Properties

Label 2736.2.cg.c.1151.7
Level $2736$
Weight $2$
Character 2736.1151
Analytic conductor $21.847$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2736,2,Mod(1151,2736)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2736.1151");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.cg (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: \(21.8470699930\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1151.7
Character \(\chi\) \(=\) 2736.1151
Dual form 2736.2.cg.c.2591.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.34408 - 0.776006i) q^{5} -2.95486i q^{7} +O(q^{10})\) \(q+(-1.34408 - 0.776006i) q^{5} -2.95486i q^{7} +3.57750 q^{11} +(2.39307 + 4.14491i) q^{13} +(3.37866 + 1.95067i) q^{17} +(-2.61248 + 3.48926i) q^{19} +(2.64157 + 4.57534i) q^{23} +(-1.29563 - 2.24410i) q^{25} +(-7.08654 + 4.09142i) q^{29} -7.52123i q^{31} +(-2.29299 + 3.97157i) q^{35} +2.32246 q^{37} +(3.70788 + 2.14074i) q^{41} +(3.48460 + 2.01183i) q^{43} +(4.08174 + 7.06978i) q^{47} -1.73120 q^{49} +(-2.03458 + 1.17467i) q^{53} +(-4.80845 - 2.77616i) q^{55} +(-3.14582 + 5.44871i) q^{59} +(-6.24917 - 10.8239i) q^{61} -7.42814i q^{65} +(9.02949 - 5.21318i) q^{67} +(2.72467 - 4.71927i) q^{71} +(-5.18870 + 8.98709i) q^{73} -10.5710i q^{77} +(8.60257 + 4.96669i) q^{79} +17.9858 q^{83} +(-3.02747 - 5.24373i) q^{85} +(7.70648 - 4.44934i) q^{89} +(12.2476 - 7.07118i) q^{91} +(6.21907 - 2.66256i) q^{95} +(6.08794 - 10.5446i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 16 q^{13} + 24 q^{25} - 16 q^{37} - 96 q^{49} - 8 q^{61} - 8 q^{73} + 16 q^{85} + 48 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).

\(n\) \(1009\) \(1217\) \(1711\) \(2053\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −1.34408 0.776006i −0.601092 0.347040i 0.168379 0.985722i \(-0.446147\pi\)
−0.769471 + 0.638682i \(0.779480\pi\)
\(6\) 0 0
\(7\) 2.95486i 1.11683i −0.829561 0.558416i \(-0.811409\pi\)
0.829561 0.558416i \(-0.188591\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 3.57750 1.07866 0.539328 0.842096i \(-0.318678\pi\)
0.539328 + 0.842096i \(0.318678\pi\)
\(12\) 0 0
\(13\) 2.39307 + 4.14491i 0.663718 + 1.14959i 0.979631 + 0.200805i \(0.0643556\pi\)
−0.315914 + 0.948788i \(0.602311\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.37866 + 1.95067i 0.819446 + 0.473108i 0.850226 0.526419i \(-0.176466\pi\)
−0.0307791 + 0.999526i \(0.509799\pi\)
\(18\) 0 0
\(19\) −2.61248 + 3.48926i −0.599343 + 0.800492i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.64157 + 4.57534i 0.550806 + 0.954025i 0.998217 + 0.0596959i \(0.0190131\pi\)
−0.447410 + 0.894329i \(0.647654\pi\)
\(24\) 0 0
\(25\) −1.29563 2.24410i −0.259126 0.448819i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −7.08654 + 4.09142i −1.31594 + 0.759757i −0.983072 0.183218i \(-0.941349\pi\)
−0.332865 + 0.942975i \(0.608015\pi\)
\(30\) 0 0
\(31\) 7.52123i 1.35085i −0.737427 0.675427i \(-0.763959\pi\)
0.737427 0.675427i \(-0.236041\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2.29299 + 3.97157i −0.387586 + 0.671319i
\(36\) 0 0
\(37\) 2.32246 0.381810 0.190905 0.981609i \(-0.438858\pi\)
0.190905 + 0.981609i \(0.438858\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 3.70788 + 2.14074i 0.579073 + 0.334328i 0.760765 0.649028i \(-0.224824\pi\)
−0.181692 + 0.983355i \(0.558157\pi\)
\(42\) 0 0
\(43\) 3.48460 + 2.01183i 0.531396 + 0.306802i 0.741585 0.670859i \(-0.234074\pi\)
−0.210189 + 0.977661i \(0.567408\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.08174 + 7.06978i 0.595383 + 1.03123i 0.993493 + 0.113896i \(0.0363329\pi\)
−0.398110 + 0.917338i \(0.630334\pi\)
\(48\) 0 0
\(49\) −1.73120 −0.247314
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −2.03458 + 1.17467i −0.279471 + 0.161353i −0.633184 0.774001i \(-0.718252\pi\)
0.353713 + 0.935354i \(0.384919\pi\)
\(54\) 0 0
\(55\) −4.80845 2.77616i −0.648371 0.374337i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −3.14582 + 5.44871i −0.409550 + 0.709362i −0.994839 0.101463i \(-0.967648\pi\)
0.585289 + 0.810825i \(0.300981\pi\)
\(60\) 0 0
\(61\) −6.24917 10.8239i −0.800125 1.38586i −0.919534 0.393011i \(-0.871433\pi\)
0.119409 0.992845i \(-0.461900\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 7.42814i 0.921347i
\(66\) 0 0
\(67\) 9.02949 5.21318i 1.10313 0.636891i 0.166087 0.986111i \(-0.446887\pi\)
0.937041 + 0.349220i \(0.113553\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 2.72467 4.71927i 0.323359 0.560074i −0.657820 0.753175i \(-0.728521\pi\)
0.981179 + 0.193101i \(0.0618545\pi\)
\(72\) 0 0
\(73\) −5.18870 + 8.98709i −0.607291 + 1.05186i 0.384394 + 0.923169i \(0.374410\pi\)
