Properties

Label 4017.2.a.i.1.6
Level $4017$
Weight $2$
Character 4017.1
Self dual yes
Analytic conductor $32.076$
Analytic rank $1$
Dimension $25$
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] = [4017,2,Mod(1,4017)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4017, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4017.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4017.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(32.0759064919\)
Analytic rank: \(1\)
Dimension: \(25\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) \(=\) 4017.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.08104 q^{2} -1.00000 q^{3} +2.33074 q^{4} +1.74075 q^{5} +2.08104 q^{6} -0.124046 q^{7} -0.688276 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.08104 q^{2} -1.00000 q^{3} +2.33074 q^{4} +1.74075 q^{5} +2.08104 q^{6} -0.124046 q^{7} -0.688276 q^{8} +1.00000 q^{9} -3.62257 q^{10} -0.521753 q^{11} -2.33074 q^{12} -1.00000 q^{13} +0.258144 q^{14} -1.74075 q^{15} -3.22914 q^{16} +3.38824 q^{17} -2.08104 q^{18} -2.62024 q^{19} +4.05723 q^{20} +0.124046 q^{21} +1.08579 q^{22} +1.07192 q^{23} +0.688276 q^{24} -1.96979 q^{25} +2.08104 q^{26} -1.00000 q^{27} -0.289118 q^{28} +1.51771 q^{29} +3.62257 q^{30} +4.90595 q^{31} +8.09653 q^{32} +0.521753 q^{33} -7.05107 q^{34} -0.215933 q^{35} +2.33074 q^{36} +5.89933 q^{37} +5.45284 q^{38} +1.00000 q^{39} -1.19812 q^{40} -10.0270 q^{41} -0.258144 q^{42} +0.753761 q^{43} -1.21607 q^{44} +1.74075 q^{45} -2.23070 q^{46} -3.90948 q^{47} +3.22914 q^{48} -6.98461 q^{49} +4.09921 q^{50} -3.38824 q^{51} -2.33074 q^{52} -13.3889 q^{53} +2.08104 q^{54} -0.908242 q^{55} +0.0853777 q^{56} +2.62024 q^{57} -3.15841 q^{58} -3.35885 q^{59} -4.05723 q^{60} +2.34011 q^{61} -10.2095 q^{62} -0.124046 q^{63} -10.3909 q^{64} -1.74075 q^{65} -1.08579 q^{66} +6.79145 q^{67} +7.89710 q^{68} -1.07192 q^{69} +0.449365 q^{70} -8.69610 q^{71} -0.688276 q^{72} -10.5845 q^{73} -12.2767 q^{74} +1.96979 q^{75} -6.10710 q^{76} +0.0647212 q^{77} -2.08104 q^{78} +11.4711 q^{79} -5.62113 q^{80} +1.00000 q^{81} +20.8666 q^{82} -15.8964 q^{83} +0.289118 q^{84} +5.89808 q^{85} -1.56861 q^{86} -1.51771 q^{87} +0.359110 q^{88} +6.43563 q^{89} -3.62257 q^{90} +0.124046 q^{91} +2.49836 q^{92} -4.90595 q^{93} +8.13579 q^{94} -4.56119 q^{95} -8.09653 q^{96} +11.4486 q^{97} +14.5353 q^{98} -0.521753 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9} + 2 q^{10} - q^{11} - 28 q^{12} - 25 q^{13} - 12 q^{14} + 3 q^{15} + 26 q^{16} - 10 q^{17} - 2 q^{18} + 22 q^{19} - 2 q^{20} + 11 q^{21} - 5 q^{22} - 49 q^{23} + 15 q^{24} + 22 q^{25} + 2 q^{26} - 25 q^{27} - 30 q^{28} - 22 q^{29} - 2 q^{30} + 8 q^{31} - 12 q^{32} + q^{33} - q^{34} - 2 q^{35} + 28 q^{36} - 26 q^{38} + 25 q^{39} - 22 q^{40} - 5 q^{41} + 12 q^{42} - 13 q^{43} - 25 q^{44} - 3 q^{45} + 13 q^{46} - 56 q^{47} - 26 q^{48} + 28 q^{49} - 31 q^{50} + 10 q^{51} - 28 q^{52} - 20 q^{53} + 2 q^{54} - 14 q^{55} - 22 q^{56} - 22 q^{57} - 21 q^{58} + 2 q^{59} + 2 q^{60} + 29 q^{61} - 39 q^{62} - 11 q^{63} + 21 q^{64} + 3 q^{65} + 5 q^{66} - 14 q^{67} - 60 q^{68} + 49 q^{69} - 31 q^{70} - 36 q^{71} - 15 q^{72} - 30 q^{73} - 64 q^{74} - 22 q^{75} + 38 q^{76} - 37 q^{77} - 2 q^{78} - 29 q^{79} + 25 q^{81} - 6 q^{82} - 17 q^{83} + 30 q^{84} + 3 q^{85} - 27 q^{86} + 22 q^{87} - 81 q^{88} - 38 q^{89} + 2 q^{90} + 11 q^{91} - 85 q^{92} - 8 q^{93} + 26 q^{94} - 71 q^{95} + 12 q^{96} + 19 q^{98} - q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.08104 −1.47152 −0.735759 0.677243i \(-0.763175\pi\)
−0.735759 + 0.677243i \(0.763175\pi\)
\(3\) −1.00000 −0.577350
\(4\) 2.33074 1.16537
\(5\) 1.74075 0.778487 0.389244 0.921135i \(-0.372736\pi\)
0.389244 + 0.921135i \(0.372736\pi\)
\(6\) 2.08104 0.849582
\(7\) −0.124046 −0.0468849 −0.0234424 0.999725i \(-0.507463\pi\)
−0.0234424 + 0.999725i \(0.507463\pi\)
\(8\) −0.688276 −0.243342
\(9\) 1.00000 0.333333
\(10\) −3.62257 −1.14556
\(11\) −0.521753 −0.157314 −0.0786572 0.996902i \(-0.525063\pi\)
−0.0786572 + 0.996902i \(0.525063\pi\)
\(12\) −2.33074 −0.672826
\(13\) −1.00000 −0.277350
\(14\) 0.258144 0.0689920
\(15\) −1.74075 −0.449460
\(16\) −3.22914 −0.807285
\(17\) 3.38824 0.821769 0.410885 0.911687i \(-0.365220\pi\)
0.410885 + 0.911687i \(0.365220\pi\)
\(18\) −2.08104 −0.490506
\(19\) −2.62024 −0.601125 −0.300563 0.953762i \(-0.597174\pi\)
−0.300563 + 0.953762i \(0.597174\pi\)
\(20\) 4.05723 0.907224
\(21\) 0.124046 0.0270690
\(22\) 1.08579 0.231491
\(23\) 1.07192 0.223510 0.111755 0.993736i \(-0.464353\pi\)
0.111755 + 0.993736i \(0.464353\pi\)
\(24\) 0.688276 0.140494
\(25\) −1.96979 −0.393958
\(26\) 2.08104 0.408126
\(27\) −1.00000 −0.192450
\(28\) −0.289118 −0.0546381
\(29\) 1.51771 0.281831 0.140916 0.990022i \(-0.454995\pi\)
0.140916 + 0.990022i \(0.454995\pi\)
\(30\) 3.62257 0.661389
\(31\) 4.90595 0.881135 0.440567 0.897720i \(-0.354777\pi\)
0.440567 + 0.897720i \(0.354777\pi\)
\(32\) 8.09653 1.43128
\(33\) 0.521753 0.0908255
\(34\) −7.05107 −1.20925
\(35\) −0.215933 −0.0364993
\(36\) 2.33074 0.388456
\(37\) 5.89933 0.969843 0.484922 0.874558i \(-0.338848\pi\)
0.484922 + 0.874558i \(0.338848\pi\)
\(38\) 5.45284 0.884567
\(39\) 1.00000 0.160128
\(40\) −1.19812 −0.189439
\(41\) −10.0270 −1.56595 −0.782977 0.622050i \(-0.786300\pi\)
