Properties

Label 6035.2.a.g.1.12
Level $6035$
Weight $2$
Character 6035.1
Self dual yes
Analytic conductor $48.190$
Analytic rank $0$
Dimension $58$
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] = [6035,2,Mod(1,6035)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6035, 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("6035.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6035 = 5 \cdot 17 \cdot 71 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6035.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: \(48.1897176198\)
Analytic rank: \(0\)
Dimension: \(58\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) \(=\) 6035.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00836 q^{2} +0.177134 q^{3} +2.03352 q^{4} +1.00000 q^{5} -0.355749 q^{6} -1.65376 q^{7} -0.0673116 q^{8} -2.96862 q^{9} +O(q^{10})\) \(q-2.00836 q^{2} +0.177134 q^{3} +2.03352 q^{4} +1.00000 q^{5} -0.355749 q^{6} -1.65376 q^{7} -0.0673116 q^{8} -2.96862 q^{9} -2.00836 q^{10} +3.65244 q^{11} +0.360205 q^{12} -3.93545 q^{13} +3.32135 q^{14} +0.177134 q^{15} -3.93185 q^{16} +1.00000 q^{17} +5.96207 q^{18} +2.30295 q^{19} +2.03352 q^{20} -0.292937 q^{21} -7.33542 q^{22} +6.71610 q^{23} -0.0119232 q^{24} +1.00000 q^{25} +7.90381 q^{26} -1.05725 q^{27} -3.36295 q^{28} +0.825756 q^{29} -0.355749 q^{30} -1.46380 q^{31} +8.03119 q^{32} +0.646971 q^{33} -2.00836 q^{34} -1.65376 q^{35} -6.03674 q^{36} -4.65274 q^{37} -4.62516 q^{38} -0.697102 q^{39} -0.0673116 q^{40} +10.9166 q^{41} +0.588324 q^{42} +2.83622 q^{43} +7.42729 q^{44} -2.96862 q^{45} -13.4884 q^{46} -5.31053 q^{47} -0.696463 q^{48} -4.26507 q^{49} -2.00836 q^{50} +0.177134 q^{51} -8.00280 q^{52} -2.16736 q^{53} +2.12333 q^{54} +3.65244 q^{55} +0.111317 q^{56} +0.407931 q^{57} -1.65842 q^{58} +5.58656 q^{59} +0.360205 q^{60} -10.4573 q^{61} +2.93984 q^{62} +4.90940 q^{63} -8.26584 q^{64} -3.93545 q^{65} -1.29935 q^{66} -9.86643 q^{67} +2.03352 q^{68} +1.18965 q^{69} +3.32135 q^{70} +1.00000 q^{71} +0.199823 q^{72} +0.726747 q^{73} +9.34439 q^{74} +0.177134 q^{75} +4.68309 q^{76} -6.04026 q^{77} +1.40003 q^{78} +12.4095 q^{79} -3.93185 q^{80} +8.71860 q^{81} -21.9244 q^{82} +4.93092 q^{83} -0.595693 q^{84} +1.00000 q^{85} -5.69616 q^{86} +0.146269 q^{87} -0.245851 q^{88} -16.6630 q^{89} +5.96207 q^{90} +6.50830 q^{91} +13.6573 q^{92} -0.259288 q^{93} +10.6655 q^{94} +2.30295 q^{95} +1.42260 q^{96} -9.51989 q^{97} +8.56580 q^{98} -10.8427 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58 q + q^{2} + 6 q^{3} + 69 q^{4} + 58 q^{5} + 10 q^{6} + 13 q^{7} - 3 q^{8} + 84 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 58 q + q^{2} + 6 q^{3} + 69 q^{4} + 58 q^{5} + 10 q^{6} + 13 q^{7} - 3 q^{8} + 84 q^{9} + q^{10} + 28 q^{11} + 18 q^{12} + 37 q^{13} + 28 q^{14} + 6 q^{15} + 83 q^{16} + 58 q^{17} - 12 q^{18} + 19 q^{19} + 69 q^{20} + 31 q^{21} + 13 q^{22} + 14 q^{23} + 13 q^{24} + 58 q^{25} + 18 q^{26} + 9 q^{27} + 8 q^{28} + 60 q^{29} + 10 q^{30} + 39 q^{31} - 30 q^{32} + 13 q^{33} + q^{34} + 13 q^{35} + 113 q^{36} + 60 q^{37} - q^{38} + 41 q^{39} - 3 q^{40} + 65 q^{41} - 30 q^{42} + 17 q^{43} + 69 q^{44} + 84 q^{45} + 24 q^{46} + 16 q^{47} + 14 q^{48} + 117 q^{49} + q^{50} + 6 q^{51} + 61 q^{52} + 5 q^{53} + 24 q^{54} + 28 q^{55} + 105 q^{56} + 8 q^{57} - 34 q^{58} + 22 q^{59} + 18 q^{60} + 113 q^{61} - 19 q^{62} + 8 q^{63} + 89 q^{64} + 37 q^{65} - 37 q^{66} + 19 q^{67} + 69 q^{68} + 75 q^{69} + 28 q^{70} + 58 q^{71} - 17 q^{72} + 49 q^{73} + 29 q^{74} + 6 q^{75} - 6 q^{76} + 17 q^{77} - 12 q^{78} + 7 q^{79} + 83 q^{80} + 134 q^{81} + 7 q^{82} - 12 q^{83} - 18 q^{84} + 58 q^{85} + 23 q^{86} - 36 q^{87} - 33 q^{88} + 52 q^{89} - 12 q^{90} + 31 q^{91} + 80 q^{92} - 37 q^{93} + 4 q^{94} + 19 q^{95} - 35 q^{96} + 26 q^{97} - 33 q^{98} + 57 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00836 −1.42013 −0.710063 0.704138i \(-0.751334\pi\)
−0.710063 + 0.704138i \(0.751334\pi\)
\(3\) 0.177134 0.102268 0.0511342 0.998692i \(-0.483716\pi\)
0.0511342 + 0.998692i \(0.483716\pi\)
\(4\) 2.03352 1.01676
\(5\) 1.00000 0.447214
\(6\) −0.355749 −0.145234
\(7\) −1.65376 −0.625063 −0.312532 0.949907i \(-0.601177\pi\)
−0.312532 + 0.949907i \(0.601177\pi\)
\(8\) −0.0673116 −0.0237982
\(9\) −2.96862 −0.989541
\(10\) −2.00836 −0.635100
\(11\) 3.65244 1.10125 0.550626 0.834752i \(-0.314389\pi\)
0.550626 + 0.834752i \(0.314389\pi\)
\(12\) 0.360205 0.103982
\(13\) −3.93545 −1.09150 −0.545749 0.837949i \(-0.683755\pi\)
−0.545749 + 0.837949i \(0.683755\pi\)
\(14\) 3.32135 0.887669
\(15\) 0.177134 0.0457358
\(16\) −3.93185 −0.982961
\(17\) 1.00000 0.242536
\(18\) 5.96207 1.40527
\(19\) 2.30295 0.528333 0.264167 0.964477i \(-0.414903\pi\)
0.264167 + 0.964477i \(0.414903\pi\)
\(20\) 2.03352 0.454708
\(21\) −0.292937 −0.0639242
\(22\) −7.33542 −1.56392
\(23\) 6.71610 1.40040 0.700202 0.713945i \(-0.253093\pi\)
0.700202 + 0.713945i \(0.253093\pi\)
\(24\) −0.0119232 −0.00243381
\(25\) 1.00000 0.200000
\(26\) 7.90381 1.55006
\(27\) −1.05725 −0.203467
\(28\) −3.36295 −0.635538
\(29\) 0.825756 0.153339 0.0766696 0.997057i \(-0.475571\pi\)
0.0766696 + 0.997057i \(0.475571\pi\)
\(30\) −0.355749 −0.0649506
\(31\) −1.46380 −0.262906 −0.131453 0.991322i \(-0.541964\pi\)
−0.131453 + 0.991322i \(0.541964\pi\)
\(32\) 8.03119 1.41973
\(33\) 0.646971 0.112623
\(34\) −2.00836 −0.344431
