Properties

Label 2005.2.a.f.1.9
Level $2005$
Weight $2$
Character 2005.1
Self dual yes
Analytic conductor $16.010$
Analytic rank $0$
Dimension $37$
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] = [2005,2,Mod(1,2005)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2005, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2005.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2005 = 5 \cdot 401 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2005.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: \(16.0100056053\)
Analytic rank: \(0\)
Dimension: \(37\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) \(=\) 2005.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.33194 q^{2} -3.14709 q^{3} -0.225946 q^{4} -1.00000 q^{5} +4.19172 q^{6} -4.67738 q^{7} +2.96482 q^{8} +6.90415 q^{9} +O(q^{10})\) \(q-1.33194 q^{2} -3.14709 q^{3} -0.225946 q^{4} -1.00000 q^{5} +4.19172 q^{6} -4.67738 q^{7} +2.96482 q^{8} +6.90415 q^{9} +1.33194 q^{10} +5.05534 q^{11} +0.711072 q^{12} +1.63013 q^{13} +6.22997 q^{14} +3.14709 q^{15} -3.49706 q^{16} -4.32572 q^{17} -9.19589 q^{18} +2.37172 q^{19} +0.225946 q^{20} +14.7201 q^{21} -6.73339 q^{22} -1.08473 q^{23} -9.33054 q^{24} +1.00000 q^{25} -2.17123 q^{26} -12.2867 q^{27} +1.05684 q^{28} -7.88273 q^{29} -4.19172 q^{30} +2.44114 q^{31} -1.27178 q^{32} -15.9096 q^{33} +5.76158 q^{34} +4.67738 q^{35} -1.55997 q^{36} -6.13003 q^{37} -3.15898 q^{38} -5.13017 q^{39} -2.96482 q^{40} -8.57579 q^{41} -19.6063 q^{42} -2.55480 q^{43} -1.14223 q^{44} -6.90415 q^{45} +1.44479 q^{46} +7.47452 q^{47} +11.0055 q^{48} +14.8779 q^{49} -1.33194 q^{50} +13.6134 q^{51} -0.368322 q^{52} +2.08798 q^{53} +16.3651 q^{54} -5.05534 q^{55} -13.8676 q^{56} -7.46400 q^{57} +10.4993 q^{58} -13.3507 q^{59} -0.711072 q^{60} -11.4901 q^{61} -3.25144 q^{62} -32.2933 q^{63} +8.68804 q^{64} -1.63013 q^{65} +21.1906 q^{66} +14.2309 q^{67} +0.977379 q^{68} +3.41373 q^{69} -6.22997 q^{70} +8.47954 q^{71} +20.4696 q^{72} +4.82319 q^{73} +8.16480 q^{74} -3.14709 q^{75} -0.535880 q^{76} -23.6457 q^{77} +6.83306 q^{78} -4.38807 q^{79} +3.49706 q^{80} +17.9549 q^{81} +11.4224 q^{82} +9.81209 q^{83} -3.32595 q^{84} +4.32572 q^{85} +3.40283 q^{86} +24.8076 q^{87} +14.9882 q^{88} -13.1613 q^{89} +9.19589 q^{90} -7.62476 q^{91} +0.245090 q^{92} -7.68247 q^{93} -9.95558 q^{94} -2.37172 q^{95} +4.00240 q^{96} -17.4022 q^{97} -19.8164 q^{98} +34.9028 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 37 q + 7 q^{2} + 3 q^{3} + 43 q^{4} - 37 q^{5} + 8 q^{6} - 16 q^{7} + 21 q^{8} + 54 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 37 q + 7 q^{2} + 3 q^{3} + 43 q^{4} - 37 q^{5} + 8 q^{6} - 16 q^{7} + 21 q^{8} + 54 q^{9} - 7 q^{10} + 42 q^{11} - 13 q^{13} + 14 q^{14} - 3 q^{15} + 63 q^{16} + 18 q^{17} + 22 q^{18} + 22 q^{19} - 43 q^{20} + 16 q^{21} - 10 q^{22} + 23 q^{23} + 23 q^{24} + 37 q^{25} + 21 q^{26} + 3 q^{27} - 18 q^{28} + 33 q^{29} - 8 q^{30} + 11 q^{31} + 54 q^{32} + 2 q^{33} + 8 q^{34} + 16 q^{35} + 91 q^{36} - 11 q^{37} + 29 q^{38} + 25 q^{39} - 21 q^{40} + 24 q^{41} + 4 q^{42} + 25 q^{43} + 84 q^{44} - 54 q^{45} + 31 q^{46} + 7 q^{47} + 4 q^{48} + 45 q^{49} + 7 q^{50} + 94 q^{51} - 43 q^{52} + 49 q^{53} + 38 q^{54} - 42 q^{55} + 46 q^{56} + 6 q^{57} + 15 q^{58} + 69 q^{59} + 9 q^{61} + 17 q^{62} - 38 q^{63} + 107 q^{64} + 13 q^{65} + 74 q^{66} + 13 q^{67} + 86 q^{68} - 14 q^{70} + 51 q^{71} + 81 q^{72} - 47 q^{73} + 79 q^{74} + 3 q^{75} + 59 q^{76} + 2 q^{77} + 20 q^{78} + 67 q^{79} - 63 q^{80} + 125 q^{81} - 24 q^{82} + 80 q^{83} + 50 q^{84} - 18 q^{85} + 69 q^{86} - 32 q^{87} - 12 q^{88} + 34 q^{89} - 22 q^{90} + 39 q^{91} + 85 q^{92} + q^{93} + 12 q^{94} - 22 q^{95} + 77 q^{96} - 14 q^{97} + 40 q^{98} + 133 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.33194 −0.941821 −0.470911 0.882181i \(-0.656075\pi\)
−0.470911 + 0.882181i \(0.656075\pi\)
\(3\) −3.14709 −1.81697 −0.908486 0.417916i \(-0.862761\pi\)
−0.908486 + 0.417916i \(0.862761\pi\)
\(4\) −0.225946 −0.112973
\(5\) −1.00000 −0.447214
\(6\) 4.19172 1.71126
\(7\) −4.67738 −1.76788 −0.883942 0.467597i \(-0.845120\pi\)
−0.883942 + 0.467597i \(0.845120\pi\)
\(8\) 2.96482 1.04822
\(9\) 6.90415 2.30138
\(10\) 1.33194 0.421195
\(11\) 5.05534 1.52424 0.762121 0.647434i \(-0.224158\pi\)
0.762121 + 0.647434i \(0.224158\pi\)
\(12\) 0.711072 0.205269
\(13\) 1.63013 0.452118 0.226059 0.974114i \(-0.427416\pi\)
0.226059 + 0.974114i \(0.427416\pi\)
\(14\) 6.22997 1.66503
\(15\) 3.14709 0.812574
\(16\) −3.49706 −0.874264
\(17\) −4.32572 −1.04914 −0.524570 0.851367i \(-0.675774\pi\)
−0.524570 + 0.851367i \(0.675774\pi\)
\(18\) −9.19589 −2.16749
\(19\) 2.37172 0.544110 0.272055 0.962282i \(-0.412297\pi\)
0.272055 + 0.962282i \(0.412297\pi\)
\(20\) 0.225946 0.0505231
\(21\) 14.7201 3.21219
\(22\) −6.73339 −1.43556
\(23\) −1.08473 −0.226181 −0.113091 0.993585i \(-0.536075\pi\)
−0.113091 + 0.993585i \(0.536075\pi\)
\(24\) −9.33054 −1.90459
\(25\) 1.00000 0.200000
\(26\) −2.17123 −0.425814
\(27\) −12.2867 −2.36458
\(28\) 1.05684 0.199723
\(29\) −7.88273 −1.46379 −0.731893 0.681419i \(-0.761363\pi\)
−0.731893 + 0.681419i \(0.761363\pi\)
\(30\) −4.19172 −0.765300
\(31\) 2.44114 0.438441 0.219221 0.975675i \(-0.429649\pi\)
0.219221 + 0.975675i \(0.429649\pi\)
