Properties

Label 1075.6.a.j.1.29
Level $1075$
Weight $6$
Character 1075.1
Self dual yes
Analytic conductor $172.413$
Analytic rank $0$
Dimension $37$
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] = [1075,6,Mod(1,1075)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1075, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1075.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1075 = 5^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1075.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: \(172.412606299\)
Analytic rank: \(0\)
Dimension: \(37\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.29
Character \(\chi\) \(=\) 1075.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+7.20077 q^{2} -5.47224 q^{3} +19.8511 q^{4} -39.4044 q^{6} +128.650 q^{7} -87.4815 q^{8} -213.055 q^{9} +O(q^{10})\) \(q+7.20077 q^{2} -5.47224 q^{3} +19.8511 q^{4} -39.4044 q^{6} +128.650 q^{7} -87.4815 q^{8} -213.055 q^{9} +74.6602 q^{11} -108.630 q^{12} -459.547 q^{13} +926.381 q^{14} -1265.17 q^{16} +1157.85 q^{17} -1534.16 q^{18} +1010.86 q^{19} -704.006 q^{21} +537.611 q^{22} -4235.90 q^{23} +478.720 q^{24} -3309.09 q^{26} +2495.64 q^{27} +2553.85 q^{28} -5891.50 q^{29} +5606.92 q^{31} -6310.78 q^{32} -408.559 q^{33} +8337.38 q^{34} -4229.36 q^{36} +13751.4 q^{37} +7278.99 q^{38} +2514.75 q^{39} +13924.9 q^{41} -5069.39 q^{42} +1849.00 q^{43} +1482.09 q^{44} -30501.8 q^{46} -4559.12 q^{47} +6923.31 q^{48} -256.094 q^{49} -6336.01 q^{51} -9122.50 q^{52} +31988.9 q^{53} +17970.5 q^{54} -11254.5 q^{56} -5531.69 q^{57} -42423.3 q^{58} -39336.2 q^{59} +738.234 q^{61} +40374.1 q^{62} -27409.5 q^{63} -4957.09 q^{64} -2941.94 q^{66} +37619.4 q^{67} +22984.5 q^{68} +23179.9 q^{69} -15610.1 q^{71} +18638.3 q^{72} -33418.5 q^{73} +99020.4 q^{74} +20066.7 q^{76} +9605.06 q^{77} +18108.1 q^{78} +1653.19 q^{79} +38115.5 q^{81} +100270. q^{82} -54366.1 q^{83} -13975.3 q^{84} +13314.2 q^{86} +32239.7 q^{87} -6531.38 q^{88} +75355.5 q^{89} -59120.8 q^{91} -84087.3 q^{92} -30682.4 q^{93} -32829.2 q^{94} +34534.1 q^{96} +76314.0 q^{97} -1844.07 q^{98} -15906.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 37 q + 630 q^{4} + 291 q^{6} + 213 q^{8} + 3535 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 37 q + 630 q^{4} + 291 q^{6} + 213 q^{8} + 3535 q^{9} + 675 q^{11} - 4446 q^{12} + 1241 q^{13} + 2375 q^{14} + 10518 q^{16} + 1153 q^{17} - 6680 q^{18} + 4065 q^{19} + 9953 q^{21} + 9283 q^{22} - 360 q^{23} + 2265 q^{24} + 23695 q^{26} + 1323 q^{27} - 30375 q^{28} + 19290 q^{29} + 23291 q^{31} + 8166 q^{32} - 10388 q^{33} - 13153 q^{34} + 148705 q^{36} + 13501 q^{37} - 8127 q^{38} - 1327 q^{39} + 38345 q^{41} - 21835 q^{42} + 68413 q^{43} + 47768 q^{44} + 48755 q^{46} + 84859 q^{47} - 208720 q^{48} + 107255 q^{49} + 62027 q^{51} + 128320 q^{52} - 53559 q^{53} + 44158 q^{54} + 107538 q^{56} + 104239 q^{57} - 85186 q^{58} + 48186 q^{59} + 82364 q^{61} + 206506 q^{62} - 75269 q^{63} + 161467 q^{64} + 91969 q^{66} + 38168 q^{67} + 95991 q^{68} + 287103 q^{69} + 155302 q^{71} + 9979 q^{72} + 31927 q^{73} + 59946 q^{74} + 225407 q^{76} - 80007 q^{77} - 67815 q^{78} + 150174 q^{79} + 417489 q^{81} + 60603 q^{82} + 266568 q^{83} + 586273 q^{84} - 57554 q^{87} + 323054 q^{88} + 334356 q^{89} + 51747 q^{91} - 258529 q^{92} - 285287 q^{93} + 302744 q^{94} + 287282 q^{96} - 78640 q^{97} - 397117 q^{98} + 362152 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.20077 1.27293 0.636464 0.771306i \(-0.280396\pi\)
0.636464 + 0.771306i \(0.280396\pi\)
\(3\) −5.47224 −0.351045 −0.175522 0.984475i \(-0.556161\pi\)
−0.175522 + 0.984475i \(0.556161\pi\)
\(4\) 19.8511 0.620347
\(5\) 0 0
\(6\) −39.4044 −0.446855
\(7\) 128.650 0.992352 0.496176 0.868222i \(-0.334737\pi\)
0.496176 + 0.868222i \(0.334737\pi\)
\(8\) −87.4815 −0.483272
\(9\) −213.055 −0.876768
\(10\) 0 0
\(11\) 74.6602 0.186040 0.0930202 0.995664i \(-0.470348\pi\)
0.0930202 + 0.995664i \(0.470348\pi\)
\(12\) −108.630 −0.217769
\(13\) −459.547 −0.754173 −0.377087 0.926178i \(-0.623074\pi\)
−0.377087 + 0.926178i \(0.623074\pi\)
\(14\) 926.381 1.26319
\(15\) 0 0
\(16\) −1265.17 −1.23552
\(17\) 1157.85 0.971691 0.485846 0.874045i \(-0.338512\pi\)
0.485846 + 0.874045i \(0.338512\pi\)
\(18\) −1534.16 −1.11606
\(19\) 1010.86 0.642404 0.321202 0.947011i \(-0.395913\pi\)
0.321202 + 0.947011i \(0.395913\pi\)
\(20\) 0 0
\(21\) −704.006 −0.348360
\(22\) 537.611 0.236816
\(23\) −4235.90 −1.66965 −0.834827 0.550513i \(-0.814432\pi\)
−0.834827 + 0.550513i \(0.814432\pi\)
\(24\) 478.720 0.169650
\(25\) 0 0
\(26\) −3309.09 −0.960008
\(27\) 2495.64 0.658829
\(28\) 2553.85 0.615602
\(29\) −5891.50 −1.30086 −0.650430 0.759566i \(-0.725411\pi\)
−0.650430 + 0.759566i \(0.725411\pi\)
\(30\) 0 0
\(31\) 5606.92 1.04790 0.523950 0.851749i \(-0.324458\pi\)
0.523950 + 0.851749i \(0.324458\pi\)
\(32\) −6310.78 −1.08945
\(33\) −408.559 −0.0653085
\(34\) 8337.38 1.23689
\(35\) 0 0
\(36\) −4229.36 −0.543900
\(37\) 13751.4 1.65136 0.825680 0.564139i \(-0.190792\pi\)
0.825680 + 0.564139i \(0.190792\pi\)
