Properties

Label 6005.2.a.d.1.1
Level $6005$
Weight $2$
Character 6005.1
Self dual yes
Analytic conductor $47.950$
Analytic rank $1$
Dimension $83$
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] = [6005,2,Mod(1,6005)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6005, 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("6005.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6005 = 5 \cdot 1201 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6005.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: \(47.9501664138\)
Analytic rank: \(1\)
Dimension: \(83\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 6005.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.64292 q^{2} +0.725582 q^{3} +4.98500 q^{4} -1.00000 q^{5} -1.91765 q^{6} -1.58856 q^{7} -7.88911 q^{8} -2.47353 q^{9} +O(q^{10})\) \(q-2.64292 q^{2} +0.725582 q^{3} +4.98500 q^{4} -1.00000 q^{5} -1.91765 q^{6} -1.58856 q^{7} -7.88911 q^{8} -2.47353 q^{9} +2.64292 q^{10} -2.20527 q^{11} +3.61703 q^{12} -1.50571 q^{13} +4.19842 q^{14} -0.725582 q^{15} +10.8802 q^{16} -0.196046 q^{17} +6.53733 q^{18} +0.106463 q^{19} -4.98500 q^{20} -1.15263 q^{21} +5.82833 q^{22} +6.89598 q^{23} -5.72419 q^{24} +1.00000 q^{25} +3.97946 q^{26} -3.97149 q^{27} -7.91896 q^{28} +2.34916 q^{29} +1.91765 q^{30} -3.29794 q^{31} -12.9773 q^{32} -1.60010 q^{33} +0.518132 q^{34} +1.58856 q^{35} -12.3306 q^{36} +2.70790 q^{37} -0.281374 q^{38} -1.09251 q^{39} +7.88911 q^{40} +6.80561 q^{41} +3.04630 q^{42} -0.922325 q^{43} -10.9933 q^{44} +2.47353 q^{45} -18.2255 q^{46} +4.83852 q^{47} +7.89450 q^{48} -4.47649 q^{49} -2.64292 q^{50} -0.142247 q^{51} -7.50596 q^{52} +10.8808 q^{53} +10.4963 q^{54} +2.20527 q^{55} +12.5323 q^{56} +0.0772479 q^{57} -6.20863 q^{58} -1.06512 q^{59} -3.61703 q^{60} -4.43798 q^{61} +8.71617 q^{62} +3.92934 q^{63} +12.5375 q^{64} +1.50571 q^{65} +4.22893 q^{66} +4.61448 q^{67} -0.977288 q^{68} +5.00360 q^{69} -4.19842 q^{70} -4.52381 q^{71} +19.5140 q^{72} +8.64022 q^{73} -7.15676 q^{74} +0.725582 q^{75} +0.530720 q^{76} +3.50319 q^{77} +2.88742 q^{78} -10.2342 q^{79} -10.8802 q^{80} +4.53895 q^{81} -17.9867 q^{82} +16.8943 q^{83} -5.74585 q^{84} +0.196046 q^{85} +2.43763 q^{86} +1.70451 q^{87} +17.3976 q^{88} -2.90154 q^{89} -6.53733 q^{90} +2.39190 q^{91} +34.3765 q^{92} -2.39292 q^{93} -12.7878 q^{94} -0.106463 q^{95} -9.41612 q^{96} +5.85530 q^{97} +11.8310 q^{98} +5.45479 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9} - q^{10} - 26 q^{11} - 12 q^{12} - 15 q^{13} - 21 q^{14} + 4 q^{15} + 5 q^{16} + 8 q^{17} - 12 q^{18} - 79 q^{19} - 61 q^{20} - 34 q^{21} - 25 q^{22} + 31 q^{23} - 42 q^{24} + 83 q^{25} - 13 q^{26} - 25 q^{27} - 16 q^{28} - 16 q^{29} + 6 q^{30} - 40 q^{31} + 15 q^{32} - 33 q^{33} - 54 q^{34} - 2 q^{35} + 11 q^{36} - 45 q^{37} + 10 q^{38} - 54 q^{39} + 3 q^{40} - 27 q^{41} - 28 q^{42} - 101 q^{43} - 51 q^{44} - 61 q^{45} - 46 q^{46} + 71 q^{47} - 14 q^{48} + 23 q^{49} + q^{50} - 71 q^{51} - 34 q^{52} - 49 q^{53} - 25 q^{54} + 26 q^{55} - 41 q^{56} - 20 q^{57} - 43 q^{58} - 60 q^{59} + 12 q^{60} - 38 q^{61} - 2 q^{62} + 36 q^{63} - 113 q^{64} + 15 q^{65} - 42 q^{66} - 164 q^{67} + 10 q^{68} - 93 q^{69} + 21 q^{70} - 78 q^{71} + q^{72} - 18 q^{73} - 23 q^{74} - 4 q^{75} - 112 q^{76} - 35 q^{77} - 44 q^{78} - 124 q^{79} - 5 q^{80} - 45 q^{81} - 34 q^{82} + 5 q^{83} - 60 q^{84} - 8 q^{85} - 25 q^{86} + 12 q^{87} - 149 q^{88} - 44 q^{89} + 12 q^{90} - 192 q^{91} + 35 q^{92} - 13 q^{93} - 32 q^{94} + 79 q^{95} - 59 q^{96} - 31 q^{97} + 25 q^{98} - 134 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.64292 −1.86882 −0.934412 0.356195i \(-0.884074\pi\)
−0.934412 + 0.356195i \(0.884074\pi\)
\(3\) 0.725582 0.418915 0.209457 0.977818i \(-0.432830\pi\)
0.209457 + 0.977818i \(0.432830\pi\)
\(4\) 4.98500 2.49250
\(5\) −1.00000 −0.447214
\(6\) −1.91765 −0.782878
\(7\) −1.58856 −0.600418 −0.300209 0.953873i \(-0.597056\pi\)
−0.300209 + 0.953873i \(0.597056\pi\)
\(8\) −7.88911 −2.78922
\(9\) −2.47353 −0.824510
\(10\) 2.64292 0.835763
\(11\) −2.20527 −0.664913 −0.332456 0.943119i \(-0.607877\pi\)
−0.332456 + 0.943119i \(0.607877\pi\)
\(12\) 3.61703 1.04415
\(13\) −1.50571 −0.417608 −0.208804 0.977957i \(-0.566957\pi\)
−0.208804 + 0.977957i \(0.566957\pi\)
\(14\) 4.19842 1.12207
\(15\) −0.725582 −0.187344
\(16\) 10.8802 2.72006
\(17\) −0.196046 −0.0475480 −0.0237740 0.999717i \(-0.507568\pi\)
−0.0237740 + 0.999717i \(0.507568\pi\)
\(18\) 6.53733 1.54086
\(19\) 0.106463 0.0244244 0.0122122 0.999925i \(-0.496113\pi\)
0.0122122 + 0.999925i \(0.496113\pi\)
\(20\) −4.98500 −1.11468
\(21\) −1.15263 −0.251524
\(22\) 5.82833 1.24260
\(23\) 6.89598 1.43791 0.718955 0.695056i \(-0.244621\pi\)
0.718955 + 0.695056i \(0.244621\pi\)
\(24\) −5.72419 −1.16845
\(25\) 1.00000 0.200000
\(26\) 3.97946 0.780436
\(27\) −3.97149 −0.764314
\(28\) −7.91896 −1.49654
\(29\) 2.34916 0.436228 0.218114 0.975923i \(-0.430010\pi\)
0.218114 + 0.975923i \(0.430010\pi\)
\(30\) 1.91765 0.350114
\(31\) −3.29794 −0.592327 −0.296164 0.955137i \(-0.595707\pi\)
−0.296164 + 0.955137i \(0.595707\pi\)
\(32\) −12.9773 −2.29409
\(33\) −1.60010 −0.278542
\(34\) 0.518132 0.0888589
\(35\) 1.58856 0.268515
\(36\) −12.3306 −2.05509
\(37\) 2.70790 0.445177 0.222588 0.974913i \(-0.428549\pi\)
0.222588 + 0.974913i \(0.428549\pi\)
