Properties

Label 6025.2.a.m.1.12
Level $6025$
Weight $2$
Character 6025.1
Self dual yes
Analytic conductor $48.110$
Analytic rank $1$
Dimension $40$
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] = [6025,2,Mod(1,6025)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6025, 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("6025.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6025.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: \(48.1098672178\)
Analytic rank: \(1\)
Dimension: \(40\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) \(=\) 6025.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.58708 q^{2} +1.81144 q^{3} +0.518823 q^{4} -2.87490 q^{6} +0.0644914 q^{7} +2.35075 q^{8} +0.281309 q^{9} +O(q^{10})\) \(q-1.58708 q^{2} +1.81144 q^{3} +0.518823 q^{4} -2.87490 q^{6} +0.0644914 q^{7} +2.35075 q^{8} +0.281309 q^{9} -3.11471 q^{11} +0.939816 q^{12} +1.08890 q^{13} -0.102353 q^{14} -4.76847 q^{16} +7.86988 q^{17} -0.446460 q^{18} -4.43016 q^{19} +0.116822 q^{21} +4.94329 q^{22} +1.31833 q^{23} +4.25823 q^{24} -1.72817 q^{26} -4.92474 q^{27} +0.0334596 q^{28} +9.34210 q^{29} -7.65119 q^{31} +2.86645 q^{32} -5.64210 q^{33} -12.4901 q^{34} +0.145950 q^{36} -5.72218 q^{37} +7.03101 q^{38} +1.97247 q^{39} -6.40082 q^{41} -0.185406 q^{42} -7.30399 q^{43} -1.61598 q^{44} -2.09230 q^{46} +5.56242 q^{47} -8.63779 q^{48} -6.99584 q^{49} +14.2558 q^{51} +0.564945 q^{52} -2.24472 q^{53} +7.81596 q^{54} +0.151603 q^{56} -8.02496 q^{57} -14.8267 q^{58} +8.40941 q^{59} -0.891498 q^{61} +12.1431 q^{62} +0.0181420 q^{63} +4.98766 q^{64} +8.95447 q^{66} -0.205157 q^{67} +4.08307 q^{68} +2.38808 q^{69} +2.18178 q^{71} +0.661287 q^{72} -1.46593 q^{73} +9.08156 q^{74} -2.29847 q^{76} -0.200872 q^{77} -3.13047 q^{78} +6.60582 q^{79} -9.76479 q^{81} +10.1586 q^{82} -11.9378 q^{83} +0.0606101 q^{84} +11.5920 q^{86} +16.9226 q^{87} -7.32189 q^{88} -3.41007 q^{89} +0.0702246 q^{91} +0.683982 q^{92} -13.8597 q^{93} -8.82800 q^{94} +5.19239 q^{96} +8.77669 q^{97} +11.1030 q^{98} -0.876197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 9 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 20 q^{7} - 27 q^{8} + 38 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 9 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 20 q^{7} - 27 q^{8} + 38 q^{9} + q^{11} - 26 q^{12} - 11 q^{13} - q^{14} + 43 q^{16} - 20 q^{17} - 18 q^{18} + 2 q^{21} - 23 q^{22} - 79 q^{23} - 2 q^{24} + 2 q^{26} - 26 q^{27} - 30 q^{28} + 2 q^{29} + q^{31} - 68 q^{32} - 20 q^{33} + 5 q^{34} + 32 q^{36} - 16 q^{37} - 45 q^{38} - 2 q^{39} - 2 q^{41} - 19 q^{42} - 25 q^{43} + 3 q^{44} + 14 q^{46} - 88 q^{47} - 75 q^{48} + 40 q^{49} - 10 q^{51} - 18 q^{52} - 34 q^{53} + 4 q^{54} - 15 q^{56} - 51 q^{57} - 53 q^{58} + q^{59} + 9 q^{61} - 39 q^{62} - 110 q^{63} + 17 q^{64} + 26 q^{66} - 30 q^{67} - 44 q^{68} - 7 q^{69} + 5 q^{71} - 18 q^{72} - 23 q^{73} - 18 q^{74} + 43 q^{76} - 30 q^{77} - 46 q^{78} + 5 q^{79} + 44 q^{81} - 5 q^{82} - 65 q^{83} - 65 q^{84} + 40 q^{86} - 33 q^{87} - 71 q^{88} - 9 q^{89} + q^{91} - 117 q^{92} - 68 q^{93} - 72 q^{94} + 83 q^{96} + 8 q^{97} - 76 q^{98} - 40 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.58708 −1.12224 −0.561118 0.827736i \(-0.689628\pi\)
−0.561118 + 0.827736i \(0.689628\pi\)
\(3\) 1.81144 1.04583 0.522917 0.852383i \(-0.324844\pi\)
0.522917 + 0.852383i \(0.324844\pi\)
\(4\) 0.518823 0.259411
\(5\) 0 0
\(6\) −2.87490 −1.17367
\(7\) 0.0644914 0.0243755 0.0121877 0.999926i \(-0.496120\pi\)
0.0121877 + 0.999926i \(0.496120\pi\)
\(8\) 2.35075 0.831114
\(9\) 0.281309 0.0937698
\(10\) 0 0
\(11\) −3.11471 −0.939120 −0.469560 0.882901i \(-0.655587\pi\)
−0.469560 + 0.882901i \(0.655587\pi\)
\(12\) 0.939816 0.271301
\(13\) 1.08890 0.302006 0.151003 0.988533i \(-0.451750\pi\)
0.151003 + 0.988533i \(0.451750\pi\)
\(14\) −0.102353 −0.0273550
\(15\) 0 0
\(16\) −4.76847 −1.19212
\(17\) 7.86988 1.90873 0.954363 0.298650i \(-0.0965363\pi\)
0.954363 + 0.298650i \(0.0965363\pi\)
\(18\) −0.446460 −0.105232
\(19\) −4.43016 −1.01635 −0.508174 0.861254i \(-0.669679\pi\)
−0.508174 + 0.861254i \(0.669679\pi\)
\(20\) 0 0
\(21\) 0.116822 0.0254927
\(22\) 4.94329 1.05391
\(23\) 1.31833 0.274892 0.137446 0.990509i \(-0.456111\pi\)
0.137446 + 0.990509i \(0.456111\pi\)
\(24\) 4.25823 0.869208
\(25\) 0 0
\(26\) −1.72817 −0.338922
\(27\) −4.92474 −0.947767
\(28\) 0.0334596 0.00632327
\(29\) 9.34210 1.73478 0.867392 0.497625i \(-0.165794\pi\)
0.867392 + 0.497625i \(0.165794\pi\)
\(30\) 0 0
\(31\) −7.65119 −1.37419 −0.687097 0.726565i \(-0.741115\pi\)
−0.687097 + 0.726565i \(0.741115\pi\)
\(32\) 2.86645 0.506721
\(33\) −5.64210 −0.982164
\(34\) −12.4901 −2.14204
\(35\) 0 0
\(36\) 0.145950 0.0243250
\(37\) −5.72218 −0.940721 −0.470360 0.882474i \(-0.655876\pi\)
−0.470360 + 0.882474i \(0.655876\pi\)
\(38\) 7.03101 1.14058
\(39\) 1.97247 0.315848
\(40\) 0 0
\(41\) −6.40082 −0.999640 −0.499820 0.866129i \(-0.666600\pi\)
