Properties

Label 4019.2.a.a.1.7
Level $4019$
Weight $2$
Character 4019.1
Self dual yes
Analytic conductor $32.092$
Analytic rank $1$
Dimension $149$
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] = [4019,2,Mod(1,4019)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4019, 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("4019.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4019 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4019.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: \(32.0918765724\)
Analytic rank: \(1\)
Dimension: \(149\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) \(=\) 4019.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.58406 q^{2} +1.99817 q^{3} +4.67739 q^{4} -2.81422 q^{5} -5.16341 q^{6} -2.01468 q^{7} -6.91855 q^{8} +0.992695 q^{9} +O(q^{10})\) \(q-2.58406 q^{2} +1.99817 q^{3} +4.67739 q^{4} -2.81422 q^{5} -5.16341 q^{6} -2.01468 q^{7} -6.91855 q^{8} +0.992695 q^{9} +7.27214 q^{10} -1.88438 q^{11} +9.34624 q^{12} -0.0851605 q^{13} +5.20607 q^{14} -5.62331 q^{15} +8.52321 q^{16} +6.33180 q^{17} -2.56519 q^{18} -3.06922 q^{19} -13.1632 q^{20} -4.02568 q^{21} +4.86936 q^{22} +5.50170 q^{23} -13.8245 q^{24} +2.91986 q^{25} +0.220060 q^{26} -4.01094 q^{27} -9.42346 q^{28} +9.63260 q^{29} +14.5310 q^{30} +2.62016 q^{31} -8.18742 q^{32} -3.76532 q^{33} -16.3618 q^{34} +5.66977 q^{35} +4.64322 q^{36} -4.41728 q^{37} +7.93107 q^{38} -0.170165 q^{39} +19.4704 q^{40} +0.552734 q^{41} +10.4026 q^{42} -8.65479 q^{43} -8.81399 q^{44} -2.79367 q^{45} -14.2168 q^{46} -2.70036 q^{47} +17.0308 q^{48} -2.94105 q^{49} -7.54510 q^{50} +12.6520 q^{51} -0.398329 q^{52} +2.57798 q^{53} +10.3645 q^{54} +5.30307 q^{55} +13.9387 q^{56} -6.13284 q^{57} -24.8913 q^{58} +5.87424 q^{59} -26.3024 q^{60} +10.0099 q^{61} -6.77066 q^{62} -1.99996 q^{63} +4.11040 q^{64} +0.239661 q^{65} +9.72983 q^{66} +2.16311 q^{67} +29.6163 q^{68} +10.9934 q^{69} -14.6510 q^{70} -5.84827 q^{71} -6.86801 q^{72} +7.40845 q^{73} +11.4145 q^{74} +5.83438 q^{75} -14.3560 q^{76} +3.79643 q^{77} +0.439719 q^{78} +0.253116 q^{79} -23.9862 q^{80} -10.9926 q^{81} -1.42830 q^{82} +6.68070 q^{83} -18.8297 q^{84} -17.8191 q^{85} +22.3645 q^{86} +19.2476 q^{87} +13.0372 q^{88} +1.64300 q^{89} +7.21901 q^{90} +0.171571 q^{91} +25.7336 q^{92} +5.23553 q^{93} +6.97791 q^{94} +8.63748 q^{95} -16.3599 q^{96} -1.03465 q^{97} +7.59987 q^{98} -1.87062 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9} - 58 q^{10} - 33 q^{11} - 33 q^{12} - 107 q^{13} - 28 q^{14} - 24 q^{15} + 74 q^{16} - 39 q^{17} - 33 q^{18} - 93 q^{19} - 63 q^{20} - 113 q^{21} - 38 q^{22} - 11 q^{23} - 130 q^{24} + 85 q^{25} - 33 q^{26} - 30 q^{27} - 94 q^{28} - 85 q^{29} - 16 q^{30} - 129 q^{31} - 35 q^{32} - 64 q^{33} - 78 q^{34} - 27 q^{35} + 79 q^{36} - 135 q^{37} - 11 q^{38} - 73 q^{39} - 146 q^{40} - 101 q^{41} + 4 q^{42} - 55 q^{43} - 82 q^{44} - 168 q^{45} - 113 q^{46} - 40 q^{47} - 65 q^{48} + 27 q^{49} - 5 q^{50} - 49 q^{51} - 177 q^{52} - 32 q^{53} - 155 q^{54} - 128 q^{55} - 44 q^{56} - 47 q^{57} - 46 q^{58} - 53 q^{59} - 11 q^{60} - 347 q^{61} - 11 q^{62} - 73 q^{63} + q^{64} - 31 q^{65} - 37 q^{66} - 40 q^{67} - 80 q^{68} - 175 q^{69} - 61 q^{70} - 31 q^{71} - 68 q^{72} - 193 q^{73} - 33 q^{74} - 56 q^{75} - 248 q^{76} - 84 q^{77} + 40 q^{78} - 111 q^{79} - 54 q^{80} + 49 q^{81} - 74 q^{82} - 24 q^{83} - 159 q^{84} - 258 q^{85} - q^{86} - 66 q^{87} - 97 q^{88} - 76 q^{89} - 75 q^{90} - 134 q^{91} + 31 q^{92} - 97 q^{93} - 111 q^{94} - 14 q^{95} - 216 q^{96} - 140 q^{97} - 13 q^{98} - 116 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.58406 −1.82721 −0.913605 0.406603i \(-0.866713\pi\)
−0.913605 + 0.406603i \(0.866713\pi\)
\(3\) 1.99817 1.15365 0.576823 0.816869i \(-0.304292\pi\)
0.576823 + 0.816869i \(0.304292\pi\)
\(4\) 4.67739 2.33870
\(5\) −2.81422 −1.25856 −0.629280 0.777179i \(-0.716650\pi\)
−0.629280 + 0.777179i \(0.716650\pi\)
\(6\) −5.16341 −2.10795
\(7\) −2.01468 −0.761478 −0.380739 0.924682i \(-0.624330\pi\)
−0.380739 + 0.924682i \(0.624330\pi\)
\(8\) −6.91855 −2.44608
\(9\) 0.992695 0.330898
\(10\) 7.27214 2.29965
\(11\) −1.88438 −0.568162 −0.284081 0.958800i \(-0.591689\pi\)
−0.284081 + 0.958800i \(0.591689\pi\)
\(12\) 9.34624 2.69803
\(13\) −0.0851605 −0.0236193 −0.0118096 0.999930i \(-0.503759\pi\)
−0.0118096 + 0.999930i \(0.503759\pi\)
\(14\) 5.20607 1.39138
\(15\) −5.62331 −1.45193
\(16\) 8.52321 2.13080
\(17\) 6.33180 1.53569 0.767843 0.640638i \(-0.221330\pi\)
0.767843 + 0.640638i \(0.221330\pi\)
\(18\) −2.56519 −0.604621
\(19\) −3.06922 −0.704128 −0.352064 0.935976i \(-0.614520\pi\)
−0.352064 + 0.935976i \(0.614520\pi\)
\(20\) −13.1632 −2.94339
\(21\) −4.02568 −0.878476
\(22\) 4.86936 1.03815
\(23\) 5.50170 1.14718 0.573592 0.819141i \(-0.305549\pi\)
0.573592 + 0.819141i \(0.305549\pi\)
\(24\) −13.8245 −2.82191
\(25\) 2.91986 0.583971
\(26\) 0.220060 0.0431574
\(27\) −4.01094 −0.771906
\(28\) −9.42346 −1.78087
\(29\) 9.63260 1.78873 0.894364 0.447340i \(-0.147629\pi\)
0.894364 + 0.447340i \(0.147629\pi\)
\(30\) 14.5310 2.65298
\(31\) 2.62016 0.470594 0.235297 0.971924i \(-0.424394\pi\)
0.235297 + 0.971924i \(0.424394\pi\)
\(32\) −8.18742 −1.44734
\(33\) −3.76532 −0.655458
\(34\) −16.3618 −2.80602
\(35\) 5.66977 0.958366
