Properties

Label 4334.2.a.c.1.6
Level $4334$
Weight $2$
Character 4334.1
Self dual yes
Analytic conductor $34.607$
Analytic rank $1$
Dimension $17$
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] = [4334,2,Mod(1,4334)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4334, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4334.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4334 = 2 \cdot 11 \cdot 197 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4334.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: \(34.6071642360\)
Analytic rank: \(1\)
Dimension: \(17\)
Coefficient field: \(\mathbb{Q}[x]/(x^{17} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{17} - 5 x^{16} - 19 x^{15} + 121 x^{14} + 112 x^{13} - 1172 x^{12} - 25 x^{11} + 5845 x^{10} - 2233 x^{9} - 16035 x^{8} + 9174 x^{7} + 23882 x^{6} - 15232 x^{5} - 17609 x^{4} + \cdots + 16 \) 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 1.6
Root \(-1.22229\) of defining polynomial
Character \(\chi\) \(=\) 4334.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.22229 q^{3} +1.00000 q^{4} +4.12347 q^{5} +1.22229 q^{6} -0.673376 q^{7} -1.00000 q^{8} -1.50600 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.22229 q^{3} +1.00000 q^{4} +4.12347 q^{5} +1.22229 q^{6} -0.673376 q^{7} -1.00000 q^{8} -1.50600 q^{9} -4.12347 q^{10} -1.00000 q^{11} -1.22229 q^{12} -1.15175 q^{13} +0.673376 q^{14} -5.04009 q^{15} +1.00000 q^{16} -5.09398 q^{17} +1.50600 q^{18} -6.95848 q^{19} +4.12347 q^{20} +0.823063 q^{21} +1.00000 q^{22} +4.97526 q^{23} +1.22229 q^{24} +12.0030 q^{25} +1.15175 q^{26} +5.50765 q^{27} -0.673376 q^{28} +4.08775 q^{29} +5.04009 q^{30} +8.14953 q^{31} -1.00000 q^{32} +1.22229 q^{33} +5.09398 q^{34} -2.77664 q^{35} -1.50600 q^{36} +1.53165 q^{37} +6.95848 q^{38} +1.40778 q^{39} -4.12347 q^{40} -10.1937 q^{41} -0.823063 q^{42} -2.45640 q^{43} -1.00000 q^{44} -6.20994 q^{45} -4.97526 q^{46} +7.13004 q^{47} -1.22229 q^{48} -6.54656 q^{49} -12.0030 q^{50} +6.22634 q^{51} -1.15175 q^{52} -5.31830 q^{53} -5.50765 q^{54} -4.12347 q^{55} +0.673376 q^{56} +8.50530 q^{57} -4.08775 q^{58} +10.9112 q^{59} -5.04009 q^{60} +2.64210 q^{61} -8.14953 q^{62} +1.01410 q^{63} +1.00000 q^{64} -4.74922 q^{65} -1.22229 q^{66} -6.43050 q^{67} -5.09398 q^{68} -6.08122 q^{69} +2.77664 q^{70} -9.86795 q^{71} +1.50600 q^{72} -8.78991 q^{73} -1.53165 q^{74} -14.6712 q^{75} -6.95848 q^{76} +0.673376 q^{77} -1.40778 q^{78} +10.3482 q^{79} +4.12347 q^{80} -2.21398 q^{81} +10.1937 q^{82} -5.79609 q^{83} +0.823063 q^{84} -21.0049 q^{85} +2.45640 q^{86} -4.99643 q^{87} +1.00000 q^{88} -2.26285 q^{89} +6.20994 q^{90} +0.775564 q^{91} +4.97526 q^{92} -9.96112 q^{93} -7.13004 q^{94} -28.6931 q^{95} +1.22229 q^{96} -19.3581 q^{97} +6.54656 q^{98} +1.50600 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9} - 6 q^{10} - 17 q^{11} + 5 q^{12} - 16 q^{13} + 9 q^{14} + 17 q^{16} - 8 q^{17} - 12 q^{18} - 23 q^{19} + 6 q^{20} - 15 q^{21} + 17 q^{22} + 12 q^{23} - 5 q^{24} + 11 q^{25} + 16 q^{26} + 17 q^{27} - 9 q^{28} - 8 q^{31} - 17 q^{32} - 5 q^{33} + 8 q^{34} + 6 q^{35} + 12 q^{36} - 7 q^{37} + 23 q^{38} - 9 q^{39} - 6 q^{40} - 27 q^{41} + 15 q^{42} - 13 q^{43} - 17 q^{44} - 11 q^{45} - 12 q^{46} + 23 q^{47} + 5 q^{48} - 8 q^{49} - 11 q^{50} - 40 q^{51} - 16 q^{52} + 14 q^{53} - 17 q^{54} - 6 q^{55} + 9 q^{56} - 18 q^{57} + 2 q^{59} - 49 q^{61} + 8 q^{62} - 42 q^{63} + 17 q^{64} - 57 q^{65} + 5 q^{66} - 5 q^{67} - 8 q^{68} - 9 q^{69} - 6 q^{70} - 5 q^{71} - 12 q^{72} - 54 q^{73} + 7 q^{74} + 7 q^{75} - 23 q^{76} + 9 q^{77} + 9 q^{78} - 11 q^{79} + 6 q^{80} - 35 q^{81} + 27 q^{82} - 8 q^{83} - 15 q^{84} - 65 q^{85} + 13 q^{86} - 20 q^{87} + 17 q^{88} - 9 q^{89} + 11 q^{90} - 9 q^{91} + 12 q^{92} - 50 q^{93} - 23 q^{94} - 27 q^{95} - 5 q^{96} - 42 q^{97} + 8 q^{98} - 12 q^{99}+O(q^{100}) \) 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
\(3\) −1.22229 −0.705692 −0.352846 0.935681i \(-0.614786\pi\)
−0.352846 + 0.935681i \(0.614786\pi\)
\(4\) 1.00000 0.500000
\(5\) 4.12347 1.84407 0.922036 0.387105i \(-0.126525\pi\)
0.922036 + 0.387105i \(0.126525\pi\)
\(6\) 1.22229 0.498999
\(7\) −0.673376 −0.254512 −0.127256 0.991870i \(-0.540617\pi\)
−0.127256 + 0.991870i \(0.540617\pi\)
\(8\) −1.00000 −0.353553
\(9\) −1.50600 −0.501999
\(10\) −4.12347 −1.30396
\(11\) −1.00000 −0.301511
\(12\) −1.22229 −0.352846
\(13\) −1.15175 −0.319439 −0.159720 0.987162i \(-0.551059\pi\)
−0.159720 + 0.987162i \(0.551059\pi\)
\(14\) 0.673376 0.179967
\(15\) −5.04009 −1.30135
\(16\) 1.00000 0.250000
\(17\) −5.09398 −1.23547 −0.617736 0.786386i \(-0.711950\pi\)
−0.617736 + 0.786386i \(0.711950\pi\)
\(18\) 1.50600 0.354967
\(19\) −6.95848 −1.59638 −0.798192 0.602403i \(-0.794210\pi\)
−0.798192 + 0.602403i \(0.794210\pi\)
\(20\) 4.12347 0.922036
\(21\) 0.823063 0.179607
\(22\) 1.00000 0.213201
\(23\) 4.97526 1.03741 0.518706 0.854953i \(-0.326414\pi\)
0.518706 + 0.854953i \(0.326414\pi\)
\(24\) 1.22229 0.249500
\(25\) 12.0030 2.40060
\(26\) 1.15175 0.225878
\(27\) 5.50765 1.05995
\(28\) −0.673376 −0.127256
\(29\) 4.08775 0.759076 0.379538 0.925176i \(-0.376083\pi\)
0.379538 + 0.925176i \(0.376083\pi\)
\(30\) 5.04009 0.920191
\(31\) 8.14953 1.46370 0.731850 0.681466i \(-0.238657\pi\)
