Properties

Label 503.2.a.f.1.2
Level $503$
Weight $2$
Character 503.1
Self dual yes
Analytic conductor $4.016$
Analytic rank $0$
Dimension $26$
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] = [503,2,Mod(1,503)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(503, 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("503.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 503 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 503.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: \(4.01647522167\)
Analytic rank: \(0\)
Dimension: \(26\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) \(=\) 503.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.69742 q^{2} +3.34519 q^{3} +5.27606 q^{4} +2.36922 q^{5} -9.02336 q^{6} -0.269938 q^{7} -8.83689 q^{8} +8.19027 q^{9} +O(q^{10})\) \(q-2.69742 q^{2} +3.34519 q^{3} +5.27606 q^{4} +2.36922 q^{5} -9.02336 q^{6} -0.269938 q^{7} -8.83689 q^{8} +8.19027 q^{9} -6.39078 q^{10} -3.44261 q^{11} +17.6494 q^{12} +0.0670783 q^{13} +0.728135 q^{14} +7.92549 q^{15} +13.2847 q^{16} +0.574750 q^{17} -22.0926 q^{18} +5.60836 q^{19} +12.5002 q^{20} -0.902992 q^{21} +9.28615 q^{22} +0.0744127 q^{23} -29.5610 q^{24} +0.613214 q^{25} -0.180938 q^{26} +17.3624 q^{27} -1.42421 q^{28} -7.68659 q^{29} -21.3783 q^{30} -10.9761 q^{31} -18.1605 q^{32} -11.5162 q^{33} -1.55034 q^{34} -0.639542 q^{35} +43.2123 q^{36} +8.85240 q^{37} -15.1281 q^{38} +0.224390 q^{39} -20.9366 q^{40} -0.941933 q^{41} +2.43574 q^{42} +0.827772 q^{43} -18.1634 q^{44} +19.4046 q^{45} -0.200722 q^{46} -10.6558 q^{47} +44.4397 q^{48} -6.92713 q^{49} -1.65409 q^{50} +1.92265 q^{51} +0.353909 q^{52} +10.1774 q^{53} -46.8336 q^{54} -8.15631 q^{55} +2.38541 q^{56} +18.7610 q^{57} +20.7339 q^{58} +0.0750789 q^{59} +41.8153 q^{60} +8.44603 q^{61} +29.6071 q^{62} -2.21086 q^{63} +22.4171 q^{64} +0.158924 q^{65} +31.0639 q^{66} +5.59158 q^{67} +3.03242 q^{68} +0.248924 q^{69} +1.72511 q^{70} -9.18424 q^{71} -72.3765 q^{72} -10.2585 q^{73} -23.8786 q^{74} +2.05132 q^{75} +29.5900 q^{76} +0.929290 q^{77} -0.605272 q^{78} +3.81855 q^{79} +31.4743 q^{80} +33.5096 q^{81} +2.54079 q^{82} -4.05258 q^{83} -4.76424 q^{84} +1.36171 q^{85} -2.23285 q^{86} -25.7131 q^{87} +30.4220 q^{88} -6.39067 q^{89} -52.3422 q^{90} -0.0181070 q^{91} +0.392606 q^{92} -36.7170 q^{93} +28.7433 q^{94} +13.2874 q^{95} -60.7502 q^{96} +7.52386 q^{97} +18.6854 q^{98} -28.1959 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9} + 4 q^{10} - 17 q^{11} + 19 q^{12} + 14 q^{13} + q^{14} + 18 q^{15} + 48 q^{16} + 17 q^{17} - 10 q^{18} - 22 q^{19} - 19 q^{20} - 16 q^{21} + 38 q^{22} + 27 q^{23} - 9 q^{24} + 93 q^{25} + q^{26} + 31 q^{27} - 9 q^{28} + 13 q^{29} - 28 q^{30} + 26 q^{31} + 5 q^{32} + 6 q^{33} - 32 q^{34} - 22 q^{35} + 52 q^{36} + 55 q^{37} - 24 q^{38} - 15 q^{39} - 7 q^{40} + 24 q^{41} - 50 q^{42} + 20 q^{43} - 27 q^{44} - 8 q^{45} + 6 q^{46} - 25 q^{47} + 29 q^{48} + 65 q^{49} - 16 q^{50} + 7 q^{51} + 32 q^{52} + 30 q^{53} - 82 q^{54} + 25 q^{55} + 3 q^{56} + 9 q^{57} + 58 q^{58} - 26 q^{59} - 68 q^{60} + 15 q^{61} - 12 q^{62} - 19 q^{63} + 44 q^{64} + 20 q^{65} - 55 q^{66} - 20 q^{67} - 4 q^{68} - 27 q^{69} + 2 q^{70} - 35 q^{71} - 26 q^{72} + 38 q^{73} - 59 q^{74} + 2 q^{75} - 42 q^{76} - 6 q^{77} - 47 q^{78} + 21 q^{79} - 100 q^{80} + 70 q^{81} - 59 q^{82} - 48 q^{83} - 116 q^{84} + 6 q^{85} - 7 q^{86} - 9 q^{87} + 106 q^{88} - 5 q^{89} - 118 q^{90} - 24 q^{91} + 26 q^{92} - 8 q^{93} - 22 q^{94} + 43 q^{95} - 100 q^{96} + 142 q^{97} - 38 q^{98} - 50 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.69742 −1.90736 −0.953681 0.300820i \(-0.902740\pi\)
−0.953681 + 0.300820i \(0.902740\pi\)
\(3\) 3.34519 1.93134 0.965672 0.259765i \(-0.0836451\pi\)
0.965672 + 0.259765i \(0.0836451\pi\)
\(4\) 5.27606 2.63803
\(5\) 2.36922 1.05955 0.529774 0.848139i \(-0.322277\pi\)
0.529774 + 0.848139i \(0.322277\pi\)
\(6\) −9.02336 −3.68377
\(7\) −0.269938 −0.102027 −0.0510134 0.998698i \(-0.516245\pi\)
−0.0510134 + 0.998698i \(0.516245\pi\)
\(8\) −8.83689 −3.12431
\(9\) 8.19027 2.73009
\(10\) −6.39078 −2.02094
\(11\) −3.44261 −1.03799 −0.518993 0.854778i \(-0.673693\pi\)
−0.518993 + 0.854778i \(0.673693\pi\)
\(12\) 17.6494 5.09494
\(13\) 0.0670783 0.0186042 0.00930209 0.999957i \(-0.497039\pi\)
0.00930209 + 0.999957i \(0.497039\pi\)
\(14\) 0.728135 0.194602
\(15\) 7.92549 2.04635
\(16\) 13.2847 3.32117
\(17\) 0.574750 0.139397 0.0696987 0.997568i \(-0.477796\pi\)
0.0696987 + 0.997568i \(0.477796\pi\)
\(18\) −22.0926 −5.20727
\(19\) 5.60836 1.28665 0.643323 0.765595i \(-0.277555\pi\)
0.643323 + 0.765595i \(0.277555\pi\)
\(20\) 12.5002 2.79512
\(21\) −0.902992 −0.197049
\(22\) 9.28615 1.97981
\(23\) 0.0744127 0.0155161 0.00775806 0.999970i \(-0.497531\pi\)
0.00775806 + 0.999970i \(0.497531\pi\)
\(24\) −29.5610 −6.03412
\(25\) 0.613214 0.122643
\(26\) −0.180938 −0.0354849
\(27\) 17.3624 3.34140
\(28\) −1.42421 −0.269150
\(29\) −7.68659 −1.42736 −0.713682 0.700470i \(-0.752974\pi\)
−0.713682 + 0.700470i \(0.752974\pi\)
\(30\) −21.3783 −3.90313
\(31\) −10.9761 −1.97136 −0.985681 0.168622i \(-0.946068\pi\)
−0.985681 + 0.168622i \(0.946068\pi\)
\(32\) −18.1605 −3.21035
\(33\) −11.5162 −2.00471
\(34\) −1.55034 −0.265881
\(35\) −0.639542 −0.108102
\(36\) 43.2123 7.20205
