Properties

Label 4011.2.a.j.1.10
Level $4011$
Weight $2$
Character 4011.1
Self dual yes
Analytic conductor $32.028$
Analytic rank $0$
Dimension $26$
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] = [4011,2,Mod(1,4011)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4011, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("4011.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4011 = 3 \cdot 7 \cdot 191 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4011.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: \(32.0279962507\)
Analytic rank: \(0\)
Dimension: \(26\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 4011.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.03703 q^{2} -1.00000 q^{3} -0.924574 q^{4} -1.10504 q^{5} +1.03703 q^{6} -1.00000 q^{7} +3.03286 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.03703 q^{2} -1.00000 q^{3} -0.924574 q^{4} -1.10504 q^{5} +1.03703 q^{6} -1.00000 q^{7} +3.03286 q^{8} +1.00000 q^{9} +1.14595 q^{10} -3.63449 q^{11} +0.924574 q^{12} -3.11689 q^{13} +1.03703 q^{14} +1.10504 q^{15} -1.29602 q^{16} -0.947106 q^{17} -1.03703 q^{18} -5.88214 q^{19} +1.02169 q^{20} +1.00000 q^{21} +3.76907 q^{22} -4.48397 q^{23} -3.03286 q^{24} -3.77889 q^{25} +3.23230 q^{26} -1.00000 q^{27} +0.924574 q^{28} -0.208014 q^{29} -1.14595 q^{30} -2.92063 q^{31} -4.72172 q^{32} +3.63449 q^{33} +0.982175 q^{34} +1.10504 q^{35} -0.924574 q^{36} +10.3878 q^{37} +6.09994 q^{38} +3.11689 q^{39} -3.35143 q^{40} +4.40926 q^{41} -1.03703 q^{42} -5.58070 q^{43} +3.36036 q^{44} -1.10504 q^{45} +4.65000 q^{46} -6.89665 q^{47} +1.29602 q^{48} +1.00000 q^{49} +3.91882 q^{50} +0.947106 q^{51} +2.88179 q^{52} +8.55990 q^{53} +1.03703 q^{54} +4.01625 q^{55} -3.03286 q^{56} +5.88214 q^{57} +0.215716 q^{58} -12.1039 q^{59} -1.02169 q^{60} -3.44450 q^{61} +3.02878 q^{62} -1.00000 q^{63} +7.48859 q^{64} +3.44427 q^{65} -3.76907 q^{66} -15.5558 q^{67} +0.875670 q^{68} +4.48397 q^{69} -1.14595 q^{70} -15.9734 q^{71} +3.03286 q^{72} -2.33818 q^{73} -10.7724 q^{74} +3.77889 q^{75} +5.43847 q^{76} +3.63449 q^{77} -3.23230 q^{78} -3.93588 q^{79} +1.43215 q^{80} +1.00000 q^{81} -4.57252 q^{82} -8.71714 q^{83} -0.924574 q^{84} +1.04659 q^{85} +5.78733 q^{86} +0.208014 q^{87} -11.0229 q^{88} -4.31048 q^{89} +1.14595 q^{90} +3.11689 q^{91} +4.14576 q^{92} +2.92063 q^{93} +7.15202 q^{94} +6.49999 q^{95} +4.72172 q^{96} +1.19390 q^{97} -1.03703 q^{98} -3.63449 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9} - q^{10} + 13 q^{11} - 34 q^{12} - q^{13} - 2 q^{15} + 54 q^{16} + q^{19} - 22 q^{20} + 26 q^{21} + 17 q^{22} - 3 q^{23} + 48 q^{25} + 6 q^{26} - 26 q^{27} - 34 q^{28} + 23 q^{29} + q^{30} + 18 q^{31} + 10 q^{32} - 13 q^{33} - 19 q^{34} - 2 q^{35} + 34 q^{36} + 23 q^{37} - 15 q^{38} + q^{39} + 14 q^{40} - 4 q^{41} + 5 q^{43} + 60 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{47} - 54 q^{48} + 26 q^{49} + 26 q^{50} + 19 q^{52} + 31 q^{53} + 41 q^{55} - q^{57} + 19 q^{58} - 2 q^{59} + 22 q^{60} - 2 q^{61} - 35 q^{62} - 26 q^{63} + 132 q^{64} + 40 q^{65} - 17 q^{66} + 47 q^{67} - 60 q^{68} + 3 q^{69} + q^{70} + 16 q^{71} - 23 q^{73} + 34 q^{74} - 48 q^{75} + 72 q^{76} - 13 q^{77} - 6 q^{78} + 14 q^{79} - 21 q^{80} + 26 q^{81} + 60 q^{82} - 4 q^{83} + 34 q^{84} + 36 q^{85} + 21 q^{86} - 23 q^{87} + 67 q^{88} + 14 q^{89} - q^{90} + q^{91} + 20 q^{92} - 18 q^{93} + 58 q^{94} - 4 q^{95} - 10 q^{96} + 48 q^{97} + 13 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.03703 −0.733289 −0.366645 0.930361i \(-0.619493\pi\)
−0.366645 + 0.930361i \(0.619493\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.924574 −0.462287
\(5\) −1.10504 −0.494188 −0.247094 0.968992i \(-0.579476\pi\)
−0.247094 + 0.968992i \(0.579476\pi\)
\(6\) 1.03703 0.423365
\(7\) −1.00000 −0.377964
\(8\) 3.03286 1.07228
\(9\) 1.00000 0.333333
\(10\) 1.14595 0.362382
\(11\) −3.63449 −1.09584 −0.547920 0.836531i \(-0.684580\pi\)
−0.547920 + 0.836531i \(0.684580\pi\)
\(12\) 0.924574 0.266901
\(13\) −3.11689 −0.864468 −0.432234 0.901761i \(-0.642275\pi\)
−0.432234 + 0.901761i \(0.642275\pi\)
\(14\) 1.03703 0.277157
\(15\) 1.10504 0.285319
\(16\) −1.29602 −0.324004
\(17\) −0.947106 −0.229707 −0.114853 0.993382i \(-0.536640\pi\)
−0.114853 + 0.993382i \(0.536640\pi\)
\(18\) −1.03703 −0.244430
\(19\) −5.88214 −1.34946 −0.674728 0.738067i \(-0.735739\pi\)
−0.674728 + 0.738067i \(0.735739\pi\)
\(20\) 1.02169 0.228457
\(21\) 1.00000 0.218218
\(22\) 3.76907 0.803568
\(23\) −4.48397 −0.934972 −0.467486 0.884000i \(-0.654840\pi\)
−0.467486 + 0.884000i \(0.654840\pi\)
\(24\) −3.03286 −0.619081
\(25\) −3.77889 −0.755779
\(26\) 3.23230 0.633905
\(27\) −1.00000 −0.192450
\(28\) 0.924574 0.174728
\(29\) −0.208014 −0.0386272 −0.0193136 0.999813i \(-0.506148\pi\)
−0.0193136 + 0.999813i \(0.506148\pi\)
\(30\) −1.14595 −0.209222
\(31\) −2.92063 −0.524561 −0.262281 0.964992i \(-0.584475\pi\)
−0.262281 + 0.964992i \(0.584475\pi\)
\(32\) −4.72172 −0.834691
\(33\) 3.63449 0.632684
\(34\) 0.982175 0.168442
\(35\) 1.10504 0.186785
\(36\) −0.924574 −0.154096
\(37\) 10.3878 1.70774 0.853870 0.520487i \(-0.174249\pi\)
0.853870 + 0.520487i \(0.174249\pi\)
\(38\) 6.09994 0.989541
\(39\) 3.11689 0.499101
\(40\) −3.35143 −0.529907
\(41\) 4.40926 0.688610 0.344305 0.938858i \(-0.388115\pi\)
