Properties

Label 4011.2.a.l.1.16
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 1.16
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)
 
\(f(q)\) \(=\) \(q-0.0484532 q^{2} -1.00000 q^{3} -1.99765 q^{4} +1.78925 q^{5} +0.0484532 q^{6} +1.00000 q^{7} +0.193699 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.0484532 q^{2} -1.00000 q^{3} -1.99765 q^{4} +1.78925 q^{5} +0.0484532 q^{6} +1.00000 q^{7} +0.193699 q^{8} +1.00000 q^{9} -0.0866947 q^{10} +3.36110 q^{11} +1.99765 q^{12} -2.05219 q^{13} -0.0484532 q^{14} -1.78925 q^{15} +3.98592 q^{16} -1.59543 q^{17} -0.0484532 q^{18} +5.14182 q^{19} -3.57429 q^{20} -1.00000 q^{21} -0.162856 q^{22} +6.94960 q^{23} -0.193699 q^{24} -1.79860 q^{25} +0.0994352 q^{26} -1.00000 q^{27} -1.99765 q^{28} +4.46629 q^{29} +0.0866947 q^{30} -3.91483 q^{31} -0.580529 q^{32} -3.36110 q^{33} +0.0773037 q^{34} +1.78925 q^{35} -1.99765 q^{36} -6.88044 q^{37} -0.249138 q^{38} +2.05219 q^{39} +0.346575 q^{40} +4.21697 q^{41} +0.0484532 q^{42} +7.27571 q^{43} -6.71431 q^{44} +1.78925 q^{45} -0.336730 q^{46} +4.83673 q^{47} -3.98592 q^{48} +1.00000 q^{49} +0.0871477 q^{50} +1.59543 q^{51} +4.09956 q^{52} -12.5504 q^{53} +0.0484532 q^{54} +6.01384 q^{55} +0.193699 q^{56} -5.14182 q^{57} -0.216406 q^{58} +7.29882 q^{59} +3.57429 q^{60} +9.05051 q^{61} +0.189686 q^{62} +1.00000 q^{63} -7.94371 q^{64} -3.67188 q^{65} +0.162856 q^{66} -12.2508 q^{67} +3.18712 q^{68} -6.94960 q^{69} -0.0866947 q^{70} -4.67775 q^{71} +0.193699 q^{72} -10.2723 q^{73} +0.333379 q^{74} +1.79860 q^{75} -10.2716 q^{76} +3.36110 q^{77} -0.0994352 q^{78} +8.94904 q^{79} +7.13179 q^{80} +1.00000 q^{81} -0.204326 q^{82} -3.69192 q^{83} +1.99765 q^{84} -2.85462 q^{85} -0.352531 q^{86} -4.46629 q^{87} +0.651042 q^{88} +1.98084 q^{89} -0.0866947 q^{90} -2.05219 q^{91} -13.8829 q^{92} +3.91483 q^{93} -0.234355 q^{94} +9.19998 q^{95} +0.580529 q^{96} +2.08239 q^{97} -0.0484532 q^{98} +3.36110 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0484532 −0.0342616 −0.0171308 0.999853i \(-0.505453\pi\)
−0.0171308 + 0.999853i \(0.505453\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.99765 −0.998826
\(5\) 1.78925 0.800175 0.400088 0.916477i \(-0.368980\pi\)
0.400088 + 0.916477i \(0.368980\pi\)
\(6\) 0.0484532 0.0197809
\(7\) 1.00000 0.377964
\(8\) 0.193699 0.0684830
\(9\) 1.00000 0.333333
\(10\) −0.0866947 −0.0274153
\(11\) 3.36110 1.01341 0.506705 0.862119i \(-0.330863\pi\)
0.506705 + 0.862119i \(0.330863\pi\)
\(12\) 1.99765 0.576673
\(13\) −2.05219 −0.569175 −0.284588 0.958650i \(-0.591857\pi\)
−0.284588 + 0.958650i \(0.591857\pi\)
\(14\) −0.0484532 −0.0129497
\(15\) −1.78925 −0.461982
\(16\) 3.98592 0.996480
\(17\) −1.59543 −0.386949 −0.193474 0.981105i \(-0.561976\pi\)
−0.193474 + 0.981105i \(0.561976\pi\)
\(18\) −0.0484532 −0.0114205
\(19\) 5.14182 1.17961 0.589807 0.807544i \(-0.299204\pi\)
0.589807 + 0.807544i \(0.299204\pi\)
\(20\) −3.57429 −0.799236
\(21\) −1.00000 −0.218218
\(22\) −0.162856 −0.0347210
\(23\) 6.94960 1.44909 0.724546 0.689227i \(-0.242050\pi\)
0.724546 + 0.689227i \(0.242050\pi\)
\(24\) −0.193699 −0.0395387
\(25\) −1.79860 −0.359719
\(26\) 0.0994352 0.0195009
\(27\) −1.00000 −0.192450
\(28\) −1.99765 −0.377521
\(29\) 4.46629 0.829370 0.414685 0.909965i \(-0.363892\pi\)
0.414685 + 0.909965i \(0.363892\pi\)
\(30\) 0.0866947 0.0158282
\(31\) −3.91483 −0.703124 −0.351562 0.936165i \(-0.614349\pi\)
−0.351562 + 0.936165i \(0.614349\pi\)
\(32\) −0.580529 −0.102624
\(33\) −3.36110 −0.585093
\(34\) 0.0773037 0.0132575
\(35\) 1.78925 0.302438
\(36\) −1.99765 −0.332942
\(37\) −6.88044 −1.13114 −0.565568 0.824701i \(-0.691343\pi\)
−0.565568 + 0.824701i \(0.691343\pi\)
\(38\) −0.249138 −0.0404155
\(39\) 2.05219 0.328614
\(40\) 0.346575 0.0547984
\(41\) 4.21697 0.658581 0.329290 0.944229i \(-0.393191\pi\)
0.329290 + 0.944229i \(0.393191\pi\)
\(42\) 0.0484532 0.00747649
\(43\) 7.27571 1.10954 0.554768 0.832005i \(-0.312807\pi\)
0.554768 + 0.832005i \(0.312807\pi\)
\(44\) −6.71431 −1.01222
\(45\) 1.78925 0.266725
\(46\) −0.336730 −0.0496482
\(47\) 4.83673 0.705509 0.352755 0.935716i \(-0.385245\pi\)
0.352755 + 0.935716i \(0.385245\pi\)
\(48\) −3.98592 −0.575318
\(49\) 1.00000 0.142857
\(50\) 0.0871477 0.0123246
\(51\) 1.59543 0.223405
\(52\) 4.09956 0.568507
\(53\) −12.5504 −1.72394 −0.861968 0.506963i \(-0.830768\pi\)
−0.861968 + 0.506963i \(0.830768\pi\)
\(54\) 0.0484532 0.00659365
\(55\) 6.01384 0.810906
\(56\) 0.193699 0.0258841
\(57\) −5.14182 −0.681051
\(58\) −0.216406 −0.0284155
\(59\) 7.29882 0.950226 0.475113 0.879925i \(-0.342407\pi\)
0.475113 + 0.879925i \(0.342407\pi\)
\(60\) 3.57429 0.461439
\(61\) 9.05051 1.15880 0.579400 0.815043i \(-0.303287\pi\)
0.579400 + 0.815043i \(0.303287\pi\)
\(62\) 0.189686 0.0240901
\(63\) 1.00000 0.125988
\(64\) −7.94371 −0.992964
\(65\) −3.67188 −0.455440
\(66\) 0.162856 0.0200462
\(67\) −12.2508 −1.49668 −0.748339 0.663316i \(-0.769148\pi\)
−0.748339 + 0.663316i \(0.769148\pi\)
\(68\) 3.18712 0.386495
\(69\) −6.94960 −0.836633
\(70\) −0.0866947 −0.0103620
\(71\) −4.67775 −0.555147 −0.277574 0.960704i \(-0.589530\pi\)
−0.277574 + 0.960704i \(0.589530\pi\)
