Properties

Label 4011.2.a.l.1.3
Level $4011$
Weight $2$
Character 4011.1
Self dual yes
Analytic conductor $32.028$
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] = [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: \(28\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
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)
 
\(f(q)\) \(=\) \(q-2.60224 q^{2} -1.00000 q^{3} +4.77168 q^{4} -2.58506 q^{5} +2.60224 q^{6} +1.00000 q^{7} -7.21258 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.60224 q^{2} -1.00000 q^{3} +4.77168 q^{4} -2.58506 q^{5} +2.60224 q^{6} +1.00000 q^{7} -7.21258 q^{8} +1.00000 q^{9} +6.72695 q^{10} -0.115915 q^{11} -4.77168 q^{12} +0.834967 q^{13} -2.60224 q^{14} +2.58506 q^{15} +9.22555 q^{16} -5.62336 q^{17} -2.60224 q^{18} +3.68328 q^{19} -12.3351 q^{20} -1.00000 q^{21} +0.301640 q^{22} +4.67180 q^{23} +7.21258 q^{24} +1.68251 q^{25} -2.17279 q^{26} -1.00000 q^{27} +4.77168 q^{28} -3.88720 q^{29} -6.72695 q^{30} +3.08830 q^{31} -9.58198 q^{32} +0.115915 q^{33} +14.6334 q^{34} -2.58506 q^{35} +4.77168 q^{36} -10.6856 q^{37} -9.58480 q^{38} -0.834967 q^{39} +18.6449 q^{40} +11.6776 q^{41} +2.60224 q^{42} -0.00633740 q^{43} -0.553111 q^{44} -2.58506 q^{45} -12.1572 q^{46} -0.636054 q^{47} -9.22555 q^{48} +1.00000 q^{49} -4.37831 q^{50} +5.62336 q^{51} +3.98420 q^{52} -2.34673 q^{53} +2.60224 q^{54} +0.299648 q^{55} -7.21258 q^{56} -3.68328 q^{57} +10.1155 q^{58} -8.43296 q^{59} +12.3351 q^{60} +13.5378 q^{61} -8.03652 q^{62} +1.00000 q^{63} +6.48354 q^{64} -2.15844 q^{65} -0.301640 q^{66} +5.15720 q^{67} -26.8328 q^{68} -4.67180 q^{69} +6.72695 q^{70} +0.734558 q^{71} -7.21258 q^{72} -9.88866 q^{73} +27.8065 q^{74} -1.68251 q^{75} +17.5754 q^{76} -0.115915 q^{77} +2.17279 q^{78} -1.05167 q^{79} -23.8486 q^{80} +1.00000 q^{81} -30.3881 q^{82} +11.9797 q^{83} -4.77168 q^{84} +14.5367 q^{85} +0.0164915 q^{86} +3.88720 q^{87} +0.836049 q^{88} -11.7675 q^{89} +6.72695 q^{90} +0.834967 q^{91} +22.2923 q^{92} -3.08830 q^{93} +1.65517 q^{94} -9.52149 q^{95} +9.58198 q^{96} -13.3662 q^{97} -2.60224 q^{98} -0.115915 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9} + 4 q^{10} - 8 q^{11} - 34 q^{12} + 26 q^{13} - 6 q^{14} - 8 q^{15} + 62 q^{16} + 9 q^{17} - 6 q^{18} + 25 q^{19} + 20 q^{20} - 28 q^{21} + 3 q^{22} - 30 q^{23} + 15 q^{24} + 42 q^{25} + 25 q^{26} - 28 q^{27} + 34 q^{28} - 5 q^{29} - 4 q^{30} + 18 q^{31} - 26 q^{32} + 8 q^{33} + 30 q^{34} + 8 q^{35} + 34 q^{36} + 36 q^{37} - 2 q^{38} - 26 q^{39} + 28 q^{40} + 21 q^{41} + 6 q^{42} + 8 q^{43} - 20 q^{44} + 8 q^{45} + 24 q^{46} + 6 q^{47} - 62 q^{48} + 28 q^{49} - 48 q^{50} - 9 q^{51} + 54 q^{52} - 12 q^{53} + 6 q^{54} + 15 q^{55} - 15 q^{56} - 25 q^{57} + 19 q^{58} + 33 q^{59} - 20 q^{60} + 48 q^{61} + 28 q^{63} + 75 q^{64} + 21 q^{65} - 3 q^{66} + 27 q^{67} + 19 q^{68} + 30 q^{69} + 4 q^{70} - 45 q^{71} - 15 q^{72} + 61 q^{73} - 31 q^{74} - 42 q^{75} + 63 q^{76} - 8 q^{77} - 25 q^{78} + 35 q^{79} + 84 q^{80} + 28 q^{81} + 11 q^{82} + 43 q^{83} - 34 q^{84} + 43 q^{85} - q^{86} + 5 q^{87} - 27 q^{88} + 25 q^{89} + 4 q^{90} + 26 q^{91} - 102 q^{92} - 18 q^{93} + 55 q^{94} - 43 q^{95} + 26 q^{96} + 40 q^{97} - 6 q^{98} - 8 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.60224 −1.84006 −0.920032 0.391842i \(-0.871838\pi\)
−0.920032 + 0.391842i \(0.871838\pi\)
\(3\) −1.00000 −0.577350
\(4\) 4.77168 2.38584
\(5\) −2.58506 −1.15607 −0.578036 0.816011i \(-0.696181\pi\)
−0.578036 + 0.816011i \(0.696181\pi\)
\(6\) 2.60224 1.06236
\(7\) 1.00000 0.377964
\(8\) −7.21258 −2.55003
\(9\) 1.00000 0.333333
\(10\) 6.72695 2.12725
\(11\) −0.115915 −0.0349498 −0.0174749 0.999847i \(-0.505563\pi\)
−0.0174749 + 0.999847i \(0.505563\pi\)
\(12\) −4.77168 −1.37746
\(13\) 0.834967 0.231578 0.115789 0.993274i \(-0.463060\pi\)
0.115789 + 0.993274i \(0.463060\pi\)
\(14\) −2.60224 −0.695479
\(15\) 2.58506 0.667459
\(16\) 9.22555 2.30639
\(17\) −5.62336 −1.36386 −0.681932 0.731415i \(-0.738860\pi\)
−0.681932 + 0.731415i \(0.738860\pi\)
\(18\) −2.60224 −0.613355
\(19\) 3.68328 0.845003 0.422501 0.906362i \(-0.361152\pi\)
0.422501 + 0.906362i \(0.361152\pi\)
\(20\) −12.3351 −2.75820
\(21\) −1.00000 −0.218218
\(22\) 0.301640 0.0643099
\(23\) 4.67180 0.974137 0.487069 0.873364i \(-0.338066\pi\)
0.487069 + 0.873364i \(0.338066\pi\)
\(24\) 7.21258 1.47226
\(25\) 1.68251 0.336503
\(26\) −2.17279 −0.426119
\(27\) −1.00000 −0.192450
\(28\) 4.77168 0.901762
\(29\) −3.88720 −0.721836 −0.360918 0.932598i \(-0.617537\pi\)
−0.360918 + 0.932598i \(0.617537\pi\)
\(30\) −6.72695 −1.22817
\(31\) 3.08830 0.554676 0.277338 0.960772i \(-0.410548\pi\)
0.277338 + 0.960772i \(0.410548\pi\)
\(32\) −9.58198 −1.69387
\(33\) 0.115915 0.0201783
\(34\) 14.6334 2.50960
\(35\) −2.58506 −0.436954
\(36\) 4.77168 0.795280
\(37\) −10.6856 −1.75670 −0.878351 0.478017i \(-0.841356\pi\)
−0.878351 + 0.478017i \(0.841356\pi\)
\(38\) −9.58480 −1.55486
\(39\) −0.834967 −0.133702
\(40\) 18.6449 2.94802
\(41\) 11.6776 1.82374 0.911871 0.410478i \(-0.134638\pi\)
0.911871 + 0.410478i \(0.134638\pi\)
\(42\) 2.60224 0.401535
\(43\) −0.00633740 −0.000966445 0 −0.000483222 1.00000i \(-0.500154\pi\)
−0.000483222 1.00000i \(0.500154\pi\)
\(44\) −0.553111 −0.0833846
