Properties

Label 25.5.c.a.7.1
Level $25$
Weight $5$
Character 25.7
Analytic conductor $2.584$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [25,5,Mod(7,25)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(25, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("25.7");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 25.c (of order \(4\), degree \(2\), minimal)

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: no
Analytic conductor: \(2.58424907710\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 5)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 7.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 25.7
Dual form 25.5.c.a.18.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(6.00000 - 6.00000i) q^{3} -14.0000i q^{4} +12.0000 q^{6} +(26.0000 + 26.0000i) q^{7} +(30.0000 - 30.0000i) q^{8} +9.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(6.00000 - 6.00000i) q^{3} -14.0000i q^{4} +12.0000 q^{6} +(26.0000 + 26.0000i) q^{7} +(30.0000 - 30.0000i) q^{8} +9.00000i q^{9} -8.00000 q^{11} +(-84.0000 - 84.0000i) q^{12} +(-139.000 + 139.000i) q^{13} +52.0000i q^{14} -164.000 q^{16} +(1.00000 + 1.00000i) q^{17} +(-9.00000 + 9.00000i) q^{18} +180.000i q^{19} +312.000 q^{21} +(-8.00000 - 8.00000i) q^{22} +(166.000 - 166.000i) q^{23} -360.000i q^{24} -278.000 q^{26} +(540.000 + 540.000i) q^{27} +(364.000 - 364.000i) q^{28} -480.000i q^{29} +572.000 q^{31} +(-644.000 - 644.000i) q^{32} +(-48.0000 + 48.0000i) q^{33} +2.00000i q^{34} +126.000 q^{36} +(251.000 + 251.000i) q^{37} +(-180.000 + 180.000i) q^{38} +1668.00i q^{39} -1688.00 q^{41} +(312.000 + 312.000i) q^{42} +(-1474.00 + 1474.00i) q^{43} +112.000i q^{44} +332.000 q^{46} +(-2474.00 - 2474.00i) q^{47} +(-984.000 + 984.000i) q^{48} -1049.00i q^{49} +12.0000 q^{51} +(1946.00 + 1946.00i) q^{52} +(3331.00 - 3331.00i) q^{53} +1080.00i q^{54} +1560.00 q^{56} +(1080.00 + 1080.00i) q^{57} +(480.000 - 480.000i) q^{58} -3660.00i q^{59} +1592.00 q^{61} +(572.000 + 572.000i) q^{62} +(-234.000 + 234.000i) q^{63} +1336.00i q^{64} -96.0000 q^{66} +(-874.000 - 874.000i) q^{67} +(14.0000 - 14.0000i) q^{68} -1992.00i q^{69} -6068.00 q^{71} +(270.000 + 270.000i) q^{72} +(791.000 - 791.000i) q^{73} +502.000i q^{74} +2520.00 q^{76} +(-208.000 - 208.000i) q^{77} +(-1668.00 + 1668.00i) q^{78} +9120.00i q^{79} +5751.00 q^{81} +(-1688.00 - 1688.00i) q^{82} +(-5654.00 + 5654.00i) q^{83} -4368.00i q^{84} -2948.00 q^{86} +(-2880.00 - 2880.00i) q^{87} +(-240.000 + 240.000i) q^{88} +2160.00i q^{89} -7228.00 q^{91} +(-2324.00 - 2324.00i) q^{92} +(3432.00 - 3432.00i) q^{93} -4948.00i q^{94} -7728.00 q^{96} +(6551.00 + 6551.00i) q^{97} +(1049.00 - 1049.00i) q^{98} -72.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} + 12 q^{3} + 24 q^{6} + 52 q^{7} + 60 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} + 12 q^{3} + 24 q^{6} + 52 q^{7} + 60 q^{8} - 16 q^{11} - 168 q^{12} - 278 q^{13} - 328 q^{16} + 2 q^{17} - 18 q^{18} + 624 q^{21} - 16 q^{22} + 332 q^{23} - 556 q^{26} + 1080 q^{27} + 728 q^{28} + 1144 q^{31} - 1288 q^{32} - 96 q^{33} + 252 q^{36} + 502 q^{37} - 360 q^{38} - 3376 q^{41} + 624 q^{42} - 2948 q^{43} + 664 q^{46} - 4948 q^{47} - 1968 q^{48} + 24 q^{51} + 3892 q^{52} + 6662 q^{53} + 3120 q^{56} + 2160 q^{57} + 960 q^{58} + 3184 q^{61} + 1144 q^{62} - 468 q^{63} - 192 q^{66} - 1748 q^{67} + 28 q^{68} - 12136 q^{71} + 540 q^{72} + 1582 q^{73} + 5040 q^{76} - 416 q^{77} - 3336 q^{78} + 11502 q^{81} - 3376 q^{82} - 11308 q^{83} - 5896 q^{86} - 5760 q^{87} - 480 q^{88} - 14456 q^{91} - 4648 q^{92} + 6864 q^{93} - 15456 q^{96} + 13102 q^{97} + 2098 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.250000 + 0.250000i 0.820971 0.570971i \(-0.193433\pi\)
−0.570971 + 0.820971i \(0.693433\pi\)
\(3\) 6.00000 6.00000i 0.666667 0.666667i −0.290276 0.956943i \(-0.593747\pi\)
0.956943 + 0.290276i \(0.0937472\pi\)
\(4\) 14.0000i 0.875000i
\(5\) 0 0
\(6\) 12.0000 0.333333
\(7\) 26.0000 + 26.0000i 0.530612 + 0.530612i 0.920755 0.390142i \(-0.127574\pi\)
−0.390142 + 0.920755i \(0.627574\pi\)
\(8\) 30.0000 30.0000i 0.468750 0.468750i
\(9\) 9.00000i 0.111111i
\(10\) 0 0
\(11\) −8.00000 −0.0661157 −0.0330579 0.999453i \(-0.510525\pi\)
−0.0330579 + 0.999453i \(0.510525\pi\)
\(12\) −84.0000 84.0000i −0.583333 0.583333i
\(13\) −139.000 + 139.000i −0.822485 + 0.822485i −0.986464 0.163979i \(-0.947567\pi\)
0.163979 + 0.986464i \(0.447567\pi\)
\(14\) 52.0000i 0.265306i
\(15\) 0 0
\(16\) −164.000 −0.640625
\(17\) 1.00000 + 1.00000i 0.00346021 + 0.00346021i 0.708835 0.705375i \(-0.249221\pi\)
−0.705375 + 0.708835i \(0.749221\pi\)
\(18\) −9.00000 + 9.00000i −0.0277778 + 0.0277778i
\(19\) 180.000i 0.498615i 0.968424 + 0.249307i \(0.0802030\pi\)
−0.968424 + 0.249307i \(0.919797\pi\)
\(20\) 0 0
\(21\) 312.000 0.707483
\(22\) −8.00000 8.00000i −0.0165289 0.0165289i
\(23\) 166.000 166.000i 0.313800 0.313800i −0.532580 0.846380i \(-0.678777\pi\)
0.846380 + 0.532580i \(0.178777\pi\)
\(24\) 360.000i 0.625000i
\(25\) 0 0
\(26\) −278.000 −0.411243
\(27\) 540.000 + 540.000i 0.740741 + 0.740741i
\(28\) 364.000 364.000i 0.464286 0.464286i
\(29\) 480.000i 0.570749i −0.958416 0.285375i \(-0.907882\pi\)
0.958416 0.285375i \(-0.0921180\pi\)
\(30\) 0 0
\(31\) 572.000 0.595213 0.297607 0.954689i \(-0.403812\pi\)
0.297607 + 0.954689i \(0.403812\pi\)
\(32\) −644.000 644.000i −0.628906 0.628906i
\(33\) −48.0000 + 48.0000i −0.0440771 + 0.0440771i
\(34\) 2.00000i 0.00173010i
\(35\) 0 0
\(36\) 126.000 0.0972222
\(37\) 251.000 + 251.000i 0.183346 + 0.183346i 0.792812 0.609466i \(-0.208616\pi\)
−0.609466 + 0.792812i \(0.708616\pi\)
\(38\) −180.000 + 180.000i −0.124654 + 0.124654i
\(39\) 1668.00i 1.09665i
\(40\) 0 0
\(41\) −1688.00 −1.00416 −0.502082 0.864820i \(-0.667432\pi\)
−0.502082 + 0.864820i \(0.667432\pi\)
\(42\) 312.000 + 312.000i 0.176871 + 0.176871i
\(43\) −1474.00 + 1474.00i −0.797188 + 0.797188i −0.982651 0.185463i \(-0.940621\pi\)
0.185463 + 0.982651i \(0.440621\pi\)
\(44\) 112.000i 0.0578512i
\(45\) 0 0
\(46\) 332.000 0.156900
\(47\) −2474.00 2474.00i −1.11996 1.11996i −0.991746 0.128218i \(-0.959074\pi\)
−0.128218 0.991746i \(-0.540926\pi\)
\(48\) −984.000 + 984.000i −0.427083 + 0.427083i