\(38\) 7278.99 0.817734
\(39\) 2514.75 0.264748
\(40\) 0 0
\(41\) 13924.9 1.29369 0.646846 0.762621i \(-0.276088\pi\)
0.646846 + 0.762621i \(0.276088\pi\)
\(42\) −5069.39 −0.443437
\(43\) 1849.00 0.152499
\(44\) 1482.09 0.115410
\(45\) 0 0
\(46\) −30501.8 −2.12535
\(47\) −4559.12 −0.301048 −0.150524 0.988606i \(-0.548096\pi\)
−0.150524 + 0.988606i \(0.548096\pi\)
\(48\) 6923.31 0.433722
\(49\) −256.094 −0.0152373
\(50\) 0 0
\(51\) −6336.01 −0.341107
\(52\) −9122.50 −0.467849
\(53\) 31988.9 1.56426 0.782131 0.623115i \(-0.214133\pi\)
0.782131 + 0.623115i \(0.214133\pi\)
\(54\) 17970.5 0.838642
\(55\) 0 0
\(56\) −11254.5 −0.479576
\(57\) −5531.69 −0.225512
\(58\) −42423.3 −1.65590
\(59\) −39336.2 −1.47117 −0.735585 0.677433i \(-0.763092\pi\)
−0.735585 + 0.677433i \(0.763092\pi\)
\(60\) 0 0
\(61\) 738.234 0.0254021 0.0127010 0.999919i \(-0.495957\pi\)
0.0127010 + 0.999919i \(0.495957\pi\)
\(62\) 40374.1 1.33390
\(63\) −27409.5 −0.870062
\(64\) −4957.09 −0.151278
\(65\) 0 0
\(66\) −2941.94 −0.0831330
\(67\) 37619.4 1.02382 0.511911 0.859039i \(-0.328938\pi\)
0.511911 + 0.859039i \(0.328938\pi\)
\(68\) 22984.5 0.602785
\(69\) 23179.9 0.586123
\(70\) 0 0
\(71\) −15610.1 −0.367502 −0.183751 0.982973i \(-0.558824\pi\)
−0.183751 + 0.982973i \(0.558824\pi\)
\(72\) 18638.3 0.423717
\(73\) −33418.5 −0.733972 −0.366986 0.930226i \(-0.619610\pi\)
−0.366986 + 0.930226i \(0.619610\pi\)
\(74\) 99020.4 2.10206
\(75\) 0 0
\(76\) 20066.7 0.398513
\(77\) 9605.06 0.184618
\(78\) 18108.1 0.337006
\(79\) 1653.19 0.0298027 0.0149013 0.999889i \(-0.495257\pi\)
0.0149013 + 0.999889i \(0.495257\pi\)
\(80\) 0 0
\(81\) 38115.5 0.645489
\(82\) 100270. 1.64678
\(83\) −54366.1 −0.866229 −0.433115 0.901339i \(-0.642585\pi\)
−0.433115 + 0.901339i \(0.642585\pi\)
\(84\) −13975.3 −0.216104
\(85\) 0 0
\(86\) 13314.2 0.194120
\(87\) 32239.7 0.456660
\(88\) −6531.38 −0.0899081
\(89\) 75355.5 1.00842 0.504208 0.863582i \(-0.331784\pi\)
0.504208 + 0.863582i \(0.331784\pi\)
\(90\) 0 0
\(91\) −59120.8 −0.748405
\(92\) −84087.3 −1.03576
\(93\) −30682.4 −0.367860
\(94\) −32829.2 −0.383213
\(95\) 0 0
\(96\) 34534.1 0.382446
\(97\) 76314.0 0.823521 0.411761 0.911292i \(-0.364914\pi\)
0.411761 + 0.911292i \(0.364914\pi\)
\(98\) −1844.07 −0.0193960
\(99\) −15906.7 −0.163114
\(100\) 0 0
\(101\) 123504. 1.20470 0.602350 0.798232i \(-0.294231\pi\)
0.602350 + 0.798232i \(0.294231\pi\)
\(102\) −45624.2 −0.434205
\(103\) 34077.8 0.316503 0.158252 0.987399i \(-0.449414\pi\)
0.158252 + 0.987399i \(0.449414\pi\)
\(104\) 40201.8 0.364471
\(105\) 0 0
\(106\) 230345. 1.99119
\(107\) 148390. 1.25298 0.626492 0.779428i \(-0.284490\pi\)
0.626492 + 0.779428i \(0.284490\pi\)
\(108\) 49541.2 0.408702
\(109\) −41193.2 −0.332093 −0.166046 0.986118i \(-0.553100\pi\)
−0.166046 + 0.986118i \(0.553100\pi\)
\(110\) 0 0
\(111\) −75250.9 −0.579701
\(112\) −162764. −1.22607
\(113\) 166815. 1.22896 0.614482 0.788931i \(-0.289365\pi\)
0.614482 + 0.788931i \(0.289365\pi\)
\(114\) −39832.4 −0.287061
\(115\) 0 0
\(116\) −116953. −0.806984
\(117\) 97908.5 0.661235
\(118\) −283251. −1.87269
\(119\) 148957. 0.964260
\(120\) 0 0
\(121\) −155477. −0.965389
\(122\) 5315.85 0.0323350
\(123\) −76200.2 −0.454144
\(124\) 111303. 0.650061
\(125\) 0 0
\(126\) −197370. −1.10753
\(127\) −292468. −1.60905 −0.804525 0.593919i \(-0.797580\pi\)
−0.804525 + 0.593919i \(0.797580\pi\)
\(128\) 166250. 0.896886
\(129\) −10118.2 −0.0535338
\(130\) 0 0
\(131\) 165082. 0.840468 0.420234 0.907416i \(-0.361948\pi\)
0.420234 + 0.907416i \(0.361948\pi\)
\(132\) −8110.33 −0.0405139
\(133\) 130048. 0.637491
\(134\) 270888. 1.30325
\(135\) 0 0
\(136\) −101290. −0.469591
\(137\) 343862. 1.56525 0.782623 0.622496i \(-0.213881\pi\)
0.782623 + 0.622496i \(0.213881\pi\)
\(138\) 166913. 0.746092
\(139\) 396100. 1.73887 0.869436 0.494045i \(-0.164482\pi\)
0.869436 + 0.494045i \(0.164482\pi\)
\(140\) 0 0
\(141\) 24948.6 0.105681
\(142\) −112405. −0.467803
\(143\) −34309.8 −0.140307
\(144\) 269550. 1.08326
\(145\) 0 0
\(146\) −240639. −0.934294
\(147\) 1401.41 0.00534899
\(148\) 272980. 1.02442
\(149\) −288486. −1.06453 −0.532266 0.846577i \(-0.678659\pi\)
−0.532266 + 0.846577i \(0.678659\pi\)
\(150\) 0 0
\(151\) 503945. 1.79863 0.899313 0.437306i \(-0.144067\pi\)
0.899313 + 0.437306i \(0.144067\pi\)
\(152\) −88431.8 −0.310456
\(153\) −246684. −0.851948
\(154\) 69163.8 0.235005
\(155\) 0 0
\(156\) 49920.5 0.164236
\(157\) −279266. −0.904210 −0.452105 0.891965i \(-0.649327\pi\)
−0.452105 + 0.891965i \(0.649327\pi\)
\(158\) 11904.2 0.0379367
\(159\) −175051. −0.549125
\(160\) 0 0
\(161\) −544950. −1.65688
\(162\) 274461. 0.821661
\(163\) 81333.7 0.239774 0.119887 0.992788i \(-0.461747\pi\)
0.119887 + 0.992788i \(0.461747\pi\)
\(164\) 276423. 0.802537
\(165\) 0 0
\(166\) −391478. −1.10265
\(167\) 369746. 1.02592 0.512959 0.858413i \(-0.328549\pi\)
0.512959 + 0.858413i \(0.328549\pi\)
\(168\) 61587.5 0.168352
\(169\) −160110. −0.431223
\(170\) 0 0
\(171\) −215369. −0.563239
\(172\) 36704.7 0.0946020
