Properties

Label 6026.2.a.m.1.19
Level $6026$
Weight $2$
Character 6026.1
Self dual yes
Analytic conductor $48.118$
Analytic rank $0$
Dimension $41$
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] = [6026,2,Mod(1,6026)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6026, 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("6026.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6026.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: \(48.1178522580\)
Analytic rank: \(0\)
Dimension: \(41\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) \(=\) 6026.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -0.352298 q^{3} +1.00000 q^{4} -1.51534 q^{5} -0.352298 q^{6} -1.04103 q^{7} +1.00000 q^{8} -2.87589 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -0.352298 q^{3} +1.00000 q^{4} -1.51534 q^{5} -0.352298 q^{6} -1.04103 q^{7} +1.00000 q^{8} -2.87589 q^{9} -1.51534 q^{10} +3.44169 q^{11} -0.352298 q^{12} -5.23410 q^{13} -1.04103 q^{14} +0.533849 q^{15} +1.00000 q^{16} -0.458447 q^{17} -2.87589 q^{18} +0.0118520 q^{19} -1.51534 q^{20} +0.366752 q^{21} +3.44169 q^{22} +1.00000 q^{23} -0.352298 q^{24} -2.70376 q^{25} -5.23410 q^{26} +2.07006 q^{27} -1.04103 q^{28} +5.71753 q^{29} +0.533849 q^{30} -7.95942 q^{31} +1.00000 q^{32} -1.21250 q^{33} -0.458447 q^{34} +1.57751 q^{35} -2.87589 q^{36} +3.61468 q^{37} +0.0118520 q^{38} +1.84396 q^{39} -1.51534 q^{40} -4.81763 q^{41} +0.366752 q^{42} +10.3818 q^{43} +3.44169 q^{44} +4.35793 q^{45} +1.00000 q^{46} +8.16294 q^{47} -0.352298 q^{48} -5.91626 q^{49} -2.70376 q^{50} +0.161510 q^{51} -5.23410 q^{52} +0.539296 q^{53} +2.07006 q^{54} -5.21532 q^{55} -1.04103 q^{56} -0.00417544 q^{57} +5.71753 q^{58} +12.5348 q^{59} +0.533849 q^{60} +2.65629 q^{61} -7.95942 q^{62} +2.99388 q^{63} +1.00000 q^{64} +7.93142 q^{65} -1.21250 q^{66} +7.91446 q^{67} -0.458447 q^{68} -0.352298 q^{69} +1.57751 q^{70} -2.66119 q^{71} -2.87589 q^{72} -15.3570 q^{73} +3.61468 q^{74} +0.952528 q^{75} +0.0118520 q^{76} -3.58290 q^{77} +1.84396 q^{78} +3.78651 q^{79} -1.51534 q^{80} +7.89838 q^{81} -4.81763 q^{82} +13.5375 q^{83} +0.366752 q^{84} +0.694702 q^{85} +10.3818 q^{86} -2.01427 q^{87} +3.44169 q^{88} -1.83019 q^{89} +4.35793 q^{90} +5.44885 q^{91} +1.00000 q^{92} +2.80409 q^{93} +8.16294 q^{94} -0.0179598 q^{95} -0.352298 q^{96} -7.88491 q^{97} -5.91626 q^{98} -9.89791 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19} + 9 q^{20} + 16 q^{21} + 4 q^{22} + 41 q^{23} + 4 q^{24} + 76 q^{25} + 16 q^{26} + 7 q^{27} + 12 q^{28} + 28 q^{29} + 10 q^{30} + 25 q^{31} + 41 q^{32} + 5 q^{33} + 10 q^{34} + 4 q^{35} + 63 q^{36} + 26 q^{37} + 16 q^{38} + 50 q^{39} + 9 q^{40} + 27 q^{41} + 16 q^{42} + 12 q^{43} + 4 q^{44} + 44 q^{45} + 41 q^{46} + 18 q^{47} + 4 q^{48} + 87 q^{49} + 76 q^{50} + 24 q^{51} + 16 q^{52} + 63 q^{53} + 7 q^{54} + 18 q^{55} + 12 q^{56} - 12 q^{57} + 28 q^{58} + 33 q^{59} + 10 q^{60} + 24 q^{61} + 25 q^{62} + 48 q^{63} + 41 q^{64} + 21 q^{65} + 5 q^{66} - 9 q^{67} + 10 q^{68} + 4 q^{69} + 4 q^{70} + 36 q^{71} + 63 q^{72} + 36 q^{73} + 26 q^{74} + 6 q^{75} + 16 q^{76} + 48 q^{77} + 50 q^{78} + 51 q^{79} + 9 q^{80} + 149 q^{81} + 27 q^{82} - 27 q^{83} + 16 q^{84} + 52 q^{85} + 12 q^{86} - 3 q^{87} + 4 q^{88} + 68 q^{89} + 44 q^{90} + 22 q^{91} + 41 q^{92} + 45 q^{93} + 18 q^{94} + 46 q^{95} + 4 q^{96} + 16 q^{97} + 87 q^{98} - 10 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −0.352298 −0.203399 −0.101700 0.994815i \(-0.532428\pi\)
−0.101700 + 0.994815i \(0.532428\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.51534 −0.677679 −0.338839 0.940844i \(-0.610034\pi\)
−0.338839 + 0.940844i \(0.610034\pi\)
\(6\) −0.352298 −0.143825
\(7\) −1.04103 −0.393472 −0.196736 0.980457i \(-0.563034\pi\)
−0.196736 + 0.980457i \(0.563034\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.87589 −0.958629
\(10\) −1.51534 −0.479191
\(11\) 3.44169 1.03771 0.518855 0.854863i \(-0.326359\pi\)
0.518855 + 0.854863i \(0.326359\pi\)
\(12\) −0.352298 −0.101700
\(13\) −5.23410 −1.45168 −0.725839 0.687865i \(-0.758548\pi\)
−0.725839 + 0.687865i \(0.758548\pi\)
\(14\) −1.04103 −0.278227
\(15\) 0.533849 0.137839
\(16\) 1.00000 0.250000
\(17\) −0.458447 −0.111190 −0.0555949 0.998453i \(-0.517706\pi\)
−0.0555949 + 0.998453i \(0.517706\pi\)
\(18\) −2.87589 −0.677853
\(19\) 0.0118520 0.00271904 0.00135952 0.999999i \(-0.499567\pi\)
0.00135952 + 0.999999i \(0.499567\pi\)
\(20\) −1.51534 −0.338839
\(21\) 0.366752 0.0800319
\(22\) 3.44169 0.733771
\(23\) 1.00000 0.208514
\(24\) −0.352298 −0.0719125
\(25\) −2.70376 −0.540751
\(26\) −5.23410 −1.02649
\(27\) 2.07006 0.398384
\(28\) −1.04103 −0.196736
\(29\) 5.71753 1.06172 0.530860 0.847460i \(-0.321869\pi\)
0.530860 + 0.847460i \(0.321869\pi\)
\(30\) 0.533849 0.0974671
\(31\) −7.95942 −1.42955 −0.714777 0.699352i \(-0.753472\pi\)
−0.714777 + 0.699352i \(0.753472\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.21250 −0.211069
\(34\) −0.458447 −0.0786231
\(35\) 1.57751 0.266648
\(36\) −2.87589 −0.479314
\(37\) 3.61468 0.594249 0.297125 0.954839i \(-0.403972\pi\)
0.297125 + 0.954839i \(0.403972\pi\)
\(38\) 0.0118520 0.00192265
\(39\) 1.84396 0.295270
\(40\) −1.51534 −0.239596
\(41\) −4.81763 −0.752387 −0.376194 0.926541i \(-0.622767\pi\)
−0.376194 + 0.926541i \(0.622767\pi\)
\(42\) 0.366752 0.0565911
