Properties

Label 4001.2.a.b.1.145
Level $4001$
Weight $2$
Character 4001.1
Self dual yes
Analytic conductor $31.948$
Analytic rank $0$
Dimension $184$
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] = [4001,2,Mod(1,4001)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4001, 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("4001.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4001 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4001.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: \(31.9481458487\)
Analytic rank: \(0\)
Dimension: \(184\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.145
Character \(\chi\) \(=\) 4001.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.92587 q^{2} +1.55925 q^{3} +1.70899 q^{4} -3.80552 q^{5} +3.00291 q^{6} -0.241535 q^{7} -0.560450 q^{8} -0.568752 q^{9} +O(q^{10})\) \(q+1.92587 q^{2} +1.55925 q^{3} +1.70899 q^{4} -3.80552 q^{5} +3.00291 q^{6} -0.241535 q^{7} -0.560450 q^{8} -0.568752 q^{9} -7.32895 q^{10} +4.51627 q^{11} +2.66473 q^{12} -2.64004 q^{13} -0.465165 q^{14} -5.93374 q^{15} -4.49733 q^{16} -0.0403322 q^{17} -1.09535 q^{18} +7.82018 q^{19} -6.50359 q^{20} -0.376612 q^{21} +8.69777 q^{22} +9.16320 q^{23} -0.873880 q^{24} +9.48199 q^{25} -5.08438 q^{26} -5.56456 q^{27} -0.412780 q^{28} +4.49399 q^{29} -11.4276 q^{30} +7.37396 q^{31} -7.54040 q^{32} +7.04198 q^{33} -0.0776747 q^{34} +0.919165 q^{35} -0.971992 q^{36} +4.70117 q^{37} +15.0607 q^{38} -4.11647 q^{39} +2.13281 q^{40} +0.360772 q^{41} -0.725306 q^{42} -8.36820 q^{43} +7.71826 q^{44} +2.16440 q^{45} +17.6472 q^{46} +9.02076 q^{47} -7.01245 q^{48} -6.94166 q^{49} +18.2611 q^{50} -0.0628878 q^{51} -4.51179 q^{52} -10.8528 q^{53} -10.7166 q^{54} -17.1868 q^{55} +0.135368 q^{56} +12.1936 q^{57} +8.65485 q^{58} -2.84122 q^{59} -10.1407 q^{60} -13.0672 q^{61} +14.2013 q^{62} +0.137373 q^{63} -5.52718 q^{64} +10.0467 q^{65} +13.5620 q^{66} +4.86140 q^{67} -0.0689273 q^{68} +14.2877 q^{69} +1.77019 q^{70} +13.0255 q^{71} +0.318758 q^{72} +13.0676 q^{73} +9.05385 q^{74} +14.7847 q^{75} +13.3646 q^{76} -1.09084 q^{77} -7.92780 q^{78} +17.0816 q^{79} +17.1147 q^{80} -6.97026 q^{81} +0.694801 q^{82} +2.70398 q^{83} -0.643625 q^{84} +0.153485 q^{85} -16.1161 q^{86} +7.00723 q^{87} -2.53115 q^{88} +17.9898 q^{89} +4.16836 q^{90} +0.637660 q^{91} +15.6598 q^{92} +11.4978 q^{93} +17.3728 q^{94} -29.7598 q^{95} -11.7573 q^{96} -10.9780 q^{97} -13.3688 q^{98} -2.56864 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9} + 46 q^{10} + 25 q^{11} + 61 q^{12} + 52 q^{13} + 28 q^{14} + 59 q^{15} + 279 q^{16} + 16 q^{17} - 2 q^{18} + 86 q^{19} + 26 q^{20} + 22 q^{21} + 54 q^{22} + 55 q^{23} + 72 q^{24} + 241 q^{25} + 32 q^{26} + 97 q^{27} + 75 q^{28} + 27 q^{29} - 10 q^{30} + 276 q^{31} + 20 q^{33} + 122 q^{34} + 30 q^{35} + 278 q^{36} + 42 q^{37} + 14 q^{38} + 113 q^{39} + 115 q^{40} + 39 q^{41} + 15 q^{42} + 65 q^{43} + 32 q^{44} + 54 q^{45} + 65 q^{46} + 82 q^{47} + 117 q^{48} + 297 q^{49} + 4 q^{50} + 45 q^{51} + 136 q^{52} + 21 q^{53} + 93 q^{54} + 252 q^{55} + 74 q^{56} + 14 q^{57} + 54 q^{58} + 95 q^{59} + 58 q^{60} + 131 q^{61} + 14 q^{62} + 88 q^{63} + 368 q^{64} - 9 q^{65} + 52 q^{66} + 90 q^{67} + 27 q^{68} + 101 q^{69} + 18 q^{70} + 117 q^{71} - 15 q^{72} + 72 q^{73} + 7 q^{74} + 150 q^{75} + 148 q^{76} + 7 q^{77} + 22 q^{78} + 287 q^{79} + 43 q^{80} + 244 q^{81} + 86 q^{82} + 25 q^{83} + 14 q^{84} + 41 q^{85} + 25 q^{86} + 82 q^{87} + 115 q^{88} + 48 q^{89} + 78 q^{90} + 272 q^{91} + 69 q^{92} + 44 q^{93} + 161 q^{94} + 37 q^{95} + 129 q^{96} + 106 q^{97} - 46 q^{98} + 53 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.92587 1.36180 0.680899 0.732377i \(-0.261589\pi\)
0.680899 + 0.732377i \(0.261589\pi\)
\(3\) 1.55925 0.900231 0.450115 0.892970i \(-0.351383\pi\)
0.450115 + 0.892970i \(0.351383\pi\)
\(4\) 1.70899 0.854494
\(5\) −3.80552 −1.70188 −0.850940 0.525263i \(-0.823967\pi\)
−0.850940 + 0.525263i \(0.823967\pi\)
\(6\) 3.00291 1.22593
\(7\) −0.241535 −0.0912915 −0.0456457 0.998958i \(-0.514535\pi\)
−0.0456457 + 0.998958i \(0.514535\pi\)
\(8\) −0.560450 −0.198149
\(9\) −0.568752 −0.189584
\(10\) −7.32895 −2.31762
\(11\) 4.51627 1.36171 0.680853 0.732420i \(-0.261609\pi\)
0.680853 + 0.732420i \(0.261609\pi\)
\(12\) 2.66473 0.769242
\(13\) −2.64004 −0.732215 −0.366107 0.930573i \(-0.619310\pi\)
−0.366107 + 0.930573i \(0.619310\pi\)
\(14\) −0.465165 −0.124321
\(15\) −5.93374 −1.53209
\(16\) −4.49733 −1.12433
\(17\) −0.0403322 −0.00978199 −0.00489100 0.999988i \(-0.501557\pi\)
−0.00489100 + 0.999988i \(0.501557\pi\)
\(18\) −1.09535 −0.258175
\(19\) 7.82018 1.79407 0.897036 0.441958i \(-0.145716\pi\)
0.897036 + 0.441958i \(0.145716\pi\)
\(20\) −6.50359 −1.45425
\(21\) −0.376612 −0.0821834
\(22\) 8.69777 1.85437
\(23\) 9.16320 1.91066 0.955330 0.295542i \(-0.0955003\pi\)
0.955330 + 0.295542i \(0.0955003\pi\)
\(24\) −0.873880 −0.178380
\(25\) 9.48199 1.89640
\(26\) −5.08438 −0.997129
\(27\) −5.56456 −1.07090
\(28\) −0.412780 −0.0780081
\(29\) 4.49399 0.834512 0.417256 0.908789i \(-0.362992\pi\)
0.417256 + 0.908789i \(0.362992\pi\)
\(30\) −11.4276 −2.08639
\(31\) 7.37396 1.32440 0.662201 0.749326i \(-0.269622\pi\)
0.662201 + 0.749326i \(0.269622\pi\)
\(32\) −7.54040 −1.33297
\(33\) 7.04198 1.22585
\(34\) −0.0776747 −0.0133211