−0.991685 + 0.128690i \(0.958923\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 10.5710i 1.20468i
\(78\) 0 0
\(79\) 8.60257 + 4.96669i 0.967864 + 0.558797i 0.898585 0.438801i \(-0.144597\pi\)
0.0692799 + 0.997597i \(0.477930\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 17.9858 1.97419 0.987097 0.160126i \(-0.0511900\pi\)
0.987097 + 0.160126i \(0.0511900\pi\)
\(84\) 0 0
\(85\) −3.02747 5.24373i −0.328375 0.568762i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 7.70648 4.44934i 0.816885 0.471629i −0.0324559 0.999473i \(-0.510333\pi\)
0.849341 + 0.527844i \(0.177000\pi\)
\(90\) 0 0
\(91\) 12.2476 7.07118i 1.28390 0.741261i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 6.21907 2.66256i 0.638063 0.273173i
\(96\) 0 0
\(97\) 6.08794 10.5446i 0.618137 1.07064i −0.371688 0.928358i \(-0.621221\pi\)
0.989825 0.142287i \(-0.0454457\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 9.47913 5.47278i 0.943209 0.544562i 0.0522441 0.998634i \(-0.483363\pi\)
0.890965 + 0.454072i \(0.150029\pi\)
\(102\) 0 0
\(103\) 10.4264i 1.02734i −0.857988 0.513670i \(-0.828286\pi\)
0.857988 0.513670i \(-0.171714\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 19.6914 1.90364 0.951820 0.306657i \(-0.0992104\pi\)
0.951820 + 0.306657i \(0.0992104\pi\)
\(108\) 0 0
\(109\) −7.94405 + 13.7595i −0.760902 + 1.31792i 0.181484 + 0.983394i \(0.441910\pi\)
−0.942386 + 0.334527i \(0.891423\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 6.66966i 0.627429i 0.949517 + 0.313715i \(0.101574\pi\)
−0.949517 + 0.313715i \(0.898426\pi\)
\(114\) 0 0
\(115\) 8.19951i 0.764608i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 5.76397 9.98348i 0.528382 0.915184i
\(120\) 0 0
\(121\) 1.79849 0.163500
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 11.7817i 1.05379i
\(126\) 0 0
\(127\) −2.29254 + 1.32360i −0.203430 + 0.117450i −0.598254 0.801306i \(-0.704139\pi\)
0.394825 + 0.918757i \(0.370805\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −9.36489 + 16.2205i −0.818214 + 1.41719i 0.0887828 + 0.996051i \(0.471702\pi\)
−0.906997 + 0.421137i \(0.861631\pi\)
\(132\) 0 0
\(133\) 10.3103 + 7.71951i 0.894015 + 0.669366i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −13.1197 + 7.57468i −1.12089 + 0.647148i −0.941629 0.336652i \(-0.890705\pi\)
−0.179265 + 0.983801i \(0.557372\pi\)
\(138\) 0 0
\(139\) 7.86612 4.54151i 0.667196 0.385206i −0.127818 0.991798i \(-0.540797\pi\)
0.795013 + 0.606592i \(0.207464\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 8.56120 + 14.8284i 0.715923 + 1.24002i
\(144\) 0 0
\(145\) 12.6999 1.05467
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −8.72619 5.03807i −0.714877 0.412735i 0.0979869 0.995188i \(-0.468760\pi\)
−0.812864 + 0.582453i \(0.802093\pi\)
\(150\) 0 0
\(151\) 15.1780i 1.23517i −0.786504 0.617586i \(-0.788111\pi\)
0.786504 0.617586i \(-0.211889\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −5.83652 + 10.1092i −0.468801 + 0.811987i
\(156\) 0 0
\(157\) 3.25867 5.64418i 0.260070 0.450454i −0.706190 0.708022i \(-0.749588\pi\)
0.966260 + 0.257568i \(0.0829210\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 13.5195 7.80549i 1.06549 0.615158i
\(162\) 0 0
\(163\) 5.36702i 0.420377i 0.977661 + 0.210189i \(0.0674078\pi\)
−0.977661 + 0.210189i \(0.932592\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −7.55271 13.0817i −0.584447 1.01229i −0.994944 0.100429i \(-0.967978\pi\)
0.410498 0.911862i \(-0.365355\pi\)
\(168\) 0 0
\(169\) −4.95354 + 8.57979i −0.381042 + 0.659984i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.97214 + 1.13862i 0.149939 + 0.0865674i 0.573093 0.819491i \(-0.305744\pi\)
−0.423153 + 0.906058i \(0.639077\pi\)
\(174\) 0 0
\(175\) −6.63099 + 3.82840i −0.501256 + 0.289400i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 13.3998 1.00155 0.500773 0.865579i \(-0.333049\pi\)
0.500773 + 0.865579i \(0.333049\pi\)
\(180\) 0 0
\(181\) 4.72566 + 8.18508i 0.351255 + 0.608392i 0.986470 0.163944i \(-0.0524215\pi\)
−0.635214 + 0.772336i \(0.719088\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −3.12157 1.80224i −0.229503 0.132503i
\(186\) 0 0
\(187\) 12.0872 + 6.97853i 0.883901 + 0.510321i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.87185 −0.135442 −0.0677210 0.997704i \(-0.521573\pi\)
−0.0677210 + 0.997704i \(0.521573\pi\)
\(192\) 0 0
\(193\) 8.91040 15.4333i 0.641385 1.11091i −0.343739 0.939065i \(-0.611694\pi\)
0.985124 0.171846i \(-0.0549731\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3.51742i 0.250606i −0.992119 0.125303i \(-0.960010\pi\)
0.992119 0.125303i \(-0.0399903\pi\)
\(198\) 0 0
\(199\) −0.896925 + 0.517840i −0.0635813 + 0.0367087i −0.531454 0.847087i \(-0.678354\pi\)
