Properties

Label 547.6.a.a.1.2
Level $547$
Weight $6$
Character 547.1
Self dual yes
Analytic conductor $87.730$
Analytic rank $1$
Dimension $111$
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: \(1\)
Dimension: \(111\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
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)
 
\(f(q)\) \(=\) \(q-11.1575 q^{2} -27.7524 q^{3} +92.4888 q^{4} -19.1317 q^{5} +309.646 q^{6} -173.776 q^{7} -674.902 q^{8} +527.195 q^{9} +O(q^{10})\) \(q-11.1575 q^{2} -27.7524 q^{3} +92.4888 q^{4} -19.1317 q^{5} +309.646 q^{6} -173.776 q^{7} -674.902 q^{8} +527.195 q^{9} +213.461 q^{10} -412.423 q^{11} -2566.79 q^{12} +68.8293 q^{13} +1938.90 q^{14} +530.951 q^{15} +4570.54 q^{16} -1218.00 q^{17} -5882.16 q^{18} +3087.57 q^{19} -1769.47 q^{20} +4822.70 q^{21} +4601.59 q^{22} -3329.84 q^{23} +18730.1 q^{24} -2758.98 q^{25} -767.960 q^{26} -7887.11 q^{27} -16072.3 q^{28} -8048.62 q^{29} -5924.06 q^{30} -537.597 q^{31} -29398.8 q^{32} +11445.7 q^{33} +13589.8 q^{34} +3324.63 q^{35} +48759.7 q^{36} -12341.0 q^{37} -34449.4 q^{38} -1910.18 q^{39} +12912.0 q^{40} +492.022 q^{41} -53809.1 q^{42} +3556.53 q^{43} -38144.5 q^{44} -10086.2 q^{45} +37152.6 q^{46} +9225.08 q^{47} -126844. q^{48} +13391.1 q^{49} +30783.2 q^{50} +33802.3 q^{51} +6365.94 q^{52} +33160.5 q^{53} +88000.0 q^{54} +7890.36 q^{55} +117282. q^{56} -85687.5 q^{57} +89802.1 q^{58} +29971.0 q^{59} +49107.1 q^{60} -11986.6 q^{61} +5998.22 q^{62} -91613.9 q^{63} +181758. q^{64} -1316.82 q^{65} -127705. q^{66} -2225.90 q^{67} -112651. q^{68} +92411.1 q^{69} -37094.5 q^{70} -83082.3 q^{71} -355805. q^{72} +27637.9 q^{73} +137694. q^{74} +76568.2 q^{75} +285566. q^{76} +71669.2 q^{77} +21312.7 q^{78} -23679.0 q^{79} -87442.4 q^{80} +90777.6 q^{81} -5489.71 q^{82} +43467.0 q^{83} +446046. q^{84} +23302.4 q^{85} -39681.8 q^{86} +223368. q^{87} +278345. q^{88} -58454.3 q^{89} +112536. q^{90} -11960.9 q^{91} -307973. q^{92} +14919.6 q^{93} -102928. q^{94} -59070.5 q^{95} +815887. q^{96} +74835.0 q^{97} -149410. q^{98} -217427. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 111 q - 28 q^{2} - 98 q^{3} + 1722 q^{4} - 801 q^{5} - 414 q^{6} - 587 q^{7} - 1344 q^{8} + 8241 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 111 q - 28 q^{2} - 98 q^{3} + 1722 q^{4} - 801 q^{5} - 414 q^{6} - 587 q^{7} - 1344 q^{8} + 8241 q^{9} - 950 q^{10} - 1832 q^{11} - 4143 q^{12} - 4369 q^{13} - 4777 q^{14} - 3487 q^{15} + 26274 q^{16} - 13648 q^{17} - 10269 q^{18} - 5446 q^{19} - 26032 q^{20} - 8428 q^{21} - 8248 q^{22} - 24142 q^{23} - 18577 q^{24} + 58062 q^{25} - 17656 q^{26} - 33269 q^{27} - 23512 q^{28} - 33752 q^{29} - 12418 q^{30} - 13781 q^{31} - 44076 q^{32} - 39186 q^{33} - 7207 q^{34} - 30833 q^{35} + 120044 q^{36} - 61582 q^{37} - 91259 q^{38} - 20077 q^{39} - 66032 q^{40} - 54181 q^{41} - 69252 q^{42} - 38600 q^{43} - 95712 q^{44} - 190880 q^{45} - 9354 q^{46} - 83886 q^{47} - 173886 q^{48} + 194148 q^{49} - 70896 q^{50} - 60673 q^{51} - 145186 q^{52} - 286874 q^{53} - 116519 q^{54} - 74821 q^{55} - 240407 q^{56} - 95180 q^{57} - 66900 q^{58} - 135740 q^{59} - 144550 q^{60} - 227450 q^{61} - 308766 q^{62} - 249721 q^{63} + 347514 q^{64} - 290374 q^{65} - 178980 q^{66} - 91006 q^{67} - 521943 q^{68} - 414510 q^{69} - 165057 q^{70} - 236165 q^{71} - 527945 q^{72} - 184618 q^{73} - 206443 q^{74} - 243897 q^{75} - 221676 q^{76} - 751131 q^{77} - 306839 q^{78} - 107446 q^{79} - 856691 q^{80} + 382187 q^{81} - 244614 q^{82} - 499547 q^{83} - 330289 q^{84} - 287103 q^{85} - 272441 q^{86} - 391281 q^{87} - 588937 q^{88} - 740774 q^{89} - 687179 q^{90} - 237213 q^{91} - 1367678 q^{92} - 754880 q^{93} - 32851 q^{94} - 295814 q^{95} - 816078 q^{96} - 320770 q^{97} - 661922 q^{98} - 547439 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −11.1575 −1.97238 −0.986189 0.165623i \(-0.947037\pi\)
−0.986189 + 0.165623i \(0.947037\pi\)
\(3\) −27.7524 −1.78032 −0.890159 0.455651i \(-0.849407\pi\)
−0.890159 + 0.455651i \(0.849407\pi\)
\(4\) 92.4888 2.89028
\(5\) −19.1317 −0.342239 −0.171119 0.985250i \(-0.554738\pi\)
−0.171119 + 0.985250i \(0.554738\pi\)
\(6\) 309.646 3.51146
\(7\) −173.776 −1.34043 −0.670216 0.742166i \(-0.733798\pi\)
−0.670216 + 0.742166i \(0.733798\pi\)
\(8\) −674.902 −3.72834
\(9\) 527.195 2.16953
\(10\) 213.461 0.675024
\(11\) −412.423 −1.02769 −0.513844 0.857884i \(-0.671779\pi\)
−0.513844 + 0.857884i \(0.671779\pi\)
\(12\) −2566.79 −5.14561
\(13\) 68.8293 0.112957 0.0564787 0.998404i \(-0.482013\pi\)
0.0564787 + 0.998404i \(0.482013\pi\)
\(14\) 1938.90 2.64384
\(15\) 530.951 0.609293
\(16\) 4570.54 4.46342
\(17\) −1218.00 −1.02217 −0.511086 0.859530i \(-0.670757\pi\)
−0.511086 + 0.859530i \(0.670757\pi\)
\(18\) −5882.16 −4.27913
\(19\) 3087.57 1.96215 0.981076 0.193621i \(-0.0620231\pi\)
0.981076 + 0.193621i \(0.0620231\pi\)
\(20\) −1769.47 −0.989164
\(21\) 4822.70 2.38639
\(22\) 4601.59 2.02699
\(23\) −3329.84 −1.31251 −0.656257 0.754537i \(-0.727861\pi\)
−0.656257 + 0.754537i \(0.727861\pi\)
\(24\) 18730.1 6.63763
\(25\) −2758.98 −0.882873
\(26\) −767.960 −0.222795
\(27\) −7887.11 −2.08213
\(28\) −16072.3 −3.87422
\(29\) −8048.62 −1.77716 −0.888579 0.458723i \(-0.848307\pi\)
−0.888579 + 0.458723i \(0.848307\pi\)
\(30\) −5924.06 −1.20176
\(31\) −537.597 −0.100474 −0.0502369 0.998737i \(-0.515998\pi\)
−0.0502369 + 0.998737i \(0.515998\pi\)
\(32\) −29398.8 −5.07522
\(33\) 11445.7 1.82961
