Properties

Label 667.2.a.b.1.2
Level $667$
Weight $2$
Character 667.1
Self dual yes
Analytic conductor $5.326$
Analytic rank $1$
Dimension $12$
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] = [667,2,Mod(1,667)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(667, 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("667.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 667 = 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 667.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: \(5.32602181482\)
Analytic rank: \(1\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 3 x^{11} - 13 x^{10} + 41 x^{9} + 54 x^{8} - 188 x^{7} - 77 x^{6} + 342 x^{5} + 13 x^{4} - 215 x^{3} + 9 x^{2} + 37 x - 5 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.58646\) of defining polynomial
Character \(\chi\) \(=\) 667.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.58646 q^{2} -2.87567 q^{3} +4.68978 q^{4} -3.69848 q^{5} +7.43782 q^{6} -0.298143 q^{7} -6.95702 q^{8} +5.26950 q^{9} +O(q^{10})\) \(q-2.58646 q^{2} -2.87567 q^{3} +4.68978 q^{4} -3.69848 q^{5} +7.43782 q^{6} -0.298143 q^{7} -6.95702 q^{8} +5.26950 q^{9} +9.56597 q^{10} -1.58434 q^{11} -13.4863 q^{12} -4.24524 q^{13} +0.771137 q^{14} +10.6356 q^{15} +8.61451 q^{16} +4.97869 q^{17} -13.6294 q^{18} +8.32429 q^{19} -17.3451 q^{20} +0.857363 q^{21} +4.09783 q^{22} -1.00000 q^{23} +20.0061 q^{24} +8.67874 q^{25} +10.9802 q^{26} -6.52634 q^{27} -1.39823 q^{28} -1.00000 q^{29} -27.5086 q^{30} -0.692531 q^{31} -8.36705 q^{32} +4.55604 q^{33} -12.8772 q^{34} +1.10268 q^{35} +24.7128 q^{36} +7.77829 q^{37} -21.5304 q^{38} +12.2079 q^{39} +25.7304 q^{40} +5.66508 q^{41} -2.21754 q^{42} -2.82585 q^{43} -7.43021 q^{44} -19.4891 q^{45} +2.58646 q^{46} +0.941070 q^{47} -24.7725 q^{48} -6.91111 q^{49} -22.4472 q^{50} -14.3171 q^{51} -19.9093 q^{52} -8.52596 q^{53} +16.8801 q^{54} +5.85965 q^{55} +2.07419 q^{56} -23.9379 q^{57} +2.58646 q^{58} -5.47010 q^{59} +49.8788 q^{60} -7.60438 q^{61} +1.79121 q^{62} -1.57107 q^{63} +4.41204 q^{64} +15.7009 q^{65} -11.7840 q^{66} +8.46657 q^{67} +23.3490 q^{68} +2.87567 q^{69} -2.85203 q^{70} +14.1339 q^{71} -36.6600 q^{72} -5.10834 q^{73} -20.1183 q^{74} -24.9572 q^{75} +39.0391 q^{76} +0.472361 q^{77} -31.5754 q^{78} -0.828407 q^{79} -31.8606 q^{80} +2.95913 q^{81} -14.6525 q^{82} -17.8414 q^{83} +4.02085 q^{84} -18.4136 q^{85} +7.30896 q^{86} +2.87567 q^{87} +11.0223 q^{88} -6.78344 q^{89} +50.4079 q^{90} +1.26569 q^{91} -4.68978 q^{92} +1.99149 q^{93} -2.43404 q^{94} -30.7872 q^{95} +24.0609 q^{96} +9.10860 q^{97} +17.8753 q^{98} -8.34868 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 16 q^{5} - 2 q^{6} - 7 q^{7} - 9 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 16 q^{5} - 2 q^{6} - 7 q^{7} - 9 q^{8} + 3 q^{9} - 6 q^{11} - 21 q^{12} - 15 q^{13} - 8 q^{14} + 6 q^{15} + 17 q^{16} - 18 q^{17} - 12 q^{18} - 6 q^{19} - 39 q^{20} - q^{21} - 5 q^{22} - 12 q^{23} + 4 q^{24} + 14 q^{25} - 3 q^{26} - 12 q^{27} - 19 q^{28} - 12 q^{29} - 11 q^{30} + 16 q^{31} - 21 q^{32} - 19 q^{33} - 7 q^{34} - 11 q^{35} - 13 q^{36} - q^{37} - 24 q^{38} + 6 q^{39} + 30 q^{40} + 3 q^{41} + 22 q^{42} - 23 q^{43} + 23 q^{44} - 22 q^{45} + 3 q^{46} - 35 q^{47} - 21 q^{48} + 3 q^{49} - 2 q^{50} - 34 q^{51} - 45 q^{53} + 55 q^{54} + 17 q^{55} - 17 q^{56} - 34 q^{57} + 3 q^{58} - 11 q^{59} + 93 q^{60} + 4 q^{61} - 7 q^{62} + q^{63} + 15 q^{64} + 5 q^{65} - 35 q^{66} - 19 q^{67} + q^{68} + 3 q^{69} + 14 q^{70} + 19 q^{71} + 4 q^{72} + 10 q^{73} - 15 q^{74} - 3 q^{75} - 4 q^{76} - 39 q^{77} + 16 q^{78} + 17 q^{79} - 90 q^{80} + 4 q^{81} - 3 q^{82} - 12 q^{83} + 42 q^{84} + 14 q^{85} + 17 q^{86} + 3 q^{87} - 2 q^{88} - 20 q^{89} + 65 q^{90} + 11 q^{91} - 11 q^{92} - 2 q^{93} + 13 q^{94} + 12 q^{95} + 14 q^{96} - 12 q^{97} + 75 q^{98} - 4 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.58646 −1.82890 −0.914452 0.404694i \(-0.867378\pi\)
−0.914452 + 0.404694i \(0.867378\pi\)
\(3\) −2.87567 −1.66027 −0.830136 0.557562i \(-0.811737\pi\)
−0.830136 + 0.557562i \(0.811737\pi\)
\(4\) 4.68978 2.34489
\(5\) −3.69848 −1.65401 −0.827005 0.562195i \(-0.809957\pi\)
−0.827005 + 0.562195i \(0.809957\pi\)
\(6\) 7.43782 3.03648
\(7\) −0.298143 −0.112688 −0.0563438 0.998411i \(-0.517944\pi\)
−0.0563438 + 0.998411i \(0.517944\pi\)
\(8\) −6.95702 −2.45968
\(9\) 5.26950 1.75650
\(10\) 9.56597 3.02503
\(11\) −1.58434 −0.477696 −0.238848 0.971057i \(-0.576770\pi\)
−0.238848 + 0.971057i \(0.576770\pi\)
\(12\) −13.4863 −3.89316
\(13\) −4.24524 −1.17742 −0.588709 0.808345i \(-0.700364\pi\)
−0.588709 + 0.808345i \(0.700364\pi\)
\(14\) 0.771137 0.206095
\(15\) 10.6356 2.74610
\(16\) 8.61451 2.15363
\(17\) 4.97869 1.20751 0.603754 0.797170i \(-0.293671\pi\)
0.603754 + 0.797170i \(0.293671\pi\)
\(18\) −13.6294 −3.21247
\(19\) 8.32429 1.90972 0.954861 0.297053i \(-0.0960037\pi\)
0.954861 + 0.297053i \(0.0960037\pi\)
\(20\) −17.3451 −3.87847
\(21\) 0.857363 0.187092
\(22\) 4.09783 0.873661
\(23\) −1.00000 −0.208514
\(24\) 20.0061 4.08374
\(25\) 8.67874 1.73575
\(26\) 10.9802 2.15339
\(27\) −6.52634 −1.25600
\(28\) −1.39823 −0.264240
\(29\) −1.00000 −0.185695
\(30\) −27.5086 −5.02236
\(31\) −0.692531 −0.124382 −0.0621911 0.998064i \(-0.519809\pi\)
−0.0621911 + 0.998064i \(0.519809\pi\)
