Properties

Label 6026.2.a.m.1.16
Level $6026$
Weight $2$
Character 6026.1
Self dual yes
Analytic conductor $48.118$
Analytic rank $0$
Dimension $41$
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] = [6026,2,Mod(1,6026)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6026, 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("6026.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6026.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: \(48.1178522580\)
Analytic rank: \(0\)
Dimension: \(41\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) \(=\) 6026.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -0.830898 q^{3} +1.00000 q^{4} -1.41489 q^{5} -0.830898 q^{6} -0.234026 q^{7} +1.00000 q^{8} -2.30961 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -0.830898 q^{3} +1.00000 q^{4} -1.41489 q^{5} -0.830898 q^{6} -0.234026 q^{7} +1.00000 q^{8} -2.30961 q^{9} -1.41489 q^{10} +3.75602 q^{11} -0.830898 q^{12} +4.10056 q^{13} -0.234026 q^{14} +1.17563 q^{15} +1.00000 q^{16} +7.34390 q^{17} -2.30961 q^{18} -2.51438 q^{19} -1.41489 q^{20} +0.194452 q^{21} +3.75602 q^{22} +1.00000 q^{23} -0.830898 q^{24} -2.99810 q^{25} +4.10056 q^{26} +4.41174 q^{27} -0.234026 q^{28} +5.16848 q^{29} +1.17563 q^{30} -8.55210 q^{31} +1.00000 q^{32} -3.12087 q^{33} +7.34390 q^{34} +0.331120 q^{35} -2.30961 q^{36} +4.10484 q^{37} -2.51438 q^{38} -3.40715 q^{39} -1.41489 q^{40} +0.450472 q^{41} +0.194452 q^{42} -12.1209 q^{43} +3.75602 q^{44} +3.26783 q^{45} +1.00000 q^{46} +5.41357 q^{47} -0.830898 q^{48} -6.94523 q^{49} -2.99810 q^{50} -6.10203 q^{51} +4.10056 q^{52} -2.60482 q^{53} +4.41174 q^{54} -5.31434 q^{55} -0.234026 q^{56} +2.08919 q^{57} +5.16848 q^{58} -9.00816 q^{59} +1.17563 q^{60} +6.21086 q^{61} -8.55210 q^{62} +0.540509 q^{63} +1.00000 q^{64} -5.80183 q^{65} -3.12087 q^{66} +9.56096 q^{67} +7.34390 q^{68} -0.830898 q^{69} +0.331120 q^{70} -4.65500 q^{71} -2.30961 q^{72} +11.6142 q^{73} +4.10484 q^{74} +2.49111 q^{75} -2.51438 q^{76} -0.879006 q^{77} -3.40715 q^{78} -0.169905 q^{79} -1.41489 q^{80} +3.26312 q^{81} +0.450472 q^{82} -0.454412 q^{83} +0.194452 q^{84} -10.3908 q^{85} -12.1209 q^{86} -4.29448 q^{87} +3.75602 q^{88} -5.74379 q^{89} +3.26783 q^{90} -0.959639 q^{91} +1.00000 q^{92} +7.10592 q^{93} +5.41357 q^{94} +3.55756 q^{95} -0.830898 q^{96} +4.99562 q^{97} -6.94523 q^{98} -8.67493 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19} + 9 q^{20} + 16 q^{21} + 4 q^{22} + 41 q^{23} + 4 q^{24} + 76 q^{25} + 16 q^{26} + 7 q^{27} + 12 q^{28} + 28 q^{29} + 10 q^{30} + 25 q^{31} + 41 q^{32} + 5 q^{33} + 10 q^{34} + 4 q^{35} + 63 q^{36} + 26 q^{37} + 16 q^{38} + 50 q^{39} + 9 q^{40} + 27 q^{41} + 16 q^{42} + 12 q^{43} + 4 q^{44} + 44 q^{45} + 41 q^{46} + 18 q^{47} + 4 q^{48} + 87 q^{49} + 76 q^{50} + 24 q^{51} + 16 q^{52} + 63 q^{53} + 7 q^{54} + 18 q^{55} + 12 q^{56} - 12 q^{57} + 28 q^{58} + 33 q^{59} + 10 q^{60} + 24 q^{61} + 25 q^{62} + 48 q^{63} + 41 q^{64} + 21 q^{65} + 5 q^{66} - 9 q^{67} + 10 q^{68} + 4 q^{69} + 4 q^{70} + 36 q^{71} + 63 q^{72} + 36 q^{73} + 26 q^{74} + 6 q^{75} + 16 q^{76} + 48 q^{77} + 50 q^{78} + 51 q^{79} + 9 q^{80} + 149 q^{81} + 27 q^{82} - 27 q^{83} + 16 q^{84} + 52 q^{85} + 12 q^{86} - 3 q^{87} + 4 q^{88} + 68 q^{89} + 44 q^{90} + 22 q^{91} + 41 q^{92} + 45 q^{93} + 18 q^{94} + 46 q^{95} + 4 q^{96} + 16 q^{97} + 87 q^{98} - 10 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −0.830898 −0.479719 −0.239859 0.970808i \(-0.577101\pi\)
−0.239859 + 0.970808i \(0.577101\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.41489 −0.632756 −0.316378 0.948633i \(-0.602467\pi\)
−0.316378 + 0.948633i \(0.602467\pi\)
\(6\) −0.830898 −0.339213
\(7\) −0.234026 −0.0884536 −0.0442268 0.999022i \(-0.514082\pi\)
−0.0442268 + 0.999022i \(0.514082\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.30961 −0.769870
\(10\) −1.41489 −0.447426
\(11\) 3.75602 1.13248 0.566241 0.824240i \(-0.308397\pi\)
0.566241 + 0.824240i \(0.308397\pi\)
\(12\) −0.830898 −0.239859
\(13\) 4.10056 1.13729 0.568646 0.822583i \(-0.307468\pi\)
0.568646 + 0.822583i \(0.307468\pi\)
\(14\) −0.234026 −0.0625461
\(15\) 1.17563 0.303545
\(16\) 1.00000 0.250000
\(17\) 7.34390 1.78116 0.890579 0.454828i \(-0.150299\pi\)
0.890579 + 0.454828i \(0.150299\pi\)
\(18\) −2.30961 −0.544380
\(19\) −2.51438 −0.576838 −0.288419 0.957504i \(-0.593130\pi\)
−0.288419 + 0.957504i \(0.593130\pi\)
\(20\) −1.41489 −0.316378
\(21\) 0.194452 0.0424328
\(22\) 3.75602 0.800786
\(23\) 1.00000 0.208514
\(24\) −0.830898 −0.169606
\(25\) −2.99810 −0.599619
\(26\) 4.10056 0.804186
\(27\) 4.41174 0.849040
\(28\) −0.234026 −0.0442268
\(29\) 5.16848 0.959762 0.479881 0.877334i \(-0.340680\pi\)
0.479881 + 0.877334i \(0.340680\pi\)
\(30\) 1.17563 0.214639
\(31\) −8.55210 −1.53600 −0.768002 0.640448i \(-0.778749\pi\)
−0.768002 + 0.640448i \(0.778749\pi\)
\(32\) 1.00000 0.176777
\(33\) −3.12087 −0.543273
\(34\) 7.34390 1.25947
\(35\) 0.331120 0.0559695
\(36\) −2.30961 −0.384935
\(37\) 4.10484 0.674831 0.337415 0.941356i \(-0.390447\pi\)
0.337415 + 0.941356i \(0.390447\pi\)
\(38\) −2.51438 −0.407886
\(39\) −3.40715 −0.545580
\(40\) −1.41489 −0.223713
\(41\) 0.450472 0.0703519 0.0351760 0.999381i \(-0.488801\pi\)
0.0351760 + 0.999381i \(0.488801\pi\)
\(42\) 0.194452 0.0300046
