Properties

Label 4015.2.a.c.1.16
Level $4015$
Weight $2$
Character 4015.1
Self dual yes
Analytic conductor $32.060$
Analytic rank $1$
Dimension $23$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4015,2,Mod(1,4015)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4015, 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("4015.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4015 = 5 \cdot 11 \cdot 73 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4015.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: \(32.0599364115\)
Analytic rank: \(1\)
Dimension: \(23\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) \(=\) 4015.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.661798 q^{2} -2.32231 q^{3} -1.56202 q^{4} +1.00000 q^{5} -1.53690 q^{6} -0.917277 q^{7} -2.35734 q^{8} +2.39311 q^{9} +O(q^{10})\) \(q+0.661798 q^{2} -2.32231 q^{3} -1.56202 q^{4} +1.00000 q^{5} -1.53690 q^{6} -0.917277 q^{7} -2.35734 q^{8} +2.39311 q^{9} +0.661798 q^{10} -1.00000 q^{11} +3.62750 q^{12} -1.28300 q^{13} -0.607052 q^{14} -2.32231 q^{15} +1.56396 q^{16} +1.41536 q^{17} +1.58376 q^{18} -0.964916 q^{19} -1.56202 q^{20} +2.13020 q^{21} -0.661798 q^{22} +6.85951 q^{23} +5.47447 q^{24} +1.00000 q^{25} -0.849085 q^{26} +1.40939 q^{27} +1.43281 q^{28} -2.38222 q^{29} -1.53690 q^{30} -0.451972 q^{31} +5.74971 q^{32} +2.32231 q^{33} +0.936683 q^{34} -0.917277 q^{35} -3.73809 q^{36} -3.55440 q^{37} -0.638580 q^{38} +2.97951 q^{39} -2.35734 q^{40} +9.63575 q^{41} +1.40976 q^{42} -10.4099 q^{43} +1.56202 q^{44} +2.39311 q^{45} +4.53961 q^{46} +3.79809 q^{47} -3.63200 q^{48} -6.15860 q^{49} +0.661798 q^{50} -3.28690 q^{51} +2.00407 q^{52} +1.82732 q^{53} +0.932729 q^{54} -1.00000 q^{55} +2.16233 q^{56} +2.24083 q^{57} -1.57655 q^{58} +7.11938 q^{59} +3.62750 q^{60} +4.53167 q^{61} -0.299114 q^{62} -2.19514 q^{63} +0.677218 q^{64} -1.28300 q^{65} +1.53690 q^{66} +4.60895 q^{67} -2.21083 q^{68} -15.9299 q^{69} -0.607052 q^{70} +13.2959 q^{71} -5.64137 q^{72} +1.00000 q^{73} -2.35229 q^{74} -2.32231 q^{75} +1.50722 q^{76} +0.917277 q^{77} +1.97184 q^{78} -15.3671 q^{79} +1.56396 q^{80} -10.4524 q^{81} +6.37692 q^{82} +10.4012 q^{83} -3.32742 q^{84} +1.41536 q^{85} -6.88922 q^{86} +5.53225 q^{87} +2.35734 q^{88} -6.54366 q^{89} +1.58376 q^{90} +1.17686 q^{91} -10.7147 q^{92} +1.04962 q^{93} +2.51357 q^{94} -0.964916 q^{95} -13.3526 q^{96} -14.5876 q^{97} -4.07575 q^{98} -2.39311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9} - 3 q^{10} - 23 q^{11} - 18 q^{12} - 5 q^{13} - 17 q^{14} - 5 q^{15} - q^{16} - 36 q^{17} + q^{18} + 6 q^{19} + 15 q^{20} - 18 q^{21} + 3 q^{22} - 14 q^{23} - 7 q^{24} + 23 q^{25} - 21 q^{26} - 29 q^{27} + 28 q^{28} - 36 q^{29} - 5 q^{30} - 16 q^{31} - 5 q^{32} + 5 q^{33} - 28 q^{34} - 14 q^{36} - 24 q^{37} + q^{38} - 10 q^{39} - 6 q^{40} - 36 q^{41} - 5 q^{42} + 17 q^{43} - 15 q^{44} + 8 q^{45} - 25 q^{46} - 21 q^{47} - 17 q^{48} - 27 q^{49} - 3 q^{50} + 19 q^{51} - 21 q^{52} - 28 q^{53} - 15 q^{54} - 23 q^{55} - 46 q^{56} - 23 q^{57} - 16 q^{58} - 61 q^{59} - 18 q^{60} - 17 q^{61} - 22 q^{62} - 9 q^{63} - 18 q^{64} - 5 q^{65} + 5 q^{66} + 2 q^{67} - 39 q^{68} - 36 q^{69} - 17 q^{70} - 50 q^{71} + 15 q^{72} + 23 q^{73} + 17 q^{74} - 5 q^{75} - 21 q^{76} + 49 q^{78} - 18 q^{79} - q^{80} - 57 q^{81} + 14 q^{82} - 20 q^{83} - 38 q^{84} - 36 q^{85} - 45 q^{86} + 37 q^{87} + 6 q^{88} - 93 q^{89} + q^{90} - 42 q^{91} - 39 q^{92} - 18 q^{93} - 6 q^{94} + 6 q^{95} - 9 q^{96} - 31 q^{97} - 31 q^{98} - 8 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.661798 0.467962 0.233981 0.972241i \(-0.424825\pi\)
0.233981 + 0.972241i \(0.424825\pi\)
\(3\) −2.32231 −1.34078 −0.670392 0.742007i \(-0.733874\pi\)
−0.670392 + 0.742007i \(0.733874\pi\)
\(4\) −1.56202 −0.781012
\(5\) 1.00000 0.447214
\(6\) −1.53690 −0.627436
\(7\) −0.917277 −0.346698 −0.173349 0.984860i \(-0.555459\pi\)
−0.173349 + 0.984860i \(0.555459\pi\)
\(8\) −2.35734 −0.833446
\(9\) 2.39311 0.797703
\(10\) 0.661798 0.209279
\(11\) −1.00000 −0.301511
\(12\) 3.62750 1.04717
\(13\) −1.28300 −0.355839 −0.177920 0.984045i \(-0.556937\pi\)
−0.177920 + 0.984045i \(0.556937\pi\)
\(14\) −0.607052 −0.162241
\(15\) −2.32231 −0.599617
\(16\) 1.56396 0.390991
\(17\) 1.41536 0.343275 0.171638 0.985160i \(-0.445094\pi\)
0.171638 + 0.985160i \(0.445094\pi\)
\(18\) 1.58376 0.373295
\(19\) −0.964916 −0.221367 −0.110684 0.993856i \(-0.535304\pi\)
−0.110684 + 0.993856i \(0.535304\pi\)
\(20\) −1.56202 −0.349279
\(21\) 2.13020 0.464847
\(22\) −0.661798 −0.141096
\(23\) 6.85951 1.43031 0.715153 0.698968i \(-0.246357\pi\)
0.715153 + 0.698968i \(0.246357\pi\)
\(24\) 5.47447 1.11747
\(25\) 1.00000 0.200000
\(26\) −0.849085 −0.166519
\(27\) 1.40939 0.271236
\(28\) 1.43281 0.270775
\(29\) −2.38222 −0.442367 −0.221184 0.975232i \(-0.570992\pi\)
−0.221184 + 0.975232i \(0.570992\pi\)
\(30\) −1.53690 −0.280598
\(31\) −0.451972 −0.0811766 −0.0405883 0.999176i \(-0.512923\pi\)
−0.0405883 + 0.999176i \(0.512923\pi\)
\(32\) 5.74971 1.01641
\(33\) 2.32231 0.404262
\(34\) 0.936683 0.160640
\(35\) −0.917277 −0.155048
\(36\) −3.73809 −0.623016
\(37\) −3.55440 −0.584339 −0.292170 0.956367i \(-0.594377\pi\)
−0.292170 + 0.956367i \(0.594377\pi\)
\(38\) −0.638580 −0.103591
\(39\) 2.97951 0.477104
\(40\) −2.35734 −0.372728
