Properties

Label 6002.2.a.d.1.6
Level $6002$
Weight $2$
Character 6002.1
Self dual yes
Analytic conductor $47.926$
Analytic rank $0$
Dimension $79$
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] = [6002,2,Mod(1,6002)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6002, 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("6002.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6002 = 2 \cdot 3001 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6002.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: \(47.9262112932\)
Analytic rank: \(0\)
Dimension: \(79\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) \(=\) 6002.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.95638 q^{3} +1.00000 q^{4} -0.704147 q^{5} -2.95638 q^{6} -0.285333 q^{7} +1.00000 q^{8} +5.74016 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.95638 q^{3} +1.00000 q^{4} -0.704147 q^{5} -2.95638 q^{6} -0.285333 q^{7} +1.00000 q^{8} +5.74016 q^{9} -0.704147 q^{10} +2.13212 q^{11} -2.95638 q^{12} -0.824474 q^{13} -0.285333 q^{14} +2.08172 q^{15} +1.00000 q^{16} +3.07908 q^{17} +5.74016 q^{18} -3.85577 q^{19} -0.704147 q^{20} +0.843551 q^{21} +2.13212 q^{22} +6.98769 q^{23} -2.95638 q^{24} -4.50418 q^{25} -0.824474 q^{26} -8.10096 q^{27} -0.285333 q^{28} +9.72258 q^{29} +2.08172 q^{30} -1.99726 q^{31} +1.00000 q^{32} -6.30336 q^{33} +3.07908 q^{34} +0.200916 q^{35} +5.74016 q^{36} +2.22155 q^{37} -3.85577 q^{38} +2.43746 q^{39} -0.704147 q^{40} -0.562653 q^{41} +0.843551 q^{42} -7.45494 q^{43} +2.13212 q^{44} -4.04192 q^{45} +6.98769 q^{46} +2.16566 q^{47} -2.95638 q^{48} -6.91859 q^{49} -4.50418 q^{50} -9.10292 q^{51} -0.824474 q^{52} -3.81629 q^{53} -8.10096 q^{54} -1.50133 q^{55} -0.285333 q^{56} +11.3991 q^{57} +9.72258 q^{58} +1.74958 q^{59} +2.08172 q^{60} +9.87230 q^{61} -1.99726 q^{62} -1.63786 q^{63} +1.00000 q^{64} +0.580551 q^{65} -6.30336 q^{66} -3.32261 q^{67} +3.07908 q^{68} -20.6582 q^{69} +0.200916 q^{70} -9.11043 q^{71} +5.74016 q^{72} -3.56037 q^{73} +2.22155 q^{74} +13.3160 q^{75} -3.85577 q^{76} -0.608365 q^{77} +2.43746 q^{78} +5.23132 q^{79} -0.704147 q^{80} +6.72900 q^{81} -0.562653 q^{82} +10.1482 q^{83} +0.843551 q^{84} -2.16813 q^{85} -7.45494 q^{86} -28.7436 q^{87} +2.13212 q^{88} +1.32183 q^{89} -4.04192 q^{90} +0.235249 q^{91} +6.98769 q^{92} +5.90464 q^{93} +2.16566 q^{94} +2.71503 q^{95} -2.95638 q^{96} -5.88876 q^{97} -6.91859 q^{98} +12.2387 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9} + 18 q^{10} + 28 q^{11} + 17 q^{12} + 47 q^{13} + 19 q^{14} + 14 q^{15} + 79 q^{16} + 36 q^{17} + 118 q^{18} + 29 q^{19} + 18 q^{20} + 45 q^{21} + 28 q^{22} + 23 q^{23} + 17 q^{24} + 161 q^{25} + 47 q^{26} + 50 q^{27} + 19 q^{28} + 53 q^{29} + 14 q^{30} + 29 q^{31} + 79 q^{32} + 34 q^{33} + 36 q^{34} + 33 q^{35} + 118 q^{36} + 89 q^{37} + 29 q^{38} - 7 q^{39} + 18 q^{40} + 58 q^{41} + 45 q^{42} + 88 q^{43} + 28 q^{44} + 45 q^{45} + 23 q^{46} + 3 q^{47} + 17 q^{48} + 162 q^{49} + 161 q^{50} + 29 q^{51} + 47 q^{52} + 88 q^{53} + 50 q^{54} + 37 q^{55} + 19 q^{56} + 54 q^{57} + 53 q^{58} + 37 q^{59} + 14 q^{60} + 55 q^{61} + 29 q^{62} + 21 q^{63} + 79 q^{64} + 55 q^{65} + 34 q^{66} + 107 q^{67} + 36 q^{68} + 39 q^{69} + 33 q^{70} - 5 q^{71} + 118 q^{72} + 71 q^{73} + 89 q^{74} + 37 q^{75} + 29 q^{76} + 61 q^{77} - 7 q^{78} + 29 q^{79} + 18 q^{80} + 215 q^{81} + 58 q^{82} + 42 q^{83} + 45 q^{84} + 84 q^{85} + 88 q^{86} + 15 q^{87} + 28 q^{88} + 72 q^{89} + 45 q^{90} + 70 q^{91} + 23 q^{92} + 97 q^{93} + 3 q^{94} - 18 q^{95} + 17 q^{96} + 93 q^{97} + 162 q^{98} + 49 q^{99}+O(q^{100}) \) 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
\(3\) −2.95638 −1.70687 −0.853433 0.521203i \(-0.825483\pi\)
−0.853433 + 0.521203i \(0.825483\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.704147 −0.314904 −0.157452 0.987527i \(-0.550328\pi\)
−0.157452 + 0.987527i \(0.550328\pi\)
\(6\) −2.95638 −1.20694
\(7\) −0.285333 −0.107846 −0.0539228 0.998545i \(-0.517172\pi\)
−0.0539228 + 0.998545i \(0.517172\pi\)
\(8\) 1.00000 0.353553
\(9\) 5.74016 1.91339
\(10\) −0.704147 −0.222671
\(11\) 2.13212 0.642860 0.321430 0.946933i \(-0.395837\pi\)
0.321430 + 0.946933i \(0.395837\pi\)
\(12\) −2.95638 −0.853433
\(13\) −0.824474 −0.228668 −0.114334 0.993442i \(-0.536473\pi\)
−0.114334 + 0.993442i \(0.536473\pi\)
\(14\) −0.285333 −0.0762584
\(15\) 2.08172 0.537499
\(16\) 1.00000 0.250000
\(17\) 3.07908 0.746787 0.373393 0.927673i \(-0.378194\pi\)
0.373393 + 0.927673i \(0.378194\pi\)
\(18\) 5.74016 1.35297
\(19\) −3.85577 −0.884574 −0.442287 0.896874i \(-0.645833\pi\)
−0.442287 + 0.896874i \(0.645833\pi\)
\(20\) −0.704147 −0.157452
\(21\) 0.843551 0.184078
\(22\) 2.13212 0.454570
\(23\) 6.98769 1.45703 0.728517 0.685028i \(-0.240210\pi\)
0.728517 + 0.685028i \(0.240210\pi\)
\(24\) −2.95638 −0.603468
\(25\) −4.50418 −0.900835
\(26\) −0.824474 −0.161693
\(27\) −8.10096 −1.55903
\(28\) −0.285333 −0.0539228
\(29\) 9.72258 1.80544 0.902719 0.430230i \(-0.141568\pi\)
0.902719 + 0.430230i \(0.141568\pi\)
\(30\) 2.08172 0.380069
\(31\) −1.99726 −0.358718 −0.179359 0.983784i \(-0.557402\pi\)
−0.179359 + 0.983784i \(0.557402\pi\)
\(32\) 1.00000 0.176777
\(33\) −6.30336 −1.09727
\(34\) 3.07908 0.528058
\(35\) 0.200916 0.0339610
\(36\) 5.74016 0.956694
\(37\) 2.22155 0.365221 0.182611 0.983185i \(-0.441545\pi\)
