Properties

Label 4027.2.a.b.1.14
Level $4027$
Weight $2$
Character 4027.1
Self dual yes
Analytic conductor $32.156$
Analytic rank $1$
Dimension $159$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4027,2,Mod(1,4027)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4027, 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("4027.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4027 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4027.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: \(32.1557568940\)
Analytic rank: \(1\)
Dimension: \(159\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) \(=\) 4027.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.54982 q^{2} +3.26459 q^{3} +4.50158 q^{4} -1.30834 q^{5} -8.32411 q^{6} +3.58480 q^{7} -6.37858 q^{8} +7.65753 q^{9} +O(q^{10})\) \(q-2.54982 q^{2} +3.26459 q^{3} +4.50158 q^{4} -1.30834 q^{5} -8.32411 q^{6} +3.58480 q^{7} -6.37858 q^{8} +7.65753 q^{9} +3.33603 q^{10} +0.411280 q^{11} +14.6958 q^{12} -6.00076 q^{13} -9.14058 q^{14} -4.27119 q^{15} +7.26106 q^{16} -6.43986 q^{17} -19.5253 q^{18} -6.79506 q^{19} -5.88959 q^{20} +11.7029 q^{21} -1.04869 q^{22} +2.21132 q^{23} -20.8234 q^{24} -3.28825 q^{25} +15.3008 q^{26} +15.2049 q^{27} +16.1372 q^{28} -9.83730 q^{29} +10.8908 q^{30} -0.964118 q^{31} -5.75724 q^{32} +1.34266 q^{33} +16.4205 q^{34} -4.69013 q^{35} +34.4710 q^{36} +4.83938 q^{37} +17.3262 q^{38} -19.5900 q^{39} +8.34534 q^{40} -8.99880 q^{41} -29.8402 q^{42} +9.23238 q^{43} +1.85141 q^{44} -10.0186 q^{45} -5.63846 q^{46} -1.06569 q^{47} +23.7044 q^{48} +5.85076 q^{49} +8.38444 q^{50} -21.0235 q^{51} -27.0129 q^{52} -10.5409 q^{53} -38.7698 q^{54} -0.538094 q^{55} -22.8659 q^{56} -22.1831 q^{57} +25.0833 q^{58} -11.4102 q^{59} -19.2271 q^{60} -11.8226 q^{61} +2.45833 q^{62} +27.4507 q^{63} +0.157808 q^{64} +7.85102 q^{65} -3.42354 q^{66} +4.27373 q^{67} -28.9896 q^{68} +7.21903 q^{69} +11.9590 q^{70} -1.28532 q^{71} -48.8441 q^{72} -2.34435 q^{73} -12.3395 q^{74} -10.7348 q^{75} -30.5885 q^{76} +1.47435 q^{77} +49.9509 q^{78} -0.336788 q^{79} -9.49993 q^{80} +26.6652 q^{81} +22.9453 q^{82} -1.65711 q^{83} +52.6814 q^{84} +8.42553 q^{85} -23.5409 q^{86} -32.1147 q^{87} -2.62338 q^{88} +10.6011 q^{89} +25.5457 q^{90} -21.5115 q^{91} +9.95442 q^{92} -3.14745 q^{93} +2.71732 q^{94} +8.89024 q^{95} -18.7950 q^{96} +5.44847 q^{97} -14.9184 q^{98} +3.14939 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9} - 23 q^{10} - 33 q^{11} - 57 q^{12} - 90 q^{13} - 28 q^{14} - 22 q^{15} + 130 q^{16} - 145 q^{17} - 50 q^{18} - 28 q^{19} - 121 q^{20} - 69 q^{21} - 26 q^{22} - 79 q^{23} - 62 q^{24} + 123 q^{25} - 40 q^{26} - 70 q^{27} - 43 q^{28} - 109 q^{29} - 43 q^{30} - 21 q^{31} - 139 q^{32} - 83 q^{33} - 93 q^{35} + 75 q^{36} - 65 q^{37} - 122 q^{38} - 18 q^{39} - 43 q^{40} - 71 q^{41} - 88 q^{42} - 72 q^{43} - 79 q^{44} - 181 q^{45} - 11 q^{46} - 114 q^{47} - 118 q^{48} + 118 q^{49} - 77 q^{50} - 29 q^{51} - 169 q^{52} - 220 q^{53} - 80 q^{54} - 37 q^{55} - 72 q^{56} - 90 q^{57} - 8 q^{58} - 60 q^{59} - 42 q^{60} - 108 q^{61} - 152 q^{62} - 65 q^{63} + 114 q^{64} - 81 q^{65} - 40 q^{66} - 50 q^{67} - 319 q^{68} - 103 q^{69} + 4 q^{70} - 7 q^{71} - 129 q^{72} - 94 q^{73} - 79 q^{74} - 59 q^{75} - 46 q^{76} - 329 q^{77} + 8 q^{78} - 18 q^{79} - 190 q^{80} + 59 q^{81} - 56 q^{82} - 201 q^{83} - 71 q^{84} - 26 q^{85} - 52 q^{86} - 126 q^{87} - 66 q^{88} - 114 q^{89} - 33 q^{90} - 30 q^{91} - 204 q^{92} - 125 q^{93} + 9 q^{94} - 84 q^{95} - 88 q^{96} - 56 q^{97} - 110 q^{98} - 46 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.54982 −1.80299 −0.901497 0.432785i \(-0.857531\pi\)
−0.901497 + 0.432785i \(0.857531\pi\)
\(3\) 3.26459 1.88481 0.942405 0.334474i \(-0.108559\pi\)
0.942405 + 0.334474i \(0.108559\pi\)
\(4\) 4.50158 2.25079
\(5\) −1.30834 −0.585107 −0.292554 0.956249i \(-0.594505\pi\)
−0.292554 + 0.956249i \(0.594505\pi\)
\(6\) −8.32411 −3.39830
\(7\) 3.58480 1.35493 0.677463 0.735557i \(-0.263080\pi\)
0.677463 + 0.735557i \(0.263080\pi\)
\(8\) −6.37858 −2.25517
\(9\) 7.65753 2.55251
\(10\) 3.33603 1.05494
\(11\) 0.411280 0.124006 0.0620028 0.998076i \(-0.480251\pi\)
0.0620028 + 0.998076i \(0.480251\pi\)
\(12\) 14.6958 4.24231
\(13\) −6.00076 −1.66431 −0.832155 0.554543i \(-0.812893\pi\)
−0.832155 + 0.554543i \(0.812893\pi\)
\(14\) −9.14058 −2.44292
\(15\) −4.27119 −1.10282
\(16\) 7.26106 1.81527
\(17\) −6.43986 −1.56190 −0.780948 0.624596i \(-0.785264\pi\)
−0.780948 + 0.624596i \(0.785264\pi\)
\(18\) −19.5253 −4.60216
\(19\) −6.79506 −1.55889 −0.779447 0.626468i \(-0.784500\pi\)
−0.779447 + 0.626468i \(0.784500\pi\)
\(20\) −5.88959 −1.31695
\(21\) 11.7029 2.55378
\(22\) −1.04869 −0.223581
\(23\) 2.21132 0.461091 0.230546 0.973062i \(-0.425949\pi\)
0.230546 + 0.973062i \(0.425949\pi\)
\(24\) −20.8234 −4.25056
\(25\) −3.28825 −0.657650
\(26\) 15.3008 3.00074
\(27\) 15.2049 2.92619
\(28\) 16.1372 3.04965
\(29\) −9.83730 −1.82674 −0.913370 0.407131i \(-0.866529\pi\)
−0.913370 + 0.407131i \(0.866529\pi\)
\(30\) 10.8908 1.98837
\(31\) −0.964118 −0.173161 −0.0865804 0.996245i \(-0.527594\pi\)
−0.0865804 + 0.996245i \(0.527594\pi\)
\(32\) −5.75724 −1.01775
\(33\) 1.34266 0.233727
\(34\) 16.4205 2.81609
\(35\) −4.69013 −0.792776