0.344305 + 0.938858i \(0.388115\pi\)
\(42\) −1.03703 −0.160017
\(43\) −5.58070 −0.851048 −0.425524 0.904947i \(-0.639910\pi\)
−0.425524 + 0.904947i \(0.639910\pi\)
\(44\) 3.36036 0.506593
\(45\) −1.10504 −0.164729
\(46\) 4.65000 0.685605
\(47\) −6.89665 −1.00598 −0.502990 0.864292i \(-0.667767\pi\)
−0.502990 + 0.864292i \(0.667767\pi\)
\(48\) 1.29602 0.187064
\(49\) 1.00000 0.142857
\(50\) 3.91882 0.554204
\(51\) 0.947106 0.132621
\(52\) 2.88179 0.399632
\(53\) 8.55990 1.17579 0.587896 0.808936i \(-0.299956\pi\)
0.587896 + 0.808936i \(0.299956\pi\)
\(54\) 1.03703 0.141122
\(55\) 4.01625 0.541551
\(56\) −3.03286 −0.405283
\(57\) 5.88214 0.779109
\(58\) 0.215716 0.0283249
\(59\) −12.1039 −1.57579 −0.787895 0.615810i \(-0.788829\pi\)
−0.787895 + 0.615810i \(0.788829\pi\)
\(60\) −1.02169 −0.131899
\(61\) −3.44450 −0.441023 −0.220512 0.975384i \(-0.570773\pi\)
−0.220512 + 0.975384i \(0.570773\pi\)
\(62\) 3.02878 0.384655
\(63\) −1.00000 −0.125988
\(64\) 7.48859 0.936074
\(65\) 3.44427 0.427210
\(66\) −3.76907 −0.463940
\(67\) −15.5558 −1.90044 −0.950220 0.311580i \(-0.899142\pi\)
−0.950220 + 0.311580i \(0.899142\pi\)
\(68\) 0.875670 0.106191
\(69\) 4.48397 0.539807
\(70\) −1.14595 −0.136968
\(71\) −15.9734 −1.89569 −0.947844 0.318733i \(-0.896743\pi\)
−0.947844 + 0.318733i \(0.896743\pi\)
\(72\) 3.03286 0.357426
\(73\) −2.33818 −0.273664 −0.136832 0.990594i \(-0.543692\pi\)
−0.136832 + 0.990594i \(0.543692\pi\)
\(74\) −10.7724 −1.25227
\(75\) 3.77889 0.436349
\(76\) 5.43847 0.623836
\(77\) 3.63449 0.414189
\(78\) −3.23230 −0.365985
\(79\) −3.93588 −0.442821 −0.221410 0.975181i \(-0.571066\pi\)
−0.221410 + 0.975181i \(0.571066\pi\)
\(80\) 1.43215 0.160119
\(81\) 1.00000 0.111111
\(82\) −4.57252 −0.504951
\(83\) −8.71714 −0.956830 −0.478415 0.878134i \(-0.658789\pi\)
−0.478415 + 0.878134i \(0.658789\pi\)
\(84\) −0.924574 −0.100879
\(85\) 1.04659 0.113518
\(86\) 5.78733 0.624064
\(87\) 0.208014 0.0223014
\(88\) −11.0229 −1.17505
\(89\) −4.31048 −0.456910 −0.228455 0.973554i \(-0.573367\pi\)
−0.228455 + 0.973554i \(0.573367\pi\)
\(90\) 1.14595 0.120794
\(91\) 3.11689 0.326738
\(92\) 4.14576 0.432226
\(93\) 2.92063 0.302856
\(94\) 7.15202 0.737674
\(95\) 6.49999 0.666884
\(96\) 4.72172 0.481909
\(97\) 1.19390 0.121222 0.0606111 0.998161i \(-0.480695\pi\)
0.0606111 + 0.998161i \(0.480695\pi\)
\(98\) −1.03703 −0.104756
\(99\) −3.63449 −0.365280
\(100\) 3.49387 0.349387
\(101\) −18.9910 −1.88968 −0.944838 0.327539i \(-0.893781\pi\)
−0.944838 + 0.327539i \(0.893781\pi\)
\(102\) −0.982175 −0.0972498
\(103\) −2.36424 −0.232955 −0.116478 0.993193i \(-0.537160\pi\)
−0.116478 + 0.993193i \(0.537160\pi\)
\(104\) −9.45309 −0.926952
\(105\) −1.10504 −0.107841
\(106\) −8.87685 −0.862196
\(107\) 3.22132 0.311417 0.155708 0.987803i \(-0.450234\pi\)
0.155708 + 0.987803i \(0.450234\pi\)
\(108\) 0.924574 0.0889672
\(109\) −0.529736 −0.0507395 −0.0253698 0.999678i \(-0.508076\pi\)
−0.0253698 + 0.999678i \(0.508076\pi\)
\(110\) −4.16496 −0.397113
\(111\) −10.3878 −0.985964
\(112\) 1.29602 0.122462
\(113\) 1.76974 0.166484 0.0832418 0.996529i \(-0.473473\pi\)
0.0832418 + 0.996529i \(0.473473\pi\)
\(114\) −6.09994 −0.571312
\(115\) 4.95495 0.462052
\(116\) 0.192324 0.0178568
\(117\) −3.11689 −0.288156
\(118\) 12.5520 1.15551
\(119\) 0.947106 0.0868211
\(120\) 3.35143 0.305942
\(121\) 2.20953 0.200867
\(122\) 3.57204 0.323398
\(123\) −4.40926 −0.397569
\(124\) 2.70034 0.242498
\(125\) 9.70100 0.867684
\(126\) 1.03703 0.0923858
\(127\) −1.32367 −0.117456 −0.0587282 0.998274i \(-0.518705\pi\)
−0.0587282 + 0.998274i \(0.518705\pi\)
\(128\) 1.67758 0.148278
\(129\) 5.58070 0.491353
\(130\) −3.57181 −0.313268
\(131\) −0.795161 −0.0694735 −0.0347368 0.999396i \(-0.511059\pi\)
−0.0347368 + 0.999396i \(0.511059\pi\)
\(132\) −3.36036 −0.292481
\(133\) 5.88214 0.510046
\(134\) 16.1318 1.39357
\(135\) 1.10504 0.0951065
\(136\) −2.87244 −0.246310
\(137\) −15.2335 −1.30148 −0.650742 0.759299i \(-0.725542\pi\)
−0.650742 + 0.759299i \(0.725542\pi\)
\(138\) −4.65000 −0.395834
\(139\) 18.7326 1.58888 0.794441 0.607342i \(-0.207764\pi\)
0.794441 + 0.607342i \(0.207764\pi\)
\(140\) −1.02169 −0.0863484
\(141\) 6.89665 0.580803
\(142\) 16.5648 1.39009
\(143\) 11.3283 0.947320
\(144\) −1.29602 −0.108001
\(145\) 0.229863 0.0190891
\(146\) 2.42476 0.200675
\(147\) −1.00000 −0.0824786
\(148\) −9.60427 −0.789466
\(149\) 5.93727 0.486400 0.243200 0.969976i \(-0.421803\pi\)
0.243200 + 0.969976i \(0.421803\pi\)
\(150\) −3.91882 −0.319970
\(151\) −7.85858 −0.639522 −0.319761 0.947498i \(-0.603603\pi\)
−0.319761 + 0.947498i \(0.603603\pi\)
\(152\) −17.8397 −1.44699
\(153\) −0.947106 −0.0765690
\(154\) −3.76907 −0.303720
\(155\) 3.22741 0.259232
\(156\) −2.88179 −0.230728
\(157\) 6.21046 0.495649 0.247824 0.968805i \(-0.420284\pi\)
0.247824 + 0.968805i \(0.420284\pi\)
\(158\) 4.08161 0.324716
\(159\) −8.55990 −0.678844
\(160\) 5.21768 0.412494
\(161\) 4.48397 0.353386
\(162\) −1.03703 −0.0814766
\(163\) 19.4849 1.52618 0.763089 0.646293i \(-0.223682\pi\)
0.763089 + 0.646293i \(0.223682\pi\)
\(164\) −4.07668 −0.318336
\(165\) −4.01625 −0.312665
\(166\) 9.03991 0.701633
\(167\) 1.48211 0.114689 0.0573445 0.998354i \(-0.481737\pi\)
0.0573445 + 0.998354i \(0.481737\pi\)
\(168\) 3.03286 0.233991
