Properties

Label 1045.6.a.e.1.17
Level $1045$
Weight $6$
Character 1045.1
Self dual yes
Analytic conductor $167.601$
Analytic rank $1$
Dimension $38$
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] = [1045,6,Mod(1,1045)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("1045.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1045.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: \(167.601091705\)
Analytic rank: \(1\)
Dimension: \(38\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) \(=\) 1045.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.59417 q^{2} +30.0518 q^{3} -25.2703 q^{4} +25.0000 q^{5} -77.9597 q^{6} -144.749 q^{7} +148.569 q^{8} +660.111 q^{9} +O(q^{10})\) \(q-2.59417 q^{2} +30.0518 q^{3} -25.2703 q^{4} +25.0000 q^{5} -77.9597 q^{6} -144.749 q^{7} +148.569 q^{8} +660.111 q^{9} -64.8544 q^{10} +121.000 q^{11} -759.417 q^{12} -665.516 q^{13} +375.505 q^{14} +751.295 q^{15} +423.234 q^{16} -777.887 q^{17} -1712.44 q^{18} -361.000 q^{19} -631.756 q^{20} -4349.98 q^{21} -313.895 q^{22} +2896.34 q^{23} +4464.77 q^{24} +625.000 q^{25} +1726.47 q^{26} +12535.0 q^{27} +3657.85 q^{28} -6731.31 q^{29} -1948.99 q^{30} +3887.42 q^{31} -5852.15 q^{32} +3636.27 q^{33} +2017.98 q^{34} -3618.73 q^{35} -16681.2 q^{36} -7108.78 q^{37} +936.497 q^{38} -20000.0 q^{39} +3714.23 q^{40} -2590.18 q^{41} +11284.6 q^{42} +4330.35 q^{43} -3057.70 q^{44} +16502.8 q^{45} -7513.60 q^{46} -13303.1 q^{47} +12719.0 q^{48} +4145.35 q^{49} -1621.36 q^{50} -23376.9 q^{51} +16817.8 q^{52} +16504.1 q^{53} -32517.9 q^{54} +3025.00 q^{55} -21505.3 q^{56} -10848.7 q^{57} +17462.2 q^{58} -10810.7 q^{59} -18985.4 q^{60} -28655.1 q^{61} -10084.6 q^{62} -95550.6 q^{63} +1638.02 q^{64} -16637.9 q^{65} -9433.12 q^{66} -39787.3 q^{67} +19657.4 q^{68} +87040.1 q^{69} +9387.62 q^{70} +51462.1 q^{71} +98072.1 q^{72} +7933.28 q^{73} +18441.4 q^{74} +18782.4 q^{75} +9122.56 q^{76} -17514.7 q^{77} +51883.4 q^{78} +69304.9 q^{79} +10580.9 q^{80} +216291. q^{81} +6719.39 q^{82} -61145.2 q^{83} +109925. q^{84} -19447.2 q^{85} -11233.7 q^{86} -202288. q^{87} +17976.9 q^{88} +34860.5 q^{89} -42811.1 q^{90} +96333.0 q^{91} -73191.1 q^{92} +116824. q^{93} +34510.6 q^{94} -9025.00 q^{95} -175868. q^{96} -152355. q^{97} -10753.8 q^{98} +79873.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 38 q - 24 q^{2} - 63 q^{3} + 594 q^{4} + 950 q^{5} - 67 q^{6} - 729 q^{7} - 1272 q^{8} + 3029 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 38 q - 24 q^{2} - 63 q^{3} + 594 q^{4} + 950 q^{5} - 67 q^{6} - 729 q^{7} - 1272 q^{8} + 3029 q^{9} - 600 q^{10} + 4598 q^{11} - 2008 q^{12} - 2663 q^{13} - 1565 q^{14} - 1575 q^{15} + 12390 q^{16} - 3311 q^{17} - 6383 q^{18} - 13718 q^{19} + 14850 q^{20} - 8179 q^{21} - 2904 q^{22} - 3412 q^{23} - 4100 q^{24} + 23750 q^{25} - 1399 q^{26} - 31596 q^{27} - 43653 q^{28} - 13633 q^{29} - 1675 q^{30} - 13789 q^{31} - 58603 q^{32} - 7623 q^{33} - 29149 q^{34} - 18225 q^{35} + 50641 q^{36} - 12103 q^{37} + 8664 q^{38} - 50960 q^{39} - 31800 q^{40} - 37885 q^{41} + 51100 q^{42} - 56119 q^{43} + 71874 q^{44} + 75725 q^{45} - 56291 q^{46} - 37532 q^{47} - 113895 q^{48} + 153501 q^{49} - 15000 q^{50} + 32882 q^{51} - 169554 q^{52} - 51511 q^{53} - 175060 q^{54} + 114950 q^{55} - 84247 q^{56} + 22743 q^{57} - 256962 q^{58} - 154267 q^{59} - 50200 q^{60} - 47165 q^{61} + 143002 q^{62} - 358780 q^{63} + 142292 q^{64} - 66575 q^{65} - 8107 q^{66} - 161712 q^{67} - 210188 q^{68} - 124602 q^{69} - 39125 q^{70} + 6118 q^{71} - 327878 q^{72} - 152182 q^{73} - 167349 q^{74} - 39375 q^{75} - 214434 q^{76} - 88209 q^{77} - 216594 q^{78} - 140433 q^{79} + 309750 q^{80} + 382874 q^{81} - 29842 q^{82} - 515287 q^{83} + 29222 q^{84} - 82775 q^{85} + 204974 q^{86} - 106764 q^{87} - 153912 q^{88} - 271610 q^{89} - 159575 q^{90} - 44332 q^{91} + 236348 q^{92} + 25202 q^{93} - 496224 q^{94} - 342950 q^{95} - 275218 q^{96} - 126390 q^{97} - 285506 q^{98} + 366509 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.59417 −0.458590 −0.229295 0.973357i \(-0.573642\pi\)
−0.229295 + 0.973357i \(0.573642\pi\)
\(3\) 30.0518 1.92782 0.963912 0.266220i \(-0.0857748\pi\)
0.963912 + 0.266220i \(0.0857748\pi\)
\(4\) −25.2703 −0.789696
\(5\) 25.0000 0.447214
\(6\) −77.9597 −0.884080
\(7\) −144.749 −1.11653 −0.558266 0.829662i \(-0.688533\pi\)
−0.558266 + 0.829662i \(0.688533\pi\)
\(8\) 148.569 0.820736
\(9\) 660.111 2.71651
\(10\) −64.8544 −0.205088
\(11\) 121.000 0.301511
\(12\) −759.417 −1.52239
\(13\) −665.516 −1.09220 −0.546098 0.837722i \(-0.683887\pi\)
−0.546098 + 0.837722i \(0.683887\pi\)
\(14\) 375.505 0.512030
\(15\) 751.295 0.862149
\(16\) 423.234 0.413315
\(17\) −777.887 −0.652821 −0.326411 0.945228i \(-0.605839\pi\)
−0.326411 + 0.945228i \(0.605839\pi\)
\(18\) −1712.44 −1.24576
\(19\) −361.000 −0.229416
\(20\) −631.756 −0.353163
\(21\) −4349.98 −2.15248
\(22\) −313.895 −0.138270
\(23\) 2896.34 1.14164 0.570820 0.821075i \(-0.306625\pi\)
0.570820 + 0.821075i \(0.306625\pi\)
\(24\) 4464.77 1.58223
\(25\) 625.000 0.200000
\(26\) 1726.47 0.500869
\(27\) 12535.0 3.30913
\(28\) 3657.85 0.881720
\(29\) −6731.31 −1.48629 −0.743147 0.669128i \(-0.766668\pi\)
−0.743147 + 0.669128i \(0.766668\pi\)
\(30\) −1948.99 −0.395373
\(31\) 3887.42 0.726536 0.363268 0.931685i \(-0.381661\pi\)
0.363268 + 0.931685i \(0.381661\pi\)
\(32\) −5852.15 −1.01028
\(33\) 3636.27 0.581261
\(34\) 2017.98 0.299377
\(35\) −3618.73 −0.499328
\(36\) −16681.2 −2.14521
