Properties

Label 504.2.q.d.121.4
Level $504$
Weight $2$
Character 504.121
Analytic conductor $4.024$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [504,2,Mod(25,504)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(504, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("504.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.q (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.02446026187\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 121.4
Character \(\chi\) \(=\) 504.121
Dual form 504.2.q.d.25.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.13364 + 1.30952i) q^{3} +(-0.170100 - 0.294622i) q^{5} +(-2.63360 - 0.253251i) q^{7} +(-0.429705 - 2.96907i) q^{9} +O(q^{10})\) \(q+(-1.13364 + 1.30952i) q^{3} +(-0.170100 - 0.294622i) q^{5} +(-2.63360 - 0.253251i) q^{7} +(-0.429705 - 2.96907i) q^{9} +(0.335794 - 0.581612i) q^{11} +(1.62370 - 2.81233i) q^{13} +(0.578647 + 0.111246i) q^{15} +(-1.10014 - 1.90550i) q^{17} +(0.242085 - 0.419303i) q^{19} +(3.31720 - 3.16167i) q^{21} +(-2.09495 - 3.62856i) q^{23} +(2.44213 - 4.22990i) q^{25} +(4.37520 + 2.80315i) q^{27} +(0.478868 + 0.829424i) q^{29} +2.08263 q^{31} +(0.380964 + 1.09907i) q^{33} +(0.373363 + 0.818995i) q^{35} +(4.81613 - 8.34178i) q^{37} +(1.84212 + 5.31445i) q^{39} +(-3.90207 + 6.75858i) q^{41} +(-3.66119 - 6.34136i) q^{43} +(-0.801659 + 0.631639i) q^{45} -2.69901 q^{47} +(6.87173 + 1.33392i) q^{49} +(3.74247 + 0.719498i) q^{51} +(-6.12335 - 10.6059i) q^{53} -0.228474 q^{55} +(0.274649 + 0.792355i) q^{57} -4.94297 q^{59} -3.52119 q^{61} +(0.379756 + 7.92816i) q^{63} -1.10477 q^{65} +12.3202 q^{67} +(7.12661 + 1.37011i) q^{69} -5.57304 q^{71} +(-3.71686 - 6.43779i) q^{73} +(2.77064 + 7.99322i) q^{75} +(-1.03164 + 1.44669i) q^{77} -10.0127 q^{79} +(-8.63071 + 2.55165i) q^{81} +(2.47376 + 4.28468i) q^{83} +(-0.374269 + 0.648252i) q^{85} +(-1.62902 - 0.313182i) q^{87} +(-8.52177 + 14.7601i) q^{89} +(-4.98840 + 6.99536i) q^{91} +(-2.36096 + 2.72725i) q^{93} -0.164714 q^{95} +(4.23657 + 7.33795i) q^{97} +(-1.87114 - 0.747072i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9} - 3 q^{11} - 3 q^{13} - q^{15} + 7 q^{17} - q^{19} + 2 q^{23} - 10 q^{25} - 4 q^{27} + 9 q^{29} + 8 q^{31} + 29 q^{33} + 14 q^{35} + 2 q^{37} - 16 q^{39} + 16 q^{41} + q^{45} - 10 q^{47} + 15 q^{49} + 7 q^{51} + 11 q^{53} + 22 q^{55} + 7 q^{57} + 38 q^{59} + 26 q^{61} + 48 q^{63} - 26 q^{65} - 52 q^{67} - 4 q^{69} - 48 q^{71} - 35 q^{73} - 23 q^{75} + 17 q^{77} - 20 q^{79} - 38 q^{81} - 28 q^{83} - 20 q^{85} - 33 q^{87} + 6 q^{89} - 37 q^{91} + 19 q^{93} - 24 q^{95} - 29 q^{97} - 56 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.13364 + 1.30952i −0.654509 + 0.756054i
\(4\) 0 0
\(5\) −0.170100 0.294622i −0.0760711 0.131759i 0.825480 0.564431i \(-0.190904\pi\)
−0.901552 + 0.432672i \(0.857571\pi\)
\(6\) 0 0
\(7\) −2.63360 0.253251i −0.995408 0.0957197i
\(8\) 0 0
\(9\) −0.429705 2.96907i −0.143235 0.989689i
\(10\) 0 0
\(11\) 0.335794 0.581612i 0.101246 0.175363i −0.810952 0.585112i \(-0.801051\pi\)
0.912198 + 0.409749i \(0.134384\pi\)
\(12\) 0 0
\(13\) 1.62370 2.81233i 0.450333 0.780000i −0.548073 0.836430i \(-0.684639\pi\)
0.998407 + 0.0564303i \(0.0179719\pi\)
\(14\) 0 0
\(15\) 0.578647 + 0.111246i 0.149406 + 0.0287236i
\(16\) 0 0
\(17\) −1.10014 1.90550i −0.266824 0.462152i 0.701216 0.712949i \(-0.252641\pi\)
−0.968040 + 0.250796i \(0.919308\pi\)
\(18\) 0 0
\(19\) 0.242085 0.419303i 0.0555380 0.0961946i −0.836920 0.547326i \(-0.815646\pi\)
0.892458 + 0.451131i \(0.148979\pi\)
\(20\) 0 0
\(21\) 3.31720 3.16167i 0.723873 0.689933i
\(22\) 0 0
\(23\) −2.09495 3.62856i −0.436827 0.756607i 0.560616 0.828076i \(-0.310565\pi\)
−0.997443 + 0.0714692i \(0.977231\pi\)
\(24\) 0 0
\(25\) 2.44213 4.22990i 0.488426 0.845979i
\(26\) 0 0
\(27\) 4.37520 + 2.80315i 0.842007 + 0.539467i
\(28\) 0 0
\(29\) 0.478868 + 0.829424i 0.0889235 + 0.154020i 0.907056 0.421009i \(-0.138324\pi\)
−0.818133 + 0.575029i \(0.804991\pi\)
\(30\) 0 0
\(31\) 2.08263 0.374052 0.187026 0.982355i \(-0.440115\pi\)
0.187026 + 0.982355i \(0.440115\pi\)
\(32\) 0 0
\(33\) 0.380964 + 1.09907i 0.0663174 + 0.191324i
\(34\) 0 0
\(35\) 0.373363 + 0.818995i 0.0631098 + 0.138435i
\(36\) 0 0
\(37\) 4.81613 8.34178i 0.791767 1.37138i −0.133105 0.991102i \(-0.542495\pi\)
0.924872 0.380278i \(-0.124172\pi\)
\(38\) 0 0
\(39\) 1.84212 + 5.31445i 0.294975 + 0.850993i
\(40\) 0 0
\(41\) −3.90207 + 6.75858i −0.609400 + 1.05551i 0.381939 + 0.924188i \(0.375256\pi\)
−0.991339 + 0.131325i \(0.958077\pi\)
\(42\) 0 0
\(43\) −3.66119 6.34136i −0.558326 0.967048i −0.997636 0.0687132i \(-0.978111\pi\)
0.439311 0.898335i \(-0.355223\pi\)
\(44\) 0 0
\(45\) −0.801659 + 0.631639i −0.119504 + 0.0941592i
\(46\) 0 0
\(47\) −2.69901 −0.393692 −0.196846 0.980434i \(-0.563070\pi\)
−0.196846 + 0.980434i \(0.563070\pi\)
\(48\) 0 0
\(49\) 6.87173 + 1.33392i 0.981675 + 0.190560i
\(50\) 0 0
\(51\) 3.74247 + 0.719498i 0.524051 + 0.100750i
\(52\) 0 0
\(53\) −6.12335 10.6059i −0.841107 1.45684i −0.888960 0.457985i \(-0.848571\pi\)
0.0478535 0.998854i \(-0.484762\pi\)
\(54\) 0 0
\(55\) −0.228474 −0.0308075
\(56\) 0 0
\(57\) 0.274649 + 0.792355i 0.0363782 + 0.104950i
\(58\) 0 0
\(59\) −4.94297 −0.643520 −0.321760 0.946821i \(-0.604274\pi\)
−0.321760 + 0.946821i \(0.604274\pi\)
\(60\) 0 0
\(61\) −3.52119 −0.450842 −0.225421 0.974261i \(-0.572376\pi\)
−0.225421 + 0.974261i \(0.572376\pi\)
\(62\) 0 0
\(63\) 0.379756 + 7.92816i 0.0478447 + 0.998855i
\(64\) 0 0
\(65\) −1.10477 −0.137029
