Properties

Label 5225.2.a.m.1.4
Level $5225$
Weight $2$
Character 5225.1
Self dual yes
Analytic conductor $41.722$
Analytic rank $0$
Dimension $7$
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] = [5225,2,Mod(1,5225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5225, 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("5225.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5225 = 5^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5225.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: \(41.7218350561\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{7} - x^{6} - 10x^{5} + 8x^{4} + 27x^{3} - 16x^{2} - 18x + 11 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1045)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(0.719047\) of defining polynomial
Character \(\chi\) \(=\) 5225.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.719047 q^{2} -0.163114 q^{3} -1.48297 q^{4} +0.117287 q^{6} -1.05678 q^{7} +2.50442 q^{8} -2.97339 q^{9} +O(q^{10})\) \(q-0.719047 q^{2} -0.163114 q^{3} -1.48297 q^{4} +0.117287 q^{6} -1.05678 q^{7} +2.50442 q^{8} -2.97339 q^{9} +1.00000 q^{11} +0.241893 q^{12} -3.88893 q^{13} +0.759873 q^{14} +1.16515 q^{16} -5.65135 q^{17} +2.13801 q^{18} -1.00000 q^{19} +0.172375 q^{21} -0.719047 q^{22} -2.78982 q^{23} -0.408506 q^{24} +2.79632 q^{26} +0.974345 q^{27} +1.56717 q^{28} +0.890165 q^{29} +6.13204 q^{31} -5.84664 q^{32} -0.163114 q^{33} +4.06359 q^{34} +4.40946 q^{36} -3.51111 q^{37} +0.719047 q^{38} +0.634339 q^{39} -2.28025 q^{41} -0.123946 q^{42} -3.91188 q^{43} -1.48297 q^{44} +2.00601 q^{46} -7.75344 q^{47} -0.190052 q^{48} -5.88322 q^{49} +0.921815 q^{51} +5.76717 q^{52} -7.61251 q^{53} -0.700600 q^{54} -2.64662 q^{56} +0.163114 q^{57} -0.640071 q^{58} -2.17640 q^{59} +0.475939 q^{61} -4.40923 q^{62} +3.14222 q^{63} +1.87372 q^{64} +0.117287 q^{66} +0.383348 q^{67} +8.38079 q^{68} +0.455059 q^{69} -2.51986 q^{71} -7.44663 q^{72} +10.7887 q^{73} +2.52465 q^{74} +1.48297 q^{76} -1.05678 q^{77} -0.456120 q^{78} -4.27374 q^{79} +8.76125 q^{81} +1.63960 q^{82} +1.39483 q^{83} -0.255628 q^{84} +2.81283 q^{86} -0.145198 q^{87} +2.50442 q^{88} +8.36845 q^{89} +4.10973 q^{91} +4.13723 q^{92} -1.00022 q^{93} +5.57509 q^{94} +0.953669 q^{96} +6.75542 q^{97} +4.23031 q^{98} -2.97339 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q - q^{2} - 3 q^{3} + 7 q^{4} + 8 q^{6} + q^{7} - 3 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 7 q - q^{2} - 3 q^{3} + 7 q^{4} + 8 q^{6} + q^{7} - 3 q^{8} + 2 q^{9} + 7 q^{11} - 13 q^{12} - q^{13} + 12 q^{14} + 3 q^{16} - q^{17} - 7 q^{18} - 7 q^{19} + 5 q^{21} - q^{22} + 8 q^{23} + 25 q^{24} - 12 q^{27} - 4 q^{28} + 11 q^{29} + 7 q^{31} - 12 q^{32} - 3 q^{33} - 14 q^{34} + 7 q^{36} + 17 q^{37} + q^{38} + 30 q^{39} + 17 q^{41} - 33 q^{42} + 3 q^{43} + 7 q^{44} + 18 q^{46} - 14 q^{47} + 12 q^{48} + 6 q^{49} + 8 q^{51} + 17 q^{52} - 7 q^{53} - 27 q^{54} + 36 q^{56} + 3 q^{57} + 15 q^{58} + 35 q^{59} + 17 q^{61} - 46 q^{62} + 22 q^{63} + 5 q^{64} + 8 q^{66} - 4 q^{67} + 35 q^{68} - 4 q^{69} + 10 q^{71} - 12 q^{72} - 22 q^{73} - 11 q^{74} - 7 q^{76} + q^{77} + 41 q^{78} + 11 q^{79} - 21 q^{81} + 14 q^{82} - 39 q^{83} + 21 q^{84} - 24 q^{86} + 2 q^{87} - 3 q^{88} + 18 q^{89} - 22 q^{91} + 51 q^{92} - 10 q^{93} + 14 q^{94} - 11 q^{96} + 4 q^{97} + 26 q^{98} + 2 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.719047 −0.508443 −0.254222 0.967146i \(-0.581819\pi\)
−0.254222 + 0.967146i \(0.581819\pi\)
\(3\) −0.163114 −0.0941739 −0.0470870 0.998891i \(-0.514994\pi\)
−0.0470870 + 0.998891i \(0.514994\pi\)
\(4\) −1.48297 −0.741486
\(5\) 0 0
\(6\) 0.117287 0.0478821
\(7\) −1.05678 −0.399424 −0.199712 0.979855i \(-0.564001\pi\)
−0.199712 + 0.979855i \(0.564001\pi\)
\(8\) 2.50442 0.885446
\(9\) −2.97339 −0.991131
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0.241893 0.0698286
\(13\) −3.88893 −1.07859 −0.539297 0.842115i \(-0.681310\pi\)
−0.539297 + 0.842115i \(0.681310\pi\)
\(14\) 0.759873 0.203085
\(15\) 0 0
\(16\) 1.16515 0.291286
\(17\) −5.65135 −1.37065 −0.685327 0.728236i \(-0.740341\pi\)
−0.685327 + 0.728236i \(0.740341\pi\)
\(18\) 2.13801 0.503934
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 0.172375 0.0376154
\(22\) −0.719047 −0.153301
\(23\) −2.78982 −0.581718 −0.290859 0.956766i \(-0.593941\pi\)
−0.290859 + 0.956766i \(0.593941\pi\)
\(24\) −0.408506 −0.0833860
\(25\) 0 0
\(26\) 2.79632 0.548404
\(27\) 0.974345 0.187513
\(28\) 1.56717 0.296167
\(29\) 0.890165 0.165299 0.0826497 0.996579i \(-0.473662\pi\)
0.0826497 + 0.996579i \(0.473662\pi\)
\(30\) 0 0
\(31\) 6.13204 1.10135 0.550673 0.834721i \(-0.314371\pi\)
0.550673 + 0.834721i \(0.314371\pi\)
\(32\) −5.84664 −1.03355
\(33\) −0.163114 −0.0283945
\(34\) 4.06359 0.696900
\(35\) 0 0
\(36\) 4.40946 0.734909
\(37\) −3.51111 −0.577223 −0.288612 0.957446i \(-0.593194\pi\)
−0.288612 + 0.957446i \(0.593194\pi\)
\(38\) 0.719047 0.116645
\(39\) 0.634339 0.101576
\(40\) 0 0
