Properties

Label 4013.2.a.c.1.4
Level $4013$
Weight $2$
Character 4013.1
Self dual yes
Analytic conductor $32.044$
Analytic rank $0$
Dimension $176$
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] = [4013,2,Mod(1,4013)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4013, 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("4013.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4013 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4013.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: \(32.0439663311\)
Analytic rank: \(0\)
Dimension: \(176\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) \(=\) 4013.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.69276 q^{2} -0.212283 q^{3} +5.25096 q^{4} -3.83789 q^{5} +0.571627 q^{6} +2.56921 q^{7} -8.75407 q^{8} -2.95494 q^{9} +O(q^{10})\) \(q-2.69276 q^{2} -0.212283 q^{3} +5.25096 q^{4} -3.83789 q^{5} +0.571627 q^{6} +2.56921 q^{7} -8.75407 q^{8} -2.95494 q^{9} +10.3345 q^{10} +2.31259 q^{11} -1.11469 q^{12} +3.08100 q^{13} -6.91826 q^{14} +0.814718 q^{15} +13.0707 q^{16} +0.494885 q^{17} +7.95694 q^{18} +6.67887 q^{19} -20.1526 q^{20} -0.545398 q^{21} -6.22725 q^{22} +8.86376 q^{23} +1.85834 q^{24} +9.72941 q^{25} -8.29641 q^{26} +1.26413 q^{27} +13.4908 q^{28} -2.15522 q^{29} -2.19384 q^{30} +0.634048 q^{31} -17.6881 q^{32} -0.490923 q^{33} -1.33261 q^{34} -9.86033 q^{35} -15.5163 q^{36} +3.65718 q^{37} -17.9846 q^{38} -0.654044 q^{39} +33.5972 q^{40} +9.17637 q^{41} +1.46863 q^{42} +7.81894 q^{43} +12.1433 q^{44} +11.3407 q^{45} -23.8680 q^{46} -6.82433 q^{47} -2.77468 q^{48} -0.399181 q^{49} -26.1990 q^{50} -0.105056 q^{51} +16.1782 q^{52} -11.3666 q^{53} -3.40400 q^{54} -8.87546 q^{55} -22.4910 q^{56} -1.41781 q^{57} +5.80351 q^{58} -1.47305 q^{59} +4.27806 q^{60} -4.25610 q^{61} -1.70734 q^{62} -7.59184 q^{63} +21.4885 q^{64} -11.8246 q^{65} +1.32194 q^{66} -2.72727 q^{67} +2.59862 q^{68} -1.88162 q^{69} +26.5515 q^{70} +12.2667 q^{71} +25.8677 q^{72} -4.18062 q^{73} -9.84792 q^{74} -2.06539 q^{75} +35.0705 q^{76} +5.94151 q^{77} +1.76119 q^{78} -4.70363 q^{79} -50.1639 q^{80} +8.59645 q^{81} -24.7098 q^{82} +0.123219 q^{83} -2.86387 q^{84} -1.89932 q^{85} -21.0545 q^{86} +0.457517 q^{87} -20.2446 q^{88} +2.64071 q^{89} -30.5379 q^{90} +7.91573 q^{91} +46.5433 q^{92} -0.134598 q^{93} +18.3763 q^{94} -25.6328 q^{95} +3.75489 q^{96} -18.0692 q^{97} +1.07490 q^{98} -6.83355 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9} + 43 q^{10} + 18 q^{11} + 95 q^{12} + 95 q^{13} + 2 q^{14} + 36 q^{15} + 225 q^{16} + 35 q^{17} + 46 q^{18} + 127 q^{19} + 4 q^{20} + 32 q^{21} + 60 q^{22} + 35 q^{23} + 26 q^{24} + 207 q^{25} + 19 q^{26} + 191 q^{27} + 87 q^{28} + 16 q^{29} + 28 q^{30} + 93 q^{31} + 73 q^{32} + 70 q^{33} + 45 q^{34} + 73 q^{35} + 206 q^{36} + 64 q^{37} + 35 q^{38} + 72 q^{39} + 139 q^{40} + 19 q^{41} + 35 q^{42} + 261 q^{43} + 11 q^{44} + 12 q^{45} + 58 q^{46} + 40 q^{47} + 130 q^{48} + 234 q^{49} - 14 q^{50} + 76 q^{51} + 263 q^{52} + 17 q^{53} + 28 q^{54} + 170 q^{55} - 10 q^{56} + 60 q^{57} + 52 q^{58} + 69 q^{59} + 37 q^{60} + 110 q^{61} + 71 q^{62} + 101 q^{63} + 250 q^{64} - q^{65} + 43 q^{66} + 190 q^{67} + 48 q^{68} + 45 q^{69} + 14 q^{70} + 9 q^{71} + 98 q^{72} + 182 q^{73} - 23 q^{74} + 219 q^{75} + 197 q^{76} + 25 q^{77} - 26 q^{78} + 105 q^{79} + 20 q^{80} + 236 q^{81} + 107 q^{82} + 130 q^{83} + 38 q^{84} + 73 q^{85} - 24 q^{86} + 171 q^{87} + 165 q^{88} + 40 q^{89} + 45 q^{90} + 182 q^{91} - 4 q^{92} + 23 q^{93} + 98 q^{94} + 30 q^{95} - 2 q^{96} + 168 q^{97} + 82 q^{98} + 50 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.69276 −1.90407 −0.952035 0.305989i \(-0.901013\pi\)
−0.952035 + 0.305989i \(0.901013\pi\)
\(3\) −0.212283 −0.122562 −0.0612808 0.998121i \(-0.519519\pi\)
−0.0612808 + 0.998121i \(0.519519\pi\)
\(4\) 5.25096 2.62548
\(5\) −3.83789 −1.71636 −0.858179 0.513351i \(-0.828404\pi\)
−0.858179 + 0.513351i \(0.828404\pi\)
\(6\) 0.571627 0.233366
\(7\) 2.56921 0.971069 0.485534 0.874218i \(-0.338625\pi\)
0.485534 + 0.874218i \(0.338625\pi\)
\(8\) −8.75407 −3.09503
\(9\) −2.95494 −0.984979
\(10\) 10.3345 3.26806
\(11\) 2.31259 0.697271 0.348636 0.937258i \(-0.386645\pi\)
0.348636 + 0.937258i \(0.386645\pi\)
\(12\) −1.11469 −0.321783
\(13\) 3.08100 0.854517 0.427258 0.904130i \(-0.359479\pi\)
0.427258 + 0.904130i \(0.359479\pi\)
\(14\) −6.91826 −1.84898
\(15\) 0.814718 0.210359
\(16\) 13.0707 3.26767
\(17\) 0.494885 0.120027 0.0600136 0.998198i \(-0.480886\pi\)
0.0600136 + 0.998198i \(0.480886\pi\)
\(18\) 7.95694 1.87547
\(19\) 6.67887 1.53224 0.766119 0.642699i \(-0.222185\pi\)
0.766119 + 0.642699i \(0.222185\pi\)
\(20\) −20.1526 −4.50626
\(21\) −0.545398 −0.119016
\(22\) −6.22725 −1.32765
\(23\) 8.86376 1.84822 0.924111 0.382125i \(-0.124808\pi\)
0.924111 + 0.382125i \(0.124808\pi\)
\(24\) 1.85834 0.379332
\(25\) 9.72941 1.94588
\(26\) −8.29641 −1.62706
\(27\) 1.26413 0.243282
\(28\) 13.4908 2.54952
\(29\) −2.15522 −0.400215 −0.200108 0.979774i \(-0.564129\pi\)
−0.200108 + 0.979774i \(0.564129\pi\)
\(30\) −2.19384 −0.400539
\(31\) 0.634048 0.113878 0.0569392 0.998378i \(-0.481866\pi\)
0.0569392 + 0.998378i \(0.481866\pi\)
\(32\) −17.6881 −3.12685
\(33\) −0.490923 −0.0854587
\(34\) −1.33261 −0.228540
\(35\) −9.86033 −1.66670
