Properties

Label 1075.6.a.j.1.14
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 1.14
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)
 
\(f(q)\) \(=\) \(q-3.78745 q^{2} -2.98047 q^{3} -17.6552 q^{4} +11.2884 q^{6} -10.8305 q^{7} +188.067 q^{8} -234.117 q^{9} +O(q^{10})\) \(q-3.78745 q^{2} -2.98047 q^{3} -17.6552 q^{4} +11.2884 q^{6} -10.8305 q^{7} +188.067 q^{8} -234.117 q^{9} -146.993 q^{11} +52.6209 q^{12} -212.624 q^{13} +41.0201 q^{14} -147.327 q^{16} -1714.81 q^{17} +886.706 q^{18} -945.260 q^{19} +32.2801 q^{21} +556.728 q^{22} +672.673 q^{23} -560.528 q^{24} +805.303 q^{26} +1422.03 q^{27} +191.215 q^{28} -7059.06 q^{29} -2752.37 q^{31} -5460.14 q^{32} +438.108 q^{33} +6494.78 q^{34} +4133.38 q^{36} +6574.22 q^{37} +3580.13 q^{38} +633.720 q^{39} -8613.44 q^{41} -122.259 q^{42} +1849.00 q^{43} +2595.19 q^{44} -2547.72 q^{46} -10163.7 q^{47} +439.103 q^{48} -16689.7 q^{49} +5110.96 q^{51} +3753.92 q^{52} +16377.9 q^{53} -5385.88 q^{54} -2036.86 q^{56} +2817.32 q^{57} +26735.8 q^{58} +5594.08 q^{59} -38842.8 q^{61} +10424.5 q^{62} +2535.61 q^{63} +25394.5 q^{64} -1659.31 q^{66} -47654.4 q^{67} +30275.4 q^{68} -2004.88 q^{69} +46426.3 q^{71} -44029.6 q^{72} -77983.9 q^{73} -24899.6 q^{74} +16688.8 q^{76} +1592.01 q^{77} -2400.18 q^{78} -16199.8 q^{79} +52652.0 q^{81} +32623.0 q^{82} -11904.1 q^{83} -569.912 q^{84} -7003.00 q^{86} +21039.3 q^{87} -27644.5 q^{88} +11983.9 q^{89} +2302.83 q^{91} -11876.2 q^{92} +8203.37 q^{93} +38494.5 q^{94} +16273.8 q^{96} -138286. q^{97} +63211.4 q^{98} +34413.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 37 q + 630 q^{4} + 291 q^{6} + 213 q^{8} + 3535 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.78745 −0.669533 −0.334767 0.942301i \(-0.608657\pi\)
−0.334767 + 0.942301i \(0.608657\pi\)
\(3\) −2.98047 −0.191197 −0.0955987 0.995420i \(-0.530477\pi\)
−0.0955987 + 0.995420i \(0.530477\pi\)
\(4\) −17.6552 −0.551725
\(5\) 0 0
\(6\) 11.2884 0.128013
\(7\) −10.8305 −0.0835419 −0.0417710 0.999127i \(-0.513300\pi\)
−0.0417710 + 0.999127i \(0.513300\pi\)
\(8\) 188.067 1.03893
\(9\) −234.117 −0.963444
\(10\) 0 0
\(11\) −146.993 −0.366281 −0.183140 0.983087i \(-0.558626\pi\)
−0.183140 + 0.983087i \(0.558626\pi\)
\(12\) 52.6209 0.105488
\(13\) −212.624 −0.348942 −0.174471 0.984662i \(-0.555822\pi\)
−0.174471 + 0.984662i \(0.555822\pi\)
\(14\) 41.0201 0.0559341
\(15\) 0 0
\(16\) −147.327 −0.143874
\(17\) −1714.81 −1.43911 −0.719556 0.694434i \(-0.755655\pi\)
−0.719556 + 0.694434i \(0.755655\pi\)
\(18\) 886.706 0.645057
\(19\) −945.260 −0.600714 −0.300357 0.953827i \(-0.597106\pi\)
−0.300357 + 0.953827i \(0.597106\pi\)
\(20\) 0 0
\(21\) 32.2801 0.0159730
\(22\) 556.728 0.245237
\(23\) 672.673 0.265145 0.132573 0.991173i \(-0.457676\pi\)
0.132573 + 0.991173i \(0.457676\pi\)
\(24\) −560.528 −0.198641
\(25\) 0 0
\(26\) 805.303 0.233628
\(27\) 1422.03 0.375405
\(28\) 191.215 0.0460922
\(29\) −7059.06 −1.55866 −0.779330 0.626613i \(-0.784441\pi\)
−0.779330 + 0.626613i \(0.784441\pi\)
\(30\) 0 0
\(31\) −2752.37 −0.514403 −0.257201 0.966358i \(-0.582800\pi\)
−0.257201 + 0.966358i \(0.582800\pi\)
\(32\) −5460.14 −0.942603
\(33\) 438.108 0.0700320
\(34\) 6494.78 0.963534
\(35\) 0 0
\(36\) 4133.38 0.531556
\(37\) 6574.22 0.789478 0.394739 0.918793i \(-0.370835\pi\)
0.394739 + 0.918793i \(0.370835\pi\)
\(38\) 3580.13 0.402198
\(39\) 633.720 0.0667169
\(40\) 0 0
\(41\) −8613.44 −0.800234 −0.400117 0.916464i \(-0.631030\pi\)
−0.400117 + 0.916464i \(0.631030\pi\)
\(42\) −122.259 −0.0106945
\(43\) 1849.00 0.152499
\(44\) 2595.19 0.202087
\(45\) 0 0
\(46\) −2547.72 −0.177524
\(47\) −10163.7 −0.671131 −0.335565 0.942017i \(-0.608927\pi\)
−0.335565 + 0.942017i \(0.608927\pi\)
\(48\) 439.103 0.0275083
\(49\) −16689.7 −0.993021
\(50\) 0 0
\(51\) 5110.96 0.275155
\(52\) 3753.92 0.192520
\(53\) 16377.9 0.800881 0.400440 0.916323i \(-0.368857\pi\)
0.400440 + 0.916323i \(0.368857\pi\)
\(54\) −5385.88 −0.251346
\(55\) 0 0
\(56\) −2036.86 −0.0867944
\(57\) 2817.32 0.114855
\(58\) 26735.8 1.04358
\(59\) 5594.08 0.209218 0.104609 0.994513i \(-0.466641\pi\)
0.104609 + 0.994513i \(0.466641\pi\)
\(60\) 0 0
\(61\) −38842.8 −1.33655 −0.668277 0.743913i \(-0.732968\pi\)
−0.668277 + 0.743913i \(0.732968\pi\)
\(62\) 10424.5 0.344410
\(63\) 2535.61 0.0804879
\(64\) 25394.5 0.774978
\(65\) 0 0
\(66\) −1659.31 −0.0468887
\(67\) −47654.4 −1.29693 −0.648464 0.761246i \(-0.724588\pi\)
−0.648464 + 0.761246i \(0.724588\pi\)
\(68\) 30275.4 0.793995
\(69\) −2004.88 −0.0506951
\(70\) 0 0
\(71\) 46426.3 1.09300 0.546498 0.837461i \(-0.315961\pi\)
0.546498 + 0.837461i \(0.315961\pi\)
\(72\) −44029.6 −1.00095
\(73\) −77983.9 −1.71276 −0.856382 0.516343i \(-0.827293\pi\)
−0.856382 + 0.516343i \(0.827293\pi\)
\(74\) −24899.6 −0.528582
\(75\) 0 0
\(76\) 16688.8 0.331429
\(77\) 1592.01 0.0305998