\(35\) 0.919165 0.155367
\(36\) −0.971992 −0.161999
\(37\) 4.70117 0.772867 0.386433 0.922317i \(-0.373707\pi\)
0.386433 + 0.922317i \(0.373707\pi\)
\(38\) 15.0607 2.44316
\(39\) −4.11647 −0.659162
\(40\) 2.13281 0.337226
\(41\) 0.360772 0.0563431 0.0281716 0.999603i \(-0.491032\pi\)
0.0281716 + 0.999603i \(0.491032\pi\)
\(42\) −0.725306 −0.111917
\(43\) −8.36820 −1.27614 −0.638069 0.769979i \(-0.720267\pi\)
−0.638069 + 0.769979i \(0.720267\pi\)
\(44\) 7.71826 1.16357
\(45\) 2.16440 0.322650
\(46\) 17.6472 2.60193
\(47\) 9.02076 1.31581 0.657906 0.753100i \(-0.271442\pi\)
0.657906 + 0.753100i \(0.271442\pi\)
\(48\) −7.01245 −1.01216
\(49\) −6.94166 −0.991666
\(50\) 18.2611 2.58251
\(51\) −0.0628878 −0.00880605
\(52\) −4.51179 −0.625673
\(53\) −10.8528 −1.49074 −0.745372 0.666649i \(-0.767728\pi\)
−0.745372 + 0.666649i \(0.767728\pi\)
\(54\) −10.7166 −1.45835
\(55\) −17.1868 −2.31746
\(56\) 0.135368 0.0180893
\(57\) 12.1936 1.61508
\(58\) 8.65485 1.13644
\(59\) −2.84122 −0.369895 −0.184948 0.982748i \(-0.559212\pi\)
−0.184948 + 0.982748i \(0.559212\pi\)
\(60\) −10.1407 −1.30916
\(61\) −13.0672 −1.67308 −0.836540 0.547906i \(-0.815425\pi\)
−0.836540 + 0.547906i \(0.815425\pi\)
\(62\) 14.2013 1.80357
\(63\) 0.137373 0.0173074
\(64\) −5.52718 −0.690898
\(65\) 10.0467 1.24614
\(66\) 13.5620 1.66936
\(67\) 4.86140 0.593914 0.296957 0.954891i \(-0.404028\pi\)
0.296957 + 0.954891i \(0.404028\pi\)
\(68\) −0.0689273 −0.00835866
\(69\) 14.2877 1.72003
\(70\) 1.77019 0.211579
\(71\) 13.0255 1.54584 0.772922 0.634501i \(-0.218794\pi\)
0.772922 + 0.634501i \(0.218794\pi\)
\(72\) 0.318758 0.0375659
\(73\) 13.0676 1.52945 0.764725 0.644357i \(-0.222875\pi\)
0.764725 + 0.644357i \(0.222875\pi\)
\(74\) 9.05385 1.05249
\(75\) 14.7847 1.70720
\(76\) 13.3646 1.53302
\(77\) −1.09084 −0.124312
\(78\) −7.92780 −0.897646
\(79\) 17.0816 1.92184 0.960918 0.276834i \(-0.0892852\pi\)
0.960918 + 0.276834i \(0.0892852\pi\)
\(80\) 17.1147 1.91348
\(81\) −6.97026 −0.774474
\(82\) 0.694801 0.0767280
\(83\) 2.70398 0.296801 0.148400 0.988927i \(-0.452588\pi\)
0.148400 + 0.988927i \(0.452588\pi\)
\(84\) −0.643625 −0.0702253
\(85\) 0.153485 0.0166478
\(86\) −16.1161 −1.73784
\(87\) 7.00723 0.751254
\(88\) −2.53115 −0.269821
\(89\) 17.9898 1.90692 0.953459 0.301522i \(-0.0974946\pi\)
0.953459 + 0.301522i \(0.0974946\pi\)
\(90\) 4.16836 0.439384
\(91\) 0.637660 0.0668450
\(92\) 15.6598 1.63265
\(93\) 11.4978 1.19227
\(94\) 17.3728 1.79187
\(95\) −29.7598 −3.05330
\(96\) −11.7573 −1.19998
\(97\) −10.9780 −1.11465 −0.557325 0.830295i \(-0.688172\pi\)
−0.557325 + 0.830295i \(0.688172\pi\)
\(98\) −13.3688 −1.35045
\(99\) −2.56864 −0.258158
\(100\) 16.2046 1.62046
\(101\) 10.4638 1.04119 0.520593 0.853805i \(-0.325711\pi\)
0.520593 + 0.853805i \(0.325711\pi\)
\(102\) −0.121114 −0.0119921
\(103\) 16.5376 1.62950 0.814749 0.579814i \(-0.196875\pi\)
0.814749 + 0.579814i \(0.196875\pi\)
\(104\) 1.47961 0.145088
\(105\) 1.43320 0.139866
\(106\) −20.9011 −2.03009
\(107\) −0.407451 −0.0393897 −0.0196949 0.999806i \(-0.506269\pi\)
−0.0196949 + 0.999806i \(0.506269\pi\)
\(108\) −9.50978 −0.915079
\(109\) 2.61906 0.250860 0.125430 0.992102i \(-0.459969\pi\)
0.125430 + 0.992102i \(0.459969\pi\)
\(110\) −33.0995 −3.15592
\(111\) 7.33027 0.695759
\(112\) 1.08626 0.102642
\(113\) −19.9364 −1.87546 −0.937729 0.347367i \(-0.887076\pi\)
−0.937729 + 0.347367i \(0.887076\pi\)
\(114\) 23.4833 2.19941
\(115\) −34.8707 −3.25171
\(116\) 7.68017 0.713086
\(117\) 1.50153 0.138816
\(118\) −5.47183 −0.503723
\(119\) 0.00974161 0.000893012 0
\(120\) 3.32557 0.303581
\(121\) 9.39670 0.854245
\(122\) −25.1657 −2.27840
\(123\) 0.562532 0.0507218
\(124\) 12.6020 1.13169
\(125\) −17.0563 −1.52556
\(126\) 0.264564 0.0235692
\(127\) 2.61364 0.231923 0.115961 0.993254i \(-0.463005\pi\)
0.115961 + 0.993254i \(0.463005\pi\)
\(128\) 4.43614 0.392103
\(129\) −13.0481 −1.14882
\(130\) 19.3487 1.69699
\(131\) 3.31099 0.289282 0.144641 0.989484i \(-0.453797\pi\)
0.144641 + 0.989484i \(0.453797\pi\)
\(132\) 12.0347 1.04748
\(133\) −1.88884 −0.163783
\(134\) 9.36244 0.808792
\(135\) 21.1761 1.82254
\(136\) 0.0226042 0.00193829
\(137\) 1.88103 0.160707 0.0803537 0.996766i \(-0.474395\pi\)
0.0803537 + 0.996766i \(0.474395\pi\)
\(138\) 27.5163 2.34234
\(139\) 1.86057 0.157811 0.0789057 0.996882i \(-0.474857\pi\)
0.0789057 + 0.996882i \(0.474857\pi\)
\(140\) 1.57084 0.132760
\(141\) 14.0656 1.18454
\(142\) 25.0855 2.10513
\(143\) −11.9231 −0.997062
\(144\) 2.55787 0.213156
\(145\) −17.1020 −1.42024
\(146\) 25.1666 2.08280
\(147\) −10.8238 −0.892728
\(148\) 8.03424 0.660410
\(149\) −12.7440 −1.04403 −0.522015 0.852936i \(-0.674819\pi\)
−0.522015 + 0.852936i \(0.674819\pi\)
\(150\) 28.4736 2.32486
\(151\) −6.49721 −0.528736 −0.264368 0.964422i \(-0.585163\pi\)
−0.264368 + 0.964422i \(0.585163\pi\)
\(152\) −4.38282 −0.355494
\(153\) 0.0229390 0.00185451
\(154\) −2.10081 −0.169288
\(155\) −28.0618 −2.25398
\(156\) −7.03500 −0.563251
\(157\) 17.2640 1.37782 0.688908 0.724849i \(-0.258090\pi\)
0.688908 + 0.724849i \(0.258090\pi\)
\(158\) 32.8971 2.61715
\(159\) −16.9222 −1.34201
\(160\) 28.6951 2.26855
\(161\) −2.21323 −0.174427
\(162\) −13.4238 −1.05468
\(163\) 4.02890 0.315568 0.157784 0.987474i \(-0.449565\pi\)
0.157784 + 0.987474i \(0.449565\pi\)
\(164\) 0.616556 0.0481449