\(41\) 9.63575 1.50485 0.752426 0.658677i \(-0.228884\pi\)
0.752426 + 0.658677i \(0.228884\pi\)
\(42\) 1.40976 0.217531
\(43\) −10.4099 −1.58749 −0.793744 0.608252i \(-0.791871\pi\)
−0.793744 + 0.608252i \(0.791871\pi\)
\(44\) 1.56202 0.235484
\(45\) 2.39311 0.356744
\(46\) 4.53961 0.669329
\(47\) 3.79809 0.554008 0.277004 0.960869i \(-0.410659\pi\)
0.277004 + 0.960869i \(0.410659\pi\)
\(48\) −3.63200 −0.524235
\(49\) −6.15860 −0.879800
\(50\) 0.661798 0.0935924
\(51\) −3.28690 −0.460258
\(52\) 2.00407 0.277915
\(53\) 1.82732 0.251002 0.125501 0.992093i \(-0.459946\pi\)
0.125501 + 0.992093i \(0.459946\pi\)
\(54\) 0.932729 0.126928
\(55\) −1.00000 −0.134840
\(56\) 2.16233 0.288954
\(57\) 2.24083 0.296805
\(58\) −1.57655 −0.207011
\(59\) 7.11938 0.926864 0.463432 0.886133i \(-0.346618\pi\)
0.463432 + 0.886133i \(0.346618\pi\)
\(60\) 3.62750 0.468308
\(61\) 4.53167 0.580220 0.290110 0.956993i \(-0.406308\pi\)
0.290110 + 0.956993i \(0.406308\pi\)
\(62\) −0.299114 −0.0379875
\(63\) −2.19514 −0.276562
\(64\) 0.677218 0.0846522
\(65\) −1.28300 −0.159136
\(66\) 1.53690 0.189179
\(67\) 4.60895 0.563072 0.281536 0.959551i \(-0.409156\pi\)
0.281536 + 0.959551i \(0.409156\pi\)
\(68\) −2.21083 −0.268102
\(69\) −15.9299 −1.91773
\(70\) −0.607052 −0.0725566
\(71\) 13.2959 1.57793 0.788966 0.614437i \(-0.210617\pi\)
0.788966 + 0.614437i \(0.210617\pi\)
\(72\) −5.64137 −0.664842
\(73\) 1.00000 0.117041
\(74\) −2.35229 −0.273448
\(75\) −2.32231 −0.268157
\(76\) 1.50722 0.172890
\(77\) 0.917277 0.104533
\(78\) 1.97184 0.223266
\(79\) −15.3671 −1.72894 −0.864468 0.502688i \(-0.832344\pi\)
−0.864468 + 0.502688i \(0.832344\pi\)
\(80\) 1.56396 0.174856
\(81\) −10.4524 −1.16137
\(82\) 6.37692 0.704213
\(83\) 10.4012 1.14168 0.570842 0.821060i \(-0.306617\pi\)
0.570842 + 0.821060i \(0.306617\pi\)
\(84\) −3.32742 −0.363051
\(85\) 1.41536 0.153517
\(86\) −6.88922 −0.742884
\(87\) 5.53225 0.593119
\(88\) 2.35734 0.251293
\(89\) −6.54366 −0.693626 −0.346813 0.937934i \(-0.612736\pi\)
−0.346813 + 0.937934i \(0.612736\pi\)
\(90\) 1.58376 0.166942
\(91\) 1.17686 0.123369
\(92\) −10.7147 −1.11709
\(93\) 1.04962 0.108840
\(94\) 2.51357 0.259255
\(95\) −0.964916 −0.0989983
\(96\) −13.3526 −1.36279
\(97\) −14.5876 −1.48114 −0.740571 0.671978i \(-0.765445\pi\)
−0.740571 + 0.671978i \(0.765445\pi\)
\(98\) −4.07575 −0.411713
\(99\) −2.39311 −0.240517
\(100\) −1.56202 −0.156202
\(101\) −12.2234 −1.21628 −0.608139 0.793830i \(-0.708084\pi\)
−0.608139 + 0.793830i \(0.708084\pi\)
\(102\) −2.17527 −0.215383
\(103\) 1.49878 0.147679 0.0738397 0.997270i \(-0.476475\pi\)
0.0738397 + 0.997270i \(0.476475\pi\)
\(104\) 3.02446 0.296573
\(105\) 2.13020 0.207886
\(106\) 1.20932 0.117459
\(107\) 8.47369 0.819183 0.409591 0.912269i \(-0.365671\pi\)
0.409591 + 0.912269i \(0.365671\pi\)
\(108\) −2.20149 −0.211839
\(109\) 1.07096 0.102580 0.0512899 0.998684i \(-0.483667\pi\)
0.0512899 + 0.998684i \(0.483667\pi\)
\(110\) −0.661798 −0.0631000
\(111\) 8.25440 0.783473
\(112\) −1.43459 −0.135556
\(113\) −17.9881 −1.69218 −0.846089 0.533042i \(-0.821049\pi\)
−0.846089 + 0.533042i \(0.821049\pi\)
\(114\) 1.48298 0.138894
\(115\) 6.85951 0.639653
\(116\) 3.72108 0.345494
\(117\) −3.07035 −0.283854
\(118\) 4.71159 0.433737
\(119\) −1.29828 −0.119013
\(120\) 5.47447 0.499748
\(121\) 1.00000 0.0909091
\(122\) 2.99905 0.271521
\(123\) −22.3772 −2.01768
\(124\) 0.705991 0.0633998
\(125\) 1.00000 0.0894427
\(126\) −1.45274 −0.129421
\(127\) −1.08985 −0.0967084 −0.0483542 0.998830i \(-0.515398\pi\)
−0.0483542 + 0.998830i \(0.515398\pi\)
\(128\) −11.0512 −0.976800
\(129\) 24.1749 2.12848
\(130\) −0.849085 −0.0744697
\(131\) 0.670209 0.0585564 0.0292782 0.999571i \(-0.490679\pi\)
0.0292782 + 0.999571i \(0.490679\pi\)
\(132\) −3.62750 −0.315733
\(133\) 0.885096 0.0767475
\(134\) 3.05019 0.263496
\(135\) 1.40939 0.121301
\(136\) −3.33649 −0.286101
\(137\) −15.9919 −1.36628 −0.683138 0.730289i \(-0.739385\pi\)
−0.683138 + 0.730289i \(0.739385\pi\)
\(138\) −10.5424 −0.897426
\(139\) −11.4484 −0.971043 −0.485521 0.874225i \(-0.661370\pi\)
−0.485521 + 0.874225i \(0.661370\pi\)
\(140\) 1.43281 0.121094
\(141\) −8.82032 −0.742805
\(142\) 8.79919 0.738412
\(143\) 1.28300 0.107290
\(144\) 3.74274 0.311895
\(145\) −2.38222 −0.197833
\(146\) 0.661798 0.0547708
\(147\) 14.3022 1.17962
\(148\) 5.55205 0.456376
\(149\) −11.8230 −0.968580 −0.484290 0.874907i \(-0.660922\pi\)
−0.484290 + 0.874907i \(0.660922\pi\)
\(150\) −1.53690 −0.125487
\(151\) 3.20301 0.260657 0.130329 0.991471i \(-0.458397\pi\)
0.130329 + 0.991471i \(0.458397\pi\)
\(152\) 2.27464 0.184497
\(153\) 3.38711 0.273832
\(154\) 0.607052 0.0489177
\(155\) −0.451972 −0.0363033
\(156\) −4.65407 −0.372624
\(157\) 18.8438 1.50390 0.751950 0.659220i \(-0.229113\pi\)
0.751950 + 0.659220i \(0.229113\pi\)
\(158\) −10.1699 −0.809076
\(159\) −4.24360 −0.336540
\(160\) 5.74971 0.454554
\(161\) −6.29207 −0.495885
\(162\) −6.91735 −0.543478
\(163\) −1.80746 −0.141571 −0.0707854 0.997492i \(-0.522551\pi\)
−0.0707854 + 0.997492i \(0.522551\pi\)
\(164\) −15.0513 −1.17531
\(165\) 2.32231 0.180791
\(166\) 6.88352 0.534265
\(167\) 12.8299 0.992806 0.496403 0.868092i \(-0.334654\pi\)
0.496403 + 0.868092i \(0.334654\pi\)
\(168\) −5.02160 −0.387425
\(169\) −11.3539 −0.873378
\(170\) 0.936683 0.0718403
