Properties

Label 2100.2.ce.d.1657.6
Level $2100$
Weight $2$
Character 2100.1657
Analytic conductor $16.769$
Analytic rank $0$
Dimension $24$
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] = [2100,2,Mod(157,2100)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2100, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2100.157");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2100.ce (of order \(12\), degree \(4\), 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: \(16.7685844245\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 1657.6
Character \(\chi\) \(=\) 2100.1657
Dual form 2100.2.ce.d.493.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.258819 - 0.965926i) q^{3} +(-0.895840 + 2.48947i) q^{7} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\) \(q+(0.258819 - 0.965926i) q^{3} +(-0.895840 + 2.48947i) q^{7} +(-0.866025 - 0.500000i) q^{9} +(-0.720993 - 1.24880i) q^{11} +(-1.97110 - 1.97110i) q^{13} +(3.65850 + 0.980291i) q^{17} +(-0.643613 + 1.11477i) q^{19} +(2.17278 + 1.50964i) q^{21} +(0.135022 + 0.503908i) q^{23} +(-0.707107 + 0.707107i) q^{27} -6.13312i q^{29} +(7.63312 - 4.40699i) q^{31} +(-1.39285 + 0.373213i) q^{33} +(4.08552 - 1.09471i) q^{37} +(-2.41409 + 1.39378i) q^{39} -9.57951i q^{41} +(1.27909 - 1.27909i) q^{43} +(-0.746427 - 2.78570i) q^{47} +(-5.39494 - 4.46034i) q^{49} +(1.89378 - 3.28012i) q^{51} +(5.83279 + 1.56289i) q^{53} +(0.910206 + 0.910206i) q^{57} +(-1.77048 - 3.06656i) q^{59} +(-1.71119 - 0.987954i) q^{61} +(2.02056 - 1.70803i) q^{63} +(0.583310 - 2.17694i) q^{67} +0.521684 q^{69} +9.24915 q^{71} +(0.920882 - 3.43678i) q^{73} +(3.75474 - 0.676169i) q^{77} +(-8.09350 - 4.67278i) q^{79} +(0.500000 + 0.866025i) q^{81} +(12.2773 + 12.2773i) q^{83} +(-5.92414 - 1.58737i) q^{87} +(3.94736 - 6.83702i) q^{89} +(6.67278 - 3.14120i) q^{91} +(-2.28122 - 8.51364i) q^{93} +(-9.35470 + 9.35470i) q^{97} +1.44199i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 8 q^{11} + 8 q^{21} - 12 q^{31} - 8 q^{51} - 48 q^{61} + 64 q^{71} + 12 q^{81} + 116 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).

\(n\) \(701\) \(1051\) \(1177\) \(1501\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{5}{6}\right)\)

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
\(3\) 0.258819 0.965926i 0.149429 0.557678i
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −0.895840 + 2.48947i −0.338596 + 0.940932i
\(8\) 0 0
\(9\) −0.866025 0.500000i −0.288675 0.166667i
\(10\) 0 0
\(11\) −0.720993 1.24880i −0.217387 0.376526i 0.736621 0.676306i \(-0.236420\pi\)
−0.954008 + 0.299780i \(0.903087\pi\)
\(12\) 0 0
\(13\) −1.97110 1.97110i −0.546684 0.546684i 0.378796 0.925480i \(-0.376338\pi\)
−0.925480 + 0.378796i \(0.876338\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.65850 + 0.980291i 0.887316 + 0.237756i 0.673561 0.739132i \(-0.264764\pi\)
0.213755 + 0.976887i \(0.431431\pi\)
\(18\) 0 0
\(19\) −0.643613 + 1.11477i −0.147655 + 0.255746i −0.930360 0.366647i \(-0.880506\pi\)
0.782705 + 0.622392i \(0.213839\pi\)
\(20\) 0 0
\(21\) 2.17278 + 1.50964i 0.474140 + 0.329430i
\(22\) 0 0
\(23\) 0.135022 + 0.503908i 0.0281540 + 0.105072i 0.978573 0.205900i \(-0.0660121\pi\)
−0.950419 + 0.310972i \(0.899345\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) 0 0
\(29\) 6.13312i 1.13889i −0.822029 0.569446i \(-0.807158\pi\)
0.822029 0.569446i \(-0.192842\pi\)
\(30\) 0 0
\(31\) 7.63312 4.40699i 1.37095 0.791518i 0.379902 0.925027i \(-0.375958\pi\)
0.991048 + 0.133509i \(0.0426244\pi\)
\(32\) 0 0
\(33\) −1.39285 + 0.373213i −0.242464 + 0.0649681i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 4.08552 1.09471i 0.671656 0.179970i 0.0931551 0.995652i \(-0.470305\pi\)
0.578500 + 0.815682i \(0.303638\pi\)
\(38\) 0 0
\(39\) −2.41409 + 1.39378i −0.386564 + 0.223183i
\(40\) 0 0
\(41\) 9.57951i 1.49607i −0.663660 0.748034i \(-0.730998\pi\)
0.663660 0.748034i \(-0.269002\pi\)
\(42\) 0 0
\(43\) 1.27909 1.27909i 0.195060 0.195060i −0.602819 0.797878i \(-0.705956\pi\)
0.797878 + 0.602819i \(0.205956\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −0.746427 2.78570i −0.108878 0.406336i 0.889879 0.456197i \(-0.150789\pi\)
−0.998756 + 0.0498609i \(0.984122\pi\)
\(48\) 0 0
\(49\) −5.39494 4.46034i −0.770706 0.637191i
\(50\) 0 0
\(51\) 1.89378 3.28012i 0.265182 0.459308i
\(52\) 0 0
\(53\) 5.83279 + 1.56289i 0.801196 + 0.214680i 0.636109 0.771599i \(-0.280543\pi\)
0.165087 + 0.986279i \(0.447210\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0.910206 + 0.910206i 0.120560 + 0.120560i
\(58\) 0 0
\(59\) −1.77048 3.06656i −0.230497 0.399232i 0.727458 0.686153i \(-0.240702\pi\)
−0.957954 + 0.286920i \(0.907368\pi\)
\(60\) 0 0
\(61\) −1.71119 0.987954i −0.219095 0.126495i 0.386436 0.922316i \(-0.373706\pi\)
−0.605531 + 0.795822i \(0.707039\pi\)
\(62\) 0 0
\(63\) 2.02056 1.70803i 0.254566 0.215191i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 0.583310 2.17694i 0.0712626 0.265956i −0.921097 0.389332i \(-0.872706\pi\)
0.992360 + 0.123377i \(0.0393724\pi\)
\(68\) 0 0
\(69\) 0.521684 0.0628034
\(70\) 0 0
\(71\) 9.24915 1.09767 0.548836 0.835930i \(-0.315071\pi\)