\(32\) −1.27178 −0.224821
\(33\) −15.9096 −2.76950
\(34\) 5.76158 0.988103
\(35\) 4.67738 0.790621
\(36\) −1.55997 −0.259994
\(37\) −6.13003 −1.00777 −0.503885 0.863771i \(-0.668097\pi\)
−0.503885 + 0.863771i \(0.668097\pi\)
\(38\) −3.15898 −0.512454
\(39\) −5.13017 −0.821485
\(40\) −2.96482 −0.468779
\(41\) −8.57579 −1.33931 −0.669657 0.742671i \(-0.733559\pi\)
−0.669657 + 0.742671i \(0.733559\pi\)
\(42\) −19.6063 −3.02531
\(43\) −2.55480 −0.389603 −0.194801 0.980843i \(-0.562406\pi\)
−0.194801 + 0.980843i \(0.562406\pi\)
\(44\) −1.14223 −0.172198
\(45\) −6.90415 −1.02921
\(46\) 1.44479 0.213022
\(47\) 7.47452 1.09027 0.545135 0.838348i \(-0.316478\pi\)
0.545135 + 0.838348i \(0.316478\pi\)
\(48\) 11.0055 1.58851
\(49\) 14.8779 2.12541
\(50\) −1.33194 −0.188364
\(51\) 13.6134 1.90626
\(52\) −0.368322 −0.0510771
\(53\) 2.08798 0.286807 0.143403 0.989664i \(-0.454195\pi\)
0.143403 + 0.989664i \(0.454195\pi\)
\(54\) 16.3651 2.22701
\(55\) −5.05534 −0.681662
\(56\) −13.8676 −1.85313
\(57\) −7.46400 −0.988631
\(58\) 10.4993 1.37862
\(59\) −13.3507 −1.73812 −0.869059 0.494709i \(-0.835275\pi\)
−0.869059 + 0.494709i \(0.835275\pi\)
\(60\) −0.711072 −0.0917990
\(61\) −11.4901 −1.47116 −0.735578 0.677440i \(-0.763089\pi\)
−0.735578 + 0.677440i \(0.763089\pi\)
\(62\) −3.25144 −0.412933
\(63\) −32.2933 −4.06858
\(64\) 8.68804 1.08601
\(65\) −1.63013 −0.202193
\(66\) 21.1906 2.60838
\(67\) 14.2309 1.73858 0.869288 0.494306i \(-0.164578\pi\)
0.869288 + 0.494306i \(0.164578\pi\)
\(68\) 0.977379 0.118525
\(69\) 3.41373 0.410965
\(70\) −6.22997 −0.744624
\(71\) 8.47954 1.00634 0.503168 0.864189i \(-0.332168\pi\)
0.503168 + 0.864189i \(0.332168\pi\)
\(72\) 20.4696 2.41236
\(73\) 4.82319 0.564511 0.282256 0.959339i \(-0.408917\pi\)
0.282256 + 0.959339i \(0.408917\pi\)
\(74\) 8.16480 0.949139
\(75\) −3.14709 −0.363394
\(76\) −0.535880 −0.0614697
\(77\) −23.6457 −2.69468
\(78\) 6.83306 0.773692
\(79\) −4.38807 −0.493697 −0.246848 0.969054i \(-0.579395\pi\)
−0.246848 + 0.969054i \(0.579395\pi\)
\(80\) 3.49706 0.390983
\(81\) 17.9549 1.99499
\(82\) 11.4224 1.26139
\(83\) 9.81209 1.07702 0.538508 0.842620i \(-0.318988\pi\)
0.538508 + 0.842620i \(0.318988\pi\)
\(84\) −3.32595 −0.362891
\(85\) 4.32572 0.469190
\(86\) 3.40283 0.366936
\(87\) 24.8076 2.65966
\(88\) 14.9882 1.59774
\(89\) −13.1613 −1.39510 −0.697549 0.716537i \(-0.745726\pi\)
−0.697549 + 0.716537i \(0.745726\pi\)
\(90\) 9.19589 0.969332
\(91\) −7.62476 −0.799292
\(92\) 0.245090 0.0255524
\(93\) −7.68247 −0.796636
\(94\) −9.95558 −1.02684
\(95\) −2.37172 −0.243333
\(96\) 4.00240 0.408494
\(97\) −17.4022 −1.76692 −0.883462 0.468503i \(-0.844793\pi\)
−0.883462 + 0.468503i \(0.844793\pi\)
\(98\) −19.8164 −2.00176
\(99\) 34.9028 3.50787
\(100\) −0.225946 −0.0225946
\(101\) −8.96048 −0.891601 −0.445801 0.895132i \(-0.647081\pi\)
−0.445801 + 0.895132i \(0.647081\pi\)
\(102\) −18.1322 −1.79535
\(103\) −6.55858 −0.646236 −0.323118 0.946359i \(-0.604731\pi\)
−0.323118 + 0.946359i \(0.604731\pi\)
\(104\) 4.83305 0.473920
\(105\) −14.7201 −1.43654
\(106\) −2.78106 −0.270121
\(107\) 0.962257 0.0930249 0.0465124 0.998918i \(-0.485189\pi\)
0.0465124 + 0.998918i \(0.485189\pi\)
\(108\) 2.77613 0.267134
\(109\) −0.925856 −0.0886809 −0.0443405 0.999016i \(-0.514119\pi\)
−0.0443405 + 0.999016i \(0.514119\pi\)
\(110\) 6.73339 0.642004
\(111\) 19.2917 1.83109
\(112\) 16.3571 1.54560
\(113\) 7.44701 0.700555 0.350278 0.936646i \(-0.386087\pi\)
0.350278 + 0.936646i \(0.386087\pi\)
\(114\) 9.94158 0.931114
\(115\) 1.08473 0.101151
\(116\) 1.78107 0.165368
\(117\) 11.2547 1.04050
\(118\) 17.7823 1.63700
\(119\) 20.2330 1.85476
\(120\) 9.33054 0.851758
\(121\) 14.5565 1.32331
\(122\) 15.3041 1.38557
\(123\) 26.9888 2.43349
\(124\) −0.551566 −0.0495321
\(125\) −1.00000 −0.0894427
\(126\) 43.0127 3.83187
\(127\) −15.0404 −1.33462 −0.667309 0.744781i \(-0.732554\pi\)
−0.667309 + 0.744781i \(0.732554\pi\)
\(128\) −9.02836 −0.798002
\(129\) 8.04017 0.707897
\(130\) 2.17123 0.190430
\(131\) −5.04718 −0.440974 −0.220487 0.975390i \(-0.570765\pi\)
−0.220487 + 0.975390i \(0.570765\pi\)
\(132\) 3.59471 0.312879
\(133\) −11.0934 −0.961922
\(134\) −18.9546 −1.63743
\(135\) 12.2867 1.05747
\(136\) −12.8250 −1.09973
\(137\) 17.8652 1.52633 0.763164 0.646204i \(-0.223645\pi\)
0.763164 + 0.646204i \(0.223645\pi\)
\(138\) −4.54687 −0.387055
\(139\) 13.0736 1.10889 0.554443 0.832221i \(-0.312931\pi\)
0.554443 + 0.832221i \(0.312931\pi\)
\(140\) −1.05684 −0.0893189
\(141\) −23.5230 −1.98099
\(142\) −11.2942 −0.947788
\(143\) 8.24088 0.689137
\(144\) −24.1442 −2.01202
\(145\) 7.88273 0.654625
\(146\) −6.42418 −0.531669
\(147\) −46.8220 −3.86181
\(148\) 1.38506 0.113851
\(149\) 4.76000 0.389954 0.194977 0.980808i \(-0.437537\pi\)
0.194977 + 0.980808i \(0.437537\pi\)
\(150\) 4.19172 0.342252
\(151\) 7.59676 0.618216 0.309108 0.951027i \(-0.399970\pi\)
0.309108 + 0.951027i \(0.399970\pi\)
\(152\) 7.03171 0.570347
\(153\) −29.8654 −2.41448
\(154\) 31.4946 2.53791
\(155\) −2.44114 −0.196077
\(156\) 1.15914 0.0928057
\(157\) −8.34378 −0.665906 −0.332953 0.942943i \(-0.608045\pi\)
−0.332953 + 0.942943i \(0.608045\pi\)
\(158\) 5.84463 0.464974
\(159\) −6.57106 −0.521119
\(160\) 1.27178 0.100543
\(161\) 5.07368 0.399862
\(162\) −23.9147 −1.87892