\(43\) −12.1209 −1.84842 −0.924212 0.381879i \(-0.875277\pi\)
−0.924212 + 0.381879i \(0.875277\pi\)
\(44\) 3.75602 0.566241
\(45\) 3.26783 0.487140
\(46\) 1.00000 0.147442
\(47\) 5.41357 0.789651 0.394825 0.918756i \(-0.370805\pi\)
0.394825 + 0.918756i \(0.370805\pi\)
\(48\) −0.830898 −0.119930
\(49\) −6.94523 −0.992176
\(50\) −2.99810 −0.423995
\(51\) −6.10203 −0.854455
\(52\) 4.10056 0.568646
\(53\) −2.60482 −0.357800 −0.178900 0.983867i \(-0.557254\pi\)
−0.178900 + 0.983867i \(0.557254\pi\)
\(54\) 4.41174 0.600362
\(55\) −5.31434 −0.716585
\(56\) −0.234026 −0.0312731
\(57\) 2.08919 0.276720
\(58\) 5.16848 0.678654
\(59\) −9.00816 −1.17276 −0.586381 0.810035i \(-0.699448\pi\)
−0.586381 + 0.810035i \(0.699448\pi\)
\(60\) 1.17563 0.151773
\(61\) 6.21086 0.795220 0.397610 0.917555i \(-0.369840\pi\)
0.397610 + 0.917555i \(0.369840\pi\)
\(62\) −8.55210 −1.08612
\(63\) 0.540509 0.0680977
\(64\) 1.00000 0.125000
\(65\) −5.80183 −0.719628
\(66\) −3.12087 −0.384152
\(67\) 9.56096 1.16806 0.584029 0.811733i \(-0.301476\pi\)
0.584029 + 0.811733i \(0.301476\pi\)
\(68\) 7.34390 0.890579
\(69\) −0.830898 −0.100028
\(70\) 0.331120 0.0395764
\(71\) −4.65500 −0.552447 −0.276223 0.961093i \(-0.589083\pi\)
−0.276223 + 0.961093i \(0.589083\pi\)
\(72\) −2.30961 −0.272190
\(73\) 11.6142 1.35933 0.679667 0.733521i \(-0.262124\pi\)
0.679667 + 0.733521i \(0.262124\pi\)
\(74\) 4.10484 0.477177
\(75\) 2.49111 0.287649
\(76\) −2.51438 −0.288419
\(77\) −0.879006 −0.100172
\(78\) −3.40715 −0.385783
\(79\) −0.169905 −0.0191158 −0.00955788 0.999954i \(-0.503042\pi\)
−0.00955788 + 0.999954i \(0.503042\pi\)
\(80\) −1.41489 −0.158189
\(81\) 3.26312 0.362569
\(82\) 0.450472 0.0497463
\(83\) −0.454412 −0.0498782 −0.0249391 0.999689i \(-0.507939\pi\)
−0.0249391 + 0.999689i \(0.507939\pi\)
\(84\) 0.194452 0.0212164
\(85\) −10.3908 −1.12704
\(86\) −12.1209 −1.30703
\(87\) −4.29448 −0.460416
\(88\) 3.75602 0.400393
\(89\) −5.74379 −0.608841 −0.304420 0.952538i \(-0.598463\pi\)
−0.304420 + 0.952538i \(0.598463\pi\)
\(90\) 3.26783 0.344460
\(91\) −0.959639 −0.100597
\(92\) 1.00000 0.104257
\(93\) 7.10592 0.736850
\(94\) 5.41357 0.558367
\(95\) 3.55756 0.364998
\(96\) −0.830898 −0.0848031
\(97\) 4.99562 0.507228 0.253614 0.967306i \(-0.418381\pi\)
0.253614 + 0.967306i \(0.418381\pi\)
\(98\) −6.94523 −0.701574
\(99\) −8.67493 −0.871864
\(100\) −2.99810 −0.299810
\(101\) −0.804159 −0.0800168 −0.0400084 0.999199i \(-0.512738\pi\)
−0.0400084 + 0.999199i \(0.512738\pi\)
\(102\) −6.10203 −0.604191
\(103\) 8.10317 0.798429 0.399215 0.916858i \(-0.369283\pi\)
0.399215 + 0.916858i \(0.369283\pi\)
\(104\) 4.10056 0.402093
\(105\) −0.275127 −0.0268497
\(106\) −2.60482 −0.253003
\(107\) 18.3164 1.77071 0.885355 0.464916i \(-0.153915\pi\)
0.885355 + 0.464916i \(0.153915\pi\)
\(108\) 4.41174 0.424520
\(109\) 7.66562 0.734233 0.367117 0.930175i \(-0.380345\pi\)
0.367117 + 0.930175i \(0.380345\pi\)
\(110\) −5.31434 −0.506702
\(111\) −3.41070 −0.323729
\(112\) −0.234026 −0.0221134
\(113\) 15.9127 1.49694 0.748469 0.663170i \(-0.230789\pi\)
0.748469 + 0.663170i \(0.230789\pi\)
\(114\) 2.08919 0.195671
\(115\) −1.41489 −0.131939
\(116\) 5.16848 0.479881
\(117\) −9.47070 −0.875566
\(118\) −9.00816 −0.829268
\(119\) −1.71867 −0.157550
\(120\) 1.17563 0.107319
\(121\) 3.10767 0.282516
\(122\) 6.21086 0.562305
\(123\) −0.374296 −0.0337492
\(124\) −8.55210 −0.768002
\(125\) 11.3164 1.01217
\(126\) 0.540509 0.0481524
\(127\) 0.658707 0.0584508 0.0292254 0.999573i \(-0.490696\pi\)
0.0292254 + 0.999573i \(0.490696\pi\)
\(128\) 1.00000 0.0883883
\(129\) 10.0713 0.886724
\(130\) −5.80183 −0.508854
\(131\) 1.00000 0.0873704
\(132\) −3.12087 −0.271637
\(133\) 0.588430 0.0510234
\(134\) 9.56096 0.825941
\(135\) −6.24211 −0.537235
\(136\) 7.34390 0.629735
\(137\) 12.3465 1.05483 0.527417 0.849606i \(-0.323161\pi\)
0.527417 + 0.849606i \(0.323161\pi\)
\(138\) −0.830898 −0.0707307
\(139\) 13.3114 1.12906 0.564530 0.825412i \(-0.309057\pi\)
0.564530 + 0.825412i \(0.309057\pi\)
\(140\) 0.331120 0.0279848
\(141\) −4.49812 −0.378810
\(142\) −4.65500 −0.390639
\(143\) 15.4018 1.28796
\(144\) −2.30961 −0.192467
\(145\) −7.31281 −0.607296
\(146\) 11.6142 0.961194
\(147\) 5.77078 0.475966
\(148\) 4.10484 0.337415
\(149\) 20.3092 1.66380 0.831898 0.554928i \(-0.187254\pi\)
0.831898 + 0.554928i \(0.187254\pi\)
\(150\) 2.49111 0.203398
\(151\) 0.496065 0.0403692 0.0201846 0.999796i \(-0.493575\pi\)
0.0201846 + 0.999796i \(0.493575\pi\)
\(152\) −2.51438 −0.203943
\(153\) −16.9615 −1.37126
\(154\) −0.879006 −0.0708324
\(155\) 12.1003 0.971916
\(156\) −3.40715 −0.272790
\(157\) −19.2148 −1.53351 −0.766753 0.641943i \(-0.778129\pi\)
−0.766753 + 0.641943i \(0.778129\pi\)
\(158\) −0.169905 −0.0135169
\(159\) 2.16434 0.171643
\(160\) −1.41489 −0.111857
\(161\) −0.234026 −0.0184438
\(162\) 3.26312 0.256375
\(163\) 5.38179 0.421534 0.210767 0.977536i \(-0.432404\pi\)
0.210767 + 0.977536i \(0.432404\pi\)
\(164\) 0.450472 0.0351760
\(165\) 4.41567 0.343760
\(166\) −0.454412 −0.0352692
\(167\) 18.2465 1.41196 0.705978 0.708234i \(-0.250508\pi\)
0.705978 + 0.708234i \(0.250508\pi\)
\(168\) 0.194452 0.0150023
\(169\) 3.81461 0.293431
\(170\) −10.3908 −0.796937
\(171\) 5.80723 0.444090
\(172\) −12.1209 −0.924212