0.548836 + 0.835930i \(0.315071\pi\)
\(72\) 0 0
\(73\) 0.920882 3.43678i 0.107781 0.402244i −0.890865 0.454269i \(-0.849901\pi\)
0.998646 + 0.0520242i \(0.0165673\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.75474 0.676169i 0.427892 0.0770566i
\(78\) 0 0
\(79\) −8.09350 4.67278i −0.910590 0.525729i −0.0299690 0.999551i \(-0.509541\pi\)
−0.880621 + 0.473821i \(0.842874\pi\)
\(80\) 0 0
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 12.2773 + 12.2773i 1.34760 + 1.34760i 0.888257 + 0.459347i \(0.151917\pi\)
0.459347 + 0.888257i \(0.348083\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −5.92414 1.58737i −0.635135 0.170184i
\(88\) 0 0
\(89\) 3.94736 6.83702i 0.418419 0.724723i −0.577362 0.816489i \(-0.695918\pi\)
0.995781 + 0.0917656i \(0.0292511\pi\)
\(90\) 0 0
\(91\) 6.67278 3.14120i 0.699498 0.329288i
\(92\) 0 0
\(93\) −2.28122 8.51364i −0.236552 0.882824i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −9.35470 + 9.35470i −0.949826 + 0.949826i −0.998800 0.0489744i \(-0.984405\pi\)
0.0489744 + 0.998800i \(0.484405\pi\)
\(98\) 0 0
\(99\) 1.44199i 0.144925i
\(100\) 0 0
\(101\) 12.0666 6.96663i 1.20067 0.693206i 0.239964 0.970782i \(-0.422864\pi\)
0.960704 + 0.277576i \(0.0895310\pi\)
\(102\) 0 0
\(103\) −2.35878 + 0.632032i −0.232417 + 0.0622760i −0.373148 0.927772i \(-0.621722\pi\)
0.140731 + 0.990048i \(0.455055\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 10.5421 2.82475i 1.01914 0.273079i 0.289698 0.957118i \(-0.406445\pi\)
0.729445 + 0.684039i \(0.239778\pi\)
\(108\) 0 0
\(109\) 3.86386 2.23080i 0.370090 0.213672i −0.303408 0.952861i \(-0.598124\pi\)
0.673498 + 0.739189i \(0.264791\pi\)
\(110\) 0 0
\(111\) 4.22964i 0.401460i
\(112\) 0 0
\(113\) −13.0939 + 13.0939i −1.23177 + 1.23177i −0.268489 + 0.963283i \(0.586524\pi\)
−0.963283 + 0.268489i \(0.913476\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0.721472 + 2.69257i 0.0667001 + 0.248928i
\(118\) 0 0
\(119\) −5.71784 + 8.22954i −0.524153 + 0.754401i
\(120\) 0 0
\(121\) 4.46034 7.72553i 0.405485 0.702321i
\(122\) 0 0
\(123\) −9.25310 2.47936i −0.834324 0.223556i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −8.94210 8.94210i −0.793483 0.793483i 0.188576 0.982059i \(-0.439613\pi\)
−0.982059 + 0.188576i \(0.939613\pi\)
\(128\) 0 0
\(129\) −0.904455 1.56656i −0.0796328 0.137928i
\(130\) 0 0
\(131\) 6.13312 + 3.54096i 0.535853 + 0.309375i 0.743397 0.668851i \(-0.233213\pi\)
−0.207543 + 0.978226i \(0.566547\pi\)
\(132\) 0 0
\(133\) −2.19861 2.60091i −0.190644 0.225528i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0.991812 3.70149i 0.0847362 0.316240i −0.910528 0.413448i \(-0.864324\pi\)
0.995264 + 0.0972077i \(0.0309911\pi\)
\(138\) 0 0
\(139\) −2.33059 −0.197678 −0.0988392 0.995103i \(-0.531513\pi\)
−0.0988392 + 0.995103i \(0.531513\pi\)
\(140\) 0 0
\(141\) −2.88397 −0.242874
\(142\) 0 0
\(143\) −1.04035 + 3.88265i −0.0869986 + 0.324683i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −5.70467 + 4.05669i −0.470513 + 0.334590i
\(148\) 0 0
\(149\) −14.2540 8.22954i −1.16773 0.674190i −0.214587 0.976705i \(-0.568841\pi\)
−0.953145 + 0.302515i \(0.902174\pi\)
\(150\) 0 0
\(151\) −2.05676 3.56240i −0.167376 0.289904i 0.770120 0.637899i \(-0.220196\pi\)
−0.937497 + 0.347994i \(0.886863\pi\)
\(152\) 0 0
\(153\) −2.67821 2.67821i −0.216520 0.216520i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −5.38514 1.44294i −0.429781 0.115159i 0.0374423 0.999299i \(-0.488079\pi\)
−0.467223 + 0.884139i \(0.654746\pi\)
\(158\) 0 0
\(159\) 3.01928 5.22954i 0.239444 0.414729i
\(160\) 0 0
\(161\) −1.37542 0.115288i −0.108399 0.00908600i
\(162\) 0 0
\(163\) −2.68973 10.0382i −0.210676 0.786252i −0.987644 0.156713i \(-0.949910\pi\)
0.776969 0.629539i \(-0.216756\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −0.450665 + 0.450665i −0.0348735 + 0.0348735i −0.724329 0.689455i \(-0.757850\pi\)
0.689455 + 0.724329i \(0.257850\pi\)
\(168\) 0 0
\(169\) 5.22954i 0.402272i
\(170\) 0 0
\(171\) 1.11477 0.643613i 0.0852486 0.0492183i
\(172\) 0 0
\(173\) −0.224151 + 0.0600611i −0.0170419 + 0.00456636i −0.267330 0.963605i \(-0.586141\pi\)
0.250288 + 0.968171i \(0.419475\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −3.42031 + 0.916468i −0.257086 + 0.0688860i
\(178\) 0 0
\(179\) −5.19615 + 3.00000i −0.388379 + 0.224231i −0.681457 0.731858i \(-0.738654\pi\)
0.293079 + 0.956088i \(0.405320\pi\)
\(180\) 0 0
\(181\) 6.68435i 0.496844i −0.968652 0.248422i \(-0.920088\pi\)
0.968652 0.248422i \(-0.0799119\pi\)
\(182\) 0 0
\(183\) −1.39718 + 1.39718i −0.103282 + 0.103282i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −1.41357 5.27550i −0.103370 0.385783i
\(188\) 0 0
\(189\) −1.12687 2.39378i −0.0819676 0.174122i
\(190\) 0 0
\(191\) 0.787555 1.36408i 0.0569854 0.0987017i −0.836125 0.548538i \(-0.815184\pi\)
0.893111 + 0.449837i \(0.148518\pi\)
\(192\) 0 0
\(193\) −10.9261 2.92765i −0.786480 0.210737i −0.156840 0.987624i \(-0.550131\pi\)
−0.629640 + 0.776887i \(0.716797\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −15.5194 15.5194i −1.10571 1.10571i −0.993708 0.112003i \(-0.964274\pi\)
−0.112003 0.993708i \(-0.535726\pi\)