\(163\) −22.7894 −1.78500 −0.892501 0.451044i \(-0.851052\pi\)
−0.892501 + 0.451044i \(0.851052\pi\)
\(164\) 1.93767 0.151306
\(165\) 15.9096 1.23856
\(166\) −13.0691 −1.01436
\(167\) −4.11836 −0.318688 −0.159344 0.987223i \(-0.550938\pi\)
−0.159344 + 0.987223i \(0.550938\pi\)
\(168\) 43.6425 3.36709
\(169\) −10.3427 −0.795589
\(170\) −5.76158 −0.441893
\(171\) 16.3747 1.25221
\(172\) 0.577246 0.0440146
\(173\) 6.33232 0.481438 0.240719 0.970595i \(-0.422617\pi\)
0.240719 + 0.970595i \(0.422617\pi\)
\(174\) −33.0422 −2.50492
\(175\) −4.67738 −0.353577
\(176\) −17.6788 −1.33259
\(177\) 42.0159 3.15811
\(178\) 17.5300 1.31393
\(179\) 6.18122 0.462006 0.231003 0.972953i \(-0.425799\pi\)
0.231003 + 0.972953i \(0.425799\pi\)
\(180\) 1.55997 0.116273
\(181\) −21.3322 −1.58561 −0.792807 0.609473i \(-0.791381\pi\)
−0.792807 + 0.609473i \(0.791381\pi\)
\(182\) 10.1557 0.752790
\(183\) 36.1603 2.67305
\(184\) −3.21602 −0.237088
\(185\) 6.13003 0.450689
\(186\) 10.2326 0.750288
\(187\) −21.8680 −1.59914
\(188\) −1.68884 −0.123171
\(189\) 57.4696 4.18030
\(190\) 3.15898 0.229176
\(191\) −16.8463 −1.21896 −0.609478 0.792803i \(-0.708621\pi\)
−0.609478 + 0.792803i \(0.708621\pi\)
\(192\) −27.3420 −1.97324
\(193\) 18.0433 1.29879 0.649394 0.760452i \(-0.275023\pi\)
0.649394 + 0.760452i \(0.275023\pi\)
\(194\) 23.1786 1.66413
\(195\) 5.13017 0.367379
\(196\) −3.36160 −0.240114
\(197\) −24.1481 −1.72048 −0.860240 0.509889i \(-0.829687\pi\)
−0.860240 + 0.509889i \(0.829687\pi\)
\(198\) −46.4884 −3.30378
\(199\) 18.5154 1.31252 0.656260 0.754535i \(-0.272138\pi\)
0.656260 + 0.754535i \(0.272138\pi\)
\(200\) 2.96482 0.209644
\(201\) −44.7857 −3.15894
\(202\) 11.9348 0.839729
\(203\) 36.8705 2.58780
\(204\) −3.07590 −0.215356
\(205\) 8.57579 0.598959
\(206\) 8.73561 0.608638
\(207\) −7.48912 −0.520530
\(208\) −5.70067 −0.395270
\(209\) 11.9898 0.829355
\(210\) 19.6063 1.35296
\(211\) 2.42963 0.167262 0.0836312 0.996497i \(-0.473348\pi\)
0.0836312 + 0.996497i \(0.473348\pi\)
\(212\) −0.471772 −0.0324014
\(213\) −26.6858 −1.82848
\(214\) −1.28166 −0.0876128
\(215\) 2.55480 0.174236
\(216\) −36.4279 −2.47860
\(217\) −11.4181 −0.775113
\(218\) 1.23318 0.0835216
\(219\) −15.1790 −1.02570
\(220\) 1.14223 0.0770094
\(221\) −7.05150 −0.474335
\(222\) −25.6953 −1.72456
\(223\) 11.4006 0.763444 0.381722 0.924277i \(-0.375331\pi\)
0.381722 + 0.924277i \(0.375331\pi\)
\(224\) 5.94860 0.397457
\(225\) 6.90415 0.460277
\(226\) −9.91894 −0.659798
\(227\) −2.39704 −0.159097 −0.0795486 0.996831i \(-0.525348\pi\)
−0.0795486 + 0.996831i \(0.525348\pi\)
\(228\) 1.68646 0.111689
\(229\) 27.3071 1.80451 0.902253 0.431208i \(-0.141912\pi\)
0.902253 + 0.431208i \(0.141912\pi\)
\(230\) −1.44479 −0.0952664
\(231\) 74.4152 4.89616
\(232\) −23.3709 −1.53437
\(233\) 23.3595 1.53033 0.765165 0.643834i \(-0.222657\pi\)
0.765165 + 0.643834i \(0.222657\pi\)
\(234\) −14.9905 −0.979962
\(235\) −7.47452 −0.487584
\(236\) 3.01654 0.196360
\(237\) 13.8096 0.897033
\(238\) −26.9491 −1.74685
\(239\) 27.2516 1.76276 0.881379 0.472409i \(-0.156616\pi\)
0.881379 + 0.472409i \(0.156616\pi\)
\(240\) −11.0055 −0.710404
\(241\) 14.0351 0.904081 0.452041 0.891997i \(-0.350696\pi\)
0.452041 + 0.891997i \(0.350696\pi\)
\(242\) −19.3883 −1.24633
\(243\) −19.6454 −1.26025
\(244\) 2.59614 0.166201
\(245\) −14.8779 −0.950513
\(246\) −35.9473 −2.29192
\(247\) 3.86622 0.246002
\(248\) 7.23753 0.459584
\(249\) −30.8795 −1.95691
\(250\) 1.33194 0.0842390
\(251\) 18.7805 1.18541 0.592706 0.805419i \(-0.298060\pi\)
0.592706 + 0.805419i \(0.298060\pi\)
\(252\) 7.29655 0.459640
\(253\) −5.48366 −0.344755
\(254\) 20.0328 1.25697
\(255\) −13.6134 −0.852505
\(256\) −5.35089 −0.334431
\(257\) −17.5562 −1.09513 −0.547564 0.836764i \(-0.684445\pi\)
−0.547564 + 0.836764i \(0.684445\pi\)
\(258\) −10.7090 −0.666713
\(259\) 28.6725 1.78162
\(260\) 0.368322 0.0228424
\(261\) −54.4236 −3.36873
\(262\) 6.72253 0.415319
\(263\) −9.79893 −0.604228 −0.302114 0.953272i \(-0.597692\pi\)
−0.302114 + 0.953272i \(0.597692\pi\)
\(264\) −47.1690 −2.90305
\(265\) −2.08798 −0.128264
\(266\) 14.7757 0.905959
\(267\) 41.4198 2.53485
\(268\) −3.21541 −0.196412
\(269\) 4.89910 0.298704 0.149352 0.988784i \(-0.452281\pi\)
0.149352 + 0.988784i \(0.452281\pi\)
\(270\) −16.3651 −0.995949
\(271\) −7.83632 −0.476022 −0.238011 0.971262i \(-0.576495\pi\)
−0.238011 + 0.971262i \(0.576495\pi\)
\(272\) 15.1273 0.917226
\(273\) 23.9958 1.45229
\(274\) −23.7953 −1.43753
\(275\) 5.05534 0.304848
\(276\) −0.771319 −0.0464279
\(277\) 14.4895 0.870592 0.435296 0.900287i \(-0.356644\pi\)
0.435296 + 0.900287i \(0.356644\pi\)
\(278\) −17.4132 −1.04437
\(279\) 16.8540 1.00902
\(280\) 13.8676 0.828746
\(281\) 11.9755 0.714399 0.357200 0.934028i \(-0.383732\pi\)
0.357200 + 0.934028i \(0.383732\pi\)
\(282\) 31.3311 1.86574
\(283\) −0.00720674 −0.000428396 0 −0.000214198 1.00000i \(-0.500068\pi\)
−0.000214198 1.00000i \(0.500068\pi\)
\(284\) −1.91592 −0.113689
\(285\) 7.46400 0.442129
\(286\) −10.9763 −0.649044
\(287\) 40.1122 2.36775
\(288\) −8.78057 −0.517400
\(289\) 1.71184 0.100696
\(290\) −10.4993 −0.616540
\(291\) 54.7662 3.21045
\(292\) −1.08978 −0.0637746
\(293\) 9.55771 0.558368 0.279184 0.960238i \(-0.409936\pi\)
0.279184 + 0.960238i \(0.409936\pi\)
\(294\) 62.3639 3.63713
