Properties

Label 6041.2.a.c.1.9
Level $6041$
Weight $2$
Character 6041.1
Self dual yes
Analytic conductor $48.238$
Analytic rank $1$
Dimension $83$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6041,2,Mod(1,6041)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6041, 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("6041.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6041 = 7 \cdot 863 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6041.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: \(48.2376278611\)
Analytic rank: \(1\)
Dimension: \(83\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) \(=\) 6041.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.25188 q^{2} -3.15195 q^{3} +3.07097 q^{4} +1.48598 q^{5} +7.09783 q^{6} +1.00000 q^{7} -2.41170 q^{8} +6.93481 q^{9} +O(q^{10})\) \(q-2.25188 q^{2} -3.15195 q^{3} +3.07097 q^{4} +1.48598 q^{5} +7.09783 q^{6} +1.00000 q^{7} -2.41170 q^{8} +6.93481 q^{9} -3.34625 q^{10} -1.80720 q^{11} -9.67956 q^{12} +0.118205 q^{13} -2.25188 q^{14} -4.68374 q^{15} -0.711080 q^{16} +4.60783 q^{17} -15.6164 q^{18} +2.60432 q^{19} +4.56340 q^{20} -3.15195 q^{21} +4.06961 q^{22} +4.16764 q^{23} +7.60156 q^{24} -2.79187 q^{25} -0.266183 q^{26} -12.4023 q^{27} +3.07097 q^{28} +1.70849 q^{29} +10.5472 q^{30} -2.00013 q^{31} +6.42467 q^{32} +5.69622 q^{33} -10.3763 q^{34} +1.48598 q^{35} +21.2966 q^{36} +10.7135 q^{37} -5.86461 q^{38} -0.372576 q^{39} -3.58373 q^{40} -0.734404 q^{41} +7.09783 q^{42} -4.62001 q^{43} -5.54987 q^{44} +10.3050 q^{45} -9.38503 q^{46} -9.25577 q^{47} +2.24129 q^{48} +1.00000 q^{49} +6.28696 q^{50} -14.5237 q^{51} +0.363003 q^{52} -6.59285 q^{53} +27.9286 q^{54} -2.68546 q^{55} -2.41170 q^{56} -8.20868 q^{57} -3.84731 q^{58} +3.63595 q^{59} -14.3836 q^{60} +6.74094 q^{61} +4.50406 q^{62} +6.93481 q^{63} -13.0454 q^{64} +0.175650 q^{65} -12.8272 q^{66} +3.40992 q^{67} +14.1505 q^{68} -13.1362 q^{69} -3.34625 q^{70} -11.0355 q^{71} -16.7247 q^{72} -10.0393 q^{73} -24.1256 q^{74} +8.79984 q^{75} +7.99778 q^{76} -1.80720 q^{77} +0.838997 q^{78} -12.9837 q^{79} -1.05665 q^{80} +18.2872 q^{81} +1.65379 q^{82} -13.0562 q^{83} -9.67956 q^{84} +6.84714 q^{85} +10.4037 q^{86} -5.38508 q^{87} +4.35843 q^{88} -9.51537 q^{89} -23.2056 q^{90} +0.118205 q^{91} +12.7987 q^{92} +6.30433 q^{93} +20.8429 q^{94} +3.86996 q^{95} -20.2502 q^{96} +3.63825 q^{97} -2.25188 q^{98} -12.5326 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9} - 20 q^{10} - 26 q^{11} - 14 q^{12} - 22 q^{13} - 8 q^{14} - 37 q^{15} - 10 q^{16} - 9 q^{17} - 27 q^{18} - 42 q^{19} - 22 q^{20} - 12 q^{21} - 44 q^{22} - 46 q^{23} - 24 q^{24} - 20 q^{25} - 9 q^{26} - 39 q^{27} + 48 q^{28} - 36 q^{29} - 11 q^{30} - 107 q^{31} - 19 q^{32} - 25 q^{33} - 24 q^{34} - 11 q^{35} - 32 q^{36} - 75 q^{37} - 16 q^{38} - 78 q^{39} - 34 q^{40} - 17 q^{41} - 8 q^{42} - 87 q^{43} - 32 q^{44} - 17 q^{45} - 56 q^{46} - 39 q^{47} - 16 q^{48} + 83 q^{49} - 26 q^{50} - 71 q^{51} - 53 q^{52} - 28 q^{53} - 25 q^{54} - 94 q^{55} - 18 q^{56} - 79 q^{57} - 69 q^{58} - 26 q^{59} - 43 q^{60} - 56 q^{61} - 6 q^{62} + 39 q^{63} - 108 q^{64} - 26 q^{65} + 10 q^{66} - 123 q^{67} - 11 q^{68} + 2 q^{69} - 20 q^{70} - 96 q^{71} - 11 q^{72} - 53 q^{73} - 26 q^{74} - 27 q^{75} - 65 q^{76} - 26 q^{77} - 43 q^{78} - 160 q^{79} + 12 q^{80} - 53 q^{81} - 20 q^{82} - 2 q^{83} - 14 q^{84} - 110 q^{85} + 24 q^{86} - 52 q^{87} - 79 q^{88} - 5 q^{89} - 4 q^{90} - 22 q^{91} - 51 q^{92} - 30 q^{93} - 9 q^{94} - 76 q^{95} - 3 q^{96} - 44 q^{97} - 8 q^{98} - 82 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.25188 −1.59232 −0.796160 0.605086i \(-0.793139\pi\)
−0.796160 + 0.605086i \(0.793139\pi\)
\(3\) −3.15195 −1.81978 −0.909891 0.414848i \(-0.863835\pi\)
−0.909891 + 0.414848i \(0.863835\pi\)
\(4\) 3.07097 1.53549
\(5\) 1.48598 0.664550 0.332275 0.943183i \(-0.392184\pi\)
0.332275 + 0.943183i \(0.392184\pi\)
\(6\) 7.09783 2.89768
\(7\) 1.00000 0.377964
\(8\) −2.41170 −0.852665
\(9\) 6.93481 2.31160
\(10\) −3.34625 −1.05818
\(11\) −1.80720 −0.544892 −0.272446 0.962171i \(-0.587833\pi\)
−0.272446 + 0.962171i \(0.587833\pi\)
\(12\) −9.67956 −2.79425
\(13\) 0.118205 0.0327841 0.0163920 0.999866i \(-0.494782\pi\)
0.0163920 + 0.999866i \(0.494782\pi\)
\(14\) −2.25188 −0.601841
\(15\) −4.68374 −1.20934
\(16\) −0.711080 −0.177770
\(17\) 4.60783 1.11756 0.558781 0.829315i \(-0.311269\pi\)
0.558781 + 0.829315i \(0.311269\pi\)
\(18\) −15.6164 −3.68081
\(19\) 2.60432 0.597471 0.298735 0.954336i \(-0.403435\pi\)
0.298735 + 0.954336i \(0.403435\pi\)
\(20\) 4.56340 1.02041
\(21\) −3.15195 −0.687813
\(22\) 4.06961 0.867643
\(23\) 4.16764 0.869013 0.434506 0.900669i \(-0.356923\pi\)
0.434506 + 0.900669i \(0.356923\pi\)
\(24\) 7.60156 1.55166
\(25\) −2.79187 −0.558373
\(26\) −0.266183 −0.0522028
\(27\) −12.4023 −2.38683
\(28\) 3.07097 0.580359
\(29\) 1.70849 0.317258 0.158629 0.987338i \(-0.449293\pi\)
0.158629 + 0.987338i \(0.449293\pi\)
\(30\) 10.5472 1.92565
\(31\) −2.00013 −0.359235 −0.179617 0.983737i \(-0.557486\pi\)
−0.179617 + 0.983737i \(0.557486\pi\)
\(32\) 6.42467 1.13573
\(33\) 5.69622 0.991584
\(34\) −10.3763 −1.77952
\(35\) 1.48598 0.251176
\(36\) 21.2966 3.54943
\(37\) 10.7135 1.76129 0.880646 0.473775i \(-0.157109\pi\)
