Properties

Label 230.6.a.f.1.5
Level $230$
Weight $6$
Character 230.1
Self dual yes
Analytic conductor $36.888$
Analytic rank $0$
Dimension $5$
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] = [230,6,Mod(1,230)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(230, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("230.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 230.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: \(36.8882785570\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - x^{4} - 774x^{3} - 197x^{2} + 66287x + 154128 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(26.5679\) of defining polynomial
Character \(\chi\) \(=\) 230.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.00000 q^{2} +26.5679 q^{3} +16.0000 q^{4} +25.0000 q^{5} -106.272 q^{6} +257.945 q^{7} -64.0000 q^{8} +462.854 q^{9} +O(q^{10})\) \(q-4.00000 q^{2} +26.5679 q^{3} +16.0000 q^{4} +25.0000 q^{5} -106.272 q^{6} +257.945 q^{7} -64.0000 q^{8} +462.854 q^{9} -100.000 q^{10} +382.346 q^{11} +425.087 q^{12} +152.988 q^{13} -1031.78 q^{14} +664.198 q^{15} +256.000 q^{16} +437.640 q^{17} -1851.41 q^{18} -2052.16 q^{19} +400.000 q^{20} +6853.05 q^{21} -1529.38 q^{22} -529.000 q^{23} -1700.35 q^{24} +625.000 q^{25} -611.951 q^{26} +5841.05 q^{27} +4127.11 q^{28} +2360.37 q^{29} -2656.79 q^{30} -4283.89 q^{31} -1024.00 q^{32} +10158.1 q^{33} -1750.56 q^{34} +6448.62 q^{35} +7405.66 q^{36} -12212.3 q^{37} +8208.63 q^{38} +4064.56 q^{39} -1600.00 q^{40} -16759.8 q^{41} -27412.2 q^{42} -4911.50 q^{43} +6117.53 q^{44} +11571.3 q^{45} +2116.00 q^{46} -21338.3 q^{47} +6801.38 q^{48} +49728.4 q^{49} -2500.00 q^{50} +11627.2 q^{51} +2447.80 q^{52} -36998.9 q^{53} -23364.2 q^{54} +9558.64 q^{55} -16508.5 q^{56} -54521.5 q^{57} -9441.48 q^{58} -29669.6 q^{59} +10627.2 q^{60} +29601.2 q^{61} +17135.6 q^{62} +119391. q^{63} +4096.00 q^{64} +3824.69 q^{65} -40632.5 q^{66} +25795.4 q^{67} +7002.25 q^{68} -14054.4 q^{69} -25794.5 q^{70} +27128.9 q^{71} -29622.6 q^{72} -49568.3 q^{73} +48849.4 q^{74} +16604.9 q^{75} -32834.5 q^{76} +98624.0 q^{77} -16258.3 q^{78} +73611.6 q^{79} +6400.00 q^{80} +42711.1 q^{81} +67039.1 q^{82} +54599.4 q^{83} +109649. q^{84} +10941.0 q^{85} +19646.0 q^{86} +62710.1 q^{87} -24470.1 q^{88} +24120.5 q^{89} -46285.4 q^{90} +39462.4 q^{91} -8464.00 q^{92} -113814. q^{93} +85353.4 q^{94} -51303.9 q^{95} -27205.5 q^{96} +103363. q^{97} -198914. q^{98} +176970. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 20 q^{2} + q^{3} + 80 q^{4} + 125 q^{5} - 4 q^{6} + 102 q^{7} - 320 q^{8} + 334 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 20 q^{2} + q^{3} + 80 q^{4} + 125 q^{5} - 4 q^{6} + 102 q^{7} - 320 q^{8} + 334 q^{9} - 500 q^{10} + 251 q^{11} + 16 q^{12} + 1743 q^{13} - 408 q^{14} + 25 q^{15} + 1280 q^{16} + 1944 q^{17} - 1336 q^{18} - 845 q^{19} + 2000 q^{20} + 4682 q^{21} - 1004 q^{22} - 2645 q^{23} - 64 q^{24} + 3125 q^{25} - 6972 q^{26} + 2428 q^{27} + 1632 q^{28} - 4021 q^{29} - 100 q^{30} - 15752 q^{31} - 5120 q^{32} + 2931 q^{33} - 7776 q^{34} + 2550 q^{35} + 5344 q^{36} - 3455 q^{37} + 3380 q^{38} - 16708 q^{39} - 8000 q^{40} - 11898 q^{41} - 18728 q^{42} + 6968 q^{43} + 4016 q^{44} + 8350 q^{45} + 10580 q^{46} + 13412 q^{47} + 256 q^{48} + 91041 q^{49} - 12500 q^{50} - 2115 q^{51} + 27888 q^{52} + 53029 q^{53} - 9712 q^{54} + 6275 q^{55} - 6528 q^{56} - 21730 q^{57} + 16084 q^{58} - 31223 q^{59} + 400 q^{60} + 71477 q^{61} + 63008 q^{62} + 262199 q^{63} + 20480 q^{64} + 43575 q^{65} - 11724 q^{66} + 76003 q^{67} + 31104 q^{68} - 529 q^{69} - 10200 q^{70} + 54418 q^{71} - 21376 q^{72} + 69418 q^{73} + 13820 q^{74} + 625 q^{75} - 13520 q^{76} + 283598 q^{77} + 66832 q^{78} + 105024 q^{79} + 32000 q^{80} + 102913 q^{81} + 47592 q^{82} + 89399 q^{83} + 74912 q^{84} + 48600 q^{85} - 27872 q^{86} + 276726 q^{87} - 16064 q^{88} + 96240 q^{89} - 33400 q^{90} + 59261 q^{91} - 42320 q^{92} + 84434 q^{93} - 53648 q^{94} - 21125 q^{95} - 1024 q^{96} + 216087 q^{97} - 364164 q^{98} + 386925 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.00000 −0.707107
\(3\) 26.5679 1.70433 0.852166 0.523272i \(-0.175289\pi\)
0.852166 + 0.523272i \(0.175289\pi\)
\(4\) 16.0000 0.500000
\(5\) 25.0000 0.447214
\(6\) −106.272 −1.20514
\(7\) 257.945 1.98967 0.994836 0.101499i \(-0.0323637\pi\)
0.994836 + 0.101499i \(0.0323637\pi\)
\(8\) −64.0000 −0.353553
\(9\) 462.854 1.90475
\(10\) −100.000 −0.316228
\(11\) 382.346 0.952740 0.476370 0.879245i \(-0.341952\pi\)
0.476370 + 0.879245i \(0.341952\pi\)
\(12\) 425.087 0.852166
\(13\) 152.988 0.251072 0.125536 0.992089i \(-0.459935\pi\)
0.125536 + 0.992089i \(0.459935\pi\)
\(14\) −1031.78 −1.40691
\(15\) 664.198 0.762200
\(16\) 256.000 0.250000
\(17\) 437.640 0.367278 0.183639 0.982994i \(-0.441212\pi\)
0.183639 + 0.982994i \(0.441212\pi\)
\(18\) −1851.41 −1.34686
\(19\) −2052.16 −1.30415 −0.652074 0.758156i \(-0.726101\pi\)
−0.652074 + 0.758156i \(0.726101\pi\)
\(20\) 400.000 0.223607
\(21\) 6853.05 3.39106
\(22\) −1529.38 −0.673689
\(23\) −529.000 −0.208514
\(24\) −1700.35 −0.602572
\(25\) 625.000 0.200000
\(26\) −611.951 −0.177535
\(27\) 5841.05 1.54199
\(28\) 4127.11 0.994836
\(29\) 2360.37 0.521177 0.260588 0.965450i \(-0.416083\pi\)
0.260588 + 0.965450i \(0.416083\pi\)
\(30\) −2656.79 −0.538957
\(31\) −4283.89 −0.800634 −0.400317 0.916377i \(-0.631100\pi\)
−0.400317 + 0.916377i \(0.631100\pi\)
\(32\) −1024.00 −0.176777
\(33\) 10158.1 1.62379
