Properties

Label 4031.2.a.e.1.5
Level $4031$
Weight $2$
Character 4031.1
Self dual yes
Analytic conductor $32.188$
Analytic rank $0$
Dimension $103$
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] = [4031,2,Mod(1,4031)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4031, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4031.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4031 = 29 \cdot 139 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4031.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(32.1876970548\)
Analytic rank: \(0\)
Dimension: \(103\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) \(=\) 4031.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.68510 q^{2} -0.634380 q^{3} +5.20976 q^{4} +1.13239 q^{5} +1.70337 q^{6} +4.26000 q^{7} -8.61852 q^{8} -2.59756 q^{9} +O(q^{10})\) \(q-2.68510 q^{2} -0.634380 q^{3} +5.20976 q^{4} +1.13239 q^{5} +1.70337 q^{6} +4.26000 q^{7} -8.61852 q^{8} -2.59756 q^{9} -3.04058 q^{10} -6.04290 q^{11} -3.30497 q^{12} +5.71769 q^{13} -11.4385 q^{14} -0.718365 q^{15} +12.7221 q^{16} +3.90610 q^{17} +6.97471 q^{18} -0.321001 q^{19} +5.89947 q^{20} -2.70246 q^{21} +16.2258 q^{22} +0.470194 q^{23} +5.46742 q^{24} -3.71770 q^{25} -15.3526 q^{26} +3.55098 q^{27} +22.1936 q^{28} -1.00000 q^{29} +1.92888 q^{30} -10.0857 q^{31} -16.9229 q^{32} +3.83350 q^{33} -10.4883 q^{34} +4.82398 q^{35} -13.5327 q^{36} +8.59551 q^{37} +0.861921 q^{38} -3.62719 q^{39} -9.75951 q^{40} -4.43703 q^{41} +7.25638 q^{42} -3.34993 q^{43} -31.4821 q^{44} -2.94145 q^{45} -1.26252 q^{46} -1.52974 q^{47} -8.07062 q^{48} +11.1476 q^{49} +9.98238 q^{50} -2.47795 q^{51} +29.7878 q^{52} +7.29192 q^{53} -9.53474 q^{54} -6.84291 q^{55} -36.7149 q^{56} +0.203637 q^{57} +2.68510 q^{58} +7.45661 q^{59} -3.74251 q^{60} -4.27509 q^{61} +27.0812 q^{62} -11.0656 q^{63} +19.9957 q^{64} +6.47465 q^{65} -10.2933 q^{66} +8.21626 q^{67} +20.3498 q^{68} -0.298282 q^{69} -12.9529 q^{70} -12.4356 q^{71} +22.3871 q^{72} +1.46047 q^{73} -23.0798 q^{74} +2.35843 q^{75} -1.67234 q^{76} -25.7428 q^{77} +9.73936 q^{78} +17.3013 q^{79} +14.4063 q^{80} +5.54001 q^{81} +11.9139 q^{82} +5.68429 q^{83} -14.0792 q^{84} +4.42322 q^{85} +8.99489 q^{86} +0.634380 q^{87} +52.0808 q^{88} +14.6303 q^{89} +7.89808 q^{90} +24.3574 q^{91} +2.44960 q^{92} +6.39818 q^{93} +4.10751 q^{94} -0.363498 q^{95} +10.7356 q^{96} -3.29050 q^{97} -29.9325 q^{98} +15.6968 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9} + 20 q^{10} + 9 q^{11} + 36 q^{13} - 10 q^{14} + 16 q^{15} + 179 q^{16} + 21 q^{17} + 7 q^{18} + 42 q^{19} + 24 q^{20} + 28 q^{21} + 32 q^{22} + 25 q^{23} + 68 q^{24} + 194 q^{25} - 5 q^{26} + 14 q^{27} + 59 q^{28} - 103 q^{29} + 84 q^{30} + 34 q^{31} + 11 q^{32} + 42 q^{33} + 54 q^{34} + 35 q^{35} + 214 q^{36} + 34 q^{37} + 9 q^{38} + 23 q^{39} + 46 q^{40} + 16 q^{41} + 13 q^{42} + 68 q^{43} - 6 q^{44} + 25 q^{45} + 60 q^{46} + 6 q^{47} + 5 q^{48} + 257 q^{49} - 51 q^{50} + 68 q^{51} + 37 q^{52} + 35 q^{53} + 30 q^{54} + 66 q^{55} - 54 q^{56} + 78 q^{57} - q^{58} + 10 q^{59} - 24 q^{60} + 70 q^{61} + 29 q^{62} + 26 q^{63} + 276 q^{64} + 95 q^{65} + 77 q^{66} + 71 q^{67} - 21 q^{68} - 20 q^{69} + 48 q^{70} + 32 q^{71} + 32 q^{72} + 94 q^{73} + 35 q^{74} + 7 q^{75} + 134 q^{76} + 17 q^{77} + 58 q^{78} + 110 q^{79} + 78 q^{80} + 267 q^{81} - 71 q^{82} + 35 q^{83} + 96 q^{84} + 71 q^{85} + 33 q^{86} - 2 q^{87} + 100 q^{88} + 22 q^{89} - 134 q^{90} + 108 q^{91} - 11 q^{92} + 78 q^{93} + 90 q^{94} + 12 q^{95} + 177 q^{96} + 44 q^{97} - 18 q^{98} + 83 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.68510 −1.89865 −0.949326 0.314293i \(-0.898232\pi\)
−0.949326 + 0.314293i \(0.898232\pi\)
\(3\) −0.634380 −0.366260 −0.183130 0.983089i \(-0.558623\pi\)
−0.183130 + 0.983089i \(0.558623\pi\)
\(4\) 5.20976 2.60488
\(5\) 1.13239 0.506420 0.253210 0.967411i \(-0.418514\pi\)
0.253210 + 0.967411i \(0.418514\pi\)
\(6\) 1.70337 0.695399
\(7\) 4.26000 1.61013 0.805065 0.593186i \(-0.202130\pi\)
0.805065 + 0.593186i \(0.202130\pi\)
\(8\) −8.61852 −3.04711
\(9\) −2.59756 −0.865854
\(10\) −3.04058 −0.961515
\(11\) −6.04290 −1.82200 −0.911002 0.412402i \(-0.864690\pi\)
−0.911002 + 0.412402i \(0.864690\pi\)
\(12\) −3.30497 −0.954062
\(13\) 5.71769 1.58580 0.792901 0.609351i \(-0.208570\pi\)
0.792901 + 0.609351i \(0.208570\pi\)
\(14\) −11.4385 −3.05708
\(15\) −0.718365 −0.185481
\(16\) 12.7221 3.18051
\(17\) 3.90610 0.947368 0.473684 0.880695i \(-0.342924\pi\)
0.473684 + 0.880695i \(0.342924\pi\)
\(18\) 6.97471 1.64396
\(19\) −0.321001 −0.0736428 −0.0368214 0.999322i \(-0.511723\pi\)
−0.0368214 + 0.999322i \(0.511723\pi\)
\(20\) 5.89947 1.31916
\(21\) −2.70246 −0.589726
\(22\) 16.2258 3.45935
\(23\) 0.470194 0.0980422 0.0490211 0.998798i \(-0.484390\pi\)
0.0490211 + 0.998798i \(0.484390\pi\)
\(24\) 5.46742 1.11603
\(25\) −3.71770 −0.743539
\(26\) −15.3526 −3.01088
\(27\) 3.55098 0.683387
\(28\) 22.1936 4.19419
\(29\) −1.00000 −0.185695
\(30\) 1.92888 0.352164
\(31\) −10.0857 −1.81145 −0.905725 0.423867i \(-0.860673\pi\)
−0.905725 + 0.423867i \(0.860673\pi\)
\(32\) −16.9229 −2.99158
\(33\) 3.83350 0.667326
\(34\) −10.4883 −1.79872
\(35\) 4.82398 0.815402
\(36\) −13.5327 −2.25544
\(37\) 8.59551 1.41309 0.706546 0.707667i \(-0.250252\pi\)
