 26.2001 1.09644 0.548221 0.836334i \(-0.315305\pi\)
0.548221 + 0.836334i \(0.315305\pi\)
\(572\) 5.73137 0.239641
\(573\) 7.63879 0.319115
\(574\) 21.8882 0.913594
\(575\) −28.8019 −1.20112
\(576\) −2.75757 −0.114899
\(577\) 42.7653 1.78034 0.890172 0.455625i \(-0.150584\pi\)
0.890172 + 0.455625i \(0.150584\pi\)
\(578\) −4.97537 −0.206948
\(579\) −10.0294 −0.416806
\(580\) −2.12304 −0.0881543
\(581\) −17.9384 −0.744210
\(582\) 0.492368 0.0204093
\(583\) −20.5794 −0.852311
\(584\) 6.47204 0.267815
\(585\) −5.10852 −0.211211
\(586\) −4.82842 −0.199460
\(587\) 19.4624 0.803299 0.401650 0.915793i \(-0.368437\pi\)
0.401650 + 0.915793i \(0.368437\pi\)
\(588\) −8.27548 −0.341275
\(589\) 3.29297 0.135684
\(590\) −1.19356 −0.0491381
\(591\) 0.512436 0.0210788
\(592\) 3.70114 0.152116
\(593\) −17.0492 −0.700128 −0.350064 0.936726i \(-0.613840\pi\)
−0.350064 + 0.936726i \(0.613840\pi\)
\(594\) −4.79935 −0.196920
\(595\) 9.25880 0.379574
\(596\) 4.82747 0.197741
\(597\) 6.56997 0.268891
\(598\) −20.7433 −0.848256
\(599\) −2.44361 −0.0998430 −0.0499215 0.998753i \(-0.515897\pi\)
−0.0499215 + 0.998753i \(0.515897\pi\)
\(600\) 2.31440 0.0944851
\(601\) 8.09623 0.330252 0.165126 0.986272i \(-0.447197\pi\)
0.165126 + 0.986272i \(0.447197\pi\)
\(602\) 25.0568 1.02124
\(603\) −36.8911 −1.50232
\(604\) −11.1519 −0.453765
\(605\) 4.45098 0.180958
\(606\) −0.933183 −0.0379079
\(607\) −24.9190 −1.01143 −0.505715 0.862701i \(-0.668771\pi\)
−0.505715 + 0.862701i \(0.668771\pi\)
\(608\) −3.29297 −0.133548
\(609\) −9.32057 −0.377688
\(610\) −5.25250 −0.212667
\(611\) −6.18766 −0.250326
\(612\) 9.56231 0.386534
\(613\) 46.2394 1.86759 0.933796 0.357806i \(-0.116475\pi\)
0.933796 + 0.357806i \(0.116475\pi\)
\(614\) 1.93106 0.0779313
\(615\) 1.20866 0.0487379
\(616\) −8.26056 −0.332828
\(617\) 3.89219 0.156694 0.0783469 0.996926i \(-0.475036\pi\)
0.0783469 + 0.996926i \(0.475036\pi\)
\(618\) −5.50117 −0.221290
\(619\) 8.36100 0.336057 0.168028 0.985782i \(-0.446260\pi\)
0.168028 + 0.985782i \(0.446260\pi\)
\(620\) 0.547220 0.0219769
\(621\) 17.3701 0.697037
\(622\) 7.45672 0.298987
\(623\) 70.1045 2.80868
\(624\) 1.66685 0.0667273
\(625\) 20.5979 0.823917
\(626\) 25.8462 1.03302
\(627\) −2.74493 −0.109622
\(628\) 23.1586 0.924129
\(629\) −12.8343 −0.511735
\(630\) 7.36285 0.293343
\(631\) −12.3082 −0.489981 −0.244990 0.969525i \(-0.578785\pi\)
−0.244990 + 0.969525i \(0.578785\pi\)
\(632\) −4.26535 −0.169666
\(633\) 5.33810 0.212170
\(634\) −12.3077 −0.488800
\(635\) −5.88782 −0.233651
\(636\) −5.98508 −0.237324
\(637\) −56.8995 −2.25444
\(638\) −6.56823 −0.260039
\(639\) −17.2305 −0.681628
\(640\) −0.547220 −0.0216308
\(641\) −20.1961 −0.797696 −0.398848 0.917017i \(-0.630590\pi\)
