Properties

Label 4029.2.a.j.1.5
Level $4029$
Weight $2$
Character 4029.1
Self dual yes
Analytic conductor $32.172$
Analytic rank $0$
Dimension $25$
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] = [4029,2,Mod(1,4029)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4029, 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("4029.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4029 = 3 \cdot 17 \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4029.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: \(32.1717269744\)
Analytic rank: \(0\)
Dimension: \(25\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) \(=\) 4029.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.73737 q^{2} +1.00000 q^{3} +1.01844 q^{4} +3.91288 q^{5} -1.73737 q^{6} +2.21072 q^{7} +1.70533 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.73737 q^{2} +1.00000 q^{3} +1.01844 q^{4} +3.91288 q^{5} -1.73737 q^{6} +2.21072 q^{7} +1.70533 q^{8} +1.00000 q^{9} -6.79810 q^{10} -0.251112 q^{11} +1.01844 q^{12} +1.93652 q^{13} -3.84083 q^{14} +3.91288 q^{15} -4.99966 q^{16} -1.00000 q^{17} -1.73737 q^{18} +1.08362 q^{19} +3.98503 q^{20} +2.21072 q^{21} +0.436274 q^{22} -0.204447 q^{23} +1.70533 q^{24} +10.3106 q^{25} -3.36445 q^{26} +1.00000 q^{27} +2.25148 q^{28} +0.225940 q^{29} -6.79810 q^{30} -2.46050 q^{31} +5.27557 q^{32} -0.251112 q^{33} +1.73737 q^{34} +8.65029 q^{35} +1.01844 q^{36} -1.51392 q^{37} -1.88265 q^{38} +1.93652 q^{39} +6.67276 q^{40} -1.25010 q^{41} -3.84083 q^{42} -6.94797 q^{43} -0.255742 q^{44} +3.91288 q^{45} +0.355200 q^{46} -0.145293 q^{47} -4.99966 q^{48} -2.11271 q^{49} -17.9134 q^{50} -1.00000 q^{51} +1.97223 q^{52} -5.50273 q^{53} -1.73737 q^{54} -0.982573 q^{55} +3.77001 q^{56} +1.08362 q^{57} -0.392540 q^{58} +12.8788 q^{59} +3.98503 q^{60} +15.2747 q^{61} +4.27479 q^{62} +2.21072 q^{63} +0.833725 q^{64} +7.57738 q^{65} +0.436274 q^{66} +12.3682 q^{67} -1.01844 q^{68} -0.204447 q^{69} -15.0287 q^{70} +6.57427 q^{71} +1.70533 q^{72} +12.3282 q^{73} +2.63023 q^{74} +10.3106 q^{75} +1.10360 q^{76} -0.555139 q^{77} -3.36445 q^{78} -1.00000 q^{79} -19.5631 q^{80} +1.00000 q^{81} +2.17188 q^{82} +0.945634 q^{83} +2.25148 q^{84} -3.91288 q^{85} +12.0712 q^{86} +0.225940 q^{87} -0.428230 q^{88} -1.35133 q^{89} -6.79810 q^{90} +4.28111 q^{91} -0.208217 q^{92} -2.46050 q^{93} +0.252426 q^{94} +4.24008 q^{95} +5.27557 q^{96} -13.8447 q^{97} +3.67056 q^{98} -0.251112 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9} + 13 q^{10} + 19 q^{11} + 26 q^{12} + 17 q^{14} + 6 q^{15} + 16 q^{16} - 25 q^{17} + 6 q^{18} + 25 q^{19} + 32 q^{20} + 4 q^{21} - 7 q^{22} + 8 q^{23} + 18 q^{24} + 15 q^{25} + 20 q^{26} + 25 q^{27} + 9 q^{28} + 21 q^{29} + 13 q^{30} + 4 q^{31} + 27 q^{32} + 19 q^{33} - 6 q^{34} + 50 q^{35} + 26 q^{36} - 8 q^{37} + 31 q^{38} + 52 q^{40} + 40 q^{41} + 17 q^{42} + 21 q^{43} + 34 q^{44} + 6 q^{45} + 29 q^{46} + 43 q^{47} + 16 q^{48} + 21 q^{49} + 13 q^{50} - 25 q^{51} + 3 q^{52} + 44 q^{53} + 6 q^{54} + 13 q^{55} + 38 q^{56} + 25 q^{57} - 5 q^{58} + 45 q^{59} + 32 q^{60} + 22 q^{61} + 4 q^{62} + 4 q^{63} + 26 q^{64} + 43 q^{65} - 7 q^{66} + 8 q^{67} - 26 q^{68} + 8 q^{69} + 29 q^{70} + 9 q^{71} + 18 q^{72} - 7 q^{73} + 18 q^{74} + 15 q^{75} + 33 q^{76} + 20 q^{77} + 20 q^{78} - 25 q^{79} + 42 q^{80} + 25 q^{81} - 43 q^{82} + 41 q^{83} + 9 q^{84} - 6 q^{85} - 12 q^{86} + 21 q^{87} - 43 q^{88} + 68 q^{89} + 13 q^{90} + 10 q^{91} + 2 q^{92} + 4 q^{93} - 17 q^{94} + 8 q^{95} + 27 q^{96} + 15 q^{97} + 11 q^{98} + 19 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.73737 −1.22850 −0.614251 0.789110i \(-0.710542\pi\)
−0.614251 + 0.789110i \(0.710542\pi\)
\(3\) 1.00000 0.577350
\(4\) 1.01844 0.509219
\(5\) 3.91288 1.74989 0.874947 0.484219i \(-0.160896\pi\)
0.874947 + 0.484219i \(0.160896\pi\)
\(6\) −1.73737 −0.709276
\(7\) 2.21072 0.835574 0.417787 0.908545i \(-0.362806\pi\)
0.417787 + 0.908545i \(0.362806\pi\)
\(8\) 1.70533 0.602926
\(9\) 1.00000 0.333333
\(10\) −6.79810 −2.14975
\(11\) −0.251112 −0.0757132 −0.0378566 0.999283i \(-0.512053\pi\)
−0.0378566 + 0.999283i \(0.512053\pi\)
\(12\) 1.01844 0.293998
\(13\) 1.93652 0.537095 0.268547 0.963267i \(-0.413456\pi\)
0.268547 + 0.963267i \(0.413456\pi\)
\(14\) −3.84083 −1.02650
\(15\) 3.91288 1.01030
\(16\) −4.99966 −1.24992
\(17\) −1.00000 −0.242536
\(18\) −1.73737 −0.409501
\(19\) 1.08362 0.248600 0.124300 0.992245i \(-0.460331\pi\)
0.124300 + 0.992245i \(0.460331\pi\)
\(20\) 3.98503 0.891079
\(21\) 2.21072 0.482419
\(22\) 0.436274 0.0930139
\(23\) −0.204447 −0.0426302 −0.0213151 0.999773i \(-0.506785\pi\)
−0.0213151 + 0.999773i \(0.506785\pi\)
\(24\) 1.70533 0.348099
\(25\) 10.3106 2.06213
\(26\) −3.36445 −0.659822
\(27\) 1.00000 0.192450
\(28\) 2.25148 0.425490
\(29\) 0.225940 0.0419560 0.0209780 0.999780i \(-0.493322\pi\)
0.0209780 + 0.999780i \(0.493322\pi\)
\(30\) −6.79810 −1.24116
\(31\) −2.46050 −0.441919 −0.220959 0.975283i \(-0.570919\pi\)
−0.220959 + 0.975283i \(0.570919\pi\)
\(32\) 5.27557 0.932598
\(33\) −0.251112 −0.0437131
\(34\) 1.73737 0.297956
\(35\) 8.65029 1.46217
\(36\) 1.01844 0.169740
\(37\) −1.51392 −0.248887 −0.124443 0.992227i \(-0.539714\pi\)
−0.124443 + 0.992227i \(0.539714\pi\)
\(38\) −1.88265 −0.305406
\(39\) 1.93652 0.310092
\(40\) 6.67276 1.05506