\(295\) 13.3507 0.777310
\(296\) −18.1744 −1.05637
\(297\) −62.1135 −3.60419
\(298\) −6.34001 −0.367267
\(299\) −1.76825 −0.102261
\(300\) 0.711072 0.0410537
\(301\) 11.9498 0.688773
\(302\) −10.1184 −0.582248
\(303\) 28.1994 1.62001
\(304\) −8.29403 −0.475695
\(305\) 11.4901 0.657921
\(306\) 39.7788 2.27400
\(307\) 6.17788 0.352590 0.176295 0.984337i \(-0.443589\pi\)
0.176295 + 0.984337i \(0.443589\pi\)
\(308\) 5.34266 0.304426
\(309\) 20.6404 1.17419
\(310\) 3.25144 0.184669
\(311\) 1.90916 0.108259 0.0541294 0.998534i \(-0.482762\pi\)
0.0541294 + 0.998534i \(0.482762\pi\)
\(312\) −15.2100 −0.861098
\(313\) −7.32354 −0.413951 −0.206975 0.978346i \(-0.566362\pi\)
−0.206975 + 0.978346i \(0.566362\pi\)
\(314\) 11.1134 0.627164
\(315\) 32.2933 1.81952
\(316\) 0.991467 0.0557744
\(317\) 1.56878 0.0881116 0.0440558 0.999029i \(-0.485972\pi\)
0.0440558 + 0.999029i \(0.485972\pi\)
\(318\) 8.75224 0.490801
\(319\) −39.8499 −2.23117
\(320\) −8.68804 −0.485676
\(321\) −3.02831 −0.169024
\(322\) −6.75782 −0.376598
\(323\) −10.2594 −0.570848
\(324\) −4.05683 −0.225380
\(325\) 1.63013 0.0904236
\(326\) 30.3540 1.68115
\(327\) 2.91375 0.161131
\(328\) −25.4257 −1.40390
\(329\) −34.9612 −1.92747
\(330\) −21.1906 −1.16650
\(331\) −34.2692 −1.88360 −0.941802 0.336168i \(-0.890869\pi\)
−0.941802 + 0.336168i \(0.890869\pi\)
\(332\) −2.21700 −0.121674
\(333\) −42.3226 −2.31927
\(334\) 5.48539 0.300147
\(335\) −14.2309 −0.777515
\(336\) −51.4771 −2.80830
\(337\) −10.3283 −0.562617 −0.281308 0.959617i \(-0.590768\pi\)
−0.281308 + 0.959617i \(0.590768\pi\)
\(338\) 13.7758 0.749303
\(339\) −23.4364 −1.27289
\(340\) −0.977379 −0.0530058
\(341\) 12.3408 0.668291
\(342\) −21.8101 −1.17935
\(343\) −36.8478 −1.98960
\(344\) −7.57451 −0.408390
\(345\) −3.41373 −0.183789
\(346\) −8.43425 −0.453428
\(347\) 36.2019 1.94342 0.971711 0.236175i \(-0.0758939\pi\)
0.971711 + 0.236175i \(0.0758939\pi\)
\(348\) −5.60519 −0.300470
\(349\) 12.0418 0.644580 0.322290 0.946641i \(-0.395547\pi\)
0.322290 + 0.946641i \(0.395547\pi\)
\(350\) 6.22997 0.333006
\(351\) −20.0290 −1.06907
\(352\) −6.42928 −0.342682
\(353\) 8.81876 0.469375 0.234688 0.972071i \(-0.424593\pi\)
0.234688 + 0.972071i \(0.424593\pi\)
\(354\) −55.9625 −2.97437
\(355\) −8.47954 −0.450047
\(356\) 2.97375 0.157608
\(357\) −63.6751 −3.37004
\(358\) −8.23299 −0.435127
\(359\) −7.74389 −0.408707 −0.204354 0.978897i \(-0.565509\pi\)
−0.204354 + 0.978897i \(0.565509\pi\)
\(360\) −20.4696 −1.07884
\(361\) −13.3750 −0.703945
\(362\) 28.4132 1.49336
\(363\) −45.8104 −2.40442
\(364\) 1.72278 0.0902984
\(365\) −4.82319 −0.252457
\(366\) −48.1632 −2.51753
\(367\) −28.7516 −1.50082 −0.750411 0.660972i \(-0.770144\pi\)
−0.750411 + 0.660972i \(0.770144\pi\)
\(368\) 3.79335 0.197742
\(369\) −59.2086 −3.08228
\(370\) −8.16480 −0.424468
\(371\) −9.76629 −0.507041
\(372\) 1.73582 0.0899983
\(373\) 10.5310 0.545277 0.272638 0.962117i \(-0.412104\pi\)
0.272638 + 0.962117i \(0.412104\pi\)
\(374\) 29.1267 1.50611
\(375\) 3.14709 0.162515
\(376\) 22.1606 1.14284
\(377\) −12.8499 −0.661804
\(378\) −76.5458 −3.93709
\(379\) −27.1783 −1.39605 −0.698027 0.716072i \(-0.745938\pi\)
−0.698027 + 0.716072i \(0.745938\pi\)
\(380\) 0.535880 0.0274901
\(381\) 47.3334 2.42496
\(382\) 22.4382 1.14804
\(383\) 12.5973 0.643692 0.321846 0.946792i \(-0.395697\pi\)
0.321846 + 0.946792i \(0.395697\pi\)
\(384\) 28.4130 1.44995
\(385\) 23.6457 1.20510
\(386\) −24.0326 −1.22323
\(387\) −17.6387 −0.896626
\(388\) 3.93195 0.199615
\(389\) −7.28219 −0.369222 −0.184611 0.982812i \(-0.559103\pi\)
−0.184611 + 0.982812i \(0.559103\pi\)
\(390\) −6.83306 −0.346006
\(391\) 4.69222 0.237296
\(392\) 44.1102 2.22790
\(393\) 15.8839 0.801238
\(394\) 32.1637 1.62039
\(395\) 4.38807 0.220788
\(396\) −7.88616 −0.396294
\(397\) 15.0633 0.756004 0.378002 0.925805i \(-0.376611\pi\)
0.378002 + 0.925805i \(0.376611\pi\)
\(398\) −24.6613 −1.23616
\(399\) 34.9120 1.74778
\(400\) −3.49706 −0.174853
\(401\) 1.00000 0.0499376
\(402\) 59.6518 2.97516
\(403\) 3.97938 0.198227
\(404\) 2.02459 0.100727
\(405\) −17.9549 −0.892185
\(406\) −49.1092 −2.43725
\(407\) −30.9894 −1.53609
\(408\) 40.3613 1.99818
\(409\) −23.6374 −1.16879 −0.584396 0.811468i \(-0.698669\pi\)
−0.584396 + 0.811468i \(0.698669\pi\)
\(410\) −11.4224 −0.564112
\(411\) −56.2234 −2.77330
\(412\) 1.48188 0.0730072
\(413\) 62.4464 3.07279
\(414\) 9.97503 0.490246
\(415\) −9.81209 −0.481657
\(416\) −2.07317 −0.101646
\(417\) −41.1437 −2.01482
\(418\) −15.9697 −0.781104
\(419\) 9.64766 0.471319 0.235660 0.971836i \(-0.424275\pi\)
0.235660 + 0.971836i \(0.424275\pi\)
\(420\) 3.32595 0.162290
\(421\) 11.2023 0.545968 0.272984 0.962019i \(-0.411989\pi\)
0.272984 + 0.962019i \(0.411989\pi\)
\(422\) −3.23611 −0.157531
\(423\) 51.6052 2.50913
\(424\) 6.19049 0.300637
\(425\) −4.32572 −0.209828
\(426\) 35.5438 1.72210
\(427\) 53.7435 2.60083
\(428\) −0.217418 −0.0105093
\(429\) −25.9348 −1.25214
\(430\) −3.40283 −0.164099
\(431\) 19.8437 0.955838 0.477919 0.878404i \(-0.341391\pi\)
0.477919 + 0.878404i \(0.341391\pi\)
\(432\) 42.9673 2.06727
\(433\) −6.53186 −0.313901 −0.156951 0.987606i \(-0.550166\pi\)
−0.156951 + 0.987606i \(0.550166\pi\)
\(434\) 15.2082 0.730018
\(435\) −24.8076 −1.18944
\(436\) 0.209194 0.0100186