−0.499820 + 0.866129i \(0.666600\pi\)
\(42\) −0.185406 −0.0286088
\(43\) −7.30399 −1.11385 −0.556924 0.830563i \(-0.688019\pi\)
−0.556924 + 0.830563i \(0.688019\pi\)
\(44\) −1.61598 −0.243618
\(45\) 0 0
\(46\) −2.09230 −0.308493
\(47\) 5.56242 0.811362 0.405681 0.914015i \(-0.367034\pi\)
0.405681 + 0.914015i \(0.367034\pi\)
\(48\) −8.63779 −1.24676
\(49\) −6.99584 −0.999406
\(50\) 0 0
\(51\) 14.2558 1.99621
\(52\) 0.564945 0.0783438
\(53\) −2.24472 −0.308336 −0.154168 0.988045i \(-0.549270\pi\)
−0.154168 + 0.988045i \(0.549270\pi\)
\(54\) 7.81596 1.06362
\(55\) 0 0
\(56\) 0.151603 0.0202588
\(57\) −8.02496 −1.06293
\(58\) −14.8267 −1.94684
\(59\) 8.40941 1.09481 0.547406 0.836867i \(-0.315615\pi\)
0.547406 + 0.836867i \(0.315615\pi\)
\(60\) 0 0
\(61\) −0.891498 −0.114145 −0.0570723 0.998370i \(-0.518177\pi\)
−0.0570723 + 0.998370i \(0.518177\pi\)
\(62\) 12.1431 1.54217
\(63\) 0.0181420 0.00228568
\(64\) 4.98766 0.623457
\(65\) 0 0
\(66\) 8.95447 1.10222
\(67\) −0.205157 −0.0250639 −0.0125319 0.999921i \(-0.503989\pi\)
−0.0125319 + 0.999921i \(0.503989\pi\)
\(68\) 4.08307 0.495145
\(69\) 2.38808 0.287491
\(70\) 0 0
\(71\) 2.18178 0.258930 0.129465 0.991584i \(-0.458674\pi\)
0.129465 + 0.991584i \(0.458674\pi\)
\(72\) 0.661287 0.0779334
\(73\) −1.46593 −0.171574 −0.0857872 0.996313i \(-0.527341\pi\)
−0.0857872 + 0.996313i \(0.527341\pi\)
\(74\) 9.08156 1.05571
\(75\) 0 0
\(76\) −2.29847 −0.263652
\(77\) −0.200872 −0.0228915
\(78\) −3.13047 −0.354456
\(79\) 6.60582 0.743213 0.371607 0.928390i \(-0.378807\pi\)
0.371607 + 0.928390i \(0.378807\pi\)
\(80\) 0 0
\(81\) −9.76479 −1.08498
\(82\) 10.1586 1.12183
\(83\) −11.9378 −1.31035 −0.655174 0.755478i \(-0.727405\pi\)
−0.655174 + 0.755478i \(0.727405\pi\)
\(84\) 0.0606101 0.00661310
\(85\) 0 0
\(86\) 11.5920 1.25000
\(87\) 16.9226 1.81430
\(88\) −7.32189 −0.780516
\(89\) −3.41007 −0.361467 −0.180734 0.983532i \(-0.557847\pi\)
−0.180734 + 0.983532i \(0.557847\pi\)
\(90\) 0 0
\(91\) 0.0702246 0.00736154
\(92\) 0.683982 0.0713100
\(93\) −13.8597 −1.43718
\(94\) −8.82800 −0.910539
\(95\) 0 0
\(96\) 5.19239 0.529946
\(97\) 8.77669 0.891137 0.445569 0.895248i \(-0.353001\pi\)
0.445569 + 0.895248i \(0.353001\pi\)
\(98\) 11.1030 1.12157
\(99\) −0.876197 −0.0880611
\(100\) 0 0
\(101\) −2.01796 −0.200794 −0.100397 0.994947i \(-0.532011\pi\)
−0.100397 + 0.994947i \(0.532011\pi\)
\(102\) −22.6251 −2.24022
\(103\) 6.47931 0.638426 0.319213 0.947683i \(-0.396582\pi\)
0.319213 + 0.947683i \(0.396582\pi\)
\(104\) 2.55972 0.251002
\(105\) 0 0
\(106\) 3.56255 0.346025
\(107\) 7.26553 0.702385 0.351193 0.936303i \(-0.385776\pi\)
0.351193 + 0.936303i \(0.385776\pi\)
\(108\) −2.55507 −0.245862
\(109\) −1.82410 −0.174717 −0.0873586 0.996177i \(-0.527843\pi\)
−0.0873586 + 0.996177i \(0.527843\pi\)
\(110\) 0 0
\(111\) −10.3654 −0.983838
\(112\) −0.307525 −0.0290584
\(113\) −3.62469 −0.340983 −0.170491 0.985359i \(-0.554535\pi\)
−0.170491 + 0.985359i \(0.554535\pi\)
\(114\) 12.7363 1.19286
\(115\) 0 0
\(116\) 4.84689 0.450023
\(117\) 0.306317 0.0283190
\(118\) −13.3464 −1.22864
\(119\) 0.507540 0.0465261
\(120\) 0 0
\(121\) −1.29859 −0.118053
\(122\) 1.41488 0.128097
\(123\) −11.5947 −1.04546
\(124\) −3.96961 −0.356482
\(125\) 0 0
\(126\) −0.0287929 −0.00256507
\(127\) −18.0032 −1.59753 −0.798764 0.601645i \(-0.794512\pi\)
−0.798764 + 0.601645i \(0.794512\pi\)
\(128\) −13.6487 −1.20639
\(129\) −13.2307 −1.16490
\(130\) 0 0
\(131\) −20.2832 −1.77216 −0.886078 0.463537i \(-0.846580\pi\)
−0.886078 + 0.463537i \(0.846580\pi\)
\(132\) −2.92725 −0.254785
\(133\) −0.285707 −0.0247740
\(134\) 0.325600 0.0281276
\(135\) 0 0
\(136\) 18.5001 1.58637
\(137\) −5.76429 −0.492477 −0.246238 0.969209i \(-0.579195\pi\)
−0.246238 + 0.969209i \(0.579195\pi\)
\(138\) −3.79007 −0.322633
\(139\) 13.2382 1.12285 0.561426 0.827527i \(-0.310253\pi\)
0.561426 + 0.827527i \(0.310253\pi\)
\(140\) 0 0
\(141\) 10.0760 0.848550
\(142\) −3.46266 −0.290580
\(143\) −3.39160 −0.283620
\(144\) −1.34141 −0.111785
\(145\) 0 0
\(146\) 2.32655 0.192547
\(147\) −12.6725 −1.04521
\(148\) −2.96880 −0.244034
\(149\) 11.0016 0.901286 0.450643 0.892704i \(-0.351195\pi\)
0.450643 + 0.892704i \(0.351195\pi\)
\(150\) 0 0
\(151\) −2.93660 −0.238977 −0.119488 0.992836i \(-0.538125\pi\)
−0.119488 + 0.992836i \(0.538125\pi\)
\(152\) −10.4142 −0.844701
\(153\) 2.21387 0.178981
\(154\) 0.318800 0.0256896
\(155\) 0 0
\(156\) 1.02336 0.0819346
\(157\) 15.5005 1.23707 0.618537 0.785755i \(-0.287726\pi\)
0.618537 + 0.785755i \(0.287726\pi\)
\(158\) −10.4840 −0.834060
\(159\) −4.06617 −0.322468
\(160\) 0 0
\(161\) 0.0850212 0.00670061
\(162\) 15.4975 1.21760
\(163\) −7.71386 −0.604196 −0.302098 0.953277i \(-0.597687\pi\)
−0.302098 + 0.953277i \(0.597687\pi\)
\(164\) −3.32089 −0.259318
\(165\) 0 0
\(166\) 18.9463 1.47052
\(167\) −10.1357 −0.784320 −0.392160 0.919897i \(-0.628272\pi\)
−0.392160 + 0.919897i \(0.628272\pi\)