\(72\) 0.193699 0.0228277
\(73\) −10.2723 −1.20228 −0.601141 0.799143i \(-0.705287\pi\)
−0.601141 + 0.799143i \(0.705287\pi\)
\(74\) 0.333379 0.0387545
\(75\) 1.79860 0.207684
\(76\) −10.2716 −1.17823
\(77\) 3.36110 0.383033
\(78\) −0.0994352 −0.0112588
\(79\) 8.94904 1.00685 0.503423 0.864040i \(-0.332074\pi\)
0.503423 + 0.864040i \(0.332074\pi\)
\(80\) 7.13179 0.797359
\(81\) 1.00000 0.111111
\(82\) −0.204326 −0.0225640
\(83\) −3.69192 −0.405240 −0.202620 0.979257i \(-0.564946\pi\)
−0.202620 + 0.979257i \(0.564946\pi\)
\(84\) 1.99765 0.217962
\(85\) −2.85462 −0.309627
\(86\) −0.352531 −0.0380144
\(87\) −4.46629 −0.478837
\(88\) 0.651042 0.0694013
\(89\) 1.98084 0.209969 0.104985 0.994474i \(-0.466521\pi\)
0.104985 + 0.994474i \(0.466521\pi\)
\(90\) −0.0866947 −0.00913843
\(91\) −2.05219 −0.215128
\(92\) −13.8829 −1.44739
\(93\) 3.91483 0.405949
\(94\) −0.234355 −0.0241719
\(95\) 9.19998 0.943899
\(96\) 0.580529 0.0592500
\(97\) 2.08239 0.211435 0.105718 0.994396i \(-0.466286\pi\)
0.105718 + 0.994396i \(0.466286\pi\)
\(98\) −0.0484532 −0.00489451
\(99\) 3.36110 0.337803
\(100\) 3.59297 0.359297
\(101\) 7.02738 0.699251 0.349625 0.936890i \(-0.386309\pi\)
0.349625 + 0.936890i \(0.386309\pi\)
\(102\) −0.0773037 −0.00765421
\(103\) −1.46585 −0.144434 −0.0722171 0.997389i \(-0.523007\pi\)
−0.0722171 + 0.997389i \(0.523007\pi\)
\(104\) −0.397507 −0.0389788
\(105\) −1.78925 −0.174613
\(106\) 0.608109 0.0590648
\(107\) 3.12126 0.301744 0.150872 0.988553i \(-0.451792\pi\)
0.150872 + 0.988553i \(0.451792\pi\)
\(108\) 1.99765 0.192224
\(109\) −5.64099 −0.540309 −0.270155 0.962817i \(-0.587075\pi\)
−0.270155 + 0.962817i \(0.587075\pi\)
\(110\) −0.291390 −0.0277829
\(111\) 6.88044 0.653062
\(112\) 3.98592 0.376634
\(113\) 6.37340 0.599559 0.299779 0.954009i \(-0.403087\pi\)
0.299779 + 0.954009i \(0.403087\pi\)
\(114\) 0.249138 0.0233339
\(115\) 12.4345 1.15953
\(116\) −8.92210 −0.828396
\(117\) −2.05219 −0.189725
\(118\) −0.353651 −0.0325562
\(119\) −1.59543 −0.146253
\(120\) −0.346575 −0.0316379
\(121\) 0.297008 0.0270007
\(122\) −0.438526 −0.0397023
\(123\) −4.21697 −0.380232
\(124\) 7.82047 0.702299
\(125\) −12.1644 −1.08801
\(126\) −0.0484532 −0.00431655
\(127\) 3.93257 0.348959 0.174480 0.984661i \(-0.444176\pi\)
0.174480 + 0.984661i \(0.444176\pi\)
\(128\) 1.54596 0.136644
\(129\) −7.27571 −0.640591
\(130\) 0.177914 0.0156041
\(131\) 12.6893 1.10867 0.554334 0.832294i \(-0.312973\pi\)
0.554334 + 0.832294i \(0.312973\pi\)
\(132\) 6.71431 0.584406
\(133\) 5.14182 0.445852
\(134\) 0.593593 0.0512786
\(135\) −1.78925 −0.153994
\(136\) −0.309033 −0.0264994
\(137\) 11.4048 0.974375 0.487188 0.873297i \(-0.338023\pi\)
0.487188 + 0.873297i \(0.338023\pi\)
\(138\) 0.336730 0.0286644
\(139\) 6.36160 0.539584 0.269792 0.962919i \(-0.413045\pi\)
0.269792 + 0.962919i \(0.413045\pi\)
\(140\) −3.57429 −0.302083
\(141\) −4.83673 −0.407326
\(142\) 0.226652 0.0190202
\(143\) −6.89762 −0.576808
\(144\) 3.98592 0.332160
\(145\) 7.99130 0.663641
\(146\) 0.497726 0.0411921
\(147\) −1.00000 −0.0824786
\(148\) 13.7447 1.12981
\(149\) 15.5309 1.27234 0.636171 0.771548i \(-0.280517\pi\)
0.636171 + 0.771548i \(0.280517\pi\)
\(150\) −0.0871477 −0.00711558
\(151\) −16.4683 −1.34017 −0.670086 0.742283i \(-0.733743\pi\)
−0.670086 + 0.742283i \(0.733743\pi\)
\(152\) 0.995966 0.0807835
\(153\) −1.59543 −0.128983
\(154\) −0.162856 −0.0131233
\(155\) −7.00460 −0.562623
\(156\) −4.09956 −0.328228
\(157\) −5.87308 −0.468723 −0.234361 0.972150i \(-0.575300\pi\)
−0.234361 + 0.972150i \(0.575300\pi\)
\(158\) −0.433610 −0.0344961
\(159\) 12.5504 0.995315
\(160\) −1.03871 −0.0821172
\(161\) 6.94960 0.547705
\(162\) −0.0484532 −0.00380684
\(163\) −5.22016 −0.408875 −0.204437 0.978880i \(-0.565536\pi\)
−0.204437 + 0.978880i \(0.565536\pi\)
\(164\) −8.42405 −0.657807
\(165\) −6.01384 −0.468177
\(166\) 0.178885 0.0138842
\(167\) 9.85654 0.762722 0.381361 0.924426i \(-0.375455\pi\)
0.381361 + 0.924426i \(0.375455\pi\)
\(168\) −0.193699 −0.0149442
\(169\) −8.78851 −0.676039
\(170\) 0.138315 0.0106083
\(171\) 5.14182 0.393205
\(172\) −14.5343 −1.10823
\(173\) 5.07979 0.386209 0.193104 0.981178i \(-0.438144\pi\)
0.193104 + 0.981178i \(0.438144\pi\)
\(174\) 0.216406 0.0164057
\(175\) −1.79860 −0.135961
\(176\) 13.3971 1.00984
\(177\) −7.29882 −0.548613
\(178\) −0.0959783 −0.00719387
\(179\) −6.71008 −0.501535 −0.250768 0.968047i \(-0.580683\pi\)
−0.250768 + 0.968047i \(0.580683\pi\)
\(180\) −3.57429 −0.266412
\(181\) 15.3178 1.13856 0.569280 0.822144i \(-0.307222\pi\)
0.569280 + 0.822144i \(0.307222\pi\)
\(182\) 0.0994352 0.00737063
\(183\) −9.05051 −0.669033
\(184\) 1.34613 0.0992381
\(185\) −12.3108 −0.905108
\(186\) −0.189686 −0.0139085
\(187\) −5.36240 −0.392138
\(188\) −9.66210 −0.704681
\(189\) −1.00000 −0.0727393
\(190\) −0.445769 −0.0323395
\(191\) −1.00000 −0.0723575
\(192\) 7.94371 0.573288
\(193\) 24.9357 1.79491 0.897454 0.441108i \(-0.145414\pi\)
0.897454 + 0.441108i \(0.145414\pi\)
\(194\) −0.100899 −0.00724410
\(195\) 3.67188 0.262948
\(196\) −1.99765 −0.142689
\(197\) 9.15332 0.652147 0.326074 0.945344i \(-0.394274\pi\)
0.326074 + 0.945344i \(0.394274\pi\)
