Properties

Label 900.3.y.a.89.16
Level $900$
Weight $3$
Character 900.89
Analytic conductor $24.523$
Analytic rank $0$
Dimension $80$
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] = [900,3,Mod(89,900)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(900, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 5, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("900.89");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 900.y (of order \(10\), degree \(4\), 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: \(24.5232237924\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 89.16
Character \(\chi\) \(=\) 900.89
Dual form 900.3.y.a.809.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.94179 - 3.07609i) q^{5} +7.41454i q^{7} +O(q^{10})\) \(q+(3.94179 - 3.07609i) q^{5} +7.41454i q^{7} +(-11.4971 - 15.8244i) q^{11} +(-4.29536 + 5.91205i) q^{13} +(8.99059 + 27.6702i) q^{17} +(9.64430 + 29.6821i) q^{19} +(-13.1297 + 9.53925i) q^{23} +(6.07535 - 24.2506i) q^{25} +(43.8931 + 14.2617i) q^{29} +(-1.23512 - 3.80131i) q^{31} +(22.8078 + 29.2265i) q^{35} +(-11.5940 + 15.9578i) q^{37} +(23.4213 - 32.2366i) q^{41} +9.31409i q^{43} +(-6.13800 + 18.8908i) q^{47} -5.97546 q^{49} +(-17.5851 + 54.1214i) q^{53} +(-93.9964 - 27.0103i) q^{55} +(41.9182 - 57.6954i) q^{59} +(-53.9280 + 39.1810i) q^{61} +(1.25462 + 36.5170i) q^{65} +(-100.605 + 32.6887i) q^{67} +(79.5907 + 25.8606i) q^{71} +(50.2620 + 69.1797i) q^{73} +(117.331 - 85.2458i) q^{77} +(22.4848 - 69.2010i) q^{79} +(-15.0766 - 46.4011i) q^{83} +(120.555 + 81.4141i) q^{85} +(74.8317 + 102.997i) q^{89} +(-43.8352 - 31.8481i) q^{91} +(129.321 + 87.3338i) q^{95} +(141.583 + 46.0030i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q+O(q^{10}) \) Copy content Toggle raw display \( 80 q + 60 q^{19} + 56 q^{25} - 120 q^{31} + 20 q^{37} - 680 q^{49} - 56 q^{55} - 80 q^{61} - 280 q^{67} - 360 q^{73} + 40 q^{79} + 192 q^{85} + 140 q^{91} - 40 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(451\) \(577\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{3}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 3.94179 3.07609i 0.788357 0.615218i
\(6\) 0 0
\(7\) 7.41454i 1.05922i 0.848241 + 0.529610i \(0.177662\pi\)
−0.848241 + 0.529610i \(0.822338\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −11.4971 15.8244i −1.04519 1.43858i −0.892905 0.450246i \(-0.851336\pi\)
−0.152286 0.988336i \(-0.548664\pi\)
\(12\) 0 0
\(13\) −4.29536 + 5.91205i −0.330412 + 0.454773i −0.941610 0.336704i \(-0.890688\pi\)
0.611198 + 0.791477i \(0.290688\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 8.99059 + 27.6702i 0.528858 + 1.62766i 0.756558 + 0.653927i \(0.226880\pi\)
−0.227700 + 0.973731i \(0.573120\pi\)
\(18\) 0 0
\(19\) 9.64430 + 29.6821i 0.507595 + 1.56222i 0.796364 + 0.604817i \(0.206754\pi\)
−0.288769 + 0.957399i \(0.593246\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −13.1297 + 9.53925i −0.570855 + 0.414750i −0.835416 0.549619i \(-0.814773\pi\)
0.264561 + 0.964369i \(0.414773\pi\)
\(24\) 0 0
\(25\) 6.07535 24.2506i 0.243014 0.970023i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 43.8931 + 14.2617i 1.51356 + 0.491784i 0.943937 0.330125i \(-0.107091\pi\)
0.569619 + 0.821909i \(0.307091\pi\)
\(30\) 0 0
\(31\) −1.23512 3.80131i −0.0398426 0.122623i 0.929157 0.369686i \(-0.120535\pi\)
−0.968999 + 0.247063i \(0.920535\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 22.8078 + 29.2265i 0.651651 + 0.835044i
\(36\) 0 0
\(37\) −11.5940 + 15.9578i −0.313351 + 0.431291i −0.936423 0.350874i \(-0.885885\pi\)
0.623071 + 0.782165i \(0.285885\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 23.4213 32.2366i 0.571251 0.786259i −0.421451 0.906851i \(-0.638479\pi\)
0.992702 + 0.120592i \(0.0384792\pi\)
\(42\) 0 0
\(43\) 9.31409i 0.216607i 0.994118 + 0.108303i \(0.0345418\pi\)
−0.994118 + 0.108303i \(0.965458\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.13800 + 18.8908i −0.130596 + 0.401932i −0.994879 0.101073i \(-0.967772\pi\)
0.864283 + 0.503005i \(0.167772\pi\)
\(48\) 0 0
\(49\) −5.97546 −0.121948
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −17.5851 + 54.1214i −0.331795 + 1.02116i 0.636485 + 0.771289i \(0.280388\pi\)
−0.968280 + 0.249870i \(0.919612\pi\)
\(54\) 0 0
\(55\) −93.9964 27.0103i −1.70903 0.491096i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 41.9182 57.6954i 0.710477 0.977888i −0.289309 0.957236i \(-0.593426\pi\)
0.999787 0.0206524i \(-0.00657435\pi\)
\(60\) 0 0
\(61\) −53.9280 + 39.1810i −0.884065 + 0.642311i −0.934324 0.356425i \(-0.883995\pi\)
0.0502585 + 0.998736i \(0.483995\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.25462 + 36.5170i 0.0193018 + 0.561799i
\(66\) 0 0
\(67\) −100.605 + 32.6887i −1.50157 + 0.487891i −0.940476 0.339859i \(-0.889621\pi\)