\(66\) 0 0
\(67\) 12.3202 1.50516 0.752579 0.658502i \(-0.228810\pi\)
0.752579 + 0.658502i \(0.228810\pi\)
\(68\) 0 0
\(69\) 7.12661 + 1.37011i 0.857943 + 0.164941i
\(70\) 0 0
\(71\) −5.57304 −0.661398 −0.330699 0.943736i \(-0.607285\pi\)
−0.330699 + 0.943736i \(0.607285\pi\)
\(72\) 0 0
\(73\) −3.71686 6.43779i −0.435026 0.753487i 0.562272 0.826952i \(-0.309927\pi\)
−0.997298 + 0.0734657i \(0.976594\pi\)
\(74\) 0 0
\(75\) 2.77064 + 7.99322i 0.319926 + 0.922978i
\(76\) 0 0
\(77\) −1.03164 + 1.44669i −0.117566 + 0.164866i
\(78\) 0 0
\(79\) −10.0127 −1.12652 −0.563260 0.826279i \(-0.690453\pi\)
−0.563260 + 0.826279i \(0.690453\pi\)
\(80\) 0 0
\(81\) −8.63071 + 2.55165i −0.958967 + 0.283516i
\(82\) 0 0
\(83\) 2.47376 + 4.28468i 0.271530 + 0.470305i 0.969254 0.246063i \(-0.0791369\pi\)
−0.697723 + 0.716367i \(0.745804\pi\)
\(84\) 0 0
\(85\) −0.374269 + 0.648252i −0.0405951 + 0.0703128i
\(86\) 0 0
\(87\) −1.62902 0.313182i −0.174649 0.0335766i
\(88\) 0 0
\(89\) −8.52177 + 14.7601i −0.903306 + 1.56457i −0.0801310 + 0.996784i \(0.525534\pi\)
−0.823175 + 0.567788i \(0.807799\pi\)
\(90\) 0 0
\(91\) −4.98840 + 6.99536i −0.522927 + 0.733313i
\(92\) 0 0
\(93\) −2.36096 + 2.72725i −0.244820 + 0.282803i
\(94\) 0 0
\(95\) −0.164714 −0.0168993
\(96\) 0 0
\(97\) 4.23657 + 7.33795i 0.430159 + 0.745056i 0.996887 0.0788485i \(-0.0251243\pi\)
−0.566728 + 0.823905i \(0.691791\pi\)
\(98\) 0 0
\(99\) −1.87114 0.747072i −0.188056 0.0750836i
\(100\) 0 0
\(101\) 2.28693 3.96107i 0.227558 0.394141i −0.729526 0.683953i \(-0.760259\pi\)
0.957084 + 0.289812i \(0.0935927\pi\)
\(102\) 0 0
\(103\) 0.903563 + 1.56502i 0.0890307 + 0.154206i 0.907102 0.420912i \(-0.138290\pi\)
−0.818071 + 0.575117i \(0.804956\pi\)
\(104\) 0 0
\(105\) −1.49575 0.439521i −0.145971 0.0428928i
\(106\) 0 0
\(107\) 3.88188 6.72361i 0.375275 0.649996i −0.615093 0.788454i \(-0.710882\pi\)
0.990368 + 0.138459i \(0.0442149\pi\)
\(108\) 0 0
\(109\) −1.07178 1.85638i −0.102658 0.177809i 0.810121 0.586263i \(-0.199401\pi\)
−0.912779 + 0.408454i \(0.866068\pi\)
\(110\) 0 0
\(111\) 5.46399 + 15.7634i 0.518619 + 1.49620i
\(112\) 0 0
\(113\) −7.91006 + 13.7006i −0.744116 + 1.28885i 0.206491 + 0.978449i \(0.433796\pi\)
−0.950607 + 0.310398i \(0.899538\pi\)
\(114\) 0 0
\(115\) −0.712702 + 1.23444i −0.0664598 + 0.115112i
\(116\) 0 0
\(117\) −9.04771 3.61240i −0.836461 0.333966i
\(118\) 0 0
\(119\) 2.41477 + 5.29695i 0.221362 + 0.485571i
\(120\) 0 0
\(121\) 5.27449 + 9.13568i 0.479499 + 0.830516i
\(122\) 0 0
\(123\) −4.42697 12.7717i −0.399166 1.15158i
\(124\) 0 0
\(125\) −3.36263 −0.300763
\(126\) 0 0
\(127\) −13.8820 −1.23183 −0.615915 0.787812i \(-0.711214\pi\)
−0.615915 + 0.787812i \(0.711214\pi\)
\(128\) 0 0
\(129\) 12.4546 + 2.39443i 1.09657 + 0.210818i
\(130\) 0 0
\(131\) 2.08769 + 3.61599i 0.182402 + 0.315930i 0.942698 0.333647i \(-0.108279\pi\)
−0.760296 + 0.649577i \(0.774946\pi\)
\(132\) 0 0
\(133\) −0.743743 + 1.04297i −0.0644907 + 0.0904369i
\(134\) 0 0
\(135\) 0.0816493 1.76585i 0.00702725 0.151980i
\(136\) 0 0
\(137\) 6.38043 11.0512i 0.545117 0.944170i −0.453483 0.891265i \(-0.649819\pi\)
0.998600 0.0529051i \(-0.0168481\pi\)
\(138\) 0 0
\(139\) 5.95986 10.3228i 0.505509 0.875567i −0.494471 0.869194i \(-0.664638\pi\)
0.999980 0.00637264i \(-0.00202849\pi\)
\(140\) 0 0
\(141\) 3.05972 3.53442i 0.257675 0.297652i
\(142\) 0 0
\(143\) −1.09046 1.88873i −0.0911885 0.157943i
\(144\) 0 0
\(145\) 0.162911 0.282170i 0.0135290 0.0234329i
\(146\) 0 0
\(147\) −9.53689 + 7.48650i −0.786590 + 0.617476i
\(148\) 0 0
\(149\) 5.37548 + 9.31060i 0.440376 + 0.762754i 0.997717 0.0675295i \(-0.0215117\pi\)
−0.557341 + 0.830284i \(0.688178\pi\)
\(150\) 0 0
\(151\) 1.29050 2.23521i 0.105019 0.181899i −0.808727 0.588184i \(-0.799843\pi\)
0.913746 + 0.406286i \(0.133176\pi\)
\(152\) 0 0
\(153\) −5.18483 + 4.08520i −0.419168 + 0.330269i
\(154\) 0 0
\(155\) −0.354256 0.613589i −0.0284545 0.0492846i
\(156\) 0 0
\(157\) 7.99693 0.638224 0.319112 0.947717i \(-0.396615\pi\)
0.319112 + 0.947717i \(0.396615\pi\)
\(158\) 0 0
\(159\) 20.8304 + 4.00469i 1.65196 + 0.317593i
\(160\) 0 0
\(161\) 4.59833 + 10.0867i 0.362399 + 0.794946i
\(162\) 0 0
\(163\) 4.13306 7.15868i 0.323727 0.560711i −0.657527 0.753431i \(-0.728398\pi\)
0.981254 + 0.192720i \(0.0617309\pi\)
\(164\) 0 0
\(165\) 0.259008 0.299192i 0.0201638 0.0232921i
\(166\) 0 0
\(167\) 8.99384 15.5778i 0.695964 1.20544i −0.273891 0.961761i \(-0.588311\pi\)
0.969855 0.243684i \(-0.0783560\pi\)
\(168\) 0 0
\(169\) 1.22720 + 2.12557i 0.0944000 + 0.163506i
\(170\) 0 0
\(171\) −1.34896 0.538588i −0.103158 0.0411869i
\(172\) 0 0
\(173\) −16.9983 −1.29236 −0.646179 0.763186i \(-0.723634\pi\)
−0.646179 + 0.763186i \(0.723634\pi\)
\(174\) 0 0
\(175\) −7.50283 + 10.5214i −0.567161 + 0.795343i
\(176\) 0 0
\(177\) 5.60356 6.47293i 0.421190 0.486536i
\(178\) 0 0
\(179\) −9.65073 16.7156i −0.721329 1.24938i −0.960467 0.278393i \(-0.910198\pi\)
0.239138 0.970986i \(-0.423135\pi\)
\(180\) 0 0
\(181\) 21.9640 1.63257 0.816287 0.577646i \(-0.196029\pi\)
0.816287 + 0.577646i \(0.196029\pi\)
\(182\) 0 0
\(183\) 3.99177 4.61108i 0.295080 0.340861i
\(184\) 0 0
\(185\) −3.27690 −0.240922
\(186\) 0 0
\(187\) −1.47768 −0.108059
\(188\) 0 0
\(189\) −10.8126 8.49041i −0.786503 0.617587i
\(190\) 0 0
\(191\) 6.65744 0.481716 0.240858 0.970560i \(-0.422571\pi\)
0.240858 + 0.970560i \(0.422571\pi\)
\(192\) 0 0
\(193\) 6.34906 0.457015 0.228508 0.973542i \(-0.426615\pi\)
0.228508 + 0.973542i \(0.426615\pi\)
\(194\) 0 0
