Properties

Label 3024.2.t.h.1873.1
Level $3024$
Weight $2$
Character 3024.1873
Analytic conductor $24.147$
Analytic rank $0$
Dimension $6$
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: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1873.1
Root \(0.500000 - 0.224437i\) of defining polynomial
Character \(\chi\) \(=\) 3024.1873
Dual form 3024.2.t.h.289.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.58836 q^{5} +(2.64400 + 0.0963576i) q^{7} +O(q^{10})\) \(q-1.58836 q^{5} +(2.64400 + 0.0963576i) q^{7} -1.58836 q^{11} +(2.40545 - 4.16635i) q^{13} +(2.69963 - 4.67589i) q^{17} +(3.54944 + 6.14781i) q^{19} +0.300372 q^{23} -2.47710 q^{25} +(-4.13781 - 7.16689i) q^{29} +(-1.35600 - 2.34867i) q^{31} +(-4.19963 - 0.153051i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-2.93818 + 5.08907i) q^{41} +(0.833104 + 1.44298i) q^{43} +(-1.33310 + 2.30900i) q^{47} +(6.98143 + 0.509538i) q^{49} +(-2.44437 + 4.23377i) q^{53} +2.52290 q^{55} +(-3.23855 - 5.60933i) q^{59} +(2.23855 - 3.87728i) q^{61} +(-3.82072 + 6.61769i) q^{65} +(-5.02654 - 8.70623i) q^{67} +12.7207 q^{71} +(8.02654 - 13.9024i) q^{73} +(-4.19963 - 0.153051i) q^{77} +(4.19344 - 7.26325i) q^{79} +(1.18292 + 2.04887i) q^{83} +(-4.28799 + 7.42702i) q^{85} +(-1.60507 - 2.78007i) q^{89} +(6.76145 - 10.7840i) q^{91} +(-5.63781 - 9.76497i) q^{95} +(0.712008 + 1.23323i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 2 q^{5} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 2 q^{5} + 4 q^{7} + 2 q^{11} + 8 q^{13} + 4 q^{17} + 3 q^{19} + 14 q^{23} - 4 q^{25} + 5 q^{29} - 20 q^{31} - 13 q^{35} + 3 q^{37} + 6 q^{43} - 9 q^{47} - 12 q^{49} - 15 q^{53} + 26 q^{55} - 14 q^{59} + 8 q^{61} + 12 q^{65} - q^{67} + 14 q^{71} + 19 q^{73} - 13 q^{77} - 5 q^{79} + 2 q^{83} - 2 q^{85} + 9 q^{89} + 46 q^{91} - 4 q^{95} + 28 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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
\(5\) −1.58836 −0.710338 −0.355169 0.934802i \(-0.615577\pi\)
−0.355169 + 0.934802i \(0.615577\pi\)
\(6\) 0 0
\(7\) 2.64400 + 0.0963576i 0.999337 + 0.0364197i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.58836 −0.478910 −0.239455 0.970907i \(-0.576969\pi\)
−0.239455 + 0.970907i \(0.576969\pi\)
\(12\) 0 0
\(13\) 2.40545 4.16635i 0.667151 1.15554i −0.311547 0.950231i \(-0.600847\pi\)
0.978697 0.205308i \(-0.0658196\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.69963 4.67589i 0.654756 1.13407i −0.327199 0.944955i \(-0.606105\pi\)
0.981955 0.189115i \(-0.0605620\pi\)
\(18\) 0 0
\(19\) 3.54944 + 6.14781i 0.814298 + 1.41041i 0.909831 + 0.414979i \(0.136211\pi\)
−0.0955331 + 0.995426i \(0.530456\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.300372 0.0626319 0.0313159 0.999510i \(-0.490030\pi\)
0.0313159 + 0.999510i \(0.490030\pi\)
\(24\) 0 0
\(25\) −2.47710 −0.495420
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4.13781 7.16689i −0.768371 1.33086i −0.938446 0.345427i \(-0.887734\pi\)
0.170074 0.985431i \(-0.445599\pi\)
\(30\) 0 0
\(31\) −1.35600 2.34867i −0.243545 0.421833i 0.718176 0.695861i \(-0.244977\pi\)
−0.961722 + 0.274028i \(0.911644\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.19963 0.153051i −0.709867 0.0258703i
\(36\) 0 0
\(37\) 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i \(-0.140472\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.93818 + 5.08907i −0.458866 + 0.794780i −0.998901 0.0468628i \(-0.985078\pi\)
0.540035 + 0.841643i \(0.318411\pi\)
\(42\) 0 0
\(43\) 0.833104 + 1.44298i 0.127047 + 0.220052i 0.922531 0.385922i \(-0.126117\pi\)
−0.795484 + 0.605974i \(0.792783\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.33310 + 2.30900i −0.194453 + 0.336803i −0.946721 0.322055i \(-0.895627\pi\)
0.752268 + 0.658857i \(0.228960\pi\)
\(48\) 0 0
\(49\) 6.98143 + 0.509538i 0.997347 + 0.0727912i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −2.44437 + 4.23377i −0.335760 + 0.581553i −0.983630 0.180197i \(-0.942326\pi\)
0.647871 + 0.761750i \(0.275660\pi\)
\(54\) 0 0
\(55\) 2.52290 0.340188
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −3.23855 5.60933i −0.421623 0.730273i 0.574475 0.818522i \(-0.305206\pi\)
−0.996098 + 0.0882491i \(0.971873\pi\)
\(60\) 0 0
\(61\) 2.23855 3.87728i 0.286617 0.496435i −0.686383 0.727240i \(-0.740803\pi\)
0.973000 + 0.230805i \(0.0741360\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −3.82072 + 6.61769i −0.473902 + 0.820823i
\(66\) 0 0
\(67\) −5.02654 8.70623i −0.614090 1.06363i −0.990543 0.137199i \(-0.956190\pi\)
0.376454 0.926435i \(-0.377143\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 12.7207 1.50967 0.754833 0.655917i \(-0.227718\pi\)
0.754833 + 0.655917i \(0.227718\pi\)
\(72\) 0 0
\(73\) 8.02654 13.9024i 0.939436 1.62715i 0.172909 0.984938i \(-0.444683\pi\)
0.766527 0.642213i \(-0.221983\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −4.19963 0.153051i −0.478592 0.0174418i
\(78\) 0 0
\(79\) 4.19344 7.26325i 0.471799 0.817179i −0.527681 0.849443i \(-0.676938\pi\)