0.706546 + 0.707667i \(0.250252\pi\)
\(38\) 0.861921 0.139822
\(39\) −3.62719 −0.580815
\(40\) −9.75951 −1.54311
\(41\) −4.43703 −0.692948 −0.346474 0.938060i \(-0.612621\pi\)
−0.346474 + 0.938060i \(0.612621\pi\)
\(42\) 7.25638 1.11968
\(43\) −3.34993 −0.510860 −0.255430 0.966828i \(-0.582217\pi\)
−0.255430 + 0.966828i \(0.582217\pi\)
\(44\) −31.4821 −4.74610
\(45\) −2.94145 −0.438485
\(46\) −1.26252 −0.186148
\(47\) −1.52974 −0.223136 −0.111568 0.993757i \(-0.535587\pi\)
−0.111568 + 0.993757i \(0.535587\pi\)
\(48\) −8.07062 −1.16489
\(49\) 11.1476 1.59252
\(50\) 9.98238 1.41172
\(51\) −2.47795 −0.346983
\(52\) 29.7878 4.13082
\(53\) 7.29192 1.00162 0.500811 0.865556i \(-0.333035\pi\)
0.500811 + 0.865556i \(0.333035\pi\)
\(54\) −9.53474 −1.29751
\(55\) −6.84291 −0.922698
\(56\) −36.7149 −4.90624
\(57\) 0.203637 0.0269724
\(58\) 2.68510 0.352571
\(59\) 7.45661 0.970768 0.485384 0.874301i \(-0.338680\pi\)
0.485384 + 0.874301i \(0.338680\pi\)
\(60\) −3.74251 −0.483156
\(61\) −4.27509 −0.547370 −0.273685 0.961819i \(-0.588243\pi\)
−0.273685 + 0.961819i \(0.588243\pi\)
\(62\) 27.0812 3.43931
\(63\) −11.0656 −1.39414
\(64\) 19.9957 2.49946
\(65\) 6.47465 0.803081
\(66\) −10.2933 −1.26702
\(67\) 8.21626 1.00378 0.501888 0.864933i \(-0.332639\pi\)
0.501888 + 0.864933i \(0.332639\pi\)
\(68\) 20.3498 2.46778
\(69\) −0.298282 −0.0359089
\(70\) −12.9529 −1.54816
\(71\) −12.4356 −1.47583 −0.737915 0.674894i \(-0.764189\pi\)
−0.737915 + 0.674894i \(0.764189\pi\)
\(72\) 22.3871 2.63835
\(73\) 1.46047 0.170935 0.0854677 0.996341i \(-0.472762\pi\)
0.0854677 + 0.996341i \(0.472762\pi\)
\(74\) −23.0798 −2.68297
\(75\) 2.35843 0.272328
\(76\) −1.67234 −0.191830
\(77\) −25.7428 −2.93366
\(78\) 9.73936 1.10277
\(79\) 17.3013 1.94655 0.973274 0.229647i \(-0.0737573\pi\)
0.973274 + 0.229647i \(0.0737573\pi\)
\(80\) 14.4063 1.61067
\(81\) 5.54001 0.615557
\(82\) 11.9139 1.31567
\(83\) 5.68429 0.623931 0.311966 0.950093i \(-0.399013\pi\)
0.311966 + 0.950093i \(0.399013\pi\)
\(84\) −14.0792 −1.53616
\(85\) 4.42322 0.479766
\(86\) 8.99489 0.969944
\(87\) 0.634380 0.0680127
\(88\) 52.0808 5.55184
\(89\) 14.6303 1.55081 0.775405 0.631465i \(-0.217546\pi\)
0.775405 + 0.631465i \(0.217546\pi\)
\(90\) 7.89808 0.832531
\(91\) 24.3574 2.55335
\(92\) 2.44960 0.255388
\(93\) 6.39818 0.663461
\(94\) 4.10751 0.423658
\(95\) −0.363498 −0.0372941
\(96\) 10.7356 1.09570
\(97\) −3.29050 −0.334099 −0.167050 0.985948i \(-0.553424\pi\)
−0.167050 + 0.985948i \(0.553424\pi\)
\(98\) −29.9325 −3.02364
\(99\) 15.6968 1.57759
\(100\) −19.3683 −1.93683
\(101\) 8.21401 0.817324 0.408662 0.912686i \(-0.365995\pi\)
0.408662 + 0.912686i \(0.365995\pi\)
\(102\) 6.65355 0.658799
\(103\) −4.17813 −0.411683 −0.205842 0.978585i \(-0.565993\pi\)
−0.205842 + 0.978585i \(0.565993\pi\)
\(104\) −49.2780 −4.83210
\(105\) −3.06024 −0.298649
\(106\) −19.5795 −1.90173
\(107\) 3.29478 0.318518 0.159259 0.987237i \(-0.449089\pi\)
0.159259 + 0.987237i \(0.449089\pi\)
\(108\) 18.4998 1.78014
\(109\) 6.35842 0.609026 0.304513 0.952508i \(-0.401506\pi\)
0.304513 + 0.952508i \(0.401506\pi\)
\(110\) 18.3739 1.75188
\(111\) −5.45282 −0.517559
\(112\) 54.1960 5.12104
\(113\) 7.01170 0.659605 0.329803 0.944050i \(-0.393018\pi\)
0.329803 + 0.944050i \(0.393018\pi\)
\(114\) −0.546785 −0.0512111
\(115\) 0.532442 0.0496505
\(116\) −5.20976 −0.483714
\(117\) −14.8520 −1.37307
\(118\) −20.0217 −1.84315
\(119\) 16.6400 1.52539
\(120\) 6.19124 0.565180
\(121\) 25.5167 2.31970
\(122\) 11.4791 1.03926
\(123\) 2.81477 0.253799
\(124\) −52.5442 −4.71861
\(125\) −9.87182 −0.882962
\(126\) 29.7123 2.64698
\(127\) 6.93898 0.615734 0.307867 0.951429i \(-0.400385\pi\)
0.307867 + 0.951429i \(0.400385\pi\)
\(128\) −19.8445 −1.75402
\(129\) 2.12513 0.187107
\(130\) −17.3851 −1.52477
\(131\) −10.2913 −0.899154 −0.449577 0.893242i \(-0.648425\pi\)
−0.449577 + 0.893242i \(0.648425\pi\)
\(132\) 19.9716 1.73830
\(133\) −1.36747 −0.118574
\(134\) −22.0615 −1.90582
\(135\) 4.02109 0.346081
\(136\) −33.6648 −2.88673
\(137\) 13.9411 1.19107 0.595536 0.803329i \(-0.296940\pi\)
0.595536 + 0.803329i \(0.296940\pi\)
\(138\) 0.800916 0.0681785
\(139\) 1.00000 0.0848189
\(140\) 25.1318 2.12402
\(141\) 0.970439 0.0817257
\(142\) 33.3907 2.80209
\(143\) −34.5514 −2.88934
\(144\) −33.0463 −2.75386
\(145\) −1.13239 −0.0940398
\(146\) −3.92151 −0.324547
\(147\) −7.07184 −0.583276
\(148\) 44.7805 3.68093
\(149\) −17.5661 −1.43907 −0.719535 0.694456i \(-0.755645\pi\)
−0.719535 + 0.694456i \(0.755645\pi\)
\(150\) −6.33263 −0.517057
\(151\) −17.1209 −1.39328 −0.696639 0.717422i \(-0.745322\pi\)
−0.696639 + 0.717422i \(0.745322\pi\)
\(152\) 2.76656 0.224397
\(153\) −10.1463 −0.820282
\(154\) 69.1219 5.57000
\(155\) −11.4210 −0.917353
\(156\) −18.8968 −1.51295
\(157\) 1.62185 0.129438 0.0647188 0.997904i \(-0.479385\pi\)
0.0647188 + 0.997904i \(0.479385\pi\)
\(158\) −46.4557 −3.69582
\(159\) −4.62585 −0.366854
\(160\) −19.1634 −1.51500
\(161\) 2.00303 0.157861
\(162\) −14.8755 −1.16873
\(163\) 7.83518 0.613699 0.306849 0.951758i \(-0.400725\pi\)
0.306849 + 0.951758i \(0.400725\pi\)
\(164\) −23.1159 −1.80505
\(165\) 4.34101 0.337947
\(166\) −15.2629 −1.18463
\(167\) −20.9838 −1.62377 −0.811887 0.583815i \(-0.801560\pi\)
