Properties

Label 547.6.a.b.1.11
Level $547$
Weight $6$
Character 547.1
Self dual yes
Analytic conductor $87.730$
Analytic rank $0$
Dimension $117$
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] = [547,6,Mod(1,547)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(547, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("547.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 547 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 547.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: \(87.7299494377\)
Analytic rank: \(0\)
Dimension: \(117\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) \(=\) 547.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-9.59008 q^{2} +16.3551 q^{3} +59.9697 q^{4} +7.17600 q^{5} -156.846 q^{6} +253.293 q^{7} -268.232 q^{8} +24.4881 q^{9} +O(q^{10})\) \(q-9.59008 q^{2} +16.3551 q^{3} +59.9697 q^{4} +7.17600 q^{5} -156.846 q^{6} +253.293 q^{7} -268.232 q^{8} +24.4881 q^{9} -68.8184 q^{10} +232.324 q^{11} +980.808 q^{12} -147.492 q^{13} -2429.10 q^{14} +117.364 q^{15} +653.334 q^{16} +32.0243 q^{17} -234.843 q^{18} +356.352 q^{19} +430.342 q^{20} +4142.62 q^{21} -2228.01 q^{22} +2571.17 q^{23} -4386.95 q^{24} -3073.51 q^{25} +1414.46 q^{26} -3573.78 q^{27} +15189.9 q^{28} +3131.09 q^{29} -1125.53 q^{30} -4885.47 q^{31} +2317.89 q^{32} +3799.68 q^{33} -307.116 q^{34} +1817.63 q^{35} +1468.55 q^{36} +8933.18 q^{37} -3417.45 q^{38} -2412.24 q^{39} -1924.83 q^{40} -235.516 q^{41} -39728.1 q^{42} +5683.28 q^{43} +13932.4 q^{44} +175.727 q^{45} -24657.7 q^{46} +29165.7 q^{47} +10685.3 q^{48} +47350.2 q^{49} +29475.2 q^{50} +523.760 q^{51} -8845.04 q^{52} -23417.4 q^{53} +34272.8 q^{54} +1667.16 q^{55} -67941.2 q^{56} +5828.17 q^{57} -30027.4 q^{58} +7454.46 q^{59} +7038.28 q^{60} +30262.1 q^{61} +46852.0 q^{62} +6202.67 q^{63} -43135.4 q^{64} -1058.40 q^{65} -36439.2 q^{66} -31380.7 q^{67} +1920.49 q^{68} +42051.6 q^{69} -17431.2 q^{70} +73810.7 q^{71} -6568.49 q^{72} +72207.8 q^{73} -85669.9 q^{74} -50267.4 q^{75} +21370.3 q^{76} +58846.1 q^{77} +23133.6 q^{78} -41830.8 q^{79} +4688.32 q^{80} -64399.9 q^{81} +2258.62 q^{82} -27176.2 q^{83} +248432. q^{84} +229.807 q^{85} -54503.1 q^{86} +51209.1 q^{87} -62316.8 q^{88} +28556.0 q^{89} -1685.23 q^{90} -37358.6 q^{91} +154192. q^{92} -79902.1 q^{93} -279701. q^{94} +2557.18 q^{95} +37909.2 q^{96} -168665. q^{97} -454093. q^{98} +5689.19 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 117 q + 24 q^{2} + 100 q^{3} + 1962 q^{4} + 749 q^{5} + 306 q^{6} + 393 q^{7} + 1152 q^{8} + 10671 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 117 q + 24 q^{2} + 100 q^{3} + 1962 q^{4} + 749 q^{5} + 306 q^{6} + 393 q^{7} + 1152 q^{8} + 10671 q^{9} + 850 q^{10} + 1798 q^{11} + 5361 q^{12} + 4419 q^{13} + 3847 q^{14} + 1913 q^{15} + 34722 q^{16} + 15252 q^{17} + 2367 q^{18} + 1052 q^{19} + 23568 q^{20} + 9212 q^{21} + 9176 q^{22} + 18178 q^{23} + 15983 q^{24} + 84312 q^{25} + 21552 q^{26} + 30883 q^{27} + 23528 q^{28} + 43620 q^{29} + 23582 q^{30} + 13127 q^{31} + 49108 q^{32} + 39222 q^{33} + 32097 q^{34} + 52467 q^{35} + 217244 q^{36} + 56152 q^{37} + 76245 q^{38} + 28595 q^{39} + 20368 q^{40} + 46679 q^{41} + 78924 q^{42} + 39058 q^{43} + 78528 q^{44} + 185770 q^{45} + 41430 q^{46} + 150268 q^{47} + 180930 q^{48} + 323802 q^{49} + 91604 q^{50} + 43367 q^{51} + 136030 q^{52} + 297398 q^{53} + 116761 q^{54} + 94579 q^{55} + 173545 q^{56} + 164740 q^{57} + 87844 q^{58} + 135778 q^{59} + 114650 q^{60} + 166976 q^{61} + 229394 q^{62} + 147179 q^{63} + 630138 q^{64} + 216626 q^{65} + 82380 q^{66} + 133444 q^{67} + 634057 q^{68} + 232986 q^{69} + 30943 q^{70} + 126787 q^{71} + 78583 q^{72} + 241702 q^{73} + 242589 q^{74} + 374853 q^{75} + 90228 q^{76} + 766693 q^{77} + 82537 q^{78} + 117230 q^{79} + 730509 q^{80} + 1051409 q^{81} + 468130 q^{82} + 368467 q^{83} + 234191 q^{84} + 261997 q^{85} + 230487 q^{86} + 214239 q^{87} + 247415 q^{88} + 494902 q^{89} + 41821 q^{90} + 259647 q^{91} + 663682 q^{92} + 767344 q^{93} + 373605 q^{94} + 426186 q^{95} + 474162 q^{96} + 733038 q^{97} + 461746 q^{98} + 334651 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −9.59008 −1.69530 −0.847652 0.530553i \(-0.821984\pi\)
−0.847652 + 0.530553i \(0.821984\pi\)
\(3\) 16.3551 1.04918 0.524589 0.851356i \(-0.324219\pi\)
0.524589 + 0.851356i \(0.324219\pi\)
\(4\) 59.9697 1.87405
\(5\) 7.17600 0.128368 0.0641841 0.997938i \(-0.479556\pi\)
0.0641841 + 0.997938i \(0.479556\pi\)
\(6\) −156.846 −1.77867
\(7\) 253.293 1.95379 0.976895 0.213721i \(-0.0685584\pi\)
0.976895 + 0.213721i \(0.0685584\pi\)
\(8\) −268.232 −1.48178
\(9\) 24.4881 0.100774
\(10\) −68.8184 −0.217623
\(11\) 232.324 0.578913 0.289456 0.957191i \(-0.406526\pi\)
0.289456 + 0.957191i \(0.406526\pi\)
\(12\) 980.808 1.96621
\(13\) −147.492 −0.242052 −0.121026 0.992649i \(-0.538619\pi\)
−0.121026 + 0.992649i \(0.538619\pi\)
\(14\) −2429.10 −3.31227
\(15\) 117.364 0.134681
\(16\) 653.334 0.638021
\(17\) 32.0243 0.0268756 0.0134378 0.999910i \(-0.495722\pi\)
0.0134378 + 0.999910i \(0.495722\pi\)
\(18\) −234.843 −0.170843
\(19\) 356.352 0.226462 0.113231 0.993569i \(-0.463880\pi\)
0.113231 + 0.993569i \(0.463880\pi\)
\(20\) 430.342 0.240569
\(21\) 4142.62 2.04987
\(22\) −2228.01 −0.981432
\(23\) 2571.17 1.01347 0.506735 0.862102i \(-0.330852\pi\)
0.506735 + 0.862102i \(0.330852\pi\)
\(24\) −4386.95 −1.55466
\(25\) −3073.51 −0.983522
\(26\) 1414.46 0.410352
\(27\) −3573.78 −0.943448
\(28\) 15189.9 3.66150