0.467872 + 0.883796i \(0.345021\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 12.0896 + 20.9397i 0.848521 + 1.46968i
\(204\) 0 0
\(205\) −3.32246 5.75467i −0.232051 0.401923i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −9.34613 + 12.4828i −0.646486 + 0.863456i
\(210\) 0 0
\(211\) 6.51358 + 3.76062i 0.448413 + 0.258892i 0.707160 0.707054i \(-0.249976\pi\)
−0.258747 + 0.965945i \(0.583309\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −3.12239 5.40814i −0.212945 0.368832i
\(216\) 0 0
\(217\) −22.2242 −1.50868
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 18.6724i 1.25604i
\(222\) 0 0
\(223\) 21.7471 + 12.5557i 1.45630 + 0.840793i 0.998826 0.0484325i \(-0.0154226\pi\)
0.457469 + 0.889225i \(0.348756\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −4.58598 −0.304382 −0.152191 0.988351i \(-0.548633\pi\)
−0.152191 + 0.988351i \(0.548633\pi\)
\(228\) 0 0
\(229\) −10.3584 −0.684503 −0.342251 0.939608i \(-0.611189\pi\)
−0.342251 + 0.939608i \(0.611189\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −16.5657 9.56419i −1.08525 0.626571i −0.152945 0.988235i \(-0.548876\pi\)
−0.932309 + 0.361664i \(0.882209\pi\)
\(234\) 0 0
\(235\) 12.6698i 0.826488i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −8.95891 −0.579504 −0.289752 0.957102i \(-0.593573\pi\)
−0.289752 + 0.957102i \(0.593573\pi\)
\(240\) 0 0
\(241\) −1.04028 1.80181i −0.0670101 0.116065i 0.830574 0.556909i \(-0.188013\pi\)
−0.897584 + 0.440844i \(0.854679\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 2.32687 + 1.34342i 0.148659 + 0.0858281i
\(246\) 0 0
\(247\) −20.7145 2.47845i −1.31803 0.157700i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 9.49712 + 16.4495i 0.599453 + 1.03828i 0.992902 + 0.118936i \(0.0379484\pi\)
−0.393449 + 0.919346i \(0.628718\pi\)
\(252\) 0 0
\(253\) 9.45023 + 16.3683i 0.594131 + 1.02906i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −19.1578 + 11.0607i −1.19503 + 0.689950i −0.959443 0.281904i \(-0.909034\pi\)
−0.235585 + 0.971854i \(0.575701\pi\)
\(258\) 0 0
\(259\) 6.86254i 0.426418i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 7.31065 12.6624i 0.450794 0.780798i −0.547641 0.836713i \(-0.684474\pi\)
0.998436 + 0.0559148i \(0.0178075\pi\)
\(264\) 0 0
\(265\) 3.64619 0.223984
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 12.7954 + 7.38740i 0.780147 + 0.450418i 0.836482 0.547994i \(-0.184608\pi\)
−0.0563356 + 0.998412i \(0.517942\pi\)
\(270\) 0 0
\(271\) −25.3521 14.6370i −1.54003 0.889136i −0.998836 0.0482382i \(-0.984639\pi\)
−0.541193 0.840898i \(-0.682027\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −4.63511 8.02825i −0.279508 0.484122i
\(276\) 0 0
\(277\) −7.08628 −0.425773 −0.212887 0.977077i \(-0.568287\pi\)
−0.212887 + 0.977077i \(0.568287\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 10.7896 6.22936i 0.643652 0.371613i −0.142368 0.989814i \(-0.545472\pi\)
0.786020 + 0.618201i \(0.212138\pi\)
\(282\) 0 0
\(283\) −16.6722 9.62572i −0.991062 0.572190i −0.0854701 0.996341i \(-0.527239\pi\)
−0.905591 + 0.424151i \(0.860573\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 6.32560 10.9563i 0.373388 0.646727i
\(288\) 0 0
\(289\) −0.889753 1.54110i −0.0523384 0.0906528i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.82121i 0.106396i −0.998584 0.0531980i \(-0.983059\pi\)
0.998584 0.0531980i \(-0.0169415\pi\)
\(294\) 0 0
\(295\) 8.45647 4.88234i 0.492355 0.284261i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −12.6429 + 21.8982i −0.731160 + 1.26641i
\(300\) 0 0
\(301\) 5.94469 10.2965i 0.342646 0.593480i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 19.3976i 1.11070i
\(306\) 0 0
\(307\) 18.0734 + 10.4347i 1.03150 + 0.595538i 0.917414 0.397933i \(-0.130272\pi\)
0.114087 + 0.993471i \(0.463606\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 21.2309 1.20389 0.601946 0.798537i \(-0.294392\pi\)
0.601946 + 0.798537i \(0.294392\pi\)
\(312\) 0 0
\(313\) 1.62822 + 2.82016i 0.0920324 + 0.159405i 0.908366 0.418176i \(-0.137330\pi\)
−0.816334 + 0.577580i \(0.803997\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 12.0712 6.96932i 0.677987 0.391436i −0.121109 0.992639i \(-0.538645\pi\)
0.799096 + 0.601203i \(0.205312\pi\)
\(318\) 0 0
\(319\) −25.3521 + 14.6370i −1.41944 + 0.819516i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −15.6331 + 6.69296i −0.869849 + 0.372406i
\(324\) 0 0
\(325\) 6.20106 10.7405i 0.343973 0.595778i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 20.8902 12.0610i 1.15171 0.664943i
\(330\) 0 0
\(331\) 7.14723i 0.392847i 0.980519 + 0.196424i \(0.0629328\pi\)
−0.980519 + 0.196424i \(0.937067\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −16.1818 −0.884108
\(336\) 0 0