\(169\) −3.28503 −0.252694
\(170\) −1.08534 −0.0832418
\(171\) −5.88214 −0.449819
\(172\) 5.15977 0.393428
\(173\) −11.0374 −0.839159 −0.419579 0.907719i \(-0.637822\pi\)
−0.419579 + 0.907719i \(0.637822\pi\)
\(174\) −0.215716 −0.0163534
\(175\) 3.77889 0.285657
\(176\) 4.71036 0.355057
\(177\) 12.1039 0.909783
\(178\) 4.47009 0.335047
\(179\) 21.9314 1.63923 0.819615 0.572914i \(-0.194187\pi\)
0.819615 + 0.572914i \(0.194187\pi\)
\(180\) 1.02169 0.0761522
\(181\) 3.88994 0.289137 0.144568 0.989495i \(-0.453821\pi\)
0.144568 + 0.989495i \(0.453821\pi\)
\(182\) −3.23230 −0.239594
\(183\) 3.44450 0.254625
\(184\) −13.5993 −1.00255
\(185\) −11.4789 −0.843944
\(186\) −3.02878 −0.222081
\(187\) 3.44225 0.251722
\(188\) 6.37646 0.465051
\(189\) 1.00000 0.0727393
\(190\) −6.74066 −0.489019
\(191\) 1.00000 0.0723575
\(192\) −7.48859 −0.540442
\(193\) 16.6386 1.19767 0.598835 0.800872i \(-0.295630\pi\)
0.598835 + 0.800872i \(0.295630\pi\)
\(194\) −1.23811 −0.0888909
\(195\) −3.44427 −0.246650
\(196\) −0.924574 −0.0660410
\(197\) −16.6427 −1.18574 −0.592870 0.805298i \(-0.702005\pi\)
−0.592870 + 0.805298i \(0.702005\pi\)
\(198\) 3.76907 0.267856
\(199\) −17.0296 −1.20720 −0.603599 0.797288i \(-0.706267\pi\)
−0.603599 + 0.797288i \(0.706267\pi\)
\(200\) −11.4609 −0.810406
\(201\) 15.5558 1.09722
\(202\) 19.6942 1.38568
\(203\) 0.208014 0.0145997
\(204\) −0.875670 −0.0613091
\(205\) −4.87239 −0.340303
\(206\) 2.45178 0.170824
\(207\) −4.48397 −0.311657
\(208\) 4.03953 0.280091
\(209\) 21.3786 1.47879
\(210\) 1.14595 0.0790783
\(211\) 21.3817 1.47197 0.735987 0.676996i \(-0.236718\pi\)
0.735987 + 0.676996i \(0.236718\pi\)
\(212\) −7.91426 −0.543554
\(213\) 15.9734 1.09448
\(214\) −3.34060 −0.228359
\(215\) 6.16688 0.420577
\(216\) −3.03286 −0.206360
\(217\) 2.92063 0.198266
\(218\) 0.549351 0.0372067
\(219\) 2.33818 0.158000
\(220\) −3.71332 −0.250352
\(221\) 2.95202 0.198574
\(222\) 10.7724 0.722997
\(223\) −5.93620 −0.397517 −0.198759 0.980048i \(-0.563691\pi\)
−0.198759 + 0.980048i \(0.563691\pi\)
\(224\) 4.72172 0.315483
\(225\) −3.77889 −0.251926
\(226\) −1.83527 −0.122081
\(227\) 7.49099 0.497195 0.248597 0.968607i \(-0.420030\pi\)
0.248597 + 0.968607i \(0.420030\pi\)
\(228\) −5.43847 −0.360172
\(229\) 29.2528 1.93308 0.966540 0.256515i \(-0.0825745\pi\)
0.966540 + 0.256515i \(0.0825745\pi\)
\(230\) −5.13842 −0.338818
\(231\) −3.63449 −0.239132
\(232\) −0.630878 −0.0414191
\(233\) −11.1443 −0.730084 −0.365042 0.930991i \(-0.618945\pi\)
−0.365042 + 0.930991i \(0.618945\pi\)
\(234\) 3.23230 0.211302
\(235\) 7.62106 0.497143
\(236\) 11.1909 0.728467
\(237\) 3.93588 0.255663
\(238\) −0.982175 −0.0636650
\(239\) 28.7312 1.85847 0.929235 0.369490i \(-0.120468\pi\)
0.929235 + 0.369490i \(0.120468\pi\)
\(240\) −1.43215 −0.0924446
\(241\) 20.8421 1.34255 0.671277 0.741206i \(-0.265746\pi\)
0.671277 + 0.741206i \(0.265746\pi\)
\(242\) −2.29135 −0.147293
\(243\) −1.00000 −0.0641500
\(244\) 3.18470 0.203879
\(245\) −1.10504 −0.0705982
\(246\) 4.57252 0.291533
\(247\) 18.3340 1.16656
\(248\) −8.85789 −0.562476
\(249\) 8.71714 0.552426
\(250\) −10.0602 −0.636263
\(251\) −1.85083 −0.116823 −0.0584116 0.998293i \(-0.518604\pi\)
−0.0584116 + 0.998293i \(0.518604\pi\)
\(252\) 0.924574 0.0582427
\(253\) 16.2970 1.02458
\(254\) 1.37268 0.0861295
\(255\) −1.04659 −0.0655399
\(256\) −16.7169 −1.04480
\(257\) −27.7137 −1.72873 −0.864366 0.502864i \(-0.832280\pi\)
−0.864366 + 0.502864i \(0.832280\pi\)
\(258\) −5.78733 −0.360304
\(259\) −10.3878 −0.645465
\(260\) −3.18449 −0.197493
\(261\) −0.208014 −0.0128757
\(262\) 0.824604 0.0509442
\(263\) 12.8633 0.793186 0.396593 0.917995i \(-0.370192\pi\)
0.396593 + 0.917995i \(0.370192\pi\)
\(264\) 11.0229 0.678414
\(265\) −9.45901 −0.581062
\(266\) −6.09994 −0.374011
\(267\) 4.31048 0.263797
\(268\) 14.3825 0.878549
\(269\) −25.0295 −1.52607 −0.763037 0.646355i \(-0.776292\pi\)
−0.763037 + 0.646355i \(0.776292\pi\)
\(270\) −1.14595 −0.0697405
\(271\) 21.1717 1.28609 0.643045 0.765829i \(-0.277671\pi\)
0.643045 + 0.765829i \(0.277671\pi\)
\(272\) 1.22746 0.0744259
\(273\) −3.11689 −0.188642
\(274\) 15.7975 0.954364
\(275\) 13.7344 0.828213
\(276\) −4.14576 −0.249546
\(277\) −8.31613 −0.499668 −0.249834 0.968289i \(-0.580376\pi\)
−0.249834 + 0.968289i \(0.580376\pi\)
\(278\) −19.4263 −1.16511
\(279\) −2.92063 −0.174854
\(280\) 3.35143 0.200286
\(281\) 7.02617 0.419146 0.209573 0.977793i \(-0.432793\pi\)
0.209573 + 0.977793i \(0.432793\pi\)
\(282\) −7.15202 −0.425896
\(283\) −12.8768 −0.765445 −0.382722 0.923863i \(-0.625013\pi\)
−0.382722 + 0.923863i \(0.625013\pi\)
\(284\) 14.7686 0.876352
\(285\) −6.49999 −0.385026
\(286\) −11.7478 −0.694659
\(287\) −4.40926 −0.260270
\(288\) −4.72172 −0.278230
\(289\) −16.1030 −0.947235
\(290\) −0.238374 −0.0139978
\(291\) −1.19390 −0.0699877
\(292\) 2.16182 0.126511
\(293\) −1.60819 −0.0939513 −0.0469757 0.998896i \(-0.514958\pi\)
−0.0469757 + 0.998896i \(0.514958\pi\)
\(294\) 1.03703 0.0604807
\(295\) 13.3752 0.778736
\(296\) 31.5047 1.83117
\(297\) 3.63449 0.210895
\(298\) −6.15711 −0.356672
\(299\) 13.9760 0.808254
\(300\) −3.49387 −0.201718
\(301\) 5.58070 0.321666
\(302\) 8.14956 0.468955
\(303\) 18.9910 1.09100
\(304\) 7.62335 0.437229
\(305\) 3.80630 0.217948
\(306\) 0.982175 0.0561472