\(198\) 0 0
\(199\) 6.18411 + 10.7112i 0.438380 + 0.759296i 0.997565 0.0697470i \(-0.0222192\pi\)
−0.559185 + 0.829043i \(0.688886\pi\)
\(200\) 0 0
\(201\) −1.95179 1.12687i −0.137669 0.0794831i
\(202\) 0 0
\(203\) 15.2682 + 5.49430i 1.07162 + 0.385624i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0.135022 0.503908i 0.00938467 0.0350241i
\(208\) 0 0
\(209\) 1.85616 0.128393
\(210\) 0 0
\(211\) 19.6886 1.35542 0.677710 0.735329i \(-0.262972\pi\)
0.677710 + 0.735329i \(0.262972\pi\)
\(212\) 0 0
\(213\) 2.39386 8.93400i 0.164024 0.612147i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 4.13301 + 22.9504i 0.280567 + 1.55797i
\(218\) 0 0
\(219\) −3.08133 1.77901i −0.208217 0.120214i
\(220\) 0 0
\(221\) −5.27901 9.14351i −0.355104 0.615059i
\(222\) 0 0
\(223\) −3.01669 3.01669i −0.202013 0.202013i 0.598849 0.800862i \(-0.295625\pi\)
−0.800862 + 0.598849i \(0.795625\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 24.3122 + 6.51443i 1.61366 + 0.432378i 0.949129 0.314886i \(-0.101966\pi\)
0.664527 + 0.747264i \(0.268633\pi\)
\(228\) 0 0
\(229\) 11.4120 19.7662i 0.754129 1.30619i −0.191677 0.981458i \(-0.561392\pi\)
0.945806 0.324732i \(-0.105274\pi\)
\(230\) 0 0
\(231\) 0.318668 3.80180i 0.0209668 0.250140i
\(232\) 0 0
\(233\) 6.79166 + 25.3468i 0.444936 + 1.66052i 0.716105 + 0.697993i \(0.245923\pi\)
−0.271169 + 0.962532i \(0.587410\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −6.60832 + 6.60832i −0.429256 + 0.429256i
\(238\) 0 0
\(239\) 22.7253i 1.46998i 0.678078 + 0.734990i \(0.262813\pi\)
−0.678078 + 0.734990i \(0.737187\pi\)
\(240\) 0 0
\(241\) −19.2070 + 11.0892i −1.23723 + 0.714315i −0.968527 0.248908i \(-0.919928\pi\)
−0.268703 + 0.963223i \(0.586595\pi\)
\(242\) 0 0
\(243\) 0.965926 0.258819i 0.0619642 0.0166032i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 3.46595 0.928697i 0.220533 0.0590916i
\(248\) 0 0
\(249\) 15.0365 8.68133i 0.952900 0.550157i
\(250\) 0 0
\(251\) 28.0971i 1.77347i 0.462275 + 0.886737i \(0.347033\pi\)
−0.462275 + 0.886737i \(0.652967\pi\)
\(252\) 0 0
\(253\) 0.531929 0.531929i 0.0334421 0.0334421i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2.19445 8.18979i −0.136886 0.510865i −0.999983 0.00582706i \(-0.998145\pi\)
0.863097 0.505038i \(-0.168521\pi\)
\(258\) 0 0
\(259\) −0.934720 + 11.1515i −0.0580807 + 0.692919i
\(260\) 0 0
\(261\) −3.06656 + 5.31144i −0.189815 + 0.328770i
\(262\) 0 0
\(263\) 9.47582 + 2.53904i 0.584304 + 0.156564i 0.538849 0.842403i \(-0.318859\pi\)
0.0454554 + 0.998966i \(0.485526\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −5.58241 5.58241i −0.341638 0.341638i
\(268\) 0 0
\(269\) 0.521684 + 0.903584i 0.0318077 + 0.0550925i 0.881491 0.472201i \(-0.156540\pi\)
−0.849683 + 0.527293i \(0.823207\pi\)
\(270\) 0 0
\(271\) −11.6148 6.70579i −0.705547 0.407348i 0.103863 0.994592i \(-0.466880\pi\)
−0.809410 + 0.587244i \(0.800213\pi\)
\(272\) 0 0
\(273\) −1.30713 7.25842i −0.0791109 0.439299i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 4.45076 16.6104i 0.267420 0.998025i −0.693332 0.720618i \(-0.743858\pi\)
0.960752 0.277407i \(-0.0894751\pi\)
\(278\) 0 0
\(279\) −8.81397 −0.527679
\(280\) 0 0
\(281\) −18.2662 −1.08967 −0.544836 0.838542i \(-0.683408\pi\)
−0.544836 + 0.838542i \(0.683408\pi\)
\(282\) 0 0
\(283\) 1.09976 4.10437i 0.0653740 0.243979i −0.925505 0.378736i \(-0.876359\pi\)
0.990879 + 0.134757i \(0.0430254\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 23.8479 + 8.58172i 1.40770 + 0.506563i
\(288\) 0 0
\(289\) −2.29880 1.32722i −0.135224 0.0780715i
\(290\) 0 0
\(291\) 6.61477 + 11.4571i 0.387765 + 0.671628i
\(292\) 0 0
\(293\) 21.4015 + 21.4015i 1.25029 + 1.25029i 0.955591 + 0.294696i \(0.0952184\pi\)
0.294696 + 0.955591i \(0.404782\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 1.39285 + 0.373213i 0.0808214 + 0.0216560i
\(298\) 0 0
\(299\) 0.727112 1.25939i 0.0420500 0.0728327i
\(300\) 0 0
\(301\) 2.03840 + 4.33013i 0.117492 + 0.249584i
\(302\) 0 0
\(303\) −3.60619 13.4585i −0.207170 0.773171i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −21.6337 + 21.6337i −1.23470 + 1.23470i −0.272565 + 0.962137i \(0.587872\pi\)
−0.962137 + 0.272565i \(0.912128\pi\)
\(308\) 0 0
\(309\) 2.44199i 0.138920i
\(310\) 0 0
\(311\) 11.1630 6.44495i 0.632994 0.365459i −0.148916 0.988850i \(-0.547579\pi\)
0.781911 + 0.623390i \(0.214245\pi\)
\(312\) 0 0
\(313\) −0.426925 + 0.114394i −0.0241312 + 0.00646594i −0.270864 0.962617i \(-0.587310\pi\)
0.246733 + 0.969083i \(0.420643\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 27.4209 7.34741i 1.54011 0.412672i 0.613810 0.789454i \(-0.289636\pi\)
0.926302 + 0.376782i \(0.122969\pi\)
\(318\) 0 0
\(319\) −7.65902 + 4.42194i −0.428823 + 0.247581i
\(320\) 0 0
\(321\) 10.9140i 0.609159i
\(322\) 0 0
\(323\) −3.44745 + 3.44745i −0.191821 + 0.191821i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −1.15475 4.30957i −0.0638576 0.238320i
\(328\) 0 0
\(329\) 7.60361 + 0.637336i 0.419200 + 0.0351375i
\(330\) 0 0
\(331\) −13.4207 + 23.2453i −0.737667 + 1.27768i 0.215876 + 0.976421i \(0.430739\pi\)
−0.953543 + 0.301256i \(0.902594\pi\)
\(332\) 0 0