\(171\) −2.30915 −0.176585
\(172\) 16.2604 1.23985
\(173\) −1.30633 −0.0993181 −0.0496591 0.998766i \(-0.515813\pi\)
−0.0496591 + 0.998766i \(0.515813\pi\)
\(174\) 3.66123 0.277557
\(175\) −0.917277 −0.0693396
\(176\) −1.56396 −0.117888
\(177\) −16.5334 −1.24272
\(178\) −4.33058 −0.324591
\(179\) 15.7126 1.17441 0.587207 0.809437i \(-0.300228\pi\)
0.587207 + 0.809437i \(0.300228\pi\)
\(180\) −3.73809 −0.278621
\(181\) −25.0696 −1.86341 −0.931704 0.363218i \(-0.881678\pi\)
−0.931704 + 0.363218i \(0.881678\pi\)
\(182\) 0.778846 0.0577319
\(183\) −10.5239 −0.777951
\(184\) −16.1702 −1.19208
\(185\) −3.55440 −0.261324
\(186\) 0.694635 0.0509331
\(187\) −1.41536 −0.103501
\(188\) −5.93270 −0.432687
\(189\) −1.29280 −0.0940372
\(190\) −0.638580 −0.0463274
\(191\) −19.1417 −1.38505 −0.692524 0.721395i \(-0.743501\pi\)
−0.692524 + 0.721395i \(0.743501\pi\)
\(192\) −1.57271 −0.113500
\(193\) 12.7752 0.919579 0.459789 0.888028i \(-0.347925\pi\)
0.459789 + 0.888028i \(0.347925\pi\)
\(194\) −9.65402 −0.693118
\(195\) 2.97951 0.213367
\(196\) 9.61988 0.687134
\(197\) 5.09996 0.363357 0.181678 0.983358i \(-0.441847\pi\)
0.181678 + 0.983358i \(0.441847\pi\)
\(198\) −1.58376 −0.112553
\(199\) −9.29350 −0.658799 −0.329399 0.944191i \(-0.606846\pi\)
−0.329399 + 0.944191i \(0.606846\pi\)
\(200\) −2.35734 −0.166689
\(201\) −10.7034 −0.754959
\(202\) −8.08945 −0.569172
\(203\) 2.18516 0.153368
\(204\) 5.13422 0.359467
\(205\) 9.63575 0.672990
\(206\) 0.991891 0.0691083
\(207\) 16.4156 1.14096
\(208\) −2.00656 −0.139130
\(209\) 0.964916 0.0667447
\(210\) 1.40976 0.0972828
\(211\) 16.2152 1.11630 0.558152 0.829739i \(-0.311511\pi\)
0.558152 + 0.829739i \(0.311511\pi\)
\(212\) −2.85432 −0.196036
\(213\) −30.8771 −2.11567
\(214\) 5.60787 0.383346
\(215\) −10.4099 −0.709946
\(216\) −3.32240 −0.226061
\(217\) 0.414583 0.0281438
\(218\) 0.708762 0.0480034
\(219\) −2.32231 −0.156927
\(220\) 1.56202 0.105312
\(221\) −1.81590 −0.122151
\(222\) 5.46274 0.366635
\(223\) −28.1438 −1.88465 −0.942323 0.334704i \(-0.891364\pi\)
−0.942323 + 0.334704i \(0.891364\pi\)
\(224\) −5.27407 −0.352389
\(225\) 2.39311 0.159541
\(226\) −11.9045 −0.791875
\(227\) 19.0019 1.26120 0.630600 0.776108i \(-0.282809\pi\)
0.630600 + 0.776108i \(0.282809\pi\)
\(228\) −3.50023 −0.231809
\(229\) −6.80519 −0.449699 −0.224850 0.974393i \(-0.572189\pi\)
−0.224850 + 0.974393i \(0.572189\pi\)
\(230\) 4.53961 0.299333
\(231\) −2.13020 −0.140157
\(232\) 5.61570 0.368689
\(233\) −3.68600 −0.241478 −0.120739 0.992684i \(-0.538526\pi\)
−0.120739 + 0.992684i \(0.538526\pi\)
\(234\) −2.03195 −0.132833
\(235\) 3.79809 0.247760
\(236\) −11.1206 −0.723891
\(237\) 35.6872 2.31813
\(238\) −0.859198 −0.0556935
\(239\) −24.2962 −1.57159 −0.785796 0.618486i \(-0.787747\pi\)
−0.785796 + 0.618486i \(0.787747\pi\)
\(240\) −3.63200 −0.234445
\(241\) −19.5774 −1.26109 −0.630544 0.776153i \(-0.717168\pi\)
−0.630544 + 0.776153i \(0.717168\pi\)
\(242\) 0.661798 0.0425420
\(243\) 20.0454 1.28591
\(244\) −7.07857 −0.453159
\(245\) −6.15860 −0.393459
\(246\) −14.8092 −0.944198
\(247\) 1.23799 0.0787711
\(248\) 1.06545 0.0676562
\(249\) −24.1549 −1.53075
\(250\) 0.661798 0.0418558
\(251\) 21.3969 1.35056 0.675280 0.737561i \(-0.264023\pi\)
0.675280 + 0.737561i \(0.264023\pi\)
\(252\) 3.42887 0.215998
\(253\) −6.85951 −0.431254
\(254\) −0.721260 −0.0452559
\(255\) −3.28690 −0.205834
\(256\) −8.66812 −0.541758
\(257\) −25.0175 −1.56055 −0.780276 0.625436i \(-0.784921\pi\)
−0.780276 + 0.625436i \(0.784921\pi\)
\(258\) 15.9989 0.996047
\(259\) 3.26037 0.202589
\(260\) 2.00407 0.124287
\(261\) −5.70092 −0.352878
\(262\) 0.443543 0.0274022
\(263\) −4.93740 −0.304453 −0.152227 0.988346i \(-0.548644\pi\)
−0.152227 + 0.988346i \(0.548644\pi\)
\(264\) −5.47447 −0.336930
\(265\) 1.82732 0.112252
\(266\) 0.585755 0.0359149
\(267\) 15.1964 0.930003
\(268\) −7.19928 −0.439766
\(269\) −0.499581 −0.0304600 −0.0152300 0.999884i \(-0.504848\pi\)
−0.0152300 + 0.999884i \(0.504848\pi\)
\(270\) 0.932729 0.0567641
\(271\) −29.5644 −1.79591 −0.897953 0.440091i \(-0.854946\pi\)
−0.897953 + 0.440091i \(0.854946\pi\)
\(272\) 2.21357 0.134218
\(273\) −2.73304 −0.165411
\(274\) −10.5834 −0.639365
\(275\) −1.00000 −0.0603023
\(276\) 24.8829 1.49777
\(277\) −9.82010 −0.590033 −0.295016 0.955492i \(-0.595325\pi\)
−0.295016 + 0.955492i \(0.595325\pi\)
\(278\) −7.57655 −0.454411
\(279\) −1.08162 −0.0647548
\(280\) 2.16233 0.129224
\(281\) −3.91159 −0.233346 −0.116673 0.993170i \(-0.537223\pi\)
−0.116673 + 0.993170i \(0.537223\pi\)
\(282\) −5.83727 −0.347604
\(283\) 0.551321 0.0327726 0.0163863 0.999866i \(-0.494784\pi\)
0.0163863 + 0.999866i \(0.494784\pi\)
\(284\) −20.7685 −1.23238
\(285\) 2.24083 0.132735
\(286\) 0.849085 0.0502074
\(287\) −8.83865 −0.521729
\(288\) 13.7597 0.810797
\(289\) −14.9968 −0.882162
\(290\) −1.57655 −0.0925781
\(291\) 33.8768 1.98589
\(292\) −1.56202 −0.0914105
\(293\) 15.1630 0.885832 0.442916 0.896563i \(-0.353944\pi\)
0.442916 + 0.896563i \(0.353944\pi\)
\(294\) 9.46515 0.552018
\(295\) 7.11938 0.414506
\(296\) 8.37892 0.487015
\(297\) −1.40939 −0.0817809
\(298\) −7.82446 −0.453259
\(299\) −8.80073 −0.508960
\(300\) 3.62750 0.209434
\(301\) 9.54872 0.550379
\(302\) 2.11975 0.121978
\(303\) 28.3866 1.63077
\(304\) −1.50909 −0.0865525