0.880646 + 0.473775i \(0.157109\pi\)
\(38\) −5.86461 −0.951365
\(39\) −0.372576 −0.0596599
\(40\) −3.58373 −0.566638
\(41\) −0.734404 −0.114695 −0.0573473 0.998354i \(-0.518264\pi\)
−0.0573473 + 0.998354i \(0.518264\pi\)
\(42\) 7.09783 1.09522
\(43\) −4.62001 −0.704545 −0.352272 0.935897i \(-0.614591\pi\)
−0.352272 + 0.935897i \(0.614591\pi\)
\(44\) −5.54987 −0.836674
\(45\) 10.3050 1.53618
\(46\) −9.38503 −1.38375
\(47\) −9.25577 −1.35009 −0.675047 0.737775i \(-0.735877\pi\)
−0.675047 + 0.737775i \(0.735877\pi\)
\(48\) 2.24129 0.323502
\(49\) 1.00000 0.142857
\(50\) 6.28696 0.889110
\(51\) −14.5237 −2.03372
\(52\) 0.363003 0.0503395
\(53\) −6.59285 −0.905598 −0.452799 0.891613i \(-0.649574\pi\)
−0.452799 + 0.891613i \(0.649574\pi\)
\(54\) 27.9286 3.80060
\(55\) −2.68546 −0.362108
\(56\) −2.41170 −0.322277
\(57\) −8.20868 −1.08727
\(58\) −3.84731 −0.505177
\(59\) 3.63595 0.473360 0.236680 0.971588i \(-0.423941\pi\)
0.236680 + 0.971588i \(0.423941\pi\)
\(60\) −14.3836 −1.85692
\(61\) 6.74094 0.863089 0.431545 0.902092i \(-0.357969\pi\)
0.431545 + 0.902092i \(0.357969\pi\)
\(62\) 4.50406 0.572017
\(63\) 6.93481 0.873704
\(64\) −13.0454 −1.63068
\(65\) 0.175650 0.0217867
\(66\) −12.8272 −1.57892
\(67\) 3.40992 0.416588 0.208294 0.978066i \(-0.433209\pi\)
0.208294 + 0.978066i \(0.433209\pi\)
\(68\) 14.1505 1.71600
\(69\) −13.1362 −1.58141
\(70\) −3.34625 −0.399953
\(71\) −11.0355 −1.30968 −0.654839 0.755769i \(-0.727263\pi\)
−0.654839 + 0.755769i \(0.727263\pi\)
\(72\) −16.7247 −1.97102
\(73\) −10.0393 −1.17501 −0.587506 0.809219i \(-0.699890\pi\)
−0.587506 + 0.809219i \(0.699890\pi\)
\(74\) −24.1256 −2.80454
\(75\) 8.79984 1.01612
\(76\) 7.99778 0.917408
\(77\) −1.80720 −0.205950
\(78\) 0.838997 0.0949977
\(79\) −12.9837 −1.46078 −0.730392 0.683028i \(-0.760663\pi\)
−0.730392 + 0.683028i \(0.760663\pi\)
\(80\) −1.05665 −0.118137
\(81\) 18.2872 2.03191
\(82\) 1.65379 0.182631
\(83\) −13.0562 −1.43311 −0.716554 0.697532i \(-0.754282\pi\)
−0.716554 + 0.697532i \(0.754282\pi\)
\(84\) −9.67956 −1.05613
\(85\) 6.84714 0.742676
\(86\) 10.4037 1.12186
\(87\) −5.38508 −0.577341
\(88\) 4.35843 0.464610
\(89\) −9.51537 −1.00863 −0.504313 0.863521i \(-0.668254\pi\)
−0.504313 + 0.863521i \(0.668254\pi\)
\(90\) −23.2056 −2.44608
\(91\) 0.118205 0.0123912
\(92\) 12.7987 1.33436
\(93\) 6.30433 0.653728
\(94\) 20.8429 2.14978
\(95\) 3.86996 0.397049
\(96\) −20.2502 −2.06678
\(97\) 3.63825 0.369408 0.184704 0.982794i \(-0.440867\pi\)
0.184704 + 0.982794i \(0.440867\pi\)
\(98\) −2.25188 −0.227474
\(99\) −12.5326 −1.25957
\(100\) −8.57374 −0.857374
\(101\) −8.44168 −0.839979 −0.419989 0.907529i \(-0.637966\pi\)
−0.419989 + 0.907529i \(0.637966\pi\)
\(102\) 32.7056 3.23833
\(103\) 3.10717 0.306159 0.153079 0.988214i \(-0.451081\pi\)
0.153079 + 0.988214i \(0.451081\pi\)
\(104\) −0.285074 −0.0279538
\(105\) −4.68374 −0.457086
\(106\) 14.8463 1.44200
\(107\) −14.8324 −1.43390 −0.716950 0.697125i \(-0.754462\pi\)
−0.716950 + 0.697125i \(0.754462\pi\)
\(108\) −38.0872 −3.66494
\(109\) −0.795075 −0.0761544 −0.0380772 0.999275i \(-0.512123\pi\)
−0.0380772 + 0.999275i \(0.512123\pi\)
\(110\) 6.04735 0.576592
\(111\) −33.7685 −3.20517
\(112\) −0.711080 −0.0671907
\(113\) 9.71076 0.913512 0.456756 0.889592i \(-0.349011\pi\)
0.456756 + 0.889592i \(0.349011\pi\)
\(114\) 18.4850 1.73128
\(115\) 6.19302 0.577502
\(116\) 5.24672 0.487146
\(117\) 0.819728 0.0757838
\(118\) −8.18773 −0.753742
\(119\) 4.60783 0.422399
\(120\) 11.2958 1.03116
\(121\) −7.73402 −0.703093
\(122\) −15.1798 −1.37432
\(123\) 2.31481 0.208719
\(124\) −6.14235 −0.551600
\(125\) −11.5785 −1.03562
\(126\) −15.6164 −1.39122
\(127\) −11.0562 −0.981078 −0.490539 0.871419i \(-0.663200\pi\)
−0.490539 + 0.871419i \(0.663200\pi\)
\(128\) 16.5274 1.46083
\(129\) 14.5621 1.28212
\(130\) −0.395542 −0.0346914
\(131\) 19.7556 1.72605 0.863027 0.505157i \(-0.168565\pi\)
0.863027 + 0.505157i \(0.168565\pi\)
\(132\) 17.4929 1.52256
\(133\) 2.60432 0.225823
\(134\) −7.67873 −0.663341
\(135\) −18.4296 −1.58617
\(136\) −11.1127 −0.952906
\(137\) 3.67314 0.313817 0.156909 0.987613i \(-0.449847\pi\)
0.156909 + 0.987613i \(0.449847\pi\)
\(138\) 29.5812 2.51812
\(139\) −19.6361 −1.66551 −0.832757 0.553638i \(-0.813239\pi\)
−0.832757 + 0.553638i \(0.813239\pi\)
\(140\) 4.56340 0.385677
\(141\) 29.1738 2.45687
\(142\) 24.8507 2.08543
\(143\) −0.213620 −0.0178638
\(144\) −4.93120 −0.410934
\(145\) 2.53878 0.210834
\(146\) 22.6073 1.87100
\(147\) −3.15195 −0.259969
\(148\) 32.9009 2.70444
\(149\) −14.9750 −1.22680 −0.613401 0.789772i \(-0.710199\pi\)
−0.613401 + 0.789772i \(0.710199\pi\)
\(150\) −19.8162 −1.61799
\(151\) −6.58328 −0.535740 −0.267870 0.963455i \(-0.586320\pi\)
−0.267870 + 0.963455i \(0.586320\pi\)
\(152\) −6.28083 −0.509442
\(153\) 31.9544 2.58336
\(154\) 4.06961 0.327938
\(155\) −2.97216 −0.238729
\(156\) −1.14417 −0.0916069
\(157\) −1.59429 −0.127238 −0.0636191 0.997974i \(-0.520264\pi\)
−0.0636191 + 0.997974i \(0.520264\pi\)
\(158\) 29.2378 2.32604
\(159\) 20.7804 1.64799
\(160\) 9.54692 0.754750
\(161\) 4.16764 0.328456
\(162\) −41.1805 −3.23545
\(163\) 3.40652 0.266819 0.133410 0.991061i \(-0.457407\pi\)
0.133410 + 0.991061i \(0.457407\pi\)
\(164\) −2.25533 −0.176112
\(165\) 8.46446 0.658957
