Properties

Label 2013.2.a.h.1.9
Level $2013$
Weight $2$
Character 2013.1
Self dual yes
Analytic conductor $16.074$
Analytic rank $0$
Dimension $14$
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] = [2013,2,Mod(1,2013)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2013, 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("2013.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2013 = 3 \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2013.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: \(16.0738859269\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} - x^{13} - 21 x^{12} + 20 x^{11} + 167 x^{10} - 148 x^{9} - 627 x^{8} + 497 x^{7} + 1123 x^{6} - 745 x^{5} - 802 x^{4} + 386 x^{3} + 74 x^{2} - 15 x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(-0.231279\) of defining polynomial
Character \(\chi\) \(=\) 2013.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.231279 q^{2} -1.00000 q^{3} -1.94651 q^{4} +3.70694 q^{5} -0.231279 q^{6} -0.911108 q^{7} -0.912746 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.231279 q^{2} -1.00000 q^{3} -1.94651 q^{4} +3.70694 q^{5} -0.231279 q^{6} -0.911108 q^{7} -0.912746 q^{8} +1.00000 q^{9} +0.857338 q^{10} -1.00000 q^{11} +1.94651 q^{12} -1.28993 q^{13} -0.210720 q^{14} -3.70694 q^{15} +3.68192 q^{16} -7.36730 q^{17} +0.231279 q^{18} +5.91624 q^{19} -7.21559 q^{20} +0.911108 q^{21} -0.231279 q^{22} +6.40611 q^{23} +0.912746 q^{24} +8.74139 q^{25} -0.298334 q^{26} -1.00000 q^{27} +1.77348 q^{28} +9.58456 q^{29} -0.857338 q^{30} -8.65847 q^{31} +2.67705 q^{32} +1.00000 q^{33} -1.70390 q^{34} -3.37742 q^{35} -1.94651 q^{36} -8.74406 q^{37} +1.36830 q^{38} +1.28993 q^{39} -3.38349 q^{40} +6.54649 q^{41} +0.210720 q^{42} +9.59278 q^{43} +1.94651 q^{44} +3.70694 q^{45} +1.48160 q^{46} +5.82694 q^{47} -3.68192 q^{48} -6.16988 q^{49} +2.02170 q^{50} +7.36730 q^{51} +2.51086 q^{52} -5.01034 q^{53} -0.231279 q^{54} -3.70694 q^{55} +0.831610 q^{56} -5.91624 q^{57} +2.21671 q^{58} +1.55369 q^{59} +7.21559 q^{60} +1.00000 q^{61} -2.00252 q^{62} -0.911108 q^{63} -6.74470 q^{64} -4.78168 q^{65} +0.231279 q^{66} +12.7209 q^{67} +14.3405 q^{68} -6.40611 q^{69} -0.781128 q^{70} -0.506871 q^{71} -0.912746 q^{72} -3.71011 q^{73} -2.02232 q^{74} -8.74139 q^{75} -11.5160 q^{76} +0.911108 q^{77} +0.298334 q^{78} -5.28303 q^{79} +13.6486 q^{80} +1.00000 q^{81} +1.51407 q^{82} +7.43641 q^{83} -1.77348 q^{84} -27.3101 q^{85} +2.21861 q^{86} -9.58456 q^{87} +0.912746 q^{88} +12.7615 q^{89} +0.857338 q^{90} +1.17526 q^{91} -12.4695 q^{92} +8.65847 q^{93} +1.34765 q^{94} +21.9311 q^{95} -2.67705 q^{96} +19.0085 q^{97} -1.42697 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9} + 6 q^{10} - 14 q^{11} - 15 q^{12} + q^{13} - 7 q^{14} - q^{15} + 17 q^{16} - 9 q^{17} - q^{18} + 22 q^{19} + 23 q^{20} - 9 q^{21} + q^{22} + q^{23} + 25 q^{25} + 4 q^{26} - 14 q^{27} + 37 q^{28} - 6 q^{29} - 6 q^{30} + 9 q^{31} + 4 q^{32} + 14 q^{33} + 8 q^{34} + 18 q^{35} + 15 q^{36} + 18 q^{37} + 8 q^{38} - q^{39} + 16 q^{40} - 25 q^{41} + 7 q^{42} + 25 q^{43} - 15 q^{44} + q^{45} + 20 q^{46} + 36 q^{47} - 17 q^{48} + 25 q^{49} + 2 q^{50} + 9 q^{51} - 13 q^{52} + q^{54} - q^{55} - 40 q^{56} - 22 q^{57} + 33 q^{58} + 17 q^{59} - 23 q^{60} + 14 q^{61} - 13 q^{62} + 9 q^{63} - 6 q^{64} - 61 q^{65} - q^{66} + 22 q^{67} + 66 q^{68} - q^{69} + 44 q^{70} - 13 q^{71} + 20 q^{73} - 12 q^{74} - 25 q^{75} + 49 q^{76} - 9 q^{77} - 4 q^{78} + 31 q^{79} + 88 q^{80} + 14 q^{81} + 2 q^{82} + 32 q^{83} - 37 q^{84} + 2 q^{85} - 14 q^{86} + 6 q^{87} - 21 q^{89} + 6 q^{90} + 45 q^{91} - 14 q^{92} - 9 q^{93} - 31 q^{94} + 23 q^{95} - 4 q^{96} + 37 q^{97} - 38 q^{98} - 14 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.231279 0.163539 0.0817696 0.996651i \(-0.473943\pi\)
0.0817696 + 0.996651i \(0.473943\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.94651 −0.973255
\(5\) 3.70694 1.65779 0.828896 0.559402i \(-0.188969\pi\)
0.828896 + 0.559402i \(0.188969\pi\)
\(6\) −0.231279 −0.0944194
\(7\) −0.911108 −0.344366 −0.172183 0.985065i \(-0.555082\pi\)
−0.172183 + 0.985065i \(0.555082\pi\)
\(8\) −0.912746 −0.322705
\(9\) 1.00000 0.333333
\(10\) 0.857338 0.271114
\(11\) −1.00000 −0.301511
\(12\) 1.94651 0.561909
\(13\) −1.28993 −0.357761 −0.178881 0.983871i \(-0.557248\pi\)
−0.178881 + 0.983871i \(0.557248\pi\)
\(14\) −0.210720 −0.0563174
\(15\) −3.70694 −0.957127
\(16\) 3.68192 0.920480
\(17\) −7.36730 −1.78683 −0.893416 0.449230i \(-0.851699\pi\)
−0.893416 + 0.449230i \(0.851699\pi\)
\(18\) 0.231279 0.0545131
\(19\) 5.91624 1.35728 0.678640 0.734472i \(-0.262570\pi\)
0.678640 + 0.734472i \(0.262570\pi\)
\(20\) −7.21559 −1.61346
\(21\) 0.911108 0.198820
\(22\) −0.231279 −0.0493089
\(23\) 6.40611 1.33577 0.667883 0.744267i \(-0.267201\pi\)
0.667883 + 0.744267i \(0.267201\pi\)
\(24\) 0.912746 0.186314
\(25\) 8.74139 1.74828
\(26\) −0.298334 −0.0585080
\(27\) −1.00000 −0.192450
\(28\) 1.77348 0.335156
\(29\) 9.58456 1.77981 0.889904 0.456147i \(-0.150771\pi\)
0.889904 + 0.456147i \(0.150771\pi\)
\(30\) −0.857338 −0.156528
\(31\) −8.65847 −1.55511 −0.777553 0.628817i \(-0.783539\pi\)
−0.777553 + 0.628817i \(0.783539\pi\)
\(32\) 2.67705 0.473239
\(33\) 1.00000 0.174078
\(34\) −1.70390 −0.292217
\(35\) −3.37742 −0.570888
\(36\) −1.94651 −0.324418
