Properties

Label 4001.2.a.b.1.14
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 1.14
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)
 
\(f(q)\) \(=\) \(q-2.61059 q^{2} -0.259768 q^{3} +4.81518 q^{4} -4.09316 q^{5} +0.678147 q^{6} +2.08780 q^{7} -7.34928 q^{8} -2.93252 q^{9} +O(q^{10})\) \(q-2.61059 q^{2} -0.259768 q^{3} +4.81518 q^{4} -4.09316 q^{5} +0.678147 q^{6} +2.08780 q^{7} -7.34928 q^{8} -2.93252 q^{9} +10.6856 q^{10} -4.54556 q^{11} -1.25083 q^{12} -2.98042 q^{13} -5.45038 q^{14} +1.06327 q^{15} +9.55560 q^{16} +4.39920 q^{17} +7.65561 q^{18} -0.751344 q^{19} -19.7093 q^{20} -0.542342 q^{21} +11.8666 q^{22} -0.781648 q^{23} +1.90911 q^{24} +11.7540 q^{25} +7.78065 q^{26} +1.54108 q^{27} +10.0531 q^{28} -4.78053 q^{29} -2.77577 q^{30} -3.90479 q^{31} -10.2472 q^{32} +1.18079 q^{33} -11.4845 q^{34} -8.54569 q^{35} -14.1206 q^{36} -6.77693 q^{37} +1.96145 q^{38} +0.774216 q^{39} +30.0818 q^{40} -11.6528 q^{41} +1.41583 q^{42} +0.552335 q^{43} -21.8877 q^{44} +12.0033 q^{45} +2.04056 q^{46} -1.35892 q^{47} -2.48224 q^{48} -2.64111 q^{49} -30.6848 q^{50} -1.14277 q^{51} -14.3512 q^{52} -8.71995 q^{53} -4.02312 q^{54} +18.6057 q^{55} -15.3438 q^{56} +0.195175 q^{57} +12.4800 q^{58} -11.9100 q^{59} +5.11984 q^{60} -0.470997 q^{61} +10.1938 q^{62} -6.12251 q^{63} +7.64001 q^{64} +12.1993 q^{65} -3.08256 q^{66} -8.34431 q^{67} +21.1830 q^{68} +0.203047 q^{69} +22.3093 q^{70} +10.0343 q^{71} +21.5519 q^{72} +7.49575 q^{73} +17.6918 q^{74} -3.05331 q^{75} -3.61786 q^{76} -9.49020 q^{77} -2.02116 q^{78} -10.3980 q^{79} -39.1126 q^{80} +8.39724 q^{81} +30.4208 q^{82} -13.4273 q^{83} -2.61147 q^{84} -18.0067 q^{85} -1.44192 q^{86} +1.24183 q^{87} +33.4066 q^{88} +11.9262 q^{89} -31.3357 q^{90} -6.22250 q^{91} -3.76378 q^{92} +1.01434 q^{93} +3.54757 q^{94} +3.07538 q^{95} +2.66189 q^{96} -18.5687 q^{97} +6.89485 q^{98} +13.3299 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.61059 −1.84597 −0.922983 0.384841i \(-0.874256\pi\)
−0.922983 + 0.384841i \(0.874256\pi\)
\(3\) −0.259768 −0.149977 −0.0749885 0.997184i \(-0.523892\pi\)
−0.0749885 + 0.997184i \(0.523892\pi\)
\(4\) 4.81518 2.40759
\(5\) −4.09316 −1.83052 −0.915259 0.402865i \(-0.868014\pi\)
−0.915259 + 0.402865i \(0.868014\pi\)
\(6\) 0.678147 0.276852
\(7\) 2.08780 0.789113 0.394556 0.918872i \(-0.370898\pi\)
0.394556 + 0.918872i \(0.370898\pi\)
\(8\) −7.34928 −2.59836
\(9\) −2.93252 −0.977507
\(10\) 10.6856 3.37907
\(11\) −4.54556 −1.37054 −0.685269 0.728290i \(-0.740315\pi\)
−0.685269 + 0.728290i \(0.740315\pi\)
\(12\) −1.25083 −0.361083
\(13\) −2.98042 −0.826619 −0.413309 0.910591i \(-0.635627\pi\)
−0.413309 + 0.910591i \(0.635627\pi\)
\(14\) −5.45038 −1.45668
\(15\) 1.06327 0.274536
\(16\) 9.55560 2.38890
\(17\) 4.39920 1.06696 0.533482 0.845812i \(-0.320883\pi\)
0.533482 + 0.845812i \(0.320883\pi\)
\(18\) 7.65561 1.80444
\(19\) −0.751344 −0.172370 −0.0861851 0.996279i \(-0.527468\pi\)
−0.0861851 + 0.996279i \(0.527468\pi\)
\(20\) −19.7093 −4.40714
\(21\) −0.542342 −0.118349
\(22\) 11.8666 2.52997
\(23\) −0.781648 −0.162985 −0.0814925 0.996674i \(-0.525969\pi\)
−0.0814925 + 0.996674i \(0.525969\pi\)
\(24\) 1.90911 0.389695
\(25\) 11.7540 2.35080
\(26\) 7.78065 1.52591
\(27\) 1.54108 0.296580
\(28\) 10.0531 1.89986
\(29\) −4.78053 −0.887723 −0.443861 0.896095i \(-0.646392\pi\)
−0.443861 + 0.896095i \(0.646392\pi\)
\(30\) −2.77577 −0.506783
\(31\) −3.90479 −0.701322 −0.350661 0.936502i \(-0.614043\pi\)
−0.350661 + 0.936502i \(0.614043\pi\)
\(32\) −10.2472 −1.81146
\(33\) 1.18079 0.205549
\(34\) −11.4845 −1.96958
\(35\) −8.54569 −1.44449
\(36\) −14.1206 −2.35344
\(37\) −6.77693 −1.11412 −0.557060 0.830472i \(-0.688071\pi\)
−0.557060 + 0.830472i \(0.688071\pi\)
\(38\) 1.96145 0.318190
\(39\) 0.774216 0.123974
\(40\) 30.0818 4.75635
\(41\) −11.6528 −1.81987 −0.909934 0.414753i \(-0.863868\pi\)
−0.909934 + 0.414753i \(0.863868\pi\)
\(42\) 1.41583 0.218468
\(43\) 0.552335 0.0842303 0.0421152 0.999113i \(-0.486590\pi\)
0.0421152 + 0.999113i \(0.486590\pi\)
\(44\) −21.8877 −3.29969
\(45\) 12.0033 1.78934
\(46\) 2.04056 0.300865
\(47\) −1.35892 −0.198218 −0.0991091 0.995077i \(-0.531599\pi\)
−0.0991091 + 0.995077i \(0.531599\pi\)
\(48\) −2.48224 −0.358280
\(49\) −2.64111 −0.377301
\(50\) −30.6848 −4.33949
\(51\) −1.14277 −0.160020
\(52\) −14.3512 −1.99016
\(53\) −8.71995 −1.19778 −0.598888 0.800833i \(-0.704391\pi\)
−0.598888 + 0.800833i \(0.704391\pi\)
\(54\) −4.02312 −0.547477
\(55\) 18.6057 2.50879
\(56\) −15.3438 −2.05040
\(57\) 0.195175 0.0258516
\(58\) 12.4800 1.63871
\(59\) −11.9100 −1.55055 −0.775275 0.631624i \(-0.782389\pi\)
−0.775275 + 0.631624i \(0.782389\pi\)
\(60\) 5.11984 0.660969
\(61\) −0.470997 −0.0603050 −0.0301525 0.999545i \(-0.509599\pi\)
−0.0301525 + 0.999545i \(0.509599\pi\)
\(62\) 10.1938 1.29462
\(63\) −6.12251 −0.771363
\(64\) 7.64001 0.955001
\(65\) 12.1993 1.51314
\(66\) −3.08256 −0.379436
\(67\) −8.34431 −1.01942 −0.509710 0.860346i \(-0.670247\pi\)
−0.509710 + 0.860346i \(0.670247\pi\)
\(68\) 21.1830 2.56881
\(69\) 0.203047 0.0244440