−0.561097 + 0.827750i \(0.689621\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 79.5907 + 25.8606i 1.12100 + 0.364233i 0.810147 0.586226i \(-0.199387\pi\)
0.310848 + 0.950460i \(0.399387\pi\)
\(72\) 0 0
\(73\) 50.2620 + 69.1797i 0.688520 + 0.947667i 0.999997 0.00258691i \(-0.000823440\pi\)
−0.311476 + 0.950254i \(0.600823\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 117.331 85.2458i 1.52378 1.10709i
\(78\) 0 0
\(79\) 22.4848 69.2010i 0.284617 0.875962i −0.701896 0.712280i \(-0.747663\pi\)
0.986513 0.163682i \(-0.0523372\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −15.0766 46.4011i −0.181646 0.559049i 0.818228 0.574893i \(-0.194956\pi\)
−0.999874 + 0.0158440i \(0.994956\pi\)
\(84\) 0 0
\(85\) 120.555 + 81.4141i 1.41829 + 0.957813i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 74.8317 + 102.997i 0.840805 + 1.15727i 0.985814 + 0.167839i \(0.0536789\pi\)
−0.145009 + 0.989430i \(0.546321\pi\)
\(90\) 0 0
\(91\) −43.8352 31.8481i −0.481705 0.349979i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 129.321 + 87.3338i 1.36127 + 0.919303i
\(96\) 0 0
\(97\) 141.583 + 46.0030i 1.45962 + 0.474258i 0.927953 0.372698i \(-0.121567\pi\)
0.531663 + 0.846956i \(0.321567\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 56.9546i 0.563907i 0.959428 + 0.281954i \(0.0909824\pi\)
−0.959428 + 0.281954i \(0.909018\pi\)
\(102\) 0 0
\(103\) 166.959 + 54.2484i 1.62096 + 0.526683i 0.972169 0.234280i \(-0.0752732\pi\)
0.648795 + 0.760963i \(0.275273\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −27.6818 −0.258708 −0.129354 0.991598i \(-0.541290\pi\)
−0.129354 + 0.991598i \(0.541290\pi\)
\(108\) 0 0
\(109\) −119.820 87.0542i −1.09926 0.798663i −0.118325 0.992975i \(-0.537752\pi\)
−0.980940 + 0.194312i \(0.937752\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 75.5907 + 54.9198i 0.668944 + 0.486016i 0.869672 0.493631i \(-0.164331\pi\)
−0.200728 + 0.979647i \(0.564331\pi\)
\(114\) 0 0
\(115\) −22.4107 + 77.9897i −0.194876 + 0.678171i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −205.162 + 66.6611i −1.72405 + 0.560177i
\(120\) 0 0
\(121\) −80.8373 + 248.792i −0.668077 + 2.05613i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −50.6492 114.279i −0.405193 0.914231i
\(126\) 0 0
\(127\) −81.9260 112.762i −0.645087 0.887886i 0.353787 0.935326i \(-0.384894\pi\)
−0.998874 + 0.0474399i \(0.984894\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −87.3442 + 28.3798i −0.666749 + 0.216640i −0.622785 0.782393i \(-0.713999\pi\)
−0.0439645 + 0.999033i \(0.513999\pi\)
\(132\) 0 0
\(133\) −220.079 + 71.5081i −1.65473 + 0.537655i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −5.43646 3.94982i −0.0396822 0.0288308i 0.567767 0.823189i \(-0.307807\pi\)
−0.607450 + 0.794358i \(0.707807\pi\)
\(138\) 0 0
\(139\) −93.1731 + 67.6942i −0.670310 + 0.487009i −0.870129 0.492824i \(-0.835965\pi\)
0.199819 + 0.979833i \(0.435965\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 142.939 0.999573
\(144\) 0 0
\(145\) 216.888 78.8024i 1.49578 0.543465i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 91.4528i 0.613777i −0.951745 0.306889i \(-0.900712\pi\)
0.951745 0.306889i \(-0.0992879\pi\)
\(150\) 0 0
\(151\) −83.0238 −0.549827 −0.274913 0.961469i \(-0.588649\pi\)
−0.274913 + 0.961469i \(0.588649\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −16.5618 11.1846i −0.106850 0.0721588i
\(156\) 0 0
\(157\) 105.588i 0.672535i −0.941766 0.336268i \(-0.890835\pi\)
0.941766 0.336268i \(-0.109165\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −70.7292 97.3504i −0.439312 0.604661i
\(162\) 0 0
\(163\) −148.647 + 204.594i −0.911942 + 1.25518i 0.0545570 + 0.998511i \(0.482625\pi\)
−0.966499 + 0.256670i \(0.917375\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 68.8019 + 211.750i 0.411987 + 1.26797i 0.914918 + 0.403640i \(0.132255\pi\)
−0.502930 + 0.864327i \(0.667745\pi\)
\(168\) 0 0
\(169\) 35.7216 + 109.940i 0.211370 + 0.650531i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −50.1311 + 36.4224i −0.289775 + 0.210534i −0.723170 0.690670i \(-0.757316\pi\)
0.433395 + 0.901204i \(0.357316\pi\)
\(174\) 0 0
\(175\) 179.807 + 45.0460i 1.02747 + 0.257406i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 20.7014 + 6.72629i 0.115650 + 0.0375770i 0.366270 0.930508i \(-0.380635\pi\)
−0.250620 + 0.968085i \(0.580635\pi\)
\(180\) 0 0
\(181\) −6.60737 20.3354i −0.0365048 0.112350i 0.931144 0.364653i \(-0.118812\pi\)
−0.967648 + 0.252302i \(0.918812\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 3.38646 + 98.5663i 0.0183052 + 0.532791i
\(186\) 0 0
\(187\) 334.499 460.398i 1.78876 2.46202i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −59.5744 + 81.9971i −0.311908 + 0.429304i −0.935975 0.352066i \(-0.885479\pi\)
0.624067 + 0.781371i \(0.285479\pi\)
\(192\) 0 0
\(193\) 300.637i 1.55770i −0.627208 0.778852i \(-0.715802\pi\)
