Properties

Label 6007.2.a.c.1.2
Level $6007$
Weight $2$
Character 6007.1
Self dual yes
Analytic conductor $47.966$
Analytic rank $0$
Dimension $261$
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] = [6007,2,Mod(1,6007)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6007, 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("6007.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6007 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6007.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: \(47.9661364942\)
Analytic rank: \(0\)
Dimension: \(261\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) \(=\) 6007.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.81023 q^{2} -2.20286 q^{3} +5.89742 q^{4} +4.33627 q^{5} +6.19056 q^{6} +0.601928 q^{7} -10.9527 q^{8} +1.85260 q^{9} +O(q^{10})\) \(q-2.81023 q^{2} -2.20286 q^{3} +5.89742 q^{4} +4.33627 q^{5} +6.19056 q^{6} +0.601928 q^{7} -10.9527 q^{8} +1.85260 q^{9} -12.1859 q^{10} -1.95095 q^{11} -12.9912 q^{12} -0.638794 q^{13} -1.69156 q^{14} -9.55220 q^{15} +18.9847 q^{16} +5.84863 q^{17} -5.20624 q^{18} -4.93353 q^{19} +25.5728 q^{20} -1.32596 q^{21} +5.48263 q^{22} -2.39688 q^{23} +24.1272 q^{24} +13.8032 q^{25} +1.79516 q^{26} +2.52756 q^{27} +3.54982 q^{28} +6.77850 q^{29} +26.8439 q^{30} -4.97453 q^{31} -31.4461 q^{32} +4.29768 q^{33} -16.4360 q^{34} +2.61012 q^{35} +10.9256 q^{36} -2.01664 q^{37} +13.8644 q^{38} +1.40718 q^{39} -47.4936 q^{40} -3.61257 q^{41} +3.72627 q^{42} +7.38229 q^{43} -11.5056 q^{44} +8.03337 q^{45} +6.73579 q^{46} +1.60762 q^{47} -41.8206 q^{48} -6.63768 q^{49} -38.7902 q^{50} -12.8837 q^{51} -3.76724 q^{52} +3.69528 q^{53} -7.10304 q^{54} -8.45985 q^{55} -6.59271 q^{56} +10.8679 q^{57} -19.0492 q^{58} -7.47114 q^{59} -56.3333 q^{60} -2.73881 q^{61} +13.9796 q^{62} +1.11513 q^{63} +50.4016 q^{64} -2.76998 q^{65} -12.0775 q^{66} +13.9681 q^{67} +34.4918 q^{68} +5.27999 q^{69} -7.33505 q^{70} -10.4090 q^{71} -20.2909 q^{72} +11.9176 q^{73} +5.66723 q^{74} -30.4066 q^{75} -29.0951 q^{76} -1.17433 q^{77} -3.95449 q^{78} -1.66559 q^{79} +82.3227 q^{80} -11.1257 q^{81} +10.1522 q^{82} -9.37613 q^{83} -7.81976 q^{84} +25.3612 q^{85} -20.7460 q^{86} -14.9321 q^{87} +21.3681 q^{88} -2.69099 q^{89} -22.5757 q^{90} -0.384508 q^{91} -14.1354 q^{92} +10.9582 q^{93} -4.51779 q^{94} -21.3931 q^{95} +69.2714 q^{96} -16.3166 q^{97} +18.6534 q^{98} -3.61434 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 261 q + 26 q^{2} + 25 q^{3} + 274 q^{4} + 66 q^{5} + 25 q^{6} + 37 q^{7} + 72 q^{8} + 310 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 261 q + 26 q^{2} + 25 q^{3} + 274 q^{4} + 66 q^{5} + 25 q^{6} + 37 q^{7} + 72 q^{8} + 310 q^{9} + 35 q^{10} + 32 q^{11} + 51 q^{12} + 60 q^{13} + 55 q^{14} + 16 q^{15} + 288 q^{16} + 270 q^{17} + 45 q^{18} + 34 q^{19} + 157 q^{20} + 27 q^{21} + 38 q^{22} + 116 q^{23} + 48 q^{24} + 335 q^{25} + 46 q^{26} + 73 q^{27} + 70 q^{28} + 99 q^{29} + 33 q^{30} + 33 q^{31} + 150 q^{32} + 172 q^{33} + 24 q^{34} + 114 q^{35} + 339 q^{36} + 36 q^{37} + 112 q^{38} + 30 q^{39} + 106 q^{40} + 209 q^{41} + 64 q^{42} + 64 q^{43} + 65 q^{44} + 153 q^{45} + 135 q^{47} + 87 q^{48} + 332 q^{49} + 82 q^{50} + 52 q^{51} + 102 q^{52} + 163 q^{53} + 52 q^{54} + 56 q^{55} + 134 q^{56} + 181 q^{57} + q^{58} + 89 q^{59} - 43 q^{60} + 112 q^{61} + 228 q^{62} + 130 q^{63} + 268 q^{64} + 248 q^{65} + 5 q^{66} + 42 q^{67} + 453 q^{68} + 51 q^{69} - 22 q^{70} + 98 q^{71} + 113 q^{72} + 206 q^{73} + 81 q^{74} + 29 q^{75} + 62 q^{76} + 185 q^{77} - 25 q^{78} + 29 q^{79} + 258 q^{80} + 393 q^{81} + 79 q^{82} + 265 q^{83} - 25 q^{84} + 84 q^{85} + 36 q^{86} + 131 q^{87} + 24 q^{88} + 195 q^{89} + 89 q^{90} - 18 q^{91} + 261 q^{92} + 52 q^{93} + 3 q^{94} + 104 q^{95} + 92 q^{96} + 213 q^{97} + 156 q^{98} + 47 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.81023 −1.98714 −0.993568 0.113239i \(-0.963878\pi\)
−0.993568 + 0.113239i \(0.963878\pi\)
\(3\) −2.20286 −1.27182 −0.635911 0.771762i \(-0.719376\pi\)
−0.635911 + 0.771762i \(0.719376\pi\)
\(4\) 5.89742 2.94871
\(5\) 4.33627 1.93924 0.969619 0.244621i \(-0.0786637\pi\)
0.969619 + 0.244621i \(0.0786637\pi\)
\(6\) 6.19056 2.52728
\(7\) 0.601928 0.227507 0.113754 0.993509i \(-0.463713\pi\)
0.113754 + 0.993509i \(0.463713\pi\)
\(8\) −10.9527 −3.87235
\(9\) 1.85260 0.617534
\(10\) −12.1859 −3.85353
\(11\) −1.95095 −0.588234 −0.294117 0.955769i \(-0.595026\pi\)
−0.294117 + 0.955769i \(0.595026\pi\)
\(12\) −12.9912 −3.75023
\(13\) −0.638794 −0.177170 −0.0885848 0.996069i \(-0.528234\pi\)
−0.0885848 + 0.996069i \(0.528234\pi\)
\(14\) −1.69156 −0.452088
\(15\) −9.55220 −2.46637
\(16\) 18.9847 4.74617
\(17\) 5.84863 1.41850 0.709251 0.704956i \(-0.249033\pi\)
0.709251 + 0.704956i \(0.249033\pi\)
\(18\) −5.20624 −1.22712
\(19\) −4.93353 −1.13183 −0.565914 0.824464i \(-0.691477\pi\)
−0.565914 + 0.824464i \(0.691477\pi\)
\(20\) 25.5728 5.71824
\(21\) −1.32596 −0.289349
\(22\) 5.48263 1.16890
\(23\) −2.39688 −0.499784 −0.249892 0.968274i \(-0.580395\pi\)
−0.249892 + 0.968274i \(0.580395\pi\)
\(24\) 24.1272 4.92494
\(25\) 13.8032 2.76064
\(26\) 1.79516 0.352060
\(27\) 2.52756 0.486430
\(28\) 3.54982 0.670853
\(29\) 6.77850 1.25874 0.629368 0.777108i \(-0.283314\pi\)
0.629368 + 0.777108i \(0.283314\pi\)