\(34\) 13589.8 2.01611
\(35\) 3324.63 0.458747
\(36\) 48759.7 6.27054
\(37\) −12341.0 −1.48199 −0.740994 0.671511i \(-0.765645\pi\)
−0.740994 + 0.671511i \(0.765645\pi\)
\(38\) −34449.4 −3.87011
\(39\) −1910.18 −0.201100
\(40\) 12912.0 1.27598
\(41\) 492.022 0.0457114 0.0228557 0.999739i \(-0.492724\pi\)
0.0228557 + 0.999739i \(0.492724\pi\)
\(42\) −53809.1 −4.70687
\(43\) 3556.53 0.293329 0.146665 0.989186i \(-0.453146\pi\)
0.146665 + 0.989186i \(0.453146\pi\)
\(44\) −38144.5 −2.97030
\(45\) −10086.2 −0.742497
\(46\) 37152.6 2.58878
\(47\) 9225.08 0.609152 0.304576 0.952488i \(-0.401485\pi\)
0.304576 + 0.952488i \(0.401485\pi\)
\(48\) −126844. −7.94631
\(49\) 13391.1 0.796756
\(50\) 30783.2 1.74136
\(51\) 33802.3 1.81979
\(52\) 6365.94 0.326478
\(53\) 33160.5 1.62155 0.810777 0.585355i \(-0.199045\pi\)
0.810777 + 0.585355i \(0.199045\pi\)
\(54\) 88000.0 4.10675
\(55\) 7890.36 0.351714
\(56\) 117282. 4.99758
\(57\) −85687.5 −3.49325
\(58\) 89802.1 3.50523
\(59\) 29971.0 1.12091 0.560456 0.828184i \(-0.310626\pi\)
0.560456 + 0.828184i \(0.310626\pi\)
\(60\) 49107.1 1.76103
\(61\) −11986.6 −0.412451 −0.206225 0.978504i \(-0.566118\pi\)
−0.206225 + 0.978504i \(0.566118\pi\)
\(62\) 5998.22 0.198172
\(63\) −91613.9 −2.90810
\(64\) 181758. 5.54682
\(65\) −1316.82 −0.0386584
\(66\) −127705. −3.60868
\(67\) −2225.90 −0.0605784 −0.0302892 0.999541i \(-0.509643\pi\)
−0.0302892 + 0.999541i \(0.509643\pi\)
\(68\) −112651. −2.95436
\(69\) 92411.1 2.33669
\(70\) −37094.5 −0.904823
\(71\) −83082.3 −1.95597 −0.977986 0.208669i \(-0.933087\pi\)
−0.977986 + 0.208669i \(0.933087\pi\)
\(72\) −355805. −8.08874
\(73\) 27637.9 0.607014 0.303507 0.952829i \(-0.401842\pi\)
0.303507 + 0.952829i \(0.401842\pi\)
\(74\) 137694. 2.92304
\(75\) 76568.2 1.57179
\(76\) 285566. 5.67116
\(77\) 71669.2 1.37754
\(78\) 21312.7 0.396645
\(79\) −23679.0 −0.426871 −0.213435 0.976957i \(-0.568465\pi\)
−0.213435 + 0.976957i \(0.568465\pi\)
\(80\) −87442.4 −1.52756
\(81\) 90777.6 1.53733
\(82\) −5489.71 −0.0901602
\(83\) 43467.0 0.692572 0.346286 0.938129i \(-0.387443\pi\)
0.346286 + 0.938129i \(0.387443\pi\)
\(84\) 446046. 6.89733
\(85\) 23302.4 0.349827
\(86\) −39681.8 −0.578556
\(87\) 223368. 3.16391
\(88\) 278345. 3.83157
\(89\) −58454.3 −0.782242 −0.391121 0.920339i \(-0.627913\pi\)
−0.391121 + 0.920339i \(0.627913\pi\)
\(90\) 112536. 1.46448
\(91\) −11960.9 −0.151412
\(92\) −307973. −3.79353
\(93\) 14919.6 0.178875
\(94\) −102928. −1.20148
\(95\) −59070.5 −0.671525
\(96\) 815887. 9.03549
\(97\) 74835.0 0.807562 0.403781 0.914856i \(-0.367696\pi\)
0.403781 + 0.914856i \(0.367696\pi\)
\(98\) −149410. −1.57150
\(99\) −217427. −2.22960
\(100\) −255175. −2.55175
\(101\) 106882. 1.04256 0.521280 0.853386i \(-0.325455\pi\)
0.521280 + 0.853386i \(0.325455\pi\)
\(102\) −377148. −3.58932
\(103\) 163475. 1.51830 0.759152 0.650913i \(-0.225614\pi\)
0.759152 + 0.650913i \(0.225614\pi\)
\(104\) −46453.0 −0.421144
\(105\) −92266.5 −0.816716
\(106\) −369987. −3.19832
\(107\) 131515. 1.11050 0.555248 0.831685i \(-0.312623\pi\)
0.555248 + 0.831685i \(0.312623\pi\)
\(108\) −729469. −6.01794
\(109\) 130163. 1.04935 0.524674 0.851303i \(-0.324187\pi\)
0.524674 + 0.851303i \(0.324187\pi\)
\(110\) −88036.3 −0.693714
\(111\) 342491. 2.63841
\(112\) −794251. −5.98291
\(113\) 136226. 1.00360 0.501802 0.864982i \(-0.332671\pi\)
0.501802 + 0.864982i \(0.332671\pi\)
\(114\) 956054. 6.89002
\(115\) 63705.6 0.449193
\(116\) −744407. −5.13648
\(117\) 36286.5 0.245064
\(118\) −334400. −2.21086
\(119\) 211659. 1.37015
\(120\) −358340. −2.27165
\(121\) 9041.53 0.0561408
\(122\) 133740. 0.813509
\(123\) −13654.8 −0.0813808
\(124\) −49721.7 −0.290397
\(125\) 112571. 0.644392
\(126\) 1.02218e6 5.73588
\(127\) 75340.2 0.414493 0.207247 0.978289i \(-0.433550\pi\)
0.207247 + 0.978289i \(0.433550\pi\)
\(128\) −1.08720e6 −5.86522
\(129\) −98702.3 −0.522219
\(130\) 14692.4 0.0762490
\(131\) 343851. 1.75062 0.875310 0.483563i \(-0.160658\pi\)
0.875310 + 0.483563i \(0.160658\pi\)
\(132\) 1.05860e6 5.28808
\(133\) −536545. −2.63013
\(134\) 24835.3 0.119484
\(135\) 150894. 0.712586
\(136\) 822029. 3.81101
\(137\) −25000.1 −0.113800 −0.0568998 0.998380i \(-0.518122\pi\)
−0.0568998 + 0.998380i \(0.518122\pi\)
\(138\) −1.03107e6 −4.60884
\(139\) 33948.3 0.149033 0.0745163 0.997220i \(-0.476259\pi\)
0.0745163 + 0.997220i \(0.476259\pi\)
\(140\) 307491. 1.32591
\(141\) −256018. −1.08448
\(142\) 926987. 3.85792
\(143\) −28386.8 −0.116085
\(144\) 2.40957e6 9.68352
\(145\) 153984. 0.608212
\(146\) −308369. −1.19726
\(147\) −371635. −1.41848
\(148\) −1.14140e6 −4.28336
\(149\) −180925. −0.667625 −0.333812 0.942640i \(-0.608335\pi\)
−0.333812 + 0.942640i \(0.608335\pi\)
\(150\) −854307. −3.10017
\(151\) −233727. −0.834192 −0.417096 0.908862i \(-0.636952\pi\)
−0.417096 + 0.908862i \(0.636952\pi\)
\(152\) −2.08381e6 −7.31557
\(153\) −642123. −2.21763
\(154\) −799645. −2.71704
\(155\) 10285.2 0.0343860
\(156\) −176670. −0.581235
\(157\) 119878. 0.388142 0.194071 0.980988i \(-0.437831\pi\)
0.194071 + 0.980988i \(0.437831\pi\)
\(158\) 264198. 0.841951
\(159\) −920284. −2.88688
\(160\) 562450. 1.73694
\(161\) 578647. 1.75934
\(162\) −1.01285e6 −3.03219
\(163\) 304780. 0.898497 0.449249 0.893407i \(-0.351692\pi\)
0.449249 + 0.893407i \(0.351692\pi\)
\(164\) 45506.5 0.132119
\(165\) −218976. −0.626163
\(166\) −484982. −1.36601
\(167\) −340121. −0.943719 −0.471859 0.881674i \(-0.656417\pi\)