0.627208 0.778852i \(-0.284198\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 53.3613 164.229i 0.270870 0.833651i −0.719413 0.694582i \(-0.755589\pi\)
0.990283 0.139069i \(-0.0444109\pi\)
\(198\) 0 0
\(199\) −294.792 −1.48137 −0.740684 0.671854i \(-0.765498\pi\)
−0.740684 + 0.671854i \(0.765498\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −105.744 + 325.447i −0.520908 + 1.60319i
\(204\) 0 0
\(205\) −6.84106 199.116i −0.0333710 0.971297i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 358.820 493.874i 1.71684 2.36303i
\(210\) 0 0
\(211\) 50.9872 37.0443i 0.241645 0.175566i −0.460371 0.887727i \(-0.652284\pi\)
0.702016 + 0.712161i \(0.252284\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 28.6510 + 36.7142i 0.133260 + 0.170764i
\(216\) 0 0
\(217\) 28.1850 9.15786i 0.129885 0.0422021i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −202.205 65.7005i −0.914957 0.297287i
\(222\) 0 0
\(223\) 109.047 + 150.091i 0.489002 + 0.673053i 0.980204 0.197993i \(-0.0634422\pi\)
−0.491202 + 0.871046i \(0.663442\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −164.163 + 119.271i −0.723183 + 0.525423i −0.887400 0.461001i \(-0.847490\pi\)
0.164217 + 0.986424i \(0.447490\pi\)
\(228\) 0 0
\(229\) 74.7205 229.966i 0.326291 1.00422i −0.644564 0.764550i \(-0.722961\pi\)
0.970855 0.239669i \(-0.0770389\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −133.667 411.386i −0.573680 1.76560i −0.640632 0.767848i \(-0.721328\pi\)
0.0669527 0.997756i \(-0.478672\pi\)
\(234\) 0 0
\(235\) 33.9152 + 93.3446i 0.144320 + 0.397211i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −131.387 180.839i −0.549736 0.756647i 0.440240 0.897880i \(-0.354893\pi\)
−0.989976 + 0.141233i \(0.954893\pi\)
\(240\) 0 0
\(241\) 154.774 + 112.450i 0.642217 + 0.466598i 0.860611 0.509262i \(-0.170082\pi\)
−0.218394 + 0.975861i \(0.570082\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −23.5540 + 18.3811i −0.0961387 + 0.0750247i
\(246\) 0 0
\(247\) −216.908 70.4777i −0.878170 0.285335i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 381.283i 1.51906i −0.650475 0.759528i \(-0.725430\pi\)
0.650475 0.759528i \(-0.274570\pi\)
\(252\) 0 0
\(253\) 301.906 + 98.0952i 1.19330 + 0.387728i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 461.439 1.79548 0.897742 0.440522i \(-0.145207\pi\)
0.897742 + 0.440522i \(0.145207\pi\)
\(258\) 0 0
\(259\) −118.320 85.9642i −0.456833 0.331908i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −369.060 268.138i −1.40327 1.01954i −0.994258 0.107008i \(-0.965873\pi\)
−0.409013 0.912528i \(-0.634127\pi\)
\(264\) 0 0
\(265\) 97.1655 + 267.428i 0.366662 + 1.00916i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −93.6036 + 30.4137i −0.347969 + 0.113062i −0.477787 0.878476i \(-0.658561\pi\)
0.129818 + 0.991538i \(0.458561\pi\)
\(270\) 0 0
\(271\) 60.5821 186.453i 0.223550 0.688017i −0.774885 0.632102i \(-0.782192\pi\)
0.998436 0.0559149i \(-0.0178075\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −453.600 + 182.672i −1.64945 + 0.664263i
\(276\) 0 0
\(277\) −104.438 143.746i −0.377032 0.518940i 0.577763 0.816204i \(-0.303926\pi\)
−0.954795 + 0.297264i \(0.903926\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −59.9546 + 19.4804i −0.213362 + 0.0693254i −0.413748 0.910392i \(-0.635780\pi\)
0.200386 + 0.979717i \(0.435780\pi\)
\(282\) 0 0
\(283\) 316.388 102.801i 1.11798 0.363254i 0.308983 0.951067i \(-0.400011\pi\)
0.808996 + 0.587814i \(0.200011\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 239.020 + 173.658i 0.832822 + 0.605081i
\(288\) 0 0
\(289\) −451.003 + 327.673i −1.56056 + 1.13382i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −307.520 −1.04956 −0.524778 0.851239i \(-0.675852\pi\)
−0.524778 + 0.851239i \(0.675852\pi\)
\(294\) 0 0
\(295\) −12.2438 356.367i −0.0415043 1.20802i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 118.598i 0.396648i
\(300\) 0 0
\(301\) −69.0597 −0.229434
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −92.0484 + 320.330i −0.301798 + 1.05026i
\(306\) 0 0
\(307\) 26.6987i 0.0869666i −0.999054 0.0434833i \(-0.986154\pi\)
0.999054 0.0434833i \(-0.0138455\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −127.356 175.290i −0.409504 0.563634i 0.553594 0.832787i \(-0.313256\pi\)
−0.963097 + 0.269153i \(0.913256\pi\)
\(312\) 0 0
\(313\) 19.9638 27.4777i 0.0637819 0.0877883i −0.775934 0.630814i \(-0.782721\pi\)
0.839716 + 0.543025i \(0.182721\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −39.3540 121.119i −0.124145 0.382079i 0.869599 0.493758i \(-0.164377\pi\)
−0.993744 + 0.111679i \(0.964377\pi\)
\(318\) 0 0
\(319\) −278.960 858.551i −0.874483 2.69138i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −734.602 + 533.719i −2.27431 + 1.65238i
\(324\) 0 0