\(30\) 26.8439 4.90100
\(31\) −4.97453 −0.893452 −0.446726 0.894671i \(-0.647410\pi\)
−0.446726 + 0.894671i \(0.647410\pi\)
\(32\) −31.4461 −5.55894
\(33\) 4.29768 0.748130
\(34\) −16.4360 −2.81875
\(35\) 2.61012 0.441191
\(36\) 10.9256 1.82093
\(37\) −2.01664 −0.331533 −0.165767 0.986165i \(-0.553010\pi\)
−0.165767 + 0.986165i \(0.553010\pi\)
\(38\) 13.8644 2.24910
\(39\) 1.40718 0.225328
\(40\) −47.4936 −7.50940
\(41\) −3.61257 −0.564188 −0.282094 0.959387i \(-0.591029\pi\)
−0.282094 + 0.959387i \(0.591029\pi\)
\(42\) 3.72627 0.574976
\(43\) 7.38229 1.12579 0.562895 0.826529i \(-0.309688\pi\)
0.562895 + 0.826529i \(0.309688\pi\)
\(44\) −11.5056 −1.73453
\(45\) 8.03337 1.19754
\(46\) 6.73579 0.993138
\(47\) 1.60762 0.234495 0.117248 0.993103i \(-0.462593\pi\)
0.117248 + 0.993103i \(0.462593\pi\)
\(48\) −41.8206 −6.03629
\(49\) −6.63768 −0.948240
\(50\) −38.7902 −5.48577
\(51\) −12.8837 −1.80408
\(52\) −3.76724 −0.522422
\(53\) 3.69528 0.507585 0.253793 0.967259i \(-0.418322\pi\)
0.253793 + 0.967259i \(0.418322\pi\)
\(54\) −7.10304 −0.966601
\(55\) −8.45985 −1.14073
\(56\) −6.59271 −0.880987
\(57\) 10.8679 1.43949
\(58\) −19.0492 −2.50128
\(59\) −7.47114 −0.972659 −0.486330 0.873775i \(-0.661665\pi\)
−0.486330 + 0.873775i \(0.661665\pi\)
\(60\) −56.3333 −7.27260
\(61\) −2.73881 −0.350669 −0.175334 0.984509i \(-0.556101\pi\)
−0.175334 + 0.984509i \(0.556101\pi\)
\(62\) 13.9796 1.77541
\(63\) 1.11513 0.140493
\(64\) 50.4016 6.30019
\(65\) −2.76998 −0.343574
\(66\) −12.0775 −1.48664
\(67\) 13.9681 1.70647 0.853236 0.521526i \(-0.174637\pi\)
0.853236 + 0.521526i \(0.174637\pi\)
\(68\) 34.4918 4.18275
\(69\) 5.27999 0.635636
\(70\) −7.33505 −0.876706
\(71\) −10.4090 −1.23533 −0.617663 0.786443i \(-0.711920\pi\)
−0.617663 + 0.786443i \(0.711920\pi\)
\(72\) −20.2909 −2.39130
\(73\) 11.9176 1.39485 0.697426 0.716657i \(-0.254329\pi\)
0.697426 + 0.716657i \(0.254329\pi\)
\(74\) 5.66723 0.658802
\(75\) −30.4066 −3.51105
\(76\) −29.0951 −3.33743
\(77\) −1.17433 −0.133828
\(78\) −3.95449 −0.447758
\(79\) −1.66559 −0.187394 −0.0936968 0.995601i \(-0.529868\pi\)
−0.0936968 + 0.995601i \(0.529868\pi\)
\(80\) 82.3227 9.20395
\(81\) −11.1257 −1.23619
\(82\) 10.1522 1.12112
\(83\) −9.37613 −1.02916 −0.514582 0.857441i \(-0.672053\pi\)
−0.514582 + 0.857441i \(0.672053\pi\)
\(84\) −7.81976 −0.853206
\(85\) 25.3612 2.75081
\(86\) −20.7460 −2.23710
\(87\) −14.9321 −1.60089
\(88\) 21.3681 2.27785
\(89\) −2.69099 −0.285244 −0.142622 0.989777i \(-0.545553\pi\)
−0.142622 + 0.989777i \(0.545553\pi\)
\(90\) −22.5757 −2.37968
\(91\) −0.384508 −0.0403074
\(92\) −14.1354 −1.47372
\(93\) 10.9582 1.13631
\(94\) −4.51779 −0.465974
\(95\) −21.3931 −2.19488
\(96\) 69.2714 7.06999
\(97\) −16.3166 −1.65670 −0.828349 0.560213i \(-0.810719\pi\)
−0.828349 + 0.560213i \(0.810719\pi\)
\(98\) 18.6534 1.88428
\(99\) −3.61434 −0.363255
\(100\) 81.4033 8.14033
\(101\) 14.7604 1.46872 0.734358 0.678762i \(-0.237483\pi\)
0.734358 + 0.678762i \(0.237483\pi\)
\(102\) 36.2063 3.58496
\(103\) 10.3421 1.01903 0.509516 0.860461i \(-0.329824\pi\)
0.509516 + 0.860461i \(0.329824\pi\)
\(104\) 6.99649 0.686063
\(105\) −5.74973 −0.561116
\(106\) −10.3846 −1.00864
\(107\) 11.7368 1.13464 0.567320 0.823497i \(-0.307980\pi\)
0.567320 + 0.823497i \(0.307980\pi\)
\(108\) 14.9061 1.43434
\(109\) 13.8887 1.33029 0.665146 0.746713i \(-0.268369\pi\)
0.665146 + 0.746713i \(0.268369\pi\)
\(110\) 23.7742 2.26678
\(111\) 4.44238 0.421652
\(112\) 11.4274 1.07979
\(113\) 9.37285 0.881723 0.440862 0.897575i \(-0.354673\pi\)
0.440862 + 0.897575i \(0.354673\pi\)
\(114\) −30.5413 −2.86045
\(115\) −10.3935 −0.969199
\(116\) 39.9756 3.71164
\(117\) −1.18343 −0.109408
\(118\) 20.9956 1.93281
\(119\) 3.52045 0.322719
\(120\) 104.622 9.55063
\(121\) −7.19378 −0.653980
\(122\) 7.69670 0.696827
\(123\) 7.95799 0.717548
\(124\) −29.3369 −2.63453
\(125\) 38.1731 3.41430
\(126\) −3.13378 −0.279179
\(127\) −10.2666 −0.911013 −0.455507 0.890232i \(-0.650542\pi\)
−0.455507 + 0.890232i \(0.650542\pi\)
\(128\) −78.7480 −6.96040
\(129\) −16.2622 −1.43180
\(130\) 7.78430 0.682728
\(131\) 15.2661 1.33381 0.666903 0.745145i \(-0.267620\pi\)
0.666903 + 0.745145i \(0.267620\pi\)
\(132\) 25.3452 2.20602
\(133\) −2.96963 −0.257499
\(134\) −39.2535 −3.39099
\(135\) 10.9602 0.943302
\(136\) −64.0580 −5.49293
\(137\) 18.5347 1.58353 0.791764 0.610827i \(-0.209163\pi\)
0.791764 + 0.610827i \(0.209163\pi\)
\(138\) −14.8380 −1.26310
\(139\) −15.2801 −1.29604 −0.648021 0.761623i \(-0.724403\pi\)
−0.648021 + 0.761623i \(0.724403\pi\)
\(140\) 15.3930 1.30094
\(141\) −3.54136 −0.298237
\(142\) 29.2518 2.45476
\(143\) 1.24626 0.104217
\(144\) 35.1710 2.93092
\(145\) 29.3934 2.44099
\(146\) −33.4913 −2.77176
\(147\) 14.6219 1.20599
\(148\) −11.8930 −0.977595
\(149\) 17.4848 1.43241 0.716207 0.697888i \(-0.245877\pi\)
0.716207 + 0.697888i \(0.245877\pi\)
\(150\) 85.4496 6.97693
\(151\) 2.38900 0.194414 0.0972072 0.995264i \(-0.469009\pi\)
0.0972072 + 0.995264i \(0.469009\pi\)
\(152\) 54.0352 4.38283
\(153\) 10.8352 0.875972
\(154\) 3.30015 0.265934
\(155\) −21.5709 −1.73261
\(156\) 8.29870 0.664428
\(157\) −3.54400 −0.282842 −0.141421 0.989950i \(-0.545167\pi\)
−0.141421 + 0.989950i \(0.545167\pi\)
\(158\) 4.68070 0.372377