\(337\) −6.47152 + 11.2090i −0.352526 + 0.610593i −0.986691 0.162605i \(-0.948011\pi\)
0.634165 + 0.773197i \(0.281344\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 26.9072i 1.45711i
\(342\) 0 0
\(343\) 15.5686i 0.840624i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7.70837 13.3513i 0.413807 0.716735i −0.581495 0.813550i \(-0.697532\pi\)
0.995302 + 0.0968150i \(0.0308655\pi\)
\(348\) 0 0
\(349\) 29.4727 1.57764 0.788820 0.614625i \(-0.210693\pi\)
0.788820 + 0.614625i \(0.210693\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 19.7000i 1.04853i −0.851556 0.524264i \(-0.824341\pi\)
0.851556 0.524264i \(-0.175659\pi\)
\(354\) 0 0
\(355\) −7.32437 + 4.22873i −0.388737 + 0.224437i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 6.64022 11.5012i 0.350457 0.607010i −0.635872 0.771794i \(-0.719360\pi\)
0.986330 + 0.164785i \(0.0526929\pi\)
\(360\) 0 0
\(361\) −5.34993 18.2312i −0.281575 0.959539i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 13.9481 8.05292i 0.730075 0.421509i
\(366\) 0 0
\(367\) −14.4570 + 8.34674i −0.754648 + 0.435696i −0.827371 0.561656i \(-0.810165\pi\)
0.0727227 + 0.997352i \(0.476831\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 3.47098 + 6.01191i 0.180204 + 0.312123i
\(372\) 0 0
\(373\) −30.7828 −1.59387 −0.796937 0.604062i \(-0.793548\pi\)
−0.796937 + 0.604062i \(0.793548\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −33.9171 19.5821i −1.74682 1.00853i
\(378\) 0 0
\(379\) 14.9927i 0.770125i 0.922890 + 0.385063i \(0.125820\pi\)
−0.922890 + 0.385063i \(0.874180\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −2.26956 + 3.93100i −0.115969 + 0.200865i −0.918167 0.396194i \(-0.870331\pi\)
0.802197 + 0.597059i \(0.203664\pi\)
\(384\) 0 0
\(385\) −8.20317 + 14.2083i −0.418072 + 0.724122i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −2.79236 + 1.61217i −0.141578 + 0.0817404i −0.569116 0.822257i \(-0.692714\pi\)
0.427538 + 0.903998i \(0.359381\pi\)
\(390\) 0 0
\(391\) 20.6114i 1.04236i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −7.70837 13.3513i −0.387850 0.671776i
\(396\) 0 0
\(397\) 6.15174 10.6551i 0.308747 0.534765i −0.669342 0.742955i \(-0.733424\pi\)
0.978088 + 0.208190i \(0.0667571\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 21.1635 + 12.2188i 1.05686 + 0.610176i 0.924561 0.381034i \(-0.124432\pi\)
0.132296 + 0.991210i \(0.457765\pi\)
\(402\) 0 0
\(403\) 31.1749 17.9988i 1.55293 0.896585i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 8.30859 0.411842
\(408\) 0 0
\(409\) 7.96304 + 13.7924i 0.393747 + 0.681990i 0.992940 0.118615i \(-0.0378453\pi\)
−0.599193 + 0.800604i \(0.704512\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 16.1002 + 9.29544i 0.792238 + 0.457399i
\(414\) 0 0
\(415\) −24.1743 13.9571i −1.18667 0.685125i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −38.2550 −1.86888 −0.934439 0.356123i \(-0.884099\pi\)
−0.934439 + 0.356123i \(0.884099\pi\)
\(420\) 0 0
\(421\) 6.06443 10.5039i 0.295562 0.511929i −0.679553 0.733626i \(-0.737826\pi\)
0.975116 + 0.221697i \(0.0711597\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 10.1094i 0.490378i
\(426\) 0 0
\(427\) −31.9831 + 18.4654i −1.54777 + 0.893605i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −12.9424 22.4169i −0.623413 1.07978i −0.988845 0.148945i \(-0.952412\pi\)
0.365433 0.930838i \(-0.380921\pi\)
\(432\) 0 0
\(433\) 11.3701 + 19.6936i 0.546413 + 0.946416i 0.998516 + 0.0544501i \(0.0173406\pi\)
−0.452103 + 0.891966i \(0.649326\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −22.8656 2.73582i −1.09381 0.130872i
\(438\) 0 0
\(439\) 30.1175 + 17.3883i 1.43743 + 0.829900i 0.997671 0.0682169i \(-0.0217310\pi\)
0.439758 + 0.898116i \(0.355064\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −4.93456 8.54692i −0.234448 0.406076i 0.724664 0.689102i \(-0.241995\pi\)
−0.959112 + 0.283026i \(0.908662\pi\)
\(444\) 0 0
\(445\) −13.8109 −0.654697
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 7.88038i 0.371898i −0.982559 0.185949i \(-0.940464\pi\)
0.982559 0.185949i \(-0.0595359\pi\)
\(450\) 0 0
\(451\) 13.2649 + 7.65850i 0.624621 + 0.360625i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −21.9491 −1.02899
\(456\) 0 0
\(457\) 7.32909 0.342840 0.171420 0.985198i \(-0.445164\pi\)
0.171420 + 0.985198i \(0.445164\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 18.1717 + 10.4914i 0.846340 + 0.488634i 0.859414 0.511280i \(-0.170829\pi\)
−0.0130745 + 0.999915i \(0.504162\pi\)
\(462\) 0 0
\(463\) 15.7207i 0.730605i 0.930889 + 0.365302i \(0.119034\pi\)
−0.930889 + 0.365302i \(0.880966\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −27.8549 −1.28897 −0.644485 0.764617i \(-0.722928\pi\)
