Properties

Label 2671.2.a.b.1.4
Level $2671$
Weight $2$
Character 2671.1
Self dual yes
Analytic conductor $21.328$
Analytic rank $0$
Dimension $122$
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] = [2671,2,Mod(1,2671)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2671, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2671.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2671 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2671.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: \(21.3280423799\)
Analytic rank: \(0\)
Dimension: \(122\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) \(=\) 2671.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.66332 q^{2} -2.18729 q^{3} +5.09325 q^{4} +2.00666 q^{5} +5.82544 q^{6} -4.67426 q^{7} -8.23831 q^{8} +1.78423 q^{9} +O(q^{10})\) \(q-2.66332 q^{2} -2.18729 q^{3} +5.09325 q^{4} +2.00666 q^{5} +5.82544 q^{6} -4.67426 q^{7} -8.23831 q^{8} +1.78423 q^{9} -5.34438 q^{10} -1.28646 q^{11} -11.1404 q^{12} +0.837420 q^{13} +12.4490 q^{14} -4.38915 q^{15} +11.7547 q^{16} -3.72116 q^{17} -4.75198 q^{18} -6.63400 q^{19} +10.2204 q^{20} +10.2240 q^{21} +3.42626 q^{22} -8.18713 q^{23} +18.0196 q^{24} -0.973304 q^{25} -2.23031 q^{26} +2.65923 q^{27} -23.8072 q^{28} -6.01804 q^{29} +11.6897 q^{30} -7.83177 q^{31} -14.8299 q^{32} +2.81387 q^{33} +9.91064 q^{34} -9.37967 q^{35} +9.08756 q^{36} -4.64698 q^{37} +17.6684 q^{38} -1.83168 q^{39} -16.5315 q^{40} +10.7890 q^{41} -27.2297 q^{42} +2.02891 q^{43} -6.55228 q^{44} +3.58036 q^{45} +21.8049 q^{46} -8.20429 q^{47} -25.7110 q^{48} +14.8487 q^{49} +2.59222 q^{50} +8.13926 q^{51} +4.26519 q^{52} -1.63209 q^{53} -7.08238 q^{54} -2.58150 q^{55} +38.5081 q^{56} +14.5105 q^{57} +16.0279 q^{58} -7.28117 q^{59} -22.3551 q^{60} +10.1621 q^{61} +20.8585 q^{62} -8.33998 q^{63} +15.9873 q^{64} +1.68042 q^{65} -7.49421 q^{66} -9.39520 q^{67} -18.9528 q^{68} +17.9076 q^{69} +24.9810 q^{70} +8.18081 q^{71} -14.6991 q^{72} -7.41648 q^{73} +12.3764 q^{74} +2.12890 q^{75} -33.7886 q^{76} +6.01327 q^{77} +4.87834 q^{78} -4.96542 q^{79} +23.5878 q^{80} -11.1692 q^{81} -28.7346 q^{82} +11.9648 q^{83} +52.0733 q^{84} -7.46712 q^{85} -5.40364 q^{86} +13.1632 q^{87} +10.5983 q^{88} -6.85860 q^{89} -9.53562 q^{90} -3.91432 q^{91} -41.6992 q^{92} +17.1304 q^{93} +21.8506 q^{94} -13.3122 q^{95} +32.4374 q^{96} -7.93820 q^{97} -39.5469 q^{98} -2.29535 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9} + 16 q^{10} + 43 q^{11} + 23 q^{12} + 25 q^{13} + 45 q^{14} + 12 q^{15} + 132 q^{16} + 103 q^{17} + 30 q^{18} + 37 q^{19} + 63 q^{20} + 81 q^{21} + 15 q^{23} + 60 q^{24} + 151 q^{25} + 59 q^{26} + 22 q^{27} - 3 q^{28} + 80 q^{29} - 9 q^{30} + 15 q^{31} + 66 q^{32} + 93 q^{33} + 30 q^{34} + 23 q^{35} + 162 q^{36} + 18 q^{37} + 41 q^{38} + 10 q^{39} + 29 q^{40} + 249 q^{41} - 8 q^{42} + 14 q^{43} + 100 q^{44} + 59 q^{45} + 11 q^{46} + 57 q^{47} + 33 q^{48} + 180 q^{49} + 63 q^{50} + 26 q^{51} + 31 q^{52} + 65 q^{53} + 65 q^{54} - 8 q^{55} + 120 q^{56} + 57 q^{57} - 31 q^{58} + 108 q^{59} - q^{60} + 70 q^{61} + 25 q^{62} - 7 q^{63} + 100 q^{64} + 171 q^{65} + 12 q^{66} - 6 q^{67} + 184 q^{68} + 64 q^{69} - 24 q^{70} + 47 q^{71} + 53 q^{72} + 76 q^{73} + 66 q^{74} + 40 q^{75} + 32 q^{76} + 73 q^{77} - 19 q^{78} + 8 q^{79} + 115 q^{80} + 250 q^{81} - 13 q^{82} + 116 q^{83} + 159 q^{84} + 31 q^{85} + 91 q^{86} + 25 q^{87} - 43 q^{88} + 361 q^{89} + 32 q^{90} + 7 q^{91} + 5 q^{92} + 18 q^{93} + 23 q^{94} + 42 q^{95} + 77 q^{96} + 79 q^{97} + 56 q^{98} + 74 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.66332 −1.88325 −0.941625 0.336665i \(-0.890701\pi\)
−0.941625 + 0.336665i \(0.890701\pi\)
\(3\) −2.18729 −1.26283 −0.631416 0.775444i \(-0.717526\pi\)
−0.631416 + 0.775444i \(0.717526\pi\)
\(4\) 5.09325 2.54663
\(5\) 2.00666 0.897407 0.448703 0.893681i \(-0.351886\pi\)
0.448703 + 0.893681i \(0.351886\pi\)
\(6\) 5.82544 2.37823
\(7\) −4.67426 −1.76671 −0.883353 0.468709i \(-0.844719\pi\)
−0.883353 + 0.468709i \(0.844719\pi\)
\(8\) −8.23831 −2.91268
\(9\) 1.78423 0.594745
\(10\) −5.34438 −1.69004
\(11\) −1.28646 −0.387883 −0.193942 0.981013i \(-0.562127\pi\)
−0.193942 + 0.981013i \(0.562127\pi\)
\(12\) −11.1404 −3.21596
\(13\) 0.837420 0.232258 0.116129 0.993234i \(-0.462951\pi\)
0.116129 + 0.993234i \(0.462951\pi\)
\(14\) 12.4490 3.32715
\(15\) −4.38915 −1.13327
\(16\) 11.7547 2.93868
\(17\) −3.72116 −0.902515 −0.451257 0.892394i \(-0.649024\pi\)
−0.451257 + 0.892394i \(0.649024\pi\)
\(18\) −4.75198 −1.12005
\(19\) −6.63400 −1.52194 −0.760972 0.648785i \(-0.775277\pi\)
−0.760972 + 0.648785i \(0.775277\pi\)
\(20\) 10.2204 2.28536
\(21\) 10.2240 2.23105
\(22\) 3.42626 0.730480
\(23\) −8.18713 −1.70714 −0.853568 0.520982i \(-0.825566\pi\)
−0.853568 + 0.520982i \(0.825566\pi\)
\(24\) 18.0196 3.67823
\(25\) −0.973304 −0.194661
\(26\) −2.23031 −0.437401
\(27\) 2.65923 0.511769
\(28\) −23.8072 −4.49914
\(29\) −6.01804 −1.11752 −0.558761 0.829329i \(-0.688723\pi\)
−0.558761 + 0.829329i \(0.688723\pi\)
\(30\) 11.6897 2.13424
\(31\) −7.83177 −1.40663 −0.703314 0.710879i \(-0.748297\pi\)
−0.703314 + 0.710879i \(0.748297\pi\)
\(32\) −14.8299 −2.62159
\(33\) 2.81387 0.489831
\(34\) 9.91064 1.69966
\(35\) −9.37967 −1.58545
