Properties

Label 6018.2.a.z.1.9
Level $6018$
Weight $2$
Character 6018.1
Self dual yes
Analytic conductor $48.054$
Analytic rank $0$
Dimension $11$
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] = [6018,2,Mod(1,6018)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6018, 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("6018.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6018.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: \(48.0539719364\)
Analytic rank: \(0\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{11} - 4 x^{10} - 27 x^{9} + 117 x^{8} + 200 x^{7} - 1023 x^{6} - 484 x^{5} + 3403 x^{4} + 562 x^{3} - 4372 x^{2} - 692 x + 1200 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(2.25950\) of defining polynomial
Character \(\chi\) \(=\) 6018.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.25950 q^{5} -1.00000 q^{6} +3.73494 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.25950 q^{5} -1.00000 q^{6} +3.73494 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.25950 q^{10} +3.84055 q^{11} -1.00000 q^{12} -4.08367 q^{13} +3.73494 q^{14} -2.25950 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -1.16453 q^{19} +2.25950 q^{20} -3.73494 q^{21} +3.84055 q^{22} +5.03855 q^{23} -1.00000 q^{24} +0.105322 q^{25} -4.08367 q^{26} -1.00000 q^{27} +3.73494 q^{28} +6.70162 q^{29} -2.25950 q^{30} -7.12027 q^{31} +1.00000 q^{32} -3.84055 q^{33} -1.00000 q^{34} +8.43907 q^{35} +1.00000 q^{36} -2.75553 q^{37} -1.16453 q^{38} +4.08367 q^{39} +2.25950 q^{40} +8.36186 q^{41} -3.73494 q^{42} +10.5441 q^{43} +3.84055 q^{44} +2.25950 q^{45} +5.03855 q^{46} +0.0503609 q^{47} -1.00000 q^{48} +6.94974 q^{49} +0.105322 q^{50} +1.00000 q^{51} -4.08367 q^{52} -0.972069 q^{53} -1.00000 q^{54} +8.67770 q^{55} +3.73494 q^{56} +1.16453 q^{57} +6.70162 q^{58} -1.00000 q^{59} -2.25950 q^{60} -6.11723 q^{61} -7.12027 q^{62} +3.73494 q^{63} +1.00000 q^{64} -9.22703 q^{65} -3.84055 q^{66} -0.356946 q^{67} -1.00000 q^{68} -5.03855 q^{69} +8.43907 q^{70} +5.02022 q^{71} +1.00000 q^{72} -5.24611 q^{73} -2.75553 q^{74} -0.105322 q^{75} -1.16453 q^{76} +14.3442 q^{77} +4.08367 q^{78} +0.531164 q^{79} +2.25950 q^{80} +1.00000 q^{81} +8.36186 q^{82} +5.67224 q^{83} -3.73494 q^{84} -2.25950 q^{85} +10.5441 q^{86} -6.70162 q^{87} +3.84055 q^{88} +13.4985 q^{89} +2.25950 q^{90} -15.2522 q^{91} +5.03855 q^{92} +7.12027 q^{93} +0.0503609 q^{94} -2.63126 q^{95} -1.00000 q^{96} -7.52852 q^{97} +6.94974 q^{98} +3.84055 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9} + 4 q^{10} + 9 q^{11} - 11 q^{12} + 6 q^{13} + 3 q^{14} - 4 q^{15} + 11 q^{16} - 11 q^{17} + 11 q^{18} - q^{19} + 4 q^{20} - 3 q^{21} + 9 q^{22} + 10 q^{23} - 11 q^{24} + 15 q^{25} + 6 q^{26} - 11 q^{27} + 3 q^{28} + 14 q^{29} - 4 q^{30} + 17 q^{31} + 11 q^{32} - 9 q^{33} - 11 q^{34} + 8 q^{35} + 11 q^{36} + 30 q^{37} - q^{38} - 6 q^{39} + 4 q^{40} + 10 q^{41} - 3 q^{42} + 11 q^{43} + 9 q^{44} + 4 q^{45} + 10 q^{46} - 6 q^{47} - 11 q^{48} + 18 q^{49} + 15 q^{50} + 11 q^{51} + 6 q^{52} + 10 q^{53} - 11 q^{54} - 11 q^{55} + 3 q^{56} + q^{57} + 14 q^{58} - 11 q^{59} - 4 q^{60} + 13 q^{61} + 17 q^{62} + 3 q^{63} + 11 q^{64} + 32 q^{65} - 9 q^{66} + 26 q^{67} - 11 q^{68} - 10 q^{69} + 8 q^{70} + 14 q^{71} + 11 q^{72} + 20 q^{73} + 30 q^{74} - 15 q^{75} - q^{76} + 26 q^{77} - 6 q^{78} + 15 q^{79} + 4 q^{80} + 11 q^{81} + 10 q^{82} + 2 q^{83} - 3 q^{84} - 4 q^{85} + 11 q^{86} - 14 q^{87} + 9 q^{88} + q^{89} + 4 q^{90} + 17 q^{91} + 10 q^{92} - 17 q^{93} - 6 q^{94} + 3 q^{95} - 11 q^{96} + 33 q^{97} + 18 q^{98} + 9 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) 2.25950 1.01048 0.505239 0.862980i \(-0.331404\pi\)
0.505239 + 0.862980i \(0.331404\pi\)
\(6\) −1.00000 −0.408248
\(7\) 3.73494 1.41167 0.705837 0.708375i \(-0.250571\pi\)
0.705837 + 0.708375i \(0.250571\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 2.25950 0.714515
\(11\) 3.84055 1.15797 0.578984 0.815339i \(-0.303449\pi\)
0.578984 + 0.815339i \(0.303449\pi\)
\(12\) −1.00000 −0.288675
\(13\) −4.08367 −1.13261 −0.566303 0.824197i \(-0.691627\pi\)
−0.566303 + 0.824197i \(0.691627\pi\)
\(14\) 3.73494 0.998204
\(15\) −2.25950 −0.583399
\(16\) 1.00000 0.250000
\(17\) −1.00000 −0.242536
\(18\) 1.00000 0.235702
\(19\) −1.16453 −0.267162 −0.133581 0.991038i \(-0.542648\pi\)
−0.133581 + 0.991038i \(0.542648\pi\)
\(20\) 2.25950 0.505239
\(21\) −3.73494 −0.815030
\(22\) 3.84055 0.818807
\(23\) 5.03855 1.05061 0.525305 0.850914i \(-0.323951\pi\)
0.525305 + 0.850914i \(0.323951\pi\)
\(24\) −1.00000 −0.204124
\(25\) 0.105322 0.0210645
\(26\) −4.08367 −0.800873
\(27\) −1.00000 −0.192450
\(28\) 3.73494 0.705837
\(29\) 6.70162 1.24446 0.622230 0.782835i \(-0.286227\pi\)
0.622230 + 0.782835i \(0.286227\pi\)
\(30\) −2.25950 −0.412526
\(31\) −7.12027 −1.27884 −0.639419 0.768859i \(-0.720825\pi\)
−0.639419 + 0.768859i \(0.720825\pi\)
\(32\) 1.00000 0.176777
\(33\) −3.84055 −0.668553
\(34\) −1.00000 −0.171499
\(35\) 8.43907 1.42646
\(36\) 1.00000 0.166667
\(37\) −2.75553 −0.453006 −0.226503 0.974011i \(-0.572729\pi\)
−0.226503 + 0.974011i \(0.572729\pi\)
\(38\) −1.16453 −0.188912
\(39\) 4.08367 0.653910
\(40\) 2.25950 0.357258
\(41\) 8.36186 1.30590 0.652951 0.757400i \(-0.273531\pi\)
0.652951 + 0.757400i \(0.273531\pi\)