−0.811887 + 0.583815i \(0.801560\pi\)
\(168\) 23.2912 1.79696
\(169\) 19.6920 1.51477
\(170\) −11.8768 −0.910908
\(171\) 0.833821 0.0637639
\(172\) −17.4523 −1.33073
\(173\) −3.13875 −0.238634 −0.119317 0.992856i \(-0.538071\pi\)
−0.119317 + 0.992856i \(0.538071\pi\)
\(174\) −1.70337 −0.129132
\(175\) −15.8374 −1.19719
\(176\) −76.8781 −5.79491
\(177\) −4.73033 −0.355553
\(178\) −39.2838 −2.94445
\(179\) −2.63246 −0.196760 −0.0983798 0.995149i \(-0.531366\pi\)
−0.0983798 + 0.995149i \(0.531366\pi\)
\(180\) −15.3242 −1.14220
\(181\) 10.2405 0.761170 0.380585 0.924746i \(-0.375723\pi\)
0.380585 + 0.924746i \(0.375723\pi\)
\(182\) −65.4020 −4.84792
\(183\) 2.71204 0.200479
\(184\) −4.05237 −0.298745
\(185\) 9.73345 0.715618
\(186\) −17.1798 −1.25968
\(187\) −23.6042 −1.72611
\(188\) −7.96959 −0.581242
\(189\) 15.1272 1.10034
\(190\) 0.976029 0.0708086
\(191\) 16.3101 1.18016 0.590078 0.807346i \(-0.299097\pi\)
0.590078 + 0.807346i \(0.299097\pi\)
\(192\) −12.6849 −0.915451
\(193\) 23.1364 1.66539 0.832697 0.553730i \(-0.186796\pi\)
0.832697 + 0.553730i \(0.186796\pi\)
\(194\) 8.83531 0.634338
\(195\) −4.10739 −0.294136
\(196\) 58.0765 4.14832
\(197\) 7.70316 0.548827 0.274414 0.961612i \(-0.411516\pi\)
0.274414 + 0.961612i \(0.411516\pi\)
\(198\) −42.1475 −2.99529
\(199\) −18.8108 −1.33346 −0.666731 0.745299i \(-0.732307\pi\)
−0.666731 + 0.745299i \(0.732307\pi\)
\(200\) 32.0410 2.26564
\(201\) −5.21223 −0.367643
\(202\) −22.0554 −1.55181
\(203\) −4.26000 −0.298994
\(204\) −12.9095 −0.903848
\(205\) −5.02444 −0.350922
\(206\) 11.2187 0.781643
\(207\) −1.22136 −0.0848902
\(208\) 72.7408 5.04366
\(209\) 1.93978 0.134177
\(210\) 8.21704 0.567030
\(211\) −4.76369 −0.327946 −0.163973 0.986465i \(-0.552431\pi\)
−0.163973 + 0.986465i \(0.552431\pi\)
\(212\) 37.9892 2.60911
\(213\) 7.88888 0.540537
\(214\) −8.84681 −0.604756
\(215\) −3.79342 −0.258709
\(216\) −30.6042 −2.08235
\(217\) −42.9652 −2.91667
\(218\) −17.0730 −1.15633
\(219\) −0.926495 −0.0626067
\(220\) −35.6499 −2.40352
\(221\) 22.3339 1.50234
\(222\) 14.6414 0.982664
\(223\) −0.485916 −0.0325393 −0.0162697 0.999868i \(-0.505179\pi\)
−0.0162697 + 0.999868i \(0.505179\pi\)
\(224\) −72.0918 −4.81684
\(225\) 9.65694 0.643796
\(226\) −18.8271 −1.25236
\(227\) 24.8926 1.65218 0.826089 0.563540i \(-0.190561\pi\)
0.826089 + 0.563540i \(0.190561\pi\)
\(228\) 1.06090 0.0702598
\(229\) 23.0702 1.52452 0.762261 0.647270i \(-0.224089\pi\)
0.762261 + 0.647270i \(0.224089\pi\)
\(230\) −1.42966 −0.0942690
\(231\) 16.3307 1.07448
\(232\) 8.61852 0.565833
\(233\) 18.9799 1.24341 0.621706 0.783251i \(-0.286440\pi\)
0.621706 + 0.783251i \(0.286440\pi\)
\(234\) 39.8792 2.60699
\(235\) −1.73226 −0.113000
\(236\) 38.8471 2.52873
\(237\) −10.9756 −0.712942
\(238\) −44.6800 −2.89618
\(239\) 5.26823 0.340773 0.170387 0.985377i \(-0.445498\pi\)
0.170387 + 0.985377i \(0.445498\pi\)
\(240\) −9.13908 −0.589925
\(241\) −27.2067 −1.75254 −0.876268 0.481824i \(-0.839974\pi\)
−0.876268 + 0.481824i \(0.839974\pi\)
\(242\) −68.5148 −4.40430
\(243\) −14.1674 −0.908841
\(244\) −22.2722 −1.42583
\(245\) 12.6235 0.806483
\(246\) −7.55792 −0.481876
\(247\) −1.83539 −0.116783
\(248\) 86.9240 5.51968
\(249\) −3.60600 −0.228521
\(250\) 26.5068 1.67644
\(251\) 13.3232 0.840956 0.420478 0.907303i \(-0.361862\pi\)
0.420478 + 0.907303i \(0.361862\pi\)
\(252\) −57.6492 −3.63156
\(253\) −2.84133 −0.178633
\(254\) −18.6318 −1.16907
\(255\) −2.80601 −0.175719
\(256\) 13.2930 0.830816
\(257\) 0.666973 0.0416046 0.0208023 0.999784i \(-0.493378\pi\)
0.0208023 + 0.999784i \(0.493378\pi\)
\(258\) −5.70618 −0.355251
\(259\) 36.6169 2.27526
\(260\) 33.7313 2.09193
\(261\) 2.59756 0.160785
\(262\) 27.6331 1.70718
\(263\) 18.4823 1.13967 0.569833 0.821761i \(-0.307008\pi\)
0.569833 + 0.821761i \(0.307008\pi\)
\(264\) −33.0391 −2.03341
\(265\) 8.25729 0.507241
\(266\) 3.67179 0.225132
\(267\) −9.28118 −0.567999
\(268\) 42.8047 2.61471
\(269\) 3.25871 0.198687 0.0993435 0.995053i \(-0.468326\pi\)
0.0993435 + 0.995053i \(0.468326\pi\)
\(270\) −10.7970 −0.657086
\(271\) −30.4341 −1.84874 −0.924369 0.381501i \(-0.875407\pi\)
−0.924369 + 0.381501i \(0.875407\pi\)
\(272\) 49.6936 3.01312
\(273\) −15.4518 −0.935188
\(274\) −37.4333 −2.26143
\(275\) 22.4657 1.35473
\(276\) −1.55397 −0.0935383
\(277\) −2.17481 −0.130672 −0.0653359 0.997863i \(-0.520812\pi\)
−0.0653359 + 0.997863i \(0.520812\pi\)
\(278\) −2.68510 −0.161042
\(279\) 26.1983 1.56845
\(280\) −41.5756 −2.48461
\(281\) 15.8763 0.947101 0.473551 0.880767i \(-0.342972\pi\)
0.473551 + 0.880767i \(0.342972\pi\)
\(282\) −2.60572 −0.155169
\(283\) 6.08870 0.361936 0.180968 0.983489i \(-0.442077\pi\)
0.180968 + 0.983489i \(0.442077\pi\)
\(284\) −64.7863 −3.84436
\(285\) 0.230596 0.0136593
\(286\) 92.7740 5.48584
\(287\) −18.9018 −1.11574
\(288\) 43.9584 2.59027
\(289\) −1.74239 −0.102493
\(290\) 3.04058 0.178549
\(291\) 2.08743 0.122367
\(292\) 7.60871 0.445266
\(293\) −27.9492 −1.63281 −0.816403 0.577482i \(-0.804035\pi\)
−0.816403 + 0.577482i \(0.804035\pi\)
\(294\) 18.9886 1.10744
\(295\) 8.44378 0.491616
\(296\) −74.0805 −4.30584
\(297\) −21.4582 −1.24513
\(298\) 47.1667 2.73229
\(299\) 2.68842 0.155475
\(300\) 12.2869 0.709382
