Properties

Label 3024.2.cc.d.881.6
Level $3024$
Weight $2$
Character 3024.881
Analytic conductor $24.147$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3024,2,Mod(881,3024)]
 
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, 5, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3024.881");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.cc (of order \(6\), 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: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 881.6
Character \(\chi\) \(=\) 3024.881
Dual form 3024.2.cc.d.2897.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.16173 + 2.01217i) q^{5} +(1.39373 + 2.24889i) q^{7} +O(q^{10})\) \(q+(-1.16173 + 2.01217i) q^{5} +(1.39373 + 2.24889i) q^{7} +(-2.17784 + 1.25738i) q^{11} +(-0.244656 - 0.141252i) q^{13} -2.01033 q^{17} -2.93904i q^{19} +(-4.32546 - 2.49731i) q^{23} +(-0.199225 - 0.345068i) q^{25} +(-4.02448 + 2.32353i) q^{29} +(-8.91154 - 5.14508i) q^{31} +(-6.14429 + 0.191820i) q^{35} +3.93132 q^{37} +(-3.44915 + 5.97410i) q^{41} +(5.66183 + 9.80657i) q^{43} +(-1.84396 - 3.19383i) q^{47} +(-3.11504 + 6.26869i) q^{49} +0.845432i q^{53} -5.84293i q^{55} +(7.27908 - 12.6077i) q^{59} +(9.59760 - 5.54118i) q^{61} +(0.568447 - 0.328193i) q^{65} +(5.59936 - 9.69838i) q^{67} -7.67879i q^{71} +6.37515i q^{73} +(-5.86303 - 3.14529i) q^{77} +(-3.71484 - 6.43430i) q^{79} +(-4.73177 - 8.19566i) q^{83} +(2.33546 - 4.04513i) q^{85} -5.12467 q^{89} +(-0.0233229 - 0.747071i) q^{91} +(5.91385 + 3.41436i) q^{95} +(-4.49852 + 2.59722i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 12 q^{23} - 24 q^{25} + 36 q^{29} - 12 q^{43} + 6 q^{49} - 36 q^{65} + 60 q^{77} + 12 q^{79} + 12 q^{91} - 108 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(757\) \(785\) \(1135\) \(2593\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

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
\(5\) −1.16173 + 2.01217i −0.519541 + 0.899871i 0.480201 + 0.877158i \(0.340564\pi\)
−0.999742 + 0.0227126i \(0.992770\pi\)
\(6\) 0 0
\(7\) 1.39373 + 2.24889i 0.526780 + 0.850002i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.17784 + 1.25738i −0.656645 + 0.379114i −0.790997 0.611820i \(-0.790438\pi\)
0.134353 + 0.990934i \(0.457105\pi\)
\(12\) 0 0
\(13\) −0.244656 0.141252i −0.0678552 0.0391762i 0.465689 0.884949i \(-0.345807\pi\)
−0.533544 + 0.845772i \(0.679140\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.01033 −0.487577 −0.243788 0.969828i \(-0.578390\pi\)
−0.243788 + 0.969828i \(0.578390\pi\)
\(18\) 0 0
\(19\) 2.93904i 0.674261i −0.941458 0.337130i \(-0.890544\pi\)
0.941458 0.337130i \(-0.109456\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.32546 2.49731i −0.901921 0.520724i −0.0240979 0.999710i \(-0.507671\pi\)
−0.877823 + 0.478985i \(0.841005\pi\)
\(24\) 0 0
\(25\) −0.199225 0.345068i −0.0398450 0.0690136i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4.02448 + 2.32353i −0.747326 + 0.431469i −0.824727 0.565531i \(-0.808671\pi\)
0.0774007 + 0.997000i \(0.475338\pi\)
\(30\) 0 0
\(31\) −8.91154 5.14508i −1.60056 0.924083i −0.991375 0.131054i \(-0.958164\pi\)
−0.609184 0.793029i \(-0.708503\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −6.14429 + 0.191820i −1.03858 + 0.0324234i
\(36\) 0 0
\(37\) 3.93132 0.646305 0.323153 0.946347i \(-0.395257\pi\)
0.323153 + 0.946347i \(0.395257\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −3.44915 + 5.97410i −0.538666 + 0.932997i 0.460310 + 0.887758i \(0.347738\pi\)
−0.998976 + 0.0452389i \(0.985595\pi\)
\(42\) 0 0
\(43\) 5.66183 + 9.80657i 0.863421 + 1.49549i 0.868607 + 0.495502i \(0.165016\pi\)
−0.00518640 + 0.999987i \(0.501651\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.84396 3.19383i −0.268969 0.465869i 0.699627 0.714509i \(-0.253350\pi\)
−0.968596 + 0.248640i \(0.920016\pi\)
\(48\) 0 0
\(49\) −3.11504 + 6.26869i −0.445006 + 0.895528i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0.845432i 0.116129i 0.998313 + 0.0580645i \(0.0184929\pi\)
−0.998313 + 0.0580645i \(0.981507\pi\)
\(54\) 0 0
\(55\) 5.84293i 0.787860i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 7.27908 12.6077i 0.947656 1.64139i 0.197312 0.980341i \(-0.436779\pi\)
0.750344 0.661048i \(-0.229888\pi\)
\(60\) 0 0
\(61\) 9.59760 5.54118i 1.22885 0.709475i 0.262058 0.965052i \(-0.415599\pi\)
0.966789 + 0.255577i \(0.0822654\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.568447 0.328193i 0.0705071 0.0407073i
\(66\) 0 0
\(67\) 5.59936 9.69838i 0.684071 1.18485i −0.289657 0.957130i \(-0.593541\pi\)
0.973728 0.227715i \(-0.0731253\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 7.67879i 0.911304i −0.890158 0.455652i \(-0.849406\pi\)
0.890158 0.455652i \(-0.150594\pi\)
\(72\) 0 0
\(73\) 6.37515i 0.746155i 0.927800 + 0.373077i \(0.121697\pi\)