\(36\) 4.64322 0.773870
\(37\) −4.41728 −0.726197 −0.363098 0.931751i \(-0.618281\pi\)
−0.363098 + 0.931751i \(0.618281\pi\)
\(38\) 7.93107 1.28659
\(39\) −0.170165 −0.0272483
\(40\) 19.4704 3.07853
\(41\) 0.552734 0.0863226 0.0431613 0.999068i \(-0.486257\pi\)
0.0431613 + 0.999068i \(0.486257\pi\)
\(42\) 10.4026 1.60516
\(43\) −8.65479 −1.31984 −0.659922 0.751334i \(-0.729411\pi\)
−0.659922 + 0.751334i \(0.729411\pi\)
\(44\) −8.81399 −1.32876
\(45\) −2.79367 −0.416455
\(46\) −14.2168 −2.09615
\(47\) −2.70036 −0.393888 −0.196944 0.980415i \(-0.563102\pi\)
−0.196944 + 0.980415i \(0.563102\pi\)
\(48\) 17.0308 2.45819
\(49\) −2.94105 −0.420151
\(50\) −7.54510 −1.06704
\(51\) 12.6520 1.77164
\(52\) −0.398329 −0.0552383
\(53\) 2.57798 0.354113 0.177057 0.984201i \(-0.443342\pi\)
0.177057 + 0.984201i \(0.443342\pi\)
\(54\) 10.3645 1.41043
\(55\) 5.30307 0.715066
\(56\) 13.9387 1.86264
\(57\) −6.13284 −0.812314
\(58\) −24.8913 −3.26838
\(59\) 5.87424 0.764761 0.382381 0.924005i \(-0.375104\pi\)
0.382381 + 0.924005i \(0.375104\pi\)
\(60\) −26.3024 −3.39563
\(61\) 10.0099 1.28164 0.640819 0.767692i \(-0.278595\pi\)
0.640819 + 0.767692i \(0.278595\pi\)
\(62\) −6.77066 −0.859874
\(63\) −1.99996 −0.251972
\(64\) 4.11040 0.513800
\(65\) 0.239661 0.0297263
\(66\) 9.72983 1.19766
\(67\) 2.16311 0.264266 0.132133 0.991232i \(-0.457817\pi\)
0.132133 + 0.991232i \(0.457817\pi\)
\(68\) 29.6163 3.59150
\(69\) 10.9934 1.32344
\(70\) −14.6510 −1.75114
\(71\) −5.84827 −0.694062 −0.347031 0.937854i \(-0.612810\pi\)
−0.347031 + 0.937854i \(0.612810\pi\)
\(72\) −6.86801 −0.809403
\(73\) 7.40845 0.867093 0.433547 0.901131i \(-0.357262\pi\)
0.433547 + 0.901131i \(0.357262\pi\)
\(74\) 11.4145 1.32691
\(75\) 5.83438 0.673696
\(76\) −14.3560 −1.64674
\(77\) 3.79643 0.432643
\(78\) 0.439719 0.0497883
\(79\) 0.253116 0.0284778 0.0142389 0.999899i \(-0.495467\pi\)
0.0142389 + 0.999899i \(0.495467\pi\)
\(80\) −23.9862 −2.68174
\(81\) −10.9926 −1.22140
\(82\) −1.42830 −0.157729
\(83\) 6.68070 0.733302 0.366651 0.930359i \(-0.380504\pi\)
0.366651 + 0.930359i \(0.380504\pi\)
\(84\) −18.8297 −2.05449
\(85\) −17.8191 −1.93275
\(86\) 22.3645 2.41163
\(87\) 19.2476 2.06356
\(88\) 13.0372 1.38977
\(89\) 1.64300 0.174158 0.0870791 0.996201i \(-0.472247\pi\)
0.0870791 + 0.996201i \(0.472247\pi\)
\(90\) 7.21901 0.760951
\(91\) 0.171571 0.0179856
\(92\) 25.7336 2.68291
\(93\) 5.23553 0.542899
\(94\) 6.97791 0.719717
\(95\) 8.63748 0.886187
\(96\) −16.3599 −1.66972
\(97\) −1.03465 −0.105053 −0.0525266 0.998620i \(-0.516727\pi\)
−0.0525266 + 0.998620i \(0.516727\pi\)
\(98\) 7.59987 0.767703
\(99\) −1.87062 −0.188004
\(100\) 13.6573 1.36573
\(101\) −14.6889 −1.46160 −0.730800 0.682591i \(-0.760853\pi\)
−0.730800 + 0.682591i \(0.760853\pi\)
\(102\) −32.6936 −3.23715
\(103\) −5.50626 −0.542548 −0.271274 0.962502i \(-0.587445\pi\)
−0.271274 + 0.962502i \(0.587445\pi\)
\(104\) 0.589188 0.0577746
\(105\) 11.3292 1.10561
\(106\) −6.66168 −0.647039
\(107\) 9.11373 0.881058 0.440529 0.897738i \(-0.354791\pi\)
0.440529 + 0.897738i \(0.354791\pi\)
\(108\) −18.7608 −1.80525
\(109\) −4.61244 −0.441792 −0.220896 0.975297i \(-0.570898\pi\)
−0.220896 + 0.975297i \(0.570898\pi\)
\(110\) −13.7035 −1.30658
\(111\) −8.82650 −0.837774
\(112\) −17.1716 −1.62256
\(113\) −4.04058 −0.380106 −0.190053 0.981774i \(-0.560866\pi\)
−0.190053 + 0.981774i \(0.560866\pi\)
\(114\) 15.8477 1.48427
\(115\) −15.4830 −1.44380
\(116\) 45.0554 4.18329
\(117\) −0.0845384 −0.00781558
\(118\) −15.1794 −1.39738
\(119\) −12.7566 −1.16939
\(120\) 38.9051 3.55154
\(121\) −7.44911 −0.677192
\(122\) −25.8663 −2.34182
\(123\) 1.10446 0.0995857
\(124\) 12.2555 1.10058
\(125\) 5.85399 0.523597
\(126\) 5.16804 0.460405
\(127\) −13.6352 −1.20993 −0.604963 0.796254i \(-0.706812\pi\)
−0.604963 + 0.796254i \(0.706812\pi\)
\(128\) 5.75329 0.508524
\(129\) −17.2938 −1.52263
\(130\) −0.619299 −0.0543161
\(131\) −19.9763 −1.74534 −0.872669 0.488312i \(-0.837613\pi\)
−0.872669 + 0.488312i \(0.837613\pi\)
\(132\) −17.6119 −1.53292
\(133\) 6.18351 0.536178
\(134\) −5.58961 −0.482869
\(135\) 11.2877 0.971490
\(136\) −43.8069 −3.75641
\(137\) −7.79908 −0.666321 −0.333160 0.942870i \(-0.608115\pi\)
−0.333160 + 0.942870i \(0.608115\pi\)
\(138\) −28.4075 −2.41821
\(139\) 10.9364 0.927611 0.463805 0.885937i \(-0.346484\pi\)
0.463805 + 0.885937i \(0.346484\pi\)
\(140\) 26.5197 2.24133
\(141\) −5.39579 −0.454408
\(142\) 15.1123 1.26820
\(143\) 0.160475 0.0134196
\(144\) 8.46094 0.705079
\(145\) −27.1083 −2.25122
\(146\) −19.1439 −1.58436
\(147\) −5.87673 −0.484705
\(148\) −20.6614 −1.69835
\(149\) −8.37092 −0.685773 −0.342886 0.939377i \(-0.611405\pi\)
−0.342886 + 0.939377i \(0.611405\pi\)
\(150\) −15.0764 −1.23098
\(151\) −19.4727 −1.58467 −0.792333 0.610088i \(-0.791134\pi\)
−0.792333 + 0.610088i \(0.791134\pi\)
\(152\) 21.2346 1.72235
\(153\) 6.28554 0.508156
\(154\) −9.81022 −0.790530
\(155\) −7.37371 −0.592271
\(156\) −0.795931 −0.0637254
\(157\) −12.4938 −0.997111 −0.498555 0.866858i \(-0.666136\pi\)
−0.498555 + 0.866858i \(0.666136\pi\)
\(158\) −0.654068 −0.0520348
\(159\) 5.15126 0.408521
\(160\) 23.0412 1.82157
\(161\) −11.0842 −0.873556
\(162\) 28.4057 2.23176
\(163\) 16.1492 1.26491 0.632453 0.774599i \(-0.282048\pi\)