\(35\) −1.65376 −0.279537
\(36\) −6.03674 −1.00612
\(37\) −4.65274 −0.764906 −0.382453 0.923975i \(-0.624921\pi\)
−0.382453 + 0.923975i \(0.624921\pi\)
\(38\) −4.62516 −0.750299
\(39\) −0.697102 −0.111626
\(40\) −0.0673116 −0.0106429
\(41\) 10.9166 1.70488 0.852442 0.522822i \(-0.175121\pi\)
0.852442 + 0.522822i \(0.175121\pi\)
\(42\) 0.588324 0.0907804
\(43\) 2.83622 0.432520 0.216260 0.976336i \(-0.430614\pi\)
0.216260 + 0.976336i \(0.430614\pi\)
\(44\) 7.42729 1.11971
\(45\) −2.96862 −0.442536
\(46\) −13.4884 −1.98875
\(47\) −5.31053 −0.774621 −0.387311 0.921949i \(-0.626596\pi\)
−0.387311 + 0.921949i \(0.626596\pi\)
\(48\) −0.696463 −0.100526
\(49\) −4.26507 −0.609296
\(50\) −2.00836 −0.284025
\(51\) 0.177134 0.0248037
\(52\) −8.00280 −1.10979
\(53\) −2.16736 −0.297710 −0.148855 0.988859i \(-0.547559\pi\)
−0.148855 + 0.988859i \(0.547559\pi\)
\(54\) 2.12333 0.288949
\(55\) 3.65244 0.492495
\(56\) 0.111317 0.0148754
\(57\) 0.407931 0.0540317
\(58\) −1.65842 −0.217761
\(59\) 5.58656 0.727308 0.363654 0.931534i \(-0.381529\pi\)
0.363654 + 0.931534i \(0.381529\pi\)
\(60\) 0.360205 0.0465022
\(61\) −10.4573 −1.33892 −0.669461 0.742847i \(-0.733475\pi\)
−0.669461 + 0.742847i \(0.733475\pi\)
\(62\) 2.93984 0.373359
\(63\) 4.90940 0.618526
\(64\) −8.26584 −1.03323
\(65\) −3.93545 −0.488132
\(66\) −1.29935 −0.159939
\(67\) −9.86643 −1.20538 −0.602688 0.797977i \(-0.705904\pi\)
−0.602688 + 0.797977i \(0.705904\pi\)
\(68\) 2.03352 0.246600
\(69\) 1.18965 0.143217
\(70\) 3.32135 0.396977
\(71\) 1.00000 0.118678
\(72\) 0.199823 0.0235493
\(73\) 0.726747 0.0850594 0.0425297 0.999095i \(-0.486458\pi\)
0.0425297 + 0.999095i \(0.486458\pi\)
\(74\) 9.34439 1.08626
\(75\) 0.177134 0.0204537
\(76\) 4.68309 0.537187
\(77\) −6.04026 −0.688352
\(78\) 1.40003 0.158522
\(79\) 12.4095 1.39618 0.698088 0.716012i \(-0.254035\pi\)
0.698088 + 0.716012i \(0.254035\pi\)
\(80\) −3.93185 −0.439594
\(81\) 8.71860 0.968733
\(82\) −21.9244 −2.42115
\(83\) 4.93092 0.541239 0.270619 0.962686i \(-0.412771\pi\)
0.270619 + 0.962686i \(0.412771\pi\)
\(84\) −0.595693 −0.0649954
\(85\) 1.00000 0.108465
\(86\) −5.69616 −0.614233
\(87\) 0.146269 0.0156817
\(88\) −0.245851 −0.0262078
\(89\) −16.6630 −1.76627 −0.883135 0.469118i \(-0.844572\pi\)
−0.883135 + 0.469118i \(0.844572\pi\)
\(90\) 5.96207 0.628457
\(91\) 6.50830 0.682255
\(92\) 13.6573 1.42387
\(93\) −0.259288 −0.0268869
\(94\) 10.6655 1.10006
\(95\) 2.30295 0.236278
\(96\) 1.42260 0.145193
\(97\) −9.51989 −0.966599 −0.483299 0.875455i \(-0.660562\pi\)
−0.483299 + 0.875455i \(0.660562\pi\)
\(98\) 8.56580 0.865277
\(99\) −10.8427 −1.08973
\(100\) 2.03352 0.203352
\(101\) 13.6698 1.36019 0.680096 0.733123i \(-0.261938\pi\)
0.680096 + 0.733123i \(0.261938\pi\)
\(102\) −0.355749 −0.0352244
\(103\) −2.43188 −0.239620 −0.119810 0.992797i \(-0.538229\pi\)
−0.119810 + 0.992797i \(0.538229\pi\)
\(104\) 0.264901 0.0259757
\(105\) −0.292937 −0.0285878
\(106\) 4.35285 0.422786
\(107\) 5.64044 0.545281 0.272641 0.962116i \(-0.412103\pi\)
0.272641 + 0.962116i \(0.412103\pi\)
\(108\) −2.14993 −0.206877
\(109\) −12.6398 −1.21067 −0.605336 0.795970i \(-0.706961\pi\)
−0.605336 + 0.795970i \(0.706961\pi\)
\(110\) −7.33542 −0.699404
\(111\) −0.824158 −0.0782256
\(112\) 6.50234 0.614413
\(113\) −5.07155 −0.477091 −0.238546 0.971131i \(-0.576671\pi\)
−0.238546 + 0.971131i \(0.576671\pi\)
\(114\) −0.819272 −0.0767319
\(115\) 6.71610 0.626280
\(116\) 1.67919 0.155909
\(117\) 11.6829 1.08008
\(118\) −11.2198 −1.03287
\(119\) −1.65376 −0.151600
\(120\) −0.0119232 −0.00108843
\(121\) 2.34030 0.212755
\(122\) 21.0021 1.90144
\(123\) 1.93370 0.174356
\(124\) −2.97666 −0.267312
\(125\) 1.00000 0.0894427
\(126\) −9.85984 −0.878385
\(127\) 0.0180324 0.00160011 0.000800057 1.00000i \(-0.499745\pi\)
0.000800057 1.00000i \(0.499745\pi\)
\(128\) 0.538417 0.0475898
\(129\) 0.502391 0.0442331
\(130\) 7.90381 0.693210
\(131\) 19.3083 1.68698 0.843488 0.537148i \(-0.180498\pi\)
0.843488 + 0.537148i \(0.180498\pi\)
\(132\) 1.31563 0.114510
\(133\) −3.80853 −0.330242
\(134\) 19.8154 1.71179
\(135\) −1.05725 −0.0909932
\(136\) −0.0673116 −0.00577192
\(137\) 18.3264 1.56573 0.782865 0.622192i \(-0.213758\pi\)
0.782865 + 0.622192i \(0.213758\pi\)
\(138\) −2.38925 −0.203386
\(139\) 5.88400 0.499074 0.249537 0.968365i \(-0.419722\pi\)
0.249537 + 0.968365i \(0.419722\pi\)
\(140\) −3.36295 −0.284221
\(141\) −0.940676 −0.0792192
\(142\) −2.00836 −0.168538
\(143\) −14.3740 −1.20201
\(144\) 11.6722 0.972681
\(145\) 0.825756 0.0685753
\(146\) −1.45957 −0.120795
\(147\) −0.755489 −0.0623117
\(148\) −9.46142 −0.777724
\(149\) 14.3188 1.17304 0.586522 0.809934i \(-0.300497\pi\)
0.586522 + 0.809934i \(0.300497\pi\)
\(150\) −0.355749 −0.0290468
\(151\) 1.10586 0.0899938 0.0449969 0.998987i \(-0.485672\pi\)
0.0449969 + 0.998987i \(0.485672\pi\)
\(152\) −0.155015 −0.0125734
\(153\) −2.96862 −0.239999
\(154\) 12.1310 0.977546
\(155\) −1.46380 −0.117575
\(156\) −1.41757 −0.113496
\(157\) −11.6735 −0.931643 −0.465821 0.884879i \(-0.654241\pi\)
−0.465821 + 0.884879i \(0.654241\pi\)
\(158\) −24.9227 −1.98274
\(159\) −0.383913 −0.0304463
\(160\) 8.03119 0.634921
\(161\) −11.1068 −0.875342
\(162\) −17.5101 −1.37572
\(163\) 5.40040 0.422992 0.211496 0.977379i \(-0.432166\pi\)
0.211496 + 0.977379i \(0.432166\pi\)
\(164\) 22.1990 1.73345
\(165\) 0.646971 0.0503666
