Properties

Label 3024.2.t.k.289.11
Level $3024$
Weight $2$
Character 3024.289
Analytic conductor $24.147$
Analytic rank $0$
Dimension $22$
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] = [3024,2,Mod(289,3024)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3024.289");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.t (of order \(3\), 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: \(24.1467615712\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 289.11
Character \(\chi\) \(=\) 3024.289
Dual form 3024.2.t.k.1873.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.22296 q^{5} +(2.37802 + 1.15974i) q^{7} +O(q^{10})\) \(q+4.22296 q^{5} +(2.37802 + 1.15974i) q^{7} +1.92915 q^{11} +(-0.291529 - 0.504943i) q^{13} +(-3.61082 - 6.25412i) q^{17} +(-2.10268 + 3.64194i) q^{19} +1.27988 q^{23} +12.8334 q^{25} +(4.20305 - 7.27990i) q^{29} +(-0.476061 + 0.824561i) q^{31} +(10.0423 + 4.89755i) q^{35} +(3.03329 - 5.25381i) q^{37} +(-1.31299 - 2.27416i) q^{41} +(-0.442349 + 0.766171i) q^{43} +(-2.88201 - 4.99178i) q^{47} +(4.30999 + 5.51579i) q^{49} +(0.962456 + 1.66702i) q^{53} +8.14673 q^{55} +(2.27614 - 3.94240i) q^{59} +(5.29008 + 9.16268i) q^{61} +(-1.23112 - 2.13236i) q^{65} +(-2.43191 + 4.21220i) q^{67} +11.5443 q^{71} +(0.446138 + 0.772734i) q^{73} +(4.58756 + 2.23732i) q^{77} +(-5.93520 - 10.2801i) q^{79} +(-5.24250 + 9.08028i) q^{83} +(-15.2484 - 26.4109i) q^{85} +(-3.87906 + 6.71874i) q^{89} +(-0.107659 - 1.53887i) q^{91} +(-8.87953 + 15.3798i) q^{95} +(-1.98651 + 3.44073i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q + 2 q^{5} + q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 22 q + 2 q^{5} + q^{7} - 6 q^{11} + 7 q^{13} + q^{17} - 13 q^{19} + 44 q^{25} + 7 q^{29} - 6 q^{31} + 2 q^{35} + 6 q^{37} - 4 q^{41} - 2 q^{43} + 17 q^{47} + 29 q^{49} - q^{53} - 2 q^{55} - 21 q^{59} + 31 q^{61} + 3 q^{65} + 26 q^{67} - 32 q^{71} + 17 q^{73} + 4 q^{77} + 16 q^{79} - 36 q^{83} + 28 q^{85} + 2 q^{89} - 15 q^{91} - 24 q^{95} + 19 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1135\) \(2593\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) 4.22296 1.88857 0.944283 0.329134i \(-0.106757\pi\)
0.944283 + 0.329134i \(0.106757\pi\)
\(6\) 0 0
\(7\) 2.37802 + 1.15974i 0.898809 + 0.438341i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.92915 0.581660 0.290830 0.956775i \(-0.406069\pi\)
0.290830 + 0.956775i \(0.406069\pi\)
\(12\) 0 0
\(13\) −0.291529 0.504943i −0.0808557 0.140046i 0.822762 0.568386i \(-0.192432\pi\)
−0.903618 + 0.428340i \(0.859099\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.61082 6.25412i −0.875753 1.51685i −0.855959 0.517044i \(-0.827032\pi\)
−0.0197936 0.999804i \(-0.506301\pi\)
\(18\) 0 0
\(19\) −2.10268 + 3.64194i −0.482387 + 0.835519i −0.999796 0.0202194i \(-0.993564\pi\)
0.517408 + 0.855739i \(0.326897\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.27988 0.266873 0.133437 0.991057i \(-0.457399\pi\)
0.133437 + 0.991057i \(0.457399\pi\)
\(24\) 0 0
\(25\) 12.8334 2.56668
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4.20305 7.27990i 0.780487 1.35184i −0.151171 0.988508i \(-0.548305\pi\)
0.931658 0.363335i \(-0.118362\pi\)
\(30\) 0 0
\(31\) −0.476061 + 0.824561i −0.0855030 + 0.148096i −0.905605 0.424121i \(-0.860583\pi\)
0.820102 + 0.572217i \(0.193916\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 10.0423 + 4.89755i 1.69746 + 0.827837i
\(36\) 0 0
\(37\) 3.03329 5.25381i 0.498669 0.863721i −0.501330 0.865256i \(-0.667156\pi\)
0.999999 + 0.00153588i \(0.000488885\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −1.31299 2.27416i −0.205054 0.355164i 0.745096 0.666957i \(-0.232404\pi\)
−0.950150 + 0.311794i \(0.899070\pi\)
\(42\) 0 0
\(43\) −0.442349 + 0.766171i −0.0674576 + 0.116840i −0.897782 0.440441i \(-0.854822\pi\)
0.830324 + 0.557281i \(0.188155\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −2.88201 4.99178i −0.420384 0.728126i 0.575593 0.817736i \(-0.304771\pi\)
−0.995977 + 0.0896103i \(0.971438\pi\)
\(48\) 0 0
\(49\) 4.30999 + 5.51579i 0.615713 + 0.787970i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0.962456 + 1.66702i 0.132204 + 0.228983i 0.924526 0.381120i \(-0.124461\pi\)
−0.792322 + 0.610103i \(0.791128\pi\)
\(54\) 0 0
\(55\) 8.14673 1.09850
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 2.27614 3.94240i 0.296329 0.513256i −0.678964 0.734171i \(-0.737571\pi\)
0.975293 + 0.220915i \(0.0709043\pi\)
\(60\) 0 0
\(61\) 5.29008 + 9.16268i 0.677325 + 1.17316i 0.975783 + 0.218739i \(0.0701943\pi\)
−0.298458 + 0.954423i \(0.596472\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.23112 2.13236i −0.152701 0.264486i
\(66\) 0 0
\(67\) −2.43191 + 4.21220i −0.297106 + 0.514602i −0.975473 0.220121i \(-0.929355\pi\)
0.678367 + 0.734723i \(0.262688\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 11.5443 1.37005 0.685027 0.728518i \(-0.259791\pi\)