\(165\) −26.7984 −2.08625
\(166\) 5.20753 0.404183
\(167\) 8.20389 0.634836 0.317418 0.948286i \(-0.397184\pi\)
0.317418 + 0.948286i \(0.397184\pi\)
\(168\) 0.211072 0.0162846
\(169\) −6.03020 −0.463862
\(170\) 0.295593 0.0226709
\(171\) −4.44775 −0.340128
\(172\) −14.3012 −1.09045
\(173\) −1.73616 −0.131998 −0.0659989 0.997820i \(-0.521023\pi\)
−0.0659989 + 0.997820i \(0.521023\pi\)
\(174\) 13.4950 1.02306
\(175\) −2.29023 −0.173125
\(176\) −20.3112 −1.53101
\(177\) −4.43016 −0.332991
\(178\) 34.6461 2.59684
\(179\) −21.9604 −1.64140 −0.820700 0.571360i \(-0.806416\pi\)
−0.820700 + 0.571360i \(0.806416\pi\)
\(180\) 3.69893 0.275702
\(181\) −11.8627 −0.881750 −0.440875 0.897569i \(-0.645332\pi\)
−0.440875 + 0.897569i \(0.645332\pi\)
\(182\) 1.22805 0.0910293
\(183\) −20.3749 −1.50616
\(184\) −5.13552 −0.378596
\(185\) −17.8904 −1.31533
\(186\) 22.1433 1.62363
\(187\) −0.182151 −0.0133202
\(188\) 15.4164 1.12435
\(189\) 1.34403 0.0977641
\(190\) −57.3137 −4.15797
\(191\) −12.0032 −0.868521 −0.434261 0.900787i \(-0.642990\pi\)
−0.434261 + 0.900787i \(0.642990\pi\)
\(192\) −8.61823 −0.621968
\(193\) −8.16426 −0.587677 −0.293838 0.955855i \(-0.594933\pi\)
−0.293838 + 0.955855i \(0.594933\pi\)
\(194\) −21.1423 −1.51793
\(195\) 15.6653 1.12182
\(196\) −11.8632 −0.847373
\(197\) −11.6872 −0.832679 −0.416339 0.909209i \(-0.636687\pi\)
−0.416339 + 0.909209i \(0.636687\pi\)
\(198\) −4.94688 −0.351559
\(199\) 10.1338 0.718364 0.359182 0.933268i \(-0.383056\pi\)
0.359182 + 0.933268i \(0.383056\pi\)
\(200\) −5.31418 −0.375770
\(201\) 7.58012 0.534660
\(202\) 20.1519 1.41788
\(203\) −1.08545 −0.0761839
\(204\) −0.107475 −0.00752472
\(205\) −1.37293 −0.0958893
\(206\) 31.8493 2.21905
\(207\) −5.21159 −0.362231
\(208\) 11.8731 0.823254
\(209\) 35.3180 2.44300
\(210\) 2.76017 0.190470
\(211\) −19.8357 −1.36555 −0.682774 0.730629i \(-0.739227\pi\)
−0.682774 + 0.730629i \(0.739227\pi\)
\(212\) −18.5473 −1.27383
\(213\) 20.3100 1.39162
\(214\) −0.784699 −0.0536409
\(215\) 31.8454 2.17184
\(216\) 3.11866 0.212198
\(217\) −1.78107 −0.120907
\(218\) 5.04397 0.341621
\(219\) 20.3756 1.37686
\(220\) −29.3720 −1.98026
\(221\) 0.106478 0.00716252
\(222\) 14.1172 0.947483
\(223\) −17.8267 −1.19377 −0.596883 0.802328i \(-0.703594\pi\)
−0.596883 + 0.802328i \(0.703594\pi\)
\(224\) 1.82127 0.121688
\(225\) −5.39290 −0.359527
\(226\) −38.3950 −2.55400
\(227\) −21.2212 −1.40850 −0.704252 0.709950i \(-0.748717\pi\)
−0.704252 + 0.709950i \(0.748717\pi\)
\(228\) 20.8387 1.38008
\(229\) −2.74103 −0.181132 −0.0905660 0.995890i \(-0.528868\pi\)
−0.0905660 + 0.995890i \(0.528868\pi\)
\(230\) −67.1566 −4.42818
\(231\) −1.70088 −0.111910
\(232\) −2.51866 −0.165358
\(233\) −5.03032 −0.329547 −0.164773 0.986331i \(-0.552689\pi\)
−0.164773 + 0.986331i \(0.552689\pi\)
\(234\) 2.89175 0.189040
\(235\) −34.3287 −2.23936
\(236\) −4.85561 −0.316073
\(237\) 26.6345 1.73010
\(238\) 0.0187611 0.00121610
\(239\) 1.48484 0.0960464 0.0480232 0.998846i \(-0.484708\pi\)
0.0480232 + 0.998846i \(0.484708\pi\)
\(240\) 26.6860 1.72258
\(241\) 9.91003 0.638361 0.319180 0.947694i \(-0.396592\pi\)
0.319180 + 0.947694i \(0.396592\pi\)
\(242\) 18.0969 1.16331
\(243\) 5.82533 0.373695
\(244\) −22.3317 −1.42964
\(245\) 26.4166 1.68770
\(246\) 1.08337 0.0690729
\(247\) −20.6456 −1.31365
\(248\) −4.13274 −0.262429
\(249\) 4.21618 0.267189
\(250\) −32.8483 −2.07751
\(251\) −15.4192 −0.973249 −0.486624 0.873611i \(-0.661772\pi\)
−0.486624 + 0.873611i \(0.661772\pi\)
\(252\) 0.234770 0.0147891
\(253\) 41.3835 2.60176
\(254\) 5.03353 0.315832
\(255\) 0.239321 0.0149868
\(256\) 19.5978 1.22486
\(257\) 21.1289 1.31799 0.658993 0.752149i \(-0.270983\pi\)
0.658993 + 0.752149i \(0.270983\pi\)
\(258\) −25.1290 −1.56446
\(259\) −1.13549 −0.0705562
\(260\) 17.1697 1.06482
\(261\) −2.55597 −0.158210
\(262\) 6.37654 0.393944
\(263\) −9.18975 −0.566664 −0.283332 0.959022i \(-0.591440\pi\)
−0.283332 + 0.959022i \(0.591440\pi\)
\(264\) −3.94668 −0.242901
\(265\) 41.3005 2.53707
\(266\) −3.63767 −0.223040
\(267\) 28.0506 1.71667
\(268\) 8.30808 0.507497
\(269\) −19.5231 −1.19034 −0.595171 0.803599i \(-0.702916\pi\)
−0.595171 + 0.803599i \(0.702916\pi\)
\(270\) 40.7824 2.48194
\(271\) 11.9398 0.725292 0.362646 0.931927i \(-0.381873\pi\)
0.362646 + 0.931927i \(0.381873\pi\)
\(272\) 0.181387 0.0109982
\(273\) 0.994269 0.0601759
\(274\) 3.62263 0.218851
\(275\) 42.8232 2.58234
\(276\) 24.4175 1.46976
\(277\) −15.0490 −0.904204 −0.452102 0.891966i \(-0.649326\pi\)
−0.452102 + 0.891966i \(0.649326\pi\)
\(278\) 3.58322 0.214907
\(279\) −4.19396 −0.251086
\(280\) −0.515146 −0.0307859
\(281\) 31.0218 1.85061 0.925303 0.379228i \(-0.123810\pi\)
0.925303 + 0.379228i \(0.123810\pi\)
\(282\) 27.0885 1.61310
\(283\) 4.60383 0.273669 0.136835 0.990594i \(-0.456307\pi\)
0.136835 + 0.990594i \(0.456307\pi\)
\(284\) 22.2605 1.32091
\(285\) −46.4029 −2.74867
\(286\) −22.9624 −1.35780
\(287\) −0.0871389 −0.00514365
\(288\) 4.28862 0.252709
\(289\) −16.9984 −0.999904
\(290\) −32.9362 −1.93408
\(291\) −17.1174 −1.00344
\(292\) 22.3324 1.30691
\(293\) 31.2883 1.82788 0.913940 0.405848i \(-0.133024\pi\)
0.913940 + 0.405848i \(0.133024\pi\)
\(294\) −20.8452 −1.21572
\(295\) 10.8123 0.629518
\(296\) −2.63477 −0.153143
\(297\) −25.1311 −1.45825
\(298\) −24.5433 −1.42176