\(29\) 3131.09 0.691353 0.345677 0.938354i \(-0.387649\pi\)
0.345677 + 0.938354i \(0.387649\pi\)
\(30\) −1125.53 −0.228325
\(31\) −4885.47 −0.913065 −0.456533 0.889707i \(-0.650909\pi\)
−0.456533 + 0.889707i \(0.650909\pi\)
\(32\) 2317.89 0.400145
\(33\) 3799.68 0.607382
\(34\) −307.116 −0.0455623
\(35\) 1817.63 0.250804
\(36\) 1468.55 0.188856
\(37\) 8933.18 1.07276 0.536379 0.843977i \(-0.319792\pi\)
0.536379 + 0.843977i \(0.319792\pi\)
\(38\) −3417.45 −0.383922
\(39\) −2412.24 −0.253956
\(40\) −1924.83 −0.190214
\(41\) −235.516 −0.0218807 −0.0109404 0.999940i \(-0.503482\pi\)
−0.0109404 + 0.999940i \(0.503482\pi\)
\(42\) −39728.1 −3.47516
\(43\) 5683.28 0.468735 0.234368 0.972148i \(-0.424698\pi\)
0.234368 + 0.972148i \(0.424698\pi\)
\(44\) 13932.4 1.08491
\(45\) 175.727 0.0129362
\(46\) −24657.7 −1.71814
\(47\) 29165.7 1.92587 0.962935 0.269732i \(-0.0869351\pi\)
0.962935 + 0.269732i \(0.0869351\pi\)
\(48\) 10685.3 0.669398
\(49\) 47350.2 2.81729
\(50\) 29475.2 1.66737
\(51\) 523.760 0.0281973
\(52\) −8845.04 −0.453619
\(53\) −23417.4 −1.14511 −0.572557 0.819865i \(-0.694048\pi\)
−0.572557 + 0.819865i \(0.694048\pi\)
\(54\) 34272.8 1.59943
\(55\) 1667.16 0.0743139
\(56\) −67941.2 −2.89510
\(57\) 5828.17 0.237599
\(58\) −30027.4 −1.17205
\(59\) 7454.46 0.278796 0.139398 0.990236i \(-0.455483\pi\)
0.139398 + 0.990236i \(0.455483\pi\)
\(60\) 7038.28 0.252399
\(61\) 30262.1 1.04130 0.520648 0.853772i \(-0.325691\pi\)
0.520648 + 0.853772i \(0.325691\pi\)
\(62\) 46852.0 1.54792
\(63\) 6202.67 0.196892
\(64\) −43135.4 −1.31639
\(65\) −1058.40 −0.0310718
\(66\) −36439.2 −1.02970
\(67\) −31380.7 −0.854035 −0.427017 0.904243i \(-0.640436\pi\)
−0.427017 + 0.904243i \(0.640436\pi\)
\(68\) 1920.49 0.0503663
\(69\) 42051.6 1.06331
\(70\) −17431.2 −0.425189
\(71\) 73810.7 1.73769 0.868847 0.495081i \(-0.164862\pi\)
0.868847 + 0.495081i \(0.164862\pi\)
\(72\) −6568.49 −0.149326
\(73\) 72207.8 1.58590 0.792952 0.609285i \(-0.208543\pi\)
0.792952 + 0.609285i \(0.208543\pi\)
\(74\) −85669.9 −1.81865
\(75\) −50267.4 −1.03189
\(76\) 21370.3 0.424402
\(77\) 58846.1 1.13107
\(78\) 23133.6 0.430533
\(79\) −41830.8 −0.754100 −0.377050 0.926193i \(-0.623061\pi\)
−0.377050 + 0.926193i \(0.623061\pi\)
\(80\) 4688.32 0.0819016
\(81\) −64399.9 −1.09062
\(82\) 2258.62 0.0370944
\(83\) −27176.2 −0.433006 −0.216503 0.976282i \(-0.569465\pi\)
−0.216503 + 0.976282i \(0.569465\pi\)
\(84\) 248432. 3.84157
\(85\) 229.807 0.00344997
\(86\) −54503.1 −0.794648
\(87\) 51209.1 0.725353
\(88\) −62316.8 −0.857824
\(89\) 28556.0 0.382139 0.191070 0.981576i \(-0.438804\pi\)
0.191070 + 0.981576i \(0.438804\pi\)
\(90\) −1685.23 −0.0219308
\(91\) −37358.6 −0.472920
\(92\) 154192. 1.89930
\(93\) −79902.1 −0.957968
\(94\) −279701. −3.26494
\(95\) 2557.18 0.0290705
\(96\) 37909.2 0.419823
\(97\) −168665. −1.82010 −0.910050 0.414499i \(-0.863957\pi\)
−0.910050 + 0.414499i \(0.863957\pi\)
\(98\) −454093. −4.77617
\(99\) 5689.19 0.0583395
\(100\) −184317. −1.84317
\(101\) −66683.6 −0.650452 −0.325226 0.945636i \(-0.605440\pi\)
−0.325226 + 0.945636i \(0.605440\pi\)
\(102\) −5022.90 −0.0478029
\(103\) −190069. −1.76530 −0.882651 0.470029i \(-0.844243\pi\)
−0.882651 + 0.470029i \(0.844243\pi\)
\(104\) 39562.0 0.358670
\(105\) 29727.4 0.263138
\(106\) 224575. 1.94131
\(107\) 66433.1 0.560951 0.280476 0.959861i \(-0.409508\pi\)
0.280476 + 0.959861i \(0.409508\pi\)
\(108\) −214318. −1.76807
\(109\) −81034.9 −0.653290 −0.326645 0.945147i \(-0.605918\pi\)
−0.326645 + 0.945147i \(0.605918\pi\)
\(110\) −15988.2 −0.125985
\(111\) 146103. 1.12551
\(112\) 165485. 1.24656
\(113\) 49830.3 0.367111 0.183555 0.983009i \(-0.441239\pi\)
0.183555 + 0.983009i \(0.441239\pi\)
\(114\) −55892.6 −0.402802
\(115\) 18450.7 0.130097
\(116\) 187770. 1.29563
\(117\) −3611.80 −0.0243926
\(118\) −71488.9 −0.472643
\(119\) 8111.54 0.0525092
\(120\) −31480.7 −0.199568
\(121\) −107076. −0.664860
\(122\) −290216. −1.76531
\(123\) −3851.88 −0.0229567
\(124\) −292980. −1.71113
\(125\) −44480.4 −0.254621
\(126\) −59484.1 −0.333791
\(127\) −195474. −1.07543 −0.537713 0.843128i \(-0.680711\pi\)
−0.537713 + 0.843128i \(0.680711\pi\)
\(128\) 339500. 1.83153
\(129\) 92950.3 0.491787
\(130\) 10150.1 0.0526762
\(131\) 195818. 0.996950 0.498475 0.866904i \(-0.333894\pi\)
0.498475 + 0.866904i \(0.333894\pi\)
\(132\) 227866. 1.13827
\(133\) 90261.5 0.442459
\(134\) 300943. 1.44785
\(135\) −25645.4 −0.121109
\(136\) −8589.94 −0.0398238
\(137\) 212839. 0.968836 0.484418 0.874837i \(-0.339031\pi\)
0.484418 + 0.874837i \(0.339031\pi\)
\(138\) −403279. −1.80263
\(139\) 281393. 1.23531 0.617656 0.786448i \(-0.288082\pi\)
0.617656 + 0.786448i \(0.288082\pi\)
\(140\) 109003. 0.470020
\(141\) 477006. 2.02058
\(142\) −707850. −2.94592
\(143\) −34265.9 −0.140127
\(144\) 15998.9 0.0642961
\(145\) 22468.7 0.0887477
\(146\) −692478. −2.68859
\(147\) 774416. 2.95584
\(148\) 535720. 2.01040
\(149\) 468800. 1.72990 0.864952 0.501855i \(-0.167349\pi\)
0.864952 + 0.501855i \(0.167349\pi\)
\(150\) 482068. 1.74936
\(151\) 80770.8 0.288278 0.144139 0.989557i \(-0.453959\pi\)
0.144139 + 0.989557i \(0.453959\pi\)
\(152\) −95585.0 −0.335568
\(153\) 784.216 0.00270837
\(154\) −564339. −1.91751
\(155\) −35058.1 −0.117208
\(156\) −144661. −0.475927
\(157\) −184657. −0.597885 −0.298942 0.954271i \(-0.596634\pi\)
−0.298942 + 0.954271i \(0.596634\pi\)
\(158\) 401161. 1.27843
\(159\) −382993. −1.20143
\(160\) 16633.1 0.0513658
\(161\) 651258. 1.98011
\(162\) 617601. 1.84893