\(32\) −8.36705 −1.47910
\(33\) 4.55604 0.793106
\(34\) −12.8772 −2.20842
\(35\) 1.10268 0.186386
\(36\) 24.7128 4.11880
\(37\) 7.77829 1.27874 0.639372 0.768898i \(-0.279194\pi\)
0.639372 + 0.768898i \(0.279194\pi\)
\(38\) −21.5304 −3.49270
\(39\) 12.2079 1.95483
\(40\) 25.7304 4.06833
\(41\) 5.66508 0.884737 0.442368 0.896833i \(-0.354138\pi\)
0.442368 + 0.896833i \(0.354138\pi\)
\(42\) −2.21754 −0.342173
\(43\) −2.82585 −0.430939 −0.215469 0.976511i \(-0.569128\pi\)
−0.215469 + 0.976511i \(0.569128\pi\)
\(44\) −7.43021 −1.12015
\(45\) −19.4891 −2.90527
\(46\) 2.58646 0.381353
\(47\) 0.941070 0.137269 0.0686346 0.997642i \(-0.478136\pi\)
0.0686346 + 0.997642i \(0.478136\pi\)
\(48\) −24.7725 −3.57561
\(49\) −6.91111 −0.987301
\(50\) −22.4472 −3.17452
\(51\) −14.3171 −2.00479
\(52\) −19.9093 −2.76092
\(53\) −8.52596 −1.17113 −0.585565 0.810625i \(-0.699127\pi\)
−0.585565 + 0.810625i \(0.699127\pi\)
\(54\) 16.8801 2.29710
\(55\) 5.85965 0.790115
\(56\) 2.07419 0.277175
\(57\) −23.9379 −3.17066
\(58\) 2.58646 0.339619
\(59\) −5.47010 −0.712146 −0.356073 0.934458i \(-0.615885\pi\)
−0.356073 + 0.934458i \(0.615885\pi\)
\(60\) 49.8788 6.43932
\(61\) −7.60438 −0.973641 −0.486820 0.873502i \(-0.661843\pi\)
−0.486820 + 0.873502i \(0.661843\pi\)
\(62\) 1.79121 0.227483
\(63\) −1.57107 −0.197936
\(64\) 4.41204 0.551505
\(65\) 15.7009 1.94746
\(66\) −11.7840 −1.45051
\(67\) 8.46657 1.03436 0.517178 0.855878i \(-0.326983\pi\)
0.517178 + 0.855878i \(0.326983\pi\)
\(68\) 23.3490 2.83148
\(69\) 2.87567 0.346190
\(70\) −2.85203 −0.340883
\(71\) 14.1339 1.67738 0.838691 0.544608i \(-0.183321\pi\)
0.838691 + 0.544608i \(0.183321\pi\)
\(72\) −36.6600 −4.32043
\(73\) −5.10834 −0.597885 −0.298943 0.954271i \(-0.596634\pi\)
−0.298943 + 0.954271i \(0.596634\pi\)
\(74\) −20.1183 −2.33870
\(75\) −24.9572 −2.88181
\(76\) 39.0391 4.47809
\(77\) 0.472361 0.0538305
\(78\) −31.5754 −3.57520
\(79\) −0.828407 −0.0932031 −0.0466016 0.998914i \(-0.514839\pi\)
−0.0466016 + 0.998914i \(0.514839\pi\)
\(80\) −31.8606 −3.56212
\(81\) 2.95913 0.328793
\(82\) −14.6525 −1.61810
\(83\) −17.8414 −1.95834 −0.979172 0.203033i \(-0.934920\pi\)
−0.979172 + 0.203033i \(0.934920\pi\)
\(84\) 4.02085 0.438711
\(85\) −18.4136 −1.99723
\(86\) 7.30896 0.788146
\(87\) 2.87567 0.308305
\(88\) 11.0223 1.17498
\(89\) −6.78344 −0.719043 −0.359522 0.933137i \(-0.617060\pi\)
−0.359522 + 0.933137i \(0.617060\pi\)
\(90\) 50.4079 5.31346
\(91\) 1.26569 0.132681
\(92\) −4.68978 −0.488944
\(93\) 1.99149 0.206508
\(94\) −2.43404 −0.251052
\(95\) −30.7872 −3.15870
\(96\) 24.0609 2.45571
\(97\) 9.10860 0.924838 0.462419 0.886661i \(-0.346982\pi\)
0.462419 + 0.886661i \(0.346982\pi\)
\(98\) 17.8753 1.80568
\(99\) −8.34868 −0.839074
\(100\) 40.7014 4.07014
\(101\) −16.9255 −1.68415 −0.842073 0.539364i \(-0.818665\pi\)
−0.842073 + 0.539364i \(0.818665\pi\)
\(102\) 37.0306 3.66657
\(103\) 0.342308 0.0337286 0.0168643 0.999858i \(-0.494632\pi\)
0.0168643 + 0.999858i \(0.494632\pi\)
\(104\) 29.5343 2.89607
\(105\) −3.17094 −0.309452
\(106\) 22.0521 2.14189
\(107\) 16.6153 1.60626 0.803130 0.595804i \(-0.203166\pi\)
0.803130 + 0.595804i \(0.203166\pi\)
\(108\) −30.6071 −2.94517
\(109\) −1.54247 −0.147742 −0.0738710 0.997268i \(-0.523535\pi\)
−0.0738710 + 0.997268i \(0.523535\pi\)
\(110\) −15.1558 −1.44504
\(111\) −22.3678 −2.12306
\(112\) −2.56836 −0.242687
\(113\) 14.7265 1.38536 0.692678 0.721247i \(-0.256431\pi\)
0.692678 + 0.721247i \(0.256431\pi\)
\(114\) 61.9145 5.79883
\(115\) 3.69848 0.344885
\(116\) −4.68978 −0.435436
\(117\) −22.3703 −2.06814
\(118\) 14.1482 1.30245
\(119\) −1.48436 −0.136071
\(120\) −73.9923 −6.75454
\(121\) −8.48987 −0.771806
\(122\) 19.6684 1.78070
\(123\) −16.2909 −1.46890
\(124\) −3.24782 −0.291663
\(125\) −13.6057 −1.21693
\(126\) 4.06350 0.362006
\(127\) −0.462641 −0.0410528 −0.0205264 0.999789i \(-0.506534\pi\)
−0.0205264 + 0.999789i \(0.506534\pi\)
\(128\) 5.32254 0.470450
\(129\) 8.12624 0.715475
\(130\) −40.6099 −3.56172
\(131\) 16.0399 1.40141 0.700707 0.713449i \(-0.252868\pi\)
0.700707 + 0.713449i \(0.252868\pi\)
\(132\) 21.3669 1.85975
\(133\) −2.48183 −0.215202
\(134\) −21.8985 −1.89174
\(135\) 24.1375 2.07743
\(136\) −34.6368 −2.97008
\(137\) −3.85509 −0.329363 −0.164681 0.986347i \(-0.552660\pi\)
−0.164681 + 0.986347i \(0.552660\pi\)
\(138\) −7.43782 −0.633149
\(139\) 8.07514 0.684924 0.342462 0.939532i \(-0.388739\pi\)
0.342462 + 0.939532i \(0.388739\pi\)
\(140\) 5.17132 0.437056
\(141\) −2.70621 −0.227904
\(142\) −36.5567 −3.06777
\(143\) 6.72591 0.562449
\(144\) 45.3942 3.78285
\(145\) 3.69848 0.307142
\(146\) 13.2125 1.09348
\(147\) 19.8741 1.63919
\(148\) 36.4785 2.99852
\(149\) 21.9397 1.79737 0.898683 0.438598i \(-0.144525\pi\)
0.898683 + 0.438598i \(0.144525\pi\)
\(150\) 64.5509 5.27056
\(151\) 0.452281 0.0368061 0.0184031 0.999831i \(-0.494142\pi\)
0.0184031 + 0.999831i \(0.494142\pi\)
\(152\) −57.9123 −4.69730
\(153\) 26.2352 2.12099
\(154\) −1.22174 −0.0984508
\(155\) 2.56131 0.205730
\(156\) 57.2526 4.58387
\(157\) −8.50054 −0.678417 −0.339208 0.940711i \(-0.610159\pi\)
−0.339208 + 0.940711i \(0.610159\pi\)
\(158\) 2.14264 0.170460
\(159\) 24.5179 1.94439
\(160\) 30.9454 2.44645
\(161\) 0.298143 0.0234970
\(162\) −7.65368 −0.601330