\(37\) 8.85240 1.45533 0.727663 0.685935i \(-0.240607\pi\)
0.727663 + 0.685935i \(0.240607\pi\)
\(38\) −15.1281 −2.45410
\(39\) 0.224390 0.0359311
\(40\) −20.9366 −3.31036
\(41\) −0.941933 −0.147105 −0.0735526 0.997291i \(-0.523434\pi\)
−0.0735526 + 0.997291i \(0.523434\pi\)
\(42\) 2.43574 0.375844
\(43\) 0.827772 0.126234 0.0631170 0.998006i \(-0.479896\pi\)
0.0631170 + 0.998006i \(0.479896\pi\)
\(44\) −18.1634 −2.73824
\(45\) 19.4046 2.89266
\(46\) −0.200722 −0.0295949
\(47\) −10.6558 −1.55431 −0.777157 0.629306i \(-0.783339\pi\)
−0.777157 + 0.629306i \(0.783339\pi\)
\(48\) 44.4397 6.41431
\(49\) −6.92713 −0.989591
\(50\) −1.65409 −0.233924
\(51\) 1.92265 0.269224
\(52\) 0.353909 0.0490784
\(53\) 10.1774 1.39797 0.698984 0.715137i \(-0.253636\pi\)
0.698984 + 0.715137i \(0.253636\pi\)
\(54\) −46.8336 −6.37325
\(55\) −8.15631 −1.09980
\(56\) 2.38541 0.318764
\(57\) 18.7610 2.48495
\(58\) 20.7339 2.72250
\(59\) 0.0750789 0.00977443 0.00488722 0.999988i \(-0.498444\pi\)
0.00488722 + 0.999988i \(0.498444\pi\)
\(60\) 41.8153 5.39834
\(61\) 8.44603 1.08140 0.540702 0.841214i \(-0.318159\pi\)
0.540702 + 0.841214i \(0.318159\pi\)
\(62\) 29.6071 3.76010
\(63\) −2.21086 −0.278542
\(64\) 22.4171 2.80214
\(65\) 0.158924 0.0197120
\(66\) 31.0639 3.82370
\(67\) 5.59158 0.683120 0.341560 0.939860i \(-0.389045\pi\)
0.341560 + 0.939860i \(0.389045\pi\)
\(68\) 3.03242 0.367734
\(69\) 0.248924 0.0299670
\(70\) 1.72511 0.206190
\(71\) −9.18424 −1.08997 −0.544984 0.838446i \(-0.683464\pi\)
−0.544984 + 0.838446i \(0.683464\pi\)
\(72\) −72.3765 −8.52965
\(73\) −10.2585 −1.20067 −0.600336 0.799748i \(-0.704966\pi\)
−0.600336 + 0.799748i \(0.704966\pi\)
\(74\) −23.8786 −2.77583
\(75\) 2.05132 0.236865
\(76\) 29.5900 3.39421
\(77\) 0.929290 0.105902
\(78\) −0.605272 −0.0685336
\(79\) 3.81855 0.429620 0.214810 0.976656i \(-0.431087\pi\)
0.214810 + 0.976656i \(0.431087\pi\)
\(80\) 31.4743 3.51894
\(81\) 33.5096 3.72329
\(82\) 2.54079 0.280583
\(83\) −4.05258 −0.444828 −0.222414 0.974952i \(-0.571394\pi\)
−0.222414 + 0.974952i \(0.571394\pi\)
\(84\) −4.76424 −0.519821
\(85\) 1.36171 0.147698
\(86\) −2.23285 −0.240774
\(87\) −25.7131 −2.75673
\(88\) 30.4220 3.24299
\(89\) −6.39067 −0.677410 −0.338705 0.940893i \(-0.609989\pi\)
−0.338705 + 0.940893i \(0.609989\pi\)
\(90\) −52.3422 −5.51735
\(91\) −0.0181070 −0.00189813
\(92\) 0.392606 0.0409320
\(93\) −36.7170 −3.80738
\(94\) 28.7433 2.96464
\(95\) 13.2874 1.36326
\(96\) −60.7502 −6.20029
\(97\) 7.52386 0.763932 0.381966 0.924176i \(-0.375247\pi\)
0.381966 + 0.924176i \(0.375247\pi\)
\(98\) 18.6854 1.88751
\(99\) −28.1959 −2.83379
\(100\) 3.23535 0.323535
\(101\) −7.46008 −0.742306 −0.371153 0.928572i \(-0.621037\pi\)
−0.371153 + 0.928572i \(0.621037\pi\)
\(102\) −5.18618 −0.513508
\(103\) −4.83695 −0.476599 −0.238300 0.971192i \(-0.576590\pi\)
−0.238300 + 0.971192i \(0.576590\pi\)
\(104\) −0.592764 −0.0581253
\(105\) −2.13939 −0.208783
\(106\) −27.4526 −2.66643
\(107\) −7.97886 −0.771345 −0.385673 0.922636i \(-0.626031\pi\)
−0.385673 + 0.922636i \(0.626031\pi\)
\(108\) 91.6050 8.81470
\(109\) 6.05695 0.580150 0.290075 0.957004i \(-0.406320\pi\)
0.290075 + 0.957004i \(0.406320\pi\)
\(110\) 22.0010 2.09771
\(111\) 29.6129 2.81073
\(112\) −3.58603 −0.338848
\(113\) 11.0788 1.04221 0.521103 0.853494i \(-0.325521\pi\)
0.521103 + 0.853494i \(0.325521\pi\)
\(114\) −50.6062 −4.73971
\(115\) 0.176300 0.0164401
\(116\) −40.5549 −3.76543
\(117\) 0.549389 0.0507911
\(118\) −0.202519 −0.0186434
\(119\) −0.155147 −0.0142223
\(120\) −70.0367 −6.39344
\(121\) 0.851566 0.0774151
\(122\) −22.7825 −2.06263
\(123\) −3.15094 −0.284111
\(124\) −57.9104 −5.20051
\(125\) −10.3933 −0.929602
\(126\) 5.96361 0.531281
\(127\) 3.26030 0.289305 0.144653 0.989483i \(-0.453794\pi\)
0.144653 + 0.989483i \(0.453794\pi\)
\(128\) −24.1473 −2.13434
\(129\) 2.76905 0.243801
\(130\) −0.428683 −0.0375980
\(131\) 20.1252 1.75835 0.879173 0.476503i \(-0.158096\pi\)
0.879173 + 0.476503i \(0.158096\pi\)
\(132\) −60.7600 −5.28848
\(133\) −1.51391 −0.131272
\(134\) −15.0828 −1.30296
\(135\) 41.1354 3.54037
\(136\) −5.07901 −0.435521
\(137\) 7.41685 0.633664 0.316832 0.948482i \(-0.397381\pi\)
0.316832 + 0.948482i \(0.397381\pi\)
\(138\) −0.671453 −0.0571579
\(139\) 2.28911 0.194160 0.0970799 0.995277i \(-0.469050\pi\)
0.0970799 + 0.995277i \(0.469050\pi\)
\(140\) −3.37426 −0.285177
\(141\) −35.6458 −3.00192
\(142\) 24.7737 2.07896
\(143\) −0.230925 −0.0193109
\(144\) 108.805 9.06708
\(145\) −18.2112 −1.51236
\(146\) 27.6716 2.29012
\(147\) −23.1725 −1.91124
\(148\) 46.7058 3.83919
\(149\) 12.4083 1.01653 0.508264 0.861202i \(-0.330288\pi\)
0.508264 + 0.861202i \(0.330288\pi\)
\(150\) −5.53325 −0.451788
\(151\) −19.3681 −1.57615 −0.788076 0.615578i \(-0.788923\pi\)
−0.788076 + 0.615578i \(0.788923\pi\)
\(152\) −49.5605 −4.01988
\(153\) 4.70736 0.380567
\(154\) −2.50668 −0.201994
\(155\) −26.0048 −2.08875
\(156\) 1.18389 0.0947872
\(157\) −6.46739 −0.516154 −0.258077 0.966124i \(-0.583089\pi\)
−0.258077 + 0.966124i \(0.583089\pi\)
\(158\) −10.3002 −0.819441
\(159\) 34.0452 2.69996
\(160\) −43.0262 −3.40152
\(161\) −0.0200868 −0.00158306
\(162\) −90.3895 −7.10167
\(163\) 11.4793 0.899126 0.449563 0.893249i \(-0.351580\pi\)
0.449563 + 0.893249i \(0.351580\pi\)
\(164\) −4.96969 −0.388068