−0.927800 + 0.373077i \(0.878303\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −5.86303 3.14529i −0.668155 0.358439i
\(78\) 0 0
\(79\) −3.71484 6.43430i −0.417953 0.723915i 0.577781 0.816192i \(-0.303919\pi\)
−0.995733 + 0.0922769i \(0.970585\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −4.73177 8.19566i −0.519379 0.899591i −0.999746 0.0225236i \(-0.992830\pi\)
0.480367 0.877067i \(-0.340503\pi\)
\(84\) 0 0
\(85\) 2.33546 4.04513i 0.253316 0.438756i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −5.12467 −0.543214 −0.271607 0.962408i \(-0.587555\pi\)
−0.271607 + 0.962408i \(0.587555\pi\)
\(90\) 0 0
\(91\) −0.0233229 0.747071i −0.00244491 0.0783143i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 5.91385 + 3.41436i 0.606748 + 0.350306i
\(96\) 0 0
\(97\) −4.49852 + 2.59722i −0.456755 + 0.263708i −0.710679 0.703517i \(-0.751612\pi\)
0.253924 + 0.967224i \(0.418279\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −4.08122 7.06888i −0.406096 0.703379i 0.588352 0.808605i \(-0.299777\pi\)
−0.994448 + 0.105225i \(0.966444\pi\)
\(102\) 0 0
\(103\) −7.91895 4.57201i −0.780278 0.450493i 0.0562511 0.998417i \(-0.482085\pi\)
−0.836529 + 0.547923i \(0.815419\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.91633i 0.958648i 0.877638 + 0.479324i \(0.159118\pi\)
−0.877638 + 0.479324i \(0.840882\pi\)
\(108\) 0 0
\(109\) 7.55063 0.723220 0.361610 0.932330i \(-0.382227\pi\)
0.361610 + 0.932330i \(0.382227\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −4.89485 2.82604i −0.460469 0.265852i 0.251773 0.967786i \(-0.418987\pi\)
−0.712241 + 0.701935i \(0.752320\pi\)
\(114\) 0 0
\(115\) 10.0500 5.80238i 0.937169 0.541075i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2.80185 4.52102i −0.256846 0.414441i
\(120\) 0 0
\(121\) −2.33800 + 4.04953i −0.212545 + 0.368139i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −10.6915 −0.956277
\(126\) 0 0
\(127\) −10.6289 −0.943160 −0.471580 0.881823i \(-0.656316\pi\)
−0.471580 + 0.881823i \(0.656316\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −2.74685 + 4.75768i −0.239993 + 0.415681i −0.960712 0.277547i \(-0.910479\pi\)
0.720719 + 0.693228i \(0.243812\pi\)
\(132\) 0 0
\(133\) 6.60958 4.09622i 0.573123 0.355187i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 17.8601 10.3115i 1.52589 0.880973i 0.526361 0.850261i \(-0.323556\pi\)
0.999528 0.0307114i \(-0.00977729\pi\)
\(138\) 0 0
\(139\) −4.80013 2.77136i −0.407142 0.235064i 0.282419 0.959291i \(-0.408863\pi\)
−0.689561 + 0.724228i \(0.742196\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0.710429 0.0594090
\(144\) 0 0
\(145\) 10.7973i 0.896663i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 3.99945 + 2.30908i 0.327648 + 0.189167i 0.654796 0.755805i \(-0.272754\pi\)
−0.327149 + 0.944973i \(0.606088\pi\)
\(150\) 0 0
\(151\) −3.38911 5.87011i −0.275802 0.477703i 0.694535 0.719459i \(-0.255610\pi\)
−0.970337 + 0.241756i \(0.922277\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 20.7056 11.9544i 1.66311 0.960198i
\(156\) 0 0
\(157\) −6.42189 3.70768i −0.512522 0.295905i 0.221347 0.975195i \(-0.428955\pi\)
−0.733870 + 0.679290i \(0.762288\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −0.412344 13.2081i −0.0324973 1.04094i
\(162\) 0 0
\(163\) −12.0227 −0.941689 −0.470844 0.882216i \(-0.656051\pi\)
−0.470844 + 0.882216i \(0.656051\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −10.4096 + 18.0300i −0.805521 + 1.39520i 0.110419 + 0.993885i \(0.464781\pi\)
−0.915939 + 0.401317i \(0.868552\pi\)
\(168\) 0 0
\(169\) −6.46010 11.1892i −0.496930 0.860709i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 3.68149 + 6.37652i 0.279898 + 0.484798i 0.971359 0.237616i \(-0.0763659\pi\)
−0.691461 + 0.722414i \(0.743033\pi\)
\(174\) 0 0
\(175\) 0.498355 0.928967i 0.0376721 0.0702233i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 16.8136i 1.25670i 0.777929 + 0.628352i \(0.216270\pi\)
−0.777929 + 0.628352i \(0.783730\pi\)
\(180\) 0 0
\(181\) 4.02239i 0.298982i 0.988763 + 0.149491i \(0.0477635\pi\)
−0.988763 + 0.149491i \(0.952236\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −4.56713 + 7.91050i −0.335782 + 0.581591i
\(186\) 0 0
\(187\) 4.37818 2.52775i 0.320165 0.184847i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −4.42466 + 2.55458i −0.320157 + 0.184843i −0.651463 0.758681i \(-0.725844\pi\)
0.331306 + 0.943524i \(0.392511\pi\)
\(192\) 0 0
\(193\) −3.54994 + 6.14868i −0.255531 + 0.442592i −0.965039 0.262105i \(-0.915583\pi\)
0.709509 + 0.704696i \(0.248917\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 15.6086i 1.11206i 0.831161 + 0.556032i \(0.187677\pi\)
−0.831161 + 0.556032i \(0.812323\pi\)
\(198\) 0 0
\(199\) 26.8155i 1.90090i −0.310875 0.950451i \(-0.600622\pi\)
0.310875 0.950451i \(-0.399378\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −10.8344 5.81224i −0.760426 0.407939i