\(38\) −0.281374 −0.0456449
\(39\) −1.09251 −0.174942
\(40\) 7.88911 1.24738
\(41\) 6.80561 1.06286 0.531429 0.847103i \(-0.321655\pi\)
0.531429 + 0.847103i \(0.321655\pi\)
\(42\) 3.04630 0.470054
\(43\) −0.922325 −0.140653 −0.0703266 0.997524i \(-0.522404\pi\)
−0.0703266 + 0.997524i \(0.522404\pi\)
\(44\) −10.9933 −1.65730
\(45\) 2.47353 0.368732
\(46\) −18.2255 −2.68720
\(47\) 4.83852 0.705770 0.352885 0.935667i \(-0.385201\pi\)
0.352885 + 0.935667i \(0.385201\pi\)
\(48\) 7.89450 1.13947
\(49\) −4.47649 −0.639498
\(50\) −2.64292 −0.373765
\(51\) −0.142247 −0.0199186
\(52\) −7.50596 −1.04089
\(53\) 10.8808 1.49460 0.747299 0.664488i \(-0.231350\pi\)
0.747299 + 0.664488i \(0.231350\pi\)
\(54\) 10.4963 1.42837
\(55\) 2.20527 0.297358
\(56\) 12.5323 1.67470
\(57\) 0.0772479 0.0102317
\(58\) −6.20863 −0.815233
\(59\) −1.06512 −0.138667 −0.0693336 0.997594i \(-0.522087\pi\)
−0.0693336 + 0.997594i \(0.522087\pi\)
\(60\) −3.61703 −0.466956
\(61\) −4.43798 −0.568225 −0.284112 0.958791i \(-0.591699\pi\)
−0.284112 + 0.958791i \(0.591699\pi\)
\(62\) 8.71617 1.10696
\(63\) 3.92934 0.495051
\(64\) 12.5375 1.56719
\(65\) 1.50571 0.186760
\(66\) 4.22893 0.520545
\(67\) 4.61448 0.563748 0.281874 0.959451i \(-0.409044\pi\)
0.281874 + 0.959451i \(0.409044\pi\)
\(68\) −0.977288 −0.118514
\(69\) 5.00360 0.602362
\(70\) −4.19842 −0.501807
\(71\) −4.52381 −0.536877 −0.268439 0.963297i \(-0.586508\pi\)
−0.268439 + 0.963297i \(0.586508\pi\)
\(72\) 19.5140 2.29974
\(73\) 8.64022 1.01126 0.505630 0.862750i \(-0.331260\pi\)
0.505630 + 0.862750i \(0.331260\pi\)
\(74\) −7.15676 −0.831956
\(75\) 0.725582 0.0837830
\(76\) 0.530720 0.0608778
\(77\) 3.50319 0.399225
\(78\) 2.88742 0.326936
\(79\) −10.2342 −1.15143 −0.575717 0.817649i \(-0.695277\pi\)
−0.575717 + 0.817649i \(0.695277\pi\)
\(80\) −10.8802 −1.21645
\(81\) 4.53895 0.504328
\(82\) −17.9867 −1.98629
\(83\) 16.8943 1.85439 0.927195 0.374580i \(-0.122213\pi\)
0.927195 + 0.374580i \(0.122213\pi\)
\(84\) −5.74585 −0.626923
\(85\) 0.196046 0.0212641
\(86\) 2.43763 0.262856
\(87\) 1.70451 0.182742
\(88\) 17.3976 1.85459
\(89\) −2.90154 −0.307563 −0.153782 0.988105i \(-0.549145\pi\)
−0.153782 + 0.988105i \(0.549145\pi\)
\(90\) −6.53733 −0.689096
\(91\) 2.39190 0.250740
\(92\) 34.3765 3.58399
\(93\) −2.39292 −0.248135
\(94\) −12.7878 −1.31896
\(95\) −0.106463 −0.0109229
\(96\) −9.41612 −0.961029
\(97\) 5.85530 0.594516 0.297258 0.954797i \(-0.403928\pi\)
0.297258 + 0.954797i \(0.403928\pi\)
\(98\) 11.8310 1.19511
\(99\) 5.45479 0.548227
\(100\) 4.98500 0.498500
\(101\) 5.86367 0.583457 0.291729 0.956501i \(-0.405770\pi\)
0.291729 + 0.956501i \(0.405770\pi\)
\(102\) 0.375947 0.0372243
\(103\) −6.26730 −0.617536 −0.308768 0.951137i \(-0.599917\pi\)
−0.308768 + 0.951137i \(0.599917\pi\)
\(104\) 11.8787 1.16480
\(105\) 1.15263 0.112485
\(106\) −28.7571 −2.79314
\(107\) 10.4352 1.00881 0.504403 0.863468i \(-0.331713\pi\)
0.504403 + 0.863468i \(0.331713\pi\)
\(108\) −19.7979 −1.90505
\(109\) 11.7361 1.12411 0.562055 0.827100i \(-0.310011\pi\)
0.562055 + 0.827100i \(0.310011\pi\)
\(110\) −5.82833 −0.555710
\(111\) 1.96480 0.186491
\(112\) −17.2839 −1.63317
\(113\) −3.92494 −0.369227 −0.184614 0.982811i \(-0.559103\pi\)
−0.184614 + 0.982811i \(0.559103\pi\)
\(114\) −0.204160 −0.0191213
\(115\) −6.89598 −0.643053
\(116\) 11.7106 1.08730
\(117\) 3.72442 0.344322
\(118\) 2.81503 0.259144
\(119\) 0.311429 0.0285487
\(120\) 5.72419 0.522545
\(121\) −6.13680 −0.557891
\(122\) 11.7292 1.06191
\(123\) 4.93803 0.445247
\(124\) −16.4402 −1.47638
\(125\) −1.00000 −0.0894427
\(126\) −10.3849 −0.925162
\(127\) −16.5053 −1.46461 −0.732304 0.680978i \(-0.761555\pi\)
−0.732304 + 0.680978i \(0.761555\pi\)
\(128\) −7.18095 −0.634712
\(129\) −0.669222 −0.0589217
\(130\) −3.97946 −0.349022
\(131\) 15.1146 1.32057 0.660285 0.751015i \(-0.270435\pi\)
0.660285 + 0.751015i \(0.270435\pi\)
\(132\) −7.97650 −0.694266
\(133\) −0.169123 −0.0146648
\(134\) −12.1957 −1.05355
\(135\) 3.97149 0.341812
\(136\) 1.54662 0.132622
\(137\) −20.7872 −1.77597 −0.887986 0.459870i \(-0.847896\pi\)
−0.887986 + 0.459870i \(0.847896\pi\)
\(138\) −13.2241 −1.12571
\(139\) −19.2498 −1.63275 −0.816373 0.577525i \(-0.804019\pi\)
−0.816373 + 0.577525i \(0.804019\pi\)
\(140\) 7.91896 0.669274
\(141\) 3.51074 0.295658
\(142\) 11.9560 1.00333
\(143\) 3.32049 0.277673
\(144\) −26.9126 −2.24272
\(145\) −2.34916 −0.195087
\(146\) −22.8354 −1.88987
\(147\) −3.24806 −0.267895
\(148\) 13.4989 1.10960
\(149\) 0.437062 0.0358056 0.0179028 0.999840i \(-0.494301\pi\)
0.0179028 + 0.999840i \(0.494301\pi\)
\(150\) −1.91765 −0.156576
\(151\) 10.1252 0.823976 0.411988 0.911189i \(-0.364835\pi\)
0.411988 + 0.911189i \(0.364835\pi\)
\(152\) −0.839902 −0.0681250
\(153\) 0.484925 0.0392039
\(154\) −9.25863 −0.746082
\(155\) 3.29794 0.264897
\(156\) −5.44619 −0.436044
\(157\) −9.04644 −0.721984 −0.360992 0.932569i \(-0.617562\pi\)
−0.360992 + 0.932569i \(0.617562\pi\)
\(158\) 27.0480 2.15183
\(159\) 7.89494 0.626109
\(160\) 12.9773 1.02595
\(161\) −10.9546 −0.863347
\(162\) −11.9961 −0.942500
\(163\) −7.83580 −0.613747 −0.306874 0.951750i \(-0.599283\pi\)
−0.306874 + 0.951750i \(0.599283\pi\)
\(164\) 33.9260 2.64917
\(165\) 1.60010 0.124568
\(166\) −44.6502 −3.46553
\(167\) −23.6721 −1.83180 −0.915902 0.401403i \(-0.868523\pi\)
