Properties

Label 8033.2.a.b.1.9
Level $8033$
Weight $2$
Character 8033.1
Self dual yes
Analytic conductor $64.144$
Analytic rank $1$
Dimension $153$
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] = [8033,2,Mod(1,8033)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8033, 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("8033.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8033 = 29 \cdot 277 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8033.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: \(64.1438279437\)
Analytic rank: \(1\)
Dimension: \(153\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) \(=\) 8033.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.59547 q^{2} +1.19515 q^{3} +4.73648 q^{4} -3.51521 q^{5} -3.10198 q^{6} +1.20876 q^{7} -7.10244 q^{8} -1.57161 q^{9} +O(q^{10})\) \(q-2.59547 q^{2} +1.19515 q^{3} +4.73648 q^{4} -3.51521 q^{5} -3.10198 q^{6} +1.20876 q^{7} -7.10244 q^{8} -1.57161 q^{9} +9.12363 q^{10} +4.18691 q^{11} +5.66080 q^{12} -4.74438 q^{13} -3.13731 q^{14} -4.20121 q^{15} +8.96125 q^{16} +1.27570 q^{17} +4.07908 q^{18} +3.12310 q^{19} -16.6497 q^{20} +1.44465 q^{21} -10.8670 q^{22} +6.80267 q^{23} -8.48849 q^{24} +7.35671 q^{25} +12.3139 q^{26} -5.46377 q^{27} +5.72527 q^{28} -1.00000 q^{29} +10.9041 q^{30} -3.50259 q^{31} -9.05377 q^{32} +5.00399 q^{33} -3.31104 q^{34} -4.24906 q^{35} -7.44391 q^{36} -8.65626 q^{37} -8.10592 q^{38} -5.67025 q^{39} +24.9666 q^{40} +10.0102 q^{41} -3.74956 q^{42} -4.89375 q^{43} +19.8312 q^{44} +5.52456 q^{45} -17.6561 q^{46} -2.81653 q^{47} +10.7100 q^{48} -5.53889 q^{49} -19.0941 q^{50} +1.52465 q^{51} -22.4717 q^{52} +2.58742 q^{53} +14.1811 q^{54} -14.7179 q^{55} -8.58517 q^{56} +3.73258 q^{57} +2.59547 q^{58} -5.11804 q^{59} -19.8989 q^{60} +12.2315 q^{61} +9.09087 q^{62} -1.89971 q^{63} +5.57633 q^{64} +16.6775 q^{65} -12.9877 q^{66} -6.35287 q^{67} +6.04232 q^{68} +8.13022 q^{69} +11.0283 q^{70} +1.20473 q^{71} +11.1623 q^{72} -11.6941 q^{73} +22.4671 q^{74} +8.79238 q^{75} +14.7925 q^{76} +5.06098 q^{77} +14.7170 q^{78} +4.93390 q^{79} -31.5007 q^{80} -1.81519 q^{81} -25.9813 q^{82} -2.91087 q^{83} +6.84257 q^{84} -4.48435 q^{85} +12.7016 q^{86} -1.19515 q^{87} -29.7373 q^{88} +5.38970 q^{89} -14.3388 q^{90} -5.73483 q^{91} +32.2207 q^{92} -4.18612 q^{93} +7.31023 q^{94} -10.9784 q^{95} -10.8206 q^{96} +19.1506 q^{97} +14.3760 q^{98} -6.58021 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9} - 30 q^{10} + 4 q^{11} - 39 q^{12} - 65 q^{13} + q^{14} - 26 q^{15} + 107 q^{16} - 20 q^{17} - 21 q^{18} - 65 q^{19} - 23 q^{20} - 24 q^{21} - 59 q^{22} - 62 q^{23} - 59 q^{24} + 102 q^{25} - 18 q^{26} - 57 q^{27} - 155 q^{28} - 153 q^{29} - 82 q^{30} - 49 q^{31} - 17 q^{32} - 59 q^{33} - 68 q^{34} - 36 q^{35} + 74 q^{36} - 30 q^{37} - 67 q^{38} - 47 q^{39} - 108 q^{40} - 9 q^{41} - 62 q^{42} - 90 q^{43} - 14 q^{44} - 56 q^{45} - 52 q^{46} - 54 q^{47} - 76 q^{48} + 101 q^{49} - 36 q^{50} - 60 q^{51} - 191 q^{52} - 38 q^{53} - 82 q^{54} - 215 q^{55} + 24 q^{56} - 52 q^{57} + 3 q^{58} - 55 q^{59} - 60 q^{60} - 90 q^{61} - 66 q^{62} - 229 q^{63} + 52 q^{64} - 67 q^{65} - 29 q^{66} - 114 q^{67} - 78 q^{68} - 68 q^{69} - 61 q^{70} - 52 q^{71} - 47 q^{72} - 83 q^{73} - 21 q^{74} - 47 q^{75} - 100 q^{76} - 32 q^{77} - 17 q^{78} - 151 q^{79} - 24 q^{80} + 81 q^{81} - 151 q^{82} - 94 q^{83} - 84 q^{84} - 77 q^{85} - 43 q^{86} + 12 q^{87} - 121 q^{88} + 11 q^{89} - 14 q^{90} - 66 q^{91} - 156 q^{92} - 66 q^{93} - 22 q^{94} - 67 q^{95} - 131 q^{96} - 78 q^{97} - 67 q^{98} - 41 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.59547 −1.83528 −0.917638 0.397417i \(-0.869907\pi\)
−0.917638 + 0.397417i \(0.869907\pi\)
\(3\) 1.19515 0.690021 0.345010 0.938599i \(-0.387875\pi\)
0.345010 + 0.938599i \(0.387875\pi\)
\(4\) 4.73648 2.36824
\(5\) −3.51521 −1.57205 −0.786025 0.618195i \(-0.787864\pi\)
−0.786025 + 0.618195i \(0.787864\pi\)
\(6\) −3.10198 −1.26638
\(7\) 1.20876 0.456869 0.228435 0.973559i \(-0.426639\pi\)
0.228435 + 0.973559i \(0.426639\pi\)
\(8\) −7.10244 −2.51109
\(9\) −1.57161 −0.523871
\(10\) 9.12363 2.88515
\(11\) 4.18691 1.26240 0.631201 0.775620i \(-0.282562\pi\)
0.631201 + 0.775620i \(0.282562\pi\)
\(12\) 5.66080 1.63413
\(13\) −4.74438 −1.31586 −0.657928 0.753081i \(-0.728567\pi\)
−0.657928 + 0.753081i \(0.728567\pi\)
\(14\) −3.13731 −0.838481
\(15\) −4.20121 −1.08475
\(16\) 8.96125 2.24031
\(17\) 1.27570 0.309402 0.154701 0.987961i \(-0.450559\pi\)
0.154701 + 0.987961i \(0.450559\pi\)
\(18\) 4.07908 0.961449
\(19\) 3.12310 0.716489 0.358244 0.933628i \(-0.383376\pi\)
0.358244 + 0.933628i \(0.383376\pi\)
\(20\) −16.6497 −3.72299
\(21\) 1.44465 0.315249
\(22\) −10.8670 −2.31685
\(23\) 6.80267 1.41845 0.709227 0.704980i \(-0.249044\pi\)
0.709227 + 0.704980i \(0.249044\pi\)
\(24\) −8.48849 −1.73271
\(25\) 7.35671 1.47134
\(26\) 12.3139 2.41496
\(27\) −5.46377 −1.05150
\(28\) 5.72527 1.08198
\(29\) −1.00000 −0.185695
\(30\) 10.9041 1.99081
\(31\) −3.50259 −0.629083 −0.314542 0.949244i \(-0.601851\pi\)
−0.314542 + 0.949244i \(0.601851\pi\)
\(32\) −9.05377 −1.60050
\(33\) 5.00399 0.871083
\(34\) −3.31104 −0.567839
\(35\) −4.24906 −0.718221
\(36\) −7.44391 −1.24065
\(37\) −8.65626 −1.42308 −0.711540 0.702645i \(-0.752002\pi\)