\(45\) −2.58506 −0.385357
\(46\) −12.1572 −1.79248
\(47\) −0.636054 −0.0927780 −0.0463890 0.998923i \(-0.514771\pi\)
−0.0463890 + 0.998923i \(0.514771\pi\)
\(48\) −9.22555 −1.33159
\(49\) 1.00000 0.142857
\(50\) −4.37831 −0.619187
\(51\) 5.62336 0.787428
\(52\) 3.98420 0.552508
\(53\) −2.34673 −0.322349 −0.161174 0.986926i \(-0.551528\pi\)
−0.161174 + 0.986926i \(0.551528\pi\)
\(54\) 2.60224 0.354121
\(55\) 0.299648 0.0404045
\(56\) −7.21258 −0.963822
\(57\) −3.68328 −0.487863
\(58\) 10.1155 1.32822
\(59\) −8.43296 −1.09788 −0.548939 0.835862i \(-0.684968\pi\)
−0.548939 + 0.835862i \(0.684968\pi\)
\(60\) 12.3351 1.59245
\(61\) 13.5378 1.73334 0.866669 0.498884i \(-0.166256\pi\)
0.866669 + 0.498884i \(0.166256\pi\)
\(62\) −8.03652 −1.02064
\(63\) 1.00000 0.125988
\(64\) 6.48354 0.810443
\(65\) −2.15844 −0.267721
\(66\) −0.301640 −0.0371293
\(67\) 5.15720 0.630052 0.315026 0.949083i \(-0.397987\pi\)
0.315026 + 0.949083i \(0.397987\pi\)
\(68\) −26.8328 −3.25396
\(69\) −4.67180 −0.562418
\(70\) 6.72695 0.804024
\(71\) 0.734558 0.0871760 0.0435880 0.999050i \(-0.486121\pi\)
0.0435880 + 0.999050i \(0.486121\pi\)
\(72\) −7.21258 −0.850011
\(73\) −9.88866 −1.15738 −0.578690 0.815548i \(-0.696436\pi\)
−0.578690 + 0.815548i \(0.696436\pi\)
\(74\) 27.8065 3.23244
\(75\) −1.68251 −0.194280
\(76\) 17.5754 2.01604
\(77\) −0.115915 −0.0132098
\(78\) 2.17279 0.246020
\(79\) −1.05167 −0.118322 −0.0591609 0.998248i \(-0.518843\pi\)
−0.0591609 + 0.998248i \(0.518843\pi\)
\(80\) −23.8486 −2.66635
\(81\) 1.00000 0.111111
\(82\) −30.3881 −3.35580
\(83\) 11.9797 1.31494 0.657470 0.753481i \(-0.271627\pi\)
0.657470 + 0.753481i \(0.271627\pi\)
\(84\) −4.77168 −0.520633
\(85\) 14.5367 1.57673
\(86\) 0.0164915 0.00177832
\(87\) 3.88720 0.416752
\(88\) 0.836049 0.0891232
\(89\) −11.7675 −1.24736 −0.623678 0.781681i \(-0.714362\pi\)
−0.623678 + 0.781681i \(0.714362\pi\)
\(90\) 6.72695 0.709083
\(91\) 0.834967 0.0875284
\(92\) 22.2923 2.32413
\(93\) −3.08830 −0.320242
\(94\) 1.65517 0.170717
\(95\) −9.52149 −0.976884
\(96\) 9.58198 0.977956
\(97\) −13.3662 −1.35714 −0.678568 0.734538i \(-0.737399\pi\)
−0.678568 + 0.734538i \(0.737399\pi\)
\(98\) −2.60224 −0.262866
\(99\) −0.115915 −0.0116499
\(100\) 8.02841 0.802841
\(101\) 4.25024 0.422915 0.211458 0.977387i \(-0.432179\pi\)
0.211458 + 0.977387i \(0.432179\pi\)
\(102\) −14.6334 −1.44892
\(103\) −10.8398 −1.06807 −0.534036 0.845461i \(-0.679325\pi\)
−0.534036 + 0.845461i \(0.679325\pi\)
\(104\) −6.02227 −0.590532
\(105\) 2.58506 0.252276
\(106\) 6.10677 0.593142
\(107\) 8.44855 0.816752 0.408376 0.912814i \(-0.366095\pi\)
0.408376 + 0.912814i \(0.366095\pi\)
\(108\) −4.77168 −0.459155
\(109\) −1.06337 −0.101852 −0.0509261 0.998702i \(-0.516217\pi\)
−0.0509261 + 0.998702i \(0.516217\pi\)
\(110\) −0.779757 −0.0743469
\(111\) 10.6856 1.01423
\(112\) 9.22555 0.871733
\(113\) −3.70684 −0.348711 −0.174355 0.984683i \(-0.555784\pi\)
−0.174355 + 0.984683i \(0.555784\pi\)
\(114\) 9.58480 0.897699
\(115\) −12.0769 −1.12617
\(116\) −18.5485 −1.72218
\(117\) 0.834967 0.0771928
\(118\) 21.9446 2.02017
\(119\) −5.62336 −0.515492
\(120\) −18.6449 −1.70204
\(121\) −10.9866 −0.998779
\(122\) −35.2287 −3.18945
\(123\) −11.6776 −1.05294
\(124\) 14.7364 1.32337
\(125\) 8.57589 0.767051
\(126\) −2.60224 −0.231826
\(127\) 9.32079 0.827086 0.413543 0.910485i \(-0.364291\pi\)
0.413543 + 0.910485i \(0.364291\pi\)
\(128\) 2.29218 0.202602
\(129\) 0.00633740 0.000557977 0
\(130\) 5.61678 0.492624
\(131\) 3.48282 0.304296 0.152148 0.988358i \(-0.451381\pi\)
0.152148 + 0.988358i \(0.451381\pi\)
\(132\) 0.553111 0.0481421
\(133\) 3.68328 0.319381
\(134\) −13.4203 −1.15934
\(135\) 2.58506 0.222486
\(136\) 40.5589 3.47790
\(137\) 1.52560 0.130341 0.0651703 0.997874i \(-0.479241\pi\)
0.0651703 + 0.997874i \(0.479241\pi\)
\(138\) 12.1572 1.03489
\(139\) 8.07704 0.685086 0.342543 0.939502i \(-0.388712\pi\)
0.342543 + 0.939502i \(0.388712\pi\)
\(140\) −12.3351 −1.04250
\(141\) 0.636054 0.0535654
\(142\) −1.91150 −0.160410
\(143\) −0.0967856 −0.00809362
\(144\) 9.22555 0.768796
\(145\) 10.0486 0.834494
\(146\) 25.7327 2.12965
\(147\) −1.00000 −0.0824786
\(148\) −50.9882 −4.19121
\(149\) −20.9577 −1.71692 −0.858461 0.512879i \(-0.828579\pi\)
−0.858461 + 0.512879i \(0.828579\pi\)
\(150\) 4.37831 0.357488
\(151\) −3.17563 −0.258429 −0.129215 0.991617i \(-0.541246\pi\)
−0.129215 + 0.991617i \(0.541246\pi\)
\(152\) −26.5660 −2.15479
\(153\) −5.62336 −0.454622
\(154\) 0.301640 0.0243069
\(155\) −7.98344 −0.641245
\(156\) −3.98420 −0.318991
\(157\) −5.31711 −0.424351 −0.212176 0.977232i \(-0.568055\pi\)
−0.212176 + 0.977232i \(0.568055\pi\)
\(158\) 2.73670 0.217720
\(159\) 2.34673 0.186108
\(160\) 24.7699 1.95824
\(161\) 4.67180 0.368189
\(162\) −2.60224 −0.204452
\(163\) 13.9648 1.09381 0.546903 0.837196i \(-0.315807\pi\)
0.546903 + 0.837196i \(0.315807\pi\)
\(164\) 55.7219 4.35115
\(165\) −0.299648 −0.0233275
\(166\) −31.1740 −2.41957
\(167\) 23.7366 1.83679 0.918397 0.395661i \(-0.129485\pi\)
0.918397 + 0.395661i \(0.129485\pi\)
\(168\) 7.21258 0.556463
\(169\) −12.3028 −0.946371
\(170\) −37.8280 −2.90128
\(171\) 3.68328 0.281668
\(172\) −0.0302400 −0.00230578
\(173\) −19.3101 −1.46812 −0.734059 0.679086i \(-0.762376\pi\)
