Properties

Label 8011.2.a.a.1.10
Level $8011$
Weight $2$
Character 8011.1
Self dual yes
Analytic conductor $63.968$
Analytic rank $1$
Dimension $309$
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] = [8011,2,Mod(1,8011)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8011, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8011.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8011 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8011.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: \(63.9681570592\)
Analytic rank: \(1\)
Dimension: \(309\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 8011.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.67443 q^{2} -1.89818 q^{3} +5.15257 q^{4} -2.43152 q^{5} +5.07654 q^{6} +2.86566 q^{7} -8.43133 q^{8} +0.603070 q^{9} +O(q^{10})\) \(q-2.67443 q^{2} -1.89818 q^{3} +5.15257 q^{4} -2.43152 q^{5} +5.07654 q^{6} +2.86566 q^{7} -8.43133 q^{8} +0.603070 q^{9} +6.50294 q^{10} +4.27299 q^{11} -9.78049 q^{12} +0.189678 q^{13} -7.66401 q^{14} +4.61546 q^{15} +12.2439 q^{16} +1.12106 q^{17} -1.61287 q^{18} -7.55968 q^{19} -12.5286 q^{20} -5.43953 q^{21} -11.4278 q^{22} -7.54256 q^{23} +16.0041 q^{24} +0.912304 q^{25} -0.507280 q^{26} +4.54979 q^{27} +14.7655 q^{28} +6.13120 q^{29} -12.3437 q^{30} +3.70580 q^{31} -15.8827 q^{32} -8.11087 q^{33} -2.99819 q^{34} -6.96792 q^{35} +3.10736 q^{36} +8.03245 q^{37} +20.2178 q^{38} -0.360042 q^{39} +20.5010 q^{40} -3.65263 q^{41} +14.5476 q^{42} +10.2794 q^{43} +22.0169 q^{44} -1.46638 q^{45} +20.1721 q^{46} +4.94177 q^{47} -23.2410 q^{48} +1.21202 q^{49} -2.43989 q^{50} -2.12796 q^{51} +0.977328 q^{52} -8.88480 q^{53} -12.1681 q^{54} -10.3899 q^{55} -24.1614 q^{56} +14.3496 q^{57} -16.3975 q^{58} -7.85765 q^{59} +23.7815 q^{60} +3.20740 q^{61} -9.91090 q^{62} +1.72819 q^{63} +17.9894 q^{64} -0.461206 q^{65} +21.6920 q^{66} +8.07005 q^{67} +5.77633 q^{68} +14.3171 q^{69} +18.6352 q^{70} +1.63264 q^{71} -5.08468 q^{72} -3.90267 q^{73} -21.4822 q^{74} -1.73171 q^{75} -38.9518 q^{76} +12.2449 q^{77} +0.962906 q^{78} -16.1114 q^{79} -29.7712 q^{80} -10.4455 q^{81} +9.76870 q^{82} -7.98861 q^{83} -28.0276 q^{84} -2.72588 q^{85} -27.4916 q^{86} -11.6381 q^{87} -36.0270 q^{88} -15.0225 q^{89} +3.92172 q^{90} +0.543552 q^{91} -38.8636 q^{92} -7.03426 q^{93} -13.2164 q^{94} +18.3815 q^{95} +30.1481 q^{96} +5.56650 q^{97} -3.24147 q^{98} +2.57691 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9} - 23 q^{10} - 72 q^{11} - 42 q^{12} - 57 q^{13} - 77 q^{14} - 44 q^{15} + 205 q^{16} - 86 q^{17} - 82 q^{18} - 58 q^{19} - 134 q^{20} - 123 q^{21} - 31 q^{22} - 94 q^{23} - 84 q^{24} + 225 q^{25} - 92 q^{26} - 48 q^{27} - 36 q^{28} - 345 q^{29} - 85 q^{30} - 36 q^{31} - 199 q^{32} - 56 q^{33} - 28 q^{34} - 168 q^{35} + 65 q^{36} - 79 q^{37} - 66 q^{38} - 145 q^{39} - 54 q^{40} - 176 q^{41} - 48 q^{42} - 58 q^{43} - 194 q^{44} - 192 q^{45} - 44 q^{46} - 82 q^{47} - 81 q^{48} + 186 q^{49} - 206 q^{50} - 145 q^{51} - 86 q^{52} - 223 q^{53} - 117 q^{54} - 58 q^{55} - 216 q^{56} - 124 q^{57} - 151 q^{59} - 91 q^{60} - 184 q^{61} - 124 q^{62} - 78 q^{63} + 101 q^{64} - 194 q^{65} - 112 q^{66} - 53 q^{67} - 182 q^{68} - 243 q^{69} - 193 q^{71} - 208 q^{72} - 69 q^{73} - 236 q^{74} - 62 q^{75} - 142 q^{76} - 324 q^{77} - 20 q^{78} - 91 q^{79} - 223 q^{80} - 27 q^{81} + 2 q^{82} - 117 q^{83} - 157 q^{84} - 171 q^{85} - 203 q^{86} - 69 q^{87} - 36 q^{88} - 172 q^{89} - 10 q^{90} - 84 q^{91} - 226 q^{92} - 220 q^{93} - 96 q^{94} - 166 q^{95} - 118 q^{96} - 12 q^{97} - 116 q^{98} - 154 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.67443 −1.89111 −0.945554 0.325466i \(-0.894479\pi\)
−0.945554 + 0.325466i \(0.894479\pi\)
\(3\) −1.89818 −1.09591 −0.547956 0.836507i \(-0.684594\pi\)
−0.547956 + 0.836507i \(0.684594\pi\)
\(4\) 5.15257 2.57629
\(5\) −2.43152 −1.08741 −0.543705 0.839276i \(-0.682979\pi\)
−0.543705 + 0.839276i \(0.682979\pi\)
\(6\) 5.07654 2.07249
\(7\) 2.86566 1.08312 0.541559 0.840663i \(-0.317834\pi\)
0.541559 + 0.840663i \(0.317834\pi\)
\(8\) −8.43133 −2.98093
\(9\) 0.603070 0.201023
\(10\) 6.50294 2.05641
\(11\) 4.27299 1.28835 0.644177 0.764877i \(-0.277200\pi\)
0.644177 + 0.764877i \(0.277200\pi\)
\(12\) −9.78049 −2.82338
\(13\) 0.189678 0.0526071 0.0263036 0.999654i \(-0.491626\pi\)
0.0263036 + 0.999654i \(0.491626\pi\)
\(14\) −7.66401 −2.04829
\(15\) 4.61546 1.19171
\(16\) 12.2439 3.06096
\(17\) 1.12106 0.271896 0.135948 0.990716i \(-0.456592\pi\)
0.135948 + 0.990716i \(0.456592\pi\)
\(18\) −1.61287 −0.380156
\(19\) −7.55968 −1.73431 −0.867155 0.498038i \(-0.834054\pi\)
−0.867155 + 0.498038i \(0.834054\pi\)
\(20\) −12.5286 −2.80148
\(21\) −5.43953 −1.18700
\(22\) −11.4278 −2.43641
\(23\) −7.54256 −1.57273 −0.786367 0.617760i \(-0.788040\pi\)
−0.786367 + 0.617760i \(0.788040\pi\)
\(24\) 16.0041 3.26683
\(25\) 0.912304 0.182461
\(26\) −0.507280 −0.0994857
\(27\) 4.54979 0.875608
\(28\) 14.7655 2.79042
\(29\) 6.13120 1.13853 0.569267 0.822152i \(-0.307227\pi\)
0.569267 + 0.822152i \(0.307227\pi\)
\(30\) −12.3437 −2.25364
\(31\) 3.70580 0.665581 0.332791 0.943001i \(-0.392010\pi\)
0.332791 + 0.943001i \(0.392010\pi\)
\(32\) −15.8827 −2.80769
\(33\) −8.11087 −1.41192
\(34\) −2.99819 −0.514185
\(35\) −6.96792 −1.17779