0.632453 + 0.774599i \(0.282048\pi\)
\(164\) 2.58535 0.201882
\(165\) 10.5965 0.824933
\(166\) −17.2634 −1.33990
\(167\) 3.06546 0.237213 0.118606 0.992941i \(-0.462157\pi\)
0.118606 + 0.992941i \(0.462157\pi\)
\(168\) 27.8519 2.14882
\(169\) −12.9927 −0.999442
\(170\) 46.0457 3.53154
\(171\) −3.04680 −0.232995
\(172\) −40.4819 −3.08671
\(173\) −14.6669 −1.11510 −0.557550 0.830143i \(-0.688259\pi\)
−0.557550 + 0.830143i \(0.688259\pi\)
\(174\) −49.7370 −3.77055
\(175\) −5.88258 −0.444681
\(176\) −16.0610 −1.21064
\(177\) 11.7378 0.882264
\(178\) −4.24563 −0.318223
\(179\) 20.6383 1.54258 0.771290 0.636483i \(-0.219612\pi\)
0.771290 + 0.636483i \(0.219612\pi\)
\(180\) −13.0671 −0.973962
\(181\) −7.04355 −0.523543 −0.261771 0.965130i \(-0.584307\pi\)
−0.261771 + 0.965130i \(0.584307\pi\)
\(182\) −0.443352 −0.0328634
\(183\) 20.0015 1.47856
\(184\) −38.0638 −2.80610
\(185\) 12.4312 0.913962
\(186\) −13.5289 −0.991990
\(187\) −11.9315 −0.872519
\(188\) −12.6307 −0.921185
\(189\) 8.08078 0.587790
\(190\) −22.3198 −1.61925
\(191\) −4.37479 −0.316549 −0.158274 0.987395i \(-0.550593\pi\)
−0.158274 + 0.987395i \(0.550593\pi\)
\(192\) 8.21329 0.592743
\(193\) −15.7237 −1.13182 −0.565908 0.824468i \(-0.691474\pi\)
−0.565908 + 0.824468i \(0.691474\pi\)
\(194\) 2.67361 0.191954
\(195\) 0.478884 0.0342936
\(196\) −13.7565 −0.982604
\(197\) −13.0423 −0.929225 −0.464613 0.885514i \(-0.653806\pi\)
−0.464613 + 0.885514i \(0.653806\pi\)
\(198\) 4.83379 0.343523
\(199\) 0.717136 0.0508364 0.0254182 0.999677i \(-0.491908\pi\)
0.0254182 + 0.999677i \(0.491908\pi\)
\(200\) −20.2012 −1.42844
\(201\) 4.32226 0.304869
\(202\) 37.9571 2.67065
\(203\) −19.4066 −1.36208
\(204\) 59.1785 4.14332
\(205\) −1.55552 −0.108642
\(206\) 14.2285 0.991349
\(207\) 5.46151 0.379601
\(208\) −0.725841 −0.0503280
\(209\) 5.78359 0.400059
\(210\) −29.2753 −2.02019
\(211\) 5.97442 0.411296 0.205648 0.978626i \(-0.434070\pi\)
0.205648 + 0.978626i \(0.434070\pi\)
\(212\) 12.0582 0.828164
\(213\) −11.6859 −0.800702
\(214\) −23.5505 −1.60988
\(215\) 24.3565 1.66110
\(216\) 27.7499 1.88814
\(217\) −5.27878 −0.358347
\(218\) 11.9188 0.807246
\(219\) 14.8034 1.00032
\(220\) 24.8045 1.67232
\(221\) −0.539219 −0.0362718
\(222\) 22.8082 1.53079
\(223\) −9.11526 −0.610403 −0.305202 0.952288i \(-0.598724\pi\)
−0.305202 + 0.952288i \(0.598724\pi\)
\(224\) 16.4950 1.10212
\(225\) 2.89853 0.193235
\(226\) 10.4411 0.694533
\(227\) −15.8179 −1.04987 −0.524936 0.851142i \(-0.675911\pi\)
−0.524936 + 0.851142i \(0.675911\pi\)
\(228\) −28.6857 −1.89976
\(229\) −2.04031 −0.134827 −0.0674137 0.997725i \(-0.521475\pi\)
−0.0674137 + 0.997725i \(0.521475\pi\)
\(230\) 40.0091 2.63812
\(231\) 7.58592 0.499117
\(232\) −66.6436 −4.37537
\(233\) 3.61776 0.237007 0.118504 0.992954i \(-0.462190\pi\)
0.118504 + 0.992954i \(0.462190\pi\)
\(234\) 0.218453 0.0142807
\(235\) 7.59943 0.495732
\(236\) 27.4761 1.78854
\(237\) 0.505769 0.0328532
\(238\) 32.9638 2.13672
\(239\) −6.95003 −0.449560 −0.224780 0.974410i \(-0.572166\pi\)
−0.224780 + 0.974410i \(0.572166\pi\)
\(240\) −47.9286 −3.09378
\(241\) −0.430829 −0.0277522 −0.0138761 0.999904i \(-0.504417\pi\)
−0.0138761 + 0.999904i \(0.504417\pi\)
\(242\) 19.2490 1.23737
\(243\) −9.93237 −0.637162
\(244\) 46.8203 2.99736
\(245\) 8.27678 0.528784
\(246\) −2.85399 −0.181964
\(247\) 0.261377 0.0166310
\(248\) −18.1277 −1.15111
\(249\) 13.3492 0.845971
\(250\) −15.1271 −0.956721
\(251\) 8.26910 0.521941 0.260970 0.965347i \(-0.415958\pi\)
0.260970 + 0.965347i \(0.415958\pi\)
\(252\) −9.35462 −0.589286
\(253\) −10.3673 −0.651787
\(254\) 35.2342 2.21079
\(255\) −35.6056 −2.22971
\(256\) −23.0877 −1.44298
\(257\) 9.72805 0.606819 0.303409 0.952860i \(-0.401875\pi\)
0.303409 + 0.952860i \(0.401875\pi\)
\(258\) 44.6882 2.78217
\(259\) 8.89942 0.552983
\(260\) 1.12099 0.0695207
\(261\) 9.56223 0.591887
\(262\) 51.6201 3.18910
\(263\) 8.72313 0.537891 0.268945 0.963155i \(-0.413325\pi\)
0.268945 + 0.963155i \(0.413325\pi\)
\(264\) 26.0506 1.60330
\(265\) −7.25503 −0.445673
\(266\) −15.9786 −0.979710
\(267\) 3.28301 0.200917
\(268\) 10.1177 0.618037
\(269\) 1.15133 0.0701980 0.0350990 0.999384i \(-0.488825\pi\)
0.0350990 + 0.999384i \(0.488825\pi\)
\(270\) −29.1681 −1.77512
\(271\) −12.3041 −0.747422 −0.373711 0.927545i \(-0.621915\pi\)
−0.373711 + 0.927545i \(0.621915\pi\)
\(272\) 53.9672 3.27224
\(273\) 0.342829 0.0207490
\(274\) 20.1533 1.21751
\(275\) −5.50212 −0.331790
\(276\) 51.4202 3.09513
\(277\) −15.5010 −0.931363 −0.465681 0.884952i \(-0.654191\pi\)
−0.465681 + 0.884952i \(0.654191\pi\)
\(278\) −28.2603 −1.69494
\(279\) 2.60102 0.155719
\(280\) −39.2266 −2.34424
\(281\) −16.6874 −0.995484 −0.497742 0.867325i \(-0.665837\pi\)
−0.497742 + 0.867325i \(0.665837\pi\)
\(282\) 13.9431 0.830298
\(283\) 7.52478 0.447301 0.223651 0.974669i \(-0.428203\pi\)
0.223651 + 0.974669i \(0.428203\pi\)
\(284\) −27.3547 −1.62320
\(285\) 17.2592 1.02235
\(286\) −0.414678 −0.0245204
\(287\) −1.11358 −0.0657328
\(288\) −8.12761 −0.478924
\(289\) 23.0916 1.35833
\(290\) 70.0496 4.11345
\(291\) −2.06742 −0.121194
\(292\) 34.6522 2.02787
\(293\) −6.22398 −0.363609 −0.181804 0.983335i \(-0.558194\pi\)
−0.181804 + 0.983335i \(0.558194\pi\)
\(294\) 15.1859 0.885658
\(295\) −16.5314 −0.962497
\(296\) 30.5612 1.77633