\(163\) 488799. 1.44099 0.720495 0.693460i \(-0.243915\pi\)
0.720495 + 0.693460i \(0.243915\pi\)
\(164\) −14123.8 −0.0410056
\(165\) 27266.5 0.0779685
\(166\) 260622. 0.734076
\(167\) 287397. 0.797427 0.398714 0.917075i \(-0.369457\pi\)
0.398714 + 0.917075i \(0.369457\pi\)
\(168\) −1.11118e6 −3.03747
\(169\) −349539. −0.941411
\(170\) −2203.86 −0.00584874
\(171\) 8726.40 0.0228215
\(172\) 340824. 0.878435
\(173\) −214167. −0.544048 −0.272024 0.962291i \(-0.587693\pi\)
−0.272024 + 0.962291i \(0.587693\pi\)
\(174\) −491100. −1.22969
\(175\) −778497. −1.92159
\(176\) 151785. 0.369359
\(177\) 121918. 0.292506
\(178\) −273854. −0.647842
\(179\) −535369. −1.24888 −0.624440 0.781072i \(-0.714673\pi\)
−0.624440 + 0.781072i \(0.714673\pi\)
\(180\) 10538.3 0.0242431
\(181\) 294854. 0.668977 0.334488 0.942400i \(-0.391437\pi\)
0.334488 + 0.942400i \(0.391437\pi\)
\(182\) 358272. 0.801742
\(183\) 494938. 1.09250
\(184\) −689669. −1.50174
\(185\) 64104.4 0.137708
\(186\) 766268. 1.62405
\(187\) 7440.03 0.0155586
\(188\) 1.74906e6 3.60918
\(189\) −905212. −1.84330
\(190\) −24523.6 −0.0492833
\(191\) 256898. 0.509540 0.254770 0.967002i \(-0.418000\pi\)
0.254770 + 0.967002i \(0.418000\pi\)
\(192\) −705482. −1.38113
\(193\) 265223. 0.512528 0.256264 0.966607i \(-0.417508\pi\)
0.256264 + 0.966607i \(0.417508\pi\)
\(194\) 1.61751e6 3.08562
\(195\) −17310.2 −0.0325999
\(196\) 2.83958e6 5.27976
\(197\) −119175. −0.218786 −0.109393 0.993999i \(-0.534891\pi\)
−0.109393 + 0.993999i \(0.534891\pi\)
\(198\) −54559.8 −0.0989031
\(199\) 346776. 0.620750 0.310375 0.950614i \(-0.399545\pi\)
0.310375 + 0.950614i \(0.399545\pi\)
\(200\) 824411. 1.45737
\(201\) −513233. −0.896034
\(202\) 639501. 1.10271
\(203\) 793082. 1.35076
\(204\) 31409.7 0.0528432
\(205\) −1690.06 −0.00280878
\(206\) 1.82278e6 2.99272
\(207\) 62963.1 0.102132
\(208\) −96361.4 −0.154435
\(209\) 82789.3 0.131102
\(210\) −285088. −0.446099
\(211\) 1.08726e6 1.68123 0.840617 0.541630i \(-0.182193\pi\)
0.840617 + 0.541630i \(0.182193\pi\)
\(212\) −1.40433e6 −2.14600
\(213\) 1.20718e6 1.82315
\(214\) −637099. −0.950982
\(215\) 40783.2 0.0601707
\(216\) 958600. 1.39799
\(217\) −1.23745e6 −1.78394
\(218\) 777132. 1.10752
\(219\) 1.18096e6 1.66389
\(220\) 99979.0 0.139268
\(221\) −4723.33 −0.00650530
\(222\) −1.40114e6 −1.90809
\(223\) 189487. 0.255162 0.127581 0.991828i \(-0.459279\pi\)
0.127581 + 0.991828i \(0.459279\pi\)
\(224\) 587104. 0.781799
\(225\) −75264.4 −0.0991136
\(226\) −477876. −0.622364
\(227\) −118108. −0.152130 −0.0760650 0.997103i \(-0.524236\pi\)
−0.0760650 + 0.997103i \(0.524236\pi\)
\(228\) 349513. 0.445273
\(229\) −1.08976e6 −1.37323 −0.686615 0.727021i \(-0.740904\pi\)
−0.686615 + 0.727021i \(0.740904\pi\)
\(230\) −176944. −0.220554
\(231\) 962432. 1.18670
\(232\) −839857. −1.02444
\(233\) −12191.7 −0.0147121 −0.00735606 0.999973i \(-0.502342\pi\)
−0.00735606 + 0.999973i \(0.502342\pi\)
\(234\) 34637.5 0.0413529
\(235\) 209293. 0.247220
\(236\) 447041. 0.522478
\(237\) −684146. −0.791185
\(238\) −77790.3 −0.0890191
\(239\) 249853. 0.282937 0.141468 0.989943i \(-0.454818\pi\)
0.141468 + 0.989943i \(0.454818\pi\)
\(240\) 76677.8 0.0859294
\(241\) 1.40842e6 1.56203 0.781017 0.624510i \(-0.214701\pi\)
0.781017 + 0.624510i \(0.214701\pi\)
\(242\) 1.02687e6 1.12714
\(243\) −184838. −0.200805
\(244\) 1.81481e6 1.95144
\(245\) 339785. 0.361651
\(246\) 36939.9 0.0389186
\(247\) −52559.0 −0.0548157
\(248\) 1.31044e6 1.35297
\(249\) −444469. −0.454300
\(250\) 426571. 0.431660
\(251\) −532829. −0.533831 −0.266915 0.963720i \(-0.586004\pi\)
−0.266915 + 0.963720i \(0.586004\pi\)
\(252\) 371972. 0.368985
\(253\) 597345. 0.586711
\(254\) 1.87461e6 1.82317
\(255\) 3758.50 0.00361963
\(256\) −1.87550e6 −1.78861
\(257\) −9092.38 −0.00858707 −0.00429353 0.999991i \(-0.501367\pi\)
−0.00429353 + 0.999991i \(0.501367\pi\)
\(258\) −891402. −0.833728
\(259\) 2.26271e6 2.09594
\(260\) −63472.0 −0.0582302
\(261\) 76674.5 0.0696706
\(262\) −1.87791e6 −1.69013
\(263\) −560522. −0.499693 −0.249847 0.968285i \(-0.580380\pi\)
−0.249847 + 0.968285i \(0.580380\pi\)
\(264\) −1.01919e6 −0.900010
\(265\) −168043. −0.146996
\(266\) −865615. −0.750103
\(267\) 467035. 0.400932
\(268\) −1.88189e6 −1.60051
\(269\) −2.09358e6 −1.76404 −0.882019 0.471214i \(-0.843816\pi\)
−0.882019 + 0.471214i \(0.843816\pi\)
\(270\) 245942. 0.205316
\(271\) 457713. 0.378591 0.189295 0.981920i \(-0.439380\pi\)
0.189295 + 0.981920i \(0.439380\pi\)
\(272\) 20922.6 0.0171472
\(273\) −611003. −0.496177
\(274\) −2.04115e6 −1.64247
\(275\) −714050. −0.569373
\(276\) 2.52182e6 1.99270
\(277\) 416800. 0.326383 0.163192 0.986594i \(-0.447821\pi\)
0.163192 + 0.986594i \(0.447821\pi\)
\(278\) −2.69859e6 −2.09423
\(279\) −119636. −0.0920134
\(280\) −487545. −0.371638
\(281\) −1.02702e6 −0.775910 −0.387955 0.921678i \(-0.626818\pi\)
−0.387955 + 0.921678i \(0.626818\pi\)
\(282\) −4.57453e6 −3.42550
\(283\) 1.68071e6 1.24746 0.623729 0.781640i \(-0.285617\pi\)
0.623729 + 0.781640i \(0.285617\pi\)
\(284\) 4.42640e6 3.25653
\(285\) 41822.9 0.0305001
\(286\) 328613. 0.237558
\(287\) −59654.6 −0.0427503
\(288\) 56760.7 0.0403243
\(289\) −1.41883e6 −0.999278
\(290\) −215476. −0.150454
\(291\) −2.75852e6 −1.90961
\(292\) 4.33028e6 2.97207
\(293\) −478521. −0.325636 −0.162818 0.986656i \(-0.552058\pi\)
−0.162818 + 0.986656i \(0.552058\pi\)
\(294\) −7.42672e6 −5.01105
\(295\) 53493.2 0.0357885
\(296\) −2.39616e6 −1.58960
\(297\) −830275. −0.546174
\(298\) −4.49583e6 −2.93271
