Properties

Label 1008.4.bt.d.593.9
Level $1008$
Weight $4$
Character 1008.593
Analytic conductor $59.474$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1008,4,Mod(17,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.17");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1008.bt (of order \(6\), degree \(2\), not 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: \(59.4739252858\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 593.9
Character \(\chi\) \(=\) 1008.593
Dual form 1008.4.bt.d.17.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.30930 + 5.73188i) q^{5} +(4.31556 + 18.0104i) q^{7} +O(q^{10})\) \(q+(-3.30930 + 5.73188i) q^{5} +(4.31556 + 18.0104i) q^{7} +(-1.54712 + 0.893230i) q^{11} -4.72915i q^{13} +(23.8462 + 41.3029i) q^{17} +(40.1443 + 23.1773i) q^{19} +(-30.2011 - 17.4366i) q^{23} +(40.5970 + 70.3161i) q^{25} +48.3459i q^{29} +(107.814 - 62.2462i) q^{31} +(-117.515 - 34.8657i) q^{35} +(-137.933 + 238.908i) q^{37} +37.3352 q^{41} +215.883 q^{43} +(53.1037 - 91.9783i) q^{47} +(-305.752 + 155.450i) q^{49} +(-233.771 + 134.968i) q^{53} -11.8239i q^{55} +(-149.592 - 259.101i) q^{59} +(-292.459 - 168.851i) q^{61} +(27.1069 + 15.6502i) q^{65} +(188.686 + 326.815i) q^{67} -816.814i q^{71} +(-596.355 + 344.306i) q^{73} +(-22.7641 - 24.0095i) q^{77} +(307.064 - 531.851i) q^{79} -1323.90 q^{83} -315.658 q^{85} +(-480.368 + 832.022i) q^{89} +(85.1741 - 20.4089i) q^{91} +(-265.699 + 153.401i) q^{95} +449.508i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 24 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 24 q^{7} - 540 q^{19} - 924 q^{25} - 648 q^{31} - 132 q^{37} + 792 q^{43} + 672 q^{49} + 12 q^{67} + 2412 q^{73} - 1680 q^{79} + 480 q^{85} - 1404 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −3.30930 + 5.73188i −0.295993 + 0.512675i −0.975215 0.221258i \(-0.928984\pi\)
0.679222 + 0.733932i \(0.262317\pi\)
\(6\) 0 0
\(7\) 4.31556 + 18.0104i 0.233019 + 0.972472i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.54712 + 0.893230i −0.0424067 + 0.0244835i −0.521053 0.853524i \(-0.674461\pi\)
0.478647 + 0.878008i \(0.341127\pi\)
\(12\) 0 0
\(13\) 4.72915i 0.100895i −0.998727 0.0504473i \(-0.983935\pi\)
0.998727 0.0504473i \(-0.0160647\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 23.8462 + 41.3029i 0.340210 + 0.589260i 0.984471 0.175545i \(-0.0561687\pi\)
−0.644262 + 0.764805i \(0.722835\pi\)
\(18\) 0 0
\(19\) 40.1443 + 23.1773i 0.484722 + 0.279855i 0.722382 0.691494i \(-0.243047\pi\)
−0.237660 + 0.971348i \(0.576380\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −30.2011 17.4366i −0.273798 0.158078i 0.356814 0.934175i \(-0.383863\pi\)
−0.630613 + 0.776098i \(0.717196\pi\)
\(24\) 0 0
\(25\) 40.5970 + 70.3161i 0.324776 + 0.562529i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 48.3459i 0.309573i 0.987948 + 0.154786i \(0.0494689\pi\)
−0.987948 + 0.154786i \(0.950531\pi\)
\(30\) 0 0
\(31\) 107.814 62.2462i 0.624642 0.360637i −0.154032 0.988066i \(-0.549226\pi\)
0.778674 + 0.627429i \(0.215893\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −117.515 34.8657i −0.567534 0.168382i
\(36\) 0 0
\(37\) −137.933 + 238.908i −0.612868 + 1.06152i 0.377887 + 0.925852i \(0.376651\pi\)
−0.990755 + 0.135667i \(0.956682\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 37.3352 0.142214 0.0711071 0.997469i \(-0.477347\pi\)
0.0711071 + 0.997469i \(0.477347\pi\)
\(42\) 0 0
\(43\) 215.883 0.765625 0.382812 0.923826i \(-0.374956\pi\)
0.382812 + 0.923826i \(0.374956\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 53.1037 91.9783i 0.164808 0.285456i −0.771779 0.635891i \(-0.780633\pi\)
0.936587 + 0.350435i \(0.113966\pi\)
\(48\) 0 0
\(49\) −305.752 + 155.450i −0.891405 + 0.453208i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −233.771 + 134.968i −0.605867 + 0.349797i −0.771346 0.636416i \(-0.780416\pi\)
0.165479 + 0.986213i \(0.447083\pi\)
\(54\) 0 0
\(55\) 11.8239i 0.0289878i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −149.592 259.101i −0.330088 0.571729i 0.652441 0.757840i \(-0.273745\pi\)
−0.982529 + 0.186110i \(0.940412\pi\)
\(60\) 0 0
\(61\) −292.459 168.851i −0.613861 0.354413i 0.160614 0.987017i \(-0.448653\pi\)
−0.774475 + 0.632604i \(0.781986\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 27.1069 + 15.6502i 0.0517261 + 0.0298641i
\(66\) 0 0
\(67\) 188.686 + 326.815i 0.344055 + 0.595922i 0.985182 0.171514i \(-0.0548658\pi\)
−0.641126 + 0.767435i \(0.721533\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 816.814i 1.36532i −0.730734 0.682662i \(-0.760822\pi\)
0.730734 0.682662i \(-0.239178\pi\)
\(72\) 0 0
\(73\) −596.355 + 344.306i −0.956139 + 0.552027i −0.894982 0.446101i \(-0.852812\pi\)