\(43\) 10.3818 1.58321 0.791603 0.611035i \(-0.209247\pi\)
0.791603 + 0.611035i \(0.209247\pi\)
\(44\) 3.44169 0.518855
\(45\) 4.35793 0.649642
\(46\) 1.00000 0.147442
\(47\) 8.16294 1.19069 0.595344 0.803471i \(-0.297016\pi\)
0.595344 + 0.803471i \(0.297016\pi\)
\(48\) −0.352298 −0.0508498
\(49\) −5.91626 −0.845180
\(50\) −2.70376 −0.382369
\(51\) 0.161510 0.0226159
\(52\) −5.23410 −0.725839
\(53\) 0.539296 0.0740779 0.0370390 0.999314i \(-0.488207\pi\)
0.0370390 + 0.999314i \(0.488207\pi\)
\(54\) 2.07006 0.281700
\(55\) −5.21532 −0.703234
\(56\) −1.04103 −0.139113
\(57\) −0.00417544 −0.000553051 0
\(58\) 5.71753 0.750749
\(59\) 12.5348 1.63190 0.815948 0.578126i \(-0.196216\pi\)
0.815948 + 0.578126i \(0.196216\pi\)
\(60\) 0.533849 0.0689197
\(61\) 2.65629 0.340104 0.170052 0.985435i \(-0.445607\pi\)
0.170052 + 0.985435i \(0.445607\pi\)
\(62\) −7.95942 −1.01085
\(63\) 2.99388 0.377193
\(64\) 1.00000 0.125000
\(65\) 7.93142 0.983771
\(66\) −1.21250 −0.149248
\(67\) 7.91446 0.966905 0.483453 0.875371i \(-0.339383\pi\)
0.483453 + 0.875371i \(0.339383\pi\)
\(68\) −0.458447 −0.0555949
\(69\) −0.352298 −0.0424117
\(70\) 1.57751 0.188548
\(71\) −2.66119 −0.315825 −0.157912 0.987453i \(-0.550476\pi\)
−0.157912 + 0.987453i \(0.550476\pi\)
\(72\) −2.87589 −0.338926
\(73\) −15.3570 −1.79740 −0.898701 0.438563i \(-0.855488\pi\)
−0.898701 + 0.438563i \(0.855488\pi\)
\(74\) 3.61468 0.420198
\(75\) 0.952528 0.109988
\(76\) 0.0118520 0.00135952
\(77\) −3.58290 −0.408309
\(78\) 1.84396 0.208788
\(79\) 3.78651 0.426016 0.213008 0.977050i \(-0.431674\pi\)
0.213008 + 0.977050i \(0.431674\pi\)
\(80\) −1.51534 −0.169420
\(81\) 7.89838 0.877598
\(82\) −4.81763 −0.532018
\(83\) 13.5375 1.48594 0.742968 0.669327i \(-0.233418\pi\)
0.742968 + 0.669327i \(0.233418\pi\)
\(84\) 0.366752 0.0400159
\(85\) 0.694702 0.0753510
\(86\) 10.3818 1.11950
\(87\) −2.01427 −0.215953
\(88\) 3.44169 0.366886
\(89\) −1.83019 −0.194000 −0.0970000 0.995284i \(-0.530925\pi\)
−0.0970000 + 0.995284i \(0.530925\pi\)
\(90\) 4.35793 0.459367
\(91\) 5.44885 0.571194
\(92\) 1.00000 0.104257
\(93\) 2.80409 0.290770
\(94\) 8.16294 0.841943
\(95\) −0.0179598 −0.00184264
\(96\) −0.352298 −0.0359562
\(97\) −7.88491 −0.800592 −0.400296 0.916386i \(-0.631093\pi\)
−0.400296 + 0.916386i \(0.631093\pi\)
\(98\) −5.91626 −0.597632
\(99\) −9.89791 −0.994778
\(100\) −2.70376 −0.270376
\(101\) 14.3080 1.42369 0.711847 0.702334i \(-0.247859\pi\)
0.711847 + 0.702334i \(0.247859\pi\)
\(102\) 0.161510 0.0159919
\(103\) 17.6647 1.74055 0.870275 0.492566i \(-0.163941\pi\)
0.870275 + 0.492566i \(0.163941\pi\)
\(104\) −5.23410 −0.513246
\(105\) −0.555753 −0.0542359
\(106\) 0.539296 0.0523810
\(107\) −0.999157 −0.0965922 −0.0482961 0.998833i \(-0.515379\pi\)
−0.0482961 + 0.998833i \(0.515379\pi\)
\(108\) 2.07006 0.199192
\(109\) −6.65393 −0.637331 −0.318666 0.947867i \(-0.603235\pi\)
−0.318666 + 0.947867i \(0.603235\pi\)
\(110\) −5.21532 −0.497261
\(111\) −1.27344 −0.120870
\(112\) −1.04103 −0.0983680
\(113\) −13.5888 −1.27833 −0.639163 0.769072i \(-0.720719\pi\)
−0.639163 + 0.769072i \(0.720719\pi\)
\(114\) −0.00417544 −0.000391066 0
\(115\) −1.51534 −0.141306
\(116\) 5.71753 0.530860
\(117\) 15.0527 1.39162
\(118\) 12.5348 1.15392
\(119\) 0.477257 0.0437501
\(120\) 0.533849 0.0487336
\(121\) 0.845244 0.0768403
\(122\) 2.65629 0.240490
\(123\) 1.69724 0.153035
\(124\) −7.95942 −0.714777
\(125\) 11.6738 1.04413
\(126\) 2.99388 0.266716
\(127\) 3.40953 0.302547 0.151273 0.988492i \(-0.451663\pi\)
0.151273 + 0.988492i \(0.451663\pi\)
\(128\) 1.00000 0.0883883
\(129\) −3.65748 −0.322023
\(130\) 7.93142 0.695631
\(131\) 1.00000 0.0873704
\(132\) −1.21250 −0.105535
\(133\) −0.0123383 −0.00106987
\(134\) 7.91446 0.683705
\(135\) −3.13684 −0.269976
\(136\) −0.458447 −0.0393115
\(137\) 18.4716 1.57814 0.789069 0.614305i \(-0.210563\pi\)
0.789069 + 0.614305i \(0.210563\pi\)
\(138\) −0.352298 −0.0299896
\(139\) −7.10422 −0.602572 −0.301286 0.953534i \(-0.597416\pi\)
−0.301286 + 0.953534i \(0.597416\pi\)
\(140\) 1.57751 0.133324
\(141\) −2.87579 −0.242185
\(142\) −2.66119 −0.223322
\(143\) −18.0142 −1.50642
\(144\) −2.87589 −0.239657
\(145\) −8.66398 −0.719505
\(146\) −15.3570 −1.27095
\(147\) 2.08428 0.171909
\(148\) 3.61468 0.297125
\(149\) 12.8693 1.05429 0.527146 0.849775i \(-0.323262\pi\)
0.527146 + 0.849775i \(0.323262\pi\)
\(150\) 0.952528 0.0777736
\(151\) −14.7178 −1.19772 −0.598860 0.800853i \(-0.704380\pi\)
−0.598860 + 0.800853i \(0.704380\pi\)
\(152\) 0.0118520 0.000961326 0
\(153\) 1.31844 0.106590
\(154\) −3.58290 −0.288718
\(155\) 12.0612 0.968779
\(156\) 1.84396 0.147635
\(157\) 17.4726 1.39447 0.697233 0.716845i \(-0.254414\pi\)
0.697233 + 0.716845i \(0.254414\pi\)
\(158\) 3.78651 0.301239
\(159\) −0.189993 −0.0150674
\(160\) −1.51534 −0.119798
\(161\) −1.04103 −0.0820446
\(162\) 7.89838 0.620555
\(163\) 7.29343 0.571265 0.285633 0.958339i \(-0.407796\pi\)
0.285633 + 0.958339i \(0.407796\pi\)
\(164\) −4.81763 −0.376194
\(165\) 1.83735 0.143037
\(166\) 13.5375 1.05071
\(167\) 7.28136 0.563448 0.281724 0.959495i \(-0.409094\pi\)
0.281724 + 0.959495i \(0.409094\pi\)
\(168\) 0.366752 0.0282955
\(169\) 14.3958 1.10737
\(170\) 0.694702 0.0532812
\(171\) −0.0340851 −0.00260655
\(172\) 10.3818 0.791603
\(173\) −22.0643 −1.67751 −0.838757 0.544505i \(-0.816717\pi\)