\(37\) −7108.78 −0.853672 −0.426836 0.904329i \(-0.640372\pi\)
−0.426836 + 0.904329i \(0.640372\pi\)
\(38\) 936.497 0.105208
\(39\) −20000.0 −2.10556
\(40\) 3714.23 0.367044
\(41\) −2590.18 −0.240642 −0.120321 0.992735i \(-0.538392\pi\)
−0.120321 + 0.992735i \(0.538392\pi\)
\(42\) 11284.6 0.987104
\(43\) 4330.35 0.357151 0.178576 0.983926i \(-0.442851\pi\)
0.178576 + 0.983926i \(0.442851\pi\)
\(44\) −3057.70 −0.238102
\(45\) 16502.8 1.21486
\(46\) −7513.60 −0.523544
\(47\) −13303.1 −0.878432 −0.439216 0.898381i \(-0.644744\pi\)
−0.439216 + 0.898381i \(0.644744\pi\)
\(48\) 12719.0 0.796798
\(49\) 4145.35 0.246644
\(50\) −1621.36 −0.0917179
\(51\) −23376.9 −1.25853
\(52\) 16817.8 0.862502
\(53\) 16504.1 0.807051 0.403525 0.914968i \(-0.367785\pi\)
0.403525 + 0.914968i \(0.367785\pi\)
\(54\) −32517.9 −1.51753
\(55\) 3025.00 0.134840
\(56\) −21505.3 −0.916378
\(57\) −10848.7 −0.442273
\(58\) 17462.2 0.681599
\(59\) −10810.7 −0.404318 −0.202159 0.979353i \(-0.564796\pi\)
−0.202159 + 0.979353i \(0.564796\pi\)
\(60\) −18985.4 −0.680835
\(61\) −28655.1 −0.985999 −0.493000 0.870029i \(-0.664100\pi\)
−0.493000 + 0.870029i \(0.664100\pi\)
\(62\) −10084.6 −0.333182
\(63\) −95550.6 −3.03307
\(64\) 1638.02 0.0499884
\(65\) −16637.9 −0.488444
\(66\) −9433.12 −0.266560
\(67\) −39787.3 −1.08282 −0.541412 0.840757i \(-0.682110\pi\)
−0.541412 + 0.840757i \(0.682110\pi\)
\(68\) 19657.4 0.515530
\(69\) 87040.1 2.20088
\(70\) 9387.62 0.228987
\(71\) 51462.1 1.21155 0.605775 0.795636i \(-0.292863\pi\)
0.605775 + 0.795636i \(0.292863\pi\)
\(72\) 98072.1 2.22954
\(73\) 7933.28 0.174239 0.0871195 0.996198i \(-0.472234\pi\)
0.0871195 + 0.996198i \(0.472234\pi\)
\(74\) 18441.4 0.391485
\(75\) 18782.4 0.385565
\(76\) 9122.56 0.181169
\(77\) −17514.7 −0.336647
\(78\) 51883.4 0.965588
\(79\) 69304.9 1.24938 0.624692 0.780871i \(-0.285224\pi\)
0.624692 + 0.780871i \(0.285224\pi\)
\(80\) 10580.9 0.184840
\(81\) 216291. 3.66291
\(82\) 6719.39 0.110356
\(83\) −61145.2 −0.974243 −0.487121 0.873334i \(-0.661953\pi\)
−0.487121 + 0.873334i \(0.661953\pi\)
\(84\) 109925. 1.69980
\(85\) −19447.2 −0.291951
\(86\) −11233.7 −0.163786
\(87\) −202288. −2.86531
\(88\) 17976.9 0.247461
\(89\) 34860.5 0.466508 0.233254 0.972416i \(-0.425063\pi\)
0.233254 + 0.972416i \(0.425063\pi\)
\(90\) −42811.1 −0.557122
\(91\) 96333.0 1.21947
\(92\) −73191.1 −0.901548
\(93\) 116824. 1.40063
\(94\) 34510.6 0.402840
\(95\) −9025.00 −0.102598
\(96\) −175868. −1.94764
\(97\) −152355. −1.64410 −0.822050 0.569415i \(-0.807170\pi\)
−0.822050 + 0.569415i \(0.807170\pi\)
\(98\) −10753.8 −0.113108
\(99\) 79873.5 0.819058
\(100\) −15793.9 −0.157939
\(101\) −12408.5 −0.121036 −0.0605181 0.998167i \(-0.519275\pi\)
−0.0605181 + 0.998167i \(0.519275\pi\)
\(102\) 60643.8 0.577147
\(103\) 8677.70 0.0805956 0.0402978 0.999188i \(-0.487169\pi\)
0.0402978 + 0.999188i \(0.487169\pi\)
\(104\) −98875.1 −0.896404
\(105\) −108749. −0.962618
\(106\) −42814.4 −0.370105
\(107\) −163744. −1.38263 −0.691314 0.722555i \(-0.742968\pi\)
−0.691314 + 0.722555i \(0.742968\pi\)
\(108\) −316761. −2.61320
\(109\) −138019. −1.11268 −0.556342 0.830953i \(-0.687796\pi\)
−0.556342 + 0.830953i \(0.687796\pi\)
\(110\) −7847.38 −0.0618362
\(111\) −213632. −1.64573
\(112\) −61262.8 −0.461479
\(113\) −74196.5 −0.546623 −0.273311 0.961926i \(-0.588119\pi\)
−0.273311 + 0.961926i \(0.588119\pi\)
\(114\) 28143.4 0.202822
\(115\) 72408.4 0.510557
\(116\) 170102. 1.17372
\(117\) −439315. −2.96696
\(118\) 28044.8 0.185416
\(119\) 112599. 0.728896
\(120\) 111619. 0.707597
\(121\) 14641.0 0.0909091
\(122\) 74336.2 0.452169
\(123\) −77839.7 −0.463915
\(124\) −98236.1 −0.573742
\(125\) 15625.0 0.0894427
\(126\) 247875. 1.39093
\(127\) 220133. 1.21109 0.605545 0.795811i \(-0.292955\pi\)
0.605545 + 0.795811i \(0.292955\pi\)
\(128\) 183020. 0.987353
\(129\) 130135. 0.688525
\(130\) 43161.6 0.223996
\(131\) −352552. −1.79492 −0.897460 0.441095i \(-0.854590\pi\)
−0.897460 + 0.441095i \(0.854590\pi\)
\(132\) −91889.5 −0.459019
\(133\) 52254.5 0.256150
\(134\) 103215. 0.496572
\(135\) 313374. 1.47989
\(136\) −115570. −0.535794
\(137\) −183588. −0.835685 −0.417842 0.908519i \(-0.637214\pi\)
−0.417842 + 0.908519i \(0.637214\pi\)
\(138\) −225797. −1.00930
\(139\) −122620. −0.538299 −0.269150 0.963098i \(-0.586743\pi\)
−0.269150 + 0.963098i \(0.586743\pi\)
\(140\) 91446.3 0.394317
\(141\) −399782. −1.69346
\(142\) −133502. −0.555604
\(143\) −80527.5 −0.329309
\(144\) 279382. 1.12277
\(145\) −168283. −0.664691
\(146\) −20580.3 −0.0799042
\(147\) 124575. 0.475487
\(148\) 179641. 0.674141
\(149\) 272693. 1.00626 0.503128 0.864212i \(-0.332183\pi\)
0.503128 + 0.864212i \(0.332183\pi\)
\(150\) −48724.8 −0.176816
\(151\) −523658. −1.86898 −0.934492 0.355985i \(-0.884145\pi\)
−0.934492 + 0.355985i \(0.884145\pi\)
\(152\) −53633.4 −0.188290
\(153\) −513492. −1.77339
\(154\) 45436.1 0.154383
\(155\) 97185.5 0.324917
\(156\) 505404. 1.66275
\(157\) −271502. −0.879072 −0.439536 0.898225i \(-0.644857\pi\)
−0.439536 + 0.898225i \(0.644857\pi\)
\(158\) −179789. −0.572955
\(159\) 495977. 1.55585
\(160\) −146304. −0.451810
\(161\) −419242. −1.27468
\(162\) −561096. −1.67977
\(163\) 280699. 0.827507 0.413753 0.910389i \(-0.364218\pi\)
0.413753 + 0.910389i \(0.364218\pi\)
\(164\) 65454.6 0.190034
\(165\) 90906.7 0.259948
\(166\) 158621. 0.446778
\(167\) 526263. 1.46020 0.730099 0.683342i \(-0.239474\pi\)
0.730099 + 0.683342i \(0.239474\pi\)
\(168\) −646272. −1.76662