−0.0611561 + 0.998128i \(0.519479\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −22.7641 24.0095i −0.0336911 0.0355342i
\(78\) 0 0
\(79\) 307.064 531.851i 0.437309 0.757442i −0.560172 0.828377i \(-0.689265\pi\)
0.997481 + 0.0709347i \(0.0225982\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −1323.90 −1.75081 −0.875406 0.483389i \(-0.839406\pi\)
−0.875406 + 0.483389i \(0.839406\pi\)
\(84\) 0 0
\(85\) −315.658 −0.402798
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −480.368 + 832.022i −0.572123 + 0.990946i 0.424225 + 0.905557i \(0.360547\pi\)
−0.996348 + 0.0853887i \(0.972787\pi\)
\(90\) 0 0
\(91\) 85.1741 20.4089i 0.0981172 0.0235103i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −265.699 + 153.401i −0.286949 + 0.165670i
\(96\) 0 0
\(97\) 449.508i 0.470522i 0.971932 + 0.235261i \(0.0755945\pi\)
−0.971932 + 0.235261i \(0.924406\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −178.518 309.203i −0.175874 0.304622i 0.764590 0.644517i \(-0.222942\pi\)
−0.940463 + 0.339895i \(0.889608\pi\)
\(102\) 0 0
\(103\) 506.565 + 292.466i 0.484596 + 0.279782i 0.722330 0.691549i \(-0.243071\pi\)
−0.237734 + 0.971330i \(0.576405\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1105.24 638.108i −0.998571 0.576525i −0.0907460 0.995874i \(-0.528925\pi\)
−0.907825 + 0.419349i \(0.862258\pi\)
\(108\) 0 0
\(109\) 318.386 + 551.461i 0.279779 + 0.484591i 0.971330 0.237737i \(-0.0764056\pi\)
−0.691551 + 0.722328i \(0.743072\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 961.802i 0.800696i 0.916363 + 0.400348i \(0.131111\pi\)
−0.916363 + 0.400348i \(0.868889\pi\)
\(114\) 0 0
\(115\) 199.889 115.406i 0.162085 0.0935797i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −640.973 + 607.726i −0.493764 + 0.468153i
\(120\) 0 0
\(121\) −663.904 + 1149.92i −0.498801 + 0.863949i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1364.72 −0.976512
\(126\) 0 0
\(127\) −144.006 −0.100618 −0.0503089 0.998734i \(-0.516021\pi\)
−0.0503089 + 0.998734i \(0.516021\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −186.107 + 322.347i −0.124124 + 0.214989i −0.921390 0.388639i \(-0.872945\pi\)
0.797266 + 0.603628i \(0.206279\pi\)
\(132\) 0 0
\(133\) −244.188 + 823.039i −0.159202 + 0.536590i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −478.822 + 276.448i −0.298602 + 0.172398i −0.641815 0.766860i \(-0.721818\pi\)
0.343213 + 0.939258i \(0.388485\pi\)
\(138\) 0 0
\(139\) 2526.72i 1.54183i 0.636941 + 0.770913i \(0.280200\pi\)
−0.636941 + 0.770913i \(0.719800\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 4.22422 + 7.31656i 0.00247026 + 0.00427861i
\(144\) 0 0
\(145\) −277.113 159.991i −0.158710 0.0916314i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2384.00 1376.40i −1.31077 0.756774i −0.328547 0.944488i \(-0.606559\pi\)
−0.982224 + 0.187714i \(0.939892\pi\)
\(150\) 0 0
\(151\) 395.046 + 684.240i 0.212903 + 0.368759i 0.952622 0.304157i \(-0.0983748\pi\)
−0.739719 + 0.672916i \(0.765041\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 823.966i 0.426984i
\(156\) 0 0
\(157\) 871.100 502.930i 0.442811 0.255657i −0.261978 0.965074i \(-0.584375\pi\)
0.704789 + 0.709417i \(0.251042\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 183.706 619.184i 0.0899260 0.303096i
\(162\) 0 0
\(163\) 8.76430 15.1802i 0.00421149 0.00729452i −0.863912 0.503643i \(-0.831993\pi\)
0.868123 + 0.496348i \(0.165326\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −195.663 −0.0906639 −0.0453320 0.998972i \(-0.514435\pi\)
−0.0453320 + 0.998972i \(0.514435\pi\)
\(168\) 0 0
\(169\) 2174.64 0.989820
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −420.902 + 729.024i −0.184975 + 0.320385i −0.943568 0.331179i \(-0.892554\pi\)
0.758593 + 0.651564i \(0.225887\pi\)
\(174\) 0 0
\(175\) −1091.23 + 1034.62i −0.471365 + 0.446916i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 766.552 442.569i 0.320083 0.184800i −0.331347 0.943509i \(-0.607503\pi\)
0.651429 + 0.758709i \(0.274170\pi\)
\(180\) 0 0
\(181\) 1011.03i 0.415190i 0.978215 + 0.207595i \(0.0665635\pi\)
−0.978215 + 0.207595i \(0.933436\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −912.927 1581.24i −0.362809 0.628404i
\(186\) 0 0
\(187\) −73.7859 42.6003i −0.0288543 0.0166591i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2760.51 1593.78i −1.04578 0.603779i −0.124312 0.992243i \(-0.539673\pi\)
−0.921464 + 0.388464i \(0.873006\pi\)
\(192\) 0 0
\(193\) 475.271 + 823.193i 0.177258 + 0.307019i 0.940940 0.338573i \(-0.109944\pi\)
−0.763683 + 0.645592i \(0.776611\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3589.52i 1.29819i −0.760709 0.649093i \(-0.775149\pi\)
0.760709 0.649093i \(-0.224851\pi\)
\(198\) 0 0
\(199\) −3985.72 + 2301.16i −1.41980 + 0.819722i −0.996281 0.0861652i \(-0.972539\pi\)