\(333\) −4.08552 1.09471i −0.223885 0.0599899i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −11.2829 11.2829i −0.614618 0.614618i 0.329528 0.944146i \(-0.393111\pi\)
−0.944146 + 0.329528i \(0.893111\pi\)
\(338\) 0 0
\(339\) 9.25880 + 16.0367i 0.502869 + 0.870994i
\(340\) 0 0
\(341\) −11.0069 6.35481i −0.596054 0.344132i
\(342\) 0 0
\(343\) 15.9369 9.43480i 0.860511 0.509431i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4.41863 16.4906i 0.237205 0.885260i −0.739938 0.672675i \(-0.765145\pi\)
0.977143 0.212585i \(-0.0681882\pi\)
\(348\) 0 0
\(349\) 13.1205 0.702323 0.351161 0.936315i \(-0.385787\pi\)
0.351161 + 0.936315i \(0.385787\pi\)
\(350\) 0 0
\(351\) 2.78755 0.148789
\(352\) 0 0
\(353\) −3.40860 + 12.7211i −0.181422 + 0.677075i 0.813947 + 0.580940i \(0.197315\pi\)
−0.995368 + 0.0961351i \(0.969352\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 6.46924 + 7.65297i 0.342388 + 0.405038i
\(358\) 0 0
\(359\) 12.8042 + 7.39252i 0.675781 + 0.390162i 0.798263 0.602308i \(-0.205752\pi\)
−0.122483 + 0.992471i \(0.539086\pi\)
\(360\) 0 0
\(361\) 8.67153 + 15.0195i 0.456396 + 0.790501i
\(362\) 0 0
\(363\) −6.30787 6.30787i −0.331077 0.331077i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 12.5381 + 3.35957i 0.654483 + 0.175368i 0.570755 0.821120i \(-0.306651\pi\)
0.0837281 + 0.996489i \(0.473317\pi\)
\(368\) 0 0
\(369\) −4.78976 + 8.29610i −0.249345 + 0.431878i
\(370\) 0 0
\(371\) −9.11603 + 13.1205i −0.473281 + 0.681181i
\(372\) 0 0
\(373\) −8.77184 32.7370i −0.454189 1.69506i −0.690461 0.723369i \(-0.742593\pi\)
0.236273 0.971687i \(-0.424074\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −12.0890 + 12.0890i −0.622615 + 0.622615i
\(378\) 0 0
\(379\) 11.6911i 0.600533i 0.953855 + 0.300267i \(0.0970757\pi\)
−0.953855 + 0.300267i \(0.902924\pi\)
\(380\) 0 0
\(381\) −10.9518 + 6.32302i −0.561077 + 0.323938i
\(382\) 0 0
\(383\) 2.78570 0.746427i 0.142343 0.0381406i −0.186944 0.982371i \(-0.559858\pi\)
0.329287 + 0.944230i \(0.393192\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −1.74727 + 0.468180i −0.0888189 + 0.0237989i
\(388\) 0 0
\(389\) 2.61288 1.50855i 0.132478 0.0764864i −0.432296 0.901732i \(-0.642296\pi\)
0.564774 + 0.825245i \(0.308963\pi\)
\(390\) 0 0
\(391\) 1.97591i 0.0999259i
\(392\) 0 0
\(393\) 5.00767 5.00767i 0.252604 0.252604i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 4.50329 + 16.8065i 0.226014 + 0.843494i 0.981996 + 0.188902i \(0.0604929\pi\)
−0.755982 + 0.654592i \(0.772840\pi\)
\(398\) 0 0
\(399\) −3.08133 + 1.45053i −0.154259 + 0.0726175i
\(400\) 0 0
\(401\) −15.0171 + 26.0104i −0.749918 + 1.29890i 0.197944 + 0.980213i \(0.436574\pi\)
−0.947862 + 0.318683i \(0.896760\pi\)
\(402\) 0 0
\(403\) −23.7322 6.35904i −1.18219 0.316766i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −4.31270 4.31270i −0.213773 0.213773i
\(408\) 0 0
\(409\) −1.18674 2.05550i −0.0586806 0.101638i 0.835193 0.549957i \(-0.185356\pi\)
−0.893873 + 0.448320i \(0.852023\pi\)
\(410\) 0 0
\(411\) −3.31867 1.91603i −0.163698 0.0945110i
\(412\) 0 0
\(413\) 9.22019 1.66041i 0.453696 0.0817035i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −0.603202 + 2.25118i −0.0295389 + 0.110241i
\(418\) 0 0
\(419\) 27.4646 1.34173 0.670867 0.741578i \(-0.265922\pi\)
0.670867 + 0.741578i \(0.265922\pi\)
\(420\) 0 0
\(421\) −31.6118 −1.54067 −0.770333 0.637642i \(-0.779910\pi\)
−0.770333 + 0.637642i \(0.779910\pi\)
\(422\) 0 0
\(423\) −0.746427 + 2.78570i −0.0362925 + 0.135445i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 3.99243 3.37490i 0.193207 0.163323i
\(428\) 0 0
\(429\) 3.48109 + 2.00981i 0.168068 + 0.0970344i
\(430\) 0 0
\(431\) −12.9036 22.3497i −0.621544 1.07655i −0.989198 0.146583i \(-0.953172\pi\)
0.367655 0.929962i \(-0.380161\pi\)
\(432\) 0 0
\(433\) 13.9376 + 13.9376i 0.669799 + 0.669799i 0.957669 0.287871i \(-0.0929473\pi\)
−0.287871 + 0.957669i \(0.592947\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.648644 0.173804i −0.0310288 0.00831415i
\(438\) 0 0
\(439\) −17.3287 + 30.0141i −0.827052 + 1.43250i 0.0732882 + 0.997311i \(0.476651\pi\)
−0.900341 + 0.435186i \(0.856683\pi\)
\(440\) 0 0
\(441\) 2.44199 + 6.56024i 0.116285 + 0.312392i
\(442\) 0 0
\(443\) −5.54547 20.6960i −0.263473 0.983295i −0.963178 0.268863i \(-0.913352\pi\)
0.699705 0.714432i \(-0.253315\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −11.6383 + 11.6383i −0.550474 + 0.550474i
\(448\) 0 0
\(449\) 12.0342i 0.567928i −0.958835 0.283964i \(-0.908350\pi\)
0.958835 0.283964i \(-0.0916497\pi\)
\(450\) 0 0
\(451\) −11.9629 + 6.90676i −0.563309 + 0.325227i
\(452\) 0 0
\(453\) −3.97335 + 1.06465i −0.186684 + 0.0500219i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 18.9073 5.06619i 0.884445 0.236986i 0.212121 0.977243i \(-0.431963\pi\)
0.672324 + 0.740257i \(0.265296\pi\)
\(458\) 0 0
\(459\) −3.28012 + 1.89378i −0.153103 + 0.0883940i
\(460\) 0 0
\(461\) 18.9284i 0.881586i 0.897609 + 0.440793i \(0.145303\pi\)
−0.897609 + 0.440793i \(0.854697\pi\)
\(462\) 0 0
\(463\) −28.6886 + 28.6886i −1.33327 + 1.33327i −0.430846 + 0.902425i \(0.641785\pi\)