\(41\) −2.28025 −0.356115 −0.178057 0.984020i \(-0.556981\pi\)
−0.178057 + 0.984020i \(0.556981\pi\)
\(42\) −0.123946 −0.0191253
\(43\) −3.91188 −0.596556 −0.298278 0.954479i \(-0.596412\pi\)
−0.298278 + 0.954479i \(0.596412\pi\)
\(44\) −1.48297 −0.223566
\(45\) 0 0
\(46\) 2.00601 0.295771
\(47\) −7.75344 −1.13096 −0.565478 0.824764i \(-0.691308\pi\)
−0.565478 + 0.824764i \(0.691308\pi\)
\(48\) −0.190052 −0.0274316
\(49\) −5.88322 −0.840460
\(50\) 0 0
\(51\) 0.921815 0.129080
\(52\) 5.76717 0.799763
\(53\) −7.61251 −1.04566 −0.522830 0.852437i \(-0.675124\pi\)
−0.522830 + 0.852437i \(0.675124\pi\)
\(54\) −0.700600 −0.0953396
\(55\) 0 0
\(56\) −2.64662 −0.353669
\(57\) 0.163114 0.0216050
\(58\) −0.640071 −0.0840454
\(59\) −2.17640 −0.283344 −0.141672 0.989914i \(-0.545248\pi\)
−0.141672 + 0.989914i \(0.545248\pi\)
\(60\) 0 0
\(61\) 0.475939 0.0609378 0.0304689 0.999536i \(-0.490300\pi\)
0.0304689 + 0.999536i \(0.490300\pi\)
\(62\) −4.40923 −0.559972
\(63\) 3.14222 0.395882
\(64\) 1.87372 0.234215
\(65\) 0 0
\(66\) 0.117287 0.0144370
\(67\) 0.383348 0.0468334 0.0234167 0.999726i \(-0.492546\pi\)
0.0234167 + 0.999726i \(0.492546\pi\)
\(68\) 8.38079 1.01632
\(69\) 0.455059 0.0547827
\(70\) 0 0
\(71\) −2.51986 −0.299052 −0.149526 0.988758i \(-0.547775\pi\)
−0.149526 + 0.988758i \(0.547775\pi\)
\(72\) −7.44663 −0.877594
\(73\) 10.7887 1.26272 0.631358 0.775491i \(-0.282498\pi\)
0.631358 + 0.775491i \(0.282498\pi\)
\(74\) 2.52465 0.293485
\(75\) 0 0
\(76\) 1.48297 0.170108
\(77\) −1.05678 −0.120431
\(78\) −0.456120 −0.0516454
\(79\) −4.27374 −0.480834 −0.240417 0.970670i \(-0.577284\pi\)
−0.240417 + 0.970670i \(0.577284\pi\)
\(80\) 0 0
\(81\) 8.76125 0.973472
\(82\) 1.63960 0.181064
\(83\) 1.39483 0.153102 0.0765512 0.997066i \(-0.475609\pi\)
0.0765512 + 0.997066i \(0.475609\pi\)
\(84\) −0.255628 −0.0278913
\(85\) 0 0
\(86\) 2.81283 0.303315
\(87\) −0.145198 −0.0155669
\(88\) 2.50442 0.266972
\(89\) 8.36845 0.887054 0.443527 0.896261i \(-0.353727\pi\)
0.443527 + 0.896261i \(0.353727\pi\)
\(90\) 0 0
\(91\) 4.10973 0.430817
\(92\) 4.13723 0.431336
\(93\) −1.00022 −0.103718
\(94\) 5.57509 0.575026
\(95\) 0 0
\(96\) 0.953669 0.0973334
\(97\) 6.75542 0.685909 0.342954 0.939352i \(-0.388572\pi\)
0.342954 + 0.939352i \(0.388572\pi\)
\(98\) 4.23031 0.427326
\(99\) −2.97339 −0.298837
\(100\) 0 0
\(101\) 9.99525 0.994565 0.497283 0.867589i \(-0.334331\pi\)
0.497283 + 0.867589i \(0.334331\pi\)
\(102\) −0.662828 −0.0656298
\(103\) −8.95835 −0.882692 −0.441346 0.897337i \(-0.645499\pi\)
−0.441346 + 0.897337i \(0.645499\pi\)
\(104\) −9.73952 −0.955038
\(105\) 0 0
\(106\) 5.47376 0.531658
\(107\) 1.97814 0.191234 0.0956171 0.995418i \(-0.469518\pi\)
0.0956171 + 0.995418i \(0.469518\pi\)
\(108\) −1.44492 −0.139038
\(109\) −0.846527 −0.0810826 −0.0405413 0.999178i \(-0.512908\pi\)
−0.0405413 + 0.999178i \(0.512908\pi\)
\(110\) 0 0
\(111\) 0.572712 0.0543594
\(112\) −1.23130 −0.116347
\(113\) −1.91728 −0.180362 −0.0901812 0.995925i \(-0.528745\pi\)
−0.0901812 + 0.995925i \(0.528745\pi\)
\(114\) −0.117287 −0.0109849
\(115\) 0 0
\(116\) −1.32009 −0.122567
\(117\) 11.5633 1.06903
\(118\) 1.56494 0.144064
\(119\) 5.97222 0.547473
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −0.342223 −0.0309834
\(123\) 0.371940 0.0335367
\(124\) −9.09364 −0.816633
\(125\) 0 0
\(126\) −2.25940 −0.201284
\(127\) −11.4902 −1.01959 −0.509795 0.860296i \(-0.670279\pi\)
−0.509795 + 0.860296i \(0.670279\pi\)
\(128\) 10.3460 0.914464
\(129\) 0.638083 0.0561801
\(130\) 0 0
\(131\) −1.00153 −0.0875044 −0.0437522 0.999042i \(-0.513931\pi\)
−0.0437522 + 0.999042i \(0.513931\pi\)
\(132\) 0.241893 0.0210541
\(133\) 1.05678 0.0916343
\(134\) −0.275645 −0.0238121
\(135\) 0 0
\(136\) −14.1534 −1.21364
\(137\) −13.7420 −1.17406 −0.587030 0.809565i \(-0.699703\pi\)
−0.587030 + 0.809565i \(0.699703\pi\)
\(138\) −0.327209 −0.0278539
\(139\) −13.4541 −1.14116 −0.570582 0.821241i \(-0.693282\pi\)
−0.570582 + 0.821241i \(0.693282\pi\)
\(140\) 0 0
\(141\) 1.26469 0.106507
\(142\) 1.81190 0.152051
\(143\) −3.88893 −0.325209
\(144\) −3.46444 −0.288703
\(145\) 0 0
\(146\) −7.75755 −0.642020
\(147\) 0.959636 0.0791494
\(148\) 5.20688 0.428003
\(149\) 15.6201 1.27965 0.639823 0.768522i \(-0.279008\pi\)
0.639823 + 0.768522i \(0.279008\pi\)
\(150\) 0 0
\(151\) −13.2415 −1.07758 −0.538790 0.842440i \(-0.681118\pi\)
−0.538790 + 0.842440i \(0.681118\pi\)
\(152\) −2.50442 −0.203135
\(153\) 16.8037 1.35850
\(154\) 0.759873 0.0612323
\(155\) 0 0
\(156\) −0.940706 −0.0753168
\(157\) 7.93760 0.633490 0.316745 0.948511i \(-0.397410\pi\)
0.316745 + 0.948511i \(0.397410\pi\)
\(158\) 3.07302 0.244477
\(159\) 1.24171 0.0984739
\(160\) 0 0
\(161\) 2.94822 0.232353
\(162\) −6.29975 −0.494955
\(163\) −4.86881 −0.381355 −0.190677 0.981653i \(-0.561068\pi\)
−0.190677 + 0.981653i \(0.561068\pi\)
\(164\) 3.38154 0.264054
\(165\) 0 0
\(166\) −1.00295 −0.0778439
\(167\) 6.78983 0.525413 0.262706 0.964876i \(-0.415385\pi\)