\(168\) 0.274620 0.0211874
\(169\) −11.8143 −0.908792
\(170\) 0 0
\(171\) −1.24624 −0.0953027
\(172\) −3.78948 −0.288945
\(173\) −6.25726 −0.475731 −0.237865 0.971298i \(-0.576448\pi\)
−0.237865 + 0.971298i \(0.576448\pi\)
\(174\) −26.8576 −2.03607
\(175\) 0 0
\(176\) 14.8524 1.11954
\(177\) 15.2331 1.14499
\(178\) 5.41206 0.405651
\(179\) −20.4876 −1.53131 −0.765657 0.643250i \(-0.777586\pi\)
−0.765657 + 0.643250i \(0.777586\pi\)
\(180\) 0 0
\(181\) −6.38386 −0.474509 −0.237254 0.971448i \(-0.576247\pi\)
−0.237254 + 0.971448i \(0.576247\pi\)
\(182\) −0.111452 −0.00826138
\(183\) −1.61489 −0.119376
\(184\) 3.09907 0.228466
\(185\) 0 0
\(186\) 21.9964 1.61285
\(187\) −24.5124 −1.79252
\(188\) 2.88591 0.210477
\(189\) −0.317604 −0.0231023
\(190\) 0 0
\(191\) 9.46713 0.685018 0.342509 0.939515i \(-0.388723\pi\)
0.342509 + 0.939515i \(0.388723\pi\)
\(192\) 9.03483 0.652033
\(193\) −2.15639 −0.155220 −0.0776102 0.996984i \(-0.524729\pi\)
−0.0776102 + 0.996984i \(0.524729\pi\)
\(194\) −13.9293 −1.00007
\(195\) 0 0
\(196\) −3.62960 −0.259257
\(197\) −4.35613 −0.310362 −0.155181 0.987886i \(-0.549596\pi\)
−0.155181 + 0.987886i \(0.549596\pi\)
\(198\) 1.39059 0.0988253
\(199\) −10.1846 −0.721967 −0.360983 0.932572i \(-0.617559\pi\)
−0.360983 + 0.932572i \(0.617559\pi\)
\(200\) 0 0
\(201\) −0.371629 −0.0262127
\(202\) 3.20266 0.225339
\(203\) 0.602485 0.0422862
\(204\) 7.39623 0.517840
\(205\) 0 0
\(206\) −10.2832 −0.716463
\(207\) 0.370860 0.0257765
\(208\) −5.19238 −0.360027
\(209\) 13.7987 0.954473
\(210\) 0 0
\(211\) 18.5472 1.27684 0.638421 0.769687i \(-0.279588\pi\)
0.638421 + 0.769687i \(0.279588\pi\)
\(212\) −1.16461 −0.0799858
\(213\) 3.95216 0.270797
\(214\) −11.5310 −0.788241
\(215\) 0 0
\(216\) −11.5768 −0.787703
\(217\) −0.493436 −0.0334966
\(218\) 2.89499 0.196074
\(219\) −2.65545 −0.179439
\(220\) 0 0
\(221\) 8.56949 0.576447
\(222\) 16.4507 1.10410
\(223\) 7.24666 0.485272 0.242636 0.970117i \(-0.421988\pi\)
0.242636 + 0.970117i \(0.421988\pi\)
\(224\) 0.184861 0.0123516
\(225\) 0 0
\(226\) 5.75268 0.382663
\(227\) −18.8256 −1.24950 −0.624748 0.780826i \(-0.714798\pi\)
−0.624748 + 0.780826i \(0.714798\pi\)
\(228\) −4.16353 −0.275737
\(229\) 24.4964 1.61877 0.809385 0.587279i \(-0.199801\pi\)
0.809385 + 0.587279i \(0.199801\pi\)
\(230\) 0 0
\(231\) −0.363867 −0.0239407
\(232\) 21.9609 1.44180
\(233\) 9.08981 0.595493 0.297747 0.954645i \(-0.403765\pi\)
0.297747 + 0.954645i \(0.403765\pi\)
\(234\) −0.486150 −0.0317806
\(235\) 0 0
\(236\) 4.36299 0.284007
\(237\) 11.9660 0.777278
\(238\) −0.805506 −0.0522132
\(239\) −5.63343 −0.364396 −0.182198 0.983262i \(-0.558321\pi\)
−0.182198 + 0.983262i \(0.558321\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) 2.06096 0.132484
\(243\) −2.91410 −0.186940
\(244\) −0.462529 −0.0296104
\(245\) 0 0
\(246\) 18.4017 1.17325
\(247\) −4.82399 −0.306943
\(248\) −17.9860 −1.14211
\(249\) −21.6247 −1.37041
\(250\) 0 0
\(251\) −14.3485 −0.905668 −0.452834 0.891595i \(-0.649587\pi\)
−0.452834 + 0.891595i \(0.649587\pi\)
\(252\) 0.00941251 0.000592932 0
\(253\) −4.10623 −0.258156
\(254\) 28.5725 1.79280
\(255\) 0 0
\(256\) 11.6863 0.730392
\(257\) 12.6265 0.787620 0.393810 0.919192i \(-0.371157\pi\)
0.393810 + 0.919192i \(0.371157\pi\)
\(258\) 20.9982 1.30729
\(259\) −0.369032 −0.0229305
\(260\) 0 0
\(261\) 2.62802 0.162670
\(262\) 32.1911 1.98877
\(263\) −16.9720 −1.04654 −0.523268 0.852168i \(-0.675287\pi\)
−0.523268 + 0.852168i \(0.675287\pi\)
\(264\) −13.2632 −0.816291
\(265\) 0 0
\(266\) 0.453440 0.0278022
\(267\) −6.17714 −0.378035
\(268\) −0.106440 −0.00650185
\(269\) −22.2900 −1.35905 −0.679523 0.733654i \(-0.737813\pi\)
−0.679523 + 0.733654i \(0.737813\pi\)
\(270\) 0 0
\(271\) −30.3970 −1.84649 −0.923243 0.384216i \(-0.874472\pi\)
−0.923243 + 0.384216i \(0.874472\pi\)
\(272\) −37.5273 −2.27542
\(273\) 0.127208 0.00769895
\(274\) 9.14840 0.552675
\(275\) 0 0
\(276\) 1.23899 0.0745785
\(277\) −3.61385 −0.217135 −0.108568 0.994089i \(-0.534626\pi\)
−0.108568 + 0.994089i \(0.534626\pi\)
\(278\) −21.0101 −1.26010
\(279\) −2.15235 −0.128858
\(280\) 0 0
\(281\) −9.01500 −0.537790 −0.268895 0.963170i \(-0.586658\pi\)
−0.268895 + 0.963170i \(0.586658\pi\)
\(282\) −15.9914 −0.952273
\(283\) 1.66251 0.0988261 0.0494131 0.998778i \(-0.484265\pi\)
0.0494131 + 0.998778i \(0.484265\pi\)
\(284\) 1.13196 0.0671693
\(285\) 0 0
\(286\) 5.38274 0.318288
\(287\) −0.412798 −0.0243667
\(288\) 0.806359 0.0475151
\(289\) 44.9350 2.64323
\(290\) 0 0
\(291\) 15.8984 0.931982
\(292\) −0.760560 −0.0445084
\(293\) −30.2574 −1.76766 −0.883828 0.467812i \(-0.845043\pi\)
−0.883828 + 0.467812i \(0.845043\pi\)
\(294\) 20.1123 1.17297
\(295\) 0 0
\(296\) −13.4514 −0.781847
\(297\) 15.3391 0.890067
\(298\) −17.4604 −1.01145
\(299\) 1.43553 0.0830189
\(300\) 0 0
\(301\) −0.471045 −0.0271506
\(302\) 4.66061 0.268188
\(303\) −3.65541 −0.209998
\(304\) 21.1251 1.21161
