Properties

Label 920.2.bv.a.17.17
Level $920$
Weight $2$
Character 920.17
Analytic conductor $7.346$
Analytic rank $0$
Dimension $720$
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [920,2,Mod(17,920)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(920, base_ring=CyclotomicField(44))
 
chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("920.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 920.bv (of order \(44\), degree \(20\), 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: \(7.34623698596\)
Analytic rank: \(0\)
Dimension: \(720\)
Relative dimension: \(36\) over \(\Q(\zeta_{44})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label 17.17
Character \(\chi\) \(=\) 920.17
Dual form 920.2.bv.a.433.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0822135 + 0.0448920i) q^{3} +(-1.59045 - 1.57177i) q^{5} +(3.12275 + 4.17150i) q^{7} +(-1.61718 + 2.51638i) q^{9} +(-3.36211 + 1.53542i) q^{11} +(-1.74996 - 1.31000i) q^{13} +(0.201316 + 0.0578226i) q^{15} +(-0.442284 - 6.18393i) q^{17} +(-2.05565 - 2.37235i) q^{19} +(-0.443999 - 0.202768i) q^{21} +(-4.77306 + 0.466813i) q^{23} +(0.0590597 + 4.99965i) q^{25} +(0.0400361 - 0.559777i) q^{27} +(-1.75914 - 1.52430i) q^{29} +(-0.693792 + 0.203716i) q^{31} +(0.207482 - 0.277164i) q^{33} +(1.59008 - 11.5428i) q^{35} +(-8.16416 + 1.77600i) q^{37} +(0.202679 + 0.0291408i) q^{39} +(-4.34358 + 2.79145i) q^{41} +(0.396781 + 0.726651i) q^{43} +(6.52722 - 1.46034i) q^{45} +(6.39744 + 6.39744i) q^{47} +(-5.67774 + 19.3366i) q^{49} +(0.313971 + 0.488548i) q^{51} +(-8.20433 + 6.14168i) q^{53} +(7.76059 + 2.84245i) q^{55} +(0.275502 + 0.102757i) q^{57} +(-1.11563 + 0.160403i) q^{59} +(1.41688 + 4.82546i) q^{61} +(-15.5471 + 1.11195i) q^{63} +(0.724194 + 4.83403i) q^{65} +(1.29574 + 3.47401i) q^{67} +(0.371454 - 0.252650i) q^{69} +(5.27911 - 11.5596i) q^{71} +(1.25599 + 0.0898299i) q^{73} +(-0.229300 - 0.408388i) q^{75} +(-16.9040 - 9.23029i) q^{77} +(0.267327 + 1.85930i) q^{79} +(-3.70596 - 8.11493i) q^{81} +(-3.06361 - 14.0832i) q^{83} +(-9.01631 + 10.5304i) q^{85} +(0.213054 + 0.0463470i) q^{87} +(11.9814 + 3.51804i) q^{89} -11.3907i q^{91} +(0.0478939 - 0.0478939i) q^{93} +(-0.459383 + 7.00411i) q^{95} +(-2.27190 + 10.4438i) q^{97} +(1.57342 - 10.9434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/920\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(281\) \(461\) \(737\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{22}\right)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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