−0.423519 + 0.905887i \(0.639205\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −870.731 + 208.640i −0.301051 + 0.0721362i
\(204\) 0 0
\(205\) −123.554 + 214.001i −0.0420944 + 0.0729097i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −82.8106 −0.0274073
\(210\) 0 0
\(211\) −3074.01 −1.00296 −0.501478 0.865171i \(-0.667210\pi\)
−0.501478 + 0.865171i \(0.667210\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −714.422 + 1237.42i −0.226620 + 0.392517i
\(216\) 0 0
\(217\) 1586.36 + 1673.14i 0.496263 + 0.523412i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 195.328 112.772i 0.0594532 0.0343253i
\(222\) 0 0
\(223\) 2057.55i 0.617866i 0.951084 + 0.308933i \(0.0999718\pi\)
−0.951084 + 0.308933i \(0.900028\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 892.967 + 1546.66i 0.261094 + 0.452228i 0.966533 0.256543i \(-0.0825835\pi\)
−0.705439 + 0.708771i \(0.749250\pi\)
\(228\) 0 0
\(229\) −1288.59 743.966i −0.371844 0.214684i 0.302420 0.953175i \(-0.402206\pi\)
−0.674264 + 0.738491i \(0.735539\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −231.289 133.535i −0.0650312 0.0375458i 0.467132 0.884188i \(-0.345287\pi\)
−0.532163 + 0.846642i \(0.678621\pi\)
\(234\) 0 0
\(235\) 351.472 + 608.768i 0.0975639 + 0.168986i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1832.70i 0.496013i 0.968758 + 0.248007i \(0.0797755\pi\)
−0.968758 + 0.248007i \(0.920225\pi\)
\(240\) 0 0
\(241\) 5639.44 3255.93i 1.50734 0.870261i 0.507373 0.861726i \(-0.330617\pi\)
0.999964 0.00853503i \(-0.00271682\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 120.802 2266.96i 0.0315011 0.591147i
\(246\) 0 0
\(247\) 109.609 189.848i 0.0282358 0.0489059i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2590.15 0.651350 0.325675 0.945482i \(-0.394409\pi\)
0.325675 + 0.945482i \(0.394409\pi\)
\(252\) 0 0
\(253\) 62.2996 0.0154812
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2367.41 + 4100.48i −0.574612 + 0.995256i 0.421472 + 0.906841i \(0.361514\pi\)
−0.996084 + 0.0884151i \(0.971820\pi\)
\(258\) 0 0
\(259\) −4898.09 1453.22i −1.17511 0.348644i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1176.48 + 679.239i −0.275835 + 0.159253i −0.631536 0.775346i \(-0.717575\pi\)
0.355701 + 0.934600i \(0.384242\pi\)
\(264\) 0 0
\(265\) 1786.60i 0.414150i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −2517.48 4360.41i −0.570608 0.988323i −0.996504 0.0835501i \(-0.973374\pi\)
0.425895 0.904772i \(-0.359959\pi\)
\(270\) 0 0
\(271\) 1678.51 + 969.091i 0.376245 + 0.217225i 0.676183 0.736733i \(-0.263633\pi\)
−0.299938 + 0.953959i \(0.596966\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −125.617 72.5250i −0.0275454 0.0159033i
\(276\) 0 0
\(277\) −986.169 1708.09i −0.213910 0.370503i 0.739025 0.673678i \(-0.235287\pi\)
−0.952935 + 0.303175i \(0.901953\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 255.262i 0.0541910i 0.999633 + 0.0270955i \(0.00862582\pi\)
−0.999633 + 0.0270955i \(0.991374\pi\)
\(282\) 0 0
\(283\) −181.330 + 104.691i −0.0380882 + 0.0219902i −0.518923 0.854821i \(-0.673667\pi\)
0.480835 + 0.876811i \(0.340334\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 161.123 + 672.424i 0.0331386 + 0.138299i
\(288\) 0 0
\(289\) 1319.21 2284.95i 0.268515 0.465082i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −7355.30 −1.46656 −0.733279 0.679928i \(-0.762011\pi\)
−0.733279 + 0.679928i \(0.762011\pi\)
\(294\) 0 0
\(295\) 1980.18 0.390815
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −82.4603 + 142.826i −0.0159492 + 0.0276248i
\(300\) 0 0
\(301\) 931.657 + 3888.15i 0.178405 + 0.744549i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1935.67 1117.56i 0.363397 0.209807i
\(306\) 0 0
\(307\) 397.297i 0.0738598i 0.999318 + 0.0369299i \(0.0117578\pi\)
−0.999318 + 0.0369299i \(0.988242\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 3349.51 + 5801.52i 0.610717 + 1.05779i 0.991120 + 0.132972i \(0.0424522\pi\)
−0.380402 + 0.924821i \(0.624214\pi\)
\(312\) 0 0
\(313\) −3683.02 2126.39i −0.665100 0.383996i 0.129117 0.991629i \(-0.458786\pi\)
−0.794218 + 0.607633i \(0.792119\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6472.98 + 3737.17i 1.14687 + 0.662147i 0.948123 0.317903i \(-0.102979\pi\)
0.198749 + 0.980050i \(0.436312\pi\)
\(318\) 0 0
\(319\) −43.1840 74.7969i −0.00757944 0.0131280i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2210.77i 0.380837i
\(324\) 0 0
\(325\) 332.536 191.989i 0.0567562 0.0327682i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1885.74 + 559.482i 0.316001 + 0.0937546i
\(330\) 0 0
\(331\) 4036.45 6991.34i 0.670283 1.16096i −0.307541 0.951535i \(-0.599506\pi\)