\(305\) 0 0
\(306\) −3.51359 −0.200859
\(307\) −29.0908 −1.66030 −0.830151 0.557539i \(-0.811746\pi\)
−0.830151 + 0.557539i \(0.811746\pi\)
\(308\) −0.104217 −0.00593831
\(309\) 11.7369 0.667687
\(310\) 0 0
\(311\) 0.202626 0.0114899 0.00574494 0.999983i \(-0.498171\pi\)
0.00574494 + 0.999983i \(0.498171\pi\)
\(312\) 4.63678 0.262506
\(313\) 15.3145 0.865627 0.432814 0.901483i \(-0.357521\pi\)
0.432814 + 0.901483i \(0.357521\pi\)
\(314\) −24.6005 −1.38829
\(315\) 0 0
\(316\) 3.42725 0.192798
\(317\) 13.4881 0.757569 0.378785 0.925485i \(-0.376342\pi\)
0.378785 + 0.925485i \(0.376342\pi\)
\(318\) 6.45333 0.361885
\(319\) −29.0979 −1.62917
\(320\) 0 0
\(321\) 13.1611 0.734579
\(322\) −0.134935 −0.00751966
\(323\) −34.8648 −1.93993
\(324\) −5.06620 −0.281455
\(325\) 0 0
\(326\) 12.2425 0.678050
\(327\) −3.30425 −0.182725
\(328\) −15.0467 −0.830815
\(329\) 0.358728 0.0197773
\(330\) 0 0
\(331\) 32.3538 1.77832 0.889162 0.457593i \(-0.151288\pi\)
0.889162 + 0.457593i \(0.151288\pi\)
\(332\) −6.19362 −0.339919
\(333\) −1.60970 −0.0882112
\(334\) 16.0861 0.880192
\(335\) 0 0
\(336\) −0.557063 −0.0303903
\(337\) −14.8297 −0.807827 −0.403913 0.914797i \(-0.632350\pi\)
−0.403913 + 0.914797i \(0.632350\pi\)
\(338\) 18.7502 1.01988
\(339\) −6.56591 −0.356611
\(340\) 0 0
\(341\) 23.8312 1.29053
\(342\) 1.97789 0.106952
\(343\) −0.902612 −0.0487365
\(344\) −17.1698 −0.925736
\(345\) 0 0
\(346\) 9.93077 0.533882
\(347\) −25.0660 −1.34561 −0.672806 0.739819i \(-0.734911\pi\)
−0.672806 + 0.739819i \(0.734911\pi\)
\(348\) 8.77985 0.470649
\(349\) 19.2180 1.02872 0.514358 0.857576i \(-0.328030\pi\)
0.514358 + 0.857576i \(0.328030\pi\)
\(350\) 0 0
\(351\) −5.36254 −0.286231
\(352\) −8.92815 −0.475872
\(353\) −22.6187 −1.20387 −0.601936 0.798544i \(-0.705604\pi\)
−0.601936 + 0.798544i \(0.705604\pi\)
\(354\) −24.1762 −1.28495
\(355\) 0 0
\(356\) −1.76922 −0.0937687
\(357\) 0.919377 0.0486586
\(358\) 32.5154 1.71849
\(359\) 9.49426 0.501088 0.250544 0.968105i \(-0.419391\pi\)
0.250544 + 0.968105i \(0.419391\pi\)
\(360\) 0 0
\(361\) 0.626297 0.0329630
\(362\) 10.1317 0.532510
\(363\) −2.35231 −0.123464
\(364\) 0.0364341 0.00190967
\(365\) 0 0
\(366\) 2.56296 0.133968
\(367\) −29.1574 −1.52201 −0.761003 0.648749i \(-0.775293\pi\)
−0.761003 + 0.648749i \(0.775293\pi\)
\(368\) −6.28643 −0.327703
\(369\) −1.80061 −0.0937360
\(370\) 0 0
\(371\) −0.144765 −0.00751583
\(372\) −7.19071 −0.372821
\(373\) 35.1988 1.82252 0.911262 0.411828i \(-0.135110\pi\)
0.911262 + 0.411828i \(0.135110\pi\)
\(374\) 38.9031 2.01163
\(375\) 0 0
\(376\) 13.0758 0.674334
\(377\) 10.1726 0.523915
\(378\) 0.504062 0.0259262
\(379\) −31.9147 −1.63935 −0.819673 0.572832i \(-0.805845\pi\)
−0.819673 + 0.572832i \(0.805845\pi\)
\(380\) 0 0
\(381\) −32.6117 −1.67075
\(382\) −15.0251 −0.768751
\(383\) −20.2534 −1.03490 −0.517451 0.855713i \(-0.673119\pi\)
−0.517451 + 0.855713i \(0.673119\pi\)
\(384\) −24.7238 −1.26168
\(385\) 0 0
\(386\) 3.42237 0.174194
\(387\) −2.05468 −0.104445
\(388\) 4.55354 0.231171
\(389\) 27.5404 1.39635 0.698176 0.715926i \(-0.253995\pi\)
0.698176 + 0.715926i \(0.253995\pi\)
\(390\) 0 0
\(391\) 10.3751 0.524692
\(392\) −16.4454 −0.830621
\(393\) −36.7418 −1.85338
\(394\) 6.91353 0.348299
\(395\) 0 0
\(396\) −0.454591 −0.0228441
\(397\) 4.77657 0.239729 0.119865 0.992790i \(-0.461754\pi\)
0.119865 + 0.992790i \(0.461754\pi\)
\(398\) 16.1638 0.810217
\(399\) −0.517541 −0.0259095
\(400\) 0 0
\(401\) −2.02237 −0.100992 −0.0504962 0.998724i \(-0.516080\pi\)
−0.0504962 + 0.998724i \(0.516080\pi\)
\(402\) 0.589804 0.0294168
\(403\) −8.33137 −0.415015
\(404\) −1.04696 −0.0520884
\(405\) 0 0
\(406\) −0.956192 −0.0474550
\(407\) 17.8229 0.883450
\(408\) 33.5118 1.65908
\(409\) −31.4714 −1.55616 −0.778082 0.628163i \(-0.783807\pi\)
−0.778082 + 0.628163i \(0.783807\pi\)
\(410\) 0 0
\(411\) −10.4417 −0.515049
\(412\) 3.36161 0.165615
\(413\) 0.542335 0.0266866
\(414\) −0.588584 −0.0289273
\(415\) 0 0
\(416\) 3.12127 0.153033
\(417\) 23.9802 1.17432
\(418\) −21.8996 −1.07114
\(419\) −18.3424 −0.896084 −0.448042 0.894012i \(-0.647879\pi\)
−0.448042 + 0.894012i \(0.647879\pi\)
\(420\) 0 0
\(421\) −27.7191 −1.35095 −0.675474 0.737384i \(-0.736061\pi\)
−0.675474 + 0.737384i \(0.736061\pi\)
\(422\) −29.4359 −1.43292
\(423\) 1.56476 0.0760812
\(424\) −5.27676 −0.256262
\(425\) 0 0
\(426\) −6.27239 −0.303898
\(427\) −0.0574940 −0.00278233
\(428\) 3.76952 0.182207
\(429\) −6.14368 −0.296619
\(430\) 0 0
\(431\) 5.86749 0.282627 0.141314 0.989965i \(-0.454867\pi\)
0.141314 + 0.989965i \(0.454867\pi\)
\(432\) 23.4835 1.12985
\(433\) −15.0366 −0.722611 −0.361306 0.932447i \(-0.617669\pi\)
−0.361306 + 0.932447i \(0.617669\pi\)
\(434\) 0.783123 0.0375911
\(435\) 0 0
\(436\) −0.946385 −0.0453236
\(437\) −5.84043 −0.279385
\(438\) 4.21441 0.201372
\(439\) 20.8095 0.993185 0.496593 0.867984i \(-0.334584\pi\)
0.496593 + 0.867984i \(0.334584\pi\)
\(440\) 0 0