\(301\) −14.2707 −0.822550
\(302\) 45.9713 2.64535
\(303\) −5.21080 −0.299353
\(304\) −4.08380 −0.234222
\(305\) −4.84107 −0.277199
\(306\) 27.2439 1.55743
\(307\) 5.10355 0.291275 0.145638 0.989338i \(-0.453477\pi\)
0.145638 + 0.989338i \(0.453477\pi\)
\(308\) −134.114 −7.64184
\(309\) 2.65052 0.150783
\(310\) 30.6664 1.74173
\(311\) 9.25161 0.524610 0.262305 0.964985i \(-0.415517\pi\)
0.262305 + 0.964985i \(0.415517\pi\)
\(312\) 31.2610 1.76980
\(313\) 12.6099 0.712755 0.356378 0.934342i \(-0.384012\pi\)
0.356378 + 0.934342i \(0.384012\pi\)
\(314\) −4.35482 −0.245757
\(315\) −12.5306 −0.706019
\(316\) 90.1355 5.07052
\(317\) −9.55673 −0.536759 −0.268380 0.963313i \(-0.586488\pi\)
−0.268380 + 0.963313i \(0.586488\pi\)
\(318\) 12.4209 0.696528
\(319\) 6.04290 0.338338
\(320\) 22.6429 1.26578
\(321\) −2.09014 −0.116660
\(322\) −5.37833 −0.299722
\(323\) −1.25386 −0.0697668
\(324\) 28.8621 1.60345
\(325\) −21.2566 −1.17911
\(326\) −21.0382 −1.16520
\(327\) −4.03365 −0.223062
\(328\) 38.2406 2.11149
\(329\) −6.51671 −0.359278
\(330\) −11.6560 −0.641644
\(331\) −17.9599 −0.987166 −0.493583 0.869699i \(-0.664313\pi\)
−0.493583 + 0.869699i \(0.664313\pi\)
\(332\) 29.6137 1.62527
\(333\) −22.3274 −1.22353
\(334\) 56.3435 3.08298
\(335\) 9.30400 0.508332
\(336\) −34.3809 −1.87563
\(337\) 0.231403 0.0126053 0.00630267 0.999980i \(-0.497994\pi\)
0.00630267 + 0.999980i \(0.497994\pi\)
\(338\) −52.8749 −2.87601
\(339\) −4.44808 −0.241587
\(340\) 23.0439 1.24973
\(341\) 60.9470 3.30047
\(342\) −2.23889 −0.121065
\(343\) 17.6690 0.954034
\(344\) 28.8714 1.55664
\(345\) −0.337771 −0.0181850
\(346\) 8.42784 0.453084
\(347\) −7.26342 −0.389921 −0.194960 0.980811i \(-0.562458\pi\)
−0.194960 + 0.980811i \(0.562458\pi\)
\(348\) 3.30497 0.177165
\(349\) −21.2600 −1.13802 −0.569012 0.822329i \(-0.692674\pi\)
−0.569012 + 0.822329i \(0.692674\pi\)
\(350\) 42.5250 2.27306
\(351\) 20.3034 1.08372
\(352\) 102.264 5.45067
\(353\) −6.98241 −0.371636 −0.185818 0.982584i \(-0.559494\pi\)
−0.185818 + 0.982584i \(0.559494\pi\)
\(354\) 12.7014 0.675072
\(355\) −14.0819 −0.747389
\(356\) 76.2203 4.03967
\(357\) −10.5561 −0.558687
\(358\) 7.06843 0.373578
\(359\) 18.7846 0.991413 0.495707 0.868490i \(-0.334909\pi\)
0.495707 + 0.868490i \(0.334909\pi\)
\(360\) 25.3509 1.33611
\(361\) −18.8970 −0.994577
\(362\) −27.4968 −1.44520
\(363\) −16.1873 −0.849611
\(364\) 126.896 6.65116
\(365\) 1.65382 0.0865650
\(366\) −7.28208 −0.380641
\(367\) 23.8213 1.24346 0.621730 0.783232i \(-0.286430\pi\)
0.621730 + 0.783232i \(0.286430\pi\)
\(368\) 5.98183 0.311824
\(369\) 11.5255 0.599992
\(370\) −26.1353 −1.35871
\(371\) 31.0636 1.61274
\(372\) 33.3330 1.72823
\(373\) −19.4035 −1.00467 −0.502337 0.864672i \(-0.667526\pi\)
−0.502337 + 0.864672i \(0.667526\pi\)
\(374\) 63.3796 3.27728
\(375\) 6.26249 0.323393
\(376\) 13.1841 0.679919
\(377\) −5.71769 −0.294476
\(378\) −40.6180 −2.08917
\(379\) 13.8163 0.709695 0.354848 0.934924i \(-0.384533\pi\)
0.354848 + 0.934924i \(0.384533\pi\)
\(380\) −1.89374 −0.0971467
\(381\) −4.40195 −0.225519
\(382\) −43.7942 −2.24070
\(383\) 7.20712 0.368266 0.184133 0.982901i \(-0.441052\pi\)
0.184133 + 0.982901i \(0.441052\pi\)
\(384\) 12.5889 0.642427
\(385\) −29.1508 −1.48566
\(386\) −62.1235 −3.16200
\(387\) 8.70165 0.442330
\(388\) −17.1427 −0.870288
\(389\) −5.19326 −0.263309 −0.131654 0.991296i \(-0.542029\pi\)
−0.131654 + 0.991296i \(0.542029\pi\)
\(390\) 11.0287 0.558462
\(391\) 1.83662 0.0928820
\(392\) −96.0761 −4.85258
\(393\) 6.52859 0.329324
\(394\) −20.6837 −1.04203
\(395\) 19.5918 0.985770
\(396\) 81.7766 4.10943
\(397\) 13.8072 0.692961 0.346481 0.938057i \(-0.387377\pi\)
0.346481 + 0.938057i \(0.387377\pi\)
\(398\) 50.5088 2.53178
\(399\) 0.867494 0.0434290
\(400\) −47.2967 −2.36484
\(401\) −25.6728 −1.28204 −0.641020 0.767524i \(-0.721488\pi\)
−0.641020 + 0.767524i \(0.721488\pi\)
\(402\) 13.9954 0.698025
\(403\) −57.6670 −2.87260
\(404\) 42.7930 2.12903
\(405\) 6.27345 0.311730
\(406\) 11.4385 0.567685
\(407\) −51.9418 −2.57466
\(408\) 21.3563 1.05729
\(409\) 9.19424 0.454626 0.227313 0.973822i \(-0.427006\pi\)
0.227313 + 0.973822i \(0.427006\pi\)
\(410\) 13.4911 0.666279
\(411\) −8.84398 −0.436241
\(412\) −21.7670 −1.07239
\(413\) 31.7652 1.56306
\(414\) 3.27947 0.161177
\(415\) 6.43682 0.315971
\(416\) −96.7601 −4.74406
\(417\) −0.634380 −0.0310657
\(418\) −5.20850 −0.254756
\(419\) 8.35548 0.408192 0.204096 0.978951i \(-0.434575\pi\)
0.204096 + 0.978951i \(0.434575\pi\)
\(420\) −15.9431 −0.777944
\(421\) −5.80266 −0.282804 −0.141402 0.989952i \(-0.545161\pi\)
−0.141402 + 0.989952i \(0.545161\pi\)
\(422\) 12.7910 0.622655
\(423\) 3.97360 0.193203
\(424\) −62.8456 −3.05205
\(425\) −14.5217 −0.704405
\(426\) −21.1824 −1.02629
\(427\) −18.2119 −0.881336
\(428\) 17.1650 0.829702
\(429\) 21.9187 1.05825
\(430\) 10.1857 0.491199
\(431\) 0.647192 0.0311741 0.0155871 0.999879i \(-0.495038\pi\)
0.0155871 + 0.999879i \(0.495038\pi\)
\(432\) 45.1758 2.17352
\(433\) 1.91751 0.0921499 0.0460749 0.998938i \(-0.485329\pi\)
0.0460749 + 0.998938i \(0.485329\pi\)
\(434\) 115.366 5.53774
\(435\) 0.718365 0.0344430
\(436\) 33.1258 1.58644
\(437\) −0.150933 −0.00722010
\(438\) 2.48773 0.118868