\(78\) −2400.18 −0.0446692
\(79\) −16199.8 −0.292039 −0.146019 0.989282i \(-0.546646\pi\)
−0.146019 + 0.989282i \(0.546646\pi\)
\(80\) 0 0
\(81\) 52652.0 0.891667
\(82\) 32623.0 0.535783
\(83\) −11904.1 −0.189671 −0.0948355 0.995493i \(-0.530233\pi\)
−0.0948355 + 0.995493i \(0.530233\pi\)
\(84\) −569.912 −0.00881271
\(85\) 0 0
\(86\) −7003.00 −0.102103
\(87\) 21039.3 0.298012
\(88\) −27644.5 −0.380541
\(89\) 11983.9 0.160370 0.0801849 0.996780i \(-0.474449\pi\)
0.0801849 + 0.996780i \(0.474449\pi\)
\(90\) 0 0
\(91\) 2302.83 0.0291513
\(92\) −11876.2 −0.146287
\(93\) 8203.37 0.0983524
\(94\) 38494.5 0.449344
\(95\) 0 0
\(96\) 16273.8 0.180223
\(97\) −138286. −1.49228 −0.746139 0.665791i \(-0.768094\pi\)
−0.746139 + 0.665791i \(0.768094\pi\)
\(98\) 63211.4 0.664860
\(99\) 34413.5 0.352891
\(100\) 0 0
\(101\) −107338. −1.04701 −0.523505 0.852022i \(-0.675376\pi\)
−0.523505 + 0.852022i \(0.675376\pi\)
\(102\) −19357.5 −0.184225
\(103\) −184140. −1.71024 −0.855118 0.518434i \(-0.826515\pi\)
−0.855118 + 0.518434i \(0.826515\pi\)
\(104\) −39987.5 −0.362527
\(105\) 0 0
\(106\) −62030.4 −0.536216
\(107\) −224246. −1.89350 −0.946748 0.321975i \(-0.895653\pi\)
−0.946748 + 0.321975i \(0.895653\pi\)
\(108\) −25106.3 −0.207121
\(109\) 45034.5 0.363061 0.181530 0.983385i \(-0.441895\pi\)
0.181530 + 0.983385i \(0.441895\pi\)
\(110\) 0 0
\(111\) −19594.3 −0.150946
\(112\) 1595.63 0.0120195
\(113\) −54906.7 −0.404510 −0.202255 0.979333i \(-0.564827\pi\)
−0.202255 + 0.979333i \(0.564827\pi\)
\(114\) −10670.5 −0.0768991
\(115\) 0 0
\(116\) 124629. 0.859953
\(117\) 49778.8 0.336186
\(118\) −21187.3 −0.140078
\(119\) 18572.3 0.120226
\(120\) 0 0
\(121\) −139444. −0.865838
\(122\) 147115. 0.894867
\(123\) 25672.1 0.153003
\(124\) 48593.7 0.283809
\(125\) 0 0
\(126\) −9603.49 −0.0538893
\(127\) 178360. 0.981272 0.490636 0.871365i \(-0.336765\pi\)
0.490636 + 0.871365i \(0.336765\pi\)
\(128\) 78544.2 0.423730
\(129\) −5510.89 −0.0291573
\(130\) 0 0
\(131\) 155441. 0.791384 0.395692 0.918383i \(-0.370505\pi\)
0.395692 + 0.918383i \(0.370505\pi\)
\(132\) −7734.89 −0.0386384
\(133\) 10237.7 0.0501848
\(134\) 180489. 0.868336
\(135\) 0 0
\(136\) −322499. −1.49514
\(137\) −72863.2 −0.331671 −0.165835 0.986153i \(-0.553032\pi\)
−0.165835 + 0.986153i \(0.553032\pi\)
\(138\) 7593.40 0.0339421
\(139\) 33628.0 0.147626 0.0738132 0.997272i \(-0.476483\pi\)
0.0738132 + 0.997272i \(0.476483\pi\)
\(140\) 0 0
\(141\) 30292.6 0.128318
\(142\) −175837. −0.731797
\(143\) 31254.2 0.127811
\(144\) 34491.7 0.138614
\(145\) 0 0
\(146\) 295360. 1.14675
\(147\) 49743.2 0.189863
\(148\) −116069. −0.435575
\(149\) −322095. −1.18855 −0.594277 0.804261i \(-0.702562\pi\)
−0.594277 + 0.804261i \(0.702562\pi\)
\(150\) 0 0
\(151\) 252170. 0.900018 0.450009 0.893024i \(-0.351421\pi\)
0.450009 + 0.893024i \(0.351421\pi\)
\(152\) −177772. −0.624100
\(153\) 401467. 1.38650
\(154\) −6029.66 −0.0204876
\(155\) 0 0
\(156\) −11188.5 −0.0368094
\(157\) −435261. −1.40929 −0.704646 0.709559i \(-0.748894\pi\)
−0.704646 + 0.709559i \(0.748894\pi\)
\(158\) 61355.8 0.195530
\(159\) −48813.8 −0.153126
\(160\) 0 0
\(161\) −7285.40 −0.0221508
\(162\) −199417. −0.597001
\(163\) 166832. 0.491825 0.245913 0.969292i \(-0.420912\pi\)
0.245913 + 0.969292i \(0.420912\pi\)
\(164\) 152072. 0.441509
\(165\) 0 0
\(166\) 45086.2 0.126991
\(167\) −380682. −1.05626 −0.528130 0.849163i \(-0.677107\pi\)
−0.528130 + 0.849163i \(0.677107\pi\)
\(168\) 6070.81 0.0165949
\(169\) −326084. −0.878239
\(170\) 0 0
\(171\) 221301. 0.578754
\(172\) −32644.5 −0.0841373
\(173\) −323531. −0.821864 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(174\) −79685.4 −0.199529
\(175\) 0 0
\(176\) 21656.0 0.0526982
\(177\) −16673.0 −0.0400019
\(178\) −45388.4 −0.107373
\(179\) −722793. −1.68609 −0.843046 0.537841i \(-0.819240\pi\)
−0.843046 + 0.537841i \(0.819240\pi\)
\(180\) 0 0
\(181\) 554674. 1.25847 0.629233 0.777217i \(-0.283369\pi\)
0.629233 + 0.777217i \(0.283369\pi\)
\(182\) −8721.85 −0.0195178
\(183\) 115770. 0.255545
\(184\) 126507. 0.275468
\(185\) 0 0
\(186\) −31069.9 −0.0658502
\(187\) 252065. 0.527120
\(188\) 179442. 0.370280
\(189\) −15401.4 −0.0313621
\(190\) 0 0
\(191\) −465840. −0.923961 −0.461980 0.886890i \(-0.652861\pi\)
−0.461980 + 0.886890i \(0.652861\pi\)
\(192\) −75687.5 −0.148174
\(193\) 685918. 1.32550 0.662749 0.748842i \(-0.269390\pi\)
0.662749 + 0.748842i \(0.269390\pi\)
\(194\) 523752. 0.999129
\(195\) 0 0
\(196\) 294660. 0.547875
\(197\) −706923. −1.29780 −0.648898 0.760875i \(-0.724770\pi\)
−0.648898 + 0.760875i \(0.724770\pi\)
\(198\) −130339. −0.236272
\(199\) 832627. 1.49045 0.745225 0.666813i \(-0.232342\pi\)
0.745225 + 0.666813i \(0.232342\pi\)
\(200\) 0 0
\(201\) 142033. 0.247969
\(202\) 406538. 0.701008
\(203\) 76453.3 0.130214
\(204\) −90235.0 −0.151810
