Properties

Label 1008.2.cz.h.607.11
Level $1008$
Weight $2$
Character 1008.607
Analytic conductor $8.049$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1008,2,Mod(367,1008)]
 
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([3, 0, 4, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.367");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.cz (of order \(6\), 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: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 607.11
Character \(\chi\) \(=\) 1008.607
Dual form 1008.2.cz.h.367.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.62154 - 0.608772i) q^{3} +(1.53539 - 0.886460i) q^{5} +(-2.64391 - 0.0987102i) q^{7} +(2.25879 - 1.97430i) q^{9} +O(q^{10})\) \(q+(1.62154 - 0.608772i) q^{3} +(1.53539 - 0.886460i) q^{5} +(-2.64391 - 0.0987102i) q^{7} +(2.25879 - 1.97430i) q^{9} +(5.33976 + 3.08291i) q^{11} +(-4.60307 - 2.65758i) q^{13} +(1.95005 - 2.37214i) q^{15} +(4.69663 - 2.71160i) q^{17} +(0.935544 - 1.62041i) q^{19} +(-4.34730 + 1.44947i) q^{21} +(-0.562751 + 0.324904i) q^{23} +(-0.928378 + 1.60800i) q^{25} +(2.46083 - 4.57649i) q^{27} +(-1.14874 - 1.98967i) q^{29} +10.2138 q^{31} +(10.5354 + 1.74837i) q^{33} +(-4.14694 + 2.19216i) q^{35} +(1.09566 - 1.89773i) q^{37} +(-9.08193 - 1.50716i) q^{39} +(-6.64391 - 3.83586i) q^{41} +(-1.07492 + 0.620607i) q^{43} +(1.71800 - 5.03365i) q^{45} -0.468259 q^{47} +(6.98051 + 0.521962i) q^{49} +(5.96504 - 7.25615i) q^{51} +(-0.941715 - 1.63110i) q^{53} +10.9315 q^{55} +(0.530564 - 3.19709i) q^{57} -9.24765 q^{59} -6.33056i q^{61} +(-6.16693 + 4.99690i) q^{63} -9.42337 q^{65} +9.93473i q^{67} +(-0.714731 + 0.869433i) q^{69} +11.1497i q^{71} +(-4.77625 + 2.75757i) q^{73} +(-0.526500 + 3.17261i) q^{75} +(-13.8135 - 8.67802i) q^{77} +10.5842i q^{79} +(1.20430 - 8.91906i) q^{81} +(4.06061 + 7.03319i) q^{83} +(4.80745 - 8.32675i) q^{85} +(-3.07398 - 2.52701i) q^{87} +(-0.228674 - 0.132025i) q^{89} +(11.9078 + 7.48078i) q^{91} +(16.5622 - 6.21790i) q^{93} -3.31729i q^{95} +(-12.5762 + 7.26089i) q^{97} +(18.1480 - 3.57861i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 3 q^{3} - 3 q^{5} - 4 q^{7} + 17 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 3 q^{3} - 3 q^{5} - 4 q^{7} + 17 q^{9} + 9 q^{11} - 3 q^{13} + 6 q^{15} - 3 q^{17} + 4 q^{19} + 13 q^{21} + 6 q^{23} + 15 q^{25} - 9 q^{27} + 18 q^{29} - 34 q^{31} - 21 q^{33} + 42 q^{35} - 3 q^{37} - 27 q^{39} + 36 q^{41} - 24 q^{43} + 21 q^{45} + 42 q^{47} + 30 q^{49} + 6 q^{51} - 12 q^{53} + 30 q^{55} - 13 q^{57} + 12 q^{59} + 3 q^{63} + 6 q^{69} + 48 q^{73} - 36 q^{75} - 48 q^{77} - 31 q^{81} + 48 q^{83} - 21 q^{85} - 15 q^{87} + 39 q^{89} - 9 q^{91} + 10 q^{93} + 3 q^{97} - 30 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) 1.62154 0.608772i 0.936197 0.351474i
\(4\) 0 0
\(5\) 1.53539 0.886460i 0.686649 0.396437i −0.115707 0.993283i \(-0.536913\pi\)
0.802355 + 0.596847i \(0.203580\pi\)
\(6\) 0 0
\(7\) −2.64391 0.0987102i −0.999304 0.0373090i
\(8\) 0 0
\(9\) 2.25879 1.97430i 0.752931 0.658099i
\(10\) 0 0
\(11\) 5.33976 + 3.08291i 1.61000 + 0.929532i 0.989369 + 0.145427i \(0.0464557\pi\)
0.620628 + 0.784105i \(0.286878\pi\)
\(12\) 0 0
\(13\) −4.60307 2.65758i −1.27666 0.737081i −0.300429 0.953804i \(-0.597130\pi\)
−0.976233 + 0.216723i \(0.930463\pi\)
\(14\) 0 0
\(15\) 1.95005 2.37214i 0.503501 0.612483i
\(16\) 0 0
\(17\) 4.69663 2.71160i 1.13910 0.657660i 0.192893 0.981220i \(-0.438213\pi\)
0.946208 + 0.323560i \(0.104880\pi\)
\(18\) 0 0
\(19\) 0.935544 1.62041i 0.214629 0.371748i −0.738529 0.674222i \(-0.764479\pi\)
0.953158 + 0.302474i \(0.0978126\pi\)
\(20\) 0 0
\(21\) −4.34730 + 1.44947i −0.948659 + 0.316301i
\(22\) 0 0
\(23\) −0.562751 + 0.324904i −0.117342 + 0.0677472i −0.557522 0.830162i \(-0.688248\pi\)
0.440180 + 0.897909i \(0.354914\pi\)
\(24\) 0 0
\(25\) −0.928378 + 1.60800i −0.185676 + 0.321600i
\(26\) 0 0
\(27\) 2.46083 4.57649i 0.473587 0.880747i
\(28\) 0 0
\(29\) −1.14874 1.98967i −0.213315 0.369472i 0.739435 0.673228i \(-0.235093\pi\)
−0.952750 + 0.303756i \(0.901759\pi\)
\(30\) 0 0
\(31\) 10.2138 1.83446 0.917230 0.398358i \(-0.130420\pi\)
0.917230 + 0.398358i \(0.130420\pi\)
\(32\) 0 0
\(33\) 10.5354 + 1.74837i 1.83398 + 0.304353i
\(34\) 0 0
\(35\) −4.14694 + 2.19216i −0.700961 + 0.370543i
\(36\) 0 0
\(37\) 1.09566 1.89773i 0.180125 0.311985i −0.761798 0.647815i \(-0.775683\pi\)
0.941923 + 0.335829i \(0.109017\pi\)
\(38\) 0 0
\(39\) −9.08193 1.50716i −1.45427 0.241339i
\(40\) 0 0
\(41\) −6.64391 3.83586i −1.03760 0.599061i −0.118450 0.992960i \(-0.537793\pi\)
−0.919154 + 0.393899i \(0.871126\pi\)
\(42\) 0 0
\(43\) −1.07492 + 0.620607i −0.163924 + 0.0946416i −0.579718 0.814817i \(-0.696837\pi\)
0.415794 + 0.909459i \(0.363504\pi\)
\(44\) 0 0
\(45\) 1.71800 5.03365i 0.256105 0.750373i
\(46\) 0 0
\(47\) −0.468259 −0.0683026 −0.0341513 0.999417i \(-0.510873\pi\)
−0.0341513 + 0.999417i \(0.510873\pi\)
\(48\) 0 0
\(49\) 6.98051 + 0.521962i 0.997216 + 0.0745660i
\(50\) 0 0
\(51\) 5.96504 7.25615i 0.835272 1.01606i
\(52\) 0 0
\(53\) −0.941715 1.63110i −0.129354 0.224048i 0.794072 0.607823i \(-0.207957\pi\)
−0.923427 + 0.383775i \(0.874624\pi\)
\(54\) 0 0
\(55\) 10.9315 1.47400
\(56\) 0 0
\(57\) 0.530564 3.19709i 0.0702749 0.423466i
\(58\) 0 0
\(59\) −9.24765 −1.20394 −0.601971 0.798518i \(-0.705618\pi\)
−0.601971 + 0.798518i \(0.705618\pi\)
\(60\) 0 0
\(61\) 6.33056i 0.810545i −0.914196 0.405273i \(-0.867177\pi\)
0.914196 0.405273i \(-0.132823\pi\)
\(62\) 0 0
\(63\) −6.16693 + 4.99690i −0.776960 + 0.629550i