\(299\) −24.1912 −1.39901
\(300\) 25.2670 1.45879
\(301\) 2.02121 0.116501
\(302\) −12.5128 −0.720031
\(303\) 16.3156 0.937307
\(304\) −35.1700 −2.01714
\(305\) 49.7274 2.84738
\(306\) 0.0441777 0.00252547
\(307\) 0.0701815 0.00400547 0.00200273 0.999998i \(-0.499363\pi\)
0.00200273 + 0.999998i \(0.499363\pi\)
\(308\) −1.86423 −0.106224
\(309\) 25.7862 1.46692
\(310\) −54.0434 −3.06946
\(311\) −20.7286 −1.17541 −0.587705 0.809075i \(-0.699968\pi\)
−0.587705 + 0.809075i \(0.699968\pi\)
\(312\) 2.30708 0.130612
\(313\) 6.24610 0.353051 0.176525 0.984296i \(-0.443514\pi\)
0.176525 + 0.984296i \(0.443514\pi\)
\(314\) 33.2483 1.87631
\(315\) −0.522777 −0.0294552
\(316\) 29.1923 1.64220
\(317\) 2.10936 0.118473 0.0592366 0.998244i \(-0.481133\pi\)
0.0592366 + 0.998244i \(0.481133\pi\)
\(318\) −32.5899 −1.82755
\(319\) 20.2961 1.13636
\(320\) 21.0338 1.17583
\(321\) −0.635316 −0.0354599
\(322\) −4.26240 −0.237534
\(323\) −0.315405 −0.0175496
\(324\) −11.9121 −0.661783
\(325\) −25.0328 −1.38857
\(326\) 7.75916 0.429740
\(327\) 4.08375 0.225832
\(328\) −0.202195 −0.0111643
\(329\) −2.17882 −0.120122
\(330\) −51.6103 −2.84105
\(331\) 20.8793 1.14763 0.573814 0.818986i \(-0.305463\pi\)
0.573814 + 0.818986i \(0.305463\pi\)
\(332\) 4.62108 0.253615
\(333\) −2.67380 −0.146523
\(334\) 15.7997 0.864519
\(335\) −18.5002 −1.01077
\(336\) 1.69375 0.0924016
\(337\) −15.8906 −0.865618 −0.432809 0.901486i \(-0.642478\pi\)
−0.432809 + 0.901486i \(0.642478\pi\)
\(338\) −11.6134 −0.631686
\(339\) −31.0857 −1.68835
\(340\) 0.262304 0.0142254
\(341\) 33.3028 1.80345
\(342\) −8.56579 −0.463185
\(343\) 3.36739 0.181822
\(344\) 4.68996 0.252866
\(345\) −54.3721 −2.92729
\(346\) −3.34363 −0.179754
\(347\) −2.36350 −0.126879 −0.0634397 0.997986i \(-0.520207\pi\)
−0.0634397 + 0.997986i \(0.520207\pi\)
\(348\) 11.9753 0.641942
\(349\) 1.27289 0.0681362 0.0340681 0.999420i \(-0.489154\pi\)
0.0340681 + 0.999420i \(0.489154\pi\)
\(350\) −4.41069 −0.235761
\(351\) 14.6907 0.784129
\(352\) −34.0545 −1.81511
\(353\) −17.5982 −0.936657 −0.468328 0.883554i \(-0.655144\pi\)
−0.468328 + 0.883554i \(0.655144\pi\)
\(354\) −8.53193 −0.453467
\(355\) −49.5688 −2.63084
\(356\) 30.7444 1.62945
\(357\) 0.0151896 0.000803917 0
\(358\) −42.2930 −2.23525
\(359\) 16.9880 0.896592 0.448296 0.893885i \(-0.352031\pi\)
0.448296 + 0.893885i \(0.352031\pi\)
\(360\) −1.21304 −0.0639327
\(361\) 42.1552 2.21869
\(362\) −22.8461 −1.20076
\(363\) 14.6518 0.769018
\(364\) 1.08975 0.0571186
\(365\) −49.7291 −2.60294
\(366\) −39.2395 −2.05108
\(367\) −5.49070 −0.286612 −0.143306 0.989678i \(-0.545773\pi\)
−0.143306 + 0.989678i \(0.545773\pi\)
\(368\) −41.2100 −2.14822
\(369\) −0.205190 −0.0106818
\(370\) −34.4546 −1.79121
\(371\) 2.62132 0.136092
\(372\) 19.6496 1.01879
\(373\) 17.0082 0.880652 0.440326 0.897838i \(-0.354863\pi\)
0.440326 + 0.897838i \(0.354863\pi\)
\(374\) −0.350800 −0.0181394
\(375\) −26.5949 −1.37336
\(376\) −5.05569 −0.260727
\(377\) −11.8643 −0.611042
\(378\) 2.58844 0.133135
\(379\) 1.87958 0.0965477 0.0482739 0.998834i \(-0.484628\pi\)
0.0482739 + 0.998834i \(0.484628\pi\)
\(380\) −50.8592 −2.60902
\(381\) 4.07530 0.208784
\(382\) −23.1166 −1.18275
\(383\) 31.8719 1.62858 0.814289 0.580459i \(-0.197127\pi\)
0.814289 + 0.580459i \(0.197127\pi\)
\(384\) 6.91703 0.352983
\(385\) 4.15120 0.211565
\(386\) −15.7233 −0.800297
\(387\) 4.75943 0.241936
\(388\) −18.7613 −0.952462
\(389\) 27.7644 1.40771 0.703854 0.710344i \(-0.251461\pi\)
0.703854 + 0.710344i \(0.251461\pi\)
\(390\) 30.1694 1.52769
\(391\) −0.369572 −0.0186901
\(392\) 3.89046 0.196498
\(393\) 5.16264 0.260421
\(394\) −22.5081 −1.13394
\(395\) −65.0046 −3.27073
\(396\) −4.38978 −0.220595
\(397\) 6.86918 0.344754 0.172377 0.985031i \(-0.444855\pi\)
0.172377 + 0.985031i \(0.444855\pi\)
\(398\) 19.5164 0.978267
\(399\) −2.94517 −0.147443
\(400\) −42.6437 −2.13218
\(401\) −26.3264 −1.31468 −0.657339 0.753595i \(-0.728318\pi\)
−0.657339 + 0.753595i \(0.728318\pi\)
\(402\) 14.5983 0.728099
\(403\) −19.4675 −0.969747
\(404\) 17.8825 0.889687
\(405\) 26.5255 1.31806
\(406\) −2.09044 −0.103747
\(407\) 21.2317 1.05242
\(408\) 0.0352455 0.00174491
\(409\) 2.97792 0.147249 0.0736244 0.997286i \(-0.476543\pi\)
0.0736244 + 0.997286i \(0.476543\pi\)
\(410\) −2.64408 −0.130582
\(411\) 2.93299 0.144674
\(412\) 28.2626 1.39240
\(413\) 0.686253 0.0337683
\(414\) −10.0369 −0.493285
\(415\) −10.2901 −0.505120
\(416\) 19.9069 0.976018
\(417\) 2.90108 0.142067
\(418\) 68.0181 3.32687
\(419\) 11.6573 0.569495 0.284748 0.958603i \(-0.408090\pi\)
0.284748 + 0.958603i \(0.408090\pi\)
\(420\) 2.44933 0.119515
\(421\) 12.1251 0.590942 0.295471 0.955352i \(-0.404523\pi\)
0.295471 + 0.955352i \(0.404523\pi\)
\(422\) −38.2011 −1.85960
\(423\) −5.13058 −0.249457
\(424\) 6.08245 0.295390
\(425\) −0.382429 −0.0185505
\(426\) 39.1144 1.89510
\(427\) 3.15617 0.152738
\(428\) −0.696329 −0.0336583
\(429\) −18.5911 −0.897586
\(430\) 61.3301 2.95760
\(431\) −15.2477 −0.734458 −0.367229 0.930131i \(-0.619693\pi\)
−0.367229 + 0.930131i \(0.619693\pi\)
\(432\) 25.0257 1.20405
\(433\) 10.6963 0.514033 0.257016 0.966407i \(-0.417261\pi\)
0.257016 + 0.966407i \(0.417261\pi\)
\(434\) −3.43011 −0.164650
\(435\) −26.6662 −1.27854
\(436\) 4.47594 0.214359
\(437\) 71.6579 3.42786
\(438\) 39.2409 1.87500