−0.711540 + 0.702645i \(0.752002\pi\)
\(38\) −8.10592 −1.31495
\(39\) −5.67025 −0.907967
\(40\) 24.9666 3.94756
\(41\) 10.0102 1.56334 0.781669 0.623694i \(-0.214369\pi\)
0.781669 + 0.623694i \(0.214369\pi\)
\(42\) −3.74956 −0.578569
\(43\) −4.89375 −0.746290 −0.373145 0.927773i \(-0.621721\pi\)
−0.373145 + 0.927773i \(0.621721\pi\)
\(44\) 19.8312 2.98967
\(45\) 5.52456 0.823552
\(46\) −17.6561 −2.60326
\(47\) −2.81653 −0.410833 −0.205417 0.978675i \(-0.565855\pi\)
−0.205417 + 0.978675i \(0.565855\pi\)
\(48\) 10.7100 1.54586
\(49\) −5.53889 −0.791270
\(50\) −19.0941 −2.70032
\(51\) 1.52465 0.213494
\(52\) −22.4717 −3.11626
\(53\) 2.58742 0.355410 0.177705 0.984084i \(-0.443133\pi\)
0.177705 + 0.984084i \(0.443133\pi\)
\(54\) 14.1811 1.92980
\(55\) −14.7179 −1.98456
\(56\) −8.58517 −1.14724
\(57\) 3.73258 0.494392
\(58\) 2.59547 0.340802
\(59\) −5.11804 −0.666312 −0.333156 0.942872i \(-0.608114\pi\)
−0.333156 + 0.942872i \(0.608114\pi\)
\(60\) −19.8989 −2.56894
\(61\) 12.2315 1.56608 0.783040 0.621972i \(-0.213668\pi\)
0.783040 + 0.621972i \(0.213668\pi\)
\(62\) 9.09087 1.15454
\(63\) −1.89971 −0.239341
\(64\) 5.57633 0.697041
\(65\) 16.6775 2.06859
\(66\) −12.9877 −1.59868
\(67\) −6.35287 −0.776127 −0.388063 0.921633i \(-0.626856\pi\)
−0.388063 + 0.921633i \(0.626856\pi\)
\(68\) 6.04232 0.732738
\(69\) 8.13022 0.978763
\(70\) 11.0283 1.31813
\(71\) 1.20473 0.142976 0.0714878 0.997441i \(-0.477225\pi\)
0.0714878 + 0.997441i \(0.477225\pi\)
\(72\) 11.1623 1.31549
\(73\) −11.6941 −1.36869 −0.684346 0.729158i \(-0.739912\pi\)
−0.684346 + 0.729158i \(0.739912\pi\)
\(74\) 22.4671 2.61175
\(75\) 8.79238 1.01526
\(76\) 14.7925 1.69682
\(77\) 5.06098 0.576752
\(78\) 14.7170 1.66637
\(79\) 4.93390 0.555107 0.277554 0.960710i \(-0.410476\pi\)
0.277554 + 0.960710i \(0.410476\pi\)
\(80\) −31.5007 −3.52188
\(81\) −1.81519 −0.201687
\(82\) −25.9813 −2.86916
\(83\) −2.91087 −0.319509 −0.159755 0.987157i \(-0.551070\pi\)
−0.159755 + 0.987157i \(0.551070\pi\)
\(84\) 6.84257 0.746585
\(85\) −4.48435 −0.486396
\(86\) 12.7016 1.36965
\(87\) −1.19515 −0.128134
\(88\) −29.7373 −3.17001
\(89\) 5.38970 0.571307 0.285654 0.958333i \(-0.407789\pi\)
0.285654 + 0.958333i \(0.407789\pi\)
\(90\) −14.3388 −1.51145
\(91\) −5.73483 −0.601174
\(92\) 32.2207 3.35924
\(93\) −4.18612 −0.434080
\(94\) 7.31023 0.753992
\(95\) −10.9784 −1.12636
\(96\) −10.8206 −1.10438
\(97\) 19.1506 1.94445 0.972224 0.234051i \(-0.0751981\pi\)
0.972224 + 0.234051i \(0.0751981\pi\)
\(98\) 14.3760 1.45220
\(99\) −6.58021 −0.661336
\(100\) 34.8449 3.48449
\(101\) −7.35382 −0.731732 −0.365866 0.930667i \(-0.619227\pi\)
−0.365866 + 0.930667i \(0.619227\pi\)
\(102\) −3.95719 −0.391820
\(103\) −17.3093 −1.70554 −0.852770 0.522287i \(-0.825079\pi\)
−0.852770 + 0.522287i \(0.825079\pi\)
\(104\) 33.6967 3.30423
\(105\) −5.07826 −0.495588
\(106\) −6.71558 −0.652275
\(107\) −0.485892 −0.0469730 −0.0234865 0.999724i \(-0.507477\pi\)
−0.0234865 + 0.999724i \(0.507477\pi\)
\(108\) −25.8790 −2.49021
\(109\) 16.1404 1.54597 0.772984 0.634426i \(-0.218763\pi\)
0.772984 + 0.634426i \(0.218763\pi\)
\(110\) 38.1998 3.64221
\(111\) −10.3455 −0.981955
\(112\) 10.8320 1.02353
\(113\) −3.56541 −0.335405 −0.167703 0.985838i \(-0.553635\pi\)
−0.167703 + 0.985838i \(0.553635\pi\)
\(114\) −9.68780 −0.907346
\(115\) −23.9128 −2.22988
\(116\) −4.73648 −0.439771
\(117\) 7.45634 0.689339
\(118\) 13.2837 1.22287
\(119\) 1.54202 0.141356
\(120\) 29.8388 2.72390
\(121\) 6.53023 0.593657
\(122\) −31.7464 −2.87419
\(123\) 11.9638 1.07874
\(124\) −16.5899 −1.48982
\(125\) −8.28432 −0.740972
\(126\) 4.93064 0.439256
\(127\) 0.342143 0.0303603 0.0151802 0.999885i \(-0.495168\pi\)
0.0151802 + 0.999885i \(0.495168\pi\)
\(128\) 3.63435 0.321234
\(129\) −5.84877 −0.514956
\(130\) −43.2860 −3.79643
\(131\) −4.78937 −0.418450 −0.209225 0.977868i \(-0.567094\pi\)
−0.209225 + 0.977868i \(0.567094\pi\)
\(132\) 23.7013 2.06293
\(133\) 3.77509 0.327342
\(134\) 16.4887 1.42441
\(135\) 19.2063 1.65302
\(136\) −9.06058 −0.776938
\(137\) 4.11028 0.351165 0.175582 0.984465i \(-0.443819\pi\)
0.175582 + 0.984465i \(0.443819\pi\)
\(138\) −21.1018 −1.79630
\(139\) 18.7856 1.59337 0.796686 0.604393i \(-0.206584\pi\)
0.796686 + 0.604393i \(0.206584\pi\)
\(140\) −20.1255 −1.70092
\(141\) −3.36618 −0.283483
\(142\) −3.12685 −0.262400
\(143\) −19.8643 −1.66114
\(144\) −14.0836 −1.17364
\(145\) 3.51521 0.291922
\(146\) 30.3517 2.51193
\(147\) −6.61981 −0.545993
\(148\) −41.0002 −3.37019
\(149\) −2.75537 −0.225729 −0.112864 0.993610i \(-0.536003\pi\)
−0.112864 + 0.993610i \(0.536003\pi\)
\(150\) −22.8204 −1.86327
\(151\) 8.75549 0.712512 0.356256 0.934388i \(-0.384053\pi\)
0.356256 + 0.934388i \(0.384053\pi\)
\(152\) −22.1817 −1.79917
\(153\) −2.00491 −0.162087
\(154\) −13.1356 −1.05850
\(155\) 12.3123 0.988950
\(156\) −26.8570 −2.15028
\(157\) 6.31833 0.504258 0.252129 0.967694i \(-0.418869\pi\)
0.252129 + 0.967694i \(0.418869\pi\)
\(158\) −12.8058 −1.01877
\(159\) 3.09236 0.245240
\(160\) 31.8259 2.51606
\(161\) 8.22281 0.648049
\(162\) 4.71126 0.370152
\(163\) −1.53713 −0.120397 −0.0601986 0.998186i \(-0.519173\pi\)
−0.0601986 + 0.998186i \(0.519173\pi\)
\(164\) 47.4133 3.70236