\(36\) −15.5163 −2.58604
\(37\) 3.65718 0.601237 0.300619 0.953744i \(-0.402807\pi\)
0.300619 + 0.953744i \(0.402807\pi\)
\(38\) −17.9846 −2.91749
\(39\) −0.654044 −0.104731
\(40\) 33.5972 5.31218
\(41\) 9.17637 1.43311 0.716554 0.697531i \(-0.245718\pi\)
0.716554 + 0.697531i \(0.245718\pi\)
\(42\) 1.46863 0.226614
\(43\) 7.81894 1.19238 0.596188 0.802845i \(-0.296681\pi\)
0.596188 + 0.802845i \(0.296681\pi\)
\(44\) 12.1433 1.83067
\(45\) 11.3407 1.69058
\(46\) −23.8680 −3.51914
\(47\) −6.82433 −0.995431 −0.497715 0.867340i \(-0.665828\pi\)
−0.497715 + 0.867340i \(0.665828\pi\)
\(48\) −2.77468 −0.400491
\(49\) −0.399181 −0.0570259
\(50\) −26.1990 −3.70509
\(51\) −0.105056 −0.0147107
\(52\) 16.1782 2.24352
\(53\) −11.3666 −1.56133 −0.780663 0.624952i \(-0.785118\pi\)
−0.780663 + 0.624952i \(0.785118\pi\)
\(54\) −3.40400 −0.463226
\(55\) −8.87546 −1.19677
\(56\) −22.4910 −3.00549
\(57\) −1.41781 −0.187793
\(58\) 5.80351 0.762038
\(59\) −1.47305 −0.191775 −0.0958877 0.995392i \(-0.530569\pi\)
−0.0958877 + 0.995392i \(0.530569\pi\)
\(60\) 4.27806 0.552295
\(61\) −4.25610 −0.544938 −0.272469 0.962165i \(-0.587840\pi\)
−0.272469 + 0.962165i \(0.587840\pi\)
\(62\) −1.70734 −0.216833
\(63\) −7.59184 −0.956482
\(64\) 21.4885 2.68606
\(65\) −11.8246 −1.46666
\(66\) 1.32194 0.162719
\(67\) −2.72727 −0.333189 −0.166594 0.986026i \(-0.553277\pi\)
−0.166594 + 0.986026i \(0.553277\pi\)
\(68\) 2.59862 0.315129
\(69\) −1.88162 −0.226521
\(70\) 26.5515 3.17351
\(71\) 12.2667 1.45579 0.727897 0.685686i \(-0.240498\pi\)
0.727897 + 0.685686i \(0.240498\pi\)
\(72\) 25.8677 3.04854
\(73\) −4.18062 −0.489304 −0.244652 0.969611i \(-0.578674\pi\)
−0.244652 + 0.969611i \(0.578674\pi\)
\(74\) −9.84792 −1.14480
\(75\) −2.06539 −0.238490
\(76\) 35.0705 4.02286
\(77\) 5.94151 0.677098
\(78\) 1.76119 0.199415
\(79\) −4.70363 −0.529199 −0.264600 0.964358i \(-0.585240\pi\)
−0.264600 + 0.964358i \(0.585240\pi\)
\(80\) −50.1639 −5.60850
\(81\) 8.59645 0.955162
\(82\) −24.7098 −2.72874
\(83\) 0.123219 0.0135250 0.00676251 0.999977i \(-0.497847\pi\)
0.00676251 + 0.999977i \(0.497847\pi\)
\(84\) −2.86387 −0.312474
\(85\) −1.89932 −0.206010
\(86\) −21.0545 −2.27037
\(87\) 0.457517 0.0490510
\(88\) −20.2446 −2.15808
\(89\) 2.64071 0.279915 0.139957 0.990158i \(-0.455303\pi\)
0.139957 + 0.990158i \(0.455303\pi\)
\(90\) −30.5379 −3.21897
\(91\) 7.91573 0.829794
\(92\) 46.5433 4.85247
\(93\) −0.134598 −0.0139571
\(94\) 18.3763 1.89537
\(95\) −25.6328 −2.62987
\(96\) 3.75489 0.383231
\(97\) −18.0692 −1.83465 −0.917325 0.398139i \(-0.869656\pi\)
−0.917325 + 0.398139i \(0.869656\pi\)
\(98\) 1.07490 0.108581
\(99\) −6.83355 −0.686797
\(100\) 51.0888 5.10888
\(101\) 7.00335 0.696859 0.348430 0.937335i \(-0.386715\pi\)
0.348430 + 0.937335i \(0.386715\pi\)
\(102\) 0.282890 0.0280103
\(103\) 1.59986 0.157639 0.0788194 0.996889i \(-0.474885\pi\)
0.0788194 + 0.996889i \(0.474885\pi\)
\(104\) −26.9713 −2.64476
\(105\) 2.09318 0.204273
\(106\) 30.6076 2.97287
\(107\) 11.7474 1.13566 0.567832 0.823145i \(-0.307782\pi\)
0.567832 + 0.823145i \(0.307782\pi\)
\(108\) 6.63791 0.638733
\(109\) −10.5930 −1.01462 −0.507311 0.861763i \(-0.669361\pi\)
−0.507311 + 0.861763i \(0.669361\pi\)
\(110\) 23.8995 2.27873
\(111\) −0.776357 −0.0736886
\(112\) 33.5813 3.17314
\(113\) 17.4276 1.63945 0.819724 0.572759i \(-0.194127\pi\)
0.819724 + 0.572759i \(0.194127\pi\)
\(114\) 3.81782 0.357572
\(115\) −34.0181 −3.17221
\(116\) −11.3170 −1.05076
\(117\) −9.10417 −0.841681
\(118\) 3.96658 0.365154
\(119\) 1.27146 0.116555
\(120\) −7.13210 −0.651069
\(121\) −5.65194 −0.513813
\(122\) 11.4607 1.03760
\(123\) −1.94799 −0.175644
\(124\) 3.32937 0.298986
\(125\) −18.1510 −1.62347
\(126\) 20.4430 1.82121
\(127\) −2.42321 −0.215025 −0.107512 0.994204i \(-0.534289\pi\)
−0.107512 + 0.994204i \(0.534289\pi\)
\(128\) −22.4872 −1.98760
\(129\) −1.65983 −0.146140
\(130\) 31.8407 2.79262
\(131\) 1.23473 0.107879 0.0539396 0.998544i \(-0.482822\pi\)
0.0539396 + 0.998544i \(0.482822\pi\)
\(132\) −2.57782 −0.224370
\(133\) 17.1594 1.48791
\(134\) 7.34388 0.634415
\(135\) −4.85160 −0.417559
\(136\) −4.33226 −0.371488
\(137\) 11.9408 1.02017 0.510084 0.860125i \(-0.329614\pi\)
0.510084 + 0.860125i \(0.329614\pi\)
\(138\) 5.06676 0.431312
\(139\) 10.1442 0.860423 0.430211 0.902728i \(-0.358439\pi\)
0.430211 + 0.902728i \(0.358439\pi\)
\(140\) −51.7763 −4.37589
\(141\) 1.44869 0.122002
\(142\) −33.0314 −2.77193
\(143\) 7.12509 0.595830
\(144\) −38.6231 −3.21859
\(145\) 8.27152 0.686912
\(146\) 11.2574 0.931669
\(147\) 0.0847393 0.00698918
\(148\) 19.2037 1.57854
\(149\) −4.03799 −0.330805 −0.165403 0.986226i \(-0.552892\pi\)
−0.165403 + 0.986226i \(0.552892\pi\)
\(150\) 5.56159 0.454102
\(151\) −20.5812 −1.67487 −0.837436 0.546535i \(-0.815946\pi\)
−0.837436 + 0.546535i \(0.815946\pi\)
\(152\) −58.4673 −4.74232
\(153\) −1.46235 −0.118224
\(154\) −15.9991 −1.28924
\(155\) −2.43341 −0.195456
\(156\) −3.43436 −0.274969
\(157\) −4.67486 −0.373094 −0.186547 0.982446i \(-0.559730\pi\)
−0.186547 + 0.982446i \(0.559730\pi\)
\(158\) 12.6657 1.00763
\(159\) 2.41294 0.191359
\(160\) 67.8851 5.36679
\(161\) 22.7728 1.79475
\(162\) −23.1482 −1.81869
\(163\) 22.8843 1.79243 0.896217 0.443615i \(-0.146304\pi\)
0.896217 + 0.443615i \(0.146304\pi\)