−0.915902 + 0.401403i \(0.868523\pi\)
\(168\) 9.09320 0.701556
\(169\) −10.7328 −0.825603
\(170\) −0.518132 −0.0397389
\(171\) −0.263341 −0.0201382
\(172\) −4.59779 −0.350578
\(173\) −22.8064 −1.73394 −0.866968 0.498363i \(-0.833935\pi\)
−0.866968 + 0.498363i \(0.833935\pi\)
\(174\) −4.50487 −0.341513
\(175\) −1.58856 −0.120084
\(176\) −23.9938 −1.80860
\(177\) −0.772833 −0.0580897
\(178\) 7.66853 0.574781
\(179\) −18.8078 −1.40576 −0.702881 0.711308i \(-0.748103\pi\)
−0.702881 + 0.711308i \(0.748103\pi\)
\(180\) 12.3306 0.919066
\(181\) −4.20617 −0.312642 −0.156321 0.987706i \(-0.549963\pi\)
−0.156321 + 0.987706i \(0.549963\pi\)
\(182\) −6.32160 −0.468588
\(183\) −3.22011 −0.238038
\(184\) −54.4031 −4.01065
\(185\) −2.70790 −0.199089
\(186\) 6.32429 0.463720
\(187\) 0.432333 0.0316153
\(188\) 24.1200 1.75913
\(189\) 6.30894 0.458908
\(190\) 0.281374 0.0204130
\(191\) 5.80324 0.419908 0.209954 0.977711i \(-0.432669\pi\)
0.209954 + 0.977711i \(0.432669\pi\)
\(192\) 9.09700 0.656519
\(193\) 19.4678 1.40132 0.700661 0.713494i \(-0.252889\pi\)
0.700661 + 0.713494i \(0.252889\pi\)
\(194\) −15.4751 −1.11104
\(195\) 1.09251 0.0782366
\(196\) −22.3153 −1.59395
\(197\) 8.73362 0.622244 0.311122 0.950370i \(-0.399295\pi\)
0.311122 + 0.950370i \(0.399295\pi\)
\(198\) −14.4166 −1.02454
\(199\) −4.34045 −0.307686 −0.153843 0.988095i \(-0.549165\pi\)
−0.153843 + 0.988095i \(0.549165\pi\)
\(200\) −7.88911 −0.557844
\(201\) 3.34818 0.236163
\(202\) −15.4972 −1.09038
\(203\) −3.73177 −0.261919
\(204\) −0.709102 −0.0496471
\(205\) −6.80561 −0.475325
\(206\) 16.5640 1.15407
\(207\) −17.0574 −1.18557
\(208\) −16.3825 −1.13592
\(209\) −0.234780 −0.0162401
\(210\) −3.04630 −0.210214
\(211\) −13.5782 −0.934762 −0.467381 0.884056i \(-0.654802\pi\)
−0.467381 + 0.884056i \(0.654802\pi\)
\(212\) 54.2410 3.72529
\(213\) −3.28239 −0.224906
\(214\) −27.5793 −1.88528
\(215\) 0.922325 0.0629020
\(216\) 31.3315 2.13184
\(217\) 5.23896 0.355644
\(218\) −31.0174 −2.10076
\(219\) 6.26918 0.423632
\(220\) 10.9933 0.741165
\(221\) 0.295188 0.0198565
\(222\) −5.19281 −0.348519
\(223\) 0.381218 0.0255282 0.0127641 0.999919i \(-0.495937\pi\)
0.0127641 + 0.999919i \(0.495937\pi\)
\(224\) 20.6152 1.37741
\(225\) −2.47353 −0.164902
\(226\) 10.3733 0.690021
\(227\) 5.43424 0.360683 0.180342 0.983604i \(-0.442280\pi\)
0.180342 + 0.983604i \(0.442280\pi\)
\(228\) 0.385081 0.0255026
\(229\) 23.9439 1.58226 0.791130 0.611648i \(-0.209493\pi\)
0.791130 + 0.611648i \(0.209493\pi\)
\(230\) 18.2255 1.20175
\(231\) 2.54185 0.167241
\(232\) −18.5328 −1.21674
\(233\) 4.56100 0.298801 0.149401 0.988777i \(-0.452266\pi\)
0.149401 + 0.988777i \(0.452266\pi\)
\(234\) −9.84332 −0.643478
\(235\) −4.83852 −0.315630
\(236\) −5.30964 −0.345628
\(237\) −7.42573 −0.482353
\(238\) −0.823082 −0.0533525
\(239\) 10.4438 0.675555 0.337778 0.941226i \(-0.390325\pi\)
0.337778 + 0.941226i \(0.390325\pi\)
\(240\) −7.89450 −0.509588
\(241\) −10.3329 −0.665601 −0.332800 0.942997i \(-0.607994\pi\)
−0.332800 + 0.942997i \(0.607994\pi\)
\(242\) 16.2190 1.04260
\(243\) 15.2079 0.975585
\(244\) −22.1233 −1.41630
\(245\) 4.47649 0.285992
\(246\) −13.0508 −0.832088
\(247\) −0.160303 −0.0101998
\(248\) 26.0178 1.65213
\(249\) 12.2582 0.776831
\(250\) 2.64292 0.167153
\(251\) −8.65525 −0.546315 −0.273157 0.961969i \(-0.588068\pi\)
−0.273157 + 0.961969i \(0.588068\pi\)
\(252\) 19.5878 1.23391
\(253\) −15.2075 −0.956085
\(254\) 43.6221 2.73709
\(255\) 0.142247 0.00890786
\(256\) −6.09641 −0.381026
\(257\) −3.72216 −0.232182 −0.116091 0.993239i \(-0.537036\pi\)
−0.116091 + 0.993239i \(0.537036\pi\)
\(258\) 1.76870 0.110114
\(259\) −4.30166 −0.267292
\(260\) 7.50596 0.465500
\(261\) −5.81072 −0.359674
\(262\) −39.9466 −2.46791
\(263\) −8.98303 −0.553917 −0.276959 0.960882i \(-0.589327\pi\)
−0.276959 + 0.960882i \(0.589327\pi\)
\(264\) 12.6234 0.776914
\(265\) −10.8808 −0.668404
\(266\) 0.446978 0.0274060
\(267\) −2.10531 −0.128843
\(268\) 23.0032 1.40514
\(269\) −20.1493 −1.22852 −0.614262 0.789102i \(-0.710546\pi\)
−0.614262 + 0.789102i \(0.710546\pi\)
\(270\) −10.4963 −0.638786
\(271\) −2.56521 −0.155825 −0.0779127 0.996960i \(-0.524826\pi\)
−0.0779127 + 0.996960i \(0.524826\pi\)
\(272\) −2.13302 −0.129334
\(273\) 1.73552 0.105038
\(274\) 54.9389 3.31898
\(275\) −2.20527 −0.132983
\(276\) 24.9429 1.50139
\(277\) −29.1691 −1.75260 −0.876301 0.481764i \(-0.839996\pi\)
−0.876301 + 0.481764i \(0.839996\pi\)
\(278\) 50.8756 3.05131
\(279\) 8.15755 0.488380
\(280\) −12.5323 −0.748948
\(281\) −2.16718 −0.129283 −0.0646416 0.997909i \(-0.520590\pi\)
−0.0646416 + 0.997909i \(0.520590\pi\)
\(282\) −9.27859 −0.552532
\(283\) 22.9618 1.36494 0.682468 0.730915i \(-0.260907\pi\)
0.682468 + 0.730915i \(0.260907\pi\)
\(284\) −22.5512 −1.33817
\(285\) −0.0772479 −0.00457577
\(286\) −8.77577 −0.518922
\(287\) −10.8111 −0.638159
\(288\) 32.0999 1.89150
\(289\) −16.9616 −0.997739
\(290\) 6.20863 0.364583
\(291\) 4.24850 0.249051
\(292\) 43.0715 2.52057
\(293\) −5.64281 −0.329657 −0.164828 0.986322i \(-0.552707\pi\)
−0.164828 + 0.986322i \(0.552707\pi\)
\(294\) 8.58434 0.500649
\(295\) 1.06512 0.0620138
\(296\) −21.3629 −1.24170
\(297\) 8.75820 0.508202
\(298\) −1.15512 −0.0669143
\(299\) −10.3833 −0.600484
\(300\) 3.61703 0.208829
