Properties

Label 8035.2.a.d.1.19
Level $8035$
Weight $2$
Character 8035.1
Self dual yes
Analytic conductor $64.160$
Analytic rank $1$
Dimension $140$
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] = [8035,2,Mod(1,8035)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8035, 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("8035.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8035 = 5 \cdot 1607 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8035.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: \(64.1597980241\)
Analytic rank: \(1\)
Dimension: \(140\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) \(=\) 8035.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.36612 q^{2} -3.07539 q^{3} +3.59854 q^{4} -1.00000 q^{5} +7.27675 q^{6} +3.28740 q^{7} -3.78235 q^{8} +6.45802 q^{9} +O(q^{10})\) \(q-2.36612 q^{2} -3.07539 q^{3} +3.59854 q^{4} -1.00000 q^{5} +7.27675 q^{6} +3.28740 q^{7} -3.78235 q^{8} +6.45802 q^{9} +2.36612 q^{10} -5.16172 q^{11} -11.0669 q^{12} -0.588339 q^{13} -7.77839 q^{14} +3.07539 q^{15} +1.75242 q^{16} -5.86859 q^{17} -15.2805 q^{18} -5.21720 q^{19} -3.59854 q^{20} -10.1100 q^{21} +12.2133 q^{22} -0.898889 q^{23} +11.6322 q^{24} +1.00000 q^{25} +1.39208 q^{26} -10.6348 q^{27} +11.8298 q^{28} -0.0172396 q^{29} -7.27675 q^{30} +10.1623 q^{31} +3.41826 q^{32} +15.8743 q^{33} +13.8858 q^{34} -3.28740 q^{35} +23.2395 q^{36} -0.677044 q^{37} +12.3445 q^{38} +1.80937 q^{39} +3.78235 q^{40} +5.24336 q^{41} +23.9216 q^{42} +0.668571 q^{43} -18.5747 q^{44} -6.45802 q^{45} +2.12688 q^{46} -10.7620 q^{47} -5.38937 q^{48} +3.80699 q^{49} -2.36612 q^{50} +18.0482 q^{51} -2.11716 q^{52} +2.11254 q^{53} +25.1632 q^{54} +5.16172 q^{55} -12.4341 q^{56} +16.0449 q^{57} +0.0407911 q^{58} +13.7279 q^{59} +11.0669 q^{60} -2.99581 q^{61} -24.0452 q^{62} +21.2301 q^{63} -11.5929 q^{64} +0.588339 q^{65} -37.5606 q^{66} -1.58919 q^{67} -21.1183 q^{68} +2.76443 q^{69} +7.77839 q^{70} +8.60165 q^{71} -24.4265 q^{72} -6.33151 q^{73} +1.60197 q^{74} -3.07539 q^{75} -18.7743 q^{76} -16.9686 q^{77} -4.28120 q^{78} +8.41599 q^{79} -1.75242 q^{80} +13.3320 q^{81} -12.4064 q^{82} -8.25560 q^{83} -36.3814 q^{84} +5.86859 q^{85} -1.58192 q^{86} +0.0530186 q^{87} +19.5234 q^{88} -5.42031 q^{89} +15.2805 q^{90} -1.93411 q^{91} -3.23469 q^{92} -31.2530 q^{93} +25.4642 q^{94} +5.21720 q^{95} -10.5125 q^{96} +11.1628 q^{97} -9.00782 q^{98} -33.3345 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9} + 20 q^{10} - 26 q^{11} - 31 q^{12} - 32 q^{13} - 37 q^{14} + 12 q^{15} + 152 q^{16} - 69 q^{17} - 64 q^{18} + 37 q^{19} - 144 q^{20} - 43 q^{21} - 25 q^{22} - 63 q^{23} - 5 q^{24} + 140 q^{25} - 16 q^{26} - 48 q^{27} - 52 q^{28} - 136 q^{29} + 25 q^{31} - 151 q^{32} - 48 q^{33} + 29 q^{34} + 15 q^{35} + 120 q^{36} - 82 q^{37} - 69 q^{38} - 26 q^{39} + 63 q^{40} - 11 q^{41} - 35 q^{42} - 54 q^{43} - 83 q^{44} - 134 q^{45} + 25 q^{46} - 39 q^{47} - 83 q^{48} + 215 q^{49} - 20 q^{50} - 75 q^{51} - 56 q^{52} - 196 q^{53} - 29 q^{54} + 26 q^{55} - 132 q^{56} - 110 q^{57} - 29 q^{58} - 31 q^{59} + 31 q^{60} - 18 q^{61} - 107 q^{62} - 67 q^{63} + 165 q^{64} + 32 q^{65} - 16 q^{66} - 50 q^{67} - 201 q^{68} - 46 q^{69} + 37 q^{70} - 84 q^{71} - 200 q^{72} - 70 q^{73} - 101 q^{74} - 12 q^{75} + 118 q^{76} - 166 q^{77} - 106 q^{78} - 35 q^{79} - 152 q^{80} + 116 q^{81} - 72 q^{82} - 66 q^{83} - 60 q^{84} + 69 q^{85} - 66 q^{86} - 75 q^{87} - 101 q^{88} + 8 q^{89} + 64 q^{90} + 2 q^{91} - 197 q^{92} - 134 q^{93} + 65 q^{94} - 37 q^{95} + 6 q^{96} - 73 q^{97} - 151 q^{98} - 51 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.36612 −1.67310 −0.836551 0.547889i \(-0.815432\pi\)
−0.836551 + 0.547889i \(0.815432\pi\)
\(3\) −3.07539 −1.77558 −0.887788 0.460252i \(-0.847759\pi\)
−0.887788 + 0.460252i \(0.847759\pi\)
\(4\) 3.59854 1.79927
\(5\) −1.00000 −0.447214
\(6\) 7.27675 2.97072
\(7\) 3.28740 1.24252 0.621260 0.783604i \(-0.286621\pi\)
0.621260 + 0.783604i \(0.286621\pi\)
\(8\) −3.78235 −1.33726
\(9\) 6.45802 2.15267
\(10\) 2.36612 0.748234
\(11\) −5.16172 −1.55632 −0.778159 0.628067i \(-0.783846\pi\)
−0.778159 + 0.628067i \(0.783846\pi\)
\(12\) −11.0669 −3.19474
\(13\) −0.588339 −0.163176 −0.0815880 0.996666i \(-0.525999\pi\)
−0.0815880 + 0.996666i \(0.525999\pi\)
\(14\) −7.77839 −2.07886
\(15\) 3.07539 0.794062
\(16\) 1.75242 0.438104
\(17\) −5.86859 −1.42334 −0.711671 0.702513i \(-0.752061\pi\)
−0.711671 + 0.702513i \(0.752061\pi\)
\(18\) −15.2805 −3.60164
\(19\) −5.21720 −1.19691 −0.598454 0.801157i \(-0.704218\pi\)
−0.598454 + 0.801157i \(0.704218\pi\)
\(20\) −3.59854 −0.804658
\(21\) −10.1100 −2.20619
\(22\) 12.2133 2.60388
\(23\) −0.898889 −0.187431 −0.0937157 0.995599i \(-0.529874\pi\)
−0.0937157 + 0.995599i \(0.529874\pi\)
\(24\) 11.6322 2.37441
\(25\) 1.00000 0.200000
\(26\) 1.39208 0.273010
\(27\) −10.6348 −2.04666
\(28\) 11.8298 2.23563
\(29\) −0.0172396 −0.00320132 −0.00160066 0.999999i \(-0.500510\pi\)
−0.00160066 + 0.999999i \(0.500510\pi\)
\(30\) −7.27675 −1.32855
\(31\) 10.1623 1.82520 0.912600 0.408853i \(-0.134071\pi\)
0.912600 + 0.408853i \(0.134071\pi\)
\(32\) 3.41826 0.604268
\(33\) 15.8743 2.76336
\(34\) 13.8858 2.38140
\(35\) −3.28740 −0.555672
\(36\) 23.2395 3.87324
\(37\) −0.677044 −0.111305 −0.0556527 0.998450i \(-0.517724\pi\)