\(439\) 18.3356 0.875109 0.437554 0.899192i \(-0.355845\pi\)
0.437554 + 0.899192i \(0.355845\pi\)
\(440\) 9.63233 0.459203
\(441\) 3.94809 0.188004
\(442\) 0.205064 0.00975390
\(443\) 1.65444 0.0786048 0.0393024 0.999227i \(-0.487486\pi\)
0.0393024 + 0.999227i \(0.487486\pi\)
\(444\) 12.5274 0.594522
\(445\) −68.4607 −3.24535
\(446\) −34.3320 −1.62567
\(447\) −19.8710 −0.939868
\(448\) 1.33501 0.0630731
\(449\) 25.7870 1.21696 0.608482 0.793568i \(-0.291779\pi\)
0.608482 + 0.793568i \(0.291779\pi\)
\(450\) −10.3860 −0.489603
\(451\) 1.62934 0.0767228
\(452\) −34.0711 −1.60257
\(453\) −10.1308 −0.475984
\(454\) −40.8694 −1.91810
\(455\) −2.42663 −0.113762
\(456\) −6.83390 −0.320027
\(457\) −0.922525 −0.0431539 −0.0215770 0.999767i \(-0.506869\pi\)
−0.0215770 + 0.999767i \(0.506869\pi\)
\(458\) −5.27887 −0.246665
\(459\) 0.224431 0.0104755
\(460\) −59.5937 −2.77857
\(461\) −36.6179 −1.70547 −0.852734 0.522346i \(-0.825057\pi\)
−0.852734 + 0.522346i \(0.825057\pi\)
\(462\) −3.27568 −0.152398
\(463\) −15.5084 −0.720737 −0.360369 0.932810i \(-0.617349\pi\)
−0.360369 + 0.932810i \(0.617349\pi\)
\(464\) −20.2110 −0.938270
\(465\) −43.7552 −2.02910
\(466\) −9.68775 −0.448776
\(467\) −23.7761 −1.10023 −0.550113 0.835090i \(-0.685415\pi\)
−0.550113 + 0.835090i \(0.685415\pi\)
\(468\) 2.56609 0.118618
\(469\) −1.17420 −0.0542193
\(470\) −66.1127 −3.04955
\(471\) 26.9188 1.24035
\(472\) 1.59236 0.0732944
\(473\) −37.7931 −1.73773
\(474\) 51.2947 2.35604
\(475\) 74.1508 3.40227
\(476\) 0.0166483 0.000763074 0
\(477\) 6.17255 0.282621
\(478\) 2.85962 0.130796
\(479\) 26.2354 1.19872 0.599362 0.800478i \(-0.295421\pi\)
0.599362 + 0.800478i \(0.295421\pi\)
\(480\) 44.7428 2.04222
\(481\) −12.4113 −0.565904
\(482\) 19.0855 0.869319
\(483\) −3.45097 −0.157024
\(484\) 16.0589 0.729948
\(485\) 41.7771 1.89700
\(486\) 11.2189 0.508898
\(487\) 4.40302 0.199520 0.0997599 0.995012i \(-0.468193\pi\)
0.0997599 + 0.995012i \(0.468193\pi\)
\(488\) 7.32350 0.331519
\(489\) 6.28205 0.284084
\(490\) 50.8751 2.29830
\(491\) −31.2403 −1.40985 −0.704927 0.709280i \(-0.749020\pi\)
−0.704927 + 0.709280i \(0.749020\pi\)
\(492\) 0.961362 0.0433415
\(493\) −0.181252 −0.00816319
\(494\) −39.7607 −1.78892
\(495\) 9.77501 0.439354
\(496\) −33.1632 −1.48907
\(497\) −3.14611 −0.141122
\(498\) 8.11982 0.363858
\(499\) −1.12984 −0.0505786 −0.0252893 0.999680i \(-0.508051\pi\)
−0.0252893 + 0.999680i \(0.508051\pi\)
\(500\) −29.1490 −1.30358
\(501\) 12.7919 0.571499
\(502\) −29.6953 −1.32537
\(503\) −17.4507 −0.778089 −0.389045 0.921219i \(-0.627195\pi\)
−0.389045 + 0.921219i \(0.627195\pi\)
\(504\) −0.0769910 −0.00342945
\(505\) −39.8201 −1.77197
\(506\) 79.6994 3.54307
\(507\) −9.40257 −0.417583
\(508\) 4.46668 0.198177
\(509\) 33.0181 1.46350 0.731750 0.681573i \(-0.238704\pi\)
0.731750 + 0.681573i \(0.238704\pi\)
\(510\) 0.460902 0.0204091
\(511\) −3.15628 −0.139626
\(512\) 28.8706 1.27591
\(513\) −43.5159 −1.92127
\(514\) 40.6916 1.79483
\(515\) −62.9342 −2.77321
\(516\) −22.2990 −0.981660
\(517\) 40.7402 1.79175
\(518\) −2.18682 −0.0960832
\(519\) −2.70710 −0.118829
\(520\) −5.63069 −0.246922
\(521\) 1.55627 0.0681815 0.0340908 0.999419i \(-0.489146\pi\)
0.0340908 + 0.999419i \(0.489146\pi\)
\(522\) −4.92247 −0.215451
\(523\) −26.4168 −1.15513 −0.577563 0.816346i \(-0.695996\pi\)
−0.577563 + 0.816346i \(0.695996\pi\)
\(524\) 5.65844 0.247190
\(525\) −3.57103 −0.155852
\(526\) −17.6983 −0.771682
\(527\) −0.297408 −0.0129553
\(528\) −31.6701 −1.37827
\(529\) 60.9642 2.65062
\(530\) 79.5395 3.45497
\(531\) 1.61595 0.0701263
\(532\) −3.22801 −0.139952
\(533\) −0.952452 −0.0412553
\(534\) 54.0219 2.33775
\(535\) 1.55056 0.0670366
\(536\) −2.72457 −0.117684
\(537\) −34.2417 −1.47764
\(538\) −37.5990 −1.62101
\(539\) −31.3504 −1.35036
\(540\) 36.1896 1.55735
\(541\) −0.463213 −0.0199151 −0.00995755 0.999950i \(-0.503170\pi\)
−0.00995755 + 0.999950i \(0.503170\pi\)
\(542\) 22.9946 0.987701
\(543\) −18.4969 −0.793778
\(544\) 0.304121 0.0130391
\(545\) −9.96688 −0.426934
\(546\) 1.91484 0.0819474
\(547\) −4.41548 −0.188792 −0.0943961 0.995535i \(-0.530092\pi\)
−0.0943961 + 0.995535i \(0.530092\pi\)
\(548\) 3.21466 0.137324
\(549\) 7.43199 0.317189
\(550\) 82.4721 3.51662
\(551\) 35.1438 1.49718
\(552\) −8.00754 −0.340823
\(553\) −4.12581 −0.175447
\(554\) −28.9824 −1.23134
\(555\) −27.8955 −1.18410
\(556\) 3.17969 0.134849
\(557\) −30.7259 −1.30190 −0.650949 0.759121i \(-0.725629\pi\)
−0.650949 + 0.759121i \(0.725629\pi\)
\(558\) −8.07703 −0.341928
\(559\) 22.0924 0.934407
\(560\) −4.13379 −0.174685
\(561\) −0.284018 −0.0119913
\(562\) 59.7441 2.52015
\(563\) 11.0243 0.464617 0.232309 0.972642i \(-0.425372\pi\)
0.232309 + 0.972642i \(0.425372\pi\)
\(564\) 24.0379 1.01218
\(565\) 75.8684 3.19181
\(566\) 8.86639 0.372682
\(567\) 1.68356 0.0707028
\(568\) −7.30015 −0.306308
\(569\) −2.47167 −0.103618 −0.0518090 0.998657i \(-0.516499\pi\)
−0.0518090 + 0.998657i \(0.516499\pi\)
\(570\) −89.3661 −3.74314
\(571\) 6.15024 0.257380 0.128690 0.991685i \(-0.458923\pi\)
0.128690 + 0.991685i \(0.458923\pi\)
\(572\) −20.3765 −0.851984
\(573\) −18.7159 −0.781870
\(574\) −0.167819 −0.00700461
\(575\) 86.8853 3.62337
\(576\) 3.14360 0.130983
\(577\) −1.34304 −0.0559114 −0.0279557 0.999609i \(-0.508900\pi\)
−0.0279557 + 0.999609i \(0.508900\pi\)