\(204\) 0 0
\(205\) −8.01394 13.8806i −0.559718 0.969460i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 3.69548 + 6.40076i 0.255622 + 0.442750i
\(210\) 0 0
\(211\) 1.15444 1.99955i 0.0794748 0.137654i −0.823549 0.567246i \(-0.808009\pi\)
0.903023 + 0.429591i \(0.141342\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −26.3100 −1.79433
\(216\) 0 0
\(217\) −0.849533 27.2119i −0.0576701 1.84727i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0.491838 + 0.283963i 0.0330846 + 0.0191014i
\(222\) 0 0
\(223\) −16.6900 + 9.63599i −1.11765 + 0.645274i −0.940799 0.338965i \(-0.889923\pi\)
−0.176847 + 0.984238i \(0.556590\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −0.124385 0.215441i −0.00825572 0.0142993i 0.861868 0.507133i \(-0.169295\pi\)
−0.870124 + 0.492833i \(0.835961\pi\)
\(228\) 0 0
\(229\) −18.2102 10.5137i −1.20336 0.694762i −0.242062 0.970261i \(-0.577824\pi\)
−0.961302 + 0.275498i \(0.911157\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 23.5168i 1.54064i 0.637659 + 0.770318i \(0.279903\pi\)
−0.637659 + 0.770318i \(0.720097\pi\)
\(234\) 0 0
\(235\) 8.56873 0.558962
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −10.6889 6.17125i −0.691409 0.399185i 0.112731 0.993626i \(-0.464040\pi\)
−0.804140 + 0.594441i \(0.797374\pi\)
\(240\) 0 0
\(241\) −4.62278 + 2.66896i −0.297780 + 0.171923i −0.641445 0.767169i \(-0.721665\pi\)
0.343665 + 0.939092i \(0.388331\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −8.99486 13.5505i −0.574661 0.865711i
\(246\) 0 0
\(247\) −0.415144 + 0.719051i −0.0264150 + 0.0457521i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 21.7872 1.37520 0.687599 0.726091i \(-0.258665\pi\)
0.687599 + 0.726091i \(0.258665\pi\)
\(252\) 0 0
\(253\) 12.5602 0.789655
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 13.0603 22.6211i 0.814679 1.41106i −0.0948796 0.995489i \(-0.530247\pi\)
0.909558 0.415576i \(-0.136420\pi\)
\(258\) 0 0
\(259\) 5.47920 + 8.84112i 0.340461 + 0.549361i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 17.1035 9.87469i 1.05464 0.608899i 0.130699 0.991422i \(-0.458278\pi\)
0.923946 + 0.382523i \(0.124945\pi\)
\(264\) 0 0
\(265\) −1.70115 0.982162i −0.104501 0.0603337i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −26.7501 −1.63098 −0.815492 0.578769i \(-0.803533\pi\)
−0.815492 + 0.578769i \(0.803533\pi\)
\(270\) 0 0
\(271\) 27.3379i 1.66066i 0.557274 + 0.830329i \(0.311847\pi\)
−0.557274 + 0.830329i \(0.688153\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.867762 + 0.501003i 0.0523280 + 0.0302116i
\(276\) 0 0
\(277\) −7.06241 12.2325i −0.424339 0.734977i 0.572019 0.820240i \(-0.306160\pi\)
−0.996358 + 0.0852630i \(0.972827\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 22.0291 12.7185i 1.31415 0.758723i 0.331366 0.943502i \(-0.392490\pi\)
0.982780 + 0.184780i \(0.0591571\pi\)
\(282\) 0 0
\(283\) 18.2802 + 10.5541i 1.08664 + 0.627374i 0.932681 0.360703i \(-0.117463\pi\)
0.153963 + 0.988077i \(0.450796\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −18.2423 + 0.569508i −1.07681 + 0.0336170i
\(288\) 0 0
\(289\) −12.9586 −0.762269
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 6.36260 11.0204i 0.371707 0.643816i −0.618121 0.786083i \(-0.712106\pi\)
0.989828 + 0.142267i \(0.0454392\pi\)
\(294\) 0 0
\(295\) 16.9126 + 29.2935i 0.984692 + 1.70554i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.705499 + 1.22196i 0.0408000 + 0.0706677i
\(300\) 0 0
\(301\) −14.1629 + 26.4005i −0.816335 + 1.52170i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 25.7494i 1.47440i
\(306\) 0 0
\(307\) 7.12625i 0.406717i 0.979104 + 0.203358i \(0.0651856\pi\)
−0.979104 + 0.203358i \(0.934814\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.67348 2.89855i 0.0948944 0.164362i −0.814670 0.579925i \(-0.803082\pi\)
0.909565 + 0.415563i \(0.136415\pi\)
\(312\) 0 0
\(313\) −3.49029 + 2.01512i −0.197283 + 0.113901i −0.595388 0.803439i \(-0.703001\pi\)
0.398105 + 0.917340i \(0.369668\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −11.9601 + 6.90518i −0.671748 + 0.387834i −0.796739 0.604324i \(-0.793443\pi\)
0.124991 + 0.992158i \(0.460110\pi\)
\(318\) 0 0
\(319\) 5.84312 10.1206i 0.327152 0.566644i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 5.90843i 0.328754i
\(324\) 0 0
\(325\) 0.112564i 0.00624391i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 4.61261 8.59821i 0.254301 0.474035i
\(330\) 0 0
\(331\) −2.71627 4.70472i −0.149300 0.258595i 0.781669 0.623693i \(-0.214369\pi\)
−0.930969 + 0.365099i \(0.881035\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 13.0099 + 22.5338i 0.710805 + 1.23115i
\(336\) 0 0
\(337\) −8.45417 + 14.6431i −0.460528 + 0.797658i −0.998987 0.0449936i \(-0.985673\pi\)
0.538459 + 0.842652i \(0.319007\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 25.8772 1.40133