\(305\) 4.53167 0.259482
\(306\) 2.24159 0.128143
\(307\) −3.00100 −0.171276 −0.0856382 0.996326i \(-0.527293\pi\)
−0.0856382 + 0.996326i \(0.527293\pi\)
\(308\) −1.43281 −0.0816418
\(309\) −3.48063 −0.198006
\(310\) −0.299114 −0.0169885
\(311\) −27.5293 −1.56104 −0.780521 0.625129i \(-0.785046\pi\)
−0.780521 + 0.625129i \(0.785046\pi\)
\(312\) −7.02373 −0.397640
\(313\) −2.10701 −0.119095 −0.0595476 0.998225i \(-0.518966\pi\)
−0.0595476 + 0.998225i \(0.518966\pi\)
\(314\) 12.4708 0.703768
\(315\) −2.19514 −0.123682
\(316\) 24.0038 1.35032
\(317\) 22.1695 1.24516 0.622582 0.782555i \(-0.286084\pi\)
0.622582 + 0.782555i \(0.286084\pi\)
\(318\) −2.80841 −0.157488
\(319\) 2.38222 0.133379
\(320\) 0.677218 0.0378576
\(321\) −19.6785 −1.09835
\(322\) −4.16408 −0.232055
\(323\) −1.36571 −0.0759899
\(324\) 16.3268 0.907046
\(325\) −1.28300 −0.0711679
\(326\) −1.19617 −0.0662497
\(327\) −2.48711 −0.137537
\(328\) −22.7147 −1.25421
\(329\) −3.48390 −0.192073
\(330\) 1.53690 0.0846035
\(331\) −31.6011 −1.73695 −0.868475 0.495732i \(-0.834900\pi\)
−0.868475 + 0.495732i \(0.834900\pi\)
\(332\) −16.2470 −0.891669
\(333\) −8.50606 −0.466129
\(334\) 8.49079 0.464595
\(335\) 4.60895 0.251814
\(336\) 3.33155 0.181751
\(337\) 15.6974 0.855090 0.427545 0.903994i \(-0.359379\pi\)
0.427545 + 0.903994i \(0.359379\pi\)
\(338\) −7.51400 −0.408708
\(339\) 41.7739 2.26885
\(340\) −2.21083 −0.119899
\(341\) 0.451972 0.0244757
\(342\) −1.52819 −0.0826351
\(343\) 12.0701 0.651723
\(344\) 24.5396 1.32308
\(345\) −15.9299 −0.857636
\(346\) −0.864524 −0.0464771
\(347\) −18.1016 −0.971744 −0.485872 0.874030i \(-0.661498\pi\)
−0.485872 + 0.874030i \(0.661498\pi\)
\(348\) −8.64150 −0.463233
\(349\) 13.0476 0.698424 0.349212 0.937044i \(-0.386449\pi\)
0.349212 + 0.937044i \(0.386449\pi\)
\(350\) −0.607052 −0.0324483
\(351\) −1.80824 −0.0965166
\(352\) −5.74971 −0.306460
\(353\) −16.9950 −0.904555 −0.452278 0.891877i \(-0.649388\pi\)
−0.452278 + 0.891877i \(0.649388\pi\)
\(354\) −10.9418 −0.581548
\(355\) 13.2959 0.705672
\(356\) 10.2213 0.541730
\(357\) 3.01500 0.159571
\(358\) 10.3986 0.549581
\(359\) 31.8130 1.67903 0.839514 0.543339i \(-0.182840\pi\)
0.839514 + 0.543339i \(0.182840\pi\)
\(360\) −5.64137 −0.297326
\(361\) −18.0689 −0.950997
\(362\) −16.5910 −0.872004
\(363\) −2.32231 −0.121890
\(364\) −1.83829 −0.0963525
\(365\) 1.00000 0.0523424
\(366\) −6.96471 −0.364051
\(367\) −24.1869 −1.26255 −0.631274 0.775560i \(-0.717468\pi\)
−0.631274 + 0.775560i \(0.717468\pi\)
\(368\) 10.7280 0.559237
\(369\) 23.0594 1.20042
\(370\) −2.35229 −0.122290
\(371\) −1.67616 −0.0870219
\(372\) −1.63953 −0.0850055
\(373\) 6.68523 0.346148 0.173074 0.984909i \(-0.444630\pi\)
0.173074 + 0.984909i \(0.444630\pi\)
\(374\) −0.936683 −0.0484347
\(375\) −2.32231 −0.119923
\(376\) −8.95338 −0.461735
\(377\) 3.05638 0.157412
\(378\) −0.855571 −0.0440058
\(379\) −28.3191 −1.45466 −0.727328 0.686290i \(-0.759238\pi\)
−0.727328 + 0.686290i \(0.759238\pi\)
\(380\) 1.50722 0.0773189
\(381\) 2.53096 0.129665
\(382\) −12.6680 −0.648149
\(383\) −24.2648 −1.23987 −0.619937 0.784652i \(-0.712842\pi\)
−0.619937 + 0.784652i \(0.712842\pi\)
\(384\) 25.6644 1.30968
\(385\) 0.917277 0.0467488
\(386\) 8.45460 0.430328
\(387\) −24.9119 −1.26634
\(388\) 22.7861 1.15679
\(389\) 23.7608 1.20472 0.602360 0.798224i \(-0.294227\pi\)
0.602360 + 0.798224i \(0.294227\pi\)
\(390\) 1.97184 0.0998478
\(391\) 9.70868 0.490989
\(392\) 14.5179 0.733266
\(393\) −1.55643 −0.0785116
\(394\) 3.37514 0.170037
\(395\) −15.3671 −0.773203
\(396\) 3.73809 0.187846
\(397\) 35.0518 1.75920 0.879599 0.475717i \(-0.157811\pi\)
0.879599 + 0.475717i \(0.157811\pi\)
\(398\) −6.15042 −0.308293
\(399\) −2.05546 −0.102902
\(400\) 1.56396 0.0781982
\(401\) 18.7538 0.936521 0.468261 0.883590i \(-0.344881\pi\)
0.468261 + 0.883590i \(0.344881\pi\)
\(402\) −7.08348 −0.353292
\(403\) 0.579879 0.0288858
\(404\) 19.0933 0.949928
\(405\) −10.4524 −0.519382
\(406\) 1.44613 0.0717703
\(407\) 3.55440 0.176185
\(408\) 7.74835 0.383600
\(409\) 29.3706 1.45228 0.726141 0.687545i \(-0.241312\pi\)
0.726141 + 0.687545i \(0.241312\pi\)
\(410\) 6.37692 0.314934
\(411\) 37.1380 1.83188
\(412\) −2.34113 −0.115339
\(413\) −6.53044 −0.321342
\(414\) 10.8638 0.533926
\(415\) 10.4012 0.510577
\(416\) −7.37686 −0.361680
\(417\) 26.5868 1.30196
\(418\) 0.638580 0.0312340
\(419\) 2.24786 0.109815 0.0549075 0.998491i \(-0.482514\pi\)
0.0549075 + 0.998491i \(0.482514\pi\)
\(420\) −3.32742 −0.162361
\(421\) −20.4664 −0.997470 −0.498735 0.866755i \(-0.666202\pi\)
−0.498735 + 0.866755i \(0.666202\pi\)
\(422\) 10.7312 0.522388
\(423\) 9.08924 0.441934
\(424\) −4.30762 −0.209197
\(425\) 1.41536 0.0686551
\(426\) −20.4344 −0.990051
\(427\) −4.15679 −0.201161
\(428\) −13.2361 −0.639791
\(429\) −2.97951 −0.143852
\(430\) −6.88922 −0.332228
\(431\) 32.6318 1.57182 0.785908 0.618343i \(-0.212196\pi\)
0.785908 + 0.618343i \(0.212196\pi\)
\(432\) 2.20423 0.106051
\(433\) −7.20781 −0.346385 −0.173193 0.984888i \(-0.555408\pi\)
−0.173193 + 0.984888i \(0.555408\pi\)
\(434\) 0.274371 0.0131702
\(435\) 5.53225 0.265251
\(436\) −1.67287 −0.0801160
\(437\) −6.61885 −0.316623
\(438\) −1.53690 −0.0734358
\(439\) −35.1285 −1.67659 −0.838296 0.545216i \(-0.816448\pi\)
−0.838296 + 0.545216i \(0.816448\pi\)