0.182611 + 0.983185i \(0.441545\pi\)
\(38\) −3.85577 −0.625488
\(39\) 2.43746 0.390305
\(40\) −0.704147 −0.111335
\(41\) −0.562653 −0.0878716 −0.0439358 0.999034i \(-0.513990\pi\)
−0.0439358 + 0.999034i \(0.513990\pi\)
\(42\) 0.843551 0.130163
\(43\) −7.45494 −1.13687 −0.568434 0.822729i \(-0.692451\pi\)
−0.568434 + 0.822729i \(0.692451\pi\)
\(44\) 2.13212 0.321430
\(45\) −4.04192 −0.602534
\(46\) 6.98769 1.03028
\(47\) 2.16566 0.315894 0.157947 0.987448i \(-0.449512\pi\)
0.157947 + 0.987448i \(0.449512\pi\)
\(48\) −2.95638 −0.426716
\(49\) −6.91859 −0.988369
\(50\) −4.50418 −0.636987
\(51\) −9.10292 −1.27466
\(52\) −0.824474 −0.114334
\(53\) −3.81629 −0.524208 −0.262104 0.965040i \(-0.584416\pi\)
−0.262104 + 0.965040i \(0.584416\pi\)
\(54\) −8.10096 −1.10240
\(55\) −1.50133 −0.202439
\(56\) −0.285333 −0.0381292
\(57\) 11.3991 1.50985
\(58\) 9.72258 1.27664
\(59\) 1.74958 0.227776 0.113888 0.993494i \(-0.463669\pi\)
0.113888 + 0.993494i \(0.463669\pi\)
\(60\) 2.08172 0.268749
\(61\) 9.87230 1.26402 0.632009 0.774961i \(-0.282230\pi\)
0.632009 + 0.774961i \(0.282230\pi\)
\(62\) −1.99726 −0.253652
\(63\) −1.63786 −0.206351
\(64\) 1.00000 0.125000
\(65\) 0.580551 0.0720085
\(66\) −6.30336 −0.775890
\(67\) −3.32261 −0.405921 −0.202961 0.979187i \(-0.565056\pi\)
−0.202961 + 0.979187i \(0.565056\pi\)
\(68\) 3.07908 0.373393
\(69\) −20.6582 −2.48696
\(70\) 0.200916 0.0240141
\(71\) −9.11043 −1.08121 −0.540604 0.841277i \(-0.681804\pi\)
−0.540604 + 0.841277i \(0.681804\pi\)
\(72\) 5.74016 0.676485
\(73\) −3.56037 −0.416710 −0.208355 0.978053i \(-0.566811\pi\)
−0.208355 + 0.978053i \(0.566811\pi\)
\(74\) 2.22155 0.258250
\(75\) 13.3160 1.53760
\(76\) −3.85577 −0.442287
\(77\) −0.608365 −0.0693296
\(78\) 2.43746 0.275988
\(79\) 5.23132 0.588570 0.294285 0.955718i \(-0.404919\pi\)
0.294285 + 0.955718i \(0.404919\pi\)
\(80\) −0.704147 −0.0787260
\(81\) 6.72900 0.747666
\(82\) −0.562653 −0.0621346
\(83\) 10.1482 1.11391 0.556955 0.830543i \(-0.311970\pi\)
0.556955 + 0.830543i \(0.311970\pi\)
\(84\) 0.843551 0.0920389
\(85\) −2.16813 −0.235166
\(86\) −7.45494 −0.803887
\(87\) −28.7436 −3.08164
\(88\) 2.13212 0.227285
\(89\) 1.32183 0.140114 0.0700570 0.997543i \(-0.477682\pi\)
0.0700570 + 0.997543i \(0.477682\pi\)
\(90\) −4.04192 −0.426056
\(91\) 0.235249 0.0246608
\(92\) 6.98769 0.728517
\(93\) 5.90464 0.612283
\(94\) 2.16566 0.223371
\(95\) 2.71503 0.278556
\(96\) −2.95638 −0.301734
\(97\) −5.88876 −0.597913 −0.298956 0.954267i \(-0.596638\pi\)
−0.298956 + 0.954267i \(0.596638\pi\)
\(98\) −6.91859 −0.698883
\(99\) 12.2387 1.23004
\(100\) −4.50418 −0.450418
\(101\) 3.20302 0.318713 0.159356 0.987221i \(-0.449058\pi\)
0.159356 + 0.987221i \(0.449058\pi\)
\(102\) −9.10292 −0.901324
\(103\) −5.94076 −0.585360 −0.292680 0.956210i \(-0.594547\pi\)
−0.292680 + 0.956210i \(0.594547\pi\)
\(104\) −0.824474 −0.0808463
\(105\) −0.593984 −0.0579669
\(106\) −3.81629 −0.370671
\(107\) 0.282513 0.0273116 0.0136558 0.999907i \(-0.495653\pi\)
0.0136558 + 0.999907i \(0.495653\pi\)
\(108\) −8.10096 −0.779515
\(109\) 9.55550 0.915251 0.457626 0.889145i \(-0.348700\pi\)
0.457626 + 0.889145i \(0.348700\pi\)
\(110\) −1.50133 −0.143146
\(111\) −6.56775 −0.623383
\(112\) −0.285333 −0.0269614
\(113\) 2.37643 0.223555 0.111778 0.993733i \(-0.464346\pi\)
0.111778 + 0.993733i \(0.464346\pi\)
\(114\) 11.3991 1.06762
\(115\) −4.92036 −0.458826
\(116\) 9.72258 0.902719
\(117\) −4.73262 −0.437531
\(118\) 1.74958 0.161062
\(119\) −0.878562 −0.0805377
\(120\) 2.08172 0.190035
\(121\) −6.45404 −0.586731
\(122\) 9.87230 0.893796
\(123\) 1.66341 0.149985
\(124\) −1.99726 −0.179359
\(125\) 6.69234 0.598581
\(126\) −1.63786 −0.145912
\(127\) 12.2521 1.08720 0.543600 0.839344i \(-0.317061\pi\)
0.543600 + 0.839344i \(0.317061\pi\)
\(128\) 1.00000 0.0883883
\(129\) 22.0396 1.94048
\(130\) 0.580551 0.0509177
\(131\) 0.754565 0.0659266 0.0329633 0.999457i \(-0.489506\pi\)
0.0329633 + 0.999457i \(0.489506\pi\)
\(132\) −6.30336 −0.548637
\(133\) 1.10018 0.0953974
\(134\) −3.32261 −0.287030
\(135\) 5.70427 0.490945
\(136\) 3.07908 0.264029
\(137\) 19.2410 1.64387 0.821936 0.569580i \(-0.192894\pi\)
0.821936 + 0.569580i \(0.192894\pi\)
\(138\) −20.6582 −1.75855
\(139\) −16.0240 −1.35914 −0.679569 0.733612i \(-0.737833\pi\)
−0.679569 + 0.733612i \(0.737833\pi\)
\(140\) 0.200916 0.0169805
\(141\) −6.40251 −0.539189
\(142\) −9.11043 −0.764530
\(143\) −1.75788 −0.147001
\(144\) 5.74016 0.478347
\(145\) −6.84613 −0.568540
\(146\) −3.56037 −0.294658
\(147\) 20.4539 1.68701
\(148\) 2.22155 0.182611
\(149\) 7.14519 0.585357 0.292678 0.956211i \(-0.405453\pi\)
0.292678 + 0.956211i \(0.405453\pi\)
\(150\) 13.3160 1.08725
\(151\) −20.0088 −1.62829 −0.814145 0.580662i \(-0.802794\pi\)
−0.814145 + 0.580662i \(0.802794\pi\)
\(152\) −3.85577 −0.312744
\(153\) 17.6744 1.42889
\(154\) −0.608365 −0.0490234
\(155\) 1.40636 0.112962
\(156\) 2.43746 0.195153
\(157\) 13.1473 1.04926 0.524632 0.851329i \(-0.324203\pi\)
0.524632 + 0.851329i \(0.324203\pi\)
\(158\) 5.23132 0.416182
\(159\) 11.2824 0.894752
\(160\) −0.704147 −0.0556677
\(161\) −1.99382 −0.157135
\(162\) 6.72900 0.528680
\(163\) 7.81901 0.612432 0.306216 0.951962i \(-0.400937\pi\)
0.306216 + 0.951962i \(0.400937\pi\)
\(164\) −0.562653 −0.0439358
\(165\) 4.43850 0.345536