\(36\) 34.4710 5.74516
\(37\) 4.83938 0.795589 0.397794 0.917475i \(-0.369776\pi\)
0.397794 + 0.917475i \(0.369776\pi\)
\(38\) 17.3262 2.81068
\(39\) −19.5900 −3.13691
\(40\) 8.34534 1.31951
\(41\) −8.99880 −1.40538 −0.702688 0.711498i \(-0.748017\pi\)
−0.702688 + 0.711498i \(0.748017\pi\)
\(42\) −29.8402 −4.60445
\(43\) 9.23238 1.40792 0.703962 0.710237i \(-0.251412\pi\)
0.703962 + 0.710237i \(0.251412\pi\)
\(44\) 1.85141 0.279111
\(45\) −10.0186 −1.49349
\(46\) −5.63846 −0.831345
\(47\) −1.06569 −0.155447 −0.0777236 0.996975i \(-0.524765\pi\)
−0.0777236 + 0.996975i \(0.524765\pi\)
\(48\) 23.7044 3.42143
\(49\) 5.85076 0.835823
\(50\) 8.38444 1.18574
\(51\) −21.0235 −2.94388
\(52\) −27.0129 −3.74601
\(53\) −10.5409 −1.44791 −0.723954 0.689848i \(-0.757677\pi\)
−0.723954 + 0.689848i \(0.757677\pi\)
\(54\) −38.7698 −5.27590
\(55\) −0.538094 −0.0725565
\(56\) −22.8659 −3.05558
\(57\) −22.1831 −2.93822
\(58\) 25.0833 3.29360
\(59\) −11.4102 −1.48549 −0.742743 0.669577i \(-0.766476\pi\)
−0.742743 + 0.669577i \(0.766476\pi\)
\(60\) −19.2271 −2.48221
\(61\) −11.8226 −1.51373 −0.756867 0.653569i \(-0.773271\pi\)
−0.756867 + 0.653569i \(0.773271\pi\)
\(62\) 2.45833 0.312208
\(63\) 27.4507 3.45846
\(64\) 0.157808 0.0197259
\(65\) 7.85102 0.973800
\(66\) −3.42354 −0.421409
\(67\) 4.27373 0.522119 0.261059 0.965323i \(-0.415928\pi\)
0.261059 + 0.965323i \(0.415928\pi\)
\(68\) −28.9896 −3.51550
\(69\) 7.21903 0.869070
\(70\) 11.9590 1.42937
\(71\) −1.28532 −0.152539 −0.0762695 0.997087i \(-0.524301\pi\)
−0.0762695 + 0.997087i \(0.524301\pi\)
\(72\) −48.8441 −5.75634
\(73\) −2.34435 −0.274386 −0.137193 0.990544i \(-0.543808\pi\)
−0.137193 + 0.990544i \(0.543808\pi\)
\(74\) −12.3395 −1.43444
\(75\) −10.7348 −1.23954
\(76\) −30.5885 −3.50874
\(77\) 1.47435 0.168018
\(78\) 49.9509 5.65583
\(79\) −0.336788 −0.0378916 −0.0189458 0.999821i \(-0.506031\pi\)
−0.0189458 + 0.999821i \(0.506031\pi\)
\(80\) −9.49993 −1.06212
\(81\) 26.6652 2.96280
\(82\) 22.9453 2.53389
\(83\) −1.65711 −0.181892 −0.0909460 0.995856i \(-0.528989\pi\)
−0.0909460 + 0.995856i \(0.528989\pi\)
\(84\) 52.6814 5.74802
\(85\) 8.42553 0.913877
\(86\) −23.5409 −2.53848
\(87\) −32.1147 −3.44306
\(88\) −2.62338 −0.279653
\(89\) 10.6011 1.12371 0.561855 0.827236i \(-0.310088\pi\)
0.561855 + 0.827236i \(0.310088\pi\)
\(90\) 25.5457 2.69276
\(91\) −21.5115 −2.25502
\(92\) 9.95442 1.03782
\(93\) −3.14745 −0.326375
\(94\) 2.71732 0.280271
\(95\) 8.89024 0.912120
\(96\) −18.7950 −1.91826
\(97\) 5.44847 0.553209 0.276604 0.960984i \(-0.410791\pi\)
0.276604 + 0.960984i \(0.410791\pi\)
\(98\) −14.9184 −1.50698
\(99\) 3.14939 0.316525
\(100\) −14.8023 −1.48023
\(101\) −11.1996 −1.11440 −0.557199 0.830379i \(-0.688124\pi\)
−0.557199 + 0.830379i \(0.688124\pi\)
\(102\) 53.6061 5.30780
\(103\) 4.75386 0.468412 0.234206 0.972187i \(-0.424751\pi\)
0.234206 + 0.972187i \(0.424751\pi\)
\(104\) 38.2763 3.75330
\(105\) −15.3113 −1.49423
\(106\) 26.8775 2.61057
\(107\) −3.17007 −0.306462 −0.153231 0.988190i \(-0.548968\pi\)
−0.153231 + 0.988190i \(0.548968\pi\)
\(108\) 68.4461 6.58623
\(109\) 5.44427 0.521466 0.260733 0.965411i \(-0.416036\pi\)
0.260733 + 0.965411i \(0.416036\pi\)
\(110\) 1.37204 0.130819
\(111\) 15.7986 1.49953
\(112\) 26.0294 2.45955
\(113\) −2.45297 −0.230756 −0.115378 0.993322i \(-0.536808\pi\)
−0.115378 + 0.993322i \(0.536808\pi\)
\(114\) 56.5628 5.29759
\(115\) −2.89315 −0.269788
\(116\) −44.2834 −4.11161
\(117\) −45.9510 −4.24817
\(118\) 29.0940 2.67832
\(119\) −23.0856 −2.11625
\(120\) 27.2441 2.48703
\(121\) −10.8308 −0.984623
\(122\) 30.1456 2.72925
\(123\) −29.3774 −2.64887
\(124\) −4.34006 −0.389749
\(125\) 10.8438 0.969903
\(126\) −69.9943 −6.23559
\(127\) 6.94291 0.616084 0.308042 0.951373i \(-0.400326\pi\)
0.308042 + 0.951373i \(0.400326\pi\)
\(128\) 11.1121 0.982181
\(129\) 30.1399 2.65367
\(130\) −20.0187 −1.75576
\(131\) −6.65546 −0.581490 −0.290745 0.956801i \(-0.593903\pi\)
−0.290745 + 0.956801i \(0.593903\pi\)
\(132\) 6.04409 0.526070
\(133\) −24.3589 −2.11218
\(134\) −10.8972 −0.941378
\(135\) −19.8932 −1.71213
\(136\) 41.0772 3.52234
\(137\) 17.1113 1.46192 0.730958 0.682422i \(-0.239073\pi\)
0.730958 + 0.682422i \(0.239073\pi\)
\(138\) −18.4072 −1.56693
\(139\) 9.05478 0.768016 0.384008 0.923330i \(-0.374543\pi\)
0.384008 + 0.923330i \(0.374543\pi\)
\(140\) −21.1130 −1.78437
\(141\) −3.47905 −0.292989
\(142\) 3.27732 0.275027
\(143\) −2.46799 −0.206384
\(144\) 55.6018 4.63348
\(145\) 12.8705 1.06884
\(146\) 5.97768 0.494716
\(147\) 19.1003 1.57537
\(148\) 21.7848 1.79070
\(149\) 10.1611 0.832429 0.416215 0.909266i \(-0.363356\pi\)
0.416215 + 0.909266i \(0.363356\pi\)
\(150\) 27.3717 2.23489
\(151\) 10.9212 0.888759 0.444379 0.895839i \(-0.353424\pi\)
0.444379 + 0.895839i \(0.353424\pi\)
\(152\) 43.3428 3.51557
\(153\) −49.3134 −3.98676
\(154\) −3.75934 −0.302936
\(155\) 1.26139 0.101318
\(156\) −88.1859 −7.06052
\(157\) −15.8883 −1.26802 −0.634011 0.773324i \(-0.718593\pi\)
−0.634011 + 0.773324i \(0.718593\pi\)
\(158\) 0.858748 0.0683183
\(159\) −34.4118 −2.72903
\(160\) 7.53243 0.595491
\(161\) 7.92712 0.624744
\(162\) −67.9913 −5.34190
\(163\) −13.7364 −1.07592 −0.537958 0.842971i \(-0.680804\pi\)
−0.537958 + 0.842971i \(0.680804\pi\)