\(198\) −0.162856 −0.0115737
\(199\) 14.9381 1.05893 0.529467 0.848331i \(-0.322392\pi\)
0.529467 + 0.848331i \(0.322392\pi\)
\(200\) −0.348386 −0.0246346
\(201\) 12.2508 0.864108
\(202\) −0.340499 −0.0239574
\(203\) 4.46629 0.313472
\(204\) −3.18712 −0.223143
\(205\) 7.54521 0.526980
\(206\) 0.0710249 0.00494854
\(207\) 6.94960 0.483030
\(208\) −8.17987 −0.567172
\(209\) 17.2822 1.19543
\(210\) 0.0866947 0.00598250
\(211\) 1.42893 0.0983719 0.0491859 0.998790i \(-0.484337\pi\)
0.0491859 + 0.998790i \(0.484337\pi\)
\(212\) 25.0714 1.72191
\(213\) 4.67775 0.320514
\(214\) −0.151235 −0.0103382
\(215\) 13.0180 0.887823
\(216\) −0.193699 −0.0131796
\(217\) −3.91483 −0.265756
\(218\) 0.273324 0.0185119
\(219\) 10.2723 0.694137
\(220\) −12.0136 −0.809954
\(221\) 3.27413 0.220242
\(222\) −0.333379 −0.0223749
\(223\) −26.8665 −1.79912 −0.899559 0.436800i \(-0.856112\pi\)
−0.899559 + 0.436800i \(0.856112\pi\)
\(224\) −0.580529 −0.0387882
\(225\) −1.79860 −0.119906
\(226\) −0.308811 −0.0205418
\(227\) −7.98868 −0.530227 −0.265114 0.964217i \(-0.585409\pi\)
−0.265114 + 0.964217i \(0.585409\pi\)
\(228\) 10.2716 0.680251
\(229\) 13.2290 0.874195 0.437097 0.899414i \(-0.356006\pi\)
0.437097 + 0.899414i \(0.356006\pi\)
\(230\) −0.602493 −0.0397272
\(231\) −3.36110 −0.221144
\(232\) 0.865116 0.0567977
\(233\) 21.9885 1.44051 0.720257 0.693707i \(-0.244024\pi\)
0.720257 + 0.693707i \(0.244024\pi\)
\(234\) 0.0994352 0.00650028
\(235\) 8.65410 0.564531
\(236\) −14.5805 −0.949111
\(237\) −8.94904 −0.581303
\(238\) 0.0773037 0.00501086
\(239\) 24.0805 1.55764 0.778818 0.627250i \(-0.215820\pi\)
0.778818 + 0.627250i \(0.215820\pi\)
\(240\) −7.13179 −0.460355
\(241\) 15.8356 1.02006 0.510032 0.860156i \(-0.329634\pi\)
0.510032 + 0.860156i \(0.329634\pi\)
\(242\) −0.0143910 −0.000925086 0
\(243\) −1.00000 −0.0641500
\(244\) −18.0798 −1.15744
\(245\) 1.78925 0.114311
\(246\) 0.204326 0.0130273
\(247\) −10.5520 −0.671407
\(248\) −0.758299 −0.0481520
\(249\) 3.69192 0.233966
\(250\) 0.589402 0.0372771
\(251\) 4.43127 0.279699 0.139850 0.990173i \(-0.455338\pi\)
0.139850 + 0.990173i \(0.455338\pi\)
\(252\) −1.99765 −0.125840
\(253\) 23.3583 1.46852
\(254\) −0.190546 −0.0119559
\(255\) 2.85462 0.178763
\(256\) 15.8125 0.988282
\(257\) −26.4282 −1.64855 −0.824273 0.566193i \(-0.808416\pi\)
−0.824273 + 0.566193i \(0.808416\pi\)
\(258\) 0.352531 0.0219476
\(259\) −6.88044 −0.427530
\(260\) 7.33513 0.454906
\(261\) 4.46629 0.276457
\(262\) −0.614836 −0.0379847
\(263\) 19.5544 1.20578 0.602889 0.797825i \(-0.294016\pi\)
0.602889 + 0.797825i \(0.294016\pi\)
\(264\) −0.651042 −0.0400689
\(265\) −22.4558 −1.37945
\(266\) −0.249138 −0.0152756
\(267\) −1.98084 −0.121226
\(268\) 24.4729 1.49492
\(269\) 22.5742 1.37637 0.688186 0.725534i \(-0.258407\pi\)
0.688186 + 0.725534i \(0.258407\pi\)
\(270\) 0.0866947 0.00527607
\(271\) 19.5448 1.18726 0.593631 0.804737i \(-0.297694\pi\)
0.593631 + 0.804737i \(0.297694\pi\)
\(272\) −6.35926 −0.385587
\(273\) 2.05219 0.124204
\(274\) −0.552598 −0.0333836
\(275\) −6.04527 −0.364543
\(276\) 13.8829 0.835651
\(277\) 15.9122 0.956069 0.478035 0.878341i \(-0.341349\pi\)
0.478035 + 0.878341i \(0.341349\pi\)
\(278\) −0.308240 −0.0184870
\(279\) −3.91483 −0.234375
\(280\) 0.346575 0.0207118
\(281\) −4.72334 −0.281771 −0.140886 0.990026i \(-0.544995\pi\)
−0.140886 + 0.990026i \(0.544995\pi\)
\(282\) 0.234355 0.0139556
\(283\) 1.09143 0.0648790 0.0324395 0.999474i \(-0.489672\pi\)
0.0324395 + 0.999474i \(0.489672\pi\)
\(284\) 9.34452 0.554496
\(285\) −9.19998 −0.544960
\(286\) 0.334212 0.0197624
\(287\) 4.21697 0.248920
\(288\) −0.580529 −0.0342080
\(289\) −14.4546 −0.850271
\(290\) −0.387204 −0.0227374
\(291\) −2.08239 −0.122072
\(292\) 20.5205 1.20087
\(293\) −30.6330 −1.78960 −0.894799 0.446468i \(-0.852682\pi\)
−0.894799 + 0.446468i \(0.852682\pi\)
\(294\) 0.0484532 0.00282585
\(295\) 13.0594 0.760347
\(296\) −1.33273 −0.0774636
\(297\) −3.36110 −0.195031
\(298\) −0.752522 −0.0435925
\(299\) −14.2619 −0.824787
\(300\) −3.59297 −0.207440
\(301\) 7.27571 0.419365
\(302\) 0.797943 0.0459164
\(303\) −7.02738 −0.403713
\(304\) 20.4949 1.17546
\(305\) 16.1936 0.927243
\(306\) 0.0773037 0.00441916
\(307\) 21.5884 1.23211 0.616057 0.787701i \(-0.288729\pi\)
0.616057 + 0.787701i \(0.288729\pi\)
\(308\) −6.71431 −0.382584
\(309\) 1.46585 0.0833891
\(310\) 0.339395 0.0192763
\(311\) −11.3055 −0.641076 −0.320538 0.947236i \(-0.603864\pi\)
−0.320538 + 0.947236i \(0.603864\pi\)
\(312\) 0.397507 0.0225044
\(313\) 27.9643 1.58063 0.790317 0.612698i \(-0.209916\pi\)
0.790317 + 0.612698i \(0.209916\pi\)
\(314\) 0.284569 0.0160592
\(315\) 1.78925 0.100813
\(316\) −17.8771 −1.00566
\(317\) −25.2148 −1.41620 −0.708102 0.706110i \(-0.750448\pi\)
−0.708102 + 0.706110i \(0.750448\pi\)
\(318\) −0.608109 −0.0341011
\(319\) 15.0117 0.840492
\(320\) −14.2133 −0.794545
\(321\) −3.12126 −0.174212
\(322\) −0.336730 −0.0187652
\(323\) −8.20342 −0.456450
\(324\) −1.99765 −0.110981
\(325\) 3.69106 0.204743
\(326\) 0.252934 0.0140087
\(327\) 5.64099 0.311948
\(328\) 0.816824 0.0451015
\(329\) 4.83673 0.266657
\(330\) 0.291390 0.0160405