0.977824 0.209429i \(-0.0671604\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −2497.68 −0.407352
\(336\) 0 0
\(337\) 5669.65 0.916455 0.458228 0.888835i \(-0.348484\pi\)
0.458228 + 0.888835i \(0.348484\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −111.200 + 192.605i −0.0176593 + 0.0305869i
\(342\) 0 0
\(343\) −4119.22 4835.87i −0.648446 0.761261i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 5238.57 3024.49i 0.810436 0.467905i −0.0366712 0.999327i \(-0.511675\pi\)
0.847107 + 0.531422i \(0.178342\pi\)
\(348\) 0 0
\(349\) 492.028i 0.0754660i 0.999288 + 0.0377330i \(0.0120136\pi\)
−0.999288 + 0.0377330i \(0.987986\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 6002.09 + 10395.9i 0.904982 + 1.56748i 0.820941 + 0.571013i \(0.193450\pi\)
0.0840416 + 0.996462i \(0.473217\pi\)
\(354\) 0 0
\(355\) 4681.88 + 2703.08i 0.699967 + 0.404126i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −3458.42 1996.72i −0.508436 0.293545i 0.223755 0.974645i \(-0.428169\pi\)
−0.732190 + 0.681100i \(0.761502\pi\)
\(360\) 0 0
\(361\) −2355.13 4079.20i −0.343363 0.594722i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 4557.65i 0.653584i
\(366\) 0 0
\(367\) 640.131 369.580i 0.0910478 0.0525665i −0.453785 0.891111i \(-0.649927\pi\)
0.544833 + 0.838545i \(0.316593\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −3439.68 3627.86i −0.481346 0.507679i
\(372\) 0 0
\(373\) −6623.43 + 11472.1i −0.919432 + 1.59250i −0.119152 + 0.992876i \(0.538018\pi\)
−0.800280 + 0.599627i \(0.795316\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 228.635 0.0312342
\(378\) 0 0
\(379\) 1420.35 0.192502 0.0962512 0.995357i \(-0.469315\pi\)
0.0962512 + 0.995357i \(0.469315\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 5835.44 10107.3i 0.778530 1.34845i −0.154258 0.988031i \(-0.549299\pi\)
0.932789 0.360424i \(-0.117368\pi\)
\(384\) 0 0
\(385\) 212.953 51.0266i 0.0281898 0.00675470i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 8840.84 5104.26i 1.15231 0.665286i 0.202861 0.979208i \(-0.434976\pi\)
0.949449 + 0.313921i \(0.101643\pi\)
\(390\) 0 0
\(391\) 1663.19i 0.215118i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2032.34 + 3520.11i 0.258881 + 0.448395i
\(396\) 0 0
\(397\) −11903.6 6872.57i −1.50485 0.868827i −0.999984 0.00563049i \(-0.998208\pi\)
−0.504868 0.863196i \(-0.668459\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 11514.5 + 6647.91i 1.43394 + 0.827883i 0.997418 0.0718132i \(-0.0228786\pi\)
0.436517 + 0.899696i \(0.356212\pi\)
\(402\) 0 0
\(403\) −294.372 509.867i −0.0363863 0.0630230i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 492.825i 0.0600207i
\(408\) 0 0
\(409\) 9944.36 5741.38i 1.20224 0.694115i 0.241189 0.970478i \(-0.422463\pi\)
0.961053 + 0.276364i \(0.0891294\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 4020.94 3812.38i 0.479074 0.454225i
\(414\) 0 0
\(415\) 4381.20 7588.46i 0.518228 0.897597i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 9092.21 1.06010 0.530052 0.847965i \(-0.322172\pi\)
0.530052 + 0.847965i \(0.322172\pi\)
\(420\) 0 0
\(421\) −7373.44 −0.853585 −0.426793 0.904349i \(-0.640357\pi\)
−0.426793 + 0.904349i \(0.640357\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1936.17 + 3353.55i −0.220984 + 0.382756i
\(426\) 0 0
\(427\) 1778.96 5996.00i 0.201616 0.679548i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 14205.0 8201.24i 1.58754 0.916566i 0.593827 0.804592i \(-0.297616\pi\)
0.993711 0.111973i \(-0.0357172\pi\)
\(432\) 0 0
\(433\) 5691.74i 0.631703i −0.948809 0.315852i \(-0.897710\pi\)
0.948809 0.315852i \(-0.102290\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −808.267 1399.96i −0.0884775 0.153248i
\(438\) 0 0
\(439\) 8196.36 + 4732.17i 0.891095 + 0.514474i 0.874301 0.485385i \(-0.161321\pi\)
0.0167945 + 0.999859i \(0.494654\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −9130.65 5271.58i −0.979255 0.565373i −0.0772101 0.997015i \(-0.524601\pi\)
−0.902045 + 0.431642i \(0.857935\pi\)
\(444\) 0 0
\(445\) −3179.37 5506.82i −0.338689 0.586626i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 9305.47i 0.978067i 0.872265 + 0.489034i \(0.162650\pi\)
−0.872265 + 0.489034i \(0.837350\pi\)
\(450\) 0 0
\(451\) −57.7621 + 33.3489i −0.00603084 + 0.00348191i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −164.885 + 555.747i −0.0169889 + 0.0572611i
\(456\) 0 0
\(457\) −4589.88 + 7949.91i −0.469815 + 0.813744i −0.999404 0.0345103i \(-0.989013\pi\)
0.529589 + 0.848254i \(0.322346\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 6418.60 0.648469 0.324234 0.945977i \(-0.394893\pi\)
0.324234 + 0.945977i \(0.394893\pi\)
\(462\) 0 0
\(463\) 9649.90 0.968615 0.484307 0.874898i \(-0.339072\pi\)