\(166\) 10.1482 0.787653
\(167\) −1.89276 −0.146466 −0.0732332 0.997315i \(-0.523332\pi\)
−0.0732332 + 0.997315i \(0.523332\pi\)
\(168\) 0.843551 0.0650814
\(169\) −12.3202 −0.947711
\(170\) −2.16813 −0.166288
\(171\) −22.1328 −1.69253
\(172\) −7.45494 −0.568434
\(173\) −2.02229 −0.153752 −0.0768760 0.997041i \(-0.524495\pi\)
−0.0768760 + 0.997041i \(0.524495\pi\)
\(174\) −28.7436 −2.17905
\(175\) 1.28519 0.0971511
\(176\) 2.13212 0.160715
\(177\) −5.17242 −0.388783
\(178\) 1.32183 0.0990756
\(179\) −12.0044 −0.897249 −0.448624 0.893720i \(-0.648086\pi\)
−0.448624 + 0.893720i \(0.648086\pi\)
\(180\) −4.04192 −0.301267
\(181\) 4.31112 0.320443 0.160221 0.987081i \(-0.448779\pi\)
0.160221 + 0.987081i \(0.448779\pi\)
\(182\) 0.235249 0.0174378
\(183\) −29.1862 −2.15751
\(184\) 6.98769 0.515139
\(185\) −1.56430 −0.115010
\(186\) 5.90464 0.432949
\(187\) 6.56498 0.480079
\(188\) 2.16566 0.157947
\(189\) 2.31147 0.168135
\(190\) 2.71503 0.196969
\(191\) 24.4644 1.77018 0.885092 0.465416i \(-0.154095\pi\)
0.885092 + 0.465416i \(0.154095\pi\)
\(192\) −2.95638 −0.213358
\(193\) 16.1289 1.16098 0.580491 0.814267i \(-0.302861\pi\)
0.580491 + 0.814267i \(0.302861\pi\)
\(194\) −5.88876 −0.422788
\(195\) −1.71633 −0.122909
\(196\) −6.91859 −0.494185
\(197\) 26.6450 1.89838 0.949191 0.314702i \(-0.101905\pi\)
0.949191 + 0.314702i \(0.101905\pi\)
\(198\) 12.2387 0.869770
\(199\) −8.63087 −0.611826 −0.305913 0.952059i \(-0.598962\pi\)
−0.305913 + 0.952059i \(0.598962\pi\)
\(200\) −4.50418 −0.318493
\(201\) 9.82289 0.692853
\(202\) 3.20302 0.225364
\(203\) −2.77417 −0.194709
\(204\) −9.10292 −0.637332
\(205\) 0.396190 0.0276711
\(206\) −5.94076 −0.413912
\(207\) 40.1105 2.78787
\(208\) −0.824474 −0.0571670
\(209\) −8.22098 −0.568657
\(210\) −0.593984 −0.0409888
\(211\) 28.0721 1.93256 0.966282 0.257486i \(-0.0828942\pi\)
0.966282 + 0.257486i \(0.0828942\pi\)
\(212\) −3.81629 −0.262104
\(213\) 26.9339 1.84548
\(214\) 0.282513 0.0193122
\(215\) 5.24938 0.358005
\(216\) −8.10096 −0.551201
\(217\) 0.569882 0.0386861
\(218\) 9.55550 0.647180
\(219\) 10.5258 0.711267
\(220\) −1.50133 −0.101220
\(221\) −2.53862 −0.170766
\(222\) −6.56775 −0.440799
\(223\) −26.0000 −1.74109 −0.870543 0.492093i \(-0.836232\pi\)
−0.870543 + 0.492093i \(0.836232\pi\)
\(224\) −0.285333 −0.0190646
\(225\) −25.8547 −1.72365
\(226\) 2.37643 0.158077
\(227\) 19.7096 1.30817 0.654084 0.756422i \(-0.273054\pi\)
0.654084 + 0.756422i \(0.273054\pi\)
\(228\) 11.3991 0.754924
\(229\) 4.04796 0.267497 0.133748 0.991015i \(-0.457299\pi\)
0.133748 + 0.991015i \(0.457299\pi\)
\(230\) −4.92036 −0.324439
\(231\) 1.79856 0.118336
\(232\) 9.72258 0.638319
\(233\) 30.1140 1.97283 0.986417 0.164259i \(-0.0525232\pi\)
0.986417 + 0.164259i \(0.0525232\pi\)
\(234\) −4.73262 −0.309381
\(235\) −1.52494 −0.0994764
\(236\) 1.74958 0.113888
\(237\) −15.4658 −1.00461
\(238\) −0.878562 −0.0569487
\(239\) 16.1795 1.04657 0.523284 0.852158i \(-0.324707\pi\)
0.523284 + 0.852158i \(0.324707\pi\)
\(240\) 2.08172 0.134375
\(241\) −28.0150 −1.80460 −0.902301 0.431106i \(-0.858123\pi\)
−0.902301 + 0.431106i \(0.858123\pi\)
\(242\) −6.45404 −0.414882
\(243\) 4.40943 0.282865
\(244\) 9.87230 0.632009
\(245\) 4.87170 0.311242
\(246\) 1.66341 0.106055
\(247\) 3.17898 0.202274
\(248\) −1.99726 −0.126826
\(249\) −30.0019 −1.90129
\(250\) 6.69234 0.423261
\(251\) −15.5728 −0.982943 −0.491472 0.870894i \(-0.663541\pi\)
−0.491472 + 0.870894i \(0.663541\pi\)
\(252\) −1.63786 −0.103175
\(253\) 14.8986 0.936669
\(254\) 12.2521 0.768767
\(255\) 6.40980 0.401397
\(256\) 1.00000 0.0625000
\(257\) 29.3394 1.83014 0.915072 0.403290i \(-0.132134\pi\)
0.915072 + 0.403290i \(0.132134\pi\)
\(258\) 22.0396 1.37213
\(259\) −0.633882 −0.0393875
\(260\) 0.580551 0.0360042
\(261\) 55.8092 3.45450
\(262\) 0.754565 0.0466172
\(263\) −7.17445 −0.442396 −0.221198 0.975229i \(-0.570997\pi\)
−0.221198 + 0.975229i \(0.570997\pi\)
\(264\) −6.30336 −0.387945
\(265\) 2.68723 0.165075
\(266\) 1.10018 0.0674562
\(267\) −3.90784 −0.239156
\(268\) −3.32261 −0.202961
\(269\) 11.3203 0.690213 0.345107 0.938564i \(-0.387843\pi\)
0.345107 + 0.938564i \(0.387843\pi\)
\(270\) 5.70427 0.347151
\(271\) −19.7521 −1.19985 −0.599927 0.800055i \(-0.704804\pi\)
−0.599927 + 0.800055i \(0.704804\pi\)
\(272\) 3.07908 0.186697
\(273\) −0.695486 −0.0420927
\(274\) 19.2410 1.16239
\(275\) −9.60347 −0.579111
\(276\) −20.6582 −1.24348
\(277\) 19.7273 1.18530 0.592649 0.805461i \(-0.298082\pi\)
0.592649 + 0.805461i \(0.298082\pi\)
\(278\) −16.0240 −0.961055
\(279\) −11.4646 −0.686366
\(280\) 0.200916 0.0120070
\(281\) 10.7098 0.638892 0.319446 0.947604i \(-0.396503\pi\)
0.319446 + 0.947604i \(0.396503\pi\)
\(282\) −6.40251 −0.381264
\(283\) −5.28438 −0.314124 −0.157062 0.987589i \(-0.550202\pi\)
−0.157062 + 0.987589i \(0.550202\pi\)
\(284\) −9.11043 −0.540604
\(285\) −8.02665 −0.475458
\(286\) −1.75788 −0.103946
\(287\) 0.160543 0.00947657
\(288\) 5.74016 0.338242
\(289\) −7.51927 −0.442310
\(290\) −6.84613 −0.402019
\(291\) 17.4094 1.02056
\(292\) −3.56037 −0.208355
\(293\) 31.5082 1.84073 0.920364 0.391063i \(-0.127893\pi\)
0.920364 + 0.391063i \(0.127893\pi\)
\(294\) 20.4539 1.19290
\(295\) −1.23196 −0.0717277
\(296\) 2.22155 0.129125
\(297\) −17.2723 −1.00224
\(298\) 7.14519 0.413910
\(299\) −5.76117 −0.333177