\(36\) 9.08756 1.51459
\(37\) −4.64698 −0.763959 −0.381980 0.924171i \(-0.624758\pi\)
−0.381980 + 0.924171i \(0.624758\pi\)
\(38\) 17.6684 2.86620
\(39\) −1.83168 −0.293303
\(40\) −16.5315 −2.61386
\(41\) 10.7890 1.68497 0.842483 0.538723i \(-0.181093\pi\)
0.842483 + 0.538723i \(0.181093\pi\)
\(42\) −27.2297 −4.20163
\(43\) 2.02891 0.309406 0.154703 0.987961i \(-0.450558\pi\)
0.154703 + 0.987961i \(0.450558\pi\)
\(44\) −6.55228 −0.987793
\(45\) 3.58036 0.533728
\(46\) 21.8049 3.21496
\(47\) −8.20429 −1.19672 −0.598359 0.801228i \(-0.704180\pi\)
−0.598359 + 0.801228i \(0.704180\pi\)
\(48\) −25.7110 −3.71106
\(49\) 14.8487 2.12125
\(50\) 2.59222 0.366595
\(51\) 8.13926 1.13972
\(52\) 4.26519 0.591476
\(53\) −1.63209 −0.224185 −0.112093 0.993698i \(-0.535755\pi\)
−0.112093 + 0.993698i \(0.535755\pi\)
\(54\) −7.08238 −0.963789
\(55\) −2.58150 −0.348089
\(56\) 38.5081 5.14585
\(57\) 14.5105 1.92196
\(58\) 16.0279 2.10457
\(59\) −7.28117 −0.947928 −0.473964 0.880544i \(-0.657177\pi\)
−0.473964 + 0.880544i \(0.657177\pi\)
\(60\) −22.3551 −2.88603
\(61\) 10.1621 1.30112 0.650560 0.759455i \(-0.274534\pi\)
0.650560 + 0.759455i \(0.274534\pi\)
\(62\) 20.8585 2.64903
\(63\) −8.33998 −1.05074
\(64\) 15.9873 1.99842
\(65\) 1.68042 0.208430
\(66\) −7.49421 −0.922474
\(67\) −9.39520 −1.14781 −0.573903 0.818923i \(-0.694572\pi\)
−0.573903 + 0.818923i \(0.694572\pi\)
\(68\) −18.9528 −2.29837
\(69\) 17.9076 2.15583
\(70\) 24.9810 2.98580
\(71\) 8.18081 0.970883 0.485442 0.874269i \(-0.338659\pi\)
0.485442 + 0.874269i \(0.338659\pi\)
\(72\) −14.6991 −1.73230
\(73\) −7.41648 −0.868034 −0.434017 0.900905i \(-0.642904\pi\)
−0.434017 + 0.900905i \(0.642904\pi\)
\(74\) 12.3764 1.43873
\(75\) 2.12890 0.245824
\(76\) −33.7886 −3.87582
\(77\) 6.01327 0.685275
\(78\) 4.87834 0.552363
\(79\) −4.96542 −0.558653 −0.279326 0.960196i \(-0.590111\pi\)
−0.279326 + 0.960196i \(0.590111\pi\)
\(80\) 23.5878 2.63719
\(81\) −11.1692 −1.24102
\(82\) −28.7346 −3.17321
\(83\) 11.9648 1.31331 0.656654 0.754192i \(-0.271971\pi\)
0.656654 + 0.754192i \(0.271971\pi\)
\(84\) 52.0733 5.68166
\(85\) −7.46712 −0.809923
\(86\) −5.40364 −0.582689
\(87\) 13.1632 1.41124
\(88\) 10.5983 1.12978
\(89\) −6.85860 −0.727010 −0.363505 0.931592i \(-0.618420\pi\)
−0.363505 + 0.931592i \(0.618420\pi\)
\(90\) −9.53562 −1.00514
\(91\) −3.91432 −0.410332
\(92\) −41.6992 −4.34744
\(93\) 17.1304 1.77634
\(94\) 21.8506 2.25372
\(95\) −13.3122 −1.36580
\(96\) 32.4374 3.31062
\(97\) −7.93820 −0.806002 −0.403001 0.915199i \(-0.632033\pi\)
−0.403001 + 0.915199i \(0.632033\pi\)
\(98\) −39.5469 −3.99484
\(99\) −2.29535 −0.230691
\(100\) −4.95728 −0.495728
\(101\) 6.48990 0.645769 0.322884 0.946438i \(-0.395347\pi\)
0.322884 + 0.946438i \(0.395347\pi\)
\(102\) −21.6774 −2.14639
\(103\) −10.3847 −1.02324 −0.511618 0.859213i \(-0.670954\pi\)
−0.511618 + 0.859213i \(0.670954\pi\)
\(104\) −6.89893 −0.676496
\(105\) 20.5161 2.00216
\(106\) 4.34678 0.422197
\(107\) −3.36124 −0.324943 −0.162472 0.986713i \(-0.551947\pi\)
−0.162472 + 0.986713i \(0.551947\pi\)
\(108\) 13.5441 1.30329
\(109\) −6.77144 −0.648587 −0.324293 0.945957i \(-0.605127\pi\)
−0.324293 + 0.945957i \(0.605127\pi\)
\(110\) 6.87534 0.655538
\(111\) 10.1643 0.964752
\(112\) −54.9447 −5.19179
\(113\) −11.4522 −1.07733 −0.538664 0.842521i \(-0.681071\pi\)
−0.538664 + 0.842521i \(0.681071\pi\)
\(114\) −38.6460 −3.61953
\(115\) −16.4288 −1.53200
\(116\) −30.6514 −2.84591
\(117\) 1.49415 0.138134
\(118\) 19.3921 1.78518
\(119\) 17.3937 1.59448
\(120\) 36.1592 3.30087
\(121\) −9.34501 −0.849547
\(122\) −27.0648 −2.45033
\(123\) −23.5988 −2.12783
\(124\) −39.8892 −3.58216
\(125\) −11.9864 −1.07210
\(126\) 22.2120 1.97880
\(127\) 6.37785 0.565942 0.282971 0.959128i \(-0.408680\pi\)
0.282971 + 0.959128i \(0.408680\pi\)
\(128\) −12.9195 −1.14193
\(129\) −4.43782 −0.390728
\(130\) −4.47549 −0.392526
\(131\) −9.70503 −0.847932 −0.423966 0.905678i \(-0.639362\pi\)
−0.423966 + 0.905678i \(0.639362\pi\)
\(132\) 14.3317 1.24742
\(133\) 31.0091 2.68883
\(134\) 25.0224 2.16161
\(135\) 5.33618 0.459265
\(136\) 30.6561 2.62874
\(137\) 16.4808 1.40805 0.704025 0.710175i \(-0.251384\pi\)
0.704025 + 0.710175i \(0.251384\pi\)
\(138\) −47.6937 −4.05996
\(139\) 2.38455 0.202255 0.101128 0.994873i \(-0.467755\pi\)
0.101128 + 0.994873i \(0.467755\pi\)
\(140\) −47.7730 −4.03756
\(141\) 17.9451 1.51125
\(142\) −21.7881 −1.82841
\(143\) −1.07731 −0.0900891
\(144\) 20.9732 1.74777
\(145\) −12.0762 −1.00287
\(146\) 19.7524 1.63472
\(147\) −32.4785 −2.67878
\(148\) −23.6683 −1.94552
\(149\) 12.3573 1.01235 0.506174 0.862431i \(-0.331059\pi\)
0.506174 + 0.862431i \(0.331059\pi\)
\(150\) −5.66993 −0.462948
\(151\) −5.65832 −0.460467 −0.230234 0.973135i \(-0.573949\pi\)
−0.230234 + 0.973135i \(0.573949\pi\)
\(152\) 54.6530 4.43294
\(153\) −6.63943 −0.536766
\(154\) −16.0152 −1.29054
\(155\) −15.7157 −1.26232
\(156\) −9.32921 −0.746935
\(157\) −22.2420 −1.77511 −0.887553 0.460706i \(-0.847596\pi\)
−0.887553 + 0.460706i \(0.847596\pi\)
\(158\) 13.2245 1.05208
\(159\) 3.56986 0.283109
\(160\) −29.7587 −2.35263
\(161\) 38.2688 3.01601
\(162\) 29.7471 2.33716
\(163\) 14.8534 1.16341 0.581703 0.813401i \(-0.302386\pi\)
0.581703 + 0.813401i \(0.302386\pi\)