0.731850 + 0.681466i \(0.238657\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.22229 0.212774
\(34\) 5.09398 0.873611
\(35\) −2.77664 −0.469339
\(36\) −1.50600 −0.251000
\(37\) 1.53165 0.251802 0.125901 0.992043i \(-0.459818\pi\)
0.125901 + 0.992043i \(0.459818\pi\)
\(38\) 6.95848 1.12881
\(39\) 1.40778 0.225426
\(40\) −4.12347 −0.651978
\(41\) −10.1937 −1.59198 −0.795992 0.605307i \(-0.793050\pi\)
−0.795992 + 0.605307i \(0.793050\pi\)
\(42\) −0.823063 −0.127001
\(43\) −2.45640 −0.374598 −0.187299 0.982303i \(-0.559973\pi\)
−0.187299 + 0.982303i \(0.559973\pi\)
\(44\) −1.00000 −0.150756
\(45\) −6.20994 −0.925723
\(46\) −4.97526 −0.733561
\(47\) 7.13004 1.04002 0.520012 0.854159i \(-0.325928\pi\)
0.520012 + 0.854159i \(0.325928\pi\)
\(48\) −1.22229 −0.176423
\(49\) −6.54656 −0.935224
\(50\) −12.0030 −1.69748
\(51\) 6.22634 0.871862
\(52\) −1.15175 −0.159720
\(53\) −5.31830 −0.730525 −0.365263 0.930905i \(-0.619021\pi\)
−0.365263 + 0.930905i \(0.619021\pi\)
\(54\) −5.50765 −0.749497
\(55\) −4.12347 −0.556008
\(56\) 0.673376 0.0899836
\(57\) 8.50530 1.12655
\(58\) −4.08775 −0.536748
\(59\) 10.9112 1.42052 0.710258 0.703942i \(-0.248578\pi\)
0.710258 + 0.703942i \(0.248578\pi\)
\(60\) −5.04009 −0.650673
\(61\) 2.64210 0.338287 0.169143 0.985591i \(-0.445900\pi\)
0.169143 + 0.985591i \(0.445900\pi\)
\(62\) −8.14953 −1.03499
\(63\) 1.01410 0.127765
\(64\) 1.00000 0.125000
\(65\) −4.74922 −0.589069
\(66\) −1.22229 −0.150454
\(67\) −6.43050 −0.785610 −0.392805 0.919622i \(-0.628495\pi\)
−0.392805 + 0.919622i \(0.628495\pi\)
\(68\) −5.09398 −0.617736
\(69\) −6.08122 −0.732093
\(70\) 2.77664 0.331873
\(71\) −9.86795 −1.17111 −0.585555 0.810633i \(-0.699123\pi\)
−0.585555 + 0.810633i \(0.699123\pi\)
\(72\) 1.50600 0.177484
\(73\) −8.78991 −1.02878 −0.514391 0.857556i \(-0.671982\pi\)
−0.514391 + 0.857556i \(0.671982\pi\)
\(74\) −1.53165 −0.178051
\(75\) −14.6712 −1.69408
\(76\) −6.95848 −0.798192
\(77\) 0.673376 0.0767383
\(78\) −1.40778 −0.159400
\(79\) 10.3482 1.16426 0.582131 0.813095i \(-0.302219\pi\)
0.582131 + 0.813095i \(0.302219\pi\)
\(80\) 4.12347 0.461018
\(81\) −2.21398 −0.245997
\(82\) 10.1937 1.12570
\(83\) −5.79609 −0.636204 −0.318102 0.948057i \(-0.603045\pi\)
−0.318102 + 0.948057i \(0.603045\pi\)
\(84\) 0.823063 0.0898036
\(85\) −21.0049 −2.27830
\(86\) 2.45640 0.264880
\(87\) −4.99643 −0.535674
\(88\) 1.00000 0.106600
\(89\) −2.26285 −0.239862 −0.119931 0.992782i \(-0.538267\pi\)
−0.119931 + 0.992782i \(0.538267\pi\)
\(90\) 6.20994 0.654585
\(91\) 0.775564 0.0813012
\(92\) 4.97526 0.518706
\(93\) −9.96112 −1.03292
\(94\) −7.13004 −0.735408
\(95\) −28.6931 −2.94385
\(96\) 1.22229 0.124750
\(97\) −19.3581 −1.96551 −0.982757 0.184901i \(-0.940803\pi\)
−0.982757 + 0.184901i \(0.940803\pi\)
\(98\) 6.54656 0.661303
\(99\) 1.50600 0.151358
\(100\) 12.0030 1.20030
\(101\) −17.2864 −1.72006 −0.860029 0.510245i \(-0.829555\pi\)
−0.860029 + 0.510245i \(0.829555\pi\)
\(102\) −6.22634 −0.616500
\(103\) 5.18480 0.510873 0.255437 0.966826i \(-0.417781\pi\)
0.255437 + 0.966826i \(0.417781\pi\)
\(104\) 1.15175 0.112939
\(105\) 3.39388 0.331208
\(106\) 5.31830 0.516559
\(107\) −4.31733 −0.417372 −0.208686 0.977983i \(-0.566919\pi\)
−0.208686 + 0.977983i \(0.566919\pi\)
\(108\) 5.50765 0.529974
\(109\) −5.07937 −0.486515 −0.243258 0.969962i \(-0.578216\pi\)
−0.243258 + 0.969962i \(0.578216\pi\)
\(110\) 4.12347 0.393157
\(111\) −1.87213 −0.177695
\(112\) −0.673376 −0.0636280
\(113\) −8.78693 −0.826605 −0.413303 0.910594i \(-0.635625\pi\)
−0.413303 + 0.910594i \(0.635625\pi\)
\(114\) −8.50530 −0.796595
\(115\) 20.5153 1.91306
\(116\) 4.08775 0.379538
\(117\) 1.73454 0.160358
\(118\) −10.9112 −1.00446
\(119\) 3.43016 0.314443
\(120\) 5.04009 0.460095
\(121\) 1.00000 0.0909091
\(122\) −2.64210 −0.239205
\(123\) 12.4597 1.12345
\(124\) 8.14953 0.731850
\(125\) 28.8767 2.58281
\(126\) −1.01410 −0.0903434
\(127\) 13.4600 1.19439 0.597193 0.802098i \(-0.296283\pi\)
0.597193 + 0.802098i \(0.296283\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 3.00244 0.264350
\(130\) 4.74922 0.416534
\(131\) 2.93923 0.256802 0.128401 0.991722i \(-0.459016\pi\)
0.128401 + 0.991722i \(0.459016\pi\)
\(132\) 1.22229 0.106387
\(133\) 4.68567 0.406299
\(134\) 6.43050 0.555510
\(135\) 22.7106 1.95462
\(136\) 5.09398 0.436805
\(137\) −6.88035 −0.587828 −0.293914 0.955832i \(-0.594958\pi\)
−0.293914 + 0.955832i \(0.594958\pi\)
\(138\) 6.08122 0.517668
\(139\) −4.21524 −0.357532 −0.178766 0.983892i \(-0.557211\pi\)
−0.178766 + 0.983892i \(0.557211\pi\)
\(140\) −2.77664 −0.234669
\(141\) −8.71500 −0.733936
\(142\) 9.86795 0.828100
\(143\) 1.15175 0.0963145
\(144\) −1.50600 −0.125500
\(145\) 16.8557 1.39979
\(146\) 8.78991 0.727458
\(147\) 8.00183 0.659979
\(148\) 1.53165 0.125901
\(149\) −14.8554 −1.21700 −0.608500 0.793554i \(-0.708228\pi\)
−0.608500 + 0.793554i \(0.708228\pi\)
\(150\) 14.6712 1.19790
\(151\) −23.9206 −1.94663 −0.973315 0.229472i \(-0.926300\pi\)
−0.973315 + 0.229472i \(0.926300\pi\)
\(152\) 6.95848 0.564407
\(153\) 7.67153 0.620206
\(154\) −0.673376 −0.0542622
\(155\) 33.6043 2.69917
\(156\) 1.40778 0.112713
\(157\) −3.88069 −0.309713 −0.154856 0.987937i \(-0.549492\pi\)
−0.154856 + 0.987937i \(0.549492\pi\)
\(158\) −10.3482 −0.823257
\(159\) 6.50053 0.515526
\(160\) −4.12347 −0.325989
\(161\) −3.35022 −0.264034