0.262706 + 0.964876i \(0.415385\pi\)
\(168\) 0.431700 0.0333064
\(169\) 2.12377 0.163367
\(170\) 0 0
\(171\) 2.97339 0.227381
\(172\) 5.80121 0.442338
\(173\) 14.6609 1.11465 0.557325 0.830295i \(-0.311828\pi\)
0.557325 + 0.830295i \(0.311828\pi\)
\(174\) 0.104405 0.00791489
\(175\) 0 0
\(176\) 1.16515 0.0878261
\(177\) 0.355002 0.0266836
\(178\) −6.01731 −0.451017
\(179\) −9.14657 −0.683647 −0.341823 0.939764i \(-0.611044\pi\)
−0.341823 + 0.939764i \(0.611044\pi\)
\(180\) 0 0
\(181\) 3.93642 0.292592 0.146296 0.989241i \(-0.453265\pi\)
0.146296 + 0.989241i \(0.453265\pi\)
\(182\) −2.95509 −0.219046
\(183\) −0.0776324 −0.00573875
\(184\) −6.98689 −0.515080
\(185\) 0 0
\(186\) 0.719207 0.0527348
\(187\) −5.65135 −0.413268
\(188\) 11.4981 0.838587
\(189\) −1.02967 −0.0748972
\(190\) 0 0
\(191\) −22.0025 −1.59204 −0.796022 0.605267i \(-0.793066\pi\)
−0.796022 + 0.605267i \(0.793066\pi\)
\(192\) −0.305630 −0.0220569
\(193\) −15.6976 −1.12994 −0.564968 0.825113i \(-0.691112\pi\)
−0.564968 + 0.825113i \(0.691112\pi\)
\(194\) −4.85746 −0.348746
\(195\) 0 0
\(196\) 8.72465 0.623189
\(197\) 9.97970 0.711024 0.355512 0.934672i \(-0.384306\pi\)
0.355512 + 0.934672i \(0.384306\pi\)
\(198\) 2.13801 0.151942
\(199\) −4.99525 −0.354104 −0.177052 0.984201i \(-0.556656\pi\)
−0.177052 + 0.984201i \(0.556656\pi\)
\(200\) 0 0
\(201\) −0.0625295 −0.00441049
\(202\) −7.18706 −0.505680
\(203\) −0.940706 −0.0660247
\(204\) −1.36702 −0.0957109
\(205\) 0 0
\(206\) 6.44147 0.448799
\(207\) 8.29524 0.576559
\(208\) −4.53117 −0.314180
\(209\) −1.00000 −0.0691714
\(210\) 0 0
\(211\) 15.2151 1.04745 0.523727 0.851886i \(-0.324541\pi\)
0.523727 + 0.851886i \(0.324541\pi\)
\(212\) 11.2891 0.775341
\(213\) 0.411024 0.0281629
\(214\) −1.42238 −0.0972317
\(215\) 0 0
\(216\) 2.44017 0.166032
\(217\) −6.48020 −0.439905
\(218\) 0.608693 0.0412259
\(219\) −1.75978 −0.118915
\(220\) 0 0
\(221\) 21.9777 1.47838
\(222\) −0.411807 −0.0276387
\(223\) 19.1508 1.28244 0.641218 0.767359i \(-0.278430\pi\)
0.641218 + 0.767359i \(0.278430\pi\)
\(224\) 6.17859 0.412825
\(225\) 0 0
\(226\) 1.37861 0.0917040
\(227\) −15.0978 −1.00207 −0.501037 0.865426i \(-0.667048\pi\)
−0.501037 + 0.865426i \(0.667048\pi\)
\(228\) −0.241893 −0.0160198
\(229\) 22.5618 1.49092 0.745461 0.666549i \(-0.232229\pi\)
0.745461 + 0.666549i \(0.232229\pi\)
\(230\) 0 0
\(231\) 0.172375 0.0113415
\(232\) 2.22935 0.146364
\(233\) 0.917101 0.0600813 0.0300406 0.999549i \(-0.490436\pi\)
0.0300406 + 0.999549i \(0.490436\pi\)
\(234\) −8.31457 −0.543541
\(235\) 0 0
\(236\) 3.22755 0.210095
\(237\) 0.697108 0.0452820
\(238\) −4.29431 −0.278359
\(239\) 28.4833 1.84243 0.921215 0.389054i \(-0.127198\pi\)
0.921215 + 0.389054i \(0.127198\pi\)
\(240\) 0 0
\(241\) 2.76910 0.178373 0.0891867 0.996015i \(-0.471573\pi\)
0.0891867 + 0.996015i \(0.471573\pi\)
\(242\) −0.719047 −0.0462221
\(243\) −4.35212 −0.279188
\(244\) −0.705804 −0.0451845
\(245\) 0 0
\(246\) −0.267443 −0.0170515
\(247\) 3.88893 0.247447
\(248\) 15.3572 0.975183
\(249\) −0.227516 −0.0144183
\(250\) 0 0
\(251\) 27.9920 1.76684 0.883419 0.468585i \(-0.155236\pi\)
0.883419 + 0.468585i \(0.155236\pi\)
\(252\) −4.65982 −0.293541
\(253\) −2.78982 −0.175395
\(254\) 8.26199 0.518403
\(255\) 0 0
\(256\) −11.1867 −0.699168
\(257\) 16.4205 1.02428 0.512140 0.858902i \(-0.328853\pi\)
0.512140 + 0.858902i \(0.328853\pi\)
\(258\) −0.458812 −0.0285644
\(259\) 3.71046 0.230557
\(260\) 0 0
\(261\) −2.64681 −0.163833
\(262\) 0.720150 0.0444910
\(263\) 5.81131 0.358340 0.179170 0.983818i \(-0.442659\pi\)
0.179170 + 0.983818i \(0.442659\pi\)
\(264\) −0.408506 −0.0251418
\(265\) 0 0
\(266\) −0.759873 −0.0465908
\(267\) −1.36501 −0.0835374
\(268\) −0.568494 −0.0347263
\(269\) −16.2245 −0.989223 −0.494611 0.869114i \(-0.664690\pi\)
−0.494611 + 0.869114i \(0.664690\pi\)
\(270\) 0 0
\(271\) 3.74012 0.227196 0.113598 0.993527i \(-0.463762\pi\)
0.113598 + 0.993527i \(0.463762\pi\)
\(272\) −6.58464 −0.399253
\(273\) −0.670355 −0.0405718
\(274\) 9.88116 0.596943
\(275\) 0 0
\(276\) −0.674840 −0.0406206
\(277\) −16.9533 −1.01863 −0.509313 0.860581i \(-0.670101\pi\)
−0.509313 + 0.860581i \(0.670101\pi\)
\(278\) 9.67414 0.580217
\(279\) −18.2330 −1.09158
\(280\) 0 0
\(281\) −18.1398 −1.08213 −0.541064 0.840981i \(-0.681978\pi\)
−0.541064 + 0.840981i \(0.681978\pi\)
\(282\) −0.909375 −0.0541525
\(283\) 18.6616 1.10932 0.554658 0.832079i \(-0.312849\pi\)
0.554658 + 0.832079i \(0.312849\pi\)
\(284\) 3.73687 0.221743
\(285\) 0 0
\(286\) 2.79632 0.165350
\(287\) 2.40971 0.142241
\(288\) 17.3844 1.02438
\(289\) 14.9378 0.878692
\(290\) 0 0
\(291\) −1.10190 −0.0645947
\(292\) −15.9993 −0.936286
\(293\) 10.5405 0.615780 0.307890 0.951422i \(-0.400377\pi\)
0.307890 + 0.951422i \(0.400377\pi\)
\(294\) −0.690024 −0.0402430
\(295\) 0 0
\(296\) −8.79330 −0.511100
\(297\) 0.974345 0.0565372
\(298\) −11.2316 −0.650628
\(299\) 10.8494 0.627438
\(300\) 0 0
\(301\) 4.13399 0.238279
\(302\) 9.52128 0.547888