\(166\) −9.90307 −0.768627
\(167\) 10.3466 0.800644 0.400322 0.916375i \(-0.368898\pi\)
0.400322 + 0.916375i \(0.368898\pi\)
\(168\) 0.0197181 0.00152128
\(169\) 2.48777 0.191367
\(170\) −2.00836 −0.154034
\(171\) −6.83659 −0.522807
\(172\) 5.76751 0.439768
\(173\) 6.20238 0.471558 0.235779 0.971807i \(-0.424236\pi\)
0.235779 + 0.971807i \(0.424236\pi\)
\(174\) −0.293762 −0.0222700
\(175\) −1.65376 −0.125013
\(176\) −14.3608 −1.08249
\(177\) 0.989569 0.0743805
\(178\) 33.4653 2.50833
\(179\) −2.29474 −0.171517 −0.0857585 0.996316i \(-0.527331\pi\)
−0.0857585 + 0.996316i \(0.527331\pi\)
\(180\) −6.03674 −0.449952
\(181\) 2.80181 0.208257 0.104128 0.994564i \(-0.466795\pi\)
0.104128 + 0.994564i \(0.466795\pi\)
\(182\) −13.0710 −0.968888
\(183\) −1.85235 −0.136929
\(184\) −0.452072 −0.0333272
\(185\) −4.65274 −0.342076
\(186\) 0.520745 0.0381828
\(187\) 3.65244 0.267093
\(188\) −10.7991 −0.787602
\(189\) 1.74843 0.127180
\(190\) −4.62516 −0.335544
\(191\) 7.82504 0.566200 0.283100 0.959090i \(-0.408637\pi\)
0.283100 + 0.959090i \(0.408637\pi\)
\(192\) −1.46416 −0.105667
\(193\) −4.79443 −0.345111 −0.172555 0.985000i \(-0.555202\pi\)
−0.172555 + 0.985000i \(0.555202\pi\)
\(194\) 19.1194 1.37269
\(195\) −0.697102 −0.0499205
\(196\) −8.67309 −0.619506
\(197\) −12.8939 −0.918653 −0.459326 0.888268i \(-0.651909\pi\)
−0.459326 + 0.888268i \(0.651909\pi\)
\(198\) 21.7761 1.54756
\(199\) 4.18811 0.296887 0.148444 0.988921i \(-0.452574\pi\)
0.148444 + 0.988921i \(0.452574\pi\)
\(200\) −0.0673116 −0.00475965
\(201\) −1.74768 −0.123272
\(202\) −27.4538 −1.93164
\(203\) −1.36560 −0.0958467
\(204\) 0.360205 0.0252194
\(205\) 10.9166 0.762447
\(206\) 4.88408 0.340290
\(207\) −19.9376 −1.38576
\(208\) 15.4736 1.07290
\(209\) 8.41138 0.581828
\(210\) 0.588324 0.0405982
\(211\) −10.2783 −0.707588 −0.353794 0.935323i \(-0.615109\pi\)
−0.353794 + 0.935323i \(0.615109\pi\)
\(212\) −4.40736 −0.302699
\(213\) 0.177134 0.0121370
\(214\) −11.3280 −0.774368
\(215\) 2.83622 0.193429
\(216\) 0.0711649 0.00484216
\(217\) 2.42077 0.164333
\(218\) 25.3852 1.71931
\(219\) 0.128732 0.00869888
\(220\) 7.42729 0.500748
\(221\) −3.93545 −0.264727
\(222\) 1.65521 0.111090
\(223\) 6.19438 0.414806 0.207403 0.978256i \(-0.433499\pi\)
0.207403 + 0.978256i \(0.433499\pi\)
\(224\) −13.2817 −0.887419
\(225\) −2.96862 −0.197908
\(226\) 10.1855 0.677530
\(227\) −15.6112 −1.03615 −0.518077 0.855334i \(-0.673352\pi\)
−0.518077 + 0.855334i \(0.673352\pi\)
\(228\) 0.829533 0.0549372
\(229\) 13.2502 0.875597 0.437799 0.899073i \(-0.355758\pi\)
0.437799 + 0.899073i \(0.355758\pi\)
\(230\) −13.4884 −0.889396
\(231\) −1.06994 −0.0703966
\(232\) −0.0555830 −0.00364920
\(233\) 3.25183 0.213034 0.106517 0.994311i \(-0.466030\pi\)
0.106517 + 0.994311i \(0.466030\pi\)
\(234\) −23.4634 −1.53385
\(235\) −5.31053 −0.346421
\(236\) 11.3604 0.739496
\(237\) 2.19814 0.142784
\(238\) 3.32135 0.215291
\(239\) 27.2189 1.76065 0.880323 0.474374i \(-0.157326\pi\)
0.880323 + 0.474374i \(0.157326\pi\)
\(240\) −0.696463 −0.0449565
\(241\) 4.37592 0.281878 0.140939 0.990018i \(-0.454988\pi\)
0.140939 + 0.990018i \(0.454988\pi\)
\(242\) −4.70018 −0.302139
\(243\) 4.71610 0.302538
\(244\) −21.2651 −1.36136
\(245\) −4.26507 −0.272485
\(246\) −3.88356 −0.247607
\(247\) −9.06315 −0.576674
\(248\) 0.0985306 0.00625670
\(249\) 0.873433 0.0553516
\(250\) −2.00836 −0.127020
\(251\) −5.87688 −0.370945 −0.185473 0.982649i \(-0.559382\pi\)
−0.185473 + 0.982649i \(0.559382\pi\)
\(252\) 9.98334 0.628891
\(253\) 24.5302 1.54220
\(254\) −0.0362155 −0.00227236
\(255\) 0.177134 0.0110926
\(256\) 15.4503 0.965647
\(257\) −9.05219 −0.564660 −0.282330 0.959317i \(-0.591107\pi\)
−0.282330 + 0.959317i \(0.591107\pi\)
\(258\) −1.00898 −0.0628166
\(259\) 7.69453 0.478115
\(260\) −8.00280 −0.496313
\(261\) −2.45136 −0.151735
\(262\) −38.7781 −2.39572
\(263\) −0.980568 −0.0604644 −0.0302322 0.999543i \(-0.509625\pi\)
−0.0302322 + 0.999543i \(0.509625\pi\)
\(264\) −0.0435486 −0.00268023
\(265\) −2.16736 −0.133140
\(266\) 7.64891 0.468985
\(267\) −2.95158 −0.180634
\(268\) −20.0635 −1.22558
\(269\) 20.4279 1.24551 0.622754 0.782417i \(-0.286014\pi\)
0.622754 + 0.782417i \(0.286014\pi\)
\(270\) 2.12333 0.129222
\(271\) 30.3650 1.84455 0.922273 0.386540i \(-0.126330\pi\)
0.922273 + 0.386540i \(0.126330\pi\)
\(272\) −3.93185 −0.238403
\(273\) 1.15284 0.0697731
\(274\) −36.8060 −2.22353
\(275\) 3.65244 0.220250
\(276\) 2.41917 0.145617
\(277\) 16.4346 0.987458 0.493729 0.869616i \(-0.335633\pi\)
0.493729 + 0.869616i \(0.335633\pi\)
\(278\) −11.8172 −0.708748
\(279\) 4.34547 0.260156
\(280\) 0.111317 0.00665248
\(281\) −12.5015 −0.745777 −0.372888 0.927876i \(-0.621633\pi\)
−0.372888 + 0.927876i \(0.621633\pi\)
\(282\) 1.88922 0.112501
\(283\) 6.98244 0.415063 0.207531 0.978228i \(-0.433457\pi\)
0.207531 + 0.978228i \(0.433457\pi\)
\(284\) 2.03352 0.120667
\(285\) 0.407931 0.0241637
\(286\) 28.8682 1.70701
\(287\) −18.0534 −1.06566
\(288\) −23.8416 −1.40488
\(289\) 1.00000 0.0588235
\(290\) −1.65842 −0.0973856
\(291\) −1.68630 −0.0988524
\(292\) 1.47785 0.0864848
\(293\) −25.2987 −1.47797 −0.738983 0.673724i \(-0.764694\pi\)
−0.738983 + 0.673724i \(0.764694\pi\)
\(294\) 1.51729 0.0884904
\(295\) 5.58656 0.325262
\(296\) 0.313183 0.0182034
\(297\) −3.86152 −0.224068
\(298\) −28.7574 −1.66587
\(299\) −26.4309 −1.52854