\(195\) 1.25241 1.44672i 0.0896870 0.103602i
\(196\) 0 0
\(197\) 23.8112 1.69648 0.848239 0.529614i \(-0.177663\pi\)
0.848239 + 0.529614i \(0.177663\pi\)
\(198\) 0 0
\(199\) −10.4771 18.1468i −0.742701 1.28640i −0.951261 0.308386i \(-0.900211\pi\)
0.208561 0.978009i \(-0.433122\pi\)
\(200\) 0 0
\(201\) −13.9668 + 16.1337i −0.985140 + 1.13798i
\(202\) 0 0
\(203\) −1.05110 2.30565i −0.0737725 0.161825i
\(204\) 0 0
\(205\) 2.65497 0.185431
\(206\) 0 0
\(207\) −9.87322 + 7.77926i −0.686236 + 0.540696i
\(208\) 0 0
\(209\) −0.162581 0.281599i −0.0112460 0.0194786i
\(210\) 0 0
\(211\) −6.32431 + 10.9540i −0.435384 + 0.754106i −0.997327 0.0730693i \(-0.976721\pi\)
0.561943 + 0.827176i \(0.310054\pi\)
\(212\) 0 0
\(213\) 6.31784 7.29803i 0.432891 0.500053i
\(214\) 0 0
\(215\) −1.24554 + 2.15733i −0.0849448 + 0.147129i
\(216\) 0 0
\(217\) −5.48482 0.527427i −0.372334 0.0358041i
\(218\) 0 0
\(219\) 12.6440 + 2.43084i 0.854405 + 0.164261i
\(220\) 0 0
\(221\) −7.14520 −0.480638
\(222\) 0 0
\(223\) −1.34432 2.32843i −0.0900225 0.155924i 0.817498 0.575932i \(-0.195361\pi\)
−0.907520 + 0.420008i \(0.862027\pi\)
\(224\) 0 0
\(225\) −13.6082 5.43324i −0.907216 0.362216i
\(226\) 0 0
\(227\) −13.9942 + 24.2387i −0.928829 + 1.60878i −0.143546 + 0.989644i \(0.545850\pi\)
−0.785284 + 0.619136i \(0.787483\pi\)
\(228\) 0 0
\(229\) −12.2695 21.2514i −0.810790 1.40433i −0.912312 0.409497i \(-0.865704\pi\)
0.101521 0.994833i \(-0.467629\pi\)
\(230\) 0 0
\(231\) −0.724968 2.99099i −0.0476994 0.196793i
\(232\) 0 0
\(233\) −4.61844 + 7.99938i −0.302564 + 0.524057i −0.976716 0.214536i \(-0.931176\pi\)
0.674152 + 0.738593i \(0.264509\pi\)
\(234\) 0 0
\(235\) 0.459103 + 0.795189i 0.0299486 + 0.0518724i
\(236\) 0 0
\(237\) 11.3509 13.1119i 0.737318 0.851711i
\(238\) 0 0
\(239\) 14.0126 24.2706i 0.906403 1.56994i 0.0873796 0.996175i \(-0.472151\pi\)
0.819023 0.573760i \(-0.194516\pi\)
\(240\) 0 0
\(241\) −9.91411 + 17.1717i −0.638624 + 1.10613i 0.347111 + 0.937824i \(0.387163\pi\)
−0.985735 + 0.168305i \(0.946171\pi\)
\(242\) 0 0
\(243\) 6.44270 14.1948i 0.413299 0.910595i
\(244\) 0 0
\(245\) −0.775879 2.25146i −0.0495691 0.143841i
\(246\) 0 0
\(247\) −0.786145 1.36164i −0.0500212 0.0866393i
\(248\) 0 0
\(249\) −8.41525 1.61785i −0.533295 0.102527i
\(250\) 0 0
\(251\) 16.5759 1.04626 0.523132 0.852252i \(-0.324764\pi\)
0.523132 + 0.852252i \(0.324764\pi\)
\(252\) 0 0
\(253\) −2.81389 −0.176907
\(254\) 0 0
\(255\) −0.424615 1.22500i −0.0265904 0.0767125i
\(256\) 0 0
\(257\) −3.64750 6.31766i −0.227525 0.394085i 0.729549 0.683929i \(-0.239730\pi\)
−0.957074 + 0.289844i \(0.906397\pi\)
\(258\) 0 0
\(259\) −14.7963 + 20.7493i −0.919399 + 1.28930i
\(260\) 0 0
\(261\) 2.25684 1.77820i 0.139695 0.110068i
\(262\) 0 0
\(263\) 13.3899 23.1920i 0.825657 1.43008i −0.0757586 0.997126i \(-0.524138\pi\)
0.901416 0.432954i \(-0.142529\pi\)
\(264\) 0 0
\(265\) −2.08316 + 3.60815i −0.127968 + 0.221647i
\(266\) 0 0
\(267\) −9.66811 27.8922i −0.591679 1.70698i
\(268\) 0 0
\(269\) 10.1791 + 17.6307i 0.620630 + 1.07496i 0.989369 + 0.145429i \(0.0464562\pi\)
−0.368739 + 0.929533i \(0.620210\pi\)
\(270\) 0 0
\(271\) 5.45842 9.45427i 0.331576 0.574306i −0.651245 0.758867i \(-0.725753\pi\)
0.982821 + 0.184561i \(0.0590864\pi\)
\(272\) 0 0
\(273\) −3.50552 14.4627i −0.212164 0.875321i
\(274\) 0 0
\(275\) −1.64011 2.84075i −0.0989021 0.171303i
\(276\) 0 0
\(277\) −8.83689 + 15.3059i −0.530957 + 0.919645i 0.468390 + 0.883522i \(0.344834\pi\)
−0.999347 + 0.0361231i \(0.988499\pi\)
\(278\) 0 0
\(279\) −0.894918 6.18347i −0.0535773 0.370195i
\(280\) 0 0
\(281\) 7.17614 + 12.4294i 0.428092 + 0.741478i 0.996704 0.0811286i \(-0.0258524\pi\)
−0.568611 + 0.822606i \(0.692519\pi\)
\(282\) 0 0
\(283\) 9.72841 0.578294 0.289147 0.957285i \(-0.406628\pi\)
0.289147 + 0.957285i \(0.406628\pi\)
\(284\) 0 0
\(285\) 0.186727 0.215697i 0.0110608 0.0127768i
\(286\) 0 0
\(287\) 11.9881 16.8112i 0.707636 0.992334i
\(288\) 0 0
\(289\) 6.07937 10.5298i 0.357610 0.619399i
\(290\) 0 0
\(291\) −14.4120 2.77073i −0.844846 0.162423i
\(292\) 0 0
\(293\) 6.26345 10.8486i 0.365915 0.633783i −0.623008 0.782216i \(-0.714089\pi\)
0.988923 + 0.148433i \(0.0474228\pi\)
\(294\) 0 0
\(295\) 0.840799 + 1.45631i 0.0489532 + 0.0847895i
\(296\) 0 0
\(297\) 3.09951 1.60338i 0.179852 0.0930378i
\(298\) 0 0
\(299\) −13.6063 −0.786871
\(300\) 0 0
\(301\) 8.03616 + 17.6278i 0.463196 + 1.01605i
\(302\) 0 0
\(303\) 2.59456 + 7.48523i 0.149054 + 0.430015i
\(304\) 0 0
\(305\) 0.598954 + 1.03742i 0.0342960 + 0.0594025i
\(306\) 0 0
\(307\) 25.8747 1.47675 0.738375 0.674391i \(-0.235594\pi\)
0.738375 + 0.674391i \(0.235594\pi\)
\(308\) 0 0
\(309\) −3.07375 0.590934i −0.174859 0.0336171i
\(310\) 0 0
\(311\) 28.4001 1.61042 0.805211 0.592988i \(-0.202052\pi\)
0.805211 + 0.592988i \(0.202052\pi\)
\(312\) 0 0
\(313\) −12.2015 −0.689668 −0.344834 0.938664i \(-0.612065\pi\)
−0.344834 + 0.938664i \(0.612065\pi\)
\(314\) 0 0
\(315\) 2.27121 1.46047i 0.127968 0.0822879i
\(316\) 0 0
\(317\) −3.95219 −0.221977 −0.110988 0.993822i \(-0.535402\pi\)
−0.110988 + 0.993822i \(0.535402\pi\)
\(318\) 0 0
\(319\) 0.643204 0.0360125
\(320\) 0 0
\(321\) 4.40406 + 12.7056i 0.245811 + 0.709156i
\(322\) 0 0
\(323\) −1.06531 −0.0592754
\(324\) 0 0
\(325\) −7.93058 13.7362i −0.439909 0.761945i
\(326\) 0 0
\(327\) 3.64600 + 0.700951i 0.201624 + 0.0387627i
\(328\) 0 0
\(329\) 7.10813 + 0.683527i 0.391884 + 0.0376841i
\(330\) 0 0
\(331\) −8.88286 −0.488246 −0.244123 0.969744i \(-0.578500\pi\)