−0.838757 + 0.544505i \(0.816717\pi\)
\(174\) −2.01427 −0.152702
\(175\) 2.81469 0.212770
\(176\) 3.44169 0.259427
\(177\) −4.41599 −0.331926
\(178\) −1.83019 −0.137179
\(179\) 24.9774 1.86690 0.933448 0.358711i \(-0.116784\pi\)
0.933448 + 0.358711i \(0.116784\pi\)
\(180\) 4.35793 0.324821
\(181\) −8.10577 −0.602497 −0.301248 0.953546i \(-0.597403\pi\)
−0.301248 + 0.953546i \(0.597403\pi\)
\(182\) 5.44885 0.403896
\(183\) −0.935806 −0.0691768
\(184\) 1.00000 0.0737210
\(185\) −5.47745 −0.402710
\(186\) 2.80409 0.205606
\(187\) −1.57783 −0.115383
\(188\) 8.16294 0.595344
\(189\) −2.15499 −0.156753
\(190\) −0.0179598 −0.00130294
\(191\) 17.2642 1.24920 0.624598 0.780946i \(-0.285263\pi\)
0.624598 + 0.780946i \(0.285263\pi\)
\(192\) −0.352298 −0.0254249
\(193\) 1.60663 0.115648 0.0578240 0.998327i \(-0.481584\pi\)
0.0578240 + 0.998327i \(0.481584\pi\)
\(194\) −7.88491 −0.566104
\(195\) −2.79422 −0.200098
\(196\) −5.91626 −0.422590
\(197\) 9.97120 0.710418 0.355209 0.934787i \(-0.384410\pi\)
0.355209 + 0.934787i \(0.384410\pi\)
\(198\) −9.89791 −0.703414
\(199\) −14.3287 −1.01574 −0.507869 0.861435i \(-0.669566\pi\)
−0.507869 + 0.861435i \(0.669566\pi\)
\(200\) −2.70376 −0.191185
\(201\) −2.78825 −0.196668
\(202\) 14.3080 1.00670
\(203\) −5.95212 −0.417757
\(204\) 0.161510 0.0113080
\(205\) 7.30033 0.509877
\(206\) 17.6647 1.23075
\(207\) −2.87589 −0.199888
\(208\) −5.23410 −0.362920
\(209\) 0.0407910 0.00282157
\(210\) −0.555753 −0.0383506
\(211\) 25.1471 1.73120 0.865600 0.500736i \(-0.166937\pi\)
0.865600 + 0.500736i \(0.166937\pi\)
\(212\) 0.539296 0.0370390
\(213\) 0.937530 0.0642385
\(214\) −0.999157 −0.0683010
\(215\) −15.7319 −1.07291
\(216\) 2.07006 0.140850
\(217\) 8.28599 0.562490
\(218\) −6.65393 −0.450661
\(219\) 5.41024 0.365590
\(220\) −5.21532 −0.351617
\(221\) 2.39956 0.161412
\(222\) −1.27344 −0.0854679
\(223\) 13.8372 0.926605 0.463303 0.886200i \(-0.346664\pi\)
0.463303 + 0.886200i \(0.346664\pi\)
\(224\) −1.04103 −0.0695567
\(225\) 7.77570 0.518380
\(226\) −13.5888 −0.903912
\(227\) −2.71032 −0.179890 −0.0899450 0.995947i \(-0.528669\pi\)
−0.0899450 + 0.995947i \(0.528669\pi\)
\(228\) −0.00417544 −0.000276525 0
\(229\) −12.8284 −0.847724 −0.423862 0.905727i \(-0.639326\pi\)
−0.423862 + 0.905727i \(0.639326\pi\)
\(230\) −1.51534 −0.0999183
\(231\) 1.26225 0.0830498
\(232\) 5.71753 0.375374
\(233\) 2.43023 0.159210 0.0796049 0.996826i \(-0.474634\pi\)
0.0796049 + 0.996826i \(0.474634\pi\)
\(234\) 15.0527 0.984024
\(235\) −12.3696 −0.806903
\(236\) 12.5348 0.815948
\(237\) −1.33398 −0.0866513
\(238\) 0.477257 0.0309360
\(239\) −15.5872 −1.00825 −0.504126 0.863630i \(-0.668185\pi\)
−0.504126 + 0.863630i \(0.668185\pi\)
\(240\) 0.533849 0.0344598
\(241\) 14.0684 0.906226 0.453113 0.891453i \(-0.350313\pi\)
0.453113 + 0.891453i \(0.350313\pi\)
\(242\) 0.845244 0.0543343
\(243\) −8.99277 −0.576886
\(244\) 2.65629 0.170052
\(245\) 8.96512 0.572760
\(246\) 1.69724 0.108212
\(247\) −0.0620347 −0.00394717
\(248\) −7.95942 −0.505424
\(249\) −4.76924 −0.302238
\(250\) 11.6738 0.738315
\(251\) 26.5809 1.67777 0.838885 0.544308i \(-0.183208\pi\)
0.838885 + 0.544308i \(0.183208\pi\)
\(252\) 2.99388 0.188597
\(253\) 3.44169 0.216377
\(254\) 3.40953 0.213933
\(255\) −0.244742 −0.0153263
\(256\) 1.00000 0.0625000
\(257\) −21.2214 −1.32376 −0.661879 0.749611i \(-0.730241\pi\)
−0.661879 + 0.749611i \(0.730241\pi\)
\(258\) −3.65748 −0.227705
\(259\) −3.76298 −0.233820
\(260\) 7.93142 0.491886
\(261\) −16.4430 −1.01779
\(262\) 1.00000 0.0617802
\(263\) 18.7421 1.15569 0.577843 0.816148i \(-0.303895\pi\)
0.577843 + 0.816148i \(0.303895\pi\)
\(264\) −1.21250 −0.0746242
\(265\) −0.817214 −0.0502011
\(266\) −0.0123383 −0.000756510 0
\(267\) 0.644773 0.0394594
\(268\) 7.91446 0.483453
\(269\) −0.923774 −0.0563235 −0.0281617 0.999603i \(-0.508965\pi\)
−0.0281617 + 0.999603i \(0.508965\pi\)
\(270\) −3.13684 −0.190902
\(271\) −4.53739 −0.275627 −0.137813 0.990458i \(-0.544007\pi\)
−0.137813 + 0.990458i \(0.544007\pi\)
\(272\) −0.458447 −0.0277974
\(273\) −1.91962 −0.116181
\(274\) 18.4716 1.11591
\(275\) −9.30550 −0.561143
\(276\) −0.352298 −0.0212058
\(277\) 22.6030 1.35808 0.679042 0.734100i \(-0.262396\pi\)
0.679042 + 0.734100i \(0.262396\pi\)
\(278\) −7.10422 −0.426083
\(279\) 22.8904 1.37041
\(280\) 1.57751 0.0942741
\(281\) −10.3379 −0.616707 −0.308354 0.951272i \(-0.599778\pi\)
−0.308354 + 0.951272i \(0.599778\pi\)
\(282\) −2.87579 −0.171251
\(283\) −20.7533 −1.23365 −0.616827 0.787098i \(-0.711582\pi\)
−0.616827 + 0.787098i \(0.711582\pi\)
\(284\) −2.66119 −0.157912
\(285\) 0.00632720 0.000374791 0
\(286\) −18.0142 −1.06520
\(287\) 5.01529 0.296043
\(288\) −2.87589 −0.169463
\(289\) −16.7898 −0.987637
\(290\) −8.66398 −0.508767
\(291\) 2.77784 0.162840
\(292\) −15.3570 −0.898701
\(293\) 7.78476 0.454791 0.227395 0.973803i \(-0.426979\pi\)
0.227395 + 0.973803i \(0.426979\pi\)
\(294\) 2.08428 0.121558
\(295\) −18.9945 −1.10590
\(296\) 3.61468 0.210099
\(297\) 7.12451 0.413406
\(298\) 12.8693 0.745496
\(299\) −5.23410 −0.302696
\(300\) 0.952528 0.0549942
\(301\) −10.8077 −0.622947
\(302\) −14.7178 −0.846917
\(303\) −5.04066 −0.289578
\(304\) 0.0118520 0.000679760 0
\(305\) −4.02518 −0.230481
\(306\) 1.31844 0.0753703
\(307\) −1.97831 −0.112908 −0.0564540 0.998405i \(-0.517979\pi\)