\(297\) 7.55815 0.438568
\(298\) 21.6310 1.25305
\(299\) −0.468528 −0.0270957
\(300\) 27.2897 1.57557
\(301\) 17.4367 1.00503
\(302\) 50.3188 2.89552
\(303\) −29.3510 −1.68617
\(304\) −26.1596 −1.50036
\(305\) −28.1701 −1.61302
\(306\) −16.2422 −0.928507
\(307\) 10.0546 0.573845 0.286922 0.957954i \(-0.407368\pi\)
0.286922 + 0.957954i \(0.407368\pi\)
\(308\) 17.7574 1.01182
\(309\) −11.0025 −0.625908
\(310\) 19.0541 1.08220
\(311\) 17.1724 0.973759 0.486880 0.873469i \(-0.338135\pi\)
0.486880 + 0.873469i \(0.338135\pi\)
\(312\) 1.17730 0.0666514
\(313\) 33.9047 1.91641 0.958203 0.286089i \(-0.0923552\pi\)
0.958203 + 0.286089i \(0.0923552\pi\)
\(314\) 32.2847 1.82193
\(315\) 5.62835 0.317122
\(316\) 1.18392 0.0666008
\(317\) −7.02071 −0.394322 −0.197161 0.980371i \(-0.563172\pi\)
−0.197161 + 0.980371i \(0.563172\pi\)
\(318\) −13.3112 −0.746454
\(319\) −18.1515 −1.01629
\(320\) −11.5676 −0.646648
\(321\) 18.2108 1.01643
\(322\) 28.6422 1.59617
\(323\) −19.4337 −1.08132
\(324\) −51.4169 −2.85649
\(325\) −0.248657 −0.0137930
\(326\) −41.7307 −2.31125
\(327\) −9.21646 −0.509671
\(328\) −3.82412 −0.211152
\(329\) 5.44037 0.299938
\(330\) −27.3819 −1.50733
\(331\) 6.34872 0.348957 0.174479 0.984661i \(-0.444176\pi\)
0.174479 + 0.984661i \(0.444176\pi\)
\(332\) 31.2483 1.71497
\(333\) −4.38501 −0.240297
\(334\) −7.92136 −0.433438
\(335\) −6.08747 −0.332594
\(336\) −34.3117 −1.87186
\(337\) −19.0227 −1.03623 −0.518115 0.855311i \(-0.673366\pi\)
−0.518115 + 0.855311i \(0.673366\pi\)
\(338\) 33.5741 1.82619
\(339\) −8.07377 −0.438507
\(340\) −83.3469 −4.52012
\(341\) −4.93737 −0.267374
\(342\) 7.87313 0.425730
\(343\) 20.0281 1.08141
\(344\) 59.8787 3.22844
\(345\) −30.9377 −1.66563
\(346\) 37.9001 2.03752
\(347\) −11.7829 −0.632537 −0.316268 0.948670i \(-0.602430\pi\)
−0.316268 + 0.948670i \(0.602430\pi\)
\(348\) 90.0285 4.82604
\(349\) −14.3263 −0.766869 −0.383434 0.923568i \(-0.625259\pi\)
−0.383434 + 0.923568i \(0.625259\pi\)
\(350\) 15.2010 0.812526
\(351\) 0.341574 0.0182319
\(352\) 15.4282 0.822327
\(353\) −34.8142 −1.85297 −0.926485 0.376331i \(-0.877186\pi\)
−0.926485 + 0.376331i \(0.877186\pi\)
\(354\) −30.3311 −1.61208
\(355\) 16.4584 0.873519
\(356\) 7.68498 0.407303
\(357\) −25.4898 −1.34906
\(358\) −53.3308 −2.81862
\(359\) 4.58096 0.241774 0.120887 0.992666i \(-0.461426\pi\)
0.120887 + 0.992666i \(0.461426\pi\)
\(360\) 19.3281 1.01868
\(361\) −9.57987 −0.504204
\(362\) 18.2010 0.956623
\(363\) −14.8846 −0.781239
\(364\) 0.802507 0.0420628
\(365\) −20.8490 −1.09129
\(366\) −51.6852 −2.70163
\(367\) 10.5221 0.549250 0.274625 0.961551i \(-0.411446\pi\)
0.274625 + 0.961551i \(0.411446\pi\)
\(368\) 46.8922 2.44442
\(369\) 0.548696 0.0285640
\(370\) −32.1231 −1.67000
\(371\) −5.19382 −0.269650
\(372\) 24.4886 1.26968
\(373\) −6.90087 −0.357314 −0.178657 0.983911i \(-0.557175\pi\)
−0.178657 + 0.983911i \(0.557175\pi\)
\(374\) 30.8318 1.59428
\(375\) 11.6973 0.604045
\(376\) 18.6826 0.963482
\(377\) −0.820317 −0.0422485
\(378\) −20.8813 −1.07402
\(379\) 24.6228 1.26479 0.632395 0.774646i \(-0.282072\pi\)
0.632395 + 0.774646i \(0.282072\pi\)
\(380\) 40.4009 2.07252
\(381\) −27.2454 −1.39583
\(382\) 11.3047 0.578401
\(383\) 29.9598 1.53087 0.765437 0.643511i \(-0.222523\pi\)
0.765437 + 0.643511i \(0.222523\pi\)
\(384\) 11.4961 0.586656
\(385\) −10.6840 −0.544507
\(386\) 40.6311 2.06807
\(387\) −8.59157 −0.436734
\(388\) −4.83948 −0.245687
\(389\) −7.63501 −0.387110 −0.193555 0.981089i \(-0.562002\pi\)
−0.193555 + 0.981089i \(0.562002\pi\)
\(390\) −1.23747 −0.0626616
\(391\) 34.8357 1.76171
\(392\) 20.3478 1.02772
\(393\) −39.9161 −2.01350
\(394\) 33.7021 1.69789
\(395\) −0.712325 −0.0358409
\(396\) −8.74960 −0.439684
\(397\) 8.76841 0.440074 0.220037 0.975492i \(-0.429382\pi\)
0.220037 + 0.975492i \(0.429382\pi\)
\(398\) −1.85313 −0.0928888
\(399\) 12.3557 0.618560
\(400\) 24.8865 1.24433
\(401\) 10.0800 0.503373 0.251687 0.967809i \(-0.419015\pi\)
0.251687 + 0.967809i \(0.419015\pi\)
\(402\) −11.1690 −0.557059
\(403\) −0.223134 −0.0111151
\(404\) −68.7058 −3.41824
\(405\) 30.9358 1.53721
\(406\) 50.1480 2.48880
\(407\) 8.32385 0.412598
\(408\) −87.5337 −4.33356
\(409\) −14.0993 −0.697165 −0.348582 0.937278i \(-0.613337\pi\)
−0.348582 + 0.937278i \(0.613337\pi\)
\(410\) 4.01956 0.198512
\(411\) −15.5839 −0.768698
\(412\) −25.7549 −1.26885
\(413\) −11.8347 −0.582349
\(414\) −14.1129 −0.693611
\(415\) −18.8010 −0.922904
\(416\) 0.697245 0.0341852
\(417\) 21.8528 1.07013
\(418\) −14.9452 −0.730992
\(419\) −27.7498 −1.35567 −0.677834 0.735215i \(-0.737081\pi\)
−0.677834 + 0.735215i \(0.737081\pi\)
\(420\) 52.9910 2.58570
\(421\) −32.5882 −1.58825 −0.794127 0.607752i \(-0.792071\pi\)
−0.794127 + 0.607752i \(0.792071\pi\)
\(422\) −15.4383 −0.751525
\(423\) −2.68064 −0.130337
\(424\) −17.8359 −0.866189
\(425\) 18.4879 0.896796
\(426\) 30.1970 1.46305
\(427\) −20.1668 −0.975939
\(428\) 42.6285 2.06053
\(429\) 0.320657 0.0154814
\(430\) −62.9388 −3.03518
\(431\) −37.2013 −1.79193 −0.895963 0.444129i \(-0.853513\pi\)
−0.895963 + 0.444129i \(0.853513\pi\)
\(432\) −34.1861 −1.64478
\(433\) −24.0137 −1.15403 −0.577014 0.816735i \(-0.695782\pi\)
−0.577014 + 0.816735i \(0.695782\pi\)
\(434\) 13.6407 0.654776
\(435\) −54.1670 −2.59711