\(70\) 22.3093 2.66647
\(71\) 10.0343 1.19085 0.595423 0.803412i \(-0.296984\pi\)
0.595423 + 0.803412i \(0.296984\pi\)
\(72\) 21.5519 2.53992
\(73\) 7.49575 0.877311 0.438656 0.898655i \(-0.355455\pi\)
0.438656 + 0.898655i \(0.355455\pi\)
\(74\) 17.6918 2.05663
\(75\) −3.05331 −0.352565
\(76\) −3.61786 −0.414997
\(77\) −9.49020 −1.08151
\(78\) −2.02116 −0.228851
\(79\) −10.3980 −1.16987 −0.584936 0.811080i \(-0.698880\pi\)
−0.584936 + 0.811080i \(0.698880\pi\)
\(80\) −39.1126 −4.37293
\(81\) 8.39724 0.933027
\(82\) 30.4208 3.35941
\(83\) −13.4273 −1.47384 −0.736920 0.675980i \(-0.763721\pi\)
−0.736920 + 0.675980i \(0.763721\pi\)
\(84\) −2.61147 −0.284935
\(85\) −18.0067 −1.95310
\(86\) −1.44192 −0.155486
\(87\) 1.24183 0.133138
\(88\) 33.4066 3.56115
\(89\) 11.9262 1.26418 0.632088 0.774897i \(-0.282198\pi\)
0.632088 + 0.774897i \(0.282198\pi\)
\(90\) −31.3357 −3.30307
\(91\) −6.22250 −0.652295
\(92\) −3.76378 −0.392401
\(93\) 1.01434 0.105182
\(94\) 3.54757 0.365904
\(95\) 3.07538 0.315527
\(96\) 2.66189 0.271678
\(97\) −18.5687 −1.88537 −0.942683 0.333689i \(-0.891706\pi\)
−0.942683 + 0.333689i \(0.891706\pi\)
\(98\) 6.89485 0.696485
\(99\) 13.3299 1.33971
\(100\) 56.5976 5.65976
\(101\) −11.1905 −1.11350 −0.556749 0.830681i \(-0.687951\pi\)
−0.556749 + 0.830681i \(0.687951\pi\)
\(102\) 2.98331 0.295391
\(103\) 10.2361 1.00859 0.504296 0.863531i \(-0.331752\pi\)
0.504296 + 0.863531i \(0.331752\pi\)
\(104\) 21.9039 2.14786
\(105\) 2.21989 0.216639
\(106\) 22.7642 2.21105
\(107\) 3.78086 0.365509 0.182755 0.983159i \(-0.441499\pi\)
0.182755 + 0.983159i \(0.441499\pi\)
\(108\) 7.42056 0.714044
\(109\) −9.49382 −0.909343 −0.454671 0.890659i \(-0.650243\pi\)
−0.454671 + 0.890659i \(0.650243\pi\)
\(110\) −48.5719 −4.63115
\(111\) 1.76043 0.167092
\(112\) 19.9501 1.88511
\(113\) −5.83525 −0.548934 −0.274467 0.961597i \(-0.588501\pi\)
−0.274467 + 0.961597i \(0.588501\pi\)
\(114\) −0.509522 −0.0477211
\(115\) 3.19942 0.298347
\(116\) −23.0191 −2.13727
\(117\) 8.74013 0.808026
\(118\) 31.0921 2.86226
\(119\) 9.18464 0.841955
\(120\) −7.81428 −0.713343
\(121\) 9.66210 0.878373
\(122\) 1.22958 0.111321
\(123\) 3.02703 0.272938
\(124\) −18.8023 −1.68850
\(125\) −27.6452 −2.47266
\(126\) 15.9834 1.42391
\(127\) −8.99415 −0.798102 −0.399051 0.916929i \(-0.630660\pi\)
−0.399051 + 0.916929i \(0.630660\pi\)
\(128\) 0.549442 0.0485643
\(129\) −0.143479 −0.0126326
\(130\) −31.8475 −2.79321
\(131\) 7.48803 0.654233 0.327116 0.944984i \(-0.393923\pi\)
0.327116 + 0.944984i \(0.393923\pi\)
\(132\) 5.68571 0.494878
\(133\) −1.56865 −0.136020
\(134\) 21.7836 1.88181
\(135\) −6.30788 −0.542896
\(136\) −32.3310 −2.77236
\(137\) 1.45083 0.123953 0.0619764 0.998078i \(-0.480260\pi\)
0.0619764 + 0.998078i \(0.480260\pi\)
\(138\) −0.530072 −0.0451228
\(139\) −12.7844 −1.08436 −0.542179 0.840263i \(-0.682401\pi\)
−0.542179 + 0.840263i \(0.682401\pi\)
\(140\) −41.1490 −3.47773
\(141\) 0.353002 0.0297282
\(142\) −26.1953 −2.19826
\(143\) 13.5477 1.13291
\(144\) −28.0220 −2.33517
\(145\) 19.5675 1.62499
\(146\) −19.5683 −1.61949
\(147\) 0.686074 0.0565865
\(148\) −32.6321 −2.68235
\(149\) −0.904473 −0.0740973 −0.0370487 0.999313i \(-0.511796\pi\)
−0.0370487 + 0.999313i \(0.511796\pi\)
\(150\) 7.97093 0.650824
\(151\) 16.4418 1.33801 0.669007 0.743256i \(-0.266720\pi\)
0.669007 + 0.743256i \(0.266720\pi\)
\(152\) 5.52184 0.447880
\(153\) −12.9008 −1.04296
\(154\) 24.7750 1.99643
\(155\) 15.9830 1.28378
\(156\) 3.72799 0.298478
\(157\) −23.7994 −1.89940 −0.949701 0.313159i \(-0.898613\pi\)
−0.949701 + 0.313159i \(0.898613\pi\)
\(158\) 27.1450 2.15954
\(159\) 2.26516 0.179639
\(160\) 41.9434 3.31592
\(161\) −1.63192 −0.128614
\(162\) −21.9218 −1.72234
\(163\) −19.3108 −1.51254 −0.756271 0.654259i \(-0.772981\pi\)
−0.756271 + 0.654259i \(0.772981\pi\)
\(164\) −56.1105 −4.38150
\(165\) −4.83316 −0.376261
\(166\) 35.0532 2.72066
\(167\) 4.19358 0.324509 0.162254 0.986749i \(-0.448123\pi\)
0.162254 + 0.986749i \(0.448123\pi\)
\(168\) 3.98582 0.307513
\(169\) −4.11712 −0.316701
\(170\) 47.0080 3.60535
\(171\) 2.20333 0.168493
\(172\) 2.65959 0.202792
\(173\) 11.4519 0.870673 0.435336 0.900268i \(-0.356629\pi\)
0.435336 + 0.900268i \(0.356629\pi\)
\(174\) −3.24190 −0.245768
\(175\) 24.5399 1.85504
\(176\) −43.4355 −3.27408
\(177\) 3.09383 0.232547
\(178\) −31.1344 −2.33362
\(179\) 4.80326 0.359013 0.179506 0.983757i \(-0.442550\pi\)
0.179506 + 0.983757i \(0.442550\pi\)
\(180\) 57.7980 4.30801
\(181\) 20.4628 1.52098 0.760492 0.649347i \(-0.224958\pi\)
0.760492 + 0.649347i \(0.224958\pi\)
\(182\) 16.2444 1.20412
\(183\) 0.122350 0.00904435
\(184\) 5.74455 0.423494
\(185\) 27.7391 2.03942
\(186\) −2.64802 −0.194163
\(187\) −19.9968 −1.46231
\(188\) −6.54342 −0.477228
\(189\) 3.21745 0.234035
\(190\) −8.02855 −0.582452
\(191\) −6.12788 −0.443398 −0.221699 0.975115i \(-0.571160\pi\)
−0.221699 + 0.975115i \(0.571160\pi\)
\(192\) −1.98463 −0.143228
\(193\) −1.47115 −0.105896 −0.0529480 0.998597i \(-0.516862\pi\)
−0.0529480 + 0.998597i \(0.516862\pi\)
\(194\) 48.4753 3.48032