\(64\) 0 0
\(65\) −9.42337 −1.16882
\(66\) 0 0
\(67\) 9.93473i 1.21372i 0.794808 + 0.606860i \(0.207571\pi\)
−0.794808 + 0.606860i \(0.792429\pi\)
\(68\) 0 0
\(69\) −0.714731 + 0.869433i −0.0860435 + 0.104667i
\(70\) 0 0
\(71\) 11.1497i 1.32322i 0.749847 + 0.661612i \(0.230127\pi\)
−0.749847 + 0.661612i \(0.769873\pi\)
\(72\) 0 0
\(73\) −4.77625 + 2.75757i −0.559018 + 0.322749i −0.752751 0.658305i \(-0.771274\pi\)
0.193733 + 0.981054i \(0.437940\pi\)
\(74\) 0 0
\(75\) −0.526500 + 3.17261i −0.0607950 + 0.366341i
\(76\) 0 0
\(77\) −13.8135 8.67802i −1.57420 0.988952i
\(78\) 0 0
\(79\) 10.5842i 1.19081i 0.803425 + 0.595406i \(0.203009\pi\)
−0.803425 + 0.595406i \(0.796991\pi\)
\(80\) 0 0
\(81\) 1.20430 8.91906i 0.133811 0.991007i
\(82\) 0 0
\(83\) 4.06061 + 7.03319i 0.445710 + 0.771992i 0.998101 0.0615925i \(-0.0196179\pi\)
−0.552391 + 0.833585i \(0.686285\pi\)
\(84\) 0 0
\(85\) 4.80745 8.32675i 0.521441 0.903163i
\(86\) 0 0
\(87\) −3.07398 2.52701i −0.329565 0.270924i
\(88\) 0 0
\(89\) −0.228674 0.132025i −0.0242394 0.0139946i 0.487831 0.872938i \(-0.337788\pi\)
−0.512071 + 0.858943i \(0.671121\pi\)
\(90\) 0 0
\(91\) 11.9078 + 7.48078i 1.24827 + 0.784199i
\(92\) 0 0
\(93\) 16.5622 6.21790i 1.71742 0.644766i
\(94\) 0 0
\(95\) 3.31729i 0.340347i
\(96\) 0 0
\(97\) −12.5762 + 7.26089i −1.27692 + 0.737231i −0.976281 0.216506i \(-0.930534\pi\)
−0.300641 + 0.953737i \(0.597201\pi\)
\(98\) 0 0
\(99\) 18.1480 3.57861i 1.82394 0.359663i
\(100\) 0 0
\(101\) 11.2127 + 6.47364i 1.11570 + 0.644151i 0.940300 0.340346i \(-0.110544\pi\)
0.175402 + 0.984497i \(0.443877\pi\)
\(102\) 0 0
\(103\) −6.24550 10.8175i −0.615387 1.06588i −0.990316 0.138829i \(-0.955666\pi\)
0.374929 0.927053i \(-0.377667\pi\)
\(104\) 0 0
\(105\) −5.38992 + 6.07922i −0.526002 + 0.593271i
\(106\) 0 0
\(107\) −9.00119 5.19684i −0.870178 0.502398i −0.00277074 0.999996i \(-0.500882\pi\)
−0.867407 + 0.497599i \(0.834215\pi\)
\(108\) 0 0
\(109\) 1.34449 + 2.32873i 0.128779 + 0.223051i 0.923204 0.384311i \(-0.125561\pi\)
−0.794425 + 0.607362i \(0.792228\pi\)
\(110\) 0 0
\(111\) 0.621367 3.74426i 0.0589775 0.355389i
\(112\) 0 0
\(113\) 6.39791 11.0815i 0.601864 1.04246i −0.390674 0.920529i \(-0.627758\pi\)
0.992539 0.121931i \(-0.0389086\pi\)
\(114\) 0 0
\(115\) −0.576029 + 0.997712i −0.0537150 + 0.0930371i
\(116\) 0 0
\(117\) −15.6443 + 3.08489i −1.44631 + 0.285198i
\(118\) 0 0
\(119\) −12.6851 + 6.70562i −1.16284 + 0.614703i
\(120\) 0 0
\(121\) 13.5087 + 23.3977i 1.22806 + 2.12706i
\(122\) 0 0
\(123\) −13.1085 2.17539i −1.18196 0.196148i
\(124\) 0 0
\(125\) 12.1565i 1.08731i
\(126\) 0 0
\(127\) 3.34509i 0.296829i 0.988925 + 0.148414i \(0.0474170\pi\)
−0.988925 + 0.148414i \(0.952583\pi\)
\(128\) 0 0
\(129\) −1.36522 + 1.66072i −0.120201 + 0.146218i
\(130\) 0 0
\(131\) 1.52532 + 2.64194i 0.133268 + 0.230827i 0.924935 0.380126i \(-0.124120\pi\)
−0.791666 + 0.610954i \(0.790786\pi\)
\(132\) 0 0
\(133\) −2.63344 + 4.19187i −0.228349 + 0.363481i
\(134\) 0 0
\(135\) −0.278532 9.20815i −0.0239722 0.792511i
\(136\) 0 0
\(137\) 6.58747 11.4098i 0.562806 0.974808i −0.434444 0.900699i \(-0.643055\pi\)
0.997250 0.0741094i \(-0.0236114\pi\)
\(138\) 0 0
\(139\) 5.78263 10.0158i 0.490476 0.849529i −0.509464 0.860492i \(-0.670156\pi\)
0.999940 + 0.0109626i \(0.00348957\pi\)
\(140\) 0 0
\(141\) −0.759302 + 0.285063i −0.0639447 + 0.0240066i
\(142\) 0 0
\(143\) −16.3862 28.3817i −1.37028 2.37340i
\(144\) 0 0
\(145\) −3.52752 2.03662i −0.292945 0.169132i
\(146\) 0 0
\(147\) 11.6369 3.40316i 0.959799 0.280688i
\(148\) 0 0
\(149\) 4.15048 + 7.18885i 0.340021 + 0.588933i 0.984436 0.175742i \(-0.0562325\pi\)
−0.644415 + 0.764676i \(0.722899\pi\)
\(150\) 0 0
\(151\) −7.77662 4.48983i −0.632852 0.365377i 0.149004 0.988837i \(-0.452393\pi\)
−0.781856 + 0.623459i \(0.785727\pi\)
\(152\) 0 0
\(153\) 5.25522 15.3975i 0.424859 1.24481i
\(154\) 0 0
\(155\) 15.6823 9.05416i 1.25963 0.727247i
\(156\) 0 0
\(157\) 0.436812i 0.0348614i −0.999848 0.0174307i \(-0.994451\pi\)
0.999848 0.0174307i \(-0.00554865\pi\)
\(158\) 0 0
\(159\) −2.52000 2.07160i −0.199849 0.164289i
\(160\) 0 0
\(161\) 1.51993 0.803468i 0.119788 0.0633222i
\(162\) 0 0
\(163\) 15.7966 + 9.12015i 1.23728 + 0.714345i 0.968538 0.248867i \(-0.0800581\pi\)
0.268744 + 0.963212i \(0.413391\pi\)
\(164\) 0 0
\(165\) 17.7259 6.65479i 1.37996 0.518075i
\(166\) 0 0
\(167\) −7.51273 + 13.0124i −0.581352 + 1.00693i 0.413967 + 0.910292i \(0.364143\pi\)
−0.995319 + 0.0966400i \(0.969190\pi\)
\(168\) 0 0
\(169\) 7.62551 + 13.2078i 0.586578 + 1.01598i
\(170\) 0 0
\(171\) −1.08597 5.50721i −0.0830461 0.421147i
\(172\) 0 0
\(173\) 2.83455i 0.215507i 0.994178 + 0.107753i \(0.0343657\pi\)
−0.994178 + 0.107753i \(0.965634\pi\)
\(174\) 0 0
\(175\) 2.61327 4.15976i 0.197545 0.314448i
\(176\) 0 0
\(177\) −14.9955 + 5.62971i −1.12713 + 0.423155i
\(178\) 0 0
\(179\) −13.0126 + 7.51284i −0.972609 + 0.561536i −0.900031 0.435827i \(-0.856456\pi\)
−0.0725782 + 0.997363i \(0.523123\pi\)
\(180\) 0 0
\(181\) 24.8091i 1.84404i 0.387137 + 0.922022i \(0.373464\pi\)
−0.387137 + 0.922022i \(0.626536\pi\)
\(182\) 0 0
\(183\) −3.85387 10.2653i −0.284886 0.758830i
\(184\) 0 0
\(185\) 3.88502i 0.285632i
\(186\) 0 0
\(187\) 33.4385 2.44526
\(188\) 0 0
\(189\) −6.95797 + 11.8569i −0.506118 + 0.862465i
\(190\) 0 0
\(191\) 25.2415i 1.82641i 0.407498 + 0.913206i \(0.366401\pi\)
−0.407498 + 0.913206i \(0.633599\pi\)
\(192\) 0 0
\(193\) −15.1601 −1.09125 −0.545623 0.838030i \(-0.683707\pi\)
−0.545623 + 0.838030i \(0.683707\pi\)