\(164\) 54.9513 4.29098
\(165\) 5.64648 0.439578
\(166\) −31.8661 −2.47329
\(167\) 9.87378 0.764056 0.382028 0.924151i \(-0.375226\pi\)
0.382028 + 0.924151i \(0.375226\pi\)
\(168\) −84.2282 −6.49835
\(169\) −12.2987 −0.946056
\(170\) 19.8873 1.52529
\(171\) −11.8366 −0.905168
\(172\) 10.3338 0.787942
\(173\) −22.6187 −1.71967 −0.859834 0.510574i \(-0.829433\pi\)
−0.859834 + 0.510574i \(0.829433\pi\)
\(174\) −35.0577 −2.65772
\(175\) 4.54948 0.343908
\(176\) −15.1220 −1.13987
\(177\) 15.9260 1.19707
\(178\) 18.2666 1.36914
\(179\) 4.78710 0.357805 0.178902 0.983867i \(-0.442745\pi\)
0.178902 + 0.983867i \(0.442745\pi\)
\(180\) 18.2357 1.35921
\(181\) −18.3074 −1.36078 −0.680389 0.732851i \(-0.738189\pi\)
−0.680389 + 0.732851i \(0.738189\pi\)
\(182\) 10.4251 0.772758
\(183\) −22.2274 −1.64310
\(184\) 67.4482 4.97235
\(185\) −9.32493 −0.685582
\(186\) −45.6236 −3.34528
\(187\) 4.78714 0.350070
\(188\) −41.7865 −3.04759
\(189\) −12.4300 −0.904146
\(190\) 35.4546 2.57215
\(191\) 10.3998 0.752501 0.376251 0.926518i \(-0.377213\pi\)
0.376251 + 0.926518i \(0.377213\pi\)
\(192\) −34.9690 −2.52367
\(193\) 7.70248 0.554437 0.277218 0.960807i \(-0.410587\pi\)
0.277218 + 0.960807i \(0.410587\pi\)
\(194\) 21.1419 1.51790
\(195\) −3.67556 −0.263213
\(196\) 75.6284 5.40203
\(197\) 8.15356 0.580917 0.290459 0.956888i \(-0.406192\pi\)
0.290459 + 0.956888i \(0.406192\pi\)
\(198\) 6.11324 0.434449
\(199\) −22.1347 −1.56909 −0.784545 0.620072i \(-0.787103\pi\)
−0.784545 + 0.620072i \(0.787103\pi\)
\(200\) 8.01838 0.566985
\(201\) 20.5500 1.44949
\(202\) −17.2846 −1.21614
\(203\) 28.1299 1.97433
\(204\) 41.4553 2.90245
\(205\) 21.6500 1.51210
\(206\) 27.6577 1.92701
\(207\) −14.6078 −1.01531
\(208\) 9.84364 0.682534
\(209\) 8.53439 0.590336
\(210\) −54.6407 −3.77057
\(211\) 9.37060 0.645098 0.322549 0.946553i \(-0.395460\pi\)
0.322549 + 0.946553i \(0.395460\pi\)
\(212\) −8.31267 −0.570917
\(213\) −17.8938 −1.22606
\(214\) 8.95205 0.611949
\(215\) 4.07134 0.277663
\(216\) −21.9076 −1.49062
\(217\) 36.6078 2.48510
\(218\) 18.0345 1.22145
\(219\) 16.2220 1.09618
\(220\) −13.1482 −0.886453
\(221\) −3.11618 −0.209617
\(222\) −27.0707 −1.81687
\(223\) −8.93203 −0.598133 −0.299066 0.954232i \(-0.596675\pi\)
−0.299066 + 0.954232i \(0.596675\pi\)
\(224\) 69.3190 4.63157
\(225\) −1.73660 −0.115773
\(226\) 30.5007 2.02888
\(227\) 26.8461 1.78184 0.890920 0.454161i \(-0.150061\pi\)
0.890920 + 0.454161i \(0.150061\pi\)
\(228\) 73.9055 4.89451
\(229\) −5.70574 −0.377046 −0.188523 0.982069i \(-0.560370\pi\)
−0.188523 + 0.982069i \(0.560370\pi\)
\(230\) 43.7551 2.88513
\(231\) −13.1527 −0.865387
\(232\) 49.5785 3.25499
\(233\) −25.1291 −1.64626 −0.823132 0.567850i \(-0.807775\pi\)
−0.823132 + 0.567850i \(0.807775\pi\)
\(234\) −3.97940 −0.260142
\(235\) −16.4632 −1.07394
\(236\) −37.0849 −2.41402
\(237\) 10.8608 0.705485
\(238\) −46.3249 −3.00280
\(239\) −14.2166 −0.919597 −0.459798 0.888023i \(-0.652078\pi\)
−0.459798 + 0.888023i \(0.652078\pi\)
\(240\) −51.5933 −3.33033
\(241\) −13.9784 −0.900428 −0.450214 0.892921i \(-0.648652\pi\)
−0.450214 + 0.892921i \(0.648652\pi\)
\(242\) 24.8887 1.59991
\(243\) 16.4526 1.05543
\(244\) 51.7580 3.31347
\(245\) 29.7964 1.90362
\(246\) 62.8510 4.00723
\(247\) −5.55544 −0.353484
\(248\) 64.5206 4.09706
\(249\) −26.1705 −1.65849
\(250\) 31.9236 2.01903
\(251\) 16.2604 1.02635 0.513175 0.858284i \(-0.328469\pi\)
0.513175 + 0.858284i \(0.328469\pi\)
\(252\) −42.4776 −2.67584
\(253\) 10.5324 0.662169
\(254\) −16.9862 −1.06581
\(255\) 16.3328 1.02280
\(256\) 2.43401 0.152126
\(257\) −2.07375 −0.129357 −0.0646785 0.997906i \(-0.520602\pi\)
−0.0646785 + 0.997906i \(0.520602\pi\)
\(258\) 11.8193 0.735838
\(259\) 21.7212 1.34969
\(260\) 8.55880 0.530794
\(261\) −10.7376 −0.664640
\(262\) 25.8476 1.59687
\(263\) −0.346995 −0.0213966 −0.0106983 0.999943i \(-0.503405\pi\)
−0.0106983 + 0.999943i \(0.503405\pi\)
\(264\) −23.1815 −1.42672
\(265\) −3.27506 −0.201186
\(266\) −82.5869 −5.06373
\(267\) 15.0017 0.918092
\(268\) −47.8522 −2.92304
\(269\) 30.8745 1.88245 0.941226 0.337776i \(-0.109675\pi\)
0.941226 + 0.337776i \(0.109675\pi\)
\(270\) −14.2119 −0.864911
\(271\) 15.4027 0.935647 0.467823 0.883822i \(-0.345038\pi\)
0.467823 + 0.883822i \(0.345038\pi\)
\(272\) −43.7413 −2.65220
\(273\) 8.56175 0.518181
\(274\) −43.8936 −2.65171
\(275\) 1.25212 0.0755056
\(276\) 91.2081 5.49008
\(277\) −26.0543 −1.56545 −0.782727 0.622365i \(-0.786172\pi\)
−0.782727 + 0.622365i \(0.786172\pi\)
\(278\) −6.35082 −0.380897
\(279\) −13.9737 −0.836585
\(280\) 77.2727 4.61793
\(281\) 12.6198 0.752835 0.376418 0.926450i \(-0.377156\pi\)
0.376418 + 0.926450i \(0.377156\pi\)
\(282\) −47.7936 −2.84607
\(283\) 22.8594 1.35885 0.679426 0.733744i \(-0.262229\pi\)
0.679426 + 0.733744i \(0.262229\pi\)
\(284\) 41.6669 2.47248
\(285\) 29.1176 1.72478
\(286\) 2.86922 0.169660
\(287\) −50.4308 −2.97684
\(288\) −26.4601 −1.55917
\(289\) −3.15294 −0.185467
\(290\) 32.1627 1.88866
\(291\) 17.3631 1.01785
\(292\) −37.7740 −2.21056
\(293\) 5.75528 0.336227 0.168114 0.985768i \(-0.446232\pi\)
0.168114 + 0.985768i \(0.446232\pi\)
\(294\) 86.5005 5.04481
\(295\) −14.6109 −0.850677
\(296\) 38.2833 2.22517
\(297\) −3.42100 −0.198507
