Properties

Label 6025.2.a.l.1.14
Level $6025$
Weight $2$
Character 6025.1
Self dual yes
Analytic conductor $48.110$
Analytic rank $1$
Dimension $40$
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] = [6025,2,Mod(1,6025)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6025, 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("6025.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6025.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: \(48.1098672178\)
Analytic rank: \(1\)
Dimension: \(40\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) \(=\) 6025.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.26445 q^{2} +0.637501 q^{3} -0.401165 q^{4} -0.806088 q^{6} +3.31632 q^{7} +3.03615 q^{8} -2.59359 q^{9} +O(q^{10})\) \(q-1.26445 q^{2} +0.637501 q^{3} -0.401165 q^{4} -0.806088 q^{6} +3.31632 q^{7} +3.03615 q^{8} -2.59359 q^{9} -4.24228 q^{11} -0.255743 q^{12} +4.96033 q^{13} -4.19333 q^{14} -3.03674 q^{16} -0.765219 q^{17} +3.27947 q^{18} -0.395721 q^{19} +2.11416 q^{21} +5.36415 q^{22} +0.736028 q^{23} +1.93555 q^{24} -6.27209 q^{26} -3.56592 q^{27} -1.33039 q^{28} +0.111486 q^{29} -4.87704 q^{31} -2.23251 q^{32} -2.70446 q^{33} +0.967582 q^{34} +1.04046 q^{36} +5.92852 q^{37} +0.500370 q^{38} +3.16221 q^{39} -10.0798 q^{41} -2.67325 q^{42} +11.7509 q^{43} +1.70186 q^{44} -0.930671 q^{46} +0.146161 q^{47} -1.93592 q^{48} +3.99800 q^{49} -0.487828 q^{51} -1.98991 q^{52} -12.9699 q^{53} +4.50893 q^{54} +10.0689 q^{56} -0.252273 q^{57} -0.140969 q^{58} -7.84684 q^{59} -4.56240 q^{61} +6.16678 q^{62} -8.60119 q^{63} +8.89637 q^{64} +3.41965 q^{66} -9.50170 q^{67} +0.306979 q^{68} +0.469218 q^{69} +1.93643 q^{71} -7.87455 q^{72} +6.60869 q^{73} -7.49631 q^{74} +0.158750 q^{76} -14.0688 q^{77} -3.99846 q^{78} +3.83638 q^{79} +5.50750 q^{81} +12.7454 q^{82} +12.1432 q^{83} -0.848127 q^{84} -14.8584 q^{86} +0.0710725 q^{87} -12.8802 q^{88} +3.43003 q^{89} +16.4500 q^{91} -0.295269 q^{92} -3.10912 q^{93} -0.184813 q^{94} -1.42323 q^{96} -3.58285 q^{97} -5.05527 q^{98} +11.0027 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9} + q^{11} - 14 q^{12} - 9 q^{13} - q^{14} + 43 q^{16} - 12 q^{17} - 42 q^{18} + 2 q^{21} - 5 q^{22} - 77 q^{23} - 2 q^{24} + 2 q^{26} - 38 q^{27} - 42 q^{28} + 2 q^{29} + q^{31} - 72 q^{32} - 20 q^{33} + 5 q^{34} + 32 q^{36} - 28 q^{37} - 23 q^{38} - 2 q^{39} - 2 q^{41} - 37 q^{42} - 31 q^{43} + 3 q^{44} + 14 q^{46} - 96 q^{47} - 13 q^{48} + 40 q^{49} - 10 q^{51} - 42 q^{52} - 54 q^{53} + 4 q^{54} - 15 q^{56} - 37 q^{57} - 27 q^{58} + q^{59} + 5 q^{61} - 39 q^{62} - 70 q^{63} + 65 q^{64} - 52 q^{66} - 34 q^{67} - 52 q^{68} + 21 q^{69} - 9 q^{71} - 70 q^{72} - 25 q^{73} + 22 q^{74} - 47 q^{76} - 54 q^{77} - 58 q^{78} + 13 q^{79} + 12 q^{81} + 5 q^{82} - 63 q^{83} + 95 q^{84} - 18 q^{86} - 47 q^{87} - 13 q^{88} + 19 q^{89} - 31 q^{91} - 137 q^{92} - 52 q^{93} + 120 q^{94} - 49 q^{96} - 36 q^{97} - 64 q^{98} + 16 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.26445 −0.894101 −0.447051 0.894509i \(-0.647526\pi\)
−0.447051 + 0.894509i \(0.647526\pi\)
\(3\) 0.637501 0.368061 0.184031 0.982921i \(-0.441085\pi\)
0.184031 + 0.982921i \(0.441085\pi\)
\(4\) −0.401165 −0.200583
\(5\) 0 0
\(6\) −0.806088 −0.329084
\(7\) 3.31632 1.25345 0.626726 0.779240i \(-0.284395\pi\)
0.626726 + 0.779240i \(0.284395\pi\)
\(8\) 3.03615 1.07344
\(9\) −2.59359 −0.864531
\(10\) 0 0
\(11\) −4.24228 −1.27910 −0.639548 0.768752i \(-0.720878\pi\)
−0.639548 + 0.768752i \(0.720878\pi\)
\(12\) −0.255743 −0.0738267
\(13\) 4.96033 1.37575 0.687874 0.725831i \(-0.258544\pi\)
0.687874 + 0.725831i \(0.258544\pi\)
\(14\) −4.19333 −1.12071
\(15\) 0 0
\(16\) −3.03674 −0.759184
\(17\) −0.765219 −0.185593 −0.0927965 0.995685i \(-0.529581\pi\)
−0.0927965 + 0.995685i \(0.529581\pi\)
\(18\) 3.27947 0.772978
\(19\) −0.395721 −0.0907847 −0.0453923 0.998969i \(-0.514454\pi\)
−0.0453923 + 0.998969i \(0.514454\pi\)
\(20\) 0 0
\(21\) 2.11416 0.461347
\(22\) 5.36415 1.14364
\(23\) 0.736028 0.153472 0.0767362 0.997051i \(-0.475550\pi\)
0.0767362 + 0.997051i \(0.475550\pi\)
\(24\) 1.93555 0.395093
\(25\) 0 0
\(26\) −6.27209 −1.23006
\(27\) −3.56592 −0.686262
\(28\) −1.33039 −0.251421
\(29\) 0.111486 0.0207024 0.0103512 0.999946i \(-0.496705\pi\)
0.0103512 + 0.999946i \(0.496705\pi\)
\(30\) 0 0
\(31\) −4.87704 −0.875942 −0.437971 0.898989i \(-0.644303\pi\)
−0.437971 + 0.898989i \(0.644303\pi\)
\(32\) −2.23251 −0.394655
\(33\) −2.70446 −0.470785
\(34\) 0.967582 0.165939
\(35\) 0 0
\(36\) 1.04046 0.173410
\(37\) 5.92852 0.974642 0.487321 0.873223i \(-0.337974\pi\)
0.487321 + 0.873223i \(0.337974\pi\)
\(38\) 0.500370 0.0811707
\(39\) 3.16221 0.506359
\(40\) 0 0
\(41\) −10.0798 −1.57420 −0.787101 0.616824i \(-0.788419\pi\)
−0.787101 + 0.616824i \(0.788419\pi\)
\(42\) −2.67325 −0.412491
\(43\) 11.7509 1.79199 0.895997 0.444061i \(-0.146463\pi\)
0.895997 + 0.444061i \(0.146463\pi\)