\(42\) −3.73494 −0.576313
\(43\) 10.5441 1.60795 0.803976 0.594661i \(-0.202714\pi\)
0.803976 + 0.594661i \(0.202714\pi\)
\(44\) 3.84055 0.578984
\(45\) 2.25950 0.336826
\(46\) 5.03855 0.742893
\(47\) 0.0503609 0.00734589 0.00367294 0.999993i \(-0.498831\pi\)
0.00367294 + 0.999993i \(0.498831\pi\)
\(48\) −1.00000 −0.144338
\(49\) 6.94974 0.992821
\(50\) 0.105322 0.0148948
\(51\) 1.00000 0.140028
\(52\) −4.08367 −0.566303
\(53\) −0.972069 −0.133524 −0.0667620 0.997769i \(-0.521267\pi\)
−0.0667620 + 0.997769i \(0.521267\pi\)
\(54\) −1.00000 −0.136083
\(55\) 8.67770 1.17010
\(56\) 3.73494 0.499102
\(57\) 1.16453 0.154246
\(58\) 6.70162 0.879966
\(59\) −1.00000 −0.130189
\(60\) −2.25950 −0.291700
\(61\) −6.11723 −0.783231 −0.391616 0.920129i \(-0.628084\pi\)
−0.391616 + 0.920129i \(0.628084\pi\)
\(62\) −7.12027 −0.904275
\(63\) 3.73494 0.470558
\(64\) 1.00000 0.125000
\(65\) −9.22703 −1.14447
\(66\) −3.84055 −0.472739
\(67\) −0.356946 −0.0436079 −0.0218040 0.999762i \(-0.506941\pi\)
−0.0218040 + 0.999762i \(0.506941\pi\)
\(68\) −1.00000 −0.121268
\(69\) −5.03855 −0.606570
\(70\) 8.43907 1.00866
\(71\) 5.02022 0.595791 0.297895 0.954599i \(-0.403715\pi\)
0.297895 + 0.954599i \(0.403715\pi\)
\(72\) 1.00000 0.117851
\(73\) −5.24611 −0.614010 −0.307005 0.951708i \(-0.599327\pi\)
−0.307005 + 0.951708i \(0.599327\pi\)
\(74\) −2.75553 −0.320323
\(75\) −0.105322 −0.0121616
\(76\) −1.16453 −0.133581
\(77\) 14.3442 1.63467
\(78\) 4.08367 0.462384
\(79\) 0.531164 0.0597606 0.0298803 0.999553i \(-0.490487\pi\)
0.0298803 + 0.999553i \(0.490487\pi\)
\(80\) 2.25950 0.252619
\(81\) 1.00000 0.111111
\(82\) 8.36186 0.923412
\(83\) 5.67224 0.622610 0.311305 0.950310i \(-0.399234\pi\)
0.311305 + 0.950310i \(0.399234\pi\)
\(84\) −3.73494 −0.407515
\(85\) −2.25950 −0.245077
\(86\) 10.5441 1.13699
\(87\) −6.70162 −0.718489
\(88\) 3.84055 0.409404
\(89\) 13.4985 1.43084 0.715421 0.698693i \(-0.246235\pi\)
0.715421 + 0.698693i \(0.246235\pi\)
\(90\) 2.25950 0.238172
\(91\) −15.2522 −1.59887
\(92\) 5.03855 0.525305
\(93\) 7.12027 0.738337
\(94\) 0.0503609 0.00519433
\(95\) −2.63126 −0.269962
\(96\) −1.00000 −0.102062
\(97\) −7.52852 −0.764405 −0.382203 0.924079i \(-0.624834\pi\)
−0.382203 + 0.924079i \(0.624834\pi\)
\(98\) 6.94974 0.702030
\(99\) 3.84055 0.385990
\(100\) 0.105322 0.0105322
\(101\) 7.36090 0.732437 0.366218 0.930529i \(-0.380652\pi\)
0.366218 + 0.930529i \(0.380652\pi\)
\(102\) 1.00000 0.0990148
\(103\) 16.9716 1.67226 0.836128 0.548534i \(-0.184814\pi\)
0.836128 + 0.548534i \(0.184814\pi\)
\(104\) −4.08367 −0.400437
\(105\) −8.43907 −0.823569
\(106\) −0.972069 −0.0944157
\(107\) 6.02420 0.582381 0.291191 0.956665i \(-0.405949\pi\)
0.291191 + 0.956665i \(0.405949\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −10.5956 −1.01487 −0.507436 0.861689i \(-0.669407\pi\)
−0.507436 + 0.861689i \(0.669407\pi\)
\(110\) 8.67770 0.827386
\(111\) 2.75553 0.261543
\(112\) 3.73494 0.352918
\(113\) −20.2421 −1.90421 −0.952107 0.305766i \(-0.901088\pi\)
−0.952107 + 0.305766i \(0.901088\pi\)
\(114\) 1.16453 0.109069
\(115\) 11.3846 1.06162
\(116\) 6.70162 0.622230
\(117\) −4.08367 −0.377535
\(118\) −1.00000 −0.0920575
\(119\) −3.73494 −0.342381
\(120\) −2.25950 −0.206263
\(121\) 3.74980 0.340891
\(122\) −6.11723 −0.553828
\(123\) −8.36186 −0.753963
\(124\) −7.12027 −0.639419
\(125\) −11.0595 −0.989192
\(126\) 3.73494 0.332735
\(127\) −7.19680 −0.638612 −0.319306 0.947652i \(-0.603450\pi\)
−0.319306 + 0.947652i \(0.603450\pi\)
\(128\) 1.00000 0.0883883
\(129\) −10.5441 −0.928352
\(130\) −9.22703 −0.809264
\(131\) −10.3416 −0.903550 −0.451775 0.892132i \(-0.649209\pi\)
−0.451775 + 0.892132i \(0.649209\pi\)
\(132\) −3.84055 −0.334277
\(133\) −4.34946 −0.377146
\(134\) −0.356946 −0.0308355
\(135\) −2.25950 −0.194466
\(136\) −1.00000 −0.0857493
\(137\) 12.5181 1.06950 0.534748 0.845012i \(-0.320407\pi\)
0.534748 + 0.845012i \(0.320407\pi\)
\(138\) −5.03855 −0.428910
\(139\) −0.485663 −0.0411934 −0.0205967 0.999788i \(-0.506557\pi\)
−0.0205967 + 0.999788i \(0.506557\pi\)
\(140\) 8.43907 0.713232
\(141\) −0.0503609 −0.00424115
\(142\) 5.02022 0.421288
\(143\) −15.6835 −1.31152
\(144\) 1.00000 0.0833333
\(145\) 15.1423 1.25750
\(146\) −5.24611 −0.434171
\(147\) −6.94974 −0.573205
\(148\) −2.75553 −0.226503
\(149\) −12.1194 −0.992861 −0.496431 0.868076i \(-0.665356\pi\)
−0.496431 + 0.868076i \(0.665356\pi\)
\(150\) −0.105322 −0.00859954
\(151\) −12.0007 −0.976600 −0.488300 0.872676i \(-0.662383\pi\)
−0.488300 + 0.872676i \(0.662383\pi\)
\(152\) −1.16453 −0.0944562
\(153\) −1.00000 −0.0808452
\(154\) 14.3442 1.15589
\(155\) −16.0882 −1.29224
\(156\) 4.08367 0.326955
\(157\) 6.65132 0.530833 0.265417 0.964134i \(-0.414490\pi\)
0.265417 + 0.964134i \(0.414490\pi\)
\(158\) 0.531164 0.0422571
\(159\) 0.972069 0.0770901
\(160\) 2.25950 0.178629
\(161\) 18.8187 1.48312
\(162\) 1.00000 0.0785674
\(163\) 15.2569 1.19501 0.597507 0.801864i \(-0.296158\pi\)
0.597507 + 0.801864i \(0.296158\pi\)
\(164\) 8.36186 0.652951
\(165\) −8.67770 −0.675558
\(166\) 5.67224 0.440251
\(167\) −18.2500 −1.41223 −0.706114 0.708098i \(-0.749554\pi\)
−0.706114 + 0.708098i \(0.749554\pi\)
\(168\) −3.73494 −0.288157
\(169\) 3.67634 0.282796
\(170\) −2.25950 −0.173295
\(171\) −1.16453 −0.0890541
\(172\) 10.5441 0.803976