\(165\) −27.2844 −2.12408
\(166\) 10.9315 0.848448
\(167\) 8.31406 0.643361 0.321680 0.946848i \(-0.395752\pi\)
0.321680 + 0.946848i \(0.395752\pi\)
\(168\) 7.97964 0.615643
\(169\) −12.9955 −0.999654
\(170\) −3.67310 −0.281714
\(171\) 45.9339 3.51266
\(172\) 4.36737 0.333009
\(173\) −3.21616 −0.244520 −0.122260 0.992498i \(-0.539014\pi\)
−0.122260 + 0.992498i \(0.539014\pi\)
\(174\) 69.3589 5.25808
\(175\) −0.165530 −0.0125129
\(176\) −45.7339 −3.44732
\(177\) 0.251153 0.0188778
\(178\) 17.2383 1.29207
\(179\) 11.6492 0.870698 0.435349 0.900262i \(-0.356625\pi\)
0.435349 + 0.900262i \(0.356625\pi\)
\(180\) 102.380 7.63092
\(181\) −5.84600 −0.434529 −0.217265 0.976113i \(-0.569713\pi\)
−0.217265 + 0.976113i \(0.569713\pi\)
\(182\) 0.0488421 0.00362041
\(183\) 28.2535 2.08856
\(184\) −0.657577 −0.0484772
\(185\) 20.9733 1.54199
\(186\) 99.0411 7.26204
\(187\) −1.97864 −0.144693
\(188\) −56.2208 −4.10033
\(189\) −4.68677 −0.340912
\(190\) −35.8418 −2.60024
\(191\) −2.85579 −0.206638 −0.103319 0.994648i \(-0.532946\pi\)
−0.103319 + 0.994648i \(0.532946\pi\)
\(192\) 74.9893 5.41189
\(193\) 17.3742 1.25063 0.625313 0.780374i \(-0.284971\pi\)
0.625313 + 0.780374i \(0.284971\pi\)
\(194\) −20.2950 −1.45709
\(195\) 0.531629 0.0380707
\(196\) −36.5480 −2.61057
\(197\) −7.87516 −0.561082 −0.280541 0.959842i \(-0.590514\pi\)
−0.280541 + 0.959842i \(0.590514\pi\)
\(198\) 76.0561 5.40507
\(199\) −22.2898 −1.58008 −0.790042 0.613052i \(-0.789941\pi\)
−0.790042 + 0.613052i \(0.789941\pi\)
\(200\) −5.41891 −0.383175
\(201\) 18.7049 1.31934
\(202\) 20.1229 1.41585
\(203\) 2.07490 0.145629
\(204\) 10.1440 0.710222
\(205\) −2.23165 −0.155865
\(206\) 13.0473 0.909047
\(207\) 0.609460 0.0423604
\(208\) 0.891113 0.0617876
\(209\) −19.3074 −1.33552
\(210\) 5.77082 0.398225
\(211\) 11.0417 0.760140 0.380070 0.924958i \(-0.375900\pi\)
0.380070 + 0.924958i \(0.375900\pi\)
\(212\) 53.6963 3.68788
\(213\) −30.7230 −2.10510
\(214\) 21.5223 1.47123
\(215\) 1.96118 0.133751
\(216\) −153.430 −10.4396
\(217\) 2.96286 0.201132
\(218\) −16.3381 −1.10656
\(219\) −34.3167 −2.31891
\(220\) −43.0332 −2.90129
\(221\) 0.0385533 0.00259338
\(222\) −79.8784 −5.36108
\(223\) −20.8389 −1.39548 −0.697738 0.716353i \(-0.745810\pi\)
−0.697738 + 0.716353i \(0.745810\pi\)
\(224\) 4.90220 0.327542
\(225\) 5.02239 0.334826
\(226\) −29.8841 −1.98786
\(227\) −3.45610 −0.229390 −0.114695 0.993401i \(-0.536589\pi\)
−0.114695 + 0.993401i \(0.536589\pi\)
\(228\) 98.9841 6.55538
\(229\) −7.66799 −0.506715 −0.253358 0.967373i \(-0.581535\pi\)
−0.253358 + 0.967373i \(0.581535\pi\)
\(230\) −0.475555 −0.0313572
\(231\) 3.10865 0.204534
\(232\) 67.9256 4.45953
\(233\) 2.09010 0.136927 0.0684635 0.997654i \(-0.478190\pi\)
0.0684635 + 0.997654i \(0.478190\pi\)
\(234\) −1.48193 −0.0968769
\(235\) −25.2461 −1.64687
\(236\) 0.396120 0.0257852
\(237\) 12.7737 0.829744
\(238\) 0.418496 0.0271270
\(239\) −7.70373 −0.498313 −0.249156 0.968463i \(-0.580153\pi\)
−0.249156 + 0.968463i \(0.580153\pi\)
\(240\) 105.287 6.79628
\(241\) −27.8018 −1.79087 −0.895434 0.445193i \(-0.853135\pi\)
−0.895434 + 0.445193i \(0.853135\pi\)
\(242\) −2.29703 −0.147659
\(243\) 60.0088 3.84957
\(244\) 44.5618 2.85277
\(245\) −16.4119 −1.04852
\(246\) 8.49940 0.541902
\(247\) 0.376199 0.0239370
\(248\) 96.9944 6.15915
\(249\) −13.5566 −0.859116
\(250\) 28.0350 1.77309
\(251\) −14.6925 −0.927382 −0.463691 0.885997i \(-0.653475\pi\)
−0.463691 + 0.885997i \(0.653475\pi\)
\(252\) −11.6646 −0.734803
\(253\) −0.256174 −0.0161055
\(254\) −8.79440 −0.551810
\(255\) 4.55518 0.285256
\(256\) 20.3010 1.26881
\(257\) 18.6366 1.16252 0.581259 0.813719i \(-0.302560\pi\)
0.581259 + 0.813719i \(0.302560\pi\)
\(258\) −7.46928 −0.465017
\(259\) −2.38960 −0.148482
\(260\) 0.838490 0.0520009
\(261\) −62.9552 −3.89683
\(262\) −54.2860 −3.35380
\(263\) −2.10250 −0.129646 −0.0648230 0.997897i \(-0.520648\pi\)
−0.0648230 + 0.997897i \(0.520648\pi\)
\(264\) 101.767 6.26333
\(265\) 24.1124 1.48121
\(266\) 4.08364 0.250384
\(267\) −21.3780 −1.30831
\(268\) 29.5015 1.80209
\(269\) 14.7598 0.899921 0.449960 0.893048i \(-0.351438\pi\)
0.449960 + 0.893048i \(0.351438\pi\)
\(270\) −110.959 −6.75277
\(271\) −5.23259 −0.317857 −0.158929 0.987290i \(-0.550804\pi\)
−0.158929 + 0.987290i \(0.550804\pi\)
\(272\) 7.63537 0.462962
\(273\) −0.0605712 −0.00366594
\(274\) −20.0063 −1.20863
\(275\) −2.11106 −0.127302
\(276\) 1.31334 0.0790537
\(277\) 22.1292 1.32961 0.664806 0.747016i \(-0.268514\pi\)
0.664806 + 0.747016i \(0.268514\pi\)
\(278\) −6.17468 −0.370333
\(279\) −89.8970 −5.38199
\(280\) 5.65157 0.337746
\(281\) 4.68344 0.279391 0.139695 0.990195i \(-0.455388\pi\)
0.139695 + 0.990195i \(0.455388\pi\)
\(282\) 96.1515 5.72574
\(283\) −15.8277 −0.940859 −0.470429 0.882438i \(-0.655901\pi\)
−0.470429 + 0.882438i \(0.655901\pi\)
\(284\) −48.4566 −2.87537
\(285\) 44.4490 2.63293
\(286\) 0.622900 0.0368328
\(287\) 0.254263 0.0150087
\(288\) −148.739 −8.76455
\(289\) −16.6697 −0.980568
\(290\) 49.1233 2.88462
\(291\) 25.1687 1.47542
\(292\) −54.1247 −3.16741
\(293\) 19.2238 1.12307 0.561534 0.827454i \(-0.310212\pi\)
0.561534 + 0.827454i \(0.310212\pi\)
\(294\) 62.5060 3.64542
\(295\) 0.177878 0.0103565
\(296\) −78.2277 −4.54689
\(297\) −59.7720 −3.46832
\(298\) −33.4703 −1.93889