\(166\) 29.4011 2.28197
\(167\) 24.0584 1.86170 0.930849 0.365404i \(-0.119069\pi\)
0.930849 + 0.365404i \(0.119069\pi\)
\(168\) 7.60156 0.586473
\(169\) −12.9860 −0.998925
\(170\) −15.4189 −1.18258
\(171\) 18.0604 1.38112
\(172\) −14.1879 −1.08182
\(173\) 22.3753 1.70116 0.850581 0.525845i \(-0.176251\pi\)
0.850581 + 0.525845i \(0.176251\pi\)
\(174\) 12.1266 0.919312
\(175\) −2.79187 −0.211045
\(176\) 1.28506 0.0968654
\(177\) −11.4603 −0.861412
\(178\) 21.4275 1.60606
\(179\) 13.7150 1.02511 0.512553 0.858656i \(-0.328700\pi\)
0.512553 + 0.858656i \(0.328700\pi\)
\(180\) 31.6463 2.35878
\(181\) −1.89955 −0.141192 −0.0705962 0.997505i \(-0.522490\pi\)
−0.0705962 + 0.997505i \(0.522490\pi\)
\(182\) −0.266183 −0.0197308
\(183\) −21.2471 −1.57063
\(184\) −10.0511 −0.740976
\(185\) 15.9201 1.17047
\(186\) −14.1966 −1.04095
\(187\) −8.32728 −0.608951
\(188\) −28.4242 −2.07305
\(189\) −12.4023 −0.902137
\(190\) −8.71468 −0.632230
\(191\) 3.58967 0.259739 0.129870 0.991531i \(-0.458544\pi\)
0.129870 + 0.991531i \(0.458544\pi\)
\(192\) 41.1186 2.96748
\(193\) 7.55714 0.543975 0.271987 0.962301i \(-0.412319\pi\)
0.271987 + 0.962301i \(0.412319\pi\)
\(194\) −8.19290 −0.588216
\(195\) −0.553640 −0.0396470
\(196\) 3.07097 0.219355
\(197\) −4.54289 −0.323667 −0.161834 0.986818i \(-0.551741\pi\)
−0.161834 + 0.986818i \(0.551741\pi\)
\(198\) 28.2219 2.00565
\(199\) −23.8856 −1.69321 −0.846603 0.532225i \(-0.821356\pi\)
−0.846603 + 0.532225i \(0.821356\pi\)
\(200\) 6.73315 0.476105
\(201\) −10.7479 −0.758098
\(202\) 19.0097 1.33752
\(203\) 1.70849 0.119912
\(204\) −44.6018 −3.12275
\(205\) −1.09131 −0.0762203
\(206\) −6.99698 −0.487503
\(207\) 28.9018 2.00881
\(208\) −0.0840530 −0.00582803
\(209\) −4.70652 −0.325557
\(210\) 10.5472 0.727827
\(211\) −18.8760 −1.29948 −0.649738 0.760158i \(-0.725121\pi\)
−0.649738 + 0.760158i \(0.725121\pi\)
\(212\) −20.2465 −1.39053
\(213\) 34.7835 2.38333
\(214\) 33.4008 2.28323
\(215\) −6.86524 −0.468205
\(216\) 29.9107 2.03517
\(217\) −2.00013 −0.135778
\(218\) 1.79042 0.121262
\(219\) 31.6435 2.13827
\(220\) −8.24698 −0.556011
\(221\) 0.544667 0.0366383
\(222\) 76.0427 5.10365
\(223\) 12.8415 0.859929 0.429965 0.902846i \(-0.358526\pi\)
0.429965 + 0.902846i \(0.358526\pi\)
\(224\) 6.42467 0.429266
\(225\) −19.3611 −1.29074
\(226\) −21.8675 −1.45460
\(227\) 22.2024 1.47362 0.736812 0.676097i \(-0.236330\pi\)
0.736812 + 0.676097i \(0.236330\pi\)
\(228\) −25.2086 −1.66948
\(229\) −22.1015 −1.46051 −0.730255 0.683175i \(-0.760599\pi\)
−0.730255 + 0.683175i \(0.760599\pi\)
\(230\) −13.9459 −0.919569
\(231\) 5.69622 0.374784
\(232\) −4.12036 −0.270515
\(233\) 6.53757 0.428290 0.214145 0.976802i \(-0.431303\pi\)
0.214145 + 0.976802i \(0.431303\pi\)
\(234\) −1.84593 −0.120672
\(235\) −13.7539 −0.897204
\(236\) 11.1659 0.726838
\(237\) 40.9241 2.65831
\(238\) −10.3763 −0.672595
\(239\) −8.06523 −0.521696 −0.260848 0.965380i \(-0.584002\pi\)
−0.260848 + 0.965380i \(0.584002\pi\)
\(240\) 3.33051 0.214983
\(241\) 25.2744 1.62807 0.814035 0.580816i \(-0.197266\pi\)
0.814035 + 0.580816i \(0.197266\pi\)
\(242\) 17.4161 1.11955
\(243\) −20.4333 −1.31079
\(244\) 20.7012 1.32526
\(245\) 1.48598 0.0949357
\(246\) −5.21267 −0.332348
\(247\) 0.307842 0.0195875
\(248\) 4.82372 0.306307
\(249\) 41.1526 2.60794
\(250\) 26.0735 1.64903
\(251\) 4.42774 0.279476 0.139738 0.990188i \(-0.455374\pi\)
0.139738 + 0.990188i \(0.455374\pi\)
\(252\) 21.2966 1.34156
\(253\) −7.53176 −0.473518
\(254\) 24.8972 1.56219
\(255\) −21.5819 −1.35151
\(256\) −11.1270 −0.695435
\(257\) −9.32220 −0.581503 −0.290752 0.956799i \(-0.593905\pi\)
−0.290752 + 0.956799i \(0.593905\pi\)
\(258\) −32.7920 −2.04154
\(259\) 10.7135 0.665706
\(260\) 0.539415 0.0334531
\(261\) 11.8480 0.733376
\(262\) −44.4873 −2.74843
\(263\) 26.5234 1.63550 0.817751 0.575572i \(-0.195221\pi\)
0.817751 + 0.575572i \(0.195221\pi\)
\(264\) −13.7376 −0.845489
\(265\) −9.79684 −0.601815
\(266\) −5.86461 −0.359582
\(267\) 29.9920 1.83548
\(268\) 10.4718 0.639664
\(269\) −11.8921 −0.725071 −0.362536 0.931970i \(-0.618089\pi\)
−0.362536 + 0.931970i \(0.618089\pi\)
\(270\) 41.5013 2.52569
\(271\) 12.5010 0.759379 0.379690 0.925114i \(-0.376031\pi\)
0.379690 + 0.925114i \(0.376031\pi\)
\(272\) −3.27653 −0.198669
\(273\) −0.372576 −0.0225493
\(274\) −8.27147 −0.499698
\(275\) 5.04547 0.304253
\(276\) −40.3409 −2.42824
\(277\) 10.4051 0.625184 0.312592 0.949887i \(-0.398803\pi\)
0.312592 + 0.949887i \(0.398803\pi\)
\(278\) 44.2182 2.65203
\(279\) −13.8705 −0.830408
\(280\) −3.58373 −0.214169
\(281\) 8.67708 0.517631 0.258816 0.965927i \(-0.416668\pi\)
0.258816 + 0.965927i \(0.416668\pi\)
\(282\) −65.6959 −3.91213
\(283\) −31.6052 −1.87874 −0.939368 0.342912i \(-0.888587\pi\)
−0.939368 + 0.342912i \(0.888587\pi\)
\(284\) −33.8898 −2.01099
\(285\) −12.1979 −0.722543
\(286\) 0.481047 0.0284449
\(287\) −0.734404 −0.0433505
\(288\) 44.5538 2.62536
\(289\) 4.23210 0.248947
\(290\) −5.71703 −0.335715
\(291\) −11.4676 −0.672242
\(292\) −30.8304 −1.80422
\(293\) 0.256704 0.0149968 0.00749841 0.999972i \(-0.497613\pi\)
0.00749841 + 0.999972i \(0.497613\pi\)
\(294\) 7.09783 0.413954
\(295\) 5.40294 0.314572
\(296\) −25.8378 −1.50179
\(297\) 22.4135 1.30057
\(298\) 33.7220 1.95346