\(205\) 0 0
\(206\) 697423. 1.14506
\(207\) −157484. −0.255453
\(208\) 31325.2 0.0502037
\(209\) 138946. 0.220030
\(210\) 0 0
\(211\) 586051. 0.906211 0.453106 0.891457i \(-0.350316\pi\)
0.453106 + 0.891457i \(0.350316\pi\)
\(212\) −289155. −0.441866
\(213\) −138372. −0.208978
\(214\) 849319. 1.26776
\(215\) 0 0
\(216\) 267437. 0.390020
\(217\) 29809.7 0.0429742
\(218\) −170566. −0.243081
\(219\) 232429. 0.327476
\(220\) 0 0
\(221\) 364610. 0.502167
\(222\) 74212.4 0.101063
\(223\) −294899. −0.397110 −0.198555 0.980090i \(-0.563625\pi\)
−0.198555 + 0.980090i \(0.563625\pi\)
\(224\) 59136.2 0.0787469
\(225\) 0 0
\(226\) 207956. 0.270833
\(227\) 1.07718e6 1.38747 0.693734 0.720232i \(-0.255965\pi\)
0.693734 + 0.720232i \(0.255965\pi\)
\(228\) −49740.4 −0.0633683
\(229\) 951704. 1.19926 0.599630 0.800277i \(-0.295314\pi\)
0.599630 + 0.800277i \(0.295314\pi\)
\(230\) 0 0
\(231\) −4744.94 −0.00585061
\(232\) −1.32757e6 −1.61934
\(233\) 151423. 0.182727 0.0913635 0.995818i \(-0.470877\pi\)
0.0913635 + 0.995818i \(0.470877\pi\)
\(234\) −188535. −0.225088
\(235\) 0 0
\(236\) −98764.6 −0.115431
\(237\) 48282.9 0.0558371
\(238\) −70341.9 −0.0804955
\(239\) 424064. 0.480216 0.240108 0.970746i \(-0.422817\pi\)
0.240108 + 0.970746i \(0.422817\pi\)
\(240\) 0 0
\(241\) 246268. 0.273127 0.136564 0.990631i \(-0.456394\pi\)
0.136564 + 0.990631i \(0.456394\pi\)
\(242\) 528138. 0.579707
\(243\) −502482. −0.545890
\(244\) 685778. 0.737410
\(245\) 0 0
\(246\) −97231.9 −0.102440
\(247\) 200985. 0.209614
\(248\) −517630. −0.534429
\(249\) 35479.8 0.0362646
\(250\) 0 0
\(251\) 490250. 0.491172 0.245586 0.969375i \(-0.421020\pi\)
0.245586 + 0.969375i \(0.421020\pi\)
\(252\) −44766.7 −0.0444072
\(253\) −98878.1 −0.0971178
\(254\) −675532. −0.656994
\(255\) 0 0
\(256\) −1.11011e6 −1.05868
\(257\) −877949. −0.829157 −0.414578 0.910014i \(-0.636071\pi\)
−0.414578 + 0.910014i \(0.636071\pi\)
\(258\) 20872.2 0.0195218
\(259\) −71202.3 −0.0659545
\(260\) 0 0
\(261\) 1.65264e6 1.50168
\(262\) −588725. −0.529858
\(263\) 543206. 0.484256 0.242128 0.970244i \(-0.422155\pi\)
0.242128 + 0.970244i \(0.422155\pi\)
\(264\) 82393.5 0.0727584
\(265\) 0 0
\(266\) −38774.7 −0.0336004
\(267\) −35717.6 −0.0306623
\(268\) 841348. 0.715548
\(269\) 1.04690e6 0.882113 0.441056 0.897479i \(-0.354604\pi\)
0.441056 + 0.897479i \(0.354604\pi\)
\(270\) 0 0
\(271\) −1.95842e6 −1.61988 −0.809939 0.586515i \(-0.800500\pi\)
−0.809939 + 0.586515i \(0.800500\pi\)
\(272\) 252638. 0.207051
\(273\) −6863.52 −0.00557366
\(274\) 275966. 0.222064
\(275\) 0 0
\(276\) 35396.6 0.0279698
\(277\) −2.30455e6 −1.80462 −0.902311 0.431086i \(-0.858131\pi\)
−0.902311 + 0.431086i \(0.858131\pi\)
\(278\) −127364. −0.0988407
\(279\) 644377. 0.495598
\(280\) 0 0
\(281\) −613724. −0.463668 −0.231834 0.972755i \(-0.574473\pi\)
−0.231834 + 0.972755i \(0.574473\pi\)
\(282\) −114732. −0.0859135
\(283\) 2.11228e6 1.56778 0.783889 0.620901i \(-0.213233\pi\)
0.783889 + 0.620901i \(0.213233\pi\)
\(284\) −819667. −0.603033
\(285\) 0 0
\(286\) −118374. −0.0855737
\(287\) 93288.1 0.0668531
\(288\) 1.27831e6 0.908145
\(289\) 1.52073e6 1.07105
\(290\) 0 0
\(291\) 412158. 0.285320
\(292\) 1.37682e6 0.944975
\(293\) −1.74950e6 −1.19054 −0.595272 0.803525i \(-0.702956\pi\)
−0.595272 + 0.803525i \(0.702956\pi\)
\(294\) −188400. −0.127120
\(295\) 0 0
\(296\) 1.23639e6 0.820214
\(297\) −209029. −0.137504
\(298\) 1.21992e6 0.795776
\(299\) −143026. −0.0925205
\(300\) 0 0
\(301\) −20025.6 −0.0127400
\(302\) −955082. −0.602592
\(303\) 319919. 0.200186
\(304\) 139262. 0.0864269
\(305\) 0 0
\(306\) −1.52054e6 −0.928310
\(307\) −485962. −0.294277 −0.147139 0.989116i \(-0.547006\pi\)
−0.147139 + 0.989116i \(0.547006\pi\)
\(308\) −28107.3 −0.0168827
\(309\) 548825. 0.326993
\(310\) 0 0
\(311\) 2.09644e6 1.22908 0.614541 0.788885i \(-0.289341\pi\)
0.614541 + 0.788885i \(0.289341\pi\)
\(312\) 119182. 0.0693143
\(313\) 1.34798e6 0.777716 0.388858 0.921298i \(-0.372870\pi\)
0.388858 + 0.921298i \(0.372870\pi\)
\(314\) 1.64853e6 0.943567
\(315\) 0 0
\(316\) 286010. 0.161125
\(317\) −2.00382e6 −1.11998 −0.559991 0.828499i \(-0.689195\pi\)
−0.559991 + 0.828499i \(0.689195\pi\)
\(318\) 184880. 0.102523
\(319\) 1.03763e6 0.570908
\(320\) 0 0
\(321\) 668358. 0.362032
\(322\) 27593.1 0.0148307
\(323\) 1.62095e6 0.864494
\(324\) −929583. −0.491955
\(325\) 0 0
\(326\) −631869. −0.329293
\(327\) −134224. −0.0694162
\(328\) −1.61990e6 −0.831388
\(329\) 110078. 0.0560676
\(330\) 0 0
\(331\) −758888. −0.380722 −0.190361 0.981714i \(-0.560966\pi\)
−0.190361 + 0.981714i \(0.560966\pi\)
\(332\) 210169. 0.104646
\(333\) −1.53914e6 −0.760618
\(334\) 1.44181e6 0.707202
\(335\) 0 0
\(336\) −4755.72 −0.00229810
\(337\) −280895. −0.134732 −0.0673658 0.997728i \(-0.521459\pi\)
−0.0673658 + 0.997728i \(0.521459\pi\)