\(299\) 0.00499148 0.000288665 0
\(300\) 10.8229 0.624858
\(301\) −0.223447 −0.0128793
\(302\) 52.2438 3.00629
\(303\) −24.9553 −1.43365
\(304\) 74.5052 4.27316
\(305\) 20.0105 1.14580
\(306\) −12.6977 −0.725880
\(307\) −5.71917 −0.326410 −0.163205 0.986592i \(-0.552183\pi\)
−0.163205 + 0.986592i \(0.552183\pi\)
\(308\) 4.90299 0.279374
\(309\) −16.1805 −0.920477
\(310\) 70.1457 3.98401
\(311\) −1.46106 −0.0828490 −0.0414245 0.999142i \(-0.513190\pi\)
−0.0414245 + 0.999142i \(0.513190\pi\)
\(312\) −1.98291 −0.112260
\(313\) −24.3208 −1.37469 −0.687345 0.726331i \(-0.741224\pi\)
−0.687345 + 0.726331i \(0.741224\pi\)
\(314\) 17.4453 0.984493
\(315\) −5.23802 −0.295129
\(316\) 20.1469 1.13335
\(317\) 16.2503 0.912708 0.456354 0.889798i \(-0.349155\pi\)
0.456354 + 0.889798i \(0.349155\pi\)
\(318\) −91.8340 −5.14979
\(319\) 26.4619 1.48158
\(320\) 53.1111 2.96900
\(321\) −26.6908 −1.48973
\(322\) 0.0541825 0.00301947
\(323\) 3.22341 0.179355
\(324\) 176.799 9.82216
\(325\) 0.0411334 0.00228167
\(326\) −30.9644 −1.71496
\(327\) 20.2616 1.12047
\(328\) 8.32376 0.459603
\(329\) 2.87641 0.158582
\(330\) 73.5973 4.05140
\(331\) 14.4154 0.792340 0.396170 0.918177i \(-0.370339\pi\)
0.396170 + 0.918177i \(0.370339\pi\)
\(332\) −21.3816 −1.17347
\(333\) 72.5035 3.97317
\(334\) −22.4265 −1.22712
\(335\) 13.2477 0.723799
\(336\) −11.9959 −0.654432
\(337\) 0.721121 0.0392820 0.0196410 0.999807i \(-0.493748\pi\)
0.0196410 + 0.999807i \(0.493748\pi\)
\(338\) 35.0543 1.90670
\(339\) 37.0606 2.01286
\(340\) 7.18447 0.389632
\(341\) 37.7864 2.04625
\(342\) −123.903 −6.69991
\(343\) 3.75946 0.202992
\(344\) −7.31493 −0.394395
\(345\) 0.589757 0.0317515
\(346\) 8.67533 0.466388
\(347\) −10.9006 −0.585174 −0.292587 0.956239i \(-0.594516\pi\)
−0.292587 + 0.956239i \(0.594516\pi\)
\(348\) −135.664 −7.27233
\(349\) 7.23410 0.387232 0.193616 0.981077i \(-0.437978\pi\)
0.193616 + 0.981077i \(0.437978\pi\)
\(350\) 0.446502 0.0238666
\(351\) 1.16464 0.0621639
\(352\) 62.5195 3.33230
\(353\) 2.79663 0.148849 0.0744247 0.997227i \(-0.476288\pi\)
0.0744247 + 0.997227i \(0.476288\pi\)
\(354\) −0.677463 −0.0360068
\(355\) −21.7595 −1.15487
\(356\) −33.7175 −1.78703
\(357\) −0.518995 −0.0274681
\(358\) −31.4226 −1.66074
\(359\) 11.4565 0.604650 0.302325 0.953205i \(-0.402237\pi\)
0.302325 + 0.953205i \(0.402237\pi\)
\(360\) −171.476 −9.03758
\(361\) 12.4537 0.655457
\(362\) 15.7691 0.828805
\(363\) 2.84864 0.149515
\(364\) −0.0955334 −0.00500731
\(365\) −24.3048 −1.27217
\(366\) −76.2116 −3.98364
\(367\) −1.24262 −0.0648644 −0.0324322 0.999474i \(-0.510325\pi\)
−0.0324322 + 0.999474i \(0.510325\pi\)
\(368\) 0.988548 0.0515316
\(369\) −7.71468 −0.401610
\(370\) −56.5737 −2.94113
\(371\) −2.74725 −0.142630
\(372\) −193.721 −10.0440
\(373\) −16.5054 −0.854619 −0.427310 0.904105i \(-0.640539\pi\)
−0.427310 + 0.904105i \(0.640539\pi\)
\(374\) 5.33722 0.275981
\(375\) −34.7674 −1.79538
\(376\) 94.1645 4.85617
\(377\) −0.515604 −0.0265549
\(378\) 12.6422 0.650243
\(379\) 13.7335 0.705442 0.352721 0.935728i \(-0.385256\pi\)
0.352721 + 0.935728i \(0.385256\pi\)
\(380\) 70.1053 3.59633
\(381\) 10.9063 0.558748
\(382\) 7.70325 0.394133
\(383\) 15.6624 0.800310 0.400155 0.916447i \(-0.368956\pi\)
0.400155 + 0.916447i \(0.368956\pi\)
\(384\) −80.7770 −4.12214
\(385\) 2.20170 0.112209
\(386\) −46.8656 −2.38539
\(387\) 6.77967 0.344630
\(388\) 39.6963 2.01527
\(389\) 20.4979 1.03928 0.519641 0.854385i \(-0.326066\pi\)
0.519641 + 0.854385i \(0.326066\pi\)
\(390\) −1.43402 −0.0726146
\(391\) 0.0427687 0.00216291
\(392\) 61.2143 3.09179
\(393\) 67.3225 3.39597
\(394\) 21.2426 1.07019
\(395\) 9.04699 0.455203
\(396\) −148.763 −7.47563
\(397\) −19.6180 −0.984601 −0.492301 0.870425i \(-0.663844\pi\)
−0.492301 + 0.870425i \(0.663844\pi\)
\(398\) 60.1250 3.01379
\(399\) −5.06430 −0.253532
\(400\) 8.14635 0.407317
\(401\) −5.59083 −0.279193 −0.139596 0.990209i \(-0.544580\pi\)
−0.139596 + 0.990209i \(0.544580\pi\)
\(402\) −50.4548 −2.51646
\(403\) −0.736257 −0.0366756
\(404\) −39.3598 −1.95822
\(405\) 79.3918 3.94501
\(406\) −5.59687 −0.277768
\(407\) −30.4754 −1.51061
\(408\) −16.9902 −0.841141
\(409\) 3.42442 0.169327 0.0846633 0.996410i \(-0.473019\pi\)
0.0846633 + 0.996410i \(0.473019\pi\)
\(410\) 6.01968 0.297291
\(411\) 24.8107 1.22382
\(412\) −25.5200 −1.25728
\(413\) −0.0202666 −0.000997255 0
\(414\) −1.64397 −0.0807966
\(415\) −9.60145 −0.471317
\(416\) −1.21818 −0.0597260
\(417\) 7.65750 0.374989
\(418\) 52.0801 2.54732
\(419\) −7.13684 −0.348658 −0.174329 0.984688i \(-0.555776\pi\)
−0.174329 + 0.984688i \(0.555776\pi\)
\(420\) −11.2875 −0.550775
\(421\) −4.24453 −0.206866 −0.103433 0.994636i \(-0.532983\pi\)
−0.103433 + 0.994636i \(0.532983\pi\)
\(422\) −29.7840 −1.44986
\(423\) −87.2742 −4.24342
\(424\) −89.9362 −4.36769
\(425\) 0.352445 0.0170961
\(426\) 82.8727 4.01520
\(427\) −2.27990 −0.110332
\(428\) −42.0969 −2.03483
\(429\) −0.772486 −0.0372960
\(430\) −5.29011 −0.255112
\(431\) −14.8999 −0.717701 −0.358850 0.933395i \(-0.616831\pi\)
−0.358850 + 0.933395i \(0.616831\pi\)
\(432\) 230.654 11.0973
\(433\) 36.7320 1.76523 0.882615 0.470097i \(-0.155781\pi\)
0.882615 + 0.470097i \(0.155781\pi\)
\(434\) −7.99206 −0.383631
\(435\) −60.9200 −2.92089
\(436\) 31.9568 1.53045
\(437\) 0.417333 0.0199638