\(173\) 749929. 1.90504 0.952522 0.304469i \(-0.0984789\pi\)
0.952522 + 0.304469i \(0.0984789\pi\)
\(174\) 232151. 0.581295
\(175\) 0 0
\(176\) −94457.7 −0.229856
\(177\) 215257. 0.516446
\(178\) 542618. 1.28364
\(179\) 245010. 0.571546 0.285773 0.958297i \(-0.407750\pi\)
0.285773 + 0.958297i \(0.407750\pi\)
\(180\) 0 0
\(181\) −864861. −1.96223 −0.981114 0.193428i \(-0.938039\pi\)
−0.981114 + 0.193428i \(0.938039\pi\)
\(182\) −425715. −0.952666
\(183\) −4039.80 −0.00891727
\(184\) 370563. 0.806896
\(185\) 0 0
\(186\) −220937. −0.468259
\(187\) 86445.0 0.180774
\(188\) −90503.5 −0.186754
\(189\) 321065. 0.653791
\(190\) 0 0
\(191\) 13437.9 0.0266531 0.0133266 0.999911i \(-0.495758\pi\)
0.0133266 + 0.999911i \(0.495758\pi\)
\(192\) 27126.4 0.0531054
\(193\) 565162. 1.09214 0.546071 0.837739i \(-0.316123\pi\)
0.546071 + 0.837739i \(0.316123\pi\)
\(194\) 549519. 1.04828
\(195\) 0 0
\(196\) −5083.74 −0.00945243
\(197\) 225656. 0.414268 0.207134 0.978313i \(-0.433586\pi\)
0.207134 + 0.978313i \(0.433586\pi\)
\(198\) −114540. −0.207633
\(199\) −555552. −0.994471 −0.497236 0.867615i \(-0.665652\pi\)
−0.497236 + 0.867615i \(0.665652\pi\)
\(200\) 0 0
\(201\) −205862. −0.359407
\(202\) 889327. 1.53350
\(203\) −757943. −1.29091
\(204\) −125777. −0.211605
\(205\) 0 0
\(206\) 245386. 0.402886
\(207\) 902478. 1.46390
\(208\) 581404. 0.931794
\(209\) 75471.2 0.119513
\(210\) 0 0
\(211\) 772768. 1.19493 0.597465 0.801895i \(-0.296175\pi\)
0.597465 + 0.801895i \(0.296175\pi\)
\(212\) 635014. 0.970384
\(213\) 85422.2 0.129010
\(214\) 1.06852e6 1.59496
\(215\) 0 0
\(216\) −218323. −0.318394
\(217\) 721332. 1.03989
\(218\) −296623. −0.422730
\(219\) 182874. 0.257657
\(220\) 0 0
\(221\) −532084. −0.732824
\(222\) −541864. −0.737918
\(223\) 315027. 0.424215 0.212107 0.977246i \(-0.431967\pi\)
0.212107 + 0.977246i \(0.431967\pi\)
\(224\) −811884. −1.08112
\(225\) 0 0
\(226\) 1.20120e6 1.56438
\(227\) −1.03800e6 −1.33700 −0.668500 0.743712i \(-0.733063\pi\)
−0.668500 + 0.743712i \(0.733063\pi\)
\(228\) −109810. −0.139896
\(229\) 607620. 0.765673 0.382837 0.923816i \(-0.374947\pi\)
0.382837 + 0.923816i \(0.374947\pi\)
\(230\) 0 0
\(231\) −52561.2 −0.0648090
\(232\) 515397. 0.628669
\(233\) −170546. −0.205803 −0.102901 0.994692i \(-0.532813\pi\)
−0.102901 + 0.994692i \(0.532813\pi\)
\(234\) 705016. 0.841704
\(235\) 0 0
\(236\) −780867. −0.912635
\(237\) −9046.66 −0.0104621
\(238\) 1.07261e6 1.22743
\(239\) 1.51509e6 1.71571 0.857856 0.513890i \(-0.171796\pi\)
0.857856 + 0.513890i \(0.171796\pi\)
\(240\) 0 0
\(241\) 565222. 0.626869 0.313434 0.949610i \(-0.398520\pi\)
0.313434 + 0.949610i \(0.398520\pi\)
\(242\) −1.11955e6 −1.22887
\(243\) −815018. −0.885425
\(244\) 14654.7 0.0157581
\(245\) 0 0
\(246\) −548700. −0.578092
\(247\) −464538. −0.484484
\(248\) −490501. −0.506420
\(249\) 297504. 0.304085
\(250\) 0 0
\(251\) −193329. −0.193693 −0.0968464 0.995299i \(-0.530876\pi\)
−0.0968464 + 0.995299i \(0.530876\pi\)
\(252\) −544109. −0.539740
\(253\) −316253. −0.310623
\(254\) −2.10600e6 −2.04820
\(255\) 0 0
\(256\) 1.35576e6 1.29295
\(257\) −2.08642e6 −1.97046 −0.985232 0.171225i \(-0.945228\pi\)
−0.985232 + 0.171225i \(0.945228\pi\)
\(258\) −72858.7 −0.0681447
\(259\) 1.76912e6 1.63873
\(260\) 0 0
\(261\) 1.25521e6 1.14055
\(262\) 1.18872e6 1.06986
\(263\) 2.22099e6 1.97996 0.989980 0.141204i \(-0.0450975\pi\)
0.989980 + 0.141204i \(0.0450975\pi\)
\(264\) 35741.3 0.0315617
\(265\) 0 0
\(266\) 936444. 0.811480
\(267\) −412364. −0.353999
\(268\) 746785. 0.635124
\(269\) −767101. −0.646356 −0.323178 0.946338i \(-0.604751\pi\)
−0.323178 + 0.946338i \(0.604751\pi\)
\(270\) 0 0
\(271\) −159729. −0.132118 −0.0660588 0.997816i \(-0.521043\pi\)
−0.0660588 + 0.997816i \(0.521043\pi\)
\(272\) −1.46487e6 −1.20054
\(273\) 323524. 0.262724
\(274\) 2.47607e6 1.99245
\(275\) 0 0
\(276\) 460146. 0.363599
\(277\) −484535. −0.379425 −0.189712 0.981840i \(-0.560756\pi\)
−0.189712 + 0.981840i \(0.560756\pi\)
\(278\) 2.85222e6 2.21346
\(279\) −1.19458e6 −0.918765
\(280\) 0 0
\(281\) 328209. 0.247962 0.123981 0.992285i \(-0.460434\pi\)
0.123981 + 0.992285i \(0.460434\pi\)
\(282\) 179649. 0.134525
\(283\) 1.03659e6 0.769380 0.384690 0.923046i \(-0.374308\pi\)
0.384690 + 0.923046i \(0.374308\pi\)
\(284\) −309877. −0.227978
\(285\) 0 0
\(286\) −247057. −0.178600
\(287\) 1.79144e6 1.28380
\(288\) 1.34454e6 0.955197
\(289\) −79250.4 −0.0558158
\(290\) 0 0
\(291\) −417609. −0.289093
\(292\) −663393. −0.455317
\(293\) 546625. 0.371981 0.185990 0.982552i \(-0.440451\pi\)
0.185990 + 0.982552i \(0.440451\pi\)
\(294\) 10091.2 0.00680888
\(295\) 0 0
\(296\) −1.20299e6 −0.798055
\(297\) 186325. 0.122569
\(298\) −2.07732e6 −1.35507
\(299\) 1.94659e6 1.25921
\(300\) 0 0
\(301\) 237874. 0.151332
\(302\) 3.62879e6 2.28952
\(303\) −675847. −0.422904
\(304\) −1.27891e6 −0.793701
\(305\) 0 0
\(306\) −1.77632e6 −1.08447
\(307\) −843892. −0.511024 −0.255512 0.966806i \(-0.582244\pi\)
−0.255512 + 0.966806i \(0.582244\pi\)
\(308\) 190671. 0.114527
\(309\) −186482. −0.111107