\(164\) 48.1848 3.76260
\(165\) 1.88411 0.146678
\(166\) −0.331799 −0.0257526
\(167\) 12.4072 0.960096 0.480048 0.877242i \(-0.340619\pi\)
0.480048 + 0.877242i \(0.340619\pi\)
\(168\) 4.77446 0.368357
\(169\) −3.50741 −0.269801
\(170\) 5.11440 0.392257
\(171\) −19.7356 −1.50922
\(172\) 41.0569 3.13056
\(173\) 13.3188 1.01261 0.506303 0.862356i \(-0.331012\pi\)
0.506303 + 0.862356i \(0.331012\pi\)
\(174\) −1.23198 −0.0933965
\(175\) 24.9969 1.88958
\(176\) 30.2271 2.27846
\(177\) 0.312704 0.0235043
\(178\) −7.11080 −0.532977
\(179\) 5.09849 0.381079 0.190540 0.981680i \(-0.438976\pi\)
0.190540 + 0.981680i \(0.438976\pi\)
\(180\) 59.5497 4.43857
\(181\) 18.9132 1.40580 0.702902 0.711286i \(-0.251887\pi\)
0.702902 + 0.711286i \(0.251887\pi\)
\(182\) −21.3152 −1.57999
\(183\) 0.903497 0.0667884
\(184\) −77.5940 −5.72030
\(185\) −14.0359 −1.03194
\(186\) 0.362439 0.0265753
\(187\) 1.14447 0.0836916
\(188\) −35.8343 −2.61349
\(189\) 3.24781 0.236244
\(190\) 69.0229 5.00745
\(191\) −22.0090 −1.59252 −0.796259 0.604955i \(-0.793191\pi\)
−0.796259 + 0.604955i \(0.793191\pi\)
\(192\) −4.56164 −0.329208
\(193\) −9.42002 −0.678068 −0.339034 0.940774i \(-0.610100\pi\)
−0.339034 + 0.940774i \(0.610100\pi\)
\(194\) 48.6561 3.49330
\(195\) 2.51015 0.179756
\(196\) −2.09609 −0.149720
\(197\) 0.134865 0.00960876 0.00480438 0.999988i \(-0.498471\pi\)
0.00480438 + 0.999988i \(0.498471\pi\)
\(198\) 18.4011 1.30771
\(199\) −23.5042 −1.66617 −0.833084 0.553147i \(-0.813427\pi\)
−0.833084 + 0.553147i \(0.813427\pi\)
\(200\) −85.1719 −6.02256
\(201\) 0.578952 0.0408361
\(202\) −18.8584 −1.32687
\(203\) −5.53722 −0.388636
\(204\) −0.551643 −0.0386228
\(205\) −35.2179 −2.45973
\(206\) −4.30804 −0.300155
\(207\) −26.1918 −1.82046
\(208\) 40.2709 2.79228
\(209\) 15.4455 1.06839
\(210\) −5.63643 −0.388951
\(211\) −15.3602 −1.05744 −0.528722 0.848795i \(-0.677328\pi\)
−0.528722 + 0.848795i \(0.677328\pi\)
\(212\) −59.6857 −4.09923
\(213\) −2.60402 −0.178424
\(214\) −31.6329 −2.16238
\(215\) −30.0082 −2.04654
\(216\) −11.0663 −0.752966
\(217\) 1.62900 0.110584
\(218\) 28.5244 1.93191
\(219\) 0.887473 0.0599699
\(220\) −46.6047 −3.14209
\(221\) 1.52474 0.102565
\(222\) 2.09054 0.140308
\(223\) 17.8160 1.19305 0.596523 0.802596i \(-0.296548\pi\)
0.596523 + 0.802596i \(0.296548\pi\)
\(224\) −45.4444 −3.03638
\(225\) −28.7498 −1.91665
\(226\) −46.9283 −3.12162
\(227\) −8.74547 −0.580458 −0.290229 0.956957i \(-0.593731\pi\)
−0.290229 + 0.956957i \(0.593731\pi\)
\(228\) −7.44486 −0.493048
\(229\) 20.0980 1.32811 0.664057 0.747682i \(-0.268833\pi\)
0.664057 + 0.747682i \(0.268833\pi\)
\(230\) 91.6027 6.04011
\(231\) −1.26128 −0.0829862
\(232\) 18.8670 1.23868
\(233\) −2.66778 −0.174772 −0.0873861 0.996175i \(-0.527851\pi\)
−0.0873861 + 0.996175i \(0.527851\pi\)
\(234\) 24.5154 1.60262
\(235\) 26.1910 1.70851
\(236\) −7.73496 −0.503503
\(237\) 0.998499 0.0648595
\(238\) −3.42374 −0.221928
\(239\) −3.37713 −0.218448 −0.109224 0.994017i \(-0.534837\pi\)
−0.109224 + 0.994017i \(0.534837\pi\)
\(240\) 10.6489 0.687386
\(241\) 18.0039 1.15973 0.579865 0.814712i \(-0.303105\pi\)
0.579865 + 0.814712i \(0.303105\pi\)
\(242\) 15.2193 0.978335
\(243\) −5.61727 −0.360348
\(244\) −22.3486 −1.43072
\(245\) 1.53201 0.0978767
\(246\) 5.24546 0.334438
\(247\) 20.5776 1.30932
\(248\) −5.55050 −0.352457
\(249\) −0.0261572 −0.00165765
\(250\) 48.8762 3.09120
\(251\) −17.3166 −1.09301 −0.546506 0.837455i \(-0.684042\pi\)
−0.546506 + 0.837455i \(0.684042\pi\)
\(252\) −39.8645 −2.51123
\(253\) 20.4982 1.28871
\(254\) 6.52512 0.409422
\(255\) 0.403192 0.0252489
\(256\) 17.5756 1.09847
\(257\) 2.99678 0.186934 0.0934671 0.995622i \(-0.470205\pi\)
0.0934671 + 0.995622i \(0.470205\pi\)
\(258\) 4.46951 0.278260
\(259\) 9.39606 0.583843
\(260\) −62.0903 −3.85068
\(261\) 6.36855 0.394203
\(262\) −3.32484 −0.205410
\(263\) 2.80380 0.172890 0.0864448 0.996257i \(-0.472449\pi\)
0.0864448 + 0.996257i \(0.472449\pi\)
\(264\) 4.29757 0.264497
\(265\) 43.6239 2.67979
\(266\) −46.2061 −2.83308
\(267\) −0.560577 −0.0343068
\(268\) −14.3208 −0.874781
\(269\) 7.41569 0.452143 0.226071 0.974111i \(-0.427412\pi\)
0.226071 + 0.974111i \(0.427412\pi\)
\(270\) 13.0642 0.795061
\(271\) −26.7479 −1.62482 −0.812410 0.583087i \(-0.801845\pi\)
−0.812410 + 0.583087i \(0.801845\pi\)
\(272\) 6.46849 0.392210
\(273\) −1.68037 −0.101701
\(274\) −32.1536 −1.94247
\(275\) 22.5001 1.35681
\(276\) −9.88034 −0.594727
\(277\) 3.99925 0.240292 0.120146 0.992756i \(-0.461664\pi\)
0.120146 + 0.992756i \(0.461664\pi\)
\(278\) −27.3160 −1.63830
\(279\) −1.87357 −0.112168
\(280\) 86.3181 5.15849
\(281\) 0.114544 0.00683314 0.00341657 0.999994i \(-0.498912\pi\)
0.00341657 + 0.999994i \(0.498912\pi\)
\(282\) −3.90097 −0.232299
\(283\) −18.4299 −1.09555 −0.547773 0.836627i \(-0.684524\pi\)
−0.547773 + 0.836627i \(0.684524\pi\)
\(284\) 64.4122 3.82216
\(285\) 5.44140 0.322321
\(286\) −19.1862 −1.13450
\(287\) 23.5760 1.39165
\(288\) 52.2673 3.07988
\(289\) −16.7551 −0.985593
\(290\) −22.2732 −1.30793
\(291\) 3.83578 0.224858
\(292\) −21.9523 −1.28466
\(293\) 8.03920 0.469655 0.234827 0.972037i \(-0.424547\pi\)
0.234827 + 0.972037i \(0.424547\pi\)
\(294\) −0.228183 −0.0133079
\(295\) 5.65342 0.329155
\(296\) −32.0152 −1.86085
\(297\) 2.92341 0.169634