−0.398848 + 0.917017i \(0.630590\pi\)
\(642\) 5.95014 0.234833
\(643\) 6.75292 0.266309 0.133155 0.991095i \(-0.457489\pi\)
0.133155 + 0.991095i \(0.457489\pi\)
\(644\) 29.8971 1.17811
\(645\) 1.38363 0.0544804
\(646\) 11.4189 0.449270
\(647\) 12.0709 0.474556 0.237278 0.971442i \(-0.423745\pi\)
0.237278 + 0.971442i \(0.423745\pi\)
\(648\) 6.87693 0.270151
\(649\) −3.69262 −0.144948
\(650\) 15.9131 0.624162
\(651\) 2.40241 0.0941578
\(652\) −5.17824 −0.202796
\(653\) 15.6983 0.614322 0.307161 0.951658i \(-0.400621\pi\)
0.307161 + 0.951658i \(0.400621\pi\)
\(654\) 5.11402 0.199974
\(655\) −1.18363 −0.0462482
\(656\) 4.48593 0.175146
\(657\) −17.8471 −0.696283
\(658\) 8.91820 0.347668
\(659\) −21.5338 −0.838839 −0.419420 0.907793i \(-0.637766\pi\)
−0.419420 + 0.907793i \(0.637766\pi\)
\(660\) −0.456147 −0.0177555
\(661\) −46.2703 −1.79971 −0.899854 0.436191i \(-0.856327\pi\)
−0.899854 + 0.436191i \(0.856327\pi\)
\(662\) −5.39932 −0.209851
\(663\) −5.78005 −0.224479
\(664\) −3.67643 −0.142673
\(665\) 8.79238 0.340954
\(666\) −10.2062 −0.395480
\(667\) 23.7721 0.920459
\(668\) −4.22756 −0.163569
\(669\) 4.57513 0.176885
\(670\) −7.32078 −0.282826
\(671\) −16.2501 −0.627329
\(672\) −2.40241 −0.0926749
\(673\) 37.5931 1.44911 0.724555 0.689217i \(-0.242045\pi\)
0.724555 + 0.689217i \(0.242045\pi\)
\(674\) −6.99344 −0.269377
\(675\) −13.3253 −0.512893
\(676\) −1.53930 −0.0592037
\(677\) −13.0532 −0.501677 −0.250838 0.968029i \(-0.580706\pi\)
−0.250838 + 0.968029i \(0.580706\pi\)
\(678\) 6.10560 0.234484
\(679\) −4.87929 −0.187250
\(680\) 1.89757 0.0727685
\(681\) 2.48067 0.0950595
\(682\) 1.69298 0.0648277
\(683\) 39.8102 1.52329 0.761647 0.647992i \(-0.224391\pi\)
0.761647 + 0.647992i \(0.224391\pi\)
\(684\) 9.08060 0.347206
\(685\) 11.8582 0.453077
\(686\) 47.8536 1.82706
\(687\) −6.31901 −0.241085
\(688\) 5.13533 0.195783
\(689\) −41.1515 −1.56775
\(690\) 1.65091 0.0628492
\(691\) 39.2479 1.49306 0.746531 0.665351i \(-0.231718\pi\)
0.746531 + 0.665351i \(0.231718\pi\)
\(692\) 13.8562 0.526735
\(693\) 22.7791 0.865307
\(694\) −12.5591 −0.476737
\(695\) −8.11094 −0.307665
\(696\) −1.91023 −0.0724071
\(697\) −15.5557 −0.589212
\(698\) 8.37399 0.316960
\(699\) 10.1553 0.384110
\(700\) −22.9354 −0.866875
\(701\) −51.5574 −1.94730 −0.973649 0.228053i \(-0.926764\pi\)
−0.973649 + 0.228053i \(0.926764\pi\)
\(702\) −9.59700 −0.362215
\(703\) −12.1877 −0.459669
\(704\) −1.69298 −0.0638067
\(705\) 0.492462 0.0185472
\(706\) −18.0438 −0.679087
\(707\) 9.24769 0.347795
\(708\) −1.07392 −0.0403604
\(709\) −24.3644 −0.915025 −0.457513 0.889203i \(-0.651260\pi\)
−0.457513 + 0.889203i \(0.651260\pi\)
\(710\) −3.41927 −0.128323
\(711\) 11.7620 0.441110