\(299\) −379226. −0.245313
\(300\) −3.01452e6 −1.93381
\(301\) 1.43953e6 0.915810
\(302\) −774598. −0.488719
\(303\) −1.09061e6 −0.682440
\(304\) 232817. 0.144488
\(305\) 217160. 0.133669
\(306\) −7520.70 −0.00459150
\(307\) 343199. 0.207826 0.103913 0.994586i \(-0.466864\pi\)
0.103913 + 0.994586i \(0.466864\pi\)
\(308\) 3.52898e6 2.11969
\(309\) −3.10860e6 −1.85212
\(310\) 336210. 0.198704
\(311\) 1.55766e6 0.913213 0.456607 0.889669i \(-0.349065\pi\)
0.456607 + 0.889669i \(0.349065\pi\)
\(312\) 647039. 0.376308
\(313\) −1.29291e6 −0.745945 −0.372973 0.927842i \(-0.621662\pi\)
−0.372973 + 0.927842i \(0.621662\pi\)
\(314\) 1.77088e6 1.01360
\(315\) 44510.3 0.0252746
\(316\) −2.50858e6 −1.41322
\(317\) 592011. 0.330888 0.165444 0.986219i \(-0.447094\pi\)
0.165444 + 0.986219i \(0.447094\pi\)
\(318\) 3.67293e6 2.03678
\(319\) 727428. 0.400233
\(320\) −309540. −0.168982
\(321\) 1.08652e6 0.588538
\(322\) −6.24562e6 −3.35688
\(323\) 11411.9 0.00608630
\(324\) −3.86205e6 −2.04388
\(325\) 453317. 0.238064
\(326\) −4.68762e6 −2.44292
\(327\) −1.32533e6 −0.685417
\(328\) 63172.9 0.0324225
\(329\) 7.38745e6 3.76275
\(330\) −261488. −0.132180
\(331\) 1.56073e6 0.782991 0.391496 0.920180i \(-0.371958\pi\)
0.391496 + 0.920180i \(0.371958\pi\)
\(332\) −1.62975e6 −0.811476
\(333\) 218757. 0.108106
\(334\) −2.75616e6 −1.35188
\(335\) −225188. −0.109631
\(336\) 2.70651e6 1.30786
\(337\) −94315.9 −0.0452387 −0.0226193 0.999744i \(-0.507201\pi\)
−0.0226193 + 0.999744i \(0.507201\pi\)
\(338\) 3.35211e6 1.59598
\(339\) 814977. 0.385164
\(340\) 13781.4 0.00646542
\(341\) −1.13501e6 −0.528585
\(342\) −83686.9 −0.0386894
\(343\) 7.73638e6 3.55061
\(344\) −1.52443e6 −0.694565
\(345\) 301762. 0.136495
\(346\) 2.05388e6 0.922326
\(347\) −3.82991e6 −1.70752 −0.853758 0.520671i \(-0.825682\pi\)
−0.853758 + 0.520671i \(0.825682\pi\)
\(348\) 3.07100e6 1.35935
\(349\) 3.56667e6 1.56747 0.783735 0.621095i \(-0.213312\pi\)
0.783735 + 0.621095i \(0.213312\pi\)
\(350\) 7.46585e6 3.25768
\(351\) 527103. 0.228364
\(352\) 538502. 0.231649
\(353\) 1.80004e6 0.768855 0.384428 0.923155i \(-0.374399\pi\)
0.384428 + 0.923155i \(0.374399\pi\)
\(354\) −1.16920e6 −0.495887
\(355\) 529665. 0.223064
\(356\) 1.71249e6 0.716149
\(357\) 132665. 0.0550915
\(358\) 5.13424e6 2.11723
\(359\) 3.58201e6 1.46687 0.733434 0.679761i \(-0.237916\pi\)
0.733434 + 0.679761i \(0.237916\pi\)
\(360\) −47135.5 −0.0191687
\(361\) −2.34911e6 −0.948715
\(362\) −2.82768e6 −1.13412
\(363\) −1.75124e6 −0.697557
\(364\) −2.24038e6 −0.886276
\(365\) 518163. 0.203579
\(366\) −4.74650e6 −1.85213
\(367\) −2.16977e6 −0.840909 −0.420454 0.907314i \(-0.638129\pi\)
−0.420454 + 0.907314i \(0.638129\pi\)
\(368\) 1.67983e6 0.646616
\(369\) −5767.35 −0.00220501
\(370\) −614767. −0.233457
\(371\) −5.93145e6 −2.23731
\(372\) −4.79170e6 −1.79528
\(373\) −4.38410e6 −1.63158 −0.815790 0.578348i \(-0.803697\pi\)
−0.815790 + 0.578348i \(0.803697\pi\)
\(374\) −71350.5 −0.0263766
\(375\) −727481. −0.267143
\(376\) −7.82315e6 −2.85373
\(377\) −461810. −0.167344
\(378\) 8.68106e6 3.12495
\(379\) 2.70002e6 0.965536 0.482768 0.875748i \(-0.339631\pi\)
0.482768 + 0.875748i \(0.339631\pi\)
\(380\) 153353. 0.0544797
\(381\) −3.19699e6 −1.12831
\(382\) −2.46368e6 −0.863824
\(383\) 1.88809e6 0.657696 0.328848 0.944383i \(-0.393340\pi\)
0.328848 + 0.944383i \(0.393340\pi\)
\(384\) 5.55254e6 1.92160
\(385\) 422279. 0.145194
\(386\) −2.54351e6 −0.868891
\(387\) 139173. 0.0472364
\(388\) −1.01148e7 −3.41096
\(389\) 3.15103e6 1.05579 0.527896 0.849309i \(-0.322981\pi\)
0.527896 + 0.849309i \(0.322981\pi\)
\(390\) 166006. 0.0552667
\(391\) 82340.0 0.0272376
\(392\) −1.27008e7 −4.17462
\(393\) 3.20261e6 1.04598
\(394\) 1.14290e6 0.370909
\(395\) −300178. −0.0968024
\(396\) 341179. 0.109331
\(397\) −1.21894e6 −0.388157 −0.194079 0.980986i \(-0.562172\pi\)
−0.194079 + 0.980986i \(0.562172\pi\)
\(398\) −3.32561e6 −1.05236
\(399\) 1.47623e6 0.464219
\(400\) −2.00803e6 −0.627508
\(401\) 2.31902e6 0.720185 0.360093 0.932917i \(-0.382745\pi\)
0.360093 + 0.932917i \(0.382745\pi\)
\(402\) 4.92195e6 1.51905
\(403\) 720566. 0.221010
\(404\) −3.99899e6 −1.21898
\(405\) −462134. −0.140001
\(406\) −7.60572e6 −2.28995
\(407\) 2.07539e6 0.621033
\(408\) −140489. −0.0417823
\(409\) −2.34601e6 −0.693461 −0.346731 0.937965i \(-0.612708\pi\)
−0.346731 + 0.937965i \(0.612708\pi\)
\(410\) 16207.9 0.00476174
\(411\) 3.48100e6 1.01648
\(412\) −1.13984e7 −3.30827
\(413\) 1.88816e6 0.544708
\(414\) −603822. −0.173144
\(415\) −195016. −0.0555841
\(416\) −341869. −0.0968561
\(417\) 4.60221e6 1.29606
\(418\) −793956. −0.222257
\(419\) 404570. 0.112579 0.0562897 0.998414i \(-0.482073\pi\)
0.0562897 + 0.998414i \(0.482073\pi\)
\(420\) 1.78274e6 0.493135
\(421\) −6.03339e6 −1.65904 −0.829518 0.558480i \(-0.811385\pi\)
−0.829518 + 0.558480i \(0.811385\pi\)
\(422\) −1.04269e7 −2.85020
\(423\) 714213. 0.194078
\(424\) 6.28128e6 1.69681
\(425\) −98427.0 −0.0264327
\(426\) −1.15769e7 −3.09079
\(427\) 7.66516e6 2.03447
\(428\) 3.98397e6 1.05125
\(429\) −560422. −0.147018
\(430\) −391114. −0.102008
\(431\) 4.40463e6 1.14213 0.571066 0.820904i \(-0.306530\pi\)
0.571066 + 0.820904i \(0.306530\pi\)
\(432\) −2.33487e6 −0.601940
\(433\) −5.79371e6 −1.48504 −0.742518 0.669826i \(-0.766369\pi\)
−0.742518 + 0.669826i \(0.766369\pi\)
\(434\) 1.18673e7 3.02431
\(435\) 367476. 0.0931122
\(436\) −4.85964e6 −1.22430
\(437\) 916242. 0.229513
\(438\) −1.13255e7 −2.82081