\(298\) −32.9114 −1.90650
\(299\) −6.85607 −0.396497
\(300\) 10.8430 0.626022
\(301\) −9.48367 −0.546630
\(302\) 15.0699 0.867175
\(303\) −14.1953 −0.815498
\(304\) −77.9808 −4.47251
\(305\) 20.3919 1.16763
\(306\) 17.6829 1.01086
\(307\) −0.529976 −0.0302473 −0.0151237 0.999886i \(-0.504814\pi\)
−0.0151237 + 0.999886i \(0.504814\pi\)
\(308\) 30.6271 1.74514
\(309\) 22.7143 1.29217
\(310\) 41.8560 2.37726
\(311\) −10.4676 −0.593565 −0.296782 0.954945i \(-0.595914\pi\)
−0.296782 + 0.954945i \(0.595914\pi\)
\(312\) 15.0900 0.854300
\(313\) 0.601656 0.0340076 0.0170038 0.999855i \(-0.494587\pi\)
0.0170038 + 0.999855i \(0.494587\pi\)
\(314\) 59.2375 3.34297
\(315\) −16.7355 −0.942940
\(316\) −25.2901 −1.42268
\(317\) 32.8675 1.84602 0.923012 0.384770i \(-0.125719\pi\)
0.923012 + 0.384770i \(0.125719\pi\)
\(318\) −9.50767 −0.533164
\(319\) 7.74198 0.433467
\(320\) 32.0812 1.79339
\(321\) 7.35200 0.410349
\(322\) −101.922 −5.67989
\(323\) 24.6862 1.37358
\(324\) −56.8876 −3.16042
\(325\) −0.815064 −0.0452116
\(326\) −39.5593 −2.19098
\(327\) 14.8111 0.819056
\(328\) −88.8835 −4.90777
\(329\) 38.3490 2.11425
\(330\) −15.0384 −0.827835
\(331\) 30.0571 1.65209 0.826044 0.563605i \(-0.190586\pi\)
0.826044 + 0.563605i \(0.190586\pi\)
\(332\) 60.9398 3.34451
\(333\) −8.29131 −0.454361
\(334\) −26.2970 −1.43891
\(335\) −18.8530 −1.03005
\(336\) 120.180 6.55635
\(337\) 0.969105 0.0527905 0.0263953 0.999652i \(-0.491597\pi\)
0.0263953 + 0.999652i \(0.491597\pi\)
\(338\) 32.7554 1.78166
\(339\) 25.0492 1.36048
\(340\) −38.0319 −2.06257
\(341\) 10.0753 0.545607
\(342\) 31.5246 1.70466
\(343\) −36.6871 −1.98092
\(344\) −16.7148 −0.901203
\(345\) 35.9346 1.93465
\(346\) 60.2407 3.23856
\(347\) 35.9887 1.93198 0.965988 0.258588i \(-0.0832570\pi\)
0.965988 + 0.258588i \(0.0832570\pi\)
\(348\) 67.0434 3.59391
\(349\) −16.1972 −0.867015 −0.433507 0.901150i \(-0.642724\pi\)
−0.433507 + 0.901150i \(0.642724\pi\)
\(350\) −12.1167 −0.647665
\(351\) 2.22689 0.118863
\(352\) 19.0782 1.01687
\(353\) 5.73632 0.305313 0.152657 0.988279i \(-0.451217\pi\)
0.152657 + 0.988279i \(0.451217\pi\)
\(354\) −42.4161 −2.25439
\(355\) 16.4161 0.871277
\(356\) −34.9326 −1.85142
\(357\) −38.0451 −2.01356
\(358\) −12.7496 −0.673835
\(359\) −14.1387 −0.746215 −0.373107 0.927788i \(-0.621708\pi\)
−0.373107 + 0.927788i \(0.621708\pi\)
\(360\) −29.4961 −1.55458
\(361\) 25.0099 1.31631
\(362\) 48.7584 2.56268
\(363\) 20.4402 1.07283
\(364\) −19.9366 −1.04496
\(365\) −14.8824 −0.778979
\(366\) 59.1986 3.09436
\(367\) −8.05407 −0.420419 −0.210210 0.977656i \(-0.567415\pi\)
−0.210210 + 0.977656i \(0.567415\pi\)
\(368\) −96.2375 −5.01673
\(369\) 19.2502 1.00212
\(370\) 24.8352 1.29112
\(371\) 7.62884 0.396070
\(372\) 87.2493 4.52366
\(373\) 3.41546 0.176846 0.0884228 0.996083i \(-0.471817\pi\)
0.0884228 + 0.996083i \(0.471817\pi\)
\(374\) −12.7497 −0.659269
\(375\) 26.2177 1.35388
\(376\) 67.5895 3.48566
\(377\) −5.03962 −0.259554
\(378\) 33.1049 1.70273
\(379\) 14.1907 0.728925 0.364463 0.931218i \(-0.381253\pi\)
0.364463 + 0.931218i \(0.381253\pi\)
\(380\) −67.8024 −3.47819
\(381\) −13.9502 −0.714690
\(382\) −27.6979 −1.41715
\(383\) −2.11868 −0.108259 −0.0541297 0.998534i \(-0.517238\pi\)
−0.0541297 + 0.998534i \(0.517238\pi\)
\(384\) 28.2587 1.44207
\(385\) 12.0666 0.614971
\(386\) −20.5141 −1.04414
\(387\) 3.62005 0.184018
\(388\) −40.4313 −2.05259
\(389\) −17.2805 −0.876158 −0.438079 0.898936i \(-0.644341\pi\)
−0.438079 + 0.898936i \(0.644341\pi\)
\(390\) 9.78919 0.495695
\(391\) 30.4657 1.54072
\(392\) −122.329 −6.17853
\(393\) 21.2277 1.07080
\(394\) −21.7155 −1.09401
\(395\) −9.96391 −0.501339
\(396\) −11.6908 −0.587485
\(397\) 18.0286 0.904830 0.452415 0.891807i \(-0.350563\pi\)
0.452415 + 0.891807i \(0.350563\pi\)
\(398\) 58.9518 2.95499
\(399\) −67.8258 −3.39554
\(400\) −11.4409 −0.572046
\(401\) −7.89119 −0.394067 −0.197034 0.980397i \(-0.563131\pi\)
−0.197034 + 0.980397i \(0.563131\pi\)
\(402\) −54.7312 −2.72975
\(403\) −6.55848 −0.326701
\(404\) 33.0547 1.64453
\(405\) −22.4128 −1.11370
\(406\) −74.9188 −3.71816
\(407\) 5.97817 0.296327
\(408\) −67.0538 −3.31966
\(409\) 7.63751 0.377651 0.188825 0.982011i \(-0.439532\pi\)
0.188825 + 0.982011i \(0.439532\pi\)
\(410\) −57.6607 −2.84766
\(411\) −36.0483 −1.77813
\(412\) −52.8919 −2.60580
\(413\) 34.0341 1.67471
\(414\) 38.9051 1.91208
\(415\) 24.0093 1.17857
\(416\) −12.4189 −0.608886
\(417\) −5.21571 −0.255414
\(418\) −22.7298 −1.11175
\(419\) −35.2617 −1.72265 −0.861323 0.508057i \(-0.830364\pi\)
−0.861323 + 0.508057i \(0.830364\pi\)
\(420\) 104.493 5.09876
\(421\) 18.3743 0.895511 0.447755 0.894156i \(-0.352224\pi\)
0.447755 + 0.894156i \(0.352224\pi\)
\(422\) −24.9569 −1.21488
\(423\) −14.6384 −0.711742
\(424\) 13.4457 0.652981
\(425\) 3.62182 0.175684
\(426\) 47.6568 2.30898
\(427\) −47.5002 −2.29870
\(428\) −17.1196 −0.827509
\(429\) 2.35639 0.113767
\(430\) −10.8433 −0.522909
\(431\) −5.93338 −0.285801 −0.142900 0.989737i \(-0.545643\pi\)
−0.142900 + 0.989737i \(0.545643\pi\)
\(432\) 31.2586 1.50393
\(433\) −26.6012 −1.27837 −0.639187 0.769051i \(-0.720729\pi\)
−0.639187 + 0.769051i \(0.720729\pi\)
\(434\) −97.4981 −4.68006
\(435\) 26.4141 1.26646
\(436\) −34.4887 −1.65171
