Properties

Label 8002.2.a.g.1.19
Level $8002$
Weight $2$
Character 8002.1
Self dual yes
Analytic conductor $63.896$
Analytic rank $0$
Dimension $95$
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] = [8002,2,Mod(1,8002)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8002, 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("8002.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8002.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: \(63.8962916974\)
Analytic rank: \(0\)
Dimension: \(95\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) \(=\) 8002.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.94136 q^{3} +1.00000 q^{4} -0.368072 q^{5} -1.94136 q^{6} -3.56861 q^{7} +1.00000 q^{8} +0.768897 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.94136 q^{3} +1.00000 q^{4} -0.368072 q^{5} -1.94136 q^{6} -3.56861 q^{7} +1.00000 q^{8} +0.768897 q^{9} -0.368072 q^{10} -1.91905 q^{11} -1.94136 q^{12} -3.88960 q^{13} -3.56861 q^{14} +0.714562 q^{15} +1.00000 q^{16} -2.31804 q^{17} +0.768897 q^{18} +2.22922 q^{19} -0.368072 q^{20} +6.92797 q^{21} -1.91905 q^{22} +3.88295 q^{23} -1.94136 q^{24} -4.86452 q^{25} -3.88960 q^{26} +4.33138 q^{27} -3.56861 q^{28} -6.88751 q^{29} +0.714562 q^{30} +3.30935 q^{31} +1.00000 q^{32} +3.72558 q^{33} -2.31804 q^{34} +1.31350 q^{35} +0.768897 q^{36} -3.47882 q^{37} +2.22922 q^{38} +7.55113 q^{39} -0.368072 q^{40} -9.31768 q^{41} +6.92797 q^{42} -9.31761 q^{43} -1.91905 q^{44} -0.283009 q^{45} +3.88295 q^{46} -7.12346 q^{47} -1.94136 q^{48} +5.73496 q^{49} -4.86452 q^{50} +4.50017 q^{51} -3.88960 q^{52} +8.17762 q^{53} +4.33138 q^{54} +0.706349 q^{55} -3.56861 q^{56} -4.32773 q^{57} -6.88751 q^{58} -5.71449 q^{59} +0.714562 q^{60} +2.14757 q^{61} +3.30935 q^{62} -2.74389 q^{63} +1.00000 q^{64} +1.43165 q^{65} +3.72558 q^{66} -8.17728 q^{67} -2.31804 q^{68} -7.53822 q^{69} +1.31350 q^{70} -10.1180 q^{71} +0.768897 q^{72} -7.91677 q^{73} -3.47882 q^{74} +9.44381 q^{75} +2.22922 q^{76} +6.84834 q^{77} +7.55113 q^{78} +10.7209 q^{79} -0.368072 q^{80} -10.7155 q^{81} -9.31768 q^{82} -5.44583 q^{83} +6.92797 q^{84} +0.853206 q^{85} -9.31761 q^{86} +13.3712 q^{87} -1.91905 q^{88} -3.11259 q^{89} -0.283009 q^{90} +13.8805 q^{91} +3.88295 q^{92} -6.42465 q^{93} -7.12346 q^{94} -0.820512 q^{95} -1.94136 q^{96} +4.37204 q^{97} +5.73496 q^{98} -1.47555 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9} + 36 q^{10} + 40 q^{11} + 24 q^{12} + 52 q^{13} + 21 q^{14} + 15 q^{15} + 95 q^{16} + 84 q^{17} + 121 q^{18} + 37 q^{19} + 36 q^{20} + 36 q^{21} + 40 q^{22} + 37 q^{23} + 24 q^{24} + 133 q^{25} + 52 q^{26} + 93 q^{27} + 21 q^{28} + 66 q^{29} + 15 q^{30} + 10 q^{31} + 95 q^{32} + 63 q^{33} + 84 q^{34} + 55 q^{35} + 121 q^{36} + 49 q^{37} + 37 q^{38} + 14 q^{39} + 36 q^{40} + 98 q^{41} + 36 q^{42} + 37 q^{43} + 40 q^{44} + 97 q^{45} + 37 q^{46} + 91 q^{47} + 24 q^{48} + 170 q^{49} + 133 q^{50} + 22 q^{51} + 52 q^{52} + 70 q^{53} + 93 q^{54} - q^{55} + 21 q^{56} + 50 q^{57} + 66 q^{58} + 72 q^{59} + 15 q^{60} + 97 q^{61} + 10 q^{62} + 75 q^{63} + 95 q^{64} + 75 q^{65} + 63 q^{66} + 39 q^{67} + 84 q^{68} + 65 q^{69} + 55 q^{70} + 28 q^{71} + 121 q^{72} + 117 q^{73} + 49 q^{74} + 62 q^{75} + 37 q^{76} + 92 q^{77} + 14 q^{78} + q^{79} + 36 q^{80} + 155 q^{81} + 98 q^{82} + 117 q^{83} + 36 q^{84} + 81 q^{85} + 37 q^{86} + 46 q^{87} + 40 q^{88} + 90 q^{89} + 97 q^{90} + 65 q^{91} + 37 q^{92} + 36 q^{93} + 91 q^{94} + 38 q^{95} + 24 q^{96} + 111 q^{97} + 170 q^{98} + 97 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.94136 −1.12085 −0.560424 0.828206i \(-0.689362\pi\)
−0.560424 + 0.828206i \(0.689362\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.368072 −0.164607 −0.0823033 0.996607i \(-0.526228\pi\)
−0.0823033 + 0.996607i \(0.526228\pi\)
\(6\) −1.94136 −0.792559
\(7\) −3.56861 −1.34881 −0.674403 0.738363i \(-0.735599\pi\)
−0.674403 + 0.738363i \(0.735599\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.768897 0.256299
\(10\) −0.368072 −0.116395
\(11\) −1.91905 −0.578616 −0.289308 0.957236i \(-0.593425\pi\)
−0.289308 + 0.957236i \(0.593425\pi\)
\(12\) −1.94136 −0.560424
\(13\) −3.88960 −1.07878 −0.539391 0.842056i \(-0.681345\pi\)
−0.539391 + 0.842056i \(0.681345\pi\)
\(14\) −3.56861 −0.953750
\(15\) 0.714562 0.184499
\(16\) 1.00000 0.250000
\(17\) −2.31804 −0.562208 −0.281104 0.959677i \(-0.590701\pi\)
−0.281104 + 0.959677i \(0.590701\pi\)
\(18\) 0.768897 0.181231
\(19\) 2.22922 0.511418 0.255709 0.966754i \(-0.417691\pi\)
0.255709 + 0.966754i \(0.417691\pi\)
\(20\) −0.368072 −0.0823033
\(21\) 6.92797 1.51181
\(22\) −1.91905 −0.409143
\(23\) 3.88295 0.809651 0.404825 0.914394i \(-0.367332\pi\)
0.404825 + 0.914394i \(0.367332\pi\)
\(24\) −1.94136 −0.396279
\(25\) −4.86452 −0.972905
\(26\) −3.88960 −0.762814
\(27\) 4.33138 0.833575
\(28\) −3.56861 −0.674403
\(29\) −6.88751 −1.27898 −0.639489 0.768800i \(-0.720854\pi\)
−0.639489 + 0.768800i \(0.720854\pi\)
\(30\) 0.714562 0.130460
\(31\) 3.30935 0.594376 0.297188 0.954819i \(-0.403951\pi\)
0.297188 + 0.954819i \(0.403951\pi\)
\(32\) 1.00000 0.176777
\(33\) 3.72558 0.648540
\(34\) −2.31804 −0.397541
\(35\) 1.31350 0.222023
\(36\) 0.768897 0.128149
\(37\) −3.47882 −0.571914 −0.285957 0.958242i \(-0.592311\pi\)
−0.285957 + 0.958242i \(0.592311\pi\)