\(169\) 71618.7 0.192890
\(170\) 50449.4 0.133886
\(171\) −238300. −0.623210
\(172\) −109429. −0.282041
\(173\) −190186. −0.483130 −0.241565 0.970385i \(-0.577661\pi\)
−0.241565 + 0.970385i \(0.577661\pi\)
\(174\) 524771. 1.31400
\(175\) −90468.3 −0.223306
\(176\) 51211.3 0.124619
\(177\) −324881. −0.779455
\(178\) −90434.3 −0.213936
\(179\) 457020. 1.06611 0.533056 0.846080i \(-0.321044\pi\)
0.533056 + 0.846080i \(0.321044\pi\)
\(180\) −417030. −0.959369
\(181\) −474720. −1.07706 −0.538531 0.842605i \(-0.681021\pi\)
−0.538531 + 0.842605i \(0.681021\pi\)
\(182\) −249905. −0.559237
\(183\) −861136. −1.90083
\(184\) 430306. 0.936985
\(185\) −177720. −0.381774
\(186\) −303062. −0.642316
\(187\) −94124.4 −0.196833
\(188\) 336173. 0.693694
\(189\) −1.81442e6 −3.69475
\(190\) 23412.4 0.0470503
\(191\) 385660. 0.764929 0.382465 0.923970i \(-0.375075\pi\)
0.382465 + 0.923970i \(0.375075\pi\)
\(192\) 49225.4 0.0963688
\(193\) −637298. −1.23154 −0.615771 0.787925i \(-0.711155\pi\)
−0.615771 + 0.787925i \(0.711155\pi\)
\(194\) 395236. 0.753967
\(195\) −499999. −0.941635
\(196\) −104754. −0.194774
\(197\) −221197. −0.406082 −0.203041 0.979170i \(-0.565082\pi\)
−0.203041 + 0.979170i \(0.565082\pi\)
\(198\) −207206. −0.375611
\(199\) −77746.7 −0.139171 −0.0695856 0.997576i \(-0.522168\pi\)
−0.0695856 + 0.997576i \(0.522168\pi\)
\(200\) 92855.7 0.164147
\(201\) −1.19568e6 −2.08749
\(202\) 32189.8 0.0555060
\(203\) 974352. 1.65949
\(204\) 590741. 0.993852
\(205\) −64754.6 −0.107618
\(206\) −22511.5 −0.0369603
\(207\) 1.91190e6 3.10127
\(208\) −281669. −0.451420
\(209\) −43681.0 −0.0691714
\(210\) 282115. 0.441446
\(211\) 2153.47 0.00332991 0.00166495 0.999999i \(-0.499470\pi\)
0.00166495 + 0.999999i \(0.499470\pi\)
\(212\) −417062. −0.637324
\(213\) 1.54653e6 2.33566
\(214\) 424780. 0.634059
\(215\) 108259. 0.159723
\(216\) 1.86231e6 2.71592
\(217\) −562701. −0.811201
\(218\) 358045. 0.510266
\(219\) 238409. 0.335902
\(220\) −76442.5 −0.106483
\(221\) 517697. 0.713008
\(222\) 554198. 0.754715
\(223\) −1.34187e6 −1.80697 −0.903483 0.428624i \(-0.858998\pi\)
−0.903483 + 0.428624i \(0.858998\pi\)
\(224\) 847095. 1.12801
\(225\) 412570. 0.543302
\(226\) 192479. 0.250675
\(227\) −272518. −0.351019 −0.175509 0.984478i \(-0.556157\pi\)
−0.175509 + 0.984478i \(0.556157\pi\)
\(228\) 274150. 0.349261
\(229\) −459425. −0.578930 −0.289465 0.957189i \(-0.593477\pi\)
−0.289465 + 0.957189i \(0.593477\pi\)
\(230\) −187840. −0.234136
\(231\) −526347. −0.648997
\(232\) −1.00006e6 −1.21985
\(233\) −189474. −0.228644 −0.114322 0.993444i \(-0.536470\pi\)
−0.114322 + 0.993444i \(0.536470\pi\)
\(234\) 1.13966e6 1.36062
\(235\) −332578. −0.392847
\(236\) 273189. 0.319288
\(237\) 2.08274e6 2.40859
\(238\) −292101. −0.334264
\(239\) 1.32750e6 1.50328 0.751642 0.659572i \(-0.229262\pi\)
0.751642 + 0.659572i \(0.229262\pi\)
\(240\) 317974. 0.356339
\(241\) 175730. 0.194897 0.0974483 0.995241i \(-0.468932\pi\)
0.0974483 + 0.995241i \(0.468932\pi\)
\(242\) −37981.3 −0.0416900
\(243\) 3.45394e6 3.75231
\(244\) 724121. 0.778639
\(245\) 103634. 0.110303
\(246\) 201930. 0.212747
\(247\) 240251. 0.250567
\(248\) 577550. 0.596294
\(249\) −1.83752e6 −1.87817
\(250\) −40534.0 −0.0410175
\(251\) −131282. −0.131529 −0.0657644 0.997835i \(-0.520949\pi\)
−0.0657644 + 0.997835i \(0.520949\pi\)
\(252\) 2.41459e6 2.39520
\(253\) 350457. 0.344217
\(254\) −571064. −0.555393
\(255\) −584423. −0.562830
\(256\) −527201. −0.502778
\(257\) −755502. −0.713514 −0.356757 0.934197i \(-0.616118\pi\)
−0.356757 + 0.934197i \(0.616118\pi\)
\(258\) −337593. −0.315751
\(259\) 1.02899e6 0.953152
\(260\) 420444. 0.385722
\(261\) −4.44341e6 −4.03753
\(262\) 914582. 0.823132
\(263\) 1.56982e6 1.39946 0.699732 0.714406i \(-0.253303\pi\)
0.699732 + 0.714406i \(0.253303\pi\)
\(264\) 540237. 0.477062
\(265\) 412601. 0.360924
\(266\) −135557. −0.117468
\(267\) 1.04762e6 0.899346
\(268\) 1.00544e6 0.855101
\(269\) −1.19913e6 −1.01038 −0.505192 0.863007i \(-0.668578\pi\)
−0.505192 + 0.863007i \(0.668578\pi\)
\(270\) −812946. −0.678660
\(271\) 436478. 0.361027 0.180513 0.983573i \(-0.442224\pi\)
0.180513 + 0.983573i \(0.442224\pi\)
\(272\) −329228. −0.269821
\(273\) 2.89498e6 2.35093
\(274\) 476259. 0.383236
\(275\) 75625.0 0.0603023
\(276\) −2.19953e6 −1.73803
\(277\) −538959. −0.422042 −0.211021 0.977481i \(-0.567679\pi\)
−0.211021 + 0.977481i \(0.567679\pi\)
\(278\) 318097. 0.246859
\(279\) 2.56613e6 1.97364
\(280\) −537632. −0.409817
\(281\) 397007. 0.299938 0.149969 0.988691i \(-0.452083\pi\)
0.149969 + 0.988691i \(0.452083\pi\)
\(282\) 1.03711e6 0.776605
\(283\) −1.76214e6 −1.30790 −0.653950 0.756537i \(-0.726890\pi\)
−0.653950 + 0.756537i \(0.726890\pi\)
\(284\) −1.30046e6 −0.956755
\(285\) −271218. −0.197791
\(286\) 208902. 0.151018
\(287\) 374927. 0.268684
\(288\) −3.86307e6 −2.74443
\(289\) −814748. −0.573824
\(290\) 436555. 0.304820
\(291\) −4.57855e6 −3.16954
\(292\) −200476. −0.137596
\(293\) 2.52332e6 1.71713 0.858565 0.512705i \(-0.171357\pi\)
0.858565 + 0.512705i \(0.171357\pi\)
\(294\) −323170. −0.218053
\(295\) −270267. −0.180817
\(296\) −1.05615e6 −0.700639
\(297\) 1.51673e6 0.997739
\(298\) −707413. −0.461458
\(299\) −1.92756e6 −1.24689
\(300\) −474636. −0.304479
\(301\) −626816. −0.398771
\(302\) 1.35846e6 0.857096
\(303\) −372897. −0.233337
\(304\) −152788. −0.0948209
\(305\) −716376. −0.440952
\(306\) 1.33209e6 0.813260
\(307\) 552768. 0.334732 0.167366 0.985895i \(-0.446474\pi\)