\(194\) 0 0
\(195\) −15.2804 + 5.73668i −1.09425 + 0.410812i
\(196\) 0 0
\(197\) −1.89234 −0.134823 −0.0674117 0.997725i \(-0.521474\pi\)
−0.0674117 + 0.997725i \(0.521474\pi\)
\(198\) 0 0
\(199\) −6.63078 11.4849i −0.470044 0.814140i 0.529370 0.848391i \(-0.322429\pi\)
−0.999413 + 0.0342518i \(0.989095\pi\)
\(200\) 0 0
\(201\) 6.04798 + 16.1096i 0.426592 + 1.13628i
\(202\) 0 0
\(203\) 2.84075 + 5.37389i 0.199382 + 0.377173i
\(204\) 0 0
\(205\) −13.6013 −0.949959
\(206\) 0 0
\(207\) −0.629681 + 1.84493i −0.0437658 + 0.128231i
\(208\) 0 0
\(209\) 9.99116 5.76840i 0.691103 0.399008i
\(210\) 0 0
\(211\) −7.44279 4.29710i −0.512383 0.295824i 0.221430 0.975176i \(-0.428928\pi\)
−0.733813 + 0.679352i \(0.762261\pi\)
\(212\) 0 0
\(213\) 6.78761 + 18.0797i 0.465079 + 1.23880i
\(214\) 0 0
\(215\) −1.10029 + 1.90575i −0.0750389 + 0.129971i
\(216\) 0 0
\(217\) −27.0045 1.00821i −1.83318 0.0684418i
\(218\) 0 0
\(219\) −6.06616 + 7.37916i −0.409913 + 0.498637i
\(220\) 0 0
\(221\) −28.8252 −1.93900
\(222\) 0 0
\(223\) 3.34744 + 5.79794i 0.224161 + 0.388259i 0.956068 0.293147i \(-0.0947024\pi\)
−0.731906 + 0.681405i \(0.761369\pi\)
\(224\) 0 0
\(225\) 1.07765 + 5.46503i 0.0718434 + 0.364336i
\(226\) 0 0
\(227\) −1.10565 + 1.91504i −0.0733843 + 0.127105i −0.900383 0.435099i \(-0.856713\pi\)
0.826998 + 0.562205i \(0.190047\pi\)
\(228\) 0 0
\(229\) 8.64408 4.99066i 0.571217 0.329792i −0.186418 0.982470i \(-0.559688\pi\)
0.757635 + 0.652678i \(0.226355\pi\)
\(230\) 0 0
\(231\) −27.6821 5.66250i −1.82135 0.372565i
\(232\) 0 0
\(233\) −11.2371 + 19.4633i −0.736169 + 1.27508i 0.218040 + 0.975940i \(0.430034\pi\)
−0.954209 + 0.299142i \(0.903300\pi\)
\(234\) 0 0
\(235\) −0.718962 + 0.415093i −0.0468999 + 0.0270777i
\(236\) 0 0
\(237\) 6.44334 + 17.1627i 0.418540 + 1.11483i
\(238\) 0 0
\(239\) −18.6203 10.7504i −1.20445 0.695387i −0.242906 0.970050i \(-0.578101\pi\)
−0.961541 + 0.274663i \(0.911434\pi\)
\(240\) 0 0
\(241\) 16.8420 + 9.72375i 1.08489 + 0.626362i 0.932211 0.361914i \(-0.117877\pi\)
0.152679 + 0.988276i \(0.451210\pi\)
\(242\) 0 0
\(243\) −3.47684 15.1958i −0.223040 0.974809i
\(244\) 0 0
\(245\) 11.1805 5.38653i 0.714298 0.344133i
\(246\) 0 0
\(247\) −8.61275 + 4.97257i −0.548016 + 0.316397i
\(248\) 0 0
\(249\) 10.8661 + 8.93262i 0.688608 + 0.566082i
\(250\) 0 0
\(251\) 11.3542 0.716674 0.358337 0.933592i \(-0.383344\pi\)
0.358337 + 0.933592i \(0.383344\pi\)
\(252\) 0 0
\(253\) −4.00660 −0.251893
\(254\) 0 0
\(255\) 2.72639 16.4288i 0.170733 1.02881i
\(256\) 0 0
\(257\) −17.7865 + 10.2691i −1.10949 + 0.640566i −0.938698 0.344741i \(-0.887967\pi\)
−0.170795 + 0.985307i \(0.554634\pi\)
\(258\) 0 0
\(259\) −3.08414 + 4.90928i −0.191639 + 0.305048i
\(260\) 0 0
\(261\) −6.52295 2.22631i −0.403761 0.137805i
\(262\) 0 0
\(263\) −9.36552 5.40719i −0.577503 0.333422i 0.182637 0.983180i \(-0.441537\pi\)
−0.760140 + 0.649759i \(0.774870\pi\)
\(264\) 0 0
\(265\) −2.89180 1.66958i −0.177642 0.102562i
\(266\) 0 0
\(267\) −0.451178 0.0748739i −0.0276116 0.00458221i
\(268\) 0 0
\(269\) −11.8170 + 6.82255i −0.720495 + 0.415978i −0.814935 0.579553i \(-0.803227\pi\)
0.0944398 + 0.995531i \(0.469894\pi\)
\(270\) 0 0
\(271\) −5.49515 + 9.51788i −0.333807 + 0.578170i −0.983255 0.182236i \(-0.941667\pi\)
0.649448 + 0.760406i \(0.275000\pi\)
\(272\) 0 0
\(273\) 23.8630 + 4.88129i 1.44426 + 0.295429i
\(274\) 0 0
\(275\) −9.91463 + 5.72421i −0.597875 + 0.345183i
\(276\) 0 0
\(277\) 10.6221 18.3980i 0.638219 1.10543i −0.347605 0.937641i \(-0.613005\pi\)
0.985823 0.167786i \(-0.0536618\pi\)
\(278\) 0 0
\(279\) 23.0710 20.1652i 1.38122 1.20726i
\(280\) 0 0
\(281\) −5.38885 9.33375i −0.321472 0.556805i 0.659320 0.751862i \(-0.270844\pi\)
−0.980792 + 0.195057i \(0.937511\pi\)
\(282\) 0 0
\(283\) 1.61290 0.0958769 0.0479385 0.998850i \(-0.484735\pi\)
0.0479385 + 0.998850i \(0.484735\pi\)
\(284\) 0 0
\(285\) −2.01947 5.37912i −0.119623 0.318632i
\(286\) 0 0
\(287\) 17.1872 + 10.7975i 1.01453 + 0.637356i
\(288\) 0 0
\(289\) 6.20556 10.7484i 0.365033 0.632256i
\(290\) 0 0
\(291\) −15.9727 + 19.4299i −0.936333 + 1.13900i
\(292\) 0 0
\(293\) −5.09618 2.94228i −0.297722 0.171890i 0.343697 0.939081i \(-0.388321\pi\)
−0.641419 + 0.767191i \(0.721654\pi\)
\(294\) 0 0
\(295\) −14.1988 + 8.19767i −0.826685 + 0.477287i
\(296\) 0 0
\(297\) 27.2492 16.8508i 1.58116 0.977785i
\(298\) 0 0
\(299\) 3.45384 0.199741
\(300\) 0 0
\(301\) 2.90326 1.53472i 0.167341 0.0884599i
\(302\) 0 0
\(303\) 22.1228 + 3.67132i 1.27092 + 0.210912i
\(304\) 0 0
\(305\) −5.61179 9.71990i −0.321330 0.556560i
\(306\) 0 0
\(307\) −4.93775 −0.281812 −0.140906 0.990023i \(-0.545002\pi\)
−0.140906 + 0.990023i \(0.545002\pi\)
\(308\) 0 0
\(309\) −16.7127 13.7390i −0.950754 0.781583i
\(310\) 0 0
\(311\) 15.7060 0.890607 0.445303 0.895380i \(-0.353096\pi\)
0.445303 + 0.895380i \(0.353096\pi\)
\(312\) 0 0
\(313\) 33.9317i 1.91794i −0.283515 0.958968i \(-0.591501\pi\)
0.283515 0.958968i \(-0.408499\pi\)
\(314\) 0 0
\(315\) −5.03912 + 13.1389i −0.283922 + 0.740295i
\(316\) 0 0
\(317\) 16.4578 0.924364 0.462182 0.886785i \(-0.347067\pi\)
0.462182 + 0.886785i \(0.347067\pi\)
\(318\) 0 0
\(319\) 14.1658i 0.793132i
\(320\) 0 0
\(321\) −17.7595 2.94722i −0.991239 0.164498i
\(322\) 0 0
\(323\) 10.1473i 0.564610i
\(324\) 0 0
\(325\) 8.54678 4.93449i 0.474090 0.273716i
\(326\) 0 0
\(327\) 3.59781 + 2.95764i 0.198959 + 0.163558i
\(328\) 0 0
\(329\) 1.23803 + 0.0462220i 0.0682550 + 0.00254830i
\(330\) 0 0
\(331\) 3.92749i 0.215875i −0.994158 0.107937i \(-0.965575\pi\)