\(163\) −7.14215 −0.559417 −0.279708 0.960085i \(-0.590238\pi\)
−0.279708 + 0.960085i \(0.590238\pi\)
\(164\) 26.5680 2.07461
\(165\) −16.8504 −1.31180
\(166\) 46.1460 3.58162
\(167\) −1.47531 −0.114163 −0.0570813 0.998370i \(-0.518179\pi\)
−0.0570813 + 0.998370i \(0.518179\pi\)
\(168\) −5.96470 −0.460186
\(169\) 5.02209 0.386314
\(170\) 47.6260 3.65275
\(171\) 43.8648 3.35443
\(172\) −13.2526 −1.01050
\(173\) −18.0111 −1.36936 −0.684678 0.728846i \(-0.740057\pi\)
−0.684678 + 0.728846i \(0.740057\pi\)
\(174\) −7.43782 −0.563860
\(175\) −2.58751 −0.195597
\(176\) −13.6483 −1.02878
\(177\) 15.7302 1.18236
\(178\) 17.5451 1.31506
\(179\) 15.7157 1.17465 0.587323 0.809353i \(-0.300182\pi\)
0.587323 + 0.809353i \(0.300182\pi\)
\(180\) −91.3998 −6.81254
\(181\) −19.1187 −1.42108 −0.710541 0.703656i \(-0.751550\pi\)
−0.710541 + 0.703656i \(0.751550\pi\)
\(182\) −3.27366 −0.242660
\(183\) 21.8677 1.61651
\(184\) 6.95702 0.512879
\(185\) −28.7679 −2.11505
\(186\) −5.15092 −0.377684
\(187\) −7.88793 −0.576823
\(188\) 4.41342 0.321882
\(189\) 1.94579 0.141535
\(190\) 79.6299 5.77696
\(191\) 3.97520 0.287636 0.143818 0.989604i \(-0.454062\pi\)
0.143818 + 0.989604i \(0.454062\pi\)
\(192\) −12.6876 −0.915647
\(193\) −20.0623 −1.44412 −0.722059 0.691832i \(-0.756804\pi\)
−0.722059 + 0.691832i \(0.756804\pi\)
\(194\) −23.5590 −1.69144
\(195\) −45.1508 −3.23331
\(196\) −32.4116 −2.31512
\(197\) 11.0730 0.788916 0.394458 0.918914i \(-0.370932\pi\)
0.394458 + 0.918914i \(0.370932\pi\)
\(198\) 21.5935 1.53459
\(199\) −18.6961 −1.32533 −0.662665 0.748916i \(-0.730575\pi\)
−0.662665 + 0.748916i \(0.730575\pi\)
\(200\) −60.3782 −4.26939
\(201\) −24.3471 −1.71731
\(202\) 43.7770 3.08014
\(203\) 0.298143 0.0209256
\(204\) −67.1440 −4.70102
\(205\) −20.9522 −1.46336
\(206\) −0.885366 −0.0616864
\(207\) −5.26950 −0.366256
\(208\) −36.5707 −2.53572
\(209\) −13.1885 −0.912267
\(210\) 8.20151 0.565958
\(211\) 4.24605 0.292310 0.146155 0.989262i \(-0.453310\pi\)
0.146155 + 0.989262i \(0.453310\pi\)
\(212\) −39.9849 −2.74617
\(213\) −40.6444 −2.78491
\(214\) −42.9748 −2.93770
\(215\) 10.4514 0.712777
\(216\) 45.4039 3.08935
\(217\) 0.206474 0.0140163
\(218\) 3.98954 0.270206
\(219\) 14.6899 0.992652
\(220\) 27.4805 1.85273
\(221\) −21.1357 −1.42174
\(222\) 57.8536 3.88288
\(223\) 18.4472 1.23532 0.617658 0.786447i \(-0.288082\pi\)
0.617658 + 0.786447i \(0.288082\pi\)
\(224\) 2.49458 0.166676
\(225\) 45.7326 3.04884
\(226\) −38.0896 −2.53368
\(227\) 20.0773 1.33257 0.666287 0.745695i \(-0.267882\pi\)
0.666287 + 0.745695i \(0.267882\pi\)
\(228\) −112.264 −7.43485
\(229\) −3.04324 −0.201103 −0.100551 0.994932i \(-0.532061\pi\)
−0.100551 + 0.994932i \(0.532061\pi\)
\(230\) −9.56597 −0.630762
\(231\) −1.35835 −0.0893732
\(232\) 6.95702 0.456751
\(233\) 5.39180 0.353228 0.176614 0.984280i \(-0.443486\pi\)
0.176614 + 0.984280i \(0.443486\pi\)
\(234\) 57.8599 3.78242
\(235\) −3.48053 −0.227045
\(236\) −25.6536 −1.66991
\(237\) 2.38223 0.154742
\(238\) 3.83925 0.248861
\(239\) −14.2539 −0.922008 −0.461004 0.887398i \(-0.652511\pi\)
−0.461004 + 0.887398i \(0.652511\pi\)
\(240\) 91.6206 5.91409
\(241\) −7.87515 −0.507283 −0.253641 0.967298i \(-0.581628\pi\)
−0.253641 + 0.967298i \(0.581628\pi\)
\(242\) 21.9587 1.41156
\(243\) 11.0695 0.710111
\(244\) −35.6629 −2.28308
\(245\) 25.5606 1.63301
\(246\) 42.1358 2.68648
\(247\) −35.3386 −2.24854
\(248\) 4.81796 0.305941
\(249\) 51.3059 3.25138
\(250\) 35.1907 2.22566
\(251\) −7.81496 −0.493276 −0.246638 0.969108i \(-0.579326\pi\)
−0.246638 + 0.969108i \(0.579326\pi\)
\(252\) −7.36797 −0.464138
\(253\) 1.58434 0.0996066
\(254\) 1.19660 0.0750816
\(255\) 52.9514 3.31595
\(256\) −22.5906 −1.41191
\(257\) −29.9598 −1.86884 −0.934419 0.356175i \(-0.884081\pi\)
−0.934419 + 0.356175i \(0.884081\pi\)
\(258\) −21.0182 −1.30854
\(259\) −2.31905 −0.144099
\(260\) 73.6340 4.56659
\(261\) −5.26950 −0.326174
\(262\) −41.4866 −2.56305
\(263\) −13.9120 −0.857853 −0.428926 0.903339i \(-0.641108\pi\)
−0.428926 + 0.903339i \(0.641108\pi\)
\(264\) −31.6965 −1.95079
\(265\) 31.5331 1.93706
\(266\) 6.41916 0.393584
\(267\) 19.5070 1.19381
\(268\) 39.7064 2.42545
\(269\) −24.8644 −1.51601 −0.758003 0.652251i \(-0.773825\pi\)
−0.758003 + 0.652251i \(0.773825\pi\)
\(270\) −62.4308 −3.79942
\(271\) −11.0533 −0.671439 −0.335720 0.941962i \(-0.608979\pi\)
−0.335720 + 0.941962i \(0.608979\pi\)
\(272\) 42.8889 2.60052
\(273\) −3.63972 −0.220286
\(274\) 9.97105 0.602373
\(275\) −13.7501 −0.829161
\(276\) 13.4863 0.811779
\(277\) −23.3758 −1.40451 −0.702257 0.711923i \(-0.747824\pi\)
−0.702257 + 0.711923i \(0.747824\pi\)
\(278\) −20.8860 −1.25266
\(279\) −3.64929 −0.218478
\(280\) −7.67135 −0.458451
\(281\) −10.6841 −0.637358 −0.318679 0.947863i \(-0.603239\pi\)
−0.318679 + 0.947863i \(0.603239\pi\)
\(282\) 6.99951 0.416815
\(283\) −18.4046 −1.09404 −0.547021 0.837119i \(-0.684238\pi\)
−0.547021 + 0.837119i \(0.684238\pi\)
\(284\) 66.2848 3.93328
\(285\) 88.5339 5.24430
\(286\) −17.3963 −1.02866
\(287\) −1.68901 −0.0996989
\(288\) −44.0902 −2.59804
\(289\) 7.78731 0.458077
\(290\) −9.56597 −0.561733
\(291\) −26.1934 −1.53548
\(292\) −23.9570 −1.40198
\(293\) −5.02693 −0.293677 −0.146838 0.989161i \(-0.546910\pi\)
−0.146838 + 0.989161i \(0.546910\pi\)
\(294\) −51.4036 −2.99792