\(159\) −8.14019 −0.645559
\(160\) −136.359 −10.7801
\(161\) −1.44275 −0.113704
\(162\) 31.2657 2.45647
\(163\) −15.8254 −1.23954 −0.619772 0.784782i \(-0.712775\pi\)
−0.619772 + 0.784782i \(0.712775\pi\)
\(164\) −21.3048 −1.66363
\(165\) 18.6359 1.45080
\(166\) 26.3491 2.04509
\(167\) 7.23168 0.559604 0.279802 0.960058i \(-0.409731\pi\)
0.279802 + 0.960058i \(0.409731\pi\)
\(168\) 14.5228 1.12046
\(169\) −12.5919 −0.968611
\(170\) −71.2710 −5.46623
\(171\) −9.13986 −0.698942
\(172\) 43.5365 3.31962
\(173\) 14.5017 1.10254 0.551271 0.834326i \(-0.314143\pi\)
0.551271 + 0.834326i \(0.314143\pi\)
\(174\) 41.9627 3.18118
\(175\) 8.30853 0.628066
\(176\) −37.0382 −2.79186
\(177\) 16.4579 1.23705
\(178\) 7.56230 0.566819
\(179\) 19.7734 1.47793 0.738967 0.673742i \(-0.235314\pi\)
0.738967 + 0.673742i \(0.235314\pi\)
\(180\) 47.3761 3.53121
\(181\) 3.13654 0.233137 0.116568 0.993183i \(-0.462811\pi\)
0.116568 + 0.993183i \(0.462811\pi\)
\(182\) 1.08056 0.0800963
\(183\) 6.03322 0.445989
\(184\) 26.2522 1.93534
\(185\) −8.74468 −0.642922
\(186\) −30.7951 −2.25801
\(187\) −11.4104 −0.834411
\(188\) 9.48080 0.691458
\(189\) 1.52141 0.110666
\(190\) 60.1196 4.36153
\(191\) −10.1409 −0.733771 −0.366885 0.930266i \(-0.619576\pi\)
−0.366885 + 0.930266i \(0.619576\pi\)
\(192\) −111.028 −8.01273
\(193\) −21.5914 −1.55418 −0.777092 0.629387i \(-0.783306\pi\)
−0.777092 + 0.629387i \(0.783306\pi\)
\(194\) 45.8534 3.29208
\(195\) 6.10189 0.436965
\(196\) −39.1452 −2.79608
\(197\) −10.8767 −0.774933 −0.387467 0.921884i \(-0.626650\pi\)
−0.387467 + 0.921884i \(0.626650\pi\)
\(198\) 10.1571 0.721836
\(199\) −9.53646 −0.676022 −0.338011 0.941142i \(-0.609754\pi\)
−0.338011 + 0.941142i \(0.609754\pi\)
\(200\) −151.182 −10.6902
\(201\) −30.7697 −2.17033
\(202\) −41.4802 −2.91854
\(203\) 4.08017 0.286371
\(204\) −75.9807 −5.31971
\(205\) −15.6651 −1.09409
\(206\) −29.0636 −2.02496
\(207\) −4.44046 −0.308633
\(208\) −12.1273 −0.840878
\(209\) 9.62508 0.665781
\(210\) 16.1581 1.11501
\(211\) 22.5473 1.55222 0.776109 0.630599i \(-0.217191\pi\)
0.776109 + 0.630599i \(0.217191\pi\)
\(212\) 21.7926 1.49672
\(213\) 22.9297 1.57112
\(214\) −32.9832 −2.25468
\(215\) 32.0116 2.18317
\(216\) −27.6835 −1.88362
\(217\) −2.99431 −0.203267
\(218\) −39.0304 −2.64347
\(219\) −26.2529 −1.77401
\(220\) −49.8913 −3.36367
\(221\) −3.73607 −0.251315
\(222\) −12.4841 −0.837879
\(223\) 18.4469 1.23529 0.617647 0.786456i \(-0.288086\pi\)
0.617647 + 0.786456i \(0.288086\pi\)
\(224\) −18.9283 −1.26470
\(225\) 25.5718 1.70479
\(226\) −26.3399 −1.75210
\(227\) −0.204980 −0.0136050 −0.00680249 0.999977i \(-0.502165\pi\)
−0.00680249 + 0.999977i \(0.502165\pi\)
\(228\) 64.0924 4.24462
\(229\) −8.18803 −0.541080 −0.270540 0.962709i \(-0.587202\pi\)
−0.270540 + 0.962709i \(0.587202\pi\)
\(230\) 29.2082 1.92593
\(231\) 2.58689 0.170205
\(232\) −74.2425 −4.87426
\(233\) −6.56071 −0.429806 −0.214903 0.976635i \(-0.568944\pi\)
−0.214903 + 0.976635i \(0.568944\pi\)
\(234\) 3.32572 0.217409
\(235\) 6.97107 0.454742
\(236\) −44.0604 −2.86809
\(237\) 3.66907 0.238332
\(238\) −9.89330 −0.641287
\(239\) 6.48662 0.419585 0.209792 0.977746i \(-0.432721\pi\)
0.209792 + 0.977746i \(0.432721\pi\)
\(240\) −181.345 −11.7058
\(241\) 4.47262 0.288107 0.144053 0.989570i \(-0.453986\pi\)
0.144053 + 0.989570i \(0.453986\pi\)
\(242\) 20.2162 1.29955
\(243\) 16.9256 1.08578
\(244\) −16.1519 −1.03402
\(245\) −28.7828 −1.83886
\(246\) −22.3638 −1.42586
\(247\) 3.15151 0.200526
\(248\) 54.4843 3.45976
\(249\) 20.6543 1.30891
\(250\) −107.275 −6.78468
\(251\) 13.0091 0.821126 0.410563 0.911832i \(-0.365332\pi\)
0.410563 + 0.911832i \(0.365332\pi\)
\(252\) 6.57640 0.414274
\(253\) 4.67620 0.293990
\(254\) 28.8515 1.81031
\(255\) −55.8673 −3.49854
\(256\) 120.497 7.53107
\(257\) −2.41731 −0.150788 −0.0753938 0.997154i \(-0.524021\pi\)
−0.0753938 + 0.997154i \(0.524021\pi\)
\(258\) 45.7005 2.84519
\(259\) −1.21387 −0.0754263
\(260\) −16.3357 −1.01310
\(261\) 12.5578 0.777311
\(262\) −42.9013 −2.65045
\(263\) 18.9696 1.16972 0.584858 0.811135i \(-0.301150\pi\)
0.584858 + 0.811135i \(0.301150\pi\)
\(264\) −47.0710 −2.89702
\(265\) 16.0237 0.984329
\(266\) 8.34535 0.511686
\(267\) 5.92787 0.362780
\(268\) 82.3755 5.03189
\(269\) −13.6485 −0.832163 −0.416082 0.909327i \(-0.636597\pi\)
−0.416082 + 0.909327i \(0.636597\pi\)
\(270\) −30.8007 −1.87447
\(271\) 7.35582 0.446834 0.223417 0.974723i \(-0.428279\pi\)
0.223417 + 0.974723i \(0.428279\pi\)
\(272\) 111.034 6.73245
\(273\) 0.847018 0.0512639
\(274\) −52.0869 −3.14669
\(275\) −26.9294 −1.62390
\(276\) 31.1383 1.87431
\(277\) 1.17446 0.0705664 0.0352832 0.999377i \(-0.488767\pi\)
0.0352832 + 0.999377i \(0.488767\pi\)
\(278\) 42.9407 2.57541
\(279\) −9.21582 −0.551736
\(280\) −28.5877 −1.70844
\(281\) −11.6490 −0.694920 −0.347460 0.937695i \(-0.612956\pi\)
−0.347460 + 0.937695i \(0.612956\pi\)
\(282\) 9.95206 0.592637
\(283\) 17.5045 1.04053 0.520266 0.854004i \(-0.325833\pi\)
0.520266 + 0.854004i \(0.325833\pi\)
\(284\) −61.3864 −3.64262
\(285\) 47.1260 2.79150
\(286\) −3.50228 −0.207094
\(287\) −2.17450 −0.128357
\(288\) −58.2571 −3.43283
\(289\) 17.2065 1.01215
\(290\) −82.6022 −4.85057
\(291\) 35.9432 2.10703
\(292\) 70.2832 4.11301
\(293\) −8.30486 −0.485175 −0.242587 0.970130i \(-0.577996\pi\)