\(712\) 14.3678 0.538455
\(713\) −6.12734 −0.229471
\(714\) 8.33072 0.311770
\(715\) −3.13632 −0.117292
\(716\) −9.02751 −0.337374
\(717\) 5.28563 0.197396
\(718\) −28.9683 −1.08109
\(719\) −42.3959 −1.58110 −0.790551 0.612397i \(-0.790205\pi\)
−0.790551 + 0.612397i \(0.790205\pi\)
\(720\) 1.50900 0.0562371
\(721\) 54.5157 2.03027
\(722\) −8.15636 −0.303548
\(723\) 4.97195 0.184909
\(724\) 6.06735 0.225491
\(725\) −18.2366 −0.677291
\(726\) 4.00483 0.148633
\(727\) −0.663978 −0.0246256 −0.0123128 0.999924i \(-0.503919\pi\)
−0.0123128 + 0.999924i \(0.503919\pi\)
\(728\) −16.5182 −0.612205
\(729\) −14.7763 −0.547269
\(730\) −3.54163 −0.131082
\(731\) −17.8075 −0.658636
\(732\) −4.72600 −0.174678
\(733\) −6.32870 −0.233756 −0.116878 0.993146i \(-0.537289\pi\)
−0.116878 + 0.993146i \(0.537289\pi\)
\(734\) 15.6555 0.577856
\(735\) 4.52851 0.167037
\(736\) 6.12734 0.225857
\(737\) −22.6489 −0.834284
\(738\) −12.3703 −0.455356
\(739\) −25.1731 −0.926007 −0.463004 0.886356i \(-0.653228\pi\)
−0.463004 + 0.886356i \(0.653228\pi\)
\(740\) −2.02534 −0.0744528
\(741\) −5.48888 −0.201639
\(742\) 59.3112 2.17738
\(743\) −6.96576 −0.255549 −0.127775 0.991803i \(-0.540783\pi\)
−0.127775 + 0.991803i \(0.540783\pi\)
\(744\) 0.492368 0.0180511
\(745\) −2.64169 −0.0967840
\(746\) −25.0761 −0.918102
\(747\) 10.1380 0.370931
\(748\) 5.87068 0.214653
\(749\) −58.9649 −2.15453
\(750\) −2.61366 −0.0954373
\(751\) 38.6055 1.40873 0.704367 0.709836i \(-0.251231\pi\)
0.704367 + 0.709836i \(0.251231\pi\)
\(752\) 1.82777 0.0666517
\(753\) 6.60982 0.240875
\(754\) −13.1341 −0.478316
\(755\) 6.10255 0.222095
\(756\) 13.8320 0.503067
\(757\) −52.9200 −1.92341 −0.961705 0.274087i \(-0.911624\pi\)
−0.961705 + 0.274087i \(0.911624\pi\)
\(758\) 22.0357 0.800374
\(759\) 5.10758 0.185393
\(760\) 1.80198 0.0653647
\(761\) −11.3999 −0.413248 −0.206624 0.978420i \(-0.566248\pi\)
−0.206624 + 0.978420i \(0.566248\pi\)
\(762\) −5.29764 −0.191913
\(763\) −50.6792 −1.83471
\(764\) −15.5144 −0.561290
\(765\) −5.23269 −0.189188
\(766\) 25.9200 0.936527
\(767\) −7.38393 −0.266618
\(768\) −0.492368 −0.0177668
\(769\) −7.60468 −0.274232 −0.137116 0.990555i \(-0.543783\pi\)
−0.137116 + 0.990555i \(0.543783\pi\)
\(770\) 4.52035 0.162902
\(771\) −5.85894 −0.211005
\(772\) 20.3696 0.733120
\(773\) −4.36699 −0.157070 −0.0785348 0.996911i \(-0.525024\pi\)
−0.0785348 + 0.996911i \(0.525024\pi\)
\(774\) −14.1610 −0.509008
\(775\) 4.70055 0.168849
\(776\) −1.00000 −0.0358979
\(777\) −8.89164 −0.318986
\(778\) −33.8834 −1.21478
\(779\) −14.7720 −0.529263
\(780\) −0.912133 −0.0326596
\(781\) −10.5785 −0.378528
\(782\) −21.2475 −0.759809
\(783\) 10.9983 0.393047
\(784\) 16.8075 0.600267
