Properties

Label 4021.2.a.c.1.17
Level $4021$
Weight $2$
Character 4021.1
Self dual yes
Analytic conductor $32.108$
Analytic rank $0$
Dimension $182$
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] = [4021,2,Mod(1,4021)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4021, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4021.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4021 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4021.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: \(32.1078466528\)
Analytic rank: \(0\)
Dimension: \(182\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) \(=\) 4021.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.38633 q^{2} -0.134750 q^{3} +3.69456 q^{4} -0.899112 q^{5} +0.321557 q^{6} -0.745765 q^{7} -4.04378 q^{8} -2.98184 q^{9} +O(q^{10})\) \(q-2.38633 q^{2} -0.134750 q^{3} +3.69456 q^{4} -0.899112 q^{5} +0.321557 q^{6} -0.745765 q^{7} -4.04378 q^{8} -2.98184 q^{9} +2.14558 q^{10} +0.293991 q^{11} -0.497841 q^{12} -1.69853 q^{13} +1.77964 q^{14} +0.121155 q^{15} +2.26067 q^{16} -4.46796 q^{17} +7.11566 q^{18} +4.09378 q^{19} -3.32183 q^{20} +0.100492 q^{21} -0.701558 q^{22} -0.899501 q^{23} +0.544898 q^{24} -4.19160 q^{25} +4.05325 q^{26} +0.806051 q^{27} -2.75528 q^{28} +1.10875 q^{29} -0.289115 q^{30} -8.42322 q^{31} +2.69286 q^{32} -0.0396151 q^{33} +10.6620 q^{34} +0.670526 q^{35} -11.0166 q^{36} -4.63360 q^{37} -9.76911 q^{38} +0.228876 q^{39} +3.63581 q^{40} +9.06142 q^{41} -0.239806 q^{42} -1.24742 q^{43} +1.08617 q^{44} +2.68101 q^{45} +2.14650 q^{46} -1.77997 q^{47} -0.304625 q^{48} -6.44383 q^{49} +10.0025 q^{50} +0.602056 q^{51} -6.27533 q^{52} +3.41414 q^{53} -1.92350 q^{54} -0.264330 q^{55} +3.01572 q^{56} -0.551636 q^{57} -2.64584 q^{58} -6.04312 q^{59} +0.447615 q^{60} -6.70671 q^{61} +20.1006 q^{62} +2.22376 q^{63} -10.9474 q^{64} +1.52717 q^{65} +0.0945346 q^{66} -3.29913 q^{67} -16.5072 q^{68} +0.121207 q^{69} -1.60010 q^{70} -2.56050 q^{71} +12.0579 q^{72} -6.89904 q^{73} +11.0573 q^{74} +0.564816 q^{75} +15.1247 q^{76} -0.219248 q^{77} -0.546174 q^{78} +14.0674 q^{79} -2.03260 q^{80} +8.83691 q^{81} -21.6235 q^{82} -11.5699 q^{83} +0.371273 q^{84} +4.01720 q^{85} +2.97675 q^{86} -0.149404 q^{87} -1.18883 q^{88} +11.3134 q^{89} -6.39777 q^{90} +1.26670 q^{91} -3.32326 q^{92} +1.13503 q^{93} +4.24760 q^{94} -3.68077 q^{95} -0.362862 q^{96} +12.5097 q^{97} +15.3771 q^{98} -0.876633 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9} + 7 q^{10} + 138 q^{11} + 47 q^{12} + 5 q^{13} + 72 q^{14} + 41 q^{15} + 256 q^{16} + 29 q^{17} + 35 q^{18} + 48 q^{19} + 56 q^{20} + 22 q^{21} + 19 q^{22} + 91 q^{23} + 46 q^{24} + 230 q^{25} + 88 q^{26} + 103 q^{27} + 15 q^{28} + 75 q^{29} + 18 q^{30} + 43 q^{31} + 116 q^{32} + 15 q^{33} + 13 q^{34} + 185 q^{35} + 364 q^{36} + 15 q^{37} + 53 q^{38} + 80 q^{39} - 13 q^{40} + 68 q^{41} + 32 q^{42} + 82 q^{43} + 259 q^{44} + 37 q^{45} + 13 q^{46} + 121 q^{47} + 53 q^{48} + 244 q^{49} + 93 q^{50} + 144 q^{51} - 16 q^{52} + 101 q^{53} + 47 q^{54} + 49 q^{55} + 199 q^{56} + 3 q^{57} + 4 q^{58} + 254 q^{59} + 24 q^{60} + 8 q^{61} + 37 q^{62} + 19 q^{63} + 326 q^{64} + 65 q^{65} + 41 q^{66} + 91 q^{67} + 50 q^{68} + 50 q^{69} + 5 q^{70} + 212 q^{71} + 77 q^{72} + 5 q^{73} + 101 q^{74} + 127 q^{75} + 22 q^{76} + 87 q^{77} - 20 q^{78} + 86 q^{79} + 71 q^{80} + 358 q^{81} - 20 q^{82} + 139 q^{83} - 30 q^{84} + 25 q^{85} + 82 q^{86} + 36 q^{87} - 8 q^{88} + 100 q^{89} - 87 q^{90} + 74 q^{91} + 171 q^{92} + 50 q^{93} - 13 q^{94} + 217 q^{95} + 42 q^{96} + 20 q^{97} + 47 q^{98} + 389 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.38633 −1.68739 −0.843695 0.536824i \(-0.819624\pi\)
−0.843695 + 0.536824i \(0.819624\pi\)
\(3\) −0.134750 −0.0777977 −0.0388989 0.999243i \(-0.512385\pi\)
−0.0388989 + 0.999243i \(0.512385\pi\)
\(4\) 3.69456 1.84728
\(5\) −0.899112 −0.402095 −0.201047 0.979581i \(-0.564435\pi\)
−0.201047 + 0.979581i \(0.564435\pi\)
\(6\) 0.321557 0.131275
\(7\) −0.745765 −0.281873 −0.140936 0.990019i \(-0.545011\pi\)
−0.140936 + 0.990019i \(0.545011\pi\)
\(8\) −4.04378 −1.42969
\(9\) −2.98184 −0.993948
\(10\) 2.14558 0.678491
\(11\) 0.293991 0.0886415 0.0443207 0.999017i \(-0.485888\pi\)
0.0443207 + 0.999017i \(0.485888\pi\)
\(12\) −0.497841 −0.143714
\(13\) −1.69853 −0.471087 −0.235544 0.971864i \(-0.575687\pi\)
−0.235544 + 0.971864i \(0.575687\pi\)
\(14\) 1.77964 0.475629
\(15\) 0.121155 0.0312821
\(16\) 2.26067 0.565168
\(17\) −4.46796 −1.08364 −0.541820 0.840495i \(-0.682265\pi\)
−0.541820 + 0.840495i \(0.682265\pi\)
\(18\) 7.11566 1.67718
\(19\) 4.09378 0.939178 0.469589 0.882885i \(-0.344402\pi\)
0.469589 + 0.882885i \(0.344402\pi\)
\(20\) −3.32183 −0.742783
\(21\) 0.100492 0.0219291
\(22\) −0.701558 −0.149573
\(23\) −0.899501 −0.187559 −0.0937794 0.995593i \(-0.529895\pi\)
−0.0937794 + 0.995593i \(0.529895\pi\)
\(24\) 0.544898 0.111227
\(25\) −4.19160 −0.838320
\(26\) 4.05325 0.794908
\(27\) 0.806051 0.155125
\(28\) −2.75528 −0.520699
\(29\) 1.10875 0.205890 0.102945 0.994687i \(-0.467173\pi\)
0.102945 + 0.994687i \(0.467173\pi\)
\(30\) −0.289115 −0.0527850
\(31\) −8.42322 −1.51285 −0.756427 0.654078i \(-0.773057\pi\)
−0.756427 + 0.654078i \(0.773057\pi\)
\(32\) 2.69286 0.476036
\(33\) −0.0396151 −0.00689610
\(34\) 10.6620 1.82852
\(35\) 0.670526 0.113340
