Properties

Label 8035.2.a.c.1.11
Level $8035$
Weight $2$
Character 8035.1
Self dual yes
Analytic conductor $64.160$
Analytic rank $0$
Dimension $127$
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] = [8035,2,Mod(1,8035)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8035, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8035.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8035 = 5 \cdot 1607 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8035.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: \(64.1597980241\)
Analytic rank: \(0\)
Dimension: \(127\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) \(=\) 8035.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.33324 q^{2} -1.40461 q^{3} +3.44401 q^{4} -1.00000 q^{5} +3.27730 q^{6} -3.84799 q^{7} -3.36922 q^{8} -1.02706 q^{9} +O(q^{10})\) \(q-2.33324 q^{2} -1.40461 q^{3} +3.44401 q^{4} -1.00000 q^{5} +3.27730 q^{6} -3.84799 q^{7} -3.36922 q^{8} -1.02706 q^{9} +2.33324 q^{10} +0.0531881 q^{11} -4.83751 q^{12} +4.09428 q^{13} +8.97829 q^{14} +1.40461 q^{15} +0.973182 q^{16} +6.43239 q^{17} +2.39637 q^{18} +3.86078 q^{19} -3.44401 q^{20} +5.40495 q^{21} -0.124101 q^{22} -1.52544 q^{23} +4.73246 q^{24} +1.00000 q^{25} -9.55294 q^{26} +5.65646 q^{27} -13.2525 q^{28} +0.386636 q^{29} -3.27730 q^{30} -5.73040 q^{31} +4.46777 q^{32} -0.0747088 q^{33} -15.0083 q^{34} +3.84799 q^{35} -3.53719 q^{36} +7.40755 q^{37} -9.00812 q^{38} -5.75089 q^{39} +3.36922 q^{40} +1.71601 q^{41} -12.6110 q^{42} +8.69101 q^{43} +0.183180 q^{44} +1.02706 q^{45} +3.55921 q^{46} +3.60357 q^{47} -1.36695 q^{48} +7.80706 q^{49} -2.33324 q^{50} -9.03503 q^{51} +14.1007 q^{52} +13.1394 q^{53} -13.1979 q^{54} -0.0531881 q^{55} +12.9647 q^{56} -5.42291 q^{57} -0.902114 q^{58} +5.87507 q^{59} +4.83751 q^{60} +14.8116 q^{61} +13.3704 q^{62} +3.95211 q^{63} -12.3708 q^{64} -4.09428 q^{65} +0.174314 q^{66} -11.5574 q^{67} +22.1532 q^{68} +2.14265 q^{69} -8.97829 q^{70} -6.81391 q^{71} +3.46038 q^{72} +7.77783 q^{73} -17.2836 q^{74} -1.40461 q^{75} +13.2966 q^{76} -0.204668 q^{77} +13.4182 q^{78} +4.31554 q^{79} -0.973182 q^{80} -4.86398 q^{81} -4.00387 q^{82} -7.65175 q^{83} +18.6147 q^{84} -6.43239 q^{85} -20.2782 q^{86} -0.543074 q^{87} -0.179203 q^{88} +9.33077 q^{89} -2.39637 q^{90} -15.7548 q^{91} -5.25363 q^{92} +8.04900 q^{93} -8.40800 q^{94} -3.86078 q^{95} -6.27550 q^{96} -0.304722 q^{97} -18.2157 q^{98} -0.0546273 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9} - 19 q^{10} + 30 q^{11} + 35 q^{12} + 30 q^{13} + 39 q^{14} - 10 q^{15} + 121 q^{16} + 63 q^{17} + 53 q^{18} - 35 q^{19} - 125 q^{20} + 33 q^{21} + 49 q^{22} + 61 q^{23} - 5 q^{24} + 127 q^{25} + 10 q^{26} + 40 q^{27} + 32 q^{28} + 134 q^{29} - 25 q^{31} + 122 q^{32} + 48 q^{33} - 21 q^{34} - 13 q^{35} + 133 q^{36} + 60 q^{37} + 33 q^{38} + 26 q^{39} - 54 q^{40} + 9 q^{41} + 45 q^{42} + 48 q^{43} + 85 q^{44} - 123 q^{45} - 11 q^{46} + 57 q^{47} + 71 q^{48} + 70 q^{49} + 19 q^{50} + 45 q^{51} + 68 q^{52} + 182 q^{53} - 29 q^{54} - 30 q^{55} + 96 q^{56} + 74 q^{57} + 47 q^{58} + 19 q^{59} - 35 q^{60} + 16 q^{61} + 43 q^{62} + 73 q^{63} + 110 q^{64} - 30 q^{65} + 8 q^{66} + 40 q^{67} + 129 q^{68} + 2 q^{69} - 39 q^{70} + 48 q^{71} + 151 q^{72} + 30 q^{73} + 117 q^{74} + 10 q^{75} - 98 q^{76} + 134 q^{77} + 54 q^{78} + 23 q^{79} - 121 q^{80} + 111 q^{81} + 4 q^{82} + 92 q^{83} + 48 q^{84} - 63 q^{85} + 42 q^{86} + 69 q^{87} + 121 q^{88} + 12 q^{89} - 53 q^{90} - 30 q^{91} + 175 q^{92} + 82 q^{93} - 23 q^{94} + 35 q^{95} + 6 q^{96} + 67 q^{97} + 122 q^{98} + 73 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.33324 −1.64985 −0.824925 0.565242i \(-0.808783\pi\)
−0.824925 + 0.565242i \(0.808783\pi\)
\(3\) −1.40461 −0.810955 −0.405477 0.914105i \(-0.632895\pi\)
−0.405477 + 0.914105i \(0.632895\pi\)
\(4\) 3.44401 1.72200
\(5\) −1.00000 −0.447214
\(6\) 3.27730 1.33795
\(7\) −3.84799 −1.45440 −0.727202 0.686423i \(-0.759180\pi\)
−0.727202 + 0.686423i \(0.759180\pi\)
\(8\) −3.36922 −1.19120
\(9\) −1.02706 −0.342352
\(10\) 2.33324 0.737835
\(11\) 0.0531881 0.0160368 0.00801841 0.999968i \(-0.497448\pi\)
0.00801841 + 0.999968i \(0.497448\pi\)
\(12\) −4.83751 −1.39647
\(13\) 4.09428 1.13555 0.567774 0.823184i \(-0.307805\pi\)
0.567774 + 0.823184i \(0.307805\pi\)
\(14\) 8.97829 2.39955
\(15\) 1.40461 0.362670
\(16\) 0.973182 0.243295
\(17\) 6.43239 1.56008 0.780042 0.625727i \(-0.215198\pi\)
0.780042 + 0.625727i \(0.215198\pi\)
\(18\) 2.39637 0.564830
\(19\) 3.86078 0.885723 0.442862 0.896590i \(-0.353963\pi\)
0.442862 + 0.896590i \(0.353963\pi\)
\(20\) −3.44401 −0.770104
\(21\) 5.40495 1.17946
\(22\) −0.124101 −0.0264584
\(23\) −1.52544 −0.318076 −0.159038 0.987272i \(-0.550839\pi\)
−0.159038 + 0.987272i \(0.550839\pi\)
\(24\) 4.73246 0.966009
\(25\) 1.00000 0.200000
\(26\) −9.55294 −1.87348
\(27\) 5.65646 1.08859
\(28\) −13.2525 −2.50449
\(29\) 0.386636 0.0717964 0.0358982 0.999355i \(-0.488571\pi\)
0.0358982 + 0.999355i \(0.488571\pi\)
\(30\) −3.27730 −0.598351
\(31\) −5.73040 −1.02921 −0.514605 0.857427i \(-0.672061\pi\)
−0.514605 + 0.857427i \(0.672061\pi\)
\(32\) 4.46777 0.789798
\(33\) −0.0747088 −0.0130051
\(34\) −15.0083 −2.57390
\(35\) 3.84799 0.650430
\(36\) −3.53719 −0.589532
\(37\) 7.40755 1.21779 0.608897 0.793249i \(-0.291612\pi\)