\(300\) 0.360205 0.0207964
\(301\) −4.69044 −0.270352
\(302\) −2.22097 −0.127802
\(303\) 2.42138 0.139105
\(304\) −9.05484 −0.519331
\(305\) −10.4573 −0.598784
\(306\) 5.96207 0.340829
\(307\) −10.4225 −0.594842 −0.297421 0.954746i \(-0.596126\pi\)
−0.297421 + 0.954746i \(0.596126\pi\)
\(308\) −12.2830 −0.699887
\(309\) −0.430768 −0.0245055
\(310\) 2.93984 0.166971
\(311\) 21.4581 1.21678 0.608389 0.793639i \(-0.291816\pi\)
0.608389 + 0.793639i \(0.291816\pi\)
\(312\) 0.0469230 0.00265649
\(313\) −29.2304 −1.65220 −0.826101 0.563523i \(-0.809446\pi\)
−0.826101 + 0.563523i \(0.809446\pi\)
\(314\) 23.4445 1.32305
\(315\) 4.90940 0.276613
\(316\) 25.2349 1.41957
\(317\) 29.7942 1.67341 0.836704 0.547656i \(-0.184480\pi\)
0.836704 + 0.547656i \(0.184480\pi\)
\(318\) 0.771037 0.0432376
\(319\) 3.01602 0.168865
\(320\) −8.26584 −0.462075
\(321\) 0.999112 0.0557650
\(322\) 22.3065 1.24310
\(323\) 2.30295 0.128140
\(324\) 17.7294 0.984967
\(325\) −3.93545 −0.218299
\(326\) −10.8460 −0.600702
\(327\) −2.23893 −0.123813
\(328\) −0.734812 −0.0405732
\(329\) 8.78236 0.484187
\(330\) −1.29935 −0.0715269
\(331\) 20.0926 1.10439 0.552195 0.833715i \(-0.313790\pi\)
0.552195 + 0.833715i \(0.313790\pi\)
\(332\) 10.0271 0.550309
\(333\) 13.8122 0.756906
\(334\) −20.7797 −1.13702
\(335\) −9.86643 −0.539060
\(336\) 1.15178 0.0628350
\(337\) −7.84023 −0.427084 −0.213542 0.976934i \(-0.568500\pi\)
−0.213542 + 0.976934i \(0.568500\pi\)
\(338\) −4.99633 −0.271765
\(339\) −0.898343 −0.0487913
\(340\) 2.03352 0.110283
\(341\) −5.34643 −0.289525
\(342\) 13.7303 0.742452
\(343\) 18.6297 1.00591
\(344\) −0.190911 −0.0102932
\(345\) 1.18965 0.0640486
\(346\) −12.4566 −0.669672
\(347\) −26.6311 −1.42963 −0.714816 0.699313i \(-0.753490\pi\)
−0.714816 + 0.699313i \(0.753490\pi\)
\(348\) 0.297441 0.0159445
\(349\) 17.5815 0.941118 0.470559 0.882368i \(-0.344052\pi\)
0.470559 + 0.882368i \(0.344052\pi\)
\(350\) 3.32135 0.177534
\(351\) 4.16074 0.222084
\(352\) 29.3334 1.56348
\(353\) 6.41713 0.341549 0.170775 0.985310i \(-0.445373\pi\)
0.170775 + 0.985310i \(0.445373\pi\)
\(354\) −1.98741 −0.105630
\(355\) 1.00000 0.0530745
\(356\) −33.8844 −1.79587
\(357\) −0.292937 −0.0155039
\(358\) 4.60867 0.243576
\(359\) −25.6463 −1.35356 −0.676779 0.736186i \(-0.736625\pi\)
−0.676779 + 0.736186i \(0.736625\pi\)
\(360\) 0.199823 0.0105316
\(361\) −13.6964 −0.720864
\(362\) −5.62704 −0.295751
\(363\) 0.414547 0.0217581
\(364\) 13.2347 0.693688
\(365\) 0.726747 0.0380397
\(366\) 3.72018 0.194457
\(367\) 15.7468 0.821976 0.410988 0.911641i \(-0.365184\pi\)
0.410988 + 0.911641i \(0.365184\pi\)
\(368\) −26.4067 −1.37654
\(369\) −32.4072 −1.68705
\(370\) 9.34439 0.485792
\(371\) 3.58430 0.186088
\(372\) −0.527267 −0.0273375
\(373\) 1.66257 0.0860846 0.0430423 0.999073i \(-0.486295\pi\)
0.0430423 + 0.999073i \(0.486295\pi\)
\(374\) −7.33542 −0.379305
\(375\) 0.177134 0.00914716
\(376\) 0.357460 0.0184346
\(377\) −3.24972 −0.167369
\(378\) −3.51149 −0.180611
\(379\) 5.14326 0.264192 0.132096 0.991237i \(-0.457829\pi\)
0.132096 + 0.991237i \(0.457829\pi\)
\(380\) 4.68309 0.240237
\(381\) 0.00319415 0.000163641 0
\(382\) −15.7155 −0.804076
\(383\) −0.311861 −0.0159354 −0.00796769 0.999968i \(-0.502536\pi\)
−0.00796769 + 0.999968i \(0.502536\pi\)
\(384\) 0.0953719 0.00486693
\(385\) −6.04026 −0.307840
\(386\) 9.62895 0.490101
\(387\) −8.41968 −0.427996
\(388\) −19.3589 −0.982797
\(389\) 22.9490 1.16356 0.581780 0.813346i \(-0.302357\pi\)
0.581780 + 0.813346i \(0.302357\pi\)
\(390\) 1.40003 0.0708934
\(391\) 6.71610 0.339648
\(392\) 0.287089 0.0145002
\(393\) 3.42016 0.172524
\(394\) 25.8956 1.30460
\(395\) 12.4095 0.624389
\(396\) −22.0488 −1.10800
\(397\) 6.68613 0.335567 0.167784 0.985824i \(-0.446339\pi\)
0.167784 + 0.985824i \(0.446339\pi\)
\(398\) −8.41124 −0.421617
\(399\) −0.674620 −0.0337733
\(400\) −3.93185 −0.196592
\(401\) 0.519070 0.0259211 0.0129606 0.999916i \(-0.495874\pi\)
0.0129606 + 0.999916i \(0.495874\pi\)
\(402\) 3.50997 0.175061
\(403\) 5.76070 0.286961
\(404\) 27.7977 1.38299
\(405\) 8.71860 0.433231
\(406\) 2.74263 0.136114
\(407\) −16.9938 −0.842354
\(408\) −0.0119232 −0.000590285 0
\(409\) 35.8801 1.77416 0.887078 0.461620i \(-0.152732\pi\)
0.887078 + 0.461620i \(0.152732\pi\)
\(410\) −21.9244 −1.08277
\(411\) 3.24623 0.160124
\(412\) −4.94526 −0.243635
\(413\) −9.23884 −0.454613
\(414\) 40.0419 1.96795
\(415\) 4.93092 0.242049
\(416\) −31.6063 −1.54963
\(417\) 1.04226 0.0510395
\(418\) −16.8931 −0.826268
\(419\) −36.1761 −1.76732 −0.883659 0.468131i \(-0.844927\pi\)
−0.883659 + 0.468131i \(0.844927\pi\)
\(420\) −0.595693 −0.0290668
\(421\) −12.6971 −0.618821 −0.309410 0.950929i \(-0.600132\pi\)
−0.309410 + 0.950929i \(0.600132\pi\)
\(422\) 20.6426 1.00486
\(423\) 15.7650 0.766519
\(424\) 0.145889 0.00708498
\(425\) 1.00000 0.0485071
\(426\) −0.355749 −0.0172361
\(427\) 17.2939 0.836911
\(428\) 11.4699 0.554419
\(429\) −2.54612 −0.122928
\(430\) −5.69616 −0.274693
\(431\) −17.0952 −0.823447 −0.411723 0.911309i \(-0.635073\pi\)
−0.411723 + 0.911309i \(0.635073\pi\)
\(432\) 4.15693 0.200000
\(433\) 29.0572 1.39640 0.698199 0.715903i \(-0.253985\pi\)
0.698199 + 0.715903i \(0.253985\pi\)
\(434\) −4.86179 −0.233373
\(435\) 0.146269 0.00701308
\(436\) −25.7032 −1.23096
\(437\) 15.4669 0.739880
\(438\) −0.258540 −0.0123535