−0.244123 + 0.969744i \(0.578500\pi\)
\(332\) 0 0
\(333\) −26.8368 10.7149i −1.47065 0.587173i
\(334\) 0 0
\(335\) −2.09567 3.62981i −0.114499 0.198318i
\(336\) 0 0
\(337\) −11.9741 + 20.7397i −0.652269 + 1.12976i 0.330302 + 0.943875i \(0.392849\pi\)
−0.982571 + 0.185887i \(0.940484\pi\)
\(338\) 0 0
\(339\) −8.97411 25.8900i −0.487407 1.40615i
\(340\) 0 0
\(341\) 0.699335 1.21128i 0.0378711 0.0655947i
\(342\) 0 0
\(343\) −17.7596 5.25329i −0.958928 0.283651i
\(344\) 0 0
\(345\) −0.808574 2.33271i −0.0435322 0.125589i
\(346\) 0 0
\(347\) 9.49059 0.509481 0.254741 0.967009i \(-0.418010\pi\)
0.254741 + 0.967009i \(0.418010\pi\)
\(348\) 0 0
\(349\) 4.26145 + 7.38104i 0.228110 + 0.395098i 0.957248 0.289269i \(-0.0934121\pi\)
−0.729138 + 0.684367i \(0.760079\pi\)
\(350\) 0 0
\(351\) 14.9874 7.75302i 0.799968 0.413825i
\(352\) 0 0
\(353\) 18.5872 32.1940i 0.989297 1.71351i 0.368279 0.929715i \(-0.379947\pi\)
0.621018 0.783797i \(-0.286719\pi\)
\(354\) 0 0
\(355\) 0.947975 + 1.64194i 0.0503133 + 0.0871451i
\(356\) 0 0
\(357\) −9.67397 2.84265i −0.512001 0.150449i
\(358\) 0 0
\(359\) −5.30964 + 9.19657i −0.280232 + 0.485376i −0.971442 0.237278i \(-0.923745\pi\)
0.691210 + 0.722654i \(0.257078\pi\)
\(360\) 0 0
\(361\) 9.38279 + 16.2515i 0.493831 + 0.855340i
\(362\) 0 0
\(363\) −17.9428 3.44953i −0.941751 0.181054i
\(364\) 0 0
\(365\) −1.26448 + 2.19014i −0.0661857 + 0.114637i
\(366\) 0 0
\(367\) −11.1799 + 19.3642i −0.583586 + 1.01080i 0.411464 + 0.911426i \(0.365018\pi\)
−0.995050 + 0.0993751i \(0.968316\pi\)
\(368\) 0 0
\(369\) 21.7434 + 8.68130i 1.13192 + 0.451930i
\(370\) 0 0
\(371\) 13.4405 + 29.4826i 0.697796 + 1.53066i
\(372\) 0 0
\(373\) 8.79264 + 15.2293i 0.455266 + 0.788544i 0.998703 0.0509059i \(-0.0162109\pi\)
−0.543438 + 0.839450i \(0.682878\pi\)
\(374\) 0 0
\(375\) 3.81202 4.40344i 0.196852 0.227393i
\(376\) 0 0
\(377\) 3.11015 0.160181
\(378\) 0 0
\(379\) 10.0443 0.515939 0.257969 0.966153i \(-0.416947\pi\)
0.257969 + 0.966153i \(0.416947\pi\)
\(380\) 0 0
\(381\) 15.7373 18.1788i 0.806245 0.931330i
\(382\) 0 0
\(383\) 3.93619 + 6.81768i 0.201130 + 0.348367i 0.948893 0.315599i \(-0.102205\pi\)
−0.747763 + 0.663966i \(0.768872\pi\)
\(384\) 0 0
\(385\) 0.601710 + 0.0578612i 0.0306660 + 0.00294888i
\(386\) 0 0
\(387\) −17.2547 + 13.5952i −0.877105 + 0.691084i
\(388\) 0 0
\(389\) 1.82417 3.15956i 0.0924893 0.160196i −0.816069 0.577955i \(-0.803851\pi\)
0.908558 + 0.417759i \(0.137184\pi\)
\(390\) 0 0
\(391\) −4.60949 + 7.98387i −0.233112 + 0.403762i
\(392\) 0 0
\(393\) −7.10192 1.36536i −0.358244 0.0688732i
\(394\) 0 0
\(395\) 1.70317 + 2.94997i 0.0856956 + 0.148429i
\(396\) 0 0
\(397\) 6.56071 11.3635i 0.329272 0.570317i −0.653095 0.757276i \(-0.726530\pi\)
0.982368 + 0.186959i \(0.0598632\pi\)
\(398\) 0 0
\(399\) −0.522653 2.15630i −0.0261654 0.107950i
\(400\) 0 0
\(401\) −5.71872 9.90511i −0.285579 0.494638i 0.687170 0.726496i \(-0.258853\pi\)
−0.972749 + 0.231859i \(0.925519\pi\)
\(402\) 0 0
\(403\) 3.38157 5.85705i 0.168448 0.291760i
\(404\) 0 0
\(405\) 2.21986 + 2.10876i 0.110305 + 0.104785i
\(406\) 0 0
\(407\) −3.23445 5.60224i −0.160326 0.277693i
\(408\) 0 0
\(409\) −18.4821 −0.913882 −0.456941 0.889497i \(-0.651055\pi\)
−0.456941 + 0.889497i \(0.651055\pi\)
\(410\) 0 0
\(411\) 7.23872 + 20.8835i 0.357060 + 1.03011i
\(412\) 0 0
\(413\) 13.0178 + 1.25181i 0.640565 + 0.0615975i
\(414\) 0 0
\(415\) 0.841574 1.45765i 0.0413112 0.0715531i
\(416\) 0 0
\(417\) 6.76157 + 19.5069i 0.331116 + 0.955258i
\(418\) 0 0
\(419\) −10.6290 + 18.4099i −0.519260 + 0.899385i 0.480489 + 0.877001i \(0.340459\pi\)
−0.999749 + 0.0223843i \(0.992874\pi\)
\(420\) 0 0
\(421\) −8.60478 14.9039i −0.419371 0.726373i 0.576505 0.817094i \(-0.304416\pi\)
−0.995876 + 0.0907211i \(0.971083\pi\)
\(422\) 0 0
\(423\) 1.15978 + 8.01355i 0.0563905 + 0.389632i
\(424\) 0 0
\(425\) −10.7468 −0.521295
\(426\) 0 0
\(427\) 9.27341 + 0.891743i 0.448772 + 0.0431545i
\(428\) 0 0
\(429\) 3.70952 + 0.713163i 0.179097 + 0.0344318i
\(430\) 0 0
\(431\) 3.02962 + 5.24745i 0.145931 + 0.252761i 0.929720 0.368267i \(-0.120049\pi\)
−0.783789 + 0.621028i \(0.786715\pi\)
\(432\) 0 0
\(433\) −17.6963 −0.850432 −0.425216 0.905092i \(-0.639802\pi\)
−0.425216 + 0.905092i \(0.639802\pi\)
\(434\) 0 0
\(435\) 0.184825 + 0.533216i 0.00886170 + 0.0255657i
\(436\) 0 0
\(437\) −2.02862 −0.0970421
\(438\) 0 0
\(439\) 27.3373 1.30474 0.652370 0.757901i \(-0.273775\pi\)
0.652370 + 0.757901i \(0.273775\pi\)
\(440\) 0 0
\(441\) 1.00769 20.9758i 0.0479851 0.998848i
\(442\) 0 0
\(443\) 1.91771 0.0911132 0.0455566 0.998962i \(-0.485494\pi\)
0.0455566 + 0.998962i \(0.485494\pi\)
\(444\) 0 0
\(445\) 5.79822 0.274862
\(446\) 0 0
\(447\) −18.2863 3.51559i −0.864914 0.166281i
\(448\) 0 0
\(449\) 28.3249 1.33674 0.668368 0.743831i \(-0.266993\pi\)
0.668368 + 0.743831i \(0.266993\pi\)
\(450\) 0 0
\(451\) 2.62058 + 4.53898i 0.123398 + 0.213732i
\(452\) 0 0
\(453\) 1.46409 + 4.22386i 0.0687891 + 0.198454i
\(454\) 0 0
\(455\) 2.90951 + 0.279782i 0.136400 + 0.0131164i
\(456\) 0 0
\(457\) 13.0085 0.608514 0.304257 0.952590i \(-0.401592\pi\)
0.304257 + 0.952590i \(0.401592\pi\)
\(458\) 0 0
\(459\) 0.528076 11.4208i 0.0246485 0.533078i
\(460\) 0 0
\(461\) −11.8278 20.4863i −0.550875 0.954144i −0.998212 0.0597782i \(-0.980961\pi\)
0.447336 0.894366i \(-0.352373\pi\)
\(462\) 0 0
\(463\) −20.2403 + 35.0572i −0.940647 + 1.62925i −0.176406 + 0.984317i \(0.556447\pi\)
−0.764241 + 0.644931i \(0.776886\pi\)
\(464\) 0 0
\(465\) 1.20511 + 0.231685i 0.0558856 + 0.0107441i
