Properties

Label 207.6.a.i.1.1
Level $207$
Weight $6$
Character 207.1
Self dual yes
Analytic conductor $33.199$
Analytic rank $0$
Dimension $10$
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] = [207,6,Mod(1,207)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(207, 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("207.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 207 = 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 207.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: \(33.1994507013\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2 x^{9} - 251 x^{8} + 296 x^{7} + 21169 x^{6} - 9042 x^{5} - 685949 x^{4} - 270764 x^{3} + 6230110 x^{2} + 11573432 x + 5446216 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{4} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(11.3536\) of defining polynomial
Character \(\chi\) \(=\) 207.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-10.3536 q^{2} +75.1975 q^{4} +71.3591 q^{5} -210.967 q^{7} -447.250 q^{8} +O(q^{10})\) \(q-10.3536 q^{2} +75.1975 q^{4} +71.3591 q^{5} -210.967 q^{7} -447.250 q^{8} -738.825 q^{10} +170.188 q^{11} +605.525 q^{13} +2184.27 q^{14} +2224.34 q^{16} +1337.03 q^{17} -1794.65 q^{19} +5366.03 q^{20} -1762.07 q^{22} +529.000 q^{23} +1967.12 q^{25} -6269.38 q^{26} -15864.2 q^{28} +3006.00 q^{29} -9214.34 q^{31} -8717.97 q^{32} -13843.1 q^{34} -15054.4 q^{35} +6021.35 q^{37} +18581.1 q^{38} -31915.4 q^{40} +6606.07 q^{41} +22934.8 q^{43} +12797.7 q^{44} -5477.07 q^{46} -20179.5 q^{47} +27700.0 q^{49} -20366.9 q^{50} +45534.0 q^{52} -3604.41 q^{53} +12144.5 q^{55} +94355.0 q^{56} -31123.0 q^{58} -37190.1 q^{59} -31681.4 q^{61} +95401.8 q^{62} +19083.7 q^{64} +43209.8 q^{65} -3782.79 q^{67} +100541. q^{68} +155868. q^{70} +6321.88 q^{71} +12637.8 q^{73} -62342.8 q^{74} -134953. q^{76} -35904.1 q^{77} +79327.3 q^{79} +158727. q^{80} -68396.7 q^{82} +114368. q^{83} +95409.1 q^{85} -237459. q^{86} -76116.8 q^{88} +63683.3 q^{89} -127746. q^{91} +39779.5 q^{92} +208931. q^{94} -128065. q^{95} +151168. q^{97} -286795. q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 8 q^{2} + 192 q^{4} + 100 q^{5} + 20 q^{7} + 384 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 8 q^{2} + 192 q^{4} + 100 q^{5} + 20 q^{7} + 384 q^{8} - 250 q^{10} + 460 q^{11} + 464 q^{13} + 3676 q^{14} + 4612 q^{16} + 4756 q^{17} - 1780 q^{19} + 10314 q^{20} - 4214 q^{22} + 5290 q^{23} + 1330 q^{25} - 5152 q^{26} + 7072 q^{28} + 4048 q^{29} + 2816 q^{31} + 27436 q^{32} + 420 q^{34} + 9452 q^{35} + 2872 q^{37} + 31038 q^{38} + 2618 q^{40} + 34056 q^{41} + 7316 q^{43} + 33562 q^{44} + 4232 q^{46} + 49300 q^{47} + 45118 q^{49} + 44764 q^{50} - 25120 q^{52} + 86676 q^{53} - 2120 q^{55} + 290684 q^{56} - 87408 q^{58} + 67100 q^{59} - 40432 q^{61} + 230992 q^{62} + 136776 q^{64} + 184000 q^{65} - 50108 q^{67} + 270592 q^{68} + 117456 q^{70} + 238584 q^{71} - 13804 q^{73} + 150074 q^{74} - 197622 q^{76} + 116248 q^{77} - 9228 q^{79} + 313010 q^{80} - 68604 q^{82} + 155300 q^{83} + 80444 q^{85} - 80914 q^{86} - 237738 q^{88} + 213732 q^{89} - 264352 q^{91} + 101568 q^{92} + 140280 q^{94} - 123612 q^{95} + 42516 q^{97} - 151388 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −10.3536 −1.83028 −0.915139 0.403137i \(-0.867920\pi\)
−0.915139 + 0.403137i \(0.867920\pi\)
\(3\) 0 0
\(4\) 75.1975 2.34992
\(5\) 71.3591 1.27651 0.638255 0.769825i \(-0.279656\pi\)
0.638255 + 0.769825i \(0.279656\pi\)
\(6\) 0 0
\(7\) −210.967 −1.62731 −0.813653 0.581351i \(-0.802524\pi\)
−0.813653 + 0.581351i \(0.802524\pi\)
\(8\) −447.250 −2.47073
\(9\) 0 0
\(10\) −738.825 −2.33637
\(11\) 170.188 0.424080 0.212040 0.977261i \(-0.431989\pi\)
0.212040 + 0.977261i \(0.431989\pi\)
\(12\) 0 0
\(13\) 605.525 0.993743 0.496871 0.867824i \(-0.334482\pi\)
0.496871 + 0.867824i \(0.334482\pi\)
\(14\) 2184.27 2.97842
\(15\) 0 0
\(16\) 2224.34 2.17221
\(17\) 1337.03 1.12207 0.561033 0.827794i \(-0.310404\pi\)
0.561033 + 0.827794i \(0.310404\pi\)
\(18\) 0 0
\(19\) −1794.65 −1.14050 −0.570251 0.821471i \(-0.693154\pi\)
−0.570251 + 0.821471i \(0.693154\pi\)
\(20\) 5366.03 2.99970
\(21\) 0 0
\(22\) −1762.07 −0.776185
\(23\) 529.000 0.208514
\(24\) 0 0
\(25\) 1967.12 0.629480
\(26\) −6269.38 −1.81883
\(27\) 0 0
\(28\) −15864.2 −3.82404
\(29\) 3006.00 0.663734 0.331867 0.943326i \(-0.392321\pi\)
0.331867 + 0.943326i \(0.392321\pi\)
\(30\) 0 0
\(31\) −9214.34 −1.72211 −0.861053 0.508515i \(-0.830195\pi\)
−0.861053 + 0.508515i \(0.830195\pi\)
\(32\) −8717.97 −1.50501
\(33\) 0 0
\(34\) −13843.1 −2.05369
\(35\) −15054.4 −2.07727
\(36\) 0 0
\(37\) 6021.35 0.723085 0.361543 0.932356i \(-0.382250\pi\)
0.361543 + 0.932356i \(0.382250\pi\)
\(38\) 18581.1 2.08744
\(39\) 0 0
\(40\) −31915.4 −3.15392