\(38\) 2.22922 0.361627
\(39\) 7.55113 1.20915
\(40\) −0.368072 −0.0581973
\(41\) −9.31768 −1.45518 −0.727589 0.686013i \(-0.759359\pi\)
−0.727589 + 0.686013i \(0.759359\pi\)
\(42\) 6.92797 1.06901
\(43\) −9.31761 −1.42092 −0.710461 0.703737i \(-0.751514\pi\)
−0.710461 + 0.703737i \(0.751514\pi\)
\(44\) −1.91905 −0.289308
\(45\) −0.283009 −0.0421885
\(46\) 3.88295 0.572509
\(47\) −7.12346 −1.03906 −0.519532 0.854451i \(-0.673894\pi\)
−0.519532 + 0.854451i \(0.673894\pi\)
\(48\) −1.94136 −0.280212
\(49\) 5.73496 0.819280
\(50\) −4.86452 −0.687947
\(51\) 4.50017 0.630149
\(52\) −3.88960 −0.539391
\(53\) 8.17762 1.12328 0.561641 0.827381i \(-0.310170\pi\)
0.561641 + 0.827381i \(0.310170\pi\)
\(54\) 4.33138 0.589427
\(55\) 0.706349 0.0952441
\(56\) −3.56861 −0.476875
\(57\) −4.32773 −0.573221
\(58\) −6.88751 −0.904374
\(59\) −5.71449 −0.743964 −0.371982 0.928240i \(-0.621322\pi\)
−0.371982 + 0.928240i \(0.621322\pi\)
\(60\) 0.714562 0.0922495
\(61\) 2.14757 0.274968 0.137484 0.990504i \(-0.456098\pi\)
0.137484 + 0.990504i \(0.456098\pi\)
\(62\) 3.30935 0.420288
\(63\) −2.74389 −0.345698
\(64\) 1.00000 0.125000
\(65\) 1.43165 0.177575
\(66\) 3.72558 0.458587
\(67\) −8.17728 −0.999014 −0.499507 0.866310i \(-0.666485\pi\)
−0.499507 + 0.866310i \(0.666485\pi\)
\(68\) −2.31804 −0.281104
\(69\) −7.53822 −0.907495
\(70\) 1.31350 0.156994
\(71\) −10.1180 −1.20079 −0.600396 0.799703i \(-0.704990\pi\)
−0.600396 + 0.799703i \(0.704990\pi\)
\(72\) 0.768897 0.0906154
\(73\) −7.91677 −0.926587 −0.463294 0.886205i \(-0.653333\pi\)
−0.463294 + 0.886205i \(0.653333\pi\)
\(74\) −3.47882 −0.404404
\(75\) 9.44381 1.09048
\(76\) 2.22922 0.255709
\(77\) 6.84834 0.780441
\(78\) 7.55113 0.854998
\(79\) 10.7209 1.20619 0.603097 0.797668i \(-0.293933\pi\)
0.603097 + 0.797668i \(0.293933\pi\)
\(80\) −0.368072 −0.0411517
\(81\) −10.7155 −1.19061
\(82\) −9.31768 −1.02897
\(83\) −5.44583 −0.597757 −0.298879 0.954291i \(-0.596613\pi\)
−0.298879 + 0.954291i \(0.596613\pi\)
\(84\) 6.92797 0.755903
\(85\) 0.853206 0.0925432
\(86\) −9.31761 −1.00474
\(87\) 13.3712 1.43354
\(88\) −1.91905 −0.204572
\(89\) −3.11259 −0.329934 −0.164967 0.986299i \(-0.552752\pi\)
−0.164967 + 0.986299i \(0.552752\pi\)
\(90\) −0.283009 −0.0298318
\(91\) 13.8805 1.45507
\(92\) 3.88295 0.404825
\(93\) −6.42465 −0.666205
\(94\) −7.12346 −0.734729
\(95\) −0.820512 −0.0841828
\(96\) −1.94136 −0.198140
\(97\) 4.37204 0.443913 0.221957 0.975057i \(-0.428756\pi\)
0.221957 + 0.975057i \(0.428756\pi\)
\(98\) 5.73496 0.579318
\(99\) −1.47555 −0.148299
\(100\) −4.86452 −0.486452
\(101\) 18.6342 1.85417 0.927087 0.374847i \(-0.122305\pi\)
0.927087 + 0.374847i \(0.122305\pi\)
\(102\) 4.50017 0.445583
\(103\) 3.72595 0.367129 0.183564 0.983008i \(-0.441236\pi\)
0.183564 + 0.983008i \(0.441236\pi\)
\(104\) −3.88960 −0.381407
\(105\) −2.54999 −0.248853
\(106\) 8.17762 0.794281
\(107\) 2.10121 0.203132 0.101566 0.994829i \(-0.467615\pi\)
0.101566 + 0.994829i \(0.467615\pi\)
\(108\) 4.33138 0.416788
\(109\) −8.20290 −0.785695 −0.392848 0.919604i \(-0.628510\pi\)
−0.392848 + 0.919604i \(0.628510\pi\)
\(110\) 0.706349 0.0673477
\(111\) 6.75365 0.641028
\(112\) −3.56861 −0.337202
\(113\) 11.9151 1.12088 0.560441 0.828194i \(-0.310632\pi\)
0.560441 + 0.828194i \(0.310632\pi\)
\(114\) −4.32773 −0.405329
\(115\) −1.42920 −0.133274
\(116\) −6.88751 −0.639489
\(117\) −2.99070 −0.276491
\(118\) −5.71449 −0.526062
\(119\) 8.27218 0.758310
\(120\) 0.714562 0.0652302
\(121\) −7.31724 −0.665203
\(122\) 2.14757 0.194432
\(123\) 18.0890 1.63103
\(124\) 3.30935 0.297188
\(125\) 3.63085 0.324753
\(126\) −2.74389 −0.244445
\(127\) 17.7895 1.57856 0.789282 0.614031i \(-0.210453\pi\)
0.789282 + 0.614031i \(0.210453\pi\)
\(128\) 1.00000 0.0883883
\(129\) 18.0889 1.59264
\(130\) 1.43165 0.125564
\(131\) 2.29304 0.200344 0.100172 0.994970i \(-0.468061\pi\)
0.100172 + 0.994970i \(0.468061\pi\)
\(132\) 3.72558 0.324270
\(133\) −7.95520 −0.689804
\(134\) −8.17728 −0.706409
\(135\) −1.59426 −0.137212
\(136\) −2.31804 −0.198771
\(137\) 16.5841 1.41688 0.708438 0.705773i \(-0.249400\pi\)
0.708438 + 0.705773i \(0.249400\pi\)
\(138\) −7.53822 −0.641696
\(139\) −17.5563 −1.48910 −0.744551 0.667566i \(-0.767336\pi\)
−0.744551 + 0.667566i \(0.767336\pi\)
\(140\) 1.31350 0.111011
\(141\) 13.8292 1.16463
\(142\) −10.1180 −0.849088
\(143\) 7.46435 0.624200
\(144\) 0.768897 0.0640747
\(145\) 2.53510 0.210528
\(146\) −7.91677 −0.655196
\(147\) −11.1336 −0.918288
\(148\) −3.47882 −0.285957
\(149\) 13.8344 1.13336 0.566678 0.823939i \(-0.308228\pi\)
0.566678 + 0.823939i \(0.308228\pi\)
\(150\) 9.44381 0.771084
\(151\) 11.7706 0.957882 0.478941 0.877847i \(-0.341021\pi\)
0.478941 + 0.877847i \(0.341021\pi\)
\(152\) 2.22922 0.180813
\(153\) −1.78234 −0.144093
\(154\) 6.84834 0.551855
\(155\) −1.21808 −0.0978383
\(156\) 7.55113 0.604575
\(157\) −2.56113 −0.204400 −0.102200 0.994764i \(-0.532588\pi\)
−0.102200 + 0.994764i \(0.532588\pi\)
\(158\) 10.7209 0.852908
\(159\) −15.8757 −1.25903
\(160\) −0.368072 −0.0290986
\(161\) −13.8567 −1.09206
\(162\) −10.7155 −0.841888
\(163\) 3.03303 0.237565 0.118783 0.992920i \(-0.462101\pi\)
0.118783 + 0.992920i \(0.462101\pi\)
\(164\) −9.31768 −0.727589
\(165\) −1.37128 −0.106754
\(166\) −5.44583 −0.422678