0.685027 + 0.728518i \(0.259791\pi\)
\(72\) 0 0
\(73\) 0.446138 + 0.772734i 0.0522165 + 0.0904417i 0.890952 0.454097i \(-0.150038\pi\)
−0.838736 + 0.544539i \(0.816705\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4.58756 + 2.23732i 0.522801 + 0.254966i
\(78\) 0 0
\(79\) −5.93520 10.2801i −0.667763 1.15660i −0.978528 0.206112i \(-0.933919\pi\)
0.310766 0.950487i \(-0.399415\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −5.24250 + 9.08028i −0.575439 + 0.996690i 0.420555 + 0.907267i \(0.361836\pi\)
−0.995994 + 0.0894227i \(0.971498\pi\)
\(84\) 0 0
\(85\) −15.2484 26.4109i −1.65392 2.86467i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −3.87906 + 6.71874i −0.411180 + 0.712185i −0.995019 0.0996849i \(-0.968217\pi\)
0.583839 + 0.811869i \(0.301550\pi\)
\(90\) 0 0
\(91\) −0.107659 1.53887i −0.0112857 0.161317i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −8.87953 + 15.3798i −0.911020 + 1.57793i
\(96\) 0 0
\(97\) −1.98651 + 3.44073i −0.201699 + 0.349353i −0.949076 0.315047i \(-0.897980\pi\)
0.747377 + 0.664400i \(0.231313\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −16.7707 −1.66874 −0.834372 0.551202i \(-0.814169\pi\)
−0.834372 + 0.551202i \(0.814169\pi\)
\(102\) 0 0
\(103\) −11.6114 −1.14410 −0.572052 0.820218i \(-0.693852\pi\)
−0.572052 + 0.820218i \(0.693852\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −10.2454 + 17.7455i −0.990460 + 1.71553i −0.375890 + 0.926664i \(0.622663\pi\)
−0.614570 + 0.788862i \(0.710671\pi\)
\(108\) 0 0
\(109\) 2.46965 + 4.27756i 0.236550 + 0.409716i 0.959722 0.280951i \(-0.0906500\pi\)
−0.723172 + 0.690668i \(0.757317\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 7.42131 + 12.8541i 0.698138 + 1.20921i 0.969111 + 0.246623i \(0.0793210\pi\)
−0.270974 + 0.962587i \(0.587346\pi\)
\(114\) 0 0
\(115\) 5.40488 0.504008
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.33344 19.0601i −0.122236 1.74723i
\(120\) 0 0
\(121\) −7.27838 −0.661671
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 33.0802 2.95879
\(126\) 0 0
\(127\) 8.53648 0.757490 0.378745 0.925501i \(-0.376356\pi\)
0.378745 + 0.925501i \(0.376356\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −2.34684 −0.205045 −0.102522 0.994731i \(-0.532691\pi\)
−0.102522 + 0.994731i \(0.532691\pi\)
\(132\) 0 0
\(133\) −9.22393 + 6.22207i −0.799817 + 0.539522i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1.28363 −0.109668 −0.0548340 0.998495i \(-0.517463\pi\)
−0.0548340 + 0.998495i \(0.517463\pi\)
\(138\) 0 0
\(139\) −0.610553 1.05751i −0.0517865 0.0896968i 0.838970 0.544177i \(-0.183158\pi\)
−0.890757 + 0.454481i \(0.849825\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −0.562403 0.974111i −0.0470305 0.0814593i
\(144\) 0 0
\(145\) 17.7493 30.7427i 1.47400 2.55305i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −6.29459 −0.515673 −0.257836 0.966189i \(-0.583010\pi\)
−0.257836 + 0.966189i \(0.583010\pi\)
\(150\) 0 0
\(151\) −2.35453 −0.191609 −0.0958044 0.995400i \(-0.530542\pi\)
−0.0958044 + 0.995400i \(0.530542\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −2.01039 + 3.48209i −0.161478 + 0.279688i
\(156\) 0 0
\(157\) 1.44437 2.50172i 0.115273 0.199659i −0.802616 0.596496i \(-0.796559\pi\)
0.917889 + 0.396838i \(0.129892\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 3.04358 + 1.48433i 0.239868 + 0.116982i
\(162\) 0 0
\(163\) −2.60538 + 4.51265i −0.204069 + 0.353458i −0.949836 0.312749i \(-0.898750\pi\)
0.745767 + 0.666207i \(0.232083\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 10.5400 + 18.2558i 0.815610 + 1.41268i 0.908889 + 0.417039i \(0.136932\pi\)
−0.0932784 + 0.995640i \(0.529735\pi\)
\(168\) 0 0
\(169\) 6.33002 10.9639i 0.486925 0.843378i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −2.03653 3.52737i −0.154834 0.268181i 0.778164 0.628061i \(-0.216151\pi\)
−0.932999 + 0.359880i \(0.882818\pi\)
\(174\) 0 0
\(175\) 30.5182 + 14.8835i 2.30696 + 1.12508i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −3.11088 5.38821i −0.232518 0.402733i 0.726030 0.687663i \(-0.241363\pi\)
−0.958549 + 0.284929i \(0.908030\pi\)
\(180\) 0 0
\(181\) 18.2396 1.35574 0.677868 0.735184i \(-0.262904\pi\)
0.677868 + 0.735184i \(0.262904\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 12.8095 22.1866i 0.941770 1.63119i
\(186\) 0 0
\(187\) −6.96581 12.0651i −0.509391 0.882290i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3.69298 + 6.39644i 0.267215 + 0.462830i 0.968142 0.250404i \(-0.0805633\pi\)
−0.700927 + 0.713233i \(0.747230\pi\)
\(192\) 0 0
\(193\) −9.75908 + 16.9032i −0.702474 + 1.21672i 0.265121 + 0.964215i \(0.414588\pi\)
−0.967595 + 0.252506i \(0.918745\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −7.77564 −0.553992 −0.276996 0.960871i \(-0.589339\pi\)