\(41\) −1.25010 −0.195233 −0.0976163 0.995224i \(-0.531122\pi\)
−0.0976163 + 0.995224i \(0.531122\pi\)
\(42\) −3.84083 −0.592653
\(43\) −6.94797 −1.05956 −0.529778 0.848136i \(-0.677725\pi\)
−0.529778 + 0.848136i \(0.677725\pi\)
\(44\) −0.255742 −0.0385546
\(45\) 3.91288 0.583298
\(46\) 0.355200 0.0523713
\(47\) −0.145293 −0.0211931 −0.0105966 0.999944i \(-0.503373\pi\)
−0.0105966 + 0.999944i \(0.503373\pi\)
\(48\) −4.99966 −0.721639
\(49\) −2.11271 −0.301816
\(50\) −17.9134 −2.53333
\(51\) −1.00000 −0.140028
\(52\) 1.97223 0.273499
\(53\) −5.50273 −0.755858 −0.377929 0.925835i \(-0.623364\pi\)
−0.377929 + 0.925835i \(0.623364\pi\)
\(54\) −1.73737 −0.236425
\(55\) −0.982573 −0.132490
\(56\) 3.77001 0.503789
\(57\) 1.08362 0.143529
\(58\) −0.392540 −0.0515430
\(59\) 12.8788 1.67668 0.838339 0.545150i \(-0.183527\pi\)
0.838339 + 0.545150i \(0.183527\pi\)
\(60\) 3.98503 0.514465
\(61\) 15.2747 1.95573 0.977863 0.209245i \(-0.0671005\pi\)
0.977863 + 0.209245i \(0.0671005\pi\)
\(62\) 4.27479 0.542898
\(63\) 2.21072 0.278525
\(64\) 0.833725 0.104216
\(65\) 7.57738 0.939858
\(66\) 0.436274 0.0537016
\(67\) 12.3682 1.51102 0.755508 0.655139i \(-0.227390\pi\)
0.755508 + 0.655139i \(0.227390\pi\)
\(68\) −1.01844 −0.123504
\(69\) −0.204447 −0.0246126
\(70\) −15.0287 −1.79627
\(71\) 6.57427 0.780222 0.390111 0.920768i \(-0.372437\pi\)
0.390111 + 0.920768i \(0.372437\pi\)
\(72\) 1.70533 0.200975
\(73\) 12.3282 1.44290 0.721452 0.692464i \(-0.243475\pi\)
0.721452 + 0.692464i \(0.243475\pi\)
\(74\) 2.63023 0.305758
\(75\) 10.3106 1.19057
\(76\) 1.10360 0.126592
\(77\) −0.555139 −0.0632640
\(78\) −3.36445 −0.380948
\(79\) −1.00000 −0.112509
\(80\) −19.5631 −2.18722
\(81\) 1.00000 0.111111
\(82\) 2.17188 0.239844
\(83\) 0.945634 0.103797 0.0518984 0.998652i \(-0.483473\pi\)
0.0518984 + 0.998652i \(0.483473\pi\)
\(84\) 2.25148 0.245657
\(85\) −3.91288 −0.424412
\(86\) 12.0712 1.30167
\(87\) 0.225940 0.0242233
\(88\) −0.428230 −0.0456495
\(89\) −1.35133 −0.143241 −0.0716206 0.997432i \(-0.522817\pi\)
−0.0716206 + 0.997432i \(0.522817\pi\)
\(90\) −6.79810 −0.716583
\(91\) 4.28111 0.448782
\(92\) −0.208217 −0.0217081
\(93\) −2.46050 −0.255142
\(94\) 0.252426 0.0260358
\(95\) 4.24008 0.435024
\(96\) 5.27557 0.538436
\(97\) −13.8447 −1.40571 −0.702856 0.711332i \(-0.748092\pi\)
−0.702856 + 0.711332i \(0.748092\pi\)
\(98\) 3.67056 0.370782
\(99\) −0.251112 −0.0252377
\(100\) 10.5007 1.05007
\(101\) 4.43251 0.441052 0.220526 0.975381i \(-0.429223\pi\)
0.220526 + 0.975381i \(0.429223\pi\)
\(102\) 1.73737 0.172025
\(103\) 11.6964 1.15248 0.576239 0.817281i \(-0.304520\pi\)
0.576239 + 0.817281i \(0.304520\pi\)
\(104\) 3.30241 0.323828
\(105\) 8.65029 0.844182
\(106\) 9.56025 0.928574
\(107\) −6.87350 −0.664487 −0.332243 0.943194i \(-0.607806\pi\)
−0.332243 + 0.943194i \(0.607806\pi\)
\(108\) 1.01844 0.0979992
\(109\) −13.4885 −1.29196 −0.645981 0.763354i \(-0.723551\pi\)
−0.645981 + 0.763354i \(0.723551\pi\)
\(110\) 1.70709 0.162764
\(111\) −1.51392 −0.143695
\(112\) −11.0529 −1.04440
\(113\) 9.32760 0.877466 0.438733 0.898617i \(-0.355427\pi\)
0.438733 + 0.898617i \(0.355427\pi\)
\(114\) −1.88265 −0.176326
\(115\) −0.799978 −0.0745983
\(116\) 0.230106 0.0213648
\(117\) 1.93652 0.179032
\(118\) −22.3752 −2.05980
\(119\) −2.21072 −0.202656
\(120\) 6.67276 0.609137
\(121\) −10.9369 −0.994268
\(122\) −26.5378 −2.40262
\(123\) −1.25010 −0.112718
\(124\) −2.50587 −0.225033
\(125\) 20.7799 1.85861
\(126\) −3.84083 −0.342168
\(127\) 7.73496 0.686366 0.343183 0.939269i \(-0.388495\pi\)
0.343183 + 0.939269i \(0.388495\pi\)
\(128\) −11.9996 −1.06063
\(129\) −6.94797 −0.611735
\(130\) −13.1647 −1.15462
\(131\) 6.07699 0.530949 0.265475 0.964118i \(-0.414471\pi\)
0.265475 + 0.964118i \(0.414471\pi\)
\(132\) −0.255742 −0.0222595
\(133\) 2.39559 0.207724
\(134\) −21.4881 −1.85629
\(135\) 3.91288 0.336767
\(136\) −1.70533 −0.146231
\(137\) 6.48607 0.554143 0.277071 0.960849i \(-0.410636\pi\)
0.277071 + 0.960849i \(0.410636\pi\)
\(138\) 0.355200 0.0302366
\(139\) −4.23617 −0.359307 −0.179654 0.983730i \(-0.557498\pi\)
−0.179654 + 0.983730i \(0.557498\pi\)
\(140\) 8.80978 0.744562
\(141\) −0.145293 −0.0122358
\(142\) −11.4219 −0.958505
\(143\) −0.486285 −0.0406652
\(144\) −4.99966 −0.416638
\(145\) 0.884076 0.0734185
\(146\) −21.4186 −1.77261
\(147\) −2.11271 −0.174254
\(148\) −1.54183 −0.126738
\(149\) −4.13335 −0.338617 −0.169309 0.985563i \(-0.554154\pi\)
−0.169309 + 0.985563i \(0.554154\pi\)
\(150\) −17.9134 −1.46262
\(151\) −16.5867 −1.34981 −0.674905 0.737905i \(-0.735815\pi\)
−0.674905 + 0.737905i \(0.735815\pi\)
\(152\) 1.84794 0.149887
\(153\) −1.00000 −0.0808452
\(154\) 0.964480 0.0777200
\(155\) −9.62764 −0.773311
\(156\) 1.97223 0.157905
\(157\) −13.0467 −1.04124 −0.520620 0.853788i \(-0.674299\pi\)
−0.520620 + 0.853788i \(0.674299\pi\)
\(158\) 1.73737 0.138217
\(159\) −5.50273 −0.436395
\(160\) 20.6427 1.63195
\(161\) −0.451976 −0.0356207
\(162\) −1.73737 −0.136500
\(163\) 21.7381 1.70266 0.851330 0.524630i \(-0.175796\pi\)
0.851330 + 0.524630i \(0.175796\pi\)
\(164\) −1.27315 −0.0994162
\(165\) −0.982573 −0.0764932
\(166\) −1.64291 −0.127515
\(167\) −4.07053 −0.314987 −0.157493 0.987520i \(-0.550341\pi\)
−0.157493 + 0.987520i \(0.550341\pi\)
\(168\) 3.77001 0.290863
\(169\) −9.24988 −0.711529