\(303\) −1.63037 −0.0936621
\(304\) −1.16515 −0.0668257
\(305\) 0 0
\(306\) −12.0826 −0.690719
\(307\) 7.13003 0.406932 0.203466 0.979082i \(-0.434779\pi\)
0.203466 + 0.979082i \(0.434779\pi\)
\(308\) 1.56717 0.0892978
\(309\) 1.46123 0.0831266
\(310\) 0 0
\(311\) 19.8839 1.12751 0.563757 0.825941i \(-0.309356\pi\)
0.563757 + 0.825941i \(0.309356\pi\)
\(312\) 1.58865 0.0899397
\(313\) 4.06293 0.229651 0.114825 0.993386i \(-0.463369\pi\)
0.114825 + 0.993386i \(0.463369\pi\)
\(314\) −5.70751 −0.322094
\(315\) 0 0
\(316\) 6.33784 0.356531
\(317\) −1.04954 −0.0589479 −0.0294739 0.999566i \(-0.509383\pi\)
−0.0294739 + 0.999566i \(0.509383\pi\)
\(318\) −0.892847 −0.0500684
\(319\) 0.890165 0.0498397
\(320\) 0 0
\(321\) −0.322663 −0.0180093
\(322\) −2.11991 −0.118138
\(323\) 5.65135 0.314450
\(324\) −12.9927 −0.721816
\(325\) 0 0
\(326\) 3.50091 0.193897
\(327\) 0.138080 0.00763587
\(328\) −5.71069 −0.315320
\(329\) 8.19366 0.451731
\(330\) 0 0
\(331\) 18.3670 1.00954 0.504772 0.863253i \(-0.331577\pi\)
0.504772 + 0.863253i \(0.331577\pi\)
\(332\) −2.06849 −0.113523
\(333\) 10.4399 0.572104
\(334\) −4.88221 −0.267142
\(335\) 0 0
\(336\) 0.200842 0.0109568
\(337\) 30.8428 1.68012 0.840058 0.542496i \(-0.182521\pi\)
0.840058 + 0.542496i \(0.182521\pi\)
\(338\) −1.52709 −0.0830628
\(339\) 0.312735 0.0169854
\(340\) 0 0
\(341\) 6.13204 0.332068
\(342\) −2.13801 −0.115610
\(343\) 13.6147 0.735125
\(344\) −9.79700 −0.528219
\(345\) 0 0
\(346\) −10.5419 −0.566736
\(347\) −12.7838 −0.686269 −0.343134 0.939286i \(-0.611489\pi\)
−0.343134 + 0.939286i \(0.611489\pi\)
\(348\) 0.215325 0.0115426
\(349\) −24.5164 −1.31233 −0.656166 0.754616i \(-0.727823\pi\)
−0.656166 + 0.754616i \(0.727823\pi\)
\(350\) 0 0
\(351\) −3.78916 −0.202250
\(352\) −5.84664 −0.311627
\(353\) 18.2615 0.971963 0.485981 0.873969i \(-0.338462\pi\)
0.485981 + 0.873969i \(0.338462\pi\)
\(354\) −0.255263 −0.0135671
\(355\) 0 0
\(356\) −12.4102 −0.657738
\(357\) −0.974153 −0.0515577
\(358\) 6.57681 0.347595
\(359\) 8.81005 0.464977 0.232488 0.972599i \(-0.425313\pi\)
0.232488 + 0.972599i \(0.425313\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) −2.83047 −0.148766
\(363\) −0.163114 −0.00856127
\(364\) −6.09462 −0.319445
\(365\) 0 0
\(366\) 0.0558213 0.00291783
\(367\) 14.5509 0.759552 0.379776 0.925079i \(-0.376001\pi\)
0.379776 + 0.925079i \(0.376001\pi\)
\(368\) −3.25055 −0.169447
\(369\) 6.78007 0.352956
\(370\) 0 0
\(371\) 8.04474 0.417662
\(372\) 1.48330 0.0769055
\(373\) 6.38135 0.330414 0.165207 0.986259i \(-0.447171\pi\)
0.165207 + 0.986259i \(0.447171\pi\)
\(374\) 4.06359 0.210123
\(375\) 0 0
\(376\) −19.4179 −1.00140
\(377\) −3.46179 −0.178291
\(378\) 0.740378 0.0380809
\(379\) −11.7023 −0.601104 −0.300552 0.953765i \(-0.597171\pi\)
−0.300552 + 0.953765i \(0.597171\pi\)
\(380\) 0 0
\(381\) 1.87421 0.0960188
\(382\) 15.8208 0.809464
\(383\) −29.3472 −1.49957 −0.749786 0.661680i \(-0.769844\pi\)
−0.749786 + 0.661680i \(0.769844\pi\)
\(384\) −1.68758 −0.0861187
\(385\) 0 0
\(386\) 11.2873 0.574509
\(387\) 11.6316 0.591266
\(388\) −10.0181 −0.508591
\(389\) −13.9988 −0.709768 −0.354884 0.934910i \(-0.615480\pi\)
−0.354884 + 0.934910i \(0.615480\pi\)
\(390\) 0 0
\(391\) 15.7663 0.797334
\(392\) −14.7341 −0.744182
\(393\) 0.163364 0.00824064
\(394\) −7.17588 −0.361515
\(395\) 0 0
\(396\) 4.40946 0.221584
\(397\) 29.3475 1.47291 0.736455 0.676487i \(-0.236498\pi\)
0.736455 + 0.676487i \(0.236498\pi\)
\(398\) 3.59182 0.180042
\(399\) −0.172375 −0.00862956
\(400\) 0 0
\(401\) −1.30870 −0.0653533 −0.0326766 0.999466i \(-0.510403\pi\)
−0.0326766 + 0.999466i \(0.510403\pi\)
\(402\) 0.0449616 0.00224248
\(403\) −23.8471 −1.18791
\(404\) −14.8227 −0.737456
\(405\) 0 0
\(406\) 0.676412 0.0335698
\(407\) −3.51111 −0.174039
\(408\) 2.30861 0.114293
\(409\) −0.0668127 −0.00330367 −0.00165184 0.999999i \(-0.500526\pi\)
−0.00165184 + 0.999999i \(0.500526\pi\)
\(410\) 0 0
\(411\) 2.24152 0.110566
\(412\) 13.2850 0.654503
\(413\) 2.29998 0.113174
\(414\) −5.96467 −0.293148
\(415\) 0 0
\(416\) 22.7372 1.11478
\(417\) 2.19456 0.107468
\(418\) 0.719047 0.0351697
\(419\) 15.1746 0.741326 0.370663 0.928767i \(-0.379131\pi\)
0.370663 + 0.928767i \(0.379131\pi\)
\(420\) 0 0
\(421\) −3.96365 −0.193177 −0.0965883 0.995324i \(-0.530793\pi\)
−0.0965883 + 0.995324i \(0.530793\pi\)
\(422\) −10.9404 −0.532570
\(423\) 23.0540 1.12093
\(424\) −19.0649 −0.925875
\(425\) 0 0
\(426\) −0.295546 −0.0143192
\(427\) −0.502962 −0.0243400
\(428\) −2.93353 −0.141797
\(429\) 0.634339 0.0306262
\(430\) 0 0
\(431\) 36.3363 1.75026 0.875129 0.483890i \(-0.160777\pi\)
0.875129 + 0.483890i \(0.160777\pi\)
\(432\) 1.13525 0.0546199
\(433\) −14.8147 −0.711950 −0.355975 0.934495i \(-0.615851\pi\)
−0.355975 + 0.934495i \(0.615851\pi\)
\(434\) 4.65957 0.223667
\(435\) 0 0
\(436\) 1.25538 0.0601216
\(437\) 2.78982 0.133455
\(438\) 1.26537 0.0604615
\(439\) 38.3087 1.82837 0.914187 0.405292i \(-0.132830\pi\)