\(3\) −0.0822135 + 0.0448920i −0.0474660 + 0.0259184i −0.502807 0.864399i \(-0.667699\pi\)
0.455341 + 0.890317i \(0.349517\pi\)
\(4\) 0 0
\(5\) −1.59045 1.57177i −0.711271 0.702918i
\(6\) 0 0
\(7\) 3.12275 + 4.17150i 1.18029 + 1.57668i 0.729381 + 0.684107i \(0.239808\pi\)
0.450906 + 0.892572i \(0.351101\pi\)
\(8\) 0 0
\(9\) −1.61718 + 2.51638i −0.539060 + 0.838793i
\(10\) 0 0
\(11\) −3.36211 + 1.53542i −1.01371 + 0.462947i −0.851805 0.523859i \(-0.824492\pi\)
−0.161908 + 0.986806i \(0.551765\pi\)
\(12\) 0 0
\(13\) −1.74996 1.31000i −0.485351 0.363329i 0.328404 0.944537i \(-0.393489\pi\)
−0.813755 + 0.581208i \(0.802580\pi\)
\(14\) 0 0
\(15\) 0.201316 + 0.0578226i 0.0519797 + 0.0149297i
\(16\) 0 0
\(17\) −0.442284 6.18393i −0.107270 1.49982i −0.711314 0.702874i \(-0.751900\pi\)
0.604045 0.796950i \(-0.293555\pi\)
\(18\) 0 0
\(19\) −2.05565 2.37235i −0.471599 0.544254i 0.469257 0.883062i \(-0.344522\pi\)
−0.940856 + 0.338808i \(0.889976\pi\)
\(20\) 0 0
\(21\) −0.443999 0.202768i −0.0968885 0.0442475i
\(22\) 0 0
\(23\) −4.77306 + 0.466813i −0.995251 + 0.0973372i
\(24\) 0 0
\(25\) 0.0590597 + 4.99965i 0.0118119 + 0.999930i
\(26\) 0 0
\(27\) 0.0400361 0.559777i 0.00770494 0.107729i
\(28\) 0 0
\(29\) −1.75914 1.52430i −0.326664 0.283056i 0.476053 0.879417i \(-0.342067\pi\)
−0.802716 + 0.596361i \(0.796613\pi\)
\(30\) 0 0
\(31\) −0.693792 + 0.203716i −0.124609 + 0.0365884i −0.343442 0.939174i \(-0.611593\pi\)
0.218834 + 0.975762i \(0.429775\pi\)
\(32\) 0 0
\(33\) 0.207482 0.277164i 0.0361181 0.0482481i
\(34\) 0 0
\(35\) 1.59008 11.5428i 0.268773 1.95109i
\(36\) 0 0
\(37\) −8.16416 + 1.77600i −1.34218 + 0.291973i −0.825595 0.564263i \(-0.809160\pi\)
−0.516584 + 0.856236i \(0.672797\pi\)
\(38\) 0 0
\(39\) 0.202679 + 0.0291408i 0.0324546 + 0.00466626i
\(40\) 0 0
\(41\) −4.34358 + 2.79145i −0.678354 + 0.435951i −0.833928 0.551873i \(-0.813913\pi\)
0.155575 + 0.987824i \(0.450277\pi\)
\(42\) 0 0
\(43\) 0.396781 + 0.726651i 0.0605086 + 0.110813i 0.906183 0.422886i \(-0.138983\pi\)
−0.845674 + 0.533700i \(0.820801\pi\)
\(44\) 0 0
\(45\) 6.52722 1.46034i 0.973020 0.217694i
\(46\) 0 0
\(47\) 6.39744 + 6.39744i 0.933163 + 0.933163i 0.997902 0.0647394i \(-0.0206216\pi\)
−0.0647394 + 0.997902i \(0.520622\pi\)
\(48\) 0 0
\(49\) −5.67774 + 19.3366i −0.811106 + 2.76237i
\(50\) 0 0
\(51\) 0.313971 + 0.488548i 0.0439647 + 0.0684104i
\(52\) 0 0