\(342\) 0 0
\(343\) −18.4391 + 1.73146i −0.995620 + 0.0934903i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −15.1375 8.73962i −0.812622 0.469168i 0.0352435 0.999379i \(-0.488779\pi\)
−0.847866 + 0.530211i \(0.822113\pi\)
\(348\) 0 0
\(349\) −27.5413 + 15.9010i −1.47425 + 0.851159i −0.999579 0.0290038i \(-0.990766\pi\)
−0.474672 + 0.880163i \(0.657433\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −16.0034 27.7187i −0.851775 1.47532i −0.879605 0.475705i \(-0.842193\pi\)
0.0278304 0.999613i \(-0.491140\pi\)
\(354\) 0 0
\(355\) 15.4510 + 8.92066i 0.820056 + 0.473460i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 5.86805i 0.309704i 0.987938 + 0.154852i \(0.0494901\pi\)
−0.987938 + 0.154852i \(0.950510\pi\)
\(360\) 0 0
\(361\) 10.3621 0.545372
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −12.8279 7.40619i −0.671443 0.387658i
\(366\) 0 0
\(367\) 20.8681 12.0482i 1.08931 0.628912i 0.155916 0.987770i \(-0.450167\pi\)
0.933392 + 0.358858i \(0.116834\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.90129 + 1.17830i −0.0987098 + 0.0611744i
\(372\) 0 0
\(373\) 15.1182 26.1855i 0.782790 1.35583i −0.147521 0.989059i \(-0.547129\pi\)
0.930311 0.366773i \(-0.119537\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.31281 0.0676133
\(378\) 0 0
\(379\) −24.6188 −1.26458 −0.632292 0.774730i \(-0.717886\pi\)
−0.632292 + 0.774730i \(0.717886\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −14.7429 + 25.5354i −0.753326 + 1.30480i 0.192876 + 0.981223i \(0.438218\pi\)
−0.946202 + 0.323576i \(0.895115\pi\)
\(384\) 0 0
\(385\) 13.1401 8.14346i 0.669683 0.415029i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 8.19930 4.73387i 0.415721 0.240017i −0.277524 0.960719i \(-0.589514\pi\)
0.693245 + 0.720702i \(0.256180\pi\)
\(390\) 0 0
\(391\) 8.69560 + 5.02041i 0.439755 + 0.253893i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 17.2626 0.868573
\(396\) 0 0
\(397\) 0.430822i 0.0216223i 0.999942 + 0.0108112i \(0.00344137\pi\)
−0.999942 + 0.0108112i \(0.996559\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −19.1407 11.0509i −0.955842 0.551856i −0.0609515 0.998141i \(-0.519413\pi\)
−0.894891 + 0.446285i \(0.852747\pi\)
\(402\) 0 0
\(403\) 1.45350 + 2.51754i 0.0724042 + 0.125408i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −8.56181 + 4.94316i −0.424393 + 0.245023i
\(408\) 0 0
\(409\) 19.6278 + 11.3321i 0.970535 + 0.560338i 0.899399 0.437128i \(-0.144004\pi\)
0.0711355 + 0.997467i \(0.477338\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 38.4985 1.20189i 1.89439 0.0591412i
\(414\) 0 0
\(415\) 21.9881 1.07935
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 6.69489 11.5959i 0.327067 0.566496i −0.654862 0.755749i \(-0.727273\pi\)
0.981928 + 0.189252i \(0.0606064\pi\)
\(420\) 0 0
\(421\) 13.6383 + 23.6223i 0.664691 + 1.15128i 0.979369 + 0.202080i \(0.0647702\pi\)
−0.314678 + 0.949199i \(0.601896\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0.400508 + 0.693700i 0.0194275 + 0.0336494i
\(426\) 0 0
\(427\) 25.8380 + 13.8611i 1.25039 + 0.670785i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 30.2430i 1.45675i 0.685177 + 0.728377i \(0.259725\pi\)
−0.685177 + 0.728377i \(0.740275\pi\)
\(432\) 0 0
\(433\) 8.03211i 0.385999i −0.981199 0.192999i \(-0.938178\pi\)
0.981199 0.192999i \(-0.0618215\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −7.33967 + 12.7127i −0.351104 + 0.608130i
\(438\) 0 0
\(439\) −25.7082 + 14.8426i −1.22699 + 0.708401i −0.966398 0.257050i \(-0.917250\pi\)
−0.260588 + 0.965450i \(0.583916\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 3.67730 2.12309i 0.174714 0.100871i −0.410093 0.912044i \(-0.634504\pi\)
0.584807 + 0.811173i \(0.301170\pi\)
\(444\) 0 0
\(445\) 5.95347 10.3117i 0.282222 0.488822i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 11.2597i 0.531376i −0.964059 0.265688i \(-0.914401\pi\)
0.964059 0.265688i \(-0.0855991\pi\)
\(450\) 0 0
\(451\) 17.3475i 0.816863i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.53033 + 0.820964i 0.0717430 + 0.0384874i
\(456\) 0 0
\(457\) 8.81254 + 15.2638i 0.412233 + 0.714009i 0.995134 0.0985348i \(-0.0314156\pi\)
−0.582900 + 0.812544i \(0.698082\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 16.7014 + 28.9277i 0.777862 + 1.34730i 0.933172 + 0.359430i \(0.117029\pi\)
−0.155310 + 0.987866i \(0.549638\pi\)
\(462\) 0 0
\(463\) 7.91102 13.7023i 0.367656 0.636799i −0.621543 0.783380i \(-0.713494\pi\)
0.989199 + 0.146581i \(0.0468270\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 7.88148 0.364711 0.182356 0.983233i \(-0.441628\pi\)
0.182356 + 0.983233i \(0.441628\pi\)
\(468\) 0 0
\(469\) 29.6146 0.924542i 1.36748 0.0426914i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −24.6612 14.2381i −1.13392 0.654670i
\(474\) 0 0
