Properties

Label 8018.2.a.j.1.23
Level $8018$
Weight $2$
Character 8018.1
Self dual yes
Analytic conductor $64.024$
Analytic rank $0$
Dimension $47$
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] = [8018,2,Mod(1,8018)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8018, 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("8018.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8018.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: \(64.0240523407\)
Analytic rank: \(0\)
Dimension: \(47\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.23
Character \(\chi\) \(=\) 8018.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +0.295377 q^{3} +1.00000 q^{4} +0.172140 q^{5} +0.295377 q^{6} -3.30669 q^{7} +1.00000 q^{8} -2.91275 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +0.295377 q^{3} +1.00000 q^{4} +0.172140 q^{5} +0.295377 q^{6} -3.30669 q^{7} +1.00000 q^{8} -2.91275 q^{9} +0.172140 q^{10} -2.45188 q^{11} +0.295377 q^{12} -2.40163 q^{13} -3.30669 q^{14} +0.0508464 q^{15} +1.00000 q^{16} -0.737190 q^{17} -2.91275 q^{18} -1.00000 q^{19} +0.172140 q^{20} -0.976721 q^{21} -2.45188 q^{22} -1.13177 q^{23} +0.295377 q^{24} -4.97037 q^{25} -2.40163 q^{26} -1.74649 q^{27} -3.30669 q^{28} +3.37680 q^{29} +0.0508464 q^{30} +2.23204 q^{31} +1.00000 q^{32} -0.724229 q^{33} -0.737190 q^{34} -0.569215 q^{35} -2.91275 q^{36} +8.49904 q^{37} -1.00000 q^{38} -0.709388 q^{39} +0.172140 q^{40} +8.47459 q^{41} -0.976721 q^{42} -10.7373 q^{43} -2.45188 q^{44} -0.501402 q^{45} -1.13177 q^{46} +10.8454 q^{47} +0.295377 q^{48} +3.93419 q^{49} -4.97037 q^{50} -0.217749 q^{51} -2.40163 q^{52} +11.0578 q^{53} -1.74649 q^{54} -0.422067 q^{55} -3.30669 q^{56} -0.295377 q^{57} +3.37680 q^{58} -2.36963 q^{59} +0.0508464 q^{60} +7.18189 q^{61} +2.23204 q^{62} +9.63157 q^{63} +1.00000 q^{64} -0.413418 q^{65} -0.724229 q^{66} -0.726963 q^{67} -0.737190 q^{68} -0.334298 q^{69} -0.569215 q^{70} +10.2530 q^{71} -2.91275 q^{72} -3.97307 q^{73} +8.49904 q^{74} -1.46813 q^{75} -1.00000 q^{76} +8.10760 q^{77} -0.709388 q^{78} +5.35217 q^{79} +0.172140 q^{80} +8.22238 q^{81} +8.47459 q^{82} +2.06586 q^{83} -0.976721 q^{84} -0.126900 q^{85} -10.7373 q^{86} +0.997430 q^{87} -2.45188 q^{88} +3.34314 q^{89} -0.501402 q^{90} +7.94145 q^{91} -1.13177 q^{92} +0.659296 q^{93} +10.8454 q^{94} -0.172140 q^{95} +0.295377 q^{96} +6.07568 q^{97} +3.93419 q^{98} +7.14171 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 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
\(3\) 0.295377 0.170536 0.0852681 0.996358i \(-0.472825\pi\)
0.0852681 + 0.996358i \(0.472825\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.172140 0.0769835 0.0384918 0.999259i \(-0.487745\pi\)
0.0384918 + 0.999259i \(0.487745\pi\)
\(6\) 0.295377 0.120587
\(7\) −3.30669 −1.24981 −0.624905 0.780700i \(-0.714862\pi\)
−0.624905 + 0.780700i \(0.714862\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.91275 −0.970917
\(10\) 0.172140 0.0544356
\(11\) −2.45188 −0.739269 −0.369635 0.929177i \(-0.620517\pi\)
−0.369635 + 0.929177i \(0.620517\pi\)
\(12\) 0.295377 0.0852681
\(13\) −2.40163 −0.666093 −0.333046 0.942910i \(-0.608077\pi\)
−0.333046 + 0.942910i \(0.608077\pi\)
\(14\) −3.30669 −0.883750
\(15\) 0.0508464 0.0131285
\(16\) 1.00000 0.250000
\(17\) −0.737190 −0.178795 −0.0893975 0.995996i \(-0.528494\pi\)
−0.0893975 + 0.995996i \(0.528494\pi\)
\(18\) −2.91275 −0.686542
\(19\) −1.00000 −0.229416
\(20\) 0.172140 0.0384918
\(21\) −0.976721 −0.213138
\(22\) −2.45188 −0.522742
\(23\) −1.13177 −0.235990 −0.117995 0.993014i \(-0.537647\pi\)
−0.117995 + 0.993014i \(0.537647\pi\)
\(24\) 0.295377 0.0602937
\(25\) −4.97037 −0.994074
\(26\) −2.40163 −0.470999
\(27\) −1.74649 −0.336113
\(28\) −3.30669 −0.624905
\(29\) 3.37680 0.627056 0.313528 0.949579i \(-0.398489\pi\)
0.313528 + 0.949579i \(0.398489\pi\)
\(30\) 0.0508464 0.00928324
\(31\) 2.23204 0.400887 0.200444 0.979705i \(-0.435762\pi\)
0.200444 + 0.979705i \(0.435762\pi\)
\(32\) 1.00000 0.176777
\(33\) −0.724229 −0.126072
\(34\) −0.737190 −0.126427
\(35\) −0.569215 −0.0962149
\(36\) −2.91275 −0.485459
\(37\) 8.49904 1.39723 0.698617 0.715496i \(-0.253799\pi\)
0.698617 + 0.715496i \(0.253799\pi\)
\(38\) −1.00000 −0.162221
\(39\) −0.709388 −0.113593
\(40\) 0.172140 0.0272178
\(41\) 8.47459 1.32351 0.661754 0.749721i \(-0.269812\pi\)
0.661754 + 0.749721i \(0.269812\pi\)
\(42\) −0.976721 −0.150711
\(43\) −10.7373 −1.63742 −0.818710 0.574207i \(-0.805310\pi\)
−0.818710 + 0.574207i \(0.805310\pi\)
\(44\) −2.45188 −0.369635
\(45\) −0.501402 −0.0747446
\(46\) −1.13177 −0.166870
\(47\) 10.8454 1.58197 0.790985 0.611836i \(-0.209569\pi\)
0.790985 + 0.611836i \(0.209569\pi\)
\(48\) 0.295377 0.0426341
\(49\) 3.93419 0.562027
\(50\) −4.97037 −0.702916
\(51\) −0.217749 −0.0304910
\(52\) −2.40163 −0.333046
\(53\) 11.0578 1.51891 0.759453 0.650562i \(-0.225467\pi\)
0.759453 + 0.650562i \(0.225467\pi\)
\(54\) −1.74649 −0.237668
\(55\) −0.422067 −0.0569115
\(56\) −3.30669 −0.441875
\(57\) −0.295377 −0.0391237
\(58\) 3.37680 0.443395
\(59\) −2.36963 −0.308499 −0.154249 0.988032i \(-0.549296\pi\)
−0.154249 + 0.988032i \(0.549296\pi\)
\(60\) 0.0508464 0.00656424