\(440\) 2.35734 0.112382
\(441\) −14.7382 −0.701820
\(442\) −1.20176 −0.0571620
\(443\) 10.1155 0.480600 0.240300 0.970699i \(-0.422754\pi\)
0.240300 + 0.970699i \(0.422754\pi\)
\(444\) −12.8936 −0.611901
\(445\) −6.54366 −0.310199
\(446\) −18.6255 −0.881943
\(447\) 27.4567 1.29866
\(448\) −0.621196 −0.0293488
\(449\) −14.1635 −0.668415 −0.334208 0.942500i \(-0.608469\pi\)
−0.334208 + 0.942500i \(0.608469\pi\)
\(450\) 1.58376 0.0746589
\(451\) −9.63575 −0.453730
\(452\) 28.0978 1.32161
\(453\) −7.43837 −0.349485
\(454\) 12.5754 0.590193
\(455\) 1.17686 0.0551722
\(456\) −5.28240 −0.247371
\(457\) 3.67434 0.171878 0.0859391 0.996300i \(-0.472611\pi\)
0.0859391 + 0.996300i \(0.472611\pi\)
\(458\) −4.50366 −0.210442
\(459\) 1.99479 0.0931088
\(460\) −10.7147 −0.499576
\(461\) 4.89385 0.227929 0.113965 0.993485i \(-0.463645\pi\)
0.113965 + 0.993485i \(0.463645\pi\)
\(462\) −1.40976 −0.0655880
\(463\) 22.0672 1.02555 0.512774 0.858523i \(-0.328618\pi\)
0.512774 + 0.858523i \(0.328618\pi\)
\(464\) −3.72571 −0.172962
\(465\) 1.04962 0.0486749
\(466\) −2.43939 −0.113002
\(467\) −8.77814 −0.406204 −0.203102 0.979158i \(-0.565102\pi\)
−0.203102 + 0.979158i \(0.565102\pi\)
\(468\) 4.79596 0.221693
\(469\) −4.22768 −0.195216
\(470\) 2.51357 0.115942
\(471\) −43.7611 −2.01641
\(472\) −16.7828 −0.772491
\(473\) 10.4099 0.478646
\(474\) 23.6177 1.08480
\(475\) −0.964916 −0.0442734
\(476\) 2.02794 0.0929505
\(477\) 4.37298 0.200225
\(478\) −16.0792 −0.735445
\(479\) 27.7489 1.26788 0.633939 0.773383i \(-0.281437\pi\)
0.633939 + 0.773383i \(0.281437\pi\)
\(480\) −13.3526 −0.609459
\(481\) 4.56028 0.207931
\(482\) −12.9563 −0.590141
\(483\) 14.6121 0.664874
\(484\) −1.56202 −0.0710011
\(485\) −14.5876 −0.662387
\(486\) 13.2660 0.601759
\(487\) 30.3206 1.37396 0.686979 0.726677i \(-0.258936\pi\)
0.686979 + 0.726677i \(0.258936\pi\)
\(488\) −10.6827 −0.483582
\(489\) 4.19747 0.189816
\(490\) −4.07575 −0.184124
\(491\) 18.5130 0.835481 0.417740 0.908566i \(-0.362822\pi\)
0.417740 + 0.908566i \(0.362822\pi\)
\(492\) 34.9537 1.57583
\(493\) −3.37170 −0.151854
\(494\) 0.819296 0.0368619
\(495\) −2.39311 −0.107562
\(496\) −0.706868 −0.0317393
\(497\) −12.1960 −0.547066
\(498\) −15.9856 −0.716334
\(499\) −33.3043 −1.49090 −0.745452 0.666560i \(-0.767766\pi\)
−0.745452 + 0.666560i \(0.767766\pi\)
\(500\) −1.56202 −0.0698558
\(501\) −29.7949 −1.33114
\(502\) 14.1604 0.632011
\(503\) 1.04345 0.0465251 0.0232626 0.999729i \(-0.492595\pi\)
0.0232626 + 0.999729i \(0.492595\pi\)
\(504\) 5.17470 0.230500
\(505\) −12.2234 −0.543936
\(506\) −4.53961 −0.201810
\(507\) 26.3673 1.17101
\(508\) 1.70237 0.0755304
\(509\) −29.7330 −1.31789 −0.658946 0.752190i \(-0.728997\pi\)
−0.658946 + 0.752190i \(0.728997\pi\)
\(510\) −2.17527 −0.0963224
\(511\) −0.917277 −0.0405779
\(512\) 16.3659 0.723279
\(513\) −1.35994 −0.0600428
\(514\) −16.5566 −0.730279
\(515\) 1.49878 0.0660443
\(516\) −37.7617 −1.66237
\(517\) −3.79809 −0.167040
\(518\) 2.15770 0.0948040
\(519\) 3.03369 0.133164
\(520\) 3.02446 0.132631
\(521\) −26.2559 −1.15029 −0.575145 0.818051i \(-0.695054\pi\)
−0.575145 + 0.818051i \(0.695054\pi\)
\(522\) −3.77285 −0.165133
\(523\) −3.97375 −0.173760 −0.0868799 0.996219i \(-0.527690\pi\)
−0.0868799 + 0.996219i \(0.527690\pi\)
\(524\) −1.04688 −0.0457333
\(525\) 2.13020 0.0929695
\(526\) −3.26756 −0.142473
\(527\) −0.639703 −0.0278659
\(528\) 3.63200 0.158063
\(529\) 24.0529 1.04578
\(530\) 1.20932 0.0525294
\(531\) 17.0374 0.739362
\(532\) −1.38254 −0.0599407
\(533\) −12.3626 −0.535485
\(534\) 10.0569 0.435206
\(535\) 8.47369 0.366350
\(536\) −10.8649 −0.469290
\(537\) −36.4894 −1.57463
\(538\) −0.330622 −0.0142541
\(539\) 6.15860 0.265270
\(540\) −2.20149 −0.0947372
\(541\) −15.6625 −0.673382 −0.336691 0.941615i \(-0.609308\pi\)
−0.336691 + 0.941615i \(0.609308\pi\)
\(542\) −19.5656 −0.840416
\(543\) 58.2193 2.49843
\(544\) 8.13791 0.348910
\(545\) 1.07096 0.0458751
\(546\) −1.80872 −0.0774061
\(547\) 14.7392 0.630202 0.315101 0.949058i \(-0.397962\pi\)
0.315101 + 0.949058i \(0.397962\pi\)
\(548\) 24.9796 1.06708
\(549\) 10.8448 0.462844
\(550\) −0.661798 −0.0282192
\(551\) 2.29864 0.0979255
\(552\) 37.5522 1.59833
\(553\) 14.0959 0.599419
\(554\) −6.49892 −0.276113
\(555\) 8.25440 0.350380
\(556\) 17.8827 0.758396
\(557\) −24.5129 −1.03864 −0.519322 0.854578i \(-0.673816\pi\)
−0.519322 + 0.854578i \(0.673816\pi\)
\(558\) −0.715813 −0.0303028
\(559\) 13.3558 0.564891
\(560\) −1.43459 −0.0606224
\(561\) 3.28690 0.138773
\(562\) −2.58868 −0.109197
\(563\) 3.42956 0.144539 0.0722694 0.997385i \(-0.476976\pi\)
0.0722694 + 0.997385i \(0.476976\pi\)
\(564\) 13.7775 0.580139
\(565\) −17.9881 −0.756765
\(566\) 0.364863 0.0153363
\(567\) 9.58770 0.402646
\(568\) −31.3429 −1.31512
\(569\) 15.0678 0.631676 0.315838 0.948813i \(-0.397714\pi\)
0.315838 + 0.948813i \(0.397714\pi\)
\(570\) 1.48298 0.0621151
\(571\) −15.7541 −0.659289 −0.329644 0.944105i \(-0.606929\pi\)
−0.329644 + 0.944105i \(0.606929\pi\)
\(572\) −2.00407 −0.0837944
\(573\) 44.4530 1.85705
\(574\) −5.84940 −0.244149
\(575\) 6.85951 0.286061
\(576\) 1.62066 0.0675273
\(577\) 22.1891 0.923744 0.461872 0.886946i \(-0.347178\pi\)
0.461872 + 0.886946i \(0.347178\pi\)
\(578\) −9.92482 −0.412818
\(579\) −29.6679 −1.23296
