Properties

Label 547.6.a.a.1.18
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 1.18
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)
 
\(f(q)\) \(=\) \(q-8.25035 q^{2} -30.3390 q^{3} +36.0683 q^{4} -26.4241 q^{5} +250.308 q^{6} -114.994 q^{7} -33.5649 q^{8} +677.458 q^{9} +O(q^{10})\) \(q-8.25035 q^{2} -30.3390 q^{3} +36.0683 q^{4} -26.4241 q^{5} +250.308 q^{6} -114.994 q^{7} -33.5649 q^{8} +677.458 q^{9} +218.008 q^{10} +428.707 q^{11} -1094.28 q^{12} -862.728 q^{13} +948.740 q^{14} +801.681 q^{15} -877.263 q^{16} -1332.74 q^{17} -5589.26 q^{18} -1168.30 q^{19} -953.071 q^{20} +3488.81 q^{21} -3536.99 q^{22} +1386.99 q^{23} +1018.33 q^{24} -2426.77 q^{25} +7117.81 q^{26} -13181.0 q^{27} -4147.64 q^{28} +3554.81 q^{29} -6614.15 q^{30} -4864.80 q^{31} +8311.81 q^{32} -13006.6 q^{33} +10995.6 q^{34} +3038.61 q^{35} +24434.7 q^{36} +11319.1 q^{37} +9638.88 q^{38} +26174.4 q^{39} +886.921 q^{40} -16580.8 q^{41} -28783.9 q^{42} -15275.3 q^{43} +15462.7 q^{44} -17901.2 q^{45} -11443.1 q^{46} +20901.7 q^{47} +26615.3 q^{48} -3583.40 q^{49} +20021.7 q^{50} +40434.1 q^{51} -31117.1 q^{52} +10132.7 q^{53} +108748. q^{54} -11328.2 q^{55} +3859.76 q^{56} +35445.1 q^{57} -29328.4 q^{58} -9394.76 q^{59} +28915.3 q^{60} +19966.7 q^{61} +40136.3 q^{62} -77903.5 q^{63} -40502.9 q^{64} +22796.8 q^{65} +107309. q^{66} -24684.5 q^{67} -48069.7 q^{68} -42079.9 q^{69} -25069.6 q^{70} +48422.0 q^{71} -22738.8 q^{72} +19511.6 q^{73} -93386.8 q^{74} +73625.8 q^{75} -42138.6 q^{76} -49298.7 q^{77} -215948. q^{78} +68131.6 q^{79} +23180.9 q^{80} +235278. q^{81} +136798. q^{82} -60589.1 q^{83} +125835. q^{84} +35216.4 q^{85} +126026. q^{86} -107849. q^{87} -14389.5 q^{88} +61096.0 q^{89} +147691. q^{90} +99208.5 q^{91} +50026.3 q^{92} +147594. q^{93} -172446. q^{94} +30871.2 q^{95} -252172. q^{96} +97304.7 q^{97} +29564.3 q^{98} +290431. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 111 q - 28 q^{2} - 98 q^{3} + 1722 q^{4} - 801 q^{5} - 414 q^{6} - 587 q^{7} - 1344 q^{8} + 8241 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −8.25035 −1.45847 −0.729235 0.684263i \(-0.760124\pi\)
−0.729235 + 0.684263i \(0.760124\pi\)
\(3\) −30.3390 −1.94625 −0.973125 0.230276i \(-0.926037\pi\)
−0.973125 + 0.230276i \(0.926037\pi\)
\(4\) 36.0683 1.12713
\(5\) −26.4241 −0.472688 −0.236344 0.971669i \(-0.575949\pi\)
−0.236344 + 0.971669i \(0.575949\pi\)
\(6\) 250.308 2.83855
\(7\) −114.994 −0.887013 −0.443506 0.896271i \(-0.646266\pi\)
−0.443506 + 0.896271i \(0.646266\pi\)
\(8\) −33.5649 −0.185422
\(9\) 677.458 2.78789
\(10\) 218.008 0.689401
\(11\) 428.707 1.06827 0.534133 0.845401i \(-0.320638\pi\)
0.534133 + 0.845401i \(0.320638\pi\)
\(12\) −1094.28 −2.19369
\(13\) −862.728 −1.41584 −0.707922 0.706290i \(-0.750367\pi\)
−0.707922 + 0.706290i \(0.750367\pi\)
\(14\) 948.740 1.29368
\(15\) 801.681 0.919969
\(16\) −877.263 −0.856702
\(17\) −1332.74 −1.11847 −0.559234 0.829010i \(-0.688905\pi\)
−0.559234 + 0.829010i \(0.688905\pi\)
\(18\) −5589.26 −4.06606
\(19\) −1168.30 −0.742455 −0.371227 0.928542i \(-0.621063\pi\)
−0.371227 + 0.928542i \(0.621063\pi\)
\(20\) −953.071 −0.532783
\(21\) 3488.81 1.72635
\(22\) −3536.99 −1.55803
\(23\) 1386.99 0.546705 0.273352 0.961914i \(-0.411867\pi\)
0.273352 + 0.961914i \(0.411867\pi\)
\(24\) 1018.33 0.360877
\(25\) −2426.77 −0.776566
\(26\) 7117.81 2.06497
\(27\) −13181.0 −3.47968
\(28\) −4147.64 −0.999782
\(29\) 3554.81 0.784912 0.392456 0.919771i \(-0.371626\pi\)
0.392456 + 0.919771i \(0.371626\pi\)
\(30\) −6614.15 −1.34175
\(31\) −4864.80 −0.909204 −0.454602 0.890695i \(-0.650218\pi\)
−0.454602 + 0.890695i \(0.650218\pi\)
\(32\) 8311.81 1.43490
\(33\) −13006.6 −2.07911
\(34\) 10995.6 1.63125
\(35\) 3038.61 0.419280
\(36\) 24434.7 3.14233
\(37\) 11319.1 1.35928 0.679640 0.733546i \(-0.262136\pi\)
0.679640 + 0.733546i \(0.262136\pi\)
\(38\) 9638.88 1.08285
\(39\) 26174.4 2.75559
\(40\) 886.921 0.0876466
\(41\) −16580.8 −1.54044 −0.770222 0.637775i \(-0.779855\pi\)
−0.770222 + 0.637775i \(0.779855\pi\)
\(42\) −28783.9 −2.51783
\(43\) −15275.3 −1.25985 −0.629924 0.776657i \(-0.716914\pi\)
−0.629924 + 0.776657i \(0.716914\pi\)
\(44\) 15462.7 1.20408
\(45\) −17901.2 −1.31780
\(46\) −11443.1 −0.797353
\(47\) 20901.7 1.38018 0.690092 0.723722i \(-0.257570\pi\)
0.690092 + 0.723722i \(0.257570\pi\)
\(48\) 26615.3 1.66736
\(49\) −3583.40 −0.213209
\(50\) 20021.7 1.13260
\(51\) 40434.1 2.17682
\(52\) −31117.1 −1.59585
\(53\) 10132.7 0.495491 0.247745 0.968825i \(-0.420310\pi\)
0.247745 + 0.968825i \(0.420310\pi\)
\(54\) 108748. 5.07501
\(55\) −11328.2 −0.504956
\(56\) 3859.76 0.164471
\(57\) 35445.1 1.44500
\(58\) −29328.4 −1.14477
\(59\) −9394.76 −0.351363 −0.175681 0.984447i \(-0.556213\pi\)
−0.175681 + 0.984447i \(0.556213\pi\)
\(60\) 28915.3 1.03693
\(61\) 19966.7 0.687039 0.343519 0.939146i \(-0.388381\pi\)
0.343519 + 0.939146i \(0.388381\pi\)
\(62\) 40136.3 1.32605
\(63\) −77903.5 −2.47289
\(64\) −40502.9 −1.23605
\(65\) 22796.8 0.669253
\(66\) 107309. 3.03232
\(67\) −24684.5 −0.671796 −0.335898 0.941898i \(-0.609040\pi\)
−0.335898 + 0.941898i \(0.609040\pi\)
\(68\) −48069.7 −1.26066
\(69\) −42079.9 −1.06402
\(70\) −25069.6 −0.611508
\(71\) 48422.0 1.13998 0.569989 0.821652i \(-0.306947\pi\)