0.999479 + 0.0322635i \(0.0102716\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1.18292 + 2.04887i 0.129842 + 0.224893i 0.923615 0.383321i \(-0.125220\pi\)
−0.793773 + 0.608214i \(0.791886\pi\)
\(84\) 0 0
\(85\) −4.28799 + 7.42702i −0.465098 + 0.805573i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1.60507 2.78007i −0.170138 0.294687i 0.768330 0.640054i \(-0.221088\pi\)
−0.938468 + 0.345367i \(0.887755\pi\)
\(90\) 0 0
\(91\) 6.76145 10.7840i 0.708793 1.13047i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −5.63781 9.76497i −0.578427 1.00186i
\(96\) 0 0
\(97\) 0.712008 + 1.23323i 0.0722934 + 0.125216i 0.899906 0.436084i \(-0.143635\pi\)
−0.827613 + 0.561300i \(0.810302\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −12.0334 −1.19737 −0.598685 0.800985i \(-0.704310\pi\)
−0.598685 + 0.800985i \(0.704310\pi\)
\(102\) 0 0
\(103\) 6.09888 0.600941 0.300470 0.953791i \(-0.402856\pi\)
0.300470 + 0.953791i \(0.402856\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.54325 2.67299i −0.149192 0.258408i 0.781737 0.623608i \(-0.214334\pi\)
−0.930929 + 0.365200i \(0.881001\pi\)
\(108\) 0 0
\(109\) 1.14400 1.98146i 0.109575 0.189789i −0.806023 0.591884i \(-0.798384\pi\)
0.915598 + 0.402095i \(0.131718\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 9.73236 16.8569i 0.915543 1.58577i 0.109440 0.993993i \(-0.465094\pi\)
0.806104 0.591774i \(-0.201572\pi\)
\(114\) 0 0
\(115\) −0.477100 −0.0444898
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 7.58836 12.1029i 0.695624 1.10947i
\(120\) 0 0
\(121\) −8.47710 −0.770645
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 11.8764 1.06225
\(126\) 0 0
\(127\) 13.4400 1.19260 0.596302 0.802760i \(-0.296636\pi\)
0.596302 + 0.802760i \(0.296636\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −3.17673 −0.277552 −0.138776 0.990324i \(-0.544317\pi\)
−0.138776 + 0.990324i \(0.544317\pi\)
\(132\) 0 0
\(133\) 8.79232 + 16.5968i 0.762391 + 1.43913i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 21.2632 1.81664 0.908320 0.418275i \(-0.137365\pi\)
0.908320 + 0.418275i \(0.137365\pi\)
\(138\) 0 0
\(139\) −6.52654 + 11.3043i −0.553574 + 0.958818i 0.444439 + 0.895809i \(0.353403\pi\)
−0.998013 + 0.0630092i \(0.979930\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −3.82072 + 6.61769i −0.319505 + 0.553399i
\(144\) 0 0
\(145\) 6.57234 + 11.3836i 0.545803 + 0.945359i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −5.20877 −0.426719 −0.213360 0.976974i \(-0.568441\pi\)
−0.213360 + 0.976974i \(0.568441\pi\)
\(150\) 0 0
\(151\) 0.522900 0.0425530 0.0212765 0.999774i \(-0.493227\pi\)
0.0212765 + 0.999774i \(0.493227\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2.15383 + 3.73054i 0.173000 + 0.299644i
\(156\) 0 0
\(157\) −4.43199 7.67643i −0.353711 0.612646i 0.633185 0.774000i \(-0.281747\pi\)
−0.986897 + 0.161354i \(0.948414\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0.794182 + 0.0289431i 0.0625903 + 0.00228104i
\(162\) 0 0
\(163\) −10.9814 19.0204i −0.860132 1.48979i −0.871801 0.489860i \(-0.837048\pi\)
0.0116689 0.999932i \(-0.496286\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.65019 2.85821i 0.127695 0.221175i −0.795088 0.606494i \(-0.792575\pi\)
0.922783 + 0.385319i \(0.125909\pi\)
\(168\) 0 0
\(169\) −5.07234 8.78555i −0.390180 0.675812i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 9.55377 16.5476i 0.726360 1.25809i −0.232052 0.972703i \(-0.574544\pi\)
0.958412 0.285389i \(-0.0921227\pi\)
\(174\) 0 0
\(175\) −6.54944 0.238687i −0.495091 0.0180431i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −8.03706 + 13.9206i −0.600718 + 1.04047i 0.391994 + 0.919968i \(0.371785\pi\)
−0.992712 + 0.120507i \(0.961548\pi\)
\(180\) 0 0
\(181\) 8.05308 0.598581 0.299291 0.954162i \(-0.403250\pi\)
0.299291 + 0.954162i \(0.403250\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −0.794182 1.37556i −0.0583894 0.101133i
\(186\) 0 0
\(187\) −4.28799 + 7.42702i −0.313569 + 0.543118i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 11.9814 20.7524i 0.866946 1.50159i 0.00184390 0.999998i \(-0.499413\pi\)
0.865102 0.501596i \(-0.167254\pi\)
\(192\) 0 0
\(193\) −4.88255 8.45682i −0.351453 0.608735i 0.635051 0.772470i \(-0.280979\pi\)
−0.986504 + 0.163735i \(0.947646\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 18.2436 1.29980 0.649900 0.760020i \(-0.274811\pi\)
0.649900 + 0.760020i \(0.274811\pi\)
\(198\) 0 0
\(199\) −9.04944 + 15.6741i −0.641498 + 1.11111i 0.343601 + 0.939116i \(0.388353\pi\)
−0.985098 + 0.171991i \(0.944980\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −10.2498 19.3479i −0.719392 1.35796i
\(204\) 0 0
\(205\) 4.66690 8.08330i 0.325950 0.564562i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −5.63781 9.76497i −0.389975 0.675457i
\(210\) 0 0
\(211\) −0.166208 + 0.287880i −0.0114422 + 0.0198185i −0.871690 0.490058i \(-0.836976\pi\)
0.860248 + 0.509877i \(0.170309\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1.32327 2.29197i −0.0902464 0.156311i