\(295\) 20.2310 1.17790
\(296\) −54.1138 −3.14530
\(297\) 10.3399 0.599984
\(298\) −56.7461 −3.28721
\(299\) 4.24524 0.245509
\(300\) −117.044 −6.75754
\(301\) 0.842510 0.0485615
\(302\) −1.16981 −0.0673149
\(303\) 48.6721 2.79614
\(304\) 71.7096 4.11283
\(305\) 28.1246 1.61041
\(306\) −67.8563 −3.87909
\(307\) −15.6946 −0.895736 −0.447868 0.894100i \(-0.647816\pi\)
−0.447868 + 0.894100i \(0.647816\pi\)
\(308\) 2.21527 0.126227
\(309\) −0.984366 −0.0559986
\(310\) −6.62474 −0.376260
\(311\) 19.4424 1.10248 0.551238 0.834348i \(-0.314156\pi\)
0.551238 + 0.834348i \(0.314156\pi\)
\(312\) −84.9309 −4.80827
\(313\) 20.3762 1.15173 0.575866 0.817544i \(-0.304665\pi\)
0.575866 + 0.817544i \(0.304665\pi\)
\(314\) 21.9863 1.24076
\(315\) 5.81056 0.327388
\(316\) −3.88505 −0.218551
\(317\) 23.6273 1.32704 0.663519 0.748159i \(-0.269062\pi\)
0.663519 + 0.748159i \(0.269062\pi\)
\(318\) −63.4145 −3.55611
\(319\) 1.58434 0.0887060
\(320\) −16.3178 −0.912194
\(321\) −47.7801 −2.66683
\(322\) −0.771137 −0.0429738
\(323\) 41.4440 2.30601
\(324\) 13.8777 0.770983
\(325\) −36.8434 −2.04370
\(326\) 18.4729 1.02312
\(327\) 4.43564 0.245292
\(328\) −39.4121 −2.17617
\(329\) −0.280574 −0.0154685
\(330\) 43.5830 2.39917
\(331\) 13.0745 0.718638 0.359319 0.933215i \(-0.383009\pi\)
0.359319 + 0.933215i \(0.383009\pi\)
\(332\) −83.6721 −4.59210
\(333\) 40.9877 2.24611
\(334\) 3.81583 0.208793
\(335\) −31.3134 −1.71083
\(336\) 7.38577 0.402927
\(337\) 14.7501 0.803490 0.401745 0.915752i \(-0.368404\pi\)
0.401745 + 0.915752i \(0.368404\pi\)
\(338\) −12.9894 −0.706532
\(339\) −42.3487 −2.30007
\(340\) −86.3556 −4.68329
\(341\) 1.09720 0.0594170
\(342\) −113.455 −6.13493
\(343\) 4.14751 0.223944
\(344\) 19.6595 1.05997
\(345\) −10.6356 −0.572602
\(346\) 46.5849 2.50442
\(347\) −21.7437 −1.16726 −0.583631 0.812019i \(-0.698369\pi\)
−0.583631 + 0.812019i \(0.698369\pi\)
\(348\) 13.4863 0.722941
\(349\) −14.7938 −0.791896 −0.395948 0.918273i \(-0.629584\pi\)
−0.395948 + 0.918273i \(0.629584\pi\)
\(350\) 6.69250 0.357729
\(351\) 27.7059 1.47883
\(352\) 13.2563 0.706561
\(353\) 4.93410 0.262615 0.131308 0.991342i \(-0.458082\pi\)
0.131308 + 0.991342i \(0.458082\pi\)
\(354\) −40.6856 −2.16242
\(355\) −52.2738 −2.77441
\(356\) −31.8129 −1.68608
\(357\) 4.26854 0.225915
\(358\) −40.6480 −2.14832
\(359\) 15.7127 0.829282 0.414641 0.909985i \(-0.363907\pi\)
0.414641 + 0.909985i \(0.363907\pi\)
\(360\) 135.586 7.14603
\(361\) 50.2937 2.64704
\(362\) 49.4498 2.59902
\(363\) 24.4141 1.28141
\(364\) 5.93582 0.311121
\(365\) 18.8931 0.988908
\(366\) −56.5600 −2.95644
\(367\) 7.48780 0.390860 0.195430 0.980718i \(-0.437390\pi\)
0.195430 + 0.980718i \(0.437390\pi\)
\(368\) −8.61451 −0.449062
\(369\) 29.8521 1.55404
\(370\) 74.4070 3.86823
\(371\) 2.54196 0.131972
\(372\) 9.33968 0.484240
\(373\) 4.44612 0.230211 0.115106 0.993353i \(-0.463279\pi\)
0.115106 + 0.993353i \(0.463279\pi\)
\(374\) 20.4018 1.05495
\(375\) 39.1257 2.02044
\(376\) −6.54705 −0.337638
\(377\) 4.24524 0.218641
\(378\) −5.03270 −0.258854
\(379\) 2.88999 0.148449 0.0742243 0.997242i \(-0.476352\pi\)
0.0742243 + 0.997242i \(0.476352\pi\)
\(380\) −144.385 −7.40681
\(381\) 1.33041 0.0681588
\(382\) −10.2817 −0.526058
\(383\) −15.5570 −0.794927 −0.397463 0.917618i \(-0.630109\pi\)
−0.397463 + 0.917618i \(0.630109\pi\)
\(384\) −15.3059 −0.781075
\(385\) −1.74702 −0.0890361
\(386\) 51.8904 2.64115
\(387\) −14.8908 −0.756944
\(388\) 42.7174 2.16865
\(389\) −27.6653 −1.40269 −0.701344 0.712823i \(-0.747416\pi\)
−0.701344 + 0.712823i \(0.747416\pi\)
\(390\) 116.781 5.91342
\(391\) −4.97869 −0.251783
\(392\) 48.0808 2.42845
\(393\) −46.1256 −2.32673
\(394\) −28.6398 −1.44285
\(395\) 3.06385 0.154159
\(396\) −39.1535 −1.96754
\(397\) 19.0031 0.953738 0.476869 0.878974i \(-0.341772\pi\)
0.476869 + 0.878974i \(0.341772\pi\)
\(398\) 48.3567 2.42390
\(399\) 7.13694 0.357294
\(400\) 74.7631 3.73816
\(401\) −16.3800 −0.817977 −0.408988 0.912540i \(-0.634118\pi\)
−0.408988 + 0.912540i \(0.634118\pi\)
\(402\) 62.9728 3.14080
\(403\) 2.93996 0.146450
\(404\) −79.3767 −3.94914
\(405\) −10.9443 −0.543826
\(406\) −0.771137 −0.0382709
\(407\) −12.3235 −0.610851
\(408\) 99.6043 4.93115
\(409\) 15.8224 0.782369 0.391184 0.920312i \(-0.372065\pi\)
0.391184 + 0.920312i \(0.372065\pi\)
\(410\) 54.1920 2.67635
\(411\) 11.0860 0.546832
\(412\) 1.60535 0.0790899
\(413\) 1.63087 0.0802500
\(414\) 13.6294 0.669847
\(415\) 65.9859 3.23912
\(416\) 35.5202 1.74152
\(417\) −23.2215 −1.13716
\(418\) 34.1115 1.66845
\(419\) −28.0107 −1.36841 −0.684206 0.729289i \(-0.739851\pi\)
−0.684206 + 0.729289i \(0.739851\pi\)
\(420\) −14.8710 −0.725632
\(421\) −4.24762 −0.207017 −0.103508 0.994629i \(-0.533007\pi\)
−0.103508 + 0.994629i \(0.533007\pi\)
\(422\) −10.9822 −0.534607
\(423\) 4.95897 0.241113
\(424\) 59.3153 2.88061
\(425\) 43.2087 2.09593
\(426\) 105.125 5.09333
\(427\) 2.26719 0.109717
\(428\) 77.9221 3.76651
\(429\) −19.3415 −0.933817
\(430\) −27.0320 −1.30360
\(431\) −3.36941 −0.162299 −0.0811495 0.996702i \(-0.525859\pi\)
−0.0811495 + 0.996702i \(0.525859\pi\)
\(432\) −56.2212 −2.70495
\(433\) 10.2719 0.493637 0.246818 0.969062i \(-0.420615\pi\)
0.246818 + 0.969062i \(0.420615\pi\)
\(434\) −0.534036 −0.0256346
\(435\) −10.6356 −0.509939