−0.471859 + 0.881674i \(0.656417\pi\)
\(168\) −3.25485e6 −8.89728
\(169\) −366556. −0.987241
\(170\) −259995. −0.689991
\(171\) 1.62775e6 4.25695
\(172\) 328939. 0.847803
\(173\) −100831. −0.256141 −0.128070 0.991765i \(-0.540878\pi\)
−0.128070 + 0.991765i \(0.540878\pi\)
\(174\) −2.49222e6 −6.24042
\(175\) 479444. 1.18343
\(176\) −1.88500e6 −4.58700
\(177\) −831767. −1.99558
\(178\) 652201. 1.54288
\(179\) −149128. −0.347878 −0.173939 0.984756i \(-0.555650\pi\)
−0.173939 + 0.984756i \(0.555650\pi\)
\(180\) −932857. −2.14602
\(181\) −380740. −0.863838 −0.431919 0.901912i \(-0.642163\pi\)
−0.431919 + 0.901912i \(0.642163\pi\)
\(182\) 133453. 0.298641
\(183\) 332658. 0.734294
\(184\) 2.24732e6 4.89350
\(185\) 236104. 0.507194
\(186\) −166465. −0.352809
\(187\) 502330. 1.05047
\(188\) 853217. 1.76062
\(189\) 1.37059e6 2.79095
\(190\) 659077. 1.32450
\(191\) 335347. 0.665138 0.332569 0.943079i \(-0.392085\pi\)
0.332569 + 0.943079i \(0.392085\pi\)
\(192\) −5.04423e6 −9.87511
\(193\) 489983. 0.946863 0.473432 0.880831i \(-0.343015\pi\)
0.473432 + 0.880831i \(0.343015\pi\)
\(194\) −834969. −1.59282
\(195\) 36545.0 0.0688242
\(196\) 1.23853e6 2.30285
\(197\) 40123.1 0.0736596 0.0368298 0.999322i \(-0.488274\pi\)
0.0368298 + 0.999322i \(0.488274\pi\)
\(198\) 2.42594e6 4.39761
\(199\) 160586. 0.287458 0.143729 0.989617i \(-0.454091\pi\)
0.143729 + 0.989617i \(0.454091\pi\)
\(200\) 1.86204e6 3.29165
\(201\) 61773.9 0.107849
\(202\) −1.19253e6 −2.05632
\(203\) 1.39866e6 2.38216
\(204\) 3.12634e6 5.25970
\(205\) −9413.23 −0.0156442
\(206\) −1.82397e6 −2.99467
\(207\) −1.75548e6 −2.84754
\(208\) 314587. 0.504177
\(209\) −1.27338e6 −2.01648
\(210\) 1.02946e6 1.61087
\(211\) −415141. −0.641932 −0.320966 0.947091i \(-0.604008\pi\)
−0.320966 + 0.947091i \(0.604008\pi\)
\(212\) 3.06698e6 4.68674
\(213\) 2.30573e6 3.48225
\(214\) −1.46738e6 −2.19032
\(215\) −68042.6 −0.100389
\(216\) 5.32302e6 7.76290
\(217\) 93421.4 0.134678
\(218\) −1.45228e6 −2.06971
\(219\) −767019. −1.08068
\(220\) 729770. 1.01655
\(221\) −83833.9 −0.115462
\(222\) −3.82133e6 −5.20394
\(223\) 775825. 1.04472 0.522362 0.852724i \(-0.325051\pi\)
0.522362 + 0.852724i \(0.325051\pi\)
\(224\) 5.10880e6 6.80298
\(225\) −1.45452e6 −1.91542
\(226\) −1.51993e6 −1.97949
\(227\) 35942.4 0.0462959 0.0231479 0.999732i \(-0.492631\pi\)
0.0231479 + 0.999732i \(0.492631\pi\)
\(228\) −7.92514e6 −10.0965
\(229\) −271606. −0.342256 −0.171128 0.985249i \(-0.554741\pi\)
−0.171128 + 0.985249i \(0.554741\pi\)
\(230\) −710793. −0.885979
\(231\) −1.98899e6 −2.45246
\(232\) 5.43202e6 6.62585
\(233\) 786471. 0.949058 0.474529 0.880240i \(-0.342618\pi\)
0.474529 + 0.880240i \(0.342618\pi\)
\(234\) −404865. −0.483360
\(235\) −176492. −0.208475
\(236\) 2.77198e6 3.23974
\(237\) 657150. 0.759965
\(238\) −2.36157e6 −2.70246
\(239\) 153700. 0.174052 0.0870260 0.996206i \(-0.472264\pi\)
0.0870260 + 0.996206i \(0.472264\pi\)
\(240\) 2.42674e6 2.71953
\(241\) 1.20367e6 1.33494 0.667472 0.744634i \(-0.267376\pi\)
0.667472 + 0.744634i \(0.267376\pi\)
\(242\) −100880. −0.110731
\(243\) −602729. −0.654796
\(244\) −1.10863e6 −1.19210
\(245\) −256194. −0.272681
\(246\) 152353. 0.160514
\(247\) 212515. 0.221640
\(248\) 362825. 0.374600
\(249\) −1.20631e6 −1.23300
\(250\) −1.25600e6 −1.27098
\(251\) 35391.8 0.0354583 0.0177292 0.999843i \(-0.494356\pi\)
0.0177292 + 0.999843i \(0.494356\pi\)
\(252\) −8.47326e6 −8.40523
\(253\) 1.37330e6 1.34885
\(254\) −840605. −0.817538
\(255\) −646697. −0.622803
\(256\) 6.31412e6 6.02161
\(257\) 49319.0 0.0465781 0.0232891 0.999729i \(-0.492586\pi\)
0.0232891 + 0.999729i \(0.492586\pi\)
\(258\) 1.10127e6 1.03001
\(259\) 2.14456e6 1.98650
\(260\) −121791. −0.111733
\(261\) −4.24319e6 −3.85560
\(262\) −3.83650e6 −3.45288
\(263\) −1.68990e6 −1.50651 −0.753254 0.657730i \(-0.771517\pi\)
−0.753254 + 0.657730i \(0.771517\pi\)
\(264\) −7.72474e6 −6.82140
\(265\) −634418. −0.554959
\(266\) 5.98648e6 5.18761
\(267\) 1.62225e6 1.39264
\(268\) −205870. −0.175088
\(269\) −1.26446e6 −1.06543 −0.532716 0.846294i \(-0.678829\pi\)
−0.532716 + 0.846294i \(0.678829\pi\)
\(270\) −1.68359e6 −1.40549
\(271\) 107918. 0.0892630 0.0446315 0.999004i \(-0.485789\pi\)
0.0446315 + 0.999004i \(0.485789\pi\)
\(272\) −5.56691e6 −4.56239
\(273\) 331943. 0.269561
\(274\) 278938. 0.224456
\(275\) 1.13786e6 0.907317
\(276\) 8.54700e6 6.75369
\(277\) −2.33180e6 −1.82596 −0.912981 0.408003i \(-0.866225\pi\)
−0.912981 + 0.408003i \(0.866225\pi\)
\(278\) −378777. −0.293949
\(279\) −283419. −0.217981
\(280\) −2.24380e6 −1.71037
\(281\) −920487. −0.695428 −0.347714 0.937601i \(-0.613042\pi\)
−0.347714 + 0.937601i \(0.613042\pi\)
\(282\) 2.85651e6 2.13901
\(283\) −182579. −0.135514 −0.0677570 0.997702i \(-0.521584\pi\)
−0.0677570 + 0.997702i \(0.521584\pi\)
\(284\) −7.68419e6 −5.65330
\(285\) 1.63935e6 1.19553
\(286\) 316724. 0.228963
\(287\) −85501.6 −0.0612730
\(288\) −1.54989e7 −11.0108
\(289\) 63660.5 0.0448359
\(290\) −1.71807e6 −1.19962
\(291\) −2.07685e6 −1.43772
\(292\) 2.55620e6 1.75444
\(293\) −1.82416e6 −1.24135 −0.620673 0.784069i \(-0.713141\pi\)
−0.620673 + 0.784069i \(0.713141\pi\)
\(294\) 4.14650e6 2.79778
\(295\) −573397. −0.383619
\(296\) 8.32894e6 5.52536
\(297\) 3.25282e6 2.13978
\(298\) 2.01866e6 1.31681
\(299\) −229191. −0.148258
\(300\) 7.08171e6 4.54292
\(301\) −618040. −0.393188
\(302\) 2.60780e6 1.64534
\(303\) −2.96623e6 −1.85609
\(304\) 1.41119e7 8.75792