\(49\) 1049.00i 0.436901i
\(50\) 0 0
\(51\) 12.0000 0.00461361
\(52\) 1946.00 + 1946.00i 0.719675 + 0.719675i
\(53\) 3331.00 3331.00i 1.18583 1.18583i 0.207622 0.978209i \(-0.433428\pi\)
0.978209 0.207622i \(-0.0665724\pi\)
\(54\) 1080.00i 0.370370i
\(55\) 0 0
\(56\) 1560.00 0.497449
\(57\) 1080.00 + 1080.00i 0.332410 + 0.332410i
\(58\) 480.000 480.000i 0.142687 0.142687i
\(59\) 3660.00i 1.05142i −0.850663 0.525711i \(-0.823799\pi\)
0.850663 0.525711i \(-0.176201\pi\)
\(60\) 0 0
\(61\) 1592.00 0.427842 0.213921 0.976851i \(-0.431376\pi\)
0.213921 + 0.976851i \(0.431376\pi\)
\(62\) 572.000 + 572.000i 0.148803 + 0.148803i
\(63\) −234.000 + 234.000i −0.0589569 + 0.0589569i
\(64\) 1336.00i 0.326172i
\(65\) 0 0
\(66\) −96.0000 −0.0220386
\(67\) −874.000 874.000i −0.194698 0.194698i 0.603025 0.797723i \(-0.293962\pi\)
−0.797723 + 0.603025i \(0.793962\pi\)
\(68\) 14.0000 14.0000i 0.00302768 0.00302768i
\(69\) 1992.00i 0.418399i
\(70\) 0 0
\(71\) −6068.00 −1.20373 −0.601865 0.798598i \(-0.705575\pi\)
−0.601865 + 0.798598i \(0.705575\pi\)
\(72\) 270.000 + 270.000i 0.0520833 + 0.0520833i
\(73\) 791.000 791.000i 0.148433 0.148433i −0.628985 0.777418i \(-0.716529\pi\)
0.777418 + 0.628985i \(0.216529\pi\)
\(74\) 502.000i 0.0916728i
\(75\) 0 0
\(76\) 2520.00 0.436288
\(77\) −208.000 208.000i −0.0350818 0.0350818i
\(78\) −1668.00 + 1668.00i −0.274162 + 0.274162i
\(79\) 9120.00i 1.46130i 0.682750 + 0.730652i \(0.260784\pi\)
−0.682750 + 0.730652i \(0.739216\pi\)
\(80\) 0 0
\(81\) 5751.00 0.876543
\(82\) −1688.00 1688.00i −0.251041 0.251041i
\(83\) −5654.00 + 5654.00i −0.820729 + 0.820729i −0.986213 0.165484i \(-0.947081\pi\)
0.165484 + 0.986213i \(0.447081\pi\)
\(84\) 4368.00i 0.619048i
\(85\) 0 0
\(86\) −2948.00 −0.398594
\(87\) −2880.00 2880.00i −0.380499 0.380499i
\(88\) −240.000 + 240.000i −0.0309917 + 0.0309917i
\(89\) 2160.00i 0.272693i 0.990661 + 0.136346i \(0.0435360\pi\)
−0.990661 + 0.136346i \(0.956464\pi\)
\(90\) 0 0
\(91\) −7228.00 −0.872841
\(92\) −2324.00 2324.00i −0.274575 0.274575i
\(93\) 3432.00 3432.00i 0.396809 0.396809i
\(94\) 4948.00i 0.559982i
\(95\) 0 0
\(96\) −7728.00 −0.838542
\(97\) 6551.00 + 6551.00i 0.696248 + 0.696248i 0.963599 0.267351i \(-0.0861483\pi\)
−0.267351 + 0.963599i \(0.586148\pi\)
\(98\) 1049.00 1049.00i 0.109225 0.109225i
\(99\) 72.0000i 0.00734619i
\(100\) 0 0
\(101\) 16102.0 1.57847 0.789236 0.614090i \(-0.210477\pi\)
0.789236 + 0.614090i \(0.210477\pi\)
\(102\) 12.0000 + 12.0000i 0.00115340 + 0.00115340i
\(103\) −994.000 + 994.000i −0.0936940 + 0.0936940i −0.752400 0.658706i \(-0.771104\pi\)
0.658706 + 0.752400i \(0.271104\pi\)
\(104\) 8340.00i 0.771080i
\(105\) 0 0
\(106\) 6662.00 0.592916
\(107\) 8326.00 + 8326.00i 0.727225 + 0.727225i 0.970066 0.242841i \(-0.0780793\pi\)
−0.242841 + 0.970066i \(0.578079\pi\)
\(108\) 7560.00 7560.00i 0.648148 0.648148i
\(109\) 17010.0i 1.43170i −0.698255 0.715849i \(-0.746040\pi\)
0.698255 0.715849i \(-0.253960\pi\)
\(110\) 0 0
\(111\) 3012.00 0.244461
\(112\) −4264.00 4264.00i −0.339923 0.339923i
\(113\) 5161.00 5161.00i 0.404182 0.404182i −0.475522 0.879704i \(-0.657741\pi\)
0.879704 + 0.475522i \(0.157741\pi\)
\(114\) 2160.00i 0.166205i
\(115\) 0 0
\(116\) −6720.00 −0.499405
\(117\) −1251.00 1251.00i −0.0913872 0.0913872i
\(118\) 3660.00 3660.00i 0.262856 0.262856i
\(119\) 52.0000i 0.00367206i
\(120\) 0 0
\(121\) −14577.0 −0.995629
\(122\) 1592.00 + 1592.00i 0.106960 + 0.106960i
\(123\) −10128.0 + 10128.0i −0.669443 + 0.669443i
\(124\) 8008.00i 0.520812i
\(125\) 0 0
\(126\) −468.000 −0.0294785
\(127\) −12574.0 12574.0i −0.779590 0.779590i 0.200171 0.979761i \(-0.435850\pi\)
−0.979761 + 0.200171i \(0.935850\pi\)
\(128\) −11640.0 + 11640.0i −0.710449 + 0.710449i
\(129\) 17688.0i 1.06292i
\(130\) 0 0
\(131\) 20272.0 1.18128 0.590642 0.806934i \(-0.298875\pi\)
0.590642 + 0.806934i \(0.298875\pi\)
\(132\) 672.000 + 672.000i 0.0385675 + 0.0385675i
\(133\) −4680.00 + 4680.00i −0.264571 + 0.264571i
\(134\) 1748.00i 0.0973491i
\(135\) 0 0
\(136\) 60.0000 0.00324394
\(137\) 10351.0 + 10351.0i 0.551494 + 0.551494i 0.926872 0.375378i \(-0.122487\pi\)
−0.375378 + 0.926872i \(0.622487\pi\)
\(138\) 1992.00 1992.00i 0.104600 0.104600i
\(139\) 27060.0i 1.40055i 0.713874 + 0.700274i \(0.246939\pi\)
−0.713874 + 0.700274i \(0.753061\pi\)
\(140\) 0 0
\(141\) −29688.0 −1.49329
\(142\) −6068.00 6068.00i −0.300932 0.300932i
\(143\) 1112.00 1112.00i 0.0543792 0.0543792i
\(144\) 1476.00i 0.0711806i
\(145\) 0 0
\(146\) 1582.00 0.0742166
\(147\) −6294.00 6294.00i −0.291268 0.291268i
\(148\) 3514.00 3514.00i 0.160427 0.160427i
\(149\) 16350.0i 0.736453i −0.929736 0.368227i \(-0.879965\pi\)
0.929736 0.368227i \(-0.120035\pi\)
\(150\) 0 0
\(151\) 1052.00 0.0461383 0.0230692 0.999734i \(-0.492656\pi\)
0.0230692 + 0.999734i \(0.492656\pi\)
\(152\) 5400.00 + 5400.00i 0.233726 + 0.233726i
\(153\) −9.00000 + 9.00000i −0.000384468 + 0.000384468i
\(154\) 416.000i 0.0175409i
\(155\) 0 0
\(156\) 23352.0 0.959566
\(157\) −6499.00 6499.00i −0.263662 0.263662i 0.562878 0.826540i \(-0.309694\pi\)
−0.826540 + 0.562878i \(0.809694\pi\)
\(158\) −9120.00 + 9120.00i −0.365326 + 0.365326i
\(159\) 39972.0i 1.58111i
\(160\) 0 0
\(161\) 8632.00 0.333012
\(162\) 5751.00 + 5751.00i 0.219136 + 0.219136i
\(163\) 19286.0 19286.0i 0.725884 0.725884i −0.243913 0.969797i \(-0.578431\pi\)
0.969797 + 0.243913i \(0.0784313\pi\)
\(164\) 23632.0i 0.878644i
\(165\) 0 0
\(166\) −11308.0 −0.410364
\(167\) 15526.0 + 15526.0i 0.556707 + 0.556707i 0.928368 0.371661i \(-0.121212\pi\)
−0.371661 + 0.928368i \(0.621212\pi\)
\(168\) 9360.00 9360.00i 0.331633 0.331633i
\(169\) 10081.0i 0.352964i
\(170\) 0 0
\(171\) −1620.00 −0.0554017
\(172\) 20636.0 + 20636.0i 0.697539 + 0.697539i
\(173\) 16891.0 16891.0i 0.564369 0.564369i −0.366176 0.930545i \(-0.619333\pi\)
0.930545 + 0.366176i \(0.119333\pi\)
\(174\) 5760.00i 0.190250i
\(175\) 0 0
\(176\) 1312.00 0.0423554
\(177\) −21960.0 21960.0i −0.700948 0.700948i
\(178\) −2160.00 + 2160.00i −0.0681732 + 0.0681732i
\(179\) 10620.0i 0.331450i 0.986172 + 0.165725i \(0.0529965\pi\)
−0.986172 + 0.165725i \(0.947004\pi\)
\(180\) 0 0
\(181\) 24122.0 0.736302 0.368151 0.929766i \(-0.379991\pi\)