\(307\) 13.6333 0.778091 0.389045 0.921219i \(-0.372805\pi\)
0.389045 + 0.921219i \(0.372805\pi\)
\(308\) −3.36036 −0.191474
\(309\) 2.36424 0.134497
\(310\) −3.34691 −0.190092
\(311\) −21.1376 −1.19861 −0.599303 0.800522i \(-0.704555\pi\)
−0.599303 + 0.800522i \(0.704555\pi\)
\(312\) 9.45309 0.535176
\(313\) 21.6650 1.22458 0.612290 0.790633i \(-0.290249\pi\)
0.612290 + 0.790633i \(0.290249\pi\)
\(314\) −6.44042 −0.363454
\(315\) 1.10504 0.0622618
\(316\) 3.63901 0.204710
\(317\) −4.02993 −0.226343 −0.113172 0.993575i \(-0.536101\pi\)
−0.113172 + 0.993575i \(0.536101\pi\)
\(318\) 8.87685 0.497789
\(319\) 0.756025 0.0423292
\(320\) −8.27517 −0.462596
\(321\) −3.22132 −0.179797
\(322\) −4.65000 −0.259134
\(323\) 5.57101 0.309979
\(324\) −0.924574 −0.0513652
\(325\) 11.7784 0.653347
\(326\) −20.2064 −1.11913
\(327\) 0.529736 0.0292945
\(328\) 13.3727 0.738383
\(329\) 6.89665 0.380225
\(330\) 4.16496 0.229274
\(331\) 32.3774 1.77962 0.889810 0.456330i \(-0.150836\pi\)
0.889810 + 0.456330i \(0.150836\pi\)
\(332\) 8.05964 0.442330
\(333\) 10.3878 0.569247
\(334\) −1.53699 −0.0841002
\(335\) 17.1897 0.939174
\(336\) −1.29602 −0.0707034
\(337\) 6.16555 0.335859 0.167930 0.985799i \(-0.446292\pi\)
0.167930 + 0.985799i \(0.446292\pi\)
\(338\) 3.40666 0.185298
\(339\) −1.76974 −0.0961193
\(340\) −0.967648 −0.0524781
\(341\) 10.6150 0.574836
\(342\) 6.09994 0.329847
\(343\) −1.00000 −0.0539949
\(344\) −16.9255 −0.912561
\(345\) −4.95495 −0.266766
\(346\) 11.4461 0.615346
\(347\) 11.9209 0.639949 0.319975 0.947426i \(-0.396326\pi\)
0.319975 + 0.947426i \(0.396326\pi\)
\(348\) −0.192324 −0.0103097
\(349\) −19.5567 −1.04684 −0.523422 0.852073i \(-0.675345\pi\)
−0.523422 + 0.852073i \(0.675345\pi\)
\(350\) −3.91882 −0.209470
\(351\) 3.11689 0.166367
\(352\) 17.1611 0.914688
\(353\) 10.6088 0.564651 0.282326 0.959319i \(-0.408894\pi\)
0.282326 + 0.959319i \(0.408894\pi\)
\(354\) −12.5520 −0.667134
\(355\) 17.6512 0.936826
\(356\) 3.98536 0.211224
\(357\) −0.947106 −0.0501262
\(358\) −22.7435 −1.20203
\(359\) −17.3249 −0.914374 −0.457187 0.889371i \(-0.651143\pi\)
−0.457187 + 0.889371i \(0.651143\pi\)
\(360\) −3.35143 −0.176636
\(361\) 15.5996 0.821031
\(362\) −4.03397 −0.212021
\(363\) −2.20953 −0.115970
\(364\) −2.88179 −0.151047
\(365\) 2.58378 0.135241
\(366\) −3.57204 −0.186714
\(367\) −16.3946 −0.855790 −0.427895 0.903828i \(-0.640745\pi\)
−0.427895 + 0.903828i \(0.640745\pi\)
\(368\) 5.81129 0.302935
\(369\) 4.40926 0.229537
\(370\) 11.9039 0.618855
\(371\) −8.55990 −0.444408
\(372\) −2.70034 −0.140006
\(373\) −14.8397 −0.768371 −0.384185 0.923256i \(-0.625518\pi\)
−0.384185 + 0.923256i \(0.625518\pi\)
\(374\) −3.56971 −0.184585
\(375\) −9.70100 −0.500958
\(376\) −20.9166 −1.07869
\(377\) 0.648355 0.0333920
\(378\) −1.03703 −0.0533389
\(379\) 4.27019 0.219345 0.109672 0.993968i \(-0.465020\pi\)
0.109672 + 0.993968i \(0.465020\pi\)
\(380\) −6.00972 −0.308292
\(381\) 1.32367 0.0678135
\(382\) −1.03703 −0.0530589
\(383\) −3.24085 −0.165600 −0.0827999 0.996566i \(-0.526386\pi\)
−0.0827999 + 0.996566i \(0.526386\pi\)
\(384\) −1.67758 −0.0856084
\(385\) −4.01625 −0.204687
\(386\) −17.2547 −0.878239
\(387\) −5.58070 −0.283683
\(388\) −1.10385 −0.0560394
\(389\) 6.13044 0.310825 0.155413 0.987850i \(-0.450329\pi\)
0.155413 + 0.987850i \(0.450329\pi\)
\(390\) 3.57181 0.180866
\(391\) 4.24680 0.214770
\(392\) 3.03286 0.153183
\(393\) 0.795161 0.0401106
\(394\) 17.2589 0.869490
\(395\) 4.34929 0.218837
\(396\) 3.36036 0.168864
\(397\) 15.5375 0.779803 0.389901 0.920857i \(-0.372509\pi\)
0.389901 + 0.920857i \(0.372509\pi\)
\(398\) 17.6602 0.885226
\(399\) −5.88214 −0.294475
\(400\) 4.89750 0.244875
\(401\) −18.2847 −0.913096 −0.456548 0.889699i \(-0.650914\pi\)
−0.456548 + 0.889699i \(0.650914\pi\)
\(402\) −16.1318 −0.804579
\(403\) 9.10328 0.453467
\(404\) 17.5586 0.873572
\(405\) −1.10504 −0.0549097
\(406\) −0.215716 −0.0107058
\(407\) −37.7543 −1.87141
\(408\) 2.87244 0.142207
\(409\) −12.4054 −0.613408 −0.306704 0.951805i \(-0.599226\pi\)
−0.306704 + 0.951805i \(0.599226\pi\)
\(410\) 5.05281 0.249540
\(411\) 15.2335 0.751412
\(412\) 2.18591 0.107692
\(413\) 12.1039 0.595593
\(414\) 4.65000 0.228535
\(415\) 9.63276 0.472854
\(416\) 14.7171 0.721564
\(417\) −18.7326 −0.917341
\(418\) −22.1702 −1.08438
\(419\) −23.4003 −1.14318 −0.571589 0.820540i \(-0.693673\pi\)
−0.571589 + 0.820540i \(0.693673\pi\)
\(420\) 1.02169 0.0498533
\(421\) −28.1342 −1.37118 −0.685589 0.727989i \(-0.740455\pi\)
−0.685589 + 0.727989i \(0.740455\pi\)
\(422\) −22.1734 −1.07938
\(423\) −6.89665 −0.335327
\(424\) 25.9610 1.26078
\(425\) 3.57901 0.173608
\(426\) −16.5648 −0.802568
\(427\) 3.44450 0.166691
\(428\) −2.97835 −0.143964
\(429\) −11.3283 −0.546935
\(430\) −6.39522 −0.308405
\(431\) −15.9764 −0.769556 −0.384778 0.923009i \(-0.625722\pi\)
−0.384778 + 0.923009i \(0.625722\pi\)
\(432\) 1.29602 0.0623546
\(433\) 6.10886 0.293573 0.146786 0.989168i \(-0.453107\pi\)
0.146786 + 0.989168i \(0.453107\pi\)
\(434\) −3.02878 −0.145386
\(435\) −0.229863 −0.0110211
\(436\) 0.489780 0.0234562
\(437\) 26.3753 1.26170
\(438\) −2.42476 −0.115860
\(439\) −27.1465 −1.29563 −0.647815 0.761798i \(-0.724317\pi\)
−0.647815 + 0.761798i \(0.724317\pi\)
\(440\) 12.1807 0.580694
\(441\) 1.00000 0.0476190