−0.734059 + 0.679086i \(0.762376\pi\)
\(174\) −10.1155 −0.766851
\(175\) 1.68251 0.127186
\(176\) −1.06938 −0.0806078
\(177\) 8.43296 0.633860
\(178\) 30.6220 2.29522
\(179\) −6.85410 −0.512299 −0.256150 0.966637i \(-0.582454\pi\)
−0.256150 + 0.966637i \(0.582454\pi\)
\(180\) −12.3351 −0.919401
\(181\) 2.43507 0.180997 0.0904985 0.995897i \(-0.471154\pi\)
0.0904985 + 0.995897i \(0.471154\pi\)
\(182\) −2.17279 −0.161058
\(183\) −13.5378 −1.00074
\(184\) −33.6957 −2.48408
\(185\) 27.6229 2.03087
\(186\) 8.03652 0.589266
\(187\) 0.651834 0.0476668
\(188\) −3.03504 −0.221353
\(189\) −1.00000 −0.0727393
\(190\) 24.7772 1.79753
\(191\) −1.00000 −0.0723575
\(192\) −6.48354 −0.467909
\(193\) −10.0769 −0.725353 −0.362676 0.931915i \(-0.618137\pi\)
−0.362676 + 0.931915i \(0.618137\pi\)
\(194\) 34.7822 2.49722
\(195\) 2.15844 0.154569
\(196\) 4.77168 0.340834
\(197\) 4.19816 0.299107 0.149553 0.988754i \(-0.452216\pi\)
0.149553 + 0.988754i \(0.452216\pi\)
\(198\) 0.301640 0.0214366
\(199\) −6.65383 −0.471677 −0.235839 0.971792i \(-0.575784\pi\)
−0.235839 + 0.971792i \(0.575784\pi\)
\(200\) −12.1353 −0.858093
\(201\) −5.15720 −0.363761
\(202\) −11.0602 −0.778191
\(203\) −3.88720 −0.272828
\(204\) 26.8328 1.87868
\(205\) −30.1874 −2.10838
\(206\) 28.2077 1.96532
\(207\) 4.67180 0.324712
\(208\) 7.70304 0.534109
\(209\) −0.426949 −0.0295327
\(210\) −6.72695 −0.464204
\(211\) 16.5266 1.13774 0.568871 0.822427i \(-0.307380\pi\)
0.568871 + 0.822427i \(0.307380\pi\)
\(212\) −11.1979 −0.769072
\(213\) −0.734558 −0.0503311
\(214\) −21.9852 −1.50288
\(215\) 0.0163825 0.00111728
\(216\) 7.21258 0.490754
\(217\) 3.08830 0.209648
\(218\) 2.76714 0.187415
\(219\) 9.88866 0.668214
\(220\) 1.42982 0.0963986
\(221\) −4.69532 −0.315841
\(222\) −27.8065 −1.86625
\(223\) −19.2287 −1.28765 −0.643825 0.765173i \(-0.722653\pi\)
−0.643825 + 0.765173i \(0.722653\pi\)
\(224\) −9.58198 −0.640223
\(225\) 1.68251 0.112168
\(226\) 9.64611 0.641650
\(227\) −3.63510 −0.241270 −0.120635 0.992697i \(-0.538493\pi\)
−0.120635 + 0.992697i \(0.538493\pi\)
\(228\) −17.5754 −1.16396
\(229\) −0.0867138 −0.00573021 −0.00286510 0.999996i \(-0.500912\pi\)
−0.00286510 + 0.999996i \(0.500912\pi\)
\(230\) 31.4269 2.07223
\(231\) 0.115915 0.00762667
\(232\) 28.0368 1.84070
\(233\) −21.3122 −1.39621 −0.698103 0.715998i \(-0.745972\pi\)
−0.698103 + 0.715998i \(0.745972\pi\)
\(234\) −2.17279 −0.142040
\(235\) 1.64423 0.107258
\(236\) −40.2394 −2.61936
\(237\) 1.05167 0.0683132
\(238\) 14.6334 0.948539
\(239\) 3.59778 0.232721 0.116361 0.993207i \(-0.462877\pi\)
0.116361 + 0.993207i \(0.462877\pi\)
\(240\) 23.8486 1.53942
\(241\) 8.40658 0.541515 0.270758 0.962648i \(-0.412726\pi\)
0.270758 + 0.962648i \(0.412726\pi\)
\(242\) 28.5897 1.83782
\(243\) −1.00000 −0.0641500
\(244\) 64.5980 4.13546
\(245\) −2.58506 −0.165153
\(246\) 30.3881 1.93747
\(247\) 3.07542 0.195684
\(248\) −22.2747 −1.41444
\(249\) −11.9797 −0.759181
\(250\) −22.3166 −1.41142
\(251\) 16.3609 1.03269 0.516344 0.856381i \(-0.327293\pi\)
0.516344 + 0.856381i \(0.327293\pi\)
\(252\) 4.77168 0.300587
\(253\) −0.541533 −0.0340459
\(254\) −24.2550 −1.52189
\(255\) −14.5367 −0.910323
\(256\) −18.9319 −1.18324
\(257\) −15.4413 −0.963199 −0.481599 0.876391i \(-0.659944\pi\)
−0.481599 + 0.876391i \(0.659944\pi\)
\(258\) −0.0164915 −0.00102671
\(259\) −10.6856 −0.663971
\(260\) −10.2994 −0.638740
\(261\) −3.88720 −0.240612
\(262\) −9.06315 −0.559924
\(263\) −32.0181 −1.97432 −0.987159 0.159740i \(-0.948935\pi\)
−0.987159 + 0.159740i \(0.948935\pi\)
\(264\) −0.836049 −0.0514553
\(265\) 6.06644 0.372658
\(266\) −9.58480 −0.587682
\(267\) 11.7675 0.720162
\(268\) 24.6085 1.50320
\(269\) 14.4482 0.880924 0.440462 0.897771i \(-0.354815\pi\)
0.440462 + 0.897771i \(0.354815\pi\)
\(270\) −6.72695 −0.409389
\(271\) −18.8960 −1.14785 −0.573925 0.818908i \(-0.694580\pi\)
−0.573925 + 0.818908i \(0.694580\pi\)
\(272\) −51.8786 −3.14560
\(273\) −0.834967 −0.0505345
\(274\) −3.96998 −0.239835
\(275\) −0.195029 −0.0117607
\(276\) −22.2923 −1.34184
\(277\) 13.7382 0.825449 0.412724 0.910856i \(-0.364577\pi\)
0.412724 + 0.910856i \(0.364577\pi\)
\(278\) −21.0184 −1.26060
\(279\) 3.08830 0.184892
\(280\) 18.6449 1.11425
\(281\) 30.0517 1.79273 0.896366 0.443314i \(-0.146197\pi\)
0.896366 + 0.443314i \(0.146197\pi\)
\(282\) −1.65517 −0.0985638
\(283\) 15.1964 0.903335 0.451668 0.892186i \(-0.350829\pi\)
0.451668 + 0.892186i \(0.350829\pi\)
\(284\) 3.50507 0.207988
\(285\) 9.52149 0.564004
\(286\) 0.251860 0.0148928
\(287\) 11.6776 0.689309
\(288\) −9.58198 −0.564623
\(289\) 14.6222 0.860127
\(290\) −26.1490 −1.53552
\(291\) 13.3662 0.783543
\(292\) −47.1855 −2.76132
\(293\) 11.6374 0.679865 0.339933 0.940450i \(-0.389596\pi\)
0.339933 + 0.940450i \(0.389596\pi\)
\(294\) 2.60224 0.151766
\(295\) 21.7997 1.26923
\(296\) 77.0708 4.47965
\(297\) 0.115915 0.00672609
\(298\) 54.5371 3.15925
\(299\) 3.90080 0.225589
\(300\) −8.02841 −0.463521
\(301\) −0.00633740 −0.000365282 0
\(302\) 8.26378 0.475527
\(303\) −4.25024 −0.244170
\(304\) 33.9803 1.94890
\(305\) −34.9960 −2.00386
\(306\) 14.6334 0.836533
\(307\) 13.1049 0.747935 0.373968 0.927442i \(-0.377997\pi\)
0.373968 + 0.927442i \(0.377997\pi\)
\(308\) −0.553111 −0.0315164