\(436\) −7.23386 −0.346439
\(437\) −8.32429 −0.398205
\(438\) −37.9949 −1.81547
\(439\) 19.4763 0.929554 0.464777 0.885428i \(-0.346135\pi\)
0.464777 + 0.885428i \(0.346135\pi\)
\(440\) −40.7657 −1.94343
\(441\) −36.4181 −1.73420
\(442\) 54.6668 2.60023
\(443\) 0.131749 0.00625956 0.00312978 0.999995i \(-0.499004\pi\)
0.00312978 + 0.999995i \(0.499004\pi\)
\(444\) −104.900 −4.97835
\(445\) 25.0884 1.18930
\(446\) −47.7130 −2.25927
\(447\) −63.0913 −2.98412
\(448\) −1.31542 −0.0621478
\(449\) −27.9352 −1.31835 −0.659173 0.751992i \(-0.729093\pi\)
−0.659173 + 0.751992i \(0.729093\pi\)
\(450\) −118.286 −5.57604
\(451\) −8.97541 −0.422636
\(452\) 69.0643 3.24851
\(453\) −1.30061 −0.0611082
\(454\) −51.9291 −2.43715
\(455\) −4.68113 −0.219455
\(456\) 166.537 7.79880
\(457\) −10.4880 −0.490608 −0.245304 0.969446i \(-0.578888\pi\)
−0.245304 + 0.969446i \(0.578888\pi\)
\(458\) 7.87122 0.367798
\(459\) −32.4926 −1.51663
\(460\) 17.3451 0.808718
\(461\) 20.0869 0.935542 0.467771 0.883850i \(-0.345057\pi\)
0.467771 + 0.883850i \(0.345057\pi\)
\(462\) 3.51333 0.163455
\(463\) 8.02831 0.373107 0.186554 0.982445i \(-0.440268\pi\)
0.186554 + 0.982445i \(0.440268\pi\)
\(464\) −8.61451 −0.399919
\(465\) −7.36550 −0.341567
\(466\) −13.9457 −0.646021
\(467\) 10.8557 0.502343 0.251171 0.967943i \(-0.419184\pi\)
0.251171 + 0.967943i \(0.419184\pi\)
\(468\) −104.912 −4.84956
\(469\) −2.52425 −0.116559
\(470\) 9.00225 0.415243
\(471\) 24.4448 1.12636
\(472\) 38.0556 1.75165
\(473\) 4.47711 0.205858
\(474\) −6.16155 −0.283009
\(475\) 72.2443 3.31480
\(476\) −6.96134 −0.319073
\(477\) −44.9275 −2.05709
\(478\) 36.8672 1.68626
\(479\) 10.0793 0.460536 0.230268 0.973127i \(-0.426040\pi\)
0.230268 + 0.973127i \(0.426040\pi\)
\(480\) −88.9888 −4.06176
\(481\) −33.0207 −1.50562
\(482\) 20.3688 0.927772
\(483\) −0.857363 −0.0390114
\(484\) −39.8156 −1.80980
\(485\) −33.6880 −1.52969
\(486\) −28.6309 −1.29872
\(487\) −41.2202 −1.86786 −0.933932 0.357450i \(-0.883646\pi\)
−0.933932 + 0.357450i \(0.883646\pi\)
\(488\) 52.9038 2.39484
\(489\) 20.5385 0.928783
\(490\) −66.1115 −2.98661
\(491\) −17.3868 −0.784655 −0.392328 0.919826i \(-0.628330\pi\)
−0.392328 + 0.919826i \(0.628330\pi\)
\(492\) −76.4009 −3.44442
\(493\) −4.97869 −0.224229
\(494\) 91.4020 4.11237
\(495\) 30.8774 1.38784
\(496\) −5.96582 −0.267873
\(497\) −4.21392 −0.189020
\(498\) −132.701 −5.94647
\(499\) 11.0205 0.493346 0.246673 0.969099i \(-0.420663\pi\)
0.246673 + 0.969099i \(0.420663\pi\)
\(500\) −63.8080 −2.85358
\(501\) 4.24250 0.189541
\(502\) 20.2131 0.902155
\(503\) −19.4469 −0.867094 −0.433547 0.901131i \(-0.642738\pi\)
−0.433547 + 0.901131i \(0.642738\pi\)
\(504\) 10.9300 0.486859
\(505\) 62.5984 2.78559
\(506\) −4.09783 −0.182171
\(507\) −14.4419 −0.641387
\(508\) −2.16969 −0.0962644
\(509\) −23.9761 −1.06272 −0.531361 0.847145i \(-0.678319\pi\)
−0.531361 + 0.847145i \(0.678319\pi\)
\(510\) −136.957 −6.06455
\(511\) 1.52302 0.0673743
\(512\) 47.7847 2.11180
\(513\) −54.3271 −2.39860
\(514\) 77.4898 3.41793
\(515\) −1.26602 −0.0557874
\(516\) 38.1103 1.67771
\(517\) −1.49098 −0.0655730
\(518\) 5.99813 0.263543
\(519\) 51.7939 2.27350
\(520\) −109.232 −4.79013
\(521\) −6.98559 −0.306044 −0.153022 0.988223i \(-0.548901\pi\)
−0.153022 + 0.988223i \(0.548901\pi\)
\(522\) 13.6294 0.596541
\(523\) 2.57278 0.112500 0.0562498 0.998417i \(-0.482086\pi\)
0.0562498 + 0.998417i \(0.482086\pi\)
\(524\) 75.2238 3.28617
\(525\) 7.44084 0.324745
\(526\) 35.9829 1.56893
\(527\) −3.44790 −0.150193
\(528\) 39.2481 1.70805
\(529\) 1.00000 0.0434783
\(530\) −81.5591 −3.54270
\(531\) −28.8247 −1.25088
\(532\) −11.6393 −0.504626
\(533\) −24.0496 −1.04171
\(534\) −50.4540 −2.18336
\(535\) −61.4513 −2.65677
\(536\) −58.9021 −2.54418
\(537\) −45.1932 −1.95023
\(538\) 64.3107 2.77263
\(539\) 10.9495 0.471630
\(540\) 113.200 4.87135
\(541\) −6.06745 −0.260860 −0.130430 0.991458i \(-0.541636\pi\)
−0.130430 + 0.991458i \(0.541636\pi\)
\(542\) 28.5889 1.22800
\(543\) 54.9791 2.35938
\(544\) −41.6569 −1.78603
\(545\) 5.70480 0.244367
\(546\) 9.41399 0.402881
\(547\) −17.8606 −0.763663 −0.381831 0.924232i \(-0.624707\pi\)
−0.381831 + 0.924232i \(0.624707\pi\)
\(548\) −18.0796 −0.772321
\(549\) −40.0713 −1.71020
\(550\) 35.5640 1.51646
\(551\) −8.32429 −0.354627
\(552\) −20.0061 −0.851518
\(553\) 0.246984 0.0105028
\(554\) 60.4605 2.56872
\(555\) 82.7270 3.51156
\(556\) 37.8707 1.60607
\(557\) −24.5101 −1.03853 −0.519264 0.854614i \(-0.673794\pi\)
−0.519264 + 0.854614i \(0.673794\pi\)
\(558\) 9.43876 0.399575
\(559\) 11.9964 0.507395
\(560\) 9.49902 0.401407
\(561\) 22.6831 0.957682
\(562\) 27.6339 1.16567
\(563\) 19.6373 0.827614 0.413807 0.910365i \(-0.364199\pi\)
0.413807 + 0.910365i \(0.364199\pi\)
\(564\) −12.6915 −0.534411
\(565\) −54.4658 −2.29139
\(566\) 47.6028 2.00090
\(567\) −0.882246 −0.0370509
\(568\) −98.3297 −4.12582
\(569\) 12.2184 0.512220 0.256110 0.966648i \(-0.417559\pi\)
0.256110 + 0.966648i \(0.417559\pi\)
\(570\) −228.990 −9.59132
\(571\) −14.8371 −0.620912 −0.310456 0.950588i \(-0.600482\pi\)
−0.310456 + 0.950588i \(0.600482\pi\)
\(572\) 31.5431 1.31888
\(573\) −11.4314 −0.477553
\(574\) 4.36855 0.182340
\(575\) −8.67874 −0.361929
\(576\) 23.2492 0.968718
\(577\) 3.27511 0.136345 0.0681724 0.997674i \(-0.478283\pi\)