\(61\) 7.18189 0.919547 0.459774 0.888036i \(-0.347931\pi\)
0.459774 + 0.888036i \(0.347931\pi\)
\(62\) 2.23204 0.283470
\(63\) 9.63157 1.21346
\(64\) 1.00000 0.125000
\(65\) −0.413418 −0.0512782
\(66\) −0.724229 −0.0891465
\(67\) −0.726963 −0.0888127 −0.0444063 0.999014i \(-0.514140\pi\)
−0.0444063 + 0.999014i \(0.514140\pi\)
\(68\) −0.737190 −0.0893975
\(69\) −0.334298 −0.0402448
\(70\) −0.569215 −0.0680342
\(71\) 10.2530 1.21681 0.608406 0.793626i \(-0.291809\pi\)
0.608406 + 0.793626i \(0.291809\pi\)
\(72\) −2.91275 −0.343271
\(73\) −3.97307 −0.465013 −0.232506 0.972595i \(-0.574693\pi\)
−0.232506 + 0.972595i \(0.574693\pi\)
\(74\) 8.49904 0.987994
\(75\) −1.46813 −0.169526
\(76\) −1.00000 −0.114708
\(77\) 8.10760 0.923947
\(78\) −0.709388 −0.0803223
\(79\) 5.35217 0.602167 0.301083 0.953598i \(-0.402652\pi\)
0.301083 + 0.953598i \(0.402652\pi\)
\(80\) 0.172140 0.0192459
\(81\) 8.22238 0.913598
\(82\) 8.47459 0.935862
\(83\) 2.06586 0.226758 0.113379 0.993552i \(-0.463833\pi\)
0.113379 + 0.993552i \(0.463833\pi\)
\(84\) −0.976721 −0.106569
\(85\) −0.126900 −0.0137643
\(86\) −10.7373 −1.15783
\(87\) 0.997430 0.106936
\(88\) −2.45188 −0.261371
\(89\) 3.34314 0.354372 0.177186 0.984177i \(-0.443301\pi\)
0.177186 + 0.984177i \(0.443301\pi\)
\(90\) −0.501402 −0.0528524
\(91\) 7.94145 0.832490
\(92\) −1.13177 −0.117995
\(93\) 0.659296 0.0683658
\(94\) 10.8454 1.11862
\(95\) −0.172140 −0.0176612
\(96\) 0.295377 0.0301468
\(97\) 6.07568 0.616892 0.308446 0.951242i \(-0.400191\pi\)
0.308446 + 0.951242i \(0.400191\pi\)
\(98\) 3.93419 0.397413
\(99\) 7.14171 0.717769
\(100\) −4.97037 −0.497037
\(101\) 6.68046 0.664730 0.332365 0.943151i \(-0.392153\pi\)
0.332365 + 0.943151i \(0.392153\pi\)
\(102\) −0.217749 −0.0215604
\(103\) −6.72207 −0.662345 −0.331173 0.943570i \(-0.607444\pi\)
−0.331173 + 0.943570i \(0.607444\pi\)
\(104\) −2.40163 −0.235499
\(105\) −0.168133 −0.0164081
\(106\) 11.0578 1.07403
\(107\) −1.11875 −0.108154 −0.0540769 0.998537i \(-0.517222\pi\)
−0.0540769 + 0.998537i \(0.517222\pi\)
\(108\) −1.74649 −0.168056
\(109\) −2.84306 −0.272315 −0.136158 0.990687i \(-0.543475\pi\)
−0.136158 + 0.990687i \(0.543475\pi\)
\(110\) −0.422067 −0.0402425
\(111\) 2.51042 0.238279
\(112\) −3.30669 −0.312453
\(113\) −8.42912 −0.792945 −0.396473 0.918047i \(-0.629766\pi\)
−0.396473 + 0.918047i \(0.629766\pi\)
\(114\) −0.295377 −0.0276646
\(115\) −0.194823 −0.0181673
\(116\) 3.37680 0.313528
\(117\) 6.99536 0.646721
\(118\) −2.36963 −0.218142
\(119\) 2.43766 0.223460
\(120\) 0.0508464 0.00464162
\(121\) −4.98829 −0.453481
\(122\) 7.18189 0.650218
\(123\) 2.50320 0.225706
\(124\) 2.23204 0.200444
\(125\) −1.71630 −0.153511
\(126\) 9.63157 0.858048
\(127\) 6.68152 0.592889 0.296445 0.955050i \(-0.404199\pi\)
0.296445 + 0.955050i \(0.404199\pi\)
\(128\) 1.00000 0.0883883
\(129\) −3.17155 −0.279239
\(130\) −0.413418 −0.0362591
\(131\) 4.29041 0.374855 0.187427 0.982278i \(-0.439985\pi\)
0.187427 + 0.982278i \(0.439985\pi\)
\(132\) −0.724229 −0.0630361
\(133\) 3.30669 0.286726
\(134\) −0.726963 −0.0628001
\(135\) −0.300642 −0.0258752
\(136\) −0.737190 −0.0632135
\(137\) 16.0219 1.36884 0.684420 0.729088i \(-0.260056\pi\)
0.684420 + 0.729088i \(0.260056\pi\)
\(138\) −0.334298 −0.0284574
\(139\) −12.8331 −1.08849 −0.544243 0.838928i \(-0.683183\pi\)
−0.544243 + 0.838928i \(0.683183\pi\)
\(140\) −0.569215 −0.0481074
\(141\) 3.20350 0.269783
\(142\) 10.2530 0.860417
\(143\) 5.88851 0.492422
\(144\) −2.91275 −0.242729
\(145\) 0.581283 0.0482730
\(146\) −3.97307 −0.328814
\(147\) 1.16207 0.0958460
\(148\) 8.49904 0.698617
\(149\) 17.3940 1.42497 0.712486 0.701686i \(-0.247569\pi\)
0.712486 + 0.701686i \(0.247569\pi\)
\(150\) −1.46813 −0.119873
\(151\) −20.5050 −1.66867 −0.834335 0.551258i \(-0.814148\pi\)
−0.834335 + 0.551258i \(0.814148\pi\)
\(152\) −1.00000 −0.0811107
\(153\) 2.14725 0.173595
\(154\) 8.10760 0.653329
\(155\) 0.384225 0.0308617
\(156\) −0.709388 −0.0567965
\(157\) 16.3390 1.30400 0.651999 0.758220i \(-0.273931\pi\)
0.651999 + 0.758220i \(0.273931\pi\)
\(158\) 5.35217 0.425796
\(159\) 3.26623 0.259029
\(160\) 0.172140 0.0136089
\(161\) 3.74240 0.294942
\(162\) 8.22238 0.646011
\(163\) 16.2441 1.27234 0.636170 0.771549i \(-0.280518\pi\)
0.636170 + 0.771549i \(0.280518\pi\)
\(164\) 8.47459 0.661754
\(165\) −0.124669 −0.00970548
\(166\) 2.06586 0.160342
\(167\) −1.51083 −0.116912 −0.0584559 0.998290i \(-0.518618\pi\)
−0.0584559 + 0.998290i \(0.518618\pi\)
\(168\) −0.976721 −0.0753557
\(169\) −7.23217 −0.556321
\(170\) −0.126900 −0.00973280
\(171\) 2.91275 0.222744
\(172\) −10.7373 −0.818710
\(173\) −20.1631 −1.53297 −0.766485 0.642262i \(-0.777996\pi\)
−0.766485 + 0.642262i \(0.777996\pi\)
\(174\) 0.997430 0.0756150
\(175\) 16.4355 1.24240
\(176\) −2.45188 −0.184817
\(177\) −0.699934 −0.0526102
\(178\) 3.34314 0.250579
\(179\) −2.74253 −0.204987 −0.102493 0.994734i \(-0.532682\pi\)
−0.102493 + 0.994734i \(0.532682\pi\)
\(180\) −0.501402 −0.0373723
\(181\) −0.968669 −0.0720006 −0.0360003 0.999352i \(-0.511462\pi\)
−0.0360003 + 0.999352i \(0.511462\pi\)
\(182\) 7.94145 0.588659
\(183\) 2.12137 0.156816
\(184\) −1.13177 −0.0834349
\(185\) 1.46303 0.107564
\(186\) 0.659296 0.0483419