\(195\) −3.16899 −0.226936
\(196\) −12.7174 −0.908386
\(197\) −0.514119 −0.0366295 −0.0183147 0.999832i \(-0.505830\pi\)
−0.0183147 + 0.999832i \(0.505830\pi\)
\(198\) −34.7990 −2.47306
\(199\) 20.6196 1.46169 0.730844 0.682545i \(-0.239127\pi\)
0.730844 + 0.682545i \(0.239127\pi\)
\(200\) −86.3834 −6.10823
\(201\) 2.16758 0.152889
\(202\) 29.2138 2.05548
\(203\) −9.98078 −0.700513
\(204\) −5.50265 −0.385262
\(205\) 47.6970 3.33130
\(206\) −26.7223 −1.86183
\(207\) 2.29220 0.159319
\(208\) −28.4797 −1.97471
\(209\) 3.41528 0.236240
\(210\) −5.79523 −0.399909
\(211\) −0.169116 −0.0116424 −0.00582122 0.999983i \(-0.501853\pi\)
−0.00582122 + 0.999983i \(0.501853\pi\)
\(212\) −41.9881 −2.88376
\(213\) −2.60657 −0.178600
\(214\) −9.87027 −0.674718
\(215\) −2.26080 −0.154185
\(216\) −11.3258 −0.770624
\(217\) −8.15242 −0.553422
\(218\) 24.7845 1.67862
\(219\) −1.94715 −0.131576
\(220\) 89.5899 6.04015
\(221\) −13.1115 −0.881972
\(222\) −4.59575 −0.308447
\(223\) −3.78724 −0.253613 −0.126806 0.991928i \(-0.540473\pi\)
−0.126806 + 0.991928i \(0.540473\pi\)
\(224\) −21.3940 −1.42945
\(225\) −34.4688 −2.29792
\(226\) 15.2334 1.01331
\(227\) −14.0626 −0.933368 −0.466684 0.884424i \(-0.654552\pi\)
−0.466684 + 0.884424i \(0.654552\pi\)
\(228\) 0.939803 0.0622400
\(229\) −6.47850 −0.428111 −0.214056 0.976821i \(-0.568667\pi\)
−0.214056 + 0.976821i \(0.568667\pi\)
\(230\) −8.35236 −0.550738
\(231\) 2.46525 0.162201
\(232\) 35.1335 2.30663
\(233\) 8.11537 0.531655 0.265828 0.964021i \(-0.414355\pi\)
0.265828 + 0.964021i \(0.414355\pi\)
\(234\) −22.8169 −1.49159
\(235\) 5.56227 0.362842
\(236\) −57.3488 −3.73309
\(237\) 2.70108 0.175454
\(238\) −23.9773 −1.55422
\(239\) −24.2326 −1.56748 −0.783739 0.621091i \(-0.786690\pi\)
−0.783739 + 0.621091i \(0.786690\pi\)
\(240\) 10.1602 0.655838
\(241\) 12.3097 0.792937 0.396469 0.918048i \(-0.370236\pi\)
0.396469 + 0.918048i \(0.370236\pi\)
\(242\) −25.2238 −1.62145
\(243\) −6.80456 −0.436513
\(244\) −2.26793 −0.145190
\(245\) 10.8105 0.690657
\(246\) −7.90234 −0.503835
\(247\) 2.23932 0.142484
\(248\) 28.6974 1.82229
\(249\) 3.48798 0.221042
\(250\) 72.1703 4.56445
\(251\) −15.5663 −0.982537 −0.491269 0.871008i \(-0.663467\pi\)
−0.491269 + 0.871008i \(0.663467\pi\)
\(252\) −29.4810 −1.85713
\(253\) 3.55303 0.223377
\(254\) 23.4800 1.47327
\(255\) 4.67755 0.292919
\(256\) −16.7144 −1.04465
\(257\) 12.3264 0.768901 0.384450 0.923146i \(-0.374391\pi\)
0.384450 + 0.923146i \(0.374391\pi\)
\(258\) 0.374564 0.0233194
\(259\) −14.1488 −0.879167
\(260\) 58.7420 3.64302
\(261\) 14.0190 0.867755
\(262\) −19.5482 −1.20769
\(263\) −5.57478 −0.343756 −0.171878 0.985118i \(-0.554983\pi\)
−0.171878 + 0.985118i \(0.554983\pi\)
\(264\) −8.67795 −0.534091
\(265\) 35.6922 2.19255
\(266\) 4.09511 0.251087
\(267\) −3.09804 −0.189597
\(268\) −40.1794 −2.45434
\(269\) 24.8679 1.51622 0.758111 0.652126i \(-0.226123\pi\)
0.758111 + 0.652126i \(0.226123\pi\)
\(270\) 16.4673 1.00217
\(271\) −14.2423 −0.865161 −0.432580 0.901595i \(-0.642397\pi\)
−0.432580 + 0.901595i \(0.642397\pi\)
\(272\) 42.0370 2.54887
\(273\) 1.61640 0.0978293
\(274\) −3.78752 −0.228813
\(275\) −53.4285 −3.22186
\(276\) 0.977708 0.0588511
\(277\) 32.3841 1.94577 0.972887 0.231282i \(-0.0742921\pi\)
0.972887 + 0.231282i \(0.0742921\pi\)
\(278\) 33.3748 2.00169
\(279\) 11.4509 0.685547
\(280\) 62.8047 3.75330
\(281\) −5.35320 −0.319345 −0.159673 0.987170i \(-0.551044\pi\)
−0.159673 + 0.987170i \(0.551044\pi\)
\(282\) −0.921545 −0.0548772
\(283\) −4.26767 −0.253687 −0.126843 0.991923i \(-0.540485\pi\)
−0.126843 + 0.991923i \(0.540485\pi\)
\(284\) 48.3167 2.86707
\(285\) −0.798883 −0.0473218
\(286\) −35.3674 −2.09132
\(287\) −24.3288 −1.43608
\(288\) 30.0501 1.77072
\(289\) 2.35299 0.138411
\(290\) −51.0827 −2.99968
\(291\) 4.82355 0.282761
\(292\) 36.0934 2.11221
\(293\) 7.60370 0.444213 0.222107 0.975022i \(-0.428707\pi\)
0.222107 + 0.975022i \(0.428707\pi\)
\(294\) −1.79106 −0.104457
\(295\) 48.7496 2.83831
\(296\) 49.8056 2.89489
\(297\) −7.00506 −0.406475
\(298\) 2.36121 0.136781
\(299\) 2.32964 0.134726
\(300\) −14.7022 −0.848833
\(301\) 1.15316 0.0664672
\(302\) −42.9228 −2.46993
\(303\) 2.90693 0.166999
\(304\) −7.17955 −0.411775
\(305\) 1.92787 0.110389
\(306\) 33.6786 1.92528
\(307\) 6.82587 0.389573 0.194786 0.980846i \(-0.437599\pi\)
0.194786 + 0.980846i \(0.437599\pi\)
\(308\) −45.6970 −2.60383
\(309\) −2.65901 −0.151266
\(310\) −41.7250 −2.36982
\(311\) −22.8574 −1.29612 −0.648061 0.761588i \(-0.724420\pi\)
−0.648061 + 0.761588i \(0.724420\pi\)
\(312\) −5.68993 −0.322129
\(313\) −1.85118 −0.104635 −0.0523175 0.998631i \(-0.516661\pi\)
−0.0523175 + 0.998631i \(0.516661\pi\)
\(314\) 62.1306 3.50623
\(315\) 25.0604 1.41199
\(316\) −50.0685 −2.81657
\(317\) −20.6041 −1.15724 −0.578621 0.815597i \(-0.696409\pi\)
−0.578621 + 0.815597i \(0.696409\pi\)
\(318\) −5.91340 −0.331607
\(319\) 21.7302 1.21666
\(320\) −31.2718 −1.74815
\(321\) −0.982145 −0.0548180
\(322\) 4.26028 0.237416
\(323\) −3.30532 −0.183913
\(324\) 40.4342 2.24635
\(325\) −35.0318 −1.94321