\(173\) −5.65681 −0.430079 −0.215040 0.976605i \(-0.568988\pi\)
−0.215040 + 0.976605i \(0.568988\pi\)
\(174\) −6.70162 −0.508048
\(175\) 0.393373 0.0297362
\(176\) 3.84055 0.289492
\(177\) 1.00000 0.0751646
\(178\) 13.4985 1.01176
\(179\) −17.5859 −1.31443 −0.657216 0.753702i \(-0.728266\pi\)
−0.657216 + 0.753702i \(0.728266\pi\)
\(180\) 2.25950 0.168413
\(181\) 15.4875 1.15118 0.575589 0.817739i \(-0.304773\pi\)
0.575589 + 0.817739i \(0.304773\pi\)
\(182\) −15.2522 −1.13057
\(183\) 6.11723 0.452199
\(184\) 5.03855 0.371447
\(185\) −6.22610 −0.457752
\(186\) 7.12027 0.522083
\(187\) −3.84055 −0.280849
\(188\) 0.0503609 0.00367294
\(189\) −3.73494 −0.271677
\(190\) −2.63126 −0.190892
\(191\) −5.98757 −0.433245 −0.216623 0.976255i \(-0.569504\pi\)
−0.216623 + 0.976255i \(0.569504\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 20.0576 1.44378 0.721888 0.692010i \(-0.243274\pi\)
0.721888 + 0.692010i \(0.243274\pi\)
\(194\) −7.52852 −0.540516
\(195\) 9.22703 0.660761
\(196\) 6.94974 0.496410
\(197\) −1.62569 −0.115826 −0.0579129 0.998322i \(-0.518445\pi\)
−0.0579129 + 0.998322i \(0.518445\pi\)
\(198\) 3.84055 0.272936
\(199\) −10.9179 −0.773952 −0.386976 0.922090i \(-0.626480\pi\)
−0.386976 + 0.922090i \(0.626480\pi\)
\(200\) 0.105322 0.00744742
\(201\) 0.356946 0.0251771
\(202\) 7.36090 0.517911
\(203\) 25.0301 1.75677
\(204\) 1.00000 0.0700140
\(205\) 18.8936 1.31958
\(206\) 16.9716 1.18246
\(207\) 5.03855 0.350203
\(208\) −4.08367 −0.283151
\(209\) −4.47245 −0.309366
\(210\) −8.43907 −0.582351
\(211\) 24.7016 1.70053 0.850264 0.526357i \(-0.176443\pi\)
0.850264 + 0.526357i \(0.176443\pi\)
\(212\) −0.972069 −0.0667620
\(213\) −5.02022 −0.343980
\(214\) 6.02420 0.411806
\(215\) 23.8242 1.62480
\(216\) −1.00000 −0.0680414
\(217\) −26.5937 −1.80530
\(218\) −10.5956 −0.717623
\(219\) 5.24611 0.354499
\(220\) 8.67770 0.585051
\(221\) 4.08367 0.274697
\(222\) 2.75553 0.184939
\(223\) −17.9650 −1.20303 −0.601513 0.798863i \(-0.705435\pi\)
−0.601513 + 0.798863i \(0.705435\pi\)
\(224\) 3.73494 0.249551
\(225\) 0.105322 0.00702150
\(226\) −20.2421 −1.34648
\(227\) −12.1520 −0.806554 −0.403277 0.915078i \(-0.632129\pi\)
−0.403277 + 0.915078i \(0.632129\pi\)
\(228\) 1.16453 0.0771231
\(229\) −10.5713 −0.698571 −0.349286 0.937016i \(-0.613576\pi\)
−0.349286 + 0.937016i \(0.613576\pi\)
\(230\) 11.3846 0.750677
\(231\) −14.3442 −0.943779
\(232\) 6.70162 0.439983
\(233\) 13.9663 0.914961 0.457480 0.889220i \(-0.348752\pi\)
0.457480 + 0.889220i \(0.348752\pi\)
\(234\) −4.08367 −0.266958
\(235\) 0.113790 0.00742285
\(236\) −1.00000 −0.0650945
\(237\) −0.531164 −0.0345028
\(238\) −3.73494 −0.242100
\(239\) 28.5324 1.84561 0.922803 0.385273i \(-0.125893\pi\)
0.922803 + 0.385273i \(0.125893\pi\)
\(240\) −2.25950 −0.145850
\(241\) −29.0203 −1.86936 −0.934682 0.355485i \(-0.884316\pi\)
−0.934682 + 0.355485i \(0.884316\pi\)
\(242\) 3.74980 0.241047
\(243\) −1.00000 −0.0641500
\(244\) −6.11723 −0.391616
\(245\) 15.7029 1.00322
\(246\) −8.36186 −0.533132
\(247\) 4.75557 0.302590
\(248\) −7.12027 −0.452137
\(249\) −5.67224 −0.359464
\(250\) −11.0595 −0.699464
\(251\) 26.4706 1.67081 0.835404 0.549636i \(-0.185234\pi\)
0.835404 + 0.549636i \(0.185234\pi\)
\(252\) 3.73494 0.235279
\(253\) 19.3508 1.21657
\(254\) −7.19680 −0.451567
\(255\) 2.25950 0.141495
\(256\) 1.00000 0.0625000
\(257\) −19.5525 −1.21965 −0.609827 0.792534i \(-0.708761\pi\)
−0.609827 + 0.792534i \(0.708761\pi\)
\(258\) −10.5441 −0.656444
\(259\) −10.2917 −0.639496
\(260\) −9.22703 −0.572236
\(261\) 6.70162 0.414820
\(262\) −10.3416 −0.638906
\(263\) −20.1022 −1.23956 −0.619778 0.784777i \(-0.712778\pi\)
−0.619778 + 0.784777i \(0.712778\pi\)
\(264\) −3.84055 −0.236369
\(265\) −2.19639 −0.134923
\(266\) −4.34946 −0.266682
\(267\) −13.4985 −0.826097
\(268\) −0.356946 −0.0218040
\(269\) −21.5907 −1.31641 −0.658205 0.752839i \(-0.728684\pi\)
−0.658205 + 0.752839i \(0.728684\pi\)
\(270\) −2.25950 −0.137509
\(271\) 11.2670 0.684419 0.342209 0.939624i \(-0.388825\pi\)
0.342209 + 0.939624i \(0.388825\pi\)
\(272\) −1.00000 −0.0606339
\(273\) 15.2522 0.923107
\(274\) 12.5181 0.756247
\(275\) 0.404496 0.0243920
\(276\) −5.03855 −0.303285
\(277\) 10.0277 0.602503 0.301252 0.953545i \(-0.402596\pi\)
0.301252 + 0.953545i \(0.402596\pi\)
\(278\) −0.485663 −0.0291281
\(279\) −7.12027 −0.426279
\(280\) 8.43907 0.504331
\(281\) 29.8315 1.77960 0.889799 0.456354i \(-0.150845\pi\)
0.889799 + 0.456354i \(0.150845\pi\)
\(282\) −0.0503609 −0.00299895
\(283\) 10.4024 0.618361 0.309180 0.951003i \(-0.399945\pi\)
0.309180 + 0.951003i \(0.399945\pi\)
\(284\) 5.02022 0.297895
\(285\) 2.63126 0.155862
\(286\) −15.6835 −0.927386
\(287\) 31.2310 1.84351
\(288\) 1.00000 0.0589256
\(289\) 1.00000 0.0588235
\(290\) 15.1423 0.889186
\(291\) 7.52852 0.441329
\(292\) −5.24611 −0.307005
\(293\) −12.9210 −0.754850 −0.377425 0.926040i \(-0.623190\pi\)
−0.377425 + 0.926040i \(0.623190\pi\)
\(294\) −6.94974 −0.405317
\(295\) −2.25950 −0.131553
\(296\) −2.75553 −0.160162
\(297\) −3.84055 −0.222851
\(298\) −12.1194 −0.702059
\(299\) −20.5758 −1.18993
\(300\) −0.105322 −0.00608080
\(301\) 39.3814 2.26990
\(302\) −12.0007 −0.690561
\(303\) −7.36090 −0.422873
\(304\) −1.16453 −0.0667906
\(305\) −13.8219 −0.791437
\(306\) −1.00000 −0.0571662