\(578\) −32.7367 −1.36167
\(579\) −12.7301 −0.529045
\(580\) −29.2271 −1.21359
\(581\) −0.653106 −0.0270954
\(582\) −32.9660 −1.36649
\(583\) −49.0141 −2.02996
\(584\) −7.32376 −0.303059
\(585\) −5.71409 −0.236249
\(586\) 60.2573 2.48920
\(587\) −28.5062 −1.17658 −0.588288 0.808651i \(-0.700198\pi\)
−0.588288 + 0.808651i \(0.700198\pi\)
\(588\) −18.4977 −0.762831
\(589\) 57.6657 2.37607
\(590\) 20.8232 0.857276
\(591\) −18.2232 −0.749603
\(592\) −21.1427 −0.868960
\(593\) 25.6786 1.05449 0.527247 0.849712i \(-0.323224\pi\)
0.527247 + 0.849712i \(0.323224\pi\)
\(594\) −48.3993 −1.98585
\(595\) −0.0370719 −0.00151980
\(596\) −21.7794 −0.892118
\(597\) 15.8010 0.646693
\(598\) −46.5892 −1.90517
\(599\) −10.4424 −0.426664 −0.213332 0.976980i \(-0.568432\pi\)
−0.213332 + 0.976980i \(0.568432\pi\)
\(600\) −8.28612 −0.338279
\(601\) 17.4730 0.712739 0.356369 0.934345i \(-0.384014\pi\)
0.356369 + 0.934345i \(0.384014\pi\)
\(602\) 3.89259 0.158650
\(603\) −2.76493 −0.112597
\(604\) −11.1037 −0.451802
\(605\) −35.7593 −1.45382
\(606\) 31.4218 1.27642
\(607\) 13.8759 0.563205 0.281602 0.959531i \(-0.409134\pi\)
0.281602 + 0.959531i \(0.409134\pi\)
\(608\) −58.9672 −2.39144
\(609\) −1.69249 −0.0685831
\(610\) 95.7687 3.87756
\(611\) −23.8151 −0.963457
\(612\) 0.0392025 0.00158467
\(613\) 30.8506 1.24605 0.623023 0.782204i \(-0.285904\pi\)
0.623023 + 0.782204i \(0.285904\pi\)
\(614\) 0.135161 0.00545464
\(615\) −2.14073 −0.0863225
\(616\) 0.611359 0.0246324
\(617\) 42.6931 1.71876 0.859379 0.511339i \(-0.170850\pi\)
0.859379 + 0.511339i \(0.170850\pi\)
\(618\) 49.6609 1.99766
\(619\) 31.4285 1.26322 0.631610 0.775286i \(-0.282394\pi\)
0.631610 + 0.775286i \(0.282394\pi\)
\(620\) −47.9572 −1.92601
\(621\) −50.9892 −2.04613
\(622\) −39.9206 −1.60067
\(623\) −4.34517 −0.174085
\(624\) 18.5131 0.741118
\(625\) 17.4981 0.699925
\(626\) 12.0292 0.480784
\(627\) 55.0695 2.19926
\(628\) 29.5040 1.17734
\(629\) −0.189608 −0.00756018
\(630\) −1.00680 −0.0401120
\(631\) 43.0799 1.71498 0.857492 0.514497i \(-0.172021\pi\)
0.857492 + 0.514497i \(0.172021\pi\)
\(632\) −9.57342 −0.380810
\(633\) −30.9288 −1.22931
\(634\) 4.06235 0.161337
\(635\) −9.94625 −0.394705
\(636\) −28.9198 −1.14674
\(637\) 18.3262 0.726112
\(638\) 39.0876 1.54749
\(639\) −7.40829 −0.293067
\(640\) −16.8818 −0.667313
\(641\) −12.1718 −0.480758 −0.240379 0.970679i \(-0.577272\pi\)
−0.240379 + 0.970679i \(0.577272\pi\)
\(642\) −1.22354 −0.0482892
\(643\) 3.48617 0.137481 0.0687406 0.997635i \(-0.478102\pi\)
0.0687406 + 0.997635i \(0.478102\pi\)
\(644\) −3.78238 −0.149047
\(645\) 49.6547 1.95515
\(646\) −0.607430 −0.0238990
\(647\) −11.6664 −0.458653 −0.229326 0.973350i \(-0.573652\pi\)
−0.229326 + 0.973350i \(0.573652\pi\)
\(648\) 3.90649 0.153461
\(649\) −12.8317 −0.503689
\(650\) −48.2100 −1.89095
\(651\) −2.77712 −0.108844
\(652\) 6.88535 0.269651
\(653\) 0.538774 0.0210838 0.0105419 0.999944i \(-0.496644\pi\)
0.0105419 + 0.999944i \(0.496644\pi\)
\(654\) 7.86480 0.307538
\(655\) −12.6000 −0.492324
\(656\) −1.62251 −0.0633485
\(657\) −7.43224 −0.289959
\(658\) −4.19614 −0.163583
\(659\) −13.1889 −0.513766 −0.256883 0.966442i \(-0.582696\pi\)
−0.256883 + 0.966442i \(0.582696\pi\)
\(660\) −45.7981 −1.78269
\(661\) 3.19662 0.124334 0.0621670 0.998066i \(-0.480199\pi\)
0.0621670 + 0.998066i \(0.480199\pi\)
\(662\) 40.2108 1.56284
\(663\) 0.166026 0.00644792
\(664\) −1.51545 −0.0588108
\(665\) 7.18803 0.278740
\(666\) −5.14940 −0.199535
\(667\) 41.1793 1.59447
\(668\) 14.0204 0.542464
\(669\) −27.7963 −1.07467
\(670\) −35.6290 −1.37647
\(671\) −59.0149 −2.27824
\(672\) 2.83980 0.109548
\(673\) 41.2058 1.58837 0.794183 0.607679i \(-0.207899\pi\)
0.794183 + 0.607679i \(0.207899\pi\)
\(674\) −30.6033 −1.17880
\(675\) −52.7631 −2.03085
\(676\) −10.3055 −0.396367
\(677\) −12.6571 −0.486452 −0.243226 0.969970i \(-0.578206\pi\)
−0.243226 + 0.969970i \(0.578206\pi\)
\(678\) −59.8672 −2.29919
\(679\) 2.65157 0.101758
\(680\) −0.0860207 −0.00329874
\(681\) −33.0891 −1.26798
\(682\) 64.1370 2.45593
\(683\) −24.6882 −0.944667 −0.472334 0.881420i \(-0.656588\pi\)
−0.472334 + 0.881420i \(0.656588\pi\)
\(684\) −7.60115 −0.290637
\(685\) −7.15831 −0.273505
\(686\) 6.48517 0.247605
\(687\) −4.27393 −0.163061
\(688\) 37.6346 1.43481
\(689\) 28.6517 1.09154
\(690\) −104.714 −3.98638
\(691\) 12.2157 0.464708 0.232354 0.972631i \(-0.425357\pi\)
0.232354 + 0.972631i \(0.425357\pi\)
\(692\) −2.96708 −0.112791
\(693\) 0.620415 0.0235676
\(694\) −4.55180 −0.172784
\(695\) −7.08043 −0.268576
\(696\) −3.92721 −0.148860
\(697\) −0.0145507 −0.000551148 0
\(698\) 2.45142 0.0927878
\(699\) −7.84350 −0.296668
\(700\) −3.91397 −0.147934
\(701\) −22.5837 −0.852974 −0.426487 0.904494i \(-0.640249\pi\)
−0.426487 + 0.904494i \(0.640249\pi\)
\(702\) 28.2923 1.06783
\(703\) 36.7640 1.38658
\(704\) −24.9622 −0.940800
\(705\) −53.5268 −2.01594
\(706\) −33.8919 −1.27554
\(707\) −2.52736 −0.0950513
\(708\) −7.57109 −0.284539
\(709\) −10.8886 −0.408930 −0.204465 0.978874i \(-0.565546\pi\)
−0.204465 + 0.978874i \(0.565546\pi\)
\(710\) −95.4633 −3.58267
\(711\) −9.71523 −0.364350
\(712\) −10.0824 −0.377854
\(713\) 67.5691 2.53048
\(714\) 0.0292532 0.00109477
\(715\) 45.3737 1.69688
\(716\) −37.5301 −1.40257
\(717\) 2.31523 0.0864640
\(718\) 32.7167 1.22098