\(34\) −1750.56 −0.259705
\(35\) 6448.62 0.889808
\(36\) 7405.66 0.952374
\(37\) −12212.3 −1.46654 −0.733271 0.679936i \(-0.762008\pi\)
−0.733271 + 0.679936i \(0.762008\pi\)
\(38\) 8208.63 0.922171
\(39\) 4064.56 0.427910
\(40\) −1600.00 −0.158114
\(41\) −16759.8 −1.55707 −0.778536 0.627600i \(-0.784037\pi\)
−0.778536 + 0.627600i \(0.784037\pi\)
\(42\) −27412.2 −2.39784
\(43\) −4911.50 −0.405082 −0.202541 0.979274i \(-0.564920\pi\)
−0.202541 + 0.979274i \(0.564920\pi\)
\(44\) 6117.53 0.476370
\(45\) 11571.3 0.851829
\(46\) 2116.00 0.147442
\(47\) −21338.3 −1.40902 −0.704508 0.709696i \(-0.748832\pi\)
−0.704508 + 0.709696i \(0.748832\pi\)
\(48\) 6801.38 0.426083
\(49\) 49728.4 2.95879
\(50\) −2500.00 −0.141421
\(51\) 11627.2 0.625964
\(52\) 2447.80 0.125536
\(53\) −36998.9 −1.80925 −0.904625 0.426208i \(-0.859849\pi\)
−0.904625 + 0.426208i \(0.859849\pi\)
\(54\) −23364.2 −1.09035
\(55\) 9558.64 0.426078
\(56\) −16508.5 −0.703455
\(57\) −54521.5 −2.22270
\(58\) −9441.48 −0.368528
\(59\) −29669.6 −1.10964 −0.554819 0.831971i \(-0.687213\pi\)
−0.554819 + 0.831971i \(0.687213\pi\)
\(60\) 10627.2 0.381100
\(61\) 29601.2 1.01856 0.509278 0.860602i \(-0.329913\pi\)
0.509278 + 0.860602i \(0.329913\pi\)
\(62\) 17135.6 0.566134
\(63\) 119391. 3.78982
\(64\) 4096.00 0.125000
\(65\) 3824.69 0.112283
\(66\) −40632.5 −1.14819
\(67\) 25795.4 0.702030 0.351015 0.936370i \(-0.385837\pi\)
0.351015 + 0.936370i \(0.385837\pi\)
\(68\) 7002.25 0.183639
\(69\) −14054.4 −0.355378
\(70\) −25794.5 −0.629189
\(71\) 27128.9 0.638684 0.319342 0.947640i \(-0.396538\pi\)
0.319342 + 0.947640i \(0.396538\pi\)
\(72\) −29622.6 −0.673430
\(73\) −49568.3 −1.08867 −0.544336 0.838867i \(-0.683218\pi\)
−0.544336 + 0.838867i \(0.683218\pi\)
\(74\) 48849.4 1.03700
\(75\) 16604.9 0.340866
\(76\) −32834.5 −0.652074
\(77\) 98624.0 1.89564
\(78\) −16258.3 −0.302578
\(79\) 73611.6 1.32702 0.663512 0.748166i \(-0.269065\pi\)
0.663512 + 0.748166i \(0.269065\pi\)
\(80\) 6400.00 0.111803
\(81\) 42711.1 0.723316
\(82\) 67039.1 1.10102
\(83\) 54599.4 0.869946 0.434973 0.900443i \(-0.356758\pi\)
0.434973 + 0.900443i \(0.356758\pi\)
\(84\) 109649. 1.69553
\(85\) 10941.0 0.164252
\(86\) 19646.0 0.286436
\(87\) 62710.1 0.888258
\(88\) −24470.1 −0.336845
\(89\) 24120.5 0.322783 0.161392 0.986890i \(-0.448402\pi\)
0.161392 + 0.986890i \(0.448402\pi\)
\(90\) −46285.4 −0.602334
\(91\) 39462.4 0.499551
\(92\) −8464.00 −0.104257
\(93\) −113814. −1.36455
\(94\) 85353.4 0.996325
\(95\) −51303.9 −0.583232
\(96\) −27205.5 −0.301286
\(97\) 103363. 1.11541 0.557705 0.830039i \(-0.311682\pi\)
0.557705 + 0.830039i \(0.311682\pi\)
\(98\) −198914. −2.09218
\(99\) 176970. 1.81473
\(100\) 10000.0 0.100000
\(101\) 45095.7 0.439877 0.219939 0.975514i \(-0.429414\pi\)
0.219939 + 0.975514i \(0.429414\pi\)
\(102\) −46508.8 −0.442623
\(103\) 89880.9 0.834784 0.417392 0.908727i \(-0.362944\pi\)
0.417392 + 0.908727i \(0.362944\pi\)
\(104\) −9791.22 −0.0887674
\(105\) 171326. 1.51653
\(106\) 147995. 1.27933
\(107\) −127029. −1.07262 −0.536309 0.844022i \(-0.680182\pi\)
−0.536309 + 0.844022i \(0.680182\pi\)
\(108\) 93456.8 0.770995
\(109\) −10406.1 −0.0838919 −0.0419459 0.999120i \(-0.513356\pi\)
−0.0419459 + 0.999120i \(0.513356\pi\)
\(110\) −38234.6 −0.301283
\(111\) −324456. −2.49948
\(112\) 66033.8 0.497418
\(113\) 3869.90 0.0285104 0.0142552 0.999898i \(-0.495462\pi\)
0.0142552 + 0.999898i \(0.495462\pi\)
\(114\) 218086. 1.57169
\(115\) −13225.0 −0.0932505
\(116\) 37765.9 0.260588
\(117\) 70810.9 0.478229
\(118\) 118678. 0.784633
\(119\) 112887. 0.730763
\(120\) −42508.7 −0.269479
\(121\) −14862.7 −0.0922858
\(122\) −118405. −0.720228
\(123\) −445272. −2.65377
\(124\) −68542.2 −0.400317
\(125\) 15625.0 0.0894427
\(126\) −477562. −2.67981
\(127\) 98019.0 0.539263 0.269632 0.962964i \(-0.413098\pi\)
0.269632 + 0.962964i \(0.413098\pi\)
\(128\) −16384.0 −0.0883883
\(129\) −130488. −0.690394
\(130\) −15298.8 −0.0793959
\(131\) −118385. −0.602723 −0.301361 0.953510i \(-0.597441\pi\)
−0.301361 + 0.953510i \(0.597441\pi\)
\(132\) 162530. 0.811893
\(133\) −529343. −2.59482
\(134\) −103182. −0.496410
\(135\) 146026. 0.689599
\(136\) −28009.0 −0.129852
\(137\) −12515.2 −0.0569688 −0.0284844 0.999594i \(-0.509068\pi\)
−0.0284844 + 0.999594i \(0.509068\pi\)
\(138\) 56217.7 0.251290
\(139\) 350905. 1.54047 0.770235 0.637760i \(-0.220139\pi\)
0.770235 + 0.637760i \(0.220139\pi\)
\(140\) 103178. 0.444904
\(141\) −566915. −2.40143
\(142\) −108516. −0.451618
\(143\) 58494.2 0.239206
\(144\) 118491. 0.476187
\(145\) 59009.3 0.233077
\(146\) 198273. 0.769808
\(147\) 1.32118e6 5.04276
\(148\) −195398. −0.733271
\(149\) 6379.53 0.0235409 0.0117704 0.999931i \(-0.496253\pi\)
0.0117704 + 0.999931i \(0.496253\pi\)
\(150\) −66419.8 −0.241029
\(151\) −516891. −1.84483 −0.922416 0.386197i \(-0.873789\pi\)
−0.922416 + 0.386197i \(0.873789\pi\)
\(152\) 131338. 0.461086
\(153\) 202563. 0.699572
\(154\) −394496. −1.34042
\(155\) −107097. −0.358054
\(156\) 65033.0 0.213955
\(157\) 187263. 0.606321 0.303161 0.952939i \(-0.401958\pi\)
0.303161 + 0.952939i \(0.401958\pi\)
\(158\) −294447. −0.938348
\(159\) −982982. −3.08356
\(160\) −25600.0 −0.0790569
\(161\) −136453. −0.414875
\(162\) −170844. −0.511461
\(163\) 616742. 1.81817 0.909086 0.416609i \(-0.136782\pi\)
0.909086 + 0.416609i \(0.136782\pi\)
\(164\) −268156. −0.778536
\(165\) 253953. 0.726179
\(166\) −218397. −0.615145
\(167\) −261863. −0.726579 −0.363290 0.931676i \(-0.618346\pi\)