−0.902425 + 0.430846i \(0.858215\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2.83598 + 10.5840i 0.131234 + 0.489770i 0.999985 0.00547816i \(-0.00174376\pi\)
−0.868751 + 0.495248i \(0.835077\pi\)
\(468\) 0 0
\(469\) 4.89688 + 3.40232i 0.226117 + 0.157105i
\(470\) 0 0
\(471\) −2.78755 + 4.82819i −0.128444 + 0.222471i
\(472\) 0 0
\(473\) −2.51954 0.675109i −0.115849 0.0310416i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −4.26990 4.26990i −0.195505 0.195505i
\(478\) 0 0
\(479\) 1.36408 + 2.36266i 0.0623266 + 0.107953i 0.895505 0.445051i \(-0.146815\pi\)
−0.833178 + 0.553004i \(0.813481\pi\)
\(480\) 0 0
\(481\) −10.2108 5.89518i −0.465570 0.268797i
\(482\) 0 0
\(483\) −0.467346 + 1.29872i −0.0212650 + 0.0590937i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −7.77124 + 29.0027i −0.352148 + 1.31424i 0.531887 + 0.846816i \(0.321483\pi\)
−0.884035 + 0.467420i \(0.845183\pi\)
\(488\) 0 0
\(489\) −10.3923 −0.469956
\(490\) 0 0
\(491\) −0.498306 −0.0224882 −0.0112441 0.999937i \(-0.503579\pi\)
−0.0112441 + 0.999937i \(0.503579\pi\)
\(492\) 0 0
\(493\) 6.01225 22.4380i 0.270778 1.01056i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −8.28577 + 23.0255i −0.371667 + 1.03284i
\(498\) 0 0
\(499\) 18.0491 + 10.4207i 0.807991 + 0.466494i 0.846258 0.532774i \(-0.178850\pi\)
−0.0382670 + 0.999268i \(0.512184\pi\)
\(500\) 0 0
\(501\) 0.318668 + 0.551950i 0.0142370 + 0.0246593i
\(502\) 0 0
\(503\) 12.7279 + 12.7279i 0.567510 + 0.567510i 0.931430 0.363920i \(-0.118562\pi\)
−0.363920 + 0.931430i \(0.618562\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −5.05135 1.35350i −0.224338 0.0601112i
\(508\) 0 0
\(509\) 14.2540 24.6886i 0.631797 1.09430i −0.355388 0.934719i \(-0.615651\pi\)
0.987184 0.159585i \(-0.0510155\pi\)
\(510\) 0 0
\(511\) 7.73080 + 5.37131i 0.341990 + 0.237613i
\(512\) 0 0
\(513\) −0.333158 1.24336i −0.0147093 0.0548959i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −2.94061 + 2.94061i −0.129328 + 0.129328i
\(518\) 0 0
\(519\) 0.232058i 0.0101862i
\(520\) 0 0
\(521\) 0.504213 0.291107i 0.0220900 0.0127536i −0.488914 0.872332i \(-0.662607\pi\)
0.511004 + 0.859578i \(0.329274\pi\)
\(522\) 0 0
\(523\) −0.0931310 + 0.0249544i −0.00407233 + 0.00109118i −0.260855 0.965378i \(-0.584004\pi\)
0.256782 + 0.966469i \(0.417338\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 32.2459 8.64026i 1.40465 0.376376i
\(528\) 0 0
\(529\) 19.6829 11.3639i 0.855778 0.494084i
\(530\) 0 0
\(531\) 3.54096i 0.153665i
\(532\) 0 0
\(533\) −18.8822 + 18.8822i −0.817877 + 0.817877i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 1.55291 + 5.79555i 0.0670132 + 0.250097i
\(538\) 0 0
\(539\) −1.68034 + 9.95305i −0.0723774 + 0.428708i
\(540\) 0 0
\(541\) −5.51709 + 9.55589i −0.237198 + 0.410840i −0.959909 0.280311i \(-0.909562\pi\)
0.722711 + 0.691150i \(0.242896\pi\)
\(542\) 0 0
\(543\) −6.45658 1.73004i −0.277078 0.0742430i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −32.0608 32.0608i −1.37082 1.37082i −0.859231 0.511588i \(-0.829057\pi\)
−0.511588 0.859231i \(-0.670943\pi\)
\(548\) 0 0
\(549\) 0.987954 + 1.71119i 0.0421648 + 0.0730316i
\(550\) 0 0
\(551\) 6.83702 + 3.94736i 0.291267 + 0.168163i
\(552\) 0 0
\(553\) 18.8833 15.9625i 0.802997 0.678793i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 9.58541 35.7732i 0.406147 1.51576i −0.395784 0.918344i \(-0.629527\pi\)
0.801931 0.597417i \(-0.203806\pi\)
\(558\) 0 0
\(559\) −5.04243 −0.213272
\(560\) 0 0
\(561\) −5.46160 −0.230589
\(562\) 0 0
\(563\) −3.04577 + 11.3670i −0.128364 + 0.479060i −0.999937 0.0112048i \(-0.996433\pi\)
0.871573 + 0.490265i \(0.163100\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −2.60387 + 0.468915i −0.109352 + 0.0196926i
\(568\) 0 0
\(569\) 18.4319 + 10.6417i 0.772706 + 0.446122i 0.833839 0.552008i \(-0.186138\pi\)
−0.0611330 + 0.998130i \(0.519471\pi\)
\(570\) 0 0
\(571\) 16.6899 + 28.9077i 0.698450 + 1.20975i 0.969004 + 0.247046i \(0.0794597\pi\)
−0.270554 + 0.962705i \(0.587207\pi\)
\(572\) 0 0
\(573\) −1.11377 1.11377i −0.0465284 0.0465284i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 1.61457 + 0.432623i 0.0672154 + 0.0180103i 0.292270 0.956336i \(-0.405589\pi\)
−0.225055 + 0.974346i \(0.572256\pi\)
\(578\) 0 0
\(579\) −5.65578 + 9.79610i −0.235046 + 0.407112i
\(580\) 0 0
\(581\) −41.5623 + 19.5654i −1.72430 + 0.811710i
\(582\) 0 0
\(583\) −2.25367 8.41080i −0.0933374 0.348340i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −19.8129 + 19.8129i −0.817764 + 0.817764i −0.985784 0.168019i \(-0.946263\pi\)
0.168019 + 0.985784i \(0.446263\pi\)
\(588\) 0 0
\(589\) 11.3456i 0.467486i
\(590\) 0 0
\(591\) −19.0073 + 10.9739i −0.781855 + 0.451404i
\(592\) 0 0
\(593\) 2.17008 0.581472i 0.0891146 0.0238782i −0.213986 0.976837i \(-0.568645\pi\)
0.303101 + 0.952958i \(0.401978\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 11.9468 3.20113i 0.488949 0.131013i
\(598\) 0 0
\(599\) −28.7089 + 16.5751i −1.17302 + 0.677241i −0.954388 0.298568i \(-0.903491\pi\)
−0.218627 + 0.975809i \(0.570158\pi\)
\(600\) 0 0
\(601\) 13.9465i 0.568891i −0.958692 0.284446i \(-0.908190\pi\)
0.958692 0.284446i \(-0.0918096\pi\)
\(602\) 0 0