\(165\) −17.5901 −1.36939
\(166\) 7.55508 0.586388
\(167\) 17.0137 1.31656 0.658279 0.752774i \(-0.271285\pi\)
0.658279 + 0.752774i \(0.271285\pi\)
\(168\) −10.2606 −0.791620
\(169\) 9.50917 0.731475
\(170\) 11.6390 0.892671
\(171\) −4.90831 −0.375348
\(172\) −23.1791 −1.76739
\(173\) 12.8909 0.980078 0.490039 0.871700i \(-0.336983\pi\)
0.490039 + 0.871700i \(0.336983\pi\)
\(174\) 3.10198 0.235161
\(175\) 8.89251 0.672211
\(176\) 37.5199 2.82817
\(177\) −6.11683 −0.459769
\(178\) −13.9888 −1.04851
\(179\) 16.4353 1.22843 0.614215 0.789139i \(-0.289473\pi\)
0.614215 + 0.789139i \(0.289473\pi\)
\(180\) 26.1669 1.95037
\(181\) −7.62309 −0.566620 −0.283310 0.959028i \(-0.591433\pi\)
−0.283310 + 0.959028i \(0.591433\pi\)
\(182\) 14.8846 1.10332
\(183\) 14.6184 1.08063
\(184\) −48.3156 −3.56187
\(185\) 30.4286 2.23715
\(186\) 10.8650 0.796657
\(187\) 5.34124 0.390590
\(188\) −13.3404 −0.972951
\(189\) −6.60440 −0.480399
\(190\) 28.4940 2.06717
\(191\) −7.83937 −0.567237 −0.283619 0.958937i \(-0.591535\pi\)
−0.283619 + 0.958937i \(0.591535\pi\)
\(192\) 6.66455 0.480973
\(193\) −8.10380 −0.583324 −0.291662 0.956521i \(-0.594208\pi\)
−0.291662 + 0.956521i \(0.594208\pi\)
\(194\) −49.7048 −3.56860
\(195\) 19.9321 1.42737
\(196\) −26.2348 −1.87392
\(197\) 22.1352 1.57706 0.788532 0.614994i \(-0.210841\pi\)
0.788532 + 0.614994i \(0.210841\pi\)
\(198\) 17.0788 1.21373
\(199\) −20.1335 −1.42722 −0.713612 0.700541i \(-0.752942\pi\)
−0.713612 + 0.700541i \(0.752942\pi\)
\(200\) −52.2506 −3.69468
\(201\) −7.59264 −0.535544
\(202\) 19.0866 1.34293
\(203\) −1.20876 −0.0848385
\(204\) 7.22148 0.505605
\(205\) −35.1881 −2.45765
\(206\) 44.9259 3.13014
\(207\) −10.6912 −0.743088
\(208\) −42.5156 −2.94793
\(209\) 13.0761 0.904496
\(210\) 13.1805 0.909540
\(211\) −21.8929 −1.50717 −0.753583 0.657352i \(-0.771676\pi\)
−0.753583 + 0.657352i \(0.771676\pi\)
\(212\) 12.2553 0.841695
\(213\) 1.43984 0.0986562
\(214\) 1.26112 0.0862084
\(215\) 17.2026 1.17321
\(216\) 38.8061 2.64042
\(217\) −4.23380 −0.287409
\(218\) −41.8919 −2.83728
\(219\) −13.9762 −0.944425
\(220\) −69.7109 −4.69990
\(221\) −6.05240 −0.407129
\(222\) 26.8516 1.80216
\(223\) −2.58770 −0.173285 −0.0866426 0.996239i \(-0.527614\pi\)
−0.0866426 + 0.996239i \(0.527614\pi\)
\(224\) −10.9439 −0.731218
\(225\) −11.5619 −0.770794
\(226\) 9.25391 0.615561
\(227\) −1.70962 −0.113471 −0.0567357 0.998389i \(-0.518069\pi\)
−0.0567357 + 0.998389i \(0.518069\pi\)
\(228\) 17.6793 1.17084
\(229\) 0.874116 0.0577632 0.0288816 0.999583i \(-0.490805\pi\)
0.0288816 + 0.999583i \(0.490805\pi\)
\(230\) 62.0651 4.09245
\(231\) 6.04864 0.397971
\(232\) 7.10244 0.466298
\(233\) −21.8141 −1.42909 −0.714543 0.699591i \(-0.753366\pi\)
−0.714543 + 0.699591i \(0.753366\pi\)
\(234\) −19.3527 −1.26513
\(235\) 9.90070 0.645850
\(236\) −24.2415 −1.57798
\(237\) 5.89676 0.383035
\(238\) −4.00226 −0.259428
\(239\) 9.85174 0.637256 0.318628 0.947880i \(-0.396778\pi\)
0.318628 + 0.947880i \(0.396778\pi\)
\(240\) −37.6481 −2.43017
\(241\) −4.52319 −0.291364 −0.145682 0.989331i \(-0.546538\pi\)
−0.145682 + 0.989331i \(0.546538\pi\)
\(242\) −16.9490 −1.08952
\(243\) 14.2219 0.912334
\(244\) 57.9340 3.70885
\(245\) 19.4704 1.24392
\(246\) −31.0516 −1.97978
\(247\) −14.8172 −0.942795
\(248\) 24.8769 1.57969
\(249\) −3.47893 −0.220468
\(250\) 21.5017 1.35989
\(251\) 19.4279 1.22628 0.613139 0.789975i \(-0.289906\pi\)
0.613139 + 0.789975i \(0.289906\pi\)
\(252\) −8.99792 −0.566816
\(253\) 28.4822 1.79066
\(254\) −0.888023 −0.0557195
\(255\) −5.35947 −0.335623
\(256\) −20.5855 −1.28659
\(257\) −6.31920 −0.394181 −0.197090 0.980385i \(-0.563149\pi\)
−0.197090 + 0.980385i \(0.563149\pi\)
\(258\) 15.1803 0.945086
\(259\) −10.4634 −0.650162
\(260\) 78.9926 4.89891
\(261\) 1.57161 0.0972805
\(262\) 12.4307 0.767970
\(263\) −11.4910 −0.708568 −0.354284 0.935138i \(-0.615275\pi\)
−0.354284 + 0.935138i \(0.615275\pi\)
\(264\) −35.5406 −2.18737
\(265\) −9.09533 −0.558722
\(266\) −9.79814 −0.600762
\(267\) 6.44151 0.394214
\(268\) −30.0902 −1.83805
\(269\) −25.2203 −1.53771 −0.768854 0.639424i \(-0.779173\pi\)
−0.768854 + 0.639424i \(0.779173\pi\)
\(270\) −49.8494 −3.03374
\(271\) −21.2041 −1.28806 −0.644029 0.765001i \(-0.722739\pi\)
−0.644029 + 0.765001i \(0.722739\pi\)
\(272\) 11.4318 0.693158
\(273\) −6.85399 −0.414822
\(274\) −10.6681 −0.644484
\(275\) 30.8019 1.85742
\(276\) 38.5086 2.31794
\(277\) −1.00000 −0.0600842
\(278\) −48.7575 −2.92428
\(279\) 5.50472 0.329559
\(280\) 30.1787 1.80352
\(281\) 18.9231 1.12885 0.564427 0.825483i \(-0.309097\pi\)
0.564427 + 0.825483i \(0.309097\pi\)
\(282\) 8.73682 0.520270
\(283\) 22.6363 1.34559 0.672793 0.739830i \(-0.265094\pi\)
0.672793 + 0.739830i \(0.265094\pi\)
\(284\) 5.70619 0.338600
\(285\) −13.1208 −0.777209
\(286\) 51.5573 3.04864
\(287\) 12.1000 0.714241
\(288\) 14.2290 0.838454
\(289\) −15.3726 −0.904270
\(290\) −9.12363 −0.535758
\(291\) 22.8879 1.34171
\(292\) −55.3888 −3.24139
\(293\) −31.4878 −1.83954 −0.919769 0.392460i \(-0.871624\pi\)
−0.919769 + 0.392460i \(0.871624\pi\)
\(294\) 17.1815 1.00205
\(295\) 17.9910 1.04748
\(296\) 61.4806 3.57349
\(297\) −22.8763 −1.32742
\(298\) 7.15149 0.414275
\(299\) −32.2745 −1.86648
\(300\) 41.6449 2.40437
\(301\) −5.91539 −0.340957