−0.0564540 + 0.998405i \(0.517979\pi\)
\(308\) −3.58290 −0.204155
\(309\) −6.22322 −0.354027
\(310\) 12.0612 0.685030
\(311\) 31.0217 1.75908 0.879540 0.475825i \(-0.157850\pi\)
0.879540 + 0.475825i \(0.157850\pi\)
\(312\) 1.84396 0.104394
\(313\) −14.2749 −0.806863 −0.403432 0.915010i \(-0.632183\pi\)
−0.403432 + 0.915010i \(0.632183\pi\)
\(314\) 17.4726 0.986036
\(315\) −4.53673 −0.255616
\(316\) 3.78651 0.213008
\(317\) −1.91311 −0.107451 −0.0537256 0.998556i \(-0.517110\pi\)
−0.0537256 + 0.998556i \(0.517110\pi\)
\(318\) −0.189993 −0.0106543
\(319\) 19.6780 1.10176
\(320\) −1.51534 −0.0847098
\(321\) 0.352001 0.0196468
\(322\) −1.04103 −0.0580143
\(323\) −0.00543353 −0.000302330 0
\(324\) 7.89838 0.438799
\(325\) 14.1517 0.784997
\(326\) 7.29343 0.403946
\(327\) 2.34417 0.129633
\(328\) −4.81763 −0.266009
\(329\) −8.49785 −0.468502
\(330\) 1.83735 0.101143
\(331\) −19.5088 −1.07230 −0.536149 0.844123i \(-0.680122\pi\)
−0.536149 + 0.844123i \(0.680122\pi\)
\(332\) 13.5375 0.742968
\(333\) −10.3954 −0.569665
\(334\) 7.28136 0.398418
\(335\) −11.9931 −0.655251
\(336\) 0.366752 0.0200080
\(337\) −16.7671 −0.913364 −0.456682 0.889630i \(-0.650962\pi\)
−0.456682 + 0.889630i \(0.650962\pi\)
\(338\) 14.3958 0.783028
\(339\) 4.78730 0.260010
\(340\) 0.694702 0.0376755
\(341\) −27.3939 −1.48346
\(342\) −0.0340851 −0.00184311
\(343\) 13.4462 0.726026
\(344\) 10.3818 0.559748
\(345\) 0.533849 0.0287415
\(346\) −22.0643 −1.18618
\(347\) 20.5624 1.10385 0.551924 0.833894i \(-0.313894\pi\)
0.551924 + 0.833894i \(0.313894\pi\)
\(348\) −2.01427 −0.107976
\(349\) 4.23107 0.226484 0.113242 0.993567i \(-0.463876\pi\)
0.113242 + 0.993567i \(0.463876\pi\)
\(350\) 2.81469 0.150451
\(351\) −10.8349 −0.578325
\(352\) 3.44169 0.183443
\(353\) 10.0342 0.534068 0.267034 0.963687i \(-0.413956\pi\)
0.267034 + 0.963687i \(0.413956\pi\)
\(354\) −4.41599 −0.234707
\(355\) 4.03259 0.214028
\(356\) −1.83019 −0.0970000
\(357\) −0.168136 −0.00889873
\(358\) 24.9774 1.32010
\(359\) 18.4158 0.971951 0.485976 0.873972i \(-0.338464\pi\)
0.485976 + 0.873972i \(0.338464\pi\)
\(360\) 4.35793 0.229683
\(361\) −18.9999 −0.999993
\(362\) −8.10577 −0.426030
\(363\) −0.297777 −0.0156293
\(364\) 5.44885 0.285597
\(365\) 23.2710 1.21806
\(366\) −0.935806 −0.0489154
\(367\) 15.9241 0.831233 0.415617 0.909540i \(-0.363566\pi\)
0.415617 + 0.909540i \(0.363566\pi\)
\(368\) 1.00000 0.0521286
\(369\) 13.8550 0.721260
\(370\) −5.47745 −0.284759
\(371\) −0.561422 −0.0291476
\(372\) 2.80409 0.145385
\(373\) 18.5232 0.959096 0.479548 0.877516i \(-0.340801\pi\)
0.479548 + 0.877516i \(0.340801\pi\)
\(374\) −1.57783 −0.0815879
\(375\) −4.11265 −0.212376
\(376\) 8.16294 0.420971
\(377\) −29.9261 −1.54127
\(378\) −2.15499 −0.110841
\(379\) 16.2185 0.833086 0.416543 0.909116i \(-0.363241\pi\)
0.416543 + 0.909116i \(0.363241\pi\)
\(380\) −0.0179598 −0.000921318 0
\(381\) −1.20117 −0.0615378
\(382\) 17.2642 0.883315
\(383\) −14.9956 −0.766242 −0.383121 0.923698i \(-0.625151\pi\)
−0.383121 + 0.923698i \(0.625151\pi\)
\(384\) −0.352298 −0.0179781
\(385\) 5.42930 0.276703
\(386\) 1.60663 0.0817755
\(387\) −29.8568 −1.51771
\(388\) −7.88491 −0.400296
\(389\) −17.4007 −0.882249 −0.441125 0.897446i \(-0.645420\pi\)
−0.441125 + 0.897446i \(0.645420\pi\)
\(390\) −2.79422 −0.141491
\(391\) −0.458447 −0.0231847
\(392\) −5.91626 −0.298816
\(393\) −0.352298 −0.0177711
\(394\) 9.97120 0.502342
\(395\) −5.73784 −0.288702
\(396\) −9.89791 −0.497389
\(397\) −4.57924 −0.229825 −0.114913 0.993376i \(-0.536659\pi\)
−0.114913 + 0.993376i \(0.536659\pi\)
\(398\) −14.3287 −0.718235
\(399\) 0.00434676 0.000217610 0
\(400\) −2.70376 −0.135188
\(401\) 5.29946 0.264642 0.132321 0.991207i \(-0.457757\pi\)
0.132321 + 0.991207i \(0.457757\pi\)
\(402\) −2.78825 −0.139065
\(403\) 41.6604 2.07525
\(404\) 14.3080 0.711847
\(405\) −11.9687 −0.594729
\(406\) −5.95212 −0.295399
\(407\) 12.4406 0.616658
\(408\) 0.161510 0.00799593
\(409\) 37.8084 1.86950 0.934752 0.355301i \(-0.115622\pi\)
0.934752 + 0.355301i \(0.115622\pi\)
\(410\) 7.30033 0.360537
\(411\) −6.50751 −0.320992
\(412\) 17.6647 0.870275
\(413\) −13.0491 −0.642105
\(414\) −2.87589 −0.141342
\(415\) −20.5139 −1.00699
\(416\) −5.23410 −0.256623
\(417\) 2.50280 0.122563
\(418\) 0.0407910 0.00199515
\(419\) 6.59183 0.322032 0.161016 0.986952i \(-0.448523\pi\)
0.161016 + 0.986952i \(0.448523\pi\)
\(420\) −0.555753 −0.0271179
\(421\) −26.7028 −1.30141 −0.650707 0.759329i \(-0.725527\pi\)
−0.650707 + 0.759329i \(0.725527\pi\)
\(422\) 25.1471 1.22414
\(423\) −23.4757 −1.14143
\(424\) 0.539296 0.0261905
\(425\) 1.23953 0.0601260
\(426\) 0.937530 0.0454235
\(427\) −2.76528 −0.133821
\(428\) −0.999157 −0.0482961
\(429\) 6.34635 0.306405
\(430\) −15.7319 −0.758659
\(431\) −22.9331 −1.10465 −0.552324 0.833629i \(-0.686259\pi\)
−0.552324 + 0.833629i \(0.686259\pi\)
\(432\) 2.07006 0.0995959
\(433\) −36.7661 −1.76687 −0.883433 0.468558i \(-0.844774\pi\)
−0.883433 + 0.468558i \(0.844774\pi\)
\(434\) 8.28599 0.397740
\(435\) 3.05230 0.146347
\(436\) −6.65393 −0.318666
\(437\) 0.0118520 0.000566959 0
\(438\) 5.41024 0.258511
\(439\) 8.54496 0.407829 0.203914 0.978989i \(-0.434634\pi\)
0.203914 + 0.978989i \(0.434634\pi\)
\(440\) −5.21532 −0.248631
\(441\) 17.0145 0.810214
\(442\) 2.39956 0.114135