\(298\) 10.8733 0.629876
\(299\) 27.3093 1.57934
\(300\) −10.8453 −0.626152
\(301\) 20.0885 1.15788
\(302\) 55.4202 3.18907
\(303\) −1.48669 −0.0854082
\(304\) 87.2975 5.00685
\(305\) 16.3344 0.935307
\(306\) 3.93777 0.225107
\(307\) −5.15724 −0.294339 −0.147169 0.989111i \(-0.547016\pi\)
−0.147169 + 0.989111i \(0.547016\pi\)
\(308\) 31.1987 1.77771
\(309\) −0.339623 −0.0193204
\(310\) 6.55259 0.372162
\(311\) 3.61155 0.204792 0.102396 0.994744i \(-0.467349\pi\)
0.102396 + 0.994744i \(0.467349\pi\)
\(312\) 5.72555 0.324145
\(313\) 26.2965 1.48637 0.743184 0.669087i \(-0.233315\pi\)
0.743184 + 0.669087i \(0.233315\pi\)
\(314\) 12.5883 0.710397
\(315\) 29.1367 1.64166
\(316\) −24.6986 −1.38940
\(317\) −31.9969 −1.79712 −0.898562 0.438847i \(-0.855387\pi\)
−0.898562 + 0.438847i \(0.855387\pi\)
\(318\) −6.49747 −0.364360
\(319\) −4.98415 −0.279059
\(320\) −82.4706 −4.61024
\(321\) −2.49377 −0.139189
\(322\) −61.3218 −3.41733
\(323\) 3.30527 0.183910
\(324\) 45.1397 2.50776
\(325\) 29.9763 1.66279
\(326\) −61.6219 −3.41292
\(327\) 2.24871 0.124354
\(328\) −80.3306 −4.43552
\(329\) −17.5331 −0.966631
\(330\) −5.07345 −0.279284
\(331\) −8.79971 −0.483676 −0.241838 0.970317i \(-0.577750\pi\)
−0.241838 + 0.970317i \(0.577750\pi\)
\(332\) 0.647018 0.0355097
\(333\) −10.8067 −0.592206
\(334\) −33.4096 −1.82809
\(335\) 10.4670 0.571871
\(336\) −7.12874 −0.388904
\(337\) 32.3009 1.75954 0.879771 0.475398i \(-0.157696\pi\)
0.879771 + 0.475398i \(0.157696\pi\)
\(338\) 9.44463 0.513720
\(339\) −3.69957 −0.200933
\(340\) −9.97324 −0.540875
\(341\) 1.46629 0.0794042
\(342\) 53.1433 2.87366
\(343\) −19.0100 −1.02644
\(344\) −68.4475 −3.69044
\(345\) 7.22147 0.388791
\(346\) −35.8642 −1.92807
\(347\) −19.8800 −1.06721 −0.533607 0.845732i \(-0.679164\pi\)
−0.533607 + 0.845732i \(0.679164\pi\)
\(348\) 2.40241 0.128782
\(349\) 27.4836 1.47116 0.735582 0.677436i \(-0.236909\pi\)
0.735582 + 0.677436i \(0.236909\pi\)
\(350\) −67.3106 −3.59790
\(351\) 3.89479 0.207889
\(352\) −40.9053 −2.18026
\(353\) 7.79486 0.414879 0.207439 0.978248i \(-0.433487\pi\)
0.207439 + 0.978248i \(0.433487\pi\)
\(354\) −0.842038 −0.0447538
\(355\) −47.0784 −2.49866
\(356\) 13.8663 0.734911
\(357\) −0.269910 −0.0142851
\(358\) −13.7290 −0.725601
\(359\) 1.36466 0.0720239 0.0360119 0.999351i \(-0.488535\pi\)
0.0360119 + 0.999351i \(0.488535\pi\)
\(360\) −99.2775 −5.23238
\(361\) 25.6073 1.34775
\(362\) −50.9286 −2.67675
\(363\) 1.19981 0.0629737
\(364\) 41.5652 2.17861
\(365\) 16.0447 0.839820
\(366\) −2.43290 −0.127170
\(367\) 30.2734 1.58026 0.790128 0.612941i \(-0.210014\pi\)
0.790128 + 0.612941i \(0.210014\pi\)
\(368\) 115.855 6.03939
\(369\) −27.1156 −1.41158
\(370\) 37.7952 1.96488
\(371\) −29.2032 −1.51615
\(372\) −0.706767 −0.0366442
\(373\) 30.9004 1.59996 0.799981 0.600025i \(-0.204843\pi\)
0.799981 + 0.600025i \(0.204843\pi\)
\(374\) −3.08177 −0.159355
\(375\) 3.85314 0.198975
\(376\) 59.7407 3.08089
\(377\) −6.64026 −0.341991
\(378\) −8.74558 −0.449824
\(379\) −1.67349 −0.0859616 −0.0429808 0.999076i \(-0.513685\pi\)
−0.0429808 + 0.999076i \(0.513685\pi\)
\(380\) −134.597 −6.90467
\(381\) 0.514405 0.0263538
\(382\) 59.2651 3.03227
\(383\) −11.5094 −0.588105 −0.294052 0.955789i \(-0.595004\pi\)
−0.294052 + 0.955789i \(0.595004\pi\)
\(384\) 4.77364 0.243604
\(385\) −22.8029 −1.16214
\(386\) 25.3659 1.29109
\(387\) −23.1045 −1.17447
\(388\) −94.8808 −4.81684
\(389\) −28.6354 −1.45187 −0.725935 0.687763i \(-0.758593\pi\)
−0.725935 + 0.687763i \(0.758593\pi\)
\(390\) −6.75924 −0.342267
\(391\) 4.38654 0.221837
\(392\) 3.49446 0.176497
\(393\) −0.262113 −0.0132218
\(394\) −0.363160 −0.0182957
\(395\) 18.0520 0.908295
\(396\) −35.8827 −1.80317
\(397\) 3.64723 0.183049 0.0915245 0.995803i \(-0.470826\pi\)
0.0915245 + 0.995803i \(0.470826\pi\)
\(398\) 63.2912 3.17250
\(399\) −3.64264 −0.182360
\(400\) 127.170 6.35851
\(401\) −6.52520 −0.325853 −0.162926 0.986638i \(-0.552093\pi\)
−0.162926 + 0.986638i \(0.552093\pi\)
\(402\) −1.55898 −0.0777548
\(403\) 1.95351 0.0973110
\(404\) 36.7743 1.82959
\(405\) −32.9923 −1.63940
\(406\) 14.9104 0.739991
\(407\) 8.45756 0.419225
\(408\) 0.919664 0.0455302
\(409\) −32.6804 −1.61594 −0.807970 0.589223i \(-0.799434\pi\)
−0.807970 + 0.589223i \(0.799434\pi\)
\(410\) 94.8334 4.68349
\(411\) −2.53482 −0.125033
\(412\) 8.40080 0.413878
\(413\) −3.78458 −0.186227
\(414\) 70.5284 3.46628
\(415\) −0.472901 −0.0232138
\(416\) −54.4972 −2.67194
\(417\) −2.15345 −0.105455
\(418\) −41.5910 −2.03428
\(419\) 6.02994 0.294582 0.147291 0.989093i \(-0.452945\pi\)
0.147291 + 0.989093i \(0.452945\pi\)
\(420\) 10.9912 0.536316
\(421\) 17.1353 0.835125 0.417562 0.908648i \(-0.362885\pi\)
0.417562 + 0.908648i \(0.362885\pi\)
\(422\) 41.3615 2.01345
\(423\) 20.1655 0.980478
\(424\) 99.5042 4.83235
\(425\) 4.81494 0.233559
\(426\) 7.01200 0.339733
\(427\) −10.9348 −0.529172
\(428\) 61.6851 2.98166
\(429\) −1.51253 −0.0730259
\(430\) 80.8050 3.89676
\(431\) −26.1267 −1.25848 −0.629241 0.777211i \(-0.716634\pi\)
−0.629241 + 0.777211i \(0.716634\pi\)
\(432\) 16.5231 0.794967
\(433\) 11.5088 0.553078 0.276539 0.961003i \(-0.410812\pi\)
0.276539 + 0.961003i \(0.410812\pi\)
\(434\) −4.38651 −0.210559
\(435\) −1.75590 −0.0841890
\(436\) −55.6233 −2.66387
\(437\) 59.1999 2.83191