−0.782977 + 0.622050i \(0.786300\pi\)
\(42\) −0.258144 −0.0398325
\(43\) 0.753761 0.114948 0.0574738 0.998347i \(-0.481695\pi\)
0.0574738 + 0.998347i \(0.481695\pi\)
\(44\) −1.21607 −0.183329
\(45\) 1.74075 0.259496
\(46\) −2.23070 −0.328899
\(47\) −3.90948 −0.570256 −0.285128 0.958489i \(-0.592036\pi\)
−0.285128 + 0.958489i \(0.592036\pi\)
\(48\) 3.22914 0.466086
\(49\) −6.98461 −0.997802
\(50\) 4.09921 0.579716
\(51\) −3.38824 −0.474449
\(52\) −2.33074 −0.323215
\(53\) −13.3889 −1.83910 −0.919552 0.392967i \(-0.871449\pi\)
−0.919552 + 0.392967i \(0.871449\pi\)
\(54\) 2.08104 0.283194
\(55\) −0.908242 −0.122467
\(56\) 0.0853777 0.0114091
\(57\) 2.62024 0.347060
\(58\) −3.15841 −0.414720
\(59\) −3.35885 −0.437285 −0.218643 0.975805i \(-0.570163\pi\)
−0.218643 + 0.975805i \(0.570163\pi\)
\(60\) −4.05723 −0.523786
\(61\) 2.34011 0.299620 0.149810 0.988715i \(-0.452134\pi\)
0.149810 + 0.988715i \(0.452134\pi\)
\(62\) −10.2095 −1.29661
\(63\) −0.124046 −0.0156283
\(64\) −10.3909 −1.29887
\(65\) −1.74075 −0.215913
\(66\) −1.08579 −0.133651
\(67\) 6.79145 0.829707 0.414854 0.909888i \(-0.363833\pi\)
0.414854 + 0.909888i \(0.363833\pi\)
\(68\) 7.89710 0.957664
\(69\) −1.07192 −0.129044
\(70\) 0.449365 0.0537094
\(71\) −8.69610 −1.03204 −0.516019 0.856577i \(-0.672587\pi\)
−0.516019 + 0.856577i \(0.672587\pi\)
\(72\) −0.688276 −0.0811141
\(73\) −10.5845 −1.23882 −0.619409 0.785068i \(-0.712628\pi\)
−0.619409 + 0.785068i \(0.712628\pi\)
\(74\) −12.2767 −1.42714
\(75\) 1.96979 0.227452
\(76\) −6.10710 −0.700532
\(77\) 0.0647212 0.00737567
\(78\) −2.08104 −0.235632
\(79\) 11.4711 1.29060 0.645301 0.763929i \(-0.276732\pi\)
0.645301 + 0.763929i \(0.276732\pi\)
\(80\) −5.62113 −0.628461
\(81\) 1.00000 0.111111
\(82\) 20.8666 2.30433
\(83\) −15.8964 −1.74485 −0.872426 0.488746i \(-0.837455\pi\)
−0.872426 + 0.488746i \(0.837455\pi\)
\(84\) 0.289118 0.0315453
\(85\) 5.89808 0.639737
\(86\) −1.56861 −0.169147
\(87\) −1.51771 −0.162715
\(88\) 0.359110 0.0382813
\(89\) 6.43563 0.682176 0.341088 0.940031i \(-0.389205\pi\)
0.341088 + 0.940031i \(0.389205\pi\)
\(90\) −3.62257 −0.381853
\(91\) 0.124046 0.0130035
\(92\) 2.49836 0.260472
\(93\) −4.90595 −0.508723
\(94\) 8.13579 0.839142
\(95\) −4.56119 −0.467968
\(96\) −8.09653 −0.826349
\(97\) 11.4486 1.16243 0.581214 0.813751i \(-0.302578\pi\)
0.581214 + 0.813751i \(0.302578\pi\)
\(98\) 14.5353 1.46828
\(99\) −0.521753 −0.0524381
\(100\) −4.59106 −0.459106
\(101\) 13.0315 1.29668 0.648341 0.761350i \(-0.275463\pi\)
0.648341 + 0.761350i \(0.275463\pi\)
\(102\) 7.05107 0.698160
\(103\) −1.00000 −0.0985329
\(104\) 0.688276 0.0674910
\(105\) 0.215933 0.0210729
\(106\) 27.8628 2.70628
\(107\) −6.66516 −0.644345 −0.322173 0.946681i \(-0.604413\pi\)
−0.322173 + 0.946681i \(0.604413\pi\)
\(108\) −2.33074 −0.224275
\(109\) 1.80728 0.173106 0.0865531 0.996247i \(-0.472415\pi\)
0.0865531 + 0.996247i \(0.472415\pi\)
\(110\) 1.89009 0.180213
\(111\) −5.89933 −0.559939
\(112\) 0.400561 0.0378495
\(113\) −1.77919 −0.167372 −0.0836861 0.996492i \(-0.526669\pi\)
−0.0836861 + 0.996492i \(0.526669\pi\)
\(114\) −5.45284 −0.510705
\(115\) 1.86594 0.174000
\(116\) 3.53738 0.328437
\(117\) −1.00000 −0.0924500
\(118\) 6.98991 0.643473
\(119\) −0.420297 −0.0385285
\(120\) 1.19812 0.109373
\(121\) −10.7278 −0.975252
\(122\) −4.86987 −0.440897
\(123\) 10.0270 0.904104
\(124\) 11.4345 1.02685
\(125\) −12.1327 −1.08518
\(126\) 0.258144 0.0229973
\(127\) −2.12556 −0.188613 −0.0943066 0.995543i \(-0.530063\pi\)
−0.0943066 + 0.995543i \(0.530063\pi\)
\(128\) 5.43092 0.480030
\(129\) −0.753761 −0.0663650
\(130\) 3.62257 0.317721
\(131\) −11.1284 −0.972289 −0.486144 0.873878i \(-0.661597\pi\)
−0.486144 + 0.873878i \(0.661597\pi\)
\(132\) 1.21607 0.105845
\(133\) 0.325030 0.0281837
\(134\) −14.1333 −1.22093
\(135\) −1.74075 −0.149820
\(136\) −2.33204 −0.199971
\(137\) 2.19152 0.187235 0.0936173 0.995608i \(-0.470157\pi\)
0.0936173 + 0.995608i \(0.470157\pi\)
\(138\) 2.23070 0.189890
\(139\) 13.0881 1.11012 0.555061 0.831810i \(-0.312695\pi\)
0.555061 + 0.831810i \(0.312695\pi\)
\(140\) −0.503282 −0.0425351
\(141\) 3.90948 0.329237
\(142\) 18.0970 1.51866
\(143\) 0.521753 0.0436312
\(144\) −3.22914 −0.269095
\(145\) 2.64195 0.219402
\(146\) 22.0267 1.82294
\(147\) 6.98461 0.576081
\(148\) 13.7498 1.13022
\(149\) 18.2394 1.49423 0.747116 0.664694i \(-0.231438\pi\)
0.747116 + 0.664694i \(0.231438\pi\)
\(150\) −4.09921 −0.334699
\(151\) −16.9669 −1.38075 −0.690375 0.723451i \(-0.742555\pi\)
−0.690375 + 0.723451i \(0.742555\pi\)
\(152\) 1.80345 0.146279
\(153\) 3.38824 0.273923
\(154\) −0.134688 −0.0108534
\(155\) 8.54003 0.685952
\(156\) 2.33074 0.186608
\(157\) −14.6396 −1.16836 −0.584182 0.811623i \(-0.698585\pi\)
−0.584182 + 0.811623i \(0.698585\pi\)
\(158\) −23.8719 −1.89914
\(159\) 13.3889 1.06181
\(160\) 14.0940 1.11423
\(161\) −0.132967 −0.0104792
\(162\) −2.08104 −0.163502
\(163\) 0.586063 0.0459040 0.0229520 0.999737i \(-0.492694\pi\)
0.0229520 + 0.999737i \(0.492694\pi\)
\(164\) −23.3703 −1.82491
\(165\) 0.908242 0.0707065
\(166\) 33.0810 2.56758
\(167\) −5.12247 −0.396389 −0.198194 0.980163i \(-0.563508\pi\)
−0.198194 + 0.980163i \(0.563508\pi\)
\(168\) −0.0853777 −0.00658703
\(169\) 1.00000 0.0769231
\(170\) −12.2742 −0.941385
\(171\) −2.62024 −0.200375