\(187\) 1.80750 0.132178
\(188\) 10.8454 0.790985
\(189\) 5.77511 0.420077
\(190\) −0.172140 −0.0124884
\(191\) −3.85353 −0.278832 −0.139416 0.990234i \(-0.544522\pi\)
−0.139416 + 0.990234i \(0.544522\pi\)
\(192\) 0.295377 0.0213170
\(193\) −6.61520 −0.476173 −0.238086 0.971244i \(-0.576520\pi\)
−0.238086 + 0.971244i \(0.576520\pi\)
\(194\) 6.07568 0.436209
\(195\) −0.122114 −0.00874478
\(196\) 3.93419 0.281014
\(197\) −5.86335 −0.417746 −0.208873 0.977943i \(-0.566980\pi\)
−0.208873 + 0.977943i \(0.566980\pi\)
\(198\) 7.14171 0.507540
\(199\) −19.8599 −1.40783 −0.703916 0.710284i \(-0.748567\pi\)
−0.703916 + 0.710284i \(0.748567\pi\)
\(200\) −4.97037 −0.351458
\(201\) −0.214729 −0.0151458
\(202\) 6.68046 0.470035
\(203\) −11.1660 −0.783701
\(204\) −0.217749 −0.0152455
\(205\) 1.45882 0.101888
\(206\) −6.72207 −0.468349
\(207\) 3.29656 0.229126
\(208\) −2.40163 −0.166523
\(209\) 2.45188 0.169600
\(210\) −0.168133 −0.0116023
\(211\) −1.00000 −0.0688428
\(212\) 11.0578 0.759453
\(213\) 3.02852 0.207511
\(214\) −1.11875 −0.0764762
\(215\) −1.84832 −0.126054
\(216\) −1.74649 −0.118834
\(217\) −7.38068 −0.501033
\(218\) −2.84306 −0.192556
\(219\) −1.17356 −0.0793015
\(220\) −0.422067 −0.0284558
\(221\) 1.77046 0.119094
\(222\) 2.51042 0.168489
\(223\) 12.8030 0.857354 0.428677 0.903458i \(-0.358980\pi\)
0.428677 + 0.903458i \(0.358980\pi\)
\(224\) −3.30669 −0.220937
\(225\) 14.4774 0.965163
\(226\) −8.42912 −0.560697
\(227\) 22.1849 1.47247 0.736233 0.676728i \(-0.236603\pi\)
0.736233 + 0.676728i \(0.236603\pi\)
\(228\) −0.295377 −0.0195618
\(229\) −1.61219 −0.106536 −0.0532682 0.998580i \(-0.516964\pi\)
−0.0532682 + 0.998580i \(0.516964\pi\)
\(230\) −0.194823 −0.0128462
\(231\) 2.39480 0.157566
\(232\) 3.37680 0.221698
\(233\) −22.0222 −1.44272 −0.721361 0.692559i \(-0.756483\pi\)
−0.721361 + 0.692559i \(0.756483\pi\)
\(234\) 6.99536 0.457301
\(235\) 1.86694 0.121786
\(236\) −2.36963 −0.154249
\(237\) 1.58091 0.102691
\(238\) 2.43766 0.158010
\(239\) 22.7925 1.47433 0.737163 0.675715i \(-0.236165\pi\)
0.737163 + 0.675715i \(0.236165\pi\)
\(240\) 0.0508464 0.00328212
\(241\) −3.70087 −0.238394 −0.119197 0.992871i \(-0.538032\pi\)
−0.119197 + 0.992871i \(0.538032\pi\)
\(242\) −4.98829 −0.320660
\(243\) 7.66819 0.491914
\(244\) 7.18189 0.459774
\(245\) 0.677233 0.0432669
\(246\) 2.50320 0.159598
\(247\) 2.40163 0.152812
\(248\) 2.23204 0.141735
\(249\) 0.610208 0.0386704
\(250\) −1.71630 −0.108549
\(251\) −23.2800 −1.46942 −0.734710 0.678382i \(-0.762682\pi\)
−0.734710 + 0.678382i \(0.762682\pi\)
\(252\) 9.63157 0.606732
\(253\) 2.77495 0.174460
\(254\) 6.68152 0.419236
\(255\) −0.0374835 −0.00234731
\(256\) 1.00000 0.0625000
\(257\) 7.83805 0.488924 0.244462 0.969659i \(-0.421389\pi\)
0.244462 + 0.969659i \(0.421389\pi\)
\(258\) −3.17155 −0.197452
\(259\) −28.1037 −1.74628
\(260\) −0.413418 −0.0256391
\(261\) −9.83578 −0.608819
\(262\) 4.29041 0.265062
\(263\) 6.33785 0.390809 0.195404 0.980723i \(-0.437398\pi\)
0.195404 + 0.980723i \(0.437398\pi\)
\(264\) −0.724229 −0.0445732
\(265\) 1.90350 0.116931
\(266\) 3.30669 0.202746
\(267\) 0.987488 0.0604333
\(268\) −0.726963 −0.0444063
\(269\) 5.60736 0.341887 0.170944 0.985281i \(-0.445318\pi\)
0.170944 + 0.985281i \(0.445318\pi\)
\(270\) −0.300642 −0.0182965
\(271\) 26.3981 1.60357 0.801786 0.597612i \(-0.203883\pi\)
0.801786 + 0.597612i \(0.203883\pi\)
\(272\) −0.737190 −0.0446987
\(273\) 2.34572 0.141970
\(274\) 16.0219 0.967916
\(275\) 12.1867 0.734888
\(276\) −0.334298 −0.0201224
\(277\) −12.5493 −0.754017 −0.377008 0.926210i \(-0.623047\pi\)
−0.377008 + 0.926210i \(0.623047\pi\)
\(278\) −12.8331 −0.769676
\(279\) −6.50139 −0.389228
\(280\) −0.569215 −0.0340171
\(281\) 10.8646 0.648127 0.324064 0.946035i \(-0.394951\pi\)
0.324064 + 0.946035i \(0.394951\pi\)
\(282\) 3.20350 0.190765
\(283\) 7.01506 0.417002 0.208501 0.978022i \(-0.433142\pi\)
0.208501 + 0.978022i \(0.433142\pi\)
\(284\) 10.2530 0.608406
\(285\) −0.0508464 −0.00301188
\(286\) 5.88851 0.348195
\(287\) −28.0228 −1.65414
\(288\) −2.91275 −0.171636
\(289\) −16.4566 −0.968032
\(290\) 0.581283 0.0341341
\(291\) 1.79462 0.105202
\(292\) −3.97307 −0.232506
\(293\) 17.7179 1.03509 0.517546 0.855655i \(-0.326846\pi\)
0.517546 + 0.855655i \(0.326846\pi\)
\(294\) 1.16207 0.0677734
\(295\) −0.407908 −0.0237493
\(296\) 8.49904 0.493997
\(297\) 4.28219 0.248478
\(298\) 17.3940 1.00761
\(299\) 2.71809 0.157191
\(300\) −1.46813 −0.0847628
\(301\) 35.5048 2.04647
\(302\) −20.5050 −1.17993
\(303\) 1.97326 0.113361
\(304\) −1.00000 −0.0573539
\(305\) 1.23629 0.0707900
\(306\) 2.14725 0.122750
\(307\) −17.9338 −1.02354 −0.511769 0.859123i \(-0.671010\pi\)
−0.511769 + 0.859123i \(0.671010\pi\)
\(308\) 8.10760 0.461973
\(309\) −1.98555 −0.112954
\(310\) 0.384225 0.0218225
\(311\) −26.3427 −1.49376 −0.746878 0.664961i \(-0.768448\pi\)
−0.746878 + 0.664961i \(0.768448\pi\)
\(312\) −0.709388 −0.0401612
\(313\) 11.0123 0.622452 0.311226 0.950336i \(-0.399260\pi\)
0.311226 + 0.950336i \(0.399260\pi\)
\(314\) 16.3390 0.922065
\(315\) 1.65798 0.0934167
\(316\) 5.35217 0.301083
\(317\) −0.0614134 −0.00344932 −0.00172466 0.999999i \(-0.500549\pi\)
−0.00172466 + 0.999999i \(0.500549\pi\)
