Properties

Label 4013.2.a.b.1.8
Level $4013$
Weight $2$
Character 4013.1
Self dual yes
Analytic conductor $32.044$
Analytic rank $1$
Dimension $157$
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] = [4013,2,Mod(1,4013)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4013, 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("4013.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4013 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4013.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: \(32.0439663311\)
Analytic rank: \(1\)
Dimension: \(157\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) \(=\) 4013.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.60727 q^{2} +1.83175 q^{3} +4.79788 q^{4} -1.15472 q^{5} -4.77588 q^{6} -1.01890 q^{7} -7.29484 q^{8} +0.355310 q^{9} +O(q^{10})\) \(q-2.60727 q^{2} +1.83175 q^{3} +4.79788 q^{4} -1.15472 q^{5} -4.77588 q^{6} -1.01890 q^{7} -7.29484 q^{8} +0.355310 q^{9} +3.01066 q^{10} -0.0753550 q^{11} +8.78852 q^{12} -0.480633 q^{13} +2.65654 q^{14} -2.11515 q^{15} +9.42388 q^{16} +4.79189 q^{17} -0.926390 q^{18} +5.38687 q^{19} -5.54019 q^{20} -1.86637 q^{21} +0.196471 q^{22} -3.84351 q^{23} -13.3623 q^{24} -3.66663 q^{25} +1.25314 q^{26} -4.84441 q^{27} -4.88855 q^{28} +6.34587 q^{29} +5.51478 q^{30} -3.87811 q^{31} -9.98096 q^{32} -0.138032 q^{33} -12.4938 q^{34} +1.17654 q^{35} +1.70473 q^{36} -8.07254 q^{37} -14.0451 q^{38} -0.880400 q^{39} +8.42346 q^{40} +6.27018 q^{41} +4.86613 q^{42} -8.53557 q^{43} -0.361544 q^{44} -0.410282 q^{45} +10.0211 q^{46} -1.62043 q^{47} +17.2622 q^{48} -5.96185 q^{49} +9.55991 q^{50} +8.77755 q^{51} -2.30602 q^{52} +3.70097 q^{53} +12.6307 q^{54} +0.0870136 q^{55} +7.43269 q^{56} +9.86741 q^{57} -16.5454 q^{58} +5.72151 q^{59} -10.1482 q^{60} +1.57985 q^{61} +10.1113 q^{62} -0.362024 q^{63} +7.17535 q^{64} +0.554995 q^{65} +0.359886 q^{66} -12.0493 q^{67} +22.9909 q^{68} -7.04036 q^{69} -3.06755 q^{70} +15.2328 q^{71} -2.59193 q^{72} +7.02673 q^{73} +21.0473 q^{74} -6.71635 q^{75} +25.8456 q^{76} +0.0767790 q^{77} +2.29544 q^{78} -2.19477 q^{79} -10.8819 q^{80} -9.93968 q^{81} -16.3481 q^{82} -8.97436 q^{83} -8.95460 q^{84} -5.53327 q^{85} +22.2546 q^{86} +11.6240 q^{87} +0.549702 q^{88} +1.48870 q^{89} +1.06972 q^{90} +0.489716 q^{91} -18.4407 q^{92} -7.10373 q^{93} +4.22489 q^{94} -6.22031 q^{95} -18.2826 q^{96} -3.54976 q^{97} +15.5442 q^{98} -0.0267744 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 157 q - 15 q^{2} - 51 q^{3} + 137 q^{4} - 13 q^{5} - 15 q^{6} - 49 q^{7} - 42 q^{8} + 144 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 157 q - 15 q^{2} - 51 q^{3} + 137 q^{4} - 13 q^{5} - 15 q^{6} - 49 q^{7} - 42 q^{8} + 144 q^{9} - 61 q^{10} - 27 q^{11} - 93 q^{12} - 97 q^{13} - 12 q^{14} - 36 q^{15} + 105 q^{16} - 45 q^{17} - 68 q^{18} - 128 q^{19} - 30 q^{20} - 26 q^{21} - 68 q^{22} - 41 q^{23} - 40 q^{24} + 102 q^{25} - 5 q^{26} - 189 q^{27} - 115 q^{28} - 26 q^{29} - 12 q^{30} - 88 q^{31} - 89 q^{32} - 52 q^{33} - 61 q^{34} - 87 q^{35} + 110 q^{36} - 62 q^{37} - 37 q^{38} - 20 q^{39} - 161 q^{40} - 34 q^{41} - 53 q^{42} - 254 q^{43} - 19 q^{44} - 46 q^{45} - 52 q^{46} - 76 q^{47} - 162 q^{48} + 96 q^{49} - 54 q^{50} - 76 q^{51} - 259 q^{52} - 48 q^{53} - 12 q^{54} - 194 q^{55} - 10 q^{56} - 30 q^{57} - 52 q^{58} - 64 q^{59} - 31 q^{60} - 107 q^{61} - 51 q^{62} - 106 q^{63} + 54 q^{64} - 17 q^{65} - 13 q^{66} - 193 q^{67} - 118 q^{68} - 55 q^{69} - 86 q^{70} - 11 q^{71} - 172 q^{72} - 173 q^{73} - 11 q^{74} - 209 q^{75} - 213 q^{76} - 84 q^{77} - 30 q^{78} - 111 q^{79} - 6 q^{80} + 157 q^{81} - 117 q^{82} - 154 q^{83} - 6 q^{84} - 91 q^{85} + 28 q^{86} - 165 q^{87} - 165 q^{88} - 32 q^{89} - 103 q^{90} - 200 q^{91} - 86 q^{92} - 39 q^{93} - 118 q^{94} - 22 q^{95} - 28 q^{96} - 151 q^{97} - 38 q^{98} - 91 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.60727 −1.84362 −0.921811 0.387641i \(-0.873290\pi\)
−0.921811 + 0.387641i \(0.873290\pi\)
\(3\) 1.83175 1.05756 0.528781 0.848758i \(-0.322649\pi\)
0.528781 + 0.848758i \(0.322649\pi\)
\(4\) 4.79788 2.39894
\(5\) −1.15472 −0.516405 −0.258202 0.966091i \(-0.583130\pi\)
−0.258202 + 0.966091i \(0.583130\pi\)
\(6\) −4.77588 −1.94974
\(7\) −1.01890 −0.385107 −0.192554 0.981286i \(-0.561677\pi\)
−0.192554 + 0.981286i \(0.561677\pi\)
\(8\) −7.29484 −2.57911
\(9\) 0.355310 0.118437
\(10\) 3.01066 0.952055
\(11\) −0.0753550 −0.0227204 −0.0113602 0.999935i \(-0.503616\pi\)
−0.0113602 + 0.999935i \(0.503616\pi\)
\(12\) 8.78852 2.53703
\(13\) −0.480633 −0.133304 −0.0666518 0.997776i \(-0.521232\pi\)
−0.0666518 + 0.997776i \(0.521232\pi\)
\(14\) 2.65654 0.709991
\(15\) −2.11515 −0.546130
\(16\) 9.42388 2.35597
\(17\) 4.79189 1.16220 0.581102 0.813831i \(-0.302622\pi\)
0.581102 + 0.813831i \(0.302622\pi\)
\(18\) −0.926390 −0.218352
\(19\) 5.38687 1.23583 0.617917 0.786243i \(-0.287977\pi\)
0.617917 + 0.786243i \(0.287977\pi\)
\(20\) −5.54019 −1.23882
\(21\) −1.86637 −0.407274
\(22\) 0.196471 0.0418878
\(23\) −3.84351 −0.801428 −0.400714 0.916203i \(-0.631238\pi\)
−0.400714 + 0.916203i \(0.631238\pi\)
\(24\) −13.3623 −2.72757
\(25\) −3.66663 −0.733326
\(26\) 1.25314 0.245761
\(27\) −4.84441 −0.932308
\(28\) −4.88855 −0.923848
\(29\) 6.34587 1.17840 0.589199 0.807988i \(-0.299443\pi\)
0.589199 + 0.807988i \(0.299443\pi\)