\(325\) 117.275 + 140.083i 0.360846 + 0.431024i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −140.067 45.5105i −0.425735 0.138330i
\(330\) 0 0
\(331\) 125.378 + 385.875i 0.378786 + 1.16578i 0.940888 + 0.338717i \(0.109993\pi\)
−0.562102 + 0.827068i \(0.690007\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −296.012 + 438.323i −0.883617 + 1.30843i
\(336\) 0 0
\(337\) 29.2691 40.2855i 0.0868520 0.119542i −0.763380 0.645950i \(-0.776462\pi\)
0.850232 + 0.526408i \(0.176462\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −45.9532 + 63.2492i −0.134760 + 0.185481i
\(342\) 0 0
\(343\) 319.007i 0.930051i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 115.083 354.189i 0.331651 1.02072i −0.636697 0.771114i \(-0.719700\pi\)
0.968348 0.249603i \(-0.0803002\pi\)
\(348\) 0 0
\(349\) 513.030 1.47000 0.735000 0.678067i \(-0.237182\pi\)
0.735000 + 0.678067i \(0.237182\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 114.892 353.603i 0.325474 1.00171i −0.645752 0.763548i \(-0.723456\pi\)
0.971226 0.238160i \(-0.0765441\pi\)
\(354\) 0 0
\(355\) 393.279 142.891i 1.10783 0.402510i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 143.229 197.138i 0.398968 0.549132i −0.561517 0.827465i \(-0.689782\pi\)
0.960485 + 0.278333i \(0.0897820\pi\)
\(360\) 0 0
\(361\) −495.960 + 360.336i −1.37385 + 0.998160i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 410.925 + 118.081i 1.12582 + 0.323510i
\(366\) 0 0
\(367\) 527.034 171.244i 1.43606 0.466604i 0.515393 0.856954i \(-0.327646\pi\)
0.920667 + 0.390350i \(0.127646\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −401.286 130.386i −1.08163 0.351444i
\(372\) 0 0
\(373\) 192.939 + 265.558i 0.517263 + 0.711952i 0.985123 0.171851i \(-0.0549748\pi\)
−0.467860 + 0.883803i \(0.654975\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −272.853 + 198.239i −0.723748 + 0.525833i
\(378\) 0 0
\(379\) −17.1823 + 52.8816i −0.0453358 + 0.139529i −0.971162 0.238420i \(-0.923371\pi\)
0.925826 + 0.377949i \(0.123371\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 89.5142 + 275.496i 0.233719 + 0.719312i 0.997289 + 0.0735870i \(0.0234446\pi\)
−0.763570 + 0.645725i \(0.776555\pi\)
\(384\) 0 0
\(385\) 200.269 696.940i 0.520179 1.81023i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −26.8740 36.9888i −0.0690847 0.0950869i 0.773076 0.634313i \(-0.218717\pi\)
−0.842161 + 0.539226i \(0.818717\pi\)
\(390\) 0 0
\(391\) −381.996 277.537i −0.976972 0.709812i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −124.238 341.941i −0.314527 0.865673i
\(396\) 0 0
\(397\) 20.7843 + 6.75323i 0.0523534 + 0.0170107i 0.335077 0.942191i \(-0.391238\pi\)
−0.282723 + 0.959202i \(0.591238\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 693.977i 1.73062i −0.501240 0.865308i \(-0.667123\pi\)
0.501240 0.865308i \(-0.332877\pi\)
\(402\) 0 0
\(403\) 27.7789 + 9.02590i 0.0689302 + 0.0223968i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 385.820 0.947960
\(408\) 0 0
\(409\) 155.964 + 113.315i 0.381331 + 0.277053i 0.761894 0.647702i \(-0.224270\pi\)
−0.380563 + 0.924755i \(0.624270\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 427.785 + 310.804i 1.03580 + 0.752552i
\(414\) 0 0
\(415\) −202.163 136.526i −0.487139 0.328979i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 78.4830 25.5007i 0.187310 0.0608608i −0.213860 0.976864i \(-0.568604\pi\)
0.401170 + 0.916004i \(0.368604\pi\)
\(420\) 0 0
\(421\) −199.344 + 613.519i −0.473502 + 1.45729i 0.374466 + 0.927241i \(0.377826\pi\)
−0.847967 + 0.530048i \(0.822174\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 725.639 49.9207i 1.70739 0.117460i
\(426\) 0 0
\(427\) −290.509 399.851i −0.680349 0.936420i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −55.8508 + 18.1470i −0.129584 + 0.0421045i −0.373091 0.927795i \(-0.621702\pi\)
0.243507 + 0.969899i \(0.421702\pi\)
\(432\) 0 0
\(433\) −23.0577 + 7.49189i −0.0532510 + 0.0173023i −0.335521 0.942033i \(-0.608912\pi\)
0.282270 + 0.959335i \(0.408912\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −409.771 297.716i −0.937692 0.681273i
\(438\) 0 0
\(439\) −89.7741 + 65.2247i −0.204497 + 0.148576i −0.685320 0.728242i \(-0.740338\pi\)
0.480823 + 0.876817i \(0.340338\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −100.429 −0.226701 −0.113351 0.993555i \(-0.536158\pi\)
−0.113351 + 0.993555i \(0.536158\pi\)
\(444\) 0 0
\(445\) 611.798 + 175.803i 1.37483 + 0.395063i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 114.908i 0.255920i 0.991779 + 0.127960i \(0.0408428\pi\)
−0.991779 + 0.127960i \(0.959157\pi\)
\(450\) 0 0
\(451\) −779.402 −1.72817
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −270.757 + 9.30243i −0.595069 + 0.0204449i
\(456\) 0 0
\(457\) 816.492i 1.78663i −0.449427 0.893317i \(-0.648372\pi\)
0.449427 0.893317i \(-0.351628\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 35.5319 + 48.9055i 0.0770758 + 0.106086i 0.845814 0.533478i \(-0.179115\pi\)