\(436\) −21.5742 −1.03322
\(437\) −16.8860 −0.807765
\(438\) −38.2528 −1.82779
\(439\) −15.4176 −0.735844 −0.367922 0.929857i \(-0.619931\pi\)
−0.367922 + 0.929857i \(0.619931\pi\)
\(440\) −36.6896 −1.74911
\(441\) −2.91957 −0.139027
\(442\) 1.39338 0.0662762
\(443\) −24.2718 −1.15319 −0.576594 0.817031i \(-0.695618\pi\)
−0.576594 + 0.817031i \(0.695618\pi\)
\(444\) −41.2850 −1.95930
\(445\) −4.62378 −0.219188
\(446\) 23.5544 1.11533
\(447\) −16.7266 −0.791139
\(448\) −8.28115 −0.391248
\(449\) −20.7160 −0.977651 −0.488825 0.872382i \(-0.662574\pi\)
−0.488825 + 0.872382i \(0.662574\pi\)
\(450\) −7.48998 −0.353081
\(451\) −1.04156 −0.0490452
\(452\) −18.8994 −0.888951
\(453\) −38.9098 −1.82814
\(454\) 40.8745 1.91834
\(455\) −0.482840 −0.0226359
\(456\) 42.4304 1.98698
\(457\) 30.5125 1.42731 0.713656 0.700496i \(-0.247038\pi\)
0.713656 + 0.700496i \(0.247038\pi\)
\(458\) 5.27229 0.246358
\(459\) −25.3965 −1.18541
\(460\) −72.4201 −3.37661
\(461\) −1.17667 −0.0548029 −0.0274014 0.999625i \(-0.508723\pi\)
−0.0274014 + 0.999625i \(0.508723\pi\)
\(462\) −19.6025 −0.911992
\(463\) −11.1730 −0.519251 −0.259626 0.965709i \(-0.583599\pi\)
−0.259626 + 0.965709i \(0.583599\pi\)
\(464\) 82.1006 3.81143
\(465\) −14.7339 −0.683270
\(466\) −9.34852 −0.433062
\(467\) 10.5786 0.489518 0.244759 0.969584i \(-0.421291\pi\)
0.244759 + 0.969584i \(0.421291\pi\)
\(468\) −0.395419 −0.0182783
\(469\) −4.35797 −0.201233
\(470\) −19.6374 −0.905806
\(471\) −24.9647 −1.15031
\(472\) −40.6413 −1.87067
\(473\) 16.3089 0.749885
\(474\) −1.30694 −0.0600298
\(475\) −8.96169 −0.411191
\(476\) −59.6674 −2.73485
\(477\) 2.55915 0.117175
\(478\) 17.9593 0.821441
\(479\) −19.1889 −0.876765 −0.438383 0.898788i \(-0.644449\pi\)
−0.438383 + 0.898788i \(0.644449\pi\)
\(480\) 46.0404 2.10145
\(481\) 0.376178 0.0171523
\(482\) 1.11329 0.0507090
\(483\) −22.1481 −1.00777
\(484\) −34.8424 −1.58375
\(485\) 2.91175 0.132216
\(486\) 25.6659 1.16423
\(487\) −10.5527 −0.478187 −0.239094 0.970997i \(-0.576850\pi\)
−0.239094 + 0.970997i \(0.576850\pi\)
\(488\) −69.2541 −3.13499
\(489\) 32.2690 1.45925
\(490\) −21.3877 −0.966200
\(491\) 20.2447 0.913631 0.456816 0.889561i \(-0.348990\pi\)
0.456816 + 0.889561i \(0.348990\pi\)
\(492\) 5.16599 0.232901
\(493\) 60.9916 2.74693
\(494\) −0.675414 −0.0303883
\(495\) 5.26433 0.236614
\(496\) 22.3321 1.00274
\(497\) 11.7824 0.528514
\(498\) −34.4952 −1.54577
\(499\) 26.4653 1.18475 0.592374 0.805663i \(-0.298191\pi\)
0.592374 + 0.805663i \(0.298191\pi\)
\(500\) 27.3814 1.22453
\(501\) 6.12533 0.273660
\(502\) −21.3679 −0.953695
\(503\) −26.6438 −1.18799 −0.593993 0.804470i \(-0.702449\pi\)
−0.593993 + 0.804470i \(0.702449\pi\)
\(504\) 13.8369 0.616343
\(505\) 41.3379 1.83951
\(506\) 26.7898 1.19095
\(507\) −25.9618 −1.15300
\(508\) −63.7770 −2.82965
\(509\) 11.2536 0.498806 0.249403 0.968400i \(-0.419766\pi\)
0.249403 + 0.968400i \(0.419766\pi\)
\(510\) 92.0072 4.07415
\(511\) −14.9257 −0.660273
\(512\) 48.1535 2.12810
\(513\) 12.3105 0.543521
\(514\) −25.1379 −1.10879
\(515\) 15.4958 0.682829
\(516\) −80.8897 −3.56097
\(517\) 5.08851 0.223793
\(518\) −22.9967 −1.01042
\(519\) −29.3069 −1.28643
\(520\) −1.65811 −0.0727128
\(521\) −4.58244 −0.200760 −0.100380 0.994949i \(-0.532006\pi\)
−0.100380 + 0.994949i \(0.532006\pi\)
\(522\) −24.7094 −1.08150
\(523\) 19.4101 0.848743 0.424372 0.905488i \(-0.360495\pi\)
0.424372 + 0.905488i \(0.360495\pi\)
\(524\) −93.4370 −4.08181
\(525\) −11.7544 −0.513005
\(526\) −22.5411 −0.982840
\(527\) 16.5903 0.722685
\(528\) −32.0926 −1.39665
\(529\) 7.26872 0.316031
\(530\) 18.7475 0.814337
\(531\) 5.83133 0.253058
\(532\) 28.9227 1.25396
\(533\) −0.0470712 −0.00203888
\(534\) −8.48350 −0.367117
\(535\) −25.6481 −1.10886
\(536\) −14.9656 −0.646414
\(537\) 41.2389 1.77959
\(538\) −2.97512 −0.128267
\(539\) 5.54207 0.238714
\(540\) 52.7970 2.27202
\(541\) 1.63895 0.0704640 0.0352320 0.999379i \(-0.488783\pi\)
0.0352320 + 0.999379i \(0.488783\pi\)
\(542\) 31.7946 1.36570
\(543\) −14.0742 −0.603983
\(544\) −51.8411 −2.22267
\(545\) 12.9804 0.556021
\(546\) −0.885894 −0.0379127
\(547\) 9.76693 0.417604 0.208802 0.977958i \(-0.433044\pi\)
0.208802 + 0.977958i \(0.433044\pi\)
\(548\) −36.4794 −1.55832
\(549\) 9.93678 0.424092
\(550\) 14.2178 0.606251
\(551\) −29.5646 −1.25949
\(552\) −76.0581 −3.23725
\(553\) −0.509948 −0.0216852
\(554\) 40.0555 1.70180
\(555\) 24.8397 1.05439
\(556\) 51.1537 2.16940
\(557\) −21.6799 −0.918606 −0.459303 0.888280i \(-0.651901\pi\)
−0.459303 + 0.888280i \(0.651901\pi\)
\(558\) −6.72119 −0.284531
\(559\) 0.737047 0.0311738
\(560\) 48.3246 2.04209
\(561\) −23.8412 −1.00658
\(562\) 43.1212 1.81896
\(563\) −25.0408 −1.05535 −0.527673 0.849448i \(-0.676935\pi\)
−0.527673 + 0.849448i \(0.676935\pi\)
\(564\) −25.2382 −1.06272
\(565\) 11.3711 0.478385
\(566\) −19.4445 −0.817314
\(567\) 22.1467 0.930073
\(568\) 40.4616 1.69773
\(569\) 4.95000 0.207515 0.103757 0.994603i \(-0.466913\pi\)
0.103757 + 0.994603i \(0.466913\pi\)
\(570\) −44.5988 −1.86804
\(571\) −25.8591 −1.08217 −0.541085 0.840968i \(-0.681986\pi\)
−0.541085 + 0.840968i \(0.681986\pi\)
\(572\) 0.750604 0.0313843
\(573\) −8.74158 −0.365185
\(574\) 2.87757 0.120108
\(575\) 16.0642 0.669922
\(576\) 4.08037 0.170016