\(326\) 50.4127 2.79210
\(327\) 2.46619 0.136380
\(328\) 85.6400 4.72868
\(329\) −2.83714 −0.156417
\(330\) 12.6174 0.694565
\(331\) −6.35867 −0.349504 −0.174752 0.984612i \(-0.555912\pi\)
−0.174752 + 0.984612i \(0.555912\pi\)
\(332\) −64.6550 −3.54840
\(333\) 19.8735 1.08906
\(334\) −10.9477 −0.599032
\(335\) 34.1546 1.86607
\(336\) −5.18240 −0.282723
\(337\) 7.40140 0.403180 0.201590 0.979470i \(-0.435389\pi\)
0.201590 + 0.979470i \(0.435389\pi\)
\(338\) 10.7481 0.584620
\(339\) 1.51581 0.0823274
\(340\) −86.7053 −4.70226
\(341\) 17.7495 0.961188
\(342\) −5.75200 −0.311033
\(343\) −20.1287 −1.08685
\(344\) −4.05927 −0.218861
\(345\) −0.831105 −0.0447452
\(346\) −29.8962 −1.60723
\(347\) 2.97440 0.159674 0.0798371 0.996808i \(-0.474560\pi\)
0.0798371 + 0.996808i \(0.474560\pi\)
\(348\) 5.97963 0.320542
\(349\) −0.315419 −0.0168840 −0.00844199 0.999964i \(-0.502687\pi\)
−0.00844199 + 0.999964i \(0.502687\pi\)
\(350\) −64.0637 −3.42435
\(351\) −4.59305 −0.245159
\(352\) 46.5792 2.48268
\(353\) −23.4323 −1.24717 −0.623587 0.781754i \(-0.714325\pi\)
−0.623587 + 0.781754i \(0.714325\pi\)
\(354\) −8.07673 −0.429273
\(355\) −41.0718 −2.17987
\(356\) 57.4268 3.04362
\(357\) −2.38587 −0.126274
\(358\) −12.5394 −0.662725
\(359\) 20.2783 1.07025 0.535124 0.844774i \(-0.320265\pi\)
0.535124 + 0.844774i \(0.320265\pi\)
\(360\) −88.2155 −4.64937
\(361\) −18.4355 −0.970289
\(362\) −53.4199 −2.80769
\(363\) −2.50990 −0.131736
\(364\) −29.9625 −1.57046
\(365\) −30.6813 −1.60593
\(366\) −0.319405 −0.0166956
\(367\) −36.3136 −1.89555 −0.947776 0.318936i \(-0.896675\pi\)
−0.947776 + 0.318936i \(0.896675\pi\)
\(368\) −7.46912 −0.389355
\(369\) 34.1722 1.77893
\(370\) −72.4154 −3.76470
\(371\) −18.2055 −0.945181
\(372\) 4.88423 0.253235
\(373\) 3.70281 0.191724 0.0958620 0.995395i \(-0.469439\pi\)
0.0958620 + 0.995395i \(0.469439\pi\)
\(374\) 52.2035 2.69938
\(375\) 7.18133 0.370842
\(376\) 9.98705 0.515043
\(377\) 14.2480 0.733808
\(378\) −8.39945 −0.432021
\(379\) 27.7795 1.42694 0.713468 0.700687i \(-0.247123\pi\)
0.713468 + 0.700687i \(0.247123\pi\)
\(380\) 14.8085 0.759659
\(381\) 2.33639 0.119697
\(382\) 15.9974 0.818497
\(383\) 31.5241 1.61081 0.805404 0.592726i \(-0.201948\pi\)
0.805404 + 0.592726i \(0.201948\pi\)
\(384\) −0.142727 −0.00728352
\(385\) 38.8449 1.97972
\(386\) 3.84058 0.195480
\(387\) −1.61973 −0.0823357
\(388\) −89.4117 −4.53919
\(389\) 23.2436 1.17850 0.589250 0.807951i \(-0.299423\pi\)
0.589250 + 0.807951i \(0.299423\pi\)
\(390\) 8.27294 0.418917
\(391\) −3.43863 −0.173899
\(392\) 19.4102 0.980365
\(393\) −1.94515 −0.0981198
\(394\) 1.34215 0.0676168
\(395\) 42.5609 2.14147
\(396\) 64.1861 3.22547
\(397\) −33.6923 −1.69097 −0.845484 0.534001i \(-0.820688\pi\)
−0.845484 + 0.534001i \(0.820688\pi\)
\(398\) −53.8294 −2.69823
\(399\) 0.407486 0.0203998
\(400\) 112.316 5.61582
\(401\) −19.3137 −0.964480 −0.482240 0.876039i \(-0.660177\pi\)
−0.482240 + 0.876039i \(0.660177\pi\)
\(402\) −5.65867 −0.282229
\(403\) 11.6379 0.579726
\(404\) −53.8843 −2.68085
\(405\) −34.3713 −1.70792
\(406\) 26.0557 1.29312
\(407\) 30.8049 1.52694
\(408\) 8.39854 0.415790
\(409\) 34.4975 1.70579 0.852896 0.522080i \(-0.174844\pi\)
0.852896 + 0.522080i \(0.174844\pi\)
\(410\) −124.517 −6.14947
\(411\) −0.376879 −0.0185901
\(412\) 49.2886 2.42828
\(413\) −24.8656 −1.22356
\(414\) −5.98400 −0.294097
\(415\) 54.9602 2.69789
\(416\) 30.5409 1.49739
\(417\) 3.32097 0.162629
\(418\) −8.91590 −0.436091
\(419\) 15.4010 0.752389 0.376194 0.926541i \(-0.377232\pi\)
0.376194 + 0.926541i \(0.377232\pi\)
\(420\) 10.6892 0.521579
\(421\) 40.2951 1.96386 0.981931 0.189241i \(-0.0606027\pi\)
0.981931 + 0.189241i \(0.0606027\pi\)
\(422\) 0.441493 0.0214916
\(423\) 3.98505 0.193760
\(424\) 64.0853 3.11226
\(425\) 51.7082 2.50822
\(426\) 6.80470 0.329689
\(427\) −0.983345 −0.0475874
\(428\) 18.2055 0.879997
\(429\) −3.51924 −0.169911
\(430\) 5.90202 0.284621
\(431\) 21.3448 1.02814 0.514072 0.857747i \(-0.328136\pi\)
0.514072 + 0.857747i \(0.328136\pi\)
\(432\) 14.7259 0.708501
\(433\) 19.7426 0.948770 0.474385 0.880317i \(-0.342670\pi\)
0.474385 + 0.880317i \(0.342670\pi\)
\(434\) 21.2826 1.02160
\(435\) −5.08301 −0.243711
\(436\) −45.7144 −2.18932
\(437\) 0.587287 0.0280938
\(438\) 5.08322 0.242886
\(439\) 20.9962 1.00209 0.501047 0.865420i \(-0.332948\pi\)
0.501047 + 0.865420i \(0.332948\pi\)
\(440\) −136.739 −6.51876
\(441\) 7.74510 0.368814
\(442\) 34.2286 1.62809
\(443\) 37.6209 1.78742 0.893711 0.448642i \(-0.148092\pi\)
0.893711 + 0.448642i \(0.148092\pi\)
\(444\) 8.47677 0.402290
\(445\) −48.8159 −2.31410
\(446\) 9.88694 0.468160
\(447\) 0.234953 0.0111129
\(448\) 15.9508 0.753604
\(449\) 17.4333 0.822727 0.411363 0.911471i \(-0.365053\pi\)
0.411363 + 0.911471i \(0.365053\pi\)
\(450\) 89.9840 4.24188
\(451\) 52.9687 2.49420
\(452\) −28.0978 −1.32161
\(453\) −4.27104 −0.200671
\(454\) 36.7117 1.72297
\(455\) 25.4697 1.19404
\(456\) −1.43440 −0.0671717
\(457\) 5.70445 0.266843 0.133421 0.991059i \(-0.457404\pi\)
0.133421 + 0.991059i \(0.457404\pi\)