\(307\) −2.59585 −0.148153 −0.0740766 0.997253i \(-0.523601\pi\)
−0.0740766 + 0.997253i \(0.523601\pi\)
\(308\) 14.3442 0.817337
\(309\) −16.9716 −0.965478
\(310\) −16.0882 −0.913749
\(311\) −18.7836 −1.06512 −0.532560 0.846392i \(-0.678770\pi\)
−0.532560 + 0.846392i \(0.678770\pi\)
\(312\) 4.08367 0.231192
\(313\) 6.07314 0.343274 0.171637 0.985160i \(-0.445094\pi\)
0.171637 + 0.985160i \(0.445094\pi\)
\(314\) 6.65132 0.375356
\(315\) 8.43907 0.475488
\(316\) 0.531164 0.0298803
\(317\) 17.1939 0.965706 0.482853 0.875701i \(-0.339601\pi\)
0.482853 + 0.875701i \(0.339601\pi\)
\(318\) 0.972069 0.0545109
\(319\) 25.7379 1.44105
\(320\) 2.25950 0.126310
\(321\) −6.02420 −0.336238
\(322\) 18.8187 1.04872
\(323\) 1.16453 0.0647964
\(324\) 1.00000 0.0555556
\(325\) −0.430102 −0.0238578
\(326\) 15.2569 0.845002
\(327\) 10.5956 0.585937
\(328\) 8.36186 0.461706
\(329\) 0.188095 0.0103700
\(330\) −8.67770 −0.477692
\(331\) −29.0385 −1.59610 −0.798049 0.602592i \(-0.794135\pi\)
−0.798049 + 0.602592i \(0.794135\pi\)
\(332\) 5.67224 0.311305
\(333\) −2.75553 −0.151002
\(334\) −18.2500 −0.998597
\(335\) −0.806519 −0.0440648
\(336\) −3.73494 −0.203757
\(337\) 25.9764 1.41503 0.707513 0.706701i \(-0.249817\pi\)
0.707513 + 0.706701i \(0.249817\pi\)
\(338\) 3.67634 0.199967
\(339\) 20.2421 1.09940
\(340\) −2.25950 −0.122538
\(341\) −27.3457 −1.48085
\(342\) −1.16453 −0.0629708
\(343\) −0.187700 −0.0101349
\(344\) 10.5441 0.568497
\(345\) −11.3846 −0.612925
\(346\) −5.65681 −0.304112
\(347\) 9.12812 0.490023 0.245012 0.969520i \(-0.421208\pi\)
0.245012 + 0.969520i \(0.421208\pi\)
\(348\) −6.70162 −0.359245
\(349\) 13.1665 0.704787 0.352394 0.935852i \(-0.385368\pi\)
0.352394 + 0.935852i \(0.385368\pi\)
\(350\) 0.393373 0.0210267
\(351\) 4.08367 0.217970
\(352\) 3.84055 0.204702
\(353\) 26.8304 1.42804 0.714018 0.700128i \(-0.246874\pi\)
0.714018 + 0.700128i \(0.246874\pi\)
\(354\) 1.00000 0.0531494
\(355\) 11.3432 0.602033
\(356\) 13.4985 0.715421
\(357\) 3.73494 0.197674
\(358\) −17.5859 −0.929444
\(359\) 7.02028 0.370516 0.185258 0.982690i \(-0.440688\pi\)
0.185258 + 0.982690i \(0.440688\pi\)
\(360\) 2.25950 0.119086
\(361\) −17.6439 −0.928624
\(362\) 15.4875 0.814006
\(363\) −3.74980 −0.196814
\(364\) −15.2522 −0.799434
\(365\) −11.8536 −0.620444
\(366\) 6.11723 0.319753
\(367\) 16.5640 0.864632 0.432316 0.901722i \(-0.357696\pi\)
0.432316 + 0.901722i \(0.357696\pi\)
\(368\) 5.03855 0.262652
\(369\) 8.36186 0.435301
\(370\) −6.22610 −0.323680
\(371\) −3.63062 −0.188492
\(372\) 7.12027 0.369169
\(373\) 3.82633 0.198120 0.0990600 0.995081i \(-0.468416\pi\)
0.0990600 + 0.995081i \(0.468416\pi\)
\(374\) −3.84055 −0.198590
\(375\) 11.0595 0.571110
\(376\) 0.0503609 0.00259716
\(377\) −27.3672 −1.40948
\(378\) −3.73494 −0.192104
\(379\) −7.12721 −0.366100 −0.183050 0.983104i \(-0.558597\pi\)
−0.183050 + 0.983104i \(0.558597\pi\)
\(380\) −2.63126 −0.134981
\(381\) 7.19680 0.368703
\(382\) −5.98757 −0.306351
\(383\) 19.2278 0.982494 0.491247 0.871020i \(-0.336541\pi\)
0.491247 + 0.871020i \(0.336541\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 32.4107 1.65180
\(386\) 20.0576 1.02090
\(387\) 10.5441 0.535984
\(388\) −7.52852 −0.382203
\(389\) 19.0883 0.967815 0.483908 0.875119i \(-0.339217\pi\)
0.483908 + 0.875119i \(0.339217\pi\)
\(390\) 9.22703 0.467229
\(391\) −5.03855 −0.254810
\(392\) 6.94974 0.351015
\(393\) 10.3416 0.521665
\(394\) −1.62569 −0.0819013
\(395\) 1.20016 0.0603867
\(396\) 3.84055 0.192995
\(397\) 21.1370 1.06084 0.530418 0.847736i \(-0.322035\pi\)
0.530418 + 0.847736i \(0.322035\pi\)
\(398\) −10.9179 −0.547267
\(399\) 4.34946 0.217745
\(400\) 0.105322 0.00526612
\(401\) 24.8782 1.24236 0.621180 0.783668i \(-0.286654\pi\)
0.621180 + 0.783668i \(0.286654\pi\)
\(402\) 0.356946 0.0178029
\(403\) 29.0768 1.44842
\(404\) 7.36090 0.366218
\(405\) 2.25950 0.112275
\(406\) 25.0301 1.24222
\(407\) −10.5827 −0.524566
\(408\) 1.00000 0.0495074
\(409\) −11.5738 −0.572287 −0.286144 0.958187i \(-0.592373\pi\)
−0.286144 + 0.958187i \(0.592373\pi\)
\(410\) 18.8936 0.933087
\(411\) −12.5181 −0.617473
\(412\) 16.9716 0.836128
\(413\) −3.73494 −0.183784
\(414\) 5.03855 0.247631
\(415\) 12.8164 0.629133
\(416\) −4.08367 −0.200218
\(417\) 0.485663 0.0237830
\(418\) −4.47245 −0.218755
\(419\) −6.59791 −0.322329 −0.161165 0.986928i \(-0.551525\pi\)
−0.161165 + 0.986928i \(0.551525\pi\)
\(420\) −8.43907 −0.411785
\(421\) 1.87461 0.0913628 0.0456814 0.998956i \(-0.485454\pi\)
0.0456814 + 0.998956i \(0.485454\pi\)
\(422\) 24.7016 1.20245
\(423\) 0.0503609 0.00244863
\(424\) −0.972069 −0.0472078
\(425\) −0.105322 −0.00510889
\(426\) −5.02022 −0.243231
\(427\) −22.8475 −1.10567
\(428\) 6.02420 0.291191
\(429\) 15.6835 0.757207
\(430\) 23.8242 1.14891
\(431\) −22.9785 −1.10684 −0.553418 0.832904i \(-0.686677\pi\)
−0.553418 + 0.832904i \(0.686677\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 0.864790 0.0415591 0.0207796 0.999784i \(-0.493385\pi\)
0.0207796 + 0.999784i \(0.493385\pi\)
\(434\) −26.5937 −1.27654
\(435\) −15.1423 −0.726017
\(436\) −10.5956 −0.507436
\(437\) −5.86756 −0.280683
\(438\) 5.24611 0.250669
\(439\) −9.41071 −0.449149 −0.224574 0.974457i \(-0.572099\pi\)
−0.224574 + 0.974457i \(0.572099\pi\)
\(440\) 8.67770 0.413693
\(441\) 6.94974 0.330940