\(36\) −11.0166 −1.83610
\(37\) −4.63360 −0.761758 −0.380879 0.924625i \(-0.624379\pi\)
−0.380879 + 0.924625i \(0.624379\pi\)
\(38\) −9.76911 −1.58476
\(39\) 0.228876 0.0366495
\(40\) 3.63581 0.574873
\(41\) 9.06142 1.41516 0.707578 0.706635i \(-0.249788\pi\)
0.707578 + 0.706635i \(0.249788\pi\)
\(42\) −0.239806 −0.0370029
\(43\) −1.24742 −0.190229 −0.0951147 0.995466i \(-0.530322\pi\)
−0.0951147 + 0.995466i \(0.530322\pi\)
\(44\) 1.08617 0.163746
\(45\) 2.68101 0.399661
\(46\) 2.14650 0.316485
\(47\) −1.77997 −0.259636 −0.129818 0.991538i \(-0.541439\pi\)
−0.129818 + 0.991538i \(0.541439\pi\)
\(48\) −0.304625 −0.0439688
\(49\) −6.44383 −0.920548
\(50\) 10.0025 1.41457
\(51\) 0.602056 0.0843047
\(52\) −6.27533 −0.870231
\(53\) 3.41414 0.468969 0.234484 0.972120i \(-0.424660\pi\)
0.234484 + 0.972120i \(0.424660\pi\)
\(54\) −1.92350 −0.261755
\(55\) −0.264330 −0.0356423
\(56\) 3.01572 0.402992
\(57\) −0.551636 −0.0730659
\(58\) −2.64584 −0.347416
\(59\) −6.04312 −0.786748 −0.393374 0.919379i \(-0.628692\pi\)
−0.393374 + 0.919379i \(0.628692\pi\)
\(60\) 0.447615 0.0577868
\(61\) −6.70671 −0.858706 −0.429353 0.903137i \(-0.641258\pi\)
−0.429353 + 0.903137i \(0.641258\pi\)
\(62\) 20.1006 2.55277
\(63\) 2.22376 0.280167
\(64\) −10.9474 −1.36843
\(65\) 1.52717 0.189422
\(66\) 0.0945346 0.0116364
\(67\) −3.29913 −0.403053 −0.201527 0.979483i \(-0.564590\pi\)
−0.201527 + 0.979483i \(0.564590\pi\)
\(68\) −16.5072 −2.00179
\(69\) 0.121207 0.0145917
\(70\) −1.60010 −0.191248
\(71\) −2.56050 −0.303875 −0.151937 0.988390i \(-0.548551\pi\)
−0.151937 + 0.988390i \(0.548551\pi\)
\(72\) 12.0579 1.42104
\(73\) −6.89904 −0.807472 −0.403736 0.914876i \(-0.632289\pi\)
−0.403736 + 0.914876i \(0.632289\pi\)
\(74\) 11.0573 1.28538
\(75\) 0.564816 0.0652193
\(76\) 15.1247 1.73493
\(77\) −0.219248 −0.0249856
\(78\) −0.546174 −0.0618420
\(79\) 14.0674 1.58270 0.791351 0.611363i \(-0.209378\pi\)
0.791351 + 0.611363i \(0.209378\pi\)
\(80\) −2.03260 −0.227251
\(81\) 8.83691 0.981879
\(82\) −21.6235 −2.38792
\(83\) −11.5699 −1.26997 −0.634983 0.772526i \(-0.718993\pi\)
−0.634983 + 0.772526i \(0.718993\pi\)
\(84\) 0.371273 0.0405092
\(85\) 4.01720 0.435726
\(86\) 2.97675 0.320991
\(87\) −0.149404 −0.0160177
\(88\) −1.18883 −0.126730
\(89\) 11.3134 1.19922 0.599608 0.800294i \(-0.295323\pi\)
0.599608 + 0.800294i \(0.295323\pi\)
\(90\) −6.39777 −0.674384
\(91\) 1.26670 0.132787
\(92\) −3.32326 −0.346474
\(93\) 1.13503 0.117697
\(94\) 4.24760 0.438107
\(95\) −3.68077 −0.377639
\(96\) −0.362862 −0.0370345
\(97\) 12.5097 1.27017 0.635083 0.772444i \(-0.280966\pi\)
0.635083 + 0.772444i \(0.280966\pi\)
\(98\) 15.3771 1.55332
\(99\) −0.876633 −0.0881050
\(100\) −15.4861 −1.54861
\(101\) 4.05913 0.403898 0.201949 0.979396i \(-0.435272\pi\)
0.201949 + 0.979396i \(0.435272\pi\)
\(102\) −1.43670 −0.142255
\(103\) 4.49373 0.442780 0.221390 0.975185i \(-0.428941\pi\)
0.221390 + 0.975185i \(0.428941\pi\)
\(104\) 6.86849 0.673511
\(105\) −0.0903532 −0.00881757
\(106\) −8.14726 −0.791332
\(107\) −3.31042 −0.320031 −0.160015 0.987115i \(-0.551154\pi\)
−0.160015 + 0.987115i \(0.551154\pi\)
\(108\) 2.97801 0.286559
\(109\) 7.11163 0.681170 0.340585 0.940214i \(-0.389375\pi\)
0.340585 + 0.940214i \(0.389375\pi\)
\(110\) 0.630779 0.0601424
\(111\) 0.624375 0.0592631
\(112\) −1.68593 −0.159305
\(113\) −11.1282 −1.04685 −0.523424 0.852072i \(-0.675346\pi\)
−0.523424 + 0.852072i \(0.675346\pi\)
\(114\) 1.31638 0.123291
\(115\) 0.808752 0.0754165
\(116\) 4.09635 0.380336
\(117\) 5.06475 0.468236
\(118\) 14.4209 1.32755
\(119\) 3.33205 0.305449
\(120\) −0.489924 −0.0447238
\(121\) −10.9136 −0.992143
\(122\) 16.0044 1.44897
\(123\) −1.22102 −0.110096
\(124\) −31.1201 −2.79467
\(125\) 8.26427 0.739179
\(126\) −5.30661 −0.472750
\(127\) −20.0668 −1.78064 −0.890321 0.455333i \(-0.849520\pi\)
−0.890321 + 0.455333i \(0.849520\pi\)
\(128\) 20.7384 1.83303
\(129\) 0.168089 0.0147994
\(130\) −3.64432 −0.319628
\(131\) 22.1672 1.93676 0.968378 0.249487i \(-0.0802619\pi\)
0.968378 + 0.249487i \(0.0802619\pi\)
\(132\) −0.146360 −0.0127390
\(133\) −3.05300 −0.264729
\(134\) 7.87281 0.680107
\(135\) −0.724730 −0.0623748
\(136\) 18.0675 1.54927
\(137\) 16.8952 1.44346 0.721728 0.692177i \(-0.243348\pi\)
0.721728 + 0.692177i \(0.243348\pi\)
\(138\) −0.289241 −0.0246218
\(139\) −2.24020 −0.190011 −0.0950057 0.995477i \(-0.530287\pi\)
−0.0950057 + 0.995477i \(0.530287\pi\)
\(140\) 2.47730 0.209370
\(141\) 0.239851 0.0201991
\(142\) 6.11018 0.512755
\(143\) −0.499352 −0.0417579
\(144\) −6.74097 −0.561747
\(145\) −0.996890 −0.0827872
\(146\) 16.4634 1.36252
\(147\) 0.868304 0.0716165
\(148\) −17.1191 −1.40718
\(149\) −3.69363 −0.302594 −0.151297 0.988488i \(-0.548345\pi\)
−0.151297 + 0.988488i \(0.548345\pi\)
\(150\) −1.34784 −0.110050
\(151\) −11.9598 −0.973273 −0.486636 0.873605i \(-0.661776\pi\)
−0.486636 + 0.873605i \(0.661776\pi\)
\(152\) −16.5544 −1.34274
\(153\) 13.3228 1.07708
\(154\) 0.523198 0.0421605
\(155\) 7.57342 0.608311
\(156\) 0.845598 0.0677020
\(157\) −8.51927 −0.679912 −0.339956 0.940441i \(-0.610412\pi\)
−0.339956 + 0.940441i \(0.610412\pi\)
\(158\) −33.5693 −2.67063
\(159\) −0.460054 −0.0364847
\(160\) −2.42119 −0.191412
\(161\) 0.670817 0.0528678
\(162\) −21.0878 −1.65681
\(163\) 1.62584 0.127345 0.0636727 0.997971i \(-0.479719\pi\)
0.0636727 + 0.997971i \(0.479719\pi\)