0.994158 0.107937i \(-0.0344246\pi\)
\(332\) 0 0
\(333\) −1.27183 6.44974i −0.0696956 0.353444i
\(334\) 0 0
\(335\) 8.80674 + 15.2537i 0.481164 + 0.833400i
\(336\) 0 0
\(337\) −17.4006 + 30.1387i −0.947870 + 1.64176i −0.197969 + 0.980208i \(0.563435\pi\)
−0.749900 + 0.661551i \(0.769899\pi\)
\(338\) 0 0
\(339\) 3.62837 21.8640i 0.197066 1.18749i
\(340\) 0 0
\(341\) 54.5394 + 31.4883i 2.95347 + 1.70519i
\(342\) 0 0
\(343\) −18.4043 2.06907i −0.993740 0.111719i
\(344\) 0 0
\(345\) −0.326677 + 1.96850i −0.0175877 + 0.105981i
\(346\) 0 0
\(347\) 2.41593i 0.129694i 0.997895 + 0.0648470i \(0.0206559\pi\)
−0.997895 + 0.0648470i \(0.979344\pi\)
\(348\) 0 0
\(349\) 3.23522 1.86785i 0.173177 0.0999840i −0.410906 0.911678i \(-0.634788\pi\)
0.584083 + 0.811694i \(0.301454\pi\)
\(350\) 0 0
\(351\) −23.4898 + 14.5261i −1.25379 + 0.775344i
\(352\) 0 0
\(353\) −26.5648 15.3372i −1.41390 0.816316i −0.418148 0.908379i \(-0.637321\pi\)
−0.995753 + 0.0920629i \(0.970654\pi\)
\(354\) 0 0
\(355\) 9.88374 + 17.1191i 0.524575 + 0.908590i
\(356\) 0 0
\(357\) −16.4873 + 18.5958i −0.872599 + 0.984194i
\(358\) 0 0
\(359\) −23.0928 13.3326i −1.21879 0.703669i −0.254132 0.967170i \(-0.581790\pi\)
−0.964659 + 0.263500i \(0.915123\pi\)
\(360\) 0 0
\(361\) 7.74951 + 13.4226i 0.407869 + 0.706450i
\(362\) 0 0
\(363\) 36.1487 + 29.7166i 1.89732 + 1.55972i
\(364\) 0 0
\(365\) −4.88895 + 8.46790i −0.255899 + 0.443230i
\(366\) 0 0
\(367\) −5.56943 + 9.64654i −0.290722 + 0.503545i −0.973981 0.226631i \(-0.927229\pi\)
0.683259 + 0.730176i \(0.260562\pi\)
\(368\) 0 0
\(369\) −22.5803 + 4.45262i −1.17549 + 0.231794i
\(370\) 0 0
\(371\) 2.32880 + 4.40543i 0.120905 + 0.228719i
\(372\) 0 0
\(373\) −9.31048 16.1262i −0.482079 0.834985i 0.517710 0.855556i \(-0.326785\pi\)
−0.999788 + 0.0205717i \(0.993451\pi\)
\(374\) 0 0
\(375\) 7.40052 + 19.7122i 0.382161 + 1.01794i
\(376\) 0 0
\(377\) 12.2114i 0.628921i
\(378\) 0 0
\(379\) 2.95154i 0.151610i 0.997123 + 0.0758051i \(0.0241527\pi\)
−0.997123 + 0.0758051i \(0.975847\pi\)
\(380\) 0 0
\(381\) 2.03640 + 5.42421i 0.104328 + 0.277891i
\(382\) 0 0
\(383\) −3.74662 6.48933i −0.191443 0.331589i 0.754285 0.656547i \(-0.227983\pi\)
−0.945729 + 0.324957i \(0.894650\pi\)
\(384\) 0 0
\(385\) −28.9019 1.07905i −1.47298 0.0549935i
\(386\) 0 0
\(387\) −1.20277 + 3.52404i −0.0611401 + 0.179137i
\(388\) 0 0
\(389\) 8.01874 13.8889i 0.406566 0.704193i −0.587936 0.808907i \(-0.700059\pi\)
0.994502 + 0.104714i \(0.0333928\pi\)
\(390\) 0 0
\(391\) −1.76202 + 3.05191i −0.0891093 + 0.154342i
\(392\) 0 0
\(393\) 4.08171 + 3.35544i 0.205895 + 0.169259i
\(394\) 0 0
\(395\) 9.38243 + 16.2509i 0.472081 + 0.817669i
\(396\) 0 0
\(397\) 24.7118 + 14.2673i 1.24025 + 0.716057i 0.969145 0.246493i \(-0.0792783\pi\)
0.271103 + 0.962550i \(0.412612\pi\)
\(398\) 0 0
\(399\) −1.71835 + 8.40046i −0.0860251 + 0.420549i
\(400\) 0 0
\(401\) −9.25499 16.0301i −0.462172 0.800506i 0.536897 0.843648i \(-0.319597\pi\)
−0.999069 + 0.0431421i \(0.986263\pi\)
\(402\) 0 0
\(403\) −47.0150 27.1441i −2.34199 1.35215i
\(404\) 0 0
\(405\) −6.05731 14.7618i −0.300990 0.733521i
\(406\) 0 0
\(407\) 11.7011 6.75562i 0.580001 0.334864i
\(408\) 0 0
\(409\) 10.1232i 0.500560i −0.968174 0.250280i \(-0.919477\pi\)
0.968174 0.250280i \(-0.0805227\pi\)
\(410\) 0 0
\(411\) 3.73588 22.5118i 0.184277 1.11042i
\(412\) 0 0
\(413\) 24.4500 + 0.912838i 1.20310 + 0.0449178i
\(414\) 0 0
\(415\) 12.4693 + 7.19914i 0.612092 + 0.353392i
\(416\) 0 0
\(417\) 3.27943 19.7613i 0.160595 0.967717i
\(418\) 0 0
\(419\) 17.3083 29.9789i 0.845566 1.46456i −0.0395630 0.999217i \(-0.512597\pi\)
0.885129 0.465346i \(-0.154070\pi\)
\(420\) 0 0
\(421\) 8.91746 + 15.4455i 0.434610 + 0.752767i 0.997264 0.0739258i \(-0.0235528\pi\)
−0.562654 + 0.826693i \(0.690219\pi\)
\(422\) 0 0
\(423\) −1.05770 + 0.924482i −0.0514272 + 0.0449499i
\(424\) 0 0
\(425\) 10.0696i 0.488446i
\(426\) 0 0
\(427\) −0.624891 + 16.7374i −0.0302406 + 0.809981i
\(428\) 0 0
\(429\) −43.8489 36.0467i −2.11704 1.74035i
\(430\) 0 0
\(431\) −12.6343 + 7.29439i −0.608571 + 0.351359i −0.772406 0.635129i \(-0.780947\pi\)
0.163835 + 0.986488i \(0.447614\pi\)
\(432\) 0 0
\(433\) 10.2683i 0.493463i 0.969084 + 0.246731i \(0.0793565\pi\)
−0.969084 + 0.246731i \(0.920643\pi\)
\(434\) 0 0
\(435\) −6.95986 1.15500i −0.333700 0.0553781i
\(436\) 0 0
\(437\) 1.21585i 0.0581620i
\(438\) 0 0
\(439\) 25.0851 1.19725 0.598623 0.801031i \(-0.295715\pi\)
0.598623 + 0.801031i \(0.295715\pi\)
\(440\) 0 0
\(441\) 16.7980 12.6026i 0.799907 0.600124i
\(442\) 0 0
\(443\) 11.9393i 0.567255i −0.958934 0.283628i \(-0.908462\pi\)
0.958934 0.283628i \(-0.0915380\pi\)
\(444\) 0 0
\(445\) −0.468140 −0.0221920
\(446\) 0 0
\(447\) 11.1065 + 9.13032i 0.525322 + 0.431849i
\(448\) 0 0
\(449\) −13.2652 −0.626026 −0.313013 0.949749i \(-0.601338\pi\)
−0.313013 + 0.949749i \(0.601338\pi\)
\(450\) 0 0
\(451\) −23.6512 40.9651i −1.11369 1.92897i
\(452\) 0 0
\(453\) −15.3434 2.54627i −0.720896 0.119634i
\(454\) 0 0
\(455\) 24.9145 + 0.930183i 1.16801 + 0.0436076i
\(456\) 0 0
\(457\) 31.1413 1.45673 0.728364 0.685190i \(-0.240281\pi\)
0.728364 + 0.685190i \(0.240281\pi\)
\(458\) 0 0
\(459\) −0.852005 28.1669i −0.0397682 1.31472i
\(460\) 0 0
\(461\) 13.4565 7.76913i 0.626733 0.361845i −0.152753 0.988264i \(-0.548814\pi\)
0.779486 + 0.626420i \(0.215480\pi\)
\(462\) 0 0
\(463\) 17.3249 + 10.0026i 0.805158 + 0.464858i 0.845272 0.534337i \(-0.179439\pi\)
−0.0401133 + 0.999195i \(0.512772\pi\)
\(464\) 0 0