\(37\) −8.74406 −1.43751 −0.718757 0.695261i \(-0.755289\pi\)
−0.718757 + 0.695261i \(0.755289\pi\)
\(38\) 1.36830 0.221968
\(39\) 1.28993 0.206554
\(40\) −3.38349 −0.534977
\(41\) 6.54649 1.02239 0.511195 0.859465i \(-0.329203\pi\)
0.511195 + 0.859465i \(0.329203\pi\)
\(42\) 0.210720 0.0325149
\(43\) 9.59278 1.46289 0.731443 0.681903i \(-0.238847\pi\)
0.731443 + 0.681903i \(0.238847\pi\)
\(44\) 1.94651 0.293447
\(45\) 3.70694 0.552598
\(46\) 1.48160 0.218450
\(47\) 5.82694 0.849946 0.424973 0.905206i \(-0.360284\pi\)
0.424973 + 0.905206i \(0.360284\pi\)
\(48\) −3.68192 −0.531439
\(49\) −6.16988 −0.881412
\(50\) 2.02170 0.285912
\(51\) 7.36730 1.03163
\(52\) 2.51086 0.348193
\(53\) −5.01034 −0.688223 −0.344111 0.938929i \(-0.611820\pi\)
−0.344111 + 0.938929i \(0.611820\pi\)
\(54\) −0.231279 −0.0314731
\(55\) −3.70694 −0.499843
\(56\) 0.831610 0.111129
\(57\) −5.91624 −0.783625
\(58\) 2.21671 0.291069
\(59\) 1.55369 0.202273 0.101137 0.994873i \(-0.467752\pi\)
0.101137 + 0.994873i \(0.467752\pi\)
\(60\) 7.21559 0.931529
\(61\) 1.00000 0.128037
\(62\) −2.00252 −0.254321
\(63\) −0.911108 −0.114789
\(64\) −6.74470 −0.843087
\(65\) −4.78168 −0.593094
\(66\) 0.231279 0.0284685
\(67\) 12.7209 1.55410 0.777052 0.629436i \(-0.216714\pi\)
0.777052 + 0.629436i \(0.216714\pi\)
\(68\) 14.3405 1.73904
\(69\) −6.40611 −0.771205
\(70\) −0.781128 −0.0933626
\(71\) −0.506871 −0.0601545 −0.0300773 0.999548i \(-0.509575\pi\)
−0.0300773 + 0.999548i \(0.509575\pi\)
\(72\) −0.912746 −0.107568
\(73\) −3.71011 −0.434236 −0.217118 0.976145i \(-0.569666\pi\)
−0.217118 + 0.976145i \(0.569666\pi\)
\(74\) −2.02232 −0.235090
\(75\) −8.74139 −1.00937
\(76\) −11.5160 −1.32098
\(77\) 0.911108 0.103830
\(78\) 0.298334 0.0337796
\(79\) −5.28303 −0.594387 −0.297194 0.954817i \(-0.596051\pi\)
−0.297194 + 0.954817i \(0.596051\pi\)
\(80\) 13.6486 1.52597
\(81\) 1.00000 0.111111
\(82\) 1.51407 0.167201
\(83\) 7.43641 0.816252 0.408126 0.912926i \(-0.366182\pi\)
0.408126 + 0.912926i \(0.366182\pi\)
\(84\) −1.77348 −0.193503
\(85\) −27.3101 −2.96220
\(86\) 2.21861 0.239239
\(87\) −9.58456 −1.02757
\(88\) 0.912746 0.0972991
\(89\) 12.7615 1.35272 0.676360 0.736571i \(-0.263556\pi\)
0.676360 + 0.736571i \(0.263556\pi\)
\(90\) 0.857338 0.0903714
\(91\) 1.17526 0.123201
\(92\) −12.4695 −1.30004
\(93\) 8.65847 0.897841
\(94\) 1.34765 0.139000
\(95\) 21.9311 2.25009
\(96\) −2.67705 −0.273225
\(97\) 19.0085 1.93002 0.965012 0.262207i \(-0.0844504\pi\)
0.965012 + 0.262207i \(0.0844504\pi\)
\(98\) −1.42697 −0.144145
\(99\) −1.00000 −0.100504
\(100\) −17.0152 −1.70152
\(101\) −5.60028 −0.557249 −0.278624 0.960400i \(-0.589878\pi\)
−0.278624 + 0.960400i \(0.589878\pi\)
\(102\) 1.70390 0.168712
\(103\) 16.0507 1.58153 0.790763 0.612122i \(-0.209684\pi\)
0.790763 + 0.612122i \(0.209684\pi\)
\(104\) 1.17738 0.115451
\(105\) 3.37742 0.329602
\(106\) −1.15879 −0.112551
\(107\) 16.1333 1.55966 0.779830 0.625991i \(-0.215305\pi\)
0.779830 + 0.625991i \(0.215305\pi\)
\(108\) 1.94651 0.187303
\(109\) −15.2826 −1.46381 −0.731905 0.681407i \(-0.761369\pi\)
−0.731905 + 0.681407i \(0.761369\pi\)
\(110\) −0.857338 −0.0817440
\(111\) 8.74406 0.829949
\(112\) −3.35463 −0.316982
\(113\) 13.4720 1.26734 0.633668 0.773605i \(-0.281549\pi\)
0.633668 + 0.773605i \(0.281549\pi\)
\(114\) −1.36830 −0.128153
\(115\) 23.7470 2.21442
\(116\) −18.6564 −1.73221
\(117\) −1.28993 −0.119254
\(118\) 0.359337 0.0330796
\(119\) 6.71240 0.615325
\(120\) 3.38349 0.308869
\(121\) 1.00000 0.0909091
\(122\) 0.231279 0.0209391
\(123\) −6.54649 −0.590277
\(124\) 16.8538 1.51352
\(125\) 13.8691 1.24049
\(126\) −0.210720 −0.0187725
\(127\) 14.9118 1.32321 0.661605 0.749852i \(-0.269875\pi\)
0.661605 + 0.749852i \(0.269875\pi\)
\(128\) −6.91400 −0.611117
\(129\) −9.59278 −0.844597
\(130\) −1.10590 −0.0969942
\(131\) 1.52367 0.133123 0.0665617 0.997782i \(-0.478797\pi\)
0.0665617 + 0.997782i \(0.478797\pi\)
\(132\) −1.94651 −0.169422
\(133\) −5.39033 −0.467401
\(134\) 2.94208 0.254157
\(135\) −3.70694 −0.319042
\(136\) 6.72448 0.576619
\(137\) 3.70337 0.316400 0.158200 0.987407i \(-0.449431\pi\)
0.158200 + 0.987407i \(0.449431\pi\)
\(138\) −1.48160 −0.126122
\(139\) 6.10661 0.517956 0.258978 0.965883i \(-0.416614\pi\)
0.258978 + 0.965883i \(0.416614\pi\)
\(140\) 6.57418 0.555620
\(141\) −5.82694 −0.490717
\(142\) −0.117229 −0.00983762
\(143\) 1.28993 0.107869
\(144\) 3.68192 0.306827
\(145\) 35.5294 2.95055
\(146\) −0.858073 −0.0710146
\(147\) 6.16988 0.508883
\(148\) 17.0204 1.39907
\(149\) −13.5246 −1.10797 −0.553987 0.832525i \(-0.686894\pi\)
−0.553987 + 0.832525i \(0.686894\pi\)
\(150\) −2.02170 −0.165071
\(151\) −1.09346 −0.0889849 −0.0444924 0.999010i \(-0.514167\pi\)
−0.0444924 + 0.999010i \(0.514167\pi\)
\(152\) −5.40003 −0.438000
\(153\) −7.36730 −0.595611
\(154\) 0.210720 0.0169803
\(155\) −32.0964 −2.57804
\(156\) −2.51086 −0.201029
\(157\) 14.4608 1.15410 0.577049 0.816709i \(-0.304204\pi\)
0.577049 + 0.816709i \(0.304204\pi\)
\(158\) −1.22186 −0.0972057
\(159\) 5.01034 0.397346
\(160\) 9.92364 0.784533
\(161\) −5.83665 −0.459993
\(162\) 0.231279 0.0181710
\(163\) 1.40734 0.110231 0.0551155 0.998480i \(-0.482447\pi\)
0.0551155 + 0.998480i \(0.482447\pi\)
\(164\) −12.7428 −0.995046
\(165\) 3.70694 0.288585
\(166\) 1.71989 0.133489
\(167\) −14.0105 −1.08416 −0.542082 0.840326i \(-0.682364\pi\)