\(30\) 5.51478 1.00686
\(31\) −3.87811 −0.696529 −0.348265 0.937396i \(-0.613229\pi\)
−0.348265 + 0.937396i \(0.613229\pi\)
\(32\) −9.98096 −1.76440
\(33\) −0.138032 −0.0240282
\(34\) −12.4938 −2.14266
\(35\) 1.17654 0.198871
\(36\) 1.70473 0.284122
\(37\) −8.07254 −1.32712 −0.663559 0.748124i \(-0.730955\pi\)
−0.663559 + 0.748124i \(0.730955\pi\)
\(38\) −14.0451 −2.27841
\(39\) −0.880400 −0.140977
\(40\) 8.42346 1.33187
\(41\) 6.27018 0.979237 0.489619 0.871937i \(-0.337136\pi\)
0.489619 + 0.871937i \(0.337136\pi\)
\(42\) 4.86613 0.750860
\(43\) −8.53557 −1.30166 −0.650831 0.759222i \(-0.725580\pi\)
−0.650831 + 0.759222i \(0.725580\pi\)
\(44\) −0.361544 −0.0545048
\(45\) −0.410282 −0.0611612
\(46\) 10.0211 1.47753
\(47\) −1.62043 −0.236363 −0.118182 0.992992i \(-0.537707\pi\)
−0.118182 + 0.992992i \(0.537707\pi\)
\(48\) 17.2622 2.49158
\(49\) −5.96185 −0.851693
\(50\) 9.55991 1.35198
\(51\) 8.77755 1.22910
\(52\) −2.30602 −0.319787
\(53\) 3.70097 0.508368 0.254184 0.967156i \(-0.418193\pi\)
0.254184 + 0.967156i \(0.418193\pi\)
\(54\) 12.6307 1.71882
\(55\) 0.0870136 0.0117329
\(56\) 7.43269 0.993235
\(57\) 9.86741 1.30697
\(58\) −16.5454 −2.17252
\(59\) 5.72151 0.744878 0.372439 0.928057i \(-0.378522\pi\)
0.372439 + 0.928057i \(0.378522\pi\)
\(60\) −10.1482 −1.31013
\(61\) 1.57985 0.202279 0.101139 0.994872i \(-0.467751\pi\)
0.101139 + 0.994872i \(0.467751\pi\)
\(62\) 10.1113 1.28414
\(63\) −0.362024 −0.0456108
\(64\) 7.17535 0.896919
\(65\) 0.554995 0.0688386
\(66\) 0.359886 0.0442989
\(67\) −12.0493 −1.47206 −0.736030 0.676949i \(-0.763302\pi\)
−0.736030 + 0.676949i \(0.763302\pi\)
\(68\) 22.9909 2.78806
\(69\) −7.04036 −0.847560
\(70\) −3.06755 −0.366643
\(71\) 15.2328 1.80780 0.903899 0.427745i \(-0.140692\pi\)
0.903899 + 0.427745i \(0.140692\pi\)
\(72\) −2.59193 −0.305461
\(73\) 7.02673 0.822416 0.411208 0.911541i \(-0.365107\pi\)
0.411208 + 0.911541i \(0.365107\pi\)
\(74\) 21.0473 2.44670
\(75\) −6.71635 −0.775538
\(76\) 25.8456 2.96469
\(77\) 0.0767790 0.00874978
\(78\) 2.29544 0.259908
\(79\) −2.19477 −0.246931 −0.123466 0.992349i \(-0.539401\pi\)
−0.123466 + 0.992349i \(0.539401\pi\)
\(80\) −10.8819 −1.21663
\(81\) −9.93968 −1.10441
\(82\) −16.3481 −1.80534
\(83\) −8.97436 −0.985064 −0.492532 0.870294i \(-0.663929\pi\)
−0.492532 + 0.870294i \(0.663929\pi\)
\(84\) −8.95460 −0.977026
\(85\) −5.53327 −0.600168
\(86\) 22.2546 2.39977
\(87\) 11.6240 1.24623
\(88\) 0.549702 0.0585985
\(89\) 1.48870 0.157802 0.0789008 0.996882i \(-0.474859\pi\)
0.0789008 + 0.996882i \(0.474859\pi\)
\(90\) 1.06972 0.112758
\(91\) 0.489716 0.0513362
\(92\) −18.4407 −1.92258
\(93\) −7.10373 −0.736623
\(94\) 4.22489 0.435764
\(95\) −6.22031 −0.638190
\(96\) −18.2826 −1.86596
\(97\) −3.54976 −0.360423 −0.180212 0.983628i \(-0.557678\pi\)
−0.180212 + 0.983628i \(0.557678\pi\)
\(98\) 15.5442 1.57020
\(99\) −0.0267744 −0.00269093
\(100\) −17.5920 −1.75920
\(101\) 3.74777 0.372918 0.186459 0.982463i \(-0.440299\pi\)
0.186459 + 0.982463i \(0.440299\pi\)
\(102\) −22.8855 −2.26600
\(103\) 2.17975 0.214777 0.107389 0.994217i \(-0.465751\pi\)
0.107389 + 0.994217i \(0.465751\pi\)
\(104\) 3.50614 0.343805
\(105\) 2.15512 0.210318
\(106\) −9.64945 −0.937237
\(107\) −13.5794 −1.31277 −0.656387 0.754424i \(-0.727916\pi\)
−0.656387 + 0.754424i \(0.727916\pi\)
\(108\) −23.2429 −2.23655
\(109\) 4.68781 0.449010 0.224505 0.974473i \(-0.427923\pi\)
0.224505 + 0.974473i \(0.427923\pi\)
\(110\) −0.226868 −0.0216310
\(111\) −14.7869 −1.40351
\(112\) −9.60196 −0.907300
\(113\) 11.0750 1.04185 0.520924 0.853603i \(-0.325588\pi\)
0.520924 + 0.853603i \(0.325588\pi\)
\(114\) −25.7270 −2.40956
\(115\) 4.43817 0.413861
\(116\) 30.4467 2.82691
\(117\) −0.170774 −0.0157880
\(118\) −14.9176 −1.37327
\(119\) −4.88245 −0.447573
\(120\) 15.4297 1.40853
\(121\) −10.9943 −0.999484
\(122\) −4.11910 −0.372925
\(123\) 11.4854 1.03560
\(124\) −18.6067 −1.67093
\(125\) 10.0075 0.895098
\(126\) 0.943896 0.0840890
\(127\) 0.427077 0.0378970 0.0189485 0.999820i \(-0.493968\pi\)
0.0189485 + 0.999820i \(0.493968\pi\)
\(128\) 1.25382 0.110823
\(129\) −15.6350 −1.37659
\(130\) −1.44702 −0.126912
\(131\) −15.9941 −1.39741 −0.698704 0.715411i \(-0.746240\pi\)
−0.698704 + 0.715411i \(0.746240\pi\)
\(132\) −0.662259 −0.0576422
\(133\) −5.48867 −0.475928
\(134\) 31.4159 2.71392
\(135\) 5.59392 0.481448
\(136\) −34.9561 −2.99746
\(137\) 15.3692 1.31308 0.656539 0.754292i \(-0.272020\pi\)
0.656539 + 0.754292i \(0.272020\pi\)
\(138\) 18.3561 1.56258
\(139\) −18.0680 −1.53250 −0.766252 0.642540i \(-0.777881\pi\)
−0.766252 + 0.642540i \(0.777881\pi\)
\(140\) 5.64488 0.477080
\(141\) −2.96821 −0.249969
\(142\) −39.7160 −3.33290
\(143\) 0.0362181 0.00302871
\(144\) 3.34840 0.279033
\(145\) −7.32767 −0.608530
\(146\) −18.3206 −1.51622
\(147\) −10.9206 −0.900717
\(148\) −38.7311 −3.18367
\(149\) −21.2328 −1.73946 −0.869731 0.493526i \(-0.835708\pi\)
−0.869731 + 0.493526i \(0.835708\pi\)
\(150\) 17.5114 1.42980
\(151\) 5.55500 0.452060 0.226030 0.974120i \(-0.427425\pi\)
0.226030 + 0.974120i \(0.427425\pi\)
\(152\) −39.2964 −3.18736
\(153\) 1.70261 0.137648
\(154\) −0.200184 −0.0161313
\(155\) 4.47812 0.359691
\(156\) −4.22405 −0.338195
\(157\) 0.915628 0.0730751 0.0365375 0.999332i \(-0.488367\pi\)
0.0365375 + 0.999332i \(0.488367\pi\)
\(158\) 5.72238 0.455248