0.569989 + 0.821652i \(0.306947\pi\)
\(72\) −22738.8 −0.516935
\(73\) 19511.6 0.428534 0.214267 0.976775i \(-0.431264\pi\)
0.214267 + 0.976775i \(0.431264\pi\)
\(74\) −93386.8 −1.98247
\(75\) 73625.8 1.51139
\(76\) −42138.6 −0.836846
\(77\) −49298.7 −0.947565
\(78\) −215948. −4.01894
\(79\) 68131.6 1.22823 0.614117 0.789215i \(-0.289512\pi\)
0.614117 + 0.789215i \(0.289512\pi\)
\(80\) 23180.9 0.404953
\(81\) 235278. 3.98445
\(82\) 136798. 2.24669
\(83\) −60589.1 −0.965381 −0.482691 0.875791i \(-0.660340\pi\)
−0.482691 + 0.875791i \(0.660340\pi\)
\(84\) 125835. 1.94583
\(85\) 35216.4 0.528686
\(86\) 126026. 1.83745
\(87\) −107849. −1.52764
\(88\) −14389.5 −0.198080
\(89\) 61096.0 0.817594 0.408797 0.912625i \(-0.365948\pi\)
0.408797 + 0.912625i \(0.365948\pi\)
\(90\) 147691. 1.92198
\(91\) 99208.5 1.25587
\(92\) 50026.3 0.616210
\(93\) 147594. 1.76954
\(94\) −172446. −2.01296
\(95\) 30871.2 0.350949
\(96\) −252172. −2.79267
\(97\) 97304.7 1.05004 0.525018 0.851091i \(-0.324058\pi\)
0.525018 + 0.851091i \(0.324058\pi\)
\(98\) 29564.3 0.310958
\(99\) 290431. 2.97821
\(100\) −87529.4 −0.875294
\(101\) 127737. 1.24599 0.622995 0.782226i \(-0.285916\pi\)
0.622995 + 0.782226i \(0.285916\pi\)
\(102\) −333595. −3.17482
\(103\) −57338.3 −0.532540 −0.266270 0.963899i \(-0.585791\pi\)
−0.266270 + 0.963899i \(0.585791\pi\)
\(104\) 28957.4 0.262528
\(105\) −92188.4 −0.816024
\(106\) −83598.3 −0.722658
\(107\) 79789.8 0.673734 0.336867 0.941552i \(-0.390633\pi\)
0.336867 + 0.941552i \(0.390633\pi\)
\(108\) −475417. −3.92207
\(109\) 91310.2 0.736128 0.368064 0.929801i \(-0.380021\pi\)
0.368064 + 0.929801i \(0.380021\pi\)
\(110\) 93461.5 0.736463
\(111\) −343411. −2.64550
\(112\) 100880. 0.759906
\(113\) −158647. −1.16879 −0.584393 0.811471i \(-0.698667\pi\)
−0.584393 + 0.811471i \(0.698667\pi\)
\(114\) −292434. −2.10749
\(115\) −36649.9 −0.258421
\(116\) 128216. 0.884701
\(117\) −584462. −3.94722
\(118\) 77510.0 0.512452
\(119\) 153257. 0.992095
\(120\) −26908.3 −0.170582
\(121\) 22738.9 0.141191
\(122\) −164732. −1.00203
\(123\) 503046. 2.99809
\(124\) −175465. −1.02479
\(125\) 146700. 0.839761
\(126\) 642731. 3.60664
\(127\) −213325. −1.17363 −0.586815 0.809721i \(-0.699619\pi\)
−0.586815 + 0.809721i \(0.699619\pi\)
\(128\) 68185.4 0.367846
\(129\) 463437. 2.45198
\(130\) −188082. −0.976085
\(131\) 303669. 1.54604 0.773022 0.634379i \(-0.218744\pi\)
0.773022 + 0.634379i \(0.218744\pi\)
\(132\) −469125. −2.34344
\(133\) 134347. 0.658567
\(134\) 203656. 0.979794
\(135\) 348296. 1.64480
\(136\) 44733.3 0.207388
\(137\) −318846. −1.45138 −0.725688 0.688024i \(-0.758478\pi\)
−0.725688 + 0.688024i \(0.758478\pi\)
\(138\) 347174. 1.55185
\(139\) 42137.1 0.184981 0.0924907 0.995714i \(-0.470517\pi\)
0.0924907 + 0.995714i \(0.470517\pi\)
\(140\) 109597. 0.472585
\(141\) −634137. −2.68618
\(142\) −399498. −1.66262
\(143\) −369858. −1.51250
\(144\) −594309. −2.38839
\(145\) −93932.4 −0.371018
\(146\) −160977. −0.625004
\(147\) 108717. 0.414958
\(148\) 408262. 1.53209
\(149\) −351854. −1.29836 −0.649182 0.760633i \(-0.724889\pi\)
−0.649182 + 0.760633i \(0.724889\pi\)
\(150\) −607439. −2.20432
\(151\) 64284.8 0.229438 0.114719 0.993398i \(-0.463403\pi\)
0.114719 + 0.993398i \(0.463403\pi\)
\(152\) 39213.8 0.137667
\(153\) −902875. −3.11817
\(154\) 406732. 1.38199
\(155\) 128548. 0.429770
\(156\) 944064. 3.10592
\(157\) −167134. −0.541147 −0.270573 0.962699i \(-0.587213\pi\)
−0.270573 + 0.962699i \(0.587213\pi\)
\(158\) −562110. −1.79134
\(159\) −307416. −0.964349
\(160\) −219632. −0.678258
\(161\) −159495. −0.484934
\(162\) −1.94112e6 −5.81119
\(163\) −28356.0 −0.0835943 −0.0417972 0.999126i \(-0.513308\pi\)
−0.0417972 + 0.999126i \(0.513308\pi\)
\(164\) −598042. −1.73629
\(165\) 343686. 0.982771
\(166\) 499881. 1.40798
\(167\) 579045. 1.60665 0.803325 0.595541i \(-0.203062\pi\)
0.803325 + 0.595541i \(0.203062\pi\)
\(168\) −117101. −0.320102
\(169\) 373007. 1.00462
\(170\) −290548. −0.771073
\(171\) −791473. −2.06988
\(172\) −550953. −1.42002
\(173\) −425916. −1.08195 −0.540977 0.841037i \(-0.681945\pi\)
−0.540977 + 0.841037i \(0.681945\pi\)
\(174\) 889796. 2.22801
\(175\) 279064. 0.688824
\(176\) −376089. −0.915186
\(177\) 285028. 0.683840
\(178\) −504063. −1.19244
\(179\) −266030. −0.620581 −0.310291 0.950642i \(-0.600426\pi\)
−0.310291 + 0.950642i \(0.600426\pi\)
\(180\) −645665. −1.48534
\(181\) 618211. 1.40262 0.701310 0.712857i \(-0.252599\pi\)
0.701310 + 0.712857i \(0.252599\pi\)
\(182\) −818505. −1.83165
\(183\) −605770. −1.33715
\(184\) −46554.1 −0.101371
\(185\) −299097. −0.642515
\(186\) −1.21770e6 −2.58082
\(187\) −571356. −1.19482
\(188\) 753889. 1.55565
\(189\) 1.51574e6 3.08652
\(190\) −254698. −0.511849
\(191\) 783722. 1.55446 0.777228 0.629219i \(-0.216625\pi\)
0.777228 + 0.629219i \(0.216625\pi\)
\(192\) 1.22882e6 2.40566
\(193\) 196320. 0.379376 0.189688 0.981844i \(-0.439252\pi\)
0.189688 + 0.981844i \(0.439252\pi\)
\(194\) −802798. −1.53145
\(195\) −691633. −1.30253
\(196\) −129247. −0.240315
\(197\) 329724. 0.605320 0.302660 0.953099i \(-0.402125\pi\)
0.302660 + 0.953099i \(0.402125\pi\)
\(198\) −2.39616e6 −4.34363
\(199\) 635923. 1.13834 0.569169 0.822220i \(-0.307265\pi\)