\(580\) 3.72108 0.154510
\(581\) −9.54082 −0.395820
\(582\) 22.4196 0.929322
\(583\) −1.82732 −0.0756800
\(584\) −2.35734 −0.0975474
\(585\) −3.07035 −0.126943
\(586\) 10.0348 0.414536
\(587\) 24.3443 1.00480 0.502398 0.864636i \(-0.332451\pi\)
0.502398 + 0.864636i \(0.332451\pi\)
\(588\) −22.3403 −0.921299
\(589\) 0.436115 0.0179698
\(590\) 4.71159 0.193973
\(591\) −11.8437 −0.487183
\(592\) −5.55895 −0.228471
\(593\) 17.7642 0.729490 0.364745 0.931107i \(-0.381156\pi\)
0.364745 + 0.931107i \(0.381156\pi\)
\(594\) −0.932729 −0.0382703
\(595\) −1.29828 −0.0532242
\(596\) 18.4679 0.756473
\(597\) 21.5824 0.883307
\(598\) −5.82431 −0.238174
\(599\) 34.4258 1.40660 0.703301 0.710893i \(-0.251709\pi\)
0.703301 + 0.710893i \(0.251709\pi\)
\(600\) 5.47447 0.223494
\(601\) 47.5927 1.94135 0.970674 0.240399i \(-0.0772783\pi\)
0.970674 + 0.240399i \(0.0772783\pi\)
\(602\) 6.31932 0.257556
\(603\) 11.0297 0.449165
\(604\) −5.00318 −0.203576
\(605\) 1.00000 0.0406558
\(606\) 18.7862 0.763137
\(607\) −7.92900 −0.321828 −0.160914 0.986968i \(-0.551444\pi\)
−0.160914 + 0.986968i \(0.551444\pi\)
\(608\) −5.54799 −0.225001
\(609\) −5.07460 −0.205633
\(610\) 2.99905 0.121428
\(611\) −4.87293 −0.197138
\(612\) −5.29075 −0.213866
\(613\) −42.2364 −1.70591 −0.852956 0.521983i \(-0.825193\pi\)
−0.852956 + 0.521983i \(0.825193\pi\)
\(614\) −1.98606 −0.0801508
\(615\) −22.3772 −0.902335
\(616\) −2.16233 −0.0871229
\(617\) 11.8654 0.477683 0.238842 0.971059i \(-0.423232\pi\)
0.238842 + 0.971059i \(0.423232\pi\)
\(618\) −2.30348 −0.0926594
\(619\) 1.88074 0.0755933 0.0377967 0.999285i \(-0.487966\pi\)
0.0377967 + 0.999285i \(0.487966\pi\)
\(620\) 0.705991 0.0283533
\(621\) 9.66770 0.387951
\(622\) −18.2188 −0.730509
\(623\) 6.00235 0.240479
\(624\) 4.65985 0.186543
\(625\) 1.00000 0.0400000
\(626\) −1.39441 −0.0557320
\(627\) −2.24083 −0.0894902
\(628\) −29.4345 −1.17456
\(629\) −5.03075 −0.200589
\(630\) −1.45274 −0.0578786
\(631\) 36.9963 1.47280 0.736400 0.676547i \(-0.236524\pi\)
0.736400 + 0.676547i \(0.236524\pi\)
\(632\) 36.2255 1.44097
\(633\) −37.6568 −1.49672
\(634\) 14.6717 0.582689
\(635\) −1.08985 −0.0432493
\(636\) 6.62861 0.262841
\(637\) 7.90147 0.313068
\(638\) 1.57655 0.0624162
\(639\) 31.8185 1.25872
\(640\) −11.0512 −0.436838
\(641\) −22.8528 −0.902630 −0.451315 0.892365i \(-0.649045\pi\)
−0.451315 + 0.892365i \(0.649045\pi\)
\(642\) −13.0232 −0.513985
\(643\) 26.9278 1.06193 0.530964 0.847394i \(-0.321830\pi\)
0.530964 + 0.847394i \(0.321830\pi\)
\(644\) 9.82836 0.387292
\(645\) 24.1749 0.951885
\(646\) −0.903821 −0.0355604
\(647\) −27.4271 −1.07827 −0.539136 0.842219i \(-0.681249\pi\)
−0.539136 + 0.842219i \(0.681249\pi\)
\(648\) 24.6398 0.967941
\(649\) −7.11938 −0.279460
\(650\) −0.849085 −0.0333039
\(651\) −0.962790 −0.0377347
\(652\) 2.82329 0.110568
\(653\) −3.01776 −0.118094 −0.0590470 0.998255i \(-0.518806\pi\)
−0.0590470 + 0.998255i \(0.518806\pi\)
\(654\) −1.64596 −0.0643622
\(655\) 0.670209 0.0261872
\(656\) 15.0700 0.588383
\(657\) 2.39311 0.0933641
\(658\) −2.30564 −0.0898830
\(659\) −26.0426 −1.01448 −0.507239 0.861806i \(-0.669334\pi\)
−0.507239 + 0.861806i \(0.669334\pi\)
\(660\) −3.62750 −0.141200
\(661\) 23.8916 0.929276 0.464638 0.885501i \(-0.346185\pi\)
0.464638 + 0.885501i \(0.346185\pi\)
\(662\) −20.9135 −0.812827
\(663\) 4.21709 0.163778
\(664\) −24.5193 −0.951532
\(665\) 0.885096 0.0343225
\(666\) −5.62929 −0.218131
\(667\) −16.3409 −0.632721
\(668\) −20.0406 −0.775393
\(669\) 65.3585 2.52690
\(670\) 3.05019 0.117839
\(671\) −4.53167 −0.174943
\(672\) 12.2480 0.472478
\(673\) −39.6098 −1.52684 −0.763422 0.645900i \(-0.776482\pi\)
−0.763422 + 0.645900i \(0.776482\pi\)
\(674\) 10.3885 0.400150
\(675\) 1.40939 0.0542473
\(676\) 17.7351 0.682119
\(677\) 41.5613 1.59733 0.798665 0.601775i \(-0.205540\pi\)
0.798665 + 0.601775i \(0.205540\pi\)
\(678\) 27.6459 1.06173
\(679\) 13.3808 0.513509
\(680\) −3.33649 −0.127948
\(681\) −44.1282 −1.69100
\(682\) 0.299114 0.0114537
\(683\) −7.14032 −0.273217 −0.136608 0.990625i \(-0.543620\pi\)
−0.136608 + 0.990625i \(0.543620\pi\)
\(684\) 3.60695 0.137915
\(685\) −15.9919 −0.611017
\(686\) 7.98796 0.304982
\(687\) 15.8037 0.602950
\(688\) −16.2806 −0.620693
\(689\) −2.34445 −0.0893164
\(690\) −10.5424 −0.401341
\(691\) 35.1901 1.33869 0.669347 0.742950i \(-0.266574\pi\)
0.669347 + 0.742950i \(0.266574\pi\)
\(692\) 2.04051 0.0775686
\(693\) 2.19514 0.0833866
\(694\) −11.9796 −0.454739
\(695\) −11.4484 −0.434264
\(696\) −13.0414 −0.494333
\(697\) 13.6381 0.516579
\(698\) 8.63490 0.326836
\(699\) 8.56002 0.323770
\(700\) 1.43281 0.0541551
\(701\) −28.9200 −1.09229 −0.546147 0.837689i \(-0.683906\pi\)
−0.546147 + 0.837689i \(0.683906\pi\)
\(702\) −1.19669 −0.0451661
\(703\) 3.42969 0.129353
\(704\) −0.677218 −0.0255236
\(705\) −8.82032 −0.332193
\(706\) −11.2473 −0.423297
\(707\) 11.2123 0.421681
\(708\) 25.8255 0.970583
\(709\) −2.03807 −0.0765415 −0.0382707 0.999267i \(-0.512185\pi\)
−0.0382707 + 0.999267i \(0.512185\pi\)
\(710\) 8.79919 0.330228
\(711\) −36.7752 −1.37918
\(712\) 15.4256 0.578100
\(713\) −3.10031 −0.116107
\(714\) 1.99532 0.0746730
\(715\) 1.28300 0.0479814
\(716\) −24.5434 −0.917230
\(717\) 56.4233 2.10717
\(718\) 21.0538 0.785721
\(719\) 15.4012 0.574367 0.287183 0.957876i \(-0.407281\pi\)