\(167\) −7.10238 −0.549599 −0.274799 0.961502i \(-0.588611\pi\)
−0.274799 + 0.961502i \(0.588611\pi\)
\(168\) 6.92797 0.534504
\(169\) 2.12900 0.163769
\(170\) 0.853206 0.0654379
\(171\) 1.71404 0.131076
\(172\) −9.31761 −0.710461
\(173\) 21.0730 1.60215 0.801074 0.598565i \(-0.204262\pi\)
0.801074 + 0.598565i \(0.204262\pi\)
\(174\) 13.3712 1.01367
\(175\) 17.3596 1.31226
\(176\) −1.91905 −0.144654
\(177\) 11.0939 0.833870
\(178\) −3.11259 −0.233298
\(179\) −12.6317 −0.944141 −0.472070 0.881561i \(-0.656493\pi\)
−0.472070 + 0.881561i \(0.656493\pi\)
\(180\) −0.283009 −0.0210943
\(181\) 24.3889 1.81282 0.906408 0.422403i \(-0.138813\pi\)
0.906408 + 0.422403i \(0.138813\pi\)
\(182\) 13.8805 1.02889
\(183\) −4.16922 −0.308198
\(184\) 3.88295 0.286255
\(185\) 1.28045 0.0941409
\(186\) −6.42465 −0.471078
\(187\) 4.44845 0.325303
\(188\) −7.12346 −0.519532
\(189\) −15.4570 −1.12433
\(190\) −0.820512 −0.0595262
\(191\) −11.7067 −0.847068 −0.423534 0.905880i \(-0.639211\pi\)
−0.423534 + 0.905880i \(0.639211\pi\)
\(192\) −1.94136 −0.140106
\(193\) 21.1088 1.51944 0.759721 0.650249i \(-0.225335\pi\)
0.759721 + 0.650249i \(0.225335\pi\)
\(194\) 4.37204 0.313894
\(195\) −2.77936 −0.199034
\(196\) 5.73496 0.409640
\(197\) −0.835550 −0.0595304 −0.0297652 0.999557i \(-0.509476\pi\)
−0.0297652 + 0.999557i \(0.509476\pi\)
\(198\) −1.47555 −0.104863
\(199\) −19.2997 −1.36812 −0.684061 0.729425i \(-0.739788\pi\)
−0.684061 + 0.729425i \(0.739788\pi\)
\(200\) −4.86452 −0.343974
\(201\) 15.8751 1.11974
\(202\) 18.6342 1.31110
\(203\) 24.5788 1.72509
\(204\) 4.50017 0.315075
\(205\) 3.42958 0.239532
\(206\) 3.72595 0.259599
\(207\) 2.98559 0.207513
\(208\) −3.88960 −0.269695
\(209\) −4.27799 −0.295915
\(210\) −2.54999 −0.175966
\(211\) −18.5858 −1.27950 −0.639751 0.768582i \(-0.720962\pi\)
−0.639751 + 0.768582i \(0.720962\pi\)
\(212\) 8.17762 0.561641
\(213\) 19.6428 1.34590
\(214\) 2.10121 0.143636
\(215\) 3.42955 0.233893
\(216\) 4.33138 0.294713
\(217\) −11.8098 −0.801699
\(218\) −8.20290 −0.555570
\(219\) 15.3693 1.03856
\(220\) 0.706349 0.0476220
\(221\) 9.01626 0.606499
\(222\) 6.75365 0.453275
\(223\) 8.83295 0.591498 0.295749 0.955266i \(-0.404431\pi\)
0.295749 + 0.955266i \(0.404431\pi\)
\(224\) −3.56861 −0.238438
\(225\) −3.74032 −0.249354
\(226\) 11.9151 0.792583
\(227\) 3.08551 0.204792 0.102396 0.994744i \(-0.467349\pi\)
0.102396 + 0.994744i \(0.467349\pi\)
\(228\) −4.32773 −0.286611
\(229\) 17.5736 1.16130 0.580648 0.814154i \(-0.302799\pi\)
0.580648 + 0.814154i \(0.302799\pi\)
\(230\) −1.42920 −0.0942389
\(231\) −13.2951 −0.874756
\(232\) −6.88751 −0.452187
\(233\) −10.1255 −0.663340 −0.331670 0.943395i \(-0.607612\pi\)
−0.331670 + 0.943395i \(0.607612\pi\)
\(234\) −2.99070 −0.195508
\(235\) 2.62194 0.171037
\(236\) −5.71449 −0.371982
\(237\) −20.8132 −1.35196
\(238\) 8.27218 0.536206
\(239\) −1.16044 −0.0750628 −0.0375314 0.999295i \(-0.511949\pi\)
−0.0375314 + 0.999295i \(0.511949\pi\)
\(240\) 0.714562 0.0461247
\(241\) 5.78703 0.372775 0.186388 0.982476i \(-0.440322\pi\)
0.186388 + 0.982476i \(0.440322\pi\)
\(242\) −7.31724 −0.470370
\(243\) 7.80852 0.500917
\(244\) 2.14757 0.137484
\(245\) −2.11088 −0.134859
\(246\) 18.0890 1.15331
\(247\) −8.67077 −0.551708
\(248\) 3.30935 0.210144
\(249\) 10.5723 0.669995
\(250\) 3.63085 0.229635
\(251\) −13.1024 −0.827015 −0.413507 0.910501i \(-0.635696\pi\)
−0.413507 + 0.910501i \(0.635696\pi\)
\(252\) −2.74389 −0.172849
\(253\) −7.45158 −0.468477
\(254\) 17.7895 1.11621
\(255\) −1.65638 −0.103727
\(256\) 1.00000 0.0625000
\(257\) 8.17694 0.510063 0.255032 0.966933i \(-0.417914\pi\)
0.255032 + 0.966933i \(0.417914\pi\)
\(258\) 18.0889 1.12616
\(259\) 12.4145 0.771401
\(260\) 1.43165 0.0887873
\(261\) −5.29578 −0.327801
\(262\) 2.29304 0.141665
\(263\) 4.43350 0.273381 0.136691 0.990614i \(-0.456353\pi\)
0.136691 + 0.990614i \(0.456353\pi\)
\(264\) 3.72558 0.229294
\(265\) −3.00995 −0.184900
\(266\) −7.95520 −0.487765
\(267\) 6.04267 0.369805
\(268\) −8.17728 −0.499507
\(269\) 16.2099 0.988338 0.494169 0.869366i \(-0.335472\pi\)
0.494169 + 0.869366i \(0.335472\pi\)
\(270\) −1.59426 −0.0970236
\(271\) −8.15583 −0.495431 −0.247716 0.968833i \(-0.579680\pi\)
−0.247716 + 0.968833i \(0.579680\pi\)
\(272\) −2.31804 −0.140552
\(273\) −26.9470 −1.63091
\(274\) 16.5841 1.00188
\(275\) 9.33527 0.562938
\(276\) −7.53822 −0.453747
\(277\) −2.96226 −0.177985 −0.0889926 0.996032i \(-0.528365\pi\)
−0.0889926 + 0.996032i \(0.528365\pi\)
\(278\) −17.5563 −1.05295
\(279\) 2.54455 0.152338
\(280\) 1.31350 0.0784969
\(281\) −15.8704 −0.946747 −0.473374 0.880862i \(-0.656964\pi\)
−0.473374 + 0.880862i \(0.656964\pi\)
\(282\) 13.8292 0.823519
\(283\) 21.7775 1.29454 0.647268 0.762263i \(-0.275912\pi\)
0.647268 + 0.762263i \(0.275912\pi\)
\(284\) −10.1180 −0.600396
\(285\) 1.59291 0.0943561
\(286\) 7.46435 0.441376
\(287\) 33.2512 1.96275
\(288\) 0.768897 0.0453077
\(289\) −11.6267 −0.683922
\(290\) 2.53510 0.148866
\(291\) −8.48772 −0.497559
\(292\) −7.91677 −0.463294
\(293\) 26.2240 1.53203 0.766013 0.642826i \(-0.222238\pi\)
0.766013 + 0.642826i \(0.222238\pi\)
\(294\) −11.1336 −0.649328
\(295\) 2.10334 0.122461
\(296\) −3.47882 −0.202202
\(297\) −8.31215 −0.482320
\(298\) 13.8344 0.801403
\(299\) −15.1031 −0.873436
\(300\) 9.44381 0.545239
\(301\) 33.2509 1.91655