0.608897 + 0.793249i \(0.291612\pi\)
\(38\) −9.00812 −1.46131
\(39\) −5.75089 −0.920879
\(40\) 3.36922 0.532721
\(41\) 1.71601 0.267996 0.133998 0.990982i \(-0.457218\pi\)
0.133998 + 0.990982i \(0.457218\pi\)
\(42\) −12.6110 −1.94593
\(43\) 8.69101 1.32537 0.662684 0.748900i \(-0.269417\pi\)
0.662684 + 0.748900i \(0.269417\pi\)
\(44\) 0.183180 0.0276155
\(45\) 1.02706 0.153105
\(46\) 3.55921 0.524778
\(47\) 3.60357 0.525635 0.262817 0.964846i \(-0.415348\pi\)
0.262817 + 0.964846i \(0.415348\pi\)
\(48\) −1.36695 −0.197302
\(49\) 7.80706 1.11529
\(50\) −2.33324 −0.329970
\(51\) −9.03503 −1.26516
\(52\) 14.1007 1.95542
\(53\) 13.1394 1.80483 0.902415 0.430868i \(-0.141793\pi\)
0.902415 + 0.430868i \(0.141793\pi\)
\(54\) −13.1979 −1.79601
\(55\) −0.0531881 −0.00717189
\(56\) 12.9647 1.73249
\(57\) −5.42291 −0.718281
\(58\) −0.902114 −0.118453
\(59\) 5.87507 0.764869 0.382434 0.923983i \(-0.375086\pi\)
0.382434 + 0.923983i \(0.375086\pi\)
\(60\) 4.83751 0.624519
\(61\) 14.8116 1.89643 0.948213 0.317635i \(-0.102889\pi\)
0.948213 + 0.317635i \(0.102889\pi\)
\(62\) 13.3704 1.69804
\(63\) 3.95211 0.497919
\(64\) −12.3708 −1.54634
\(65\) −4.09428 −0.507833
\(66\) 0.174314 0.0214565
\(67\) −11.5574 −1.41196 −0.705978 0.708233i \(-0.749492\pi\)
−0.705978 + 0.708233i \(0.749492\pi\)
\(68\) 22.1532 2.68647
\(69\) 2.14265 0.257945
\(70\) −8.97829 −1.07311
\(71\) −6.81391 −0.808663 −0.404331 0.914613i \(-0.632496\pi\)
−0.404331 + 0.914613i \(0.632496\pi\)
\(72\) 3.46038 0.407810
\(73\) 7.77783 0.910326 0.455163 0.890408i \(-0.349581\pi\)
0.455163 + 0.890408i \(0.349581\pi\)
\(74\) −17.2836 −2.00918
\(75\) −1.40461 −0.162191
\(76\) 13.2966 1.52522
\(77\) −0.204668 −0.0233240
\(78\) 13.4182 1.51931
\(79\) 4.31554 0.485536 0.242768 0.970084i \(-0.421945\pi\)
0.242768 + 0.970084i \(0.421945\pi\)
\(80\) −0.973182 −0.108805
\(81\) −4.86398 −0.540442
\(82\) −4.00387 −0.442153
\(83\) −7.65175 −0.839889 −0.419945 0.907550i \(-0.637950\pi\)
−0.419945 + 0.907550i \(0.637950\pi\)
\(84\) 18.6147 2.03103
\(85\) −6.43239 −0.697691
\(86\) −20.2782 −2.18666
\(87\) −0.543074 −0.0582237
\(88\) −0.179203 −0.0191031
\(89\) 9.33077 0.989059 0.494530 0.869161i \(-0.335340\pi\)
0.494530 + 0.869161i \(0.335340\pi\)
\(90\) −2.39637 −0.252600
\(91\) −15.7548 −1.65155
\(92\) −5.25363 −0.547728
\(93\) 8.04900 0.834643
\(94\) −8.40800 −0.867219
\(95\) −3.86078 −0.396107
\(96\) −6.27550 −0.640491
\(97\) −0.304722 −0.0309398 −0.0154699 0.999880i \(-0.504924\pi\)
−0.0154699 + 0.999880i \(0.504924\pi\)
\(98\) −18.2157 −1.84007
\(99\) −0.0546273 −0.00549025
\(100\) 3.44401 0.344401
\(101\) −16.0684 −1.59887 −0.799434 0.600754i \(-0.794867\pi\)
−0.799434 + 0.600754i \(0.794867\pi\)
\(102\) 21.0809 2.08732
\(103\) −3.48132 −0.343024 −0.171512 0.985182i \(-0.554865\pi\)
−0.171512 + 0.985182i \(0.554865\pi\)
\(104\) −13.7945 −1.35266
\(105\) −5.40495 −0.527469
\(106\) −30.6573 −2.97770
\(107\) −10.6835 −1.03281 −0.516406 0.856344i \(-0.672730\pi\)
−0.516406 + 0.856344i \(0.672730\pi\)
\(108\) 19.4809 1.87455
\(109\) −1.66031 −0.159029 −0.0795143 0.996834i \(-0.525337\pi\)
−0.0795143 + 0.996834i \(0.525337\pi\)
\(110\) 0.124101 0.0118325
\(111\) −10.4048 −0.987575
\(112\) −3.74480 −0.353850
\(113\) 11.4399 1.07618 0.538089 0.842888i \(-0.319146\pi\)
0.538089 + 0.842888i \(0.319146\pi\)
\(114\) 12.6529 1.18506
\(115\) 1.52544 0.142248
\(116\) 1.33158 0.123634
\(117\) −4.20506 −0.388758
\(118\) −13.7079 −1.26192
\(119\) −24.7518 −2.26899
\(120\) −4.73246 −0.432012
\(121\) −10.9972 −0.999743
\(122\) −34.5589 −3.12882
\(123\) −2.41033 −0.217333
\(124\) −19.7355 −1.77230
\(125\) −1.00000 −0.0894427
\(126\) −9.22122 −0.821492
\(127\) 4.87444 0.432536 0.216268 0.976334i \(-0.430611\pi\)
0.216268 + 0.976334i \(0.430611\pi\)
\(128\) 19.9284 1.76144
\(129\) −12.2075 −1.07481
\(130\) 9.55294 0.837848
\(131\) 6.94772 0.607025 0.303513 0.952827i \(-0.401841\pi\)
0.303513 + 0.952827i \(0.401841\pi\)
\(132\) −0.257298 −0.0223949
\(133\) −14.8562 −1.28820
\(134\) 26.9661 2.32952
\(135\) −5.65646 −0.486831
\(136\) −21.6721 −1.85837
\(137\) 3.53942 0.302393 0.151196 0.988504i \(-0.451687\pi\)
0.151196 + 0.988504i \(0.451687\pi\)
\(138\) −4.99933 −0.425571
\(139\) −5.60196 −0.475152 −0.237576 0.971369i \(-0.576353\pi\)
−0.237576 + 0.971369i \(0.576353\pi\)
\(140\) 13.2525 1.12004
\(141\) −5.06163 −0.426266
\(142\) 15.8985 1.33417
\(143\) 0.217767 0.0182106
\(144\) −0.999514 −0.0832928
\(145\) −0.386636 −0.0321083
\(146\) −18.1475 −1.50190
\(147\) −10.9659 −0.904453
\(148\) 25.5117 2.09705
\(149\) −3.55897 −0.291563 −0.145781 0.989317i \(-0.546570\pi\)
−0.145781 + 0.989317i \(0.546570\pi\)
\(150\) 3.27730 0.267591
\(151\) 12.7853 1.04045 0.520227 0.854028i \(-0.325847\pi\)
0.520227 + 0.854028i \(0.325847\pi\)
\(152\) −13.0078 −1.05507
\(153\) −6.60643 −0.534099
\(154\) 0.477539 0.0384812
\(155\) 5.73040 0.460277
\(156\) −19.8061 −1.58576
\(157\) 20.3533 1.62437 0.812186 0.583398i \(-0.198277\pi\)
0.812186 + 0.583398i \(0.198277\pi\)
\(158\) −10.0692 −0.801062
\(159\) −18.4557 −1.46364
\(160\) −4.46777 −0.353209
\(161\) 5.86988 0.462611
\(162\) 11.3488 0.891649
\(163\) 8.28586 0.648999 0.324499 0.945886i \(-0.394804\pi\)
0.324499 + 0.945886i \(0.394804\pi\)
\(164\) 5.90996 0.461490
\(165\) 0.0747088 0.00581607
