Properties

Label 4029.2.a.g.1.19
Level $4029$
Weight $2$
Character 4029.1
Self dual yes
Analytic conductor $32.172$
Analytic rank $1$
Dimension $22$
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] = [4029,2,Mod(1,4029)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4029, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("4029.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4029 = 3 \cdot 17 \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4029.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: \(32.1717269744\)
Analytic rank: \(1\)
Dimension: \(22\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) \(=\) 4029.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.08589 q^{2} -1.00000 q^{3} +2.35095 q^{4} +0.140268 q^{5} -2.08589 q^{6} +1.76887 q^{7} +0.732041 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.08589 q^{2} -1.00000 q^{3} +2.35095 q^{4} +0.140268 q^{5} -2.08589 q^{6} +1.76887 q^{7} +0.732041 q^{8} +1.00000 q^{9} +0.292585 q^{10} -2.44783 q^{11} -2.35095 q^{12} +1.47150 q^{13} +3.68967 q^{14} -0.140268 q^{15} -3.17494 q^{16} -1.00000 q^{17} +2.08589 q^{18} -5.38878 q^{19} +0.329763 q^{20} -1.76887 q^{21} -5.10591 q^{22} -7.77124 q^{23} -0.732041 q^{24} -4.98032 q^{25} +3.06938 q^{26} -1.00000 q^{27} +4.15852 q^{28} -5.37989 q^{29} -0.292585 q^{30} +2.36220 q^{31} -8.08666 q^{32} +2.44783 q^{33} -2.08589 q^{34} +0.248116 q^{35} +2.35095 q^{36} +1.32119 q^{37} -11.2404 q^{38} -1.47150 q^{39} +0.102682 q^{40} +3.53576 q^{41} -3.68967 q^{42} -4.67768 q^{43} -5.75472 q^{44} +0.140268 q^{45} -16.2100 q^{46} +11.1381 q^{47} +3.17494 q^{48} -3.87111 q^{49} -10.3884 q^{50} +1.00000 q^{51} +3.45941 q^{52} -0.209911 q^{53} -2.08589 q^{54} -0.343353 q^{55} +1.29488 q^{56} +5.38878 q^{57} -11.2219 q^{58} +9.96744 q^{59} -0.329763 q^{60} +1.71172 q^{61} +4.92729 q^{62} +1.76887 q^{63} -10.5180 q^{64} +0.206404 q^{65} +5.10591 q^{66} -9.81778 q^{67} -2.35095 q^{68} +7.77124 q^{69} +0.517543 q^{70} +3.49626 q^{71} +0.732041 q^{72} +5.72483 q^{73} +2.75585 q^{74} +4.98032 q^{75} -12.6687 q^{76} -4.32989 q^{77} -3.06938 q^{78} -1.00000 q^{79} -0.445343 q^{80} +1.00000 q^{81} +7.37522 q^{82} -17.4586 q^{83} -4.15852 q^{84} -0.140268 q^{85} -9.75714 q^{86} +5.37989 q^{87} -1.79191 q^{88} +5.07693 q^{89} +0.292585 q^{90} +2.60288 q^{91} -18.2698 q^{92} -2.36220 q^{93} +23.2328 q^{94} -0.755874 q^{95} +8.08666 q^{96} -9.54399 q^{97} -8.07472 q^{98} -2.44783 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9} - 5 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 7 q^{14} - 5 q^{15} - 22 q^{17} + 2 q^{18} - 36 q^{19} + 4 q^{21} - 9 q^{22} + 21 q^{23} - 6 q^{24} + 9 q^{25} - 16 q^{26} - 22 q^{27} - 17 q^{28} - q^{29} + 5 q^{30} - 12 q^{31} - 11 q^{32} + 2 q^{33} - 2 q^{34} - 14 q^{35} + 16 q^{36} - 6 q^{37} + q^{38} + 11 q^{39} - 24 q^{40} - 17 q^{41} + 7 q^{42} - 36 q^{43} + 16 q^{44} + 5 q^{45} - 23 q^{46} - 17 q^{47} - 6 q^{49} - 33 q^{50} + 22 q^{51} - 57 q^{52} - 2 q^{53} - 2 q^{54} - 24 q^{55} - 64 q^{56} + 36 q^{57} - 7 q^{58} - 59 q^{59} - 30 q^{61} - 4 q^{62} - 4 q^{63} - 22 q^{64} + 36 q^{65} + 9 q^{66} - 16 q^{67} - 16 q^{68} - 21 q^{69} - 39 q^{70} - 11 q^{71} + 6 q^{72} - 19 q^{73} - 28 q^{74} - 9 q^{75} - 77 q^{76} + 2 q^{77} + 16 q^{78} - 22 q^{79} - 2 q^{80} + 22 q^{81} + 33 q^{82} - 23 q^{83} + 17 q^{84} - 5 q^{85} + 6 q^{86} + q^{87} - 23 q^{88} + 12 q^{89} - 5 q^{90} - 24 q^{91} + 66 q^{92} + 12 q^{93} - 61 q^{94} - 11 q^{95} + 11 q^{96} - 9 q^{97} + 17 q^{98} - 2 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.08589 1.47495 0.737474 0.675375i \(-0.236018\pi\)
0.737474 + 0.675375i \(0.236018\pi\)
\(3\) −1.00000 −0.577350
\(4\) 2.35095 1.17547
\(5\) 0.140268 0.0627299 0.0313649 0.999508i \(-0.490015\pi\)
0.0313649 + 0.999508i \(0.490015\pi\)
\(6\) −2.08589 −0.851562
\(7\) 1.76887 0.668569 0.334285 0.942472i \(-0.391505\pi\)
0.334285 + 0.942472i \(0.391505\pi\)
\(8\) 0.732041 0.258816
\(9\) 1.00000 0.333333
\(10\) 0.292585 0.0925234
\(11\) −2.44783 −0.738048 −0.369024 0.929420i \(-0.620308\pi\)
−0.369024 + 0.929420i \(0.620308\pi\)
\(12\) −2.35095 −0.678660
\(13\) 1.47150 0.408120 0.204060 0.978958i \(-0.434586\pi\)
0.204060 + 0.978958i \(0.434586\pi\)
\(14\) 3.68967 0.986105
\(15\) −0.140268 −0.0362171
\(16\) −3.17494 −0.793734
\(17\) −1.00000 −0.242536
\(18\) 2.08589 0.491650
\(19\) −5.38878 −1.23627 −0.618135 0.786072i \(-0.712112\pi\)
−0.618135 + 0.786072i \(0.712112\pi\)
\(20\) 0.329763 0.0737374
\(21\) −1.76887 −0.385999
\(22\) −5.10591 −1.08858
\(23\) −7.77124 −1.62042 −0.810208 0.586143i \(-0.800646\pi\)
−0.810208 + 0.586143i \(0.800646\pi\)
\(24\) −0.732041 −0.149427
\(25\) −4.98032 −0.996065
\(26\) 3.06938 0.601956
\(27\) −1.00000 −0.192450
\(28\) 4.15852 0.785886
\(29\) −5.37989 −0.999020 −0.499510 0.866308i \(-0.666487\pi\)
−0.499510 + 0.866308i \(0.666487\pi\)
\(30\) −0.292585 −0.0534184
\(31\) 2.36220 0.424264 0.212132 0.977241i \(-0.431959\pi\)
0.212132 + 0.977241i \(0.431959\pi\)
\(32\) −8.08666 −1.42953
\(33\) 2.44783 0.426112
\(34\) −2.08589 −0.357728
\(35\) 0.248116 0.0419393
\(36\) 2.35095 0.391825
\(37\) 1.32119 0.217202 0.108601 0.994085i \(-0.465363\pi\)
0.108601 + 0.994085i \(0.465363\pi\)
\(38\) −11.2404 −1.82344
\(39\) −1.47150 −0.235628
\(40\) 0.102682 0.0162355