−0.363290 + 0.931676i \(0.618346\pi\)
\(168\) −438595. −1.19892
\(169\) −347888. −0.936963
\(170\) −43764.0 −0.116144
\(171\) −949848. −2.48407
\(172\) −78583.9 −0.202541
\(173\) −452537. −1.14958 −0.574790 0.818301i \(-0.694916\pi\)
−0.574790 + 0.818301i \(0.694916\pi\)
\(174\) −250840. −0.628094
\(175\) 161215. 0.397934
\(176\) 97880.5 0.238185
\(177\) −788259. −1.89119
\(178\) −96482.0 −0.228242
\(179\) 391812. 0.913998 0.456999 0.889467i \(-0.348924\pi\)
0.456999 + 0.889467i \(0.348924\pi\)
\(180\) 185141. 0.425914
\(181\) −709815. −1.61046 −0.805228 0.592965i \(-0.797957\pi\)
−0.805228 + 0.592965i \(0.797957\pi\)
\(182\) −157849. −0.353236
\(183\) 786442. 1.73596
\(184\) 33856.0 0.0737210
\(185\) −305309. −0.655858
\(186\) 455256. 0.964880
\(187\) 167330. 0.349921
\(188\) −341413. −0.704508
\(189\) 1.50667e6 3.06805
\(190\) 205216. 0.412408
\(191\) 158111. 0.313602 0.156801 0.987630i \(-0.449882\pi\)
0.156801 + 0.987630i \(0.449882\pi\)
\(192\) 108822. 0.213041
\(193\) 326743. 0.631413 0.315707 0.948857i \(-0.397758\pi\)
0.315707 + 0.948857i \(0.397758\pi\)
\(194\) −413451. −0.788714
\(195\) 101614. 0.191367
\(196\) 795655. 1.47940
\(197\) 94961.8 0.174335 0.0871673 0.996194i \(-0.472219\pi\)
0.0871673 + 0.996194i \(0.472219\pi\)
\(198\) −707881. −1.28321
\(199\) −159731. −0.285928 −0.142964 0.989728i \(-0.545663\pi\)
−0.142964 + 0.989728i \(0.545663\pi\)
\(200\) −40000.0 −0.0707107
\(201\) 685330. 1.19649
\(202\) −180383. −0.311040
\(203\) 608845. 1.03697
\(204\) 186035. 0.312982
\(205\) −418994. −0.696344
\(206\) −359523. −0.590281
\(207\) −244850. −0.397167
\(208\) 39164.9 0.0627680
\(209\) −784634. −1.24251
\(210\) −685305. −1.07235
\(211\) 1.03326e6 1.59774 0.798868 0.601506i \(-0.205433\pi\)
0.798868 + 0.601506i \(0.205433\pi\)
\(212\) −591982. −0.904625
\(213\) 720758. 1.08853
\(214\) 508118. 0.758455
\(215\) −122787. −0.181158
\(216\) −373827. −0.545176
\(217\) −1.10501e6 −1.59300
\(218\) 41624.2 0.0593205
\(219\) −1.31693e6 −1.85546
\(220\) 152938. 0.213039
\(221\) 66953.6 0.0922133
\(222\) 1.29783e6 1.76740
\(223\) 566494. 0.762839 0.381420 0.924402i \(-0.375435\pi\)
0.381420 + 0.924402i \(0.375435\pi\)
\(224\) −264135. −0.351728
\(225\) 289284. 0.380950
\(226\) −15479.6 −0.0201599
\(227\) 1.00552e6 1.29517 0.647587 0.761992i \(-0.275778\pi\)
0.647587 + 0.761992i \(0.275778\pi\)
\(228\) −872344. −1.11135
\(229\) 1.00056e6 1.26082 0.630412 0.776260i \(-0.282886\pi\)
0.630412 + 0.776260i \(0.282886\pi\)
\(230\) 52900.0 0.0659380
\(231\) 2.62023e6 3.23080
\(232\) −151064. −0.184264
\(233\) −1.02845e6 −1.24106 −0.620532 0.784181i \(-0.713083\pi\)
−0.620532 + 0.784181i \(0.713083\pi\)
\(234\) −283244. −0.338159
\(235\) −533458. −0.630131
\(236\) −474713. −0.554819
\(237\) 1.95571e6 2.26169
\(238\) −451548. −0.516727
\(239\) 701099. 0.793934 0.396967 0.917833i \(-0.370063\pi\)
0.396967 + 0.917833i \(0.370063\pi\)
\(240\) 170035. 0.190550
\(241\) −504212. −0.559204 −0.279602 0.960116i \(-0.590203\pi\)
−0.279602 + 0.960116i \(0.590203\pi\)
\(242\) 59450.9 0.0652559
\(243\) −284632. −0.309220
\(244\) 473619. 0.509278
\(245\) 1.24321e6 1.32321
\(246\) 1.78109e6 1.87650
\(247\) −313955. −0.327435
\(248\) 274169. 0.283067
\(249\) 1.45059e6 1.48268
\(250\) −62500.0 −0.0632456
\(251\) −1.23699e6 −1.23932 −0.619659 0.784871i \(-0.712729\pi\)
−0.619659 + 0.784871i \(0.712729\pi\)
\(252\) 1.91025e6 1.89491
\(253\) −202261. −0.198660
\(254\) −392076. −0.381317
\(255\) 290680. 0.279940
\(256\) 65536.0 0.0625000
\(257\) 191965. 0.181296 0.0906482 0.995883i \(-0.471106\pi\)
0.0906482 + 0.995883i \(0.471106\pi\)
\(258\) 521953. 0.488182
\(259\) −3.15011e6 −2.91794
\(260\) 61195.1 0.0561414
\(261\) 1.09251e6 0.992710
\(262\) 473539. 0.426189
\(263\) −857405. −0.764358 −0.382179 0.924088i \(-0.624826\pi\)
−0.382179 + 0.924088i \(0.624826\pi\)
\(264\) −650120. −0.574095
\(265\) −924972. −0.809122
\(266\) 2.11737e6 1.83482
\(267\) 640831. 0.550130
\(268\) 412727. 0.351015
\(269\) 423229. 0.356611 0.178305 0.983975i \(-0.442938\pi\)
0.178305 + 0.983975i \(0.442938\pi\)
\(270\) −584105. −0.487620
\(271\) −2.21758e6 −1.83424 −0.917119 0.398613i \(-0.869492\pi\)
−0.917119 + 0.398613i \(0.869492\pi\)
\(272\) 112036. 0.0918196
\(273\) 1.04843e6 0.851400
\(274\) 50060.8 0.0402830
\(275\) 238966. 0.190548
\(276\) −224871. −0.177689
\(277\) 770934. 0.603695 0.301848 0.953356i \(-0.402397\pi\)
0.301848 + 0.953356i \(0.402397\pi\)
\(278\) −1.40362e6 −1.08928
\(279\) −1.98281e6 −1.52501
\(280\) −412711. −0.314595
\(281\) −2.54824e6 −1.92519 −0.962597 0.270939i \(-0.912666\pi\)
−0.962597 + 0.270939i \(0.912666\pi\)
\(282\) 2.26766e6 1.69807
\(283\) 378353. 0.280822 0.140411 0.990093i \(-0.455158\pi\)
0.140411 + 0.990093i \(0.455158\pi\)
\(284\) 434062. 0.319342
\(285\) −1.36304e6 −0.994022
\(286\) −233977. −0.169144
\(287\) −4.32309e6 −3.09806
\(288\) −473962. −0.336715
\(289\) −1.22833e6 −0.865107
\(290\) −236037. −0.164811
\(291\) 2.74613e6 1.90103
\(292\) −793093. −0.544336
\(293\) −1.31258e6 −0.893215 −0.446608 0.894730i \(-0.647368\pi\)
−0.446608 + 0.894730i \(0.647368\pi\)
\(294\) −5.28472e6 −3.56577
\(295\) −741740. −0.496245
\(296\) 781590. 0.518501
\(297\) 2.23330e6 1.46912
\(298\) −25518.1 −0.0166459
\(299\) −80930.5 −0.0523521
\(300\) 265679. 0.170433
\(301\) −1.26689e6 −0.805980
\(302\) 2.06757e6 1.30449
\(303\) 1.19810e6 0.749697
\(304\) −525352. −0.326037
\(305\) 740030. 0.455512
\(306\) −810254. −0.494672