−0.0556527 + 0.998450i \(0.517724\pi\)
\(38\) 12.3445 2.00255
\(39\) 1.80937 0.289731
\(40\) 3.78235 0.598042
\(41\) 5.24336 0.818875 0.409437 0.912338i \(-0.365725\pi\)
0.409437 + 0.912338i \(0.365725\pi\)
\(42\) 23.9216 3.69118
\(43\) 0.668571 0.101956 0.0509781 0.998700i \(-0.483766\pi\)
0.0509781 + 0.998700i \(0.483766\pi\)
\(44\) −18.5747 −2.80024
\(45\) −6.45802 −0.962705
\(46\) 2.12688 0.313592
\(47\) −10.7620 −1.56980 −0.784898 0.619625i \(-0.787285\pi\)
−0.784898 + 0.619625i \(0.787285\pi\)
\(48\) −5.38937 −0.777888
\(49\) 3.80699 0.543856
\(50\) −2.36612 −0.334620
\(51\) 18.0482 2.52725
\(52\) −2.11716 −0.293598
\(53\) 2.11254 0.290179 0.145090 0.989419i \(-0.453653\pi\)
0.145090 + 0.989419i \(0.453653\pi\)
\(54\) 25.1632 3.42427
\(55\) 5.16172 0.696007
\(56\) −12.4341 −1.66157
\(57\) 16.0449 2.12520
\(58\) 0.0407911 0.00535614
\(59\) 13.7279 1.78723 0.893613 0.448838i \(-0.148162\pi\)
0.893613 + 0.448838i \(0.148162\pi\)
\(60\) 11.0669 1.42873
\(61\) −2.99581 −0.383574 −0.191787 0.981437i \(-0.561428\pi\)
−0.191787 + 0.981437i \(0.561428\pi\)
\(62\) −24.0452 −3.05375
\(63\) 21.2301 2.67474
\(64\) −11.5929 −1.44911
\(65\) 0.588339 0.0729745
\(66\) −37.5606 −4.62339
\(67\) −1.58919 −0.194151 −0.0970755 0.995277i \(-0.530949\pi\)
−0.0970755 + 0.995277i \(0.530949\pi\)
\(68\) −21.1183 −2.56098
\(69\) 2.76443 0.332799
\(70\) 7.77839 0.929696
\(71\) 8.60165 1.02083 0.510414 0.859929i \(-0.329492\pi\)
0.510414 + 0.859929i \(0.329492\pi\)
\(72\) −24.4265 −2.87869
\(73\) −6.33151 −0.741047 −0.370523 0.928823i \(-0.620822\pi\)
−0.370523 + 0.928823i \(0.620822\pi\)
\(74\) 1.60197 0.186225
\(75\) −3.07539 −0.355115
\(76\) −18.7743 −2.15356
\(77\) −16.9686 −1.93376
\(78\) −4.28120 −0.484750
\(79\) 8.41599 0.946873 0.473436 0.880828i \(-0.343013\pi\)
0.473436 + 0.880828i \(0.343013\pi\)
\(80\) −1.75242 −0.195926
\(81\) 13.3320 1.48133
\(82\) −12.4064 −1.37006
\(83\) −8.25560 −0.906170 −0.453085 0.891467i \(-0.649677\pi\)
−0.453085 + 0.891467i \(0.649677\pi\)
\(84\) −36.3814 −3.96953
\(85\) 5.86859 0.636537
\(86\) −1.58192 −0.170583
\(87\) 0.0530186 0.00568419
\(88\) 19.5234 2.08120
\(89\) −5.42031 −0.574551 −0.287276 0.957848i \(-0.592750\pi\)
−0.287276 + 0.957848i \(0.592750\pi\)
\(90\) 15.2805 1.61070
\(91\) −1.93411 −0.202749
\(92\) −3.23469 −0.337240
\(93\) −31.2530 −3.24078
\(94\) 25.4642 2.62643
\(95\) 5.21720 0.535273
\(96\) −10.5125 −1.07292
\(97\) 11.1628 1.13341 0.566703 0.823922i \(-0.308219\pi\)
0.566703 + 0.823922i \(0.308219\pi\)
\(98\) −9.00782 −0.909927
\(99\) −33.3345 −3.35025
\(100\) 3.59854 0.359854
\(101\) −2.23367 −0.222258 −0.111129 0.993806i \(-0.535447\pi\)
−0.111129 + 0.993806i \(0.535447\pi\)
\(102\) −42.7042 −4.22835
\(103\) −9.11025 −0.897659 −0.448830 0.893617i \(-0.648159\pi\)
−0.448830 + 0.893617i \(0.648159\pi\)
\(104\) 2.22530 0.218209
\(105\) 10.1100 0.986638
\(106\) −4.99852 −0.485499
\(107\) −13.6076 −1.31549 −0.657747 0.753239i \(-0.728490\pi\)
−0.657747 + 0.753239i \(0.728490\pi\)
\(108\) −38.2696 −3.68250
\(109\) 11.1141 1.06454 0.532268 0.846576i \(-0.321340\pi\)
0.532268 + 0.846576i \(0.321340\pi\)
\(110\) −12.2133 −1.16449
\(111\) 2.08217 0.197631
\(112\) 5.76090 0.544353
\(113\) −3.85274 −0.362436 −0.181218 0.983443i \(-0.558004\pi\)
−0.181218 + 0.983443i \(0.558004\pi\)
\(114\) −37.9643 −3.55568
\(115\) 0.898889 0.0838218
\(116\) −0.0620376 −0.00576004
\(117\) −3.79951 −0.351264
\(118\) −32.4820 −2.99021
\(119\) −19.2924 −1.76853
\(120\) −11.6322 −1.06187
\(121\) 15.6434 1.42213
\(122\) 7.08845 0.641758
\(123\) −16.1254 −1.45397
\(124\) 36.5694 3.28403
\(125\) −1.00000 −0.0894427
\(126\) −50.2330 −4.47511
\(127\) 5.74292 0.509602 0.254801 0.966994i \(-0.417990\pi\)
0.254801 + 0.966994i \(0.417990\pi\)
\(128\) 20.5936 1.82024
\(129\) −2.05612 −0.181031
\(130\) −1.39208 −0.122094
\(131\) 21.2655 1.85797 0.928986 0.370115i \(-0.120682\pi\)
0.928986 + 0.370115i \(0.120682\pi\)
\(132\) 57.1244 4.97204
\(133\) −17.1510 −1.48718
\(134\) 3.76023 0.324834
\(135\) 10.6348 0.915294
\(136\) 22.1970 1.90338
\(137\) 1.45751 0.124524 0.0622618 0.998060i \(-0.480169\pi\)
0.0622618 + 0.998060i \(0.480169\pi\)
\(138\) −6.54099 −0.556806
\(139\) 17.5384 1.48758 0.743792 0.668411i \(-0.233025\pi\)
0.743792 + 0.668411i \(0.233025\pi\)
\(140\) −11.8298 −0.999804
\(141\) 33.0973 2.78729
\(142\) −20.3526 −1.70795
\(143\) 3.03684 0.253954
\(144\) 11.3171 0.943096
\(145\) 0.0172396 0.00143167
\(146\) 14.9811 1.23985
\(147\) −11.7080 −0.965659
\(148\) −2.43637 −0.200268
\(149\) −14.1271 −1.15733 −0.578667 0.815564i \(-0.696427\pi\)
−0.578667 + 0.815564i \(0.696427\pi\)
\(150\) 7.27675 0.594144
\(151\) −0.306774 −0.0249649 −0.0124825 0.999922i \(-0.503973\pi\)
−0.0124825 + 0.999922i \(0.503973\pi\)
\(152\) 19.7333 1.60058
\(153\) −37.8994 −3.06399
\(154\) 40.1499 3.23537
\(155\) −10.1623 −0.816254
\(156\) 6.51110 0.521305
\(157\) 17.3500 1.38468 0.692341 0.721570i \(-0.256579\pi\)
0.692341 + 0.721570i \(0.256579\pi\)
\(158\) −19.9133 −1.58421
\(159\) −6.49687 −0.515235
\(160\) −3.41826 −0.270237
\(161\) −2.95501 −0.232887
\(162\) −31.5451 −2.47842
\(163\) 2.35349 0.184339 0.0921696 0.995743i \(-0.470620\pi\)
0.0921696 + 0.995743i \(0.470620\pi\)
\(164\) 18.8684 1.47338
\(165\) −15.8743 −1.23581