\(437\) −2.57267 −0.123067
\(438\) 20.2174 0.966027
\(439\) −19.2152 −0.917093 −0.458547 0.888670i \(-0.651630\pi\)
−0.458547 + 0.888670i \(0.651630\pi\)
\(440\) −14.9882 −0.714533
\(441\) 102.719 4.89139
\(442\) 9.39215 0.446739
\(443\) −1.76374 −0.0837980 −0.0418990 0.999122i \(-0.513341\pi\)
−0.0418990 + 0.999122i \(0.513341\pi\)
\(444\) −4.35889 −0.206864
\(445\) 13.1613 0.623907
\(446\) −15.1849 −0.719027
\(447\) −14.9801 −0.708535
\(448\) −40.6373 −1.91993
\(449\) 11.0092 0.519559 0.259779 0.965668i \(-0.416350\pi\)
0.259779 + 0.965668i \(0.416350\pi\)
\(450\) −9.19589 −0.433498
\(451\) −43.3535 −2.04144
\(452\) −1.68262 −0.0791439
\(453\) −23.9077 −1.12328
\(454\) 3.19271 0.149841
\(455\) 7.62476 0.357454
\(456\) −22.1294 −1.03630
\(457\) −19.3983 −0.907417 −0.453708 0.891150i \(-0.649899\pi\)
−0.453708 + 0.891150i \(0.649899\pi\)
\(458\) −36.3713 −1.69952
\(459\) 53.1488 2.48078
\(460\) −0.245090 −0.0114274
\(461\) 23.7034 1.10398 0.551988 0.833852i \(-0.313869\pi\)
0.551988 + 0.833852i \(0.313869\pi\)
\(462\) −99.1163 −4.61131
\(463\) −19.7966 −0.920026 −0.460013 0.887912i \(-0.652155\pi\)
−0.460013 + 0.887912i \(0.652155\pi\)
\(464\) 27.5664 1.27974
\(465\) 7.68247 0.356266
\(466\) −31.1133 −1.44130
\(467\) 24.7579 1.14566 0.572829 0.819675i \(-0.305846\pi\)
0.572829 + 0.819675i \(0.305846\pi\)
\(468\) −2.54295 −0.117548
\(469\) −66.5631 −3.07360
\(470\) 9.95558 0.459217
\(471\) 26.2586 1.20993
\(472\) −39.5825 −1.82193
\(473\) −12.9154 −0.593849
\(474\) −18.3936 −0.844844
\(475\) 2.37172 0.108822
\(476\) −4.57157 −0.209538
\(477\) 14.4158 0.660052
\(478\) −36.2974 −1.66020
\(479\) 14.5018 0.662603 0.331302 0.943525i \(-0.392512\pi\)
0.331302 + 0.943525i \(0.392512\pi\)
\(480\) −4.00240 −0.182684
\(481\) −9.99277 −0.455631
\(482\) −18.6939 −0.851483
\(483\) −15.9673 −0.726538
\(484\) −3.28897 −0.149499
\(485\) 17.4022 0.790192
\(486\) 26.1664 1.18693
\(487\) 33.3055 1.50922 0.754609 0.656174i \(-0.227826\pi\)
0.754609 + 0.656174i \(0.227826\pi\)
\(488\) −34.0660 −1.54210
\(489\) 71.7202 3.24330
\(490\) 19.8164 0.895213
\(491\) 19.5046 0.880232 0.440116 0.897941i \(-0.354937\pi\)
0.440116 + 0.897941i \(0.354937\pi\)
\(492\) −6.09800 −0.274919
\(493\) 34.0985 1.53572
\(494\) −5.14956 −0.231690
\(495\) −34.9028 −1.56877
\(496\) −8.53680 −0.383314
\(497\) −39.6620 −1.77908
\(498\) 41.1295 1.84306
\(499\) −21.8187 −0.976741 −0.488370 0.872637i \(-0.662408\pi\)
−0.488370 + 0.872637i \(0.662408\pi\)
\(500\) 0.225946 0.0101046
\(501\) 12.9608 0.579047
\(502\) −25.0144 −1.11645
\(503\) −32.2929 −1.43987 −0.719935 0.694041i \(-0.755829\pi\)
−0.719935 + 0.694041i \(0.755829\pi\)
\(504\) −95.7439 −4.26477
\(505\) 8.96048 0.398736
\(506\) 7.30389 0.324697
\(507\) 32.5493 1.44556
\(508\) 3.39831 0.150776
\(509\) 14.0154 0.621220 0.310610 0.950537i \(-0.399467\pi\)
0.310610 + 0.950537i \(0.399467\pi\)
\(510\) 18.1322 0.802907
\(511\) −22.5599 −0.997990
\(512\) 25.1838 1.11298
\(513\) −29.1406 −1.28659
\(514\) 23.3838 1.03141
\(515\) 6.55858 0.289005
\(516\) −1.81664 −0.0799733
\(517\) 37.7862 1.66184
\(518\) −38.1899 −1.67797
\(519\) −19.9284 −0.874758
\(520\) −4.83305 −0.211943
\(521\) 7.64852 0.335088 0.167544 0.985865i \(-0.446416\pi\)
0.167544 + 0.985865i \(0.446416\pi\)
\(522\) 72.4887 3.17275
\(523\) 19.7800 0.864919 0.432459 0.901653i \(-0.357646\pi\)
0.432459 + 0.901653i \(0.357646\pi\)
\(524\) 1.14039 0.0498182
\(525\) 14.7201 0.642439
\(526\) 13.0516 0.569075
\(527\) −10.5597 −0.459987
\(528\) 55.6367 2.42128
\(529\) −21.8234 −0.948842
\(530\) 2.78106 0.120802
\(531\) −92.1755 −4.00008
\(532\) 2.50652 0.108671
\(533\) −13.9797 −0.605528
\(534\) −55.1686 −2.38738
\(535\) −0.962257 −0.0416020
\(536\) 42.1919 1.82241
\(537\) −19.4528 −0.839451
\(538\) −6.52529 −0.281325
\(539\) 75.2127 3.23964
\(540\) −2.77613 −0.119466
\(541\) 32.0621 1.37846 0.689229 0.724544i \(-0.257950\pi\)
0.689229 + 0.724544i \(0.257950\pi\)
\(542\) 10.4375 0.448328
\(543\) 67.1344 2.88101
\(544\) 5.50136 0.235869
\(545\) 0.925856 0.0396593
\(546\) −31.9608 −1.36780
\(547\) 39.9796 1.70940 0.854702 0.519118i \(-0.173740\pi\)
0.854702 + 0.519118i \(0.173740\pi\)
\(548\) −4.03658 −0.172434
\(549\) −79.3293 −3.38569
\(550\) −6.73339 −0.287113
\(551\) −18.6956 −0.796460
\(552\) 10.1211 0.430782
\(553\) 20.5247 0.872798
\(554\) −19.2991 −0.819942
\(555\) −19.2917 −0.818888
\(556\) −2.95392 −0.125274
\(557\) −6.03776 −0.255828 −0.127914 0.991785i \(-0.540828\pi\)
−0.127914 + 0.991785i \(0.540828\pi\)
\(558\) −22.4484 −0.950319
\(559\) −4.16466 −0.176146
\(560\) −16.3571 −0.691212
\(561\) 68.8204 2.90560
\(562\) −15.9506 −0.672836
\(563\) 6.16676 0.259898 0.129949 0.991521i \(-0.458519\pi\)
0.129949 + 0.991521i \(0.458519\pi\)
\(564\) 5.31492 0.223798
\(565\) −7.44701 −0.313298
\(566\) 0.00959891 0.000403472 0
\(567\) −83.9817 −3.52690
\(568\) 25.1403 1.05486
\(569\) 6.94361 0.291091 0.145546 0.989352i \(-0.453506\pi\)
0.145546 + 0.989352i \(0.453506\pi\)
\(570\) −9.94158 −0.416407
\(571\) 25.3313 1.06008 0.530040 0.847972i \(-0.322177\pi\)
0.530040 + 0.847972i \(0.322177\pi\)
\(572\) −1.86199 −0.0778539
\(573\) 53.0167 2.21481
\(574\) −53.4269 −2.23000
\(575\) −1.08473 −0.0452362
\(576\) 59.9836 2.49932
\(577\) −5.04835 −0.210165 −0.105083 0.994463i \(-0.533511\pi\)