\(305\) 229325. 0.141157
\(306\) 7.16446e6 4.37401
\(307\) 2.88314e6 1.74590 0.872951 0.487808i \(-0.162203\pi\)
0.872951 + 0.487808i \(0.162203\pi\)
\(308\) 6.62860e6 3.98148
\(309\) −4.53683e6 −2.70306
\(310\) −114756. −0.0678222
\(311\) 2.79704e6 1.63983 0.819913 0.572488i \(-0.194022\pi\)
0.819913 + 0.572488i \(0.194022\pi\)
\(312\) 1.28918e6 0.749770
\(313\) −1.12104e6 −0.646788 −0.323394 0.946264i \(-0.604824\pi\)
−0.323394 + 0.946264i \(0.604824\pi\)
\(314\) −1.33753e6 −0.765562
\(315\) 1.75273e6 0.995266
\(316\) −2.19005e6 −1.23377
\(317\) −762781. −0.426336 −0.213168 0.977016i \(-0.568378\pi\)
−0.213168 + 0.977016i \(0.568378\pi\)
\(318\) 1.02680e7 5.69402
\(319\) 3.31943e6 1.82636
\(320\) −3.47735e6 −1.89834
\(321\) −3.64987e6 −1.97704
\(322\) −6.45623e6 −3.47008
\(323\) −3.76065e6 −2.00566
\(324\) 8.39591e6 4.44330
\(325\) −189898. −0.0997271
\(326\) −3.40056e6 −1.77218
\(327\) −3.61232e6 −1.86817
\(328\) −332066. −0.170428
\(329\) −1.60310e6 −0.816526
\(330\) 2.44322e6 1.23503
\(331\) 1.60937e6 0.807397 0.403699 0.914892i \(-0.367724\pi\)
0.403699 + 0.914892i \(0.367724\pi\)
\(332\) 4.02022e6 2.00172
\(333\) −6.50610e6 −3.21522
\(334\) 3.79489e6 1.86137
\(335\) 42585.2 0.0207323
\(336\) 2.20424e7 10.6515
\(337\) −448429. −0.215090 −0.107545 0.994200i \(-0.534299\pi\)
−0.107545 + 0.994200i \(0.534299\pi\)
\(338\) 4.08983e6 1.94721
\(339\) −3.78059e6 −1.78673
\(340\) 2.15521e6 1.01110
\(341\) 221717. 0.103256
\(342\) −1.81616e7 −8.39631
\(343\) 593605. 0.272435
\(344\) −2.40031e6 −1.09363
\(345\) −1.76798e6 −0.799707
\(346\) 1.12502e6 0.505206
\(347\) 763023. 0.340184 0.170092 0.985428i \(-0.445594\pi\)
0.170092 + 0.985428i \(0.445594\pi\)
\(348\) 2.06591e7 9.14456
\(349\) −2.24983e6 −0.988748 −0.494374 0.869249i \(-0.664603\pi\)
−0.494374 + 0.869249i \(0.664603\pi\)
\(350\) −5.34937e6 −2.33417
\(351\) −542864. −0.235192
\(352\) 1.21247e7 5.21573
\(353\) −1.25844e6 −0.537522 −0.268761 0.963207i \(-0.586614\pi\)
−0.268761 + 0.963207i \(0.586614\pi\)
\(354\) 9.28041e6 3.93603
\(355\) 1.58951e6 0.669409
\(356\) −5.40637e6 −2.26090
\(357\) −5.87403e6 −2.43930
\(358\) 1.66389e6 0.686147
\(359\) −1.81972e6 −0.745194 −0.372597 0.927993i \(-0.621533\pi\)
−0.372597 + 0.927993i \(0.621533\pi\)
\(360\) 6.80717e6 2.76828
\(361\) 7.05699e6 2.85004
\(362\) 4.24809e6 1.70382
\(363\) −250924. −0.0999484
\(364\) −1.10625e6 −0.437622
\(365\) −528761. −0.207744
\(366\) −3.71161e6 −1.44830
\(367\) 3.95001e6 1.53085 0.765426 0.643524i \(-0.222528\pi\)
0.765426 + 0.643524i \(0.222528\pi\)
\(368\) −1.52192e7 −5.85831
\(369\) 259392. 0.0991723
\(370\) −2.63432e6 −1.00038
\(371\) −5.76250e6 −2.17358
\(372\) 1.37990e6 0.516999
\(373\) 2.65077e6 0.986505 0.493252 0.869886i \(-0.335808\pi\)
0.493252 + 0.869886i \(0.335808\pi\)
\(374\) −5.60472e6 −2.07193
\(375\) −3.12410e6 −1.14722
\(376\) −6.22602e6 −2.27113
\(377\) −553981. −0.200743
\(378\) −1.52923e7 −5.50482
\(379\) −987497. −0.353133 −0.176566 0.984289i \(-0.556499\pi\)
−0.176566 + 0.984289i \(0.556499\pi\)
\(380\) −5.46337e6 −1.94089
\(381\) −2.09087e6 −0.737930
\(382\) −3.74162e6 −1.31190
\(383\) 2.77254e6 0.965787 0.482893 0.875679i \(-0.339586\pi\)
0.482893 + 0.875679i \(0.339586\pi\)
\(384\) 3.01724e7 10.4420
\(385\) −1.37115e6 −0.471449
\(386\) −5.46696e6 −1.86757
\(387\) 1.87499e6 0.636386
\(388\) 6.92141e6 2.33408
\(389\) −1.22855e6 −0.411642 −0.205821 0.978590i \(-0.565987\pi\)
−0.205821 + 0.978590i \(0.565987\pi\)
\(390\) −407749. −0.135747
\(391\) 4.05574e6 1.34162
\(392\) −9.03766e6 −2.97058
\(393\) −9.54268e6 −3.11666
\(394\) −447672. −0.145285
\(395\) 453021. 0.146092
\(396\) −2.01096e7 −6.44415
\(397\) −628198. −0.200042 −0.100021 0.994985i \(-0.531891\pi\)
−0.100021 + 0.994985i \(0.531891\pi\)
\(398\) −1.79173e6 −0.566975
\(399\) 1.48904e7 4.68247
\(400\) −1.26100e7 −3.94063
\(401\) −504475. −0.156667 −0.0783337 0.996927i \(-0.524960\pi\)
−0.0783337 + 0.996927i \(0.524960\pi\)
\(402\) −689240. −0.212719
\(403\) −37002.4 −0.0113493
\(404\) 9.88539e6 3.01329
\(405\) −1.73673e6 −0.526132
\(406\) −1.56054e7 −4.69852
\(407\) 5.08970e6 1.52302
\(408\) −2.28133e7 −6.78480
\(409\) 292189. 0.0863687 0.0431843 0.999067i \(-0.486250\pi\)
0.0431843 + 0.999067i \(0.486250\pi\)
\(410\) 105028. 0.0308563
\(411\) 693813. 0.202599
\(412\) 1.51196e7 4.38832
\(413\) −5.20824e6 −1.50250
\(414\) 1.95867e7 5.61642
\(415\) −831600. −0.237025
\(416\) −2.02350e6 −0.573284
\(417\) −942147. −0.265325
\(418\) 1.42077e7 3.97726
\(419\) 811721. 0.225877 0.112938 0.993602i \(-0.463974\pi\)
0.112938 + 0.993602i \(0.463974\pi\)
\(420\) −8.53363e6 −2.36053
\(421\) −607784. −0.167126 −0.0835631 0.996502i \(-0.526630\pi\)
−0.0835631 + 0.996502i \(0.526630\pi\)
\(422\) 4.63192e6 1.26613
\(423\) 4.86342e6 1.32157
\(424\) −2.23801e7 −6.04571
\(425\) 3.36043e6 0.902448
\(426\) −2.57261e7 −6.86832
\(427\) 2.08299e6 0.552862
\(428\) 1.21637e7 3.20964
\(429\) 787801. 0.206668
\(430\) 759182. 0.198004
\(431\) 4.05571e6 1.05166 0.525828 0.850591i \(-0.323756\pi\)
0.525828 + 0.850591i \(0.323756\pi\)
\(432\) −3.60484e7 −9.29343
\(433\) −1.44028e6 −0.369171 −0.184585 0.982817i \(-0.559094\pi\)
−0.184585 + 0.982817i \(0.559094\pi\)
\(434\) −1.04235e6 −0.265636
\(435\) −4.27342e6 −1.08281
\(436\) 1.20386e7 3.03291
\(437\) −1.02811e7 −2.57535
\(438\) 8.55798e6 2.13150
\(439\) −4.89840e6 −1.21309 −0.606545 0.795049i \(-0.707445\pi\)
−0.606545 + 0.795049i \(0.707445\pi\)
\(440\) −5.32522e6 −1.31131