\(166\) 19.5338 1.51612
\(167\) 13.6983 1.06001 0.530005 0.847995i \(-0.322190\pi\)
0.530005 + 0.847995i \(0.322190\pi\)
\(168\) 38.2396 2.95025
\(169\) −12.6539 −0.973374
\(170\) −13.8858 −1.06499
\(171\) −33.6928 −2.57655
\(172\) 2.40588 0.183447
\(173\) −4.21847 −0.320724 −0.160362 0.987058i \(-0.551266\pi\)
−0.160362 + 0.987058i \(0.551266\pi\)
\(174\) −0.125449 −0.00951023
\(175\) 3.28740 0.248504
\(176\) −9.04549 −0.681830
\(177\) −42.2188 −3.17336
\(178\) 12.8251 0.961283
\(179\) −13.0669 −0.976663 −0.488332 0.872658i \(-0.662394\pi\)
−0.488332 + 0.872658i \(0.662394\pi\)
\(180\) −23.2395 −1.73217
\(181\) 0.0904172 0.00672066 0.00336033 0.999994i \(-0.498930\pi\)
0.00336033 + 0.999994i \(0.498930\pi\)
\(182\) 4.57633 0.339220
\(183\) 9.21327 0.681065
\(184\) 3.39991 0.250645
\(185\) 0.677044 0.0497773
\(186\) 73.9484 5.42216
\(187\) 30.2920 2.21517
\(188\) −38.7274 −2.82449
\(189\) −34.9607 −2.54302
\(190\) −12.3445 −0.895567
\(191\) 3.42710 0.247976 0.123988 0.992284i \(-0.460432\pi\)
0.123988 + 0.992284i \(0.460432\pi\)
\(192\) 35.6525 2.57300
\(193\) −8.29879 −0.597360 −0.298680 0.954353i \(-0.596546\pi\)
−0.298680 + 0.954353i \(0.596546\pi\)
\(194\) −26.4124 −1.89630
\(195\) −1.80937 −0.129572
\(196\) 13.6996 0.978545
\(197\) 11.1523 0.794568 0.397284 0.917696i \(-0.369953\pi\)
0.397284 + 0.917696i \(0.369953\pi\)
\(198\) 78.8736 5.60530
\(199\) 21.8295 1.54745 0.773727 0.633520i \(-0.218390\pi\)
0.773727 + 0.633520i \(0.218390\pi\)
\(200\) −3.78235 −0.267452
\(201\) 4.88739 0.344730
\(202\) 5.28513 0.371860
\(203\) −0.0566736 −0.00397771
\(204\) 64.9471 4.54721
\(205\) −5.24336 −0.366212
\(206\) 21.5560 1.50188
\(207\) −5.80504 −0.403478
\(208\) −1.03102 −0.0714881
\(209\) 26.9297 1.86277
\(210\) −23.9216 −1.65075
\(211\) −18.7450 −1.29046 −0.645230 0.763989i \(-0.723238\pi\)
−0.645230 + 0.763989i \(0.723238\pi\)
\(212\) 7.60205 0.522111
\(213\) −26.4534 −1.81256
\(214\) 32.1972 2.20096
\(215\) −0.668571 −0.0455962
\(216\) 40.2243 2.73692
\(217\) 33.4075 2.26785
\(218\) −26.2973 −1.78108
\(219\) 19.4718 1.31579
\(220\) 18.5747 1.25230
\(221\) 3.45272 0.232255
\(222\) −4.92668 −0.330657
\(223\) −10.4204 −0.697803 −0.348901 0.937159i \(-0.613445\pi\)
−0.348901 + 0.937159i \(0.613445\pi\)
\(224\) 11.2372 0.750815
\(225\) 6.45802 0.430535
\(226\) 9.11607 0.606392
\(227\) −6.01240 −0.399057 −0.199529 0.979892i \(-0.563941\pi\)
−0.199529 + 0.979892i \(0.563941\pi\)
\(228\) 57.7383 3.82381
\(229\) 17.5419 1.15920 0.579600 0.814901i \(-0.303209\pi\)
0.579600 + 0.814901i \(0.303209\pi\)
\(230\) −2.12688 −0.140243
\(231\) 52.1852 3.43353
\(232\) 0.0652063 0.00428100
\(233\) −4.30961 −0.282332 −0.141166 0.989986i \(-0.545085\pi\)
−0.141166 + 0.989986i \(0.545085\pi\)
\(234\) 8.99010 0.587701
\(235\) 10.7620 0.702034
\(236\) 49.4006 3.21570
\(237\) −25.8824 −1.68125
\(238\) 45.6482 2.95893
\(239\) 27.1554 1.75653 0.878267 0.478170i \(-0.158700\pi\)
0.878267 + 0.478170i \(0.158700\pi\)
\(240\) 5.38937 0.347882
\(241\) 27.9422 1.79992 0.899958 0.435976i \(-0.143597\pi\)
0.899958 + 0.435976i \(0.143597\pi\)
\(242\) −37.0142 −2.37936
\(243\) −9.09671 −0.583554
\(244\) −10.7805 −0.690153
\(245\) −3.80699 −0.243220
\(246\) 38.1546 2.43265
\(247\) 3.06948 0.195307
\(248\) −38.4373 −2.44077
\(249\) 25.3892 1.60897
\(250\) 2.36612 0.149647
\(251\) −30.3794 −1.91753 −0.958766 0.284198i \(-0.908273\pi\)
−0.958766 + 0.284198i \(0.908273\pi\)
\(252\) 76.3974 4.81258
\(253\) 4.63982 0.291703
\(254\) −13.5885 −0.852616
\(255\) −18.0482 −1.13022
\(256\) −25.5413 −1.59633
\(257\) 10.5086 0.655508 0.327754 0.944763i \(-0.393708\pi\)
0.327754 + 0.944763i \(0.393708\pi\)
\(258\) 4.86503 0.302883
\(259\) −2.22571 −0.138299
\(260\) 2.11716 0.131301
\(261\) −0.111334 −0.00689140
\(262\) −50.3167 −3.10858
\(263\) 7.69863 0.474718 0.237359 0.971422i \(-0.423718\pi\)
0.237359 + 0.971422i \(0.423718\pi\)
\(264\) −60.0421 −3.69534
\(265\) −2.11254 −0.129772
\(266\) 40.5814 2.48821
\(267\) 16.6696 1.02016
\(268\) −5.71878 −0.349330
\(269\) −10.1928 −0.621465 −0.310733 0.950497i \(-0.600574\pi\)
−0.310733 + 0.950497i \(0.600574\pi\)
\(270\) −25.1632 −1.53138
\(271\) −28.1002 −1.70696 −0.853481 0.521123i \(-0.825513\pi\)
−0.853481 + 0.521123i \(0.825513\pi\)
\(272\) −10.2842 −0.623572
\(273\) 5.94813 0.359997
\(274\) −3.44865 −0.208341
\(275\) −5.16172 −0.311264
\(276\) 9.94793 0.598795
\(277\) −12.8701 −0.773291 −0.386645 0.922229i \(-0.626366\pi\)
−0.386645 + 0.922229i \(0.626366\pi\)
\(278\) −41.4979 −2.48888
\(279\) 65.6282 3.92906
\(280\) 12.4341 0.743079
\(281\) −14.6774 −0.875578 −0.437789 0.899078i \(-0.644238\pi\)
−0.437789 + 0.899078i \(0.644238\pi\)
\(282\) −78.3123 −4.66343
\(283\) 17.7741 1.05656 0.528282 0.849069i \(-0.322837\pi\)
0.528282 + 0.849069i \(0.322837\pi\)
\(284\) 30.9534 1.83675
\(285\) −16.0449 −0.950419
\(286\) −7.18555 −0.424890
\(287\) 17.2370 1.01747
\(288\) 22.0752 1.30079
\(289\) 17.4403 1.02590
\(290\) −0.0407911 −0.00239534
\(291\) −34.3298 −2.01245
\(292\) −22.7842 −1.33334
\(293\) −5.41529 −0.316365 −0.158182 0.987410i \(-0.550563\pi\)
−0.158182 + 0.987410i \(0.550563\pi\)
\(294\) 27.7025 1.61565
\(295\) −13.7279 −0.799272
\(296\) 2.56081 0.148844
\(297\) 54.8937 3.18525
\(298\) 33.4264 1.93634
\(299\) 0.528852 0.0305843