\(441\) −1.96800 −0.0937141
\(442\) −13.6005 −0.646908
\(443\) 10.0002 0.475124 0.237562 0.971372i \(-0.423652\pi\)
0.237562 + 0.971372i \(0.423652\pi\)
\(444\) −5.37780 −0.255219
\(445\) 0 0
\(446\) −11.5010 −0.544589
\(447\) 19.9287 0.942596
\(448\) 0.321661 0.0151971
\(449\) −2.65024 −0.125072 −0.0625362 0.998043i \(-0.519919\pi\)
−0.0625362 + 0.998043i \(0.519919\pi\)
\(450\) 0 0
\(451\) 19.9367 0.938782
\(452\) −1.88057 −0.0884548
\(453\) −5.31946 −0.249930
\(454\) 29.8777 1.40223
\(455\) 0 0
\(456\) −18.8646 −0.883418
\(457\) 5.43669 0.254318 0.127159 0.991882i \(-0.459414\pi\)
0.127159 + 0.991882i \(0.459414\pi\)
\(458\) −38.8778 −1.81664
\(459\) −38.7571 −1.80903
\(460\) 0 0
\(461\) 16.0079 0.745564 0.372782 0.927919i \(-0.378404\pi\)
0.372782 + 0.927919i \(0.378404\pi\)
\(462\) 0.577487 0.0268671
\(463\) 1.33278 0.0619394 0.0309697 0.999520i \(-0.490140\pi\)
0.0309697 + 0.999520i \(0.490140\pi\)
\(464\) −44.5475 −2.06807
\(465\) 0 0
\(466\) −14.4263 −0.668284
\(467\) −7.86721 −0.364051 −0.182026 0.983294i \(-0.558265\pi\)
−0.182026 + 0.983294i \(0.558265\pi\)
\(468\) 0.158924 0.00734628
\(469\) −0.0132308 −0.000610944 0
\(470\) 0 0
\(471\) 28.0782 1.29378
\(472\) 19.7684 0.909914
\(473\) 22.7498 1.04604
\(474\) −18.9911 −0.872288
\(475\) 0 0
\(476\) 0.263323 0.0120694
\(477\) −0.631460 −0.0289126
\(478\) 8.94070 0.408938
\(479\) 7.30904 0.333958 0.166979 0.985960i \(-0.446599\pi\)
0.166979 + 0.985960i \(0.446599\pi\)
\(480\) 0 0
\(481\) −6.23087 −0.284103
\(482\) −1.58708 −0.0722895
\(483\) 0.154011 0.00700773
\(484\) −0.673736 −0.0306244
\(485\) 0 0
\(486\) 4.62491 0.209790
\(487\) 24.3739 1.10449 0.552243 0.833683i \(-0.313772\pi\)
0.552243 + 0.833683i \(0.313772\pi\)
\(488\) −2.09569 −0.0948672
\(489\) −13.9732 −0.631890
\(490\) 0 0
\(491\) 15.6542 0.706465 0.353232 0.935536i \(-0.385083\pi\)
0.353232 + 0.935536i \(0.385083\pi\)
\(492\) −6.01559 −0.271204
\(493\) 73.5212 3.31123
\(494\) 7.65606 0.344462
\(495\) 0 0
\(496\) 36.4845 1.63820
\(497\) 0.140706 0.00631153
\(498\) 34.3201 1.53792
\(499\) −28.7368 −1.28644 −0.643218 0.765683i \(-0.722401\pi\)
−0.643218 + 0.765683i \(0.722401\pi\)
\(500\) 0 0
\(501\) −18.3601 −0.820269
\(502\) 22.7722 1.01637
\(503\) −0.207761 −0.00926360 −0.00463180 0.999989i \(-0.501474\pi\)
−0.00463180 + 0.999989i \(0.501474\pi\)
\(504\) 0.0426473 0.00189966
\(505\) 0 0
\(506\) 6.51691 0.289712
\(507\) −21.4009 −0.950446
\(508\) −9.34048 −0.414417
\(509\) 9.52541 0.422206 0.211103 0.977464i \(-0.432294\pi\)
0.211103 + 0.977464i \(0.432294\pi\)
\(510\) 0 0
\(511\) −0.0945401 −0.00418221
\(512\) 8.75036 0.386715
\(513\) 21.8174 0.963261
\(514\) −20.0393 −0.883894
\(515\) 0 0
\(516\) −6.86441 −0.302189
\(517\) −17.3253 −0.761966
\(518\) 0.585683 0.0257334
\(519\) −11.3346 −0.497536
\(520\) 0 0
\(521\) 34.1721 1.49711 0.748553 0.663075i \(-0.230749\pi\)
0.748553 + 0.663075i \(0.230749\pi\)
\(522\) −4.17088 −0.182554
\(523\) 19.9061 0.870432 0.435216 0.900326i \(-0.356672\pi\)
0.435216 + 0.900326i \(0.356672\pi\)
\(524\) −10.5234 −0.459717
\(525\) 0 0
\(526\) 26.9359 1.17446
\(527\) −60.2139 −2.62296
\(528\) 26.9042 1.17085
\(529\) −21.2620 −0.924435
\(530\) 0 0
\(531\) 2.36565 0.102660
\(532\) −0.148231 −0.00642665
\(533\) −6.96984 −0.301897
\(534\) 9.80362 0.424244
\(535\) 0 0
\(536\) −0.482271 −0.0208309
\(537\) −37.1120 −1.60150
\(538\) 35.3760 1.52517
\(539\) 21.7900 0.938562
\(540\) 0 0
\(541\) −14.8350 −0.637808 −0.318904 0.947787i \(-0.603315\pi\)
−0.318904 + 0.947787i \(0.603315\pi\)
\(542\) 48.2425 2.07219
\(543\) −11.5640 −0.496258
\(544\) 22.5586 0.967191
\(545\) 0 0
\(546\) −0.201889 −0.00864003
\(547\) −26.9418 −1.15195 −0.575974 0.817468i \(-0.695377\pi\)
−0.575974 + 0.817468i \(0.695377\pi\)
\(548\) −2.99065 −0.127754
\(549\) −0.250787 −0.0107033
\(550\) 0 0
\(551\) −41.3870 −1.76314
\(552\) 5.61377 0.238938
\(553\) 0.426019 0.0181162
\(554\) 5.73546 0.243677
\(555\) 0 0
\(556\) 6.86829 0.291280
\(557\) −35.8208 −1.51777 −0.758887 0.651222i \(-0.774257\pi\)
−0.758887 + 0.651222i \(0.774257\pi\)
\(558\) 3.41596 0.144609
\(559\) −7.95331 −0.336389
\(560\) 0 0
\(561\) −44.4027 −1.87468
\(562\) 14.3075 0.603526
\(563\) 39.5803 1.66811 0.834055 0.551682i \(-0.186014\pi\)
0.834055 + 0.551682i \(0.186014\pi\)
\(564\) 5.22765 0.220124
\(565\) 0 0
\(566\) −2.63854 −0.110906
\(567\) −0.629745 −0.0264468
\(568\) 5.12881 0.215200
\(569\) 7.96023 0.333710 0.166855 0.985981i \(-0.446639\pi\)
0.166855 + 0.985981i \(0.446639\pi\)
\(570\) 0 0
\(571\) 3.11420 0.130325 0.0651625 0.997875i \(-0.479243\pi\)
0.0651625 + 0.997875i \(0.479243\pi\)
\(572\) −1.75964 −0.0735742
\(573\) 17.1491 0.716415
\(574\) 0.655143 0.0273452
\(575\) 0 0
\(576\) 1.40307 0.0584614
\(577\) −1.43705 −0.0598250 −0.0299125 0.999553i \(-0.509523\pi\)
−0.0299125 + 0.999553i \(0.509523\pi\)
\(578\) −71.3154 −2.96633
\(579\) −3.90617 −0.162335
\(580\) 0 0
\(581\) −0.769888 −0.0319403