\(300\) 13.3160 0.768802
\(301\) 2.12714 0.122606
\(302\) −20.0088 −1.15137
\(303\) −9.46935 −0.544000
\(304\) −3.85577 −0.221144
\(305\) −6.95155 −0.398045
\(306\) 17.6744 1.01038
\(307\) 12.6660 0.722889 0.361444 0.932394i \(-0.382284\pi\)
0.361444 + 0.932394i \(0.382284\pi\)
\(308\) −0.608365 −0.0346648
\(309\) 17.5631 0.999131
\(310\) 1.40636 0.0798760
\(311\) 25.2909 1.43412 0.717058 0.697013i \(-0.245488\pi\)
0.717058 + 0.697013i \(0.245488\pi\)
\(312\) 2.43746 0.137994
\(313\) −2.81859 −0.159316 −0.0796582 0.996822i \(-0.525383\pi\)
−0.0796582 + 0.996822i \(0.525383\pi\)
\(314\) 13.1473 0.741942
\(315\) 1.15329 0.0649806
\(316\) 5.23132 0.294285
\(317\) −9.50407 −0.533802 −0.266901 0.963724i \(-0.586000\pi\)
−0.266901 + 0.963724i \(0.586000\pi\)
\(318\) 11.2824 0.632685
\(319\) 20.7298 1.16064
\(320\) −0.704147 −0.0393630
\(321\) −0.835216 −0.0466172
\(322\) −1.99382 −0.111111
\(323\) −11.8722 −0.660588
\(324\) 6.72900 0.373833
\(325\) 3.71358 0.205992
\(326\) 7.81901 0.433055
\(327\) −28.2497 −1.56221
\(328\) −0.562653 −0.0310673
\(329\) −0.617934 −0.0340678
\(330\) 4.43850 0.244331
\(331\) 19.0048 1.04460 0.522298 0.852763i \(-0.325075\pi\)
0.522298 + 0.852763i \(0.325075\pi\)
\(332\) 10.1482 0.556955
\(333\) 12.7521 0.698810
\(334\) −1.89276 −0.103567
\(335\) 2.33961 0.127826
\(336\) 0.843551 0.0460195
\(337\) −9.92416 −0.540604 −0.270302 0.962776i \(-0.587123\pi\)
−0.270302 + 0.962776i \(0.587123\pi\)
\(338\) −12.3202 −0.670133
\(339\) −7.02561 −0.381579
\(340\) −2.16813 −0.117583
\(341\) −4.25840 −0.230605
\(342\) −22.1328 −1.19680
\(343\) 3.97143 0.214437
\(344\) −7.45494 −0.401944
\(345\) 14.5464 0.783154
\(346\) −2.02229 −0.108719
\(347\) −12.7437 −0.684116 −0.342058 0.939679i \(-0.611124\pi\)
−0.342058 + 0.939679i \(0.611124\pi\)
\(348\) −28.7436 −1.54082
\(349\) −12.7200 −0.680886 −0.340443 0.940265i \(-0.610577\pi\)
−0.340443 + 0.940265i \(0.610577\pi\)
\(350\) 1.28519 0.0686962
\(351\) 6.67903 0.356500
\(352\) 2.13212 0.113643
\(353\) −15.5391 −0.827064 −0.413532 0.910490i \(-0.635705\pi\)
−0.413532 + 0.910490i \(0.635705\pi\)
\(354\) −5.17242 −0.274911
\(355\) 6.41508 0.340477
\(356\) 1.32183 0.0700570
\(357\) 2.59736 0.137467
\(358\) −12.0044 −0.634451
\(359\) 23.8705 1.25984 0.629920 0.776660i \(-0.283088\pi\)
0.629920 + 0.776660i \(0.283088\pi\)
\(360\) −4.04192 −0.213028
\(361\) −4.13304 −0.217529
\(362\) 4.31112 0.226587
\(363\) 19.0806 1.00147
\(364\) 0.235249 0.0123304
\(365\) 2.50702 0.131224
\(366\) −29.1862 −1.52559
\(367\) 28.9891 1.51322 0.756610 0.653866i \(-0.226854\pi\)
0.756610 + 0.653866i \(0.226854\pi\)
\(368\) 6.98769 0.364259
\(369\) −3.22972 −0.168133
\(370\) −1.56430 −0.0813241
\(371\) 1.08891 0.0565335
\(372\) 5.90464 0.306141
\(373\) 10.7208 0.555101 0.277551 0.960711i \(-0.410477\pi\)
0.277551 + 0.960711i \(0.410477\pi\)
\(374\) 6.56498 0.339467
\(375\) −19.7851 −1.02170
\(376\) 2.16566 0.111685
\(377\) −8.01602 −0.412846
\(378\) 2.31147 0.118889
\(379\) 26.4805 1.36021 0.680106 0.733114i \(-0.261934\pi\)
0.680106 + 0.733114i \(0.261934\pi\)
\(380\) 2.71503 0.139278
\(381\) −36.2219 −1.85570
\(382\) 24.4644 1.25171
\(383\) 12.9398 0.661195 0.330597 0.943772i \(-0.392750\pi\)
0.330597 + 0.943772i \(0.392750\pi\)
\(384\) −2.95638 −0.150867
\(385\) 0.428378 0.0218322
\(386\) 16.1289 0.820938
\(387\) −42.7926 −2.17527
\(388\) −5.88876 −0.298956
\(389\) 5.05213 0.256153 0.128077 0.991764i \(-0.459120\pi\)
0.128077 + 0.991764i \(0.459120\pi\)
\(390\) −1.71633 −0.0869096
\(391\) 21.5157 1.08809
\(392\) −6.91859 −0.349441
\(393\) −2.23078 −0.112528
\(394\) 26.6450 1.34236
\(395\) −3.68362 −0.185343
\(396\) 12.2387 0.615020
\(397\) 29.8019 1.49571 0.747856 0.663860i \(-0.231083\pi\)
0.747856 + 0.663860i \(0.231083\pi\)
\(398\) −8.63087 −0.432626
\(399\) −3.25254 −0.162831
\(400\) −4.50418 −0.225209
\(401\) −13.1336 −0.655863 −0.327931 0.944702i \(-0.606351\pi\)
−0.327931 + 0.944702i \(0.606351\pi\)
\(402\) 9.82289 0.489921
\(403\) 1.64669 0.0820273
\(404\) 3.20302 0.159356
\(405\) −4.73820 −0.235443
\(406\) −2.77417 −0.137680
\(407\) 4.73663 0.234786
\(408\) −9.10292 −0.450662
\(409\) −2.53363 −0.125280 −0.0626399 0.998036i \(-0.519952\pi\)
−0.0626399 + 0.998036i \(0.519952\pi\)
\(410\) 0.396190 0.0195665
\(411\) −56.8837 −2.80587
\(412\) −5.94076 −0.292680
\(413\) −0.499213 −0.0245647
\(414\) 40.1105 1.97132
\(415\) −7.14583 −0.350775
\(416\) −0.824474 −0.0404232
\(417\) 47.3730 2.31986
\(418\) −8.22098 −0.402101
\(419\) −38.1765 −1.86504 −0.932521 0.361116i \(-0.882396\pi\)
−0.932521 + 0.361116i \(0.882396\pi\)
\(420\) −0.593984 −0.0289834
\(421\) 33.4945 1.63242 0.816211 0.577754i \(-0.196071\pi\)
0.816211 + 0.577754i \(0.196071\pi\)
\(422\) 28.0721 1.36653
\(423\) 12.4313 0.604428
\(424\) −3.81629 −0.185335
\(425\) −13.8687 −0.672732
\(426\) 26.9339 1.30495
\(427\) −2.81689 −0.136319
\(428\) 0.282513 0.0136558
\(429\) 5.19696 0.250912
\(430\) 5.24938 0.253147
\(431\) 30.0466 1.44730 0.723648 0.690170i \(-0.242464\pi\)
0.723648 + 0.690170i \(0.242464\pi\)
\(432\) −8.10096 −0.389758
\(433\) 34.8119 1.67295 0.836476 0.548004i \(-0.184612\pi\)
0.836476 + 0.548004i \(0.184612\pi\)
\(434\) 0.569882 0.0273552
\(435\) 20.2397 0.970421
\(436\) 9.55550 0.457626
\(437\) −26.9429 −1.28885
\(438\) 10.5258 0.502942
\(439\) −1.05540 −0.0503716 −0.0251858 0.999683i \(-0.508018\pi\)