0.167366 + 0.985895i \(0.446474\pi\)
\(308\) 442600. 0.265849
\(309\) 260781. 0.155374
\(310\) −252116. −0.149003
\(311\) 3.00558e6 1.76209 0.881045 0.473033i \(-0.156841\pi\)
0.881045 + 0.473033i \(0.156841\pi\)
\(312\) −2.97138e6 −1.72811
\(313\) −2.59535e6 −1.49739 −0.748694 0.662915i \(-0.769319\pi\)
−0.748694 + 0.662915i \(0.769319\pi\)
\(314\) 704324. 0.403133
\(315\) −2.38877e6 −1.35643
\(316\) −1.75135e6 −0.986634
\(317\) −1.88311e6 −1.05251 −0.526255 0.850327i \(-0.676404\pi\)
−0.526255 + 0.850327i \(0.676404\pi\)
\(318\) −1.28665e6 −0.713498
\(319\) −814488. −0.448134
\(320\) 40950.5 0.0223555
\(321\) −4.92080e6 −2.66546
\(322\) 1.08759e6 0.584554
\(323\) 280817. 0.149768
\(324\) −5.46573e6 −2.89258
\(325\) −415948. −0.218439
\(326\) −728182. −0.379486
\(327\) −4.14771e6 −2.14506
\(328\) −384821. −0.197503
\(329\) 1.92561e6 0.980798
\(330\) −235828. −0.119209
\(331\) 1.45682e6 0.730861 0.365430 0.930839i \(-0.380922\pi\)
0.365430 + 0.930839i \(0.380922\pi\)
\(332\) 1.54516e6 0.769355
\(333\) −4.69259e6 −2.31901
\(334\) −1.36522e6 −0.669631
\(335\) −994683. −0.484254
\(336\) −1.84106e6 −0.889651
\(337\) −1.53753e6 −0.737476 −0.368738 0.929533i \(-0.620210\pi\)
−0.368738 + 0.929533i \(0.620210\pi\)
\(338\) −185792. −0.0884574
\(339\) −2.22974e6 −1.05379
\(340\) 491435. 0.230552
\(341\) 470378. 0.219059
\(342\) 618192. 0.285797
\(343\) 1.83276e6 0.841146
\(344\) 643357. 0.293127
\(345\) 2.17600e6 0.984264
\(346\) 493376. 0.221558
\(347\) −684400. −0.305131 −0.152565 0.988293i \(-0.548754\pi\)
−0.152565 + 0.988293i \(0.548754\pi\)
\(348\) 5.11187e6 2.26272
\(349\) −226242. −0.0994281 −0.0497140 0.998763i \(-0.515831\pi\)
−0.0497140 + 0.998763i \(0.515831\pi\)
\(350\) 234691. 0.102406
\(351\) −8.34221e6 −3.61421
\(352\) −708111. −0.304610
\(353\) −3.71916e6 −1.58858 −0.794289 0.607540i \(-0.792156\pi\)
−0.794289 + 0.607540i \(0.792156\pi\)
\(354\) 842798. 0.357450
\(355\) 1.28655e6 0.541822
\(356\) −880935. −0.368399
\(357\) 3.38379e6 1.40518
\(358\) −1.18559e6 −0.488908
\(359\) −463313. −0.189731 −0.0948655 0.995490i \(-0.530242\pi\)
−0.0948655 + 0.995490i \(0.530242\pi\)
\(360\) 2.45180e6 0.997078
\(361\) 130321. 0.0526316
\(362\) 1.23151e6 0.493930
\(363\) 439989. 0.175257
\(364\) −2.43436e6 −0.963011
\(365\) 198332. 0.0779221
\(366\) 2.23394e6 0.871703
\(367\) 2.33654e6 0.905539 0.452770 0.891628i \(-0.350436\pi\)
0.452770 + 0.891628i \(0.350436\pi\)
\(368\) 1.22583e6 0.471856
\(369\) −1.70981e6 −0.653705
\(370\) 461036. 0.175077
\(371\) −2.38895e6 −0.901098
\(372\) −2.95217e6 −1.10607
\(373\) 4.95822e6 1.84525 0.922623 0.385704i \(-0.126041\pi\)
0.922623 + 0.385704i \(0.126041\pi\)
\(374\) 244175. 0.0902656
\(375\) 469560. 0.172430
\(376\) −1.97643e6 −0.720961
\(377\) 4.47980e6 1.62332
\(378\) 4.70694e6 1.69437
\(379\) −5.33490e6 −1.90778 −0.953891 0.300154i \(-0.902962\pi\)
−0.953891 + 0.300154i \(0.902962\pi\)
\(380\) 228064. 0.0810211
\(381\) 6.61541e6 2.33477
\(382\) −1.00047e6 −0.350789
\(383\) −175997. −0.0613069 −0.0306534 0.999530i \(-0.509759\pi\)
−0.0306534 + 0.999530i \(0.509759\pi\)
\(384\) 5.50007e6 1.90344
\(385\) −437867. −0.150553
\(386\) 1.65326e6 0.564772
\(387\) 2.85852e6 0.970204
\(388\) 3.85006e6 1.29834
\(389\) −969606. −0.324879 −0.162439 0.986719i \(-0.551936\pi\)
−0.162439 + 0.986719i \(0.551936\pi\)
\(390\) 1.29709e6 0.431824
\(391\) −2.25302e6 −0.745287
\(392\) 615871. 0.202430
\(393\) −1.05948e7 −3.46029
\(394\) 573823. 0.186225
\(395\) 1.73262e6 0.558742
\(396\) −2.01842e6 −0.646806
\(397\) −1.72016e6 −0.547764 −0.273882 0.961763i \(-0.588308\pi\)
−0.273882 + 0.961763i \(0.588308\pi\)
\(398\) 201689. 0.0638225
\(399\) 1.57034e6 0.493812
\(400\) 264521. 0.0826629
\(401\) −2.55022e6 −0.791985 −0.395993 0.918254i \(-0.629599\pi\)
−0.395993 + 0.918254i \(0.629599\pi\)
\(402\) 3.10181e6 0.957303
\(403\) −2.58714e6 −0.793519
\(404\) 313566. 0.0955818
\(405\) 5.40727e6 1.63810
\(406\) −2.52764e6 −0.761027
\(407\) −860163. −0.257392
\(408\) −3.47309e6 −1.03292
\(409\) 254985. 0.0753714 0.0376857 0.999290i \(-0.488001\pi\)
0.0376857 + 0.999290i \(0.488001\pi\)
\(410\) 167985. 0.0493526
\(411\) −5.51715e6 −1.61105
\(412\) −219288. −0.0636460
\(413\) 1.56484e6 0.451434
\(414\) −4.95981e6 −1.42221
\(415\) −1.52863e6 −0.435695
\(416\) 3.89470e6 1.10342
\(417\) −3.68495e6 −1.03775
\(418\) 113316. 0.0317213
\(419\) 3.25431e6 0.905573 0.452787 0.891619i \(-0.350430\pi\)
0.452787 + 0.891619i \(0.350430\pi\)
\(420\) 2.74813e6 0.760175
\(421\) −2.08852e6 −0.574292 −0.287146 0.957887i \(-0.592707\pi\)
−0.287146 + 0.957887i \(0.592707\pi\)
\(422\) −5586.47 −0.00152706
\(423\) −8.78153e6 −2.38627
\(424\) 2.45199e6 0.662376
\(425\) −486180. −0.130564
\(426\) −4.01196e6 −1.07111
\(427\) 4.14780e6 1.10090
\(428\) 4.13785e6 1.09185
\(429\) −2.42000e6 −0.634850
\(430\) −280842. −0.0732473
\(431\) −362649. −0.0940358 −0.0470179 0.998894i \(-0.514972\pi\)
−0.0470179 + 0.998894i \(0.514972\pi\)
\(432\) 5.30522e6 1.36771
\(433\) −4.47651e6 −1.14741 −0.573706 0.819061i \(-0.694495\pi\)
−0.573706 + 0.819061i \(0.694495\pi\)
\(434\) 1.45974e6 0.372008
\(435\) −5.05720e6 −1.28141
\(436\) 3.48777e6 0.878682
\(437\) −1.04558e6 −0.261910
\(438\) −618476. −0.154041
\(439\) 1.41522e6 0.350480 0.175240 0.984526i \(-0.443930\pi\)
0.175240 + 0.984526i \(0.443930\pi\)
\(440\) 449421. 0.110668
\(441\) 2.73639e6 0.670011
\(442\) −1.34300e6 −0.326978
\(443\) −740508. −0.179275 −0.0896377 0.995974i \(-0.528571\pi\)