\(300\) −11.0669 −0.638949
\(301\) 2.19786 0.126683
\(302\) 0.725866 0.0417689
\(303\) 6.86939 0.394636
\(304\) −9.14271 −0.524371
\(305\) 2.99581 0.171539
\(306\) 89.6748 5.12637
\(307\) −1.20893 −0.0689976 −0.0344988 0.999405i \(-0.510983\pi\)
−0.0344988 + 0.999405i \(0.510983\pi\)
\(308\) −61.0624 −3.47935
\(309\) 28.0176 1.59386
\(310\) 24.0452 1.36568
\(311\) 12.5722 0.712903 0.356452 0.934314i \(-0.383986\pi\)
0.356452 + 0.934314i \(0.383986\pi\)
\(312\) −6.84367 −0.387447
\(313\) 10.7037 0.605011 0.302506 0.953148i \(-0.402177\pi\)
0.302506 + 0.953148i \(0.402177\pi\)
\(314\) −41.0523 −2.31672
\(315\) −21.2301 −1.19618
\(316\) 30.2853 1.70368
\(317\) −23.0882 −1.29676 −0.648381 0.761316i \(-0.724553\pi\)
−0.648381 + 0.761316i \(0.724553\pi\)
\(318\) 15.3724 0.862041
\(319\) 0.0889863 0.00498227
\(320\) 11.5929 0.648060
\(321\) 41.8486 2.33576
\(322\) 6.99191 0.389644
\(323\) 30.6176 1.70361
\(324\) 47.9756 2.66531
\(325\) −0.588339 −0.0326352
\(326\) −5.56864 −0.308418
\(327\) −34.1801 −1.89016
\(328\) −19.8322 −1.09505
\(329\) −35.3789 −1.95050
\(330\) 37.5606 2.06764
\(331\) −9.07569 −0.498845 −0.249423 0.968395i \(-0.580241\pi\)
−0.249423 + 0.968395i \(0.580241\pi\)
\(332\) −29.7081 −1.63045
\(333\) −4.37236 −0.239604
\(334\) −32.4120 −1.77350
\(335\) 1.58919 0.0868270
\(336\) −17.7170 −0.966541
\(337\) −1.84113 −0.100293 −0.0501464 0.998742i \(-0.515969\pi\)
−0.0501464 + 0.998742i \(0.515969\pi\)
\(338\) 29.9406 1.62855
\(339\) 11.8487 0.643532
\(340\) 21.1183 1.14530
\(341\) −52.4549 −2.84059
\(342\) 79.7213 4.31083
\(343\) −10.4967 −0.566768
\(344\) −2.52877 −0.136342
\(345\) −2.76443 −0.148832
\(346\) 9.98142 0.536605
\(347\) 27.8846 1.49692 0.748462 0.663177i \(-0.230792\pi\)
0.748462 + 0.663177i \(0.230792\pi\)
\(348\) 0.190790 0.0102274
\(349\) −34.1007 −1.82537 −0.912683 0.408668i \(-0.865993\pi\)
−0.912683 + 0.408668i \(0.865993\pi\)
\(350\) −7.77839 −0.415773
\(351\) 6.25685 0.333966
\(352\) −17.6441 −0.940434
\(353\) −10.0598 −0.535431 −0.267716 0.963498i \(-0.586269\pi\)
−0.267716 + 0.963498i \(0.586269\pi\)
\(354\) 99.8949 5.30935
\(355\) −8.60165 −0.456528
\(356\) −19.5052 −1.03377
\(357\) 59.3316 3.14016
\(358\) 30.9178 1.63406
\(359\) −3.59741 −0.189864 −0.0949320 0.995484i \(-0.530263\pi\)
−0.0949320 + 0.995484i \(0.530263\pi\)
\(360\) 24.4265 1.28739
\(361\) 8.21918 0.432588
\(362\) −0.213938 −0.0112443
\(363\) −48.1095 −2.52510
\(364\) −6.95996 −0.364801
\(365\) 6.33151 0.331406
\(366\) −21.7997 −1.13949
\(367\) 6.66468 0.347893 0.173947 0.984755i \(-0.444348\pi\)
0.173947 + 0.984755i \(0.444348\pi\)
\(368\) −1.57523 −0.0821145
\(369\) 33.8617 1.76277
\(370\) −1.60197 −0.0832824
\(371\) 6.94475 0.360553
\(372\) −112.465 −5.83105
\(373\) 5.81113 0.300889 0.150444 0.988618i \(-0.451930\pi\)
0.150444 + 0.988618i \(0.451930\pi\)
\(374\) −71.6747 −3.70621
\(375\) 3.07539 0.158812
\(376\) 40.7055 2.09923
\(377\) 0.0101428 0.000522379 0
\(378\) 82.7213 4.25473
\(379\) −21.3947 −1.09897 −0.549487 0.835502i \(-0.685177\pi\)
−0.549487 + 0.835502i \(0.685177\pi\)
\(380\) 18.7743 0.963102
\(381\) −17.6617 −0.904837
\(382\) −8.10893 −0.414889
\(383\) 19.8857 1.01611 0.508055 0.861325i \(-0.330365\pi\)
0.508055 + 0.861325i \(0.330365\pi\)
\(384\) −63.3334 −3.23197
\(385\) 16.9686 0.864802
\(386\) 19.6360 0.999445
\(387\) 4.31765 0.219478
\(388\) 40.1696 2.03930
\(389\) 10.3201 0.523251 0.261625 0.965169i \(-0.415741\pi\)
0.261625 + 0.965169i \(0.415741\pi\)
\(390\) 4.28120 0.216787
\(391\) 5.27521 0.266779
\(392\) −14.3994 −0.727278
\(393\) −65.3996 −3.29897
\(394\) −26.3877 −1.32939
\(395\) −8.41599 −0.423454
\(396\) −119.956 −6.02800
\(397\) 0.116493 0.00584659 0.00292330 0.999996i \(-0.499069\pi\)
0.00292330 + 0.999996i \(0.499069\pi\)
\(398\) −51.6513 −2.58905
\(399\) 52.7461 2.64061
\(400\) 1.75242 0.0876209
\(401\) −14.5740 −0.727790 −0.363895 0.931440i \(-0.618553\pi\)
−0.363895 + 0.931440i \(0.618553\pi\)
\(402\) −11.5642 −0.576768
\(403\) −5.97887 −0.297829
\(404\) −8.03794 −0.399902
\(405\) −13.3320 −0.662471
\(406\) 0.134097 0.00665511
\(407\) 3.49471 0.173227
\(408\) −68.2645 −3.37960
\(409\) 12.0558 0.596121 0.298060 0.954547i \(-0.403660\pi\)
0.298060 + 0.954547i \(0.403660\pi\)
\(410\) 12.4064 0.612710
\(411\) −4.48241 −0.221101
\(412\) −32.7836 −1.61513
\(413\) 45.1292 2.22066
\(414\) 13.7355 0.675061
\(415\) 8.25560 0.405252
\(416\) −2.01109 −0.0986020
\(417\) −53.9373 −2.64132
\(418\) −63.7191 −3.11660
\(419\) −16.6203 −0.811957 −0.405979 0.913883i \(-0.633069\pi\)
−0.405979 + 0.913883i \(0.633069\pi\)
\(420\) 36.3814 1.77523
\(421\) −7.30206 −0.355881 −0.177940 0.984041i \(-0.556943\pi\)
−0.177940 + 0.984041i \(0.556943\pi\)
\(422\) 44.3530 2.15907
\(423\) −69.5011 −3.37926
\(424\) −7.99034 −0.388045
\(425\) −5.86859 −0.284668
\(426\) 62.5921 3.03260
\(427\) −9.84841 −0.476598
\(428\) −48.9674 −2.36693
\(429\) −9.33948 −0.450914
\(430\) 1.58192 0.0762870
\(431\) 33.8206 1.62908 0.814541 0.580106i \(-0.196989\pi\)
0.814541 + 0.580106i \(0.196989\pi\)
\(432\) −18.6365 −0.896651
\(433\) −1.81250 −0.0871033 −0.0435516 0.999051i \(-0.513867\pi\)
−0.0435516 + 0.999051i \(0.513867\pi\)
\(434\) −79.0462 −3.79434
\(435\) −0.0530186 −0.00254205
\(436\) 39.9945 1.91539
\(437\) 4.68968 0.224338