\(443\) 20.9058 0.993263 0.496631 0.867962i \(-0.334570\pi\)
0.496631 + 0.867962i \(0.334570\pi\)
\(444\) −1.27344 −0.0604349
\(445\) 2.77336 0.131470
\(446\) 13.8372 0.655209
\(447\) −4.53381 −0.214442
\(448\) −1.04103 −0.0491840
\(449\) −22.2619 −1.05060 −0.525301 0.850917i \(-0.676047\pi\)
−0.525301 + 0.850917i \(0.676047\pi\)
\(450\) 7.77570 0.366550
\(451\) −16.5808 −0.780759
\(452\) −13.5888 −0.639163
\(453\) 5.18506 0.243615
\(454\) −2.71032 −0.127201
\(455\) −8.25684 −0.387086
\(456\) −0.00417544 −0.000195533 0
\(457\) 30.7283 1.43741 0.718705 0.695315i \(-0.244735\pi\)
0.718705 + 0.695315i \(0.244735\pi\)
\(458\) −12.8284 −0.599431
\(459\) −0.949014 −0.0442962
\(460\) −1.51534 −0.0706529
\(461\) 1.84511 0.0859352 0.0429676 0.999076i \(-0.486319\pi\)
0.0429676 + 0.999076i \(0.486319\pi\)
\(462\) 1.26225 0.0587251
\(463\) −18.9409 −0.880258 −0.440129 0.897935i \(-0.645067\pi\)
−0.440129 + 0.897935i \(0.645067\pi\)
\(464\) 5.71753 0.265430
\(465\) −4.24913 −0.197049
\(466\) 2.43023 0.112578
\(467\) −27.4815 −1.27169 −0.635846 0.771816i \(-0.719349\pi\)
−0.635846 + 0.771816i \(0.719349\pi\)
\(468\) 15.0527 0.695810
\(469\) −8.23918 −0.380450
\(470\) −12.3696 −0.570567
\(471\) −6.15556 −0.283633
\(472\) 12.5348 0.576962
\(473\) 35.7309 1.64291
\(474\) −1.33398 −0.0612717
\(475\) −0.0320450 −0.00147033
\(476\) 0.477257 0.0218750
\(477\) −1.55095 −0.0710132
\(478\) −15.5872 −0.712942
\(479\) 31.3647 1.43309 0.716545 0.697541i \(-0.245722\pi\)
0.716545 + 0.697541i \(0.245722\pi\)
\(480\) 0.533849 0.0243668
\(481\) −18.9196 −0.862659
\(482\) 14.0684 0.640799
\(483\) 0.366752 0.0166878
\(484\) 0.845244 0.0384202
\(485\) 11.9483 0.542544
\(486\) −8.99277 −0.407920
\(487\) 17.6248 0.798655 0.399328 0.916808i \(-0.369244\pi\)
0.399328 + 0.916808i \(0.369244\pi\)
\(488\) 2.65629 0.120245
\(489\) −2.56946 −0.116195
\(490\) 8.96512 0.405003
\(491\) 24.4755 1.10456 0.552282 0.833658i \(-0.313757\pi\)
0.552282 + 0.833658i \(0.313757\pi\)
\(492\) 1.69724 0.0765175
\(493\) −2.62119 −0.118052
\(494\) −0.0620347 −0.00279107
\(495\) 14.9987 0.674140
\(496\) −7.95942 −0.357389
\(497\) 2.77037 0.124268
\(498\) −4.76924 −0.213715
\(499\) 31.3949 1.40543 0.702713 0.711473i \(-0.251972\pi\)
0.702713 + 0.711473i \(0.251972\pi\)
\(500\) 11.6738 0.522067
\(501\) −2.56521 −0.114605
\(502\) 26.5809 1.18636
\(503\) 15.5797 0.694665 0.347333 0.937742i \(-0.387087\pi\)
0.347333 + 0.937742i \(0.387087\pi\)
\(504\) 2.99388 0.133358
\(505\) −21.6814 −0.964808
\(506\) 3.44169 0.153002
\(507\) −5.07161 −0.225238
\(508\) 3.40953 0.151273
\(509\) −11.8461 −0.525070 −0.262535 0.964923i \(-0.584558\pi\)
−0.262535 + 0.964923i \(0.584558\pi\)
\(510\) −0.244742 −0.0108373
\(511\) 15.9871 0.707227
\(512\) 1.00000 0.0441942
\(513\) 0.0245344 0.00108322
\(514\) −21.2214 −0.936038
\(515\) −26.7679 −1.17953
\(516\) −3.65748 −0.161012
\(517\) 28.0943 1.23559
\(518\) −3.76298 −0.165336
\(519\) 7.77319 0.341205
\(520\) 7.93142 0.347816
\(521\) −27.8162 −1.21865 −0.609324 0.792921i \(-0.708559\pi\)
−0.609324 + 0.792921i \(0.708559\pi\)
\(522\) −16.4430 −0.719690
\(523\) −15.9098 −0.695689 −0.347844 0.937552i \(-0.613086\pi\)
−0.347844 + 0.937552i \(0.613086\pi\)
\(524\) 1.00000 0.0436852
\(525\) −0.991609 −0.0432773
\(526\) 18.7421 0.817193
\(527\) 3.64898 0.158952
\(528\) −1.21250 −0.0527673
\(529\) 1.00000 0.0434783
\(530\) −0.817214 −0.0354975
\(531\) −36.0487 −1.56438
\(532\) −0.0123383 −0.000534933 0
\(533\) 25.2160 1.09222
\(534\) 0.644773 0.0279020
\(535\) 1.51406 0.0654585
\(536\) 7.91446 0.341853
\(537\) −8.79948 −0.379725
\(538\) −0.923774 −0.0398267
\(539\) −20.3619 −0.877051
\(540\) −3.13684 −0.134988
\(541\) 30.0126 1.29034 0.645172 0.764037i \(-0.276786\pi\)
0.645172 + 0.764037i \(0.276786\pi\)
\(542\) −4.53739 −0.194898
\(543\) 2.85564 0.122547
\(544\) −0.458447 −0.0196558
\(545\) 10.0829 0.431906
\(546\) −1.91962 −0.0821520
\(547\) −43.2762 −1.85035 −0.925177 0.379535i \(-0.876084\pi\)
−0.925177 + 0.379535i \(0.876084\pi\)
\(548\) 18.4716 0.789069
\(549\) −7.63920 −0.326033
\(550\) −9.30550 −0.396788
\(551\) 0.0677644 0.00288686
\(552\) −0.352298 −0.0149948
\(553\) −3.94187 −0.167625
\(554\) 22.6030 0.960310
\(555\) 1.92969 0.0819109
\(556\) −7.10422 −0.301286
\(557\) 13.3302 0.564820 0.282410 0.959294i \(-0.408866\pi\)
0.282410 + 0.959294i \(0.408866\pi\)
\(558\) 22.8904 0.969028
\(559\) −54.3393 −2.29831
\(560\) 1.57751 0.0666619
\(561\) 0.555867 0.0234687
\(562\) −10.3379 −0.436078
\(563\) −26.2627 −1.10684 −0.553420 0.832903i \(-0.686677\pi\)
−0.553420 + 0.832903i \(0.686677\pi\)
\(564\) −2.87579 −0.121092
\(565\) 20.5916 0.866294
\(566\) −20.7533 −0.872326
\(567\) −8.22244 −0.345310
\(568\) −2.66119 −0.111661
\(569\) 26.0421 1.09174 0.545871 0.837869i \(-0.316199\pi\)
0.545871 + 0.837869i \(0.316199\pi\)
\(570\) 0.00632720 0.000265017 0
\(571\) −45.9614 −1.92342 −0.961712 0.274062i \(-0.911633\pi\)
−0.961712 + 0.274062i \(0.911633\pi\)
\(572\) −18.0142 −0.753210
\(573\) −6.08215 −0.254086
\(574\) 5.01529 0.209334
\(575\) −2.70376 −0.112754
\(576\) −2.87589 −0.119829
\(577\) −27.5783 −1.14810 −0.574050 0.818821i \(-0.694628\pi\)
−0.574050 + 0.818821i \(0.694628\pi\)
\(578\) −16.7898 −0.698365
\(579\) −0.566013 −0.0235227
\(580\) −8.66398 −0.359752
\(581\) −14.0929 −0.584674
\(582\) 2.77784 0.115145