−0.276996 + 0.960871i \(0.589339\pi\)
\(198\) 0 0
\(199\) 3.85734 + 6.68110i 0.273439 + 0.473611i 0.969740 0.244139i \(-0.0785054\pi\)
−0.696301 + 0.717750i \(0.745172\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 18.4378 12.4373i 1.29408 0.872928i
\(204\) 0 0
\(205\) −5.54469 9.60368i −0.387258 0.670750i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −4.05638 + 7.02585i −0.280586 + 0.485989i
\(210\) 0 0
\(211\) −11.7645 20.3767i −0.809899 1.40279i −0.912933 0.408109i \(-0.866188\pi\)
0.103034 0.994678i \(-0.467145\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1.86802 + 3.23551i −0.127398 + 0.220660i
\(216\) 0 0
\(217\) −2.08836 + 1.40872i −0.141767 + 0.0956301i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2.10532 + 3.64652i −0.141619 + 0.245291i
\(222\) 0 0
\(223\) 4.83093 8.36742i 0.323503 0.560324i −0.657705 0.753275i \(-0.728473\pi\)
0.981208 + 0.192952i \(0.0618061\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 17.9718 1.19283 0.596417 0.802675i \(-0.296591\pi\)
0.596417 + 0.802675i \(0.296591\pi\)
\(228\) 0 0
\(229\) −7.91668 −0.523149 −0.261574 0.965183i \(-0.584242\pi\)
−0.261574 + 0.965183i \(0.584242\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3.27796 + 5.67759i −0.214746 + 0.371951i −0.953194 0.302359i \(-0.902226\pi\)
0.738448 + 0.674311i \(0.235559\pi\)
\(234\) 0 0
\(235\) −12.1706 21.0801i −0.793922 1.37511i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −8.01922 13.8897i −0.518720 0.898450i −0.999763 0.0217529i \(-0.993075\pi\)
0.481043 0.876697i \(-0.340258\pi\)
\(240\) 0 0
\(241\) 11.1791 0.720112 0.360056 0.932931i \(-0.382758\pi\)
0.360056 + 0.932931i \(0.382758\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 18.2009 + 23.2930i 1.16282 + 1.48813i
\(246\) 0 0
\(247\) 2.45197 0.156015
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 14.6169 0.922613 0.461307 0.887241i \(-0.347381\pi\)
0.461307 + 0.887241i \(0.347381\pi\)
\(252\) 0 0
\(253\) 2.46908 0.155230
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −14.9187 −0.930605 −0.465302 0.885152i \(-0.654054\pi\)
−0.465302 + 0.885152i \(0.654054\pi\)
\(258\) 0 0
\(259\) 13.3063 8.97585i 0.826813 0.557732i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −22.2114 −1.36962 −0.684808 0.728724i \(-0.740114\pi\)
−0.684808 + 0.728724i \(0.740114\pi\)
\(264\) 0 0
\(265\) 4.06442 + 7.03978i 0.249675 + 0.432450i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 4.73590 + 8.20281i 0.288753 + 0.500134i 0.973512 0.228635i \(-0.0734261\pi\)
−0.684760 + 0.728769i \(0.740093\pi\)
\(270\) 0 0
\(271\) −8.78188 + 15.2107i −0.533461 + 0.923982i 0.465775 + 0.884903i \(0.345776\pi\)
−0.999236 + 0.0390786i \(0.987558\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 24.7576 1.49294
\(276\) 0 0
\(277\) 13.5530 0.814322 0.407161 0.913356i \(-0.366519\pi\)
0.407161 + 0.913356i \(0.366519\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −6.14196 + 10.6382i −0.366398 + 0.634621i −0.989000 0.147919i \(-0.952743\pi\)
0.622601 + 0.782539i \(0.286076\pi\)
\(282\) 0 0
\(283\) 7.02415 12.1662i 0.417542 0.723204i −0.578149 0.815931i \(-0.696225\pi\)
0.995692 + 0.0927267i \(0.0295583\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.484873 6.93072i −0.0286212 0.409108i
\(288\) 0 0
\(289\) −17.5760 + 30.4426i −1.03388 + 1.79074i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −4.05863 7.02975i −0.237108 0.410682i 0.722776 0.691083i \(-0.242866\pi\)
−0.959883 + 0.280401i \(0.909533\pi\)
\(294\) 0 0
\(295\) 9.61207 16.6486i 0.559636 0.969319i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −0.373122 0.646266i −0.0215782 0.0373746i
\(300\) 0 0
\(301\) −1.94048 + 1.30896i −0.111847 + 0.0754473i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 22.3398 + 38.6937i 1.27917 + 2.21559i
\(306\) 0 0
\(307\) −6.61556 −0.377570 −0.188785 0.982018i \(-0.560455\pi\)
−0.188785 + 0.982018i \(0.560455\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 4.17980 7.23963i 0.237015 0.410522i −0.722841 0.691014i \(-0.757164\pi\)
0.959856 + 0.280492i \(0.0904976\pi\)
\(312\) 0 0
\(313\) −13.0542 22.6105i −0.737864 1.27802i −0.953455 0.301535i \(-0.902501\pi\)
0.215591 0.976484i \(-0.430832\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 5.60741 + 9.71231i 0.314943 + 0.545498i 0.979425 0.201806i \(-0.0646812\pi\)
−0.664482 + 0.747304i \(0.731348\pi\)
\(318\) 0 0
\(319\) 8.10831 14.0440i 0.453978 0.786314i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 30.3696 1.68981
\(324\) 0 0
\(325\) −3.74132 6.48015i −0.207531 0.359454i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1.06430 15.2130i −0.0586766 0.838717i
\(330\) 0 0
\(331\) −9.11645 15.7902i −0.501086 0.867906i −0.999999 0.00125391i \(-0.999601\pi\)
0.498914 0.866652i \(-0.333732\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −10.2699 + 17.7880i −0.561104 + 0.971860i