−0.105083 + 0.994463i \(0.533511\pi\)
\(578\) −2.28006 −0.0948380
\(579\) −56.7839 −2.35986
\(580\) −1.78107 −0.0739550
\(581\) −45.8949 −1.90404
\(582\) −72.9450 −3.02367
\(583\) 10.5555 0.437163
\(584\) 14.2999 0.591733
\(585\) −11.2547 −0.465324
\(586\) −12.7303 −0.525882
\(587\) 1.41615 0.0584509 0.0292255 0.999573i \(-0.490696\pi\)
0.0292255 + 0.999573i \(0.490696\pi\)
\(588\) 10.5792 0.436280
\(589\) 5.78969 0.238560
\(590\) −17.7823 −0.732087
\(591\) 75.9962 3.12606
\(592\) 21.4370 0.881057
\(593\) 37.5146 1.54054 0.770270 0.637718i \(-0.220122\pi\)
0.770270 + 0.637718i \(0.220122\pi\)
\(594\) 82.7312 3.39450
\(595\) −20.2330 −0.829473
\(596\) −1.07550 −0.0440543
\(597\) −58.2694 −2.38481
\(598\) 2.35520 0.0963111
\(599\) 26.8331 1.09637 0.548185 0.836357i \(-0.315319\pi\)
0.548185 + 0.836357i \(0.315319\pi\)
\(600\) −9.33054 −0.380918
\(601\) 9.40978 0.383833 0.191916 0.981411i \(-0.438530\pi\)
0.191916 + 0.981411i \(0.438530\pi\)
\(602\) −15.9163 −0.648700
\(603\) 98.2520 4.00113
\(604\) −1.71646 −0.0698417
\(605\) −14.5565 −0.591804
\(606\) −37.5598 −1.52576
\(607\) −36.4057 −1.47766 −0.738830 0.673892i \(-0.764621\pi\)
−0.738830 + 0.673892i \(0.764621\pi\)
\(608\) −3.01630 −0.122327
\(609\) −116.035 −4.70196
\(610\) −15.3041 −0.619644
\(611\) 12.1845 0.492931
\(612\) 6.74797 0.272771
\(613\) 40.1766 1.62272 0.811358 0.584549i \(-0.198729\pi\)
0.811358 + 0.584549i \(0.198729\pi\)
\(614\) −8.22854 −0.332077
\(615\) −26.9888 −1.08829
\(616\) −70.1053 −2.82462
\(617\) 19.8434 0.798866 0.399433 0.916762i \(-0.369207\pi\)
0.399433 + 0.916762i \(0.369207\pi\)
\(618\) −27.4917 −1.10588
\(619\) −15.0648 −0.605505 −0.302752 0.953069i \(-0.597905\pi\)
−0.302752 + 0.953069i \(0.597905\pi\)
\(620\) 0.551566 0.0221514
\(621\) 13.3277 0.534823
\(622\) −2.54288 −0.101960
\(623\) 61.5605 2.46637
\(624\) 17.9405 0.718195
\(625\) 1.00000 0.0400000
\(626\) 9.75448 0.389868
\(627\) −37.7331 −1.50691
\(628\) 1.88524 0.0752294
\(629\) 26.5168 1.05729
\(630\) −43.0127 −1.71367
\(631\) 17.0579 0.679062 0.339531 0.940595i \(-0.389732\pi\)
0.339531 + 0.940595i \(0.389732\pi\)
\(632\) −13.0098 −0.517503
\(633\) −7.64624 −0.303911
\(634\) −2.08952 −0.0829853
\(635\) 15.0404 0.596859
\(636\) 1.48471 0.0588724
\(637\) 24.2529 0.960936
\(638\) 53.0775 2.10136
\(639\) 58.5440 2.31597
\(640\) 9.02836 0.356877
\(641\) −30.5408 −1.20629 −0.603145 0.797631i \(-0.706086\pi\)
−0.603145 + 0.797631i \(0.706086\pi\)
\(642\) 4.03351 0.159190
\(643\) 2.11400 0.0833680 0.0416840 0.999131i \(-0.486728\pi\)
0.0416840 + 0.999131i \(0.486728\pi\)
\(644\) −1.14638 −0.0451736
\(645\) −8.04017 −0.316581
\(646\) 13.6648 0.537636
\(647\) −9.90786 −0.389518 −0.194759 0.980851i \(-0.562393\pi\)
−0.194759 + 0.980851i \(0.562393\pi\)
\(648\) 53.2329 2.09119
\(649\) −67.4925 −2.64931
\(650\) −2.17123 −0.0851628
\(651\) 35.9338 1.40836
\(652\) 5.14917 0.201657
\(653\) −36.5645 −1.43088 −0.715439 0.698675i \(-0.753773\pi\)
−0.715439 + 0.698675i \(0.753773\pi\)
\(654\) −3.88093 −0.151756
\(655\) 5.04718 0.197210
\(656\) 29.9900 1.17091
\(657\) 33.3000 1.29916
\(658\) 46.5660 1.81533
\(659\) 29.4584 1.14754 0.573768 0.819018i \(-0.305481\pi\)
0.573768 + 0.819018i \(0.305481\pi\)
\(660\) −3.59471 −0.139924
\(661\) 32.9103 1.28006 0.640030 0.768350i \(-0.278922\pi\)
0.640030 + 0.768350i \(0.278922\pi\)
\(662\) 45.6443 1.77402
\(663\) 22.1917 0.861854
\(664\) 29.0911 1.12895
\(665\) 11.0934 0.430185
\(666\) 56.3711 2.18433
\(667\) 8.55061 0.331081
\(668\) 0.930526 0.0360031
\(669\) −35.8788 −1.38716
\(670\) 18.9546 0.732280
\(671\) −58.0863 −2.24240
\(672\) −18.7208 −0.722169
\(673\) 21.2481 0.819055 0.409528 0.912298i \(-0.365693\pi\)
0.409528 + 0.912298i \(0.365693\pi\)
\(674\) 13.7566 0.529884
\(675\) −12.2867 −0.472916
\(676\) 2.33688 0.0898801
\(677\) −31.1394 −1.19678 −0.598392 0.801203i \(-0.704194\pi\)
−0.598392 + 0.801203i \(0.704194\pi\)
\(678\) 31.2158 1.19883
\(679\) 81.3966 3.12371
\(680\) 12.8250 0.491815
\(681\) 7.54369 0.289075
\(682\) −16.4371 −0.629411
\(683\) 7.31863 0.280040 0.140020 0.990149i \(-0.455283\pi\)
0.140020 + 0.990149i \(0.455283\pi\)
\(684\) −3.69980 −0.141465
\(685\) −17.8652 −0.682595
\(686\) 49.0789 1.87384
\(687\) −85.9379 −3.27873
\(688\) 8.93427 0.340616
\(689\) 3.40369 0.129670
\(690\) 4.54687 0.173096
\(691\) 37.7841 1.43738 0.718688 0.695332i \(-0.244743\pi\)
0.718688 + 0.695332i \(0.244743\pi\)
\(692\) −1.43076 −0.0543895
\(693\) −163.254 −6.20150
\(694\) −48.2186 −1.83035
\(695\) −13.0736 −0.495909
\(696\) 73.5501 2.78791
\(697\) 37.0965 1.40513
\(698\) −16.0388 −0.607079
\(699\) −73.5143 −2.78057
\(700\) 1.05684 0.0399446
\(701\) −21.4200 −0.809024 −0.404512 0.914533i \(-0.632559\pi\)
−0.404512 + 0.914533i \(0.632559\pi\)
\(702\) 26.6773 1.00687
\(703\) −14.5387 −0.548337
\(704\) 43.9210 1.65534
\(705\) 23.5230 0.885926
\(706\) −11.7460 −0.442068
\(707\) 41.9116 1.57625
\(708\) −9.49333 −0.356781
\(709\) 30.4194 1.14242 0.571212 0.820803i \(-0.306474\pi\)
0.571212 + 0.820803i \(0.306474\pi\)
\(710\) 11.2942 0.423864
\(711\) −30.2959 −1.13619
\(712\) −39.0209 −1.46237
\(713\) −2.64797 −0.0991672
\(714\) 84.8111 3.17398
\(715\) −8.24088 −0.308192
\(716\) −1.39662 −0.0521942
\(717\) −85.7631 −3.20288
\(718\) 10.3144 0.384929