\(53\) −8.20433 + 6.14168i −1.12695 + 0.843625i −0.989161 0.146836i \(-0.953091\pi\)
−0.137790 + 0.990461i \(0.544000\pi\)
\(54\) 0 0
\(55\) 7.76059 + 2.84245i 1.04644 + 0.383277i
\(56\) 0 0
\(57\) 0.275502 + 0.102757i 0.0364911 + 0.0136105i
\(58\) 0 0
\(59\) −1.11563 + 0.160403i −0.145242 + 0.0208827i −0.214552 0.976712i \(-0.568829\pi\)
0.0693102 + 0.997595i \(0.477920\pi\)
\(60\) 0 0
\(61\) 1.41688 + 4.82546i 0.181413 + 0.617837i 0.999110 + 0.0421875i \(0.0134327\pi\)
−0.817696 + 0.575650i \(0.804749\pi\)
\(62\) 0 0
\(63\) −15.5471 + 1.11195i −1.95875 + 0.140093i
\(64\) 0 0
\(65\) 0.724194 + 4.83403i 0.0898252 + 0.599587i
\(66\) 0 0
\(67\) 1.29574 + 3.47401i 0.158300 + 0.424418i 0.991752 0.128174i \(-0.0409115\pi\)
−0.833452 + 0.552592i \(0.813639\pi\)
\(68\) 0 0
\(69\) 0.371454 0.252650i 0.0447178 0.0304155i
\(70\) 0 0
\(71\) 5.27911 11.5596i 0.626515 1.37188i −0.284169 0.958774i \(-0.591718\pi\)
0.910684 0.413103i \(-0.135555\pi\)
\(72\) 0 0
\(73\) 1.25599 + 0.0898299i 0.147002 + 0.0105138i 0.144646 0.989483i \(-0.453796\pi\)
0.00235582 + 0.999997i \(0.499250\pi\)
\(74\) 0 0
\(75\) −0.229300 0.408388i −0.0264773 0.0471565i
\(76\) 0 0
\(77\) −16.9040 9.23029i −1.92639 1.05189i
\(78\) 0 0
\(79\) 0.267327 + 1.85930i 0.0300766 + 0.209187i 0.999318 0.0369245i \(-0.0117561\pi\)
−0.969241 + 0.246112i \(0.920847\pi\)
\(80\) 0 0
\(81\) −3.70596 8.11493i −0.411774 0.901658i
\(82\) 0 0
\(83\) −3.06361 14.0832i −0.336275 1.54583i −0.765982 0.642862i \(-0.777747\pi\)
0.429708 0.902968i \(-0.358617\pi\)
\(84\) 0 0
\(85\) −9.01631 + 10.5304i −0.977956 + 1.14218i
\(86\) 0 0
\(87\) 0.213054 + 0.0463470i 0.0228418 + 0.00496892i
\(88\) 0 0
\(89\) 11.9814 + 3.51804i 1.27002 + 0.372912i 0.846215 0.532841i \(-0.178876\pi\)
0.423806 + 0.905753i \(0.360694\pi\)
\(90\) 0 0
\(91\) 11.3907i 1.19407i
\(92\) 0 0
\(93\) 0.0478939 0.0478939i 0.00496637 0.00496637i
\(94\) 0 0
\(95\) −0.459383 + 7.00411i −0.0471317 + 0.718607i
\(96\) 0 0
\(97\) −2.27190 + 10.4438i −0.230677 + 1.06040i 0.705455 + 0.708754i \(0.250743\pi\)
−0.936132 + 0.351649i \(0.885621\pi\)
\(98\) 0 0
\(99\) 1.57342 10.9434i 0.158135 1.09985i
\(100\) 0 0
\(101\) −1.66564 1.07044i −0.165738 0.106513i 0.455142 0.890419i \(-0.349588\pi\)
−0.620880 + 0.783905i \(0.713225\pi\)
\(102\) 0 0
\(103\) 2.67522 7.17254i 0.263597 0.706731i −0.735962 0.677023i \(-0.763270\pi\)
0.999559 0.0297077i \(-0.00945764\pi\)
\(104\) 0 0
\(105\) 0.387453 + 1.02036i 0.0378116 + 0.0995766i
\(106\) 0 0