\(603\) −1.59363 + 1.59363i −0.0648977 + 0.0648977i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −10.2267 38.1665i −0.415088 1.54913i −0.784659 0.619928i \(-0.787162\pi\)
0.369570 0.929203i \(-0.379505\pi\)
\(608\) 0 0
\(609\) 9.25880 13.3260i 0.375185 0.539995i
\(610\) 0 0
\(611\) −4.01961 + 6.96217i −0.162616 + 0.281659i
\(612\) 0 0
\(613\) 19.7952 + 5.30411i 0.799521 + 0.214231i 0.635374 0.772205i \(-0.280846\pi\)
0.164147 + 0.986436i \(0.447513\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −23.5210 23.5210i −0.946918 0.946918i 0.0517425 0.998660i \(-0.483522\pi\)
−0.998660 + 0.0517425i \(0.983522\pi\)
\(618\) 0 0
\(619\) 16.9289 + 29.3217i 0.680431 + 1.17854i 0.974850 + 0.222864i \(0.0715406\pi\)
−0.294419 + 0.955676i \(0.595126\pi\)
\(620\) 0 0
\(621\) −0.451792 0.260842i −0.0181298 0.0104672i
\(622\) 0 0
\(623\) 13.4844 + 15.9517i 0.540240 + 0.639092i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0.480410 1.79291i 0.0191857 0.0716021i
\(628\) 0 0
\(629\) 16.0200 0.638759
\(630\) 0 0
\(631\) −20.4933 −0.815824 −0.407912 0.913021i \(-0.633743\pi\)
−0.407912 + 0.913021i \(0.633743\pi\)
\(632\) 0 0
\(633\) 5.09579 19.0177i 0.202539 0.755888i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 1.84219 + 19.4257i 0.0729902 + 0.769675i
\(638\) 0 0
\(639\) −8.01000 4.62458i −0.316871 0.182945i
\(640\) 0 0
\(641\) −10.4915 18.1717i −0.414387 0.717740i 0.580976 0.813920i \(-0.302671\pi\)
−0.995364 + 0.0961802i \(0.969337\pi\)
\(642\) 0 0
\(643\) 23.0444 + 23.0444i 0.908782 + 0.908782i 0.996174 0.0873921i \(-0.0278533\pi\)
−0.0873921 + 0.996174i \(0.527853\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 14.9924 + 4.01721i 0.589413 + 0.157933i 0.541185 0.840904i \(-0.317976\pi\)
0.0482282 + 0.998836i \(0.484643\pi\)
\(648\) 0 0
\(649\) −2.55301 + 4.42194i −0.100214 + 0.173576i
\(650\) 0 0
\(651\) 23.2381 + 1.94782i 0.910772 + 0.0763412i
\(652\) 0 0
\(653\) 1.11117 + 4.14693i 0.0434833 + 0.162282i 0.984253 0.176763i \(-0.0565627\pi\)
−0.940770 + 0.339045i \(0.889896\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −2.51590 + 2.51590i −0.0981545 + 0.0981545i
\(658\) 0 0
\(659\) 22.4591i 0.874882i −0.899247 0.437441i \(-0.855885\pi\)
0.899247 0.437441i \(-0.144115\pi\)
\(660\) 0 0
\(661\) −2.52257 + 1.45640i −0.0981165 + 0.0566476i −0.548255 0.836311i \(-0.684708\pi\)
0.450139 + 0.892959i \(0.351374\pi\)
\(662\) 0 0
\(663\) −10.1983 + 2.73262i −0.396068 + 0.106126i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 3.09053 0.828106i 0.119666 0.0320644i
\(668\) 0 0
\(669\) −3.69468 + 2.13312i −0.142845 + 0.0824713i
\(670\) 0 0
\(671\) 2.84923i 0.109993i
\(672\) 0 0
\(673\) −11.9120 + 11.9120i −0.459173 + 0.459173i −0.898384 0.439211i \(-0.855258\pi\)
0.439211 + 0.898384i \(0.355258\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −11.9284 44.5176i −0.458448 1.71095i −0.677750 0.735293i \(-0.737045\pi\)
0.219302 0.975657i \(-0.429622\pi\)
\(678\) 0 0
\(679\) −14.9079 31.6686i −0.572114 1.21533i
\(680\) 0 0
\(681\) 12.5849 21.7977i 0.482255 0.835290i
\(682\) 0 0
\(683\) −22.2077 5.95053i −0.849754 0.227691i −0.192441 0.981309i \(-0.561640\pi\)
−0.657313 + 0.753618i \(0.728307\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −16.1391 16.1391i −0.615744 0.615744i
\(688\) 0 0
\(689\) −8.41640 14.5776i −0.320639 0.555363i
\(690\) 0 0
\(691\) 13.4182 + 7.74698i 0.510451 + 0.294709i 0.733019 0.680208i \(-0.238111\pi\)
−0.222568 + 0.974917i \(0.571444\pi\)
\(692\) 0 0
\(693\) −3.58978 1.29179i −0.136365 0.0490710i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 9.39071 35.0466i 0.355699 1.32749i
\(698\) 0 0
\(699\) 26.2409 0.992524
\(700\) 0 0
\(701\) 22.8585 0.863352 0.431676 0.902029i \(-0.357922\pi\)
0.431676 + 0.902029i \(0.357922\pi\)
\(702\) 0 0
\(703\) −1.40914 + 5.25899i −0.0531468 + 0.198346i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 6.53352 + 36.2804i 0.245718 + 1.36446i
\(708\) 0 0
\(709\) −9.58768 5.53545i −0.360073 0.207888i 0.309040 0.951049i \(-0.399992\pi\)
−0.669113 + 0.743161i \(0.733326\pi\)
\(710\) 0 0
\(711\) 4.67278 + 8.09350i 0.175243 + 0.303530i
\(712\) 0 0
\(713\) 3.25136 + 3.25136i 0.121764 + 0.121764i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 21.9510 + 5.88175i 0.819774 + 0.219658i
\(718\) 0 0
\(719\) −22.4694 + 38.9182i −0.837968 + 1.45140i 0.0536236 + 0.998561i \(0.482923\pi\)
−0.891591 + 0.452841i \(0.850410\pi\)
\(720\) 0 0
\(721\) 0.539661 6.43831i 0.0200980 0.239775i
\(722\) 0 0
\(723\) 5.74017 + 21.4226i 0.213479 + 0.796715i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −25.9289 + 25.9289i −0.961650 + 0.961650i −0.999291 0.0376415i \(-0.988016\pi\)
0.0376415 + 0.999291i \(0.488016\pi\)
\(728\) 0 0
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 5.93344 3.42567i 0.219456 0.126703i
\(732\) 0 0
\(733\) −31.7034 + 8.49489i −1.17099 + 0.313766i −0.791347 0.611367i \(-0.790620\pi\)
−0.379643 + 0.925133i \(0.623953\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3.13912 + 0.841124i −0.115631 + 0.0309832i
\(738\) 0 0
\(739\) 21.7785 12.5738i 0.801137 0.462537i −0.0427317 0.999087i \(-0.513606\pi\)
0.843869 + 0.536550i \(0.180273\pi\)