0.368151 + 0.929766i \(0.379991\pi\)
\(182\) −7228.00 7228.00i −0.218210 0.218210i
\(183\) 9552.00 9552.00i 0.285228 0.285228i
\(184\) 9960.00i 0.294187i
\(185\) 0 0
\(186\) 6864.00 0.198404
\(187\) −8.00000 8.00000i −0.000228774 0.000228774i
\(188\) −34636.0 + 34636.0i −0.979968 + 0.979968i
\(189\) 28080.0i 0.786092i
\(190\) 0 0
\(191\) −45188.0 −1.23867 −0.619336 0.785126i \(-0.712598\pi\)
−0.619336 + 0.785126i \(0.712598\pi\)
\(192\) 8016.00 + 8016.00i 0.217448 + 0.217448i
\(193\) −39199.0 + 39199.0i −1.05235 + 1.05235i −0.0537986 + 0.998552i \(0.517133\pi\)
−0.998552 + 0.0537986i \(0.982867\pi\)
\(194\) 13102.0i 0.348124i
\(195\) 0 0
\(196\) −14686.0 −0.382289
\(197\) −28349.0 28349.0i −0.730475 0.730475i 0.240239 0.970714i \(-0.422774\pi\)
−0.970714 + 0.240239i \(0.922774\pi\)
\(198\) 72.0000 72.0000i 0.00183655 0.00183655i
\(199\) 1800.00i 0.0454534i −0.999742 0.0227267i \(-0.992765\pi\)
0.999742 0.0227267i \(-0.00723476\pi\)
\(200\) 0 0
\(201\) −10488.0 −0.259598
\(202\) 16102.0 + 16102.0i 0.394618 + 0.394618i
\(203\) 12480.0 12480.0i 0.302846 0.302846i
\(204\) 168.000i 0.00403691i
\(205\) 0 0
\(206\) −1988.00 −0.0468470
\(207\) 1494.00 + 1494.00i 0.0348666 + 0.0348666i
\(208\) 22796.0 22796.0i 0.526905 0.526905i
\(209\) 1440.00i 0.0329663i
\(210\) 0 0
\(211\) 18392.0 0.413108 0.206554 0.978435i \(-0.433775\pi\)
0.206554 + 0.978435i \(0.433775\pi\)
\(212\) −46634.0 46634.0i −1.03760 1.03760i
\(213\) −36408.0 + 36408.0i −0.802486 + 0.802486i
\(214\) 16652.0i 0.363613i
\(215\) 0 0
\(216\) 32400.0 0.694444
\(217\) 14872.0 + 14872.0i 0.315827 + 0.315827i
\(218\) 17010.0 17010.0i 0.357924 0.357924i
\(219\) 9492.00i 0.197911i
\(220\) 0 0
\(221\) −278.000 −0.00569194
\(222\) 3012.00 + 3012.00i 0.0611152 + 0.0611152i
\(223\) 866.000 866.000i 0.0174144 0.0174144i −0.698346 0.715760i \(-0.746080\pi\)
0.715760 + 0.698346i \(0.246080\pi\)
\(224\) 33488.0i 0.667411i
\(225\) 0 0
\(226\) 10322.0 0.202091
\(227\) 45226.0 + 45226.0i 0.877681 + 0.877681i 0.993294 0.115614i \(-0.0368835\pi\)
−0.115614 + 0.993294i \(0.536883\pi\)
\(228\) 15120.0 15120.0i 0.290859 0.290859i
\(229\) 39120.0i 0.745981i 0.927835 + 0.372991i \(0.121668\pi\)
−0.927835 + 0.372991i \(0.878332\pi\)
\(230\) 0 0
\(231\) −2496.00 −0.0467757
\(232\) −14400.0 14400.0i −0.267539 0.267539i
\(233\) 33121.0 33121.0i 0.610087 0.610087i −0.332882 0.942969i \(-0.608021\pi\)
0.942969 + 0.332882i \(0.108021\pi\)
\(234\) 2502.00i 0.0456936i
\(235\) 0 0
\(236\) −51240.0 −0.919994
\(237\) 54720.0 + 54720.0i 0.974203 + 0.974203i
\(238\) −52.0000 + 52.0000i −0.000918014 + 0.000918014i
\(239\) 88440.0i 1.54829i −0.633007 0.774146i \(-0.718180\pi\)
0.633007 0.774146i \(-0.281820\pi\)
\(240\) 0 0
\(241\) 20312.0 0.349718 0.174859 0.984593i \(-0.444053\pi\)
0.174859 + 0.984593i \(0.444053\pi\)
\(242\) −14577.0 14577.0i −0.248907 0.248907i
\(243\) −9234.00 + 9234.00i −0.156379 + 0.156379i
\(244\) 22288.0i 0.374362i
\(245\) 0 0
\(246\) −20256.0 −0.334721
\(247\) −25020.0 25020.0i −0.410103 0.410103i
\(248\) 17160.0 17160.0i 0.279006 0.279006i
\(249\) 67848.0i 1.09430i
\(250\) 0 0
\(251\) 74752.0 1.18652 0.593260 0.805011i \(-0.297840\pi\)
0.593260 + 0.805011i \(0.297840\pi\)
\(252\) 3276.00 + 3276.00i 0.0515873 + 0.0515873i
\(253\) −1328.00 + 1328.00i −0.0207471 + 0.0207471i
\(254\) 25148.0i 0.389795i
\(255\) 0 0
\(256\) −1904.00 −0.0290527
\(257\) −37799.0 37799.0i −0.572287 0.572287i 0.360480 0.932767i \(-0.382613\pi\)
−0.932767 + 0.360480i \(0.882613\pi\)
\(258\) −17688.0 + 17688.0i −0.265729 + 0.265729i
\(259\) 13052.0i 0.194571i
\(260\) 0 0
\(261\) 4320.00 0.0634166
\(262\) 20272.0 + 20272.0i 0.295321 + 0.295321i
\(263\) 33586.0 33586.0i 0.485564 0.485564i −0.421339 0.906903i \(-0.638440\pi\)
0.906903 + 0.421339i \(0.138440\pi\)
\(264\) 2880.00i 0.0413223i
\(265\) 0 0
\(266\) −9360.00 −0.132286
\(267\) 12960.0 + 12960.0i 0.181795 + 0.181795i
\(268\) −12236.0 + 12236.0i −0.170361 + 0.170361i
\(269\) 28530.0i 0.394273i 0.980376 + 0.197137i \(0.0631642\pi\)
−0.980376 + 0.197137i \(0.936836\pi\)
\(270\) 0 0
\(271\) −7468.00 −0.101687 −0.0508435 0.998707i \(-0.516191\pi\)
−0.0508435 + 0.998707i \(0.516191\pi\)
\(272\) −164.000 164.000i −0.00221670 0.00221670i
\(273\) −43368.0 + 43368.0i −0.581894 + 0.581894i
\(274\) 20702.0i 0.275747i
\(275\) 0 0
\(276\) −27888.0 −0.366100
\(277\) −6499.00 6499.00i −0.0847007 0.0847007i 0.663487 0.748188i \(-0.269076\pi\)
−0.748188 + 0.663487i \(0.769076\pi\)
\(278\) −27060.0 + 27060.0i −0.350137 + 0.350137i
\(279\) 5148.00i 0.0661348i
\(280\) 0 0
\(281\) −97928.0 −1.24021 −0.620104 0.784520i \(-0.712909\pi\)
−0.620104 + 0.784520i \(0.712909\pi\)
\(282\) −29688.0 29688.0i −0.373321 0.373321i
\(283\) −59854.0 + 59854.0i −0.747344 + 0.747344i −0.973980 0.226636i \(-0.927227\pi\)
0.226636 + 0.973980i \(0.427227\pi\)
\(284\) 84952.0i 1.05326i
\(285\) 0 0
\(286\) 2224.00 0.0271896
\(287\) −43888.0 43888.0i −0.532822 0.532822i
\(288\) 5796.00 5796.00i 0.0698785 0.0698785i
\(289\) 83519.0i 0.999976i
\(290\) 0 0
\(291\) 78612.0 0.928331
\(292\) −11074.0 11074.0i −0.129879 0.129879i
\(293\) −28499.0 + 28499.0i −0.331967 + 0.331967i −0.853333 0.521366i \(-0.825423\pi\)
0.521366 + 0.853333i \(0.325423\pi\)
\(294\) 12588.0i 0.145634i
\(295\) 0 0
\(296\) 15060.0 0.171886
\(297\) −4320.00 4320.00i −0.0489746 0.0489746i
\(298\) 16350.0 16350.0i 0.184113 0.184113i
\(299\) 46148.0i 0.516191i
\(300\) 0 0
\(301\) −76648.0 −0.845995
\(302\) 1052.00 + 1052.00i 0.0115346 + 0.0115346i
\(303\) 96612.0 96612.0i 1.05232 1.05232i
\(304\) 29520.0i 0.319425i
\(305\) 0 0
\(306\) −18.0000 −0.000192234
\(307\) 117926. + 117926.i 1.25122 + 1.25122i 0.955175 + 0.296043i \(0.0956671\pi\)
0.296043 + 0.955175i \(0.404333\pi\)
\(308\) −2912.00 + 2912.00i −0.0306966 + 0.0306966i
\(309\) 11928.0i 0.124925i
\(310\) 0 0
\(311\) 3892.00 0.0402395 0.0201197 0.999798i \(-0.493595\pi\)
0.0201197 + 0.999798i \(0.493595\pi\)
\(312\) 50040.0 + 50040.0i 0.514053 + 0.514053i
\(313\) 49961.0 49961.0i 0.509967 0.509967i −0.404549 0.914516i \(-0.632571\pi\)
0.914516 + 0.404549i \(0.132571\pi\)
\(314\) 12998.0i 0.131831i
\(315\) 0 0
\(316\) 127680. 1.27864
\(317\) −17099.0 17099.0i −0.170158 0.170158i 0.616891 0.787049i \(-0.288392\pi\)