\(166\) 17.8534 1.38569
\(167\) 18.8878 1.46158 0.730791 0.682602i \(-0.239152\pi\)
0.730791 + 0.682602i \(0.239152\pi\)
\(168\) −18.2105 −1.40497
\(169\) 3.76312 0.289471
\(170\) 15.0083 1.15109
\(171\) −3.96524 −0.303229
\(172\) 29.9319 2.28229
\(173\) 13.1948 1.00318 0.501592 0.865104i \(-0.332748\pi\)
0.501592 + 0.865104i \(0.332748\pi\)
\(174\) 1.26712 0.0960603
\(175\) −3.84799 −0.290881
\(176\) 0.0517617 0.00390169
\(177\) −8.25221 −0.620274
\(178\) −21.7709 −1.63180
\(179\) 7.98969 0.597178 0.298589 0.954382i \(-0.403484\pi\)
0.298589 + 0.954382i \(0.403484\pi\)
\(180\) 3.53719 0.263647
\(181\) 2.65337 0.197223 0.0986117 0.995126i \(-0.468560\pi\)
0.0986117 + 0.995126i \(0.468560\pi\)
\(182\) 36.7596 2.72481
\(183\) −20.8045 −1.53792
\(184\) 5.13954 0.378892
\(185\) −7.40755 −0.544614
\(186\) −18.7803 −1.37704
\(187\) 0.342127 0.0250188
\(188\) 12.4107 0.905146
\(189\) −21.7660 −1.58325
\(190\) 9.00812 0.653518
\(191\) −12.1539 −0.879424 −0.439712 0.898139i \(-0.644919\pi\)
−0.439712 + 0.898139i \(0.644919\pi\)
\(192\) 17.3761 1.25402
\(193\) −18.9896 −1.36690 −0.683452 0.729996i \(-0.739522\pi\)
−0.683452 + 0.729996i \(0.739522\pi\)
\(194\) 0.710989 0.0510461
\(195\) 5.75089 0.411829
\(196\) 26.8876 1.92054
\(197\) −8.51495 −0.606665 −0.303333 0.952885i \(-0.598099\pi\)
−0.303333 + 0.952885i \(0.598099\pi\)
\(198\) 0.127458 0.00905808
\(199\) 0.501648 0.0355609 0.0177804 0.999842i \(-0.494340\pi\)
0.0177804 + 0.999842i \(0.494340\pi\)
\(200\) −3.36922 −0.238240
\(201\) 16.2336 1.14503
\(202\) 37.4915 2.63789
\(203\) −1.48777 −0.104421
\(204\) −31.1167 −2.17861
\(205\) −1.71601 −0.119851
\(206\) 8.12274 0.565938
\(207\) 1.56671 0.108894
\(208\) 3.98448 0.276274
\(209\) 0.205348 0.0142042
\(210\) 12.6110 0.870245
\(211\) −24.1263 −1.66092 −0.830462 0.557075i \(-0.811923\pi\)
−0.830462 + 0.557075i \(0.811923\pi\)
\(212\) 45.2521 3.10793
\(213\) 9.57092 0.655789
\(214\) 24.9271 1.70398
\(215\) −8.69101 −0.592722
\(216\) −19.0579 −1.29672
\(217\) 22.0505 1.49689
\(218\) 3.87390 0.262373
\(219\) −10.9249 −0.738233
\(220\) −0.183180 −0.0123500
\(221\) 26.3360 1.77155
\(222\) 24.2768 1.62935
\(223\) −20.6011 −1.37955 −0.689775 0.724024i \(-0.742291\pi\)
−0.689775 + 0.724024i \(0.742291\pi\)
\(224\) −17.1920 −1.14869
\(225\) −1.02706 −0.0684705
\(226\) −26.6921 −1.77553
\(227\) 15.1957 1.00857 0.504286 0.863536i \(-0.331756\pi\)
0.504286 + 0.863536i \(0.331756\pi\)
\(228\) −18.6765 −1.23688
\(229\) −12.8564 −0.849573 −0.424786 0.905294i \(-0.639651\pi\)
−0.424786 + 0.905294i \(0.639651\pi\)
\(230\) −3.55921 −0.234688
\(231\) 0.287479 0.0189147
\(232\) −1.30266 −0.0855239
\(233\) 7.59265 0.497411 0.248706 0.968579i \(-0.419995\pi\)
0.248706 + 0.968579i \(0.419995\pi\)
\(234\) 9.81141 0.641392
\(235\) −3.60357 −0.235071
\(236\) 20.2338 1.31711
\(237\) −6.06167 −0.393748
\(238\) 57.7519 3.74350
\(239\) 4.62598 0.299230 0.149615 0.988744i \(-0.452197\pi\)
0.149615 + 0.988744i \(0.452197\pi\)
\(240\) 1.36695 0.0882360
\(241\) −15.9888 −1.02993 −0.514964 0.857212i \(-0.672195\pi\)
−0.514964 + 0.857212i \(0.672195\pi\)
\(242\) 25.6590 1.64943
\(243\) −10.1374 −0.650313
\(244\) 51.0112 3.26566
\(245\) −7.80706 −0.498775
\(246\) 5.62389 0.358566
\(247\) 15.8071 1.00578
\(248\) 19.3070 1.22599
\(249\) 10.7478 0.681112
\(250\) 2.33324 0.147567
\(251\) −0.581135 −0.0366809 −0.0183405 0.999832i \(-0.505838\pi\)
−0.0183405 + 0.999832i \(0.505838\pi\)
\(252\) 13.6111 0.857419
\(253\) −0.0811352 −0.00510093
\(254\) −11.3732 −0.713620
\(255\) 9.03503 0.565796
\(256\) −21.7562 −1.35976
\(257\) 16.8480 1.05095 0.525474 0.850810i \(-0.323888\pi\)
0.525474 + 0.850810i \(0.323888\pi\)
\(258\) 28.4831 1.77328
\(259\) −28.5042 −1.77116
\(260\) −14.1007 −0.874491
\(261\) −0.397097 −0.0245797
\(262\) −16.2107 −1.00150
\(263\) −7.42969 −0.458134 −0.229067 0.973411i \(-0.573568\pi\)
−0.229067 + 0.973411i \(0.573568\pi\)
\(264\) 0.251711 0.0154917
\(265\) −13.1394 −0.807144
\(266\) 34.6632 2.12534
\(267\) −13.1061 −0.802082
\(268\) −39.8037 −2.43140
\(269\) −7.18438 −0.438040 −0.219020 0.975720i \(-0.570286\pi\)
−0.219020 + 0.975720i \(0.570286\pi\)
\(270\) 13.1979 0.803198
\(271\) 12.1383 0.737348 0.368674 0.929559i \(-0.379812\pi\)
0.368674 + 0.929559i \(0.379812\pi\)
\(272\) 6.25989 0.379561
\(273\) 22.1294 1.33933
\(274\) −8.25831 −0.498903
\(275\) 0.0531881 0.00320736
\(276\) 7.37932 0.444183
\(277\) −19.3545 −1.16290 −0.581449 0.813583i \(-0.697514\pi\)
−0.581449 + 0.813583i \(0.697514\pi\)
\(278\) 13.0707 0.783929
\(279\) 5.88545 0.352352
\(280\) −12.9647 −0.774791
\(281\) 33.3153 1.98742 0.993711 0.111972i \(-0.0357166\pi\)
0.993711 + 0.111972i \(0.0357166\pi\)
\(282\) 11.8100 0.703275
\(283\) −9.55179 −0.567795 −0.283897 0.958855i \(-0.591628\pi\)
−0.283897 + 0.958855i \(0.591628\pi\)
\(284\) −23.4672 −1.39252
\(285\) 5.42291 0.321225
\(286\) −0.508103 −0.0300447
\(287\) −6.60320 −0.389775
\(288\) −4.58866 −0.270389
\(289\) 24.3757 1.43386
\(290\) 0.902114 0.0529739
\(291\) 0.428017 0.0250908
\(292\) 26.7869 1.56759
\(293\) −21.2837 −1.24341 −0.621703 0.783253i \(-0.713559\pi\)
−0.621703 + 0.783253i \(0.713559\pi\)
\(294\) 25.5861 1.49221
\(295\) −5.87507 −0.342060
\(296\) −24.9577 −1.45063
\(297\) 0.300857 0.0174575
\(298\) 8.30394 0.481034