\(577\) 36.3126 1.51172 0.755858 0.654736i \(-0.227220\pi\)
0.755858 + 0.654736i \(0.227220\pi\)
\(578\) −59.6703 −2.48196
\(579\) −31.4187 −1.30572
\(580\) −126.796 −5.26492
\(581\) −13.4595 −0.558394
\(582\) 5.34234 0.221447
\(583\) −4.85791 −0.201194
\(584\) −51.2558 −2.12098
\(585\) 0.237910 0.00983637
\(586\) 16.0832 0.664389
\(587\) 21.7060 0.895905 0.447952 0.894057i \(-0.352153\pi\)
0.447952 + 0.894057i \(0.352153\pi\)
\(588\) −27.4878 −1.13358
\(589\) −8.04185 −0.331359
\(590\) 42.7183 1.75868
\(591\) −26.0608 −1.07200
\(592\) −37.6494 −1.54738
\(593\) 32.2149 1.32291 0.661453 0.749987i \(-0.269940\pi\)
0.661453 + 0.749987i \(0.269940\pi\)
\(594\) −19.5307 −0.801356
\(595\) 35.8998 1.47175
\(596\) −39.1541 −1.60381
\(597\) 1.43296 0.0586472
\(598\) 1.21071 0.0495095
\(599\) 37.2563 1.52225 0.761125 0.648605i \(-0.224647\pi\)
0.761125 + 0.648605i \(0.224647\pi\)
\(600\) −40.3655 −1.64791
\(601\) −38.6749 −1.57758 −0.788792 0.614661i \(-0.789293\pi\)
−0.788792 + 0.614661i \(0.789293\pi\)
\(602\) −45.0575 −1.83641
\(603\) 2.14730 0.0874450
\(604\) −91.0815 −3.70605
\(605\) 20.9635 0.852286
\(606\) 75.8448 3.08099
\(607\) 5.61301 0.227825 0.113913 0.993491i \(-0.463662\pi\)
0.113913 + 0.993491i \(0.463662\pi\)
\(608\) 25.1290 1.01912
\(609\) −38.7778 −1.57136
\(610\) 72.7934 2.94732
\(611\) 0.229964 0.00930336
\(612\) 29.3999 1.18842
\(613\) −24.8597 −1.00408 −0.502038 0.864846i \(-0.667416\pi\)
−0.502038 + 0.864846i \(0.667416\pi\)
\(614\) −25.9817 −1.04854
\(615\) −3.10819 −0.125334
\(616\) −26.2658 −1.05828
\(617\) 47.7644 1.92292 0.961462 0.274938i \(-0.0886572\pi\)
0.961462 + 0.274938i \(0.0886572\pi\)
\(618\) 28.4311 1.14367
\(619\) −40.9876 −1.64743 −0.823716 0.567003i \(-0.808103\pi\)
−0.823716 + 0.567003i \(0.808103\pi\)
\(620\) −34.4897 −1.38514
\(621\) −22.0670 −0.885519
\(622\) −44.3747 −1.77926
\(623\) −3.31013 −0.132618
\(624\) −1.45036 −0.0580607
\(625\) −31.0737 −1.24295
\(626\) −87.6119 −3.50168
\(627\) 11.5566 0.461526
\(628\) −58.4382 −2.33194
\(629\) −27.9693 −1.11521
\(630\) −14.5440 −0.579448
\(631\) −2.61434 −0.104075 −0.0520376 0.998645i \(-0.516572\pi\)
−0.0520376 + 0.998645i \(0.516572\pi\)
\(632\) −1.75120 −0.0696588
\(633\) 11.9379 0.474490
\(634\) 18.1420 0.720509
\(635\) 38.3724 1.52276
\(636\) 24.0945 0.955407
\(637\) 0.250462 0.00992366
\(638\) 46.9046 1.85697
\(639\) −5.80555 −0.229664
\(640\) −16.1910 −0.640007
\(641\) 28.2018 1.11391 0.556953 0.830544i \(-0.311971\pi\)
0.556953 + 0.830544i \(0.311971\pi\)
\(642\) −47.0579 −1.85723
\(643\) 45.8642 1.80871 0.904354 0.426783i \(-0.140353\pi\)
0.904354 + 0.426783i \(0.140353\pi\)
\(644\) −51.8451 −2.04298
\(645\) 48.6685 1.91632
\(646\) 50.2179 1.97580
\(647\) 18.7169 0.735838 0.367919 0.929858i \(-0.380070\pi\)
0.367919 + 0.929858i \(0.380070\pi\)
\(648\) 76.0532 2.98765
\(649\) −11.0693 −0.434509
\(650\) 0.642545 0.0252027
\(651\) −10.5479 −0.413406
\(652\) 75.5363 2.95823
\(653\) −40.3245 −1.57802 −0.789011 0.614380i \(-0.789406\pi\)
−0.789011 + 0.614380i \(0.789406\pi\)
\(654\) 23.8159 0.931276
\(655\) 56.2178 2.19661
\(656\) 4.71107 0.183936
\(657\) 7.35433 0.286920
\(658\) −14.0583 −0.548049
\(659\) −47.5350 −1.85170 −0.925850 0.377891i \(-0.876649\pi\)
−0.925850 + 0.377891i \(0.876649\pi\)
\(660\) 49.5638 1.92927
\(661\) 17.4038 0.676931 0.338465 0.940979i \(-0.390092\pi\)
0.338465 + 0.940979i \(0.390092\pi\)
\(662\) −16.4055 −0.637618
\(663\) −1.07745 −0.0418448
\(664\) −46.2208 −1.79371
\(665\) −17.4018 −0.674812
\(666\) 11.3312 0.439074
\(667\) 52.9957 2.05200
\(668\) 14.3384 0.554769
\(669\) −18.2139 −0.704189
\(670\) 15.7304 0.607719
\(671\) −18.8625 −0.728178
\(672\) 32.9600 1.27146
\(673\) 36.2160 1.39602 0.698012 0.716086i \(-0.254068\pi\)
0.698012 + 0.716086i \(0.254068\pi\)
\(674\) 49.1558 1.89341
\(675\) −11.7114 −0.450771
\(676\) −60.7722 −2.33739
\(677\) 27.2841 1.04861 0.524307 0.851529i \(-0.324324\pi\)
0.524307 + 0.851529i \(0.324324\pi\)
\(678\) 20.8632 0.801245
\(679\) 2.08450 0.0799957
\(680\) 123.282 4.72766
\(681\) −31.6069 −1.21118
\(682\) 12.7585 0.488548
\(683\) −24.8704 −0.951638 −0.475819 0.879543i \(-0.657848\pi\)
−0.475819 + 0.879543i \(0.657848\pi\)
\(684\) −14.2511 −0.544904
\(685\) 21.9484 0.838604
\(686\) −51.7538 −1.97597
\(687\) −4.07689 −0.155543
\(688\) −73.7666 −2.81233
\(689\) −0.219543 −0.00836390
\(690\) 79.9452 3.04346
\(691\) 10.1426 0.385844 0.192922 0.981214i \(-0.438203\pi\)
0.192922 + 0.981214i \(0.438203\pi\)
\(692\) −68.6027 −2.60788
\(693\) 3.76870 0.143161
\(694\) 30.4477 1.15578
\(695\) −30.7774 −1.16745
\(696\) −133.166 −5.04763
\(697\) 3.49980 0.132564
\(698\) 37.0201 1.40123
\(699\) 7.22891 0.273422
\(700\) −27.5151 −1.03997
\(701\) −13.6799 −0.516682 −0.258341 0.966054i \(-0.583176\pi\)
−0.258341 + 0.966054i \(0.583176\pi\)
\(702\) −0.882650 −0.0333135
\(703\) 13.5576 0.511336
\(704\) −7.74556 −0.291922
\(705\) 15.1850 0.571899
\(706\) 89.9620 3.38577
\(707\) 29.5935 1.11298
\(708\) 54.9021 2.06335
\(709\) −39.7672 −1.49349 −0.746745 0.665111i \(-0.768384\pi\)
−0.746745 + 0.665111i \(0.768384\pi\)
\(710\) −42.5294 −1.59610
\(711\) 0.251267 0.00942324
\(712\) −11.3672 −0.426004
\(713\) 14.4153 0.539858
\(714\) 65.8673 2.46502
\(715\) −0.451612 −0.0168893
\(716\) 96.5335 3.60763
\(717\) −13.8874 −0.518633