\(338\) 1.23503e6 0.588010
\(339\) 163648. 0.0773413
\(340\) 0 0
\(341\) 404579. 0.188416
\(342\) −838168. −0.387495
\(343\) 362787. 0.166501
\(344\) 347735. 0.158436
\(345\) 0 0
\(346\) 1.22536e6 0.550266
\(347\) 765330. 0.341213 0.170606 0.985339i \(-0.445427\pi\)
0.170606 + 0.985339i \(0.445427\pi\)
\(348\) −371454. −0.164421
\(349\) −2.25701e6 −0.991906 −0.495953 0.868349i \(-0.665181\pi\)
−0.495953 + 0.868349i \(0.665181\pi\)
\(350\) 0 0
\(351\) −302358. −0.130995
\(352\) 802602. 0.345258
\(353\) 4.13031e6 1.76419 0.882096 0.471071i \(-0.156132\pi\)
0.882096 + 0.471071i \(0.156132\pi\)
\(354\) 63148.2 0.0267826
\(355\) 0 0
\(356\) −211578. −0.0884801
\(357\) −55354.4 −0.0229869
\(358\) 2.73754e6 1.12889
\(359\) 2.18583e6 0.895116 0.447558 0.894255i \(-0.352294\pi\)
0.447558 + 0.894255i \(0.352294\pi\)
\(360\) 0 0
\(361\) −1.58258e6 −0.639143
\(362\) −2.10080e6 −0.842585
\(363\) 415609. 0.165546
\(364\) −40656.9 −0.0160835
\(365\) 0 0
\(366\) −438473. −0.171096
\(367\) 970044. 0.375947 0.187973 0.982174i \(-0.439808\pi\)
0.187973 + 0.982174i \(0.439808\pi\)
\(368\) −99102.7 −0.0381475
\(369\) 2.01655e6 0.770980
\(370\) 0 0
\(371\) −177381. −0.0669071
\(372\) −144832. −0.0542635
\(373\) 1.00486e6 0.373969 0.186984 0.982363i \(-0.440129\pi\)
0.186984 + 0.982363i \(0.440129\pi\)
\(374\) −954685. −0.352924
\(375\) 0 0
\(376\) −1.91145e6 −0.697259
\(377\) 1.50092e6 0.543883
\(378\) 58332.0 0.0209980
\(379\) 2.83101e6 1.01238 0.506190 0.862422i \(-0.331054\pi\)
0.506190 + 0.862422i \(0.331054\pi\)
\(380\) 0 0
\(381\) −531599. −0.187617
\(382\) 1.76435e6 0.618623
\(383\) 4.39503e6 1.53096 0.765482 0.643458i \(-0.222501\pi\)
0.765482 + 0.643458i \(0.222501\pi\)
\(384\) −234099. −0.0810160
\(385\) 0 0
\(386\) −2.59788e6 −0.887465
\(387\) −432882. −0.146924
\(388\) 2.44147e6 0.823327
\(389\) 1.76227e6 0.590470 0.295235 0.955425i \(-0.404602\pi\)
0.295235 + 0.955425i \(0.404602\pi\)
\(390\) 0 0
\(391\) −1.15351e6 −0.381574
\(392\) −3.13878e6 −1.03168
\(393\) −463288. −0.151311
\(394\) 2.67744e6 0.868918
\(395\) 0 0
\(396\) −607577. −0.194699
\(397\) 2.47331e6 0.787595 0.393798 0.919197i \(-0.371161\pi\)
0.393798 + 0.919197i \(0.371161\pi\)
\(398\) −3.15353e6 −0.997906
\(399\) −30513.1 −0.00959520
\(400\) 0 0
\(401\) −1.64980e6 −0.512355 −0.256177 0.966630i \(-0.582463\pi\)
−0.256177 + 0.966630i \(0.582463\pi\)
\(402\) −537941. −0.166024
\(403\) 585220. 0.179497
\(404\) 1.89508e6 0.577662
\(405\) 0 0
\(406\) −289563. −0.0871823
\(407\) −966364. −0.289171
\(408\) 961201. 0.285867
\(409\) −1.68762e6 −0.498845 −0.249422 0.968395i \(-0.580241\pi\)
−0.249422 + 0.968395i \(0.580241\pi\)
\(410\) 0 0
\(411\) 217167. 0.0634145
\(412\) 3.25104e6 0.943580
\(413\) −60586.8 −0.0174785
\(414\) 596463. 0.171034
\(415\) 0 0
\(416\) 1.16096e6 0.328914
\(417\) −100227. −0.0282258
\(418\) −526253. −0.147317
\(419\) 5.53289e6 1.53963 0.769816 0.638266i \(-0.220348\pi\)
0.769816 + 0.638266i \(0.220348\pi\)
\(420\) 0 0
\(421\) 5.66009e6 1.55639 0.778194 0.628024i \(-0.216136\pi\)
0.778194 + 0.628024i \(0.216136\pi\)
\(422\) −2.21964e6 −0.606738
\(423\) 2.37949e6 0.646597
\(424\) 3.08013e6 0.832060
\(425\) 0 0
\(426\) 524079. 0.139918
\(427\) 420688. 0.111658
\(428\) 3.95910e6 1.04469
\(429\) −93152.2 −0.0244371
\(430\) 0 0
\(431\) 6.71981e6 1.74247 0.871233 0.490871i \(-0.163321\pi\)
0.871233 + 0.490871i \(0.163321\pi\)
\(432\) −209504. −0.0540110
\(433\) 909356. 0.233085 0.116542 0.993186i \(-0.462819\pi\)
0.116542 + 0.993186i \(0.462819\pi\)
\(434\) −112903. −0.0287726
\(435\) 0 0
\(436\) −795094. −0.200310
\(437\) −635851. −0.159276
\(438\) −880313. −0.219256
\(439\) −3.11990e6 −0.772644 −0.386322 0.922364i \(-0.626255\pi\)
−0.386322 + 0.922364i \(0.626255\pi\)
\(440\) 0 0
\(441\) 3.90734e6 0.956719
\(442\) −1.38094e6 −0.336218
\(443\) −3.60692e6 −0.873228 −0.436614 0.899649i \(-0.643822\pi\)
−0.436614 + 0.899649i \(0.643822\pi\)
\(444\) 345941. 0.0832808
\(445\) 0 0
\(446\) 1.11691e6 0.265878
\(447\) 959996. 0.227248
\(448\) −275036. −0.0647432
\(449\) 6.14057e6 1.43745 0.718726 0.695294i \(-0.244726\pi\)
0.718726 + 0.695294i \(0.244726\pi\)
\(450\) 0 0
\(451\) 1.26611e6 0.293110
\(452\) 969389. 0.223178
\(453\) −751586. −0.172081
\(454\) −4.07976e6 −0.928955
\(455\) 0 0
\(456\) 529845. 0.119326
\(457\) 2.84240e6 0.636642 0.318321 0.947983i \(-0.396881\pi\)
0.318321 + 0.947983i \(0.396881\pi\)
\(458\) −3.60453e6 −0.802944
\(459\) −2.43852e6 −0.540251
\(460\) 0 0
\(461\) −4.87847e6 −1.06913 −0.534566 0.845127i \(-0.679525\pi\)
−0.534566 + 0.845127i \(0.679525\pi\)
\(462\) 17971.2 0.00391718
\(463\) −6.64392e6 −1.44036 −0.720182 0.693786i \(-0.755942\pi\)
−0.720182 + 0.693786i \(0.755942\pi\)
\(464\) 1.03999e6 0.224250
\(465\) 0 0
\(466\) −573508. −0.122342
\(467\) −569835. −0.120908 −0.0604542 0.998171i \(-0.519255\pi\)