\(438\) −2.38975 −0.114187
\(439\) 29.8291 1.42367 0.711833 0.702349i \(-0.247865\pi\)
0.711833 + 0.702349i \(0.247865\pi\)
\(440\) 77.6964 3.70403
\(441\) 1.17955 0.0561692
\(442\) −4.10577 −0.195292
\(443\) 31.6635 1.50438 0.752188 0.658948i \(-0.228998\pi\)
0.752188 + 0.658948i \(0.228998\pi\)
\(444\) −4.07662 −0.193468
\(445\) −10.1348 −0.480434
\(446\) −47.9742 −2.27164
\(447\) 0.857196 0.0405440
\(448\) 55.2084 2.60835
\(449\) 32.0724 1.51359 0.756794 0.653653i \(-0.226764\pi\)
0.756794 + 0.653653i \(0.226764\pi\)
\(450\) 77.4163 3.64944
\(451\) 21.2212 0.999265
\(452\) 91.5115 4.30434
\(453\) 4.36903 0.205275
\(454\) 23.5495 1.10523
\(455\) −30.3797 −1.42422
\(456\) 12.4116 0.581226
\(457\) 22.3672 1.04629 0.523147 0.852242i \(-0.324758\pi\)
0.523147 + 0.852242i \(0.324758\pi\)
\(458\) −54.1192 −2.52882
\(459\) 0.625599 0.0292005
\(460\) −178.628 −8.32857
\(461\) 31.6791 1.47544 0.737721 0.675105i \(-0.235902\pi\)
0.737721 + 0.675105i \(0.235902\pi\)
\(462\) 3.39633 0.158012
\(463\) 15.7833 0.733510 0.366755 0.930318i \(-0.380469\pi\)
0.366755 + 0.930318i \(0.380469\pi\)
\(464\) −28.1703 −1.30777
\(465\) 0.516571 0.0239554
\(466\) 7.18370 0.332778
\(467\) 42.9220 1.98619 0.993097 0.117300i \(-0.0374239\pi\)
0.993097 + 0.117300i \(0.0374239\pi\)
\(468\) −47.8057 −2.20982
\(469\) −7.00691 −0.323549
\(470\) −70.5262 −3.25313
\(471\) 0.992392 0.0457270
\(472\) 12.8952 0.593551
\(473\) 18.0820 0.831410
\(474\) −2.68872 −0.123497
\(475\) 64.9814 2.98155
\(476\) 6.67640 0.306012
\(477\) 33.5876 1.53787
\(478\) 9.09381 0.415941
\(479\) −24.0204 −1.09752 −0.548760 0.835980i \(-0.684900\pi\)
−0.548760 + 0.835980i \(0.684900\pi\)
\(480\) −14.4108 −0.657762
\(481\) 11.2678 0.513767
\(482\) −48.4801 −2.20821
\(483\) −4.83428 −0.219967
\(484\) −29.6781 −1.34901
\(485\) 69.3477 3.14892
\(486\) 15.1260 0.686128
\(487\) 7.47270 0.338620 0.169310 0.985563i \(-0.445846\pi\)
0.169310 + 0.985563i \(0.445846\pi\)
\(488\) 37.2582 1.68660
\(489\) −4.85794 −0.219684
\(490\) −4.12535 −0.186364
\(491\) 11.5032 0.519132 0.259566 0.965725i \(-0.416421\pi\)
0.259566 + 0.965725i \(0.416421\pi\)
\(492\) −10.2288 −0.461150
\(493\) −1.06659 −0.0480367
\(494\) −55.4106 −2.49304
\(495\) 26.2264 1.17879
\(496\) 8.28745 0.372118
\(497\) 31.5158 1.41368
\(498\) 0.0704352 0.00315628
\(499\) −27.1099 −1.21361 −0.606804 0.794852i \(-0.707549\pi\)
−0.606804 + 0.794852i \(0.707549\pi\)
\(500\) −95.3100 −4.26239
\(501\) −2.63383 −0.117671
\(502\) 46.6294 2.08117
\(503\) −21.8364 −0.973637 −0.486819 0.873503i \(-0.661843\pi\)
−0.486819 + 0.873503i \(0.661843\pi\)
\(504\) 66.4595 2.96034
\(505\) −26.8781 −1.19606
\(506\) −55.1968 −2.45380
\(507\) 0.744564 0.0330672
\(508\) −12.7242 −0.564544
\(509\) −6.85343 −0.303773 −0.151886 0.988398i \(-0.548535\pi\)
−0.151886 + 0.988398i \(0.548535\pi\)
\(510\) −1.08570 −0.0480756
\(511\) −10.7409 −0.475148
\(512\) −2.35252 −0.103968
\(513\) 8.44296 0.372766
\(514\) −8.06962 −0.355936
\(515\) −6.14008 −0.270564
\(516\) −8.71569 −0.383687
\(517\) −15.7819 −0.694085
\(518\) −25.3013 −1.11168
\(519\) −2.82734 −0.124107
\(520\) 103.513 4.53935
\(521\) 17.0675 0.747740 0.373870 0.927481i \(-0.378031\pi\)
0.373870 + 0.927481i \(0.378031\pi\)
\(522\) −17.1490 −0.750591
\(523\) 6.49693 0.284091 0.142045 0.989860i \(-0.454632\pi\)
0.142045 + 0.989860i \(0.454632\pi\)
\(524\) 6.48354 0.283235
\(525\) −5.30640 −0.231590
\(526\) −7.54996 −0.329194
\(527\) 0.313781 0.0136685
\(528\) −6.41670 −0.279251
\(529\) 55.5662 2.41592
\(530\) −117.469 −5.10251
\(531\) 4.35278 0.188895
\(532\) 90.1033 3.90647
\(533\) 28.2724 1.22462
\(534\) 1.50950 0.0653225
\(535\) −45.0852 −1.94920
\(536\) 23.8747 1.03123
\(537\) −1.08232 −0.0467056
\(538\) −19.9687 −0.860911
\(539\) −0.923141 −0.0397625
\(540\) −25.4756 −1.09629
\(541\) 40.2835 1.73192 0.865961 0.500111i \(-0.166708\pi\)
0.865961 + 0.500111i \(0.166708\pi\)
\(542\) 72.0257 3.09377
\(543\) −4.01494 −0.172298
\(544\) −8.75359 −0.375307
\(545\) 40.6547 1.74146
\(546\) 4.52485 0.193646
\(547\) 28.5300 1.21986 0.609928 0.792457i \(-0.291198\pi\)
0.609928 + 0.792457i \(0.291198\pi\)
\(548\) 62.7005 2.67843
\(549\) 12.5765 0.536752
\(550\) −60.5874 −2.58346
\(551\) −14.3945 −0.613225
\(552\) 16.4719 0.701089
\(553\) −12.0846 −0.513889
\(554\) −10.7690 −0.457533
\(555\) 2.97957 0.126476
\(556\) 53.2670 2.25902
\(557\) −36.9379 −1.56511 −0.782555 0.622582i \(-0.786084\pi\)
−0.782555 + 0.622582i \(0.786084\pi\)
\(558\) 5.04508 0.213575
\(559\) 24.0902 1.01891
\(560\) −128.881 −5.44623
\(561\) −0.242950 −0.0102574
\(562\) −0.308440 −0.0130108
\(563\) −23.5729 −0.993478 −0.496739 0.867900i \(-0.665469\pi\)
−0.496739 + 0.867900i \(0.665469\pi\)
\(564\) 7.60701 0.320313
\(565\) −66.8851 −2.81388
\(566\) 49.6275 2.08600
\(567\) 22.0861 0.927527
\(568\) −107.384 −4.50573
\(569\) −21.7507 −0.911838 −0.455919 0.890021i \(-0.650689\pi\)
−0.455919 + 0.890021i \(0.650689\pi\)
\(570\) −14.6524 −0.613721
\(571\) 18.4990 0.774158 0.387079 0.922047i \(-0.373484\pi\)
0.387079 + 0.922047i \(0.373484\pi\)
\(572\) 37.4136 1.56434
\(573\) 4.67214 0.195182
\(574\) −63.4845 −2.64979
\(575\) 86.2391 3.59642
\(576\) −63.4972 −2.64572
\(577\) −34.6022 −1.44051 −0.720255 0.693709i \(-0.755975\pi\)
−0.720255 + 0.693709i \(0.755975\pi\)