−0.242587 + 0.970130i \(0.577996\pi\)
\(294\) −41.0910 −2.39647
\(295\) −32.3968 −1.88622
\(296\) 22.0875 1.28381
\(297\) −4.93115 −0.286135
\(298\) −49.1365 −2.84640
\(299\) 1.53111 0.0885465
\(300\) −179.320 −10.3531
\(301\) 4.44361 0.256125
\(302\) −6.71366 −0.386328
\(303\) −32.5152 −1.86795
\(304\) −93.6615 −5.37185
\(305\) −11.8762 −0.680030
\(306\) −30.4494 −1.74068
\(307\) 25.1241 1.43391 0.716954 0.697121i \(-0.245536\pi\)
0.716954 + 0.697121i \(0.245536\pi\)
\(308\) −6.92553 −0.394619
\(309\) −22.7821 −1.29603
\(310\) 60.6192 3.44294
\(311\) 27.2114 1.54301 0.771507 0.636220i \(-0.219503\pi\)
0.771507 + 0.636220i \(0.219503\pi\)
\(312\) −15.4123 −0.872550
\(313\) 27.0965 1.53158 0.765792 0.643089i \(-0.222347\pi\)
0.765792 + 0.643089i \(0.222347\pi\)
\(314\) 9.95947 0.562046
\(315\) 4.83551 0.272450
\(316\) −9.82268 −0.552569
\(317\) 9.31869 0.523390 0.261695 0.965151i \(-0.415719\pi\)
0.261695 + 0.965151i \(0.415719\pi\)
\(318\) 22.8758 1.28281
\(319\) −13.2245 −0.740431
\(320\) 218.555 12.2176
\(321\) −25.8546 −1.44306
\(322\) 4.05446 0.225946
\(323\) −28.8544 −1.60550
\(324\) −65.6127 −3.64515
\(325\) −8.81741 −0.489102
\(326\) 44.4732 2.46314
\(327\) −30.5948 −1.69190
\(328\) 39.5672 2.18473
\(329\) 0.967671 0.0533494
\(330\) −52.3712 −2.88294
\(331\) −30.3209 −1.66659 −0.833293 0.552832i \(-0.813547\pi\)
−0.833293 + 0.552832i \(0.813547\pi\)
\(332\) −55.2950 −3.03471
\(333\) −3.73603 −0.204733
\(334\) −20.3227 −1.11201
\(335\) 60.5693 3.30925
\(336\) −25.1730 −1.37330
\(337\) −27.6976 −1.50878 −0.754392 0.656424i \(-0.772068\pi\)
−0.754392 + 0.656424i \(0.772068\pi\)
\(338\) 35.3863 1.92476
\(339\) −20.6471 −1.12140
\(340\) 149.566 8.11134
\(341\) 9.70507 0.525559
\(342\) 25.6851 1.38889
\(343\) −8.20890 −0.443239
\(344\) −80.8557 −4.35945
\(345\) 22.8954 1.23265
\(346\) −40.7531 −2.19090
\(347\) −12.2633 −0.658328 −0.329164 0.944273i \(-0.606767\pi\)
−0.329164 + 0.944273i \(0.606767\pi\)
\(348\) −88.0608 −4.72055
\(349\) 11.4521 0.613016 0.306508 0.951868i \(-0.400839\pi\)
0.306508 + 0.951868i \(0.400839\pi\)
\(350\) −23.3489 −1.24805
\(351\) −1.61459 −0.0861806
\(352\) 61.3499 3.26996
\(353\) 13.2465 0.705039 0.352519 0.935805i \(-0.385325\pi\)
0.352519 + 0.935805i \(0.385325\pi\)
\(354\) −46.2505 −2.45819
\(355\) −45.1364 −2.39559
\(356\) −15.8699 −0.841101
\(357\) −7.75507 −0.410442
\(358\) −55.5679 −2.93685
\(359\) −8.99862 −0.474929 −0.237464 0.971396i \(-0.576316\pi\)
−0.237464 + 0.971396i \(0.576316\pi\)
\(360\) −87.9867 −4.63731
\(361\) 5.33969 0.281036
\(362\) −8.81440 −0.463275
\(363\) 15.8469 0.831747
\(364\) −2.26760 −0.118855
\(365\) 51.6780 2.70495
\(366\) −16.9548 −0.886240
\(367\) −8.65967 −0.452031 −0.226016 0.974124i \(-0.572570\pi\)
−0.226016 + 0.974124i \(0.572570\pi\)
\(368\) −45.5040 −2.37206
\(369\) −6.69265 −0.348405
\(370\) 24.5746 1.27757
\(371\) 2.22429 0.115479
\(372\) 64.6251 3.35065
\(373\) −0.483945 −0.0250577 −0.0125288 0.999922i \(-0.503988\pi\)
−0.0125288 + 0.999922i \(0.503988\pi\)
\(374\) 32.0659 1.65809
\(375\) −84.0900 −4.34239
\(376\) −17.6077 −0.908047
\(377\) −4.33007 −0.223010
\(378\) −4.27552 −0.219909
\(379\) −34.2709 −1.76038 −0.880190 0.474622i \(-0.842585\pi\)
−0.880190 + 0.474622i \(0.842585\pi\)
\(380\) −126.164 −6.47207
\(381\) 22.6159 1.15865
\(382\) 28.4983 1.45810
\(383\) 3.82752 0.195577 0.0977885 0.995207i \(-0.468823\pi\)
0.0977885 + 0.995207i \(0.468823\pi\)
\(384\) 173.471 8.85240
\(385\) −5.09222 −0.259524
\(386\) 60.6769 3.08837
\(387\) 13.6764 0.695213
\(388\) −96.2256 −4.88512
\(389\) −4.10693 −0.208230 −0.104115 0.994565i \(-0.533201\pi\)
−0.104115 + 0.994565i \(0.533201\pi\)
\(390\) −17.1477 −0.868309
\(391\) −14.0185 −0.708944
\(392\) 72.7002 3.67192
\(393\) −33.6291 −1.69636
\(394\) 30.5661 1.53990
\(395\) −7.22245 −0.363401
\(396\) −21.3152 −1.07113
\(397\) 12.4633 0.625513 0.312756 0.949833i \(-0.398748\pi\)
0.312756 + 0.949833i \(0.398748\pi\)
\(398\) 26.7997 1.34335
\(399\) 6.54168 0.327494
\(400\) 262.050 13.1025
\(401\) 37.5303 1.87417 0.937087 0.349096i \(-0.113511\pi\)
0.937087 + 0.349096i \(0.113511\pi\)
\(402\) 86.4701 4.31274
\(403\) 3.17770 0.158293
\(404\) 87.0483 4.33082
\(405\) −48.2439 −2.39726
\(406\) −11.4662 −0.569059
\(407\) 3.93437 0.195019
\(408\) 141.111 6.98603
\(409\) −17.7285 −0.876620 −0.438310 0.898824i \(-0.644423\pi\)
−0.438310 + 0.898824i \(0.644423\pi\)
\(410\) 44.0225 2.17411
\(411\) −40.8294 −2.01397
\(412\) 60.9914 3.00483
\(413\) −4.49709 −0.221287
\(414\) 12.4787 0.613296
\(415\) −40.6574 −1.99579
\(416\) 20.0876 0.984875
\(417\) 33.6600 1.64833
\(418\) −27.0487 −1.32300
\(419\) 20.0610 0.980043 0.490021 0.871710i \(-0.336989\pi\)
0.490021 + 0.871710i \(0.336989\pi\)
\(420\) −33.9086 −1.65457
\(421\) −3.46014 −0.168637 −0.0843185 0.996439i \(-0.526871\pi\)
−0.0843185 + 0.996439i \(0.526871\pi\)
\(422\) −63.3631 −3.08447
\(423\) 2.97828 0.144809
\(424\) −40.4731 −1.96555
\(425\) 80.7299 3.91597
\(426\) −64.4378 −3.12202
\(427\) −1.64857 −0.0797797
\(428\) 69.2168 3.34572
\(429\) −2.74533 −0.132546
\(430\) −89.9601 −4.33826
\(431\) 34.9359 1.68280 0.841402 0.540410i \(-0.181731\pi\)
0.841402 + 0.540410i \(0.181731\pi\)
\(432\) 47.9850 2.30868
\(433\) −3.03823 −0.146008 −0.0730039 0.997332i \(-0.523259\pi\)