\(442\) 4.08367 0.194240
\(443\) −13.5800 −0.645206 −0.322603 0.946534i \(-0.604558\pi\)
−0.322603 + 0.946534i \(0.604558\pi\)
\(444\) 2.75553 0.130771
\(445\) 30.4999 1.44583
\(446\) −17.9650 −0.850668
\(447\) 12.1194 0.573229
\(448\) 3.73494 0.176459
\(449\) 29.3480 1.38502 0.692510 0.721408i \(-0.256505\pi\)
0.692510 + 0.721408i \(0.256505\pi\)
\(450\) 0.105322 0.00496495
\(451\) 32.1141 1.51219
\(452\) −20.2421 −0.952107
\(453\) 12.0007 0.563840
\(454\) −12.1520 −0.570320
\(455\) −34.4624 −1.61562
\(456\) 1.16453 0.0545343
\(457\) −37.0754 −1.73431 −0.867157 0.498035i \(-0.834055\pi\)
−0.867157 + 0.498035i \(0.834055\pi\)
\(458\) −10.5713 −0.493965
\(459\) 1.00000 0.0466760
\(460\) 11.3846 0.530809
\(461\) −34.0342 −1.58513 −0.792566 0.609786i \(-0.791255\pi\)
−0.792566 + 0.609786i \(0.791255\pi\)
\(462\) −14.3442 −0.667352
\(463\) −1.56747 −0.0728466 −0.0364233 0.999336i \(-0.511596\pi\)
−0.0364233 + 0.999336i \(0.511596\pi\)
\(464\) 6.70162 0.311115
\(465\) 16.0882 0.746073
\(466\) 13.9663 0.646975
\(467\) −9.32331 −0.431431 −0.215716 0.976456i \(-0.569208\pi\)
−0.215716 + 0.976456i \(0.569208\pi\)
\(468\) −4.08367 −0.188768
\(469\) −1.33317 −0.0615601
\(470\) 0.113790 0.00524875
\(471\) −6.65132 −0.306477
\(472\) −1.00000 −0.0460287
\(473\) 40.4949 1.86196
\(474\) −0.531164 −0.0243972
\(475\) −0.122652 −0.00562764
\(476\) −3.73494 −0.171190
\(477\) −0.972069 −0.0445080
\(478\) 28.5324 1.30504
\(479\) −18.8986 −0.863501 −0.431750 0.901993i \(-0.642104\pi\)
−0.431750 + 0.901993i \(0.642104\pi\)
\(480\) −2.25950 −0.103131
\(481\) 11.2527 0.513077
\(482\) −29.0203 −1.32184
\(483\) −18.8187 −0.856278
\(484\) 3.74980 0.170446
\(485\) −17.0107 −0.772414
\(486\) −1.00000 −0.0453609
\(487\) −2.21739 −0.100479 −0.0502397 0.998737i \(-0.515999\pi\)
−0.0502397 + 0.998737i \(0.515999\pi\)
\(488\) −6.11723 −0.276914
\(489\) −15.2569 −0.689942
\(490\) 15.7029 0.709386
\(491\) −25.7217 −1.16080 −0.580401 0.814331i \(-0.697104\pi\)
−0.580401 + 0.814331i \(0.697104\pi\)
\(492\) −8.36186 −0.376982
\(493\) −6.70162 −0.301826
\(494\) 4.75557 0.213963
\(495\) 8.67770 0.390034
\(496\) −7.12027 −0.319709
\(497\) 18.7502 0.841062
\(498\) −5.67224 −0.254179
\(499\) 28.1068 1.25823 0.629116 0.777311i \(-0.283417\pi\)
0.629116 + 0.777311i \(0.283417\pi\)
\(500\) −11.0595 −0.494596
\(501\) 18.2500 0.815351
\(502\) 26.4706 1.18144
\(503\) −23.9722 −1.06887 −0.534434 0.845210i \(-0.679475\pi\)
−0.534434 + 0.845210i \(0.679475\pi\)
\(504\) 3.73494 0.166367
\(505\) 16.6319 0.740111
\(506\) 19.3508 0.860247
\(507\) −3.67634 −0.163272
\(508\) −7.19680 −0.319306
\(509\) −32.5485 −1.44269 −0.721343 0.692578i \(-0.756475\pi\)
−0.721343 + 0.692578i \(0.756475\pi\)
\(510\) 2.25950 0.100052
\(511\) −19.5939 −0.866782
\(512\) 1.00000 0.0441942
\(513\) 1.16453 0.0514154
\(514\) −19.5525 −0.862426
\(515\) 38.3472 1.68978
\(516\) −10.5441 −0.464176
\(517\) 0.193413 0.00850630
\(518\) −10.2917 −0.452192
\(519\) 5.65681 0.248306
\(520\) −9.22703 −0.404632
\(521\) 26.6450 1.16734 0.583670 0.811991i \(-0.301616\pi\)
0.583670 + 0.811991i \(0.301616\pi\)
\(522\) 6.70162 0.293322
\(523\) −7.84479 −0.343029 −0.171514 0.985182i \(-0.554866\pi\)
−0.171514 + 0.985182i \(0.554866\pi\)
\(524\) −10.3416 −0.451775
\(525\) −0.393373 −0.0171682
\(526\) −20.1022 −0.876499
\(527\) 7.12027 0.310164
\(528\) −3.84055 −0.167138
\(529\) 2.38697 0.103781
\(530\) −2.19639 −0.0954049
\(531\) −1.00000 −0.0433963
\(532\) −4.34946 −0.188573
\(533\) −34.1470 −1.47907
\(534\) −13.4985 −0.584139
\(535\) 13.6117 0.588483
\(536\) −0.356946 −0.0154177
\(537\) 17.5859 0.758888
\(538\) −21.5907 −0.930843
\(539\) 26.6908 1.14966
\(540\) −2.25950 −0.0972332
\(541\) 14.3164 0.615511 0.307756 0.951465i \(-0.400422\pi\)
0.307756 + 0.951465i \(0.400422\pi\)
\(542\) 11.2670 0.483957
\(543\) −15.4875 −0.664633
\(544\) −1.00000 −0.0428746
\(545\) −23.9407 −1.02551
\(546\) 15.2522 0.652735
\(547\) 7.81064 0.333959 0.166979 0.985960i \(-0.446599\pi\)
0.166979 + 0.985960i \(0.446599\pi\)
\(548\) 12.5181 0.534748
\(549\) −6.11723 −0.261077
\(550\) 0.404496 0.0172478
\(551\) −7.80426 −0.332473
\(552\) −5.03855 −0.214455
\(553\) 1.98386 0.0843624
\(554\) 10.0277 0.426034
\(555\) 6.22610 0.264283
\(556\) −0.485663 −0.0205967
\(557\) 31.0526 1.31574 0.657871 0.753130i \(-0.271457\pi\)
0.657871 + 0.753130i \(0.271457\pi\)
\(558\) −7.12027 −0.301425
\(559\) −43.0584 −1.82118
\(560\) 8.43907 0.356616
\(561\) 3.84055 0.162148
\(562\) 29.8315 1.25837
\(563\) −23.7356 −1.00034 −0.500168 0.865928i \(-0.666728\pi\)
−0.500168 + 0.865928i \(0.666728\pi\)
\(564\) −0.0503609 −0.00212057
\(565\) −45.7369 −1.92416
\(566\) 10.4024 0.437247
\(567\) 3.73494 0.156853
\(568\) 5.02022 0.210644
\(569\) −18.0113 −0.755072 −0.377536 0.925995i \(-0.623229\pi\)
−0.377536 + 0.925995i \(0.623229\pi\)
\(570\) 2.63126 0.110211
\(571\) 13.2665 0.555185 0.277592 0.960699i \(-0.410464\pi\)
0.277592 + 0.960699i \(0.410464\pi\)
\(572\) −15.6835 −0.655761
\(573\) 5.98757 0.250134
\(574\) 31.2310 1.30356
\(575\) 0.530672 0.0221306
\(576\) 1.00000 0.0416667
\(577\) 6.08544 0.253340 0.126670 0.991945i \(-0.459571\pi\)
0.126670 + 0.991945i \(0.459571\pi\)
\(578\) 1.00000 0.0415945
\(579\) −20.0576 −0.833565
\(580\) 15.1423 0.628749
\(581\) 21.1855 0.878921
\(582\) 7.52852 0.312067