−0.542082 + 0.840326i \(0.682364\pi\)
\(168\) −0.831610 −0.0641601
\(169\) −11.3361 −0.872007
\(170\) −6.31627 −0.484436
\(171\) 5.91624 0.452426
\(172\) −18.6724 −1.42376
\(173\) 2.67772 0.203584 0.101792 0.994806i \(-0.467542\pi\)
0.101792 + 0.994806i \(0.467542\pi\)
\(174\) −2.21671 −0.168048
\(175\) −7.96434 −0.602048
\(176\) −3.68192 −0.277535
\(177\) −1.55369 −0.116783
\(178\) 2.95148 0.221223
\(179\) 2.14059 0.159995 0.0799977 0.996795i \(-0.474509\pi\)
0.0799977 + 0.996795i \(0.474509\pi\)
\(180\) −7.21559 −0.537818
\(181\) 10.4522 0.776903 0.388451 0.921469i \(-0.373010\pi\)
0.388451 + 0.921469i \(0.373010\pi\)
\(182\) 0.271814 0.0201482
\(183\) −1.00000 −0.0739221
\(184\) −5.84715 −0.431058
\(185\) −32.4137 −2.38310
\(186\) 2.00252 0.146832
\(187\) 7.36730 0.538750
\(188\) −11.3422 −0.827214
\(189\) 0.911108 0.0662733
\(190\) 5.07222 0.367978
\(191\) 6.90631 0.499723 0.249862 0.968282i \(-0.419615\pi\)
0.249862 + 0.968282i \(0.419615\pi\)
\(192\) 6.74470 0.486756
\(193\) 13.5215 0.973300 0.486650 0.873597i \(-0.338219\pi\)
0.486650 + 0.873597i \(0.338219\pi\)
\(194\) 4.39628 0.315634
\(195\) 4.78168 0.342423
\(196\) 12.0097 0.857838
\(197\) −12.6509 −0.901342 −0.450671 0.892690i \(-0.648815\pi\)
−0.450671 + 0.892690i \(0.648815\pi\)
\(198\) −0.231279 −0.0164363
\(199\) 3.63188 0.257457 0.128728 0.991680i \(-0.458910\pi\)
0.128728 + 0.991680i \(0.458910\pi\)
\(200\) −7.97867 −0.564177
\(201\) −12.7209 −0.897263
\(202\) −1.29523 −0.0911320
\(203\) −8.73257 −0.612906
\(204\) −14.3405 −1.00404
\(205\) 24.2674 1.69491
\(206\) 3.71220 0.258642
\(207\) 6.40611 0.445255
\(208\) −4.74941 −0.329312
\(209\) −5.91624 −0.409235
\(210\) 0.781128 0.0539029
\(211\) −18.3470 −1.26306 −0.631530 0.775352i \(-0.717573\pi\)
−0.631530 + 0.775352i \(0.717573\pi\)
\(212\) 9.75267 0.669816
\(213\) 0.506871 0.0347302
\(214\) 3.73129 0.255066
\(215\) 35.5598 2.42516
\(216\) 0.912746 0.0621045
\(217\) 7.88880 0.535526
\(218\) −3.53456 −0.239390
\(219\) 3.71011 0.250706
\(220\) 7.21559 0.486475
\(221\) 9.50328 0.639260
\(222\) 2.02232 0.135729
\(223\) 6.99961 0.468729 0.234364 0.972149i \(-0.424699\pi\)
0.234364 + 0.972149i \(0.424699\pi\)
\(224\) −2.43908 −0.162968
\(225\) 8.74139 0.582759
\(226\) 3.11579 0.207259
\(227\) 6.85426 0.454933 0.227467 0.973786i \(-0.426956\pi\)
0.227467 + 0.973786i \(0.426956\pi\)
\(228\) 11.5160 0.762667
\(229\) −2.15050 −0.142109 −0.0710544 0.997472i \(-0.522636\pi\)
−0.0710544 + 0.997472i \(0.522636\pi\)
\(230\) 5.49220 0.362145
\(231\) −0.911108 −0.0599465
\(232\) −8.74827 −0.574352
\(233\) −0.0878610 −0.00575597 −0.00287798 0.999996i \(-0.500916\pi\)
−0.00287798 + 0.999996i \(0.500916\pi\)
\(234\) −0.298334 −0.0195027
\(235\) 21.6001 1.40903
\(236\) −3.02428 −0.196864
\(237\) 5.28303 0.343170
\(238\) 1.55244 0.100630
\(239\) −1.34617 −0.0870763 −0.0435382 0.999052i \(-0.513863\pi\)
−0.0435382 + 0.999052i \(0.513863\pi\)
\(240\) −13.6486 −0.881016
\(241\) 4.54006 0.292451 0.146225 0.989251i \(-0.453288\pi\)
0.146225 + 0.989251i \(0.453288\pi\)
\(242\) 0.231279 0.0148672
\(243\) −1.00000 −0.0641500
\(244\) −1.94651 −0.124613
\(245\) −22.8714 −1.46120
\(246\) −1.51407 −0.0965334
\(247\) −7.63152 −0.485582
\(248\) 7.90298 0.501840
\(249\) −7.43641 −0.471263
\(250\) 3.20763 0.202869
\(251\) −5.83748 −0.368458 −0.184229 0.982883i \(-0.558979\pi\)
−0.184229 + 0.982883i \(0.558979\pi\)
\(252\) 1.77348 0.111719
\(253\) −6.40611 −0.402748
\(254\) 3.44880 0.216397
\(255\) 27.3101 1.71023
\(256\) 11.8903 0.743145
\(257\) 19.2484 1.20068 0.600341 0.799744i \(-0.295032\pi\)
0.600341 + 0.799744i \(0.295032\pi\)
\(258\) −2.21861 −0.138125
\(259\) 7.96678 0.495032
\(260\) 9.30759 0.577232
\(261\) 9.58456 0.593270
\(262\) 0.352393 0.0217709
\(263\) −12.4662 −0.768698 −0.384349 0.923188i \(-0.625574\pi\)
−0.384349 + 0.923188i \(0.625574\pi\)
\(264\) −0.912746 −0.0561757
\(265\) −18.5730 −1.14093
\(266\) −1.24667 −0.0764384
\(267\) −12.7615 −0.780993
\(268\) −24.7614 −1.51254
\(269\) −10.9441 −0.667276 −0.333638 0.942701i \(-0.608276\pi\)
−0.333638 + 0.942701i \(0.608276\pi\)
\(270\) −0.857338 −0.0521759
\(271\) −17.9716 −1.09169 −0.545847 0.837885i \(-0.683792\pi\)
−0.545847 + 0.837885i \(0.683792\pi\)
\(272\) −27.1258 −1.64474
\(273\) −1.17526 −0.0711301
\(274\) 0.856514 0.0517439
\(275\) −8.74139 −0.527125
\(276\) 12.4695 0.750579
\(277\) −5.74306 −0.345067 −0.172534 0.985004i \(-0.555195\pi\)
−0.172534 + 0.985004i \(0.555195\pi\)
\(278\) 1.41233 0.0847061
\(279\) −8.65847 −0.518369
\(280\) 3.08273 0.184228
\(281\) −31.3802 −1.87199 −0.935993 0.352019i \(-0.885495\pi\)
−0.935993 + 0.352019i \(0.885495\pi\)
\(282\) −1.34765 −0.0802514
\(283\) −22.4497 −1.33450 −0.667248 0.744835i \(-0.732528\pi\)
−0.667248 + 0.744835i \(0.732528\pi\)
\(284\) 0.986629 0.0585457
\(285\) −21.9311 −1.29909
\(286\) 0.298334 0.0176408
\(287\) −5.96456 −0.352077
\(288\) 2.67705 0.157746
\(289\) 37.2771 2.19277
\(290\) 8.21721 0.482531
\(291\) −19.0085 −1.11430
\(292\) 7.22177 0.422622
\(293\) −15.8824 −0.927861 −0.463931 0.885872i \(-0.653561\pi\)
−0.463931 + 0.885872i \(0.653561\pi\)
\(294\) 1.42697 0.0832224
\(295\) 5.75944 0.335327
\(296\) 7.98111 0.463893
\(297\) 1.00000 0.0580259
\(298\) −3.12795 −0.181197
\(299\) −8.26341 −0.477885
\(300\) 17.0152 0.982373
\(301\) −8.74006 −0.503769