\(107\) −8.22621 + 15.0652i −0.795258 + 1.45641i 0.0923106 + 0.995730i \(0.470575\pi\)
−0.887568 + 0.460676i \(0.847607\pi\)
\(108\) 0 0
\(109\) 10.7923 12.4550i 1.03372 1.19297i 0.0527863 0.998606i \(-0.483190\pi\)
0.980929 0.194365i \(-0.0622648\pi\)
\(110\) 0 0
\(111\) 0.591476 0.512517i 0.0561404 0.0486459i
\(112\) 0 0
\(113\) 3.33266 1.24302i 0.313510 0.116933i −0.187784 0.982210i \(-0.560130\pi\)
0.501294 + 0.865277i \(0.332858\pi\)
\(114\) 0 0
\(115\) 8.32503 + 6.75972i 0.776313 + 0.630347i
\(116\) 0 0
\(117\) 6.12645 2.28505i 0.566391 0.211253i
\(118\) 0 0
\(119\) 24.4151 21.1558i 2.23813 1.93935i
\(120\) 0 0
\(121\) 1.74276 2.01126i 0.158433 0.182841i
\(122\) 0 0
\(123\) 0.231788 0.424487i 0.0208996 0.0382747i
\(124\) 0 0
\(125\) 7.76438 8.04452i 0.694468 0.719524i
\(126\) 0 0
\(127\) 1.08271 2.90286i 0.0960751 0.257587i −0.880018 0.474940i \(-0.842470\pi\)
0.976093 + 0.217353i \(0.0697423\pi\)
\(128\) 0 0
\(129\) −0.0652416 0.0419282i −0.00574420 0.00369157i
\(130\) 0 0
\(131\) 0.187109 1.30137i 0.0163478 0.113701i −0.980014 0.198931i \(-0.936253\pi\)
0.996361 + 0.0852292i \(0.0271623\pi\)
\(132\) 0 0
\(133\) 3.47697 15.9834i 0.301492 1.38594i
\(134\) 0 0
\(135\) −0.943518 + 0.827370i −0.0812051 + 0.0712087i
\(136\) 0 0
\(137\) −13.6508 + 13.6508i −1.16627 + 1.16627i −0.183188 + 0.983078i \(0.558642\pi\)
−0.983078 + 0.183188i \(0.941358\pi\)
\(138\) 0 0
\(139\) 14.1071i 1.19655i 0.801291 + 0.598275i \(0.204147\pi\)
−0.801291 + 0.598275i \(0.795853\pi\)
\(140\) 0 0
\(141\) −0.813150 0.238762i −0.0684796 0.0201074i
\(142\) 0 0
\(143\) 7.89495 + 1.71744i 0.660208 + 0.143620i
\(144\) 0 0
\(145\) 0.401964 + 5.18929i 0.0333813 + 0.430947i
\(146\) 0 0
\(147\) −0.401272 1.84462i −0.0330963 0.152141i
\(148\) 0 0
\(149\) −4.09582 8.96860i −0.335543 0.734736i 0.664377 0.747398i \(-0.268697\pi\)
−0.999920 + 0.0126614i \(0.995970\pi\)
\(150\) 0 0
\(151\) −0.807321 5.61504i −0.0656989 0.456946i −0.995942 0.0900011i \(-0.971313\pi\)
0.930243 0.366945i \(-0.119596\pi\)
\(152\) 0 0
\(153\) 16.2764 + 8.88757i 1.31587 + 0.718518i
\(154\) 0 0
\(155\) 1.42364 + 0.766484i 0.114349 + 0.0615655i
\(156\) 0 0
\(157\) 13.9863 + 1.00032i 1.11623 + 0.0798340i 0.617239 0.786776i \(-0.288251\pi\)
0.498987 + 0.866610i \(0.333706\pi\)
\(158\) 0 0
\(159\) 0.398795 0.873238i 0.0316265 0.0692523i
\(160\) 0 0
\(161\) −16.8524 18.4531i −1.32815 1.45431i
\(162\) 0 0
\(163\) 7.18895 + 19.2743i 0.563082 + 1.50968i 0.836600 + 0.547815i \(0.184540\pi\)
−0.273518 + 0.961867i \(0.588187\pi\)