\(466\) 0 0
\(467\) −18.6010 + 32.2179i −0.860753 + 1.49087i 0.0104492 + 0.999945i \(0.496674\pi\)
−0.871203 + 0.490923i \(0.836659\pi\)
\(468\) 0 0
\(469\) −32.4466 3.12011i −1.49825 0.144073i
\(470\) 0 0
\(471\) −9.06566 + 10.4722i −0.417724 + 0.482532i
\(472\) 0 0
\(473\) −4.91761 −0.226112
\(474\) 0 0
\(475\) −1.18240 2.04799i −0.0542525 0.0939680i
\(476\) 0 0
\(477\) −28.8585 + 22.7381i −1.32134 + 1.04110i
\(478\) 0 0
\(479\) −20.2918 + 35.1463i −0.927154 + 1.60588i −0.139094 + 0.990279i \(0.544419\pi\)
−0.788060 + 0.615598i \(0.788914\pi\)
\(480\) 0 0
\(481\) −15.6399 27.0891i −0.713118 1.23516i
\(482\) 0 0
\(483\) −18.4217 5.41313i −0.838216 0.246306i
\(484\) 0 0
\(485\) 1.44128 2.49637i 0.0654452 0.113354i
\(486\) 0 0
\(487\) 10.5255 + 18.2307i 0.476956 + 0.826113i 0.999651 0.0264072i \(-0.00840666\pi\)
−0.522695 + 0.852520i \(0.675073\pi\)
\(488\) 0 0
\(489\) 4.68904 + 13.5277i 0.212046 + 0.611745i
\(490\) 0 0
\(491\) −4.97925 + 8.62432i −0.224711 + 0.389210i −0.956233 0.292608i \(-0.905477\pi\)
0.731522 + 0.681818i \(0.238810\pi\)
\(492\) 0 0
\(493\) 1.05365 1.82497i 0.0474538 0.0821924i
\(494\) 0 0
\(495\) 0.0981766 + 0.678355i 0.00441271 + 0.0304898i
\(496\) 0 0
\(497\) 14.6772 + 1.41138i 0.658361 + 0.0633088i
\(498\) 0 0
\(499\) −11.3150 19.5982i −0.506531 0.877337i −0.999971 0.00755788i \(-0.997594\pi\)
0.493440 0.869780i \(-0.335739\pi\)
\(500\) 0 0
\(501\) 10.2037 + 29.4373i 0.455867 + 1.31516i
\(502\) 0 0
\(503\) −43.4520 −1.93743 −0.968714 0.248179i \(-0.920168\pi\)
−0.968714 + 0.248179i \(0.920168\pi\)
\(504\) 0 0
\(505\) −1.55602 −0.0692422
\(506\) 0 0
\(507\) −4.17470 0.802594i −0.185405 0.0356444i
\(508\) 0 0
\(509\) 4.77739 + 8.27468i 0.211754 + 0.366769i 0.952264 0.305277i \(-0.0987491\pi\)
−0.740510 + 0.672046i \(0.765416\pi\)
\(510\) 0 0
\(511\) 8.15836 + 17.8959i 0.360905 + 0.791667i
\(512\) 0 0
\(513\) 2.23454 1.15593i 0.0986572 0.0510356i
\(514\) 0 0
\(515\) 0.307392 0.532419i 0.0135453 0.0234612i
\(516\) 0 0
\(517\) −0.906312 + 1.56978i −0.0398596 + 0.0690388i
\(518\) 0 0
\(519\) 19.2700 22.2597i 0.845860 0.977092i
\(520\) 0 0
\(521\) 0.581462 + 1.00712i 0.0254743 + 0.0441228i 0.878482 0.477776i \(-0.158557\pi\)
−0.853007 + 0.521899i \(0.825224\pi\)
\(522\) 0 0
\(523\) −3.20567 + 5.55239i −0.140174 + 0.242789i −0.927562 0.373669i \(-0.878100\pi\)
0.787388 + 0.616458i \(0.211433\pi\)
\(524\) 0 0
\(525\) −5.27249 21.7526i −0.230110 0.949363i
\(526\) 0 0
\(527\) −2.29119 3.96846i −0.0998059 0.172869i
\(528\) 0 0
\(529\) 2.72237 4.71528i 0.118364 0.205012i
\(530\) 0 0
\(531\) 2.12402 + 14.6760i 0.0921746 + 0.636884i
\(532\) 0 0
\(533\) 12.6716 + 21.9478i 0.548866 + 0.950665i
\(534\) 0 0
\(535\) −2.64123 −0.114190
\(536\) 0 0
\(537\) 32.8299 + 6.31162i 1.41671 + 0.272366i
\(538\) 0 0
\(539\) 3.08331 3.54876i 0.132808 0.152856i
\(540\) 0 0
\(541\) −7.37443 + 12.7729i −0.317052 + 0.549150i −0.979871 0.199629i \(-0.936026\pi\)
0.662820 + 0.748779i \(0.269360\pi\)
\(542\) 0 0
\(543\) −24.8994 + 28.7624i −1.06854 + 1.23431i
\(544\) 0 0
\(545\) −0.364621 + 0.631542i −0.0156187 + 0.0270523i
\(546\) 0 0
\(547\) 6.57905 + 11.3952i 0.281300 + 0.487226i 0.971705 0.236197i \(-0.0759011\pi\)
−0.690405 + 0.723423i \(0.742568\pi\)
\(548\) 0 0
\(549\) 1.51307 + 10.4546i 0.0645764 + 0.446193i
\(550\) 0 0
\(551\) 0.463706 0.0197545
\(552\) 0 0
\(553\) 26.3696 + 2.53573i 1.12135 + 0.107830i
\(554\) 0 0
\(555\) 3.71483 4.29117i 0.157686 0.182150i
\(556\) 0 0
\(557\) −12.1869 21.1083i −0.516374 0.894385i −0.999819 0.0190111i \(-0.993948\pi\)
0.483446 0.875374i \(-0.339385\pi\)
\(558\) 0 0
\(559\) −23.7787 −1.00573
\(560\) 0 0
\(561\) 1.67517 1.93506i 0.0707256 0.0816984i
\(562\) 0 0
\(563\) −3.11965 −0.131478 −0.0657388 0.997837i \(-0.520940\pi\)
−0.0657388 + 0.997837i \(0.520940\pi\)
\(564\) 0 0
\(565\) 5.38201 0.226423
\(566\) 0 0
\(567\) 23.3761 4.53429i 0.981702 0.190422i
\(568\) 0 0
\(569\) −21.4769 −0.900358 −0.450179 0.892938i \(-0.648640\pi\)
−0.450179 + 0.892938i \(0.648640\pi\)
\(570\) 0 0
\(571\) 33.0460 1.38293 0.691466 0.722409i \(-0.256965\pi\)
0.691466 + 0.722409i \(0.256965\pi\)
\(572\) 0 0
\(573\) −7.54717 + 8.71808i −0.315287 + 0.364203i
\(574\) 0 0
\(575\) −20.4646 −0.853432
\(576\) 0 0
\(577\) 0.904826 + 1.56720i 0.0376684 + 0.0652436i 0.884245 0.467023i \(-0.154674\pi\)
−0.846577 + 0.532267i \(0.821340\pi\)
\(578\) 0 0
\(579\) −7.19757 + 8.31425i −0.299121 + 0.345528i
\(580\) 0 0
\(581\) −5.42980 11.9106i −0.225266 0.494136i
\(582\) 0 0
\(583\) −8.22473 −0.340633
\(584\) 0 0
\(585\) 0.474724 + 3.28012i 0.0196274 + 0.135616i
\(586\) 0 0
\(587\) 1.65901 + 2.87349i 0.0684746 + 0.118601i 0.898230 0.439526i \(-0.144853\pi\)
−0.829755 + 0.558127i \(0.811520\pi\)
\(588\) 0 0
\(589\) 0.504173 0.873253i 0.0207741 0.0359818i
\(590\) 0 0
\(591\) −26.9934 + 31.1813i −1.11036 + 1.28263i
\(592\) 0 0
\(593\) 15.3784 26.6362i 0.631516 1.09382i −0.355726 0.934590i \(-0.615766\pi\)
0.987242 0.159228i \(-0.0509005\pi\)
\(594\) 0 0
\(595\) 1.14985 1.61246i 0.0471391 0.0661042i
\(596\) 0 0
\(597\) 35.6410 + 6.85205i 1.45869 + 0.280436i
\(598\) 0 0
\(599\) 13.9705 0.570817 0.285409 0.958406i \(-0.407871\pi\)
0.285409 + 0.958406i \(0.407871\pi\)
\(600\) 0 0
\(601\) −7.50432 12.9979i −0.306108 0.530194i 0.671400 0.741096i \(-0.265693\pi\)
−0.977507 + 0.210901i \(0.932360\pi\)
\(602\) 0 0
\(603\) −5.29408 36.5796i −0.215591 1.48964i
\(604\) 0 0
\(605\) 1.79438 3.10796i 0.0729519 0.126356i
\(606\) 0 0
\(607\) −11.6644 20.2034i −0.473444 0.820030i 0.526093 0.850427i \(-0.323656\pi\)