−0.787049 + 0.616891i \(0.788392\pi\)
\(318\) 39972.0 39972.0i 0.395277 0.395277i
\(319\) 3840.00i 0.0377355i
\(320\) 0 0
\(321\) 99912.0 0.969633
\(322\) 8632.00 + 8632.00i 0.0832530 + 0.0832530i
\(323\) −180.000 + 180.000i −0.00172531 + 0.00172531i
\(324\) 80514.0i 0.766975i
\(325\) 0 0
\(326\) 38572.0 0.362942
\(327\) −102060. 102060.i −0.954465 0.954465i
\(328\) −50640.0 + 50640.0i −0.470702 + 0.470702i
\(329\) 128648.i 1.18853i
\(330\) 0 0
\(331\) −143128. −1.30638 −0.653189 0.757195i \(-0.726569\pi\)
−0.653189 + 0.757195i \(0.726569\pi\)
\(332\) 79156.0 + 79156.0i 0.718138 + 0.718138i
\(333\) −2259.00 + 2259.00i −0.0203717 + 0.0203717i
\(334\) 31052.0i 0.278353i
\(335\) 0 0
\(336\) −51168.0 −0.453231
\(337\) −103249. 103249.i −0.909130 0.909130i 0.0870719 0.996202i \(-0.472249\pi\)
−0.996202 + 0.0870719i \(0.972249\pi\)
\(338\) 10081.0 10081.0i 0.0882410 0.0882410i
\(339\) 61932.0i 0.538909i
\(340\) 0 0
\(341\) −4576.00 −0.0393529
\(342\) −1620.00 1620.00i −0.0138504 0.0138504i
\(343\) 89700.0 89700.0i 0.762437 0.762437i
\(344\) 88440.0i 0.747363i
\(345\) 0 0
\(346\) 33782.0 0.282185
\(347\) 104626. + 104626.i 0.868922 + 0.868922i 0.992353 0.123431i \(-0.0393899\pi\)
−0.123431 + 0.992353i \(0.539390\pi\)
\(348\) −40320.0 + 40320.0i −0.332937 + 0.332937i
\(349\) 94800.0i 0.778319i 0.921170 + 0.389159i \(0.127234\pi\)
−0.921170 + 0.389159i \(0.872766\pi\)
\(350\) 0 0
\(351\) −150120. −1.21850
\(352\) 5152.00 + 5152.00i 0.0415806 + 0.0415806i
\(353\) −63569.0 + 63569.0i −0.510148 + 0.510148i −0.914572 0.404424i \(-0.867472\pi\)
0.404424 + 0.914572i \(0.367472\pi\)
\(354\) 43920.0i 0.350474i
\(355\) 0 0
\(356\) 30240.0 0.238606
\(357\) 312.000 + 312.000i 0.00244804 + 0.00244804i
\(358\) −10620.0 + 10620.0i −0.0828626 + 0.0828626i
\(359\) 141840.i 1.10055i 0.834983 + 0.550275i \(0.185477\pi\)
−0.834983 + 0.550275i \(0.814523\pi\)
\(360\) 0 0
\(361\) 97921.0 0.751383
\(362\) 24122.0 + 24122.0i 0.184076 + 0.184076i
\(363\) −87462.0 + 87462.0i −0.663752 + 0.663752i
\(364\) 101192.i 0.763736i
\(365\) 0 0
\(366\) 19104.0 0.142614
\(367\) −142174. 142174.i −1.05557 1.05557i −0.998362 0.0572103i \(-0.981779\pi\)
−0.0572103 0.998362i \(-0.518221\pi\)
\(368\) −27224.0 + 27224.0i −0.201028 + 0.201028i
\(369\) 15192.0i 0.111574i
\(370\) 0 0
\(371\) 173212. 1.25843
\(372\) −48048.0 48048.0i −0.347208 0.347208i
\(373\) −10309.0 + 10309.0i −0.0740967 + 0.0740967i −0.743184 0.669087i \(-0.766685\pi\)
0.669087 + 0.743184i \(0.266685\pi\)
\(374\) 16.0000i 0.000114387i
\(375\) 0 0
\(376\) −148440. −1.04997
\(377\) 66720.0 + 66720.0i 0.469433 + 0.469433i
\(378\) −28080.0 + 28080.0i −0.196523 + 0.196523i
\(379\) 115380.i 0.803253i −0.915804 0.401626i \(-0.868445\pi\)
0.915804 0.401626i \(-0.131555\pi\)
\(380\) 0 0
\(381\) −150888. −1.03945
\(382\) −45188.0 45188.0i −0.309668 0.309668i
\(383\) −62654.0 + 62654.0i −0.427121 + 0.427121i −0.887647 0.460525i \(-0.847661\pi\)
0.460525 + 0.887647i \(0.347661\pi\)
\(384\) 139680.i 0.947266i
\(385\) 0 0
\(386\) −78398.0 −0.526175
\(387\) −13266.0 13266.0i −0.0885764 0.0885764i
\(388\) 91714.0 91714.0i 0.609217 0.609217i
\(389\) 132690.i 0.876878i −0.898761 0.438439i \(-0.855532\pi\)
0.898761 0.438439i \(-0.144468\pi\)
\(390\) 0 0
\(391\) 332.000 0.00217162
\(392\) −31470.0 31470.0i −0.204797 0.204797i
\(393\) 121632. 121632.i 0.787522 0.787522i
\(394\) 56698.0i 0.365237i
\(395\) 0 0
\(396\) −1008.00 −0.00642792
\(397\) 88451.0 + 88451.0i 0.561205 + 0.561205i 0.929650 0.368444i \(-0.120110\pi\)
−0.368444 + 0.929650i \(0.620110\pi\)
\(398\) 1800.00 1800.00i 0.0113633 0.0113633i
\(399\) 56160.0i 0.352762i
\(400\) 0 0
\(401\) 63202.0 0.393045 0.196522 0.980499i \(-0.437035\pi\)
0.196522 + 0.980499i \(0.437035\pi\)
\(402\) −10488.0 10488.0i −0.0648994 0.0648994i
\(403\) −79508.0 + 79508.0i −0.489554 + 0.489554i
\(404\) 225428.i 1.38116i
\(405\) 0 0
\(406\) 24960.0 0.151423
\(407\) −2008.00 2008.00i −0.0121220 0.0121220i
\(408\) 360.000 360.000i 0.00216263 0.00216263i
\(409\) 52890.0i 0.316175i 0.987425 + 0.158087i \(0.0505327\pi\)
−0.987425 + 0.158087i \(0.949467\pi\)
\(410\) 0 0
\(411\) 124212. 0.735326
\(412\) 13916.0 + 13916.0i 0.0819823 + 0.0819823i
\(413\) 95160.0 95160.0i 0.557897 0.557897i
\(414\) 2988.00i 0.0174333i
\(415\) 0 0
\(416\) 179032. 1.03453
\(417\) 162360. + 162360.i 0.933699 + 0.933699i
\(418\) 1440.00 1440.00i 0.00824157 0.00824157i
\(419\) 256980.i 1.46376i 0.681431 + 0.731882i \(0.261358\pi\)
−0.681431 + 0.731882i \(0.738642\pi\)
\(420\) 0 0
\(421\) 186632. 1.05298 0.526492 0.850180i \(-0.323507\pi\)
0.526492 + 0.850180i \(0.323507\pi\)
\(422\) 18392.0 + 18392.0i 0.103277 + 0.103277i
\(423\) 22266.0 22266.0i 0.124440 0.124440i
\(424\) 199860.i 1.11172i
\(425\) 0 0
\(426\) −72816.0 −0.401243
\(427\) 41392.0 + 41392.0i 0.227018 + 0.227018i
\(428\) 116564. 116564.i 0.636322 0.636322i
\(429\) 13344.0i 0.0725056i
\(430\) 0 0
\(431\) −208028. −1.11987 −0.559935 0.828537i \(-0.689174\pi\)
−0.559935 + 0.828537i \(0.689174\pi\)
\(432\) −88560.0 88560.0i −0.474537 0.474537i
\(433\) 151271. 151271.i 0.806826 0.806826i −0.177326 0.984152i \(-0.556745\pi\)
0.984152 + 0.177326i \(0.0567447\pi\)
\(434\) 29744.0i 0.157914i
\(435\) 0 0
\(436\) −238140. −1.25274
\(437\) 29880.0 + 29880.0i 0.156465 + 0.156465i
\(438\) 9492.00 9492.00i 0.0494777 0.0494777i
\(439\) 158640.i 0.823159i −0.911374 0.411579i \(-0.864977\pi\)
0.911374 0.411579i \(-0.135023\pi\)
\(440\) 0 0
\(441\) 9441.00 0.0485446
\(442\) −278.000 278.000i −0.00142298 0.00142298i
\(443\) −252974. + 252974.i −1.28905 + 1.28905i −0.353679 + 0.935367i \(0.615070\pi\)
−0.935367 + 0.353679i \(0.884930\pi\)
\(444\) 42168.0i 0.213903i
\(445\) 0 0
\(446\) 1732.00 0.00870719
\(447\) −98100.0 98100.0i −0.490969 0.490969i
\(448\) −34736.0 + 34736.0i −0.173071 + 0.173071i
\(449\) 123750.i 0.613836i 0.951736 + 0.306918i \(0.0992978\pi\)
−0.951736 + 0.306918i \(0.900702\pi\)
\(450\) 0 0
\(451\) 13504.0 0.0663910
\(452\) −72254.0 72254.0i −0.353659 0.353659i
\(453\) 6312.00 6312.00i 0.0307589 0.0307589i
\(454\) 90452.0i 0.438840i
\(455\) 0 0
\(456\) 64800.0 0.311634
\(457\) 32201.0 + 32201.0i 0.154183 + 0.154183i 0.779983 0.625800i \(-0.215227\pi\)