\(578\) 45.1175 1.87664
\(579\) 1.99971 0.0831050
\(580\) 43.4334 1.80348
\(581\) 0.316575 0.0131337
\(582\) −10.3288 −0.428145
\(583\) −26.2863 −1.08867
\(584\) 36.5974 1.51441
\(585\) 34.9408 1.44462
\(586\) −21.6476 −0.894256
\(587\) 35.8441 1.47945 0.739723 0.672911i \(-0.234956\pi\)
0.739723 + 0.672911i \(0.234956\pi\)
\(588\) 0.444963 0.0183500
\(589\) 4.23472 0.174489
\(590\) −15.2233 −0.626734
\(591\) −0.0286296 −0.00117766
\(592\) 47.8019 1.96465
\(593\) 6.29377 0.258454 0.129227 0.991615i \(-0.458750\pi\)
0.129227 + 0.991615i \(0.458750\pi\)
\(594\) −7.87205 −0.322994
\(595\) −4.87973 −0.200050
\(596\) −21.2033 −0.868523
\(597\) 4.98953 0.204208
\(598\) −73.5374 −3.00717
\(599\) 12.0416 0.492007 0.246004 0.969269i \(-0.420882\pi\)
0.246004 + 0.969269i \(0.420882\pi\)
\(600\) 18.0805 0.738135
\(601\) −11.8147 −0.481930 −0.240965 0.970534i \(-0.577464\pi\)
−0.240965 + 0.970534i \(0.577464\pi\)
\(602\) −54.0934 −2.20468
\(603\) 8.05890 0.328184
\(604\) −108.071 −4.39735
\(605\) 21.6915 0.881886
\(606\) 4.00330 0.162623
\(607\) 36.7972 1.49355 0.746777 0.665075i \(-0.231600\pi\)
0.746777 + 0.665075i \(0.231600\pi\)
\(608\) −118.137 −4.79107
\(609\) 1.17546 0.0476319
\(610\) −43.9848 −1.78089
\(611\) −21.0258 −0.850612
\(612\) −7.67877 −0.310396
\(613\) −28.9840 −1.17065 −0.585325 0.810798i \(-0.699033\pi\)
−0.585325 + 0.810798i \(0.699033\pi\)
\(614\) 13.8872 0.560442
\(615\) 7.47616 0.301468
\(616\) −52.0124 −2.09564
\(617\) −18.3585 −0.739085 −0.369542 0.929214i \(-0.620486\pi\)
−0.369542 + 0.929214i \(0.620486\pi\)
\(618\) 0.914522 0.0367875
\(619\) −10.2532 −0.412111 −0.206056 0.978540i \(-0.566063\pi\)
−0.206056 + 0.978540i \(0.566063\pi\)
\(620\) −12.7777 −0.513166
\(621\) 11.2049 0.449639
\(622\) −9.72504 −0.389938
\(623\) 6.78453 0.271816
\(624\) −8.54881 −0.342226
\(625\) 21.0143 0.840574
\(626\) −70.8103 −2.83015
\(627\) −3.27881 −0.130943
\(628\) −24.5475 −0.979552
\(629\) 1.80989 0.0721649
\(630\) −78.4581 −3.12584
\(631\) 24.1928 0.963101 0.481551 0.876418i \(-0.340074\pi\)
0.481551 + 0.876418i \(0.340074\pi\)
\(632\) 41.1759 1.63789
\(633\) 3.26072 0.129602
\(634\) 86.1600 3.42185
\(635\) 9.30000 0.369059
\(636\) 12.6703 0.502408
\(637\) −1.22988 −0.0487295
\(638\) 13.4211 0.531347
\(639\) −36.2474 −1.43393
\(640\) 86.3034 3.41144
\(641\) −19.7245 −0.779069 −0.389535 0.921012i \(-0.627364\pi\)
−0.389535 + 0.921012i \(0.627364\pi\)
\(642\) 6.71513 0.265025
\(643\) −13.1272 −0.517685 −0.258842 0.965920i \(-0.583341\pi\)
−0.258842 + 0.965920i \(0.583341\pi\)
\(644\) 119.579 4.71208
\(645\) 6.37023 0.250828
\(646\) −8.90031 −0.350178
\(647\) −2.68577 −0.105589 −0.0527943 0.998605i \(-0.516813\pi\)
−0.0527943 + 0.998605i \(0.516813\pi\)
\(648\) −75.2540 −2.95626
\(649\) −3.40657 −0.133719
\(650\) −80.7191 −3.16607
\(651\) −0.345809 −0.0135533
\(652\) 120.165 4.70601
\(653\) 42.5622 1.66559 0.832793 0.553584i \(-0.186740\pi\)
0.832793 + 0.553584i \(0.186740\pi\)
\(654\) −6.05523 −0.236778
\(655\) −4.73877 −0.185159
\(656\) 119.942 4.68293
\(657\) 12.3535 0.481954
\(658\) 47.2125 1.84053
\(659\) −29.3377 −1.14284 −0.571418 0.820659i \(-0.693606\pi\)
−0.571418 + 0.820659i \(0.693606\pi\)
\(660\) 9.89338 0.385099
\(661\) 26.6044 1.03479 0.517396 0.855746i \(-0.326901\pi\)
0.517396 + 0.855746i \(0.326901\pi\)
\(662\) 23.6955 0.920953
\(663\) −0.323677 −0.0125706
\(664\) −1.07867 −0.0418604
\(665\) −65.8559 −2.55378
\(666\) 29.1000 1.12760
\(667\) −19.1034 −0.739686
\(668\) 65.1496 2.52072
\(669\) −3.78203 −0.146222
\(670\) −28.1850 −1.08888
\(671\) −9.84260 −0.379969
\(672\) 9.64707 0.372144
\(673\) 27.3260 1.05334 0.526670 0.850070i \(-0.323440\pi\)
0.526670 + 0.850070i \(0.323440\pi\)
\(674\) −86.9786 −3.35029
\(675\) 12.2992 0.473398
\(676\) −18.4173 −0.708358
\(677\) 0.296493 0.0113951 0.00569757 0.999984i \(-0.498186\pi\)
0.00569757 + 0.999984i \(0.498186\pi\)
\(678\) 9.96207 0.382591
\(679\) −46.4235 −1.78157
\(680\) 16.6267 0.637606
\(681\) 1.85651 0.0711418
\(682\) −3.94838 −0.151191
\(683\) 31.6912 1.21263 0.606315 0.795225i \(-0.292647\pi\)
0.606315 + 0.795225i \(0.292647\pi\)
\(684\) −103.631 −3.96243
\(685\) −45.8273 −1.75097
\(686\) 51.1894 1.95442
\(687\) −4.26647 −0.162776
\(688\) 102.199 3.89630
\(689\) −35.0206 −1.33418
\(690\) −19.4457 −0.740285
\(691\) 2.21915 0.0844205 0.0422103 0.999109i \(-0.486560\pi\)
0.0422103 + 0.999109i \(0.486560\pi\)
\(692\) 69.9363 2.65858
\(693\) −17.5568 −0.666927
\(694\) 53.5321 2.03205
\(695\) −38.9325 −1.47679
\(696\) −4.00514 −0.151814
\(697\) 4.54125 0.172012
\(698\) −74.0068 −2.80120
\(699\) 0.566324 0.0214203
\(700\) 131.258 4.96107
\(701\) −25.7608 −0.972973 −0.486487 0.873688i \(-0.661722\pi\)
−0.486487 + 0.873688i \(0.661722\pi\)
\(702\) −10.4877 −0.395834
\(703\) 24.4258 0.921238
\(704\) 49.6941 1.87292
\(705\) −5.55991 −0.209398
\(706\) −20.9897 −0.789958
\(707\) 17.9930 0.676698
\(708\) 1.64200 0.0617101
\(709\) 5.41832 0.203489 0.101745 0.994811i \(-0.467558\pi\)
0.101745 + 0.994811i \(0.467558\pi\)
\(710\) 126.771 4.75763
\(711\) 13.8989 0.521250
\(712\) −23.1170 −0.866345
\(713\) 5.62005 0.210473
\(714\) 0.726802 0.0271999
\(715\) −27.3453 −1.02266
\(716\) 26.7720 1.00052
\(717\) 0.716907 0.0267734
\(718\) −3.67470 −0.137139
\(719\) −0.452797 −0.0168865 −0.00844324 0.999964i \(-0.502688\pi\)