\(41\) 3.53576 0.552194 0.276097 0.961130i \(-0.410959\pi\)
0.276097 + 0.961130i \(0.410959\pi\)
\(42\) −3.68967 −0.569328
\(43\) −4.67768 −0.713340 −0.356670 0.934230i \(-0.616088\pi\)
−0.356670 + 0.934230i \(0.616088\pi\)
\(44\) −5.75472 −0.867557
\(45\) 0.140268 0.0209100
\(46\) −16.2100 −2.39003
\(47\) 11.1381 1.62466 0.812328 0.583201i \(-0.198200\pi\)
0.812328 + 0.583201i \(0.198200\pi\)
\(48\) 3.17494 0.458263
\(49\) −3.87111 −0.553015
\(50\) −10.3884 −1.46914
\(51\) 1.00000 0.140028
\(52\) 3.45941 0.479734
\(53\) −0.209911 −0.0288334 −0.0144167 0.999896i \(-0.504589\pi\)
−0.0144167 + 0.999896i \(0.504589\pi\)
\(54\) −2.08589 −0.283854
\(55\) −0.343353 −0.0462977
\(56\) 1.29488 0.173036
\(57\) 5.38878 0.713761
\(58\) −11.2219 −1.47350
\(59\) 9.96744 1.29765 0.648825 0.760938i \(-0.275261\pi\)
0.648825 + 0.760938i \(0.275261\pi\)
\(60\) −0.329763 −0.0425723
\(61\) 1.71172 0.219163 0.109581 0.993978i \(-0.465049\pi\)
0.109581 + 0.993978i \(0.465049\pi\)
\(62\) 4.92729 0.625767
\(63\) 1.76887 0.222856
\(64\) −10.5180 −1.31475
\(65\) 0.206404 0.0256013
\(66\) 5.10591 0.628494
\(67\) −9.81778 −1.19943 −0.599716 0.800213i \(-0.704720\pi\)
−0.599716 + 0.800213i \(0.704720\pi\)
\(68\) −2.35095 −0.285094
\(69\) 7.77124 0.935548
\(70\) 0.517543 0.0618583
\(71\) 3.49626 0.414929 0.207465 0.978243i \(-0.433479\pi\)
0.207465 + 0.978243i \(0.433479\pi\)
\(72\) 0.732041 0.0862719
\(73\) 5.72483 0.670040 0.335020 0.942211i \(-0.391257\pi\)
0.335020 + 0.942211i \(0.391257\pi\)
\(74\) 2.75585 0.320361
\(75\) 4.98032 0.575078
\(76\) −12.6687 −1.45320
\(77\) −4.32989 −0.493436
\(78\) −3.06938 −0.347539
\(79\) −1.00000 −0.112509
\(80\) −0.445343 −0.0497909
\(81\) 1.00000 0.111111
\(82\) 7.37522 0.814457
\(83\) −17.4586 −1.91633 −0.958165 0.286217i \(-0.907602\pi\)
−0.958165 + 0.286217i \(0.907602\pi\)
\(84\) −4.15852 −0.453731
\(85\) −0.140268 −0.0152142
\(86\) −9.75714 −1.05214
\(87\) 5.37989 0.576785
\(88\) −1.79191 −0.191018
\(89\) 5.07693 0.538154 0.269077 0.963119i \(-0.413281\pi\)
0.269077 + 0.963119i \(0.413281\pi\)
\(90\) 0.292585 0.0308411
\(91\) 2.60288 0.272856
\(92\) −18.2698 −1.90476
\(93\) −2.36220 −0.244949
\(94\) 23.2328 2.39628
\(95\) −0.755874 −0.0775511
\(96\) 8.08666 0.825342
\(97\) −9.54399 −0.969045 −0.484523 0.874779i \(-0.661007\pi\)
−0.484523 + 0.874779i \(0.661007\pi\)
\(98\) −8.07472 −0.815669
\(99\) −2.44783 −0.246016
\(100\) −11.7085 −1.17085
\(101\) −2.06114 −0.205091 −0.102545 0.994728i \(-0.532699\pi\)
−0.102545 + 0.994728i \(0.532699\pi\)
\(102\) 2.08589 0.206534
\(103\) −5.73622 −0.565207 −0.282603 0.959237i \(-0.591198\pi\)
−0.282603 + 0.959237i \(0.591198\pi\)
\(104\) 1.07720 0.105628
\(105\) −0.248116 −0.0242136
\(106\) −0.437851 −0.0425278
\(107\) −12.4941 −1.20785 −0.603925 0.797041i \(-0.706398\pi\)
−0.603925 + 0.797041i \(0.706398\pi\)
\(108\) −2.35095 −0.226220
\(109\) −6.84570 −0.655699 −0.327850 0.944730i \(-0.606324\pi\)
−0.327850 + 0.944730i \(0.606324\pi\)
\(110\) −0.716197 −0.0682867
\(111\) −1.32119 −0.125401
\(112\) −5.61604 −0.530666
\(113\) 14.0784 1.32439 0.662194 0.749332i \(-0.269625\pi\)
0.662194 + 0.749332i \(0.269625\pi\)
\(114\) 11.2404 1.05276
\(115\) −1.09006 −0.101648
\(116\) −12.6478 −1.17432
\(117\) 1.47150 0.136040
\(118\) 20.7910 1.91397
\(119\) −1.76887 −0.162152
\(120\) −0.102682 −0.00937355
\(121\) −5.00813 −0.455285
\(122\) 3.57046 0.323254
\(123\) −3.53576 −0.318809
\(124\) 5.55341 0.498711
\(125\) −1.39992 −0.125213
\(126\) 3.68967 0.328702
\(127\) 19.6610 1.74463 0.872316 0.488943i \(-0.162617\pi\)
0.872316 + 0.488943i \(0.162617\pi\)
\(128\) −5.76617 −0.509662
\(129\) 4.67768 0.411847
\(130\) 0.430537 0.0377606
\(131\) 8.36193 0.730586 0.365293 0.930893i \(-0.380969\pi\)
0.365293 + 0.930893i \(0.380969\pi\)
\(132\) 5.75472 0.500884
\(133\) −9.53203 −0.826532
\(134\) −20.4788 −1.76910
\(135\) −0.140268 −0.0120724
\(136\) −0.732041 −0.0627720
\(137\) 15.8738 1.35619 0.678093 0.734976i \(-0.262806\pi\)
0.678093 + 0.734976i \(0.262806\pi\)
\(138\) 16.2100 1.37988
\(139\) −18.7464 −1.59005 −0.795026 0.606575i \(-0.792543\pi\)
−0.795026 + 0.606575i \(0.792543\pi\)
\(140\) 0.583308 0.0492985
\(141\) −11.1381 −0.937996
\(142\) 7.29282 0.611999
\(143\) −3.60197 −0.301212
\(144\) −3.17494 −0.264578
\(145\) −0.754628 −0.0626684
\(146\) 11.9414 0.988275
\(147\) 3.87111 0.319284
\(148\) 3.10604 0.255315
\(149\) −10.7818 −0.883277 −0.441638 0.897193i \(-0.645603\pi\)
−0.441638 + 0.897193i \(0.645603\pi\)
\(150\) 10.3884 0.848211
\(151\) −18.4500 −1.50144 −0.750720 0.660621i \(-0.770293\pi\)
−0.750720 + 0.660621i \(0.770293\pi\)
\(152\) −3.94481 −0.319966
\(153\) −1.00000 −0.0808452
\(154\) −9.03168 −0.727793
\(155\) 0.331342 0.0266140
\(156\) −3.45941 −0.276975
\(157\) −15.5799 −1.24341 −0.621706 0.783251i \(-0.713560\pi\)
−0.621706 + 0.783251i \(0.713560\pi\)
\(158\) −2.08589 −0.165945
\(159\) 0.209911 0.0166470
\(160\) −1.13430 −0.0896745
\(161\) −13.7463 −1.08336
\(162\) 2.08589 0.163883
\(163\) −14.5802 −1.14201 −0.571006 0.820946i \(-0.693447\pi\)
−0.571006 + 0.820946i \(0.693447\pi\)
\(164\) 8.31240 0.649089
\(165\) 0.343353 0.0267300
\(166\) −36.4168 −2.82649
\(167\) 7.87714 0.609551 0.304776 0.952424i \(-0.401419\pi\)
0.304776 + 0.952424i \(0.401419\pi\)
\(168\) −1.29488 −0.0999025
\(169\) −10.8347 −0.833438