\(583\) 1.85609 0.0768714
\(584\) −15.3570 −0.635477
\(585\) −22.8099 −0.943072
\(586\) 7.78476 0.321586
\(587\) −18.8978 −0.779997 −0.389999 0.920815i \(-0.627524\pi\)
−0.389999 + 0.920815i \(0.627524\pi\)
\(588\) 2.08428 0.0859545
\(589\) −0.0943353 −0.00388702
\(590\) −18.9945 −0.781990
\(591\) −3.51283 −0.144499
\(592\) 3.61468 0.148562
\(593\) 1.83243 0.0752491 0.0376245 0.999292i \(-0.488021\pi\)
0.0376245 + 0.999292i \(0.488021\pi\)
\(594\) 7.12451 0.292322
\(595\) −0.723204 −0.0296485
\(596\) 12.8693 0.527146
\(597\) 5.04798 0.206600
\(598\) −5.23410 −0.214038
\(599\) 2.05151 0.0838225 0.0419113 0.999121i \(-0.486655\pi\)
0.0419113 + 0.999121i \(0.486655\pi\)
\(600\) 0.952528 0.0388868
\(601\) 1.95094 0.0795805 0.0397903 0.999208i \(-0.487331\pi\)
0.0397903 + 0.999208i \(0.487331\pi\)
\(602\) −10.8077 −0.440490
\(603\) −22.7611 −0.926903
\(604\) −14.7178 −0.598860
\(605\) −1.28083 −0.0520731
\(606\) −5.04066 −0.204763
\(607\) −23.4770 −0.952902 −0.476451 0.879201i \(-0.658077\pi\)
−0.476451 + 0.879201i \(0.658077\pi\)
\(608\) 0.0118520 0.000480663 0
\(609\) 2.09692 0.0849714
\(610\) −4.02518 −0.162975
\(611\) −42.7256 −1.72849
\(612\) 1.31844 0.0532949
\(613\) −43.5415 −1.75862 −0.879312 0.476247i \(-0.841997\pi\)
−0.879312 + 0.476247i \(0.841997\pi\)
\(614\) −1.97831 −0.0798380
\(615\) −2.57189 −0.103709
\(616\) −3.58290 −0.144359
\(617\) 14.4099 0.580120 0.290060 0.957008i \(-0.406325\pi\)
0.290060 + 0.957008i \(0.406325\pi\)
\(618\) −6.22322 −0.250335
\(619\) 47.8848 1.92465 0.962327 0.271895i \(-0.0876504\pi\)
0.962327 + 0.271895i \(0.0876504\pi\)
\(620\) 12.0612 0.484390
\(621\) 2.07006 0.0830687
\(622\) 31.0217 1.24386
\(623\) 1.90528 0.0763335
\(624\) 1.84396 0.0738175
\(625\) −4.17091 −0.166836
\(626\) −14.2749 −0.570538
\(627\) −0.0143706 −0.000573906 0
\(628\) 17.4726 0.697233
\(629\) −1.65714 −0.0660745
\(630\) −4.53673 −0.180748
\(631\) 13.0687 0.520256 0.260128 0.965574i \(-0.416235\pi\)
0.260128 + 0.965574i \(0.416235\pi\)
\(632\) 3.78651 0.150619
\(633\) −8.85928 −0.352125
\(634\) −1.91311 −0.0759794
\(635\) −5.16658 −0.205030
\(636\) −0.189993 −0.00753370
\(637\) 30.9663 1.22693
\(638\) 19.6780 0.779059
\(639\) 7.65327 0.302759
\(640\) −1.51534 −0.0598989
\(641\) −21.8563 −0.863271 −0.431635 0.902048i \(-0.642063\pi\)
−0.431635 + 0.902048i \(0.642063\pi\)
\(642\) 0.352001 0.0138924
\(643\) 21.2264 0.837088 0.418544 0.908196i \(-0.362541\pi\)
0.418544 + 0.908196i \(0.362541\pi\)
\(644\) −1.04103 −0.0410223
\(645\) 5.54231 0.218228
\(646\) −0.00543353 −0.000213779 0
\(647\) −43.9680 −1.72856 −0.864281 0.503010i \(-0.832226\pi\)
−0.864281 + 0.503010i \(0.832226\pi\)
\(648\) 7.89838 0.310278
\(649\) 43.1410 1.69343
\(650\) 14.1517 0.555077
\(651\) −2.91914 −0.114410
\(652\) 7.29343 0.285633
\(653\) 37.9204 1.48394 0.741970 0.670433i \(-0.233892\pi\)
0.741970 + 0.670433i \(0.233892\pi\)
\(654\) 2.34417 0.0916641
\(655\) −1.51534 −0.0592091
\(656\) −4.81763 −0.188097
\(657\) 44.1650 1.72304
\(658\) −8.49785 −0.331281
\(659\) 2.91481 0.113545 0.0567725 0.998387i \(-0.481919\pi\)
0.0567725 + 0.998387i \(0.481919\pi\)
\(660\) 1.83735 0.0715186
\(661\) 12.7634 0.496439 0.248219 0.968704i \(-0.420155\pi\)
0.248219 + 0.968704i \(0.420155\pi\)
\(662\) −19.5088 −0.758230
\(663\) −0.845359 −0.0328310
\(664\) 13.5375 0.525357
\(665\) 0.0186967 0.000725026 0
\(666\) −10.3954 −0.402814
\(667\) 5.71753 0.221384
\(668\) 7.28136 0.281724
\(669\) −4.87480 −0.188471
\(670\) −11.9931 −0.463333
\(671\) 9.14214 0.352929
\(672\) 0.366752 0.0141478
\(673\) −12.7395 −0.491071 −0.245536 0.969388i \(-0.578964\pi\)
−0.245536 + 0.969388i \(0.578964\pi\)
\(674\) −16.7671 −0.645846
\(675\) −5.59694 −0.215426
\(676\) 14.3958 0.553685
\(677\) −41.6208 −1.59962 −0.799808 0.600256i \(-0.795066\pi\)
−0.799808 + 0.600256i \(0.795066\pi\)
\(678\) 4.78730 0.183855
\(679\) 8.20842 0.315010
\(680\) 0.694702 0.0266406
\(681\) 0.954839 0.0365895
\(682\) −27.3939 −1.04897
\(683\) −23.2670 −0.890286 −0.445143 0.895460i \(-0.646847\pi\)
−0.445143 + 0.895460i \(0.646847\pi\)
\(684\) −0.0340851 −0.00130328
\(685\) −27.9907 −1.06947
\(686\) 13.4462 0.513378
\(687\) 4.51941 0.172426
\(688\) 10.3818 0.395802
\(689\) −2.82273 −0.107537
\(690\) 0.533849 0.0203233
\(691\) 21.1975 0.806391 0.403196 0.915114i \(-0.367899\pi\)
0.403196 + 0.915114i \(0.367899\pi\)
\(692\) −22.0643 −0.838757
\(693\) 10.3040 0.391417
\(694\) 20.5624 0.780539
\(695\) 10.7653 0.408350
\(696\) −2.01427 −0.0763509
\(697\) 2.20863 0.0836578
\(698\) 4.23107 0.160148
\(699\) −0.856166 −0.0323832
\(700\) 2.81469 0.106385
\(701\) 44.6793 1.68752 0.843758 0.536724i \(-0.180338\pi\)
0.843758 + 0.536724i \(0.180338\pi\)
\(702\) −10.8349 −0.408937
\(703\) 0.0428413 0.00161579
\(704\) 3.44169 0.129714
\(705\) 4.35778 0.164124
\(706\) 10.0342 0.377643
\(707\) −14.8950 −0.560184
\(708\) −4.41599 −0.165963
\(709\) −1.11972 −0.0420520 −0.0210260 0.999779i \(-0.506693\pi\)
−0.0210260 + 0.999779i \(0.506693\pi\)
\(710\) 4.03259 0.151340
\(711\) −10.8896 −0.408391
\(712\) −1.83019 −0.0685893
\(713\) −7.95942 −0.298083
\(714\) −0.168136 −0.00629235
\(715\) 27.2975 1.02087
\(716\) 24.9774 0.933448
\(717\) 5.49134 0.205078
\(718\) 18.4158 0.687273
\(719\) −12.6106 −0.470298 −0.235149 0.971959i \(-0.575558\pi\)
−0.235149 + 0.971959i \(0.575558\pi\)