\(36\) 3.10736 0.517893
\(37\) 8.03245 1.32053 0.660264 0.751034i \(-0.270445\pi\)
0.660264 + 0.751034i \(0.270445\pi\)
\(38\) 20.2178 3.27977
\(39\) −0.360042 −0.0576528
\(40\) 20.5010 3.24149
\(41\) −3.65263 −0.570445 −0.285223 0.958461i \(-0.592068\pi\)
−0.285223 + 0.958461i \(0.592068\pi\)
\(42\) 14.5476 2.24475
\(43\) 10.2794 1.56760 0.783798 0.621016i \(-0.213280\pi\)
0.783798 + 0.621016i \(0.213280\pi\)
\(44\) 22.0169 3.31917
\(45\) −1.46638 −0.218595
\(46\) 20.1721 2.97421
\(47\) 4.94177 0.720831 0.360415 0.932792i \(-0.382635\pi\)
0.360415 + 0.932792i \(0.382635\pi\)
\(48\) −23.2410 −3.35455
\(49\) 1.21202 0.173146
\(50\) −2.43989 −0.345053
\(51\) −2.12796 −0.297974
\(52\) 0.977328 0.135531
\(53\) −8.88480 −1.22042 −0.610211 0.792239i \(-0.708915\pi\)
−0.610211 + 0.792239i \(0.708915\pi\)
\(54\) −12.1681 −1.65587
\(55\) −10.3899 −1.40097
\(56\) −24.1614 −3.22870
\(57\) 14.3496 1.90065
\(58\) −16.3975 −2.15309
\(59\) −7.85765 −1.02298 −0.511489 0.859290i \(-0.670906\pi\)
−0.511489 + 0.859290i \(0.670906\pi\)
\(60\) 23.7815 3.07018
\(61\) 3.20740 0.410666 0.205333 0.978692i \(-0.434172\pi\)
0.205333 + 0.978692i \(0.434172\pi\)
\(62\) −9.91090 −1.25869
\(63\) 1.72819 0.217732
\(64\) 17.9894 2.24867
\(65\) −0.461206 −0.0572055
\(66\) 21.6920 2.67010
\(67\) 8.07005 0.985913 0.492957 0.870054i \(-0.335916\pi\)
0.492957 + 0.870054i \(0.335916\pi\)
\(68\) 5.77633 0.700482
\(69\) 14.3171 1.72358
\(70\) 18.6352 2.22734
\(71\) 1.63264 0.193759 0.0968796 0.995296i \(-0.469114\pi\)
0.0968796 + 0.995296i \(0.469114\pi\)
\(72\) −5.08468 −0.599235
\(73\) −3.90267 −0.456772 −0.228386 0.973571i \(-0.573345\pi\)
−0.228386 + 0.973571i \(0.573345\pi\)
\(74\) −21.4822 −2.49726
\(75\) −1.73171 −0.199961
\(76\) −38.9518 −4.46808
\(77\) 12.2449 1.39544
\(78\) 0.962906 0.109028
\(79\) −16.1114 −1.81267 −0.906336 0.422558i \(-0.861132\pi\)
−0.906336 + 0.422558i \(0.861132\pi\)
\(80\) −29.7712 −3.32852
\(81\) −10.4455 −1.16061
\(82\) 9.76870 1.07877
\(83\) −7.98861 −0.876864 −0.438432 0.898764i \(-0.644466\pi\)
−0.438432 + 0.898764i \(0.644466\pi\)
\(84\) −28.0276 −3.05806
\(85\) −2.72588 −0.295663
\(86\) −27.4916 −2.96449
\(87\) −11.6381 −1.24773
\(88\) −36.0270 −3.84049
\(89\) −15.0225 −1.59238 −0.796189 0.605048i \(-0.793154\pi\)
−0.796189 + 0.605048i \(0.793154\pi\)
\(90\) 3.92172 0.413386
\(91\) 0.543552 0.0569798
\(92\) −38.8636 −4.05181
\(93\) −7.03426 −0.729418
\(94\) −13.2164 −1.36317
\(95\) 18.3815 1.88591
\(96\) 30.1481 3.07698
\(97\) 5.56650 0.565192 0.282596 0.959239i \(-0.408804\pi\)
0.282596 + 0.959239i \(0.408804\pi\)
\(98\) −3.24147 −0.327438
\(99\) 2.57691 0.258989
\(100\) 4.70071 0.470071
\(101\) −2.09406 −0.208366 −0.104183 0.994558i \(-0.533223\pi\)
−0.104183 + 0.994558i \(0.533223\pi\)
\(102\) 5.69108 0.563501
\(103\) 9.41699 0.927883 0.463942 0.885866i \(-0.346435\pi\)
0.463942 + 0.885866i \(0.346435\pi\)
\(104\) −1.59924 −0.156818
\(105\) 13.2263 1.29076
\(106\) 23.7618 2.30795
\(107\) −5.75346 −0.556207 −0.278104 0.960551i \(-0.589706\pi\)
−0.278104 + 0.960551i \(0.589706\pi\)
\(108\) 23.4431 2.25582
\(109\) −5.94102 −0.569047 −0.284523 0.958669i \(-0.591835\pi\)
−0.284523 + 0.958669i \(0.591835\pi\)
\(110\) 27.7870 2.64938
\(111\) −15.2470 −1.44718
\(112\) 35.0868 3.31539
\(113\) −4.08957 −0.384714 −0.192357 0.981325i \(-0.561613\pi\)
−0.192357 + 0.981325i \(0.561613\pi\)
\(114\) −38.3770 −3.59434
\(115\) 18.3399 1.71021
\(116\) 31.5914 2.93319
\(117\) 0.114389 0.0105753
\(118\) 21.0147 1.93456
\(119\) 3.21257 0.294496
\(120\) −38.9145 −3.55239
\(121\) 7.25840 0.659855
\(122\) −8.57798 −0.776614
\(123\) 6.93333 0.625158
\(124\) 19.0944 1.71473
\(125\) 9.93933 0.889000
\(126\) −4.62193 −0.411754
\(127\) 13.1736 1.16896 0.584482 0.811407i \(-0.301298\pi\)
0.584482 + 0.811407i \(0.301298\pi\)
\(128\) −16.3459 −1.44479
\(129\) −19.5121 −1.71795
\(130\) 1.23346 0.108182
\(131\) −10.7144 −0.936121 −0.468061 0.883696i \(-0.655047\pi\)
−0.468061 + 0.883696i \(0.655047\pi\)
\(132\) −41.7919 −3.63752
\(133\) −21.6635 −1.87846
\(134\) −21.5828 −1.86447
\(135\) −11.0629 −0.952145
\(136\) −9.45200 −0.810503
\(137\) 1.07823 0.0921191 0.0460595 0.998939i \(-0.485334\pi\)
0.0460595 + 0.998939i \(0.485334\pi\)
\(138\) −38.2901 −3.25947
\(139\) 17.8734 1.51600 0.757999 0.652256i \(-0.226177\pi\)
0.757999 + 0.652256i \(0.226177\pi\)
\(140\) −35.9027 −3.03434
\(141\) −9.38034 −0.789967
\(142\) −4.36639 −0.366419
\(143\) 0.810490 0.0677766
\(144\) 7.38390 0.615325
\(145\) −14.9081 −1.23805
\(146\) 10.4374 0.863806
\(147\) −2.30063 −0.189753
\(148\) 41.3878 3.40206
\(149\) 11.7423 0.961965 0.480983 0.876730i \(-0.340280\pi\)
0.480983 + 0.876730i \(0.340280\pi\)
\(150\) 4.63134 0.378148
\(151\) 1.26006 0.102542 0.0512710 0.998685i \(-0.483673\pi\)
0.0512710 + 0.998685i \(0.483673\pi\)
\(152\) 63.7382 5.16985
\(153\) 0.676075 0.0546574
\(154\) −32.7482 −2.63893
\(155\) −9.01074 −0.723760
\(156\) −1.85514 −0.148530
\(157\) −11.8205 −0.943382 −0.471691 0.881764i \(-0.656356\pi\)
−0.471691 + 0.881764i \(0.656356\pi\)
\(158\) 43.0887 3.42796
\(159\) 16.8649 1.33747
\(160\) 38.6191 3.05311
\(161\) −21.6144 −1.70346
\(162\) 27.9358 2.19484
\(163\) −24.4130 −1.91217 −0.956085 0.293088i \(-0.905317\pi\)
−0.956085 + 0.293088i \(0.905317\pi\)