\(170\) −0.292585 −0.0224402
\(171\) −5.38878 −0.412090
\(172\) −10.9970 −0.838513
\(173\) 2.59830 0.197545 0.0987726 0.995110i \(-0.468508\pi\)
0.0987726 + 0.995110i \(0.468508\pi\)
\(174\) 11.2219 0.850728
\(175\) −8.80953 −0.665938
\(176\) 7.77171 0.585814
\(177\) −9.96744 −0.749198
\(178\) 10.5899 0.793749
\(179\) 6.06085 0.453009 0.226504 0.974010i \(-0.427270\pi\)
0.226504 + 0.974010i \(0.427270\pi\)
\(180\) 0.329763 0.0245791
\(181\) 1.82586 0.135715 0.0678574 0.997695i \(-0.478384\pi\)
0.0678574 + 0.997695i \(0.478384\pi\)
\(182\) 5.42933 0.402449
\(183\) −1.71172 −0.126534
\(184\) −5.68887 −0.419389
\(185\) 0.185320 0.0136250
\(186\) −4.92729 −0.361287
\(187\) 2.44783 0.179003
\(188\) 26.1851 1.90974
\(189\) −1.76887 −0.128666
\(190\) −1.57667 −0.114384
\(191\) −3.46885 −0.250997 −0.125499 0.992094i \(-0.540053\pi\)
−0.125499 + 0.992094i \(0.540053\pi\)
\(192\) 10.5180 0.759074
\(193\) 26.3873 1.89940 0.949699 0.313165i \(-0.101389\pi\)
0.949699 + 0.313165i \(0.101389\pi\)
\(194\) −19.9077 −1.42929
\(195\) −0.206404 −0.0147809
\(196\) −9.10078 −0.650055
\(197\) 18.7104 1.33306 0.666531 0.745477i \(-0.267778\pi\)
0.666531 + 0.745477i \(0.267778\pi\)
\(198\) −5.10591 −0.362861
\(199\) −26.0633 −1.84758 −0.923790 0.382899i \(-0.874926\pi\)
−0.923790 + 0.382899i \(0.874926\pi\)
\(200\) −3.64580 −0.257797
\(201\) 9.81778 0.692493
\(202\) −4.29931 −0.302498
\(203\) −9.51631 −0.667914
\(204\) 2.35095 0.164599
\(205\) 0.495955 0.0346390
\(206\) −11.9651 −0.833651
\(207\) −7.77124 −0.540139
\(208\) −4.67191 −0.323939
\(209\) 13.1908 0.912427
\(210\) −0.517543 −0.0357139
\(211\) 20.8950 1.43847 0.719235 0.694767i \(-0.244493\pi\)
0.719235 + 0.694767i \(0.244493\pi\)
\(212\) −0.493489 −0.0338930
\(213\) −3.49626 −0.239560
\(214\) −26.0614 −1.78152
\(215\) −0.656130 −0.0447477
\(216\) −0.732041 −0.0498091
\(217\) 4.17842 0.283649
\(218\) −14.2794 −0.967123
\(219\) −5.72483 −0.386848
\(220\) −0.807205 −0.0544217
\(221\) −1.47150 −0.0989836
\(222\) −2.75585 −0.184961
\(223\) −6.89174 −0.461505 −0.230753 0.973012i \(-0.574119\pi\)
−0.230753 + 0.973012i \(0.574119\pi\)
\(224\) −14.3042 −0.955742
\(225\) −4.98032 −0.332022
\(226\) 29.3661 1.95341
\(227\) −16.4113 −1.08925 −0.544627 0.838679i \(-0.683329\pi\)
−0.544627 + 0.838679i \(0.683329\pi\)
\(228\) 12.6687 0.839008
\(229\) −15.9846 −1.05629 −0.528146 0.849153i \(-0.677113\pi\)
−0.528146 + 0.849153i \(0.677113\pi\)
\(230\) −2.27375 −0.149926
\(231\) 4.32989 0.284886
\(232\) −3.93830 −0.258562
\(233\) 6.04582 0.396075 0.198037 0.980194i \(-0.436543\pi\)
0.198037 + 0.980194i \(0.436543\pi\)
\(234\) 3.06938 0.200652
\(235\) 1.56232 0.101914
\(236\) 23.4329 1.52535
\(237\) 1.00000 0.0649570
\(238\) −3.68967 −0.239166
\(239\) −10.6450 −0.688568 −0.344284 0.938866i \(-0.611878\pi\)
−0.344284 + 0.938866i \(0.611878\pi\)
\(240\) 0.445343 0.0287468
\(241\) 2.95261 0.190195 0.0950973 0.995468i \(-0.469684\pi\)
0.0950973 + 0.995468i \(0.469684\pi\)
\(242\) −10.4464 −0.671521
\(243\) −1.00000 −0.0641500
\(244\) 4.02416 0.257620
\(245\) −0.542994 −0.0346906
\(246\) −7.37522 −0.470227
\(247\) −7.92957 −0.504546
\(248\) 1.72923 0.109806
\(249\) 17.4586 1.10639
\(250\) −2.92009 −0.184683
\(251\) 15.6584 0.988349 0.494174 0.869363i \(-0.335470\pi\)
0.494174 + 0.869363i \(0.335470\pi\)
\(252\) 4.15852 0.261962
\(253\) 19.0227 1.19595
\(254\) 41.0107 2.57324
\(255\) 0.140268 0.00878394
\(256\) 9.00846 0.563029
\(257\) −22.2563 −1.38831 −0.694155 0.719825i \(-0.744222\pi\)
−0.694155 + 0.719825i \(0.744222\pi\)
\(258\) 9.75714 0.607453
\(259\) 2.33700 0.145214
\(260\) 0.485246 0.0300937
\(261\) −5.37989 −0.333007
\(262\) 17.4421 1.07758
\(263\) 3.39626 0.209422 0.104711 0.994503i \(-0.466608\pi\)
0.104711 + 0.994503i \(0.466608\pi\)
\(264\) 1.79191 0.110285
\(265\) −0.0294438 −0.00180872
\(266\) −19.8828 −1.21909
\(267\) −5.07693 −0.310703
\(268\) −23.0811 −1.40990
\(269\) 20.1378 1.22783 0.613913 0.789374i \(-0.289594\pi\)
0.613913 + 0.789374i \(0.289594\pi\)
\(270\) −0.292585 −0.0178061
\(271\) 27.4628 1.66825 0.834125 0.551576i \(-0.185973\pi\)
0.834125 + 0.551576i \(0.185973\pi\)
\(272\) 3.17494 0.192509
\(273\) −2.60288 −0.157534
\(274\) 33.1110 2.00031
\(275\) 12.1910 0.735144
\(276\) 18.2698 1.09971
\(277\) −22.0555 −1.32519 −0.662593 0.748980i \(-0.730544\pi\)
−0.662593 + 0.748980i \(0.730544\pi\)
\(278\) −39.1031 −2.34525
\(279\) 2.36220 0.141421
\(280\) 0.181631 0.0108545
\(281\) 18.0037 1.07401 0.537004 0.843579i \(-0.319556\pi\)
0.537004 + 0.843579i \(0.319556\pi\)
\(282\) −23.2328 −1.38350
\(283\) 19.1507 1.13839 0.569196 0.822202i \(-0.307255\pi\)
0.569196 + 0.822202i \(0.307255\pi\)
\(284\) 8.21952 0.487739
\(285\) 0.755874 0.0447741
\(286\) −7.51333 −0.444273
\(287\) 6.25430 0.369180
\(288\) −8.08666 −0.476511
\(289\) 1.00000 0.0588235
\(290\) −1.57407 −0.0924327
\(291\) 9.54399 0.559479
\(292\) 13.4588 0.787615
\(293\) −9.45058 −0.552109 −0.276054 0.961142i \(-0.589027\pi\)
−0.276054 + 0.961142i \(0.589027\pi\)
\(294\) 8.07472 0.470927
\(295\) 1.39811 0.0814014
\(296\) 0.967162 0.0562151
\(297\) 2.44783 0.142037
\(298\) −22.4896 −1.30279
\(299\) −11.4354 −0.661324
\(300\) 11.7085 0.675990
\(301\) −8.27420 −0.476917
\(302\) −38.4847 −2.21455
\(303\) 2.06114 0.118409
\(304\) 17.1090 0.981270