\(583\) −3.73328 −0.154617
\(584\) −5.24611 −0.217085
\(585\) −9.22703 −0.381491
\(586\) −12.9210 −0.533760
\(587\) 8.53687 0.352354 0.176177 0.984358i \(-0.443627\pi\)
0.176177 + 0.984358i \(0.443627\pi\)
\(588\) −6.94974 −0.286603
\(589\) 8.29179 0.341657
\(590\) −2.25950 −0.0930220
\(591\) 1.62569 0.0668721
\(592\) −2.75553 −0.113251
\(593\) 23.7012 0.973293 0.486647 0.873599i \(-0.338220\pi\)
0.486647 + 0.873599i \(0.338220\pi\)
\(594\) −3.84055 −0.157580
\(595\) −8.43907 −0.345968
\(596\) −12.1194 −0.496431
\(597\) 10.9179 0.446841
\(598\) −20.5758 −0.841405
\(599\) −2.08309 −0.0851129 −0.0425564 0.999094i \(-0.513550\pi\)
−0.0425564 + 0.999094i \(0.513550\pi\)
\(600\) −0.105322 −0.00429977
\(601\) 4.30685 0.175680 0.0878401 0.996135i \(-0.472004\pi\)
0.0878401 + 0.996135i \(0.472004\pi\)
\(602\) 39.3814 1.60506
\(603\) −0.356946 −0.0145360
\(604\) −12.0007 −0.488300
\(605\) 8.47267 0.344463
\(606\) −7.36090 −0.299016
\(607\) −1.62235 −0.0658491 −0.0329246 0.999458i \(-0.510482\pi\)
−0.0329246 + 0.999458i \(0.510482\pi\)
\(608\) −1.16453 −0.0472281
\(609\) −25.0301 −1.01427
\(610\) −13.8219 −0.559631
\(611\) −0.205657 −0.00831999
\(612\) −1.00000 −0.0404226
\(613\) −25.1016 −1.01385 −0.506923 0.861992i \(-0.669217\pi\)
−0.506923 + 0.861992i \(0.669217\pi\)
\(614\) −2.59585 −0.104760
\(615\) −18.8936 −0.761863
\(616\) 14.3442 0.577944
\(617\) 1.41959 0.0571505 0.0285753 0.999592i \(-0.490903\pi\)
0.0285753 + 0.999592i \(0.490903\pi\)
\(618\) −16.9716 −0.682696
\(619\) −33.0372 −1.32788 −0.663938 0.747788i \(-0.731116\pi\)
−0.663938 + 0.747788i \(0.731116\pi\)
\(620\) −16.0882 −0.646118
\(621\) −5.03855 −0.202190
\(622\) −18.7836 −0.753154
\(623\) 50.4162 2.01988
\(624\) 4.08367 0.163478
\(625\) −25.5155 −1.02062
\(626\) 6.07314 0.242731
\(627\) 4.47245 0.178612
\(628\) 6.65132 0.265417
\(629\) 2.75553 0.109870
\(630\) 8.43907 0.336221
\(631\) −37.6015 −1.49689 −0.748446 0.663196i \(-0.769200\pi\)
−0.748446 + 0.663196i \(0.769200\pi\)
\(632\) 0.531164 0.0211286
\(633\) −24.7016 −0.981800
\(634\) 17.1939 0.682857
\(635\) −16.2611 −0.645303
\(636\) 0.972069 0.0385450
\(637\) −28.3804 −1.12447
\(638\) 25.7379 1.01897
\(639\) 5.02022 0.198597
\(640\) 2.25950 0.0893144
\(641\) 0.103096 0.00407206 0.00203603 0.999998i \(-0.499352\pi\)
0.00203603 + 0.999998i \(0.499352\pi\)
\(642\) −6.02420 −0.237756
\(643\) 17.7498 0.699986 0.349993 0.936752i \(-0.386184\pi\)
0.349993 + 0.936752i \(0.386184\pi\)
\(644\) 18.8187 0.741559
\(645\) −23.8242 −0.938079
\(646\) 1.16453 0.0458180
\(647\) 26.9828 1.06080 0.530401 0.847747i \(-0.322041\pi\)
0.530401 + 0.847747i \(0.322041\pi\)
\(648\) 1.00000 0.0392837
\(649\) −3.84055 −0.150755
\(650\) −0.430102 −0.0168700
\(651\) 26.5937 1.04229
\(652\) 15.2569 0.597507
\(653\) −34.5877 −1.35352 −0.676761 0.736202i \(-0.736617\pi\)
−0.676761 + 0.736202i \(0.736617\pi\)
\(654\) 10.5956 0.414320
\(655\) −23.3668 −0.913017
\(656\) 8.36186 0.326476
\(657\) −5.24611 −0.204670
\(658\) 0.188095 0.00733269
\(659\) −9.03242 −0.351853 −0.175927 0.984403i \(-0.556292\pi\)
−0.175927 + 0.984403i \(0.556292\pi\)
\(660\) −8.67770 −0.337779
\(661\) 14.1662 0.551003 0.275502 0.961301i \(-0.411156\pi\)
0.275502 + 0.961301i \(0.411156\pi\)
\(662\) −29.0385 −1.12861
\(663\) −4.08367 −0.158597
\(664\) 5.67224 0.220126
\(665\) −9.82758 −0.381097
\(666\) −2.75553 −0.106774
\(667\) 33.7664 1.30744
\(668\) −18.2500 −0.706114
\(669\) 17.9650 0.694567
\(670\) −0.806519 −0.0311585
\(671\) −23.4935 −0.906957
\(672\) −3.73494 −0.144078
\(673\) −45.0241 −1.73555 −0.867776 0.496955i \(-0.834451\pi\)
−0.867776 + 0.496955i \(0.834451\pi\)
\(674\) 25.9764 1.00057
\(675\) −0.105322 −0.00405386
\(676\) 3.67634 0.141398
\(677\) 12.1851 0.468312 0.234156 0.972199i \(-0.424767\pi\)
0.234156 + 0.972199i \(0.424767\pi\)
\(678\) 20.2421 0.777392
\(679\) −28.1185 −1.07909
\(680\) −2.25950 −0.0866477
\(681\) 12.1520 0.465664
\(682\) −27.3457 −1.04712
\(683\) −34.0667 −1.30353 −0.651763 0.758423i \(-0.725970\pi\)
−0.651763 + 0.758423i \(0.725970\pi\)
\(684\) −1.16453 −0.0445271
\(685\) 28.2846 1.08070
\(686\) −0.187700 −0.00716643
\(687\) 10.5713 0.403320
\(688\) 10.5441 0.401988
\(689\) 3.96961 0.151230
\(690\) −11.3846 −0.433404
\(691\) 16.1644 0.614923 0.307461 0.951561i \(-0.400520\pi\)
0.307461 + 0.951561i \(0.400520\pi\)
\(692\) −5.65681 −0.215040
\(693\) 14.3442 0.544891
\(694\) 9.12812 0.346499
\(695\) −1.09735 −0.0416250
\(696\) −6.70162 −0.254024
\(697\) −8.36186 −0.316728
\(698\) 13.1665 0.498360
\(699\) −13.9663 −0.528253
\(700\) 0.393373 0.0148681
\(701\) 35.3391 1.33474 0.667369 0.744727i \(-0.267420\pi\)
0.667369 + 0.744727i \(0.267420\pi\)
\(702\) 4.08367 0.154128
\(703\) 3.20890 0.121026
\(704\) 3.84055 0.144746
\(705\) −0.113790 −0.00428558
\(706\) 26.8304 1.00977
\(707\) 27.4925 1.03396
\(708\) 1.00000 0.0375823
\(709\) −41.0406 −1.54131 −0.770656 0.637251i \(-0.780071\pi\)
−0.770656 + 0.637251i \(0.780071\pi\)
\(710\) 11.3432 0.425702
\(711\) 0.531164 0.0199202
\(712\) 13.4985 0.505879
\(713\) −35.8758 −1.34356
\(714\) 3.73494 0.139776
\(715\) −35.4369 −1.32526
\(716\) −17.5859 −0.657216
\(717\) −28.5324 −1.06556
\(718\) 7.02028 0.261995
\(719\) −17.1001 −0.637728 −0.318864 0.947800i \(-0.603301\pi\)
−0.318864 + 0.947800i \(0.603301\pi\)