\(785\) −12.6729 −0.452314
\(786\) −1.06498 −0.0379868
\(787\) −10.6198 −0.378555 −0.189277 0.981924i \(-0.560615\pi\)
−0.189277 + 0.981924i \(0.560615\pi\)
\(788\) −1.04076 −0.0370755
\(789\) −9.05676 −0.322429
\(790\) 2.33409 0.0830430
\(791\) −60.5055 −2.15133
\(792\) 4.66853 0.165889
\(793\) −32.4944 −1.15391
\(794\) 1.42616 0.0506127
\(795\) 3.27516 0.116158
\(796\) −13.3436 −0.472951
\(797\) 33.7283 1.19472 0.597358 0.801975i \(-0.296217\pi\)
0.597358 + 0.801975i \(0.296217\pi\)
\(798\) 7.91106 0.280048
\(799\) −6.33806 −0.224224
\(800\) −4.70055 −0.166190
\(801\) −39.6202 −1.39991
\(802\) 17.0063 0.600515
\(803\) −10.9571 −0.386666
\(804\) −6.58696 −0.232304
\(805\) −16.3603 −0.576624
\(806\) 3.38537 0.119244
\(807\) −13.6246 −0.479607
\(808\) 1.89529 0.0666762
\(809\) −38.9582 −1.36970 −0.684849 0.728685i \(-0.740132\pi\)
−0.684849 + 0.728685i \(0.740132\pi\)
\(810\) −3.76320 −0.132225
\(811\) 43.0000 1.50994 0.754968 0.655762i \(-0.227653\pi\)
0.754968 + 0.655762i \(0.227653\pi\)
\(812\) 18.9301 0.664315
\(813\) 15.7012 0.550666
\(814\) −6.26596 −0.219622
\(815\) 2.83364 0.0992581
\(816\) 1.70736 0.0597697
\(817\) −16.9105 −0.591623
\(818\) 11.6724 0.408115
\(819\) 45.5501 1.59165
\(820\) −2.45479 −0.0857250
\(821\) −5.23412 −0.182672 −0.0913360 0.995820i \(-0.529114\pi\)
−0.0913360 + 0.995820i \(0.529114\pi\)
\(822\) 10.6695 0.372143
\(823\) −18.2220 −0.635178 −0.317589 0.948229i \(-0.602873\pi\)
−0.317589 + 0.948229i \(0.602873\pi\)
\(824\) 11.1729 0.389226
\(825\) −3.91825 −0.136416
\(826\) 10.6424 0.370296
\(827\) 18.9358 0.658463 0.329231 0.944249i \(-0.393210\pi\)
0.329231 + 0.944249i \(0.393210\pi\)
\(828\) −16.8966 −0.587197
\(829\) 13.2920 0.461649 0.230825 0.972995i \(-0.425858\pi\)
0.230825 + 0.972995i \(0.425858\pi\)
\(830\) 2.01182 0.0698312
\(831\) 4.02029 0.139462
\(832\) −3.38537 −0.117366
\(833\) −58.2826 −2.01937
\(834\) −7.29792 −0.252706
\(835\) 2.31340 0.0800587
\(836\) 5.57494 0.192813
\(837\) −2.83485 −0.0979867
\(838\) 18.4560 0.637552
\(839\) 21.9369 0.757348 0.378674 0.925530i \(-0.376380\pi\)
0.378674 + 0.925530i \(0.376380\pi\)
\(840\) 1.31465 0.0453596
\(841\) −13.9481 −0.480970
\(842\) −16.7262 −0.576424
\(843\) −10.8517 −0.373753
\(844\) −10.8417 −0.373186
\(845\) 0.842334 0.0289772
\(846\) −5.04020 −0.173286
\(847\) −39.6872 −1.36367
\(848\) 12.1557 0.417428
\(849\) −11.0405 −0.378908
\(850\) 16.2999 0.559081
\(851\) 22.6781 0.777396
\(852\) −3.07653 −0.105400
\(853\) 40.2841 1.37930 0.689650 0.724143i \(-0.257764\pi\)
0.689650 + 0.724143i \(0.257764\pi\)
\(854\) 46.8339 1.60262
\(855\) −4.96909 −0.169939
\(856\) −12.0847 −0.413048
\(857\) −55.4421 −1.89387 −0.946934 0.321429i \(-0.895837\pi\)
−0.946934 + 0.321429i \(0.895837\pi\)