\(299\) −6.24557 −0.361191
\(300\) −4.83751 −0.279294
\(301\) −33.4430 −1.92762
\(302\) −29.8312 −1.71659
\(303\) 22.5700 1.29661
\(304\) 3.75724 0.215492
\(305\) −14.8116 −0.848108
\(306\) 15.4144 0.881182
\(307\) −25.7525 −1.46977 −0.734887 0.678190i \(-0.762765\pi\)
−0.734887 + 0.678190i \(0.762765\pi\)
\(308\) −0.704877 −0.0401641
\(309\) 4.88991 0.278177
\(310\) −13.3704 −0.759387
\(311\) 33.7565 1.91416 0.957079 0.289827i \(-0.0935979\pi\)
0.957079 + 0.289827i \(0.0935979\pi\)
\(312\) 19.3760 1.09695
\(313\) 14.3243 0.809658 0.404829 0.914392i \(-0.367331\pi\)
0.404829 + 0.914392i \(0.367331\pi\)
\(314\) −47.4892 −2.67997
\(315\) −3.95211 −0.222676
\(316\) 14.8628 0.836095
\(317\) 32.1227 1.80419 0.902095 0.431537i \(-0.142029\pi\)
0.902095 + 0.431537i \(0.142029\pi\)
\(318\) 43.0617 2.41478
\(319\) 0.0205644 0.00115139
\(320\) 12.3708 0.691546
\(321\) 15.0062 0.837564
\(322\) −13.6958 −0.763239
\(323\) 24.8340 1.38180
\(324\) −16.7516 −0.930644
\(325\) 4.09428 0.227110
\(326\) −19.3329 −1.07075
\(327\) 2.33209 0.128965
\(328\) −5.78162 −0.319237
\(329\) −13.8665 −0.764486
\(330\) −0.174314 −0.00959565
\(331\) −25.9993 −1.42905 −0.714525 0.699610i \(-0.753357\pi\)
−0.714525 + 0.699610i \(0.753357\pi\)
\(332\) −26.3527 −1.44629
\(333\) −7.60798 −0.416915
\(334\) −44.0698 −2.41139
\(335\) 11.5574 0.631446
\(336\) 5.26000 0.286956
\(337\) −4.58480 −0.249750 −0.124875 0.992172i \(-0.539853\pi\)
−0.124875 + 0.992172i \(0.539853\pi\)
\(338\) −8.78027 −0.477584
\(339\) −16.0687 −0.872732
\(340\) −22.1532 −1.20143
\(341\) −0.304789 −0.0165053
\(342\) 9.25186 0.500283
\(343\) −3.10555 −0.167684
\(344\) −29.2819 −1.57878
\(345\) −2.14265 −0.115357
\(346\) −30.7867 −1.65510
\(347\) −15.5934 −0.837096 −0.418548 0.908195i \(-0.637461\pi\)
−0.418548 + 0.908195i \(0.637461\pi\)
\(348\) −1.87035 −0.100261
\(349\) −35.0544 −1.87642 −0.938210 0.346067i \(-0.887517\pi\)
−0.938210 + 0.346067i \(0.887517\pi\)
\(350\) 8.97829 0.479910
\(351\) 23.1591 1.23614
\(352\) 0.237633 0.0126659
\(353\) −4.71655 −0.251037 −0.125518 0.992091i \(-0.540059\pi\)
−0.125518 + 0.992091i \(0.540059\pi\)
\(354\) 19.2544 1.02336
\(355\) 6.81391 0.361645
\(356\) 32.1352 1.70316
\(357\) 34.7667 1.84005
\(358\) −18.6419 −0.985254
\(359\) −2.33013 −0.122980 −0.0614899 0.998108i \(-0.519585\pi\)
−0.0614899 + 0.998108i \(0.519585\pi\)
\(360\) −3.46038 −0.182378
\(361\) −4.09440 −0.215495
\(362\) −6.19095 −0.325389
\(363\) 15.4468 0.810746
\(364\) −54.2595 −2.84397
\(365\) −7.77783 −0.407110
\(366\) 48.5420 2.53733
\(367\) 34.8477 1.81904 0.909518 0.415664i \(-0.136451\pi\)
0.909518 + 0.415664i \(0.136451\pi\)
\(368\) −1.48453 −0.0773864
\(369\) −1.76244 −0.0917490
\(370\) 17.2836 0.898531
\(371\) −50.5602 −2.62495
\(372\) 27.7208 1.43726
\(373\) −7.35432 −0.380792 −0.190396 0.981707i \(-0.560977\pi\)
−0.190396 + 0.981707i \(0.560977\pi\)
\(374\) −0.798264 −0.0412773
\(375\) 1.40461 0.0725340
\(376\) −12.1412 −0.626136
\(377\) 1.58299 0.0815283
\(378\) 50.7854 2.61212
\(379\) 1.83124 0.0940644 0.0470322 0.998893i \(-0.485024\pi\)
0.0470322 + 0.998893i \(0.485024\pi\)
\(380\) −13.2966 −0.682099
\(381\) −6.84670 −0.350767
\(382\) 28.3579 1.45092
\(383\) −22.4259 −1.14591 −0.572954 0.819588i \(-0.694203\pi\)
−0.572954 + 0.819588i \(0.694203\pi\)
\(384\) −27.9917 −1.42845
\(385\) 0.204668 0.0104308
\(386\) 44.3074 2.25519
\(387\) −8.92617 −0.453743
\(388\) −1.04947 −0.0532785
\(389\) 4.27589 0.216796 0.108398 0.994108i \(-0.465428\pi\)
0.108398 + 0.994108i \(0.465428\pi\)
\(390\) −13.4182 −0.679457
\(391\) −9.81222 −0.496225
\(392\) −26.3037 −1.32854
\(393\) −9.75887 −0.492270
\(394\) 19.8674 1.00091
\(395\) −4.31554 −0.217138
\(396\) −0.188137 −0.00945423
\(397\) 2.89010 0.145050 0.0725249 0.997367i \(-0.476894\pi\)
0.0725249 + 0.997367i \(0.476894\pi\)
\(398\) −1.17047 −0.0586701
\(399\) 20.8673 1.04467
\(400\) 0.973182 0.0486591
\(401\) −6.62421 −0.330797 −0.165399 0.986227i \(-0.552891\pi\)
−0.165399 + 0.986227i \(0.552891\pi\)
\(402\) −37.8770 −1.88913
\(403\) −23.4619 −1.16872
\(404\) −55.3398 −2.75326
\(405\) 4.86398 0.241693
\(406\) 3.47133 0.172279
\(407\) 0.393994 0.0195295
\(408\) 30.4410 1.50705
\(409\) −10.6685 −0.527525 −0.263763 0.964588i \(-0.584964\pi\)
−0.263763 + 0.964588i \(0.584964\pi\)
\(410\) 4.00387 0.197737
\(411\) −4.97152 −0.245227
\(412\) −11.9897 −0.590689
\(413\) −22.6072 −1.11243
\(414\) −3.65552 −0.179659
\(415\) 7.65175 0.375610
\(416\) 18.2923 0.896855
\(417\) 7.86859 0.385327
\(418\) −0.479125 −0.0234348
\(419\) 9.04484 0.441869 0.220935 0.975289i \(-0.429089\pi\)
0.220935 + 0.975289i \(0.429089\pi\)
\(420\) −18.6147 −0.908304
\(421\) −6.50841 −0.317201 −0.158600 0.987343i \(-0.550698\pi\)
−0.158600 + 0.987343i \(0.550698\pi\)
\(422\) 56.2925 2.74028
\(423\) −3.70107 −0.179952
\(424\) −44.2694 −2.14991
\(425\) 6.43239 0.312017
\(426\) −22.3313 −1.08195
\(427\) −56.9948 −2.75817
\(428\) −36.7940 −1.77851
\(429\) −0.305879 −0.0147680
\(430\) 20.2782 0.977903
\(431\) 6.92237 0.333439 0.166720 0.986004i \(-0.446683\pi\)
0.166720 + 0.986004i \(0.446683\pi\)
\(432\) 5.50477 0.264848
\(433\) −23.2515 −1.11739 −0.558697 0.829372i \(-0.688698\pi\)
−0.558697 + 0.829372i \(0.688698\pi\)
\(434\) −51.4492 −2.46964
\(435\) 0.543074 0.0260384
\(436\) −5.71812 −0.273848