\(336\) 0 0
\(337\) 4.62148 + 8.00465i 0.251748 + 0.436041i 0.964007 0.265876i \(-0.0856612\pi\)
−0.712259 + 0.701917i \(0.752328\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −0.918392 + 1.59070i −0.0497337 + 0.0861413i
\(342\) 0 0
\(343\) 3.85237 + 18.1152i 0.208009 + 0.978127i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 15.8325 27.4226i 0.849931 1.47212i −0.0313384 0.999509i \(-0.509977\pi\)
0.881269 0.472615i \(-0.156690\pi\)
\(348\) 0 0
\(349\) −18.2112 + 31.5427i −0.974821 + 1.68844i −0.294296 + 0.955714i \(0.595085\pi\)
−0.680525 + 0.732725i \(0.738248\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −7.19777 −0.383098 −0.191549 0.981483i \(-0.561351\pi\)
−0.191549 + 0.981483i \(0.561351\pi\)
\(354\) 0 0
\(355\) 48.7510 2.58744
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −7.39891 + 12.8153i −0.390499 + 0.676365i −0.992515 0.122119i \(-0.961031\pi\)
0.602016 + 0.798484i \(0.294364\pi\)
\(360\) 0 0
\(361\) 0.657495 + 1.13881i 0.0346050 + 0.0599376i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.88402 + 3.26323i 0.0986144 + 0.170805i
\(366\) 0 0
\(367\) −4.19100 −0.218768 −0.109384 0.994000i \(-0.534888\pi\)
−0.109384 + 0.994000i \(0.534888\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0.355426 + 5.08042i 0.0184528 + 0.263762i
\(372\) 0 0
\(373\) 17.4175 0.901844 0.450922 0.892563i \(-0.351095\pi\)
0.450922 + 0.892563i \(0.351095\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −4.90125 −0.252427
\(378\) 0 0
\(379\) 11.1732 0.573927 0.286964 0.957941i \(-0.407354\pi\)
0.286964 + 0.957941i \(0.407354\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −25.1016 −1.28263 −0.641316 0.767276i \(-0.721611\pi\)
−0.641316 + 0.767276i \(0.721611\pi\)
\(384\) 0 0
\(385\) 19.3731 + 9.44811i 0.987345 + 0.481520i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.46402 −0.0742289 −0.0371144 0.999311i \(-0.511817\pi\)
−0.0371144 + 0.999311i \(0.511817\pi\)
\(390\) 0 0
\(391\) −4.62141 8.00452i −0.233715 0.404806i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −25.0641 43.4124i −1.26111 2.18431i
\(396\) 0 0
\(397\) −1.49591 + 2.59100i −0.0750778 + 0.130039i −0.901120 0.433570i \(-0.857254\pi\)
0.826042 + 0.563608i \(0.190587\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 26.3371 1.31521 0.657605 0.753363i \(-0.271570\pi\)
0.657605 + 0.753363i \(0.271570\pi\)
\(402\) 0 0
\(403\) 0.555142 0.0276536
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5.85166 10.1354i 0.290056 0.502392i
\(408\) 0 0
\(409\) −1.50392 + 2.60487i −0.0743642 + 0.128803i −0.900810 0.434214i \(-0.857026\pi\)
0.826445 + 0.563017i \(0.190359\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 9.98489 6.73537i 0.491324 0.331426i
\(414\) 0 0
\(415\) −22.1389 + 38.3457i −1.08676 + 1.88232i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −17.2414 29.8630i −0.842297 1.45890i −0.887948 0.459944i \(-0.847869\pi\)
0.0456508 0.998957i \(-0.485464\pi\)
\(420\) 0 0
\(421\) 9.86151 17.0806i 0.480620 0.832459i −0.519132 0.854694i \(-0.673745\pi\)
0.999753 + 0.0222349i \(0.00707818\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −46.3392 80.2618i −2.24778 3.89327i
\(426\) 0 0
\(427\) 1.95358 + 27.9242i 0.0945402 + 1.35135i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 10.4257 + 18.0578i 0.502188 + 0.869816i 0.999997 + 0.00252883i \(0.000804953\pi\)
−0.497808 + 0.867287i \(0.665862\pi\)
\(432\) 0 0
\(433\) 15.6324 0.751247 0.375624 0.926772i \(-0.377429\pi\)
0.375624 + 0.926772i \(0.377429\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.69117 + 4.66125i −0.128736 + 0.222978i
\(438\) 0 0
\(439\) 17.8495 + 30.9162i 0.851909 + 1.47555i 0.879483 + 0.475930i \(0.157888\pi\)
−0.0275746 + 0.999620i \(0.508778\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −9.05787 15.6887i −0.430352 0.745392i 0.566551 0.824027i \(-0.308277\pi\)
−0.996904 + 0.0786344i \(0.974944\pi\)
\(444\) 0 0
\(445\) −16.3811 + 28.3730i −0.776541 + 1.34501i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −17.4189 −0.822051 −0.411025 0.911624i \(-0.634829\pi\)
−0.411025 + 0.911624i \(0.634829\pi\)
\(450\) 0 0
\(451\) −2.53294 4.38719i −0.119272 0.206585i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −0.454640 6.49858i −0.0213139 0.304658i
\(456\) 0 0
\(457\) −7.67918 13.3007i −0.359217 0.622182i 0.628613 0.777718i \(-0.283623\pi\)
−0.987830 + 0.155536i \(0.950290\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 6.15140 10.6545i 0.286499 0.496231i −0.686472 0.727156i \(-0.740842\pi\)
0.972972 + 0.230924i \(0.0741750\pi\)
\(462\) 0 0
\(463\) −9.18922 15.9162i −0.427059 0.739688i 0.569551 0.821956i \(-0.307117\pi\)
−0.996610 + 0.0822677i \(0.973784\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −11.1020 + 19.2292i −0.513738 + 0.889820i 0.486135 + 0.873884i \(0.338406\pi\)