−0.625800 + 0.779983i \(0.715227\pi\)
\(458\) −39120.0 + 39120.0i −0.186495 + 0.186495i
\(459\) 1080.00i 0.00512623i
\(460\) 0 0
\(461\) 75142.0 0.353574 0.176787 0.984249i \(-0.443430\pi\)
0.176787 + 0.984249i \(0.443430\pi\)
\(462\) −2496.00 2496.00i −0.0116939 0.0116939i
\(463\) −235714. + 235714.i −1.09957 + 1.09957i −0.105111 + 0.994461i \(0.533520\pi\)
−0.994461 + 0.105111i \(0.966480\pi\)
\(464\) 78720.0i 0.365636i
\(465\) 0 0
\(466\) 66242.0 0.305043
\(467\) −28574.0 28574.0i −0.131020 0.131020i 0.638556 0.769576i \(-0.279532\pi\)
−0.769576 + 0.638556i \(0.779532\pi\)
\(468\) −17514.0 + 17514.0i −0.0799638 + 0.0799638i
\(469\) 45448.0i 0.206618i
\(470\) 0 0
\(471\) −77988.0 −0.351549
\(472\) −109800. 109800.i −0.492854 0.492854i
\(473\) 11792.0 11792.0i 0.0527066 0.0527066i
\(474\) 109440.i 0.487101i
\(475\) 0 0
\(476\) 728.000 0.00321305
\(477\) 29979.0 + 29979.0i 0.131759 + 0.131759i
\(478\) 88440.0 88440.0i 0.387073 0.387073i
\(479\) 26520.0i 0.115585i 0.998329 + 0.0577926i \(0.0184062\pi\)
−0.998329 + 0.0577926i \(0.981594\pi\)
\(480\) 0 0
\(481\) −69778.0 −0.301598
\(482\) 20312.0 + 20312.0i 0.0874296 + 0.0874296i
\(483\) 51792.0 51792.0i 0.222008 0.222008i
\(484\) 204078.i 0.871175i
\(485\) 0 0
\(486\) −18468.0 −0.0781893
\(487\) −41374.0 41374.0i −0.174449 0.174449i 0.614482 0.788931i \(-0.289365\pi\)
−0.788931 + 0.614482i \(0.789365\pi\)
\(488\) 47760.0 47760.0i 0.200551 0.200551i
\(489\) 231432.i 0.967845i
\(490\) 0 0
\(491\) −149288. −0.619244 −0.309622 0.950860i \(-0.600203\pi\)
−0.309622 + 0.950860i \(0.600203\pi\)
\(492\) 141792. + 141792.i 0.585762 + 0.585762i
\(493\) 480.000 480.000i 0.00197491 0.00197491i
\(494\) 50040.0i 0.205052i
\(495\) 0 0
\(496\) −93808.0 −0.381309
\(497\) −157768. 157768.i −0.638714 0.638714i
\(498\) −67848.0 + 67848.0i −0.273576 + 0.273576i
\(499\) 284100.i 1.14096i 0.821312 + 0.570480i \(0.193243\pi\)
−0.821312 + 0.570480i \(0.806757\pi\)
\(500\) 0 0
\(501\) 186312. 0.742276
\(502\) 74752.0 + 74752.0i 0.296630 + 0.296630i
\(503\) 117406. 117406.i 0.464039 0.464039i −0.435938 0.899977i \(-0.643583\pi\)
0.899977 + 0.435938i \(0.143583\pi\)
\(504\) 14040.0i 0.0552721i
\(505\) 0 0
\(506\) −2656.00 −0.0103735
\(507\) −60486.0 60486.0i −0.235309 0.235309i
\(508\) −176036. + 176036.i −0.682141 + 0.682141i
\(509\) 234960.i 0.906898i −0.891282 0.453449i \(-0.850193\pi\)
0.891282 0.453449i \(-0.149807\pi\)
\(510\) 0 0
\(511\) 41132.0 0.157521
\(512\) 184336. + 184336.i 0.703186 + 0.703186i
\(513\) −97200.0 + 97200.0i −0.369344 + 0.369344i
\(514\) 75598.0i 0.286144i
\(515\) 0 0
\(516\) 247632. 0.930052
\(517\) 19792.0 + 19792.0i 0.0740472 + 0.0740472i
\(518\) −13052.0 + 13052.0i −0.0486427 + 0.0486427i
\(519\) 202692.i 0.752492i
\(520\) 0 0
\(521\) −171218. −0.630774 −0.315387 0.948963i \(-0.602134\pi\)
−0.315387 + 0.948963i \(0.602134\pi\)
\(522\) 4320.00 + 4320.00i 0.0158541 + 0.0158541i
\(523\) 332666. 332666.i 1.21620 1.21620i 0.247248 0.968952i \(-0.420474\pi\)
0.968952 0.247248i \(-0.0795262\pi\)
\(524\) 283808.i 1.03362i
\(525\) 0 0
\(526\) 67172.0 0.242782
\(527\) 572.000 + 572.000i 0.00205956 + 0.00205956i
\(528\) 7872.00 7872.00i 0.0282369 0.0282369i
\(529\) 224729.i 0.803060i
\(530\) 0 0
\(531\) 32940.0 0.116825
\(532\) 65520.0 + 65520.0i 0.231500 + 0.231500i
\(533\) 234632. 234632.i 0.825910 0.825910i
\(534\) 25920.0i 0.0908976i
\(535\) 0 0
\(536\) −52440.0 −0.182530
\(537\) 63720.0 + 63720.0i 0.220967 + 0.220967i
\(538\) −28530.0 + 28530.0i −0.0985683 + 0.0985683i
\(539\) 8392.00i 0.0288860i
\(540\) 0 0
\(541\) 13862.0 0.0473621 0.0236811 0.999720i \(-0.492461\pi\)
0.0236811 + 0.999720i \(0.492461\pi\)
\(542\) −7468.00 7468.00i −0.0254218 0.0254218i
\(543\) 144732. 144732.i 0.490868 0.490868i
\(544\) 1288.00i 0.00435229i
\(545\) 0 0
\(546\) −86736.0 −0.290947
\(547\) 180026. + 180026.i 0.601673 + 0.601673i 0.940756 0.339083i \(-0.110117\pi\)
−0.339083 + 0.940756i \(0.610117\pi\)
\(548\) 144914. 144914.i 0.482558 0.482558i
\(549\) 14328.0i 0.0475380i
\(550\) 0 0
\(551\) 86400.0 0.284584
\(552\) −59760.0 59760.0i −0.196125 0.196125i
\(553\) −237120. + 237120.i −0.775386 + 0.775386i
\(554\) 12998.0i 0.0423503i
\(555\) 0 0
\(556\) 378840. 1.22548
\(557\) −422549. 422549.i −1.36197 1.36197i −0.871408 0.490560i \(-0.836792\pi\)
−0.490560 0.871408i \(-0.663208\pi\)
\(558\) −5148.00 + 5148.00i −0.0165337 + 0.0165337i
\(559\) 409772.i 1.31135i
\(560\) 0 0
\(561\) −96.0000 −0.000305032
\(562\) −97928.0 97928.0i −0.310052 0.310052i
\(563\) −105314. + 105314.i −0.332253 + 0.332253i −0.853442 0.521188i \(-0.825489\pi\)
0.521188 + 0.853442i \(0.325489\pi\)
\(564\) 415632.i 1.30662i
\(565\) 0 0
\(566\) −119708. −0.373672
\(567\) 149526. + 149526.i 0.465105 + 0.465105i
\(568\) −182040. + 182040.i −0.564248 + 0.564248i
\(569\) 85830.0i 0.265103i 0.991176 + 0.132551i \(0.0423170\pi\)
−0.991176 + 0.132551i \(0.957683\pi\)
\(570\) 0 0
\(571\) −142168. −0.436043 −0.218022 0.975944i \(-0.569960\pi\)
−0.218022 + 0.975944i \(0.569960\pi\)
\(572\) −15568.0 15568.0i −0.0475818 0.0475818i
\(573\) −271128. + 271128.i −0.825781 + 0.825781i
\(574\) 87776.0i 0.266411i
\(575\) 0 0
\(576\) −12024.0 −0.0362413
\(577\) 154601. + 154601.i 0.464366 + 0.464366i 0.900084 0.435717i \(-0.143505\pi\)
−0.435717 + 0.900084i \(0.643505\pi\)
\(578\) 83519.0 83519.0i 0.249994 0.249994i
\(579\) 470388.i 1.40313i
\(580\) 0 0
\(581\) −294008. −0.870977
\(582\) 78612.0 + 78612.0i 0.232083 + 0.232083i
\(583\) −26648.0 + 26648.0i −0.0784021 + 0.0784021i
\(584\) 47460.0i 0.139156i
\(585\) 0 0
\(586\) −56998.0 −0.165983
\(587\) −222974. 222974.i −0.647110 0.647110i 0.305184 0.952294i \(-0.401282\pi\)
−0.952294 + 0.305184i \(0.901282\pi\)
\(588\) −88116.0 + 88116.0i −0.254859 + 0.254859i
\(589\) 102960.i 0.296782i
\(590\) 0 0
\(591\) −340188. −0.973967
\(592\) −41164.0 41164.0i −0.117456 0.117456i
\(593\) −148049. + 148049.i −0.421014 + 0.421014i −0.885553 0.464539i \(-0.846220\pi\)
0.464539 + 0.885553i \(0.346220\pi\)
\(594\) 8640.00i 0.0244873i
\(595\) 0 0
\(596\) −228900. −0.644397
\(597\) −10800.0 10800.0i −0.0303023 0.0303023i
\(598\) −46148.0 + 46148.0i −0.129048 + 0.129048i