\(720\) 4.35793 0.162411
\(721\) −18.3894 −0.684858
\(722\) −18.9999 −0.707102
\(723\) −4.95627 −0.184326
\(724\) −8.10577 −0.301248
\(725\) −15.4588 −0.574126
\(726\) −0.297777 −0.0110516
\(727\) −0.00700972 −0.000259976 0 −0.000129988 1.00000i \(-0.500041\pi\)
−0.000129988 1.00000i \(0.500041\pi\)
\(728\) 5.44885 0.201948
\(729\) −20.5270 −0.760260
\(730\) 23.2710 0.861299
\(731\) −4.75950 −0.176036
\(732\) −0.935806 −0.0345884
\(733\) 8.83525 0.326337 0.163169 0.986598i \(-0.447829\pi\)
0.163169 + 0.986598i \(0.447829\pi\)
\(734\) 15.9241 0.587771
\(735\) −3.15839 −0.116499
\(736\) 1.00000 0.0368605
\(737\) 27.2391 1.00337
\(738\) 13.8550 0.510008
\(739\) 8.14061 0.299457 0.149729 0.988727i \(-0.452160\pi\)
0.149729 + 0.988727i \(0.452160\pi\)
\(740\) −5.47745 −0.201355
\(741\) 0.0218547 0.000802852 0
\(742\) −0.561422 −0.0206105
\(743\) −8.30326 −0.304617 −0.152309 0.988333i \(-0.548671\pi\)
−0.152309 + 0.988333i \(0.548671\pi\)
\(744\) 2.80409 0.102803
\(745\) −19.5013 −0.714471
\(746\) 18.5232 0.678183
\(747\) −38.9324 −1.42446
\(748\) −1.57783 −0.0576913
\(749\) 1.04015 0.0380063
\(750\) −4.11265 −0.150173
\(751\) 45.6034 1.66409 0.832045 0.554708i \(-0.187170\pi\)
0.832045 + 0.554708i \(0.187170\pi\)
\(752\) 8.16294 0.297672
\(753\) −9.36439 −0.341257
\(754\) −29.9261 −1.08985
\(755\) 22.3025 0.811670
\(756\) −2.15499 −0.0783764
\(757\) 29.8653 1.08547 0.542737 0.839903i \(-0.317388\pi\)
0.542737 + 0.839903i \(0.317388\pi\)
\(758\) 16.2185 0.589081
\(759\) −1.21250 −0.0440110
\(760\) −0.0179598 −0.000651470 0
\(761\) 22.4368 0.813334 0.406667 0.913576i \(-0.366691\pi\)
0.406667 + 0.913576i \(0.366691\pi\)
\(762\) −1.20117 −0.0435138
\(763\) 6.92693 0.250772
\(764\) 17.2642 0.624598
\(765\) −1.99788 −0.0722336
\(766\) −14.9956 −0.541815
\(767\) −65.6085 −2.36899
\(768\) −0.352298 −0.0127125
\(769\) 0.992382 0.0357862 0.0178931 0.999840i \(-0.494304\pi\)
0.0178931 + 0.999840i \(0.494304\pi\)
\(770\) 5.42930 0.195658
\(771\) 7.47627 0.269251
\(772\) 1.60663 0.0578240
\(773\) −6.05231 −0.217687 −0.108843 0.994059i \(-0.534715\pi\)
−0.108843 + 0.994059i \(0.534715\pi\)
\(774\) −29.8568 −1.07318
\(775\) 21.5204 0.773034
\(776\) −7.88491 −0.283052
\(777\) 1.32569 0.0475589
\(778\) −17.4007 −0.623844
\(779\) −0.0570987 −0.00204577
\(780\) −2.79422 −0.100049
\(781\) −9.15898 −0.327734
\(782\) −0.458447 −0.0163940
\(783\) 11.8356 0.422972
\(784\) −5.91626 −0.211295
\(785\) −26.4769 −0.945000
\(786\) −0.352298 −0.0125660
\(787\) −46.0925 −1.64302 −0.821511 0.570193i \(-0.806868\pi\)
−0.821511 + 0.570193i \(0.806868\pi\)
\(788\) 9.97120 0.355209
\(789\) −6.60279 −0.235065
\(790\) −5.73784 −0.204143
\(791\) 14.1463 0.502985
\(792\) −9.89791 −0.351707
\(793\) −13.9033 −0.493721
\(794\) −4.57924 −0.162511
\(795\) 0.287903 0.0102109
\(796\) −14.3287 −0.507869
\(797\) 2.66924 0.0945494 0.0472747 0.998882i \(-0.484946\pi\)
0.0472747 + 0.998882i \(0.484946\pi\)
\(798\) 0.00434676 0.000153873 0
\(799\) −3.74228 −0.132392
\(800\) −2.70376 −0.0955923
\(801\) 5.26342 0.185974
\(802\) 5.29946 0.187130
\(803\) −52.8541 −1.86518
\(804\) −2.78825 −0.0983339
\(805\) 1.57751 0.0555999
\(806\) 41.6604 1.46743
\(807\) 0.325443 0.0114562
\(808\) 14.3080 0.503352
\(809\) 19.3720 0.681084 0.340542 0.940229i \(-0.389390\pi\)
0.340542 + 0.940229i \(0.389390\pi\)
\(810\) −11.9687 −0.420537
\(811\) 16.0883 0.564938 0.282469 0.959276i \(-0.408847\pi\)
0.282469 + 0.959276i \(0.408847\pi\)
\(812\) −5.95212 −0.208878
\(813\) 1.59851 0.0560623
\(814\) 12.4406 0.436043
\(815\) −11.0520 −0.387134
\(816\) 0.161510 0.00565398
\(817\) 0.123045 0.00430480
\(818\) 37.8084 1.32194
\(819\) −15.6703 −0.547563
\(820\) 7.30033 0.254938
\(821\) −31.6776 −1.10555 −0.552777 0.833329i \(-0.686432\pi\)
−0.552777 + 0.833329i \(0.686432\pi\)
\(822\) −6.50751 −0.226976
\(823\) 11.4619 0.399537 0.199769 0.979843i \(-0.435981\pi\)
0.199769 + 0.979843i \(0.435981\pi\)
\(824\) 17.6647 0.615377
\(825\) 3.27831 0.114136
\(826\) −13.0491 −0.454037
\(827\) −42.9348 −1.49299 −0.746495 0.665391i \(-0.768265\pi\)
−0.746495 + 0.665391i \(0.768265\pi\)
\(828\) −2.87589 −0.0999440
\(829\) −8.00365 −0.277978 −0.138989 0.990294i \(-0.544385\pi\)
−0.138989 + 0.990294i \(0.544385\pi\)
\(830\) −20.5139 −0.712047
\(831\) −7.96299 −0.276233
\(832\) −5.23410 −0.181460
\(833\) 2.71229 0.0939754
\(834\) 2.50280 0.0866649
\(835\) −11.0337 −0.381837
\(836\) 0.0407910 0.00141079
\(837\) −16.4765 −0.569511
\(838\) 6.59183 0.227711
\(839\) 17.7537 0.612926 0.306463 0.951883i \(-0.400854\pi\)
0.306463 + 0.951883i \(0.400854\pi\)
\(840\) −0.555753 −0.0191753
\(841\) 3.69019 0.127248
\(842\) −26.7028 −0.920238
\(843\) 3.64202 0.125438
\(844\) 25.1471 0.865600
\(845\) −21.8145 −0.750441
\(846\) −23.4757 −0.807111
\(847\) −0.879923 −0.0302345
\(848\) 0.539296 0.0185195
\(849\) 7.31134 0.250924
\(850\) 1.23953 0.0425155
\(851\) 3.61468 0.123910
\(852\) 0.937530 0.0321192
\(853\) 3.05897 0.104737 0.0523685 0.998628i \(-0.483323\pi\)
0.0523685 + 0.998628i \(0.483323\pi\)
\(854\) −2.76528 −0.0946259
\(855\) 0.0516503 0.00176640
\(856\) −0.999157 −0.0341505
\(857\) 4.03841 0.137949 0.0689747 0.997618i \(-0.478027\pi\)
0.0689747 + 0.997618i \(0.478027\pi\)
\(858\) 6.34635 0.216661
\(859\) 12.8894 0.439780 0.219890 0.975525i \(-0.429430\pi\)
0.219890 + 0.975525i \(0.429430\pi\)