0.569169 + 0.822220i \(0.307265\pi\)
\(200\) 81454.3 0.143992
\(201\) 748904. 1.30748
\(202\) −1.05388e6 −1.81724
\(203\) −408781. −0.696227
\(204\) 1.45839e6 2.45357
\(205\) 438132. 0.728150
\(206\) 473061. 0.776693
\(207\) 939625. 1.52415
\(208\) 756840. 1.21296
\(209\) −500858. −0.793139
\(210\) 760587. 1.19015
\(211\) 488148. 0.754824 0.377412 0.926045i \(-0.376814\pi\)
0.377412 + 0.926045i \(0.376814\pi\)
\(212\) 365469. 0.558484
\(213\) −1.46908e6 −2.21868
\(214\) −658294. −0.982620
\(215\) 403635. 0.595515
\(216\) 442420. 0.645209
\(217\) 559423. 0.806475
\(218\) −753341. −1.07362
\(219\) −591963. −0.834035
\(220\) −408588. −0.569153
\(221\) 1.14979e6 1.58358
\(222\) 2.83327e6 3.85838
\(223\) 1.00289e6 1.35049 0.675243 0.737596i \(-0.264039\pi\)
0.675243 + 0.737596i \(0.264039\pi\)
\(224\) −955807. −1.27277
\(225\) −1.64403e6 −2.16498
\(226\) 1.30889e6 1.70464
\(227\) −252146. −0.324779 −0.162390 0.986727i \(-0.551920\pi\)
−0.162390 + 0.986727i \(0.551920\pi\)
\(228\) 1.27844e6 1.62871
\(229\) −64290.8 −0.0810140 −0.0405070 0.999179i \(-0.512897\pi\)
−0.0405070 + 0.999179i \(0.512897\pi\)
\(230\) 302374. 0.376899
\(231\) 1.49568e6 1.84420
\(232\) −119317. −0.145540
\(233\) 1.06891e6 1.28989 0.644945 0.764229i \(-0.276880\pi\)
0.644945 + 0.764229i \(0.276880\pi\)
\(234\) 4.82202e6 5.75690
\(235\) −552308. −0.652396
\(236\) −338853. −0.396033
\(237\) −2.06705e6 −2.39045
\(238\) −1.26442e6 −1.44694
\(239\) 1.65221e6 1.87099 0.935493 0.353345i \(-0.114956\pi\)
0.935493 + 0.353345i \(0.114956\pi\)
\(240\) −703285. −0.788140
\(241\) −551406. −0.611546 −0.305773 0.952104i \(-0.598915\pi\)
−0.305773 + 0.952104i \(0.598915\pi\)
\(242\) −187604. −0.205922
\(243\) −3.93511e6 −4.27505
\(244\) 720164. 0.774385
\(245\) 94687.9 0.100781
\(246\) −4.15031e6 −4.37263
\(247\) 1.00792e6 1.05120
\(248\) 163287. 0.168586
\(249\) 1.83821e6 1.87887
\(250\) −1.21033e6 −1.22477
\(251\) 79390.5 0.0795397 0.0397699 0.999209i \(-0.487338\pi\)
0.0397699 + 0.999209i \(0.487338\pi\)
\(252\) −2.80985e6 −2.78728
\(253\) 594612. 0.584026
\(254\) 1.76000e6 1.71171
\(255\) −1.06843e6 −1.02896
\(256\) 733540. 0.699558
\(257\) −1.82046e6 −1.71929 −0.859645 0.510892i \(-0.829315\pi\)
−0.859645 + 0.510892i \(0.829315\pi\)
\(258\) −3.82352e6 −3.57614
\(259\) −1.30163e6 −1.20570
\(260\) 822241. 0.754338
\(261\) 2.40823e6 2.18825
\(262\) −2.50537e6 −2.25486
\(263\) −211531. −0.188576 −0.0942878 0.995545i \(-0.530057\pi\)
−0.0942878 + 0.995545i \(0.530057\pi\)
\(264\) 436564. 0.385512
\(265\) −267747. −0.234212
\(266\) −1.10841e6 −0.960500
\(267\) −1.85359e6 −1.59124
\(268\) −890328. −0.757204
\(269\) 1.16045e6 0.977792 0.488896 0.872342i \(-0.337400\pi\)
0.488896 + 0.872342i \(0.337400\pi\)
\(270\) −2.87357e6 −2.39890
\(271\) −1.25402e6 −1.03724 −0.518621 0.855004i \(-0.673554\pi\)
−0.518621 + 0.855004i \(0.673554\pi\)
\(272\) 1.16916e6 0.958194
\(273\) −3.00989e6 −2.44424
\(274\) 2.63059e6 2.11679
\(275\) −1.04037e6 −0.829579
\(276\) −1.51775e6 −1.19930
\(277\) 1.14668e6 0.897932 0.448966 0.893549i \(-0.351792\pi\)
0.448966 + 0.893549i \(0.351792\pi\)
\(278\) −347646. −0.269790
\(279\) −3.29570e6 −2.53476
\(280\) −101991. −0.0777436
\(281\) 228129. 0.172351 0.0861755 0.996280i \(-0.472535\pi\)
0.0861755 + 0.996280i \(0.472535\pi\)
\(282\) 5.23186e6 3.91772
\(283\) −280999. −0.208564 −0.104282 0.994548i \(-0.533254\pi\)
−0.104282 + 0.994548i \(0.533254\pi\)
\(284\) 1.74650e6 1.28491
\(285\) −936603. −0.683036
\(286\) 3.05146e6 2.20593
\(287\) 1.90669e6 1.36639
\(288\) 5.63090e6 4.00033
\(289\) 356341. 0.250970
\(290\) 774975. 0.541119
\(291\) −2.95213e6 −2.04363
\(292\) 703750. 0.483016
\(293\) −1.84060e6 −1.25253 −0.626267 0.779608i \(-0.715418\pi\)
−0.626267 + 0.779608i \(0.715418\pi\)
\(294\) −896952. −0.605203
\(295\) 248248. 0.166085
\(296\) −379925. −0.252040
\(297\) −5.65080e6 −3.71723
\(298\) 2.90292e6 1.89363
\(299\) −1.19659e6 −0.774049
\(300\) 2.65556e6 1.70354
\(301\) 1.75656e6 1.11750
\(302\) −530372. −0.334629
\(303\) −3.87543e6 −2.42501
\(304\) 1.02491e6 0.636063
\(305\) −527601. −0.324755
\(306\) 7.44904e6 4.54775
\(307\) 1.36190e6 0.824709 0.412354 0.911024i \(-0.364707\pi\)
0.412354 + 0.911024i \(0.364707\pi\)
\(308\) −1.77812e6 −1.06803
\(309\) 1.73959e6 1.03646
\(310\) −1.06057e6 −0.626806
\(311\) −1.43376e6 −0.840574 −0.420287 0.907391i \(-0.638071\pi\)
−0.420287 + 0.907391i \(0.638071\pi\)
\(312\) −878540. −0.510946
\(313\) 2.05782e6 1.18726 0.593630 0.804738i \(-0.297694\pi\)
0.593630 + 0.804738i \(0.297694\pi\)
\(314\) 1.37891e6 0.789246
\(315\) 2.05853e6 1.16891
\(316\) 2.45739e6 1.38438
\(317\) −694380. −0.388105 −0.194052 0.980991i \(-0.562163\pi\)
−0.194052 + 0.980991i \(0.562163\pi\)
\(318\) 2.53629e6 1.40647
\(319\) 1.52397e6 0.838494
\(320\) 1.07025e6 0.584266
\(321\) −2.42075e6 −1.31125
\(322\) 1.31589e6 0.707262
\(323\) 1.55704e6 0.830412
\(324\) 8.48606e6 4.49101
\(325\) 2.09364e6 1.09950
\(326\) 233947. 0.121920
\(327\) −2.77026e6 −1.43269
\(328\) 556533. 0.285632
\(329\) −2.40357e6 −1.22424
\(330\) −2.83553e6 −1.43334
\(331\) 1.40117e6 0.702943 0.351472 0.936199i \(-0.385681\pi\)
0.351472 + 0.936199i \(0.385681\pi\)
\(332\) −2.18534e6 −1.08811
\(333\) 7.66823e6 3.78952