\(438\) −46.0728 −2.20144
\(439\) −7.76897 −0.370793 −0.185396 0.982664i \(-0.559357\pi\)
−0.185396 + 0.982664i \(0.559357\pi\)
\(440\) −19.5234 −0.930743
\(441\) 24.5856 1.17074
\(442\) −8.16956 −0.388586
\(443\) −10.7822 −0.512280 −0.256140 0.966640i \(-0.582451\pi\)
−0.256140 + 0.966640i \(0.582451\pi\)
\(444\) 7.49279 0.355592
\(445\) 5.42031 0.256947
\(446\) 24.6560 1.16749
\(447\) 43.4462 2.05493
\(448\) −38.1103 −1.80054
\(449\) 9.06052 0.427592 0.213796 0.976878i \(-0.431417\pi\)
0.213796 + 0.976878i \(0.431417\pi\)
\(450\) −15.2805 −0.720328
\(451\) −27.0648 −1.27443
\(452\) −13.8643 −0.652120
\(453\) 0.943451 0.0443272
\(454\) 14.2261 0.667663
\(455\) 1.93411 0.0906723
\(456\) −60.6875 −2.84195
\(457\) −21.8343 −1.02136 −0.510682 0.859770i \(-0.670607\pi\)
−0.510682 + 0.859770i \(0.670607\pi\)
\(458\) −41.5062 −1.93946
\(459\) 62.4110 2.91310
\(460\) 3.23469 0.150818
\(461\) 10.0497 0.468062 0.234031 0.972229i \(-0.424808\pi\)
0.234031 + 0.972229i \(0.424808\pi\)
\(462\) −123.477 −5.74465
\(463\) 33.3348 1.54920 0.774599 0.632452i \(-0.217951\pi\)
0.774599 + 0.632452i \(0.217951\pi\)
\(464\) −0.0302110 −0.00140251
\(465\) 31.2530 1.44932
\(466\) 10.1971 0.472370
\(467\) 26.0048 1.20336 0.601678 0.798738i \(-0.294499\pi\)
0.601678 + 0.798738i \(0.294499\pi\)
\(468\) −13.6727 −0.632020
\(469\) −5.22432 −0.241236
\(470\) −25.4642 −1.17457
\(471\) −53.3581 −2.45861
\(472\) −51.9239 −2.38999
\(473\) −3.45098 −0.158676
\(474\) 61.2411 2.81289
\(475\) −5.21720 −0.239382
\(476\) −69.4244 −3.18206
\(477\) 13.6428 0.624661
\(478\) −64.2529 −2.93886
\(479\) −5.92247 −0.270604 −0.135302 0.990804i \(-0.543201\pi\)
−0.135302 + 0.990804i \(0.543201\pi\)
\(480\) 10.5125 0.479827
\(481\) 0.398331 0.0181623
\(482\) −66.1147 −3.01144
\(483\) 9.08780 0.413509
\(484\) 56.2934 2.55879
\(485\) −11.1628 −0.506874
\(486\) 21.5239 0.976346
\(487\) 35.8580 1.62488 0.812442 0.583042i \(-0.198138\pi\)
0.812442 + 0.583042i \(0.198138\pi\)
\(488\) 11.3312 0.512938
\(489\) −7.23789 −0.327309
\(490\) 9.00782 0.406932
\(491\) 21.2768 0.960208 0.480104 0.877211i \(-0.340599\pi\)
0.480104 + 0.877211i \(0.340599\pi\)
\(492\) −58.0278 −2.61609
\(493\) 0.101172 0.00455657
\(494\) −7.26278 −0.326768
\(495\) 33.3345 1.49828
\(496\) 17.8086 0.799628
\(497\) 28.2771 1.26840
\(498\) −60.0740 −2.69198
\(499\) 36.6870 1.64233 0.821167 0.570688i \(-0.193323\pi\)
0.821167 + 0.570688i \(0.193323\pi\)
\(500\) −3.59854 −0.160932
\(501\) −42.1277 −1.88213
\(502\) 71.8814 3.20823
\(503\) −20.2739 −0.903970 −0.451985 0.892026i \(-0.649284\pi\)
−0.451985 + 0.892026i \(0.649284\pi\)
\(504\) −80.2996 −3.57683
\(505\) 2.23367 0.0993968
\(506\) −10.9784 −0.488049
\(507\) 38.9155 1.72830
\(508\) 20.6661 0.916911
\(509\) −1.62790 −0.0721555 −0.0360777 0.999349i \(-0.511486\pi\)
−0.0360777 + 0.999349i \(0.511486\pi\)
\(510\) 42.7042 1.89098
\(511\) −20.8142 −0.920766
\(512\) 19.2467 0.850593
\(513\) 55.4837 2.44966
\(514\) −24.8646 −1.09673
\(515\) 9.11025 0.401445
\(516\) −7.39902 −0.325724
\(517\) 55.5504 2.44310
\(518\) 5.26631 0.231389
\(519\) 12.9734 0.569471
\(520\) −2.22530 −0.0975860
\(521\) 18.9189 0.828852 0.414426 0.910083i \(-0.363982\pi\)
0.414426 + 0.910083i \(0.363982\pi\)
\(522\) 0.263430 0.0115300
\(523\) −5.81238 −0.254157 −0.127079 0.991893i \(-0.540560\pi\)
−0.127079 + 0.991893i \(0.540560\pi\)
\(524\) 76.5246 3.34299
\(525\) −10.1100 −0.441238
\(526\) −18.2159 −0.794251
\(527\) −59.6382 −2.59788
\(528\) 27.8184 1.21064
\(529\) −22.1920 −0.964869
\(530\) 4.99852 0.217122
\(531\) 88.6554 3.84731
\(532\) −61.7187 −2.67584
\(533\) −3.08487 −0.133621
\(534\) −39.4422 −1.70683
\(535\) 13.6076 0.588307
\(536\) 6.01088 0.259631
\(537\) 40.1857 1.73414
\(538\) 24.1174 1.03977
\(539\) −19.6507 −0.846413
\(540\) 38.2696 1.64686
\(541\) 9.28912 0.399370 0.199685 0.979860i \(-0.436008\pi\)
0.199685 + 0.979860i \(0.436008\pi\)
\(542\) 66.4884 2.85592
\(543\) −0.278068 −0.0119330
\(544\) −20.0603 −0.860080
\(545\) −11.1141 −0.476075
\(546\) −14.0740 −0.602312
\(547\) 16.3683 0.699858 0.349929 0.936776i \(-0.386206\pi\)
0.349929 + 0.936776i \(0.386206\pi\)
\(548\) 5.24491 0.224052
\(549\) −19.3470 −0.825709
\(550\) 12.2133 0.520776
\(551\) 0.0899427 0.00383169
\(552\) −10.4560 −0.445039
\(553\) 27.6667 1.17651
\(554\) 30.4523 1.29379
\(555\) −2.08217 −0.0883833
\(556\) 63.1125 2.67657
\(557\) −8.66389 −0.367101 −0.183550 0.983010i \(-0.558759\pi\)
−0.183550 + 0.983010i \(0.558759\pi\)
\(558\) −155.285 −6.57372
\(559\) −0.393347 −0.0166368
\(560\) −5.76090 −0.243442
\(561\) −93.1598 −3.93321
\(562\) 34.7285 1.46493
\(563\) 44.9070 1.89260 0.946302 0.323283i \(-0.104787\pi\)
0.946302 + 0.323283i \(0.104787\pi\)
\(564\) 119.102 5.01510
\(565\) 3.85274 0.162086
\(566\) −42.0558 −1.76774
\(567\) 43.8275 1.84058
\(568\) −32.5344 −1.36511
\(569\) 26.8612 1.12608 0.563040 0.826430i \(-0.309632\pi\)
0.563040 + 0.826430i \(0.309632\pi\)
\(570\) 37.9643 1.59015
\(571\) 10.9228 0.457104 0.228552 0.973532i \(-0.426601\pi\)
0.228552 + 0.973532i \(0.426601\pi\)
\(572\) 10.9282 0.456931
\(573\) −10.5397 −0.440300
\(574\) −40.7849 −1.70233
\(575\) −0.898889 −0.0374863
\(576\) −74.8669 −3.11945
\(577\) 8.39183 0.349356 0.174678 0.984626i \(-0.444112\pi\)
0.174678 + 0.984626i \(0.444112\pi\)