\(437\) −5.88938 −0.281727
\(438\) 25.4903 1.21797
\(439\) 25.8361 1.23309 0.616545 0.787319i \(-0.288532\pi\)
0.616545 + 0.787319i \(0.288532\pi\)
\(440\) 0.179203 0.00854315
\(441\) −8.01829 −0.381824
\(442\) −61.4482 −2.92279
\(443\) −0.285867 −0.0135820 −0.00679098 0.999977i \(-0.502162\pi\)
−0.00679098 + 0.999977i \(0.502162\pi\)
\(444\) −35.8341 −1.70061
\(445\) −9.33077 −0.442321
\(446\) 48.0673 2.27605
\(447\) 4.99899 0.236444
\(448\) 47.6026 2.24901
\(449\) −12.7000 −0.599348 −0.299674 0.954042i \(-0.596878\pi\)
−0.299674 + 0.954042i \(0.596878\pi\)
\(450\) 2.39637 0.112966
\(451\) 0.0912714 0.00429780
\(452\) 39.3993 1.85318
\(453\) −17.9584 −0.843761
\(454\) −35.4552 −1.66399
\(455\) 15.7548 0.738595
\(456\) 18.2710 0.855616
\(457\) 34.5110 1.61436 0.807178 0.590307i \(-0.200994\pi\)
0.807178 + 0.590307i \(0.200994\pi\)
\(458\) 29.9970 1.40167
\(459\) 36.3846 1.69829
\(460\) 5.25363 0.244952
\(461\) −1.31095 −0.0610571 −0.0305285 0.999534i \(-0.509719\pi\)
−0.0305285 + 0.999534i \(0.509719\pi\)
\(462\) −0.670758 −0.0312065
\(463\) 8.97271 0.416997 0.208499 0.978023i \(-0.433142\pi\)
0.208499 + 0.978023i \(0.433142\pi\)
\(464\) 0.376267 0.0174677
\(465\) −8.04900 −0.373264
\(466\) −17.7155 −0.820654
\(467\) 31.5143 1.45831 0.729154 0.684350i \(-0.239914\pi\)
0.729154 + 0.684350i \(0.239914\pi\)
\(468\) −14.4823 −0.669443
\(469\) 44.4727 2.05356
\(470\) 8.40800 0.387832
\(471\) −28.5886 −1.31729
\(472\) −19.7944 −0.911111
\(473\) 0.462259 0.0212547
\(474\) 14.1433 0.649625
\(475\) 3.86078 0.177145
\(476\) −85.2454 −3.90722
\(477\) −13.4949 −0.617888
\(478\) −10.7935 −0.493684
\(479\) 23.6211 1.07927 0.539637 0.841898i \(-0.318561\pi\)
0.539637 + 0.841898i \(0.318561\pi\)
\(480\) 6.27550 0.286436
\(481\) 30.3286 1.38286
\(482\) 37.3057 1.69923
\(483\) −8.24492 −0.375157
\(484\) −37.8744 −1.72156
\(485\) 0.304722 0.0138367
\(486\) 23.6529 1.07292
\(487\) 38.7504 1.75595 0.877975 0.478707i \(-0.158894\pi\)
0.877975 + 0.478707i \(0.158894\pi\)
\(488\) −49.9034 −2.25902
\(489\) −11.6384 −0.526308
\(490\) 18.2157 0.822903
\(491\) 13.3406 0.602055 0.301027 0.953615i \(-0.402670\pi\)
0.301027 + 0.953615i \(0.402670\pi\)
\(492\) −8.30121 −0.374248
\(493\) 2.48699 0.112008
\(494\) −36.8818 −1.65939
\(495\) 0.0546273 0.00245531
\(496\) −5.57672 −0.250402
\(497\) 26.2199 1.17612
\(498\) −25.0771 −1.12373
\(499\) −9.83177 −0.440130 −0.220065 0.975485i \(-0.570627\pi\)
−0.220065 + 0.975485i \(0.570627\pi\)
\(500\) −3.44401 −0.154021
\(501\) −26.5301 −1.18528
\(502\) 1.35593 0.0605180
\(503\) −22.0632 −0.983748 −0.491874 0.870666i \(-0.663688\pi\)
−0.491874 + 0.870666i \(0.663688\pi\)
\(504\) −13.3155 −0.593121
\(505\) 16.0684 0.715036
\(506\) 0.189308 0.00841577
\(507\) −5.28574 −0.234748
\(508\) 16.7876 0.744829
\(509\) 31.2126 1.38348 0.691738 0.722149i \(-0.256845\pi\)
0.691738 + 0.722149i \(0.256845\pi\)
\(510\) −21.0809 −0.933478
\(511\) −29.9290 −1.32398
\(512\) 10.9057 0.481968
\(513\) 21.8384 0.964187
\(514\) −39.3104 −1.73391
\(515\) 3.48132 0.153405
\(516\) −42.0428 −1.85083
\(517\) 0.191667 0.00842951
\(518\) 66.5071 2.92216
\(519\) −18.5336 −0.813536
\(520\) 13.7945 0.604930
\(521\) 27.4114 1.20091 0.600457 0.799657i \(-0.294986\pi\)
0.600457 + 0.799657i \(0.294986\pi\)
\(522\) 0.926522 0.0405528
\(523\) −17.2473 −0.754173 −0.377086 0.926178i \(-0.623074\pi\)
−0.377086 + 0.926178i \(0.623074\pi\)
\(524\) 23.9280 1.04530
\(525\) 5.40495 0.235891
\(526\) 17.3353 0.755853
\(527\) −36.8602 −1.60565
\(528\) −0.0727053 −0.00316409
\(529\) −20.6730 −0.898828
\(530\) 30.6573 1.33167
\(531\) −6.03403 −0.261855
\(532\) −51.1651 −2.21829
\(533\) 7.02583 0.304322
\(534\) 30.5798 1.32332
\(535\) 10.6835 0.461888
\(536\) 38.9393 1.68192
\(537\) −11.2224 −0.484284
\(538\) 16.7629 0.722700
\(539\) 0.415243 0.0178858
\(540\) −19.4809 −0.838325
\(541\) −7.60227 −0.326847 −0.163424 0.986556i \(-0.552254\pi\)
−0.163424 + 0.986556i \(0.552254\pi\)
\(542\) −28.3215 −1.21651
\(543\) −3.72696 −0.159939
\(544\) 28.7385 1.23215
\(545\) 1.66031 0.0711198
\(546\) −51.6331 −2.20969
\(547\) 12.1411 0.519115 0.259558 0.965728i \(-0.416423\pi\)
0.259558 + 0.965728i \(0.416423\pi\)
\(548\) 12.1898 0.520722
\(549\) −15.2123 −0.649246
\(550\) −0.124101 −0.00529167
\(551\) 1.49271 0.0635918
\(552\) −7.21907 −0.307264
\(553\) −16.6062 −0.706166
\(554\) 45.1587 1.91861
\(555\) 10.4048 0.441657
\(556\) −19.2932 −0.818214
\(557\) −22.6142 −0.958196 −0.479098 0.877761i \(-0.659036\pi\)
−0.479098 + 0.877761i \(0.659036\pi\)
\(558\) −13.7322 −0.581329
\(559\) 35.5834 1.50502
\(560\) 3.74480 0.158247
\(561\) −0.480556 −0.0202891
\(562\) −77.7325 −3.27895
\(563\) 41.2958 1.74041 0.870206 0.492689i \(-0.163986\pi\)
0.870206 + 0.492689i \(0.163986\pi\)
\(564\) −17.4323 −0.734032
\(565\) −11.4399 −0.481282
\(566\) 22.2866 0.936776
\(567\) 18.7166 0.786022
\(568\) 22.9576 0.963278
\(569\) −18.1614 −0.761365 −0.380683 0.924706i \(-0.624311\pi\)
−0.380683 + 0.924706i \(0.624311\pi\)
\(570\) −12.6529 −0.529973
\(571\) 36.1298 1.51198 0.755992 0.654581i \(-0.227155\pi\)
0.755992 + 0.654581i \(0.227155\pi\)
\(572\) 0.749992 0.0313587
\(573\) 17.0715 0.713173
\(574\) 15.4068 0.643069
\(575\) −1.52544 −0.0636152
\(576\) 12.7055 0.529395
\(577\) 10.0358 0.417794 0.208897 0.977938i \(-0.433013\pi\)