−0.0896377 + 0.995974i \(0.528571\pi\)
\(444\) 5.39853e6 1.29963
\(445\) 871514. 0.208629
\(446\) 3.48106e6 0.828656
\(447\) 8.19491e6 1.93988
\(448\) −237102. −0.0558136
\(449\) −4.15714e6 −0.973147 −0.486574 0.873640i \(-0.661753\pi\)
−0.486574 + 0.873640i \(0.661753\pi\)
\(450\) −1.07028e6 −0.249152
\(451\) −313412. −0.0725562
\(452\) 1.87497e6 0.431665
\(453\) −1.57369e7 −3.60307
\(454\) 706959. 0.160974
\(455\) 2.40832e6 0.545364
\(456\) −1.61178e6 −0.362990
\(457\) 8.65673e6 1.93893 0.969467 0.245220i \(-0.0788602\pi\)
0.969467 + 0.245220i \(0.0788602\pi\)
\(458\) 1.19183e6 0.265492
\(459\) −9.75078e6 −2.16027
\(460\) −1.82978e6 −0.403185
\(461\) 2.80291e6 0.614266 0.307133 0.951667i \(-0.400630\pi\)
0.307133 + 0.951667i \(0.400630\pi\)
\(462\) 1.36544e6 0.297623
\(463\) −5.90007e6 −1.27910 −0.639550 0.768749i \(-0.720879\pi\)
−0.639550 + 0.768749i \(0.720879\pi\)
\(464\) −2.84892e6 −0.614307
\(465\) 2.92060e6 0.626383
\(466\) 491529. 0.104854
\(467\) 5.86542e6 1.24453 0.622267 0.782805i \(-0.286212\pi\)
0.622267 + 0.782805i \(0.286212\pi\)
\(468\) 1.11016e7 2.34299
\(469\) 5.75919e6 1.20901
\(470\) 862764. 0.180156
\(471\) −8.15914e6 −1.69470
\(472\) −1.60613e6 −0.331839
\(473\) 523973. 0.107685
\(474\) −5.40299e6 −1.10456
\(475\) −225625. −0.0458831
\(476\) −2.84540e6 −0.575606
\(477\) 1.08945e7 2.19236
\(478\) −3.44378e6 −0.689390
\(479\) −5.37524e6 −1.07043 −0.535216 0.844715i \(-0.679770\pi\)
−0.535216 + 0.844715i \(0.679770\pi\)
\(480\) −4.39670e6 −0.871010
\(481\) 4.73101e6 0.932376
\(482\) −455875. −0.0893776
\(483\) −1.25990e7 −2.45736
\(484\) −369982. −0.0717905
\(485\) −3.80888e6 −0.735264
\(486\) −8.96013e6 −1.72077
\(487\) −8.03326e6 −1.53486 −0.767431 0.641132i \(-0.778465\pi\)
−0.767431 + 0.641132i \(0.778465\pi\)
\(488\) −4.25725e6 −0.809245
\(489\) 8.43551e6 1.59529
\(490\) −268844. −0.0505836
\(491\) 3.32940e6 0.623251 0.311625 0.950205i \(-0.399127\pi\)
0.311625 + 0.950205i \(0.399127\pi\)
\(492\) 1.96703e6 0.366352
\(493\) 5.23620e6 0.970284
\(494\) −623254. −0.114907
\(495\) 1.99684e6 0.366294
\(496\) 1.64529e6 0.300288
\(497\) −7.44909e6 −1.35273
\(498\) 4.76686e6 0.861309
\(499\) −4.80316e6 −0.863527 −0.431763 0.901987i \(-0.642108\pi\)
−0.431763 + 0.901987i \(0.642108\pi\)
\(500\) −394848. −0.0706325
\(501\) 1.58152e7 2.81500
\(502\) 340569. 0.0603178
\(503\) 1.24139e6 0.218770 0.109385 0.993999i \(-0.465112\pi\)
0.109385 + 0.993999i \(0.465112\pi\)
\(504\) −1.41959e7 −2.48935
\(505\) −310212. −0.0541290
\(506\) −909146. −0.157855
\(507\) 2.15227e6 0.371858
\(508\) −5.56283e6 −0.956393
\(509\) −9.62858e6 −1.64728 −0.823640 0.567113i \(-0.808060\pi\)
−0.823640 + 0.567113i \(0.808060\pi\)
\(510\) 1.51610e6 0.258108
\(511\) −1.14834e6 −0.194544
\(512\) −4.48897e6 −0.756784
\(513\) −4.52512e6 −0.759165
\(514\) 1.95990e6 0.327210
\(515\) 216943. 0.0360435
\(516\) −3.28854e6 −0.543725
\(517\) −1.60968e6 −0.264857
\(518\) −2.66938e6 −0.437106
\(519\) −5.71544e6 −0.931389
\(520\) −2.47188e6 −0.400884
\(521\) 569169. 0.0918644 0.0459322 0.998945i \(-0.485374\pi\)
0.0459322 + 0.998945i \(0.485374\pi\)
\(522\) 1.15270e7 1.85157
\(523\) 2.23753e6 0.357697 0.178848 0.983877i \(-0.442763\pi\)
0.178848 + 0.983877i \(0.442763\pi\)
\(524\) 8.90909e6 1.41744
\(525\) −2.71874e6 −0.430496
\(526\) −4.07240e6 −0.641780
\(527\) −3.02397e6 −0.474298
\(528\) 1.53899e6 0.240244
\(529\) 1.95242e6 0.303342
\(530\) −1.07036e6 −0.165516
\(531\) −7.13626e6 −1.09833
\(532\) −1.32048e6 −0.202281
\(533\) 1.72381e6 0.262828
\(534\) −2.71772e6 −0.412431
\(535\) −4.09359e6 −0.618330
\(536\) −5.91117e6 −0.888712
\(537\) 1.37343e7 2.05528
\(538\) 3.11076e6 0.463352
\(539\) 501587. 0.0743660
\(540\) −7.91904e6 −1.16866
\(541\) −1.39018e6 −0.204210 −0.102105 0.994774i \(-0.532558\pi\)
−0.102105 + 0.994774i \(0.532558\pi\)
\(542\) −1.13230e6 −0.165563
\(543\) −1.42662e7 −2.07639
\(544\) 4.55232e6 0.659531
\(545\) −3.45047e6 −0.497608
\(546\) −7.51009e6 −1.07811
\(547\) −8.62746e6 −1.23286 −0.616431 0.787409i \(-0.711422\pi\)
−0.616431 + 0.787409i \(0.711422\pi\)
\(548\) 4.63931e6 0.659937
\(549\) −1.89155e7 −2.67847
\(550\) −196184. −0.0276540
\(551\) 2.43000e6 0.340979
\(552\) 1.29315e7 1.80634
\(553\) −1.00318e7 −1.39498
\(554\) 1.39815e6 0.193544
\(555\) −5.34080e6 −0.735993
\(556\) 3.09864e6 0.425093
\(557\) 9.32183e6 1.27310 0.636551 0.771234i \(-0.280360\pi\)
0.636551 + 0.771234i \(0.280360\pi\)
\(558\) −6.65699e6 −0.905091
\(559\) −2.88192e6 −0.390079
\(560\) −1.53157e6 −0.206380
\(561\) −2.82861e6 −0.379460
\(562\) −1.02990e6 −0.137549
\(563\) 3.35530e6 0.446128 0.223064 0.974804i \(-0.428394\pi\)
0.223064 + 0.974804i \(0.428394\pi\)
\(564\) 1.01026e7 1.33732
\(565\) −1.85491e6 −0.244457
\(566\) 4.57130e6 0.599790
\(567\) −3.13080e7 −4.08975
\(568\) 7.64567e6 0.994362
\(569\) 1.10414e6 0.142970 0.0714849 0.997442i \(-0.477226\pi\)
0.0714849 + 0.997442i \(0.477226\pi\)
\(570\) 703586. 0.0907047
\(571\) −1.15796e7 −1.48629 −0.743146 0.669129i \(-0.766667\pi\)
−0.743146 + 0.669129i \(0.766667\pi\)
\(572\) 2.03495e6 0.260054
\(573\) 1.15898e7 1.47465
\(574\) −972627. −0.123216
\(575\) 1.81021e6 0.228328
\(576\) 1.08127e6 0.135794
\(577\) 9.06103e6 1.13302 0.566510 0.824055i \(-0.308293\pi\)
0.566510 + 0.824055i \(0.308293\pi\)
\(578\) 2.11360e6 0.263150
\(579\) −1.91520e7 −2.37420
\(580\) 4.25255e6 0.524903
\(581\) 8.85072e6 1.08777
\(582\) 1.18776e7 1.45352
\(583\) 1.99699e6 0.243335
\(584\) 1.17864e6 0.143004