\(318\) 3.26623 0.183161
\(319\) −8.27950 −0.463563
\(320\) 0.172140 0.00962294
\(321\) −0.330454 −0.0184441
\(322\) 3.74240 0.208556
\(323\) 0.737190 0.0410184
\(324\) 8.22238 0.456799
\(325\) 11.9370 0.662145
\(326\) 16.2441 0.899680
\(327\) −0.839774 −0.0464396
\(328\) 8.47459 0.467931
\(329\) −35.8625 −1.97716
\(330\) −0.124669 −0.00686281
\(331\) −7.06512 −0.388334 −0.194167 0.980968i \(-0.562200\pi\)
−0.194167 + 0.980968i \(0.562200\pi\)
\(332\) 2.06586 0.113379
\(333\) −24.7556 −1.35660
\(334\) −1.51083 −0.0826691
\(335\) −0.125140 −0.00683711
\(336\) −0.976721 −0.0532845
\(337\) −30.0402 −1.63640 −0.818198 0.574937i \(-0.805026\pi\)
−0.818198 + 0.574937i \(0.805026\pi\)
\(338\) −7.23217 −0.393378
\(339\) −2.48977 −0.135226
\(340\) −0.126900 −0.00688213
\(341\) −5.47270 −0.296363
\(342\) 2.91275 0.157504
\(343\) 10.1377 0.547383
\(344\) −10.7373 −0.578915
\(345\) −0.0575462 −0.00309819
\(346\) −20.1631 −1.08397
\(347\) 13.2232 0.709858 0.354929 0.934893i \(-0.384505\pi\)
0.354929 + 0.934893i \(0.384505\pi\)
\(348\) 0.997430 0.0534679
\(349\) 21.7286 1.16310 0.581552 0.813509i \(-0.302446\pi\)
0.581552 + 0.813509i \(0.302446\pi\)
\(350\) 16.4355 0.878512
\(351\) 4.19443 0.223882
\(352\) −2.45188 −0.130686
\(353\) 5.47856 0.291594 0.145797 0.989315i \(-0.453425\pi\)
0.145797 + 0.989315i \(0.453425\pi\)
\(354\) −0.699934 −0.0372011
\(355\) 1.76496 0.0936746
\(356\) 3.34314 0.177186
\(357\) 0.720029 0.0381080
\(358\) −2.74253 −0.144947
\(359\) 28.8807 1.52426 0.762132 0.647422i \(-0.224153\pi\)
0.762132 + 0.647422i \(0.224153\pi\)
\(360\) −0.501402 −0.0264262
\(361\) 1.00000 0.0526316
\(362\) −0.968669 −0.0509121
\(363\) −1.47343 −0.0773350
\(364\) 7.94145 0.416245
\(365\) −0.683926 −0.0357983
\(366\) 2.12137 0.110886
\(367\) 28.7707 1.50182 0.750910 0.660405i \(-0.229615\pi\)
0.750910 + 0.660405i \(0.229615\pi\)
\(368\) −1.13177 −0.0589974
\(369\) −24.6844 −1.28502
\(370\) 1.46303 0.0760592
\(371\) −36.5647 −1.89835
\(372\) 0.659296 0.0341829
\(373\) −27.5792 −1.42800 −0.713999 0.700146i \(-0.753118\pi\)
−0.713999 + 0.700146i \(0.753118\pi\)
\(374\) 1.80750 0.0934636
\(375\) −0.506957 −0.0261792
\(376\) 10.8454 0.559311
\(377\) −8.10982 −0.417677
\(378\) 5.77511 0.297040
\(379\) 22.5703 1.15936 0.579680 0.814844i \(-0.303178\pi\)
0.579680 + 0.814844i \(0.303178\pi\)
\(380\) −0.172140 −0.00883062
\(381\) 1.97357 0.101109
\(382\) −3.85353 −0.197164
\(383\) 24.5709 1.25552 0.627758 0.778409i \(-0.283973\pi\)
0.627758 + 0.778409i \(0.283973\pi\)
\(384\) 0.295377 0.0150734
\(385\) 1.39565 0.0711287
\(386\) −6.61520 −0.336705
\(387\) 31.2750 1.58980
\(388\) 6.07568 0.308446
\(389\) 17.2012 0.872135 0.436067 0.899914i \(-0.356371\pi\)
0.436067 + 0.899914i \(0.356371\pi\)
\(390\) −0.122114 −0.00618350
\(391\) 0.834327 0.0421937
\(392\) 3.93419 0.198707
\(393\) 1.26729 0.0639263
\(394\) −5.86335 −0.295391
\(395\) 0.921325 0.0463569
\(396\) 7.14171 0.358885
\(397\) 25.7587 1.29279 0.646395 0.763003i \(-0.276276\pi\)
0.646395 + 0.763003i \(0.276276\pi\)
\(398\) −19.8599 −0.995487
\(399\) 0.976721 0.0488972
\(400\) −4.97037 −0.248518
\(401\) −9.53177 −0.475994 −0.237997 0.971266i \(-0.576491\pi\)
−0.237997 + 0.971266i \(0.576491\pi\)
\(402\) −0.214729 −0.0107097
\(403\) −5.36055 −0.267028
\(404\) 6.68046 0.332365
\(405\) 1.41540 0.0703320
\(406\) −11.1660 −0.554160
\(407\) −20.8386 −1.03293
\(408\) −0.217749 −0.0107802
\(409\) −20.5341 −1.01534 −0.507672 0.861550i \(-0.669494\pi\)
−0.507672 + 0.861550i \(0.669494\pi\)
\(410\) 1.45882 0.0720460
\(411\) 4.73250 0.233437
\(412\) −6.72207 −0.331173
\(413\) 7.83561 0.385565
\(414\) 3.29656 0.162017
\(415\) 0.355618 0.0174566
\(416\) −2.40163 −0.117750
\(417\) −3.79060 −0.185626
\(418\) 2.45188 0.119925
\(419\) −27.3905 −1.33811 −0.669057 0.743211i \(-0.733302\pi\)
−0.669057 + 0.743211i \(0.733302\pi\)
\(420\) −0.168133 −0.00820406
\(421\) −20.3757 −0.993053 −0.496527 0.868021i \(-0.665391\pi\)
−0.496527 + 0.868021i \(0.665391\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −31.5901 −1.53596
\(424\) 11.0578 0.537015
\(425\) 3.66411 0.177735
\(426\) 3.02852 0.146732
\(427\) −23.7483 −1.14926
\(428\) −1.11875 −0.0540769
\(429\) 1.73933 0.0839757
\(430\) −1.84832 −0.0891339
\(431\) 5.25951 0.253342 0.126671 0.991945i \(-0.459571\pi\)
0.126671 + 0.991945i \(0.459571\pi\)
\(432\) −1.74649 −0.0840282
\(433\) 34.9253 1.67840 0.839202 0.543820i \(-0.183022\pi\)
0.839202 + 0.543820i \(0.183022\pi\)
\(434\) −7.38068 −0.354284
\(435\) 0.171698 0.00823229
\(436\) −2.84306 −0.136158
\(437\) 1.13177 0.0541397
\(438\) −1.17356 −0.0560746
\(439\) −14.4547 −0.689885 −0.344943 0.938624i \(-0.612102\pi\)
−0.344943 + 0.938624i \(0.612102\pi\)
\(440\) −0.422067 −0.0201213
\(441\) −11.4593 −0.545682
\(442\) 1.77046 0.0842122
\(443\) 1.17908 0.0560200 0.0280100 0.999608i \(-0.491083\pi\)
0.0280100 + 0.999608i \(0.491083\pi\)
\(444\) 2.51042 0.119139
\(445\) 0.575489 0.0272808
\(446\) 12.8030 0.606241
\(447\) 5.13780 0.243009
\(448\) −3.30669 −0.156226
\(449\) −27.3337 −1.28996 −0.644978 0.764201i \(-0.723134\pi\)
−0.644978 + 0.764201i \(0.723134\pi\)
\(450\) 14.4774 0.682474
\(451\) −20.7787 −0.978429
\(452\) −8.42912 −0.396473