\(578\) −41.2659 −1.71644
\(579\) 25.5220 1.06066
\(580\) 0.0620376 0.00257597
\(581\) −27.1395 −1.12593
\(582\) 81.2286 3.36703
\(583\) −10.9043 −0.451611
\(584\) 23.9480 0.990973
\(585\) 3.79951 0.157090
\(586\) 12.8133 0.529311
\(587\) −5.46457 −0.225547 −0.112773 0.993621i \(-0.535973\pi\)
−0.112773 + 0.993621i \(0.535973\pi\)
\(588\) −42.1317 −1.73748
\(589\) −53.0187 −2.18460
\(590\) 32.4820 1.33726
\(591\) −34.2976 −1.41082
\(592\) −1.18646 −0.0487633
\(593\) 6.14451 0.252325 0.126162 0.992010i \(-0.459734\pi\)
0.126162 + 0.992010i \(0.459734\pi\)
\(594\) −129.885 −5.32926
\(595\) 19.2924 0.790911
\(596\) −50.8368 −2.08236
\(597\) −67.1342 −2.74762
\(598\) −1.25133 −0.0511706
\(599\) −10.3899 −0.424521 −0.212261 0.977213i \(-0.568083\pi\)
−0.212261 + 0.977213i \(0.568083\pi\)
\(600\) 11.6322 0.474882
\(601\) −29.1871 −1.19057 −0.595284 0.803516i \(-0.702960\pi\)
−0.595284 + 0.803516i \(0.702960\pi\)
\(602\) −5.20041 −0.211953
\(603\) −10.2630 −0.417944
\(604\) −1.10394 −0.0449187
\(605\) −15.6434 −0.635994
\(606\) −16.2538 −0.660267
\(607\) 36.0792 1.46441 0.732204 0.681085i \(-0.238492\pi\)
0.732204 + 0.681085i \(0.238492\pi\)
\(608\) −17.8337 −0.723253
\(609\) 0.174293 0.00706272
\(610\) −7.08845 −0.287003
\(611\) 6.33169 0.256153
\(612\) −136.383 −5.51294
\(613\) −26.4548 −1.06850 −0.534250 0.845327i \(-0.679406\pi\)
−0.534250 + 0.845327i \(0.679406\pi\)
\(614\) 2.86049 0.115440
\(615\) 16.1254 0.650237
\(616\) 64.1813 2.58594
\(617\) −28.9200 −1.16427 −0.582137 0.813091i \(-0.697783\pi\)
−0.582137 + 0.813091i \(0.697783\pi\)
\(618\) −66.2930 −2.66670
\(619\) 43.9134 1.76503 0.882514 0.470286i \(-0.155849\pi\)
0.882514 + 0.470286i \(0.155849\pi\)
\(620\) −36.5694 −1.46866
\(621\) 9.55947 0.383608
\(622\) −29.7473 −1.19276
\(623\) −17.8187 −0.713892
\(624\) 3.17077 0.126933
\(625\) 1.00000 0.0400000
\(626\) −25.3264 −1.01225
\(627\) −82.8195 −3.30749
\(628\) 62.4348 2.49142
\(629\) 3.97329 0.158425
\(630\) 50.2330 2.00133
\(631\) −9.39118 −0.373857 −0.186928 0.982374i \(-0.559853\pi\)
−0.186928 + 0.982374i \(0.559853\pi\)
\(632\) −31.8322 −1.26622
\(633\) 57.6482 2.29131
\(634\) 54.6295 2.16961
\(635\) −5.74292 −0.227901
\(636\) −23.3793 −0.927048
\(637\) −2.23980 −0.0887442
\(638\) −0.210553 −0.00833585
\(639\) 55.5496 2.19751
\(640\) −20.5936 −0.814034
\(641\) 17.8921 0.706695 0.353348 0.935492i \(-0.385043\pi\)
0.353348 + 0.935492i \(0.385043\pi\)
\(642\) −99.0190 −3.90797
\(643\) −4.94125 −0.194864 −0.0974320 0.995242i \(-0.531063\pi\)
−0.0974320 + 0.995242i \(0.531063\pi\)
\(644\) −10.6337 −0.419027
\(645\) 2.05612 0.0809595
\(646\) −72.4450 −2.85031
\(647\) −29.0644 −1.14264 −0.571320 0.820727i \(-0.693568\pi\)
−0.571320 + 0.820727i \(0.693568\pi\)
\(648\) −50.4261 −1.98092
\(649\) −70.8599 −2.78149
\(650\) 1.39208 0.0546020
\(651\) −102.741 −4.02674
\(652\) 8.46912 0.331676
\(653\) 4.18506 0.163774 0.0818870 0.996642i \(-0.473905\pi\)
0.0818870 + 0.996642i \(0.473905\pi\)
\(654\) 80.8744 3.16244
\(655\) −21.2655 −0.830910
\(656\) 9.18855 0.358753
\(657\) −40.8890 −1.59523
\(658\) 83.7109 3.26339
\(659\) −7.20160 −0.280535 −0.140267 0.990114i \(-0.544796\pi\)
−0.140267 + 0.990114i \(0.544796\pi\)
\(660\) −57.1244 −2.22356
\(661\) −1.65025 −0.0641873 −0.0320937 0.999485i \(-0.510217\pi\)
−0.0320937 + 0.999485i \(0.510217\pi\)
\(662\) 21.4742 0.834619
\(663\) −10.6185 −0.412387
\(664\) 31.2256 1.21179
\(665\) 17.1510 0.665088
\(666\) 10.3456 0.400882
\(667\) 0.0154965 0.000600028 0
\(668\) 49.2940 1.90724
\(669\) 32.0468 1.23900
\(670\) −3.76023 −0.145270
\(671\) 15.4635 0.596963
\(672\) −34.5587 −1.33313
\(673\) 9.04261 0.348567 0.174284 0.984696i \(-0.444239\pi\)
0.174284 + 0.984696i \(0.444239\pi\)
\(674\) 4.35634 0.167800
\(675\) −10.6348 −0.409332
\(676\) −45.5354 −1.75136
\(677\) 23.9548 0.920657 0.460328 0.887749i \(-0.347732\pi\)
0.460328 + 0.887749i \(0.347732\pi\)
\(678\) −28.0355 −1.07670
\(679\) 36.6964 1.40828
\(680\) −22.1970 −0.851217
\(681\) 18.4905 0.708557
\(682\) 124.115 4.75260
\(683\) 16.0727 0.615005 0.307503 0.951547i \(-0.400507\pi\)
0.307503 + 0.951547i \(0.400507\pi\)
\(684\) −121.245 −4.63591
\(685\) −1.45751 −0.0556886
\(686\) 24.8365 0.948260
\(687\) −53.9481 −2.05825
\(688\) 1.17162 0.0446674
\(689\) −1.24289 −0.0473502
\(690\) 6.54099 0.249011
\(691\) −28.0749 −1.06802 −0.534009 0.845479i \(-0.679315\pi\)
−0.534009 + 0.845479i \(0.679315\pi\)
\(692\) −15.1803 −0.577070
\(693\) −109.584 −4.16275
\(694\) −65.9785 −2.50451
\(695\) −17.5384 −0.665268
\(696\) −0.200535 −0.00760125
\(697\) −30.7711 −1.16554
\(698\) 80.6864 3.05402
\(699\) 13.2537 0.501302
\(700\) 11.8298 0.447126
\(701\) −1.44616 −0.0546208 −0.0273104 0.999627i \(-0.508694\pi\)
−0.0273104 + 0.999627i \(0.508694\pi\)
\(702\) −14.8045 −0.558759
\(703\) 3.53227 0.133222
\(704\) 59.8391 2.25527
\(705\) −33.0973 −1.24652
\(706\) 23.8028 0.895831
\(707\) −7.34295 −0.276160
\(708\) −151.926 −5.70973
\(709\) −17.8710 −0.671161 −0.335580 0.942012i \(-0.608932\pi\)
−0.335580 + 0.942012i \(0.608932\pi\)
\(710\) 20.3526 0.763818
\(711\) 54.3506 2.03831
\(712\) 20.5015 0.768325
\(713\) −9.13477 −0.342100
\(714\) −140.386 −5.25381
\(715\) −3.03684 −0.113572
\(716\) −47.0216 −1.75728
\(717\) −83.5133 −3.11886
\(718\) 8.51191 0.317662