\(465\) 19.9175 24.2286i 0.923653 1.12357i
\(466\) 0 0
\(467\) −4.56009 + 7.89831i −0.211016 + 0.365490i −0.952033 0.305996i \(-0.901010\pi\)
0.741017 + 0.671486i \(0.234344\pi\)
\(468\) 0 0
\(469\) 0.980660 26.2665i 0.0452827 1.21288i
\(470\) 0 0
\(471\) −0.265919 0.708309i −0.0122529 0.0326372i
\(472\) 0 0
\(473\) −7.65310 −0.351890
\(474\) 0 0
\(475\) 1.73708 + 3.00871i 0.0797026 + 0.138049i
\(476\) 0 0
\(477\) −5.34741 1.82509i −0.244841 0.0835651i
\(478\) 0 0
\(479\) 7.22232 12.5094i 0.329996 0.571570i −0.652514 0.757776i \(-0.726286\pi\)
0.982511 + 0.186206i \(0.0596192\pi\)
\(480\) 0 0
\(481\) −10.0868 + 5.82360i −0.459917 + 0.265533i
\(482\) 0 0
\(483\) 1.97551 2.22815i 0.0898887 0.101384i
\(484\) 0 0
\(485\) −12.8730 + 22.2966i −0.584531 + 1.01244i
\(486\) 0 0
\(487\) −7.70646 + 4.44933i −0.349213 + 0.201618i −0.664339 0.747432i \(-0.731287\pi\)
0.315126 + 0.949050i \(0.397953\pi\)
\(488\) 0 0
\(489\) 31.1669 + 5.17220i 1.40941 + 0.233895i
\(490\) 0 0
\(491\) −6.76842 3.90775i −0.305455 0.176354i 0.339436 0.940629i \(-0.389764\pi\)
−0.644891 + 0.764275i \(0.723097\pi\)
\(492\) 0 0
\(493\) −10.7904 6.22982i −0.485974 0.280577i
\(494\) 0 0
\(495\) 24.6920 21.5820i 1.10982 0.970040i
\(496\) 0 0
\(497\) 1.10059 29.4787i 0.0493681 1.32230i
\(498\) 0 0
\(499\) 2.29721 1.32629i 0.102837 0.0593730i −0.447699 0.894184i \(-0.647757\pi\)
0.550536 + 0.834811i \(0.314423\pi\)
\(500\) 0 0
\(501\) −4.26061 + 25.6737i −0.190350 + 1.14702i
\(502\) 0 0
\(503\) −12.8732 −0.573986 −0.286993 0.957933i \(-0.592656\pi\)
−0.286993 + 0.957933i \(0.592656\pi\)
\(504\) 0 0
\(505\) 22.9545 1.02146
\(506\) 0 0
\(507\) 20.4056 + 16.7748i 0.906244 + 0.744993i
\(508\) 0 0
\(509\) 9.02324 5.20957i 0.399948 0.230910i −0.286514 0.958076i \(-0.592496\pi\)
0.686462 + 0.727166i \(0.259163\pi\)
\(510\) 0 0
\(511\) 12.9002 6.81930i 0.570670 0.301668i
\(512\) 0 0
\(513\) −5.11358 8.26907i −0.225770 0.365088i
\(514\) 0 0
\(515\) −19.1786 11.0728i −0.845110 0.487924i
\(516\) 0 0
\(517\) −2.50039 1.44360i −0.109967 0.0634895i
\(518\) 0 0
\(519\) 1.72559 + 4.59634i 0.0757451 + 0.201757i
\(520\) 0 0
\(521\) 1.91461 1.10540i 0.0838807 0.0484285i −0.457473 0.889224i \(-0.651245\pi\)
0.541354 + 0.840795i \(0.317912\pi\)
\(522\) 0 0
\(523\) 12.8836 22.3151i 0.563361 0.975770i −0.433839 0.900990i \(-0.642841\pi\)
0.997200 0.0747794i \(-0.0238253\pi\)
\(524\) 0 0
\(525\) 1.70519 8.33611i 0.0744205 0.363818i
\(526\) 0 0
\(527\) 47.9706 27.6959i 2.08963 1.20645i
\(528\) 0 0
\(529\) −11.2889 + 19.5529i −0.490821 + 0.850126i
\(530\) 0 0
\(531\) −20.8885 + 18.2576i −0.906486 + 0.792313i
\(532\) 0 0
\(533\) 20.3882 + 35.3135i 0.883113 + 1.52960i
\(534\) 0 0
\(535\) −18.4272 −0.796676
\(536\) 0 0
\(537\) −16.5269 + 20.1041i −0.713188 + 0.867556i
\(538\) 0 0
\(539\) 35.6651 + 24.3074i 1.53620 + 1.04700i
\(540\) 0 0
\(541\) 18.0878 31.3289i 0.777653 1.34694i −0.155638 0.987814i \(-0.549743\pi\)
0.933291 0.359121i \(-0.116923\pi\)
\(542\) 0 0
\(543\) 15.1031 + 40.2289i 0.648134 + 1.72639i
\(544\) 0 0
\(545\) 4.12864 + 2.38367i 0.176852 + 0.102105i
\(546\) 0 0
\(547\) 29.1084 16.8057i 1.24458 0.718561i 0.274560 0.961570i \(-0.411468\pi\)
0.970024 + 0.243009i \(0.0781346\pi\)
\(548\) 0 0
\(549\) −12.4984 14.2994i −0.533419 0.610285i
\(550\) 0 0
\(551\) −4.29877 −0.183134
\(552\) 0 0
\(553\) 1.04477 27.9836i 0.0444279 1.18998i
\(554\) 0 0
\(555\) −2.36509 6.29972i −0.100393 0.267408i
\(556\) 0 0
\(557\) −20.2862 35.1367i −0.859552 1.48879i −0.872357 0.488870i \(-0.837409\pi\)
0.0128047 0.999918i \(-0.495924\pi\)
\(558\) 0 0
\(559\) 6.59726 0.279034
\(560\) 0 0
\(561\) 54.2219 20.3564i 2.28925 0.859448i
\(562\) 0 0
\(563\) 17.5148 0.738159 0.369080 0.929398i \(-0.379673\pi\)
0.369080 + 0.929398i \(0.379673\pi\)
\(564\) 0 0
\(565\) 22.6859i 0.954405i
\(566\) 0 0
\(567\) −4.06447 + 23.4623i −0.170692 + 0.985324i
\(568\) 0 0
\(569\) −3.93338 −0.164896 −0.0824480 0.996595i \(-0.526274\pi\)
−0.0824480 + 0.996595i \(0.526274\pi\)
\(570\) 0 0
\(571\) 3.65160i 0.152815i −0.997077 0.0764074i \(-0.975655\pi\)
0.997077 0.0764074i \(-0.0243449\pi\)
\(572\) 0 0
\(573\) 15.3663 + 40.9302i 0.641937 + 1.70988i
\(574\) 0 0
\(575\) 1.20654i 0.0503161i
\(576\) 0 0
\(577\) 19.6944 11.3706i 0.819889 0.473363i −0.0304894 0.999535i \(-0.509707\pi\)
0.850378 + 0.526172i \(0.176373\pi\)
\(578\) 0 0
\(579\) −24.5827 + 9.22903i −1.02162 + 0.383545i
\(580\) 0 0
\(581\) −10.0416 18.9959i −0.416597 0.788084i
\(582\) 0 0
\(583\) 11.6129i 0.480957i
\(584\) 0 0
\(585\) −21.2854 + 18.6045i −0.880045 + 0.769202i
\(586\) 0 0
\(587\) 5.83767 + 10.1111i 0.240947 + 0.417332i 0.960984 0.276603i \(-0.0892088\pi\)
−0.720038 + 0.693935i \(0.755875\pi\)
\(588\) 0 0
\(589\) 9.55550 16.5506i 0.393727 0.681956i
\(590\) 0 0
\(591\) −3.06850 + 1.15200i −0.126221 + 0.0473870i
\(592\) 0 0
\(593\) 14.8178 + 8.55508i 0.608496 + 0.351315i 0.772376 0.635165i \(-0.219068\pi\)
−0.163881 + 0.986480i \(0.552401\pi\)
\(594\) 0 0
\(595\) −13.5324 + 21.5406i −0.554774 + 0.883079i
\(596\) 0 0
\(597\) −17.7437 14.5865i −0.726203 0.596987i
\(598\) 0 0
\(599\) 34.0410i 1.39088i −0.718584 0.695440i \(-0.755210\pi\)
0.718584 0.695440i \(-0.244790\pi\)
\(600\) 0 0
\(601\) 15.9273 9.19561i 0.649686 0.375097i −0.138650 0.990341i \(-0.544276\pi\)
0.788336 + 0.615245i \(0.210943\pi\)
\(602\) 0 0
\(603\) 19.6141 + 22.4405i 0.798749 + 0.913849i
\(604\) 0 0
\(605\) 41.4822 + 23.9498i 1.68649 + 0.973697i
\(606\) 0 0
\(607\) −3.78485 6.55555i −0.153622 0.266082i 0.778934 0.627106i \(-0.215761\pi\)