\(216\) 0 0
\(217\) −3.35896 6.34053i −0.228021 0.430423i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −12.9876 22.4952i −0.873642 1.51319i
\(222\) 0 0
\(223\) −3.16621 5.48403i −0.212025 0.367238i 0.740323 0.672251i \(-0.234672\pi\)
−0.952348 + 0.305013i \(0.901339\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −23.3090 −1.54707 −0.773537 0.633751i \(-0.781515\pi\)
−0.773537 + 0.633751i \(0.781515\pi\)
\(228\) 0 0
\(229\) −4.95420 −0.327383 −0.163691 0.986512i \(-0.552340\pi\)
−0.163691 + 0.986512i \(0.552340\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 7.13781 + 12.3630i 0.467613 + 0.809930i 0.999315 0.0370017i \(-0.0117807\pi\)
−0.531702 + 0.846932i \(0.678447\pi\)
\(234\) 0 0
\(235\) 2.11745 3.66754i 0.138127 0.239244i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 2.48762 4.30868i 0.160911 0.278706i −0.774285 0.632837i \(-0.781890\pi\)
0.935196 + 0.354132i \(0.115224\pi\)
\(240\) 0 0
\(241\) −13.0000 −0.837404 −0.418702 0.908124i \(-0.637515\pi\)
−0.418702 + 0.908124i \(0.637515\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −11.0891 0.809332i −0.708454 0.0517063i
\(246\) 0 0
\(247\) 34.1520 2.17304
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2.43268 0.153549 0.0767746 0.997048i \(-0.475538\pi\)
0.0767746 + 0.997048i \(0.475538\pi\)
\(252\) 0 0
\(253\) −0.477100 −0.0299950
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0.987620 0.0616061 0.0308030 0.999525i \(-0.490194\pi\)
0.0308030 + 0.999525i \(0.490194\pi\)
\(258\) 0 0
\(259\) 1.23855 + 2.33795i 0.0769597 + 0.145273i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 17.1854 1.05970 0.529848 0.848092i \(-0.322249\pi\)
0.529848 + 0.848092i \(0.322249\pi\)
\(264\) 0 0
\(265\) 3.88255 6.72477i 0.238503 0.413099i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −11.4523 + 19.8360i −0.698262 + 1.20942i 0.270807 + 0.962634i \(0.412709\pi\)
−0.969069 + 0.246791i \(0.920624\pi\)
\(270\) 0 0
\(271\) −7.00364 12.1307i −0.425441 0.736885i 0.571021 0.820936i \(-0.306548\pi\)
−0.996462 + 0.0840504i \(0.973214\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 3.93454 0.237261
\(276\) 0 0
\(277\) 28.2953 1.70010 0.850049 0.526703i \(-0.176572\pi\)
0.850049 + 0.526703i \(0.176572\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 8.79782 + 15.2383i 0.524834 + 0.909039i 0.999582 + 0.0289175i \(0.00920600\pi\)
−0.474748 + 0.880122i \(0.657461\pi\)
\(282\) 0 0
\(283\) −9.26145 16.0413i −0.550536 0.953556i −0.998236 0.0593725i \(-0.981090\pi\)
0.447700 0.894184i \(-0.352243\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −8.25890 + 13.1724i −0.487508 + 0.777541i
\(288\) 0 0
\(289\) −6.07598 10.5239i −0.357411 0.619054i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 7.04256 12.1981i 0.411431 0.712619i −0.583616 0.812030i \(-0.698362\pi\)
0.995046 + 0.0994108i \(0.0316958\pi\)
\(294\) 0 0
\(295\) 5.14400 + 8.90966i 0.299495 + 0.518741i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.722528 1.25146i 0.0417849 0.0723736i
\(300\) 0 0
\(301\) 2.06368 + 3.89550i 0.118949 + 0.224533i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −3.55563 + 6.15854i −0.203595 + 0.352637i
\(306\) 0 0
\(307\) 5.85532 0.334180 0.167090 0.985942i \(-0.446563\pi\)
0.167090 + 0.985942i \(0.446563\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −0.405446 0.702253i −0.0229907 0.0398211i 0.854301 0.519778i \(-0.173985\pi\)
−0.877292 + 0.479957i \(0.840652\pi\)
\(312\) 0 0
\(313\) −5.28799 + 9.15907i −0.298895 + 0.517701i −0.975883 0.218292i \(-0.929951\pi\)
0.676988 + 0.735994i \(0.263285\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6.09820 10.5624i 0.342509 0.593243i −0.642389 0.766379i \(-0.722057\pi\)
0.984898 + 0.173136i \(0.0553900\pi\)
\(318\) 0 0
\(319\) 6.57234 + 11.3836i 0.367981 + 0.637361i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 38.3287 2.13267
\(324\) 0 0
\(325\) −5.95853 + 10.3205i −0.330520 + 0.572477i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −3.74721 + 5.97654i −0.206590 + 0.329497i
\(330\) 0 0
\(331\) −7.83310 + 13.5673i −0.430546 + 0.745728i −0.996920 0.0784202i \(-0.975012\pi\)
0.566374 + 0.824148i \(0.308346\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 7.98398 + 13.8287i 0.436211 + 0.755540i
\(336\) 0 0
\(337\) −4.21201 + 7.29541i −0.229443 + 0.397406i −0.957643 0.287958i \(-0.907024\pi\)
0.728200 + 0.685364i \(0.240357\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2.15383 + 3.73054i 0.116636 + 0.202020i
\(342\) 0 0
\(343\) 18.4098 + 2.01993i 0.994035 + 0.109066i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −0.283662 0.491316i −0.0152277 0.0263752i 0.858311 0.513130i \(-0.171514\pi\)
−0.873539 + 0.486754i \(0.838181\pi\)
\(348\) 0 0
\(349\) −0.00364189 0.00630794i −0.000194946 0.000337656i 0.865928 0.500169i \(-0.166729\pi\)
−0.866123 + 0.499831i \(0.833395\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −6.65383 −0.354148 −0.177074 0.984198i \(-0.556663\pi\)