\(164\) −18.8204 −1.46963
\(165\) 19.7218 1.53534
\(166\) 21.3650 1.65824
\(167\) 15.0925 1.16790 0.583948 0.811791i \(-0.301507\pi\)
0.583948 + 0.811791i \(0.301507\pi\)
\(168\) 45.8625 3.53837
\(169\) −12.9640 −0.997232
\(170\) 7.29016 0.559130
\(171\) −4.55902 −0.348637
\(172\) 52.9654 4.03858
\(173\) −0.580461 −0.0441317 −0.0220658 0.999757i \(-0.507024\pi\)
−0.0220658 + 0.999757i \(0.507024\pi\)
\(174\) 31.1252 2.35960
\(175\) 2.61435 0.197627
\(176\) 52.3178 3.94360
\(177\) 14.9152 1.12109
\(178\) 40.1765 3.01136
\(179\) −15.7726 −1.17890 −0.589450 0.807805i \(-0.700655\pi\)
−0.589450 + 0.807805i \(0.700655\pi\)
\(180\) −7.55562 −0.563162
\(181\) 22.9087 1.70279 0.851395 0.524525i \(-0.175757\pi\)
0.851395 + 0.524525i \(0.175757\pi\)
\(182\) −1.45369 −0.107755
\(183\) −6.08822 −0.450054
\(184\) 63.5939 4.68820
\(185\) −19.5311 −1.43595
\(186\) 18.8126 1.37941
\(187\) 4.79026 0.350298
\(188\) 25.4628 1.85707
\(189\) 13.0382 0.948388
\(190\) −49.1601 −3.56645
\(191\) −18.4589 −1.33564 −0.667818 0.744325i \(-0.732772\pi\)
−0.667818 + 0.744325i \(0.732772\pi\)
\(192\) −34.1470 −2.46435
\(193\) −5.36127 −0.385912 −0.192956 0.981207i \(-0.561808\pi\)
−0.192956 + 0.981207i \(0.561808\pi\)
\(194\) −14.8872 −1.06884
\(195\) 0.875449 0.0626922
\(196\) 6.24504 0.446074
\(197\) 24.2824 1.73005 0.865023 0.501732i \(-0.167304\pi\)
0.865023 + 0.501732i \(0.167304\pi\)
\(198\) −6.89176 −0.489776
\(199\) 22.8423 1.61924 0.809622 0.586951i \(-0.199672\pi\)
0.809622 + 0.586951i \(0.199672\pi\)
\(200\) −7.69194 −0.543902
\(201\) −15.3184 −1.08047
\(202\) 5.60041 0.394043
\(203\) 17.5699 1.23317
\(204\) −10.9645 −0.767667
\(205\) 8.88145 0.620308
\(206\) −25.1851 −1.75473
\(207\) −4.54869 −0.316156
\(208\) 2.32239 0.161029
\(209\) −32.3024 −2.23441
\(210\) −35.3729 −2.44096
\(211\) −20.4977 −1.41112 −0.705560 0.708650i \(-0.749305\pi\)
−0.705560 + 0.708650i \(0.749305\pi\)
\(212\) −45.7796 −3.14415
\(213\) −3.09904 −0.212343
\(214\) 15.3872 1.05185
\(215\) −24.9946 −1.70462
\(216\) −38.3608 −2.61012
\(217\) 10.6196 0.720903
\(218\) 15.8889 1.07613
\(219\) 7.40794 0.500582
\(220\) −53.5345 −3.60930
\(221\) 0.212640 0.0143037
\(222\) 40.7770 2.73678
\(223\) 26.0517 1.74455 0.872275 0.489015i \(-0.162644\pi\)
0.872275 + 0.489015i \(0.162644\pi\)
\(224\) −45.5144 −3.04106
\(225\) 0.550183 0.0366788
\(226\) 10.9373 0.727536
\(227\) −19.9624 −1.32495 −0.662475 0.749084i \(-0.730494\pi\)
−0.662475 + 0.749084i \(0.730494\pi\)
\(228\) 73.9374 4.89662
\(229\) −21.5385 −1.42330 −0.711651 0.702533i \(-0.752052\pi\)
−0.711651 + 0.702533i \(0.752052\pi\)
\(230\) −49.0488 −3.23418
\(231\) −23.2430 −1.52928
\(232\) −51.6942 −3.39389
\(233\) 3.27507 0.214557 0.107279 0.994229i \(-0.465786\pi\)
0.107279 + 0.994229i \(0.465786\pi\)
\(234\) −0.305925 −0.0199989
\(235\) −12.0160 −0.783839
\(236\) −40.4871 −2.63549
\(237\) 30.5822 1.98653
\(238\) −8.59179 −0.556923
\(239\) −26.2737 −1.69950 −0.849752 0.527182i \(-0.823249\pi\)
−0.849752 + 0.527182i \(0.823249\pi\)
\(240\) 56.5110 3.64777
\(241\) 1.75603 0.113116 0.0565580 0.998399i \(-0.481987\pi\)
0.0565580 + 0.998399i \(0.481987\pi\)
\(242\) −19.4121 −1.24786
\(243\) 6.17804 0.396321
\(244\) 16.5264 1.05799
\(245\) −2.94706 −0.188281
\(246\) −18.5427 −1.18224
\(247\) −1.43390 −0.0912371
\(248\) −31.2448 −1.98405
\(249\) 15.1638 0.960966
\(250\) −26.5820 −1.68120
\(251\) 0.464826 0.0293395 0.0146698 0.999892i \(-0.495330\pi\)
0.0146698 + 0.999892i \(0.495330\pi\)
\(252\) 8.90464 0.560940
\(253\) −32.2293 −2.02624
\(254\) −35.2317 −2.21064
\(255\) 5.17419 0.324020
\(256\) 7.73734 0.483584
\(257\) 27.6326 1.72368 0.861838 0.507184i \(-0.169314\pi\)
0.861838 + 0.507184i \(0.169314\pi\)
\(258\) 52.1838 3.24882
\(259\) 23.0183 1.43029
\(260\) −2.37640 −0.147378
\(261\) 3.69754 0.228872
\(262\) 28.6549 1.77031
\(263\) 9.09253 0.560669 0.280335 0.959902i \(-0.409555\pi\)
0.280335 + 0.959902i \(0.409555\pi\)
\(264\) 68.3855 4.20884
\(265\) 21.6036 1.32710
\(266\) 57.9375 3.55238
\(267\) 28.5153 1.74511
\(268\) 41.5815 2.53999
\(269\) 24.5820 1.49879 0.749395 0.662123i \(-0.230344\pi\)
0.749395 + 0.662123i \(0.230344\pi\)
\(270\) 29.5870 1.80061
\(271\) 29.8402 1.81266 0.906331 0.422567i \(-0.138871\pi\)
0.906331 + 0.422567i \(0.138871\pi\)
\(272\) 13.7261 0.832265
\(273\) −1.03176 −0.0624448
\(274\) −2.88364 −0.174207
\(275\) 3.89826 0.235074
\(276\) 73.7699 4.44043
\(277\) −0.921441 −0.0553640 −0.0276820 0.999617i \(-0.508813\pi\)
−0.0276820 + 0.999617i \(0.508813\pi\)
\(278\) −47.8010 −2.86692
\(279\) 2.23485 0.133797
\(280\) 58.7489 3.51092
\(281\) −1.49617 −0.0892541 −0.0446270 0.999004i \(-0.514210\pi\)
−0.0446270 + 0.999004i \(0.514210\pi\)
\(282\) 25.0871 1.49391
\(283\) 12.8917 0.766334 0.383167 0.923679i \(-0.374833\pi\)
0.383167 + 0.923679i \(0.374833\pi\)
\(284\) 8.41231 0.499179
\(285\) −34.8914 −2.06679
\(286\) −2.16760 −0.128173
\(287\) −10.4672 −0.617860
\(288\) −9.57836 −0.564410
\(289\) −15.7432 −0.926072
\(290\) 39.8708 2.34129
\(291\) −10.5662 −0.619401
\(292\) −20.1088 −1.17678
\(293\) 3.73575 0.218245 0.109122 0.994028i \(-0.465196\pi\)
0.109122 + 0.994028i \(0.465196\pi\)
\(294\) 6.15288 0.358843
\(295\) 19.1060 1.11240
\(296\) −67.7243 −3.93639
\(297\) 19.4412 1.12809