0.914187 + 0.405292i \(0.132830\pi\)
\(440\) 0 0
\(441\) 17.4931 0.833006
\(442\) −15.8030 −0.751672
\(443\) −1.84952 −0.0878734 −0.0439367 0.999034i \(-0.513990\pi\)
−0.0439367 + 0.999034i \(0.513990\pi\)
\(444\) −0.849315 −0.0403067
\(445\) 0 0
\(446\) −13.7704 −0.652045
\(447\) −2.54785 −0.120509
\(448\) −1.98010 −0.0935510
\(449\) 32.8639 1.55094 0.775472 0.631382i \(-0.217512\pi\)
0.775472 + 0.631382i \(0.217512\pi\)
\(450\) 0 0
\(451\) −2.28025 −0.107373
\(452\) 2.84327 0.133736
\(453\) 2.15988 0.101480
\(454\) 10.8560 0.509498
\(455\) 0 0
\(456\) 0.408506 0.0191301
\(457\) 10.8486 0.507478 0.253739 0.967273i \(-0.418340\pi\)
0.253739 + 0.967273i \(0.418340\pi\)
\(458\) −16.2230 −0.758049
\(459\) −5.50636 −0.257015
\(460\) 0 0
\(461\) 2.26284 0.105391 0.0526954 0.998611i \(-0.483219\pi\)
0.0526954 + 0.998611i \(0.483219\pi\)
\(462\) −0.123946 −0.00576649
\(463\) 32.1970 1.49632 0.748160 0.663518i \(-0.230937\pi\)
0.748160 + 0.663518i \(0.230937\pi\)
\(464\) 1.03717 0.0481495
\(465\) 0 0
\(466\) −0.659439 −0.0305479
\(467\) −37.3807 −1.72977 −0.864887 0.501967i \(-0.832610\pi\)
−0.864887 + 0.501967i \(0.832610\pi\)
\(468\) −17.1481 −0.792670
\(469\) −0.405114 −0.0187064
\(470\) 0 0
\(471\) −1.29473 −0.0596582
\(472\) −5.45063 −0.250886
\(473\) −3.91188 −0.179869
\(474\) −0.501254 −0.0230233
\(475\) 0 0
\(476\) −8.85663 −0.405943
\(477\) 22.6350 1.03639
\(478\) −20.4808 −0.936771
\(479\) 22.4365 1.02515 0.512574 0.858643i \(-0.328692\pi\)
0.512574 + 0.858643i \(0.328692\pi\)
\(480\) 0 0
\(481\) 13.6545 0.622590
\(482\) −1.99111 −0.0906927
\(483\) −0.480897 −0.0218816
\(484\) −1.48297 −0.0674078
\(485\) 0 0
\(486\) 3.12938 0.141951
\(487\) 7.74046 0.350754 0.175377 0.984501i \(-0.443886\pi\)
0.175377 + 0.984501i \(0.443886\pi\)
\(488\) 1.19195 0.0539571
\(489\) 0.794172 0.0359137
\(490\) 0 0
\(491\) 2.94721 0.133006 0.0665028 0.997786i \(-0.478816\pi\)
0.0665028 + 0.997786i \(0.478816\pi\)
\(492\) −0.551576 −0.0248670
\(493\) −5.03063 −0.226568
\(494\) −2.79632 −0.125813
\(495\) 0 0
\(496\) 7.14472 0.320807
\(497\) 2.66293 0.119449
\(498\) 0.163595 0.00733087
\(499\) 8.36252 0.374358 0.187179 0.982326i \(-0.440066\pi\)
0.187179 + 0.982326i \(0.440066\pi\)
\(500\) 0 0
\(501\) −1.10752 −0.0494802
\(502\) −20.1275 −0.898336
\(503\) −3.93785 −0.175580 −0.0877901 0.996139i \(-0.527980\pi\)
−0.0877901 + 0.996139i \(0.527980\pi\)
\(504\) 7.86943 0.350532
\(505\) 0 0
\(506\) 2.00601 0.0891782
\(507\) −0.346417 −0.0153849
\(508\) 17.0396 0.756011
\(509\) −26.3613 −1.16844 −0.584221 0.811595i \(-0.698600\pi\)
−0.584221 + 0.811595i \(0.698600\pi\)
\(510\) 0 0
\(511\) −11.4012 −0.504360
\(512\) −12.6482 −0.558977
\(513\) −0.974345 −0.0430184
\(514\) −11.8071 −0.520788
\(515\) 0 0
\(516\) −0.946259 −0.0416567
\(517\) −7.75344 −0.340996
\(518\) −2.66800 −0.117225
\(519\) −2.39140 −0.104971
\(520\) 0 0
\(521\) 5.27680 0.231181 0.115590 0.993297i \(-0.463124\pi\)
0.115590 + 0.993297i \(0.463124\pi\)
\(522\) 1.90318 0.0833000
\(523\) −27.9611 −1.22265 −0.611327 0.791378i \(-0.709364\pi\)
−0.611327 + 0.791378i \(0.709364\pi\)
\(524\) 1.48525 0.0648833
\(525\) 0 0
\(526\) −4.17860 −0.182196
\(527\) −34.6543 −1.50956
\(528\) −0.190052 −0.00827093
\(529\) −15.2169 −0.661604
\(530\) 0 0
\(531\) 6.47131 0.280831
\(532\) −1.56717 −0.0679455
\(533\) 8.86771 0.384103
\(534\) 0.981509 0.0424740
\(535\) 0 0
\(536\) 0.960065 0.0414685
\(537\) 1.49193 0.0643817
\(538\) 11.6662 0.502963
\(539\) −5.88322 −0.253408
\(540\) 0 0
\(541\) −20.8098 −0.894683 −0.447342 0.894363i \(-0.647629\pi\)
−0.447342 + 0.894363i \(0.647629\pi\)
\(542\) −2.68932 −0.115516
\(543\) −0.642086 −0.0275545
\(544\) 33.0414 1.41664
\(545\) 0 0
\(546\) 0.482017 0.0206284
\(547\) −15.6205 −0.667885 −0.333942 0.942593i \(-0.608379\pi\)
−0.333942 + 0.942593i \(0.608379\pi\)
\(548\) 20.3790 0.870549
\(549\) −1.41515 −0.0603973
\(550\) 0 0
\(551\) −0.890165 −0.0379223
\(552\) 1.13966 0.0485072
\(553\) 4.51640 0.192057
\(554\) 12.1902 0.517914
\(555\) 0 0
\(556\) 19.9521 0.846156
\(557\) 19.8995 0.843171 0.421585 0.906789i \(-0.361474\pi\)
0.421585 + 0.906789i \(0.361474\pi\)
\(558\) 13.1104 0.555006
\(559\) 15.2130 0.643443
\(560\) 0 0
\(561\) 0.921815 0.0389190
\(562\) 13.0434 0.550201
\(563\) 19.0668 0.803570 0.401785 0.915734i \(-0.368390\pi\)
0.401785 + 0.915734i \(0.368390\pi\)
\(564\) −1.87551 −0.0789730
\(565\) 0 0
\(566\) −13.4186 −0.564024
\(567\) −9.25870 −0.388829
\(568\) −6.31078 −0.264794
\(569\) −4.26584 −0.178833 −0.0894166 0.995994i \(-0.528500\pi\)
−0.0894166 + 0.995994i \(0.528500\pi\)
\(570\) 0 0
\(571\) −4.97199 −0.208071 −0.104036 0.994574i \(-0.533176\pi\)
−0.104036 + 0.994574i \(0.533176\pi\)
\(572\) 5.76717 0.241137
\(573\) 3.58892 0.149929
\(574\) −1.73270 −0.0723214
\(575\) 0 0
\(576\) −5.57130 −0.232137
\(577\) 19.1116 0.795627 0.397814 0.917466i \(-0.369769\pi\)
0.397814 + 0.917466i \(0.369769\pi\)
\(578\) −10.7410 −0.446765
\(579\) 2.56050 0.106411
\(580\) 0 0
\(581\) −1.47402 −0.0611528