−0.932557 + 0.361024i \(0.882427\pi\)
\(608\) 0 0
\(609\) 7.87787 + 6.98462i 0.319227 + 0.283031i
\(610\) 0 0
\(611\) 2.15543 + 1.24444i 0.0871994 + 0.0503446i
\(612\) 0 0
\(613\) −3.18881 5.52319i −0.128795 0.223080i 0.794415 0.607375i \(-0.207778\pi\)
−0.923210 + 0.384296i \(0.874444\pi\)
\(614\) 0 0
\(615\) −22.0551 + 8.28011i −0.889349 + 0.333886i
\(616\) 0 0
\(617\) 7.53848 13.0570i 0.303488 0.525656i −0.673436 0.739246i \(-0.735182\pi\)
0.976924 + 0.213589i \(0.0685155\pi\)
\(618\) 0 0
\(619\) −3.70692 + 6.42058i −0.148994 + 0.258065i −0.930856 0.365387i \(-0.880937\pi\)
0.781862 + 0.623451i \(0.214270\pi\)
\(620\) 0 0
\(621\) 0.102087 + 3.37496i 0.00409662 + 0.135433i
\(622\) 0 0
\(623\) 0.591562 + 0.371635i 0.0237004 + 0.0148892i
\(624\) 0 0
\(625\) 6.13433 + 10.6250i 0.245373 + 0.424999i
\(626\) 0 0
\(627\) 12.6894 15.4360i 0.506767 0.616455i
\(628\) 0 0
\(629\) 11.8839i 0.473843i
\(630\) 0 0
\(631\) 4.50590i 0.179377i 0.995970 + 0.0896885i \(0.0285872\pi\)
−0.995970 + 0.0896885i \(0.971413\pi\)
\(632\) 0 0
\(633\) −14.6847 2.43696i −0.583666 0.0968606i
\(634\) 0 0
\(635\) 2.96529 + 5.13603i 0.117674 + 0.203817i
\(636\) 0 0
\(637\) −30.7446 20.9539i −1.21815 0.830225i
\(638\) 0 0
\(639\) 22.0128 + 25.1848i 0.870812 + 0.996297i
\(640\) 0 0
\(641\) 22.2663 38.5664i 0.879467 1.52328i 0.0275404 0.999621i \(-0.491233\pi\)
0.851927 0.523661i \(-0.175434\pi\)
\(642\) 0 0
\(643\) −5.01024 + 8.67799i −0.197585 + 0.342227i −0.947745 0.319030i \(-0.896643\pi\)
0.750160 + 0.661256i \(0.229976\pi\)
\(644\) 0 0
\(645\) −0.623992 + 3.76008i −0.0245697 + 0.148053i
\(646\) 0 0
\(647\) −7.17309 12.4242i −0.282003 0.488444i 0.689875 0.723929i \(-0.257666\pi\)
−0.971878 + 0.235485i \(0.924332\pi\)
\(648\) 0 0
\(649\) −49.3802 28.5097i −1.93834 1.11910i
\(650\) 0 0
\(651\) −44.4026 + 14.8047i −1.74028 + 0.580242i
\(652\) 0 0
\(653\) 5.09260 + 8.82064i 0.199289 + 0.345178i 0.948298 0.317381i \(-0.102804\pi\)
−0.749009 + 0.662559i \(0.769470\pi\)
\(654\) 0 0
\(655\) 4.68394 + 2.70428i 0.183017 + 0.105665i
\(656\) 0 0
\(657\) −5.34430 + 15.6585i −0.208501 + 0.610897i
\(658\) 0 0
\(659\) 13.1154 7.57216i 0.510902 0.294970i −0.222302 0.974978i \(-0.571357\pi\)
0.733205 + 0.680008i \(0.238024\pi\)
\(660\) 0 0
\(661\) 7.28596i 0.283391i −0.989910 0.141695i \(-0.954745\pi\)
0.989910 0.141695i \(-0.0452554\pi\)
\(662\) 0 0
\(663\) −46.7413 + 17.5480i −1.81528 + 0.681507i
\(664\) 0 0
\(665\) −0.327450 + 8.77061i −0.0126980 + 0.340110i
\(666\) 0 0
\(667\) 1.29290 + 0.746458i 0.0500614 + 0.0289030i
\(668\) 0 0
\(669\) 8.95764 + 7.36378i 0.346322 + 0.284700i
\(670\) 0 0
\(671\) 19.5165 33.8037i 0.753428 1.30498i
\(672\) 0 0
\(673\) 9.14049 + 15.8318i 0.352340 + 0.610271i 0.986659 0.162801i \(-0.0520528\pi\)
−0.634319 + 0.773071i \(0.718719\pi\)
\(674\) 0 0
\(675\) 5.07441 + 8.20573i 0.195314 + 0.315839i
\(676\) 0 0
\(677\) 6.06704i 0.233175i −0.993180 0.116588i \(-0.962804\pi\)
0.993180 0.116588i \(-0.0371956\pi\)
\(678\) 0 0
\(679\) 33.9671 17.9557i 1.30354 0.689078i
\(680\) 0 0
\(681\) −0.627032 + 3.77840i −0.0240279 + 0.144788i
\(682\) 0 0
\(683\) 19.2524 11.1154i 0.736672 0.425318i −0.0841862 0.996450i \(-0.526829\pi\)
0.820858 + 0.571132i \(0.193496\pi\)
\(684\) 0 0
\(685\) 23.3581i 0.892468i
\(686\) 0 0
\(687\) 10.9786 13.3548i 0.418858 0.509519i
\(688\) 0 0
\(689\) 10.0107i 0.381379i
\(690\) 0 0
\(691\) −29.0317 −1.10442 −0.552209 0.833706i \(-0.686215\pi\)
−0.552209 + 0.833706i \(0.686215\pi\)
\(692\) 0 0
\(693\) −48.3349 + 7.67012i −1.83609 + 0.291364i
\(694\) 0 0
\(695\) 20.5043i 0.777771i
\(696\) 0 0
\(697\) −41.6053 −1.57591
\(698\) 0 0
\(699\) −6.37278 + 38.4014i −0.241041 + 1.45247i
\(700\) 0 0
\(701\) −26.6798 −1.00768 −0.503841 0.863796i \(-0.668080\pi\)
−0.503841 + 0.863796i \(0.668080\pi\)
\(702\) 0 0
\(703\) −2.05007 3.55083i −0.0773198 0.133922i
\(704\) 0 0
\(705\) −0.913130 + 1.11077i −0.0343905 + 0.0418342i
\(706\) 0 0
\(707\) −29.0063 18.2225i −1.09089 0.685328i
\(708\) 0 0
\(709\) 40.8942 1.53581 0.767907 0.640561i \(-0.221298\pi\)
0.767907 + 0.640561i \(0.221298\pi\)
\(710\) 0 0
\(711\) 20.8963 + 23.9074i 0.783672 + 0.896599i
\(712\) 0 0
\(713\) −5.74785 + 3.31852i −0.215259 + 0.124280i
\(714\) 0 0
\(715\) −50.3185 29.0514i −1.88180 1.08646i
\(716\) 0 0
\(717\) −36.7381 6.09676i −1.37201 0.227688i
\(718\) 0 0
\(719\) −3.01395 + 5.22031i −0.112401 + 0.194685i −0.916738 0.399489i \(-0.869188\pi\)
0.804337 + 0.594174i \(0.202521\pi\)
\(720\) 0 0
\(721\) 15.4447 + 29.2170i 0.575192 + 1.08810i
\(722\) 0 0
\(723\) 33.2296 + 5.51452i 1.23582 + 0.205087i
\(724\) 0 0
\(725\) 4.26584 0.158429
\(726\) 0 0
\(727\) −9.28363 16.0797i −0.344311 0.596364i 0.640918 0.767610i \(-0.278554\pi\)
−0.985228 + 0.171246i \(0.945221\pi\)
\(728\) 0 0
\(729\) −14.8886 22.5240i −0.551430 0.834221i
\(730\) 0 0
\(731\) −3.36568 + 5.82952i −0.124484 + 0.215613i
\(732\) 0 0
\(733\) 24.2957 14.0272i 0.897384 0.518105i 0.0210332 0.999779i \(-0.493304\pi\)
0.876350 + 0.481674i \(0.159971\pi\)
\(734\) 0 0
\(735\) 14.8505 15.5409i 0.547770 0.573233i
\(736\) 0 0
\(737\) −30.6279 + 53.0491i −1.12819 + 1.95409i
\(738\) 0 0
\(739\) −41.9757 + 24.2347i −1.54410 + 0.891488i −0.545529 + 0.838092i \(0.683671\pi\)
−0.998573 + 0.0533962i \(0.982995\pi\)
\(740\) 0 0
\(741\) −10.9388 + 13.3064i −0.401846 + 0.488824i
\(742\) 0 0
\(743\) 0.173090 + 0.0999335i 0.00635005 + 0.00366620i 0.503172 0.864186i \(-0.332166\pi\)
−0.496822 + 0.867853i \(0.665500\pi\)
\(744\) 0 0
\(745\) 12.7452 + 7.35847i 0.466950 + 0.269594i
\(746\) 0 0