\(310\) 0 0
\(311\) 2.66748e6 1.56387 0.781933 0.623362i \(-0.214234\pi\)
0.781933 + 0.623362i \(0.214234\pi\)
\(312\) −219994. −0.127945
\(313\) 211659. 0.122117 0.0610586 0.998134i \(-0.480552\pi\)
0.0610586 + 0.998134i \(0.480552\pi\)
\(314\) −2.01093e6 −1.15099
\(315\) 0 0
\(316\) 32817.6 0.0184880
\(317\) −2.76558e6 −1.54574 −0.772872 0.634562i \(-0.781181\pi\)
−0.772872 + 0.634562i \(0.781181\pi\)
\(318\) −1.26050e6 −0.698997
\(319\) −439860. −0.242013
\(320\) 0 0
\(321\) −812027. −0.439854
\(322\) −3.92406e6 −2.10909
\(323\) 1.17042e6 0.624218
\(324\) 756634. 0.400427
\(325\) 0 0
\(326\) 585665. 0.305215
\(327\) 225419. 0.116579
\(328\) −1.21817e6 −0.625205
\(329\) −586532. −0.298746
\(330\) 0 0
\(331\) 2.10223e6 1.05465 0.527327 0.849662i \(-0.323194\pi\)
0.527327 + 0.849662i \(0.323194\pi\)
\(332\) −1.07923e6 −0.537362
\(333\) −2.92979e6 −1.44786
\(334\) 2.66246e6 1.30592
\(335\) 0 0
\(336\) 890687. 0.430404
\(337\) 247202. 0.118570 0.0592852 0.998241i \(-0.481118\pi\)
0.0592852 + 0.998241i \(0.481118\pi\)
\(338\) −1.15292e6 −0.548916
\(339\) −912852. −0.431421
\(340\) 0 0
\(341\) 418613. 0.194952
\(342\) −1.55082e6 −0.716963
\(343\) −2.19517e6 −1.00747
\(344\) −161753. −0.0736982
\(345\) 0 0
\(346\) 5.40007e6 2.42499
\(347\) −674766. −0.300836 −0.150418 0.988622i \(-0.548062\pi\)
−0.150418 + 0.988622i \(0.548062\pi\)
\(348\) 639993. 0.283287
\(349\) 3.49441e6 1.53572 0.767858 0.640620i \(-0.221323\pi\)
0.767858 + 0.640620i \(0.221323\pi\)
\(350\) 0 0
\(351\) −1.14686e6 −0.496871
\(352\) −471164. −0.202682
\(353\) 3.12311e6 1.33398 0.666992 0.745065i \(-0.267582\pi\)
0.666992 + 0.745065i \(0.267582\pi\)
\(354\) 1.55002e6 0.657399
\(355\) 0 0
\(356\) 1.49589e6 0.625568
\(357\) −815130. −0.338498
\(358\) 1.76426e6 0.727537
\(359\) 3.02885e6 1.24034 0.620172 0.784466i \(-0.287063\pi\)
0.620172 + 0.784466i \(0.287063\pi\)
\(360\) 0 0
\(361\) −1.45426e6 −0.587317
\(362\) −6.22766e6 −2.49778
\(363\) 850807. 0.338895
\(364\) −1.17361e6 −0.464271
\(365\) 0 0
\(366\) −29089.7 −0.0113510
\(367\) −4.62366e6 −1.79193 −0.895965 0.444125i \(-0.853515\pi\)
−0.895965 + 0.444125i \(0.853515\pi\)
\(368\) 5.35913e6 2.06288
\(369\) −2.96675e6 −1.13427
\(370\) 0 0
\(371\) 4.11538e6 1.55230
\(372\) −609079. −0.228200
\(373\) −1.75855e6 −0.654461 −0.327230 0.944945i \(-0.606115\pi\)
−0.327230 + 0.944945i \(0.606115\pi\)
\(374\) 622470. 0.230112
\(375\) 0 0
\(376\) 398839. 0.145488
\(377\) 2.70742e6 0.981074
\(378\) 2.31192e6 0.832229
\(379\) 3.77525e6 1.35004 0.675021 0.737799i \(-0.264135\pi\)
0.675021 + 0.737799i \(0.264135\pi\)
\(380\) 0 0
\(381\) 1.60046e6 0.564848
\(382\) 96763.3 0.0339275
\(383\) −1.85816e6 −0.647272 −0.323636 0.946182i \(-0.604905\pi\)
−0.323636 + 0.946182i \(0.604905\pi\)
\(384\) −909762. −0.314847
\(385\) 0 0
\(386\) 4.06960e6 1.39022
\(387\) −393938. −0.133706
\(388\) 1.51492e6 0.510869
\(389\) 468713. 0.157048 0.0785241 0.996912i \(-0.474979\pi\)
0.0785241 + 0.996912i \(0.474979\pi\)
\(390\) 0 0
\(391\) −4.90452e6 −1.62239
\(392\) 22403.5 0.00736377
\(393\) −903368. −0.295042
\(394\) 1.62490e6 0.527334
\(395\) 0 0
\(396\) −315765. −0.101187
\(397\) 2.30778e6 0.734883 0.367442 0.930047i \(-0.380234\pi\)
0.367442 + 0.930047i \(0.380234\pi\)
\(398\) −4.00041e6 −1.26589
\(399\) −711653. −0.223788
\(400\) 0 0
\(401\) 2.86726e6 0.890444 0.445222 0.895420i \(-0.353125\pi\)
0.445222 + 0.895420i \(0.353125\pi\)
\(402\) −1.48237e6 −0.457500
\(403\) −2.57664e6 −0.790298
\(404\) 2.45170e6 0.747332
\(405\) 0 0
\(406\) −5.45777e6 −1.64324
\(407\) 1.02668e6 0.307220
\(408\) 554284. 0.164847
\(409\) −2.17707e6 −0.643523 −0.321761 0.946821i \(-0.604275\pi\)
−0.321761 + 0.946821i \(0.604275\pi\)
\(410\) 0 0
\(411\) −1.88170e6 −0.549471
\(412\) 676481. 0.196342
\(413\) −5.06062e6 −1.45992
\(414\) 6.49854e6 1.86344
\(415\) 0 0
\(416\) 2.90010e6 0.821636
\(417\) −2.16756e6 −0.610422
\(418\) 543451. 0.152132
\(419\) −2.47893e6 −0.689810 −0.344905 0.938638i \(-0.612089\pi\)
−0.344905 + 0.938638i \(0.612089\pi\)
\(420\) 0 0
\(421\) 2.02419e6 0.556605 0.278302 0.960494i \(-0.410228\pi\)
0.278302 + 0.960494i \(0.410228\pi\)
\(422\) 5.56452e6 1.52106
\(423\) 971341. 0.263950
\(424\) −2.79844e6 −0.755963
\(425\) 0 0
\(426\) 615106. 0.164220
\(427\) 94974.1 0.0252078
\(428\) 2.94571e6 0.777285
\(429\) 187752. 0.0492539
\(430\) 0 0
\(431\) 2.48747e6 0.645006 0.322503 0.946568i \(-0.395476\pi\)
0.322503 + 0.946568i \(0.395476\pi\)
\(432\) −3.15741e6 −0.813995
\(433\) 1.34938e6 0.345871 0.172935 0.984933i \(-0.444675\pi\)
0.172935 + 0.984933i \(0.444675\pi\)
\(434\) 5.19414e6 1.32370
\(435\) 0 0
\(436\) −817730. −0.206012
\(437\) −4.28191e6 −1.07259
\(438\) 1.31683e6 0.327979
\(439\) −4.37772e6 −1.08414 −0.542071 0.840332i \(-0.682360\pi\)
−0.542071 + 0.840332i \(0.682360\pi\)
\(440\) 0 0
\(441\) 54562.0 0.0133596
\(442\) −3.83141e6 −0.932832
\(443\) −6.46353e6 −1.56481 −0.782403 0.622772i \(-0.786006\pi\)
−0.782403 + 0.622772i \(0.786006\pi\)
\(444\) −1.49381e6 −0.359615
\(445\) 0 0
\(446\) 2.26844e6 0.539995