\(718\) −11.8375 −0.441771
\(719\) 12.3541 0.460729 0.230365 0.973104i \(-0.426008\pi\)
0.230365 + 0.973104i \(0.426008\pi\)
\(720\) −23.8110 −0.887383
\(721\) 11.0934 0.413139
\(722\) 24.7550 0.921286
\(723\) −0.860872 −0.0320162
\(724\) −32.9454 −1.22441
\(725\) 28.1258 1.04457
\(726\) 38.4628 1.42749
\(727\) −6.08668 −0.225743 −0.112871 0.993610i \(-0.536005\pi\)
−0.112871 + 0.993610i \(0.536005\pi\)
\(728\) −1.18703 −0.0439941
\(729\) 13.1313 0.486346
\(730\) 53.8753 1.99401
\(731\) −54.8004 −2.02687
\(732\) 93.5550 3.45789
\(733\) −27.3540 −1.01034 −0.505172 0.863019i \(-0.668571\pi\)
−0.505172 + 0.863019i \(0.668571\pi\)
\(734\) −27.1898 −1.00359
\(735\) 16.5384 0.610030
\(736\) −45.0447 −1.66037
\(737\) −4.07612 −0.150146
\(738\) −1.41787 −0.0521924
\(739\) −27.2589 −1.00273 −0.501367 0.865235i \(-0.667169\pi\)
−0.501367 + 0.865235i \(0.667169\pi\)
\(740\) 58.1457 2.13748
\(741\) 0.522276 0.0191863
\(742\) 13.4212 0.492707
\(743\) −21.8287 −0.800818 −0.400409 0.916336i \(-0.631132\pi\)
−0.400409 + 0.916336i \(0.631132\pi\)
\(744\) −36.2223 −1.32797
\(745\) 23.5577 0.863086
\(746\) 17.8323 0.652887
\(747\) 6.63190 0.242648
\(748\) −55.8084 −2.04056
\(749\) −18.3613 −0.670907
\(750\) −30.2265 −1.10372
\(751\) 49.8303 1.81833 0.909166 0.416433i \(-0.136720\pi\)
0.909166 + 0.416433i \(0.136720\pi\)
\(752\) −23.0158 −0.839298
\(753\) 16.5231 0.602135
\(754\) 2.11975 0.0771968
\(755\) 54.8006 1.99440
\(756\) 37.7970 1.37466
\(757\) −2.35011 −0.0854162 −0.0427081 0.999088i \(-0.513599\pi\)
−0.0427081 + 0.999088i \(0.513599\pi\)
\(758\) −63.6270 −2.31104
\(759\) −20.7157 −0.751931
\(760\) −59.7589 −2.16768
\(761\) −49.6973 −1.80153 −0.900763 0.434311i \(-0.856992\pi\)
−0.900763 + 0.434311i \(0.856992\pi\)
\(762\) 70.4040 2.55047
\(763\) 9.29261 0.336415
\(764\) −20.4626 −0.740311
\(765\) −17.6889 −0.639544
\(766\) −77.4181 −2.79723
\(767\) −0.500254 −0.0180631
\(768\) −46.1332 −1.66469
\(769\) −21.7073 −0.782785 −0.391392 0.920224i \(-0.628007\pi\)
−0.391392 + 0.920224i \(0.628007\pi\)
\(770\) 27.6082 0.994929
\(771\) 19.4383 0.700054
\(772\) −73.5459 −2.64697
\(773\) −32.2112 −1.15856 −0.579278 0.815130i \(-0.696666\pi\)
−0.579278 + 0.815130i \(0.696666\pi\)
\(774\) 22.2012 0.798005
\(775\) 7.65048 0.274813
\(776\) 7.15831 0.256968
\(777\) 17.7826 0.637947
\(778\) 19.7294 0.707332
\(779\) −1.69646 −0.0607822
\(780\) 2.23993 0.0802022
\(781\) 11.0204 0.394340
\(782\) −90.0176 −3.21902
\(783\) −38.6358 −1.38073
\(784\) −25.0672 −0.895258
\(785\) 35.1602 1.25492
\(786\) 103.146 3.67909
\(787\) −45.6872 −1.62857 −0.814287 0.580462i \(-0.802872\pi\)
−0.814287 + 0.580462i \(0.802872\pi\)
\(788\) −61.0039 −2.17317
\(789\) 17.4303 0.620536
\(790\) 1.84069 0.0654889
\(791\) 8.14048 0.289442
\(792\) 12.9420 0.459872
\(793\) −0.852449 −0.0302714
\(794\) −22.6582 −0.804108
\(795\) −14.4968 −0.514148
\(796\) 3.35432 0.118891
\(797\) −24.0236 −0.850960 −0.425480 0.904968i \(-0.639895\pi\)
−0.425480 + 0.904968i \(0.639895\pi\)
\(798\) −31.9280 −1.13024
\(799\) −17.0981 −0.604889
\(800\) −23.9061 −0.845208
\(801\) 1.63100 0.0576286
\(802\) −26.0475 −0.919769
\(803\) −13.9603 −0.492650
\(804\) 20.2169 0.712995
\(805\) 31.1934 1.09942
\(806\) 0.576593 0.0203096
\(807\) 2.30056 0.0809837
\(808\) 101.626 3.57519
\(809\) 6.45845 0.227067 0.113534 0.993534i \(-0.463783\pi\)
0.113534 + 0.993534i \(0.463783\pi\)
\(810\) −79.9400 −2.80881
\(811\) −9.76960 −0.343057 −0.171529 0.985179i \(-0.554871\pi\)
−0.171529 + 0.985179i \(0.554871\pi\)
\(812\) −90.7724 −3.18549
\(813\) −24.5857 −0.862260
\(814\) −21.5094 −0.753903
\(815\) −45.4476 −1.59196
\(816\) 107.836 3.77501
\(817\) 26.5635 0.929339
\(818\) 36.4335 1.27387
\(819\) 0.170318 0.00595140
\(820\) −7.27577 −0.254081
\(821\) 55.1034 1.92312 0.961561 0.274592i \(-0.0885427\pi\)
0.961561 + 0.274592i \(0.0885427\pi\)
\(822\) 40.2699 1.40457
\(823\) 36.0072 1.25513 0.627566 0.778564i \(-0.284051\pi\)
0.627566 + 0.778564i \(0.284051\pi\)
\(824\) 38.0954 1.32711
\(825\) −10.9942 −0.382769
\(826\) 30.5817 1.06407
\(827\) 0.485395 0.0168788 0.00843942 0.999964i \(-0.497314\pi\)
0.00843942 + 0.999964i \(0.497314\pi\)
\(828\) 25.5456 0.887772
\(829\) −37.9508 −1.31808 −0.659042 0.752106i \(-0.729038\pi\)
−0.659042 + 0.752106i \(0.729038\pi\)
\(830\) 48.5830 1.68634
\(831\) −30.9736 −1.07446
\(832\) −0.350044 −0.0121356
\(833\) −18.6222 −0.645219
\(834\) −56.4689 −1.95536
\(835\) −8.62690 −0.298546
\(836\) 27.0521 0.935616
\(837\) −10.5093 −0.363255
\(838\) 71.7074 2.47709
\(839\) 13.2483 0.457383 0.228691 0.973499i \(-0.426555\pi\)
0.228691 + 0.973499i \(0.426555\pi\)
\(840\) −78.3815 −2.70442
\(841\) 63.7869 2.19955
\(842\) 84.2101 2.90207
\(843\) −33.3442 −1.14844
\(844\) 27.9447 0.961897
\(845\) 36.5645 1.25786
\(846\) 6.92694 0.238153
\(847\) 15.0076 0.515667
\(848\) 21.9727 0.754546
\(849\) 15.0358 0.516027
\(850\) −47.7740 −1.63864
\(851\) −24.3026 −0.833082
\(852\) −54.6594 −1.87260
\(853\) 35.3907 1.21175 0.605877 0.795558i \(-0.292822\pi\)
0.605877 + 0.795558i \(0.292822\pi\)
\(854\) 52.1123 1.78325
\(855\) 8.57438 0.293238
\(856\) −63.0538 −2.15514
\(857\) 1.47580 0.0504123 0.0252062 0.999682i \(-0.491976\pi\)
0.0252062 + 0.999682i \(0.491976\pi\)
\(858\) −0.828598 −0.0282879