\(301\) 1.46516 0.0844507
\(302\) −26.7600 −1.53987
\(303\) 4.25457 0.244419
\(304\) 1.15835 0.0664358
\(305\) 4.43798 0.254118
\(306\) −1.28162 −0.0732651
\(307\) −6.50334 −0.371165 −0.185582 0.982629i \(-0.559417\pi\)
−0.185582 + 0.982629i \(0.559417\pi\)
\(308\) 17.4634 0.995070
\(309\) −4.54744 −0.258695
\(310\) −8.71617 −0.495045
\(311\) −27.1012 −1.53677 −0.768383 0.639990i \(-0.778939\pi\)
−0.768383 + 0.639990i \(0.778939\pi\)
\(312\) 8.61896 0.487953
\(313\) 17.5031 0.989332 0.494666 0.869083i \(-0.335290\pi\)
0.494666 + 0.869083i \(0.335290\pi\)
\(314\) 23.9090 1.34926
\(315\) −3.92934 −0.221393
\(316\) −51.0174 −2.86995
\(317\) 22.1024 1.24139 0.620697 0.784050i \(-0.286850\pi\)
0.620697 + 0.784050i \(0.286850\pi\)
\(318\) −20.8656 −1.17009
\(319\) −5.18052 −0.290053
\(320\) −12.5375 −0.700869
\(321\) 7.57157 0.422604
\(322\) 28.9522 1.61344
\(323\) −0.0208717 −0.00116133
\(324\) 22.6267 1.25704
\(325\) −1.50571 −0.0835217
\(326\) 20.7094 1.14699
\(327\) 8.51547 0.470906
\(328\) −53.6902 −2.96455
\(329\) −7.68626 −0.423757
\(330\) −4.22893 −0.232795
\(331\) −12.8352 −0.705485 −0.352743 0.935720i \(-0.614751\pi\)
−0.352743 + 0.935720i \(0.614751\pi\)
\(332\) 84.2181 4.62207
\(333\) −6.69808 −0.367053
\(334\) 62.5634 3.42332
\(335\) −4.61448 −0.252116
\(336\) −12.5409 −0.684160
\(337\) −4.86167 −0.264832 −0.132416 0.991194i \(-0.542273\pi\)
−0.132416 + 0.991194i \(0.542273\pi\)
\(338\) 28.3660 1.54291
\(339\) −2.84786 −0.154675
\(340\) 0.977288 0.0530009
\(341\) 7.27283 0.393846
\(342\) 0.695987 0.0376347
\(343\) 18.2310 0.984384
\(344\) 7.27632 0.392313
\(345\) −5.00360 −0.269385
\(346\) 60.2753 3.24042
\(347\) 28.4873 1.52928 0.764638 0.644460i \(-0.222918\pi\)
0.764638 + 0.644460i \(0.222918\pi\)
\(348\) 8.49697 0.455485
\(349\) 2.95588 0.158224 0.0791122 0.996866i \(-0.474791\pi\)
0.0791122 + 0.996866i \(0.474791\pi\)
\(350\) 4.19842 0.224415
\(351\) 5.97991 0.319184
\(352\) 28.6185 1.52537
\(353\) −18.4537 −0.982193 −0.491096 0.871105i \(-0.663404\pi\)
−0.491096 + 0.871105i \(0.663404\pi\)
\(354\) 2.04253 0.108559
\(355\) 4.52381 0.240099
\(356\) −14.4642 −0.766601
\(357\) 0.225967 0.0119595
\(358\) 49.7075 2.62712
\(359\) −7.90800 −0.417368 −0.208684 0.977983i \(-0.566918\pi\)
−0.208684 + 0.977983i \(0.566918\pi\)
\(360\) −19.5140 −1.02848
\(361\) −18.9887 −0.999403
\(362\) 11.1165 0.584273
\(363\) −4.45275 −0.233709
\(364\) 11.9236 0.624968
\(365\) −8.64022 −0.452250
\(366\) 8.51049 0.444851
\(367\) −8.17603 −0.426785 −0.213393 0.976967i \(-0.568451\pi\)
−0.213393 + 0.976967i \(0.568451\pi\)
\(368\) 75.0299 3.91120
\(369\) −16.8339 −0.876338
\(370\) 7.15676 0.372062
\(371\) −17.2848 −0.897383
\(372\) −11.9287 −0.618476
\(373\) 18.9560 0.981507 0.490753 0.871299i \(-0.336722\pi\)
0.490753 + 0.871299i \(0.336722\pi\)
\(374\) −1.14262 −0.0590834
\(375\) −0.725582 −0.0374689
\(376\) −38.1716 −1.96855
\(377\) −3.53715 −0.182172
\(378\) −16.6740 −0.857618
\(379\) 4.90940 0.252179 0.126089 0.992019i \(-0.459757\pi\)
0.126089 + 0.992019i \(0.459757\pi\)
\(380\) −0.530720 −0.0272254
\(381\) −11.9759 −0.613546
\(382\) −15.3375 −0.784734
\(383\) 6.72804 0.343787 0.171893 0.985116i \(-0.445012\pi\)
0.171893 + 0.985116i \(0.445012\pi\)
\(384\) −5.21037 −0.265890
\(385\) −3.50319 −0.178539
\(386\) −51.4517 −2.61882
\(387\) 2.28140 0.115970
\(388\) 29.1887 1.48183
\(389\) 11.7736 0.596947 0.298473 0.954418i \(-0.403523\pi\)
0.298473 + 0.954418i \(0.403523\pi\)
\(390\) −2.88742 −0.146210
\(391\) −1.35193 −0.0683698
\(392\) 35.3155 1.78370
\(393\) 10.9669 0.553206
\(394\) −23.0822 −1.16286
\(395\) 10.2342 0.514937
\(396\) 27.1922 1.36646
\(397\) −20.2666 −1.01715 −0.508575 0.861018i \(-0.669827\pi\)
−0.508575 + 0.861018i \(0.669827\pi\)
\(398\) 11.4714 0.575012
\(399\) −0.122713 −0.00614332
\(400\) 10.8802 0.544012
\(401\) −24.1730 −1.20714 −0.603571 0.797310i \(-0.706256\pi\)
−0.603571 + 0.797310i \(0.706256\pi\)
\(402\) −8.84896 −0.441346
\(403\) 4.96573 0.247361
\(404\) 29.2304 1.45427
\(405\) −4.53895 −0.225542
\(406\) 9.86275 0.489480
\(407\) −5.97165 −0.296004
\(408\) 1.12220 0.0555573
\(409\) 1.31937 0.0652387 0.0326194 0.999468i \(-0.489615\pi\)
0.0326194 + 0.999468i \(0.489615\pi\)
\(410\) 17.9867 0.888298
\(411\) −15.0828 −0.743981
\(412\) −31.2425 −1.53921
\(413\) 1.69201 0.0832582
\(414\) 45.0813 2.21563
\(415\) −16.8943 −0.829308
\(416\) 19.5401 0.958032
\(417\) −13.9673 −0.683982
\(418\) 0.620504 0.0303499
\(419\) 5.46987 0.267221 0.133610 0.991034i \(-0.457343\pi\)
0.133610 + 0.991034i \(0.457343\pi\)
\(420\) 5.74585 0.280369
\(421\) 19.3563 0.943367 0.471683 0.881768i \(-0.343647\pi\)
0.471683 + 0.881768i \(0.343647\pi\)
\(422\) 35.8860 1.74690
\(423\) −11.9682 −0.581915
\(424\) −85.8401 −4.16876
\(425\) −0.196046 −0.00950961
\(426\) 8.67508 0.420309
\(427\) 7.04998 0.341172
\(428\) 52.0194 2.51445
\(429\) 2.40929 0.116321
\(430\) −2.43763 −0.117553
\(431\) 25.5736 1.23184 0.615919 0.787810i \(-0.288785\pi\)
0.615919 + 0.787810i \(0.288785\pi\)
\(432\) −43.2108 −2.07898
\(433\) −2.95021 −0.141778 −0.0708891 0.997484i \(-0.522584\pi\)
−0.0708891 + 0.997484i \(0.522584\pi\)
\(434\) −13.8461 −0.664635
\(435\) −1.70451 −0.0817248
\(436\) 58.5043 2.80185
\(437\) 0.734170 0.0351201
\(438\) −16.5689 −0.791693
\(439\) 21.2335 1.01342 0.506710 0.862117i \(-0.330862\pi\)