\(164\) 33.4780 2.61419
\(165\) 0.0356184 0.00277289
\(166\) 27.6097 2.14293
\(167\) 19.1385 1.48098 0.740491 0.672066i \(-0.234593\pi\)
0.740491 + 0.672066i \(0.234593\pi\)
\(168\) −0.406366 −0.0313518
\(169\) −10.1150 −0.778077
\(170\) −9.58635 −0.735239
\(171\) −12.2070 −0.933494
\(172\) −4.60867 −0.351407
\(173\) −0.0957593 −0.00728044 −0.00364022 0.999993i \(-0.501159\pi\)
−0.00364022 + 0.999993i \(0.501159\pi\)
\(174\) 0.356526 0.0270282
\(175\) 3.12595 0.236300
\(176\) 0.664616 0.0500973
\(177\) 0.814309 0.0612072
\(178\) −26.9974 −2.02354
\(179\) −15.7268 −1.17548 −0.587740 0.809050i \(-0.699982\pi\)
−0.587740 + 0.809050i \(0.699982\pi\)
\(180\) 9.90516 0.738287
\(181\) 18.7410 1.39301 0.696504 0.717553i \(-0.254738\pi\)
0.696504 + 0.717553i \(0.254738\pi\)
\(182\) −3.02277 −0.224063
\(183\) 0.903726 0.0668054
\(184\) 3.63739 0.268152
\(185\) 4.16612 0.306299
\(186\) −2.70854 −0.198600
\(187\) −1.31354 −0.0960554
\(188\) −6.57622 −0.479620
\(189\) −0.601125 −0.0437254
\(190\) 8.78352 0.637224
\(191\) −14.3635 −1.03931 −0.519655 0.854376i \(-0.673939\pi\)
−0.519655 + 0.854376i \(0.673939\pi\)
\(192\) 1.47516 0.106460
\(193\) −5.14580 −0.370403 −0.185201 0.982701i \(-0.559294\pi\)
−0.185201 + 0.982701i \(0.559294\pi\)
\(194\) −29.8522 −2.14327
\(195\) −0.205785 −0.0147366
\(196\) −23.8072 −1.70051
\(197\) −8.52683 −0.607511 −0.303756 0.952750i \(-0.598241\pi\)
−0.303756 + 0.952750i \(0.598241\pi\)
\(198\) 2.09194 0.148667
\(199\) 6.38700 0.452762 0.226381 0.974039i \(-0.427310\pi\)
0.226381 + 0.974039i \(0.427310\pi\)
\(200\) 16.9499 1.19854
\(201\) 0.444557 0.0313566
\(202\) −9.68642 −0.681534
\(203\) −0.826867 −0.0580347
\(204\) 2.22433 0.155735
\(205\) −8.14723 −0.569027
\(206\) −10.7235 −0.747143
\(207\) 2.68217 0.186424
\(208\) −3.83982 −0.266243
\(209\) 1.20353 0.0832502
\(210\) 0.215612 0.0148787
\(211\) 3.41872 0.235354 0.117677 0.993052i \(-0.462455\pi\)
0.117677 + 0.993052i \(0.462455\pi\)
\(212\) 12.6138 0.866317
\(213\) 0.345026 0.0236408
\(214\) 7.89976 0.540016
\(215\) 1.12157 0.0764903
\(216\) −3.25950 −0.221781
\(217\) 6.28175 0.426433
\(218\) −16.9707 −1.14940
\(219\) 0.929643 0.0628195
\(220\) −0.976585 −0.0658414
\(221\) 7.58897 0.510489
\(222\) −1.48996 −0.0999998
\(223\) −23.6932 −1.58661 −0.793306 0.608823i \(-0.791642\pi\)
−0.793306 + 0.608823i \(0.791642\pi\)
\(224\) −2.00825 −0.134182
\(225\) 12.4987 0.833246
\(226\) 26.5554 1.76644
\(227\) 1.89021 0.125458 0.0627288 0.998031i \(-0.480020\pi\)
0.0627288 + 0.998031i \(0.480020\pi\)
\(228\) −2.03805 −0.134973
\(229\) −17.3718 −1.14796 −0.573979 0.818870i \(-0.694601\pi\)
−0.573979 + 0.818870i \(0.694601\pi\)
\(230\) −1.92995 −0.127257
\(231\) 0.0295436 0.00194382
\(232\) −4.48354 −0.294359
\(233\) 10.4577 0.685105 0.342553 0.939499i \(-0.388708\pi\)
0.342553 + 0.939499i \(0.388708\pi\)
\(234\) −12.0862 −0.790097
\(235\) 1.60039 0.104398
\(236\) −22.3267 −1.45334
\(237\) −1.89557 −0.123131
\(238\) −7.95137 −0.515411
\(239\) 8.81120 0.569949 0.284975 0.958535i \(-0.408015\pi\)
0.284975 + 0.958535i \(0.408015\pi\)
\(240\) 0.273892 0.0176796
\(241\) 25.1670 1.62115 0.810574 0.585636i \(-0.199155\pi\)
0.810574 + 0.585636i \(0.199155\pi\)
\(242\) 26.0434 1.67413
\(243\) −3.60892 −0.231513
\(244\) −24.7784 −1.58627
\(245\) 5.79373 0.370148
\(246\) 2.91376 0.185775
\(247\) −6.95341 −0.442435
\(248\) 34.0617 2.16292
\(249\) 1.55905 0.0988005
\(250\) −19.7213 −1.24728
\(251\) −20.6573 −1.30388 −0.651938 0.758272i \(-0.726044\pi\)
−0.651938 + 0.758272i \(0.726044\pi\)
\(252\) 8.21580 0.517547
\(253\) −0.264445 −0.0166255
\(254\) 47.8860 3.00464
\(255\) −0.541316 −0.0338985
\(256\) −27.5938 −1.72461
\(257\) 20.0198 1.24880 0.624402 0.781103i \(-0.285343\pi\)
0.624402 + 0.781103i \(0.285343\pi\)
\(258\) −0.401116 −0.0249724
\(259\) 3.45558 0.214719
\(260\) 5.64222 0.349916
\(261\) −3.30612 −0.204643
\(262\) −52.8982 −3.26806
\(263\) 10.9410 0.674652 0.337326 0.941388i \(-0.390478\pi\)
0.337326 + 0.941388i \(0.390478\pi\)
\(264\) 0.160195 0.00985932
\(265\) −3.06970 −0.188570
\(266\) 7.28547 0.446701
\(267\) −1.52447 −0.0932962
\(268\) −12.1889 −0.744553
\(269\) 0.521301 0.0317843 0.0158921 0.999874i \(-0.494941\pi\)
0.0158921 + 0.999874i \(0.494941\pi\)
\(270\) 1.72944 0.105251
\(271\) −1.71921 −0.104435 −0.0522174 0.998636i \(-0.516629\pi\)
−0.0522174 + 0.998636i \(0.516629\pi\)
\(272\) −10.1006 −0.612438
\(273\) −0.170688 −0.0103305
\(274\) −40.3175 −2.43567
\(275\) −1.23229 −0.0743099
\(276\) 0.447808 0.0269549
\(277\) 13.4311 0.806999 0.403500 0.914980i \(-0.367794\pi\)
0.403500 + 0.914980i \(0.367794\pi\)
\(278\) 5.34586 0.320623
\(279\) 25.1167 1.50370
\(280\) −2.71146 −0.162041
\(281\) 19.0008 1.13349 0.566747 0.823892i \(-0.308202\pi\)
0.566747 + 0.823892i \(0.308202\pi\)
\(282\) −0.572362 −0.0340837
\(283\) 23.3534 1.38822 0.694108 0.719871i \(-0.255799\pi\)
0.694108 + 0.719871i \(0.255799\pi\)
\(284\) −9.45991 −0.561343
\(285\) 0.495982 0.0293794
\(286\) 1.19162 0.0704618
\(287\) −6.75769 −0.398894
\(288\) −8.02970 −0.473154
\(289\) 2.96268 0.174275
\(290\) 2.37891 0.139694
\(291\) −1.68568 −0.0988161
\(292\) −25.4889 −1.49163
\(293\) −2.98491 −0.174380 −0.0871901 0.996192i \(-0.527789\pi\)
−0.0871901 + 0.996192i \(0.527789\pi\)
\(294\) −2.07206 −0.120845
\(295\) 5.43344 0.316347
\(296\) 18.7373 1.08908