−0.0730039 + 0.997332i \(0.523259\pi\)
\(434\) 8.41470 0.403919
\(435\) −64.7495 −3.10450
\(436\) 81.9072 3.92264
\(437\) 11.8251 0.565669
\(438\) 73.7767 3.52519
\(439\) −0.359735 −0.0171692 −0.00858462 0.999963i \(-0.502733\pi\)
−0.00858462 + 0.999963i \(0.502733\pi\)
\(440\) 92.6578 4.41729
\(441\) −12.2970 −0.585570
\(442\) 10.4992 0.499398
\(443\) −4.85741 −0.230783 −0.115391 0.993320i \(-0.536812\pi\)
−0.115391 + 0.993320i \(0.536812\pi\)
\(444\) 26.1985 1.24333
\(445\) −11.6688 −0.553156
\(446\) −51.8400 −2.45470
\(447\) −38.5167 −1.82178
\(448\) 30.3381 1.43334
\(449\) −9.62024 −0.454007 −0.227004 0.973894i \(-0.572893\pi\)
−0.227004 + 0.973894i \(0.572893\pi\)
\(450\) −71.8628 −3.38765
\(451\) 7.04795 0.331875
\(452\) 55.2756 2.59994
\(453\) −5.26265 −0.247261
\(454\) 0.576041 0.0270349
\(455\) −1.66733 −0.0781656
\(456\) −119.032 −5.57419
\(457\) 15.6366 0.731450 0.365725 0.930723i \(-0.380821\pi\)
0.365725 + 0.930723i \(0.380821\pi\)
\(458\) 23.0103 1.07520
\(459\) 14.7828 0.690001
\(460\) −61.2948 −2.85788
\(461\) −25.1096 −1.16947 −0.584735 0.811225i \(-0.698801\pi\)
−0.584735 + 0.811225i \(0.698801\pi\)
\(462\) −7.26977 −0.338221
\(463\) 30.8776 1.43500 0.717501 0.696557i \(-0.245286\pi\)
0.717501 + 0.696557i \(0.245286\pi\)
\(464\) 128.688 5.97417
\(465\) 47.5177 2.20358
\(466\) 18.4371 0.854084
\(467\) −3.11904 −0.144332 −0.0721660 0.997393i \(-0.522991\pi\)
−0.0721660 + 0.997393i \(0.522991\pi\)
\(468\) −6.97919 −0.322613
\(469\) 8.40777 0.388235
\(470\) −19.5903 −0.903634
\(471\) 7.80694 0.359725
\(472\) 81.8288 3.76647
\(473\) −14.4025 −0.662228
\(474\) −10.3109 −0.473597
\(475\) −68.0985 −3.12457
\(476\) 20.7616 0.951605
\(477\) 6.84587 0.313451
\(478\) −18.2289 −0.833771
\(479\) 20.0049 0.914049 0.457025 0.889454i \(-0.348915\pi\)
0.457025 + 0.889454i \(0.348915\pi\)
\(480\) 300.379 13.7104
\(481\) 1.28822 0.0587377
\(482\) −12.5691 −0.572508
\(483\) 3.17817 0.144612
\(484\) −42.4247 −1.92840
\(485\) −70.7530 −3.21273
\(486\) −47.5650 −2.15759
\(487\) −16.3250 −0.739756 −0.369878 0.929080i \(-0.620600\pi\)
−0.369878 + 0.929080i \(0.620600\pi\)
\(488\) 29.9973 1.35791
\(489\) 34.8613 1.57648
\(490\) 80.8863 3.65407
\(491\) 35.3819 1.59676 0.798382 0.602152i \(-0.205690\pi\)
0.798382 + 0.602152i \(0.205690\pi\)
\(492\) 46.9316 2.11584
\(493\) 39.6449 1.78552
\(494\) −8.85648 −0.398472
\(495\) −15.6727 −0.704437
\(496\) −94.4399 −4.24047
\(497\) −6.26549 −0.281046
\(498\) −58.0435 −2.60099
\(499\) −13.6407 −0.610641 −0.305321 0.952250i \(-0.598764\pi\)
−0.305321 + 0.952250i \(0.598764\pi\)
\(500\) 225.122 10.0678
\(501\) −15.9304 −0.711718
\(502\) −36.5586 −1.63169
\(503\) −7.74060 −0.345136 −0.172568 0.984998i \(-0.555206\pi\)
−0.172568 + 0.984998i \(0.555206\pi\)
\(504\) −12.2137 −0.544039
\(505\) 64.0051 2.84819
\(506\) −13.1412 −0.584198
\(507\) 27.7383 1.23190
\(508\) −60.5464 −2.68631
\(509\) −6.80080 −0.301440 −0.150720 0.988576i \(-0.548159\pi\)
−0.150720 + 0.988576i \(0.548159\pi\)
\(510\) 157.000 6.95208
\(511\) 7.17355 0.317339
\(512\) −181.129 −8.00485
\(513\) −12.4698 −0.550555
\(514\) 6.79320 0.299635
\(515\) 44.8459 1.97615
\(516\) −95.9048 −4.22197
\(517\) −3.13639 −0.137938
\(518\) 3.41126 0.149882
\(519\) −31.9452 −1.40224
\(520\) 30.3387 1.33044
\(521\) −2.82595 −0.123807 −0.0619036 0.998082i \(-0.519717\pi\)
−0.0619036 + 0.998082i \(0.519717\pi\)
\(522\) −35.2905 −1.54462
\(523\) 35.6118 1.55719 0.778597 0.627524i \(-0.215932\pi\)
0.778597 + 0.627524i \(0.215932\pi\)
\(524\) 90.0305 3.93300
\(525\) −18.3026 −0.798789
\(526\) −53.3091 −2.32439
\(527\) −29.0942 −1.26736
\(528\) 81.5901 3.55075
\(529\) −17.2550 −0.750216
\(530\) −45.0304 −1.95599
\(531\) −13.8410 −0.600650
\(532\) −17.5131 −0.759290
\(533\) 2.30769 0.0999570
\(534\) −16.6587 −0.720893
\(535\) 50.8939 2.20034
\(536\) −152.987 −6.60805
\(537\) −43.5581 −1.87967
\(538\) 38.3555 1.65362
\(539\) 12.9498 0.557788
\(540\) 64.6368 2.78152
\(541\) 6.24023 0.268288 0.134144 0.990962i \(-0.457171\pi\)
0.134144 + 0.990962i \(0.457171\pi\)
\(542\) −20.6716 −0.887920
\(543\) −6.90935 −0.296509
\(544\) −183.917 −7.88536
\(545\) 60.2249 2.57975
\(546\) −2.38032 −0.101868
\(547\) −0.777847 −0.0332583 −0.0166292 0.999862i \(-0.505293\pi\)
−0.0166292 + 0.999862i \(0.505293\pi\)
\(548\) 109.307 4.66936
\(549\) −5.07392 −0.216550
\(550\) 75.6779 3.22692
\(551\) −33.4419 −1.42467
\(552\) −57.8299 −2.46140
\(553\) −1.00257 −0.0426334
\(554\) −3.30050 −0.140225
\(555\) 19.2633 0.817683
\(556\) −90.1131 −3.82165
\(557\) −0.518257 −0.0219593 −0.0109796 0.999940i \(-0.503495\pi\)
−0.0109796 + 0.999940i \(0.503495\pi\)
\(558\) 25.8986 1.09638
\(559\) −4.71577 −0.199456
\(560\) 49.5523 2.09397
\(561\) 25.1355 1.06122
\(562\) 32.7364 1.38090
\(563\) 5.23265 0.220530 0.110265 0.993902i \(-0.464830\pi\)
0.110265 + 0.993902i \(0.464830\pi\)
\(564\) −20.8849 −0.879413
\(565\) 40.6432 1.70987
\(566\) −49.1916 −2.06768
\(567\) −6.69685 −0.281241
\(568\) 114.007 4.78361
\(569\) −22.6443 −0.949299 −0.474650 0.880175i \(-0.657425\pi\)
−0.474650 + 0.880175i \(0.657425\pi\)
\(570\) −132.435 −5.54710
\(571\) 16.8049 0.703263 0.351632 0.936138i \(-0.385627\pi\)
0.351632 + 0.936138i \(0.385627\pi\)
\(572\) 7.34970 0.307306
\(573\) 22.3390 0.933227
\(574\) 6.11087 0.255063