\(740\) 0 0
\(741\) 3.58821i 0.131816i
\(742\) 0 0
\(743\) 20.3996 20.3996i 0.748388 0.748388i −0.225788 0.974176i \(-0.572496\pi\)
0.974176 + 0.225788i \(0.0724957\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −4.49379 16.7710i −0.164419 0.613620i
\(748\) 0 0
\(749\) −2.41191 + 28.7748i −0.0881293 + 1.05141i
\(750\) 0 0
\(751\) 20.2082 35.0017i 0.737409 1.27723i −0.216249 0.976338i \(-0.569382\pi\)
0.953658 0.300892i \(-0.0972842\pi\)
\(752\) 0 0
\(753\) 27.1397 + 7.27207i 0.989026 + 0.265009i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 17.8174 + 17.8174i 0.647584 + 0.647584i 0.952408 0.304825i \(-0.0985979\pi\)
−0.304825 + 0.952408i \(0.598598\pi\)
\(758\) 0 0
\(759\) −0.376131 0.651477i −0.0136527 0.0236471i
\(760\) 0 0
\(761\) 29.9104 + 17.2688i 1.08425 + 0.625993i 0.932040 0.362354i \(-0.118027\pi\)
0.152212 + 0.988348i \(0.451360\pi\)
\(762\) 0 0
\(763\) 2.09211 + 11.6174i 0.0757395 + 0.420578i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −2.55470 + 9.53429i −0.0922450 + 0.344263i
\(768\) 0 0
\(769\) −29.1538 −1.05131 −0.525656 0.850697i \(-0.676180\pi\)
−0.525656 + 0.850697i \(0.676180\pi\)
\(770\) 0 0
\(771\) −8.47869 −0.305353
\(772\) 0 0
\(773\) 4.82370 18.0023i 0.173496 0.647497i −0.823307 0.567597i \(-0.807873\pi\)
0.996803 0.0799002i \(-0.0254602\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 10.5296 + 3.78909i 0.377746 + 0.135933i
\(778\) 0 0
\(779\) 10.6790 + 6.16550i 0.382613 + 0.220902i
\(780\) 0 0
\(781\) −6.66857 11.5503i −0.238620 0.413302i
\(782\) 0 0
\(783\) 4.33677 + 4.33677i 0.154984 + 0.154984i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 4.31201 + 1.15540i 0.153706 + 0.0411855i 0.334852 0.942271i \(-0.391314\pi\)
−0.181145 + 0.983456i \(0.557980\pi\)
\(788\) 0 0
\(789\) 4.90504 8.49579i 0.174624 0.302458i
\(790\) 0 0
\(791\) −20.8669 44.3270i −0.741941 1.57609i
\(792\) 0 0
\(793\) 1.42556 + 5.32027i 0.0506232 + 0.188928i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −21.5240 + 21.5240i −0.762418 + 0.762418i −0.976759 0.214341i \(-0.931240\pi\)
0.214341 + 0.976759i \(0.431240\pi\)
\(798\) 0 0
\(799\) 10.9232i 0.386435i
\(800\) 0 0
\(801\) −6.83702 + 3.94736i −0.241574 + 0.139473i
\(802\) 0 0
\(803\) −4.95578 + 1.32790i −0.174886 + 0.0468605i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 1.00782 0.270044i 0.0354768 0.00950599i
\(808\) 0 0
\(809\) −19.4501 + 11.2295i −0.683830 + 0.394810i −0.801297 0.598267i \(-0.795856\pi\)
0.117466 + 0.993077i \(0.462523\pi\)
\(810\) 0 0
\(811\) 11.5465i 0.405453i 0.979235 + 0.202726i \(0.0649802\pi\)
−0.979235 + 0.202726i \(0.935020\pi\)
\(812\) 0 0
\(813\) −9.48342 + 9.48342i −0.332598 + 0.332598i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0.602654 + 2.24913i 0.0210842 + 0.0786872i
\(818\) 0 0
\(819\) −7.34940 0.616029i −0.256809 0.0215258i
\(820\) 0 0
\(821\) 1.62458 2.81385i 0.0566981 0.0982040i −0.836283 0.548298i \(-0.815276\pi\)
0.892981 + 0.450094i \(0.148609\pi\)
\(822\) 0 0
\(823\) −32.8568 8.80397i −1.14532 0.306887i −0.364230 0.931309i \(-0.618668\pi\)
−0.781087 + 0.624422i \(0.785335\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −5.41936 5.41936i −0.188450 0.188450i 0.606576 0.795026i \(-0.292543\pi\)
−0.795026 + 0.606576i \(0.792543\pi\)
\(828\) 0 0
\(829\) −12.5670 21.7667i −0.436470 0.755988i 0.560944 0.827853i \(-0.310438\pi\)
−0.997414 + 0.0718654i \(0.977105\pi\)
\(830\) 0 0
\(831\) −14.8925 8.59820i −0.516616 0.298268i
\(832\) 0 0
\(833\) −15.3649 21.6067i −0.532364 0.748629i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −2.28122 + 8.51364i −0.0788506 + 0.294275i
\(838\) 0 0
\(839\) −18.7482 −0.647259 −0.323629 0.946184i \(-0.604903\pi\)
−0.323629 + 0.946184i \(0.604903\pi\)
\(840\) 0 0
\(841\) −8.61521 −0.297076
\(842\) 0 0
\(843\) −4.72765 + 17.6438i −0.162829 + 0.607686i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 15.2367 + 18.0247i 0.523541 + 0.619337i
\(848\) 0 0
\(849\) −3.67987 2.12458i −0.126293 0.0729153i
\(850\) 0 0
\(851\) 1.10327 + 1.91092i 0.0378196 + 0.0655054i
\(852\) 0 0
\(853\) 10.0238 + 10.0238i 0.343207 + 0.343207i 0.857572 0.514365i \(-0.171972\pi\)
−0.514365 + 0.857572i \(0.671972\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −44.7417 11.9885i −1.52835 0.409520i −0.605869 0.795565i \(-0.707174\pi\)
−0.922480 + 0.386045i \(0.873841\pi\)
\(858\) 0 0
\(859\) 9.95564 17.2437i 0.339682 0.588347i −0.644691 0.764444i \(-0.723014\pi\)
0.984373 + 0.176097i \(0.0563472\pi\)
\(860\) 0 0
\(861\) 14.4616 20.8142i 0.492850 0.709347i
\(862\) 0 0
\(863\) −12.7112 47.4388i −0.432694 1.61484i −0.746525 0.665358i \(-0.768279\pi\)
0.313831 0.949479i \(-0.398388\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −1.87697 + 1.87697i −0.0637451 + 0.0637451i
\(868\) 0 0
\(869\) 13.4762i 0.457148i
\(870\) 0 0
\(871\) −5.44073 + 3.14120i −0.184352 + 0.106436i
\(872\) 0 0
\(873\) 12.7788 3.42406i 0.432495 0.115887i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 35.3278 9.46606i 1.19294 0.319646i 0.392890 0.919586i \(-0.371475\pi\)
0.800045 + 0.599940i \(0.204809\pi\)
\(878\) 0 0
\(879\) 26.2113 15.1331i 0.884087 0.510428i