\(170\) 6.79810 0.521391
\(171\) 1.08362 0.0828666
\(172\) −7.07608 −0.539546
\(173\) 14.9989 1.14035 0.570174 0.821524i \(-0.306876\pi\)
0.570174 + 0.821524i \(0.306876\pi\)
\(174\) −0.392540 −0.0297584
\(175\) 22.7940 1.72306
\(176\) 1.25548 0.0946351
\(177\) 12.8788 0.968030
\(178\) 2.34776 0.175972
\(179\) 5.32282 0.397847 0.198923 0.980015i \(-0.436256\pi\)
0.198923 + 0.980015i \(0.436256\pi\)
\(180\) 3.98503 0.297026
\(181\) −22.9663 −1.70707 −0.853534 0.521036i \(-0.825546\pi\)
−0.853534 + 0.521036i \(0.825546\pi\)
\(182\) −7.43785 −0.551330
\(183\) 15.2747 1.12914
\(184\) −0.348651 −0.0257029
\(185\) −5.92378 −0.435525
\(186\) 4.27479 0.313443
\(187\) 0.251112 0.0183632
\(188\) −0.147971 −0.0107919
\(189\) 2.21072 0.160806
\(190\) −7.36658 −0.534428
\(191\) 8.04363 0.582016 0.291008 0.956721i \(-0.406009\pi\)
0.291008 + 0.956721i \(0.406009\pi\)
\(192\) 0.833725 0.0601689
\(193\) 7.87585 0.566916 0.283458 0.958985i \(-0.408518\pi\)
0.283458 + 0.958985i \(0.408518\pi\)
\(194\) 24.0532 1.72692
\(195\) 7.57738 0.542628
\(196\) −2.15167 −0.153691
\(197\) −7.23692 −0.515609 −0.257805 0.966197i \(-0.582999\pi\)
−0.257805 + 0.966197i \(0.582999\pi\)
\(198\) 0.436274 0.0310046
\(199\) −8.61742 −0.610873 −0.305437 0.952212i \(-0.598802\pi\)
−0.305437 + 0.952212i \(0.598802\pi\)
\(200\) 17.5831 1.24331
\(201\) 12.3682 0.872385
\(202\) −7.70089 −0.541833
\(203\) 0.499490 0.0350573
\(204\) −1.01844 −0.0713049
\(205\) −4.89149 −0.341636
\(206\) −20.3209 −1.41582
\(207\) −0.204447 −0.0142101
\(208\) −9.68195 −0.671323
\(209\) −0.272111 −0.0188223
\(210\) −15.0287 −1.03708
\(211\) −21.3932 −1.47277 −0.736385 0.676563i \(-0.763469\pi\)
−0.736385 + 0.676563i \(0.763469\pi\)
\(212\) −5.60419 −0.384897
\(213\) 6.57427 0.450462
\(214\) 11.9418 0.816324
\(215\) −27.1866 −1.85411
\(216\) 1.70533 0.116033
\(217\) −5.43948 −0.369256
\(218\) 23.4344 1.58718
\(219\) 12.3282 0.833062
\(220\) −1.00069 −0.0674665
\(221\) −1.93652 −0.130265
\(222\) 2.63023 0.176529
\(223\) −10.5593 −0.707101 −0.353550 0.935416i \(-0.615026\pi\)
−0.353550 + 0.935416i \(0.615026\pi\)
\(224\) 11.6628 0.779255
\(225\) 10.3106 0.687376
\(226\) −16.2054 −1.07797
\(227\) 7.61930 0.505711 0.252855 0.967504i \(-0.418630\pi\)
0.252855 + 0.967504i \(0.418630\pi\)
\(228\) 1.10360 0.0730878
\(229\) −24.1252 −1.59424 −0.797120 0.603821i \(-0.793644\pi\)
−0.797120 + 0.603821i \(0.793644\pi\)
\(230\) 1.38985 0.0916443
\(231\) −0.555139 −0.0365255
\(232\) 0.385303 0.0252964
\(233\) −12.6213 −0.826848 −0.413424 0.910539i \(-0.635667\pi\)
−0.413424 + 0.910539i \(0.635667\pi\)
\(234\) −3.36445 −0.219941
\(235\) −0.568513 −0.0370857
\(236\) 13.1163 0.853796
\(237\) −1.00000 −0.0649570
\(238\) 3.84083 0.248964
\(239\) 27.0754 1.75136 0.875680 0.482892i \(-0.160414\pi\)
0.875680 + 0.482892i \(0.160414\pi\)
\(240\) −19.5631 −1.26279
\(241\) −6.79346 −0.437605 −0.218802 0.975769i \(-0.570215\pi\)
−0.218802 + 0.975769i \(0.570215\pi\)
\(242\) 19.0015 1.22146
\(243\) 1.00000 0.0641500
\(244\) 15.5563 0.995893
\(245\) −8.26680 −0.528147
\(246\) 2.17188 0.138474
\(247\) 2.09846 0.133522
\(248\) −4.19597 −0.266444
\(249\) 0.945634 0.0599271
\(250\) −36.1023 −2.28331
\(251\) −11.5630 −0.729848 −0.364924 0.931037i \(-0.618905\pi\)
−0.364924 + 0.931037i \(0.618905\pi\)
\(252\) 2.25148 0.141830
\(253\) 0.0513392 0.00322767
\(254\) −13.4384 −0.843203
\(255\) −3.91288 −0.245034
\(256\) 19.1803 1.19877
\(257\) 4.91211 0.306409 0.153204 0.988195i \(-0.451041\pi\)
0.153204 + 0.988195i \(0.451041\pi\)
\(258\) 12.0712 0.751518
\(259\) −3.34685 −0.207963
\(260\) 7.71709 0.478594
\(261\) 0.225940 0.0139853
\(262\) −10.5580 −0.652273
\(263\) −2.63845 −0.162694 −0.0813470 0.996686i \(-0.525922\pi\)
−0.0813470 + 0.996686i \(0.525922\pi\)
\(264\) −0.428230 −0.0263557
\(265\) −21.5315 −1.32267
\(266\) −4.16201 −0.255189
\(267\) −1.35133 −0.0827004
\(268\) 12.5962 0.769438
\(269\) −13.2737 −0.809314 −0.404657 0.914468i \(-0.632609\pi\)
−0.404657 + 0.914468i \(0.632609\pi\)
\(270\) −6.79810 −0.413719
\(271\) −10.0676 −0.611562 −0.305781 0.952102i \(-0.598918\pi\)
−0.305781 + 0.952102i \(0.598918\pi\)
\(272\) 4.99966 0.303149
\(273\) 4.28111 0.259105
\(274\) −11.2687 −0.680766
\(275\) −2.58913 −0.156130
\(276\) −0.208217 −0.0125332
\(277\) −8.38310 −0.503692 −0.251846 0.967767i \(-0.581038\pi\)
−0.251846 + 0.967767i \(0.581038\pi\)
\(278\) 7.35977 0.441410
\(279\) −2.46050 −0.147306
\(280\) 14.7516 0.881577
\(281\) 30.8757 1.84189 0.920945 0.389692i \(-0.127419\pi\)
0.920945 + 0.389692i \(0.127419\pi\)
\(282\) 0.252426 0.0150318
\(283\) −4.62332 −0.274828 −0.137414 0.990514i \(-0.543879\pi\)
−0.137414 + 0.990514i \(0.543879\pi\)
\(284\) 6.69549 0.397304
\(285\) 4.24008 0.251161
\(286\) 0.844854 0.0499573
\(287\) −2.76362 −0.163131
\(288\) 5.27557 0.310866
\(289\) 1.00000 0.0588235
\(290\) −1.53596 −0.0901949
\(291\) −13.8447 −0.811588
\(292\) 12.5555 0.734755
\(293\) 20.4561 1.19506 0.597530 0.801846i \(-0.296149\pi\)
0.597530 + 0.801846i \(0.296149\pi\)
\(294\) 3.67056 0.214071
\(295\) 50.3932 2.93401
\(296\) −2.58173 −0.150060
\(297\) −0.251112 −0.0145710
\(298\) 7.18114 0.415993
\(299\) −0.395917 −0.0228965
\(300\) 10.5007 0.606261
\(301\) −15.3600 −0.885337
\(302\) 28.8172 1.65824
\(303\) 4.43251 0.254641
\(304\) −5.41774 −0.310729