\(439\) 26.5405 1.26671 0.633354 0.773862i \(-0.281678\pi\)
0.633354 + 0.773862i \(0.281678\pi\)
\(440\) 58.9758 2.81156
\(441\) −28.9567 −1.37889
\(442\) −59.9686 −2.85242
\(443\) 18.3116 0.870011 0.435006 0.900428i \(-0.356746\pi\)
0.435006 + 0.900428i \(0.356746\pi\)
\(444\) −28.4079 −1.34818
\(445\) 16.5672 0.785360
\(446\) 1.30473 0.0617808
\(447\) 11.1436 0.527073
\(448\) 85.1817 4.02446
\(449\) 18.2634 0.861905 0.430952 0.902375i \(-0.358178\pi\)
0.430952 + 0.902375i \(0.358178\pi\)
\(450\) −25.9299 −1.22234
\(451\) 26.8125 1.26255
\(452\) 36.5293 1.71819
\(453\) 10.8612 0.510301
\(454\) −66.8390 −3.13691
\(455\) 27.5820 1.29307
\(456\) −1.75505 −0.0821877
\(457\) 35.4383 1.65773 0.828866 0.559447i \(-0.188987\pi\)
0.828866 + 0.559447i \(0.188987\pi\)
\(458\) −61.9458 −2.89454
\(459\) 13.8705 0.647419
\(460\) 2.77389 0.129333
\(461\) 13.6366 0.635121 0.317560 0.948238i \(-0.397136\pi\)
0.317560 + 0.948238i \(0.397136\pi\)
\(462\) −43.8496 −2.04007
\(463\) 25.5791 1.18876 0.594381 0.804183i \(-0.297397\pi\)
0.594381 + 0.804183i \(0.297397\pi\)
\(464\) −12.7221 −0.590607
\(465\) 7.24523 0.335990
\(466\) −50.9628 −2.36081
\(467\) 20.1031 0.930261 0.465131 0.885242i \(-0.346007\pi\)
0.465131 + 0.885242i \(0.346007\pi\)
\(468\) −77.3756 −3.57669
\(469\) 35.0013 1.61621
\(470\) 4.65130 0.214548
\(471\) −1.02887 −0.0474078
\(472\) −64.2649 −2.95803
\(473\) 20.2433 0.930788
\(474\) 29.4706 1.35363
\(475\) 1.19339 0.0547563
\(476\) 86.6904 3.97345
\(477\) −18.9412 −0.867259
\(478\) −14.1457 −0.647010
\(479\) −15.3045 −0.699281 −0.349640 0.936884i \(-0.613696\pi\)
−0.349640 + 0.936884i \(0.613696\pi\)
\(480\) 12.1569 0.554882
\(481\) 49.1464 2.24088
\(482\) 73.0526 3.32746
\(483\) −1.27068 −0.0578180
\(484\) 132.936 6.04253
\(485\) −3.72612 −0.169194
\(486\) 38.0409 1.72557
\(487\) −15.8113 −0.716480 −0.358240 0.933630i \(-0.616623\pi\)
−0.358240 + 0.933630i \(0.616623\pi\)
\(488\) 36.8450 1.66789
\(489\) −4.97048 −0.224773
\(490\) −33.8952 −1.53123
\(491\) −20.4391 −0.922404 −0.461202 0.887295i \(-0.652582\pi\)
−0.461202 + 0.887295i \(0.652582\pi\)
\(492\) 14.6642 0.661115
\(493\) −3.90610 −0.175922
\(494\) 4.92819 0.221730
\(495\) 17.7749 0.798922
\(496\) −128.311 −5.76134
\(497\) −52.9756 −2.37628
\(498\) 9.68246 0.433882
\(499\) 26.2082 1.17324 0.586620 0.809862i \(-0.300458\pi\)
0.586620 + 0.809862i \(0.300458\pi\)
\(500\) −51.4298 −2.30001
\(501\) 13.3117 0.594723
\(502\) −35.7742 −1.59668
\(503\) 25.3318 1.12949 0.564744 0.825266i \(-0.308975\pi\)
0.564744 + 0.825266i \(0.308975\pi\)
\(504\) 95.3693 4.24808
\(505\) 9.30145 0.413909
\(506\) 7.62927 0.339162
\(507\) −12.4922 −0.554798
\(508\) 36.1504 1.60391
\(509\) 38.0122 1.68486 0.842431 0.538805i \(-0.181124\pi\)
0.842431 + 0.538805i \(0.181124\pi\)
\(510\) 7.53440 0.333629
\(511\) 6.22162 0.275228
\(512\) 3.99581 0.176592
\(513\) −1.13987 −0.0503265
\(514\) −1.79089 −0.0789927
\(515\) −4.73127 −0.208485
\(516\) 11.0714 0.487392
\(517\) 9.24409 0.406555
\(518\) −98.3200 −4.31993
\(519\) 1.99116 0.0874022
\(520\) −55.8018 −2.44707
\(521\) −33.5830 −1.47130 −0.735648 0.677364i \(-0.763122\pi\)
−0.735648 + 0.677364i \(0.763122\pi\)
\(522\) −6.97471 −0.305275
\(523\) −14.5752 −0.637331 −0.318666 0.947867i \(-0.603235\pi\)
−0.318666 + 0.947867i \(0.603235\pi\)
\(524\) −53.6151 −2.34219
\(525\) 10.0469 0.438484
\(526\) −49.6267 −2.16383
\(527\) −39.3958 −1.71611
\(528\) 48.7700 2.12244
\(529\) −22.7789 −0.990388
\(530\) −22.1716 −0.963075
\(531\) −19.3690 −0.840543
\(532\) −7.12417 −0.308872
\(533\) −25.3696 −1.09888
\(534\) 24.9209 1.07843
\(535\) 3.73097 0.161304
\(536\) −70.8120 −3.05861
\(537\) 1.66998 0.0720651
\(538\) −8.74996 −0.377237
\(539\) −67.3641 −2.90158
\(540\) 20.9489 0.901498
\(541\) 21.4791 0.923460 0.461730 0.887021i \(-0.347229\pi\)
0.461730 + 0.887021i \(0.347229\pi\)
\(542\) 81.7184 3.51011
\(543\) −6.49637 −0.278786
\(544\) −66.1027 −2.83413
\(545\) 7.20020 0.308423
\(546\) 41.4897 1.77560
\(547\) −40.4651 −1.73016 −0.865081 0.501632i \(-0.832733\pi\)
−0.865081 + 0.501632i \(0.832733\pi\)
\(548\) 72.6299 3.10260
\(549\) 11.1048 0.473942
\(550\) −60.3226 −2.57216
\(551\) 0.321001 0.0136751
\(552\) 2.57074 0.109418
\(553\) 73.7036 3.13420
\(554\) 5.83959 0.248100
\(555\) −6.17471 −0.262102
\(556\) 5.20976 0.220943
\(557\) −23.5219 −0.996654 −0.498327 0.866989i \(-0.666052\pi\)
−0.498327 + 0.866989i \(0.666052\pi\)
\(558\) −70.3450 −2.97794
\(559\) −19.1539 −0.810122
\(560\) 61.3709 2.59340
\(561\) 14.9740 0.632204
\(562\) −42.6295 −1.79822
\(563\) 1.99192 0.0839494 0.0419747 0.999119i \(-0.486635\pi\)
0.0419747 + 0.999119i \(0.486635\pi\)
\(564\) 5.05575 0.212886
\(565\) 7.93997 0.334037
\(566\) −16.3488 −0.687190
\(567\) 23.6005 0.991127
\(568\) 107.176 4.49701
\(569\) −16.2491 −0.681196 −0.340598 0.940209i \(-0.610630\pi\)
−0.340598 + 0.940209i \(0.610630\pi\)
\(570\) −0.619174 −0.0259343
\(571\) 20.4182 0.854476 0.427238 0.904139i \(-0.359487\pi\)
0.427238 + 0.904139i \(0.359487\pi\)
\(572\) −180.005 −7.52637
\(573\) −10.3468 −0.432243
\(574\) 50.7531 2.11839
\(575\) −1.74804 −0.0728982
\(576\) −51.9400 −2.16417
\(577\) −47.9364 −1.99562 −0.997810 0.0661520i \(-0.978928\pi\)
−0.997810 + 0.0661520i \(0.978928\pi\)
\(578\) 4.67849 0.194599