\(299\) 0.492635 0.0284898
\(300\) 27.0240 1.56023
\(301\) −4.62001 −0.266293
\(302\) 14.8248 0.853069
\(303\) 26.6078 1.52858
\(304\) −1.85188 −0.106212
\(305\) 10.0169 0.573566
\(306\) −71.9576 −4.11354
\(307\) −21.6675 −1.23663 −0.618316 0.785930i \(-0.712185\pi\)
−0.618316 + 0.785930i \(0.712185\pi\)
\(308\) −5.54987 −0.316233
\(309\) −9.79366 −0.557142
\(310\) 6.69294 0.380134
\(311\) 10.8042 0.612652 0.306326 0.951927i \(-0.400900\pi\)
0.306326 + 0.951927i \(0.400900\pi\)
\(312\) 0.898541 0.0508699
\(313\) 11.1276 0.628971 0.314485 0.949262i \(-0.398168\pi\)
0.314485 + 0.949262i \(0.398168\pi\)
\(314\) 3.59015 0.202604
\(315\) 10.3050 0.580620
\(316\) −39.8727 −2.24301
\(317\) −18.3815 −1.03241 −0.516205 0.856465i \(-0.672656\pi\)
−0.516205 + 0.856465i \(0.672656\pi\)
\(318\) −46.7949 −2.62413
\(319\) −3.08759 −0.172872
\(320\) −19.3852 −1.08367
\(321\) 46.7510 2.60938
\(322\) −9.38503 −0.523007
\(323\) 12.0002 0.667711
\(324\) 56.1593 3.11996
\(325\) −0.330012 −0.0183058
\(326\) −7.67108 −0.424862
\(327\) 2.50604 0.138584
\(328\) 1.77116 0.0977960
\(329\) −9.25577 −0.510287
\(330\) −19.0610 −1.04927
\(331\) −11.6571 −0.640730 −0.320365 0.947294i \(-0.603805\pi\)
−0.320365 + 0.947294i \(0.603805\pi\)
\(332\) −40.0953 −2.20052
\(333\) 74.2962 4.07141
\(334\) −54.1768 −2.96442
\(335\) 5.06706 0.276843
\(336\) 2.24129 0.122272
\(337\) −4.97204 −0.270844 −0.135422 0.990788i \(-0.543239\pi\)
−0.135422 + 0.990788i \(0.543239\pi\)
\(338\) 29.2430 1.59061
\(339\) −30.6079 −1.66239
\(340\) 21.0274 1.14037
\(341\) 3.61465 0.195744
\(342\) −40.6700 −2.19918
\(343\) 1.00000 0.0539949
\(344\) 11.1421 0.600741
\(345\) −19.5201 −1.05093
\(346\) −50.3865 −2.70879
\(347\) 25.4043 1.36378 0.681888 0.731456i \(-0.261159\pi\)
0.681888 + 0.731456i \(0.261159\pi\)
\(348\) −16.5374 −0.886499
\(349\) −4.68626 −0.250850 −0.125425 0.992103i \(-0.540029\pi\)
−0.125425 + 0.992103i \(0.540029\pi\)
\(350\) 6.28696 0.336052
\(351\) −1.46602 −0.0782501
\(352\) −11.6107 −0.618851
\(353\) 7.76895 0.413499 0.206750 0.978394i \(-0.433711\pi\)
0.206750 + 0.978394i \(0.433711\pi\)
\(354\) 25.8073 1.37164
\(355\) −16.3986 −0.870346
\(356\) −29.2214 −1.54873
\(357\) −14.5237 −0.768674
\(358\) −30.8845 −1.63230
\(359\) −3.90140 −0.205908 −0.102954 0.994686i \(-0.532829\pi\)
−0.102954 + 0.994686i \(0.532829\pi\)
\(360\) −24.8525 −1.30984
\(361\) −12.2175 −0.643029
\(362\) 4.27756 0.224823
\(363\) 24.3773 1.27947
\(364\) 0.363003 0.0190265
\(365\) −14.9182 −0.780855
\(366\) 47.8460 2.50095
\(367\) −36.7223 −1.91689 −0.958446 0.285276i \(-0.907915\pi\)
−0.958446 + 0.285276i \(0.907915\pi\)
\(368\) −2.96352 −0.154484
\(369\) −5.09295 −0.265128
\(370\) −35.8501 −1.86376
\(371\) −6.59285 −0.342284
\(372\) 19.3604 1.00379
\(373\) 12.1354 0.628346 0.314173 0.949366i \(-0.398273\pi\)
0.314173 + 0.949366i \(0.398273\pi\)
\(374\) 18.7520 0.969645
\(375\) 36.4950 1.88460
\(376\) 22.3221 1.15118
\(377\) 0.201952 0.0104010
\(378\) 27.9286 1.43649
\(379\) −28.3692 −1.45723 −0.728614 0.684924i \(-0.759835\pi\)
−0.728614 + 0.684924i \(0.759835\pi\)
\(380\) 11.8845 0.609663
\(381\) 34.8486 1.78535
\(382\) −8.08350 −0.413588
\(383\) −11.2115 −0.572880 −0.286440 0.958098i \(-0.592472\pi\)
−0.286440 + 0.958098i \(0.592472\pi\)
\(384\) −52.0937 −2.65839
\(385\) −2.68546 −0.136864
\(386\) −17.0178 −0.866182
\(387\) −32.0389 −1.62863
\(388\) 11.1729 0.567221
\(389\) 15.6303 0.792487 0.396244 0.918145i \(-0.370314\pi\)
0.396244 + 0.918145i \(0.370314\pi\)
\(390\) 1.24673 0.0631307
\(391\) 19.2038 0.971176
\(392\) −2.41170 −0.121809
\(393\) −62.2687 −3.14104
\(394\) 10.2300 0.515382
\(395\) −19.2936 −0.970764
\(396\) −38.4873 −1.93406
\(397\) 23.4557 1.17721 0.588604 0.808422i \(-0.299678\pi\)
0.588604 + 0.808422i \(0.299678\pi\)
\(398\) 53.7876 2.69613
\(399\) −8.20868 −0.410948
\(400\) 1.98524 0.0992620
\(401\) 10.4508 0.521888 0.260944 0.965354i \(-0.415966\pi\)
0.260944 + 0.965354i \(0.415966\pi\)
\(402\) 24.2030 1.20714
\(403\) −0.236425 −0.0117772
\(404\) −25.9242 −1.28978
\(405\) 27.1743 1.35030
\(406\) −3.84731 −0.190939
\(407\) −19.3615 −0.959714
\(408\) 35.0267 1.73408
\(409\) −6.69689 −0.331140 −0.165570 0.986198i \(-0.552946\pi\)
−0.165570 + 0.986198i \(0.552946\pi\)
\(410\) 2.45750 0.121367
\(411\) −11.5776 −0.571079
\(412\) 9.54204 0.470102
\(413\) 3.63595 0.178913
\(414\) −65.0834 −3.19867
\(415\) −19.4013 −0.952372
\(416\) 0.759426 0.0372339
\(417\) 61.8922 3.03087
\(418\) 10.5985 0.518391
\(419\) 3.51411 0.171675 0.0858377 0.996309i \(-0.472643\pi\)
0.0858377 + 0.996309i \(0.472643\pi\)
\(420\) −14.3836 −0.701849
\(421\) −21.5476 −1.05016 −0.525082 0.851052i \(-0.675965\pi\)
−0.525082 + 0.851052i \(0.675965\pi\)
\(422\) 42.5065 2.06918
\(423\) −64.1870 −3.12088
\(424\) 15.9000 0.772171
\(425\) −12.8645 −0.624018
\(426\) −78.3283 −3.79502
\(427\) 6.74094 0.326217
\(428\) −45.5498 −2.20173
\(429\) 0.673320 0.0325082
\(430\) 15.4597 0.745533
\(431\) −31.3170 −1.50848 −0.754242 0.656596i \(-0.771996\pi\)
−0.754242 + 0.656596i \(0.771996\pi\)
\(432\) 8.81905 0.424307
\(433\) −12.0671 −0.579908 −0.289954 0.957041i \(-0.593640\pi\)
−0.289954 + 0.957041i \(0.593640\pi\)
\(434\) 4.50406 0.216202
\(435\) −8.00211 −0.383672
\(436\) −2.44165 −0.116934
\(437\) 10.8538 0.519210