\(719\) −37.7154 −1.40655 −0.703274 0.710919i \(-0.748279\pi\)
−0.703274 + 0.710919i \(0.748279\pi\)
\(720\) 24.1442 0.899802
\(721\) 30.6770 1.14247
\(722\) 17.8146 0.662990
\(723\) −44.1697 −1.64269
\(724\) 4.81994 0.179132
\(725\) −7.88273 −0.292757
\(726\) 61.0166 2.26454
\(727\) 4.05298 0.150317 0.0751583 0.997172i \(-0.476054\pi\)
0.0751583 + 0.997172i \(0.476054\pi\)
\(728\) −22.6060 −0.837835
\(729\) 7.96118 0.294859
\(730\) 6.42418 0.237769
\(731\) 11.0513 0.408748
\(732\) −8.17028 −0.301982
\(733\) −12.0939 −0.446699 −0.223350 0.974738i \(-0.571699\pi\)
−0.223350 + 0.974738i \(0.571699\pi\)
\(734\) 38.2953 1.41351
\(735\) 46.8220 1.72705
\(736\) 1.37953 0.0508503
\(737\) 71.9418 2.65001
\(738\) 78.8620 2.90295
\(739\) 52.6129 1.93540 0.967699 0.252110i \(-0.0811243\pi\)
0.967699 + 0.252110i \(0.0811243\pi\)
\(740\) −1.38506 −0.0509156
\(741\) −12.1673 −0.446978
\(742\) 13.0081 0.477542
\(743\) −26.3937 −0.968289 −0.484145 0.874988i \(-0.660869\pi\)
−0.484145 + 0.874988i \(0.660869\pi\)
\(744\) −22.7771 −0.835050
\(745\) −4.76000 −0.174393
\(746\) −14.0267 −0.513553
\(747\) 67.7442 2.47863
\(748\) 4.94098 0.180660
\(749\) −4.50084 −0.164457
\(750\) −4.19172 −0.153060
\(751\) 23.5431 0.859099 0.429549 0.903043i \(-0.358672\pi\)
0.429549 + 0.903043i \(0.358672\pi\)
\(752\) −26.1388 −0.953184
\(753\) −59.1037 −2.15386
\(754\) 17.1153 0.623301
\(755\) −7.59676 −0.276474
\(756\) −12.9850 −0.472261
\(757\) −38.4230 −1.39651 −0.698255 0.715849i \(-0.746040\pi\)
−0.698255 + 0.715849i \(0.746040\pi\)
\(758\) 36.1997 1.31483
\(759\) 17.2576 0.626410
\(760\) −7.03171 −0.255067
\(761\) 48.1681 1.74609 0.873046 0.487637i \(-0.162141\pi\)
0.873046 + 0.487637i \(0.162141\pi\)
\(762\) −63.0450 −2.28388
\(763\) 4.33058 0.156778
\(764\) 3.80635 0.137709
\(765\) 29.8654 1.07979
\(766\) −16.7788 −0.606243
\(767\) −21.7635 −0.785834
\(768\) 16.8397 0.607651
\(769\) 21.7647 0.784857 0.392428 0.919783i \(-0.371635\pi\)
0.392428 + 0.919783i \(0.371635\pi\)
\(770\) −31.4946 −1.13499
\(771\) 55.2510 1.98982
\(772\) −4.07682 −0.146728
\(773\) 14.7284 0.529743 0.264872 0.964284i \(-0.414670\pi\)
0.264872 + 0.964284i \(0.414670\pi\)
\(774\) 23.4936 0.844461
\(775\) 2.44114 0.0876883
\(776\) −51.5943 −1.85213
\(777\) −90.2347 −3.23715
\(778\) 9.69942 0.347741
\(779\) −20.3394 −0.728733
\(780\) −1.15914 −0.0415040
\(781\) 42.8669 1.53390
\(782\) −6.24974 −0.223490
\(783\) 96.8528 3.46124
\(784\) −52.0288 −1.85817
\(785\) 8.34378 0.297802
\(786\) −21.1564 −0.754623
\(787\) 0.908663 0.0323903 0.0161952 0.999869i \(-0.494845\pi\)
0.0161952 + 0.999869i \(0.494845\pi\)
\(788\) 5.45617 0.194368
\(789\) 30.8381 1.09786
\(790\) −5.84463 −0.207943
\(791\) −34.8325 −1.23850
\(792\) 103.481 3.67702
\(793\) −18.7304 −0.665136
\(794\) −20.0633 −0.712021
\(795\) 6.57106 0.233052
\(796\) −4.18347 −0.148279
\(797\) 0.320200 0.0113421 0.00567104 0.999984i \(-0.498195\pi\)
0.00567104 + 0.999984i \(0.498195\pi\)
\(798\) −46.5005 −1.64610
\(799\) −32.3327 −1.14385
\(800\) −1.27178 −0.0449642
\(801\) −90.8678 −3.21066
\(802\) −1.33194 −0.0470323
\(803\) 24.3828 0.860452
\(804\) 10.1192 0.356875
\(805\) −5.07368 −0.178824
\(806\) −5.30029 −0.186695
\(807\) −15.4179 −0.542736
\(808\) −26.5662 −0.934596
\(809\) 5.59585 0.196740 0.0983699 0.995150i \(-0.468637\pi\)
0.0983699 + 0.995150i \(0.468637\pi\)
\(810\) 23.9147 0.840278
\(811\) 0.469348 0.0164810 0.00824051 0.999966i \(-0.497377\pi\)
0.00824051 + 0.999966i \(0.497377\pi\)
\(812\) −8.33075 −0.292352
\(813\) 24.6616 0.864919
\(814\) 41.2759 1.44672
\(815\) 22.7894 0.798278
\(816\) −47.6069 −1.66657
\(817\) −6.05926 −0.211987
\(818\) 31.4835 1.10079
\(819\) −52.6425 −1.83948
\(820\) −1.93767 −0.0676662
\(821\) 6.52091 0.227581 0.113791 0.993505i \(-0.463701\pi\)
0.113791 + 0.993505i \(0.463701\pi\)
\(822\) 74.8860 2.61195
\(823\) −23.7373 −0.827430 −0.413715 0.910406i \(-0.635769\pi\)
−0.413715 + 0.910406i \(0.635769\pi\)
\(824\) −19.4450 −0.677398
\(825\) −15.9096 −0.553901
\(826\) −83.1747 −2.89402
\(827\) 47.1198 1.63852 0.819259 0.573424i \(-0.194385\pi\)
0.819259 + 0.573424i \(0.194385\pi\)
\(828\) 1.69214 0.0588058
\(829\) −4.22231 −0.146647 −0.0733234 0.997308i \(-0.523361\pi\)
−0.0733234 + 0.997308i \(0.523361\pi\)
\(830\) 13.0691 0.453634
\(831\) −45.5998 −1.58184
\(832\) 14.1627 0.491002
\(833\) −64.3575 −2.22986
\(834\) 54.8008 1.89760
\(835\) 4.11836 0.142522
\(836\) −2.70906 −0.0936947
\(837\) −29.9936 −1.03673
\(838\) −12.8501 −0.443898
\(839\) 1.91583 0.0661419 0.0330710 0.999453i \(-0.489471\pi\)
0.0330710 + 0.999453i \(0.489471\pi\)
\(840\) −43.6425 −1.50581
\(841\) 33.1374 1.14267
\(842\) −14.9208 −0.514205
\(843\) −37.6880 −1.29804
\(844\) −0.548964 −0.0188961
\(845\) 10.3427 0.355798
\(846\) −68.7349 −2.36315
\(847\) −68.0861 −2.33947
\(848\) −7.30180 −0.250745
\(849\) 0.0226802 0.000778383 0
\(850\) 5.76158 0.197621
\(851\) 6.64940 0.227939
\(852\) 6.02956 0.206569
\(853\) −0.367949 −0.0125983 −0.00629916 0.999980i \(-0.502005\pi\)
−0.00629916 + 0.999980i \(0.502005\pi\)
\(854\) −71.5829 −2.44952
\(855\) −16.3747 −0.560003
\(856\) 2.85292 0.0975107
\(857\) −1.29518 −0.0442424 −0.0221212 0.999755i \(-0.507042\pi\)
−0.0221212 + 0.999755i \(0.507042\pi\)
\(858\) 34.5435 1.17929
\(859\) −39.6041 −1.35127 −0.675637 0.737235i \(-0.736131\pi\)