\(302\) −0.252896 −0.0145525
\(303\) 5.60028 0.321728
\(304\) 21.7831 1.24935
\(305\) 3.70694 0.212259
\(306\) −1.70390 −0.0974057
\(307\) 13.2053 0.753665 0.376832 0.926281i \(-0.377013\pi\)
0.376832 + 0.926281i \(0.377013\pi\)
\(308\) −1.77348 −0.101053
\(309\) −16.0507 −0.913095
\(310\) −7.42323 −0.421611
\(311\) 7.86121 0.445768 0.222884 0.974845i \(-0.428453\pi\)
0.222884 + 0.974845i \(0.428453\pi\)
\(312\) −1.17738 −0.0666558
\(313\) −17.6385 −0.996988 −0.498494 0.866893i \(-0.666113\pi\)
−0.498494 + 0.866893i \(0.666113\pi\)
\(314\) 3.34449 0.188740
\(315\) −3.37742 −0.190296
\(316\) 10.2835 0.578490
\(317\) 10.5734 0.593859 0.296930 0.954899i \(-0.404037\pi\)
0.296930 + 0.954899i \(0.404037\pi\)
\(318\) 1.15879 0.0649816
\(319\) −9.58456 −0.536632
\(320\) −25.0022 −1.39766
\(321\) −16.1333 −0.900471
\(322\) −1.34990 −0.0752268
\(323\) −43.5867 −2.42523
\(324\) −1.94651 −0.108139
\(325\) −11.2758 −0.625466
\(326\) 0.325488 0.0180271
\(327\) 15.2826 0.845131
\(328\) −5.97528 −0.329930
\(329\) −5.30897 −0.292693
\(330\) 0.857338 0.0471949
\(331\) −25.7221 −1.41381 −0.706906 0.707307i \(-0.749910\pi\)
−0.706906 + 0.707307i \(0.749910\pi\)
\(332\) −14.4750 −0.794421
\(333\) −8.74406 −0.479172
\(334\) −3.24034 −0.177303
\(335\) 47.1556 2.57638
\(336\) 3.35463 0.183010
\(337\) −22.1471 −1.20643 −0.603216 0.797578i \(-0.706114\pi\)
−0.603216 + 0.797578i \(0.706114\pi\)
\(338\) −2.62180 −0.142607
\(339\) −13.4720 −0.731696
\(340\) 53.1594 2.88297
\(341\) 8.65847 0.468882
\(342\) 1.36830 0.0739895
\(343\) 11.9992 0.647895
\(344\) −8.75578 −0.472080
\(345\) −23.7470 −1.27850
\(346\) 0.619303 0.0332939
\(347\) 16.8724 0.905757 0.452879 0.891572i \(-0.350397\pi\)
0.452879 + 0.891572i \(0.350397\pi\)
\(348\) 18.6564 1.00009
\(349\) −36.7014 −1.96458 −0.982291 0.187362i \(-0.940006\pi\)
−0.982291 + 0.187362i \(0.940006\pi\)
\(350\) −1.84199 −0.0984584
\(351\) 1.28993 0.0688512
\(352\) −2.67705 −0.142687
\(353\) 0.505931 0.0269280 0.0134640 0.999909i \(-0.495714\pi\)
0.0134640 + 0.999909i \(0.495714\pi\)
\(354\) −0.359337 −0.0190985
\(355\) −1.87894 −0.0997237
\(356\) −24.8405 −1.31654
\(357\) −6.71240 −0.355258
\(358\) 0.495075 0.0261655
\(359\) 6.62258 0.349527 0.174763 0.984610i \(-0.444084\pi\)
0.174763 + 0.984610i \(0.444084\pi\)
\(360\) −3.38349 −0.178326
\(361\) 16.0019 0.842206
\(362\) 2.41737 0.127054
\(363\) −1.00000 −0.0524864
\(364\) −2.28766 −0.119906
\(365\) −13.7532 −0.719873
\(366\) −0.231279 −0.0120892
\(367\) 19.2989 1.00739 0.503696 0.863881i \(-0.331973\pi\)
0.503696 + 0.863881i \(0.331973\pi\)
\(368\) 23.5868 1.22955
\(369\) 6.54649 0.340797
\(370\) −7.49662 −0.389731
\(371\) 4.56496 0.237001
\(372\) −16.8538 −0.873828
\(373\) −33.3340 −1.72597 −0.862985 0.505229i \(-0.831408\pi\)
−0.862985 + 0.505229i \(0.831408\pi\)
\(374\) 1.70390 0.0881068
\(375\) −13.8691 −0.716196
\(376\) −5.31852 −0.274282
\(377\) −12.3634 −0.636747
\(378\) 0.210720 0.0108383
\(379\) 38.6940 1.98757 0.993787 0.111294i \(-0.0354997\pi\)
0.993787 + 0.111294i \(0.0354997\pi\)
\(380\) −42.6892 −2.18991
\(381\) −14.9118 −0.763956
\(382\) 1.59729 0.0817244
\(383\) −9.35020 −0.477773 −0.238886 0.971048i \(-0.576782\pi\)
−0.238886 + 0.971048i \(0.576782\pi\)
\(384\) 6.91400 0.352829
\(385\) 3.37742 0.172129
\(386\) 3.12725 0.159173
\(387\) 9.59278 0.487629
\(388\) −37.0003 −1.87840
\(389\) 22.9294 1.16257 0.581283 0.813701i \(-0.302551\pi\)
0.581283 + 0.813701i \(0.302551\pi\)
\(390\) 1.10590 0.0559996
\(391\) −47.1957 −2.38679
\(392\) 5.63154 0.284436
\(393\) −1.52367 −0.0768589
\(394\) −2.92590 −0.147405
\(395\) −19.5839 −0.985371
\(396\) 1.94651 0.0978158
\(397\) 17.2747 0.866993 0.433496 0.901155i \(-0.357280\pi\)
0.433496 + 0.901155i \(0.357280\pi\)
\(398\) 0.839978 0.0421043
\(399\) 5.39033 0.269854
\(400\) 32.1851 1.60925
\(401\) −31.6046 −1.57826 −0.789129 0.614228i \(-0.789468\pi\)
−0.789129 + 0.614228i \(0.789468\pi\)
\(402\) −2.94208 −0.146738
\(403\) 11.1688 0.556357
\(404\) 10.9010 0.542345
\(405\) 3.70694 0.184199
\(406\) −2.01966 −0.100234
\(407\) 8.74406 0.433427
\(408\) −6.72448 −0.332911
\(409\) 20.8224 1.02960 0.514800 0.857310i \(-0.327866\pi\)
0.514800 + 0.857310i \(0.327866\pi\)
\(410\) 5.61255 0.277184
\(411\) −3.70337 −0.182674
\(412\) −31.2429 −1.53923
\(413\) −1.41558 −0.0696561
\(414\) 1.48160 0.0728167
\(415\) 27.5663 1.35318
\(416\) −3.45319 −0.169307
\(417\) −6.10661 −0.299042
\(418\) −1.36830 −0.0669260
\(419\) −12.4302 −0.607256 −0.303628 0.952791i \(-0.598198\pi\)
−0.303628 + 0.952791i \(0.598198\pi\)
\(420\) −6.57418 −0.320787
\(421\) −9.53980 −0.464942 −0.232471 0.972603i \(-0.574681\pi\)
−0.232471 + 0.972603i \(0.574681\pi\)
\(422\) −4.24328 −0.206560
\(423\) 5.82694 0.283315
\(424\) 4.57317 0.222093
\(425\) −64.4004 −3.12388
\(426\) 0.117229 0.00567975
\(427\) −0.911108 −0.0440916
\(428\) −31.4035 −1.51795
\(429\) −1.28993 −0.0622783
\(430\) 8.22426 0.396609
\(431\) −12.5341 −0.603745 −0.301872 0.953348i \(-0.597612\pi\)
−0.301872 + 0.953348i \(0.597612\pi\)
\(432\) −3.68192 −0.177146
\(433\) −18.0140 −0.865696 −0.432848 0.901467i \(-0.642491\pi\)
−0.432848 + 0.901467i \(0.642491\pi\)
\(434\) 1.82452 0.0875796
\(435\) −35.5294 −1.70350
\(436\) 29.7478 1.42466
\(437\) 37.9001 1.81301
\(438\) 0.858073 0.0410003
\(439\) −4.17247 −0.199141 −0.0995707 0.995030i \(-0.531747\pi\)