\(719\) 52.4303 1.95532 0.977660 0.210193i \(-0.0674091\pi\)
0.977660 + 0.210193i \(0.0674091\pi\)
\(720\) −11.3171 −0.421765
\(721\) −29.9490 −1.11536
\(722\) −19.4476 −0.723765
\(723\) −85.9332 −3.19589
\(724\) 0.325370 0.0120923
\(725\) −0.0172396 −0.000640264 0
\(726\) 113.833 4.22474
\(727\) 26.8833 0.997046 0.498523 0.866876i \(-0.333876\pi\)
0.498523 + 0.866876i \(0.333876\pi\)
\(728\) 7.31546 0.271129
\(729\) −12.0200 −0.445184
\(730\) −14.9811 −0.554476
\(731\) −3.92357 −0.145118
\(732\) 33.1543 1.22542
\(733\) −11.1616 −0.412265 −0.206132 0.978524i \(-0.566088\pi\)
−0.206132 + 0.978524i \(0.566088\pi\)
\(734\) −15.7695 −0.582061
\(735\) 11.7080 0.431856
\(736\) −3.07263 −0.113259
\(737\) 8.20298 0.302161
\(738\) −80.1210 −2.94929
\(739\) 12.7281 0.468212 0.234106 0.972211i \(-0.424784\pi\)
0.234106 + 0.972211i \(0.424784\pi\)
\(740\) 2.43637 0.0895628
\(741\) −9.43986 −0.346782
\(742\) −16.4321 −0.603243
\(743\) −48.6917 −1.78633 −0.893163 0.449732i \(-0.851519\pi\)
−0.893163 + 0.449732i \(0.851519\pi\)
\(744\) 118.210 4.33377
\(745\) 14.1271 0.517575
\(746\) −13.7499 −0.503418
\(747\) −53.3149 −1.95069
\(748\) 109.007 3.98569
\(749\) −44.7335 −1.63453
\(750\) −7.27675 −0.265709
\(751\) −54.4956 −1.98857 −0.994287 0.106744i \(-0.965957\pi\)
−0.994287 + 0.106744i \(0.965957\pi\)
\(752\) −18.8595 −0.687734
\(753\) 93.4285 3.40472
\(754\) −0.0239990 −0.000873993 0
\(755\) 0.306774 0.0111647
\(756\) −125.808 −4.57558
\(757\) −22.6406 −0.822888 −0.411444 0.911435i \(-0.634975\pi\)
−0.411444 + 0.911435i \(0.634975\pi\)
\(758\) 50.6226 1.83870
\(759\) −14.2692 −0.517941
\(760\) −19.7333 −0.715801
\(761\) 45.4808 1.64868 0.824339 0.566097i \(-0.191547\pi\)
0.824339 + 0.566097i \(0.191547\pi\)
\(762\) 41.7898 1.51388
\(763\) 36.5364 1.32271
\(764\) 12.3325 0.446176
\(765\) 37.8994 1.37026
\(766\) −47.0519 −1.70005
\(767\) −8.07669 −0.291632
\(768\) 78.5495 2.83441
\(769\) −29.6728 −1.07003 −0.535013 0.844844i \(-0.679693\pi\)
−0.535013 + 0.844844i \(0.679693\pi\)
\(770\) −40.1499 −1.44690
\(771\) −32.3180 −1.16391
\(772\) −29.8636 −1.07481
\(773\) 5.69643 0.204886 0.102443 0.994739i \(-0.467334\pi\)
0.102443 + 0.994739i \(0.467334\pi\)
\(774\) −10.2161 −0.367210
\(775\) 10.1623 0.365040
\(776\) −42.2214 −1.51566
\(777\) 6.84494 0.245561
\(778\) −24.4187 −0.875452
\(779\) −27.3556 −0.980117
\(780\) −6.51110 −0.233135
\(781\) −44.3993 −1.58873
\(782\) −12.4818 −0.446348
\(783\) 0.183339 0.00655202
\(784\) 6.67144 0.238266
\(785\) −17.3500 −0.619249
\(786\) 154.743 5.51952
\(787\) 13.5510 0.483042 0.241521 0.970396i \(-0.422354\pi\)
0.241521 + 0.970396i \(0.422354\pi\)
\(788\) 40.1320 1.42964
\(789\) −23.6763 −0.842898
\(790\) 19.9133 0.708482
\(791\) −12.6655 −0.450334
\(792\) 126.083 4.48015
\(793\) 1.76255 0.0625900
\(794\) −0.275636 −0.00978195
\(795\) 6.49687 0.230420
\(796\) 78.5544 2.78429
\(797\) −1.90869 −0.0676094 −0.0338047 0.999428i \(-0.510762\pi\)
−0.0338047 + 0.999428i \(0.510762\pi\)
\(798\) −124.804 −4.41800
\(799\) 63.1576 2.23436
\(800\) 3.41826 0.120854
\(801\) −35.0045 −1.23682
\(802\) 34.4838 1.21767
\(803\) 32.6815 1.15330
\(804\) 17.5875 0.620263
\(805\) 2.95501 0.104150
\(806\) 14.1467 0.498298
\(807\) 31.3468 1.10346
\(808\) 8.44850 0.297217
\(809\) 44.7879 1.57466 0.787330 0.616532i \(-0.211463\pi\)
0.787330 + 0.616532i \(0.211463\pi\)
\(810\) 31.5451 1.10838
\(811\) −9.37215 −0.329101 −0.164550 0.986369i \(-0.552617\pi\)
−0.164550 + 0.986369i \(0.552617\pi\)
\(812\) −0.203942 −0.00715697
\(813\) 86.4189 3.03084
\(814\) −8.26892 −0.289826
\(815\) −2.35349 −0.0824390
\(816\) 31.6280 1.10720
\(817\) −3.48807 −0.122032
\(818\) −28.5255 −0.997371
\(819\) −12.4905 −0.436453
\(820\) −18.8684 −0.658914
\(821\) −27.2939 −0.952565 −0.476283 0.879292i \(-0.658016\pi\)
−0.476283 + 0.879292i \(0.658016\pi\)
\(822\) 10.6059 0.369925
\(823\) −8.22499 −0.286705 −0.143353 0.989672i \(-0.545788\pi\)
−0.143353 + 0.989672i \(0.545788\pi\)
\(824\) 34.4581 1.20041
\(825\) 15.8743 0.552673
\(826\) −106.781 −3.71540
\(827\) −41.2479 −1.43433 −0.717165 0.696904i \(-0.754560\pi\)
−0.717165 + 0.696904i \(0.754560\pi\)
\(828\) −20.8897 −0.725967
\(829\) −5.81355 −0.201913 −0.100956 0.994891i \(-0.532190\pi\)
−0.100956 + 0.994891i \(0.532190\pi\)
\(830\) −19.5338 −0.678027
\(831\) 39.5806 1.37304
\(832\) 6.82053 0.236459
\(833\) −22.3417 −0.774093
\(834\) 127.622 4.41920
\(835\) −13.6983 −0.474051
\(836\) 96.9078 3.35163
\(837\) −108.073 −3.73556
\(838\) 39.3258 1.35849
\(839\) −29.2434 −1.00959 −0.504797 0.863238i \(-0.668433\pi\)
−0.504797 + 0.863238i \(0.668433\pi\)
\(840\) −38.2396 −1.31939
\(841\) −28.9997 −0.999990
\(842\) 17.2776 0.595425
\(843\) 45.1386 1.55466
\(844\) −67.4547 −2.32189
\(845\) 12.6539 0.435306
\(846\) 164.448 5.65384
\(847\) 51.4261 1.76702
\(848\) 3.70204 0.127129
\(849\) −54.6624 −1.87601
\(850\) 13.8858 0.476279
\(851\) 0.608587 0.0208621
\(852\) −95.1937 −3.26128
\(853\) −36.5160 −1.25028 −0.625142 0.780511i \(-0.714959\pi\)
−0.625142 + 0.780511i \(0.714959\pi\)
\(854\) 23.3026 0.797397
\(855\) 33.6928 1.15227
\(856\) 51.4686 1.75916
\(857\) −31.8144 −1.08676 −0.543380 0.839487i \(-0.682856\pi\)
−0.543380 + 0.839487i \(0.682856\pi\)
\(858\) 22.0984 0.754426
\(859\) −36.2894 −1.23818 −0.619089 0.785321i \(-0.712498\pi\)