\(447\) 1.57866e6 0.373698
\(448\) −637731. −0.150121
\(449\) 5.49347e6 1.28597 0.642985 0.765879i \(-0.277696\pi\)
0.642985 + 0.765879i \(0.277696\pi\)
\(450\) 0 0
\(451\) 1.03963e6 0.240679
\(452\) 3.31146e6 0.762383
\(453\) −2.75771e6 −0.631398
\(454\) −7.47438e6 −1.70191
\(455\) 0 0
\(456\) 483920. 0.108984
\(457\) −7.91228e6 −1.77219 −0.886097 0.463500i \(-0.846593\pi\)
−0.886097 + 0.463500i \(0.846593\pi\)
\(458\) 4.37533e6 0.974647
\(459\) 2.88957e6 0.640179
\(460\) 0 0
\(461\) 5.65524e6 1.23936 0.619682 0.784853i \(-0.287262\pi\)
0.619682 + 0.784853i \(0.287262\pi\)
\(462\) −378481. −0.0824972
\(463\) −7.19442e6 −1.55971 −0.779854 0.625962i \(-0.784706\pi\)
−0.779854 + 0.625962i \(0.784706\pi\)
\(464\) 7.45374e6 1.60723
\(465\) 0 0
\(466\) −1.22806e6 −0.261972
\(467\) −5.30058e6 −1.12468 −0.562342 0.826904i \(-0.690100\pi\)
−0.562342 + 0.826904i \(0.690100\pi\)
\(468\) 1.94359e6 0.410195
\(469\) 4.83974e6 1.01599
\(470\) 0 0
\(471\) 1.52821e6 0.317418
\(472\) 3.44119e6 0.710974
\(473\) 138047. 0.0283709
\(474\) −65142.9 −0.0133175
\(475\) 0 0
\(476\) 2.95696e6 0.598175
\(477\) −6.81537e6 −1.37149
\(478\) 1.09098e7 2.18398
\(479\) 4.42947e6 0.882091 0.441045 0.897485i \(-0.354608\pi\)
0.441045 + 0.897485i \(0.354608\pi\)
\(480\) 0 0
\(481\) −6.31939e6 −1.24541
\(482\) 4.07004e6 0.797959
\(483\) 2.98210e6 0.581640
\(484\) −3.08638e6 −0.598876
\(485\) 0 0
\(486\) −5.86876e6 −1.12708
\(487\) −4.07803e6 −0.779162 −0.389581 0.920992i \(-0.627380\pi\)
−0.389581 + 0.920992i \(0.627380\pi\)
\(488\) −64581.8 −0.0122761
\(489\) −445078. −0.0841713
\(490\) 0 0
\(491\) −2.18961e6 −0.409886 −0.204943 0.978774i \(-0.565701\pi\)
−0.204943 + 0.978774i \(0.565701\pi\)
\(492\) −1.51266e6 −0.281726
\(493\) −6.82144e6 −1.26403
\(494\) −3.34503e6 −0.616713
\(495\) 0 0
\(496\) −7.09370e6 −1.29470
\(497\) −2.00824e6 −0.364691
\(498\) 2.14226e6 0.387079
\(499\) −1.03583e7 −1.86224 −0.931119 0.364715i \(-0.881166\pi\)
−0.931119 + 0.364715i \(0.881166\pi\)
\(500\) 0 0
\(501\) −2.02334e6 −0.360143
\(502\) −1.39212e6 −0.246557
\(503\) 5.77249e6 1.01729 0.508643 0.860978i \(-0.330147\pi\)
0.508643 + 0.860978i \(0.330147\pi\)
\(504\) 2.39783e6 0.420476
\(505\) 0 0
\(506\) −2.27727e6 −0.395401
\(507\) 876161. 0.151378
\(508\) −5.80581e6 −0.998168
\(509\) −6.19636e6 −1.06009 −0.530044 0.847970i \(-0.677825\pi\)
−0.530044 + 0.847970i \(0.677825\pi\)
\(510\) 0 0
\(511\) −4.29930e6 −0.728359
\(512\) 4.44248e6 0.748947
\(513\) 2.52275e6 0.423234
\(514\) −1.50238e7 −2.50826
\(515\) 0 0
\(516\) −200857. −0.0332095
\(517\) −340385. −0.0560072
\(518\) 1.27390e7 2.08599
\(519\) −4.10380e6 −0.668756
\(520\) 0 0
\(521\) −8.73637e6 −1.41006 −0.705028 0.709179i \(-0.749066\pi\)
−0.705028 + 0.709179i \(0.749066\pi\)
\(522\) 9.03848e6 1.45184
\(523\) −1.53756e6 −0.245798 −0.122899 0.992419i \(-0.539219\pi\)
−0.122899 + 0.992419i \(0.539219\pi\)
\(524\) 3.27705e6 0.521381
\(525\) 0 0
\(526\) 1.59928e7 2.52035
\(527\) 6.49194e6 1.01824
\(528\) 516896. 0.0806897
\(529\) 1.15065e7 1.78774
\(530\) 0 0
\(531\) 8.38076e6 1.28987
\(532\) 2.58159e6 0.395465
\(533\) −6.39912e6 −0.975668
\(534\) −2.96934e6 −0.450616
\(535\) 0 0
\(536\) −3.29100e6 −0.494784
\(537\) −1.34075e6 −0.200638
\(538\) −5.52372e6 −0.822765
\(539\) −19120.0 −0.00283476
\(540\) 0 0
\(541\) 2.59108e6 0.380617 0.190308 0.981724i \(-0.439051\pi\)
0.190308 + 0.981724i \(0.439051\pi\)
\(542\) −1.15017e6 −0.168176
\(543\) 4.73273e6 0.688830
\(544\) −7.30691e6 −1.05861
\(545\) 0 0
\(546\) 2.32962e6 0.334428
\(547\) −1.67024e6 −0.238677 −0.119338 0.992854i \(-0.538077\pi\)
−0.119338 + 0.992854i \(0.538077\pi\)
\(548\) 6.82603e6 0.970995
\(549\) −157284. −0.0222717
\(550\) 0 0
\(551\) −5.95549e6 −0.835678
\(552\) −2.02781e6 −0.283257
\(553\) 212683. 0.0295747
\(554\) −3.48903e6 −0.482981
\(555\) 0 0
\(556\) 7.86301e6 1.07870
\(557\) −6.91475e6 −0.944362 −0.472181 0.881502i \(-0.656533\pi\)
−0.472181 + 0.881502i \(0.656533\pi\)
\(558\) −8.60189e6 −1.16952
\(559\) −849701. −0.115010
\(560\) 0 0
\(561\) −473048. −0.0634597
\(562\) 2.36336e6 0.315638
\(563\) −5.76254e6 −0.766202 −0.383101 0.923706i \(-0.625144\pi\)
−0.383101 + 0.923706i \(0.625144\pi\)
\(564\) 495257. 0.0655591
\(565\) 0 0
\(566\) 7.46424e6 0.979365
\(567\) 4.90357e6 0.640553
\(568\) 1.36559e6 0.177603
\(569\) −5.44028e6 −0.704434 −0.352217 0.935918i \(-0.614572\pi\)
−0.352217 + 0.935918i \(0.614572\pi\)
\(570\) 0 0
\(571\) 6.87704e6 0.882696 0.441348 0.897336i \(-0.354500\pi\)
0.441348 + 0.897336i \(0.354500\pi\)
\(572\) −681087. −0.0870388
\(573\) −73535.6 −0.00935644
\(574\) 1.28997e7 1.63418
\(575\) 0 0
\(576\) 1.05613e6 0.132636
\(577\) −1.71198e6 −0.214072 −0.107036 0.994255i \(-0.534136\pi\)
−0.107036 + 0.994255i \(0.534136\pi\)
\(578\) −570664. −0.0710495
\(579\) −3.09270e6 −0.383391
\(580\) 0 0
\(581\) −6.99421e6 −0.859604
\(582\) −3.00711e6 −0.367994
\(583\) 2.38829e6 0.291016
\(584\) 2.92350e6 0.354708
\(585\) 0 0
\(586\) 3.93612e6 0.473505
\(587\) −9.59837e6 −1.14975 −0.574874 0.818242i \(-0.694949\pi\)