\(41\) 6606.07 0.613739 0.306869 0.951752i \(-0.400719\pi\)
0.306869 + 0.951752i \(0.400719\pi\)
\(42\) 0 0
\(43\) 22934.8 1.89158 0.945790 0.324779i \(-0.105290\pi\)
0.945790 + 0.324779i \(0.105290\pi\)
\(44\) 12797.7 0.996555
\(45\) 0 0
\(46\) −5477.07 −0.381640
\(47\) −20179.5 −1.33250 −0.666249 0.745729i \(-0.732101\pi\)
−0.666249 + 0.745729i \(0.732101\pi\)
\(48\) 0 0
\(49\) 27700.0 1.64812
\(50\) −20366.9 −1.15212
\(51\) 0 0
\(52\) 45534.0 2.33522
\(53\) −3604.41 −0.176256 −0.0881281 0.996109i \(-0.528088\pi\)
−0.0881281 + 0.996109i \(0.528088\pi\)
\(54\) 0 0
\(55\) 12144.5 0.541343
\(56\) 94355.0 4.02064
\(57\) 0 0
\(58\) −31123.0 −1.21482
\(59\) −37190.1 −1.39090 −0.695452 0.718572i \(-0.744796\pi\)
−0.695452 + 0.718572i \(0.744796\pi\)
\(60\) 0 0
\(61\) −31681.4 −1.09013 −0.545067 0.838392i \(-0.683496\pi\)
−0.545067 + 0.838392i \(0.683496\pi\)
\(62\) 95401.8 3.15194
\(63\) 0 0
\(64\) 19083.7 0.582388
\(65\) 43209.8 1.26852
\(66\) 0 0
\(67\) −3782.79 −0.102950 −0.0514749 0.998674i \(-0.516392\pi\)
−0.0514749 + 0.998674i \(0.516392\pi\)
\(68\) 100541. 2.63677
\(69\) 0 0
\(70\) 155868. 3.80199
\(71\) 6321.88 0.148833 0.0744167 0.997227i \(-0.476291\pi\)
0.0744167 + 0.997227i \(0.476291\pi\)
\(72\) 0 0
\(73\) 12637.8 0.277564 0.138782 0.990323i \(-0.455681\pi\)
0.138782 + 0.990323i \(0.455681\pi\)
\(74\) −62342.8 −1.32345
\(75\) 0 0
\(76\) −134953. −2.68009
\(77\) −35904.1 −0.690108
\(78\) 0 0
\(79\) 79327.3 1.43006 0.715032 0.699092i \(-0.246412\pi\)
0.715032 + 0.699092i \(0.246412\pi\)
\(80\) 158727. 2.77285
\(81\) 0 0
\(82\) −68396.7 −1.12331
\(83\) 114368. 1.82226 0.911130 0.412118i \(-0.135211\pi\)
0.911130 + 0.412118i \(0.135211\pi\)
\(84\) 0 0
\(85\) 95409.1 1.43233
\(86\) −237459. −3.46212
\(87\) 0 0
\(88\) −76116.8 −1.04779
\(89\) 63683.3 0.852217 0.426109 0.904672i \(-0.359884\pi\)
0.426109 + 0.904672i \(0.359884\pi\)
\(90\) 0 0
\(91\) −127746. −1.61712
\(92\) 39779.5 0.489992
\(93\) 0 0
\(94\) 208931. 2.43884
\(95\) −128065. −1.45586
\(96\) 0 0
\(97\) 151168. 1.63129 0.815644 0.578553i \(-0.196383\pi\)
0.815644 + 0.578553i \(0.196383\pi\)
\(98\) −286795. −3.01652
\(99\) 0 0
\(100\) 147923. 1.47923
\(101\) 188855. 1.84215 0.921074 0.389387i \(-0.127313\pi\)
0.921074 + 0.389387i \(0.127313\pi\)
\(102\) 0 0
\(103\) 143432. 1.33215 0.666074 0.745886i \(-0.267974\pi\)
0.666074 + 0.745886i \(0.267974\pi\)
\(104\) −270821. −2.45527
\(105\) 0 0
\(106\) 37318.7 0.322598
\(107\) 88610.8 0.748216 0.374108 0.927385i \(-0.377949\pi\)
0.374108 + 0.927385i \(0.377949\pi\)
\(108\) 0 0
\(109\) −94789.3 −0.764176 −0.382088 0.924126i \(-0.624795\pi\)
−0.382088 + 0.924126i \(0.624795\pi\)
\(110\) −125739. −0.990809
\(111\) 0 0
\(112\) −469262. −3.53485
\(113\) 84969.6 0.625990 0.312995 0.949755i \(-0.398668\pi\)
0.312995 + 0.949755i \(0.398668\pi\)
\(114\) 0 0
\(115\) 37749.0 0.266171
\(116\) 226044. 1.55972
\(117\) 0 0
\(118\) 385052. 2.54574
\(119\) −282069. −1.82594
\(120\) 0 0
\(121\) −132087. −0.820156
\(122\) 328018. 1.99525
\(123\) 0 0
\(124\) −692895. −4.04681
\(125\) −82625.0 −0.472973
\(126\) 0 0
\(127\) −826.453 −0.00454683 −0.00227342 0.999997i \(-0.500724\pi\)
−0.00227342 + 0.999997i \(0.500724\pi\)
\(128\) 81389.9 0.439082
\(129\) 0 0
\(130\) −447378. −2.32175
\(131\) 262321. 1.33554 0.667768 0.744370i \(-0.267250\pi\)
0.667768 + 0.744370i \(0.267250\pi\)
\(132\) 0 0
\(133\) 378612. 1.85594
\(134\) 39165.6 0.188427
\(135\) 0 0
\(136\) −597986. −2.77232
\(137\) −12970.6 −0.0590415 −0.0295207 0.999564i \(-0.509398\pi\)
−0.0295207 + 0.999564i \(0.509398\pi\)
\(138\) 0 0
\(139\) −89440.8 −0.392644 −0.196322 0.980539i \(-0.562900\pi\)
−0.196322 + 0.980539i \(0.562900\pi\)
\(140\) −1.13205e6 −4.88143
\(141\) 0 0
\(142\) −65454.4 −0.272407
\(143\) 103053. 0.421427
\(144\) 0 0
\(145\) 214506. 0.847264
\(146\) −130847. −0.508020
\(147\) 0 0
\(148\) 452790. 1.69919
\(149\) 317159. 1.17034 0.585170 0.810911i \(-0.301028\pi\)
0.585170 + 0.810911i \(0.301028\pi\)
\(150\) 0 0
\(151\) −96753.6 −0.345322 −0.172661 0.984981i \(-0.555237\pi\)
−0.172661 + 0.984981i \(0.555237\pi\)
\(152\) 802658. 2.81787
\(153\) 0 0
\(154\) 371737. 1.26309
\(155\) −657527. −2.19829
\(156\) 0 0
\(157\) 133196. 0.431261 0.215631 0.976475i \(-0.430819\pi\)
0.215631 + 0.976475i \(0.430819\pi\)
\(158\) −821325. −2.61741
\(159\) 0 0
\(160\) −622107. −1.92117
\(161\) −111601. −0.339317
\(162\) 0 0
\(163\) 45781.6 0.134965 0.0674827 0.997720i \(-0.478503\pi\)
0.0674827 + 0.997720i \(0.478503\pi\)
\(164\) 496760. 1.44224
\(165\) 0 0
\(166\) −1.18413e6 −3.33525
\(167\) −38039.4 −0.105546 −0.0527731 0.998607i \(-0.516806\pi\)
−0.0527731 + 0.998607i \(0.516806\pi\)
\(168\) 0 0
\(169\) −4631.97 −0.0124752
\(170\) −987830. −2.62156