\(585\) −1.09829e7 −1.32686
\(586\) −6.54593e6 −0.787458
\(587\) −8.08821e6 −0.968852 −0.484426 0.874832i \(-0.660972\pi\)
−0.484426 + 0.874832i \(0.660972\pi\)
\(588\) −3.14805e6 −0.375490
\(589\) −1.40336e6 −0.166679
\(590\) 701121. 0.0829207
\(591\) −6.64737e6 −0.782854
\(592\) −3.00868e6 −0.352835
\(593\) −2.61518e6 −0.305397 −0.152698 0.988273i \(-0.548796\pi\)
−0.152698 + 0.988273i \(0.548796\pi\)
\(594\) −3.93466e6 −0.457553
\(595\) 2.81497e6 0.325972
\(596\) −6.89102e6 −0.794635
\(597\) −2.33643e6 −0.268298
\(598\) 5.00042e6 0.571813
\(599\) 1.58662e7 1.80678 0.903391 0.428817i \(-0.141069\pi\)
0.903391 + 0.428817i \(0.141069\pi\)
\(600\) 2.79048e6 0.316447
\(601\) 3.38022e6 0.381732 0.190866 0.981616i \(-0.438870\pi\)
0.190866 + 0.981616i \(0.438870\pi\)
\(602\) 1.62607e6 0.182872
\(603\) −2.62641e7 −2.94150
\(604\) 1.32330e7 1.47593
\(605\) 366025. 0.0406558
\(606\) 967361. 0.107006
\(607\) 6.05529e6 0.667057 0.333529 0.942740i \(-0.391761\pi\)
0.333529 + 0.942740i \(0.391761\pi\)
\(608\) 2.11263e6 0.231774
\(609\) 2.92810e7 3.19921
\(610\) 1.85841e6 0.202216
\(611\) 8.85343e6 0.959420
\(612\) 1.29761e7 1.40044
\(613\) 2.34791e6 0.252365 0.126183 0.992007i \(-0.459727\pi\)
0.126183 + 0.992007i \(0.459727\pi\)
\(614\) −1.43398e6 −0.153505
\(615\) −1.94599e6 −0.207469
\(616\) −2.60214e6 −0.276298
\(617\) −2786.40 −0.000294666 0 −0.000147333 1.00000i \(-0.500047\pi\)
−0.000147333 1.00000i \(0.500047\pi\)
\(618\) −676511. −0.0712530
\(619\) 7.38249e6 0.774420 0.387210 0.921992i \(-0.373439\pi\)
0.387210 + 0.921992i \(0.373439\pi\)
\(620\) −2.45590e6 −0.256585
\(621\) 3.63054e7 3.77783
\(622\) −7.79701e6 −0.808076
\(623\) −5.04604e6 −0.520871
\(624\) −8.46467e6 −0.870259
\(625\) 390625. 0.0400000
\(626\) 6.73278e6 0.686687
\(627\) −1.31269e6 −0.133350
\(628\) 6.86093e6 0.694199
\(629\) 5.52983e6 0.557295
\(630\) 6.19688e6 0.622044
\(631\) 1.43702e7 1.43678 0.718389 0.695642i \(-0.244880\pi\)
0.718389 + 0.695642i \(0.244880\pi\)
\(632\) 1.02966e7 1.02541
\(633\) 64715.6 0.00641948
\(634\) 4.88510e6 0.482670
\(635\) 5.50333e6 0.541616
\(636\) −1.25335e7 −1.22865
\(637\) −2.75880e6 −0.269384
\(638\) 2.11293e6 0.205510
\(639\) 3.39707e7 3.29118
\(640\) 4.57549e6 0.441558
\(641\) 814356. 0.0782833 0.0391417 0.999234i \(-0.487538\pi\)
0.0391417 + 0.999234i \(0.487538\pi\)
\(642\) 1.27654e7 1.22235
\(643\) −1.58604e7 −1.51282 −0.756408 0.654100i \(-0.773048\pi\)
−0.756408 + 0.654100i \(0.773048\pi\)
\(644\) 1.05944e7 1.00661
\(645\) 3.25338e6 0.307918
\(646\) −728489. −0.0686818
\(647\) 1.48375e7 1.39348 0.696738 0.717326i \(-0.254634\pi\)
0.696738 + 0.717326i \(0.254634\pi\)
\(648\) 3.21341e7 3.00628
\(649\) −1.30809e6 −0.121907
\(650\) 1.07904e6 0.100174
\(651\) −1.69102e7 −1.56385
\(652\) −7.09333e6 −0.653478
\(653\) 9.80135e6 0.899504 0.449752 0.893153i \(-0.351512\pi\)
0.449752 + 0.893153i \(0.351512\pi\)
\(654\) 1.07599e7 0.983702
\(655\) −8.81381e6 −0.802713
\(656\) −1.09625e6 −0.0994607
\(657\) 5.23685e6 0.473322
\(658\) −4.99538e6 −0.449784
\(659\) 5.03359e6 0.451507 0.225753 0.974185i \(-0.427516\pi\)
0.225753 + 0.974185i \(0.427516\pi\)
\(660\) −2.29724e6 −0.205280
\(661\) −1.47344e7 −1.31168 −0.655840 0.754900i \(-0.727685\pi\)
−0.655840 + 0.754900i \(0.727685\pi\)
\(662\) −3.77923e6 −0.335165
\(663\) 1.55577e7 1.37456
\(664\) −9.08429e6 −0.799596
\(665\) 1.30636e6 0.114554
\(666\) 1.21734e7 1.06347
\(667\) −1.94961e7 −1.69681
\(668\) −1.32988e7 −1.15311
\(669\) −4.03258e7 −3.48351
\(670\) 2.58038e6 0.222074
\(671\) −3.46726e6 −0.297290
\(672\) 2.54567e7 2.17460
\(673\) 1.09990e7 0.936088 0.468044 0.883705i \(-0.344959\pi\)
0.468044 + 0.883705i \(0.344959\pi\)
\(674\) 3.98861e6 0.338199
\(675\) 7.83434e6 0.661825
\(676\) −1.80982e6 −0.152324
\(677\) −1.29517e7 −1.08606 −0.543031 0.839713i \(-0.682723\pi\)
−0.543031 + 0.839713i \(0.682723\pi\)
\(678\) 5.78434e6 0.483258
\(679\) 2.20533e7 1.83569
\(680\) −2.88925e6 −0.239614
\(681\) −8.18966e6 −0.676703
\(682\) −1.22024e6 −0.100458
\(683\) 2.26814e7 1.86045 0.930226 0.366987i \(-0.119610\pi\)
0.930226 + 0.366987i \(0.119610\pi\)
\(684\) 6.02191e6 0.492146
\(685\) −4.58970e6 −0.373730
\(686\) −4.75451e6 −0.385741
\(687\) −1.38066e7 −1.11608
\(688\) 1.83275e6 0.147616
\(689\) −1.09837e7 −0.881457
\(690\) −5.64493e6 −0.451373
\(691\) −5.78332e6 −0.460768 −0.230384 0.973100i \(-0.573998\pi\)
−0.230384 + 0.973100i \(0.573998\pi\)
\(692\) 4.80605e6 0.381525
\(693\) −1.15616e7 −0.914504
\(694\) 1.77545e6 0.139930
\(695\) −3.06550e6 −0.240735
\(696\) −3.00537e7 −2.35167
\(697\) 2.01487e6 0.157096
\(698\) 586911. 0.0455967
\(699\) −5.69404e6 −0.440786
\(700\) 2.28616e6 0.176344
\(701\) −2.58390e6 −0.198601 −0.0993004 0.995057i \(-0.531660\pi\)
−0.0993004 + 0.995057i \(0.531660\pi\)
\(702\) 2.16412e7 1.65744
\(703\) 2.56627e6 0.195846
\(704\) 198200. 0.0150721
\(705\) −9.99456e6 −0.757340
\(706\) 9.64816e6 0.728506
\(707\) 1.79612e6 0.135141
\(708\) 8.20982e6 0.615532
\(709\) 2.55024e7 1.90531 0.952655 0.304053i \(-0.0983401\pi\)
0.952655 + 0.304053i \(0.0983401\pi\)
\(710\) −3.33754e6 −0.248474
\(711\) 4.57490e7 3.39396
\(712\) 5.17920e6 0.382880
\(713\) 1.12593e7 0.829443
\(714\) −8.77815e6 −0.644403
\(715\) −2.01319e6 −0.147272
\(716\) −1.15490e7 −0.841904
\(717\) 3.98939e7 2.89807
\(718\) 1.20192e6 0.0870087
\(719\) 2.36466e7 1.70587 0.852935 0.522017i \(-0.174820\pi\)
0.852935 + 0.522017i \(0.174820\pi\)
\(720\) 6.98454e6 0.502119
\(721\) −1.25609e6 −0.0899876