\(599\) 31800.0i 0.0886285i 0.999018 + 0.0443143i \(0.0141103\pi\)
−0.999018 + 0.0443143i \(0.985890\pi\)
\(600\) 0 0
\(601\) −71848.0 −0.198914 −0.0994571 0.995042i \(-0.531711\pi\)
−0.0994571 + 0.995042i \(0.531711\pi\)
\(602\) −76648.0 76648.0i −0.211499 0.211499i
\(603\) 7866.00 7866.00i 0.0216331 0.0216331i
\(604\) 14728.0i 0.0403710i
\(605\) 0 0
\(606\) 193224. 0.526158
\(607\) 13526.0 + 13526.0i 0.0367106 + 0.0367106i 0.725224 0.688513i \(-0.241736\pi\)
−0.688513 + 0.725224i \(0.741736\pi\)
\(608\) 115920. 115920.i 0.313582 0.313582i
\(609\) 149760.i 0.403795i
\(610\) 0 0
\(611\) 687772. 1.84231
\(612\) 126.000 + 126.000i 0.000336409 + 0.000336409i
\(613\) 303461. 303461.i 0.807573 0.807573i −0.176693 0.984266i \(-0.556540\pi\)
0.984266 + 0.176693i \(0.0565399\pi\)
\(614\) 235852.i 0.625609i
\(615\) 0 0
\(616\) −12480.0 −0.0328892
\(617\) −122399. 122399.i −0.321520 0.321520i 0.527830 0.849350i \(-0.323006\pi\)
−0.849350 + 0.527830i \(0.823006\pi\)
\(618\) −11928.0 + 11928.0i −0.0312313 + 0.0312313i
\(619\) 110220.i 0.287660i −0.989602 0.143830i \(-0.954058\pi\)
0.989602 0.143830i \(-0.0459418\pi\)
\(620\) 0 0
\(621\) 179280. 0.464888
\(622\) 3892.00 + 3892.00i 0.0100599 + 0.0100599i
\(623\) −56160.0 + 56160.0i −0.144694 + 0.144694i
\(624\) 273552.i 0.702539i
\(625\) 0 0
\(626\) 99922.0 0.254984
\(627\) −8640.00 8640.00i −0.0219775 0.0219775i
\(628\) −90986.0 + 90986.0i −0.230704 + 0.230704i
\(629\) 502.000i 0.00126883i
\(630\) 0 0
\(631\) 620372. 1.55809 0.779047 0.626966i \(-0.215703\pi\)
0.779047 + 0.626966i \(0.215703\pi\)
\(632\) 273600. + 273600.i 0.684986 + 0.684986i
\(633\) 110352. 110352.i 0.275406 0.275406i
\(634\) 34198.0i 0.0850790i
\(635\) 0 0
\(636\) −559608. −1.38347
\(637\) 145811. + 145811.i 0.359345 + 0.359345i
\(638\) −3840.00 + 3840.00i −0.00943387 + 0.00943387i
\(639\) 54612.0i 0.133748i
\(640\) 0 0
\(641\) −722888. −1.75936 −0.879680 0.475565i \(-0.842244\pi\)
−0.879680 + 0.475565i \(0.842244\pi\)
\(642\) 99912.0 + 99912.0i 0.242408 + 0.242408i
\(643\) 393026. 393026.i 0.950603 0.950603i −0.0482328 0.998836i \(-0.515359\pi\)
0.998836 + 0.0482328i \(0.0153589\pi\)
\(644\) 120848.i 0.291385i
\(645\) 0 0
\(646\) −360.000 −0.000862656
\(647\) 338626. + 338626.i 0.808931 + 0.808931i 0.984472 0.175541i \(-0.0561674\pi\)
−0.175541 + 0.984472i \(0.556167\pi\)
\(648\) 172530. 172530.i 0.410880 0.410880i
\(649\) 29280.0i 0.0695155i
\(650\) 0 0
\(651\) 178464. 0.421103
\(652\) −270004. 270004.i −0.635148 0.635148i
\(653\) −254669. + 254669.i −0.597241 + 0.597241i −0.939577 0.342336i \(-0.888782\pi\)
0.342336 + 0.939577i \(0.388782\pi\)
\(654\) 204120.i 0.477233i
\(655\) 0 0
\(656\) 276832. 0.643293
\(657\) 7119.00 + 7119.00i 0.0164926 + 0.0164926i
\(658\) 128648. 128648.i 0.297133 0.297133i
\(659\) 603660.i 1.39002i −0.718999 0.695011i \(-0.755400\pi\)
0.718999 0.695011i \(-0.244600\pi\)
\(660\) 0 0
\(661\) 14792.0 0.0338551 0.0169275 0.999857i \(-0.494612\pi\)
0.0169275 + 0.999857i \(0.494612\pi\)
\(662\) −143128. 143128.i −0.326594 0.326594i
\(663\) −1668.00 + 1668.00i −0.00379463 + 0.00379463i
\(664\) 339240.i 0.769433i
\(665\) 0 0
\(666\) −4518.00 −0.0101859
\(667\) −79680.0 79680.0i −0.179101 0.179101i
\(668\) 217364. 217364.i 0.487119 0.487119i
\(669\) 10392.0i 0.0232192i
\(670\) 0 0
\(671\) −12736.0 −0.0282871
\(672\) −200928. 200928.i −0.444940 0.444940i
\(673\) −300409. + 300409.i −0.663258 + 0.663258i −0.956147 0.292888i \(-0.905384\pi\)
0.292888 + 0.956147i \(0.405384\pi\)
\(674\) 206498.i 0.454565i
\(675\) 0 0
\(676\) −141134. −0.308843
\(677\) 256051. + 256051.i 0.558662 + 0.558662i 0.928926 0.370264i \(-0.120733\pi\)
−0.370264 + 0.928926i \(0.620733\pi\)
\(678\) 61932.0 61932.0i 0.134727 0.134727i
\(679\) 340652.i 0.738876i
\(680\) 0 0
\(681\) 542712. 1.17024
\(682\) −4576.00 4576.00i −0.00983824 0.00983824i
\(683\) −341954. + 341954.i −0.733038 + 0.733038i −0.971220 0.238183i \(-0.923448\pi\)
0.238183 + 0.971220i \(0.423448\pi\)
\(684\) 22680.0i 0.0484765i
\(685\) 0 0
\(686\) 179400. 0.381219
\(687\) 234720. + 234720.i 0.497321 + 0.497321i
\(688\) 241736. 241736.i 0.510698 0.510698i
\(689\) 926018.i 1.95066i
\(690\) 0 0
\(691\) −717688. −1.50307 −0.751536 0.659692i \(-0.770687\pi\)
−0.751536 + 0.659692i \(0.770687\pi\)
\(692\) −236474. 236474.i −0.493823 0.493823i
\(693\) 1872.00 1872.00i 0.00389798 0.00389798i
\(694\) 209252.i 0.434461i
\(695\) 0 0
\(696\) −172800. −0.356718
\(697\) −1688.00 1688.00i −0.00347462 0.00347462i
\(698\) −94800.0 + 94800.0i −0.194580 + 0.194580i
\(699\) 397452.i 0.813449i
\(700\) 0 0
\(701\) 267352. 0.544061 0.272030 0.962289i \(-0.412305\pi\)
0.272030 + 0.962289i \(0.412305\pi\)
\(702\) −150120. 150120.i −0.304624 0.304624i
\(703\) −45180.0 + 45180.0i −0.0914188 + 0.0914188i
\(704\) 10688.0i 0.0215651i
\(705\) 0 0
\(706\) −127138. −0.255074
\(707\) 418652. + 418652.i 0.837557 + 0.837557i
\(708\) −307440. + 307440.i −0.613330 + 0.613330i
\(709\) 159360.i 0.317020i −0.987357 0.158510i \(-0.949331\pi\)
0.987357 0.158510i \(-0.0506690\pi\)
\(710\) 0 0
\(711\) −82080.0 −0.162367
\(712\) 64800.0 + 64800.0i 0.127825 + 0.127825i
\(713\) 94952.0 94952.0i 0.186778 0.186778i
\(714\) 624.000i 0.00122402i
\(715\) 0 0
\(716\) 148680. 0.290019
\(717\) −530640. 530640.i −1.03219 1.03219i
\(718\) −141840. + 141840.i −0.275138 + 0.275138i
\(719\) 364680.i 0.705430i 0.935731 + 0.352715i \(0.114742\pi\)
−0.935731 + 0.352715i \(0.885258\pi\)
\(720\) 0 0
\(721\) −51688.0 −0.0994304
\(722\) 97921.0 + 97921.0i 0.187846 + 0.187846i
\(723\) 121872. 121872.i 0.233146 0.233146i
\(724\) 337708.i 0.644265i
\(725\) 0 0
\(726\) −174924. −0.331876
\(727\) −716374. 716374.i −1.35541 1.35541i −0.879486 0.475925i \(-0.842113\pi\)
−0.475925 0.879486i \(-0.657887\pi\)
\(728\) −216840. + 216840.i −0.409144 + 0.409144i
\(729\) 576639.i 1.08505i
\(730\) 0 0
\(731\) −2948.00 −0.00551687
\(732\) −133728. 133728.i −0.249574 0.249574i
\(733\) −641029. + 641029.i −1.19308 + 1.19308i −0.216883 + 0.976198i \(0.569589\pi\)
−0.976198 + 0.216883i \(0.930411\pi\)
\(734\) 284348.i 0.527786i
\(735\) 0 0
\(736\) −213808. −0.394701
\(737\) 6992.00 + 6992.00i 0.0128726 + 0.0128726i
\(738\) 15192.0 15192.0i 0.0278934 0.0278934i