\(438\) 92.5665 4.42300
\(439\) −34.9016 −1.66576 −0.832881 0.553453i \(-0.813310\pi\)
−0.832881 + 0.553453i \(0.813310\pi\)
\(440\) 72.0764 3.43611
\(441\) −56.7351 −2.70167
\(442\) −0.103994 −0.00494651
\(443\) −9.46514 −0.449702 −0.224851 0.974393i \(-0.572190\pi\)
−0.224851 + 0.974393i \(0.572190\pi\)
\(444\) 156.239 7.41479
\(445\) −15.1409 −0.717748
\(446\) 56.2112 2.66168
\(447\) 41.5081 1.96326
\(448\) −6.05122 −0.285893
\(449\) −9.57151 −0.451708 −0.225854 0.974161i \(-0.572517\pi\)
−0.225854 + 0.974161i \(0.572517\pi\)
\(450\) −13.5475 −0.638634
\(451\) 3.24271 0.152693
\(452\) 58.4523 2.74937
\(453\) −64.7898 −3.04409
\(454\) 9.32255 0.437529
\(455\) −0.0428995 −0.00201116
\(456\) −165.789 −7.76378
\(457\) 28.0582 1.31251 0.656253 0.754541i \(-0.272140\pi\)
0.656253 + 0.754541i \(0.272140\pi\)
\(458\) 20.6838 0.966489
\(459\) 9.97905 0.465782
\(460\) 0.930170 0.0433694
\(461\) −10.2702 −0.478330 −0.239165 0.970979i \(-0.576874\pi\)
−0.239165 + 0.970979i \(0.576874\pi\)
\(462\) −8.38532 −0.390120
\(463\) −3.40138 −0.158076 −0.0790378 0.996872i \(-0.525185\pi\)
−0.0790378 + 0.996872i \(0.525185\pi\)
\(464\) −102.114 −4.74051
\(465\) −86.9908 −4.03410
\(466\) −5.63787 −0.261169
\(467\) 0.206542 0.00955762 0.00477881 0.999989i \(-0.498479\pi\)
0.00477881 + 0.999989i \(0.498479\pi\)
\(468\) 2.89861 0.133988
\(469\) −1.50938 −0.0696966
\(470\) 68.0992 3.14118
\(471\) −21.6346 −0.996871
\(472\) −0.663464 −0.0305384
\(473\) −2.84970 −0.131029
\(474\) −34.4561 −1.58262
\(475\) 3.43913 0.157798
\(476\) −0.818564 −0.0375188
\(477\) 83.3553 3.81658
\(478\) 20.7802 0.950463
\(479\) 18.2434 0.833563 0.416781 0.909007i \(-0.363158\pi\)
0.416781 + 0.909007i \(0.363158\pi\)
\(480\) −143.931 −6.56951
\(481\) 0.593804 0.0270751
\(482\) 74.9929 3.41583
\(483\) −0.0671941 −0.00305744
\(484\) 4.49291 0.204223
\(485\) 17.8257 0.809423
\(486\) −161.869 −7.34251
\(487\) 21.9324 0.993851 0.496925 0.867793i \(-0.334462\pi\)
0.496925 + 0.867793i \(0.334462\pi\)
\(488\) −74.6367 −3.37864
\(489\) 38.4003 1.73652
\(490\) 44.2698 1.99991
\(491\) −17.1433 −0.773666 −0.386833 0.922150i \(-0.626431\pi\)
−0.386833 + 0.922150i \(0.626431\pi\)
\(492\) −16.6245 −0.749492
\(493\) −4.41787 −0.198971
\(494\) −1.01477 −0.0456565
\(495\) −66.8023 −3.00254
\(496\) −145.814 −6.54722
\(497\) 2.47917 0.111206
\(498\) 36.5678 1.63864
\(499\) 8.94274 0.400332 0.200166 0.979762i \(-0.435852\pi\)
0.200166 + 0.979762i \(0.435852\pi\)
\(500\) −54.8355 −2.45232
\(501\) 27.8121 1.24255
\(502\) 39.6318 1.76885
\(503\) 1.00000 0.0445878
\(504\) 19.5371 0.870254
\(505\) −17.6746 −0.786509
\(506\) 0.691008 0.0307191
\(507\) −43.4724 −1.93068
\(508\) 17.2015 0.763195
\(509\) −24.0244 −1.06486 −0.532432 0.846473i \(-0.678722\pi\)
−0.532432 + 0.846473i \(0.678722\pi\)
\(510\) −12.2872 −0.544087
\(511\) 2.76917 0.122501
\(512\) −6.46580 −0.285751
\(513\) 97.3746 4.29919
\(514\) −50.2706 −2.21734
\(515\) −11.4598 −0.504980
\(516\) 14.6097 0.643155
\(517\) 36.6839 1.61336
\(518\) 6.44574 0.283209
\(519\) −10.7587 −0.472253
\(520\) −1.40439 −0.0615866
\(521\) 33.6897 1.47597 0.737986 0.674816i \(-0.235777\pi\)
0.737986 + 0.674816i \(0.235777\pi\)
\(522\) 169.816 7.43267
\(523\) 38.0576 1.66414 0.832071 0.554669i \(-0.187155\pi\)
0.832071 + 0.554669i \(0.187155\pi\)
\(524\) 106.182 4.63857
\(525\) −0.553727 −0.0241666
\(526\) 5.67133 0.247282
\(527\) −6.30851 −0.274803
\(528\) −152.988 −6.65797
\(529\) −22.9945 −0.999759
\(530\) −65.0413 −2.82521
\(531\) 0.614916 0.0266851
\(532\) −7.98746 −0.346300
\(533\) −0.0631833 −0.00273677
\(534\) 57.6653 2.49542
\(535\) −18.9037 −0.817278
\(536\) −49.4122 −2.13428
\(537\) 38.9686 1.68162
\(538\) −39.8133 −1.71647
\(539\) 23.8474 1.02718
\(540\) 217.033 9.33960
\(541\) 13.6023 0.584808 0.292404 0.956295i \(-0.405545\pi\)
0.292404 + 0.956295i \(0.405545\pi\)
\(542\) 14.1145 0.606269
\(543\) −19.5559 −0.839226
\(544\) −10.4378 −0.447515
\(545\) 14.3503 0.614697
\(546\) 0.163386 0.00699226
\(547\) −8.79579 −0.376081 −0.188040 0.982161i \(-0.560214\pi\)
−0.188040 + 0.982161i \(0.560214\pi\)
\(548\) 39.1317 1.67162
\(549\) 69.1752 2.95233
\(550\) 5.69440 0.242810
\(551\) −43.1092 −1.83651
\(552\) −2.19972 −0.0936262
\(553\) −1.03077 −0.0438328
\(554\) −59.6916 −2.53605
\(555\) 70.1596 2.97811
\(556\) 12.0775 0.512199
\(557\) 25.0480 1.06132 0.530660 0.847585i \(-0.321944\pi\)
0.530660 + 0.847585i \(0.321944\pi\)
\(558\) 242.490 10.2654
\(559\) 0.0555256 0.00234848
\(560\) −8.49611 −0.359026
\(561\) −6.61892 −0.279451
\(562\) −12.6332 −0.532899
\(563\) 25.2455 1.06397 0.531986 0.846753i \(-0.321446\pi\)
0.531986 + 0.846753i \(0.321446\pi\)
\(564\) −188.069 −7.91914
\(565\) 26.2481 1.10427
\(566\) 42.6939 1.79456
\(567\) −9.04552 −0.379876
\(568\) 81.1601 3.40540
\(569\) 37.7144 1.58107 0.790534 0.612418i \(-0.209803\pi\)
0.790534 + 0.612418i \(0.209803\pi\)
\(570\) −119.897 −5.02195
\(571\) 25.7219 1.07643 0.538214 0.842809i \(-0.319099\pi\)
0.538214 + 0.842809i \(0.319099\pi\)
\(572\) −1.21837 −0.0509427
\(573\) −9.55314 −0.399088
\(574\) −0.685854 −0.0286270
\(575\) 0.0456309 0.00190294
\(576\) 183.602 7.65008
\(577\) 16.6129 0.691605 0.345802 0.938307i \(-0.387607\pi\)
0.345802 + 0.938307i \(0.387607\pi\)
\(578\) 44.9650 1.87030
\(579\) 58.1201 2.41539