\(297\) 0.236971 0.0137505
\(298\) 8.81422 0.510594
\(299\) 1.52783 0.0883566
\(300\) 2.08675 0.120479
\(301\) 0.930281 0.0536205
\(302\) 28.5400 1.64229
\(303\) −0.546966 −0.0314224
\(304\) 9.25470 0.530793
\(305\) 6.03008 0.345281
\(306\) −31.7925 −1.81745
\(307\) −4.27511 −0.243994 −0.121997 0.992530i \(-0.538930\pi\)
−0.121997 + 0.992530i \(0.538930\pi\)
\(308\) −0.810026 −0.0461555
\(309\) −0.605528 −0.0344473
\(310\) −18.0727 −1.02646
\(311\) 13.3739 0.758366 0.379183 0.925322i \(-0.376205\pi\)
0.379183 + 0.925322i \(0.376205\pi\)
\(312\) −0.925526 −0.0523976
\(313\) −26.9168 −1.52142 −0.760712 0.649089i \(-0.775150\pi\)
−0.760712 + 0.649089i \(0.775150\pi\)
\(314\) 20.3298 1.14728
\(315\) −1.99940 −0.112654
\(316\) 51.9727 2.92369
\(317\) 11.1875 0.628353 0.314176 0.949365i \(-0.398272\pi\)
0.314176 + 0.949365i \(0.398272\pi\)
\(318\) 1.09784 0.0615638
\(319\) 0.325962 0.0182504
\(320\) 9.84294 0.550237
\(321\) 0.446078 0.0248977
\(322\) −1.60079 −0.0892085
\(323\) −18.2909 −1.01773
\(324\) 32.6485 1.81381
\(325\) 7.11955 0.394922
\(326\) −3.87978 −0.214881
\(327\) −0.958289 −0.0529935
\(328\) −36.6424 −2.02324
\(329\) 1.32744 0.0731843
\(330\) −0.0849972 −0.00467894
\(331\) 11.3715 0.625035 0.312518 0.949912i \(-0.398828\pi\)
0.312518 + 0.949912i \(0.398828\pi\)
\(332\) −42.7459 −2.34599
\(333\) 13.8167 0.757148
\(334\) −45.6708 −2.49899
\(335\) 2.96629 0.162066
\(336\) 0.227178 0.0123936
\(337\) −9.40268 −0.512196 −0.256098 0.966651i \(-0.582437\pi\)
−0.256098 + 0.966651i \(0.582437\pi\)
\(338\) 24.1377 1.31292
\(339\) 1.49951 0.0814424
\(340\) 14.8418 0.804909
\(341\) −2.47635 −0.134102
\(342\) 29.1300 1.57517
\(343\) 10.0259 0.541350
\(344\) 5.04429 0.271970
\(345\) −0.108979 −0.00586723
\(346\) 0.228513 0.0122849
\(347\) −6.56082 −0.352203 −0.176102 0.984372i \(-0.556349\pi\)
−0.176102 + 0.984372i \(0.556349\pi\)
\(348\) −0.551981 −0.0295893
\(349\) 24.3552 1.30371 0.651853 0.758346i \(-0.273992\pi\)
0.651853 + 0.758346i \(0.273992\pi\)
\(350\) −7.45954 −0.398729
\(351\) −1.36910 −0.0730772
\(352\) 0.791677 0.0421965
\(353\) −33.6719 −1.79218 −0.896088 0.443877i \(-0.853603\pi\)
−0.896088 + 0.443877i \(0.853603\pi\)
\(354\) −1.94321 −0.103280
\(355\) 2.30217 0.122187
\(356\) 41.7980 2.21529
\(357\) −0.448993 −0.0237632
\(358\) 37.5294 1.98349
\(359\) 12.6353 0.666865 0.333432 0.942774i \(-0.391793\pi\)
0.333432 + 0.942774i \(0.391793\pi\)
\(360\) −10.8414 −0.571393
\(361\) −2.24094 −0.117944
\(362\) −44.7222 −2.35055
\(363\) 1.47060 0.0771864
\(364\) 4.67992 0.245295
\(365\) 6.20301 0.324680
\(366\) −2.15659 −0.112727
\(367\) −10.1017 −0.527303 −0.263652 0.964618i \(-0.584927\pi\)
−0.263652 + 0.964618i \(0.584927\pi\)
\(368\) −2.03348 −0.106002
\(369\) −27.0197 −1.40659
\(370\) −9.94173 −0.516846
\(371\) −2.54615 −0.132189
\(372\) 4.19342 0.217419
\(373\) 14.5014 0.750856 0.375428 0.926852i \(-0.377496\pi\)
0.375428 + 0.926852i \(0.377496\pi\)
\(374\) 3.13453 0.162083
\(375\) −1.11361 −0.0575064
\(376\) 7.19783 0.371200
\(377\) −1.88324 −0.0969920
\(378\) 1.43448 0.0737818
\(379\) 9.84652 0.505782 0.252891 0.967495i \(-0.418619\pi\)
0.252891 + 0.967495i \(0.418619\pi\)
\(380\) −13.5988 −0.697605
\(381\) 2.70400 0.138530
\(382\) 34.2761 1.75372
\(383\) 13.4721 0.688394 0.344197 0.938898i \(-0.388151\pi\)
0.344197 + 0.938898i \(0.388151\pi\)
\(384\) −2.79449 −0.142606
\(385\) 0.197128 0.0100466
\(386\) 12.2796 0.625014
\(387\) 3.71960 0.189078
\(388\) 46.2179 2.34636
\(389\) −27.7948 −1.40925 −0.704627 0.709578i \(-0.748886\pi\)
−0.704627 + 0.709578i \(0.748886\pi\)
\(390\) 0.491071 0.0248664
\(391\) 4.01893 0.203246
\(392\) 26.0575 1.31610
\(393\) −2.98702 −0.150675
\(394\) 20.3478 1.02511
\(395\) −12.6481 −0.636396
\(396\) −3.23878 −0.162755
\(397\) 13.2872 0.666866 0.333433 0.942774i \(-0.391793\pi\)
0.333433 + 0.942774i \(0.391793\pi\)
\(398\) −15.2415 −0.763986
\(399\) 0.411391 0.0205953
\(400\) −9.47583 −0.473791
\(401\) 37.6536 1.88033 0.940165 0.340719i \(-0.110671\pi\)
0.940165 + 0.340719i \(0.110671\pi\)
\(402\) −1.06086 −0.0529108
\(403\) 14.3071 0.712687
\(404\) 14.9967 0.746114
\(405\) −7.94537 −0.394809
\(406\) 1.97318 0.0979271
\(407\) −1.36223 −0.0675234
\(408\) −2.43458 −0.120530
\(409\) 11.3610 0.561767 0.280884 0.959742i \(-0.409373\pi\)
0.280884 + 0.959742i \(0.409373\pi\)
\(410\) 19.4420 0.960170
\(411\) −2.27662 −0.112298
\(412\) 16.6024 0.817940
\(413\) 4.50675 0.221763
\(414\) −6.40054 −0.314569
\(415\) 10.4027 0.510647
\(416\) −4.57391 −0.224254
\(417\) 0.301866 0.0147825
\(418\) −2.87203 −0.140475
\(419\) 33.0110 1.61270 0.806348 0.591442i \(-0.201441\pi\)
0.806348 + 0.591442i \(0.201441\pi\)
\(420\) −0.333816 −0.0162885
\(421\) 34.3417 1.67371 0.836855 0.547425i \(-0.184392\pi\)
0.836855 + 0.547425i \(0.184392\pi\)
\(422\) −8.15819 −0.397134
\(423\) 5.30760 0.258064
\(424\) −13.8061 −0.670481
\(425\) 18.7279 0.908437
\(426\) −0.823345 −0.0398912
\(427\) 5.00163 0.242046
\(428\) −12.2306 −0.591187
\(429\) 0.0672874 0.00324867
\(430\) −2.67643 −0.129069
\(431\) 12.6756 0.610560 0.305280 0.952263i \(-0.401250\pi\)
0.305280 + 0.952263i \(0.401250\pi\)
\(432\) 1.82222 0.0876714
\(433\) 2.19496 0.105483 0.0527414 0.998608i \(-0.483204\pi\)
0.0527414 + 0.998608i \(0.483204\pi\)
\(434\) −14.9903 −0.719558
\(435\) 0.134330 0.00644065
\(436\) 26.2744 1.25831
\(437\) −3.68236 −0.176151