\(437\) 54.3134 2.59816
\(438\) −43.2043 −2.06438
\(439\) −9.42551 −0.449855 −0.224927 0.974376i \(-0.572215\pi\)
−0.224927 + 0.974376i \(0.572215\pi\)
\(440\) 21.2672 1.01387
\(441\) 26.4936 1.26160
\(442\) 8.29936 0.394761
\(443\) −9.78308 −0.464808 −0.232404 0.972619i \(-0.574659\pi\)
−0.232404 + 0.972619i \(0.574659\pi\)
\(444\) 51.7693 2.45686
\(445\) −13.7629 −0.652424
\(446\) 23.7888 1.12643
\(447\) −27.0290 −1.27843
\(448\) −74.7291 −3.53062
\(449\) −9.56221 −0.451269 −0.225634 0.974212i \(-0.572445\pi\)
−0.225634 + 0.974212i \(0.572445\pi\)
\(450\) 4.62512 0.218030
\(451\) −13.8797 −0.653570
\(452\) −58.3288 −2.74355
\(453\) 12.3764 0.581493
\(454\) −71.4997 −3.35565
\(455\) −7.85472 −0.368235
\(456\) −119.542 −5.59806
\(457\) −8.30614 −0.388545 −0.194272 0.980948i \(-0.562235\pi\)
−0.194272 + 0.980948i \(0.562235\pi\)
\(458\) 15.1962 0.710071
\(459\) −9.89544 −0.461879
\(460\) −83.6761 −3.90142
\(461\) 5.81176 0.270681 0.135340 0.990799i \(-0.456787\pi\)
0.135340 + 0.990799i \(0.456787\pi\)
\(462\) 35.0299 1.62974
\(463\) −38.7694 −1.80176 −0.900882 0.434063i \(-0.857079\pi\)
−0.900882 + 0.434063i \(0.857079\pi\)
\(464\) −70.7404 −3.28404
\(465\) 34.3748 1.59410
\(466\) 66.9268 3.10033
\(467\) 15.2641 0.706340 0.353170 0.935559i \(-0.385104\pi\)
0.353170 + 0.935559i \(0.385104\pi\)
\(468\) 7.61010 0.351777
\(469\) 43.9157 2.02784
\(470\) 43.8468 2.02250
\(471\) 48.6497 2.24166
\(472\) 59.9846 2.76101
\(473\) −2.61012 −0.120013
\(474\) −28.9257 −1.32860
\(475\) 6.45690 0.296263
\(476\) 88.5905 4.06054
\(477\) −2.91204 −0.133333
\(478\) 37.8634 1.73183
\(479\) −30.0271 −1.37197 −0.685987 0.727614i \(-0.740629\pi\)
−0.685987 + 0.727614i \(0.740629\pi\)
\(480\) 65.0908 2.97098
\(481\) −3.89148 −0.177436
\(482\) 37.2289 1.69573
\(483\) −83.7050 −3.80871
\(484\) −47.5965 −2.16348
\(485\) −15.9293 −0.723312
\(486\) −43.8185 −1.98765
\(487\) 23.4168 1.06112 0.530559 0.847648i \(-0.321982\pi\)
0.530559 + 0.847648i \(0.321982\pi\)
\(488\) −83.7183 −3.78975
\(489\) −32.4886 −1.46919
\(490\) −79.3573 −3.58500
\(491\) −25.0575 −1.13083 −0.565415 0.824807i \(-0.691284\pi\)
−0.565415 + 0.824807i \(0.691284\pi\)
\(492\) −120.194 −5.41879
\(493\) 22.3941 1.00858
\(494\) 14.7959 0.665699
\(495\) −4.60599 −0.207024
\(496\) −92.0604 −4.13363
\(497\) −38.2392 −1.71526
\(498\) 69.7003 3.12335
\(499\) −8.85100 −0.396225 −0.198112 0.980179i \(-0.563481\pi\)
−0.198112 + 0.980179i \(0.563481\pi\)
\(500\) −61.0498 −2.73023
\(501\) −21.5968 −0.964874
\(502\) −43.3067 −1.93287
\(503\) −13.8848 −0.619092 −0.309546 0.950884i \(-0.600177\pi\)
−0.309546 + 0.950884i \(0.600177\pi\)
\(504\) 68.7074 3.06047
\(505\) 13.0230 0.579517
\(506\) −28.0512 −1.24703
\(507\) 26.9009 1.19471
\(508\) 32.4840 1.44124
\(509\) −15.3759 −0.681523 −0.340762 0.940150i \(-0.610685\pi\)
−0.340762 + 0.940150i \(0.610685\pi\)
\(510\) −43.4993 −1.92618
\(511\) 34.6666 1.53356
\(512\) 19.3564 0.855442
\(513\) −17.6413 −0.778884
\(514\) 5.52305 0.243611
\(515\) −20.8386 −0.918258
\(516\) −22.6029 −0.995039
\(517\) 10.5545 0.464187
\(518\) −57.8505 −2.54180
\(519\) 49.4736 2.17165
\(520\) −13.8438 −0.607092
\(521\) 29.3976 1.28793 0.643967 0.765053i \(-0.277287\pi\)
0.643967 + 0.765053i \(0.277287\pi\)
\(522\) 28.5976 1.25168
\(523\) −25.8707 −1.13125 −0.565624 0.824663i \(-0.691365\pi\)
−0.565624 + 0.824663i \(0.691365\pi\)
\(524\) −49.4302 −2.15937
\(525\) −9.95103 −0.434298
\(526\) 0.924158 0.0402952
\(527\) 29.1433 1.26950
\(528\) 33.0762 1.43946
\(529\) 44.0292 1.91431
\(530\) 8.72253 0.378883
\(531\) −12.9913 −0.563775
\(532\) 157.937 6.84744
\(533\) 9.03496 0.391348
\(534\) −39.9544 −1.72899
\(535\) −6.74488 −0.291606
\(536\) 77.4006 3.34320
\(537\) −10.4708 −0.451847
\(538\) −82.2286 −3.54513
\(539\) −19.1023 −0.822796
\(540\) 27.1785 1.16958
\(541\) 23.3694 1.00473 0.502365 0.864656i \(-0.332463\pi\)
0.502365 + 0.864656i \(0.332463\pi\)
\(542\) −41.0222 −1.76206
\(543\) 40.0436 1.71843
\(544\) 55.1846 2.36602
\(545\) −13.5880 −0.582046
\(546\) −22.8027 −0.975864
\(547\) 34.3858 1.47023 0.735116 0.677942i \(-0.237128\pi\)
0.735116 + 0.677942i \(0.237128\pi\)
\(548\) 83.9409 3.58578
\(549\) 18.1315 0.773834
\(550\) −3.33479 −0.142196
\(551\) 39.9236 1.70080
\(552\) −147.529 −6.27924
\(553\) 23.2097 0.986975
\(554\) 69.3910 2.94814
\(555\) 20.3963 0.865775
\(556\) 12.1451 0.515069
\(557\) 14.8010 0.627137 0.313569 0.949566i \(-0.398475\pi\)
0.313569 + 0.949566i \(0.398475\pi\)
\(558\) 37.2164 1.57550
\(559\) 1.69905 0.0718622
\(560\) −110.255 −4.65914
\(561\) −10.4709 −0.442080
\(562\) −33.6106 −1.41778
\(563\) 15.6915 0.661317 0.330659 0.943750i \(-0.392729\pi\)
0.330659 + 0.943750i \(0.392729\pi\)
\(564\) 91.3992 3.84860
\(565\) −22.9806 −0.966802
\(566\) −60.8819 −2.55906
\(567\) 52.2078 2.19252
\(568\) −67.3961 −2.82788
\(569\) 17.6535 0.740074 0.370037 0.929017i \(-0.379345\pi\)
0.370037 + 0.929017i \(0.379345\pi\)
\(570\) −77.5494 −3.24819
\(571\) −27.1355 −1.13558 −0.567792 0.823172i \(-0.692202\pi\)
−0.567792 + 0.823172i \(0.692202\pi\)
\(572\) −5.48701 −0.229423
\(573\) −22.7473 −0.950283
\(574\) 134.313 5.60613
\(575\) 7.96857 0.332312
\(576\) 28.5252 1.18855
\(577\) 18.8841 0.786155 0.393078 0.919505i \(-0.371410\pi\)