\(579\) −14.6773 −0.609966
\(580\) −5.89947 −0.244962
\(581\) 24.2151 1.00461
\(582\) −5.60494 −0.232332
\(583\) −44.0644 −1.82496
\(584\) −12.5871 −0.520858
\(585\) −16.8183 −0.695351
\(586\) 75.0462 3.10013
\(587\) 14.8599 0.613332 0.306666 0.951817i \(-0.400787\pi\)
0.306666 + 0.951817i \(0.400787\pi\)
\(588\) −36.8426 −1.51936
\(589\) 3.23753 0.133400
\(590\) −22.6724 −0.933408
\(591\) −4.88673 −0.201013
\(592\) 109.353 4.49436
\(593\) 16.4235 0.674432 0.337216 0.941427i \(-0.390515\pi\)
0.337216 + 0.941427i \(0.390515\pi\)
\(594\) 57.6175 2.36407
\(595\) 18.8429 0.772486
\(596\) −91.5151 −3.74860
\(597\) 11.9332 0.488393
\(598\) −7.21868 −0.295194
\(599\) 17.0152 0.695222 0.347611 0.937639i \(-0.386993\pi\)
0.347611 + 0.937639i \(0.386993\pi\)
\(600\) −20.3262 −0.829813
\(601\) −26.2279 −1.06986 −0.534930 0.844896i \(-0.679662\pi\)
−0.534930 + 0.844896i \(0.679662\pi\)
\(602\) 38.3183 1.56174
\(603\) −21.3422 −0.869123
\(604\) −89.1956 −3.62932
\(605\) 28.8948 1.17474
\(606\) 13.9915 0.568367
\(607\) 40.8876 1.65958 0.829789 0.558078i \(-0.188461\pi\)
0.829789 + 0.558078i \(0.188461\pi\)
\(608\) 5.43229 0.220308
\(609\) 2.70246 0.109509
\(610\) 12.9987 0.526304
\(611\) −8.74660 −0.353849
\(612\) −52.8599 −2.13674
\(613\) 38.0298 1.53601 0.768005 0.640444i \(-0.221250\pi\)
0.768005 + 0.640444i \(0.221250\pi\)
\(614\) −13.7035 −0.553030
\(615\) 3.18741 0.128529
\(616\) 221.865 8.93918
\(617\) 39.3160 1.58280 0.791401 0.611298i \(-0.209352\pi\)
0.791401 + 0.611298i \(0.209352\pi\)
\(618\) −7.11692 −0.286284
\(619\) 24.6865 0.992234 0.496117 0.868256i \(-0.334759\pi\)
0.496117 + 0.868256i \(0.334759\pi\)
\(620\) −59.5004 −2.38959
\(621\) 1.66965 0.0670007
\(622\) −24.8415 −0.996053
\(623\) 62.3252 2.49700
\(624\) −46.1453 −1.84729
\(625\) 7.40974 0.296390
\(626\) −33.8589 −1.35327
\(627\) −1.23056 −0.0491438
\(628\) 8.44944 0.337169
\(629\) 33.5749 1.33872
\(630\) 33.6459 1.34048
\(631\) −25.3344 −1.00855 −0.504274 0.863544i \(-0.668240\pi\)
−0.504274 + 0.863544i \(0.668240\pi\)
\(632\) −149.111 −5.93134
\(633\) 3.02199 0.120113
\(634\) 25.6608 1.01912
\(635\) 7.85762 0.311820
\(636\) −24.0996 −0.955610
\(637\) 63.7387 2.52542
\(638\) −16.2258 −0.642385
\(639\) 32.3021 1.27785
\(640\) −22.4717 −0.888271
\(641\) 23.6091 0.932502 0.466251 0.884653i \(-0.345604\pi\)
0.466251 + 0.884653i \(0.345604\pi\)
\(642\) 5.61224 0.221498
\(643\) −5.45055 −0.214949 −0.107474 0.994208i \(-0.534276\pi\)
−0.107474 + 0.994208i \(0.534276\pi\)
\(644\) 10.4353 0.411208
\(645\) 2.40647 0.0947548
\(646\) 3.36675 0.132463
\(647\) 18.6662 0.733845 0.366923 0.930252i \(-0.380411\pi\)
0.366923 + 0.930252i \(0.380411\pi\)
\(648\) −47.7467 −1.87567
\(649\) −45.0596 −1.76874
\(650\) 57.0762 2.23871
\(651\) 27.2563 1.06826
\(652\) 40.8194 1.59861
\(653\) −25.7106 −1.00613 −0.503066 0.864248i \(-0.667795\pi\)
−0.503066 + 0.864248i \(0.667795\pi\)
\(654\) 10.8308 0.423516
\(655\) −11.6537 −0.455349
\(656\) −56.4482 −2.20393
\(657\) −3.79367 −0.148005
\(658\) 17.4980 0.682144
\(659\) 25.0477 0.975720 0.487860 0.872922i \(-0.337778\pi\)
0.487860 + 0.872922i \(0.337778\pi\)
\(660\) 22.6156 0.880311
\(661\) 50.5272 1.96528 0.982640 0.185523i \(-0.0593981\pi\)
0.982640 + 0.185523i \(0.0593981\pi\)
\(662\) 48.2241 1.87428
\(663\) −14.1682 −0.550246
\(664\) −48.9901 −1.90118
\(665\) −1.54850 −0.0600484
\(666\) 59.9512 2.32306
\(667\) −0.470194 −0.0182060
\(668\) −109.320 −4.22973
\(669\) 0.308255 0.0119178
\(670\) −24.9822 −0.965145
\(671\) 25.8340 0.997309
\(672\) 45.7336 1.76421
\(673\) 28.4760 1.09767 0.548835 0.835931i \(-0.315072\pi\)
0.548835 + 0.835931i \(0.315072\pi\)
\(674\) −0.621341 −0.0239332
\(675\) −13.2015 −0.508125
\(676\) 102.590 3.94578
\(677\) −11.0606 −0.425092 −0.212546 0.977151i \(-0.568175\pi\)
−0.212546 + 0.977151i \(0.568175\pi\)
\(678\) 11.9435 0.458689
\(679\) −14.0175 −0.537943
\(680\) −38.1216 −1.46190
\(681\) −15.7914 −0.605126
\(682\) −163.649 −6.26644
\(683\) 2.60973 0.0998584 0.0499292 0.998753i \(-0.484100\pi\)
0.0499292 + 0.998753i \(0.484100\pi\)
\(684\) 4.34401 0.166097
\(685\) 15.7868 0.603182
\(686\) −47.4429 −1.81138
\(687\) −14.6353 −0.558371
\(688\) −42.6180 −1.62480
\(689\) 41.6930 1.58837
\(690\) 0.906948 0.0345269
\(691\) 9.76080 0.371318 0.185659 0.982614i \(-0.440558\pi\)
0.185659 + 0.982614i \(0.440558\pi\)
\(692\) −16.3521 −0.621614
\(693\) 66.8685 2.54012
\(694\) 19.5030 0.740324
\(695\) 1.13239 0.0429540
\(696\) −5.46742 −0.207242
\(697\) −17.3315 −0.656477
\(698\) 57.0853 2.16071
\(699\) −12.0404 −0.455412
\(700\) −82.5090 −3.11855
\(701\) 34.5710 1.30573 0.652864 0.757475i \(-0.273567\pi\)
0.652864 + 0.757475i \(0.273567\pi\)
\(702\) −54.5167 −2.05760
\(703\) −2.75917 −0.104064
\(704\) −120.832 −4.55402
\(705\) 1.09891 0.0413875
\(706\) 18.7485 0.705608
\(707\) 34.9917 1.31600
\(708\) −24.6439 −0.926173
\(709\) −45.0495 −1.69187 −0.845934 0.533288i \(-0.820956\pi\)
−0.845934 + 0.533288i \(0.820956\pi\)
\(710\) 37.8113 1.41903
\(711\) −44.9412 −1.68543
\(712\) −126.092 −4.72548
\(713\) −4.74224 −0.177598
\(714\) 28.3441 1.06075
\(715\) −39.1257 −1.46322
\(716\) −13.7145 −0.512535
\(717\) −3.34206 −0.124811
\(718\) −50.4385 −1.88235
\(719\) 21.8477 0.814781 0.407390 0.913254i \(-0.366439\pi\)