\(438\) −2.21843 −0.106001
\(439\) 6.94039 0.331247 0.165623 0.986189i \(-0.447036\pi\)
0.165623 + 0.986189i \(0.447036\pi\)
\(440\) 1.06889 0.0509576
\(441\) 19.2145 0.914976
\(442\) −18.1098 −0.861394
\(443\) −26.3745 −1.25309 −0.626546 0.779384i \(-0.715532\pi\)
−0.626546 + 0.779384i \(0.715532\pi\)
\(444\) 2.30679 0.109476
\(445\) −10.1720 −0.482198
\(446\) 56.5397 2.67723
\(447\) 0.497715 0.0235411
\(448\) 8.16419 0.385722
\(449\) 38.8633 1.83407 0.917035 0.398806i \(-0.130575\pi\)
0.917035 + 0.398806i \(0.130575\pi\)
\(450\) −29.8260 −1.40601
\(451\) 2.66397 0.125441
\(452\) −41.1137 −1.93382
\(453\) 1.61157 0.0757184
\(454\) −4.51066 −0.211696
\(455\) −1.13891 −0.0533929
\(456\) 2.23070 0.104462
\(457\) 0.806934 0.0377468 0.0188734 0.999822i \(-0.493992\pi\)
0.0188734 + 0.999822i \(0.493992\pi\)
\(458\) 41.4547 1.93705
\(459\) −3.60140 −0.168099
\(460\) 2.98798 0.139315
\(461\) −35.9208 −1.67300 −0.836498 0.547969i \(-0.815401\pi\)
−0.836498 + 0.547969i \(0.815401\pi\)
\(462\) −0.0705007 −0.00327999
\(463\) 27.7359 1.28900 0.644499 0.764605i \(-0.277066\pi\)
0.644499 + 0.764605i \(0.277066\pi\)
\(464\) 2.50652 0.116362
\(465\) −1.02051 −0.0473252
\(466\) −24.9555 −1.15604
\(467\) −2.24571 −0.103919 −0.0519596 0.998649i \(-0.516547\pi\)
−0.0519596 + 0.998649i \(0.516547\pi\)
\(468\) 18.7120 0.864964
\(469\) 2.46038 0.113610
\(470\) −3.81907 −0.176160
\(471\) 1.14797 0.0528956
\(472\) 24.4371 1.12481
\(473\) −0.366729 −0.0168622
\(474\) 4.52345 0.207769
\(475\) −17.1595 −0.787332
\(476\) 12.3105 0.564250
\(477\) −10.1804 −0.466130
\(478\) −21.0264 −0.961726
\(479\) −15.9507 −0.728806 −0.364403 0.931241i \(-0.618727\pi\)
−0.364403 + 0.931241i \(0.618727\pi\)
\(480\) 0.326254 0.0148914
\(481\) 7.87030 0.358855
\(482\) −60.0567 −2.73551
\(483\) −0.0903923 −0.00411299
\(484\) −40.3209 −1.83277
\(485\) −11.2476 −0.510728
\(486\) 8.61208 0.390652
\(487\) 1.91964 0.0869870 0.0434935 0.999054i \(-0.486151\pi\)
0.0434935 + 0.999054i \(0.486151\pi\)
\(488\) 27.1205 1.22769
\(489\) −0.219081 −0.00990717
\(490\) −13.8257 −0.624583
\(491\) 14.1953 0.640626 0.320313 0.947312i \(-0.396212\pi\)
0.320313 + 0.947312i \(0.396212\pi\)
\(492\) −4.51114 −0.203378
\(493\) −4.95385 −0.223110
\(494\) 16.5931 0.746560
\(495\) 0.788191 0.0354266
\(496\) −19.0421 −0.855017
\(497\) 1.90953 0.0856541
\(498\) −3.72039 −0.166715
\(499\) 42.5164 1.90329 0.951647 0.307194i \(-0.0993902\pi\)
0.951647 + 0.307194i \(0.0993902\pi\)
\(500\) 30.5329 1.36547
\(501\) −2.57891 −0.115217
\(502\) 49.2950 2.20015
\(503\) 21.3422 0.951602 0.475801 0.879553i \(-0.342158\pi\)
0.475801 + 0.879553i \(0.342158\pi\)
\(504\) −8.99239 −0.400553
\(505\) −3.64961 −0.162406
\(506\) 0.631052 0.0280537
\(507\) 1.36299 0.0605326
\(508\) −74.1382 −3.28935
\(509\) 29.1281 1.29108 0.645540 0.763727i \(-0.276633\pi\)
0.645540 + 0.763727i \(0.276633\pi\)
\(510\) 1.29176 0.0572000
\(511\) 5.14507 0.227604
\(512\) 24.3710 1.07706
\(513\) 3.29980 0.145690
\(514\) −47.7739 −2.10722
\(515\) −4.04037 −0.178040
\(516\) 0.621016 0.0273387
\(517\) −0.523295 −0.0230145
\(518\) −8.24614 −0.362315
\(519\) 0.0129035 0.000566402 0
\(520\) −6.17554 −0.270815
\(521\) 41.6966 1.82676 0.913380 0.407108i \(-0.133463\pi\)
0.913380 + 0.407108i \(0.133463\pi\)
\(522\) 7.88948 0.345313
\(523\) 34.8138 1.52230 0.761151 0.648575i \(-0.224635\pi\)
0.761151 + 0.648575i \(0.224635\pi\)
\(524\) 81.8981 3.57773
\(525\) −0.421220 −0.0183836
\(526\) −26.1089 −1.13840
\(527\) 37.6346 1.63939
\(528\) −0.0895567 −0.00389746
\(529\) −22.1909 −0.964822
\(530\) 7.32530 0.318191
\(531\) 18.0196 0.781986
\(532\) −11.2795 −0.489029
\(533\) −15.3911 −0.666662
\(534\) 3.63789 0.157427
\(535\) 2.97644 0.128683
\(536\) 13.3410 0.576243
\(537\) 2.11919 0.0914496
\(538\) −1.24400 −0.0536325
\(539\) −1.89443 −0.0815987
\(540\) −2.67756 −0.115224
\(541\) 23.5117 1.01085 0.505423 0.862871i \(-0.331336\pi\)
0.505423 + 0.862871i \(0.331336\pi\)
\(542\) 4.10261 0.176222
\(543\) −2.52534 −0.108373
\(544\) −12.0316 −0.515851
\(545\) −6.39415 −0.273895
\(546\) 0.407318 0.0174316
\(547\) 10.7515 0.459699 0.229850 0.973226i \(-0.426177\pi\)
0.229850 + 0.973226i \(0.426177\pi\)
\(548\) 62.4204 2.66647
\(549\) 19.9984 0.853509
\(550\) 2.94065 0.125390
\(551\) 4.53898 0.193367
\(552\) −0.490136 −0.0208616
\(553\) −10.4909 −0.446120
\(554\) −32.0511 −1.36172
\(555\) −0.561383 −0.0238294
\(556\) −8.27657 −0.351005
\(557\) −15.9100 −0.674130 −0.337065 0.941481i \(-0.609434\pi\)
−0.337065 + 0.941481i \(0.609434\pi\)
\(558\) −59.9367 −2.53732
\(559\) 2.11878 0.0896147
\(560\) 1.51584 0.0640559
\(561\) 0.176999 0.00747289
\(562\) −45.3422 −1.91265
\(563\) −23.0125 −0.969863 −0.484932 0.874552i \(-0.661156\pi\)
−0.484932 + 0.874552i \(0.661156\pi\)
\(564\) 0.886143 0.0373134
\(565\) 10.0055 0.420933
\(566\) −55.7289 −2.34246
\(567\) −6.59026 −0.276765
\(568\) 10.3541 0.434448
\(569\) 43.7241 1.83301 0.916504 0.400025i \(-0.130999\pi\)
0.916504 + 0.400025i \(0.130999\pi\)
\(570\) −1.18358 −0.0495745
\(571\) 7.93582 0.332104 0.166052 0.986117i \(-0.446898\pi\)
0.166052 + 0.986117i \(0.446898\pi\)
\(572\) −1.84489 −0.0771386
\(573\) 1.93548 0.0808559
\(574\) 16.1261 0.673089
\(575\) 3.77035 0.157234
\(576\) 32.6434 1.36014
\(577\) 19.8752 0.827417 0.413708 0.910409i \(-0.364233\pi\)
0.413708 + 0.910409i \(0.364233\pi\)