−0.0604542 + 0.998171i \(0.519255\pi\)
\(468\) −878856. −0.185482
\(469\) 516122. 0.108348
\(470\) 0 0
\(471\) 1.29728e6 0.269453
\(472\) 1.05206e6 0.217363
\(473\) −271790. −0.0558573
\(474\) −182869. −0.0373848
\(475\) 0 0
\(476\) −327899. −0.0663319
\(477\) −3.83433e6 −0.771603
\(478\) −1.60612e6 −0.321520
\(479\) −3.00681e6 −0.598779 −0.299390 0.954131i \(-0.596783\pi\)
−0.299390 + 0.954131i \(0.596783\pi\)
\(480\) 0 0
\(481\) −1.39784e6 −0.275482
\(482\) −932727. −0.182868
\(483\) 21713.9 0.00423517
\(484\) 2.46192e6 0.477705
\(485\) 0 0
\(486\) 1.90313e6 0.365491
\(487\) 316355. 0.0604438 0.0302219 0.999543i \(-0.490379\pi\)
0.0302219 + 0.999543i \(0.490379\pi\)
\(488\) −7.30504e6 −1.38859
\(489\) −497239. −0.0940357
\(490\) 0 0
\(491\) −1.00469e7 −1.88074 −0.940368 0.340158i \(-0.889519\pi\)
−0.940368 + 0.340158i \(0.889519\pi\)
\(492\) −453247. −0.0844154
\(493\) 1.21050e7 2.24309
\(494\) −761221. −0.140344
\(495\) 0 0
\(496\) 405498. 0.0740091
\(497\) −502822. −0.0913110
\(498\) −134378. −0.0242804
\(499\) 1.04539e7 1.87944 0.939719 0.341949i \(-0.111087\pi\)
0.939719 + 0.341949i \(0.111087\pi\)
\(500\) 0 0
\(501\) 1.13461e6 0.201954
\(502\) −1.85680e6 −0.328856
\(503\) 6.03763e6 1.06401 0.532006 0.846741i \(-0.321438\pi\)
0.532006 + 0.846741i \(0.321438\pi\)
\(504\) 476864. 0.0836215
\(505\) 0 0
\(506\) 374496. 0.0650236
\(507\) 971885. 0.167917
\(508\) −3.14899e6 −0.541393
\(509\) −136721. −0.0233905 −0.0116953 0.999932i \(-0.503723\pi\)
−0.0116953 + 0.999932i \(0.503723\pi\)
\(510\) 0 0
\(511\) 844606. 0.143088
\(512\) 1.69106e6 0.285091
\(513\) −1.34419e6 −0.225511
\(514\) 3.32519e6 0.555148
\(515\) 0 0
\(516\) 97296.0 0.0160868
\(517\) 1.49399e6 0.245822
\(518\) 269675. 0.0441588
\(519\) 964274. 0.157138
\(520\) 0 0
\(521\) 9.40395e6 1.51781 0.758903 0.651204i \(-0.225736\pi\)
0.758903 + 0.651204i \(0.225736\pi\)
\(522\) −6.25931e6 −1.00543
\(523\) 21599.2 0.00345290 0.00172645 0.999999i \(-0.499450\pi\)
0.00172645 + 0.999999i \(0.499450\pi\)
\(524\) −2.74434e6 −0.436627
\(525\) 0 0
\(526\) −2.05736e6 −0.324225
\(527\) 4.71981e6 0.740283
\(528\) −64545.0 −0.0100758
\(529\) −5.98385e6 −0.929698
\(530\) 0 0
\(531\) −1.30967e6 −0.201569
\(532\) −180748. −0.0276882
\(533\) 1.83142e6 0.279235
\(534\) 135279. 0.0205294
\(535\) 0 0
\(536\) −8.96220e6 −1.34742
\(537\) 2.15426e6 0.322376
\(538\) −3.96508e6 −0.590604
\(539\) 2.45327e6 0.363725
\(540\) 0 0
\(541\) −7.40079e6 −1.08714 −0.543570 0.839364i \(-0.682928\pi\)
−0.543570 + 0.839364i \(0.682928\pi\)
\(542\) 7.41741e6 1.08456
\(543\) −1.65319e6 −0.240615
\(544\) 9.36313e6 1.35651
\(545\) 0 0
\(546\) 25995.2 0.00373175
\(547\) −4.12820e6 −0.589919 −0.294960 0.955510i \(-0.595306\pi\)
−0.294960 + 0.955510i \(0.595306\pi\)
\(548\) 1.28642e6 0.182991
\(549\) 9.09376e6 1.28769
\(550\) 0 0
\(551\) 6.67265e6 0.936309
\(552\) −377052. −0.0526688
\(553\) 175452. 0.0243975
\(554\) 8.72836e6 1.20825
\(555\) 0 0
\(556\) −593709. −0.0814492
\(557\) 4.99309e6 0.681916 0.340958 0.940078i \(-0.389249\pi\)
0.340958 + 0.940078i \(0.389249\pi\)
\(558\) −2.44055e6 −0.331819
\(559\) −393142. −0.0532132
\(560\) 0 0
\(561\) −751274. −0.100784
\(562\) 2.32445e6 0.310441
\(563\) −6.88378e6 −0.915285 −0.457642 0.889136i \(-0.651306\pi\)
−0.457642 + 0.889136i \(0.651306\pi\)
\(564\) −534823. −0.0707965
\(565\) 0 0
\(566\) −8.00014e6 −1.04968
\(567\) −570249. −0.0744916
\(568\) 8.73125e6 1.13555
\(569\) −9.36390e6 −1.21248 −0.606242 0.795280i \(-0.707324\pi\)
−0.606242 + 0.795280i \(0.707324\pi\)
\(570\) 0 0
\(571\) 1.30552e7 1.67569 0.837846 0.545907i \(-0.183815\pi\)
0.837846 + 0.545907i \(0.183815\pi\)
\(572\) −551799. −0.0705165
\(573\) 1.38842e6 0.176659
\(574\) −353324. −0.0447603
\(575\) 0 0
\(576\) −5.94527e6 −0.746648
\(577\) −1.07959e7 −1.34996 −0.674978 0.737838i \(-0.735847\pi\)
−0.674978 + 0.737838i \(0.735847\pi\)
\(578\) −5.75969e6 −0.717100
\(579\) −2.04436e6 −0.253432
\(580\) 0 0
\(581\) 128928. 0.0158455
\(582\) −1.56103e6 −0.191031
\(583\) −2.40743e6 −0.293347
\(584\) −1.46662e7 −1.77944
\(585\) 0 0
\(586\) 6.62615e6 0.797108
\(587\) 5.25307e6 0.629242 0.314621 0.949217i \(-0.398123\pi\)
0.314621 + 0.949217i \(0.398123\pi\)
\(588\) −878227. −0.104752
\(589\) 2.60171e6 0.309009
\(590\) 0 0
\(591\) 2.10697e6 0.248135
\(592\) −968559. −0.113585
\(593\) −2.99811e6 −0.350116 −0.175058 0.984558i \(-0.556011\pi\)
−0.175058 + 0.984558i \(0.556011\pi\)
\(594\) 791686. 0.0920634
\(595\) 0 0
\(596\) 5.68666e6 0.655755
\(597\) −2.48162e6 −0.284970
\(598\) 541705. 0.0619455
\(599\) −1.24700e7 −1.42004 −0.710019 0.704183i \(-0.751314\pi\)
−0.710019 + 0.704183i \(0.751314\pi\)
\(600\) 0 0
\(601\) −5.04108e6 −0.569295 −0.284647 0.958632i \(-0.591877\pi\)
−0.284647 + 0.958632i \(0.591877\pi\)
\(602\) 75846.2 0.00852987
\(603\) 1.11567e7 1.24952