\(164\) −40.5088 −3.16321
\(165\) −1.75665 −0.136755
\(166\) 4.22534 0.327950
\(167\) −1.80503 −0.139677 −0.0698386 0.997558i \(-0.522248\pi\)
−0.0698386 + 0.997558i \(0.522248\pi\)
\(168\) −74.6477 −5.75920
\(169\) 23.0091 1.76993
\(170\) −21.4836 −1.64771
\(171\) −52.0334 −3.97909
\(172\) 41.5603 3.16894
\(173\) −3.27531 −0.249017 −0.124509 0.992219i \(-0.539735\pi\)
−0.124509 + 0.992219i \(0.539735\pi\)
\(174\) 81.8867 6.20782
\(175\) −11.7877 −0.891066
\(176\) 2.98633 0.225103
\(177\) −37.2497 −2.79986
\(178\) −27.0308 −2.02604
\(179\) 13.0586 0.976045 0.488022 0.872831i \(-0.337718\pi\)
0.488022 + 0.872831i \(0.337718\pi\)
\(180\) −45.0997 −3.36154
\(181\) −11.8647 −0.881893 −0.440947 0.897533i \(-0.645357\pi\)
−0.440947 + 0.897533i \(0.645357\pi\)
\(182\) 54.8504 4.06578
\(183\) −38.5960 −2.85310
\(184\) −14.1051 −1.03984
\(185\) −6.33155 −0.465505
\(186\) 8.02543 0.588453
\(187\) −2.64859 −0.193684
\(188\) −4.79730 −0.349879
\(189\) 54.5065 3.96476
\(190\) −22.6685 −1.64455
\(191\) 11.9273 0.863029 0.431514 0.902106i \(-0.357979\pi\)
0.431514 + 0.902106i \(0.357979\pi\)
\(192\) 0.515177 0.0371797
\(193\) 17.4408 1.25542 0.627710 0.778447i \(-0.283992\pi\)
0.627710 + 0.778447i \(0.283992\pi\)
\(194\) −13.8926 −0.997432
\(195\) 25.6303 1.83543
\(196\) 26.3377 1.88126
\(197\) −22.5623 −1.60749 −0.803747 0.594971i \(-0.797163\pi\)
−0.803747 + 0.594971i \(0.797163\pi\)
\(198\) −8.03037 −0.570694
\(199\) 19.7135 1.39745 0.698726 0.715389i \(-0.253751\pi\)
0.698726 + 0.715389i \(0.253751\pi\)
\(200\) 20.9743 1.48311
\(201\) 13.9520 0.984095
\(202\) 28.5569 2.00925
\(203\) −35.2647 −2.47510
\(204\) −94.6390 −6.62605
\(205\) 11.7735 0.822296
\(206\) −12.1215 −0.844544
\(207\) 16.9332 1.17694
\(208\) −43.5719 −3.02116
\(209\) −2.79467 −0.193312
\(210\) 39.0411 2.69409
\(211\) 1.48029 0.101907 0.0509536 0.998701i \(-0.483774\pi\)
0.0509536 + 0.998701i \(0.483774\pi\)
\(212\) −47.4508 −3.25894
\(213\) −4.19603 −0.287507
\(214\) 8.08310 0.552549
\(215\) −12.0791 −0.823787
\(216\) −96.9857 −6.59904
\(217\) −3.45617 −0.234620
\(218\) −13.8819 −0.940201
\(219\) −7.65335 −0.517165
\(220\) −2.42227 −0.163310
\(221\) 38.6441 2.59948
\(222\) −40.2835 −2.70365
\(223\) 26.7924 1.79415 0.897076 0.441876i \(-0.145687\pi\)
0.897076 + 0.441876i \(0.145687\pi\)
\(224\) −20.6385 −1.37897
\(225\) −25.1799 −1.67866
\(226\) 6.25463 0.416052
\(227\) −4.25407 −0.282353 −0.141176 0.989984i \(-0.545088\pi\)
−0.141176 + 0.989984i \(0.545088\pi\)
\(228\) −99.8588 −6.61331
\(229\) 18.4264 1.21765 0.608824 0.793305i \(-0.291641\pi\)
0.608824 + 0.793305i \(0.291641\pi\)
\(230\) 7.37701 0.486426
\(231\) 4.81316 0.316683
\(232\) 62.7480 4.11960
\(233\) 17.6588 1.15687 0.578433 0.815730i \(-0.303664\pi\)
0.578433 + 0.815730i \(0.303664\pi\)
\(234\) 117.167 7.65942
\(235\) 1.39429 0.0909533
\(236\) −51.3641 −3.34352
\(237\) −1.09947 −0.0714184
\(238\) 58.8641 3.81559
\(239\) 19.5435 1.26416 0.632081 0.774903i \(-0.282201\pi\)
0.632081 + 0.774903i \(0.282201\pi\)
\(240\) −31.0134 −2.00190
\(241\) 21.1757 1.36405 0.682024 0.731330i \(-0.261100\pi\)
0.682024 + 0.731330i \(0.261100\pi\)
\(242\) 27.6167 1.77527
\(243\) 41.4360 2.65812
\(244\) −53.2205 −3.40710
\(245\) −7.65478 −0.489046
\(246\) 74.9070 4.77589
\(247\) 40.7755 2.59448
\(248\) 6.14970 0.390507
\(249\) −5.40980 −0.342832
\(250\) −27.6498 −1.74873
\(251\) −1.43428 −0.0905311 −0.0452656 0.998975i \(-0.514413\pi\)
−0.0452656 + 0.998975i \(0.514413\pi\)
\(252\) 123.571 7.78427
\(253\) 0.909470 0.0571779
\(254\) −17.7032 −1.11080
\(255\) 27.5059 1.72248
\(256\) −28.6495 −1.79059
\(257\) −23.2274 −1.44888 −0.724442 0.689336i \(-0.757903\pi\)
−0.724442 + 0.689336i \(0.757903\pi\)
\(258\) −76.8513 −4.78456
\(259\) 17.3482 1.07796
\(260\) 35.3420 2.19182
\(261\) −75.3294 −4.66277
\(262\) 16.9702 1.04842
\(263\) 18.5577 1.14432 0.572158 0.820144i \(-0.306107\pi\)
0.572158 + 0.820144i \(0.306107\pi\)
\(264\) −8.56426 −0.527094
\(265\) 13.7911 0.847181
\(266\) 62.1108 3.80826
\(267\) 34.6081 2.11798
\(268\) 19.2385 1.17518
\(269\) −8.08164 −0.492746 −0.246373 0.969175i \(-0.579239\pi\)
−0.246373 + 0.969175i \(0.579239\pi\)
\(270\) 50.7240 3.08696
\(271\) −4.84411 −0.294258 −0.147129 0.989117i \(-0.547003\pi\)
−0.147129 + 0.989117i \(0.547003\pi\)
\(272\) −46.7603 −2.83526
\(273\) −70.2261 −4.25028
\(274\) −43.6307 −2.63583
\(275\) −1.35239 −0.0815522
\(276\) 32.4971 1.95609
\(277\) −17.6155 −1.05841 −0.529207 0.848493i \(-0.677511\pi\)
−0.529207 + 0.848493i \(0.677511\pi\)
\(278\) −23.0880 −1.38473
\(279\) −7.38276 −0.441995
\(280\) 29.9163 1.78784
\(281\) 31.7310 1.89291 0.946456 0.322833i \(-0.104635\pi\)
0.946456 + 0.322833i \(0.104635\pi\)
\(282\) 8.87094 0.528257
\(283\) 8.20055 0.487472 0.243736 0.969842i \(-0.421627\pi\)
0.243736 + 0.969842i \(0.421627\pi\)
\(284\) −5.78595 −0.343333
\(285\) 29.0230 1.71917
\(286\) 6.29293 0.372109
\(287\) −32.2589 −1.90418
\(288\) −44.0863 −2.59781
\(289\) 24.4719 1.43952
\(290\) −32.8175 −1.92711
\(291\) 17.7870 1.04269
\(292\) −10.5533 −0.617585
\(293\) −19.9298 −1.16431 −0.582157 0.813077i \(-0.697791\pi\)
−0.582157 + 0.813077i \(0.697791\pi\)
\(294\) −48.7024 −2.84038
\(295\) 14.9285 0.869168
\(296\) −30.8683 −1.79419
\(297\) 6.25347 0.362863