\(334\) −4.77733e6 −2.34325
\(335\) 652265. 0.317550
\(336\) −3.06060e6 −1.47897
\(337\) −3.16105e6 −1.51620 −0.758101 0.652138i \(-0.773872\pi\)
−0.758101 + 0.652138i \(0.773872\pi\)
\(338\) −3.07744e6 −1.46520
\(339\) 4.81319e6 2.27475
\(340\) 1.27020e6 0.595900
\(341\) −2.08558e6 −0.971271
\(342\) 6.52993e6 3.01886
\(343\) 2.34477e6 1.07613
\(344\) 512713. 0.233603
\(345\) 1.11192e6 0.502952
\(346\) 3.51396e6 1.57800
\(347\) 2.41305e6 1.07583 0.537914 0.842999i \(-0.319212\pi\)
0.537914 + 0.842999i \(0.319212\pi\)
\(348\) −3.88994e6 −1.72185
\(349\) −3.04701e6 −1.33909 −0.669546 0.742771i \(-0.733511\pi\)
−0.669546 + 0.742771i \(0.733511\pi\)
\(350\) −2.30237e6 −1.00463
\(351\) 1.13716e7 4.92669
\(352\) 3.56333e6 1.53285
\(353\) 4.05547e6 1.73222 0.866112 0.499849i \(-0.166611\pi\)
0.866112 + 0.499849i \(0.166611\pi\)
\(354\) −2.35158e6 −0.997359
\(355\) −1.27951e6 −0.538854
\(356\) 2.20363e6 0.921538
\(357\) −4.64967e6 −1.93087
\(358\) 2.19484e6 0.905099
\(359\) −3.26666e6 −1.33773 −0.668865 0.743384i \(-0.733219\pi\)
−0.668865 + 0.743384i \(0.733219\pi\)
\(360\) 600851. 0.244349
\(361\) −1.11118e6 −0.448761
\(362\) −5.10045e6 −2.04568
\(363\) −689877. −0.274792
\(364\) 3.57828e6 1.41554
\(365\) −515576. −0.202563
\(366\) 4.99781e6 1.95019
\(367\) 2.35078e6 0.911058 0.455529 0.890221i \(-0.349450\pi\)
0.455529 + 0.890221i \(0.349450\pi\)
\(368\) −1.21675e6 −0.468363
\(369\) −1.12328e7 −4.29459
\(370\) 2.46766e6 0.937089
\(371\) −1.16520e6 −0.439506
\(372\) 5.32345e6 1.99451
\(373\) 226137. 0.0841589 0.0420794 0.999114i \(-0.486602\pi\)
0.0420794 + 0.999114i \(0.486602\pi\)
\(374\) 4.71389e6 1.74261
\(375\) −4.45075e6 −1.63439
\(376\) −701563. −0.255916
\(377\) −3.06683e6 −1.11131
\(378\) −1.25054e7 −4.50160
\(379\) 373040. 0.133400 0.0667002 0.997773i \(-0.478753\pi\)
0.0667002 + 0.997773i \(0.478753\pi\)
\(380\) 1.11347e6 0.395567
\(381\) 6.47206e6 2.28418
\(382\) −6.46598e6 −2.26713
\(383\) 5.27984e6 1.83918 0.919589 0.392882i \(-0.128522\pi\)
0.919589 + 0.392882i \(0.128522\pi\)
\(384\) −2.06868e6 −0.715921
\(385\) 1.30267e6 0.447902
\(386\) −1.61970e6 −0.553309
\(387\) −1.03484e7 −3.51232
\(388\) 3.50961e6 1.18353
\(389\) −4.31256e6 −1.44498 −0.722488 0.691383i \(-0.757002\pi\)
−0.722488 + 0.691383i \(0.757002\pi\)
\(390\) 5.70621e6 1.89971
\(391\) −1.84850e6 −0.611472
\(392\) 120276. 0.0395335
\(393\) −9.21302e6 −3.00899
\(394\) −2.72034e6 −0.882842
\(395\) −1.80031e6 −0.580571
\(396\) 1.04754e7 3.35684
\(397\) −4.90018e6 −1.56040 −0.780199 0.625531i \(-0.784882\pi\)
−0.780199 + 0.625531i \(0.784882\pi\)
\(398\) −5.24658e6 −1.66023
\(399\) −4.07597e6 −1.28174
\(400\) 2.12892e6 0.665286
\(401\) −1.85639e6 −0.576511 −0.288255 0.957554i \(-0.593075\pi\)
−0.288255 + 0.957554i \(0.593075\pi\)
\(402\) −6.17872e6 −1.90692
\(403\) 4.19700e6 1.28729
\(404\) 4.60727e6 1.40440
\(405\) −6.21699e6 −1.88340
\(406\) 3.37259e6 1.01543
\(407\) 4.85259e6 1.45207
\(408\) −1.35717e6 −0.403629
\(409\) 6.10123e6 1.80347 0.901736 0.432288i \(-0.142294\pi\)
0.901736 + 0.432288i \(0.142294\pi\)
\(410\) −3.61475e6 −1.06198
\(411\) 9.67349e6 2.82474
\(412\) −2.06810e6 −0.600244
\(413\) 1.08034e6 0.311663
\(414\) −7.75224e6 −2.22293
\(415\) 1.60101e6 0.456324
\(416\) −7.17083e6 −2.03159
\(417\) −1.27840e6 −0.360020
\(418\) 4.13226e6 1.15677
\(419\) −4.65495e6 −1.29533 −0.647665 0.761925i \(-0.724254\pi\)
−0.647665 + 0.761925i \(0.724254\pi\)
\(420\) −3.32508e6 −0.919769
\(421\) −1.22677e6 −0.337331 −0.168665 0.985673i \(-0.553946\pi\)
−0.168665 + 0.985673i \(0.553946\pi\)
\(422\) −4.02740e6 −1.10089
\(423\) 1.41600e7 3.84780
\(424\) −340103. −0.0918747
\(425\) 3.23425e6 0.868564
\(426\) 1.21204e7 3.23588
\(427\) −2.29605e6 −0.609412
\(428\) 2.87788e6 0.759388
\(429\) 1.12211e7 2.94370
\(430\) −3.33013e6 −0.868541
\(431\) 174437. 0.0452320 0.0226160 0.999744i \(-0.492800\pi\)
0.0226160 + 0.999744i \(0.492800\pi\)
\(432\) 1.15632e7 2.98105
\(433\) −5.91829e6 −1.51697 −0.758485 0.651691i \(-0.774060\pi\)
−0.758485 + 0.651691i \(0.774060\pi\)
\(434\) −4.61544e6 −1.17622
\(435\) 2.84982e6 0.722095
\(436\) 3.29340e6 0.829715
\(437\) −1.62042e6 −0.405904
\(438\) 4.88390e6 1.21641
\(439\) 4.22650e6 1.04669 0.523346 0.852120i \(-0.324683\pi\)
0.523346 + 0.852120i \(0.324683\pi\)
\(440\) 380230. 0.0936298
\(441\) −2.42760e6 −0.594403
\(442\) −9.48620e6 −2.30960
\(443\) 2.13728e6 0.517431 0.258715 0.965954i \(-0.416701\pi\)
0.258715 + 0.965954i \(0.416701\pi\)
\(444\) −1.23863e7 −2.98183
\(445\) −1.61440e6 −0.386467
\(446\) −8.27417e6 −1.96964
\(447\) 1.06749e7 2.52694
\(448\) 4.65759e6 1.09639
\(449\) −2.81178e6 −0.658210 −0.329105 0.944293i \(-0.606747\pi\)
−0.329105 + 0.944293i \(0.606747\pi\)
\(450\) 1.35638e7 3.15756
\(451\) −7.10831e6 −1.64560
\(452\) −5.72212e6 −1.31738
\(453\) −1.95034e6 −0.446544
\(454\) 2.08030e6 0.473680
\(455\) −2.62149e6 −0.593636
\(456\) −1.18971e6 −0.267935
\(457\) 2.30364e6 0.515970 0.257985 0.966149i \(-0.416941\pi\)
0.257985 + 0.966149i \(0.416941\pi\)
\(458\) 530422. 0.118157
\(459\) 1.75669e7 3.89191
\(460\) −1.32190e6 −0.291275
\(461\) −8.76118e6 −1.92004 −0.960020 0.279930i \(-0.909689\pi\)
−0.960020 + 0.279930i \(0.909689\pi\)
\(462\) −1.23399e7 −2.68971