\(159\) 6.77926 0.537630
\(160\) 11.5252 0.911145
\(161\) 3.91615 0.308636
\(162\) 25.9155 2.03611
\(163\) 11.4408 0.896115 0.448057 0.894005i \(-0.352116\pi\)
0.448057 + 0.894005i \(0.352116\pi\)
\(164\) 30.0835 2.34913
\(165\) 0.159387 0.0124083
\(166\) 23.3986 1.81609
\(167\) −13.1313 −1.01613 −0.508066 0.861318i \(-0.669639\pi\)
−0.508066 + 0.861318i \(0.669639\pi\)
\(168\) 13.6148 1.05041
\(169\) −12.7690 −0.982230
\(170\) 14.4268 1.10648
\(171\) 1.91401 0.146368
\(172\) −40.9526 −3.12261
\(173\) −23.9185 −1.81849 −0.909245 0.416262i \(-0.863340\pi\)
−0.909245 + 0.416262i \(0.863340\pi\)
\(174\) −30.3071 −2.29757
\(175\) 3.73592 0.282409
\(176\) −0.710136 −0.0535285
\(177\) 10.4804 0.787754
\(178\) −3.88144 −0.290926
\(179\) −19.3904 −1.44930 −0.724652 0.689115i \(-0.758000\pi\)
−0.724652 + 0.689115i \(0.758000\pi\)
\(180\) −1.96848 −0.146722
\(181\) 11.0732 0.823065 0.411533 0.911395i \(-0.364994\pi\)
0.411533 + 0.911395i \(0.364994\pi\)
\(182\) −1.27682 −0.0946444
\(183\) 2.89389 0.213922
\(184\) 28.0378 2.06697
\(185\) 9.32149 0.685330
\(186\) 18.5214 1.35805
\(187\) −0.361093 −0.0264057
\(188\) −7.77460 −0.567021
\(189\) 4.93596 0.359038
\(190\) 16.2181 1.17658
\(191\) −16.6181 −1.20244 −0.601221 0.799083i \(-0.705319\pi\)
−0.601221 + 0.799083i \(0.705319\pi\)
\(192\) 13.1435 0.948547
\(193\) −13.5168 −0.972962 −0.486481 0.873691i \(-0.661720\pi\)
−0.486481 + 0.873691i \(0.661720\pi\)
\(194\) 9.25519 0.664484
\(195\) 1.01661 0.0728011
\(196\) −28.6042 −2.04316
\(197\) 3.04756 0.217130 0.108565 0.994089i \(-0.465374\pi\)
0.108565 + 0.994089i \(0.465374\pi\)
\(198\) 0.0698081 0.00496105
\(199\) 24.0733 1.70651 0.853255 0.521493i \(-0.174625\pi\)
0.853255 + 0.521493i \(0.174625\pi\)
\(200\) 26.7475 1.89133
\(201\) −22.0714 −1.55679
\(202\) −9.77148 −0.687519
\(203\) −6.46579 −0.453809
\(204\) 42.1136 2.94854
\(205\) −7.24027 −0.505683
\(206\) −5.68321 −0.395968
\(207\) −1.36564 −0.0949184
\(208\) −4.52943 −0.314059
\(209\) −0.405928 −0.0280786
\(210\) −5.61899 −0.387747
\(211\) −7.44328 −0.512416 −0.256208 0.966622i \(-0.582473\pi\)
−0.256208 + 0.966622i \(0.582473\pi\)
\(212\) 17.7568 1.21954
\(213\) 27.9027 1.91186
\(214\) 35.4053 2.42026
\(215\) 9.85616 0.672185
\(216\) 35.3392 2.40453
\(217\) 3.95140 0.268238
\(218\) −12.2224 −0.827805
\(219\) 12.8712 0.869756
\(220\) 0.417481 0.0281465
\(221\) −2.30314 −0.154926
\(222\) 38.5535 2.58754
\(223\) 4.37262 0.292812 0.146406 0.989225i \(-0.453229\pi\)
0.146406 + 0.989225i \(0.453229\pi\)
\(224\) 10.1696 0.679483
\(225\) −1.30279 −0.0868527
\(226\) −28.8755 −1.92077
\(227\) −14.3997 −0.955743 −0.477872 0.878430i \(-0.658592\pi\)
−0.477872 + 0.878430i \(0.658592\pi\)
\(228\) 47.3426 3.13534
\(229\) −2.94469 −0.194590 −0.0972951 0.995256i \(-0.531019\pi\)
−0.0972951 + 0.995256i \(0.531019\pi\)
\(230\) −11.5715 −0.763003
\(231\) 0.140640 0.00925343
\(232\) −46.2921 −3.03922
\(233\) −4.55987 −0.298727 −0.149363 0.988782i \(-0.547722\pi\)
−0.149363 + 0.988782i \(0.547722\pi\)
\(234\) 0.445254 0.0291071
\(235\) 1.87113 0.122059
\(236\) 27.4511 1.78692
\(237\) −4.02028 −0.261145
\(238\) 12.7299 0.825155
\(239\) −18.4957 −1.19639 −0.598194 0.801351i \(-0.704115\pi\)
−0.598194 + 0.801351i \(0.704115\pi\)
\(240\) −19.9329 −1.28667
\(241\) 5.05414 0.325566 0.162783 0.986662i \(-0.447953\pi\)
0.162783 + 0.986662i \(0.447953\pi\)
\(242\) 28.6652 1.84267
\(243\) −3.67378 −0.235673
\(244\) 7.57992 0.485254
\(245\) 6.88424 0.439818
\(246\) −29.9456 −1.90926
\(247\) −2.58911 −0.164741
\(248\) 28.2902 1.79643
\(249\) −16.4388 −1.04177
\(250\) −26.0923 −1.65022
\(251\) −22.5966 −1.42629 −0.713143 0.701018i \(-0.752729\pi\)
−0.713143 + 0.701018i \(0.752729\pi\)
\(252\) −1.73695 −0.109417
\(253\) 0.289628 0.0182088
\(254\) −1.11351 −0.0698677
\(255\) −10.1356 −0.634714
\(256\) −17.6198 −1.10123
\(257\) −1.82103 −0.113593 −0.0567964 0.998386i \(-0.518089\pi\)
−0.0567964 + 0.998386i \(0.518089\pi\)
\(258\) 40.7648 2.53791
\(259\) 8.22509 0.511082
\(260\) 2.66280 0.165140
\(261\) 2.25475 0.139565
\(262\) 41.7009 2.57629
\(263\) 23.2240 1.43206 0.716028 0.698071i \(-0.245958\pi\)
0.716028 + 0.698071i \(0.245958\pi\)
\(264\) 1.00692 0.0619715
\(265\) −4.27357 −0.262523
\(266\) 14.3105 0.877431
\(267\) 2.72692 0.166885
\(268\) −57.8112 −3.53138
\(269\) 15.9970 0.975352 0.487676 0.873025i \(-0.337845\pi\)
0.487676 + 0.873025i \(0.337845\pi\)
\(270\) −14.5849 −0.887608
\(271\) −4.35694 −0.264665 −0.132333 0.991205i \(-0.542247\pi\)
−0.132333 + 0.991205i \(0.542247\pi\)
\(272\) 45.1582 2.73812
\(273\) 0.897037 0.0542911
\(274\) −40.0717 −2.42082
\(275\) 0.276299 0.0166615
\(276\) −33.7788 −2.03324
\(277\) 1.09551 0.0658230 0.0329115 0.999458i \(-0.489522\pi\)
0.0329115 + 0.999458i \(0.489522\pi\)
\(278\) 47.1081 2.82536
\(279\) −1.37793 −0.0824946
\(280\) −8.58264 −0.512911
\(281\) 21.1359 1.26086 0.630430 0.776246i \(-0.282879\pi\)
0.630430 + 0.776246i \(0.282879\pi\)
\(282\) 7.73895 0.460848
\(283\) 4.55851 0.270975 0.135488 0.990779i \(-0.456740\pi\)
0.135488 + 0.990779i \(0.456740\pi\)
\(284\) 73.0850 4.33680
\(285\) −11.3941 −0.674926
\(286\) −0.0944305 −0.00558379
\(287\) −6.38867 −0.377111
\(288\) −3.54633 −0.208970
\(289\) 5.96223 0.350719
\(290\) 19.1053 1.12190
\(291\) −6.50227 −0.381170
\(292\) 33.7134 1.97293
\(293\) −13.6257 −0.796023 −0.398012 0.917380i \(-0.630300\pi\)