\(298\) −25.9090 −1.50087
\(299\) −13.2696 −0.767399
\(300\) −48.3234 −2.78996
\(301\) 33.0962 1.90763
\(302\) −27.8472 −1.60243
\(303\) −36.5620 −2.10043
\(304\) −49.3394 −2.82981
\(305\) 15.4680 0.885696
\(306\) 125.740 7.18810
\(307\) −14.2019 −0.810545 −0.405272 0.914196i \(-0.632823\pi\)
−0.405272 + 0.914196i \(0.632823\pi\)
\(308\) 6.63693 0.378174
\(309\) 15.5194 0.882867
\(310\) −3.21633 −0.182675
\(311\) −21.6827 −1.22952 −0.614758 0.788716i \(-0.710746\pi\)
−0.614758 + 0.788716i \(0.710746\pi\)
\(312\) 124.956 7.07425
\(313\) −13.8563 −0.783205 −0.391603 0.920134i \(-0.628079\pi\)
−0.391603 + 0.920134i \(0.628079\pi\)
\(314\) 40.5122 2.28624
\(315\) −35.9148 −2.02357
\(316\) −1.51608 −0.0852860
\(317\) 9.68610 0.544025 0.272013 0.962294i \(-0.412311\pi\)
0.272013 + 0.962294i \(0.412311\pi\)
\(318\) 87.7438 4.92043
\(319\) −4.04588 −0.226526
\(320\) −0.206466 −0.0115418
\(321\) −10.3490 −0.577623
\(322\) −20.2127 −1.12641
\(323\) 43.7593 2.43483
\(324\) 120.035 6.66863
\(325\) 19.7320 1.09453
\(326\) 35.0253 1.93987
\(327\) 17.7733 0.982865
\(328\) 57.3995 3.16936
\(329\) −3.82029 −0.210619
\(330\) 4.47915 0.246569
\(331\) 11.6817 0.642085 0.321042 0.947065i \(-0.395967\pi\)
0.321042 + 0.947065i \(0.395967\pi\)
\(332\) −7.45964 −0.409401
\(333\) 37.0577 2.03075
\(334\) 4.60249 0.251837
\(335\) −5.59148 −0.305495
\(336\) 84.9753 4.63578
\(337\) 35.1362 1.91399 0.956996 0.290101i \(-0.0936888\pi\)
0.956996 + 0.290101i \(0.0936888\pi\)
\(338\) −58.6690 −3.19117
\(339\) −8.00793 −0.434931
\(340\) 37.9282 2.05694
\(341\) −0.396523 −0.0214729
\(342\) 132.676 7.17428
\(343\) −4.11979 −0.222448
\(344\) −58.8895 −3.17511
\(345\) −9.44495 −0.508499
\(346\) 8.35145 0.448977
\(347\) 6.39188 0.343134 0.171567 0.985172i \(-0.445117\pi\)
0.171567 + 0.985172i \(0.445117\pi\)
\(348\) −144.567 −7.74960
\(349\) −19.9636 −1.06863 −0.534313 0.845286i \(-0.679430\pi\)
−0.534313 + 0.845286i \(0.679430\pi\)
\(350\) 30.0565 1.60659
\(351\) −91.2409 −4.87008
\(352\) −2.36784 −0.126206
\(353\) −2.29044 −0.121908 −0.0609538 0.998141i \(-0.519414\pi\)
−0.0609538 + 0.998141i \(0.519414\pi\)
\(354\) 94.9800 5.04813
\(355\) 1.68163 0.0892516
\(356\) 47.7215 2.52924
\(357\) −75.3650 −3.98874
\(358\) −33.2971 −1.75980
\(359\) −10.0595 −0.530920 −0.265460 0.964122i \(-0.585524\pi\)
−0.265460 + 0.964122i \(0.585524\pi\)
\(360\) 63.9047 3.36807
\(361\) 27.1728 1.43015
\(362\) 30.2528 1.59005
\(363\) −35.3582 −1.85583
\(364\) −96.8357 −5.07557
\(365\) 3.06721 0.160545
\(366\) 98.4129 5.14412
\(367\) −28.6183 −1.49386 −0.746931 0.664902i \(-0.768473\pi\)
−0.746931 + 0.664902i \(0.768473\pi\)
\(368\) 16.0565 0.837003
\(369\) −68.9086 −3.58724
\(370\) 16.1443 0.839302
\(371\) −37.7871 −1.96181
\(372\) −14.1685 −0.734602
\(373\) 0.0767872 0.00397589 0.00198795 0.999998i \(-0.499367\pi\)
0.00198795 + 0.999998i \(0.499367\pi\)
\(374\) 6.75342 0.349211
\(375\) 35.4007 1.82808
\(376\) 6.79760 0.350560
\(377\) 59.0312 3.04026
\(378\) −138.982 −7.14845
\(379\) −16.5756 −0.851431 −0.425715 0.904857i \(-0.639978\pi\)
−0.425715 + 0.904857i \(0.639978\pi\)
\(380\) 40.0201 2.05299
\(381\) 22.6657 1.16120
\(382\) −30.4124 −1.55604
\(383\) −9.53902 −0.487421 −0.243711 0.969848i \(-0.578365\pi\)
−0.243711 + 0.969848i \(0.578365\pi\)
\(384\) 36.2764 1.85122
\(385\) −1.92896 −0.0983087
\(386\) −44.4710 −2.26351
\(387\) 70.6972 3.59374
\(388\) 24.5267 1.24516
\(389\) −12.1337 −0.615203 −0.307601 0.951515i \(-0.599526\pi\)
−0.307601 + 0.951515i \(0.599526\pi\)
\(390\) −65.3528 −3.30927
\(391\) −14.2406 −0.720177
\(392\) −37.3195 −1.88492
\(393\) −21.7273 −1.09600
\(394\) 57.5297 2.89830
\(395\) 0.440632 0.0221706
\(396\) 14.1772 0.712432
\(397\) −8.36633 −0.419894 −0.209947 0.977713i \(-0.567329\pi\)
−0.209947 + 0.977713i \(0.567329\pi\)
\(398\) −50.2658 −2.51960
\(399\) −79.5218 −3.98107
\(400\) −23.8762 −1.19381
\(401\) −22.0525 −1.10125 −0.550625 0.834752i \(-0.685611\pi\)
−0.550625 + 0.834752i \(0.685611\pi\)
\(402\) −35.5750 −1.77432
\(403\) 5.78544 0.288193
\(404\) −50.4157 −2.50828
\(405\) −34.8871 −1.73355
\(406\) 89.9186 4.46259
\(407\) 1.99034 0.0986575
\(408\) 134.100 6.63894
\(409\) −14.6263 −0.723222 −0.361611 0.932329i \(-0.617773\pi\)
−0.361611 + 0.932329i \(0.617773\pi\)
\(410\) −30.0203 −1.48259
\(411\) 55.8613 2.75544
\(412\) 21.3999 1.05430
\(413\) −40.9034 −2.01272
\(414\) −43.1766 −2.12202
\(415\) 2.16807 0.106426
\(416\) 34.5478 1.69385
\(417\) 29.5601 1.44756
\(418\) 7.12591 0.348540
\(419\) −19.6119 −0.958104 −0.479052 0.877787i \(-0.659019\pi\)
−0.479052 + 0.877787i \(0.659019\pi\)
\(420\) −68.9252 −3.36320
\(421\) 20.4536 0.996849 0.498424 0.866933i \(-0.333912\pi\)
0.498424 + 0.866933i \(0.333912\pi\)
\(422\) −3.77447 −0.183738
\(423\) −8.16057 −0.396781
\(424\) 67.2361 3.26527
\(425\) 21.1759 1.02718
\(426\) 10.6991 0.518373
\(427\) −42.3817 −2.05100
\(428\) −14.2703 −0.689781
\(429\) −8.05697 −0.388994
\(430\) 30.7995 1.48528
\(431\) 26.9400 1.29765 0.648827 0.760936i \(-0.275260\pi\)
0.648827 + 0.760936i \(0.275260\pi\)
\(432\) 110.404 5.31180
\(433\) 11.3900 0.547370 0.273685 0.961819i \(-0.411757\pi\)
0.273685 + 0.961819i \(0.411757\pi\)
\(434\) 8.81260 0.423019
\(435\) 42.0169 2.01456
\(436\) 24.5078 1.17371