\(580\) −96.0836 −3.98965
\(581\) 1.09394 0.0453844
\(582\) −67.8905 −2.81415
\(583\) −35.0367 −1.45107
\(584\) 90.6536 3.75127
\(585\) 1.30163 0.0538156
\(586\) −51.8546 −2.14209
\(587\) 8.40276 0.346819 0.173409 0.984850i \(-0.444522\pi\)
0.173409 + 0.984850i \(0.444522\pi\)
\(588\) −122.260 −5.04190
\(589\) −61.5578 −2.53644
\(590\) −0.479812 −0.0197536
\(591\) −26.3439 −1.08364
\(592\) 117.601 4.83338
\(593\) −22.0943 −0.907303 −0.453651 0.891179i \(-0.649879\pi\)
−0.453651 + 0.891179i \(0.649879\pi\)
\(594\) 161.230 6.61534
\(595\) −0.367577 −0.0150692
\(596\) 65.4669 2.68163
\(597\) −74.5636 −3.05169
\(598\) −0.0134641 −0.000550588 0
\(599\) 8.13507 0.332390 0.166195 0.986093i \(-0.446852\pi\)
0.166195 + 0.986093i \(0.446852\pi\)
\(600\) −18.1273 −0.740042
\(601\) 26.1570 1.06697 0.533484 0.845810i \(-0.320882\pi\)
0.533484 + 0.845810i \(0.320882\pi\)
\(602\) 0.602729 0.0245654
\(603\) 45.7965 1.86498
\(604\) −102.187 −4.15793
\(605\) 2.01755 0.0820250
\(606\) 67.3150 2.73448
\(607\) −25.2595 −1.02525 −0.512626 0.858612i \(-0.671327\pi\)
−0.512626 + 0.858612i \(0.671327\pi\)
\(608\) −101.851 −4.13059
\(609\) 6.94093 0.281261
\(610\) −53.9767 −2.18545
\(611\) −0.714776 −0.0289168
\(612\) 24.8363 1.00395
\(613\) −10.0650 −0.406520 −0.203260 0.979125i \(-0.565154\pi\)
−0.203260 + 0.979125i \(0.565154\pi\)
\(614\) 15.4270 0.622582
\(615\) −7.46528 −0.301029
\(616\) −8.21204 −0.330872
\(617\) 36.2555 1.45959 0.729796 0.683665i \(-0.239615\pi\)
0.729796 + 0.683665i \(0.239615\pi\)
\(618\) 43.6456 1.75568
\(619\) 21.4552 0.862359 0.431180 0.902266i \(-0.358098\pi\)
0.431180 + 0.902266i \(0.358098\pi\)
\(620\) −137.203 −5.51019
\(621\) 1.29198 0.0518455
\(622\) 3.94108 0.158023
\(623\) 1.72508 0.0691140
\(624\) 2.98094 0.119333
\(625\) −27.6900 −1.10760
\(626\) 65.6032 2.62203
\(627\) −64.5868 −2.57935
\(628\) −34.1223 −1.36163
\(629\) 5.08792 0.202869
\(630\) 14.1291 0.562918
\(631\) 8.56590 0.341003 0.170501 0.985357i \(-0.445461\pi\)
0.170501 + 0.985357i \(0.445461\pi\)
\(632\) −33.7441 −1.34227
\(633\) 36.9364 1.46809
\(634\) −43.8339 −1.74086
\(635\) 7.72438 0.306533
\(636\) 179.624 7.12256
\(637\) −0.464661 −0.0184105
\(638\) −71.3789 −2.82592
\(639\) −75.2214 −2.97571
\(640\) −57.2102 −2.26143
\(641\) 24.9910 0.987086 0.493543 0.869721i \(-0.335702\pi\)
0.493543 + 0.869721i \(0.335702\pi\)
\(642\) 71.9961 2.84146
\(643\) −8.63372 −0.340481 −0.170240 0.985403i \(-0.554454\pi\)
−0.170240 + 0.985403i \(0.554454\pi\)
\(644\) −0.105979 −0.00417616
\(645\) 6.56050 0.258319
\(646\) −8.69487 −0.342095
\(647\) −0.879218 −0.0345656 −0.0172828 0.999851i \(-0.505502\pi\)
−0.0172828 + 0.999851i \(0.505502\pi\)
\(648\) −296.121 −11.6327
\(649\) −0.258467 −0.0101457
\(650\) −0.110954 −0.00435197
\(651\) 9.91131 0.388455
\(652\) 60.5653 2.37192
\(653\) 32.6080 1.27605 0.638024 0.770016i \(-0.279752\pi\)
0.638024 + 0.770016i \(0.279752\pi\)
\(654\) −54.6540 −2.13714
\(655\) 47.6810 1.86305
\(656\) −12.5133 −0.488561
\(657\) −84.0202 −3.27794
\(658\) −7.75889 −0.302473
\(659\) −37.2484 −1.45099 −0.725497 0.688226i \(-0.758390\pi\)
−0.725497 + 0.688226i \(0.758390\pi\)
\(660\) −143.954 −5.60340
\(661\) 15.2171 0.591875 0.295938 0.955207i \(-0.404368\pi\)
0.295938 + 0.955207i \(0.404368\pi\)
\(662\) −38.8843 −1.51128
\(663\) 0.128968 0.00500870
\(664\) 35.8122 1.38978
\(665\) −3.58678 −0.139089
\(666\) −195.572 −7.57827
\(667\) −0.571980 −0.0221472
\(668\) 43.8654 1.69720
\(669\) −69.7100 −2.69514
\(670\) −35.7346 −1.38055
\(671\) −29.0764 −1.12248
\(672\) 16.3988 0.632597
\(673\) 29.8552 1.15083 0.575416 0.817861i \(-0.304840\pi\)
0.575416 + 0.817861i \(0.304840\pi\)
\(674\) −1.94516 −0.0749249
\(675\) 10.6469 0.409798
\(676\) −68.5650 −2.63712
\(677\) −33.4292 −1.28479 −0.642395 0.766374i \(-0.722059\pi\)
−0.642395 + 0.766374i \(0.722059\pi\)
\(678\) −99.9679 −3.83925
\(679\) −2.03097 −0.0779416
\(680\) −12.0333 −0.461456
\(681\) −11.5613 −0.443030
\(682\) −101.926 −3.90293
\(683\) −9.08193 −0.347510 −0.173755 0.984789i \(-0.555590\pi\)
−0.173755 + 0.984789i \(0.555590\pi\)
\(684\) 242.350 9.26649
\(685\) 17.5722 0.671398
\(686\) −10.1408 −0.387179
\(687\) −25.6509 −0.978641
\(688\) 10.9967 0.419244
\(689\) 0.682681 0.0260081
\(690\) −1.59082 −0.0605615
\(691\) 25.9196 0.986029 0.493015 0.870021i \(-0.335895\pi\)
0.493015 + 0.870021i \(0.335895\pi\)
\(692\) −16.9687 −0.645051
\(693\) 7.61113 0.289123
\(694\) 29.4034 1.11614
\(695\) 5.42341 0.205722
\(696\) 227.224 8.61289
\(697\) −0.541376 −0.0205061
\(698\) −19.5134 −0.738592
\(699\) 6.99177 0.264453
\(700\) −0.873344 −0.0330093
\(701\) 31.1296 1.17575 0.587874 0.808953i \(-0.299965\pi\)
0.587874 + 0.808953i \(0.299965\pi\)
\(702\) −3.14152 −0.118569
\(703\) 49.6474 1.87249
\(704\) −77.1733 −2.90858
\(705\) −84.4528 −3.18068
\(706\) −7.54367 −0.283910
\(707\) 2.01376 0.0757351
\(708\) 1.32510 0.0498002
\(709\) −26.1278 −0.981251 −0.490625 0.871371i \(-0.663232\pi\)
−0.490625 + 0.871371i \(0.663232\pi\)
\(710\) 58.6945 2.20276
\(711\) 31.2749 1.17290
\(712\) 56.4737 2.11644
\(713\) −0.816760 −0.0305879
\(714\) 1.39995 0.0523916
\(715\) −0.547112 −0.0204608
\(716\) 61.4616 2.29693
\(717\) −25.7704 −0.962414
\(718\) −30.9029 −1.15329
\(719\) −46.0980 −1.71916 −0.859582 0.510997i \(-0.829276\pi\)
−0.859582 + 0.510997i \(0.829276\pi\)