\(458\) 16.9127 0.790278
\(459\) 6.77951 0.316440
\(460\) 15.4058 0.718297
\(461\) 41.5258 1.93405 0.967025 0.254682i \(-0.0819709\pi\)
0.967025 + 0.254682i \(0.0819709\pi\)
\(462\) −6.43575 −0.299418
\(463\) −11.1028 −0.515989 −0.257994 0.966146i \(-0.583062\pi\)
−0.257994 + 0.966146i \(0.583062\pi\)
\(464\) −45.6809 −2.12068
\(465\) −4.15186 −0.192538
\(466\) −21.1859 −0.981418
\(467\) −36.6735 −1.69705 −0.848524 0.529157i \(-0.822508\pi\)
−0.848524 + 0.529157i \(0.822508\pi\)
\(468\) 42.0853 1.94539
\(469\) −17.4212 −0.804437
\(470\) −14.5208 −0.669794
\(471\) 6.18232 0.284866
\(472\) 87.5299 4.02889
\(473\) −2.51067 −0.115441
\(474\) −7.05140 −0.323882
\(475\) −8.83130 −0.405208
\(476\) 44.2257 2.02708
\(477\) 25.5714 1.17083
\(478\) 63.2614 2.89351
\(479\) −22.7530 −1.03961 −0.519807 0.854284i \(-0.673996\pi\)
−0.519807 + 0.854284i \(0.673996\pi\)
\(480\) −10.8955 −0.497311
\(481\) 20.1981 0.920953
\(482\) −32.1356 −1.46374
\(483\) 0.423921 0.0192891
\(484\) 46.5248 2.11476
\(485\) 76.0047 3.45120
\(486\) 17.7639 0.805788
\(487\) −25.5086 −1.15590 −0.577952 0.816071i \(-0.696148\pi\)
−0.577952 + 0.816071i \(0.696148\pi\)
\(488\) 3.46149 0.156694
\(489\) 5.01633 0.226846
\(490\) −28.2217 −1.27493
\(491\) −12.1885 −0.550059 −0.275030 0.961436i \(-0.588688\pi\)
−0.275030 + 0.961436i \(0.588688\pi\)
\(492\) 14.5757 0.657123
\(493\) −21.0305 −0.947168
\(494\) −5.84594 −0.263021
\(495\) −54.5616 −2.45236
\(496\) −37.3127 −1.67539
\(497\) 20.9495 0.939712
\(498\) −9.10570 −0.408036
\(499\) 35.7400 1.59994 0.799970 0.600039i \(-0.204848\pi\)
0.799970 + 0.600039i \(0.204848\pi\)
\(500\) −133.117 −5.95315
\(501\) −1.08936 −0.0486688
\(502\) 40.6373 1.81373
\(503\) −5.33213 −0.237748 −0.118874 0.992909i \(-0.537928\pi\)
−0.118874 + 0.992909i \(0.537928\pi\)
\(504\) 44.9960 2.00428
\(505\) 45.8046 2.03828
\(506\) −9.27550 −0.412346
\(507\) 1.06949 0.0474979
\(508\) −43.3085 −1.92150
\(509\) 8.18131 0.362630 0.181315 0.983425i \(-0.441965\pi\)
0.181315 + 0.983425i \(0.441965\pi\)
\(510\) −12.2112 −0.540719
\(511\) 15.6496 0.692297
\(512\) 42.5355 1.87982
\(513\) −1.15788 −0.0511216
\(514\) −32.1792 −1.41936
\(515\) −41.8980 −1.84625
\(516\) −0.690876 −0.0304141
\(517\) 6.17703 0.271666
\(518\) 36.9368 1.62291
\(519\) −2.97484 −0.130581
\(520\) −89.6563 −3.93169
\(521\) −10.1797 −0.445979 −0.222990 0.974821i \(-0.571582\pi\)
−0.222990 + 0.974821i \(0.571582\pi\)
\(522\) −36.5979 −1.60185
\(523\) 4.14289 0.181156 0.0905780 0.995889i \(-0.471129\pi\)
0.0905780 + 0.995889i \(0.471129\pi\)
\(524\) 36.0562 1.57512
\(525\) −6.37468 −0.278214
\(526\) 14.5535 0.634562
\(527\) −17.1780 −0.748285
\(528\) 11.2831 0.491036
\(529\) −22.3890 −0.973436
\(530\) −93.1776 −4.04738
\(531\) 34.9263 1.51567
\(532\) −7.55335 −0.327479
\(533\) 34.7303 1.50434
\(534\) 8.08772 0.349990
\(535\) −15.4757 −0.669072
\(536\) 61.3247 2.64882
\(537\) −1.24773 −0.0538436
\(538\) −64.9198 −2.79889
\(539\) 12.0053 0.517105
\(540\) −30.3736 −1.30707
\(541\) 43.9279 1.88861 0.944303 0.329077i \(-0.106738\pi\)
0.944303 + 0.329077i \(0.106738\pi\)
\(542\) 37.1809 1.59706
\(543\) −5.31556 −0.228113
\(544\) −45.0795 −1.93277
\(545\) 38.8597 1.66457
\(546\) −4.21977 −0.180589
\(547\) 1.21345 0.0518835 0.0259418 0.999663i \(-0.491742\pi\)
0.0259418 + 0.999663i \(0.491742\pi\)
\(548\) 6.98601 0.298427
\(549\) 1.38121 0.0589485
\(550\) 139.480 5.94744
\(551\) 3.59183 0.153017
\(552\) −1.49225 −0.0635143
\(553\) −21.7090 −0.923160
\(554\) −84.5417 −3.59183
\(555\) −7.20572 −0.305866
\(556\) −61.5592 −2.61069
\(557\) 4.58400 0.194230 0.0971152 0.995273i \(-0.469038\pi\)
0.0971152 + 0.995273i \(0.469038\pi\)
\(558\) −29.8936 −1.26550
\(559\) −1.64619 −0.0696264
\(560\) −81.6592 −3.45073
\(561\) 5.19453 0.219313
\(562\) 13.9750 0.589500
\(563\) 10.8044 0.455351 0.227675 0.973737i \(-0.426888\pi\)
0.227675 + 0.973737i \(0.426888\pi\)
\(564\) 1.69977 0.0715732
\(565\) 23.8846 1.00483
\(566\) 11.1411 0.468297
\(567\) 17.5317 0.736263
\(568\) −73.7445 −3.09425
\(569\) −10.1723 −0.426444 −0.213222 0.977004i \(-0.568396\pi\)
−0.213222 + 0.977004i \(0.568396\pi\)
\(570\) 2.08556 0.0873543
\(571\) 14.4371 0.604172 0.302086 0.953281i \(-0.402317\pi\)
0.302086 + 0.953281i \(0.402317\pi\)
\(572\) 65.2344 2.72759
\(573\) 1.59182 0.0664994
\(574\) 63.5124 2.65096
\(575\) −9.18749 −0.383145
\(576\) −22.4045 −0.933520
\(577\) −6.36585 −0.265014 −0.132507 0.991182i \(-0.542303\pi\)
−0.132507 + 0.991182i \(0.542303\pi\)
\(578\) −6.14269 −0.255502
\(579\) 0.382158 0.0158820
\(580\) 94.2211 3.91232
\(581\) −28.0335 −1.16303
\(582\) −12.5923 −0.521968
\(583\) 39.6370 1.64160
\(584\) −55.0884 −2.27957
\(585\) −35.7748 −1.47911
\(586\) −19.8502 −0.820002
\(587\) 27.5890 1.13872 0.569361 0.822088i \(-0.307191\pi\)
0.569361 + 0.822088i \(0.307191\pi\)
\(588\) 3.30357 0.136237
\(589\) 2.93385 0.120887
\(590\) −127.265 −5.23942
\(591\) 0.133552 0.00549358
\(592\) −64.7576 −2.66152
\(593\) 7.29011 0.299369 0.149684 0.988734i \(-0.452174\pi\)
0.149684 + 0.988734i \(0.452174\pi\)
\(594\) 18.2873 0.750338