−0.999873 + 0.0159363i \(0.994927\pi\)
\(468\) 0 0
\(469\) −10.6682 + 7.19631i −0.492612 + 0.332295i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −0.853358 + 1.47806i −0.0392374 + 0.0679612i
\(474\) 0 0
\(475\) −26.9845 + 46.7386i −1.23814 + 2.14451i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −34.5938 −1.58063 −0.790317 0.612699i \(-0.790084\pi\)
−0.790317 + 0.612699i \(0.790084\pi\)
\(480\) 0 0
\(481\) −3.53717 −0.161281
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −8.38895 + 14.5301i −0.380922 + 0.659777i
\(486\) 0 0
\(487\) −6.79789 11.7743i −0.308042 0.533544i 0.669892 0.742458i \(-0.266340\pi\)
−0.977934 + 0.208915i \(0.933007\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −7.01841 12.1563i −0.316737 0.548604i 0.663069 0.748559i \(-0.269254\pi\)
−0.979805 + 0.199955i \(0.935920\pi\)
\(492\) 0 0
\(493\) −60.7058 −2.73405
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 27.4526 + 13.3884i 1.23142 + 0.600551i
\(498\) 0 0
\(499\) 30.2816 1.35559 0.677794 0.735251i \(-0.262936\pi\)
0.677794 + 0.735251i \(0.262936\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −35.5942 −1.58707 −0.793533 0.608527i \(-0.791761\pi\)
−0.793533 + 0.608527i \(0.791761\pi\)
\(504\) 0 0
\(505\) −70.8219 −3.15153
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 6.47349 0.286932 0.143466 0.989655i \(-0.454175\pi\)
0.143466 + 0.989655i \(0.454175\pi\)
\(510\) 0 0
\(511\) 0.164755 + 2.35499i 0.00728832 + 0.104178i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −49.0344 −2.16072
\(516\) 0 0
\(517\) −5.55982 9.62989i −0.244521 0.423522i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −6.18988 10.7212i −0.271184 0.469704i 0.697982 0.716116i \(-0.254082\pi\)
−0.969165 + 0.246412i \(0.920748\pi\)
\(522\) 0 0
\(523\) −11.0290 + 19.1028i −0.482265 + 0.835308i −0.999793 0.0203585i \(-0.993519\pi\)
0.517527 + 0.855667i \(0.326853\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 6.87588 0.299518
\(528\) 0 0
\(529\) −21.3619 −0.928779
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −0.765547 + 1.32597i −0.0331595 + 0.0574340i
\(534\) 0 0
\(535\) −43.2659 + 74.9388i −1.87055 + 3.23989i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 8.31462 + 10.6408i 0.358136 + 0.458331i
\(540\) 0 0
\(541\) 7.24989 12.5572i 0.311697 0.539875i −0.667033 0.745028i \(-0.732436\pi\)
0.978730 + 0.205153i \(0.0657693\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 10.4293 + 18.0640i 0.446740 + 0.773777i
\(546\) 0 0
\(547\) 12.4034 21.4834i 0.530332 0.918562i −0.469042 0.883176i \(-0.655401\pi\)
0.999374 0.0353858i \(-0.0112660\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 17.6753 + 30.6146i 0.752994 + 1.30422i
\(552\) 0 0
\(553\) −2.19182 31.3296i −0.0932055 1.33227i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −9.02336 15.6289i −0.382332 0.662219i 0.609063 0.793122i \(-0.291546\pi\)
−0.991395 + 0.130903i \(0.958212\pi\)
\(558\) 0 0
\(559\) 0.515831 0.0218173
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −9.51748 + 16.4848i −0.401114 + 0.694749i −0.993861 0.110639i \(-0.964710\pi\)
0.592747 + 0.805389i \(0.298043\pi\)
\(564\) 0 0
\(565\) 31.3399 + 54.2823i 1.31848 + 2.28367i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 4.68018 + 8.10631i 0.196203 + 0.339834i 0.947294 0.320364i \(-0.103805\pi\)
−0.751091 + 0.660199i \(0.770472\pi\)
\(570\) 0 0
\(571\) 17.6805 30.6236i 0.739907 1.28156i −0.212630 0.977133i \(-0.568203\pi\)
0.952537 0.304424i \(-0.0984638\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 16.4252 0.684979
\(576\) 0 0
\(577\) 14.0160 + 24.2764i 0.583493 + 1.01064i 0.995061 + 0.0992610i \(0.0316479\pi\)
−0.411568 + 0.911379i \(0.635019\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −22.9976 + 15.5132i −0.954100 + 0.643595i
\(582\) 0 0
\(583\) 1.85672 + 3.21594i 0.0768976 + 0.133190i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 13.7305 23.7819i 0.566718 0.981585i −0.430169 0.902748i \(-0.641546\pi\)
0.996888 0.0788364i \(-0.0251205\pi\)
\(588\) 0 0
\(589\) −2.00200 3.46757i −0.0824912 0.142879i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 11.1267 19.2719i 0.456917 0.791404i −0.541879 0.840457i \(-0.682287\pi\)
0.998796 + 0.0490525i \(0.0156202\pi\)
\(594\) 0 0
\(595\) −5.63108 80.4900i −0.230852 3.29977i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −3.37059 + 5.83804i −0.137719 + 0.238536i −0.926633 0.375968i \(-0.877310\pi\)
0.788914 + 0.614504i \(0.210644\pi\)
\(600\) 0 0
\(601\) 4.04153 7.00013i 0.164857 0.285541i −0.771747 0.635929i \(-0.780617\pi\)
0.936605 + 0.350388i \(0.113950\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −30.7363 −1.24961
\(606\) 0 0
\(607\) −31.6039 −1.28276 −0.641382 0.767222i \(-0.721639\pi\)