0.484307 + 0.874898i \(0.339072\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 4082.03 7070.29i 0.404484 0.700587i −0.589777 0.807566i \(-0.700784\pi\)
0.994261 + 0.106979i \(0.0341178\pi\)
\(468\) 0 0
\(469\) −5071.78 + 4808.71i −0.499346 + 0.473445i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −333.997 + 192.833i −0.0324676 + 0.0187452i
\(474\) 0 0
\(475\) 3763.72i 0.363561i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 3688.53 + 6388.72i 0.351844 + 0.609412i 0.986573 0.163324i \(-0.0522214\pi\)
−0.634729 + 0.772735i \(0.718888\pi\)
\(480\) 0 0
\(481\) 1129.83 + 652.308i 0.107101 + 0.0618351i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2576.53 1487.56i −0.241225 0.139271i
\(486\) 0 0
\(487\) −5919.10 10252.2i −0.550760 0.953944i −0.998220 0.0596401i \(-0.981005\pi\)
0.447460 0.894304i \(-0.352329\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 3932.63i 0.361460i 0.983533 + 0.180730i \(0.0578461\pi\)
−0.983533 + 0.180730i \(0.942154\pi\)
\(492\) 0 0
\(493\) −1996.83 + 1152.87i −0.182419 + 0.105320i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 14711.2 3525.01i 1.32774 0.318146i
\(498\) 0 0
\(499\) 7852.94 13601.7i 0.704500 1.22023i −0.262371 0.964967i \(-0.584505\pi\)
0.966872 0.255263i \(-0.0821622\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 1461.52 0.129555 0.0647773 0.997900i \(-0.479366\pi\)
0.0647773 + 0.997900i \(0.479366\pi\)
\(504\) 0 0
\(505\) 2363.08 0.208229
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −3690.38 + 6391.93i −0.321362 + 0.556616i −0.980769 0.195170i \(-0.937474\pi\)
0.659407 + 0.751786i \(0.270807\pi\)
\(510\) 0 0
\(511\) −8774.71 9254.75i −0.759629 0.801186i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −3352.76 + 1935.71i −0.286874 + 0.165627i
\(516\) 0 0
\(517\) 189.735i 0.0161403i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 5116.53 + 8862.09i 0.430248 + 0.745211i 0.996894 0.0787498i \(-0.0250928\pi\)
−0.566646 + 0.823961i \(0.691759\pi\)
\(522\) 0 0
\(523\) 16679.3 + 9629.78i 1.39452 + 0.805126i 0.993812 0.111080i \(-0.0354308\pi\)
0.400708 + 0.916206i \(0.368764\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 5141.90 + 2968.68i 0.425018 + 0.245384i
\(528\) 0 0
\(529\) −5475.43 9483.72i −0.450023 0.779463i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 176.564i 0.0143487i
\(534\) 0 0
\(535\) 7315.11 4223.38i 0.591140 0.341295i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 334.182 513.607i 0.0267054 0.0410438i
\(540\) 0 0
\(541\) −5087.07 + 8811.07i −0.404270 + 0.700217i −0.994236 0.107211i \(-0.965808\pi\)
0.589966 + 0.807428i \(0.299141\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −4214.55 −0.331250
\(546\) 0 0
\(547\) −14637.4 −1.14415 −0.572076 0.820201i \(-0.693862\pi\)
−0.572076 + 0.820201i \(0.693862\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1120.53 + 1940.81i −0.0866354 + 0.150057i
\(552\) 0 0
\(553\) 10904.0 + 3235.13i 0.838492 + 0.248773i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 2573.96 1486.07i 0.195803 0.113047i −0.398894 0.916997i \(-0.630606\pi\)
0.594696 + 0.803951i \(0.297272\pi\)
\(558\) 0 0
\(559\) 1020.94i 0.0772474i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 6713.27 + 11627.7i 0.502541 + 0.870427i 0.999996 + 0.00293687i \(0.000934837\pi\)
−0.497454 + 0.867490i \(0.665732\pi\)
\(564\) 0 0
\(565\) −5512.93 3182.89i −0.410497 0.237001i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 20925.0 + 12081.0i 1.54169 + 0.890094i 0.998732 + 0.0503329i \(0.0160282\pi\)
0.542956 + 0.839761i \(0.317305\pi\)
\(570\) 0 0
\(571\) −2748.17 4759.96i −0.201414 0.348859i 0.747571 0.664182i \(-0.231220\pi\)
−0.948984 + 0.315324i \(0.897887\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2831.50i 0.205359i
\(576\) 0 0
\(577\) 18614.4 10747.0i 1.34303 0.775398i 0.355778 0.934571i \(-0.384216\pi\)
0.987251 + 0.159173i \(0.0508826\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −5713.39 23844.1i −0.407971 1.70262i
\(582\) 0 0
\(583\) 241.114 417.623i 0.0171285 0.0296675i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −15656.5 −1.10087 −0.550437 0.834877i \(-0.685539\pi\)
−0.550437 + 0.834877i \(0.685539\pi\)
\(588\) 0 0
\(589\) 5770.80 0.403704
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −12134.6 + 21017.8i −0.840319 + 1.45547i 0.0493069 + 0.998784i \(0.484299\pi\)
−0.889625 + 0.456691i \(0.849035\pi\)
\(594\) 0 0
\(595\) −1362.24 5685.13i −0.0938595 0.391710i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 11862.8 6848.98i 0.809182 0.467181i −0.0374897 0.999297i \(-0.511936\pi\)
0.846672 + 0.532116i \(0.178603\pi\)
\(600\) 0 0
\(601\) 8670.98i 0.588514i −0.955726 0.294257i \(-0.904928\pi\)
0.955726 0.294257i \(-0.0950721\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −4394.12 7610.84i −0.295283 0.511446i