\(305\) 59.7681 3.42231
\(306\) 1.73737 0.0993186
\(307\) 26.1751 1.49389 0.746946 0.664885i \(-0.231519\pi\)
0.746946 + 0.664885i \(0.231519\pi\)
\(308\) −0.565375 −0.0322152
\(309\) 11.6964 0.665384
\(310\) 16.7267 0.950015
\(311\) 32.0019 1.81466 0.907331 0.420417i \(-0.138116\pi\)
0.907331 + 0.420417i \(0.138116\pi\)
\(312\) 3.30241 0.186962
\(313\) −18.7322 −1.05881 −0.529404 0.848370i \(-0.677584\pi\)
−0.529404 + 0.848370i \(0.677584\pi\)
\(314\) 22.6669 1.27917
\(315\) 8.65029 0.487389
\(316\) −1.01844 −0.0572916
\(317\) −20.1536 −1.13194 −0.565968 0.824427i \(-0.691498\pi\)
−0.565968 + 0.824427i \(0.691498\pi\)
\(318\) 9.56025 0.536112
\(319\) −0.0567363 −0.00317662
\(320\) 3.26227 0.182366
\(321\) −6.87350 −0.383642
\(322\) 0.785247 0.0437601
\(323\) −1.08362 −0.0602943
\(324\) 1.01844 0.0565799
\(325\) 19.9668 1.10756
\(326\) −37.7670 −2.09172
\(327\) −13.4885 −0.745915
\(328\) −2.13183 −0.117711
\(329\) −0.321201 −0.0177084
\(330\) 1.70709 0.0939721
\(331\) −21.2552 −1.16829 −0.584145 0.811649i \(-0.698570\pi\)
−0.584145 + 0.811649i \(0.698570\pi\)
\(332\) 0.963070 0.0528553
\(333\) −1.51392 −0.0829622
\(334\) 7.07199 0.386962
\(335\) 48.3953 2.64412
\(336\) −11.0529 −0.602982
\(337\) −1.26935 −0.0691460 −0.0345730 0.999402i \(-0.511007\pi\)
−0.0345730 + 0.999402i \(0.511007\pi\)
\(338\) 16.0704 0.874116
\(339\) 9.32760 0.506605
\(340\) −3.98503 −0.216118
\(341\) 0.617862 0.0334591
\(342\) −1.88265 −0.101802
\(343\) −20.1457 −1.08776
\(344\) −11.8486 −0.638834
\(345\) −0.799978 −0.0430694
\(346\) −26.0586 −1.40092
\(347\) 15.6083 0.837900 0.418950 0.908009i \(-0.362398\pi\)
0.418950 + 0.908009i \(0.362398\pi\)
\(348\) 0.230106 0.0123350
\(349\) 17.1071 0.915720 0.457860 0.889024i \(-0.348616\pi\)
0.457860 + 0.889024i \(0.348616\pi\)
\(350\) −39.6014 −2.11678
\(351\) 1.93652 0.103364
\(352\) −1.32476 −0.0706100
\(353\) 14.2995 0.761084 0.380542 0.924764i \(-0.375738\pi\)
0.380542 + 0.924764i \(0.375738\pi\)
\(354\) −22.3752 −1.18923
\(355\) 25.7243 1.36531
\(356\) −1.37625 −0.0729411
\(357\) −2.21072 −0.117004
\(358\) −9.24769 −0.488756
\(359\) −7.56972 −0.399514 −0.199757 0.979845i \(-0.564015\pi\)
−0.199757 + 0.979845i \(0.564015\pi\)
\(360\) 6.67276 0.351685
\(361\) −17.8258 −0.938198
\(362\) 39.9008 2.09714
\(363\) −10.9369 −0.574041
\(364\) 4.36004 0.228528
\(365\) 48.2387 2.52493
\(366\) −26.5378 −1.38715
\(367\) −7.29852 −0.380980 −0.190490 0.981689i \(-0.561008\pi\)
−0.190490 + 0.981689i \(0.561008\pi\)
\(368\) 1.02217 0.0532841
\(369\) −1.25010 −0.0650776
\(370\) 10.2918 0.535044
\(371\) −12.1650 −0.631575
\(372\) −2.50587 −0.129923
\(373\) 12.9327 0.669631 0.334816 0.942284i \(-0.391326\pi\)
0.334816 + 0.942284i \(0.391326\pi\)
\(374\) −0.436274 −0.0225592
\(375\) 20.7799 1.07307
\(376\) −0.247772 −0.0127779
\(377\) 0.437538 0.0225343
\(378\) −3.84083 −0.197551
\(379\) 0.752794 0.0386684 0.0193342 0.999813i \(-0.493845\pi\)
0.0193342 + 0.999813i \(0.493845\pi\)
\(380\) 4.31826 0.221522
\(381\) 7.73496 0.396274
\(382\) −13.9747 −0.715009
\(383\) 6.43116 0.328617 0.164309 0.986409i \(-0.447461\pi\)
0.164309 + 0.986409i \(0.447461\pi\)
\(384\) −11.9996 −0.612353
\(385\) −2.17219 −0.110705
\(386\) −13.6832 −0.696458
\(387\) −6.94797 −0.353185
\(388\) −14.0999 −0.715815
\(389\) 7.87471 0.399264 0.199632 0.979871i \(-0.436025\pi\)
0.199632 + 0.979871i \(0.436025\pi\)
\(390\) −13.1647 −0.666619
\(391\) 0.204447 0.0103393
\(392\) −3.60288 −0.181973
\(393\) 6.07699 0.306544
\(394\) 12.5732 0.633428
\(395\) −3.91288 −0.196878
\(396\) −0.255742 −0.0128515
\(397\) −22.3825 −1.12335 −0.561674 0.827359i \(-0.689842\pi\)
−0.561674 + 0.827359i \(0.689842\pi\)
\(398\) 14.9716 0.750459
\(399\) 2.39559 0.119929
\(400\) −51.5497 −2.57749
\(401\) −24.4098 −1.21897 −0.609483 0.792799i \(-0.708623\pi\)
−0.609483 + 0.792799i \(0.708623\pi\)
\(402\) −21.4881 −1.07173
\(403\) −4.76481 −0.237352
\(404\) 4.51424 0.224592
\(405\) 3.91288 0.194433
\(406\) −0.867797 −0.0430680
\(407\) 0.380164 0.0188440
\(408\) −1.70533 −0.0844265
\(409\) −6.57814 −0.325268 −0.162634 0.986686i \(-0.551999\pi\)
−0.162634 + 0.986686i \(0.551999\pi\)
\(410\) 8.49830 0.419701
\(411\) 6.48607 0.319934
\(412\) 11.9120 0.586864
\(413\) 28.4714 1.40099
\(414\) 0.355200 0.0174571
\(415\) 3.70016 0.181633
\(416\) 10.2163 0.500893
\(417\) −4.23617 −0.207446
\(418\) 0.472756 0.0231233
\(419\) 1.03889 0.0507532 0.0253766 0.999678i \(-0.491922\pi\)
0.0253766 + 0.999678i \(0.491922\pi\)
\(420\) 8.80978 0.429873
\(421\) 34.1288 1.66334 0.831668 0.555273i \(-0.187386\pi\)
0.831668 + 0.555273i \(0.187386\pi\)
\(422\) 37.1678 1.80930
\(423\) −0.145293 −0.00706437
\(424\) −9.38398 −0.455726
\(425\) −10.3106 −0.500140
\(426\) −11.4219 −0.553393
\(427\) 33.7681 1.63415
\(428\) −7.00024 −0.338369
\(429\) −0.486285 −0.0234780
\(430\) 47.2330 2.27778
\(431\) −12.3414 −0.594464 −0.297232 0.954805i \(-0.596063\pi\)
−0.297232 + 0.954805i \(0.596063\pi\)
\(432\) −4.99966 −0.240546
\(433\) 9.62887 0.462734 0.231367 0.972867i \(-0.425680\pi\)
0.231367 + 0.972867i \(0.425680\pi\)
\(434\) 9.45036 0.453632
\(435\) 0.884076 0.0423882
\(436\) −13.7372 −0.657891
\(437\) −0.221544 −0.0105979
\(438\) −21.4186 −1.02342
\(439\) 7.22772 0.344960 0.172480 0.985013i \(-0.444822\pi\)
0.172480 + 0.985013i \(0.444822\pi\)