0.0681724 + 0.997674i \(0.478283\pi\)
\(578\) −20.1416 −0.837780
\(579\) 57.6927 2.39763
\(580\) 17.3451 0.720215
\(581\) 5.31928 0.220681
\(582\) 67.7481 2.80825
\(583\) 13.5080 0.559445
\(584\) 35.5388 1.47061
\(585\) 82.7361 3.42072
\(586\) 13.0020 0.537107
\(587\) −3.32253 −0.137135 −0.0685677 0.997646i \(-0.521843\pi\)
−0.0685677 + 0.997646i \(0.521843\pi\)
\(588\) 93.2052 3.84372
\(589\) −5.76483 −0.237536
\(590\) −52.3268 −2.15426
\(591\) −31.8422 −1.30981
\(592\) 67.0062 2.75394
\(593\) 5.26774 0.216320 0.108160 0.994133i \(-0.465504\pi\)
0.108160 + 0.994133i \(0.465504\pi\)
\(594\) −26.7439 −1.09731
\(595\) 5.48988 0.225063
\(596\) 102.892 4.21463
\(597\) 53.7639 2.20041
\(598\) −10.9802 −0.449012
\(599\) −27.8838 −1.13930 −0.569651 0.821887i \(-0.692922\pi\)
−0.569651 + 0.821887i \(0.692922\pi\)
\(600\) 173.628 7.08834
\(601\) −41.4467 −1.69064 −0.845322 0.534256i \(-0.820592\pi\)
−0.845322 + 0.534256i \(0.820592\pi\)
\(602\) −2.17912 −0.0888143
\(603\) 44.6146 1.81685
\(604\) 2.12110 0.0863064
\(605\) 31.3996 1.27657
\(606\) −125.888 −5.11387
\(607\) −9.60082 −0.389685 −0.194843 0.980835i \(-0.562420\pi\)
−0.194843 + 0.980835i \(0.562420\pi\)
\(608\) −69.6497 −2.82467
\(609\) −0.857363 −0.0347421
\(610\) −72.7433 −2.94529
\(611\) −3.99507 −0.161623
\(612\) 123.037 4.97349
\(613\) −9.71648 −0.392445 −0.196222 0.980559i \(-0.562867\pi\)
−0.196222 + 0.980559i \(0.562867\pi\)
\(614\) 40.5934 1.63822
\(615\) 60.2516 2.42958
\(616\) −3.28622 −0.132406
\(617\) 15.4612 0.622446 0.311223 0.950337i \(-0.399261\pi\)
0.311223 + 0.950337i \(0.399261\pi\)
\(618\) 2.54602 0.102416
\(619\) −32.2470 −1.29612 −0.648058 0.761591i \(-0.724419\pi\)
−0.648058 + 0.761591i \(0.724419\pi\)
\(620\) 12.0120 0.482414
\(621\) 6.52634 0.261893
\(622\) −50.2870 −2.01632
\(623\) 2.02244 0.0810273
\(624\) 105.165 4.20998
\(625\) 6.92685 0.277074
\(626\) −52.7023 −2.10641
\(627\) 37.9258 1.51461
\(628\) −39.8657 −1.59081
\(629\) 38.7257 1.54409
\(630\) −15.0288 −0.598761
\(631\) −0.388206 −0.0154543 −0.00772713 0.999970i \(-0.502460\pi\)
−0.00772713 + 0.999970i \(0.502460\pi\)
\(632\) 5.76325 0.229250
\(633\) −12.2102 −0.485314
\(634\) −61.1110 −2.42703
\(635\) 1.71107 0.0679017
\(636\) 114.984 4.55939
\(637\) 29.3393 1.16247
\(638\) −4.09783 −0.162235
\(639\) 74.4784 2.94632
\(640\) −19.6853 −0.778129
\(641\) −10.1116 −0.399382 −0.199691 0.979859i \(-0.563994\pi\)
−0.199691 + 0.979859i \(0.563994\pi\)
\(642\) 123.582 4.87737
\(643\) −2.00502 −0.0790702 −0.0395351 0.999218i \(-0.512588\pi\)
−0.0395351 + 0.999218i \(0.512588\pi\)
\(644\) 1.39823 0.0550979
\(645\) −30.0547 −1.18340
\(646\) −107.193 −4.21747
\(647\) −6.03637 −0.237314 −0.118657 0.992935i \(-0.537859\pi\)
−0.118657 + 0.992935i \(0.537859\pi\)
\(648\) −20.5868 −0.808724
\(649\) 8.66649 0.340190
\(650\) 95.2940 3.73774
\(651\) −0.593751 −0.0232709
\(652\) −33.4952 −1.31177
\(653\) 29.0646 1.13739 0.568693 0.822550i \(-0.307449\pi\)
0.568693 + 0.822550i \(0.307449\pi\)
\(654\) −11.4726 −0.448615
\(655\) −59.3233 −2.31795
\(656\) 48.8019 1.90539
\(657\) −26.9184 −1.05019
\(658\) 0.725694 0.0282905
\(659\) 3.50863 0.136677 0.0683383 0.997662i \(-0.478230\pi\)
0.0683383 + 0.997662i \(0.478230\pi\)
\(660\) −79.0249 −3.07604
\(661\) −24.1713 −0.940154 −0.470077 0.882625i \(-0.655774\pi\)
−0.470077 + 0.882625i \(0.655774\pi\)
\(662\) −33.8166 −1.31432
\(663\) 60.7795 2.36048
\(664\) 124.123 4.81690
\(665\) 9.17900 0.355946
\(666\) −106.013 −4.10793
\(667\) 1.00000 0.0387202
\(668\) −6.91887 −0.267699
\(669\) −53.0481 −2.05096
\(670\) 80.9910 3.12895
\(671\) 12.0479 0.465105
\(672\) −7.17360 −0.276728
\(673\) −21.8007 −0.840356 −0.420178 0.907442i \(-0.638032\pi\)
−0.420178 + 0.907442i \(0.638032\pi\)
\(674\) −38.1506 −1.46951
\(675\) −56.6404 −2.18009
\(676\) 23.5525 0.905865
\(677\) −25.6377 −0.985338 −0.492669 0.870217i \(-0.663979\pi\)
−0.492669 + 0.870217i \(0.663979\pi\)
\(678\) 109.533 4.20660
\(679\) −2.71567 −0.104218
\(680\) 128.104 4.91255
\(681\) −57.7357 −2.21244
\(682\) −2.83788 −0.108668
\(683\) 22.5840 0.864153 0.432077 0.901837i \(-0.357781\pi\)
0.432077 + 0.901837i \(0.357781\pi\)
\(684\) 205.717 7.86577
\(685\) 14.2580 0.544769
\(686\) −10.7274 −0.409573
\(687\) 8.75136 0.333885
\(688\) −24.3434 −0.928082
\(689\) 36.1948 1.37891
\(690\) 27.5086 1.04724
\(691\) 18.2063 0.692601 0.346301 0.938124i \(-0.387438\pi\)
0.346301 + 0.938124i \(0.387438\pi\)
\(692\) −84.4680 −3.21099
\(693\) 2.48910 0.0945532
\(694\) 56.2392 2.13481
\(695\) −29.8657 −1.13287
\(696\) −20.0061 −0.758331
\(697\) 28.2046 1.06833
\(698\) 38.2637 1.44830
\(699\) −15.5051 −0.586455
\(700\) −12.1349 −0.458655
\(701\) −26.0625 −0.984367 −0.492183 0.870492i \(-0.663801\pi\)
−0.492183 + 0.870492i \(0.663801\pi\)
\(702\) −71.6603 −2.70464
\(703\) 64.7487 2.44205
\(704\) −6.99017 −0.263452
\(705\) 10.0089 0.376956
\(706\) −12.7618 −0.480299
\(707\) 5.04621 0.189782
\(708\) 73.7713 2.77250
\(709\) −8.21955 −0.308692 −0.154346 0.988017i \(-0.549327\pi\)
−0.154346 + 0.988017i \(0.549327\pi\)
\(710\) 135.204 5.07412
\(711\) −4.36529 −0.163711
\(712\) 47.1926 1.76862
\(713\) 0.692531 0.0259355
\(714\) −11.0404 −0.413177
\(715\) −24.8756 −0.930296
\(716\) 73.7032 2.75442
\(717\) 40.9896 1.53078
\(718\) −40.6402 −1.51668