−0.619089 + 0.785321i \(0.712498\pi\)
\(860\) −2.40588 −0.0820398
\(861\) −53.0105 −1.80659
\(862\) −80.0238 −2.72562
\(863\) −41.4523 −1.41105 −0.705526 0.708684i \(-0.749289\pi\)
−0.705526 + 0.708684i \(0.749289\pi\)
\(864\) −36.3523 −1.23673
\(865\) 4.21847 0.143432
\(866\) 4.28860 0.145733
\(867\) −53.6357 −1.82156
\(868\) 120.218 4.08047
\(869\) −43.4410 −1.47364
\(870\) 0.125449 0.00425311
\(871\) 0.934985 0.0316808
\(872\) −42.0373 −1.42356
\(873\) 72.0893 2.43985
\(874\) −11.0964 −0.375340
\(875\) −3.28740 −0.111134
\(876\) 70.0703 2.36745
\(877\) 36.7965 1.24253 0.621265 0.783600i \(-0.286619\pi\)
0.621265 + 0.783600i \(0.286619\pi\)
\(878\) 18.3823 0.620374
\(879\) 16.6541 0.561730
\(880\) 9.04549 0.304924
\(881\) 42.3021 1.42520 0.712598 0.701573i \(-0.247519\pi\)
0.712598 + 0.701573i \(0.247519\pi\)
\(882\) −58.1727 −1.95878
\(883\) 14.8430 0.499507 0.249754 0.968309i \(-0.419650\pi\)
0.249754 + 0.968309i \(0.419650\pi\)
\(884\) 12.4248 0.417890
\(885\) 42.2188 1.41917
\(886\) 25.5121 0.857096
\(887\) 36.1070 1.21235 0.606177 0.795330i \(-0.292702\pi\)
0.606177 + 0.795330i \(0.292702\pi\)
\(888\) −7.87550 −0.264285
\(889\) 18.8793 0.633190
\(890\) −12.8251 −0.429899
\(891\) −68.8159 −2.30542
\(892\) −37.4983 −1.25554
\(893\) 56.1474 1.87890
\(894\) −102.799 −3.43812
\(895\) 13.0669 0.436777
\(896\) 67.6994 2.26168
\(897\) −1.62642 −0.0543047
\(898\) −21.4383 −0.715406
\(899\) −0.175194 −0.00584305
\(900\) 23.2395 0.774648
\(901\) −12.3976 −0.413024
\(902\) 64.0386 2.13225
\(903\) −6.75928 −0.224935
\(904\) 14.5724 0.484671
\(905\) −0.0904172 −0.00300557
\(906\) −2.23232 −0.0741639
\(907\) −25.5209 −0.847409 −0.423704 0.905800i \(-0.639270\pi\)
−0.423704 + 0.905800i \(0.639270\pi\)
\(908\) −21.6359 −0.718012
\(909\) −14.4251 −0.478449
\(910\) −4.57633 −0.151704
\(911\) −26.3449 −0.872846 −0.436423 0.899742i \(-0.643755\pi\)
−0.436423 + 0.899742i \(0.643755\pi\)
\(912\) 28.1174 0.931060
\(913\) 42.6131 1.41029
\(914\) 51.6626 1.70885
\(915\) −9.21327 −0.304581
\(916\) 63.1251 2.08571
\(917\) 69.9081 2.30857
\(918\) −147.672 −4.87391
\(919\) −38.8064 −1.28011 −0.640053 0.768331i \(-0.721087\pi\)
−0.640053 + 0.768331i \(0.721087\pi\)
\(920\) −3.39991 −0.112092
\(921\) 3.71795 0.122510
\(922\) −23.7789 −0.783115
\(923\) −5.06069 −0.166575
\(924\) 187.791 6.17786
\(925\) −0.677044 −0.0222611
\(926\) −78.8742 −2.59197
\(927\) −58.8342 −1.93237
\(928\) −0.0589295 −0.00193446
\(929\) 9.65784 0.316864 0.158432 0.987370i \(-0.449356\pi\)
0.158432 + 0.987370i \(0.449356\pi\)
\(930\) −73.9484 −2.42486
\(931\) −19.8618 −0.650946
\(932\) −15.5083 −0.507991
\(933\) −38.6644 −1.26581
\(934\) −61.5305 −2.01334
\(935\) −30.2920 −0.990655
\(936\) 14.3710 0.469732
\(937\) −53.1044 −1.73484 −0.867422 0.497572i \(-0.834225\pi\)
−0.867422 + 0.497572i \(0.834225\pi\)
\(938\) 12.3614 0.403613
\(939\) −32.9182 −1.07424
\(940\) 38.7274 1.26315
\(941\) −50.8426 −1.65742 −0.828710 0.559678i \(-0.810925\pi\)
−0.828710 + 0.559678i \(0.810925\pi\)
\(942\) 126.252 4.11351
\(943\) −4.71320 −0.153483
\(944\) 24.0571 0.782992
\(945\) 34.9607 1.13727
\(946\) 8.16544 0.265481
\(947\) 7.21175 0.234350 0.117175 0.993111i \(-0.462616\pi\)
0.117175 + 0.993111i \(0.462616\pi\)
\(948\) −93.1390 −3.02501
\(949\) 3.72507 0.120921
\(950\) 12.3445 0.400510
\(951\) 71.0051 2.30250
\(952\) 72.9705 2.36499
\(953\) −43.7221 −1.41630 −0.708149 0.706063i \(-0.750469\pi\)
−0.708149 + 0.706063i \(0.750469\pi\)
\(954\) −32.2805 −1.04512
\(955\) −3.42710 −0.110898
\(956\) 97.7197 3.16048
\(957\) −0.273667 −0.00884641
\(958\) 14.0133 0.452749
\(959\) 4.79142 0.154723
\(960\) −35.6525 −1.15068
\(961\) 72.2720 2.33136
\(962\) −0.942501 −0.0303875
\(963\) −87.8780 −2.83183
\(964\) 100.551 3.23854
\(965\) 8.29879 0.267148
\(966\) −21.5029 −0.691843
\(967\) −6.07106 −0.195232 −0.0976160 0.995224i \(-0.531122\pi\)
−0.0976160 + 0.995224i \(0.531122\pi\)
\(968\) −59.1687 −1.90176
\(969\) −94.1610 −3.02489
\(970\) 26.4124 0.848053
\(971\) −22.4637 −0.720895 −0.360447 0.932780i \(-0.617376\pi\)
−0.360447 + 0.932780i \(0.617376\pi\)
\(972\) −32.7349 −1.04997
\(973\) 57.6556 1.84835
\(974\) −84.8446 −2.71860
\(975\) 1.80937 0.0579463
\(976\) −5.24990 −0.168045
\(977\) 27.8058 0.889585 0.444793 0.895634i \(-0.353277\pi\)
0.444793 + 0.895634i \(0.353277\pi\)
\(978\) 17.1257 0.547621
\(979\) 27.9781 0.894185
\(980\) −13.6996 −0.437618
\(981\) 71.7749 2.29160
\(982\) −50.3435 −1.60653
\(983\) 18.1185 0.577891 0.288945 0.957346i \(-0.406695\pi\)
0.288945 + 0.957346i \(0.406695\pi\)
\(984\) 60.9917 1.94434
\(985\) −11.1523 −0.355342
\(986\) −0.239386 −0.00762361
\(987\) 108.804 3.46327
\(988\) 11.0457 0.351409
\(989\) −0.600971 −0.0191098
\(990\) −78.8736 −2.50677
\(991\) 54.8813 1.74336 0.871681 0.490073i \(-0.163030\pi\)
0.871681 + 0.490073i \(0.163030\pi\)
\(992\) 34.7373 1.10291
\(993\) 27.9113 0.885738
\(994\) −66.9070 −2.12216
\(995\) −21.8295 −0.692042
\(996\) 91.3641 2.89498
\(997\) −56.0612 −1.77548 −0.887738 0.460350i \(-0.847724\pi\)
−0.887738 + 0.460350i \(0.847724\pi\)
\(998\) −86.8059 −2.74779
\(999\) 7.20020 0.227804
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 8035.2.a.d.1.19 140
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8035.2.a.d.1.19 140 1.1 even 1 trivial