\(739\) 607140.i 1.11173i −0.831272 0.555866i \(-0.812387\pi\)
0.831272 0.555866i \(-0.187613\pi\)
\(740\) 0 0
\(741\) −300240. −0.546805
\(742\) 173212. + 173212.i 0.314608 + 0.314608i
\(743\) 248026. 248026.i 0.449283 0.449283i −0.445833 0.895116i \(-0.647093\pi\)
0.895116 + 0.445833i \(0.147093\pi\)
\(744\) 205920.i 0.372008i
\(745\) 0 0
\(746\) −20618.0 −0.0370484
\(747\) −50886.0 50886.0i −0.0911921 0.0911921i
\(748\) −112.000 + 112.000i −0.000200177 + 0.000200177i
\(749\) 432952.i 0.771749i
\(750\) 0 0
\(751\) 169052. 0.299737 0.149869 0.988706i \(-0.452115\pi\)
0.149869 + 0.988706i \(0.452115\pi\)
\(752\) 405736. + 405736.i 0.717477 + 0.717477i
\(753\) 448512. 448512.i 0.791014 0.791014i
\(754\) 133440.i 0.234716i
\(755\) 0 0
\(756\) 393120. 0.687831
\(757\) 166301. + 166301.i 0.290204 + 0.290204i 0.837161 0.546957i \(-0.184214\pi\)
−0.546957 + 0.837161i \(0.684214\pi\)
\(758\) 115380. 115380.i 0.200813 0.200813i
\(759\) 15936.0i 0.0276628i
\(760\) 0 0
\(761\) 557842. 0.963256 0.481628 0.876376i \(-0.340046\pi\)
0.481628 + 0.876376i \(0.340046\pi\)
\(762\) −150888. 150888.i −0.259863 0.259863i
\(763\) 442260. 442260.i 0.759676 0.759676i
\(764\) 632632.i 1.08384i
\(765\) 0 0
\(766\) −125308. −0.213561
\(767\) 508740. + 508740.i 0.864779 + 0.864779i
\(768\) −11424.0 + 11424.0i −0.0193685 + 0.0193685i
\(769\) 678720.i 1.14773i −0.818952 0.573863i \(-0.805444\pi\)
0.818952 0.573863i \(-0.194556\pi\)
\(770\) 0 0
\(771\) −453588. −0.763050
\(772\) 548786. + 548786.i 0.920807 + 0.920807i
\(773\) 164341. 164341.i 0.275034 0.275034i −0.556089 0.831123i \(-0.687699\pi\)
0.831123 + 0.556089i \(0.187699\pi\)
\(774\) 26532.0i 0.0442882i
\(775\) 0 0
\(776\) 393060. 0.652733
\(777\) 78312.0 + 78312.0i 0.129714 + 0.129714i
\(778\) 132690. 132690.i 0.219219 0.219219i
\(779\) 303840.i 0.500691i
\(780\) 0 0
\(781\) 48544.0 0.0795854
\(782\) 332.000 + 332.000i 0.000542906 + 0.000542906i
\(783\) 259200. 259200.i 0.422777 0.422777i
\(784\) 172036.i 0.279890i
\(785\) 0 0
\(786\) 243264. 0.393761
\(787\) −323074. 323074.i −0.521618 0.521618i 0.396442 0.918060i \(-0.370245\pi\)
−0.918060 + 0.396442i \(0.870245\pi\)
\(788\) −396886. + 396886.i −0.639166 + 0.639166i
\(789\) 403032.i 0.647419i
\(790\) 0 0
\(791\) 268372. 0.428928
\(792\) −2160.00 2160.00i −0.00344353 0.00344353i
\(793\) −221288. + 221288.i −0.351894 + 0.351894i
\(794\) 176902.i 0.280603i
\(795\) 0 0
\(796\) −25200.0 −0.0397717
\(797\) −510299. 510299.i −0.803356 0.803356i 0.180262 0.983619i \(-0.442305\pi\)
−0.983619 + 0.180262i \(0.942305\pi\)
\(798\) −56160.0 + 56160.0i −0.0881904 + 0.0881904i
\(799\) 4948.00i 0.00775061i
\(800\) 0 0
\(801\) −19440.0 −0.0302992
\(802\) 63202.0 + 63202.0i 0.0982612 + 0.0982612i
\(803\) −6328.00 + 6328.00i −0.00981376 + 0.00981376i
\(804\) 146832.i 0.227148i
\(805\) 0 0
\(806\) −159016. −0.244777
\(807\) 171180. + 171180.i 0.262849 + 0.262849i
\(808\) 483060. 483060.i 0.739909 0.739909i
\(809\) 1.18656e6i 1.81298i −0.422229 0.906489i \(-0.638752\pi\)
0.422229 0.906489i \(-0.361248\pi\)
\(810\) 0 0
\(811\) −431008. −0.655305 −0.327653 0.944798i \(-0.606258\pi\)
−0.327653 + 0.944798i \(0.606258\pi\)
\(812\) −174720. 174720.i −0.264991 0.264991i
\(813\) −44808.0 + 44808.0i −0.0677914 + 0.0677914i
\(814\) 4016.00i 0.00606101i
\(815\) 0 0
\(816\) −1968.00 −0.00295559
\(817\) −265320. 265320.i −0.397490 0.397490i
\(818\) −52890.0 + 52890.0i −0.0790436 + 0.0790436i
\(819\) 65052.0i 0.0969824i
\(820\) 0 0
\(821\) −639368. −0.948560 −0.474280 0.880374i \(-0.657291\pi\)
−0.474280 + 0.880374i \(0.657291\pi\)
\(822\) 124212. + 124212.i 0.183831 + 0.183831i
\(823\) 74966.0 74966.0i 0.110679 0.110679i −0.649599 0.760277i \(-0.725063\pi\)
0.760277 + 0.649599i \(0.225063\pi\)
\(824\) 59640.0i 0.0878382i
\(825\) 0 0
\(826\) 190320. 0.278949
\(827\) 144226. + 144226.i 0.210879 + 0.210879i 0.804641 0.593762i \(-0.202358\pi\)
−0.593762 + 0.804641i \(0.702358\pi\)
\(828\) 20916.0 20916.0i 0.0305083 0.0305083i
\(829\) 685170.i 0.996987i 0.866894 + 0.498493i \(0.166113\pi\)
−0.866894 + 0.498493i \(0.833887\pi\)
\(830\) 0 0
\(831\) −77988.0 −0.112934
\(832\) −185704. 185704.i −0.268272 0.268272i
\(833\) 1049.00 1049.00i 0.00151177 0.00151177i
\(834\) 324720.i 0.466850i
\(835\) 0 0
\(836\) −20160.0 −0.0288455
\(837\) 308880. + 308880.i 0.440899 + 0.440899i
\(838\) −256980. + 256980.i −0.365941 + 0.365941i
\(839\) 445560.i 0.632969i 0.948598 + 0.316484i \(0.102502\pi\)
−0.948598 + 0.316484i \(0.897498\pi\)
\(840\) 0 0
\(841\) 476881. 0.674245
\(842\) 186632. + 186632.i 0.263246 + 0.263246i
\(843\) −587568. + 587568.i −0.826805 + 0.826805i
\(844\) 257488.i 0.361470i
\(845\) 0 0
\(846\) 44532.0 0.0622202
\(847\) −379002. 379002.i −0.528293 0.528293i
\(848\) −546284. + 546284.i −0.759673 + 0.759673i
\(849\) 718248.i 0.996458i
\(850\) 0 0
\(851\) 83332.0 0.115068
\(852\) 509712. + 509712.i 0.702175 + 0.702175i
\(853\) 319781. 319781.i 0.439496 0.439496i −0.452347 0.891842i \(-0.649413\pi\)
0.891842 + 0.452347i \(0.149413\pi\)
\(854\) 82784.0i 0.113509i
\(855\) 0 0
\(856\) 499560. 0.681774
\(857\) −576449. 576449.i −0.784873 0.784873i 0.195776 0.980649i \(-0.437277\pi\)
−0.980649 + 0.195776i \(0.937277\pi\)
\(858\) 13344.0 13344.0i 0.0181264 0.0181264i
\(859\) 807540.i 1.09440i 0.837001 + 0.547202i \(0.184307\pi\)
−0.837001 + 0.547202i \(0.815693\pi\)
\(860\) 0 0
\(861\) −526656. −0.710429
\(862\) −208028. 208028.i −0.279967 0.279967i
\(863\) −507914. + 507914.i −0.681975 + 0.681975i −0.960445 0.278470i \(-0.910173\pi\)
0.278470 + 0.960445i \(0.410173\pi\)
\(864\) 695520.i 0.931713i
\(865\) 0 0
\(866\) 302542. 0.403413
\(867\) −501114. 501114.i −0.666651 0.666651i
\(868\) 208208. 208208.i 0.276349 0.276349i
\(869\) 72960.0i 0.0966152i
\(870\) 0 0
\(871\) 242972. 0.320273
\(872\) −510300. 510300.i −0.671108 0.671108i
\(873\) −58959.0 + 58959.0i −0.0773609 + 0.0773609i
\(874\) 59760.0i 0.0782326i
\(875\) 0 0
\(876\) −132888. −0.173172
\(877\) 673901. + 673901.i 0.876187 + 0.876187i 0.993138 0.116951i \(-0.0373119\pi\)
−0.116951 + 0.993138i \(0.537312\pi\)
\(878\) 158640. 158640.i 0.205790 0.205790i
\(879\) 341988.i 0.442622i
\(880\) 0 0
\(881\) −1.33753e6 −1.72326 −0.861631 0.507536i \(-0.830556\pi\)