\(173\) 17.5575 1.33487 0.667435 0.744668i \(-0.267392\pi\)
0.667435 + 0.744668i \(0.267392\pi\)
\(174\) −4.29448 −0.325563
\(175\) 0.701633 0.0530385
\(176\) 3.75602 0.283121
\(177\) 7.48486 0.562596
\(178\) −5.74379 −0.430515
\(179\) 3.41719 0.255413 0.127706 0.991812i \(-0.459238\pi\)
0.127706 + 0.991812i \(0.459238\pi\)
\(180\) 3.26783 0.243570
\(181\) −20.4216 −1.51793 −0.758964 0.651132i \(-0.774294\pi\)
−0.758964 + 0.651132i \(0.774294\pi\)
\(182\) −0.959639 −0.0711331
\(183\) −5.16059 −0.381482
\(184\) 1.00000 0.0737210
\(185\) −5.80787 −0.427003
\(186\) 7.10592 0.521032
\(187\) 27.5838 2.01713
\(188\) 5.41357 0.394825
\(189\) −1.03246 −0.0751006
\(190\) 3.55756 0.258093
\(191\) −18.1162 −1.31084 −0.655420 0.755264i \(-0.727508\pi\)
−0.655420 + 0.755264i \(0.727508\pi\)
\(192\) −0.830898 −0.0599649
\(193\) 1.03366 0.0744045 0.0372022 0.999308i \(-0.488155\pi\)
0.0372022 + 0.999308i \(0.488155\pi\)
\(194\) 4.99562 0.358664
\(195\) 4.82073 0.345219
\(196\) −6.94523 −0.496088
\(197\) 3.09375 0.220421 0.110210 0.993908i \(-0.464848\pi\)
0.110210 + 0.993908i \(0.464848\pi\)
\(198\) −8.67493 −0.616501
\(199\) 5.97114 0.423283 0.211641 0.977347i \(-0.432119\pi\)
0.211641 + 0.977347i \(0.432119\pi\)
\(200\) −2.99810 −0.211997
\(201\) −7.94418 −0.560339
\(202\) −0.804159 −0.0565804
\(203\) −1.20956 −0.0848944
\(204\) −6.10203 −0.427228
\(205\) −0.637367 −0.0445156
\(206\) 8.10317 0.564575
\(207\) −2.30961 −0.160529
\(208\) 4.10056 0.284323
\(209\) −9.44405 −0.653259
\(210\) −0.275127 −0.0189856
\(211\) 4.47685 0.308199 0.154099 0.988055i \(-0.450752\pi\)
0.154099 + 0.988055i \(0.450752\pi\)
\(212\) −2.60482 −0.178900
\(213\) 3.86783 0.265019
\(214\) 18.3164 1.25208
\(215\) 17.1497 1.16960
\(216\) 4.41174 0.300181
\(217\) 2.00142 0.135865
\(218\) 7.66562 0.519181
\(219\) −9.65017 −0.652098
\(220\) −5.31434 −0.358293
\(221\) 30.1141 2.02570
\(222\) −3.41070 −0.228911
\(223\) −10.2941 −0.689342 −0.344671 0.938723i \(-0.612010\pi\)
−0.344671 + 0.938723i \(0.612010\pi\)
\(224\) −0.234026 −0.0156365
\(225\) 6.92443 0.461629
\(226\) 15.9127 1.05850
\(227\) 26.6259 1.76722 0.883612 0.468220i \(-0.155104\pi\)
0.883612 + 0.468220i \(0.155104\pi\)
\(228\) 2.08919 0.138360
\(229\) 18.4674 1.22036 0.610182 0.792262i \(-0.291096\pi\)
0.610182 + 0.792262i \(0.291096\pi\)
\(230\) −1.41489 −0.0932948
\(231\) 0.730364 0.0480544
\(232\) 5.16848 0.339327
\(233\) −1.95218 −0.127892 −0.0639459 0.997953i \(-0.520369\pi\)
−0.0639459 + 0.997953i \(0.520369\pi\)
\(234\) −9.47070 −0.619119
\(235\) −7.65959 −0.499656
\(236\) −9.00816 −0.586381
\(237\) 0.141173 0.00917019
\(238\) −1.71867 −0.111405
\(239\) −1.46566 −0.0948056 −0.0474028 0.998876i \(-0.515094\pi\)
−0.0474028 + 0.998876i \(0.515094\pi\)
\(240\) 1.17563 0.0758863
\(241\) −29.9828 −1.93136 −0.965681 0.259732i \(-0.916366\pi\)
−0.965681 + 0.259732i \(0.916366\pi\)
\(242\) 3.10767 0.199769
\(243\) −15.9465 −1.02297
\(244\) 6.21086 0.397610
\(245\) 9.82671 0.627806
\(246\) −0.374296 −0.0238643
\(247\) −10.3104 −0.656033
\(248\) −8.55210 −0.543059
\(249\) 0.377570 0.0239275
\(250\) 11.3164 0.715712
\(251\) −4.98723 −0.314791 −0.157396 0.987536i \(-0.550310\pi\)
−0.157396 + 0.987536i \(0.550310\pi\)
\(252\) 0.540509 0.0340489
\(253\) 3.75602 0.236139
\(254\) 0.658707 0.0413309
\(255\) 8.63368 0.540662
\(256\) 1.00000 0.0625000
\(257\) 23.8339 1.48672 0.743358 0.668894i \(-0.233232\pi\)
0.743358 + 0.668894i \(0.233232\pi\)
\(258\) 10.0713 0.627009
\(259\) −0.960639 −0.0596912
\(260\) −5.80183 −0.359814
\(261\) −11.9372 −0.738892
\(262\) 1.00000 0.0617802
\(263\) 7.87510 0.485600 0.242800 0.970076i \(-0.421934\pi\)
0.242800 + 0.970076i \(0.421934\pi\)
\(264\) −3.12087 −0.192076
\(265\) 3.68553 0.226400
\(266\) 0.588430 0.0360790
\(267\) 4.77250 0.292072
\(268\) 9.56096 0.584029
\(269\) 9.11359 0.555665 0.277833 0.960630i \(-0.410384\pi\)
0.277833 + 0.960630i \(0.410384\pi\)
\(270\) −6.24211 −0.379883
\(271\) −6.46382 −0.392649 −0.196325 0.980539i \(-0.562901\pi\)
−0.196325 + 0.980539i \(0.562901\pi\)
\(272\) 7.34390 0.445290
\(273\) 0.797361 0.0482585
\(274\) 12.3465 0.745880
\(275\) −11.2609 −0.679058
\(276\) −0.830898 −0.0500142
\(277\) 2.70561 0.162564 0.0812822 0.996691i \(-0.474099\pi\)
0.0812822 + 0.996691i \(0.474099\pi\)
\(278\) 13.3114 0.798367
\(279\) 19.7520 1.18252
\(280\) 0.331120 0.0197882
\(281\) −7.31543 −0.436402 −0.218201 0.975904i \(-0.570019\pi\)
−0.218201 + 0.975904i \(0.570019\pi\)
\(282\) −4.49812 −0.267859
\(283\) −5.09365 −0.302786 −0.151393 0.988474i \(-0.548376\pi\)
−0.151393 + 0.988474i \(0.548376\pi\)
\(284\) −4.65500 −0.276223
\(285\) −2.95597 −0.175096
\(286\) 15.4018 0.910727
\(287\) −0.105422 −0.00622288
\(288\) −2.30961 −0.136095
\(289\) 36.9329 2.17252
\(290\) −7.31281 −0.429423
\(291\) −4.15084 −0.243327
\(292\) 11.6142 0.679667
\(293\) −15.9117 −0.929573 −0.464786 0.885423i \(-0.653869\pi\)
−0.464786 + 0.885423i \(0.653869\pi\)
\(294\) 5.77078 0.336559
\(295\) 12.7455 0.742073
\(296\) 4.10484 0.238589
\(297\) 16.5706 0.961523
\(298\) 20.3092 1.17648
\(299\) 4.10056 0.237142
\(300\) 2.49111 0.143824
\(301\) 2.83661 0.163500
\(302\) 0.496065 0.0285453
\(303\) 0.668173 0.0383856
\(304\) −2.51438 −0.144210
\(305\) −8.78767 −0.503180
\(306\) −16.9615 −0.969627
\(307\) 18.8530 1.07600 0.538000 0.842945i \(-0.319180\pi\)