\(309\) 10.8398 0.616652
\(310\) 20.7749 1.17993
\(311\) 27.8159 1.57729 0.788647 0.614846i \(-0.210782\pi\)
0.788647 + 0.614846i \(0.210782\pi\)
\(312\) 6.02227 0.340944
\(313\) 22.2381 1.25697 0.628485 0.777822i \(-0.283675\pi\)
0.628485 + 0.777822i \(0.283675\pi\)
\(314\) 13.8364 0.780834
\(315\) −2.58506 −0.145651
\(316\) −5.01822 −0.282297
\(317\) −6.15878 −0.345912 −0.172956 0.984930i \(-0.555332\pi\)
−0.172956 + 0.984930i \(0.555332\pi\)
\(318\) −6.10677 −0.342451
\(319\) 0.450587 0.0252280
\(320\) −16.7603 −0.936931
\(321\) −8.44855 −0.471552
\(322\) −12.1572 −0.677492
\(323\) −20.7124 −1.15247
\(324\) 4.77168 0.265093
\(325\) 1.40484 0.0779267
\(326\) −36.3397 −2.01267
\(327\) 1.06337 0.0588044
\(328\) −84.2260 −4.65060
\(329\) −0.636054 −0.0350668
\(330\) 0.779757 0.0429242
\(331\) −2.93153 −0.161131 −0.0805656 0.996749i \(-0.525673\pi\)
−0.0805656 + 0.996749i \(0.525673\pi\)
\(332\) 57.1631 3.13723
\(333\) −10.6856 −0.585567
\(334\) −61.7684 −3.37982
\(335\) −13.3317 −0.728386
\(336\) −9.22555 −0.503295
\(337\) −16.4073 −0.893764 −0.446882 0.894593i \(-0.647466\pi\)
−0.446882 + 0.894593i \(0.647466\pi\)
\(338\) 32.0150 1.74138
\(339\) 3.70684 0.201328
\(340\) 69.3644 3.76181
\(341\) −0.357982 −0.0193858
\(342\) −9.58480 −0.518287
\(343\) 1.00000 0.0539949
\(344\) 0.0457090 0.00246447
\(345\) 12.0769 0.650196
\(346\) 50.2495 2.70143
\(347\) −18.4212 −0.988902 −0.494451 0.869205i \(-0.664631\pi\)
−0.494451 + 0.869205i \(0.664631\pi\)
\(348\) 18.5485 0.994303
\(349\) −7.60569 −0.407123 −0.203562 0.979062i \(-0.565252\pi\)
−0.203562 + 0.979062i \(0.565252\pi\)
\(350\) −4.37831 −0.234031
\(351\) −0.834967 −0.0445673
\(352\) 1.11070 0.0592004
\(353\) 14.4737 0.770355 0.385178 0.922842i \(-0.374140\pi\)
0.385178 + 0.922842i \(0.374140\pi\)
\(354\) −21.9446 −1.16634
\(355\) −1.89887 −0.100782
\(356\) −56.1509 −2.97599
\(357\) 5.62336 0.297620
\(358\) 17.8360 0.942664
\(359\) 3.77612 0.199296 0.0996479 0.995023i \(-0.468228\pi\)
0.0996479 + 0.995023i \(0.468228\pi\)
\(360\) 18.6449 0.982674
\(361\) −5.43343 −0.285970
\(362\) −6.33664 −0.333046
\(363\) 10.9866 0.576645
\(364\) 3.98420 0.208829
\(365\) 25.5627 1.33801
\(366\) 35.2287 1.84143
\(367\) 31.1477 1.62590 0.812949 0.582335i \(-0.197861\pi\)
0.812949 + 0.582335i \(0.197861\pi\)
\(368\) 43.0999 2.24674
\(369\) 11.6776 0.607914
\(370\) −71.8815 −3.73694
\(371\) −2.34673 −0.121836
\(372\) −14.7364 −0.764046
\(373\) 10.4761 0.542431 0.271216 0.962519i \(-0.412574\pi\)
0.271216 + 0.962519i \(0.412574\pi\)
\(374\) −1.69623 −0.0877100
\(375\) −8.57589 −0.442857
\(376\) 4.58759 0.236587
\(377\) −3.24569 −0.167161
\(378\) 2.60224 0.133845
\(379\) 24.1122 1.23856 0.619281 0.785169i \(-0.287424\pi\)
0.619281 + 0.785169i \(0.287424\pi\)
\(380\) −45.4335 −2.33069
\(381\) −9.32079 −0.477518
\(382\) 2.60224 0.133142
\(383\) 11.0766 0.565988 0.282994 0.959122i \(-0.408672\pi\)
0.282994 + 0.959122i \(0.408672\pi\)
\(384\) −2.29218 −0.116973
\(385\) 0.299648 0.0152715
\(386\) 26.2226 1.33470
\(387\) −0.00633740 −0.000322148 0
\(388\) −63.7794 −3.23791
\(389\) 24.8098 1.25791 0.628954 0.777442i \(-0.283483\pi\)
0.628954 + 0.777442i \(0.283483\pi\)
\(390\) −5.61678 −0.284417
\(391\) −26.2712 −1.32859
\(392\) −7.21258 −0.364290
\(393\) −3.48282 −0.175685
\(394\) −10.9246 −0.550375
\(395\) 2.71862 0.136789
\(396\) −0.553111 −0.0277949
\(397\) 28.6238 1.43659 0.718293 0.695741i \(-0.244924\pi\)
0.718293 + 0.695741i \(0.244924\pi\)
\(398\) 17.3149 0.867917
\(399\) −3.68328 −0.184395
\(400\) 15.5221 0.776106
\(401\) 11.8383 0.591177 0.295589 0.955315i \(-0.404484\pi\)
0.295589 + 0.955315i \(0.404484\pi\)
\(402\) 13.4203 0.669344
\(403\) 2.57863 0.128451
\(404\) 20.2808 1.00901
\(405\) −2.58506 −0.128452
\(406\) 10.1155 0.502022
\(407\) 1.23863 0.0613964
\(408\) −40.5589 −2.00797
\(409\) −4.56857 −0.225901 −0.112951 0.993601i \(-0.536030\pi\)
−0.112951 + 0.993601i \(0.536030\pi\)
\(410\) 78.5549 3.87955
\(411\) −1.52560 −0.0752522
\(412\) −51.7238 −2.54825
\(413\) −8.43296 −0.414959
\(414\) −12.1572 −0.597492
\(415\) −30.9681 −1.52016
\(416\) −8.00064 −0.392264
\(417\) −8.07704 −0.395534
\(418\) 1.11103 0.0543421
\(419\) 26.9077 1.31453 0.657265 0.753660i \(-0.271713\pi\)
0.657265 + 0.753660i \(0.271713\pi\)
\(420\) 12.3351 0.601889
\(421\) 14.4110 0.702348 0.351174 0.936310i \(-0.385783\pi\)
0.351174 + 0.936310i \(0.385783\pi\)
\(422\) −43.0064 −2.09352
\(423\) −0.636054 −0.0309260
\(424\) 16.9260 0.822000
\(425\) −9.46138 −0.458944
\(426\) 1.91150 0.0926125
\(427\) 13.5378 0.655140
\(428\) 40.3137 1.94864
\(429\) 0.0967856 0.00467285
\(430\) −0.0426314 −0.00205587
\(431\) 2.99499 0.144264 0.0721319 0.997395i \(-0.477020\pi\)
0.0721319 + 0.997395i \(0.477020\pi\)
\(432\) −9.22555 −0.443865
\(433\) 19.3718 0.930950 0.465475 0.885061i \(-0.345884\pi\)
0.465475 + 0.885061i \(0.345884\pi\)
\(434\) −8.03652 −0.385765
\(435\) −10.0486 −0.481795
\(436\) −5.07405 −0.243003
\(437\) 17.2076 0.823149
\(438\) −25.7327 −1.22956
\(439\) 22.9468 1.09519 0.547595 0.836743i \(-0.315543\pi\)
0.547595 + 0.836743i \(0.315543\pi\)
\(440\) −2.16123 −0.103033
\(441\) 1.00000 0.0476190
\(442\) 12.2184 0.581169
\(443\) 16.4169 0.779990 0.389995 0.920817i \(-0.372477\pi\)
0.389995 + 0.920817i \(0.372477\pi\)