−0.177074 + 0.984198i \(0.556663\pi\)
\(354\) 0 0
\(355\) −20.2051 −1.07237
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −0.398568 0.690339i −0.0210356 0.0364347i 0.855316 0.518107i \(-0.173363\pi\)
−0.876352 + 0.481672i \(0.840030\pi\)
\(360\) 0 0
\(361\) −15.6971 + 27.1881i −0.826162 + 1.43095i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −12.7491 + 22.0820i −0.667317 + 1.15583i
\(366\) 0 0
\(367\) 15.4327 0.805579 0.402790 0.915293i \(-0.368041\pi\)
0.402790 + 0.915293i \(0.368041\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −6.87085 + 10.9585i −0.356717 + 0.568939i
\(372\) 0 0
\(373\) 10.2422 0.530321 0.265160 0.964204i \(-0.414575\pi\)
0.265160 + 0.964204i \(0.414575\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −39.8131 −2.05048
\(378\) 0 0
\(379\) −25.0087 −1.28461 −0.642304 0.766450i \(-0.722021\pi\)
−0.642304 + 0.766450i \(0.722021\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −6.26695 −0.320226 −0.160113 0.987099i \(-0.551186\pi\)
−0.160113 + 0.987099i \(0.551186\pi\)
\(384\) 0 0
\(385\) 6.67054 + 0.243101i 0.339962 + 0.0123896i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 21.6342 1.09690 0.548448 0.836185i \(-0.315219\pi\)
0.548448 + 0.836185i \(0.315219\pi\)
\(390\) 0 0
\(391\) 0.810892 1.40451i 0.0410086 0.0710290i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −6.66071 + 11.5367i −0.335137 + 0.580473i
\(396\) 0 0
\(397\) 2.05308 + 3.55605i 0.103041 + 0.178473i 0.912936 0.408102i \(-0.133809\pi\)
−0.809895 + 0.586575i \(0.800476\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −16.7417 −0.836041 −0.418021 0.908438i \(-0.637276\pi\)
−0.418021 + 0.908438i \(0.637276\pi\)
\(402\) 0 0
\(403\) −13.0472 −0.649926
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −0.794182 1.37556i −0.0393661 0.0681842i
\(408\) 0 0
\(409\) 4.38255 + 7.59079i 0.216703 + 0.375341i 0.953798 0.300449i \(-0.0971364\pi\)
−0.737095 + 0.675789i \(0.763803\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −8.02221 15.1431i −0.394747 0.745144i
\(414\) 0 0
\(415\) −1.87890 3.25436i −0.0922318 0.159750i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −0.210149 + 0.363988i −0.0102664 + 0.0177820i −0.871113 0.491083i \(-0.836601\pi\)
0.860847 + 0.508865i \(0.169935\pi\)
\(420\) 0 0
\(421\) 3.28799 + 5.69497i 0.160247 + 0.277556i 0.934957 0.354761i \(-0.115438\pi\)
−0.774710 + 0.632316i \(0.782104\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −6.68725 + 11.5827i −0.324379 + 0.561841i
\(426\) 0 0
\(427\) 6.29232 10.0358i 0.304507 0.485667i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 11.0439 19.1287i 0.531968 0.921395i −0.467336 0.884080i \(-0.654786\pi\)
0.999304 0.0373155i \(-0.0118806\pi\)
\(432\) 0 0
\(433\) −9.43268 −0.453306 −0.226653 0.973976i \(-0.572778\pi\)
−0.226653 + 0.973976i \(0.572778\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.06615 + 1.84663i 0.0510010 + 0.0883363i
\(438\) 0 0
\(439\) −15.6032 + 27.0256i −0.744701 + 1.28986i 0.205634 + 0.978629i \(0.434074\pi\)
−0.950334 + 0.311231i \(0.899259\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6.52723 + 11.3055i −0.310118 + 0.537140i −0.978388 0.206779i \(-0.933702\pi\)
0.668270 + 0.743919i \(0.267035\pi\)
\(444\) 0 0
\(445\) 2.54944 + 4.41576i 0.120855 + 0.209327i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 9.91706 0.468015 0.234008 0.972235i \(-0.424816\pi\)
0.234008 + 0.972235i \(0.424816\pi\)
\(450\) 0 0
\(451\) 4.66690 8.08330i 0.219756 0.380628i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −10.7396 + 17.1290i −0.503482 + 0.803019i
\(456\) 0 0
\(457\) 12.2615 21.2375i 0.573566 0.993446i −0.422629 0.906303i \(-0.638893\pi\)
0.996196 0.0871436i \(-0.0277739\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.75526 3.04020i −0.0817506 0.141596i 0.822251 0.569125i \(-0.192718\pi\)
−0.904002 + 0.427528i \(0.859384\pi\)
\(462\) 0 0
\(463\) −8.69413 + 15.0587i −0.404050 + 0.699836i −0.994210 0.107451i \(-0.965731\pi\)
0.590160 + 0.807286i \(0.299065\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 6.69894 + 11.6029i 0.309990 + 0.536918i 0.978360 0.206911i \(-0.0663410\pi\)
−0.668370 + 0.743829i \(0.733008\pi\)
\(468\) 0 0
\(469\) −12.4512 23.5036i −0.574945 1.08529i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1.32327 2.29197i −0.0608441 0.105385i
\(474\) 0 0
\(475\) −8.79232 15.2287i −0.403419 0.698743i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 20.8058 0.950641 0.475321 0.879813i \(-0.342332\pi\)
0.475321 + 0.879813i \(0.342332\pi\)
\(480\) 0 0
\(481\) 4.81089 0.219358
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.13093 1.95882i −0.0513528 0.0889456i
\(486\) 0 0
\(487\) −16.2472 + 28.1410i −0.736231 + 1.27519i 0.217950 + 0.975960i \(0.430063\pi\)
−0.954181 + 0.299230i \(0.903270\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −9.66071 + 16.7328i −0.435982 + 0.755142i −0.997375 0.0724067i \(-0.976932\pi\)
0.561394 + 0.827549i \(0.310265\pi\)