−0.641382 + 0.767222i \(0.721639\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.68038 + 2.91050i −0.0679808 + 0.117746i
\(612\) 0 0
\(613\) −3.10601 5.37977i −0.125451 0.217287i 0.796458 0.604693i \(-0.206704\pi\)
−0.921909 + 0.387407i \(0.873371\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.309009 + 0.535218i 0.0124402 + 0.0215471i 0.872178 0.489188i \(-0.162707\pi\)
−0.859738 + 0.510735i \(0.829373\pi\)
\(618\) 0 0
\(619\) −40.0206 −1.60857 −0.804283 0.594247i \(-0.797450\pi\)
−0.804283 + 0.594247i \(0.797450\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −17.0165 + 11.4786i −0.681752 + 0.459880i
\(624\) 0 0
\(625\) 75.5295 3.02118
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −43.8106 −1.74684
\(630\) 0 0
\(631\) −5.20154 −0.207070 −0.103535 0.994626i \(-0.533015\pi\)
−0.103535 + 0.994626i \(0.533015\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 36.0492 1.43057
\(636\) 0 0
\(637\) 1.52867 3.78432i 0.0605682 0.149940i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0.274587 0.0108455 0.00542277 0.999985i \(-0.498274\pi\)
0.00542277 + 0.999985i \(0.498274\pi\)
\(642\) 0 0
\(643\) −11.2657 19.5128i −0.444277 0.769510i 0.553725 0.832700i \(-0.313206\pi\)
−0.998002 + 0.0631900i \(0.979873\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 12.2737 + 21.2586i 0.482528 + 0.835763i 0.999799 0.0200588i \(-0.00638534\pi\)
−0.517271 + 0.855822i \(0.673052\pi\)
\(648\) 0 0
\(649\) 4.39102 7.60547i 0.172363 0.298541i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −33.0308 −1.29260 −0.646298 0.763085i \(-0.723684\pi\)
−0.646298 + 0.763085i \(0.723684\pi\)
\(654\) 0 0
\(655\) −9.91064 −0.387241
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 21.3813 37.0335i 0.832897 1.44262i −0.0628336 0.998024i \(-0.520014\pi\)
0.895731 0.444596i \(-0.146653\pi\)
\(660\) 0 0
\(661\) 9.55416 16.5483i 0.371614 0.643654i −0.618200 0.786021i \(-0.712138\pi\)
0.989814 + 0.142367i \(0.0454713\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −38.9523 + 26.2756i −1.51051 + 1.01892i
\(666\) 0 0
\(667\) 5.37940 9.31739i 0.208291 0.360771i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 10.2054 + 17.6762i 0.393973 + 0.682382i
\(672\) 0 0
\(673\) −12.9345 + 22.4032i −0.498588 + 0.863579i −0.999999 0.00162995i \(-0.999481\pi\)
0.501411 + 0.865209i \(0.332815\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 0.946686 + 1.63971i 0.0363841 + 0.0630191i 0.883644 0.468159i \(-0.155083\pi\)
−0.847260 + 0.531178i \(0.821749\pi\)
\(678\) 0 0
\(679\) −8.71432 + 5.87830i −0.334425 + 0.225589i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −6.39573 11.0777i −0.244726 0.423878i 0.717329 0.696735i \(-0.245365\pi\)
−0.962055 + 0.272857i \(0.912031\pi\)
\(684\) 0 0
\(685\) −5.42072 −0.207115
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0.561168 0.971972i 0.0213788 0.0370292i
\(690\) 0 0
\(691\) −18.0349 31.2373i −0.686079 1.18832i −0.973096 0.230399i \(-0.925997\pi\)
0.287017 0.957925i \(-0.407336\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.57834 4.46582i −0.0978022 0.169398i
\(696\) 0 0
\(697\) −9.48191 + 16.4231i −0.359153 + 0.622071i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 20.2524 0.764922 0.382461 0.923972i \(-0.375077\pi\)
0.382461 + 0.923972i \(0.375077\pi\)
\(702\) 0 0
\(703\) 12.7560 + 22.0941i 0.481103 + 0.833296i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −39.8811 19.4497i −1.49988 0.731480i
\(708\) 0 0
\(709\) 3.38318 + 5.85984i 0.127058 + 0.220071i 0.922536 0.385912i \(-0.126113\pi\)
−0.795478 + 0.605983i \(0.792780\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −0.609300 + 1.05534i −0.0228185 + 0.0395227i
\(714\) 0 0
\(715\) −2.37501 4.11364i −0.0888203 0.153841i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 6.43767 11.1504i 0.240084 0.415839i −0.720654 0.693295i \(-0.756158\pi\)
0.960738 + 0.277457i \(0.0894915\pi\)
\(720\) 0 0
\(721\) −27.6121 13.4662i −1.02833 0.501508i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 53.9395 93.4260i 2.00326 3.46975i
\(726\) 0 0
\(727\) −14.3621 + 24.8758i −0.532659 + 0.922593i 0.466613 + 0.884461i \(0.345474\pi\)
−0.999273 + 0.0381316i \(0.987859\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 6.38897 0.236305
\(732\) 0 0
\(733\) 4.66050 0.172139 0.0860697 0.996289i \(-0.472569\pi\)
0.0860697 + 0.996289i \(0.472569\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −4.69153 + 8.12596i −0.172815 + 0.299324i
\(738\) 0 0
\(739\) −9.46395 16.3920i −0.348137 0.602991i 0.637782 0.770217i \(-0.279852\pi\)
−0.985919 + 0.167227i \(0.946519\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 6.64732 + 11.5135i 0.243867 + 0.422389i 0.961812 0.273710i \(-0.0882507\pi\)
−0.717946 + 0.696099i \(0.754917\pi\)
\(744\) 0 0
\(745\) −26.5818 −0.973882
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −44.9441 + 30.3173i −1.64222 + 1.10777i