\(331\) 1.93245 0.106217 0.0531086 0.998589i \(-0.483087\pi\)
0.0531086 + 0.998589i \(0.483087\pi\)
\(332\) 7.37516 0.404765
\(333\) −6.88044 −0.377046
\(334\) −0.477581 −0.0261321
\(335\) −21.9198 −1.19761
\(336\) −3.98592 −0.217450
\(337\) 23.3954 1.27443 0.637215 0.770686i \(-0.280086\pi\)
0.637215 + 0.770686i \(0.280086\pi\)
\(338\) 0.425832 0.0231622
\(339\) −6.37340 −0.346155
\(340\) 5.70254 0.309263
\(341\) −13.1581 −0.712553
\(342\) −0.249138 −0.0134718
\(343\) 1.00000 0.0539949
\(344\) 1.40930 0.0759843
\(345\) −12.4345 −0.669453
\(346\) −0.246132 −0.0132321
\(347\) −3.03197 −0.162765 −0.0813824 0.996683i \(-0.525933\pi\)
−0.0813824 + 0.996683i \(0.525933\pi\)
\(348\) 8.92210 0.478275
\(349\) 17.7162 0.948325 0.474163 0.880437i \(-0.342751\pi\)
0.474163 + 0.880437i \(0.342751\pi\)
\(350\) 0.0871477 0.00465824
\(351\) 2.05219 0.109538
\(352\) −1.95122 −0.104000
\(353\) 28.7717 1.53136 0.765681 0.643221i \(-0.222402\pi\)
0.765681 + 0.643221i \(0.222402\pi\)
\(354\) 0.353651 0.0187964
\(355\) −8.36965 −0.444215
\(356\) −3.95704 −0.209723
\(357\) 1.59543 0.0844391
\(358\) 0.325125 0.0171834
\(359\) −10.1813 −0.537351 −0.268675 0.963231i \(-0.586586\pi\)
−0.268675 + 0.963231i \(0.586586\pi\)
\(360\) 0.346575 0.0182661
\(361\) 7.43832 0.391490
\(362\) −0.742194 −0.0390089
\(363\) −0.297008 −0.0155889
\(364\) 4.09956 0.214876
\(365\) −18.3797 −0.962036
\(366\) 0.438526 0.0229221
\(367\) 7.63791 0.398696 0.199348 0.979929i \(-0.436118\pi\)
0.199348 + 0.979929i \(0.436118\pi\)
\(368\) 27.7005 1.44399
\(369\) 4.21697 0.219527
\(370\) 0.596498 0.0310104
\(371\) −12.5504 −0.651587
\(372\) −7.82047 −0.405472
\(373\) −24.9217 −1.29040 −0.645199 0.764014i \(-0.723226\pi\)
−0.645199 + 0.764014i \(0.723226\pi\)
\(374\) 0.259826 0.0134353
\(375\) 12.1644 0.628165
\(376\) 0.936870 0.0483154
\(377\) −9.16568 −0.472057
\(378\) 0.0484532 0.00249216
\(379\) 25.5207 1.31091 0.655456 0.755234i \(-0.272477\pi\)
0.655456 + 0.755234i \(0.272477\pi\)
\(380\) −18.3784 −0.942791
\(381\) −3.93257 −0.201472
\(382\) 0.0484532 0.00247908
\(383\) −35.9304 −1.83596 −0.917978 0.396631i \(-0.870179\pi\)
−0.917978 + 0.396631i \(0.870179\pi\)
\(384\) −1.54596 −0.0788917
\(385\) 6.01384 0.306494
\(386\) −1.20821 −0.0614964
\(387\) 7.27571 0.369845
\(388\) −4.15990 −0.211187
\(389\) 16.2508 0.823950 0.411975 0.911195i \(-0.364839\pi\)
0.411975 + 0.911195i \(0.364839\pi\)
\(390\) −0.177914 −0.00900903
\(391\) −11.0876 −0.560724
\(392\) 0.193699 0.00978328
\(393\) −12.6893 −0.640090
\(394\) −0.443508 −0.0223436
\(395\) 16.0120 0.805654
\(396\) −6.71431 −0.337407
\(397\) 27.0683 1.35852 0.679259 0.733898i \(-0.262301\pi\)
0.679259 + 0.733898i \(0.262301\pi\)
\(398\) −0.723798 −0.0362807
\(399\) −5.14182 −0.257413
\(400\) −7.16906 −0.358453
\(401\) −11.8162 −0.590071 −0.295035 0.955486i \(-0.595331\pi\)
−0.295035 + 0.955486i \(0.595331\pi\)
\(402\) −0.593593 −0.0296057
\(403\) 8.03398 0.400201
\(404\) −14.0383 −0.698430
\(405\) 1.78925 0.0889084
\(406\) −0.216406 −0.0107401
\(407\) −23.1259 −1.14631
\(408\) 0.309033 0.0152994
\(409\) 7.28958 0.360446 0.180223 0.983626i \(-0.442318\pi\)
0.180223 + 0.983626i \(0.442318\pi\)
\(410\) −0.365589 −0.0180552
\(411\) −11.4048 −0.562556
\(412\) 2.92825 0.144265
\(413\) 7.29882 0.359152
\(414\) −0.336730 −0.0165494
\(415\) −6.60575 −0.324263
\(416\) 1.19136 0.0584110
\(417\) −6.36160 −0.311529
\(418\) −0.837377 −0.0409575
\(419\) −7.22568 −0.352997 −0.176499 0.984301i \(-0.556477\pi\)
−0.176499 + 0.984301i \(0.556477\pi\)
\(420\) 3.57429 0.174408
\(421\) −5.07452 −0.247317 −0.123658 0.992325i \(-0.539463\pi\)
−0.123658 + 0.992325i \(0.539463\pi\)
\(422\) −0.0692364 −0.00337038
\(423\) 4.83673 0.235170
\(424\) −2.43101 −0.118060
\(425\) 2.86954 0.139193
\(426\) −0.226652 −0.0109813
\(427\) 9.05051 0.437985
\(428\) −6.23520 −0.301390
\(429\) 6.89762 0.333020
\(430\) −0.630766 −0.0304182
\(431\) −7.33911 −0.353513 −0.176756 0.984255i \(-0.556560\pi\)
−0.176756 + 0.984255i \(0.556560\pi\)
\(432\) −3.98592 −0.191773
\(433\) 5.68241 0.273079 0.136540 0.990635i \(-0.456402\pi\)
0.136540 + 0.990635i \(0.456402\pi\)
\(434\) 0.189686 0.00910522
\(435\) −7.99130 −0.383153
\(436\) 11.2687 0.539675
\(437\) 35.7336 1.70937
\(438\) −0.497726 −0.0237822
\(439\) 7.65415 0.365313 0.182656 0.983177i \(-0.441530\pi\)
0.182656 + 0.983177i \(0.441530\pi\)
\(440\) 1.16488 0.0555332
\(441\) 1.00000 0.0476190
\(442\) −0.158642 −0.00754583
\(443\) −25.3486 −1.20435 −0.602173 0.798365i \(-0.705698\pi\)
−0.602173 + 0.798365i \(0.705698\pi\)
\(444\) −13.7447 −0.652296
\(445\) 3.54422 0.168012
\(446\) 1.30177 0.0616406
\(447\) −15.5309 −0.734587
\(448\) −7.94371 −0.375305
\(449\) −26.3344 −1.24280 −0.621399 0.783494i \(-0.713436\pi\)
−0.621399 + 0.783494i \(0.713436\pi\)
\(450\) 0.0871477 0.00410818
\(451\) 14.1737 0.667412
\(452\) −12.7318 −0.598855
\(453\) 16.4683 0.773749
\(454\) 0.387077 0.0181664
\(455\) −3.67188 −0.172140
\(456\) −0.995966 −0.0466404
\(457\) −21.8870 −1.02383 −0.511915 0.859036i \(-0.671064\pi\)
−0.511915 + 0.859036i \(0.671064\pi\)
\(458\) −0.640986 −0.0299513
\(459\) 1.59543 0.0744683
\(460\) −24.8399 −1.15817