\(302\) −22.7246 −1.30766
\(303\) −8.78892 −0.504910
\(304\) 27.9869 1.60516
\(305\) −42.9962 −2.46195
\(306\) 5.20368 0.297475
\(307\) −4.93345 −0.281567 −0.140784 0.990040i \(-0.544962\pi\)
−0.140784 + 0.990040i \(0.544962\pi\)
\(308\) 23.9712 1.36589
\(309\) −20.6873 −1.17686
\(310\) −31.9563 −1.81500
\(311\) −26.0780 −1.47875 −0.739374 0.673295i \(-0.764878\pi\)
−0.739374 + 0.673295i \(0.764878\pi\)
\(312\) 40.2727 2.27999
\(313\) −31.3904 −1.77429 −0.887144 0.461492i \(-0.847314\pi\)
−0.887144 + 0.461492i \(0.847314\pi\)
\(314\) −16.3991 −0.925452
\(315\) 6.67788 0.376256
\(316\) 23.3693 1.31463
\(317\) 11.3222 0.635921 0.317960 0.948104i \(-0.397002\pi\)
0.317960 + 0.948104i \(0.397002\pi\)
\(318\) −8.02613 −0.450083
\(319\) −4.18691 −0.234422
\(320\) −19.6020 −1.09578
\(321\) −0.580715 −0.0324123
\(322\) −21.3421 −1.18935
\(323\) 3.98414 0.221683
\(324\) −8.59758 −0.477643
\(325\) −34.9030 −1.93607
\(326\) 3.98958 0.220962
\(327\) 19.2902 1.06675
\(328\) −71.0972 −3.92569
\(329\) −3.40452 −0.187697
\(330\) 45.6546 2.51320
\(331\) −21.2962 −1.17055 −0.585273 0.810836i \(-0.699013\pi\)
−0.585273 + 0.810836i \(0.699013\pi\)
\(332\) −13.7873 −0.756674
\(333\) 13.6043 0.745511
\(334\) −44.1585 −2.41625
\(335\) 22.3317 1.22011
\(336\) 12.9459 0.706257
\(337\) −13.9059 −0.757500 −0.378750 0.925499i \(-0.623646\pi\)
−0.378750 + 0.925499i \(0.623646\pi\)
\(338\) −24.6808 −1.34246
\(339\) −4.26120 −0.231437
\(340\) −21.2400 −1.15190
\(341\) −14.6650 −0.794155
\(342\) 12.7394 0.688867
\(343\) −15.1565 −0.818377
\(344\) 34.7576 1.87400
\(345\) −28.5794 −1.53866
\(346\) −33.4580 −1.79871
\(347\) −17.1101 −0.918518 −0.459259 0.888302i \(-0.651885\pi\)
−0.459259 + 0.888302i \(0.651885\pi\)
\(348\) −5.66080 −0.303451
\(349\) −18.3144 −0.980350 −0.490175 0.871624i \(-0.663067\pi\)
−0.490175 + 0.871624i \(0.663067\pi\)
\(350\) −23.0803 −1.23369
\(351\) 25.9222 1.38363
\(352\) −37.9074 −2.02047
\(353\) −0.813463 −0.0432963 −0.0216481 0.999766i \(-0.506891\pi\)
−0.0216481 + 0.999766i \(0.506891\pi\)
\(354\) 15.8761 0.843803
\(355\) −4.23490 −0.224765
\(356\) 25.5282 1.35299
\(357\) 1.84294 0.0975389
\(358\) −42.6573 −2.25451
\(359\) −25.0221 −1.32062 −0.660308 0.750995i \(-0.729574\pi\)
−0.660308 + 0.750995i \(0.729574\pi\)
\(360\) −39.2379 −2.06802
\(361\) −9.24624 −0.486644
\(362\) 19.7855 1.03990
\(363\) 7.80461 0.409636
\(364\) −27.1629 −1.42372
\(365\) 41.1072 2.15165
\(366\) −37.9418 −1.98325
\(367\) 14.0266 0.732185 0.366093 0.930578i \(-0.380695\pi\)
0.366093 + 0.930578i \(0.380695\pi\)
\(368\) 60.9604 3.17778
\(369\) −15.7322 −0.818988
\(370\) −78.9765 −4.10579
\(371\) 3.12758 0.162376
\(372\) −19.8274 −1.02801
\(373\) 14.9927 0.776291 0.388146 0.921598i \(-0.373116\pi\)
0.388146 + 0.921598i \(0.373116\pi\)
\(374\) −13.8630 −0.716840
\(375\) −9.90102 −0.511286
\(376\) 20.0042 1.03164
\(377\) 4.74438 0.244348
\(378\) 17.1415 0.881665
\(379\) 19.7808 1.01607 0.508035 0.861336i \(-0.330372\pi\)
0.508035 + 0.861336i \(0.330372\pi\)
\(380\) −51.9987 −2.66748
\(381\) 0.408913 0.0209492
\(382\) 20.3469 1.04104
\(383\) −4.66112 −0.238172 −0.119086 0.992884i \(-0.537996\pi\)
−0.119086 + 0.992884i \(0.537996\pi\)
\(384\) 4.34360 0.221658
\(385\) −17.7904 −0.906684
\(386\) 21.0332 1.07056
\(387\) 7.69109 0.390960
\(388\) 90.7063 4.60492
\(389\) 17.2193 0.873051 0.436526 0.899692i \(-0.356209\pi\)
0.436526 + 0.899692i \(0.356209\pi\)
\(390\) −51.7333 −2.61962
\(391\) 8.67816 0.438873
\(392\) 39.3397 1.98695
\(393\) −5.72403 −0.288739
\(394\) −57.4512 −2.89435
\(395\) −17.3437 −0.872656
\(396\) −31.1670 −1.56620
\(397\) −7.96676 −0.399840 −0.199920 0.979812i \(-0.564068\pi\)
−0.199920 + 0.979812i \(0.564068\pi\)
\(398\) 52.2559 2.61935
\(399\) 4.51180 0.225873
\(400\) 65.9253 3.29626
\(401\) 17.4253 0.870178 0.435089 0.900387i \(-0.356717\pi\)
0.435089 + 0.900387i \(0.356717\pi\)
\(402\) 19.7065 0.982870
\(403\) 16.6176 0.827782
\(404\) −34.8312 −1.73292
\(405\) 6.38076 0.317062
\(406\) 3.13731 0.155702
\(407\) −36.2430 −1.79650
\(408\) −10.8288 −0.536103
\(409\) 8.19295 0.405115 0.202558 0.979270i \(-0.435075\pi\)
0.202558 + 0.979270i \(0.435075\pi\)
\(410\) 91.3298 4.51046
\(411\) 4.91240 0.242311
\(412\) −81.9852 −4.03912
\(413\) −6.18649 −0.304417
\(414\) 27.7486 1.36377
\(415\) 10.2323 0.502285
\(416\) 42.9546 2.10602
\(417\) 22.4516 1.09946
\(418\) −33.9388 −1.66000
\(419\) 8.05920 0.393718 0.196859 0.980432i \(-0.436926\pi\)
0.196859 + 0.980432i \(0.436926\pi\)
\(420\) −24.0531 −1.17367
\(421\) −26.1683 −1.27537 −0.637683 0.770299i \(-0.720107\pi\)
−0.637683 + 0.770299i \(0.720107\pi\)
\(422\) 56.8223 2.76607
\(423\) 4.42650 0.215224
\(424\) −18.3770 −0.892467
\(425\) 9.38494 0.455237
\(426\) −3.73706 −0.181061
\(427\) 14.7849 0.715493
\(428\) −2.30142 −0.111243
\(429\) −23.7408 −1.14622
\(430\) −44.6488 −2.15316
\(431\) 8.51845 0.410319 0.205160 0.978729i \(-0.434229\pi\)
0.205160 + 0.978729i \(0.434229\pi\)
\(432\) −48.9622 −2.35569
\(433\) −17.1435 −0.823864 −0.411932 0.911215i \(-0.635146\pi\)
−0.411932 + 0.911215i \(0.635146\pi\)
\(434\) 10.9887 0.527474
\(435\) 4.20121 0.201432
\(436\) 76.4485 3.66122
\(437\) 21.2454 1.01631
\(438\) 36.2749 1.73328
\(439\) 10.3646 0.494673 0.247337 0.968930i \(-0.420445\pi\)