0.208897 + 0.977938i \(0.433013\pi\)
\(578\) −56.8743 −2.36566
\(579\) 26.6731 1.10850
\(580\) −1.33158 −0.0552907
\(581\) 29.4439 1.22154
\(582\) −0.998666 −0.0413961
\(583\) 0.698858 0.0289437
\(584\) −26.2052 −1.08438
\(585\) 4.20506 0.173858
\(586\) 49.6599 2.05143
\(587\) −22.2221 −0.917206 −0.458603 0.888641i \(-0.651650\pi\)
−0.458603 + 0.888641i \(0.651650\pi\)
\(588\) −37.7667 −1.55747
\(589\) −22.1238 −0.911595
\(590\) 13.7079 0.564347
\(591\) 11.9602 0.491978
\(592\) 7.20889 0.296284
\(593\) 20.6748 0.849013 0.424507 0.905425i \(-0.360448\pi\)
0.424507 + 0.905425i \(0.360448\pi\)
\(594\) −0.701971 −0.0288022
\(595\) 24.7518 1.01472
\(596\) −12.2571 −0.502072
\(597\) −0.704622 −0.0288383
\(598\) 14.5724 0.595911
\(599\) 20.2471 0.827275 0.413638 0.910442i \(-0.364258\pi\)
0.413638 + 0.910442i \(0.364258\pi\)
\(600\) 4.73246 0.193202
\(601\) 10.9073 0.444917 0.222458 0.974942i \(-0.428592\pi\)
0.222458 + 0.974942i \(0.428592\pi\)
\(602\) 78.0305 3.18028
\(603\) 11.8701 0.483387
\(604\) 44.0327 1.79167
\(605\) 10.9972 0.447099
\(606\) −52.6611 −2.13921
\(607\) −1.26576 −0.0513755 −0.0256877 0.999670i \(-0.508178\pi\)
−0.0256877 + 0.999670i \(0.508178\pi\)
\(608\) 17.2491 0.699543
\(609\) 2.08975 0.0846808
\(610\) 34.5589 1.39925
\(611\) 14.7540 0.596884
\(612\) −22.7526 −0.919720
\(613\) 8.15339 0.329312 0.164656 0.986351i \(-0.447349\pi\)
0.164656 + 0.986351i \(0.447349\pi\)
\(614\) 60.0868 2.42491
\(615\) 2.41033 0.0971941
\(616\) 0.689570 0.0277836
\(617\) 6.83241 0.275063 0.137531 0.990497i \(-0.456083\pi\)
0.137531 + 0.990497i \(0.456083\pi\)
\(618\) −11.4093 −0.458950
\(619\) −18.0731 −0.726419 −0.363209 0.931708i \(-0.618319\pi\)
−0.363209 + 0.931708i \(0.618319\pi\)
\(620\) 19.7355 0.792599
\(621\) −8.62859 −0.346253
\(622\) −78.7621 −3.15807
\(623\) −35.9047 −1.43849
\(624\) −5.59666 −0.224046
\(625\) 1.00000 0.0400000
\(626\) −33.4221 −1.33581
\(627\) −0.288434 −0.0115190
\(628\) 70.0971 2.79718
\(629\) 47.6482 1.89986
\(630\) 9.22122 0.367382
\(631\) −34.8105 −1.38579 −0.692893 0.721041i \(-0.743664\pi\)
−0.692893 + 0.721041i \(0.743664\pi\)
\(632\) −14.5400 −0.578370
\(633\) 33.8882 1.34693
\(634\) −74.9500 −2.97664
\(635\) −4.87444 −0.193436
\(636\) −63.5617 −2.52039
\(637\) 31.9643 1.26647
\(638\) −0.0479817 −0.00189962
\(639\) 6.99828 0.276848
\(640\) −19.9284 −0.787739
\(641\) −12.3625 −0.488289 −0.244144 0.969739i \(-0.578507\pi\)
−0.244144 + 0.969739i \(0.578507\pi\)
\(642\) −35.0130 −1.38185
\(643\) −24.1796 −0.953550 −0.476775 0.879025i \(-0.658194\pi\)
−0.476775 + 0.879025i \(0.658194\pi\)
\(644\) 20.2159 0.796619
\(645\) 12.2075 0.480671
\(646\) −57.9438 −2.27977
\(647\) −8.62444 −0.339062 −0.169531 0.985525i \(-0.554225\pi\)
−0.169531 + 0.985525i \(0.554225\pi\)
\(648\) 16.3878 0.643775
\(649\) 0.312484 0.0122661
\(650\) −9.55294 −0.374697
\(651\) −30.9725 −1.21391
\(652\) 28.5366 1.11758
\(653\) −29.4156 −1.15112 −0.575561 0.817759i \(-0.695216\pi\)
−0.575561 + 0.817759i \(0.695216\pi\)
\(654\) −5.44133 −0.212773
\(655\) −6.94772 −0.271470
\(656\) 1.66999 0.0652022
\(657\) −7.98827 −0.311652
\(658\) 32.3539 1.26129
\(659\) −20.7071 −0.806634 −0.403317 0.915060i \(-0.632143\pi\)
−0.403317 + 0.915060i \(0.632143\pi\)
\(660\) 0.257298 0.0100153
\(661\) 27.3892 1.06532 0.532658 0.846331i \(-0.321193\pi\)
0.532658 + 0.846331i \(0.321193\pi\)
\(662\) 60.6625 2.35772
\(663\) −36.9919 −1.43665
\(664\) 25.7804 1.00048
\(665\) 14.8562 0.576101
\(666\) 17.7512 0.687846
\(667\) −0.589789 −0.0228367
\(668\) 65.0497 2.51685
\(669\) 28.9366 1.11875
\(670\) −26.9661 −1.04179
\(671\) 0.787799 0.0304127
\(672\) 24.1481 0.931533
\(673\) −31.3578 −1.20875 −0.604377 0.796698i \(-0.706578\pi\)
−0.604377 + 0.796698i \(0.706578\pi\)
\(674\) 10.6974 0.412050
\(675\) 5.65646 0.217717
\(676\) 12.9602 0.498470
\(677\) −48.4275 −1.86122 −0.930611 0.366011i \(-0.880723\pi\)
−0.930611 + 0.366011i \(0.880723\pi\)
\(678\) 37.4921 1.43988
\(679\) 1.17257 0.0449990
\(680\) 21.6721 0.831089
\(681\) −21.3441 −0.817907
\(682\) 0.711146 0.0272312
\(683\) 0.565404 0.0216346 0.0108173 0.999941i \(-0.496557\pi\)
0.0108173 + 0.999941i \(0.496557\pi\)
\(684\) −13.6563 −0.522163
\(685\) −3.53942 −0.135234
\(686\) 7.24599 0.276653
\(687\) 18.0582 0.688965
\(688\) 8.45794 0.322456
\(689\) 53.7962 2.04947
\(690\) 4.99933 0.190321
\(691\) 21.7559 0.827634 0.413817 0.910360i \(-0.364195\pi\)
0.413817 + 0.910360i \(0.364195\pi\)
\(692\) 45.4431 1.72749
\(693\) 0.210205 0.00798504
\(694\) 36.3831 1.38108
\(695\) 5.60196 0.212494
\(696\) 1.82974 0.0693560
\(697\) 11.0381 0.418096
\(698\) 81.7904 3.09581
\(699\) −10.6647 −0.403378
\(700\) −13.2525 −0.500898
\(701\) 3.07596 0.116177 0.0580887 0.998311i \(-0.481499\pi\)
0.0580887 + 0.998311i \(0.481499\pi\)
\(702\) −54.0358 −2.03945
\(703\) 28.5989 1.07863
\(704\) −0.657977 −0.0247984
\(705\) 5.06163 0.190632
\(706\) 11.0048 0.414173
\(707\) 61.8312 2.32540
\(708\) −28.4207 −1.06811
\(709\) 37.1833 1.39645 0.698223 0.715880i \(-0.253974\pi\)
0.698223 + 0.715880i \(0.253974\pi\)
\(710\) −15.8985 −0.596660
\(711\) −4.43231 −0.166224
\(712\) −31.4374 −1.17817
\(713\) 8.74137 0.327367
\(714\) −81.1192 −3.03581
\(715\) −0.217767 −0.00814403
\(716\) 27.5166 1.02834
\(717\) −6.49772 −0.242662
\(718\) 5.43676 0.202898