\(439\) −5.74057e6 −1.42165 −0.710827 0.703367i \(-0.751679\pi\)
−0.710827 + 0.703367i \(0.751679\pi\)
\(440\) −447185. −0.110117
\(441\) 1.15952e6 0.283911
\(442\) 45297.1 0.0110285
\(443\) 5.56239e6 1.34664 0.673321 0.739350i \(-0.264867\pi\)
0.673321 + 0.739350i \(0.264867\pi\)
\(444\) 8.76173e6 2.10927
\(445\) 204917. 0.0490545
\(446\) −1.81719e6 −0.432577
\(447\) 7.66725e6 1.81498
\(448\) −1.09259e7 −2.57195
\(449\) 999227. 0.233910 0.116955 0.993137i \(-0.462687\pi\)
0.116955 + 0.993137i \(0.462687\pi\)
\(450\) 721792. 0.168028
\(451\) −54716.2 −0.0126670
\(452\) 2.98831e6 0.687985
\(453\) 1.32101e6 0.302455
\(454\) 1.13267e6 0.257906
\(455\) −268085. −0.0607078
\(456\) −1.56330e6 −0.352071
\(457\) 3.18082e6 0.712441 0.356220 0.934402i \(-0.384065\pi\)
0.356220 + 0.934402i \(0.384065\pi\)
\(458\) 1.04509e7 2.32804
\(459\) −114448. −0.0253557
\(460\) 1.10648e6 0.243809
\(461\) 2.73926e6 0.600317 0.300159 0.953889i \(-0.402960\pi\)
0.300159 + 0.953889i \(0.402960\pi\)
\(462\) −9.22980e6 −2.01181
\(463\) 1.54179e6 0.334252 0.167126 0.985936i \(-0.446551\pi\)
0.167126 + 0.985936i \(0.446551\pi\)
\(464\) 2.04565e6 0.441098
\(465\) −573377. −0.122973
\(466\) 116920. 0.0249415
\(467\) 6.14108e6 1.30302 0.651512 0.758638i \(-0.274135\pi\)
0.651512 + 0.758638i \(0.274135\pi\)
\(468\) −216598. −0.0457131
\(469\) −7.94850e6 −1.66860
\(470\) −2.00713e6 −0.419114
\(471\) −3.02008e6 −0.627288
\(472\) −1.99952e6 −0.413115
\(473\) 1.32036e6 0.271357
\(474\) 6.56102e6 1.34130
\(475\) −1.09525e6 −0.222730
\(476\) 486446. 0.0984051
\(477\) −573448. −0.115398
\(478\) −2.39611e6 −0.479663
\(479\) 1.31361e6 0.261594 0.130797 0.991409i \(-0.458246\pi\)
0.130797 + 0.991409i \(0.458246\pi\)
\(480\) 272036. 0.0538919
\(481\) −1.31757e6 −0.259664
\(482\) −1.35069e7 −2.64812
\(483\) 1.06514e7 2.07748
\(484\) −6.42134e6 −1.24598
\(485\) −1.21034e6 −0.233643
\(486\) 1.77261e6 0.340426
\(487\) −6.71405e6 −1.28281 −0.641405 0.767203i \(-0.721648\pi\)
−0.641405 + 0.767203i \(0.721648\pi\)
\(488\) −8.11724e6 −1.54298
\(489\) 7.99433e6 1.51186
\(490\) −3.25857e6 −0.613107
\(491\) −5.21717e6 −0.976632 −0.488316 0.872667i \(-0.662389\pi\)
−0.488316 + 0.872667i \(0.662389\pi\)
\(492\) −230996. −0.0430222
\(493\) 100271. 0.0185805
\(494\) 504046. 0.0929293
\(495\) 40825.6 0.00748893
\(496\) −3.19184e6 −0.582555
\(497\) 1.86957e7 3.39509
\(498\) 4.26249e6 0.770177
\(499\) 9.90693e6 1.78110 0.890549 0.454887i \(-0.150320\pi\)
0.890549 + 0.454887i \(0.150320\pi\)
\(500\) −2.66748e6 −0.477173
\(501\) 4.70040e6 0.836643
\(502\) 5.10987e6 0.905005
\(503\) −9.57206e6 −1.68689 −0.843443 0.537219i \(-0.819475\pi\)
−0.843443 + 0.537219i \(0.819475\pi\)
\(504\) −1.66375e6 −0.291751
\(505\) −478521. −0.0834974
\(506\) −5.72859e6 −0.994652
\(507\) −5.71674e6 −0.987707
\(508\) −1.17225e7 −2.01540
\(509\) −6.64078e6 −1.13612 −0.568060 0.822987i \(-0.692306\pi\)
−0.568060 + 0.822987i \(0.692306\pi\)
\(510\) −36044.3 −0.00613637
\(511\) 1.82897e7 3.09852
\(512\) 7.12219e6 1.20071
\(513\) −1.27352e6 −0.213655
\(514\) 87196.7 0.0145577
\(515\) −1.36394e6 −0.226608
\(516\) 5.57420e6 0.921634
\(517\) 6.77589e6 1.11491
\(518\) −2.16996e7 −3.55326
\(519\) −3.50271e6 −0.570803
\(520\) 283897. 0.0460417
\(521\) 512688. 0.0827483 0.0413741 0.999144i \(-0.486826\pi\)
0.0413741 + 0.999144i \(0.486826\pi\)
\(522\) −735314. −0.118113
\(523\) −2.33631e6 −0.373487 −0.186743 0.982409i \(-0.559793\pi\)
−0.186743 + 0.982409i \(0.559793\pi\)
\(524\) 1.17431e7 1.86834
\(525\) −1.27324e7 −2.01609
\(526\) 5.37546e6 0.847132
\(527\) −156454. −0.0245392
\(528\) 2.48246e6 0.387523
\(529\) 174563. 0.0271215
\(530\) 1.61155e6 0.249203
\(531\) 182546. 0.0280954
\(532\) 5.41295e6 0.829192
\(533\) 34736.7 0.00529628
\(534\) −4.47890e6 −0.679702
\(535\) 476724. 0.0720082
\(536\) 8.41730e6 1.26550
\(537\) −8.75600e6 −1.31030
\(538\) 2.00776e7 2.99058
\(539\) 1.10006e7 1.63097
\(540\) −1.53795e6 −0.226964
\(541\) −7.19645e6 −1.05712 −0.528561 0.848895i \(-0.677268\pi\)
−0.528561 + 0.848895i \(0.677268\pi\)
\(542\) −4.38951e6 −0.641826
\(543\) 4.82236e6 0.701875
\(544\) 74228.8 0.0107541
\(545\) −581506. −0.0838616
\(546\) 5.85956e6 0.841170
\(547\) 299209. 0.0427569
\(548\) 1.27639e7 1.81565
\(549\) 741061. 0.104936
\(550\) 6.84780e6 0.965260
\(551\) 1.11577e6 0.156565
\(552\) −1.12796e7 −1.57560
\(553\) −1.05955e7 −1.47335
\(554\) −3.99714e6 −0.553319
\(555\) 1.04843e6 0.144480
\(556\) 1.68751e7 2.31504
\(557\) 2.09970e6 0.286760 0.143380 0.989668i \(-0.454203\pi\)
0.143380 + 0.989668i \(0.454203\pi\)
\(558\) 1.14732e6 0.155991
\(559\) −838237. −0.113459
\(560\) 1.18752e6 0.160019
\(561\) 121682. 0.0163238
\(562\) 9.84917e6 1.31540
\(563\) −7.60608e6 −1.01132 −0.505662 0.862732i \(-0.668752\pi\)
−0.505662 + 0.862732i \(0.668752\pi\)
\(564\) 2.86059e7 3.78668
\(565\) 357582. 0.0471253
\(566\) −1.61181e7 −2.11482
\(567\) −1.63120e7 −2.13084
\(568\) −1.97984e7 −2.57489
\(569\) 7.62657e6 0.987526 0.493763 0.869597i \(-0.335621\pi\)
0.493763 + 0.869597i \(0.335621\pi\)
\(570\) −401085. −0.0517070
\(571\) 4.09627e6 0.525773 0.262887 0.964827i \(-0.415325\pi\)
0.262887 + 0.964827i \(0.415325\pi\)
\(572\) −2.05492e6 −0.262606
\(573\) 4.20159e6 0.534598
\(574\) 572092. 0.0724747
\(575\) −7.90250e6 −0.996770
\(576\) −1.05631e6 −0.132658
\(577\) −7.49194e6 −0.936817 −0.468409 0.883512i \(-0.655172\pi\)
−0.468409 + 0.883512i \(0.655172\pi\)
\(578\) 1.36067e7 1.69408
\(579\) 4.33774e6 0.537733
\(580\) 1.34744e6 0.166318
\(581\) −6.88354e6 −0.846002