\(441\) 7.05972e6 1.72859
\(442\) 935373. 0.227735
\(443\) −6.73786e6 −1.63122 −0.815611 0.578601i \(-0.803599\pi\)
−0.815611 + 0.578601i \(0.803599\pi\)
\(444\) 3.16766e7 7.62573
\(445\) 1.11833e6 0.267714
\(446\) −8.65624e6 −2.06059
\(447\) 5.02110e6 1.18858
\(448\) −3.15852e7 −7.43514
\(449\) 3.90647e6 0.914468 0.457234 0.889347i \(-0.348840\pi\)
0.457234 + 0.889347i \(0.348840\pi\)
\(450\) 1.62287e7 3.77793
\(451\) −202921. −0.0469771
\(452\) 1.25993e7 2.90069
\(453\) 6.48648e6 1.48513
\(454\) −401025. −0.0913129
\(455\) 228832. 0.0518189
\(456\) 5.78306e7 13.0240
\(457\) −7.34036e6 −1.64409 −0.822047 0.569419i \(-0.807168\pi\)
−0.822047 + 0.569419i \(0.807168\pi\)
\(458\) 3.03044e6 0.675059
\(459\) 9.60647e6 2.12830
\(460\) 5.89206e6 1.29829
\(461\) 4.09372e6 0.897152 0.448576 0.893745i \(-0.351931\pi\)
0.448576 + 0.893745i \(0.351931\pi\)
\(462\) 2.21921e7 4.83719
\(463\) 3.96085e6 0.858689 0.429345 0.903141i \(-0.358745\pi\)
0.429345 + 0.903141i \(0.358745\pi\)
\(464\) −3.67865e7 −7.93221
\(465\) −285438. −0.0612180
\(466\) −8.77501e6 −1.87190
\(467\) 1.63277e6 0.346444 0.173222 0.984883i \(-0.444582\pi\)
0.173222 + 0.984883i \(0.444582\pi\)
\(468\) 3.35610e6 0.708304
\(469\) 386807. 0.0812012
\(470\) 1.96920e6 0.411192
\(471\) −3.32690e6 −0.691015
\(472\) −2.02275e7 −4.17914
\(473\) −1.46679e6 −0.301451
\(474\) −7.33213e6 −1.49894
\(475\) −8.51854e6 −1.73233
\(476\) 1.95761e7 3.96012
\(477\) 1.74821e7 3.51801
\(478\) −1.71490e6 −0.343296
\(479\) 2.91116e6 0.579732 0.289866 0.957067i \(-0.406389\pi\)
0.289866 + 0.957067i \(0.406389\pi\)
\(480\) −1.56093e7 −3.09230
\(481\) −849420. −0.167402
\(482\) −1.34299e7 −2.63302
\(483\) −1.60588e7 −3.13218
\(484\) 836240. 0.162262
\(485\) −1.43172e6 −0.276379
\(486\) 6.72492e6 1.29151
\(487\) −2.89689e6 −0.553490 −0.276745 0.960943i \(-0.589256\pi\)
−0.276745 + 0.960943i \(0.589256\pi\)
\(488\) 8.08979e6 1.53776
\(489\) −8.45836e6 −1.59961
\(490\) 2.85848e6 0.537830
\(491\) −2.70718e6 −0.506773 −0.253386 0.967365i \(-0.581544\pi\)
−0.253386 + 0.967365i \(0.581544\pi\)
\(492\) −1.26292e6 −0.235213
\(493\) 9.80319e6 1.81656
\(494\) −2.37113e6 −0.437158
\(495\) 4.15976e6 0.763054
\(496\) −2.45711e6 −0.448457
\(497\) 1.44377e7 2.62185
\(498\) 1.34594e7 2.43194
\(499\) −330570. −0.0594308 −0.0297154 0.999558i \(-0.509460\pi\)
−0.0297154 + 0.999558i \(0.509460\pi\)
\(500\) 1.04115e7 1.86247
\(501\) 9.43918e6 1.68012
\(502\) −394882. −0.0699372
\(503\) 494040. 0.0870646 0.0435323 0.999052i \(-0.486139\pi\)
0.0435323 + 0.999052i \(0.486139\pi\)
\(504\) 6.18304e7 10.8424
\(505\) −2.04484e6 −0.356804
\(506\) −1.53226e7 −2.66045
\(507\) 1.01728e7 1.75760
\(508\) 6.96813e6 1.19800
\(509\) −3.92159e6 −0.670915 −0.335457 0.942055i \(-0.608891\pi\)
−0.335457 + 0.942055i \(0.608891\pi\)
\(510\) 7.21550e6 1.22840
\(511\) −4.80281e6 −0.813660
\(512\) −3.56591e7 −6.01167
\(513\) −2.43520e7 −4.08546
\(514\) −550275. −0.0918696
\(515\) −3.12756e6 −0.519623
\(516\) −9.12886e6 −1.50936
\(517\) −3.80463e6 −0.626018
\(518\) −2.39279e7 −3.91814
\(519\) 2.79830e6 0.456011
\(520\) 888726. 0.144132
\(521\) −5.05932e6 −0.816578 −0.408289 0.912853i \(-0.633875\pi\)
−0.408289 + 0.912853i \(0.633875\pi\)
\(522\) 4.73433e7 7.60470
\(523\) 3.22834e6 0.516090 0.258045 0.966133i \(-0.416922\pi\)
0.258045 + 0.966133i \(0.416922\pi\)
\(524\) 3.18024e7 5.05977
\(525\) −1.33057e7 −2.10688
\(526\) 1.88550e7 2.97140
\(527\) 654792. 0.102701
\(528\) 5.23132e7 8.16632
\(529\) 4.65151e6 0.722695
\(530\) 7.07849e6 1.09459
\(531\) 1.58006e7 2.43185
\(532\) −4.96245e7 −7.60181
\(533\) 33865.5 0.00516345
\(534\) −1.81001e7 −2.74681
\(535\) −2.51612e6 −0.380055
\(536\) 1.50226e6 0.225857
\(537\) 4.13867e6 0.619334
\(538\) 1.41082e7 2.10143
\(539\) −5.52279e6 −0.818816
\(540\) 1.39560e7 2.05957
\(541\) −2.41717e6 −0.355071 −0.177535 0.984114i \(-0.556812\pi\)
−0.177535 + 0.984114i \(0.556812\pi\)
\(542\) −1.20409e6 −0.176060
\(543\) 1.05665e7 1.53791
\(544\) 3.58076e7 5.18774
\(545\) −2.49023e6 −0.359128
\(546\) −3.70364e6 −0.531676
\(547\) −299209. −0.0427569
\(548\) −2.31223e6 −0.328912
\(549\) −6.31929e6 −0.894824
\(550\) −1.26957e7 −1.78957
\(551\) −2.48507e7 −3.48706
\(552\) −6.23684e7 −8.71199
\(553\) 4.11485e6 0.572191
\(554\) 2.60169e7 3.60149
\(555\) −6.55245e6 −0.902966
\(556\) 3.13984e6 0.430745
\(557\) −891752. −0.121788 −0.0608942 0.998144i \(-0.519395\pi\)
−0.0608942 + 0.998144i \(0.519395\pi\)
\(558\) 3.16223e6 0.429940
\(559\) 244794. 0.0331337
\(560\) 1.51954e7 2.04758
\(561\) −1.39409e7 −1.87018
\(562\) 1.02703e7 1.37165
\(563\) 1.21958e7 1.62158 0.810792 0.585335i \(-0.199037\pi\)
0.810792 + 0.585335i \(0.199037\pi\)
\(564\) −2.36788e7 −3.13446
\(565\) −2.60623e6 −0.343472
\(566\) 2.03712e6 0.267285
\(567\) −1.57750e7 −2.06068
\(568\) 5.60724e7 7.29253
\(569\) −17154.0 −0.00222119 −0.00111059 0.999999i \(-0.500354\pi\)
−0.00111059 + 0.999999i \(0.500354\pi\)
\(570\) −1.82910e7 −2.35803
\(571\) 2.64958e6 0.340085 0.170042 0.985437i \(-0.445610\pi\)
0.170042 + 0.985437i \(0.445610\pi\)
\(572\) −2.62546e6 −0.335518
\(573\) −9.30670e6 −1.18416
\(574\) 953980. 0.120854
\(575\) 9.18696e6 1.15878
\(576\) 9.58222e7 12.0340
\(577\) −8.44674e6 −1.05621 −0.528104 0.849180i \(-0.677097\pi\)
−0.528104 + 0.849180i \(0.677097\pi\)
\(578\) −710290. −0.0884333
\(579\) −1.35982e7 −1.68572
\(580\) 1.42418e7 1.75790
\(581\) −7.55353e6 −0.928345
\(582\) 2.31724e7 2.83572
\(583\) −1.36761e7 −1.66645