\(720\) 2.25950 0.0842064
\(721\) 63.3877 2.36068
\(722\) −17.6439 −0.656637
\(723\) 29.0203 1.07928
\(724\) 15.4875 0.575589
\(725\) 0.705831 0.0262139
\(726\) −3.74980 −0.139168
\(727\) −17.2349 −0.639205 −0.319603 0.947552i \(-0.603549\pi\)
−0.319603 + 0.947552i \(0.603549\pi\)
\(728\) −15.2522 −0.565285
\(729\) 1.00000 0.0370370
\(730\) −11.8536 −0.438720
\(731\) −10.5441 −0.389986
\(732\) 6.11723 0.226099
\(733\) −39.5708 −1.46158 −0.730790 0.682602i \(-0.760848\pi\)
−0.730790 + 0.682602i \(0.760848\pi\)
\(734\) 16.5640 0.611387
\(735\) −15.7029 −0.579211
\(736\) 5.03855 0.185723
\(737\) −1.37087 −0.0504966
\(738\) 8.36186 0.307804
\(739\) 26.2005 0.963799 0.481900 0.876226i \(-0.339947\pi\)
0.481900 + 0.876226i \(0.339947\pi\)
\(740\) −6.22610 −0.228876
\(741\) −4.75557 −0.174700
\(742\) −3.63062 −0.133284
\(743\) −25.0926 −0.920559 −0.460280 0.887774i \(-0.652251\pi\)
−0.460280 + 0.887774i \(0.652251\pi\)
\(744\) 7.12027 0.261042
\(745\) −27.3838 −1.00326
\(746\) 3.82633 0.140092
\(747\) 5.67224 0.207537
\(748\) −3.84055 −0.140424
\(749\) 22.5000 0.822132
\(750\) 11.0595 0.403836
\(751\) −25.1869 −0.919082 −0.459541 0.888157i \(-0.651986\pi\)
−0.459541 + 0.888157i \(0.651986\pi\)
\(752\) 0.0503609 0.00183647
\(753\) −26.4706 −0.964642
\(754\) −27.3672 −0.996654
\(755\) −27.1155 −0.986833
\(756\) −3.73494 −0.135838
\(757\) 42.0424 1.52806 0.764028 0.645183i \(-0.223219\pi\)
0.764028 + 0.645183i \(0.223219\pi\)
\(758\) −7.12721 −0.258872
\(759\) −19.3508 −0.702389
\(760\) −2.63126 −0.0954458
\(761\) 40.5003 1.46814 0.734068 0.679076i \(-0.237619\pi\)
0.734068 + 0.679076i \(0.237619\pi\)
\(762\) 7.19680 0.260712
\(763\) −39.5738 −1.43267
\(764\) −5.98757 −0.216623
\(765\) −2.25950 −0.0816923
\(766\) 19.2278 0.694728
\(767\) 4.08367 0.147453
\(768\) −1.00000 −0.0360844
\(769\) −47.3385 −1.70707 −0.853535 0.521036i \(-0.825546\pi\)
−0.853535 + 0.521036i \(0.825546\pi\)
\(770\) 32.4107 1.16800
\(771\) 19.5525 0.704168
\(772\) 20.0576 0.721888
\(773\) −20.0210 −0.720105 −0.360053 0.932932i \(-0.617241\pi\)
−0.360053 + 0.932932i \(0.617241\pi\)
\(774\) 10.5441 0.378998
\(775\) −0.749924 −0.0269381
\(776\) −7.52852 −0.270258
\(777\) 10.2917 0.369213
\(778\) 19.0883 0.684349
\(779\) −9.73766 −0.348888
\(780\) 9.22703 0.330381
\(781\) 19.2804 0.689907
\(782\) −5.03855 −0.180178
\(783\) −6.70162 −0.239496
\(784\) 6.94974 0.248205
\(785\) 15.0286 0.536395
\(786\) 10.3416 0.368873
\(787\) 16.7688 0.597745 0.298872 0.954293i \(-0.403390\pi\)
0.298872 + 0.954293i \(0.403390\pi\)
\(788\) −1.62569 −0.0579129
\(789\) 20.1022 0.715658
\(790\) 1.20016 0.0426999
\(791\) −75.6028 −2.68813
\(792\) 3.84055 0.136468
\(793\) 24.9807 0.887092
\(794\) 21.1370 0.750124
\(795\) 2.19639 0.0778978
\(796\) −10.9179 −0.386976
\(797\) 39.5968 1.40259 0.701296 0.712870i \(-0.252605\pi\)
0.701296 + 0.712870i \(0.252605\pi\)
\(798\) 4.34946 0.153969
\(799\) −0.0503609 −0.00178164
\(800\) 0.105322 0.00372371
\(801\) 13.4985 0.476948
\(802\) 24.8782 0.878481
\(803\) −20.1479 −0.711005
\(804\) 0.356946 0.0125885
\(805\) 42.5207 1.49866
\(806\) 29.0768 1.02419
\(807\) 21.5907 0.760030
\(808\) 7.36090 0.258956
\(809\) 49.7068 1.74760 0.873800 0.486286i \(-0.161649\pi\)
0.873800 + 0.486286i \(0.161649\pi\)
\(810\) 2.25950 0.0793906
\(811\) −51.6865 −1.81496 −0.907480 0.420095i \(-0.861997\pi\)
−0.907480 + 0.420095i \(0.861997\pi\)
\(812\) 25.0301 0.878385
\(813\) −11.2670 −0.395149
\(814\) −10.5827 −0.370924
\(815\) 34.4729 1.20753
\(816\) 1.00000 0.0350070
\(817\) −12.2789 −0.429584
\(818\) −11.5738 −0.404668
\(819\) −15.2522 −0.532956
\(820\) 18.8936 0.659792
\(821\) −31.8857 −1.11282 −0.556410 0.830908i \(-0.687822\pi\)
−0.556410 + 0.830908i \(0.687822\pi\)
\(822\) −12.5181 −0.436620
\(823\) −38.7694 −1.35142 −0.675708 0.737170i \(-0.736162\pi\)
−0.675708 + 0.737170i \(0.736162\pi\)
\(824\) 16.9716 0.591232
\(825\) −0.404496 −0.0140827
\(826\) −3.73494 −0.129955
\(827\) −18.4879 −0.642886 −0.321443 0.946929i \(-0.604168\pi\)
−0.321443 + 0.946929i \(0.604168\pi\)
\(828\) 5.03855 0.175102
\(829\) 32.0706 1.11386 0.556928 0.830561i \(-0.311980\pi\)
0.556928 + 0.830561i \(0.311980\pi\)
\(830\) 12.8164 0.444864
\(831\) −10.0277 −0.347855
\(832\) −4.08367 −0.141576
\(833\) −6.94974 −0.240794
\(834\) 0.485663 0.0168171
\(835\) −41.2358 −1.42703
\(836\) −4.47245 −0.154683
\(837\) 7.12027 0.246112
\(838\) −6.59791 −0.227921
\(839\) 2.64124 0.0911857 0.0455928 0.998960i \(-0.485482\pi\)
0.0455928 + 0.998960i \(0.485482\pi\)
\(840\) −8.43907 −0.291176
\(841\) 15.9117 0.548680
\(842\) 1.87461 0.0646033
\(843\) −29.8315 −1.02745
\(844\) 24.7016 0.850264
\(845\) 8.30668 0.285759
\(846\) 0.0503609 0.00173144
\(847\) 14.0053 0.481227
\(848\) −0.972069 −0.0333810
\(849\) −10.4024 −0.357011
\(850\) −0.105322 −0.00361253
\(851\) −13.8839 −0.475932
\(852\) −5.02022 −0.171990
\(853\) 22.5016 0.770440 0.385220 0.922825i \(-0.374126\pi\)
0.385220 + 0.922825i \(0.374126\pi\)
\(854\) −22.8475 −0.781824
\(855\) −2.63126 −0.0899872
\(856\) 6.02420 0.205903
\(857\) −47.8504 −1.63454 −0.817269 0.576256i \(-0.804513\pi\)
−0.817269 + 0.576256i \(0.804513\pi\)
\(858\) 15.6835 0.535427
\(859\) −7.48499 −0.255385 −0.127692 0.991814i \(-0.540757\pi\)
−0.127692 + 0.991814i \(0.540757\pi\)
\(860\) 23.8242 0.812400