\(747\) 23.0577 + 7.86967i 0.843637 + 0.287936i
\(748\) 0 0
\(749\) 23.2854 + 14.6285i 0.850828 + 0.534513i
\(750\) 0 0
\(751\) −30.6319 + 17.6853i −1.11777 + 0.645347i −0.940832 0.338874i \(-0.889954\pi\)
−0.176942 + 0.984221i \(0.556621\pi\)
\(752\) 0 0
\(753\) 18.4114 6.91214i 0.670948 0.251893i
\(754\) 0 0
\(755\) −15.9202 −0.579396
\(756\) 0 0
\(757\) −32.7804 −1.19142 −0.595712 0.803198i \(-0.703130\pi\)
−0.595712 + 0.803198i \(0.703130\pi\)
\(758\) 0 0
\(759\) −6.49687 + 2.43911i −0.235822 + 0.0885339i
\(760\) 0 0
\(761\) 20.7302 11.9686i 0.751470 0.433861i −0.0747551 0.997202i \(-0.523818\pi\)
0.826225 + 0.563341i \(0.190484\pi\)
\(762\) 0 0
\(763\) −3.32484 6.28965i −0.120367 0.227701i
\(764\) 0 0
\(765\) −5.58043 28.2997i −0.201761 1.02318i
\(766\) 0 0
\(767\) 42.5676 + 24.5764i 1.53703 + 0.887403i
\(768\) 0 0
\(769\) −3.09015 1.78410i −0.111434 0.0643363i 0.443247 0.896399i \(-0.353826\pi\)
−0.554681 + 0.832063i \(0.687160\pi\)
\(770\) 0 0
\(771\) −22.5901 + 27.4796i −0.813562 + 0.989655i
\(772\) 0 0
\(773\) 7.21515 4.16567i 0.259511 0.149829i −0.364600 0.931164i \(-0.618794\pi\)
0.624111 + 0.781335i \(0.285461\pi\)
\(774\) 0 0
\(775\) −9.48231 + 16.4238i −0.340615 + 0.589962i
\(776\) 0 0
\(777\) −2.01243 + 9.83814i −0.0721957 + 0.352941i
\(778\) 0 0
\(779\) −12.4313 + 7.17723i −0.445399 + 0.257151i
\(780\) 0 0
\(781\) −34.3735 + 59.5366i −1.22998 + 2.13039i
\(782\) 0 0
\(783\) −11.9326 + 0.360941i −0.426435 + 0.0128990i
\(784\) 0 0
\(785\) −0.387217 0.670679i −0.0138204 0.0239376i
\(786\) 0 0
\(787\) 11.6617 0.415693 0.207847 0.978161i \(-0.433355\pi\)
0.207847 + 0.978161i \(0.433355\pi\)
\(788\) 0 0
\(789\) −18.4783 3.06651i −0.657846 0.109171i
\(790\) 0 0
\(791\) −18.0093 + 28.6669i −0.640338 + 1.01928i
\(792\) 0 0
\(793\) −16.8240 + 29.1400i −0.597438 + 1.03479i
\(794\) 0 0
\(795\) −5.70558 0.946852i −0.202356 0.0335814i
\(796\) 0 0
\(797\) 7.96836 + 4.60053i 0.282254 + 0.162959i 0.634443 0.772969i \(-0.281229\pi\)
−0.352190 + 0.935929i \(0.614563\pi\)
\(798\) 0 0
\(799\) −2.19924 + 1.26973i −0.0778035 + 0.0449199i
\(800\) 0 0
\(801\) −0.777185 + 0.153253i −0.0274605 + 0.00541494i
\(802\) 0 0
\(803\) −34.0053 −1.20002
\(804\) 0 0
\(805\) 1.62145 2.58100i 0.0571487 0.0909683i
\(806\) 0 0
\(807\) −15.0084 + 18.2569i −0.528320 + 0.642673i
\(808\) 0 0
\(809\) 12.5382 + 21.7168i 0.440820 + 0.763523i 0.997751 0.0670362i \(-0.0213543\pi\)
−0.556930 + 0.830559i \(0.688021\pi\)
\(810\) 0 0
\(811\) −28.4265 −0.998191 −0.499095 0.866547i \(-0.666334\pi\)
−0.499095 + 0.866547i \(0.666334\pi\)
\(812\) 0 0
\(813\) −3.11640 + 18.7789i −0.109297 + 0.658606i
\(814\) 0 0
\(815\) 32.3386 1.13277
\(816\) 0 0
\(817\) 2.32242i 0.0812512i
\(818\) 0 0
\(819\) 41.6665 6.61193i 1.45595 0.231040i
\(820\) 0 0
\(821\) −43.1755 −1.50684 −0.753418 0.657542i \(-0.771596\pi\)
−0.753418 + 0.657542i \(0.771596\pi\)
\(822\) 0 0
\(823\) 31.1928i 1.08731i 0.839308 + 0.543656i \(0.182960\pi\)
−0.839308 + 0.543656i \(0.817040\pi\)
\(824\) 0 0
\(825\) −12.5922 + 15.3178i −0.438406 + 0.533297i
\(826\) 0 0
\(827\) 28.5280i 0.992015i 0.868318 + 0.496008i \(0.165201\pi\)
−0.868318 + 0.496008i \(0.834799\pi\)
\(828\) 0 0
\(829\) 11.4834 6.62996i 0.398836 0.230268i −0.287146 0.957887i \(-0.592706\pi\)
0.685982 + 0.727619i \(0.259373\pi\)
\(830\) 0 0
\(831\) 6.02397 36.2995i 0.208969 1.25922i
\(832\) 0 0
\(833\) 34.2002 16.4769i 1.18497 0.570891i
\(834\) 0 0
\(835\) 26.6389i 0.921878i
\(836\) 0 0
\(837\) 25.1346 46.7436i 0.868777 1.61569i
\(838\) 0 0
\(839\) 25.8498 + 44.7732i 0.892434 + 1.54574i 0.836949 + 0.547281i \(0.184337\pi\)
0.0554852 + 0.998460i \(0.482329\pi\)
\(840\) 0 0
\(841\) 11.8608 20.5435i 0.408994 0.708398i
\(842\) 0 0
\(843\) −14.4204 11.8545i −0.496664 0.408290i
\(844\) 0 0
\(845\) 23.4163 + 13.5194i 0.805546 + 0.465082i
\(846\) 0 0
\(847\) −33.4061 63.1948i −1.14785 2.17140i
\(848\) 0 0
\(849\) 2.61538 0.981888i 0.0897598 0.0336983i
\(850\) 0 0
\(851\) 1.42393i 0.0488118i
\(852\) 0 0
\(853\) −7.05764 + 4.07473i −0.241649 + 0.139516i −0.615934 0.787798i \(-0.711221\pi\)
0.374285 + 0.927314i \(0.377888\pi\)
\(854\) 0 0
\(855\) −6.54931 7.49307i −0.223982 0.256258i
\(856\) 0 0
\(857\) −10.1744 5.87421i −0.347552 0.200659i 0.316055 0.948741i \(-0.397642\pi\)
−0.663606 + 0.748082i \(0.730975\pi\)
\(858\) 0 0
\(859\) −5.47139 9.47672i −0.186681 0.323342i 0.757460 0.652881i \(-0.226440\pi\)
−0.944142 + 0.329539i \(0.893107\pi\)
\(860\) 0 0
\(861\) 34.4430 + 7.04547i 1.17382 + 0.240109i
\(862\) 0 0
\(863\) −2.81866 1.62735i −0.0959482 0.0553957i 0.451258 0.892393i \(-0.350975\pi\)
−0.547206 + 0.836998i \(0.684309\pi\)
\(864\) 0 0
\(865\) 2.51271 + 4.35215i 0.0854348 + 0.147977i
\(866\) 0 0
\(867\) 3.51929 21.2067i 0.119521 0.720216i
\(868\) 0 0
\(869\) −32.6300 + 56.5168i −1.10690 + 1.91720i
\(870\) 0 0
\(871\) 26.4024 45.7303i 0.894611 1.54951i
\(872\) 0 0
\(873\) −14.0720 + 41.2301i −0.476264 + 1.39543i
\(874\) 0 0
\(875\) 1.19997 32.1406i 0.0405664 1.08655i
\(876\) 0 0
\(877\) 6.94971 + 12.0373i 0.234675 + 0.406469i 0.959178 0.282802i \(-0.0912641\pi\)
−0.724503 + 0.689271i \(0.757931\pi\)
\(878\) 0 0
\(879\) −10.0549 1.66862i −0.339142 0.0562812i
\(880\) 0 0
\(881\) 18.1825i 0.612583i −0.951938 0.306292i \(-0.900912\pi\)
0.951938 0.306292i \(-0.0990882\pi\)
\(882\) 0 0
\(883\) 8.80976i 0.296472i 0.988952 + 0.148236i \(0.0473595\pi\)
−0.988952 + 0.148236i \(0.952640\pi\)
\(884\) 0 0
\(885\) −18.0334 + 21.9367i −0.606186 + 0.737394i
\(886\) 0 0