\(439\) −30.9008 −1.47481 −0.737406 0.675449i \(-0.763950\pi\)
−0.737406 + 0.675449i \(0.763950\pi\)
\(440\) −0.245851 −0.0117205
\(441\) 12.6614 0.602923
\(442\) 7.90381 0.375946
\(443\) 14.0348 0.666812 0.333406 0.942783i \(-0.391802\pi\)
0.333406 + 0.942783i \(0.391802\pi\)
\(444\) −1.67594 −0.0795365
\(445\) −16.6630 −0.789900
\(446\) −12.4405 −0.589077
\(447\) 2.53635 0.119965
\(448\) 13.6697 0.645834
\(449\) −9.79645 −0.462323 −0.231162 0.972915i \(-0.574253\pi\)
−0.231162 + 0.972915i \(0.574253\pi\)
\(450\) 5.96207 0.281055
\(451\) 39.8721 1.87751
\(452\) −10.3131 −0.485086
\(453\) 0.195886 0.00920351
\(454\) 31.3530 1.47147
\(455\) 6.50830 0.305114
\(456\) −0.0274585 −0.00128586
\(457\) −39.8414 −1.86370 −0.931851 0.362841i \(-0.881807\pi\)
−0.931851 + 0.362841i \(0.881807\pi\)
\(458\) −26.6112 −1.24346
\(459\) −1.05725 −0.0493480
\(460\) 13.6573 0.636775
\(461\) −0.123718 −0.00576211 −0.00288105 0.999996i \(-0.500917\pi\)
−0.00288105 + 0.999996i \(0.500917\pi\)
\(462\) 2.14882 0.0999720
\(463\) 33.0773 1.53723 0.768615 0.639712i \(-0.220946\pi\)
0.768615 + 0.639712i \(0.220946\pi\)
\(464\) −3.24675 −0.150726
\(465\) −0.259288 −0.0120242
\(466\) −6.53084 −0.302536
\(467\) −4.33109 −0.200419 −0.100210 0.994966i \(-0.531951\pi\)
−0.100210 + 0.994966i \(0.531951\pi\)
\(468\) 23.7573 1.09818
\(469\) 16.3167 0.753436
\(470\) 10.6655 0.491962
\(471\) −2.06776 −0.0952776
\(472\) −0.376040 −0.0173086
\(473\) 10.3591 0.476313
\(474\) −4.41466 −0.202772
\(475\) 2.30295 0.105667
\(476\) −3.36295 −0.154141
\(477\) 6.43408 0.294596
\(478\) −54.6655 −2.50034
\(479\) 30.1415 1.37720 0.688600 0.725141i \(-0.258226\pi\)
0.688600 + 0.725141i \(0.258226\pi\)
\(480\) 1.42260 0.0649323
\(481\) 18.3106 0.834893
\(482\) −8.78843 −0.400302
\(483\) −1.96740 −0.0895197
\(484\) 4.75904 0.216320
\(485\) −9.51989 −0.432276
\(486\) −9.47163 −0.429642
\(487\) 22.1133 1.00205 0.501025 0.865433i \(-0.332956\pi\)
0.501025 + 0.865433i \(0.332956\pi\)
\(488\) 0.703898 0.0318640
\(489\) 0.956594 0.0432587
\(490\) 8.56580 0.386964
\(491\) 14.2567 0.643397 0.321698 0.946842i \(-0.395746\pi\)
0.321698 + 0.946842i \(0.395746\pi\)
\(492\) 3.93220 0.177277
\(493\) 0.825756 0.0371902
\(494\) 18.2021 0.818950
\(495\) −10.8427 −0.487344
\(496\) 5.75543 0.258426
\(497\) −1.65376 −0.0741814
\(498\) −1.75417 −0.0786062
\(499\) 24.1031 1.07900 0.539502 0.841984i \(-0.318613\pi\)
0.539502 + 0.841984i \(0.318613\pi\)
\(500\) 2.03352 0.0909416
\(501\) 1.83273 0.0818805
\(502\) 11.8029 0.526789
\(503\) 22.1111 0.985886 0.492943 0.870061i \(-0.335921\pi\)
0.492943 + 0.870061i \(0.335921\pi\)
\(504\) −0.330459 −0.0147198
\(505\) 13.6698 0.608296
\(506\) −49.2654 −2.19011
\(507\) 0.440668 0.0195707
\(508\) 0.0366691 0.00162693
\(509\) −4.83268 −0.214205 −0.107102 0.994248i \(-0.534157\pi\)
−0.107102 + 0.994248i \(0.534157\pi\)
\(510\) −0.355749 −0.0157528
\(511\) −1.20187 −0.0531675
\(512\) −32.1067 −1.41893
\(513\) −2.43478 −0.107498
\(514\) 18.1801 0.801889
\(515\) −2.43188 −0.107161
\(516\) 1.02162 0.0449743
\(517\) −19.3964 −0.853053
\(518\) −15.4534 −0.678983
\(519\) 1.09865 0.0482255
\(520\) 0.264901 0.0116167
\(521\) 30.1778 1.32211 0.661056 0.750336i \(-0.270108\pi\)
0.661056 + 0.750336i \(0.270108\pi\)
\(522\) 4.92322 0.215483
\(523\) 44.8735 1.96218 0.981092 0.193544i \(-0.0619983\pi\)
0.981092 + 0.193544i \(0.0619983\pi\)
\(524\) 39.2638 1.71525
\(525\) −0.292937 −0.0127848
\(526\) 1.96933 0.0858671
\(527\) −1.46380 −0.0637640
\(528\) −2.54379 −0.110704
\(529\) 22.1061 0.961133
\(530\) 4.35285 0.189076
\(531\) −16.5844 −0.719701
\(532\) −7.74471 −0.335776
\(533\) −42.9617 −1.86088
\(534\) 5.92783 0.256522
\(535\) 5.64044 0.243857
\(536\) 0.664125 0.0286858
\(537\) −0.406477 −0.0175408
\(538\) −41.0265 −1.76878
\(539\) −15.5779 −0.670988
\(540\) −2.14993 −0.0925181
\(541\) 42.4678 1.82583 0.912916 0.408148i \(-0.133825\pi\)
0.912916 + 0.408148i \(0.133825\pi\)
\(542\) −60.9840 −2.61949
\(543\) 0.496295 0.0212981
\(544\) 8.03119 0.344334
\(545\) −12.6398 −0.541429
\(546\) −2.31532 −0.0990866
\(547\) −6.80140 −0.290807 −0.145404 0.989372i \(-0.546448\pi\)
−0.145404 + 0.989372i \(0.546448\pi\)
\(548\) 37.2670 1.59197
\(549\) 31.0438 1.32492
\(550\) −7.33542 −0.312783
\(551\) 1.90168 0.0810141
\(552\) −0.0800772 −0.00340831
\(553\) −20.5223 −0.872698
\(554\) −33.0066 −1.40232
\(555\) −0.824158 −0.0349836
\(556\) 11.9652 0.507437
\(557\) −17.6436 −0.747582 −0.373791 0.927513i \(-0.621942\pi\)
−0.373791 + 0.927513i \(0.621942\pi\)
\(558\) −8.72726 −0.369455
\(559\) −11.1618 −0.472095
\(560\) 6.50234 0.274774
\(561\) 0.646971 0.0273151
\(562\) 25.1075 1.05910
\(563\) 28.7571 1.21197 0.605983 0.795478i \(-0.292780\pi\)
0.605983 + 0.795478i \(0.292780\pi\)
\(564\) −1.91288 −0.0805467
\(565\) −5.07155 −0.213362
\(566\) −14.0233 −0.589442
\(567\) −14.4185 −0.605519
\(568\) −0.0673116 −0.00282433
\(569\) −25.7672 −1.08022 −0.540109 0.841595i \(-0.681617\pi\)
−0.540109 + 0.841595i \(0.681617\pi\)
\(570\) −0.819272 −0.0343155
\(571\) −31.0067 −1.29759 −0.648794 0.760964i \(-0.724726\pi\)
−0.648794 + 0.760964i \(0.724726\pi\)
\(572\) −29.2297 −1.22216
\(573\) 1.38608 0.0579043
\(574\) 36.2578 1.51337
\(575\) 6.71610 0.280081
\(576\) 24.5382 1.02242
\(577\) −34.6463 −1.44235 −0.721173 0.692755i \(-0.756397\pi\)
−0.721173 + 0.692755i \(0.756397\pi\)
\(578\) −2.00836 −0.0835368