\(307\) −2.74167e6 −1.66023 −0.830117 0.557589i \(-0.811727\pi\)
−0.830117 + 0.557589i \(0.811727\pi\)
\(308\) 1.57798e6 0.947820
\(309\) 2.38795e6 1.42275
\(310\) 428389. 0.253183
\(311\) 457160. 0.268020 0.134010 0.990980i \(-0.457215\pi\)
0.134010 + 0.990980i \(0.457215\pi\)
\(312\) −260132. −0.151289
\(313\) 2.30247e6 1.32841 0.664206 0.747549i \(-0.268770\pi\)
0.664206 + 0.747549i \(0.268770\pi\)
\(314\) −749052. −0.428734
\(315\) 2.98477e6 1.69486
\(316\) 1.17779e6 0.663512
\(317\) 605094. 0.338201 0.169100 0.985599i \(-0.445914\pi\)
0.169100 + 0.985599i \(0.445914\pi\)
\(318\) 3.93193e6 2.18041
\(319\) 902478. 0.496546
\(320\) 102400. 0.0559017
\(321\) −3.37491e6 −1.82810
\(322\) 545811. 0.293361
\(323\) −898107. −0.478985
\(324\) 683377. 0.361658
\(325\) 95617.3 0.0502144
\(326\) −2.46697e6 −1.28564
\(327\) −276467. −0.142980
\(328\) 1.07263e6 0.550508
\(329\) −5.50411e6 −2.80348
\(330\) −1.01581e6 −0.513486
\(331\) 733658. 0.368064 0.184032 0.982920i \(-0.441085\pi\)
0.184032 + 0.982920i \(0.441085\pi\)
\(332\) 873590. 0.434973
\(333\) −5.65253e6 −2.79339
\(334\) 1.04745e6 0.513769
\(335\) 644885. 0.313957
\(336\) 1.75438e6 0.847765
\(337\) 1.62914e6 0.781417 0.390709 0.920514i \(-0.372230\pi\)
0.390709 + 0.920514i \(0.372230\pi\)
\(338\) 1.39155e6 0.662533
\(339\) 102815. 0.0485912
\(340\) 175056. 0.0821259
\(341\) −1.63793e6 −0.762796
\(342\) 3.79939e6 1.75650
\(343\) 8.49190e6 3.89735
\(344\) 314336. 0.143218
\(345\) −351361. −0.158930
\(346\) 1.81015e6 0.812875
\(347\) 3.37477e6 1.50460 0.752300 0.658821i \(-0.228945\pi\)
0.752300 + 0.658821i \(0.228945\pi\)
\(348\) 1.00336e6 0.444129
\(349\) 537073. 0.236031 0.118016 0.993012i \(-0.462347\pi\)
0.118016 + 0.993012i \(0.462347\pi\)
\(350\) −644862. −0.281382
\(351\) 893609. 0.387151
\(352\) −391522. −0.168422
\(353\) 1.16518e6 0.497685 0.248842 0.968544i \(-0.419950\pi\)
0.248842 + 0.968544i \(0.419950\pi\)
\(354\) 3.15303e6 1.33727
\(355\) 678222. 0.285628
\(356\) 385928. 0.161392
\(357\) 2.99917e6 1.24546
\(358\) −1.56725e6 −0.646294
\(359\) 2.18962e6 0.896668 0.448334 0.893866i \(-0.352017\pi\)
0.448334 + 0.893866i \(0.352017\pi\)
\(360\) −740566. −0.301167
\(361\) 1.73525e6 0.700800
\(362\) 2.83926e6 1.13876
\(363\) −394871. −0.157286
\(364\) 631398. 0.249775
\(365\) −1.23921e6 −0.486869
\(366\) −3.14577e6 −1.22751
\(367\) 4.62473e6 1.79234 0.896172 0.443707i \(-0.146337\pi\)
0.896172 + 0.443707i \(0.146337\pi\)
\(368\) −135424. −0.0521286
\(369\) −7.75732e6 −2.96583
\(370\) 1.22123e6 0.463762
\(371\) −9.54366e6 −3.59981
\(372\) −1.82102e6 −0.682273
\(373\) 4.31479e6 1.60579 0.802893 0.596123i \(-0.203293\pi\)
0.802893 + 0.596123i \(0.203293\pi\)
\(374\) −669320. −0.247431
\(375\) 415124. 0.152440
\(376\) 1.36565e6 0.498162
\(377\) 361108. 0.130853
\(378\) −6.02667e6 −2.16944
\(379\) −2.49537e6 −0.892352 −0.446176 0.894945i \(-0.647214\pi\)
−0.446176 + 0.894945i \(0.647214\pi\)
\(380\) −820863. −0.291616
\(381\) 2.60416e6 0.919084
\(382\) −632444. −0.221750
\(383\) −1.49289e6 −0.520034 −0.260017 0.965604i \(-0.583728\pi\)
−0.260017 + 0.965604i \(0.583728\pi\)
\(384\) −435289. −0.150643
\(385\) 2.46560e6 0.847756
\(386\) −1.30697e6 −0.446476
\(387\) −2.27330e6 −0.771578
\(388\) 1.65380e6 0.557705
\(389\) 5.36234e6 1.79672 0.898360 0.439260i \(-0.144759\pi\)
0.898360 + 0.439260i \(0.144759\pi\)
\(390\) −406456. −0.135317
\(391\) −231512. −0.0765828
\(392\) −3.18262e6 −1.04609
\(393\) −3.14524e6 −1.02724
\(394\) −379847. −0.123273
\(395\) 1.84029e6 0.593463
\(396\) 2.83152e6 0.907365
\(397\) −1.83492e6 −0.584307 −0.292153 0.956371i \(-0.594372\pi\)
−0.292153 + 0.956371i \(0.594372\pi\)
\(398\) 638923. 0.202181
\(399\) −1.40635e7 −4.42244
\(400\) 160000. 0.0500000
\(401\) 877209. 0.272422 0.136211 0.990680i \(-0.456508\pi\)
0.136211 + 0.990680i \(0.456508\pi\)
\(402\) −2.74132e6 −0.846047
\(403\) −655383. −0.201017
\(404\) 721531. 0.219939
\(405\) 1.06778e6 0.323477
\(406\) −2.43538e6 −0.733249
\(407\) −4.66934e6 −1.39723
\(408\) −744140. −0.221312
\(409\) 2.45886e6 0.726819 0.363409 0.931630i \(-0.381613\pi\)
0.363409 + 0.931630i \(0.381613\pi\)
\(410\) 1.67598e6 0.492389
\(411\) −332503. −0.0970937
\(412\) 1.43809e6 0.417392
\(413\) −7.65311e6 −2.20782
\(414\) 979398. 0.280840
\(415\) 1.36498e6 0.389052
\(416\) −156659. −0.0443837
\(417\) 9.32282e6 2.62547
\(418\) 3.13853e6 0.878590
\(419\) −5.08361e6 −1.41461 −0.707305 0.706908i \(-0.750089\pi\)
−0.707305 + 0.706908i \(0.750089\pi\)
\(420\) 2.74122e6 0.758264
\(421\) 1.91427e6 0.526378 0.263189 0.964744i \(-0.415226\pi\)
0.263189 + 0.964744i \(0.415226\pi\)
\(422\) −4.13306e6 −1.12977
\(423\) −9.87653e6 −2.68382
\(424\) 2.36793e6 0.639667
\(425\) 273525. 0.0734556
\(426\) −2.88303e6 −0.769707
\(427\) 7.63547e6 2.02659
\(428\) −2.03247e6 −0.536309
\(429\) 1.55407e6 0.407687
\(430\) 491150. 0.128098
\(431\) −1.01147e6 −0.262278 −0.131139 0.991364i \(-0.541863\pi\)
−0.131139 + 0.991364i \(0.541863\pi\)
\(432\) 1.49531e6 0.385498
\(433\) 1.13027e6 0.289709 0.144855 0.989453i \(-0.453729\pi\)
0.144855 + 0.989453i \(0.453729\pi\)
\(434\) 4.42002e6 1.12642
\(435\) 1.56775e6 0.397241
\(436\) −166497. −0.0419459
\(437\) 1.08559e6 0.271933
\(438\) 5.26771e6 1.31201
\(439\) −3.62722e6 −0.898282 −0.449141 0.893461i \(-0.648270\pi\)
−0.449141 + 0.893461i \(0.648270\pi\)
\(440\) −611753. −0.150641
\(441\) 2.30170e7 5.63575
\(442\) −267815. −0.0652046
\(443\) 2.60561e6 0.630812 0.315406 0.948957i \(-0.397859\pi\)