\(475\) −1.01417 + 0.585529i −0.0465332 + 0.0268659i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 2.64131 + 4.57489i 0.120685 + 0.209032i 0.920038 0.391830i \(-0.128158\pi\)
−0.799353 + 0.600861i \(0.794824\pi\)
\(480\) 0 0
\(481\) −0.961820 0.555307i −0.0438552 0.0253198i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 12.0691i 0.548027i
\(486\) 0 0
\(487\) −3.90074 −0.176760 −0.0883798 0.996087i \(-0.528169\pi\)
−0.0883798 + 0.996087i \(0.528169\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −15.6506 9.03585i −0.706300 0.407782i 0.103390 0.994641i \(-0.467031\pi\)
−0.809689 + 0.586859i \(0.800364\pi\)
\(492\) 0 0
\(493\) 8.09052 4.67106i 0.364379 0.210374i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 17.2688 10.7021i 0.774610 0.480057i
\(498\) 0 0
\(499\) 1.95896 3.39301i 0.0876949 0.151892i −0.818841 0.574020i \(-0.805383\pi\)
0.906536 + 0.422128i \(0.138717\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −0.565207 −0.0252013 −0.0126007 0.999921i \(-0.504011\pi\)
−0.0126007 + 0.999921i \(0.504011\pi\)
\(504\) 0 0
\(505\) 18.9651 0.843934
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −5.68974 + 9.85492i −0.252193 + 0.436812i −0.964129 0.265433i \(-0.914485\pi\)
0.711936 + 0.702244i \(0.247819\pi\)
\(510\) 0 0
\(511\) −14.3370 + 8.88523i −0.634233 + 0.393059i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 18.3993 10.6229i 0.810772 0.468099i
\(516\) 0 0
\(517\) 8.03172 + 4.63711i 0.353235 + 0.203940i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 6.78433 0.297227 0.148613 0.988895i \(-0.452519\pi\)
0.148613 + 0.988895i \(0.452519\pi\)
\(522\) 0 0
\(523\) 43.4601i 1.90038i 0.311672 + 0.950190i \(0.399111\pi\)
−0.311672 + 0.950190i \(0.600889\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 17.9151 + 10.3433i 0.780395 + 0.450561i
\(528\) 0 0
\(529\) 0.973072 + 1.68541i 0.0423075 + 0.0732787i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.68771 0.974397i 0.0731026 0.0422058i
\(534\) 0 0
\(535\) −19.9534 11.5201i −0.862659 0.498057i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.09805 17.5690i −0.0472963 0.756751i
\(540\) 0 0
\(541\) −34.1486 −1.46816 −0.734082 0.679061i \(-0.762387\pi\)
−0.734082 + 0.679061i \(0.762387\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −8.77179 + 15.1932i −0.375742 + 0.650804i
\(546\) 0 0
\(547\) −17.5029 30.3159i −0.748369 1.29621i −0.948604 0.316466i \(-0.897504\pi\)
0.200234 0.979748i \(-0.435830\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 6.82894 + 11.8281i 0.290923 + 0.503893i
\(552\) 0 0
\(553\) 9.29256 17.3219i 0.395160 0.736604i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.61299i 0.0683444i −0.999416 0.0341722i \(-0.989121\pi\)
0.999416 0.0341722i \(-0.0108795\pi\)
\(558\) 0 0
\(559\) 3.19898i 0.135302i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 16.6209 28.7883i 0.700488 1.21328i −0.267808 0.963472i \(-0.586299\pi\)
0.968295 0.249808i \(-0.0803674\pi\)
\(564\) 0 0
\(565\) 11.3730 6.56619i 0.478465 0.276242i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −6.49511 + 3.74995i −0.272289 + 0.157206i −0.629927 0.776654i \(-0.716915\pi\)
0.357638 + 0.933860i \(0.383582\pi\)
\(570\) 0 0
\(571\) −15.7805 + 27.3327i −0.660395 + 1.14384i 0.320117 + 0.947378i \(0.396278\pi\)
−0.980512 + 0.196459i \(0.937056\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.99010i 0.0829931i
\(576\) 0 0
\(577\) 26.3137i 1.09545i 0.836658 + 0.547726i \(0.184506\pi\)
−0.836658 + 0.547726i \(0.815494\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 11.8364 22.0638i 0.491055 0.915360i
\(582\) 0 0
\(583\) −1.06303 1.84122i −0.0440261 0.0762555i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 14.8116 + 25.6545i 0.611341 + 1.05887i 0.991015 + 0.133753i \(0.0427029\pi\)
−0.379674 + 0.925120i \(0.623964\pi\)
\(588\) 0 0
\(589\) −15.1216 + 26.1913i −0.623073 + 1.07919i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 10.8344 0.444916 0.222458 0.974942i \(-0.428592\pi\)
0.222458 + 0.974942i \(0.428592\pi\)
\(594\) 0 0
\(595\) 12.3521 0.385621i 0.506385 0.0158089i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −21.3274 12.3134i −0.871413 0.503111i −0.00359567 0.999994i \(-0.501145\pi\)
−0.867818 + 0.496883i \(0.834478\pi\)
\(600\) 0 0
\(601\) −34.8096 + 20.0973i −1.41991 + 0.819786i −0.996291 0.0860533i \(-0.972574\pi\)
−0.423621 + 0.905840i \(0.639241\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −5.43223 9.40891i −0.220852 0.382526i
\(606\) 0 0
\(607\) −20.5906 11.8880i −0.835747 0.482519i 0.0200693 0.999799i \(-0.493611\pi\)
−0.855816 + 0.517280i \(0.826945\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.04185i 0.0421488i
\(612\) 0 0
\(613\) −26.0354 −1.05156 −0.525780 0.850620i \(-0.676227\pi\)
−0.525780 + 0.850620i \(0.676227\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −4.94660 2.85592i −0.199143 0.114975i 0.397113 0.917770i \(-0.370012\pi\)