\(720\) 257.783 9.60701
\(721\) 1.30568 0.0486259
\(722\) −33.5928 −1.25019
\(723\) −93.0020 −3.45878
\(724\) −30.8438 −1.14630
\(725\) −4.71353 −0.175056
\(726\) −7.68398 −0.285179
\(727\) −13.2838 −0.492670 −0.246335 0.969185i \(-0.579226\pi\)
−0.246335 + 0.969185i \(0.579226\pi\)
\(728\) 0.160009 0.00593034
\(729\) 100.212 3.71154
\(730\) 65.5601 2.42649
\(731\) 0.475762 0.0175967
\(732\) 149.067 5.50969
\(733\) 28.9552 1.06949 0.534743 0.845015i \(-0.320408\pi\)
0.534743 + 0.845015i \(0.320408\pi\)
\(734\) 3.35187 0.123720
\(735\) −54.9009 −2.02505
\(736\) −1.35137 −0.0498122
\(737\) −19.2496 −0.709069
\(738\) 20.8097 0.766016
\(739\) 27.6806 1.01825 0.509124 0.860693i \(-0.329969\pi\)
0.509124 + 0.860693i \(0.329969\pi\)
\(740\) 110.656 4.06781
\(741\) 1.25846 0.0462306
\(742\) 7.41049 0.272048
\(743\) 18.1835 0.667090 0.333545 0.942734i \(-0.391755\pi\)
0.333545 + 0.942734i \(0.391755\pi\)
\(744\) 324.464 11.8954
\(745\) 29.3980 1.07706
\(746\) 44.5221 1.63007
\(747\) −33.1917 −1.21442
\(748\) −10.4394 −0.381703
\(749\) 2.15379 0.0786979
\(750\) 93.7822 3.42444
\(751\) −25.4018 −0.926926 −0.463463 0.886116i \(-0.653393\pi\)
−0.463463 + 0.886116i \(0.653393\pi\)
\(752\) −141.559 −5.16214
\(753\) −49.1491 −1.79109
\(754\) 1.39080 0.0506499
\(755\) −45.8873 −1.67001
\(756\) −24.7276 −0.899336
\(757\) −16.8536 −0.612554 −0.306277 0.951942i \(-0.599083\pi\)
−0.306277 + 0.951942i \(0.599083\pi\)
\(758\) −37.0450 −1.34553
\(759\) −0.856950 −0.0311053
\(760\) −117.420 −4.25926
\(761\) 35.4748 1.28596 0.642980 0.765883i \(-0.277698\pi\)
0.642980 + 0.765883i \(0.277698\pi\)
\(762\) −29.4189 −1.06573
\(763\) −1.63500 −0.0591909
\(764\) −15.0673 −0.545116
\(765\) 11.1528 0.403230
\(766\) −42.2480 −1.52648
\(767\) 0.00503617 0.000181845 0
\(768\) 67.9107 2.45052
\(769\) −21.3691 −0.770589 −0.385294 0.922794i \(-0.625900\pi\)
−0.385294 + 0.922794i \(0.625900\pi\)
\(770\) −5.93889 −0.214023
\(771\) 62.3428 2.24522
\(772\) 91.6675 3.29918
\(773\) 33.7070 1.21236 0.606179 0.795328i \(-0.292702\pi\)
0.606179 + 0.795328i \(0.292702\pi\)
\(774\) −18.2876 −0.657334
\(775\) −6.73069 −0.241773
\(776\) −66.4875 −2.38676
\(777\) −7.99364 −0.286770
\(778\) −55.2913 −1.98229
\(779\) −5.28270 −0.189272
\(780\) 2.80490 0.100432
\(781\) 31.6178 1.13137
\(782\) −0.115365 −0.00412545
\(783\) −133.458 −4.76939
\(784\) −92.0246 −3.28659
\(785\) −15.3227 −0.546890
\(786\) −181.597 −6.47734
\(787\) 37.8925 1.35072 0.675360 0.737488i \(-0.263988\pi\)
0.675360 + 0.737488i \(0.263988\pi\)
\(788\) −41.5498 −1.48015
\(789\) −7.03326 −0.250391
\(790\) −24.4035 −0.868237
\(791\) −2.99058 −0.106333
\(792\) 249.164 8.85366
\(793\) 0.566546 0.0201186
\(794\) 52.9180 1.87799
\(795\) 80.6605 2.86073
\(796\) −117.602 −4.16831
\(797\) −40.7165 −1.44225 −0.721127 0.692803i \(-0.756375\pi\)
−0.721127 + 0.692803i \(0.756375\pi\)
\(798\) 13.6605 0.483578
\(799\) −6.12445 −0.216668
\(800\) −11.1363 −0.393727
\(801\) −52.3413 −1.84939
\(802\) 15.0808 0.532521
\(803\) 35.3162 1.24628
\(804\) 98.6880 3.48046
\(805\) −0.0475901 −0.00167733
\(806\) 1.98599 0.0699536
\(807\) 49.3743 1.73806
\(808\) 65.9239 2.31919
\(809\) −32.4835 −1.14206 −0.571030 0.820929i \(-0.693456\pi\)
−0.571030 + 0.820929i \(0.693456\pi\)
\(810\) −214.153 −7.52456
\(811\) 22.7836 0.800041 0.400021 0.916506i \(-0.369003\pi\)
0.400021 + 0.916506i \(0.369003\pi\)
\(812\) 10.9473 0.384175
\(813\) −17.5040 −0.613892
\(814\) 82.2047 2.88127
\(815\) 27.1970 0.952668
\(816\) 25.5417 0.894139
\(817\) 4.64244 0.162418
\(818\) −9.23708 −0.322967
\(819\) −0.148301 −0.00518205
\(820\) −11.7743 −0.411176
\(821\) 10.5774 0.369154 0.184577 0.982818i \(-0.440909\pi\)
0.184577 + 0.982818i \(0.440909\pi\)
\(822\) −66.9249 −2.33427
\(823\) −49.0401 −1.70943 −0.854715 0.519098i \(-0.826268\pi\)
−0.854715 + 0.519098i \(0.826268\pi\)
\(824\) 42.7436 1.48904
\(825\) −7.06188 −0.245863
\(826\) 0.0546675 0.00190213
\(827\) −49.1811 −1.71019 −0.855096 0.518469i \(-0.826502\pi\)
−0.855096 + 0.518469i \(0.826502\pi\)
\(828\) 3.21555 0.111748
\(829\) −0.279492 −0.00970717 −0.00485359 0.999988i \(-0.501545\pi\)
−0.00485359 + 0.999988i \(0.501545\pi\)
\(830\) 25.8991 0.898971
\(831\) 74.0262 2.56794
\(832\) 1.50370 0.0521315
\(833\) −3.98137 −0.137946
\(834\) −20.6555 −0.715240
\(835\) 19.6978 0.681672
\(836\) −101.867 −3.52314
\(837\) −190.571 −6.58710
\(838\) 19.2510 0.665016
\(839\) −13.5763 −0.468707 −0.234353 0.972151i \(-0.575297\pi\)
−0.234353 + 0.972151i \(0.575297\pi\)
\(840\) 18.9055 0.652303
\(841\) 30.0837 1.03737
\(842\) 11.4493 0.394568
\(843\) 15.6670 0.539600
\(844\) 58.2565 2.00527
\(845\) −30.7892 −1.05918
\(846\) 235.415 8.09373
\(847\) −0.229870 −0.00789842
\(848\) 135.203 4.64288
\(849\) −52.9466 −1.81712
\(850\) −0.950692 −0.0326084
\(851\) 0.658731 0.0225810
\(852\) −162.096 −5.55333
\(853\) 43.3481 1.48421 0.742105 0.670284i \(-0.233828\pi\)
0.742105 + 0.670284i \(0.233828\pi\)
\(854\) 6.14985 0.210443
\(855\) 108.828 3.72183
\(856\) 70.5083 2.40992
\(857\) −40.2106 −1.37357 −0.686783 0.726862i \(-0.740978\pi\)
−0.686783 + 0.726862i \(0.740978\pi\)
\(858\) 2.08372 0.0711369
\(859\) 45.8000 1.56268 0.781338 0.624108i \(-0.214537\pi\)
0.781338 + 0.624108i \(0.214537\pi\)
\(860\) 10.3473 0.352839
\(861\) 0.850557 0.0289869