\(305\) 0.240100 0.0137481
\(306\) −2.08589 −0.119243
\(307\) −1.88031 −0.107315 −0.0536574 0.998559i \(-0.517088\pi\)
−0.0536574 + 0.998559i \(0.517088\pi\)
\(308\) −10.1793 −0.580022
\(309\) 5.73622 0.326322
\(310\) 0.691143 0.0392543
\(311\) 20.9805 1.18969 0.594847 0.803839i \(-0.297213\pi\)
0.594847 + 0.803839i \(0.297213\pi\)
\(312\) −1.07720 −0.0609842
\(313\) 33.9738 1.92031 0.960157 0.279460i \(-0.0901555\pi\)
0.960157 + 0.279460i \(0.0901555\pi\)
\(314\) −32.4980 −1.83397
\(315\) 0.248116 0.0139798
\(316\) −2.35095 −0.132251
\(317\) 18.0211 1.01217 0.506083 0.862485i \(-0.331093\pi\)
0.506083 + 0.862485i \(0.331093\pi\)
\(318\) 0.437851 0.0245535
\(319\) 13.1691 0.737325
\(320\) −1.47535 −0.0824744
\(321\) 12.4941 0.697353
\(322\) −28.6733 −1.59790
\(323\) 5.38878 0.299840
\(324\) 2.35095 0.130608
\(325\) −7.32853 −0.406514
\(326\) −30.4128 −1.68441
\(327\) 6.84570 0.378568
\(328\) 2.58832 0.142916
\(329\) 19.7018 1.08619
\(330\) 0.716197 0.0394254
\(331\) 18.2450 1.00284 0.501418 0.865205i \(-0.332812\pi\)
0.501418 + 0.865205i \(0.332812\pi\)
\(332\) −41.0443 −2.25260
\(333\) 1.32119 0.0724005
\(334\) 16.4309 0.899057
\(335\) −1.37712 −0.0752403
\(336\) 5.61604 0.306380
\(337\) 18.9468 1.03210 0.516049 0.856559i \(-0.327402\pi\)
0.516049 + 0.856559i \(0.327402\pi\)
\(338\) −22.6000 −1.22928
\(339\) −14.0784 −0.764636
\(340\) −0.329763 −0.0178839
\(341\) −5.78226 −0.313127
\(342\) −11.2404 −0.607812
\(343\) −19.2295 −1.03830
\(344\) −3.42426 −0.184624
\(345\) 1.09006 0.0586868
\(346\) 5.41978 0.291369
\(347\) 28.8043 1.54630 0.773149 0.634225i \(-0.218681\pi\)
0.773149 + 0.634225i \(0.218681\pi\)
\(348\) 12.6478 0.677996
\(349\) 26.0275 1.39322 0.696609 0.717451i \(-0.254691\pi\)
0.696609 + 0.717451i \(0.254691\pi\)
\(350\) −18.3757 −0.982225
\(351\) −1.47150 −0.0785427
\(352\) 19.7948 1.05506
\(353\) −29.6973 −1.58063 −0.790315 0.612701i \(-0.790083\pi\)
−0.790315 + 0.612701i \(0.790083\pi\)
\(354\) −20.7910 −1.10503
\(355\) 0.490414 0.0260285
\(356\) 11.9356 0.632586
\(357\) 1.76887 0.0936184
\(358\) 12.6423 0.668165
\(359\) −24.1413 −1.27413 −0.637064 0.770811i \(-0.719852\pi\)
−0.637064 + 0.770811i \(0.719852\pi\)
\(360\) 0.102682 0.00541182
\(361\) 10.0389 0.528364
\(362\) 3.80854 0.200172
\(363\) 5.00813 0.262859
\(364\) 6.11924 0.320736
\(365\) 0.803011 0.0420315
\(366\) −3.57046 −0.186631
\(367\) −11.1079 −0.579828 −0.289914 0.957053i \(-0.593627\pi\)
−0.289914 + 0.957053i \(0.593627\pi\)
\(368\) 24.6732 1.28618
\(369\) 3.53576 0.184065
\(370\) 0.386558 0.0200962
\(371\) −0.371304 −0.0192771
\(372\) −5.55341 −0.287931
\(373\) −33.2434 −1.72128 −0.860639 0.509216i \(-0.829936\pi\)
−0.860639 + 0.509216i \(0.829936\pi\)
\(374\) 5.10591 0.264020
\(375\) 1.39992 0.0722917
\(376\) 8.15353 0.420486
\(377\) −7.91649 −0.407720
\(378\) −3.68967 −0.189776
\(379\) −23.2407 −1.19379 −0.596897 0.802318i \(-0.703600\pi\)
−0.596897 + 0.802318i \(0.703600\pi\)
\(380\) −1.77702 −0.0911593
\(381\) −19.6610 −1.00726
\(382\) −7.23565 −0.370208
\(383\) −23.6303 −1.20745 −0.603725 0.797193i \(-0.706317\pi\)
−0.603725 + 0.797193i \(0.706317\pi\)
\(384\) 5.76617 0.294253
\(385\) −0.607346 −0.0309532
\(386\) 55.0410 2.80151
\(387\) −4.67768 −0.237780
\(388\) −22.4374 −1.13909
\(389\) 14.2837 0.724212 0.362106 0.932137i \(-0.382058\pi\)
0.362106 + 0.932137i \(0.382058\pi\)
\(390\) −0.430537 −0.0218011
\(391\) 7.77124 0.393009
\(392\) −2.83381 −0.143129
\(393\) −8.36193 −0.421804
\(394\) 39.0279 1.96620
\(395\) −0.140268 −0.00705766
\(396\) −5.75472 −0.289186
\(397\) 31.1662 1.56419 0.782093 0.623162i \(-0.214152\pi\)
0.782093 + 0.623162i \(0.214152\pi\)
\(398\) −54.3653 −2.72509
\(399\) 9.53203 0.477199
\(400\) 15.8122 0.790611
\(401\) 6.19151 0.309189 0.154595 0.987978i \(-0.450593\pi\)
0.154595 + 0.987978i \(0.450593\pi\)
\(402\) 20.4788 1.02139
\(403\) 3.47597 0.173150
\(404\) −4.84563 −0.241079
\(405\) 0.140268 0.00696999
\(406\) −19.8500 −0.985139
\(407\) −3.23404 −0.160305
\(408\) 0.732041 0.0362414
\(409\) −26.6687 −1.31868 −0.659342 0.751843i \(-0.729165\pi\)
−0.659342 + 0.751843i \(0.729165\pi\)
\(410\) 1.03451 0.0510908
\(411\) −15.8738 −0.782995
\(412\) −13.4856 −0.664386
\(413\) 17.6311 0.867568
\(414\) −16.2100 −0.796677
\(415\) −2.44889 −0.120211
\(416\) −11.8995 −0.583421
\(417\) 18.7464 0.918017
\(418\) 27.5146 1.34578
\(419\) −4.41752 −0.215810 −0.107905 0.994161i \(-0.534414\pi\)
−0.107905 + 0.994161i \(0.534414\pi\)
\(420\) −0.583308 −0.0284625
\(421\) 0.965972 0.0470786 0.0235393 0.999723i \(-0.492507\pi\)
0.0235393 + 0.999723i \(0.492507\pi\)
\(422\) 43.5847 2.12167
\(423\) 11.1381 0.541552
\(424\) −0.153663 −0.00746254
\(425\) 4.98032 0.241581
\(426\) −7.29282 −0.353338
\(427\) 3.02780 0.146526
\(428\) −29.3730 −1.41980
\(429\) 3.60197 0.173905
\(430\) −1.36862 −0.0660006
\(431\) 15.1526 0.729877 0.364939 0.931032i \(-0.381090\pi\)
0.364939 + 0.931032i \(0.381090\pi\)
\(432\) 3.17494 0.152754
\(433\) −5.53821 −0.266149 −0.133075 0.991106i \(-0.542485\pi\)
−0.133075 + 0.991106i \(0.542485\pi\)
\(434\) 8.71573 0.418368
\(435\) 0.754628 0.0361816
\(436\) −16.0939 −0.770758
\(437\) 41.8775 2.00327
\(438\) −11.9414 −0.570581
\(439\) −12.1857 −0.581592 −0.290796 0.956785i \(-0.593920\pi\)
−0.290796 + 0.956785i \(0.593920\pi\)