\(302\) 11.7706 0.677325
\(303\) −36.1758 −2.07825
\(304\) 2.22922 0.127854
\(305\) −0.790461 −0.0452616
\(306\) −1.78234 −0.101889
\(307\) 20.0487 1.14424 0.572121 0.820170i \(-0.306121\pi\)
0.572121 + 0.820170i \(0.306121\pi\)
\(308\) 6.84834 0.390221
\(309\) −7.23343 −0.411496
\(310\) −1.21808 −0.0691822
\(311\) −25.0170 −1.41858 −0.709291 0.704916i \(-0.750985\pi\)
−0.709291 + 0.704916i \(0.750985\pi\)
\(312\) 7.55113 0.427499
\(313\) 29.9847 1.69484 0.847418 0.530926i \(-0.178156\pi\)
0.847418 + 0.530926i \(0.178156\pi\)
\(314\) −2.56113 −0.144533
\(315\) 1.00995 0.0569042
\(316\) 10.7209 0.603097
\(317\) −20.8808 −1.17278 −0.586392 0.810027i \(-0.699452\pi\)
−0.586392 + 0.810027i \(0.699452\pi\)
\(318\) −15.8757 −0.890267
\(319\) 13.2175 0.740037
\(320\) −0.368072 −0.0205758
\(321\) −4.07922 −0.227680
\(322\) −13.8567 −0.772205
\(323\) −5.16742 −0.287523
\(324\) −10.7155 −0.595305
\(325\) 18.9211 1.04955
\(326\) 3.03303 0.167984
\(327\) 15.9248 0.880644
\(328\) −9.31768 −0.514483
\(329\) 25.4208 1.40150
\(330\) −1.37128 −0.0754865
\(331\) −5.96917 −0.328095 −0.164048 0.986452i \(-0.552455\pi\)
−0.164048 + 0.986452i \(0.552455\pi\)
\(332\) −5.44583 −0.298879
\(333\) −2.67485 −0.146581
\(334\) −7.10238 −0.388625
\(335\) 3.00983 0.164444
\(336\) 6.92797 0.377952
\(337\) −24.3089 −1.32419 −0.662096 0.749419i \(-0.730333\pi\)
−0.662096 + 0.749419i \(0.730333\pi\)
\(338\) 2.12900 0.115802
\(339\) −23.1316 −1.25634
\(340\) 0.853206 0.0462716
\(341\) −6.35081 −0.343916
\(342\) 1.71404 0.0926846
\(343\) 4.51443 0.243756
\(344\) −9.31761 −0.502372
\(345\) 2.77461 0.149380
\(346\) 21.0730 1.13289
\(347\) 9.89764 0.531333 0.265667 0.964065i \(-0.414408\pi\)
0.265667 + 0.964065i \(0.414408\pi\)
\(348\) 13.3712 0.716770
\(349\) −6.73425 −0.360476 −0.180238 0.983623i \(-0.557687\pi\)
−0.180238 + 0.983623i \(0.557687\pi\)
\(350\) 17.3596 0.927908
\(351\) −16.8474 −0.899246
\(352\) −1.91905 −0.102286
\(353\) −10.7229 −0.570723 −0.285361 0.958420i \(-0.592114\pi\)
−0.285361 + 0.958420i \(0.592114\pi\)
\(354\) 11.0939 0.589635
\(355\) 3.72417 0.197658
\(356\) −3.11259 −0.164967
\(357\) −16.0593 −0.849950
\(358\) −12.6317 −0.667608
\(359\) 11.2548 0.594006 0.297003 0.954877i \(-0.404013\pi\)
0.297003 + 0.954877i \(0.404013\pi\)
\(360\) −0.283009 −0.0149159
\(361\) −14.0306 −0.738452
\(362\) 24.3889 1.28185
\(363\) 14.2054 0.745592
\(364\) 13.8805 0.727534
\(365\) 2.91394 0.152522
\(366\) −4.16922 −0.217929
\(367\) 23.1135 1.20651 0.603256 0.797547i \(-0.293870\pi\)
0.603256 + 0.797547i \(0.293870\pi\)
\(368\) 3.88295 0.202413
\(369\) −7.16434 −0.372961
\(370\) 1.28045 0.0665676
\(371\) −29.1827 −1.51509
\(372\) −6.42465 −0.333103
\(373\) 0.504509 0.0261225 0.0130613 0.999915i \(-0.495842\pi\)
0.0130613 + 0.999915i \(0.495842\pi\)
\(374\) 4.44845 0.230024
\(375\) −7.04881 −0.363999
\(376\) −7.12346 −0.367364
\(377\) 26.7897 1.37974
\(378\) −15.4570 −0.795023
\(379\) 0.664947 0.0341560 0.0170780 0.999854i \(-0.494564\pi\)
0.0170780 + 0.999854i \(0.494564\pi\)
\(380\) −0.820512 −0.0420914
\(381\) −34.5359 −1.76933
\(382\) −11.7067 −0.598968
\(383\) −22.9062 −1.17045 −0.585227 0.810870i \(-0.698995\pi\)
−0.585227 + 0.810870i \(0.698995\pi\)
\(384\) −1.94136 −0.0990699
\(385\) −2.52068 −0.128466
\(386\) 21.1088 1.07441
\(387\) −7.16428 −0.364181
\(388\) 4.37204 0.221957
\(389\) −7.85157 −0.398090 −0.199045 0.979990i \(-0.563784\pi\)
−0.199045 + 0.979990i \(0.563784\pi\)
\(390\) −2.77936 −0.140738
\(391\) −9.00084 −0.455192
\(392\) 5.73496 0.289659
\(393\) −4.45163 −0.224555
\(394\) −0.835550 −0.0420944
\(395\) −3.94606 −0.198548
\(396\) −1.47555 −0.0741493
\(397\) −0.347756 −0.0174534 −0.00872668 0.999962i \(-0.502778\pi\)
−0.00872668 + 0.999962i \(0.502778\pi\)
\(398\) −19.2997 −0.967408
\(399\) 15.4440 0.773165
\(400\) −4.86452 −0.243226
\(401\) −9.74717 −0.486750 −0.243375 0.969932i \(-0.578255\pi\)
−0.243375 + 0.969932i \(0.578255\pi\)
\(402\) 15.8751 0.791777
\(403\) −12.8720 −0.641202
\(404\) 18.6342 0.927087
\(405\) 3.94407 0.195982
\(406\) 24.5788 1.21983
\(407\) 6.67603 0.330919
\(408\) 4.50017 0.222791
\(409\) 16.0797 0.795091 0.397545 0.917582i \(-0.369862\pi\)
0.397545 + 0.917582i \(0.369862\pi\)
\(410\) 3.42958 0.169375
\(411\) −32.1958 −1.58810
\(412\) 3.72595 0.183564
\(413\) 20.3928 1.00346
\(414\) 2.98559 0.146734
\(415\) 2.00446 0.0983949
\(416\) −3.88960 −0.190703
\(417\) 34.0831 1.66906
\(418\) −4.27799 −0.209243
\(419\) −25.0498 −1.22376 −0.611881 0.790949i \(-0.709587\pi\)
−0.611881 + 0.790949i \(0.709587\pi\)
\(420\) −2.54999 −0.124427
\(421\) 28.5639 1.39212 0.696061 0.717983i \(-0.254934\pi\)
0.696061 + 0.717983i \(0.254934\pi\)
\(422\) −18.5858 −0.904744
\(423\) −5.47721 −0.266311
\(424\) 8.17762 0.397140
\(425\) 11.2762 0.546975
\(426\) 19.6428 0.951698
\(427\) −7.66384 −0.370879
\(428\) 2.10121 0.101566
\(429\) −14.4910 −0.699633
\(430\) 3.42955 0.165388
\(431\) 35.7111 1.72014 0.860071 0.510174i \(-0.170419\pi\)
0.860071 + 0.510174i \(0.170419\pi\)
\(432\) 4.33138 0.208394
\(433\) −31.9940 −1.53753 −0.768767 0.639529i \(-0.779130\pi\)
−0.768767 + 0.639529i \(0.779130\pi\)
\(434\) −11.8098 −0.566887
\(435\) −4.92155 −0.235970
\(436\) −8.20290 −0.392848
\(437\) 8.65594 0.414070
\(438\) 15.3693 0.734375