−0.596256 + 0.802795i \(0.703345\pi\)
\(618\) 0 0
\(619\) 39.4955 22.8027i 1.58746 0.916520i 0.593734 0.804661i \(-0.297653\pi\)
0.993724 0.111859i \(-0.0356803\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −7.14239 11.5248i −0.286154 0.461732i
\(624\) 0 0
\(625\) 13.4167 23.2385i 0.536670 0.929539i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −7.90325 −0.315123
\(630\) 0 0
\(631\) 39.5756 1.57548 0.787739 0.616009i \(-0.211252\pi\)
0.787739 + 0.616009i \(0.211252\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 12.3479 21.3871i 0.490010 0.848722i
\(636\) 0 0
\(637\) 1.64758 1.09367i 0.0652794 0.0433326i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −19.1080 + 11.0320i −0.754719 + 0.435737i −0.827396 0.561618i \(-0.810179\pi\)
0.0726775 + 0.997355i \(0.476846\pi\)
\(642\) 0 0
\(643\) 17.9250 + 10.3490i 0.706894 + 0.408126i 0.809910 0.586554i \(-0.199516\pi\)
−0.103016 + 0.994680i \(0.532849\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 13.6007 0.534697 0.267348 0.963600i \(-0.413853\pi\)
0.267348 + 0.963600i \(0.413853\pi\)
\(648\) 0 0
\(649\) 36.6103i 1.43708i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 33.8994 + 19.5718i 1.32659 + 0.765905i 0.984770 0.173862i \(-0.0556246\pi\)
0.341816 + 0.939767i \(0.388958\pi\)
\(654\) 0 0
\(655\) −6.38218 11.0543i −0.249373 0.431926i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −8.36427 + 4.82911i −0.325826 + 0.188116i −0.653986 0.756506i \(-0.726905\pi\)
0.328161 + 0.944622i \(0.393571\pi\)
\(660\) 0 0
\(661\) 11.2955 + 6.52145i 0.439343 + 0.253655i 0.703319 0.710874i \(-0.251701\pi\)
−0.263976 + 0.964529i \(0.585034\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0.563765 + 18.0583i 0.0218618 + 0.700271i
\(666\) 0 0
\(667\) 23.2103 0.898706
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −13.9347 + 24.1356i −0.537944 + 0.931746i
\(672\) 0 0
\(673\) −10.2742 17.7955i −0.396042 0.685965i 0.597192 0.802099i \(-0.296283\pi\)
−0.993234 + 0.116134i \(0.962950\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 12.3014 + 21.3067i 0.472782 + 0.818882i 0.999515 0.0311486i \(-0.00991650\pi\)
−0.526733 + 0.850031i \(0.676583\pi\)
\(678\) 0 0
\(679\) −12.1106 6.49686i −0.464761 0.249327i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 34.7249i 1.32871i −0.747416 0.664357i \(-0.768706\pi\)
0.747416 0.664357i \(-0.231294\pi\)
\(684\) 0 0
\(685\) 47.9167i 1.83080i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0.119419 0.206840i 0.00454950 0.00787996i
\(690\) 0 0
\(691\) −12.5120 + 7.22382i −0.475980 + 0.274807i −0.718740 0.695279i \(-0.755281\pi\)
0.242760 + 0.970086i \(0.421947\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 11.1529 6.43913i 0.423054 0.244250i
\(696\) 0 0
\(697\) 6.93392 12.0099i 0.262641 0.454907i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 30.9550i 1.16915i −0.811338 0.584577i \(-0.801261\pi\)
0.811338 0.584577i \(-0.198739\pi\)
\(702\) 0 0
\(703\) 11.5543i 0.435778i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 10.2090 19.0303i 0.383950 0.715709i
\(708\) 0 0
\(709\) 2.64988 + 4.58973i 0.0995184 + 0.172371i 0.911485 0.411332i \(-0.134936\pi\)
−0.811967 + 0.583703i \(0.801603\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 25.6977 + 44.5097i 0.962385 + 1.66690i
\(714\) 0 0
\(715\) −0.825325 + 1.42951i −0.0308654 + 0.0534605i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 23.8427 0.889184 0.444592 0.895733i \(-0.353349\pi\)
0.444592 + 0.895733i \(0.353349\pi\)
\(720\) 0 0
\(721\) −0.754911 24.1810i −0.0281143 0.900548i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1.60355 + 0.925812i 0.0595545 + 0.0343838i
\(726\) 0 0
\(727\) −41.8426 + 24.1579i −1.55186 + 0.895965i −0.553866 + 0.832606i \(0.686848\pi\)
−0.997991 + 0.0633594i \(0.979819\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −11.3821 19.7144i −0.420984 0.729165i
\(732\) 0 0
\(733\) 14.9281 + 8.61872i 0.551381 + 0.318340i 0.749679 0.661802i \(-0.230208\pi\)
−0.198298 + 0.980142i \(0.563541\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 28.1621i 1.03736i
\(738\) 0 0
\(739\) 11.0251 0.405567 0.202783 0.979224i \(-0.435001\pi\)
0.202783 + 0.979224i \(0.435001\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −14.2819 8.24567i −0.523953 0.302504i 0.214598 0.976703i \(-0.431156\pi\)
−0.738550 + 0.674198i \(0.764489\pi\)
\(744\) 0 0
\(745\) −9.29254 + 5.36505i −0.340452 + 0.196560i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −22.3008 + 13.8207i −0.814852 + 0.504996i
\(750\) 0 0
\(751\) −7.08239 + 12.2671i −0.258440 + 0.447631i −0.965824 0.259198i \(-0.916542\pi\)
0.707384 + 0.706829i \(0.249875\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 15.7489 0.573161
\(756\) 0 0
\(757\) −24.3048 −0.883374 −0.441687 0.897169i \(-0.645620\pi\)