0.315406 + 0.948957i \(0.397859\pi\)
\(444\) −5.19130e6 −1.24974
\(445\) 603013. 0.144353
\(446\) −2.26598e6 −0.539409
\(447\) 169491. 0.0401215
\(448\) 1.05654e6 0.248709
\(449\) −636675. −0.149040 −0.0745198 0.997220i \(-0.523742\pi\)
−0.0745198 + 0.997220i \(0.523742\pi\)
\(450\) −1.15713e6 −0.269372
\(451\) −6.40803e6 −1.48348
\(452\) 61918.3 0.0142552
\(453\) −1.37327e7 −3.14421
\(454\) −4.02210e6 −0.915826
\(455\) 986559. 0.223406
\(456\) 3.48938e6 0.785843
\(457\) −2.44658e6 −0.547986 −0.273993 0.961732i \(-0.588345\pi\)
−0.273993 + 0.961732i \(0.588345\pi\)
\(458\) −4.00224e6 −0.891538
\(459\) 2.55628e6 0.566339
\(460\) −211600. −0.0466252
\(461\) 8.31672e6 1.82263 0.911317 0.411705i \(-0.135066\pi\)
0.911317 + 0.411705i \(0.135066\pi\)
\(462\) −1.04809e7 −2.28452
\(463\) 3.27620e6 0.710260 0.355130 0.934817i \(-0.384437\pi\)
0.355130 + 0.934817i \(0.384437\pi\)
\(464\) 604255. 0.130294
\(465\) −2.84535e6 −0.610244
\(466\) 4.11381e6 0.877564
\(467\) −8.51659e6 −1.80706 −0.903532 0.428521i \(-0.859035\pi\)
−0.903532 + 0.428521i \(0.859035\pi\)
\(468\) 1.13297e6 0.239114
\(469\) 6.65379e6 1.39681
\(470\) 2.13383e6 0.445570
\(471\) 4.97519e6 1.03337
\(472\) 1.89885e6 0.392316
\(473\) −1.87789e6 −0.385938
\(474\) −7.82283e6 −1.59926
\(475\) −1.28260e6 −0.260829
\(476\) 1.80619e6 0.365381
\(477\) −1.71251e7 −3.44617
\(478\) −2.80439e6 −0.561396
\(479\) 1.70961e6 0.340454 0.170227 0.985405i \(-0.445550\pi\)
0.170227 + 0.985405i \(0.445550\pi\)
\(480\) −680138. −0.134739
\(481\) −1.86834e6 −0.368208
\(482\) 2.01685e6 0.395417
\(483\) −3.62526e6 −0.707085
\(484\) −237803. −0.0461429
\(485\) 2.58407e6 0.498827
\(486\) 1.13853e6 0.218652
\(487\) 7.87548e6 1.50472 0.752358 0.658754i \(-0.228916\pi\)
0.752358 + 0.658754i \(0.228916\pi\)
\(488\) −1.89448e6 −0.360114
\(489\) 1.63856e7 3.09877
\(490\) −4.97284e6 −0.935652
\(491\) 99613.8 0.0186473 0.00932365 0.999957i \(-0.497032\pi\)
0.00932365 + 0.999957i \(0.497032\pi\)
\(492\) −7.12435e6 −1.32688
\(493\) 1.03299e6 0.191417
\(494\) 1.25582e6 0.231531
\(495\) 4.42425e6 0.811572
\(496\) −1.09668e6 −0.200159
\(497\) 6.99775e6 1.27077
\(498\) −5.80236e6 −1.04841
\(499\) −4.03670e6 −0.725730 −0.362865 0.931842i \(-0.618201\pi\)
−0.362865 + 0.931842i \(0.618201\pi\)
\(500\) 250000. 0.0447214
\(501\) −6.95715e6 −1.23833
\(502\) 4.94797e6 0.876331
\(503\) −5.09894e6 −0.898586 −0.449293 0.893385i \(-0.648324\pi\)
−0.449293 + 0.893385i \(0.648324\pi\)
\(504\) −7.64100e6 −1.33990
\(505\) 1.12739e6 0.196719
\(506\) 809044. 0.140474
\(507\) −9.24265e6 −1.59690
\(508\) 1.56830e6 0.269632
\(509\) 3.39724e6 0.581208 0.290604 0.956843i \(-0.406144\pi\)
0.290604 + 0.956843i \(0.406144\pi\)
\(510\) −1.16272e6 −0.197947
\(511\) −1.27859e7 −2.16610
\(512\) −262144. −0.0441942
\(513\) −1.19868e7 −2.01098
\(514\) −767860. −0.128196
\(515\) 2.24702e6 0.373327
\(516\) −2.08781e6 −0.345197
\(517\) −8.15862e6 −1.34243
\(518\) 1.26004e7 2.06329
\(519\) −1.20230e7 −1.95926
\(520\) −244780. −0.0396980
\(521\) −6.06716e6 −0.979245 −0.489622 0.871935i \(-0.662865\pi\)
−0.489622 + 0.871935i \(0.662865\pi\)
\(522\) −4.37002e6 −0.701952
\(523\) −2.33142e6 −0.372706 −0.186353 0.982483i \(-0.559667\pi\)
−0.186353 + 0.982483i \(0.559667\pi\)
\(524\) −1.89416e6 −0.301361
\(525\) 4.28316e6 0.678212
\(526\) 3.42962e6 0.540483
\(527\) −1.87480e6 −0.294055
\(528\) 2.60048e6 0.405946
\(529\) 279841. 0.0434783
\(530\) 3.69989e6 0.572135
\(531\) −1.37327e7 −2.11358
\(532\) −8.46949e6 −1.29741
\(533\) −2.56404e6 −0.390937
\(534\) −2.56332e6 −0.389001
\(535\) −3.17574e6 −0.479689
\(536\) −1.65091e6 −0.248205
\(537\) 1.04096e7 1.55776
\(538\) −1.69292e6 −0.252162
\(539\) 1.90135e7 2.81896
\(540\) 2.33642e6 0.344799
\(541\) 206989. 0.0304056 0.0152028 0.999884i \(-0.495161\pi\)
0.0152028 + 0.999884i \(0.495161\pi\)
\(542\) 8.87032e6 1.29700
\(543\) −1.88583e7 −2.74475
\(544\) −448144. −0.0649262
\(545\) −260151. −0.0375176
\(546\) −4.19373e6 −0.602031
\(547\) 9.25725e6 1.32286 0.661430 0.750007i \(-0.269950\pi\)
0.661430 + 0.750007i \(0.269950\pi\)
\(548\) −200243. −0.0284844
\(549\) 1.37010e7 1.94009
\(550\) −955864. −0.134738
\(551\) −4.84385e6 −0.679691
\(552\) 899483. 0.125645
\(553\) 1.89877e7 2.64034
\(554\) −3.08374e6 −0.426877
\(555\) −8.11141e6 −1.11780
\(556\) 5.61449e6 0.770235
\(557\) 9.55108e6 1.30441 0.652206 0.758042i \(-0.273844\pi\)
0.652206 + 0.758042i \(0.273844\pi\)
\(558\) 7.93126e6 1.07834
\(559\) −751399. −0.101705
\(560\) 1.65085e6 0.222452
\(561\) 4.44561e6 0.596381
\(562\) 1.01930e7 1.36132
\(563\) −1.21668e7 −1.61772 −0.808862 0.587999i \(-0.799916\pi\)
−0.808862 + 0.587999i \(0.799916\pi\)
\(564\) −9.07064e6 −1.20072
\(565\) 96747.4 0.0127502
\(566\) −1.51341e6 −0.198571
\(567\) 1.10171e7 1.43916
\(568\) −1.73625e6 −0.225809
\(569\) 3.88469e6 0.503009 0.251505 0.967856i \(-0.419075\pi\)
0.251505 + 0.967856i \(0.419075\pi\)
\(570\) 5.45215e6 0.702879
\(571\) 148768. 0.0190950 0.00954748 0.999954i \(-0.496961\pi\)
0.00954748 + 0.999954i \(0.496961\pi\)
\(572\) 935907. 0.119603
\(573\) 4.20068e6 0.534482
\(574\) 1.72924e7 2.19066
\(575\) −330625. −0.0417029
\(576\) 1.89585e6 0.238093
\(577\) 7.60448e6 0.950890 0.475445 0.879746i \(-0.342287\pi\)
0.475445 + 0.879746i \(0.342287\pi\)
\(578\) 4.91331e6 0.611723
\(579\) 8.68089e6 1.07614
\(580\) 944148. 0.116539
\(581\) 1.40836e7 1.73091
\(582\) −1.09845e7 −1.34423
\(583\) −1.41464e7 −1.72375
\(584\) 3.17237e6 0.384904
\(585\) 1.77027e6 0.213870