\(44\) 1.70186 0.256564
\(45\) 0 0
\(46\) −0.930671 −0.137220
\(47\) 0.146161 0.0213198 0.0106599 0.999943i \(-0.496607\pi\)
0.0106599 + 0.999943i \(0.496607\pi\)
\(48\) −1.93592 −0.279426
\(49\) 3.99800 0.571142
\(50\) 0 0
\(51\) −0.487828 −0.0683096
\(52\) −1.98991 −0.275951
\(53\) −12.9699 −1.78155 −0.890776 0.454442i \(-0.849839\pi\)
−0.890776 + 0.454442i \(0.849839\pi\)
\(54\) 4.50893 0.613588
\(55\) 0 0
\(56\) 10.0689 1.34551
\(57\) −0.252273 −0.0334143
\(58\) −0.140969 −0.0185101
\(59\) −7.84684 −1.02157 −0.510786 0.859708i \(-0.670646\pi\)
−0.510786 + 0.859708i \(0.670646\pi\)
\(60\) 0 0
\(61\) −4.56240 −0.584156 −0.292078 0.956395i \(-0.594347\pi\)
−0.292078 + 0.956395i \(0.594347\pi\)
\(62\) 6.16678 0.783181
\(63\) −8.60119 −1.08365
\(64\) 8.89637 1.11205
\(65\) 0 0
\(66\) 3.41965 0.420930
\(67\) −9.50170 −1.16082 −0.580409 0.814325i \(-0.697107\pi\)
−0.580409 + 0.814325i \(0.697107\pi\)
\(68\) 0.306979 0.0372267
\(69\) 0.469218 0.0564873
\(70\) 0 0
\(71\) 1.93643 0.229812 0.114906 0.993376i \(-0.463343\pi\)
0.114906 + 0.993376i \(0.463343\pi\)
\(72\) −7.87455 −0.928024
\(73\) 6.60869 0.773488 0.386744 0.922187i \(-0.373600\pi\)
0.386744 + 0.922187i \(0.373600\pi\)
\(74\) −7.49631 −0.871429
\(75\) 0 0
\(76\) 0.158750 0.0182098
\(77\) −14.0688 −1.60328
\(78\) −3.99846 −0.452737
\(79\) 3.83638 0.431627 0.215813 0.976435i \(-0.430760\pi\)
0.215813 + 0.976435i \(0.430760\pi\)
\(80\) 0 0
\(81\) 5.50750 0.611945
\(82\) 12.7454 1.40750
\(83\) 12.1432 1.33289 0.666446 0.745553i \(-0.267815\pi\)
0.666446 + 0.745553i \(0.267815\pi\)
\(84\) −0.848127 −0.0925383
\(85\) 0 0
\(86\) −14.8584 −1.60222
\(87\) 0.0710725 0.00761977
\(88\) −12.8802 −1.37304
\(89\) 3.43003 0.363582 0.181791 0.983337i \(-0.441810\pi\)
0.181791 + 0.983337i \(0.441810\pi\)
\(90\) 0 0
\(91\) 16.4500 1.72443
\(92\) −0.295269 −0.0307839
\(93\) −3.10912 −0.322400
\(94\) −0.184813 −0.0190620
\(95\) 0 0
\(96\) −1.42323 −0.145257
\(97\) −3.58285 −0.363783 −0.181891 0.983319i \(-0.558222\pi\)
−0.181891 + 0.983319i \(0.558222\pi\)
\(98\) −5.05527 −0.510659
\(99\) 11.0027 1.10582
\(100\) 0 0
\(101\) −14.2822 −1.42113 −0.710565 0.703631i \(-0.751561\pi\)
−0.710565 + 0.703631i \(0.751561\pi\)
\(102\) 0.616834 0.0610757
\(103\) −17.4214 −1.71658 −0.858289 0.513166i \(-0.828473\pi\)
−0.858289 + 0.513166i \(0.828473\pi\)
\(104\) 15.0603 1.47679
\(105\) 0 0
\(106\) 16.3998 1.59289
\(107\) 2.69267 0.260310 0.130155 0.991494i \(-0.458453\pi\)
0.130155 + 0.991494i \(0.458453\pi\)
\(108\) 1.43052 0.137652
\(109\) −11.9114 −1.14091 −0.570454 0.821330i \(-0.693233\pi\)
−0.570454 + 0.821330i \(0.693233\pi\)
\(110\) 0 0
\(111\) 3.77943 0.358728
\(112\) −10.0708 −0.951601
\(113\) 9.95943 0.936905 0.468452 0.883489i \(-0.344812\pi\)
0.468452 + 0.883489i \(0.344812\pi\)
\(114\) 0.318986 0.0298758
\(115\) 0 0
\(116\) −0.0447243 −0.00415255
\(117\) −12.8651 −1.18938
\(118\) 9.92194 0.913389
\(119\) −2.53771 −0.232632
\(120\) 0 0
\(121\) 6.99693 0.636085
\(122\) 5.76893 0.522295
\(123\) −6.42589 −0.579403
\(124\) 1.95650 0.175699
\(125\) 0 0
\(126\) 10.8758 0.968891
\(127\) −4.52799 −0.401794 −0.200897 0.979612i \(-0.564386\pi\)
−0.200897 + 0.979612i \(0.564386\pi\)
\(128\) −6.78400 −0.599626
\(129\) 7.49120 0.659563
\(130\) 0 0
\(131\) −11.0767 −0.967774 −0.483887 0.875131i \(-0.660775\pi\)
−0.483887 + 0.875131i \(0.660775\pi\)
\(132\) 1.08493 0.0944314
\(133\) −1.31234 −0.113794
\(134\) 12.0144 1.03789
\(135\) 0 0
\(136\) −2.32332 −0.199223
\(137\) −17.3794 −1.48482 −0.742411 0.669944i \(-0.766318\pi\)
−0.742411 + 0.669944i \(0.766318\pi\)
\(138\) −0.593303 −0.0505053
\(139\) 18.1370 1.53836 0.769182 0.639030i \(-0.220664\pi\)
0.769182 + 0.639030i \(0.220664\pi\)
\(140\) 0 0
\(141\) 0.0931778 0.00784698
\(142\) −2.44852 −0.205475
\(143\) −21.0431 −1.75971
\(144\) 7.87606 0.656338
\(145\) 0 0
\(146\) −8.35636 −0.691577
\(147\) 2.54873 0.210215
\(148\) −2.37832 −0.195496
\(149\) 3.84207 0.314755 0.157377 0.987539i \(-0.449696\pi\)
0.157377 + 0.987539i \(0.449696\pi\)
\(150\) 0 0
\(151\) 2.56714 0.208911 0.104455 0.994530i \(-0.466690\pi\)
0.104455 + 0.994530i \(0.466690\pi\)
\(152\) −1.20147 −0.0974521
\(153\) 1.98467 0.160451
\(154\) 17.7893 1.43350
\(155\) 0 0
\(156\) −1.26857 −0.101567
\(157\) 17.2668 1.37804 0.689019 0.724744i \(-0.258042\pi\)
0.689019 + 0.724744i \(0.258042\pi\)
\(158\) −4.85092 −0.385918
\(159\) −8.26832 −0.655720
\(160\) 0 0
\(161\) 2.44091 0.192370
\(162\) −6.96396 −0.547140
\(163\) −23.3540 −1.82922 −0.914612 0.404334i \(-0.867503\pi\)
−0.914612 + 0.404334i \(0.867503\pi\)
\(164\) 4.04367 0.315758
\(165\) 0 0
\(166\) −15.3545 −1.19174
\(167\) −8.41952 −0.651522 −0.325761 0.945452i \(-0.605621\pi\)
−0.325761 + 0.945452i \(0.605621\pi\)
\(168\) 6.41891 0.495230
\(169\) 11.6048 0.892680
\(170\) 0 0
\(171\) 1.02634 0.0784862
\(172\) −4.71405 −0.359443