0.506710 + 0.862117i \(0.330862\pi\)
\(440\) −17.3976 −0.829397
\(441\) 11.0727 0.527273
\(442\) −0.780156 −0.0371082
\(443\) −3.61334 −0.171675 −0.0858376 0.996309i \(-0.527357\pi\)
−0.0858376 + 0.996309i \(0.527357\pi\)
\(444\) 9.79455 0.464829
\(445\) 2.90154 0.137546
\(446\) −1.00753 −0.0477077
\(447\) 0.317124 0.0149995
\(448\) −19.9166 −0.940969
\(449\) −14.8918 −0.702789 −0.351395 0.936227i \(-0.614292\pi\)
−0.351395 + 0.936227i \(0.614292\pi\)
\(450\) 6.53733 0.308173
\(451\) −15.0082 −0.706708
\(452\) −19.5658 −0.920299
\(453\) 7.34665 0.345176
\(454\) −14.3622 −0.674054
\(455\) −2.39190 −0.112134
\(456\) −0.609417 −0.0285386
\(457\) 15.7572 0.737089 0.368545 0.929610i \(-0.379856\pi\)
0.368545 + 0.929610i \(0.379856\pi\)
\(458\) −63.2818 −2.95696
\(459\) 0.778594 0.0363417
\(460\) −34.3765 −1.60281
\(461\) −21.8079 −1.01570 −0.507848 0.861447i \(-0.669559\pi\)
−0.507848 + 0.861447i \(0.669559\pi\)
\(462\) −6.71789 −0.312545
\(463\) 31.8937 1.48223 0.741113 0.671381i \(-0.234298\pi\)
0.741113 + 0.671381i \(0.234298\pi\)
\(464\) 25.5594 1.18657
\(465\) 2.39292 0.110969
\(466\) −12.0543 −0.558407
\(467\) 25.3220 1.17176 0.585882 0.810397i \(-0.300748\pi\)
0.585882 + 0.810397i \(0.300748\pi\)
\(468\) 18.5662 0.858224
\(469\) −7.33036 −0.338485
\(470\) 12.7878 0.589857
\(471\) −6.56393 −0.302450
\(472\) 8.40286 0.386773
\(473\) 2.03397 0.0935221
\(474\) 19.6256 0.901432
\(475\) 0.106463 0.00488488
\(476\) 1.55248 0.0711576
\(477\) −26.9141 −1.23231
\(478\) −27.6022 −1.26249
\(479\) −6.57375 −0.300362 −0.150181 0.988658i \(-0.547986\pi\)
−0.150181 + 0.988658i \(0.547986\pi\)
\(480\) 9.41612 0.429785
\(481\) −4.07731 −0.185909
\(482\) 27.3090 1.24389
\(483\) −7.94849 −0.361669
\(484\) −30.5920 −1.39054
\(485\) −5.85530 −0.265875
\(486\) −40.1931 −1.82320
\(487\) −27.1114 −1.22853 −0.614267 0.789098i \(-0.710548\pi\)
−0.614267 + 0.789098i \(0.710548\pi\)
\(488\) 35.0117 1.58490
\(489\) −5.68551 −0.257108
\(490\) −11.8310 −0.534469
\(491\) −6.01516 −0.271460 −0.135730 0.990746i \(-0.543338\pi\)
−0.135730 + 0.990746i \(0.543338\pi\)
\(492\) 24.6161 1.10978
\(493\) −0.460542 −0.0207418
\(494\) 0.423667 0.0190617
\(495\) −5.45479 −0.245175
\(496\) −35.8824 −1.61117
\(497\) 7.18632 0.322351
\(498\) −32.3973 −1.45176
\(499\) −2.72643 −0.122052 −0.0610259 0.998136i \(-0.519437\pi\)
−0.0610259 + 0.998136i \(0.519437\pi\)
\(500\) −4.98500 −0.222936
\(501\) −17.1761 −0.767369
\(502\) 22.8751 1.02097
\(503\) 19.6780 0.877400 0.438700 0.898633i \(-0.355439\pi\)
0.438700 + 0.898633i \(0.355439\pi\)
\(504\) −30.9990 −1.38081
\(505\) −5.86367 −0.260930
\(506\) 40.1920 1.78675
\(507\) −7.78755 −0.345857
\(508\) −82.2789 −3.65054
\(509\) 39.7918 1.76374 0.881870 0.471492i \(-0.156285\pi\)
0.881870 + 0.471492i \(0.156285\pi\)
\(510\) −0.375947 −0.0166472
\(511\) −13.7255 −0.607179
\(512\) 30.4742 1.34678
\(513\) −0.422819 −0.0186679
\(514\) 9.83736 0.433908
\(515\) 6.26730 0.276170
\(516\) −3.33607 −0.146862
\(517\) −10.6702 −0.469276
\(518\) 11.3689 0.499521
\(519\) −16.5479 −0.726372
\(520\) −11.8787 −0.520915
\(521\) −25.1736 −1.10287 −0.551437 0.834216i \(-0.685920\pi\)
−0.551437 + 0.834216i \(0.685920\pi\)
\(522\) 15.3572 0.672168
\(523\) −30.9819 −1.35475 −0.677373 0.735640i \(-0.736881\pi\)
−0.677373 + 0.735640i \(0.736881\pi\)
\(524\) 75.3464 3.29152
\(525\) −1.15263 −0.0503048
\(526\) 23.7414 1.03517
\(527\) 0.646546 0.0281640
\(528\) −17.4095 −0.757650
\(529\) 24.5545 1.06759
\(530\) 28.7571 1.24913
\(531\) 2.63461 0.114332
\(532\) −0.843079 −0.0365521
\(533\) −10.2473 −0.443858
\(534\) 5.56415 0.240784
\(535\) −10.4352 −0.451152
\(536\) −36.4041 −1.57242
\(537\) −13.6466 −0.588894
\(538\) 53.2529 2.29589
\(539\) 9.87185 0.425211
\(540\) 19.7979 0.851966
\(541\) −5.90962 −0.254074 −0.127037 0.991898i \(-0.540547\pi\)
−0.127037 + 0.991898i \(0.540547\pi\)
\(542\) 6.77963 0.291210
\(543\) −3.05192 −0.130970
\(544\) 2.54415 0.109080
\(545\) −11.7361 −0.502717
\(546\) −4.58683 −0.196298
\(547\) 29.0896 1.24378 0.621891 0.783104i \(-0.286365\pi\)
0.621891 + 0.783104i \(0.286365\pi\)
\(548\) −103.624 −4.42661
\(549\) 10.9775 0.468507
\(550\) 5.82833 0.248521
\(551\) 0.250099 0.0106546
\(552\) −39.4739 −1.68012
\(553\) 16.2576 0.691342
\(554\) 77.0915 3.27530
\(555\) −1.96480 −0.0834013
\(556\) −95.9603 −4.06962
\(557\) −41.8074 −1.77144 −0.885718 0.464224i \(-0.846333\pi\)
−0.885718 + 0.464224i \(0.846333\pi\)
\(558\) −21.5597 −0.912696
\(559\) 1.38875 0.0587379
\(560\) 17.2839 0.730377
\(561\) 0.313693 0.0132441
\(562\) 5.72768 0.241608
\(563\) −4.68519 −0.197457 −0.0987286 0.995114i \(-0.531478\pi\)
−0.0987286 + 0.995114i \(0.531478\pi\)
\(564\) 17.5010 0.736927
\(565\) 3.92494 0.165123
\(566\) −60.6861 −2.55083
\(567\) −7.21038 −0.302807
\(568\) 35.6888 1.49747
\(569\) 26.2582 1.10080 0.550401 0.834900i \(-0.314475\pi\)
0.550401 + 0.834900i \(0.314475\pi\)
\(570\) 0.204160 0.00855131
\(571\) −33.9283 −1.41986 −0.709928 0.704274i \(-0.751272\pi\)
−0.709928 + 0.704274i \(0.751272\pi\)
\(572\) 16.5526 0.692101
\(573\) 4.21073 0.175906
\(574\) 28.5728 1.19261
\(575\) 6.89598 0.287582
\(576\) −31.0120 −1.29217
\(577\) −8.47874 −0.352974 −0.176487 0.984303i \(-0.556473\pi\)
−0.176487 + 0.984303i \(0.556473\pi\)
\(578\) 44.8280 1.86460
\(579\) 14.1255 0.587034