\(582\) −25.2321 −1.04590
\(583\) 6.99164 0.289564
\(584\) −3.44604 −0.142598
\(585\) 0 0
\(586\) 48.0209 1.98373
\(587\) −13.8048 −0.569783 −0.284892 0.958560i \(-0.591958\pi\)
−0.284892 + 0.958560i \(0.591958\pi\)
\(588\) −6.57480 −0.271140
\(589\) 33.8960 1.39666
\(590\) 0 0
\(591\) −7.89087 −0.324587
\(592\) 27.2860 1.12145
\(593\) 6.55202 0.269059 0.134530 0.990910i \(-0.457048\pi\)
0.134530 + 0.990910i \(0.457048\pi\)
\(594\) −24.3444 −0.998864
\(595\) 0 0
\(596\) 5.70788 0.233804
\(597\) −18.4488 −0.755058
\(598\) −2.27830 −0.0931667
\(599\) −0.304293 −0.0124331 −0.00621653 0.999981i \(-0.501979\pi\)
−0.00621653 + 0.999981i \(0.501979\pi\)
\(600\) 0 0
\(601\) −5.74779 −0.234457 −0.117229 0.993105i \(-0.537401\pi\)
−0.117229 + 0.993105i \(0.537401\pi\)
\(602\) 0.747586 0.0304693
\(603\) −0.0577125 −0.00235023
\(604\) −1.52357 −0.0619933
\(605\) 0 0
\(606\) 5.80143 0.235667
\(607\) 8.27242 0.335767 0.167884 0.985807i \(-0.446307\pi\)
0.167884 + 0.985807i \(0.446307\pi\)
\(608\) −12.6988 −0.515005
\(609\) 1.09137 0.0442243
\(610\) 0 0
\(611\) 6.05690 0.245036
\(612\) 1.14861 0.0464297
\(613\) −7.23604 −0.292261 −0.146130 0.989265i \(-0.546682\pi\)
−0.146130 + 0.989265i \(0.546682\pi\)
\(614\) 46.1695 1.86325
\(615\) 0 0
\(616\) −0.472199 −0.0190255
\(617\) 38.1701 1.53667 0.768335 0.640048i \(-0.221086\pi\)
0.768335 + 0.640048i \(0.221086\pi\)
\(618\) −18.6274 −0.749302
\(619\) 19.8009 0.795865 0.397932 0.917415i \(-0.369728\pi\)
0.397932 + 0.917415i \(0.369728\pi\)
\(620\) 0 0
\(621\) −6.49245 −0.260533
\(622\) −0.321584 −0.0128943
\(623\) −0.219921 −0.00881093
\(624\) −9.40567 −0.376528
\(625\) 0 0
\(626\) −24.3054 −0.971437
\(627\) 24.9954 0.998221
\(628\) 8.04201 0.320911
\(629\) −45.0329 −1.79558
\(630\) 0 0
\(631\) −34.7838 −1.38472 −0.692362 0.721551i \(-0.743430\pi\)
−0.692362 + 0.721551i \(0.743430\pi\)
\(632\) 15.5286 0.617695
\(633\) 33.5971 1.33537
\(634\) −21.4067 −0.850171
\(635\) 0 0
\(636\) −2.10962 −0.0836519
\(637\) −7.61776 −0.301827
\(638\) 46.1807 1.82831
\(639\) 0.613755 0.0242798
\(640\) 0 0
\(641\) −45.1011 −1.78139 −0.890694 0.454603i \(-0.849781\pi\)
−0.890694 + 0.454603i \(0.849781\pi\)
\(642\) −20.8876 −0.824370
\(643\) 22.6840 0.894569 0.447285 0.894392i \(-0.352391\pi\)
0.447285 + 0.894392i \(0.352391\pi\)
\(644\) 0.0441109 0.00173821
\(645\) 0 0
\(646\) 55.3332 2.17706
\(647\) 5.70435 0.224261 0.112131 0.993693i \(-0.464233\pi\)
0.112131 + 0.993693i \(0.464233\pi\)
\(648\) −22.9546 −0.901740
\(649\) −26.1929 −1.02816
\(650\) 0 0
\(651\) −0.893830 −0.0350319
\(652\) −4.00213 −0.156735
\(653\) −9.26570 −0.362595 −0.181297 0.983428i \(-0.558030\pi\)
−0.181297 + 0.983428i \(0.558030\pi\)
\(654\) 5.24410 0.205061
\(655\) 0 0
\(656\) 30.5221 1.19169
\(657\) −0.412381 −0.0160885
\(658\) −0.569330 −0.0221948
\(659\) 33.4266 1.30212 0.651058 0.759028i \(-0.274325\pi\)
0.651058 + 0.759028i \(0.274325\pi\)
\(660\) 0 0
\(661\) −38.9425 −1.51469 −0.757345 0.653015i \(-0.773504\pi\)
−0.757345 + 0.653015i \(0.773504\pi\)
\(662\) −51.3480 −1.99570
\(663\) 15.5231 0.602868
\(664\) −28.0628 −1.08905
\(665\) 0 0
\(666\) 2.55473 0.0989937
\(667\) 12.3160 0.476878
\(668\) −5.25861 −0.203462
\(669\) 13.1269 0.507514
\(670\) 0 0
\(671\) 2.77676 0.107195
\(672\) 0.334865 0.0129177
\(673\) −27.0760 −1.04370 −0.521851 0.853037i \(-0.674758\pi\)
−0.521851 + 0.853037i \(0.674758\pi\)
\(674\) 23.5360 0.906572
\(675\) 0 0
\(676\) −6.12953 −0.235751
\(677\) −40.1184 −1.54187 −0.770937 0.636911i \(-0.780212\pi\)
−0.770937 + 0.636911i \(0.780212\pi\)
\(678\) 10.4206 0.400202
\(679\) 0.566021 0.0217219
\(680\) 0 0
\(681\) −34.1014 −1.30677
\(682\) −37.8221 −1.44828
\(683\) 9.16420 0.350658 0.175329 0.984510i \(-0.443901\pi\)
0.175329 + 0.984510i \(0.443901\pi\)
\(684\) −0.646580 −0.0247226
\(685\) 0 0
\(686\) 1.43252 0.0546938
\(687\) 44.3738 1.69297
\(688\) 34.8289 1.32784
\(689\) −2.44427 −0.0931192
\(690\) 0 0
\(691\) −3.48079 −0.132415 −0.0662077 0.997806i \(-0.521090\pi\)
−0.0662077 + 0.997806i \(0.521090\pi\)
\(692\) −3.24641 −0.123410
\(693\) −0.0565072 −0.00214653
\(694\) 39.7817 1.51009
\(695\) 0 0
\(696\) 39.7808 1.50789
\(697\) −50.3736 −1.90804
\(698\) −30.5005 −1.15446
\(699\) 16.4656 0.622788
\(700\) 0 0
\(701\) −15.3573 −0.580036 −0.290018 0.957021i \(-0.593661\pi\)
−0.290018 + 0.957021i \(0.593661\pi\)
\(702\) 8.51078 0.321219
\(703\) 25.3502 0.956100
\(704\) −15.5351 −0.585501
\(705\) 0 0
\(706\) 35.8977 1.35103
\(707\) −0.130141 −0.00489446
\(708\) 7.90329 0.297024
\(709\) −46.4365 −1.74396 −0.871979 0.489543i \(-0.837164\pi\)
−0.871979 + 0.489543i \(0.837164\pi\)
\(710\) 0 0
\(711\) 1.85828 0.0696909
\(712\) −8.01622 −0.300421
\(713\) −10.0868 −0.377755
\(714\) −1.45912 −0.0546064
\(715\) 0 0
\(716\) −10.6294 −0.397240
\(717\) −10.2046 −0.381098
\(718\) −15.0682 −0.562338
\(719\) 31.5267 1.17575 0.587875 0.808952i \(-0.299965\pi\)
0.587875 + 0.808952i \(0.299965\pi\)