0.287183 + 0.957876i \(0.407281\pi\)
\(720\) 3.74274 0.139484
\(721\) −1.37480 −0.0512002
\(722\) −11.9580 −0.445030
\(723\) 45.4646 1.69085
\(724\) 39.1593 1.45534
\(725\) −2.38222 −0.0884735
\(726\) −1.53690 −0.0570396
\(727\) 32.7586 1.21495 0.607475 0.794339i \(-0.292182\pi\)
0.607475 + 0.794339i \(0.292182\pi\)
\(728\) −2.77427 −0.102821
\(729\) −15.1946 −0.562761
\(730\) 0.661798 0.0244942
\(731\) −14.7337 −0.544946
\(732\) 16.4386 0.607589
\(733\) −26.5594 −0.980993 −0.490496 0.871443i \(-0.663184\pi\)
−0.490496 + 0.871443i \(0.663184\pi\)
\(734\) −16.0069 −0.590824
\(735\) 14.3022 0.527543
\(736\) 39.4402 1.45378
\(737\) −4.60895 −0.169773
\(738\) 15.2607 0.561753
\(739\) 40.2441 1.48040 0.740202 0.672384i \(-0.234730\pi\)
0.740202 + 0.672384i \(0.234730\pi\)
\(740\) 5.55205 0.204097
\(741\) −2.87498 −0.105615
\(742\) −1.10928 −0.0407230
\(743\) 26.7560 0.981584 0.490792 0.871277i \(-0.336707\pi\)
0.490792 + 0.871277i \(0.336707\pi\)
\(744\) −2.47431 −0.0907124
\(745\) −11.8230 −0.433162
\(746\) 4.42427 0.161984
\(747\) 24.8913 0.910725
\(748\) 2.21083 0.0808358
\(749\) −7.77272 −0.284009
\(750\) −1.53690 −0.0561196
\(751\) −28.9489 −1.05636 −0.528179 0.849133i \(-0.677125\pi\)
−0.528179 + 0.849133i \(0.677125\pi\)
\(752\) 5.94007 0.216612
\(753\) −49.6902 −1.81081
\(754\) 2.02271 0.0736627
\(755\) 3.20301 0.116569
\(756\) 2.01938 0.0734441
\(757\) 21.0738 0.765940 0.382970 0.923761i \(-0.374901\pi\)
0.382970 + 0.923761i \(0.374901\pi\)
\(758\) −18.7415 −0.680724
\(759\) 15.9299 0.578218
\(760\) 2.27464 0.0825097
\(761\) −32.6056 −1.18195 −0.590975 0.806690i \(-0.701257\pi\)
−0.590975 + 0.806690i \(0.701257\pi\)
\(762\) 1.67499 0.0606784
\(763\) −0.982371 −0.0355642
\(764\) 29.8998 1.08174
\(765\) 3.38711 0.122461
\(766\) −16.0584 −0.580213
\(767\) −9.13414 −0.329815
\(768\) 20.1300 0.726380
\(769\) −39.0585 −1.40848 −0.704242 0.709960i \(-0.748713\pi\)
−0.704242 + 0.709960i \(0.748713\pi\)
\(770\) 0.607052 0.0218766
\(771\) 58.0984 2.09236
\(772\) −19.9552 −0.718202
\(773\) 9.80518 0.352668 0.176334 0.984330i \(-0.443576\pi\)
0.176334 + 0.984330i \(0.443576\pi\)
\(774\) −16.4867 −0.592601
\(775\) −0.451972 −0.0162353
\(776\) 34.3878 1.23445
\(777\) −7.57157 −0.271629
\(778\) 15.7249 0.563763
\(779\) −9.29769 −0.333124
\(780\) −4.65407 −0.166642
\(781\) −13.2959 −0.475764
\(782\) 6.42519 0.229764
\(783\) −3.35747 −0.119986
\(784\) −9.63183 −0.343994
\(785\) 18.8438 0.672565
\(786\) −1.03004 −0.0367404
\(787\) −8.11030 −0.289101 −0.144551 0.989497i \(-0.546174\pi\)
−0.144551 + 0.989497i \(0.546174\pi\)
\(788\) −7.96625 −0.283786
\(789\) 11.4662 0.408206
\(790\) −10.1699 −0.361830
\(791\) 16.5001 0.586675
\(792\) 5.64137 0.200457
\(793\) −5.81412 −0.206465
\(794\) 23.1972 0.823237
\(795\) −4.24360 −0.150505
\(796\) 14.5167 0.514530
\(797\) −36.5238 −1.29374 −0.646869 0.762601i \(-0.723922\pi\)
−0.646869 + 0.762601i \(0.723922\pi\)
\(798\) −1.36030 −0.0481542
\(799\) 5.37566 0.190177
\(800\) 5.74971 0.203283
\(801\) −15.6597 −0.553308
\(802\) 12.4112 0.438256
\(803\) −1.00000 −0.0352892
\(804\) 16.7189 0.589632
\(805\) −6.29207 −0.221766
\(806\) 0.383763 0.0135175
\(807\) 1.16018 0.0408403
\(808\) 28.8148 1.01370
\(809\) 6.14707 0.216119 0.108060 0.994144i \(-0.465536\pi\)
0.108060 + 0.994144i \(0.465536\pi\)
\(810\) −6.91735 −0.243051
\(811\) 37.3371 1.31108 0.655541 0.755160i \(-0.272441\pi\)
0.655541 + 0.755160i \(0.272441\pi\)
\(812\) −3.41327 −0.119782
\(813\) 68.6575 2.40792
\(814\) 2.35229 0.0824478
\(815\) −1.80746 −0.0633124
\(816\) −5.14060 −0.179957
\(817\) 10.0446 0.351417
\(818\) 19.4374 0.679613
\(819\) 2.81636 0.0984117
\(820\) −15.0513 −0.525613
\(821\) −45.1683 −1.57638 −0.788191 0.615430i \(-0.788982\pi\)
−0.788191 + 0.615430i \(0.788982\pi\)
\(822\) 24.5778 0.857251
\(823\) −33.2099 −1.15762 −0.578811 0.815461i \(-0.696483\pi\)
−0.578811 + 0.815461i \(0.696483\pi\)
\(824\) −3.53314 −0.123083
\(825\) 2.32231 0.0808524
\(826\) −4.32183 −0.150376
\(827\) 40.8527 1.42059 0.710293 0.703906i \(-0.248562\pi\)
0.710293 + 0.703906i \(0.248562\pi\)
\(828\) −25.6415 −0.891103
\(829\) −43.8791 −1.52398 −0.761991 0.647587i \(-0.775778\pi\)
−0.761991 + 0.647587i \(0.775778\pi\)
\(830\) 6.88352 0.238930
\(831\) 22.8053 0.791107
\(832\) −0.868868 −0.0301226
\(833\) −8.71665 −0.302014
\(834\) 17.5951 0.609267
\(835\) 12.8299 0.443996
\(836\) −1.50722 −0.0521284
\(837\) −0.637003 −0.0220180
\(838\) 1.48763 0.0513893
\(839\) 21.0451 0.726556 0.363278 0.931681i \(-0.381658\pi\)
0.363278 + 0.931681i \(0.381658\pi\)
\(840\) −5.02160 −0.173262
\(841\) −23.3250 −0.804311
\(842\) −13.5446 −0.466778
\(843\) 9.08391 0.312866
\(844\) −25.3286 −0.871846
\(845\) −11.3539 −0.390587
\(846\) 6.01524 0.206808
\(847\) −0.917277 −0.0315180
\(848\) 2.85787 0.0981395
\(849\) −1.28034 −0.0439410
\(850\) 0.936683 0.0321280
\(851\) −24.3814 −0.835784
\(852\) 48.2308 1.65236
\(853\) 57.2895 1.96156 0.980778 0.195129i \(-0.0625125\pi\)
0.980778 + 0.195129i \(0.0625125\pi\)
\(854\) −2.75096 −0.0941358
\(855\) −2.30915 −0.0789713
\(856\) −19.9754 −0.682744
\(857\) −20.5171 −0.700850 −0.350425 0.936591i \(-0.613963\pi\)
−0.350425 + 0.936591i \(0.613963\pi\)
\(858\) −1.97184 −0.0673174
\(859\) −23.5681 −0.804133 −0.402067 0.915610i \(-0.631708\pi\)