\(586\) 5.25031e6 0.631599
\(587\) 1.43808e7 1.72262 0.861309 0.508082i \(-0.169645\pi\)
0.861309 + 0.508082i \(0.169645\pi\)
\(588\) 2.11389e7 2.52138
\(589\) 8.79121e6 1.04414
\(590\) 2.96696e6 0.350898
\(591\) 2.52294e6 0.297124
\(592\) −3.12636e6 −0.366636
\(593\) −1.16050e7 −1.35522 −0.677610 0.735421i \(-0.736984\pi\)
−0.677610 + 0.735421i \(0.736984\pi\)
\(594\) −8.93320e6 −1.03882
\(595\) 2.82217e6 0.326807
\(596\) 102072. 0.0117704
\(597\) −4.24371e6 −0.487316
\(598\) 323722. 0.0370185
\(599\) 1.04099e7 1.18544 0.592720 0.805409i \(-0.298054\pi\)
0.592720 + 0.805409i \(0.298054\pi\)
\(600\) −1.06272e6 −0.120514
\(601\) 7.62102e6 0.860651 0.430326 0.902674i \(-0.358399\pi\)
0.430326 + 0.902674i \(0.358399\pi\)
\(602\) 5.06758e6 0.569914
\(603\) 1.19395e7 1.33719
\(604\) −8.27026e6 −0.922416
\(605\) −371568. −0.0412715
\(606\) −4.79239e6 −0.530116
\(607\) 36429.8 0.00401314 0.00200657 0.999998i \(-0.499361\pi\)
0.00200657 + 0.999998i \(0.499361\pi\)
\(608\) 2.10141e6 0.230543
\(609\) 1.61757e7 1.76734
\(610\) −2.96012e6 −0.322096
\(611\) −3.26450e6 −0.353764
\(612\) 3.24102e6 0.349786
\(613\) −5.16547e6 −0.555212 −0.277606 0.960695i \(-0.589541\pi\)
−0.277606 + 0.960695i \(0.589541\pi\)
\(614\) 1.09667e7 1.17396
\(615\) −1.11318e7 −1.18680
\(616\) −6.31194e6 −0.670210
\(617\) −1.64300e7 −1.73750 −0.868752 0.495248i \(-0.835077\pi\)
−0.868752 + 0.495248i \(0.835077\pi\)
\(618\) −9.55178e6 −1.00604
\(619\) −1.33143e7 −1.39666 −0.698329 0.715777i \(-0.746073\pi\)
−0.698329 + 0.715777i \(0.746073\pi\)
\(620\) −1.71356e6 −0.179027
\(621\) −3.08992e6 −0.321527
\(622\) −1.82864e6 −0.189519
\(623\) 6.22175e6 0.642233
\(624\) 1.04053e6 0.106978
\(625\) 390625. 0.0400000
\(626\) −9.20988e6 −0.939330
\(627\) −2.08461e7 −2.11766
\(628\) 2.99621e6 0.303161
\(629\) −5.34462e6 −0.538629
\(630\) −1.19391e7 −1.19845
\(631\) 911454. 0.0911300 0.0455650 0.998961i \(-0.485491\pi\)
0.0455650 + 0.998961i \(0.485491\pi\)
\(632\) −4.71114e6 −0.469174
\(633\) 2.74517e7 2.72307
\(634\) −2.42037e6 −0.239144
\(635\) 2.45047e6 0.241166
\(636\) −1.57277e7 −1.54178
\(637\) 7.60784e6 0.742870
\(638\) −3.60991e6 −0.351111
\(639\) 1.25567e7 1.21653
\(640\) −409600. −0.0395285
\(641\) 1.88172e6 0.180888 0.0904438 0.995902i \(-0.471171\pi\)
0.0904438 + 0.995902i \(0.471171\pi\)
\(642\) 1.34996e7 1.29266
\(643\) −1.48647e7 −1.41784 −0.708922 0.705287i \(-0.750818\pi\)
−0.708922 + 0.705287i \(0.750818\pi\)
\(644\) −2.18324e6 −0.207438
\(645\) −3.26220e6 −0.308753
\(646\) 3.59243e6 0.338693
\(647\) −34099.0 −0.00320244 −0.00160122 0.999999i \(-0.500510\pi\)
−0.00160122 + 0.999999i \(0.500510\pi\)
\(648\) −2.73351e6 −0.255731
\(649\) −1.13440e7 −1.05720
\(650\) −382469. −0.0355069
\(651\) −2.93577e7 −2.71500
\(652\) 9.86788e6 0.909086
\(653\) 5.21815e6 0.478888 0.239444 0.970910i \(-0.423035\pi\)
0.239444 + 0.970910i \(0.423035\pi\)
\(654\) 1.10587e6 0.101102
\(655\) −2.95962e6 −0.269546
\(656\) −4.29050e6 −0.389268
\(657\) −2.29429e7 −2.07365
\(658\) 2.20164e7 1.98236
\(659\) −3.56361e6 −0.319651 −0.159826 0.987145i \(-0.551093\pi\)
−0.159826 + 0.987145i \(0.551093\pi\)
\(660\) 4.06325e6 0.363090
\(661\) 7.48892e6 0.666677 0.333339 0.942807i \(-0.391825\pi\)
0.333339 + 0.942807i \(0.391825\pi\)
\(662\) −2.93463e6 −0.260261
\(663\) 1.77882e6 0.157162
\(664\) −3.49436e6 −0.307572
\(665\) −1.32336e7 −1.16044
\(666\) 2.26101e7 1.97523
\(667\) −1.24864e6 −0.108673
\(668\) −4.18981e6 −0.363290
\(669\) 1.50506e7 1.30013
\(670\) −2.57954e6 −0.222001
\(671\) 1.13179e7 0.970419
\(672\) −7.01752e6 −0.599460
\(673\) −4.25849e6 −0.362424 −0.181212 0.983444i \(-0.558002\pi\)
−0.181212 + 0.983444i \(0.558002\pi\)
\(674\) −6.51655e6 −0.552545
\(675\) 3.65066e6 0.308398
\(676\) −5.56620e6 −0.468481
\(677\) −9.44304e6 −0.791845 −0.395923 0.918284i \(-0.629575\pi\)
−0.395923 + 0.918284i \(0.629575\pi\)
\(678\) −411260. −0.0343591
\(679\) 2.66619e7 2.21930
\(680\) −700225. −0.0580718
\(681\) 2.67147e7 2.20741
\(682\) 6.55171e6 0.539378
\(683\) 881961. 0.0723431 0.0361716 0.999346i \(-0.488484\pi\)
0.0361716 + 0.999346i \(0.488484\pi\)
\(684\) −1.51976e7 −1.24204
\(685\) −312880. −0.0254772
\(686\) −3.39676e7 −2.75584
\(687\) 2.65828e7 2.14886
\(688\) −1.25734e6 −0.101270
\(689\) −5.66037e6 −0.454252
\(690\) 1.40544e6 0.112380
\(691\) 5.02713e6 0.400521 0.200260 0.979743i \(-0.435821\pi\)
0.200260 + 0.979743i \(0.435821\pi\)
\(692\) −7.24059e6 −0.574790
\(693\) 4.56485e7 3.61072
\(694\) −1.34991e7 −1.06391
\(695\) 8.77264e6 0.688919
\(696\) −4.01345e6 −0.314047
\(697\) −7.33476e6 −0.571878
\(698\) −2.14829e6 −0.166899
\(699\) −2.73238e7 −2.11518
\(700\) 2.57945e6 0.198967
\(701\) −2.19117e7 −1.68415 −0.842076 0.539359i \(-0.818667\pi\)
−0.842076 + 0.539359i \(0.818667\pi\)
\(702\) −3.57444e6 −0.273757
\(703\) 2.50617e7 1.91259
\(704\) 1.56609e6 0.119093
\(705\) −1.41729e7 −1.07395
\(706\) −4.66070e6 −0.351916
\(707\) 1.16322e7 0.875211
\(708\) −1.26121e7 −0.945596
\(709\) 1.18099e7 0.882330 0.441165 0.897426i \(-0.354565\pi\)
0.441165 + 0.897426i \(0.354565\pi\)
\(710\) −2.71289e6 −0.201970
\(711\) 3.40714e7 2.52765
\(712\) −1.54371e6 −0.114121
\(713\) 2.26618e6 0.166944
\(714\) −1.19967e7 −0.880675
\(715\) 1.46236e6 0.106976
\(716\) 6.26899e6 0.456999
\(717\) 1.86267e7 1.35313
\(718\) −8.75846e6 −0.634040
\(719\) 1.49758e7 1.08036 0.540180 0.841550i \(-0.318356\pi\)
0.540180 + 0.841550i \(0.318356\pi\)
\(720\) 2.96226e6 0.212957
\(721\) 2.31843e7 1.66095