\(575\) −33.0846 −1.37972
\(576\) 93.3740 3.89058
\(577\) −12.1208 −0.504594 −0.252297 0.967650i \(-0.581186\pi\)
−0.252297 + 0.967650i \(0.581186\pi\)
\(578\) −48.3543 −2.01127
\(579\) 47.5629 1.97665
\(580\) 173.345 7.19776
\(581\) −5.64376 −0.234142
\(582\) −101.009 −4.18695
\(583\) −7.20931 −0.298579
\(584\) −130.530 −5.40135
\(585\) −5.13167 −0.212169
\(586\) 23.3386 0.964108
\(587\) −8.08414 −0.333668 −0.166834 0.985985i \(-0.553354\pi\)
−0.166834 + 0.985985i \(0.553354\pi\)
\(588\) 86.2314 3.55612
\(589\) 24.5420 1.01123
\(590\) 91.0427 3.74817
\(591\) 23.9599 0.985578
\(592\) −38.2853 −1.57351
\(593\) 22.8739 0.939320 0.469660 0.882847i \(-0.344376\pi\)
0.469660 + 0.882847i \(0.344376\pi\)
\(594\) 13.8577 0.568588
\(595\) 15.2656 0.625830
\(596\) 103.115 4.22377
\(597\) 21.0075 0.859780
\(598\) −4.30278 −0.175954
\(599\) −13.0049 −0.531367 −0.265683 0.964060i \(-0.585598\pi\)
−0.265683 + 0.964060i \(0.585598\pi\)
\(600\) 333.032 13.5960
\(601\) 40.3384 1.64544 0.822718 0.568450i \(-0.192457\pi\)
0.822718 + 0.568450i \(0.192457\pi\)
\(602\) −12.4876 −0.508956
\(603\) 25.8773 1.05380
\(604\) 14.0890 0.573271
\(605\) −31.1942 −1.26822
\(606\) 91.3752 3.71187
\(607\) −32.0494 −1.30084 −0.650422 0.759573i \(-0.725408\pi\)
−0.650422 + 0.759573i \(0.725408\pi\)
\(608\) 155.140 6.29177
\(609\) −8.98804 −0.364214
\(610\) 33.3750 1.35131
\(611\) −1.02694 −0.0415455
\(612\) 63.8996 2.58299
\(613\) −38.7926 −1.56682 −0.783410 0.621505i \(-0.786521\pi\)
−0.783410 + 0.621505i \(0.786521\pi\)
\(614\) −70.6046 −2.84937
\(615\) 34.5080 1.39150
\(616\) 12.8621 0.518227
\(617\) 31.8709 1.28307 0.641537 0.767092i \(-0.278297\pi\)
0.641537 + 0.767092i \(0.278297\pi\)
\(618\) 64.0231 2.57539
\(619\) −1.26527 −0.0508555 −0.0254278 0.999677i \(-0.508095\pi\)
−0.0254278 + 0.999677i \(0.508095\pi\)
\(620\) −127.212 −5.10898
\(621\) −6.05826 −0.243109
\(622\) −76.4703 −3.06618
\(623\) −1.61978 −0.0648951
\(624\) 26.7148 1.06945
\(625\) 96.5125 3.86050
\(626\) −76.1474 −3.04346
\(627\) −21.2027 −0.846755
\(628\) −20.9004 −0.834019
\(629\) −11.7946 −0.470281
\(630\) −13.5889 −0.541395
\(631\) −0.820938 −0.0326810 −0.0163405 0.999866i \(-0.505202\pi\)
−0.0163405 + 0.999866i \(0.505202\pi\)
\(632\) 18.2426 0.725653
\(633\) −49.6685 −1.97415
\(634\) −26.1877 −1.04005
\(635\) −44.5187 −1.76667
\(636\) −48.0061 −1.90356
\(637\) 4.24011 0.167999
\(638\) 37.1640 1.47134
\(639\) −19.2838 −0.762855
\(640\) −341.472 −13.4979
\(641\) 4.19240 0.165590 0.0827950 0.996567i \(-0.473615\pi\)
0.0827950 + 0.996567i \(0.473615\pi\)
\(642\) 72.6574 2.86756
\(643\) −22.8109 −0.899573 −0.449787 0.893136i \(-0.648500\pi\)
−0.449787 + 0.893136i \(0.648500\pi\)
\(644\) −8.50848 −0.335281
\(645\) −70.5171 −2.77661
\(646\) 81.0876 3.19035
\(647\) 10.7325 0.421940 0.210970 0.977493i \(-0.432338\pi\)
0.210970 + 0.977493i \(0.432338\pi\)
\(648\) 121.856 4.78694
\(649\) 14.5758 0.572152
\(650\) 24.7790 0.971912
\(651\) 6.59604 0.258519
\(652\) −93.3292 −3.65506
\(653\) −46.7824 −1.83074 −0.915368 0.402619i \(-0.868100\pi\)
−0.915368 + 0.402619i \(0.868100\pi\)
\(654\) 85.9785 3.36203
\(655\) 66.1979 2.58656
\(656\) −68.5835 −2.67773
\(657\) 22.0786 0.861368
\(658\) −2.71938 −0.106013
\(659\) −40.8992 −1.59321 −0.796604 0.604502i \(-0.793372\pi\)
−0.796604 + 0.604502i \(0.793372\pi\)
\(660\) 109.904 4.27799
\(661\) −32.0598 −1.24698 −0.623491 0.781830i \(-0.714286\pi\)
−0.623491 + 0.781830i \(0.714286\pi\)
\(662\) 85.2087 3.31173
\(663\) 8.23005 0.319629
\(664\) 102.694 3.98528
\(665\) −12.8771 −0.499352
\(666\) 10.4991 0.406832
\(667\) −16.2472 −0.629095
\(668\) 42.6482 1.65011
\(669\) −40.6359 −1.57107
\(670\) −170.214 −6.57593
\(671\) 5.34329 0.206276
\(672\) 41.6964 1.60847
\(673\) 5.46201 0.210545 0.105273 0.994443i \(-0.466428\pi\)
0.105273 + 0.994443i \(0.466428\pi\)
\(674\) 77.8367 2.99816
\(675\) 34.8885 1.34286
\(676\) −74.2599 −2.85615
\(677\) 15.5063 0.595956 0.297978 0.954573i \(-0.403688\pi\)
0.297978 + 0.954573i \(0.403688\pi\)
\(678\) 58.0231 2.22837
\(679\) −9.82140 −0.376911
\(680\) −277.773 −10.6521
\(681\) 0.451542 0.0173031
\(682\) −27.2735 −1.04436
\(683\) −11.5023 −0.440124 −0.220062 0.975486i \(-0.570626\pi\)
−0.220062 + 0.975486i \(0.570626\pi\)
\(684\) −53.9015 −2.06098
\(685\) 80.3715 3.07084
\(686\) 23.0689 0.880776
\(687\) 18.0371 0.688158
\(688\) 140.151 5.34319
\(689\) −2.36052 −0.0899287
\(690\) −64.3416 −2.44944
\(691\) −44.0188 −1.67455 −0.837277 0.546778i \(-0.815854\pi\)
−0.837277 + 0.546778i \(0.815854\pi\)
\(692\) 85.5224 3.25107
\(693\) −2.17557 −0.0826431
\(694\) 34.4627 1.30819
\(695\) −66.2586 −2.51333
\(696\) 163.546 6.19920
\(697\) −21.1286 −0.800302
\(698\) −32.1830 −1.21815
\(699\) 14.4523 0.546638
\(700\) 48.9989 1.85198
\(701\) 36.4824 1.37792 0.688960 0.724799i \(-0.258067\pi\)
0.688960 + 0.724799i \(0.258067\pi\)
\(702\) 4.53738 0.171252
\(703\) 9.94914 0.375239
\(704\) −98.3311 −3.70599
\(705\) −15.3563 −0.578352
\(706\) −37.2257 −1.40101
\(707\) 8.88471 0.334144
\(708\) 97.0590 3.64770
\(709\) 27.8191 1.04477 0.522385 0.852710i \(-0.325042\pi\)
0.522385 + 0.852710i \(0.325042\pi\)
\(710\) 126.844 4.76036
\(711\) −3.08568 −0.115722
\(712\) 29.4734 1.10456
\(713\) 11.9233 0.446532
\(714\) 21.7936 0.815604
\(715\) 5.40411 0.202102