\(440\) −1.67561 −0.0798817
\(441\) −2.11271 −0.100605
\(442\) 3.36445 0.160030
\(443\) −28.2387 −1.34166 −0.670830 0.741612i \(-0.734062\pi\)
−0.670830 + 0.741612i \(0.734062\pi\)
\(444\) −1.54183 −0.0731721
\(445\) −5.28761 −0.250657
\(446\) 18.3453 0.868675
\(447\) −4.13335 −0.195501
\(448\) 1.84313 0.0870799
\(449\) 18.8981 0.891857 0.445929 0.895069i \(-0.352874\pi\)
0.445929 + 0.895069i \(0.352874\pi\)
\(450\) −17.9134 −0.844444
\(451\) 0.313915 0.0147817
\(452\) 9.49958 0.446823
\(453\) −16.5867 −0.779313
\(454\) −13.2375 −0.621267
\(455\) 16.7515 0.785321
\(456\) 1.84794 0.0865375
\(457\) −4.80011 −0.224540 −0.112270 0.993678i \(-0.535812\pi\)
−0.112270 + 0.993678i \(0.535812\pi\)
\(458\) 41.9143 1.95853
\(459\) −1.00000 −0.0466760
\(460\) −0.814728 −0.0379869
\(461\) −11.0763 −0.515873 −0.257937 0.966162i \(-0.583043\pi\)
−0.257937 + 0.966162i \(0.583043\pi\)
\(462\) 0.964480 0.0448717
\(463\) −20.9078 −0.971667 −0.485834 0.874051i \(-0.661484\pi\)
−0.485834 + 0.874051i \(0.661484\pi\)
\(464\) −1.12962 −0.0524414
\(465\) −9.62764 −0.446471
\(466\) 21.9278 1.01579
\(467\) 12.2481 0.566776 0.283388 0.959005i \(-0.408542\pi\)
0.283388 + 0.959005i \(0.408542\pi\)
\(468\) 1.97223 0.0911662
\(469\) 27.3426 1.26257
\(470\) 0.987714 0.0455599
\(471\) −13.0467 −0.601160
\(472\) 21.9626 1.01091
\(473\) 1.74472 0.0802224
\(474\) 1.73737 0.0797998
\(475\) 11.1728 0.512645
\(476\) −2.25148 −0.103196
\(477\) −5.50273 −0.251953
\(478\) −47.0398 −2.15155
\(479\) −5.73414 −0.262000 −0.131000 0.991382i \(-0.541819\pi\)
−0.131000 + 0.991382i \(0.541819\pi\)
\(480\) 20.6427 0.942205
\(481\) −2.93174 −0.133676
\(482\) 11.8027 0.537599
\(483\) −0.451976 −0.0205656
\(484\) −11.1386 −0.506300
\(485\) −54.1725 −2.45985
\(486\) −1.73737 −0.0788085
\(487\) 34.1870 1.54916 0.774581 0.632475i \(-0.217961\pi\)
0.774581 + 0.632475i \(0.217961\pi\)
\(488\) 26.0485 1.17916
\(489\) 21.7381 0.983031
\(490\) 14.3625 0.648829
\(491\) 2.08344 0.0940244 0.0470122 0.998894i \(-0.485030\pi\)
0.0470122 + 0.998894i \(0.485030\pi\)
\(492\) −1.27315 −0.0573980
\(493\) −0.225940 −0.0101758
\(494\) −3.64579 −0.164032
\(495\) −0.982573 −0.0441634
\(496\) 12.3017 0.552361
\(497\) 14.5339 0.651933
\(498\) −1.64291 −0.0736207
\(499\) −26.5308 −1.18768 −0.593841 0.804583i \(-0.702389\pi\)
−0.593841 + 0.804583i \(0.702389\pi\)
\(500\) 21.1631 0.946441
\(501\) −4.07053 −0.181858
\(502\) 20.0891 0.896620
\(503\) −32.8461 −1.46453 −0.732267 0.681017i \(-0.761538\pi\)
−0.732267 + 0.681017i \(0.761538\pi\)
\(504\) 3.77001 0.167930
\(505\) 17.3439 0.771793
\(506\) −0.0891950 −0.00396520
\(507\) −9.24988 −0.410802
\(508\) 7.87757 0.349511
\(509\) 2.18583 0.0968850 0.0484425 0.998826i \(-0.484574\pi\)
0.0484425 + 0.998826i \(0.484574\pi\)
\(510\) 6.79810 0.301025
\(511\) 27.2542 1.20565
\(512\) −9.32391 −0.412062
\(513\) 1.08362 0.0478431
\(514\) −8.53413 −0.376424
\(515\) 45.7666 2.01672
\(516\) −7.07608 −0.311507
\(517\) 0.0364848 0.00160460
\(518\) 5.81470 0.255483
\(519\) 14.9989 0.658381
\(520\) 12.9219 0.566665
\(521\) −29.1503 −1.27710 −0.638549 0.769581i \(-0.720465\pi\)
−0.638549 + 0.769581i \(0.720465\pi\)
\(522\) −0.392540 −0.0171810
\(523\) 3.72874 0.163046 0.0815232 0.996671i \(-0.474022\pi\)
0.0815232 + 0.996671i \(0.474022\pi\)
\(524\) 6.18904 0.270370
\(525\) 22.7940 0.994810
\(526\) 4.58396 0.199870
\(527\) 2.46050 0.107181
\(528\) 1.25548 0.0546376
\(529\) −22.9582 −0.998183
\(530\) 37.4081 1.62491
\(531\) 12.8788 0.558892
\(532\) 2.43976 0.105777
\(533\) −2.42084 −0.104858
\(534\) 2.34776 0.101598
\(535\) −26.8952 −1.16278
\(536\) 21.0919 0.911031
\(537\) 5.32282 0.229697
\(538\) 23.0613 0.994245
\(539\) 0.530529 0.0228515
\(540\) 3.98503 0.171488
\(541\) 30.4126 1.30754 0.653769 0.756694i \(-0.273187\pi\)
0.653769 + 0.756694i \(0.273187\pi\)
\(542\) 17.4911 0.751306
\(543\) −22.9663 −0.985577
\(544\) −5.27557 −0.226188
\(545\) −52.7788 −2.26080
\(546\) −7.43785 −0.318311
\(547\) 6.09974 0.260806 0.130403 0.991461i \(-0.458373\pi\)
0.130403 + 0.991461i \(0.458373\pi\)
\(548\) 6.60566 0.282180
\(549\) 15.2747 0.651909
\(550\) 4.49826 0.191807
\(551\) 0.244833 0.0104303
\(552\) −0.348651 −0.0148396
\(553\) −2.21072 −0.0940094
\(554\) 14.5645 0.618787
\(555\) −5.92378 −0.251451
\(556\) −4.31428 −0.182966
\(557\) −8.11702 −0.343929 −0.171965 0.985103i \(-0.555011\pi\)
−0.171965 + 0.985103i \(0.555011\pi\)
\(558\) 4.27479 0.180966
\(559\) −13.4549 −0.569082
\(560\) −43.2485 −1.82758
\(561\) 0.251112 0.0106020
\(562\) −53.6424 −2.26277
\(563\) −47.2869 −1.99291 −0.996453 0.0841553i \(-0.973181\pi\)
−0.996453 + 0.0841553i \(0.973181\pi\)
\(564\) −0.147971 −0.00623072
\(565\) 36.4978 1.53547
\(566\) 8.03239 0.337626
\(567\) 2.21072 0.0928415
\(568\) 11.2113 0.470416
\(569\) 39.3622 1.65015 0.825075 0.565023i \(-0.191133\pi\)
0.825075 + 0.565023i \(0.191133\pi\)
\(570\) −7.36658 −0.308552
\(571\) 4.72298 0.197650 0.0988252 0.995105i \(-0.468492\pi\)
0.0988252 + 0.995105i \(0.468492\pi\)
\(572\) −0.495251 −0.0207075
\(573\) 8.04363 0.336027
\(574\) 4.80142 0.200407
\(575\) −2.10798 −0.0879090
\(576\) 0.833725 0.0347386
\(577\) 6.85425 0.285346 0.142673 0.989770i \(-0.454430\pi\)
0.142673 + 0.989770i \(0.454430\pi\)
\(578\) −1.73737 −0.0722649
\(579\) 7.87585 0.327309
\(580\) 0.900377 0.0373861