\(578\) −7.06993 −0.294070
\(579\) 0.693395 0.0288165
\(580\) −3.68307 −0.152931
\(581\) 8.62847 0.357969
\(582\) 4.02258 0.166741
\(583\) 1.00373 0.0415701
\(584\) 27.8982 1.15444
\(585\) −4.55377 −0.188275
\(586\) 7.12297 0.294247
\(587\) −29.7160 −1.22651 −0.613255 0.789885i \(-0.710140\pi\)
−0.613255 + 0.789885i \(0.710140\pi\)
\(588\) 3.20800 0.132296
\(589\) −34.4828 −1.42084
\(590\) −12.9660 −0.533801
\(591\) 1.14899 0.0472630
\(592\) −10.4750 −0.430521
\(593\) 1.18232 0.0485521 0.0242761 0.999705i \(-0.492272\pi\)
0.0242761 + 0.999705i \(0.492272\pi\)
\(594\) −0.565491 −0.0232024
\(595\) −2.99589 −0.122819
\(596\) −13.6464 −0.558977
\(597\) −0.860646 −0.0352239
\(598\) −3.64590 −0.149092
\(599\) −25.1601 −1.02802 −0.514008 0.857785i \(-0.671840\pi\)
−0.514008 + 0.857785i \(0.671840\pi\)
\(600\) −2.28399 −0.0932437
\(601\) −8.90263 −0.363146 −0.181573 0.983377i \(-0.558119\pi\)
−0.181573 + 0.983377i \(0.558119\pi\)
\(602\) −2.21996 −0.0904787
\(603\) 9.83749 0.400614
\(604\) −44.1861 −1.79791
\(605\) 9.81252 0.398936
\(606\) 1.30524 0.0530218
\(607\) 1.08194 0.0439144 0.0219572 0.999759i \(-0.493010\pi\)
0.0219572 + 0.999759i \(0.493010\pi\)
\(608\) 11.0240 0.447082
\(609\) 0.111420 0.00451497
\(610\) −14.3898 −0.582624
\(611\) 3.02334 0.122311
\(612\) 49.2218 1.98967
\(613\) −2.96150 −0.119614 −0.0598068 0.998210i \(-0.519048\pi\)
−0.0598068 + 0.998210i \(0.519048\pi\)
\(614\) 10.2018 0.411712
\(615\) 1.09784 0.0442690
\(616\) 0.886592 0.0357218
\(617\) 45.0514 1.81370 0.906850 0.421453i \(-0.138480\pi\)
0.906850 + 0.421453i \(0.138480\pi\)
\(618\) 1.44499 0.0581260
\(619\) −21.9683 −0.882981 −0.441491 0.897266i \(-0.645550\pi\)
−0.441491 + 0.897266i \(0.645550\pi\)
\(620\) 27.9805 1.12372
\(621\) −0.725043 −0.0290950
\(622\) −31.9146 −1.27966
\(623\) −8.43712 −0.338026
\(624\) 0.517414 0.0207131
\(625\) 13.5275 0.541099
\(626\) 64.2322 2.56724
\(627\) −0.162176 −0.00647667
\(628\) −31.4750 −1.25599
\(629\) 20.7027 0.825472
\(630\) 4.77124 0.190091
\(631\) 18.9448 0.754182 0.377091 0.926176i \(-0.376924\pi\)
0.377091 + 0.926176i \(0.376924\pi\)
\(632\) −56.8854 −2.26278
\(633\) −0.460671 −0.0183100
\(634\) −26.6971 −1.06028
\(635\) 18.0423 0.715987
\(636\) −1.69970 −0.0673975
\(637\) 10.9450 0.433658
\(638\) −0.777852 −0.0307955
\(639\) 7.63499 0.302036
\(640\) −18.6461 −0.737052
\(641\) −6.97141 −0.275354 −0.137677 0.990477i \(-0.543964\pi\)
−0.137677 + 0.990477i \(0.543964\pi\)
\(642\) −1.06449 −0.0420120
\(643\) 1.09525 0.0431925 0.0215962 0.999767i \(-0.493125\pi\)
0.0215962 + 0.999767i \(0.493125\pi\)
\(644\) 2.47837 0.0976616
\(645\) −0.151131 −0.00595077
\(646\) 43.6480 1.71731
\(647\) −3.11802 −0.122582 −0.0612910 0.998120i \(-0.519522\pi\)
−0.0612910 + 0.998120i \(0.519522\pi\)
\(648\) −35.7346 −1.40379
\(649\) −1.77662 −0.0697385
\(650\) −16.9896 −0.666387
\(651\) −0.846463 −0.0331755
\(652\) 6.00675 0.235243
\(653\) −23.5756 −0.922586 −0.461293 0.887248i \(-0.652614\pi\)
−0.461293 + 0.887248i \(0.652614\pi\)
\(654\) 2.28679 0.0894206
\(655\) −19.9308 −0.778760
\(656\) 20.4849 0.799801
\(657\) 20.5719 0.802585
\(658\) −3.16771 −0.123490
\(659\) 2.03433 0.0792463 0.0396231 0.999215i \(-0.487384\pi\)
0.0396231 + 0.999215i \(0.487384\pi\)
\(660\) 0.131594 0.00512231
\(661\) −49.8867 −1.94037 −0.970183 0.242373i \(-0.922074\pi\)
−0.970183 + 0.242373i \(0.922074\pi\)
\(662\) −27.1362 −1.05468
\(663\) −1.02261 −0.0397149
\(664\) 46.7864 1.81566
\(665\) 2.74499 0.106446
\(666\) −32.9711 −1.27760
\(667\) −0.997321 −0.0386164
\(668\) 70.7084 2.73579
\(669\) 3.19265 0.123435
\(670\) −7.07854 −0.273468
\(671\) −1.97171 −0.0761170
\(672\) 0.270610 0.0104390
\(673\) 6.01826 0.231987 0.115994 0.993250i \(-0.462995\pi\)
0.115994 + 0.993250i \(0.462995\pi\)
\(674\) 22.4379 0.864274
\(675\) −3.37864 −0.130044
\(676\) −37.3705 −1.43733
\(677\) 42.7474 1.64292 0.821459 0.570268i \(-0.193161\pi\)
0.821459 + 0.570268i \(0.193161\pi\)
\(678\) −3.57833 −0.137425
\(679\) −9.32930 −0.358026
\(680\) −16.2447 −0.622955
\(681\) −0.254705 −0.00976031
\(682\) 5.90938 0.226282
\(683\) 47.2430 1.80770 0.903852 0.427845i \(-0.140727\pi\)
0.903852 + 0.427845i \(0.140727\pi\)
\(684\) −45.0996 −1.72443
\(685\) −15.1907 −0.580406
\(686\) −23.9252 −0.913469
\(687\) 2.34084 0.0893085
\(688\) −2.82000 −0.107512
\(689\) −5.79902 −0.220925
\(690\) 0.260060 0.00990030
\(691\) 38.6412 1.46998 0.734990 0.678078i \(-0.237187\pi\)
0.734990 + 0.678078i \(0.237187\pi\)
\(692\) −0.353789 −0.0134490
\(693\) 0.653763 0.0248344
\(694\) 15.6563 0.594304
\(695\) 2.01419 0.0764027
\(696\) 0.604156 0.0229005
\(697\) −40.4861 −1.53352
\(698\) −58.1196 −2.19986
\(699\) −1.40917 −0.0532996
\(700\) 11.5490 0.436512
\(701\) −6.47991 −0.244743 −0.122371 0.992484i \(-0.539050\pi\)
−0.122371 + 0.992484i \(0.539050\pi\)
\(702\) 3.26713 0.123310
\(703\) −18.9689 −0.715427
\(704\) −3.21843 −0.121299
\(705\) −0.215653 −0.00812194
\(706\) 80.3523 3.02410
\(707\) −3.02716 −0.113848
\(708\) 3.00851 0.113067
\(709\) −22.6081 −0.849067 −0.424533 0.905412i \(-0.639562\pi\)
−0.424533 + 0.905412i \(0.639562\pi\)
\(710\) −5.49374 −0.206176
\(711\) −41.9466 −1.57312
\(712\) −45.7488 −1.71451
\(713\) 7.57669 0.283749
\(714\) 1.07144 0.0400978
\(715\) 0.448973 0.0167906
\(716\) −58.1038 −2.17144
\(717\) −1.18731 −0.0443407
\(718\) −30.1519 −1.12526