\(171\) 0 0
\(172\) 1.72464e6 4.44506
\(173\) 685175. 1.74055 0.870275 0.492566i \(-0.163941\pi\)
0.870275 + 0.492566i \(0.163941\pi\)
\(174\) 0 0
\(175\) −414998. −1.02436
\(176\) 378557. 0.921190
\(177\) 0 0
\(178\) −659352. −1.55980
\(179\) 326298. 0.761170 0.380585 0.924746i \(-0.375723\pi\)
0.380585 + 0.924746i \(0.375723\pi\)
\(180\) 0 0
\(181\) −359932. −0.816627 −0.408313 0.912842i \(-0.633883\pi\)
−0.408313 + 0.912842i \(0.633883\pi\)
\(182\) 1.32263e6 2.95979
\(183\) 0 0
\(184\) −236595. −0.515183
\(185\) 429678. 0.923026
\(186\) 0 0
\(187\) 227547. 0.475846
\(188\) −1.51745e6 −3.13126
\(189\) 0 0
\(190\) 1.32593e6 2.66463
\(191\) −310829. −0.616508 −0.308254 0.951304i \(-0.599745\pi\)
−0.308254 + 0.951304i \(0.599745\pi\)
\(192\) 0 0
\(193\) −136244. −0.263284 −0.131642 0.991297i \(-0.542025\pi\)
−0.131642 + 0.991297i \(0.542025\pi\)
\(194\) −1.56514e6 −2.98571
\(195\) 0 0
\(196\) 2.08297e6 3.87296
\(197\) −823205. −1.51127 −0.755635 0.654992i \(-0.772672\pi\)
−0.755635 + 0.654992i \(0.772672\pi\)
\(198\) 0 0
\(199\) 654175. 1.17101 0.585506 0.810668i \(-0.300896\pi\)
0.585506 + 0.810668i \(0.300896\pi\)
\(200\) −879797. −1.55528
\(201\) 0 0
\(202\) −1.95533e6 −3.37165
\(203\) −634167. −1.08010
\(204\) 0 0
\(205\) 471403. 0.783444
\(206\) −1.48504e6 −2.43820
\(207\) 0 0
\(208\) 1.34689e6 2.15862
\(209\) −305428. −0.483664
\(210\) 0 0
\(211\) 812196. 1.25590 0.627950 0.778254i \(-0.283894\pi\)
0.627950 + 0.778254i \(0.283894\pi\)
\(212\) −271043. −0.414188
\(213\) 0 0
\(214\) −917442. −1.36944
\(215\) 1.63661e6 2.41462
\(216\) 0 0
\(217\) 1.94392e6 2.80239
\(218\) 981413. 1.39865
\(219\) 0 0
\(220\) 913235. 1.27211
\(221\) 809604. 1.11504
\(222\) 0 0
\(223\) −252062. −0.339426 −0.169713 0.985494i \(-0.554284\pi\)
−0.169713 + 0.985494i \(0.554284\pi\)
\(224\) 1.83920e6 2.44912
\(225\) 0 0
\(226\) −879744. −1.14574
\(227\) 999309. 1.28717 0.643584 0.765376i \(-0.277447\pi\)
0.643584 + 0.765376i \(0.277447\pi\)
\(228\) 0 0
\(229\) 963621. 1.21428 0.607138 0.794596i \(-0.292317\pi\)
0.607138 + 0.794596i \(0.292317\pi\)
\(230\) −390839. −0.487167
\(231\) 0 0
\(232\) −1.34444e6 −1.63991
\(233\) −86902.2 −0.104868 −0.0524338 0.998624i \(-0.516698\pi\)
−0.0524338 + 0.998624i \(0.516698\pi\)
\(234\) 0 0
\(235\) −1.43999e6 −1.70095
\(236\) −2.79660e6 −3.26852
\(237\) 0 0
\(238\) 2.92043e6 3.34199
\(239\) 1.42740e6 1.61641 0.808206 0.588900i \(-0.200439\pi\)
0.808206 + 0.588900i \(0.200439\pi\)
\(240\) 0 0
\(241\) −137084. −0.152035 −0.0760176 0.997106i \(-0.524221\pi\)
−0.0760176 + 0.997106i \(0.524221\pi\)
\(242\) 1.36758e6 1.50111
\(243\) 0 0
\(244\) −2.38236e6 −2.56173
\(245\) 1.97665e6 2.10385
\(246\) 0 0
\(247\) −1.08671e6 −1.13336
\(248\) 4.12112e6 4.25486
\(249\) 0 0
\(250\) 855468. 0.865672
\(251\) −947694. −0.949476 −0.474738 0.880127i \(-0.657457\pi\)
−0.474738 + 0.880127i \(0.657457\pi\)
\(252\) 0 0
\(253\) 90029.6 0.0884269
\(254\) 8556.78 0.00832197
\(255\) 0 0
\(256\) −1.45336e6 −1.38603
\(257\) 1.25100e6 1.18148 0.590739 0.806862i \(-0.298836\pi\)
0.590739 + 0.806862i \(0.298836\pi\)
\(258\) 0 0
\(259\) −1.27030e6 −1.17668
\(260\) 3.24926e6 2.98093
\(261\) 0 0
\(262\) −2.71598e6 −2.44440
\(263\) −305663. −0.272492 −0.136246 0.990675i \(-0.543504\pi\)
−0.136246 + 0.990675i \(0.543504\pi\)
\(264\) 0 0
\(265\) −257208. −0.224993
\(266\) −3.92000e6 −3.39689
\(267\) 0 0
\(268\) −284456. −0.241924
\(269\) −712.235 −0.000600127 0 −0.000300063 1.00000i \(-0.500096\pi\)
−0.000300063 1.00000i \(0.500096\pi\)
\(270\) 0 0
\(271\) −726592. −0.600990 −0.300495 0.953783i \(-0.597152\pi\)
−0.300495 + 0.953783i \(0.597152\pi\)
\(272\) 2.97401e6 2.43736
\(273\) 0 0
\(274\) 134292. 0.108062
\(275\) 334782. 0.266950
\(276\) 0 0
\(277\) −650868. −0.509675 −0.254837 0.966984i \(-0.582022\pi\)
−0.254837 + 0.966984i \(0.582022\pi\)
\(278\) 926036. 0.718648
\(279\) 0 0
\(280\) 6.73309e6 5.13238
\(281\) −667888. −0.504589 −0.252294 0.967650i \(-0.581185\pi\)
−0.252294 + 0.967650i \(0.581185\pi\)
\(282\) 0 0
\(283\) −1.91825e6 −1.42377 −0.711883 0.702298i \(-0.752157\pi\)
−0.711883 + 0.702298i \(0.752157\pi\)
\(284\) 475390. 0.349747
\(285\) 0 0
\(286\) −1.06698e6 −0.771328
\(287\) −1.39366e6 −0.998740
\(288\) 0 0
\(289\) 367787. 0.259031
\(290\) −2.22091e6 −1.55073
\(291\) 0 0
\(292\) 950328. 0.652254
\(293\) −357387. −0.243203 −0.121602 0.992579i \(-0.538803\pi\)
−0.121602 + 0.992579i \(0.538803\pi\)
\(294\) 0 0
\(295\) −2.65385e6 −1.77550
\(296\) −2.69305e6 −1.78655
\(297\) 0 0
\(298\) −3.28375e6 −2.14205
\(299\) 320323. 0.207210
\(300\) 0 0
\(301\) −4.83849e6 −3.07818
\(302\) 1.00175e6 0.632036
\(303\) 0 0
\(304\) −3.99191e6 −2.47741
\(305\) −2.26076e6 −1.39157
\(306\) 0 0
\(307\) 242810. 0.147035 0.0735176 0.997294i \(-0.476577\pi\)