\(719\) 11.7301 0.437459 0.218729 0.975786i \(-0.429809\pi\)
0.218729 + 0.975786i \(0.429809\pi\)
\(720\) −9.73403 −0.362766
\(721\) −3.99440 −0.148759
\(722\) 81.1855 3.02141
\(723\) 15.4522 0.574672
\(724\) −20.2733 −0.753450
\(725\) 42.6119 1.58257
\(726\) 28.2174 1.04725
\(727\) 0.372335 0.0138091 0.00690457 0.999976i \(-0.497802\pi\)
0.00690457 + 0.999976i \(0.497802\pi\)
\(728\) −0.357377 −0.0132453
\(729\) 29.9939 1.11089
\(730\) −95.7720 −3.54468
\(731\) 0.337508 0.0124832
\(732\) −34.8205 −1.28700
\(733\) −25.9204 −0.957393 −0.478696 0.877980i \(-0.658891\pi\)
−0.478696 + 0.877980i \(0.658891\pi\)
\(734\) −10.5744 −0.390308
\(735\) 41.1900 1.51932
\(736\) −69.0942 −2.54684
\(737\) 21.9554 0.808737
\(738\) −0.395170 −0.0145464
\(739\) 4.69958 0.172877 0.0864385 0.996257i \(-0.472451\pi\)
0.0864385 + 0.996257i \(0.472451\pi\)
\(740\) −30.5745 −1.12394
\(741\) −32.1915 −1.18258
\(742\) 5.04833 0.185330
\(743\) −43.9654 −1.61294 −0.806468 0.591278i \(-0.798624\pi\)
−0.806468 + 0.591278i \(0.798624\pi\)
\(744\) −6.44396 −0.236247
\(745\) 48.4976 1.77681
\(746\) 32.7557 1.19927
\(747\) −1.53790 −0.0562687
\(748\) −0.311294 −0.0113820
\(749\) 0.0984134 0.00359595
\(750\) −51.2185 −1.87024
\(751\) −2.88688 −0.105344 −0.0526719 0.998612i \(-0.516774\pi\)
−0.0526719 + 0.998612i \(0.516774\pi\)
\(752\) −40.5694 −1.47941
\(753\) −24.0423 −0.876149
\(754\) −22.8491 −0.832116
\(755\) 24.7253 0.899845
\(756\) 2.29694 0.0835389
\(757\) −19.7532 −0.717943 −0.358971 0.933349i \(-0.616872\pi\)
−0.358971 + 0.933349i \(0.616872\pi\)
\(758\) 3.61984 0.131479
\(759\) 64.5270 2.34218
\(760\) 16.6789 0.605008
\(761\) 7.29433 0.264419 0.132210 0.991222i \(-0.457793\pi\)
0.132210 + 0.991222i \(0.457793\pi\)
\(762\) 7.84852 0.284322
\(763\) −0.632593 −0.0229014
\(764\) −20.5133 −0.742146
\(765\) −0.0872949 −0.00315615
\(766\) 61.3813 2.21780
\(767\) 7.50093 0.270843
\(768\) 30.5578 1.10266
\(769\) −14.7248 −0.530988 −0.265494 0.964112i \(-0.585535\pi\)
−0.265494 + 0.964112i \(0.585535\pi\)
\(770\) 7.99468 0.288108
\(771\) 32.9452 1.18649
\(772\) −13.9526 −0.502166
\(773\) −43.4277 −1.56199 −0.780993 0.624540i \(-0.785287\pi\)
−0.780993 + 0.624540i \(0.785287\pi\)
\(774\) 9.16607 0.329468
\(775\) 69.9198 2.51159
\(776\) 6.15264 0.220867
\(777\) −1.77051 −0.0635168
\(778\) 53.4706 1.91702
\(779\) 2.82130 0.101084
\(780\) 26.7718 0.958585
\(781\) 58.8267 2.10499
\(782\) −0.711749 −0.0254521
\(783\) −25.0071 −0.893680
\(784\) 31.2190 1.11496
\(785\) −65.6985 −2.34488
\(786\) 9.94260 0.354641
\(787\) 2.36935 0.0844583 0.0422292 0.999108i \(-0.486554\pi\)
0.0422292 + 0.999108i \(0.486554\pi\)
\(788\) −19.9733 −0.711519
\(789\) −14.3291 −0.510129
\(790\) −125.191 −4.45408
\(791\) 4.81533 0.171213
\(792\) 1.43960 0.0511538
\(793\) 34.4978 1.22505
\(794\) 13.2292 0.469486
\(795\) 64.3976 2.28395
\(796\) 17.3185 0.613838
\(797\) 16.0573 0.568778 0.284389 0.958709i \(-0.408209\pi\)
0.284389 + 0.958709i \(0.408209\pi\)
\(798\) −5.67203 −0.200788
\(799\) −0.363827 −0.0128713
\(800\) −71.4979 −2.52783
\(801\) −10.2318 −0.361522
\(802\) −50.7013 −1.79033
\(803\) 59.0169 2.08266
\(804\) 12.9543 0.456864
\(805\) 8.42249 0.296854
\(806\) −37.4920 −1.32060
\(807\) −30.4413 −1.07158
\(808\) −5.86443 −0.206310
\(809\) −52.1316 −1.83285 −0.916424 0.400208i \(-0.868938\pi\)
−0.916424 + 0.400208i \(0.868938\pi\)
\(810\) 51.0847 1.79493
\(811\) −18.6496 −0.654875 −0.327438 0.944873i \(-0.606185\pi\)
−0.327438 + 0.944873i \(0.606185\pi\)
\(812\) −1.85503 −0.0650987
\(813\) 18.6171 0.652930
\(814\) 40.8896 1.43318
\(815\) −15.3321 −0.537059
\(816\) 0.282827 0.00990094
\(817\) −65.4408 −2.28948
\(818\) 5.73510 0.200523
\(819\) −0.362671 −0.0126727
\(820\) −2.34631 −0.0819369
\(821\) −23.9677 −0.836479 −0.418239 0.908337i \(-0.637353\pi\)
−0.418239 + 0.908337i \(0.637353\pi\)
\(822\) 5.64857 0.197017
\(823\) −12.1227 −0.422569 −0.211285 0.977425i \(-0.567765\pi\)
−0.211285 + 0.977425i \(0.567765\pi\)
\(824\) −9.26851 −0.322884
\(825\) 66.7719 2.32470
\(826\) 1.32164 0.0459856
\(827\) 8.86514 0.308271 0.154136 0.988050i \(-0.450741\pi\)
0.154136 + 0.988050i \(0.450741\pi\)
\(828\) −8.90655 −0.309524
\(829\) 32.7052 1.13590 0.567949 0.823064i \(-0.307737\pi\)
0.567949 + 0.823064i \(0.307737\pi\)
\(830\) −19.8174 −0.687871
\(831\) −23.4650 −0.813992
\(832\) 14.5920 0.505885
\(833\) 0.279972 0.00970047
\(834\) 5.58712 0.193466
\(835\) −31.2201 −1.08042
\(836\) 60.3581 2.08753
\(837\) −41.0329 −1.41830
\(838\) 22.4504 0.775537
\(839\) 14.2915 0.493396 0.246698 0.969092i \(-0.420654\pi\)
0.246698 + 0.969092i \(0.420654\pi\)
\(840\) −0.803240 −0.0277144
\(841\) −8.80409 −0.303589
\(842\) 23.3515 0.804744
\(843\) 48.3706 1.66597
\(844\) −33.8991 −1.16685
\(845\) 22.9481 0.789437
\(846\) −9.88084 −0.339710
\(847\) −2.26963 −0.0779853
\(848\) 48.8086 1.67609
\(849\) 7.17850 0.246365
\(850\) −0.736510 −0.0252621
\(851\) 43.0777 1.47669
\(852\) 34.7095 1.18913
\(853\) −9.49025 −0.324940 −0.162470 0.986713i \(-0.551946\pi\)
−0.162470 + 0.986713i \(0.551946\pi\)
\(854\) 6.07839 0.207998
\(855\) 16.9260 0.578856
\(856\) 0.228356 0.00780505
\(857\) −19.5854 −0.669025 −0.334513 0.942391i \(-0.608572\pi\)
−0.334513 + 0.942391i \(0.608572\pi\)
\(858\) −35.8041 −1.22233
\(859\) 35.4819 1.21063 0.605313 0.795987i \(-0.293048\pi\)