\(581\) 2.09053 0.0867299
\(582\) 24.0532 0.997038
\(583\) 1.38180 0.0572284
\(584\) 21.0236 0.869965
\(585\) 7.57738 0.313286
\(586\) −35.5398 −1.46813
\(587\) 15.9574 0.658631 0.329316 0.944220i \(-0.393182\pi\)
0.329316 + 0.944220i \(0.393182\pi\)
\(588\) −2.15167 −0.0887333
\(589\) −2.66625 −0.109861
\(590\) −87.5514 −3.60444
\(591\) −7.23692 −0.297687
\(592\) 7.56907 0.311087
\(593\) 12.8763 0.528767 0.264383 0.964418i \(-0.414832\pi\)
0.264383 + 0.964418i \(0.414832\pi\)
\(594\) 0.436274 0.0179005
\(595\) −8.65029 −0.354627
\(596\) −4.20956 −0.172430
\(597\) −8.61742 −0.352688
\(598\) 0.687852 0.0281284
\(599\) 14.2486 0.582180 0.291090 0.956696i \(-0.405982\pi\)
0.291090 + 0.956696i \(0.405982\pi\)
\(600\) 17.5831 0.717826
\(601\) −17.2942 −0.705445 −0.352722 0.935728i \(-0.614744\pi\)
−0.352722 + 0.935728i \(0.614744\pi\)
\(602\) 26.6860 1.08764
\(603\) 12.3682 0.503672
\(604\) −16.8926 −0.687349
\(605\) −42.7950 −1.73986
\(606\) −7.70089 −0.312827
\(607\) 2.81368 0.114204 0.0571019 0.998368i \(-0.481814\pi\)
0.0571019 + 0.998368i \(0.481814\pi\)
\(608\) 5.71673 0.231844
\(609\) 0.499490 0.0202404
\(610\) −103.839 −4.20432
\(611\) −0.281362 −0.0113827
\(612\) −1.01844 −0.0411679
\(613\) −14.2980 −0.577489 −0.288744 0.957406i \(-0.593238\pi\)
−0.288744 + 0.957406i \(0.593238\pi\)
\(614\) −45.4757 −1.83525
\(615\) −4.89149 −0.197244
\(616\) −0.946697 −0.0381435
\(617\) −47.3397 −1.90582 −0.952912 0.303247i \(-0.901929\pi\)
−0.952912 + 0.303247i \(0.901929\pi\)
\(618\) −20.3209 −0.817426
\(619\) 13.1078 0.526849 0.263424 0.964680i \(-0.415148\pi\)
0.263424 + 0.964680i \(0.415148\pi\)
\(620\) −9.80516 −0.393785
\(621\) −0.204447 −0.00820419
\(622\) −55.5990 −2.22932
\(623\) −2.98742 −0.119689
\(624\) −9.68195 −0.387588
\(625\) 29.7561 1.19025
\(626\) 32.5447 1.30075
\(627\) −0.272111 −0.0108671
\(628\) −13.2873 −0.530219
\(629\) 1.51392 0.0603639
\(630\) −15.0287 −0.598758
\(631\) 1.39625 0.0555840 0.0277920 0.999614i \(-0.491152\pi\)
0.0277920 + 0.999614i \(0.491152\pi\)
\(632\) −1.70533 −0.0678345
\(633\) −21.3932 −0.850304
\(634\) 35.0141 1.39059
\(635\) 30.2660 1.20107
\(636\) −5.60419 −0.222221
\(637\) −4.09132 −0.162104
\(638\) 0.0985717 0.00390249
\(639\) 6.57427 0.260074
\(640\) −46.9531 −1.85599
\(641\) 41.6634 1.64560 0.822802 0.568328i \(-0.192410\pi\)
0.822802 + 0.568328i \(0.192410\pi\)
\(642\) 11.9418 0.471305
\(643\) 40.3886 1.59277 0.796386 0.604789i \(-0.206743\pi\)
0.796386 + 0.604789i \(0.206743\pi\)
\(644\) −0.460309 −0.0181387
\(645\) −27.1866 −1.07047
\(646\) 1.88265 0.0740718
\(647\) −21.2985 −0.837331 −0.418666 0.908140i \(-0.637502\pi\)
−0.418666 + 0.908140i \(0.637502\pi\)
\(648\) 1.70533 0.0669918
\(649\) −3.23403 −0.126947
\(650\) −34.6896 −1.36064
\(651\) −5.43948 −0.213190
\(652\) 22.1389 0.867027
\(653\) −13.5145 −0.528865 −0.264433 0.964404i \(-0.585185\pi\)
−0.264433 + 0.964404i \(0.585185\pi\)
\(654\) 23.4344 0.916358
\(655\) 23.7786 0.929105
\(656\) 6.25007 0.244024
\(657\) 12.3282 0.480968
\(658\) 0.558044 0.0217548
\(659\) 39.6021 1.54268 0.771340 0.636423i \(-0.219587\pi\)
0.771340 + 0.636423i \(0.219587\pi\)
\(660\) −1.00069 −0.0389518
\(661\) −0.739657 −0.0287693 −0.0143847 0.999897i \(-0.504579\pi\)
−0.0143847 + 0.999897i \(0.504579\pi\)
\(662\) 36.9280 1.43525
\(663\) −1.93652 −0.0752083
\(664\) 1.61262 0.0625818
\(665\) 9.37364 0.363494
\(666\) 2.63023 0.101919
\(667\) −0.0461928 −0.00178859
\(668\) −4.14558 −0.160397
\(669\) −10.5593 −0.408245
\(670\) −84.0803 −3.24831
\(671\) −3.83567 −0.148074
\(672\) 11.6628 0.449903
\(673\) −10.7466 −0.414253 −0.207126 0.978314i \(-0.566411\pi\)
−0.207126 + 0.978314i \(0.566411\pi\)
\(674\) 2.20533 0.0849461
\(675\) 10.3106 0.396857
\(676\) −9.42043 −0.362324
\(677\) −10.4011 −0.399749 −0.199874 0.979822i \(-0.564053\pi\)
−0.199874 + 0.979822i \(0.564053\pi\)
\(678\) −16.2054 −0.622366
\(679\) −30.6067 −1.17458
\(680\) −6.67276 −0.255889
\(681\) 7.61930 0.291972
\(682\) −1.07345 −0.0411046
\(683\) −13.8578 −0.530253 −0.265127 0.964214i \(-0.585414\pi\)
−0.265127 + 0.964214i \(0.585414\pi\)
\(684\) 1.10360 0.0421973
\(685\) 25.3792 0.969691
\(686\) 35.0004 1.33632
\(687\) −24.1252 −0.920435
\(688\) 34.7375 1.32435
\(689\) −10.6562 −0.405967
\(690\) 1.38985 0.0529108
\(691\) 32.1785 1.22413 0.612063 0.790809i \(-0.290340\pi\)
0.612063 + 0.790809i \(0.290340\pi\)
\(692\) 15.2755 0.580687
\(693\) −0.555139 −0.0210880
\(694\) −27.1174 −1.02936
\(695\) −16.5756 −0.628750
\(696\) 0.385303 0.0146049
\(697\) 1.25010 0.0473509
\(698\) −29.7212 −1.12496
\(699\) −12.6213 −0.477381
\(700\) 23.2142 0.877415
\(701\) −11.5234 −0.435232 −0.217616 0.976034i \(-0.569828\pi\)
−0.217616 + 0.976034i \(0.569828\pi\)
\(702\) −3.36445 −0.126983
\(703\) −1.64051 −0.0618732
\(704\) −0.209359 −0.00789051
\(705\) −0.568513 −0.0214114
\(706\) −24.8434 −0.934993
\(707\) 9.79905 0.368531
\(708\) 13.1163 0.492939
\(709\) 19.4682 0.731142 0.365571 0.930783i \(-0.380874\pi\)
0.365571 + 0.930783i \(0.380874\pi\)
\(710\) −44.6926 −1.67728
\(711\) −1.00000 −0.0375029
\(712\) −2.30447 −0.0863638
\(713\) 0.503043 0.0188391
\(714\) 3.84083 0.143739
\(715\) −1.90277 −0.0711597
\(716\) 5.42097 0.202591
\(717\) 27.0754 1.01115
\(718\) 13.1514 0.490804
\(719\) 11.5836 0.431997 0.215998 0.976394i \(-0.430699\pi\)