\(453\) −6.05670 −0.284569
\(454\) 22.1849 1.04119
\(455\) 1.36704 0.0640880
\(456\) −0.295377 −0.0138323
\(457\) 28.6036 1.33802 0.669009 0.743254i \(-0.266719\pi\)
0.669009 + 0.743254i \(0.266719\pi\)
\(458\) −1.61219 −0.0753326
\(459\) 1.28750 0.0600953
\(460\) −0.194823 −0.00908366
\(461\) 14.9798 0.697681 0.348841 0.937182i \(-0.386575\pi\)
0.348841 + 0.937182i \(0.386575\pi\)
\(462\) 2.39480 0.111416
\(463\) −32.3245 −1.50225 −0.751123 0.660162i \(-0.770488\pi\)
−0.751123 + 0.660162i \(0.770488\pi\)
\(464\) 3.37680 0.156764
\(465\) 0.113491 0.00526304
\(466\) −22.0222 −1.02016
\(467\) 2.71335 0.125559 0.0627795 0.998027i \(-0.480004\pi\)
0.0627795 + 0.998027i \(0.480004\pi\)
\(468\) 6.99536 0.323360
\(469\) 2.40384 0.110999
\(470\) 1.86694 0.0861154
\(471\) 4.82618 0.222379
\(472\) −2.36963 −0.109071
\(473\) 26.3265 1.21049
\(474\) 1.58091 0.0726137
\(475\) 4.97037 0.228056
\(476\) 2.43766 0.111730
\(477\) −32.2086 −1.47473
\(478\) 22.7925 1.04251
\(479\) 27.1385 1.23999 0.619995 0.784605i \(-0.287134\pi\)
0.619995 + 0.784605i \(0.287134\pi\)
\(480\) 0.0508464 0.00232081
\(481\) −20.4116 −0.930687
\(482\) −3.70087 −0.168570
\(483\) 1.10542 0.0502984
\(484\) −4.98829 −0.226741
\(485\) 1.04587 0.0474905
\(486\) 7.66819 0.347836
\(487\) 38.8091 1.75861 0.879304 0.476260i \(-0.158008\pi\)
0.879304 + 0.476260i \(0.158008\pi\)
\(488\) 7.18189 0.325109
\(489\) 4.79815 0.216980
\(490\) 0.677233 0.0305943
\(491\) −32.8313 −1.48166 −0.740828 0.671694i \(-0.765567\pi\)
−0.740828 + 0.671694i \(0.765567\pi\)
\(492\) 2.50320 0.112853
\(493\) −2.48934 −0.112114
\(494\) 2.40163 0.108054
\(495\) 1.22938 0.0552564
\(496\) 2.23204 0.100222
\(497\) −33.9036 −1.52079
\(498\) 0.610208 0.0273441
\(499\) 9.63830 0.431470 0.215735 0.976452i \(-0.430785\pi\)
0.215735 + 0.976452i \(0.430785\pi\)
\(500\) −1.71630 −0.0767554
\(501\) −0.446266 −0.0199377
\(502\) −23.2800 −1.03904
\(503\) −32.7166 −1.45876 −0.729381 0.684108i \(-0.760192\pi\)
−0.729381 + 0.684108i \(0.760192\pi\)
\(504\) 9.63157 0.429024
\(505\) 1.14998 0.0511733
\(506\) 2.77495 0.123362
\(507\) −2.13622 −0.0948728
\(508\) 6.68152 0.296445
\(509\) 11.7606 0.521278 0.260639 0.965436i \(-0.416067\pi\)
0.260639 + 0.965436i \(0.416067\pi\)
\(510\) −0.0374835 −0.00165980
\(511\) 13.1377 0.581178
\(512\) 1.00000 0.0441942
\(513\) 1.74649 0.0771096
\(514\) 7.83805 0.345721
\(515\) −1.15714 −0.0509897
\(516\) −3.17155 −0.139620
\(517\) −26.5917 −1.16950
\(518\) −28.1037 −1.23481
\(519\) −5.95572 −0.261427
\(520\) −0.413418 −0.0181296
\(521\) −19.6619 −0.861403 −0.430702 0.902494i \(-0.641734\pi\)
−0.430702 + 0.902494i \(0.641734\pi\)
\(522\) −9.83578 −0.430500
\(523\) −42.5510 −1.86062 −0.930312 0.366768i \(-0.880464\pi\)
−0.930312 + 0.366768i \(0.880464\pi\)
\(524\) 4.29041 0.187427
\(525\) 4.85466 0.211875
\(526\) 6.33785 0.276344
\(527\) −1.64544 −0.0716766
\(528\) −0.724229 −0.0315180
\(529\) −21.7191 −0.944309
\(530\) 1.90350 0.0826825
\(531\) 6.90213 0.299527
\(532\) 3.30669 0.143363
\(533\) −20.3528 −0.881580
\(534\) 0.987488 0.0427328
\(535\) −0.192582 −0.00832606
\(536\) −0.726963 −0.0314000
\(537\) −0.810083 −0.0349576
\(538\) 5.60736 0.241751
\(539\) −9.64616 −0.415490
\(540\) −0.300642 −0.0129376
\(541\) 20.8524 0.896516 0.448258 0.893904i \(-0.352045\pi\)
0.448258 + 0.893904i \(0.352045\pi\)
\(542\) 26.3981 1.13390
\(543\) −0.286123 −0.0122787
\(544\) −0.737190 −0.0316068
\(545\) −0.489405 −0.0209638
\(546\) 2.34572 0.100388
\(547\) 22.0066 0.940936 0.470468 0.882417i \(-0.344085\pi\)
0.470468 + 0.882417i \(0.344085\pi\)
\(548\) 16.0219 0.684420
\(549\) −20.9191 −0.892805
\(550\) 12.1867 0.519644
\(551\) −3.37680 −0.143856
\(552\) −0.334298 −0.0142287
\(553\) −17.6980 −0.752594
\(554\) −12.5493 −0.533171
\(555\) 0.432146 0.0183436
\(556\) −12.8331 −0.544243
\(557\) 1.29275 0.0547756 0.0273878 0.999625i \(-0.491281\pi\)
0.0273878 + 0.999625i \(0.491281\pi\)
\(558\) −6.50139 −0.275226
\(559\) 25.7870 1.09067
\(560\) −0.569215 −0.0240537
\(561\) 0.533895 0.0225411
\(562\) 10.8646 0.458295
\(563\) 1.62339 0.0684177 0.0342088 0.999415i \(-0.489109\pi\)
0.0342088 + 0.999415i \(0.489109\pi\)
\(564\) 3.20350 0.134892
\(565\) −1.45099 −0.0610437
\(566\) 7.01506 0.294865
\(567\) −27.1889 −1.14182
\(568\) 10.2530 0.430208
\(569\) 30.4307 1.27572 0.637861 0.770152i \(-0.279820\pi\)
0.637861 + 0.770152i \(0.279820\pi\)
\(570\) −0.0508464 −0.00212972
\(571\) 2.90148 0.121423 0.0607117 0.998155i \(-0.480663\pi\)
0.0607117 + 0.998155i \(0.480663\pi\)
\(572\) 5.88851 0.246211
\(573\) −1.13825 −0.0475509
\(574\) −28.0228 −1.16965
\(575\) 5.62530 0.234591
\(576\) −2.91275 −0.121365
\(577\) −7.52091 −0.313100 −0.156550 0.987670i \(-0.550037\pi\)
−0.156550 + 0.987670i \(0.550037\pi\)
\(578\) −16.4566 −0.684502
\(579\) −1.95398 −0.0812047
\(580\) 0.581283 0.0241365
\(581\) −6.83116 −0.283404
\(582\) 1.79462 0.0743894
\(583\) −27.1124 −1.12288
\(584\) −3.97307 −0.164407
\(585\) 1.20418 0.0497869
\(586\) 17.7179 0.731920
\(587\) −11.8648 −0.489714 −0.244857 0.969559i \(-0.578741\pi\)
−0.244857 + 0.969559i \(0.578741\pi\)
\(588\) 1.16207 0.0479230
\(589\) −2.23204 −0.0919698
\(590\) −0.407908 −0.0167933
\(591\) −1.73190 −0.0712408
\(592\) 8.49904 0.349308