\(584\) −1.86529e7 −2.26315
\(585\) −694223. −0.0838705
\(586\) 2.03530e7 2.44841
\(587\) −458654. −0.0549402 −0.0274701 0.999623i \(-0.508745\pi\)
−0.0274701 + 0.999623i \(0.508745\pi\)
\(588\) −3.43720e7 −4.09979
\(589\) −1.65987e6 −0.197145
\(590\) 6.39765e6 0.756642
\(591\) −1.11351e6 −0.131137
\(592\) −5.64049e7 −6.61474
\(593\) −7.42864e6 −0.867506 −0.433753 0.901032i \(-0.642811\pi\)
−0.433753 + 0.901032i \(0.642811\pi\)
\(594\) −3.62932e7 −4.22046
\(595\) −4.04939e6 −0.468919
\(596\) −1.67335e7 −1.92962
\(597\) −4.45664e6 −0.511766
\(598\) 2.55719e6 0.292422
\(599\) −1.04362e7 −1.18843 −0.594216 0.804305i \(-0.702538\pi\)
−0.594216 + 0.804305i \(0.702538\pi\)
\(600\) −5.16760e7 −5.86018
\(601\) 2.64233e6 0.298401 0.149201 0.988807i \(-0.452330\pi\)
0.149201 + 0.988807i \(0.452330\pi\)
\(602\) 6.89575e6 0.775515
\(603\) −1.17348e6 −0.131427
\(604\) −2.16171e7 −2.41105
\(605\) −172980. −0.0192135
\(606\) 3.30956e7 3.66091
\(607\) 6.72243e6 0.740550 0.370275 0.928922i \(-0.379263\pi\)
0.370275 + 0.928922i \(0.379263\pi\)
\(608\) −9.07708e7 −9.95835
\(609\) −3.88160e7 −4.24100
\(610\) −2.55868e6 −0.278414
\(611\) 634956. 0.0688083
\(612\) −5.93892e7 −6.40957
\(613\) −1.84145e7 −1.97928 −0.989641 0.143562i \(-0.954144\pi\)
−0.989641 + 0.143562i \(0.954144\pi\)
\(614\) −3.21685e7 −3.44358
\(615\) 261240. 0.0278517
\(616\) −4.83696e7 −5.13595
\(617\) 1.35918e7 1.43735 0.718675 0.695346i \(-0.244749\pi\)
0.718675 + 0.695346i \(0.244749\pi\)
\(618\) 5.06195e7 5.33146
\(619\) 1.12109e7 1.17602 0.588009 0.808855i \(-0.299912\pi\)
0.588009 + 0.808855i \(0.299912\pi\)
\(620\) 951262. 0.0993851
\(621\) 2.62628e7 2.73283
\(622\) −3.12079e7 −3.23436
\(623\) 1.01579e7 1.04854
\(624\) −8.73055e6 −0.897595
\(625\) 6.46813e6 0.662337
\(626\) 1.25080e7 1.27571
\(627\) 3.53395e7 3.58997
\(628\) 1.10874e7 1.12184
\(629\) 1.50313e7 1.51485
\(630\) −1.95560e7 −1.96304
\(631\) 7.62809e6 0.762680 0.381340 0.924435i \(-0.375463\pi\)
0.381340 + 0.924435i \(0.375463\pi\)
\(632\) 1.59810e7 1.59152
\(633\) 1.15212e7 1.14284
\(634\) 8.51070e6 0.840896
\(635\) −1.44139e6 −0.141856
\(636\) −8.51160e7 −8.34388
\(637\) 921698. 0.0899995
\(638\) −3.70364e7 −3.60228
\(639\) −4.38006e7 −4.24354
\(640\) 2.08000e7 2.00731
\(641\) 1.83128e7 1.76039 0.880196 0.474611i \(-0.157411\pi\)
0.880196 + 0.474611i \(0.157411\pi\)
\(642\) 4.07233e7 3.89946
\(643\) 1.91637e6 0.182790 0.0913950 0.995815i \(-0.470867\pi\)
0.0913950 + 0.995815i \(0.470867\pi\)
\(644\) 5.35184e7 5.08497
\(645\) 1.88834e6 0.178724
\(646\) 4.19593e7 3.95592
\(647\) 3.57012e6 0.335291 0.167646 0.985847i \(-0.446384\pi\)
0.167646 + 0.985847i \(0.446384\pi\)
\(648\) −6.12659e7 −5.73168
\(649\) −1.23607e7 −1.15195
\(650\) 2.11878e6 0.196699
\(651\) −2.59267e6 −0.239770
\(652\) 2.81887e7 2.59691
\(653\) −4.41723e6 −0.405385 −0.202692 0.979242i \(-0.564969\pi\)
−0.202692 + 0.979242i \(0.564969\pi\)
\(654\) 4.03043e7 3.68475
\(655\) −6.57846e6 −0.599130
\(656\) 2.24881e6 0.204029
\(657\) 1.45706e7 1.31693
\(658\) 1.78865e7 1.61050
\(659\) −424525. −0.0380794 −0.0190397 0.999819i \(-0.506061\pi\)
−0.0190397 + 0.999819i \(0.506061\pi\)
\(660\) −2.02529e7 −1.80978
\(661\) 5.28141e6 0.470161 0.235080 0.971976i \(-0.424465\pi\)
0.235080 + 0.971976i \(0.424465\pi\)
\(662\) −1.79565e7 −1.59249
\(663\) 2.32659e6 0.205559
\(664\) −2.93360e7 −2.58214
\(665\) 1.02650e7 0.900133
\(666\) 7.25916e7 6.34162
\(667\) 2.68006e7 2.33255
\(668\) −3.14574e7 −2.72761
\(669\) −2.15310e7 −1.85994
\(670\) −475143. −0.0408919
\(671\) 4.94356e6 0.423871
\(672\) −1.41782e8 −12.1115
\(673\) −1.33158e7 −1.13326 −0.566631 0.823972i \(-0.691753\pi\)
−0.566631 + 0.823972i \(0.691753\pi\)
\(674\) 5.00333e6 0.424238
\(675\) 2.17603e7 1.83826
\(676\) −3.39023e7 −2.85340
\(677\) 5.07423e6 0.425499 0.212750 0.977107i \(-0.431758\pi\)
0.212750 + 0.977107i \(0.431758\pi\)
\(678\) 4.21817e7 3.52411
\(679\) −1.30045e7 −1.08248
\(680\) −1.57268e7 −1.30427
\(681\) −997487. −0.0824213
\(682\) −2.47380e6 −0.203659
\(683\) −1.06491e7 −0.873496 −0.436748 0.899584i \(-0.643870\pi\)
−0.436748 + 0.899584i \(0.643870\pi\)
\(684\) 1.50549e8 12.3038
\(685\) 478295. 0.0389466
\(686\) −6.62312e6 −0.537344
\(687\) 7.53773e6 0.609324
\(688\) 1.62553e7 1.30925
\(689\) 2.28241e6 0.183167
\(690\) 1.97262e7 1.57732
\(691\) −9.29758e6 −0.740755 −0.370378 0.928881i \(-0.620772\pi\)
−0.370378 + 0.928881i \(0.620772\pi\)
\(692\) −9.32573e6 −0.740317
\(693\) 3.77837e7 2.98862
\(694\) −8.51339e6 −0.670971
\(695\) −649490. −0.0510047
\(696\) −1.50752e8 −11.7961
\(697\) −599281. −0.0467250
\(698\) 2.51024e7 1.95019
\(699\) −2.18264e7 −1.68962
\(700\) 4.43432e7 3.42044
\(701\) 2.43226e7 1.86946 0.934729 0.355361i \(-0.115642\pi\)
0.934729 + 0.355361i \(0.115642\pi\)
\(702\) 6.05698e6 0.463888
\(703\) −3.81036e7 −2.90789
\(704\) −7.49613e7 −5.70040
\(705\) 4.89807e6 0.371152
\(706\) 1.40410e7 1.06020
\(707\) −1.85735e7 −1.39748
\(708\) −7.69292e7 −5.76777
\(709\) 1.61653e7 1.20772 0.603862 0.797089i \(-0.293628\pi\)
0.603862 + 0.797089i \(0.293628\pi\)
\(710\) −1.77349e7 −1.32033
\(711\) −1.24835e7 −0.926108
\(712\) 3.94509e7 2.91647
\(713\) 1.79011e6 0.131873
\(714\) 6.55393e7 4.81123
\(715\) 543088. 0.0397288
\(716\) −1.37927e7 −1.00546
\(717\) −4.26554e6 −0.309868
\(718\) 2.03035e7 1.46981
\(719\) −2.51635e7 −1.81530 −0.907652 0.419723i \(-0.862127\pi\)
−0.907652 + 0.419723i \(0.862127\pi\)
\(720\) −4.60992e7 −3.31408