0.0735176 + 0.997294i \(0.476577\pi\)
\(308\) −2.69990e6 −1.62170
\(309\) 0 0
\(310\) 6.80779e6 4.02348
\(311\) 510526. 0.299307 0.149654 0.988738i \(-0.452184\pi\)
0.149654 + 0.988738i \(0.452184\pi\)
\(312\) 0 0
\(313\) 268272. 0.154780 0.0773901 0.997001i \(-0.475341\pi\)
0.0773901 + 0.997001i \(0.475341\pi\)
\(314\) −1.37906e6 −0.789328
\(315\) 0 0
\(316\) 5.96522e6 3.36054
\(317\) −1.17566e6 −0.657102 −0.328551 0.944486i \(-0.606560\pi\)
−0.328551 + 0.944486i \(0.606560\pi\)
\(318\) 0 0
\(319\) 511586. 0.281477
\(320\) 1.36180e6 0.743424
\(321\) 0 0
\(322\) 1.15548e6 0.621044
\(323\) −2.39950e6 −1.27972
\(324\) 0 0
\(325\) 1.19114e6 0.625541
\(326\) −474006. −0.247024
\(327\) 0 0
\(328\) −2.95457e6 −1.51638
\(329\) 4.25721e6 2.16838
\(330\) 0 0
\(331\) 3.74833e6 1.88047 0.940237 0.340520i \(-0.110603\pi\)
0.940237 + 0.340520i \(0.110603\pi\)
\(332\) 8.60021e6 4.28217
\(333\) 0 0
\(334\) 393846. 0.193179
\(335\) −269937. −0.131417
\(336\) 0 0
\(337\) −3.05514e6 −1.46540 −0.732701 0.680551i \(-0.761740\pi\)
−0.732701 + 0.680551i \(0.761740\pi\)
\(338\) 47957.7 0.0228332
\(339\) 0 0
\(340\) 7.17453e6 3.36586
\(341\) −1.56817e6 −0.730312
\(342\) 0 0
\(343\) −2.29806e6 −1.05469
\(344\) −1.02576e7 −4.67359
\(345\) 0 0
\(346\) −7.09405e6 −3.18569
\(347\) 4.00997e6 1.78779 0.893896 0.448274i \(-0.147961\pi\)
0.893896 + 0.448274i \(0.147961\pi\)
\(348\) 0 0
\(349\) 1.17172e6 0.514944 0.257472 0.966286i \(-0.417111\pi\)
0.257472 + 0.966286i \(0.417111\pi\)
\(350\) 4.29673e6 1.87486
\(351\) 0 0
\(352\) −1.48370e6 −0.638247
\(353\) −2.17711e6 −0.929917 −0.464958 0.885333i \(-0.653931\pi\)
−0.464958 + 0.885333i \(0.653931\pi\)
\(354\) 0 0
\(355\) 451124. 0.189988
\(356\) 4.78882e6 2.00264
\(357\) 0 0
\(358\) −3.37837e6 −1.39315
\(359\) −1.01162e6 −0.414269 −0.207135 0.978312i \(-0.566414\pi\)
−0.207135 + 0.978312i \(0.566414\pi\)
\(360\) 0 0
\(361\) 744669. 0.300743
\(362\) 3.72660e6 1.49465
\(363\) 0 0
\(364\) −9.60616e6 −3.80011
\(365\) 901820. 0.354313
\(366\) 0 0
\(367\) −1.83005e6 −0.709249 −0.354625 0.935009i \(-0.615391\pi\)
−0.354625 + 0.935009i \(0.615391\pi\)
\(368\) 1.17668e6 0.452937
\(369\) 0 0
\(370\) −4.44872e6 −1.68939
\(371\) 760411. 0.286823
\(372\) 0 0
\(373\) 206897. 0.0769986 0.0384993 0.999259i \(-0.487742\pi\)
0.0384993 + 0.999259i \(0.487742\pi\)
\(374\) −2.35593e6 −0.870931
\(375\) 0 0
\(376\) 9.02530e6 3.29225
\(377\) 1.82021e6 0.659581
\(378\) 0 0
\(379\) 4.49105e6 1.60602 0.803008 0.595968i \(-0.203232\pi\)
0.803008 + 0.595968i \(0.203232\pi\)
\(380\) −9.63014e6 −3.42116
\(381\) 0 0
\(382\) 3.21821e6 1.12838
\(383\) 2.30581e6 0.803204 0.401602 0.915814i \(-0.368453\pi\)
0.401602 + 0.915814i \(0.368453\pi\)
\(384\) 0 0
\(385\) −2.56208e6 −0.880930
\(386\) 1.41062e6 0.481883
\(387\) 0 0
\(388\) 1.13675e7 3.83340
\(389\) −1.17176e6 −0.392612 −0.196306 0.980543i \(-0.562895\pi\)
−0.196306 + 0.980543i \(0.562895\pi\)
\(390\) 0 0
\(391\) 707288. 0.233967
\(392\) −1.23888e7 −4.07207
\(393\) 0 0
\(394\) 8.52315e6 2.76605
\(395\) 5.66073e6 1.82549
\(396\) 0 0
\(397\) 1.03765e6 0.330428 0.165214 0.986258i \(-0.447169\pi\)
0.165214 + 0.986258i \(0.447169\pi\)
\(398\) −6.77308e6 −2.14328
\(399\) 0 0
\(400\) 4.37556e6 1.36736
\(401\) −6.13691e6 −1.90585 −0.952925 0.303205i \(-0.901943\pi\)
−0.952925 + 0.303205i \(0.901943\pi\)
\(402\) 0 0
\(403\) −5.57952e6 −1.71133
\(404\) 1.42014e7 4.32890
\(405\) 0 0
\(406\) 6.56592e6 1.97688
\(407\) 1.02476e6 0.306646
\(408\) 0 0
\(409\) −2.13261e6 −0.630380 −0.315190 0.949029i \(-0.602068\pi\)
−0.315190 + 0.949029i \(0.602068\pi\)
\(410\) −4.88073e6 −1.43392
\(411\) 0 0
\(412\) 1.07857e7 3.13044
\(413\) 7.84588e6 2.26343
\(414\) 0 0
\(415\) 8.16122e6 2.32614
\(416\) −5.27895e6 −1.49560
\(417\) 0 0
\(418\) 3.16229e6 0.885240
\(419\) 6.05469e6 1.68483 0.842417 0.538826i \(-0.181132\pi\)
0.842417 + 0.538826i \(0.181132\pi\)
\(420\) 0 0
\(421\) −4.62140e6 −1.27077 −0.635386 0.772194i \(-0.719159\pi\)
−0.635386 + 0.772194i \(0.719159\pi\)
\(422\) −8.40917e6 −2.29865
\(423\) 0 0
\(424\) 1.61207e6 0.435482
\(425\) 2.63010e6 0.706318
\(426\) 0 0
\(427\) 6.68373e6 1.77398
\(428\) 6.66331e6 1.75825
\(429\) 0 0
\(430\) −1.69448e7 −4.41943
\(431\) −1.49369e6 −0.387319 −0.193659 0.981069i \(-0.562036\pi\)
−0.193659 + 0.981069i \(0.562036\pi\)
\(432\) 0 0
\(433\) −7.44271e6 −1.90770 −0.953852 0.300276i \(-0.902921\pi\)
−0.953852 + 0.300276i \(0.902921\pi\)
\(434\) −2.01266e7 −5.12916
\(435\) 0 0
\(436\) −7.12792e6 −1.79575
\(437\) −949370. −0.237811
\(438\) 0 0
\(439\) −2.11446e6 −0.523647 −0.261823 0.965116i \(-0.584324\pi\)
−0.261823 + 0.965116i \(0.584324\pi\)
\(440\) −5.43163e6 −1.33751
\(441\) 0 0
\(442\) −8.38234e6 −2.04084