−0.768738 + 0.639563i \(0.779115\pi\)
\(462\) 0 0
\(463\) −234.495 + 322.755i −0.506469 + 0.697094i −0.983319 0.181890i \(-0.941778\pi\)
0.476850 + 0.878985i \(0.341778\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −40.9533 126.041i −0.0876944 0.269895i 0.897587 0.440838i \(-0.145319\pi\)
−0.985281 + 0.170943i \(0.945319\pi\)
\(468\) 0 0
\(469\) −242.372 745.943i −0.516784 1.59050i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 147.390 107.085i 0.311607 0.226395i
\(474\) 0 0
\(475\) 778.401 53.5505i 1.63874 0.112738i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 445.196 + 144.653i 0.929427 + 0.301989i 0.734328 0.678794i \(-0.237497\pi\)
0.195099 + 0.980784i \(0.437497\pi\)
\(480\) 0 0
\(481\) −44.5428 137.089i −0.0926046 0.285008i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 699.598 254.187i 1.44247 0.524097i
\(486\) 0 0
\(487\) −233.802 + 321.801i −0.480087 + 0.660783i −0.978522 0.206144i \(-0.933908\pi\)
0.498435 + 0.866927i \(0.333908\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 70.8954 97.5791i 0.144390 0.198735i −0.730697 0.682702i \(-0.760805\pi\)
0.875086 + 0.483967i \(0.160805\pi\)
\(492\) 0 0
\(493\) 1342.75i 2.72364i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −191.744 + 590.129i −0.385804 + 1.18738i
\(498\) 0 0
\(499\) −713.310 −1.42948 −0.714739 0.699391i \(-0.753455\pi\)
−0.714739 + 0.699391i \(0.753455\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −72.9299 + 224.455i −0.144990 + 0.446233i −0.997010 0.0772767i \(-0.975378\pi\)
0.852020 + 0.523509i \(0.175378\pi\)
\(504\) 0 0
\(505\) 175.197 + 224.503i 0.346926 + 0.444560i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −50.1595 + 69.0386i −0.0985452 + 0.135636i −0.855442 0.517898i \(-0.826714\pi\)
0.756897 + 0.653534i \(0.226714\pi\)
\(510\) 0 0
\(511\) −512.936 + 372.670i −1.00379 + 0.729295i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 824.991 299.746i 1.60192 0.582032i
\(516\) 0 0
\(517\) 369.505 120.059i 0.714710 0.232223i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −563.754 183.175i −1.08206 0.351583i −0.286888 0.957964i \(-0.592621\pi\)
−0.795174 + 0.606381i \(0.792621\pi\)
\(522\) 0 0
\(523\) −46.6987 64.2752i −0.0892900 0.122897i 0.762035 0.647536i \(-0.224200\pi\)
−0.851325 + 0.524639i \(0.824200\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 94.0786 68.3521i 0.178517 0.129700i
\(528\) 0 0
\(529\) −82.0795 + 252.615i −0.155160 + 0.477533i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 89.9819 + 276.936i 0.168822 + 0.519579i
\(534\) 0 0
\(535\) −109.116 + 85.1515i −0.203954 + 0.159162i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 68.7005 + 94.5581i 0.127459 + 0.175433i
\(540\) 0 0
\(541\) −146.918 106.742i −0.271567 0.197305i 0.443664 0.896193i \(-0.353678\pi\)
−0.715231 + 0.698888i \(0.753678\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −740.091 + 25.4274i −1.35796 + 0.0466558i
\(546\) 0 0
\(547\) −252.310 81.9804i −0.461261 0.149873i 0.0691628 0.997605i \(-0.477967\pi\)
−0.530424 + 0.847733i \(0.677967\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1440.38i 2.61413i
\(552\) 0 0
\(553\) 513.094 + 166.714i 0.927837 + 0.301473i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 779.122 1.39878 0.699392 0.714739i \(-0.253454\pi\)
0.699392 + 0.714739i \(0.253454\pi\)
\(558\) 0 0
\(559\) −55.0654 40.0074i −0.0985070 0.0715695i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 379.921 + 276.029i 0.674816 + 0.490282i 0.871634 0.490158i \(-0.163061\pi\)
−0.196818 + 0.980440i \(0.563061\pi\)
\(564\) 0 0
\(565\) 466.901 16.0414i 0.826373 0.0283918i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 498.674 162.029i 0.876404 0.284761i 0.163941 0.986470i \(-0.447579\pi\)
0.712463 + 0.701709i \(0.247579\pi\)
\(570\) 0 0
\(571\) 162.539 500.242i 0.284656 0.876081i −0.701846 0.712329i \(-0.747640\pi\)
0.986502 0.163752i \(-0.0523596\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 151.565 + 376.356i 0.263591 + 0.654532i
\(576\) 0 0
\(577\) −45.9051 63.1830i −0.0795583 0.109503i 0.767383 0.641189i \(-0.221559\pi\)
−0.846941 + 0.531686i \(0.821559\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 344.043 111.786i 0.592157 0.192403i
\(582\) 0 0
\(583\) 1058.62 343.965i 1.81581 0.589992i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9.15368 + 6.65053i 0.0155940 + 0.0113297i 0.595555 0.803315i \(-0.296932\pi\)
−0.579961 + 0.814644i \(0.696932\pi\)
\(588\) 0 0
\(589\) 100.919 73.3220i 0.171340 0.124486i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −390.250 −0.658094 −0.329047 0.944313i \(-0.606728\pi\)
−0.329047 + 0.944313i \(0.606728\pi\)
\(594\) 0 0
\(595\) −603.649 + 893.860i −1.01454 + 1.50229i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 45.7243i 0.0763343i 0.999271 + 0.0381672i \(0.0121519\pi\)