\(722\) −6.94100e6 −0.495540
\(723\) −1.33958e7 −0.953069
\(724\) −1.13570e7 −0.805228
\(725\) 1.47523e6 0.104235
\(726\) 1.57949e6 0.111218
\(727\) 1.01581e7 0.712812 0.356406 0.934331i \(-0.384002\pi\)
0.356406 + 0.934331i \(0.384002\pi\)
\(728\) −2.52559e6 −0.176618
\(729\) −1.79409e7 −1.25033
\(730\) 4.95683e6 0.344268
\(731\) −2.14947e6 −0.148778
\(732\) 1.25831e7 0.867978
\(733\) −1.96629e7 −1.35172 −0.675861 0.737029i \(-0.736228\pi\)
−0.675861 + 0.737029i \(0.736228\pi\)
\(734\) −1.84989e7 −1.26738
\(735\) 3.30295e7 2.25519
\(736\) 541696. 0.0368605
\(737\) 9.86277e6 0.668852
\(738\) 3.10293e7 2.09716
\(739\) −8.71300e6 −0.586890 −0.293445 0.955976i \(-0.594802\pi\)
−0.293445 + 0.955976i \(0.594802\pi\)
\(740\) −4.88494e6 −0.327929
\(741\) −8.34112e6 −0.558058
\(742\) 3.81746e7 2.54545
\(743\) 1.28335e7 0.852854 0.426427 0.904522i \(-0.359772\pi\)
0.426427 + 0.904522i \(0.359772\pi\)
\(744\) 7.28409e6 0.482440
\(745\) 159488. 0.0105278
\(746\) −1.72592e7 −1.13546
\(747\) 2.52715e7 1.65703
\(748\) 2.67728e6 0.174960
\(749\) −3.27666e7 −2.13416
\(750\) −1.66049e6 −0.107791
\(751\) 5.80666e6 0.375687 0.187844 0.982199i \(-0.439850\pi\)
0.187844 + 0.982199i \(0.439850\pi\)
\(752\) −5.46262e6 −0.352254
\(753\) −3.28643e7 −2.11221
\(754\) −1.44443e6 −0.0925270
\(755\) −1.29223e7 −0.825034
\(756\) 2.41067e7 1.53403
\(757\) −2.36785e7 −1.50181 −0.750905 0.660410i \(-0.770383\pi\)
−0.750905 + 0.660410i \(0.770383\pi\)
\(758\) 9.98146e6 0.630988
\(759\) −5.37365e6 −0.338583
\(760\) 3.28345e6 0.206204
\(761\) −1.08104e7 −0.676672 −0.338336 0.941025i \(-0.609864\pi\)
−0.338336 + 0.941025i \(0.609864\pi\)
\(762\) −1.04166e7 −0.649890
\(763\) −2.68419e6 −0.166917
\(764\) 2.52978e6 0.156801
\(765\) 5.06409e6 0.312858
\(766\) 5.97157e6 0.367720
\(767\) −4.53908e6 −0.278599
\(768\) 1.74115e6 0.106521
\(769\) 2.04035e7 1.24420 0.622098 0.782939i \(-0.286280\pi\)
0.622098 + 0.782939i \(0.286280\pi\)
\(770\) −9.86240e6 −0.599454
\(771\) 5.10011e6 0.308989
\(772\) 5.22789e6 0.315707
\(773\) 1.26279e7 0.760119 0.380059 0.924962i \(-0.375904\pi\)
0.380059 + 0.924962i \(0.375904\pi\)
\(774\) 9.09322e6 0.545588
\(775\) −2.67743e6 −0.160127
\(776\) −6.61522e6 −0.394357
\(777\) −8.36918e7 −4.97314
\(778\) −2.14494e7 −1.27047
\(779\) 3.43937e7 2.03065
\(780\) 1.62583e6 0.0956836
\(781\) 1.03726e7 0.608500
\(782\) 926047. 0.0541522
\(783\) 1.37870e7 0.803650
\(784\) 1.27305e7 0.739698
\(785\) 4.68158e6 0.271155
\(786\) 1.25809e7 0.726368
\(787\) −1.15243e7 −0.663252 −0.331626 0.943411i \(-0.607597\pi\)
−0.331626 + 0.943411i \(0.607597\pi\)
\(788\) 1.51939e6 0.0871673
\(789\) −2.27795e7 −1.30272
\(790\) −7.36116e6 −0.419642
\(791\) 998219. 0.0567263
\(792\) −1.13261e7 −0.641604
\(793\) 4.52862e6 0.255731
\(794\) 7.33968e6 0.413167
\(795\) −2.45746e7 −1.37901
\(796\) −2.55569e6 −0.142964
\(797\) 2.38509e7 1.33002 0.665010 0.746834i \(-0.268427\pi\)
0.665010 + 0.746834i \(0.268427\pi\)
\(798\) 5.62541e7 3.12714
\(799\) −9.33852e6 −0.517501
\(800\) −640000. −0.0353553
\(801\) 1.11643e7 0.614821
\(802\) −3.50884e6 −0.192631
\(803\) −1.89522e7 −1.03722
\(804\) 1.09653e7 0.598246
\(805\) −3.41132e6 −0.185538
\(806\) 2.62153e6 0.142140
\(807\) 1.12443e7 0.607783
\(808\) −2.88612e6 −0.155520
\(809\) −1.75973e7 −0.945311 −0.472656 0.881247i \(-0.656705\pi\)
−0.472656 + 0.881247i \(0.656705\pi\)
\(810\) −4.27111e6 −0.228732
\(811\) −2.13966e7 −1.14233 −0.571167 0.820834i \(-0.693509\pi\)
−0.571167 + 0.820834i \(0.693509\pi\)
\(812\) 9.74152e6 0.518485
\(813\) −5.89164e7 −3.12615
\(814\) 1.86774e7 0.987994
\(815\) 1.54186e7 0.813111
\(816\) 2.97656e6 0.156491
\(817\) 1.00792e7 0.528286
\(818\) −9.83546e6 −0.513939
\(819\) 1.82653e7 0.951518
\(820\) −6.70391e6 −0.348172
\(821\) 5.53624e6 0.286653 0.143327 0.989675i \(-0.454220\pi\)
0.143327 + 0.989675i \(0.454220\pi\)
\(822\) 1.33001e6 0.0686556
\(823\) 2.12780e7 1.09504 0.547522 0.836792i \(-0.315571\pi\)
0.547522 + 0.836792i \(0.315571\pi\)
\(824\) −5.75237e6 −0.295141
\(825\) 6.34883e6 0.324757
\(826\) 3.06124e7 1.56116
\(827\) −1.64976e7 −0.838795 −0.419397 0.907803i \(-0.637759\pi\)
−0.419397 + 0.907803i \(0.637759\pi\)
\(828\) −3.91759e6 −0.198584
\(829\) 6.72349e6 0.339788 0.169894 0.985462i \(-0.445657\pi\)
0.169894 + 0.985462i \(0.445657\pi\)
\(830\) −5.45994e6 −0.275101
\(831\) 2.04821e7 1.02890
\(832\) 626638. 0.0313840
\(833\) 2.17632e7 1.08670
\(834\) −3.72913e7 −1.85649
\(835\) −6.54658e6 −0.324936
\(836\) −1.25541e7 −0.621257
\(837\) −2.50224e7 −1.23457
\(838\) 2.03344e7 1.00028
\(839\) 6.09269e6 0.298816 0.149408 0.988776i \(-0.452263\pi\)
0.149408 + 0.988776i \(0.452263\pi\)
\(840\) −1.09649e7 −0.536174
\(841\) −1.49398e7 −0.728375
\(842\) −7.65707e6 −0.372205
\(843\) −6.77014e7 −3.28117
\(844\) 1.65322e7 0.798868
\(845\) −8.69719e6 −0.419023
\(846\) 3.95061e7 1.89775
\(847\) −3.83376e6 −0.183618
\(848\) −9.47171e6 −0.452313
\(849\) 1.00520e7 0.478614
\(850\) −1.09410e6 −0.0519410
\(851\) 6.46033e6 0.305795
\(852\) 1.15321e7 0.544265
\(853\) 1.92555e7 0.906111 0.453055 0.891482i \(-0.350334\pi\)
0.453055 + 0.891482i \(0.350334\pi\)
\(854\) −3.05419e7 −1.43302
\(855\) −2.37462e7 −1.11091
\(856\) 8.12989e6 0.379228
\(857\) −1.64010e7 −0.762815 −0.381408 0.924407i \(-0.624561\pi\)
−0.381408 + 0.924407i \(0.624561\pi\)
\(858\) −6.21628e6 −0.288278
\(859\) −2.54001e6 −0.117450 −0.0587250 0.998274i \(-0.518704\pi\)
−0.0587250 + 0.998274i \(0.518704\pi\)
\(860\) −1.96460e6 −0.0905790