\(461\) 2.02297 0.0942193 0.0471097 0.998890i \(-0.484999\pi\)
0.0471097 + 0.998890i \(0.484999\pi\)
\(462\) 0.162856 0.00757675
\(463\) 29.8958 1.38937 0.694687 0.719312i \(-0.255543\pi\)
0.694687 + 0.719312i \(0.255543\pi\)
\(464\) 17.8023 0.826450
\(465\) 7.00460 0.324830
\(466\) −1.06541 −0.0493543
\(467\) −29.7906 −1.37854 −0.689272 0.724503i \(-0.742069\pi\)
−0.689272 + 0.724503i \(0.742069\pi\)
\(468\) 4.09956 0.189502
\(469\) −12.2508 −0.565691
\(470\) −0.419319 −0.0193417
\(471\) 5.87308 0.270617
\(472\) 1.41378 0.0650743
\(473\) 24.4544 1.12441
\(474\) 0.433610 0.0199164
\(475\) −9.24806 −0.424330
\(476\) 3.18712 0.146081
\(477\) −12.5504 −0.574645
\(478\) −1.16678 −0.0533671
\(479\) −28.7260 −1.31252 −0.656262 0.754533i \(-0.727863\pi\)
−0.656262 + 0.754533i \(0.727863\pi\)
\(480\) 1.03871 0.0474104
\(481\) 14.1200 0.643815
\(482\) −0.767287 −0.0349490
\(483\) −6.94960 −0.316218
\(484\) −0.593318 −0.0269690
\(485\) 3.72592 0.169185
\(486\) 0.0484532 0.00219788
\(487\) 26.6979 1.20980 0.604898 0.796303i \(-0.293214\pi\)
0.604898 + 0.796303i \(0.293214\pi\)
\(488\) 1.75308 0.0793580
\(489\) 5.22016 0.236064
\(490\) −0.0866947 −0.00391647
\(491\) −5.42719 −0.244926 −0.122463 0.992473i \(-0.539079\pi\)
−0.122463 + 0.992473i \(0.539079\pi\)
\(492\) 8.42405 0.379785
\(493\) −7.12566 −0.320924
\(494\) 0.511278 0.0230035
\(495\) 6.01384 0.270302
\(496\) −15.6042 −0.700649
\(497\) −4.67775 −0.209826
\(498\) −0.178885 −0.00801603
\(499\) −12.4354 −0.556684 −0.278342 0.960482i \(-0.589785\pi\)
−0.278342 + 0.960482i \(0.589785\pi\)
\(500\) 24.3002 1.08674
\(501\) −9.85654 −0.440358
\(502\) −0.214709 −0.00958294
\(503\) 20.4994 0.914021 0.457010 0.889461i \(-0.348920\pi\)
0.457010 + 0.889461i \(0.348920\pi\)
\(504\) 0.193699 0.00862804
\(505\) 12.5737 0.559523
\(506\) −1.13178 −0.0503140
\(507\) 8.78851 0.390312
\(508\) −7.85591 −0.348550
\(509\) 42.4578 1.88191 0.940955 0.338531i \(-0.109930\pi\)
0.940955 + 0.338531i \(0.109930\pi\)
\(510\) −0.138315 −0.00612471
\(511\) −10.2723 −0.454420
\(512\) −3.85808 −0.170505
\(513\) −5.14182 −0.227017
\(514\) 1.28053 0.0564818
\(515\) −2.62276 −0.115573
\(516\) 14.5343 0.639839
\(517\) 16.2567 0.714971
\(518\) 0.333379 0.0146478
\(519\) −5.07979 −0.222978
\(520\) −0.711239 −0.0311899
\(521\) −5.94373 −0.260400 −0.130200 0.991488i \(-0.541562\pi\)
−0.130200 + 0.991488i \(0.541562\pi\)
\(522\) −0.216406 −0.00947184
\(523\) −10.7362 −0.469460 −0.234730 0.972061i \(-0.575421\pi\)
−0.234730 + 0.972061i \(0.575421\pi\)
\(524\) −25.3488 −1.10737
\(525\) 1.79860 0.0784972
\(526\) −0.947475 −0.0413119
\(527\) 6.24584 0.272073
\(528\) −13.3971 −0.583033
\(529\) 25.2969 1.09987
\(530\) 1.08806 0.0472622
\(531\) 7.29882 0.316742
\(532\) −10.2716 −0.445329
\(533\) −8.65403 −0.374848
\(534\) 0.0959783 0.00415339
\(535\) 5.58471 0.241448
\(536\) −2.37298 −0.102497
\(537\) 6.71008 0.289561
\(538\) −1.09379 −0.0471567
\(539\) 3.36110 0.144773
\(540\) 3.57429 0.153813
\(541\) 2.83501 0.121887 0.0609433 0.998141i \(-0.480589\pi\)
0.0609433 + 0.998141i \(0.480589\pi\)
\(542\) −0.947008 −0.0406775
\(543\) −15.3178 −0.657348
\(544\) 0.926193 0.0397102
\(545\) −10.0931 −0.432342
\(546\) −0.0994352 −0.00425543
\(547\) −37.5183 −1.60416 −0.802082 0.597214i \(-0.796274\pi\)
−0.802082 + 0.597214i \(0.796274\pi\)
\(548\) −22.7828 −0.973231
\(549\) 9.05051 0.386267
\(550\) 0.292912 0.0124898
\(551\) 22.9649 0.978336
\(552\) −1.34613 −0.0572951
\(553\) 8.94904 0.380552
\(554\) −0.770995 −0.0327565
\(555\) 12.3108 0.522564
\(556\) −12.7083 −0.538950
\(557\) −25.4342 −1.07768 −0.538840 0.842408i \(-0.681137\pi\)
−0.538840 + 0.842408i \(0.681137\pi\)
\(558\) 0.189686 0.00803005
\(559\) −14.9311 −0.631520
\(560\) 7.13179 0.301373
\(561\) 5.36240 0.226401
\(562\) 0.228861 0.00965392
\(563\) 45.1734 1.90383 0.951916 0.306359i \(-0.0991109\pi\)
0.951916 + 0.306359i \(0.0991109\pi\)
\(564\) 9.66210 0.406848
\(565\) 11.4036 0.479752
\(566\) −0.0528834 −0.00222286
\(567\) 1.00000 0.0419961
\(568\) −0.906076 −0.0380181
\(569\) 10.4488 0.438036 0.219018 0.975721i \(-0.429715\pi\)
0.219018 + 0.975721i \(0.429715\pi\)
\(570\) 0.445769 0.0186712
\(571\) −45.4229 −1.90089 −0.950445 0.310891i \(-0.899372\pi\)
−0.950445 + 0.310891i \(0.899372\pi\)
\(572\) 13.7791 0.576131
\(573\) 1.00000 0.0417756
\(574\) −0.204326 −0.00852840
\(575\) −12.4995 −0.521266
\(576\) −7.94371 −0.330988
\(577\) −34.1089 −1.41997 −0.709986 0.704216i \(-0.751299\pi\)
−0.709986 + 0.704216i \(0.751299\pi\)
\(578\) 0.700372 0.0291316
\(579\) −24.9357 −1.03629
\(580\) −15.9638 −0.662862
\(581\) −3.69192 −0.153166
\(582\) 0.100899 0.00418238
\(583\) −42.1833 −1.74705
\(584\) −1.98973 −0.0823358
\(585\) −3.67188 −0.151813
\(586\) 1.48427 0.0613145
\(587\) 0.697154 0.0287746 0.0143873 0.999896i \(-0.495420\pi\)
0.0143873 + 0.999896i \(0.495420\pi\)
\(588\) 1.99765 0.0823818
\(589\) −20.1294 −0.829415
\(590\) −0.632770 −0.0260507
\(591\) −9.15332 −0.376517
\(592\) −27.4249 −1.12716
\(593\) 15.3082 0.628632 0.314316 0.949318i \(-0.398225\pi\)
0.314316 + 0.949318i \(0.398225\pi\)
\(594\) 0.162856 0.00668207
\(595\) −2.85462 −0.117028
\(596\) −31.0254 −1.27085