\(582\) 0.792321 0.0328427
\(583\) −7.61251 −0.315278
\(584\) 27.0193 1.11807
\(585\) 0 0
\(586\) −7.57909 −0.313089
\(587\) 2.43947 0.100688 0.0503438 0.998732i \(-0.483968\pi\)
0.0503438 + 0.998732i \(0.483968\pi\)
\(588\) −1.42311 −0.0586882
\(589\) −6.13204 −0.252666
\(590\) 0 0
\(591\) −1.62783 −0.0669600
\(592\) −4.09096 −0.168137
\(593\) −42.8982 −1.76162 −0.880809 0.473472i \(-0.843000\pi\)
−0.880809 + 0.473472i \(0.843000\pi\)
\(594\) −0.700600 −0.0287460
\(595\) 0 0
\(596\) −23.1641 −0.948839
\(597\) 0.814796 0.0333474
\(598\) −7.80125 −0.319017
\(599\) 11.9181 0.486962 0.243481 0.969906i \(-0.421711\pi\)
0.243481 + 0.969906i \(0.421711\pi\)
\(600\) 0 0
\(601\) −35.3304 −1.44116 −0.720579 0.693373i \(-0.756124\pi\)
−0.720579 + 0.693373i \(0.756124\pi\)
\(602\) −2.97253 −0.121151
\(603\) −1.13984 −0.0464181
\(604\) 19.6368 0.799010
\(605\) 0 0
\(606\) 1.17231 0.0476219
\(607\) −2.12778 −0.0863638 −0.0431819 0.999067i \(-0.513750\pi\)
−0.0431819 + 0.999067i \(0.513750\pi\)
\(608\) 5.84664 0.237112
\(609\) 0.153442 0.00621780
\(610\) 0 0
\(611\) 30.1526 1.21984
\(612\) −24.9194 −1.00731
\(613\) 25.7794 1.04122 0.520611 0.853794i \(-0.325704\pi\)
0.520611 + 0.853794i \(0.325704\pi\)
\(614\) −5.12683 −0.206902
\(615\) 0 0
\(616\) −2.64662 −0.106635
\(617\) 25.0524 1.00857 0.504286 0.863537i \(-0.331756\pi\)
0.504286 + 0.863537i \(0.331756\pi\)
\(618\) −1.05070 −0.0422652
\(619\) 34.6510 1.39274 0.696372 0.717681i \(-0.254797\pi\)
0.696372 + 0.717681i \(0.254797\pi\)
\(620\) 0 0
\(621\) −2.71825 −0.109080
\(622\) −14.2975 −0.573276
\(623\) −8.84360 −0.354311
\(624\) 0.739097 0.0295876
\(625\) 0 0
\(626\) −2.92144 −0.116764
\(627\) 0.163114 0.00651415
\(628\) −11.7712 −0.469723
\(629\) 19.8425 0.791173
\(630\) 0 0
\(631\) −9.38162 −0.373476 −0.186738 0.982410i \(-0.559792\pi\)
−0.186738 + 0.982410i \(0.559792\pi\)
\(632\) −10.7033 −0.425753
\(633\) −2.48180 −0.0986428
\(634\) 0.754667 0.0299717
\(635\) 0 0
\(636\) −1.84142 −0.0730169
\(637\) 22.8794 0.906516
\(638\) −0.640071 −0.0253406
\(639\) 7.49252 0.296400
\(640\) 0 0
\(641\) −45.9392 −1.81449 −0.907245 0.420601i \(-0.861819\pi\)
−0.907245 + 0.420601i \(0.861819\pi\)
\(642\) 0.232010 0.00915670
\(643\) 20.4152 0.805097 0.402548 0.915399i \(-0.368125\pi\)
0.402548 + 0.915399i \(0.368125\pi\)
\(644\) −4.37213 −0.172286
\(645\) 0 0
\(646\) −4.06359 −0.159880
\(647\) −17.2966 −0.680000 −0.340000 0.940425i \(-0.610427\pi\)
−0.340000 + 0.940425i \(0.610427\pi\)
\(648\) 21.9419 0.861958
\(649\) −2.17640 −0.0854314
\(650\) 0 0
\(651\) 1.05701 0.0414276
\(652\) 7.22031 0.282769
\(653\) −17.4074 −0.681204 −0.340602 0.940208i \(-0.610631\pi\)
−0.340602 + 0.940208i \(0.610631\pi\)
\(654\) −0.0992864 −0.00388241
\(655\) 0 0
\(656\) −2.65682 −0.103731
\(657\) −32.0789 −1.25152
\(658\) −5.89163 −0.229680
\(659\) 19.7517 0.769415 0.384708 0.923038i \(-0.374302\pi\)
0.384708 + 0.923038i \(0.374302\pi\)
\(660\) 0 0
\(661\) −8.59246 −0.334208 −0.167104 0.985939i \(-0.553442\pi\)
−0.167104 + 0.985939i \(0.553442\pi\)
\(662\) −13.2068 −0.513295
\(663\) −3.58487 −0.139225
\(664\) 3.49324 0.135564
\(665\) 0 0
\(666\) −7.50679 −0.290882
\(667\) −2.48340 −0.0961577
\(668\) −10.0691 −0.389586
\(669\) −3.12377 −0.120772
\(670\) 0 0
\(671\) 0.475939 0.0183734
\(672\) −1.00782 −0.0388773
\(673\) 13.8476 0.533787 0.266893 0.963726i \(-0.414003\pi\)
0.266893 + 0.963726i \(0.414003\pi\)
\(674\) −22.1775 −0.854244
\(675\) 0 0
\(676\) −3.14949 −0.121134
\(677\) −42.0501 −1.61612 −0.808058 0.589102i \(-0.799481\pi\)
−0.808058 + 0.589102i \(0.799481\pi\)
\(678\) −0.224871 −0.00863613
\(679\) −7.13897 −0.273969
\(680\) 0 0
\(681\) 2.46266 0.0943693
\(682\) −4.40923 −0.168838
\(683\) 37.7020 1.44263 0.721313 0.692609i \(-0.243539\pi\)
0.721313 + 0.692609i \(0.243539\pi\)
\(684\) −4.40946 −0.168600
\(685\) 0 0
\(686\) −9.78961 −0.373769
\(687\) −3.68014 −0.140406
\(688\) −4.55791 −0.173769
\(689\) 29.6045 1.12784
\(690\) 0 0
\(691\) −48.8445 −1.85813 −0.929066 0.369913i \(-0.879387\pi\)
−0.929066 + 0.369913i \(0.879387\pi\)
\(692\) −21.7417 −0.826497
\(693\) 3.14222 0.119363
\(694\) 9.19213 0.348929
\(695\) 0 0
\(696\) −0.363638 −0.0137837
\(697\) 12.8865 0.488110
\(698\) 17.6284 0.667246
\(699\) −0.149592 −0.00565809
\(700\) 0 0
\(701\) −23.7536 −0.897160 −0.448580 0.893743i \(-0.648070\pi\)
−0.448580 + 0.893743i \(0.648070\pi\)
\(702\) 2.72458 0.102833
\(703\) 3.51111 0.132424
\(704\) 1.87372 0.0706184
\(705\) 0 0
\(706\) −13.1309 −0.494188
\(707\) −10.5628 −0.397254
\(708\) −0.526458 −0.0197855
\(709\) 27.0551 1.01607 0.508037 0.861335i \(-0.330371\pi\)
0.508037 + 0.861335i \(0.330371\pi\)
\(710\) 0 0
\(711\) 12.7075 0.476569
\(712\) 20.9581 0.785439
\(713\) −17.1073 −0.640673
\(714\) 0.700462 0.0262141
\(715\) 0 0
\(716\) 13.5641 0.506914
\(717\) −4.64602 −0.173509
\(718\) −6.33485 −0.236414
\(719\) −31.5836 −1.17787 −0.588934 0.808181i \(-0.700452\pi\)
−0.588934 + 0.808181i \(0.700452\pi\)