\(442\) −3.06133 −0.145612
\(443\) −0.710893 −0.0337755 −0.0168878 0.999857i \(-0.505376\pi\)
−0.0168878 + 0.999857i \(0.505376\pi\)
\(444\) 9.60427 0.455798
\(445\) 4.76325 0.225800
\(446\) 6.15600 0.291495
\(447\) −5.93727 −0.280823
\(448\) −7.48859 −0.353803
\(449\) 8.87985 0.419066 0.209533 0.977802i \(-0.432806\pi\)
0.209533 + 0.977802i \(0.432806\pi\)
\(450\) 3.91882 0.184735
\(451\) −16.0254 −0.754607
\(452\) −1.63626 −0.0769632
\(453\) 7.85858 0.369228
\(454\) −7.76836 −0.364587
\(455\) −3.44427 −0.161470
\(456\) 17.8397 0.835422
\(457\) 12.0478 0.563571 0.281785 0.959477i \(-0.409073\pi\)
0.281785 + 0.959477i \(0.409073\pi\)
\(458\) −30.3360 −1.41751
\(459\) 0.947106 0.0442071
\(460\) −4.58122 −0.213601
\(461\) 26.5290 1.23558 0.617790 0.786343i \(-0.288028\pi\)
0.617790 + 0.786343i \(0.288028\pi\)
\(462\) 3.76907 0.175353
\(463\) 16.2694 0.756102 0.378051 0.925785i \(-0.376594\pi\)
0.378051 + 0.925785i \(0.376594\pi\)
\(464\) 0.269589 0.0125154
\(465\) −3.22741 −0.149668
\(466\) 11.5569 0.535363
\(467\) −11.6417 −0.538713 −0.269356 0.963041i \(-0.586811\pi\)
−0.269356 + 0.963041i \(0.586811\pi\)
\(468\) 2.88179 0.133211
\(469\) 15.5558 0.718299
\(470\) −7.90325 −0.364550
\(471\) −6.21046 −0.286163
\(472\) −36.7094 −1.68969
\(473\) 20.2830 0.932613
\(474\) −4.08161 −0.187475
\(475\) 22.2280 1.01989
\(476\) −0.875670 −0.0401363
\(477\) 8.55990 0.391931
\(478\) −29.7951 −1.36280
\(479\) −13.9042 −0.635298 −0.317649 0.948208i \(-0.602893\pi\)
−0.317649 + 0.948208i \(0.602893\pi\)
\(480\) −5.21768 −0.238153
\(481\) −32.3775 −1.47629
\(482\) −21.6138 −0.984481
\(483\) −4.48397 −0.204028
\(484\) −2.04288 −0.0928580
\(485\) −1.31930 −0.0599065
\(486\) 1.03703 0.0470405
\(487\) 20.0714 0.909521 0.454760 0.890614i \(-0.349725\pi\)
0.454760 + 0.890614i \(0.349725\pi\)
\(488\) −10.4467 −0.472900
\(489\) −19.4849 −0.881139
\(490\) 1.14595 0.0517689
\(491\) −25.7718 −1.16306 −0.581532 0.813524i \(-0.697546\pi\)
−0.581532 + 0.813524i \(0.697546\pi\)
\(492\) 4.07668 0.183791
\(493\) 0.197011 0.00887294
\(494\) −19.0128 −0.855427
\(495\) 4.01625 0.180517
\(496\) 3.78519 0.169960
\(497\) 15.9734 0.716503
\(498\) −9.03991 −0.405088
\(499\) −10.1009 −0.452179 −0.226089 0.974107i \(-0.572594\pi\)
−0.226089 + 0.974107i \(0.572594\pi\)
\(500\) −8.96929 −0.401119
\(501\) −1.48211 −0.0662157
\(502\) 1.91936 0.0856652
\(503\) −36.5060 −1.62772 −0.813861 0.581060i \(-0.802638\pi\)
−0.813861 + 0.581060i \(0.802638\pi\)
\(504\) −3.03286 −0.135094
\(505\) 20.9858 0.933854
\(506\) −16.9004 −0.751314
\(507\) 3.28503 0.145893
\(508\) 1.22383 0.0542986
\(509\) 27.7174 1.22855 0.614275 0.789092i \(-0.289448\pi\)
0.614275 + 0.789092i \(0.289448\pi\)
\(510\) 1.08534 0.0480597
\(511\) 2.33818 0.103435
\(512\) 13.9807 0.617866
\(513\) 5.88214 0.259703
\(514\) 28.7398 1.26766
\(515\) 2.61257 0.115124
\(516\) −5.15977 −0.227146
\(517\) 25.0658 1.10239
\(518\) 10.7724 0.473312
\(519\) 11.0374 0.484489
\(520\) 10.4460 0.458088
\(521\) 32.4414 1.42128 0.710641 0.703554i \(-0.248405\pi\)
0.710641 + 0.703554i \(0.248405\pi\)
\(522\) 0.215716 0.00944164
\(523\) 8.70652 0.380709 0.190355 0.981715i \(-0.439036\pi\)
0.190355 + 0.981715i \(0.439036\pi\)
\(524\) 0.735185 0.0321167
\(525\) −3.77889 −0.164924
\(526\) −13.3396 −0.581635
\(527\) 2.76615 0.120495
\(528\) −4.71036 −0.204992
\(529\) −2.89401 −0.125827
\(530\) 9.80925 0.426087
\(531\) −12.1039 −0.525263
\(532\) −5.43847 −0.235788
\(533\) −13.7432 −0.595282
\(534\) −4.47009 −0.193440
\(535\) −3.55968 −0.153898
\(536\) −47.1785 −2.03780
\(537\) −21.9314 −0.946410
\(538\) 25.9562 1.11905
\(539\) −3.63449 −0.156549
\(540\) −1.02169 −0.0439665
\(541\) 27.5515 1.18453 0.592265 0.805743i \(-0.298234\pi\)
0.592265 + 0.805743i \(0.298234\pi\)
\(542\) −21.9556 −0.943075
\(543\) −3.88994 −0.166933
\(544\) 4.47197 0.191734
\(545\) 0.585378 0.0250748
\(546\) 3.23230 0.138329
\(547\) 26.9337 1.15160 0.575801 0.817590i \(-0.304690\pi\)
0.575801 + 0.817590i \(0.304690\pi\)
\(548\) 14.0845 0.601659
\(549\) −3.44450 −0.147008
\(550\) −14.2429 −0.607319
\(551\) 1.22357 0.0521257
\(552\) 13.5993 0.578823
\(553\) 3.93588 0.167371
\(554\) 8.62406 0.366401
\(555\) 11.4789 0.487251
\(556\) −17.3197 −0.734519
\(557\) −34.4089 −1.45795 −0.728975 0.684540i \(-0.760003\pi\)
−0.728975 + 0.684540i \(0.760003\pi\)
\(558\) 3.02878 0.128218
\(559\) 17.3944 0.735704
\(560\) −1.43215 −0.0605192
\(561\) −3.44225 −0.145332
\(562\) −7.28633 −0.307355
\(563\) −11.5076 −0.484986 −0.242493 0.970153i \(-0.577965\pi\)
−0.242493 + 0.970153i \(0.577965\pi\)
\(564\) −6.37646 −0.268498
\(565\) −1.95563 −0.0822741
\(566\) 13.3536 0.561292
\(567\) −1.00000 −0.0419961
\(568\) −48.4450 −2.03271
\(569\) −7.35747 −0.308441 −0.154221 0.988036i \(-0.549287\pi\)
−0.154221 + 0.988036i \(0.549287\pi\)
\(570\) 6.74066 0.282335
\(571\) −3.16207 −0.132328 −0.0661642 0.997809i \(-0.521076\pi\)
−0.0661642 + 0.997809i \(0.521076\pi\)
\(572\) −10.4738 −0.437933
\(573\) −1.00000 −0.0417756
\(574\) 4.57252 0.190853
\(575\) 16.9444 0.706632
\(576\) 7.48859 0.312025
\(577\) 1.29342 0.0538459 0.0269229 0.999638i \(-0.491429\pi\)
0.0269229 + 0.999638i \(0.491429\pi\)
\(578\) 16.6992 0.694597
\(579\) −16.6386 −0.691476
\(580\) −0.212525 −0.00882463
\(581\) 8.71714 0.361648
\(582\) 1.23811 0.0513212