−0.441687 + 0.897169i \(0.645620\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −7.29941 + 12.6429i −0.264603 + 0.458306i −0.967460 0.253025i \(-0.918574\pi\)
0.702856 + 0.711332i \(0.251908\pi\)
\(762\) 0 0
\(763\) 10.5235 + 16.9806i 0.380978 + 0.614738i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −3.56174 + 2.05637i −0.128607 + 0.0742512i
\(768\) 0 0
\(769\) 20.5263 + 11.8509i 0.740198 + 0.427353i 0.822141 0.569284i \(-0.192779\pi\)
−0.0819433 + 0.996637i \(0.526113\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −33.3407 −1.19918 −0.599591 0.800307i \(-0.704670\pi\)
−0.599591 + 0.800307i \(0.704670\pi\)
\(774\) 0 0
\(775\) 4.10011i 0.147280i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 17.5581 + 10.1372i 0.629083 + 0.363202i
\(780\) 0 0
\(781\) 9.65514 + 16.7232i 0.345488 + 0.598403i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 14.9210 8.61463i 0.532552 0.307469i
\(786\) 0 0
\(787\) 9.81353 + 5.66584i 0.349815 + 0.201966i 0.664604 0.747196i \(-0.268600\pi\)
−0.314789 + 0.949162i \(0.601934\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −0.466624 14.9467i −0.0165912 0.531445i
\(792\) 0 0
\(793\) −3.13081 −0.111178
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −16.3604 + 28.3370i −0.579515 + 1.00375i 0.416020 + 0.909356i \(0.363425\pi\)
−0.995535 + 0.0943942i \(0.969909\pi\)
\(798\) 0 0
\(799\) 3.70697 + 6.42066i 0.131143 + 0.227147i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −8.01597 13.8841i −0.282878 0.489958i
\(804\) 0 0
\(805\) 27.0559 + 14.5145i 0.953596 + 0.511568i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 24.6586i 0.866951i 0.901165 + 0.433475i \(0.142713\pi\)
−0.901165 + 0.433475i \(0.857287\pi\)
\(810\) 0 0
\(811\) 24.8675i 0.873216i 0.899652 + 0.436608i \(0.143820\pi\)
−0.899652 + 0.436608i \(0.856180\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 13.9671 24.1917i 0.489246 0.847398i
\(816\) 0 0
\(817\) 28.8219 16.6403i 1.00835 0.582171i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 41.7660 24.1136i 1.45764 0.841570i 0.458747 0.888567i \(-0.348299\pi\)
0.998895 + 0.0469972i \(0.0149652\pi\)
\(822\) 0 0
\(823\) −24.1616 + 41.8492i −0.842221 + 1.45877i 0.0457915 + 0.998951i \(0.485419\pi\)
−0.888013 + 0.459819i \(0.847914\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 50.5791i 1.75881i 0.476078 + 0.879403i \(0.342058\pi\)
−0.476078 + 0.879403i \(0.657942\pi\)
\(828\) 0 0
\(829\) 14.9456i 0.519082i 0.965732 + 0.259541i \(0.0835713\pi\)
−0.965732 + 0.259541i \(0.916429\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 6.26226 12.6021i 0.216974 0.436638i
\(834\) 0 0
\(835\) −24.1863 41.8919i −0.837001 1.44973i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 3.25434 + 5.63669i 0.112352 + 0.194600i 0.916718 0.399534i \(-0.130828\pi\)
−0.804366 + 0.594134i \(0.797495\pi\)
\(840\) 0 0
\(841\) −3.70240 + 6.41274i −0.127669 + 0.221129i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 30.0195 1.03270
\(846\) 0 0
\(847\) −12.3655 + 0.386040i −0.424883 + 0.0132645i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −17.0048 9.81771i −0.582916 0.336547i
\(852\) 0 0
\(853\) 14.8966 8.60053i 0.510049 0.294477i −0.222805 0.974863i \(-0.571521\pi\)
0.732854 + 0.680386i \(0.238188\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 20.2073 + 35.0001i 0.690269 + 1.19558i 0.971750 + 0.236014i \(0.0758411\pi\)
−0.281481 + 0.959567i \(0.590826\pi\)
\(858\) 0 0
\(859\) −20.1957 11.6600i −0.689068 0.397834i 0.114195 0.993458i \(-0.463571\pi\)
−0.803263 + 0.595625i \(0.796905\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 9.03284i 0.307481i 0.988111 + 0.153741i \(0.0491320\pi\)
−0.988111 + 0.153741i \(0.950868\pi\)
\(864\) 0 0
\(865\) −17.1076 −0.581674
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 16.1807 + 9.34193i 0.548893 + 0.316903i
\(870\) 0 0
\(871\) −2.73983 + 1.58184i −0.0928356 + 0.0535986i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −14.9011 24.0440i −0.503747 0.812837i
\(876\) 0 0
\(877\) 8.21638 14.2312i 0.277447 0.480553i −0.693302 0.720647i \(-0.743845\pi\)
0.970750 + 0.240094i \(0.0771782\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 20.8143 0.701252 0.350626 0.936516i \(-0.385969\pi\)
0.350626 + 0.936516i \(0.385969\pi\)
\(882\) 0 0
\(883\) −29.8412 −1.00424 −0.502119 0.864799i \(-0.667446\pi\)
−0.502119 + 0.864799i \(0.667446\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −8.25876 + 14.3046i −0.277302 + 0.480301i −0.970713 0.240241i \(-0.922774\pi\)
0.693411 + 0.720542i \(0.256107\pi\)
\(888\) 0 0
\(889\) −14.8138 23.9032i −0.496838 0.801688i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −9.38679 + 5.41947i −0.314117 + 0.181356i
\(894\) 0 0
\(895\) −33.8318 19.5328i −1.13087 0.652909i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 47.8190 1.59485
\(900\) 0 0