\(593\) 21.2835 0.874008 0.437004 0.899460i \(-0.356040\pi\)
0.437004 + 0.899460i \(0.356040\pi\)
\(594\) 4.28219 0.175700
\(595\) 0.419620 0.0172027
\(596\) 17.3940 0.712486
\(597\) −5.86617 −0.240086
\(598\) 2.71809 0.111151
\(599\) −2.67523 −0.109307 −0.0546534 0.998505i \(-0.517405\pi\)
−0.0546534 + 0.998505i \(0.517405\pi\)
\(600\) −1.46813 −0.0599363
\(601\) 42.1168 1.71798 0.858989 0.511994i \(-0.171093\pi\)
0.858989 + 0.511994i \(0.171093\pi\)
\(602\) 35.5048 1.44707
\(603\) 2.11746 0.0862298
\(604\) −20.5050 −0.834335
\(605\) −0.858687 −0.0349106
\(606\) 1.97326 0.0801580
\(607\) −37.0344 −1.50318 −0.751590 0.659631i \(-0.770713\pi\)
−0.751590 + 0.659631i \(0.770713\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −3.29819 −0.133649
\(610\) 1.23629 0.0500561
\(611\) −26.0467 −1.05374
\(612\) 2.14725 0.0867975
\(613\) −39.7141 −1.60404 −0.802018 0.597300i \(-0.796240\pi\)
−0.802018 + 0.597300i \(0.796240\pi\)
\(614\) −17.9338 −0.723750
\(615\) 0.430902 0.0173757
\(616\) 8.10760 0.326664
\(617\) 32.3712 1.30321 0.651607 0.758557i \(-0.274095\pi\)
0.651607 + 0.758557i \(0.274095\pi\)
\(618\) −1.98555 −0.0798705
\(619\) 43.6604 1.75486 0.877430 0.479705i \(-0.159256\pi\)
0.877430 + 0.479705i \(0.159256\pi\)
\(620\) 0.384225 0.0154308
\(621\) 1.97662 0.0793191
\(622\) −26.3427 −1.05625
\(623\) −11.0547 −0.442898
\(624\) −0.709388 −0.0283982
\(625\) 24.5564 0.982256
\(626\) 11.0123 0.440140
\(627\) 0.724229 0.0289229
\(628\) 16.3390 0.651999
\(629\) −6.26541 −0.249818
\(630\) 1.65798 0.0660556
\(631\) −26.3425 −1.04868 −0.524339 0.851509i \(-0.675688\pi\)
−0.524339 + 0.851509i \(0.675688\pi\)
\(632\) 5.35217 0.212898
\(633\) −0.295377 −0.0117402
\(634\) −0.0614134 −0.00243904
\(635\) 1.15016 0.0456427
\(636\) 3.26623 0.129514
\(637\) −9.44848 −0.374362
\(638\) −8.27950 −0.327788
\(639\) −29.8646 −1.18142
\(640\) 0.172140 0.00680445
\(641\) 33.1176 1.30807 0.654034 0.756465i \(-0.273075\pi\)
0.654034 + 0.756465i \(0.273075\pi\)
\(642\) −0.330454 −0.0130420
\(643\) −9.32860 −0.367884 −0.183942 0.982937i \(-0.558886\pi\)
−0.183942 + 0.982937i \(0.558886\pi\)
\(644\) 3.74240 0.147471
\(645\) −0.545952 −0.0214968
\(646\) 0.737190 0.0290044
\(647\) 8.26257 0.324835 0.162418 0.986722i \(-0.448071\pi\)
0.162418 + 0.986722i \(0.448071\pi\)
\(648\) 8.22238 0.323006
\(649\) 5.81003 0.228064
\(650\) 11.9370 0.468207
\(651\) −2.18009 −0.0854443
\(652\) 16.2441 0.636170
\(653\) 38.8783 1.52142 0.760712 0.649089i \(-0.224850\pi\)
0.760712 + 0.649089i \(0.224850\pi\)
\(654\) −0.839774 −0.0328378
\(655\) 0.738552 0.0288576
\(656\) 8.47459 0.330877
\(657\) 11.5726 0.451489
\(658\) −35.8625 −1.39807
\(659\) −17.2662 −0.672594 −0.336297 0.941756i \(-0.609175\pi\)
−0.336297 + 0.941756i \(0.609175\pi\)
\(660\) −0.124669 −0.00485274
\(661\) 46.5289 1.80977 0.904883 0.425661i \(-0.139958\pi\)
0.904883 + 0.425661i \(0.139958\pi\)
\(662\) −7.06512 −0.274594
\(663\) 0.522954 0.0203098
\(664\) 2.06586 0.0801709
\(665\) 0.569215 0.0220732
\(666\) −24.7556 −0.959260
\(667\) −3.82175 −0.147979
\(668\) −1.51083 −0.0584559
\(669\) 3.78173 0.146210
\(670\) −0.125140 −0.00483457
\(671\) −17.6091 −0.679793
\(672\) −0.976721 −0.0376778
\(673\) 43.8931 1.69195 0.845977 0.533220i \(-0.179018\pi\)
0.845977 + 0.533220i \(0.179018\pi\)
\(674\) −30.0402 −1.15711
\(675\) 8.68071 0.334121
\(676\) −7.23217 −0.278160
\(677\) −4.57794 −0.175944 −0.0879722 0.996123i \(-0.528039\pi\)
−0.0879722 + 0.996123i \(0.528039\pi\)
\(678\) −2.48977 −0.0956191
\(679\) −20.0904 −0.770999
\(680\) −0.126900 −0.00486640
\(681\) 6.55293 0.251109
\(682\) −5.47270 −0.209561
\(683\) 42.0730 1.60988 0.804939 0.593358i \(-0.202198\pi\)
0.804939 + 0.593358i \(0.202198\pi\)
\(684\) 2.91275 0.111372
\(685\) 2.75801 0.105378
\(686\) 10.1377 0.387058
\(687\) −0.476204 −0.0181683
\(688\) −10.7373 −0.409355
\(689\) −26.5568 −1.01173
\(690\) −0.0575462 −0.00219075
\(691\) 20.8317 0.792474 0.396237 0.918148i \(-0.370316\pi\)
0.396237 + 0.918148i \(0.370316\pi\)
\(692\) −20.1631 −0.766485
\(693\) −23.6154 −0.897076
\(694\) 13.2232 0.501945
\(695\) −2.20909 −0.0837955
\(696\) 0.997430 0.0378075
\(697\) −6.24739 −0.236637
\(698\) 21.7286 0.822439
\(699\) −6.50486 −0.246037
\(700\) 16.4355 0.621202
\(701\) 30.5069 1.15223 0.576116 0.817368i \(-0.304568\pi\)
0.576116 + 0.817368i \(0.304568\pi\)
\(702\) 4.19443 0.158309
\(703\) −8.49904 −0.320547
\(704\) −2.45188 −0.0924086
\(705\) 0.551451 0.0207689
\(706\) 5.47856 0.206188
\(707\) −22.0902 −0.830787
\(708\) −0.699934 −0.0263051
\(709\) −8.31447 −0.312257 −0.156128 0.987737i \(-0.549901\pi\)
−0.156128 + 0.987737i \(0.549901\pi\)
\(710\) 1.76496 0.0662379
\(711\) −15.5896 −0.584654
\(712\) 3.34314 0.125289
\(713\) −2.52615 −0.0946052
\(714\) 0.720029 0.0269464
\(715\) 1.01365 0.0379084
\(716\) −2.74253 −0.102493
\(717\) 6.73240 0.251426
\(718\) 28.8807 1.07782
\(719\) 22.4595 0.837598 0.418799 0.908079i \(-0.362451\pi\)
0.418799 + 0.908079i \(0.362451\pi\)
\(720\) −0.501402 −0.0186862
\(721\) 22.2278 0.827806
\(722\) 1.00000 0.0372161
\(723\) −1.09315 −0.0406548
\(724\) −0.968669 −0.0360003
\(725\) −16.7839 −0.623339
\(726\) −1.47343 −0.0546841