\(438\) −71.2573 −3.40481
\(439\) 26.5970 1.26940 0.634702 0.772757i \(-0.281123\pi\)
0.634702 + 0.772757i \(0.281123\pi\)
\(440\) 6.47653 0.308757
\(441\) 6.93481 0.330229
\(442\) −1.22653 −0.0583399
\(443\) 17.1679 0.815673 0.407837 0.913055i \(-0.366283\pi\)
0.407837 + 0.913055i \(0.366283\pi\)
\(444\) −103.702 −4.92149
\(445\) −14.1396 −0.670283
\(446\) −28.9175 −1.36928
\(447\) 47.2006 2.23251
\(448\) −13.0454 −0.616339
\(449\) 22.3309 1.05386 0.526931 0.849908i \(-0.323343\pi\)
0.526931 + 0.849908i \(0.323343\pi\)
\(450\) 43.5988 2.05527
\(451\) 1.32722 0.0624962
\(452\) 29.8215 1.40268
\(453\) 20.7502 0.974929
\(454\) −49.9972 −2.34648
\(455\) 0.175650 0.00823459
\(456\) 19.7969 0.927073
\(457\) −22.1697 −1.03705 −0.518527 0.855061i \(-0.673519\pi\)
−0.518527 + 0.855061i \(0.673519\pi\)
\(458\) 49.7700 2.32560
\(459\) −57.1479 −2.66743
\(460\) 19.0186 0.886746
\(461\) −4.59956 −0.214223 −0.107111 0.994247i \(-0.534160\pi\)
−0.107111 + 0.994247i \(0.534160\pi\)
\(462\) −12.8272 −0.596776
\(463\) −31.2323 −1.45149 −0.725744 0.687965i \(-0.758504\pi\)
−0.725744 + 0.687965i \(0.758504\pi\)
\(464\) −1.21487 −0.0563990
\(465\) 9.36810 0.434435
\(466\) −14.7218 −0.681976
\(467\) −5.60616 −0.259422 −0.129711 0.991552i \(-0.541405\pi\)
−0.129711 + 0.991552i \(0.541405\pi\)
\(468\) 2.51736 0.116365
\(469\) 3.40992 0.157455
\(470\) 30.9721 1.42864
\(471\) 5.02513 0.231546
\(472\) −8.76882 −0.403618
\(473\) 8.34929 0.383901
\(474\) −92.1563 −4.23288
\(475\) −7.27090 −0.333612
\(476\) 14.1505 0.648588
\(477\) −45.7202 −2.09338
\(478\) 18.1619 0.830707
\(479\) −3.99643 −0.182602 −0.0913009 0.995823i \(-0.529102\pi\)
−0.0913009 + 0.995823i \(0.529102\pi\)
\(480\) −30.0914 −1.37348
\(481\) 1.26639 0.0577424
\(482\) −56.9150 −2.59241
\(483\) −13.1362 −0.597718
\(484\) −23.7510 −1.07959
\(485\) 5.40636 0.245490
\(486\) 46.0133 2.08721
\(487\) 26.6685 1.20847 0.604234 0.796807i \(-0.293479\pi\)
0.604234 + 0.796807i \(0.293479\pi\)
\(488\) −16.2571 −0.735926
\(489\) −10.7372 −0.485553
\(490\) −3.34625 −0.151168
\(491\) 7.72807 0.348763 0.174381 0.984678i \(-0.444207\pi\)
0.174381 + 0.984678i \(0.444207\pi\)
\(492\) 7.10870 0.320485
\(493\) 7.87243 0.354556
\(494\) −0.693225 −0.0311897
\(495\) −18.6232 −0.837050
\(496\) 1.42225 0.0638611
\(497\) −11.0355 −0.495012
\(498\) −92.6709 −4.15268
\(499\) 0.0786257 0.00351977 0.00175989 0.999998i \(-0.499440\pi\)
0.00175989 + 0.999998i \(0.499440\pi\)
\(500\) −35.5574 −1.59017
\(501\) −75.8311 −3.38788
\(502\) −9.97074 −0.445016
\(503\) −21.3721 −0.952936 −0.476468 0.879192i \(-0.658083\pi\)
−0.476468 + 0.879192i \(0.658083\pi\)
\(504\) −16.7247 −0.744976
\(505\) −12.5442 −0.558208
\(506\) 16.9606 0.753992
\(507\) 40.9314 1.81783
\(508\) −33.9532 −1.50643
\(509\) −24.0236 −1.06483 −0.532415 0.846484i \(-0.678715\pi\)
−0.532415 + 0.846484i \(0.678715\pi\)
\(510\) 48.5998 2.15203
\(511\) −10.0393 −0.444113
\(512\) −7.99827 −0.353477
\(513\) −32.2996 −1.42606
\(514\) 20.9925 0.925940
\(515\) 4.61719 0.203458
\(516\) 44.7197 1.96867
\(517\) 16.7271 0.735655
\(518\) −24.1256 −1.06002
\(519\) −70.5258 −3.09574
\(520\) −0.423614 −0.0185767
\(521\) 7.44491 0.326167 0.163084 0.986612i \(-0.447856\pi\)
0.163084 + 0.986612i \(0.447856\pi\)
\(522\) −26.6804 −1.16777
\(523\) −8.03508 −0.351349 −0.175675 0.984448i \(-0.556211\pi\)
−0.175675 + 0.984448i \(0.556211\pi\)
\(524\) 60.6689 2.65033
\(525\) 8.79984 0.384056
\(526\) −59.7275 −2.60424
\(527\) −9.21628 −0.401467
\(528\) −4.05046 −0.176274
\(529\) −5.63080 −0.244817
\(530\) 22.0613 0.958283
\(531\) 25.2146 1.09422
\(532\) 7.99778 0.346748
\(533\) −0.0868100 −0.00376016
\(534\) −67.5384 −2.92267
\(535\) −22.0406 −0.952898
\(536\) −8.22370 −0.355210
\(537\) −43.2290 −1.86547
\(538\) 26.7795 1.15455
\(539\) −1.80720 −0.0778417
\(540\) −56.5968 −2.43554
\(541\) −4.06658 −0.174836 −0.0874180 0.996172i \(-0.527862\pi\)
−0.0874180 + 0.996172i \(0.527862\pi\)
\(542\) −28.1507 −1.20918
\(543\) 5.98729 0.256939
\(544\) 29.6038 1.26925
\(545\) −1.18146 −0.0506084
\(546\) 0.838997 0.0359057
\(547\) 29.9747 1.28163 0.640813 0.767697i \(-0.278597\pi\)
0.640813 + 0.767697i \(0.278597\pi\)
\(548\) 11.2801 0.481862
\(549\) 46.7472 1.99512
\(550\) −11.3618 −0.484469
\(551\) 4.44944 0.189553
\(552\) 31.6806 1.34841
\(553\) −12.9837 −0.552125
\(554\) −23.4311 −0.995493
\(555\) −50.1793 −2.12999
\(556\) −60.3020 −2.55737
\(557\) −3.14757 −0.133367 −0.0666833 0.997774i \(-0.521242\pi\)
−0.0666833 + 0.997774i \(0.521242\pi\)
\(558\) 31.2348 1.32228
\(559\) −0.546107 −0.0230979
\(560\) −1.05665 −0.0446516
\(561\) 26.2472 1.10816
\(562\) −19.5398 −0.824235
\(563\) 9.24699 0.389714 0.194857 0.980832i \(-0.437576\pi\)
0.194857 + 0.980832i \(0.437576\pi\)
\(564\) 89.5918 3.77250
\(565\) 14.4300 0.607074
\(566\) 71.1712 2.99155
\(567\) 18.2872 0.767989
\(568\) 26.6144 1.11672
\(569\) −26.8669 −1.12632 −0.563159 0.826349i \(-0.690414\pi\)
−0.563159 + 0.826349i \(0.690414\pi\)
\(570\) 27.4683 1.15052
\(571\) −16.9462 −0.709177 −0.354589 0.935022i \(-0.615379\pi\)
−0.354589 + 0.935022i \(0.615379\pi\)
\(572\) −0.656020 −0.0274296
\(573\) −11.3145 −0.472668
\(574\) 1.65379 0.0690279
\(575\) −11.6355 −0.485234
\(576\) −90.4676 −3.76948
\(577\) 6.92784 0.288410 0.144205 0.989548i \(-0.453938\pi\)