\(443\) −2.16454e6 −0.524031 −0.262015 0.965064i \(-0.584387\pi\)
−0.262015 + 0.965064i \(0.584387\pi\)
\(444\) 0 0
\(445\) 4.54438e6 1.08786
\(446\) 2.60975e6 0.621244
\(447\) 0 0
\(448\) −4.02602e6 −0.947723
\(449\) −5.65548e6 −1.32390 −0.661948 0.749550i \(-0.730270\pi\)
−0.661948 + 0.749550i \(0.730270\pi\)
\(450\) 0 0
\(451\) 1.12428e6 0.260274
\(452\) 6.38950e6 1.47103
\(453\) 0 0
\(454\) −1.03465e7 −2.35588
\(455\) −9.11583e6 −2.06427
\(456\) 0 0
\(457\) 213062. 0.0477216 0.0238608 0.999715i \(-0.492404\pi\)
0.0238608 + 0.999715i \(0.492404\pi\)
\(458\) −9.97697e6 −2.22246
\(459\) 0 0
\(460\) 2.83863e6 0.625481
\(461\) −2.84868e6 −0.624296 −0.312148 0.950033i \(-0.601049\pi\)
−0.312148 + 0.950033i \(0.601049\pi\)
\(462\) 0 0
\(463\) −981530. −0.212790 −0.106395 0.994324i \(-0.533931\pi\)
−0.106395 + 0.994324i \(0.533931\pi\)
\(464\) 6.68637e6 1.44177
\(465\) 0 0
\(466\) 899753. 0.191937
\(467\) −1.12083e6 −0.237820 −0.118910 0.992905i \(-0.537940\pi\)
−0.118910 + 0.992905i \(0.537940\pi\)
\(468\) 0 0
\(469\) 798043. 0.167531
\(470\) 1.49092e7 3.11321
\(471\) 0 0
\(472\) 1.66333e7 3.43655
\(473\) 3.90324e6 0.802182
\(474\) 0 0
\(475\) −3.53030e6 −0.717923
\(476\) −2.12108e7 −4.29082
\(477\) 0 0
\(478\) −1.47788e7 −2.95848
\(479\) −8.75292e6 −1.74307 −0.871534 0.490335i \(-0.836874\pi\)
−0.871534 + 0.490335i \(0.836874\pi\)
\(480\) 0 0
\(481\) 3.64608e6 0.718561
\(482\) 1.41932e6 0.278267
\(483\) 0 0
\(484\) −9.93260e6 −1.92730
\(485\) 1.07872e7 2.08236
\(486\) 0 0
\(487\) 4.58029e6 0.875126 0.437563 0.899188i \(-0.355842\pi\)
0.437563 + 0.899188i \(0.355842\pi\)
\(488\) 1.41695e7 2.69343
\(489\) 0 0
\(490\) −2.04655e7 −3.85062
\(491\) −3.32030e6 −0.621546 −0.310773 0.950484i \(-0.600588\pi\)
−0.310773 + 0.950484i \(0.600588\pi\)
\(492\) 0 0
\(493\) 4.01911e6 0.744753
\(494\) 1.12513e7 2.07437
\(495\) 0 0
\(496\) −2.04958e7 −3.74077
\(497\) −1.33371e6 −0.242197
\(498\) 0 0
\(499\) 9.33617e6 1.67848 0.839242 0.543758i \(-0.182999\pi\)
0.839242 + 0.543758i \(0.182999\pi\)
\(500\) −6.21319e6 −1.11145
\(501\) 0 0
\(502\) 9.81207e6 1.73781
\(503\) −7.75961e6 −1.36748 −0.683738 0.729728i \(-0.739647\pi\)
−0.683738 + 0.729728i \(0.739647\pi\)
\(504\) 0 0
\(505\) 1.34765e7 2.35152
\(506\) −932133. −0.161846
\(507\) 0 0
\(508\) −62147.2 −0.0106847
\(509\) 8.78414e6 1.50281 0.751406 0.659840i \(-0.229376\pi\)
0.751406 + 0.659840i \(0.229376\pi\)
\(510\) 0 0
\(511\) −2.66615e6 −0.451681
\(512\) 1.24430e7 2.09774
\(513\) 0 0
\(514\) −1.29524e7 −2.16244
\(515\) 1.02352e7 1.70050
\(516\) 0 0
\(517\) −3.43432e6 −0.565086
\(518\) 1.31523e7 2.15365
\(519\) 0 0
\(520\) −1.93256e7 −3.13418
\(521\) −6.42822e6 −1.03752 −0.518760 0.854920i \(-0.673606\pi\)
−0.518760 + 0.854920i \(0.673606\pi\)
\(522\) 0 0
\(523\) −4.75955e6 −0.760872 −0.380436 0.924807i \(-0.624226\pi\)
−0.380436 + 0.924807i \(0.624226\pi\)
\(524\) 1.97259e7 3.13840
\(525\) 0 0
\(526\) 3.16472e6 0.498736
\(527\) −1.23198e7 −1.93232
\(528\) 0 0
\(529\) 279841. 0.0434783
\(530\) 2.66303e6 0.411800
\(531\) 0 0
\(532\) 2.84706e7 4.36132
\(533\) 4.00014e6 0.609898
\(534\) 0 0
\(535\) 6.32319e6 0.955106
\(536\) 1.69185e6 0.254361
\(537\) 0 0
\(538\) 7374.22 0.00109840
\(539\) 4.71422e6 0.698936
\(540\) 0 0
\(541\) 7.85812e6 1.15432 0.577159 0.816632i \(-0.304161\pi\)
0.577159 + 0.816632i \(0.304161\pi\)
\(542\) 7.52286e6 1.09998
\(543\) 0 0
\(544\) −1.16562e7 −1.68872
\(545\) −6.76408e6 −0.975479
\(546\) 0 0
\(547\) 1.00196e7 1.43180 0.715902 0.698201i \(-0.246016\pi\)
0.715902 + 0.698201i \(0.246016\pi\)
\(548\) −975353. −0.138743
\(549\) 0 0
\(550\) −3.46620e6 −0.488593
\(551\) −5.39472e6 −0.756990
\(552\) 0 0
\(553\) −1.67354e7 −2.32715
\(554\) 6.73884e6 0.932847
\(555\) 0 0
\(556\) −6.72572e6 −0.922682
\(557\) −5.74512e6 −0.784623 −0.392312 0.919832i \(-0.628325\pi\)
−0.392312 + 0.919832i \(0.628325\pi\)
\(558\) 0 0
\(559\) 1.38876e7 1.87974
\(560\) −3.34861e7 −4.51227
\(561\) 0 0
\(562\) 6.91506e6 0.923539
\(563\) 1.23215e6 0.163829 0.0819146 0.996639i \(-0.473897\pi\)
0.0819146 + 0.996639i \(0.473897\pi\)
\(564\) 0 0
\(565\) 6.06336e6 0.799084
\(566\) 1.98608e7 2.60589
\(567\) 0 0
\(568\) −2.82746e6 −0.367728
\(569\) 8.80266e6 1.13981 0.569906 0.821710i \(-0.306980\pi\)
0.569906 + 0.821710i \(0.306980\pi\)
\(570\) 0 0
\(571\) −7.49333e6 −0.961800 −0.480900 0.876776i \(-0.659690\pi\)
−0.480900 + 0.876776i \(0.659690\pi\)
\(572\) 7.74935e6 0.990320
\(573\) 0 0
\(574\) 1.44294e7 1.82797
\(575\) 1.04061e6 0.131256
\(576\) 0 0
\(577\) −1.36469e7 −1.70646 −0.853228 0.521538i \(-0.825358\pi\)
−0.853228 + 0.521538i \(0.825358\pi\)
\(578\) −3.80793e6 −0.474099
\(579\) 0 0
\(580\) 1.61303e7 1.99100
\(581\) −2.41279e7 −2.96537
\(582\) 0 0
\(583\) −613429. −0.0747468
\(584\) −5.65224e6 −0.685786