\(606\) 0 0
\(607\) 10404.7 + 6007.18i 0.695742 + 0.401687i 0.805760 0.592243i \(-0.201757\pi\)
−0.110017 + 0.993930i \(0.535091\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −434.979 251.135i −0.0288009 0.0166282i
\(612\) 0 0
\(613\) −8647.55 14978.0i −0.569773 0.986877i −0.996588 0.0825374i \(-0.973698\pi\)
0.426815 0.904339i \(-0.359636\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 9886.44i 0.645078i 0.946556 + 0.322539i \(0.104536\pi\)
−0.946556 + 0.322539i \(0.895464\pi\)
\(618\) 0 0
\(619\) −8751.96 + 5052.94i −0.568289 + 0.328102i −0.756466 0.654033i \(-0.773076\pi\)
0.188177 + 0.982135i \(0.439742\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −17058.1 5061.00i −1.09698 0.325465i
\(624\) 0 0
\(625\) −558.371 + 967.126i −0.0357357 + 0.0618961i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −13156.8 −0.834014
\(630\) 0 0
\(631\) −22892.4 −1.44427 −0.722133 0.691754i \(-0.756838\pi\)
−0.722133 + 0.691754i \(0.756838\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 476.559 825.424i 0.0297821 0.0515842i
\(636\) 0 0
\(637\) 735.148 + 1445.95i 0.0457263 + 0.0899379i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 12723.7 7346.04i 0.784019 0.452654i −0.0538337 0.998550i \(-0.517144\pi\)
0.837853 + 0.545896i \(0.183811\pi\)
\(642\) 0 0
\(643\) 28388.0i 1.74108i 0.492099 + 0.870539i \(0.336230\pi\)
−0.492099 + 0.870539i \(0.663770\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 15705.6 + 27202.9i 0.954331 + 1.65295i 0.735893 + 0.677098i \(0.236763\pi\)
0.218438 + 0.975851i \(0.429904\pi\)
\(648\) 0 0
\(649\) 462.873 + 267.240i 0.0279959 + 0.0161634i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −20102.2 11606.0i −1.20468 0.695525i −0.243091 0.970003i \(-0.578161\pi\)
−0.961593 + 0.274479i \(0.911495\pi\)
\(654\) 0 0
\(655\) −1231.77 2133.49i −0.0734797 0.127271i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 4092.54i 0.241916i 0.992658 + 0.120958i \(0.0385966\pi\)
−0.992658 + 0.120958i \(0.961403\pi\)
\(660\) 0 0
\(661\) 17750.7 10248.4i 1.04451 0.603050i 0.123405 0.992356i \(-0.460619\pi\)
0.921108 + 0.389306i \(0.127285\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −3909.47 4123.34i −0.227974 0.240446i
\(666\) 0 0
\(667\) 842.989 1460.10i 0.0489365 0.0847606i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 603.292 0.0347091
\(672\) 0 0
\(673\) 11264.6 0.645198 0.322599 0.946536i \(-0.395443\pi\)
0.322599 + 0.946536i \(0.395443\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 7916.23 13711.3i 0.449403 0.778388i −0.548945 0.835859i \(-0.684970\pi\)
0.998347 + 0.0574706i \(0.0183035\pi\)
\(678\) 0 0
\(679\) −8095.84 + 1939.88i −0.457570 + 0.109640i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 10545.0 6088.16i 0.590766 0.341079i −0.174634 0.984633i \(-0.555874\pi\)
0.765400 + 0.643554i \(0.222541\pi\)
\(684\) 0 0
\(685\) 3659.40i 0.204114i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 638.283 + 1105.54i 0.0352927 + 0.0611287i
\(690\) 0 0
\(691\) −7657.82 4421.24i −0.421588 0.243404i 0.274169 0.961682i \(-0.411597\pi\)
−0.695756 + 0.718278i \(0.744931\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −14482.9 8361.68i −0.790455 0.456369i
\(696\) 0 0
\(697\) 890.305 + 1542.05i 0.0483826 + 0.0838012i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 22086.4i 1.19000i −0.803726 0.595000i \(-0.797152\pi\)
0.803726 0.595000i \(-0.202848\pi\)
\(702\) 0 0
\(703\) −11074.5 + 6393.85i −0.594142 + 0.343028i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 4798.47 4549.57i 0.255255 0.242015i
\(708\) 0 0
\(709\) −14042.2 + 24321.9i −0.743818 + 1.28833i 0.206927 + 0.978356i \(0.433654\pi\)
−0.950745 + 0.309974i \(0.899680\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −4341.45 −0.228035
\(714\) 0 0
\(715\) −55.9168 −0.00292471
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 2227.62 3858.36i 0.115544 0.200129i −0.802453 0.596715i \(-0.796472\pi\)
0.917997 + 0.396587i \(0.129805\pi\)
\(720\) 0 0
\(721\) −3081.32 + 10385.6i −0.159160 + 0.536450i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −3399.50 + 1962.70i −0.174144 + 0.100542i
\(726\) 0 0
\(727\) 11915.8i 0.607884i 0.952690 + 0.303942i \(0.0983030\pi\)
−0.952690 + 0.303942i \(0.901697\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 5148.00 + 8916.60i 0.260473 + 0.451152i
\(732\) 0 0
\(733\) 6157.69 + 3555.14i 0.310286 + 0.179143i 0.647054 0.762444i \(-0.276001\pi\)
−0.336769 + 0.941587i \(0.609334\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −583.841 337.081i −0.0291805 0.0168474i
\(738\) 0 0
\(739\) −15356.0 26597.3i −0.764382 1.32395i −0.940573 0.339593i \(-0.889711\pi\)