0.144205 + 0.989548i \(0.453938\pi\)
\(578\) −9.53018 −0.396403
\(579\) −23.8197 −0.989915
\(580\) 7.79651 0.323733
\(581\) −13.0562 −0.541664
\(582\) 25.8236 1.07042
\(583\) 11.9146 0.493453
\(584\) 24.2118 1.00189
\(585\) 1.21810 0.0503621
\(586\) −0.578068 −0.0238798
\(587\) −29.6401 −1.22338 −0.611689 0.791098i \(-0.709510\pi\)
−0.611689 + 0.791098i \(0.709510\pi\)
\(588\) −9.67956 −0.399178
\(589\) −5.20898 −0.214632
\(590\) −12.1668 −0.500899
\(591\) 14.3190 0.589004
\(592\) −7.61817 −0.313105
\(593\) −17.5073 −0.718940 −0.359470 0.933157i \(-0.617042\pi\)
−0.359470 + 0.933157i \(0.617042\pi\)
\(594\) −50.4726 −2.07092
\(595\) 6.84714 0.280705
\(596\) −45.9878 −1.88374
\(597\) 75.2863 3.08126
\(598\) −1.10935 −0.0453649
\(599\) 3.33470 0.136252 0.0681260 0.997677i \(-0.478298\pi\)
0.0681260 + 0.997677i \(0.478298\pi\)
\(600\) −21.2226 −0.866407
\(601\) 2.40141 0.0979556 0.0489778 0.998800i \(-0.484404\pi\)
0.0489778 + 0.998800i \(0.484404\pi\)
\(602\) 10.4037 0.424024
\(603\) 23.6471 0.962985
\(604\) −20.2171 −0.822620
\(605\) −11.4926 −0.467240
\(606\) −59.9176 −2.43399
\(607\) −10.0650 −0.408525 −0.204262 0.978916i \(-0.565480\pi\)
−0.204262 + 0.978916i \(0.565480\pi\)
\(608\) 16.7319 0.678566
\(609\) −5.38508 −0.218214
\(610\) −22.5569 −0.913301
\(611\) −1.09408 −0.0442616
\(612\) 98.1311 3.96671
\(613\) −4.46403 −0.180300 −0.0901502 0.995928i \(-0.528735\pi\)
−0.0901502 + 0.995928i \(0.528735\pi\)
\(614\) 48.7927 1.96911
\(615\) 3.43975 0.138704
\(616\) 4.35843 0.175606
\(617\) −15.8111 −0.636530 −0.318265 0.948002i \(-0.603100\pi\)
−0.318265 + 0.948002i \(0.603100\pi\)
\(618\) 22.0542 0.887149
\(619\) 29.7501 1.19576 0.597879 0.801586i \(-0.296010\pi\)
0.597879 + 0.801586i \(0.296010\pi\)
\(620\) −9.12740 −0.366565
\(621\) −51.6884 −2.07419
\(622\) −24.3299 −0.975538
\(623\) −9.51537 −0.381225
\(624\) 0.264931 0.0106057
\(625\) −3.24614 −0.129846
\(626\) −25.0581 −1.00152
\(627\) 14.8347 0.592443
\(628\) −4.89602 −0.195372
\(629\) 49.3661 1.96835
\(630\) −23.2056 −0.924533
\(631\) 31.8015 1.26600 0.632999 0.774153i \(-0.281824\pi\)
0.632999 + 0.774153i \(0.281824\pi\)
\(632\) 31.3129 1.24556
\(633\) 59.4962 2.36476
\(634\) 41.3931 1.64393
\(635\) −16.4293 −0.651975
\(636\) 63.8159 2.53047
\(637\) 0.118205 0.00468344
\(638\) 6.95288 0.275267
\(639\) −76.5294 −3.02745
\(640\) 24.5594 0.970796
\(641\) 16.4744 0.650699 0.325350 0.945594i \(-0.394518\pi\)
0.325350 + 0.945594i \(0.394518\pi\)
\(642\) −105.278 −4.15498
\(643\) 13.0067 0.512932 0.256466 0.966553i \(-0.417442\pi\)
0.256466 + 0.966553i \(0.417442\pi\)
\(644\) 12.7987 0.504339
\(645\) 21.6389 0.852031
\(646\) −27.0231 −1.06321
\(647\) −37.1849 −1.46189 −0.730944 0.682438i \(-0.760920\pi\)
−0.730944 + 0.682438i \(0.760920\pi\)
\(648\) −44.1031 −1.73253
\(649\) −6.57090 −0.257930
\(650\) 0.743148 0.0291487
\(651\) 6.30433 0.247086
\(652\) 10.4613 0.409697
\(653\) 40.4935 1.58463 0.792317 0.610110i \(-0.208875\pi\)
0.792317 + 0.610110i \(0.208875\pi\)
\(654\) −5.64331 −0.220671
\(655\) 29.3564 1.14705
\(656\) 0.522220 0.0203892
\(657\) −69.6207 −2.71616
\(658\) 20.8429 0.812541
\(659\) 20.5019 0.798640 0.399320 0.916812i \(-0.369246\pi\)
0.399320 + 0.916812i \(0.369246\pi\)
\(660\) 25.9941 1.01182
\(661\) 31.8266 1.23791 0.618956 0.785426i \(-0.287556\pi\)
0.618956 + 0.785426i \(0.287556\pi\)
\(662\) 26.2503 1.02025
\(663\) −1.71677 −0.0666737
\(664\) 31.4877 1.22196
\(665\) 3.86996 0.150070
\(666\) −167.306 −6.48299
\(667\) 7.12036 0.275702
\(668\) 73.8828 2.85861
\(669\) −40.4758 −1.56488
\(670\) −11.4104 −0.440823
\(671\) −12.1822 −0.470290
\(672\) −20.2502 −0.781170
\(673\) −29.7117 −1.14530 −0.572651 0.819800i \(-0.694085\pi\)
−0.572651 + 0.819800i \(0.694085\pi\)
\(674\) 11.1965 0.431271
\(675\) 34.6257 1.33274
\(676\) −39.8797 −1.53384
\(677\) 40.7669 1.56680 0.783400 0.621517i \(-0.213484\pi\)
0.783400 + 0.621517i \(0.213484\pi\)
\(678\) 68.9253 2.64706
\(679\) 3.63825 0.139623
\(680\) −16.5132 −0.633254
\(681\) −69.9809 −2.68167
\(682\) −8.13976 −0.311687
\(683\) 18.2699 0.699079 0.349539 0.936922i \(-0.386338\pi\)
0.349539 + 0.936922i \(0.386338\pi\)
\(684\) 55.4631 2.12068
\(685\) 5.45820 0.208547
\(686\) −2.25188 −0.0859772
\(687\) 69.6630 2.65781
\(688\) 3.28520 0.125247
\(689\) −0.779307 −0.0296892
\(690\) 43.9570 1.67341
\(691\) 42.6438 1.62225 0.811123 0.584876i \(-0.198857\pi\)
0.811123 + 0.584876i \(0.198857\pi\)
\(692\) 68.7138 2.61211
\(693\) −12.5326 −0.476074
\(694\) −57.2076 −2.17157
\(695\) −29.1789 −1.10682
\(696\) 12.9872 0.492278
\(697\) −3.38401 −0.128178
\(698\) 10.5529 0.399434
\(699\) −20.6061 −0.779395
\(700\) −8.57374 −0.324057
\(701\) 7.66940 0.289669 0.144835 0.989456i \(-0.453735\pi\)
0.144835 + 0.989456i \(0.453735\pi\)
\(702\) 3.30129 0.124599
\(703\) 27.9014 1.05232
\(704\) 23.5757 0.888544
\(705\) 43.3516 1.63272
\(706\) −17.4948 −0.658424
\(707\) −8.44168 −0.317482
\(708\) −35.1944 −1.32269
\(709\) −22.5595 −0.847239 −0.423620 0.905840i \(-0.639241\pi\)
−0.423620 + 0.905840i \(0.639241\pi\)
\(710\) 36.9276 1.38587
\(711\) −90.0398 −3.37676
\(712\) 22.9482 0.860020
\(713\) −8.33583 −0.312179
\(714\) 32.7056 1.22398
\(715\) −0.317435 −0.0118714
\(716\) 42.1183 1.57403
\(717\) 25.4212 0.949373