\(162\) 2.21398 0.173946
\(163\) 15.7845 1.23633 0.618167 0.786047i \(-0.287876\pi\)
0.618167 + 0.786047i \(0.287876\pi\)
\(164\) −10.1937 −0.795992
\(165\) 5.04009 0.392371
\(166\) 5.79609 0.449864
\(167\) 9.48967 0.734333 0.367166 0.930155i \(-0.380328\pi\)
0.367166 + 0.930155i \(0.380328\pi\)
\(168\) −0.823063 −0.0635007
\(169\) −11.6735 −0.897959
\(170\) 21.0049 1.61100
\(171\) 10.4794 0.801384
\(172\) −2.45640 −0.187299
\(173\) 3.55523 0.270299 0.135150 0.990825i \(-0.456848\pi\)
0.135150 + 0.990825i \(0.456848\pi\)
\(174\) 4.99643 0.378779
\(175\) −8.08253 −0.610982
\(176\) −1.00000 −0.0753778
\(177\) −13.3367 −1.00245
\(178\) 2.26285 0.169608
\(179\) −23.0257 −1.72102 −0.860511 0.509431i \(-0.829856\pi\)
−0.860511 + 0.509431i \(0.829856\pi\)
\(180\) −6.20994 −0.462861
\(181\) 1.67191 0.124272 0.0621360 0.998068i \(-0.480209\pi\)
0.0621360 + 0.998068i \(0.480209\pi\)
\(182\) −0.775564 −0.0574886
\(183\) −3.22943 −0.238726
\(184\) −4.97526 −0.366781
\(185\) 6.31573 0.464342
\(186\) 9.96112 0.730385
\(187\) 5.09398 0.372509
\(188\) 7.13004 0.520012
\(189\) −3.70872 −0.269770
\(190\) 28.6931 2.08161
\(191\) −21.4595 −1.55275 −0.776376 0.630270i \(-0.782944\pi\)
−0.776376 + 0.630270i \(0.782944\pi\)
\(192\) −1.22229 −0.0882115
\(193\) 12.4401 0.895456 0.447728 0.894170i \(-0.352233\pi\)
0.447728 + 0.894170i \(0.352233\pi\)
\(194\) 19.3581 1.38983
\(195\) 5.80495 0.415701
\(196\) −6.54656 −0.467612
\(197\) −1.00000 −0.0712470
\(198\) −1.50600 −0.107027
\(199\) −11.2537 −0.797751 −0.398875 0.917005i \(-0.630599\pi\)
−0.398875 + 0.917005i \(0.630599\pi\)
\(200\) −12.0030 −0.848740
\(201\) 7.85996 0.554398
\(202\) 17.2864 1.21626
\(203\) −2.75259 −0.193194
\(204\) 6.22634 0.435931
\(205\) −42.0333 −2.93573
\(206\) −5.18480 −0.361242
\(207\) −7.49272 −0.520780
\(208\) −1.15175 −0.0798598
\(209\) 6.95848 0.481328
\(210\) −3.39388 −0.234200
\(211\) 4.83153 0.332616 0.166308 0.986074i \(-0.446815\pi\)
0.166308 + 0.986074i \(0.446815\pi\)
\(212\) −5.31830 −0.365263
\(213\) 12.0615 0.826442
\(214\) 4.31733 0.295127
\(215\) −10.1289 −0.690785
\(216\) −5.50765 −0.374748
\(217\) −5.48770 −0.372529
\(218\) 5.07937 0.344018
\(219\) 10.7439 0.726002
\(220\) −4.12347 −0.278004
\(221\) 5.86702 0.394658
\(222\) 1.87213 0.125649
\(223\) −21.1240 −1.41456 −0.707282 0.706931i \(-0.750079\pi\)
−0.707282 + 0.706931i \(0.750079\pi\)
\(224\) 0.673376 0.0449918
\(225\) −18.0765 −1.20510
\(226\) 8.78693 0.584498
\(227\) −14.6606 −0.973061 −0.486530 0.873664i \(-0.661738\pi\)
−0.486530 + 0.873664i \(0.661738\pi\)
\(228\) 8.50530 0.563277
\(229\) 2.79269 0.184546 0.0922730 0.995734i \(-0.470587\pi\)
0.0922730 + 0.995734i \(0.470587\pi\)
\(230\) −20.5153 −1.35274
\(231\) −0.823063 −0.0541536
\(232\) −4.08775 −0.268374
\(233\) 7.45053 0.488101 0.244050 0.969763i \(-0.421524\pi\)
0.244050 + 0.969763i \(0.421524\pi\)
\(234\) −1.73454 −0.113390
\(235\) 29.4005 1.91788
\(236\) 10.9112 0.710258
\(237\) −12.6485 −0.821609
\(238\) −3.43016 −0.222345
\(239\) 2.13371 0.138018 0.0690091 0.997616i \(-0.478016\pi\)
0.0690091 + 0.997616i \(0.478016\pi\)
\(240\) −5.04009 −0.325336
\(241\) −7.12792 −0.459150 −0.229575 0.973291i \(-0.573734\pi\)
−0.229575 + 0.973291i \(0.573734\pi\)
\(242\) −1.00000 −0.0642824
\(243\) −13.8168 −0.886350
\(244\) 2.64210 0.169143
\(245\) −26.9946 −1.72462
\(246\) −12.4597 −0.794399
\(247\) 8.01445 0.509948
\(248\) −8.14953 −0.517496
\(249\) 7.08453 0.448964
\(250\) −28.8767 −1.82632
\(251\) 26.5391 1.67513 0.837566 0.546337i \(-0.183978\pi\)
0.837566 + 0.546337i \(0.183978\pi\)
\(252\) 1.01410 0.0638825
\(253\) −4.97526 −0.312792
\(254\) −13.4600 −0.844558
\(255\) 25.6741 1.60778
\(256\) 1.00000 0.0625000
\(257\) −30.0195 −1.87257 −0.936283 0.351247i \(-0.885758\pi\)
−0.936283 + 0.351247i \(0.885758\pi\)
\(258\) −3.00244 −0.186924
\(259\) −1.03138 −0.0640868
\(260\) −4.74922 −0.294534
\(261\) −6.15614 −0.381056
\(262\) −2.93923 −0.181586
\(263\) 28.7291 1.77151 0.885757 0.464149i \(-0.153640\pi\)
0.885757 + 0.464149i \(0.153640\pi\)
\(264\) −1.22229 −0.0752270
\(265\) −21.9299 −1.34714
\(266\) −4.68567 −0.287297
\(267\) 2.76587 0.169268
\(268\) −6.43050 −0.392805
\(269\) −1.92518 −0.117380 −0.0586901 0.998276i \(-0.518692\pi\)
−0.0586901 + 0.998276i \(0.518692\pi\)
\(270\) −22.7106 −1.38213
\(271\) 7.33014 0.445275 0.222637 0.974901i \(-0.428533\pi\)
0.222637 + 0.974901i \(0.428533\pi\)
\(272\) −5.09398 −0.308868
\(273\) −0.947967 −0.0573735
\(274\) 6.88035 0.415657
\(275\) −12.0030 −0.723808
\(276\) −6.08122 −0.366047
\(277\) −6.73088 −0.404420 −0.202210 0.979342i \(-0.564812\pi\)
−0.202210 + 0.979342i \(0.564812\pi\)
\(278\) 4.21524 0.252813
\(279\) −12.2732 −0.734776
\(280\) 2.77664 0.165936
\(281\) 9.12854 0.544563 0.272281 0.962218i \(-0.412222\pi\)
0.272281 + 0.962218i \(0.412222\pi\)
\(282\) 8.71500 0.518971
\(283\) −7.30638 −0.434319 −0.217160 0.976136i \(-0.569679\pi\)
−0.217160 + 0.976136i \(0.569679\pi\)
\(284\) −9.86795 −0.585555
\(285\) 35.0714 2.07745
\(286\) −1.15175 −0.0681047
\(287\) 6.86417 0.405179
\(288\) 1.50600 0.0887418
\(289\) 8.94865 0.526391
\(290\) −16.8557 −0.989802
\(291\) 23.6612 1.38705
\(292\) −8.78991 −0.514391
\(293\) 1.70904 0.0998434 0.0499217 0.998753i \(-0.484103\pi\)
0.0499217 + 0.998753i \(0.484103\pi\)
\(294\) −8.00183 −0.466676