\(579\) −0.849256 −0.0352939
\(580\) 1.67919 0.0697245
\(581\) −8.15457 −0.338309
\(582\) 3.38669 0.140383
\(583\) −7.91616 −0.327854
\(584\) −0.0489185 −0.00202426
\(585\) 11.6829 0.483027
\(586\) 50.8089 2.09890
\(587\) 27.4750 1.13401 0.567007 0.823713i \(-0.308101\pi\)
0.567007 + 0.823713i \(0.308101\pi\)
\(588\) −1.53630 −0.0633559
\(589\) −3.37105 −0.138902
\(590\) −11.2198 −0.461913
\(591\) −2.28395 −0.0939491
\(592\) 18.2939 0.751873
\(593\) 0.336283 0.0138095 0.00690474 0.999976i \(-0.497802\pi\)
0.00690474 + 0.999976i \(0.497802\pi\)
\(594\) 7.75534 0.318205
\(595\) −1.65376 −0.0677976
\(596\) 29.1175 1.19270
\(597\) 0.741856 0.0303622
\(598\) 53.0828 2.17072
\(599\) 41.1644 1.68193 0.840967 0.541087i \(-0.181987\pi\)
0.840967 + 0.541087i \(0.181987\pi\)
\(600\) −0.0119232 −0.000486761 0
\(601\) −22.5177 −0.918516 −0.459258 0.888303i \(-0.651885\pi\)
−0.459258 + 0.888303i \(0.651885\pi\)
\(602\) 9.42010 0.383934
\(603\) 29.2897 1.19277
\(604\) 2.24879 0.0915019
\(605\) 2.34030 0.0951469
\(606\) −4.86300 −0.197546
\(607\) −44.1978 −1.79394 −0.896968 0.442096i \(-0.854235\pi\)
−0.896968 + 0.442096i \(0.854235\pi\)
\(608\) 18.4954 0.750089
\(609\) −0.241895 −0.00980208
\(610\) 21.0021 0.850349
\(611\) 20.8993 0.845497
\(612\) −6.03674 −0.244021
\(613\) 41.6637 1.68278 0.841390 0.540428i \(-0.181738\pi\)
0.841390 + 0.540428i \(0.181738\pi\)
\(614\) 20.9321 0.844750
\(615\) 1.93370 0.0779742
\(616\) 0.406580 0.0163816
\(617\) 9.38216 0.377711 0.188856 0.982005i \(-0.439522\pi\)
0.188856 + 0.982005i \(0.439522\pi\)
\(618\) 0.865137 0.0348009
\(619\) 24.4679 0.983449 0.491725 0.870751i \(-0.336367\pi\)
0.491725 + 0.870751i \(0.336367\pi\)
\(620\) −2.97666 −0.119545
\(621\) −7.10057 −0.284936
\(622\) −43.0957 −1.72798
\(623\) 27.5566 1.10403
\(624\) 2.74090 0.109724
\(625\) 1.00000 0.0400000
\(626\) 58.7053 2.34633
\(627\) 1.48994 0.0595025
\(628\) −23.7381 −0.947255
\(629\) −4.65274 −0.185517
\(630\) −9.85984 −0.392826
\(631\) 19.6827 0.783557 0.391779 0.920060i \(-0.371860\pi\)
0.391779 + 0.920060i \(0.371860\pi\)
\(632\) −0.835302 −0.0332265
\(633\) −1.82064 −0.0723639
\(634\) −59.8375 −2.37645
\(635\) 0.0180324 0.000715593 0
\(636\) −0.780694 −0.0309565
\(637\) 16.7850 0.665045
\(638\) −6.05727 −0.239810
\(639\) −2.96862 −0.117437
\(640\) 0.538417 0.0212828
\(641\) 36.8693 1.45625 0.728124 0.685446i \(-0.240393\pi\)
0.728124 + 0.685446i \(0.240393\pi\)
\(642\) −2.00658 −0.0791934
\(643\) −48.1641 −1.89941 −0.949703 0.313151i \(-0.898615\pi\)
−0.949703 + 0.313151i \(0.898615\pi\)
\(644\) −22.5859 −0.890010
\(645\) 0.502391 0.0197816
\(646\) −4.62516 −0.181974
\(647\) 0.840589 0.0330470 0.0165235 0.999863i \(-0.494740\pi\)
0.0165235 + 0.999863i \(0.494740\pi\)
\(648\) −0.586863 −0.0230541
\(649\) 20.4046 0.800949
\(650\) 7.90381 0.310013
\(651\) 0.428801 0.0168060
\(652\) 10.9818 0.430081
\(653\) −3.81467 −0.149279 −0.0746397 0.997211i \(-0.523781\pi\)
−0.0746397 + 0.997211i \(0.523781\pi\)
\(654\) 4.49659 0.175830
\(655\) 19.3083 0.754439
\(656\) −42.9223 −1.67583
\(657\) −2.15744 −0.0841697
\(658\) −17.6382 −0.687607
\(659\) 42.0446 1.63782 0.818912 0.573919i \(-0.194578\pi\)
0.818912 + 0.573919i \(0.194578\pi\)
\(660\) 1.31563 0.0512106
\(661\) 49.1719 1.91257 0.956284 0.292441i \(-0.0944676\pi\)
0.956284 + 0.292441i \(0.0944676\pi\)
\(662\) −40.3533 −1.56837
\(663\) −0.697102 −0.0270732
\(664\) −0.331908 −0.0128805
\(665\) −3.80853 −0.147689
\(666\) −27.7400 −1.07490
\(667\) 5.54587 0.214737
\(668\) 21.0400 0.814061
\(669\) 1.09723 0.0424215
\(670\) 19.8154 0.765534
\(671\) −38.1947 −1.47449
\(672\) −2.35264 −0.0907549
\(673\) 39.8547 1.53629 0.768144 0.640278i \(-0.221181\pi\)
0.768144 + 0.640278i \(0.221181\pi\)
\(674\) 15.7460 0.606514
\(675\) −1.05725 −0.0406934
\(676\) 5.05891 0.194574
\(677\) 40.5156 1.55714 0.778571 0.627557i \(-0.215945\pi\)
0.778571 + 0.627557i \(0.215945\pi\)
\(678\) 1.80420 0.0692898
\(679\) 15.7436 0.604185
\(680\) −0.0673116 −0.00258128
\(681\) −2.76528 −0.105966
\(682\) 10.7376 0.411163
\(683\) 38.5400 1.47469 0.737346 0.675516i \(-0.236079\pi\)
0.737346 + 0.675516i \(0.236079\pi\)
\(684\) −13.9023 −0.531568
\(685\) 18.3264 0.700215
\(686\) −37.4153 −1.42852
\(687\) 2.34706 0.0895459
\(688\) −11.1516 −0.425150
\(689\) 8.52954 0.324950
\(690\) −2.38925 −0.0909571
\(691\) 1.55240 0.0590560 0.0295280 0.999564i \(-0.490600\pi\)
0.0295280 + 0.999564i \(0.490600\pi\)
\(692\) 12.6126 0.479461
\(693\) 17.9313 0.681153
\(694\) 53.4849 2.03026
\(695\) 5.88400 0.223193
\(696\) −0.00984563 −0.000373198 0
\(697\) 10.9166 0.413495
\(698\) −35.3101 −1.33651
\(699\) 0.576009 0.0217867
\(700\) −3.36295 −0.127108
\(701\) 4.21754 0.159294 0.0796471 0.996823i \(-0.474621\pi\)
0.0796471 + 0.996823i \(0.474621\pi\)
\(702\) −8.35626 −0.315387
\(703\) −10.7150 −0.404125
\(704\) −30.1905 −1.13785
\(705\) −0.940676 −0.0354279
\(706\) −12.8879 −0.485043
\(707\) −22.6065 −0.850206
\(708\) 2.01230 0.0756270
\(709\) −15.4181 −0.579037 −0.289519 0.957172i \(-0.593495\pi\)
−0.289519 + 0.957172i \(0.593495\pi\)
\(710\) −2.00836 −0.0753725
\(711\) −36.8391 −1.38157
\(712\) 1.12161 0.0420341
\(713\) −9.83102 −0.368175
\(714\) 0.588324 0.0220175
\(715\) −14.3740 −0.537557
\(716\) −4.66639 −0.174391
\(717\) 4.82140 0.180058
\(718\) 51.5070 1.92222
\(719\) 28.7877 1.07360 0.536801 0.843709i \(-0.319633\pi\)