−0.644485 + 0.764617i \(0.722928\pi\)
\(468\) 0 0
\(469\) −15.4042 26.6809i −0.711301 1.23201i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 12.4661 + 7.19733i 0.573194 + 0.330934i
\(474\) 0 0
\(475\) 11.2150 + 1.34186i 0.514582 + 0.0615686i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −5.78739 10.0241i −0.264433 0.458011i 0.702982 0.711207i \(-0.251851\pi\)
−0.967415 + 0.253197i \(0.918518\pi\)
\(480\) 0 0
\(481\) 5.55780 + 9.62639i 0.253414 + 0.438926i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −16.3654 + 9.44856i −0.743114 + 0.429037i
\(486\) 0 0
\(487\) 4.00714i 0.181581i 0.995870 + 0.0907905i \(0.0289394\pi\)
−0.995870 + 0.0907905i \(0.971061\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −2.72467 + 4.71927i −0.122963 + 0.212978i −0.920935 0.389717i \(-0.872573\pi\)
0.797972 + 0.602695i \(0.205906\pi\)
\(492\) 0 0
\(493\) −31.9240 −1.43779
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −13.9448 8.05103i −0.625509 0.361138i
\(498\) 0 0
\(499\) 2.76253 + 1.59495i 0.123668 + 0.0713997i 0.560558 0.828115i \(-0.310587\pi\)
−0.436890 + 0.899515i \(0.643920\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −19.2446 33.3326i −0.858072 1.48623i −0.873765 0.486348i \(-0.838329\pi\)
0.0156927 0.999877i \(-0.495005\pi\)
\(504\) 0 0
\(505\) −16.9876 −0.755940
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −8.72135 + 5.03527i −0.386567 + 0.223185i −0.680672 0.732589i \(-0.738312\pi\)
0.294105 + 0.955773i \(0.404979\pi\)
\(510\) 0 0
\(511\) 26.5556 + 15.3319i 1.17475 + 0.678242i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −8.09092 + 14.0139i −0.356529 + 0.617526i
\(516\) 0 0
\(517\) 14.6024 + 25.2921i 0.642213 + 1.11235i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 34.7688i 1.52325i 0.648018 + 0.761625i \(0.275598\pi\)
−0.648018 + 0.761625i \(0.724402\pi\)
\(522\) 0 0
\(523\) −4.64797 + 2.68351i −0.203242 + 0.117342i −0.598167 0.801372i \(-0.704104\pi\)
0.394925 + 0.918713i \(0.370771\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 14.6715 25.4117i 0.639099 1.10695i
\(528\) 0 0
\(529\) −2.45584 + 4.25363i −0.106775 + 0.184941i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 20.4918i 0.887597i
\(534\) 0 0
\(535\) −26.4669 15.2807i −1.14426 0.660640i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −6.19337 −0.266767
\(540\) 0 0
\(541\) −6.23120 10.7928i −0.267900 0.464017i 0.700419 0.713732i \(-0.252996\pi\)
−0.968319 + 0.249715i \(0.919663\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 21.3549 12.3293i 0.914744 0.528128i
\(546\) 0 0
\(547\) 1.10047 0.635358i 0.0470528 0.0271659i −0.476289 0.879289i \(-0.658018\pi\)
0.523342 + 0.852123i \(0.324685\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 4.23739 35.4155i 0.180519 1.50875i
\(552\) 0 0
\(553\) 14.6759 25.4194i 0.624082 1.08094i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −37.0099 + 21.3677i −1.56816 + 0.905378i −0.571776 + 0.820409i \(0.693746\pi\)
−0.996384 + 0.0849682i \(0.972921\pi\)
\(558\) 0 0
\(559\) 19.2578i 0.814519i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −15.0540 −0.634451 −0.317226 0.948350i \(-0.602751\pi\)
−0.317226 + 0.948350i \(0.602751\pi\)
\(564\) 0 0
\(565\) 5.17570 8.96457i 0.217743 0.377142i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 27.3871i 1.14813i 0.818811 + 0.574064i \(0.194634\pi\)
−0.818811 + 0.574064i \(0.805366\pi\)
\(570\) 0 0
\(571\) 20.0687i 0.839848i 0.907559 + 0.419924i \(0.137943\pi\)
−0.907559 + 0.419924i \(0.862057\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 6.84500 11.8559i 0.285456 0.494425i
\(576\) 0 0
\(577\) 27.6632 1.15163 0.575816 0.817579i \(-0.304684\pi\)
0.575816 + 0.817579i \(0.304684\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 53.1454i 2.20484i
\(582\) 0 0
\(583\) −7.27871 + 4.20237i −0.301454 + 0.174044i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 6.24250 10.8123i 0.257655 0.446272i −0.707958 0.706255i \(-0.750383\pi\)
0.965613 + 0.259982i \(0.0837167\pi\)
\(588\) 0 0
\(589\) 26.2436 + 19.6490i 1.08135 + 0.809625i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −22.7999 + 13.1635i −0.936280 + 0.540562i −0.888792 0.458310i \(-0.848455\pi\)
−0.0474878 + 0.998872i \(0.515122\pi\)
\(594\) 0 0
\(595\) −15.4945 + 8.94574i −0.635212 + 0.366740i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 8.90978 + 15.4322i 0.364044 + 0.630542i 0.988622 0.150420i \(-0.0480625\pi\)
−0.624578 + 0.780962i \(0.714729\pi\)
\(600\) 0 0
\(601\) 4.14657 0.169142 0.0845711 0.996417i \(-0.473048\pi\)
0.0845711 + 0.996417i \(0.473048\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2.41732 1.39564i −0.0982782 0.0567409i
\(606\) 0 0