\(716\) 116.612 4.35799
\(717\) −14.2891 −0.533637
\(718\) 25.2882 0.943748
\(719\) −24.1092 −0.899121 −0.449561 0.893250i \(-0.648419\pi\)
−0.449561 + 0.893250i \(0.648419\pi\)
\(720\) 152.511 5.68375
\(721\) 6.22517 0.231837
\(722\) −15.0058 −0.558458
\(723\) −9.85257 −0.366421
\(724\) 18.4975 0.687452
\(725\) 93.5650 3.47492
\(726\) −44.5335 −1.65279
\(727\) −3.39388 −0.125872 −0.0629360 0.998018i \(-0.520046\pi\)
−0.0629360 + 0.998018i \(0.520046\pi\)
\(728\) 4.21138 0.156084
\(729\) −3.90782 −0.144734
\(730\) −145.227 −5.37510
\(731\) 43.1763 1.59693
\(732\) 35.5804 1.31509
\(733\) 0.368534 0.0136121 0.00680606 0.999977i \(-0.497834\pi\)
0.00680606 + 0.999977i \(0.497834\pi\)
\(734\) 24.3357 0.898247
\(735\) 63.4045 2.33871
\(736\) 75.3725 2.77827
\(737\) −27.2510 −1.00381
\(738\) 18.8079 0.692328
\(739\) −9.68622 −0.356313 −0.178157 0.984002i \(-0.557013\pi\)
−0.178157 + 0.984002i \(0.557013\pi\)
\(740\) −51.5710 −1.89579
\(741\) −6.94234 −0.255033
\(742\) −6.25078 −0.229473
\(743\) 25.7129 0.943315 0.471657 0.881782i \(-0.343656\pi\)
0.471657 + 0.881782i \(0.343656\pi\)
\(744\) −120.021 −4.40020
\(745\) 75.8189 2.77779
\(746\) 1.36000 0.0497930
\(747\) −17.3702 −0.635544
\(748\) −67.2919 −2.46044
\(749\) 7.06471 0.258139
\(750\) 236.313 8.62891
\(751\) 0.560399 0.0204493 0.0102246 0.999948i \(-0.496745\pi\)
0.0102246 + 0.999948i \(0.496745\pi\)
\(752\) 30.5201 1.11296
\(753\) −28.6572 −1.04433
\(754\) 12.1685 0.443151
\(755\) 10.3594 0.377016
\(756\) 8.97239 0.326323
\(757\) −4.20040 −0.152666 −0.0763330 0.997082i \(-0.524321\pi\)
−0.0763330 + 0.997082i \(0.524321\pi\)
\(758\) 96.3093 3.49811
\(759\) −10.3010 −0.373903
\(760\) 234.311 8.49936
\(761\) 44.1877 1.60180 0.800902 0.598796i \(-0.204354\pi\)
0.800902 + 0.598796i \(0.204354\pi\)
\(762\) −63.5560 −2.30239
\(763\) 8.35997 0.302651
\(764\) −59.8052 −2.16368
\(765\) 46.9842 1.69872
\(766\) −10.7562 −0.388638
\(767\) 4.77252 0.172326
\(768\) −265.438 −9.57819
\(769\) −1.36477 −0.0492148 −0.0246074 0.999697i \(-0.507834\pi\)
−0.0246074 + 0.999697i \(0.507834\pi\)
\(770\) 14.3103 0.515708
\(771\) 5.32500 0.191775
\(772\) −127.334 −4.58283
\(773\) 7.34616 0.264223 0.132112 0.991235i \(-0.457824\pi\)
0.132112 + 0.991235i \(0.457824\pi\)
\(774\) −38.4340 −1.38148
\(775\) −68.6644 −2.46650
\(776\) 178.710 6.41531
\(777\) 2.67399 0.0959289
\(778\) 11.5414 0.413781
\(779\) 17.8227 0.638565
\(780\) 35.9854 1.28848
\(781\) 20.3075 0.726661
\(782\) 39.3951 1.40877
\(783\) 17.1331 0.612286
\(784\) −126.014 −4.50051
\(785\) −15.3677 −0.548498
\(786\) 94.5057 3.37091
\(787\) −28.2164 −1.00581 −0.502903 0.864343i \(-0.667735\pi\)
−0.502903 + 0.864343i \(0.667735\pi\)
\(788\) −64.1445 −2.28505
\(789\) −41.7875 −1.48767
\(790\) 20.2968 0.722127
\(791\) 5.64178 0.200598
\(792\) 39.5866 1.40665
\(793\) 1.74954 0.0621279
\(794\) −35.0247 −1.24298
\(795\) −35.2980 −1.25189
\(796\) −56.2405 −1.99339
\(797\) 9.54848 0.338225 0.169112 0.985597i \(-0.445910\pi\)
0.169112 + 0.985597i \(0.445910\pi\)
\(798\) −18.3836 −0.650774
\(799\) 9.40237 0.332632
\(800\) −434.057 −15.3462
\(801\) −4.98533 −0.176148
\(802\) −105.469 −3.72424
\(803\) −23.2507 −0.820500
\(804\) −181.462 −6.39967
\(805\) −6.25614 −0.220500
\(806\) −8.93008 −0.314549
\(807\) 30.0657 1.05836
\(808\) −161.666 −5.68738
\(809\) −9.45189 −0.332311 −0.166155 0.986100i \(-0.553135\pi\)
−0.166155 + 0.986100i \(0.553135\pi\)
\(810\) 135.577 4.76368
\(811\) 31.5941 1.10942 0.554709 0.832044i \(-0.312830\pi\)
0.554709 + 0.832044i \(0.312830\pi\)
\(812\) 24.0624 0.844426
\(813\) −16.2038 −0.568294
\(814\) −11.0565 −0.387530
\(815\) −68.6234 −2.40377
\(816\) −244.594 −8.56249
\(817\) −36.4207 −1.27420
\(818\) 49.8213 1.74196
\(819\) −0.712340 −0.0248912
\(820\) −92.3833 −3.22617
\(821\) −6.17822 −0.215621 −0.107811 0.994171i \(-0.534384\pi\)
−0.107811 + 0.994171i \(0.534384\pi\)
\(822\) 114.740 4.00203
\(823\) 53.9967 1.88221 0.941103 0.338120i \(-0.109791\pi\)
0.941103 + 0.338120i \(0.109791\pi\)
\(824\) −113.273 −3.94605
\(825\) 59.3218 2.06532
\(826\) 12.6379 0.439727
\(827\) −2.17653 −0.0756853 −0.0378426 0.999284i \(-0.512049\pi\)
−0.0378426 + 0.999284i \(0.512049\pi\)
\(828\) −26.1872 −0.910069
\(829\) 10.3874 0.360771 0.180385 0.983596i \(-0.442265\pi\)
0.180385 + 0.983596i \(0.442265\pi\)
\(830\) 114.257 3.96591
\(831\) −2.58717 −0.0897480
\(832\) −32.1962 −1.11620
\(833\) −38.8214 −1.34508
\(834\) −94.5923 −3.27547
\(835\) 31.3585 1.08521
\(836\) 56.7631 1.96319
\(837\) −12.5734 −0.434601
\(838\) −56.3760 −1.94748
\(839\) −12.7492 −0.440153 −0.220076 0.975483i \(-0.570631\pi\)
−0.220076 + 0.975483i \(0.570631\pi\)
\(840\) 62.9748 2.17284
\(841\) 16.9480 0.584414
\(842\) 9.72381 0.335105
\(843\) 25.6611 0.883815
\(844\) 132.971 4.57704
\(845\) −54.6020 −1.87837
\(846\) −8.36966 −0.287755
\(847\) −4.33014 −0.148785
\(848\) 70.1537 2.40909
\(849\) −38.5599 −1.32337
\(850\) −226.870 −7.78157
\(851\) 4.83364 0.165695
\(852\) 135.226 4.63276
\(853\) 23.4556 0.803106 0.401553 0.915836i \(-0.368471\pi\)
0.401553 + 0.915836i \(0.368471\pi\)
\(854\) 4.63286 0.158533
\(855\) −39.6329 −1.35542
\(856\) −128.549 −4.39372
\(857\) −9.48708 −0.324073 −0.162036 0.986785i \(-0.551806\pi\)
−0.162036 + 0.986785i \(0.551806\pi\)
\(858\) 7.71503 0.263387