\(437\) −15.0260 −0.718792
\(438\) 19.5147 0.932446
\(439\) 31.2537 1.49166 0.745829 0.666138i \(-0.232054\pi\)
0.745829 + 0.666138i \(0.232054\pi\)
\(440\) 3.43227 0.163627
\(441\) 44.8024 2.13345
\(442\) −98.5354 −4.68685
\(443\) −9.11996 −0.433302 −0.216651 0.976249i \(-0.569513\pi\)
−0.216651 + 0.976249i \(0.569513\pi\)
\(444\) 71.1185 3.37514
\(445\) −13.8698 −0.657491
\(446\) −68.3158 −3.23485
\(447\) 33.1718 1.56897
\(448\) 0.565708 0.0267272
\(449\) −0.313559 −0.0147978 −0.00739888 0.999973i \(-0.502355\pi\)
−0.00739888 + 0.999973i \(0.502355\pi\)
\(450\) 64.2041 3.02661
\(451\) −3.70103 −0.174275
\(452\) −11.0422 −0.519383
\(453\) 35.6534 1.67514
\(454\) 10.8471 0.509080
\(455\) 28.1443 1.31943
\(456\) 141.496 6.62618
\(457\) −32.1299 −1.50297 −0.751487 0.659748i \(-0.770663\pi\)
−0.751487 + 0.659748i \(0.770663\pi\)
\(458\) −46.9839 −2.19541
\(459\) −97.9175 −4.57040
\(460\) −13.0238 −0.607236
\(461\) 32.3718 1.50771 0.753853 0.657043i \(-0.228193\pi\)
0.753853 + 0.657043i \(0.228193\pi\)
\(462\) −12.2727 −0.570977
\(463\) −31.9572 −1.48517 −0.742587 0.669749i \(-0.766402\pi\)
−0.742587 + 0.669749i \(0.766402\pi\)
\(464\) −71.4292 −3.31602
\(465\) 4.11793 0.190964
\(466\) −45.0268 −2.08582
\(467\) 6.17443 0.285719 0.142859 0.989743i \(-0.454370\pi\)
0.142859 + 0.989743i \(0.454370\pi\)
\(468\) −206.852 −9.56173
\(469\) 15.3204 0.707432
\(470\) −3.55518 −0.163988
\(471\) −51.8687 −2.38998
\(472\) 72.7811 3.35002
\(473\) 3.79709 0.174591
\(474\) 2.80346 0.128767
\(475\) 22.3438 1.02521
\(476\) −103.922 −4.76324
\(477\) −80.7174 −3.69580
\(478\) −49.8323 −2.27928
\(479\) 5.68226 0.259629 0.129815 0.991538i \(-0.458562\pi\)
0.129815 + 0.991538i \(0.458562\pi\)
\(480\) 24.5903 1.12239
\(481\) −29.0399 −1.32411
\(482\) −53.9942 −2.45937
\(483\) 25.8788 1.17752
\(484\) −48.7559 −2.21618
\(485\) −7.12845 −0.323686
\(486\) −105.654 −4.79258
\(487\) −21.8856 −0.991731 −0.495866 0.868399i \(-0.665149\pi\)
−0.495866 + 0.868399i \(0.665149\pi\)
\(488\) 75.4116 3.41372
\(489\) −44.8436 −2.02790
\(490\) 19.5183 0.881747
\(491\) 35.9607 1.62289 0.811443 0.584432i \(-0.198683\pi\)
0.811443 + 0.584432i \(0.198683\pi\)
\(492\) −132.245 −5.96205
\(493\) 63.3509 2.85318
\(494\) −103.970 −4.67784
\(495\) −4.12047 −0.185201
\(496\) −7.00052 −0.314333
\(497\) −4.60759 −0.206679
\(498\) 13.7940 0.618124
\(499\) −13.9074 −0.622581 −0.311291 0.950315i \(-0.600761\pi\)
−0.311291 + 0.950315i \(0.600761\pi\)
\(500\) 48.8144 2.18305
\(501\) −5.89267 −0.263265
\(502\) 3.65716 0.163227
\(503\) −7.28881 −0.324992 −0.162496 0.986709i \(-0.551954\pi\)
−0.162496 + 0.986709i \(0.551954\pi\)
\(504\) −175.096 −7.79941
\(505\) 14.6528 0.652042
\(506\) −2.31898 −0.103091
\(507\) 75.1151 3.33598
\(508\) 31.2541 1.38668
\(509\) 3.05791 0.135540 0.0677698 0.997701i \(-0.478412\pi\)
0.0677698 + 0.997701i \(0.478412\pi\)
\(510\) −70.1350 −3.10563
\(511\) −8.40403 −0.371772
\(512\) 50.8268 2.24625
\(513\) −103.318 −4.56161
\(514\) 59.2256 2.61233
\(515\) −6.21966 −0.274071
\(516\) 135.677 5.97286
\(517\) −0.438298 −0.0192763
\(518\) −44.2347 −1.94356
\(519\) −10.6925 −0.469350
\(520\) −50.0784 −2.19608
\(521\) 22.3066 0.977272 0.488636 0.872488i \(-0.337495\pi\)
0.488636 + 0.872488i \(0.337495\pi\)
\(522\) 192.076 8.40695
\(523\) 16.8476 0.736693 0.368346 0.929689i \(-0.379924\pi\)
0.368346 + 0.929689i \(0.379924\pi\)
\(524\) −29.9601 −1.30881
\(525\) −38.4820 −1.67949
\(526\) −47.3187 −2.06319
\(527\) 6.20879 0.270459
\(528\) 9.74913 0.424277
\(529\) −18.1101 −0.787395
\(530\) −35.1648 −1.52746
\(531\) −87.3742 −3.79172
\(532\) −109.654 −4.75408
\(533\) 53.9996 2.33898
\(534\) −88.2444 −3.81871
\(535\) 4.14752 0.179313
\(536\) −27.2603 −1.17747
\(537\) 42.6309 1.83966
\(538\) 20.6067 0.888419
\(539\) 2.40630 0.103647
\(540\) −89.5507 −3.85365
\(541\) 4.11699 0.177003 0.0885016 0.996076i \(-0.471792\pi\)
0.0885016 + 0.996076i \(0.471792\pi\)
\(542\) 12.3516 0.530546
\(543\) −38.7332 −1.66220
\(544\) 37.0759 1.58961
\(545\) −7.12295 −0.305114
\(546\) 179.064 7.66323
\(547\) −22.7473 −0.972606 −0.486303 0.873790i \(-0.661655\pi\)
−0.486303 + 0.873790i \(0.661655\pi\)
\(548\) 77.0279 3.29047
\(549\) −90.5322 −3.86382
\(550\) 3.44835 0.147038
\(551\) 66.8450 2.84769
\(552\) −46.0472 −1.95990
\(553\) −1.20732 −0.0513403
\(554\) 44.9164 1.90832
\(555\) −20.6699 −0.877388
\(556\) 40.7608 1.72864
\(557\) −3.26824 −0.138480 −0.0692399 0.997600i \(-0.522057\pi\)
−0.0692399 + 0.997600i \(0.522057\pi\)
\(558\) 18.8247 0.796914
\(559\) −55.4013 −2.34322
\(560\) −34.0553 −1.43910
\(561\) −8.64655 −0.365057
\(562\) −80.9083 −3.41291
\(563\) −3.33565 −0.140581 −0.0702905 0.997527i \(-0.522393\pi\)
−0.0702905 + 0.997527i \(0.522393\pi\)
\(564\) −15.6612 −0.659456
\(565\) 3.20931 0.135017
\(566\) −20.9099 −0.878910
\(567\) 95.5891 4.01437
\(568\) 8.19849 0.344001
\(569\) −36.7685 −1.54142 −0.770709 0.637187i \(-0.780098\pi\)
−0.770709 + 0.637187i \(0.780098\pi\)
\(570\) −74.0033 −3.09966
\(571\) −37.8739 −1.58497 −0.792487 0.609888i \(-0.791214\pi\)
−0.792487 + 0.609888i \(0.791214\pi\)
\(572\) −11.1099 −0.464526
\(573\) 38.9377 1.62665
\(574\) 82.2543 3.43323
\(575\) −7.27136 −0.303237
\(576\) 1.20842 0.0503507
\(577\) 3.73009 0.155286 0.0776429 0.996981i \(-0.475261\pi\)