\(444\) 50.9882 2.41979
\(445\) 30.4197 1.44203
\(446\) 50.0378 2.36936
\(447\) 20.9577 0.991265
\(448\) 6.48354 0.306319
\(449\) 9.72314 0.458864 0.229432 0.973325i \(-0.426313\pi\)
0.229432 + 0.973325i \(0.426313\pi\)
\(450\) −4.37831 −0.206396
\(451\) −1.35362 −0.0637394
\(452\) −17.6879 −0.831967
\(453\) 3.17563 0.149204
\(454\) 9.45942 0.443953
\(455\) −2.15844 −0.101189
\(456\) 26.5660 1.24407
\(457\) 8.35758 0.390951 0.195475 0.980709i \(-0.437375\pi\)
0.195475 + 0.980709i \(0.437375\pi\)
\(458\) 0.225650 0.0105440
\(459\) 5.62336 0.262476
\(460\) −57.6269 −2.68687
\(461\) 10.6655 0.496742 0.248371 0.968665i \(-0.420105\pi\)
0.248371 + 0.968665i \(0.420105\pi\)
\(462\) −0.301640 −0.0140336
\(463\) 30.3694 1.41139 0.705693 0.708518i \(-0.250636\pi\)
0.705693 + 0.708518i \(0.250636\pi\)
\(464\) −35.8616 −1.66483
\(465\) 7.98344 0.370223
\(466\) 55.4594 2.56911
\(467\) 0.0640863 0.00296556 0.00148278 0.999999i \(-0.499528\pi\)
0.00148278 + 0.999999i \(0.499528\pi\)
\(468\) 3.98420 0.184169
\(469\) 5.15720 0.238137
\(470\) −4.27870 −0.197362
\(471\) 5.31711 0.244999
\(472\) 60.8234 2.79963
\(473\) 0.000734603 0 3.37771e−5 0
\(474\) −2.73670 −0.125701
\(475\) 6.19717 0.284346
\(476\) −26.8328 −1.22988
\(477\) −2.34673 −0.107450
\(478\) −9.36231 −0.428222
\(479\) 32.9683 1.50636 0.753179 0.657816i \(-0.228519\pi\)
0.753179 + 0.657816i \(0.228519\pi\)
\(480\) −24.7699 −1.13059
\(481\) −8.92213 −0.406814
\(482\) −21.8760 −0.996423
\(483\) −4.67180 −0.212574
\(484\) −52.4243 −2.38292
\(485\) 34.5525 1.56895
\(486\) 2.60224 0.118040
\(487\) 18.3674 0.832306 0.416153 0.909295i \(-0.363378\pi\)
0.416153 + 0.909295i \(0.363378\pi\)
\(488\) −97.6425 −4.42007
\(489\) −13.9648 −0.631509
\(490\) 6.72695 0.303893
\(491\) −12.3677 −0.558146 −0.279073 0.960270i \(-0.590027\pi\)
−0.279073 + 0.960270i \(0.590027\pi\)
\(492\) −55.7219 −2.51214
\(493\) 21.8591 0.984486
\(494\) −8.00300 −0.360072
\(495\) 0.299648 0.0134682
\(496\) 28.4913 1.27930
\(497\) 0.734558 0.0329494
\(498\) 31.1740 1.39694
\(499\) 9.77414 0.437550 0.218775 0.975775i \(-0.429794\pi\)
0.218775 + 0.975775i \(0.429794\pi\)
\(500\) 40.9214 1.83006
\(501\) −23.7366 −1.06047
\(502\) −42.5749 −1.90021
\(503\) 1.28839 0.0574467 0.0287233 0.999587i \(-0.490856\pi\)
0.0287233 + 0.999587i \(0.490856\pi\)
\(504\) −7.21258 −0.321274
\(505\) −10.9871 −0.488920
\(506\) 1.40920 0.0626467
\(507\) 12.3028 0.546388
\(508\) 44.4758 1.97329
\(509\) 7.27679 0.322538 0.161269 0.986910i \(-0.448441\pi\)
0.161269 + 0.986910i \(0.448441\pi\)
\(510\) 37.8280 1.67505
\(511\) −9.88866 −0.437448
\(512\) 44.6811 1.97464
\(513\) −3.68328 −0.162621
\(514\) 40.1819 1.77235
\(515\) 28.0214 1.23477
\(516\) 0.0302400 0.00133124
\(517\) 0.0737284 0.00324257
\(518\) 27.8065 1.22175
\(519\) 19.3101 0.847618
\(520\) 15.5679 0.682698
\(521\) 37.8831 1.65969 0.829844 0.557995i \(-0.188429\pi\)
0.829844 + 0.557995i \(0.188429\pi\)
\(522\) 10.1155 0.442741
\(523\) 20.0741 0.877780 0.438890 0.898541i \(-0.355372\pi\)
0.438890 + 0.898541i \(0.355372\pi\)
\(524\) 16.6189 0.726000
\(525\) −1.68251 −0.0734309
\(526\) 83.3188 3.63287
\(527\) −17.3666 −0.756503
\(528\) 1.06938 0.0465389
\(529\) −1.17430 −0.0510565
\(530\) −15.7863 −0.685715
\(531\) −8.43296 −0.365959
\(532\) 17.5754 0.761992
\(533\) 9.75045 0.422339
\(534\) −30.6220 −1.32514
\(535\) −21.8400 −0.944224
\(536\) −37.1967 −1.60665
\(537\) 6.85410 0.295776
\(538\) −37.5978 −1.62096
\(539\) −0.115915 −0.00499283
\(540\) 12.3351 0.530816
\(541\) 27.4397 1.17973 0.589863 0.807503i \(-0.299182\pi\)
0.589863 + 0.807503i \(0.299182\pi\)
\(542\) 49.1720 2.11212
\(543\) −2.43507 −0.104499
\(544\) 53.8829 2.31021
\(545\) 2.74887 0.117749
\(546\) 2.17279 0.0929868
\(547\) −9.06312 −0.387511 −0.193756 0.981050i \(-0.562067\pi\)
−0.193756 + 0.981050i \(0.562067\pi\)
\(548\) 7.27967 0.310972
\(549\) 13.5378 0.577779
\(550\) 0.507514 0.0216405
\(551\) −14.3177 −0.609953
\(552\) 33.6957 1.43419
\(553\) −1.05167 −0.0447215
\(554\) −35.7502 −1.51888
\(555\) −27.6229 −1.17253
\(556\) 38.5410 1.63450
\(557\) −3.14559 −0.133283 −0.0666415 0.997777i \(-0.521228\pi\)
−0.0666415 + 0.997777i \(0.521228\pi\)
\(558\) −8.03652 −0.340213
\(559\) −0.00529152 −0.000223808 0
\(560\) −23.8486 −1.00779
\(561\) −0.651834 −0.0275204
\(562\) −78.2018 −3.29874
\(563\) −28.0855 −1.18366 −0.591831 0.806062i \(-0.701595\pi\)
−0.591831 + 0.806062i \(0.701595\pi\)
\(564\) 3.03504 0.127798
\(565\) 9.58240 0.403135
\(566\) −39.5449 −1.66220
\(567\) 1.00000 0.0419961
\(568\) −5.29806 −0.222302
\(569\) 13.0055 0.545217 0.272609 0.962125i \(-0.412114\pi\)
0.272609 + 0.962125i \(0.412114\pi\)
\(570\) −24.7772 −1.03780
\(571\) −22.7871 −0.953609 −0.476805 0.879009i \(-0.658205\pi\)
−0.476805 + 0.879009i \(0.658205\pi\)
\(572\) −0.461830 −0.0193101
\(573\) 1.00000 0.0417756
\(574\) −30.3881 −1.26837
\(575\) 7.86037 0.327800
\(576\) 6.48354 0.270148
\(577\) −4.11858 −0.171459 −0.0857294 0.996318i \(-0.527322\pi\)
−0.0857294 + 0.996318i \(0.527322\pi\)
\(578\) −38.0504 −1.58269
\(579\) 10.0769 0.418783
\(580\) 47.9489 1.99097
\(581\) 11.9797 0.497000
\(582\) −34.7822 −1.44177
\(583\) 0.272022 0.0112660
\(584\) 71.3228 2.95136
\(585\) −2.15844 −0.0892404