\(172\) 1.75682 0.133956
\(173\) 5.66494 0.430697 0.215349 0.976537i \(-0.430911\pi\)
0.215349 + 0.976537i \(0.430911\pi\)
\(174\) 3.15841 0.239439
\(175\) 0.244344 0.0184707
\(176\) 1.68481 0.126998
\(177\) 3.35885 0.252467
\(178\) −13.3928 −1.00383
\(179\) −17.1537 −1.28213 −0.641064 0.767487i \(-0.721507\pi\)
−0.641064 + 0.767487i \(0.721507\pi\)
\(180\) 4.05723 0.302408
\(181\) 5.79668 0.430864 0.215432 0.976519i \(-0.430884\pi\)
0.215432 + 0.976519i \(0.430884\pi\)
\(182\) −0.258144 −0.0191349
\(183\) −2.34011 −0.172986
\(184\) −0.737775 −0.0543895
\(185\) 10.2693 0.755010
\(186\) 10.2095 0.748596
\(187\) −1.76782 −0.129276
\(188\) −9.11196 −0.664558
\(189\) 0.124046 0.00902300
\(190\) 9.49203 0.688624
\(191\) 10.0894 0.730044 0.365022 0.930999i \(-0.381062\pi\)
0.365022 + 0.930999i \(0.381062\pi\)
\(192\) 10.3909 0.749901
\(193\) 21.3866 1.53944 0.769722 0.638379i \(-0.220395\pi\)
0.769722 + 0.638379i \(0.220395\pi\)
\(194\) −23.8250 −1.71054
\(195\) 1.74075 0.124658
\(196\) −16.2793 −1.16281
\(197\) 14.6160 1.04135 0.520673 0.853756i \(-0.325681\pi\)
0.520673 + 0.853756i \(0.325681\pi\)
\(198\) 1.08579 0.0771637
\(199\) 19.4870 1.38140 0.690699 0.723143i \(-0.257303\pi\)
0.690699 + 0.723143i \(0.257303\pi\)
\(200\) 1.35576 0.0958666
\(201\) −6.79145 −0.479032
\(202\) −27.1191 −1.90809
\(203\) −0.188265 −0.0132136
\(204\) −7.89710 −0.552907
\(205\) −17.4545 −1.21908
\(206\) 2.08104 0.144993
\(207\) 1.07192 0.0745034
\(208\) 3.22914 0.223901
\(209\) 1.36712 0.0945657
\(210\) −0.449365 −0.0310091
\(211\) −22.4629 −1.54641 −0.773206 0.634155i \(-0.781348\pi\)
−0.773206 + 0.634155i \(0.781348\pi\)
\(212\) −31.2060 −2.14323
\(213\) 8.69610 0.595847
\(214\) 13.8705 0.948166
\(215\) 1.31211 0.0894852
\(216\) 0.688276 0.0468312
\(217\) −0.608562 −0.0413119
\(218\) −3.76103 −0.254729
\(219\) 10.5845 0.715232
\(220\) −2.11687 −0.142719
\(221\) −3.38824 −0.227918
\(222\) 12.2767 0.823961
\(223\) 1.58222 0.105953 0.0529765 0.998596i \(-0.483129\pi\)
0.0529765 + 0.998596i \(0.483129\pi\)
\(224\) −1.00434 −0.0671053
\(225\) −1.96979 −0.131319
\(226\) 3.70257 0.246291
\(227\) −26.3243 −1.74721 −0.873603 0.486639i \(-0.838223\pi\)
−0.873603 + 0.486639i \(0.838223\pi\)
\(228\) 6.10710 0.404453
\(229\) 12.3705 0.817468 0.408734 0.912654i \(-0.365970\pi\)
0.408734 + 0.912654i \(0.365970\pi\)
\(230\) −3.88310 −0.256044
\(231\) −0.0647212 −0.00425834
\(232\) −1.04460 −0.0685815
\(233\) −8.60177 −0.563521 −0.281760 0.959485i \(-0.590918\pi\)
−0.281760 + 0.959485i \(0.590918\pi\)
\(234\) 2.08104 0.136042
\(235\) −6.80542 −0.443937
\(236\) −7.82860 −0.509598
\(237\) −11.4711 −0.745129
\(238\) 0.874655 0.0566955
\(239\) 2.22240 0.143755 0.0718774 0.997413i \(-0.477101\pi\)
0.0718774 + 0.997413i \(0.477101\pi\)
\(240\) 5.62113 0.362842
\(241\) 26.3501 1.69736 0.848679 0.528908i \(-0.177398\pi\)
0.848679 + 0.528908i \(0.177398\pi\)
\(242\) 22.3249 1.43510
\(243\) −1.00000 −0.0641500
\(244\) 5.45418 0.349168
\(245\) −12.1585 −0.776776
\(246\) −20.8666 −1.33041
\(247\) 2.62024 0.166722
\(248\) −3.37665 −0.214417
\(249\) 15.8964 1.00739
\(250\) 25.2486 1.59686
\(251\) 16.9216 1.06808 0.534041 0.845458i \(-0.320673\pi\)
0.534041 + 0.845458i \(0.320673\pi\)
\(252\) −0.289118 −0.0182127
\(253\) −0.559276 −0.0351614
\(254\) 4.42338 0.277548
\(255\) −5.89808 −0.369352
\(256\) 9.47991 0.592494
\(257\) −14.9316 −0.931411 −0.465705 0.884940i \(-0.654199\pi\)
−0.465705 + 0.884940i \(0.654199\pi\)
\(258\) 1.56861 0.0976573
\(259\) −0.731786 −0.0454710
\(260\) −4.05723 −0.251619
\(261\) 1.51771 0.0939438
\(262\) 23.1586 1.43074
\(263\) −7.43575 −0.458508 −0.229254 0.973367i \(-0.573629\pi\)
−0.229254 + 0.973367i \(0.573629\pi\)
\(264\) −0.359110 −0.0221017
\(265\) −23.3067 −1.43172
\(266\) −0.676401 −0.0414728
\(267\) −6.43563 −0.393854
\(268\) 15.8291 0.966914
\(269\) −3.21442 −0.195987 −0.0979934 0.995187i \(-0.531242\pi\)
−0.0979934 + 0.995187i \(0.531242\pi\)
\(270\) 3.62257 0.220463
\(271\) −23.8045 −1.44602 −0.723011 0.690836i \(-0.757243\pi\)
−0.723011 + 0.690836i \(0.757243\pi\)
\(272\) −10.9411 −0.663402
\(273\) −0.124046 −0.00750759
\(274\) −4.56065 −0.275519
\(275\) 1.02774 0.0619752
\(276\) −2.49836 −0.150383
\(277\) 11.1743 0.671397 0.335699 0.941969i \(-0.391028\pi\)
0.335699 + 0.941969i \(0.391028\pi\)
\(278\) −27.2370 −1.63357
\(279\) 4.90595 0.293712
\(280\) 0.148621 0.00888182
\(281\) −3.08517 −0.184046 −0.0920230 0.995757i \(-0.529333\pi\)
−0.0920230 + 0.995757i \(0.529333\pi\)
\(282\) −8.13579 −0.484479
\(283\) −24.0540 −1.42986 −0.714931 0.699195i \(-0.753542\pi\)
−0.714931 + 0.699195i \(0.753542\pi\)
\(284\) −20.2683 −1.20270
\(285\) 4.56119 0.270182
\(286\) −1.08579 −0.0642041
\(287\) 1.24381 0.0734196
\(288\) 8.09653 0.477093
\(289\) −5.51982 −0.324695
\(290\) −5.49801 −0.322854
\(291\) −11.4486 −0.671128
\(292\) −24.6696 −1.44368
\(293\) 20.9087 1.22150 0.610750 0.791824i \(-0.290868\pi\)
0.610750 + 0.791824i \(0.290868\pi\)
\(294\) −14.5353 −0.847714
\(295\) −5.84692 −0.340421
\(296\) −4.06036 −0.236004
\(297\) 0.521753 0.0302752
\(298\) −37.9570 −2.19879
\(299\) −1.07192 −0.0619906
\(300\) 4.59106 0.265065
\(301\) −0.0935009 −0.00538930
\(302\) 35.3089 2.03180
\(303\) −13.0315 −0.748639
\(304\) 8.46114 0.485280
\(305\) 4.07355 0.233251