\(295\) 44.9920 2.61953
\(296\) −1.53165 −0.0890256
\(297\) −5.50765 −0.319586
\(298\) 14.8554 0.860549
\(299\) −5.73027 −0.331390
\(300\) −14.6712 −0.847042
\(301\) 1.65408 0.0953396
\(302\) 23.9206 1.37648
\(303\) 21.1290 1.21383
\(304\) −6.95848 −0.399096
\(305\) 10.8946 0.623825
\(306\) −7.67153 −0.438552
\(307\) −29.7495 −1.69789 −0.848947 0.528479i \(-0.822763\pi\)
−0.848947 + 0.528479i \(0.822763\pi\)
\(308\) 0.673376 0.0383692
\(309\) −6.33735 −0.360519
\(310\) −33.6043 −1.90860
\(311\) −26.8202 −1.52084 −0.760418 0.649434i \(-0.775006\pi\)
−0.760418 + 0.649434i \(0.775006\pi\)
\(312\) −1.40778 −0.0797000
\(313\) 20.3744 1.15163 0.575816 0.817579i \(-0.304685\pi\)
0.575816 + 0.817579i \(0.304685\pi\)
\(314\) 3.88069 0.219000
\(315\) 4.18162 0.235608
\(316\) 10.3482 0.582131
\(317\) 8.97894 0.504308 0.252154 0.967687i \(-0.418861\pi\)
0.252154 + 0.967687i \(0.418861\pi\)
\(318\) −6.50053 −0.364532
\(319\) −4.08775 −0.228870
\(320\) 4.12347 0.230509
\(321\) 5.27705 0.294536
\(322\) 3.35022 0.186700
\(323\) 35.4463 1.97229
\(324\) −2.21398 −0.122999
\(325\) −13.8245 −0.766846
\(326\) −15.7845 −0.874220
\(327\) 6.20848 0.343330
\(328\) 10.1937 0.562851
\(329\) −4.80120 −0.264699
\(330\) −5.04009 −0.277448
\(331\) 3.66781 0.201601 0.100801 0.994907i \(-0.467860\pi\)
0.100801 + 0.994907i \(0.467860\pi\)
\(332\) −5.79609 −0.318102
\(333\) −2.30667 −0.126405
\(334\) −9.48967 −0.519252
\(335\) −26.5160 −1.44872
\(336\) 0.823063 0.0449018
\(337\) 27.7733 1.51291 0.756455 0.654046i \(-0.226930\pi\)
0.756455 + 0.654046i \(0.226930\pi\)
\(338\) 11.6735 0.634953
\(339\) 10.7402 0.583328
\(340\) −21.0049 −1.13915
\(341\) −8.14953 −0.441322
\(342\) −10.4794 −0.566664
\(343\) 9.12193 0.492538
\(344\) 2.45640 0.132440
\(345\) −25.0757 −1.35003
\(346\) −3.55523 −0.191131
\(347\) −4.48980 −0.241025 −0.120513 0.992712i \(-0.538454\pi\)
−0.120513 + 0.992712i \(0.538454\pi\)
\(348\) −4.99643 −0.267837
\(349\) 9.48557 0.507751 0.253876 0.967237i \(-0.418295\pi\)
0.253876 + 0.967237i \(0.418295\pi\)
\(350\) 8.08253 0.432029
\(351\) −6.34346 −0.338589
\(352\) 1.00000 0.0533002
\(353\) −35.7101 −1.90066 −0.950329 0.311247i \(-0.899253\pi\)
−0.950329 + 0.311247i \(0.899253\pi\)
\(354\) 13.3367 0.708836
\(355\) −40.6902 −2.15961
\(356\) −2.26285 −0.119931
\(357\) −4.19267 −0.221900
\(358\) 23.0257 1.21695
\(359\) 23.3915 1.23456 0.617279 0.786744i \(-0.288235\pi\)
0.617279 + 0.786744i \(0.288235\pi\)
\(360\) 6.20994 0.327292
\(361\) 29.4204 1.54844
\(362\) −1.67191 −0.0878736
\(363\) −1.22229 −0.0641538
\(364\) 0.775564 0.0406506
\(365\) −36.2449 −1.89715
\(366\) 3.22943 0.168805
\(367\) −37.1698 −1.94025 −0.970123 0.242612i \(-0.921996\pi\)
−0.970123 + 0.242612i \(0.921996\pi\)
\(368\) 4.97526 0.259353
\(369\) 15.3516 0.799175
\(370\) −6.31573 −0.328339
\(371\) 3.58122 0.185928
\(372\) −9.96112 −0.516460
\(373\) 21.2940 1.10256 0.551280 0.834321i \(-0.314140\pi\)
0.551280 + 0.834321i \(0.314140\pi\)
\(374\) −5.09398 −0.263404
\(375\) −35.2958 −1.82266
\(376\) −7.13004 −0.367704
\(377\) −4.70808 −0.242479
\(378\) 3.70872 0.190756
\(379\) −21.1655 −1.08720 −0.543600 0.839345i \(-0.682939\pi\)
−0.543600 + 0.839345i \(0.682939\pi\)
\(380\) −28.6931 −1.47192
\(381\) −16.4521 −0.842868
\(382\) 21.4595 1.09796
\(383\) −24.0635 −1.22959 −0.614793 0.788689i \(-0.710760\pi\)
−0.614793 + 0.788689i \(0.710760\pi\)
\(384\) 1.22229 0.0623749
\(385\) 2.77664 0.141511
\(386\) −12.4401 −0.633183
\(387\) 3.69933 0.188048
\(388\) −19.3581 −0.982757
\(389\) 6.92942 0.351336 0.175668 0.984449i \(-0.443792\pi\)
0.175668 + 0.984449i \(0.443792\pi\)
\(390\) −5.80495 −0.293945
\(391\) −25.3439 −1.28169
\(392\) 6.54656 0.330651
\(393\) −3.59260 −0.181223
\(394\) 1.00000 0.0503793
\(395\) 42.6704 2.14698
\(396\) 1.50600 0.0756792
\(397\) −2.47881 −0.124408 −0.0622039 0.998063i \(-0.519813\pi\)
−0.0622039 + 0.998063i \(0.519813\pi\)
\(398\) 11.2537 0.564095
\(399\) −5.72727 −0.286722
\(400\) 12.0030 0.600150
\(401\) −14.5549 −0.726835 −0.363417 0.931626i \(-0.618390\pi\)
−0.363417 + 0.931626i \(0.618390\pi\)
\(402\) −7.85996 −0.392019
\(403\) −9.38626 −0.467563
\(404\) −17.2864 −0.860029
\(405\) −9.12927 −0.453637
\(406\) 2.75259 0.136609
\(407\) −1.53165 −0.0759213
\(408\) −6.22634 −0.308250
\(409\) −8.66702 −0.428557 −0.214278 0.976773i \(-0.568740\pi\)
−0.214278 + 0.976773i \(0.568740\pi\)
\(410\) 42.0333 2.07588
\(411\) 8.40982 0.414826
\(412\) 5.18480 0.255437
\(413\) −7.34733 −0.361539
\(414\) 7.49272 0.368247
\(415\) −23.9000 −1.17321
\(416\) 1.15175 0.0564694
\(417\) 5.15226 0.252307
\(418\) −6.95848 −0.340350
\(419\) −25.8782 −1.26423 −0.632117 0.774873i \(-0.717814\pi\)
−0.632117 + 0.774873i \(0.717814\pi\)
\(420\) 3.39388 0.165604
\(421\) −7.93816 −0.386882 −0.193441 0.981112i \(-0.561965\pi\)
−0.193441 + 0.981112i \(0.561965\pi\)
\(422\) −4.83153 −0.235195
\(423\) −10.7378 −0.522091
\(424\) 5.31830 0.258280
\(425\) −61.1431 −2.96587
\(426\) −12.0615 −0.584383
\(427\) −1.77913 −0.0860981
\(428\) −4.31733 −0.208686
\(429\) −1.40778 −0.0679684
\(430\) 10.1289 0.488458
\(431\) 28.7579 1.38522 0.692610 0.721312i \(-0.256461\pi\)
0.692610 + 0.721312i \(0.256461\pi\)
\(432\) 5.50765 0.264987
\(433\) 36.1236 1.73599 0.867995 0.496572i \(-0.165408\pi\)
0.867995 + 0.496572i \(0.165408\pi\)
\(434\) 5.48770 0.263418