−0.398012 + 0.917380i \(0.630300\pi\)
\(294\) 28.4730 1.66058
\(295\) −6.60672 −0.384658
\(296\) 58.8879 3.42279
\(297\) 0.365051 0.0211824
\(298\) 55.3598 3.20691
\(299\) 1.84732 0.106833
\(300\) −32.2242 −1.86047
\(301\) 8.69687 0.501280
\(302\) −14.4834 −0.833426
\(303\) 6.86499 0.394383
\(304\) 50.7652 2.91159
\(305\) −1.82428 −0.104458
\(306\) −4.43916 −0.253770
\(307\) 32.1118 1.83271 0.916357 0.400362i \(-0.131116\pi\)
0.916357 + 0.400362i \(0.131116\pi\)
\(308\) 0.368376 0.0209902
\(309\) 3.99276 0.227140
\(310\) −11.6757 −0.663134
\(311\) −3.36747 −0.190952 −0.0954759 0.995432i \(-0.530437\pi\)
−0.0954759 + 0.995432i \(0.530437\pi\)
\(312\) 6.42237 0.363595
\(313\) −24.2343 −1.36980 −0.684901 0.728636i \(-0.740155\pi\)
−0.684901 + 0.728636i \(0.740155\pi\)
\(314\) −2.38729 −0.134723
\(315\) 0.418035 0.0235536
\(316\) −10.5303 −0.592374
\(317\) 7.33522 0.411987 0.205993 0.978553i \(-0.433957\pi\)
0.205993 + 0.978553i \(0.433957\pi\)
\(318\) −17.6754 −0.991186
\(319\) −0.478193 −0.0267737
\(320\) −8.28549 −0.463173
\(321\) −24.8741 −1.38834
\(322\) −10.2105 −0.569007
\(323\) 25.8133 1.43629
\(324\) −47.6894 −2.64941
\(325\) 1.76230 0.0977550
\(326\) −29.8294 −1.65210
\(327\) 8.58689 0.474856
\(328\) −45.7399 −2.52556
\(329\) 1.65105 0.0910252
\(330\) −0.415566 −0.0228762
\(331\) −5.15352 −0.283263 −0.141632 0.989919i \(-0.545235\pi\)
−0.141632 + 0.989919i \(0.545235\pi\)
\(332\) −43.0579 −2.36311
\(333\) −2.86825 −0.157179
\(334\) 34.2369 1.87336
\(335\) 13.9136 0.760179
\(336\) −17.5884 −0.959526
\(337\) −17.3320 −0.944135 −0.472067 0.881563i \(-0.656492\pi\)
−0.472067 + 0.881563i \(0.656492\pi\)
\(338\) 33.2923 1.81086
\(339\) 20.2866 1.10182
\(340\) −26.5480 −1.43977
\(341\) 0.292235 0.0158254
\(342\) −4.99035 −0.269847
\(343\) 13.2068 0.713100
\(344\) 62.2656 3.35714
\(345\) 8.12961 0.437684
\(346\) 62.3621 3.35261
\(347\) −30.4509 −1.63469 −0.817345 0.576149i \(-0.804555\pi\)
−0.817345 + 0.576149i \(0.804555\pi\)
\(348\) 55.7708 2.98963
\(349\) 13.8507 0.741409 0.370705 0.928751i \(-0.379116\pi\)
0.370705 + 0.928751i \(0.379116\pi\)
\(350\) −9.74057 −0.520655
\(351\) 2.32838 0.124280
\(352\) 0.752115 0.0400879
\(353\) 4.87813 0.259637 0.129818 0.991538i \(-0.458561\pi\)
0.129818 + 0.991538i \(0.458561\pi\)
\(354\) −27.3252 −1.45232
\(355\) −17.5895 −0.933556
\(356\) 7.14259 0.378556
\(357\) −8.94342 −0.473336
\(358\) 50.5560 2.67197
\(359\) −35.6623 −1.88218 −0.941091 0.338153i \(-0.890198\pi\)
−0.941091 + 0.338153i \(0.890198\pi\)
\(360\) 2.99294 0.157742
\(361\) 10.0184 0.527285
\(362\) −28.8709 −1.51742
\(363\) −20.1389 −1.05702
\(364\) 2.34960 0.123152
\(365\) −8.11388 −0.424700
\(366\) −7.54516 −0.394392
\(367\) −33.5515 −1.75137 −0.875687 0.482878i \(-0.839591\pi\)
−0.875687 + 0.482878i \(0.839591\pi\)
\(368\) −36.2208 −1.88814
\(369\) 2.22786 0.115978
\(370\) −24.3037 −1.26349
\(371\) −3.77091 −0.195776
\(372\) −34.0828 −1.76711
\(373\) −18.9687 −0.982160 −0.491080 0.871114i \(-0.663398\pi\)
−0.491080 + 0.871114i \(0.663398\pi\)
\(374\) 0.941469 0.0486822
\(375\) 18.3312 0.946621
\(376\) 11.8207 0.609608
\(377\) −3.05003 −0.157085
\(378\) −12.8694 −0.661930
\(379\) −33.7463 −1.73343 −0.866715 0.498804i \(-0.833773\pi\)
−0.866715 + 0.498804i \(0.833773\pi\)
\(380\) −29.8443 −1.53098
\(381\) 0.782299 0.0400784
\(382\) 43.3279 2.21685
\(383\) 26.4576 1.35192 0.675960 0.736938i \(-0.263729\pi\)
0.675960 + 0.736938i \(0.263729\pi\)
\(384\) 2.29669 0.117202
\(385\) −0.0886579 −0.00451843
\(386\) 35.2421 1.79377
\(387\) −3.03277 −0.154165
\(388\) −17.0313 −0.864634
\(389\) 4.33977 0.220035 0.110018 0.993930i \(-0.464909\pi\)
0.110018 + 0.993930i \(0.464909\pi\)
\(390\) −2.65058 −0.134218
\(391\) −18.4177 −0.931423
\(392\) 43.4907 2.19661
\(393\) −29.2971 −1.47785
\(394\) −7.94584 −0.400305
\(395\) 2.53434 0.127517
\(396\) −0.128460 −0.00645537
\(397\) −28.0190 −1.40623 −0.703117 0.711074i \(-0.748209\pi\)
−0.703117 + 0.711074i \(0.748209\pi\)
\(398\) −62.7657 −3.14616
\(399\) −10.0539 −0.503323
\(400\) −34.5539 −1.72769
\(401\) −31.0130 −1.54872 −0.774358 0.632747i \(-0.781927\pi\)
−0.774358 + 0.632747i \(0.781927\pi\)
\(402\) 57.5461 2.87014
\(403\) 1.86395 0.0928499
\(404\) 17.9814 0.894606
\(405\) 11.4775 0.570322
\(406\) 16.8581 0.836653
\(407\) 0.608307 0.0301526
\(408\) −64.0308 −3.17000
\(409\) 9.95578 0.492282 0.246141 0.969234i \(-0.420837\pi\)
0.246141 + 0.969234i \(0.420837\pi\)
\(410\) 18.8774 0.932287
\(411\) 28.1525 1.38866
\(412\) 10.4582 0.515237
\(413\) −5.82964 −0.286858
\(414\) 3.56059 0.174994
\(415\) 10.3628 0.508692
\(416\) 4.79718 0.235201
\(417\) −33.0960 −1.62072
\(418\) 1.05837 0.0517663
\(419\) −4.83309 −0.236112 −0.118056 0.993007i \(-0.537666\pi\)
−0.118056 + 0.993007i \(0.537666\pi\)
\(420\) 10.3400 0.504541
\(421\) 17.1174 0.834252 0.417126 0.908849i \(-0.363037\pi\)
0.417126 + 0.908849i \(0.363037\pi\)
\(422\) 19.4067 0.944701
\(423\) −0.575753 −0.0279941
\(424\) −26.9980 −1.31114
\(425\) −17.5701 −0.852275
\(426\) −72.7499 −3.52474
\(427\) −1.60970 −0.0778990
\(428\) −65.1525 −3.14926
\(429\) 0.0663425 0.00320305
\(430\) −25.6977 −1.23925
\(431\) −11.6025 −0.558874 −0.279437 0.960164i \(-0.590148\pi\)
−0.279437 + 0.960164i \(0.590148\pi\)
\(432\) −45.6532 −2.19649
\(433\) −24.1896 −1.16248 −0.581240 0.813732i \(-0.697432\pi\)