0.536801 + 0.843709i \(0.319633\pi\)
\(720\) 11.6722 0.434996
\(721\) 4.02174 0.149778
\(722\) 27.5074 1.02372
\(723\) 0.775124 0.0288272
\(724\) 5.69752 0.211747
\(725\) 0.825756 0.0306678
\(726\) −0.832561 −0.0308992
\(727\) −10.0382 −0.372296 −0.186148 0.982522i \(-0.559600\pi\)
−0.186148 + 0.982522i \(0.559600\pi\)
\(728\) −0.438084 −0.0162365
\(729\) −25.3204 −0.937793
\(730\) −1.45957 −0.0540212
\(731\) 2.83622 0.104902
\(732\) −3.76677 −0.139224
\(733\) −34.2867 −1.26641 −0.633204 0.773985i \(-0.718261\pi\)
−0.633204 + 0.773985i \(0.718261\pi\)
\(734\) −31.6253 −1.16731
\(735\) −0.755489 −0.0278666
\(736\) 53.9383 1.98819
\(737\) −36.0365 −1.32742
\(738\) 65.0854 2.39583
\(739\) 21.6428 0.796142 0.398071 0.917355i \(-0.369680\pi\)
0.398071 + 0.917355i \(0.369680\pi\)
\(740\) −9.46142 −0.347809
\(741\) −1.60539 −0.0589755
\(742\) −7.19857 −0.264268
\(743\) −5.84064 −0.214272 −0.107136 0.994244i \(-0.534168\pi\)
−0.107136 + 0.994244i \(0.534168\pi\)
\(744\) 0.0174531 0.000639862 0
\(745\) 14.3188 0.524601
\(746\) −3.33904 −0.122251
\(747\) −14.6380 −0.535578
\(748\) 7.42729 0.271569
\(749\) −9.32794 −0.340835
\(750\) −0.355749 −0.0129901
\(751\) 4.83817 0.176547 0.0882737 0.996096i \(-0.471865\pi\)
0.0882737 + 0.996096i \(0.471865\pi\)
\(752\) 20.8802 0.761423
\(753\) −1.04099 −0.0379359
\(754\) 6.52662 0.237685
\(755\) 1.10586 0.0402464
\(756\) 3.55547 0.129311
\(757\) 34.5801 1.25684 0.628418 0.777875i \(-0.283703\pi\)
0.628418 + 0.777875i \(0.283703\pi\)
\(758\) −10.3295 −0.375186
\(759\) 4.34512 0.157718
\(760\) −0.155015 −0.00562299
\(761\) 0.122668 0.00444671 0.00222335 0.999998i \(-0.499292\pi\)
0.00222335 + 0.999998i \(0.499292\pi\)
\(762\) −0.00641500 −0.000232391 0
\(763\) 20.9032 0.756746
\(764\) 15.9123 0.575689
\(765\) −2.96862 −0.107331
\(766\) 0.626331 0.0226302
\(767\) −21.9856 −0.793855
\(768\) 2.73678 0.0987551
\(769\) −5.25406 −0.189466 −0.0947331 0.995503i \(-0.530200\pi\)
−0.0947331 + 0.995503i \(0.530200\pi\)
\(770\) 12.1310 0.437172
\(771\) −1.60345 −0.0577469
\(772\) −9.74955 −0.350894
\(773\) 44.8626 1.61360 0.806798 0.590828i \(-0.201199\pi\)
0.806798 + 0.590828i \(0.201199\pi\)
\(774\) 16.9098 0.607809
\(775\) −1.46380 −0.0525812
\(776\) 0.640799 0.0230033
\(777\) 1.36296 0.0488960
\(778\) −46.0898 −1.65240
\(779\) 25.1403 0.900746
\(780\) −1.41757 −0.0507570
\(781\) 3.65244 0.130695
\(782\) −13.4884 −0.482343
\(783\) −0.873027 −0.0311995
\(784\) 16.7696 0.598914
\(785\) −11.6735 −0.416643
\(786\) −6.86892 −0.245006
\(787\) −13.1881 −0.470106 −0.235053 0.971983i \(-0.575526\pi\)
−0.235053 + 0.971983i \(0.575526\pi\)
\(788\) −26.2200 −0.934047
\(789\) −0.173692 −0.00618359
\(790\) −24.9227 −0.886710
\(791\) 8.38714 0.298212
\(792\) 0.729840 0.0259337
\(793\) 41.1542 1.46143
\(794\) −13.4282 −0.476547
\(795\) −0.383913 −0.0136160
\(796\) 8.51659 0.301862
\(797\) 1.34147 0.0475173 0.0237586 0.999718i \(-0.492437\pi\)
0.0237586 + 0.999718i \(0.492437\pi\)
\(798\) 1.35488 0.0479623
\(799\) −5.31053 −0.187873
\(800\) 8.03119 0.283945
\(801\) 49.4661 1.74780
\(802\) −1.04248 −0.0368112
\(803\) 2.65440 0.0936717
\(804\) −3.55393 −0.125338
\(805\) −11.1068 −0.391465
\(806\) −11.5696 −0.407521
\(807\) 3.61847 0.127376
\(808\) −0.920133 −0.0323702
\(809\) −25.6195 −0.900732 −0.450366 0.892844i \(-0.648707\pi\)
−0.450366 + 0.892844i \(0.648707\pi\)
\(810\) −17.5101 −0.615242
\(811\) 22.0020 0.772596 0.386298 0.922374i \(-0.373754\pi\)
0.386298 + 0.922374i \(0.373754\pi\)
\(812\) −2.77698 −0.0974528
\(813\) 5.37868 0.188639
\(814\) 34.1298 1.19625
\(815\) 5.40040 0.189168
\(816\) −0.696463 −0.0243811
\(817\) 6.53168 0.228515
\(818\) −72.0602 −2.51952
\(819\) −19.3207 −0.675119
\(820\) 22.1990 0.775224
\(821\) −2.30062 −0.0802920 −0.0401460 0.999194i \(-0.512782\pi\)
−0.0401460 + 0.999194i \(0.512782\pi\)
\(822\) −6.51959 −0.227397
\(823\) 27.4210 0.955837 0.477919 0.878404i \(-0.341391\pi\)
0.477919 + 0.878404i \(0.341391\pi\)
\(824\) 0.163693 0.00570253
\(825\) 0.646971 0.0225246
\(826\) 18.5549 0.645608
\(827\) 15.7534 0.547799 0.273900 0.961758i \(-0.411686\pi\)
0.273900 + 0.961758i \(0.411686\pi\)
\(828\) −40.5434 −1.40898
\(829\) 25.8772 0.898751 0.449376 0.893343i \(-0.351646\pi\)
0.449376 + 0.893343i \(0.351646\pi\)
\(830\) −9.90307 −0.343741
\(831\) 2.91112 0.100986
\(832\) 32.5298 1.12777
\(833\) −4.26507 −0.147776
\(834\) −2.09323 −0.0724825
\(835\) 10.3466 0.358059
\(836\) 17.1047 0.591578
\(837\) 1.54759 0.0534927
\(838\) 72.6547 2.50981
\(839\) 35.5601 1.22767 0.613835 0.789434i \(-0.289626\pi\)
0.613835 + 0.789434i \(0.289626\pi\)
\(840\) 0.0197181 0.000680338 0
\(841\) −28.3181 −0.976487
\(842\) 25.5005 0.878804
\(843\) −2.21444 −0.0762693
\(844\) −20.9011 −0.719446
\(845\) 2.48777 0.0855818
\(846\) −31.6618 −1.08855
\(847\) −3.87031 −0.132985
\(848\) 8.52173 0.292637
\(849\) 1.23683 0.0424478
\(850\) −2.00836 −0.0688862
\(851\) −31.2483 −1.07118
\(852\) 0.360205 0.0123404
\(853\) −25.2721 −0.865299 −0.432649 0.901562i \(-0.642421\pi\)
−0.432649 + 0.901562i \(0.642421\pi\)
\(854\) −34.7324 −1.18852
\(855\) −6.83659 −0.233807
\(856\) −0.379667 −0.0129767
\(857\) 16.0224 0.547316 0.273658 0.961827i \(-0.411766\pi\)
0.273658 + 0.961827i \(0.411766\pi\)
\(858\) 5.11353 0.174573
\(859\) 25.0244 0.853822 0.426911 0.904294i \(-0.359602\pi\)
0.426911 + 0.904294i \(0.359602\pi\)