−0.0995707 + 0.995030i \(0.531747\pi\)
\(440\) 3.38349 0.161302
\(441\) −6.16988 −0.293804
\(442\) 2.19791 0.104544
\(443\) −31.4449 −1.49399 −0.746995 0.664830i \(-0.768504\pi\)
−0.746995 + 0.664830i \(0.768504\pi\)
\(444\) −17.0204 −0.807752
\(445\) 47.3062 2.24253
\(446\) 1.61887 0.0766556
\(447\) 13.5246 0.639690
\(448\) 6.14514 0.290331
\(449\) 13.4654 0.635471 0.317735 0.948179i \(-0.397078\pi\)
0.317735 + 0.948179i \(0.397078\pi\)
\(450\) 2.02170 0.0953040
\(451\) −6.54649 −0.308262
\(452\) −26.2233 −1.23344
\(453\) 1.09346 0.0513755
\(454\) 1.58525 0.0743994
\(455\) 4.35663 0.204242
\(456\) 5.40003 0.252880
\(457\) 16.0392 0.750280 0.375140 0.926968i \(-0.377595\pi\)
0.375140 + 0.926968i \(0.377595\pi\)
\(458\) −0.497365 −0.0232404
\(459\) 7.36730 0.343876
\(460\) −46.2238 −2.15520
\(461\) −2.07719 −0.0967444 −0.0483722 0.998829i \(-0.515403\pi\)
−0.0483722 + 0.998829i \(0.515403\pi\)
\(462\) −0.210720 −0.00980360
\(463\) 22.3955 1.04081 0.520404 0.853920i \(-0.325781\pi\)
0.520404 + 0.853920i \(0.325781\pi\)
\(464\) 35.2896 1.63828
\(465\) 32.0964 1.48843
\(466\) −0.0203204 −0.000941327 0
\(467\) 7.84551 0.363047 0.181523 0.983387i \(-0.441897\pi\)
0.181523 + 0.983387i \(0.441897\pi\)
\(468\) 2.51086 0.116064
\(469\) −11.5901 −0.535181
\(470\) 4.99566 0.230432
\(471\) −14.4608 −0.666319
\(472\) −1.41813 −0.0652745
\(473\) −9.59278 −0.441077
\(474\) 1.22186 0.0561217
\(475\) 51.7162 2.37290
\(476\) −13.0658 −0.598868
\(477\) −5.01034 −0.229408
\(478\) −0.311341 −0.0142404
\(479\) −23.9318 −1.09347 −0.546736 0.837305i \(-0.684130\pi\)
−0.546736 + 0.837305i \(0.684130\pi\)
\(480\) −9.92364 −0.452950
\(481\) 11.2792 0.514287
\(482\) 1.05002 0.0478272
\(483\) 5.83665 0.265577
\(484\) −1.94651 −0.0884777
\(485\) 70.4634 3.19958
\(486\) −0.231279 −0.0104910
\(487\) 25.8238 1.17019 0.585094 0.810965i \(-0.301058\pi\)
0.585094 + 0.810965i \(0.301058\pi\)
\(488\) −0.912746 −0.0413181
\(489\) −1.40734 −0.0636419
\(490\) −5.28968 −0.238963
\(491\) −31.3212 −1.41351 −0.706754 0.707459i \(-0.749841\pi\)
−0.706754 + 0.707459i \(0.749841\pi\)
\(492\) 12.7428 0.574490
\(493\) −70.6123 −3.18022
\(494\) −1.76501 −0.0794117
\(495\) −3.70694 −0.166614
\(496\) −31.8798 −1.43144
\(497\) 0.461814 0.0207152
\(498\) −1.71989 −0.0770700
\(499\) 24.5909 1.10084 0.550420 0.834888i \(-0.314467\pi\)
0.550420 + 0.834888i \(0.314467\pi\)
\(500\) −26.9963 −1.20731
\(501\) 14.0105 0.625942
\(502\) −1.35009 −0.0602574
\(503\) −2.31095 −0.103040 −0.0515200 0.998672i \(-0.516407\pi\)
−0.0515200 + 0.998672i \(0.516407\pi\)
\(504\) 0.831610 0.0370429
\(505\) −20.7599 −0.923803
\(506\) −1.48160 −0.0658652
\(507\) 11.3361 0.503453
\(508\) −29.0260 −1.28782
\(509\) −29.9915 −1.32935 −0.664676 0.747132i \(-0.731430\pi\)
−0.664676 + 0.747132i \(0.731430\pi\)
\(510\) 6.31627 0.279689
\(511\) 3.38031 0.149536
\(512\) 16.5780 0.732650
\(513\) −5.91624 −0.261208
\(514\) 4.45176 0.196359
\(515\) 59.4991 2.62184
\(516\) 18.6724 0.822009
\(517\) −5.82694 −0.256268
\(518\) 1.84255 0.0809571
\(519\) −2.67772 −0.117539
\(520\) 4.36446 0.191394
\(521\) −17.7422 −0.777300 −0.388650 0.921385i \(-0.627058\pi\)
−0.388650 + 0.921385i \(0.627058\pi\)
\(522\) 2.21671 0.0970228
\(523\) −16.2858 −0.712129 −0.356064 0.934461i \(-0.615882\pi\)
−0.356064 + 0.934461i \(0.615882\pi\)
\(524\) −2.96583 −0.129563
\(525\) 7.96434 0.347592
\(526\) −2.88317 −0.125712
\(527\) 63.7895 2.77872
\(528\) 3.68192 0.160235
\(529\) 18.0382 0.784269
\(530\) −4.29555 −0.186587
\(531\) 1.55369 0.0674245
\(532\) 10.4923 0.454901
\(533\) −8.44449 −0.365772
\(534\) −2.95148 −0.127723
\(535\) 59.8050 2.58559
\(536\) −11.6110 −0.501517
\(537\) −2.14059 −0.0923734
\(538\) −2.53115 −0.109126
\(539\) 6.16988 0.265756
\(540\) 7.21559 0.310510
\(541\) −4.81097 −0.206840 −0.103420 0.994638i \(-0.532979\pi\)
−0.103420 + 0.994638i \(0.532979\pi\)
\(542\) −4.15645 −0.178535
\(543\) −10.4522 −0.448545
\(544\) −19.7226 −0.845599
\(545\) −56.6517 −2.42669
\(546\) −0.271814 −0.0116326
\(547\) 12.5709 0.537491 0.268745 0.963211i \(-0.413391\pi\)
0.268745 + 0.963211i \(0.413391\pi\)
\(548\) −7.20865 −0.307938
\(549\) 1.00000 0.0426790
\(550\) −2.02170 −0.0862057
\(551\) 56.7046 2.41570
\(552\) 5.84715 0.248871
\(553\) 4.81341 0.204687
\(554\) −1.32825 −0.0564320
\(555\) 32.4137 1.37588
\(556\) −11.8866 −0.504103
\(557\) −31.8497 −1.34951 −0.674757 0.738040i \(-0.735752\pi\)
−0.674757 + 0.738040i \(0.735752\pi\)
\(558\) −2.00252 −0.0847736
\(559\) −12.3740 −0.523364
\(560\) −12.4354 −0.525491
\(561\) −7.36730 −0.311048
\(562\) −7.25759 −0.306143
\(563\) 37.6429 1.58646 0.793229 0.608923i \(-0.208398\pi\)
0.793229 + 0.608923i \(0.208398\pi\)
\(564\) 11.3422 0.477592
\(565\) 49.9397 2.10098
\(566\) −5.19216 −0.218243
\(567\) −0.911108 −0.0382629
\(568\) 0.462645 0.0194121
\(569\) −3.93199 −0.164838 −0.0824189 0.996598i \(-0.526265\pi\)
−0.0824189 + 0.996598i \(0.526265\pi\)
\(570\) −5.07222 −0.212452
\(571\) 18.8819 0.790185 0.395092 0.918641i \(-0.370713\pi\)
0.395092 + 0.918641i \(0.370713\pi\)
\(572\) −2.51086 −0.104984
\(573\) −6.90631 −0.288515
\(574\) −1.37948 −0.0575783
\(575\) 55.9982 2.33529
\(576\) −6.74470 −0.281029
\(577\) 34.1619 1.42218 0.711088 0.703103i \(-0.248203\pi\)
0.711088 + 0.703103i \(0.248203\pi\)
\(578\) 8.62143 0.358604
\(579\) −13.5215 −0.561935