−0.581240 + 0.813732i \(0.697432\pi\)
\(434\) −10.3024 −0.494530
\(435\) −13.4225 −0.643558
\(436\) 22.4915 1.07715
\(437\) −20.7045 −0.990432
\(438\) −33.5588 −1.60350
\(439\) 4.11750 0.196517 0.0982587 0.995161i \(-0.468673\pi\)
0.0982587 + 0.995161i \(0.468673\pi\)
\(440\) −0.634750 −0.0302605
\(441\) −2.11830 −0.100872
\(442\) 6.00492 0.285625
\(443\) −26.1064 −1.24035 −0.620175 0.784463i \(-0.712939\pi\)
−0.620175 + 0.784463i \(0.712939\pi\)
\(444\) −70.9457 −3.36693
\(445\) −1.71902 −0.0814895
\(446\) −11.4006 −0.539835
\(447\) −38.8933 −1.83959
\(448\) −7.31094 −0.345410
\(449\) −4.22039 −0.199172 −0.0995862 0.995029i \(-0.531752\pi\)
−0.0995862 + 0.995029i \(0.531752\pi\)
\(450\) 3.39673 0.160123
\(451\) −0.472489 −0.0222487
\(452\) 53.1365 2.49933
\(453\) 10.1754 0.478081
\(454\) 37.5440 1.76203
\(455\) −0.565482 −0.0265102
\(456\) −71.9811 −3.37083
\(457\) −3.22372 −0.150799 −0.0753996 0.997153i \(-0.524023\pi\)
−0.0753996 + 0.997153i \(0.524023\pi\)
\(458\) 7.67760 0.358751
\(459\) −23.2139 −1.08353
\(460\) 21.2938 0.992828
\(461\) 1.00504 0.0468093 0.0234046 0.999726i \(-0.492549\pi\)
0.0234046 + 0.999726i \(0.492549\pi\)
\(462\) −0.366687 −0.0170598
\(463\) −3.22289 −0.149781 −0.0748903 0.997192i \(-0.523861\pi\)
−0.0748903 + 0.997192i \(0.523861\pi\)
\(464\) 59.8027 2.77627
\(465\) 8.20279 0.380395
\(466\) 11.8888 0.550739
\(467\) −17.3202 −0.801483 −0.400741 0.916191i \(-0.631247\pi\)
−0.400741 + 0.916191i \(0.631247\pi\)
\(468\) −0.819351 −0.0378745
\(469\) 12.2770 0.566901
\(470\) −4.87855 −0.225031
\(471\) 1.67720 0.0772814
\(472\) −41.7375 −1.92112
\(473\) 0.643198 0.0295743
\(474\) 10.4820 0.481453
\(475\) −19.7517 −0.906269
\(476\) −23.4254 −1.07370
\(477\) 1.31499 0.0602093
\(478\) 48.2234 2.20569
\(479\) 38.1310 1.74225 0.871125 0.491061i \(-0.163391\pi\)
0.871125 + 0.491061i \(0.163391\pi\)
\(480\) 21.1112 0.963592
\(481\) 3.87993 0.176910
\(482\) −13.1775 −0.600220
\(483\) 7.17340 0.326401
\(484\) −52.7494 −2.39770
\(485\) 4.09896 0.186124
\(486\) 9.57856 0.434492
\(487\) −1.75904 −0.0797098 −0.0398549 0.999205i \(-0.512690\pi\)
−0.0398549 + 0.999205i \(0.512690\pi\)
\(488\) −11.5247 −0.521700
\(489\) 20.9567 0.947697
\(490\) −17.9491 −0.810858
\(491\) −6.66025 −0.300573 −0.150286 0.988642i \(-0.548020\pi\)
−0.150286 + 0.988642i \(0.548020\pi\)
\(492\) 55.1056 2.48435
\(493\) 30.4087 1.36954
\(494\) 6.75052 0.303720
\(495\) 0.0309168 0.00138961
\(496\) −36.5469 −1.64100
\(497\) −15.5206 −0.696196
\(498\) 42.8604 1.92062
\(499\) 35.2943 1.57999 0.789994 0.613115i \(-0.210084\pi\)
0.789994 + 0.613115i \(0.210084\pi\)
\(500\) 48.0148 2.14728
\(501\) −24.0533 −1.07462
\(502\) 58.9156 2.62953
\(503\) 19.5774 0.872913 0.436456 0.899725i \(-0.356233\pi\)
0.436456 + 0.899725i \(0.356233\pi\)
\(504\) 2.64091 0.117635
\(505\) −4.32762 −0.192576
\(506\) −0.755140 −0.0335701
\(507\) −23.3896 −1.03877
\(508\) 2.04906 0.0909125
\(509\) 21.8081 0.966627 0.483313 0.875447i \(-0.339433\pi\)
0.483313 + 0.875447i \(0.339433\pi\)
\(510\) 26.4262 1.17017
\(511\) −7.15952 −0.316718
\(512\) 43.4319 1.91944
\(513\) −26.0962 −1.15218
\(514\) 4.74793 0.209422
\(515\) −2.51699 −0.110912
\(516\) −75.0150 −3.30235
\(517\) 0.122107 0.00537027
\(518\) −21.4451 −0.942242
\(519\) −43.8127 −1.92317
\(520\) −4.04859 −0.177543
\(521\) −32.4806 −1.42300 −0.711500 0.702686i \(-0.751984\pi\)
−0.711500 + 0.702686i \(0.751984\pi\)
\(522\) −5.87875 −0.257306
\(523\) −1.86675 −0.0816274 −0.0408137 0.999167i \(-0.512995\pi\)
−0.0408137 + 0.999167i \(0.512995\pi\)
\(524\) −76.7376 −3.35230
\(525\) 6.84327 0.298665
\(526\) −60.5515 −2.64017
\(527\) −18.5835 −0.809510
\(528\) −1.30079 −0.0566097
\(529\) −8.22740 −0.357713
\(530\) 11.1424 0.483994
\(531\) 2.03291 0.0882208
\(532\) −26.3340 −1.14172
\(533\) −3.01365 −0.130536
\(534\) −7.10983 −0.307672
\(535\) 15.6804 0.677922
\(536\) 87.8979 3.79661
\(537\) −35.5183 −1.53273
\(538\) −41.7085 −1.79818
\(539\) 0.449255 0.0193508
\(540\) 26.8389 1.15496
\(541\) −20.1723 −0.867275 −0.433637 0.901088i \(-0.642770\pi\)
−0.433637 + 0.901088i \(0.642770\pi\)
\(542\) 11.3597 0.487942
\(543\) 20.2834 0.870442
\(544\) −47.8277 −2.05060
\(545\) −5.41309 −0.231871
\(546\) −2.33882 −0.100092
\(547\) 25.5123 1.09083 0.545414 0.838167i \(-0.316373\pi\)
0.545414 + 0.838167i \(0.316373\pi\)
\(548\) 73.7395 3.14999
\(549\) 0.561335 0.0239572
\(550\) −0.720387 −0.0307174
\(551\) 34.1844 1.45630
\(552\) 51.3583 2.18595
\(553\) 2.23625 0.0950950
\(554\) −2.85630 −0.121353
\(555\) 17.0747 0.724779
\(556\) −86.6879 −3.67638
\(557\) 5.41060 0.229255 0.114627 0.993409i \(-0.463433\pi\)
0.114627 + 0.993409i \(0.463433\pi\)
\(558\) 3.59264 0.152089
\(559\) 4.10248 0.173516
\(560\) 11.0875 0.468534
\(561\) −0.661432 −0.0279257
\(562\) −55.1070 −2.32455
\(563\) 26.5761 1.12005 0.560024 0.828476i \(-0.310792\pi\)
0.560024 + 0.828476i \(0.310792\pi\)
\(564\) −14.2411 −0.599660
\(565\) −12.7885 −0.538015
\(566\) −11.8853 −0.499576
\(567\) 10.1275 0.425316
\(568\) −111.121 −4.66252
\(569\) 36.9142 1.54753 0.773763 0.633475i \(-0.218372\pi\)
0.773763 + 0.633475i \(0.218372\pi\)
\(570\) 29.7074 1.24431
\(571\) 4.26468 0.178471 0.0892356 0.996011i \(-0.471558\pi\)
0.0892356 + 0.996011i \(0.471558\pi\)
\(572\) 0.173770 0.00726569
\(573\) −30.4402 −1.27166
\(574\) 16.6570 0.695250