−0.999271 + 0.0381672i \(0.987848\pi\)
\(600\) 0 0
\(601\) 408.687 0.680012 0.340006 0.940423i \(-0.389571\pi\)
0.340006 + 0.940423i \(0.389571\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 446.662 + 1229.35i 0.738284 + 2.03198i
\(606\) 0 0
\(607\) 401.268i 0.661068i 0.943794 + 0.330534i \(0.107229\pi\)
−0.943794 + 0.330534i \(0.892771\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −85.3186 117.431i −0.139638 0.192195i
\(612\) 0 0
\(613\) −465.247 + 640.358i −0.758968 + 1.04463i 0.238331 + 0.971184i \(0.423400\pi\)
−0.997299 + 0.0734459i \(0.976600\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 287.494 + 884.816i 0.465955 + 1.43406i 0.857778 + 0.514021i \(0.171845\pi\)
−0.391823 + 0.920041i \(0.628155\pi\)
\(618\) 0 0
\(619\) −140.385 432.061i −0.226793 0.697998i −0.998105 0.0615399i \(-0.980399\pi\)
0.771311 0.636458i \(-0.219601\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −763.676 + 554.843i −1.22580 + 0.890598i
\(624\) 0 0
\(625\) −551.180 294.662i −0.881888 0.471459i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −545.792 177.338i −0.867713 0.281937i
\(630\) 0 0
\(631\) 368.588 + 1134.40i 0.584133 + 1.79778i 0.602725 + 0.797949i \(0.294081\pi\)
−0.0185925 + 0.999827i \(0.505919\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −669.799 192.470i −1.05480 0.303102i
\(636\) 0 0
\(637\) 25.6668 35.3273i 0.0402932 0.0554588i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 559.013 769.415i 0.872095 1.20034i −0.106453 0.994318i \(-0.533949\pi\)
0.978548 0.206018i \(-0.0660506\pi\)
\(642\) 0 0
\(643\) 983.678i 1.52983i 0.644134 + 0.764913i \(0.277218\pi\)
−0.644134 + 0.764913i \(0.722782\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 283.311 871.942i 0.437885 1.34767i −0.452217 0.891908i \(-0.649367\pi\)
0.890102 0.455762i \(-0.150633\pi\)
\(648\) 0 0
\(649\) −1394.93 −2.14936
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 74.2283 228.451i 0.113673 0.349849i −0.877995 0.478670i \(-0.841119\pi\)
0.991668 + 0.128821i \(0.0411192\pi\)
\(654\) 0 0
\(655\) −256.993 + 380.546i −0.392356 + 0.580986i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 419.142 576.900i 0.636028 0.875417i −0.362368 0.932035i \(-0.618032\pi\)
0.998396 + 0.0566182i \(0.0180318\pi\)
\(660\) 0 0
\(661\) −142.102 + 103.243i −0.214980 + 0.156192i −0.690064 0.723748i \(-0.742418\pi\)
0.475084 + 0.879940i \(0.342418\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −647.540 + 958.853i −0.973745 + 1.44188i
\(666\) 0 0
\(667\) −712.348 + 231.456i −1.06799 + 0.347010i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1240.03 + 402.911i 1.84803 + 0.600463i
\(672\) 0 0
\(673\) −639.821 880.639i −0.950700 1.30853i −0.951216 0.308527i \(-0.900164\pi\)
0.000515262 1.00000i \(-0.499836\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 967.184 702.700i 1.42863 1.03796i 0.438363 0.898798i \(-0.355558\pi\)
0.990269 0.139164i \(-0.0444416\pi\)
\(678\) 0 0
\(679\) −341.092 + 1049.77i −0.502344 + 1.54606i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −163.918 504.488i −0.239997 0.738635i −0.996419 0.0845514i \(-0.973054\pi\)
0.756422 0.654084i \(-0.226946\pi\)
\(684\) 0 0
\(685\) −33.5793 + 1.15369i −0.0490209 + 0.00168422i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −244.434 336.435i −0.354767 0.488295i
\(690\) 0 0
\(691\) 331.197 + 240.629i 0.479301 + 0.348233i 0.801055 0.598591i \(-0.204272\pi\)
−0.321754 + 0.946823i \(0.604272\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −159.035 + 553.445i −0.228827 + 0.796324i
\(696\) 0 0
\(697\) 1102.56 + 358.245i 1.58187 + 0.513981i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 446.906i 0.637527i −0.947834 0.318763i \(-0.896732\pi\)
0.947834 0.318763i \(-0.103268\pi\)
\(702\) 0 0
\(703\) −585.476 190.233i −0.832826 0.270601i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −422.293 −0.597302
\(708\) 0 0
\(709\) 426.777 + 310.072i 0.601942 + 0.437337i 0.846568 0.532281i \(-0.178665\pi\)
−0.244625 + 0.969618i \(0.578665\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 52.4784 + 38.1278i 0.0736023 + 0.0534752i
\(714\) 0 0
\(715\) 563.435 439.693i 0.788020 0.614955i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 595.734 193.566i 0.828558 0.269215i 0.136120 0.990692i \(-0.456537\pi\)
0.692438 + 0.721477i \(0.256537\pi\)
\(720\) 0 0
\(721\) −402.227 + 1237.93i −0.557874 + 1.71696i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 612.522 977.788i 0.844857 1.34867i
\(726\) 0 0
\(727\) 108.843 + 149.809i 0.149715 + 0.206065i 0.877287 0.479966i \(-0.159351\pi\)
−0.727572 + 0.686032i \(0.759351\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −257.723 + 83.7392i −0.352562 + 0.114554i
\(732\) 0 0
\(733\) 249.865 81.1861i 0.340880 0.110759i −0.133574 0.991039i \(-0.542645\pi\)