0.247337 + 0.968930i \(0.420445\pi\)
\(440\) 104.533 4.98341
\(441\) 8.70500 0.414524
\(442\) 15.7088 0.747193
\(443\) 3.36989 0.160108 0.0800541 0.996791i \(-0.474491\pi\)
0.0800541 + 0.996791i \(0.474491\pi\)
\(444\) −49.0014 −2.32550
\(445\) −18.9459 −0.898123
\(446\) 6.71630 0.318026
\(447\) −3.29309 −0.155758
\(448\) 6.74045 0.318457
\(449\) 9.22512 0.435360 0.217680 0.976020i \(-0.430151\pi\)
0.217680 + 0.976020i \(0.430151\pi\)
\(450\) 30.0086 1.41462
\(451\) 41.9120 1.97356
\(452\) −16.8875 −0.794319
\(453\) 10.4641 0.491648
\(454\) 4.43727 0.208251
\(455\) 20.1591 0.945075
\(456\) −26.5104 −1.24146
\(457\) 34.3169 1.60528 0.802639 0.596466i \(-0.203429\pi\)
0.802639 + 0.596466i \(0.203429\pi\)
\(458\) −2.26874 −0.106011
\(459\) −6.97012 −0.325337
\(460\) −113.262 −5.28089
\(461\) −34.2515 −1.59525 −0.797625 0.603154i \(-0.793911\pi\)
−0.797625 + 0.603154i \(0.793911\pi\)
\(462\) −15.6991 −0.730387
\(463\) −18.0716 −0.839858 −0.419929 0.907557i \(-0.637945\pi\)
−0.419929 + 0.907557i \(0.637945\pi\)
\(464\) −8.96125 −0.416015
\(465\) 14.7151 0.682396
\(466\) 56.6178 2.62277
\(467\) −1.88839 −0.0873843 −0.0436921 0.999045i \(-0.513912\pi\)
−0.0436921 + 0.999045i \(0.513912\pi\)
\(468\) 35.3168 1.63252
\(469\) −7.67911 −0.354589
\(470\) −25.6970 −1.18531
\(471\) 7.55136 0.347948
\(472\) 36.3506 1.67317
\(473\) −20.4897 −0.942118
\(474\) −15.3049 −0.702976
\(475\) 22.9757 1.05420
\(476\) 7.30372 0.334766
\(477\) −4.06643 −0.186189
\(478\) −25.5699 −1.16954
\(479\) −21.2788 −0.972252 −0.486126 0.873889i \(-0.661590\pi\)
−0.486126 + 0.873889i \(0.661590\pi\)
\(480\) 38.0368 1.73613
\(481\) 41.0686 1.87257
\(482\) 11.7398 0.534734
\(483\) 9.82750 0.447167
\(484\) 30.9303 1.40592
\(485\) −67.3184 −3.05677
\(486\) −36.9125 −1.67439
\(487\) −36.9935 −1.67633 −0.838167 0.545414i \(-0.816372\pi\)
−0.838167 + 0.545414i \(0.816372\pi\)
\(488\) −86.8733 −3.93257
\(489\) −1.83710 −0.0830766
\(490\) −50.5348 −2.28293
\(491\) 10.9179 0.492720 0.246360 0.969178i \(-0.420765\pi\)
0.246360 + 0.969178i \(0.420765\pi\)
\(492\) 56.6660 2.55470
\(493\) −1.27570 −0.0574546
\(494\) 38.4576 1.73029
\(495\) 23.1308 1.03965
\(496\) −31.3875 −1.40934
\(497\) 1.45624 0.0653212
\(498\) 9.02946 0.404620
\(499\) 31.4617 1.40842 0.704210 0.709992i \(-0.251302\pi\)
0.704210 + 0.709992i \(0.251302\pi\)
\(500\) −39.2385 −1.75480
\(501\) 20.3339 0.908452
\(502\) −50.4246 −2.25056
\(503\) −20.9221 −0.932872 −0.466436 0.884555i \(-0.654462\pi\)
−0.466436 + 0.884555i \(0.654462\pi\)
\(504\) 13.4926 0.601007
\(505\) 25.8502 1.15032
\(506\) −73.9247 −3.28635
\(507\) 11.3649 0.504733
\(508\) 1.62055 0.0719004
\(509\) 18.6651 0.827318 0.413659 0.910432i \(-0.364251\pi\)
0.413659 + 0.910432i \(0.364251\pi\)
\(510\) 13.9104 0.615961
\(511\) −14.1354 −0.625313
\(512\) 46.1604 2.04002
\(513\) −17.0639 −0.753390
\(514\) 16.4013 0.723430
\(515\) 60.8460 2.68119
\(516\) −27.7026 −1.21954
\(517\) −11.7926 −0.518636
\(518\) 27.1574 1.19323
\(519\) 15.4066 0.676274
\(520\) −118.451 −5.19442
\(521\) 23.3120 1.02132 0.510659 0.859783i \(-0.329401\pi\)
0.510659 + 0.859783i \(0.329401\pi\)
\(522\) −4.07908 −0.178537
\(523\) −22.0354 −0.963540 −0.481770 0.876298i \(-0.660006\pi\)
−0.481770 + 0.876298i \(0.660006\pi\)
\(524\) −22.6848 −0.990988
\(525\) 10.6279 0.463839
\(526\) 29.8247 1.30042
\(527\) −4.46824 −0.194640
\(528\) 44.8420 1.95150
\(529\) 23.2763 1.01201
\(530\) 23.6067 1.02541
\(531\) 8.04358 0.349062
\(532\) 17.8806 0.775223
\(533\) −47.4924 −2.05713
\(534\) −16.7187 −0.723491
\(535\) 1.70801 0.0738439
\(536\) 45.1209 1.94893
\(537\) 19.6426 0.847641
\(538\) 65.4586 2.82212
\(539\) −23.1909 −0.998901
\(540\) 90.9702 3.91473
\(541\) 19.0266 0.818016 0.409008 0.912531i \(-0.365875\pi\)
0.409008 + 0.912531i \(0.365875\pi\)
\(542\) 55.0347 2.36394
\(543\) −9.11075 −0.390980
\(544\) −11.5499 −0.495197
\(545\) −56.7368 −2.43034
\(546\) 17.7893 0.761314
\(547\) 25.7110 1.09932 0.549662 0.835387i \(-0.314757\pi\)
0.549662 + 0.835387i \(0.314757\pi\)
\(548\) 19.4682 0.831642
\(549\) −19.2232 −0.820424
\(550\) −79.9454 −3.40888
\(551\) −3.12310 −0.133049
\(552\) −57.7444 −2.45777
\(553\) 5.96391 0.253611
\(554\) 2.59547 0.110271
\(555\) 36.3667 1.54368
\(556\) 88.9775 3.77348
\(557\) −23.2382 −0.984632 −0.492316 0.870416i \(-0.663850\pi\)
−0.492316 + 0.870416i \(0.663850\pi\)
\(558\) −14.2873 −0.604831
\(559\) 23.2178 0.982010
\(560\) −38.0768 −1.60904
\(561\) 6.38358 0.269515
\(562\) −49.1143 −2.07176
\(563\) 26.2317 1.10554 0.552768 0.833335i \(-0.313571\pi\)
0.552768 + 0.833335i \(0.313571\pi\)
\(564\) −15.9438 −0.671356
\(565\) 12.5332 0.527274
\(566\) −58.7518 −2.46952
\(567\) −2.19413 −0.0921447
\(568\) −8.55656 −0.359025
\(569\) −8.10312 −0.339700 −0.169850 0.985470i \(-0.554328\pi\)
−0.169850 + 0.985470i \(0.554328\pi\)
\(570\) 34.0547 1.42639
\(571\) −26.7954 −1.12135 −0.560676 0.828035i \(-0.689459\pi\)
−0.560676 + 0.828035i \(0.689459\pi\)
\(572\) −94.0868 −3.93397
\(573\) −9.36923 −0.391405
\(574\) −31.4052 −1.31083
\(575\) 50.0453 2.08703
\(576\) −8.76383 −0.365160
\(577\) −4.05206 −0.168690 −0.0843448 0.996437i \(-0.526880\pi\)
−0.0843448 + 0.996437i \(0.526880\pi\)
\(578\) 39.8991 1.65959
\(579\) −9.68526 −0.402506