\(435\) −20.6026 −0.987821
\(436\) −5.07937 −0.243258
\(437\) −34.6202 −1.65611
\(438\) −10.7439 −0.513361
\(439\) −15.7448 −0.751458 −0.375729 0.926730i \(-0.622608\pi\)
−0.375729 + 0.926730i \(0.622608\pi\)
\(440\) 4.12347 0.196579
\(441\) 9.85911 0.469482
\(442\) −5.86702 −0.279065
\(443\) 1.08946 0.0517616 0.0258808 0.999665i \(-0.491761\pi\)
0.0258808 + 0.999665i \(0.491761\pi\)
\(444\) −1.87213 −0.0888474
\(445\) −9.33080 −0.442322
\(446\) 21.1240 1.00025
\(447\) 18.1576 0.858827
\(448\) −0.673376 −0.0318140
\(449\) 38.4864 1.81629 0.908144 0.418659i \(-0.137500\pi\)
0.908144 + 0.418659i \(0.137500\pi\)
\(450\) 18.0765 0.852134
\(451\) 10.1937 0.480001
\(452\) −8.78693 −0.413303
\(453\) 29.2380 1.37372
\(454\) 14.6606 0.688058
\(455\) 3.19801 0.149925
\(456\) −8.50530 −0.398297
\(457\) 8.25625 0.386211 0.193105 0.981178i \(-0.438144\pi\)
0.193105 + 0.981178i \(0.438144\pi\)
\(458\) −2.79269 −0.130494
\(459\) −28.0559 −1.30954
\(460\) 20.5153 0.956531
\(461\) 16.1195 0.750762 0.375381 0.926871i \(-0.377512\pi\)
0.375381 + 0.926871i \(0.377512\pi\)
\(462\) 0.823063 0.0382924
\(463\) −11.3407 −0.527046 −0.263523 0.964653i \(-0.584884\pi\)
−0.263523 + 0.964653i \(0.584884\pi\)
\(464\) 4.08775 0.189769
\(465\) −41.0744 −1.90478
\(466\) −7.45053 −0.345139
\(467\) 10.0432 0.464742 0.232371 0.972627i \(-0.425352\pi\)
0.232371 + 0.972627i \(0.425352\pi\)
\(468\) 1.73454 0.0801791
\(469\) 4.33014 0.199947
\(470\) −29.4005 −1.35614
\(471\) 4.74335 0.218562
\(472\) −10.9112 −0.502228
\(473\) 2.45640 0.112945
\(474\) 12.6485 0.580966
\(475\) −83.5226 −3.83228
\(476\) 3.43016 0.157221
\(477\) 8.00935 0.366723
\(478\) −2.13371 −0.0975936
\(479\) 18.2396 0.833388 0.416694 0.909047i \(-0.363189\pi\)
0.416694 + 0.909047i \(0.363189\pi\)
\(480\) 5.04009 0.230048
\(481\) −1.76409 −0.0804355
\(482\) 7.12792 0.324668
\(483\) 4.09495 0.186327
\(484\) 1.00000 0.0454545
\(485\) −79.8224 −3.62455
\(486\) 13.8168 0.626744
\(487\) 10.1976 0.462098 0.231049 0.972942i \(-0.425784\pi\)
0.231049 + 0.972942i \(0.425784\pi\)
\(488\) −2.64210 −0.119602
\(489\) −19.2932 −0.872470
\(490\) 26.9946 1.21949
\(491\) 3.23379 0.145939 0.0729694 0.997334i \(-0.476752\pi\)
0.0729694 + 0.997334i \(0.476752\pi\)
\(492\) 12.4597 0.561725
\(493\) −20.8229 −0.937817
\(494\) −8.01445 −0.360587
\(495\) 6.20994 0.279116
\(496\) 8.14953 0.365925
\(497\) 6.64484 0.298062
\(498\) −7.08453 −0.317465
\(499\) −42.2098 −1.88957 −0.944785 0.327691i \(-0.893729\pi\)
−0.944785 + 0.327691i \(0.893729\pi\)
\(500\) 28.8767 1.29140
\(501\) −11.5992 −0.518212
\(502\) −26.5391 −1.18450
\(503\) 41.0664 1.83106 0.915530 0.402251i \(-0.131772\pi\)
0.915530 + 0.402251i \(0.131772\pi\)
\(504\) −1.01410 −0.0451717
\(505\) −71.2798 −3.17191
\(506\) 4.97526 0.221177
\(507\) 14.2684 0.633682
\(508\) 13.4600 0.597193
\(509\) −27.0798 −1.20029 −0.600146 0.799890i \(-0.704891\pi\)
−0.600146 + 0.799890i \(0.704891\pi\)
\(510\) −25.6741 −1.13687
\(511\) 5.91891 0.261837
\(512\) −1.00000 −0.0441942
\(513\) −38.3249 −1.69208
\(514\) 30.0195 1.32410
\(515\) 21.3794 0.942087
\(516\) 3.00244 0.132175
\(517\) −7.13004 −0.313579
\(518\) 1.03138 0.0453162
\(519\) −4.34554 −0.190748
\(520\) 4.74922 0.208267
\(521\) 22.0852 0.967570 0.483785 0.875187i \(-0.339262\pi\)
0.483785 + 0.875187i \(0.339262\pi\)
\(522\) 6.15614 0.269447
\(523\) 1.49629 0.0654283 0.0327141 0.999465i \(-0.489585\pi\)
0.0327141 + 0.999465i \(0.489585\pi\)
\(524\) 2.93923 0.128401
\(525\) 9.87923 0.431165
\(526\) −28.7291 −1.25265
\(527\) −41.5136 −1.80836
\(528\) 1.22229 0.0531935
\(529\) 1.75317 0.0762248
\(530\) 21.9299 0.952572
\(531\) −16.4322 −0.713098
\(532\) 4.68567 0.203150
\(533\) 11.7406 0.508542
\(534\) −2.76587 −0.119691
\(535\) −17.8024 −0.769664
\(536\) 6.43050 0.277755
\(537\) 28.1442 1.21451
\(538\) 1.92518 0.0830003
\(539\) 6.54656 0.281981
\(540\) 22.7106 0.977310
\(541\) −20.4706 −0.880100 −0.440050 0.897973i \(-0.645039\pi\)
−0.440050 + 0.897973i \(0.645039\pi\)
\(542\) −7.33014 −0.314857
\(543\) −2.04356 −0.0876978
\(544\) 5.09398 0.218403
\(545\) −20.9446 −0.897169
\(546\) 0.947967 0.0405692
\(547\) −3.28950 −0.140649 −0.0703243 0.997524i \(-0.522403\pi\)
−0.0703243 + 0.997524i \(0.522403\pi\)
\(548\) −6.88035 −0.293914
\(549\) −3.97900 −0.169820
\(550\) 12.0030 0.511810
\(551\) −28.4445 −1.21178
\(552\) 6.08122 0.258834
\(553\) −6.96821 −0.296319
\(554\) 6.73088 0.285968
\(555\) −7.71968 −0.327682
\(556\) −4.21524 −0.178766
\(557\) 3.37251 0.142898 0.0714489 0.997444i \(-0.477238\pi\)
0.0714489 + 0.997444i \(0.477238\pi\)
\(558\) 12.2732 0.519565
\(559\) 2.82917 0.119661
\(560\) −2.77664 −0.117335
\(561\) −6.22634 −0.262876
\(562\) −9.12854 −0.385064
\(563\) 19.1962 0.809022 0.404511 0.914533i \(-0.367442\pi\)
0.404511 + 0.914533i \(0.367442\pi\)
\(564\) −8.71500 −0.366968
\(565\) −36.2327 −1.52432
\(566\) 7.30638 0.307110
\(567\) 1.49084 0.0626093
\(568\) 9.86795 0.414050
\(569\) −32.9852 −1.38281 −0.691406 0.722467i \(-0.743008\pi\)
−0.691406 + 0.722467i \(0.743008\pi\)
\(570\) −35.0714 −1.46898
\(571\) 33.3904 1.39735 0.698673 0.715441i \(-0.253774\pi\)
0.698673 + 0.715441i \(0.253774\pi\)
\(572\) 1.15175 0.0481573
\(573\) 26.2298 1.09576
\(574\) −6.86417 −0.286505
\(575\) 59.7180 2.49041
\(576\) −1.50600 −0.0627499