\(750\) 0 0
\(751\) 15.2353 0.555945 0.277972 0.960589i \(-0.410338\pi\)
0.277972 + 0.960589i \(0.410338\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −9.94308 −0.361866
\(756\) 0 0
\(757\) 15.6279 0.568004 0.284002 0.958824i \(-0.408338\pi\)
0.284002 + 0.958824i \(0.408338\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −7.09595 −0.257228 −0.128614 0.991695i \(-0.541053\pi\)
−0.128614 + 0.991695i \(0.541053\pi\)
\(762\) 0 0
\(763\) 0.912020 + 13.0363i 0.0330173 + 0.471946i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −2.65425 −0.0958394
\(768\) 0 0
\(769\) 5.71618 + 9.90071i 0.206131 + 0.357029i 0.950492 0.310748i \(-0.100579\pi\)
−0.744362 + 0.667777i \(0.767246\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −7.40125 12.8193i −0.266204 0.461080i 0.701674 0.712498i \(-0.252436\pi\)
−0.967878 + 0.251418i \(0.919103\pi\)
\(774\) 0 0
\(775\) −6.10949 + 10.5819i −0.219459 + 0.380114i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 11.0431 0.395661
\(780\) 0 0
\(781\) 22.2706 0.796906
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 6.09951 10.5647i 0.217701 0.377069i
\(786\) 0 0
\(787\) −9.85887 + 17.0761i −0.351431 + 0.608696i −0.986500 0.163759i \(-0.947638\pi\)
0.635070 + 0.772455i \(0.280971\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 2.74062 + 39.1741i 0.0974452 + 1.39287i
\(792\) 0 0
\(793\) 3.08442 5.34238i 0.109531 0.189713i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −22.2215 38.4887i −0.787125 1.36334i −0.927722 0.373273i \(-0.878236\pi\)
0.140597 0.990067i \(-0.455098\pi\)
\(798\) 0 0
\(799\) −20.8128 + 36.0488i −0.736304 + 1.27532i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0.860667 + 1.49072i 0.0303723 + 0.0526063i
\(804\) 0 0
\(805\) 12.8529 + 6.26827i 0.453007 + 0.220928i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 5.34657 + 9.26053i 0.187975 + 0.325583i 0.944575 0.328296i \(-0.106474\pi\)
−0.756600 + 0.653878i \(0.773141\pi\)
\(810\) 0 0
\(811\) 13.1292 0.461030 0.230515 0.973069i \(-0.425959\pi\)
0.230515 + 0.973069i \(0.425959\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −11.0024 + 19.0567i −0.385398 + 0.667529i
\(816\) 0 0
\(817\) −1.86024 3.22202i −0.0650814 0.112724i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 1.31404 + 2.27598i 0.0458602 + 0.0794323i 0.888044 0.459758i \(-0.152064\pi\)
−0.842184 + 0.539190i \(0.818730\pi\)
\(822\) 0 0
\(823\) −23.1960 + 40.1767i −0.808563 + 1.40047i 0.105296 + 0.994441i \(0.466421\pi\)
−0.913859 + 0.406031i \(0.866912\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −15.2072 −0.528807 −0.264404 0.964412i \(-0.585175\pi\)
−0.264404 + 0.964412i \(0.585175\pi\)
\(828\) 0 0
\(829\) 19.0782 + 33.0445i 0.662615 + 1.14768i 0.979926 + 0.199361i \(0.0638867\pi\)
−0.317311 + 0.948322i \(0.602780\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 18.9338 46.8718i 0.656018 1.62401i
\(834\) 0 0
\(835\) 44.5101 + 77.0937i 1.54033 + 2.66794i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −5.52298 + 9.56608i −0.190674 + 0.330258i −0.945474 0.325698i \(-0.894401\pi\)
0.754800 + 0.655955i \(0.227734\pi\)
\(840\) 0 0
\(841\) −20.8313 36.0808i −0.718320 1.24417i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 26.7314 46.3002i 0.919590 1.59278i
\(846\) 0 0
\(847\) −17.3082 8.44105i −0.594716 0.290038i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 3.88224 6.72424i 0.133081 0.230504i
\(852\) 0 0
\(853\) 22.4259 38.8428i 0.767847 1.32995i −0.170881 0.985292i \(-0.554661\pi\)
0.938728 0.344659i \(-0.112005\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −6.09527 −0.208211 −0.104105 0.994566i \(-0.533198\pi\)
−0.104105 + 0.994566i \(0.533198\pi\)
\(858\) 0 0
\(859\) −30.2137 −1.03088 −0.515438 0.856927i \(-0.672371\pi\)
−0.515438 + 0.856927i \(0.672371\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −21.3315 + 36.9472i −0.726131 + 1.25770i 0.232375 + 0.972626i \(0.425350\pi\)
−0.958507 + 0.285070i \(0.907983\pi\)
\(864\) 0 0
\(865\) −8.60018 14.8959i −0.292415 0.506477i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −11.4499 19.8318i −0.388411 0.672748i
\(870\) 0 0
\(871\) 2.83590 0.0960907
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 78.6656 + 38.3645i 2.65938 + 1.29696i
\(876\) 0 0
\(877\) 20.6751 0.698147 0.349074 0.937095i \(-0.386496\pi\)
0.349074 + 0.937095i \(0.386496\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −5.40674 −0.182158 −0.0910789 0.995844i \(-0.529032\pi\)
−0.0910789 + 0.995844i \(0.529032\pi\)
\(882\) 0 0
\(883\) 3.16348 0.106460 0.0532299 0.998582i \(-0.483048\pi\)
0.0532299 + 0.998582i \(0.483048\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −10.0863 −0.338666 −0.169333 0.985559i \(-0.554161\pi\)
−0.169333 + 0.985559i \(0.554161\pi\)
\(888\) 0 0