0.393078 + 0.919505i \(0.371410\pi\)
\(578\) 8.39727 0.349281
\(579\) −16.8475 −0.700160
\(580\) −61.5070 −2.55394
\(581\) −55.9267 −2.32023
\(582\) −46.2436 −1.91686
\(583\) 2.09963 0.0869577
\(584\) 61.0993 2.52831
\(585\) 2.99826 0.123963
\(586\) −15.3281 −0.633199
\(587\) 18.9962 0.784057 0.392029 0.919953i \(-0.371773\pi\)
0.392029 + 0.919953i \(0.371773\pi\)
\(588\) −165.421 −6.82185
\(589\) 51.9560 2.14081
\(590\) 38.9133 1.60204
\(591\) −17.8342 −0.733601
\(592\) −54.6240 −2.24503
\(593\) 5.71365 0.234631 0.117316 0.993095i \(-0.462571\pi\)
0.117316 + 0.993095i \(0.462571\pi\)
\(594\) 9.11121 0.373838
\(595\) 34.9033 1.43090
\(596\) 62.9388 2.57807
\(597\) 48.4151 1.98150
\(598\) 18.2599 0.746702
\(599\) 20.0897 0.820841 0.410421 0.911896i \(-0.365382\pi\)
0.410421 + 0.911896i \(0.365382\pi\)
\(600\) −17.5385 −0.716007
\(601\) 22.1512 0.903566 0.451783 0.892128i \(-0.350788\pi\)
0.451783 + 0.892128i \(0.350788\pi\)
\(602\) 25.2580 1.02944
\(603\) −16.7632 −0.682652
\(604\) −28.8192 −1.17264
\(605\) −18.7523 −0.762389
\(606\) 37.8065 1.53578
\(607\) −26.8138 −1.08834 −0.544169 0.838975i \(-0.683155\pi\)
−0.544169 + 0.838975i \(0.683155\pi\)
\(608\) 98.3817 3.98991
\(609\) −61.5282 −2.49325
\(610\) −54.3100 −2.19895
\(611\) −6.87043 −0.277948
\(612\) −33.8163 −1.36694
\(613\) 14.7552 0.595956 0.297978 0.954573i \(-0.403688\pi\)
0.297978 + 0.954573i \(0.403688\pi\)
\(614\) 1.41149 0.0569632
\(615\) −47.3548 −1.90953
\(616\) −49.5392 −1.99599
\(617\) 2.63305 0.106003 0.0530013 0.998594i \(-0.483121\pi\)
0.0530013 + 0.998594i \(0.483121\pi\)
\(618\) −60.4955 −2.43349
\(619\) 2.49230 0.100174 0.0500870 0.998745i \(-0.484050\pi\)
0.0500870 + 0.998745i \(0.484050\pi\)
\(620\) −80.0442 −3.21465
\(621\) −21.7715 −0.873660
\(622\) 27.8786 1.11783
\(623\) 32.0589 1.28441
\(624\) −21.5309 −0.861926
\(625\) −19.1862 −0.767446
\(626\) −1.60240 −0.0640448
\(627\) −18.6672 −0.745495
\(628\) −113.284 −4.52053
\(629\) 17.2922 0.689485
\(630\) 44.5720 1.77579
\(631\) 18.8200 0.749213 0.374606 0.927184i \(-0.377778\pi\)
0.374606 + 0.927184i \(0.377778\pi\)
\(632\) 40.9067 1.62718
\(633\) −20.4962 −0.814651
\(634\) −87.5366 −3.47652
\(635\) 12.7982 0.507881
\(636\) 18.1822 0.720972
\(637\) 12.4346 0.492678
\(638\) −20.6193 −0.816327
\(639\) 14.5965 0.577428
\(640\) −25.9251 −1.02478
\(641\) −36.5787 −1.44477 −0.722385 0.691491i \(-0.756954\pi\)
−0.722385 + 0.691491i \(0.756954\pi\)
\(642\) −19.5807 −0.772789
\(643\) 1.98930 0.0784502 0.0392251 0.999230i \(-0.487511\pi\)
0.0392251 + 0.999230i \(0.487511\pi\)
\(644\) 194.913 7.68064
\(645\) −8.90520 −0.350642
\(646\) −65.7471 −2.58679
\(647\) −28.5149 −1.12104 −0.560518 0.828142i \(-0.689398\pi\)
−0.560518 + 0.828142i \(0.689398\pi\)
\(648\) 92.0155 3.61471
\(649\) 9.36696 0.367685
\(650\) 2.17077 0.0851448
\(651\) −80.0718 −3.13826
\(652\) 75.6521 2.96276
\(653\) −30.6079 −1.19778 −0.598890 0.800831i \(-0.704391\pi\)
−0.598890 + 0.800831i \(0.704391\pi\)
\(654\) −39.4467 −1.54249
\(655\) −19.4747 −0.760940
\(656\) 126.822 4.95158
\(657\) −13.2327 −0.516258
\(658\) −102.135 −3.98166
\(659\) 19.6933 0.767142 0.383571 0.923511i \(-0.374694\pi\)
0.383571 + 0.923511i \(0.374694\pi\)
\(660\) 28.7590 1.11944
\(661\) −2.38827 −0.0928929 −0.0464465 0.998921i \(-0.514790\pi\)
−0.0464465 + 0.998921i \(0.514790\pi\)
\(662\) −80.0516 −3.11129
\(663\) 6.81598 0.264711
\(664\) −98.5699 −3.82525
\(665\) 62.2247 2.41297
\(666\) 22.0824 0.855674
\(667\) 49.2705 1.90776
\(668\) 50.2897 1.94577
\(669\) 19.5369 0.755341
\(670\) 50.2115 1.93984
\(671\) −13.0731 −0.504682
\(672\) −151.621 −5.84890
\(673\) 14.9143 0.574902 0.287451 0.957795i \(-0.407192\pi\)
0.287451 + 0.957795i \(0.407192\pi\)
\(674\) −2.58103 −0.0994177
\(675\) −2.58824 −0.0996214
\(676\) −62.6405 −2.40925
\(677\) 8.38079 0.322100 0.161050 0.986946i \(-0.448512\pi\)
0.161050 + 0.986946i \(0.448512\pi\)
\(678\) −66.7139 −2.56213
\(679\) 37.1053 1.42397
\(680\) 61.5165 2.35905
\(681\) −58.7202 −2.25016
\(682\) −26.8337 −1.02751
\(683\) 6.69871 0.256319 0.128159 0.991754i \(-0.459093\pi\)
0.128159 + 0.991754i \(0.459093\pi\)
\(684\) −60.2868 −2.30512
\(685\) 33.0714 1.26359
\(686\) 97.7093 3.73056
\(687\) 12.4801 0.476145
\(688\) 23.8493 0.909247
\(689\) −1.36675 −0.0520690
\(690\) −95.7051 −3.64343
\(691\) −41.5507 −1.58066 −0.790332 0.612679i \(-0.790092\pi\)
−0.790332 + 0.612679i \(0.790092\pi\)
\(692\) −115.203 −4.37935
\(693\) 10.7291 0.407564
\(694\) −95.8493 −3.63839
\(695\) 4.78500 0.181505
\(696\) −108.442 −4.11050
\(697\) −40.1478 −1.52071
\(698\) 43.1382 1.63280
\(699\) 54.9647 2.07896
\(700\) 23.1717 0.875806
\(701\) −23.2463 −0.878001 −0.439000 0.898487i \(-0.644667\pi\)
−0.439000 + 0.898487i \(0.644667\pi\)
\(702\) −5.93092 −0.223848
\(703\) 30.8281 1.16270
\(704\) −20.5671 −0.775153
\(705\) 36.0099 1.35621
\(706\) −15.2776 −0.574981
\(707\) −30.3355 −1.14088
\(708\) 81.1153 3.04850
\(709\) −47.3562 −1.77850 −0.889249 0.457423i \(-0.848773\pi\)
−0.889249 + 0.457423i \(0.848773\pi\)
\(710\) −43.7213 −1.64083
\(711\) −8.85946 −0.332256
\(712\) 56.5033 2.11755
\(713\) 64.1198 2.40130
\(714\) 101.326 3.79203
\(715\) −2.16180 −0.0808466
\(716\) 24.3819 0.911195
\(717\) 31.0959 1.16130
\(718\) 37.6560 1.40531