\(901\) 1.69960i 0.0566218i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −8.09375 4.67293i −0.269045 0.155333i
\(906\) 0 0
\(907\) 9.12715 + 15.8087i 0.303062 + 0.524919i 0.976828 0.214026i \(-0.0686577\pi\)
−0.673766 + 0.738945i \(0.735324\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 2.75798 1.59232i 0.0913758 0.0527559i −0.453616 0.891197i \(-0.649866\pi\)
0.544992 + 0.838441i \(0.316533\pi\)
\(912\) 0 0
\(913\) 20.6101 + 11.8993i 0.682095 + 0.393808i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −14.5279 + 0.453548i −0.479753 + 0.0149775i
\(918\) 0 0
\(919\) 13.7624 0.453980 0.226990 0.973897i \(-0.427111\pi\)
0.226990 + 0.973897i \(0.427111\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −1.08464 + 1.87866i −0.0357015 + 0.0618368i
\(924\) 0 0
\(925\) −0.783218 1.35657i −0.0257520 0.0446038i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −0.638392 1.10573i −0.0209450 0.0362778i 0.855363 0.518029i \(-0.173334\pi\)
−0.876308 + 0.481751i \(0.840001\pi\)
\(930\) 0 0
\(931\) 18.4239 + 9.15521i 0.603819 + 0.300050i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 11.7462i 0.384142i
\(936\) 0 0
\(937\) 54.0092i 1.76440i 0.470873 + 0.882201i \(0.343939\pi\)
−0.470873 + 0.882201i \(0.656061\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 3.40019 5.88931i 0.110843 0.191986i −0.805267 0.592912i \(-0.797978\pi\)
0.916110 + 0.400926i \(0.131312\pi\)
\(942\) 0 0
\(943\) 29.8383 17.2271i 0.971668 0.560993i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −26.2915 + 15.1794i −0.854359 + 0.493265i −0.862119 0.506705i \(-0.830863\pi\)
0.00776004 + 0.999970i \(0.497530\pi\)
\(948\) 0 0
\(949\) 0.900502 1.55972i 0.0292315 0.0506305i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 36.0446i 1.16760i 0.811897 + 0.583800i \(0.198435\pi\)
−0.811897 + 0.583800i \(0.801565\pi\)
\(954\) 0 0
\(955\) 11.8709i 0.384133i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 48.0816 + 25.7939i 1.55264 + 0.832930i
\(960\) 0 0
\(961\) 37.4436 + 64.8543i 1.20786 + 2.09207i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −8.24814 14.2862i −0.265517 0.459889i
\(966\) 0 0
\(967\) 10.7710 18.6560i 0.346373 0.599936i −0.639229 0.769016i \(-0.720747\pi\)
0.985602 + 0.169081i \(0.0540798\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −9.00760 −0.289068 −0.144534 0.989500i \(-0.546168\pi\)
−0.144534 + 0.989500i \(0.546168\pi\)
\(972\) 0 0
\(973\) −0.457595 14.6575i −0.0146698 0.469898i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −19.8654 11.4693i −0.635550 0.366935i 0.147348 0.989085i \(-0.452926\pi\)
−0.782898 + 0.622150i \(0.786260\pi\)
\(978\) 0 0
\(979\) 11.1607 6.44365i 0.356698 0.205940i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −4.18439 7.24758i −0.133461 0.231162i 0.791547 0.611108i \(-0.209276\pi\)
−0.925009 + 0.379946i \(0.875943\pi\)
\(984\) 0 0
\(985\) −31.4071 18.1329i −1.00071 0.577762i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 56.5573i 1.79842i
\(990\) 0 0
\(991\) −26.2476 −0.833781 −0.416891 0.908957i \(-0.636880\pi\)
−0.416891 + 0.908957i \(0.636880\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 53.9574 + 31.1523i 1.71057 + 0.987596i
\(996\) 0 0
\(997\) 29.5387 17.0542i 0.935499 0.540111i 0.0469525 0.998897i \(-0.485049\pi\)
0.888547 + 0.458786i \(0.151716\pi\)
\(998\) 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.cc.d.881.6 48
3.2 odd 2 1008.2.cc.d.545.9 48
4.3 odd 2 1512.2.bu.a.881.6 48
7.6 odd 2 inner 3024.2.cc.d.881.19 48
9.2 odd 6 inner 3024.2.cc.d.2897.19 48
9.7 even 3 1008.2.cc.d.209.16 48
12.11 even 2 504.2.bu.a.41.16 yes 48
21.20 even 2 1008.2.cc.d.545.16 48
28.27 even 2 1512.2.bu.a.881.19 48
36.7 odd 6 504.2.bu.a.209.9 yes 48
36.11 even 6 1512.2.bu.a.1385.19 48
36.23 even 6 4536.2.k.a.3401.11 48
36.31 odd 6 4536.2.k.a.3401.38 48
63.20 even 6 inner 3024.2.cc.d.2897.6 48
63.34 odd 6 1008.2.cc.d.209.9 48
84.83 odd 2 504.2.bu.a.41.9 48
252.83 odd 6 1512.2.bu.a.1385.6 48
252.139 even 6 4536.2.k.a.3401.12 48
252.167 odd 6 4536.2.k.a.3401.37 48
252.223 even 6 504.2.bu.a.209.16 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.bu.a.41.9 48 84.83 odd 2
504.2.bu.a.41.16 yes 48 12.11 even 2
504.2.bu.a.209.9 yes 48 36.7 odd 6
504.2.bu.a.209.16 yes 48 252.223 even 6
1008.2.cc.d.209.9 48 63.34 odd 6
1008.2.cc.d.209.16 48 9.7 even 3
1008.2.cc.d.545.9 48 3.2 odd 2
1008.2.cc.d.545.16 48 21.20 even 2
1512.2.bu.a.881.6 48 4.3 odd 2
1512.2.bu.a.881.19 48 28.27 even 2
1512.2.bu.a.1385.6 48 252.83 odd 6
1512.2.bu.a.1385.19 48 36.11 even 6
3024.2.cc.d.881.6 48 1.1 even 1 trivial
3024.2.cc.d.881.19 48 7.6 odd 2 inner
3024.2.cc.d.2897.6 48 63.20 even 6 inner
3024.2.cc.d.2897.19 48 9.2 odd 6 inner
4536.2.k.a.3401.11 48 36.23 even 6
4536.2.k.a.3401.12 48 252.139 even 6
4536.2.k.a.3401.37 48 252.167 odd 6
4536.2.k.a.3401.38 48 36.31 odd 6