\(439\) −17.7250 −0.845966 −0.422983 0.906138i \(-0.639017\pi\)
−0.422983 + 0.906138i \(0.639017\pi\)
\(440\) 0.706349 0.0336739
\(441\) 4.40959 0.209981
\(442\) 9.01626 0.428860
\(443\) 10.9315 0.519370 0.259685 0.965693i \(-0.416381\pi\)
0.259685 + 0.965693i \(0.416381\pi\)
\(444\) 6.75365 0.320514
\(445\) 1.14566 0.0543093
\(446\) 8.83295 0.418252
\(447\) −26.8576 −1.27032
\(448\) −3.56861 −0.168601
\(449\) 17.7727 0.838744 0.419372 0.907814i \(-0.362250\pi\)
0.419372 + 0.907814i \(0.362250\pi\)
\(450\) −3.74032 −0.176320
\(451\) 17.8811 0.841989
\(452\) 11.9151 0.560441
\(453\) −22.8511 −1.07364
\(454\) 3.08551 0.144810
\(455\) −5.10901 −0.239514
\(456\) −4.32773 −0.202664
\(457\) 21.9371 1.02618 0.513088 0.858336i \(-0.328502\pi\)
0.513088 + 0.858336i \(0.328502\pi\)
\(458\) 17.5736 0.821161
\(459\) −10.0403 −0.468643
\(460\) −1.42920 −0.0666370
\(461\) −31.8456 −1.48320 −0.741599 0.670843i \(-0.765932\pi\)
−0.741599 + 0.670843i \(0.765932\pi\)
\(462\) −13.2951 −0.618546
\(463\) −21.8179 −1.01397 −0.506983 0.861956i \(-0.669239\pi\)
−0.506983 + 0.861956i \(0.669239\pi\)
\(464\) −6.88751 −0.319745
\(465\) 2.36473 0.109662
\(466\) −10.1255 −0.469052
\(467\) 10.0246 0.463881 0.231941 0.972730i \(-0.425492\pi\)
0.231941 + 0.972730i \(0.425492\pi\)
\(468\) −2.99070 −0.138245
\(469\) 29.1815 1.34748
\(470\) 2.62194 0.120941
\(471\) 4.97208 0.229101
\(472\) −5.71449 −0.263031
\(473\) 17.8810 0.822168
\(474\) −20.8132 −0.955980
\(475\) −10.8441 −0.497561
\(476\) 8.27218 0.379155
\(477\) 6.28775 0.287896
\(478\) −1.16044 −0.0530774
\(479\) −7.55660 −0.345270 −0.172635 0.984986i \(-0.555228\pi\)
−0.172635 + 0.984986i \(0.555228\pi\)
\(480\) 0.714562 0.0326151
\(481\) 13.5312 0.616970
\(482\) 5.78703 0.263592
\(483\) 26.9009 1.22404
\(484\) −7.31724 −0.332602
\(485\) −1.60922 −0.0730711
\(486\) 7.80852 0.354201
\(487\) −11.7964 −0.534545 −0.267272 0.963621i \(-0.586122\pi\)
−0.267272 + 0.963621i \(0.586122\pi\)
\(488\) 2.14757 0.0972160
\(489\) −5.88821 −0.266274
\(490\) −2.11088 −0.0953597
\(491\) −40.3707 −1.82190 −0.910952 0.412513i \(-0.864651\pi\)
−0.910952 + 0.412513i \(0.864651\pi\)
\(492\) 18.0890 0.815516
\(493\) 15.9655 0.719052
\(494\) −8.67077 −0.390116
\(495\) 0.543109 0.0244110
\(496\) 3.30935 0.148594
\(497\) 36.1073 1.61964
\(498\) 10.5723 0.473758
\(499\) −18.8301 −0.842950 −0.421475 0.906840i \(-0.638487\pi\)
−0.421475 + 0.906840i \(0.638487\pi\)
\(500\) 3.63085 0.162377
\(501\) 13.7883 0.616016
\(502\) −13.1024 −0.584788
\(503\) 0.944486 0.0421125 0.0210563 0.999778i \(-0.493297\pi\)
0.0210563 + 0.999778i \(0.493297\pi\)
\(504\) −2.74389 −0.122223
\(505\) −6.85873 −0.305209
\(506\) −7.45158 −0.331263
\(507\) −4.13316 −0.183560
\(508\) 17.7895 0.789282
\(509\) −16.5720 −0.734542 −0.367271 0.930114i \(-0.619708\pi\)
−0.367271 + 0.930114i \(0.619708\pi\)
\(510\) −1.65638 −0.0733459
\(511\) 28.2518 1.24979
\(512\) 1.00000 0.0441942
\(513\) 9.65560 0.426305
\(514\) 8.17694 0.360669
\(515\) −1.37142 −0.0604319
\(516\) 18.0889 0.796318
\(517\) 13.6703 0.601219
\(518\) 12.4145 0.545463
\(519\) −40.9103 −1.79576
\(520\) 1.43165 0.0627821
\(521\) 38.4143 1.68296 0.841480 0.540289i \(-0.181685\pi\)
0.841480 + 0.540289i \(0.181685\pi\)
\(522\) −5.29578 −0.231790
\(523\) 9.89196 0.432545 0.216273 0.976333i \(-0.430610\pi\)
0.216273 + 0.976333i \(0.430610\pi\)
\(524\) 2.29304 0.100172
\(525\) −33.7013 −1.47084
\(526\) 4.43350 0.193310
\(527\) −7.67121 −0.334163
\(528\) 3.72558 0.162135
\(529\) −7.92271 −0.344466
\(530\) −3.00995 −0.130744
\(531\) −4.39386 −0.190677
\(532\) −7.95520 −0.344902
\(533\) 36.2421 1.56982
\(534\) 6.04267 0.261492
\(535\) −0.773396 −0.0334368
\(536\) −8.17728 −0.353205
\(537\) 24.5228 1.05824
\(538\) 16.2099 0.698860
\(539\) −11.0057 −0.474049
\(540\) −1.59426 −0.0686060
\(541\) 20.9733 0.901714 0.450857 0.892596i \(-0.351118\pi\)
0.450857 + 0.892596i \(0.351118\pi\)
\(542\) −8.15583 −0.350323
\(543\) −47.3478 −2.03189
\(544\) −2.31804 −0.0993853
\(545\) 3.01925 0.129331
\(546\) −26.9470 −1.15323
\(547\) −1.97621 −0.0844968 −0.0422484 0.999107i \(-0.513452\pi\)
−0.0422484 + 0.999107i \(0.513452\pi\)
\(548\) 16.5841 0.708438
\(549\) 1.65126 0.0704741
\(550\) 9.33527 0.398057
\(551\) −15.3538 −0.654092
\(552\) −7.53822 −0.320848
\(553\) −38.2586 −1.62692
\(554\) −2.96226 −0.125855
\(555\) −2.48583 −0.105518
\(556\) −17.5563 −0.744551
\(557\) −19.3740 −0.820904 −0.410452 0.911882i \(-0.634629\pi\)
−0.410452 + 0.911882i \(0.634629\pi\)
\(558\) 2.54455 0.107719
\(559\) 36.2418 1.53286
\(560\) 1.31350 0.0555057
\(561\) −8.63606 −0.364615
\(562\) −15.8704 −0.669451
\(563\) −11.2287 −0.473234 −0.236617 0.971603i \(-0.576039\pi\)
−0.236617 + 0.971603i \(0.576039\pi\)
\(564\) 13.8292 0.582316
\(565\) −4.38563 −0.184505
\(566\) 21.7775 0.915375
\(567\) 38.2394 1.60590
\(568\) −10.1180 −0.424544
\(569\) 32.8491 1.37710 0.688552 0.725187i \(-0.258247\pi\)
0.688552 + 0.725187i \(0.258247\pi\)
\(570\) 1.59291 0.0667198
\(571\) −3.99094 −0.167016 −0.0835078 0.996507i \(-0.526612\pi\)
−0.0835078 + 0.996507i \(0.526612\pi\)
\(572\) 7.46435 0.312100
\(573\) 22.7270 0.949434
\(574\) 33.2512 1.38788
\(575\) −18.8887 −0.787713
\(576\) 0.768897 0.0320374
\(577\) 28.4674 1.18511 0.592557 0.805529i \(-0.298118\pi\)
0.592557 + 0.805529i \(0.298118\pi\)
\(578\) −11.6267 −0.483606