0.0776429 + 0.996981i \(0.475261\pi\)
\(578\) −62.3988 −2.59545
\(579\) 56.9372 2.36623
\(580\) 57.9377 2.40573
\(581\) −5.94042 −0.246450
\(582\) −45.3537 −1.87997
\(583\) −4.33527 −0.179549
\(584\) 14.9536 0.618786
\(585\) 60.1194 2.48563
\(586\) 50.8175 2.09925
\(587\) −18.2255 −0.752249 −0.376124 0.926569i \(-0.622743\pi\)
−0.376124 + 0.926569i \(0.622743\pi\)
\(588\) 85.9816 3.54582
\(589\) 6.55124 0.269939
\(590\) −38.0649 −1.56711
\(591\) −73.6564 −3.02982
\(592\) 35.1390 1.44421
\(593\) −48.2860 −1.98287 −0.991435 0.130603i \(-0.958309\pi\)
−0.991435 + 0.130603i \(0.958309\pi\)
\(594\) −15.9452 −0.654241
\(595\) 30.2038 1.23823
\(596\) 45.7410 1.87362
\(597\) 64.3564 2.63393
\(598\) 33.8350 1.38362
\(599\) −28.7434 −1.17442 −0.587211 0.809434i \(-0.699774\pi\)
−0.587211 + 0.809434i \(0.699774\pi\)
\(600\) 68.4726 2.79538
\(601\) −21.4289 −0.874104 −0.437052 0.899436i \(-0.643977\pi\)
−0.437052 + 0.899436i \(0.643977\pi\)
\(602\) −84.3893 −3.43945
\(603\) 32.7262 1.33271
\(604\) 49.1629 2.00041
\(605\) 14.1704 0.576110
\(606\) 93.2264 3.78706
\(607\) −26.6178 −1.08038 −0.540192 0.841542i \(-0.681648\pi\)
−0.540192 + 0.841542i \(0.681648\pi\)
\(608\) 39.1208 1.58656
\(609\) −115.125 −4.66509
\(610\) −39.4407 −1.59691
\(611\) 6.39496 0.258712
\(612\) −221.988 −8.97335
\(613\) −3.50119 −0.141412 −0.0707058 0.997497i \(-0.522525\pi\)
−0.0707058 + 0.997497i \(0.522525\pi\)
\(614\) 36.2123 1.46141
\(615\) 38.4356 1.54987
\(616\) −9.40429 −0.378910
\(617\) −14.3979 −0.579638 −0.289819 0.957082i \(-0.593595\pi\)
−0.289819 + 0.957082i \(0.593595\pi\)
\(618\) −39.5716 −1.59180
\(619\) 26.5743 1.06811 0.534055 0.845450i \(-0.320668\pi\)
0.534055 + 0.845450i \(0.320668\pi\)
\(620\) 5.67827 0.228045
\(621\) 33.6229 1.34924
\(622\) 55.2871 2.21681
\(623\) 38.0026 1.52254
\(624\) −142.244 −5.69432
\(625\) 2.25382 0.0901529
\(626\) 35.3311 1.41212
\(627\) −9.12345 −0.364356
\(628\) −71.5224 −2.85405
\(629\) −31.1649 −1.24263
\(630\) 91.5762 3.64849
\(631\) −44.2818 −1.76283 −0.881415 0.472342i \(-0.843409\pi\)
−0.881415 + 0.472342i \(0.843409\pi\)
\(632\) 2.14823 0.0854519
\(633\) 4.83253 0.192076
\(634\) −24.6978 −0.980875
\(635\) −9.08368 −0.360475
\(636\) −154.907 −6.14248
\(637\) −35.1090 −1.39107
\(638\) 10.3163 0.408425
\(639\) −9.84234 −0.389357
\(640\) −14.5384 −0.574681
\(641\) 39.5854 1.56353 0.781764 0.623575i \(-0.214320\pi\)
0.781764 + 0.623575i \(0.214320\pi\)
\(642\) 26.3880 1.04145
\(643\) −8.67869 −0.342254 −0.171127 0.985249i \(-0.554741\pi\)
−0.171127 + 0.985249i \(0.554741\pi\)
\(644\) 35.6846 1.40617
\(645\) −39.4332 −1.55268
\(646\) −111.578 −4.38999
\(647\) −14.4066 −0.566382 −0.283191 0.959064i \(-0.591393\pi\)
−0.283191 + 0.959064i \(0.591393\pi\)
\(648\) −170.086 −6.68160
\(649\) −4.69280 −0.184209
\(650\) −50.3130 −1.97344
\(651\) −11.2830 −0.442214
\(652\) −61.8355 −2.42166
\(653\) 46.4250 1.81675 0.908374 0.418158i \(-0.137324\pi\)
0.908374 + 0.418158i \(0.137324\pi\)
\(654\) −45.3187 −1.77210
\(655\) 8.70760 0.340234
\(656\) −65.3408 −2.55113
\(657\) −17.9520 −0.700372
\(658\) 9.74105 0.379746
\(659\) 5.30176 0.206527 0.103264 0.994654i \(-0.467071\pi\)
0.103264 + 0.994654i \(0.467071\pi\)
\(660\) −7.90772 −0.307808
\(661\) 47.3720 1.84256 0.921278 0.388904i \(-0.127146\pi\)
0.921278 + 0.388904i \(0.127146\pi\)
\(662\) −29.7862 −1.15768
\(663\) 126.157 4.89953
\(664\) 10.5700 0.410197
\(665\) 31.8697 1.23585
\(666\) −94.4904 −3.66143
\(667\) −21.7534 −0.842294
\(668\) −8.12547 −0.314384
\(669\) 87.4661 3.38164
\(670\) 14.2573 0.550807
\(671\) −4.86241 −0.187711
\(672\) −67.3763 −2.59910
\(673\) 10.4408 0.402464 0.201232 0.979544i \(-0.435506\pi\)
0.201232 + 0.979544i \(0.435506\pi\)
\(674\) −89.5910 −3.45092
\(675\) −49.9975 −1.92441
\(676\) 103.577 3.98374
\(677\) 1.68708 0.0648396 0.0324198 0.999474i \(-0.489679\pi\)
0.0324198 + 0.999474i \(0.489679\pi\)
\(678\) 20.4188 0.784178
\(679\) 19.5317 0.749557
\(680\) −53.7429 −2.06095
\(681\) −13.8878 −0.532181
\(682\) 1.01106 0.0387155
\(683\) −34.2998 −1.31245 −0.656223 0.754567i \(-0.727847\pi\)
−0.656223 + 0.754567i \(0.727847\pi\)
\(684\) −234.232 −8.95610
\(685\) −22.3874 −0.855378
\(686\) 10.5047 0.401072
\(687\) 60.1545 2.29504
\(688\) 67.0369 2.55576
\(689\) 63.2535 2.40977
\(690\) 24.0829 0.916821
\(691\) −11.7251 −0.446046 −0.223023 0.974813i \(-0.571592\pi\)
−0.223023 + 0.974813i \(0.571592\pi\)
\(692\) −14.7441 −0.560485
\(693\) 11.2899 0.428868
\(694\) −16.2981 −0.618669
\(695\) −11.8467 −0.449372
\(696\) 204.846 7.76467
\(697\) 57.9511 2.19505
\(698\) 50.9036 1.92673
\(699\) 57.6487 2.18047
\(700\) −53.0633 −2.00560
\(701\) −8.25435 −0.311762 −0.155881 0.987776i \(-0.549822\pi\)
−0.155881 + 0.987776i \(0.549822\pi\)
\(702\) 232.648 8.78073
\(703\) −32.8839 −1.24024
\(704\) 0.0649031 0.00244613
\(705\) 4.55177 0.171430
\(706\) 5.84020 0.219799
\(707\) −40.1481 −1.50993
\(708\) −167.683 −6.30190
\(709\) −19.3772 −0.727725 −0.363863 0.931453i \(-0.618542\pi\)
−0.363863 + 0.931453i \(0.618542\pi\)
\(710\) −4.28785 −0.160920
\(711\) −2.57896 −0.0967186
\(712\) −67.6197 −2.53415
\(713\) −2.13197 −0.0798429
\(714\) 192.167 7.19167
\(715\) 3.22897 0.120757
\(716\) 58.7843 2.19687
\(717\) 63.8013 2.38270