\(722\) −338075. −0.0241363
\(723\) 5.28102e6 0.375727
\(724\) 1.19963e7 0.850552
\(725\) −4.20707e6 −0.297259
\(726\) −1.14141e6 −0.0803709
\(727\) 8.37216e6 0.587491 0.293746 0.955884i \(-0.405098\pi\)
0.293746 + 0.955884i \(0.405098\pi\)
\(728\) 1.43121e7 1.00086
\(729\) 5.12385e7 3.57090
\(730\) −514508. −0.0357343
\(731\) −3.36853e6 −0.233156
\(732\) 2.17611e7 1.50108
\(733\) −1.26328e7 −0.868439 −0.434219 0.900807i \(-0.642976\pi\)
−0.434219 + 0.900807i \(0.642976\pi\)
\(734\) −6.06138e6 −0.415271
\(735\) 3.11438e6 0.212644
\(736\) −1.69498e7 −1.15337
\(737\) −4.81427e6 −0.326484
\(738\) 4.43555e6 0.299782
\(739\) 1.86296e7 1.25485 0.627427 0.778675i \(-0.284108\pi\)
0.627427 + 0.778675i \(0.284108\pi\)
\(740\) 4.49102e6 0.301485
\(741\) 7.21999e6 0.483049
\(742\) 6.19735e6 0.413234
\(743\) 1.94042e7 1.28950 0.644752 0.764392i \(-0.276961\pi\)
0.644752 + 0.764392i \(0.276961\pi\)
\(744\) 1.73564e7 1.14955
\(745\) 6.81732e6 0.450011
\(746\) −1.28625e7 −0.846210
\(747\) −4.03626e7 −2.64654
\(748\) 2.37855e6 0.155438
\(749\) 2.37018e7 1.54375
\(750\) −1.21812e6 −0.0790746
\(751\) −3.36122e6 −0.217469 −0.108734 0.994071i \(-0.534680\pi\)
−0.108734 + 0.994071i \(0.534680\pi\)
\(752\) −5.63033e6 −0.363069
\(753\) −3.94526e6 −0.253564
\(754\) −1.16214e7 −0.744439
\(755\) −1.30915e7 −0.835835
\(756\) 4.58510e7 2.91772
\(757\) −2.29717e6 −0.145698 −0.0728489 0.997343i \(-0.523209\pi\)
−0.0728489 + 0.997343i \(0.523209\pi\)
\(758\) 1.38397e7 0.874889
\(759\) 1.05319e7 0.663591
\(760\) −1.34084e6 −0.0842057
\(761\) −2.81089e7 −1.75947 −0.879736 0.475462i \(-0.842281\pi\)
−0.879736 + 0.475462i \(0.842281\pi\)
\(762\) −1.71615e7 −1.07070
\(763\) 1.99781e7 1.24235
\(764\) −9.74573e6 −0.604061
\(765\) −1.28373e7 −0.793086
\(766\) 456568. 0.0281147
\(767\) 7.19469e6 0.441595
\(768\) −1.58434e7 −0.969269
\(769\) 1.39588e7 0.851202 0.425601 0.904911i \(-0.360063\pi\)
0.425601 + 0.904911i \(0.360063\pi\)
\(770\) 1.13590e6 0.0690421
\(771\) −2.27042e7 −1.37553
\(772\) 1.61047e7 0.972543
\(773\) −6.58993e6 −0.396673 −0.198336 0.980134i \(-0.563554\pi\)
−0.198336 + 0.980134i \(0.563554\pi\)
\(774\) −7.41549e6 −0.444926
\(775\) 2.42964e6 0.145307
\(776\) −2.26353e7 −1.34937
\(777\) 3.09230e7 1.83751
\(778\) 2.51533e6 0.148986
\(779\) 935056. 0.0552070
\(780\) 1.26351e7 0.743605
\(781\) 6.22691e6 0.365296
\(782\) 5.84474e6 0.341781
\(783\) −8.43766e7 −4.91833
\(784\) 1.75445e6 0.101942
\(785\) −6.78756e6 −0.393133
\(786\) 2.74848e7 1.58685
\(787\) −8.37335e6 −0.481906 −0.240953 0.970537i \(-0.577460\pi\)
−0.240953 + 0.970537i \(0.577460\pi\)
\(788\) 5.58970e6 0.320681
\(789\) 4.71761e7 2.69792
\(790\) −4.49473e6 −0.256233
\(791\) 1.07399e7 0.610322
\(792\) 1.18667e7 0.672230
\(793\) 1.90704e7 1.07690
\(794\) 4.46241e6 0.251199
\(795\) 1.23994e7 0.695798
\(796\) 1.96468e6 0.109903
\(797\) −2.51179e7 −1.40067 −0.700337 0.713812i \(-0.746967\pi\)
−0.700337 + 0.713812i \(0.746967\pi\)
\(798\) −4.07374e6 −0.226457
\(799\) 1.03483e7 0.573460
\(800\) −3.65760e6 −0.202056
\(801\) 2.30118e7 1.26727
\(802\) 6.61572e6 0.363196
\(803\) 959927. 0.0525351
\(804\) 3.02152e7 1.64848
\(805\) −1.04811e7 −0.570053
\(806\) 6.71149e6 0.363900
\(807\) −3.60361e7 −1.94784
\(808\) −1.84352e6 −0.0993388
\(809\) −3.35330e7 −1.80136 −0.900682 0.434478i \(-0.856933\pi\)
−0.900682 + 0.434478i \(0.856933\pi\)
\(810\) −1.40274e7 −0.751216
\(811\) 3.03912e7 1.62254 0.811271 0.584670i \(-0.198776\pi\)
0.811271 + 0.584670i \(0.198776\pi\)
\(812\) −2.46221e7 −1.31050
\(813\) 1.31170e7 0.695996
\(814\) 2.23141e6 0.118037
\(815\) 7.01747e6 0.370072
\(816\) −9.89391e6 −0.520167
\(817\) −1.56326e6 −0.0819361
\(818\) −661476. −0.0345645
\(819\) 6.35905e7 3.31270
\(820\) 1.63637e6 0.0849857
\(821\) 1.12359e7 0.581768 0.290884 0.956758i \(-0.406051\pi\)
0.290884 + 0.956758i \(0.406051\pi\)
\(822\) 1.43124e7 0.738813
\(823\) 3.15343e7 1.62287 0.811434 0.584445i \(-0.198688\pi\)
0.811434 + 0.584445i \(0.198688\pi\)
\(824\) 1.28924e6 0.0661477
\(825\) 2.27267e6 0.116252
\(826\) −4.05947e6 −0.207023
\(827\) −6.25717e6 −0.318137 −0.159068 0.987268i \(-0.550849\pi\)
−0.159068 + 0.987268i \(0.550849\pi\)
\(828\) −4.83143e7 −2.44906
\(829\) −1.05136e7 −0.531331 −0.265665 0.964065i \(-0.585592\pi\)
−0.265665 + 0.964065i \(0.585592\pi\)
\(830\) 3.96553e6 0.199805
\(831\) −1.61967e7 −0.813624
\(832\) −1.09013e6 −0.0545970
\(833\) −3.22461e6 −0.161015
\(834\) 9.55940e6 0.475900
\(835\) 1.31566e7 0.653020
\(836\) 1.10383e6 0.0546244
\(837\) 4.87286e7 2.40420
\(838\) −8.44224e6 −0.415287
\(839\) 1.60935e7 0.789308 0.394654 0.918830i \(-0.370864\pi\)
0.394654 + 0.918830i \(0.370864\pi\)
\(840\) −1.61568e7 −0.790055
\(841\) 2.47994e7 1.20907
\(842\) 5.41798e6 0.263365
\(843\) 1.19308e7 0.578228
\(844\) −54418.7 −0.00262961
\(845\) 1.79047e6 0.0862631
\(846\) 2.27808e7 1.09432
\(847\) −2.11927e6 −0.101503
\(848\) 6.98508e6 0.333566
\(849\) −5.29556e7 −2.52140
\(850\) 1.26124e6 0.0598754
\(851\) −2.05894e7 −0.974586
\(852\) −3.90812e7 −1.84446
\(853\) 4.17886e6 0.196646 0.0983230 0.995155i \(-0.468652\pi\)
0.0983230 + 0.995155i \(0.468652\pi\)
\(854\) −1.07601e7 −0.504861
\(855\) −5.95750e6 −0.278708
\(856\) −2.43272e7 −1.13477
\(857\) 2.18794e7 1.01762 0.508808 0.860880i \(-0.330086\pi\)
0.508808 + 0.860880i \(0.330086\pi\)
\(858\) 6.27789e6 0.291136
\(859\) 5.19684e6 0.240302 0.120151 0.992756i \(-0.461662\pi\)
0.120151 + 0.992756i \(0.461662\pi\)
\(860\) −2.73573e6 −0.126133
\(861\) 1.12672e7 0.517976