\(580\) −69.1583 −2.87164
\(581\) −6.77537 −0.281090
\(582\) −4.39628 −0.182232
\(583\) 5.01034 0.207507
\(584\) 3.38639 0.140130
\(585\) −4.78168 −0.197698
\(586\) −3.67328 −0.151742
\(587\) −4.92186 −0.203147 −0.101573 0.994828i \(-0.532388\pi\)
−0.101573 + 0.994828i \(0.532388\pi\)
\(588\) −12.0097 −0.495273
\(589\) −51.2256 −2.11071
\(590\) 1.33204 0.0548392
\(591\) 12.6509 0.520390
\(592\) −32.1949 −1.32320
\(593\) 38.0886 1.56411 0.782056 0.623208i \(-0.214171\pi\)
0.782056 + 0.623208i \(0.214171\pi\)
\(594\) 0.231279 0.00948951
\(595\) 24.8825 1.02008
\(596\) 26.3257 1.07834
\(597\) −3.63188 −0.148643
\(598\) −1.91116 −0.0781530
\(599\) −35.5566 −1.45280 −0.726401 0.687271i \(-0.758809\pi\)
−0.726401 + 0.687271i \(0.758809\pi\)
\(600\) 7.97867 0.325728
\(601\) −3.34841 −0.136584 −0.0682922 0.997665i \(-0.521755\pi\)
−0.0682922 + 0.997665i \(0.521755\pi\)
\(602\) −2.02140 −0.0823859
\(603\) 12.7209 0.518035
\(604\) 2.12844 0.0866050
\(605\) 3.70694 0.150708
\(606\) 1.29523 0.0526151
\(607\) −24.1878 −0.981753 −0.490877 0.871229i \(-0.663323\pi\)
−0.490877 + 0.871229i \(0.663323\pi\)
\(608\) 15.8380 0.642318
\(609\) 8.73257 0.353862
\(610\) 0.857338 0.0347126
\(611\) −7.51633 −0.304078
\(612\) 14.3405 0.579681
\(613\) −19.1329 −0.772769 −0.386384 0.922338i \(-0.626276\pi\)
−0.386384 + 0.922338i \(0.626276\pi\)
\(614\) 3.05411 0.123254
\(615\) −24.2674 −0.978557
\(616\) −0.831610 −0.0335065
\(617\) 22.2994 0.897741 0.448870 0.893597i \(-0.351827\pi\)
0.448870 + 0.893597i \(0.351827\pi\)
\(618\) −3.71220 −0.149327
\(619\) 31.9197 1.28296 0.641480 0.767140i \(-0.278321\pi\)
0.641480 + 0.767140i \(0.278321\pi\)
\(620\) 62.4759 2.50909
\(621\) −6.40611 −0.257068
\(622\) 1.81814 0.0729006
\(623\) −11.6271 −0.465831
\(624\) 4.74941 0.190129
\(625\) 7.70489 0.308196
\(626\) −4.07943 −0.163047
\(627\) 5.91624 0.236272
\(628\) −28.1481 −1.12323
\(629\) 64.4201 2.56860
\(630\) −0.781128 −0.0311209
\(631\) 0.258718 0.0102994 0.00514971 0.999987i \(-0.498361\pi\)
0.00514971 + 0.999987i \(0.498361\pi\)
\(632\) 4.82207 0.191812
\(633\) 18.3470 0.729228
\(634\) 2.44540 0.0971193
\(635\) 55.2772 2.19361
\(636\) −9.75267 −0.386719
\(637\) 7.95870 0.315335
\(638\) −2.21671 −0.0877605
\(639\) −0.506871 −0.0200515
\(640\) −25.6298 −1.01311
\(641\) −26.1212 −1.03173 −0.515863 0.856671i \(-0.672529\pi\)
−0.515863 + 0.856671i \(0.672529\pi\)
\(642\) −3.73129 −0.147262
\(643\) 7.45790 0.294111 0.147056 0.989128i \(-0.453020\pi\)
0.147056 + 0.989128i \(0.453020\pi\)
\(644\) 11.3611 0.447690
\(645\) −35.5598 −1.40017
\(646\) −10.0807 −0.396620
\(647\) −44.3581 −1.74390 −0.871949 0.489597i \(-0.837144\pi\)
−0.871949 + 0.489597i \(0.837144\pi\)
\(648\) −0.912746 −0.0358561
\(649\) −1.55369 −0.0609877
\(650\) −2.60785 −0.102288
\(651\) −7.88880 −0.309186
\(652\) −2.73939 −0.107283
\(653\) −6.14521 −0.240481 −0.120240 0.992745i \(-0.538367\pi\)
−0.120240 + 0.992745i \(0.538367\pi\)
\(654\) 3.53456 0.138212
\(655\) 5.64814 0.220691
\(656\) 24.1036 0.941089
\(657\) −3.71011 −0.144745
\(658\) −1.22785 −0.0478668
\(659\) 27.8267 1.08398 0.541988 0.840387i \(-0.317672\pi\)
0.541988 + 0.840387i \(0.317672\pi\)
\(660\) −7.21559 −0.280866
\(661\) 41.3110 1.60681 0.803406 0.595431i \(-0.203019\pi\)
0.803406 + 0.595431i \(0.203019\pi\)
\(662\) −5.94898 −0.231214
\(663\) −9.50328 −0.369077
\(664\) −6.78756 −0.263408
\(665\) −19.9816 −0.774854
\(666\) −2.02232 −0.0783633
\(667\) 61.3997 2.37741
\(668\) 27.2716 1.05517
\(669\) −6.99961 −0.270621
\(670\) 10.9061 0.421340
\(671\) −1.00000 −0.0386046
\(672\) 2.43908 0.0940894
\(673\) −19.1769 −0.739214 −0.369607 0.929188i \(-0.620508\pi\)
−0.369607 + 0.929188i \(0.620508\pi\)
\(674\) −5.12218 −0.197299
\(675\) −8.74139 −0.336456
\(676\) 22.0658 0.848685
\(677\) −6.49815 −0.249744 −0.124872 0.992173i \(-0.539852\pi\)
−0.124872 + 0.992173i \(0.539852\pi\)
\(678\) −3.11579 −0.119661
\(679\) −17.3188 −0.664635
\(680\) 24.9272 0.955915
\(681\) −6.85426 −0.262656
\(682\) 2.00252 0.0766806
\(683\) −30.5994 −1.17085 −0.585426 0.810726i \(-0.699073\pi\)
−0.585426 + 0.810726i \(0.699073\pi\)
\(684\) −11.5160 −0.440326
\(685\) 13.7282 0.524526
\(686\) 2.77516 0.105956
\(687\) 2.15050 0.0820465
\(688\) 35.3199 1.34656
\(689\) 6.46297 0.246220
\(690\) −5.49220 −0.209084
\(691\) 21.3756 0.813166 0.406583 0.913614i \(-0.366720\pi\)
0.406583 + 0.913614i \(0.366720\pi\)
\(692\) −5.21222 −0.198139
\(693\) 0.911108 0.0346101
\(694\) 3.90224 0.148127
\(695\) 22.6368 0.858663
\(696\) 8.74827 0.331603
\(697\) −48.2299 −1.82684
\(698\) −8.48828 −0.321286
\(699\) 0.0878610 0.00332321
\(700\) 15.5027 0.585946
\(701\) −13.7805 −0.520483 −0.260241 0.965544i \(-0.583802\pi\)
−0.260241 + 0.965544i \(0.583802\pi\)
\(702\) 0.298334 0.0112599
\(703\) −51.7320 −1.95111
\(704\) 6.74470 0.254200
\(705\) −21.6001 −0.813507
\(706\) 0.117012 0.00440379
\(707\) 5.10246 0.191898
\(708\) 3.02428 0.113659
\(709\) 19.3933 0.728332 0.364166 0.931334i \(-0.381354\pi\)
0.364166 + 0.931334i \(0.381354\pi\)
\(710\) −0.434560 −0.0163087
\(711\) −5.28303 −0.198129
\(712\) −11.6480 −0.436529
\(713\) −55.4671 −2.07726
\(714\) −1.55244 −0.0580986
\(715\) 4.78168 0.178825
\(716\) −4.16669 −0.155716
\(717\) 1.34617 0.0502735
\(718\) 1.53167 0.0571613
\(719\) 6.37432 0.237722 0.118861 0.992911i \(-0.462076\pi\)