0.538000 + 0.842945i \(0.319180\pi\)
\(308\) −0.879006 −0.0500860
\(309\) −6.73290 −0.383022
\(310\) 12.1003 0.687248
\(311\) −13.4179 −0.760862 −0.380431 0.924809i \(-0.624224\pi\)
−0.380431 + 0.924809i \(0.624224\pi\)
\(312\) −3.40715 −0.192892
\(313\) 16.6992 0.943893 0.471946 0.881627i \(-0.343552\pi\)
0.471946 + 0.881627i \(0.343552\pi\)
\(314\) −19.2148 −1.08435
\(315\) −0.764758 −0.0430893
\(316\) −0.169905 −0.00955788
\(317\) −28.0772 −1.57698 −0.788488 0.615051i \(-0.789136\pi\)
−0.788488 + 0.615051i \(0.789136\pi\)
\(318\) 2.16434 0.121370
\(319\) 19.4129 1.08691
\(320\) −1.41489 −0.0790945
\(321\) −15.2190 −0.849443
\(322\) −0.234026 −0.0130418
\(323\) −18.4654 −1.02744
\(324\) 3.26312 0.181285
\(325\) −12.2939 −0.681942
\(326\) 5.38179 0.298070
\(327\) −6.36935 −0.352226
\(328\) 0.450472 0.0248732
\(329\) −1.26692 −0.0698474
\(330\) 4.41567 0.243075
\(331\) −1.21324 −0.0666855 −0.0333428 0.999444i \(-0.510615\pi\)
−0.0333428 + 0.999444i \(0.510615\pi\)
\(332\) −0.454412 −0.0249391
\(333\) −9.48056 −0.519532
\(334\) 18.2465 0.998403
\(335\) −13.5277 −0.739096
\(336\) 0.194452 0.0106082
\(337\) 0.992259 0.0540518 0.0270259 0.999635i \(-0.491396\pi\)
0.0270259 + 0.999635i \(0.491396\pi\)
\(338\) 3.81461 0.207487
\(339\) −13.2218 −0.718110
\(340\) −10.3908 −0.563520
\(341\) −32.1219 −1.73950
\(342\) 5.80723 0.314019
\(343\) 3.26355 0.176215
\(344\) −12.1209 −0.653517
\(345\) 1.17563 0.0632936
\(346\) 17.5575 0.943896
\(347\) −10.7069 −0.574777 −0.287388 0.957814i \(-0.592787\pi\)
−0.287388 + 0.957814i \(0.592787\pi\)
\(348\) −4.29448 −0.230208
\(349\) −18.7164 −1.00187 −0.500934 0.865485i \(-0.667010\pi\)
−0.500934 + 0.865485i \(0.667010\pi\)
\(350\) 0.701633 0.0375039
\(351\) 18.0906 0.965606
\(352\) 3.75602 0.200196
\(353\) 37.3705 1.98903 0.994516 0.104584i \(-0.0333512\pi\)
0.994516 + 0.104584i \(0.0333512\pi\)
\(354\) 7.48486 0.397816
\(355\) 6.58629 0.349564
\(356\) −5.74379 −0.304420
\(357\) 1.42803 0.0755796
\(358\) 3.41719 0.180604
\(359\) −5.79181 −0.305680 −0.152840 0.988251i \(-0.548842\pi\)
−0.152840 + 0.988251i \(0.548842\pi\)
\(360\) 3.26783 0.172230
\(361\) −12.6779 −0.667258
\(362\) −20.4216 −1.07334
\(363\) −2.58216 −0.135528
\(364\) −0.959639 −0.0502987
\(365\) −16.4327 −0.860127
\(366\) −5.16059 −0.269749
\(367\) −20.8003 −1.08577 −0.542884 0.839807i \(-0.682668\pi\)
−0.542884 + 0.839807i \(0.682668\pi\)
\(368\) 1.00000 0.0521286
\(369\) −1.04041 −0.0541618
\(370\) −5.80787 −0.301937
\(371\) 0.609597 0.0316487
\(372\) 7.10592 0.368425
\(373\) 29.8137 1.54369 0.771847 0.635809i \(-0.219333\pi\)
0.771847 + 0.635809i \(0.219333\pi\)
\(374\) 27.5838 1.42633
\(375\) −9.40277 −0.485557
\(376\) 5.41357 0.279184
\(377\) 21.1937 1.09153
\(378\) −1.03246 −0.0531042
\(379\) 21.9308 1.12651 0.563254 0.826284i \(-0.309549\pi\)
0.563254 + 0.826284i \(0.309549\pi\)
\(380\) 3.55756 0.182499
\(381\) −0.547318 −0.0280399
\(382\) −18.1162 −0.926904
\(383\) −10.3428 −0.528494 −0.264247 0.964455i \(-0.585123\pi\)
−0.264247 + 0.964455i \(0.585123\pi\)
\(384\) −0.830898 −0.0424016
\(385\) 1.24369 0.0633845
\(386\) 1.03366 0.0526119
\(387\) 27.9946 1.42305
\(388\) 4.99562 0.253614
\(389\) 0.575240 0.0291658 0.0145829 0.999894i \(-0.495358\pi\)
0.0145829 + 0.999894i \(0.495358\pi\)
\(390\) 4.82073 0.244107
\(391\) 7.34390 0.371397
\(392\) −6.94523 −0.350787
\(393\) −0.830898 −0.0419132
\(394\) 3.09375 0.155861
\(395\) 0.240396 0.0120956
\(396\) −8.67493 −0.435932
\(397\) −9.25444 −0.464467 −0.232234 0.972660i \(-0.574603\pi\)
−0.232234 + 0.972660i \(0.574603\pi\)
\(398\) 5.97114 0.299306
\(399\) −0.488925 −0.0244769
\(400\) −2.99810 −0.149905
\(401\) −15.9794 −0.797971 −0.398986 0.916957i \(-0.630638\pi\)
−0.398986 + 0.916957i \(0.630638\pi\)
\(402\) −7.94418 −0.396220
\(403\) −35.0684 −1.74688
\(404\) −0.804159 −0.0400084
\(405\) −4.61695 −0.229418
\(406\) −1.20956 −0.0600294
\(407\) 15.4178 0.764234
\(408\) −6.10203 −0.302096
\(409\) −23.7683 −1.17527 −0.587633 0.809127i \(-0.699940\pi\)
−0.587633 + 0.809127i \(0.699940\pi\)
\(410\) −0.637367 −0.0314773
\(411\) −10.2587 −0.506024
\(412\) 8.10317 0.399215
\(413\) 2.10814 0.103735
\(414\) −2.30961 −0.113511
\(415\) 0.642941 0.0315608
\(416\) 4.10056 0.201047
\(417\) −11.0604 −0.541632
\(418\) −9.44405 −0.461924
\(419\) 31.5720 1.54240 0.771198 0.636596i \(-0.219658\pi\)
0.771198 + 0.636596i \(0.219658\pi\)
\(420\) −0.275127 −0.0134248
\(421\) −21.3439 −1.04024 −0.520118 0.854094i \(-0.674112\pi\)
−0.520118 + 0.854094i \(0.674112\pi\)
\(422\) 4.47685 0.217929
\(423\) −12.5032 −0.607928
\(424\) −2.60482 −0.126501
\(425\) −22.0177 −1.06802
\(426\) 3.86783 0.187397
\(427\) −1.45350 −0.0703400
\(428\) 18.3164 0.885355
\(429\) −12.7973 −0.617860
\(430\) 17.1497 0.827034
\(431\) −7.09641 −0.341822 −0.170911 0.985286i \(-0.554671\pi\)
−0.170911 + 0.985286i \(0.554671\pi\)
\(432\) 4.41174 0.212260
\(433\) −7.58377 −0.364453 −0.182226 0.983257i \(-0.558330\pi\)
−0.182226 + 0.983257i \(0.558330\pi\)
\(434\) 2.00142 0.0960710
\(435\) 6.07620 0.291331
\(436\) 7.66562 0.367117
\(437\) −2.51438 −0.120279
\(438\) −9.65017 −0.461103
\(439\) 25.1129 1.19858 0.599288 0.800534i \(-0.295451\pi\)
0.599288 + 0.800534i \(0.295451\pi\)
\(440\) −5.31434 −0.253351
\(441\) 16.0408 0.763846
\(442\) 30.1141 1.43238