\(720\) 0 0
\(721\) 9.46698 0.352569
\(722\) −0.719047 −0.0267602
\(723\) −0.451679 −0.0167981
\(724\) −5.83760 −0.216953
\(725\) 0 0
\(726\) 0.117287 0.00435292
\(727\) 13.1743 0.488607 0.244303 0.969699i \(-0.421441\pi\)
0.244303 + 0.969699i \(0.421441\pi\)
\(728\) 10.2925 0.381466
\(729\) −25.5739 −0.947180
\(730\) 0 0
\(731\) 22.1074 0.817672
\(732\) 0.115127 0.00425520
\(733\) −13.5227 −0.499472 −0.249736 0.968314i \(-0.580344\pi\)
−0.249736 + 0.968314i \(0.580344\pi\)
\(734\) −10.4628 −0.386189
\(735\) 0 0
\(736\) 16.3111 0.601234
\(737\) 0.383348 0.0141208
\(738\) −4.87519 −0.179458
\(739\) 20.7838 0.764544 0.382272 0.924050i \(-0.375142\pi\)
0.382272 + 0.924050i \(0.375142\pi\)
\(740\) 0 0
\(741\) −0.634339 −0.0233030
\(742\) −5.78454 −0.212357
\(743\) −39.5592 −1.45129 −0.725644 0.688070i \(-0.758458\pi\)
−0.725644 + 0.688070i \(0.758458\pi\)
\(744\) −2.50498 −0.0918369
\(745\) 0 0
\(746\) −4.58849 −0.167997
\(747\) −4.14738 −0.151745
\(748\) 8.38079 0.306432
\(749\) −2.09046 −0.0763836
\(750\) 0 0
\(751\) −45.2335 −1.65059 −0.825297 0.564698i \(-0.808993\pi\)
−0.825297 + 0.564698i \(0.808993\pi\)
\(752\) −9.03388 −0.329432
\(753\) −4.56588 −0.166390
\(754\) 2.48919 0.0906509
\(755\) 0 0
\(756\) 1.52696 0.0555352
\(757\) −9.13639 −0.332068 −0.166034 0.986120i \(-0.553096\pi\)
−0.166034 + 0.986120i \(0.553096\pi\)
\(758\) 8.41447 0.305627
\(759\) 0.455059 0.0165176
\(760\) 0 0
\(761\) 4.46096 0.161710 0.0808549 0.996726i \(-0.474235\pi\)
0.0808549 + 0.996726i \(0.474235\pi\)
\(762\) −1.34765 −0.0488201
\(763\) 0.894591 0.0323864
\(764\) 32.6291 1.18048
\(765\) 0 0
\(766\) 21.1020 0.762447
\(767\) 8.46389 0.305613
\(768\) 1.82471 0.0658434
\(769\) −49.3765 −1.78056 −0.890282 0.455410i \(-0.849493\pi\)
−0.890282 + 0.455410i \(0.849493\pi\)
\(770\) 0 0
\(771\) −2.67841 −0.0964605
\(772\) 23.2791 0.837832
\(773\) −28.1145 −1.01121 −0.505605 0.862765i \(-0.668731\pi\)
−0.505605 + 0.862765i \(0.668731\pi\)
\(774\) −8.36364 −0.300625
\(775\) 0 0
\(776\) 16.9184 0.607335
\(777\) −0.605229 −0.0217125
\(778\) 10.0658 0.360877
\(779\) 2.28025 0.0816983
\(780\) 0 0
\(781\) −2.51986 −0.0901675
\(782\) −11.3367 −0.405399
\(783\) 0.867327 0.0309958
\(784\) −6.85481 −0.244815
\(785\) 0 0
\(786\) −0.117467 −0.00418990
\(787\) 29.8108 1.06264 0.531320 0.847171i \(-0.321696\pi\)
0.531320 + 0.847171i \(0.321696\pi\)
\(788\) −14.7996 −0.527214
\(789\) −0.947906 −0.0337463
\(790\) 0 0
\(791\) 2.02614 0.0720412
\(792\) −7.44663 −0.264604
\(793\) −1.85089 −0.0657272
\(794\) −21.1023 −0.748891
\(795\) 0 0
\(796\) 7.40782 0.262563
\(797\) 50.0474 1.77277 0.886385 0.462948i \(-0.153208\pi\)
0.886385 + 0.462948i \(0.153208\pi\)
\(798\) 0.123946 0.00438764
\(799\) 43.8174 1.55015
\(800\) 0 0
\(801\) −24.8827 −0.879187
\(802\) 0.941016 0.0332284
\(803\) 10.7887 0.380723
\(804\) 0.0927294 0.00327031
\(805\) 0 0
\(806\) 17.1472 0.603983
\(807\) 2.64644 0.0931590
\(808\) 25.0323 0.880634
\(809\) −27.8648 −0.979675 −0.489837 0.871814i \(-0.662944\pi\)
−0.489837 + 0.871814i \(0.662944\pi\)
\(810\) 0 0
\(811\) 49.6627 1.74389 0.871947 0.489600i \(-0.162857\pi\)
0.871947 + 0.489600i \(0.162857\pi\)
\(812\) 1.39504 0.0489563
\(813\) −0.610066 −0.0213960
\(814\) 2.52465 0.0884891
\(815\) 0 0
\(816\) 1.07405 0.0375992
\(817\) 3.91188 0.136859
\(818\) 0.0480415 0.00167973
\(819\) −12.2199 −0.426996
\(820\) 0 0
\(821\) −21.1699 −0.738836 −0.369418 0.929263i \(-0.620443\pi\)
−0.369418 + 0.929263i \(0.620443\pi\)
\(822\) −1.61176 −0.0562165
\(823\) 14.6145 0.509430 0.254715 0.967016i \(-0.418018\pi\)
0.254715 + 0.967016i \(0.418018\pi\)
\(824\) −22.4355 −0.781577
\(825\) 0 0
\(826\) −1.65379 −0.0575428
\(827\) −23.5899 −0.820302 −0.410151 0.912018i \(-0.634524\pi\)
−0.410151 + 0.912018i \(0.634524\pi\)
\(828\) −12.3016 −0.427510
\(829\) 18.9224 0.657204 0.328602 0.944469i \(-0.393423\pi\)
0.328602 + 0.944469i \(0.393423\pi\)
\(830\) 0 0
\(831\) 2.76533 0.0959281
\(832\) −7.28675 −0.252623
\(833\) 33.2481 1.15198
\(834\) −1.57799 −0.0546413
\(835\) 0 0
\(836\) 1.48297 0.0512896
\(837\) 5.97472 0.206516
\(838\) −10.9112 −0.376922
\(839\) −30.5617 −1.05511 −0.527553 0.849522i \(-0.676890\pi\)
−0.527553 + 0.849522i \(0.676890\pi\)
\(840\) 0 0
\(841\) −28.2076 −0.972676
\(842\) 2.85005 0.0982193
\(843\) 2.95885 0.101908
\(844\) −22.5636 −0.776671
\(845\) 0 0
\(846\) −16.5769 −0.569927
\(847\) −1.05678 −0.0363113
\(848\) −8.86968 −0.304586
\(849\) −3.04397 −0.104469
\(850\) 0 0
\(851\) 9.79538 0.335781
\(852\) −0.609537 −0.0208824
\(853\) −35.0082 −1.19866 −0.599329 0.800503i \(-0.704566\pi\)
−0.599329 + 0.800503i \(0.704566\pi\)
\(854\) 0.361653 0.0123755
\(855\) 0 0
\(856\) 4.95410 0.169328
\(857\) 20.5089 0.700569 0.350285 0.936643i \(-0.386085\pi\)
0.350285 + 0.936643i \(0.386085\pi\)
\(858\) −0.456120 −0.0155717
\(859\) −39.8526 −1.35975 −0.679877 0.733326i \(-0.737967\pi\)
−0.679877 + 0.733326i \(0.737967\pi\)
\(860\) 0 0
\(861\) −0.393058 −0.0133954
\(862\) −26.1275 −0.889906