0.118861 + 0.992911i \(0.462076\pi\)
\(720\) 13.6486 0.508655
\(721\) −14.6240 −0.544624
\(722\) 3.70091 0.137734
\(723\) −4.54006 −0.168847
\(724\) −20.3452 −0.756124
\(725\) 83.7824 3.11160
\(726\) −0.231279 −0.00858358
\(727\) −21.3988 −0.793637 −0.396819 0.917897i \(-0.629886\pi\)
−0.396819 + 0.917897i \(0.629886\pi\)
\(728\) −1.07272 −0.0397575
\(729\) 1.00000 0.0370370
\(730\) −3.18082 −0.117728
\(731\) −70.6729 −2.61393
\(732\) 1.94651 0.0719451
\(733\) 23.1610 0.855470 0.427735 0.903904i \(-0.359312\pi\)
0.427735 + 0.903904i \(0.359312\pi\)
\(734\) 4.46343 0.164748
\(735\) 22.8714 0.843623
\(736\) 17.1494 0.632137
\(737\) −12.7209 −0.468580
\(738\) 1.51407 0.0557336
\(739\) −31.1840 −1.14712 −0.573561 0.819163i \(-0.694439\pi\)
−0.573561 + 0.819163i \(0.694439\pi\)
\(740\) 63.0936 2.31937
\(741\) 7.63152 0.280351
\(742\) 1.05578 0.0387589
\(743\) −11.7663 −0.431663 −0.215831 0.976431i \(-0.569246\pi\)
−0.215831 + 0.976431i \(0.569246\pi\)
\(744\) −7.90298 −0.289737
\(745\) −50.1347 −1.83679
\(746\) −7.70947 −0.282264
\(747\) 7.43641 0.272084
\(748\) −14.3405 −0.524341
\(749\) −14.6991 −0.537095
\(750\) −3.20763 −0.117126
\(751\) −0.685367 −0.0250094 −0.0125047 0.999922i \(-0.503980\pi\)
−0.0125047 + 0.999922i \(0.503980\pi\)
\(752\) 21.4543 0.782359
\(753\) 5.83748 0.212730
\(754\) −2.85940 −0.104133
\(755\) −4.05341 −0.147519
\(756\) −1.77348 −0.0645009
\(757\) −32.9419 −1.19730 −0.598648 0.801013i \(-0.704295\pi\)
−0.598648 + 0.801013i \(0.704295\pi\)
\(758\) 8.94911 0.325046
\(759\) 6.40611 0.232527
\(760\) −20.0176 −0.726114
\(761\) 24.4080 0.884791 0.442396 0.896820i \(-0.354129\pi\)
0.442396 + 0.896820i \(0.354129\pi\)
\(762\) −3.44880 −0.124937
\(763\) 13.9241 0.504087
\(764\) −13.4432 −0.486358
\(765\) −27.3101 −0.987399
\(766\) −2.16251 −0.0781346
\(767\) −2.00415 −0.0723656
\(768\) −11.8903 −0.429055
\(769\) −0.979264 −0.0353132 −0.0176566 0.999844i \(-0.505621\pi\)
−0.0176566 + 0.999844i \(0.505621\pi\)
\(770\) 0.781128 0.0281499
\(771\) −19.2484 −0.693214
\(772\) −26.3198 −0.947269
\(773\) −47.3585 −1.70337 −0.851683 0.524057i \(-0.824418\pi\)
−0.851683 + 0.524057i \(0.824418\pi\)
\(774\) 2.21861 0.0797464
\(775\) −75.6870 −2.71876
\(776\) −17.3500 −0.622827
\(777\) −7.96678 −0.285807
\(778\) 5.30310 0.190125
\(779\) 38.7306 1.38767
\(780\) −9.30759 −0.333265
\(781\) 0.506871 0.0181373
\(782\) −10.9154 −0.390334
\(783\) −9.58456 −0.342524
\(784\) −22.7170 −0.811322
\(785\) 53.6053 1.91326
\(786\) −0.352393 −0.0125694
\(787\) −21.9000 −0.780651 −0.390326 0.920677i \(-0.627638\pi\)
−0.390326 + 0.920677i \(0.627638\pi\)
\(788\) 24.6252 0.877235
\(789\) 12.4662 0.443808
\(790\) −4.52934 −0.161147
\(791\) −12.2744 −0.436428
\(792\) 0.912746 0.0324330
\(793\) −1.28993 −0.0458067
\(794\) 3.99528 0.141787
\(795\) 18.5730 0.658717
\(796\) −7.06948 −0.250571
\(797\) 16.0797 0.569571 0.284785 0.958591i \(-0.408078\pi\)
0.284785 + 0.958591i \(0.408078\pi\)
\(798\) 1.24667 0.0441318
\(799\) −42.9288 −1.51871
\(800\) 23.4011 0.827353
\(801\) 12.7615 0.450907
\(802\) −7.30949 −0.258107
\(803\) 3.71011 0.130927
\(804\) 24.7614 0.873265
\(805\) −21.6361 −0.762573
\(806\) 2.58311 0.0909862
\(807\) 10.9441 0.385252
\(808\) 5.11164 0.179827
\(809\) −11.8133 −0.415333 −0.207667 0.978200i \(-0.566587\pi\)
−0.207667 + 0.978200i \(0.566587\pi\)
\(810\) 0.857338 0.0301238
\(811\) 29.4126 1.03281 0.516407 0.856343i \(-0.327269\pi\)
0.516407 + 0.856343i \(0.327269\pi\)
\(812\) 16.9980 0.596514
\(813\) 17.9716 0.630290
\(814\) 2.02232 0.0708823
\(815\) 5.21691 0.182740
\(816\) 27.1258 0.949593
\(817\) 56.7532 1.98554
\(818\) 4.81579 0.168380
\(819\) 1.17526 0.0410670
\(820\) −47.2368 −1.64958
\(821\) −30.6948 −1.07125 −0.535627 0.844454i \(-0.679925\pi\)
−0.535627 + 0.844454i \(0.679925\pi\)
\(822\) −0.856514 −0.0298743
\(823\) 31.6432 1.10301 0.551505 0.834171i \(-0.314054\pi\)
0.551505 + 0.834171i \(0.314054\pi\)
\(824\) −14.6503 −0.510366
\(825\) 8.74139 0.304336
\(826\) −0.327394 −0.0113915
\(827\) −13.0222 −0.452825 −0.226413 0.974031i \(-0.572700\pi\)
−0.226413 + 0.974031i \(0.572700\pi\)
\(828\) −12.4695 −0.433347
\(829\) 47.5998 1.65321 0.826604 0.562783i \(-0.190269\pi\)
0.826604 + 0.562783i \(0.190269\pi\)
\(830\) 6.37552 0.221298
\(831\) 5.74306 0.199225
\(832\) 8.70017 0.301624
\(833\) 45.4554 1.57494
\(834\) −1.41233 −0.0489051
\(835\) −51.9360 −1.79732
\(836\) 11.5160 0.398290
\(837\) 8.65847 0.299280
\(838\) −2.87485 −0.0993102
\(839\) −2.77869 −0.0959309 −0.0479655 0.998849i \(-0.515274\pi\)
−0.0479655 + 0.998849i \(0.515274\pi\)
\(840\) −3.08273 −0.106364
\(841\) 62.8638 2.16772
\(842\) −2.20636 −0.0760362
\(843\) 31.3802 1.08079
\(844\) 35.7126 1.22928
\(845\) −42.0222 −1.44561
\(846\) 1.34765 0.0463332
\(847\) −0.911108 −0.0313060
\(848\) −18.4477 −0.633495
\(849\) 22.4497 0.770472
\(850\) −14.8945 −0.510877
\(851\) −56.0154 −1.92018
\(852\) −0.986629 −0.0338014
\(853\) 19.4760 0.666845 0.333423 0.942777i \(-0.391796\pi\)
0.333423 + 0.942777i \(0.391796\pi\)
\(854\) −0.210720 −0.00721071
\(855\) 21.9311 0.750029
\(856\) −14.7256 −0.503310
\(857\) −34.8220 −1.18950 −0.594749 0.803912i \(-0.702748\pi\)
−0.594749 + 0.803912i \(0.702748\pi\)
\(858\) −0.298334 −0.0101849
\(859\) −8.18830 −0.279381 −0.139691 0.990195i \(-0.544611\pi\)
−0.139691 + 0.990195i \(0.544611\pi\)