−0.0251858 + 0.999683i \(0.508018\pi\)
\(440\) −1.50133 −0.0715731
\(441\) −39.7138 −1.89113
\(442\) −2.53862 −0.120750
\(443\) −30.0688 −1.42861 −0.714306 0.699834i \(-0.753257\pi\)
−0.714306 + 0.699834i \(0.753257\pi\)
\(444\) −6.56775 −0.311692
\(445\) −0.930765 −0.0441225
\(446\) −26.0000 −1.23113
\(447\) −21.1239 −0.999125
\(448\) −0.285333 −0.0134807
\(449\) 20.0551 0.946457 0.473229 0.880940i \(-0.343088\pi\)
0.473229 + 0.880940i \(0.343088\pi\)
\(450\) −25.8547 −1.21880
\(451\) −1.19965 −0.0564891
\(452\) 2.37643 0.111778
\(453\) 59.1534 2.77927
\(454\) 19.7096 0.925015
\(455\) −0.165650 −0.00776580
\(456\) 11.3991 0.533812
\(457\) −19.1140 −0.894117 −0.447058 0.894505i \(-0.647528\pi\)
−0.447058 + 0.894505i \(0.647528\pi\)
\(458\) 4.04796 0.189149
\(459\) −24.9435 −1.16426
\(460\) −4.92036 −0.229413
\(461\) 11.4975 0.535492 0.267746 0.963489i \(-0.413721\pi\)
0.267746 + 0.963489i \(0.413721\pi\)
\(462\) 1.79856 0.0836764
\(463\) −12.4145 −0.576949 −0.288475 0.957488i \(-0.593148\pi\)
−0.288475 + 0.957488i \(0.593148\pi\)
\(464\) 9.72258 0.451360
\(465\) −4.15774 −0.192810
\(466\) 30.1140 1.39500
\(467\) −9.23241 −0.427225 −0.213613 0.976918i \(-0.568523\pi\)
−0.213613 + 0.976918i \(0.568523\pi\)
\(468\) −4.73262 −0.218765
\(469\) 0.948049 0.0437768
\(470\) −1.52494 −0.0703404
\(471\) −38.8682 −1.79095
\(472\) 1.74958 0.0805310
\(473\) −15.8949 −0.730847
\(474\) −15.4658 −0.710366
\(475\) 17.3671 0.796856
\(476\) −0.878562 −0.0402688
\(477\) −21.9061 −1.00301
\(478\) 16.1795 0.740035
\(479\) −22.6355 −1.03424 −0.517121 0.855912i \(-0.672996\pi\)
−0.517121 + 0.855912i \(0.672996\pi\)
\(480\) 2.08172 0.0950173
\(481\) −1.83161 −0.0835144
\(482\) −28.0150 −1.27605
\(483\) 5.89447 0.268208
\(484\) −6.45404 −0.293366
\(485\) 4.14655 0.188285
\(486\) 4.40943 0.200016
\(487\) 12.0008 0.543807 0.271904 0.962324i \(-0.412347\pi\)
0.271904 + 0.962324i \(0.412347\pi\)
\(488\) 9.87230 0.446898
\(489\) −23.1160 −1.04534
\(490\) 4.87170 0.220081
\(491\) 37.5969 1.69672 0.848361 0.529418i \(-0.177590\pi\)
0.848361 + 0.529418i \(0.177590\pi\)
\(492\) 1.66341 0.0749925
\(493\) 29.9366 1.34828
\(494\) 3.17898 0.143029
\(495\) −8.61788 −0.387345
\(496\) −1.99726 −0.0896794
\(497\) 2.59950 0.116604
\(498\) −30.0019 −1.34442
\(499\) −5.33365 −0.238767 −0.119384 0.992848i \(-0.538092\pi\)
−0.119384 + 0.992848i \(0.538092\pi\)
\(500\) 6.69234 0.299290
\(501\) 5.59572 0.249998
\(502\) −15.5728 −0.695046
\(503\) 1.73557 0.0773852 0.0386926 0.999251i \(-0.487681\pi\)
0.0386926 + 0.999251i \(0.487681\pi\)
\(504\) −1.63786 −0.0729559
\(505\) −2.25540 −0.100364
\(506\) 14.8986 0.662325
\(507\) 36.4233 1.61761
\(508\) 12.2521 0.543600
\(509\) 12.6870 0.562341 0.281170 0.959658i \(-0.409277\pi\)
0.281170 + 0.959658i \(0.409277\pi\)
\(510\) 6.40980 0.283831
\(511\) 1.01589 0.0449403
\(512\) 1.00000 0.0441942
\(513\) 31.2354 1.37908
\(514\) 29.3394 1.29411
\(515\) 4.18317 0.184332
\(516\) 22.0396 0.970240
\(517\) 4.61746 0.203076
\(518\) −0.633882 −0.0278512
\(519\) 5.97866 0.262434
\(520\) 0.580551 0.0254588
\(521\) 11.3962 0.499275 0.249638 0.968339i \(-0.419688\pi\)
0.249638 + 0.968339i \(0.419688\pi\)
\(522\) 55.8092 2.44270
\(523\) 13.9379 0.609462 0.304731 0.952439i \(-0.401434\pi\)
0.304731 + 0.952439i \(0.401434\pi\)
\(524\) 0.754565 0.0329633
\(525\) −3.79950 −0.165824
\(526\) −7.17445 −0.312821
\(527\) −6.14971 −0.267886
\(528\) −6.30336 −0.274319
\(529\) 25.8278 1.12295
\(530\) 2.68723 0.116726
\(531\) 10.0429 0.435824
\(532\) 1.10018 0.0476987
\(533\) 0.463893 0.0200934
\(534\) −3.90784 −0.169109
\(535\) −0.198931 −0.00860054
\(536\) −3.32261 −0.143515
\(537\) 35.4895 1.53148
\(538\) 11.3203 0.488054
\(539\) −14.7513 −0.635383
\(540\) 5.70427 0.245473
\(541\) −3.69759 −0.158972 −0.0794858 0.996836i \(-0.525328\pi\)
−0.0794858 + 0.996836i \(0.525328\pi\)
\(542\) −19.7521 −0.848425
\(543\) −12.7453 −0.546953
\(544\) 3.07908 0.132014
\(545\) −6.72848 −0.288216
\(546\) −0.695486 −0.0297640
\(547\) −3.52377 −0.150666 −0.0753329 0.997158i \(-0.524002\pi\)
−0.0753329 + 0.997158i \(0.524002\pi\)
\(548\) 19.2410 0.821936
\(549\) 56.6686 2.41856
\(550\) −9.60347 −0.409493
\(551\) −37.4880 −1.59704
\(552\) −20.6582 −0.879273
\(553\) −1.49267 −0.0634747
\(554\) 19.7273 0.838133
\(555\) 4.62466 0.196306
\(556\) −16.0240 −0.679569
\(557\) 13.6072 0.576554 0.288277 0.957547i \(-0.406918\pi\)
0.288277 + 0.957547i \(0.406918\pi\)
\(558\) −11.4646 −0.485334
\(559\) 6.14641 0.259965
\(560\) 0.200916 0.00849026
\(561\) −19.4086 −0.819430
\(562\) 10.7098 0.451765
\(563\) −5.31204 −0.223876 −0.111938 0.993715i \(-0.535706\pi\)
−0.111938 + 0.993715i \(0.535706\pi\)
\(564\) −6.40251 −0.269594
\(565\) −1.67335 −0.0703985
\(566\) −5.28438 −0.222119
\(567\) −1.92000 −0.0806325
\(568\) −9.11043 −0.382265
\(569\) −0.806131 −0.0337948 −0.0168974 0.999857i \(-0.505379\pi\)
−0.0168974 + 0.999857i \(0.505379\pi\)
\(570\) −8.02665 −0.336199
\(571\) −37.5543 −1.57160 −0.785800 0.618480i \(-0.787749\pi\)
−0.785800 + 0.618480i \(0.787749\pi\)
\(572\) −1.75788 −0.0735007
\(573\) −72.3261 −3.02147
\(574\) 0.160543 0.00670095
\(575\) −31.4738 −1.31255
\(576\) 5.74016 0.239174
\(577\) −26.4069 −1.09933 −0.549667 0.835384i \(-0.685246\pi\)
−0.549667 + 0.835384i \(0.685246\pi\)
\(578\) −7.51927 −0.312760