\(718\) 25.6499 0.957247
\(719\) −37.2591 −1.38953 −0.694766 0.719236i \(-0.744492\pi\)
−0.694766 + 0.719236i \(0.744492\pi\)
\(720\) −72.7460 −2.71108
\(721\) 17.0416 0.634663
\(722\) −69.2859 −2.57855
\(723\) 69.1299 2.57097
\(724\) −53.4097 −1.98496
\(725\) 32.3475 1.20136
\(726\) 90.1572 3.34605
\(727\) 11.1107 0.412073 0.206036 0.978544i \(-0.433943\pi\)
0.206036 + 0.978544i \(0.433943\pi\)
\(728\) 137.213 5.08544
\(729\) 55.2760 2.04726
\(730\) −7.82083 −0.289462
\(731\) −59.4553 −2.19903
\(732\) −173.743 −6.42173
\(733\) −8.17948 −0.302116 −0.151058 0.988525i \(-0.548268\pi\)
−0.151058 + 0.988525i \(0.548268\pi\)
\(734\) 72.9714 2.69342
\(735\) −24.9897 −0.921759
\(736\) −12.7311 −0.469274
\(737\) 1.75770 0.0647457
\(738\) 175.704 6.46777
\(739\) 18.9959 0.698777 0.349389 0.936978i \(-0.386389\pi\)
0.349389 + 0.936978i \(0.386389\pi\)
\(740\) −28.5020 −1.04775
\(741\) 133.115 4.89011
\(742\) 96.3502 3.53713
\(743\) 5.81776 0.213433 0.106716 0.994289i \(-0.465966\pi\)
0.106716 + 0.994289i \(0.465966\pi\)
\(744\) 20.0762 0.736031
\(745\) −13.2942 −0.487060
\(746\) −0.195794 −0.00716851
\(747\) −12.6894 −0.464281
\(748\) −11.9228 −0.435942
\(749\) −11.3640 −0.415233
\(750\) −90.2653 −3.29602
\(751\) −53.5728 −1.95490 −0.977450 0.211167i \(-0.932273\pi\)
−0.977450 + 0.211167i \(0.932273\pi\)
\(752\) −7.73806 −0.282178
\(753\) −4.68234 −0.170634
\(754\) −150.519 −5.48158
\(755\) −14.2887 −0.520019
\(756\) 245.365 8.92385
\(757\) −23.3108 −0.847244 −0.423622 0.905839i \(-0.639242\pi\)
−0.423622 + 0.905839i \(0.639242\pi\)
\(758\) 42.2648 1.53513
\(759\) 2.96904 0.107769
\(760\) −56.7071 −2.05698
\(761\) 22.9700 0.832662 0.416331 0.909213i \(-0.363316\pi\)
0.416331 + 0.909213i \(0.363316\pi\)
\(762\) −57.7935 −2.09364
\(763\) 19.5166 0.706548
\(764\) 53.6917 1.94250
\(765\) 64.5187 2.33268
\(766\) 24.3228 0.878818
\(767\) 68.4700 2.47231
\(768\) −93.5287 −3.37493
\(769\) −1.93400 −0.0697418 −0.0348709 0.999392i \(-0.511102\pi\)
−0.0348709 + 0.999392i \(0.511102\pi\)
\(770\) 4.91849 0.177250
\(771\) −75.8278 −2.73087
\(772\) 78.5114 2.82569
\(773\) 14.9331 0.537107 0.268553 0.963265i \(-0.413454\pi\)
0.268553 + 0.963265i \(0.413454\pi\)
\(774\) −180.265 −6.47950
\(775\) 3.17026 0.113879
\(776\) −34.7535 −1.24758
\(777\) 56.6347 2.03176
\(778\) 30.9387 1.10921
\(779\) 61.1474 2.19083
\(780\) 115.377 4.13116
\(781\) −0.528625 −0.0189157
\(782\) 36.3109 1.29848
\(783\) −149.575 −5.34538
\(784\) 42.4827 1.51724
\(785\) 20.7873 0.741929
\(786\) 55.4008 1.97608
\(787\) 10.8527 0.386858 0.193429 0.981114i \(-0.438039\pi\)
0.193429 + 0.981114i \(0.438039\pi\)
\(788\) −101.566 −3.61813
\(789\) 60.5831 2.15682
\(790\) −1.12353 −0.0399735
\(791\) −8.79339 −0.312657
\(792\) −20.0886 −0.713818
\(793\) 70.9447 2.51932
\(794\) 21.3326 0.757067
\(795\) 45.0223 1.59678
\(796\) 88.7418 3.14537
\(797\) −47.8515 −1.69499 −0.847494 0.530805i \(-0.821890\pi\)
−0.847494 + 0.530805i \(0.821890\pi\)
\(798\) 202.766 7.17784
\(799\) 6.86292 0.242793
\(800\) 18.9312 0.669321
\(801\) 81.1779 2.86828
\(802\) 56.2300 1.98555
\(803\) −0.964186 −0.0340254
\(804\) 62.8058 2.21499
\(805\) −10.3714 −0.365542
\(806\) −14.7518 −0.519611
\(807\) −26.3832 −0.928733
\(808\) 71.4373 2.51315
\(809\) 19.3790 0.681328 0.340664 0.940185i \(-0.389348\pi\)
0.340664 + 0.940185i \(0.389348\pi\)
\(810\) 88.9557 3.12559
\(811\) 25.9855 0.912476 0.456238 0.889858i \(-0.349197\pi\)
0.456238 + 0.889858i \(0.349197\pi\)
\(812\) −158.747 −5.57092
\(813\) −15.8140 −0.554621
\(814\) −5.07501 −0.177879
\(815\) 17.9719 0.629527
\(816\) −152.653 −5.34392
\(817\) −62.7346 −2.19481
\(818\) 37.2943 1.30397
\(819\) −164.725 −5.75595
\(820\) 52.9993 1.85081
\(821\) 20.6028 0.719041 0.359521 0.933137i \(-0.382940\pi\)
0.359521 + 0.933137i \(0.382940\pi\)
\(822\) −142.436 −4.96803
\(823\) −30.9010 −1.07714 −0.538570 0.842581i \(-0.681035\pi\)
−0.538570 + 0.842581i \(0.681035\pi\)
\(824\) −30.3229 −1.05635
\(825\) −4.41500 −0.153711
\(826\) 104.296 3.62893
\(827\) 45.7225 1.58993 0.794964 0.606657i \(-0.207490\pi\)
0.794964 + 0.606657i \(0.207490\pi\)
\(828\) 76.2262 2.64904
\(829\) −38.8858 −1.35056 −0.675279 0.737562i \(-0.735977\pi\)
−0.675279 + 0.737562i \(0.735977\pi\)
\(830\) −5.52818 −0.191886
\(831\) −57.5074 −1.99491
\(832\) −0.946965 −0.0328301
\(833\) −37.6781 −1.30547
\(834\) −75.3729 −2.60995
\(835\) 2.36159 0.0817261
\(836\) −12.5804 −0.435104
\(837\) −14.6593 −0.506701
\(838\) 50.0068 1.72746
\(839\) −9.34091 −0.322484 −0.161242 0.986915i \(-0.551550\pi\)
−0.161242 + 0.986915i \(0.551550\pi\)
\(840\) 97.6645 3.36975
\(841\) 67.7724 2.33698
\(842\) −52.1531 −1.79731
\(843\) 103.589 3.56778
\(844\) 6.66363 0.229372
\(845\) −30.1037 −1.03560
\(846\) 20.8080 0.715393
\(847\) −38.8264 −1.33409
\(848\) −76.5383 −2.62834
\(849\) 26.7714 0.918793
\(850\) −53.9947 −1.85200
\(851\) 10.7014 0.366839
\(852\) −18.8887 −0.647118
\(853\) −4.43051 −0.151698 −0.0758490 0.997119i \(-0.524167\pi\)
−0.0758490 + 0.997119i \(0.524167\pi\)
\(854\) 108.066 3.69794
\(855\) 68.0773 2.32819
\(856\) 20.2205 0.691123
\(857\) −39.5153 −1.34982 −0.674909 0.737901i \(-0.735817\pi\)
−0.674909 + 0.737901i \(0.735817\pi\)
\(858\) 20.5438 0.701355
\(859\) −41.9086 −1.42990 −0.714951 0.699174i \(-0.753551\pi\)