\(582\) 2.64545e7 3.23736
\(583\) −5.44043e6 −0.662921
\(584\) −1.93684e7 −2.34997
\(585\) −25918.3 −0.00313124
\(586\) 4.58906e6 0.552051
\(587\) 1.33786e6 0.160257 0.0801283 0.996785i \(-0.474467\pi\)
0.0801283 + 0.996785i \(0.474467\pi\)
\(588\) 4.64415e7 5.53940
\(589\) −1.74095e6 −0.206775
\(590\) −513004. −0.0606723
\(591\) −1.94911e6 −0.229545
\(592\) 5.83635e6 0.684442
\(593\) −8.52167e6 −0.995149 −0.497574 0.867421i \(-0.665776\pi\)
−0.497574 + 0.867421i \(0.665776\pi\)
\(594\) 7.96241e6 0.925930
\(595\) 58208.3 0.00674051
\(596\) 2.81138e7 3.24193
\(597\) 5.67155e6 0.651277
\(598\) 3.63681e6 0.415880
\(599\) 5.82269e6 0.663066 0.331533 0.943444i \(-0.392434\pi\)
0.331533 + 0.943444i \(0.392434\pi\)
\(600\) 1.34833e7 1.52904
\(601\) 1.57854e7 1.78266 0.891332 0.453351i \(-0.149772\pi\)
0.891332 + 0.453351i \(0.149772\pi\)
\(602\) −1.38052e7 −1.55258
\(603\) −768455. −0.0860647
\(604\) 4.84380e6 0.540249
\(605\) −768380. −0.0853469
\(606\) 1.04591e7 1.15694
\(607\) −5.66946e6 −0.624554 −0.312277 0.949991i \(-0.601092\pi\)
−0.312277 + 0.949991i \(0.601092\pi\)
\(608\) 825984. 0.0906177
\(609\) 1.29709e7 1.41719
\(610\) −2.08259e6 −0.226610
\(611\) −4.30170e6 −0.466162
\(612\) 47029.2 0.00507562
\(613\) −1.48861e7 −1.60004 −0.800020 0.599974i \(-0.795178\pi\)
−0.800020 + 0.599974i \(0.795178\pi\)
\(614\) −3.29130e6 −0.352328
\(615\) −27641.1 −0.00294691
\(616\) −1.57844e7 −1.67601
\(617\) −4.64218e6 −0.490918 −0.245459 0.969407i \(-0.578939\pi\)
−0.245459 + 0.969407i \(0.578939\pi\)
\(618\) 2.98117e7 3.13990
\(619\) 1.12810e7 1.18337 0.591687 0.806168i \(-0.298462\pi\)
0.591687 + 0.806168i \(0.298462\pi\)
\(620\) −2.10242e6 −0.219655
\(621\) −9.18878e6 −0.956156
\(622\) −1.49381e7 −1.54817
\(623\) 7.23302e6 0.746620
\(624\) −1.57600e6 −0.162029
\(625\) 9.28551e6 0.950836
\(626\) 1.23991e7 1.26460
\(627\) 1.35402e6 0.137549
\(628\) −1.10738e7 −1.12047
\(629\) 286079. 0.0288310
\(630\) −426858. −0.0428481
\(631\) 8.32225e6 0.832084 0.416042 0.909345i \(-0.363417\pi\)
0.416042 + 0.909345i \(0.363417\pi\)
\(632\) 1.12204e7 1.11741
\(633\) 1.77822e7 1.76391
\(634\) −5.67743e6 −0.560956
\(635\) −1.40272e6 −0.138050
\(636\) −2.29680e7 −2.25154
\(637\) −6.98377e6 −0.681933
\(638\) −6.97609e6 −0.678517
\(639\) 1.80749e6 0.175115
\(640\) 2.43625e6 0.235110
\(641\) −8.11956e6 −0.780526 −0.390263 0.920703i \(-0.627616\pi\)
−0.390263 + 0.920703i \(0.627616\pi\)
\(642\) −1.04198e7 −0.997750
\(643\) −1.17963e7 −1.12517 −0.562587 0.826738i \(-0.690194\pi\)
−0.562587 + 0.826738i \(0.690194\pi\)
\(644\) 3.90558e7 3.71083
\(645\) 667011. 0.0631297
\(646\) −109442. −0.0103181
\(647\) 1.92066e7 1.80381 0.901903 0.431938i \(-0.142170\pi\)
0.901903 + 0.431938i \(0.142170\pi\)
\(648\) 1.72741e7 1.61606
\(649\) 1.73185e6 0.161398
\(650\) −4.34735e6 −0.403590
\(651\) −2.02386e7 −1.87167
\(652\) 2.93131e7 2.70049
\(653\) −1.46736e7 −1.34664 −0.673321 0.739350i \(-0.735133\pi\)
−0.673321 + 0.739350i \(0.735133\pi\)
\(654\) 1.27100e7 1.16199
\(655\) 1.40519e6 0.127977
\(656\) −153871. −0.0139604
\(657\) 1.76823e6 0.159818
\(658\) −7.08463e7 −6.37900
\(659\) −1.80634e7 −1.62027 −0.810133 0.586247i \(-0.800605\pi\)
−0.810133 + 0.586247i \(0.800605\pi\)
\(660\) 1.63516e6 0.146117
\(661\) −1.94465e6 −0.173116 −0.0865580 0.996247i \(-0.527587\pi\)
−0.0865580 + 0.996247i \(0.527587\pi\)
\(662\) −1.49675e7 −1.32741
\(663\) −77250.3 −0.00682522
\(664\) 7.28952e6 0.641621
\(665\) 647716. 0.0567977
\(666\) −2.09790e6 −0.183273
\(667\) 8.05055e6 0.700666
\(668\) 1.72351e7 1.49442
\(669\) 3.09907e6 0.267711
\(670\) 2.15957e6 0.185857
\(671\) 7.03061e6 0.602819
\(672\) 9.60212e6 0.820246
\(673\) 9.47231e6 0.806154 0.403077 0.915166i \(-0.367941\pi\)
0.403077 + 0.915166i \(0.367941\pi\)
\(674\) 904497. 0.0766933
\(675\) 1.09840e7 0.927901
\(676\) −2.09618e7 −1.76425
\(677\) 4.21500e6 0.353449 0.176724 0.984260i \(-0.443450\pi\)
0.176724 + 0.984260i \(0.443450\pi\)
\(678\) −7.81570e6 −0.652971
\(679\) −4.27216e7 −3.55609
\(680\) −61641.4 −0.00511211
\(681\) −1.93166e6 −0.159611
\(682\) 1.08849e7 0.896112
\(683\) 1.20346e7 0.987147 0.493573 0.869704i \(-0.335690\pi\)
0.493573 + 0.869704i \(0.335690\pi\)
\(684\) 523320. 0.0427688
\(685\) 1.52733e6 0.124368
\(686\) −7.41926e7 −6.01936
\(687\) −1.78231e7 −1.44076
\(688\) 3.71308e6 0.299063
\(689\) 3.45387e6 0.277178
\(690\) −2.89393e6 −0.231401
\(691\) 1.48943e7 1.18665 0.593327 0.804962i \(-0.297814\pi\)
0.593327 + 0.804962i \(0.297814\pi\)
\(692\) −1.28435e7 −1.01957
\(693\) 1.44103e6 0.113983
\(694\) 3.67291e7 2.89476
\(695\) 2.01928e6 0.158575
\(696\) −1.37359e7 −1.07482
\(697\) −7542.25 −0.000588057 0
\(698\) −3.42047e7 −2.65734
\(699\) −199396. −0.0154356
\(700\) −4.66862e7 −3.60117
\(701\) −2.58343e6 −0.198564 −0.0992822 0.995059i \(-0.531655\pi\)
−0.0992822 + 0.995059i \(0.531655\pi\)
\(702\) −5.05496e6 −0.387146
\(703\) 3.18336e6 0.242939
\(704\) −1.00214e7 −0.762074
\(705\) 3.42300e6 0.259378
\(706\) −1.72625e7 −1.30344
\(707\) −1.68905e7 −1.27085
\(708\) 7.31139e6 0.548172
\(709\) −8.76096e6 −0.654540 −0.327270 0.944931i \(-0.606129\pi\)
−0.327270 + 0.944931i \(0.606129\pi\)
\(710\) −5.07953e6 −0.378162
\(711\) −1.02436e6 −0.0759938
\(712\) −7.65961e6 −0.566248
\(713\) −1.25614e7 −0.925364
\(714\) −1.27227e6 −0.0933968
\(715\) −245892. −0.0179879
\(716\) −3.21059e7 −2.34047
\(717\) 4.08636e6 0.296851
\(718\) −3.43518e7 −2.48679
\(719\) −2.55779e7 −1.84520 −0.922599 0.385761i \(-0.873939\pi\)
−0.922599 + 0.385761i \(0.873939\pi\)