−0.999538 + 0.0303969i \(0.990323\pi\)
\(608\) 0 0
\(609\) 4.21087 + 1.23734i 0.170633 + 0.0501397i
\(610\) 0 0
\(611\) −4.38239 + 7.59052i −0.177292 + 0.307080i
\(612\) 0 0
\(613\) 22.3374 + 38.6895i 0.902198 + 1.56265i 0.824635 + 0.565666i \(0.191381\pi\)
0.0775635 + 0.996987i \(0.475286\pi\)
\(614\) 0 0
\(615\) −3.00979 + 3.47674i −0.121366 + 0.140196i
\(616\) 0 0
\(617\) −1.18488 + 2.05227i −0.0477013 + 0.0826212i −0.888890 0.458120i \(-0.848523\pi\)
0.841189 + 0.540741i \(0.181856\pi\)
\(618\) 0 0
\(619\) 11.3863 19.7217i 0.457655 0.792682i −0.541181 0.840906i \(-0.682023\pi\)
0.998837 + 0.0482236i \(0.0153560\pi\)
\(620\) 0 0
\(621\) 1.00559 21.7481i 0.0403530 0.872722i
\(622\) 0 0
\(623\) 26.1810 36.7142i 1.04892 1.47092i
\(624\) 0 0
\(625\) −11.6387 20.1588i −0.465547 0.806351i
\(626\) 0 0
\(627\) 0.553069 + 0.106329i 0.0220874 + 0.00424636i
\(628\) 0 0
\(629\) −21.1937 −0.845049
\(630\) 0 0
\(631\) 17.8652 0.711201 0.355600 0.934638i \(-0.384276\pi\)
0.355600 + 0.934638i \(0.384276\pi\)
\(632\) 0 0
\(633\) −7.17505 20.6998i −0.285183 0.822743i
\(634\) 0 0
\(635\) 2.36133 + 4.08995i 0.0937067 + 0.162305i
\(636\) 0 0
\(637\) 14.9091 17.1597i 0.590718 0.679891i
\(638\) 0 0
\(639\) 2.39477 + 16.5467i 0.0947355 + 0.654578i
\(640\) 0 0
\(641\) 12.7900 22.1529i 0.505175 0.874988i −0.494808 0.869003i \(-0.664761\pi\)
0.999982 0.00598543i \(-0.00190523\pi\)
\(642\) 0 0
\(643\) 7.99334 13.8449i 0.315227 0.545989i −0.664259 0.747503i \(-0.731253\pi\)
0.979486 + 0.201514i \(0.0645861\pi\)
\(644\) 0 0
\(645\) −1.41308 4.07670i −0.0556401 0.160520i
\(646\) 0 0
\(647\) 7.47306 + 12.9437i 0.293796 + 0.508870i 0.974704 0.223499i \(-0.0717479\pi\)
−0.680908 + 0.732369i \(0.738415\pi\)
\(648\) 0 0
\(649\) −1.65982 + 2.87489i −0.0651536 + 0.112849i
\(650\) 0 0
\(651\) 6.90851 6.58459i 0.270766 0.258070i
\(652\) 0 0
\(653\) 4.82885 + 8.36381i 0.188967 + 0.327301i 0.944906 0.327341i \(-0.106153\pi\)
−0.755939 + 0.654642i \(0.772819\pi\)
\(654\) 0 0
\(655\) 0.710233 1.23016i 0.0277511 0.0480663i
\(656\) 0 0
\(657\) −17.5171 + 13.8020i −0.683406 + 0.538466i
\(658\) 0 0
\(659\) 9.80353 + 16.9802i 0.381891 + 0.661455i 0.991333 0.131376i \(-0.0419396\pi\)
−0.609441 + 0.792831i \(0.708606\pi\)
\(660\) 0 0
\(661\) −10.2655 −0.399281 −0.199641 0.979869i \(-0.563977\pi\)
−0.199641 + 0.979869i \(0.563977\pi\)
\(662\) 0 0
\(663\) 8.10011 9.35682i 0.314582 0.363389i
\(664\) 0 0
\(665\) 0.433792 + 0.0417140i 0.0168217 + 0.00161760i
\(666\) 0 0
\(667\) 2.00641 3.47520i 0.0776885 0.134560i
\(668\) 0 0
\(669\) 4.57312 + 0.879192i 0.176807 + 0.0339915i
\(670\) 0 0
\(671\) −1.18239 + 2.04797i −0.0456458 + 0.0790608i
\(672\) 0 0
\(673\) −17.1584 29.7191i −0.661406 1.14559i −0.980246 0.197780i \(-0.936627\pi\)
0.318840 0.947808i \(-0.396707\pi\)
\(674\) 0 0
\(675\) 22.5419 11.6610i 0.867636 0.448830i
\(676\) 0 0
\(677\) 7.47419 0.287256 0.143628 0.989632i \(-0.454123\pi\)
0.143628 + 0.989632i \(0.454123\pi\)
\(678\) 0 0
\(679\) −9.29910 20.3982i −0.356867 0.782810i
\(680\) 0 0
\(681\) −15.8767 45.8038i −0.608397 1.75521i
\(682\) 0 0
\(683\) −18.1577 31.4501i −0.694786 1.20340i −0.970253 0.242094i \(-0.922166\pi\)
0.275467 0.961310i \(-0.411167\pi\)
\(684\) 0 0
\(685\) −4.34125 −0.165871
\(686\) 0 0
\(687\) 41.7384 + 8.02429i 1.59242 + 0.306146i
\(688\) 0 0
\(689\) −39.7699 −1.51511
\(690\) 0 0
\(691\) 50.9624 1.93870 0.969350 0.245684i \(-0.0790126\pi\)
0.969350 + 0.245684i \(0.0790126\pi\)
\(692\) 0 0
\(693\) 4.73863 + 2.44136i 0.180006 + 0.0927395i
\(694\) 0 0
\(695\) −4.05509 −0.153818
\(696\) 0 0
\(697\) 17.1713 0.650410
\(698\) 0 0
\(699\) −5.23971 15.1164i −0.198184 0.571755i
\(700\) 0 0
\(701\) 36.6075 1.38265 0.691324 0.722545i \(-0.257028\pi\)
0.691324 + 0.722545i \(0.257028\pi\)
\(702\) 0 0
\(703\) −2.33182 4.03883i −0.0879463 0.152327i
\(704\) 0 0
\(705\) −1.56178 0.300255i −0.0588199 0.0113083i
\(706\) 0 0
\(707\) −7.02600 + 9.85272i −0.264240 + 0.370550i
\(708\) 0 0
\(709\) −5.87578 −0.220670 −0.110335 0.993894i \(-0.535192\pi\)
−0.110335 + 0.993894i \(0.535192\pi\)
\(710\) 0 0
\(711\) 4.30253 + 29.7285i 0.161357 + 1.11491i
\(712\) 0 0
\(713\) −4.36301 7.55695i −0.163396 0.283010i
\(714\) 0 0
\(715\) −0.370973 + 0.642545i −0.0138736 + 0.0240298i
\(716\) 0 0
\(717\) 15.8976 + 45.8641i 0.593707 + 1.71283i
\(718\) 0 0
\(719\) −8.09642 + 14.0234i −0.301945 + 0.522985i −0.976577 0.215170i \(-0.930969\pi\)
0.674631 + 0.738155i \(0.264303\pi\)
\(720\) 0 0
\(721\) −1.98328 4.35046i −0.0738614 0.162020i
\(722\) 0 0
\(723\) −11.2477 32.4494i −0.418308 1.20681i
\(724\) 0 0
\(725\) 4.67783 0.173730
\(726\) 0 0
\(727\) −22.8771 39.6243i −0.848464 1.46958i −0.882578 0.470166i \(-0.844194\pi\)
0.0341138 0.999418i \(-0.489139\pi\)
\(728\) 0 0
\(729\) 11.2847 + 24.5287i 0.417951 + 0.908470i
\(730\) 0 0
\(731\) −8.05565 + 13.9528i −0.297949 + 0.516063i
\(732\) 0 0
\(733\) −13.5916 23.5414i −0.502019 0.869522i −0.999997 0.00233276i \(-0.999257\pi\)
0.497978 0.867189i \(-0.334076\pi\)
\(734\) 0 0
\(735\) 3.82791 + 1.53632i 0.141195 + 0.0566682i
\(736\) 0 0
\(737\) 4.13706 7.16560i 0.152391 0.263948i
\(738\) 0 0
\(739\) 12.1738 + 21.0856i 0.447821 + 0.775648i 0.998244 0.0592377i \(-0.0188670\pi\)
−0.550423 + 0.834886i \(0.685534\pi\)
\(740\) 0 0
\(741\) 2.67431 + 0.514142i 0.0982433 + 0.0188875i
\(742\) 0 0
\(743\) −0.0683178 + 0.118330i −0.00250634 + 0.00434110i −0.867276 0.497828i \(-0.834131\pi\)
0.864770 + 0.502169i \(0.167464\pi\)
\(744\) 0 0