\(586\) −30.2834 −1.25100
\(587\) 38.0283 1.56960 0.784798 0.619752i \(-0.212767\pi\)
0.784798 + 0.619752i \(0.212767\pi\)
\(588\) −4.77168 −0.196781
\(589\) 11.3751 0.468703
\(590\) −56.7281 −2.33546
\(591\) −4.19816 −0.172689
\(592\) −98.5805 −4.05163
\(593\) 2.36301 0.0970370 0.0485185 0.998822i \(-0.484550\pi\)
0.0485185 + 0.998822i \(0.484550\pi\)
\(594\) −0.301640 −0.0123764
\(595\) 14.5367 0.595946
\(596\) −100.003 −4.09630
\(597\) 6.65383 0.272323
\(598\) −10.1508 −0.415099
\(599\) 43.2745 1.76815 0.884074 0.467346i \(-0.154790\pi\)
0.884074 + 0.467346i \(0.154790\pi\)
\(600\) 12.1353 0.495420
\(601\) 14.0998 0.575143 0.287572 0.957759i \(-0.407152\pi\)
0.287572 + 0.957759i \(0.407152\pi\)
\(602\) 0.0164915 0.000672142 0
\(603\) 5.15720 0.210017
\(604\) −15.1531 −0.616571
\(605\) 28.4009 1.15466
\(606\) 11.0602 0.449289
\(607\) −27.2079 −1.10434 −0.552168 0.833733i \(-0.686199\pi\)
−0.552168 + 0.833733i \(0.686199\pi\)
\(608\) −35.2931 −1.43133
\(609\) 3.88720 0.157517
\(610\) 91.0681 3.68724
\(611\) −0.531084 −0.0214854
\(612\) −26.8328 −1.08465
\(613\) −25.8090 −1.04242 −0.521209 0.853429i \(-0.674519\pi\)
−0.521209 + 0.853429i \(0.674519\pi\)
\(614\) −34.1021 −1.37625
\(615\) 30.1874 1.21727
\(616\) 0.836049 0.0336854
\(617\) −7.13740 −0.287341 −0.143670 0.989626i \(-0.545891\pi\)
−0.143670 + 0.989626i \(0.545891\pi\)
\(618\) −28.2077 −1.13468
\(619\) −21.7294 −0.873377 −0.436689 0.899613i \(-0.643849\pi\)
−0.436689 + 0.899613i \(0.643849\pi\)
\(620\) −38.0944 −1.52991
\(621\) −4.67180 −0.187473
\(622\) −72.3838 −2.90232
\(623\) −11.7675 −0.471457
\(624\) −7.70304 −0.308368
\(625\) −30.5817 −1.22327
\(626\) −57.8689 −2.31291
\(627\) 0.426949 0.0170507
\(628\) −25.3715 −1.01243
\(629\) 60.0889 2.39590
\(630\) 6.72695 0.268008
\(631\) −14.3936 −0.573000 −0.286500 0.958080i \(-0.592492\pi\)
−0.286500 + 0.958080i \(0.592492\pi\)
\(632\) 7.58524 0.301725
\(633\) −16.5266 −0.656875
\(634\) 16.0267 0.636500
\(635\) −24.0948 −0.956171
\(636\) 11.1979 0.444024
\(637\) 0.834967 0.0330826
\(638\) −1.17254 −0.0464212
\(639\) 0.734558 0.0290587
\(640\) −5.92542 −0.234223
\(641\) −9.79728 −0.386969 −0.193485 0.981103i \(-0.561979\pi\)
−0.193485 + 0.981103i \(0.561979\pi\)
\(642\) 21.9852 0.867686
\(643\) 3.56650 0.140649 0.0703245 0.997524i \(-0.477597\pi\)
0.0703245 + 0.997524i \(0.477597\pi\)
\(644\) 22.2923 0.878440
\(645\) −0.0163825 −0.000645062 0
\(646\) 53.8988 2.12062
\(647\) 3.46572 0.136251 0.0681257 0.997677i \(-0.478298\pi\)
0.0681257 + 0.997677i \(0.478298\pi\)
\(648\) −7.21258 −0.283337
\(649\) 0.977510 0.0383706
\(650\) −3.65575 −0.143390
\(651\) −3.08830 −0.121040
\(652\) 66.6354 2.60964
\(653\) −47.2089 −1.84743 −0.923714 0.383083i \(-0.874862\pi\)
−0.923714 + 0.383083i \(0.874862\pi\)
\(654\) −2.76714 −0.108204
\(655\) −9.00329 −0.351788
\(656\) 107.733 4.20626
\(657\) −9.88866 −0.385793
\(658\) 1.65517 0.0645251
\(659\) −32.1506 −1.25241 −0.626204 0.779659i \(-0.715392\pi\)
−0.626204 + 0.779659i \(0.715392\pi\)
\(660\) −1.42982 −0.0556558
\(661\) −6.28777 −0.244566 −0.122283 0.992495i \(-0.539022\pi\)
−0.122283 + 0.992495i \(0.539022\pi\)
\(662\) 7.62855 0.296492
\(663\) 4.69532 0.182351
\(664\) −86.4044 −3.35314
\(665\) −9.52149 −0.369228
\(666\) 27.8065 1.07748
\(667\) −18.1602 −0.703167
\(668\) 113.263 4.38229
\(669\) 19.2287 0.743425
\(670\) 34.6922 1.34028
\(671\) −1.56924 −0.0605798
\(672\) 9.58198 0.369633
\(673\) −7.11712 −0.274345 −0.137172 0.990547i \(-0.543801\pi\)
−0.137172 + 0.990547i \(0.543801\pi\)
\(674\) 42.6959 1.64458
\(675\) −1.68251 −0.0647600
\(676\) −58.7051 −2.25789
\(677\) 49.5207 1.90323 0.951617 0.307288i \(-0.0994215\pi\)
0.951617 + 0.307288i \(0.0994215\pi\)
\(678\) −9.64611 −0.370457
\(679\) −13.3662 −0.512949
\(680\) −104.847 −4.02070
\(681\) 3.63510 0.139297
\(682\) 0.931557 0.0356712
\(683\) −7.26253 −0.277893 −0.138946 0.990300i \(-0.544372\pi\)
−0.138946 + 0.990300i \(0.544372\pi\)
\(684\) 17.5754 0.672014
\(685\) −3.94376 −0.150683
\(686\) −2.60224 −0.0993542
\(687\) 0.0867138 0.00330834
\(688\) −0.0584660 −0.00222900
\(689\) −1.95945 −0.0746489
\(690\) −31.4269 −1.19640
\(691\) 43.8977 1.66995 0.834973 0.550291i \(-0.185483\pi\)
0.834973 + 0.550291i \(0.185483\pi\)
\(692\) −92.1415 −3.50269
\(693\) −0.115915 −0.00440326
\(694\) 47.9365 1.81964
\(695\) −20.8796 −0.792009
\(696\) −28.0368 −1.06273
\(697\) −65.6676 −2.48734
\(698\) 19.7919 0.749133
\(699\) 21.3122 0.806100
\(700\) 8.02841 0.303445
\(701\) 24.9864 0.943724 0.471862 0.881673i \(-0.343582\pi\)
0.471862 + 0.881673i \(0.343582\pi\)
\(702\) 2.17279 0.0820067
\(703\) −39.3581 −1.48442
\(704\) −0.751543 −0.0283248
\(705\) −1.64423 −0.0619254
\(706\) −37.6640 −1.41750
\(707\) 4.25024 0.159847
\(708\) 40.2394 1.51229
\(709\) 45.5102 1.70917 0.854586 0.519309i \(-0.173811\pi\)
0.854586 + 0.519309i \(0.173811\pi\)
\(710\) 4.94133 0.185445
\(711\) −1.05167 −0.0394406
\(712\) 84.8744 3.18080
\(713\) 14.4279 0.540330
\(714\) −14.6334 −0.547639
\(715\) 0.250196 0.00935680
\(716\) −32.7055 −1.22226
\(717\) −3.59778 −0.134362
\(718\) −9.82638 −0.366717
\(719\) −3.28730 −0.122596 −0.0612979 0.998120i \(-0.519524\pi\)
−0.0612979 + 0.998120i \(0.519524\pi\)
\(720\) −23.8486 −0.888784
\(721\) −10.8398 −0.403694