\(720\) 114808. 0.00825357
\(721\) −4.81432e7 −3.44903
\(722\) 2.25282e7 1.60836
\(723\) 2.30348e7 1.63885
\(724\) 1.76823e7 1.25370
\(725\) −9.62341e6 −0.679961
\(726\) 1.67946e7 1.18257
\(727\) 6.23788e6 0.437725 0.218862 0.975756i \(-0.429765\pi\)
0.218862 + 0.975756i \(0.429765\pi\)
\(728\) 1.00208e7 0.700765
\(729\) 1.26262e7 0.879938
\(730\) −4.96922e6 −0.345129
\(731\) 182003. 0.0125975
\(732\) 2.96813e7 2.04741
\(733\) 1.16371e7 0.799992 0.399996 0.916517i \(-0.369012\pi\)
0.399996 + 0.916517i \(0.369012\pi\)
\(734\) 2.08083e7 1.42559
\(735\) 5.55721e6 0.379436
\(736\) 5.95968e6 0.405535
\(737\) −7.29050e6 −0.494411
\(738\) 55309.4 0.00373816
\(739\) 3.60083e6 0.242545 0.121272 0.992619i \(-0.461303\pi\)
0.121272 + 0.992619i \(0.461303\pi\)
\(740\) 3.84432e6 0.258072
\(741\) −859607. −0.0575114
\(742\) 5.68831e7 3.79292
\(743\) 2.66981e6 0.177422 0.0887111 0.996057i \(-0.471725\pi\)
0.0887111 + 0.996057i \(0.471725\pi\)
\(744\) 2.14323e7 1.41950
\(745\) 3.36411e6 0.222064
\(746\) 4.20439e7 2.76602
\(747\) −665495. −0.0436358
\(748\) 446177. 0.0291577
\(749\) 1.68270e7 1.09598
\(750\) 6.97660e6 0.452888
\(751\) −4.71505e6 −0.305061 −0.152530 0.988299i \(-0.548742\pi\)
−0.152530 + 0.988299i \(0.548742\pi\)
\(752\) 1.90549e7 1.22875
\(753\) −8.71445e6 −0.560083
\(754\) 4.42879e6 0.283698
\(755\) 579611. 0.0370057
\(756\) −5.42853e7 −3.45444
\(757\) −931738. −0.0590954 −0.0295477 0.999563i \(-0.509407\pi\)
−0.0295477 + 0.999563i \(0.509407\pi\)
\(758\) −2.58934e7 −1.63688
\(759\) 9.76962e6 0.615564
\(760\) −685917. −0.0430762
\(761\) −6.36554e6 −0.398450 −0.199225 0.979954i \(-0.563842\pi\)
−0.199225 + 0.979954i \(0.563842\pi\)
\(762\) 3.06594e7 1.91283
\(763\) −2.05256e7 −1.27639
\(764\) 1.54061e7 0.954904
\(765\) 5627.53 0.000347668 0
\(766\) −1.81069e7 −1.11499
\(767\) −1.09947e6 −0.0674832
\(768\) −3.06739e7 −1.87657
\(769\) 1.83708e6 0.112024 0.0560121 0.998430i \(-0.482161\pi\)
0.0560121 + 0.998430i \(0.482161\pi\)
\(770\) −4.04969e6 −0.246147
\(771\) −148706. −0.00900936
\(772\) 1.59053e7 0.960505
\(773\) 2.34910e7 1.41401 0.707007 0.707207i \(-0.250045\pi\)
0.707007 + 0.707207i \(0.250045\pi\)
\(774\) −1.33468e6 −0.0800801
\(775\) 1.50155e7 0.898019
\(776\) 4.52412e7 2.69700
\(777\) 3.70068e7 2.19902
\(778\) −3.02186e7 −1.78989
\(779\) −83926.8 −0.00495515
\(780\) −1.03809e6 −0.0610939
\(781\) 1.71480e7 1.00597
\(782\) −789647. −0.0461760
\(783\) −1.11898e7 −0.652256
\(784\) 3.09355e7 1.79749
\(785\) −1.32510e6 −0.0767494
\(786\) −3.07133e7 −1.77325
\(787\) 2.63184e6 0.151469 0.0757343 0.997128i \(-0.475870\pi\)
0.0757343 + 0.997128i \(0.475870\pi\)
\(788\) −7.14689e6 −0.410017
\(789\) −9.16738e6 −0.524267
\(790\) 2.87873e6 0.164109
\(791\) 1.26216e7 0.717257
\(792\) −1.52602e6 −0.0864465
\(793\) −4.46341e6 −0.252048
\(794\) 1.16898e7 0.658044
\(795\) −2.74835e6 −0.154225
\(796\) 2.07961e7 1.16332
\(797\) −7.57868e6 −0.422618 −0.211309 0.977419i \(-0.567773\pi\)
−0.211309 + 0.977419i \(0.567773\pi\)
\(798\) −1.41572e7 −0.786991
\(799\) 934011. 0.0517589
\(800\) −7.12404e6 −0.393551
\(801\) 699282. 0.0385098
\(802\) −2.22396e7 −1.22093
\(803\) 1.67756e7 0.918099
\(804\) −3.07784e7 −1.67922
\(805\) 4.67343e6 0.254183
\(806\) −6.91029e6 −0.374678
\(807\) −3.42406e7 −1.85079
\(808\) 1.78867e7 0.963830
\(809\) −2.29499e6 −0.123285 −0.0616423 0.998098i \(-0.519634\pi\)
−0.0616423 + 0.998098i \(0.519634\pi\)
\(810\) 4.43190e6 0.237344
\(811\) −1.81498e7 −0.968993 −0.484496 0.874793i \(-0.660997\pi\)
−0.484496 + 0.874793i \(0.660997\pi\)
\(812\) 4.75609e7 2.53139
\(813\) 7.48593e6 0.397209
\(814\) −1.99032e7 −1.05284
\(815\) 3.50762e6 0.184977
\(816\) 342190. 0.0179905
\(817\) 2.02525e6 0.106151
\(818\) 2.24985e7 1.17563
\(819\) −914843. −0.0476581
\(820\) −101353. −0.00526381
\(821\) −2.15947e7 −1.11812 −0.559060 0.829127i \(-0.688838\pi\)
−0.559060 + 0.829127i \(0.688838\pi\)
\(822\) −3.33831e7 −1.72324
\(823\) 2.14246e7 1.10259 0.551293 0.834311i \(-0.314135\pi\)
0.551293 + 0.834311i \(0.314135\pi\)
\(824\) 5.09826e7 2.61580
\(825\) −1.16783e7 −0.597374
\(826\) −1.81076e7 −0.923445
\(827\) 2.04251e7 1.03849 0.519244 0.854626i \(-0.326214\pi\)
0.519244 + 0.854626i \(0.326214\pi\)
\(828\) 3.77588e6 0.191400
\(829\) 1.19639e7 0.604624 0.302312 0.953209i \(-0.402242\pi\)
0.302312 + 0.953209i \(0.402242\pi\)
\(830\) 1.87022e6 0.0942320
\(831\) 6.81679e6 0.342434
\(832\) 6.36212e6 0.318635
\(833\) 1.51636e6 0.0757164
\(834\) −4.41356e7 −2.19722
\(835\) 2.06236e6 0.102364
\(836\) 4.96485e6 0.245692
\(837\) 1.74596e7 0.861429
\(838\) −3.87986e6 −0.190856
\(839\) 1.76289e7 0.864612 0.432306 0.901727i \(-0.357700\pi\)
0.432306 + 0.901727i \(0.357700\pi\)
\(840\) −7.97384e6 −0.389914
\(841\) −1.07074e7 −0.522031
\(842\) 5.78607e7 2.81257
\(843\) −1.67969e7 −0.814068
\(844\) 6.52028e7 3.15072
\(845\) −2.50829e6 −0.120847
\(846\) −6.84936e6 −0.329021
\(847\) −2.71217e7 −1.29900
\(848\) −1.52994e7 −0.730607
\(849\) 2.74881e7 1.30881
\(850\) 943923. 0.0448115
\(851\) 2.29687e7 1.08721
\(852\) 7.23941e7 3.41668
\(853\) −1.36691e7 −0.643233 −0.321616 0.946870i \(-0.604226\pi\)
−0.321616 + 0.946870i \(0.604226\pi\)
\(854\) −7.35095e7 −3.44905
\(855\) 62620.6 0.00292956
\(856\) −1.78195e7 −0.831209
\(857\) 1.76341e7 0.820164 0.410082 0.912049i \(-0.365500\pi\)
0.410082 + 0.912049i \(0.365500\pi\)
\(858\) 5.37449e6 0.249241
\(859\) −1.52978e7 −0.707367 −0.353684 0.935365i \(-0.615071\pi\)
−0.353684 + 0.935365i \(0.615071\pi\)
\(860\) 2.44575e6 0.112763