\(860\) −69.2176 −2.36030
\(861\) 5.96456 0.203272
\(862\) −2.89887 −0.0987359
\(863\) 34.4697 1.17336 0.586681 0.809818i \(-0.300434\pi\)
0.586681 + 0.809818i \(0.300434\pi\)
\(864\) −2.67705 −0.0910749
\(865\) 9.92616 0.337500
\(866\) −4.16626 −0.141575
\(867\) −37.2771 −1.26600
\(868\) −15.3556 −0.521204
\(869\) 5.28303 0.179215
\(870\) −8.21721 −0.278590
\(871\) −16.4090 −0.555999
\(872\) 13.9492 0.472378
\(873\) 19.0085 0.643341
\(874\) 8.76551 0.296498
\(875\) −12.6362 −0.427182
\(876\) −7.22177 −0.244001
\(877\) 22.6206 0.763845 0.381922 0.924194i \(-0.375262\pi\)
0.381922 + 0.924194i \(0.375262\pi\)
\(878\) −0.965007 −0.0325674
\(879\) 15.8824 0.535701
\(880\) −13.6486 −0.460096
\(881\) 20.0360 0.675029 0.337514 0.941320i \(-0.390414\pi\)
0.337514 + 0.941320i \(0.390414\pi\)
\(882\) −1.42697 −0.0480485
\(883\) −16.1716 −0.544217 −0.272108 0.962267i \(-0.587721\pi\)
−0.272108 + 0.962267i \(0.587721\pi\)
\(884\) −18.4982 −0.622163
\(885\) −5.75944 −0.193601
\(886\) −7.27255 −0.244326
\(887\) −14.1009 −0.473460 −0.236730 0.971575i \(-0.576076\pi\)
−0.236730 + 0.971575i \(0.576076\pi\)
\(888\) −7.98111 −0.267829
\(889\) −13.5863 −0.455669
\(890\) 10.9410 0.366742
\(891\) −1.00000 −0.0335013
\(892\) −13.6248 −0.456193
\(893\) 34.4736 1.15361
\(894\) 3.12795 0.104614
\(895\) 7.93504 0.265239
\(896\) 6.29940 0.210448
\(897\) 8.26341 0.275907
\(898\) 3.11427 0.103924
\(899\) −82.9876 −2.76779
\(900\) −17.0152 −0.567173
\(901\) 36.9127 1.22974
\(902\) −1.51407 −0.0504129
\(903\) 8.74006 0.290851
\(904\) −12.2965 −0.408975
\(905\) 38.7455 1.28794
\(906\) 0.252896 0.00840190
\(907\) −36.0807 −1.19804 −0.599019 0.800735i \(-0.704443\pi\)
−0.599019 + 0.800735i \(0.704443\pi\)
\(908\) −13.3419 −0.442766
\(909\) −5.60028 −0.185750
\(910\) 1.00760 0.0334015
\(911\) −20.4544 −0.677684 −0.338842 0.940843i \(-0.610035\pi\)
−0.338842 + 0.940843i \(0.610035\pi\)
\(912\) −21.7831 −0.721312
\(913\) −7.43641 −0.246109
\(914\) 3.70953 0.122700
\(915\) −3.70694 −0.122548
\(916\) 4.18596 0.138308
\(917\) −1.38823 −0.0458432
\(918\) 1.70390 0.0562372
\(919\) 43.7171 1.44209 0.721046 0.692887i \(-0.243662\pi\)
0.721046 + 0.692887i \(0.243662\pi\)
\(920\) −21.6750 −0.714604
\(921\) −13.2053 −0.435129
\(922\) −0.480411 −0.0158215
\(923\) 0.653827 0.0215210
\(924\) 1.77348 0.0583432
\(925\) −76.4352 −2.51317
\(926\) 5.17962 0.170213
\(927\) 16.0507 0.527175
\(928\) 25.6583 0.842275
\(929\) −34.9056 −1.14521 −0.572607 0.819830i \(-0.694068\pi\)
−0.572607 + 0.819830i \(0.694068\pi\)
\(930\) 7.42323 0.243417
\(931\) −36.5025 −1.19632
\(932\) 0.171022 0.00560202
\(933\) −7.86121 −0.257364
\(934\) 1.81451 0.0593724
\(935\) 27.3101 0.893136
\(936\) 1.17738 0.0384838
\(937\) 27.5062 0.898589 0.449294 0.893384i \(-0.351675\pi\)
0.449294 + 0.893384i \(0.351675\pi\)
\(938\) −2.68055 −0.0875232
\(939\) 17.6385 0.575612
\(940\) −42.0448 −1.37135
\(941\) 35.8790 1.16962 0.584811 0.811170i \(-0.301169\pi\)
0.584811 + 0.811170i \(0.301169\pi\)
\(942\) −3.34449 −0.108969
\(943\) 41.9375 1.36567
\(944\) 5.72057 0.186189
\(945\) 3.37742 0.109867
\(946\) −2.21861 −0.0721333
\(947\) −11.3161 −0.367724 −0.183862 0.982952i \(-0.558860\pi\)
−0.183862 + 0.982952i \(0.558860\pi\)
\(948\) −10.2835 −0.333992
\(949\) 4.78578 0.155353
\(950\) 11.9609 0.388062
\(951\) −10.5734 −0.342865
\(952\) −6.12672 −0.198568
\(953\) −2.13994 −0.0693195 −0.0346598 0.999399i \(-0.511035\pi\)
−0.0346598 + 0.999399i \(0.511035\pi\)
\(954\) −1.15879 −0.0375171
\(955\) 25.6013 0.828438
\(956\) 2.62033 0.0847475
\(957\) 9.58456 0.309825
\(958\) −5.53493 −0.178826
\(959\) −3.37417 −0.108958
\(960\) 25.0022 0.806941
\(961\) 43.9690 1.41836
\(962\) 2.60865 0.0841062
\(963\) 16.1333 0.519887
\(964\) −8.83727 −0.284629
\(965\) 50.1234 1.61353
\(966\) 1.34990 0.0434322
\(967\) 28.0975 0.903555 0.451778 0.892131i \(-0.350790\pi\)
0.451778 + 0.892131i \(0.350790\pi\)
\(968\) −0.912746 −0.0293368
\(969\) 43.5867 1.40021
\(970\) 16.2967 0.523257
\(971\) −50.8194 −1.63087 −0.815436 0.578847i \(-0.803503\pi\)
−0.815436 + 0.578847i \(0.803503\pi\)
\(972\) 1.94651 0.0624343
\(973\) −5.56378 −0.178366
\(974\) 5.97251 0.191372
\(975\) 11.2758 0.361113
\(976\) 3.68192 0.117855
\(977\) −27.5896 −0.882670 −0.441335 0.897342i \(-0.645495\pi\)
−0.441335 + 0.897342i \(0.645495\pi\)
\(978\) −0.325488 −0.0104080
\(979\) −12.7615 −0.407860
\(980\) 44.5193 1.42212
\(981\) −15.2826 −0.487937
\(982\) −7.24396 −0.231164
\(983\) 28.6548 0.913945 0.456973 0.889481i \(-0.348934\pi\)
0.456973 + 0.889481i \(0.348934\pi\)
\(984\) 5.97528 0.190485
\(985\) −46.8962 −1.49424
\(986\) −16.3312 −0.520091
\(987\) 5.30897 0.168986
\(988\) 14.8548 0.472595
\(989\) 61.4524 1.95407
\(990\) −0.857338 −0.0272480
\(991\) 19.1844 0.609412 0.304706 0.952447i \(-0.401442\pi\)
0.304706 + 0.952447i \(0.401442\pi\)
\(992\) −23.1791 −0.735937
\(993\) 25.7221 0.816265
\(994\) 0.106808 0.00338775
\(995\) 13.4631 0.426810
\(996\) 14.4750 0.458659
\(997\) −4.14208 −0.131181 −0.0655905 0.997847i \(-0.520893\pi\)
−0.0655905 + 0.997847i \(0.520893\pi\)
\(998\) 5.68737 0.180031
\(999\) 8.74406 0.276650
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 2013.2.a.h.1.9 14
3.2 odd 2 6039.2.a.j.1.6 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2013.2.a.h.1.9 14 1.1 even 1 trivial
6039.2.a.j.1.6 14 3.2 odd 2