\(580\) −11.7106 −0.486254
\(581\) −26.8375 −1.11341
\(582\) −11.2284 −0.465433
\(583\) −23.9951 −0.993777
\(584\) −68.1636 −2.82063
\(585\) −3.72442 −0.153986
\(586\) 14.9135 0.616070
\(587\) 5.70816 0.235601 0.117801 0.993037i \(-0.462416\pi\)
0.117801 + 0.993037i \(0.462416\pi\)
\(588\) −16.1916 −0.667729
\(589\) −0.351110 −0.0144672
\(590\) −2.81503 −0.115893
\(591\) 6.33695 0.260667
\(592\) 29.4626 1.21091
\(593\) 1.98524 0.0815239 0.0407620 0.999169i \(-0.487021\pi\)
0.0407620 + 0.999169i \(0.487021\pi\)
\(594\) −23.1472 −0.949740
\(595\) −0.311429 −0.0127674
\(596\) 2.17876 0.0892454
\(597\) −3.14935 −0.128894
\(598\) 27.4423 1.12220
\(599\) −18.5941 −0.759733 −0.379867 0.925041i \(-0.624030\pi\)
−0.379867 + 0.925041i \(0.624030\pi\)
\(600\) −5.72419 −0.233689
\(601\) 18.5747 0.757678 0.378839 0.925463i \(-0.376323\pi\)
0.378839 + 0.925463i \(0.376323\pi\)
\(602\) −3.87231 −0.157823
\(603\) −11.4141 −0.464816
\(604\) 50.4741 2.05376
\(605\) 6.13680 0.249496
\(606\) −11.2445 −0.456775
\(607\) −0.730606 −0.0296544 −0.0148272 0.999890i \(-0.504720\pi\)
−0.0148272 + 0.999890i \(0.504720\pi\)
\(608\) −1.38161 −0.0560318
\(609\) −2.70770 −0.109722
\(610\) −11.7292 −0.474901
\(611\) −7.28540 −0.294736
\(612\) 2.41735 0.0977157
\(613\) −24.6791 −0.996781 −0.498390 0.866953i \(-0.666075\pi\)
−0.498390 + 0.866953i \(0.666075\pi\)
\(614\) 17.1878 0.693642
\(615\) −4.93803 −0.199120
\(616\) −27.6370 −1.11353
\(617\) 44.7941 1.80334 0.901672 0.432421i \(-0.142341\pi\)
0.901672 + 0.432421i \(0.142341\pi\)
\(618\) 12.0185 0.483455
\(619\) 0.750312 0.0301576 0.0150788 0.999886i \(-0.495200\pi\)
0.0150788 + 0.999886i \(0.495200\pi\)
\(620\) 16.4402 0.660256
\(621\) −27.3873 −1.09902
\(622\) 71.6261 2.87195
\(623\) 4.60927 0.184666
\(624\) −11.8868 −0.475854
\(625\) 1.00000 0.0400000
\(626\) −46.2591 −1.84889
\(627\) −0.170352 −0.00680321
\(628\) −45.0965 −1.79955
\(629\) −0.530872 −0.0211673
\(630\) 10.3849 0.413745
\(631\) −4.85918 −0.193441 −0.0967205 0.995312i \(-0.530835\pi\)
−0.0967205 + 0.995312i \(0.530835\pi\)
\(632\) 80.7385 3.21160
\(633\) −9.85209 −0.391585
\(634\) −58.4148 −2.31995
\(635\) 16.5053 0.654993
\(636\) 39.3563 1.56058
\(637\) 6.74029 0.267060
\(638\) 13.6917 0.542059
\(639\) 11.1898 0.442661
\(640\) 7.18095 0.283852
\(641\) −0.703440 −0.0277842 −0.0138921 0.999904i \(-0.504422\pi\)
−0.0138921 + 0.999904i \(0.504422\pi\)
\(642\) −20.0110 −0.789772
\(643\) −39.2347 −1.54726 −0.773632 0.633635i \(-0.781562\pi\)
−0.773632 + 0.633635i \(0.781562\pi\)
\(644\) −54.6089 −2.15189
\(645\) 0.669222 0.0263506
\(646\) 0.0551621 0.00217032
\(647\) −26.5099 −1.04221 −0.521107 0.853492i \(-0.674481\pi\)
−0.521107 + 0.853492i \(0.674481\pi\)
\(648\) −35.8083 −1.40668
\(649\) 2.34888 0.0922015
\(650\) 3.97946 0.156087
\(651\) 3.80129 0.148984
\(652\) −39.0615 −1.52977
\(653\) 18.6994 0.731763 0.365881 0.930661i \(-0.380768\pi\)
0.365881 + 0.930661i \(0.380768\pi\)
\(654\) −22.5057 −0.880041
\(655\) −15.1146 −0.590577
\(656\) 74.0467 2.89104
\(657\) −21.3718 −0.833795
\(658\) 20.3141 0.791927
\(659\) −37.8549 −1.47462 −0.737308 0.675557i \(-0.763903\pi\)
−0.737308 + 0.675557i \(0.763903\pi\)
\(660\) 7.97650 0.310485
\(661\) −22.6193 −0.879790 −0.439895 0.898049i \(-0.644984\pi\)
−0.439895 + 0.898049i \(0.644984\pi\)
\(662\) 33.9223 1.31843
\(663\) 0.214183 0.00831817
\(664\) −133.281 −5.17230
\(665\) 0.169123 0.00655831
\(666\) 17.7025 0.685957
\(667\) 16.1997 0.627257
\(668\) −118.006 −4.56577
\(669\) 0.276605 0.0106942
\(670\) 12.1957 0.471160
\(671\) 9.78692 0.377820
\(672\) 14.9580 0.577019
\(673\) 0.472818 0.0182258 0.00911289 0.999958i \(-0.497099\pi\)
0.00911289 + 0.999958i \(0.497099\pi\)
\(674\) 12.8490 0.494924
\(675\) −3.97149 −0.152863
\(676\) −53.5032 −2.05782
\(677\) −45.2312 −1.73838 −0.869189 0.494480i \(-0.835359\pi\)
−0.869189 + 0.494480i \(0.835359\pi\)
\(678\) 7.52666 0.289060
\(679\) −9.30147 −0.356958
\(680\) −1.54662 −0.0593104
\(681\) 3.94299 0.151096
\(682\) −19.2215 −0.736028
\(683\) −12.8065 −0.490028 −0.245014 0.969520i \(-0.578793\pi\)
−0.245014 + 0.969520i \(0.578793\pi\)
\(684\) −1.31275 −0.0501944
\(685\) 20.7872 0.794239
\(686\) −48.1831 −1.83964
\(687\) 17.3733 0.662832
\(688\) −10.0351 −0.382585
\(689\) −16.3834 −0.624157
\(690\) 13.2241 0.503432
\(691\) −3.26394 −0.124166 −0.0620830 0.998071i \(-0.519774\pi\)
−0.0620830 + 0.998071i \(0.519774\pi\)
\(692\) −113.690 −4.32184
\(693\) −8.66525 −0.329166
\(694\) −75.2894 −2.85795
\(695\) 19.2498 0.730186
\(696\) −13.4470 −0.509708
\(697\) −1.33421 −0.0505368
\(698\) −7.81213 −0.295694
\(699\) 3.30938 0.125172
\(700\) −7.91896 −0.299308
\(701\) −5.12310 −0.193497 −0.0967485 0.995309i \(-0.530844\pi\)
−0.0967485 + 0.995309i \(0.530844\pi\)
\(702\) −15.8044 −0.596499
\(703\) 0.288293 0.0108732
\(704\) −27.6486 −1.04205
\(705\) −3.51074 −0.132222
\(706\) 48.7716 1.83554
\(707\) −9.31477 −0.350318
\(708\) −3.85257 −0.144789
\(709\) 21.6961 0.814815 0.407407 0.913247i \(-0.366433\pi\)
0.407407 + 0.913247i \(0.366433\pi\)
\(710\) −11.9560 −0.448702
\(711\) 25.3145 0.949369
\(712\) 22.8906 0.857861
\(713\) −22.7425 −0.851714
\(714\) −0.597213 −0.0223501
\(715\) −3.32049 −0.124179
\(716\) −93.7570 −3.50386
\(717\) 7.57785 0.283000
\(718\) 20.9002 0.779987