\(575\) 14.0927 0.587708
\(576\) 2.54947 0.106228
\(577\) −34.2167 −1.42446 −0.712229 0.701947i \(-0.752314\pi\)
−0.712229 + 0.701947i \(0.752314\pi\)
\(578\) −15.5452 −0.646594
\(579\) −24.7594 −1.02897
\(580\) −35.1573 −1.45983
\(581\) 9.14395 0.379355
\(582\) 16.9532 0.702733
\(583\) −0.278887 −0.0115503
\(584\) −51.2588 −2.12111
\(585\) 0.197195 0.00815301
\(586\) 35.5260 1.46757
\(587\) 40.7025 1.67997 0.839986 0.542609i \(-0.182563\pi\)
0.839986 + 0.542609i \(0.182563\pi\)
\(588\) −52.3958 −2.16077
\(589\) −20.8909 −0.860795
\(590\) 17.2255 0.709164
\(591\) 5.58238 0.229628
\(592\) −76.0747 −3.12665
\(593\) −15.2334 −0.625562 −0.312781 0.949825i \(-0.601261\pi\)
−0.312781 + 0.949825i \(0.601261\pi\)
\(594\) −0.951787 −0.0390523
\(595\) 5.63784 0.231129
\(596\) −101.873 −4.17286
\(597\) 44.0963 1.80474
\(598\) −4.81647 −0.196960
\(599\) 41.3147 1.68807 0.844037 0.536285i \(-0.180173\pi\)
0.844037 + 0.536285i \(0.180173\pi\)
\(600\) 48.9947 2.00020
\(601\) 10.0865 0.411437 0.205719 0.978611i \(-0.434047\pi\)
0.205719 + 0.978611i \(0.434047\pi\)
\(602\) −22.6751 −0.924170
\(603\) −4.28125 −0.174346
\(604\) 26.6522 1.08446
\(605\) 12.6953 0.516138
\(606\) −17.8989 −0.727093
\(607\) −23.8802 −0.969266 −0.484633 0.874717i \(-0.661047\pi\)
−0.484633 + 0.874717i \(0.661047\pi\)
\(608\) −53.7662 −2.18051
\(609\) −11.8437 −0.479931
\(610\) 4.75639 0.192580
\(611\) 0.778830 0.0315081
\(612\) 8.16890 0.330208
\(613\) −29.8943 −1.20742 −0.603709 0.797204i \(-0.706311\pi\)
−0.603709 + 0.797204i \(0.706311\pi\)
\(614\) −83.7241 −3.37883
\(615\) −13.2624 −0.534791
\(616\) −0.560090 −0.0225667
\(617\) −38.0974 −1.53374 −0.766872 0.641800i \(-0.778188\pi\)
−0.766872 + 0.641800i \(0.778188\pi\)
\(618\) −10.4102 −0.418760
\(619\) 44.4171 1.78527 0.892637 0.450776i \(-0.148853\pi\)
0.892637 + 0.450776i \(0.148853\pi\)
\(620\) 21.4855 0.862877
\(621\) 18.6196 0.747178
\(622\) 8.77992 0.352043
\(623\) −1.51683 −0.0607705
\(624\) −8.29678 −0.332137
\(625\) 6.77734 0.271094
\(626\) 63.1854 2.52540
\(627\) −0.743559 −0.0296949
\(628\) 4.39307 0.175303
\(629\) −38.6828 −1.54238
\(630\) −1.08993 −0.0434239
\(631\) −41.4048 −1.64830 −0.824150 0.566371i \(-0.808347\pi\)
−0.824150 + 0.566371i \(0.808347\pi\)
\(632\) 16.0105 0.636864
\(633\) −13.6342 −0.541912
\(634\) −19.1249 −0.759548
\(635\) −0.493153 −0.0195702
\(636\) 32.5261 1.28974
\(637\) 2.86546 0.113534
\(638\) 1.24678 0.0493605
\(639\) 5.41236 0.214110
\(640\) −1.44781 −0.0572297
\(641\) −4.95359 −0.195655 −0.0978275 0.995203i \(-0.531189\pi\)
−0.0978275 + 0.995203i \(0.531189\pi\)
\(642\) 64.8537 2.55957
\(643\) −13.4679 −0.531121 −0.265560 0.964094i \(-0.585557\pi\)
−0.265560 + 0.964094i \(0.585557\pi\)
\(644\) 18.7892 0.740398
\(645\) 18.0540 0.710877
\(646\) −67.3024 −2.64798
\(647\) −28.2537 −1.11077 −0.555383 0.831594i \(-0.687428\pi\)
−0.555383 + 0.831594i \(0.687428\pi\)
\(648\) 72.5084 2.84840
\(649\) −0.431145 −0.0169239
\(650\) −4.59481 −0.180223
\(651\) 7.23798 0.283679
\(652\) 54.8917 2.14972
\(653\) 21.8515 0.855116 0.427558 0.903988i \(-0.359374\pi\)
0.427558 + 0.903988i \(0.359374\pi\)
\(654\) −22.3884 −0.875455
\(655\) 18.4686 0.721628
\(656\) 59.0894 2.30705
\(657\) 2.49667 0.0974042
\(658\) −4.30473 −0.167816
\(659\) −48.2531 −1.87967 −0.939836 0.341625i \(-0.889023\pi\)
−0.939836 + 0.341625i \(0.889023\pi\)
\(660\) 0.764721 0.0297667
\(661\) 21.2733 0.827437 0.413719 0.910405i \(-0.364230\pi\)
0.413719 + 0.910405i \(0.364230\pi\)
\(662\) 13.4366 0.522230
\(663\) −4.21878 −0.163844
\(664\) 65.4665 2.54059
\(665\) 6.33786 0.245772
\(666\) 7.47832 0.289779
\(667\) −24.3904 −0.944401
\(668\) −63.0024 −2.43764
\(669\) 8.00954 0.309667
\(670\) −36.2765 −1.40148
\(671\) −0.119049 −0.00459585
\(672\) 18.6281 0.718596
\(673\) 16.5835 0.639246 0.319623 0.947545i \(-0.396444\pi\)
0.319623 + 0.947545i \(0.396444\pi\)
\(674\) 45.1893 1.74063
\(675\) 17.7627 0.683686
\(676\) −61.2641 −2.35631
\(677\) 26.1285 1.00420 0.502100 0.864809i \(-0.332561\pi\)
0.502100 + 0.864809i \(0.332561\pi\)
\(678\) −52.8928 −2.03134
\(679\) 3.61684 0.138802
\(680\) 40.3643 1.54790
\(681\) −26.3767 −1.01076
\(682\) −0.761937 −0.0291761
\(683\) −38.9697 −1.49113 −0.745566 0.666432i \(-0.767821\pi\)
−0.745566 + 0.666432i \(0.767821\pi\)
\(684\) 9.18318 0.351128
\(685\) −17.7470 −0.678080
\(686\) −34.4337 −1.31469
\(687\) −5.39393 −0.205791
\(688\) −80.4382 −3.06668
\(689\) −1.77881 −0.0677672
\(690\) −21.1961 −0.806923
\(691\) −20.2103 −0.768835 −0.384418 0.923159i \(-0.625598\pi\)
−0.384418 + 0.923159i \(0.625598\pi\)
\(692\) −114.758 −4.36245
\(693\) 0.0272803 0.00103629
\(694\) 79.3938 3.01375
\(695\) 20.8634 0.791392
\(696\) −84.7955 −3.21417
\(697\) 30.0460 1.13807
\(698\) −36.1125 −1.36688
\(699\) −8.35254 −0.315922
\(700\) 17.9245 0.677482
\(701\) 26.2971 0.993228 0.496614 0.867971i \(-0.334576\pi\)
0.496614 + 0.867971i \(0.334576\pi\)
\(702\) −6.07074 −0.229125
\(703\) −43.4858 −1.64010
\(704\) −0.540698 −0.0203783
\(705\) 3.42744 0.129085
\(706\) −12.7186 −0.478672
\(707\) −3.81860 −0.143613
\(708\) 50.2836 1.88977
\(709\) 12.7455 0.478667 0.239333 0.970937i \(-0.423071\pi\)
0.239333 + 0.970937i \(0.423071\pi\)
\(710\) 45.8607 1.72112
\(711\) −0.779825 −0.0292457
\(712\) −10.8598 −0.406988
\(713\) 14.9056 0.558218
\(714\) 23.3180 0.872653