\(595\) −37.5942 −1.54121
\(596\) −4.35520 −0.178396
\(597\) −5.35632 −0.219219
\(598\) −6.08173 −0.248700
\(599\) 4.71237 0.192542 0.0962712 0.995355i \(-0.469308\pi\)
0.0962712 + 0.995355i \(0.469308\pi\)
\(600\) 22.4396 0.916093
\(601\) −39.4421 −1.60888 −0.804439 0.594035i \(-0.797534\pi\)
−0.804439 + 0.594035i \(0.797534\pi\)
\(602\) −3.01044 −0.122696
\(603\) 24.4699 0.996490
\(604\) 79.1701 3.22139
\(605\) −39.5486 −1.60788
\(606\) −7.58881 −0.308274
\(607\) −3.10118 −0.125873 −0.0629364 0.998018i \(-0.520047\pi\)
−0.0629364 + 0.998018i \(0.520047\pi\)
\(608\) 7.69917 0.312243
\(609\) 2.59268 0.105061
\(610\) −5.03287 −0.203775
\(611\) 4.05014 0.163851
\(612\) −62.1195 −2.51103
\(613\) −4.68215 −0.189110 −0.0945552 0.995520i \(-0.530143\pi\)
−0.0945552 + 0.995520i \(0.530143\pi\)
\(614\) −17.8195 −0.719138
\(615\) −12.3901 −0.499618
\(616\) 69.7461 2.81015
\(617\) −11.6286 −0.468150 −0.234075 0.972219i \(-0.575206\pi\)
−0.234075 + 0.972219i \(0.575206\pi\)
\(618\) 6.94158 0.279231
\(619\) −24.8642 −0.999377 −0.499689 0.866205i \(-0.666552\pi\)
−0.499689 + 0.866205i \(0.666552\pi\)
\(620\) 76.9609 3.09082
\(621\) −1.20458 −0.0483381
\(622\) 59.6712 2.39260
\(623\) 24.8995 0.997577
\(624\) 7.39810 0.296161
\(625\) 54.3863 2.17545
\(626\) 4.83268 0.193153
\(627\) −0.887179 −0.0354305
\(628\) −114.599 −4.57298
\(629\) −29.8131 −1.18873
\(630\) −65.4225 −2.60649
\(631\) −43.7745 −1.74264 −0.871318 0.490719i \(-0.836734\pi\)
−0.871318 + 0.490719i \(0.836734\pi\)
\(632\) 76.4181 3.03975
\(633\) 0.0439310 0.00174610
\(634\) 53.7889 2.13623
\(635\) 36.8145 1.46094
\(636\) 10.9072 0.432497
\(637\) 7.87160 0.311884
\(638\) −56.7286 −2.24591
\(639\) −29.4257 −1.16406
\(640\) −2.24896 −0.0888978
\(641\) −32.1088 −1.26822 −0.634111 0.773242i \(-0.718634\pi\)
−0.634111 + 0.773242i \(0.718634\pi\)
\(642\) 2.56398 0.101192
\(643\) −36.6281 −1.44447 −0.722235 0.691648i \(-0.756885\pi\)
−0.722235 + 0.691648i \(0.756885\pi\)
\(644\) −7.85800 −0.309649
\(645\) 0.587282 0.0231242
\(646\) 8.62883 0.339497
\(647\) −26.4551 −1.04006 −0.520028 0.854149i \(-0.674079\pi\)
−0.520028 + 0.854149i \(0.674079\pi\)
\(648\) −61.7137 −2.42434
\(649\) 54.1376 2.12509
\(650\) 91.4536 3.58711
\(651\) 2.11773 0.0830005
\(652\) −92.9852 −3.64158
\(653\) 40.1265 1.57027 0.785136 0.619324i \(-0.212593\pi\)
0.785136 + 0.619324i \(0.212593\pi\)
\(654\) −6.43820 −0.251754
\(655\) −30.6497 −1.19758
\(656\) −111.350 −4.34748
\(657\) −21.9814 −0.857578
\(658\) 7.40661 0.288740
\(659\) −28.2317 −1.09975 −0.549876 0.835246i \(-0.685325\pi\)
−0.549876 + 0.835246i \(0.685325\pi\)
\(660\) −23.2726 −0.905883
\(661\) 0.299228 0.0116386 0.00581931 0.999983i \(-0.498148\pi\)
0.00581931 + 0.999983i \(0.498148\pi\)
\(662\) 16.5999 0.645173
\(663\) 3.40593 0.132275
\(664\) 98.6812 3.82957
\(665\) 6.42076 0.248986
\(666\) −51.8815 −2.01037
\(667\) 3.73670 0.144685
\(668\) 20.1928 0.781284
\(669\) 0.983803 0.0380360
\(670\) −89.1637 −3.44470
\(671\) 2.14094 0.0826502
\(672\) 5.55748 0.214384
\(673\) −1.75600 −0.0676889 −0.0338445 0.999427i \(-0.510775\pi\)
−0.0338445 + 0.999427i \(0.510775\pi\)
\(674\) −19.3220 −0.744256
\(675\) 18.1138 0.697201
\(676\) −19.8247 −0.762487
\(677\) 7.46432 0.286877 0.143439 0.989659i \(-0.454184\pi\)
0.143439 + 0.989659i \(0.454184\pi\)
\(678\) −3.95715 −0.151974
\(679\) −38.7677 −1.48777
\(680\) 132.336 5.07485
\(681\) 3.65301 0.139984
\(682\) −46.3366 −1.77432
\(683\) 20.7657 0.794577 0.397288 0.917694i \(-0.369951\pi\)
0.397288 + 0.917694i \(0.369951\pi\)
\(684\) 10.6094 0.405662
\(685\) −5.93848 −0.226898
\(686\) 52.5477 2.00628
\(687\) 1.68290 0.0642068
\(688\) 5.27789 0.201218
\(689\) 25.9891 0.990105
\(690\) 2.16967 0.0825980
\(691\) 27.7378 1.05520 0.527598 0.849494i \(-0.323093\pi\)
0.527598 + 0.849494i \(0.323093\pi\)
\(692\) 55.1430 2.09622
\(693\) 27.8302 1.05718
\(694\) −7.76494 −0.294753
\(695\) 52.3286 1.98494
\(696\) −9.12654 −0.345941
\(697\) −51.2632 −1.94173
\(698\) 0.823429 0.0311672
\(699\) −2.10811 −0.0797360
\(700\) 118.164 4.46619
\(701\) 12.9063 0.487466 0.243733 0.969842i \(-0.421628\pi\)
0.243733 + 0.969842i \(0.421628\pi\)
\(702\) 11.9906 0.452555
\(703\) 5.09181 0.192041
\(704\) −34.7281 −1.30887
\(705\) −1.44490 −0.0544180
\(706\) 61.1721 2.30224
\(707\) −23.3635 −0.878675
\(708\) 14.8974 0.559877
\(709\) −16.2486 −0.610228 −0.305114 0.952316i \(-0.598695\pi\)
−0.305114 + 0.952316i \(0.598695\pi\)
\(710\) 107.222 4.02396
\(711\) 30.4925 1.14356
\(712\) −87.6490 −3.28479
\(713\) 3.05218 0.114305
\(714\) 6.22853 0.233097
\(715\) −55.4528 −2.07382
\(716\) 23.1286 0.864356
\(717\) 6.29485 0.235085
\(718\) −52.9383 −1.97564
\(719\) 33.5096 1.24970 0.624849 0.780745i \(-0.285160\pi\)
0.624849 + 0.780745i \(0.285160\pi\)
\(720\) 114.699 4.27456
\(721\) 21.3709 0.795893
\(722\) 48.1275 1.79112
\(723\) −3.19766 −0.118922
\(724\) 98.5318 3.66191
\(725\) −56.1904 −2.08686
\(726\) 6.55232 0.243180
\(727\) −25.6974 −0.953065 −0.476532 0.879157i \(-0.658107\pi\)
−0.476532 + 0.879157i \(0.658107\pi\)
\(728\) 45.7309 1.69490
\(729\) −23.4241 −0.867560