\(579\) −40.9798 −1.70306
\(580\) 2.53510 0.105264
\(581\) 19.4340 0.806259
\(582\) −8.48772 −0.351827
\(583\) −15.6933 −0.649949
\(584\) −7.91677 −0.327598
\(585\) 1.10079 0.0455122
\(586\) 26.2240 1.08331
\(587\) 6.07953 0.250929 0.125464 0.992098i \(-0.459958\pi\)
0.125464 + 0.992098i \(0.459958\pi\)
\(588\) −11.1336 −0.459144
\(589\) 7.37726 0.303975
\(590\) 2.10334 0.0865933
\(591\) 1.62211 0.0667245
\(592\) −3.47882 −0.142978
\(593\) −23.6754 −0.972231 −0.486116 0.873894i \(-0.661587\pi\)
−0.486116 + 0.873894i \(0.661587\pi\)
\(594\) −8.31215 −0.341052
\(595\) −3.04476 −0.124823
\(596\) 13.8344 0.566678
\(597\) 37.4678 1.53346
\(598\) −15.1031 −0.617613
\(599\) −18.2448 −0.745462 −0.372731 0.927939i \(-0.621579\pi\)
−0.372731 + 0.927939i \(0.621579\pi\)
\(600\) 9.44381 0.385542
\(601\) 29.9960 1.22356 0.611781 0.791027i \(-0.290453\pi\)
0.611781 + 0.791027i \(0.290453\pi\)
\(602\) 33.2509 1.35521
\(603\) −6.28748 −0.256046
\(604\) 11.7706 0.478941
\(605\) 2.69327 0.109497
\(606\) −36.1758 −1.46954
\(607\) −35.7697 −1.45185 −0.725923 0.687776i \(-0.758587\pi\)
−0.725923 + 0.687776i \(0.758587\pi\)
\(608\) 2.22922 0.0904067
\(609\) −47.7164 −1.93357
\(610\) −0.790461 −0.0320048
\(611\) 27.7074 1.12092
\(612\) −1.78234 −0.0720467
\(613\) 4.85430 0.196063 0.0980317 0.995183i \(-0.468745\pi\)
0.0980317 + 0.995183i \(0.468745\pi\)
\(614\) 20.0487 0.809101
\(615\) −6.65806 −0.268479
\(616\) 6.84834 0.275928
\(617\) 2.80918 0.113093 0.0565467 0.998400i \(-0.481991\pi\)
0.0565467 + 0.998400i \(0.481991\pi\)
\(618\) −7.23343 −0.290971
\(619\) −12.8612 −0.516937 −0.258468 0.966020i \(-0.583218\pi\)
−0.258468 + 0.966020i \(0.583218\pi\)
\(620\) −1.21808 −0.0489192
\(621\) 16.8185 0.674905
\(622\) −25.0170 −1.00309
\(623\) 11.1076 0.445017
\(624\) 7.55113 0.302287
\(625\) 22.9862 0.919448
\(626\) 29.9847 1.19843
\(627\) 8.30513 0.331675
\(628\) −2.56113 −0.102200
\(629\) 8.06405 0.321535
\(630\) 1.00995 0.0402373
\(631\) −9.72097 −0.386986 −0.193493 0.981102i \(-0.561982\pi\)
−0.193493 + 0.981102i \(0.561982\pi\)
\(632\) 10.7209 0.426454
\(633\) 36.0819 1.43413
\(634\) −20.8808 −0.829283
\(635\) −6.54782 −0.259842
\(636\) −15.8757 −0.629514
\(637\) −22.3067 −0.883824
\(638\) 13.2175 0.523285
\(639\) −7.77973 −0.307762
\(640\) −0.368072 −0.0145493
\(641\) 34.6409 1.36823 0.684116 0.729373i \(-0.260188\pi\)
0.684116 + 0.729373i \(0.260188\pi\)
\(642\) −4.07922 −0.160994
\(643\) 23.1065 0.911230 0.455615 0.890177i \(-0.349419\pi\)
0.455615 + 0.890177i \(0.349419\pi\)
\(644\) −13.8567 −0.546031
\(645\) −6.65800 −0.262159
\(646\) −5.16742 −0.203310
\(647\) 40.9944 1.61166 0.805828 0.592150i \(-0.201721\pi\)
0.805828 + 0.592150i \(0.201721\pi\)
\(648\) −10.7155 −0.420944
\(649\) 10.9664 0.430469
\(650\) 18.9211 0.742145
\(651\) 22.9271 0.898582
\(652\) 3.03303 0.118783
\(653\) 1.79881 0.0703928 0.0351964 0.999380i \(-0.488794\pi\)
0.0351964 + 0.999380i \(0.488794\pi\)
\(654\) 15.9248 0.622710
\(655\) −0.844004 −0.0329780
\(656\) −9.31768 −0.363794
\(657\) −6.08718 −0.237483
\(658\) 25.4208 0.991007
\(659\) 15.7513 0.613584 0.306792 0.951777i \(-0.400744\pi\)
0.306792 + 0.951777i \(0.400744\pi\)
\(660\) −1.37128 −0.0533770
\(661\) 24.2869 0.944651 0.472326 0.881424i \(-0.343415\pi\)
0.472326 + 0.881424i \(0.343415\pi\)
\(662\) −5.96917 −0.231998
\(663\) −17.5039 −0.679793
\(664\) −5.44583 −0.211339
\(665\) 2.92809 0.113546
\(666\) −2.67485 −0.103648
\(667\) −26.7438 −1.03553
\(668\) −7.10238 −0.274799
\(669\) −17.1480 −0.662979
\(670\) 3.00983 0.116280
\(671\) −4.12130 −0.159101
\(672\) 6.92797 0.267252
\(673\) 34.8560 1.34360 0.671799 0.740733i \(-0.265522\pi\)
0.671799 + 0.740733i \(0.265522\pi\)
\(674\) −24.3089 −0.936346
\(675\) −21.0701 −0.810989
\(676\) 2.12900 0.0818846
\(677\) 10.3717 0.398619 0.199309 0.979937i \(-0.436130\pi\)
0.199309 + 0.979937i \(0.436130\pi\)
\(678\) −23.1316 −0.888365
\(679\) −15.6021 −0.598753
\(680\) 0.853206 0.0327190
\(681\) −5.99009 −0.229541
\(682\) −6.35081 −0.243185
\(683\) −35.2014 −1.34694 −0.673472 0.739213i \(-0.735198\pi\)
−0.673472 + 0.739213i \(0.735198\pi\)
\(684\) 1.71404 0.0655379
\(685\) −6.10414 −0.233227
\(686\) 4.51443 0.172362
\(687\) −34.1168 −1.30164
\(688\) −9.31761 −0.355230
\(689\) −31.8077 −1.21178
\(690\) 2.77461 0.105627
\(691\) 41.0402 1.56124 0.780622 0.625003i \(-0.214902\pi\)
0.780622 + 0.625003i \(0.214902\pi\)
\(692\) 21.0730 0.801074
\(693\) 5.26567 0.200026
\(694\) 9.89764 0.375709
\(695\) 6.46196 0.245116
\(696\) 13.3712 0.506833
\(697\) 21.5988 0.818113
\(698\) −6.73425 −0.254895
\(699\) 19.6572 0.743503
\(700\) 17.3596 0.656130
\(701\) 6.41561 0.242314 0.121157 0.992633i \(-0.461339\pi\)
0.121157 + 0.992633i \(0.461339\pi\)
\(702\) −16.8474 −0.635863
\(703\) −7.75504 −0.292487
\(704\) −1.91905 −0.0723270
\(705\) −5.09015 −0.191706
\(706\) −10.7229 −0.403562
\(707\) −66.4982 −2.50092
\(708\) 11.0939 0.416935
\(709\) 23.0074 0.864062 0.432031 0.901859i \(-0.357797\pi\)
0.432031 + 0.901859i \(0.357797\pi\)
\(710\) 3.72417 0.139766
\(711\) 8.24326 0.309146
\(712\) −3.11259 −0.116649
\(713\) 12.8500 0.481237
\(714\) −16.0593 −0.601005
\(715\) −2.74742 −0.102748
\(716\) −12.6317 −0.472070
\(717\) 2.25284 0.0841340
\(718\) 11.2548 0.420026
\(719\) 38.7884 1.44656 0.723282 0.690553i \(-0.242633\pi\)