0.215998 + 0.976394i \(0.430699\pi\)
\(720\) −19.5631 −0.729073
\(721\) 25.8574 0.962981
\(722\) 30.9699 1.15258
\(723\) −6.79346 −0.252651
\(724\) −23.3897 −0.869272
\(725\) 2.32959 0.0865186
\(726\) 19.0015 0.705210
\(727\) −6.87787 −0.255086 −0.127543 0.991833i \(-0.540709\pi\)
−0.127543 + 0.991833i \(0.540709\pi\)
\(728\) 7.30071 0.270582
\(729\) 1.00000 0.0370370
\(730\) −83.8083 −3.10188
\(731\) 6.94797 0.256980
\(732\) 15.5563 0.574979
\(733\) −44.7822 −1.65407 −0.827034 0.562153i \(-0.809973\pi\)
−0.827034 + 0.562153i \(0.809973\pi\)
\(734\) 12.6802 0.468035
\(735\) −8.26680 −0.304926
\(736\) −1.07858 −0.0397569
\(737\) −3.10581 −0.114404
\(738\) 2.17188 0.0799479
\(739\) −7.46477 −0.274596 −0.137298 0.990530i \(-0.543842\pi\)
−0.137298 + 0.990530i \(0.543842\pi\)
\(740\) −6.03300 −0.221778
\(741\) 2.09846 0.0770888
\(742\) 21.1350 0.775892
\(743\) 40.0866 1.47063 0.735317 0.677724i \(-0.237033\pi\)
0.735317 + 0.677724i \(0.237033\pi\)
\(744\) −4.19597 −0.153832
\(745\) −16.1733 −0.592545
\(746\) −22.4689 −0.822644
\(747\) 0.945634 0.0345990
\(748\) 0.255742 0.00935087
\(749\) −15.1954 −0.555228
\(750\) −36.1023 −1.31827
\(751\) 25.7287 0.938852 0.469426 0.882972i \(-0.344461\pi\)
0.469426 + 0.882972i \(0.344461\pi\)
\(752\) 0.726414 0.0264896
\(753\) −11.5630 −0.421378
\(754\) −0.760163 −0.0276835
\(755\) −64.9020 −2.36202
\(756\) 2.25148 0.0818856
\(757\) −51.0981 −1.85719 −0.928596 0.371092i \(-0.878984\pi\)
−0.928596 + 0.371092i \(0.878984\pi\)
\(758\) −1.30788 −0.0475043
\(759\) 0.0513392 0.00186350
\(760\) 7.23075 0.262287
\(761\) −40.4674 −1.46694 −0.733471 0.679720i \(-0.762101\pi\)
−0.733471 + 0.679720i \(0.762101\pi\)
\(762\) −13.4384 −0.486823
\(763\) −29.8193 −1.07953
\(764\) 8.19194 0.296374
\(765\) −3.91288 −0.141471
\(766\) −11.1733 −0.403707
\(767\) 24.9401 0.900534
\(768\) 19.1803 0.692109
\(769\) 43.8169 1.58008 0.790038 0.613058i \(-0.210061\pi\)
0.790038 + 0.613058i \(0.210061\pi\)
\(770\) 3.77389 0.136002
\(771\) 4.91211 0.176905
\(772\) 8.02106 0.288684
\(773\) 4.94099 0.177715 0.0888576 0.996044i \(-0.471678\pi\)
0.0888576 + 0.996044i \(0.471678\pi\)
\(774\) 12.0712 0.433889
\(775\) −25.3693 −0.911293
\(776\) −23.6097 −0.847540
\(777\) −3.34685 −0.120068
\(778\) −13.6812 −0.490496
\(779\) −1.35463 −0.0485348
\(780\) 7.71709 0.276316
\(781\) −1.65088 −0.0590732
\(782\) −0.355200 −0.0127019
\(783\) 0.225940 0.00807443
\(784\) 10.5629 0.377245
\(785\) −51.0502 −1.82206
\(786\) −10.5580 −0.376590
\(787\) −28.8053 −1.02680 −0.513399 0.858150i \(-0.671614\pi\)
−0.513399 + 0.858150i \(0.671614\pi\)
\(788\) −7.37036 −0.262558
\(789\) −2.63845 −0.0939314
\(790\) 6.79810 0.241866
\(791\) 20.6207 0.733188
\(792\) −0.428230 −0.0152165
\(793\) 29.5798 1.05041
\(794\) 38.8867 1.38004
\(795\) −21.5315 −0.763645
\(796\) −8.77631 −0.311068
\(797\) 13.8433 0.490354 0.245177 0.969478i \(-0.421154\pi\)
0.245177 + 0.969478i \(0.421154\pi\)
\(798\) −4.16201 −0.147333
\(799\) 0.145293 0.00514008
\(800\) 54.3945 1.92314
\(801\) −1.35133 −0.0477471
\(802\) 42.4087 1.49750
\(803\) −3.09576 −0.109247
\(804\) 12.5962 0.444235
\(805\) −1.76853 −0.0623324
\(806\) 8.27822 0.291588
\(807\) −13.2737 −0.467258
\(808\) 7.55891 0.265921
\(809\) −16.7477 −0.588818 −0.294409 0.955679i \(-0.595123\pi\)
−0.294409 + 0.955679i \(0.595123\pi\)
\(810\) −6.79810 −0.238861
\(811\) −17.0947 −0.600275 −0.300138 0.953896i \(-0.597033\pi\)
−0.300138 + 0.953896i \(0.597033\pi\)
\(812\) 0.508700 0.0178519
\(813\) −10.0676 −0.353086
\(814\) −0.660483 −0.0231499
\(815\) 85.0587 2.97947
\(816\) 4.99966 0.175023
\(817\) −7.52898 −0.263406
\(818\) 11.4286 0.399593
\(819\) 4.28111 0.149594
\(820\) −4.98168 −0.173968
\(821\) −18.4262 −0.643079 −0.321539 0.946896i \(-0.604200\pi\)
−0.321539 + 0.946896i \(0.604200\pi\)
\(822\) −11.2687 −0.393040
\(823\) 9.22044 0.321404 0.160702 0.987003i \(-0.448624\pi\)
0.160702 + 0.987003i \(0.448624\pi\)
\(824\) 19.9462 0.694859
\(825\) −2.58913 −0.0901419
\(826\) −49.4653 −1.72112
\(827\) −36.5561 −1.27118 −0.635590 0.772027i \(-0.719243\pi\)
−0.635590 + 0.772027i \(0.719243\pi\)
\(828\) −0.208217 −0.00723604
\(829\) 31.4955 1.09388 0.546942 0.837170i \(-0.315792\pi\)
0.546942 + 0.837170i \(0.315792\pi\)
\(830\) −6.42852 −0.223137
\(831\) −8.38310 −0.290807
\(832\) 1.61453 0.0559737
\(833\) 2.11271 0.0732012
\(834\) 7.35977 0.254848
\(835\) −15.9275 −0.551194
\(836\) −0.277128 −0.00958467
\(837\) −2.46050 −0.0850473
\(838\) −1.80494 −0.0623505
\(839\) 40.5201 1.39891 0.699455 0.714676i \(-0.253426\pi\)
0.699455 + 0.714676i \(0.253426\pi\)
\(840\) 14.7516 0.508979
\(841\) −28.9490 −0.998240
\(842\) −59.2942 −2.04341
\(843\) 30.8757 1.06342
\(844\) −21.7877 −0.749963
\(845\) −36.1937 −1.24510
\(846\) 0.252426 0.00867860
\(847\) −24.1785 −0.830784
\(848\) 27.5118 0.944758
\(849\) −4.62332 −0.158672
\(850\) 17.9134 0.614423
\(851\) 0.309516 0.0106101
\(852\) 6.69549 0.229384
\(853\) 43.9649 1.50533 0.752665 0.658403i \(-0.228768\pi\)
0.752665 + 0.658403i \(0.228768\pi\)
\(854\) −58.6676 −2.00756
\(855\) 4.24008 0.145008
\(856\) −11.7216 −0.400636
\(857\) −37.2423 −1.27217 −0.636087 0.771618i \(-0.719448\pi\)
−0.636087 + 0.771618i \(0.719448\pi\)
\(858\) 0.844854 0.0288428
\(859\) −30.4889 −1.04027 −0.520134 0.854085i \(-0.674118\pi\)
−0.520134 + 0.854085i \(0.674118\pi\)