\(492\) 0 0
\(493\) −44.6822 −2.01238
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 33.6334 + 1.22573i 1.50866 + 0.0549816i
\(498\) 0 0
\(499\) 11.1506 0.499169 0.249585 0.968353i \(-0.419706\pi\)
0.249585 + 0.968353i \(0.419706\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −40.7651 −1.81763 −0.908813 0.417204i \(-0.863010\pi\)
−0.908813 + 0.417204i \(0.863010\pi\)
\(504\) 0 0
\(505\) 19.1135 0.850537
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1.44506 −0.0640510 −0.0320255 0.999487i \(-0.510196\pi\)
−0.0320255 + 0.999487i \(0.510196\pi\)
\(510\) 0 0
\(511\) 22.5617 35.9844i 0.998073 1.59186i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −9.68725 −0.426871
\(516\) 0 0
\(517\) 2.11745 3.66754i 0.0931255 0.161298i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −9.64214 + 16.7007i −0.422430 + 0.731670i −0.996177 0.0873630i \(-0.972156\pi\)
0.573747 + 0.819033i \(0.305489\pi\)
\(522\) 0 0
\(523\) 18.3454 + 31.7752i 0.802189 + 1.38943i 0.918173 + 0.396180i \(0.129665\pi\)
−0.115984 + 0.993251i \(0.537002\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −14.6428 −0.637851
\(528\) 0 0
\(529\) −22.9098 −0.996077
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 14.1353 + 24.4830i 0.612266 + 1.06048i
\(534\) 0 0
\(535\) 2.45125 + 4.24568i 0.105977 + 0.183557i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −11.0891 0.809332i −0.477639 0.0348604i
\(540\) 0 0
\(541\) −1.62543 2.81532i −0.0698825 0.121040i 0.828967 0.559298i \(-0.188929\pi\)
−0.898849 + 0.438258i \(0.855596\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1.81708 + 3.14728i −0.0778352 + 0.134815i
\(546\) 0 0
\(547\) 2.95853 + 5.12432i 0.126498 + 0.219100i 0.922317 0.386433i \(-0.126293\pi\)
−0.795820 + 0.605534i \(0.792960\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 29.3738 50.8769i 1.25137 2.16743i
\(552\) 0 0
\(553\) 11.7873 18.7999i 0.501247 0.799454i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −12.8040 + 22.1772i −0.542523 + 0.939678i 0.456235 + 0.889859i \(0.349198\pi\)
−0.998758 + 0.0498188i \(0.984136\pi\)
\(558\) 0 0
\(559\) 8.01594 0.339038
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 23.3189 + 40.3895i 0.982773 + 1.70221i 0.651443 + 0.758698i \(0.274164\pi\)
0.331330 + 0.943515i \(0.392503\pi\)
\(564\) 0 0
\(565\) −15.4585 + 26.7750i −0.650345 + 1.12643i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 15.5989 27.0181i 0.653939 1.13266i −0.328219 0.944602i \(-0.606449\pi\)
0.982159 0.188054i \(-0.0602182\pi\)
\(570\) 0 0
\(571\) −7.83812 13.5760i −0.328015 0.568139i 0.654103 0.756406i \(-0.273046\pi\)
−0.982118 + 0.188267i \(0.939713\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −0.744051 −0.0310291
\(576\) 0 0
\(577\) 6.99567 12.1169i 0.291234 0.504431i −0.682868 0.730542i \(-0.739268\pi\)
0.974102 + 0.226110i \(0.0726010\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 2.93021 + 5.53120i 0.121565 + 0.229473i
\(582\) 0 0
\(583\) 3.88255 6.72477i 0.160799 0.278511i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.44801 + 2.50803i 0.0597658 + 0.103517i 0.894360 0.447348i \(-0.147631\pi\)
−0.834594 + 0.550865i \(0.814298\pi\)
\(588\) 0 0
\(589\) 9.62612 16.6729i 0.396637 0.686996i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 2.04394 + 3.54021i 0.0839346 + 0.145379i 0.904937 0.425546i \(-0.139918\pi\)
−0.821002 + 0.570925i \(0.806585\pi\)
\(594\) 0 0
\(595\) −12.0531 + 19.2238i −0.494128 + 0.788100i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 9.88255 + 17.1171i 0.403790 + 0.699385i 0.994180 0.107734i \(-0.0343593\pi\)
−0.590390 + 0.807118i \(0.701026\pi\)
\(600\) 0 0
\(601\) −13.4320 23.2649i −0.547902 0.948994i −0.998418 0.0562261i \(-0.982093\pi\)
0.450516 0.892768i \(-0.351240\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 13.4647 0.547419
\(606\) 0 0
\(607\) 15.2422 0.618661 0.309331 0.950955i \(-0.399895\pi\)
0.309331 + 0.950955i \(0.399895\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.41342 + 11.1084i 0.259459 + 0.449396i
\(612\) 0 0
\(613\) −1.36033 + 2.35617i −0.0549434 + 0.0951648i −0.892189 0.451662i \(-0.850831\pi\)
0.837246 + 0.546827i \(0.184165\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 9.21812 15.9663i 0.371108 0.642777i −0.618629 0.785684i \(-0.712311\pi\)
0.989736 + 0.142906i \(0.0456448\pi\)
\(618\) 0 0
\(619\) −0.107546 −0.00432262 −0.00216131 0.999998i \(-0.500688\pi\)
−0.00216131 + 0.999998i \(0.500688\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −3.97593 7.50516i −0.159292 0.300688i
\(624\) 0 0
\(625\) −6.47848 −0.259139
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 5.39926 0.215282
\(630\) 0 0
\(631\) −35.7266 −1.42225 −0.711126 0.703064i \(-0.751815\pi\)
−0.711126 + 0.703064i \(0.751815\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −21.3475 −0.847152
\(636\) 0 0
\(637\) 18.9164 27.8615i 0.749494 1.10391i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −17.3128 −0.683813 −0.341906 0.939734i \(-0.611073\pi\)