\(863\) −26.4251 −0.899520 −0.449760 0.893149i \(-0.648491\pi\)
−0.449760 + 0.893149i \(0.648491\pi\)
\(864\) −5.69664 −0.193804
\(865\) 0 0
\(866\) 10.6525 0.361986
\(867\) −2.43656 −0.0827499
\(868\) 9.60995 0.326183
\(869\) −4.27374 −0.144977
\(870\) 0 0
\(871\) −1.49081 −0.0505143
\(872\) −2.12006 −0.0717943
\(873\) −20.0865 −0.679825
\(874\) −2.00601 −0.0678545
\(875\) 0 0
\(876\) 2.60970 0.0881737
\(877\) 25.0363 0.845415 0.422707 0.906266i \(-0.361080\pi\)
0.422707 + 0.906266i \(0.361080\pi\)
\(878\) −27.5458 −0.929625
\(879\) −1.71930 −0.0579904
\(880\) 0 0
\(881\) 35.9933 1.21264 0.606322 0.795219i \(-0.292644\pi\)
0.606322 + 0.795219i \(0.292644\pi\)
\(882\) −12.5784 −0.423536
\(883\) 9.56372 0.321845 0.160922 0.986967i \(-0.448553\pi\)
0.160922 + 0.986967i \(0.448553\pi\)
\(884\) −32.5923 −1.09620
\(885\) 0 0
\(886\) 1.32989 0.0446786
\(887\) −19.4058 −0.651583 −0.325792 0.945442i \(-0.605631\pi\)
−0.325792 + 0.945442i \(0.605631\pi\)
\(888\) 1.43431 0.0481323
\(889\) 12.1426 0.407249
\(890\) 0 0
\(891\) 8.76125 0.293513
\(892\) −28.4001 −0.950907
\(893\) 7.75344 0.259459
\(894\) 1.83203 0.0612722
\(895\) 0 0
\(896\) −10.9334 −0.365259
\(897\) −1.76969 −0.0590884
\(898\) −23.6307 −0.788567
\(899\) 5.45853 0.182052
\(900\) 0 0
\(901\) 43.0210 1.43324
\(902\) 1.63960 0.0545929
\(903\) −0.674312 −0.0224397
\(904\) −4.80167 −0.159701
\(905\) 0 0
\(906\) −1.55305 −0.0515968
\(907\) 41.6012 1.38134 0.690672 0.723168i \(-0.257315\pi\)
0.690672 + 0.723168i \(0.257315\pi\)
\(908\) 22.3896 0.743024
\(909\) −29.7198 −0.985744
\(910\) 0 0
\(911\) −41.9843 −1.39100 −0.695501 0.718525i \(-0.744818\pi\)
−0.695501 + 0.718525i \(0.744818\pi\)
\(912\) 0.190052 0.00629324
\(913\) 1.39483 0.0461621
\(914\) −7.80068 −0.258023
\(915\) 0 0
\(916\) −33.4584 −1.10550
\(917\) 1.05840 0.0349514
\(918\) 3.95933 0.130678
\(919\) −23.2518 −0.767007 −0.383504 0.923539i \(-0.625283\pi\)
−0.383504 + 0.923539i \(0.625283\pi\)
\(920\) 0 0
\(921\) −1.16301 −0.0383224
\(922\) −1.62709 −0.0535852
\(923\) 9.79954 0.322556
\(924\) −0.255628 −0.00840953
\(925\) 0 0
\(926\) −23.1512 −0.760794
\(927\) 26.6367 0.874864
\(928\) −5.20447 −0.170845
\(929\) −11.0442 −0.362348 −0.181174 0.983451i \(-0.557990\pi\)
−0.181174 + 0.983451i \(0.557990\pi\)
\(930\) 0 0
\(931\) 5.88322 0.192815
\(932\) −1.36003 −0.0445494
\(933\) −3.24335 −0.106182
\(934\) 26.8785 0.879492
\(935\) 0 0
\(936\) 28.9594 0.946568
\(937\) 11.1871 0.365468 0.182734 0.983162i \(-0.441505\pi\)
0.182734 + 0.983162i \(0.441505\pi\)
\(938\) 0.291296 0.00951115
\(939\) −0.662722 −0.0216271
\(940\) 0 0
\(941\) 10.2267 0.333380 0.166690 0.986009i \(-0.446692\pi\)
0.166690 + 0.986009i \(0.446692\pi\)
\(942\) 0.930975 0.0303328
\(943\) 6.36148 0.207158
\(944\) −2.53583 −0.0825342
\(945\) 0 0
\(946\) 2.81283 0.0914529
\(947\) 21.1154 0.686157 0.343079 0.939307i \(-0.388530\pi\)
0.343079 + 0.939307i \(0.388530\pi\)
\(948\) −1.03379 −0.0335760
\(949\) −41.9563 −1.36196
\(950\) 0 0
\(951\) 0.171194 0.00555136
\(952\) 14.9570 0.484758
\(953\) 15.7726 0.510925 0.255463 0.966819i \(-0.417772\pi\)
0.255463 + 0.966819i \(0.417772\pi\)
\(954\) −16.2756 −0.526943
\(955\) 0 0
\(956\) −42.2399 −1.36614
\(957\) −0.145198 −0.00469360
\(958\) −16.1329 −0.521230
\(959\) 14.5223 0.468948
\(960\) 0 0
\(961\) 6.60189 0.212964
\(962\) −9.81820 −0.316552
\(963\) −5.88180 −0.189538
\(964\) −4.10650 −0.132261
\(965\) 0 0
\(966\) 0.345787 0.0111255
\(967\) 45.7966 1.47272 0.736359 0.676591i \(-0.236543\pi\)
0.736359 + 0.676591i \(0.236543\pi\)
\(968\) 2.50442 0.0804951
\(969\) −0.921815 −0.0296130
\(970\) 0 0
\(971\) 0.966326 0.0310109 0.0155054 0.999880i \(-0.495064\pi\)
0.0155054 + 0.999880i \(0.495064\pi\)
\(972\) 6.45406 0.207014
\(973\) 14.2180 0.455808
\(974\) −5.56575 −0.178338
\(975\) 0 0
\(976\) 0.554538 0.0177503
\(977\) 42.9904 1.37539 0.687693 0.726002i \(-0.258624\pi\)
0.687693 + 0.726002i \(0.258624\pi\)
\(978\) −0.571047 −0.0182601
\(979\) 8.36845 0.267457
\(980\) 0 0
\(981\) 2.51706 0.0803635
\(982\) −2.11918 −0.0676258
\(983\) −1.22382 −0.0390337 −0.0195169 0.999810i \(-0.506213\pi\)
−0.0195169 + 0.999810i \(0.506213\pi\)
\(984\) 0.931495 0.0296950
\(985\) 0 0
\(986\) 3.61726 0.115197
\(987\) −1.33650 −0.0425413
\(988\) −5.76717 −0.183478
\(989\) 10.9135 0.347028
\(990\) 0 0
\(991\) −54.2437 −1.72311 −0.861554 0.507666i \(-0.830508\pi\)
−0.861554 + 0.507666i \(0.830508\pi\)
\(992\) −35.8518 −1.13830
\(993\) −2.99592 −0.0950727
\(994\) −1.91477 −0.0607328
\(995\) 0 0
\(996\) 0.337400 0.0106909
\(997\) 36.8826 1.16808 0.584041 0.811724i \(-0.301471\pi\)
0.584041 + 0.811724i \(0.301471\pi\)
\(998\) −6.01305 −0.190340
\(999\) −3.42103 −0.108237
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 5225.2.a.m.1.4 7
5.4 even 2 1045.2.a.h.1.4 7
15.14 odd 2 9405.2.a.bd.1.4 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.2.a.h.1.4 7 5.4 even 2
5225.2.a.m.1.4 7 1.1 even 1 trivial
9405.2.a.bd.1.4 7 15.14 odd 2