\(583\) −31.1109 −1.28848
\(584\) −7.09139 −0.293444
\(585\) 3.44427 0.142403
\(586\) 1.66773 0.0688935
\(587\) 11.8711 0.489973 0.244986 0.969527i \(-0.421217\pi\)
0.244986 + 0.969527i \(0.421217\pi\)
\(588\) 0.924574 0.0381288
\(589\) 17.1796 0.707872
\(590\) −13.8705 −0.571039
\(591\) 16.6427 0.684587
\(592\) −13.4627 −0.553314
\(593\) −25.9049 −1.06379 −0.531894 0.846811i \(-0.678520\pi\)
−0.531894 + 0.846811i \(0.678520\pi\)
\(594\) −3.76907 −0.154647
\(595\) −1.04659 −0.0429059
\(596\) −5.48944 −0.224856
\(597\) 17.0296 0.696976
\(598\) −14.4935 −0.592684
\(599\) 10.1528 0.414831 0.207416 0.978253i \(-0.433495\pi\)
0.207416 + 0.978253i \(0.433495\pi\)
\(600\) 11.4609 0.467888
\(601\) 42.6428 1.73943 0.869717 0.493550i \(-0.164301\pi\)
0.869717 + 0.493550i \(0.164301\pi\)
\(602\) −5.78733 −0.235874
\(603\) −15.5558 −0.633480
\(604\) 7.26583 0.295643
\(605\) −2.44162 −0.0992658
\(606\) −19.6942 −0.800022
\(607\) 8.63548 0.350503 0.175252 0.984524i \(-0.443926\pi\)
0.175252 + 0.984524i \(0.443926\pi\)
\(608\) 27.7738 1.12638
\(609\) −0.208014 −0.00842915
\(610\) −3.94724 −0.159819
\(611\) 21.4961 0.869638
\(612\) 0.875670 0.0353968
\(613\) −20.5553 −0.830219 −0.415109 0.909771i \(-0.636257\pi\)
−0.415109 + 0.909771i \(0.636257\pi\)
\(614\) −14.1381 −0.570566
\(615\) 4.87239 0.196474
\(616\) 11.0229 0.444126
\(617\) −4.93511 −0.198680 −0.0993401 0.995054i \(-0.531673\pi\)
−0.0993401 + 0.995054i \(0.531673\pi\)
\(618\) −2.45178 −0.0986251
\(619\) 20.5246 0.824952 0.412476 0.910968i \(-0.364664\pi\)
0.412476 + 0.910968i \(0.364664\pi\)
\(620\) −2.98398 −0.119839
\(621\) 4.48397 0.179936
\(622\) 21.9203 0.878924
\(623\) 4.31048 0.172696
\(624\) −4.03953 −0.161711
\(625\) 8.17449 0.326980
\(626\) −22.4672 −0.897971
\(627\) −21.3786 −0.853779
\(628\) −5.74203 −0.229132
\(629\) −9.83833 −0.392280
\(630\) −1.14595 −0.0456559
\(631\) −7.49153 −0.298233 −0.149117 0.988820i \(-0.547643\pi\)
−0.149117 + 0.988820i \(0.547643\pi\)
\(632\) −11.9370 −0.474828
\(633\) −21.3817 −0.849845
\(634\) 4.17915 0.165975
\(635\) 1.46270 0.0580455
\(636\) 7.91426 0.313821
\(637\) −3.11689 −0.123495
\(638\) −0.784018 −0.0310396
\(639\) −15.9734 −0.631896
\(640\) −1.85378 −0.0732772
\(641\) −32.0169 −1.26459 −0.632295 0.774727i \(-0.717887\pi\)
−0.632295 + 0.774727i \(0.717887\pi\)
\(642\) 3.34060 0.131843
\(643\) 8.94738 0.352850 0.176425 0.984314i \(-0.443547\pi\)
0.176425 + 0.984314i \(0.443547\pi\)
\(644\) −4.14576 −0.163366
\(645\) −6.16688 −0.242821
\(646\) −5.77729 −0.227305
\(647\) −35.5722 −1.39849 −0.699243 0.714884i \(-0.746479\pi\)
−0.699243 + 0.714884i \(0.746479\pi\)
\(648\) 3.03286 0.119142
\(649\) 43.9914 1.72681
\(650\) −12.2145 −0.479092
\(651\) −2.92063 −0.114469
\(652\) −18.0153 −0.705532
\(653\) 18.8391 0.737231 0.368616 0.929582i \(-0.379832\pi\)
0.368616 + 0.929582i \(0.379832\pi\)
\(654\) −0.549351 −0.0214813
\(655\) 0.878682 0.0343330
\(656\) −5.71447 −0.223112
\(657\) −2.33818 −0.0912212
\(658\) −7.15202 −0.278815
\(659\) −1.61347 −0.0628519 −0.0314259 0.999506i \(-0.510005\pi\)
−0.0314259 + 0.999506i \(0.510005\pi\)
\(660\) 3.71332 0.144541
\(661\) −19.2672 −0.749407 −0.374703 0.927145i \(-0.622255\pi\)
−0.374703 + 0.927145i \(0.622255\pi\)
\(662\) −33.5762 −1.30498
\(663\) −2.95202 −0.114647
\(664\) −26.4379 −1.02599
\(665\) −6.49999 −0.252059
\(666\) −10.7724 −0.417422
\(667\) 0.932728 0.0361154
\(668\) −1.37032 −0.0530192
\(669\) 5.93620 0.229507
\(670\) −17.8262 −0.688686
\(671\) 12.5190 0.483291
\(672\) −4.72172 −0.182144
\(673\) 21.5656 0.831293 0.415646 0.909526i \(-0.363555\pi\)
0.415646 + 0.909526i \(0.363555\pi\)
\(674\) −6.39385 −0.246282
\(675\) 3.77889 0.145450
\(676\) 3.03725 0.116817
\(677\) 29.6716 1.14037 0.570186 0.821516i \(-0.306871\pi\)
0.570186 + 0.821516i \(0.306871\pi\)
\(678\) 1.83527 0.0704833
\(679\) −1.19390 −0.0458177
\(680\) 3.17416 0.121723
\(681\) −7.49099 −0.287055
\(682\) −11.0081 −0.421521
\(683\) 5.48534 0.209891 0.104945 0.994478i \(-0.466533\pi\)
0.104945 + 0.994478i \(0.466533\pi\)
\(684\) 5.43847 0.207945
\(685\) 16.8336 0.643177
\(686\) 1.03703 0.0395939
\(687\) −29.2528 −1.11606
\(688\) 7.23267 0.275743
\(689\) −26.6802 −1.01644
\(690\) 5.13842 0.195616
\(691\) −18.4418 −0.701560 −0.350780 0.936458i \(-0.614084\pi\)
−0.350780 + 0.936458i \(0.614084\pi\)
\(692\) 10.2049 0.387932
\(693\) 3.63449 0.138063
\(694\) −12.3623 −0.469268
\(695\) −20.7003 −0.785206
\(696\) 0.630878 0.0239134
\(697\) −4.17603 −0.158179
\(698\) 20.2808 0.767640
\(699\) 11.1443 0.421514
\(700\) −3.49387 −0.132056
\(701\) 5.75346 0.217305 0.108653 0.994080i \(-0.465346\pi\)
0.108653 + 0.994080i \(0.465346\pi\)
\(702\) −3.23230 −0.121995
\(703\) −61.1024 −2.30452
\(704\) −27.2172 −1.02579
\(705\) −7.62106 −0.287026
\(706\) −11.0017 −0.414053
\(707\) 18.9910 0.714230
\(708\) −11.1909 −0.420581
\(709\) 37.2116 1.39751 0.698755 0.715361i \(-0.253738\pi\)
0.698755 + 0.715361i \(0.253738\pi\)
\(710\) −18.3047 −0.686964
\(711\) −3.93588 −0.147607
\(712\) −13.0731 −0.489936
\(713\) 13.0960 0.490450
\(714\) 0.982175 0.0367570
\(715\) −12.5182 −0.468154
\(716\) −20.2772 −0.757795
\(717\) −28.7312 −1.07299
\(718\) 17.9664 0.670501
\(719\) −7.63506 −0.284740 −0.142370 0.989814i \(-0.545472\pi\)
−0.142370 + 0.989814i \(0.545472\pi\)