\(463\) 4.29017e6 0.930083 0.465042 0.885289i \(-0.346039\pi\)
0.465042 + 0.885289i \(0.346039\pi\)
\(464\) −3.11850e6 −0.672436
\(465\) −3.90002e6 −0.836439
\(466\) −8.81891e6 −1.88127
\(467\) 940648. 0.199588 0.0997941 0.995008i \(-0.468182\pi\)
0.0997941 + 0.995008i \(0.468182\pi\)
\(468\) −2.10805e7 −4.44905
\(469\) 2.83857e6 0.595891
\(470\) 4.55673e6 0.951500
\(471\) 5.07068e6 1.05321
\(472\) 315334. 0.0651502
\(473\) −6.54862e6 −1.34585
\(474\) 1.70539e7 3.48640
\(475\) 2.83519e6 0.576565
\(476\) 5.52772e6 1.11822
\(477\) 6.86447e6 1.38137
\(478\) −1.36313e7 −2.72878
\(479\) −301446. −0.0600303 −0.0300152 0.999549i \(-0.509556\pi\)
−0.0300152 + 0.999549i \(0.509556\pi\)
\(480\) 6.66342e6 1.32006
\(481\) −9.76533e6 −1.92453
\(482\) 4.54929e6 0.891921
\(483\) 4.83893e6 0.943803
\(484\) 820154. 0.159141
\(485\) −2.57119e6 −0.496340
\(486\) 3.24660e7 6.23502
\(487\) −1.90919e6 −0.364777 −0.182389 0.983227i \(-0.558383\pi\)
−0.182389 + 0.983227i \(0.558383\pi\)
\(488\) −670179. −0.127392
\(489\) 860295. 0.162695
\(490\) −781209. −0.146986
\(491\) 8.26815e6 1.54776 0.773881 0.633331i \(-0.218313\pi\)
0.773881 + 0.633331i \(0.218313\pi\)
\(492\) 1.81440e7 3.37925
\(493\) −4.73764e6 −0.877899
\(494\) −8.31573e6 −1.53314
\(495\) −7.67437e6 −1.40776
\(496\) 4.26771e6 0.778917
\(497\) −5.56823e6 −1.01118
\(498\) −1.51659e7 −2.74028
\(499\) −7.84281e6 −1.41000 −0.705002 0.709206i \(-0.749054\pi\)
−0.705002 + 0.709206i \(0.749054\pi\)
\(500\) 5.29123e6 0.946524
\(501\) −1.75677e7 −3.12694
\(502\) −654999. −0.116006
\(503\) 9.28502e6 1.63630 0.818150 0.575005i \(-0.195000\pi\)
0.818150 + 0.575005i \(0.195000\pi\)
\(504\) 2.61482e6 0.458528
\(505\) −3.37534e6 −0.588965
\(506\) −4.90576e6 −0.851784
\(507\) −1.13167e7 −1.95524
\(508\) −7.69425e6 −1.32284
\(509\) −44924.0 −0.00768570 −0.00384285 0.999993i \(-0.501223\pi\)
−0.00384285 + 0.999993i \(0.501223\pi\)
\(510\) 8.81495e6 1.50070
\(511\) −2.24371e6 −0.380115
\(512\) −8.23389e6 −1.38813
\(513\) 1.53994e7 2.58351
\(514\) 1.50195e7 2.50753
\(515\) 1.51511e6 0.251725
\(516\) 1.67154e7 2.76371
\(517\) 8.96071e6 1.47440
\(518\) 1.07389e7 1.75847
\(519\) 1.29219e7 2.10575
\(520\) −765172. −0.124094
\(521\) −6.43306e6 −1.03830 −0.519150 0.854683i \(-0.673751\pi\)
−0.519150 + 0.854683i \(0.673751\pi\)
\(522\) −1.98687e7 −3.19150
\(523\) −6.75944e6 −1.08058 −0.540290 0.841479i \(-0.681685\pi\)
−0.540290 + 0.841479i \(0.681685\pi\)
\(524\) 1.09528e7 1.74260
\(525\) −8.46652e6 −1.34062
\(526\) 1.74521e6 0.275032
\(527\) 6.48352e6 1.01691
\(528\) 1.14102e7 1.78118
\(529\) −4.51261e6 −0.701114
\(530\) 2.20901e6 0.341592
\(531\) −6.36455e6 −0.979561
\(532\) 4.84568e6 0.742293
\(533\) 1.43047e7 2.18103
\(534\) 1.52928e7 2.32078
\(535\) −2.10837e6 −0.318466
\(536\) 828533. 0.124565
\(537\) 8.07111e6 1.20781
\(538\) −9.57413e6 −1.42608
\(539\) −1.53623e6 −0.227763
\(540\) 1.25625e7 1.85392
\(541\) 7.73077e6 1.13561 0.567806 0.823163i \(-0.307793\pi\)
0.567806 + 0.823163i \(0.307793\pi\)
\(542\) 1.03461e7 1.51279
\(543\) −1.87559e7 −2.72985
\(544\) −1.10775e7 −1.60489
\(545\) −2.41279e6 −0.347959
\(546\) 2.48327e7 3.56485
\(547\) −299209. −0.0427569
\(548\) −1.15002e7 −1.63590
\(549\) 1.35266e7 1.91539
\(550\) 8.58345e6 1.20992
\(551\) −4.15308e6 −0.582762
\(552\) 1.41241e6 0.197293
\(553\) −7.83472e6 −1.08946
\(554\) −9.46052e6 −1.30961
\(555\) 9.07433e6 1.25050
\(556\) 1.51981e6 0.208499
\(557\) −40290.3 −0.00550253 −0.00275127 0.999996i \(-0.500876\pi\)
−0.00275127 + 0.999996i \(0.500876\pi\)
\(558\) 2.71907e7 3.69687
\(559\) 1.31784e7 1.78375
\(560\) −2.66566e6 −0.359198
\(561\) 1.73344e7 2.32542
\(562\) −1.88214e6 −0.251369
\(563\) 1.65062e6 0.219470 0.109735 0.993961i \(-0.465000\pi\)
0.109735 + 0.993961i \(0.465000\pi\)
\(564\) −2.28723e7 −3.02769
\(565\) 4.19209e6 0.552471
\(566\) 2.31834e6 0.304184
\(567\) −2.70555e7 −3.53425
\(568\) −1.62528e6 −0.211377
\(569\) 3.75963e6 0.486816 0.243408 0.969924i \(-0.421735\pi\)
0.243408 + 0.969924i \(0.421735\pi\)
\(570\) 7.72730e6 0.996187
\(571\) −3.48656e6 −0.447514 −0.223757 0.974645i \(-0.571832\pi\)
−0.223757 + 0.974645i \(0.571832\pi\)
\(572\) −1.33401e7 −1.70479
\(573\) −2.37774e7 −3.02536
\(574\) −1.57309e7 −1.99284
\(575\) −3.36590e6 −0.424553
\(576\) −2.74390e7 −3.44597
\(577\) −7.35700e6 −0.919944 −0.459972 0.887933i \(-0.652141\pi\)
−0.459972 + 0.887933i \(0.652141\pi\)
\(578\) −2.93994e6 −0.366032
\(579\) −5.95615e6 −0.738361
\(580\) −3.38798e6 −0.418188
\(581\) 6.96737e6 0.856306
\(582\) 2.43561e7 2.98058
\(583\) 4.34396e6 0.529315
\(584\) −654905. −0.0794595
\(585\) 1.54439e7 1.86580
\(586\) 1.51856e7 1.82678
\(587\) 4.49819e6 0.538819 0.269410 0.963026i \(-0.413171\pi\)
0.269410 + 0.963026i \(0.413171\pi\)
\(588\) 3.92123e6 0.467713
\(589\) 5.68355e6 0.675043
\(590\) −2.04813e6 −0.242230
\(591\) −1.00035e7 −1.17811
\(592\) −9.92986e6 −1.16450
\(593\) −1.40730e7 −1.64343 −0.821715 0.569899i \(-0.806982\pi\)
−0.821715 + 0.569899i \(0.806982\pi\)
\(594\) 4.66211e7 5.42146
\(595\) −4.04968e6 −0.468951
\(596\) −1.26908e7 −1.46343
\(597\) −1.92933e7 −2.21549
\(598\) 9.87232e6 1.12893
\(599\) 282573. 0.0321784 0.0160892 0.999871i \(-0.494878\pi\)
0.0160892 + 0.999871i \(0.494878\pi\)
\(600\) −2.47124e6 −0.280245