−0.402067 + 0.915610i \(0.631708\pi\)
\(860\) 16.2604 0.554476
\(861\) 20.5261 0.699526
\(862\) 21.5956 0.735550
\(863\) −18.1177 −0.616734 −0.308367 0.951267i \(-0.599783\pi\)
−0.308367 + 0.951267i \(0.599783\pi\)
\(864\) 8.10356 0.275689
\(865\) −1.30633 −0.0444164
\(866\) −4.77012 −0.162095
\(867\) 34.8271 1.18279
\(868\) −0.647589 −0.0219806
\(869\) 15.3671 0.521294
\(870\) 3.66123 0.124127
\(871\) −5.91327 −0.200363
\(872\) −2.52463 −0.0854946
\(873\) −34.9096 −1.18151
\(874\) −4.38034 −0.148167
\(875\) −0.917277 −0.0310096
\(876\) 3.62750 0.122562
\(877\) 23.4541 0.791989 0.395994 0.918253i \(-0.370400\pi\)
0.395994 + 0.918253i \(0.370400\pi\)
\(878\) −23.2480 −0.784581
\(879\) −35.2132 −1.18771
\(880\) −1.56396 −0.0527212
\(881\) 30.6090 1.03124 0.515622 0.856816i \(-0.327561\pi\)
0.515622 + 0.856816i \(0.327561\pi\)
\(882\) −9.75372 −0.328425
\(883\) −45.0103 −1.51472 −0.757359 0.652998i \(-0.773511\pi\)
−0.757359 + 0.652998i \(0.773511\pi\)
\(884\) 2.83648 0.0954013
\(885\) −16.5334 −0.555763
\(886\) 6.69439 0.224902
\(887\) −15.9761 −0.536426 −0.268213 0.963360i \(-0.586433\pi\)
−0.268213 + 0.963360i \(0.586433\pi\)
\(888\) −19.4584 −0.652982
\(889\) 0.999693 0.0335286
\(890\) −4.33058 −0.145161
\(891\) 10.4524 0.350167
\(892\) 43.9612 1.47193
\(893\) −3.66484 −0.122639
\(894\) 18.1708 0.607722
\(895\) 15.7126 0.525214
\(896\) 10.1370 0.338655
\(897\) 20.4380 0.682405
\(898\) −9.37335 −0.312793
\(899\) 1.07670 0.0359099
\(900\) −3.73809 −0.124603
\(901\) 2.58632 0.0861629
\(902\) −6.37692 −0.212328
\(903\) −22.1751 −0.737940
\(904\) 42.4041 1.41034
\(905\) −25.0696 −0.833342
\(906\) −4.92270 −0.163546
\(907\) 22.8758 0.759578 0.379789 0.925073i \(-0.375997\pi\)
0.379789 + 0.925073i \(0.375997\pi\)
\(908\) −29.6814 −0.985012
\(909\) −29.2520 −0.970229
\(910\) 0.778846 0.0258185
\(911\) 5.38740 0.178492 0.0892462 0.996010i \(-0.471554\pi\)
0.0892462 + 0.996010i \(0.471554\pi\)
\(912\) 3.50458 0.116048
\(913\) −10.4012 −0.344231
\(914\) 2.43167 0.0804325
\(915\) −10.5239 −0.347910
\(916\) 10.6299 0.351221
\(917\) −0.614767 −0.0203014
\(918\) 1.32015 0.0435714
\(919\) −9.81772 −0.323857 −0.161928 0.986803i \(-0.551771\pi\)
−0.161928 + 0.986803i \(0.551771\pi\)
\(920\) −16.1702 −0.533116
\(921\) 6.96925 0.229645
\(922\) 3.23874 0.106662
\(923\) −17.0586 −0.561490
\(924\) 3.32742 0.109464
\(925\) −3.55440 −0.116868
\(926\) 14.6040 0.479918
\(927\) 3.58675 0.117804
\(928\) −13.6971 −0.449628
\(929\) 2.41234 0.0791463 0.0395732 0.999217i \(-0.487400\pi\)
0.0395732 + 0.999217i \(0.487400\pi\)
\(930\) 0.694635 0.0227780
\(931\) 5.94254 0.194759
\(932\) 5.75762 0.188597
\(933\) 63.9315 2.09302
\(934\) −5.80936 −0.190088
\(935\) −1.41536 −0.0462873
\(936\) 7.23787 0.236577
\(937\) −19.4876 −0.636631 −0.318315 0.947985i \(-0.603117\pi\)
−0.318315 + 0.947985i \(0.603117\pi\)
\(938\) −2.79787 −0.0913537
\(939\) 4.89312 0.159681
\(940\) −5.93270 −0.193503
\(941\) −41.5585 −1.35477 −0.677383 0.735630i \(-0.736886\pi\)
−0.677383 + 0.735630i \(0.736886\pi\)
\(942\) −28.9610 −0.943602
\(943\) 66.0965 2.15240
\(944\) 11.1344 0.362395
\(945\) −1.29280 −0.0420547
\(946\) 6.88922 0.223988
\(947\) 11.7014 0.380244 0.190122 0.981760i \(-0.439112\pi\)
0.190122 + 0.981760i \(0.439112\pi\)
\(948\) −55.7442 −1.81049
\(949\) −1.28300 −0.0416479
\(950\) −0.638580 −0.0207183
\(951\) −51.4844 −1.66950
\(952\) 3.06048 0.0991908
\(953\) 54.8326 1.77620 0.888102 0.459647i \(-0.152024\pi\)
0.888102 + 0.459647i \(0.152024\pi\)
\(954\) 2.89403 0.0936977
\(955\) −19.1417 −0.619412
\(956\) 37.9513 1.22743
\(957\) −5.53225 −0.178832
\(958\) 18.3642 0.593319
\(959\) 14.6690 0.473685
\(960\) −1.57271 −0.0507589
\(961\) −30.7957 −0.993410
\(962\) 3.01798 0.0973037
\(963\) 20.2785 0.653465
\(964\) 30.5803 0.984925
\(965\) 12.7752 0.411248
\(966\) 9.67027 0.311136
\(967\) −16.3740 −0.526552 −0.263276 0.964721i \(-0.584803\pi\)
−0.263276 + 0.964721i \(0.584803\pi\)
\(968\) −2.35734 −0.0757678
\(969\) 3.17159 0.101886
\(970\) −9.65402 −0.309972
\(971\) −6.92576 −0.222258 −0.111129 0.993806i \(-0.535447\pi\)
−0.111129 + 0.993806i \(0.535447\pi\)
\(972\) −31.3114 −1.00431
\(973\) 10.5014 0.336659
\(974\) 20.0661 0.642960
\(975\) 2.97951 0.0954208
\(976\) 7.08736 0.226861
\(977\) 44.9939 1.43948 0.719741 0.694242i \(-0.244260\pi\)
0.719741 + 0.694242i \(0.244260\pi\)
\(978\) 2.77787 0.0888266
\(979\) 6.54366 0.209136
\(980\) 9.61988 0.307296
\(981\) 2.56293 0.0818282
\(982\) 12.2519 0.390973
\(983\) −41.6828 −1.32947 −0.664737 0.747078i \(-0.731456\pi\)
−0.664737 + 0.747078i \(0.731456\pi\)
\(984\) 52.7506 1.68163
\(985\) 5.09996 0.162498
\(986\) −2.23139 −0.0710618
\(987\) 8.09068 0.257529
\(988\) −1.93376 −0.0615212
\(989\) −71.4065 −2.27059
\(990\) −1.58376 −0.0503350
\(991\) 10.6280 0.337611 0.168806 0.985649i \(-0.446009\pi\)
0.168806 + 0.985649i \(0.446009\pi\)
\(992\) −2.59871 −0.0825090
\(993\) 73.3873 2.32888
\(994\) −8.07129 −0.256006
\(995\) −9.29350 −0.294624
\(996\) 37.7305 1.19554
\(997\) −49.3544 −1.56307 −0.781535 0.623862i \(-0.785563\pi\)
−0.781535 + 0.623862i \(0.785563\pi\)
\(998\) −22.0407 −0.697686
\(999\) −5.00951 −0.158494
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 4015.2.a.c.1.16 23
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4015.2.a.c.1.16 23 1.1 even 1 trivial