−0.00844324 + 0.999964i \(0.502688\pi\)
\(720\) 148.231 5.52425
\(721\) 4.11037 0.153078
\(722\) −68.9543 −2.56621
\(723\) −3.82191 −0.142138
\(724\) 99.3124 3.69091
\(725\) −20.9691 −0.778771
\(726\) −3.23080 −0.119906
\(727\) 36.8824 1.36789 0.683945 0.729533i \(-0.260263\pi\)
0.683945 + 0.729533i \(0.260263\pi\)
\(728\) −69.2949 −2.56824
\(729\) −24.5969 −0.910997
\(730\) −43.2047 −1.59908
\(731\) 3.86947 0.143118
\(732\) 4.74423 0.175352
\(733\) −1.45650 −0.0537969 −0.0268984 0.999638i \(-0.508563\pi\)
−0.0268984 + 0.999638i \(0.508563\pi\)
\(734\) −81.5190 −3.00892
\(735\) −0.325220 −0.0119959
\(736\) −156.783 −5.77911
\(737\) −6.30704 −0.232323
\(738\) 73.0158 2.68775
\(739\) −21.7336 −0.799484 −0.399742 0.916628i \(-0.630900\pi\)
−0.399742 + 0.916628i \(0.630900\pi\)
\(740\) −73.7019 −2.70933
\(741\) −4.36828 −0.160473
\(742\) 78.6372 2.88686
\(743\) −22.9147 −0.840660 −0.420330 0.907371i \(-0.638086\pi\)
−0.420330 + 0.907371i \(0.638086\pi\)
\(744\) 1.17828 0.0431977
\(745\) 15.4974 0.567780
\(746\) −83.2074 −3.04644
\(747\) −0.364104 −0.0133219
\(748\) 6.00955 0.219731
\(749\) 30.1815 1.10281
\(750\) −10.3756 −0.378862
\(751\) −27.2152 −0.993096 −0.496548 0.868009i \(-0.665399\pi\)
−0.496548 + 0.868009i \(0.665399\pi\)
\(752\) −89.1987 −3.25274
\(753\) 3.67601 0.133961
\(754\) 17.8806 0.651174
\(755\) 78.9883 2.87468
\(756\) 17.0541 0.620253
\(757\) −35.8836 −1.30421 −0.652105 0.758129i \(-0.726114\pi\)
−0.652105 + 0.758129i \(0.726114\pi\)
\(758\) 4.50632 0.163677
\(759\) −4.35142 −0.157947
\(760\) 224.391 8.13952
\(761\) −53.4913 −1.93906 −0.969529 0.244978i \(-0.921219\pi\)
−0.969529 + 0.244978i \(0.921219\pi\)
\(762\) −1.38517 −0.0501794
\(763\) −27.2155 −0.985268
\(764\) −115.569 −4.18113
\(765\) 5.61235 0.202915
\(766\) 30.9922 1.11979
\(767\) −4.53849 −0.163875
\(768\) −3.73100 −0.134631
\(769\) −11.4276 −0.412088 −0.206044 0.978543i \(-0.566059\pi\)
−0.206044 + 0.978543i \(0.566059\pi\)
\(770\) 61.4027 2.21280
\(771\) −0.636165 −0.0229109
\(772\) −49.4642 −1.78025
\(773\) 19.2055 0.690774 0.345387 0.938460i \(-0.387748\pi\)
0.345387 + 0.938460i \(0.387748\pi\)
\(774\) 62.2148 2.23626
\(775\) 6.16892 0.221594
\(776\) 158.179 5.67830
\(777\) −1.99462 −0.0715566
\(778\) 77.1082 2.76446
\(779\) 61.2878 2.19586
\(780\) 13.1807 0.471945
\(781\) 28.3679 1.01508
\(782\) −11.8119 −0.422393
\(783\) −2.72449 −0.0973652
\(784\) −5.21757 −0.186342
\(785\) 17.9416 0.640363
\(786\) 0.705807 0.0251753
\(787\) −23.4461 −0.835763 −0.417882 0.908501i \(-0.637227\pi\)
−0.417882 + 0.908501i \(0.637227\pi\)
\(788\) 0.708173 0.0252276
\(789\) −0.595199 −0.0211896
\(790\) −48.6097 −1.72946
\(791\) 44.7750 1.59202
\(792\) 59.8214 2.12566
\(793\) −13.1131 −0.465658
\(794\) −9.82111 −0.348538
\(795\) −9.26060 −0.328440
\(796\) −123.420 −4.37449
\(797\) 7.75286 0.274620 0.137310 0.990528i \(-0.456154\pi\)
0.137310 + 0.990528i \(0.456154\pi\)
\(798\) 9.80877 0.347227
\(799\) −3.37726 −0.119479
\(800\) −172.095 −6.08448
\(801\) −7.80313 −0.275710
\(802\) 17.5708 0.620446
\(803\) −9.66804 −0.341178
\(804\) 3.04006 0.107215
\(805\) −87.3996 −3.08043
\(806\) −5.26032 −0.185287
\(807\) −1.57422 −0.0554153
\(808\) −61.3078 −2.15680
\(809\) 23.6375 0.831049 0.415525 0.909582i \(-0.363598\pi\)
0.415525 + 0.909582i \(0.363598\pi\)
\(810\) 88.8403 3.12153
\(811\) 16.1854 0.568346 0.284173 0.958773i \(-0.408281\pi\)
0.284173 + 0.958773i \(0.408281\pi\)
\(812\) −29.0757 −1.02036
\(813\) 5.67812 0.199140
\(814\) −22.7742 −0.798235
\(815\) −87.8274 −3.07646
\(816\) −1.37315 −0.0480699
\(817\) 52.2216 1.82700
\(818\) 88.0005 3.07686
\(819\) −23.3905 −0.817330
\(820\) −184.928 −6.45797
\(821\) −50.9450 −1.77799 −0.888996 0.457916i \(-0.848596\pi\)
−0.888996 + 0.457916i \(0.848596\pi\)
\(822\) 6.82566 0.238072
\(823\) 22.1304 0.771418 0.385709 0.922621i \(-0.373957\pi\)
0.385709 + 0.922621i \(0.373957\pi\)
\(824\) −14.0053 −0.487897
\(825\) −4.77639 −0.166292
\(826\) 10.1910 0.354589
\(827\) 15.6426 0.543946 0.271973 0.962305i \(-0.412324\pi\)
0.271973 + 0.962305i \(0.412324\pi\)
\(828\) −137.532 −4.77958
\(829\) −7.36837 −0.255914 −0.127957 0.991780i \(-0.540842\pi\)
−0.127957 + 0.991780i \(0.540842\pi\)
\(830\) 1.27341 0.0442006
\(831\) −0.848973 −0.0294506
\(832\) 66.2062 2.29529
\(833\) −0.197549 −0.00684466
\(834\) 5.79872 0.200793
\(835\) −47.6174 −1.64787
\(836\) 81.1036 2.80503
\(837\) 0.801520 0.0277046
\(838\) −16.2372 −0.560904
\(839\) −49.1602 −1.69720 −0.848600 0.529035i \(-0.822554\pi\)
−0.848600 + 0.529035i \(0.822554\pi\)
\(840\) −18.3238 −0.632233
\(841\) −24.3550 −0.839828
\(842\) −46.1413 −1.59014
\(843\) −0.0243158 −0.000837480 0
\(844\) −80.6561 −2.77630
\(845\) 13.4611 0.463075
\(846\) −54.3008 −1.86690
\(847\) −14.5210 −0.498947
\(848\) −148.570 −5.10190
\(849\) 3.91236 0.134272
\(850\) −12.9655 −0.444712
\(851\) 32.4164 1.11122
\(852\) −13.6736 −0.468450
\(853\) −23.0639 −0.789694 −0.394847 0.918747i \(-0.629202\pi\)
−0.394847 + 0.918747i \(0.629202\pi\)
\(854\) 29.4448 1.00758
\(855\) 75.7432 2.59036
\(856\) −102.837 −3.51491
\(857\) 54.7957 1.87179 0.935893 0.352283i \(-0.114595\pi\)
0.935893 + 0.352283i \(0.114595\pi\)
\(858\) 4.07290 0.139046
\(859\) 4.43429 0.151296 0.0756481 0.997135i \(-0.475897\pi\)