\(719\) 21.9924 0.820178 0.410089 0.912045i \(-0.365498\pi\)
0.410089 + 0.912045i \(0.365498\pi\)
\(720\) 0.999514 0.0372497
\(721\) 13.3961 0.498896
\(722\) 9.55321 0.355534
\(723\) 22.4581 0.835225
\(724\) 9.13823 0.339619
\(725\) 0.386636 0.0143593
\(726\) −36.0411 −1.33761
\(727\) 51.8150 1.92171 0.960855 0.277051i \(-0.0893572\pi\)
0.960855 + 0.277051i \(0.0893572\pi\)
\(728\) 53.0813 1.96732
\(729\) 28.8310 1.06782
\(730\) 18.1475 0.671670
\(731\) 55.9040 2.06768
\(732\) −71.6510 −2.64830
\(733\) −4.51528 −0.166776 −0.0833878 0.996517i \(-0.526574\pi\)
−0.0833878 + 0.996517i \(0.526574\pi\)
\(734\) −81.3081 −3.00114
\(735\) 10.9659 0.404484
\(736\) −6.81532 −0.251216
\(737\) −0.614714 −0.0226433
\(738\) 4.11220 0.151372
\(739\) −18.9263 −0.696217 −0.348108 0.937454i \(-0.613176\pi\)
−0.348108 + 0.937454i \(0.613176\pi\)
\(740\) −25.5117 −0.937828
\(741\) −22.2029 −0.815643
\(742\) 117.969 4.33078
\(743\) −44.9459 −1.64890 −0.824452 0.565932i \(-0.808516\pi\)
−0.824452 + 0.565932i \(0.808516\pi\)
\(744\) −27.1189 −0.994226
\(745\) 3.55897 0.130391
\(746\) 17.1594 0.628250
\(747\) 7.85879 0.287538
\(748\) 1.17829 0.0430825
\(749\) 41.1100 1.50213
\(750\) −3.27730 −0.119670
\(751\) −46.7124 −1.70456 −0.852281 0.523085i \(-0.824781\pi\)
−0.852281 + 0.523085i \(0.824781\pi\)
\(752\) 3.50693 0.127885
\(753\) 0.816271 0.0297466
\(754\) −3.69351 −0.134510
\(755\) −12.7853 −0.465305
\(756\) −74.9624 −2.72636
\(757\) −23.7932 −0.864777 −0.432388 0.901687i \(-0.642329\pi\)
−0.432388 + 0.901687i \(0.642329\pi\)
\(758\) −4.27272 −0.155192
\(759\) 0.113964 0.00413662
\(760\) 13.0078 0.471843
\(761\) 19.6816 0.713457 0.356729 0.934208i \(-0.383892\pi\)
0.356729 + 0.934208i \(0.383892\pi\)
\(762\) 15.9750 0.578713
\(763\) 6.38886 0.231292
\(764\) −41.8581 −1.51437
\(765\) 6.60643 0.238856
\(766\) 52.3249 1.89058
\(767\) 24.0542 0.868546
\(768\) 30.5591 1.10271
\(769\) 14.5815 0.525821 0.262911 0.964820i \(-0.415318\pi\)
0.262911 + 0.964820i \(0.415318\pi\)
\(770\) −0.477539 −0.0172093
\(771\) −23.6649 −0.852272
\(772\) −65.4004 −2.35381
\(773\) 41.1355 1.47954 0.739770 0.672860i \(-0.234934\pi\)
0.739770 + 0.672860i \(0.234934\pi\)
\(774\) 20.8269 0.748607
\(775\) −5.73040 −0.205842
\(776\) 1.02668 0.0368555
\(777\) 40.0374 1.43633
\(778\) −9.97668 −0.357681
\(779\) 6.62514 0.237370
\(780\) 19.8061 0.709172
\(781\) −0.362419 −0.0129684
\(782\) 22.8943 0.818697
\(783\) 2.18699 0.0781567
\(784\) 7.59769 0.271346
\(785\) −20.3533 −0.726442
\(786\) 22.7698 0.812171
\(787\) 30.7943 1.09770 0.548850 0.835921i \(-0.315066\pi\)
0.548850 + 0.835921i \(0.315066\pi\)
\(788\) −29.3256 −1.04468
\(789\) 10.4359 0.371526
\(790\) 10.0692 0.358246
\(791\) −44.0208 −1.56520
\(792\) 0.184051 0.00653998
\(793\) 60.6427 2.15348
\(794\) −6.74329 −0.239310
\(795\) 18.4557 0.654558
\(796\) 1.72768 0.0612360
\(797\) 21.4084 0.758323 0.379162 0.925330i \(-0.376212\pi\)
0.379162 + 0.925330i \(0.376212\pi\)
\(798\) −48.6884 −1.72355
\(799\) 23.1796 0.820035
\(800\) 4.46777 0.157960
\(801\) −9.58323 −0.338607
\(802\) 15.4559 0.545766
\(803\) 0.413688 0.0145987
\(804\) 55.9088 1.97175
\(805\) −5.86988 −0.206886
\(806\) 54.7421 1.92821
\(807\) 10.0913 0.355230
\(808\) 54.1381 1.90457
\(809\) −32.3824 −1.13850 −0.569252 0.822163i \(-0.692767\pi\)
−0.569252 + 0.822163i \(0.692767\pi\)
\(810\) −11.3488 −0.398757
\(811\) −10.0458 −0.352755 −0.176378 0.984323i \(-0.556438\pi\)
−0.176378 + 0.984323i \(0.556438\pi\)
\(812\) −5.12390 −0.179814
\(813\) −17.0496 −0.597956
\(814\) −0.919282 −0.0322208
\(815\) −8.28586 −0.290241
\(816\) −8.79273 −0.307807
\(817\) 33.5541 1.17391
\(818\) 24.8923 0.870337
\(819\) 16.1810 0.565411
\(820\) −5.90996 −0.206385
\(821\) 38.0383 1.32755 0.663773 0.747934i \(-0.268954\pi\)
0.663773 + 0.747934i \(0.268954\pi\)
\(822\) 11.5998 0.404588
\(823\) −47.9458 −1.67128 −0.835642 0.549274i \(-0.814904\pi\)
−0.835642 + 0.549274i \(0.814904\pi\)
\(824\) 11.7293 0.408610
\(825\) −0.0747088 −0.00260103
\(826\) 52.7481 1.83534
\(827\) −14.4004 −0.500750 −0.250375 0.968149i \(-0.580554\pi\)
−0.250375 + 0.968149i \(0.580554\pi\)
\(828\) 5.39577 0.187516
\(829\) 12.2891 0.426819 0.213410 0.976963i \(-0.431543\pi\)
0.213410 + 0.976963i \(0.431543\pi\)
\(830\) −17.8534 −0.619700
\(831\) 27.1856 0.943058
\(832\) −50.6493 −1.75595
\(833\) 50.2180 1.73995
\(834\) −18.3593 −0.635731
\(835\) −18.8878 −0.653639
\(836\) 0.707219 0.0244597
\(837\) −32.4138 −1.12038
\(838\) −21.1038 −0.729018
\(839\) −41.1144 −1.41943 −0.709713 0.704491i \(-0.751175\pi\)
−0.709713 + 0.704491i \(0.751175\pi\)
\(840\) 18.2105 0.628321
\(841\) −28.8505 −0.994845
\(842\) 15.1857 0.523334
\(843\) −46.7951 −1.61171
\(844\) −83.0913 −2.86012
\(845\) −3.76312 −0.129455
\(846\) 8.63549 0.296894
\(847\) 42.3170 1.45403
\(848\) 12.7870 0.439107
\(849\) 13.4166 0.460456
\(850\) −15.0083 −0.514781
\(851\) −11.2998 −0.387351
\(852\) 32.9623 1.12927
\(853\) −18.8087 −0.643996 −0.321998 0.946740i \(-0.604355\pi\)
−0.321998 + 0.946740i \(0.604355\pi\)
\(854\) 132.983 4.55057
\(855\) 3.96524 0.135608
\(856\) 35.9950 1.23029
\(857\) −1.16400 −0.0397616 −0.0198808 0.999802i \(-0.506329\pi\)
−0.0198808 + 0.999802i \(0.506329\pi\)
\(858\) 0.713689 0.0243649
\(859\) 12.3624 0.421800 0.210900 0.977508i \(-0.432360\pi\)