0.407390 + 0.913254i \(0.366439\pi\)
\(720\) −37.4213 −1.39461
\(721\) −17.7989 −0.662864
\(722\) 50.7402 1.88835
\(723\) 17.2594 0.641883
\(724\) 53.3505 1.98276
\(725\) 3.71770 0.138072
\(726\) 43.4644 1.61312
\(727\) −18.5984 −0.689777 −0.344889 0.938644i \(-0.612083\pi\)
−0.344889 + 0.938644i \(0.612083\pi\)
\(728\) −209.924 −7.78032
\(729\) −7.63250 −0.282685
\(730\) −4.44068 −0.164357
\(731\) −13.0852 −0.483972
\(732\) 14.1290 0.522224
\(733\) −15.1682 −0.560252 −0.280126 0.959963i \(-0.590376\pi\)
−0.280126 + 0.959963i \(0.590376\pi\)
\(734\) −63.9624 −2.36090
\(735\) −8.00807 −0.295382
\(736\) −7.95706 −0.293301
\(737\) −49.6500 −1.82888
\(738\) −30.9470 −1.13918
\(739\) −2.01974 −0.0742974 −0.0371487 0.999310i \(-0.511828\pi\)
−0.0371487 + 0.999310i \(0.511828\pi\)
\(740\) 50.7089 1.86410
\(741\) 1.16433 0.0427728
\(742\) −83.4089 −3.06204
\(743\) −35.1505 −1.28955 −0.644773 0.764374i \(-0.723048\pi\)
−0.644773 + 0.764374i \(0.723048\pi\)
\(744\) −55.1428 −2.02163
\(745\) −19.8916 −0.728773
\(746\) 52.1003 1.90753
\(747\) −14.7653 −0.540233
\(748\) −122.972 −4.49630
\(749\) 14.0358 0.512856
\(750\) −16.8154 −0.614012
\(751\) 4.09745 0.149518 0.0747590 0.997202i \(-0.476181\pi\)
0.0747590 + 0.997202i \(0.476181\pi\)
\(752\) −19.4615 −0.709687
\(753\) −8.45200 −0.308008
\(754\) 15.3526 0.559107
\(755\) −19.3875 −0.705583
\(756\) 78.8090 2.86626
\(757\) 0.746758 0.0271414 0.0135707 0.999908i \(-0.495680\pi\)
0.0135707 + 0.999908i \(0.495680\pi\)
\(758\) −37.0981 −1.34746
\(759\) 1.80249 0.0654261
\(760\) 3.13282 0.113639
\(761\) 43.5503 1.57870 0.789348 0.613946i \(-0.210419\pi\)
0.789348 + 0.613946i \(0.210419\pi\)
\(762\) 11.8197 0.428181
\(763\) 27.0869 0.980611
\(764\) 84.9715 3.07416
\(765\) −11.4896 −0.415407
\(766\) −19.3518 −0.699210
\(767\) 42.6346 1.53945
\(768\) −8.43285 −0.304294
\(769\) 34.0282 1.22709 0.613544 0.789661i \(-0.289743\pi\)
0.613544 + 0.789661i \(0.289743\pi\)
\(770\) 78.2729 2.82076
\(771\) −0.423114 −0.0152381
\(772\) 120.535 4.33815
\(773\) 8.61160 0.309738 0.154869 0.987935i \(-0.450504\pi\)
0.154869 + 0.987935i \(0.450504\pi\)
\(774\) −23.3648 −0.839830
\(775\) 37.4956 1.34688
\(776\) 28.3592 1.01804
\(777\) −23.2290 −0.833337
\(778\) 13.9444 0.499932
\(779\) 1.42429 0.0510306
\(780\) −21.3985 −0.766189
\(781\) 75.1469 2.68897
\(782\) −4.93152 −0.176351
\(783\) −3.55098 −0.126902
\(784\) 141.821 5.06503
\(785\) 1.83656 0.0655497
\(786\) −17.5299 −0.625271
\(787\) 47.3681 1.68849 0.844246 0.535956i \(-0.180049\pi\)
0.844246 + 0.535956i \(0.180049\pi\)
\(788\) 40.1316 1.42963
\(789\) −11.7248 −0.417414
\(790\) −52.6059 −1.87163
\(791\) 29.8699 1.06205
\(792\) −135.283 −4.80708
\(793\) −24.4437 −0.868020
\(794\) −37.0736 −1.31569
\(795\) −5.23826 −0.185782
\(796\) −97.9996 −3.47350
\(797\) −20.8267 −0.737720 −0.368860 0.929485i \(-0.620252\pi\)
−0.368860 + 0.929485i \(0.620252\pi\)
\(798\) −2.32931 −0.0824566
\(799\) −5.97533 −0.211392
\(800\) 62.9144 2.22436
\(801\) −38.0031 −1.34277
\(802\) 68.9341 2.43415
\(803\) −8.82549 −0.311445
\(804\) −27.1545 −0.957664
\(805\) 2.26821 0.0799437
\(806\) 154.842 5.45407
\(807\) −2.06726 −0.0727710
\(808\) −70.7925 −2.49047
\(809\) 2.88780 0.101530 0.0507648 0.998711i \(-0.483834\pi\)
0.0507648 + 0.998711i \(0.483834\pi\)
\(810\) −16.8448 −0.591867
\(811\) −16.0209 −0.562569 −0.281285 0.959624i \(-0.590761\pi\)
−0.281285 + 0.959624i \(0.590761\pi\)
\(812\) −22.1936 −0.778842
\(813\) 19.3068 0.677118
\(814\) 139.469 4.88838
\(815\) 8.87247 0.310789
\(816\) −31.5246 −1.10358
\(817\) 1.07533 0.0376211
\(818\) −24.6874 −0.863176
\(819\) −63.2698 −2.21083
\(820\) −26.1761 −0.914110
\(821\) −45.6331 −1.59261 −0.796303 0.604897i \(-0.793214\pi\)
−0.796303 + 0.604897i \(0.793214\pi\)
\(822\) 23.7470 0.828270
\(823\) 34.8963 1.21641 0.608205 0.793780i \(-0.291890\pi\)
0.608205 + 0.793780i \(0.291890\pi\)
\(824\) 36.0093 1.25444
\(825\) −14.2518 −0.496183
\(826\) −85.2927 −2.96771
\(827\) −53.7904 −1.87047 −0.935237 0.354022i \(-0.884814\pi\)
−0.935237 + 0.354022i \(0.884814\pi\)
\(828\) −6.36297 −0.221129
\(829\) 20.6428 0.716954 0.358477 0.933539i \(-0.383296\pi\)
0.358477 + 0.933539i \(0.383296\pi\)
\(830\) −17.2835 −0.599919
\(831\) 1.37966 0.0478598
\(832\) 114.329 3.96365
\(833\) 43.5438 1.50870
\(834\) 1.70337 0.0589830
\(835\) −23.7618 −0.822311
\(836\) 10.1058 0.349516
\(837\) −35.8142 −1.23792
\(838\) −22.4353 −0.775014
\(839\) −36.3213 −1.25395 −0.626975 0.779039i \(-0.715707\pi\)
−0.626975 + 0.779039i \(0.715707\pi\)
\(840\) 26.3747 0.910014
\(841\) 1.00000 0.0344828
\(842\) 15.5807 0.536947
\(843\) −10.0716 −0.346885
\(844\) −24.8177 −0.854259
\(845\) 22.2990 0.767108
\(846\) −10.6695 −0.366826
\(847\) 108.701 3.73501
\(848\) 92.7683 3.18567
\(849\) −3.86255 −0.132562
\(850\) 38.9922 1.33742
\(851\) 4.04155 0.138543
\(852\) 41.0991 1.40803
\(853\) −42.1635 −1.44365 −0.721825 0.692075i \(-0.756697\pi\)
−0.721825 + 0.692075i \(0.756697\pi\)
\(854\) 48.9008 1.67335
\(855\) 0.944210 0.0322913
\(856\) −28.3961 −0.970559
\(857\) 28.5722 0.976007 0.488003 0.872842i \(-0.337725\pi\)
0.488003 + 0.872842i \(0.337725\pi\)
\(858\) −58.8540 −2.00924
\(859\) −2.54750 −0.0869196 −0.0434598 0.999055i \(-0.513838\pi\)