\(173\) 17.0232 1.29425 0.647125 0.762384i \(-0.275971\pi\)
0.647125 + 0.762384i \(0.275971\pi\)
\(174\) −0.0898676 −0.00681284
\(175\) 0 0
\(176\) 12.8827 0.971068
\(177\) −5.00237 −0.376001
\(178\) −4.33710 −0.325080
\(179\) −6.03220 −0.450868 −0.225434 0.974258i \(-0.572380\pi\)
−0.225434 + 0.974258i \(0.572380\pi\)
\(180\) 0 0
\(181\) 1.22485 0.0910422 0.0455211 0.998963i \(-0.485505\pi\)
0.0455211 + 0.998963i \(0.485505\pi\)
\(182\) −20.8003 −1.54182
\(183\) −2.90854 −0.215005
\(184\) 2.23469 0.164744
\(185\) 0 0
\(186\) 3.93132 0.288259
\(187\) 3.24627 0.237391
\(188\) −0.0586347 −0.00427638
\(189\) −11.8257 −0.860196
\(190\) 0 0
\(191\) −14.8963 −1.07786 −0.538930 0.842350i \(-0.681171\pi\)
−0.538930 + 0.842350i \(0.681171\pi\)
\(192\) 5.67144 0.409301
\(193\) 10.1687 0.731959 0.365979 0.930623i \(-0.380734\pi\)
0.365979 + 0.930623i \(0.380734\pi\)
\(194\) 4.53033 0.325259
\(195\) 0 0
\(196\) −1.60386 −0.114561
\(197\) −7.97563 −0.568240 −0.284120 0.958789i \(-0.591701\pi\)
−0.284120 + 0.958789i \(0.591701\pi\)
\(198\) −13.9124 −0.988713
\(199\) 11.9098 0.844266 0.422133 0.906534i \(-0.361282\pi\)
0.422133 + 0.906534i \(0.361282\pi\)
\(200\) 0 0
\(201\) −6.05734 −0.427252
\(202\) 18.0591 1.27063
\(203\) 0.369724 0.0259495
\(204\) 0.195700 0.0137017
\(205\) 0 0
\(206\) 22.0285 1.53480
\(207\) −1.90896 −0.132682
\(208\) −15.0632 −1.04445
\(209\) 1.67876 0.116122
\(210\) 0 0
\(211\) −8.78994 −0.605125 −0.302562 0.953130i \(-0.597842\pi\)
−0.302562 + 0.953130i \(0.597842\pi\)
\(212\) 5.20307 0.357349
\(213\) 1.23448 0.0845850
\(214\) −3.40474 −0.232743
\(215\) 0 0
\(216\) −10.8267 −0.736663
\(217\) −16.1738 −1.09795
\(218\) 15.0614 1.02009
\(219\) 4.21304 0.284691
\(220\) 0 0
\(221\) −3.79574 −0.255329
\(222\) −4.77891 −0.320739
\(223\) 21.1387 1.41555 0.707777 0.706436i \(-0.249698\pi\)
0.707777 + 0.706436i \(0.249698\pi\)
\(224\) −7.40371 −0.494681
\(225\) 0 0
\(226\) −12.5932 −0.837688
\(227\) −14.0271 −0.931014 −0.465507 0.885044i \(-0.654128\pi\)
−0.465507 + 0.885044i \(0.654128\pi\)
\(228\) 0.101203 0.00670233
\(229\) −11.7594 −0.777086 −0.388543 0.921431i \(-0.627021\pi\)
−0.388543 + 0.921431i \(0.627021\pi\)
\(230\) 0 0
\(231\) −8.96885 −0.590107
\(232\) 0.338489 0.0222229
\(233\) 23.7103 1.55331 0.776657 0.629924i \(-0.216914\pi\)
0.776657 + 0.629924i \(0.216914\pi\)
\(234\) 16.2672 1.06342
\(235\) 0 0
\(236\) 3.14788 0.204910
\(237\) 2.44570 0.158865
\(238\) 3.20881 0.207996
\(239\) 11.9660 0.774018 0.387009 0.922076i \(-0.373508\pi\)
0.387009 + 0.922076i \(0.373508\pi\)
\(240\) 0 0
\(241\) −1.00000 −0.0644157
\(242\) −8.84727 −0.568724
\(243\) 14.2088 0.911495
\(244\) 1.83028 0.117172
\(245\) 0 0
\(246\) 8.12522 0.518045
\(247\) −1.96291 −0.124897
\(248\) −14.8074 −0.940274
\(249\) 7.74132 0.490586
\(250\) 0 0
\(251\) −14.0885 −0.889255 −0.444628 0.895715i \(-0.646664\pi\)
−0.444628 + 0.895715i \(0.646664\pi\)
\(252\) 3.45050 0.217361
\(253\) −3.12244 −0.196306
\(254\) 5.72542 0.359245
\(255\) 0 0
\(256\) −9.21470 −0.575919
\(257\) −17.9138 −1.11743 −0.558716 0.829359i \(-0.688706\pi\)
−0.558716 + 0.829359i \(0.688706\pi\)
\(258\) −9.47225 −0.589716
\(259\) 19.6609 1.22167
\(260\) 0 0
\(261\) −0.289149 −0.0178979
\(262\) 14.0059 0.865288
\(263\) 29.1480 1.79734 0.898671 0.438624i \(-0.144534\pi\)
0.898671 + 0.438624i \(0.144534\pi\)
\(264\) −8.21115 −0.505361
\(265\) 0 0
\(266\) 1.65939 0.101744
\(267\) 2.18665 0.133821
\(268\) 3.81175 0.232840
\(269\) 2.13547 0.130202 0.0651010 0.997879i \(-0.479263\pi\)
0.0651010 + 0.997879i \(0.479263\pi\)
\(270\) 0 0
\(271\) −26.0330 −1.58139 −0.790696 0.612209i \(-0.790281\pi\)
−0.790696 + 0.612209i \(0.790281\pi\)
\(272\) 2.32377 0.140899
\(273\) 10.4869 0.634697
\(274\) 21.9754 1.32758
\(275\) 0 0
\(276\) −0.188234 −0.0113304
\(277\) 28.6489 1.72134 0.860672 0.509160i \(-0.170044\pi\)
0.860672 + 0.509160i \(0.170044\pi\)
\(278\) −22.9334 −1.37545
\(279\) 12.6491 0.757279
\(280\) 0 0
\(281\) −12.4049 −0.740017 −0.370008 0.929028i \(-0.620645\pi\)
−0.370008 + 0.929028i \(0.620645\pi\)
\(282\) −0.117819 −0.00701600
\(283\) −11.8834 −0.706397 −0.353199 0.935548i \(-0.614906\pi\)
−0.353199 + 0.935548i \(0.614906\pi\)
\(284\) −0.776830 −0.0460964
\(285\) 0 0
\(286\) 26.6079 1.57336
\(287\) −33.4279 −1.97319
\(288\) 5.79021 0.341192
\(289\) −16.4144 −0.965555
\(290\) 0 0
\(291\) −2.28407 −0.133894
\(292\) −2.65118 −0.155148
\(293\) −22.2128 −1.29769 −0.648844 0.760921i \(-0.724747\pi\)
−0.648844 + 0.760921i \(0.724747\pi\)
\(294\) −3.22274 −0.187954
\(295\) 0 0
\(296\) 17.9999 1.04622
\(297\) 15.1276 0.877794
\(298\) −4.85811 −0.281423
\(299\) 3.65094 0.211139
\(300\) 0 0
\(301\) 38.9697 2.24618
\(302\) −3.24602 −0.186787
\(303\) −9.10491 −0.523063
\(304\) 1.20170 0.0689223
\(305\) 0 0
\(306\) −2.50951 −0.143459
\(307\) 17.1344 0.977913 0.488956 0.872308i \(-0.337378\pi\)
0.488956 + 0.872308i \(0.337378\pi\)