\(306\) −7.05107 −0.403083
\(307\) −29.4633 −1.68156 −0.840780 0.541377i \(-0.817903\pi\)
−0.840780 + 0.541377i \(0.817903\pi\)
\(308\) 0.150848 0.00859537
\(309\) 1.00000 0.0568880
\(310\) −17.7722 −1.00939
\(311\) −8.55254 −0.484970 −0.242485 0.970155i \(-0.577963\pi\)
−0.242485 + 0.970155i \(0.577963\pi\)
\(312\) −0.688276 −0.0389660
\(313\) 17.0478 0.963598 0.481799 0.876282i \(-0.339984\pi\)
0.481799 + 0.876282i \(0.339984\pi\)
\(314\) 30.4655 1.71927
\(315\) −0.215933 −0.0121664
\(316\) 26.7362 1.50403
\(317\) −20.9238 −1.17520 −0.587598 0.809153i \(-0.699926\pi\)
−0.587598 + 0.809153i \(0.699926\pi\)
\(318\) −27.8628 −1.56247
\(319\) −0.791869 −0.0443361
\(320\) −18.0880 −1.01115
\(321\) 6.66516 0.372013
\(322\) 0.276709 0.0154204
\(323\) −8.87802 −0.493986
\(324\) 2.33074 0.129485
\(325\) 1.96979 0.109264
\(326\) −1.21962 −0.0675486
\(327\) −1.80728 −0.0999429
\(328\) 6.90134 0.381063
\(329\) 0.484954 0.0267364
\(330\) −1.89009 −0.104046
\(331\) −14.1579 −0.778186 −0.389093 0.921198i \(-0.627212\pi\)
−0.389093 + 0.921198i \(0.627212\pi\)
\(332\) −37.0502 −2.03340
\(333\) 5.89933 0.323281
\(334\) 10.6601 0.583293
\(335\) 11.8222 0.645916
\(336\) −0.400561 −0.0218524
\(337\) −9.46821 −0.515766 −0.257883 0.966176i \(-0.583025\pi\)
−0.257883 + 0.966176i \(0.583025\pi\)
\(338\) −2.08104 −0.113194
\(339\) 1.77919 0.0966324
\(340\) 13.7469 0.745529
\(341\) −2.55969 −0.138615
\(342\) 5.45284 0.294856
\(343\) 1.73473 0.0936667
\(344\) −0.518796 −0.0279716
\(345\) −1.86594 −0.100459
\(346\) −11.7890 −0.633779
\(347\) −24.3508 −1.30722 −0.653610 0.756832i \(-0.726746\pi\)
−0.653610 + 0.756832i \(0.726746\pi\)
\(348\) −3.53738 −0.189623
\(349\) 21.2313 1.13649 0.568243 0.822861i \(-0.307623\pi\)
0.568243 + 0.822861i \(0.307623\pi\)
\(350\) −0.508490 −0.0271799
\(351\) 1.00000 0.0533761
\(352\) −4.22439 −0.225161
\(353\) −17.0348 −0.906671 −0.453336 0.891340i \(-0.649766\pi\)
−0.453336 + 0.891340i \(0.649766\pi\)
\(354\) −6.98991 −0.371510
\(355\) −15.1377 −0.803428
\(356\) 14.9998 0.794986
\(357\) 0.420297 0.0222445
\(358\) 35.6976 1.88668
\(359\) −28.3209 −1.49472 −0.747359 0.664420i \(-0.768678\pi\)
−0.747359 + 0.664420i \(0.768678\pi\)
\(360\) −1.19812 −0.0631463
\(361\) −12.1343 −0.638648
\(362\) −12.0631 −0.634024
\(363\) 10.7278 0.563062
\(364\) 0.289118 0.0151539
\(365\) −18.4249 −0.964404
\(366\) 4.86987 0.254552
\(367\) 13.2963 0.694061 0.347031 0.937854i \(-0.387190\pi\)
0.347031 + 0.937854i \(0.387190\pi\)
\(368\) −3.46137 −0.180436
\(369\) −10.0270 −0.521985
\(370\) −21.3707 −1.11101
\(371\) 1.66083 0.0862262
\(372\) −11.4345 −0.592850
\(373\) −21.7336 −1.12532 −0.562661 0.826688i \(-0.690222\pi\)
−0.562661 + 0.826688i \(0.690222\pi\)
\(374\) 3.67892 0.190232
\(375\) 12.1327 0.626528
\(376\) 2.69080 0.138767
\(377\) −1.51771 −0.0781660
\(378\) −0.258144 −0.0132775
\(379\) −25.0970 −1.28914 −0.644572 0.764544i \(-0.722964\pi\)
−0.644572 + 0.764544i \(0.722964\pi\)
\(380\) −10.6309 −0.545355
\(381\) 2.12556 0.108896
\(382\) −20.9965 −1.07427
\(383\) −37.4375 −1.91296 −0.956482 0.291790i \(-0.905749\pi\)
−0.956482 + 0.291790i \(0.905749\pi\)
\(384\) −5.43092 −0.277145
\(385\) 0.112663 0.00574186
\(386\) −44.5065 −2.26532
\(387\) 0.753761 0.0383158
\(388\) 26.6836 1.35466
\(389\) −0.692861 −0.0351294 −0.0175647 0.999846i \(-0.505591\pi\)
−0.0175647 + 0.999846i \(0.505591\pi\)
\(390\) −3.62257 −0.183436
\(391\) 3.63191 0.183674
\(392\) 4.80734 0.242807
\(393\) 11.1284 0.561351
\(394\) −30.4165 −1.53236
\(395\) 19.9684 1.00472
\(396\) −1.21607 −0.0611097
\(397\) −17.3398 −0.870258 −0.435129 0.900368i \(-0.643297\pi\)
−0.435129 + 0.900368i \(0.643297\pi\)
\(398\) −40.5533 −2.03275
\(399\) −0.325030 −0.0162719
\(400\) 6.36073 0.318036
\(401\) 5.79042 0.289160 0.144580 0.989493i \(-0.453817\pi\)
0.144580 + 0.989493i \(0.453817\pi\)
\(402\) 14.1333 0.704904
\(403\) −4.90595 −0.244383
\(404\) 30.3730 1.51111
\(405\) 1.74075 0.0864986
\(406\) 0.391788 0.0194441
\(407\) −3.07799 −0.152570
\(408\) 2.33204 0.115453
\(409\) 20.0783 0.992810 0.496405 0.868091i \(-0.334653\pi\)
0.496405 + 0.868091i \(0.334653\pi\)
\(410\) 36.3236 1.79389
\(411\) −2.19152 −0.108100
\(412\) −2.33074 −0.114827
\(413\) 0.416651 0.0205021
\(414\) −2.23070 −0.109633
\(415\) −27.6716 −1.35835
\(416\) −8.09653 −0.396965
\(417\) −13.0881 −0.640929
\(418\) −2.84504 −0.139155
\(419\) −4.01294 −0.196045 −0.0980224 0.995184i \(-0.531252\pi\)
−0.0980224 + 0.995184i \(0.531252\pi\)
\(420\) 0.503282 0.0245576
\(421\) 24.6861 1.20313 0.601564 0.798824i \(-0.294544\pi\)
0.601564 + 0.798824i \(0.294544\pi\)
\(422\) 46.7463 2.27558
\(423\) −3.90948 −0.190085
\(424\) 9.21525 0.447532
\(425\) −6.67412 −0.323742
\(426\) −18.0970 −0.876800
\(427\) −0.290281 −0.0140477
\(428\) −15.5347 −0.750900
\(429\) −0.521753 −0.0251905
\(430\) −2.73056 −0.131679
\(431\) −4.02554 −0.193903 −0.0969516 0.995289i \(-0.530909\pi\)
−0.0969516 + 0.995289i \(0.530909\pi\)
\(432\) 3.22914 0.155362
\(433\) 6.38826 0.307000 0.153500 0.988149i \(-0.450945\pi\)
0.153500 + 0.988149i \(0.450945\pi\)
\(434\) 1.26644 0.0607912
\(435\) −2.64195 −0.126672
\(436\) 4.21230 0.201732
\(437\) −2.80869 −0.134358
\(438\) −22.0267 −1.05248
\(439\) −31.2808 −1.49295 −0.746476 0.665413i \(-0.768256\pi\)
−0.746476 + 0.665413i \(0.768256\pi\)