\(298\) −31.4039 −1.81918
\(299\) −1.43066 −0.0827370
\(300\) −8.92277 −0.515157
\(301\) 29.4573 1.69789
\(302\) −3.36993 −0.193918
\(303\) 3.97489 0.228351
\(304\) −92.5597 −5.30866
\(305\) −7.79888 −0.446562
\(306\) −1.80812 −0.103363
\(307\) −19.8036 −1.13025 −0.565126 0.825005i \(-0.691172\pi\)
−0.565126 + 0.825005i \(0.691172\pi\)
\(308\) 63.0929 3.59505
\(309\) −17.8751 −1.01688
\(310\) 24.0986 1.36871
\(311\) 30.9600 1.75558 0.877791 0.479043i \(-0.159016\pi\)
0.877791 + 0.479043i \(0.159016\pi\)
\(312\) 3.03563 0.171859
\(313\) −13.5594 −0.766420 −0.383210 0.923661i \(-0.625181\pi\)
−0.383210 + 0.923661i \(0.625181\pi\)
\(314\) 31.6132 1.78404
\(315\) −4.20214 −0.236764
\(316\) −83.0150 −4.66996
\(317\) 11.2934 0.634301 0.317151 0.948375i \(-0.397274\pi\)
0.317151 + 0.948375i \(0.397274\pi\)
\(318\) −45.1040 −2.52931
\(319\) 26.1985 1.46684
\(320\) −43.7416 −2.44523
\(321\) 10.9211 0.609554
\(322\) 57.8063 3.22142
\(323\) −8.47484 −0.471552
\(324\) −53.8213 −2.99007
\(325\) 0.173044 0.00959874
\(326\) 65.2907 3.61612
\(327\) 11.2771 0.623625
\(328\) 30.7965 1.70045
\(329\) 14.1614 0.780745
\(330\) −52.7445 −2.90349
\(331\) 1.20630 0.0663041 0.0331521 0.999450i \(-0.489445\pi\)
0.0331521 + 0.999450i \(0.489445\pi\)
\(332\) −41.1619 −2.25905
\(333\) 4.84413 0.265457
\(334\) −40.3640 −2.20862
\(335\) −19.6225 −1.07209
\(336\) −66.6008 −3.63337
\(337\) −3.94495 −0.214895 −0.107448 0.994211i \(-0.534268\pi\)
−0.107448 + 0.994211i \(0.534268\pi\)
\(338\) 34.6714 1.88587
\(339\) 7.76272 0.421613
\(340\) −14.0453 −0.761712
\(341\) 15.8348 0.857504
\(342\) 12.1928 0.659309
\(343\) −16.5864 −0.895581
\(344\) −86.6692 −4.67289
\(345\) −34.8124 −1.87424
\(346\) 1.55240 0.0834577
\(347\) 15.3008 0.821388 0.410694 0.911773i \(-0.365286\pi\)
0.410694 + 0.911773i \(0.365286\pi\)
\(348\) −59.9661 −3.21452
\(349\) 3.13791 0.167969 0.0839844 0.996467i \(-0.473235\pi\)
0.0839844 + 0.996467i \(0.473235\pi\)
\(350\) −6.99191 −0.373733
\(351\) 0.862995 0.0460633
\(352\) −67.8664 −3.61729
\(353\) 27.0654 1.44054 0.720272 0.693692i \(-0.244017\pi\)
0.720272 + 0.693692i \(0.244017\pi\)
\(354\) −39.8896 −2.12011
\(355\) −3.96981 −0.210696
\(356\) −77.4044 −4.10242
\(357\) −6.09802 −0.322742
\(358\) 42.1827 2.22943
\(359\) 6.82906 0.360424 0.180212 0.983628i \(-0.442322\pi\)
0.180212 + 0.983628i \(0.442322\pi\)
\(360\) 12.3635 0.651615
\(361\) 38.1488 2.00783
\(362\) −61.2677 −3.22016
\(363\) −13.7777 −0.723143
\(364\) 2.80069 0.146796
\(365\) 9.48942 0.496699
\(366\) 16.2825 0.851100
\(367\) −27.2296 −1.42137 −0.710687 0.703508i \(-0.751616\pi\)
−0.710687 + 0.703508i \(0.751616\pi\)
\(368\) −92.3501 −4.81408
\(369\) −2.20279 −0.114673
\(370\) 52.2345 2.71554
\(371\) −25.4608 −1.32186
\(372\) −36.2445 −1.87919
\(373\) 18.8394 0.975466 0.487733 0.872993i \(-0.337824\pi\)
0.487733 + 0.872993i \(0.337824\pi\)
\(374\) −12.8112 −0.662452
\(375\) −18.8666 −0.974266
\(376\) −41.6657 −2.14874
\(377\) 1.16295 0.0598951
\(378\) −34.8697 −1.79350
\(379\) −0.301390 −0.0154814 −0.00774069 0.999970i \(-0.502464\pi\)
−0.00774069 + 0.999970i \(0.502464\pi\)
\(380\) 94.7123 4.85864
\(381\) −25.0057 −1.28108
\(382\) 49.3669 2.52583
\(383\) −7.99148 −0.408346 −0.204173 0.978935i \(-0.565450\pi\)
−0.204173 + 0.978935i \(0.565450\pi\)
\(384\) 31.0275 1.58336
\(385\) −29.7738 −1.51742
\(386\) 14.3383 0.729802
\(387\) 6.19920 0.315123
\(388\) 28.6818 1.45610
\(389\) 5.29913 0.268677 0.134338 0.990936i \(-0.457109\pi\)
0.134338 + 0.990936i \(0.457109\pi\)
\(390\) −2.34133 −0.118558
\(391\) −8.45564 −0.427620
\(392\) −10.2190 −0.516136
\(393\) 20.3378 1.02591
\(394\) −64.9415 −3.27170
\(395\) 39.1752 1.97112
\(396\) 13.2777 0.667230
\(397\) −17.1476 −0.860615 −0.430307 0.902682i \(-0.641595\pi\)
−0.430307 + 0.902682i \(0.641595\pi\)
\(398\) −61.0900 −3.06216
\(399\) 41.1211 2.05863
\(400\) 11.1701 0.558506
\(401\) 8.42097 0.420523 0.210262 0.977645i \(-0.432568\pi\)
0.210262 + 0.977645i \(0.432568\pi\)
\(402\) 40.9679 2.04329
\(403\) 0.702908 0.0350143
\(404\) −10.7898 −0.536811
\(405\) 25.3985 1.26206
\(406\) −46.9896 −2.33205
\(407\) 34.3226 1.70131
\(408\) 17.9416 0.888239
\(409\) 13.2027 0.652832 0.326416 0.945226i \(-0.394159\pi\)
0.326416 + 0.945226i \(0.394159\pi\)
\(410\) −23.7528 −1.17307
\(411\) −2.04666 −0.100954
\(412\) 48.5217 2.39049
\(413\) −22.5174 −1.10801
\(414\) 12.1652 0.597885
\(415\) 19.4245 0.953511
\(416\) −3.01259 −0.147704
\(417\) −33.9268 −1.66140
\(418\) 86.3905 4.22550
\(419\) 1.55567 0.0759994 0.0379997 0.999278i \(-0.487901\pi\)
0.0379997 + 0.999278i \(0.487901\pi\)
\(420\) 68.1497 3.32536
\(421\) −9.34657 −0.455524 −0.227762 0.973717i \(-0.573141\pi\)
−0.227762 + 0.973717i \(0.573141\pi\)
\(422\) 54.8197 2.66858
\(423\) 2.98023 0.144904
\(424\) 74.9107 3.63799
\(425\) 1.02274 0.0496104
\(426\) 8.28817 0.401563
\(427\) 9.19134 0.444800
\(428\) −29.6451 −1.43295
\(429\) −1.53845 −0.0742772
\(430\) 66.8464 3.22362
\(431\) −33.2187 −1.60009 −0.800044 0.599941i \(-0.795191\pi\)
−0.800044 + 0.599941i \(0.795191\pi\)
\(432\) 55.7070 2.68021
\(433\) 23.9988 1.15331 0.576655 0.816988i \(-0.304358\pi\)
0.576655 + 0.816988i \(0.304358\pi\)
\(434\) −28.4013 −1.36331
\(435\) 28.2983 1.35680
\(436\) −30.6116 −1.46603
\(437\) 57.0194 2.72761