−0.574874 + 0.818242i \(0.694949\pi\)
\(588\) 27819.5 0.00331823
\(589\) 5.66782e6 0.673175
\(590\) 0 0
\(591\) −1.23485e6 −0.145427
\(592\) −1.73978e7 −2.04028
\(593\) −1.23992e7 −1.44796 −0.723982 0.689818i \(-0.757690\pi\)
−0.723982 + 0.689818i \(0.757690\pi\)
\(594\) 1.34168e6 0.156021
\(595\) 0 0
\(596\) −5.72675e6 −0.660378
\(597\) 3.04012e6 0.349104
\(598\) 1.40170e7 1.60288
\(599\) 1.10058e7 1.25330 0.626648 0.779303i \(-0.284426\pi\)
0.626648 + 0.779303i \(0.284426\pi\)
\(600\) 0 0
\(601\) −1.63639e7 −1.84800 −0.923998 0.382397i \(-0.875099\pi\)
−0.923998 + 0.382397i \(0.875099\pi\)
\(602\) 1.71288e6 0.192635
\(603\) −8.01497e6 −0.897654
\(604\) 1.00039e7 1.11577
\(605\) 0 0
\(606\) −4.86662e6 −0.538326
\(607\) −2.89375e6 −0.318779 −0.159390 0.987216i \(-0.550953\pi\)
−0.159390 + 0.987216i \(0.550953\pi\)
\(608\) −6.37933e6 −0.699868
\(609\) 4.14765e6 0.453168
\(610\) 0 0
\(611\) 2.09513e6 0.227043
\(612\) −4.89695e6 −0.528503
\(613\) 362110. 0.0389215 0.0194607 0.999811i \(-0.493805\pi\)
0.0194607 + 0.999811i \(0.493805\pi\)
\(614\) −6.07668e6 −0.650497
\(615\) 0 0
\(616\) −840265. −0.0892204
\(617\) 3.10076e6 0.327911 0.163955 0.986468i \(-0.447575\pi\)
0.163955 + 0.986468i \(0.447575\pi\)
\(618\) −1.34281e6 −0.141431
\(619\) −8.22211e6 −0.862495 −0.431248 0.902234i \(-0.641927\pi\)
−0.431248 + 0.902234i \(0.641927\pi\)
\(620\) 0 0
\(621\) −1.05713e7 −1.10002
\(622\) 1.92079e7 1.99069
\(623\) 9.69451e6 1.00070
\(624\) −3.18159e6 −0.327101
\(625\) 0 0
\(626\) 1.52411e6 0.155446
\(627\) −412997. −0.0419544
\(628\) −5.54374e6 −0.560923
\(629\) 1.59220e7 1.60461
\(630\) 0 0
\(631\) −3.91402e6 −0.391336 −0.195668 0.980670i \(-0.562687\pi\)
−0.195668 + 0.980670i \(0.562687\pi\)
\(632\) −144624. −0.0144028
\(633\) −4.22877e6 −0.419474
\(634\) −1.99143e7 −1.96762
\(635\) 0 0
\(636\) −3.47495e6 −0.340648
\(637\) 117687. 0.0114916
\(638\) −3.16733e6 −0.308065
\(639\) 3.32580e6 0.322214
\(640\) 0 0
\(641\) 1.88259e6 0.180972 0.0904859 0.995898i \(-0.471158\pi\)
0.0904859 + 0.995898i \(0.471158\pi\)
\(642\) −5.84722e6 −0.559902
\(643\) −975076. −0.0930060 −0.0465030 0.998918i \(-0.514808\pi\)
−0.0465030 + 0.998918i \(0.514808\pi\)
\(644\) −1.08179e7 −1.02784
\(645\) 0 0
\(646\) 8.42795e6 0.794585
\(647\) 1.46477e7 1.37565 0.687827 0.725875i \(-0.258565\pi\)
0.687827 + 0.725875i \(0.258565\pi\)
\(648\) −3.33440e6 −0.311947
\(649\) −2.93685e6 −0.273697
\(650\) 0 0
\(651\) −3.94730e6 −0.365046
\(652\) 1.61456e6 0.148743
\(653\) 1.95004e7 1.78962 0.894810 0.446446i \(-0.147311\pi\)
0.894810 + 0.446446i \(0.147311\pi\)
\(654\) 1.62319e6 0.148397
\(655\) 0 0
\(656\) −1.76173e7 −1.59838
\(657\) 7.11996e6 0.643523
\(658\) −4.22348e6 −0.380282
\(659\) 1.69056e7 1.51641 0.758206 0.652015i \(-0.226076\pi\)
0.758206 + 0.652015i \(0.226076\pi\)
\(660\) 0 0
\(661\) −5.48642e6 −0.488411 −0.244206 0.969723i \(-0.578527\pi\)
−0.244206 + 0.969723i \(0.578527\pi\)
\(662\) 1.51377e7 1.34250
\(663\) 2.91169e6 0.257254
\(664\) 4.75603e6 0.418624
\(665\) 0 0
\(666\) −2.10968e7 −1.84302
\(667\) 2.49558e7 2.17199
\(668\) 7.33987e6 0.636425
\(669\) −1.72390e6 −0.148918
\(670\) 0 0
\(671\) 55116.7 0.00472582
\(672\) 4.44283e6 0.379522
\(673\) 6.45667e6 0.549504 0.274752 0.961515i \(-0.411404\pi\)
0.274752 + 0.961515i \(0.411404\pi\)
\(674\) 1.78004e6 0.150932
\(675\) 0 0
\(676\) −3.17836e6 −0.267508
\(677\) −1.08003e6 −0.0905658 −0.0452829 0.998974i \(-0.514419\pi\)
−0.0452829 + 0.998974i \(0.514419\pi\)
\(678\) −6.57324e6 −0.549168
\(679\) 9.81782e6 0.817223
\(680\) 0 0
\(681\) 5.68018e6 0.469347
\(682\) 3.01434e6 0.248160
\(683\) −1.27130e7 −1.04279 −0.521395 0.853315i \(-0.674588\pi\)
−0.521395 + 0.853315i \(0.674588\pi\)
\(684\) −4.27531e6 −0.349403
\(685\) 0 0
\(686\) −1.58069e7 −1.28244
\(687\) −3.32505e6 −0.268785
\(688\) −2.33930e6 −0.188415
\(689\) −1.47004e7 −1.17972
\(690\) 0 0
\(691\) 351123. 0.0279747 0.0139873 0.999902i \(-0.495548\pi\)
0.0139873 + 0.999902i \(0.495548\pi\)
\(692\) 1.48869e7 1.18179
\(693\) −2.04640e6 −0.161867
\(694\) −4.85884e6 −0.382943
\(695\) 0 0
\(696\) −2.82038e6 −0.220691
\(697\) 1.61228e7 1.25707
\(698\) 2.51625e7 1.95486
\(699\) 933268. 0.0722459
\(700\) 0 0
\(701\) 9.65153e6 0.741825 0.370912 0.928668i \(-0.379045\pi\)
0.370912 + 0.928668i \(0.379045\pi\)
\(702\) −8.25830e6 −0.632482
\(703\) 1.39007e7 1.06084
\(704\) −370097. −0.0281439
\(705\) 0 0
\(706\) 2.24888e7 1.69806
\(707\) 1.58889e7 1.19549
\(708\) 4.27309e6 0.320375
\(709\) −5.18551e6 −0.387414 −0.193707 0.981059i \(-0.562051\pi\)
−0.193707 + 0.981059i \(0.562051\pi\)
\(710\) 0 0
\(711\) −352220. −0.0261300
\(712\) −6.59221e6 −0.487339
\(713\) −2.37503e7 −1.74963
\(714\) −5.86957e6 −0.430884
\(715\) 0 0
\(716\) 4.86371e6 0.354556
\(717\) −8.29096e6 −0.602292
\(718\) 2.18101e7 1.57887
\(719\) 1.11492e7 0.804306 0.402153 0.915572i \(-0.368262\pi\)
0.402153 + 0.915572i \(0.368262\pi\)
\(720\) 0 0
\(721\) 4.38412e6 0.314083
\(722\) −1.04718e7 −0.747613
\(723\) −3.09303e6 −0.220059
\(724\) −1.71684e7 −1.21726