\(715\) −0.0418216 −0.00156404
\(716\) −93.0327 −3.47679
\(717\) −33.8795 −1.26525
\(718\) 92.9813 3.47003
\(719\) 36.3325 1.35498 0.677488 0.735534i \(-0.263069\pi\)
0.677488 + 0.735534i \(0.263069\pi\)
\(720\) −3.86645 −0.144094
\(721\) −2.22094 −0.0827122
\(722\) −26.1208 −0.972114
\(723\) 9.25792 0.344306
\(724\) 53.1279 1.97448
\(725\) −23.2680 −0.864150
\(726\) 52.5075 1.94874
\(727\) −7.22985 −0.268140 −0.134070 0.990972i \(-0.542805\pi\)
−0.134070 + 0.990972i \(0.542805\pi\)
\(728\) −3.57239 −0.132402
\(729\) 23.0896 0.855170
\(730\) 21.1551 0.782985
\(731\) −40.9016 −1.51280
\(732\) 13.8845 0.513186
\(733\) 2.47865 0.0915510 0.0457755 0.998952i \(-0.485424\pi\)
0.0457755 + 0.998952i \(0.485424\pi\)
\(734\) 87.4780 3.22887
\(735\) 12.6102 0.465135
\(736\) 38.3620 1.41404
\(737\) 0.907977 0.0334458
\(738\) −5.80863 −0.213819
\(739\) 30.8999 1.13667 0.568335 0.822797i \(-0.307588\pi\)
0.568335 + 0.822797i \(0.307588\pi\)
\(740\) 44.7234 1.64406
\(741\) −4.74260 −0.174224
\(742\) 9.83180 0.360937
\(743\) −21.4036 −0.785223 −0.392612 0.919704i \(-0.628428\pi\)
−0.392612 + 0.919704i \(0.628428\pi\)
\(744\) 51.8206 1.89983
\(745\) 24.5179 0.898266
\(746\) 49.4565 1.81073
\(747\) −3.18868 −0.116668
\(748\) −1.73248 −0.0633458
\(749\) 13.8361 0.505558
\(750\) −47.7946 −1.74521
\(751\) 15.9269 0.581182 0.290591 0.956847i \(-0.406148\pi\)
0.290591 + 0.956847i \(0.406148\pi\)
\(752\) −15.2707 −0.556865
\(753\) −41.3914 −1.50839
\(754\) 7.95227 0.289605
\(755\) −6.41445 −0.233446
\(756\) 23.6821 0.861311
\(757\) 12.7141 0.462102 0.231051 0.972942i \(-0.425784\pi\)
0.231051 + 0.972942i \(0.425784\pi\)
\(758\) 87.9858 3.19579
\(759\) 0.530526 0.0192569
\(760\) 45.3761 1.64597
\(761\) −12.7971 −0.463893 −0.231946 0.972729i \(-0.574509\pi\)
−0.231946 + 0.972729i \(0.574509\pi\)
\(762\) −2.03967 −0.0738894
\(763\) −4.77639 −0.172917
\(764\) −79.7315 −2.88459
\(765\) −1.96603 −0.0710818
\(766\) −68.9822 −2.49243
\(767\) −2.74995 −0.0992949
\(768\) −32.2750 −1.16462
\(769\) −17.5407 −0.632534 −0.316267 0.948670i \(-0.602430\pi\)
−0.316267 + 0.948670i \(0.602430\pi\)
\(770\) 0.231156 0.00833027
\(771\) −3.33567 −0.120131
\(772\) −64.8521 −2.33408
\(773\) 45.6066 1.64036 0.820178 0.572109i \(-0.193874\pi\)
0.820178 + 0.572109i \(0.193874\pi\)
\(774\) 7.90727 0.284221
\(775\) 14.2196 0.510783
\(776\) 25.8949 0.929573
\(777\) 15.0663 0.540501
\(778\) −11.3150 −0.405662
\(779\) 33.7767 1.21017
\(780\) 4.87758 0.174645
\(781\) −1.14787 −0.0410739
\(782\) 48.0200 1.71719
\(783\) −30.7420 −1.09863
\(784\) −56.1837 −2.00656
\(785\) −1.05729 −0.0377363
\(786\) 76.3857 2.72459
\(787\) −51.0311 −1.81906 −0.909531 0.415635i \(-0.863559\pi\)
−0.909531 + 0.415635i \(0.863559\pi\)
\(788\) 14.6218 0.520882
\(789\) 42.5407 1.51449
\(790\) −6.60772 −0.235092
\(791\) −11.2843 −0.401223
\(792\) 0.195315 0.00694020
\(793\) −0.759327 −0.0269645
\(794\) 73.0533 2.59256
\(795\) −7.82812 −0.277635
\(796\) 115.501 4.09382
\(797\) −17.9409 −0.635500 −0.317750 0.948175i \(-0.602927\pi\)
−0.317750 + 0.948175i \(0.602927\pi\)
\(798\) 26.2132 0.927938
\(799\) −7.76490 −0.274702
\(800\) 36.5965 1.29388
\(801\) 0.528949 0.0186895
\(802\) 80.8595 2.85525
\(803\) −0.529499 −0.0186856
\(804\) −105.896 −3.73465
\(805\) −4.52204 −0.159381
\(806\) −4.85982 −0.171180
\(807\) 29.3025 1.03150
\(808\) −27.3394 −0.961797
\(809\) 12.6932 0.446269 0.223134 0.974788i \(-0.428371\pi\)
0.223134 + 0.974788i \(0.428371\pi\)
\(810\) −29.9250 −1.05146
\(811\) 24.6581 0.865862 0.432931 0.901427i \(-0.357479\pi\)
0.432931 + 0.901427i \(0.357479\pi\)
\(812\) −31.0221 −1.08866
\(813\) −7.98082 −0.279900
\(814\) −1.58602 −0.0555900
\(815\) −13.2109 −0.462758
\(816\) 82.7186 2.89573
\(817\) −45.9801 −1.60864
\(818\) −25.9574 −0.907581
\(819\) 0.174001 0.00608008
\(820\) −34.7380 −1.21310
\(821\) −36.4455 −1.27196 −0.635978 0.771707i \(-0.719403\pi\)
−0.635978 + 0.771707i \(0.719403\pi\)
\(822\) −73.4013 −2.56017
\(823\) 4.72736 0.164786 0.0823928 0.996600i \(-0.473744\pi\)
0.0823928 + 0.996600i \(0.473744\pi\)
\(824\) −15.9009 −0.553935
\(825\) 0.506111 0.0176205
\(826\) 15.1995 0.528857
\(827\) 47.7679 1.66105 0.830527 0.556979i \(-0.188040\pi\)
0.830527 + 0.556979i \(0.188040\pi\)
\(828\) −6.55217 −0.227704
\(829\) −8.47959 −0.294508 −0.147254 0.989099i \(-0.547043\pi\)
−0.147254 + 0.989099i \(0.547043\pi\)
\(830\) −27.0188 −0.937835
\(831\) 2.00671 0.0696118
\(832\) −3.44871 −0.119562
\(833\) −28.5685 −0.989841
\(834\) 86.2903 2.98799
\(835\) 15.1629 0.524735
\(836\) −1.94759 −0.0673589
\(837\) 18.7872 0.649380
\(838\) 12.6012 0.435300
\(839\) 55.8042 1.92658 0.963288 0.268470i \(-0.0865180\pi\)
0.963288 + 0.268470i \(0.0865180\pi\)
\(840\) −15.7213 −0.542435
\(841\) 11.2700 0.388622
\(842\) −44.6298 −1.53804
\(843\) 38.7156 1.33344
\(844\) −35.7119 −1.22926
\(845\) 14.7446 0.507228
\(846\) 1.50115 0.0516104
\(847\) 11.2021 0.384908
\(848\) 34.8775 1.19770
\(849\) 8.35005 0.286573
\(850\) 45.8101 1.57127
\(851\) 31.0269 1.06359
\(852\) 133.874 4.58643
\(853\) 17.1626 0.587637 0.293819 0.955861i \(-0.405074\pi\)
0.293819 + 0.955861i \(0.405074\pi\)
\(854\) 4.19694 0.143616
\(855\) −2.21014 −0.0755851
\(856\) 99.0598 3.38579
\(857\) −18.8202 −0.642887 −0.321444 0.946929i \(-0.604168\pi\)
−0.321444 + 0.946929i \(0.604168\pi\)
\(858\) −0.172973 −0.00590521