\(721\) −2.84081e7 −2.03518
\(722\) −7.87381e7 −5.62137
\(723\) −3.34046e7 −2.37663
\(724\) −3.52142e7 −2.49673
\(725\) 2.22059e7 1.56900
\(726\) 2.79967e6 0.197136
\(727\) −1.21831e7 −0.854913 −0.427457 0.904036i \(-0.640590\pi\)
−0.427457 + 0.904036i \(0.640590\pi\)
\(728\) 8.07242e6 0.564514
\(729\) −5.33179e6 −0.371582
\(730\) 5.89963e6 0.409749
\(731\) −4.33185e6 −0.299833
\(732\) 3.07671e7 2.12231
\(733\) 1.20161e7 0.826046 0.413023 0.910721i \(-0.364473\pi\)
0.413023 + 0.910721i \(0.364473\pi\)
\(734\) −4.40721e7 −3.01942
\(735\) 7.11001e6 0.485458
\(736\) 9.78934e7 6.66130
\(737\) 918010. 0.0622556
\(738\) −2.89415e6 −0.195605
\(739\) −4.56003e6 −0.307154 −0.153577 0.988137i \(-0.549079\pi\)
−0.153577 + 0.988137i \(0.549079\pi\)
\(740\) 2.18370e7 1.46593
\(741\) −5.89781e6 −0.394589
\(742\) 6.42948e7 4.28713
\(743\) 1.05670e7 0.702233 0.351116 0.936332i \(-0.385802\pi\)
0.351116 + 0.936332i \(0.385802\pi\)
\(744\) −1.00693e7 −0.666907
\(745\) 3.46140e6 0.228487
\(746\) −2.95758e7 −1.94576
\(747\) 2.29156e7 1.50255
\(748\) 4.64599e7 3.03616
\(749\) −2.28542e7 −1.48854
\(750\) 3.48571e7 2.26276
\(751\) −1.31974e7 −0.853865 −0.426933 0.904283i \(-0.640406\pi\)
−0.426933 + 0.904283i \(0.640406\pi\)
\(752\) 4.21636e7 2.71890
\(753\) −982206. −0.0631270
\(754\) 6.18101e6 0.395942
\(755\) 4.47160e6 0.285493
\(756\) 1.26764e8 8.06663
\(757\) −3.35942e6 −0.213071 −0.106535 0.994309i \(-0.533976\pi\)
−0.106535 + 0.994309i \(0.533976\pi\)
\(758\) 1.10180e7 0.696511
\(759\) −3.81125e7 −2.40139
\(760\) 3.98668e7 2.50367
\(761\) 1.18755e7 0.743342 0.371671 0.928365i \(-0.378785\pi\)
0.371671 + 0.928365i \(0.378785\pi\)
\(762\) 2.33288e7 1.45548
\(763\) −2.26191e7 −1.40658
\(764\) 3.10159e7 1.92243
\(765\) 1.22849e7 0.758959
\(766\) −3.09345e7 −1.90490
\(767\) 2.06288e6 0.126615
\(768\) −1.75232e8 −10.7204
\(769\) 2.63124e7 1.60452 0.802260 0.596975i \(-0.203631\pi\)
0.802260 + 0.596975i \(0.203631\pi\)
\(770\) 1.52986e7 0.929875
\(771\) −1.36872e6 −0.0829238
\(772\) 4.53179e7 2.73670
\(773\) 6.59751e6 0.397129 0.198564 0.980088i \(-0.436372\pi\)
0.198564 + 0.980088i \(0.436372\pi\)
\(774\) −2.09201e7 −1.25519
\(775\) 1.48322e6 0.0887055
\(776\) −5.05063e7 −3.01086
\(777\) −5.95168e7 −3.53661
\(778\) 1.37075e7 0.811915
\(779\) 1.51915e6 0.0896928
\(780\) 3.38000e6 0.198921
\(781\) 3.42650e7 2.01013
\(782\) −4.52518e7 −2.64617
\(783\) 6.34803e7 3.70028
\(784\) 6.12045e7 3.55626
\(785\) −2.29347e6 −0.132837
\(786\) 1.06472e8 6.14723
\(787\) 2.24658e7 1.29296 0.646481 0.762930i \(-0.276240\pi\)
0.646481 + 0.762930i \(0.276240\pi\)
\(788\) 3.71094e6 0.212896
\(789\) 4.68988e7 2.68206
\(790\) −5.05456e6 −0.288148
\(791\) −2.36727e7 −1.34526
\(792\) 1.46742e8 8.31270
\(793\) −825031. −0.0465894
\(794\) 7.00909e6 0.394558
\(795\) 1.76066e7 0.988002
\(796\) 1.48524e7 0.830832
\(797\) −1.47289e7 −0.821344 −0.410672 0.911783i \(-0.634706\pi\)
−0.410672 + 0.911783i \(0.634706\pi\)
\(798\) −1.66139e8 −9.23560
\(799\) −1.12361e7 −0.622658
\(800\) 8.11106e7 4.48077
\(801\) −3.08168e7 −1.69710
\(802\) 5.62866e6 0.309007
\(803\) −1.13985e7 −0.623820
\(804\) 5.71340e6 0.311713
\(805\) −1.10705e7 −0.602113
\(806\) 412853. 0.0223850
\(807\) 3.50919e7 1.89681
\(808\) −7.21348e7 −3.88702
\(809\) −8.37974e6 −0.450152 −0.225076 0.974341i \(-0.572263\pi\)
−0.225076 + 0.974341i \(0.572263\pi\)
\(810\) 1.93775e7 1.03773
\(811\) 3.13647e7 1.67451 0.837257 0.546809i \(-0.184158\pi\)
0.837257 + 0.546809i \(0.184158\pi\)
\(812\) 1.29360e8 6.88510
\(813\) −2.99499e6 −0.158916
\(814\) −5.67881e7 −3.00397
\(815\) −5.83096e6 −0.307501
\(816\) 1.54495e8 8.12249
\(817\) 1.09810e7 0.575557
\(818\) −3.26009e6 −0.170352
\(819\) −6.30572e6 −0.328492
\(820\) −870619. −0.0452161
\(821\) 1.31639e7 0.681594 0.340797 0.940137i \(-0.389303\pi\)
0.340797 + 0.940137i \(0.389303\pi\)
\(822\) −7.74119e6 −0.399603
\(823\) −2.47626e7 −1.27437 −0.637187 0.770709i \(-0.719902\pi\)
−0.637187 + 0.770709i \(0.719902\pi\)
\(824\) −1.10330e8 −5.66076
\(825\) −3.15785e7 −1.61531
\(826\) 5.81107e7 2.96351
\(827\) −1.56468e7 −0.795539 −0.397770 0.917485i \(-0.630216\pi\)
−0.397770 + 0.917485i \(0.630216\pi\)
\(828\) −1.62362e8 −8.23017
\(829\) −3.67510e7 −1.85730 −0.928652 0.370951i \(-0.879032\pi\)
−0.928652 + 0.370951i \(0.879032\pi\)
\(830\) 9.27854e6 0.467503
\(831\) 6.47130e7 3.25079
\(832\) 1.25103e7 0.626555
\(833\) −1.63103e7 −0.814422
\(834\) 1.05120e7 0.523322
\(835\) 6.50711e6 0.322977
\(836\) −1.17774e8 −5.82818
\(837\) 4.24008e6 0.209200
\(838\) −9.05674e6 −0.445515
\(839\) 1.31090e7 0.642931 0.321466 0.946921i \(-0.395825\pi\)
0.321466 + 0.946921i \(0.395825\pi\)
\(840\) 6.22708e7 3.04499
\(841\) 4.42691e7 2.15829
\(842\) 6.78133e6 0.329636
\(843\) 2.55457e7 1.23808
\(844\) −3.83959e7 −1.85536
\(845\) 7.01284e6 0.337872
\(846\) −5.42634e7 −2.60664
\(847\) −1.57120e6 −0.0752528
\(848\) 1.51562e8 7.23768
\(849\) 5.06700e6 0.241258
\(850\) −3.74938e7 −1.77997
\(851\) 4.10935e7 1.94513
\(852\) 2.13255e8 10.0647
\(853\) 2.86732e7 1.34928 0.674641 0.738146i \(-0.264298\pi\)
0.674641 + 0.738146i \(0.264298\pi\)
\(854\) −2.32408e7 −1.09045
\(855\) −3.11417e7 −1.45689
\(856\) −8.87600e7 −4.14031
\(857\) 2.23024e7 1.03729 0.518644 0.854990i \(-0.326437\pi\)
0.518644 + 0.854990i \(0.326437\pi\)
\(858\) −8.78985e6 −0.407627
\(859\) −3.25219e7 −1.50381 −0.751905 0.659271i \(-0.770865\pi\)
−0.751905 + 0.659271i \(0.770865\pi\)
\(860\) −6.29318e6 −0.290151