\(438\) −19.8120 −0.946655
\(439\) −21.4411 −1.02333 −0.511664 0.859186i \(-0.670971\pi\)
−0.511664 + 0.859186i \(0.670971\pi\)
\(440\) 87.6004 4.17618
\(441\) 0.730934 0.0348064
\(442\) −0.568689 −0.0270498
\(443\) −40.2156 −1.91070 −0.955351 0.295474i \(-0.904523\pi\)
−0.955351 + 0.295474i \(0.904523\pi\)
\(444\) −78.5613 −3.72835
\(445\) 36.5275 1.73157
\(446\) −69.6734 −3.29913
\(447\) −22.2889 −1.05423
\(448\) 51.5515 2.43558
\(449\) 7.52202 0.354986 0.177493 0.984122i \(-0.443201\pi\)
0.177493 + 0.984122i \(0.443201\pi\)
\(450\) −1.47142 −0.0693636
\(451\) −15.6076 −0.734935
\(452\) −21.0718 −0.991135
\(453\) −2.39181 −0.112377
\(454\) 53.3880 2.50562
\(455\) −1.32166 −0.0619604
\(456\) −120.986 −5.66570
\(457\) −5.96681 −0.279115 −0.139558 0.990214i \(-0.544568\pi\)
−0.139558 + 0.990214i \(0.544568\pi\)
\(458\) 57.6031 2.69162
\(459\) 5.10058 0.238075
\(460\) 94.4977 4.40598
\(461\) −34.2658 −1.59592 −0.797959 0.602712i \(-0.794087\pi\)
−0.797959 + 0.602712i \(0.794087\pi\)
\(462\) 62.1618 2.89203
\(463\) 13.2956 0.617901 0.308950 0.951078i \(-0.400022\pi\)
0.308950 + 0.951078i \(0.400022\pi\)
\(464\) 75.0695 3.48502
\(465\) 17.1040 0.793177
\(466\) −8.75895 −0.405750
\(467\) 17.1853 0.795241 0.397621 0.917550i \(-0.369836\pi\)
0.397621 + 0.917550i \(0.369836\pi\)
\(468\) 0.589397 0.0272449
\(469\) 23.1260 1.06786
\(470\) 32.1360 1.48232
\(471\) 22.4375 1.03386
\(472\) 66.2504 3.04942
\(473\) 43.9238 2.01962
\(474\) −81.7900 −3.75674
\(475\) −6.89673 −0.316444
\(476\) 16.5530 0.758706
\(477\) −5.35815 −0.245333
\(478\) 70.2672 3.21395
\(479\) 29.5529 1.35031 0.675153 0.737677i \(-0.264077\pi\)
0.675153 + 0.737677i \(0.264077\pi\)
\(480\) −73.3058 −3.34594
\(481\) 1.52358 0.0694692
\(482\) −4.69638 −0.213914
\(483\) 41.0280 1.86684
\(484\) 37.3994 1.69997
\(485\) −13.5351 −0.614596
\(486\) −16.5227 −0.749486
\(487\) −22.5082 −1.01994 −0.509972 0.860191i \(-0.670344\pi\)
−0.509972 + 0.860191i \(0.670344\pi\)
\(488\) −27.0427 −1.22417
\(489\) 46.3401 2.09557
\(490\) 7.88171 0.356059
\(491\) −25.5461 −1.15288 −0.576440 0.817139i \(-0.695559\pi\)
−0.576440 + 0.817139i \(0.695559\pi\)
\(492\) 35.7245 1.61058
\(493\) 6.87342 0.309563
\(494\) 3.83487 0.172539
\(495\) −6.26581 −0.281627
\(496\) 45.3733 2.03732
\(497\) 4.67861 0.209864
\(498\) −40.5545 −1.81729
\(499\) −27.0222 −1.20968 −0.604839 0.796348i \(-0.706763\pi\)
−0.604839 + 0.796348i \(0.706763\pi\)
\(500\) 51.2131 2.29032
\(501\) −28.6483 −1.27991
\(502\) −1.24314 −0.0554842
\(503\) −33.2675 −1.48333 −0.741663 0.670773i \(-0.765963\pi\)
−0.741663 + 0.670773i \(0.765963\pi\)
\(504\) −14.5710 −0.649043
\(505\) 5.09175 0.226580
\(506\) 86.1949 3.83183
\(507\) 24.6080 1.09288
\(508\) 67.8777 3.01158
\(509\) 13.7336 0.608731 0.304365 0.952555i \(-0.401556\pi\)
0.304365 + 0.952555i \(0.401556\pi\)
\(510\) −13.8380 −0.612757
\(511\) −11.1837 −0.494739
\(512\) 11.9989 0.530282
\(513\) −34.3950 −1.51858
\(514\) −73.9015 −3.25965
\(515\) −22.8976 −1.00899
\(516\) −100.538 −4.42592
\(517\) 21.1161 0.928685
\(518\) −61.5608 −2.70483
\(519\) 1.10182 0.0483644
\(520\) 3.88858 0.170525
\(521\) 14.5729 0.638450 0.319225 0.947679i \(-0.396577\pi\)
0.319225 + 0.947679i \(0.396577\pi\)
\(522\) −9.88881 −0.432821
\(523\) −7.99304 −0.349511 −0.174756 0.984612i \(-0.555914\pi\)
−0.174756 + 0.984612i \(0.555914\pi\)
\(524\) −55.2067 −2.41172
\(525\) −4.96250 −0.216581
\(526\) −24.3173 −1.06029
\(527\) 4.15441 0.180969
\(528\) −99.3084 −4.32184
\(529\) 33.8903 1.47349
\(530\) −57.7773 −2.50969
\(531\) −4.73871 −0.205642
\(532\) −111.623 −4.83946
\(533\) −0.692823 −0.0300095
\(534\) −76.2621 −3.30018
\(535\) 13.9897 0.604826
\(536\) −68.0413 −2.93893
\(537\) 29.9392 1.29197
\(538\) −65.7428 −2.83437
\(539\) 5.17896 0.223073
\(540\) −57.0025 −2.45300
\(541\) 13.0723 0.562023 0.281012 0.959704i \(-0.409330\pi\)
0.281012 + 0.959704i \(0.409330\pi\)
\(542\) −79.8055 −3.42794
\(543\) −43.4847 −1.86611
\(544\) −17.8054 −0.763399
\(545\) 14.4457 0.618787
\(546\) 2.75936 0.118090
\(547\) 34.6375 1.48099 0.740495 0.672062i \(-0.234591\pi\)
0.740495 + 0.672062i \(0.234591\pi\)
\(548\) 5.55564 0.237325
\(549\) 1.93429 0.0825534
\(550\) −10.4256 −0.444550
\(551\) −46.3499 −1.97457
\(552\) −120.712 −5.13786
\(553\) −46.1698 −1.96334
\(554\) 2.46433 0.104699
\(555\) 37.0734 1.57368
\(556\) 92.0938 3.90565
\(557\) −15.5134 −0.657322 −0.328661 0.944448i \(-0.606597\pi\)
−0.328661 + 0.944448i \(0.606597\pi\)
\(558\) −5.97696 −0.253025
\(559\) 1.94978 0.0824667
\(560\) −85.3143 −3.60519
\(561\) −9.09275 −0.383896
\(562\) 4.00140 0.168789
\(563\) −19.5000 −0.821826 −0.410913 0.911675i \(-0.634790\pi\)
−0.410913 + 0.911675i \(0.634790\pi\)
\(564\) −48.3329 −2.03518
\(565\) 9.94389 0.418342
\(566\) −34.4780 −1.44922
\(567\) −29.9333 −1.25708
\(568\) −13.7654 −0.577582
\(569\) 16.4359 0.689027 0.344514 0.938781i \(-0.388044\pi\)
0.344514 + 0.938781i \(0.388044\pi\)
\(570\) 93.3146 3.90852
\(571\) 34.6767 1.45118 0.725588 0.688130i \(-0.241568\pi\)
0.725588 + 0.688130i \(0.241568\pi\)
\(572\) 4.17611 0.174612
\(573\) 35.0381 1.46374
\(574\) 27.9938 1.16844
\(575\) −6.88111 −0.286962
\(576\) 10.8488 0.452035
\(577\) 36.4051 1.51556 0.757782 0.652507i \(-0.226283\pi\)
0.757782 + 0.652507i \(0.226283\pi\)