\(719\) 42.5913 1.58839 0.794193 0.607665i \(-0.207894\pi\)
0.794193 + 0.607665i \(0.207894\pi\)
\(720\) 6.06088 0.225876
\(721\) −3.35127 −0.124808
\(722\) 5.34761 0.199017
\(723\) −3.39124 −0.126122
\(724\) 69.2398 2.57328
\(725\) −4.64743 −0.172601
\(726\) −3.50933 −0.130244
\(727\) −28.6844 −1.06384 −0.531922 0.846793i \(-0.678530\pi\)
−0.531922 + 0.846793i \(0.678530\pi\)
\(728\) −5.12228 −0.189844
\(729\) −26.0244 −0.963868
\(730\) −14.8024 −0.547862
\(731\) 5.57342 0.206140
\(732\) 3.33887 0.123408
\(733\) −31.5571 −1.16559 −0.582793 0.812620i \(-0.698040\pi\)
−0.582793 + 0.812620i \(0.698040\pi\)
\(734\) 24.1059 0.889766
\(735\) −0.780702 −0.0287966
\(736\) −2.42223 −0.0892847
\(737\) −0.969914 −0.0357272
\(738\) 64.4779 2.37347
\(739\) 7.59773 0.279487 0.139744 0.990188i \(-0.455372\pi\)
0.139744 + 0.990188i \(0.455372\pi\)
\(740\) 15.3920 0.565821
\(741\) 0.936970 0.0344204
\(742\) 6.07595 0.223055
\(743\) −44.6133 −1.63670 −0.818351 0.574719i \(-0.805111\pi\)
−0.818351 + 0.574719i \(0.805111\pi\)
\(744\) −4.58980 −0.168270
\(745\) 3.32099 0.121672
\(746\) −34.6052 −1.26699
\(747\) 34.4998 1.26228
\(748\) −4.85295 −0.177441
\(749\) 2.46880 0.0902080
\(750\) 2.65743 0.0970357
\(751\) 40.4760 1.47699 0.738496 0.674258i \(-0.235537\pi\)
0.738496 + 0.674258i \(0.235537\pi\)
\(752\) −4.02393 −0.146738
\(753\) 2.78356 0.101439
\(754\) 4.49404 0.163663
\(755\) 10.7532 0.391348
\(756\) −2.22089 −0.0807731
\(757\) −44.5469 −1.61908 −0.809542 0.587061i \(-0.800285\pi\)
−0.809542 + 0.587061i \(0.800285\pi\)
\(758\) −23.4970 −0.853450
\(759\) 0.0356338 0.00129343
\(760\) 14.8842 0.539908
\(761\) −44.7811 −1.62331 −0.811656 0.584135i \(-0.801434\pi\)
−0.811656 + 0.584135i \(0.801434\pi\)
\(762\) −6.45262 −0.233754
\(763\) −5.30361 −0.192003
\(764\) −53.0670 −1.91990
\(765\) −11.9786 −0.433089
\(766\) −32.1489 −1.16159
\(767\) 10.2644 0.370627
\(768\) 3.71825 0.134171
\(769\) 19.0504 0.686975 0.343487 0.939157i \(-0.388392\pi\)
0.343487 + 0.939157i \(0.388392\pi\)
\(770\) −0.470413 −0.0169525
\(771\) −2.69767 −0.0971541
\(772\) −19.0115 −0.684238
\(773\) −32.9792 −1.18618 −0.593090 0.805136i \(-0.702092\pi\)
−0.593090 + 0.805136i \(0.702092\pi\)
\(774\) −8.87620 −0.319048
\(775\) 35.3068 1.26826
\(776\) −50.5865 −1.81595
\(777\) −0.465637 −0.0167046
\(778\) 66.3276 2.37796
\(779\) 37.0955 1.32908
\(780\) −0.760287 −0.0272226
\(781\) −0.752761 −0.0269359
\(782\) −9.59050 −0.342956
\(783\) 0.893708 0.0319385
\(784\) −14.5674 −0.520264
\(785\) 7.65978 0.273389
\(786\) 7.12801 0.254248
\(787\) −54.0061 −1.92511 −0.962556 0.271085i \(-0.912618\pi\)
−0.962556 + 0.271085i \(0.912618\pi\)
\(788\) −31.5029 −1.12224
\(789\) −1.47430 −0.0524864
\(790\) 30.1826 1.07385
\(791\) 8.29899 0.295078
\(792\) 3.54492 0.125963
\(793\) 11.3915 0.404526
\(794\) −31.7076 −1.12526
\(795\) 0.413640 0.0146703
\(796\) 23.5972 0.836380
\(797\) 12.8405 0.454833 0.227416 0.973798i \(-0.426972\pi\)
0.227416 + 0.973798i \(0.426972\pi\)
\(798\) −0.981714 −0.0347523
\(799\) 7.95285 0.281352
\(800\) −11.2874 −0.399070
\(801\) −33.7347 −1.19196
\(802\) −89.8538 −3.17285
\(803\) −2.02825 −0.0715755
\(804\) 1.64244 0.0579245
\(805\) −0.603139 −0.0212579
\(806\) −34.1414 −1.20258
\(807\) −0.0702451 −0.00247275
\(808\) −16.4142 −0.577451
\(809\) −18.9626 −0.666691 −0.333345 0.942805i \(-0.608177\pi\)
−0.333345 + 0.942805i \(0.608177\pi\)
\(810\) 18.9603 0.666196
\(811\) −18.5559 −0.651585 −0.325792 0.945441i \(-0.605631\pi\)
−0.325792 + 0.945441i \(0.605631\pi\)
\(812\) −3.05491 −0.107206
\(813\) 0.231663 0.00812479
\(814\) 3.25074 0.113938
\(815\) −1.46181 −0.0512049
\(816\) 1.36105 0.0476463
\(817\) −5.10666 −0.178659
\(818\) −27.1112 −0.947920
\(819\) −3.77711 −0.131983
\(820\) −30.1004 −1.05115
\(821\) −1.16442 −0.0406384 −0.0203192 0.999794i \(-0.506468\pi\)
−0.0203192 + 0.999794i \(0.506468\pi\)
\(822\) 5.43277 0.189490
\(823\) −42.1364 −1.46878 −0.734392 0.678726i \(-0.762532\pi\)
−0.734392 + 0.678726i \(0.762532\pi\)
\(824\) −18.1717 −0.633040
\(825\) 0.166051 0.00578114
\(826\) −10.7546 −0.374200
\(827\) 35.8714 1.24737 0.623686 0.781675i \(-0.285634\pi\)
0.623686 + 0.781675i \(0.285634\pi\)
\(828\) 9.90945 0.344377
\(829\) 0.142024 0.00493270 0.00246635 0.999997i \(-0.499215\pi\)
0.00246635 + 0.999997i \(0.499215\pi\)
\(830\) −24.8242 −0.861660
\(831\) −1.80984 −0.0627827
\(832\) 18.5945 0.644648
\(833\) 28.7908 0.997542
\(834\) −0.720352 −0.0249438
\(835\) −17.2077 −0.595496
\(836\) 4.44653 0.153786
\(837\) −6.78954 −0.234681
\(838\) −78.7752 −2.72124
\(839\) 40.7197 1.40580 0.702901 0.711288i \(-0.251888\pi\)
0.702901 + 0.711288i \(0.251888\pi\)
\(840\) 0.365369 0.0126064
\(841\) −27.7707 −0.957609
\(842\) −81.9505 −2.82420
\(843\) −2.56035 −0.0881833
\(844\) 12.6307 0.434766
\(845\) 9.09451 0.312861
\(846\) −12.6657 −0.435455
\(847\) 8.13896 0.279658
\(848\) 7.71825 0.265046
\(849\) −3.14686 −0.108000
\(850\) −44.6909 −1.53289
\(851\) 4.16792 0.142875
\(852\) 1.27472 0.0436712
\(853\) −39.2328 −1.34331 −0.671653 0.740865i \(-0.734416\pi\)
−0.671653 + 0.740865i \(0.734416\pi\)
\(854\) −11.9355 −0.408426
\(855\) 10.9755 0.375353
\(856\) 13.3866 0.457546
\(857\) −23.5497 −0.804443 −0.402221 0.915542i \(-0.631762\pi\)
−0.402221 + 0.915542i \(0.631762\pi\)
\(858\) −0.160570 −0.00548177
\(859\) −34.1860 −1.16641 −0.583205 0.812325i \(-0.698201\pi\)