\(727\) 5.67953 0.210642 0.105321 0.994438i \(-0.466413\pi\)
0.105321 + 0.994438i \(0.466413\pi\)
\(728\) 7.94145 0.294330
\(729\) −22.4021 −0.829709
\(730\) −0.683926 −0.0253132
\(731\) 7.91542 0.292762
\(732\) 2.12137 0.0784081
\(733\) 26.8685 0.992411 0.496206 0.868205i \(-0.334726\pi\)
0.496206 + 0.868205i \(0.334726\pi\)
\(734\) 28.7707 1.06195
\(735\) 0.200039 0.00737857
\(736\) −1.13177 −0.0417175
\(737\) 1.78243 0.0656565
\(738\) −24.6844 −0.908645
\(739\) −42.7357 −1.57206 −0.786030 0.618189i \(-0.787867\pi\)
−0.786030 + 0.618189i \(0.787867\pi\)
\(740\) 1.46303 0.0537820
\(741\) 0.709388 0.0260600
\(742\) −36.5647 −1.34233
\(743\) −24.6981 −0.906084 −0.453042 0.891489i \(-0.649661\pi\)
−0.453042 + 0.891489i \(0.649661\pi\)
\(744\) 0.659296 0.0241709
\(745\) 2.99421 0.109699
\(746\) −27.5792 −1.00975
\(747\) −6.01734 −0.220163
\(748\) 1.80750 0.0660888
\(749\) 3.69936 0.135172
\(750\) −0.506957 −0.0185115
\(751\) −31.5967 −1.15298 −0.576490 0.817104i \(-0.695578\pi\)
−0.576490 + 0.817104i \(0.695578\pi\)
\(752\) 10.8454 0.395492
\(753\) −6.87638 −0.250589
\(754\) −8.10982 −0.295342
\(755\) −3.52973 −0.128460
\(756\) 5.77511 0.210039
\(757\) 42.4597 1.54322 0.771612 0.636094i \(-0.219451\pi\)
0.771612 + 0.636094i \(0.219451\pi\)
\(758\) 22.5703 0.819791
\(759\) 0.819659 0.0297517
\(760\) −0.172140 −0.00624419
\(761\) −24.8255 −0.899924 −0.449962 0.893048i \(-0.648562\pi\)
−0.449962 + 0.893048i \(0.648562\pi\)
\(762\) 1.97357 0.0714949
\(763\) 9.40110 0.340343
\(764\) −3.85353 −0.139416
\(765\) 0.369629 0.0133640
\(766\) 24.5709 0.887783
\(767\) 5.69097 0.205489
\(768\) 0.295377 0.0106585
\(769\) 50.3009 1.81390 0.906948 0.421243i \(-0.138406\pi\)
0.906948 + 0.421243i \(0.138406\pi\)
\(770\) 1.39565 0.0502956
\(771\) 2.31518 0.0833792
\(772\) −6.61520 −0.238086
\(773\) 9.73526 0.350153 0.175077 0.984555i \(-0.443983\pi\)
0.175077 + 0.984555i \(0.443983\pi\)
\(774\) 31.2750 1.12416
\(775\) −11.0941 −0.398511
\(776\) 6.07568 0.218104
\(777\) −8.30119 −0.297804
\(778\) 17.2012 0.616692
\(779\) −8.47459 −0.303634
\(780\) −0.122114 −0.00437239
\(781\) −25.1392 −0.899552
\(782\) 0.834327 0.0298355
\(783\) −5.89756 −0.210761
\(784\) 3.93419 0.140507
\(785\) 2.81261 0.100386
\(786\) 1.26729 0.0452027
\(787\) −2.85611 −0.101809 −0.0509047 0.998704i \(-0.516210\pi\)
−0.0509047 + 0.998704i \(0.516210\pi\)
\(788\) −5.86335 −0.208873
\(789\) 1.87206 0.0666471
\(790\) 0.921325 0.0327793
\(791\) 27.8725 0.991031
\(792\) 7.14171 0.253770
\(793\) −17.2483 −0.612504
\(794\) 25.7587 0.914140
\(795\) 0.562249 0.0199409
\(796\) −19.8599 −0.703916
\(797\) −37.1655 −1.31647 −0.658235 0.752812i \(-0.728697\pi\)
−0.658235 + 0.752812i \(0.728697\pi\)
\(798\) 0.976721 0.0345756
\(799\) −7.99515 −0.282848
\(800\) −4.97037 −0.175729
\(801\) −9.73774 −0.344066
\(802\) −9.53177 −0.336579
\(803\) 9.74149 0.343770
\(804\) −0.214729 −0.00757289
\(805\) 0.644218 0.0227057
\(806\) −5.36055 −0.188817
\(807\) 1.65629 0.0583041
\(808\) 6.68046 0.235018
\(809\) 44.6198 1.56875 0.784373 0.620289i \(-0.212985\pi\)
0.784373 + 0.620289i \(0.212985\pi\)
\(810\) 1.41540 0.0497322
\(811\) −52.2489 −1.83471 −0.917354 0.398072i \(-0.869680\pi\)
−0.917354 + 0.398072i \(0.869680\pi\)
\(812\) −11.1660 −0.391851
\(813\) 7.79741 0.273467
\(814\) −20.8386 −0.730393
\(815\) 2.79627 0.0979492
\(816\) −0.217749 −0.00762275
\(817\) 10.7373 0.375650
\(818\) −20.5341 −0.717957
\(819\) −23.1315 −0.808279
\(820\) 1.45882 0.0509442
\(821\) 1.09622 0.0382583 0.0191291 0.999817i \(-0.493911\pi\)
0.0191291 + 0.999817i \(0.493911\pi\)
\(822\) 4.73250 0.165065
\(823\) −45.7684 −1.59539 −0.797693 0.603063i \(-0.793947\pi\)
−0.797693 + 0.603063i \(0.793947\pi\)
\(824\) −6.72207 −0.234174
\(825\) 3.59969 0.125325
\(826\) 7.83561 0.272636
\(827\) 25.4957 0.886572 0.443286 0.896380i \(-0.353813\pi\)
0.443286 + 0.896380i \(0.353813\pi\)
\(828\) 3.29656 0.114563
\(829\) 28.5484 0.991528 0.495764 0.868457i \(-0.334888\pi\)
0.495764 + 0.868457i \(0.334888\pi\)
\(830\) 0.355618 0.0123437
\(831\) −3.70679 −0.128587
\(832\) −2.40163 −0.0832616
\(833\) −2.90025 −0.100488
\(834\) −3.79060 −0.131258
\(835\) −0.260076 −0.00900029
\(836\) 2.45188 0.0848000
\(837\) −3.89825 −0.134743
\(838\) −27.3905 −0.946189
\(839\) 57.2754 1.97737 0.988684 0.150015i \(-0.0479323\pi\)
0.988684 + 0.150015i \(0.0479323\pi\)
\(840\) −0.168133 −0.00580115
\(841\) −17.5972 −0.606801
\(842\) −20.3757 −0.702195
\(843\) 3.20915 0.110529
\(844\) −1.00000 −0.0344214
\(845\) −1.24495 −0.0428275
\(846\) −31.5901 −1.08609
\(847\) 16.4947 0.566766
\(848\) 11.0578 0.379727
\(849\) 2.07209 0.0711140
\(850\) 3.66411 0.125678
\(851\) −9.61893 −0.329733
\(852\) 3.02852 0.103755
\(853\) 24.5099 0.839204 0.419602 0.907708i \(-0.362170\pi\)
0.419602 + 0.907708i \(0.362170\pi\)
\(854\) −23.7483 −0.812650
\(855\) 0.501402 0.0171476
\(856\) −1.11875 −0.0382381
\(857\) 54.1694 1.85039 0.925196 0.379490i \(-0.123900\pi\)
0.925196 + 0.379490i \(0.123900\pi\)
\(858\) 1.73933 0.0593798
\(859\) 23.5060 0.802013 0.401006 0.916075i \(-0.368660\pi\)
0.401006 + 0.916075i \(0.368660\pi\)
\(860\) −1.84832 −0.0630272
\(861\) −8.27731 −0.282090
\(862\) 5.25951 0.179140
\(863\) −34.1086 −1.16107 −0.580534 0.814236i \(-0.697156\pi\)