\(443\) −29.8716 −1.41924 −0.709621 0.704583i \(-0.751134\pi\)
−0.709621 + 0.704583i \(0.751134\pi\)
\(444\) −3.41070 −0.161865
\(445\) 8.12681 0.385248
\(446\) −10.2941 −0.487439
\(447\) −16.8749 −0.798155
\(448\) −0.234026 −0.0110567
\(449\) −7.12677 −0.336333 −0.168167 0.985759i \(-0.553785\pi\)
−0.168167 + 0.985759i \(0.553785\pi\)
\(450\) 6.92443 0.326421
\(451\) 1.69198 0.0796723
\(452\) 15.9127 0.748469
\(453\) −0.412179 −0.0193659
\(454\) 26.6259 1.24962
\(455\) 1.35778 0.0636537
\(456\) 2.08919 0.0978354
\(457\) −29.1112 −1.36177 −0.680883 0.732392i \(-0.738404\pi\)
−0.680883 + 0.732392i \(0.738404\pi\)
\(458\) 18.4674 0.862927
\(459\) 32.3994 1.51227
\(460\) −1.41489 −0.0659694
\(461\) 33.8785 1.57788 0.788940 0.614471i \(-0.210630\pi\)
0.788940 + 0.614471i \(0.210630\pi\)
\(462\) 0.730364 0.0339796
\(463\) 4.68072 0.217532 0.108766 0.994067i \(-0.465310\pi\)
0.108766 + 0.994067i \(0.465310\pi\)
\(464\) 5.16848 0.239941
\(465\) −10.0541 −0.466246
\(466\) −1.95218 −0.0904332
\(467\) −28.6923 −1.32772 −0.663860 0.747857i \(-0.731083\pi\)
−0.663860 + 0.747857i \(0.731083\pi\)
\(468\) −9.47070 −0.437783
\(469\) −2.23751 −0.103319
\(470\) −7.65959 −0.353310
\(471\) 15.9655 0.735652
\(472\) −9.00816 −0.414634
\(473\) −45.5264 −2.09331
\(474\) 0.141173 0.00648431
\(475\) 7.53835 0.345883
\(476\) −1.71867 −0.0787749
\(477\) 6.01612 0.275459
\(478\) −1.46566 −0.0670377
\(479\) −32.2915 −1.47544 −0.737719 0.675108i \(-0.764097\pi\)
−0.737719 + 0.675108i \(0.764097\pi\)
\(480\) 1.17563 0.0536597
\(481\) 16.8321 0.767479
\(482\) −29.9828 −1.36568
\(483\) 0.194452 0.00884786
\(484\) 3.10767 0.141258
\(485\) −7.06823 −0.320952
\(486\) −15.9465 −0.723350
\(487\) −32.0737 −1.45340 −0.726698 0.686957i \(-0.758946\pi\)
−0.726698 + 0.686957i \(0.758946\pi\)
\(488\) 6.21086 0.281153
\(489\) −4.47172 −0.202218
\(490\) 9.82671 0.443926
\(491\) −6.59041 −0.297421 −0.148711 0.988881i \(-0.547512\pi\)
−0.148711 + 0.988881i \(0.547512\pi\)
\(492\) −0.374296 −0.0168746
\(493\) 37.9568 1.70949
\(494\) −10.3104 −0.463885
\(495\) 12.2740 0.551677
\(496\) −8.55210 −0.384001
\(497\) 1.08939 0.0488659
\(498\) 0.377570 0.0169193
\(499\) 7.32680 0.327993 0.163996 0.986461i \(-0.447561\pi\)
0.163996 + 0.986461i \(0.447561\pi\)
\(500\) 11.3164 0.506085
\(501\) −15.1610 −0.677342
\(502\) −4.98723 −0.222591
\(503\) −33.3411 −1.48660 −0.743302 0.668956i \(-0.766741\pi\)
−0.743302 + 0.668956i \(0.766741\pi\)
\(504\) 0.540509 0.0240762
\(505\) 1.13779 0.0506311
\(506\) 3.75602 0.166975
\(507\) −3.16955 −0.140765
\(508\) 0.658707 0.0292254
\(509\) 26.8676 1.19089 0.595443 0.803398i \(-0.296977\pi\)
0.595443 + 0.803398i \(0.296977\pi\)
\(510\) 8.63368 0.382306
\(511\) −2.71801 −0.120238
\(512\) 1.00000 0.0441942
\(513\) −11.0928 −0.489759
\(514\) 23.8339 1.05127
\(515\) −11.4651 −0.505211
\(516\) 10.0713 0.443362
\(517\) 20.3335 0.894265
\(518\) −0.960639 −0.0422080
\(519\) −14.5885 −0.640363
\(520\) −5.80183 −0.254427
\(521\) −24.5976 −1.07764 −0.538820 0.842421i \(-0.681130\pi\)
−0.538820 + 0.842421i \(0.681130\pi\)
\(522\) −11.9372 −0.522475
\(523\) 21.8706 0.956335 0.478167 0.878269i \(-0.341301\pi\)
0.478167 + 0.878269i \(0.341301\pi\)
\(524\) 1.00000 0.0436852
\(525\) −0.582985 −0.0254436
\(526\) 7.87510 0.343371
\(527\) −62.8058 −2.73586
\(528\) −3.12087 −0.135818
\(529\) 1.00000 0.0434783
\(530\) 3.68553 0.160089
\(531\) 20.8053 0.902874
\(532\) 0.588430 0.0255117
\(533\) 1.84719 0.0800107
\(534\) 4.77250 0.206526
\(535\) −25.9156 −1.12043
\(536\) 9.56096 0.412971
\(537\) −2.83934 −0.122526
\(538\) 9.11359 0.392915
\(539\) −26.0864 −1.12362
\(540\) −6.24211 −0.268618
\(541\) −24.0710 −1.03489 −0.517446 0.855716i \(-0.673117\pi\)
−0.517446 + 0.855716i \(0.673117\pi\)
\(542\) −6.46382 −0.277645
\(543\) 16.9683 0.728179
\(544\) 7.34390 0.314867
\(545\) −10.8460 −0.464591
\(546\) 0.797361 0.0341239
\(547\) 38.5541 1.64845 0.824227 0.566260i \(-0.191610\pi\)
0.824227 + 0.566260i \(0.191610\pi\)
\(548\) 12.3465 0.527417
\(549\) −14.3447 −0.612216
\(550\) −11.2609 −0.480167
\(551\) −12.9955 −0.553627
\(552\) −0.830898 −0.0353654
\(553\) 0.0397621 0.00169086
\(554\) 2.70561 0.114950
\(555\) 4.82575 0.204842
\(556\) 13.3114 0.564530
\(557\) 18.1129 0.767470 0.383735 0.923443i \(-0.374638\pi\)
0.383735 + 0.923443i \(0.374638\pi\)
\(558\) 19.7520 0.836170
\(559\) −49.7026 −2.10220
\(560\) 0.331120 0.0139924
\(561\) −22.9193 −0.967656
\(562\) −7.31543 −0.308583
\(563\) −12.9892 −0.547429 −0.273715 0.961811i \(-0.588252\pi\)
−0.273715 + 0.961811i \(0.588252\pi\)
\(564\) −4.49812 −0.189405
\(565\) −22.5146 −0.947197
\(566\) −5.09365 −0.214102
\(567\) −0.763656 −0.0320705
\(568\) −4.65500 −0.195319
\(569\) −5.17296 −0.216862 −0.108431 0.994104i \(-0.534583\pi\)
−0.108431 + 0.994104i \(0.534583\pi\)
\(570\) −2.95597 −0.123812
\(571\) 16.5056 0.690737 0.345368 0.938467i \(-0.387754\pi\)
0.345368 + 0.938467i \(0.387754\pi\)
\(572\) 15.4018 0.643981
\(573\) 15.0527 0.628835
\(574\) −0.105422 −0.00440024
\(575\) −2.99810 −0.125029
\(576\) −2.30961 −0.0962337
\(577\) 21.7339 0.904793 0.452397 0.891817i \(-0.350569\pi\)
0.452397 + 0.891817i \(0.350569\pi\)
\(578\) 36.9329 1.53621
\(579\) −0.858866 −0.0356932
\(580\) −7.31281 −0.303648
\(581\) 0.106344 0.00441190
\(582\) −4.15084 −0.172058