\(580\) 16.6497 0.691342
\(581\) −3.51855 −0.145974
\(582\) −59.4048 −2.46241
\(583\) 10.8333 0.448670
\(584\) 83.0567 3.43691
\(585\) −26.2106 −1.08368
\(586\) 81.7257 3.37606
\(587\) −6.15403 −0.254004 −0.127002 0.991902i \(-0.540535\pi\)
−0.127002 + 0.991902i \(0.540535\pi\)
\(588\) −31.3546 −1.29304
\(589\) −10.9389 −0.450731
\(590\) −46.6951 −1.92241
\(591\) 26.4548 1.08821
\(592\) −77.5709 −3.18814
\(593\) −38.8296 −1.59454 −0.797270 0.603623i \(-0.793723\pi\)
−0.797270 + 0.603623i \(0.793723\pi\)
\(594\) 59.3748 2.43618
\(595\) −5.42051 −0.222219
\(596\) −13.0508 −0.534580
\(597\) −24.0625 −0.984814
\(598\) 83.7675 3.42551
\(599\) −31.1787 −1.27393 −0.636964 0.770894i \(-0.719810\pi\)
−0.636964 + 0.770894i \(0.719810\pi\)
\(600\) −62.4474 −2.54940
\(601\) 18.7786 0.765994 0.382997 0.923749i \(-0.374892\pi\)
0.382997 + 0.923749i \(0.374892\pi\)
\(602\) 15.3532 0.625750
\(603\) 9.98427 0.406591
\(604\) 41.4702 1.68740
\(605\) −22.9551 −0.933258
\(606\) 22.8114 0.926650
\(607\) −34.2672 −1.39086 −0.695431 0.718593i \(-0.744787\pi\)
−0.695431 + 0.718593i \(0.744787\pi\)
\(608\) −28.2759 −1.14674
\(609\) −1.44465 −0.0585403
\(610\) 111.595 4.51837
\(611\) 13.3627 0.540597
\(612\) −9.49619 −0.383861
\(613\) −28.1065 −1.13521 −0.567606 0.823300i \(-0.692130\pi\)
−0.567606 + 0.823300i \(0.692130\pi\)
\(614\) 12.8046 0.516753
\(615\) −42.0551 −1.69583
\(616\) −35.9453 −1.44828
\(617\) −6.40885 −0.258011 −0.129005 0.991644i \(-0.541178\pi\)
−0.129005 + 0.991644i \(0.541178\pi\)
\(618\) 53.6932 2.15986
\(619\) −39.1342 −1.57294 −0.786469 0.617630i \(-0.788093\pi\)
−0.786469 + 0.617630i \(0.788093\pi\)
\(620\) 58.3170 2.34207
\(621\) −37.1682 −1.49151
\(622\) 67.6847 2.71391
\(623\) 6.51487 0.261013
\(624\) −50.8125 −2.03413
\(625\) −7.66239 −0.306496
\(626\) 81.4728 3.25631
\(627\) 15.6280 0.624121
\(628\) 29.9266 1.19420
\(629\) −11.0428 −0.440305
\(630\) −17.3322 −0.690533
\(631\) −28.0061 −1.11491 −0.557453 0.830208i \(-0.688221\pi\)
−0.557453 + 0.830208i \(0.688221\pi\)
\(632\) −35.0428 −1.39393
\(633\) −26.1653 −1.03998
\(634\) −29.3866 −1.16709
\(635\) −1.20271 −0.0477279
\(636\) 14.6469 0.580787
\(637\) 26.2786 1.04120
\(638\) 10.8670 0.430229
\(639\) −1.89338 −0.0749009
\(640\) −12.7755 −0.504996
\(641\) −41.6314 −1.64434 −0.822172 0.569240i \(-0.807238\pi\)
−0.822172 + 0.569240i \(0.807238\pi\)
\(642\) 1.50723 0.0594856
\(643\) 34.6942 1.36820 0.684102 0.729386i \(-0.260194\pi\)
0.684102 + 0.729386i \(0.260194\pi\)
\(644\) 38.9472 1.53473
\(645\) 20.5597 0.809536
\(646\) −10.3407 −0.406850
\(647\) −36.2524 −1.42523 −0.712614 0.701556i \(-0.752489\pi\)
−0.712614 + 0.701556i \(0.752489\pi\)
\(648\) 12.8923 0.506455
\(649\) −21.4288 −0.841153
\(650\) 90.5899 3.55323
\(651\) −5.06002 −0.198318
\(652\) −7.28057 −0.285129
\(653\) 42.5915 1.66673 0.833367 0.552719i \(-0.186410\pi\)
0.833367 + 0.552719i \(0.186410\pi\)
\(654\) −50.0671 −1.95778
\(655\) 16.8357 0.657824
\(656\) 89.7043 3.50236
\(657\) 18.3786 0.717018
\(658\) 8.83633 0.344476
\(659\) 33.1995 1.29327 0.646634 0.762801i \(-0.276176\pi\)
0.646634 + 0.762801i \(0.276176\pi\)
\(660\) −83.3150 −3.24303
\(661\) −28.1030 −1.09308 −0.546539 0.837433i \(-0.684055\pi\)
−0.546539 + 0.837433i \(0.684055\pi\)
\(662\) 55.2738 2.14828
\(663\) −7.23354 −0.280927
\(664\) 20.6743 0.802318
\(665\) −13.2702 −0.514597
\(666\) −35.3096 −1.36822
\(667\) −6.80267 −0.263400
\(668\) 80.5848 3.11792
\(669\) −3.09269 −0.119570
\(670\) −57.9613 −2.23924
\(671\) 51.2121 1.97702
\(672\) −13.0796 −0.504555
\(673\) 3.46345 0.133506 0.0667531 0.997770i \(-0.478736\pi\)
0.0667531 + 0.997770i \(0.478736\pi\)
\(674\) 36.0923 1.39022
\(675\) −40.1953 −1.54712
\(676\) 45.0399 1.73231
\(677\) −24.9028 −0.957093 −0.478546 0.878062i \(-0.658836\pi\)
−0.478546 + 0.878062i \(0.658836\pi\)
\(678\) 11.0598 0.424750
\(679\) 23.1485 0.888359
\(680\) 31.8498 1.22139
\(681\) −2.04325 −0.0782977
\(682\) 38.0626 1.45749
\(683\) 34.8449 1.33330 0.666651 0.745370i \(-0.267727\pi\)
0.666651 + 0.745370i \(0.267727\pi\)
\(684\) −23.2481 −0.888913
\(685\) −14.4485 −0.552049
\(686\) 39.3384 1.50195
\(687\) 1.04470 0.0398578
\(688\) −43.8541 −1.67192
\(689\) −12.2757 −0.467668
\(690\) 74.1771 2.82387
\(691\) −0.341332 −0.0129849 −0.00649243 0.999979i \(-0.502067\pi\)
−0.00649243 + 0.999979i \(0.502067\pi\)
\(692\) 61.0575 2.32106
\(693\) −7.95391 −0.302144
\(694\) 44.4088 1.68573
\(695\) −66.0353 −2.50486
\(696\) 8.48849 0.321755
\(697\) 12.7701 0.483700
\(698\) 47.5346 1.79921
\(699\) −26.0711 −0.986100
\(700\) 42.1192 1.59195
\(701\) 6.85905 0.259063 0.129531 0.991575i \(-0.458653\pi\)
0.129531 + 0.991575i \(0.458653\pi\)
\(702\) −67.2804 −2.53933
\(703\) −27.0344 −1.01962
\(704\) 23.3476 0.879945
\(705\) 11.8328 0.445650
\(706\) 2.11132 0.0794606
\(707\) −8.88902 −0.334306
\(708\) −28.9722 −1.08884
\(709\) 25.1923 0.946115 0.473057 0.881032i \(-0.343150\pi\)
0.473057 + 0.881032i \(0.343150\pi\)
\(710\) 10.9916 0.412506
\(711\) −7.75419 −0.290805
\(712\) −38.2801 −1.43461
\(713\) −23.8269 −0.892326
\(714\) −4.78331 −0.179011
\(715\) 69.8272 2.61139
\(716\) 77.8452 2.90921
\(717\) 11.7743 0.439720
\(718\) 64.9442 2.42370
\(719\) 19.8187 0.739113 0.369557 0.929208i \(-0.379510\pi\)