\(607\) 9.01676i 0.365979i 0.983115 + 0.182989i \(0.0585774\pi\)
−0.983115 + 0.182989i \(0.941423\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −19.5358 + 33.8369i −0.790332 + 1.36890i
\(612\) 0 0
\(613\) 9.07558 15.7194i 0.366559 0.634900i −0.622466 0.782647i \(-0.713869\pi\)
0.989025 + 0.147748i \(0.0472023\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −17.3186 + 9.99891i −0.697221 + 0.402541i −0.806312 0.591491i \(-0.798540\pi\)
0.109090 + 0.994032i \(0.465206\pi\)
\(618\) 0 0
\(619\) 6.82304i 0.274241i −0.990554 0.137120i \(-0.956215\pi\)
0.990554 0.137120i \(-0.0437848\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −13.1472 22.7716i −0.526730 0.912324i
\(624\) 0 0
\(625\) 2.66454 4.61513i 0.106582 0.184605i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 7.84681 + 4.53036i 0.312873 + 0.180637i
\(630\) 0 0
\(631\) −33.3500 + 19.2546i −1.32764 + 0.766515i −0.984935 0.172927i \(-0.944677\pi\)
−0.342708 + 0.939442i \(0.611344\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 4.10847 0.163040
\(636\) 0 0
\(637\) −4.14288 7.17568i −0.164147 0.284311i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 20.7653 + 11.9889i 0.820181 + 0.473532i 0.850479 0.526009i \(-0.176312\pi\)
−0.0302978 + 0.999541i \(0.509646\pi\)
\(642\) 0 0
\(643\) −3.05767 1.76535i −0.120583 0.0696185i 0.438495 0.898733i \(-0.355512\pi\)
−0.559078 + 0.829115i \(0.688845\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 8.83957 0.347519 0.173760 0.984788i \(-0.444408\pi\)
0.173760 + 0.984788i \(0.444408\pi\)
\(648\) 0 0
\(649\) −11.2541 + 19.4928i −0.441764 + 0.765158i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.10915i 0.0434042i 0.999764 + 0.0217021i \(0.00690854\pi\)
−0.999764 + 0.0217021i \(0.993091\pi\)
\(654\) 0 0
\(655\) 25.1744 14.5344i 0.983643 0.567907i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −7.73179 13.3919i −0.301188 0.521673i 0.675217 0.737619i \(-0.264050\pi\)
−0.976405 + 0.215946i \(0.930716\pi\)
\(660\) 0 0
\(661\) 5.32246 + 9.21877i 0.207020 + 0.358569i 0.950774 0.309884i \(-0.100290\pi\)
−0.743755 + 0.668453i \(0.766957\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −7.86749 18.3765i −0.305088 0.712610i
\(666\) 0 0
\(667\) −37.4392 21.6156i −1.44965 0.836958i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −22.3564 38.7224i −0.863060 1.49486i
\(672\) 0 0
\(673\) −39.8299 −1.53533 −0.767664 0.640852i \(-0.778581\pi\)
−0.767664 + 0.640852i \(0.778581\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 30.7547i 1.18200i 0.806671 + 0.591000i \(0.201267\pi\)
−0.806671 + 0.591000i \(0.798733\pi\)
\(678\) 0 0
\(679\) −31.1579 17.9890i −1.19573 0.690355i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 20.2903 0.776387 0.388194 0.921578i \(-0.373099\pi\)
0.388194 + 0.921578i \(0.373099\pi\)
\(684\) 0 0
\(685\) 23.5120 0.898347
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −9.73778 5.62211i −0.370980 0.214185i
\(690\) 0 0
\(691\) 8.66267i 0.329544i 0.986332 + 0.164772i \(0.0526888\pi\)
−0.986332 + 0.164772i \(0.947311\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −14.0969 −0.534728
\(696\) 0 0
\(697\) 8.35178 + 14.4657i 0.316346 + 0.547927i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −20.2447 11.6883i −0.764634 0.441461i 0.0663234 0.997798i \(-0.478873\pi\)
−0.830957 + 0.556337i \(0.812206\pi\)
\(702\) 0 0
\(703\) −6.06737 + 8.10367i −0.228835 + 0.305636i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −16.1713 28.0095i −0.608184 1.05341i
\(708\) 0 0
\(709\) 26.0163 + 45.0616i 0.977063 + 1.69232i 0.672951 + 0.739687i \(0.265027\pi\)
0.304113 + 0.952636i \(0.401640\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 34.4122 19.8679i 1.28875 0.744059i
\(714\) 0 0
\(715\) 26.5742i 0.993817i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −11.2859 + 19.5477i −0.420892 + 0.729006i −0.996027 0.0890524i \(-0.971616\pi\)
0.575135 + 0.818058i \(0.304949\pi\)
\(720\) 0 0
\(721\) −30.8084 −1.14737
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 18.3631 + 10.6019i 0.681987 + 0.393745i
\(726\) 0 0
\(727\) −2.24947 1.29873i −0.0834281 0.0481672i 0.457706 0.889104i \(-0.348671\pi\)
−0.541134 + 0.840937i \(0.682005\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 7.84886 + 13.5946i 0.290300 + 0.502815i
\(732\) 0 0
\(733\) −24.7135 −0.912813 −0.456407 0.889771i \(-0.650864\pi\)
−0.456407 + 0.889771i \(0.650864\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 32.3030 18.6501i 1.18990 0.686987i
\(738\) 0 0
\(739\) 33.8487 + 19.5425i 1.24514 + 0.718884i 0.970137 0.242558i \(-0.0779865\pi\)
0.275007 + 0.961442i \(0.411320\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −5.14989 + 8.91988i −0.188931 + 0.327238i −0.944894 0.327376i \(-0.893836\pi\)