\(604\) −4.45212e6 −0.496563
\(605\) 0 0
\(606\) −1.21168e6 −0.134031
\(607\) 6.79133e6 0.748140 0.374070 0.927400i \(-0.377962\pi\)
0.374070 + 0.927400i \(0.377962\pi\)
\(608\) 5.16126e6 0.566235
\(609\) −227867. −0.0248965
\(610\) 0 0
\(611\) 2.16105e6 0.234186
\(612\) −7.08798e6 −0.764969
\(613\) −483060. −0.0519218 −0.0259609 0.999663i \(-0.508265\pi\)
−0.0259609 + 0.999663i \(0.508265\pi\)
\(614\) 1.84056e6 0.197028
\(615\) 0 0
\(616\) 299404. 0.0317911
\(617\) −5.47210e6 −0.578683 −0.289342 0.957226i \(-0.593436\pi\)
−0.289342 + 0.957226i \(0.593436\pi\)
\(618\) −2.07865e6 −0.218932
\(619\) −9.25381e6 −0.970720 −0.485360 0.874314i \(-0.661311\pi\)
−0.485360 + 0.874314i \(0.661311\pi\)
\(620\) 0 0
\(621\) 956563. 0.0995370
\(622\) −7.94016e6 −0.822911
\(623\) −129792. −0.0133976
\(624\) −93363.9 −0.00959881
\(625\) 0 0
\(626\) −5.10539e6 −0.520707
\(627\) −414126. −0.0420692
\(628\) 7.68463e6 0.777542
\(629\) −1.12736e7 −1.13615
\(630\) 0 0
\(631\) 1.73727e6 0.173698 0.0868490 0.996221i \(-0.472320\pi\)
0.0868490 + 0.996221i \(0.472320\pi\)
\(632\) −3.04664e6 −0.303409
\(633\) −1.74671e6 −0.173265
\(634\) 7.58937e6 0.749865
\(635\) 0 0
\(636\) 861818. 0.0844836
\(637\) 3.54863e6 0.346507
\(638\) −3.92998e6 −0.382242
\(639\) −1.08692e7 −1.05304
\(640\) 0 0
\(641\) 1.39085e7 1.33701 0.668506 0.743707i \(-0.266934\pi\)
0.668506 + 0.743707i \(0.266934\pi\)
\(642\) −2.53137e6 −0.242392
\(643\) −9.27278e6 −0.884468 −0.442234 0.896900i \(-0.645814\pi\)
−0.442234 + 0.896900i \(0.645814\pi\)
\(644\) 128625. 0.0122211
\(645\) 0 0
\(646\) −6.13925e6 −0.578808
\(647\) 8.98311e6 0.843657 0.421828 0.906676i \(-0.361388\pi\)
0.421828 + 0.906676i \(0.361388\pi\)
\(648\) 9.90210e6 0.926381
\(649\) −822289. −0.0766325
\(650\) 0 0
\(651\) −88846.9 −0.00821655
\(652\) −2.94546e6 −0.271352
\(653\) −2.57150e6 −0.235995 −0.117998 0.993014i \(-0.537647\pi\)
−0.117998 + 0.993014i \(0.537647\pi\)
\(654\) 508367. 0.0464765
\(655\) 0 0
\(656\) 1.26899e6 0.115133
\(657\) 1.82573e7 1.65015
\(658\) −416916. −0.0375391
\(659\) −1.46805e7 −1.31683 −0.658413 0.752657i \(-0.728772\pi\)
−0.658413 + 0.752657i \(0.728772\pi\)
\(660\) 0 0
\(661\) −1.36060e7 −1.21123 −0.605617 0.795756i \(-0.707074\pi\)
−0.605617 + 0.795756i \(0.707074\pi\)
\(662\) 2.87425e6 0.254906
\(663\) −1.08671e6 −0.0960131
\(664\) −2.23876e6 −0.197055
\(665\) 0 0
\(666\) 5.82940e6 0.509259
\(667\) −4.74843e6 −0.413272
\(668\) 6.72102e6 0.582766
\(669\) 878937. 0.0759263
\(670\) 0 0
\(671\) 5.70962e6 0.489554
\(672\) −176254. −0.0150562
\(673\) −7.41285e6 −0.630882 −0.315441 0.948945i \(-0.602152\pi\)
−0.315441 + 0.948945i \(0.602152\pi\)
\(674\) 1.06388e6 0.0902073
\(675\) 0 0
\(676\) 5.75708e6 0.484547
\(677\) −1.02447e7 −0.859066 −0.429533 0.903051i \(-0.641322\pi\)
−0.429533 + 0.903051i \(0.641322\pi\)
\(678\) −619809. −0.0517825
\(679\) 1.49771e6 0.124668
\(680\) 0 0
\(681\) −3.21050e6 −0.265280
\(682\) −1.53232e6 −0.126151
\(683\) −1.68904e7 −1.38544 −0.692722 0.721204i \(-0.743589\pi\)
−0.692722 + 0.721204i \(0.743589\pi\)
\(684\) −3.90712e6 −0.319313
\(685\) 0 0
\(686\) −1.37404e6 −0.111478
\(687\) −2.83653e6 −0.229295
\(688\) −272407. −0.0219405
\(689\) −3.48233e6 −0.279461
\(690\) 0 0
\(691\) 1.55786e7 1.24117 0.620587 0.784138i \(-0.286894\pi\)
0.620587 + 0.784138i \(0.286894\pi\)
\(692\) 5.71200e6 0.453443
\(693\) −372716. −0.0294812
\(694\) −2.89865e6 −0.228453
\(695\) 0 0
\(696\) 3.95680e6 0.309614
\(697\) 1.47704e7 1.15163
\(698\) 8.54832e6 0.664114
\(699\) −451313. −0.0349369
\(700\) 0 0
\(701\) −9.98268e6 −0.767277 −0.383638 0.923483i \(-0.625329\pi\)
−0.383638 + 0.923483i \(0.625329\pi\)
\(702\) 1.14517e6 0.0877054
\(703\) −6.21435e6 −0.474250
\(704\) −3.73281e6 −0.283860
\(705\) 0 0
\(706\) −1.56433e7 −1.18118
\(707\) 1.16253e6 0.0874693
\(708\) 294365. 0.0220701
\(709\) 7.97811e6 0.596052 0.298026 0.954558i \(-0.403672\pi\)
0.298026 + 0.954558i \(0.403672\pi\)
\(710\) 0 0
\(711\) 3.79264e6 0.281363
\(712\) 2.25377e6 0.166613
\(713\) −1.85145e6 −0.136392
\(714\) 209652. 0.0153905
\(715\) 0 0
\(716\) 1.27611e7 0.930260
\(717\) −1.26391e6 −0.0918160
\(718\) −8.27871e6 −0.599310
\(719\) −1.13203e7 −0.816647 −0.408323 0.912837i \(-0.633886\pi\)
−0.408323 + 0.912837i \(0.633886\pi\)
\(720\) 0 0
\(721\) 1.99434e6 0.142876
\(722\) 5.99395e6 0.427928
\(723\) −733994. −0.0522212
\(724\) −9.79289e6 −0.694328
\(725\) 0 0
\(726\) −1.57410e6 −0.110839
\(727\) −7.31325e6 −0.513186 −0.256593 0.966520i \(-0.582600\pi\)
−0.256593 + 0.966520i \(0.582600\pi\)
\(728\) 433085. 0.0302862
\(729\) −1.12968e7 −0.787294
\(730\) 0 0
\(731\) −3.17069e6 −0.219463
\(732\) −2.04394e6 −0.140991
\(733\) −3.97186e6 −0.273045 −0.136522 0.990637i \(-0.543593\pi\)
−0.136522 + 0.990637i \(0.543593\pi\)
\(734\) −3.67400e6 −0.251709
\(735\) 0 0
\(736\) −3.67289e6 −0.249927