\(577\) −13.9148 −0.579280 −0.289640 0.957136i \(-0.593536\pi\)
−0.289640 + 0.957136i \(0.593536\pi\)
\(578\) −8.94865 −0.372215
\(579\) −15.2054 −0.631916
\(580\) 16.8557 0.699895
\(581\) 3.90295 0.161922
\(582\) −23.6612 −0.980790
\(583\) 5.31830 0.220262
\(584\) 8.78991 0.363729
\(585\) 7.15232 0.295712
\(586\) −1.70904 −0.0705999
\(587\) −38.3362 −1.58230 −0.791152 0.611620i \(-0.790518\pi\)
−0.791152 + 0.611620i \(0.790518\pi\)
\(588\) 8.00183 0.329990
\(589\) −56.7083 −2.33663
\(590\) −44.9920 −1.85229
\(591\) 1.22229 0.0502784
\(592\) 1.53165 0.0629506
\(593\) 23.0526 0.946656 0.473328 0.880886i \(-0.343053\pi\)
0.473328 + 0.880886i \(0.343053\pi\)
\(594\) 5.50765 0.225982
\(595\) 14.1442 0.579855
\(596\) −14.8554 −0.608500
\(597\) 13.7553 0.562966
\(598\) 5.73027 0.234328
\(599\) 22.4220 0.916138 0.458069 0.888917i \(-0.348541\pi\)
0.458069 + 0.888917i \(0.348541\pi\)
\(600\) 14.6712 0.598949
\(601\) 12.3455 0.503584 0.251792 0.967781i \(-0.418980\pi\)
0.251792 + 0.967781i \(0.418980\pi\)
\(602\) −1.65408 −0.0674153
\(603\) 9.68431 0.394376
\(604\) −23.9206 −0.973315
\(605\) 4.12347 0.167643
\(606\) −21.1290 −0.858308
\(607\) 18.4267 0.747917 0.373958 0.927446i \(-0.378000\pi\)
0.373958 + 0.927446i \(0.378000\pi\)
\(608\) 6.95848 0.282203
\(609\) 3.36448 0.136335
\(610\) −10.8946 −0.441111
\(611\) −8.21206 −0.332224
\(612\) 7.67153 0.310103
\(613\) −0.931220 −0.0376116 −0.0188058 0.999823i \(-0.505986\pi\)
−0.0188058 + 0.999823i \(0.505986\pi\)
\(614\) 29.7495 1.20059
\(615\) 51.3770 2.07172
\(616\) −0.673376 −0.0271311
\(617\) 12.2372 0.492650 0.246325 0.969187i \(-0.420777\pi\)
0.246325 + 0.969187i \(0.420777\pi\)
\(618\) 6.33735 0.254926
\(619\) −33.4532 −1.34460 −0.672298 0.740281i \(-0.734693\pi\)
−0.672298 + 0.740281i \(0.734693\pi\)
\(620\) 33.6043 1.34958
\(621\) 27.4020 1.09960
\(622\) 26.8202 1.07539
\(623\) 1.52375 0.0610477
\(624\) 1.40778 0.0563564
\(625\) 59.0570 2.36228
\(626\) −20.3744 −0.814327
\(627\) −8.50530 −0.339669
\(628\) −3.88069 −0.154856
\(629\) −7.80222 −0.311095
\(630\) −4.18162 −0.166600
\(631\) −31.3216 −1.24689 −0.623447 0.781866i \(-0.714268\pi\)
−0.623447 + 0.781866i \(0.714268\pi\)
\(632\) −10.3482 −0.411628
\(633\) −5.90555 −0.234725
\(634\) −8.97894 −0.356599
\(635\) 55.5020 2.20253
\(636\) 6.50053 0.257763
\(637\) 7.54003 0.298747
\(638\) 4.08775 0.161836
\(639\) 14.8611 0.587896
\(640\) −4.12347 −0.162994
\(641\) −3.80763 −0.150392 −0.0751962 0.997169i \(-0.523958\pi\)
−0.0751962 + 0.997169i \(0.523958\pi\)
\(642\) −5.27705 −0.208268
\(643\) 20.8352 0.821661 0.410831 0.911712i \(-0.365239\pi\)
0.410831 + 0.911712i \(0.365239\pi\)
\(644\) −3.35022 −0.132017
\(645\) 12.3805 0.487481
\(646\) −35.4463 −1.39462
\(647\) 18.4623 0.725828 0.362914 0.931823i \(-0.381782\pi\)
0.362914 + 0.931823i \(0.381782\pi\)
\(648\) 2.21398 0.0869732
\(649\) −10.9112 −0.428302
\(650\) 13.8245 0.542242
\(651\) 6.70758 0.262891
\(652\) 15.7845 0.618167
\(653\) 42.7436 1.67268 0.836342 0.548208i \(-0.184690\pi\)
0.836342 + 0.548208i \(0.184690\pi\)
\(654\) −6.20848 −0.242771
\(655\) 12.1198 0.473561
\(656\) −10.1937 −0.397996
\(657\) 13.2376 0.516447
\(658\) 4.80120 0.187170
\(659\) 10.3164 0.401871 0.200935 0.979605i \(-0.435602\pi\)
0.200935 + 0.979605i \(0.435602\pi\)
\(660\) 5.04009 0.196185
\(661\) −36.2688 −1.41069 −0.705346 0.708863i \(-0.749208\pi\)
−0.705346 + 0.708863i \(0.749208\pi\)
\(662\) −3.66781 −0.142553
\(663\) −7.17122 −0.278507
\(664\) 5.79609 0.224932
\(665\) 19.3212 0.749245
\(666\) 2.30667 0.0893816
\(667\) 20.3376 0.787475
\(668\) 9.48967 0.367166
\(669\) 25.8197 0.998246
\(670\) 26.5160 1.02440
\(671\) −2.64210 −0.101997
\(672\) −0.823063 −0.0317504
\(673\) 12.1381 0.467888 0.233944 0.972250i \(-0.424837\pi\)
0.233944 + 0.972250i \(0.424837\pi\)
\(674\) −27.7733 −1.06979
\(675\) 66.1084 2.54451
\(676\) −11.6735 −0.448979
\(677\) 32.0543 1.23195 0.615973 0.787767i \(-0.288763\pi\)
0.615973 + 0.787767i \(0.288763\pi\)
\(678\) −10.7402 −0.412475
\(679\) 13.0353 0.500247
\(680\) 21.0049 0.805500
\(681\) 17.9196 0.686681
\(682\) 8.14953 0.312062
\(683\) 41.5937 1.59154 0.795770 0.605599i \(-0.207066\pi\)
0.795770 + 0.605599i \(0.207066\pi\)
\(684\) 10.4794 0.400692
\(685\) −28.3709 −1.08400
\(686\) −9.12193 −0.348277
\(687\) −3.41348 −0.130233
\(688\) −2.45640 −0.0936494
\(689\) 6.12538 0.233358
\(690\) 25.0757 0.954617
\(691\) 34.3074 1.30511 0.652557 0.757740i \(-0.273696\pi\)
0.652557 + 0.757740i \(0.273696\pi\)
\(692\) 3.55523 0.135150
\(693\) −1.01410 −0.0385226
\(694\) 4.48980 0.170430
\(695\) −17.3814 −0.659315
\(696\) 4.99643 0.189389
\(697\) 51.9264 1.96685
\(698\) −9.48557 −0.359034
\(699\) −9.10674 −0.344449
\(700\) −8.08253 −0.305491
\(701\) −44.9691 −1.69846 −0.849229 0.528025i \(-0.822933\pi\)
−0.849229 + 0.528025i \(0.822933\pi\)
\(702\) 6.34346 0.239419
\(703\) −10.6580 −0.401973
\(704\) −1.00000 −0.0376889
\(705\) −35.9361 −1.35343
\(706\) 35.7101 1.34397
\(707\) 11.6402 0.437776
\(708\) −13.3367 −0.501223
\(709\) −39.8948 −1.49828 −0.749141 0.662411i \(-0.769533\pi\)
−0.749141 + 0.662411i \(0.769533\pi\)
\(710\) 40.6902 1.52708
\(711\) −15.5843 −0.584458
\(712\) 2.26285 0.0848039
\(713\) 40.5460 1.51846
\(714\) 4.19267 0.156907
\(715\) 4.74922 0.177611
\(716\) −23.0257 −0.860511
\(717\) −2.60802 −0.0973983