\(440\) −0.251348 −0.0119826
\(441\) −3.87111 −0.184338
\(442\) −3.06938 −0.145996
\(443\) 5.77436 0.274348 0.137174 0.990547i \(-0.456198\pi\)
0.137174 + 0.990547i \(0.456198\pi\)
\(444\) −3.10604 −0.147406
\(445\) 0.712132 0.0337583
\(446\) −14.3754 −0.680697
\(447\) 10.7818 0.509960
\(448\) −18.6050 −0.879004
\(449\) −3.28196 −0.154885 −0.0774426 0.996997i \(-0.524675\pi\)
−0.0774426 + 0.996997i \(0.524675\pi\)
\(450\) −10.3884 −0.489715
\(451\) −8.65495 −0.407546
\(452\) 33.0977 1.55679
\(453\) 18.4500 0.866857
\(454\) −34.2321 −1.60659
\(455\) 0.365102 0.0171162
\(456\) 3.94481 0.184732
\(457\) 34.4508 1.61154 0.805770 0.592229i \(-0.201752\pi\)
0.805770 + 0.592229i \(0.201752\pi\)
\(458\) −33.3422 −1.55798
\(459\) 1.00000 0.0466760
\(460\) −2.56267 −0.119485
\(461\) 21.9961 1.02446 0.512231 0.858848i \(-0.328819\pi\)
0.512231 + 0.858848i \(0.328819\pi\)
\(462\) 9.03168 0.420192
\(463\) 1.56414 0.0726920 0.0363460 0.999339i \(-0.488428\pi\)
0.0363460 + 0.999339i \(0.488428\pi\)
\(464\) 17.0808 0.792957
\(465\) −0.331342 −0.0153656
\(466\) 12.6109 0.584190
\(467\) −11.7478 −0.543622 −0.271811 0.962351i \(-0.587623\pi\)
−0.271811 + 0.962351i \(0.587623\pi\)
\(468\) 3.45941 0.159911
\(469\) −17.3664 −0.801904
\(470\) 3.25883 0.150319
\(471\) 15.5799 0.717884
\(472\) 7.29657 0.335852
\(473\) 11.4502 0.526479
\(474\) 2.08589 0.0958082
\(475\) 26.8379 1.23141
\(476\) −4.15852 −0.190605
\(477\) −0.209911 −0.00961114
\(478\) −22.2043 −1.01560
\(479\) −34.6987 −1.58542 −0.792711 0.609597i \(-0.791331\pi\)
−0.792711 + 0.609597i \(0.791331\pi\)
\(480\) 1.13430 0.0517736
\(481\) 1.94412 0.0886442
\(482\) 6.15884 0.280527
\(483\) 13.7463 0.625478
\(484\) −11.7739 −0.535175
\(485\) −1.33872 −0.0607881
\(486\) −2.08589 −0.0946180
\(487\) −18.5027 −0.838435 −0.419218 0.907886i \(-0.637696\pi\)
−0.419218 + 0.907886i \(0.637696\pi\)
\(488\) 1.25305 0.0567228
\(489\) 14.5802 0.659341
\(490\) −1.13263 −0.0511668
\(491\) −24.0229 −1.08414 −0.542069 0.840334i \(-0.682359\pi\)
−0.542069 + 0.840334i \(0.682359\pi\)
\(492\) −8.31240 −0.374752
\(493\) 5.37989 0.242298
\(494\) −16.5402 −0.744180
\(495\) −0.343353 −0.0154326
\(496\) −7.49984 −0.336753
\(497\) 6.18441 0.277409
\(498\) 36.4168 1.63187
\(499\) −2.78339 −0.124602 −0.0623008 0.998057i \(-0.519844\pi\)
−0.0623008 + 0.998057i \(0.519844\pi\)
\(500\) −3.29115 −0.147185
\(501\) −7.87714 −0.351925
\(502\) 32.6617 1.45776
\(503\) −1.15409 −0.0514585 −0.0257292 0.999669i \(-0.508191\pi\)
−0.0257292 + 0.999669i \(0.508191\pi\)
\(504\) 1.29488 0.0576787
\(505\) −0.289112 −0.0128653
\(506\) 39.6793 1.76396
\(507\) 10.8347 0.481186
\(508\) 46.2220 2.05077
\(509\) 4.25435 0.188571 0.0942853 0.995545i \(-0.469943\pi\)
0.0942853 + 0.995545i \(0.469943\pi\)
\(510\) 0.292585 0.0129559
\(511\) 10.1265 0.447968
\(512\) 30.3230 1.34010
\(513\) 5.38878 0.237920
\(514\) −46.4243 −2.04769
\(515\) −0.804610 −0.0354553
\(516\) 10.9970 0.484116
\(517\) −27.2641 −1.19908
\(518\) 4.87473 0.214184
\(519\) −2.59830 −0.114053
\(520\) 0.151096 0.00662602
\(521\) −32.4163 −1.42018 −0.710091 0.704110i \(-0.751346\pi\)
−0.710091 + 0.704110i \(0.751346\pi\)
\(522\) −11.2219 −0.491168
\(523\) 2.15610 0.0942796 0.0471398 0.998888i \(-0.484989\pi\)
0.0471398 + 0.998888i \(0.484989\pi\)
\(524\) 19.6585 0.858785
\(525\) 8.80953 0.384480
\(526\) 7.08423 0.308887
\(527\) −2.36220 −0.102899
\(528\) −7.77171 −0.338220
\(529\) 37.3922 1.62575
\(530\) −0.0614166 −0.00266777
\(531\) 9.96744 0.432550
\(532\) −22.4093 −0.971567
\(533\) 5.20287 0.225361
\(534\) −10.5899 −0.458271
\(535\) −1.75253 −0.0757683
\(536\) −7.18702 −0.310432
\(537\) −6.06085 −0.261545
\(538\) 42.0054 1.81098
\(539\) 9.47581 0.408152
\(540\) −0.329763 −0.0141908
\(541\) 32.6923 1.40555 0.702777 0.711411i \(-0.251943\pi\)
0.702777 + 0.711411i \(0.251943\pi\)
\(542\) 57.2846 2.46058
\(543\) −1.82586 −0.0783550
\(544\) 8.08666 0.346713
\(545\) −0.960235 −0.0411319
\(546\) −5.42933 −0.232354
\(547\) −28.1774 −1.20478 −0.602389 0.798203i \(-0.705784\pi\)
−0.602389 + 0.798203i \(0.705784\pi\)
\(548\) 37.3184 1.59416
\(549\) 1.71172 0.0730543
\(550\) 25.4291 1.08430
\(551\) 28.9910 1.23506
\(552\) 5.68887 0.242134
\(553\) −1.76887 −0.0752199
\(554\) −46.0054 −1.95458
\(555\) −0.185320 −0.00786641
\(556\) −44.0719 −1.86907
\(557\) −9.44003 −0.399987 −0.199993 0.979797i \(-0.564092\pi\)
−0.199993 + 0.979797i \(0.564092\pi\)
\(558\) 4.92729 0.208589
\(559\) −6.88319 −0.291128
\(560\) −0.787753 −0.0332886
\(561\) −2.44783 −0.103347
\(562\) 37.5537 1.58411
\(563\) −41.1339 −1.73359 −0.866794 0.498667i \(-0.833823\pi\)
−0.866794 + 0.498667i \(0.833823\pi\)
\(564\) −26.1851 −1.10259
\(565\) 1.97476 0.0830787
\(566\) 39.9463 1.67907
\(567\) 1.76887 0.0742855
\(568\) 2.55940 0.107390
\(569\) −17.4857 −0.733037 −0.366519 0.930411i \(-0.619450\pi\)
−0.366519 + 0.930411i \(0.619450\pi\)
\(570\) 1.57667 0.0660396
\(571\) 26.7210 1.11824 0.559120 0.829087i \(-0.311139\pi\)
0.559120 + 0.829087i \(0.311139\pi\)
\(572\) −8.46805 −0.354067
\(573\) 3.46885 0.144913
\(574\) 13.0458 0.544521
\(575\) 38.7033 1.61404
\(576\) −10.5180 −0.438251
\(577\) 36.1461 1.50478 0.752390 0.658717i \(-0.228901\pi\)
0.752390 + 0.658717i \(0.228901\pi\)
\(578\) 2.08589 0.0867617
\(579\) −26.3873 −1.09662
\(580\) −1.77409 −0.0736651