\(737\) 7.00485e6 0.475040
\(738\) −7.63759e6 −0.516197
\(739\) −2.00272e7 −1.34899 −0.674495 0.738279i \(-0.735639\pi\)
−0.674495 + 0.738279i \(0.735639\pi\)
\(740\) 0 0
\(741\) −599030. −0.0400777
\(742\) 671822. 0.0447965
\(743\) −1.61504e7 −1.07327 −0.536637 0.843813i \(-0.680306\pi\)
−0.536637 + 0.843813i \(0.680306\pi\)
\(744\) 1.54278e6 0.102181
\(745\) 0 0
\(746\) −3.80587e6 −0.250384
\(747\) 2.78695e6 0.182737
\(748\) −4.45027e6 −0.290825
\(749\) 2.42870e6 0.158186
\(750\) 0 0
\(751\) 2.43119e7 1.57297 0.786484 0.617611i \(-0.211899\pi\)
0.786484 + 0.617611i \(0.211899\pi\)
\(752\) 1.49738e6 0.0965581
\(753\) −1.46118e6 −0.0939107
\(754\) −5.68468e6 −0.364148
\(755\) 0 0
\(756\) 271914. 0.0173033
\(757\) −5.71154e6 −0.362254 −0.181127 0.983460i \(-0.557975\pi\)
−0.181127 + 0.983460i \(0.557975\pi\)
\(758\) −1.07223e7 −0.677822
\(759\) 294703. 0.0185687
\(760\) 0 0
\(761\) −9.33266e6 −0.584176 −0.292088 0.956391i \(-0.594350\pi\)
−0.292088 + 0.956391i \(0.594350\pi\)
\(762\) 2.01340e6 0.125616
\(763\) −487747. −0.0303308
\(764\) 8.22451e6 0.509773
\(765\) 0 0
\(766\) −1.66460e7 −1.02503
\(767\) −1.18943e6 −0.0730049
\(768\) 3.30864e6 0.202417
\(769\) −1.06417e7 −0.648928 −0.324464 0.945898i \(-0.605184\pi\)
−0.324464 + 0.945898i \(0.605184\pi\)
\(770\) 0 0
\(771\) 2.61670e6 0.158533
\(772\) −1.21100e7 −0.731311
\(773\) 6.61915e6 0.398431 0.199216 0.979956i \(-0.436161\pi\)
0.199216 + 0.979956i \(0.436161\pi\)
\(774\) 1.63952e6 0.0983703
\(775\) 0 0
\(776\) −2.60070e7 −1.55037
\(777\) 212217. 0.0126103
\(778\) −6.67450e6 −0.395339
\(779\) 8.14194e6 0.480711
\(780\) 0 0
\(781\) −6.82434e6 −0.400344
\(782\) 4.36886e6 0.255477
\(783\) −1.00382e7 −0.585130
\(784\) 2.45884e6 0.142870
\(785\) 0 0
\(786\) 1.75468e6 0.101307
\(787\) −1.82917e7 −1.05273 −0.526367 0.850258i \(-0.676446\pi\)
−0.526367 + 0.850258i \(0.676446\pi\)
\(788\) 1.24809e7 0.716027
\(789\) −1.61901e6 −0.0925884
\(790\) 0 0
\(791\) 594669. 0.0337935
\(792\) 6.47203e6 0.366630
\(793\) 8.25891e6 0.466380
\(794\) −9.36756e6 −0.527321
\(795\) 0 0
\(796\) −1.47002e7 −0.822319
\(797\) 1.38959e7 0.774889 0.387444 0.921893i \(-0.373358\pi\)
0.387444 + 0.921893i \(0.373358\pi\)
\(798\) 115567. 0.00642430
\(799\) 1.74289e7 0.965833
\(800\) 0 0
\(801\) −2.80563e6 −0.154507
\(802\) 6.24854e6 0.343038
\(803\) 1.14631e7 0.627353
\(804\) −2.50761e6 −0.136811
\(805\) 0 0
\(806\) −2.21649e6 −0.120179
\(807\) −3.12025e6 −0.168658
\(808\) −2.01867e7 −1.08777
\(809\) −2.37890e7 −1.27792 −0.638961 0.769239i \(-0.720636\pi\)
−0.638961 + 0.769239i \(0.720636\pi\)
\(810\) 0 0
\(811\) −6.19292e6 −0.330631 −0.165315 0.986241i \(-0.552864\pi\)
−0.165315 + 0.986241i \(0.552864\pi\)
\(812\) −1.34980e6 −0.0718421
\(813\) 5.83701e6 0.309716
\(814\) 3.66006e6 0.193609
\(815\) 0 0
\(816\) −752981. −0.0395875
\(817\) −1.74779e6 −0.0916080
\(818\) 6.39177e6 0.333993
\(819\) −539131. −0.0280857
\(820\) 0 0
\(821\) −1.66592e7 −0.862575 −0.431288 0.902215i \(-0.641941\pi\)
−0.431288 + 0.902215i \(0.641941\pi\)
\(822\) −822509. −0.0424581
\(823\) 2.43775e6 0.125455 0.0627277 0.998031i \(-0.480020\pi\)
0.0627277 + 0.998031i \(0.480020\pi\)
\(824\) −3.46307e7 −1.77682
\(825\) 0 0
\(826\) 229470. 0.0117024
\(827\) 1.14098e7 0.580116 0.290058 0.957009i \(-0.406325\pi\)
0.290058 + 0.957009i \(0.406325\pi\)
\(828\) 2.78041e6 0.140940
\(829\) −1.29460e7 −0.654259 −0.327129 0.944980i \(-0.606081\pi\)
−0.327129 + 0.944980i \(0.606081\pi\)
\(830\) 0 0
\(831\) 6.86864e6 0.345039
\(832\) −5.39947e6 −0.270423
\(833\) 2.86197e7 1.42907
\(834\) 379606. 0.0188981
\(835\) 0 0
\(836\) −2.45313e6 −0.121396
\(837\) −3.91397e6 −0.193109
\(838\) −2.09556e7 −1.03083
\(839\) 1.34123e7 0.657804 0.328902 0.944364i \(-0.393321\pi\)
0.328902 + 0.944364i \(0.393321\pi\)
\(840\) 0 0
\(841\) 2.93191e7 1.42942
\(842\) −2.14373e7 −1.04205
\(843\) 1.82919e6 0.0886522
\(844\) −1.03469e7 −0.499980
\(845\) 0 0
\(846\) −9.01221e6 −0.432918
\(847\) 1.51025e6 0.0723338
\(848\) −2.41290e6 −0.115226
\(849\) −6.29558e6 −0.299755
\(850\) 0 0
\(851\) 4.42230e6 0.209327
\(852\) 2.44299e6 0.115298
\(853\) −3.55781e7 −1.67421 −0.837105 0.547042i \(-0.815754\pi\)
−0.837105 + 0.547042i \(0.815754\pi\)
\(854\) −1.59334e6 −0.0747589
\(855\) 0 0
\(856\) −4.21731e7 −1.96721
\(857\) 1.51251e7 0.703469 0.351735 0.936100i \(-0.385592\pi\)
0.351735 + 0.936100i \(0.385592\pi\)
\(858\) 352810. 0.0163615
\(859\) 5.71909e6 0.264450 0.132225 0.991220i \(-0.457788\pi\)
0.132225 + 0.991220i \(0.457788\pi\)
\(860\) 0 0
\(861\) −278042. −0.0127821
\(862\) −2.54510e7 −1.16664
\(863\) −3.51869e7 −1.60825 −0.804125 0.594460i \(-0.797366\pi\)
−0.804125 + 0.594460i \(0.797366\pi\)
\(864\) −7.76450e6 −0.353858
\(865\) 0 0
\(866\) −3.44414e6 −0.156058
\(867\) −4.53250e6 −0.204781
\(868\) −526296. −0.0237099
\(869\) 2.38125e6 0.106968