\(579\) −47.6830 −1.98164
\(580\) −6.84613 −0.284270
\(581\) −2.89561 −0.120130
\(582\) 17.4094 0.721642
\(583\) −8.13681 −0.336992
\(584\) −3.56037 −0.147329
\(585\) 3.33246 0.137780
\(586\) 31.5082 1.30159
\(587\) −39.4487 −1.62822 −0.814110 0.580711i \(-0.802775\pi\)
−0.814110 + 0.580711i \(0.802775\pi\)
\(588\) 20.4539 0.843507
\(589\) 7.70096 0.317312
\(590\) −1.23196 −0.0507191
\(591\) −78.7728 −3.24028
\(592\) 2.22155 0.0913053
\(593\) −33.5736 −1.37870 −0.689350 0.724428i \(-0.742104\pi\)
−0.689350 + 0.724428i \(0.742104\pi\)
\(594\) −17.2723 −0.708689
\(595\) 0.618637 0.0253616
\(596\) 7.14519 0.292678
\(597\) 25.5161 1.04430
\(598\) −5.76117 −0.235592
\(599\) 13.8852 0.567333 0.283666 0.958923i \(-0.408449\pi\)
0.283666 + 0.958923i \(0.408449\pi\)
\(600\) 13.3160 0.543625
\(601\) −36.4806 −1.48807 −0.744036 0.668139i \(-0.767091\pi\)
−0.744036 + 0.668139i \(0.767091\pi\)
\(602\) 2.12714 0.0866957
\(603\) −19.0723 −0.776685
\(604\) −20.0088 −0.814145
\(605\) 4.54460 0.184764
\(606\) −9.46935 −0.384666
\(607\) 10.0795 0.409116 0.204558 0.978854i \(-0.434424\pi\)
0.204558 + 0.978854i \(0.434424\pi\)
\(608\) −3.85577 −0.156372
\(609\) 8.20149 0.332341
\(610\) −6.95155 −0.281460
\(611\) −1.78553 −0.0722349
\(612\) 17.6744 0.714446
\(613\) −7.67662 −0.310056 −0.155028 0.987910i \(-0.549547\pi\)
−0.155028 + 0.987910i \(0.549547\pi\)
\(614\) 12.6660 0.511160
\(615\) −1.17129 −0.0472309
\(616\) −0.608365 −0.0245117
\(617\) −13.0932 −0.527111 −0.263556 0.964644i \(-0.584895\pi\)
−0.263556 + 0.964644i \(0.584895\pi\)
\(618\) 17.5631 0.706492
\(619\) 17.9421 0.721155 0.360577 0.932729i \(-0.382580\pi\)
0.360577 + 0.932729i \(0.382580\pi\)
\(620\) 1.40636 0.0564809
\(621\) −56.6070 −2.27156
\(622\) 25.2909 1.01407
\(623\) −0.377162 −0.0151107
\(624\) 2.43746 0.0975763
\(625\) 17.8085 0.712340
\(626\) −2.81859 −0.112654
\(627\) 24.3043 0.970621
\(628\) 13.1473 0.524632
\(629\) 6.84034 0.272742
\(630\) 1.15329 0.0459483
\(631\) −31.4797 −1.25319 −0.626594 0.779345i \(-0.715552\pi\)
−0.626594 + 0.779345i \(0.715552\pi\)
\(632\) 5.23132 0.208091
\(633\) −82.9917 −3.29863
\(634\) −9.50407 −0.377455
\(635\) −8.62730 −0.342364
\(636\) 11.2824 0.447376
\(637\) 5.70419 0.226008
\(638\) 20.7298 0.820699
\(639\) −52.2954 −2.06877
\(640\) −0.704147 −0.0278339
\(641\) −8.32710 −0.328901 −0.164450 0.986385i \(-0.552585\pi\)
−0.164450 + 0.986385i \(0.552585\pi\)
\(642\) −0.835216 −0.0329633
\(643\) −36.2734 −1.43048 −0.715242 0.698876i \(-0.753684\pi\)
−0.715242 + 0.698876i \(0.753684\pi\)
\(644\) −1.99382 −0.0785674
\(645\) −15.5191 −0.611065
\(646\) −11.8722 −0.467106
\(647\) −24.4198 −0.960041 −0.480020 0.877257i \(-0.659371\pi\)
−0.480020 + 0.877257i \(0.659371\pi\)
\(648\) 6.72900 0.264340
\(649\) 3.73033 0.146428
\(650\) 3.71358 0.145658
\(651\) −1.68479 −0.0660320
\(652\) 7.81901 0.306216
\(653\) −4.03721 −0.157988 −0.0789942 0.996875i \(-0.525171\pi\)
−0.0789942 + 0.996875i \(0.525171\pi\)
\(654\) −28.2497 −1.10465
\(655\) −0.531325 −0.0207606
\(656\) −0.562653 −0.0219679
\(657\) −20.4371 −0.797328
\(658\) −0.617934 −0.0240896
\(659\) −26.6748 −1.03910 −0.519551 0.854439i \(-0.673901\pi\)
−0.519551 + 0.854439i \(0.673901\pi\)
\(660\) 4.43850 0.172768
\(661\) −28.5012 −1.10857 −0.554285 0.832327i \(-0.687008\pi\)
−0.554285 + 0.832327i \(0.687008\pi\)
\(662\) 19.0048 0.738641
\(663\) 7.50512 0.291475
\(664\) 10.1482 0.393827
\(665\) −0.774686 −0.0300411
\(666\) 12.7521 0.494133
\(667\) 67.9384 2.63059
\(668\) −1.89276 −0.0732332
\(669\) 76.8657 2.97180
\(670\) 2.33961 0.0903869
\(671\) 21.0490 0.812587
\(672\) 0.843551 0.0325407
\(673\) 0.343447 0.0132389 0.00661945 0.999978i \(-0.497893\pi\)
0.00661945 + 0.999978i \(0.497893\pi\)
\(674\) −9.92416 −0.382264
\(675\) 36.4882 1.40443
\(676\) −12.3202 −0.473855
\(677\) 35.2177 1.35353 0.676764 0.736200i \(-0.263382\pi\)
0.676764 + 0.736200i \(0.263382\pi\)
\(678\) −7.02561 −0.269817
\(679\) 1.68025 0.0644822
\(680\) −2.16813 −0.0831438
\(681\) −58.2689 −2.23287
\(682\) −4.25840 −0.163063
\(683\) 9.12479 0.349150 0.174575 0.984644i \(-0.444145\pi\)
0.174575 + 0.984644i \(0.444145\pi\)
\(684\) −22.1328 −0.846267
\(685\) −13.5485 −0.517662
\(686\) 3.97143 0.151630
\(687\) −11.9673 −0.456580
\(688\) −7.45494 −0.284217
\(689\) 3.14643 0.119870
\(690\) 14.5464 0.553774
\(691\) −9.79494 −0.372617 −0.186309 0.982491i \(-0.559652\pi\)
−0.186309 + 0.982491i \(0.559652\pi\)
\(692\) −2.02229 −0.0768760
\(693\) −3.49211 −0.132654
\(694\) −12.7437 −0.483743
\(695\) 11.2833 0.427998
\(696\) −28.7436 −1.08952
\(697\) −1.73245 −0.0656214
\(698\) −12.7200 −0.481459
\(699\) −89.0284 −3.36736
\(700\) 1.28519 0.0485756
\(701\) 19.3181 0.729635 0.364818 0.931079i \(-0.381131\pi\)
0.364818 + 0.931079i \(0.381131\pi\)
\(702\) 6.67903 0.252084
\(703\) −8.56580 −0.323065
\(704\) 2.13212 0.0803575
\(705\) 4.50831 0.169793
\(706\) −15.5391 −0.584823
\(707\) −0.913927 −0.0343718
\(708\) −5.17242 −0.194392
\(709\) 3.12558 0.117384 0.0586919 0.998276i \(-0.481307\pi\)
0.0586919 + 0.998276i \(0.481307\pi\)
\(710\) 6.41508 0.240754
\(711\) 30.0286 1.12616
\(712\) 1.32183 0.0495378
\(713\) −13.9562 −0.522664
\(714\) 2.59736 0.0972038
\(715\) 1.23781 0.0462914
\(716\) −12.0044 −0.448624
\(717\) −47.8328 −1.78635
\(718\) 23.8705 0.890841