−0.341906 + 0.939734i \(0.611073\pi\)
\(642\) 0 0
\(643\) −14.4821 + 25.0838i −0.571119 + 0.989207i 0.425332 + 0.905037i \(0.360157\pi\)
−0.996451 + 0.0841700i \(0.973176\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.27816 2.21384i 0.0502497 0.0870350i −0.839807 0.542886i \(-0.817332\pi\)
0.890056 + 0.455851i \(0.150665\pi\)
\(648\) 0 0
\(649\) 5.14400 + 8.90966i 0.201920 + 0.349735i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −29.9766 −1.17308 −0.586538 0.809922i \(-0.699509\pi\)
−0.586538 + 0.809922i \(0.699509\pi\)
\(654\) 0 0
\(655\) 5.04580 0.197156
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −7.63162 13.2183i −0.297286 0.514914i 0.678228 0.734851i \(-0.262748\pi\)
−0.975514 + 0.219937i \(0.929415\pi\)
\(660\) 0 0
\(661\) 13.6261 + 23.6011i 0.529994 + 0.917977i 0.999388 + 0.0349881i \(0.0111393\pi\)
−0.469393 + 0.882989i \(0.655527\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −13.9654 26.3618i −0.541555 1.02227i
\(666\) 0 0
\(667\) −1.24288 2.15273i −0.0481245 0.0833541i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −3.55563 + 6.15854i −0.137264 + 0.237748i
\(672\) 0 0
\(673\) 23.2280 + 40.2320i 0.895372 + 1.55083i 0.833344 + 0.552755i \(0.186423\pi\)
0.0620280 + 0.998074i \(0.480243\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 2.54944 4.41576i 0.0979830 0.169712i −0.812867 0.582450i \(-0.802094\pi\)
0.910850 + 0.412738i \(0.135428\pi\)
\(678\) 0 0
\(679\) 1.76371 + 3.32927i 0.0676852 + 0.127766i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −7.77197 + 13.4614i −0.297386 + 0.515088i −0.975537 0.219835i \(-0.929448\pi\)
0.678151 + 0.734923i \(0.262782\pi\)
\(684\) 0 0
\(685\) −33.7738 −1.29043
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 11.7596 + 20.3682i 0.448005 + 0.775967i
\(690\) 0 0
\(691\) 11.6483 20.1755i 0.443123 0.767512i −0.554796 0.831986i \(-0.687204\pi\)
0.997919 + 0.0644744i \(0.0205371\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 10.3665 17.9553i 0.393225 0.681085i
\(696\) 0 0
\(697\) 15.8640 + 27.4772i 0.600891 + 1.04077i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 45.6464 1.72404 0.862020 0.506874i \(-0.169199\pi\)
0.862020 + 0.506874i \(0.169199\pi\)
\(702\) 0 0
\(703\) −3.54944 + 6.14781i −0.133870 + 0.231869i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −31.8163 1.15951i −1.19658 0.0436079i
\(708\) 0 0
\(709\) −9.00069 + 15.5897i −0.338028 + 0.585482i −0.984062 0.177827i \(-0.943093\pi\)
0.646034 + 0.763309i \(0.276427\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −0.407305 0.705474i −0.0152537 0.0264202i
\(714\) 0 0
\(715\) 6.06870 10.5113i 0.226957 0.393100i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 18.4389 + 31.9371i 0.687654 + 1.19105i 0.972595 + 0.232506i \(0.0746926\pi\)
−0.284941 + 0.958545i \(0.591974\pi\)
\(720\) 0 0
\(721\) 16.1254 + 0.587674i 0.600542 + 0.0218861i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 10.2498 + 17.7531i 0.380666 + 0.659334i
\(726\) 0 0
\(727\) −15.2429 26.4014i −0.565327 0.979175i −0.997019 0.0771543i \(-0.975417\pi\)
0.431692 0.902021i \(-0.357917\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 8.99628 0.332739
\(732\) 0 0
\(733\) 6.15059 0.227177 0.113589 0.993528i \(-0.463765\pi\)
0.113589 + 0.993528i \(0.463765\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 7.98398 + 13.8287i 0.294094 + 0.509385i
\(738\) 0 0
\(739\) 20.3912 35.3186i 0.750103 1.29922i −0.197670 0.980269i \(-0.563337\pi\)
0.947772 0.318947i \(-0.103329\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 7.25271 12.5621i 0.266076 0.460858i −0.701769 0.712405i \(-0.747606\pi\)
0.967845 + 0.251547i \(0.0809394\pi\)
\(744\) 0 0
\(745\) 8.27342 0.303115
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3.82279 7.21608i −0.139682 0.263670i
\(750\) 0 0
\(751\) −4.18911 −0.152863 −0.0764314 0.997075i \(-0.524353\pi\)
−0.0764314 + 0.997075i \(0.524353\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −0.830556 −0.0302270
\(756\) 0 0
\(757\) 2.38688 0.0867525 0.0433763 0.999059i \(-0.486189\pi\)
0.0433763 + 0.999059i \(0.486189\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −3.63416 −0.131738 −0.0658692 0.997828i \(-0.520982\pi\)
−0.0658692 + 0.997828i \(0.520982\pi\)
\(762\) 0 0
\(763\) 3.21565 5.12874i 0.116414 0.185673i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −31.1606 −1.12515
\(768\) 0 0
\(769\) −19.9672 + 34.5842i −0.720035 + 1.24714i 0.240950 + 0.970538i \(0.422541\pi\)
−0.960985 + 0.276600i \(0.910792\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −18.0698 + 31.2978i −0.649925 + 1.12570i 0.333215 + 0.942851i \(0.391867\pi\)
−0.983140 + 0.182853i \(0.941467\pi\)
\(774\) 0 0
\(775\) 3.35896 + 5.81788i 0.120657 + 0.208985i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −41.7156 −1.49462
\(780\) 0 0
\(781\) −20.2051 −0.722994
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 7.03961 + 12.1930i 0.251254 + 0.435186i
\(786\) 0 0