\(719\) −23.8369 −0.888967 −0.444483 0.895787i \(-0.646613\pi\)
−0.444483 + 0.895787i \(0.646613\pi\)
\(720\) 26.9126 1.00297
\(721\) 9.95596 0.370779
\(722\) 50.1854 1.86771
\(723\) −7.49737 −0.278830
\(724\) −20.9678 −0.779260
\(725\) 2.34916 0.0872455
\(726\) 11.7682 0.436760
\(727\) 31.0562 1.15181 0.575905 0.817517i \(-0.304650\pi\)
0.575905 + 0.817517i \(0.304650\pi\)
\(728\) −18.8700 −0.699368
\(729\) −2.58231 −0.0956410
\(730\) 22.8354 0.845175
\(731\) 0.180818 0.00668778
\(732\) −16.0523 −0.593309
\(733\) −30.2746 −1.11822 −0.559109 0.829094i \(-0.688857\pi\)
−0.559109 + 0.829094i \(0.688857\pi\)
\(734\) 21.6086 0.797586
\(735\) 3.24806 0.119806
\(736\) −89.4914 −3.29870
\(737\) −10.1762 −0.374844
\(738\) 44.4906 1.63772
\(739\) −15.6635 −0.576192 −0.288096 0.957602i \(-0.593022\pi\)
−0.288096 + 0.957602i \(0.593022\pi\)
\(740\) −13.4989 −0.496229
\(741\) −0.116313 −0.00427286
\(742\) 45.6823 1.67705
\(743\) −13.5579 −0.497390 −0.248695 0.968582i \(-0.580002\pi\)
−0.248695 + 0.968582i \(0.580002\pi\)
\(744\) 18.8780 0.692102
\(745\) −0.437062 −0.0160127
\(746\) −50.0992 −1.83426
\(747\) −41.7886 −1.52896
\(748\) 2.15518 0.0788012
\(749\) −16.5769 −0.605705
\(750\) 1.91765 0.0700227
\(751\) −17.7221 −0.646690 −0.323345 0.946281i \(-0.604807\pi\)
−0.323345 + 0.946281i \(0.604807\pi\)
\(752\) 52.6442 1.91974
\(753\) −6.28009 −0.228859
\(754\) 9.34838 0.340448
\(755\) −10.1252 −0.368493
\(756\) 31.4501 1.14383
\(757\) −16.3245 −0.593324 −0.296662 0.954983i \(-0.595873\pi\)
−0.296662 + 0.954983i \(0.595873\pi\)
\(758\) −12.9751 −0.471278
\(759\) −11.0343 −0.400518
\(760\) 0.839902 0.0304664
\(761\) −6.27548 −0.227486 −0.113743 0.993510i \(-0.536284\pi\)
−0.113743 + 0.993510i \(0.536284\pi\)
\(762\) 31.6514 1.14661
\(763\) −18.6434 −0.674936
\(764\) 28.9292 1.04662
\(765\) −0.484925 −0.0175325
\(766\) −17.7816 −0.642477
\(767\) 1.60376 0.0579086
\(768\) −4.42344 −0.159617
\(769\) 17.8973 0.645392 0.322696 0.946503i \(-0.395411\pi\)
0.322696 + 0.946503i \(0.395411\pi\)
\(770\) 9.25863 0.333658
\(771\) −2.70073 −0.0972645
\(772\) 97.0469 3.49280
\(773\) 14.7341 0.529950 0.264975 0.964255i \(-0.414636\pi\)
0.264975 + 0.964255i \(0.414636\pi\)
\(774\) −6.02954 −0.216727
\(775\) −3.29794 −0.118465
\(776\) −46.1931 −1.65824
\(777\) −3.12120 −0.111973
\(778\) −31.1167 −1.11559
\(779\) 0.724549 0.0259597
\(780\) 5.44619 0.195005
\(781\) 9.97620 0.356976
\(782\) 3.57303 0.127771
\(783\) −9.32967 −0.333415
\(784\) −48.7053 −1.73947
\(785\) 9.04644 0.322881
\(786\) −28.9846 −1.03384
\(787\) 18.2463 0.650409 0.325204 0.945644i \(-0.394567\pi\)
0.325204 + 0.945644i \(0.394567\pi\)
\(788\) 43.5371 1.55094
\(789\) −6.51792 −0.232044
\(790\) −27.0480 −0.962326
\(791\) 6.23499 0.221691
\(792\) −43.0335 −1.52913
\(793\) 6.68230 0.237295
\(794\) 53.5628 1.90087
\(795\) −7.89494 −0.280005
\(796\) −21.6372 −0.766909
\(797\) −33.4749 −1.18574 −0.592871 0.805297i \(-0.702006\pi\)
−0.592871 + 0.805297i \(0.702006\pi\)
\(798\) 0.324319 0.0114808
\(799\) −0.948570 −0.0335580
\(800\) −12.9773 −0.458818
\(801\) 7.17706 0.253589
\(802\) 63.8871 2.25593
\(803\) −19.0540 −0.672400
\(804\) 16.6907 0.588635
\(805\) 10.9546 0.386101
\(806\) −13.1240 −0.462274
\(807\) −14.6200 −0.514647
\(808\) −46.2591 −1.62739
\(809\) 1.36726 0.0480702 0.0240351 0.999711i \(-0.492349\pi\)
0.0240351 + 0.999711i \(0.492349\pi\)
\(810\) 11.9961 0.421499
\(811\) 12.2338 0.429587 0.214794 0.976659i \(-0.431092\pi\)
0.214794 + 0.976659i \(0.431092\pi\)
\(812\) −18.6029 −0.652833
\(813\) −1.86127 −0.0652776
\(814\) 15.7826 0.553178
\(815\) 7.83580 0.274476
\(816\) −1.54768 −0.0541797
\(817\) −0.0981938 −0.00343537
\(818\) −3.48699 −0.121920
\(819\) −5.91645 −0.206737
\(820\) −33.9260 −1.18475
\(821\) −17.0960 −0.596654 −0.298327 0.954464i \(-0.596429\pi\)
−0.298327 + 0.954464i \(0.596429\pi\)
\(822\) 39.8627 1.39037
\(823\) −34.6417 −1.20753 −0.603767 0.797161i \(-0.706334\pi\)
−0.603767 + 0.797161i \(0.706334\pi\)
\(824\) 49.4434 1.72244
\(825\) −1.60010 −0.0557084
\(826\) −4.47183 −0.155595
\(827\) 4.58823 0.159548 0.0797742 0.996813i \(-0.474580\pi\)
0.0797742 + 0.996813i \(0.474580\pi\)
\(828\) −85.0313 −2.95504
\(829\) 19.9524 0.692974 0.346487 0.938055i \(-0.387374\pi\)
0.346487 + 0.938055i \(0.387374\pi\)
\(830\) 44.6502 1.54983
\(831\) −21.1646 −0.734191
\(832\) −18.8779 −0.654472
\(833\) 0.877596 0.0304069
\(834\) 36.9144 1.27824
\(835\) 23.6721 0.819207
\(836\) −1.17038 −0.0404784
\(837\) 13.0977 0.452724
\(838\) −14.4564 −0.499388
\(839\) −18.7009 −0.645626 −0.322813 0.946463i \(-0.604629\pi\)
−0.322813 + 0.946463i \(0.604629\pi\)
\(840\) −9.09320 −0.313745
\(841\) −23.4815 −0.809705
\(842\) −51.1570 −1.76299
\(843\) −1.57247 −0.0541587
\(844\) −67.6873 −2.32989
\(845\) 10.7328 0.369221
\(846\) 31.6310 1.08750
\(847\) 9.74865 0.334968
\(848\) 118.386 4.06540
\(849\) 16.6606 0.571792
\(850\) 0.518132 0.0177718
\(851\) 18.6736 0.640124
\(852\) −16.3627 −0.560578
\(853\) −19.0246 −0.651391 −0.325696 0.945475i \(-0.605598\pi\)
−0.325696 + 0.945475i \(0.605598\pi\)
\(854\) −18.6325 −0.637591
\(855\) 0.263341 0.00900606
\(856\) −82.3242 −2.81378
\(857\) 2.40859 0.0822757 0.0411379 0.999153i \(-0.486902\pi\)
0.0411379 + 0.999153i \(0.486902\pi\)
\(858\) −6.36754 −0.217384
\(859\) −25.1119 −0.856807 −0.428403 0.903588i \(-0.640924\pi\)