\(859\) −18.6000 −0.634625 −0.317313 0.948321i \(-0.602780\pi\)
−0.317313 + 0.948321i \(0.602780\pi\)
\(860\) 113.925 3.88481
\(861\) −2.22513 −0.0758324
\(862\) 96.1307 3.27422
\(863\) 20.6823 0.704035 0.352018 0.935993i \(-0.385496\pi\)
0.352018 + 0.935993i \(0.385496\pi\)
\(864\) 32.8393 1.11721
\(865\) 41.2758 1.40342
\(866\) 62.0531 2.10865
\(867\) 46.1411 1.56703
\(868\) −24.6909 −0.838065
\(869\) −0.476967 −0.0161800
\(870\) 139.971 4.74547
\(871\) −0.184211 −0.00624176
\(872\) 31.9114 1.08066
\(873\) −1.02710 −0.0347619
\(874\) 43.6344 1.47596
\(875\) −11.7939 −0.398708
\(876\) 69.2411 2.33944
\(877\) 34.0967 1.15136 0.575682 0.817674i \(-0.304737\pi\)
0.575682 + 0.817674i \(0.304737\pi\)
\(878\) 39.8402 1.34454
\(879\) −12.4366 −0.419475
\(880\) 45.1992 1.52366
\(881\) −19.9193 −0.671100 −0.335550 0.942022i \(-0.608922\pi\)
−0.335550 + 0.942022i \(0.608922\pi\)
\(882\) 7.54436 0.254032
\(883\) −49.9854 −1.68214 −0.841071 0.540925i \(-0.818074\pi\)
−0.841071 + 0.540925i \(0.818074\pi\)
\(884\) −2.52214 −0.0848287
\(885\) −33.0327 −1.11038
\(886\) 62.7199 2.10712
\(887\) 43.2001 1.45052 0.725258 0.688477i \(-0.241720\pi\)
0.725258 + 0.688477i \(0.241720\pi\)
\(888\) 61.0666 2.04926
\(889\) 27.4705 0.921332
\(890\) 11.9482 0.400503
\(891\) 20.7143 0.693956
\(892\) −42.6357 −1.42755
\(893\) 8.28802 0.277348
\(894\) 43.2225 1.44558
\(895\) −58.0809 −1.94143
\(896\) −11.5911 −0.387230
\(897\) −0.936200 −0.0312588
\(898\) 53.5316 1.78637
\(899\) 25.2389 0.841765
\(900\) 13.5575 0.451918
\(901\) 16.3233 0.543807
\(902\) 2.69146 0.0896159
\(903\) 34.8415 1.15945
\(904\) 27.9550 0.929768
\(905\) 19.8221 0.658910
\(906\) 100.546 3.34040
\(907\) 15.3488 0.509647 0.254824 0.966988i \(-0.417983\pi\)
0.254824 + 0.966988i \(0.417983\pi\)
\(908\) −73.9866 −2.45533
\(909\) −14.5816 −0.483641
\(910\) 1.24769 0.0413606
\(911\) −47.9111 −1.58737 −0.793683 0.608331i \(-0.791839\pi\)
−0.793683 + 0.608331i \(0.791839\pi\)
\(912\) −52.2715 −1.73088
\(913\) −12.5890 −0.416635
\(914\) −78.8462 −2.60800
\(915\) −56.2888 −1.86085
\(916\) −9.54332 −0.315320
\(917\) 40.2459 1.32904
\(918\) 65.6261 2.16599
\(919\) −54.6443 −1.80255 −0.901274 0.433249i \(-0.857367\pi\)
−0.901274 + 0.433249i \(0.857367\pi\)
\(920\) 107.120 3.53165
\(921\) 20.0908 0.662014
\(922\) 3.04058 0.100136
\(923\) 0.498042 0.0163933
\(924\) 35.4823 1.16728
\(925\) −12.8978 −0.424078
\(926\) 28.8716 0.948781
\(927\) −5.46604 −0.179528
\(928\) −78.8661 −2.58891
\(929\) 38.9931 1.27932 0.639662 0.768657i \(-0.279075\pi\)
0.639662 + 0.768657i \(0.279075\pi\)
\(930\) 38.0735 1.24848
\(931\) 9.02675 0.295840
\(932\) 16.9217 0.554288
\(933\) 34.3135 1.12337
\(934\) −27.3357 −0.894452
\(935\) 33.5780 1.09812
\(936\) 0.584884 0.0191175
\(937\) 29.0815 0.950053 0.475026 0.879972i \(-0.342439\pi\)
0.475026 + 0.879972i \(0.342439\pi\)
\(938\) 11.2613 0.367694
\(939\) 67.7474 2.21085
\(940\) 35.5455 1.15937
\(941\) 10.3075 0.336016 0.168008 0.985786i \(-0.446267\pi\)
0.168008 + 0.985786i \(0.446267\pi\)
\(942\) 64.5104 2.10186
\(943\) 3.04098 0.0990279
\(944\) 50.0674 1.62956
\(945\) −22.7411 −0.739769
\(946\) −42.1433 −1.37020
\(947\) −27.4293 −0.891331 −0.445666 0.895199i \(-0.647033\pi\)
−0.445666 + 0.895199i \(0.647033\pi\)
\(948\) 2.36568 0.0768337
\(949\) −0.630908 −0.0204801
\(950\) 23.1576 0.751331
\(951\) −14.0286 −0.454908
\(952\) 88.2569 2.86042
\(953\) 32.3115 1.04667 0.523336 0.852126i \(-0.324687\pi\)
0.523336 + 0.852126i \(0.324687\pi\)
\(954\) −6.61301 −0.214104
\(955\) 12.3116 0.398395
\(956\) −32.5080 −1.05138
\(957\) −36.2698 −1.17244
\(958\) 49.5855 1.60203
\(959\) 15.7127 0.507389
\(960\) −23.1140 −0.746003
\(961\) −24.1348 −0.778541
\(962\) −0.972069 −0.0313408
\(963\) 9.04715 0.291540
\(964\) −2.01516 −0.0649039
\(965\) 44.2500 1.42446
\(966\) 57.2322 1.84141
\(967\) 41.6259 1.33860 0.669299 0.742993i \(-0.266594\pi\)
0.669299 + 0.742993i \(0.266594\pi\)
\(968\) 51.5371 1.65646
\(969\) −38.8319 −1.24746
\(970\) −7.52415 −0.241586
\(971\) −1.83879 −0.0590094 −0.0295047 0.999565i \(-0.509393\pi\)
−0.0295047 + 0.999565i \(0.509393\pi\)
\(972\) −46.4576 −1.49013
\(973\) −22.0333 −0.706355
\(974\) 27.2688 0.873748
\(975\) −0.496859 −0.0159122
\(976\) 85.3165 2.73092
\(977\) 27.9225 0.893319 0.446659 0.894704i \(-0.352614\pi\)
0.446659 + 0.894704i \(0.352614\pi\)
\(978\) −83.3851 −2.66636
\(979\) −3.09605 −0.0989501
\(980\) 38.7138 1.23667
\(981\) −4.57875 −0.146188
\(982\) −52.3137 −1.66940
\(983\) 11.9973 0.382656 0.191328 0.981526i \(-0.438721\pi\)
0.191328 + 0.981526i \(0.438721\pi\)
\(984\) −7.64126 −0.243594
\(985\) 36.7039 1.16948
\(986\) −157.606 −5.01921
\(987\) 10.8708 0.346022
\(988\) 1.22256 0.0388949
\(989\) −47.6161 −1.51410
\(990\) −13.6034 −0.432344
\(991\) 18.8382 0.598415 0.299208 0.954188i \(-0.403278\pi\)
0.299208 + 0.954188i \(0.403278\pi\)
\(992\) −21.4523 −0.681112
\(993\) 12.6858 0.402573
\(994\) −30.4465 −0.965705
\(995\) −2.01818 −0.0639806
\(996\) 62.4394 1.97847
\(997\) −16.8183 −0.532641 −0.266320 0.963885i \(-0.585808\pi\)
−0.266320 + 0.963885i \(0.585808\pi\)
\(998\) −68.3880 −2.16478
\(999\) 17.7175 0.560556
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 4019.2.a.a.1.7 149
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4019.2.a.a.1.7 149 1.1 even 1 trivial