\(718\) 8.78550 0.327872
\(719\) −14.3607 −0.535564 −0.267782 0.963479i \(-0.586291\pi\)
−0.267782 + 0.963479i \(0.586291\pi\)
\(720\) −7.32766 −0.273086
\(721\) 3.10717 0.115717
\(722\) 27.5125 1.02391
\(723\) −79.6639 −2.96273
\(724\) −5.83346 −0.216799
\(725\) −4.76987 −0.177149
\(726\) −54.8947 −2.03733
\(727\) 33.5933 1.24591 0.622953 0.782260i \(-0.285933\pi\)
0.622953 + 0.782260i \(0.285933\pi\)
\(728\) −0.285074 −0.0105656
\(729\) 9.54321 0.353452
\(730\) 33.5940 1.24337
\(731\) −21.2882 −0.787373
\(732\) −65.2493 −2.41169
\(733\) 42.9532 1.58651 0.793257 0.608887i \(-0.208384\pi\)
0.793257 + 0.608887i \(0.208384\pi\)
\(734\) 82.6944 3.05231
\(735\) −4.68374 −0.172762
\(736\) 26.7757 0.986965
\(737\) −6.16241 −0.226995
\(738\) 11.4687 0.422169
\(739\) −24.1401 −0.888009 −0.444005 0.896025i \(-0.646443\pi\)
−0.444005 + 0.896025i \(0.646443\pi\)
\(740\) 48.8901 1.79723
\(741\) −0.970305 −0.0356450
\(742\) 14.8463 0.545026
\(743\) 3.72572 0.136683 0.0683416 0.997662i \(-0.478229\pi\)
0.0683416 + 0.997662i \(0.478229\pi\)
\(744\) −15.2041 −0.557411
\(745\) −22.2526 −0.815271
\(746\) −27.3275 −1.00053
\(747\) −90.5425 −3.31278
\(748\) −25.5728 −0.935035
\(749\) −14.8324 −0.541963
\(750\) −82.1825 −3.00088
\(751\) −51.1766 −1.86746 −0.933731 0.357975i \(-0.883467\pi\)
−0.933731 + 0.357975i \(0.883467\pi\)
\(752\) 6.58159 0.240006
\(753\) −13.9560 −0.508586
\(754\) −0.454771 −0.0165618
\(755\) −9.78261 −0.356026
\(756\) −38.0872 −1.38522
\(757\) −0.103777 −0.00377182 −0.00188591 0.999998i \(-0.500600\pi\)
−0.00188591 + 0.999998i \(0.500600\pi\)
\(758\) 63.8841 2.32038
\(759\) 23.7398 0.861699
\(760\) −9.33317 −0.338550
\(761\) −49.4710 −1.79332 −0.896661 0.442718i \(-0.854014\pi\)
−0.896661 + 0.442718i \(0.854014\pi\)
\(762\) −78.4749 −2.84284
\(763\) −0.795075 −0.0287837
\(764\) 11.0238 0.398826
\(765\) 47.4836 1.71677
\(766\) 25.2469 0.912209
\(767\) 0.429787 0.0155187
\(768\) 35.0716 1.26554
\(769\) 12.2913 0.443234 0.221617 0.975134i \(-0.428867\pi\)
0.221617 + 0.975134i \(0.428867\pi\)
\(770\) 6.04735 0.217931
\(771\) 29.3832 1.05821
\(772\) 23.2077 0.835265
\(773\) 47.0409 1.69194 0.845972 0.533228i \(-0.179021\pi\)
0.845972 + 0.533228i \(0.179021\pi\)
\(774\) 72.1478 2.59330
\(775\) 5.58411 0.200587
\(776\) −8.77436 −0.314981
\(777\) −33.7685 −1.21144
\(778\) −35.1976 −1.26189
\(779\) −1.91262 −0.0685267
\(780\) −1.70021 −0.0608773
\(781\) 19.9434 0.713633
\(782\) −43.2446 −1.54642
\(783\) −21.1893 −0.757242
\(784\) −0.711080 −0.0253957
\(785\) −2.36908 −0.0845561
\(786\) 140.222 5.00155
\(787\) −27.0970 −0.965904 −0.482952 0.875647i \(-0.660435\pi\)
−0.482952 + 0.875647i \(0.660435\pi\)
\(788\) −13.9511 −0.496987
\(789\) −83.6005 −2.97626
\(790\) 43.4468 1.54577
\(791\) 9.71076 0.345275
\(792\) 30.2249 1.07399
\(793\) 0.796812 0.0282956
\(794\) −52.8194 −1.87449
\(795\) 30.8792 1.09517
\(796\) −73.3520 −2.59989
\(797\) 9.52599 0.337428 0.168714 0.985665i \(-0.446039\pi\)
0.168714 + 0.985665i \(0.446039\pi\)
\(798\) 18.4850 0.654361
\(799\) −42.6490 −1.50881
\(800\) −17.9368 −0.634162
\(801\) −65.9873 −2.33154
\(802\) −23.5340 −0.831013
\(803\) 18.1431 0.640255
\(804\) −33.0065 −1.16405
\(805\) 6.19302 0.218275
\(806\) 0.532402 0.0187531
\(807\) 37.4832 1.31947
\(808\) 20.3588 0.716220
\(809\) −34.7609 −1.22213 −0.611065 0.791581i \(-0.709259\pi\)
−0.611065 + 0.791581i \(0.709259\pi\)
\(810\) −61.1934 −2.15012
\(811\) 4.50178 0.158079 0.0790394 0.996871i \(-0.474815\pi\)
0.0790394 + 0.996871i \(0.474815\pi\)
\(812\) 5.24672 0.184124
\(813\) −39.4025 −1.38190
\(814\) 43.5998 1.52817
\(815\) 5.06202 0.177315
\(816\) 10.3275 0.361534
\(817\) −12.0320 −0.420945
\(818\) 15.0806 0.527281
\(819\) 0.819728 0.0286436
\(820\) −3.35138 −0.117035
\(821\) −31.0748 −1.08452 −0.542259 0.840212i \(-0.682431\pi\)
−0.542259 + 0.840212i \(0.682431\pi\)
\(822\) 26.0713 0.909340
\(823\) −19.0671 −0.664636 −0.332318 0.943167i \(-0.607831\pi\)
−0.332318 + 0.943167i \(0.607831\pi\)
\(824\) −7.49357 −0.261051
\(825\) −15.9031 −0.553674
\(826\) −8.18773 −0.284888
\(827\) 11.2551 0.391379 0.195689 0.980666i \(-0.437306\pi\)
0.195689 + 0.980666i \(0.437306\pi\)
\(828\) 88.7565 3.08450
\(829\) 25.6029 0.889227 0.444613 0.895723i \(-0.353341\pi\)
0.444613 + 0.895723i \(0.353341\pi\)
\(830\) 43.6894 1.51648
\(831\) −32.7965 −1.13770
\(832\) −1.54203 −0.0534603
\(833\) 4.60783 0.159652
\(834\) −139.374 −4.82612
\(835\) 35.7503 1.23719
\(836\) −14.4536 −0.499888
\(837\) 24.8063 0.857432
\(838\) −7.91335 −0.273362
\(839\) −36.0320 −1.24396 −0.621981 0.783032i \(-0.713672\pi\)
−0.621981 + 0.783032i \(0.713672\pi\)
\(840\) 11.2958 0.389741
\(841\) −26.0811 −0.899347
\(842\) 48.5225 1.67220
\(843\) −27.3498 −0.941976
\(844\) −57.9676 −1.99533
\(845\) −19.2970 −0.663836
\(846\) 144.542 4.96944
\(847\) −7.73402 −0.265744
\(848\) 4.68804 0.160988
\(849\) 99.6182 3.41889
\(850\) 28.9692 0.993636
\(851\) 44.6501 1.53059
\(852\) 106.819 3.65956
\(853\) 12.6237 0.432226 0.216113 0.976368i \(-0.430662\pi\)
0.216113 + 0.976368i \(0.430662\pi\)
\(854\) −15.1798 −0.519442
\(855\) 26.8374 0.917820
\(856\) 35.7712 1.22264
\(857\) −25.3711 −0.866660 −0.433330 0.901235i \(-0.642661\pi\)
−0.433330 + 0.901235i \(0.642661\pi\)
\(858\) −1.51624 −0.0517635