\(583\) −9.78376 −0.405202
\(584\) 11.6142 0.480597
\(585\) 13.4000 0.554020
\(586\) −15.9117 −0.657307
\(587\) −2.84193 −0.117299 −0.0586496 0.998279i \(-0.518679\pi\)
−0.0586496 + 0.998279i \(0.518679\pi\)
\(588\) 5.77078 0.237983
\(589\) 21.5032 0.886025
\(590\) 12.7455 0.524725
\(591\) −2.57059 −0.105740
\(592\) 4.10484 0.168708
\(593\) −3.74209 −0.153669 −0.0768346 0.997044i \(-0.524481\pi\)
−0.0768346 + 0.997044i \(0.524481\pi\)
\(594\) 16.5706 0.679899
\(595\) 2.43172 0.0996906
\(596\) 20.3092 0.831898
\(597\) −4.96140 −0.203057
\(598\) 4.10056 0.167684
\(599\) 17.3354 0.708304 0.354152 0.935188i \(-0.384770\pi\)
0.354152 + 0.935188i \(0.384770\pi\)
\(600\) 2.49111 0.101699
\(601\) 15.4098 0.628577 0.314289 0.949328i \(-0.398234\pi\)
0.314289 + 0.949328i \(0.398234\pi\)
\(602\) 2.83661 0.115612
\(603\) −22.0821 −0.899252
\(604\) 0.496065 0.0201846
\(605\) −4.39701 −0.178764
\(606\) 0.668173 0.0271427
\(607\) 17.9299 0.727750 0.363875 0.931448i \(-0.381453\pi\)
0.363875 + 0.931448i \(0.381453\pi\)
\(608\) −2.51438 −0.101972
\(609\) 1.00502 0.0407254
\(610\) −8.78767 −0.355802
\(611\) 22.1987 0.898063
\(612\) −16.9615 −0.685630
\(613\) 23.0127 0.929474 0.464737 0.885449i \(-0.346149\pi\)
0.464737 + 0.885449i \(0.346149\pi\)
\(614\) 18.8530 0.760846
\(615\) 0.529587 0.0213550
\(616\) −0.879006 −0.0354162
\(617\) 47.2047 1.90039 0.950195 0.311655i \(-0.100883\pi\)
0.950195 + 0.311655i \(0.100883\pi\)
\(618\) −6.73290 −0.270837
\(619\) −16.9935 −0.683025 −0.341513 0.939877i \(-0.610939\pi\)
−0.341513 + 0.939877i \(0.610939\pi\)
\(620\) 12.1003 0.485958
\(621\) 4.41174 0.177037
\(622\) −13.4179 −0.538011
\(623\) 1.34420 0.0538541
\(624\) −3.40715 −0.136395
\(625\) −1.02093 −0.0408371
\(626\) 16.6992 0.667433
\(627\) 7.84704 0.313381
\(628\) −19.2148 −0.766753
\(629\) 30.1455 1.20198
\(630\) −0.764758 −0.0304687
\(631\) 40.8166 1.62488 0.812442 0.583041i \(-0.198138\pi\)
0.812442 + 0.583041i \(0.198138\pi\)
\(632\) −0.169905 −0.00675844
\(633\) −3.71980 −0.147849
\(634\) −28.0772 −1.11509
\(635\) −0.931995 −0.0369851
\(636\) 2.16434 0.0858217
\(637\) −28.4794 −1.12839
\(638\) 19.4129 0.768564
\(639\) 10.7512 0.425312
\(640\) −1.41489 −0.0559283
\(641\) 43.0727 1.70127 0.850634 0.525758i \(-0.176218\pi\)
0.850634 + 0.525758i \(0.176218\pi\)
\(642\) −15.2190 −0.600647
\(643\) 13.4348 0.529818 0.264909 0.964273i \(-0.414658\pi\)
0.264909 + 0.964273i \(0.414658\pi\)
\(644\) −0.234026 −0.00922192
\(645\) −14.2497 −0.561080
\(646\) −18.4654 −0.726510
\(647\) 2.28741 0.0899275 0.0449638 0.998989i \(-0.485683\pi\)
0.0449638 + 0.998989i \(0.485683\pi\)
\(648\) 3.26312 0.128188
\(649\) −33.8348 −1.32813
\(650\) −12.2939 −0.482206
\(651\) −1.66297 −0.0651770
\(652\) 5.38179 0.210767
\(653\) 32.2933 1.26374 0.631868 0.775076i \(-0.282288\pi\)
0.631868 + 0.775076i \(0.282288\pi\)
\(654\) −6.36935 −0.249061
\(655\) −1.41489 −0.0552842
\(656\) 0.450472 0.0175880
\(657\) −26.8241 −1.04651
\(658\) −1.26692 −0.0493896
\(659\) −49.3134 −1.92098 −0.960488 0.278322i \(-0.910222\pi\)
−0.960488 + 0.278322i \(0.910222\pi\)
\(660\) 4.41567 0.171880
\(661\) 7.79175 0.303064 0.151532 0.988452i \(-0.451579\pi\)
0.151532 + 0.988452i \(0.451579\pi\)
\(662\) −1.21324 −0.0471538
\(663\) −25.0218 −0.971765
\(664\) −0.454412 −0.0176346
\(665\) −0.832562 −0.0322854
\(666\) −9.48056 −0.367364
\(667\) 5.16848 0.200124
\(668\) 18.2465 0.705978
\(669\) 8.55332 0.330691
\(670\) −13.5277 −0.522619
\(671\) 23.3281 0.900572
\(672\) 0.194452 0.00750114
\(673\) 13.3627 0.515094 0.257547 0.966266i \(-0.417086\pi\)
0.257547 + 0.966266i \(0.417086\pi\)
\(674\) 0.992259 0.0382204
\(675\) −13.2268 −0.509101
\(676\) 3.81461 0.146716
\(677\) 5.47408 0.210386 0.105193 0.994452i \(-0.466454\pi\)
0.105193 + 0.994452i \(0.466454\pi\)
\(678\) −13.2218 −0.507780
\(679\) −1.16910 −0.0448661
\(680\) −10.3908 −0.398469
\(681\) −22.1234 −0.847771
\(682\) −32.1219 −1.23001
\(683\) 28.7084 1.09850 0.549249 0.835659i \(-0.314914\pi\)
0.549249 + 0.835659i \(0.314914\pi\)
\(684\) 5.80723 0.222045
\(685\) −17.4689 −0.667453
\(686\) 3.26355 0.124603
\(687\) −15.3446 −0.585431
\(688\) −12.1209 −0.462106
\(689\) −10.6812 −0.406923
\(690\) 1.17563 0.0447553
\(691\) −50.0073 −1.90237 −0.951184 0.308624i \(-0.900132\pi\)
−0.951184 + 0.308624i \(0.900132\pi\)
\(692\) 17.5575 0.667435
\(693\) 2.03016 0.0771194
\(694\) −10.7069 −0.406429
\(695\) −18.8342 −0.714420
\(696\) −4.29448 −0.162782
\(697\) 3.30822 0.125308
\(698\) −18.7164 −0.708428
\(699\) 1.62206 0.0613521
\(700\) 0.701633 0.0265192
\(701\) 46.4162 1.75312 0.876559 0.481295i \(-0.159833\pi\)
0.876559 + 0.481295i \(0.159833\pi\)
\(702\) 18.0906 0.682786
\(703\) −10.3211 −0.389268
\(704\) 3.75602 0.141560
\(705\) 6.36433 0.239695
\(706\) 37.3705 1.40646
\(707\) 0.188194 0.00707777
\(708\) 7.48486 0.281298
\(709\) 30.4219 1.14252 0.571259 0.820770i \(-0.306455\pi\)
0.571259 + 0.820770i \(0.306455\pi\)
\(710\) 6.58629 0.247179
\(711\) 0.392413 0.0147166
\(712\) −5.74379 −0.215258
\(713\) −8.55210 −0.320279
\(714\) 1.42803 0.0534429
\(715\) −21.7918 −0.814966
\(716\) 3.41719 0.127706
\(717\) 1.21781 0.0454801
\(718\) −5.79181 −0.216148
\(719\) 27.2627 1.01673 0.508364 0.861142i \(-0.330251\pi\)
0.508364 + 0.861142i \(0.330251\pi\)
\(720\) 3.26783 0.121785