0.755963 + 0.654614i \(0.227169\pi\)
\(744\) 0 0
\(745\) 7.81914 + 13.5432i 0.286471 + 0.496183i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 58.1854i 2.12605i
\(750\) 0 0
\(751\) −37.7889 + 21.8174i −1.37894 + 0.796129i −0.992031 0.125990i \(-0.959789\pi\)
−0.386905 + 0.922120i \(0.626456\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −11.7783 + 20.4005i −0.428654 + 0.742451i
\(756\) 0 0
\(757\) −9.69201 + 16.7871i −0.352262 + 0.610136i −0.986645 0.162883i \(-0.947921\pi\)
0.634383 + 0.773019i \(0.281254\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 41.1351i 1.49115i 0.666423 + 0.745574i \(0.267824\pi\)
−0.666423 + 0.745574i \(0.732176\pi\)
\(762\) 0 0
\(763\) 40.6574 + 23.4736i 1.47190 + 0.849800i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −30.1126 −1.08730
\(768\) 0 0
\(769\) −20.9257 36.2444i −0.754600 1.30701i −0.945573 0.325410i \(-0.894498\pi\)
0.190973 0.981595i \(-0.438836\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 27.7846 16.0414i 0.999342 0.576970i 0.0912886 0.995824i \(-0.470901\pi\)
0.908054 + 0.418854i \(0.137568\pi\)
\(774\) 0 0
\(775\) −16.8784 + 9.74473i −0.606289 + 0.350041i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −17.1564 + 7.34511i −0.614690 + 0.263166i
\(780\) 0 0
\(781\) 9.74751 16.8832i 0.348793 0.604128i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −8.75983 + 5.05749i −0.312652 + 0.180510i
\(786\) 0 0
\(787\) 9.20538i 0.328136i −0.986449 0.164068i \(-0.947538\pi\)
0.986449 0.164068i \(-0.0524617\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 19.7079 0.700733
\(792\) 0 0
\(793\) 29.9094 51.8046i 1.06211 1.83963i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 23.2175i 0.822404i −0.911544 0.411202i \(-0.865109\pi\)
0.911544 0.411202i \(-0.134891\pi\)
\(798\) 0 0
\(799\) 31.8485i 1.12672i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −18.5626 + 32.1513i −0.655058 + 1.13459i
\(804\) 0 0
\(805\) −24.2284 −0.853939
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 53.1510i 1.86869i −0.356371 0.934345i \(-0.615986\pi\)
0.356371 0.934345i \(-0.384014\pi\)
\(810\) 0 0
\(811\) −4.76280 + 2.74980i −0.167244 + 0.0965586i −0.581286 0.813699i \(-0.697450\pi\)
0.414041 + 0.910258i \(0.364117\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 4.16484 7.21371i 0.145888 0.252685i
\(816\) 0 0
\(817\) −16.1233 + 6.90281i −0.564081 + 0.241499i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −35.0362 + 20.2282i −1.22277 + 0.705968i −0.965508 0.260373i \(-0.916154\pi\)
−0.257264 + 0.966341i \(0.582821\pi\)
\(822\) 0 0
\(823\) −19.3542 + 11.1741i −0.674643 + 0.389506i −0.797834 0.602878i \(-0.794021\pi\)
0.123190 + 0.992383i \(0.460687\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −23.6175 40.9067i −0.821261 1.42247i −0.904744 0.425956i \(-0.859938\pi\)
0.0834832 0.996509i \(-0.473395\pi\)
\(828\) 0 0
\(829\) 23.4010 0.812750 0.406375 0.913706i \(-0.366793\pi\)
0.406375 + 0.913706i \(0.366793\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −5.84914 3.37700i −0.202661 0.117006i
\(834\) 0 0
\(835\) 23.4438i 0.811306i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 15.1780 26.2890i 0.524002 0.907599i −0.475607 0.879658i \(-0.657772\pi\)
0.999610 0.0279408i \(-0.00889500\pi\)
\(840\) 0 0
\(841\) 18.9794 32.8732i 0.654461 1.13356i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 13.3159 7.68796i 0.458082 0.264474i
\(846\) 0 0
\(847\) 5.31430i 0.182602i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 6.13495 + 10.6260i 0.210303 + 0.364256i
\(852\) 0 0
\(853\) −3.86624 + 6.69652i −0.132377 + 0.229285i −0.924593 0.380957i \(-0.875594\pi\)
0.792215 + 0.610242i \(0.208928\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 2.16835 + 1.25190i 0.0740695 + 0.0427641i 0.536577 0.843851i \(-0.319717\pi\)
−0.462508 + 0.886615i \(0.653050\pi\)
\(858\) 0 0
\(859\) 14.8497 8.57348i 0.506665 0.292523i −0.224797 0.974406i \(-0.572172\pi\)
0.731462 + 0.681882i \(0.238838\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −56.7183 −1.93071 −0.965356 0.260937i \(-0.915969\pi\)
−0.965356 + 0.260937i \(0.915969\pi\)
\(864\) 0 0
\(865\) −1.76715 3.06079i −0.0600848 0.104070i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 30.7757 + 17.7683i 1.04399 + 0.602750i
\(870\) 0 0
\(871\) 43.2164 + 24.9510i 1.46433 + 0.845432i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 34.8134 1.17691
\(876\) 0 0
\(877\) −19.0768 + 33.0420i −0.644178 + 1.11575i 0.340313 + 0.940312i \(0.389467\pi\)
−0.984491 + 0.175436i \(0.943866\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 23.3654i 0.787202i 0.919281 + 0.393601i \(0.128771\pi\)
−0.919281 + 0.393601i \(0.871229\pi\)