0.369557 + 0.929208i \(0.379510\pi\)
\(720\) 49.5069 1.84501
\(721\) −20.9229 −0.779209
\(722\) 23.9984 0.893126
\(723\) −5.40589 −0.201047
\(724\) −36.1066 −1.34189
\(725\) −7.35671 −0.273221
\(726\) −20.2566 −0.751794
\(727\) 46.8615 1.73800 0.868998 0.494815i \(-0.164764\pi\)
0.868998 + 0.494815i \(0.164764\pi\)
\(728\) 40.7313 1.50960
\(729\) 22.4429 0.831217
\(730\) −106.693 −3.94887
\(731\) −6.24295 −0.230904
\(732\) 69.2399 2.55918
\(733\) −8.94812 −0.330506 −0.165253 0.986251i \(-0.552844\pi\)
−0.165253 + 0.986251i \(0.552844\pi\)
\(734\) −36.4058 −1.34376
\(735\) 23.2700 0.858328
\(736\) −61.5898 −2.27023
\(737\) −26.5989 −0.979784
\(738\) 40.8326 1.50307
\(739\) 27.5019 1.01167 0.505837 0.862629i \(-0.331184\pi\)
0.505837 + 0.862629i \(0.331184\pi\)
\(740\) 144.124 5.29811
\(741\) −17.7088 −0.650548
\(742\) −8.11754 −0.298004
\(743\) −32.7046 −1.19982 −0.599908 0.800069i \(-0.704796\pi\)
−0.599908 + 0.800069i \(0.704796\pi\)
\(744\) 29.7317 1.09002
\(745\) 9.68572 0.354857
\(746\) −38.9131 −1.42471
\(747\) 4.57476 0.167382
\(748\) 25.2986 0.925010
\(749\) −0.587328 −0.0214605
\(750\) 25.6978 0.938351
\(751\) −6.75891 −0.246636 −0.123318 0.992367i \(-0.539354\pi\)
−0.123318 + 0.992367i \(0.539354\pi\)
\(752\) −25.2396 −0.920394
\(753\) 23.2193 0.846158
\(754\) −12.3139 −0.448446
\(755\) −30.7774 −1.12010
\(756\) −31.2816 −1.13770
\(757\) 16.3912 0.595748 0.297874 0.954605i \(-0.403722\pi\)
0.297874 + 0.954605i \(0.403722\pi\)
\(758\) −51.3405 −1.86477
\(759\) 34.0405 1.23559
\(760\) 77.9732 2.82838
\(761\) 21.4598 0.777916 0.388958 0.921255i \(-0.372835\pi\)
0.388958 + 0.921255i \(0.372835\pi\)
\(762\) −1.06132 −0.0384476
\(763\) 19.5099 0.706305
\(764\) −37.1310 −1.34335
\(765\) 7.04767 0.254809
\(766\) 12.0978 0.437112
\(767\) 24.2819 0.876770
\(768\) −24.6028 −0.887777
\(769\) 37.2079 1.34175 0.670876 0.741570i \(-0.265918\pi\)
0.670876 + 0.741570i \(0.265918\pi\)
\(770\) 46.1745 1.66401
\(771\) −7.55239 −0.271993
\(772\) −38.3834 −1.38145
\(773\) 4.40043 0.158272 0.0791362 0.996864i \(-0.474784\pi\)
0.0791362 + 0.996864i \(0.474784\pi\)
\(774\) −19.9620 −0.717520
\(775\) −25.7675 −0.925596
\(776\) −136.016 −4.88269
\(777\) −12.5053 −0.448625
\(778\) −44.6921 −1.60229
\(779\) 31.2630 1.12011
\(780\) 94.4081 3.38035
\(781\) 5.04412 0.180493
\(782\) −22.5239 −0.805454
\(783\) 5.46377 0.195259
\(784\) −49.6354 −1.77269
\(785\) −22.2103 −0.792718
\(786\) 14.8565 0.529915
\(787\) −1.75508 −0.0625620 −0.0312810 0.999511i \(-0.509959\pi\)
−0.0312810 + 0.999511i \(0.509959\pi\)
\(788\) 104.843 3.73486
\(789\) −13.7335 −0.488927
\(790\) 45.0151 1.60156
\(791\) −4.30973 −0.153236
\(792\) 46.7356 1.66068
\(793\) −58.0308 −2.06073
\(794\) 20.6775 0.733817
\(795\) −10.8703 −0.385530
\(796\) −95.3617 −3.38000
\(797\) −27.4055 −0.970753 −0.485377 0.874305i \(-0.661317\pi\)
−0.485377 + 0.874305i \(0.661317\pi\)
\(798\) −11.7103 −0.414538
\(799\) −3.59304 −0.127113
\(800\) −66.6060 −2.35488
\(801\) −8.47053 −0.299292
\(802\) −45.2269 −1.59702
\(803\) −48.9622 −1.72784
\(804\) −35.9624 −1.26829
\(805\) −28.9049 −1.01876
\(806\) −43.1305 −1.51921
\(807\) −30.1421 −1.06105
\(808\) 52.2301 1.83745
\(809\) −43.0475 −1.51347 −0.756736 0.653721i \(-0.773207\pi\)
−0.756736 + 0.653721i \(0.773207\pi\)
\(810\) −16.5611 −0.581897
\(811\) −31.4746 −1.10522 −0.552612 0.833439i \(-0.686369\pi\)
−0.552612 + 0.833439i \(0.686369\pi\)
\(812\) −5.72527 −0.200918
\(813\) −25.3421 −0.888787
\(814\) 94.0677 3.29707
\(815\) 5.40333 0.189271
\(816\) 13.6628 0.478293
\(817\) −15.2837 −0.534708
\(818\) −21.2646 −0.743498
\(819\) 9.01295 0.314938
\(820\) −166.668 −5.82029
\(821\) −3.32560 −0.116064 −0.0580320 0.998315i \(-0.518483\pi\)
−0.0580320 + 0.998315i \(0.518483\pi\)
\(822\) −12.7500 −0.444708
\(823\) −48.8380 −1.70239 −0.851193 0.524853i \(-0.824120\pi\)
−0.851193 + 0.524853i \(0.824120\pi\)
\(824\) 122.939 4.28277
\(825\) 36.8129 1.28166
\(826\) 16.0569 0.558690
\(827\) −15.1141 −0.525568 −0.262784 0.964855i \(-0.584641\pi\)
−0.262784 + 0.964855i \(0.584641\pi\)
\(828\) −50.6385 −1.75981
\(829\) −9.62165 −0.334174 −0.167087 0.985942i \(-0.553436\pi\)
−0.167087 + 0.985942i \(0.553436\pi\)
\(830\) −26.5577 −0.921831
\(831\) −1.19515 −0.0414593
\(832\) −26.4562 −0.917205
\(833\) −7.06596 −0.244821
\(834\) −58.2725 −2.01781
\(835\) −59.8067 −2.06969
\(836\) 61.9348 2.14206
\(837\) 19.1373 0.661483
\(838\) −20.9174 −0.722581
\(839\) 30.2720 1.04510 0.522552 0.852607i \(-0.324980\pi\)
0.522552 + 0.852607i \(0.324980\pi\)
\(840\) 36.0681 1.24447
\(841\) 1.00000 0.0344828
\(842\) 67.9191 2.34065
\(843\) 22.6159 0.778933
\(844\) −103.695 −3.56933
\(845\) −33.4267 −1.14991
\(846\) −11.4889 −0.394995
\(847\) 7.89349 0.271224
\(848\) 23.1865 0.796228
\(849\) 27.0538 0.928483
\(850\) −24.3584 −0.835485
\(851\) −58.8857 −2.01858
\(852\) 6.81976 0.233641
\(853\) −11.3716 −0.389356 −0.194678 0.980867i \(-0.562366\pi\)
−0.194678 + 0.980867i \(0.562366\pi\)
\(854\) −38.3739 −1.31313
\(855\) 17.2537 0.590066
\(856\) 3.45102 0.117954
\(857\) −43.9805 −1.50235 −0.751173 0.660105i \(-0.770512\pi\)
−0.751173 + 0.660105i \(0.770512\pi\)
\(858\) 61.6187 2.10363
\(859\) 1.11221 0.0379481 0.0189741 0.999820i \(-0.493960\pi\)
0.0189741 + 0.999820i \(0.493960\pi\)