\(722\) 14.1391 0.526204
\(723\) −8.40658 −0.312644
\(724\) 11.6194 0.431830
\(725\) −6.54027 −0.242900
\(726\) −28.5897 −1.06106
\(727\) 2.37891 0.0882289 0.0441144 0.999026i \(-0.485953\pi\)
0.0441144 + 0.999026i \(0.485953\pi\)
\(728\) −6.02227 −0.223200
\(729\) 1.00000 0.0370370
\(730\) −66.5205 −2.46203
\(731\) 0.0356375 0.00131810
\(732\) −64.5980 −2.38761
\(733\) −19.7643 −0.730010 −0.365005 0.931006i \(-0.618933\pi\)
−0.365005 + 0.931006i \(0.618933\pi\)
\(734\) −81.0540 −2.99176
\(735\) 2.58506 0.0953512
\(736\) −44.7651 −1.65006
\(737\) −0.597799 −0.0220202
\(738\) −30.3881 −1.11860
\(739\) −5.78584 −0.212836 −0.106418 0.994322i \(-0.533938\pi\)
−0.106418 + 0.994322i \(0.533938\pi\)
\(740\) 131.807 4.84534
\(741\) −3.07542 −0.112978
\(742\) 6.10677 0.224187
\(743\) −14.3473 −0.526350 −0.263175 0.964748i \(-0.584770\pi\)
−0.263175 + 0.964748i \(0.584770\pi\)
\(744\) 22.2747 0.816628
\(745\) 54.1768 1.98489
\(746\) −27.2613 −0.998108
\(747\) 11.9797 0.438313
\(748\) 3.11034 0.113725
\(749\) 8.44855 0.308703
\(750\) 22.3166 0.814885
\(751\) −51.4173 −1.87624 −0.938122 0.346306i \(-0.887436\pi\)
−0.938122 + 0.346306i \(0.887436\pi\)
\(752\) −5.86795 −0.213982
\(753\) −16.3609 −0.596223
\(754\) 8.44608 0.307588
\(755\) 8.20919 0.298763
\(756\) −4.77168 −0.173544
\(757\) 11.9672 0.434954 0.217477 0.976065i \(-0.430217\pi\)
0.217477 + 0.976065i \(0.430217\pi\)
\(758\) −62.7460 −2.27904
\(759\) 0.541533 0.0196564
\(760\) 68.6745 2.49109
\(761\) 49.4610 1.79296 0.896480 0.443085i \(-0.146116\pi\)
0.896480 + 0.443085i \(0.146116\pi\)
\(762\) 24.2550 0.878665
\(763\) −1.06337 −0.0384965
\(764\) −4.77168 −0.172633
\(765\) 14.5367 0.525575
\(766\) −28.8240 −1.04145
\(767\) −7.04125 −0.254245
\(768\) 18.9319 0.683147
\(769\) −28.9451 −1.04379 −0.521894 0.853010i \(-0.674774\pi\)
−0.521894 + 0.853010i \(0.674774\pi\)
\(770\) −0.779757 −0.0281005
\(771\) 15.4413 0.556103
\(772\) −48.0838 −1.73057
\(773\) 27.1893 0.977932 0.488966 0.872303i \(-0.337374\pi\)
0.488966 + 0.872303i \(0.337374\pi\)
\(774\) 0.0164915 0.000592774 0
\(775\) 5.19611 0.186650
\(776\) 96.4051 3.46074
\(777\) 10.6856 0.383344
\(778\) −64.5612 −2.31463
\(779\) 43.0121 1.54107
\(780\) 10.2994 0.368777
\(781\) −0.0851466 −0.00304678
\(782\) 68.3641 2.44469
\(783\) 3.88720 0.138917
\(784\) 9.22555 0.329484
\(785\) 13.7450 0.490581
\(786\) 9.06315 0.323272
\(787\) 27.5386 0.981646 0.490823 0.871259i \(-0.336696\pi\)
0.490823 + 0.871259i \(0.336696\pi\)
\(788\) 20.0323 0.713620
\(789\) 32.0181 1.13987
\(790\) −7.07451 −0.251700
\(791\) −3.70684 −0.131800
\(792\) 0.836049 0.0297077
\(793\) 11.3036 0.401403
\(794\) −74.4860 −2.64341
\(795\) −6.06644 −0.215154
\(796\) −31.7499 −1.12535
\(797\) −15.2187 −0.539075 −0.269537 0.962990i \(-0.586871\pi\)
−0.269537 + 0.962990i \(0.586871\pi\)
\(798\) 9.58480 0.339298
\(799\) 3.57676 0.126537
\(800\) −16.1218 −0.569992
\(801\) −11.7675 −0.415786
\(802\) −30.8062 −1.08780
\(803\) 1.14625 0.0404502
\(804\) −24.6085 −0.867875
\(805\) −12.0769 −0.425653
\(806\) −6.71024 −0.236358
\(807\) −14.4482 −0.508602
\(808\) −30.6552 −1.07845
\(809\) −18.6770 −0.656648 −0.328324 0.944565i \(-0.606484\pi\)
−0.328324 + 0.944565i \(0.606484\pi\)
\(810\) 6.72695 0.236361
\(811\) 40.3502 1.41689 0.708444 0.705767i \(-0.249398\pi\)
0.708444 + 0.705767i \(0.249398\pi\)
\(812\) −18.5485 −0.650924
\(813\) 18.8960 0.662711
\(814\) −3.22321 −0.112973
\(815\) −36.0997 −1.26452
\(816\) 51.8786 1.81611
\(817\) −0.0233424 −0.000816649 0
\(818\) 11.8885 0.415673
\(819\) 0.834967 0.0291761
\(820\) −144.044 −5.03025
\(821\) 39.1286 1.36560 0.682799 0.730607i \(-0.260763\pi\)
0.682799 + 0.730607i \(0.260763\pi\)
\(822\) 3.96998 0.138469
\(823\) −26.6637 −0.929440 −0.464720 0.885458i \(-0.653845\pi\)
−0.464720 + 0.885458i \(0.653845\pi\)
\(824\) 78.1826 2.72362
\(825\) 0.195029 0.00679005
\(826\) 21.9446 0.763551
\(827\) 7.03774 0.244726 0.122363 0.992485i \(-0.460953\pi\)
0.122363 + 0.992485i \(0.460953\pi\)
\(828\) 22.2923 0.774712
\(829\) 3.27809 0.113853 0.0569264 0.998378i \(-0.481870\pi\)
0.0569264 + 0.998378i \(0.481870\pi\)
\(830\) 80.5866 2.79720
\(831\) −13.7382 −0.476573
\(832\) 5.41355 0.187681
\(833\) −5.62336 −0.194838
\(834\) 21.0184 0.727809
\(835\) −61.3604 −2.12347
\(836\) −2.03726 −0.0704602
\(837\) −3.08830 −0.106747
\(838\) −70.0205 −2.41882
\(839\) −34.5841 −1.19398 −0.596988 0.802250i \(-0.703636\pi\)
−0.596988 + 0.802250i \(0.703636\pi\)
\(840\) −18.6449 −0.643311
\(841\) −13.8896 −0.478953
\(842\) −37.5009 −1.29237
\(843\) −30.0517 −1.03503
\(844\) 78.8598 2.71447
\(845\) 31.8035 1.09407
\(846\) 1.65517 0.0569058
\(847\) −10.9866 −0.377503
\(848\) −21.6499 −0.743461
\(849\) −15.1964 −0.521541
\(850\) 24.6208 0.844487
\(851\) −49.9210 −1.71127
\(852\) −3.50507 −0.120082
\(853\) −25.9995 −0.890204 −0.445102 0.895480i \(-0.646833\pi\)
−0.445102 + 0.895480i \(0.646833\pi\)
\(854\) −35.2287 −1.20550
\(855\) −9.52149 −0.325628
\(856\) −60.9359 −2.08274
\(857\) −30.9279 −1.05648 −0.528238 0.849096i \(-0.677147\pi\)
−0.528238 + 0.849096i \(0.677147\pi\)
\(858\) −0.251860 −0.00859835
\(859\) 2.78374 0.0949801 0.0474900 0.998872i \(-0.484878\pi\)
0.0474900 + 0.998872i \(0.484878\pi\)
\(860\) 0.0781722 0.00266565