\(719\) 31.5663 1.17723 0.588613 0.808415i \(-0.299674\pi\)
0.588613 + 0.808415i \(0.299674\pi\)
\(720\) 42.0861 1.56846
\(721\) 48.5408 1.80776
\(722\) −66.6093 −2.47894
\(723\) 30.5748 1.13709
\(724\) −93.2442 −3.46539
\(725\) 5.85738 0.217538
\(726\) −54.4388 −2.02042
\(727\) 39.5751 1.46776 0.733880 0.679279i \(-0.237707\pi\)
0.733880 + 0.679279i \(0.237707\pi\)
\(728\) 32.2474 1.19517
\(729\) −2.47896 −0.0918133
\(730\) 39.6365 1.46701
\(731\) −7.54992 −0.279244
\(732\) −113.210 −4.18435
\(733\) −13.2902 −0.490885 −0.245443 0.969411i \(-0.578933\pi\)
−0.245443 + 0.969411i \(0.578933\pi\)
\(734\) 21.4505 0.791754
\(735\) −65.1734 −2.40396
\(736\) 121.415 4.47540
\(737\) 12.0866 0.445215
\(738\) −51.2693 −1.88725
\(739\) −33.1110 −1.21801 −0.609003 0.793168i \(-0.708430\pi\)
−0.609003 + 0.793168i \(0.708430\pi\)
\(740\) −47.4942 −1.74592
\(741\) 12.1514 0.446391
\(742\) −20.3180 −0.745898
\(743\) −13.5021 −0.495345 −0.247673 0.968844i \(-0.579666\pi\)
−0.247673 + 0.968844i \(0.579666\pi\)
\(744\) −141.125 −5.17390
\(745\) 24.7969 0.908489
\(746\) −9.09644 −0.333044
\(747\) 21.3480 0.781083
\(748\) 24.3821 0.891498
\(749\) 15.7113 0.574079
\(750\) −69.8261 −2.54969
\(751\) 33.2807 1.21443 0.607214 0.794538i \(-0.292287\pi\)
0.607214 + 0.794538i \(0.292287\pi\)
\(752\) −96.4392 −3.51677
\(753\) −35.5663 −1.29611
\(754\) 13.4221 0.488804
\(755\) −11.3543 −0.413227
\(756\) −63.3089 −2.30252
\(757\) −39.1617 −1.42336 −0.711678 0.702506i \(-0.752064\pi\)
−0.711678 + 0.702506i \(0.752064\pi\)
\(758\) −37.7942 −1.37275
\(759\) −23.0375 −0.836208
\(760\) 109.670 3.97815
\(761\) 23.7429 0.860681 0.430340 0.902667i \(-0.358394\pi\)
0.430340 + 0.902667i \(0.358394\pi\)
\(762\) 37.1538 1.34594
\(763\) 31.6515 1.14586
\(764\) 52.9687 1.91634
\(765\) −13.3231 −0.481697
\(766\) 5.64271 0.203879
\(767\) −6.09740 −0.220164
\(768\) −5.32389 −0.192109
\(769\) 34.6048 1.24788 0.623940 0.781473i \(-0.285531\pi\)
0.623940 + 0.781473i \(0.285531\pi\)
\(770\) −32.1372 −1.15814
\(771\) 4.53589 0.163356
\(772\) 39.2307 1.41194
\(773\) 50.9737 1.83340 0.916698 0.399581i \(-0.130844\pi\)
0.916698 + 0.399581i \(0.130844\pi\)
\(774\) −9.64135 −0.346551
\(775\) 7.62270 0.273815
\(776\) 65.3974 2.34763
\(777\) −47.5106 −1.70443
\(778\) 46.0236 1.65002
\(779\) −71.5745 −2.56442
\(780\) −18.7206 −0.670304
\(781\) −10.5243 −0.376589
\(782\) −81.1397 −2.90155
\(783\) −16.0034 −0.571913
\(784\) 174.543 6.23368
\(785\) −44.6322 −1.59299
\(786\) −56.5361 −2.01658
\(787\) −41.2984 −1.47213 −0.736065 0.676911i \(-0.763318\pi\)
−0.736065 + 0.676911i \(0.763318\pi\)
\(788\) 41.5282 1.47938
\(789\) 0.758979 0.0270204
\(790\) 26.5371 0.944146
\(791\) 53.5304 1.90332
\(792\) 18.9098 0.671931
\(793\) 8.50992 0.302196
\(794\) −48.0159 −1.70402
\(795\) 7.16351 0.254064
\(796\) −112.738 −3.99589
\(797\) −27.6170 −0.978244 −0.489122 0.872215i \(-0.662683\pi\)
−0.489122 + 0.872215i \(0.662683\pi\)
\(798\) 180.641 6.39464
\(799\) 30.5295 1.08006
\(800\) 14.4340 0.510320
\(801\) −12.2373 −0.432385
\(802\) 21.0167 0.742127
\(803\) 9.54103 0.336696
\(804\) 104.667 3.69130
\(805\) 76.7926 2.70658
\(806\) 17.4673 0.615260
\(807\) −67.5315 −2.37722
\(808\) −53.4658 −1.88092
\(809\) −45.9752 −1.61640 −0.808201 0.588906i \(-0.799559\pi\)
−0.808201 + 0.588906i \(0.799559\pi\)
\(810\) 59.6925 2.09738
\(811\) −16.7481 −0.588105 −0.294052 0.955789i \(-0.595004\pi\)
−0.294052 + 0.955789i \(0.595004\pi\)
\(812\) 143.273 5.02788
\(813\) −33.6901 −1.18156
\(814\) −15.9218 −0.558057
\(815\) 29.8057 1.04405
\(816\) 95.6748 3.34929
\(817\) −13.4598 −0.470899
\(818\) −20.3411 −0.711211
\(819\) −6.98406 −0.244043
\(820\) 110.269 3.85075
\(821\) 16.5734 0.578417 0.289208 0.957266i \(-0.406608\pi\)
0.289208 + 0.957266i \(0.406608\pi\)
\(822\) 96.0079 3.34866
\(823\) 7.66199 0.267080 0.133540 0.991043i \(-0.457366\pi\)
0.133540 + 0.991043i \(0.457366\pi\)
\(824\) 85.5524 2.98036
\(825\) −2.73875 −0.0953509
\(826\) −90.6436 −3.15390
\(827\) 17.5652 0.610803 0.305401 0.952224i \(-0.401209\pi\)
0.305401 + 0.952224i \(0.401209\pi\)
\(828\) −74.4010 −2.58562
\(829\) −13.0915 −0.454688 −0.227344 0.973815i \(-0.573004\pi\)
−0.227344 + 0.973815i \(0.573004\pi\)
\(830\) −63.9445 −2.21955
\(831\) 56.9884 1.97691
\(832\) 13.3881 0.464150
\(833\) −55.2546 −1.91446
\(834\) 13.8911 0.481009
\(835\) 19.8133 0.685669
\(836\) 43.4678 1.50337
\(837\) −20.8265 −0.719869
\(838\) 93.9130 3.24417
\(839\) −36.3461 −1.25481 −0.627404 0.778694i \(-0.715883\pi\)
−0.627404 + 0.778694i \(0.715883\pi\)
\(840\) −169.018 −5.83166
\(841\) 7.21675 0.248853
\(842\) −48.9367 −1.68647
\(843\) −27.6032 −0.950705
\(844\) 47.7268 1.64283
\(845\) −24.6794 −0.848997
\(846\) 38.9866 1.34039
\(847\) 43.6811 1.50090
\(848\) −19.1848 −0.658810
\(849\) −50.0002 −1.71600
\(850\) −9.64606 −0.330857
\(851\) 38.0455 1.30418
\(852\) −91.1376 −3.12232
\(853\) −24.6209 −0.843004 −0.421502 0.906828i \(-0.638497\pi\)
−0.421502 + 0.906828i \(0.638497\pi\)
\(854\) 126.508 4.32902
\(855\) −23.7521 −0.812304
\(856\) 27.6910 0.946457
\(857\) 22.9754 0.784825 0.392412 0.919789i \(-0.371641\pi\)
0.392412 + 0.919789i \(0.371641\pi\)
\(858\) −6.27580 −0.214252
\(859\) −12.2651 −0.418480 −0.209240 0.977864i \(-0.567099\pi\)