0.605313 + 0.795987i \(0.293048\pi\)
\(860\) 54.4234 1.85582
\(861\) −0.135871 −0.00463047
\(862\) −29.3652 −1.00018
\(863\) −13.4238 −0.456952 −0.228476 0.973550i \(-0.573374\pi\)
−0.228476 + 0.973550i \(0.573374\pi\)
\(864\) 41.9590 1.42747
\(865\) 6.60699 0.224645
\(866\) 20.5998 0.700009
\(867\) −26.5046 −0.900145
\(868\) −3.04382 −0.103314
\(869\) 77.1453 2.61698
\(870\) −51.3556 −1.74112
\(871\) −12.8343 −0.434873
\(872\) −1.46785 −0.0497077
\(873\) 6.24378 0.211320
\(874\) 138.004 4.66805
\(875\) 4.11968 0.139271
\(876\) 34.8217 1.17652
\(877\) −3.75641 −0.126845 −0.0634225 0.997987i \(-0.520202\pi\)
−0.0634225 + 0.997987i \(0.520202\pi\)
\(878\) 35.3120 1.19172
\(879\) 48.7861 1.64552
\(880\) 77.2946 2.60560
\(881\) −49.4564 −1.66623 −0.833114 0.553101i \(-0.813444\pi\)
−0.833114 + 0.553101i \(0.813444\pi\)
\(882\) 7.60352 0.256024
\(883\) −14.2351 −0.479049 −0.239524 0.970890i \(-0.576991\pi\)
−0.239524 + 0.970890i \(0.576991\pi\)
\(884\) 0.181971 0.00612033
\(885\) 16.8591 0.566711
\(886\) 3.18624 0.107044
\(887\) −2.67754 −0.0899031 −0.0449516 0.998989i \(-0.514313\pi\)
−0.0449516 + 0.998989i \(0.514313\pi\)
\(888\) −4.10826 −0.137864
\(889\) −0.631283 −0.0211726
\(890\) −131.847 −4.41951
\(891\) −31.4796 −1.05461
\(892\) −30.4657 −1.02007
\(893\) 70.5439 2.36066
\(894\) −38.2691 −1.27991
\(895\) 83.5708 2.79347
\(896\) −1.07148 −0.0357957
\(897\) −37.7200 −1.25943
\(898\) 49.6625 1.65726
\(899\) 33.1385 1.10523
\(900\) −9.21641 −0.307214
\(901\) 0.437716 0.0145824
\(902\) 3.13791 0.104481
\(903\) 3.15156 0.104877
\(904\) 11.1734 0.371621
\(905\) 45.1438 1.50063
\(906\) −19.5105 −0.648194
\(907\) 12.0947 0.401598 0.200799 0.979632i \(-0.435646\pi\)
0.200799 + 0.979632i \(0.435646\pi\)
\(908\) −36.2669 −1.20356
\(909\) −5.95130 −0.197392
\(910\) −4.67338 −0.154921
\(911\) −0.443134 −0.0146817 −0.00734083 0.999973i \(-0.502337\pi\)
−0.00734083 + 0.999973i \(0.502337\pi\)
\(912\) −54.8386 −1.81589
\(913\) 12.2119 0.404156
\(914\) −1.77667 −0.0587669
\(915\) 77.5372 2.56330
\(916\) −4.68438 −0.154776
\(917\) −0.799718 −0.0264090
\(918\) 0.432226 0.0142656
\(919\) −37.4751 −1.23619 −0.618094 0.786104i \(-0.712095\pi\)
−0.618094 + 0.786104i \(0.712095\pi\)
\(920\) 19.5433 0.644324
\(921\) 0.109430 0.00360585
\(922\) −70.5215 −2.32250
\(923\) −34.3878 −1.13189
\(924\) −2.90679 −0.0956262
\(925\) 44.5764 1.46566
\(926\) −29.8673 −0.981499
\(927\) −9.40580 −0.308927
\(928\) −33.8864 −1.11238
\(929\) 45.4912 1.49252 0.746259 0.665656i \(-0.231848\pi\)
0.746259 + 0.665656i \(0.231848\pi\)
\(930\) −84.2670 −2.76322
\(931\) −54.2850 −1.77912
\(932\) −8.59675 −0.281596
\(933\) −32.3210 −1.05814
\(934\) −45.7897 −1.49829
\(935\) 0.693179 0.0226694
\(936\) −0.841532 −0.0275063
\(937\) −38.7947 −1.26737 −0.633684 0.773592i \(-0.718458\pi\)
−0.633684 + 0.773592i \(0.718458\pi\)
\(938\) −2.26135 −0.0738358
\(939\) 9.73921 0.317827
\(940\) −58.6673 −1.91352
\(941\) 29.6821 0.967607 0.483804 0.875177i \(-0.339255\pi\)
0.483804 + 0.875177i \(0.339255\pi\)
\(942\) 51.8422 1.68911
\(943\) 3.30583 0.107653
\(944\) 12.7779 0.415886
\(945\) −5.11475 −0.166383
\(946\) −72.7846 −2.36643
\(947\) 13.4750 0.437880 0.218940 0.975738i \(-0.429740\pi\)
0.218940 + 0.975738i \(0.429740\pi\)
\(948\) 45.5180 1.47836
\(949\) −34.4990 −1.11989
\(950\) 142.805 4.63321
\(951\) 3.28900 0.106653
\(952\) −0.00545969 −0.000176950 0
\(953\) −22.8306 −0.739557 −0.369779 0.929120i \(-0.620566\pi\)
−0.369779 + 0.929120i \(0.620566\pi\)
\(954\) 11.8875 0.384873
\(955\) 45.6784 1.47812
\(956\) 2.53758 0.0820711
\(957\) 31.6465 1.02299
\(958\) 50.5260 1.63242
\(959\) −0.454334 −0.0146712
\(960\) 32.7969 1.05851
\(961\) 23.3753 0.754042
\(962\) −23.9025 −0.770648
\(963\) 0.231739 0.00746767
\(964\) 16.9361 0.545476
\(965\) 31.0693 1.00016
\(966\) −6.64613 −0.213836
\(967\) 38.8447 1.24916 0.624581 0.780960i \(-0.285270\pi\)
0.624581 + 0.780960i \(0.285270\pi\)
\(968\) −5.26638 −0.169268
\(969\) −0.491794 −0.0157987
\(970\) 80.4574 2.58333
\(971\) −29.8372 −0.957521 −0.478761 0.877945i \(-0.658914\pi\)
−0.478761 + 0.877945i \(0.658914\pi\)
\(972\) 9.95543 0.319321
\(973\) −0.449392 −0.0144068
\(974\) 8.47966 0.271706
\(975\) −39.0323 −1.25003
\(976\) 58.7674 1.88110
\(977\) −3.35840 −0.107445 −0.0537224 0.998556i \(-0.517109\pi\)
−0.0537224 + 0.998556i \(0.517109\pi\)
\(978\) 12.0984 0.386865
\(979\) 81.2470 2.59666
\(980\) 45.1457 1.44213
\(981\) −1.48960 −0.0475591
\(982\) −60.1648 −1.91994
\(983\) 16.5818 0.528876 0.264438 0.964403i \(-0.414814\pi\)
0.264438 + 0.964403i \(0.414814\pi\)
\(984\) −0.315272 −0.0100505
\(985\) 44.4759 1.41712
\(986\) −0.349069 −0.0111166
\(987\) −3.39732 −0.108138
\(988\) −35.2830 −1.12250
\(989\) −76.6795 −2.43827
\(990\) 18.8254 0.598312
\(991\) 27.2203 0.864681 0.432341 0.901710i \(-0.357688\pi\)
0.432341 + 0.901710i \(0.357688\pi\)
\(992\) −55.6026 −1.76538
\(993\) 32.5559 1.03313
\(994\) −6.05901 −0.192180
\(995\) −38.5643 −1.22257
\(996\) 7.20540 0.228312
\(997\) 7.36253 0.233174 0.116587 0.993181i \(-0.462805\pi\)
0.116587 + 0.993181i \(0.462805\pi\)
\(998\) −2.17593 −0.0688778
\(999\) −26.1599 −0.827664
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 4001.2.a.b.1.145 184
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4001.2.a.b.1.145 184 1.1 even 1 trivial