\(578\) 42.1042 1.75130
\(579\) 10.1766 0.422926
\(580\) −76.8153 −3.18958
\(581\) −22.8927 −0.949748
\(582\) 28.2585 1.17135
\(583\) −37.9646 −1.57233
\(584\) 32.9047 1.36161
\(585\) −0.278139 −0.0114996
\(586\) −9.99100 −0.412725
\(587\) 15.4475 0.637588 0.318794 0.947824i \(-0.396722\pi\)
0.318794 + 0.947824i \(0.396722\pi\)
\(588\) −11.8542 −0.488858
\(589\) −28.0147 −1.15432
\(590\) −51.0978 −2.10366
\(591\) −46.0922 −1.89598
\(592\) 98.3482 4.04209
\(593\) −38.5590 −1.58343 −0.791713 0.610893i \(-0.790811\pi\)
−0.791713 + 0.610893i \(0.790811\pi\)
\(594\) −51.9941 −2.13334
\(595\) −7.81144 −0.320238
\(596\) 60.5030 2.47830
\(597\) −43.3586 −1.77455
\(598\) 3.82619 0.156465
\(599\) 24.5528 1.00320 0.501600 0.865100i \(-0.332745\pi\)
0.501600 + 0.865100i \(0.332745\pi\)
\(600\) 14.6006 0.596069
\(601\) 22.6814 0.925193 0.462596 0.886569i \(-0.346918\pi\)
0.462596 + 0.886569i \(0.346918\pi\)
\(602\) −78.7815 −3.21090
\(603\) 4.86680 0.198191
\(604\) 6.49253 0.264177
\(605\) −17.6490 −0.717533
\(606\) −10.6306 −0.431837
\(607\) 33.1908 1.34717 0.673586 0.739109i \(-0.264753\pi\)
0.673586 + 0.739109i \(0.264753\pi\)
\(608\) 120.068 4.86940
\(609\) −33.3508 −1.35144
\(610\) 20.8575 0.844497
\(611\) 0.937343 0.0379209
\(612\) 3.48353 0.140813
\(613\) 27.8533 1.12498 0.562492 0.826803i \(-0.309843\pi\)
0.562492 + 0.826803i \(0.309843\pi\)
\(614\) 52.9634 2.13743
\(615\) −16.8586 −0.679803
\(616\) −103.241 −4.15970
\(617\) −10.2016 −0.410699 −0.205350 0.978689i \(-0.565833\pi\)
−0.205350 + 0.978689i \(0.565833\pi\)
\(618\) 47.8057 1.92303
\(619\) −38.3478 −1.54133 −0.770664 0.637242i \(-0.780075\pi\)
−0.770664 + 0.637242i \(0.780075\pi\)
\(620\) −46.4285 −1.86461
\(621\) −34.3171 −1.37710
\(622\) −82.8004 −3.32000
\(623\) −43.0493 −1.72473
\(624\) −4.40830 −0.176473
\(625\) −28.7292 −1.14917
\(626\) 36.2635 1.44938
\(627\) 61.3157 2.44871
\(628\) −60.9062 −2.43042
\(629\) 9.00484 0.359046
\(630\) 11.2383 0.447746
\(631\) −27.0621 −1.07732 −0.538662 0.842522i \(-0.681070\pi\)
−0.538662 + 0.842522i \(0.681070\pi\)
\(632\) 135.840 5.40344
\(633\) 38.9083 1.54646
\(634\) −30.2034 −1.19953
\(635\) −32.0318 −1.27114
\(636\) 86.8977 3.44572
\(637\) 0.229894 0.00910872
\(638\) −70.0661 −2.77394
\(639\) 0.984598 0.0389501
\(640\) 39.7455 1.57108
\(641\) −28.2050 −1.11403 −0.557015 0.830503i \(-0.688053\pi\)
−0.557015 + 0.830503i \(0.688053\pi\)
\(642\) −29.2076 −1.15273
\(643\) 25.3480 0.999629 0.499815 0.866132i \(-0.333401\pi\)
0.499815 + 0.866132i \(0.333401\pi\)
\(644\) −111.370 −4.38859
\(645\) 47.4442 1.86811
\(646\) 22.6653 0.891756
\(647\) −7.02393 −0.276139 −0.138070 0.990423i \(-0.544090\pi\)
−0.138070 + 0.990423i \(0.544090\pi\)
\(648\) 88.0696 3.45970
\(649\) −33.5756 −1.31796
\(650\) −0.462793 −0.0181522
\(651\) −20.1578 −0.790047
\(652\) −125.790 −4.92630
\(653\) −42.6366 −1.66850 −0.834249 0.551388i \(-0.814098\pi\)
−0.834249 + 0.551388i \(0.814098\pi\)
\(654\) −30.1598 −1.17934
\(655\) 26.0523 1.01795
\(656\) −44.7223 −1.74611
\(657\) −2.35358 −0.0918219
\(658\) −37.8738 −1.47647
\(659\) −26.9096 −1.04825 −0.524124 0.851642i \(-0.675607\pi\)
−0.524124 + 0.851642i \(0.675607\pi\)
\(660\) 101.618 3.95547
\(661\) 41.0374 1.59617 0.798085 0.602544i \(-0.205846\pi\)
0.798085 + 0.602544i \(0.205846\pi\)
\(662\) −3.22616 −0.125388
\(663\) −0.403627 −0.0156756
\(664\) 67.3546 2.61387
\(665\) 52.6753 2.04266
\(666\) −12.9553 −0.502007
\(667\) −46.2449 −1.79061
\(668\) 77.7654 3.00884
\(669\) −49.4507 −1.91187
\(670\) 52.4790 2.02744
\(671\) 13.7052 0.529083
\(672\) 86.3943 3.33273
\(673\) −23.3272 −0.899199 −0.449600 0.893230i \(-0.648433\pi\)
−0.449600 + 0.893230i \(0.648433\pi\)
\(674\) 10.5505 0.406390
\(675\) 4.15079 0.159764
\(676\) −66.7981 −2.56916
\(677\) −3.54650 −0.136303 −0.0681515 0.997675i \(-0.521710\pi\)
−0.0681515 + 0.997675i \(0.521710\pi\)
\(678\) −20.7609 −0.797316
\(679\) 15.9517 0.612170
\(680\) 22.9828 0.881349
\(681\) 37.8921 1.45203
\(682\) −42.3491 −1.62163
\(683\) −18.5294 −0.709007 −0.354504 0.935055i \(-0.615350\pi\)
−0.354504 + 0.935055i \(0.615350\pi\)
\(684\) −23.4907 −0.898188
\(685\) −2.62173 −0.100171
\(686\) 44.3591 1.69364
\(687\) 40.8838 1.55981
\(688\) 125.860 4.79836
\(689\) −1.68525 −0.0642029
\(690\) 93.1032 3.54438
\(691\) −11.1841 −0.425464 −0.212732 0.977111i \(-0.568236\pi\)
−0.212732 + 0.977111i \(0.568236\pi\)
\(692\) −2.99087 −0.113696
\(693\) 7.38455 0.280516
\(694\) −40.9208 −1.55333
\(695\) −43.4595 −1.64851
\(696\) 98.1246 3.71940
\(697\) −4.09481 −0.155102
\(698\) −8.39213 −0.317647
\(699\) −6.21666 −0.235136
\(700\) 13.4707 0.509143
\(701\) −37.3875 −1.41211 −0.706054 0.708158i \(-0.749526\pi\)
−0.706054 + 0.708158i \(0.749526\pi\)
\(702\) −2.30802 −0.0871105
\(703\) −60.7228 −2.29020
\(704\) 76.8683 2.89708
\(705\) 22.8085 0.859018
\(706\) −72.3844 −2.72422
\(707\) −6.00086 −0.225686
\(708\) 76.8516 2.88826
\(709\) −29.8194 −1.11989 −0.559945 0.828530i \(-0.689178\pi\)
−0.559945 + 0.828530i \(0.689178\pi\)
\(710\) 10.6170 0.398448
\(711\) −9.71628 −0.364389
\(712\) 126.659 4.74676
\(713\) −27.9512 −1.04678
\(714\) 16.3087 0.610339
\(715\) −1.97073 −0.0737010
\(716\) −81.2695 −3.03718
\(717\) 49.8721 1.86251
\(718\) −18.2638 −0.681601