\(440\) 0.625121 0.0298015
\(441\) −6.98461 −0.332601
\(442\) 7.05107 0.335385
\(443\) 3.76786 0.179016 0.0895081 0.995986i \(-0.471470\pi\)
0.0895081 + 0.995986i \(0.471470\pi\)
\(444\) −13.7498 −0.652535
\(445\) 11.2028 0.531065
\(446\) −3.29266 −0.155912
\(447\) −18.2394 −0.862695
\(448\) 1.28895 0.0608972
\(449\) −26.5743 −1.25412 −0.627060 0.778971i \(-0.715742\pi\)
−0.627060 + 0.778971i \(0.715742\pi\)
\(450\) 4.09921 0.193239
\(451\) 5.23162 0.246347
\(452\) −4.14683 −0.195050
\(453\) 16.9669 0.797177
\(454\) 54.7820 2.57105
\(455\) 0.215933 0.0101231
\(456\) −1.80345 −0.0844544
\(457\) −27.1593 −1.27046 −0.635229 0.772323i \(-0.719094\pi\)
−0.635229 + 0.772323i \(0.719094\pi\)
\(458\) −25.7436 −1.20292
\(459\) −3.38824 −0.158150
\(460\) 4.34901 0.202774
\(461\) 37.8715 1.76385 0.881926 0.471388i \(-0.156247\pi\)
0.881926 + 0.471388i \(0.156247\pi\)
\(462\) 0.134688 0.00626623
\(463\) 18.4681 0.858285 0.429143 0.903237i \(-0.358816\pi\)
0.429143 + 0.903237i \(0.358816\pi\)
\(464\) −4.90089 −0.227518
\(465\) −8.54003 −0.396035
\(466\) 17.9006 0.829231
\(467\) −21.0049 −0.971989 −0.485995 0.873962i \(-0.661543\pi\)
−0.485995 + 0.873962i \(0.661543\pi\)
\(468\) −2.33074 −0.107738
\(469\) −0.842450 −0.0389007
\(470\) 14.1624 0.653262
\(471\) 14.6396 0.674555
\(472\) 2.31182 0.106410
\(473\) −0.393277 −0.0180829
\(474\) 23.8719 1.09647
\(475\) 5.16133 0.236818
\(476\) −0.979601 −0.0448999
\(477\) −13.3889 −0.613035
\(478\) −4.62490 −0.211538
\(479\) 16.9260 0.773368 0.386684 0.922212i \(-0.373620\pi\)
0.386684 + 0.922212i \(0.373620\pi\)
\(480\) −14.0940 −0.643302
\(481\) −5.89933 −0.268986
\(482\) −54.8356 −2.49769
\(483\) 0.132967 0.00605020
\(484\) −25.0036 −1.13653
\(485\) 19.9291 0.904936
\(486\) 2.08104 0.0943980
\(487\) −7.12339 −0.322791 −0.161396 0.986890i \(-0.551600\pi\)
−0.161396 + 0.986890i \(0.551600\pi\)
\(488\) −1.61064 −0.0729103
\(489\) −0.586063 −0.0265027
\(490\) 25.3023 1.14304
\(491\) 14.7857 0.667267 0.333634 0.942703i \(-0.391725\pi\)
0.333634 + 0.942703i \(0.391725\pi\)
\(492\) 23.3703 1.05361
\(493\) 5.14236 0.231600
\(494\) −5.45284 −0.245335
\(495\) −0.908242 −0.0408224
\(496\) −15.8420 −0.711327
\(497\) 1.07871 0.0483869
\(498\) −33.0810 −1.48239
\(499\) 34.1869 1.53042 0.765208 0.643783i \(-0.222636\pi\)
0.765208 + 0.643783i \(0.222636\pi\)
\(500\) −28.2780 −1.26463
\(501\) 5.12247 0.228855
\(502\) −35.2146 −1.57170
\(503\) −32.8667 −1.46545 −0.732727 0.680522i \(-0.761753\pi\)
−0.732727 + 0.680522i \(0.761753\pi\)
\(504\) 0.0853777 0.00380302
\(505\) 22.6846 1.00945
\(506\) 1.16388 0.0517406
\(507\) −1.00000 −0.0444116
\(508\) −4.95412 −0.219804
\(509\) −22.3042 −0.988614 −0.494307 0.869287i \(-0.664578\pi\)
−0.494307 + 0.869287i \(0.664578\pi\)
\(510\) 12.2742 0.543509
\(511\) 1.31296 0.0580818
\(512\) −30.5899 −1.35190
\(513\) 2.62024 0.115687
\(514\) 31.0734 1.37059
\(515\) −1.74075 −0.0767066
\(516\) −1.75682 −0.0773396
\(517\) 2.03978 0.0897095
\(518\) 1.52288 0.0669114
\(519\) −5.66494 −0.248663
\(520\) 1.19812 0.0525409
\(521\) 3.02739 0.132632 0.0663162 0.997799i \(-0.478875\pi\)
0.0663162 + 0.997799i \(0.478875\pi\)
\(522\) −3.15841 −0.138240
\(523\) −25.5829 −1.11866 −0.559332 0.828944i \(-0.688942\pi\)
−0.559332 + 0.828944i \(0.688942\pi\)
\(524\) −25.9373 −1.13307
\(525\) −0.244344 −0.0106640
\(526\) 15.4741 0.674703
\(527\) 16.6225 0.724089
\(528\) −1.68481 −0.0733221
\(529\) −21.8510 −0.950043
\(530\) 48.5022 2.10680
\(531\) −3.35885 −0.145762
\(532\) 0.757560 0.0328444
\(533\) 10.0270 0.434318
\(534\) 13.3928 0.579564
\(535\) −11.6024 −0.501615
\(536\) −4.67439 −0.201903
\(537\) 17.1537 0.740237
\(538\) 6.68935 0.288398
\(539\) 3.64424 0.156969
\(540\) −4.05723 −0.174595
\(541\) 0.0872630 0.00375173 0.00187586 0.999998i \(-0.499403\pi\)
0.00187586 + 0.999998i \(0.499403\pi\)
\(542\) 49.5382 2.12785
\(543\) −5.79668 −0.248759
\(544\) 27.4330 1.17618
\(545\) 3.14602 0.134761
\(546\) 0.258144 0.0110476
\(547\) −26.4282 −1.12999 −0.564994 0.825095i \(-0.691121\pi\)
−0.564994 + 0.825095i \(0.691121\pi\)
\(548\) 5.10786 0.218197
\(549\) 2.34011 0.0998735
\(550\) −2.13878 −0.0911977
\(551\) −3.97677 −0.169416
\(552\) 0.737775 0.0314018
\(553\) −1.42294 −0.0605097
\(554\) −23.2541 −0.987973
\(555\) −10.2693 −0.435905
\(556\) 30.5050 1.29370
\(557\) −9.63573 −0.408279 −0.204140 0.978942i \(-0.565440\pi\)
−0.204140 + 0.978942i \(0.565440\pi\)
\(558\) −10.2095 −0.432202
\(559\) −0.753761 −0.0318807
\(560\) 0.697277 0.0294653
\(561\) 1.76782 0.0746376
\(562\) 6.42038 0.270827
\(563\) 18.7778 0.791392 0.395696 0.918382i \(-0.370503\pi\)
0.395696 + 0.918382i \(0.370503\pi\)
\(564\) 9.11196 0.383683
\(565\) −3.09713 −0.130297
\(566\) 50.0574 2.10407
\(567\) −0.124046 −0.00520943
\(568\) 5.98532 0.251138
\(569\) −14.5123 −0.608389 −0.304194 0.952610i \(-0.598387\pi\)
−0.304194 + 0.952610i \(0.598387\pi\)
\(570\) −9.49203 −0.397578
\(571\) 11.9296 0.499240 0.249620 0.968344i \(-0.419694\pi\)
0.249620 + 0.968344i \(0.419694\pi\)
\(572\) 1.21607 0.0508464
\(573\) −10.0894 −0.421491
\(574\) −2.58841 −0.108038
\(575\) −2.11145 −0.0880536
\(576\) −10.3909 −0.432956
\(577\) −28.9260 −1.20420 −0.602102 0.798419i \(-0.705670\pi\)
−0.602102 + 0.798419i \(0.705670\pi\)
\(578\) 11.4870 0.477795
\(579\) −21.3866 −0.888799