\(718\) −23.3915 −0.872964
\(719\) 3.20406 0.119491 0.0597456 0.998214i \(-0.480971\pi\)
0.0597456 + 0.998214i \(0.480971\pi\)
\(720\) −6.20994 −0.231431
\(721\) −3.49132 −0.130024
\(722\) −29.4204 −1.09491
\(723\) 8.71241 0.324018
\(724\) 1.67191 0.0621360
\(725\) 49.0653 1.82224
\(726\) 1.22229 0.0453636
\(727\) 0.822265 0.0304961 0.0152481 0.999884i \(-0.495146\pi\)
0.0152481 + 0.999884i \(0.495146\pi\)
\(728\) −0.775564 −0.0287443
\(729\) 23.5302 0.871487
\(730\) 36.2449 1.34148
\(731\) 12.5129 0.462805
\(732\) −3.22943 −0.119363
\(733\) −15.2451 −0.563092 −0.281546 0.959548i \(-0.590847\pi\)
−0.281546 + 0.959548i \(0.590847\pi\)
\(734\) 37.1698 1.37196
\(735\) 32.9953 1.21705
\(736\) −4.97526 −0.183390
\(737\) 6.43050 0.236870
\(738\) −15.3516 −0.565102
\(739\) −15.3207 −0.563581 −0.281790 0.959476i \(-0.590928\pi\)
−0.281790 + 0.959476i \(0.590928\pi\)
\(740\) 6.31573 0.232171
\(741\) −9.79602 −0.359866
\(742\) −3.58122 −0.131471
\(743\) −30.1120 −1.10470 −0.552350 0.833612i \(-0.686269\pi\)
−0.552350 + 0.833612i \(0.686269\pi\)
\(744\) 9.96112 0.365192
\(745\) −61.2557 −2.24423
\(746\) −21.2940 −0.779627
\(747\) 8.72890 0.319374
\(748\) 5.09398 0.186254
\(749\) 2.90719 0.106226
\(750\) 35.2958 1.28882
\(751\) −40.4198 −1.47494 −0.737470 0.675380i \(-0.763980\pi\)
−0.737470 + 0.675380i \(0.763980\pi\)
\(752\) 7.13004 0.260006
\(753\) −32.4385 −1.18213
\(754\) 4.70808 0.171458
\(755\) −98.6358 −3.58973
\(756\) −3.70872 −0.134885
\(757\) 10.1324 0.368269 0.184134 0.982901i \(-0.441052\pi\)
0.184134 + 0.982901i \(0.441052\pi\)
\(758\) 21.1655 0.768766
\(759\) 6.08122 0.220734
\(760\) 28.6931 1.04081
\(761\) −17.5957 −0.637844 −0.318922 0.947781i \(-0.603321\pi\)
−0.318922 + 0.947781i \(0.603321\pi\)
\(762\) 16.4521 0.595997
\(763\) 3.42032 0.123824
\(764\) −21.4595 −0.776376
\(765\) 31.6333 1.14370
\(766\) 24.0635 0.869448
\(767\) −12.5670 −0.453768
\(768\) −1.22229 −0.0441057
\(769\) −41.0784 −1.48133 −0.740663 0.671877i \(-0.765488\pi\)
−0.740663 + 0.671877i \(0.765488\pi\)
\(770\) −2.77664 −0.100063
\(771\) 36.6927 1.32145
\(772\) 12.4401 0.447728
\(773\) 39.1151 1.40687 0.703437 0.710758i \(-0.251648\pi\)
0.703437 + 0.710758i \(0.251648\pi\)
\(774\) −3.69933 −0.132970
\(775\) 97.8188 3.51376
\(776\) 19.3581 0.694914
\(777\) 1.26065 0.0452255
\(778\) −6.92942 −0.248432
\(779\) 70.9324 2.54142
\(780\) 5.80495 0.207850
\(781\) 9.86795 0.353103
\(782\) 25.3439 0.906295
\(783\) 22.5139 0.804582
\(784\) −6.54656 −0.233806
\(785\) −16.0019 −0.571133
\(786\) 3.59260 0.128144
\(787\) 24.1034 0.859195 0.429597 0.903021i \(-0.358656\pi\)
0.429597 + 0.903021i \(0.358656\pi\)
\(788\) −1.00000 −0.0356235
\(789\) −35.1154 −1.25014
\(790\) −42.6704 −1.51814
\(791\) 5.91691 0.210381
\(792\) −1.50600 −0.0535133
\(793\) −3.04305 −0.108062
\(794\) 2.47881 0.0879696
\(795\) 26.8047 0.950666
\(796\) −11.2537 −0.398875
\(797\) 28.3313 1.00355 0.501774 0.864999i \(-0.332681\pi\)
0.501774 + 0.864999i \(0.332681\pi\)
\(798\) 5.72727 0.202743
\(799\) −36.3203 −1.28492
\(800\) −12.0030 −0.424370
\(801\) 3.40785 0.120410
\(802\) 14.5549 0.513950
\(803\) 8.78991 0.310189
\(804\) 7.85996 0.277199
\(805\) −13.8145 −0.486898
\(806\) 9.38626 0.330617
\(807\) 2.35313 0.0828342
\(808\) 17.2864 0.608132
\(809\) 17.6178 0.619409 0.309704 0.950833i \(-0.399770\pi\)
0.309704 + 0.950833i \(0.399770\pi\)
\(810\) 9.12927 0.320770
\(811\) −30.0729 −1.05600 −0.528001 0.849244i \(-0.677058\pi\)
−0.528001 + 0.849244i \(0.677058\pi\)
\(812\) −2.75259 −0.0965971
\(813\) −8.95959 −0.314227
\(814\) 1.53165 0.0536845
\(815\) 65.0867 2.27989
\(816\) 6.22634 0.217966
\(817\) 17.0928 0.598001
\(818\) 8.66702 0.303035
\(819\) −1.16800 −0.0408131
\(820\) −42.0333 −1.46787
\(821\) −55.6644 −1.94270 −0.971350 0.237652i \(-0.923622\pi\)
−0.971350 + 0.237652i \(0.923622\pi\)
\(822\) −8.40982 −0.293326
\(823\) 0.710759 0.0247755 0.0123877 0.999923i \(-0.496057\pi\)
0.0123877 + 0.999923i \(0.496057\pi\)
\(824\) −5.18480 −0.180621
\(825\) 14.6712 0.510785
\(826\) 7.34733 0.255646
\(827\) 30.6740 1.06664 0.533320 0.845913i \(-0.320944\pi\)
0.533320 + 0.845913i \(0.320944\pi\)
\(828\) −7.49272 −0.260390
\(829\) 5.14186 0.178584 0.0892921 0.996005i \(-0.471540\pi\)
0.0892921 + 0.996005i \(0.471540\pi\)
\(830\) 23.9000 0.829581
\(831\) 8.22712 0.285395
\(832\) −1.15175 −0.0399299
\(833\) 33.3481 1.15544
\(834\) −5.15226 −0.178408
\(835\) 39.1304 1.35416
\(836\) 6.95848 0.240664
\(837\) 44.8848 1.55145
\(838\) 25.8782 0.893948
\(839\) 8.81758 0.304417 0.152208 0.988348i \(-0.451362\pi\)
0.152208 + 0.988348i \(0.451362\pi\)
\(840\) −3.39388 −0.117100
\(841\) −12.2903 −0.423803
\(842\) 7.93816 0.273567
\(843\) −11.1578 −0.384294
\(844\) 4.83153 0.166308
\(845\) −48.1352 −1.65590
\(846\) 10.7378 0.369174
\(847\) −0.673376 −0.0231375
\(848\) −5.31830 −0.182631
\(849\) 8.93055 0.306496
\(850\) 61.1431 2.09719
\(851\) 7.62037 0.261223
\(852\) 12.0615 0.413221
\(853\) −40.1406 −1.37439 −0.687194 0.726474i \(-0.741158\pi\)
−0.687194 + 0.726474i \(0.741158\pi\)
\(854\) 1.77913 0.0608805
\(855\) 43.2117 1.47781
\(856\) 4.31733 0.147563
\(857\) 10.0182 0.342216 0.171108 0.985252i \(-0.445265\pi\)
0.171108 + 0.985252i \(0.445265\pi\)
\(858\) 1.40778 0.0480609
\(859\) 57.3877 1.95804 0.979022 0.203756i \(-0.0653150\pi\)