\(745\) 1.82874 3.16747i 0.0669998 0.116047i
\(746\) 0 0
\(747\) 11.6585 9.18591i 0.426562 0.336095i
\(748\) 0 0
\(749\) −11.9261 + 16.7242i −0.435769 + 0.611090i
\(750\) 0 0
\(751\) −3.71446 6.43364i −0.135543 0.234767i 0.790262 0.612769i \(-0.209944\pi\)
−0.925805 + 0.378002i \(0.876611\pi\)
\(752\) 0 0
\(753\) −18.7912 + 21.7066i −0.684789 + 0.791031i
\(754\) 0 0
\(755\) −0.878055 −0.0319557
\(756\) 0 0
\(757\) −14.0794 −0.511723 −0.255861 0.966713i \(-0.582359\pi\)
−0.255861 + 0.966713i \(0.582359\pi\)
\(758\) 0 0
\(759\) 3.18994 3.68485i 0.115788 0.133752i
\(760\) 0 0
\(761\) −19.3616 33.5353i −0.701858 1.21565i −0.967813 0.251669i \(-0.919021\pi\)
0.265955 0.963985i \(-0.414313\pi\)
\(762\) 0 0
\(763\) 2.35252 + 5.16041i 0.0851671 + 0.186819i
\(764\) 0 0
\(765\) 2.08553 + 0.832671i 0.0754025 + 0.0301053i
\(766\) 0 0
\(767\) −8.02589 + 13.9013i −0.289798 + 0.501945i
\(768\) 0 0
\(769\) 5.14295 8.90786i 0.185460 0.321226i −0.758272 0.651939i \(-0.773956\pi\)
0.943731 + 0.330713i \(0.107289\pi\)
\(770\) 0 0
\(771\) 12.4081 + 2.38548i 0.446867 + 0.0859111i
\(772\) 0 0
\(773\) −22.6768 39.2773i −0.815627 1.41271i −0.908877 0.417064i \(-0.863059\pi\)
0.0932501 0.995643i \(-0.470274\pi\)
\(774\) 0 0
\(775\) 5.08606 8.80931i 0.182697 0.316440i
\(776\) 0 0
\(777\) −10.3979 42.8984i −0.373022 1.53897i
\(778\) 0 0
\(779\) 1.88926 + 3.27229i 0.0676898 + 0.117242i
\(780\) 0 0
\(781\) −1.87139 + 3.24135i −0.0669637 + 0.115985i
\(782\) 0 0
\(783\) −0.229860 + 4.97123i −0.00821453 + 0.177657i
\(784\) 0 0
\(785\) −1.36028 2.35607i −0.0485504 0.0840917i
\(786\) 0 0
\(787\) 26.1087 0.930675 0.465337 0.885133i \(-0.345933\pi\)
0.465337 + 0.885133i \(0.345933\pi\)
\(788\) 0 0
\(789\) 15.1911 + 43.8259i 0.540818 + 1.56024i
\(790\) 0 0
\(791\) 24.3017 34.0788i 0.864067 1.21170i
\(792\) 0 0
\(793\) −5.71735 + 9.90274i −0.203029 + 0.351657i
\(794\) 0 0
\(795\) −2.36339 6.81830i −0.0838207 0.241820i
\(796\) 0 0
\(797\) −16.1618 + 27.9931i −0.572481 + 0.991567i 0.423829 + 0.905742i \(0.360686\pi\)
−0.996310 + 0.0858244i \(0.972648\pi\)
\(798\) 0 0
\(799\) 2.96930 + 5.14298i 0.105046 + 0.181946i
\(800\) 0 0
\(801\) 47.4857 + 18.9592i 1.67782 + 0.669890i
\(802\) 0 0
\(803\) −4.99240 −0.176178
\(804\) 0 0
\(805\) 2.18960 3.07052i 0.0771731 0.108222i
\(806\) 0 0
\(807\) −34.6273 6.65716i −1.21894 0.234343i
\(808\) 0 0
\(809\) 22.4553 + 38.8938i 0.789488 + 1.36743i 0.926281 + 0.376833i \(0.122987\pi\)
−0.136793 + 0.990600i \(0.543680\pi\)
\(810\) 0 0
\(811\) 42.8204 1.50363 0.751813 0.659376i \(-0.229180\pi\)
0.751813 + 0.659376i \(0.229180\pi\)
\(812\) 0 0
\(813\) 6.19268 + 17.8657i 0.217187 + 0.626578i
\(814\) 0 0
\(815\) −2.81214 −0.0985049
\(816\) 0 0
\(817\) −3.54527 −0.124033
\(818\) 0 0
\(819\) 22.9132 + 11.8050i 0.800653 + 0.412499i
\(820\) 0 0
\(821\) −32.2200 −1.12448 −0.562242 0.826972i \(-0.690061\pi\)
−0.562242 + 0.826972i \(0.690061\pi\)
\(822\) 0 0
\(823\) 4.38841 0.152970 0.0764851 0.997071i \(-0.475630\pi\)
0.0764851 + 0.997071i \(0.475630\pi\)
\(824\) 0 0
\(825\) 5.57932 + 1.07264i 0.194247 + 0.0373444i
\(826\) 0 0
\(827\) −42.0996 −1.46395 −0.731973 0.681333i \(-0.761400\pi\)
−0.731973 + 0.681333i \(0.761400\pi\)
\(828\) 0 0
\(829\) −5.55838 9.62739i −0.193050 0.334373i 0.753209 0.657781i \(-0.228505\pi\)
−0.946260 + 0.323408i \(0.895171\pi\)
\(830\) 0 0
\(831\) −10.0256 28.9236i −0.347785 1.00335i
\(832\) 0 0
\(833\) −5.01809 14.5616i −0.173866 0.504530i
\(834\) 0 0
\(835\) −6.11941 −0.211771
\(836\) 0 0
\(837\) 9.11192 + 5.83793i 0.314954 + 0.201788i
\(838\) 0 0
\(839\) −27.2669 47.2277i −0.941360 1.63048i −0.762881 0.646539i \(-0.776216\pi\)
−0.178479 0.983944i \(-0.557118\pi\)
\(840\) 0 0
\(841\) 14.0414 24.3204i 0.484185 0.838633i
\(842\) 0 0
\(843\) −24.4118 4.69322i −0.840788 0.161643i
\(844\) 0 0
\(845\) 0.417494 0.723120i 0.0143622 0.0248761i
\(846\) 0 0
\(847\) −11.5773 25.3955i −0.397800 0.872600i
\(848\) 0 0
\(849\) −11.0285 + 12.7396i −0.378499 + 0.437221i
\(850\) 0 0
\(851\) −40.3582 −1.38346
\(852\) 0 0
\(853\) −11.3669 19.6880i −0.389194 0.674105i 0.603147 0.797630i \(-0.293913\pi\)
−0.992341 + 0.123526i \(0.960580\pi\)
\(854\) 0 0
\(855\) 0.0707787 + 0.489048i 0.00242058 + 0.0167251i
\(856\) 0 0
\(857\) −5.61928 + 9.73288i −0.191951 + 0.332469i −0.945897 0.324468i \(-0.894815\pi\)
0.753946 + 0.656937i \(0.228148\pi\)
\(858\) 0 0
\(859\) −25.4024 43.9983i −0.866720 1.50120i −0.865329 0.501204i \(-0.832891\pi\)
−0.00139066 0.999999i \(-0.500443\pi\)
\(860\) 0 0
\(861\) 8.42444 + 34.7566i 0.287104 + 1.18450i
\(862\) 0 0
\(863\) −0.340985 + 0.590603i −0.0116073 + 0.0201044i −0.871771 0.489914i \(-0.837028\pi\)
0.860163 + 0.510018i \(0.170361\pi\)
\(864\) 0 0
\(865\) 2.89141 + 5.00807i 0.0983110 + 0.170280i
\(866\) 0 0
\(867\) 6.89716 + 19.8981i 0.234240 + 0.675775i
\(868\) 0 0
\(869\) −3.36222 + 5.82353i −0.114055 + 0.197550i
\(870\) 0 0
\(871\) 20.0044 34.6486i 0.677822 1.17402i
\(872\) 0 0
\(873\) 19.9664 15.7318i 0.675760 0.532441i
\(874\) 0 0
\(875\) 8.85583 + 0.851587i 0.299382 + 0.0287889i
\(876\) 0 0
\(877\) 12.6595 + 21.9269i 0.427480 + 0.740418i 0.996648 0.0818035i \(-0.0260680\pi\)
−0.569168 + 0.822221i \(0.692735\pi\)
\(878\) 0 0
\(879\) 7.10600 + 20.5006i 0.239680 + 0.691468i
\(880\) 0 0
\(881\) −30.9482 −1.04267 −0.521335 0.853352i \(-0.674566\pi\)
−0.521335 + 0.853352i \(0.674566\pi\)
\(882\) 0 0
\(883\) 9.48501 0.319196 0.159598 0.987182i \(-0.448980\pi\)
0.159598 + 0.987182i \(0.448980\pi\)
\(884\) 0 0
\(885\) −2.86024 0.549886i −0.0961458 0.0184842i