\(580\) 6.15769 0.255684
\(581\) 1.97188 0.0818072
\(582\) 23.8250 0.987578
\(583\) 6.98569 0.289318
\(584\) 7.28504 0.301457
\(585\) −1.74075 −0.0719712
\(586\) −43.5119 −1.79746
\(587\) 4.30846 0.177829 0.0889146 0.996039i \(-0.471660\pi\)
0.0889146 + 0.996039i \(0.471660\pi\)
\(588\) 16.2793 0.671347
\(589\) −12.8548 −0.529672
\(590\) 12.1677 0.500936
\(591\) −14.6160 −0.601222
\(592\) −19.0498 −0.782940
\(593\) −26.2928 −1.07971 −0.539857 0.841757i \(-0.681522\pi\)
−0.539857 + 0.841757i \(0.681522\pi\)
\(594\) −1.08579 −0.0445505
\(595\) −0.731632 −0.0299940
\(596\) 42.5113 1.74133
\(597\) −19.4870 −0.797550
\(598\) 2.23070 0.0912203
\(599\) −14.5575 −0.594803 −0.297402 0.954752i \(-0.596120\pi\)
−0.297402 + 0.954752i \(0.596120\pi\)
\(600\) −1.35576 −0.0553486
\(601\) 2.12829 0.0868146 0.0434073 0.999057i \(-0.486179\pi\)
0.0434073 + 0.999057i \(0.486179\pi\)
\(602\) 0.194579 0.00793046
\(603\) 6.79145 0.276569
\(604\) −39.5455 −1.60908
\(605\) −18.6744 −0.759221
\(606\) 27.1191 1.10164
\(607\) 36.7833 1.49299 0.746494 0.665392i \(-0.231736\pi\)
0.746494 + 0.665392i \(0.231736\pi\)
\(608\) −21.2149 −0.860378
\(609\) 0.188265 0.00762889
\(610\) −8.47723 −0.343233
\(611\) 3.90948 0.158161
\(612\) 7.89710 0.319221
\(613\) 9.47479 0.382683 0.191341 0.981524i \(-0.438716\pi\)
0.191341 + 0.981524i \(0.438716\pi\)
\(614\) 61.3144 2.47445
\(615\) 17.4545 0.703833
\(616\) −0.0445461 −0.00179481
\(617\) −29.7893 −1.19927 −0.599636 0.800273i \(-0.704688\pi\)
−0.599636 + 0.800273i \(0.704688\pi\)
\(618\) −2.08104 −0.0837118
\(619\) 9.38507 0.377218 0.188609 0.982052i \(-0.439602\pi\)
0.188609 + 0.982052i \(0.439602\pi\)
\(620\) 19.9046 0.799387
\(621\) −1.07192 −0.0430146
\(622\) 17.7982 0.713642
\(623\) −0.798313 −0.0319837
\(624\) −3.22914 −0.129269
\(625\) −11.2710 −0.450840
\(626\) −35.4772 −1.41795
\(627\) −1.36712 −0.0545975
\(628\) −34.1210 −1.36157
\(629\) 19.9883 0.796987
\(630\) 0.449365 0.0179031
\(631\) 18.8535 0.750547 0.375273 0.926914i \(-0.377549\pi\)
0.375273 + 0.926914i \(0.377549\pi\)
\(632\) −7.89529 −0.314058
\(633\) 22.4629 0.892822
\(634\) 43.5432 1.72932
\(635\) −3.70007 −0.146833
\(636\) 31.2060 1.23740
\(637\) 6.98461 0.276740
\(638\) 1.64791 0.0652415
\(639\) −8.69610 −0.344013
\(640\) 9.45387 0.373697
\(641\) −14.3596 −0.567169 −0.283584 0.958947i \(-0.591524\pi\)
−0.283584 + 0.958947i \(0.591524\pi\)
\(642\) −13.8705 −0.547424
\(643\) −16.1661 −0.637527 −0.318763 0.947834i \(-0.603268\pi\)
−0.318763 + 0.947834i \(0.603268\pi\)
\(644\) −0.309910 −0.0122122
\(645\) −1.31211 −0.0516643
\(646\) 18.4755 0.726910
\(647\) −44.2051 −1.73788 −0.868940 0.494917i \(-0.835198\pi\)
−0.868940 + 0.494917i \(0.835198\pi\)
\(648\) −0.688276 −0.0270380
\(649\) 1.75249 0.0687913
\(650\) −4.09921 −0.160784
\(651\) 0.608562 0.0238514
\(652\) 1.36596 0.0534950
\(653\) 48.2627 1.88867 0.944333 0.328992i \(-0.106709\pi\)
0.944333 + 0.328992i \(0.106709\pi\)
\(654\) 3.76103 0.147068
\(655\) −19.3717 −0.756914
\(656\) 32.3786 1.26417
\(657\) −10.5845 −0.412939
\(658\) −1.00921 −0.0393431
\(659\) −1.98083 −0.0771623 −0.0385811 0.999255i \(-0.512284\pi\)
−0.0385811 + 0.999255i \(0.512284\pi\)
\(660\) 2.11687 0.0823991
\(661\) −0.846173 −0.0329123 −0.0164562 0.999865i \(-0.505238\pi\)
−0.0164562 + 0.999865i \(0.505238\pi\)
\(662\) 29.4631 1.14512
\(663\) 3.38824 0.131588
\(664\) 10.9411 0.424596
\(665\) 0.565796 0.0219406
\(666\) −12.2767 −0.475714
\(667\) 1.62686 0.0629922
\(668\) −11.9391 −0.461939
\(669\) −1.58222 −0.0611720
\(670\) −24.6025 −0.950478
\(671\) −1.22096 −0.0471346
\(672\) 1.00434 0.0387433
\(673\) 20.4834 0.789577 0.394789 0.918772i \(-0.370818\pi\)
0.394789 + 0.918772i \(0.370818\pi\)
\(674\) 19.7037 0.758960
\(675\) 1.96979 0.0758172
\(676\) 2.33074 0.0896437
\(677\) 7.47659 0.287349 0.143674 0.989625i \(-0.454108\pi\)
0.143674 + 0.989625i \(0.454108\pi\)
\(678\) −3.70257 −0.142196
\(679\) −1.42015 −0.0545003
\(680\) −4.05951 −0.155675
\(681\) 26.3243 1.00875
\(682\) 5.32683 0.203975
\(683\) −43.3259 −1.65782 −0.828909 0.559384i \(-0.811038\pi\)
−0.828909 + 0.559384i \(0.811038\pi\)
\(684\) −6.10710 −0.233511
\(685\) 3.81490 0.145760
\(686\) −3.61005 −0.137832
\(687\) −12.3705 −0.471965
\(688\) −2.43400 −0.0927955
\(689\) 13.3889 0.510076
\(690\) 3.88310 0.147827
\(691\) 40.1250 1.52643 0.763214 0.646146i \(-0.223620\pi\)
0.763214 + 0.646146i \(0.223620\pi\)
\(692\) 13.2035 0.501921
\(693\) 0.0647212 0.00245856
\(694\) 50.6750 1.92360
\(695\) 22.7832 0.864216
\(696\) 1.04460 0.0395955
\(697\) −33.9739 −1.28685
\(698\) −44.1832 −1.67236
\(699\) 8.60177 0.325349
\(700\) 0.569501 0.0215251
\(701\) 1.66315 0.0628163 0.0314082 0.999507i \(-0.490001\pi\)
0.0314082 + 0.999507i \(0.490001\pi\)
\(702\) −2.08104 −0.0785439
\(703\) −15.4577 −0.582997
\(704\) 5.42150 0.204331
\(705\) 6.80542 0.256307
\(706\) 35.4502 1.33418
\(707\) −1.61650 −0.0607947
\(708\) 7.82860 0.294217
\(709\) −18.3290 −0.688360 −0.344180 0.938904i \(-0.611843\pi\)
−0.344180 + 0.938904i \(0.611843\pi\)
\(710\) 31.5023 1.18226
\(711\) 11.4711 0.430201
\(712\) −4.42949 −0.166002
\(713\) 5.25877 0.196943
\(714\) −0.874655 −0.0327332
\(715\) 0.908242 0.0339663
\(716\) −39.9808 −1.49415
\(717\) −2.22240 −0.0829969
\(718\) 58.9369 2.19951
\(719\) −3.48289 −0.129890 −0.0649449 0.997889i \(-0.520687\pi\)