−0.675637 + 0.737235i \(0.736131\pi\)
\(860\) −0.577246 −0.0196839
\(861\) −126.237 −4.30213
\(862\) −26.4306 −0.900229
\(863\) 3.56282 0.121280 0.0606398 0.998160i \(-0.480686\pi\)
0.0606398 + 0.998160i \(0.480686\pi\)
\(864\) 15.6260 0.531607
\(865\) −6.33232 −0.215305
\(866\) 8.70002 0.295639
\(867\) −5.38731 −0.182963
\(868\) 2.57988 0.0875669
\(869\) −22.1832 −0.752513
\(870\) 33.0422 1.12024
\(871\) 23.1982 0.786041
\(872\) −2.74499 −0.0929572
\(873\) −120.147 −4.06637
\(874\) 3.42663 0.115907
\(875\) 4.67738 0.158124
\(876\) 3.42963 0.115877
\(877\) 49.2908 1.66443 0.832216 0.554451i \(-0.187072\pi\)
0.832216 + 0.554451i \(0.187072\pi\)
\(878\) 25.5935 0.863738
\(879\) −30.0790 −1.01454
\(880\) 17.6788 0.595952
\(881\) −0.118580 −0.00399505 −0.00199753 0.999998i \(-0.500636\pi\)
−0.00199753 + 0.999998i \(0.500636\pi\)
\(882\) −136.815 −4.60681
\(883\) −10.4373 −0.351242 −0.175621 0.984458i \(-0.556193\pi\)
−0.175621 + 0.984458i \(0.556193\pi\)
\(884\) 1.59326 0.0535871
\(885\) −42.0159 −1.41235
\(886\) 2.34919 0.0789227
\(887\) −23.4582 −0.787648 −0.393824 0.919186i \(-0.628848\pi\)
−0.393824 + 0.919186i \(0.628848\pi\)
\(888\) 57.1965 1.91939
\(889\) 70.3496 2.35945
\(890\) −17.5300 −0.587609
\(891\) 90.7680 3.04084
\(892\) −2.57593 −0.0862485
\(893\) 17.7275 0.593227
\(894\) 19.9526 0.667314
\(895\) −6.18122 −0.206615
\(896\) 42.2291 1.41077
\(897\) 5.56484 0.185804
\(898\) −14.6636 −0.489331
\(899\) −19.2428 −0.641785
\(900\) −1.55997 −0.0519989
\(901\) −9.03203 −0.300901
\(902\) 57.7441 1.92267
\(903\) −37.6069 −1.25148
\(904\) 22.0790 0.734337
\(905\) 21.3322 0.709108
\(906\) 31.8435 1.05793
\(907\) 27.9135 0.926854 0.463427 0.886135i \(-0.346620\pi\)
0.463427 + 0.886135i \(0.346620\pi\)
\(908\) 0.541602 0.0179737
\(909\) −61.8645 −2.05192
\(910\) −10.1557 −0.336658
\(911\) 5.66976 0.187847 0.0939237 0.995579i \(-0.470059\pi\)
0.0939237 + 0.995579i \(0.470059\pi\)
\(912\) 26.1020 0.864325
\(913\) 49.6034 1.64163
\(914\) 25.8374 0.854624
\(915\) −36.1603 −1.19542
\(916\) −6.16994 −0.203860
\(917\) 23.6076 0.779591
\(918\) −70.7909 −2.33645
\(919\) 11.4842 0.378828 0.189414 0.981897i \(-0.439341\pi\)
0.189414 + 0.981897i \(0.439341\pi\)
\(920\) 3.21602 0.106029
\(921\) −19.4423 −0.640647
\(922\) −31.5714 −1.03975
\(923\) 13.8228 0.454982
\(924\) −16.8138 −0.553134
\(925\) −6.13003 −0.201554
\(926\) 26.3678 0.866500
\(927\) −45.2814 −1.48724
\(928\) 10.0251 0.329090
\(929\) 8.31839 0.272918 0.136459 0.990646i \(-0.456428\pi\)
0.136459 + 0.990646i \(0.456428\pi\)
\(930\) −10.2326 −0.335539
\(931\) 35.2861 1.15646
\(932\) −5.27798 −0.172886
\(933\) −6.00830 −0.196703
\(934\) −32.9759 −1.07900
\(935\) 21.8680 0.715159
\(936\) 33.3681 1.09067
\(937\) 28.1015 0.918037 0.459019 0.888427i \(-0.348201\pi\)
0.459019 + 0.888427i \(0.348201\pi\)
\(938\) 88.6578 2.89478
\(939\) 23.0478 0.752137
\(940\) 1.68884 0.0550838
\(941\) 46.5808 1.51849 0.759245 0.650805i \(-0.225568\pi\)
0.759245 + 0.650805i \(0.225568\pi\)
\(942\) −34.9748 −1.13954
\(943\) 9.30239 0.302928
\(944\) 46.6883 1.51957
\(945\) −57.4696 −1.86949
\(946\) 17.2024 0.559300
\(947\) 32.9615 1.07111 0.535553 0.844502i \(-0.320103\pi\)
0.535553 + 0.844502i \(0.320103\pi\)
\(948\) −3.12023 −0.101340
\(949\) 7.86244 0.255226
\(950\) −3.15898 −0.102491
\(951\) −4.93709 −0.160096
\(952\) 59.9872 1.94420
\(953\) −29.7819 −0.964729 −0.482365 0.875971i \(-0.660222\pi\)
−0.482365 + 0.875971i \(0.660222\pi\)
\(954\) −19.2009 −0.621651
\(955\) 16.8463 0.545133
\(956\) −6.15739 −0.199144
\(957\) 125.411 4.05396
\(958\) −19.3154 −0.624054
\(959\) −83.5624 −2.69837
\(960\) 27.3420 0.882460
\(961\) −25.0408 −0.807769
\(962\) 13.3097 0.429123
\(963\) 6.64357 0.214086
\(964\) −3.17118 −0.102137
\(965\) −18.0433 −0.580836
\(966\) 21.2674 0.684268
\(967\) −7.62327 −0.245148 −0.122574 0.992459i \(-0.539115\pi\)
−0.122574 + 0.992459i \(0.539115\pi\)
\(968\) 43.1573 1.38713
\(969\) 32.2872 1.03721
\(970\) −23.1786 −0.744220
\(971\) 19.5160 0.626298 0.313149 0.949704i \(-0.398616\pi\)
0.313149 + 0.949704i \(0.398616\pi\)
\(972\) 4.43880 0.142375
\(973\) −61.1501 −1.96038
\(974\) −44.3609 −1.42141
\(975\) −5.13017 −0.164297
\(976\) 40.1815 1.28618
\(977\) 27.4804 0.879176 0.439588 0.898200i \(-0.355125\pi\)
0.439588 + 0.898200i \(0.355125\pi\)
\(978\) −95.5267 −3.05461
\(979\) −66.5350 −2.12647
\(980\) 3.36160 0.107382
\(981\) −6.39225 −0.204089
\(982\) −25.9789 −0.829021
\(983\) −17.4876 −0.557769 −0.278884 0.960325i \(-0.589965\pi\)
−0.278884 + 0.960325i \(0.589965\pi\)
\(984\) 80.0167 2.55084
\(985\) 24.1481 0.769422
\(986\) −45.4170 −1.44637
\(987\) 110.026 3.50216
\(988\) −0.873557 −0.0277915
\(989\) 2.77126 0.0881209
\(990\) 46.4884 1.47750
\(991\) −3.09511 −0.0983195 −0.0491598 0.998791i \(-0.515654\pi\)
−0.0491598 + 0.998791i \(0.515654\pi\)
\(992\) −3.10459 −0.0985709
\(993\) 107.848 3.42245
\(994\) 52.8273 1.67558
\(995\) −18.5154 −0.586976
\(996\) 6.97710 0.221078
\(997\) −18.9149 −0.599041 −0.299521 0.954090i \(-0.596827\pi\)
−0.299521 + 0.954090i \(0.596827\pi\)
\(998\) 29.0612 0.919915
\(999\) 75.3178 2.38295
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 2005.2.a.f.1.9 37
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2005.2.a.f.1.9 37 1.1 even 1 trivial