\(601\) −2.47863e6 −0.279915 −0.139958 0.990158i \(-0.544697\pi\)
−0.139958 + 0.990158i \(0.544697\pi\)
\(602\) −1.44923e7 −1.62984
\(603\) −1.67227e7 −1.87289
\(604\) 2.31864e6 0.258608
\(605\) −600854. −0.0667392
\(606\) 3.19737e7 3.53680
\(607\) 5.36046e6 0.590515 0.295257 0.955418i \(-0.404595\pi\)
0.295257 + 0.955418i \(0.404595\pi\)
\(608\) −9.71068e6 −1.06535
\(609\) 1.24020e7 1.35503
\(610\) 4.35289e6 0.473645
\(611\) −1.80325e7 −1.95413
\(612\) −3.25652e7 −3.51459
\(613\) 8.50924e6 0.914617 0.457309 0.889308i \(-0.348813\pi\)
0.457309 + 0.889308i \(0.348813\pi\)
\(614\) −1.12362e7 −1.20281
\(615\) −1.32925e7 −1.41716
\(616\) 1.65471e6 0.175699
\(617\) −1.27611e7 −1.34951 −0.674754 0.738042i \(-0.735750\pi\)
−0.674754 + 0.738042i \(0.735750\pi\)
\(618\) −1.43522e7 −1.51164
\(619\) −1.47029e7 −1.54232 −0.771161 0.636640i \(-0.780324\pi\)
−0.771161 + 0.636640i \(0.780324\pi\)
\(620\) 4.63650e6 0.484408
\(621\) −1.82819e7 −1.90236
\(622\) 1.18290e7 1.22595
\(623\) −7.02567e6 −0.725216
\(624\) −2.29618e7 −2.36072
\(625\) 3.70723e6 0.379621
\(626\) −1.69777e7 −1.73158
\(627\) 1.51956e7 1.54365
\(628\) −6.02823e6 −0.609945
\(629\) −1.50855e7 −1.52031
\(630\) −1.69836e7 −1.70482
\(631\) 8.23332e6 0.823193 0.411596 0.911366i \(-0.364971\pi\)
0.411596 + 0.911366i \(0.364971\pi\)
\(632\) −2.28683e6 −0.227741
\(633\) −1.48100e7 −1.46908
\(634\) 5.72888e6 0.566039
\(635\) 5.63690e6 0.554761
\(636\) −1.10880e7 −1.08695
\(637\) 3.09150e6 0.301870
\(638\) −1.25733e7 −1.22292
\(639\) 3.28038e7 3.17814
\(640\) −1.80173e6 −0.173877
\(641\) 7.54288e6 0.725090 0.362545 0.931966i \(-0.381908\pi\)
0.362545 + 0.931966i \(0.381908\pi\)
\(642\) 1.99720e7 1.91242
\(643\) −4.00008e6 −0.381541 −0.190771 0.981635i \(-0.561099\pi\)
−0.190771 + 0.981635i \(0.561099\pi\)
\(644\) −5.75272e6 −0.546586
\(645\) −1.22459e7 −1.15902
\(646\) −1.28461e7 −1.21113
\(647\) −8.82323e6 −0.828642 −0.414321 0.910131i \(-0.635981\pi\)
−0.414321 + 0.910131i \(0.635981\pi\)
\(648\) −7.89707e6 −0.738802
\(649\) −4.02760e6 −0.375348
\(650\) −1.72733e7 −1.60358
\(651\) −1.69724e7 −1.56960
\(652\) −1.02275e6 −0.0942220
\(653\) −1.36679e7 −1.25435 −0.627174 0.778879i \(-0.715789\pi\)
−0.627174 + 0.778879i \(0.715789\pi\)
\(654\) 2.28557e7 2.08953
\(655\) −8.02416e6 −0.730797
\(656\) 1.45457e7 1.31970
\(657\) 1.32183e7 1.19471
\(658\) 1.98303e7 1.78552
\(659\) −1.19060e6 −0.106796 −0.0533979 0.998573i \(-0.517005\pi\)
−0.0533979 + 0.998573i \(0.517005\pi\)
\(660\) 1.23962e7 1.10772
\(661\) 3.25548e6 0.289809 0.144905 0.989446i \(-0.453713\pi\)
0.144905 + 0.989446i \(0.453713\pi\)
\(662\) −1.15601e7 −1.02522
\(663\) −3.48836e7 −3.08204
\(664\) 2.03367e6 0.179003
\(665\) −3.55000e6 −0.311297
\(666\) −6.32656e7 −5.52690
\(667\) 4.93047e6 0.429115
\(668\) 2.08852e7 1.81091
\(669\) −3.04266e7 −2.62838
\(670\) −5.38141e6 −0.463137
\(671\) 8.55986e6 0.733939
\(672\) 2.89983e7 2.47713
\(673\) −3.53355e6 −0.300728 −0.150364 0.988631i \(-0.548045\pi\)
−0.150364 + 0.988631i \(0.548045\pi\)
\(674\) 2.60798e7 2.21133
\(675\) 3.19873e7 2.70220
\(676\) 1.34537e7 1.13234
\(677\) 1.94898e7 1.63431 0.817157 0.576416i \(-0.195549\pi\)
0.817157 + 0.576416i \(0.195549\pi\)
\(678\) −3.97105e7 −3.31765
\(679\) −1.11894e7 −0.931396
\(680\) −1.18204e6 −0.0980299
\(681\) 7.64988e6 0.632101
\(682\) 1.72067e7 1.41657
\(683\) −9.28219e6 −0.761375 −0.380688 0.924704i \(-0.624313\pi\)
−0.380688 + 0.924704i \(0.624313\pi\)
\(684\) −2.85471e7 −2.33304
\(685\) 8.42521e6 0.686048
\(686\) −1.93452e7 −1.56951
\(687\) 1.95052e6 0.157674
\(688\) 1.34004e7 1.07931
\(689\) −8.74176e6 −0.701538
\(690\) −9.17374e6 −0.733540
\(691\) −1.78949e7 −1.42572 −0.712862 0.701305i \(-0.752601\pi\)
−0.712862 + 0.701305i \(0.752601\pi\)
\(692\) −1.53621e7 −1.21951
\(693\) −3.33978e7 −2.64171
\(694\) −1.99085e7 −1.56906
\(695\) −1.11343e6 −0.0874385
\(696\) 3.61995e6 0.283257
\(697\) 2.20979e7 1.72294
\(698\) 2.51389e7 1.95303
\(699\) −3.24298e7 −2.51045
\(700\) 1.00654e7 0.776397
\(701\) −1.18883e7 −0.913743 −0.456871 0.889533i \(-0.651030\pi\)
−0.456871 + 0.889533i \(0.651030\pi\)
\(702\) −9.38201e7 −7.18543
\(703\) −1.32241e7 −1.00920
\(704\) −1.73639e7 −1.32043
\(705\) 1.67565e7 1.26973
\(706\) −3.34590e7 −2.52640
\(707\) −1.46890e7 −1.10521
\(708\) 1.02805e7 0.770779
\(709\) −1.49479e7 −1.11677 −0.558387 0.829580i \(-0.688580\pi\)
−0.558387 + 0.829580i \(0.688580\pi\)
\(710\) 1.05564e7 0.785903
\(711\) 4.61563e7 3.42418
\(712\) −2.05068e6 −0.151600
\(713\) −6.74742e6 −0.497066
\(714\) 3.83614e7 2.81611
\(715\) 9.77315e6 0.714940
\(716\) −9.59526e6 −0.699479
\(717\) −5.01265e7 −3.64141
\(718\) 2.69511e7 1.95104
\(719\) 1.60953e7 1.16112 0.580560 0.814218i \(-0.302834\pi\)
0.580560 + 0.814218i \(0.302834\pi\)
\(720\) 1.57040e7 1.12896
\(721\) 6.59356e6 0.472369
\(722\) 9.16760e6 0.654504
\(723\) 1.67291e7 1.19022
\(724\) 2.22978e7 1.58094
\(725\) −8.62669e6 −0.609536
\(726\) 5.69172e6 0.400777
\(727\) −1.92489e7 −1.35073 −0.675366 0.737483i \(-0.736014\pi\)
−0.675366 + 0.737483i \(0.736014\pi\)
\(728\) −3.32992e6 −0.232866
\(729\) 6.22149e7 4.33586
\(730\) 4.25368e6 0.295432
\(731\) 2.03580e7 1.40910
\(732\) −2.18491e7 −1.50715
\(733\) 1.17391e7 0.807003 0.403502 0.914979i \(-0.367793\pi\)