\(887\) 21.8229 + 37.7984i 0.732742 + 1.26915i 0.955707 + 0.294320i \(0.0950933\pi\)
−0.222964 + 0.974827i \(0.571573\pi\)
\(888\) 0 0
\(889\) 0.330195 8.84412i 0.0110744 0.296622i
\(890\) 0 0
\(891\) 33.9273 43.9129i 1.13661 1.47114i
\(892\) 0 0
\(893\) −0.438077 + 0.758772i −0.0146597 + 0.0253913i
\(894\) 0 0
\(895\) −13.3197 + 23.0703i −0.445227 + 0.771156i
\(896\) 0 0
\(897\) 5.60055 2.10260i 0.186997 0.0702038i
\(898\) 0 0
\(899\) −11.7330 20.3222i −0.391317 0.677782i
\(900\) 0 0
\(901\) −8.84577 5.10711i −0.294695 0.170142i
\(902\) 0 0
\(903\) 3.77346 4.25604i 0.125573 0.141632i
\(904\) 0 0
\(905\) 21.9922 + 38.0917i 0.731047 + 1.26621i
\(906\) 0 0
\(907\) 0.424560 + 0.245120i 0.0140973 + 0.00813907i 0.507032 0.861927i \(-0.330743\pi\)
−0.492935 + 0.870066i \(0.664076\pi\)
\(908\) 0 0
\(909\) 38.1080 7.51453i 1.26396 0.249241i
\(910\) 0 0
\(911\) −27.7336 + 16.0120i −0.918857 + 0.530502i −0.883270 0.468864i \(-0.844663\pi\)
−0.0355865 + 0.999367i \(0.511330\pi\)
\(912\) 0 0
\(913\) 50.0740i 1.65721i
\(914\) 0 0
\(915\) −15.0169 12.3449i −0.496445 0.408111i
\(916\) 0 0
\(917\) −3.77203 7.13561i −0.124563 0.235639i
\(918\) 0 0
\(919\) −37.3319 21.5536i −1.23146 0.710986i −0.264129 0.964487i \(-0.585085\pi\)
−0.967335 + 0.253501i \(0.918418\pi\)
\(920\) 0 0
\(921\) −8.00677 + 3.00596i −0.263832 + 0.0990498i
\(922\) 0 0
\(923\) 29.6312 51.3228i 0.975323 1.68931i
\(924\) 0 0
\(925\) 2.03437 + 3.52363i 0.0668896 + 0.115856i
\(926\) 0 0
\(927\) −35.4643 12.1041i −1.16480 0.397550i
\(928\) 0 0
\(929\) 26.4825i 0.868863i −0.900705 0.434432i \(-0.856949\pi\)
0.900705 0.434432i \(-0.143051\pi\)
\(930\) 0 0
\(931\) 7.37637 10.8230i 0.241751 0.354709i
\(932\) 0 0
\(933\) 25.4680 9.56138i 0.833784 0.313026i
\(934\) 0 0
\(935\) 51.3412 29.6419i 1.67904 0.969393i
\(936\) 0 0
\(937\) 42.2140i 1.37907i −0.724252 0.689535i \(-0.757815\pi\)
0.724252 0.689535i \(-0.242185\pi\)
\(938\) 0 0
\(939\) −20.6567 55.0217i −0.674105 1.79557i
\(940\) 0 0
\(941\) 32.9583i 1.07441i 0.843452 + 0.537204i \(0.180520\pi\)
−0.843452 + 0.537204i \(0.819480\pi\)
\(942\) 0 0
\(943\) 4.98515 0.162339
\(944\) 0 0
\(945\) −0.172525 + 24.3730i −0.00561225 + 0.792854i
\(946\) 0 0
\(947\) 47.1913i 1.53351i −0.641939 0.766755i \(-0.721870\pi\)
0.641939 0.766755i \(-0.278130\pi\)
\(948\) 0 0
\(949\) 29.3139 0.951569
\(950\) 0 0
\(951\) 26.6871 10.0191i 0.865387 0.324890i
\(952\) 0 0
\(953\) −51.1369 −1.65649 −0.828244 0.560368i \(-0.810660\pi\)
−0.828244 + 0.560368i \(0.810660\pi\)
\(954\) 0 0
\(955\) 22.3756 + 38.7556i 0.724057 + 1.25410i
\(956\) 0 0
\(957\) −8.62373 22.9704i −0.278766 0.742528i
\(958\) 0 0
\(959\) −18.5429 + 29.5163i −0.598783 + 0.953132i
\(960\) 0 0
\(961\) 73.3225 2.36524
\(962\) 0 0
\(963\) −30.5920 + 6.03243i −0.985812 + 0.194392i
\(964\) 0 0
\(965\) −23.2767 + 13.4388i −0.749303 + 0.432610i
\(966\) 0 0
\(967\) −8.10631 4.68018i −0.260681 0.150504i 0.363964 0.931413i \(-0.381423\pi\)
−0.624645 + 0.780909i \(0.714756\pi\)
\(968\) 0 0
\(969\) −6.17738 16.4543i −0.198446 0.528587i
\(970\) 0 0
\(971\) −11.1378 + 19.2913i −0.357429 + 0.619086i −0.987531 0.157427i \(-0.949680\pi\)
0.630101 + 0.776513i \(0.283013\pi\)
\(972\) 0 0
\(973\) −16.2774 + 25.9101i −0.521830 + 0.830639i
\(974\) 0 0
\(975\) 10.8550 13.2045i 0.347638 0.422883i
\(976\) 0 0
\(977\) −57.7424 −1.84734 −0.923671 0.383186i \(-0.874827\pi\)
−0.923671 + 0.383186i \(0.874827\pi\)
\(978\) 0 0
\(979\) −0.814043 1.40996i −0.0260169 0.0450627i
\(980\) 0 0
\(981\) 7.63452 + 2.60569i 0.243752 + 0.0831932i
\(982\) 0 0
\(983\) −0.946409 + 1.63923i −0.0301858 + 0.0522833i −0.880724 0.473631i \(-0.842943\pi\)
0.850538 + 0.525914i \(0.176277\pi\)
\(984\) 0 0
\(985\) −2.90548 + 1.67748i −0.0925763 + 0.0534490i
\(986\) 0 0
\(987\) 2.03566 0.678729i 0.0647959 0.0216042i
\(988\) 0 0
\(989\) 0.403276 0.698494i 0.0128234 0.0222108i
\(990\) 0 0
\(991\) 13.3910 7.73132i 0.425380 0.245594i −0.271996 0.962298i \(-0.587684\pi\)
0.697377 + 0.716705i \(0.254350\pi\)
\(992\) 0 0
\(993\) −2.39095 6.36860i −0.0758744 0.202101i
\(994\) 0 0
\(995\) −20.3617 11.7558i −0.645510 0.372685i
\(996\) 0 0
\(997\) 7.70115 + 4.44626i 0.243898 + 0.140815i 0.616967 0.786989i \(-0.288361\pi\)
−0.373069 + 0.927804i \(0.621695\pi\)
\(998\) 0 0
\(999\) −5.98874 9.68427i −0.189475 0.306397i
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 1008.2.cz.h.607.11 yes 24
3.2 odd 2 3024.2.cz.g.1279.5 24
4.3 odd 2 1008.2.cz.g.607.2 yes 24
7.3 odd 6 1008.2.bf.h.31.9 yes 24
9.2 odd 6 3024.2.bf.h.2287.5 24
9.7 even 3 1008.2.bf.g.943.4 yes 24
12.11 even 2 3024.2.cz.h.1279.5 24
21.17 even 6 3024.2.bf.g.1711.8 24
28.3 even 6 1008.2.bf.g.31.4 24
36.7 odd 6 1008.2.bf.h.943.9 yes 24
36.11 even 6 3024.2.bf.g.2287.5 24
63.38 even 6 3024.2.cz.h.2719.5 24
63.52 odd 6 1008.2.cz.g.367.2 yes 24
84.59 odd 6 3024.2.bf.h.1711.8 24
252.115 even 6 inner 1008.2.cz.h.367.11 yes 24
252.227 odd 6 3024.2.cz.g.2719.5 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1008.2.bf.g.31.4 24 28.3 even 6
1008.2.bf.g.943.4 yes 24 9.7 even 3
1008.2.bf.h.31.9 yes 24 7.3 odd 6
1008.2.bf.h.943.9 yes 24 36.7 odd 6
1008.2.cz.g.367.2 yes 24 63.52 odd 6
1008.2.cz.g.607.2 yes 24 4.3 odd 2
1008.2.cz.h.367.11 yes 24 252.115 even 6 inner
1008.2.cz.h.607.11 yes 24 1.1 even 1 trivial
3024.2.bf.g.1711.8 24 21.17 even 6
3024.2.bf.g.2287.5 24 36.11 even 6
3024.2.bf.h.1711.8 24 84.59 odd 6
3024.2.bf.h.2287.5 24 9.2 odd 6
3024.2.cz.g.1279.5 24 3.2 odd 2
3024.2.cz.g.2719.5 24 252.227 odd 6
3024.2.cz.h.1279.5 24 12.11 even 2
3024.2.cz.h.2719.5 24 63.38 even 6