\(889\) 20.3000 + 9.90012i 0.680839 + 0.332039i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 24.2397 0.811151
\(894\) 0 0
\(895\) −13.1371 22.7542i −0.439126 0.760589i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 4.00181 + 6.93135i 0.133468 + 0.231173i
\(900\) 0 0
\(901\) 6.95051 12.0386i 0.231555 0.401065i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 77.0249 2.56040
\(906\) 0 0
\(907\) 23.8637 0.792380 0.396190 0.918169i \(-0.370332\pi\)
0.396190 + 0.918169i \(0.370332\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 9.67946 16.7653i 0.320695 0.555460i −0.659937 0.751321i \(-0.729417\pi\)
0.980632 + 0.195862i \(0.0627503\pi\)
\(912\) 0 0
\(913\) −10.1136 + 17.5172i −0.334710 + 0.579735i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −5.58085 2.72174i −0.184296 0.0898796i
\(918\) 0 0
\(919\) 25.2052 43.6567i 0.831444 1.44010i −0.0654498 0.997856i \(-0.520848\pi\)
0.896893 0.442247i \(-0.145818\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −3.36549 5.82920i −0.110777 0.191871i
\(924\) 0 0
\(925\) 38.9274 67.4243i 1.27993 2.21690i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 21.1465 + 36.6267i 0.693793 + 1.20168i 0.970586 + 0.240755i \(0.0773950\pi\)
−0.276793 + 0.960930i \(0.589272\pi\)
\(930\) 0 0
\(931\) −29.1507 + 4.09883i −0.955377 + 0.134334i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −29.4164 50.9506i −0.962018 1.66626i
\(936\) 0 0
\(937\) 20.6771 0.675490 0.337745 0.941238i \(-0.390336\pi\)
0.337745 + 0.941238i \(0.390336\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −17.1646 + 29.7300i −0.559550 + 0.969170i 0.437983 + 0.898983i \(0.355693\pi\)
−0.997534 + 0.0701867i \(0.977640\pi\)
\(942\) 0 0
\(943\) −1.68046 2.91065i −0.0547234 0.0947837i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 13.8650 + 24.0149i 0.450551 + 0.780378i 0.998420 0.0561863i \(-0.0178941\pi\)
−0.547869 + 0.836564i \(0.684561\pi\)
\(948\) 0 0
\(949\) 0.260125 0.450549i 0.00844400 0.0146254i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 22.8102 0.738894 0.369447 0.929252i \(-0.379547\pi\)
0.369447 + 0.929252i \(0.379547\pi\)
\(954\) 0 0
\(955\) 15.5953 + 27.0119i 0.504653 + 0.874085i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −3.05250 1.48868i −0.0985705 0.0480720i
\(960\) 0 0
\(961\) 15.0467 + 26.0617i 0.485378 + 0.840700i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −41.2123 + 71.3817i −1.32667 + 2.29786i
\(966\) 0 0
\(967\) −10.8697 18.8269i −0.349546 0.605432i 0.636623 0.771175i \(-0.280331\pi\)
−0.986169 + 0.165744i \(0.946998\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −19.7959 + 34.2875i −0.635281 + 1.10034i 0.351174 + 0.936310i \(0.385782\pi\)
−0.986455 + 0.164029i \(0.947551\pi\)
\(972\) 0 0
\(973\) −0.225472 3.22287i −0.00722829 0.103320i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −22.8724 + 39.6161i −0.731752 + 1.26743i 0.224382 + 0.974501i \(0.427964\pi\)
−0.956134 + 0.292930i \(0.905370\pi\)
\(978\) 0 0
\(979\) −7.48329 + 12.9614i −0.239167 + 0.414250i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 15.0498 0.480014 0.240007 0.970771i \(-0.422850\pi\)
0.240007 + 0.970771i \(0.422850\pi\)
\(984\) 0 0
\(985\) −32.8363 −1.04625
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −0.566154 + 0.980607i −0.0180026 + 0.0311815i
\(990\) 0 0
\(991\) 11.3516 + 19.6616i 0.360596 + 0.624570i 0.988059 0.154076i \(-0.0492400\pi\)
−0.627463 + 0.778646i \(0.715907\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 16.2894 + 28.2140i 0.516408 + 0.894445i
\(996\) 0 0
\(997\) −55.5352 −1.75882 −0.879408 0.476069i \(-0.842061\pi\)
−0.879408 + 0.476069i \(0.842061\pi\)
\(998\) 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 3024.2.t.k.289.11 22
3.2 odd 2 1008.2.t.l.961.11 22
4.3 odd 2 1512.2.t.c.289.11 22
7.4 even 3 3024.2.q.l.2881.1 22
9.4 even 3 3024.2.q.l.2305.1 22
9.5 odd 6 1008.2.q.l.625.5 22
12.11 even 2 504.2.t.c.457.1 yes 22
21.11 odd 6 1008.2.q.l.529.5 22
28.11 odd 6 1512.2.q.d.1369.1 22
36.23 even 6 504.2.q.c.121.7 yes 22
36.31 odd 6 1512.2.q.d.793.1 22
63.4 even 3 inner 3024.2.t.k.1873.11 22
63.32 odd 6 1008.2.t.l.193.11 22
84.11 even 6 504.2.q.c.25.7 22
252.67 odd 6 1512.2.t.c.361.11 22
252.95 even 6 504.2.t.c.193.1 yes 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.q.c.25.7 22 84.11 even 6
504.2.q.c.121.7 yes 22 36.23 even 6
504.2.t.c.193.1 yes 22 252.95 even 6
504.2.t.c.457.1 yes 22 12.11 even 2
1008.2.q.l.529.5 22 21.11 odd 6
1008.2.q.l.625.5 22 9.5 odd 6
1008.2.t.l.193.11 22 63.32 odd 6
1008.2.t.l.961.11 22 3.2 odd 2
1512.2.q.d.793.1 22 36.31 odd 6
1512.2.q.d.1369.1 22 28.11 odd 6
1512.2.t.c.289.11 22 4.3 odd 2
1512.2.t.c.361.11 22 252.67 odd 6
3024.2.q.l.2305.1 22 9.4 even 3
3024.2.q.l.2881.1 22 7.4 even 3
3024.2.t.k.289.11 22 1.1 even 1 trivial
3024.2.t.k.1873.11 22 63.4 even 3 inner