\(861\) −975654. −0.0448527
\(862\) −4.22407e7 −1.93626
\(863\) −3.39009e7 −1.54947 −0.774736 0.632285i \(-0.782117\pi\)
−0.774736 + 0.632285i \(0.782117\pi\)
\(864\) −8.28361e6 −0.377516
\(865\) −1.53686e6 −0.0698384
\(866\) 5.55622e7 2.51759
\(867\) −2.32051e7 −1.04842
\(868\) −7.42097e7 −3.34319
\(869\) −9.71832e6 −0.436558
\(870\) −3.52413e6 −0.157853
\(871\) 4.62839e6 0.206721
\(872\) 2.17361e7 0.968035
\(873\) −4.13029e6 −0.183419
\(874\) −8.78683e6 −0.389093
\(875\) −1.12666e7 −0.497476
\(876\) 7.08220e7 3.11823
\(877\) 1.05119e7 0.461513 0.230756 0.973012i \(-0.425880\pi\)
0.230756 + 0.973012i \(0.425880\pi\)
\(878\) 5.50525e7 2.41013
\(879\) −7.82624e6 −0.341650
\(880\) 1.08921e6 0.0474139
\(881\) −3.89606e7 −1.69116 −0.845581 0.533847i \(-0.820746\pi\)
−0.845581 + 0.533847i \(0.820746\pi\)
\(882\) −1.11199e7 −0.481314
\(883\) 1.11872e7 0.482857 0.241428 0.970419i \(-0.422384\pi\)
0.241428 + 0.970419i \(0.422384\pi\)
\(884\) −283257. −0.0121913
\(885\) 874884. 0.0375485
\(886\) −5.33438e7 −2.28297
\(887\) 2.48580e7 1.06086 0.530428 0.847730i \(-0.322031\pi\)
0.530428 + 0.847730i \(0.322031\pi\)
\(888\) −3.91894e7 −1.66777
\(889\) −4.95122e7 −2.10115
\(890\) −1.96518e6 −0.0831623
\(891\) −1.49617e7 −0.631373
\(892\) 1.13635e7 0.478187
\(893\) 1.03933e7 0.436137
\(894\) −7.35296e7 −3.07694
\(895\) −3.84181e6 −0.160316
\(896\) 8.59929e7 3.57843
\(897\) −6.20227e6 −0.257377
\(898\) −9.58267e6 −0.396548
\(899\) −1.52968e7 −0.631251
\(900\) −4.51358e6 −0.185744
\(901\) −749926. −0.0307756
\(902\) 524733. 0.0214744
\(903\) 2.35437e7 0.960848
\(904\) −1.33661e7 −0.543979
\(905\) 2.11587e6 0.0858753
\(906\) −1.26686e7 −0.512753
\(907\) 2.60929e7 1.05318 0.526592 0.850118i \(-0.323470\pi\)
0.526592 + 0.850118i \(0.323470\pi\)
\(908\) −7.08290e6 −0.285100
\(909\) −1.63296e6 −0.0655488
\(910\) 2.57096e6 0.102918
\(911\) −2.70240e7 −1.07883 −0.539415 0.842040i \(-0.681355\pi\)
−0.539415 + 0.842040i \(0.681355\pi\)
\(912\) 3.80774e6 0.151593
\(913\) −6.31370e6 −0.250673
\(914\) −3.05043e7 −1.20780
\(915\) 3.55167e6 0.140243
\(916\) −6.53527e7 −2.57350
\(917\) 4.95992e7 1.94783
\(918\) 1.09756e6 0.0429856
\(919\) −5.01531e7 −1.95888 −0.979442 0.201727i \(-0.935345\pi\)
−0.979442 + 0.201727i \(0.935345\pi\)
\(920\) −4.94906e6 −0.192776
\(921\) 5.61303e6 0.218046
\(922\) −2.62697e7 −1.01772
\(923\) −1.08865e7 −0.420613
\(924\) 5.77167e7 2.22393
\(925\) −2.74562e7 −1.05508
\(926\) −1.47859e7 −0.566658
\(927\) −4.65444e6 −0.177897
\(928\) 7.25750e6 0.276642
\(929\) −1.17678e7 −0.447360 −0.223680 0.974663i \(-0.571807\pi\)
−0.223680 + 0.974663i \(0.571807\pi\)
\(930\) 5.49873e6 0.208476
\(931\) 1.68734e7 0.638010
\(932\) −731134. −0.0275713
\(933\) 2.54757e7 0.958123
\(934\) −5.88934e7 −2.20902
\(935\) 53389.7 0.00199723
\(936\) 968799. 0.0361447
\(937\) −4.04239e7 −1.50414 −0.752072 0.659081i \(-0.770945\pi\)
−0.752072 + 0.659081i \(0.770945\pi\)
\(938\) 7.62268e7 2.82879
\(939\) −2.11456e7 −0.782630
\(940\) 1.25512e7 0.463304
\(941\) 8.74255e6 0.321858 0.160929 0.986966i \(-0.448551\pi\)
0.160929 + 0.986966i \(0.448551\pi\)
\(942\) 2.89629e7 1.06344
\(943\) −605552. −0.0221754
\(944\) 4.87025e6 0.177878
\(945\) −6.49580e6 −0.236621
\(946\) −1.26624e7 −0.460032
\(947\) 1.28481e7 0.465546 0.232773 0.972531i \(-0.425220\pi\)
0.232773 + 0.972531i \(0.425220\pi\)
\(948\) −4.10280e7 −1.48272
\(949\) −1.06501e7 −0.383872
\(950\) 1.05035e7 0.377596
\(951\) 9.68237e6 0.347161
\(952\) −2.17577e6 −0.0778074
\(953\) −4.17412e7 −1.48879 −0.744393 0.667742i \(-0.767261\pi\)
−0.744393 + 0.667742i \(0.767261\pi\)
\(954\) 5.49941e6 0.195634
\(955\) 1.84350e6 0.0654087
\(956\) 1.49836e7 0.530238
\(957\) 1.18971e7 0.419916
\(958\) −1.25976e7 −0.443481
\(959\) 5.39107e7 1.89290
\(960\) −5.06254e6 −0.177292
\(961\) −4.76138e6 −0.166312
\(962\) 1.26356e7 0.440209
\(963\) 1.62682e6 0.0565294
\(964\) 8.44627e7 2.92733
\(965\) 1.90324e6 0.0657923
\(966\) −1.02148e8 −3.52197
\(967\) 1.12651e7 0.387407 0.193703 0.981060i \(-0.437950\pi\)
0.193703 + 0.981060i \(0.437950\pi\)
\(968\) 2.87213e7 0.985180
\(969\) 186643. 0.00638561
\(970\) 1.16072e7 0.396095
\(971\) 1.76257e7 0.599926 0.299963 0.953951i \(-0.403026\pi\)
0.299963 + 0.953951i \(0.403026\pi\)
\(972\) −1.10847e7 −0.376320
\(973\) 7.12749e7 2.41354
\(974\) 6.43883e7 2.17475
\(975\) 7.41403e6 0.249771
\(976\) 1.97712e7 0.664369
\(977\) −1.23278e6 −0.0413189 −0.0206594 0.999787i \(-0.506577\pi\)
−0.0206594 + 0.999787i \(0.506577\pi\)
\(978\) −7.66663e7 −2.56305
\(979\) 6.63425e6 0.221225
\(980\) 2.03768e7 0.677752
\(981\) −1.98439e6 −0.0658348
\(982\) 5.00331e7 1.65569
\(983\) 4.04820e7 1.33622 0.668110 0.744063i \(-0.267104\pi\)
0.668110 + 0.744063i \(0.267104\pi\)
\(984\) 1.03320e6 0.0340170
\(985\) −855199. −0.0280852
\(986\) −961607. −0.0314996
\(987\) 1.20822e8 3.94779
\(988\) −3.15195e6 −0.102728
\(989\) 1.46127e7 0.475049
\(990\) −391521. −0.0126960
\(991\) −3.85983e7 −1.24849 −0.624243 0.781230i \(-0.714592\pi\)
−0.624243 + 0.781230i \(0.714592\pi\)
\(992\) −1.13240e7 −0.365358
\(993\) 2.55258e7 0.821497
\(994\) −1.79293e8 −5.75570
\(995\) 2.48847e6 0.0796845
\(996\) −2.66547e7 −0.851383
\(997\) 3.04171e7 0.969125 0.484562 0.874757i \(-0.338979\pi\)
0.484562 + 0.874757i \(0.338979\pi\)
\(998\) −9.50083e7 −3.01950
\(999\) −3.19252e7 −1.01209
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 547.6.a.b.1.11 117
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
547.6.a.b.1.11 117 1.1 even 1 trivial