\(725\) 0 0
\(726\) 6.12647e6 0.431389
\(727\) 2.54905e7 1.78872 0.894361 0.447347i \(-0.147631\pi\)
0.894361 + 0.447347i \(0.147631\pi\)
\(728\) 5.17198e6 0.361683
\(729\) −4.80208e6 −0.334666
\(730\) 0 0
\(731\) 2.14086e6 0.148182
\(732\) −80194.4 −0.00553180
\(733\) −1.87850e7 −1.29137 −0.645687 0.763602i \(-0.723429\pi\)
−0.645687 + 0.763602i \(0.723429\pi\)
\(734\) −3.32939e7 −2.28100
\(735\) 0 0
\(736\) 2.67319e7 1.81901
\(737\) 2.80867e6 0.190472
\(738\) −2.13629e7 −1.44384
\(739\) 8.16688e6 0.550104 0.275052 0.961429i \(-0.411305\pi\)
0.275052 + 0.961429i \(0.411305\pi\)
\(740\) 0 0
\(741\) 2.54207e6 0.170075
\(742\) 2.96339e7 1.97596
\(743\) −3.71670e6 −0.246993 −0.123497 0.992345i \(-0.539411\pi\)
−0.123497 + 0.992345i \(0.539411\pi\)
\(744\) 2.68414e6 0.177776
\(745\) 0 0
\(746\) −1.26629e7 −0.833081
\(747\) 1.15829e7 0.759482
\(748\) 1.71603e6 0.112142
\(749\) 1.90904e7 1.24340
\(750\) 0 0
\(751\) −1.60827e7 −1.04054 −0.520269 0.854002i \(-0.674168\pi\)
−0.520269 + 0.854002i \(0.674168\pi\)
\(752\) 5.76806e6 0.371950
\(753\) 1.05795e6 0.0679948
\(754\) 1.94955e7 1.24884
\(755\) 0 0
\(756\) 6.37349e6 0.405577
\(757\) 2.47457e7 1.56950 0.784749 0.619814i \(-0.212792\pi\)
0.784749 + 0.619814i \(0.212792\pi\)
\(758\) 2.71847e7 1.71851
\(759\) 1.73061e6 0.109043
\(760\) 0 0
\(761\) 2.22532e7 1.39294 0.696469 0.717587i \(-0.254753\pi\)
0.696469 + 0.717587i \(0.254753\pi\)
\(762\) 1.15245e7 0.719011
\(763\) −5.29952e6 −0.329553
\(764\) 266757. 0.0165342
\(765\) 0 0
\(766\) −1.33802e7 −0.823931
\(767\) 1.80768e7 1.10952
\(768\) −7.41903e6 −0.453883
\(769\) −1.98413e7 −1.20991 −0.604956 0.796259i \(-0.706809\pi\)
−0.604956 + 0.796259i \(0.706809\pi\)
\(770\) 0 0
\(771\) 1.14174e7 0.691721
\(772\) 1.12191e7 0.677507
\(773\) −7.62070e6 −0.458718 −0.229359 0.973342i \(-0.573663\pi\)
−0.229359 + 0.973342i \(0.573663\pi\)
\(774\) −2.83666e6 −0.170198
\(775\) 0 0
\(776\) −6.67606e6 −0.397985
\(777\) −9.68105e6 −0.575267
\(778\) 3.37509e6 0.199911
\(779\) 1.40761e7 0.831073
\(780\) 0 0
\(781\) −1.16545e6 −0.0683702
\(782\) −3.53163e7 −2.06518
\(783\) −1.47031e7 −0.857045
\(784\) 324002. 0.0188260
\(785\) 0 0
\(786\) −6.50495e6 −0.375567
\(787\) 1.94358e7 1.11858 0.559290 0.828972i \(-0.311074\pi\)
0.559290 + 0.828972i \(0.311074\pi\)
\(788\) 4.47952e6 0.256990
\(789\) −1.21538e7 −0.695055
\(790\) 0 0
\(791\) 2.14608e7 1.21956
\(792\) 1.39154e6 0.0788285
\(793\) −339253. −0.0191576
\(794\) 1.66178e7 0.935454
\(795\) 0 0
\(796\) −1.10283e7 −0.616917
\(797\) −3.86599e6 −0.215583 −0.107792 0.994174i \(-0.534378\pi\)
−0.107792 + 0.994174i \(0.534378\pi\)
\(798\) −5.12445e6 −0.284866
\(799\) −5.27876e6 −0.292526
\(800\) 0 0
\(801\) −1.60548e7 −0.884147
\(802\) 2.06465e7 1.13347
\(803\) −2.49503e6 −0.136549
\(804\) −4.08659e6 −0.222957
\(805\) 0 0
\(806\) −1.85538e7 −1.00599
\(807\) 4.19776e6 0.226900
\(808\) −1.08044e7 −0.582198
\(809\) −1.94431e7 −1.04446 −0.522232 0.852803i \(-0.674901\pi\)
−0.522232 + 0.852803i \(0.674901\pi\)
\(810\) 0 0
\(811\) −1.30552e7 −0.696995 −0.348498 0.937310i \(-0.613308\pi\)
−0.348498 + 0.937310i \(0.613308\pi\)
\(812\) −1.50460e7 −0.800812
\(813\) 874077. 0.0463792
\(814\) 7.39288e6 0.391069
\(815\) 0 0
\(816\) 8.01613e6 0.421443
\(817\) 1.86908e6 0.0979657
\(818\) −1.56766e7 −0.819158
\(819\) 1.25960e7 0.656178
\(820\) 0 0
\(821\) 1.03522e7 0.536013 0.268006 0.963417i \(-0.413635\pi\)
0.268006 + 0.963417i \(0.413635\pi\)
\(822\) −1.35497e7 −0.699437
\(823\) 2.95055e7 1.51846 0.759230 0.650823i \(-0.225576\pi\)
0.759230 + 0.650823i \(0.225576\pi\)
\(824\) −2.98118e6 −0.152957
\(825\) 0 0
\(826\) −3.64403e7 −1.85837
\(827\) −2.36807e6 −0.120401 −0.0602005 0.998186i \(-0.519174\pi\)
−0.0602005 + 0.998186i \(0.519174\pi\)
\(828\) 1.79152e7 0.908124
\(829\) −5.54371e6 −0.280165 −0.140082 0.990140i \(-0.544737\pi\)
−0.140082 + 0.990140i \(0.544737\pi\)
\(830\) 0 0
\(831\) 2.65149e6 0.133195
\(832\) 2.27801e6 0.114090
\(833\) −296517. −0.0148060
\(834\) −1.56081e7 −0.777023
\(835\) 0 0
\(836\) 1.49818e6 0.0741395
\(837\) 1.39929e7 0.690387
\(838\) −1.78502e7 −0.878079
\(839\) 2.61550e7 1.28277 0.641386 0.767218i \(-0.278360\pi\)
0.641386 + 0.767218i \(0.278360\pi\)
\(840\) 0 0
\(841\) 1.41986e7 0.692237
\(842\) 1.45758e7 0.708518
\(843\) −1.79604e6 −0.0870457
\(844\) 1.53403e7 0.741271
\(845\) 0 0
\(846\) 6.99440e6 0.335989
\(847\) −2.00021e7 −0.958006
\(848\) −4.04713e7 −1.93267
\(849\) −5.67247e6 −0.270087
\(850\) 0 0
\(851\) −5.82494e7 −2.75720
\(852\) 1.69572e6 0.0800306
\(853\) 1.50861e7 0.709911 0.354956 0.934883i \(-0.384496\pi\)
0.354956 + 0.934883i \(0.384496\pi\)
\(854\) 683886. 0.0320877
\(855\) 0 0
\(856\) −1.29814e7 −0.605532
\(857\) −3.93634e7 −1.83080 −0.915398 0.402550i \(-0.868124\pi\)
−0.915398 + 0.402550i \(0.868124\pi\)
\(858\) 1.35196e6 0.0626967
\(859\) 7.93682e6 0.366998 0.183499 0.983020i \(-0.441258\pi\)
0.183499 + 0.983020i \(0.441258\pi\)
\(860\) 0 0
\(861\) −9.80318e6 −0.450670
\(862\) 1.79117e7 0.821047
\(863\) −4.07079e7 −1.86060 −0.930298 0.366804i \(-0.880452\pi\)