\(859\) 41.0539 1.40074 0.700371 0.713779i \(-0.253018\pi\)
0.700371 + 0.713779i \(0.253018\pi\)
\(860\) 188.786 6.43754
\(861\) 4.79013 0.163247
\(862\) −98.1781 −3.34396
\(863\) 19.8301 0.675024 0.337512 0.941321i \(-0.390415\pi\)
0.337512 + 0.941321i \(0.390415\pi\)
\(864\) −79.4820 −2.70403
\(865\) 62.8831 2.13809
\(866\) 8.53813 0.290137
\(867\) −37.9035 −1.28727
\(868\) −17.6587 −0.599374
\(869\) 3.24949 0.110231
\(870\) 181.961 6.16907
\(871\) −8.92272 −0.302335
\(872\) −152.118 −5.15135
\(873\) −30.2281 −1.02307
\(874\) −33.2312 −1.12406
\(875\) 22.9774 0.776779
\(876\) −154.824 −5.23102
\(877\) 2.01793 0.0681407 0.0340704 0.999419i \(-0.489153\pi\)
0.0340704 + 0.999419i \(0.489153\pi\)
\(878\) 1.01094 0.0341176
\(879\) 18.2944 0.617056
\(880\) −160.608 −5.41408
\(881\) 23.6623 0.797203 0.398602 0.917124i \(-0.369496\pi\)
0.398602 + 0.917124i \(0.369496\pi\)
\(882\) 34.5574 1.16361
\(883\) 4.87025 0.163897 0.0819484 0.996637i \(-0.473886\pi\)
0.0819484 + 0.996637i \(0.473886\pi\)
\(884\) −22.0332 −0.741056
\(885\) 71.3658 2.39893
\(886\) 13.6505 0.458596
\(887\) −51.2537 −1.72093 −0.860466 0.509508i \(-0.829827\pi\)
−0.860466 + 0.509508i \(0.829827\pi\)
\(888\) −48.6558 −1.63278
\(889\) −6.17975 −0.207262
\(890\) 32.7922 1.09920
\(891\) 21.7057 0.727167
\(892\) 108.789 3.64252
\(893\) −7.93123 −0.265409
\(894\) 108.241 3.62012
\(895\) 85.7427 2.86606
\(896\) −47.4006 −1.58354
\(897\) −3.37283 −0.112615
\(898\) 27.0351 0.902174
\(899\) −33.7198 −1.12462
\(900\) 150.808 5.02693
\(901\) 21.6123 0.720011
\(902\) −19.8064 −0.659481
\(903\) −9.78865 −0.325746
\(904\) −102.658 −3.41434
\(905\) 13.6009 0.452108
\(906\) 14.7893 0.491341
\(907\) 26.9780 0.895789 0.447894 0.894086i \(-0.352174\pi\)
0.447894 + 0.894086i \(0.352174\pi\)
\(908\) −1.20885 −0.0401171
\(909\) 27.3452 0.906982
\(910\) 4.68559 0.155326
\(911\) 23.2476 0.770227 0.385114 0.922869i \(-0.374162\pi\)
0.385114 + 0.922869i \(0.374162\pi\)
\(912\) 206.323 6.83205
\(913\) 18.2924 0.605390
\(914\) −43.9425 −1.45349
\(915\) 26.1617 0.864878
\(916\) −48.2882 −1.59549
\(917\) 9.18909 0.303450
\(918\) −41.5431 −1.37113
\(919\) 57.3422 1.89154 0.945772 0.324831i \(-0.105307\pi\)
0.945772 + 0.324831i \(0.105307\pi\)
\(920\) 113.836 3.75308
\(921\) −55.3449 −1.82368
\(922\) 70.5638 2.32389
\(923\) 6.64924 0.218862
\(924\) 15.2560 0.501885
\(925\) −27.8361 −0.915245
\(926\) −86.7732 −2.85155
\(927\) 19.1597 0.629287
\(928\) −213.157 −6.99723
\(929\) 36.9933 1.21371 0.606856 0.794812i \(-0.292430\pi\)
0.606856 + 0.794812i \(0.292430\pi\)
\(930\) −133.536 −4.37881
\(931\) 32.7472 1.07325
\(932\) −38.6912 −1.26737
\(933\) −59.9429 −1.96244
\(934\) 8.76524 0.286807
\(935\) −49.4786 −1.61812
\(936\) 12.9617 0.423667
\(937\) 53.7816 1.75697 0.878484 0.477771i \(-0.158555\pi\)
0.878484 + 0.477771i \(0.158555\pi\)
\(938\) −23.6278 −0.771475
\(939\) −59.6898 −1.94790
\(940\) 41.1113 1.34090
\(941\) 24.4449 0.796880 0.398440 0.917195i \(-0.369552\pi\)
0.398440 + 0.917195i \(0.369552\pi\)
\(942\) −21.9393 −0.714822
\(943\) 8.65888 0.281972
\(944\) −141.837 −4.61641
\(945\) 6.59724 0.214608
\(946\) 40.4744 1.31594
\(947\) −23.1945 −0.753719 −0.376860 0.926270i \(-0.622996\pi\)
−0.376860 + 0.926270i \(0.622996\pi\)
\(948\) 21.6380 0.702770
\(949\) −7.61291 −0.247126
\(950\) 191.373 6.20895
\(951\) −20.5278 −0.665659
\(952\) −38.5583 −1.24968
\(953\) 27.7451 0.898751 0.449376 0.893343i \(-0.351646\pi\)
0.449376 + 0.893343i \(0.351646\pi\)
\(954\) −19.2385 −0.622870
\(955\) −43.9737 −1.42296
\(956\) 38.2543 1.23723
\(957\) 29.1318 0.941698
\(958\) −56.2186 −1.81634
\(959\) 11.1566 0.360264
\(960\) −481.446 −15.5386
\(961\) −6.25407 −0.201744
\(962\) −3.62019 −0.116720
\(963\) 21.7436 0.700678
\(964\) 26.3769 0.849543
\(965\) −93.6261 −3.01393
\(966\) −8.93141 −0.287363
\(967\) 22.6922 0.729731 0.364865 0.931060i \(-0.381115\pi\)
0.364865 + 0.931060i \(0.381115\pi\)
\(968\) 78.7910 2.53244
\(969\) 63.5622 2.04191
\(970\) 198.833 6.38413
\(971\) 9.93520 0.318836 0.159418 0.987211i \(-0.449038\pi\)
0.159418 + 0.987211i \(0.449038\pi\)
\(972\) 99.8175 3.20165
\(973\) −9.19752 −0.294859
\(974\) 45.8770 1.47000
\(975\) 19.4235 0.622051
\(976\) −51.9955 −1.66433
\(977\) 61.0006 1.95158 0.975791 0.218707i \(-0.0701837\pi\)
0.975791 + 0.218707i \(0.0701837\pi\)
\(978\) −97.9683 −3.13268
\(979\) 5.24999 0.167790
\(980\) −169.744 −5.42227
\(981\) 25.7301 0.821500
\(982\) −99.4314 −3.17298
\(983\) −14.3390 −0.457343 −0.228672 0.973504i \(-0.573438\pi\)
−0.228672 + 0.973504i \(0.573438\pi\)
\(984\) −87.1611 −2.77859
\(985\) −47.1643 −1.50278
\(986\) −111.412 −3.54807
\(987\) −2.13164 −0.0678510
\(988\) 18.5858 0.591292
\(989\) −17.6945 −0.562651
\(990\) 44.0440 1.39981
\(991\) −46.4309 −1.47493 −0.737463 0.675388i \(-0.763976\pi\)
−0.737463 + 0.675388i \(0.763976\pi\)
\(992\) 156.430 4.96664
\(993\) 66.7927 2.11960
\(994\) 17.6075 0.558476
\(995\) −41.3526 −1.31097
\(996\) 121.807 3.85961
\(997\) −52.2752 −1.65557 −0.827786 0.561044i \(-0.810400\pi\)
−0.827786 + 0.561044i \(0.810400\pi\)
\(998\) 38.3335 1.21343
\(999\) −5.09718 −0.161268
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 6007.2.a.c.1.2 261
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6007.2.a.c.1.2 261 1.1 even 1 trivial