\(860\) −27.6879 −0.944148
\(861\) −2.76362 −0.0941839
\(862\) 21.4415 0.730300
\(863\) 8.19926 0.279106 0.139553 0.990215i \(-0.455433\pi\)
0.139553 + 0.990215i \(0.455433\pi\)
\(864\) 5.27557 0.179479
\(865\) 58.6891 1.99549
\(866\) −16.7289 −0.568470
\(867\) 1.00000 0.0339618
\(868\) −5.53977 −0.188032
\(869\) 0.251112 0.00851840
\(870\) −1.53596 −0.0520740
\(871\) 23.9513 0.811558
\(872\) −23.0023 −0.778957
\(873\) −13.8447 −0.468571
\(874\) 0.384902 0.0130195
\(875\) 45.9386 1.55301
\(876\) 12.5555 0.424211
\(877\) −34.2171 −1.15543 −0.577715 0.816238i \(-0.696056\pi\)
−0.577715 + 0.816238i \(0.696056\pi\)
\(878\) −12.5572 −0.423785
\(879\) 20.4561 0.689968
\(880\) 4.91253 0.165601
\(881\) −57.3270 −1.93139 −0.965697 0.259671i \(-0.916386\pi\)
−0.965697 + 0.259671i \(0.916386\pi\)
\(882\) 3.67056 0.123594
\(883\) −31.5028 −1.06015 −0.530077 0.847950i \(-0.677837\pi\)
−0.530077 + 0.847950i \(0.677837\pi\)
\(884\) −1.97223 −0.0663332
\(885\) 50.3932 1.69395
\(886\) 49.0609 1.64823
\(887\) −6.35239 −0.213292 −0.106646 0.994297i \(-0.534011\pi\)
−0.106646 + 0.994297i \(0.534011\pi\)
\(888\) −2.58173 −0.0866373
\(889\) 17.0998 0.573510
\(890\) 9.18652 0.307933
\(891\) −0.251112 −0.00841258
\(892\) −10.7540 −0.360069
\(893\) −0.157442 −0.00526860
\(894\) 7.18114 0.240173
\(895\) 20.8276 0.696189
\(896\) −26.5278 −0.886232
\(897\) −0.395917 −0.0132193
\(898\) −32.8329 −1.09565
\(899\) −0.555925 −0.0185411
\(900\) 10.5007 0.350025
\(901\) 5.50273 0.183322
\(902\) −0.545386 −0.0181594
\(903\) −15.3600 −0.511150
\(904\) 15.9066 0.529047
\(905\) −89.8643 −2.98719
\(906\) 28.8172 0.957388
\(907\) 1.03147 0.0342495 0.0171248 0.999853i \(-0.494549\pi\)
0.0171248 + 0.999853i \(0.494549\pi\)
\(908\) 7.75979 0.257518
\(909\) 4.43251 0.147017
\(910\) −29.1034 −0.964769
\(911\) 10.6471 0.352753 0.176377 0.984323i \(-0.443562\pi\)
0.176377 + 0.984323i \(0.443562\pi\)
\(912\) −5.41774 −0.179399
\(913\) −0.237460 −0.00785879
\(914\) 8.33955 0.275848
\(915\) 59.7681 1.97587
\(916\) −24.5700 −0.811817
\(917\) 13.4345 0.443647
\(918\) 1.73737 0.0573416
\(919\) −21.1582 −0.697944 −0.348972 0.937133i \(-0.613469\pi\)
−0.348972 + 0.937133i \(0.613469\pi\)
\(920\) −1.36423 −0.0449773
\(921\) 26.1751 0.862499
\(922\) 19.2435 0.633752
\(923\) 12.7312 0.419053
\(924\) −0.565375 −0.0185995
\(925\) −15.6095 −0.513236
\(926\) 36.3245 1.19370
\(927\) 11.6964 0.384160
\(928\) 1.19196 0.0391281
\(929\) 47.3661 1.55403 0.777015 0.629482i \(-0.216733\pi\)
0.777015 + 0.629482i \(0.216733\pi\)
\(930\) 16.7267 0.548491
\(931\) −2.28938 −0.0750315
\(932\) −12.8540 −0.421047
\(933\) 32.0019 1.04770
\(934\) −21.2795 −0.696286
\(935\) 0.982573 0.0321336
\(936\) 3.30241 0.107943
\(937\) 23.8234 0.778276 0.389138 0.921179i \(-0.372773\pi\)
0.389138 + 0.921179i \(0.372773\pi\)
\(938\) −47.5041 −1.55106
\(939\) −18.7322 −0.611303
\(940\) −0.578995 −0.0188847
\(941\) −37.3366 −1.21714 −0.608570 0.793501i \(-0.708256\pi\)
−0.608570 + 0.793501i \(0.708256\pi\)
\(942\) 22.6669 0.738527
\(943\) 0.255579 0.00832281
\(944\) −64.3896 −2.09570
\(945\) 8.65029 0.281394
\(946\) −3.03122 −0.0985534
\(947\) 2.93765 0.0954606 0.0477303 0.998860i \(-0.484801\pi\)
0.0477303 + 0.998860i \(0.484801\pi\)
\(948\) −1.01844 −0.0330773
\(949\) 23.8738 0.774976
\(950\) −19.4113 −0.629786
\(951\) −20.1536 −0.653524
\(952\) −3.77001 −0.122187
\(953\) −48.7093 −1.57785 −0.788924 0.614490i \(-0.789362\pi\)
−0.788924 + 0.614490i \(0.789362\pi\)
\(954\) 9.56025 0.309525
\(955\) 31.4738 1.01847
\(956\) 27.5746 0.891825
\(957\) −0.0567363 −0.00183402
\(958\) 9.96230 0.321867
\(959\) 14.3389 0.463027
\(960\) 3.26227 0.105289
\(961\) −24.9459 −0.804708
\(962\) 5.09349 0.164221
\(963\) −6.87350 −0.221496
\(964\) −6.91871 −0.222837
\(965\) 30.8173 0.992043
\(966\) 0.785247 0.0252649
\(967\) −6.44367 −0.207215 −0.103607 0.994618i \(-0.533039\pi\)
−0.103607 + 0.994618i \(0.533039\pi\)
\(968\) −18.6511 −0.599470
\(969\) −1.08362 −0.0348110
\(970\) 94.1174 3.02193
\(971\) −40.4855 −1.29924 −0.649621 0.760258i \(-0.725072\pi\)
−0.649621 + 0.760258i \(0.725072\pi\)
\(972\) 1.01844 0.0326664
\(973\) −9.36499 −0.300228
\(974\) −59.3954 −1.90315
\(975\) 19.9668 0.639449
\(976\) −76.3684 −2.44449
\(977\) 18.4251 0.589470 0.294735 0.955579i \(-0.404769\pi\)
0.294735 + 0.955579i \(0.404769\pi\)
\(978\) −37.7670 −1.20766
\(979\) 0.339337 0.0108453
\(980\) −8.41922 −0.268942
\(981\) −13.4885 −0.430654
\(982\) −3.61970 −0.115509
\(983\) −13.6544 −0.435507 −0.217754 0.976004i \(-0.569873\pi\)
−0.217754 + 0.976004i \(0.569873\pi\)
\(984\) −2.13183 −0.0679604
\(985\) −28.3172 −0.902262
\(986\) 0.392540 0.0125010
\(987\) −0.321201 −0.0102240
\(988\) 2.13715 0.0679918
\(989\) 1.42049 0.0451691
\(990\) 1.70709 0.0542548
\(991\) −21.1235 −0.671010 −0.335505 0.942038i \(-0.608907\pi\)
−0.335505 + 0.942038i \(0.608907\pi\)
\(992\) −12.9805 −0.412133
\(993\) −21.2552 −0.674512
\(994\) −25.2507 −0.800902
\(995\) −33.7190 −1.06896
\(996\) 0.963070 0.0305160
\(997\) 46.1042 1.46013 0.730067 0.683375i \(-0.239489\pi\)
0.730067 + 0.683375i \(0.239489\pi\)
\(998\) 46.0937 1.45907
\(999\) −1.51392 −0.0478982
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 4029.2.a.j.1.5 25
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.j.1.5 25 1.1 even 1 trivial