\(719\) 22.3796 0.834620 0.417310 0.908764i \(-0.362973\pi\)
0.417310 + 0.908764i \(0.362973\pi\)
\(720\) −167.889 −6.25687
\(721\) −0.102057 −0.00380080
\(722\) −130.083 −4.84118
\(723\) 22.6464 0.842227
\(724\) −89.6626 −3.33228
\(725\) −8.67874 −0.322320
\(726\) −63.1461 −2.34357
\(727\) −22.5875 −0.837724 −0.418862 0.908050i \(-0.637571\pi\)
−0.418862 + 0.908050i \(0.637571\pi\)
\(728\) −8.80545 −0.326352
\(729\) −40.7098 −1.50777
\(730\) −48.8662 −1.80862
\(731\) −14.0690 −0.520362
\(732\) 102.555 3.79054
\(733\) −18.1058 −0.668752 −0.334376 0.942440i \(-0.608526\pi\)
−0.334376 + 0.942440i \(0.608526\pi\)
\(734\) −19.3669 −0.714845
\(735\) −73.5039 −2.71123
\(736\) 8.36705 0.308414
\(737\) −13.4139 −0.494108
\(738\) −77.2114 −2.84219
\(739\) 35.0206 1.28825 0.644126 0.764919i \(-0.277221\pi\)
0.644126 + 0.764919i \(0.277221\pi\)
\(740\) −134.915 −4.95958
\(741\) 101.622 3.73319
\(742\) −6.57468 −0.241364
\(743\) −49.7154 −1.82388 −0.911940 0.410324i \(-0.865416\pi\)
−0.911940 + 0.410324i \(0.865416\pi\)
\(744\) −13.8549 −0.507944
\(745\) −81.1433 −2.97286
\(746\) −11.4997 −0.421035
\(747\) −94.0150 −3.43983
\(748\) −36.9927 −1.35259
\(749\) −4.95374 −0.181006
\(750\) −101.197 −3.69520
\(751\) −15.7405 −0.574378 −0.287189 0.957874i \(-0.592721\pi\)
−0.287189 + 0.957874i \(0.592721\pi\)
\(752\) 8.10686 0.295627
\(753\) 22.4733 0.818972
\(754\) −10.9802 −0.399874
\(755\) −1.67275 −0.0608777
\(756\) 9.12532 0.331885
\(757\) 1.52963 0.0555952 0.0277976 0.999614i \(-0.491151\pi\)
0.0277976 + 0.999614i \(0.491151\pi\)
\(758\) −7.47484 −0.271498
\(759\) −4.55604 −0.165374
\(760\) 214.187 7.76939
\(761\) −5.19360 −0.188268 −0.0941339 0.995560i \(-0.530008\pi\)
−0.0941339 + 0.995560i \(0.530008\pi\)
\(762\) −3.44104 −0.124656
\(763\) 0.459878 0.0166487
\(764\) 18.6429 0.674475
\(765\) −97.0303 −3.50814
\(766\) 40.2376 1.45385
\(767\) 23.2219 0.838494
\(768\) 64.9632 2.34416
\(769\) 0.710853 0.0256340 0.0128170 0.999918i \(-0.495920\pi\)
0.0128170 + 0.999918i \(0.495920\pi\)
\(770\) 4.51859 0.162839
\(771\) 86.1545 3.10278
\(772\) −94.0880 −3.38630
\(773\) −11.8426 −0.425950 −0.212975 0.977058i \(-0.568315\pi\)
−0.212975 + 0.977058i \(0.568315\pi\)
\(774\) 38.5146 1.38438
\(775\) −6.01030 −0.215896
\(776\) −63.3688 −2.27481
\(777\) 6.66882 0.239243
\(778\) 71.5553 2.56538
\(779\) 47.1577 1.68960
\(780\) −211.747 −7.58177
\(781\) −22.3929 −0.801279
\(782\) 12.8772 0.460487
\(783\) 6.52634 0.233232
\(784\) −59.5358 −2.12628
\(785\) 31.4391 1.12211
\(786\) 119.302 4.25536
\(787\) 18.9698 0.676199 0.338100 0.941110i \(-0.390216\pi\)
0.338100 + 0.941110i \(0.390216\pi\)
\(788\) 51.9298 1.84992
\(789\) 40.0065 1.42427
\(790\) −7.92452 −0.281942
\(791\) −4.39062 −0.156112
\(792\) 58.0820 2.06385
\(793\) 32.2824 1.14638
\(794\) −49.1508 −1.74430
\(795\) −90.6788 −3.21605
\(796\) −87.6806 −3.10776
\(797\) −15.6956 −0.555967 −0.277984 0.960586i \(-0.589666\pi\)
−0.277984 + 0.960586i \(0.589666\pi\)
\(798\) −18.4594 −0.653456
\(799\) 4.68529 0.165754
\(800\) −72.6155 −2.56734
\(801\) −35.7454 −1.26300
\(802\) 42.3662 1.49600
\(803\) 8.09334 0.285608
\(804\) −114.183 −4.02691
\(805\) −1.10268 −0.0388643
\(806\) −7.60410 −0.267843
\(807\) 71.5018 2.51698
\(808\) 117.751 4.14246
\(809\) −1.92393 −0.0676419 −0.0338209 0.999428i \(-0.510768\pi\)
−0.0338209 + 0.999428i \(0.510768\pi\)
\(810\) 28.3070 0.994606
\(811\) −33.0097 −1.15913 −0.579563 0.814927i \(-0.696777\pi\)
−0.579563 + 0.814927i \(0.696777\pi\)
\(812\) 1.39823 0.0490682
\(813\) 31.7856 1.11477
\(814\) 31.8742 1.11719
\(815\) 26.4151 0.925281
\(816\) −123.335 −4.31757
\(817\) −23.5232 −0.822973
\(818\) −40.9241 −1.43088
\(819\) 6.66956 0.233053
\(820\) −98.2612 −3.43143
\(821\) 10.3352 0.360700 0.180350 0.983602i \(-0.442277\pi\)
0.180350 + 0.983602i \(0.442277\pi\)
\(822\) −28.6735 −1.00010
\(823\) 7.36395 0.256691 0.128346 0.991730i \(-0.459033\pi\)
0.128346 + 0.991730i \(0.459033\pi\)
\(824\) −2.38144 −0.0829615
\(825\) 39.5407 1.37663
\(826\) −4.21819 −0.146770
\(827\) −28.2030 −0.980713 −0.490357 0.871522i \(-0.663133\pi\)
−0.490357 + 0.871522i \(0.663133\pi\)
\(828\) −24.7128 −0.858830
\(829\) 47.8749 1.66277 0.831383 0.555700i \(-0.187550\pi\)
0.831383 + 0.555700i \(0.187550\pi\)
\(830\) −170.670 −5.92404
\(831\) 67.2211 2.33187
\(832\) −18.7302 −0.649352
\(833\) −34.4082 −1.19218
\(834\) 60.0614 2.07976
\(835\) 5.45639 0.188826
\(836\) −61.8512 −2.13917
\(837\) 4.51970 0.156224
\(838\) 72.4486 2.50270
\(839\) −21.2537 −0.733760 −0.366880 0.930268i \(-0.619574\pi\)
−0.366880 + 0.930268i \(0.619574\pi\)
\(840\) 22.0603 0.761153
\(841\) 1.00000 0.0344828
\(842\) 10.9863 0.378613
\(843\) 30.7239 1.05819
\(844\) 19.9130 0.685435
\(845\) −18.5741 −0.638968
\(846\) −12.8262 −0.440973
\(847\) 2.53120 0.0869730
\(848\) −73.4469 −2.52218
\(849\) 52.9257 1.81640
\(850\) −111.758 −3.83326
\(851\) −7.77829 −0.266636
\(852\) −190.613 −6.53031
\(853\) 37.7663 1.29309 0.646547 0.762874i \(-0.276212\pi\)
0.646547 + 0.762874i \(0.276212\pi\)
\(854\) −5.86401 −0.200662
\(855\) −162.233 −5.54826
\(856\) −115.593 −3.95089
\(857\) 21.6219 0.738591 0.369296 0.929312i \(-0.379599\pi\)
0.369296 + 0.929312i \(0.379599\pi\)
\(858\) 50.0261 1.70786
\(859\) −28.5224 −0.973171 −0.486586 0.873633i \(-0.661758\pi\)