0.176190 0.984356i \(-0.443623\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 14280.3i 0.705104i 0.935792 + 0.352552i \(0.114686\pi\)
−0.935792 + 0.352552i \(0.885314\pi\)
\(744\) 0 0
\(745\) 15778.7 9109.87i 0.775958 0.448000i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 6722.89 22659.6i 0.327969 1.10542i
\(750\) 0 0
\(751\) −9233.47 + 15992.8i −0.448647 + 0.777080i −0.998298 0.0583146i \(-0.981427\pi\)
0.549651 + 0.835394i \(0.314761\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −5229.31 −0.252071
\(756\) 0 0
\(757\) 9297.14 0.446381 0.223190 0.974775i \(-0.428353\pi\)
0.223190 + 0.974775i \(0.428353\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1751.42 + 3033.56i −0.0834285 + 0.144502i −0.904720 0.426006i \(-0.859920\pi\)
0.821292 + 0.570508i \(0.193254\pi\)
\(762\) 0 0
\(763\) −8558.05 + 8114.15i −0.406058 + 0.384996i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1225.33 + 707.442i −0.0576844 + 0.0333041i
\(768\) 0 0
\(769\) 16857.8i 0.790517i 0.918570 + 0.395258i \(0.129345\pi\)
−0.918570 + 0.395258i \(0.870655\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −7410.77 12835.8i −0.344821 0.597248i 0.640500 0.767958i \(-0.278727\pi\)
−0.985321 + 0.170710i \(0.945394\pi\)
\(774\) 0 0
\(775\) 8753.83 + 5054.02i 0.405738 + 0.234253i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1498.80 + 865.330i 0.0689344 + 0.0397993i
\(780\) 0 0
\(781\) 729.602 + 1263.71i 0.0334279 + 0.0578989i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 6657.39i 0.302691i
\(786\) 0 0
\(787\) −7423.05 + 4285.70i −0.336218 + 0.194115i −0.658598 0.752495i \(-0.728850\pi\)
0.322381 + 0.946610i \(0.395517\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −17322.5 + 4150.72i −0.778655 + 0.186577i
\(792\) 0 0
\(793\) −798.523 + 1383.08i −0.0357584 + 0.0619353i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −44804.8 −1.99130 −0.995651 0.0931611i \(-0.970303\pi\)
−0.995651 + 0.0931611i \(0.970303\pi\)
\(798\) 0 0
\(799\) 5065.29 0.224277
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 615.088 1065.36i 0.0270311 0.0468193i
\(804\) 0 0
\(805\) 2941.15 + 3102.05i 0.128772 + 0.135817i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −482.120 + 278.352i −0.0209523 + 0.0120968i −0.510440 0.859914i \(-0.670517\pi\)
0.489487 + 0.872010i \(0.337184\pi\)
\(810\) 0 0
\(811\) 16892.8i 0.731426i 0.930728 + 0.365713i \(0.119175\pi\)
−0.930728 + 0.365713i \(0.880825\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 58.0074 + 100.472i 0.00249314 + 0.00431825i
\(816\) 0 0
\(817\) 8666.47 + 5003.59i 0.371115 + 0.214264i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −4445.18 2566.43i −0.188962 0.109097i 0.402535 0.915405i \(-0.368129\pi\)
−0.591497 + 0.806308i \(0.701463\pi\)
\(822\) 0 0
\(823\) 20153.2 + 34906.4i 0.853581 + 1.47845i 0.877955 + 0.478743i \(0.158907\pi\)
−0.0243743 + 0.999703i \(0.507759\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 24795.5i 1.04259i 0.853375 + 0.521297i \(0.174552\pi\)
−0.853375 + 0.521297i \(0.825448\pi\)
\(828\) 0 0
\(829\) −413.706 + 238.854i −0.0173325 + 0.0100069i −0.508641 0.860979i \(-0.669852\pi\)
0.491309 + 0.870985i \(0.336519\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −13711.6 8921.53i −0.570322 0.371084i
\(834\) 0 0
\(835\) 647.509 1121.52i 0.0268359 0.0464811i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −46068.4 −1.89566 −0.947829 0.318780i \(-0.896727\pi\)
−0.947829 + 0.318780i \(0.896727\pi\)
\(840\) 0 0
\(841\) 22051.7 0.904165
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −7196.52 + 12464.7i −0.292980 + 0.507456i
\(846\) 0 0
\(847\) −23575.6 6994.67i −0.956396 0.283754i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 8331.48 4810.18i 0.335605 0.193761i
\(852\) 0 0
\(853\) 5319.60i 0.213528i 0.994284 + 0.106764i \(0.0340490\pi\)
−0.994284 + 0.106764i \(0.965951\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 18690.5 + 32372.9i 0.744989 + 1.29036i 0.950200 + 0.311641i \(0.100879\pi\)
−0.205211 + 0.978718i \(0.565788\pi\)
\(858\) 0 0
\(859\) 32236.0 + 18611.5i 1.28042 + 0.739249i 0.976925 0.213585i \(-0.0685139\pi\)
0.303493 + 0.952834i \(0.401847\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −8993.16 5192.20i −0.354728 0.204803i 0.312037 0.950070i \(-0.398989\pi\)
−0.666766 + 0.745267i \(0.732322\pi\)
\(864\) 0 0
\(865\) −2785.78 4825.12i −0.109502 0.189664i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 1097.12i 0.0428275i
\(870\) 0 0
\(871\) 1545.55 892.326i 0.0601253 0.0347133i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −5889.52 24579.2i −0.227545 0.949631i
\(876\) 0 0
\(877\) −5046.94 + 8741.56i −0.194325 + 0.336581i −0.946679 0.322178i \(-0.895585\pi\)