\(719\) 14.8603 0.554196 0.277098 0.960842i \(-0.410627\pi\)
0.277098 + 0.960842i \(0.410627\pi\)
\(720\) −17.9541 −0.669111
\(721\) 26.9859 1.00501
\(722\) −102.026 −3.79703
\(723\) −3.33326 −0.123965
\(724\) 118.039 4.38688
\(725\) 5.59352 0.207738
\(726\) 36.8475 1.36754
\(727\) −16.3593 −0.606732 −0.303366 0.952874i \(-0.598111\pi\)
−0.303366 + 0.952874i \(0.598111\pi\)
\(728\) −4.58287 −0.169853
\(729\) 19.6095 0.726280
\(730\) −25.3788 −0.939311
\(731\) 11.5238 0.426223
\(732\) −31.3700 −1.15947
\(733\) 12.6695 0.467960 0.233980 0.972241i \(-0.424825\pi\)
0.233980 + 0.972241i \(0.424825\pi\)
\(734\) 72.8237 2.68797
\(735\) 5.59404 0.206339
\(736\) 119.796 4.41574
\(737\) 34.4832 1.27020
\(738\) 5.89121 0.216858
\(739\) −7.46822 −0.274723 −0.137361 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(740\) −100.635 −3.69943
\(741\) 2.72180 0.0999879
\(742\) 68.0932 2.49978
\(743\) 17.8826 0.656051 0.328025 0.944669i \(-0.393617\pi\)
0.328025 + 0.944669i \(0.393617\pi\)
\(744\) 59.3082 2.17434
\(745\) −28.5516 −1.04605
\(746\) −50.3846 −1.84471
\(747\) −4.81769 −0.176270
\(748\) 24.6822 0.902469
\(749\) −16.4875 −0.602439
\(750\) 50.4574 1.84244
\(751\) 3.70986 0.135375 0.0676874 0.997707i \(-0.478438\pi\)
0.0676874 + 0.997707i \(0.478438\pi\)
\(752\) 60.5063 2.20644
\(753\) −0.882321 −0.0321536
\(754\) −3.11023 −0.113268
\(755\) −3.06386 −0.111505
\(756\) 67.1801 2.44332
\(757\) −48.0669 −1.74702 −0.873510 0.486807i \(-0.838162\pi\)
−0.873510 + 0.486807i \(0.838162\pi\)
\(758\) 0.806048 0.0292770
\(759\) 61.1768 2.22058
\(760\) −154.981 −5.62175
\(761\) 0.514146 0.0186378 0.00931890 0.999957i \(-0.497034\pi\)
0.00931890 + 0.999957i \(0.497034\pi\)
\(762\) 66.8760 2.42266
\(763\) −17.0250 −0.616345
\(764\) −95.1106 −3.44098
\(765\) −1.64389 −0.0594351
\(766\) 21.3727 0.772225
\(767\) −1.49042 −0.0538160
\(768\) −14.6868 −0.529966
\(769\) 15.4661 0.557723 0.278862 0.960331i \(-0.410043\pi\)
0.278862 + 0.960331i \(0.410043\pi\)
\(770\) 79.6280 2.86959
\(771\) −52.4516 −1.88900
\(772\) −27.6243 −0.994221
\(773\) −14.9912 −0.539197 −0.269599 0.962973i \(-0.586891\pi\)
−0.269599 + 0.962973i \(0.586891\pi\)
\(774\) −16.5793 −0.595932
\(775\) 3.38081 0.121442
\(776\) −46.9330 −1.68480
\(777\) −43.6928 −1.56747
\(778\) −14.1722 −0.508097
\(779\) 27.6127 0.989329
\(780\) 4.51082 0.161513
\(781\) 6.97626 0.249630
\(782\) 22.6140 0.808676
\(783\) 27.8957 0.996911
\(784\) 14.8398 0.529994
\(785\) 28.7419 1.02584
\(786\) −54.3920 −1.94010
\(787\) −26.0738 −0.929430 −0.464715 0.885460i \(-0.653843\pi\)
−0.464715 + 0.885460i \(0.653843\pi\)
\(788\) 125.117 4.45710
\(789\) −17.2592 −0.614444
\(790\) −104.771 −3.72759
\(791\) −11.7193 −0.416691
\(792\) −21.7268 −0.772027
\(793\) 0.608373 0.0216040
\(794\) 45.8601 1.62751
\(795\) −41.0074 −1.45438
\(796\) 117.696 4.17164
\(797\) −30.1737 −1.06881 −0.534403 0.845230i \(-0.679464\pi\)
−0.534403 + 0.845230i \(0.679464\pi\)
\(798\) −109.976 −3.89309
\(799\) 5.54000 0.195991
\(800\) −14.4898 −0.512293
\(801\) −9.05959 −0.320105
\(802\) −22.5213 −0.795255
\(803\) −16.6760 −0.588484
\(804\) −78.9290 −2.78361
\(805\) 52.5560 1.85236
\(806\) −1.87988 −0.0662158
\(807\) −46.6609 −1.64254
\(808\) 17.6557 0.621125
\(809\) −55.1431 −1.93873 −0.969364 0.245630i \(-0.921005\pi\)
−0.969364 + 0.245630i \(0.921005\pi\)
\(810\) −67.9265 −2.38669
\(811\) −19.0594 −0.669265 −0.334633 0.942349i \(-0.608612\pi\)
−0.334633 + 0.942349i \(0.608612\pi\)
\(812\) 90.5304 3.17699
\(813\) −56.6419 −1.98652
\(814\) −91.7933 −3.21735
\(815\) 59.3607 2.07931
\(816\) −26.0545 −0.912089
\(817\) −77.7091 −2.71870
\(818\) −35.3097 −1.23458
\(819\) 0.327800 0.0114543
\(820\) 45.7623 1.59809
\(821\) −9.79040 −0.341687 −0.170844 0.985298i \(-0.554649\pi\)
−0.170844 + 0.985298i \(0.554649\pi\)
\(822\) 5.47365 0.190916
\(823\) 4.78542 0.166809 0.0834046 0.996516i \(-0.473421\pi\)
0.0834046 + 0.996516i \(0.473421\pi\)
\(824\) −79.3978 −2.76595
\(825\) −7.39958 −0.257620
\(826\) 60.2211 2.09536
\(827\) 12.6197 0.438832 0.219416 0.975631i \(-0.429585\pi\)
0.219416 + 0.975631i \(0.429585\pi\)
\(828\) −23.4375 −0.814508
\(829\) 4.46812 0.155184 0.0775922 0.996985i \(-0.475277\pi\)
0.0775922 + 0.996985i \(0.475277\pi\)
\(830\) −51.9494 −1.80319
\(831\) 1.74906 0.0606741
\(832\) 3.41218 0.118296
\(833\) 1.35875 0.0470778
\(834\) 90.7347 3.14189
\(835\) −36.6979 −1.26998
\(836\) −166.441 −5.75647
\(837\) 16.8606 0.582788
\(838\) −4.16053 −0.143723
\(839\) 6.17131 0.213057 0.106529 0.994310i \(-0.466026\pi\)
0.106529 + 0.994310i \(0.466026\pi\)
\(840\) −111.516 −3.84766
\(841\) 8.59159 0.296262
\(842\) 24.9967 0.861445
\(843\) 2.83999 0.0978146
\(844\) −105.616 −3.63545
\(845\) 31.5223 1.08440
\(846\) −7.97041 −0.274028
\(847\) 20.8001 0.714701
\(848\) −108.784 −3.73567
\(849\) −24.4708 −0.839835
\(850\) −2.73526 −0.0938186
\(851\) −60.5853 −2.07684
\(852\) −15.9680 −0.547056
\(853\) −45.2450 −1.54916 −0.774580 0.632476i \(-0.782039\pi\)
−0.774580 + 0.632476i \(0.782039\pi\)
\(854\) −24.5816 −0.841165
\(855\) 11.0854 0.379111
\(856\) 48.5093 1.65801
\(857\) 41.7727 1.42693 0.713464 0.700691i \(-0.247125\pi\)
0.713464 + 0.700691i \(0.247125\pi\)
\(858\) 4.11448 0.140466
\(859\) −28.1620 −0.960875 −0.480438 0.877029i \(-0.659522\pi\)