0.0756481 + 0.997135i \(0.475897\pi\)
\(860\) −157.572 −5.37316
\(861\) −5.00478 −0.170562
\(862\) 70.3531 2.39624
\(863\) 15.8507 0.539565 0.269782 0.962921i \(-0.413048\pi\)
0.269782 + 0.962921i \(0.413048\pi\)
\(864\) −22.3601 −0.760706
\(865\) −51.1159 −1.73799
\(866\) −30.9905 −1.05310
\(867\) 3.55682 0.120796
\(868\) 8.55382 0.290336
\(869\) −10.8775 −0.368996
\(870\) 4.72822 0.160302
\(871\) −8.40272 −0.284715
\(872\) 92.7316 3.14029
\(873\) 53.3934 1.80709
\(874\) −159.411 −5.39216
\(875\) −46.6335 −1.57650
\(876\) 4.66009 0.157450
\(877\) −56.8995 −1.92136 −0.960680 0.277660i \(-0.910441\pi\)
−0.960680 + 0.277660i \(0.910441\pi\)
\(878\) −80.3227 −2.71076
\(879\) −1.70658 −0.0575616
\(880\) −116.008 −3.91064
\(881\) −36.3670 −1.22523 −0.612617 0.790380i \(-0.709883\pi\)
−0.612617 + 0.790380i \(0.709883\pi\)
\(882\) −3.17626 −0.106950
\(883\) 44.1168 1.48465 0.742325 0.670040i \(-0.233723\pi\)
0.742325 + 0.670040i \(0.233723\pi\)
\(884\) 8.00637 0.269283
\(885\) −1.20012 −0.0403417
\(886\) −85.2621 −2.86444
\(887\) −15.2649 −0.512546 −0.256273 0.966604i \(-0.582495\pi\)
−0.256273 + 0.966604i \(0.582495\pi\)
\(888\) 6.79629 0.228068
\(889\) −6.22572 −0.208804
\(890\) 27.2905 0.914779
\(891\) 19.8801 0.666007
\(892\) 93.5511 3.13232
\(893\) −45.5788 −1.52524
\(894\) −2.30823 −0.0771986
\(895\) −19.5675 −0.654068
\(896\) −57.7742 −1.93010
\(897\) −5.79729 −0.193566
\(898\) −86.3632 −2.88198
\(899\) −1.36652 −0.0455759
\(900\) −150.964 −5.03214
\(901\) −5.62517 −0.187402
\(902\) −57.1435 −1.90267
\(903\) −4.26443 −0.141911
\(904\) −152.562 −5.07414
\(905\) −72.5867 −2.41286
\(906\) −11.7648 −0.390858
\(907\) 23.8486 0.791881 0.395941 0.918276i \(-0.370419\pi\)
0.395941 + 0.918276i \(0.370419\pi\)
\(908\) −45.9222 −1.52398
\(909\) −20.6945 −0.686392
\(910\) 81.8054 2.71182
\(911\) −0.356916 −0.0118251 −0.00591257 0.999983i \(-0.501882\pi\)
−0.00591257 + 0.999983i \(0.501882\pi\)
\(912\) −18.5318 −0.613648
\(913\) 0.284954 0.00943061
\(914\) −60.2296 −1.99222
\(915\) −3.46752 −0.114633
\(916\) 105.534 3.48694
\(917\) 3.17229 0.104758
\(918\) −1.68459 −0.0555998
\(919\) −3.89679 −0.128543 −0.0642717 0.997932i \(-0.520472\pi\)
−0.0642717 + 0.997932i \(0.520472\pi\)
\(920\) 297.797 9.81808
\(921\) 1.09479 0.0360746
\(922\) −85.3043 −2.80935
\(923\) 37.7939 1.24400
\(924\) −6.62294 −0.217879
\(925\) 35.5822 1.16994
\(926\) −42.5006 −1.39665
\(927\) −4.72748 −0.155271
\(928\) 38.1219 1.25141
\(929\) −16.6041 −0.544762 −0.272381 0.962189i \(-0.587811\pi\)
−0.272381 + 0.962189i \(0.587811\pi\)
\(930\) −1.39100 −0.0456128
\(931\) −2.66608 −0.0873771
\(932\) −14.0084 −0.458861
\(933\) −0.766670 −0.0250996
\(934\) −115.579 −3.78185
\(935\) −4.39233 −0.143645
\(936\) 79.6985 2.60503
\(937\) −40.2957 −1.31640 −0.658202 0.752841i \(-0.728683\pi\)
−0.658202 + 0.752841i \(0.728683\pi\)
\(938\) 18.8679 0.616060
\(939\) −5.58230 −0.182172
\(940\) 137.528 4.48567
\(941\) 37.7868 1.23182 0.615908 0.787818i \(-0.288789\pi\)
0.615908 + 0.787818i \(0.288789\pi\)
\(942\) −2.67227 −0.0870674
\(943\) 81.3371 2.64870
\(944\) −19.2538 −0.626659
\(945\) −12.4647 −0.405478
\(946\) −48.6904 −1.58306
\(947\) −50.1060 −1.62823 −0.814114 0.580706i \(-0.802777\pi\)
−0.814114 + 0.580706i \(0.802777\pi\)
\(948\) 5.24308 0.170287
\(949\) −12.8805 −0.418118
\(950\) −174.979 −5.67708
\(951\) 6.79239 0.220258
\(952\) −11.1305 −0.360741
\(953\) −31.9329 −1.03441 −0.517204 0.855862i \(-0.673027\pi\)
−0.517204 + 0.855862i \(0.673027\pi\)
\(954\) −90.4435 −2.92822
\(955\) 84.4683 2.73333
\(956\) −17.7332 −0.573532
\(957\) 1.05805 0.0342019
\(958\) 64.6812 2.08975
\(959\) 30.6783 0.990653
\(960\) 17.5071 0.565039
\(961\) −30.5980 −0.987032
\(962\) −30.3415 −0.978249
\(963\) −34.7128 −1.11860
\(964\) 94.5376 3.04485
\(965\) 36.1530 1.16381
\(966\) 13.0176 0.418833
\(967\) 48.7518 1.56775 0.783876 0.620918i \(-0.213240\pi\)
0.783876 + 0.620918i \(0.213240\pi\)
\(968\) 49.4775 1.59027
\(969\) −0.701653 −0.0225403
\(970\) −186.737 −5.99575
\(971\) 3.75936 0.120644 0.0603219 0.998179i \(-0.480787\pi\)
0.0603219 + 0.998179i \(0.480787\pi\)
\(972\) −29.4961 −0.946088
\(973\) 26.0626 0.835529
\(974\) −20.1222 −0.644756
\(975\) −6.36346 −0.203794
\(976\) −55.6302 −1.78068
\(977\) 19.2510 0.615893 0.307946 0.951404i \(-0.400358\pi\)
0.307946 + 0.951404i \(0.400358\pi\)
\(978\) 13.0813 0.418293
\(979\) 6.10687 0.195177
\(980\) 8.04455 0.256974
\(981\) 31.3016 0.999382
\(982\) −30.9753 −0.988463
\(983\) −20.2320 −0.645302 −0.322651 0.946518i \(-0.604574\pi\)
−0.322651 + 0.946518i \(0.604574\pi\)
\(984\) 17.0528 0.543624
\(985\) −0.517599 −0.0164921
\(986\) 2.87207 0.0914653
\(987\) 3.72198 0.118472
\(988\) 108.052 3.43760
\(989\) 69.3051 2.20378
\(990\) −70.6215 −2.24450
\(991\) 35.1450 1.11642 0.558208 0.829701i \(-0.311489\pi\)
0.558208 + 0.829701i \(0.311489\pi\)
\(992\) −11.2151 −0.356081
\(993\) 1.86803 0.0592801
\(994\) −84.8645 −2.69174
\(995\) 90.2065 2.85974
\(996\) −0.137351 −0.00435213
\(997\) −1.98283 −0.0627967 −0.0313984 0.999507i \(-0.509996\pi\)
−0.0313984 + 0.999507i \(0.509996\pi\)
\(998\) 73.0006 2.31079
\(999\) 4.62316 0.146270
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 4013.2.a.c.1.4 176
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4013.2.a.c.1.4 176 1.1 even 1 trivial