\(858\) −2.82195 −0.0963396
\(859\) 48.7949 1.66486 0.832431 0.554129i \(-0.186949\pi\)
0.832431 + 0.554129i \(0.186949\pi\)
\(860\) −2.81016 −0.0958255
\(861\) −10.7770 −0.367280
\(862\) −21.6759 −0.738283
\(863\) −13.5015 −0.459596 −0.229798 0.973238i \(-0.573806\pi\)
−0.229798 + 0.973238i \(0.573806\pi\)
\(864\) 2.83485 0.0964435
\(865\) −7.58241 −0.257810
\(866\) 31.9479 1.08563
\(867\) 2.44972 0.0831968
\(868\) −4.87929 −0.165614
\(869\) 7.22117 0.244961
\(870\) 1.04532 0.0354395
\(871\) −45.2898 −1.53459
\(872\) −10.3866 −0.351734
\(873\) 2.75757 0.0933297
\(874\) −20.1771 −0.682502
\(875\) 25.9009 0.875611
\(876\) −3.18663 −0.107666
\(877\) −47.2392 −1.59516 −0.797578 0.603216i \(-0.793886\pi\)
−0.797578 + 0.603216i \(0.793886\pi\)
\(878\) −39.3101 −1.32665
\(879\) 2.37736 0.0801865
\(880\) 0.926435 0.0312301
\(881\) 18.6818 0.629404 0.314702 0.949190i \(-0.398095\pi\)
0.314702 + 0.949190i \(0.398095\pi\)
\(882\) −46.3479 −1.56061
\(883\) 24.2524 0.816157 0.408079 0.912947i \(-0.366199\pi\)
0.408079 + 0.912947i \(0.366199\pi\)
\(884\) 11.7393 0.394835
\(885\) 0.587671 0.0197544
\(886\) 4.44918 0.149473
\(887\) −41.9282 −1.40781 −0.703906 0.710293i \(-0.748562\pi\)
−0.703906 + 0.710293i \(0.748562\pi\)
\(888\) −1.82232 −0.0611531
\(889\) 52.4988 1.76075
\(890\) −7.86233 −0.263546
\(891\) −11.6425 −0.390039
\(892\) −9.29209 −0.311122
\(893\) −6.01877 −0.201411
\(894\) −2.37689 −0.0794952
\(895\) 4.94004 0.165127
\(896\) 4.87929 0.163006
\(897\) 10.2133 0.341013
\(898\) −22.2100 −0.741157
\(899\) −3.87968 −0.129394
\(900\) 12.9621 0.432070
\(901\) −42.1517 −1.40428
\(902\) −7.59460 −0.252873
\(903\) −12.3372 −0.410555
\(904\) −12.4005 −0.412433
\(905\) −3.32018 −0.110366
\(906\) 5.49085 0.182421
\(907\) 10.2331 0.339786 0.169893 0.985463i \(-0.445658\pi\)
0.169893 + 0.985463i \(0.445658\pi\)
\(908\) −5.03824 −0.167200
\(909\) −5.22641 −0.173349
\(910\) 9.03909 0.299643
\(911\) 57.2366 1.89633 0.948166 0.317774i \(-0.102935\pi\)
0.948166 + 0.317774i \(0.102935\pi\)
\(912\) 1.62135 0.0536884
\(913\) 6.22414 0.205989
\(914\) 1.37570 0.0455042
\(915\) 2.58616 0.0854959
\(916\) 12.8339 0.424044
\(917\) 10.5538 0.348518
\(918\) −9.83027 −0.324447
\(919\) −53.4502 −1.76316 −0.881579 0.472036i \(-0.843519\pi\)
−0.881579 + 0.472036i \(0.843519\pi\)
\(920\) −3.35300 −0.110545
\(921\) −0.950793 −0.0313297
\(922\) 11.1892 0.368496
\(923\) −21.1532 −0.696266
\(924\) 4.06724 0.133802
\(925\) −17.3974 −0.572022
\(926\) 37.2506 1.22413
\(927\) −30.8100 −1.01193
\(928\) 3.87968 0.127357
\(929\) −35.7928 −1.17432 −0.587162 0.809469i \(-0.699755\pi\)
−0.587162 + 0.809469i \(0.699755\pi\)
\(930\) −0.269434 −0.00883509
\(931\) −55.3465 −1.81391