\(861\) −11.6776 −0.397973
\(862\) −7.79371 −0.265455
\(863\) −38.6082 −1.31424 −0.657120 0.753786i \(-0.728225\pi\)
−0.657120 + 0.753786i \(0.728225\pi\)
\(864\) 9.58198 0.325985
\(865\) 49.9176 1.69725
\(866\) −50.4102 −1.71301
\(867\) −14.6222 −0.496594
\(868\) 14.7364 0.500186
\(869\) 0.121904 0.00413533
\(870\) 26.1490 0.886535
\(871\) 4.30610 0.145906
\(872\) 7.66963 0.259727
\(873\) −13.3662 −0.452378
\(874\) −44.7783 −1.51465
\(875\) 8.57589 0.289918
\(876\) 47.1855 1.59425
\(877\) 30.5332 1.03103 0.515517 0.856879i \(-0.327600\pi\)
0.515517 + 0.856879i \(0.327600\pi\)
\(878\) −59.7132 −2.01522
\(879\) −11.6374 −0.392520
\(880\) 2.76442 0.0931884
\(881\) −51.9298 −1.74956 −0.874780 0.484520i \(-0.838994\pi\)
−0.874780 + 0.484520i \(0.838994\pi\)
\(882\) −2.60224 −0.0876221
\(883\) 5.34872 0.179999 0.0899994 0.995942i \(-0.471313\pi\)
0.0899994 + 0.995942i \(0.471313\pi\)
\(884\) −22.4046 −0.753547
\(885\) −21.7997 −0.732788
\(886\) −42.7207 −1.43523
\(887\) 6.54742 0.219841 0.109920 0.993940i \(-0.464940\pi\)
0.109920 + 0.993940i \(0.464940\pi\)
\(888\) −77.0708 −2.58633
\(889\) 9.32079 0.312609
\(890\) −79.1596 −2.65344
\(891\) −0.115915 −0.00388331
\(892\) −91.7532 −3.07212
\(893\) −2.34276 −0.0783976
\(894\) −54.5371 −1.82399
\(895\) 17.7182 0.592255
\(896\) 2.29218 0.0765765
\(897\) −3.90080 −0.130244
\(898\) −25.3020 −0.844339
\(899\) −12.0049 −0.400385
\(900\) 8.02841 0.267614
\(901\) 13.1965 0.439640
\(902\) 3.52245 0.117285
\(903\) 0.00633740 0.000210896 0
\(904\) 26.7359 0.889223
\(905\) −6.29478 −0.209246
\(906\) −8.26378 −0.274546
\(907\) −7.51348 −0.249481 −0.124741 0.992189i \(-0.539810\pi\)
−0.124741 + 0.992189i \(0.539810\pi\)
\(908\) −17.3455 −0.575632
\(909\) 4.25024 0.140972
\(910\) 5.61678 0.186195
\(911\) 9.60176 0.318121 0.159060 0.987269i \(-0.449154\pi\)
0.159060 + 0.987269i \(0.449154\pi\)
\(912\) −33.9803 −1.12520
\(913\) −1.38863 −0.0459569
\(914\) −21.7485 −0.719375
\(915\) 34.9960 1.15693
\(916\) −0.413770 −0.0136714
\(917\) 3.48282 0.115013
\(918\) −14.6334 −0.482973
\(919\) 31.9826 1.05501 0.527505 0.849552i \(-0.323128\pi\)
0.527505 + 0.849552i \(0.323128\pi\)
\(920\) 87.1054 2.87178
\(921\) −13.1049 −0.431821
\(922\) −27.7542 −0.914037
\(923\) 0.613332 0.0201881
\(924\) 0.553111 0.0181960
\(925\) −17.9787 −0.591135
\(926\) −79.0286 −2.59704
\(927\) −10.8398 −0.356024
\(928\) 37.2471 1.22270
\(929\) 39.1814 1.28550 0.642750 0.766076i \(-0.277793\pi\)
0.642750 + 0.766076i \(0.277793\pi\)
\(930\) −20.7749 −0.681235
\(931\) 3.68328 0.120715
\(932\) −101.695 −3.33112
\(933\) −27.8159 −0.910651
\(934\) −0.166768 −0.00545682
\(935\) −1.68503 −0.0551063
\(936\) −6.02227 −0.196844
\(937\) 22.6694 0.740575 0.370288 0.928917i \(-0.379259\pi\)
0.370288 + 0.928917i \(0.379259\pi\)
\(938\) −13.4203 −0.438188
\(939\) −22.2381 −0.725712
\(940\) 7.84576 0.255900
\(941\) −32.3551 −1.05475 −0.527373 0.849634i \(-0.676823\pi\)
−0.527373 + 0.849634i \(0.676823\pi\)
\(942\) −13.8364 −0.450815
\(943\) 54.5556 1.77657
\(944\) −77.7987 −2.53213
\(945\) 2.58506 0.0840919
\(946\) −0.00191162 −6.21520e−5 0
\(947\) −17.1025 −0.555756 −0.277878 0.960616i \(-0.589631\pi\)
−0.277878 + 0.960616i \(0.589631\pi\)
\(948\) 5.01822 0.162984
\(949\) −8.25671 −0.268024
\(950\) −16.1266 −0.523215
\(951\) 6.15878 0.199712
\(952\) 40.5589 1.31452
\(953\) 27.0201 0.875267 0.437634 0.899153i \(-0.355817\pi\)
0.437634 + 0.899153i \(0.355817\pi\)
\(954\) 6.10677 0.197714
\(955\) 2.58506 0.0836504
\(956\) 17.1675 0.555235
\(957\) −0.450587 −0.0145654
\(958\) −85.7915 −2.77180
\(959\) 1.52560 0.0492642
\(960\) 16.7603 0.540937
\(961\) −21.4624 −0.692335
\(962\) 23.2176 0.748564
\(963\) 8.44855 0.272251
\(964\) 40.1135 1.29197
\(965\) 26.0494 0.838560
\(966\) 12.1572 0.391150
\(967\) 39.9680 1.28529 0.642643 0.766166i \(-0.277838\pi\)
0.642643 + 0.766166i \(0.277838\pi\)
\(968\) 79.2415 2.54692
\(969\) 20.7124 0.665379
\(970\) −89.9140 −2.88696
\(971\) −1.35538 −0.0434961 −0.0217481 0.999763i \(-0.506923\pi\)
−0.0217481 + 0.999763i \(0.506923\pi\)
\(972\) −4.77168 −0.153052
\(973\) 8.07704 0.258938
\(974\) −47.7965 −1.53150
\(975\) −1.40484 −0.0449910
\(976\) 124.894 3.99775
\(977\) 1.14587 0.0366596 0.0183298 0.999832i \(-0.494165\pi\)
0.0183298 + 0.999832i \(0.494165\pi\)
\(978\) 36.3397 1.16202
\(979\) 1.36404 0.0435949
\(980\) −12.3351 −0.394029
\(981\) −1.06337 −0.0339507
\(982\) 32.1838 1.02703
\(983\) −34.2850 −1.09352 −0.546761 0.837289i \(-0.684139\pi\)
−0.546761 + 0.837289i \(0.684139\pi\)
\(984\) 84.2260 2.68503
\(985\) −10.8525 −0.345789
\(986\) −56.8828 −1.81152
\(987\) 0.636054 0.0202458
\(988\) 14.6749 0.466871
\(989\) −0.0296071 −0.000941450 0
\(990\) −0.779757 −0.0247823
\(991\) −1.61563 −0.0513221 −0.0256610 0.999671i \(-0.508169\pi\)
−0.0256610 + 0.999671i \(0.508169\pi\)
\(992\) −29.5921 −0.939549
\(993\) 2.93153 0.0930292
\(994\) −1.91150 −0.0606291
\(995\) 17.2005 0.545293
\(996\) −57.1631 −1.81128
\(997\) 41.3066 1.30819 0.654096 0.756411i \(-0.273049\pi\)
0.654096 + 0.756411i \(0.273049\pi\)
\(998\) −25.4347 −0.805121
\(999\) 10.6856 0.338077
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.l.1.3 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4011.2.a.l.1.3 28 1.1 even 1 trivial