−0.0434598 + 0.999055i \(0.513838\pi\)
\(860\) −19.7628 −0.673906
\(861\) 11.9909 0.408649
\(862\) −1.73777 −0.0591888
\(863\) −21.4878 −0.731452 −0.365726 0.930723i \(-0.619179\pi\)
−0.365726 + 0.930723i \(0.619179\pi\)
\(864\) −60.0931 −2.04441
\(865\) −3.55428 −0.120849
\(866\) −5.14872 −0.174961
\(867\) 1.10534 0.0375392
\(868\) −223.838 −7.59757
\(869\) −104.550 −3.54662
\(870\) −1.92888 −0.0653952
\(871\) 46.9780 1.59179
\(872\) −54.8001 −1.85577
\(873\) 8.54727 0.289281
\(874\) 0.405270 0.0137085
\(875\) −42.0540 −1.42168
\(876\) −4.82681 −0.163083
\(877\) 4.34207 0.146621 0.0733106 0.997309i \(-0.476644\pi\)
0.0733106 + 0.997309i \(0.476644\pi\)
\(878\) −71.2638 −2.40504
\(879\) 17.7304 0.598031
\(880\) −87.0559 −2.93465
\(881\) −5.38871 −0.181550 −0.0907752 0.995871i \(-0.528934\pi\)
−0.0907752 + 0.995871i \(0.528934\pi\)
\(882\) 77.7515 2.61803
\(883\) 7.71472 0.259621 0.129810 0.991539i \(-0.458563\pi\)
0.129810 + 0.991539i \(0.458563\pi\)
\(884\) 116.354 3.91341
\(885\) −5.35657 −0.180059
\(886\) −49.1685 −1.65185
\(887\) 42.8186 1.43771 0.718854 0.695161i \(-0.244667\pi\)
0.718854 + 0.695161i \(0.244667\pi\)
\(888\) 46.9952 1.57706
\(889\) 29.5601 0.991413
\(890\) −44.4845 −1.49113
\(891\) −33.4777 −1.12155
\(892\) −2.53150 −0.0847610
\(893\) 0.491050 0.0164324
\(894\) −29.9216 −1.00073
\(895\) −2.98097 −0.0996430
\(896\) −84.5376 −2.82420
\(897\) −1.70548 −0.0569444
\(898\) −49.0391 −1.63646
\(899\) 10.0857 0.336378
\(900\) 50.3103 1.67701
\(901\) 28.4830 0.948906
\(902\) −71.9943 −2.39715
\(903\) 9.05306 0.301267
\(904\) −60.4304 −2.00989
\(905\) 11.5962 0.385472
\(906\) −29.1633 −0.968885
\(907\) −40.7737 −1.35387 −0.676934 0.736044i \(-0.736692\pi\)
−0.676934 + 0.736044i \(0.736692\pi\)
\(908\) 129.684 4.30372
\(909\) −21.3364 −0.707683
\(910\) −74.0605 −2.45508
\(911\) −52.8775 −1.75191 −0.875955 0.482393i \(-0.839768\pi\)
−0.875955 + 0.482393i \(0.839768\pi\)
\(912\) 2.59068 0.0857860
\(913\) −34.3496 −1.13681
\(914\) −95.1552 −3.14746
\(915\) 3.07108 0.101527
\(916\) 120.190 3.97119
\(917\) −43.8409 −1.44776
\(918\) −37.2436 −1.22922
\(919\) 49.9161 1.64658 0.823290 0.567621i \(-0.192136\pi\)
0.823290 + 0.567621i \(0.192136\pi\)
\(920\) −4.58886 −0.151290
\(921\) −3.23759 −0.106682
\(922\) −36.6157 −1.20587
\(923\) −71.1027 −2.34037
\(924\) 85.0791 2.79890
\(925\) −31.9555 −1.05069
\(926\) −68.6825 −2.25705
\(927\) 10.8530 0.356458
\(928\) 16.9229 0.555523
\(929\) −29.5273 −0.968760 −0.484380 0.874858i \(-0.660955\pi\)
−0.484380 + 0.874858i \(0.660955\pi\)
\(930\) −19.4542 −0.637927
\(931\) −3.57841 −0.117278
\(932\) 98.8804 3.23894
\(933\) −5.86904 −0.192144
\(934\) −53.9789 −1.76624
\(935\) −26.7291 −0.874135
\(936\) 128.003 4.18390
\(937\) 48.9587 1.59941 0.799705 0.600393i \(-0.204989\pi\)
0.799705 + 0.600393i \(0.204989\pi\)
\(938\) −93.9820 −3.06862
\(939\) −7.99949 −0.261053
\(940\) −9.02467 −0.294352
\(941\) 28.9821 0.944789 0.472395 0.881387i \(-0.343390\pi\)
0.472395 + 0.881387i \(0.343390\pi\)
\(942\) 2.76261 0.0900108
\(943\) −2.08626 −0.0679381
\(944\) 94.8634 3.08754
\(945\) 17.1299 0.557235
\(946\) −54.3553 −1.76724
\(947\) 25.4621 0.827408 0.413704 0.910411i \(-0.364235\pi\)
0.413704 + 0.910411i \(0.364235\pi\)
\(948\) −57.1802 −1.85713
\(949\) 8.35053 0.271070
\(950\) −3.20436 −0.103963
\(951\) 6.06260 0.196593
\(952\) −143.412 −4.64801
\(953\) 39.9532 1.29421 0.647105 0.762401i \(-0.275980\pi\)
0.647105 + 0.762401i \(0.275980\pi\)
\(954\) 50.8591 1.64662
\(955\) 18.4693 0.597654
\(956\) 27.4462 0.887673
\(957\) −3.83350 −0.123919
\(958\) 41.0941 1.32769
\(959\) 59.3893 1.91778
\(960\) −14.3642 −0.463602
\(961\) 70.7218 2.28135
\(962\) −131.963 −4.25466
\(963\) −8.55840 −0.275790
\(964\) −141.740 −4.56514
\(965\) 26.1994 0.843388
\(966\) 3.41190 0.109776
\(967\) −11.6841 −0.375736 −0.187868 0.982194i \(-0.560158\pi\)
−0.187868 + 0.982194i \(0.560158\pi\)
\(968\) −219.916 −7.06836
\(969\) 0.795426 0.0255528
\(970\) 10.0050 0.321241
\(971\) −35.2887 −1.13247 −0.566234 0.824245i \(-0.691600\pi\)
−0.566234 + 0.824245i \(0.691600\pi\)
\(972\) −73.8088 −2.36742
\(973\) 4.26000 0.136569
\(974\) 42.4550 1.36035
\(975\) 13.4848 0.431859
\(976\) −54.3880 −1.74092
\(977\) 52.4786 1.67894 0.839470 0.543407i \(-0.182866\pi\)
0.839470 + 0.543407i \(0.182866\pi\)
\(978\) 13.3462 0.426766
\(979\) −88.4095 −2.82558
\(980\) 65.7652 2.10079
\(981\) −16.5164 −0.527327
\(982\) 54.8811 1.75132
\(983\) −16.7031 −0.532747 −0.266374 0.963870i \(-0.585826\pi\)
−0.266374 + 0.963870i \(0.585826\pi\)
\(984\) −24.2591 −0.773352
\(985\) 8.72297 0.277937
\(986\) 10.4883 0.334014
\(987\) 4.13407 0.131589
\(988\) −9.56192 −0.304205
\(989\) −1.57512 −0.0500858
\(990\) −47.7273 −1.51687
\(991\) 18.7711 0.596284 0.298142 0.954522i \(-0.403633\pi\)
0.298142 + 0.954522i \(0.403633\pi\)
\(992\) 170.680 5.41910
\(993\) 11.3934 0.361559
\(994\) 142.245 4.51173
\(995\) −21.3011 −0.675291
\(996\) −18.7864 −0.595269
\(997\) 25.8249 0.817883 0.408942 0.912561i \(-0.365898\pi\)
0.408942 + 0.912561i \(0.365898\pi\)
\(998\) −70.3716 −2.22757
\(999\) 30.5225 0.965689
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 4031.2.a.e.1.5 103
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4031.2.a.e.1.5 103 1.1 even 1 trivial