\(860\) −15.7319 −0.536453
\(861\) −1.76688 −0.0602150
\(862\) −22.9331 −0.781104
\(863\) 34.8251 1.18546 0.592730 0.805401i \(-0.298050\pi\)
0.592730 + 0.805401i \(0.298050\pi\)
\(864\) 2.07006 0.0704249
\(865\) 33.4348 1.13682
\(866\) −36.7661 −1.24936
\(867\) 5.91502 0.200885
\(868\) 8.28599 0.281245
\(869\) 13.0320 0.442081
\(870\) 3.05230 0.103483
\(871\) −41.4251 −1.40364
\(872\) −6.65393 −0.225331
\(873\) 22.6761 0.767470
\(874\) 0.0118520 0.000400901 0
\(875\) −12.1527 −0.410838
\(876\) 5.41024 0.182795
\(877\) 15.4051 0.520192 0.260096 0.965583i \(-0.416246\pi\)
0.260096 + 0.965583i \(0.416246\pi\)
\(878\) 8.54496 0.288378
\(879\) −2.74255 −0.0925041
\(880\) −5.21532 −0.175808
\(881\) −17.7793 −0.599000 −0.299500 0.954096i \(-0.596820\pi\)
−0.299500 + 0.954096i \(0.596820\pi\)
\(882\) 17.0145 0.572908
\(883\) 8.30671 0.279543 0.139772 0.990184i \(-0.455363\pi\)
0.139772 + 0.990184i \(0.455363\pi\)
\(884\) 2.39956 0.0807059
\(885\) 6.69171 0.224939
\(886\) 20.9058 0.702343
\(887\) −32.9362 −1.10589 −0.552944 0.833218i \(-0.686496\pi\)
−0.552944 + 0.833218i \(0.686496\pi\)
\(888\) −1.27344 −0.0427339
\(889\) −3.54942 −0.119044
\(890\) 2.77336 0.0929631
\(891\) 27.1838 0.910691
\(892\) 13.8372 0.463303
\(893\) 0.0967474 0.00323753
\(894\) −4.53381 −0.151633
\(895\) −37.8491 −1.26516
\(896\) −1.04103 −0.0347783
\(897\) 1.84396 0.0615681
\(898\) −22.2619 −0.742888
\(899\) −45.5083 −1.51779
\(900\) 7.77570 0.259190
\(901\) −0.247239 −0.00823671
\(902\) −16.5808 −0.552080
\(903\) 3.80754 0.126707
\(904\) −13.5888 −0.451956
\(905\) 12.2830 0.408299
\(906\) 5.18506 0.172262
\(907\) −37.8218 −1.25585 −0.627927 0.778272i \(-0.716096\pi\)
−0.627927 + 0.778272i \(0.716096\pi\)
\(908\) −2.71032 −0.0899450
\(909\) −41.1481 −1.36479
\(910\) −8.25684 −0.273711
\(911\) −32.5061 −1.07697 −0.538487 0.842634i \(-0.681004\pi\)
−0.538487 + 0.842634i \(0.681004\pi\)
\(912\) −0.00417544 −0.000138263 0
\(913\) 46.5920 1.54197
\(914\) 30.7283 1.01640
\(915\) 1.41806 0.0468796
\(916\) −12.8284 −0.423862
\(917\) −1.04103 −0.0343778
\(918\) −0.949014 −0.0313221
\(919\) 29.7529 0.981456 0.490728 0.871313i \(-0.336731\pi\)
0.490728 + 0.871313i \(0.336731\pi\)
\(920\) −1.51534 −0.0499591
\(921\) 0.696954 0.0229654
\(922\) 1.84511 0.0607653
\(923\) 13.9289 0.458476
\(924\) 1.26225 0.0415249
\(925\) −9.77321 −0.321341
\(926\) −18.9409 −0.622436
\(927\) −50.8015 −1.66854
\(928\) 5.71753 0.187687
\(929\) 25.3941 0.833152 0.416576 0.909101i \(-0.363230\pi\)
0.416576 + 0.909101i \(0.363230\pi\)
\(930\) −4.24913 −0.139335
\(931\) −0.0701197 −0.00229808
\(932\) 2.43023 0.0796049
\(933\) −10.9289 −0.357795
\(934\) −27.4815 −0.899223
\(935\) 2.39095 0.0781924
\(936\) 15.0527 0.492012
\(937\) −46.1233 −1.50678 −0.753391 0.657573i \(-0.771583\pi\)
−0.753391 + 0.657573i \(0.771583\pi\)
\(938\) −8.23918 −0.269019
\(939\) 5.02900 0.164115
\(940\) −12.3696 −0.403452
\(941\) 28.6549 0.934123 0.467061 0.884225i \(-0.345313\pi\)
0.467061 + 0.884225i \(0.345313\pi\)
\(942\) −6.15556 −0.200559
\(943\) −4.81763 −0.156884
\(944\) 12.5348 0.407974
\(945\) 3.26554 0.106228
\(946\) 35.7309 1.16171
\(947\) −49.8271 −1.61916 −0.809582 0.587007i \(-0.800306\pi\)
−0.809582 + 0.587007i \(0.800306\pi\)
\(948\) −1.33398 −0.0433256
\(949\) 80.3801 2.60925
\(950\) −0.0320450 −0.00103968
\(951\) 0.673985 0.0218555
\(952\) 0.477257 0.0154680
\(953\) 24.3678 0.789350 0.394675 0.918821i \(-0.370857\pi\)
0.394675 + 0.918821i \(0.370857\pi\)
\(954\) −1.55095 −0.0502139
\(955\) −26.1611 −0.846554
\(956\) −15.5872 −0.504126
\(957\) −6.93251 −0.224096
\(958\) 31.3647 1.01335
\(959\) −19.2295 −0.620953
\(960\) 0.533849 0.0172299
\(961\) 32.3524 1.04363
\(962\) −18.9196 −0.609992
\(963\) 2.87346 0.0925960
\(964\) 14.0684 0.453113
\(965\) −2.43459 −0.0783722
\(966\) 0.366752 0.0118001
\(967\) −47.1092 −1.51493 −0.757465 0.652875i \(-0.773562\pi\)
−0.757465 + 0.652875i \(0.773562\pi\)
\(968\) 0.845244 0.0271672
\(969\) 0.00191422 6.14936e−5 0
\(970\) 11.9483 0.383637
\(971\) 18.4833 0.593156 0.296578 0.955009i \(-0.404154\pi\)
0.296578 + 0.955009i \(0.404154\pi\)
\(972\) −8.99277 −0.288443
\(973\) 7.39570 0.237095
\(974\) 17.6248 0.564735
\(975\) −4.98562 −0.159668
\(976\) 2.65629 0.0850259
\(977\) −8.44066 −0.270041 −0.135020 0.990843i \(-0.543110\pi\)
−0.135020 + 0.990843i \(0.543110\pi\)
\(978\) −2.56946 −0.0821622
\(979\) −6.29896 −0.201316
\(980\) 8.96512 0.286380
\(981\) 19.1360 0.610964
\(982\) 24.4755 0.781044
\(983\) 30.8450 0.983803 0.491901 0.870651i \(-0.336302\pi\)
0.491901 + 0.870651i \(0.336302\pi\)
\(984\) 1.69724 0.0541060
\(985\) −15.1097 −0.481435
\(986\) −2.62119 −0.0834756
\(987\) 2.99378 0.0952929
\(988\) −0.0620347 −0.00197359
\(989\) 10.3818 0.330121
\(990\) 14.9987 0.476689
\(991\) −12.7016 −0.403479 −0.201739 0.979439i \(-0.564659\pi\)
−0.201739 + 0.979439i \(0.564659\pi\)
\(992\) −7.95942 −0.252712
\(993\) 6.87290 0.218105
\(994\) 2.77037 0.0878708
\(995\) 21.7129 0.688344
\(996\) −4.76924 −0.151119
\(997\) −49.9103 −1.58067 −0.790337 0.612672i \(-0.790095\pi\)
−0.790337 + 0.612672i \(0.790095\pi\)
\(998\) 31.3949 0.993787
\(999\) 7.48261 0.236739
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 6026.2.a.m.1.19 41
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6026.2.a.m.1.19 41 1.1 even 1 trivial