\(787\) −22.3189 38.6574i −0.795582 1.37799i −0.922469 0.386071i \(-0.873832\pi\)
0.126888 0.991917i \(-0.459501\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 27.3566 43.6319i 0.972689 1.55137i
\(792\) 0 0
\(793\) −10.7694 18.6532i −0.382433 0.662394i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −26.2836 + 45.5245i −0.931012 + 1.61256i −0.149418 + 0.988774i \(0.547740\pi\)
−0.781595 + 0.623786i \(0.785593\pi\)
\(798\) 0 0
\(799\) 7.19777 + 12.4669i 0.254639 + 0.441047i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −12.7491 + 22.0820i −0.449905 + 0.779258i
\(804\) 0 0
\(805\) −1.26145 0.0459722i −0.0444603 0.00162031i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −7.40290 + 12.8222i −0.260272 + 0.450804i −0.966314 0.257365i \(-0.917146\pi\)
0.706042 + 0.708170i \(0.250479\pi\)
\(810\) 0 0
\(811\) −27.0704 −0.950571 −0.475285 0.879832i \(-0.657655\pi\)
−0.475285 + 0.879832i \(0.657655\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 17.4425 + 30.2113i 0.610984 + 1.05826i
\(816\) 0 0
\(817\) −5.91411 + 10.2435i −0.206908 + 0.358376i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 21.9091 37.9477i 0.764632 1.32438i −0.175808 0.984424i \(-0.556254\pi\)
0.940441 0.339958i \(-0.110413\pi\)
\(822\) 0 0
\(823\) 15.6712 + 27.1434i 0.546265 + 0.946158i 0.998526 + 0.0542727i \(0.0172840\pi\)
−0.452262 + 0.891885i \(0.649383\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −14.7665 −0.513480 −0.256740 0.966480i \(-0.582648\pi\)
−0.256740 + 0.966480i \(0.582648\pi\)
\(828\) 0 0
\(829\) −15.0036 + 25.9871i −0.521098 + 0.902568i 0.478601 + 0.878033i \(0.341144\pi\)
−0.999699 + 0.0245357i \(0.992189\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 21.2298 31.2689i 0.735569 1.08340i
\(834\) 0 0
\(835\) −2.62110 + 4.53987i −0.0907068 + 0.157109i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 18.0167 + 31.2059i 0.622006 + 1.07735i 0.989112 + 0.147167i \(0.0470154\pi\)
−0.367106 + 0.930179i \(0.619651\pi\)
\(840\) 0 0
\(841\) −19.7429 + 34.1957i −0.680789 + 1.17916i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 8.05673 + 13.9547i 0.277160 + 0.480055i
\(846\) 0 0
\(847\) −22.4134 0.816833i −0.770134 0.0280667i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0.150186 + 0.260130i 0.00514831 + 0.00891713i
\(852\) 0 0
\(853\) −12.2658 21.2450i −0.419972 0.727413i 0.575964 0.817475i \(-0.304627\pi\)
−0.995936 + 0.0900617i \(0.971294\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −29.0480 −0.992260 −0.496130 0.868248i \(-0.665246\pi\)
−0.496130 + 0.868248i \(0.665246\pi\)
\(858\) 0 0
\(859\) −25.2953 −0.863064 −0.431532 0.902098i \(-0.642027\pi\)
−0.431532 + 0.902098i \(0.642027\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −1.34981 2.33795i −0.0459482 0.0795846i 0.842137 0.539264i \(-0.181298\pi\)
−0.888085 + 0.459680i \(0.847964\pi\)
\(864\) 0 0
\(865\) −15.1749 + 26.2836i −0.515961 + 0.893671i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −6.66071 + 11.5367i −0.225949 + 0.391355i
\(870\) 0 0
\(871\) −48.3643 −1.63876
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 31.4010 + 1.14438i 1.06155 + 0.0386870i
\(876\) 0 0
\(877\) −11.0916 −0.374537 −0.187268 0.982309i \(-0.559963\pi\)
−0.187268 + 0.982309i \(0.559963\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 40.3942 1.36091 0.680457 0.732788i \(-0.261781\pi\)
0.680457 + 0.732788i \(0.261781\pi\)
\(882\) 0 0
\(883\) 33.2581 1.11923 0.559613 0.828754i \(-0.310950\pi\)
0.559613 + 0.828754i \(0.310950\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 40.5672 1.36211 0.681056 0.732231i \(-0.261521\pi\)
0.681056 + 0.732231i \(0.261521\pi\)
\(888\) 0 0
\(889\) 35.5352 + 1.29504i 1.19181 + 0.0434343i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −18.9271 −0.633371
\(894\) 0 0
\(895\) 12.7658 22.1110i 0.426713 0.739089i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −11.2218 + 19.4367i −0.374267 + 0.648249i
\(900\) 0 0
\(901\) 13.1978 + 22.8592i 0.439681 + 0.761551i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −12.7912 −0.425195
\(906\) 0 0
\(907\) −30.1135 −0.999901 −0.499950 0.866054i \(-0.666648\pi\)
−0.499950 + 0.866054i \(0.666648\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 14.6113 + 25.3075i 0.484093 + 0.838473i 0.999833 0.0182717i \(-0.00581638\pi\)
−0.515740 + 0.856745i \(0.672483\pi\)
\(912\) 0 0
\(913\) −1.87890 3.25436i −0.0621826 0.107704i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −8.39926 0.306102i −0.277368 0.0101084i
\(918\) 0 0
\(919\) 5.52359 + 9.56714i 0.182206 + 0.315591i 0.942632 0.333835i \(-0.108343\pi\)
−0.760425 + 0.649426i \(0.775009\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 30.5989 52.9988i 1.00717 1.74448i
\(924\) 0 0
\(925\) −1.23855 2.14523i −0.0407233 0.0705348i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −21.1669 + 36.6621i −0.694463 + 1.20285i 0.275898 + 0.961187i \(0.411025\pi\)
−0.970361 + 0.241659i \(0.922309\pi\)
\(930\) 0 0