0.403502 + 0.914979i \(0.367793\pi\)
\(734\) −1.93947e7 −1.32875
\(735\) −2.87274e6 −0.196145
\(736\) 1.15284e7 0.784465
\(737\) −1.05824e7 −0.717656
\(738\) 9.26745e7 6.26353
\(739\) 2.06300e7 1.38960 0.694799 0.719204i \(-0.255493\pi\)
0.694799 + 0.719204i \(0.255493\pi\)
\(740\) −1.07879e7 −0.724201
\(741\) −3.05795e7 −2.04590
\(742\) 9.61330e6 0.641007
\(743\) 9.09475e6 0.604392 0.302196 0.953246i \(-0.402280\pi\)
0.302196 + 0.953246i \(0.402280\pi\)
\(744\) −4.95396e6 −0.328111
\(745\) 9.29741e6 0.613721
\(746\) −1.86571e6 −0.122743
\(747\) −4.10465e7 −2.69138
\(748\) −2.06078e7 −1.34672
\(749\) −9.17535e6 −0.597610
\(750\) 3.67202e7 2.38370
\(751\) −1.71018e7 −1.10647 −0.553237 0.833024i \(-0.686608\pi\)
−0.553237 + 0.833024i \(0.686608\pi\)
\(752\) −1.83363e7 −1.18241
\(753\) −2.40863e6 −0.154804
\(754\) 2.53024e7 1.62082
\(755\) −1.69867e6 −0.108453
\(756\) 5.46701e7 3.47893
\(757\) −693046. −0.0439564 −0.0219782 0.999758i \(-0.506996\pi\)
−0.0219782 + 0.999758i \(0.506996\pi\)
\(758\) −3.07771e6 −0.194560
\(759\) −1.80399e7 −1.13666
\(760\) −1.03619e6 −0.0650736
\(761\) −1.87009e7 −1.17058 −0.585291 0.810824i \(-0.699020\pi\)
−0.585291 + 0.810824i \(0.699020\pi\)
\(762\) −5.33968e7 −3.33141
\(763\) −1.05001e7 −0.652955
\(764\) 2.82675e7 1.75208
\(765\) 2.38576e7 1.47392
\(766\) −4.35605e7 −2.68239
\(767\) 8.10512e6 0.497475
\(768\) −2.22549e7 −1.36152
\(769\) −3.10535e7 −1.89363 −0.946814 0.321781i \(-0.895719\pi\)
−0.946814 + 0.321781i \(0.895719\pi\)
\(770\) −1.07475e7 −0.653252
\(771\) 5.52311e7 3.34617
\(772\) 7.08091e6 0.427608
\(773\) −1.86406e7 −1.12205 −0.561023 0.827800i \(-0.689592\pi\)
−0.561023 + 0.827800i \(0.689592\pi\)
\(774\) 8.53776e7 5.12261
\(775\) 1.18058e7 0.706057
\(776\) −3.26602e6 −0.194700
\(777\) 3.94902e7 2.34659
\(778\) 3.55801e7 2.10745
\(779\) 1.93713e7 1.14371
\(780\) −2.49460e7 −1.46813
\(781\) 2.07589e7 1.21780
\(782\) 1.52507e7 0.891813
\(783\) −4.68560e7 −2.73125
\(784\) 3.14358e6 0.182656
\(785\) 4.41635e6 0.255793
\(786\) 7.60107e7 4.38852
\(787\) 2.07834e7 1.19613 0.598067 0.801446i \(-0.295936\pi\)
0.598067 + 0.801446i \(0.295936\pi\)
\(788\) 1.18926e7 0.682277
\(789\) 6.41766e6 0.367015
\(790\) 1.48532e7 0.846746
\(791\) 1.82434e7 1.03673
\(792\) −9.74829e6 −0.552224
\(793\) −1.72258e7 −0.972740
\(794\) 4.04282e7 2.27579
\(795\) 8.12319e6 0.455836
\(796\) 2.29366e7 1.28306
\(797\) 1.28133e7 0.714522 0.357261 0.934005i \(-0.383711\pi\)
0.357261 + 0.934005i \(0.383711\pi\)
\(798\) 3.36282e7 1.86937
\(799\) −2.78565e7 −1.54369
\(800\) −2.01708e7 −1.11429
\(801\) 4.13899e7 2.27936
\(802\) 1.53158e7 0.840823
\(803\) 8.36476e6 0.457788
\(804\) 2.70117e7 1.47371
\(805\) 4.21451e6 0.229223
\(806\) −3.46268e7 −1.87748
\(807\) −3.52070e7 −1.90303
\(808\) −4.28749e6 −0.231034
\(809\) 1.35114e7 0.725821 0.362910 0.931824i \(-0.381783\pi\)
0.362910 + 0.931824i \(0.381783\pi\)
\(810\) 5.12923e7 2.74688
\(811\) −8.79590e6 −0.469600 −0.234800 0.972044i \(-0.575443\pi\)
−0.234800 + 0.972044i \(0.575443\pi\)
\(812\) −1.47440e7 −0.784741
\(813\) 3.80457e7 2.01873
\(814\) −4.00356e7 −2.11780
\(815\) 749282. 0.0395140
\(816\) −3.54713e7 −1.86489
\(817\) 1.78461e7 0.935380
\(818\) −5.03373e7 −2.63031
\(819\) 6.72095e7 3.50123
\(820\) 1.58027e7 0.820723
\(821\) −6.26640e6 −0.324459 −0.162230 0.986753i \(-0.551869\pi\)
−0.162230 + 0.986753i \(0.551869\pi\)
\(822\) −7.98097e7 −4.11980
\(823\) −669279. −0.0344435 −0.0172218 0.999852i \(-0.505482\pi\)
−0.0172218 + 0.999852i \(0.505482\pi\)
\(824\) 1.92456e6 0.0987444
\(825\) 3.15639e7 1.61457
\(826\) −8.91318e6 −0.454551
\(827\) 1.63500e7 0.831294 0.415647 0.909526i \(-0.363555\pi\)
0.415647 + 0.909526i \(0.363555\pi\)
\(828\) 3.38907e7 1.71793
\(829\) −1.20501e6 −0.0608982 −0.0304491 0.999536i \(-0.509694\pi\)
−0.0304491 + 0.999536i \(0.509694\pi\)
\(830\) −1.32089e7 −0.665535
\(831\) −3.47892e7 −1.74760
\(832\) 3.49430e7 1.75006
\(833\) 4.77574e6 0.238467
\(834\) 1.05473e7 0.525078
\(835\) −1.53007e7 −0.759444
\(836\) −1.80651e7 −0.893974
\(837\) 6.41231e7 3.16374
\(838\) 3.84050e7 1.88920
\(839\) 9.09313e6 0.445973 0.222987 0.974822i \(-0.428419\pi\)
0.222987 + 0.974822i \(0.428419\pi\)
\(840\) 3.09430e6 0.151309
\(841\) −7.87450e6 −0.383913
\(842\) 1.01212e7 0.491987
\(843\) −6.92120e6 −0.335438
\(844\) 1.76067e7 0.850788
\(845\) −9.85636e6 −0.474870
\(846\) −1.16825e8 −5.61190
\(847\) −2.61484e6 −0.125238
\(848\) −8.88904e6 −0.424488
\(849\) 8.52525e6 0.405918
\(850\) −2.66837e7 −1.26677
\(851\) 1.56995e7 0.743125
\(852\) −5.29871e7 −2.50076
\(853\) −1.35894e7 −0.639482 −0.319741 0.947505i \(-0.603596\pi\)
−0.319741 + 0.947505i \(0.603596\pi\)
\(854\) 1.89432e7 0.888809
\(855\) 2.09139e7 0.978409
\(856\) −2.67814e6 −0.124925
\(857\) 4.02924e7 1.87401 0.937003 0.349322i \(-0.113588\pi\)
0.937003 + 0.349322i \(0.113588\pi\)
\(858\) −9.25783e7 −4.29330
\(859\) −2.40344e7 −1.11135 −0.555675 0.831400i \(-0.687540\pi\)
−0.555675 + 0.831400i \(0.687540\pi\)
\(860\) 1.45584e7 0.671225
\(861\) −5.78472e7 −2.65935
\(862\) −1.43917e6 −0.0659694
\(863\) −3.82161e7 −1.74670 −0.873352 0.487089i \(-0.838059\pi\)
−0.873352 + 0.487089i \(0.838059\pi\)
\(864\) −1.09558e8 −4.99299
\(865\) 1.12544e7 0.511427