0.752354 + 0.658759i \(0.228918\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −27322.1 −1.04484 −0.522420 0.852688i \(-0.674971\pi\)
−0.522420 + 0.852688i \(0.674971\pi\)
\(882\) 0 0
\(883\) −638.558 −0.0243366 −0.0121683 0.999926i \(-0.503873\pi\)
−0.0121683 + 0.999926i \(0.503873\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −4090.12 + 7084.29i −0.154828 + 0.268170i −0.932996 0.359885i \(-0.882816\pi\)
0.778168 + 0.628056i \(0.216149\pi\)
\(888\) 0 0
\(889\) −621.466 2593.61i −0.0234458 0.0978480i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 4263.62 2461.60i 0.159772 0.0922444i
\(894\) 0 0
\(895\) 5858.38i 0.218798i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 3009.35 + 5212.35i 0.111643 + 0.193372i
\(900\) 0 0
\(901\) −11149.1 6436.95i −0.412243 0.238009i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −5795.11 3345.81i −0.212857 0.122893i
\(906\) 0 0
\(907\) −4866.48 8429.00i −0.178158 0.308578i 0.763092 0.646290i \(-0.223680\pi\)
−0.941250 + 0.337712i \(0.890347\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 12619.6i 0.458953i −0.973314 0.229477i \(-0.926299\pi\)
0.973314 0.229477i \(-0.0737015\pi\)
\(912\) 0 0
\(913\) 2048.24 1182.55i 0.0742462 0.0428660i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −6608.77 1960.76i −0.237994 0.0706108i
\(918\) 0 0
\(919\) −12207.5 + 21144.1i −0.438183 + 0.758954i −0.997549 0.0699658i \(-0.977711\pi\)
0.559367 + 0.828920i \(0.311044\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −3862.84 −0.137754
\(924\) 0 0
\(925\) −22398.8 −0.796180
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −9360.78 + 16213.4i −0.330589 + 0.572597i −0.982628 0.185589i \(-0.940581\pi\)
0.652038 + 0.758186i \(0.273914\pi\)
\(930\) 0 0
\(931\) −15877.1 846.061i −0.558916 0.0297836i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 488.360 281.955i 0.0170814 0.00986193i
\(936\) 0 0
\(937\) 19693.0i 0.686598i 0.939226 + 0.343299i \(0.111544\pi\)
−0.939226 + 0.343299i \(0.888456\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 1511.66 + 2618.27i 0.0523685 + 0.0907049i 0.891021 0.453961i \(-0.149990\pi\)
−0.838653 + 0.544666i \(0.816656\pi\)
\(942\) 0 0
\(943\) −1127.57 651.000i −0.0389380 0.0224809i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −34975.0 20192.8i −1.20014 0.692903i −0.239556 0.970882i \(-0.577002\pi\)
−0.960587 + 0.277979i \(0.910335\pi\)
\(948\) 0 0
\(949\) 1628.27 + 2820.25i 0.0556965 + 0.0964692i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 17126.4i 0.582137i 0.956702 + 0.291069i \(0.0940108\pi\)
−0.956702 + 0.291069i \(0.905989\pi\)
\(954\) 0 0
\(955\) 18270.7 10548.6i 0.619085 0.357429i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −7045.33 7430.76i −0.237232 0.250210i
\(960\) 0 0
\(961\) −7146.32 + 12377.8i −0.239882 + 0.415488i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −6291.26 −0.209868
\(966\) 0 0
\(967\) 50418.3 1.67667 0.838336 0.545154i \(-0.183529\pi\)
0.838336 + 0.545154i \(0.183529\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −25399.4 + 43993.0i −0.839448 + 1.45397i 0.0509082 + 0.998703i \(0.483788\pi\)
−0.890357 + 0.455264i \(0.849545\pi\)
\(972\) 0 0
\(973\) −45507.4 + 10904.2i −1.49938 + 0.359274i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 20845.4 12035.1i 0.682605 0.394102i −0.118231 0.992986i \(-0.537722\pi\)
0.800836 + 0.598884i \(0.204389\pi\)
\(978\) 0 0
\(979\) 1716.32i 0.0560303i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 2209.58 + 3827.10i 0.0716933 + 0.124176i 0.899644 0.436625i \(-0.143826\pi\)
−0.827950 + 0.560802i \(0.810493\pi\)
\(984\) 0 0
\(985\) 20574.7 + 11878.8i 0.665547 + 0.384254i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −6519.91 3764.27i −0.209627 0.121028i
\(990\) 0 0
\(991\) −18648.8 32300.6i −0.597777 1.03538i −0.993148 0.116859i \(-0.962717\pi\)
0.395371 0.918521i \(-0.370616\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 30460.9i 0.970528i
\(996\) 0 0
\(997\) −9609.73 + 5548.18i −0.305259 + 0.176241i −0.644803 0.764349i \(-0.723061\pi\)
0.339544 + 0.940590i \(0.389727\pi\)
\(998\) 0 0
\(999\) 0 0
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 1008.4.bt.d.593.9 48
3.2 odd 2 inner 1008.4.bt.d.593.16 48
4.3 odd 2 504.4.bl.a.89.9 yes 48
7.3 odd 6 inner 1008.4.bt.d.17.16 48
12.11 even 2 504.4.bl.a.89.16 yes 48
21.17 even 6 inner 1008.4.bt.d.17.9 48
28.3 even 6 504.4.bl.a.17.16 yes 48
84.59 odd 6 504.4.bl.a.17.9 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.4.bl.a.17.9 48 84.59 odd 6
504.4.bl.a.17.16 yes 48 28.3 even 6
504.4.bl.a.89.9 yes 48 4.3 odd 2
504.4.bl.a.89.16 yes 48 12.11 even 2
1008.4.bt.d.17.9 48 21.17 even 6 inner
1008.4.bt.d.17.16 48 7.3 odd 6 inner
1008.4.bt.d.593.9 48 1.1 even 1 trivial
1008.4.bt.d.593.16 48 3.2 odd 2 inner