\(719\) −0.0899969 −0.00335632 −0.00167816 0.999999i \(-0.500534\pi\)
−0.00167816 + 0.999999i \(0.500534\pi\)
\(720\) −4.04192 −0.150633
\(721\) 1.69509 0.0631285
\(722\) −4.13304 −0.153816
\(723\) 82.8228 3.08021
\(724\) 4.31112 0.160221
\(725\) −43.7922 −1.62640
\(726\) 19.0806 0.708147
\(727\) −21.2534 −0.788246 −0.394123 0.919058i \(-0.628952\pi\)
−0.394123 + 0.919058i \(0.628952\pi\)
\(728\) 0.235249 0.00871892
\(729\) −33.2229 −1.23048
\(730\) 2.50702 0.0927891
\(731\) −22.9544 −0.848998
\(732\) −29.1862 −1.07875
\(733\) −5.35020 −0.197614 −0.0988071 0.995107i \(-0.531503\pi\)
−0.0988071 + 0.995107i \(0.531503\pi\)
\(734\) 28.9891 1.07001
\(735\) −14.4026 −0.531247
\(736\) 6.98769 0.257570
\(737\) −7.08422 −0.260951
\(738\) −3.22972 −0.118888
\(739\) 47.1241 1.73349 0.866744 0.498754i \(-0.166209\pi\)
0.866744 + 0.498754i \(0.166209\pi\)
\(740\) −1.56430 −0.0575048
\(741\) −9.39827 −0.345254
\(742\) 1.08891 0.0399752
\(743\) 6.81194 0.249906 0.124953 0.992163i \(-0.460122\pi\)
0.124953 + 0.992163i \(0.460122\pi\)
\(744\) 5.90464 0.216475
\(745\) −5.03127 −0.184331
\(746\) 10.7208 0.392516
\(747\) 58.2524 2.13134
\(748\) 6.56498 0.240040
\(749\) −0.0806103 −0.00294544
\(750\) −19.7851 −0.722449
\(751\) −24.4179 −0.891023 −0.445512 0.895276i \(-0.646978\pi\)
−0.445512 + 0.895276i \(0.646978\pi\)
\(752\) 2.16566 0.0789735
\(753\) 46.0389 1.67775
\(754\) −8.01602 −0.291926
\(755\) 14.0891 0.512755
\(756\) 2.31147 0.0840673
\(757\) 9.76422 0.354887 0.177443 0.984131i \(-0.443217\pi\)
0.177443 + 0.984131i \(0.443217\pi\)
\(758\) 26.4805 0.961815
\(759\) −44.0460 −1.59877
\(760\) 2.71503 0.0984845
\(761\) −3.43046 −0.124354 −0.0621770 0.998065i \(-0.519804\pi\)
−0.0621770 + 0.998065i \(0.519804\pi\)
\(762\) −36.2219 −1.31218
\(763\) −2.72650 −0.0987058
\(764\) 24.4644 0.885092
\(765\) −12.4454 −0.449964
\(766\) 12.9398 0.467535
\(767\) −1.44248 −0.0520851
\(768\) −2.95638 −0.106679
\(769\) 37.3099 1.34543 0.672715 0.739902i \(-0.265128\pi\)
0.672715 + 0.739902i \(0.265128\pi\)
\(770\) 0.428378 0.0154377
\(771\) −86.7385 −3.12381
\(772\) 16.1289 0.580491
\(773\) −18.3212 −0.658967 −0.329484 0.944161i \(-0.606875\pi\)
−0.329484 + 0.944161i \(0.606875\pi\)
\(774\) −42.7926 −1.53815
\(775\) 8.99599 0.323146
\(776\) −5.88876 −0.211394
\(777\) 1.87399 0.0672292
\(778\) 5.05213 0.181128
\(779\) 2.16946 0.0777290
\(780\) −1.71633 −0.0614544
\(781\) −19.4246 −0.695066
\(782\) 21.5157 0.769398
\(783\) −78.7623 −2.81473
\(784\) −6.91859 −0.247092
\(785\) −9.25760 −0.330418
\(786\) −2.23078 −0.0795692
\(787\) −6.71808 −0.239474 −0.119737 0.992806i \(-0.538205\pi\)
−0.119737 + 0.992806i \(0.538205\pi\)
\(788\) 26.6450 0.949191
\(789\) 21.2104 0.755110
\(790\) −3.68362 −0.131057
\(791\) −0.678072 −0.0241095
\(792\) 12.2387 0.434885
\(793\) −8.13946 −0.289041
\(794\) 29.8019 1.05763
\(795\) −7.94446 −0.281761
\(796\) −8.63087 −0.305913
\(797\) 39.4318 1.39675 0.698374 0.715733i \(-0.253907\pi\)
0.698374 + 0.715733i \(0.253907\pi\)
\(798\) −3.25254 −0.115139
\(799\) 6.66824 0.235906
\(800\) −4.50418 −0.159247
\(801\) 7.58754 0.268092
\(802\) −13.1336 −0.463765
\(803\) −7.59115 −0.267886
\(804\) 9.82289 0.346427
\(805\) 1.40394 0.0494824
\(806\) 1.64669 0.0580020
\(807\) −33.4672 −1.17810
\(808\) 3.20302 0.112682
\(809\) −39.5274 −1.38971 −0.694854 0.719151i \(-0.744531\pi\)
−0.694854 + 0.719151i \(0.744531\pi\)
\(810\) −4.73820 −0.166484
\(811\) −5.83106 −0.204756 −0.102378 0.994746i \(-0.532645\pi\)
−0.102378 + 0.994746i \(0.532645\pi\)
\(812\) −2.77417 −0.0973543
\(813\) 58.3946 2.04799
\(814\) 4.73663 0.166019
\(815\) −5.50574 −0.192858
\(816\) −9.10292 −0.318666
\(817\) 28.7445 1.00564
\(818\) −2.53363 −0.0885862
\(819\) 1.35037 0.0471858
\(820\) 0.396190 0.0138356
\(821\) −5.56543 −0.194235 −0.0971173 0.995273i \(-0.530962\pi\)
−0.0971173 + 0.995273i \(0.530962\pi\)
\(822\) −56.8837 −1.98405
\(823\) 22.4957 0.784149 0.392075 0.919933i \(-0.371758\pi\)
0.392075 + 0.919933i \(0.371758\pi\)
\(824\) −5.94076 −0.206956
\(825\) 28.3915 0.988464
\(826\) −0.499213 −0.0173698
\(827\) 2.38134 0.0828073 0.0414037 0.999143i \(-0.486817\pi\)
0.0414037 + 0.999143i \(0.486817\pi\)
\(828\) 40.1105 1.39394
\(829\) 0.101100 0.00351135 0.00175568 0.999998i \(-0.499441\pi\)
0.00175568 + 0.999998i \(0.499441\pi\)
\(830\) −7.14583 −0.248035
\(831\) −58.3213 −2.02314
\(832\) −0.824474 −0.0285835
\(833\) −21.3029 −0.738101
\(834\) 47.3730 1.64039
\(835\) 1.33278 0.0461229
\(836\) −8.22098 −0.284329
\(837\) 16.1797 0.559252
\(838\) −38.1765 −1.31878
\(839\) −37.3398 −1.28911 −0.644557 0.764556i \(-0.722958\pi\)
−0.644557 + 0.764556i \(0.722958\pi\)
\(840\) −0.593984 −0.0204944
\(841\) 65.5286 2.25961
\(842\) 33.4945 1.15430
\(843\) −31.6622 −1.09050
\(844\) 28.0721 0.966282
\(845\) 8.67526 0.298438
\(846\) 12.4313 0.427395
\(847\) 1.84155 0.0632764
\(848\) −3.81629 −0.131052
\(849\) 15.6226 0.536167
\(850\) −13.8687 −0.475693
\(851\) 15.5235 0.532140
\(852\) 26.9339 0.922739
\(853\) 30.5829 1.04714 0.523569 0.851983i \(-0.324600\pi\)
0.523569 + 0.851983i \(0.324600\pi\)
\(854\) −2.81689 −0.0963920
\(855\) 15.5847 0.532986
\(856\) 0.282513 0.00965611
\(857\) 48.0912 1.64276 0.821382 0.570378i \(-0.193203\pi\)
0.821382 + 0.570378i \(0.193203\pi\)
\(858\) 5.19696 0.177421
\(859\) 25.9453 0.885243 0.442622 0.896708i \(-0.354048\pi\)