\(597\) −14.9381 −0.611375
\(598\) 0.691035 0.0282585
\(599\) −28.1956 −1.15204 −0.576021 0.817435i \(-0.695396\pi\)
−0.576021 + 0.817435i \(0.695396\pi\)
\(600\) 0.348386 0.0142228
\(601\) −17.7830 −0.725383 −0.362692 0.931909i \(-0.618142\pi\)
−0.362692 + 0.931909i \(0.618142\pi\)
\(602\) −0.352531 −0.0143681
\(603\) −12.2508 −0.498893
\(604\) 32.8980 1.33860
\(605\) 0.531420 0.0216053
\(606\) 0.340499 0.0138318
\(607\) 29.0832 1.18045 0.590226 0.807238i \(-0.299039\pi\)
0.590226 + 0.807238i \(0.299039\pi\)
\(608\) −2.98497 −0.121057
\(609\) −4.46629 −0.180983
\(610\) −0.784632 −0.0317688
\(611\) −9.92589 −0.401559
\(612\) 3.18712 0.128832
\(613\) 24.4517 0.987595 0.493797 0.869577i \(-0.335608\pi\)
0.493797 + 0.869577i \(0.335608\pi\)
\(614\) −1.04603 −0.0422142
\(615\) −7.54521 −0.304252
\(616\) 0.651042 0.0262312
\(617\) −42.6450 −1.71683 −0.858413 0.512960i \(-0.828549\pi\)
−0.858413 + 0.512960i \(0.828549\pi\)
\(618\) −0.0710249 −0.00285704
\(619\) 12.0403 0.483941 0.241971 0.970284i \(-0.422206\pi\)
0.241971 + 0.970284i \(0.422206\pi\)
\(620\) 13.9927 0.561962
\(621\) −6.94960 −0.278878
\(622\) 0.547787 0.0219643
\(623\) 1.98084 0.0793609
\(624\) 8.17987 0.327457
\(625\) −12.7721 −0.510883
\(626\) −1.35496 −0.0541550
\(627\) −17.2822 −0.690184
\(628\) 11.7324 0.468172
\(629\) 10.9773 0.437692
\(630\) −0.0866947 −0.00345400
\(631\) 10.4861 0.417444 0.208722 0.977975i \(-0.433070\pi\)
0.208722 + 0.977975i \(0.433070\pi\)
\(632\) 1.73342 0.0689518
\(633\) −1.42893 −0.0567950
\(634\) 1.22174 0.0485214
\(635\) 7.03634 0.279229
\(636\) −25.0714 −0.994147
\(637\) −2.05219 −0.0813108
\(638\) −0.727363 −0.0287966
\(639\) −4.67775 −0.185049
\(640\) 2.76610 0.109340
\(641\) −8.60640 −0.339932 −0.169966 0.985450i \(-0.554366\pi\)
−0.169966 + 0.985450i \(0.554366\pi\)
\(642\) 0.151235 0.00596877
\(643\) −33.6841 −1.32837 −0.664186 0.747567i \(-0.731222\pi\)
−0.664186 + 0.747567i \(0.731222\pi\)
\(644\) −13.8829 −0.547062
\(645\) −13.0180 −0.512585
\(646\) 0.397482 0.0156387
\(647\) −40.4104 −1.58870 −0.794349 0.607462i \(-0.792188\pi\)
−0.794349 + 0.607462i \(0.792188\pi\)
\(648\) 0.193699 0.00760922
\(649\) 24.5321 0.962969
\(650\) −0.178844 −0.00701483
\(651\) 3.91483 0.153434
\(652\) 10.4281 0.408395
\(653\) −13.2584 −0.518842 −0.259421 0.965764i \(-0.583532\pi\)
−0.259421 + 0.965764i \(0.583532\pi\)
\(654\) −0.273324 −0.0106878
\(655\) 22.7043 0.887129
\(656\) 16.8085 0.656262
\(657\) −10.2723 −0.400760
\(658\) −0.234355 −0.00913611
\(659\) 8.43096 0.328423 0.164212 0.986425i \(-0.447492\pi\)
0.164212 + 0.986425i \(0.447492\pi\)
\(660\) 12.0136 0.467627
\(661\) −29.5292 −1.14855 −0.574276 0.818662i \(-0.694716\pi\)
−0.574276 + 0.818662i \(0.694716\pi\)
\(662\) −0.0936335 −0.00363917
\(663\) −3.27413 −0.127157
\(664\) −0.715121 −0.0277521
\(665\) 9.19998 0.356760
\(666\) 0.333379 0.0129182
\(667\) 31.0389 1.20183
\(668\) −19.6899 −0.761827
\(669\) 26.8665 1.03872
\(670\) 1.06208 0.0410319
\(671\) 30.4197 1.17434
\(672\) 0.580529 0.0223944
\(673\) 37.0666 1.42881 0.714406 0.699732i \(-0.246697\pi\)
0.714406 + 0.699732i \(0.246697\pi\)
\(674\) −1.13358 −0.0436640
\(675\) 1.79860 0.0692280
\(676\) 17.5564 0.675246
\(677\) −24.9038 −0.957130 −0.478565 0.878052i \(-0.658843\pi\)
−0.478565 + 0.878052i \(0.658843\pi\)
\(678\) 0.308811 0.0118598
\(679\) 2.08239 0.0799149
\(680\) −0.552937 −0.0212042
\(681\) 7.98868 0.306127
\(682\) 0.637554 0.0244132
\(683\) 3.07880 0.117807 0.0589034 0.998264i \(-0.481240\pi\)
0.0589034 + 0.998264i \(0.481240\pi\)
\(684\) −10.2716 −0.392743
\(685\) 20.4059 0.779671
\(686\) −0.0484532 −0.00184995
\(687\) −13.2290 −0.504717
\(688\) 29.0004 1.10563
\(689\) 25.7559 0.981222
\(690\) 0.602493 0.0229365
\(691\) 14.6114 0.555844 0.277922 0.960604i \(-0.410354\pi\)
0.277922 + 0.960604i \(0.410354\pi\)
\(692\) −10.1476 −0.385756
\(693\) 3.36110 0.127678
\(694\) 0.146909 0.00557658
\(695\) 11.3825 0.431762
\(696\) −0.865116 −0.0327922
\(697\) −6.72789 −0.254837
\(698\) −0.858405 −0.0324911
\(699\) −21.9885 −0.831681
\(700\) 3.59297 0.135802
\(701\) −35.4543 −1.33909 −0.669545 0.742772i \(-0.733511\pi\)
−0.669545 + 0.742772i \(0.733511\pi\)
\(702\) −0.0994352 −0.00375294
\(703\) −35.3780 −1.33431
\(704\) −26.6996 −1.00628
\(705\) −8.65410 −0.325932
\(706\) −1.39408 −0.0524669
\(707\) 7.02738 0.264292
\(708\) 14.5805 0.547969
\(709\) −4.75894 −0.178726 −0.0893629 0.995999i \(-0.528483\pi\)
−0.0893629 + 0.995999i \(0.528483\pi\)
\(710\) 0.405537 0.0152195
\(711\) 8.94904 0.335615
\(712\) 0.383688 0.0143793
\(713\) −27.2065 −1.01889
\(714\) −0.0773037 −0.00289302
\(715\) −12.3415 −0.461548
\(716\) 13.4044 0.500946
\(717\) −24.0805 −0.899301
\(718\) 0.493319 0.0184105
\(719\) −4.12971 −0.154012 −0.0770061 0.997031i \(-0.524536\pi\)
−0.0770061 + 0.997031i \(0.524536\pi\)
\(720\) 7.13179 0.265786
\(721\) −1.46585 −0.0545910
\(722\) −0.360410 −0.0134131
\(723\) −15.8356 −0.588934
\(724\) −30.5995 −1.13722
\(725\) −8.03306 −0.298340
\(726\) 0.0143910 0.000534099 0
\(727\) −14.8186 −0.549590 −0.274795 0.961503i \(-0.588610\pi\)
−0.274795 + 0.961503i \(0.588610\pi\)
\(728\) −0.397507 −0.0147326
\(729\) 1.00000 0.0370370