−0.0649449 + 0.997889i \(0.520687\pi\)
\(720\) −5.62113 −0.209487
\(721\) 0.124046 0.00461970
\(722\) 25.2520 0.939783
\(723\) −26.3501 −0.979970
\(724\) 13.5105 0.502115
\(725\) −2.98956 −0.111030
\(726\) −22.3249 −0.828557
\(727\) 22.9774 0.852185 0.426092 0.904680i \(-0.359890\pi\)
0.426092 + 0.904680i \(0.359890\pi\)
\(728\) −0.0853777 −0.00316431
\(729\) 1.00000 0.0370370
\(730\) 38.3430 1.41914
\(731\) 2.55393 0.0944603
\(732\) −5.45418 −0.201592
\(733\) −4.39702 −0.162407 −0.0812037 0.996698i \(-0.525876\pi\)
−0.0812037 + 0.996698i \(0.525876\pi\)
\(734\) −27.6702 −1.02132
\(735\) 12.1585 0.448472
\(736\) 8.67881 0.319905
\(737\) −3.54346 −0.130525
\(738\) 20.8666 0.768110
\(739\) 15.1383 0.556873 0.278436 0.960455i \(-0.410184\pi\)
0.278436 + 0.960455i \(0.410184\pi\)
\(740\) 23.9349 0.879865
\(741\) −2.62024 −0.0962571
\(742\) −3.45626 −0.126883
\(743\) 4.92880 0.180820 0.0904101 0.995905i \(-0.471182\pi\)
0.0904101 + 0.995905i \(0.471182\pi\)
\(744\) 3.37665 0.123794
\(745\) 31.7503 1.16324
\(746\) 45.2285 1.65593
\(747\) −15.8964 −0.581617
\(748\) −4.12033 −0.150654
\(749\) 0.826785 0.0302101
\(750\) −25.2486 −0.921948
\(751\) −33.0389 −1.20561 −0.602804 0.797890i \(-0.705950\pi\)
−0.602804 + 0.797890i \(0.705950\pi\)
\(752\) 12.6243 0.460359
\(753\) −16.9216 −0.616658
\(754\) 3.15841 0.115023
\(755\) −29.5352 −1.07490
\(756\) 0.289118 0.0105151
\(757\) −42.9269 −1.56020 −0.780102 0.625652i \(-0.784833\pi\)
−0.780102 + 0.625652i \(0.784833\pi\)
\(758\) 52.2278 1.89700
\(759\) 0.559276 0.0203004
\(760\) 3.13936 0.113877
\(761\) −28.4025 −1.02959 −0.514795 0.857313i \(-0.672132\pi\)
−0.514795 + 0.857313i \(0.672132\pi\)
\(762\) −4.42338 −0.160242
\(763\) −0.224185 −0.00811606
\(764\) 23.5157 0.850770
\(765\) 5.89808 0.213246
\(766\) 77.9089 2.81496
\(767\) 3.35885 0.121281
\(768\) −9.47991 −0.342077
\(769\) 12.8874 0.464732 0.232366 0.972628i \(-0.425353\pi\)
0.232366 + 0.972628i \(0.425353\pi\)
\(770\) −0.234457 −0.00844926
\(771\) 14.9316 0.537750
\(772\) 49.8466 1.79402
\(773\) 30.0515 1.08088 0.540439 0.841383i \(-0.318258\pi\)
0.540439 + 0.841383i \(0.318258\pi\)
\(774\) −1.56861 −0.0563825
\(775\) −9.66368 −0.347130
\(776\) −7.87979 −0.282868
\(777\) 0.731786 0.0262527
\(778\) 1.44187 0.0516936
\(779\) 26.2732 0.941335
\(780\) 4.05723 0.145272
\(781\) 4.53722 0.162354
\(782\) −7.55817 −0.270279
\(783\) −1.51771 −0.0542385
\(784\) 22.5543 0.805511
\(785\) −25.4838 −0.909557
\(786\) −23.1586 −0.826039
\(787\) 46.1545 1.64523 0.822615 0.568599i \(-0.192514\pi\)
0.822615 + 0.568599i \(0.192514\pi\)
\(788\) 34.0660 1.21355
\(789\) 7.43575 0.264720
\(790\) −41.5550 −1.47846
\(791\) 0.220701 0.00784723
\(792\) 0.359110 0.0127604
\(793\) −2.34011 −0.0830998
\(794\) 36.0848 1.28060
\(795\) 23.3067 0.826604
\(796\) 45.4191 1.60984
\(797\) −37.0747 −1.31325 −0.656627 0.754215i \(-0.728018\pi\)
−0.656627 + 0.754215i \(0.728018\pi\)
\(798\) 0.676401 0.0239444
\(799\) −13.2463 −0.468619
\(800\) −15.9485 −0.563863
\(801\) 6.43563 0.227392
\(802\) −12.0501 −0.425504
\(803\) 5.52248 0.194884
\(804\) −15.8291 −0.558248
\(805\) −0.231462 −0.00815796
\(806\) 10.2095 0.359614
\(807\) 3.21442 0.113153
\(808\) −8.96926 −0.315537
\(809\) 28.3290 0.995993 0.497996 0.867179i \(-0.334069\pi\)
0.497996 + 0.867179i \(0.334069\pi\)
\(810\) −3.62257 −0.127284
\(811\) 52.7307 1.85163 0.925813 0.377983i \(-0.123382\pi\)
0.925813 + 0.377983i \(0.123382\pi\)
\(812\) −0.438797 −0.0153987
\(813\) 23.8045 0.834862
\(814\) 6.40543 0.224510
\(815\) 1.02019 0.0357357
\(816\) 10.9411 0.383015
\(817\) −1.97504 −0.0690979
\(818\) −41.7839 −1.46094
\(819\) 0.124046 0.00433451
\(820\) −40.6818 −1.42067
\(821\) −0.760391 −0.0265378 −0.0132689 0.999912i \(-0.504224\pi\)
−0.0132689 + 0.999912i \(0.504224\pi\)
\(822\) 4.56065 0.159071
\(823\) −17.7904 −0.620133 −0.310067 0.950715i \(-0.600351\pi\)
−0.310067 + 0.950715i \(0.600351\pi\)
\(824\) 0.688276 0.0239772
\(825\) −1.02774 −0.0357814
\(826\) −0.867068 −0.0301692
\(827\) 19.2396 0.669025 0.334512 0.942391i \(-0.391428\pi\)
0.334512 + 0.942391i \(0.391428\pi\)
\(828\) 2.49836 0.0868239
\(829\) −0.830396 −0.0288408 −0.0144204 0.999896i \(-0.504590\pi\)
−0.0144204 + 0.999896i \(0.504590\pi\)
\(830\) 57.5858 1.99883
\(831\) −11.1743 −0.387631
\(832\) 10.3909 0.360241
\(833\) −23.6656 −0.819963
\(834\) 27.2370 0.943140
\(835\) −8.91694 −0.308583
\(836\) 3.18640 0.110204
\(837\) −4.90595 −0.169574
\(838\) 8.35109 0.288484
\(839\) 31.4278 1.08501 0.542504 0.840053i \(-0.317476\pi\)
0.542504 + 0.840053i \(0.317476\pi\)
\(840\) −0.148621 −0.00512792
\(841\) −26.6966 −0.920571
\(842\) −51.3729 −1.77043
\(843\) 3.08517 0.106259
\(844\) −52.3552 −1.80214
\(845\) 1.74075 0.0598836
\(846\) 8.13579 0.279714
\(847\) 1.33073 0.0457246
\(848\) 43.2346 1.48468
\(849\) 24.0540 0.825532
\(850\) 13.8891 0.476393
\(851\) 6.32359 0.216770
\(852\) 20.2683 0.694381
\(853\) −51.9791 −1.77973 −0.889864 0.456225i \(-0.849201\pi\)
−0.889864 + 0.456225i \(0.849201\pi\)
\(854\) 0.604086 0.0206714
\(855\) −4.56119 −0.155989
\(856\) 4.58747 0.156796
\(857\) 40.0693 1.36874 0.684371 0.729134i \(-0.260077\pi\)
0.684371 + 0.729134i \(0.260077\pi\)
\(858\) 1.08579 0.0370683
\(859\) −45.7856 −1.56218 −0.781092 0.624416i \(-0.785337\pi\)