−0.930298 + 0.366804i \(0.880452\pi\)
\(864\) −1.57495e7 −0.717763
\(865\) 0 0
\(866\) 9.71656e6 0.440269
\(867\) 433678. 0.0195938
\(868\) 1.43192e7 0.645089
\(869\) 123427. 0.00554450
\(870\) 0 0
\(871\) −1.72878e7 −0.772139
\(872\) 3.60364e6 0.160491
\(873\) −1.62590e7 −0.722037
\(874\) −3.08331e7 −1.36533
\(875\) 0 0
\(876\) 3.63025e6 0.159837
\(877\) −1.74592e7 −0.766523 −0.383262 0.923640i \(-0.625199\pi\)
−0.383262 + 0.923640i \(0.625199\pi\)
\(878\) −3.15229e7 −1.38004
\(879\) −2.99127e6 −0.130582
\(880\) 0 0
\(881\) 3.98363e7 1.72918 0.864588 0.502482i \(-0.167580\pi\)
0.864588 + 0.502482i \(0.167580\pi\)
\(882\) 392888. 0.0170058
\(883\) −2.37277e6 −0.102413 −0.0512063 0.998688i \(-0.516307\pi\)
−0.0512063 + 0.998688i \(0.516307\pi\)
\(884\) −1.05624e7 −0.454605
\(885\) 0 0
\(886\) −4.65424e7 −1.99189
\(887\) 2.89221e7 1.23430 0.617150 0.786846i \(-0.288287\pi\)
0.617150 + 0.786846i \(0.288287\pi\)
\(888\) 6.58306e6 0.280153
\(889\) −3.76261e7 −1.59674
\(890\) 0 0
\(891\) 2.84571e6 0.120087
\(892\) 6.25363e6 0.263160
\(893\) −4.60864e6 −0.193395
\(894\) 1.13676e7 0.475691
\(895\) 0 0
\(896\) 2.13881e7 0.890027
\(897\) −1.06522e7 −0.442038
\(898\) 3.95572e7 1.63695
\(899\) −3.30331e7 −1.36317
\(900\) 0 0
\(901\) 3.70382e7 1.51998
\(902\) 7.48615e6 0.306367
\(903\) −1.30171e6 −0.0531244
\(904\) −1.45932e7 −0.593923
\(905\) 0 0
\(906\) −1.98576e7 −0.803724
\(907\) −3.07512e7 −1.24120 −0.620602 0.784126i \(-0.713112\pi\)
−0.620602 + 0.784126i \(0.713112\pi\)
\(908\) −2.06054e7 −0.829404
\(909\) −2.63132e7 −1.05624
\(910\) 0 0
\(911\) 9.59162e6 0.382909 0.191455 0.981501i \(-0.438680\pi\)
0.191455 + 0.981501i \(0.438680\pi\)
\(912\) 6.99852e6 0.278624
\(913\) −4.05898e6 −0.161154
\(914\) −5.69745e7 −2.25588
\(915\) 0 0
\(916\) 1.20619e7 0.474983
\(917\) 2.12378e7 0.834040
\(918\) 2.08071e7 0.814902
\(919\) −3.67365e7 −1.43486 −0.717429 0.696631i \(-0.754681\pi\)
−0.717429 + 0.696631i \(0.754681\pi\)
\(920\) 0 0
\(921\) 4.61799e6 0.179392
\(922\) 4.07221e7 1.57762
\(923\) 7.17356e6 0.277160
\(924\) −1.04340e6 −0.0402040
\(925\) 0 0
\(926\) −5.18053e7 −1.98540
\(927\) −7.26042e6 −0.277500
\(928\) 3.71800e7 1.41723
\(929\) −7.37467e6 −0.280352 −0.140176 0.990127i \(-0.544767\pi\)
−0.140176 + 0.990127i \(0.544767\pi\)
\(930\) 0 0
\(931\) −258876. −0.00978852
\(932\) −3.38552e6 −0.127669
\(933\) −1.45971e7 −0.548987
\(934\) −3.81682e7 −1.43164
\(935\) 0 0
\(936\) −8.56518e6 −0.319556
\(937\) −3.02596e7 −1.12594 −0.562968 0.826478i \(-0.690341\pi\)
−0.562968 + 0.826478i \(0.690341\pi\)
\(938\) 3.48499e7 1.29328
\(939\) −1.15825e6 −0.0428686
\(940\) 0 0
\(941\) −4.19735e7 −1.54526 −0.772629 0.634858i \(-0.781059\pi\)
−0.772629 + 0.634858i \(0.781059\pi\)
\(942\) 1.10043e7 0.404050
\(943\) −5.89843e7 −2.16002
\(944\) 4.97670e7 1.81765
\(945\) 0 0
\(946\) 994042. 0.0361141
\(947\) −3.18458e7 −1.15392 −0.576961 0.816772i \(-0.695762\pi\)
−0.576961 + 0.816772i \(0.695762\pi\)
\(948\) −179586. −0.00649011
\(949\) 1.53574e7 0.553542
\(950\) 0 0
\(951\) 1.51339e7 0.542625
\(952\) −1.30310e7 −0.466000
\(953\) −2.50519e7 −0.893529 −0.446765 0.894652i \(-0.647424\pi\)
−0.446765 + 0.894652i \(0.647424\pi\)
\(954\) −4.90759e7 −1.74581
\(955\) 0 0
\(956\) 3.00762e7 1.06434
\(957\) 2.40702e6 0.0849572
\(958\) 3.18956e7 1.12284
\(959\) 4.42379e7 1.55327
\(960\) 0 0
\(961\) 2.80835e6 0.0980942
\(962\) −4.55045e7 −1.58532
\(963\) −3.16152e7 −1.09858
\(964\) 1.12203e7 0.388876
\(965\) 0 0
\(966\) 2.14734e7 0.740386
\(967\) −2.06439e7 −0.709946 −0.354973 0.934877i \(-0.615510\pi\)
−0.354973 + 0.934877i \(0.615510\pi\)
\(968\) 1.36014e7 0.466545
\(969\) −6.40484e6 −0.219128
\(970\) 0 0
\(971\) 2.05204e7 0.698455 0.349227 0.937038i \(-0.386444\pi\)
0.349227 + 0.937038i \(0.386444\pi\)
\(972\) −1.61790e7 −0.549270
\(973\) 5.09584e7 1.72557
\(974\) −2.93649e7 −0.991817
\(975\) 0 0
\(976\) −933991. −0.0313847
\(977\) −2.39254e7 −0.801904 −0.400952 0.916099i \(-0.631321\pi\)
−0.400952 + 0.916099i \(0.631321\pi\)
\(978\) −3.20490e6 −0.107144
\(979\) 5.62605e6 0.187606
\(980\) 0 0
\(981\) 8.77639e6 0.291168
\(982\) −1.57669e7 −0.521755
\(983\) −3.15675e7 −1.04197 −0.520987 0.853565i \(-0.674436\pi\)
−0.520987 + 0.853565i \(0.674436\pi\)
\(984\) 6.66611e6 0.219475
\(985\) 0 0
\(986\) −4.91196e7 −1.60903
\(987\) 3.20965e6 0.104873
\(988\) −9.22159e6 −0.300548
\(989\) −7.83218e6 −0.254620
\(990\) 0 0
\(991\) −1.05732e7 −0.341997 −0.170999 0.985271i \(-0.554699\pi\)
−0.170999 + 0.985271i \(0.554699\pi\)
\(992\) −3.53840e7 −1.14164
\(993\) −1.15039e7 −0.370231
\(994\) −1.44609e7 −0.464226
\(995\) 0 0
\(996\) 5.90579e6 0.188638
\(997\) 4.35315e7 1.38697 0.693484 0.720472i \(-0.256075\pi\)
0.693484 + 0.720472i \(0.256075\pi\)
\(998\) −7.45874e7 −2.37050
\(999\) 3.43185e7 1.08796
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 1075.6.a.j.1.29 yes 37
5.4 even 2 1075.6.a.i.1.9 37
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1075.6.a.i.1.9 37 5.4 even 2
1075.6.a.j.1.29 yes 37 1.1 even 1 trivial