\(308\) 5.64390 0.321591
\(309\) −11.1061 −0.631806
\(310\) 0 0
\(311\) 12.1453 0.688699 0.344349 0.938842i \(-0.388100\pi\)
0.344349 + 0.938842i \(0.388100\pi\)
\(312\) 9.60097 0.543548
\(313\) −13.8694 −0.783945 −0.391972 0.919977i \(-0.628207\pi\)
−0.391972 + 0.919977i \(0.628207\pi\)
\(314\) −21.8330 −1.23210
\(315\) 0 0
\(316\) −1.53902 −0.0865769
\(317\) 31.9236 1.79301 0.896504 0.443035i \(-0.146098\pi\)
0.896504 + 0.443035i \(0.146098\pi\)
\(318\) 10.4549 0.586281
\(319\) −0.472955 −0.0264804
\(320\) 0 0
\(321\) 1.71658 0.0958100
\(322\) −3.08640 −0.171999
\(323\) 0.302813 0.0168490
\(324\) −2.20942 −0.122745
\(325\) 0 0
\(326\) 29.5299 1.63551
\(327\) −7.59354 −0.419924
\(328\) −30.6039 −1.68982
\(329\) 0.484717 0.0267233
\(330\) 0 0
\(331\) −16.6477 −0.915041 −0.457521 0.889199i \(-0.651262\pi\)
−0.457521 + 0.889199i \(0.651262\pi\)
\(332\) −4.87144 −0.267355
\(333\) −15.3762 −0.842608
\(334\) 10.6461 0.582527
\(335\) 0 0
\(336\) −6.42014 −0.350247
\(337\) −7.65951 −0.417240 −0.208620 0.977997i \(-0.566897\pi\)
−0.208620 + 0.977997i \(0.566897\pi\)
\(338\) −14.6737 −0.798147
\(339\) 6.34915 0.344838
\(340\) 0 0
\(341\) 20.6898 1.12041
\(342\) −1.29776 −0.0701746
\(343\) −9.95562 −0.537553
\(344\) 35.6775 1.92360
\(345\) 0 0
\(346\) −21.5250 −1.15719
\(347\) −19.9181 −1.06926 −0.534629 0.845087i \(-0.679549\pi\)
−0.534629 + 0.845087i \(0.679549\pi\)
\(348\) −0.0285118 −0.00152839
\(349\) −22.4664 −1.20260 −0.601300 0.799023i \(-0.705351\pi\)
−0.601300 + 0.799023i \(0.705351\pi\)
\(350\) 0 0
\(351\) −17.6881 −0.944122
\(352\) 9.47092 0.504802
\(353\) 7.94392 0.422812 0.211406 0.977398i \(-0.432196\pi\)
0.211406 + 0.977398i \(0.432196\pi\)
\(354\) 6.32525 0.336183
\(355\) 0 0
\(356\) −1.37601 −0.0729283
\(357\) −1.61779 −0.0856228
\(358\) 7.62741 0.403121
\(359\) −33.5124 −1.76872 −0.884359 0.466808i \(-0.845404\pi\)
−0.884359 + 0.466808i \(0.845404\pi\)
\(360\) 0 0
\(361\) −18.8434 −0.991758
\(362\) −1.54876 −0.0814009
\(363\) 4.46055 0.234118
\(364\) −6.59919 −0.345891
\(365\) 0 0
\(366\) 3.67770 0.192236
\(367\) 7.64133 0.398874 0.199437 0.979911i \(-0.436089\pi\)
0.199437 + 0.979911i \(0.436089\pi\)
\(368\) −2.23512 −0.116514
\(369\) 26.1429 1.36095
\(370\) 0 0
\(371\) −43.0124 −2.23309
\(372\) 1.24727 0.0646679
\(373\) 14.5227 0.751954 0.375977 0.926629i \(-0.377307\pi\)
0.375977 + 0.926629i \(0.377307\pi\)
\(374\) −4.10475 −0.212252
\(375\) 0 0
\(376\) 0.443767 0.0228856
\(377\) 0.553007 0.0284813
\(378\) 14.9531 0.769103
\(379\) −1.63841 −0.0841594 −0.0420797 0.999114i \(-0.513398\pi\)
−0.0420797 + 0.999114i \(0.513398\pi\)
\(380\) 0 0
\(381\) −2.88660 −0.147885
\(382\) 18.8357 0.963716
\(383\) 7.38637 0.377426 0.188713 0.982032i \(-0.439568\pi\)
0.188713 + 0.982032i \(0.439568\pi\)
\(384\) −4.32480 −0.220699
\(385\) 0 0
\(386\) −12.8578 −0.654445
\(387\) −30.4770 −1.54923
\(388\) 1.43731 0.0729685
\(389\) −17.6275 −0.893752 −0.446876 0.894596i \(-0.647463\pi\)
−0.446876 + 0.894596i \(0.647463\pi\)
\(390\) 0 0
\(391\) −0.563223 −0.0284834
\(392\) 12.1385 0.613088
\(393\) −7.06139 −0.356200
\(394\) 10.0848 0.508064
\(395\) 0 0
\(396\) −4.41392 −0.221808
\(397\) −16.2623 −0.816180 −0.408090 0.912942i \(-0.633805\pi\)
−0.408090 + 0.912942i \(0.633805\pi\)
\(398\) −15.0594 −0.754859
\(399\) −0.836617 −0.0418833
\(400\) 0 0
\(401\) 16.8733 0.842613 0.421306 0.906918i \(-0.361572\pi\)
0.421306 + 0.906918i \(0.361572\pi\)
\(402\) 7.65921 0.382007
\(403\) −24.1917 −1.20508
\(404\) 5.72952 0.285054
\(405\) 0 0
\(406\) −0.467497 −0.0232015
\(407\) −25.1504 −1.24666
\(408\) −1.48112 −0.0733264
\(409\) −24.7239 −1.22252 −0.611258 0.791431i \(-0.709336\pi\)
−0.611258 + 0.791431i \(0.709336\pi\)
\(410\) 0 0
\(411\) −11.0794 −0.546506
\(412\) 6.98885 0.344316
\(413\) −26.0227 −1.28049
\(414\) 2.41378 0.118631
\(415\) 0 0
\(416\) −11.0740 −0.542946
\(417\) 11.5624 0.566212
\(418\) −2.12271 −0.103825
\(419\) −7.14295 −0.348956 −0.174478 0.984661i \(-0.555824\pi\)
−0.174478 + 0.984661i \(0.555824\pi\)
\(420\) 0 0
\(421\) 30.7862 1.50043 0.750213 0.661196i \(-0.229951\pi\)
0.750213 + 0.661196i \(0.229951\pi\)
\(422\) 11.1144 0.541043
\(423\) −0.379082 −0.0184316
\(424\) −39.3786 −1.91239
\(425\) 0 0
\(426\) −1.56094 −0.0756276
\(427\) −15.1304 −0.732211
\(428\) −1.08020 −0.0522137
\(429\) −13.4150 −0.647682
\(430\) 0 0
\(431\) −34.8620 −1.67924 −0.839622 0.543172i \(-0.817223\pi\)
−0.839622 + 0.543172i \(0.817223\pi\)
\(432\) 10.8288 0.520999
\(433\) −23.9224 −1.14964 −0.574819 0.818281i \(-0.694928\pi\)
−0.574819 + 0.818281i \(0.694928\pi\)
\(434\) 20.4510 0.981680
\(435\) 0 0
\(436\) 4.77845 0.228846
\(437\) −0.291262 −0.0139329
\(438\) −5.32718 −0.254543
\(439\) −12.4505 −0.594228 −0.297114 0.954842i \(-0.596024\pi\)
−0.297114 + 0.954842i \(0.596024\pi\)
\(440\) 0 0
\(441\) −10.3692 −0.493770
\(442\) 4.79952 0.228290
\(443\) −3.23466 −0.153683 −0.0768416 0.997043i \(-0.524484\pi\)