\(860\) 81.4796 2.77843
\(861\) 14.4613 0.492841
\(862\) −22.1094 −0.753049
\(863\) −11.2556 −0.383144 −0.191572 0.981479i \(-0.561359\pi\)
−0.191572 + 0.981479i \(0.561359\pi\)
\(864\) 49.4677 1.68293
\(865\) −45.3143 −1.54073
\(866\) 44.4955 1.51202
\(867\) −18.3726 −0.623965
\(868\) −20.0533 −0.680652
\(869\) 20.6578 0.700768
\(870\) −10.9041 −0.369684
\(871\) 30.1405 1.02127
\(872\) −114.636 −3.88207
\(873\) −30.0974 −1.01864
\(874\) −55.1419 −1.86520
\(875\) −10.0138 −0.338528
\(876\) −66.1980 −2.23662
\(877\) 19.5806 0.661189 0.330595 0.943773i \(-0.392751\pi\)
0.330595 + 0.943773i \(0.392751\pi\)
\(878\) −26.9009 −0.907862
\(879\) −37.6327 −1.26932
\(880\) −131.891 −4.44603
\(881\) −2.61183 −0.0879947 −0.0439973 0.999032i \(-0.514009\pi\)
−0.0439973 + 0.999032i \(0.514009\pi\)
\(882\) −22.5936 −0.760766
\(883\) −40.0782 −1.34874 −0.674369 0.738395i \(-0.735584\pi\)
−0.674369 + 0.738395i \(0.735584\pi\)
\(884\) −28.6671 −0.964177
\(885\) 21.5019 0.722780
\(886\) −8.74645 −0.293843
\(887\) −33.6910 −1.13123 −0.565616 0.824668i \(-0.691362\pi\)
−0.565616 + 0.824668i \(0.691362\pi\)
\(888\) 73.4786 2.46578
\(889\) 0.413570 0.0138707
\(890\) 49.1736 1.64830
\(891\) −7.60002 −0.254610
\(892\) −12.2566 −0.410380
\(893\) −8.79631 −0.294357
\(894\) 8.54711 0.285858
\(895\) −57.7734 −1.93115
\(896\) 4.39307 0.146762
\(897\) −38.5729 −1.28791
\(898\) −23.9435 −0.799006
\(899\) 3.50259 0.116818
\(900\) −54.7627 −1.82542
\(901\) 3.30077 0.109965
\(902\) −108.781 −3.62203
\(903\) −7.06978 −0.235268
\(904\) 25.3231 0.842234
\(905\) 26.7968 0.890755
\(906\) −27.1594 −0.902309
\(907\) 3.23262 0.107338 0.0536688 0.998559i \(-0.482908\pi\)
0.0536688 + 0.998559i \(0.482908\pi\)
\(908\) −8.09757 −0.268727
\(909\) 11.5574 0.383334
\(910\) −52.3225 −1.73447
\(911\) −10.8448 −0.359304 −0.179652 0.983730i \(-0.557497\pi\)
−0.179652 + 0.983730i \(0.557497\pi\)
\(912\) 33.4485 1.10759
\(913\) −12.1875 −0.403349
\(914\) −89.0686 −2.94613
\(915\) −51.3869 −1.69880
\(916\) 4.14023 0.136797
\(917\) −5.78922 −0.191177
\(918\) 18.0908 0.597084
\(919\) 20.7175 0.683409 0.341704 0.939808i \(-0.388996\pi\)
0.341704 + 0.939808i \(0.388996\pi\)
\(920\) 169.839 5.59944
\(921\) −5.89622 −0.194287
\(922\) 88.8987 2.92772
\(923\) −5.71572 −0.188135
\(924\) 28.6492 0.942490
\(925\) −63.6816 −2.09384
\(926\) 46.9043 1.54137
\(927\) 27.2036 0.893483
\(928\) 9.05377 0.297205
\(929\) −14.7468 −0.483826 −0.241913 0.970298i \(-0.577775\pi\)
−0.241913 + 0.970298i \(0.577775\pi\)
\(930\) −38.1926 −1.25238
\(931\) −17.2985 −0.566936
\(932\) −103.322 −3.38442
\(933\) −31.1672 −1.02037
\(934\) 4.90126 0.160374
\(935\) −18.7756 −0.614027
\(936\) −52.9582 −1.73099
\(937\) −14.3318 −0.468201 −0.234100 0.972212i \(-0.575214\pi\)
−0.234100 + 0.972212i \(0.575214\pi\)
\(938\) 19.9309 0.650768
\(939\) −37.5162 −1.22430
\(940\) 46.8944 1.52953
\(941\) −52.9303 −1.72548 −0.862739 0.505650i \(-0.831253\pi\)
−0.862739 + 0.505650i \(0.831253\pi\)
\(942\) −19.5993 −0.638581
\(943\) 68.0964 2.21752
\(944\) −45.8640 −1.49275
\(945\) 23.2159 0.755212
\(946\) 53.1805 1.72905
\(947\) 2.38532 0.0775124 0.0387562 0.999249i \(-0.487660\pi\)
0.0387562 + 0.999249i \(0.487660\pi\)
\(948\) 27.9298 0.907119
\(949\) 55.4813 1.80100
\(950\) −59.6329 −1.93475
\(951\) 13.5318 0.438798
\(952\) −10.9521 −0.354959
\(953\) 16.5195 0.535120 0.267560 0.963541i \(-0.413783\pi\)
0.267560 + 0.963541i \(0.413783\pi\)
\(954\) 10.5543 0.341708
\(955\) 27.5571 0.891725
\(956\) 46.6625 1.50917
\(957\) −5.00399 −0.161756
\(958\) 55.2285 1.78435
\(959\) 4.96835 0.160436
\(960\) −23.4273 −0.756113
\(961\) −18.7319 −0.604254
\(962\) −106.592 −3.43668
\(963\) 0.763635 0.0246078
\(964\) −21.4240 −0.690020
\(965\) 28.4866 0.917015
\(966\) −25.5070 −0.820675
\(967\) −53.7935 −1.72988 −0.864942 0.501873i \(-0.832645\pi\)
−0.864942 + 0.501873i \(0.832645\pi\)
\(968\) −46.3806 −1.49073
\(969\) 4.76164 0.152966
\(970\) 174.723 5.61002
\(971\) 27.2423 0.874248 0.437124 0.899401i \(-0.355997\pi\)
0.437124 + 0.899401i \(0.355997\pi\)
\(972\) 67.3616 2.16062
\(973\) 22.7073 0.727963
\(974\) 96.0155 3.07653
\(975\) −41.7144 −1.33593
\(976\) 109.609 3.50850
\(977\) −41.3841 −1.32400 −0.661998 0.749506i \(-0.730291\pi\)
−0.661998 + 0.749506i \(0.730291\pi\)
\(978\) 4.76815 0.152468
\(979\) 22.5662 0.721219
\(980\) 92.2210 2.94589
\(981\) −25.3664 −0.809888
\(982\) −28.3372 −0.904277
\(983\) −53.6967 −1.71266 −0.856330 0.516429i \(-0.827261\pi\)
−0.856330 + 0.516429i \(0.827261\pi\)
\(984\) −84.9719 −2.70881
\(985\) −77.8097 −2.47922
\(986\) 3.31104 0.105445
\(987\) −4.06891 −0.129515
\(988\) −70.1812 −2.23276
\(989\) −33.2906 −1.05858
\(990\) −60.0354 −1.90805
\(991\) −39.1892 −1.24489 −0.622443 0.782665i \(-0.713860\pi\)
−0.622443 + 0.782665i \(0.713860\pi\)
\(992\) 31.7116 1.00685
\(993\) −25.4522 −0.807702
\(994\) −3.77962 −0.119882
\(995\) 70.7734 2.24367
\(996\) −16.4779 −0.522121
\(997\) −12.6043 −0.399182 −0.199591 0.979879i \(-0.563961\pi\)
−0.199591 + 0.979879i \(0.563961\pi\)
\(998\) −81.6580 −2.58484
\(999\) 47.2958 1.49637
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 8033.2.a.b.1.9 153
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8033.2.a.b.1.9 153 1.1 even 1 trivial