\(581\) −30.8819 −1.28120
\(582\) 19.9077 0.825202
\(583\) 0.513825 0.0212805
\(584\) 4.19081 0.173417
\(585\) 0.206404 0.00853377
\(586\) −19.7129 −0.814332
\(587\) 18.3268 0.756428 0.378214 0.925718i \(-0.376538\pi\)
0.378214 + 0.925718i \(0.376538\pi\)
\(588\) 9.10078 0.375310
\(589\) −12.7294 −0.524504
\(590\) 2.91632 0.120063
\(591\) −18.7104 −0.769644
\(592\) −4.19468 −0.172400
\(593\) −35.0087 −1.43763 −0.718817 0.695200i \(-0.755316\pi\)
−0.718817 + 0.695200i \(0.755316\pi\)
\(594\) 5.10591 0.209498
\(595\) −0.248116 −0.0101718
\(596\) −25.3474 −1.03827
\(597\) 26.0633 1.06670
\(598\) −23.8529 −0.975419
\(599\) 17.8087 0.727644 0.363822 0.931468i \(-0.381472\pi\)
0.363822 + 0.931468i \(0.381472\pi\)
\(600\) 3.64580 0.148839
\(601\) −46.4446 −1.89451 −0.947257 0.320475i \(-0.896157\pi\)
−0.947257 + 0.320475i \(0.896157\pi\)
\(602\) −17.2591 −0.703428
\(603\) −9.81778 −0.399811
\(604\) −43.3750 −1.76490
\(605\) −0.702482 −0.0285599
\(606\) 4.29931 0.174648
\(607\) 24.2122 0.982741 0.491371 0.870951i \(-0.336496\pi\)
0.491371 + 0.870951i \(0.336496\pi\)
\(608\) 43.5772 1.76729
\(609\) 9.51631 0.385620
\(610\) 0.500822 0.0202777
\(611\) 16.3897 0.663054
\(612\) −2.35095 −0.0950315
\(613\) −42.9836 −1.73609 −0.868045 0.496485i \(-0.834624\pi\)
−0.868045 + 0.496485i \(0.834624\pi\)
\(614\) −3.92212 −0.158284
\(615\) −0.495955 −0.0199989
\(616\) −3.16965 −0.127709
\(617\) −32.1545 −1.29449 −0.647247 0.762281i \(-0.724080\pi\)
−0.647247 + 0.762281i \(0.724080\pi\)
\(618\) 11.9651 0.481309
\(619\) 4.57705 0.183967 0.0919836 0.995761i \(-0.470679\pi\)
0.0919836 + 0.995761i \(0.470679\pi\)
\(620\) 0.778967 0.0312841
\(621\) 7.77124 0.311849
\(622\) 43.7631 1.75474
\(623\) 8.98042 0.359793
\(624\) 4.67191 0.187026
\(625\) 24.7053 0.988210
\(626\) 70.8658 2.83237
\(627\) −13.1908 −0.526790
\(628\) −36.6276 −1.46160
\(629\) −1.32119 −0.0526791
\(630\) 0.517543 0.0206194
\(631\) −12.3671 −0.492327 −0.246163 0.969228i \(-0.579170\pi\)
−0.246163 + 0.969228i \(0.579170\pi\)
\(632\) −0.732041 −0.0291190
\(633\) −20.8950 −0.830501
\(634\) 37.5901 1.49289
\(635\) 2.75781 0.109440
\(636\) 0.493489 0.0195681
\(637\) −5.69632 −0.225697
\(638\) 27.4692 1.08752
\(639\) 3.49626 0.138310
\(640\) −0.808810 −0.0319710
\(641\) 25.4989 1.00715 0.503573 0.863953i \(-0.332019\pi\)
0.503573 + 0.863953i \(0.332019\pi\)
\(642\) 26.0614 1.02856
\(643\) −40.1968 −1.58521 −0.792604 0.609737i \(-0.791275\pi\)
−0.792604 + 0.609737i \(0.791275\pi\)
\(644\) −32.3168 −1.27346
\(645\) 0.656130 0.0258351
\(646\) 11.2404 0.442248
\(647\) −34.0661 −1.33928 −0.669638 0.742688i \(-0.733551\pi\)
−0.669638 + 0.742688i \(0.733551\pi\)
\(648\) 0.732041 0.0287573
\(649\) −24.3986 −0.957728
\(650\) −15.2865 −0.599587
\(651\) −4.17842 −0.163765
\(652\) −34.2774 −1.34241
\(653\) 3.99738 0.156429 0.0782147 0.996937i \(-0.475078\pi\)
0.0782147 + 0.996937i \(0.475078\pi\)
\(654\) 14.2794 0.558369
\(655\) 1.17291 0.0458295
\(656\) −11.2258 −0.438295
\(657\) 5.72483 0.223347
\(658\) 41.0958 1.60208
\(659\) 34.3326 1.33741 0.668704 0.743528i \(-0.266849\pi\)
0.668704 + 0.743528i \(0.266849\pi\)
\(660\) 0.807205 0.0314204
\(661\) 12.3659 0.480976 0.240488 0.970652i \(-0.422693\pi\)
0.240488 + 0.970652i \(0.422693\pi\)
\(662\) 38.0571 1.47913
\(663\) 1.47150 0.0571482
\(664\) −12.7804 −0.495976
\(665\) −1.33704 −0.0518483
\(666\) 2.75585 0.106787
\(667\) 41.8084 1.61883
\(668\) 18.5187 0.716512
\(669\) 6.89174 0.266450
\(670\) −2.87253 −0.110976
\(671\) −4.18999 −0.161753
\(672\) 14.3042 0.551798
\(673\) −23.5698 −0.908548 −0.454274 0.890862i \(-0.650101\pi\)
−0.454274 + 0.890862i \(0.650101\pi\)
\(674\) 39.5210 1.52229
\(675\) 4.98032 0.191693
\(676\) −25.4718 −0.979685
\(677\) 0.0626834 0.00240912 0.00120456 0.999999i \(-0.499617\pi\)
0.00120456 + 0.999999i \(0.499617\pi\)
\(678\) −29.3661 −1.12780
\(679\) −16.8821 −0.647874
\(680\) −0.102682 −0.00393768
\(681\) 16.4113 0.628881
\(682\) −12.0612 −0.461846
\(683\) −0.157880 −0.00604111 −0.00302056 0.999995i \(-0.500961\pi\)
−0.00302056 + 0.999995i \(0.500961\pi\)
\(684\) −12.6687 −0.484401
\(685\) 2.22658 0.0850734
\(686\) −40.1108 −1.53144
\(687\) 15.9846 0.609851
\(688\) 14.8514 0.566202
\(689\) −0.308883 −0.0117675
\(690\) 2.27375 0.0865600
\(691\) 6.15612 0.234190 0.117095 0.993121i \(-0.462642\pi\)
0.117095 + 0.993121i \(0.462642\pi\)
\(692\) 6.10847 0.232209
\(693\) −4.32989 −0.164479
\(694\) 60.0828 2.28071
\(695\) −2.62953 −0.0997438
\(696\) 3.93830 0.149281
\(697\) −3.53576 −0.133927
\(698\) 54.2905 2.05492
\(699\) −6.04582 −0.228674
\(700\) −20.7108 −0.782793
\(701\) −33.1235 −1.25106 −0.625529 0.780201i \(-0.715117\pi\)
−0.625529 + 0.780201i \(0.715117\pi\)
\(702\) −3.06938 −0.115846
\(703\) −7.11957 −0.268520
\(704\) 25.7464 0.970352
\(705\) −1.56232 −0.0588404
\(706\) −61.9454 −2.33135
\(707\) −3.64588 −0.137117
\(708\) −23.4329 −0.880663
\(709\) 5.19852 0.195235 0.0976173 0.995224i \(-0.468878\pi\)
0.0976173 + 0.995224i \(0.468878\pi\)
\(710\) 1.02295 0.0383906
\(711\) −1.00000 −0.0375029
\(712\) 3.71652 0.139283
\(713\) −18.3572 −0.687483
\(714\) 3.68967 0.138082
\(715\) −0.505243 −0.0188950
\(716\) 14.2487 0.532500
\(717\) 10.6450 0.397545
\(718\) −50.3562 −1.87928
\(719\) 12.3466 0.460449 0.230225 0.973137i \(-0.426054\pi\)