−0.583205 + 0.812325i \(0.698201\pi\)
\(860\) 4.14370 0.141299
\(861\) 0.910596 0.0310330
\(862\) −30.2480 −1.03025
\(863\) 8.90175 0.303019 0.151510 0.988456i \(-0.451587\pi\)
0.151510 + 0.988456i \(0.451587\pi\)
\(864\) 2.17059 0.0738448
\(865\) 0.0860983 0.00292743
\(866\) −5.23789 −0.177991
\(867\) −0.399220 −0.0135582
\(868\) 23.2083 0.787741
\(869\) 4.13567 0.140293
\(870\) −0.320557 −0.0108679
\(871\) 5.60367 0.189873
\(872\) −28.7579 −0.973865
\(873\) −37.3019 −1.26248
\(874\) 8.78732 0.297236
\(875\) −6.16321 −0.208355
\(876\) 3.43463 0.116045
\(877\) −43.2807 −1.46148 −0.730742 0.682653i \(-0.760826\pi\)
−0.730742 + 0.682653i \(0.760826\pi\)
\(878\) −16.5620 −0.558942
\(879\) 0.402215 0.0135664
\(880\) −0.597564 −0.0201439
\(881\) 35.7833 1.20557 0.602785 0.797903i \(-0.294058\pi\)
0.602785 + 0.797903i \(0.294058\pi\)
\(882\) −45.8521 −1.54392
\(883\) −29.3600 −0.988044 −0.494022 0.869449i \(-0.664474\pi\)
−0.494022 + 0.869449i \(0.664474\pi\)
\(884\) 28.0379 0.943017
\(885\) −0.732154 −0.0246111
\(886\) 62.9383 2.11445
\(887\) 5.48260 0.184088 0.0920438 0.995755i \(-0.470660\pi\)
0.0920438 + 0.995755i \(0.470660\pi\)
\(888\) −2.52484 −0.0847280
\(889\) 14.9651 0.501915
\(890\) 24.2737 0.813656
\(891\) 2.59797 0.0870352
\(892\) −87.5360 −2.93092
\(893\) −7.28683 −0.243844
\(894\) −1.18771 −0.0397230
\(895\) 14.1402 0.472654
\(896\) −15.4660 −0.516681
\(897\) −0.205874 −0.00687394
\(898\) −92.7405 −3.09479
\(899\) −9.33924 −0.311481
\(900\) 46.1772 1.53924
\(901\) −15.2543 −0.508193
\(902\) −6.35711 −0.211669
\(903\) −0.125355 −0.00417155
\(904\) 44.9999 1.49667
\(905\) −16.8503 −0.560121
\(906\) −3.84575 −0.127766
\(907\) 36.3331 1.20642 0.603210 0.797582i \(-0.293888\pi\)
0.603210 + 0.797582i \(0.293888\pi\)
\(908\) 6.98349 0.231755
\(909\) −12.1037 −0.401454
\(910\) 2.71781 0.0900946
\(911\) −13.7228 −0.454657 −0.227328 0.973818i \(-0.572999\pi\)
−0.227328 + 0.973818i \(0.572999\pi\)
\(912\) −1.24707 −0.0412945
\(913\) −3.40145 −0.112572
\(914\) −1.92561 −0.0636935
\(915\) −0.812551 −0.0268621
\(916\) −64.1811 −2.12060
\(917\) −16.5315 −0.545919
\(918\) 8.59413 0.283649
\(919\) −3.27377 −0.107992 −0.0539959 0.998541i \(-0.517196\pi\)
−0.0539959 + 0.998541i \(0.517196\pi\)
\(920\) −3.27042 −0.107822
\(921\) 0.576070 0.0189821
\(922\) 85.7187 2.82300
\(923\) 4.34908 0.143152
\(924\) 0.109151 0.00359079
\(925\) 19.4222 0.638597
\(926\) −66.1870 −2.17504
\(927\) −13.3996 −0.440100
\(928\) 2.98571 0.0980108
\(929\) −13.2236 −0.433853 −0.216926 0.976188i \(-0.569603\pi\)
−0.216926 + 0.976188i \(0.569603\pi\)
\(930\) 2.43528 0.0798561
\(931\) −26.3797 −0.864558
\(932\) 38.6366 1.26558
\(933\) −1.80213 −0.0589991
\(934\) 5.35901 0.175352
\(935\) 1.18102 0.0386234
\(936\) −20.4808 −0.669434
\(937\) 8.82152 0.288186 0.144093 0.989564i \(-0.453973\pi\)
0.144093 + 0.989564i \(0.453973\pi\)
\(938\) −5.87127 −0.191704
\(939\) 3.62702 0.118363
\(940\) 5.91276 0.192853
\(941\) −17.9741 −0.585938 −0.292969 0.956122i \(-0.594643\pi\)
−0.292969 + 0.956122i \(0.594643\pi\)
\(942\) −2.73943 −0.0892555
\(943\) −8.15075 −0.265425
\(944\) −13.6615 −0.444645
\(945\) 0.540478 0.0175818
\(946\) 0.875136 0.0284531
\(947\) −37.9267 −1.23245 −0.616226 0.787569i \(-0.711339\pi\)
−0.616226 + 0.787569i \(0.711339\pi\)
\(948\) −7.00330 −0.227457
\(949\) 11.7182 0.380390
\(950\) 40.9482 1.32853
\(951\) −1.50751 −0.0488844
\(952\) −13.4741 −0.436698
\(953\) 47.6473 1.54345 0.771724 0.635957i \(-0.219395\pi\)
0.771724 + 0.635957i \(0.219395\pi\)
\(954\) 24.2939 0.786543
\(955\) 12.9144 0.417901
\(956\) 32.5535 1.05286
\(957\) −0.0439232 −0.00141984
\(958\) 38.0636 1.22978
\(959\) −12.5999 −0.406871
\(960\) −1.32633 −0.0428072
\(961\) 39.9506 1.28873
\(962\) −18.7811 −0.605528
\(963\) 9.87116 0.318094
\(964\) 92.9811 2.99472
\(965\) 4.62665 0.148937
\(966\) 0.215706 0.00694021
\(967\) 31.1632 1.00214 0.501071 0.865406i \(-0.332940\pi\)
0.501071 + 0.865406i \(0.332940\pi\)
\(968\) 44.1321 1.41846
\(969\) 2.46469 0.0791771
\(970\) 26.8405 0.861796
\(971\) 29.8070 0.956553 0.478277 0.878209i \(-0.341262\pi\)
0.478277 + 0.878209i \(0.341262\pi\)
\(972\) −13.3334 −0.427669
\(973\) 1.67067 0.0535591
\(974\) −4.58088 −0.146781
\(975\) −0.959357 −0.0307240
\(976\) −15.1617 −0.485313
\(977\) −49.5819 −1.58626 −0.793132 0.609050i \(-0.791551\pi\)
−0.793132 + 0.609050i \(0.791551\pi\)
\(978\) 0.522799 0.0167173
\(979\) 3.32602 0.106300
\(980\) 21.4053 0.683767
\(981\) −21.2058 −0.677048
\(982\) −33.8747 −1.08098
\(983\) 30.2078 0.963479 0.481739 0.876315i \(-0.340005\pi\)
0.481739 + 0.876315i \(0.340005\pi\)
\(984\) 4.93755 0.157403
\(985\) 7.66657 0.244277
\(986\) 11.8215 0.376474
\(987\) −0.178872 −0.00569357
\(988\) −25.6898 −0.817302
\(989\) 1.12205 0.0356792
\(990\) −1.88088 −0.0597784
\(991\) 12.6417 0.401577 0.200788 0.979635i \(-0.435650\pi\)
0.200788 + 0.979635i \(0.435650\pi\)
\(992\) −22.6826 −0.720173
\(993\) −1.53231 −0.0486263
\(994\) −4.55676 −0.144532
\(995\) −5.74263 −0.182054
\(996\) 5.75999 0.182512
\(997\) 6.83372 0.216426 0.108213 0.994128i \(-0.465487\pi\)
0.108213 + 0.994128i \(0.465487\pi\)
\(998\) −101.458 −3.21160
\(999\) −3.73491 −0.118167
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 4021.2.a.c.1.17 182
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4021.2.a.c.1.17 182 1.1 even 1 trivial