\(882\) 0 0
\(883\) −10.0755 + 5.81707i −0.339066 + 0.195760i −0.659859 0.751389i \(-0.729384\pi\)
0.320793 + 0.947149i \(0.396051\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 2.63103 + 4.55708i 0.0883415 + 0.153012i 0.906810 0.421539i \(-0.138510\pi\)
−0.818469 + 0.574551i \(0.805177\pi\)
\(888\) 0 0
\(889\) 3.91104 + 6.77412i 0.131172 + 0.227197i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −35.3318 4.22737i −1.18233 0.141464i
\(894\) 0 0
\(895\) −18.0104 10.3983i −0.602021 0.347577i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 30.7725 + 53.2995i 1.02632 + 1.77764i
\(900\) 0 0
\(901\) −9.16556 −0.305349
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 14.6686i 0.487599i
\(906\) 0 0
\(907\) −27.4669 15.8580i −0.912023 0.526557i −0.0309416 0.999521i \(-0.509851\pi\)
−0.881082 + 0.472964i \(0.843184\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −26.4605 −0.876677 −0.438338 0.898810i \(-0.644433\pi\)
−0.438338 + 0.898810i \(0.644433\pi\)
\(912\) 0 0
\(913\) 64.3440 2.12948
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 47.9292 + 27.6719i 1.58276 + 0.913808i
\(918\) 0 0
\(919\) 53.0421i 1.74970i −0.484395 0.874849i \(-0.660960\pi\)
0.484395 0.874849i \(-0.339040\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 26.0813 0.858477
\(924\) 0 0
\(925\) −3.00905 5.21182i −0.0989368 0.171364i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −8.56206 4.94331i −0.280912 0.162185i 0.352924 0.935652i \(-0.385187\pi\)
−0.633836 + 0.773467i \(0.718521\pi\)
\(930\) 0 0
\(931\) 4.52272 6.04061i 0.148226 0.197973i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −10.8308 18.7594i −0.354204 0.613499i
\(936\) 0 0
\(937\) −11.5017 19.9215i −0.375743 0.650806i 0.614695 0.788765i \(-0.289279\pi\)
−0.990438 + 0.137959i \(0.955946\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −41.2656 + 23.8247i −1.34522 + 0.776663i −0.987568 0.157192i \(-0.949756\pi\)
−0.357652 + 0.933855i \(0.616423\pi\)
\(942\) 0 0
\(943\) 22.6197i 0.736600i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −4.94511 + 8.56517i −0.160694 + 0.278331i −0.935118 0.354337i \(-0.884707\pi\)
0.774424 + 0.632667i \(0.218040\pi\)
\(948\) 0 0
\(949\) −49.6676 −1.61228
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 27.5341 + 15.8968i 0.891915 + 0.514948i 0.874569 0.484902i \(-0.161145\pi\)
0.0173469 + 0.999850i \(0.494478\pi\)
\(954\) 0 0
\(955\) 2.51592 + 1.45256i 0.0814131 + 0.0470039i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 22.3821 + 38.7670i 0.722756 + 1.25185i
\(960\) 0 0
\(961\) −25.5689 −0.824805
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −23.9526 + 13.8291i −0.771062 + 0.445173i
\(966\) 0 0
\(967\) −39.3678 22.7290i −1.26598 0.730915i −0.291757 0.956493i \(-0.594240\pi\)
−0.974225 + 0.225578i \(0.927573\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 11.8498 20.5244i 0.380278 0.658660i −0.610824 0.791766i \(-0.709162\pi\)
0.991102 + 0.133106i \(0.0424951\pi\)
\(972\) 0 0
\(973\) −13.4195 23.2433i −0.430210 0.745146i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 21.4168i 0.685184i −0.939484 0.342592i \(-0.888695\pi\)
0.939484 0.342592i \(-0.111305\pi\)
\(978\) 0 0
\(979\) 27.5699 15.9175i 0.881138 0.508726i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −1.17570 + 2.03638i −0.0374991 + 0.0649504i −0.884166 0.467173i \(-0.845272\pi\)
0.846667 + 0.532124i \(0.178606\pi\)
\(984\) 0 0
\(985\) −2.72954 + 4.72770i −0.0869703 + 0.150637i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 21.2576i 0.675954i
\(990\) 0 0
\(991\) −46.7179 26.9726i −1.48404 0.856813i −0.484209 0.874952i \(-0.660893\pi\)
−0.999835 + 0.0181390i \(0.994226\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 1.60739 0.0509576
\(996\) 0 0
\(997\) 15.0931 + 26.1420i 0.478004 + 0.827926i 0.999682 0.0252157i \(-0.00802727\pi\)
−0.521678 + 0.853142i \(0.674694\pi\)
\(998\) 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 2736.2.cg.c.1151.7 32
3.2 odd 2 inner 2736.2.cg.c.1151.9 yes 32
4.3 odd 2 inner 2736.2.cg.c.1151.8 yes 32
12.11 even 2 inner 2736.2.cg.c.1151.10 yes 32
19.7 even 3 inner 2736.2.cg.c.2591.10 yes 32
57.26 odd 6 inner 2736.2.cg.c.2591.8 yes 32
76.7 odd 6 inner 2736.2.cg.c.2591.9 yes 32
228.83 even 6 inner 2736.2.cg.c.2591.7 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2736.2.cg.c.1151.7 32 1.1 even 1 trivial
2736.2.cg.c.1151.8 yes 32 4.3 odd 2 inner
2736.2.cg.c.1151.9 yes 32 3.2 odd 2 inner
2736.2.cg.c.1151.10 yes 32 12.11 even 2 inner
2736.2.cg.c.2591.7 yes 32 228.83 even 6 inner
2736.2.cg.c.2591.8 yes 32 57.26 odd 6 inner
2736.2.cg.c.2591.9 yes 32 76.7 odd 6 inner
2736.2.cg.c.2591.10 yes 32 19.7 even 3 inner