−0.861631 + 0.507536i \(0.830556\pi\)
\(882\) 9441.00 + 9441.00i 0.0121361 + 0.0121361i
\(883\) −131554. + 131554.i −0.168726 + 0.168726i −0.786419 0.617693i \(-0.788067\pi\)
0.617693 + 0.786419i \(0.288067\pi\)
\(884\) 3892.00i 0.00498045i
\(885\) 0 0
\(886\) −505948. −0.644523
\(887\) 327826. + 327826.i 0.416674 + 0.416674i 0.884056 0.467382i \(-0.154803\pi\)
−0.467382 + 0.884056i \(0.654803\pi\)
\(888\) 90360.0 90360.0i 0.114591 0.114591i
\(889\) 653848.i 0.827320i
\(890\) 0 0
\(891\) −46008.0 −0.0579533
\(892\) −12124.0 12124.0i −0.0152376 0.0152376i
\(893\) 445320. 445320.i 0.558431 0.558431i
\(894\) 196200.i 0.245484i
\(895\) 0 0
\(896\) −605280. −0.753946
\(897\) 276888. + 276888.i 0.344127 + 0.344127i
\(898\) −123750. + 123750.i −0.153459 + 0.153459i
\(899\) 274560.i 0.339717i
\(900\) 0 0
\(901\) 6662.00 0.00820644
\(902\) 13504.0 + 13504.0i 0.0165978 + 0.0165978i
\(903\) −459888. + 459888.i −0.563997 + 0.563997i
\(904\) 309660.i 0.378921i
\(905\) 0 0
\(906\) 12624.0 0.0153794
\(907\) −105274. 105274.i −0.127970 0.127970i 0.640221 0.768191i \(-0.278843\pi\)
−0.768191 + 0.640221i \(0.778843\pi\)
\(908\) 633164. 633164.i 0.767970 0.767970i
\(909\) 144918.i 0.175386i
\(910\) 0 0
\(911\) 1.59209e6 1.91837 0.959183 0.282787i \(-0.0912588\pi\)
0.959183 + 0.282787i \(0.0912588\pi\)
\(912\) −177120. 177120.i −0.212950 0.212950i
\(913\) 45232.0 45232.0i 0.0542631 0.0542631i
\(914\) 64402.0i 0.0770916i
\(915\) 0 0
\(916\) 547680. 0.652734
\(917\) 527072. + 527072.i 0.626803 + 0.626803i
\(918\) −1080.00 + 1080.00i −0.00128156 + 0.00128156i
\(919\) 515880.i 0.610826i 0.952220 + 0.305413i \(0.0987946\pi\)
−0.952220 + 0.305413i \(0.901205\pi\)
\(920\) 0 0
\(921\) 1.41511e6 1.66829
\(922\) 75142.0 + 75142.0i 0.0883936 + 0.0883936i
\(923\) 843452. 843452.i 0.990050 0.990050i
\(924\) 34944.0i 0.0409288i
\(925\) 0 0
\(926\) −471428. −0.549786
\(927\) −8946.00 8946.00i −0.0104104 0.0104104i
\(928\) −309120. + 309120.i −0.358948 + 0.358948i
\(929\) 1.60023e6i 1.85418i −0.374844 0.927088i \(-0.622304\pi\)
0.374844 0.927088i \(-0.377696\pi\)
\(930\) 0 0
\(931\) 188820. 0.217846
\(932\) −463694. 463694.i −0.533826 0.533826i
\(933\) 23352.0 23352.0i 0.0268263 0.0268263i
\(934\) 57148.0i 0.0655100i
\(935\) 0 0
\(936\) −75060.0 −0.0856755
\(937\) 908801. + 908801.i 1.03512 + 1.03512i 0.999361 + 0.0357569i \(0.0113842\pi\)
0.0357569 + 0.999361i \(0.488616\pi\)
\(938\) 45448.0 45448.0i 0.0516546 0.0516546i
\(939\) 599532.i 0.679957i
\(940\) 0 0
\(941\) 455962. 0.514931 0.257466 0.966287i \(-0.417113\pi\)
0.257466 + 0.966287i \(0.417113\pi\)
\(942\) −77988.0 77988.0i −0.0878873 0.0878873i
\(943\) −280208. + 280208.i −0.315106 + 0.315106i
\(944\) 600240.i 0.673567i
\(945\) 0 0
\(946\) 23584.0 0.0263533
\(947\) −463274. 463274.i −0.516580 0.516580i 0.399955 0.916535i \(-0.369026\pi\)
−0.916535 + 0.399955i \(0.869026\pi\)
\(948\) 766080. 766080.i 0.852427 0.852427i
\(949\) 219898.i 0.244168i
\(950\) 0 0
\(951\) −205188. −0.226877
\(952\) 1560.00 + 1560.00i 0.00172128 + 0.00172128i
\(953\) 1.03428e6 1.03428e6i 1.13881 1.13881i 0.150151 0.988663i \(-0.452024\pi\)
0.988663 0.150151i \(-0.0479759\pi\)
\(954\) 59958.0i 0.0658795i
\(955\) 0 0
\(956\) −1.23816e6 −1.35476
\(957\) 23040.0 + 23040.0i 0.0251570 + 0.0251570i
\(958\) −26520.0 + 26520.0i −0.0288963 + 0.0288963i
\(959\) 538252.i 0.585259i
\(960\) 0 0
\(961\) −596337. −0.645721
\(962\) −69778.0 69778.0i −0.0753995 0.0753995i
\(963\) −74934.0 + 74934.0i −0.0808028 + 0.0808028i
\(964\) 284368.i 0.306004i
\(965\) 0 0
\(966\) 103584. 0.111004
\(967\) 1.10253e6 + 1.10253e6i 1.17906 + 1.17906i 0.979984 + 0.199076i \(0.0637940\pi\)
0.199076 + 0.979984i \(0.436206\pi\)
\(968\) −437310. + 437310.i −0.466701 + 0.466701i
\(969\) 2160.00i 0.00230042i
\(970\) 0 0
\(971\) −264368. −0.280395 −0.140198 0.990124i \(-0.544774\pi\)
−0.140198 + 0.990124i \(0.544774\pi\)
\(972\) 129276. + 129276.i 0.136831 + 0.136831i
\(973\) −703560. + 703560.i −0.743148 + 0.743148i
\(974\) 82748.0i 0.0872247i
\(975\) 0 0
\(976\) −261088. −0.274086
\(977\) −866249. 866249.i −0.907515 0.907515i 0.0885566 0.996071i \(-0.471775\pi\)
−0.996071 + 0.0885566i \(0.971775\pi\)
\(978\) 231432. 231432.i 0.241961 0.241961i
\(979\) 17280.0i 0.0180293i
\(980\) 0 0
\(981\) 153090. 0.159078
\(982\) −149288. 149288.i −0.154811 0.154811i
\(983\) −1.08205e6 + 1.08205e6i −1.11980 + 1.11980i −0.128034 + 0.991770i \(0.540867\pi\)
−0.991770 + 0.128034i \(0.959133\pi\)
\(984\) 607680.i 0.627603i
\(985\) 0 0
\(986\) 960.000 0.000987455
\(987\) −771888. 771888.i −0.792355 0.792355i
\(988\) −350280. + 350280.i −0.358840 + 0.358840i
\(989\) 489368.i 0.500314i
\(990\) 0 0
\(991\) −54988.0 −0.0559913 −0.0279957 0.999608i \(-0.508912\pi\)
−0.0279957 + 0.999608i \(0.508912\pi\)
\(992\) −368368. 368368.i −0.374333 0.374333i
\(993\) −858768. + 858768.i −0.870918 + 0.870918i
\(994\) 315536.i 0.319357i
\(995\) 0 0
\(996\) 949872. 0.957517
\(997\) −73099.0 73099.0i −0.0735396 0.0735396i 0.669380 0.742920i \(-0.266560\pi\)
−0.742920 + 0.669380i \(0.766560\pi\)
\(998\) −284100. + 284100.i −0.285240 + 0.285240i
\(999\) 271080.i 0.271623i
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 25.5.c.a.7.1 2
3.2 odd 2 225.5.g.b.82.1 2
4.3 odd 2 400.5.p.a.257.1 2
5.2 odd 4 5.5.c.a.3.1 yes 2
5.3 odd 4 inner 25.5.c.a.18.1 2
5.4 even 2 5.5.c.a.2.1 2
15.2 even 4 45.5.g.b.28.1 2
15.8 even 4 225.5.g.b.118.1 2
15.14 odd 2 45.5.g.b.37.1 2
20.3 even 4 400.5.p.a.193.1 2
20.7 even 4 80.5.p.d.33.1 2
20.19 odd 2 80.5.p.d.17.1 2
40.19 odd 2 320.5.p.c.257.1 2
40.27 even 4 320.5.p.c.193.1 2
40.29 even 2 320.5.p.h.257.1 2
40.37 odd 4 320.5.p.h.193.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5.5.c.a.2.1 2 5.4 even 2
5.5.c.a.3.1 yes 2 5.2 odd 4
25.5.c.a.7.1 2 1.1 even 1 trivial
25.5.c.a.18.1 2 5.3 odd 4 inner
45.5.g.b.28.1 2 15.2 even 4
45.5.g.b.37.1 2 15.14 odd 2
80.5.p.d.17.1 2 20.19 odd 2
80.5.p.d.33.1 2 20.7 even 4
225.5.g.b.82.1 2 3.2 odd 2
225.5.g.b.118.1 2 15.8 even 4
320.5.p.c.193.1 2 40.27 even 4
320.5.p.c.257.1 2 40.19 odd 2
320.5.p.h.193.1 2 40.37 odd 4
320.5.p.h.257.1 2 40.29 even 2
400.5.p.a.193.1 2 20.3 even 4
400.5.p.a.257.1 2 4.3 odd 2