\(720\) 0 0
\(721\) 0.417860 0.0155619
\(722\) −0.993984 −0.0369923
\(723\) 1.81144 0.0673681
\(724\) −3.31209 −0.123093
\(725\) 0 0
\(726\) 3.73330 0.138556
\(727\) −3.11621 −0.115574 −0.0577870 0.998329i \(-0.518404\pi\)
−0.0577870 + 0.998329i \(0.518404\pi\)
\(728\) 0.165080 0.00611828
\(729\) 24.0157 0.889469
\(730\) 0 0
\(731\) −57.4815 −2.12603
\(732\) −0.837843 −0.0309676
\(733\) −12.7951 −0.472599 −0.236299 0.971680i \(-0.575935\pi\)
−0.236299 + 0.971680i \(0.575935\pi\)
\(734\) 46.2752 1.70805
\(735\) 0 0
\(736\) 3.77893 0.139293
\(737\) 0.639003 0.0235380
\(738\) 2.85771 0.105194
\(739\) −30.5478 −1.12372 −0.561860 0.827232i \(-0.689914\pi\)
−0.561860 + 0.827232i \(0.689914\pi\)
\(740\) 0 0
\(741\) −8.73836 −0.321012
\(742\) 0.229754 0.00843452
\(743\) 2.28803 0.0839397 0.0419699 0.999119i \(-0.486637\pi\)
0.0419699 + 0.999119i \(0.486637\pi\)
\(744\) −32.5806 −1.19446
\(745\) 0 0
\(746\) −55.8633 −2.04530
\(747\) −3.35823 −0.122871
\(748\) −12.7176 −0.465001
\(749\) 0.468564 0.0171210
\(750\) 0 0
\(751\) −40.3570 −1.47265 −0.736323 0.676630i \(-0.763440\pi\)
−0.736323 + 0.676630i \(0.763440\pi\)
\(752\) −26.5242 −0.967238
\(753\) −25.9914 −0.947179
\(754\) −16.1447 −0.587956
\(755\) 0 0
\(756\) −0.164780 −0.00599299
\(757\) −2.91012 −0.105770 −0.0528851 0.998601i \(-0.516842\pi\)
−0.0528851 + 0.998601i \(0.516842\pi\)
\(758\) 50.6511 1.83973
\(759\) −7.43818 −0.269989
\(760\) 0 0
\(761\) −37.6866 −1.36614 −0.683069 0.730354i \(-0.739355\pi\)
−0.683069 + 0.730354i \(0.739355\pi\)
\(762\) 51.7574 1.87497
\(763\) −0.117639 −0.00425881
\(764\) 4.91176 0.177701
\(765\) 0 0
\(766\) 32.1438 1.16140
\(767\) 9.15699 0.330640
\(768\) 21.1690 0.763869
\(769\) 5.83460 0.210401 0.105201 0.994451i \(-0.466452\pi\)
0.105201 + 0.994451i \(0.466452\pi\)
\(770\) 0 0
\(771\) 22.8721 0.823720
\(772\) −1.11878 −0.0402659
\(773\) 15.0568 0.541554 0.270777 0.962642i \(-0.412719\pi\)
0.270777 + 0.962642i \(0.412719\pi\)
\(774\) 3.26094 0.117212
\(775\) 0 0
\(776\) 20.6318 0.740637
\(777\) −0.668478 −0.0239815
\(778\) −43.7087 −1.56703
\(779\) 28.3566 1.01598
\(780\) 0 0
\(781\) −6.79561 −0.243166
\(782\) −16.4661 −0.588828
\(783\) −46.0074 −1.64417
\(784\) 33.3594 1.19141
\(785\) 0 0
\(786\) 58.3122 2.07993
\(787\) −8.82663 −0.314635 −0.157318 0.987548i \(-0.550285\pi\)
−0.157318 + 0.987548i \(0.550285\pi\)
\(788\) −2.26006 −0.0805114
\(789\) −30.7437 −1.09450
\(790\) 0 0
\(791\) −0.233762 −0.00831161
\(792\) −2.05972 −0.0731889
\(793\) −0.970750 −0.0344723
\(794\) −7.58079 −0.269032
\(795\) 0 0
\(796\) −5.28400 −0.187286
\(797\) 17.7244 0.627831 0.313916 0.949451i \(-0.398359\pi\)
0.313916 + 0.949451i \(0.398359\pi\)
\(798\) 0.821379 0.0290765
\(799\) 43.7755 1.54867
\(800\) 0 0
\(801\) −0.959286 −0.0338947
\(802\) 3.20966 0.113337
\(803\) 4.56596 0.161129
\(804\) −0.192809 −0.00679986
\(805\) 0 0
\(806\) 13.2225 0.465744
\(807\) −40.3770 −1.42134
\(808\) −4.74371 −0.166883
\(809\) −23.8068 −0.837003 −0.418502 0.908216i \(-0.637445\pi\)
−0.418502 + 0.908216i \(0.637445\pi\)
\(810\) 0 0
\(811\) −40.4561 −1.42061 −0.710303 0.703896i \(-0.751442\pi\)
−0.710303 + 0.703896i \(0.751442\pi\)
\(812\) 0.312583 0.0109695
\(813\) −55.0623 −1.93112
\(814\) −28.2864 −0.991438
\(815\) 0 0
\(816\) −67.9783 −2.37972
\(817\) 32.3578 1.13206
\(818\) 49.9477 1.74638
\(819\) 0.0197548 0.000690290 0
\(820\) 0 0
\(821\) 3.14174 0.109647 0.0548237 0.998496i \(-0.482540\pi\)
0.0548237 + 0.998496i \(0.482540\pi\)
\(822\) 16.5718 0.578006
\(823\) −8.01920 −0.279532 −0.139766 0.990185i \(-0.544635\pi\)
−0.139766 + 0.990185i \(0.544635\pi\)
\(824\) 15.2312 0.530605
\(825\) 0 0
\(826\) −0.860729 −0.0299486
\(827\) −8.81985 −0.306696 −0.153348 0.988172i \(-0.549006\pi\)
−0.153348 + 0.988172i \(0.549006\pi\)
\(828\) 0.192410 0.00668672
\(829\) 32.1961 1.11822 0.559109 0.829094i \(-0.311143\pi\)
0.559109 + 0.829094i \(0.311143\pi\)
\(830\) 0 0
\(831\) −6.54626 −0.227087
\(832\) 5.43105 0.188288
\(833\) −55.0564 −1.90759
\(834\) −38.0585 −1.31786
\(835\) 0 0
\(836\) 7.15906 0.247601
\(837\) 37.6801 1.30242
\(838\) 29.1108 1.00562
\(839\) −28.0117 −0.967070 −0.483535 0.875325i \(-0.660647\pi\)
−0.483535 + 0.875325i \(0.660647\pi\)
\(840\) 0 0
\(841\) 58.2748 2.00948
\(842\) 43.9925 1.51608
\(843\) −16.3301 −0.562439
\(844\) 9.62272 0.331228
\(845\) 0 0
\(846\) −2.48340 −0.0853810
\(847\) −0.0837477 −0.00287761
\(848\) 10.7039 0.367572
\(849\) 3.01154 0.103356
\(850\) 0 0
\(851\) −7.54374 −0.258596
\(852\) 2.05047 0.0702480
\(853\) 55.6683 1.90605 0.953023 0.302898i \(-0.0979541\pi\)
0.953023 + 0.302898i \(0.0979541\pi\)
\(854\) 0.0912475 0.00312243
\(855\) 0 0
\(856\) 17.0794 0.583762
\(857\) 8.05803 0.275257 0.137629 0.990484i \(-0.456052\pi\)
0.137629 + 0.990484i \(0.456052\pi\)
\(858\) 9.75051 0.332877
\(859\) 24.6779 0.841999 0.421000 0.907061i \(-0.361679\pi\)
0.421000 + 0.907061i \(0.361679\pi\)
\(860\) 0 0
\(861\) −0.747758 −0.0254835