\(585\) 0 0
\(586\) 3.70024e6 0.445130
\(587\) 2.92745e6 0.350666 0.175333 0.984509i \(-0.443900\pi\)
0.175333 + 0.984509i \(0.443900\pi\)
\(588\) 0 0
\(589\) 1.65365e7 1.96406
\(590\) 2.74770e7 3.24967
\(591\) 0 0
\(592\) 1.33935e7 1.57069
\(593\) 5.29722e6 0.618603 0.309301 0.950964i \(-0.399905\pi\)
0.309301 + 0.950964i \(0.399905\pi\)
\(594\) 0 0
\(595\) −2.01282e7 −2.33084
\(596\) 2.38496e7 2.75020
\(597\) 0 0
\(598\) −3.31650e6 −0.379252
\(599\) −1.35436e7 −1.54229 −0.771147 0.636657i \(-0.780317\pi\)
−0.771147 + 0.636657i \(0.780317\pi\)
\(600\) 0 0
\(601\) −3.10785e6 −0.350973 −0.175486 0.984482i \(-0.556150\pi\)
−0.175486 + 0.984482i \(0.556150\pi\)
\(602\) 5.00959e7 5.63392
\(603\) 0 0
\(604\) −7.27562e6 −0.811480
\(605\) −9.42561e6 −1.04694
\(606\) 0 0
\(607\) −5.80425e6 −0.639402 −0.319701 0.947518i \(-0.603582\pi\)
−0.319701 + 0.947518i \(0.603582\pi\)
\(608\) 1.56457e7 1.71647
\(609\) 0 0
\(610\) 2.34070e7 2.54696
\(611\) −1.22192e7 −1.32416
\(612\) 0 0
\(613\) −2.53122e6 −0.272069 −0.136035 0.990704i \(-0.543436\pi\)
−0.136035 + 0.990704i \(0.543436\pi\)
\(614\) −2.51397e6 −0.269115
\(615\) 0 0
\(616\) 1.60581e7 1.70507
\(617\) 1.03128e7 1.09059 0.545296 0.838244i \(-0.316417\pi\)
0.545296 + 0.838244i \(0.316417\pi\)
\(618\) 0 0
\(619\) −4.15021e6 −0.435355 −0.217677 0.976021i \(-0.569848\pi\)
−0.217677 + 0.976021i \(0.569848\pi\)
\(620\) −4.94444e7 −5.16580
\(621\) 0 0
\(622\) −5.28580e6 −0.547816
\(623\) −1.34351e7 −1.38682
\(624\) 0 0
\(625\) −1.20433e7 −1.23323
\(626\) −2.77759e6 −0.283291
\(627\) 0 0
\(628\) 1.00160e7 1.01343
\(629\) 8.05071e6 0.811349
\(630\) 0 0
\(631\) 1.70512e7 1.70483 0.852416 0.522864i \(-0.175136\pi\)
0.852416 + 0.522864i \(0.175136\pi\)
\(632\) −3.54792e7 −3.53330
\(633\) 0 0
\(634\) 1.21723e7 1.20268
\(635\) −58975.0 −0.00580408
\(636\) 0 0
\(637\) 1.67730e7 1.63781
\(638\) −5.29677e6 −0.515181
\(639\) 0 0
\(640\) 5.80791e6 0.560493
\(641\) 1.64702e7 1.58327 0.791633 0.610997i \(-0.209231\pi\)
0.791633 + 0.610997i \(0.209231\pi\)
\(642\) 0 0
\(643\) 6.28693e6 0.599668 0.299834 0.953991i \(-0.403069\pi\)
0.299834 + 0.953991i \(0.403069\pi\)
\(644\) −8.39215e6 −0.797367
\(645\) 0 0
\(646\) 2.48435e7 2.34224
\(647\) −5.21472e6 −0.489746 −0.244873 0.969555i \(-0.578746\pi\)
−0.244873 + 0.969555i \(0.578746\pi\)
\(648\) 0 0
\(649\) −6.32932e6 −0.589855
\(650\) −1.23327e7 −1.14491
\(651\) 0 0
\(652\) 3.44266e6 0.317158
\(653\) 4.72335e6 0.433479 0.216739 0.976230i \(-0.430458\pi\)
0.216739 + 0.976230i \(0.430458\pi\)
\(654\) 0 0
\(655\) 1.87190e7 1.70483
\(656\) 1.46941e7 1.33317
\(657\) 0 0
\(658\) −4.40776e7 −3.96874
\(659\) 5.27529e6 0.473187 0.236593 0.971609i \(-0.423969\pi\)
0.236593 + 0.971609i \(0.423969\pi\)
\(660\) 0 0
\(661\) 2.64941e6 0.235855 0.117928 0.993022i \(-0.462375\pi\)
0.117928 + 0.993022i \(0.462375\pi\)
\(662\) −3.88088e7 −3.44179
\(663\) 0 0
\(664\) −5.11513e7 −4.50232
\(665\) 2.70174e7 2.36913
\(666\) 0 0
\(667\) 1.59018e6 0.138398
\(668\) −2.86047e6 −0.248025
\(669\) 0 0
\(670\) 2.79482e6 0.240529
\(671\) −5.39181e6 −0.462305
\(672\) 0 0
\(673\) −2.58779e6 −0.220237 −0.110119 0.993918i \(-0.535123\pi\)
−0.110119 + 0.993918i \(0.535123\pi\)
\(674\) 3.16318e7 2.68209
\(675\) 0 0
\(676\) −348313. −0.0293158
\(677\) 1.06620e7 0.894064 0.447032 0.894518i \(-0.352481\pi\)
0.447032 + 0.894518i \(0.352481\pi\)
\(678\) 0 0
\(679\) −3.18915e7 −2.65461
\(680\) −4.26718e7 −3.53890
\(681\) 0 0
\(682\) 1.62363e7 1.33667
\(683\) −1.21075e7 −0.993119 −0.496559 0.868003i \(-0.665404\pi\)
−0.496559 + 0.868003i \(0.665404\pi\)
\(684\) 0 0
\(685\) −925568. −0.0753671
\(686\) 2.37932e7 1.93038
\(687\) 0 0
\(688\) 5.10149e7 4.10890
\(689\) −2.18256e6 −0.175153
\(690\) 0 0
\(691\) 1.66501e7 1.32654 0.663271 0.748379i \(-0.269168\pi\)
0.663271 + 0.748379i \(0.269168\pi\)
\(692\) 5.15235e7 4.09015
\(693\) 0 0
\(694\) −4.15177e7 −3.27216
\(695\) −6.38242e6 −0.501214
\(696\) 0 0
\(697\) 8.83250e6 0.688655
\(698\) −1.21315e7 −0.942490
\(699\) 0 0
\(700\) −3.12068e7 −2.40716
\(701\) −569003. −0.0437340 −0.0218670 0.999761i \(-0.506961\pi\)
−0.0218670 + 0.999761i \(0.506961\pi\)
\(702\) 0 0
\(703\) −1.08062e7 −0.824679
\(704\) 3.24782e6 0.246979
\(705\) 0 0
\(706\) 2.25410e7 1.70201
\(707\) −3.98421e7 −2.99774
\(708\) 0 0
\(709\) −1.70513e6 −0.127392 −0.0636959 0.997969i \(-0.520289\pi\)
−0.0636959 + 0.997969i \(0.520289\pi\)
\(710\) −4.67077e6 −0.347730
\(711\) 0 0
\(712\) −2.84824e7 −2.10560
\(713\) −4.87439e6 −0.359084
\(714\) 0 0
\(715\) 7.35380e6 0.537956
\(716\) 2.45368e7 1.78869
\(717\) 0 0
\(718\) 1.04740e7 0.758228
\(719\) −7.59885e6 −0.548183 −0.274092 0.961704i \(-0.588377\pi\)
−0.274092 + 0.961704i \(0.588377\pi\)
\(720\) 0 0
\(721\) −3.02593e7 −2.16781