−0.0768416 + 0.997043i \(0.524484\pi\)
\(444\) −1.51618 −0.0719546
\(445\) 0 0
\(446\) −26.7289 −1.26565
\(447\) 2.44932 0.115849
\(448\) 29.5032 1.39390
\(449\) −9.28417 −0.438147 −0.219073 0.975708i \(-0.570303\pi\)
−0.219073 + 0.975708i \(0.570303\pi\)
\(450\) 0 0
\(451\) 42.7614 2.01355
\(452\) −3.99538 −0.187927
\(453\) 1.63655 0.0768920
\(454\) 17.7366 0.832421
\(455\) 0 0
\(456\) −0.765939 −0.0358684
\(457\) −33.9918 −1.59007 −0.795034 0.606565i \(-0.792547\pi\)
−0.795034 + 0.606565i \(0.792547\pi\)
\(458\) 14.8692 0.694793
\(459\) 2.72871 0.127365
\(460\) 0 0
\(461\) 5.28714 0.246247 0.123123 0.992391i \(-0.460709\pi\)
0.123123 + 0.992391i \(0.460709\pi\)
\(462\) 11.3407 0.527615
\(463\) −37.1728 −1.72757 −0.863783 0.503865i \(-0.831911\pi\)
−0.863783 + 0.503865i \(0.831911\pi\)
\(464\) −0.338554 −0.0157170
\(465\) 0 0
\(466\) −29.9805 −1.38882
\(467\) 1.01602 0.0470159 0.0235080 0.999724i \(-0.492516\pi\)
0.0235080 + 0.999724i \(0.492516\pi\)
\(468\) 5.16102 0.238568
\(469\) −31.5107 −1.45503
\(470\) 0 0
\(471\) 11.0076 0.507202
\(472\) −23.8242 −1.09660
\(473\) −49.8505 −2.29213
\(474\) −3.09246 −0.142042
\(475\) 0 0
\(476\) 1.01804 0.0466619
\(477\) 33.6386 1.54021
\(478\) −15.1305 −0.692051
\(479\) 22.0556 1.00775 0.503874 0.863777i \(-0.331908\pi\)
0.503874 + 0.863777i \(0.331908\pi\)
\(480\) 0 0
\(481\) 29.4074 1.34086
\(482\) 1.26445 0.0575941
\(483\) 1.55608 0.0708041
\(484\) −2.80693 −0.127588
\(485\) 0 0
\(486\) −17.9663 −0.814969
\(487\) 2.46699 0.111790 0.0558949 0.998437i \(-0.482199\pi\)
0.0558949 + 0.998437i \(0.482199\pi\)
\(488\) −13.8522 −0.627058
\(489\) −14.8882 −0.673266
\(490\) 0 0
\(491\) −27.5530 −1.24345 −0.621725 0.783236i \(-0.713568\pi\)
−0.621725 + 0.783236i \(0.713568\pi\)
\(492\) 2.57784 0.116218
\(493\) −0.0853113 −0.00384223
\(494\) 2.48200 0.111670
\(495\) 0 0
\(496\) 14.8103 0.665001
\(497\) 6.42183 0.288059
\(498\) −9.78851 −0.438634
\(499\) −1.27747 −0.0571873 −0.0285937 0.999591i \(-0.509103\pi\)
−0.0285937 + 0.999591i \(0.509103\pi\)
\(500\) 0 0
\(501\) −5.36745 −0.239800
\(502\) 17.8141 0.795084
\(503\) 16.4394 0.732996 0.366498 0.930419i \(-0.380557\pi\)
0.366498 + 0.930419i \(0.380557\pi\)
\(504\) −26.1145 −1.16323
\(505\) 0 0
\(506\) 3.94816 0.175517
\(507\) 7.39810 0.328561
\(508\) 1.81647 0.0805929
\(509\) −14.2702 −0.632514 −0.316257 0.948674i \(-0.602426\pi\)
−0.316257 + 0.948674i \(0.602426\pi\)
\(510\) 0 0
\(511\) 21.9165 0.969530
\(512\) 25.2195 1.11456
\(513\) 1.41111 0.0623020
\(514\) 22.6511 0.999097
\(515\) 0 0
\(516\) −3.00521 −0.132297
\(517\) −0.620056 −0.0272700
\(518\) −24.8602 −1.09229
\(519\) 10.8523 0.476363
\(520\) 0 0
\(521\) −5.63068 −0.246685 −0.123342 0.992364i \(-0.539361\pi\)
−0.123342 + 0.992364i \(0.539361\pi\)
\(522\) 0.365615 0.0160025
\(523\) −19.1152 −0.835848 −0.417924 0.908482i \(-0.637242\pi\)
−0.417924 + 0.908482i \(0.637242\pi\)
\(524\) 4.44358 0.194119
\(525\) 0 0
\(526\) −36.8562 −1.60701
\(527\) 3.73201 0.162569
\(528\) 8.21272 0.357413
\(529\) −22.4583 −0.976446
\(530\) 0 0
\(531\) 20.3515 0.883180
\(532\) 0.526465 0.0228252
\(533\) −49.9992 −2.16570
\(534\) −2.76491 −0.119649
\(535\) 0 0
\(536\) −28.8486 −1.24607
\(537\) −3.84553 −0.165947
\(538\) −2.70020 −0.116414
\(539\) −16.9606 −0.730545
\(540\) 0 0
\(541\) −23.9837 −1.03114 −0.515569 0.856848i \(-0.672420\pi\)
−0.515569 + 0.856848i \(0.672420\pi\)
\(542\) 32.9174 1.41392
\(543\) 0.780841 0.0335091
\(544\) 1.70836 0.0732452
\(545\) 0 0
\(546\) −13.2602 −0.567484
\(547\) −2.05189 −0.0877326 −0.0438663 0.999037i \(-0.513968\pi\)
−0.0438663 + 0.999037i \(0.513968\pi\)
\(548\) 6.97201 0.297830
\(549\) 11.8330 0.505021
\(550\) 0 0
\(551\) −0.0441174 −0.00187946
\(552\) 1.42462 0.0606358
\(553\) 12.7227 0.541024
\(554\) −36.2251 −1.53906
\(555\) 0 0
\(556\) −7.27595 −0.308569
\(557\) −15.2105 −0.644488 −0.322244 0.946657i \(-0.604437\pi\)
−0.322244 + 0.946657i \(0.604437\pi\)
\(558\) −15.9941 −0.677084
\(559\) 58.2882 2.46533
\(560\) 0 0
\(561\) 2.06950 0.0873744
\(562\) 15.6854 0.661650
\(563\) −39.9537 −1.68385 −0.841924 0.539597i \(-0.818577\pi\)
−0.841924 + 0.539597i \(0.818577\pi\)
\(564\) −0.0373797 −0.00157397
\(565\) 0 0
\(566\) 15.0260 0.631591
\(567\) 18.2646 0.767043
\(568\) 5.87931 0.246690
\(569\) −14.4798 −0.607025 −0.303513 0.952827i \(-0.598159\pi\)
−0.303513 + 0.952827i \(0.598159\pi\)
\(570\) 0 0
\(571\) 40.0730 1.67700 0.838501 0.544901i \(-0.183433\pi\)
0.838501 + 0.544901i \(0.183433\pi\)
\(572\) 8.44176 0.352968
\(573\) −9.49642 −0.396719
\(574\) 42.2679 1.76423
\(575\) 0 0
\(576\) −23.0735 −0.961398
\(577\) −8.10574 −0.337446 −0.168723 0.985663i \(-0.553964\pi\)
−0.168723 + 0.985663i \(0.553964\pi\)
\(578\) 20.7552 0.863304
\(579\) 6.48255 0.269406
\(580\) 0 0
\(581\) 40.2709 1.67072
\(582\) 2.88809 0.119715
\(583\) 55.0219 2.27878
\(584\) 20.0650 0.830295