0.474454 + 0.880280i \(0.342645\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1673.95 + 1216.20i 2.27130 + 1.65020i
\(738\) 0 0
\(739\) 932.258 677.325i 1.26151 0.916543i 0.262683 0.964882i \(-0.415393\pi\)
0.998831 + 0.0483391i \(0.0153928\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 239.970 0.322974 0.161487 0.986875i \(-0.448371\pi\)
0.161487 + 0.986875i \(0.448371\pi\)
\(744\) 0 0
\(745\) −281.317 360.488i −0.377607 0.483876i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 205.248i 0.274029i
\(750\) 0 0
\(751\) 526.348 0.700863 0.350432 0.936588i \(-0.386035\pi\)
0.350432 + 0.936588i \(0.386035\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −327.262 + 255.389i −0.433460 + 0.338263i
\(756\) 0 0
\(757\) 643.956i 0.850669i −0.905036 0.425334i \(-0.860157\pi\)
0.905036 0.425334i \(-0.139843\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −260.104 358.003i −0.341792 0.470437i 0.603171 0.797612i \(-0.293903\pi\)
−0.944964 + 0.327175i \(0.893903\pi\)
\(762\) 0 0
\(763\) 645.467 888.410i 0.845960 1.16436i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 161.045 + 495.645i 0.209967 + 0.646212i
\(768\) 0 0
\(769\) 154.778 + 476.357i 0.201271 + 0.619450i 0.999846 + 0.0175537i \(0.00558780\pi\)
−0.798575 + 0.601896i \(0.794412\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −92.1756 + 66.9695i −0.119244 + 0.0866358i −0.645809 0.763499i \(-0.723480\pi\)
0.526565 + 0.850135i \(0.323480\pi\)
\(774\) 0 0
\(775\) −99.6878 + 6.85808i −0.128629 + 0.00884913i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1182.73 + 384.293i 1.51827 + 0.493316i
\(780\) 0 0
\(781\) −505.834 1556.80i −0.647675 1.99334i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −324.798 416.205i −0.413756 0.530198i
\(786\) 0 0
\(787\) 739.560 1017.92i 0.939720 1.29341i −0.0162253 0.999868i \(-0.505165\pi\)
0.955945 0.293545i \(-0.0948351\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −407.206 + 560.470i −0.514798 + 0.708559i
\(792\) 0 0
\(793\) 487.121i 0.614277i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −370.640 + 1140.71i −0.465043 + 1.43126i 0.393885 + 0.919160i \(0.371131\pi\)
−0.858928 + 0.512096i \(0.828869\pi\)
\(798\) 0 0
\(799\) −577.897 −0.723275
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 516.860 1590.73i 0.643661 1.98099i
\(804\) 0 0
\(805\) −578.258 166.165i −0.718333 0.206416i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −234.795 + 323.168i −0.290229 + 0.399466i −0.929088 0.369858i \(-0.879406\pi\)
0.638860 + 0.769323i \(0.279406\pi\)
\(810\) 0 0
\(811\) 585.320 425.260i 0.721727 0.524365i −0.165209 0.986259i \(-0.552830\pi\)
0.886935 + 0.461894i \(0.152830\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 43.4177 + 1263.72i 0.0532733 + 1.55057i
\(816\) 0 0
\(817\) −276.462 + 89.8279i −0.338387 + 0.109948i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −893.252 290.235i −1.08800 0.353514i −0.290529 0.956866i \(-0.593831\pi\)
−0.797475 + 0.603352i \(0.793831\pi\)
\(822\) 0 0
\(823\) −502.715 691.928i −0.610832 0.840738i 0.385813 0.922577i \(-0.373921\pi\)
−0.996646 + 0.0818385i \(0.973921\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 331.899 241.139i 0.401329 0.291583i −0.368753 0.929527i \(-0.620215\pi\)
0.770082 + 0.637945i \(0.220215\pi\)
\(828\) 0 0
\(829\) −422.256 + 1299.57i −0.509356 + 1.56764i 0.283967 + 0.958834i \(0.408349\pi\)
−0.793323 + 0.608801i \(0.791651\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −53.7229 165.342i −0.0644933 0.198490i
\(834\) 0 0
\(835\) 922.566 + 623.034i 1.10487 + 0.746149i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −239.913 330.212i −0.285951 0.393578i 0.641743 0.766920i \(-0.278212\pi\)
−0.927694 + 0.373342i \(0.878212\pi\)
\(840\) 0 0
\(841\) 1042.83 + 757.657i 1.23998 + 0.900900i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 478.991 + 323.476i 0.566854 + 0.382812i
\(846\) 0 0
\(847\) −1844.68 599.372i −2.17790 0.707641i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 320.118i 0.376167i
\(852\) 0 0
\(853\) −1289.30 418.919i −1.51149 0.491113i −0.568145 0.822928i \(-0.692339\pi\)
−0.943344 + 0.331816i \(0.892339\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −1412.12 −1.64775 −0.823876 0.566770i \(-0.808193\pi\)
−0.823876 + 0.566770i \(0.808193\pi\)
\(858\) 0 0
\(859\) 50.9579 + 37.0231i 0.0593223 + 0.0431002i 0.617051 0.786923i \(-0.288327\pi\)
−0.557729 + 0.830023i \(0.688327\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 788.212 + 572.669i 0.913339 + 0.663580i 0.941857 0.336013i \(-0.109079\pi\)
−0.0285178 + 0.999593i \(0.509079\pi\)
\(864\) 0 0
\(865\) −85.5676 + 297.777i −0.0989221 + 0.344251i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −1353.57 + 439.803i −1.55762 + 0.506102i
\(870\) 0 0