\(730\) 0.890554 0.0329609
\(731\) −11.6079 −0.429333
\(732\) 18.0798 0.668248
\(733\) 37.2268 1.37500 0.687501 0.726183i \(-0.258708\pi\)
0.687501 + 0.726183i \(0.258708\pi\)
\(734\) −0.370081 −0.0136599
\(735\) −1.78925 −0.0659974
\(736\) −4.03444 −0.148711
\(737\) −41.1763 −1.51675
\(738\) −0.204326 −0.00752134
\(739\) 25.0811 0.922625 0.461312 0.887238i \(-0.347379\pi\)
0.461312 + 0.887238i \(0.347379\pi\)
\(740\) 24.5927 0.904046
\(741\) 10.5520 0.387637
\(742\) 0.608109 0.0223244
\(743\) 22.8081 0.836747 0.418374 0.908275i \(-0.362600\pi\)
0.418374 + 0.908275i \(0.362600\pi\)
\(744\) 0.758299 0.0278006
\(745\) 27.7886 1.01810
\(746\) 1.20754 0.0442111
\(747\) −3.69192 −0.135080
\(748\) 10.7122 0.391678
\(749\) 3.12126 0.114048
\(750\) −0.589402 −0.0215219
\(751\) −11.4218 −0.416788 −0.208394 0.978045i \(-0.566824\pi\)
−0.208394 + 0.978045i \(0.566824\pi\)
\(752\) 19.2788 0.703026
\(753\) −4.43127 −0.161485
\(754\) 0.444107 0.0161734
\(755\) −29.4659 −1.07237
\(756\) 1.99765 0.0726539
\(757\) −35.8118 −1.30160 −0.650801 0.759249i \(-0.725567\pi\)
−0.650801 + 0.759249i \(0.725567\pi\)
\(758\) −1.23656 −0.0449139
\(759\) −23.3583 −0.847853
\(760\) 1.78203 0.0646410
\(761\) −32.2880 −1.17044 −0.585220 0.810874i \(-0.698992\pi\)
−0.585220 + 0.810874i \(0.698992\pi\)
\(762\) 0.190546 0.00690274
\(763\) −5.64099 −0.204218
\(764\) 1.99765 0.0722725
\(765\) −2.85462 −0.103209
\(766\) 1.74094 0.0629028
\(767\) −14.9786 −0.540845
\(768\) −15.8125 −0.570585
\(769\) 39.3988 1.42076 0.710378 0.703821i \(-0.248524\pi\)
0.710378 + 0.703821i \(0.248524\pi\)
\(770\) −0.291390 −0.0105010
\(771\) 26.4282 0.951788
\(772\) −49.8128 −1.79280
\(773\) 40.7233 1.46472 0.732358 0.680920i \(-0.238420\pi\)
0.732358 + 0.680920i \(0.238420\pi\)
\(774\) −0.352531 −0.0126715
\(775\) 7.04120 0.252927
\(776\) 0.403358 0.0144797
\(777\) 6.88044 0.246834
\(778\) −0.787405 −0.0282298
\(779\) 21.6829 0.776871
\(780\) −7.33513 −0.262640
\(781\) −15.7224 −0.562592
\(782\) 0.537230 0.0192113
\(783\) −4.46629 −0.159612
\(784\) 3.98592 0.142354
\(785\) −10.5084 −0.375060
\(786\) 0.614836 0.0219305
\(787\) −35.2079 −1.25503 −0.627513 0.778606i \(-0.715927\pi\)
−0.627513 + 0.778606i \(0.715927\pi\)
\(788\) −18.2852 −0.651382
\(789\) −19.5544 −0.696156
\(790\) −0.775835 −0.0276030
\(791\) 6.37340 0.226612
\(792\) 0.651042 0.0231338
\(793\) −18.5734 −0.659560
\(794\) −1.31155 −0.0465450
\(795\) 22.4558 0.796427
\(796\) −29.8411 −1.05769
\(797\) 9.19566 0.325727 0.162863 0.986649i \(-0.447927\pi\)
0.162863 + 0.986649i \(0.447927\pi\)
\(798\) 0.249138 0.00881938
\(799\) −7.71666 −0.272996
\(800\) 1.04414 0.0369158
\(801\) 1.98084 0.0699897
\(802\) 0.572531 0.0202168
\(803\) −34.5262 −1.21840
\(804\) −24.4729 −0.863093
\(805\) 12.4345 0.438260
\(806\) −0.389272 −0.0137115
\(807\) −22.5742 −0.794649
\(808\) 1.36120 0.0478868
\(809\) 46.6349 1.63960 0.819799 0.572652i \(-0.194085\pi\)
0.819799 + 0.572652i \(0.194085\pi\)
\(810\) −0.0866947 −0.00304614
\(811\) −52.8259 −1.85497 −0.927485 0.373861i \(-0.878034\pi\)
−0.927485 + 0.373861i \(0.878034\pi\)
\(812\) −8.92210 −0.313104
\(813\) −19.5448 −0.685466
\(814\) 1.12052 0.0392743
\(815\) −9.34016 −0.327172
\(816\) 6.35926 0.222619
\(817\) 37.4104 1.30882
\(818\) −0.353203 −0.0123495
\(819\) −2.05219 −0.0717094
\(820\) −15.0727 −0.526361
\(821\) −55.0376 −1.92083 −0.960413 0.278579i \(-0.910137\pi\)
−0.960413 + 0.278579i \(0.910137\pi\)
\(822\) 0.552598 0.0192741
\(823\) −14.2825 −0.497857 −0.248929 0.968522i \(-0.580078\pi\)
−0.248929 + 0.968522i \(0.580078\pi\)
\(824\) −0.283933 −0.00989128
\(825\) 6.04527 0.210469
\(826\) −0.353651 −0.0123051
\(827\) 29.3836 1.02177 0.510884 0.859650i \(-0.329318\pi\)
0.510884 + 0.859650i \(0.329318\pi\)
\(828\) −13.8829 −0.482463
\(829\) −13.2860 −0.461443 −0.230722 0.973020i \(-0.574109\pi\)
−0.230722 + 0.973020i \(0.574109\pi\)
\(830\) 0.320070 0.0111098
\(831\) −15.9122 −0.551987
\(832\) 16.3020 0.565170
\(833\) −1.59543 −0.0552784
\(834\) 0.308240 0.0106735
\(835\) 17.6358 0.610311
\(836\) −34.5238 −1.19403
\(837\) 3.91483 0.135316
\(838\) 0.350107 0.0120943
\(839\) 6.56697 0.226717 0.113359 0.993554i \(-0.463839\pi\)
0.113359 + 0.993554i \(0.463839\pi\)
\(840\) −0.346575 −0.0119580
\(841\) −9.05224 −0.312146
\(842\) 0.245877 0.00847347
\(843\) 4.72334 0.162681
\(844\) −2.85451 −0.0982564
\(845\) −15.7248 −0.540950
\(846\) −0.234355 −0.00805729
\(847\) 0.297008 0.0102053
\(848\) −50.0251 −1.71787
\(849\) −1.09143 −0.0374579
\(850\) −0.139038 −0.00476897
\(851\) −47.8163 −1.63912
\(852\) −9.34452 −0.320138
\(853\) −4.41670 −0.151225 −0.0756125 0.997137i \(-0.524091\pi\)
−0.0756125 + 0.997137i \(0.524091\pi\)
\(854\) −0.438526 −0.0150061
\(855\) 9.19998 0.314633
\(856\) 0.604585 0.0206643
\(857\) 8.88418 0.303478 0.151739 0.988421i \(-0.451513\pi\)
0.151739 + 0.988421i \(0.451513\pi\)
\(858\) −0.334212 −0.0114098
\(859\) 12.2457 0.417818 0.208909 0.977935i \(-0.433009\pi\)
0.208909 + 0.977935i \(0.433009\pi\)
\(860\) −26.0055 −0.886781
\(861\) −4.21697 −0.143714
\(862\) 0.355604 0.0121119
\(863\) −40.1757 −1.36760 −0.683798 0.729671i \(-0.739673\pi\)