\(585\) 0 0
\(586\) 28.0870 1.16026
\(587\) −18.2675 −0.753981 −0.376991 0.926217i \(-0.623041\pi\)
−0.376991 + 0.926217i \(0.623041\pi\)
\(588\) −1.02246 −0.0421656
\(589\) 1.92995 0.0795221
\(590\) 0 0
\(591\) −5.08447 −0.209147
\(592\) −18.0033 −0.739933
\(593\) 36.5874 1.50246 0.751232 0.660038i \(-0.229460\pi\)
0.751232 + 0.660038i \(0.229460\pi\)
\(594\) −19.1281 −0.784837
\(595\) 0 0
\(596\) −1.54131 −0.0631344
\(597\) 7.59253 0.310742
\(598\) −4.61643 −0.188780
\(599\) 38.6587 1.57955 0.789775 0.613396i \(-0.210197\pi\)
0.789775 + 0.613396i \(0.210197\pi\)
\(600\) 0 0
\(601\) 16.7738 0.684219 0.342110 0.939660i \(-0.388859\pi\)
0.342110 + 0.939660i \(0.388859\pi\)
\(602\) −49.2753 −2.00831
\(603\) 24.6435 1.00356
\(604\) −1.02985 −0.0419039
\(605\) 0 0
\(606\) 11.5127 0.467672
\(607\) 21.6480 0.878664 0.439332 0.898325i \(-0.355215\pi\)
0.439332 + 0.898325i \(0.355215\pi\)
\(608\) 0.883450 0.0358286
\(609\) 0.235699 0.00955101
\(610\) 0 0
\(611\) 0.725006 0.0293306
\(612\) −0.796180 −0.0321837
\(613\) −30.5788 −1.23507 −0.617533 0.786545i \(-0.711868\pi\)
−0.617533 + 0.786545i \(0.711868\pi\)
\(614\) −21.6656 −0.874353
\(615\) 0 0
\(616\) −42.7149 −1.72103
\(617\) −31.9095 −1.28463 −0.642314 0.766442i \(-0.722026\pi\)
−0.642314 + 0.766442i \(0.722026\pi\)
\(618\) 14.0432 0.564899
\(619\) −2.60539 −0.104720 −0.0523598 0.998628i \(-0.516674\pi\)
−0.0523598 + 0.998628i \(0.516674\pi\)
\(620\) 0 0
\(621\) −2.62462 −0.105322
\(622\) −15.3572 −0.615766
\(623\) 11.3751 0.455733
\(624\) −9.60280 −0.384420
\(625\) 0 0
\(626\) 17.5372 0.700926
\(627\) 1.07021 0.0427401
\(628\) −6.92682 −0.276410
\(629\) −4.53661 −0.180887
\(630\) 0 0
\(631\) −4.43947 −0.176732 −0.0883662 0.996088i \(-0.528165\pi\)
−0.0883662 + 0.996088i \(0.528165\pi\)
\(632\) 11.6479 0.463327
\(633\) −5.60360 −0.222723
\(634\) −40.3658 −1.60313
\(635\) 0 0
\(636\) 3.31696 0.131526
\(637\) 19.8314 0.785747
\(638\) 0.598028 0.0236762
\(639\) −5.02232 −0.198680
\(640\) 0 0
\(641\) 17.0249 0.672441 0.336221 0.941783i \(-0.390851\pi\)
0.336221 + 0.941783i \(0.390851\pi\)
\(642\) −2.17053 −0.0856639
\(643\) 27.2144 1.07323 0.536616 0.843827i \(-0.319702\pi\)
0.536616 + 0.843827i \(0.319702\pi\)
\(644\) −0.979207 −0.0385862
\(645\) 0 0
\(646\) −0.382893 −0.0150647
\(647\) 34.5285 1.35745 0.678727 0.734391i \(-0.262532\pi\)
0.678727 + 0.734391i \(0.262532\pi\)
\(648\) 16.7216 0.656887
\(649\) 33.2885 1.30669
\(650\) 0 0
\(651\) −10.3108 −0.404114
\(652\) 9.36880 0.366910
\(653\) 28.1181 1.10035 0.550173 0.835051i \(-0.314562\pi\)
0.550173 + 0.835051i \(0.314562\pi\)
\(654\) 9.60166 0.375455
\(655\) 0 0
\(656\) 30.6097 1.19511
\(657\) −17.1402 −0.668704
\(658\) −0.612901 −0.0238934
\(659\) −30.6584 −1.19428 −0.597142 0.802136i \(-0.703697\pi\)
−0.597142 + 0.802136i \(0.703697\pi\)
\(660\) 0 0
\(661\) 19.2109 0.747219 0.373610 0.927586i \(-0.378120\pi\)
0.373610 + 0.927586i \(0.378120\pi\)
\(662\) 21.0502 0.818139
\(663\) −2.41979 −0.0939767
\(664\) 36.8687 1.43078
\(665\) 0 0
\(666\) 19.4424 0.753377
\(667\) 0.0820568 0.00317725
\(668\) 3.37762 0.130684
\(669\) 13.4760 0.521011
\(670\) 0 0
\(671\) 19.3550 0.747191
\(672\) −4.71987 −0.182073
\(673\) −24.0589 −0.927401 −0.463700 0.885992i \(-0.653479\pi\)
−0.463700 + 0.885992i \(0.653479\pi\)
\(674\) 9.68507 0.373055
\(675\) 0 0
\(676\) −4.65546 −0.179056
\(677\) 11.7427 0.451308 0.225654 0.974208i \(-0.427548\pi\)
0.225654 + 0.974208i \(0.427548\pi\)
\(678\) −8.02818 −0.308320
\(679\) −11.8819 −0.455984
\(680\) 0 0
\(681\) −8.94231 −0.342670
\(682\) −26.1612 −1.00176
\(683\) −19.2688 −0.737301 −0.368650 0.929568i \(-0.620180\pi\)
−0.368650 + 0.929568i \(0.620180\pi\)
\(684\) −0.411732 −0.0157430
\(685\) 0 0
\(686\) 12.5884 0.480627
\(687\) −7.49665 −0.286015
\(688\) −35.6843 −1.36045
\(689\) −64.3349 −2.45097
\(690\) 0 0
\(691\) 0.497698 0.0189333 0.00946666 0.999955i \(-0.496987\pi\)
0.00946666 + 0.999955i \(0.496987\pi\)
\(692\) −6.82912 −0.259604
\(693\) 36.4886 1.38609
\(694\) 25.1854 0.956025
\(695\) 0 0
\(696\) 0.215787 0.00817938
\(697\) 7.71327 0.292161
\(698\) 28.4077 1.07525
\(699\) 15.1153 0.571715
\(700\) 0 0
\(701\) −26.5246 −1.00182 −0.500910 0.865499i \(-0.667001\pi\)
−0.500910 + 0.865499i \(0.667001\pi\)
\(702\) 22.3658 0.844141
\(703\) −2.34604 −0.0884826
\(704\) −37.7409 −1.42241
\(705\) 0 0
\(706\) −10.0447 −0.378037
\(707\) −47.3643 −1.78132
\(708\) 2.00678 0.0754193
\(709\) −23.0989 −0.867497 −0.433748 0.901034i \(-0.642809\pi\)
−0.433748 + 0.901034i \(0.642809\pi\)
\(710\) 0 0
\(711\) −9.95002 −0.373155
\(712\) 10.4141 0.390285
\(713\) −3.58964 −0.134433
\(714\) 2.04562 0.0765554
\(715\) 0 0
\(716\) 2.41991 0.0904362
\(717\) 7.62836 0.284886
\(718\) 42.3748 1.58141
\(719\) −29.3624 −1.09503 −0.547516 0.836795i \(-0.684427\pi\)
−0.547516 + 0.836795i \(0.684427\pi\)
\(720\) 0 0
\(721\) −57.7749 −2.15165
\(722\) 23.8265 0.886732