\(931\) 21.6476 + 44.7291i 0.709473 + 1.46594i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 6.81089 11.7968i 0.222740 0.385797i
\(936\) 0 0
\(937\) −11.7651 −0.384349 −0.192174 0.981361i \(-0.561554\pi\)
−0.192174 + 0.981361i \(0.561554\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 7.28799 + 12.6232i 0.237582 + 0.411504i 0.960020 0.279932i \(-0.0903119\pi\)
−0.722438 + 0.691436i \(0.756979\pi\)
\(942\) 0 0
\(943\) −0.882546 + 1.52861i −0.0287397 + 0.0497785i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −3.12178 + 5.40709i −0.101444 + 0.175707i −0.912280 0.409567i \(-0.865680\pi\)
0.810836 + 0.585274i \(0.199013\pi\)
\(948\) 0 0
\(949\) −38.6148 66.8828i −1.25349 2.17111i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −28.0173 −0.907570 −0.453785 0.891111i \(-0.649927\pi\)
−0.453785 + 0.891111i \(0.649927\pi\)
\(954\) 0 0
\(955\) −19.0309 + 32.9624i −0.615825 + 1.06664i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 56.2199 + 2.04887i 1.81544 + 0.0661616i
\(960\) 0 0
\(961\) 11.8225 20.4772i 0.381371 0.660554i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 7.75526 + 13.4325i 0.249651 + 0.432408i
\(966\) 0 0
\(967\) −15.7837 + 27.3381i −0.507568 + 0.879134i 0.492393 + 0.870373i \(0.336122\pi\)
−0.999962 + 0.00876132i \(0.997211\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 2.82141 + 4.88683i 0.0905434 + 0.156826i 0.907740 0.419533i \(-0.137806\pi\)
−0.817196 + 0.576359i \(0.804473\pi\)
\(972\) 0 0
\(973\) −18.3454 + 29.2596i −0.588127 + 0.938021i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 3.24652 + 5.62314i 0.103865 + 0.179900i 0.913274 0.407346i \(-0.133546\pi\)
−0.809409 + 0.587246i \(0.800212\pi\)
\(978\) 0 0
\(979\) 2.54944 + 4.41576i 0.0814805 + 0.141128i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −30.3063 −0.966620 −0.483310 0.875449i \(-0.660566\pi\)
−0.483310 + 0.875449i \(0.660566\pi\)
\(984\) 0 0
\(985\) −28.9774 −0.923298
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0.250241 + 0.433430i 0.00795720 + 0.0137823i
\(990\) 0 0
\(991\) −11.1669 + 19.3416i −0.354728 + 0.614407i −0.987071 0.160281i \(-0.948760\pi\)
0.632343 + 0.774688i \(0.282093\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 14.3738 24.8962i 0.455680 0.789262i
\(996\) 0 0
\(997\) −8.76509 −0.277593 −0.138797 0.990321i \(-0.544323\pi\)
−0.138797 + 0.990321i \(0.544323\pi\)
\(998\) 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.h.1873.1 6
3.2 odd 2 1008.2.t.h.193.1 6
4.3 odd 2 378.2.h.c.361.1 6
7.2 even 3 3024.2.q.g.2305.3 6
9.2 odd 6 1008.2.q.g.529.3 6
9.7 even 3 3024.2.q.g.2881.3 6
12.11 even 2 126.2.h.d.67.3 yes 6
21.2 odd 6 1008.2.q.g.625.3 6
28.3 even 6 2646.2.f.m.1765.1 6
28.11 odd 6 2646.2.f.l.1765.3 6
28.19 even 6 2646.2.e.p.1549.1 6
28.23 odd 6 378.2.e.d.37.3 6
28.27 even 2 2646.2.h.o.361.3 6
36.7 odd 6 378.2.e.d.235.3 6
36.11 even 6 126.2.e.c.25.1 6
36.23 even 6 1134.2.g.m.487.1 6
36.31 odd 6 1134.2.g.l.487.3 6
63.2 odd 6 1008.2.t.h.961.1 6
63.16 even 3 inner 3024.2.t.h.289.1 6
84.11 even 6 882.2.f.n.589.3 6
84.23 even 6 126.2.e.c.121.1 yes 6
84.47 odd 6 882.2.e.o.373.3 6
84.59 odd 6 882.2.f.o.589.1 6
84.83 odd 2 882.2.h.p.67.1 6
252.11 even 6 882.2.f.n.295.3 6
252.23 even 6 1134.2.g.m.163.1 6
252.31 even 6 7938.2.a.bz.1.3 3
252.47 odd 6 882.2.h.p.79.1 6
252.59 odd 6 7938.2.a.bw.1.1 3
252.67 odd 6 7938.2.a.ca.1.1 3
252.79 odd 6 378.2.h.c.289.1 6
252.83 odd 6 882.2.e.o.655.3 6
252.95 even 6 7938.2.a.bv.1.3 3
252.115 even 6 2646.2.f.m.883.1 6
252.151 odd 6 2646.2.f.l.883.3 6
252.187 even 6 2646.2.h.o.667.3 6
252.191 even 6 126.2.h.d.79.3 yes 6
252.223 even 6 2646.2.e.p.2125.1 6
252.227 odd 6 882.2.f.o.295.1 6
252.247 odd 6 1134.2.g.l.163.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.e.c.25.1 6 36.11 even 6
126.2.e.c.121.1 yes 6 84.23 even 6
126.2.h.d.67.3 yes 6 12.11 even 2
126.2.h.d.79.3 yes 6 252.191 even 6
378.2.e.d.37.3 6 28.23 odd 6
378.2.e.d.235.3 6 36.7 odd 6
378.2.h.c.289.1 6 252.79 odd 6
378.2.h.c.361.1 6 4.3 odd 2
882.2.e.o.373.3 6 84.47 odd 6
882.2.e.o.655.3 6 252.83 odd 6
882.2.f.n.295.3 6 252.11 even 6
882.2.f.n.589.3 6 84.11 even 6
882.2.f.o.295.1 6 252.227 odd 6
882.2.f.o.589.1 6 84.59 odd 6
882.2.h.p.67.1 6 84.83 odd 2
882.2.h.p.79.1 6 252.47 odd 6
1008.2.q.g.529.3 6 9.2 odd 6
1008.2.q.g.625.3 6 21.2 odd 6
1008.2.t.h.193.1 6 3.2 odd 2
1008.2.t.h.961.1 6 63.2 odd 6
1134.2.g.l.163.3 6 252.247 odd 6
1134.2.g.l.487.3 6 36.31 odd 6
1134.2.g.m.163.1 6 252.23 even 6
1134.2.g.m.487.1 6 36.23 even 6
2646.2.e.p.1549.1 6 28.19 even 6
2646.2.e.p.2125.1 6 252.223 even 6
2646.2.f.l.883.3 6 252.151 odd 6
2646.2.f.l.1765.3 6 28.11 odd 6
2646.2.f.m.883.1 6 252.115 even 6
2646.2.f.m.1765.1 6 28.3 even 6
2646.2.h.o.361.3 6 28.27 even 2
2646.2.h.o.667.3 6 252.187 even 6
3024.2.q.g.2305.3 6 7.2 even 3
3024.2.q.g.2881.3 6 9.7 even 3
3024.2.t.h.289.1 6 63.16 even 3 inner
3024.2.t.h.1873.1 6 1.1 even 1 trivial
7938.2.a.bv.1.3 3 252.95 even 6
7938.2.a.bw.1.1 3 252.59 odd 6
7938.2.a.bz.1.3 3 252.31 even 6
7938.2.a.ca.1.1 3 252.67 odd 6