\(859\) −11.5195 −0.393041 −0.196521 0.980500i \(-0.562964\pi\)
−0.196521 + 0.980500i \(0.562964\pi\)
\(860\) 47.2887 1.61253
\(861\) −11.7024 −0.398818
\(862\) 30.2509 1.03035
\(863\) −42.0945 −1.43291 −0.716456 0.697632i \(-0.754237\pi\)
−0.716456 + 0.697632i \(0.754237\pi\)
\(864\) 48.3519 1.64497
\(865\) 27.6191 0.939077
\(866\) 63.0690 2.14317
\(867\) 10.9213 0.370907
\(868\) 18.9583 0.643488
\(869\) 0.165387 0.00561038
\(870\) 34.9961 1.18648
\(871\) 5.79131 0.196231
\(872\) −34.1968 −1.15805
\(873\) −1.26126 −0.0426873
\(874\) 53.9824 1.82598
\(875\) −10.1966 −0.344708
\(876\) 61.7545 2.08649
\(877\) 0.647423 0.0218619 0.0109310 0.999940i \(-0.496520\pi\)
0.0109310 + 0.999940i \(0.496520\pi\)
\(878\) −10.7354 −0.362304
\(879\) −24.9589 −0.841844
\(880\) 0.820006 0.0276424
\(881\) 44.3105 1.49286 0.746429 0.665465i \(-0.231767\pi\)
0.746429 + 0.665465i \(0.231767\pi\)
\(882\) 5.52300 0.185969
\(883\) 19.5057 0.656419 0.328209 0.944605i \(-0.393555\pi\)
0.328209 + 0.944605i \(0.393555\pi\)
\(884\) −11.0502 −0.371658
\(885\) −12.1019 −0.406800
\(886\) 68.0665 2.28674
\(887\) 34.3705 1.15405 0.577024 0.816727i \(-0.304214\pi\)
0.577024 + 0.816727i \(0.304214\pi\)
\(888\) 107.868 3.61981
\(889\) −0.435148 −0.0145944
\(890\) 4.48196 0.150236
\(891\) 0.749005 0.0250926
\(892\) 20.9793 0.702438
\(893\) −8.72903 −0.292106
\(894\) 101.405 3.39150
\(895\) 22.3904 0.748428
\(896\) −1.27752 −0.0426788
\(897\) 3.38383 0.112983
\(898\) 11.0037 0.367198
\(899\) −24.6100 −0.820789
\(900\) −6.25063 −0.208354
\(901\) 17.7347 0.590827
\(902\) 1.23191 0.0410181
\(903\) 15.9305 0.530134
\(904\) −80.7903 −2.68704
\(905\) −12.7864 −0.425035
\(906\) −26.5300 −0.881400
\(907\) 11.2174 0.372467 0.186233 0.982506i \(-0.440372\pi\)
0.186233 + 0.982506i \(0.440372\pi\)
\(908\) −69.0881 −2.29277
\(909\) 1.33162 0.0441671
\(910\) 1.47437 0.0488748
\(911\) 26.0372 0.862651 0.431326 0.902196i \(-0.358046\pi\)
0.431326 + 0.902196i \(0.358046\pi\)
\(912\) 92.9893 3.07918
\(913\) 0.676263 0.0223810
\(914\) 8.40512 0.278017
\(915\) −3.34162 −0.110470
\(916\) −14.1282 −0.466810
\(917\) 16.2963 0.538152
\(918\) 60.5250 1.99762
\(919\) −9.37181 −0.309147 −0.154574 0.987981i \(-0.549400\pi\)
−0.154574 + 0.987981i \(0.549400\pi\)
\(920\) −32.3757 −1.06740
\(921\) 58.8207 1.93821
\(922\) −2.62041 −0.0862986
\(923\) −7.32138 −0.240986
\(924\) 0.674774 0.0221984
\(925\) 29.5990 0.973210
\(926\) 8.40296 0.276139
\(927\) 0.774487 0.0254375
\(928\) −63.3379 −2.07917
\(929\) 47.2204 1.54925 0.774626 0.632419i \(-0.217938\pi\)
0.774626 + 0.632419i \(0.217938\pi\)
\(930\) −21.3869 −0.701305
\(931\) −32.1157 −1.05255
\(932\) −21.8777 −0.716627
\(933\) −6.16837 −0.201943
\(934\) 45.1585 1.47763
\(935\) 0.416960 0.0136360
\(936\) 1.24577 0.0407191
\(937\) 26.0269 0.850261 0.425131 0.905132i \(-0.360228\pi\)
0.425131 + 0.905132i \(0.360228\pi\)
\(938\) −32.0096 −1.04515
\(939\) −44.3912 −1.44865
\(940\) 8.97746 0.292812
\(941\) 53.0192 1.72838 0.864189 0.503168i \(-0.167832\pi\)
0.864189 + 0.503168i \(0.167832\pi\)
\(942\) −4.37293 −0.142478
\(943\) −24.0995 −0.784788
\(944\) 53.9189 1.75491
\(945\) −5.69963 −0.185409
\(946\) −1.67699 −0.0545238
\(947\) 9.26704 0.301138 0.150569 0.988599i \(-0.451889\pi\)
0.150569 + 0.988599i \(0.451889\pi\)
\(948\) −19.2888 −0.626472
\(949\) −3.37728 −0.109631
\(950\) 51.4980 1.67082
\(951\) 13.4363 0.435701
\(952\) 35.6166 1.15434
\(953\) −28.0583 −0.908899 −0.454449 0.890773i \(-0.650164\pi\)
−0.454449 + 0.890773i \(0.650164\pi\)
\(954\) −3.42854 −0.111003
\(955\) 19.1892 0.620947
\(956\) −88.7401 −2.87006
\(957\) −0.875930 −0.0283148
\(958\) −99.4180 −3.21205
\(959\) −15.6596 −0.505676
\(960\) −15.1770 −0.489834
\(961\) −15.9602 −0.514847
\(962\) −10.1160 −0.326154
\(963\) −4.82491 −0.155480
\(964\) 24.2491 0.781012
\(965\) 15.6081 0.502442
\(966\) −18.7030 −0.601760
\(967\) −51.8873 −1.66858 −0.834292 0.551323i \(-0.814123\pi\)
−0.834292 + 0.551323i \(0.814123\pi\)
\(968\) 80.2018 2.57778
\(969\) 47.2836 1.51897
\(970\) −10.6871 −0.343143
\(971\) 45.6433 1.46476 0.732382 0.680894i \(-0.238409\pi\)
0.732382 + 0.680894i \(0.238409\pi\)
\(972\) −17.6264 −0.565366
\(973\) 18.4094 0.590178
\(974\) 4.58631 0.146955
\(975\) 3.22810 0.103382
\(976\) 14.8883 0.476563
\(977\) −12.7401 −0.407593 −0.203797 0.979013i \(-0.565328\pi\)
−0.203797 + 0.979013i \(0.565328\pi\)
\(978\) −54.6400 −1.74719
\(979\) −0.112181 −0.00358531
\(980\) 33.0297 1.05510
\(981\) 1.66562 0.0531793
\(982\) 17.3651 0.554143
\(983\) 39.2025 1.25037 0.625184 0.780478i \(-0.285024\pi\)
0.625184 + 0.780478i \(0.285024\pi\)
\(984\) −83.7841 −2.67094
\(985\) −3.51907 −0.112127
\(986\) −79.2839 −2.52491
\(987\) 3.02431 0.0962647
\(988\) −12.4222 −0.395204
\(989\) 32.8066 1.04319
\(990\) −0.0806085 −0.00256191
\(991\) −49.8832 −1.58459 −0.792296 0.610137i \(-0.791115\pi\)
−0.792296 + 0.610137i \(0.791115\pi\)
\(992\) 38.7073 1.22896
\(993\) −9.43996 −0.299568
\(994\) 40.4666 1.28352
\(995\) −27.7978 −0.881250
\(996\) −78.8713 −2.49913
\(997\) 22.8494 0.723649 0.361825 0.932246i \(-0.382154\pi\)
0.361825 + 0.932246i \(0.382154\pi\)
\(998\) −92.0218 −2.91290
\(999\) 39.1067 1.23728
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 4013.2.a.b.1.8 157
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4013.2.a.b.1.8 157 1.1 even 1 trivial