\(862\) 40.1911 1.36891
\(863\) 17.8762 0.608512 0.304256 0.952590i \(-0.401592\pi\)
0.304256 + 0.952590i \(0.401592\pi\)
\(864\) −315.310 −10.7271
\(865\) −7.61980 −0.259081
\(866\) −99.0816 −3.36693
\(867\) −55.7631 −1.89381
\(868\) 15.6322 0.530592
\(869\) −13.1458 −0.445940
\(870\) 164.327 5.57119
\(871\) 0.375074 0.0127089
\(872\) −53.5246 −1.81257
\(873\) 61.6224 2.08560
\(874\) −1.12572 −0.0380781
\(875\) 2.80554 0.0948444
\(876\) −181.057 −6.11735
\(877\) 17.8965 0.604323 0.302162 0.953257i \(-0.402292\pi\)
0.302162 + 0.953257i \(0.402292\pi\)
\(878\) 94.1441 3.17721
\(879\) 64.3072 2.16903
\(880\) −108.354 −3.65261
\(881\) −55.9274 −1.88424 −0.942121 0.335273i \(-0.891171\pi\)
−0.942121 + 0.335273i \(0.891171\pi\)
\(882\) 153.038 5.15306
\(883\) −18.9197 −0.636699 −0.318349 0.947973i \(-0.603128\pi\)
−0.318349 + 0.947973i \(0.603128\pi\)
\(884\) 0.203409 0.00684140
\(885\) 0.595037 0.0200019
\(886\) 25.5314 0.857745
\(887\) −49.9115 −1.67586 −0.837932 0.545775i \(-0.816235\pi\)
−0.837932 + 0.545775i \(0.816235\pi\)
\(888\) −261.686 −8.78161
\(889\) −0.880079 −0.0295169
\(890\) 40.8414 1.36901
\(891\) −115.361 −3.86473
\(892\) −109.947 −3.68130
\(893\) −59.7618 −1.99985
\(894\) −111.965 −3.74465
\(895\) 27.5994 0.922547
\(896\) 6.51825 0.217760
\(897\) 0.0166974 0.000557511 0
\(898\) 25.8184 0.861570
\(899\) 84.3686 2.81385
\(900\) 26.4984 0.883280
\(901\) 5.84944 0.194873
\(902\) −8.74693 −0.291241
\(903\) −0.747471 −0.0248743
\(904\) −97.9021 −3.25618
\(905\) −13.8505 −0.460405
\(906\) 174.765 5.80618
\(907\) 46.5770 1.54656 0.773281 0.634063i \(-0.218614\pi\)
0.773281 + 0.634063i \(0.218614\pi\)
\(908\) −18.2346 −0.605136
\(909\) −61.1000 −2.02656
\(910\) 0.115718 0.00383600
\(911\) 18.8115 0.623252 0.311626 0.950205i \(-0.399126\pi\)
0.311626 + 0.950205i \(0.399126\pi\)
\(912\) 249.234 8.25295
\(913\) 13.9514 0.461725
\(914\) −75.6846 −2.50343
\(915\) 66.9389 2.21293
\(916\) −40.4568 −1.33673
\(917\) −5.43255 −0.179398
\(918\) −26.9176 −0.888415
\(919\) −43.3197 −1.42898 −0.714492 0.699644i \(-0.753342\pi\)
−0.714492 + 0.699644i \(0.753342\pi\)
\(920\) −1.55795 −0.0513640
\(921\) −19.1317 −0.630410
\(922\) 27.7030 0.912349
\(923\) −0.616064 −0.0202780
\(924\) 16.4014 0.539567
\(925\) 5.42842 0.178485
\(926\) 9.17494 0.301507
\(927\) −39.6159 −1.30116
\(928\) 139.592 4.58234
\(929\) 33.0870 1.08555 0.542775 0.839878i \(-0.317374\pi\)
0.542775 + 0.839878i \(0.317374\pi\)
\(930\) 234.650 7.69449
\(931\) −38.8498 −1.27325
\(932\) 11.0275 0.361217
\(933\) −4.88751 −0.160010
\(934\) −0.557130 −0.0182298
\(935\) −4.68784 −0.153309
\(936\) −4.85490 −0.158687
\(937\) 56.3809 1.84188 0.920941 0.389702i \(-0.127422\pi\)
0.920941 + 0.389702i \(0.127422\pi\)
\(938\) 4.07142 0.132937
\(939\) −81.3575 −2.65500
\(940\) −133.200 −4.34449
\(941\) 34.4900 1.12434 0.562170 0.827022i \(-0.309967\pi\)
0.562170 + 0.827022i \(0.309967\pi\)
\(942\) 58.3576 1.90139
\(943\) −0.0700918 −0.00228250
\(944\) 0.997397 0.0324625
\(945\) −11.1040 −0.361213
\(946\) 7.68682 0.249920
\(947\) −17.2579 −0.560807 −0.280403 0.959882i \(-0.590468\pi\)
−0.280403 + 0.959882i \(0.590468\pi\)
\(948\) 67.3950 2.18889
\(949\) −0.688126 −0.0223375
\(950\) −9.27675 −0.300978
\(951\) 54.3603 1.76275
\(952\) 1.37102 0.0444349
\(953\) −15.2486 −0.493950 −0.246975 0.969022i \(-0.579437\pi\)
−0.246975 + 0.969022i \(0.579437\pi\)
\(954\) −224.844 −7.27959
\(955\) −6.76600 −0.218943
\(956\) −40.6453 −1.31456
\(957\) 88.5201 2.86145
\(958\) −49.2101 −1.58991
\(959\) −2.00209 −0.0646508
\(960\) 177.666 5.73416
\(961\) 89.4743 2.88627
\(962\) −1.60174 −0.0516421
\(963\) −65.3490 −2.10584
\(964\) −146.684 −4.72436
\(965\) 41.1634 1.32510
\(966\) 0.181250 0.00583164
\(967\) −46.6263 −1.49940 −0.749701 0.661777i \(-0.769802\pi\)
−0.749701 + 0.661777i \(0.769802\pi\)
\(968\) −7.52519 −0.241869
\(969\) 10.7829 0.346396
\(970\) −48.0833 −1.54386
\(971\) 31.2297 1.00221 0.501105 0.865387i \(-0.332927\pi\)
0.501105 + 0.865387i \(0.332927\pi\)
\(972\) 316.610 10.1553
\(973\) −0.617917 −0.0198095
\(974\) −59.1608 −1.89563
\(975\) 0.137599 0.00440669
\(976\) 112.203 3.59152
\(977\) 16.3462 0.522961 0.261480 0.965209i \(-0.415789\pi\)
0.261480 + 0.965209i \(0.415789\pi\)
\(978\) −103.582 −3.31218
\(979\) 22.0006 0.703142
\(980\) −86.5902 −2.76602
\(981\) 49.6080 1.58386
\(982\) 46.2426 1.47566
\(983\) −1.84855 −0.0589597 −0.0294798 0.999565i \(-0.509385\pi\)
−0.0294798 + 0.999565i \(0.509385\pi\)
\(984\) 27.8445 0.887651
\(985\) −18.6580 −0.594494
\(986\) 11.9168 0.379510
\(987\) 9.62214 0.306276
\(988\) 1.98485 0.0631465
\(989\) 0.0615968 0.00195866
\(990\) 180.194 5.72693
\(991\) −39.5986 −1.25789 −0.628946 0.777449i \(-0.716513\pi\)
−0.628946 + 0.777449i \(0.716513\pi\)
\(992\) 199.331 6.32877
\(993\) 48.2221 1.53028
\(994\) −6.68736 −0.212110
\(995\) −52.8096 −1.67418
\(996\) −71.5255 −2.26637
\(997\) 13.1127 0.415283 0.207642 0.978205i \(-0.433421\pi\)
0.207642 + 0.978205i \(0.433421\pi\)
\(998\) −24.1223 −0.763578
\(999\) 153.699 4.86282
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 503.2.a.f.1.2 26
3.2 odd 2 4527.2.a.o.1.25 26
4.3 odd 2 8048.2.a.u.1.1 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
503.2.a.f.1.2 26 1.1 even 1 trivial
4527.2.a.o.1.25 26 3.2 odd 2
8048.2.a.u.1.1 26 4.3 odd 2