\(932\) −20.6255 −0.675611
\(933\) −3.67145 −0.120198
\(934\) −35.7101 −1.16847
\(935\) −3.21256 −0.105062
\(936\) 9.33540 0.305137
\(937\) −46.9515 −1.53384 −0.766920 0.641743i \(-0.778212\pi\)
−0.766920 + 0.641743i \(0.778212\pi\)
\(938\) 65.2757 2.13133
\(939\) −12.7259 −0.415293
\(940\) −1.00019 −0.0326226
\(941\) −11.5442 −0.376329 −0.188164 0.982138i \(-0.560254\pi\)
−0.188164 + 0.982138i \(0.560254\pi\)
\(942\) −11.4026 −0.371516
\(943\) 27.4868 0.895093
\(944\) 2.18113 0.0709898
\(945\) −7.56918 −0.246225
\(946\) −8.69403 −0.282667
\(947\) 12.6232 0.410200 0.205100 0.978741i \(-0.434248\pi\)
0.205100 + 0.978741i \(0.434248\pi\)
\(948\) 2.10012 0.0682088
\(949\) −21.9102 −0.711236
\(950\) 15.4788 0.502197
\(951\) 6.05991 0.196506
\(952\) −16.9197 −0.548370
\(953\) 14.5446 0.471147 0.235574 0.971857i \(-0.424303\pi\)
0.235574 + 0.971857i \(0.424303\pi\)
\(954\) −33.5202 −1.08526
\(955\) 8.48978 0.274723
\(956\) −10.7351 −0.347199
\(957\) 3.23399 0.104540
\(958\) 3.85971 0.124702
\(959\) −105.733 −3.41431
\(960\) 0.269434 0.00869594
\(961\) 1.00000 0.0322581
\(962\) −12.5297 −0.403974
\(963\) 33.3245 1.07387
\(964\) −10.0980 −0.325236
\(965\) −11.1467 −0.358824
\(966\) −14.7204 −0.473620
\(967\) −4.68434 −0.150638 −0.0753191 0.997159i \(-0.523998\pi\)
−0.0753191 + 0.997159i \(0.523998\pi\)
\(968\) −8.13381 −0.261430
\(969\) −5.62229 −0.180614
\(970\) 0.547220 0.0175702
\(971\) 16.1261 0.517512 0.258756 0.965943i \(-0.416688\pi\)
0.258756 + 0.965943i \(0.416688\pi\)
\(972\) −11.8905 −0.381389
\(973\) 72.3212 2.31851
\(974\) 37.9468 1.21589
\(975\) −7.83510 −0.250924
\(976\) 9.59850 0.307241
\(977\) 8.67755 0.277619 0.138810 0.990319i \(-0.455672\pi\)
0.138810 + 0.990319i \(0.455672\pi\)
\(978\) 2.54960 0.0815273
\(979\) −24.3244 −0.777411
\(980\) −9.19740 −0.293800
\(981\) 28.6418 0.914461
\(982\) 29.7247 0.948554
\(983\) −23.0280 −0.734479 −0.367239 0.930126i \(-0.619697\pi\)
−0.367239 + 0.930126i \(0.619697\pi\)
\(984\) −2.20873 −0.0704117
\(985\) 0.569524 0.0181465
\(986\) −13.4534 −0.428443
\(987\) −4.39104 −0.139768
\(988\) 11.1479 0.354662
\(989\) 31.4659 1.00056
\(990\) −2.55471 −0.0811941
\(991\) −11.0579 −0.351266 −0.175633 0.984456i \(-0.556197\pi\)
−0.175633 + 0.984456i \(0.556197\pi\)
\(992\) −1.00000 −0.0317500
\(993\) 2.65846 0.0843636
\(994\) 30.4879 0.967017
\(995\) 7.30189 0.231485
\(996\) 1.81016 0.0573571
\(997\) −25.4366 −0.805586 −0.402793 0.915291i \(-0.631961\pi\)
−0.402793 + 0.915291i \(0.631961\pi\)
\(998\) 21.6164 0.684256
\(999\) 10.4922 0.331957
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 6014.2.a.i.1.11 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6014.2.a.i.1.11 28 1.1 even 1 trivial