\(862\) 940775. 0.0431238
\(863\) −9.08022e6 −0.415020 −0.207510 0.978233i \(-0.566536\pi\)
−0.207510 + 0.978233i \(0.566536\pi\)
\(864\) −7.33565e7 −3.34314
\(865\) −4.75465e6 −0.216062
\(866\) 1.16128e7 0.526192
\(867\) −2.44847e7 −1.10623
\(868\) 1.42196e7 0.640602
\(869\) 8.38589e6 0.376704
\(870\) 1.31193e7 0.587640
\(871\) 2.64791e7 1.18265
\(872\) −2.05053e7 −0.913220
\(873\) −1.00571e8 −4.46621
\(874\) 2.71241e6 0.120109
\(875\) −2.26171e6 −0.0998657
\(876\) −6.02467e6 −0.265261
\(877\) −2.78324e7 −1.22195 −0.610973 0.791651i \(-0.709222\pi\)
−0.610973 + 0.791651i \(0.709222\pi\)
\(878\) −3.67133e6 −0.160726
\(879\) 7.58303e7 3.31032
\(880\) 1.28028e6 0.0557313
\(881\) 3.03635e7 1.31799 0.658994 0.752148i \(-0.270982\pi\)
0.658994 + 0.752148i \(0.270982\pi\)
\(882\) −7.09868e6 −0.307260
\(883\) −2.09839e7 −0.905700 −0.452850 0.891587i \(-0.649593\pi\)
−0.452850 + 0.891587i \(0.649593\pi\)
\(884\) −1.30823e7 −0.563060
\(885\) −8.12202e6 −0.348583
\(886\) 1.92101e6 0.0822138
\(887\) 3.45134e7 1.47292 0.736458 0.676483i \(-0.236497\pi\)
0.736458 + 0.676483i \(0.236497\pi\)
\(888\) −3.17391e7 −1.35071
\(889\) −3.18641e7 −1.35222
\(890\) −2.26086e6 −0.0956750
\(891\) 2.61712e7 1.10441
\(892\) 3.39095e7 1.42695
\(893\) 4.80242e6 0.201526
\(894\) −2.12590e7 −0.889610
\(895\) 1.14255e7 0.476780
\(896\) −2.64920e7 −1.10241
\(897\) −5.79266e7 −2.40379
\(898\) 1.07843e7 0.446275
\(899\) −2.61674e7 −1.07985
\(900\) −1.04257e7 −0.429043
\(901\) −1.28383e7 −0.526860
\(902\) 813046. 0.0332735
\(903\) −1.88369e7 −0.768761
\(904\) −1.10233e7 −0.448633
\(905\) −1.18680e7 −0.481677
\(906\) 4.08242e7 1.65233
\(907\) 4.21126e7 1.69978 0.849892 0.526957i \(-0.176667\pi\)
0.849892 + 0.526957i \(0.176667\pi\)
\(908\) 6.88660e6 0.277198
\(909\) −8.19098e6 −0.328796
\(910\) −6.24761e6 −0.250098
\(911\) 2.24069e7 0.894510 0.447255 0.894406i \(-0.352402\pi\)
0.447255 + 0.894406i \(0.352402\pi\)
\(912\) −4.59154e6 −0.182798
\(913\) −7.39857e6 −0.293745
\(914\) −2.24571e7 −0.889175
\(915\) −2.15284e7 −0.850079
\(916\) 1.16098e7 0.457179
\(917\) 5.10317e7 2.00409
\(918\) 2.52952e7 0.990677
\(919\) 7.90951e6 0.308930 0.154465 0.987998i \(-0.450635\pi\)
0.154465 + 0.987998i \(0.450635\pi\)
\(920\) 1.07576e7 0.419032
\(921\) 1.66117e7 0.645304
\(922\) −7.27123e6 −0.281696
\(923\) −3.42488e7 −1.32325
\(924\) 1.33009e7 0.512510
\(925\) −4.44299e6 −0.170734
\(926\) 1.53058e7 0.586582
\(927\) 5.72825e6 0.218939
\(928\) 3.93927e7 1.50157
\(929\) 668234. 0.0254032 0.0127016 0.999919i \(-0.495957\pi\)
0.0127016 + 0.999919i \(0.495957\pi\)
\(930\) −7.57655e6 −0.287253
\(931\) −1.49647e6 −0.0565841
\(932\) 4.78806e6 0.180559
\(933\) 9.03233e7 3.39700
\(934\) −1.52159e7 −0.570730
\(935\) −2.35311e6 −0.0880264
\(936\) −6.52686e7 −2.43509
\(937\) 2.14457e7 0.797979 0.398989 0.916956i \(-0.369361\pi\)
0.398989 + 0.916956i \(0.369361\pi\)
\(938\) −1.49403e7 −0.554438
\(939\) −7.79949e7 −2.88670
\(940\) 8.40432e6 0.310229
\(941\) 3.60761e7 1.32815 0.664073 0.747667i \(-0.268826\pi\)
0.664073 + 0.747667i \(0.268826\pi\)
\(942\) 2.11662e7 0.777170
\(943\) −7.50204e6 −0.274726
\(944\) −4.57545e6 −0.167111
\(945\) −4.53606e7 −1.65234
\(946\) −1.35928e6 −0.0493833
\(947\) −9.57308e6 −0.346878 −0.173439 0.984845i \(-0.555488\pi\)
−0.173439 + 0.984845i \(0.555488\pi\)
\(948\) −5.26313e7 −1.90206
\(949\) −5.27972e6 −0.190303
\(950\) 585311. 0.0210415
\(951\) −5.65907e7 −2.02906
\(952\) 1.67287e7 0.598231
\(953\) −1.23929e6 −0.0442018 −0.0221009 0.999756i \(-0.507036\pi\)
−0.0221009 + 0.999756i \(0.507036\pi\)
\(954\) −2.82623e7 −1.00539
\(955\) 9.64150e6 0.342087
\(956\) −3.35464e7 −1.18714
\(957\) −2.44769e7 −0.863924
\(958\) 1.39443e7 0.490889
\(959\) 2.65742e7 0.933069
\(960\) 1.23064e6 0.0430974
\(961\) −1.35171e7 −0.472145
\(962\) −1.22731e7 −0.427578
\(963\) −1.08089e8 −3.75592
\(964\) −4.44075e6 −0.153909
\(965\) −1.59324e7 −0.550762
\(966\) 3.26840e7 1.12692
\(967\) 1.45327e7 0.499781 0.249890 0.968274i \(-0.419605\pi\)
0.249890 + 0.968274i \(0.419605\pi\)
\(968\) 2.17520e6 0.0746124
\(969\) 8.43907e6 0.288726
\(970\) 9.88091e6 0.337184
\(971\) −9.42194e6 −0.320695 −0.160348 0.987061i \(-0.551262\pi\)
−0.160348 + 0.987061i \(0.551262\pi\)
\(972\) −8.72820e7 −2.96319
\(973\) 1.77491e7 0.601029
\(974\) 2.08397e7 0.703872
\(975\) −1.25000e7 −0.421112
\(976\) −1.21278e7 −0.407528
\(977\) 4.50753e7 1.51078 0.755392 0.655274i \(-0.227447\pi\)
0.755392 + 0.655274i \(0.227447\pi\)
\(978\) −2.18832e7 −0.731582
\(979\) 4.21813e6 0.140657
\(980\) −2.61885e6 −0.0871055
\(981\) −9.11078e7 −3.02262
\(982\) −8.63705e6 −0.285816
\(983\) 1.41997e6 0.0468702 0.0234351 0.999725i \(-0.492540\pi\)
0.0234351 + 0.999725i \(0.492540\pi\)
\(984\) −1.15646e7 −0.380752
\(985\) −5.52992e6 −0.181605
\(986\) −1.35836e7 −0.444962
\(987\) 5.78682e7 1.89081
\(988\) −6.07121e6 −0.197871
\(989\) 1.25422e7 0.407738
\(990\) −5.18014e6 −0.167979
\(991\) 1.85275e7 0.599285 0.299643 0.954052i \(-0.403133\pi\)
0.299643 + 0.954052i \(0.403133\pi\)
\(992\) −2.27498e7 −0.734003
\(993\) 4.37800e7 1.40897
\(994\) 1.93243e7 0.620350
\(995\) −1.94367e6 −0.0622393
\(996\) 4.64347e7 1.48318
\(997\) −6.24362e7 −1.98929 −0.994646 0.103337i \(-0.967048\pi\)
−0.994646 + 0.103337i \(0.967048\pi\)
\(998\) 1.24602e7 0.396005
\(999\) −8.91082e7 −2.82491
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 1045.6.a.e.1.17 38
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.6.a.e.1.17 38 1.1 even 1 trivial