\(860\) 5.76751 0.196670
\(861\) −3.19788 −0.108983
\(862\) 34.3333 1.16940
\(863\) −1.75853 −0.0598610 −0.0299305 0.999552i \(-0.509529\pi\)
−0.0299305 + 0.999552i \(0.509529\pi\)
\(864\) −8.49094 −0.288868
\(865\) 6.20238 0.210887
\(866\) −58.3573 −1.98306
\(867\) 0.177134 0.00601578
\(868\) 4.92268 0.167087
\(869\) 45.3248 1.53754
\(870\) −0.293762 −0.00995946
\(871\) 38.8288 1.31566
\(872\) 0.850803 0.0288118
\(873\) 28.2610 0.956489
\(874\) −31.0630 −1.05072
\(875\) −1.65376 −0.0559074
\(876\) 0.261778 0.00884465
\(877\) −49.8773 −1.68424 −0.842118 0.539294i \(-0.818691\pi\)
−0.842118 + 0.539294i \(0.818691\pi\)
\(878\) 62.0599 2.09442
\(879\) −4.48126 −0.151149
\(880\) −14.3608 −0.484103
\(881\) −1.57314 −0.0530003 −0.0265001 0.999649i \(-0.508436\pi\)
−0.0265001 + 0.999649i \(0.508436\pi\)
\(882\) −25.4286 −0.856227
\(883\) −14.2007 −0.477893 −0.238947 0.971033i \(-0.576802\pi\)
−0.238947 + 0.971033i \(0.576802\pi\)
\(884\) −8.00280 −0.269163
\(885\) 0.989569 0.0332640
\(886\) −28.1869 −0.946957
\(887\) −41.0553 −1.37850 −0.689250 0.724523i \(-0.742060\pi\)
−0.689250 + 0.724523i \(0.742060\pi\)
\(888\) 0.0554754 0.00186163
\(889\) −0.0298213 −0.00100017
\(890\) 33.4653 1.12176
\(891\) 31.8441 1.06682
\(892\) 12.5964 0.421757
\(893\) −12.2299 −0.409258
\(894\) −5.09390 −0.170366
\(895\) −2.29474 −0.0767047
\(896\) −0.890414 −0.0297466
\(897\) −4.68181 −0.156321
\(898\) 19.6748 0.656557
\(899\) −1.20874 −0.0403138
\(900\) −6.03674 −0.201225
\(901\) −2.16736 −0.0722053
\(902\) −80.0777 −2.66630
\(903\) −0.830836 −0.0276485
\(904\) 0.341374 0.0113539
\(905\) 2.80181 0.0931352
\(906\) −0.393409 −0.0130701
\(907\) −25.7429 −0.854780 −0.427390 0.904067i \(-0.640567\pi\)
−0.427390 + 0.904067i \(0.640567\pi\)
\(908\) −31.7457 −1.05352
\(909\) −40.5804 −1.34597
\(910\) −13.0710 −0.433300
\(911\) −54.4958 −1.80553 −0.902764 0.430136i \(-0.858466\pi\)
−0.902764 + 0.430136i \(0.858466\pi\)
\(912\) −1.60392 −0.0531111
\(913\) 18.0099 0.596040
\(914\) 80.0159 2.64669
\(915\) −1.85235 −0.0612366
\(916\) 26.9445 0.890270
\(917\) −31.9314 −1.05447
\(918\) 2.12333 0.0700804
\(919\) 39.5948 1.30611 0.653056 0.757309i \(-0.273487\pi\)
0.653056 + 0.757309i \(0.273487\pi\)
\(920\) −0.452072 −0.0149044
\(921\) −1.84617 −0.0608335
\(922\) 0.248470 0.00818292
\(923\) −3.93545 −0.129537
\(924\) −2.17573 −0.0715763
\(925\) −4.65274 −0.152981
\(926\) −66.4311 −2.18306
\(927\) 7.21932 0.237114
\(928\) 6.63181 0.217700
\(929\) −0.205805 −0.00675225 −0.00337612 0.999994i \(-0.501075\pi\)
−0.00337612 + 0.999994i \(0.501075\pi\)
\(930\) 0.520745 0.0170759
\(931\) −9.82225 −0.321911
\(932\) 6.61264 0.216604
\(933\) 3.80096 0.124438
\(934\) 8.69840 0.284620
\(935\) 3.65244 0.119447
\(936\) −0.786392 −0.0257040
\(937\) 45.9808 1.50213 0.751063 0.660231i \(-0.229542\pi\)
0.751063 + 0.660231i \(0.229542\pi\)
\(938\) −32.7699 −1.06997
\(939\) −5.17770 −0.168968
\(940\) −10.7991 −0.352226
\(941\) −28.6038 −0.932459 −0.466229 0.884664i \(-0.654388\pi\)
−0.466229 + 0.884664i \(0.654388\pi\)
\(942\) 4.15282 0.135306
\(943\) 73.3169 2.38753
\(944\) −21.9655 −0.714915
\(945\) 1.74843 0.0568765
\(946\) −20.8049 −0.676425
\(947\) −7.73287 −0.251284 −0.125642 0.992076i \(-0.540099\pi\)
−0.125642 + 0.992076i \(0.540099\pi\)
\(948\) 4.46995 0.145177
\(949\) −2.86008 −0.0928421
\(950\) −4.62516 −0.150060
\(951\) 5.27756 0.171137
\(952\) 0.111317 0.00360782
\(953\) 41.9645 1.35936 0.679681 0.733507i \(-0.262118\pi\)
0.679681 + 0.733507i \(0.262118\pi\)
\(954\) −12.9220 −0.418364
\(955\) 7.82504 0.253212
\(956\) 55.3501 1.79015
\(957\) 0.534240 0.0172695
\(958\) −60.5350 −1.95580
\(959\) −30.3075 −0.978680
\(960\) −1.46416 −0.0472556
\(961\) −28.8573 −0.930881
\(962\) −36.7744 −1.18565
\(963\) −16.7443 −0.539578
\(964\) 8.89851 0.286602
\(965\) −4.79443 −0.154338
\(966\) 3.95125 0.127129
\(967\) 0.842616 0.0270967 0.0135483 0.999908i \(-0.495687\pi\)
0.0135483 + 0.999908i \(0.495687\pi\)
\(968\) −0.157530 −0.00506319
\(969\) 0.407931 0.0131046
\(970\) 19.1194 0.613887
\(971\) 25.2873 0.811509 0.405755 0.913982i \(-0.367009\pi\)
0.405755 + 0.913982i \(0.367009\pi\)
\(972\) 9.59026 0.307608
\(973\) −9.73073 −0.311953
\(974\) −44.4116 −1.42304
\(975\) −0.697102 −0.0223251
\(976\) 41.1165 1.31611
\(977\) 17.8565 0.571281 0.285640 0.958337i \(-0.407794\pi\)
0.285640 + 0.958337i \(0.407794\pi\)
\(978\) −1.92119 −0.0614328
\(979\) −60.8605 −1.94511
\(980\) −8.67309 −0.277052
\(981\) 37.5227 1.19801
\(982\) −28.6326 −0.913704
\(983\) 6.31868 0.201535 0.100767 0.994910i \(-0.467870\pi\)
0.100767 + 0.994910i \(0.467870\pi\)
\(984\) −0.130160 −0.00414936
\(985\) −12.8939 −0.410834
\(986\) −1.65842 −0.0528148
\(987\) 1.55565 0.0495170
\(988\) −18.4300 −0.586338
\(989\) 19.0484 0.605703
\(990\) 21.7761 0.692090
\(991\) −12.1787 −0.386868 −0.193434 0.981113i \(-0.561963\pi\)
−0.193434 + 0.981113i \(0.561963\pi\)
\(992\) −11.7560 −0.373255
\(993\) 3.55909 0.112944
\(994\) 3.32135 0.105347
\(995\) 4.18811 0.132772
\(996\) 1.77614 0.0562792
\(997\) 1.37060 0.0434075 0.0217037 0.999764i \(-0.493091\pi\)
0.0217037 + 0.999764i \(0.493091\pi\)
\(998\) −48.4078 −1.53232
\(999\) 4.91909 0.155633
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 6035.2.a.g.1.12 58
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6035.2.a.g.1.12 58 1.1 even 1 trivial