0.442622 + 0.896708i \(0.354048\pi\)
\(860\) 5.24938 0.179002
\(861\) −0.474626 −0.0161752
\(862\) 30.0466 1.02339
\(863\) −18.5722 −0.632205 −0.316103 0.948725i \(-0.602374\pi\)
−0.316103 + 0.948725i \(0.602374\pi\)
\(864\) −8.10096 −0.275600
\(865\) 1.42399 0.0484171
\(866\) 34.8119 1.18296
\(867\) 22.2298 0.754963
\(868\) 0.569882 0.0193431
\(869\) 11.1538 0.378368
\(870\) 20.2397 0.686191
\(871\) 2.73941 0.0928212
\(872\) 9.55550 0.323590
\(873\) −33.8024 −1.14404
\(874\) −26.9429 −0.911358
\(875\) −1.90954 −0.0645543
\(876\) 10.5258 0.355634
\(877\) −24.0744 −0.812935 −0.406468 0.913665i \(-0.633240\pi\)
−0.406468 + 0.913665i \(0.633240\pi\)
\(878\) −1.05540 −0.0356181
\(879\) −93.1501 −3.14187
\(880\) −1.50133 −0.0506098
\(881\) −52.1740 −1.75779 −0.878893 0.477019i \(-0.841717\pi\)
−0.878893 + 0.477019i \(0.841717\pi\)
\(882\) −39.7138 −1.33723
\(883\) −34.5789 −1.16367 −0.581836 0.813306i \(-0.697666\pi\)
−0.581836 + 0.813306i \(0.697666\pi\)
\(884\) −2.53862 −0.0853831
\(885\) 3.64215 0.122429
\(886\) −30.0688 −1.01018
\(887\) 27.1937 0.913076 0.456538 0.889704i \(-0.349089\pi\)
0.456538 + 0.889704i \(0.349089\pi\)
\(888\) −6.56775 −0.220399
\(889\) −3.49593 −0.117250
\(890\) −0.930765 −0.0311993
\(891\) 14.3471 0.480645
\(892\) −26.0000 −0.870543
\(893\) −8.35029 −0.279432
\(894\) −21.1239 −0.706488
\(895\) 8.45284 0.282547
\(896\) −0.285333 −0.00953230
\(897\) 17.0322 0.568688
\(898\) 20.0551 0.669246
\(899\) −19.4185 −0.647643
\(900\) −25.8547 −0.861824
\(901\) −11.7507 −0.391471
\(902\) −1.19965 −0.0399438
\(903\) −6.28862 −0.209272
\(904\) 2.37643 0.0790387
\(905\) −3.03566 −0.100909
\(906\) 59.1534 1.96524
\(907\) −28.3537 −0.941469 −0.470734 0.882275i \(-0.656011\pi\)
−0.470734 + 0.882275i \(0.656011\pi\)
\(908\) 19.7096 0.654084
\(909\) 18.3859 0.609821
\(910\) −0.165650 −0.00549125
\(911\) −13.5599 −0.449259 −0.224629 0.974444i \(-0.572117\pi\)
−0.224629 + 0.974444i \(0.572117\pi\)
\(912\) 11.3991 0.377462
\(913\) 21.6372 0.716088
\(914\) −19.1140 −0.632236
\(915\) 20.5514 0.679409
\(916\) 4.04796 0.133748
\(917\) −0.215302 −0.00710990
\(918\) −24.9435 −0.823258
\(919\) 12.2663 0.404629 0.202314 0.979321i \(-0.435154\pi\)
0.202314 + 0.979321i \(0.435154\pi\)
\(920\) −4.92036 −0.162220
\(921\) −37.4456 −1.23387
\(922\) 11.4975 0.378650
\(923\) 7.51131 0.247238
\(924\) 1.79856 0.0591681
\(925\) −10.0063 −0.329004
\(926\) −12.4145 −0.407965
\(927\) −34.1009 −1.12002
\(928\) 9.72258 0.319159
\(929\) 16.6035 0.544743 0.272372 0.962192i \(-0.412192\pi\)
0.272372 + 0.962192i \(0.412192\pi\)
\(930\) −4.15774 −0.136338
\(931\) 26.6765 0.874286
\(932\) 30.1140 0.986417
\(933\) −74.7695 −2.44784
\(934\) −9.23241 −0.302094
\(935\) −4.62271 −0.151179
\(936\) −4.73262 −0.154690
\(937\) 44.4184 1.45109 0.725543 0.688177i \(-0.241589\pi\)
0.725543 + 0.688177i \(0.241589\pi\)
\(938\) 0.948049 0.0309549
\(939\) 8.33283 0.271932
\(940\) −1.52494 −0.0497382
\(941\) −23.1607 −0.755016 −0.377508 0.926006i \(-0.623219\pi\)
−0.377508 + 0.926006i \(0.623219\pi\)
\(942\) −38.8682 −1.26640
\(943\) −3.93164 −0.128032
\(944\) 1.74958 0.0569440
\(945\) −1.62761 −0.0529463
\(946\) −15.8949 −0.516787
\(947\) −53.7244 −1.74581 −0.872904 0.487892i \(-0.837766\pi\)
−0.872904 + 0.487892i \(0.837766\pi\)
\(948\) −15.4658 −0.502304
\(949\) 2.93543 0.0952882
\(950\) 17.3671 0.563462
\(951\) 28.0976 0.911128
\(952\) −0.878562 −0.0284744
\(953\) −36.8374 −1.19328 −0.596640 0.802509i \(-0.703498\pi\)
−0.596640 + 0.802509i \(0.703498\pi\)
\(954\) −21.9061 −0.709237
\(955\) −17.2266 −0.557438
\(956\) 16.1795 0.523284
\(957\) −61.2850 −1.98106
\(958\) −22.6355 −0.731320
\(959\) −5.49009 −0.177284
\(960\) 2.08172 0.0671874
\(961\) −27.0110 −0.871322
\(962\) −1.83161 −0.0590536
\(963\) 1.62167 0.0522577
\(964\) −28.0150 −0.902301
\(965\) −11.3571 −0.365598
\(966\) 5.89447 0.189652
\(967\) 58.3548 1.87656 0.938282 0.345872i \(-0.112417\pi\)
0.938282 + 0.345872i \(0.112417\pi\)
\(968\) −6.45404 −0.207441
\(969\) 35.0988 1.12753
\(970\) 4.14655 0.133138
\(971\) 25.0537 0.804012 0.402006 0.915637i \(-0.368313\pi\)
0.402006 + 0.915637i \(0.368313\pi\)
\(972\) 4.40943 0.141432
\(973\) 4.57217 0.146577
\(974\) 12.0008 0.384530
\(975\) −10.9787 −0.351601
\(976\) 9.87230 0.316005
\(977\) 39.9809 1.27910 0.639551 0.768749i \(-0.279120\pi\)
0.639551 + 0.768749i \(0.279120\pi\)
\(978\) −23.1160 −0.739167
\(979\) 2.81831 0.0900737
\(980\) 4.87170 0.155621
\(981\) 54.8502 1.75123
\(982\) 37.5969 1.19976
\(983\) −5.20270 −0.165941 −0.0829703 0.996552i \(-0.526441\pi\)
−0.0829703 + 0.996552i \(0.526441\pi\)
\(984\) 1.66341 0.0530277
\(985\) −18.7620 −0.597808
\(986\) 29.9366 0.953376
\(987\) 1.82685 0.0581491
\(988\) 3.17898 0.101137
\(989\) −52.0928 −1.65646
\(990\) −8.61788 −0.273894
\(991\) 51.6907 1.64201 0.821004 0.570922i \(-0.193414\pi\)
0.821004 + 0.570922i \(0.193414\pi\)
\(992\) −1.99726 −0.0634129
\(993\) −56.1852 −1.78298
\(994\) 2.59950 0.0824512
\(995\) 6.07740 0.192667
\(996\) −30.0019 −0.950647
\(997\) −45.8094 −1.45080 −0.725400 0.688328i \(-0.758345\pi\)
−0.725400 + 0.688328i \(0.758345\pi\)
\(998\) −5.33365 −0.168834
\(999\) −17.9967 −0.569391
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 6002.2.a.d.1.6 79
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6002.2.a.d.1.6 79 1.1 even 1 trivial