−0.781092 + 0.624416i \(0.785337\pi\)
\(860\) 3.05818 0.104283
\(861\) −1.24381 −0.0423888
\(862\) 8.37731 0.285332
\(863\) 44.4216 1.51213 0.756064 0.654498i \(-0.227120\pi\)
0.756064 + 0.654498i \(0.227120\pi\)
\(864\) −8.09653 −0.275450
\(865\) 9.86124 0.335292
\(866\) −13.2942 −0.451757
\(867\) 5.51982 0.187463
\(868\) −1.41840 −0.0481436
\(869\) −5.98509 −0.203030
\(870\) 5.49801 0.186400
\(871\) −6.79145 −0.230119
\(872\) −1.24391 −0.0421240
\(873\) 11.4486 0.387476
\(874\) 5.84499 0.197710
\(875\) 1.50500 0.0508784
\(876\) 24.6696 0.833509
\(877\) 42.7401 1.44323 0.721615 0.692295i \(-0.243400\pi\)
0.721615 + 0.692295i \(0.243400\pi\)
\(878\) 65.0967 2.19691
\(879\) −20.9087 −0.705233
\(880\) 2.93284 0.0988660
\(881\) −37.5588 −1.26539 −0.632694 0.774402i \(-0.718051\pi\)
−0.632694 + 0.774402i \(0.718051\pi\)
\(882\) 14.5353 0.489428
\(883\) −56.5648 −1.90356 −0.951778 0.306786i \(-0.900746\pi\)
−0.951778 + 0.306786i \(0.900746\pi\)
\(884\) −7.89710 −0.265608
\(885\) 5.84692 0.196542
\(886\) −7.84107 −0.263426
\(887\) −22.9713 −0.771301 −0.385651 0.922645i \(-0.626023\pi\)
−0.385651 + 0.922645i \(0.626023\pi\)
\(888\) 4.06036 0.136257
\(889\) 0.263667 0.00884310
\(890\) −23.3136 −0.781473
\(891\) −0.521753 −0.0174794
\(892\) 3.68773 0.123474
\(893\) 10.2438 0.342795
\(894\) 37.9570 1.26947
\(895\) −29.8603 −0.998120
\(896\) −0.673682 −0.0225061
\(897\) 1.07192 0.0357903
\(898\) 55.3023 1.84546
\(899\) 7.44580 0.248331
\(900\) −4.59106 −0.153035
\(901\) −45.3648 −1.51132
\(902\) −10.8872 −0.362505
\(903\) 0.0935009 0.00311151
\(904\) 1.22457 0.0407288
\(905\) 10.0906 0.335422
\(906\) −35.3089 −1.17306
\(907\) 51.8600 1.72198 0.860991 0.508620i \(-0.169844\pi\)
0.860991 + 0.508620i \(0.169844\pi\)
\(908\) −61.3550 −2.03614
\(909\) 13.0315 0.432227
\(910\) −0.449365 −0.0148963
\(911\) −8.44497 −0.279794 −0.139897 0.990166i \(-0.544677\pi\)
−0.139897 + 0.990166i \(0.544677\pi\)
\(912\) −8.46114 −0.280176
\(913\) 8.29397 0.274490
\(914\) 56.5197 1.86950
\(915\) −4.07355 −0.134667
\(916\) 28.8325 0.952651
\(917\) 1.38042 0.0455856
\(918\) 7.05107 0.232720
\(919\) −7.14499 −0.235691 −0.117846 0.993032i \(-0.537599\pi\)
−0.117846 + 0.993032i \(0.537599\pi\)
\(920\) −1.28428 −0.0423415
\(921\) 29.4633 0.970849
\(922\) −78.8122 −2.59554
\(923\) 8.69610 0.286236
\(924\) −0.150848 −0.00496254
\(925\) −11.6204 −0.382077
\(926\) −38.4329 −1.26298
\(927\) −1.00000 −0.0328443
\(928\) 12.2882 0.403379
\(929\) 49.7567 1.63246 0.816232 0.577724i \(-0.196059\pi\)
0.816232 + 0.577724i \(0.196059\pi\)
\(930\) 17.7722 0.582772
\(931\) 18.3014 0.599804
\(932\) −20.0485 −0.656709
\(933\) 8.55254 0.279998
\(934\) 43.7120 1.43030
\(935\) −3.07734 −0.100640
\(936\) 0.688276 0.0224970
\(937\) −56.9541 −1.86061 −0.930305 0.366786i \(-0.880458\pi\)
−0.930305 + 0.366786i \(0.880458\pi\)
\(938\) 1.75317 0.0572431
\(939\) −17.0478 −0.556334
\(940\) −15.8616 −0.517350
\(941\) 47.9269 1.56237 0.781186 0.624299i \(-0.214615\pi\)
0.781186 + 0.624299i \(0.214615\pi\)
\(942\) −30.4655 −0.992621
\(943\) −10.7481 −0.350007
\(944\) 10.8462 0.353014
\(945\) 0.215933 0.00702429
\(946\) 0.818426 0.0266093
\(947\) −28.2081 −0.916641 −0.458321 0.888787i \(-0.651549\pi\)
−0.458321 + 0.888787i \(0.651549\pi\)
\(948\) −26.7362 −0.868350
\(949\) 10.5845 0.343586
\(950\) −10.7409 −0.348482
\(951\) 20.9238 0.678499
\(952\) 0.289280 0.00937562
\(953\) 46.5837 1.50899 0.754497 0.656304i \(-0.227881\pi\)
0.754497 + 0.656304i \(0.227881\pi\)
\(954\) 27.8628 0.902093
\(955\) 17.5631 0.568330
\(956\) 5.17982 0.167527
\(957\) 0.791869 0.0255975
\(958\) −35.2237 −1.13803
\(959\) −0.271849 −0.00877847
\(960\) 18.0880 0.583789
\(961\) −6.93165 −0.223602
\(962\) 12.2767 0.395818
\(963\) −6.66516 −0.214782
\(964\) 61.4151 1.97805
\(965\) 37.2288 1.19844
\(966\) −0.276709 −0.00890298
\(967\) 27.8886 0.896838 0.448419 0.893823i \(-0.351987\pi\)
0.448419 + 0.893823i \(0.351987\pi\)
\(968\) 7.38367 0.237320
\(969\) 8.87802 0.285203
\(970\) −41.4734 −1.33163
\(971\) −49.7229 −1.59569 −0.797843 0.602866i \(-0.794025\pi\)
−0.797843 + 0.602866i \(0.794025\pi\)
\(972\) −2.33074 −0.0747584
\(973\) −1.62353 −0.0520479
\(974\) 14.8241 0.474994
\(975\) −1.96979 −0.0630837
\(976\) −7.55655 −0.241879
\(977\) 33.0058 1.05595 0.527974 0.849260i \(-0.322952\pi\)
0.527974 + 0.849260i \(0.322952\pi\)
\(978\) 1.21962 0.0389992
\(979\) −3.35781 −0.107316
\(980\) −28.3382 −0.905230
\(981\) 1.80728 0.0577020
\(982\) −30.7696 −0.981897
\(983\) 34.7938 1.10975 0.554876 0.831933i \(-0.312766\pi\)
0.554876 + 0.831933i \(0.312766\pi\)
\(984\) −6.90134 −0.220007
\(985\) 25.4428 0.810675
\(986\) −10.7015 −0.340804
\(987\) −0.484954 −0.0154363
\(988\) 6.10710 0.194293
\(989\) 0.807970 0.0256919
\(990\) 1.89009 0.0600710
\(991\) 44.6099 1.41708 0.708540 0.705671i \(-0.249354\pi\)
0.708540 + 0.705671i \(0.249354\pi\)
\(992\) 39.7212 1.26115
\(993\) 14.1579 0.449286
\(994\) −2.24485 −0.0712023
\(995\) 33.9220 1.07540
\(996\) 37.0502 1.17398
\(997\) 32.1140 1.01706 0.508531 0.861044i \(-0.330189\pi\)
0.508531 + 0.861044i \(0.330189\pi\)
\(998\) −71.1444 −2.25204
\(999\) −5.89933 −0.186646
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 4017.2.a.i.1.6 25
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4017.2.a.i.1.6 25 1.1 even 1 trivial