\(722\) −7.71002e6 −0.550443
\(723\) 0 0
\(724\) −2.70660e7 −1.91901
\(725\) 5.91318e6 0.417807
\(726\) 0 0
\(727\) 7.24703e6 0.508539 0.254269 0.967133i \(-0.418165\pi\)
0.254269 + 0.967133i \(0.418165\pi\)
\(728\) 5.71343e7 3.99548
\(729\) 0 0
\(730\) −9.33710e6 −0.648493
\(731\) 3.06645e7 2.12248
\(732\) 0 0
\(733\) 4.57843e6 0.314743 0.157372 0.987539i \(-0.449698\pi\)
0.157372 + 0.987539i \(0.449698\pi\)
\(734\) 1.89477e7 1.29812
\(735\) 0 0
\(736\) −4.61181e6 −0.313817
\(737\) −643787. −0.0436590
\(738\) 0 0
\(739\) −1.79403e7 −1.20842 −0.604211 0.796825i \(-0.706511\pi\)
−0.604211 + 0.796825i \(0.706511\pi\)
\(740\) 3.23107e7 2.16904
\(741\) 0 0
\(742\) −7.87301e6 −0.524966
\(743\) 1.58719e7 1.05477 0.527383 0.849628i \(-0.323173\pi\)
0.527383 + 0.849628i \(0.323173\pi\)
\(744\) 0 0
\(745\) 2.26322e7 1.49395
\(746\) −2.14214e6 −0.140929
\(747\) 0 0
\(748\) 1.71109e7 1.11820
\(749\) −1.86939e7 −1.21758
\(750\) 0 0
\(751\) −2.95699e7 −1.91316 −0.956578 0.291478i \(-0.905853\pi\)
−0.956578 + 0.291478i \(0.905853\pi\)
\(752\) −4.48862e7 −2.89446
\(753\) 0 0
\(754\) −1.88458e7 −1.20722
\(755\) −6.90425e6 −0.440808
\(756\) 0 0
\(757\) 9.81021e6 0.622212 0.311106 0.950375i \(-0.399301\pi\)
0.311106 + 0.950375i \(0.399301\pi\)
\(758\) −4.64986e7 −2.93946
\(759\) 0 0
\(760\) 5.72769e7 3.59704
\(761\) 1.09443e7 0.685056 0.342528 0.939508i \(-0.388717\pi\)
0.342528 + 0.939508i \(0.388717\pi\)
\(762\) 0 0
\(763\) 1.99974e7 1.24355
\(764\) −2.33736e7 −1.44874
\(765\) 0 0
\(766\) −2.38735e7 −1.47009
\(767\) −2.25196e7 −1.38220
\(768\) 0 0
\(769\) 4.68373e6 0.285612 0.142806 0.989751i \(-0.454388\pi\)
0.142806 + 0.989751i \(0.454388\pi\)
\(770\) 2.65269e7 1.61235
\(771\) 0 0
\(772\) −1.02452e7 −0.618697
\(773\) 1.32674e7 0.798612 0.399306 0.916818i \(-0.369251\pi\)
0.399306 + 0.916818i \(0.369251\pi\)
\(774\) 0 0
\(775\) −1.81258e7 −1.08403
\(776\) −6.76100e7 −4.03048
\(777\) 0 0
\(778\) 1.21319e7 0.718589
\(779\) −1.18556e7 −0.699970
\(780\) 0 0
\(781\) 1.07591e6 0.0631173
\(782\) −7.32299e6 −0.428225
\(783\) 0 0
\(784\) 6.16142e7 3.58006
\(785\) 9.50472e6 0.550510
\(786\) 0 0
\(787\) 1.05678e7 0.608204 0.304102 0.952639i \(-0.401644\pi\)
0.304102 + 0.952639i \(0.401644\pi\)
\(788\) −6.19029e7 −3.55137
\(789\) 0 0
\(790\) −5.86091e7 −3.34116
\(791\) −1.79258e7 −1.01868
\(792\) 0 0
\(793\) −1.91839e7 −1.08331
\(794\) −1.07435e7 −0.604775
\(795\) 0 0
\(796\) 4.91923e7 2.75178
\(797\) 6.69757e6 0.373483 0.186742 0.982409i \(-0.440207\pi\)
0.186742 + 0.982409i \(0.440207\pi\)
\(798\) 0 0
\(799\) −2.69806e7 −1.49515
\(800\) −1.71493e7 −0.947376
\(801\) 0 0
\(802\) 6.35393e7 3.48824
\(803\) 2.15080e6 0.117709
\(804\) 0 0
\(805\) −7.96378e6 −0.433141
\(806\) 5.77682e7 3.13221
\(807\) 0 0
\(808\) −8.44654e7 −4.55145
\(809\) −2.87439e7 −1.54409 −0.772047 0.635566i \(-0.780767\pi\)
−0.772047 + 0.635566i \(0.780767\pi\)
\(810\) 0 0
\(811\) 6.11987e6 0.326731 0.163365 0.986566i \(-0.447765\pi\)
0.163365 + 0.986566i \(0.447765\pi\)
\(812\) −4.76877e7 −2.53815
\(813\) 0 0
\(814\) −1.06100e7 −0.561248
\(815\) 3.26694e6 0.172285
\(816\) 0 0
\(817\) −4.11600e7 −2.15735
\(818\) 2.20802e7 1.15377
\(819\) 0 0
\(820\) 3.54483e7 1.84103
\(821\) −2.55802e7 −1.32448 −0.662241 0.749291i \(-0.730395\pi\)
−0.662241 + 0.749291i \(0.730395\pi\)
\(822\) 0 0
\(823\) −1.38465e7 −0.712589 −0.356295 0.934374i \(-0.615960\pi\)
−0.356295 + 0.934374i \(0.615960\pi\)
\(824\) −6.41499e7 −3.29138
\(825\) 0 0
\(826\) −8.12332e7 −4.14270
\(827\) 6.70325e6 0.340817 0.170409 0.985373i \(-0.445491\pi\)
0.170409 + 0.985373i \(0.445491\pi\)
\(828\) 0 0
\(829\) −1.66094e7 −0.839395 −0.419698 0.907664i \(-0.637864\pi\)
−0.419698 + 0.907664i \(0.637864\pi\)
\(830\) −8.44982e7 −4.25748
\(831\) 0 0
\(832\) 1.15557e7 0.578744
\(833\) 3.70357e7 1.84930
\(834\) 0 0
\(835\) −2.71446e6 −0.134731
\(836\) −2.29674e7 −1.13657
\(837\) 0 0
\(838\) −6.26880e7 −3.08372
\(839\) −1.49591e7 −0.733668 −0.366834 0.930286i \(-0.619558\pi\)
−0.366834 + 0.930286i \(0.619558\pi\)
\(840\) 0 0
\(841\) −1.14751e7 −0.559457
\(842\) 4.78482e7 2.32587
\(843\) 0 0
\(844\) 6.10751e7 2.95126
\(845\) −330533. −0.0159248
\(846\) 0 0
\(847\) 2.78660e7 1.33464
\(848\) −8.01744e6 −0.382865
\(849\) 0 0
\(850\) −2.72311e7 −1.29276
\(851\) 3.18529e6 0.150774
\(852\) 0 0
\(853\) 3.51212e7 1.65271 0.826356 0.563148i \(-0.190410\pi\)
0.826356 + 0.563148i \(0.190410\pi\)
\(854\) −6.92008e7 −3.24688
\(855\) 0 0
\(856\) −3.96312e7 −1.84864
\(857\) 2.92814e7 1.36188 0.680941 0.732338i \(-0.261571\pi\)
0.680941 + 0.732338i \(0.261571\pi\)
\(858\) 0 0
\(859\) −2.71049e7 −1.25333 −0.626664 0.779289i \(-0.715580\pi\)
−0.626664 + 0.779289i \(0.715580\pi\)
\(860\) 1.23069e8 5.67417
\(861\) 0 0