−0.428403 + 0.903588i \(0.640924\pi\)
\(860\) 4.59779 0.156783
\(861\) −7.84433 −0.267334
\(862\) −67.5889 −2.30209
\(863\) −34.4222 −1.17174 −0.585872 0.810403i \(-0.699248\pi\)
−0.585872 + 0.810403i \(0.699248\pi\)
\(864\) 51.5394 1.75341
\(865\) 22.8064 0.775440
\(866\) 7.79717 0.264958
\(867\) −12.3070 −0.417968
\(868\) 26.1162 0.886443
\(869\) 22.5691 0.765603
\(870\) 4.50487 0.152729
\(871\) −6.94806 −0.235426
\(872\) −92.5870 −3.13539
\(873\) −14.4833 −0.490184
\(874\) −1.94035 −0.0656333
\(875\) 1.58856 0.0537030
\(876\) 31.2519 1.05590
\(877\) −2.73222 −0.0922607 −0.0461303 0.998935i \(-0.514689\pi\)
−0.0461303 + 0.998935i \(0.514689\pi\)
\(878\) −56.1183 −1.89390
\(879\) −4.09432 −0.138098
\(880\) 23.9938 0.808832
\(881\) −29.0709 −0.979423 −0.489712 0.871884i \(-0.662898\pi\)
−0.489712 + 0.871884i \(0.662898\pi\)
\(882\) −29.2643 −0.985380
\(883\) −23.8399 −0.802276 −0.401138 0.916018i \(-0.631385\pi\)
−0.401138 + 0.916018i \(0.631385\pi\)
\(884\) 1.47151 0.0494923
\(885\) 0.772833 0.0259785
\(886\) 9.54976 0.320830
\(887\) 8.48623 0.284940 0.142470 0.989799i \(-0.454496\pi\)
0.142470 + 0.989799i \(0.454496\pi\)
\(888\) −15.5006 −0.520165
\(889\) 26.2196 0.879377
\(890\) −7.66853 −0.257050
\(891\) −10.0096 −0.335334
\(892\) 1.90037 0.0636291
\(893\) 0.515125 0.0172380
\(894\) −0.838133 −0.0280314
\(895\) 18.8078 0.628676
\(896\) 11.4073 0.381093
\(897\) −7.53396 −0.251551
\(898\) 39.3579 1.31339
\(899\) −7.74738 −0.258390
\(900\) −12.3306 −0.411019
\(901\) −2.13314 −0.0710652
\(902\) 39.6654 1.32071
\(903\) 1.06310 0.0353776
\(904\) 30.9643 1.02986
\(905\) 4.20617 0.139818
\(906\) −19.4166 −0.645072
\(907\) −52.7608 −1.75189 −0.875947 0.482407i \(-0.839763\pi\)
−0.875947 + 0.482407i \(0.839763\pi\)
\(908\) 27.0897 0.899004
\(909\) −14.5040 −0.481066
\(910\) 6.32160 0.209559
\(911\) −5.96419 −0.197603 −0.0988013 0.995107i \(-0.531501\pi\)
−0.0988013 + 0.995107i \(0.531501\pi\)
\(912\) 0.840476 0.0278309
\(913\) −37.2564 −1.23301
\(914\) −41.6449 −1.37749
\(915\) 3.22011 0.106454
\(916\) 119.361 3.94378
\(917\) −24.0104 −0.792894
\(918\) −2.05776 −0.0679161
\(919\) 23.8602 0.787075 0.393538 0.919308i \(-0.371251\pi\)
0.393538 + 0.919308i \(0.371251\pi\)
\(920\) 54.4031 1.79362
\(921\) −4.71870 −0.155486
\(922\) 57.6365 1.89816
\(923\) 6.81153 0.224204
\(924\) 12.6711 0.416849
\(925\) 2.70790 0.0890353
\(926\) −84.2923 −2.77002
\(927\) 15.5024 0.509165
\(928\) −30.4858 −1.00075
\(929\) 53.5677 1.75750 0.878750 0.477282i \(-0.158378\pi\)
0.878750 + 0.477282i \(0.158378\pi\)
\(930\) −6.32429 −0.207382
\(931\) −0.476582 −0.0156194
\(932\) 22.7366 0.744762
\(933\) −19.6641 −0.643774
\(934\) −66.9239 −2.18982
\(935\) −0.432333 −0.0141388
\(936\) −29.3823 −0.960391
\(937\) 36.9692 1.20773 0.603866 0.797086i \(-0.293626\pi\)
0.603866 + 0.797086i \(0.293626\pi\)
\(938\) 19.3735 0.632568
\(939\) 12.6999 0.414446
\(940\) −24.1200 −0.786708
\(941\) 27.6823 0.902419 0.451209 0.892418i \(-0.350993\pi\)
0.451209 + 0.892418i \(0.350993\pi\)
\(942\) 17.3479 0.565226
\(943\) 46.9314 1.52830
\(944\) −11.5888 −0.377183
\(945\) −6.30894 −0.205230
\(946\) −5.37561 −0.174776
\(947\) 16.2867 0.529248 0.264624 0.964352i \(-0.414752\pi\)
0.264624 + 0.964352i \(0.414752\pi\)
\(948\) −37.0173 −1.20226
\(949\) −13.0096 −0.422311
\(950\) −0.281374 −0.00912897
\(951\) 16.0371 0.520038
\(952\) −2.45690 −0.0796286
\(953\) 28.9689 0.938396 0.469198 0.883093i \(-0.344543\pi\)
0.469198 + 0.883093i \(0.344543\pi\)
\(954\) 71.1317 2.30297
\(955\) −5.80324 −0.187789
\(956\) 52.0625 1.68382
\(957\) −3.75889 −0.121508
\(958\) 17.3739 0.561324
\(959\) 33.0217 1.06633
\(960\) −9.09700 −0.293604
\(961\) −20.1236 −0.649148
\(962\) 10.7760 0.347432
\(963\) −25.8117 −0.831771
\(964\) −51.5095 −1.65901
\(965\) −19.4678 −0.626690
\(966\) 21.0072 0.675895
\(967\) 41.0047 1.31862 0.659310 0.751871i \(-0.270848\pi\)
0.659310 + 0.751871i \(0.270848\pi\)
\(968\) 48.4139 1.55608
\(969\) −0.0151441 −0.000486499 0
\(970\) 15.4751 0.496874
\(971\) −0.504941 −0.0162043 −0.00810216 0.999967i \(-0.502579\pi\)
−0.00810216 + 0.999967i \(0.502579\pi\)
\(972\) 75.8112 2.43165
\(973\) 30.5794 0.980330
\(974\) 71.6531 2.29591
\(975\) −1.09251 −0.0349885
\(976\) −48.2863 −1.54561
\(977\) −12.9340 −0.413794 −0.206897 0.978363i \(-0.566337\pi\)
−0.206897 + 0.978363i \(0.566337\pi\)
\(978\) 15.0263 0.480489
\(979\) 6.39868 0.204503
\(980\) 22.3153 0.712836
\(981\) −29.0295 −0.926841
\(982\) 15.8976 0.507312
\(983\) −44.5059 −1.41952 −0.709759 0.704445i \(-0.751196\pi\)
−0.709759 + 0.704445i \(0.751196\pi\)
\(984\) −38.9566 −1.24189
\(985\) −8.73362 −0.278276
\(986\) 1.21717 0.0387627
\(987\) −5.57701 −0.177518
\(988\) −0.799110 −0.0254231
\(989\) −6.36033 −0.202247
\(990\) 14.4166 0.458188
\(991\) 26.9874 0.857282 0.428641 0.903475i \(-0.358992\pi\)
0.428641 + 0.903475i \(0.358992\pi\)
\(992\) 42.7985 1.35885
\(993\) −9.31297 −0.295538
\(994\) −18.9928 −0.602416
\(995\) 4.34045 0.137602
\(996\) 61.1071 1.93625
\(997\) 10.9214 0.345883 0.172941 0.984932i \(-0.444673\pi\)
0.172941 + 0.984932i \(0.444673\pi\)
\(998\) 7.20572 0.228093
\(999\) −10.7544 −0.340255
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 6005.2.a.d.1.1 83
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6005.2.a.d.1.1 83 1.1 even 1 trivial