\(866\) 4.88280e7 2.21245
\(867\) −1.08111e7 −0.488450
\(868\) 2.01774e7 0.909006
\(869\) 2.92085e7 1.31208
\(870\) −2.35120e7 −1.05315
\(871\) 2.12960e7 0.951158
\(872\) −3.06482e6 −0.136494
\(873\) 6.59198e7 2.92739
\(874\) 1.33690e7 0.591998
\(875\) −1.68696e7 −0.744879
\(876\) −2.13511e7 −0.940070
\(877\) −2.00451e7 −0.880055 −0.440028 0.897984i \(-0.645031\pi\)
−0.440028 + 0.897984i \(0.645031\pi\)
\(878\) −3.48701e7 −1.52657
\(879\) 5.58420e7 2.43775
\(880\) 9.93780e6 0.432597
\(881\) −4.25741e7 −1.84802 −0.924009 0.382372i \(-0.875107\pi\)
−0.924009 + 0.382372i \(0.875107\pi\)
\(882\) 2.00286e7 0.866918
\(883\) 976214. 0.0421350 0.0210675 0.999778i \(-0.493294\pi\)
0.0210675 + 0.999778i \(0.493294\pi\)
\(884\) 4.14711e7 1.78490
\(885\) −7.53160e6 −0.323243
\(886\) −1.76333e7 −0.754657
\(887\) 4.23359e7 1.80676 0.903379 0.428843i \(-0.141078\pi\)
0.903379 + 0.428843i \(0.141078\pi\)
\(888\) 1.15266e7 0.490533
\(889\) 2.45310e7 1.04103
\(890\) 1.33194e7 0.563650
\(891\) 1.00865e8 4.25644
\(892\) 3.61724e7 1.52218
\(893\) −2.44194e7 −1.02472
\(894\) −8.80717e7 −3.68547
\(895\) 7.02960e6 0.293341
\(896\) −7.84090e6 −0.326284
\(897\) 3.63035e7 1.50649
\(898\) 2.31981e7 0.959980
\(899\) −1.72934e7 −0.713645
\(900\) −5.92975e7 −2.44023
\(901\) −1.35043e7 −0.554190
\(902\) 5.86461e7 2.40006
\(903\) −5.32925e7 −2.17494
\(904\) 5.32496e6 0.216718
\(905\) −1.63356e7 −0.663002
\(906\) 1.60910e7 0.651272
\(907\) 4.23365e6 0.170882 0.0854411 0.996343i \(-0.472770\pi\)
0.0854411 + 0.996343i \(0.472770\pi\)
\(908\) −9.09449e6 −0.366070
\(909\) 8.65367e7 3.47369
\(910\) 2.16282e7 0.865800
\(911\) −2.27781e6 −0.0909330 −0.0454665 0.998966i \(-0.514477\pi\)
−0.0454665 + 0.998966i \(0.514477\pi\)
\(912\) −3.10947e7 −1.23794
\(913\) −2.59750e7 −1.03128
\(914\) −1.90059e7 −0.752527
\(915\) 1.60069e7 0.632054
\(916\) −2.31886e6 −0.0913137
\(917\) −3.49201e7 −1.37136
\(918\) −1.44933e8 −5.67624
\(919\) 1.14014e6 0.0445318 0.0222659 0.999752i \(-0.492912\pi\)
0.0222659 + 0.999752i \(0.492912\pi\)
\(920\) 1.23015e6 0.0479168
\(921\) −4.13189e7 −1.60509
\(922\) 7.22828e7 2.80032
\(923\) −4.17750e7 −1.61403
\(924\) 5.39465e7 2.07866
\(925\) −2.74689e7 −1.05557
\(926\) −3.53954e7 −1.35650
\(927\) −3.88443e7 −1.48466
\(928\) 2.95469e7 1.12627
\(929\) −1.88340e6 −0.0715985 −0.0357993 0.999359i \(-0.511398\pi\)
−0.0357993 + 0.999359i \(0.511398\pi\)
\(930\) 3.21765e7 1.21992
\(931\) 4.18648e6 0.158298
\(932\) 3.85539e7 1.45388
\(933\) 4.34989e7 1.63597
\(934\) −7.76068e6 −0.291093
\(935\) 1.50975e7 0.564777
\(936\) 1.96174e7 0.731900
\(937\) 3.16256e7 1.17676 0.588382 0.808583i \(-0.299765\pi\)
0.588382 + 0.808583i \(0.299765\pi\)
\(938\) −2.34192e7 −0.869089
\(939\) −6.24322e7 −2.31071
\(940\) −1.99208e7 −0.735338
\(941\) 4.16449e7 1.53316 0.766581 0.642148i \(-0.221956\pi\)
0.766581 + 0.642148i \(0.221956\pi\)
\(942\) −4.18349e7 −1.53607
\(943\) −2.29974e7 −0.842169
\(944\) 8.24168e6 0.301013
\(945\) −4.00520e7 −1.45896
\(946\) 5.40284e7 1.96288
\(947\) 9.04562e6 0.327766 0.163883 0.986480i \(-0.447598\pi\)
0.163883 + 0.986480i \(0.447598\pi\)
\(948\) −7.45549e7 −2.69436
\(949\) −1.68332e7 −0.606738
\(950\) −2.33913e7 −0.840903
\(951\) 2.10668e7 0.755349
\(952\) −5.14406e6 −0.183956
\(953\) 3.55147e7 1.26671 0.633353 0.773863i \(-0.281678\pi\)
0.633353 + 0.773863i \(0.281678\pi\)
\(954\) −5.66343e7 −2.01469
\(955\) −2.07091e7 −0.734773
\(956\) 5.95924e7 2.10885
\(957\) −4.62358e7 −1.63192
\(958\) 2.48704e6 0.0875524
\(959\) 3.66654e7 1.28739
\(960\) −3.24704e7 −1.13713
\(961\) −4.96283e6 −0.173349
\(962\) 8.05674e7 2.80687
\(963\) 5.40542e7 1.87830
\(964\) −1.98883e7 −0.689294
\(965\) −5.18756e6 −0.179327
\(966\) −3.99229e7 −1.37651
\(967\) 4.89615e7 1.68379 0.841896 0.539640i \(-0.181440\pi\)
0.841896 + 0.539640i \(0.181440\pi\)
\(968\) −763229. −0.0261798
\(969\) −4.72391e7 −1.61619
\(970\) 2.12132e7 0.723896
\(971\) 1.50444e7 0.512067 0.256034 0.966668i \(-0.417584\pi\)
0.256034 + 0.966668i \(0.417584\pi\)
\(972\) −1.41933e8 −4.81855
\(973\) −4.84551e6 −0.164081
\(974\) 1.57515e7 0.532016
\(975\) −6.35191e7 −2.13990
\(976\) −1.75160e7 −0.588588
\(977\) 1.54848e7 0.519002 0.259501 0.965743i \(-0.416442\pi\)
0.259501 + 0.965743i \(0.416442\pi\)
\(978\) −7.09774e6 −0.237286
\(979\) 2.61923e7 0.873407
\(980\) 3.41523e6 0.113594
\(981\) 6.18588e7 2.05224
\(982\) −6.82151e7 −2.25737
\(983\) −3.31785e7 −1.09515 −0.547574 0.836757i \(-0.684448\pi\)
−0.547574 + 0.836757i \(0.684448\pi\)
\(984\) −1.68847e7 −0.555911
\(985\) −8.71265e6 −0.286128
\(986\) 3.90872e7 1.28039
\(987\) 7.29219e7 2.38268
\(988\) 3.63541e7 1.18484
\(989\) −2.11866e7 −0.688765
\(990\) 6.33162e7 2.05318
\(991\) 4.10318e7 1.32720 0.663600 0.748088i \(-0.269028\pi\)
0.663600 + 0.748088i \(0.269028\pi\)
\(992\) −4.04353e7 −1.30461
\(993\) −4.25101e7 −1.36810
\(994\) 4.59399e7 1.47477
\(995\) −1.68037e7 −0.538079
\(996\) 6.63013e7 2.11774
\(997\) −1.82199e6 −0.0580507 −0.0290254 0.999579i \(-0.509240\pi\)
−0.0290254 + 0.999579i \(0.509240\pi\)
\(998\) 6.47059e7 2.05645
\(999\) −1.49198e8 −4.72986
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.1.18 111
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
547.6.a.a.1.18 111 1.1 even 1 trivial