\(861\) −1.14856e8 −5.28012
\(862\) 4.04590e6 0.185458
\(863\) 1.59304e7 0.728114 0.364057 0.931377i \(-0.381391\pi\)
0.364057 + 0.931377i \(0.381391\pi\)
\(864\) −5.98124e6 −0.272588
\(865\) −1.13134e7 −0.514107
\(866\) −4.52108e6 −0.204855
\(867\) −3.26341e7 −1.47443
\(868\) −1.76801e7 −0.796499
\(869\) 2.81451e7 1.26431
\(870\) −6.27101e6 −0.280892
\(871\) 3.94638e6 0.176260
\(872\) 665988. 0.0296603
\(873\) 4.78418e7 2.12458
\(874\) −4.34236e6 −0.192286
\(875\) 4.03038e6 0.177962
\(876\) −2.10708e7 −0.927730
\(877\) −1.21324e7 −0.532656 −0.266328 0.963882i \(-0.585810\pi\)
−0.266328 + 0.963882i \(0.585810\pi\)
\(878\) 1.45089e7 0.635181
\(879\) −3.48725e7 −1.52234
\(880\) 2.44701e6 0.106520
\(881\) 1.34649e7 0.584473 0.292236 0.956346i \(-0.405601\pi\)
0.292236 + 0.956346i \(0.405601\pi\)
\(882\) −9.20679e7 −3.98508
\(883\) 780486. 0.0336871 0.0168435 0.999858i \(-0.494638\pi\)
0.0168435 + 0.999858i \(0.494638\pi\)
\(884\) 1.07126e6 0.0461066
\(885\) −1.97065e7 −0.845767
\(886\) −1.04224e7 −0.446052
\(887\) −1.29634e7 −0.553235 −0.276617 0.960980i \(-0.589213\pi\)
−0.276617 + 0.960980i \(0.589213\pi\)
\(888\) 2.07652e7 0.883698
\(889\) 2.52835e7 1.07296
\(890\) −2.41205e6 −0.102073
\(891\) 1.63304e7 0.689132
\(892\) 9.06390e6 0.381420
\(893\) 4.37896e7 1.83756
\(894\) −677963. −0.0283702
\(895\) 9.79530e6 0.408752
\(896\) −4.22616e6 −0.175864
\(897\) −2.15015e6 −0.0892254
\(898\) 2.54670e6 0.105387
\(899\) −1.01116e7 −0.417272
\(900\) 4.62854e6 0.190475
\(901\) −1.61922e7 −0.664498
\(902\) 2.56321e7 1.04898
\(903\) −3.36587e7 −1.37366
\(904\) −247673. −0.0100799
\(905\) −1.77454e7 −0.720218
\(906\) 5.49309e7 2.22329
\(907\) −3.31097e7 −1.33640 −0.668201 0.743981i \(-0.732935\pi\)
−0.668201 + 0.743981i \(0.732935\pi\)
\(908\) 1.60884e7 0.647587
\(909\) 2.08727e7 0.837855
\(910\) −3.94624e6 −0.157972
\(911\) −4.57024e7 −1.82450 −0.912248 0.409637i \(-0.865655\pi\)
−0.912248 + 0.409637i \(0.865655\pi\)
\(912\) −1.39575e7 −0.555675
\(913\) 2.08758e7 0.828833
\(914\) 9.78633e6 0.387485
\(915\) 1.96610e7 0.776344
\(916\) 1.60090e7 0.630412
\(917\) −3.05367e7 −1.19922
\(918\) −1.02251e7 −0.400462
\(919\) −5.81218e6 −0.227013 −0.113506 0.993537i \(-0.536208\pi\)
−0.113506 + 0.993537i \(0.536208\pi\)
\(920\) 846400. 0.0329690
\(921\) −7.28405e7 −2.82959
\(922\) −3.32669e7 −1.28880
\(923\) 4.15039e6 0.160356
\(924\) 4.19237e7 1.61540
\(925\) −7.63272e6 −0.293309
\(926\) −1.31048e7 −0.502230
\(927\) 4.16017e7 1.59005
\(928\) −2.41702e6 −0.0921319
\(929\) 2.41127e6 0.0916657 0.0458328 0.998949i \(-0.485406\pi\)
0.0458328 + 0.998949i \(0.485406\pi\)
\(930\) 1.13814e7 0.431507
\(931\) −1.02051e8 −3.85870
\(932\) −1.64552e7 −0.620532
\(933\) 1.21458e7 0.456795
\(934\) 3.40663e7 1.27779
\(935\) 4.18325e6 0.156489
\(936\) −4.53190e6 −0.169079
\(937\) −4.01649e7 −1.49451 −0.747253 0.664540i \(-0.768627\pi\)
−0.747253 + 0.664540i \(0.768627\pi\)
\(938\) −2.66152e7 −0.987693
\(939\) 6.11718e7 2.26406
\(940\) −8.53534e6 −0.315066
\(941\) −1.31127e7 −0.482744 −0.241372 0.970433i \(-0.577597\pi\)
−0.241372 + 0.970433i \(0.577597\pi\)
\(942\) −1.99007e7 −0.730705
\(943\) 8.86592e6 0.324672
\(944\) −7.59541e6 −0.277410
\(945\) 3.76667e7 1.37208
\(946\) 7.51156e6 0.272899
\(947\) 3.67023e7 1.32990 0.664949 0.746889i \(-0.268453\pi\)
0.664949 + 0.746889i \(0.268453\pi\)
\(948\) 3.12913e7 1.13084
\(949\) −7.58335e6 −0.273335
\(950\) 5.13039e6 0.184434
\(951\) 1.60761e7 0.576406
\(952\) −7.22477e6 −0.258364
\(953\) −1.55702e7 −0.555346 −0.277673 0.960676i \(-0.589563\pi\)
−0.277673 + 0.960676i \(0.589563\pi\)
\(954\) 6.85002e7 2.43681
\(955\) 3.95278e6 0.140247
\(956\) 1.12176e7 0.396967
\(957\) 2.39769e7 0.846280
\(958\) −6.83845e6 −0.240738
\(959\) −3.22823e6 −0.113349
\(960\) 2.72055e6 0.0952751
\(961\) −1.02774e7 −0.358985
\(962\) 7.47336e6 0.260362
\(963\) −5.87960e7 −2.04307
\(964\) −8.06739e6 −0.279602
\(965\) 8.16859e6 0.282377
\(966\) 1.45010e7 0.499985
\(967\) 3.65611e7 1.25734 0.628670 0.777672i \(-0.283600\pi\)
0.628670 + 0.777672i \(0.283600\pi\)
\(968\) 951214. 0.0326280
\(969\) −2.38608e7 −0.816349
\(970\) −1.03363e7 −0.352724
\(971\) 3.92822e7 1.33705 0.668524 0.743690i \(-0.266926\pi\)
0.668524 + 0.743690i \(0.266926\pi\)
\(972\) −4.55411e6 −0.154610
\(973\) 9.05142e7 3.06503
\(974\) −3.15019e7 −1.06400
\(975\) 2.54035e6 0.0855820
\(976\) 7.57791e6 0.254639
\(977\) 2.11757e7 0.709743 0.354872 0.934915i \(-0.384525\pi\)
0.354872 + 0.934915i \(0.384525\pi\)
\(978\) −6.55422e7 −2.19116
\(979\) 9.22237e6 0.307529
\(980\) 1.98914e7 0.661606
\(981\) −4.81648e6 −0.159793
\(982\) −398455. −0.0131856
\(983\) −2.99811e7 −0.989610 −0.494805 0.869004i \(-0.664761\pi\)
−0.494805 + 0.869004i \(0.664761\pi\)
\(984\) 2.84974e7 0.938248
\(985\) 2.37405e6 0.0779648
\(986\) −4.13197e6 −0.135352
\(987\) −1.46233e8 −4.77806
\(988\) −5.02328e6 −0.163717
\(989\) 2.59818e6 0.0844654
\(990\) −1.76970e7 −0.573868
\(991\) −1.61393e7 −0.522036 −0.261018 0.965334i \(-0.584058\pi\)
−0.261018 + 0.965334i \(0.584058\pi\)
\(992\) 4.38670e6 0.141533
\(993\) 1.94918e7 0.627304
\(994\) −2.79910e7 −0.898571
\(995\) −3.99327e6 −0.127871
\(996\) 2.32095e7 0.741338
\(997\) 4.42811e7 1.41085 0.705425 0.708784i \(-0.250756\pi\)
0.705425 + 0.708784i \(0.250756\pi\)
\(998\) 1.61468e7 0.513168
\(999\) −7.13329e7 −2.26139
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 230.6.a.f.1.5 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.6.a.f.1.5 5 1.1 even 1 trivial