\(720\) 1.43215 0.0533729
\(721\) 2.36424 0.0880488
\(722\) −16.1772 −0.602053
\(723\) −20.8421 −0.775124
\(724\) −3.59654 −0.133664
\(725\) 0.786062 0.0291936
\(726\) 2.29135 0.0850398
\(727\) 22.6101 0.838561 0.419280 0.907857i \(-0.362282\pi\)
0.419280 + 0.907857i \(0.362282\pi\)
\(728\) 9.45309 0.350355
\(729\) 1.00000 0.0370370
\(730\) −2.67945 −0.0991709
\(731\) 5.28551 0.195492
\(732\) −3.18470 −0.117710
\(733\) −2.30605 −0.0851760 −0.0425880 0.999093i \(-0.513560\pi\)
−0.0425880 + 0.999093i \(0.513560\pi\)
\(734\) 17.0016 0.627541
\(735\) 1.10504 0.0407599
\(736\) 21.1721 0.780413
\(737\) 56.5373 2.08258
\(738\) −4.57252 −0.168317
\(739\) 32.8528 1.20851 0.604256 0.796791i \(-0.293471\pi\)
0.604256 + 0.796791i \(0.293471\pi\)
\(740\) 10.6131 0.390144
\(741\) −18.3340 −0.673515
\(742\) 8.87685 0.325879
\(743\) 39.8459 1.46180 0.730902 0.682483i \(-0.239100\pi\)
0.730902 + 0.682483i \(0.239100\pi\)
\(744\) 8.85789 0.324746
\(745\) −6.56090 −0.240373
\(746\) 15.3892 0.563438
\(747\) −8.71714 −0.318943
\(748\) −3.18261 −0.116368
\(749\) −3.22132 −0.117705
\(750\) 10.0602 0.367347
\(751\) 49.7512 1.81545 0.907724 0.419567i \(-0.137818\pi\)
0.907724 + 0.419567i \(0.137818\pi\)
\(752\) 8.93817 0.325941
\(753\) 1.85083 0.0674479
\(754\) −0.672362 −0.0244860
\(755\) 8.68402 0.316044
\(756\) −0.924574 −0.0336264
\(757\) −33.2413 −1.20817 −0.604087 0.796918i \(-0.706462\pi\)
−0.604087 + 0.796918i \(0.706462\pi\)
\(758\) −4.42831 −0.160843
\(759\) −16.2970 −0.591542
\(760\) 19.7136 0.715086
\(761\) −22.7486 −0.824635 −0.412317 0.911040i \(-0.635281\pi\)
−0.412317 + 0.911040i \(0.635281\pi\)
\(762\) −1.37268 −0.0497269
\(763\) 0.529736 0.0191777
\(764\) −0.924574 −0.0334499
\(765\) 1.04659 0.0378395
\(766\) 3.36085 0.121433
\(767\) 37.7264 1.36222
\(768\) 16.7169 0.603218
\(769\) −26.7163 −0.963413 −0.481706 0.876333i \(-0.659983\pi\)
−0.481706 + 0.876333i \(0.659983\pi\)
\(770\) 4.16496 0.150095
\(771\) 27.7137 0.998083
\(772\) −15.3836 −0.553668
\(773\) 40.9745 1.47375 0.736875 0.676029i \(-0.236301\pi\)
0.736875 + 0.676029i \(0.236301\pi\)
\(774\) 5.78733 0.208021
\(775\) 11.0368 0.396452
\(776\) 3.62094 0.129984
\(777\) 10.3878 0.372659
\(778\) −6.35743 −0.227925
\(779\) −25.9359 −0.929249
\(780\) 3.18449 0.114023
\(781\) 58.0550 2.07737
\(782\) −4.40404 −0.157488
\(783\) 0.208014 0.00743381
\(784\) −1.29602 −0.0462863
\(785\) −6.86279 −0.244944
\(786\) −0.824604 −0.0294126
\(787\) −37.0708 −1.32143 −0.660715 0.750637i \(-0.729747\pi\)
−0.660715 + 0.750637i \(0.729747\pi\)
\(788\) 15.3874 0.548152
\(789\) −12.8633 −0.457946
\(790\) −4.51034 −0.160471
\(791\) −1.76974 −0.0629249
\(792\) −11.0229 −0.391682
\(793\) 10.7361 0.381251
\(794\) −16.1128 −0.571821
\(795\) 9.45901 0.335476
\(796\) 15.7452 0.558072
\(797\) −34.8433 −1.23421 −0.617107 0.786879i \(-0.711695\pi\)
−0.617107 + 0.786879i \(0.711695\pi\)
\(798\) 6.09994 0.215936
\(799\) 6.53186 0.231081
\(800\) 17.8429 0.630841
\(801\) −4.31048 −0.152303
\(802\) 18.9618 0.669564
\(803\) 8.49811 0.299892
\(804\) −14.3825 −0.507230
\(805\) −4.95495 −0.174639
\(806\) −9.44035 −0.332522
\(807\) 25.0295 0.881079
\(808\) −57.5971 −2.02626
\(809\) 0.459425 0.0161525 0.00807626 0.999967i \(-0.497429\pi\)
0.00807626 + 0.999967i \(0.497429\pi\)
\(810\) 1.14595 0.0402647
\(811\) 5.84158 0.205125 0.102563 0.994727i \(-0.467296\pi\)
0.102563 + 0.994727i \(0.467296\pi\)
\(812\) −0.192324 −0.00674925
\(813\) −21.1717 −0.742524
\(814\) 39.1522 1.37229
\(815\) −21.5316 −0.754219
\(816\) −1.22746 −0.0429698
\(817\) 32.8264 1.14845
\(818\) 12.8648 0.449805
\(819\) 3.11689 0.108913
\(820\) 4.50489 0.157318
\(821\) 36.5554 1.27579 0.637895 0.770123i \(-0.279805\pi\)
0.637895 + 0.770123i \(0.279805\pi\)
\(822\) −15.7975 −0.551002
\(823\) −11.2049 −0.390579 −0.195290 0.980746i \(-0.562565\pi\)
−0.195290 + 0.980746i \(0.562565\pi\)
\(824\) −7.17041 −0.249793
\(825\) −13.7344 −0.478169
\(826\) −12.5520 −0.436742
\(827\) −28.9897 −1.00807 −0.504036 0.863683i \(-0.668152\pi\)
−0.504036 + 0.863683i \(0.668152\pi\)
\(828\) 4.14576 0.144075
\(829\) 22.3728 0.777040 0.388520 0.921440i \(-0.372987\pi\)
0.388520 + 0.921440i \(0.372987\pi\)
\(830\) −9.98944 −0.346738
\(831\) 8.31613 0.288483
\(832\) −23.3411 −0.809206
\(833\) −0.947106 −0.0328153
\(834\) 19.4263 0.672676
\(835\) −1.63779 −0.0566779
\(836\) −19.7661 −0.683625
\(837\) 2.92063 0.100952
\(838\) 24.2667 0.838280
\(839\) −44.5582 −1.53832 −0.769159 0.639057i \(-0.779325\pi\)
−0.769159 + 0.639057i \(0.779325\pi\)
\(840\) −3.35143 −0.115635
\(841\) −28.9567 −0.998508
\(842\) 29.1760 1.00547
\(843\) −7.02617 −0.241994
\(844\) −19.7689 −0.680474
\(845\) 3.63008 0.124878
\(846\) 7.15202 0.245891
\(847\) −2.20953 −0.0759204
\(848\) −11.0938 −0.380961
\(849\) 12.8768 0.441930
\(850\) −3.71153 −0.127305
\(851\) −46.5785 −1.59669
\(852\) −14.7686 −0.505962
\(853\) −57.6634 −1.97436 −0.987179 0.159620i \(-0.948973\pi\)
−0.987179 + 0.159620i \(0.948973\pi\)
\(854\) −3.57204 −0.122233
\(855\) 6.49999 0.222295
\(856\) 9.76983 0.333926
\(857\) −46.7267 −1.59615 −0.798077 0.602555i \(-0.794149\pi\)
−0.798077 + 0.602555i \(0.794149\pi\)
\(858\) 11.7478 0.401062
\(859\) −32.3796 −1.10478 −0.552389 0.833587i \(-0.686284\pi\)
−0.552389 + 0.833587i \(0.686284\pi\)
\(860\) −5.70173 −0.194427