\(862\) −9.31218 −0.317174
\(863\) 4.35714 0.148319 0.0741594 0.997246i \(-0.476373\pi\)
0.0741594 + 0.997246i \(0.476373\pi\)
\(864\) −14.1165 −0.480253
\(865\) 0 0
\(866\) 23.8642 0.810940
\(867\) 81.3969 2.76438
\(868\) −0.256006 −0.00868941
\(869\) −20.5752 −0.697966
\(870\) 0 0
\(871\) −0.223395 −0.00756944
\(872\) −4.28800 −0.145210
\(873\) 2.46896 0.0835618
\(874\) 9.26922 0.313536
\(875\) 0 0
\(876\) −1.37771 −0.0465484
\(877\) −33.5278 −1.13215 −0.566076 0.824353i \(-0.691539\pi\)
−0.566076 + 0.824353i \(0.691539\pi\)
\(878\) −33.0264 −1.11459
\(879\) −54.8094 −1.84868
\(880\) 0 0
\(881\) 2.62147 0.0883196 0.0441598 0.999024i \(-0.485939\pi\)
0.0441598 + 0.999024i \(0.485939\pi\)
\(882\) 3.12337 0.105169
\(883\) −18.5159 −0.623109 −0.311554 0.950228i \(-0.600850\pi\)
−0.311554 + 0.950228i \(0.600850\pi\)
\(884\) 4.44605 0.149537
\(885\) 0 0
\(886\) −15.8711 −0.533201
\(887\) 38.9847 1.30898 0.654489 0.756072i \(-0.272884\pi\)
0.654489 + 0.756072i \(0.272884\pi\)
\(888\) −24.3664 −0.817682
\(889\) −1.16105 −0.0389405
\(890\) 0 0
\(891\) 30.4145 1.01892
\(892\) 3.75973 0.125885
\(893\) −24.6424 −0.824626
\(894\) −31.6285 −1.05781
\(895\) 0 0
\(896\) −0.880224 −0.0294062
\(897\) 2.60038 0.0868240
\(898\) 4.20614 0.140361
\(899\) −71.4782 −2.38393
\(900\) 0 0
\(901\) −17.6657 −0.588528
\(902\) −31.6411 −1.05353
\(903\) −0.853269 −0.0283950
\(904\) −8.52074 −0.283396
\(905\) 0 0
\(906\) 8.44241 0.280480
\(907\) −24.5838 −0.816292 −0.408146 0.912917i \(-0.633825\pi\)
−0.408146 + 0.912917i \(0.633825\pi\)
\(908\) −9.76714 −0.324134
\(909\) −0.567671 −0.0188285
\(910\) 0 0
\(911\) −1.85950 −0.0616080 −0.0308040 0.999525i \(-0.509807\pi\)
−0.0308040 + 0.999525i \(0.509807\pi\)
\(912\) 38.2668 1.26714
\(913\) 37.1829 1.23057
\(914\) −8.62847 −0.285404
\(915\) 0 0
\(916\) 12.7093 0.419927
\(917\) −1.30810 −0.0431971
\(918\) 61.5106 2.03015
\(919\) −52.9084 −1.74529 −0.872644 0.488357i \(-0.837597\pi\)
−0.872644 + 0.488357i \(0.837597\pi\)
\(920\) 0 0
\(921\) −52.6963 −1.73640
\(922\) −25.4059 −0.836698
\(923\) 2.37574 0.0781983
\(924\) −0.188783 −0.00621049
\(925\) 0 0
\(926\) −2.11522 −0.0695106
\(927\) 1.82269 0.0598650
\(928\) 26.7786 0.879052
\(929\) 44.0809 1.44625 0.723124 0.690718i \(-0.242705\pi\)
0.723124 + 0.690718i \(0.242705\pi\)
\(930\) 0 0
\(931\) 30.9927 1.01574
\(932\) 4.71600 0.154478
\(933\) 0.367045 0.0120165
\(934\) 12.4859 0.408551
\(935\) 0 0
\(936\) 0.720074 0.0235364
\(937\) −52.8193 −1.72553 −0.862765 0.505604i \(-0.831270\pi\)
−0.862765 + 0.505604i \(0.831270\pi\)
\(938\) 0.0209984 0.000685622 0
\(939\) 27.7413 0.905303
\(940\) 0 0
\(941\) 12.3015 0.401017 0.200508 0.979692i \(-0.435741\pi\)
0.200508 + 0.979692i \(0.435741\pi\)
\(942\) −44.5624 −1.45192
\(943\) −8.43841 −0.274793
\(944\) −40.1000 −1.30514
\(945\) 0 0
\(946\) −36.1058 −1.17390
\(947\) 7.11954 0.231354 0.115677 0.993287i \(-0.463096\pi\)
0.115677 + 0.993287i \(0.463096\pi\)
\(948\) 6.20826 0.201635
\(949\) −1.59625 −0.0518165
\(950\) 0 0
\(951\) 24.4329 0.792292
\(952\) 1.19310 0.0386685
\(953\) −11.3501 −0.367665 −0.183832 0.982958i \(-0.558850\pi\)
−0.183832 + 0.982958i \(0.558850\pi\)
\(954\) 1.00218 0.0324467
\(955\) 0 0
\(956\) −2.92275 −0.0945285
\(957\) −52.7091 −1.70384
\(958\) −11.6000 −0.374780
\(959\) −0.371748 −0.0120044
\(960\) 0 0
\(961\) 27.5408 0.888412
\(962\) 9.88889 0.318831
\(963\) 2.04386 0.0658625
\(964\) 0.518823 0.0167102
\(965\) 0 0
\(966\) −0.244427 −0.00786432
\(967\) 51.3389 1.65095 0.825473 0.564441i \(-0.190908\pi\)
0.825473 + 0.564441i \(0.190908\pi\)
\(968\) −3.05265 −0.0981158
\(969\) −63.1554 −2.02884
\(970\) 0 0
\(971\) 45.3139 1.45419 0.727097 0.686535i \(-0.240869\pi\)
0.727097 + 0.686535i \(0.240869\pi\)
\(972\) −1.51190 −0.0484943
\(973\) 0.853752 0.0273700
\(974\) −38.6833 −1.23949
\(975\) 0 0
\(976\) 4.25108 0.136074
\(977\) 49.5972 1.58675 0.793377 0.608730i \(-0.208321\pi\)
0.793377 + 0.608730i \(0.208321\pi\)
\(978\) 22.1766 0.709129
\(979\) 10.6214 0.339461
\(980\) 0 0
\(981\) −0.513137 −0.0163832
\(982\) −24.8445 −0.792819
\(983\) −43.7321 −1.39484 −0.697418 0.716665i \(-0.745668\pi\)
−0.697418 + 0.716665i \(0.745668\pi\)
\(984\) −27.2562 −0.868895
\(985\) 0 0
\(986\) −116.684 −3.71597
\(987\) 0.649814 0.0206838
\(988\) −2.50280 −0.0796246
\(989\) −9.62910 −0.306188
\(990\) 0 0
\(991\) 45.7710 1.45396 0.726981 0.686657i \(-0.240923\pi\)
0.726981 + 0.686657i \(0.240923\pi\)
\(992\) −21.9317 −0.696334
\(993\) 58.6068 1.85983
\(994\) −0.223312 −0.00708302
\(995\) 0 0
\(996\) −11.2194 −0.355499
\(997\) 38.4455 1.21758 0.608790 0.793331i \(-0.291655\pi\)
0.608790 + 0.793331i \(0.291655\pi\)
\(998\) 45.6076 1.44368
\(999\) 28.1803 0.891584
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 6025.2.a.m.1.12 40
5.4 even 2 6025.2.a.n.1.29 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6025.2.a.m.1.12 40 1.1 even 1 trivial
6025.2.a.n.1.29 yes 40 5.4 even 2