−0.714951 + 0.699174i \(0.753551\pi\)
\(860\) −54.3750 −1.85417
\(861\) −105.312 −3.58902
\(862\) −68.6921 −2.33966
\(863\) −7.80570 −0.265709 −0.132855 0.991136i \(-0.542414\pi\)
−0.132855 + 0.991136i \(0.542414\pi\)
\(864\) −87.5384 −2.97812
\(865\) 4.28522 0.145702
\(866\) −29.0425 −0.986906
\(867\) 79.8905 2.71322
\(868\) −15.5582 −0.528080
\(869\) −0.138514 −0.00469877
\(870\) −107.136 −3.63224
\(871\) −25.6456 −0.868968
\(872\) −34.7267 −1.17599
\(873\) 41.7218 1.41207
\(874\) 38.3137 1.29598
\(875\) 38.8730 1.31415
\(876\) −34.4522 −1.16403
\(877\) −21.8789 −0.738796 −0.369398 0.929271i \(-0.620436\pi\)
−0.369398 + 0.929271i \(0.620436\pi\)
\(878\) −79.6913 −2.68945
\(879\) −65.0627 −2.19451
\(880\) −3.90713 −0.131709
\(881\) −30.4737 −1.02669 −0.513343 0.858183i \(-0.671593\pi\)
−0.513343 + 0.858183i \(0.671593\pi\)
\(882\) −114.238 −3.84659
\(883\) −15.5433 −0.523075 −0.261537 0.965193i \(-0.584229\pi\)
−0.261537 + 0.965193i \(0.584229\pi\)
\(884\) 173.959 5.85088
\(885\) 48.7352 1.63822
\(886\) 23.2542 0.781242
\(887\) 14.7229 0.494347 0.247174 0.968971i \(-0.420498\pi\)
0.247174 + 0.968971i \(0.420498\pi\)
\(888\) −100.772 −3.38170
\(889\) 24.8889 0.834748
\(890\) 35.3654 1.18545
\(891\) 10.9668 0.367403
\(892\) 120.608 4.03826
\(893\) 7.24145 0.242326
\(894\) −84.5821 −2.82885
\(895\) −17.0851 −0.571091
\(896\) 39.8346 1.33078
\(897\) −43.3197 −1.44640
\(898\) 0.799518 0.0266803
\(899\) 9.48432 0.316320
\(900\) −113.349 −3.77830
\(901\) 67.8821 2.26148
\(902\) 9.43695 0.314216
\(903\) 108.045 3.59553
\(904\) 15.6465 0.520393
\(905\) 15.5230 0.516002
\(906\) −90.9096 −3.02027
\(907\) 6.99966 0.232420 0.116210 0.993225i \(-0.462925\pi\)
0.116210 + 0.993225i \(0.462925\pi\)
\(908\) −19.1500 −0.635516
\(909\) −85.7610 −2.84451
\(910\) −71.7629 −2.37892
\(911\) −31.3243 −1.03782 −0.518910 0.854829i \(-0.673662\pi\)
−0.518910 + 0.854829i \(0.673662\pi\)
\(912\) −161.073 −5.33365
\(913\) −0.681538 −0.0225556
\(914\) 81.9255 2.70985
\(915\) 50.4967 1.66937
\(916\) 82.9477 2.74067
\(917\) −23.8585 −0.787876
\(918\) 249.672 8.24041
\(919\) −14.8413 −0.489568 −0.244784 0.969578i \(-0.578717\pi\)
−0.244784 + 0.969578i \(0.578717\pi\)
\(920\) 18.4542 0.608417
\(921\) −46.3633 −1.52772
\(922\) −82.5423 −2.71839
\(923\) 7.71287 0.253872
\(924\) 21.6668 0.712786
\(925\) −15.9131 −0.523219
\(926\) 81.4850 2.67776
\(927\) 36.4028 1.19563
\(928\) 56.6357 1.85916
\(929\) 23.7271 0.778461 0.389230 0.921140i \(-0.372741\pi\)
0.389230 + 0.921140i \(0.372741\pi\)
\(930\) −10.5000 −0.344308
\(931\) −39.7563 −1.30296
\(932\) 79.4925 2.60386
\(933\) −70.7852 −2.31740
\(934\) −15.7437 −0.515149
\(935\) 3.46525 0.113326
\(936\) 293.102 9.58033
\(937\) −17.9739 −0.587182 −0.293591 0.955931i \(-0.594850\pi\)
−0.293591 + 0.955931i \(0.594850\pi\)
\(938\) −39.0644 −1.27550
\(939\) −45.2352 −1.47619
\(940\) 6.27650 0.204717
\(941\) −20.0900 −0.654916 −0.327458 0.944866i \(-0.606192\pi\)
−0.327458 + 0.944866i \(0.606192\pi\)
\(942\) 132.256 4.30913
\(943\) −19.8992 −0.648007
\(944\) −82.8504 −2.69655
\(945\) −71.3130 −2.31981
\(946\) −9.68190 −0.314786
\(947\) 19.3138 0.627613 0.313807 0.949487i \(-0.398396\pi\)
0.313807 + 0.949487i \(0.398396\pi\)
\(948\) −4.94936 −0.160748
\(949\) 14.0679 0.456663
\(950\) −56.9728 −1.84844
\(951\) 31.6211 1.02538
\(952\) 147.253 4.77251
\(953\) −31.4249 −1.01795 −0.508977 0.860780i \(-0.669976\pi\)
−0.508977 + 0.860780i \(0.669976\pi\)
\(954\) 205.815 6.66350
\(955\) −15.6049 −0.504964
\(956\) 87.9764 2.84536
\(957\) −13.2081 −0.426958
\(958\) −14.4887 −0.468110
\(959\) 61.3405 1.98079
\(960\) −0.674026 −0.0217541
\(961\) −30.0705 −0.970015
\(962\) 74.0466 2.38736
\(963\) −24.2749 −0.782247
\(964\) 95.3241 3.07018
\(965\) −22.8185 −0.734555
\(966\) −65.9862 −2.12307
\(967\) −38.1062 −1.22541 −0.612707 0.790310i \(-0.709919\pi\)
−0.612707 + 0.790310i \(0.709919\pi\)
\(968\) 69.0854 2.22049
\(969\) 142.856 4.58919
\(970\) 18.1763 0.583605
\(971\) 47.7544 1.53251 0.766256 0.642536i \(-0.222118\pi\)
0.766256 + 0.642536i \(0.222118\pi\)
\(972\) 186.527 5.98287
\(973\) 32.4595 1.04060
\(974\) 55.8043 1.78809
\(975\) 64.4167 2.06299
\(976\) −85.8449 −2.74783
\(977\) 40.5852 1.29843 0.649217 0.760603i \(-0.275097\pi\)
0.649217 + 0.760603i \(0.275097\pi\)
\(978\) 114.343 3.65629
\(979\) 4.36000 0.139346
\(980\) −34.4586 −1.10074
\(981\) 41.6896 1.33105
\(982\) −91.6934 −2.92605
\(983\) 5.83521 0.186114 0.0930571 0.995661i \(-0.470336\pi\)
0.0930571 + 0.995661i \(0.470336\pi\)
\(984\) 187.386 5.97364
\(985\) 29.5191 0.940556
\(986\) −161.533 −5.14427
\(987\) −12.4717 −0.396978
\(988\) 183.554 5.83964
\(989\) 20.4157 0.649182
\(990\) 10.5065 0.333917
\(991\) −25.4460 −0.808320 −0.404160 0.914688i \(-0.632436\pi\)
−0.404160 + 0.914688i \(0.632436\pi\)
\(992\) 5.55066 0.176234
\(993\) 38.1359 1.21021
\(994\) 11.7485 0.372641
\(995\) −25.7919 −0.817659
\(996\) −24.3526 −0.771643
\(997\) −45.2344 −1.43259 −0.716294 0.697798i \(-0.754163\pi\)
−0.716294 + 0.697798i \(0.754163\pi\)
\(998\) 35.4614 1.12251
\(999\) 73.5823 2.32804
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 4027.2.a.b.1.14 159
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4027.2.a.b.1.14 159 1.1 even 1 trivial