\(861\) 4.40926 0.150267
\(862\) 16.5680 0.564307
\(863\) 19.3716 0.659418 0.329709 0.944083i \(-0.393049\pi\)
0.329709 + 0.944083i \(0.393049\pi\)
\(864\) 4.72172 0.160636
\(865\) 12.1968 0.414702
\(866\) −6.33505 −0.215274
\(867\) 16.1030 0.546886
\(868\) −2.70034 −0.0916556
\(869\) 14.3049 0.485261
\(870\) 0.238374 0.00808164
\(871\) 48.4856 1.64287
\(872\) −1.60662 −0.0544069
\(873\) 1.19390 0.0404074
\(874\) −27.3520 −0.925194
\(875\) −9.70100 −0.327954
\(876\) −2.16182 −0.0730413
\(877\) −1.03135 −0.0348261 −0.0174130 0.999848i \(-0.505543\pi\)
−0.0174130 + 0.999848i \(0.505543\pi\)
\(878\) 28.1516 0.950072
\(879\) 1.60819 0.0542428
\(880\) −5.20512 −0.175465
\(881\) 32.3845 1.09106 0.545530 0.838091i \(-0.316328\pi\)
0.545530 + 0.838091i \(0.316328\pi\)
\(882\) −1.03703 −0.0349185
\(883\) 23.8220 0.801673 0.400837 0.916150i \(-0.368719\pi\)
0.400837 + 0.916150i \(0.368719\pi\)
\(884\) −2.72936 −0.0917984
\(885\) −13.3752 −0.449603
\(886\) 0.737215 0.0247672
\(887\) −15.0118 −0.504046 −0.252023 0.967721i \(-0.581096\pi\)
−0.252023 + 0.967721i \(0.581096\pi\)
\(888\) −31.5047 −1.05723
\(889\) 1.32367 0.0443944
\(890\) −4.93962 −0.165576
\(891\) −3.63449 −0.121760
\(892\) 5.48846 0.183767
\(893\) 40.5671 1.35753
\(894\) 6.15711 0.205925
\(895\) −24.2350 −0.810087
\(896\) −1.67758 −0.0560439
\(897\) −13.9760 −0.466646
\(898\) −9.20865 −0.307297
\(899\) 0.607532 0.0202623
\(900\) 3.49387 0.116462
\(901\) −8.10713 −0.270088
\(902\) 16.6188 0.553345
\(903\) −5.58070 −0.185714
\(904\) 5.36739 0.178517
\(905\) −4.29853 −0.142888
\(906\) −8.14956 −0.270751
\(907\) −55.8019 −1.85287 −0.926436 0.376453i \(-0.877144\pi\)
−0.926436 + 0.376453i \(0.877144\pi\)
\(908\) −6.92597 −0.229847
\(909\) −18.9910 −0.629892
\(910\) 3.57181 0.118404
\(911\) 16.4212 0.544058 0.272029 0.962289i \(-0.412305\pi\)
0.272029 + 0.962289i \(0.412305\pi\)
\(912\) −7.62335 −0.252434
\(913\) 31.6824 1.04853
\(914\) −12.4939 −0.413260
\(915\) −3.80630 −0.125833
\(916\) −27.0464 −0.893638
\(917\) 0.795161 0.0262585
\(918\) −0.982175 −0.0324166
\(919\) 27.8004 0.917050 0.458525 0.888682i \(-0.348378\pi\)
0.458525 + 0.888682i \(0.348378\pi\)
\(920\) 15.0277 0.495449
\(921\) −13.6333 −0.449231
\(922\) −27.5114 −0.906038
\(923\) 49.7871 1.63876
\(924\) 3.36036 0.110548
\(925\) −39.2543 −1.29067
\(926\) −16.8718 −0.554442
\(927\) −2.36424 −0.0776518
\(928\) 0.982184 0.0322418
\(929\) −0.361276 −0.0118531 −0.00592654 0.999982i \(-0.501886\pi\)
−0.00592654 + 0.999982i \(0.501886\pi\)
\(930\) 3.34691 0.109750
\(931\) −5.88214 −0.192779
\(932\) 10.3037 0.337508
\(933\) 21.1376 0.692015
\(934\) 12.0727 0.395032
\(935\) −3.80381 −0.124398
\(936\) −9.45309 −0.308984
\(937\) −21.6264 −0.706504 −0.353252 0.935528i \(-0.614924\pi\)
−0.353252 + 0.935528i \(0.614924\pi\)
\(938\) −16.1318 −0.526721
\(939\) −21.6650 −0.707011
\(940\) −7.04623 −0.229823
\(941\) 23.9308 0.780123 0.390061 0.920789i \(-0.372454\pi\)
0.390061 + 0.920789i \(0.372454\pi\)
\(942\) 6.44042 0.209840
\(943\) −19.7710 −0.643832
\(944\) 15.6868 0.510562
\(945\) −1.10504 −0.0359469
\(946\) −21.0340 −0.683875
\(947\) −53.5317 −1.73955 −0.869774 0.493451i \(-0.835735\pi\)
−0.869774 + 0.493451i \(0.835735\pi\)
\(948\) −3.63901 −0.118190
\(949\) 7.28785 0.236574
\(950\) −23.0510 −0.747874
\(951\) 4.02993 0.130679
\(952\) 2.87244 0.0930964
\(953\) −8.96549 −0.290421 −0.145210 0.989401i \(-0.546386\pi\)
−0.145210 + 0.989401i \(0.546386\pi\)
\(954\) −8.87685 −0.287399
\(955\) −1.10504 −0.0357582
\(956\) −26.5642 −0.859146
\(957\) −0.756025 −0.0244388
\(958\) 14.4190 0.465857
\(959\) 15.2335 0.491915
\(960\) 8.27517 0.267080
\(961\) −22.4699 −0.724835
\(962\) 33.5764 1.08255
\(963\) 3.22132 0.103806
\(964\) −19.2700 −0.620646
\(965\) −18.3862 −0.591874
\(966\) 4.65000 0.149611
\(967\) −55.2643 −1.77718 −0.888590 0.458703i \(-0.848314\pi\)
−0.888590 + 0.458703i \(0.848314\pi\)
\(968\) 6.70121 0.215385
\(969\) −5.57101 −0.178967
\(970\) 1.36815 0.0439288
\(971\) −7.68789 −0.246716 −0.123358 0.992362i \(-0.539366\pi\)
−0.123358 + 0.992362i \(0.539366\pi\)
\(972\) 0.924574 0.0296557
\(973\) −18.7326 −0.600541
\(974\) −20.8146 −0.666942
\(975\) −11.7784 −0.377210
\(976\) 4.46413 0.142893
\(977\) 17.2569 0.552098 0.276049 0.961144i \(-0.410975\pi\)
0.276049 + 0.961144i \(0.410975\pi\)
\(978\) 20.2064 0.646130
\(979\) 15.6664 0.500701
\(980\) 1.02169 0.0326366
\(981\) −0.529736 −0.0169132
\(982\) 26.7260 0.852862
\(983\) 2.96957 0.0947147 0.0473574 0.998878i \(-0.484920\pi\)
0.0473574 + 0.998878i \(0.484920\pi\)
\(984\) −13.3727 −0.426305
\(985\) 18.3908 0.585978
\(986\) −0.204306 −0.00650643
\(987\) −6.89665 −0.219523
\(988\) −16.9511 −0.539286
\(989\) 25.0237 0.795706
\(990\) −4.16496 −0.132371
\(991\) 6.79748 0.215929 0.107965 0.994155i \(-0.465567\pi\)
0.107965 + 0.994155i \(0.465567\pi\)
\(992\) 13.7904 0.437847
\(993\) −32.3774 −1.02746
\(994\) −16.5648 −0.525404
\(995\) 18.8184 0.596583
\(996\) −8.05964 −0.255379
\(997\) 12.8536 0.407079 0.203540 0.979067i \(-0.434755\pi\)
0.203540 + 0.979067i \(0.434755\pi\)
\(998\) 10.4749 0.331578
\(999\) −10.3878 −0.328655
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 4011.2.a.j.1.10 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4011.2.a.j.1.10 26 1.1 even 1 trivial