0.230225 + 0.973137i \(0.426054\pi\)
\(720\) −0.445343 −0.0165970
\(721\) −10.1466 −0.377880
\(722\) 20.9401 0.779310
\(723\) −2.95261 −0.109809
\(724\) 4.29249 0.159529
\(725\) 26.7936 0.995089
\(726\) 10.4464 0.387703
\(727\) −35.7172 −1.32468 −0.662339 0.749204i \(-0.730436\pi\)
−0.662339 + 0.749204i \(0.730436\pi\)
\(728\) 1.90542 0.0706195
\(729\) 1.00000 0.0370370
\(730\) 1.67500 0.0619944
\(731\) 4.67768 0.173010
\(732\) −4.02416 −0.148737
\(733\) −35.9278 −1.32702 −0.663512 0.748165i \(-0.730935\pi\)
−0.663512 + 0.748165i \(0.730935\pi\)
\(734\) −23.1699 −0.855216
\(735\) 0.542994 0.0200286
\(736\) 62.8434 2.31644
\(737\) 24.0323 0.885240
\(738\) 7.37522 0.271486
\(739\) 45.9551 1.69048 0.845242 0.534383i \(-0.179456\pi\)
0.845242 + 0.534383i \(0.179456\pi\)
\(740\) 0.435679 0.0160159
\(741\) 7.92957 0.291300
\(742\) −0.774500 −0.0284328
\(743\) −19.6847 −0.722163 −0.361081 0.932534i \(-0.617592\pi\)
−0.361081 + 0.932534i \(0.617592\pi\)
\(744\) −1.72923 −0.0633965
\(745\) −1.51234 −0.0554078
\(746\) −69.3422 −2.53880
\(747\) −17.4586 −0.638777
\(748\) 5.75472 0.210413
\(749\) −22.1004 −0.807532
\(750\) 2.92009 0.106627
\(751\) 20.0946 0.733263 0.366632 0.930366i \(-0.380511\pi\)
0.366632 + 0.930366i \(0.380511\pi\)
\(752\) −35.3627 −1.28955
\(753\) −15.6584 −0.570623
\(754\) −16.5129 −0.601366
\(755\) −2.58795 −0.0941851
\(756\) −4.15852 −0.151244
\(757\) −14.5966 −0.530523 −0.265262 0.964176i \(-0.585458\pi\)
−0.265262 + 0.964176i \(0.585458\pi\)
\(758\) −48.4776 −1.76079
\(759\) −19.0227 −0.690479
\(760\) −0.553331 −0.0200714
\(761\) −8.77877 −0.318230 −0.159115 0.987260i \(-0.550864\pi\)
−0.159115 + 0.987260i \(0.550864\pi\)
\(762\) −41.0107 −1.48566
\(763\) −12.1091 −0.438380
\(764\) −8.15509 −0.295041
\(765\) −0.140268 −0.00507141
\(766\) −49.2902 −1.78093
\(767\) 14.6670 0.529596
\(768\) −9.00846 −0.325065
\(769\) 31.1511 1.12334 0.561669 0.827362i \(-0.310159\pi\)
0.561669 + 0.827362i \(0.310159\pi\)
\(770\) −1.26686 −0.0456544
\(771\) 22.2563 0.801541
\(772\) 62.0351 2.23269
\(773\) 6.06133 0.218011 0.109005 0.994041i \(-0.465233\pi\)
0.109005 + 0.994041i \(0.465233\pi\)
\(774\) −9.75714 −0.350713
\(775\) −11.7645 −0.422594
\(776\) −6.98659 −0.250804
\(777\) −2.33700 −0.0838395
\(778\) 29.7942 1.06818
\(779\) −19.0534 −0.682660
\(780\) −0.485246 −0.0173746
\(781\) −8.55824 −0.306238
\(782\) 16.2100 0.579668
\(783\) 5.37989 0.192262
\(784\) 12.2905 0.438947
\(785\) −2.18537 −0.0779991
\(786\) −17.4421 −0.622139
\(787\) 2.88069 0.102686 0.0513428 0.998681i \(-0.483650\pi\)
0.0513428 + 0.998681i \(0.483650\pi\)
\(788\) 43.9872 1.56698
\(789\) −3.39626 −0.120910
\(790\) −0.292585 −0.0104097
\(791\) 24.9029 0.885445
\(792\) −1.79191 −0.0636728
\(793\) 2.51879 0.0894447
\(794\) 65.0093 2.30709
\(795\) 0.0294438 0.00104426
\(796\) −61.2735 −2.17178
\(797\) 15.3069 0.542198 0.271099 0.962551i \(-0.412613\pi\)
0.271099 + 0.962551i \(0.412613\pi\)
\(798\) 19.8828 0.703843
\(799\) −11.1381 −0.394037
\(800\) 40.2742 1.42391
\(801\) 5.07693 0.179385
\(802\) 12.9148 0.456039
\(803\) −14.0134 −0.494522
\(804\) 23.0811 0.814008
\(805\) −1.92817 −0.0679590
\(806\) 7.25050 0.255388
\(807\) −20.1378 −0.708886
\(808\) −1.50884 −0.0530807
\(809\) −46.3098 −1.62817 −0.814084 0.580747i \(-0.802760\pi\)
−0.814084 + 0.580747i \(0.802760\pi\)
\(810\) 0.292585 0.0102804
\(811\) −16.4120 −0.576305 −0.288152 0.957585i \(-0.593041\pi\)
−0.288152 + 0.957585i \(0.593041\pi\)
\(812\) −22.3724 −0.785116
\(813\) −27.4628 −0.963164
\(814\) −6.74585 −0.236442
\(815\) −2.04514 −0.0716382
\(816\) −3.17494 −0.111145
\(817\) 25.2070 0.881881
\(818\) −55.6281 −1.94499
\(819\) 2.60288 0.0909521
\(820\) 1.16597 0.0407173
\(821\) −19.4459 −0.678668 −0.339334 0.940666i \(-0.610202\pi\)
−0.339334 + 0.940666i \(0.610202\pi\)
\(822\) −33.1110 −1.15488
\(823\) 12.9908 0.452832 0.226416 0.974031i \(-0.427299\pi\)
0.226416 + 0.974031i \(0.427299\pi\)
\(824\) −4.19915 −0.146284
\(825\) −12.1910 −0.424436
\(826\) 36.7765 1.27962
\(827\) 49.0775 1.70659 0.853296 0.521427i \(-0.174600\pi\)
0.853296 + 0.521427i \(0.174600\pi\)
\(828\) −18.2698 −0.634919
\(829\) 29.5132 1.02504 0.512518 0.858677i \(-0.328713\pi\)
0.512518 + 0.858677i \(0.328713\pi\)
\(830\) −5.10811 −0.177305
\(831\) 22.0555 0.765096
\(832\) −15.4773 −0.536577
\(833\) 3.87111 0.134126
\(834\) 39.1031 1.35403
\(835\) 1.10491 0.0382371
\(836\) 31.0109 1.07253
\(837\) −2.36220 −0.0816496
\(838\) −9.21446 −0.318308
\(839\) 26.6810 0.921132 0.460566 0.887626i \(-0.347647\pi\)
0.460566 + 0.887626i \(0.347647\pi\)
\(840\) −0.181631 −0.00626687
\(841\) −0.0567871 −0.00195818
\(842\) 2.01491 0.0694385
\(843\) −18.0037 −0.620079
\(844\) 49.1230 1.69088
\(845\) −1.51976 −0.0522815
\(846\) 23.2328 0.798762
\(847\) −8.85872 −0.304389
\(848\) 0.666453 0.0228861
\(849\) −19.1507 −0.657251
\(850\) 10.3884 0.356320
\(851\) −10.2672 −0.351957
\(852\) −8.21952 −0.281596
\(853\) 7.72389 0.264461 0.132230 0.991219i \(-0.457786\pi\)
0.132230 + 0.991219i \(0.457786\pi\)
\(854\) 6.31567 0.216118
\(855\) −0.755874 −0.0258504
\(856\) −9.14620 −0.312611
\(857\) 17.4470 0.595977 0.297989 0.954569i \(-0.403684\pi\)
0.297989 + 0.954569i \(0.403684\pi\)
\(858\) 7.51333 0.256501
\(859\) −49.0330 −1.67299 −0.836493 0.547978i \(-0.815398\pi\)
−0.836493 + 0.547978i \(0.815398\pi\)