0.979022 + 0.203756i \(0.0653150\pi\)
\(860\) −10.1289 −0.345392
\(861\) −8.39003 −0.285932
\(862\) −28.7579 −0.979499
\(863\) 30.7325 1.04615 0.523074 0.852287i \(-0.324785\pi\)
0.523074 + 0.852287i \(0.324785\pi\)
\(864\) −5.50765 −0.187374
\(865\) 14.6599 0.498451
\(866\) −36.1236 −1.22753
\(867\) −10.9379 −0.371470
\(868\) −5.48770 −0.186265
\(869\) −10.3482 −0.351038
\(870\) 20.6026 0.698495
\(871\) 7.40635 0.250955
\(872\) 5.07937 0.172009
\(873\) 29.1532 0.986687
\(874\) 34.6202 1.17105
\(875\) −19.4448 −0.657356
\(876\) 10.7439 0.363001
\(877\) −12.0207 −0.405909 −0.202955 0.979188i \(-0.565054\pi\)
−0.202955 + 0.979188i \(0.565054\pi\)
\(878\) 15.7448 0.531361
\(879\) −2.08895 −0.0704586
\(880\) −4.12347 −0.139002
\(881\) −19.2054 −0.647047 −0.323524 0.946220i \(-0.604868\pi\)
−0.323524 + 0.946220i \(0.604868\pi\)
\(882\) −9.85911 −0.331974
\(883\) 30.5119 1.02681 0.513403 0.858147i \(-0.328385\pi\)
0.513403 + 0.858147i \(0.328385\pi\)
\(884\) 5.86702 0.197329
\(885\) −54.9934 −1.84858
\(886\) −1.08946 −0.0366010
\(887\) 36.4429 1.22363 0.611817 0.790999i \(-0.290439\pi\)
0.611817 + 0.790999i \(0.290439\pi\)
\(888\) 1.87213 0.0628246
\(889\) −9.06366 −0.303986
\(890\) 9.33080 0.312769
\(891\) 2.21398 0.0741710
\(892\) −21.1240 −0.707282
\(893\) −49.6142 −1.66028
\(894\) −18.1576 −0.607282
\(895\) −94.9458 −3.17369
\(896\) 0.673376 0.0224959
\(897\) 7.00408 0.233859
\(898\) −38.4864 −1.28431
\(899\) 33.3133 1.11106
\(900\) −18.0765 −0.602550
\(901\) 27.0913 0.902543
\(902\) −10.1937 −0.339412
\(903\) −2.02177 −0.0672804
\(904\) 8.78693 0.292249
\(905\) 6.89407 0.229167
\(906\) −29.2380 −0.971367
\(907\) −33.6974 −1.11890 −0.559451 0.828863i \(-0.688988\pi\)
−0.559451 + 0.828863i \(0.688988\pi\)
\(908\) −14.6606 −0.486530
\(909\) 26.0332 0.863468
\(910\) −3.19801 −0.106013
\(911\) −19.0867 −0.632370 −0.316185 0.948698i \(-0.602402\pi\)
−0.316185 + 0.948698i \(0.602402\pi\)
\(912\) 8.50530 0.281639
\(913\) 5.79609 0.191823
\(914\) −8.25625 −0.273092
\(915\) −13.3164 −0.440228
\(916\) 2.79269 0.0922730
\(917\) −1.97921 −0.0653592
\(918\) 28.0559 0.925982
\(919\) −30.3199 −1.00016 −0.500080 0.865979i \(-0.666696\pi\)
−0.500080 + 0.865979i \(0.666696\pi\)
\(920\) −20.5153 −0.676370
\(921\) 36.3626 1.19819
\(922\) −16.1195 −0.530869
\(923\) 11.3655 0.374098
\(924\) −0.823063 −0.0270768
\(925\) 18.3844 0.604477
\(926\) 11.3407 0.372678
\(927\) −7.80830 −0.256458
\(928\) −4.08775 −0.134187
\(929\) 14.3780 0.471727 0.235863 0.971786i \(-0.424208\pi\)
0.235863 + 0.971786i \(0.424208\pi\)
\(930\) 41.0744 1.34688
\(931\) 45.5541 1.49298
\(932\) 7.45053 0.244050
\(933\) 32.7822 1.07324
\(934\) −10.0432 −0.328622
\(935\) 21.0049 0.686933
\(936\) −1.73454 −0.0566952
\(937\) −27.2551 −0.890387 −0.445193 0.895435i \(-0.646865\pi\)
−0.445193 + 0.895435i \(0.646865\pi\)
\(938\) −4.33014 −0.141384
\(939\) −24.9036 −0.812697
\(940\) 29.4005 0.958939
\(941\) 38.9972 1.27127 0.635636 0.771989i \(-0.280738\pi\)
0.635636 + 0.771989i \(0.280738\pi\)
\(942\) −4.74335 −0.154547
\(943\) −50.7161 −1.65154
\(944\) 10.9112 0.355129
\(945\) −15.2928 −0.497475
\(946\) −2.45640 −0.0798645
\(947\) −10.4985 −0.341157 −0.170578 0.985344i \(-0.554564\pi\)
−0.170578 + 0.985344i \(0.554564\pi\)
\(948\) −12.6485 −0.410805
\(949\) 10.1238 0.328633
\(950\) 83.5226 2.70983
\(951\) −10.9749 −0.355886
\(952\) −3.43016 −0.111172
\(953\) −59.2223 −1.91840 −0.959199 0.282731i \(-0.908760\pi\)
−0.959199 + 0.282731i \(0.908760\pi\)
\(954\) −8.00935 −0.259312
\(955\) −88.4874 −2.86339
\(956\) 2.13371 0.0690091
\(957\) 4.99643 0.161512
\(958\) −18.2396 −0.589294
\(959\) 4.63307 0.149609
\(960\) −5.04009 −0.162668
\(961\) 35.4149 1.14242
\(962\) 1.76409 0.0568765
\(963\) 6.50189 0.209520
\(964\) −7.12792 −0.229575
\(965\) 51.2963 1.65128
\(966\) −4.09495 −0.131753
\(967\) 44.4173 1.42836 0.714182 0.699960i \(-0.246799\pi\)
0.714182 + 0.699960i \(0.246799\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −43.3259 −1.39183
\(970\) 79.8224 2.56294
\(971\) 7.97497 0.255929 0.127965 0.991779i \(-0.459156\pi\)
0.127965 + 0.991779i \(0.459156\pi\)
\(972\) −13.8168 −0.443175
\(973\) 2.83844 0.0909963
\(974\) −10.1976 −0.326752
\(975\) 16.8976 0.541157
\(976\) 2.64210 0.0845717
\(977\) −22.2031 −0.710341 −0.355171 0.934802i \(-0.615577\pi\)
−0.355171 + 0.934802i \(0.615577\pi\)
\(978\) 19.2932 0.616930
\(979\) 2.26285 0.0723210
\(980\) −26.9946 −0.862310
\(981\) 7.64952 0.244230
\(982\) −3.23379 −0.103194
\(983\) −3.91753 −0.124950 −0.0624749 0.998047i \(-0.519899\pi\)
−0.0624749 + 0.998047i \(0.519899\pi\)
\(984\) −12.4597 −0.397199
\(985\) −4.12347 −0.131385
\(986\) 20.8229 0.663137
\(987\) 5.86847 0.186796
\(988\) 8.01445 0.254974
\(989\) −12.2212 −0.388612
\(990\) −6.20994 −0.197365
\(991\) −5.75332 −0.182760 −0.0913801 0.995816i \(-0.529128\pi\)
−0.0913801 + 0.995816i \(0.529128\pi\)
\(992\) −8.14953 −0.258748
\(993\) −4.48314 −0.142268
\(994\) −6.64484 −0.210761
\(995\) −46.4041 −1.47111
\(996\) 7.08453 0.224482
\(997\) −26.1214 −0.827272 −0.413636 0.910442i \(-0.635741\pi\)
−0.413636 + 0.910442i \(0.635741\pi\)
\(998\) 42.2098 1.33613
\(999\) 8.43582 0.266898
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 4334.2.a.c.1.6 17
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4334.2.a.c.1.6 17 1.1 even 1 trivial