\(721\) −1.89635 −0.0706239
\(722\) −12.6779 −0.471823
\(723\) 24.9126 0.926511
\(724\) −20.4216 −0.758964
\(725\) −15.4956 −0.575492
\(726\) −2.58216 −0.0958329
\(727\) 26.3797 0.978369 0.489185 0.872180i \(-0.337294\pi\)
0.489185 + 0.872180i \(0.337294\pi\)
\(728\) −0.959639 −0.0355666
\(729\) 3.46058 0.128170
\(730\) −16.4327 −0.608202
\(731\) −89.0149 −3.29234
\(732\) −5.16059 −0.190741
\(733\) 44.4526 1.64189 0.820946 0.571005i \(-0.193447\pi\)
0.820946 + 0.571005i \(0.193447\pi\)
\(734\) −20.8003 −0.767755
\(735\) −8.16499 −0.301170
\(736\) 1.00000 0.0368605
\(737\) 35.9111 1.32280
\(738\) −1.04041 −0.0382982
\(739\) −32.3513 −1.19006 −0.595030 0.803703i \(-0.702860\pi\)
−0.595030 + 0.803703i \(0.702860\pi\)
\(740\) −5.80787 −0.213502
\(741\) 8.56686 0.314711
\(742\) 0.609597 0.0223790
\(743\) 12.1524 0.445827 0.222914 0.974838i \(-0.428443\pi\)
0.222914 + 0.974838i \(0.428443\pi\)
\(744\) 7.10592 0.260516
\(745\) −28.7352 −1.05278
\(746\) 29.8137 1.09156
\(747\) 1.04951 0.0383997
\(748\) 27.5838 1.00856
\(749\) −4.28651 −0.156626
\(750\) −9.40277 −0.343341
\(751\) 30.9411 1.12906 0.564528 0.825414i \(-0.309058\pi\)
0.564528 + 0.825414i \(0.309058\pi\)
\(752\) 5.41357 0.197413
\(753\) 4.14388 0.151011
\(754\) 21.1937 0.771828
\(755\) −0.701875 −0.0255438
\(756\) −1.03246 −0.0375503
\(757\) −20.8625 −0.758261 −0.379131 0.925343i \(-0.623777\pi\)
−0.379131 + 0.925343i \(0.623777\pi\)
\(758\) 21.9308 0.796562
\(759\) −3.12087 −0.113280
\(760\) 3.55756 0.129046
\(761\) −34.0386 −1.23390 −0.616949 0.787003i \(-0.711632\pi\)
−0.616949 + 0.787003i \(0.711632\pi\)
\(762\) −0.547318 −0.0198272
\(763\) −1.79396 −0.0649455
\(764\) −18.1162 −0.655420
\(765\) 23.9987 0.867673
\(766\) −10.3428 −0.373702
\(767\) −36.9385 −1.33377
\(768\) −0.830898 −0.0299824
\(769\) −42.9030 −1.54712 −0.773561 0.633722i \(-0.781527\pi\)
−0.773561 + 0.633722i \(0.781527\pi\)
\(770\) 1.24369 0.0448196
\(771\) −19.8035 −0.713206
\(772\) 1.03366 0.0372022
\(773\) −45.7995 −1.64729 −0.823647 0.567103i \(-0.808064\pi\)
−0.823647 + 0.567103i \(0.808064\pi\)
\(774\) 27.9946 1.00625
\(775\) 25.6400 0.921017
\(776\) 4.99562 0.179332
\(777\) 0.798192 0.0286350
\(778\) 0.575240 0.0206233
\(779\) −1.13266 −0.0405817
\(780\) 4.82073 0.172610
\(781\) −17.4843 −0.625636
\(782\) 7.34390 0.262617
\(783\) 22.8020 0.814877
\(784\) −6.94523 −0.248044
\(785\) 27.1867 0.970335
\(786\) −0.830898 −0.0296371
\(787\) 29.8640 1.06454 0.532269 0.846575i \(-0.321340\pi\)
0.532269 + 0.846575i \(0.321340\pi\)
\(788\) 3.09375 0.110210
\(789\) −6.54341 −0.232951
\(790\) 0.240396 0.00855289
\(791\) −3.72398 −0.132410
\(792\) −8.67493 −0.308250
\(793\) 25.4680 0.904396
\(794\) −9.25444 −0.328428
\(795\) −3.06230 −0.108608
\(796\) 5.97114 0.211641
\(797\) −42.0432 −1.48925 −0.744623 0.667485i \(-0.767371\pi\)
−0.744623 + 0.667485i \(0.767371\pi\)
\(798\) −0.488925 −0.0173078
\(799\) 39.7568 1.40649
\(800\) −2.99810 −0.105999
\(801\) 13.2659 0.468728
\(802\) −15.9794 −0.564251
\(803\) 43.6230 1.53942
\(804\) −7.94418 −0.280170
\(805\) 0.331120 0.0116705
\(806\) −35.0684 −1.23523
\(807\) −7.57246 −0.266563
\(808\) −0.804159 −0.0282902
\(809\) −31.1472 −1.09508 −0.547538 0.836781i \(-0.684435\pi\)
−0.547538 + 0.836781i \(0.684435\pi\)
\(810\) −4.61695 −0.162223
\(811\) 46.0408 1.61671 0.808356 0.588694i \(-0.200358\pi\)
0.808356 + 0.588694i \(0.200358\pi\)
\(812\) −1.20956 −0.0424472
\(813\) 5.37078 0.188361
\(814\) 15.4178 0.540395
\(815\) −7.61462 −0.266729
\(816\) −6.10203 −0.213614
\(817\) 30.4766 1.06624
\(818\) −23.7683 −0.831039
\(819\) 2.21639 0.0774469
\(820\) −0.637367 −0.0222578
\(821\) −14.1999 −0.495578 −0.247789 0.968814i \(-0.579704\pi\)
−0.247789 + 0.968814i \(0.579704\pi\)
\(822\) −10.2587 −0.357813
\(823\) −0.278519 −0.00970855 −0.00485427 0.999988i \(-0.501545\pi\)
−0.00485427 + 0.999988i \(0.501545\pi\)
\(824\) 8.10317 0.282287
\(825\) 9.35666 0.325757
\(826\) 2.10814 0.0733517
\(827\) −33.7245 −1.17272 −0.586358 0.810052i \(-0.699439\pi\)
−0.586358 + 0.810052i \(0.699439\pi\)
\(828\) −2.30961 −0.0802645
\(829\) −40.4962 −1.40649 −0.703246 0.710947i \(-0.748267\pi\)
−0.703246 + 0.710947i \(0.748267\pi\)
\(830\) 0.642941 0.0223168
\(831\) −2.24808 −0.0779852
\(832\) 4.10056 0.142161
\(833\) −51.0051 −1.76722
\(834\) −11.0604 −0.382992
\(835\) −25.8167 −0.893424
\(836\) −9.44405 −0.326629
\(837\) −37.7297 −1.30413
\(838\) 31.5720 1.09064
\(839\) 15.1626 0.523470 0.261735 0.965140i \(-0.415705\pi\)
0.261735 + 0.965140i \(0.415705\pi\)
\(840\) −0.275127 −0.00949279
\(841\) −2.28683 −0.0788563
\(842\) −21.3439 −0.735558
\(843\) 6.07837 0.209350
\(844\) 4.47685 0.154099
\(845\) −5.39724 −0.185671
\(846\) −12.5032 −0.429870
\(847\) −0.727277 −0.0249895
\(848\) −2.60482 −0.0894500
\(849\) 4.23230 0.145252
\(850\) −22.0177 −0.755202
\(851\) 4.10484 0.140712
\(852\) 3.86783 0.132510
\(853\) 2.84635 0.0974572 0.0487286 0.998812i \(-0.484483\pi\)
0.0487286 + 0.998812i \(0.484483\pi\)
\(854\) −1.45350 −0.0497379
\(855\) −8.21657 −0.281001
\(856\) 18.3164 0.626040
\(857\) 28.7344 0.981547 0.490774 0.871287i \(-0.336714\pi\)
0.490774 + 0.871287i \(0.336714\pi\)
\(858\) −12.7973 −0.436893
\(859\) −53.3194 −1.81923 −0.909617 0.415448i \(-0.863625\pi\)
−0.909617 + 0.415448i \(0.863625\pi\)
\(860\) 17.1497 0.584801