\(862\) 1.54651e7 0.708901
\(863\) 1.47872e7 0.675863 0.337931 0.941171i \(-0.390273\pi\)
0.337931 + 0.941171i \(0.390273\pi\)
\(864\) 0 0
\(865\) 4.88935e7 2.22183
\(866\) 7.70590e7 3.49163
\(867\) 0 0
\(868\) 1.46178e8 6.58540
\(869\) 1.35006e7 0.606462
\(870\) 0 0
\(871\) −2.29058e6 −0.102306
\(872\) 4.23946e7 1.88807
\(873\) 0 0
\(874\) 9.82941e6 0.435260
\(875\) 1.74311e7 0.769671
\(876\) 0 0
\(877\) −1.07960e7 −0.473982 −0.236991 0.971512i \(-0.576161\pi\)
−0.236991 + 0.971512i \(0.576161\pi\)
\(878\) 2.18923e7 0.958420
\(879\) 0 0
\(880\) 2.70135e7 1.17591
\(881\) 6.00778e6 0.260780 0.130390 0.991463i \(-0.458377\pi\)
0.130390 + 0.991463i \(0.458377\pi\)
\(882\) 0 0
\(883\) 1.06315e7 0.458875 0.229437 0.973323i \(-0.426311\pi\)
0.229437 + 0.973323i \(0.426311\pi\)
\(884\) 6.08802e7 2.62027
\(885\) 0 0
\(886\) 2.24109e7 0.959123
\(887\) 3.31806e6 0.141604 0.0708020 0.997490i \(-0.477444\pi\)
0.0708020 + 0.997490i \(0.477444\pi\)
\(888\) 0 0
\(889\) 174354. 0.00739908
\(890\) −4.70508e7 −1.99110
\(891\) 0 0
\(892\) −1.89544e7 −0.797623
\(893\) 3.62152e7 1.51972
\(894\) 0 0
\(895\) 2.32843e7 0.971642
\(896\) −1.71706e7 −0.714520
\(897\) 0 0
\(898\) 5.85547e7 2.42310
\(899\) −2.76983e7 −1.14302
\(900\) 0 0
\(901\) −4.81920e6 −0.197771
\(902\) −1.16403e7 −0.476375
\(903\) 0 0
\(904\) −3.80027e7 −1.54665
\(905\) −2.56844e7 −1.04243
\(906\) 0 0
\(907\) −4.63923e7 −1.87253 −0.936263 0.351301i \(-0.885739\pi\)
−0.936263 + 0.351301i \(0.885739\pi\)
\(908\) 7.51455e7 3.02474
\(909\) 0 0
\(910\) 9.43818e7 3.77820
\(911\) 1.40524e7 0.560987 0.280494 0.959856i \(-0.409502\pi\)
0.280494 + 0.959856i \(0.409502\pi\)
\(912\) 0 0
\(913\) 1.94642e7 0.772785
\(914\) −2.20596e6 −0.0873439
\(915\) 0 0
\(916\) 7.24619e7 2.85345
\(917\) −5.53411e7 −2.17332
\(918\) 0 0
\(919\) 6.17102e6 0.241028 0.120514 0.992712i \(-0.461546\pi\)
0.120514 + 0.992712i \(0.461546\pi\)
\(920\) −1.68832e7 −0.657637
\(921\) 0 0
\(922\) 2.94941e7 1.14264
\(923\) 3.82806e6 0.147902
\(924\) 0 0
\(925\) 1.18447e7 0.455168
\(926\) 1.01624e7 0.389465
\(927\) 0 0
\(928\) −2.62062e7 −0.998930
\(929\) 4.76811e6 0.181262 0.0906310 0.995885i \(-0.471112\pi\)
0.0906310 + 0.995885i \(0.471112\pi\)
\(930\) 0 0
\(931\) −4.97118e7 −1.87969
\(932\) −6.53483e6 −0.246430
\(933\) 0 0
\(934\) 1.16047e7 0.435277
\(935\) 1.62375e7 0.607422
\(936\) 0 0
\(937\) −5.20047e6 −0.193506 −0.0967528 0.995308i \(-0.530846\pi\)
−0.0967528 + 0.995308i \(0.530846\pi\)
\(938\) −8.26264e6 −0.306628
\(939\) 0 0
\(940\) −1.08284e8 −3.99709
\(941\) 2.95702e7 1.08863 0.544316 0.838881i \(-0.316789\pi\)
0.544316 + 0.838881i \(0.316789\pi\)
\(942\) 0 0
\(943\) 3.49461e6 0.127973
\(944\) −8.27235e7 −3.02133
\(945\) 0 0
\(946\) −4.04127e7 −1.46822
\(947\) −3.00430e7 −1.08860 −0.544299 0.838891i \(-0.683204\pi\)
−0.544299 + 0.838891i \(0.683204\pi\)
\(948\) 0 0
\(949\) 7.65249e6 0.275827
\(950\) 3.65514e7 1.31400
\(951\) 0 0
\(952\) 1.26155e8 4.51142
\(953\) 2.08186e7 0.742540 0.371270 0.928525i \(-0.378922\pi\)
0.371270 + 0.928525i \(0.378922\pi\)
\(954\) 0 0
\(955\) −2.21805e7 −0.786979
\(956\) 1.07337e8 3.79844
\(957\) 0 0
\(958\) 9.06245e7 3.19030
\(959\) 2.73636e6 0.0960785
\(960\) 0 0
\(961\) 5.62749e7 1.96565
\(962\) −3.77501e7 −1.31517
\(963\) 0 0
\(964\) −1.03084e7 −0.357271
\(965\) −9.72226e6 −0.336085
\(966\) 0 0
\(967\) −1.35812e7 −0.467058 −0.233529 0.972350i \(-0.575027\pi\)
−0.233529 + 0.972350i \(0.575027\pi\)
\(968\) 5.90759e7 2.02639
\(969\) 0 0
\(970\) −1.11687e8 −3.81130
\(971\) −809935. −0.0275678 −0.0137839 0.999905i \(-0.504388\pi\)
−0.0137839 + 0.999905i \(0.504388\pi\)
\(972\) 0 0
\(973\) 1.88690e7 0.638951
\(974\) −4.74226e7 −1.60172
\(975\) 0 0
\(976\) −7.04703e7 −2.36800
\(977\) 5.74719e6 0.192628 0.0963140 0.995351i \(-0.469295\pi\)
0.0963140 + 0.995351i \(0.469295\pi\)
\(978\) 0 0
\(979\) 1.08381e7 0.361409
\(980\) 1.48639e8 4.94387
\(981\) 0 0
\(982\) 3.43771e7 1.13760
\(983\) −1.84120e7 −0.607740 −0.303870 0.952714i \(-0.598279\pi\)
−0.303870 + 0.952714i \(0.598279\pi\)
\(984\) 0 0
\(985\) −5.87432e7 −1.92915
\(986\) −4.16123e7 −1.36311
\(987\) 0 0
\(988\) −8.17176e7 −2.66332
\(989\) 1.21325e7 0.394422
\(990\) 0 0
\(991\) 1.13190e6 0.0366120 0.0183060 0.999832i \(-0.494173\pi\)
0.0183060 + 0.999832i \(0.494173\pi\)
\(992\) 8.03304e7 2.59180
\(993\) 0 0
\(994\) 1.38087e7 0.443289
\(995\) 4.66813e7 1.49481
\(996\) 0 0
\(997\) 3.72081e7 1.18549 0.592747 0.805389i \(-0.298043\pi\)
0.592747 + 0.805389i \(0.298043\pi\)
\(998\) −9.66631e7 −3.07209
\(999\) 0 0
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 207.6.a.i.1.1 yes 10
3.2 odd 2 207.6.a.h.1.10 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
207.6.a.h.1.10 10 3.2 odd 2
207.6.a.i.1.1 yes 10 1.1 even 1 trivial