−0.580534 + 0.814236i \(0.697156\pi\)
\(864\) −1.74649 −0.0594169
\(865\) −3.47088 −0.118014
\(866\) 34.9253 1.18681
\(867\) −4.86089 −0.165085
\(868\) −7.38068 −0.250516
\(869\) −13.1229 −0.445163
\(870\) 0.171698 0.00582111
\(871\) 1.74590 0.0591575
\(872\) −2.84306 −0.0962780
\(873\) −17.6970 −0.598951
\(874\) 1.13177 0.0382826
\(875\) 5.67528 0.191859
\(876\) −1.17356 −0.0396508
\(877\) −39.6840 −1.34003 −0.670016 0.742346i \(-0.733713\pi\)
−0.670016 + 0.742346i \(0.733713\pi\)
\(878\) −14.4547 −0.487823
\(879\) 5.23347 0.176521
\(880\) −0.422067 −0.0142279
\(881\) −5.91419 −0.199254 −0.0996270 0.995025i \(-0.531765\pi\)
−0.0996270 + 0.995025i \(0.531765\pi\)
\(882\) −11.4593 −0.385856
\(883\) 52.2003 1.75668 0.878340 0.478036i \(-0.158651\pi\)
0.878340 + 0.478036i \(0.158651\pi\)
\(884\) 1.77046 0.0595470
\(885\) −0.120487 −0.00405012
\(886\) 1.17908 0.0396121
\(887\) 37.9827 1.27533 0.637667 0.770312i \(-0.279900\pi\)
0.637667 + 0.770312i \(0.279900\pi\)
\(888\) 2.51042 0.0842443
\(889\) −22.0937 −0.741000
\(890\) 0.575489 0.0192904
\(891\) −20.1603 −0.675395
\(892\) 12.8030 0.428677
\(893\) −10.8454 −0.362929
\(894\) 5.13780 0.171834
\(895\) −0.472101 −0.0157806
\(896\) −3.30669 −0.110469
\(897\) 0.802861 0.0268068
\(898\) −27.3337 −0.912137
\(899\) 7.53716 0.251378
\(900\) 14.4774 0.482582
\(901\) −8.15171 −0.271573
\(902\) −20.7787 −0.691854
\(903\) 10.4873 0.348996
\(904\) −8.42912 −0.280348
\(905\) −0.166747 −0.00554286
\(906\) −6.05670 −0.201220
\(907\) −10.9524 −0.363667 −0.181833 0.983329i \(-0.558203\pi\)
−0.181833 + 0.983329i \(0.558203\pi\)
\(908\) 22.1849 0.736233
\(909\) −19.4585 −0.645398
\(910\) 1.36704 0.0453171
\(911\) 18.1890 0.602629 0.301314 0.953525i \(-0.402575\pi\)
0.301314 + 0.953525i \(0.402575\pi\)
\(912\) −0.295377 −0.00978092
\(913\) −5.06524 −0.167635
\(914\) 28.6036 0.946122
\(915\) 0.365173 0.0120723
\(916\) −1.61219 −0.0532682
\(917\) −14.1870 −0.468497
\(918\) 1.28750 0.0424938
\(919\) 25.0964 0.827855 0.413927 0.910310i \(-0.364157\pi\)
0.413927 + 0.910310i \(0.364157\pi\)
\(920\) −0.194823 −0.00642312
\(921\) −5.29725 −0.174550
\(922\) 14.9798 0.493335
\(923\) −24.6240 −0.810510
\(924\) 2.39480 0.0787832
\(925\) −42.2434 −1.38895
\(926\) −32.3245 −1.06225
\(927\) 19.5797 0.643083
\(928\) 3.37680 0.110849
\(929\) 29.3290 0.962255 0.481127 0.876651i \(-0.340227\pi\)
0.481127 + 0.876651i \(0.340227\pi\)
\(930\) 0.113491 0.00372153
\(931\) −3.93419 −0.128938
\(932\) −22.0222 −0.721361
\(933\) −7.78103 −0.254740
\(934\) 2.71335 0.0887837
\(935\) 0.311144 0.0101755
\(936\) 6.99536 0.228650
\(937\) −33.4242 −1.09192 −0.545961 0.837811i \(-0.683835\pi\)
−0.545961 + 0.837811i \(0.683835\pi\)
\(938\) 2.40384 0.0784882
\(939\) 3.25279 0.106151
\(940\) 1.86694 0.0608928
\(941\) −7.23354 −0.235807 −0.117903 0.993025i \(-0.537617\pi\)
−0.117903 + 0.993025i \(0.537617\pi\)
\(942\) 4.82618 0.157246
\(943\) −9.59126 −0.312334
\(944\) −2.36963 −0.0771247
\(945\) 0.994130 0.0323390
\(946\) 26.3265 0.855948
\(947\) 6.88631 0.223775 0.111887 0.993721i \(-0.464310\pi\)
0.111887 + 0.993721i \(0.464310\pi\)
\(948\) 1.58091 0.0513456
\(949\) 9.54185 0.309742
\(950\) 4.97037 0.161260
\(951\) −0.0181401 −0.000588234 0
\(952\) 2.43766 0.0790050
\(953\) 29.2317 0.946908 0.473454 0.880819i \(-0.343007\pi\)
0.473454 + 0.880819i \(0.343007\pi\)
\(954\) −32.2086 −1.04279
\(955\) −0.663348 −0.0214654
\(956\) 22.7925 0.737163
\(957\) −2.44558 −0.0790543
\(958\) 27.1385 0.876806
\(959\) −52.9793 −1.71079
\(960\) 0.0508464 0.00164106
\(961\) −26.0180 −0.839290
\(962\) −20.4116 −0.658095
\(963\) 3.25864 0.105008
\(964\) −3.70087 −0.119197
\(965\) −1.13874 −0.0366575
\(966\) 1.10542 0.0355663
\(967\) −23.8692 −0.767582 −0.383791 0.923420i \(-0.625382\pi\)
−0.383791 + 0.923420i \(0.625382\pi\)
\(968\) −4.98829 −0.160330
\(969\) 0.217749 0.00699512
\(970\) 1.04587 0.0335809
\(971\) −12.9613 −0.415947 −0.207973 0.978134i \(-0.566687\pi\)
−0.207973 + 0.978134i \(0.566687\pi\)
\(972\) 7.66819 0.245957
\(973\) 42.4349 1.36040
\(974\) 38.8091 1.24352
\(975\) 3.52592 0.112920
\(976\) 7.18189 0.229887
\(977\) 2.20374 0.0705037 0.0352519 0.999378i \(-0.488777\pi\)
0.0352519 + 0.999378i \(0.488777\pi\)
\(978\) 4.79815 0.153428
\(979\) −8.19697 −0.261976
\(980\) 0.677233 0.0216334
\(981\) 8.28112 0.264396
\(982\) −32.8313 −1.04769
\(983\) −37.5214 −1.19675 −0.598374 0.801217i \(-0.704186\pi\)
−0.598374 + 0.801217i \(0.704186\pi\)
\(984\) 2.50320 0.0797992
\(985\) −1.00932 −0.0321596
\(986\) −2.48934 −0.0792768
\(987\) −10.5930 −0.337178
\(988\) 2.40163 0.0764061
\(989\) 12.1521 0.386414
\(990\) 1.22938 0.0390722
\(991\) 44.7112 1.42030 0.710149 0.704052i \(-0.248628\pi\)
0.710149 + 0.704052i \(0.248628\pi\)
\(992\) 2.23204 0.0708675
\(993\) −2.08688 −0.0662250
\(994\) −33.9036 −1.07536
\(995\) −3.41869 −0.108380
\(996\) 0.610208 0.0193352
\(997\) −2.87454 −0.0910377 −0.0455189 0.998963i \(-0.514494\pi\)
−0.0455189 + 0.998963i \(0.514494\pi\)
\(998\) 9.63830 0.305095
\(999\) −14.8435 −0.469628
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 8018.2.a.j.1.23 47
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8018.2.a.j.1.23 47 1.1 even 1 trivial