\(860\) −1.54253 −0.0525998
\(861\) −6.25430 −0.213146
\(862\) 31.6068 1.07653
\(863\) −12.9665 −0.441385 −0.220693 0.975343i \(-0.570832\pi\)
−0.220693 + 0.975343i \(0.570832\pi\)
\(864\) 8.08666 0.275114
\(865\) 0.364459 0.0123920
\(866\) −11.5521 −0.392557
\(867\) −1.00000 −0.0339618
\(868\) 9.82324 0.333423
\(869\) 2.44783 0.0830369
\(870\) 1.57407 0.0533661
\(871\) −14.4468 −0.489512
\(872\) −5.01133 −0.169705
\(873\) −9.54399 −0.323015
\(874\) 87.3520 2.95472
\(875\) −2.47628 −0.0837135
\(876\) −13.4588 −0.454730
\(877\) 27.5641 0.930774 0.465387 0.885107i \(-0.345915\pi\)
0.465387 + 0.885107i \(0.345915\pi\)
\(878\) −25.4181 −0.857818
\(879\) 9.45058 0.318760
\(880\) 1.09012 0.0367481
\(881\) 23.7321 0.799553 0.399777 0.916613i \(-0.369088\pi\)
0.399777 + 0.916613i \(0.369088\pi\)
\(882\) −8.07472 −0.271890
\(883\) 29.4934 0.992532 0.496266 0.868170i \(-0.334704\pi\)
0.496266 + 0.868170i \(0.334704\pi\)
\(884\) −3.45941 −0.116353
\(885\) −1.39811 −0.0469971
\(886\) 12.0447 0.404649
\(887\) −5.65133 −0.189753 −0.0948766 0.995489i \(-0.530246\pi\)
−0.0948766 + 0.995489i \(0.530246\pi\)
\(888\) −0.967162 −0.0324558
\(889\) 34.7777 1.16641
\(890\) 1.48543 0.0497918
\(891\) −2.44783 −0.0820054
\(892\) −16.2021 −0.542488
\(893\) −60.0206 −2.00851
\(894\) 22.4896 0.752165
\(895\) 0.850144 0.0284172
\(896\) −10.1996 −0.340744
\(897\) 11.4354 0.381815
\(898\) −6.84582 −0.228448
\(899\) −12.7084 −0.423848
\(900\) −11.7085 −0.390283
\(901\) 0.209911 0.00699313
\(902\) −18.0533 −0.601109
\(903\) 8.27420 0.275348
\(904\) 10.3060 0.342773
\(905\) 0.256110 0.00851337
\(906\) 38.4847 1.27857
\(907\) −16.8237 −0.558623 −0.279312 0.960201i \(-0.590106\pi\)
−0.279312 + 0.960201i \(0.590106\pi\)
\(908\) −38.5820 −1.28039
\(909\) −2.06114 −0.0683636
\(910\) 0.761563 0.0252456
\(911\) 36.0202 1.19340 0.596701 0.802464i \(-0.296478\pi\)
0.596701 + 0.802464i \(0.296478\pi\)
\(912\) −17.1090 −0.566537
\(913\) 42.7357 1.41434
\(914\) 71.8606 2.37694
\(915\) −0.240100 −0.00793745
\(916\) −37.5790 −1.24165
\(917\) 14.7912 0.488447
\(918\) 2.08589 0.0688447
\(919\) −53.8788 −1.77730 −0.888649 0.458588i \(-0.848355\pi\)
−0.888649 + 0.458588i \(0.848355\pi\)
\(920\) −0.797968 −0.0263082
\(921\) 1.88031 0.0619582
\(922\) 45.8816 1.51103
\(923\) 5.14473 0.169341
\(924\) 10.1793 0.334876
\(925\) −6.57993 −0.216347
\(926\) 3.26264 0.107217
\(927\) −5.73622 −0.188402
\(928\) 43.5054 1.42813
\(929\) 34.6314 1.13622 0.568110 0.822953i \(-0.307675\pi\)
0.568110 + 0.822953i \(0.307675\pi\)
\(930\) −0.691143 −0.0226635
\(931\) 20.8605 0.683676
\(932\) 14.2134 0.465576
\(933\) −20.9805 −0.686870
\(934\) −24.5046 −0.801815
\(935\) 0.343353 0.0112288
\(936\) 1.07720 0.0352093
\(937\) 15.5029 0.506459 0.253229 0.967406i \(-0.418507\pi\)
0.253229 + 0.967406i \(0.418507\pi\)
\(938\) −36.2244 −1.18277
\(939\) −33.9738 −1.10869
\(940\) 3.67293 0.119798
\(941\) 34.0338 1.10947 0.554736 0.832027i \(-0.312819\pi\)
0.554736 + 0.832027i \(0.312819\pi\)
\(942\) 32.4980 1.05884
\(943\) −27.4773 −0.894783
\(944\) −31.6460 −1.02999
\(945\) −0.248116 −0.00807121
\(946\) 23.8838 0.776530
\(947\) −1.96102 −0.0637246 −0.0318623 0.999492i \(-0.510144\pi\)
−0.0318623 + 0.999492i \(0.510144\pi\)
\(948\) 2.35095 0.0763553
\(949\) 8.42406 0.273457
\(950\) 55.9809 1.81626
\(951\) −18.0211 −0.584375
\(952\) −1.29488 −0.0419674
\(953\) 33.3348 1.07982 0.539910 0.841723i \(-0.318458\pi\)
0.539910 + 0.841723i \(0.318458\pi\)
\(954\) −0.437851 −0.0141759
\(955\) −0.486570 −0.0157450
\(956\) −25.0258 −0.809393
\(957\) −13.1691 −0.425695
\(958\) −72.3777 −2.33842
\(959\) 28.0786 0.906705
\(960\) 1.47535 0.0476166
\(961\) −25.4200 −0.820000
\(962\) 4.05523 0.130746
\(963\) −12.4941 −0.402617
\(964\) 6.94144 0.223569
\(965\) 3.70130 0.119149
\(966\) 28.6733 0.922548
\(967\) −47.6659 −1.53283 −0.766416 0.642345i \(-0.777962\pi\)
−0.766416 + 0.642345i \(0.777962\pi\)
\(968\) −3.66616 −0.117835
\(969\) −5.38878 −0.173112
\(970\) −2.79242 −0.0896593
\(971\) −39.3174 −1.26176 −0.630878 0.775882i \(-0.717305\pi\)
−0.630878 + 0.775882i \(0.717305\pi\)
\(972\) −2.35095 −0.0754067
\(973\) −33.1600 −1.06306
\(974\) −38.5946 −1.23665
\(975\) 7.32853 0.234701
\(976\) −5.43460 −0.173957
\(977\) 53.4361 1.70957 0.854786 0.518981i \(-0.173689\pi\)
0.854786 + 0.518981i \(0.173689\pi\)
\(978\) 30.4128 0.972494
\(979\) −12.4275 −0.397183
\(980\) −1.27655 −0.0407779
\(981\) −6.84570 −0.218566
\(982\) −50.1092 −1.59905
\(983\) 53.0299 1.69139 0.845696 0.533665i \(-0.179186\pi\)
0.845696 + 0.533665i \(0.179186\pi\)
\(984\) −2.58832 −0.0825128
\(985\) 2.62448 0.0836228
\(986\) 11.2219 0.357377
\(987\) −19.7018 −0.627115
\(988\) −18.6420 −0.593081
\(989\) 36.3514 1.15591
\(990\) −0.716197 −0.0227622
\(991\) 10.4399 0.331633 0.165816 0.986157i \(-0.446974\pi\)
0.165816 + 0.986157i \(0.446974\pi\)
\(992\) −19.1023 −0.606499
\(993\) −18.2450 −0.578988
\(994\) 12.9000 0.409164
\(995\) −3.65586 −0.115898
\(996\) 41.0443 1.30054
\(997\) −10.1949 −0.322875 −0.161437 0.986883i \(-0.551613\pi\)
−0.161437 + 0.986883i \(0.551613\pi\)
\(998\) −5.80585 −0.183781
\(999\) −1.32119 −0.0418004
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 4029.2.a.g.1.19 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.g.1.19 22 1.1 even 1 trivial