0.723282 + 0.690553i \(0.242633\pi\)
\(720\) −0.283009 −0.0105471
\(721\) −13.2965 −0.495186
\(722\) −14.0306 −0.522164
\(723\) −11.2347 −0.417824
\(724\) 24.3889 0.906408
\(725\) 33.5044 1.24432
\(726\) 14.2054 0.527213
\(727\) 2.79495 0.103659 0.0518295 0.998656i \(-0.483495\pi\)
0.0518295 + 0.998656i \(0.483495\pi\)
\(728\) 13.8805 0.514444
\(729\) 16.9873 0.629159
\(730\) 2.91394 0.107850
\(731\) 21.5986 0.798854
\(732\) −4.16922 −0.154099
\(733\) −42.3818 −1.56541 −0.782704 0.622394i \(-0.786160\pi\)
−0.782704 + 0.622394i \(0.786160\pi\)
\(734\) 23.1135 0.853133
\(735\) 4.09798 0.151156
\(736\) 3.88295 0.143127
\(737\) 15.6926 0.578045
\(738\) −7.16434 −0.263723
\(739\) 0.853744 0.0314055 0.0157027 0.999877i \(-0.495001\pi\)
0.0157027 + 0.999877i \(0.495001\pi\)
\(740\) 1.28045 0.0470704
\(741\) 16.8331 0.618380
\(742\) −29.1827 −1.07133
\(743\) −1.78970 −0.0656577 −0.0328288 0.999461i \(-0.510452\pi\)
−0.0328288 + 0.999461i \(0.510452\pi\)
\(744\) −6.42465 −0.235539
\(745\) −5.09204 −0.186558
\(746\) 0.504509 0.0184714
\(747\) −4.18728 −0.153205
\(748\) 4.44845 0.162651
\(749\) −7.49840 −0.273985
\(750\) −7.04881 −0.257386
\(751\) −33.0545 −1.20617 −0.603087 0.797675i \(-0.706063\pi\)
−0.603087 + 0.797675i \(0.706063\pi\)
\(752\) −7.12346 −0.259766
\(753\) 25.4365 0.926957
\(754\) 26.7897 0.975622
\(755\) −4.33244 −0.157674
\(756\) −15.4570 −0.562166
\(757\) −10.6843 −0.388327 −0.194164 0.980969i \(-0.562199\pi\)
−0.194164 + 0.980969i \(0.562199\pi\)
\(758\) 0.664947 0.0241520
\(759\) 14.4662 0.525091
\(760\) −0.820512 −0.0297631
\(761\) −35.5396 −1.28831 −0.644154 0.764896i \(-0.722791\pi\)
−0.644154 + 0.764896i \(0.722791\pi\)
\(762\) −34.5359 −1.25111
\(763\) 29.2729 1.05975
\(764\) −11.7067 −0.423534
\(765\) 0.656027 0.0237187
\(766\) −22.9062 −0.827636
\(767\) 22.2271 0.802574
\(768\) −1.94136 −0.0700530
\(769\) 17.0629 0.615303 0.307651 0.951499i \(-0.400457\pi\)
0.307651 + 0.951499i \(0.400457\pi\)
\(770\) −2.52068 −0.0908391
\(771\) −15.8744 −0.571703
\(772\) 21.1088 0.759721
\(773\) −31.2002 −1.12219 −0.561097 0.827750i \(-0.689621\pi\)
−0.561097 + 0.827750i \(0.689621\pi\)
\(774\) −7.16428 −0.257515
\(775\) −16.0984 −0.578272
\(776\) 4.37204 0.156947
\(777\) −24.1011 −0.864623
\(778\) −7.85157 −0.281492
\(779\) −20.7712 −0.744204
\(780\) −2.77936 −0.0995170
\(781\) 19.4171 0.694797
\(782\) −9.00084 −0.321869
\(783\) −29.8324 −1.06612
\(784\) 5.73496 0.204820
\(785\) 0.942678 0.0336456
\(786\) −4.45163 −0.158784
\(787\) 23.6894 0.844436 0.422218 0.906494i \(-0.361252\pi\)
0.422218 + 0.906494i \(0.361252\pi\)
\(788\) −0.835550 −0.0297652
\(789\) −8.60703 −0.306418
\(790\) −3.94606 −0.140394
\(791\) −42.5205 −1.51185
\(792\) −1.47555 −0.0524315
\(793\) −8.35320 −0.296631
\(794\) −0.347756 −0.0123414
\(795\) 5.84341 0.207244
\(796\) −19.2997 −0.684061
\(797\) −20.3125 −0.719506 −0.359753 0.933048i \(-0.617139\pi\)
−0.359753 + 0.933048i \(0.617139\pi\)
\(798\) 15.4440 0.546710
\(799\) 16.5125 0.584170
\(800\) −4.86452 −0.171987
\(801\) −2.39326 −0.0845617
\(802\) −9.74717 −0.344185
\(803\) 15.1927 0.536138
\(804\) 15.8751 0.559871
\(805\) 5.10027 0.179761
\(806\) −12.8720 −0.453398
\(807\) −31.4694 −1.10778
\(808\) 18.6342 0.655549
\(809\) 27.5303 0.967912 0.483956 0.875092i \(-0.339199\pi\)
0.483956 + 0.875092i \(0.339199\pi\)
\(810\) 3.94407 0.138580
\(811\) −36.7980 −1.29215 −0.646076 0.763273i \(-0.723591\pi\)
−0.646076 + 0.763273i \(0.723591\pi\)
\(812\) 24.5788 0.862547
\(813\) 15.8334 0.555303
\(814\) 6.67603 0.233995
\(815\) −1.11637 −0.0391048
\(816\) 4.50017 0.157537
\(817\) −20.7710 −0.726685
\(818\) 16.0797 0.562214
\(819\) 10.6726 0.372932
\(820\) 3.42958 0.119766
\(821\) −36.7610 −1.28297 −0.641483 0.767137i \(-0.721681\pi\)
−0.641483 + 0.767137i \(0.721681\pi\)
\(822\) −32.1958 −1.12296
\(823\) −42.2714 −1.47349 −0.736744 0.676172i \(-0.763638\pi\)
−0.736744 + 0.676172i \(0.763638\pi\)
\(824\) 3.72595 0.129800
\(825\) −18.1232 −0.630968
\(826\) 20.3928 0.709556
\(827\) −10.7708 −0.374536 −0.187268 0.982309i \(-0.559963\pi\)
−0.187268 + 0.982309i \(0.559963\pi\)
\(828\) 2.98559 0.103756
\(829\) −39.5879 −1.37494 −0.687472 0.726211i \(-0.741279\pi\)
−0.687472 + 0.726211i \(0.741279\pi\)
\(830\) 2.00446 0.0695757
\(831\) 5.75084 0.199494
\(832\) −3.88960 −0.134848
\(833\) −13.2939 −0.460606
\(834\) 34.0831 1.18020
\(835\) 2.61418 0.0904676
\(836\) −4.27799 −0.147957
\(837\) 14.3341 0.495458
\(838\) −25.0498 −0.865331
\(839\) 27.4820 0.948784 0.474392 0.880314i \(-0.342668\pi\)
0.474392 + 0.880314i \(0.342668\pi\)
\(840\) −2.54999 −0.0879830
\(841\) 18.4378 0.635785
\(842\) 28.5639 0.984379
\(843\) 30.8102 1.06116
\(844\) −18.5858 −0.639751
\(845\) −0.783625 −0.0269575
\(846\) −5.47721 −0.188310
\(847\) 26.1124 0.897231
\(848\) 8.17762 0.280821
\(849\) −42.2780 −1.45098
\(850\) 11.2762 0.386770
\(851\) −13.5081 −0.463051
\(852\) 19.6428 0.672952
\(853\) 9.70272 0.332215 0.166107 0.986108i \(-0.446880\pi\)
0.166107 + 0.986108i \(0.446880\pi\)
\(854\) −7.66384 −0.262251
\(855\) −0.630889 −0.0215760
\(856\) 2.10121 0.0718179
\(857\) 14.3097 0.488809 0.244405 0.969673i \(-0.421407\pi\)
0.244405 + 0.969673i \(0.421407\pi\)
\(858\) −14.4910 −0.494715
\(859\) −20.8000 −0.709685 −0.354843 0.934926i \(-0.615466\pi\)