\(730\) 80.0964 2.96450
\(731\) 2.42983 0.0898707
\(732\) 0.589136 0.0217751
\(733\) −2.69767 −0.0996407 −0.0498203 0.998758i \(-0.515865\pi\)
−0.0498203 + 0.998758i \(0.515865\pi\)
\(734\) 94.7998 3.49913
\(735\) −2.80821 −0.103583
\(736\) 8.00970 0.295241
\(737\) 37.9296 1.39715
\(738\) −89.2096 −3.28385
\(739\) 6.64878 0.244579 0.122290 0.992494i \(-0.460976\pi\)
0.122290 + 0.992494i \(0.460976\pi\)
\(740\) 133.569 4.91008
\(741\) −0.581703 −0.0213694
\(742\) 47.5270 1.74477
\(743\) −26.3333 −0.966074 −0.483037 0.875600i \(-0.660466\pi\)
−0.483037 + 0.875600i \(0.660466\pi\)
\(744\) −7.45467 −0.273301
\(745\) 3.70216 0.135637
\(746\) −9.66651 −0.353916
\(747\) 39.3759 1.44069
\(748\) −96.2884 −3.52065
\(749\) 7.89366 0.288428
\(750\) −18.7475 −0.684562
\(751\) −32.0977 −1.17126 −0.585630 0.810578i \(-0.699153\pi\)
−0.585630 + 0.810578i \(0.699153\pi\)
\(752\) −12.9853 −0.473524
\(753\) 4.04362 0.147358
\(754\) −37.1956 −1.35459
\(755\) −67.2989 −2.44926
\(756\) 15.4926 0.563461
\(757\) 35.0330 1.27330 0.636648 0.771155i \(-0.280320\pi\)
0.636648 + 0.771155i \(0.280320\pi\)
\(758\) −72.5209 −2.63408
\(759\) −0.922962 −0.0335014
\(760\) −22.6018 −0.819853
\(761\) −29.3804 −1.06504 −0.532520 0.846417i \(-0.678755\pi\)
−0.532520 + 0.846417i \(0.678755\pi\)
\(762\) −6.09935 −0.220956
\(763\) −19.8212 −0.717574
\(764\) −29.5068 −1.06752
\(765\) 52.8049 1.90917
\(766\) −82.2966 −2.97350
\(767\) 35.4968 1.28171
\(768\) 4.34186 0.156673
\(769\) 9.96773 0.359446 0.179723 0.983717i \(-0.442480\pi\)
0.179723 + 0.983717i \(0.442480\pi\)
\(770\) −101.408 −3.65450
\(771\) −3.20200 −0.115317
\(772\) −7.08387 −0.254954
\(773\) −17.4115 −0.626249 −0.313124 0.949712i \(-0.601376\pi\)
−0.313124 + 0.949712i \(0.601376\pi\)
\(774\) 4.22846 0.151989
\(775\) −45.8969 −1.64867
\(776\) 136.467 4.89887
\(777\) 3.67541 0.131855
\(778\) −60.6796 −2.17547
\(779\) 8.75530 0.313691
\(780\) −15.2593 −0.546369
\(781\) −45.6113 −1.63210
\(782\) 8.97685 0.321012
\(783\) −7.36717 −0.263281
\(784\) −25.2374 −0.901334
\(785\) 97.4150 3.47689
\(786\) 5.07799 0.181126
\(787\) 36.6531 1.30654 0.653271 0.757124i \(-0.273396\pi\)
0.653271 + 0.757124i \(0.273396\pi\)
\(788\) −2.47558 −0.0881888
\(789\) 1.44815 0.0515554
\(790\) −111.109 −3.95308
\(791\) −12.1828 −0.433171
\(792\) −97.9655 −3.48105
\(793\) 1.40377 0.0498492
\(794\) 87.9568 3.12147
\(795\) −9.27167 −0.328832
\(796\) 99.2873 3.51915
\(797\) −2.56965 −0.0910217 −0.0455108 0.998964i \(-0.514492\pi\)
−0.0455108 + 0.998964i \(0.514492\pi\)
\(798\) −1.06378 −0.0376573
\(799\) −5.97815 −0.211492
\(800\) −120.445 −4.25839
\(801\) −34.9738 −1.23574
\(802\) 50.4201 1.78040
\(803\) −34.0724 −1.20239
\(804\) 10.4373 0.368095
\(805\) 6.67973 0.235429
\(806\) −30.3818 −1.07015
\(807\) −6.45987 −0.227398
\(808\) 82.2422 2.89327
\(809\) −27.1561 −0.954758 −0.477379 0.878698i \(-0.658413\pi\)
−0.477379 + 0.878698i \(0.658413\pi\)
\(810\) 89.7293 3.15277
\(811\) 17.6456 0.619621 0.309810 0.950798i \(-0.399734\pi\)
0.309810 + 0.950798i \(0.399734\pi\)
\(812\) −48.0593 −1.68655
\(813\) 3.69970 0.129754
\(814\) −80.4190 −2.81869
\(815\) 79.0424 2.76874
\(816\) −10.9199 −0.382271
\(817\) −0.414994 −0.0145188
\(818\) −90.0589 −3.14884
\(819\) 18.2476 0.637623
\(820\) 229.670 8.02041
\(821\) 16.6200 0.580042 0.290021 0.957020i \(-0.406338\pi\)
0.290021 + 0.957020i \(0.406338\pi\)
\(822\) 0.983876 0.0343166
\(823\) 19.9273 0.694622 0.347311 0.937750i \(-0.387095\pi\)
0.347311 + 0.937750i \(0.387095\pi\)
\(824\) −75.2280 −2.62069
\(825\) 13.8790 0.483204
\(826\) 64.9140 2.25865
\(827\) −26.3134 −0.915006 −0.457503 0.889208i \(-0.651256\pi\)
−0.457503 + 0.889208i \(0.651256\pi\)
\(828\) 11.0374 0.383575
\(829\) 37.8647 1.31510 0.657548 0.753413i \(-0.271594\pi\)
0.657548 + 0.753413i \(0.271594\pi\)
\(830\) −143.479 −4.98022
\(831\) −8.41235 −0.291821
\(832\) −22.7704 −0.789422
\(833\) −11.6188 −0.402566
\(834\) −8.66970 −0.300207
\(835\) −17.1650 −0.594019
\(836\) 16.4452 0.568769
\(837\) −6.01759 −0.207998
\(838\) −40.2057 −1.38888
\(839\) −40.8660 −1.41085 −0.705425 0.708785i \(-0.749244\pi\)
−0.705425 + 0.708785i \(0.749244\pi\)
\(840\) −16.3146 −0.562908
\(841\) −6.14649 −0.211948
\(842\) −105.194 −3.62522
\(843\) 1.39059 0.0478944
\(844\) −0.814326 −0.0280302
\(845\) 16.8520 0.579728
\(846\) −10.4033 −0.357674
\(847\) 20.1725 0.693135
\(848\) −83.3243 −2.86137
\(849\) 1.10860 0.0380471
\(850\) −134.989 −4.63008
\(851\) 5.29718 0.181585
\(852\) −12.5511 −0.429994
\(853\) −9.64903 −0.330376 −0.165188 0.986262i \(-0.552823\pi\)
−0.165188 + 0.986262i \(0.552823\pi\)
\(854\) 2.56711 0.0878447
\(855\) −9.01860 −0.308430
\(856\) −27.7866 −0.949726
\(857\) 21.3960 0.730873 0.365437 0.930836i \(-0.380920\pi\)
0.365437 + 0.930836i \(0.380920\pi\)
\(858\) 9.18730 0.313649
\(859\) −30.2944 −1.03363 −0.516815 0.856097i \(-0.672882\pi\)
−0.516815 + 0.856097i \(0.672882\pi\)
\(860\) −10.8862 −0.371215
\(861\) 6.31982 0.215379
\(862\) −55.7226 −1.89792
\(863\) 30.0519 1.02298 0.511489 0.859290i \(-0.329094\pi\)
0.511489 + 0.859290i \(0.329094\pi\)