\(859\) −1.50264 −0.0512694 −0.0256347 0.999671i \(-0.508161\pi\)
−0.0256347 + 0.999671i \(0.508161\pi\)
\(860\) −21.0829 −0.718922
\(861\) 2.31481 0.0788884
\(862\) 70.5221 2.40199
\(863\) 1.00000 0.0340404
\(864\) −79.6809 −2.71080
\(865\) 33.2492 1.13051
\(866\) 27.1737 0.923399
\(867\) −13.3394 −0.453029
\(868\) −6.14235 −0.208485
\(869\) 23.4642 0.795970
\(870\) 18.0198 0.610929
\(871\) 0.403068 0.0136575
\(872\) 1.91748 0.0649342
\(873\) 25.2305 0.853925
\(874\) −24.4416 −0.826748
\(875\) −11.5785 −0.391426
\(876\) 97.1761 3.28328
\(877\) −54.6977 −1.84701 −0.923505 0.383587i \(-0.874689\pi\)
−0.923505 + 0.383587i \(0.874689\pi\)
\(878\) −59.8932 −2.02130
\(879\) −0.809120 −0.0272909
\(880\) 1.90958 0.0643719
\(881\) 15.4681 0.521135 0.260567 0.965456i \(-0.416090\pi\)
0.260567 + 0.965456i \(0.416090\pi\)
\(882\) −15.6164 −0.525831
\(883\) −48.4282 −1.62974 −0.814869 0.579645i \(-0.803191\pi\)
−0.814869 + 0.579645i \(0.803191\pi\)
\(884\) 1.67266 0.0562576
\(885\) −17.0298 −0.572451
\(886\) −38.6602 −1.29881
\(887\) 24.2238 0.813357 0.406679 0.913571i \(-0.366687\pi\)
0.406679 + 0.913571i \(0.366687\pi\)
\(888\) 81.4395 2.73293
\(889\) −11.0562 −0.370812
\(890\) 31.8408 1.06731
\(891\) −33.0486 −1.10717
\(892\) 39.4358 1.32041
\(893\) −24.1050 −0.806642
\(894\) −106.290 −3.55487
\(895\) 20.3802 0.681234
\(896\) 16.5274 0.552143
\(897\) −1.55276 −0.0518452
\(898\) −50.2866 −1.67809
\(899\) −3.41721 −0.113970
\(900\) −59.4573 −1.98191
\(901\) −30.3787 −1.01206
\(902\) −2.98873 −0.0995139
\(903\) 14.5621 0.484595
\(904\) −23.4194 −0.778919
\(905\) −2.82269 −0.0938293
\(906\) −46.7270 −1.55240
\(907\) 12.8585 0.426959 0.213479 0.976948i \(-0.431520\pi\)
0.213479 + 0.976948i \(0.431520\pi\)
\(908\) 68.1829 2.26273
\(909\) −58.5415 −1.94170
\(910\) −0.395542 −0.0131121
\(911\) −14.4293 −0.478064 −0.239032 0.971012i \(-0.576830\pi\)
−0.239032 + 0.971012i \(0.576830\pi\)
\(912\) 5.83703 0.193283
\(913\) 23.5953 0.780889
\(914\) 49.9235 1.65132
\(915\) −31.5728 −1.04376
\(916\) −67.8731 −2.24259
\(917\) 19.7556 0.652387
\(918\) 128.690 4.24741
\(919\) −47.4295 −1.56455 −0.782277 0.622930i \(-0.785942\pi\)
−0.782277 + 0.622930i \(0.785942\pi\)
\(920\) −14.9357 −0.492416
\(921\) 68.2950 2.25040
\(922\) 10.3577 0.341112
\(923\) −1.30445 −0.0429366
\(924\) 17.4929 0.575475
\(925\) −29.9107 −0.983459
\(926\) 70.3314 2.31123
\(927\) 21.5477 0.707718
\(928\) 10.9765 0.360320
\(929\) 32.9381 1.08066 0.540332 0.841452i \(-0.318299\pi\)
0.540332 + 0.841452i \(0.318299\pi\)
\(930\) −21.0958 −0.691760
\(931\) 2.60432 0.0853530
\(932\) 20.0767 0.657634
\(933\) −34.0544 −1.11489
\(934\) 12.6244 0.413084
\(935\) −12.3742 −0.404678
\(936\) −1.97694 −0.0646182
\(937\) −39.4371 −1.28835 −0.644177 0.764877i \(-0.722800\pi\)
−0.644177 + 0.764877i \(0.722800\pi\)
\(938\) −7.67873 −0.250719
\(939\) −35.0738 −1.14459
\(940\) −42.2378 −1.37764
\(941\) 45.7441 1.49121 0.745607 0.666386i \(-0.232160\pi\)
0.745607 + 0.666386i \(0.232160\pi\)
\(942\) −11.3160 −0.368695
\(943\) −3.06073 −0.0996710
\(944\) −2.58545 −0.0841492
\(945\) −18.4296 −0.599515
\(946\) −18.8016 −0.611293
\(947\) −2.09714 −0.0681479 −0.0340740 0.999419i \(-0.510848\pi\)
−0.0340740 + 0.999419i \(0.510848\pi\)
\(948\) 125.677 4.08179
\(949\) −1.18669 −0.0385217
\(950\) 16.3732 0.531217
\(951\) 57.9378 1.87876
\(952\) −11.1127 −0.360165
\(953\) 16.5559 0.536300 0.268150 0.963377i \(-0.413588\pi\)
0.268150 + 0.963377i \(0.413588\pi\)
\(954\) 102.956 3.33334
\(955\) 5.33417 0.172610
\(956\) −24.7681 −0.801057
\(957\) 9.73192 0.314588
\(958\) 8.99950 0.290761
\(959\) 3.67314 0.118612
\(960\) 61.1013 1.97204
\(961\) −26.9995 −0.870950
\(962\) −2.85176 −0.0919444
\(963\) −102.860 −3.31461
\(964\) 77.6171 2.49988
\(965\) 11.2297 0.361498
\(966\) 29.5812 0.951758
\(967\) −19.0406 −0.612303 −0.306151 0.951983i \(-0.599041\pi\)
−0.306151 + 0.951983i \(0.599041\pi\)
\(968\) 18.6521 0.599502
\(969\) −37.8242 −1.21509
\(970\) −12.1745 −0.390899
\(971\) 14.5439 0.466736 0.233368 0.972389i \(-0.425025\pi\)
0.233368 + 0.972389i \(0.425025\pi\)
\(972\) −62.7500 −2.01271
\(973\) −19.6361 −0.629505
\(974\) −60.0544 −1.92427
\(975\) 1.04018 0.0333125
\(976\) −4.79335 −0.153431
\(977\) 4.82827 0.154470 0.0772350 0.997013i \(-0.475391\pi\)
0.0772350 + 0.997013i \(0.475391\pi\)
\(978\) 24.1789 0.773156
\(979\) 17.1962 0.549593
\(980\) 4.56340 0.145772
\(981\) −5.51370 −0.176039
\(982\) −17.4027 −0.555343
\(983\) −16.6018 −0.529515 −0.264758 0.964315i \(-0.585292\pi\)
−0.264758 + 0.964315i \(0.585292\pi\)
\(984\) −5.58262 −0.177967
\(985\) −6.75064 −0.215093
\(986\) −17.7278 −0.564567
\(987\) 29.1738 0.928611
\(988\) 0.945375 0.0300764
\(989\) −19.2545 −0.612258
\(990\) 41.9372 1.33285
\(991\) 11.7533 0.373357 0.186679 0.982421i \(-0.440228\pi\)
0.186679 + 0.982421i \(0.440228\pi\)
\(992\) −12.8502 −0.407994
\(993\) 36.7425 1.16599
\(994\) 24.8507 0.788217
\(995\) −35.4935 −1.12522
\(996\) 126.379 4.00446
\(997\) −36.3309 −1.15061 −0.575306 0.817938i \(-0.695117\pi\)
−0.575306 + 0.817938i \(0.695117\pi\)
\(998\) −0.177056 −0.00560460
\(999\) −132.873 −4.20391
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 6041.2.a.c.1.9 83
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6041.2.a.c.1.9 83 1.1 even 1 trivial