−0.354843 + 0.934926i \(0.615466\pi\)
\(860\) 3.42955 0.116947
\(861\) −64.5526 −2.19995
\(862\) 35.7111 1.21632
\(863\) 13.1248 0.446774 0.223387 0.974730i \(-0.428289\pi\)
0.223387 + 0.974730i \(0.428289\pi\)
\(864\) 4.33138 0.147357
\(865\) −7.75637 −0.263724
\(866\) −31.9940 −1.08720
\(867\) 22.5716 0.766572
\(868\) −11.8098 −0.400849
\(869\) −20.5739 −0.697923
\(870\) −4.92155 −0.166856
\(871\) 31.8064 1.07772
\(872\) −8.20290 −0.277785
\(873\) 3.36165 0.113774
\(874\) 8.65594 0.292791
\(875\) −12.9571 −0.438029
\(876\) 15.3693 0.519282
\(877\) 38.4578 1.29863 0.649314 0.760520i \(-0.275056\pi\)
0.649314 + 0.760520i \(0.275056\pi\)
\(878\) −17.7250 −0.598188
\(879\) −50.9104 −1.71717
\(880\) 0.706349 0.0238110
\(881\) −58.5360 −1.97213 −0.986064 0.166368i \(-0.946796\pi\)
−0.986064 + 0.166368i \(0.946796\pi\)
\(882\) 4.40959 0.148479
\(883\) 0.460368 0.0154926 0.00774631 0.999970i \(-0.497534\pi\)
0.00774631 + 0.999970i \(0.497534\pi\)
\(884\) 9.01626 0.303250
\(885\) −4.08336 −0.137261
\(886\) 10.9315 0.367250
\(887\) −36.3069 −1.21907 −0.609533 0.792761i \(-0.708643\pi\)
−0.609533 + 0.792761i \(0.708643\pi\)
\(888\) 6.75365 0.226638
\(889\) −63.4838 −2.12918
\(890\) 1.14566 0.0384025
\(891\) 20.5636 0.688906
\(892\) 8.83295 0.295749
\(893\) −15.8797 −0.531395
\(894\) −26.8576 −0.898251
\(895\) 4.64939 0.155412
\(896\) −3.56861 −0.119219
\(897\) 29.3207 0.978989
\(898\) 17.7727 0.593082
\(899\) −22.7932 −0.760194
\(900\) −3.74032 −0.124677
\(901\) −18.9561 −0.631518
\(902\) 17.8811 0.595376
\(903\) −64.5521 −2.14816
\(904\) 11.9151 0.396292
\(905\) −8.97688 −0.298402
\(906\) −22.8511 −0.759178
\(907\) −14.0232 −0.465634 −0.232817 0.972521i \(-0.574794\pi\)
−0.232817 + 0.972521i \(0.574794\pi\)
\(908\) 3.08551 0.102396
\(909\) 14.3278 0.475223
\(910\) −5.10901 −0.169362
\(911\) −39.7705 −1.31765 −0.658827 0.752294i \(-0.728947\pi\)
−0.658827 + 0.752294i \(0.728947\pi\)
\(912\) −4.32773 −0.143305
\(913\) 10.4508 0.345872
\(914\) 21.9371 0.725615
\(915\) 1.53457 0.0507314
\(916\) 17.5736 0.580648
\(917\) −8.18296 −0.270225
\(918\) −10.0403 −0.331380
\(919\) −48.0695 −1.58567 −0.792833 0.609439i \(-0.791395\pi\)
−0.792833 + 0.609439i \(0.791395\pi\)
\(920\) −1.42920 −0.0471194
\(921\) −38.9219 −1.28252
\(922\) −31.8456 −1.04878
\(923\) 39.3552 1.29539
\(924\) −13.2951 −0.437378
\(925\) 16.9228 0.556418
\(926\) −21.8179 −0.716982
\(927\) 2.86487 0.0940948
\(928\) −6.88751 −0.226094
\(929\) −39.0133 −1.27998 −0.639992 0.768382i \(-0.721062\pi\)
−0.639992 + 0.768382i \(0.721062\pi\)
\(930\) 2.36473 0.0775426
\(931\) 12.7845 0.418994
\(932\) −10.1255 −0.331670
\(933\) 48.5670 1.59001
\(934\) 10.0246 0.328014
\(935\) −1.63735 −0.0535470
\(936\) −2.99070 −0.0977542
\(937\) −5.51911 −0.180301 −0.0901507 0.995928i \(-0.528735\pi\)
−0.0901507 + 0.995928i \(0.528735\pi\)
\(938\) 29.1815 0.952810
\(939\) −58.2113 −1.89965
\(940\) 2.62194 0.0855184
\(941\) −22.1329 −0.721512 −0.360756 0.932660i \(-0.617481\pi\)
−0.360756 + 0.932660i \(0.617481\pi\)
\(942\) 4.97208 0.161999
\(943\) −36.1801 −1.17819
\(944\) −5.71449 −0.185991
\(945\) 5.68929 0.185073
\(946\) 17.8810 0.581361
\(947\) −3.45336 −0.112219 −0.0561095 0.998425i \(-0.517870\pi\)
−0.0561095 + 0.998425i \(0.517870\pi\)
\(948\) −20.8132 −0.675980
\(949\) 30.7931 0.999585
\(950\) −10.8441 −0.351829
\(951\) 40.5373 1.31451
\(952\) 8.27218 0.268103
\(953\) −49.4303 −1.60120 −0.800602 0.599197i \(-0.795487\pi\)
−0.800602 + 0.599197i \(0.795487\pi\)
\(954\) 6.28775 0.203573
\(955\) 4.30891 0.139433
\(956\) −1.16044 −0.0375314
\(957\) −25.6600 −0.829469
\(958\) −7.55660 −0.244143
\(959\) −59.1822 −1.91109
\(960\) 0.714562 0.0230624
\(961\) −20.0482 −0.646717
\(962\) 13.5312 0.436264
\(963\) 1.61561 0.0520624
\(964\) 5.78703 0.186388
\(965\) −7.76954 −0.250110
\(966\) 26.9009 0.865524
\(967\) −24.6541 −0.792824 −0.396412 0.918073i \(-0.629745\pi\)
−0.396412 + 0.918073i \(0.629745\pi\)
\(968\) −7.31724 −0.235185
\(969\) 10.0319 0.322270
\(970\) −1.60922 −0.0516690
\(971\) 13.1696 0.422632 0.211316 0.977418i \(-0.432225\pi\)
0.211316 + 0.977418i \(0.432225\pi\)
\(972\) 7.80852 0.250458
\(973\) 62.6514 2.00851
\(974\) −11.7964 −0.377980
\(975\) −36.7327 −1.17639
\(976\) 2.14757 0.0687421
\(977\) 29.3879 0.940202 0.470101 0.882613i \(-0.344218\pi\)
0.470101 + 0.882613i \(0.344218\pi\)
\(978\) −5.88821 −0.188284
\(979\) 5.97322 0.190905
\(980\) −2.11088 −0.0674295
\(981\) −6.30718 −0.201373
\(982\) −40.3707 −1.28828
\(983\) 36.5176 1.16473 0.582366 0.812927i \(-0.302127\pi\)
0.582366 + 0.812927i \(0.302127\pi\)
\(984\) 18.0890 0.576657
\(985\) 0.307542 0.00979911
\(986\) 15.9655 0.508446
\(987\) −49.3511 −1.57086
\(988\) −8.67077 −0.275854
\(989\) −36.1798 −1.15045
\(990\) 0.543109 0.0172612
\(991\) −50.2638 −1.59668 −0.798342 0.602205i \(-0.794289\pi\)
−0.798342 + 0.602205i \(0.794289\pi\)
\(992\) 3.30935 0.105072
\(993\) 11.5883 0.367745
\(994\) 36.1073 1.14526
\(995\) 7.10368 0.225202
\(996\) 10.5723 0.334997
\(997\) −32.6714 −1.03472 −0.517358 0.855769i \(-0.673084\pi\)
−0.517358 + 0.855769i \(0.673084\pi\)
\(998\) −18.8301 −0.596055
\(999\) −15.0681 −0.476733
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 8002.2.a.g.1.19 95
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8002.2.a.g.1.19 95 1.1 even 1 trivial