\(864\) −15.7917 −0.537245
\(865\) −46.8745 −1.59378
\(866\) −51.5399 −1.75140
\(867\) −0.611230 −0.0207585
\(868\) −39.2553 −1.33241
\(869\) 47.2649 1.60335
\(870\) 13.2696 0.449883
\(871\) 24.8695 0.842672
\(872\) 69.7727 2.36280
\(873\) 54.4531 1.84296
\(874\) −1.53317 −0.0518601
\(875\) −57.7175 −1.95121
\(876\) −9.37589 −0.316782
\(877\) −26.0876 −0.880916 −0.440458 0.897773i \(-0.645184\pi\)
−0.440458 + 0.897773i \(0.645184\pi\)
\(878\) −54.8125 −1.84983
\(879\) −1.97520 −0.0666217
\(880\) 177.789 5.99326
\(881\) 34.4083 1.15925 0.579623 0.814885i \(-0.303200\pi\)
0.579623 + 0.814885i \(0.303200\pi\)
\(882\) −20.2193 −0.680819
\(883\) −40.6746 −1.36881 −0.684405 0.729102i \(-0.739938\pi\)
−0.684405 + 0.729102i \(0.739938\pi\)
\(884\) −63.1340 −2.12343
\(885\) −12.6636 −0.425681
\(886\) −98.2127 −3.29952
\(887\) −40.9423 −1.37471 −0.687354 0.726322i \(-0.741228\pi\)
−0.687354 + 0.726322i \(0.741228\pi\)
\(888\) −12.9379 −0.434167
\(889\) −18.7780 −0.629792
\(890\) 127.438 4.27174
\(891\) −38.1701 −1.27875
\(892\) −18.2363 −0.610595
\(893\) 1.02101 0.0341669
\(894\) −0.613366 −0.0205140
\(895\) −19.6605 −0.657180
\(896\) 1.14712 0.0383227
\(897\) −0.605165 −0.0202059
\(898\) −45.5111 −1.51873
\(899\) 18.6670 0.622579
\(900\) −165.974 −5.53245
\(901\) −38.3608 −1.27798
\(902\) −138.279 −4.60420
\(903\) −0.299554 −0.00996855
\(904\) 42.8849 1.42633
\(905\) −83.7574 −2.78419
\(906\) 11.1499 0.370432
\(907\) −52.5203 −1.74391 −0.871953 0.489589i \(-0.837147\pi\)
−0.871953 + 0.489589i \(0.837147\pi\)
\(908\) −67.7140 −2.24717
\(909\) 32.8164 1.08845
\(910\) −66.4910 −2.20416
\(911\) 18.6592 0.618206 0.309103 0.951029i \(-0.399971\pi\)
0.309103 + 0.951029i \(0.399971\pi\)
\(912\) 1.86501 0.0617568
\(913\) 61.0347 2.01995
\(914\) −14.8920 −0.492583
\(915\) −0.500798 −0.0165559
\(916\) −31.1951 −1.03072
\(917\) 15.6335 0.516263
\(918\) −17.6985 −0.584138
\(919\) −18.8814 −0.622840 −0.311420 0.950272i \(-0.600805\pi\)
−0.311420 + 0.950272i \(0.600805\pi\)
\(920\) −23.5134 −0.775214
\(921\) −1.77314 −0.0584269
\(922\) −108.407 −3.57019
\(923\) −29.9063 −0.984376
\(924\) 11.8706 0.390514
\(925\) −79.6560 −2.61907
\(926\) 28.9848 0.952498
\(927\) −30.0176 −0.985906
\(928\) 48.9870 1.60808
\(929\) −6.17839 −0.202706 −0.101353 0.994851i \(-0.532317\pi\)
−0.101353 + 0.994851i \(0.532317\pi\)
\(930\) 10.8388 0.355418
\(931\) 1.98438 0.0650355
\(932\) 39.0769 1.28001
\(933\) 5.93761 0.194388
\(934\) 95.7395 3.13269
\(935\) 81.8503 2.67679
\(936\) −64.2337 −2.09954
\(937\) 7.14764 0.233503 0.116752 0.993161i \(-0.462752\pi\)
0.116752 + 0.993161i \(0.462752\pi\)
\(938\) 45.4797 1.48496
\(939\) 0.480877 0.0156928
\(940\) 26.7833 0.873575
\(941\) −31.8887 −1.03954 −0.519770 0.854306i \(-0.673982\pi\)
−0.519770 + 0.854306i \(0.673982\pi\)
\(942\) −16.1395 −0.525854
\(943\) 9.10843 0.296611
\(944\) −113.807 −3.70411
\(945\) −13.1696 −0.428406
\(946\) 6.55433 0.213100
\(947\) 21.9422 0.713027 0.356513 0.934290i \(-0.383965\pi\)
0.356513 + 0.934290i \(0.383965\pi\)
\(948\) 13.0062 0.422421
\(949\) −22.3405 −0.725202
\(950\) 23.0549 0.747999
\(951\) 5.35228 0.173560
\(952\) −67.5005 −2.18770
\(953\) −46.7805 −1.51537 −0.757684 0.652621i \(-0.773669\pi\)
−0.757684 + 0.652621i \(0.773669\pi\)
\(954\) −66.7565 −2.16132
\(955\) 25.0824 0.811648
\(956\) −116.684 −3.77384
\(957\) −5.64480 −0.182471
\(958\) 59.3989 1.91909
\(959\) 3.02904 0.0978127
\(960\) 8.12341 0.262182
\(961\) −15.7526 −0.508148
\(962\) −52.7289 −1.70005
\(963\) −11.0874 −0.357288
\(964\) 59.2734 1.90907
\(965\) 6.02167 0.193845
\(966\) −1.10668 −0.0356069
\(967\) 27.2626 0.876706 0.438353 0.898803i \(-0.355562\pi\)
0.438353 + 0.898803i \(0.355562\pi\)
\(968\) −71.0095 −2.28233
\(969\) 0.858614 0.0275827
\(970\) −198.417 −6.37079
\(971\) 30.5592 0.980692 0.490346 0.871528i \(-0.336870\pi\)
0.490346 + 0.871528i \(0.336870\pi\)
\(972\) −32.7652 −1.05094
\(973\) −26.6912 −0.855681
\(974\) 66.5924 2.13376
\(975\) 9.10013 0.291437
\(976\) −4.50066 −0.144063
\(977\) 31.6056 1.01115 0.505576 0.862782i \(-0.331280\pi\)
0.505576 + 0.862782i \(0.331280\pi\)
\(978\) −13.0956 −0.418751
\(979\) −54.2113 −1.73260
\(980\) 52.0544 1.66282
\(981\) 27.8408 0.888889
\(982\) 31.8192 1.01539
\(983\) 2.31068 0.0736993 0.0368496 0.999321i \(-0.488268\pi\)
0.0368496 + 0.999321i \(0.488268\pi\)
\(984\) −22.2465 −0.709193
\(985\) 2.10437 0.0670509
\(986\) 54.9021 1.74844
\(987\) 0.736997 0.0234589
\(988\) 10.7827 0.343044
\(989\) −0.431732 −0.0137283
\(990\) 142.438 4.52698
\(991\) 53.3558 1.69490 0.847451 0.530873i \(-0.178136\pi\)
0.847451 + 0.530873i \(0.178136\pi\)
\(992\) 40.0132 1.27042
\(993\) 1.65178 0.0524176
\(994\) −54.6905 −1.73468
\(995\) −84.3996 −2.67565
\(996\) 16.7953 0.532178
\(997\) −6.96753 −0.220664 −0.110332 0.993895i \(-0.535191\pi\)
−0.110332 + 0.993895i \(0.535191\pi\)
\(998\) −93.3024 −2.95344
\(999\) −10.4438 −0.330426
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.1.14 184
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4001.2.a.b.1.14 184 1.1 even 1 trivial