−0.209240 + 0.977864i \(0.567099\pi\)
\(860\) 20.7364 0.707105
\(861\) 110.307 3.75925
\(862\) 15.8025 0.538234
\(863\) −47.2349 −1.60790 −0.803948 0.594700i \(-0.797271\pi\)
−0.803948 + 0.594700i \(0.797271\pi\)
\(864\) −39.4362 −1.34165
\(865\) −45.3881 −1.54324
\(866\) 70.8475 2.40750
\(867\) 6.89639 0.234214
\(868\) 186.453 6.32862
\(869\) 6.38782 0.216692
\(870\) −70.3490 −2.38506
\(871\) −7.86773 −0.266588
\(872\) 55.7853 1.88913
\(873\) −14.1636 −0.479366
\(874\) −144.654 −4.89299
\(875\) 56.0276 1.89408
\(876\) 82.6227 2.79156
\(877\) −31.1956 −1.05340 −0.526701 0.850051i \(-0.676571\pi\)
−0.526701 + 0.850051i \(0.676571\pi\)
\(878\) 25.1031 0.847189
\(879\) −12.5885 −0.424598
\(880\) −30.3448 −1.02292
\(881\) −10.2898 −0.346671 −0.173336 0.984863i \(-0.555455\pi\)
−0.173336 + 0.984863i \(0.555455\pi\)
\(882\) −70.5609 −2.37591
\(883\) 2.47592 0.0833213 0.0416607 0.999132i \(-0.486735\pi\)
0.0416607 + 0.999132i \(0.486735\pi\)
\(884\) −15.8715 −0.533816
\(885\) 31.9582 1.07426
\(886\) 26.0554 0.875349
\(887\) 39.5772 1.32887 0.664435 0.747346i \(-0.268672\pi\)
0.664435 + 0.747346i \(0.268672\pi\)
\(888\) −83.7367 −2.81002
\(889\) −29.8117 −0.999854
\(890\) 36.6549 1.22868
\(891\) 14.3688 0.481372
\(892\) −45.4931 −1.52322
\(893\) 54.4272 1.82134
\(894\) 71.9867 2.40759
\(895\) 9.60609 0.321096
\(896\) 60.3891 2.01746
\(897\) 14.9962 0.500709
\(898\) 25.4672 0.849852
\(899\) 47.1319 1.57194
\(900\) −8.84496 −0.294832
\(901\) 6.07329 0.202331
\(902\) 36.9660 1.23083
\(903\) 20.7435 0.690301
\(904\) 94.3465 3.13792
\(905\) −36.7368 −1.22117
\(906\) −32.9622 −1.09510
\(907\) 26.7368 0.887780 0.443890 0.896081i \(-0.353598\pi\)
0.443890 + 0.896081i \(0.353598\pi\)
\(908\) 136.734 4.53768
\(909\) 11.5795 0.384068
\(910\) 20.9196 0.693478
\(911\) −39.7030 −1.31542 −0.657709 0.753272i \(-0.728474\pi\)
−0.657709 + 0.753272i \(0.728474\pi\)
\(912\) 170.567 5.64803
\(913\) −15.3923 −0.509410
\(914\) 22.1219 0.731727
\(915\) −44.6029 −1.47453
\(916\) −29.0608 −0.960195
\(917\) 45.3639 1.49805
\(918\) 26.3547 0.869834
\(919\) 24.7787 0.817373 0.408687 0.912675i \(-0.365987\pi\)
0.408687 + 0.912675i \(0.365987\pi\)
\(920\) 135.346 4.46222
\(921\) 1.15921 0.0381973
\(922\) −15.4786 −0.509759
\(923\) 6.85077 0.225496
\(924\) −66.9903 −2.20382
\(925\) 4.52293 0.148713
\(926\) 103.255 3.39317
\(927\) −18.5287 −0.608564
\(928\) 89.2471 2.92968
\(929\) −47.5142 −1.55889 −0.779446 0.626470i \(-0.784499\pi\)
−0.779446 + 0.626470i \(0.784499\pi\)
\(930\) −91.5511 −3.00208
\(931\) −98.5065 −3.22842
\(932\) −127.989 −4.19242
\(933\) 22.8957 0.749572
\(934\) −40.6532 −1.33021
\(935\) 9.60617 0.314155
\(936\) −12.3093 −0.402342
\(937\) −53.4347 −1.74563 −0.872817 0.488047i \(-0.837709\pi\)
−0.872817 + 0.488047i \(0.837709\pi\)
\(938\) −116.961 −3.81892
\(939\) −1.31600 −0.0429459
\(940\) −83.8514 −2.73493
\(941\) −20.6464 −0.673053 −0.336527 0.941674i \(-0.609252\pi\)
−0.336527 + 0.941674i \(0.609252\pi\)
\(942\) −129.570 −4.22160
\(943\) −88.3313 −2.87646
\(944\) −85.5882 −2.78566
\(945\) −24.9427 −0.811387
\(946\) 6.95157 0.226015
\(947\) −38.4098 −1.24815 −0.624075 0.781364i \(-0.714524\pi\)
−0.624075 + 0.781364i \(0.714524\pi\)
\(948\) 55.3168 1.79661
\(949\) −6.21071 −0.201608
\(950\) −17.1968 −0.557937
\(951\) −71.8908 −2.33122
\(952\) −143.295 −4.64421
\(953\) 13.5699 0.439573 0.219786 0.975548i \(-0.429464\pi\)
0.219786 + 0.975548i \(0.429464\pi\)
\(954\) 7.75568 0.251099
\(955\) 20.8688 0.675300
\(956\) −72.4089 −2.34187
\(957\) −16.9339 −0.547397
\(958\) 79.9717 2.58377
\(959\) −77.0356 −2.48761
\(960\) −70.1709 −2.26476
\(961\) 30.3367 0.978603
\(962\) 10.3642 0.334156
\(963\) −5.99724 −0.193258
\(964\) −71.1955 −2.29305
\(965\) 15.4563 0.497555
\(966\) 222.933 7.17275
\(967\) −50.8960 −1.63671 −0.818353 0.574716i \(-0.805113\pi\)
−0.818353 + 0.574716i \(0.805113\pi\)
\(968\) 76.9872 2.47446
\(969\) −53.9958 −1.73460
\(970\) 42.4248 1.36218
\(971\) −24.3240 −0.780594 −0.390297 0.920689i \(-0.627628\pi\)
−0.390297 + 0.920689i \(0.627628\pi\)
\(972\) 83.7973 2.68780
\(973\) −11.1460 −0.357326
\(974\) −62.3664 −1.99835
\(975\) 1.78278 0.0570947
\(976\) 119.452 3.82358
\(977\) 53.5290 1.71254 0.856272 0.516525i \(-0.172775\pi\)
0.856272 + 0.516525i \(0.172775\pi\)
\(978\) 86.5275 2.76685
\(979\) 8.82333 0.281995
\(980\) 151.761 4.84782
\(981\) −12.0818 −0.385744
\(982\) 66.7361 2.12963
\(983\) −12.4734 −0.397839 −0.198920 0.980016i \(-0.563743\pi\)
−0.198920 + 0.980016i \(0.563743\pi\)
\(984\) 194.414 6.19769
\(985\) 16.3615 0.521319
\(986\) −59.6426 −1.89941
\(987\) −83.8803 −2.66994
\(988\) −28.2953 −0.900193
\(989\) −16.6110 −0.528198
\(990\) 12.2672 0.389878
\(991\) −52.8785 −1.67974 −0.839871 0.542787i \(-0.817369\pi\)
−0.839871 + 0.542787i \(0.817369\pi\)
\(992\) 116.145 3.68760
\(993\) −65.7436 −2.08631
\(994\) 101.843 3.23027
\(995\) −44.4170 −1.40811
\(996\) −133.293 −4.22355
\(997\) 1.52848 0.0484074 0.0242037 0.999707i \(-0.492295\pi\)
0.0242037 + 0.999707i \(0.492295\pi\)
\(998\) 23.5730 0.746190
\(999\) −12.3574 −0.390971
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 2671.2.a.b.1.4 122
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2671.2.a.b.1.4 122 1.1 even 1 trivial