\(870\) 0 0
\(871\) 1.01325e7 0.452553
\(872\) 8.46949e6 0.377195
\(873\) 3.23751e7 1.43773
\(874\) 2.40825e6 0.106641
\(875\) 0 0
\(876\) −4.10358e6 −0.180677
\(877\) −2.79568e7 −1.22740 −0.613702 0.789537i \(-0.710320\pi\)
−0.613702 + 0.789537i \(0.710320\pi\)
\(878\) 1.18165e7 0.517310
\(879\) 5.21434e6 0.227629
\(880\) 0 0
\(881\) 3.91377e7 1.69885 0.849425 0.527709i \(-0.176949\pi\)
0.849425 + 0.527709i \(0.176949\pi\)
\(882\) −1.47989e7 −0.640555
\(883\) −4.10119e7 −1.77014 −0.885071 0.465456i \(-0.845890\pi\)
−0.885071 + 0.465456i \(0.845890\pi\)
\(884\) −6.43728e6 −0.277058
\(885\) 0 0
\(886\) 1.36610e7 0.584655
\(887\) 4.27594e7 1.82483 0.912415 0.409267i \(-0.134215\pi\)
0.912415 + 0.409267i \(0.134215\pi\)
\(888\) −3.68503e6 −0.156823
\(889\) −1.93174e6 −0.0819774
\(890\) 0 0
\(891\) −7.73947e6 −0.326601
\(892\) 5.20650e6 0.219095
\(893\) 9.60734e6 0.403157
\(894\) −3.63594e6 −0.152150
\(895\) 0 0
\(896\) −850675. −0.0353992
\(897\) 426286. 0.0176897
\(898\) −2.32571e7 −0.962421
\(899\) 1.94292e7 0.801779
\(900\) 0 0
\(901\) −2.80850e7 −1.15256
\(902\) −4.79534e6 −0.196247
\(903\) 59685.9 0.00243586
\(904\) −1.03261e7 −0.420258
\(905\) 0 0
\(906\) 2.84660e6 0.115214
\(907\) 3.87469e7 1.56394 0.781968 0.623319i \(-0.214216\pi\)
0.781968 + 0.623319i \(0.214216\pi\)
\(908\) −1.90178e7 −0.765501
\(909\) 2.51297e7 1.00874
\(910\) 0 0
\(911\) −2.26167e7 −0.902885 −0.451443 0.892300i \(-0.649090\pi\)
−0.451443 + 0.892300i \(0.649090\pi\)
\(912\) −415067. −0.0165246
\(913\) 1.74982e6 0.0694729
\(914\) −1.07655e7 −0.426253
\(915\) 0 0
\(916\) −1.68025e7 −0.661662
\(917\) −1.68351e6 −0.0661138
\(918\) 9.23579e6 0.361716
\(919\) −3.75628e7 −1.46713 −0.733566 0.679618i \(-0.762146\pi\)
−0.733566 + 0.679618i \(0.762146\pi\)
\(920\) 0 0
\(921\) 1.44840e6 0.0562650
\(922\) 1.84770e7 0.715820
\(923\) −9.87135e6 −0.381392
\(924\) 83772.9 0.00322793
\(925\) 0 0
\(926\) 2.51635e7 0.964371
\(927\) 4.31104e7 1.64772
\(928\) 3.85434e7 1.46920
\(929\) −2.92453e7 −1.11177 −0.555887 0.831258i \(-0.687621\pi\)
−0.555887 + 0.831258i \(0.687621\pi\)
\(930\) 0 0
\(931\) 1.57761e7 0.596521
\(932\) −2.67341e6 −0.100815
\(933\) −6.24838e6 −0.234997
\(934\) 2.15822e6 0.0809522
\(935\) 0 0
\(936\) 9.36174e6 0.349275
\(937\) 1.98213e6 0.0737536 0.0368768 0.999320i \(-0.488259\pi\)
0.0368768 + 0.999320i \(0.488259\pi\)
\(938\) −1.95479e6 −0.0725425
\(939\) −4.01760e6 −0.148697
\(940\) 0 0
\(941\) 3.31164e7 1.21918 0.609592 0.792715i \(-0.291333\pi\)
0.609592 + 0.792715i \(0.291333\pi\)
\(942\) −4.91340e6 −0.180408
\(943\) −5.79402e6 −0.212178
\(944\) −824157. −0.0301010
\(945\) 0 0
\(946\) 1.02939e6 0.0373983
\(947\) −6.56401e6 −0.237845 −0.118923 0.992904i \(-0.537944\pi\)
−0.118923 + 0.992904i \(0.537944\pi\)
\(948\) −852445. −0.0308067
\(949\) 1.65812e7 0.597656
\(950\) 0 0
\(951\) 5.97233e6 0.214137
\(952\) 3.49284e6 0.124907
\(953\) −564124. −0.0201207 −0.0100603 0.999949i \(-0.503202\pi\)
−0.0100603 + 0.999949i \(0.503202\pi\)
\(954\) 1.45224e7 0.516614
\(955\) 0 0
\(956\) −7.48693e6 −0.264947
\(957\) −3.09263e6 −0.109156
\(958\) 1.13881e7 0.400903
\(959\) 789147. 0.0277084
\(960\) 0 0
\(961\) −2.10536e7 −0.735390
\(962\) 5.29424e6 0.184445
\(963\) 5.24997e7 1.82428
\(964\) −4.34791e6 −0.150691
\(965\) 0 0
\(966\) −82240.5 −0.00283559
\(967\) −8.57276e6 −0.294818 −0.147409 0.989076i \(-0.547093\pi\)
−0.147409 + 0.989076i \(0.547093\pi\)
\(968\) −2.62248e7 −0.899547
\(969\) −4.83118e6 −0.165289
\(970\) 0 0
\(971\) −2.06221e7 −0.701917 −0.350958 0.936391i \(-0.614144\pi\)
−0.350958 + 0.936391i \(0.614144\pi\)
\(972\) 8.87143e6 0.301181
\(973\) −364209. −0.0123330
\(974\) −1.19818e6 −0.0404691
\(975\) 0 0
\(976\) 5.72259e6 0.192295
\(977\) 4.10422e6 0.137561 0.0687803 0.997632i \(-0.478089\pi\)
0.0687803 + 0.997632i \(0.478089\pi\)
\(978\) 1.88327e6 0.0629600
\(979\) −1.76155e6 −0.0587404
\(980\) 0 0
\(981\) −1.05433e7 −0.349788
\(982\) 3.80521e7 1.25922
\(983\) 2.18189e7 0.720193 0.360096 0.932915i \(-0.382744\pi\)
0.360096 + 0.932915i \(0.382744\pi\)
\(984\) 4.82807e6 0.158959
\(985\) 0 0
\(986\) −4.58470e7 −1.50182
\(987\) −328085. −0.0107200
\(988\) −3.54843e6 −0.115650
\(989\) 1.24377e6 0.0404343
\(990\) 0 0
\(991\) −2.69387e7 −0.871349 −0.435675 0.900104i \(-0.643490\pi\)
−0.435675 + 0.900104i \(0.643490\pi\)
\(992\) 1.50283e7 0.484878
\(993\) 2.26185e6 0.0727930
\(994\) 1.90441e6 0.0611357
\(995\) 0 0
\(996\) −626404. −0.0200081
\(997\) 5.10386e7 1.62615 0.813076 0.582158i \(-0.197791\pi\)
0.813076 + 0.582158i \(0.197791\pi\)
\(998\) −3.95937e7 −1.25835
\(999\) 9.34877e6 0.296374
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.1.14 yes 37
5.4 even 2 1075.6.a.i.1.24 37
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1075.6.a.i.1.24 37 5.4 even 2
1075.6.a.j.1.14 yes 37 1.1 even 1 trivial