−0.683798 + 0.729671i \(0.739673\pi\)
\(864\) 0.580529 0.0197500
\(865\) 9.08899 0.309035
\(866\) −0.275331 −0.00935613
\(867\) 14.4546 0.490904
\(868\) 7.82047 0.265444
\(869\) 30.0787 1.02035
\(870\) 0.387204 0.0131274
\(871\) 25.1411 0.851873
\(872\) −1.09266 −0.0370020
\(873\) 2.08239 0.0704784
\(874\) −1.73141 −0.0585657
\(875\) −12.1644 −0.411231
\(876\) −20.5205 −0.693323
\(877\) 51.6084 1.74269 0.871346 0.490669i \(-0.163247\pi\)
0.871346 + 0.490669i \(0.163247\pi\)
\(878\) −0.370868 −0.0125162
\(879\) 30.6330 1.03323
\(880\) 23.9707 0.808052
\(881\) 15.9384 0.536978 0.268489 0.963283i \(-0.413476\pi\)
0.268489 + 0.963283i \(0.413476\pi\)
\(882\) −0.0484532 −0.00163150
\(883\) 8.01850 0.269844 0.134922 0.990856i \(-0.456922\pi\)
0.134922 + 0.990856i \(0.456922\pi\)
\(884\) −6.54057 −0.219983
\(885\) −13.0594 −0.438987
\(886\) 1.22822 0.0412628
\(887\) 19.3084 0.648312 0.324156 0.946004i \(-0.394920\pi\)
0.324156 + 0.946004i \(0.394920\pi\)
\(888\) 1.33273 0.0447236
\(889\) 3.93257 0.131894
\(890\) −0.171729 −0.00575636
\(891\) 3.36110 0.112601
\(892\) 53.6700 1.79701
\(893\) 24.8696 0.832229
\(894\) 0.752522 0.0251681
\(895\) −12.0060 −0.401316
\(896\) 1.54596 0.0516467
\(897\) 14.2619 0.476191
\(898\) 1.27599 0.0425803
\(899\) −17.4848 −0.583150
\(900\) 3.59297 0.119766
\(901\) 20.0234 0.667075
\(902\) −0.686760 −0.0228666
\(903\) −7.27571 −0.242120
\(904\) 1.23452 0.0410595
\(905\) 27.4072 0.911048
\(906\) −0.797943 −0.0265099
\(907\) −35.8103 −1.18906 −0.594531 0.804073i \(-0.702662\pi\)
−0.594531 + 0.804073i \(0.702662\pi\)
\(908\) 15.9586 0.529605
\(909\) 7.02738 0.233084
\(910\) 0.177914 0.00589780
\(911\) 13.2358 0.438521 0.219260 0.975666i \(-0.429636\pi\)
0.219260 + 0.975666i \(0.429636\pi\)
\(912\) −20.4949 −0.678653
\(913\) −12.4089 −0.410675
\(914\) 1.06049 0.0350780
\(915\) −16.1936 −0.535344
\(916\) −26.4269 −0.873169
\(917\) 12.6893 0.419037
\(918\) −0.0773037 −0.00255140
\(919\) 19.3419 0.638031 0.319015 0.947750i \(-0.396648\pi\)
0.319015 + 0.947750i \(0.396648\pi\)
\(920\) 2.40856 0.0794079
\(921\) −21.5884 −0.711362
\(922\) −0.0980196 −0.00322810
\(923\) 9.59964 0.315976
\(924\) 6.71431 0.220885
\(925\) 12.3751 0.406892
\(926\) −1.44854 −0.0476021
\(927\) −1.46585 −0.0481447
\(928\) −2.59281 −0.0851132
\(929\) 4.29706 0.140982 0.0704910 0.997512i \(-0.477543\pi\)
0.0704910 + 0.997512i \(0.477543\pi\)
\(930\) −0.339395 −0.0111292
\(931\) 5.14182 0.168516
\(932\) −43.9254 −1.43882
\(933\) 11.3055 0.370125
\(934\) 1.44345 0.0472311
\(935\) −9.59467 −0.313779
\(936\) −0.397507 −0.0129929
\(937\) −26.3441 −0.860624 −0.430312 0.902680i \(-0.641596\pi\)
−0.430312 + 0.902680i \(0.641596\pi\)
\(938\) 0.593593 0.0193815
\(939\) −27.9643 −0.912580
\(940\) −17.2879 −0.563869
\(941\) 35.9318 1.17134 0.585671 0.810549i \(-0.300831\pi\)
0.585671 + 0.810549i \(0.300831\pi\)
\(942\) −0.284569 −0.00927177
\(943\) 29.3063 0.954343
\(944\) 29.0925 0.946881
\(945\) −1.78925 −0.0582042
\(946\) −1.18489 −0.0385242
\(947\) −16.6353 −0.540575 −0.270288 0.962780i \(-0.587119\pi\)
−0.270288 + 0.962780i \(0.587119\pi\)
\(948\) 17.8771 0.580621
\(949\) 21.0807 0.684309
\(950\) 0.448098 0.0145382
\(951\) 25.2148 0.817646
\(952\) −0.309033 −0.0100158
\(953\) −40.5799 −1.31451 −0.657256 0.753667i \(-0.728283\pi\)
−0.657256 + 0.753667i \(0.728283\pi\)
\(954\) 0.608109 0.0196883
\(955\) −1.78925 −0.0578987
\(956\) −48.1044 −1.55581
\(957\) −15.0117 −0.485258
\(958\) 1.39187 0.0449691
\(959\) 11.4048 0.368279
\(960\) 14.2133 0.458731
\(961\) −15.6741 −0.505616
\(962\) −0.684158 −0.0220581
\(963\) 3.12126 0.100581
\(964\) −31.6341 −1.01887
\(965\) 44.6161 1.43624
\(966\) 0.336730 0.0108341
\(967\) 54.4939 1.75241 0.876203 0.481942i \(-0.160068\pi\)
0.876203 + 0.481942i \(0.160068\pi\)
\(968\) 0.0575301 0.00184909
\(969\) 8.20342 0.263532
\(970\) −0.180533 −0.00579655
\(971\) −18.9209 −0.607201 −0.303601 0.952799i \(-0.598189\pi\)
−0.303601 + 0.952799i \(0.598189\pi\)
\(972\) 1.99765 0.0640747
\(973\) 6.36160 0.203943
\(974\) −1.29360 −0.0414496
\(975\) −3.69106 −0.118209
\(976\) 36.0746 1.15472
\(977\) −22.5176 −0.720402 −0.360201 0.932875i \(-0.617292\pi\)
−0.360201 + 0.932875i \(0.617292\pi\)
\(978\) −0.252934 −0.00808793
\(979\) 6.65782 0.212785
\(980\) −3.57429 −0.114177
\(981\) −5.64099 −0.180103
\(982\) 0.262965 0.00839154
\(983\) 33.4256 1.06611 0.533055 0.846080i \(-0.321044\pi\)
0.533055 + 0.846080i \(0.321044\pi\)
\(984\) −0.816824 −0.0260394
\(985\) 16.3776 0.521832
\(986\) 0.345261 0.0109953
\(987\) −4.83673 −0.153955
\(988\) 21.0792 0.670619
\(989\) 50.5633 1.60782
\(990\) −0.291390 −0.00926098
\(991\) −61.5492 −1.95518 −0.977588 0.210529i \(-0.932481\pi\)
−0.977588 + 0.210529i \(0.932481\pi\)
\(992\) 2.27267 0.0721574
\(993\) −1.93245 −0.0613246
\(994\) 0.226652 0.00718897
\(995\) 26.7279 0.847332
\(996\) −7.37516 −0.233691
\(997\) 22.1771 0.702357 0.351179 0.936309i \(-0.385781\pi\)
0.351179 + 0.936309i \(0.385781\pi\)
\(998\) 0.602533 0.0190729
\(999\) 6.88044 0.217687
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.1.16 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4011.2.a.l.1.16 28 1.1 even 1 trivial