0.210900 + 0.977508i \(0.432360\pi\)
\(860\) −29.9319 −1.02067
\(861\) 9.27495 0.316090
\(862\) −16.1516 −0.550124
\(863\) −5.47739 −0.186453 −0.0932263 0.995645i \(-0.529718\pi\)
−0.0932263 + 0.995645i \(0.529718\pi\)
\(864\) 25.2718 0.859764
\(865\) −13.1948 −0.448637
\(866\) 54.2512 1.84353
\(867\) −34.2384 −1.16280
\(868\) 75.9423 2.57765
\(869\) 0.229535 0.00778646
\(870\) −1.26712 −0.0429595
\(871\) −47.3191 −1.60335
\(872\) 5.59394 0.189435
\(873\) 0.312967 0.0105923
\(874\) 13.7413 0.464808
\(875\) 3.84799 0.130086
\(876\) −37.6253 −1.27124
\(877\) −13.9132 −0.469817 −0.234908 0.972018i \(-0.575479\pi\)
−0.234908 + 0.972018i \(0.575479\pi\)
\(878\) −60.2819 −2.03441
\(879\) 29.8954 1.00835
\(880\) −0.0517617 −0.00174489
\(881\) 28.8897 0.973319 0.486660 0.873592i \(-0.338215\pi\)
0.486660 + 0.873592i \(0.338215\pi\)
\(882\) 18.7086 0.629952
\(883\) −6.75278 −0.227249 −0.113625 0.993524i \(-0.536246\pi\)
−0.113625 + 0.993524i \(0.536246\pi\)
\(884\) 90.7014 3.05062
\(885\) 8.25221 0.277395
\(886\) 0.666997 0.0224082
\(887\) 3.28827 0.110409 0.0552046 0.998475i \(-0.482419\pi\)
0.0552046 + 0.998475i \(0.482419\pi\)
\(888\) 35.0559 1.17640
\(889\) −18.7568 −0.629083
\(890\) 21.7709 0.729763
\(891\) −0.258706 −0.00866698
\(892\) −70.9503 −2.37559
\(893\) 13.9126 0.465567
\(894\) −11.6638 −0.390097
\(895\) −7.98969 −0.267066
\(896\) −76.6843 −2.56184
\(897\) 8.77262 0.292909
\(898\) 29.6321 0.988835
\(899\) −2.21558 −0.0738936
\(900\) −3.53719 −0.117906
\(901\) 84.5175 2.81569
\(902\) −0.212958 −0.00709073
\(903\) 46.9745 1.56321
\(904\) −38.5437 −1.28194
\(905\) −2.65337 −0.0882009
\(906\) 41.9013 1.39208
\(907\) −3.33682 −0.110797 −0.0553986 0.998464i \(-0.517643\pi\)
−0.0553986 + 0.998464i \(0.517643\pi\)
\(908\) 52.3341 1.73677
\(909\) 16.5032 0.547376
\(910\) −36.7596 −1.21857
\(911\) 24.7103 0.818688 0.409344 0.912380i \(-0.365758\pi\)
0.409344 + 0.912380i \(0.365758\pi\)
\(912\) −5.27747 −0.174755
\(913\) −0.406982 −0.0134692
\(914\) −80.5225 −2.66345
\(915\) 20.8045 0.687777
\(916\) −44.2775 −1.46297
\(917\) −26.7348 −0.882860
\(918\) −84.8940 −2.80192
\(919\) 51.9195 1.71267 0.856333 0.516425i \(-0.172737\pi\)
0.856333 + 0.516425i \(0.172737\pi\)
\(920\) −5.13954 −0.169446
\(921\) 36.1724 1.19192
\(922\) 3.05876 0.100735
\(923\) −27.8981 −0.918276
\(924\) 0.990081 0.0325713
\(925\) 7.40755 0.243559
\(926\) −20.9355 −0.687983
\(927\) 3.57551 0.117435
\(928\) 1.72740 0.0567047
\(929\) −4.14538 −0.136005 −0.0680027 0.997685i \(-0.521663\pi\)
−0.0680027 + 0.997685i \(0.521663\pi\)
\(930\) 18.7803 0.615829
\(931\) 30.1413 0.987842
\(932\) 26.1492 0.856544
\(933\) −47.4149 −1.55230
\(934\) −73.5304 −2.40599
\(935\) −0.342127 −0.0111887
\(936\) 14.1678 0.463088
\(937\) 20.3672 0.665367 0.332684 0.943038i \(-0.392046\pi\)
0.332684 + 0.943038i \(0.392046\pi\)
\(938\) −103.765 −3.38806
\(939\) −20.1201 −0.656596
\(940\) −12.4107 −0.404793
\(941\) 44.4236 1.44817 0.724084 0.689712i \(-0.242263\pi\)
0.724084 + 0.689712i \(0.242263\pi\)
\(942\) 66.7040 2.17334
\(943\) −2.61767 −0.0852430
\(944\) 5.71751 0.186089
\(945\) 21.7660 0.708049
\(946\) −1.07856 −0.0350670
\(947\) 31.9869 1.03943 0.519717 0.854339i \(-0.326037\pi\)
0.519717 + 0.854339i \(0.326037\pi\)
\(948\) −20.8764 −0.678036
\(949\) 31.8446 1.03372
\(950\) −9.00812 −0.292262
\(951\) −45.1200 −1.46312
\(952\) 83.3943 2.70282
\(953\) 33.2877 1.07830 0.539148 0.842211i \(-0.318747\pi\)
0.539148 + 0.842211i \(0.318747\pi\)
\(954\) 31.4868 1.01942
\(955\) 12.1539 0.393290
\(956\) 15.9319 0.515275
\(957\) −0.0288851 −0.000933722 0
\(958\) −55.1136 −1.78064
\(959\) −13.6197 −0.439802
\(960\) −17.3761 −0.560813
\(961\) 1.83746 0.0592730
\(962\) −70.7638 −2.28152
\(963\) 10.9726 0.353586
\(964\) −55.0655 −1.77354
\(965\) 18.9896 0.611298
\(966\) 19.2374 0.618952
\(967\) −43.1904 −1.38891 −0.694455 0.719536i \(-0.744355\pi\)
−0.694455 + 0.719536i \(0.744355\pi\)
\(968\) 37.0519 1.19089
\(969\) −34.8822 −1.12058
\(970\) −0.710989 −0.0228285
\(971\) 33.0915 1.06196 0.530978 0.847386i \(-0.321825\pi\)
0.530978 + 0.847386i \(0.321825\pi\)
\(972\) −34.9132 −1.11984
\(973\) 21.5563 0.691063
\(974\) −90.4140 −2.89705
\(975\) −5.75089 −0.184176
\(976\) 14.4143 0.461392
\(977\) −7.34002 −0.234828 −0.117414 0.993083i \(-0.537460\pi\)
−0.117414 + 0.993083i \(0.537460\pi\)
\(978\) 27.1553 0.868330
\(979\) 0.496286 0.0158614
\(980\) −26.8876 −0.858892
\(981\) 1.70523 0.0544439
\(982\) −31.1269 −0.993300
\(983\) 19.1746 0.611575 0.305787 0.952100i \(-0.401080\pi\)
0.305787 + 0.952100i \(0.401080\pi\)
\(984\) 8.12095 0.258886
\(985\) 8.51495 0.271309
\(986\) −5.80275 −0.184797
\(987\) 19.4771 0.619964
\(988\) 54.4398 1.73196
\(989\) −13.2576 −0.421567
\(990\) −0.127458 −0.00405090
\(991\) −29.6556 −0.942042 −0.471021 0.882122i \(-0.656114\pi\)
−0.471021 + 0.882122i \(0.656114\pi\)
\(992\) −25.6021 −0.812868
\(993\) 36.5190 1.15889
\(994\) −61.1773 −1.94043
\(995\) −0.501648 −0.0159033
\(996\) 37.0154 1.17288
\(997\) 27.9012 0.883641 0.441820 0.897104i \(-0.354333\pi\)
0.441820 + 0.897104i \(0.354333\pi\)
\(998\) 22.9399 0.726149
\(999\) 41.9005 1.32567
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 8035.2.a.c.1.11 127
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8035.2.a.c.1.11 127 1.1 even 1 trivial