\(723\) −0.637501 −0.0237089
\(724\) −0.491366 −0.0182615
\(725\) 0 0
\(726\) −5.64014 −0.209325
\(727\) −17.0424 −0.632069 −0.316035 0.948748i \(-0.602352\pi\)
−0.316035 + 0.948748i \(0.602352\pi\)
\(728\) 49.9449 1.85108
\(729\) −7.46438 −0.276459
\(730\) 0 0
\(731\) −8.99200 −0.332581
\(732\) 1.16680 0.0431263
\(733\) 43.2745 1.59838 0.799190 0.601079i \(-0.205262\pi\)
0.799190 + 0.601079i \(0.205262\pi\)
\(734\) −9.66209 −0.356634
\(735\) 0 0
\(736\) −1.64319 −0.0605687
\(737\) 40.3089 1.48480
\(738\) −33.0564 −1.21682
\(739\) −12.5494 −0.461639 −0.230819 0.972997i \(-0.574141\pi\)
−0.230819 + 0.972997i \(0.574141\pi\)
\(740\) 0 0
\(741\) −1.25135 −0.0459697
\(742\) 54.3870 1.99661
\(743\) 11.7612 0.431475 0.215737 0.976451i \(-0.430784\pi\)
0.215737 + 0.976451i \(0.430784\pi\)
\(744\) −9.43976 −0.346078
\(745\) 0 0
\(746\) −18.3632 −0.672323
\(747\) −31.4946 −1.15233
\(748\) −1.30229 −0.0476165
\(749\) 8.92975 0.326286
\(750\) 0 0
\(751\) 21.9386 0.800552 0.400276 0.916395i \(-0.368914\pi\)
0.400276 + 0.916395i \(0.368914\pi\)
\(752\) −0.443852 −0.0161856
\(753\) −8.98140 −0.327300
\(754\) −0.699250 −0.0254652
\(755\) 0 0
\(756\) 4.74408 0.172540
\(757\) 31.1830 1.13337 0.566683 0.823936i \(-0.308226\pi\)
0.566683 + 0.823936i \(0.308226\pi\)
\(758\) 2.07169 0.0752470
\(759\) −1.99056 −0.0722526
\(760\) 0 0
\(761\) 23.5289 0.852922 0.426461 0.904506i \(-0.359760\pi\)
0.426461 + 0.904506i \(0.359760\pi\)
\(762\) 3.64996 0.132224
\(763\) −39.5021 −1.43007
\(764\) 5.97589 0.216200
\(765\) 0 0
\(766\) −9.33970 −0.337457
\(767\) −38.9229 −1.40542
\(768\) −5.87438 −0.211973
\(769\) −32.4863 −1.17148 −0.585742 0.810497i \(-0.699197\pi\)
−0.585742 + 0.810497i \(0.699197\pi\)
\(770\) 0 0
\(771\) −11.4201 −0.411283
\(772\) −4.07933 −0.146818
\(773\) 1.41782 0.0509955 0.0254977 0.999675i \(-0.491883\pi\)
0.0254977 + 0.999675i \(0.491883\pi\)
\(774\) 38.5367 1.38517
\(775\) 0 0
\(776\) −10.8781 −0.390500
\(777\) 12.5338 0.449648
\(778\) 22.2892 0.799105
\(779\) 3.98880 0.142913
\(780\) 0 0
\(781\) −8.21489 −0.293952
\(782\) 0.712167 0.0254670
\(783\) −0.397550 −0.0142073
\(784\) −12.1409 −0.433602
\(785\) 0 0
\(786\) 8.92878 0.318479
\(787\) −24.1473 −0.860759 −0.430380 0.902648i \(-0.641620\pi\)
−0.430380 + 0.902648i \(0.641620\pi\)
\(788\) 3.19955 0.113979
\(789\) 18.5819 0.661532
\(790\) 0 0
\(791\) 33.0287 1.17437
\(792\) 33.4060 1.18703
\(793\) −22.6310 −0.803651
\(794\) 20.5628 0.729748
\(795\) 0 0
\(796\) −4.77781 −0.169345
\(797\) −47.3782 −1.67822 −0.839111 0.543960i \(-0.816924\pi\)
−0.839111 + 0.543960i \(0.816924\pi\)
\(798\) 1.05786 0.0374479
\(799\) −0.111845 −0.00395680
\(800\) 0 0
\(801\) −8.89610 −0.314328
\(802\) −21.3355 −0.753381
\(803\) −28.0359 −0.989365
\(804\) 2.43000 0.0856994
\(805\) 0 0
\(806\) 30.5892 1.07746
\(807\) 1.36136 0.0479223
\(808\) −43.3629 −1.52550
\(809\) −4.46224 −0.156884 −0.0784420 0.996919i \(-0.524995\pi\)
−0.0784420 + 0.996919i \(0.524995\pi\)
\(810\) 0 0
\(811\) −1.09836 −0.0385685 −0.0192843 0.999814i \(-0.506139\pi\)
−0.0192843 + 0.999814i \(0.506139\pi\)
\(812\) −0.148320 −0.00520502
\(813\) −16.5961 −0.582049
\(814\) 31.8015 1.11464
\(815\) 0 0
\(816\) 1.48140 0.0518595
\(817\) −4.65007 −0.162686
\(818\) 31.2621 1.09305
\(819\) −42.6647 −1.49083
\(820\) 0 0
\(821\) 36.8213 1.28507 0.642536 0.766255i \(-0.277882\pi\)
0.642536 + 0.766255i \(0.277882\pi\)
\(822\) 14.0093 0.488631
\(823\) −37.0100 −1.29009 −0.645043 0.764146i \(-0.723161\pi\)
−0.645043 + 0.764146i \(0.723161\pi\)
\(824\) −52.8940 −1.84265
\(825\) 0 0
\(826\) 32.9044 1.14489
\(827\) 25.5191 0.887388 0.443694 0.896178i \(-0.353668\pi\)
0.443694 + 0.896178i \(0.353668\pi\)
\(828\) 0.765807 0.0266136
\(829\) −16.4498 −0.571324 −0.285662 0.958330i \(-0.592214\pi\)
−0.285662 + 0.958330i \(0.592214\pi\)
\(830\) 0 0
\(831\) 18.2637 0.633560
\(832\) 44.1289 1.52989
\(833\) −3.05934 −0.106000
\(834\) −14.6200 −0.506251
\(835\) 0 0
\(836\) −0.673460 −0.0232921
\(837\) 17.3911 0.601126
\(838\) 9.03191 0.312002
\(839\) 51.1330 1.76531 0.882653 0.470025i \(-0.155755\pi\)
0.882653 + 0.470025i \(0.155755\pi\)
\(840\) 0 0
\(841\) −28.9876 −0.999571
\(842\) −38.9276 −1.34153
\(843\) −7.90816 −0.272371
\(844\) 3.52622 0.121377
\(845\) 0 0
\(846\) 0.479330 0.0164797
\(847\) 23.2041 0.797301
\(848\) 39.3862 1.35253
\(849\) −7.57570 −0.259997
\(850\) 0 0
\(851\) 4.36355 0.149581
\(852\) −0.495230 −0.0169663
\(853\) −45.0455 −1.54233 −0.771164 0.636636i \(-0.780325\pi\)
−0.771164 + 0.636636i \(0.780325\pi\)
\(854\) 19.1316 0.654671
\(855\) 0 0
\(856\) 8.17535 0.279428
\(857\) 0.941226 0.0321517 0.0160758 0.999871i \(-0.494883\pi\)
0.0160758 + 0.999871i \(0.494883\pi\)
\(858\) 16.9626 0.579093
\(859\) 4.59938 0.156929 0.0784644 0.996917i \(-0.474998\pi\)
0.0784644 + 0.996917i \(0.474998\pi\)
\(860\) 0 0
\(861\) −21.3103 −0.726254
\(862\) 44.0813 1.50141