\(861\) 2.37287e6 0.109085
\(862\) −4.52514e7 −2.07426
\(863\) −2.35901e7 −1.07821 −0.539104 0.842239i \(-0.681237\pi\)
−0.539104 + 0.842239i \(0.681237\pi\)
\(864\) 2.31871e8 10.5673
\(865\) 1.92907e6 0.0876612
\(866\) 1.60699e7 0.728144
\(867\) −1.76673e6 −0.0798221
\(868\) 8.64044e6 0.389257
\(869\) 9.76578e6 0.438690
\(870\) 4.76805e7 2.13571
\(871\) −153207. −0.00684278
\(872\) −8.78470e7 −3.91233
\(873\) 3.94527e7 1.75203
\(874\) 1.14711e8 5.07957
\(875\) −1.95621e7 −0.863763
\(876\) −7.09407e7 −3.12345
\(877\) −3.50444e7 −1.53858 −0.769290 0.638900i \(-0.779390\pi\)
−0.769290 + 0.638900i \(0.779390\pi\)
\(878\) 5.46537e7 2.39267
\(879\) 5.06247e7 2.20999
\(880\) 3.60632e7 1.56985
\(881\) 2.88177e6 0.125089 0.0625446 0.998042i \(-0.480078\pi\)
0.0625446 + 0.998042i \(0.480078\pi\)
\(882\) −7.87685e7 −3.40942
\(883\) −3.10076e7 −1.33834 −0.669170 0.743110i \(-0.733350\pi\)
−0.669170 + 0.743110i \(0.733350\pi\)
\(884\) −7.75370e6 −0.333717
\(885\) 1.59131e7 0.682964
\(886\) 7.51774e7 3.21739
\(887\) −3.08394e7 −1.31612 −0.658062 0.752964i \(-0.728624\pi\)
−0.658062 + 0.752964i \(0.728624\pi\)
\(888\) −2.31148e8 −9.83689
\(889\) −1.30923e7 −0.555600
\(890\) −1.24777e7 −0.528032
\(891\) −3.74387e7 −1.57989
\(892\) 7.17552e7 3.01954
\(893\) 2.84831e7 1.19525
\(894\) −5.60227e7 −2.34434
\(895\) 2.85308e6 0.119057
\(896\) 1.88929e8 7.86193
\(897\) 6.36059e6 0.263947
\(898\) −4.35862e7 −1.80368
\(899\) 4.32691e6 0.178558
\(900\) −1.34527e8 −5.53609
\(901\) −4.03894e7 −1.65751
\(902\) 2.26408e6 0.0926565
\(903\) 1.71521e7 0.699999
\(904\) −9.19389e7 −3.74178
\(905\) 7.28422e6 0.295639
\(906\) −7.23726e7 −2.92923
\(907\) 1.08662e7 0.438591 0.219296 0.975658i \(-0.429624\pi\)
0.219296 + 0.975658i \(0.429624\pi\)
\(908\) 3.32427e6 0.133808
\(909\) 5.63477e7 2.26186
\(910\) −2.55318e6 −0.102207
\(911\) 4.02309e7 1.60607 0.803034 0.595933i \(-0.203217\pi\)
0.803034 + 0.595933i \(0.203217\pi\)
\(912\) −3.91638e8 −15.5919
\(913\) −1.79268e7 −0.711747
\(914\) 8.18997e7 3.24278
\(915\) −6.36431e6 −0.251304
\(916\) −2.51206e7 −0.989215
\(917\) −5.97530e7 −2.34658
\(918\) −1.07184e8 −4.19781
\(919\) 1.70270e7 0.665043 0.332521 0.943096i \(-0.392101\pi\)
0.332521 + 0.943096i \(0.392101\pi\)
\(920\) −4.29950e7 −1.67475
\(921\) −8.00141e7 −3.10826
\(922\) −4.56755e7 −1.76952
\(923\) −5.71850e6 −0.220942
\(924\) −1.83959e8 −7.08830
\(925\) 3.40484e7 1.30841
\(926\) −4.41930e7 −1.69366
\(927\) 8.61834e7 3.29401
\(928\) 2.36620e8 9.01946
\(929\) 1.01384e7 0.385416 0.192708 0.981256i \(-0.438273\pi\)
0.192708 + 0.981256i \(0.438273\pi\)
\(930\) 3.18476e6 0.120745
\(931\) 4.13459e7 1.56336
\(932\) 7.27398e7 2.74304
\(933\) −7.76246e7 −2.91941
\(934\) −1.82176e7 −0.683318
\(935\) −9.61044e6 −0.359513
\(936\) −2.44898e7 −0.913684
\(937\) −3.63635e7 −1.35306 −0.676529 0.736416i \(-0.736517\pi\)
−0.676529 + 0.736416i \(0.736517\pi\)
\(938\) −4.31578e6 −0.160159
\(939\) 3.11117e7 1.15149
\(940\) −1.63235e7 −0.602551
\(941\) 8.48490e6 0.312372 0.156186 0.987728i \(-0.450080\pi\)
0.156186 + 0.987728i \(0.450080\pi\)
\(942\) 3.71198e7 1.36294
\(943\) −1.63836e6 −0.0599969
\(944\) 1.36984e8 5.00310
\(945\) −2.62217e7 −0.955173
\(946\) 1.63657e7 0.594575
\(947\) 246640. 0.00893693 0.00446847 0.999990i \(-0.498578\pi\)
0.00446847 + 0.999990i \(0.498578\pi\)
\(948\) 6.07791e7 2.19651
\(949\) 1.90230e6 0.0685667
\(950\) 9.50452e7 3.41681
\(951\) 2.11690e7 0.759013
\(952\) −1.42849e8 −5.10839
\(953\) 1.84803e6 0.0659137 0.0329569 0.999457i \(-0.489508\pi\)
0.0329569 + 0.999457i \(0.489508\pi\)
\(954\) −1.95055e8 −6.93884
\(955\) −6.41577e6 −0.227636
\(956\) 1.42155e7 0.503058
\(957\) −9.21222e7 −3.25151
\(958\) −3.24811e7 −1.14345
\(959\) 4.34442e6 0.152541
\(960\) 9.65048e7 3.37964
\(961\) −2.83401e7 −0.989905
\(962\) 9.47737e6 0.330179
\(963\) 6.93344e7 2.40925
\(964\) 1.11326e8 3.85836
\(965\) −9.37421e6 −0.324053
\(966\) 1.79176e8 6.17784
\(967\) −3.71164e7 −1.27644 −0.638219 0.769855i \(-0.720329\pi\)
−0.638219 + 0.769855i \(0.720329\pi\)
\(968\) −6.10214e6 −0.209312
\(969\) 1.04367e8 3.57071
\(970\) 1.59744e7 0.545124
\(971\) 5.58644e7 1.90146 0.950730 0.310020i \(-0.100336\pi\)
0.950730 + 0.310020i \(0.100336\pi\)
\(972\) −5.57457e7 −1.89254
\(973\) −5.89940e6 −0.199768
\(974\) 3.23219e7 1.09169
\(975\) 5.27014e6 0.177546
\(976\) −5.47854e7 −1.84094
\(977\) 1.89734e7 0.635930 0.317965 0.948102i \(-0.397000\pi\)
0.317965 + 0.948102i \(0.397000\pi\)
\(978\) 9.43738e7 3.15504
\(979\) 2.41079e7 0.803900
\(980\) −2.36951e7 −0.788123
\(981\) 6.86211e7 2.27659
\(982\) 3.02052e7 0.999548
\(983\) −4.34136e7 −1.43299 −0.716494 0.697593i \(-0.754254\pi\)
−0.716494 + 0.697593i \(0.754254\pi\)
\(984\) 9.21564e6 0.303416
\(985\) −767624. −0.0252092
\(986\) −1.09379e8 −3.58295
\(987\) 4.44898e7 1.45368
\(988\) 1.96553e7 0.640600
\(989\) −1.18427e7 −0.384999
\(990\) −4.64124e7 −1.50503
\(991\) −8.70314e6 −0.281509 −0.140754 0.990045i \(-0.544953\pi\)
−0.140754 + 0.990045i \(0.544953\pi\)
\(992\) 1.58047e7 0.509926
\(993\) −4.46640e7 −1.43742
\(994\) −1.61088e8 −5.17127
\(995\) −3.07228e6 −0.0983791
\(996\) −1.11571e8 −3.56370
\(997\) 2.13851e7 0.681355 0.340678 0.940180i \(-0.389344\pi\)
0.340678 + 0.940180i \(0.389344\pi\)
\(998\) 3.68832e6 0.117220
\(999\) 9.73345e7 3.08570
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.a.1.2 111
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
547.6.a.a.1.2 111 1.1 even 1 trivial