\(880\) 0 0
\(881\) 21.4260i 0.721862i 0.932593 + 0.360931i \(0.117541\pi\)
−0.932593 + 0.360931i \(0.882459\pi\)
\(882\) 0 0
\(883\) 7.71427 7.71427i 0.259606 0.259606i −0.565288 0.824894i \(-0.691235\pi\)
0.824894 + 0.565288i \(0.191235\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 9.29035 + 34.6721i 0.311939 + 1.16417i 0.926805 + 0.375542i \(0.122543\pi\)
−0.614866 + 0.788632i \(0.710790\pi\)
\(888\) 0 0
\(889\) 30.2718 14.2504i 1.01528 0.477943i
\(890\) 0 0
\(891\) 0.720993 1.24880i 0.0241542 0.0418362i
\(892\) 0 0
\(893\) 3.58583 + 0.960819i 0.119995 + 0.0321526i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −1.02829 1.02829i −0.0343336 0.0343336i
\(898\) 0 0
\(899\) −27.0286 46.8149i −0.901454 1.56136i
\(900\) 0 0
\(901\) 19.8072 + 11.4357i 0.659872 + 0.380978i
\(902\) 0 0
\(903\) 4.71016 0.848226i 0.156744 0.0282272i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 4.72080 17.6183i 0.156752 0.585005i −0.842197 0.539169i \(-0.818738\pi\)
0.998949 0.0458355i \(-0.0145950\pi\)
\(908\) 0 0
\(909\) −13.9333 −0.462137
\(910\) 0 0
\(911\) 37.9403 1.25702 0.628509 0.777802i \(-0.283666\pi\)
0.628509 + 0.777802i \(0.283666\pi\)
\(912\) 0 0
\(913\) 6.47998 24.1836i 0.214456 0.800360i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −14.3094 + 12.0961i −0.472539 + 0.399449i
\(918\) 0 0
\(919\) −20.7477 11.9787i −0.684404 0.395141i 0.117109 0.993119i \(-0.462637\pi\)
−0.801512 + 0.597979i \(0.795971\pi\)
\(920\) 0 0
\(921\) 15.2974 + 26.4958i 0.504065 + 0.873067i
\(922\) 0 0
\(923\) −18.2310 18.2310i −0.600080 0.600080i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 2.35878 + 0.632032i 0.0774724 + 0.0207587i
\(928\) 0 0
\(929\) 13.7278 23.7773i 0.450396 0.780108i −0.548015 0.836469i \(-0.684616\pi\)
0.998410 + 0.0563603i \(0.0179496\pi\)
\(930\) 0 0
\(931\) 8.44450 3.14339i 0.276757 0.103020i
\(932\) 0 0
\(933\) −3.33615 12.4507i −0.109221 0.407617i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −19.0774 + 19.0774i −0.623231 + 0.623231i −0.946356 0.323125i \(-0.895267\pi\)
0.323125 + 0.946356i \(0.395267\pi\)
\(938\) 0 0
\(939\) 0.441985i 0.0144236i
\(940\) 0 0
\(941\) 51.3328 29.6370i 1.67340 0.966139i 0.707690 0.706523i \(-0.249737\pi\)
0.965712 0.259616i \(-0.0835958\pi\)
\(942\) 0 0
\(943\) 4.82720 1.29344i 0.157195 0.0421203i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 35.5007 9.51238i 1.15362 0.309111i 0.369203 0.929349i \(-0.379631\pi\)
0.784414 + 0.620238i \(0.212964\pi\)
\(948\) 0 0
\(949\) −8.58938 + 4.95908i −0.278823 + 0.160979i
\(950\) 0 0
\(951\) 28.3882i 0.920551i
\(952\) 0 0
\(953\) −36.0464 + 36.0464i −1.16766 + 1.16766i −0.184902 + 0.982757i \(0.559197\pi\)
−0.982757 + 0.184902i \(0.940803\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 2.28896 + 8.54253i 0.0739917 + 0.276141i
\(958\) 0 0
\(959\) 8.32626 + 5.78504i 0.268869 + 0.186809i
\(960\) 0 0
\(961\) 23.3431 40.4313i 0.753002 1.30424i
\(962\) 0 0
\(963\) −10.5421 2.82475i −0.339715 0.0910262i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −34.6587 34.6587i −1.11455 1.11455i −0.992528 0.122020i \(-0.961063\pi\)
−0.122020 0.992528i \(-0.538937\pi\)
\(968\) 0 0
\(969\) 2.43772 + 4.22225i 0.0783108 + 0.135638i
\(970\) 0 0
\(971\) 26.0964 + 15.0668i 0.837474 + 0.483516i 0.856405 0.516305i \(-0.172693\pi\)
−0.0189309 + 0.999821i \(0.506026\pi\)
\(972\) 0 0
\(973\) 2.08784 5.80195i 0.0669331 0.186002i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 2.97544 11.1045i 0.0951926 0.355264i −0.901856 0.432037i \(-0.857795\pi\)
0.997049 + 0.0767731i \(0.0244617\pi\)
\(978\) 0 0
\(979\) −11.3841 −0.363836
\(980\) 0 0
\(981\) −4.46160 −0.142448
\(982\) 0 0
\(983\) 6.45437 24.0880i 0.205862 0.768289i −0.783323 0.621616i \(-0.786477\pi\)
0.989185 0.146674i \(-0.0468567\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 2.58358 7.17956i 0.0822362 0.228528i
\(988\) 0 0
\(989\) 0.817251 + 0.471840i 0.0259871 + 0.0150036i
\(990\) 0 0
\(991\) −8.34431 14.4528i −0.265066 0.459107i 0.702515 0.711669i \(-0.252060\pi\)
−0.967581 + 0.252562i \(0.918727\pi\)
\(992\) 0 0
\(993\) 18.9797 + 18.9797i 0.602303 + 0.602303i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 24.1235 + 6.46387i 0.763999 + 0.204713i 0.619719 0.784824i \(-0.287247\pi\)
0.144280 + 0.989537i \(0.453913\pi\)
\(998\) 0 0
\(999\) −2.11482 + 3.66298i −0.0669100 + 0.115891i
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 2100.2.ce.d.1657.6 yes 24
5.2 odd 4 inner 2100.2.ce.d.1993.3 yes 24
5.3 odd 4 inner 2100.2.ce.d.1993.6 yes 24
5.4 even 2 inner 2100.2.ce.d.1657.3 yes 24
7.3 odd 6 inner 2100.2.ce.d.157.5 yes 24
35.3 even 12 inner 2100.2.ce.d.493.6 yes 24
35.17 even 12 inner 2100.2.ce.d.493.3 yes 24
35.24 odd 6 inner 2100.2.ce.d.157.3 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2100.2.ce.d.157.3 24 35.24 odd 6 inner
2100.2.ce.d.157.5 yes 24 7.3 odd 6 inner
2100.2.ce.d.493.3 yes 24 35.17 even 12 inner
2100.2.ce.d.493.6 yes 24 35.3 even 12 inner
2100.2.ce.d.1657.3 yes 24 5.4 even 2 inner
2100.2.ce.d.1657.6 yes 24 1.1 even 1 trivial
2100.2.ce.d.1993.3 yes 24 5.2 odd 4 inner
2100.2.ce.d.1993.6 yes 24 5.3 odd 4 inner