\(863\) −12.8946 −0.438937 −0.219469 0.975620i \(-0.570432\pi\)
−0.219469 + 0.975620i \(0.570432\pi\)
\(864\) 7.96094 0.270837
\(865\) 0 0
\(866\) 30.2487 1.02789
\(867\) −10.4642 −0.355384
\(868\) 6.48838 0.220230
\(869\) −16.2750 −0.552092
\(870\) 0 0
\(871\) −47.1316 −1.59699
\(872\) −36.1649 −1.22470
\(873\) 9.29244 0.314501
\(874\) 0.368286 0.0124575
\(875\) 0 0
\(876\) −1.69013 −0.0571041
\(877\) −1.28343 −0.0433383 −0.0216691 0.999765i \(-0.506898\pi\)
−0.0216691 + 0.999765i \(0.506898\pi\)
\(878\) 15.7430 0.531300
\(879\) −14.1607 −0.477629
\(880\) 0 0
\(881\) −5.72028 −0.192721 −0.0963606 0.995346i \(-0.530720\pi\)
−0.0963606 + 0.995346i \(0.530720\pi\)
\(882\) 13.1113 0.441481
\(883\) −20.1652 −0.678614 −0.339307 0.940676i \(-0.610192\pi\)
−0.339307 + 0.940676i \(0.610192\pi\)
\(884\) 1.52272 0.0512146
\(885\) 0 0
\(886\) 4.09006 0.137408
\(887\) 13.7132 0.460443 0.230221 0.973138i \(-0.426055\pi\)
0.230221 + 0.973138i \(0.426055\pi\)
\(888\) 11.4749 0.385074
\(889\) −15.0163 −0.503630
\(890\) 0 0
\(891\) −23.3644 −0.782735
\(892\) −8.48013 −0.283936
\(893\) −0.0578390 −0.00193551
\(894\) −3.09705 −0.103581
\(895\) 0 0
\(896\) −22.4979 −0.751603
\(897\) 2.32748 0.0777122
\(898\) 11.7394 0.391748
\(899\) −0.543722 −0.0181341
\(900\) 0 0
\(901\) 9.92481 0.330644
\(902\) −54.0696 −1.80032
\(903\) 24.8432 0.826731
\(904\) 30.2384 1.00571
\(905\) 0 0
\(906\) −2.06934 −0.0687492
\(907\) 11.7711 0.390853 0.195427 0.980718i \(-0.437391\pi\)
0.195427 + 0.980718i \(0.437391\pi\)
\(908\) 5.62720 0.186745
\(909\) 37.0422 1.22861
\(910\) 0 0
\(911\) 12.3287 0.408469 0.204234 0.978922i \(-0.434530\pi\)
0.204234 + 0.978922i \(0.434530\pi\)
\(912\) 0.766085 0.0253676
\(913\) −51.5150 −1.70490
\(914\) 42.9809 1.42168
\(915\) 0 0
\(916\) 4.71748 0.155870
\(917\) −36.7338 −1.21306
\(918\) −3.45032 −0.113878
\(919\) 27.1688 0.896216 0.448108 0.893980i \(-0.352098\pi\)
0.448108 + 0.893980i \(0.352098\pi\)
\(920\) 0 0
\(921\) 10.9232 0.359932
\(922\) −6.68533 −0.220170
\(923\) 9.60534 0.316164
\(924\) 3.59799 0.118365
\(925\) 0 0
\(926\) 47.0031 1.54462
\(927\) 45.1839 1.48404
\(928\) −0.248893 −0.00817033
\(929\) 6.23154 0.204450 0.102225 0.994761i \(-0.467404\pi\)
0.102225 + 0.994761i \(0.467404\pi\)
\(930\) 0 0
\(931\) −1.58209 −0.0518510
\(932\) −9.51176 −0.311568
\(933\) 7.74266 0.253483
\(934\) −1.28471 −0.0420370
\(935\) 0 0
\(936\) −39.0603 −1.27673
\(937\) 33.4598 1.09308 0.546542 0.837432i \(-0.315944\pi\)
0.546542 + 0.837432i \(0.315944\pi\)
\(938\) 39.8437 1.30094
\(939\) −8.84175 −0.288540
\(940\) 0 0
\(941\) −28.9090 −0.942406 −0.471203 0.882025i \(-0.656180\pi\)
−0.471203 + 0.882025i \(0.656180\pi\)
\(942\) −13.9185 −0.453490
\(943\) −7.41902 −0.241597
\(944\) 23.8288 0.775561
\(945\) 0 0
\(946\) 63.0335 2.04940
\(947\) −12.2378 −0.397675 −0.198837 0.980033i \(-0.563717\pi\)
−0.198837 + 0.980033i \(0.563717\pi\)
\(948\) −0.981129 −0.0318656
\(949\) 32.7812 1.06412
\(950\) 0 0
\(951\) 20.3513 0.659937
\(952\) −7.70489 −0.249717
\(953\) 29.2078 0.946133 0.473066 0.881027i \(-0.343147\pi\)
0.473066 + 0.881027i \(0.343147\pi\)
\(954\) −42.5344 −1.37710
\(955\) 0 0
\(956\) −4.80036 −0.155255
\(957\) −0.301509 −0.00974641
\(958\) −27.8883 −0.901029
\(959\) −57.6357 −1.86115
\(960\) 0 0
\(961\) −7.21448 −0.232725
\(962\) −37.1842 −1.19887
\(963\) −6.98368 −0.225046
\(964\) 0.401165 0.0129207
\(965\) 0 0
\(966\) −1.96759 −0.0633060
\(967\) −2.99676 −0.0963693 −0.0481847 0.998838i \(-0.515344\pi\)
−0.0481847 + 0.998838i \(0.515344\pi\)
\(968\) 21.2438 0.682800
\(969\) 0.193044 0.00620146
\(970\) 0 0
\(971\) −35.6237 −1.14322 −0.571609 0.820526i \(-0.693681\pi\)
−0.571609 + 0.820526i \(0.693681\pi\)
\(972\) −5.70008 −0.182830
\(973\) 60.1483 1.92826
\(974\) −3.11938 −0.0999515
\(975\) 0 0
\(976\) 13.8548 0.443482
\(977\) −32.0035 −1.02388 −0.511942 0.859020i \(-0.671074\pi\)
−0.511942 + 0.859020i \(0.671074\pi\)
\(978\) 18.8253 0.601968
\(979\) −14.5511 −0.465057
\(980\) 0 0
\(981\) 30.8934 0.986350
\(982\) 34.8394 1.11177
\(983\) −36.9419 −1.17826 −0.589132 0.808037i \(-0.700530\pi\)
−0.589132 + 0.808037i \(0.700530\pi\)
\(984\) −19.5100 −0.621956
\(985\) 0 0
\(986\) 0.107872 0.00343534
\(987\) 0.309008 0.00983582
\(988\) 0.787450 0.0250521
\(989\) 8.64898 0.275022
\(990\) 0 0
\(991\) 37.2274 1.18257 0.591283 0.806464i \(-0.298622\pi\)
0.591283 + 0.806464i \(0.298622\pi\)
\(992\) 10.8880 0.345695
\(993\) −10.6129 −0.336791
\(994\) −8.12009 −0.257554
\(995\) 0 0
\(996\) −3.10555 −0.0984031
\(997\) 56.6610 1.79447 0.897237 0.441550i \(-0.145571\pi\)
0.897237 + 0.441550i \(0.145571\pi\)
\(998\) 1.61529 0.0511313
\(999\) −21.1406 −0.668859
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 6025.2.a.l.1.14 40
5.4 even 2 6025.2.a.o.1.27 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6025.2.a.l.1.14 40 1.1 even 1 trivial
6025.2.a.o.1.27 yes 40 5.4 even 2