−0.480438 + 0.877029i \(0.659522\pi\)
\(860\) −128.787 −4.39159
\(861\) 19.8686 0.677120
\(862\) 88.8411 3.02594
\(863\) −42.1317 −1.43418 −0.717090 0.696981i \(-0.754526\pi\)
−0.717090 + 0.696981i \(0.754526\pi\)
\(864\) −72.2629 −2.45843
\(865\) 1.41141 0.0479892
\(866\) −64.1832 −2.18103
\(867\) 29.8834 1.01489
\(868\) 54.7181 1.85725
\(869\) −68.8437 −2.33536
\(870\) −75.6817 −2.56585
\(871\) 1.53071 0.0518661
\(872\) 50.0908 1.69629
\(873\) 3.35698 0.113617
\(874\) −152.494 −5.15820
\(875\) 28.4828 0.962893
\(876\) 38.1700 1.28964
\(877\) −14.0536 −0.474557 −0.237279 0.971442i \(-0.576255\pi\)
−0.237279 + 0.971442i \(0.576255\pi\)
\(878\) 57.3427 1.93522
\(879\) −7.09111 −0.239177
\(880\) −127.212 −4.28832
\(881\) −19.8655 −0.669285 −0.334642 0.942345i \(-0.608616\pi\)
−0.334642 + 0.942345i \(0.608616\pi\)
\(882\) −1.95483 −0.0658226
\(883\) 14.9354 0.502616 0.251308 0.967907i \(-0.419139\pi\)
0.251308 + 0.967907i \(0.419139\pi\)
\(884\) 1.09564 0.0368504
\(885\) −36.2666 −1.21909
\(886\) 107.554 3.61334
\(887\) 51.6223 1.73331 0.866654 0.498910i \(-0.166266\pi\)
0.866654 + 0.498910i \(0.166266\pi\)
\(888\) 128.553 4.31394
\(889\) 37.7510 1.26613
\(890\) −97.6902 −3.27458
\(891\) −44.6335 −1.49528
\(892\) 134.233 4.49446
\(893\) −37.3582 −1.25014
\(894\) 59.6101 1.99366
\(895\) 38.3514 1.28195
\(896\) −46.8420 −1.56488
\(897\) 2.71564 0.0906725
\(898\) −20.1171 −0.671317
\(899\) 22.7210 0.757787
\(900\) 2.83486 0.0944952
\(901\) −9.96037 −0.331828
\(902\) 41.7415 1.38984
\(903\) −55.9152 −1.86074
\(904\) 34.4805 1.14681
\(905\) −55.7030 −1.85163
\(906\) 6.39672 0.212517
\(907\) −18.8826 −0.626985 −0.313493 0.949591i \(-0.601499\pi\)
−0.313493 + 0.949591i \(0.601499\pi\)
\(908\) −102.858 −3.41345
\(909\) −1.26286 −0.0418865
\(910\) 3.53469 0.117174
\(911\) 37.1336 1.23029 0.615145 0.788414i \(-0.289097\pi\)
0.615145 + 0.788414i \(0.289097\pi\)
\(912\) 175.695 5.81783
\(913\) −34.1352 −1.12971
\(914\) 15.9578 0.527837
\(915\) 14.8036 0.489393
\(916\) −110.978 −3.66683
\(917\) −30.7038 −1.01393
\(918\) −13.6411 −0.450225
\(919\) 5.35187 0.176542 0.0882710 0.996097i \(-0.471866\pi\)
0.0882710 + 0.996097i \(0.471866\pi\)
\(920\) −154.630 −5.09800
\(921\) 37.5907 1.23866
\(922\) 91.6415 3.01805
\(923\) 0.309676 0.0101931
\(924\) −119.761 −3.93986
\(925\) 7.32804 0.240944
\(926\) −35.5582 −1.16852
\(927\) 5.67910 0.186526
\(928\) −97.3798 −3.19665
\(929\) −36.8448 −1.20884 −0.604419 0.796666i \(-0.706595\pi\)
−0.604419 + 0.796666i \(0.706595\pi\)
\(930\) −45.7433 −1.49998
\(931\) −9.16251 −0.300289
\(932\) 16.8750 0.552760
\(933\) −58.7676 −1.92396
\(934\) −45.9609 −1.50389
\(935\) −11.6476 −0.380918
\(936\) −0.964451 −0.0315241
\(937\) 17.0304 0.556357 0.278179 0.960529i \(-0.410269\pi\)
0.278179 + 0.960529i \(0.410269\pi\)
\(938\) −61.8490 −2.01944
\(939\) 25.7380 0.839929
\(940\) −61.9134 −2.01939
\(941\) −3.02953 −0.0987598 −0.0493799 0.998780i \(-0.515725\pi\)
−0.0493799 + 0.998780i \(0.515725\pi\)
\(942\) −60.0074 −1.95515
\(943\) 27.5502 0.897158
\(944\) −96.2079 −3.13130
\(945\) −31.7026 −1.03129
\(946\) −117.471 −3.81931
\(947\) 57.9829 1.88419 0.942096 0.335345i \(-0.108853\pi\)
0.942096 + 0.335345i \(0.108853\pi\)
\(948\) 157.577 5.11787
\(949\) −0.740249 −0.0240295
\(950\) 18.4448 0.598429
\(951\) −21.4369 −0.695139
\(952\) −27.0863 −0.877870
\(953\) −7.37054 −0.238755 −0.119378 0.992849i \(-0.538090\pi\)
−0.119378 + 0.992849i \(0.538090\pi\)
\(954\) 14.3300 0.463951
\(955\) 44.8831 1.45238
\(956\) −135.377 −4.37841
\(957\) −49.7294 −1.60752
\(958\) −79.0372 −2.55357
\(959\) 3.08983 0.0997759
\(960\) 83.0291 2.67975
\(961\) −17.2671 −0.557002
\(962\) −4.07470 −0.131374
\(963\) −3.46973 −0.111811
\(964\) 9.04808 0.291419
\(965\) 13.0360 0.419645
\(966\) −109.726 −3.53039
\(967\) 14.7334 0.473793 0.236897 0.971535i \(-0.423870\pi\)
0.236897 + 0.971535i \(0.423870\pi\)
\(968\) −61.1980 −1.96698
\(969\) 16.0867 0.516780
\(970\) 36.1986 1.16227
\(971\) −2.43397 −0.0781097 −0.0390548 0.999237i \(-0.512435\pi\)
−0.0390548 + 0.999237i \(0.512435\pi\)
\(972\) 31.8328 1.02104
\(973\) 51.2190 1.64201
\(974\) 60.1966 1.92882
\(975\) −0.328467 −0.0105194
\(976\) 39.2710 1.25703
\(977\) −35.0855 −1.12248 −0.561242 0.827651i \(-0.689676\pi\)
−0.561242 + 0.827651i \(0.689676\pi\)
\(978\) −123.933 −3.96295
\(979\) −64.1908 −2.05155
\(980\) −15.1849 −0.485065
\(981\) −3.58285 −0.114392
\(982\) 68.3213 2.18022
\(983\) 39.0926 1.24686 0.623431 0.781879i \(-0.285738\pi\)
0.623431 + 0.781879i \(0.285738\pi\)
\(984\) −58.4572 −1.86355
\(985\) −59.0431 −1.88127
\(986\) −18.3825 −0.585417
\(987\) −26.8809 −0.855628
\(988\) −7.38829 −0.235053
\(989\) −77.5331 −2.46541
\(990\) 16.7575 0.532587
\(991\) −6.90753 −0.219425 −0.109712 0.993963i \(-0.534993\pi\)
−0.109712 + 0.993963i \(0.534993\pi\)
\(992\) −58.8580 −1.86874
\(993\) −2.28977 −0.0726635
\(994\) −12.5126 −0.396876
\(995\) −55.5415 −1.76078
\(996\) 78.1325 2.47572
\(997\) 34.3234 1.08703 0.543517 0.839398i \(-0.317092\pi\)
0.543517 + 0.839398i \(0.317092\pi\)
\(998\) 72.2689 2.28763
\(999\) 36.5460 1.15626
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 8011.2.a.a.1.10 309
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8011.2.a.a.1.10 309 1.1 even 1 trivial