−0.486586 + 0.873633i \(0.661758\pi\)
\(860\) 49.0146 1.67139
\(861\) 4.85703 0.165527
\(862\) 8.71486 0.296829
\(863\) −6.71401 −0.228548 −0.114274 0.993449i \(-0.536454\pi\)
−0.114274 + 0.993449i \(0.536454\pi\)
\(864\) 54.6062 1.85774
\(865\) 66.6135 2.26493
\(866\) −26.5679 −0.902815
\(867\) −22.3938 −0.760532
\(868\) 0.968317 0.0328668
\(869\) 1.31248 0.0445228
\(870\) 27.5086 0.932630
\(871\) −35.9426 −1.21787
\(872\) 10.7310 0.363398
\(873\) 47.9978 1.62448
\(874\) 21.5304 0.728278
\(875\) 4.05646 0.137134
\(876\) 68.8925 2.32766
\(877\) 29.1648 0.984826 0.492413 0.870362i \(-0.336115\pi\)
0.492413 + 0.870362i \(0.336115\pi\)
\(878\) −50.3748 −1.70007
\(879\) 14.4558 0.487583
\(880\) 50.4780 1.70161
\(881\) −39.6009 −1.33419 −0.667095 0.744973i \(-0.732462\pi\)
−0.667095 + 0.744973i \(0.732462\pi\)
\(882\) 94.1940 3.17168
\(883\) −51.2378 −1.72429 −0.862145 0.506662i \(-0.830879\pi\)
−0.862145 + 0.506662i \(0.830879\pi\)
\(884\) −99.1220 −3.33383
\(885\) −58.1779 −1.95563
\(886\) −0.340763 −0.0114481
\(887\) −28.2673 −0.949123 −0.474561 0.880222i \(-0.657393\pi\)
−0.474561 + 0.880222i \(0.657393\pi\)
\(888\) 155.614 5.22205
\(889\) 0.137934 0.00462614
\(890\) −64.8902 −2.17513
\(891\) −4.68827 −0.157063
\(892\) 86.5134 2.89668
\(893\) 7.83374 0.262146
\(894\) 163.183 5.45766
\(895\) −58.1241 −1.94288
\(896\) −1.58688 −0.0530139
\(897\) −12.2079 −0.407611
\(898\) 72.2534 2.41113
\(899\) 0.692531 0.0230972
\(900\) 214.476 7.14921
\(901\) −42.4481 −1.41415
\(902\) 23.2146 0.772960
\(903\) −2.42278 −0.0806252
\(904\) −102.453 −3.40753
\(905\) 70.7101 2.35048
\(906\) 3.36399 0.111761
\(907\) −14.9606 −0.496759 −0.248380 0.968663i \(-0.579898\pi\)
−0.248380 + 0.968663i \(0.579898\pi\)
\(908\) 94.1580 3.12474
\(909\) −89.1887 −2.95820
\(910\) 12.1076 0.401362
\(911\) 46.5789 1.54323 0.771614 0.636091i \(-0.219450\pi\)
0.771614 + 0.636091i \(0.219450\pi\)
\(912\) −206.214 −6.82841
\(913\) 28.2668 0.935494
\(914\) 27.1268 0.897274
\(915\) −80.8772 −2.67372
\(916\) −14.2721 −0.471564
\(917\) −4.78220 −0.157922
\(918\) 84.0409 2.77376
\(919\) −13.2992 −0.438701 −0.219351 0.975646i \(-0.570394\pi\)
−0.219351 + 0.975646i \(0.570394\pi\)
\(920\) −25.7304 −0.848306
\(921\) 45.1324 1.48716
\(922\) −51.9541 −1.71102
\(923\) −60.0017 −1.97498
\(924\) −6.37039 −0.209571
\(925\) 67.5058 2.21958
\(926\) −20.7649 −0.682378
\(927\) 1.80379 0.0592443
\(928\) 8.36705 0.274662
\(929\) −53.8440 −1.76657 −0.883283 0.468840i \(-0.844672\pi\)
−0.883283 + 0.468840i \(0.844672\pi\)
\(930\) 19.0506 0.624693
\(931\) −57.5301 −1.88547
\(932\) 25.2864 0.828283
\(933\) −55.9100 −1.83041
\(934\) −28.0779 −0.918737
\(935\) 29.1733 0.954070
\(936\) 155.631 5.08695
\(937\) −52.1527 −1.70375 −0.851877 0.523742i \(-0.824536\pi\)
−0.851877 + 0.523742i \(0.824536\pi\)
\(938\) 6.52888 0.213176
\(939\) −58.5953 −1.91219
\(940\) −16.3229 −0.532395
\(941\) 52.5915 1.71443 0.857217 0.514956i \(-0.172192\pi\)
0.857217 + 0.514956i \(0.172192\pi\)
\(942\) −63.2255 −2.06000
\(943\) −5.66508 −0.184480
\(944\) −47.1222 −1.53370
\(945\) −7.19645 −0.234101
\(946\) −11.5799 −0.376494
\(947\) 43.6115 1.41718 0.708592 0.705618i \(-0.249331\pi\)
0.708592 + 0.705618i \(0.249331\pi\)
\(948\) 11.1721 0.362854
\(949\) 21.6861 0.703961
\(950\) −186.857 −6.06245
\(951\) −67.9443 −2.20324
\(952\) 10.3267 0.334692
\(953\) 29.9990 0.971763 0.485882 0.874025i \(-0.338499\pi\)
0.485882 + 0.874025i \(0.338499\pi\)
\(954\) 116.203 3.76222
\(955\) −14.7022 −0.475752
\(956\) −66.8477 −2.16201
\(957\) −4.55604 −0.147276
\(958\) −26.0698 −0.842276
\(959\) 1.14937 0.0371151
\(960\) 46.9247 1.51449
\(961\) −30.5204 −0.984529
\(962\) 85.4069 2.75363
\(963\) 87.5543 2.82140
\(964\) −36.9328 −1.18952
\(965\) 74.2001 2.38858
\(966\) 2.21754 0.0713481
\(967\) 13.5790 0.436670 0.218335 0.975874i \(-0.429937\pi\)
0.218335 + 0.975874i \(0.429937\pi\)
\(968\) 59.0642 1.89840
\(969\) −119.179 −3.82860
\(970\) 87.1326 2.79766
\(971\) 31.8369 1.02169 0.510847 0.859672i \(-0.329332\pi\)
0.510847 + 0.859672i \(0.329332\pi\)
\(972\) 51.9137 1.66513
\(973\) −2.40755 −0.0771825
\(974\) 106.614 3.41615
\(975\) 105.950 3.39310
\(976\) −65.5080 −2.09686
\(977\) −25.6319 −0.820038 −0.410019 0.912077i \(-0.634478\pi\)
−0.410019 + 0.912077i \(0.634478\pi\)
\(978\) −53.1221 −1.69866
\(979\) 10.7473 0.343485
\(980\) 119.874 3.82922
\(981\) −8.12805 −0.259509
\(982\) 44.9703 1.43506
\(983\) −32.7361 −1.04412 −0.522060 0.852909i \(-0.674836\pi\)
−0.522060 + 0.852909i \(0.674836\pi\)
\(984\) 113.336 3.61303
\(985\) −40.9531 −1.30487
\(986\) 12.8772 0.410093
\(987\) 0.806839 0.0256820
\(988\) −165.730 −5.27259
\(989\) 2.82585 0.0898569
\(990\) −79.8632 −2.53822
\(991\) −2.56233 −0.0813950 −0.0406975 0.999172i \(-0.512958\pi\)
−0.0406975 + 0.999172i \(0.512958\pi\)
\(992\) 5.79444 0.183974
\(993\) −37.5979 −1.19313
\(994\) 10.8991 0.345700
\(995\) 69.1471 2.19211
\(996\) 240.614 7.62414
\(997\) 39.5107 1.25132 0.625658 0.780097i \(-0.284830\pi\)
0.625658 + 0.780097i \(0.284830\pi\)
\(998\) −28.5041 −0.902283
\(999\) −50.7638 −1.60610
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 667.2.a.b.1.2 12
3.2 odd 2 6003.2.a.n.1.11 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
667.2.a.b.1.2 12 1.1 even 1 trivial
6003.2.a.n.1.11 12 3.2 odd 2