\(861\) −31.2310 −1.06435
\(862\) −22.9785 −0.782651
\(863\) −14.7692 −0.502748 −0.251374 0.967890i \(-0.580882\pi\)
−0.251374 + 0.967890i \(0.580882\pi\)
\(864\) −1.00000 −0.0340207
\(865\) −12.7815 −0.434585
\(866\) 0.864790 0.0293868
\(867\) −1.00000 −0.0339618
\(868\) −26.5937 −0.902650
\(869\) 2.03996 0.0692009
\(870\) −15.1423 −0.513371
\(871\) 1.45765 0.0493906
\(872\) −10.5956 −0.358811
\(873\) −7.52852 −0.254802
\(874\) −5.86756 −0.198473
\(875\) −41.3065 −1.39642
\(876\) 5.24611 0.177250
\(877\) 37.6775 1.27228 0.636139 0.771574i \(-0.280530\pi\)
0.636139 + 0.771574i \(0.280530\pi\)
\(878\) −9.41071 −0.317596
\(879\) 12.9210 0.435813
\(880\) 8.67770 0.292525
\(881\) 17.7856 0.599211 0.299606 0.954063i \(-0.403145\pi\)
0.299606 + 0.954063i \(0.403145\pi\)
\(882\) 6.94974 0.234010
\(883\) −13.1203 −0.441533 −0.220767 0.975327i \(-0.570856\pi\)
−0.220767 + 0.975327i \(0.570856\pi\)
\(884\) 4.08367 0.137349
\(885\) 2.25950 0.0759521
\(886\) −13.5800 −0.456229
\(887\) −51.2070 −1.71936 −0.859681 0.510832i \(-0.829337\pi\)
−0.859681 + 0.510832i \(0.829337\pi\)
\(888\) 2.75553 0.0924694
\(889\) −26.8796 −0.901512
\(890\) 30.4999 1.02236
\(891\) 3.84055 0.128663
\(892\) −17.9650 −0.601513
\(893\) −0.0586469 −0.00196254
\(894\) 12.1194 0.405334
\(895\) −39.7353 −1.32820
\(896\) 3.73494 0.124775
\(897\) 20.5758 0.687005
\(898\) 29.3480 0.979357
\(899\) −47.7173 −1.59146
\(900\) 0.105322 0.00351075
\(901\) 0.972069 0.0323843
\(902\) 32.1141 1.06928
\(903\) −39.3814 −1.31053
\(904\) −20.2421 −0.673241
\(905\) 34.9940 1.16324
\(906\) 12.0007 0.398695
\(907\) −4.09384 −0.135934 −0.0679669 0.997688i \(-0.521651\pi\)
−0.0679669 + 0.997688i \(0.521651\pi\)
\(908\) −12.1520 −0.403277
\(909\) 7.36090 0.244146
\(910\) −34.4624 −1.14242
\(911\) −32.0931 −1.06329 −0.531646 0.846967i \(-0.678426\pi\)
−0.531646 + 0.846967i \(0.678426\pi\)
\(912\) 1.16453 0.0385616
\(913\) 21.7845 0.720962
\(914\) −37.0754 −1.22634
\(915\) 13.8219 0.456937
\(916\) −10.5713 −0.349286
\(917\) −38.6252 −1.27552
\(918\) 1.00000 0.0330049
\(919\) −28.9217 −0.954039 −0.477019 0.878893i \(-0.658283\pi\)
−0.477019 + 0.878893i \(0.658283\pi\)
\(920\) 11.3846 0.375338
\(921\) 2.59585 0.0855363
\(922\) −34.0342 −1.12086
\(923\) −20.5009 −0.674796
\(924\) −14.3442 −0.471889
\(925\) −0.290219 −0.00954234
\(926\) −1.56747 −0.0515103
\(927\) 16.9716 0.557419
\(928\) 6.70162 0.219991
\(929\) −57.8829 −1.89908 −0.949539 0.313650i \(-0.898448\pi\)
−0.949539 + 0.313650i \(0.898448\pi\)
\(930\) 16.0882 0.527553
\(931\) −8.09321 −0.265244
\(932\) 13.9663 0.457480
\(933\) 18.7836 0.614948
\(934\) −9.32331 −0.305068
\(935\) −8.67770 −0.283791
\(936\) −4.08367 −0.133479
\(937\) 19.6569 0.642162 0.321081 0.947052i \(-0.395954\pi\)
0.321081 + 0.947052i \(0.395954\pi\)
\(938\) −1.33317 −0.0435296
\(939\) −6.07314 −0.198189
\(940\) 0.113790 0.00371143
\(941\) 25.7217 0.838505 0.419252 0.907870i \(-0.362292\pi\)
0.419252 + 0.907870i \(0.362292\pi\)
\(942\) −6.65132 −0.216712
\(943\) 42.1316 1.37199
\(944\) −1.00000 −0.0325472
\(945\) −8.43907 −0.274523
\(946\) 40.4949 1.31660
\(947\) 21.6020 0.701971 0.350986 0.936381i \(-0.385847\pi\)
0.350986 + 0.936381i \(0.385847\pi\)
\(948\) −0.531164 −0.0172514
\(949\) 21.4234 0.695432
\(950\) −0.122652 −0.00397934
\(951\) −17.1939 −0.557551
\(952\) −3.73494 −0.121050
\(953\) 10.1110 0.327526 0.163763 0.986500i \(-0.447637\pi\)
0.163763 + 0.986500i \(0.447637\pi\)
\(954\) −0.972069 −0.0314719
\(955\) −13.5289 −0.437784
\(956\) 28.5324 0.922803
\(957\) −25.7379 −0.831988
\(958\) −18.8986 −0.610587
\(959\) 46.7544 1.50978
\(960\) −2.25950 −0.0729249
\(961\) 19.6982 0.635425
\(962\) 11.2527 0.362800
\(963\) 6.02420 0.194127
\(964\) −29.0203 −0.934682
\(965\) 45.3200 1.45890
\(966\) −18.8187 −0.605480
\(967\) 56.0564 1.80265 0.901327 0.433139i \(-0.142594\pi\)
0.901327 + 0.433139i \(0.142594\pi\)
\(968\) 3.74980 0.120523
\(969\) −1.16453 −0.0374102
\(970\) −17.0107 −0.546179
\(971\) −13.8417 −0.444203 −0.222101 0.975024i \(-0.571292\pi\)
−0.222101 + 0.975024i \(0.571292\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −1.81392 −0.0581516
\(974\) −2.21739 −0.0710497
\(975\) 0.430102 0.0137743
\(976\) −6.11723 −0.195808
\(977\) −35.7335 −1.14322 −0.571609 0.820526i \(-0.693680\pi\)
−0.571609 + 0.820526i \(0.693680\pi\)
\(978\) −15.2569 −0.487862
\(979\) 51.8418 1.65687
\(980\) 15.7029 0.501611
\(981\) −10.5956 −0.338291
\(982\) −25.7217 −0.820811
\(983\) −40.9912 −1.30742 −0.653708 0.756747i \(-0.726788\pi\)
−0.653708 + 0.756747i \(0.726788\pi\)
\(984\) −8.36186 −0.266566
\(985\) −3.67325 −0.117039
\(986\) −6.70162 −0.213423
\(987\) −0.188095 −0.00598712
\(988\) 4.75557 0.151295
\(989\) 53.1267 1.68933
\(990\) 8.67770 0.275795
\(991\) 1.54052 0.0489361 0.0244680 0.999701i \(-0.492211\pi\)
0.0244680 + 0.999701i \(0.492211\pi\)
\(992\) −7.12027 −0.226069
\(993\) 29.0385 0.921508
\(994\) 18.7502 0.594720
\(995\) −24.6690 −0.782061
\(996\) −5.67224 −0.179732
\(997\) 0.664495 0.0210448 0.0105224 0.999945i \(-0.496651\pi\)
0.0105224 + 0.999945i \(0.496651\pi\)
\(998\) 28.1068 0.889705
\(999\) 2.75553 0.0871810
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 6018.2.a.z.1.9 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6018.2.a.z.1.9 11 1.1 even 1 trivial