\(886\) 0 0
\(887\) −1.97469 3.42026i −0.0663036 0.114841i 0.830968 0.556320i \(-0.187787\pi\)
−0.897272 + 0.441479i \(0.854454\pi\)
\(888\) 0 0
\(889\) 36.5597 + 3.51563i 1.22617 + 0.117910i
\(890\) 0 0
\(891\) −1.41407 + 5.87655i −0.0473731 + 0.196872i
\(892\) 0 0
\(893\) −0.653390 + 1.13170i −0.0218649 + 0.0378710i
\(894\) 0 0
\(895\) −3.28318 + 5.68663i −0.109745 + 0.190083i
\(896\) 0 0
\(897\) 15.4247 17.8177i 0.515015 0.594917i
\(898\) 0 0
\(899\) 0.997305 + 1.72738i 0.0332620 + 0.0576115i
\(900\) 0 0
\(901\) −13.4731 + 23.3361i −0.448854 + 0.777439i
\(902\) 0 0
\(903\) −32.1942 9.46012i −1.07136 0.314813i
\(904\) 0 0
\(905\) −3.73609 6.47109i −0.124192 0.215106i
\(906\) 0 0
\(907\) 16.7531 29.0171i 0.556276 0.963498i −0.441527 0.897248i \(-0.645563\pi\)
0.997803 0.0662505i \(-0.0211036\pi\)
\(908\) 0 0
\(909\) −12.7434 5.08794i −0.422671 0.168756i
\(910\) 0 0
\(911\) 5.26585 + 9.12072i 0.174465 + 0.302183i 0.939976 0.341240i \(-0.110847\pi\)
−0.765511 + 0.643423i \(0.777514\pi\)
\(912\) 0 0
\(913\) 3.32269 0.109965
\(914\) 0 0
\(915\) −2.03753 0.391719i −0.0673585 0.0129498i
\(916\) 0 0
\(917\) −4.58240 10.0518i −0.151324 0.331939i
\(918\) 0 0
\(919\) 1.81600 3.14540i 0.0599042 0.103757i −0.834518 0.550981i \(-0.814254\pi\)
0.894422 + 0.447224i \(0.147587\pi\)
\(920\) 0 0
\(921\) −29.3327 + 33.8836i −0.966546 + 1.11650i
\(922\) 0 0
\(923\) −9.04894 + 15.6732i −0.297850 + 0.515891i
\(924\) 0 0
\(925\) −23.5232 40.7435i −0.773440 1.33964i
\(926\) 0 0
\(927\) 4.25837 3.35523i 0.139863 0.110200i
\(928\) 0 0
\(929\) 13.6058 0.446392 0.223196 0.974774i \(-0.428351\pi\)
0.223196 + 0.974774i \(0.428351\pi\)
\(930\) 0 0
\(931\) 2.22286 2.55841i 0.0728512 0.0838486i
\(932\) 0 0
\(933\) −32.1956 + 37.1906i −1.05404 + 1.21757i
\(934\) 0 0
\(935\) 0.251354 + 0.435358i 0.00822016 + 0.0142377i
\(936\) 0 0
\(937\) 9.98770 0.326284 0.163142 0.986603i \(-0.447837\pi\)
0.163142 + 0.986603i \(0.447837\pi\)
\(938\) 0 0
\(939\) 13.8321 15.9781i 0.451394 0.521426i
\(940\) 0 0
\(941\) 34.6209 1.12861 0.564305 0.825566i \(-0.309144\pi\)
0.564305 + 0.825566i \(0.309144\pi\)
\(942\) 0 0
\(943\) 32.6985 1.06481
\(944\) 0 0
\(945\) −0.662233 + 4.62986i −0.0215424 + 0.150609i
\(946\) 0 0
\(947\) 49.2171 1.59934 0.799670 0.600440i \(-0.205008\pi\)
0.799670 + 0.600440i \(0.205008\pi\)
\(948\) 0 0
\(949\) −24.1403 −0.783626
\(950\) 0 0
\(951\) 4.48037 5.17548i 0.145286 0.167827i
\(952\) 0 0
\(953\) 14.2310 0.460987 0.230494 0.973074i \(-0.425966\pi\)
0.230494 + 0.973074i \(0.425966\pi\)
\(954\) 0 0
\(955\) −1.13243 1.96143i −0.0366446 0.0634704i
\(956\) 0 0
\(957\) −0.729163 + 0.842290i −0.0235705 + 0.0272274i
\(958\) 0 0
\(959\) −19.6022 + 27.4887i −0.632990 + 0.887656i
\(960\) 0 0
\(961\) −26.6626 −0.860085
\(962\) 0 0
\(963\) −21.6309 8.63638i −0.697046 0.278303i
\(964\) 0 0
\(965\) −1.07998 1.87057i −0.0347657 0.0602159i
\(966\) 0 0
\(967\) −19.4246 + 33.6443i −0.624652 + 1.08193i 0.363956 + 0.931416i \(0.381426\pi\)
−0.988608 + 0.150513i \(0.951908\pi\)
\(968\) 0 0
\(969\) 1.20768 1.39505i 0.0387963 0.0448154i
\(970\) 0 0
\(971\) −4.13629 + 7.16427i −0.132740 + 0.229912i −0.924732 0.380619i \(-0.875711\pi\)
0.791992 + 0.610532i \(0.209044\pi\)
\(972\) 0 0
\(973\) −18.3102 + 25.6768i −0.586997 + 0.823159i
\(974\) 0 0
\(975\) 26.9783 + 5.18663i 0.863996 + 0.166105i
\(976\) 0 0
\(977\) 7.37473 0.235938 0.117969 0.993017i \(-0.462362\pi\)
0.117969 + 0.993017i \(0.462362\pi\)
\(978\) 0 0
\(979\) 5.72312 + 9.91273i 0.182912 + 0.316812i
\(980\) 0 0
\(981\) −5.05118 + 3.97990i −0.161272 + 0.127068i
\(982\) 0 0
\(983\) 2.39181 4.14274i 0.0762870 0.132133i −0.825358 0.564609i \(-0.809027\pi\)
0.901645 + 0.432476i \(0.142360\pi\)
\(984\) 0 0
\(985\) −4.05029 7.01530i −0.129053 0.223526i
\(986\) 0 0
\(987\) −8.95318 + 8.53339i −0.284983 + 0.271621i
\(988\) 0 0
\(989\) −15.3400 + 26.5697i −0.487784 + 0.844866i
\(990\) 0 0
\(991\) 18.4932 + 32.0312i 0.587456 + 1.01750i 0.994564 + 0.104124i \(0.0332038\pi\)
−0.407108 + 0.913380i \(0.633463\pi\)
\(992\) 0 0
\(993\) 10.0700 11.6323i 0.319562 0.369140i
\(994\) 0 0
\(995\) −3.56430 + 6.17356i −0.112996 + 0.195715i
\(996\) 0 0
\(997\) −24.3285 + 42.1382i −0.770491 + 1.33453i 0.166803 + 0.985990i \(0.446656\pi\)
−0.937294 + 0.348539i \(0.886678\pi\)
\(998\) 0 0
\(999\) 44.4548 22.9966i 1.40649 0.727579i
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 504.2.q.d.121.4 yes 22
3.2 odd 2 1512.2.q.c.793.7 22
4.3 odd 2 1008.2.q.k.625.8 22
7.4 even 3 504.2.t.d.193.11 yes 22
9.2 odd 6 1512.2.t.d.289.5 22
9.7 even 3 504.2.t.d.457.11 yes 22
12.11 even 2 3024.2.q.k.2305.7 22
21.11 odd 6 1512.2.t.d.361.5 22
28.11 odd 6 1008.2.t.k.193.1 22
36.7 odd 6 1008.2.t.k.961.1 22
36.11 even 6 3024.2.t.l.289.5 22
63.11 odd 6 1512.2.q.c.1369.7 22
63.25 even 3 inner 504.2.q.d.25.4 22
84.11 even 6 3024.2.t.l.1873.5 22
252.11 even 6 3024.2.q.k.2881.7 22
252.151 odd 6 1008.2.q.k.529.8 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.q.d.25.4 22 63.25 even 3 inner
504.2.q.d.121.4 yes 22 1.1 even 1 trivial
504.2.t.d.193.11 yes 22 7.4 even 3
504.2.t.d.457.11 yes 22 9.7 even 3
1008.2.q.k.529.8 22 252.151 odd 6
1008.2.q.k.625.8 22 4.3 odd 2
1008.2.t.k.193.1 22 28.11 odd 6
1008.2.t.k.961.1 22 36.7 odd 6
1512.2.q.c.793.7 22 3.2 odd 2
1512.2.q.c.1369.7 22 63.11 odd 6
1512.2.t.d.289.5 22 9.2 odd 6
1512.2.t.d.361.5 22 21.11 odd 6
3024.2.q.k.2305.7 22 12.11 even 2
3024.2.q.k.2881.7 22 252.11 even 6
3024.2.t.l.289.5 22 36.11 even 6
3024.2.t.l.1873.5 22 84.11 even 6