\(861\) 0.0875951 0.00298523
\(862\) −7.09641 −0.241705
\(863\) −15.8333 −0.538972 −0.269486 0.963004i \(-0.586854\pi\)
−0.269486 + 0.963004i \(0.586854\pi\)
\(864\) 4.41174 0.150090
\(865\) −24.8418 −0.844648
\(866\) −7.58377 −0.257707
\(867\) −30.6875 −1.04220
\(868\) 2.00142 0.0679325
\(869\) −0.638165 −0.0216483
\(870\) 6.07620 0.206002
\(871\) 39.2053 1.32842
\(872\) 7.66562 0.259591
\(873\) −11.5379 −0.390499
\(874\) −2.51438 −0.0850501
\(875\) −2.64833 −0.0895300
\(876\) −9.65017 −0.326049
\(877\) 46.9103 1.58405 0.792023 0.610491i \(-0.209028\pi\)
0.792023 + 0.610491i \(0.209028\pi\)
\(878\) 25.1129 0.847521
\(879\) 13.2210 0.445934
\(880\) −5.31434 −0.179146
\(881\) 4.70541 0.158529 0.0792646 0.996854i \(-0.474743\pi\)
0.0792646 + 0.996854i \(0.474743\pi\)
\(882\) 16.0408 0.540121
\(883\) 5.74717 0.193408 0.0967039 0.995313i \(-0.469170\pi\)
0.0967039 + 0.995313i \(0.469170\pi\)
\(884\) 30.1141 1.01285
\(885\) −10.5902 −0.355986
\(886\) −29.8716 −1.00356
\(887\) −2.10416 −0.0706507 −0.0353253 0.999376i \(-0.511247\pi\)
−0.0353253 + 0.999376i \(0.511247\pi\)
\(888\) −3.41070 −0.114456
\(889\) −0.154155 −0.00517018
\(890\) 8.12681 0.272411
\(891\) 12.2563 0.410603
\(892\) −10.2941 −0.344671
\(893\) −13.6118 −0.455501
\(894\) −16.8749 −0.564381
\(895\) −4.83494 −0.161614
\(896\) −0.234026 −0.00781826
\(897\) −3.40715 −0.113761
\(898\) −7.12677 −0.237823
\(899\) −44.2014 −1.47420
\(900\) 6.92443 0.230814
\(901\) −19.1296 −0.637298
\(902\) 1.69198 0.0563368
\(903\) −2.35694 −0.0784339
\(904\) 15.9127 0.529248
\(905\) 28.8943 0.960479
\(906\) −0.412179 −0.0136937
\(907\) −41.6827 −1.38405 −0.692025 0.721873i \(-0.743281\pi\)
−0.692025 + 0.721873i \(0.743281\pi\)
\(908\) 26.6259 0.883612
\(909\) 1.85729 0.0616025
\(910\) 1.35778 0.0450099
\(911\) 31.9920 1.05994 0.529972 0.848015i \(-0.322202\pi\)
0.529972 + 0.848015i \(0.322202\pi\)
\(912\) 2.08919 0.0691800
\(913\) −1.70678 −0.0564862
\(914\) −29.1112 −0.962914
\(915\) 7.30165 0.241385
\(916\) 18.4674 0.610182
\(917\) −0.234026 −0.00772822
\(918\) 32.3994 1.06934
\(919\) 43.0366 1.41965 0.709824 0.704379i \(-0.248775\pi\)
0.709824 + 0.704379i \(0.248775\pi\)
\(920\) −1.41489 −0.0466474
\(921\) −15.6649 −0.516177
\(922\) 33.8785 1.11573
\(923\) −19.0881 −0.628293
\(924\) 0.730364 0.0240272
\(925\) −12.3067 −0.404642
\(926\) 4.68072 0.153818
\(927\) −18.7152 −0.614686
\(928\) 5.16848 0.169664
\(929\) −17.3584 −0.569509 −0.284755 0.958600i \(-0.591912\pi\)
−0.284755 + 0.958600i \(0.591912\pi\)
\(930\) −10.0541 −0.329686
\(931\) 17.4629 0.572325
\(932\) −1.95218 −0.0639459
\(933\) 11.1489 0.365000
\(934\) −28.6923 −0.938839
\(935\) −39.0280 −1.27635
\(936\) −9.47070 −0.309559
\(937\) 38.3766 1.25371 0.626854 0.779136i \(-0.284342\pi\)
0.626854 + 0.779136i \(0.284342\pi\)
\(938\) −2.23751 −0.0730574
\(939\) −13.8753 −0.452803
\(940\) −7.65959 −0.249828
\(941\) −10.6999 −0.348807 −0.174404 0.984674i \(-0.555800\pi\)
−0.174404 + 0.984674i \(0.555800\pi\)
\(942\) 15.9655 0.520184
\(943\) 0.450472 0.0146694
\(944\) −9.00816 −0.293191
\(945\) 1.46082 0.0475204
\(946\) −45.5264 −1.48019
\(947\) −41.6905 −1.35476 −0.677380 0.735634i \(-0.736885\pi\)
−0.677380 + 0.735634i \(0.736885\pi\)
\(948\) 0.141173 0.00458510
\(949\) 47.6245 1.54596
\(950\) 7.53835 0.244576
\(951\) 23.3293 0.756505
\(952\) −1.71867 −0.0557023
\(953\) 10.5881 0.342982 0.171491 0.985186i \(-0.445141\pi\)
0.171491 + 0.985186i \(0.445141\pi\)
\(954\) 6.01612 0.194779
\(955\) 25.6323 0.829443
\(956\) −1.46566 −0.0474028
\(957\) −16.1301 −0.521413
\(958\) −32.2915 −1.04329
\(959\) −2.88941 −0.0933038
\(960\) 1.17563 0.0379432
\(961\) 42.1385 1.35931
\(962\) 16.8321 0.542690
\(963\) −42.3036 −1.36322
\(964\) −29.9828 −0.965681
\(965\) −1.46251 −0.0470799
\(966\) 0.194452 0.00625638
\(967\) 1.37294 0.0441508 0.0220754 0.999756i \(-0.492973\pi\)
0.0220754 + 0.999756i \(0.492973\pi\)
\(968\) 3.10767 0.0998844
\(969\) 15.3428 0.492882
\(970\) −7.06823 −0.226947
\(971\) −36.7515 −1.17941 −0.589706 0.807618i \(-0.700756\pi\)
−0.589706 + 0.807618i \(0.700756\pi\)
\(972\) −15.9465 −0.511486
\(973\) −3.11522 −0.0998695
\(974\) −32.0737 −1.02771
\(975\) 10.2150 0.327140
\(976\) 6.21086 0.198805
\(977\) −33.7415 −1.07949 −0.539743 0.841830i \(-0.681478\pi\)
−0.539743 + 0.841830i \(0.681478\pi\)
\(978\) −4.47172 −0.142990
\(979\) −21.5738 −0.689501
\(980\) 9.82671 0.313903
\(981\) −17.7046 −0.565264
\(982\) −6.59041 −0.210308
\(983\) 6.19255 0.197512 0.0987559 0.995112i \(-0.468514\pi\)
0.0987559 + 0.995112i \(0.468514\pi\)
\(984\) −0.374296 −0.0119321
\(985\) −4.37731 −0.139473
\(986\) 37.9568 1.20879
\(987\) 1.05268 0.0335071
\(988\) −10.3104 −0.328016
\(989\) −12.1209 −0.385423
\(990\) 12.2740 0.390095
\(991\) −45.1645 −1.43470 −0.717349 0.696714i \(-0.754645\pi\)
−0.717349 + 0.696714i \(0.754645\pi\)
\(992\) −8.55210 −0.271530
\(993\) 1.00808 0.0319903
\(994\) 1.08939 0.0345534
\(995\) −8.44848 −0.267835
\(996\) 0.377570 0.0119638
\(997\) −35.3467 −1.11944 −0.559720 0.828682i \(-0.689091\pi\)
−0.559720 + 0.828682i \(0.689091\pi\)
\(998\) 7.32680 0.231926
\(999\) 18.1095 0.572958
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 6026.2.a.m.1.16 41
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6026.2.a.m.1.16 41 1.1 even 1 trivial