\(871\) 238.879 735.194i 0.274258 0.844081i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 847.326 375.540i 0.968372 0.429189i
\(876\) 0 0
\(877\) 423.700 + 583.173i 0.483125 + 0.664964i 0.979102 0.203372i \(-0.0651900\pi\)
−0.495977 + 0.868336i \(0.665190\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −595.534 + 193.501i −0.675975 + 0.219637i −0.626832 0.779154i \(-0.715649\pi\)
−0.0491424 + 0.998792i \(0.515649\pi\)
\(882\) 0 0
\(883\) 217.128 70.5493i 0.245899 0.0798973i −0.183475 0.983024i \(-0.558735\pi\)
0.429373 + 0.903127i \(0.358735\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −552.382 401.329i −0.622754 0.452457i 0.231129 0.972923i \(-0.425758\pi\)
−0.853882 + 0.520466i \(0.825758\pi\)
\(888\) 0 0
\(889\) 836.075 607.444i 0.940467 0.683289i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −619.916 −0.694195
\(894\) 0 0
\(895\) 102.291 37.1657i 0.114292 0.0415260i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 184.467i 0.205191i
\(900\) 0 0
\(901\) −1655.65 −1.83757
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −88.5984 59.8329i −0.0978987 0.0661137i
\(906\) 0 0
\(907\) 359.601i 0.396473i 0.980154 + 0.198236i \(0.0635214\pi\)
−0.980154 + 0.198236i \(0.936479\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −152.344 209.683i −0.167227 0.230168i 0.717176 0.696892i \(-0.245434\pi\)
−0.884403 + 0.466724i \(0.845434\pi\)
\(912\) 0 0
\(913\) −560.932 + 772.057i −0.614383 + 0.845626i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −210.424 647.617i −0.229470 0.706235i
\(918\) 0 0
\(919\) 222.003 + 683.256i 0.241571 + 0.743478i 0.996182 + 0.0873053i \(0.0278256\pi\)
−0.754611 + 0.656172i \(0.772174\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −494.760 + 359.464i −0.536034 + 0.389452i
\(924\) 0 0
\(925\) 316.547 + 378.110i 0.342213 + 0.408768i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 268.545 + 87.2554i 0.289068 + 0.0939240i 0.449962 0.893048i \(-0.351438\pi\)
−0.160893 + 0.986972i \(0.551438\pi\)
\(930\) 0 0
\(931\) −57.6292 177.364i −0.0619003 0.190509i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −97.7027 2843.74i −0.104495 3.04143i
\(936\) 0 0
\(937\) 235.993 324.816i 0.251860 0.346656i −0.664302 0.747465i \(-0.731271\pi\)
0.916162 + 0.400809i \(0.131271\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −299.227 + 411.850i −0.317988 + 0.437673i −0.937852 0.347037i \(-0.887188\pi\)
0.619864 + 0.784710i \(0.287188\pi\)
\(942\) 0 0
\(943\) 646.677i 0.685766i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 6.77217 20.8426i 0.00715118 0.0220091i −0.947417 0.320001i \(-0.896317\pi\)
0.954568 + 0.297992i \(0.0963168\pi\)
\(948\) 0 0
\(949\) −624.887 −0.658469
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −20.6943 + 63.6905i −0.0217149 + 0.0668316i −0.961327 0.275410i \(-0.911186\pi\)
0.939612 + 0.342242i \(0.111186\pi\)
\(954\) 0 0
\(955\) 17.4009 + 506.471i 0.0182208 + 0.530336i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 29.2861 40.3089i 0.0305382 0.0420322i
\(960\) 0 0
\(961\) 764.541 555.471i 0.795568 0.578014i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −924.785 1185.05i −0.958327 1.22803i
\(966\) 0 0
\(967\) −405.451 + 131.739i −0.419287 + 0.136235i −0.511059 0.859545i \(-0.670747\pi\)
0.0917723 + 0.995780i \(0.470747\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −310.284 100.818i −0.319551 0.103829i 0.144849 0.989454i \(-0.453730\pi\)
−0.464401 + 0.885625i \(0.653730\pi\)
\(972\) 0 0
\(973\) −501.922 690.836i −0.515850 0.710006i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −39.2546 + 28.5201i −0.0401787 + 0.0291915i −0.607693 0.794172i \(-0.707905\pi\)
0.567515 + 0.823363i \(0.307905\pi\)
\(978\) 0 0
\(979\) 769.518 2368.33i 0.786025 2.41914i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 4.61928 + 14.2167i 0.00469916 + 0.0144625i 0.953379 0.301777i \(-0.0975797\pi\)
−0.948679 + 0.316239i \(0.897580\pi\)
\(984\) 0 0
\(985\) −294.845 811.501i −0.299335 0.823859i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −88.8495 122.291i −0.0898377 0.123651i
\(990\) 0 0
\(991\) −307.992 223.769i −0.310789 0.225801i 0.421446 0.906853i \(-0.361523\pi\)
−0.732235 + 0.681052i \(0.761523\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −1162.01 + 906.807i −1.16785 + 0.911364i
\(996\) 0 0
\(997\) 1099.82 + 357.353i 1.10313 + 0.358428i 0.803306 0.595567i \(-0.203073\pi\)
0.299822 + 0.953995i \(0.403073\pi\)
\(998\) 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 900.3.y.a.89.16 yes 80
3.2 odd 2 inner 900.3.y.a.89.5 80
25.9 even 10 inner 900.3.y.a.809.5 yes 80
75.59 odd 10 inner 900.3.y.a.809.16 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
900.3.y.a.89.5 80 3.2 odd 2 inner
900.3.y.a.89.16 yes 80 1.1 even 1 trivial
900.3.y.a.809.5 yes 80 25.9 even 10 inner
900.3.y.a.809.16 yes 80 75.59 odd 10 inner