\(164\) 0 0
\(165\) −0.765629 + 0.114700i −0.0596042 + 0.00892940i
\(166\) 0 0
\(167\) −20.3718 + 1.45702i −1.57642 + 0.112748i −0.831927 0.554886i \(-0.812762\pi\)
−0.744490 + 0.667633i \(0.767307\pi\)
\(168\) 0 0
\(169\) −2.31628 7.88852i −0.178175 0.606809i
\(170\) 0 0
\(171\) 9.29408 1.33629i 0.710736 0.102188i
\(172\) 0 0
\(173\) 4.03657 + 1.50556i 0.306895 + 0.114466i 0.498193 0.867066i \(-0.333997\pi\)
−0.191298 + 0.981532i \(0.561270\pi\)
\(174\) 0 0
\(175\) −20.6716 + 15.8590i −1.56263 + 1.19883i
\(176\) 0 0
\(177\) 0.0845188 0.0632700i 0.00635282 0.00475566i
\(178\) 0 0
\(179\) 8.73930 + 13.5986i 0.653206 + 1.01641i 0.997003 + 0.0773644i \(0.0246505\pi\)
−0.343797 + 0.939044i \(0.611713\pi\)
\(180\) 0 0
\(181\) 2.83153 9.64330i 0.210466 0.716781i −0.784814 0.619732i \(-0.787241\pi\)
0.995280 0.0970491i \(-0.0309404\pi\)
\(182\) 0 0
\(183\) −0.333112 0.333112i −0.0246243 0.0246243i
\(184\) 0 0
\(185\) 15.7762 + 10.0076i 1.15989 + 0.735770i
\(186\) 0 0
\(187\) 10.9820 + 20.1119i 0.803080 + 1.47073i
\(188\) 0 0
\(189\) 2.46013 1.58103i 0.178948 0.115003i
\(190\) 0 0
\(191\) 13.5513 + 1.94839i 0.980541 + 0.140980i 0.613901 0.789383i \(-0.289599\pi\)
0.366639 + 0.930363i \(0.380508\pi\)
\(192\) 0 0
\(193\) −23.9812 + 5.21680i −1.72621 + 0.375513i −0.962760 0.270358i \(-0.912858\pi\)
−0.763446 + 0.645871i \(0.776494\pi\)
\(194\) 0 0
\(195\) −0.276548 0.364912i −0.0198040 0.0261319i
\(196\) 0 0
\(197\) −6.33826 + 8.46693i −0.451582 + 0.603243i −0.967337 0.253493i \(-0.918421\pi\)
0.515755 + 0.856736i \(0.327512\pi\)
\(198\) 0 0
\(199\) −4.47558 + 1.31415i −0.317265 + 0.0931575i −0.436488 0.899710i \(-0.643778\pi\)
0.119223 + 0.992868i \(0.461960\pi\)
\(200\) 0 0
\(201\) −0.262483 0.227443i −0.0185141 0.0160426i
\(202\) 0 0
\(203\) 0.865284 12.0982i 0.0607310 0.849130i
\(204\) 0 0
\(205\) 11.2958 + 2.38746i 0.788931 + 0.166748i
\(206\) 0 0
\(207\) 6.54421 12.7657i 0.454854 0.887281i
\(208\) 0 0
\(209\) 10.5539 + 4.81979i 0.730026 + 0.333392i
\(210\) 0 0
\(211\) 0.725033 + 0.836732i 0.0499133 + 0.0576030i 0.780157 0.625584i \(-0.215139\pi\)
−0.730244 + 0.683187i \(0.760594\pi\)
\(212\) 0 0
\(213\) 0.0849209 + 1.18735i 0.00581868 + 0.0813558i
\(214\) 0 0
\(215\) 0.511069 1.77935i 0.0348546 0.121351i
\(216\) 0 0
\(217\) −3.01634 2.25800i −0.204762 0.153283i
\(218\) 0 0
\(219\) −0.107292 + 0.0489985i −0.00725010 + 0.00331101i
\(220\) 0 0
\(221\) −7.32699 + 11.4010i −0.492866 + 0.766915i
\(222\) 0 0
\(223\) −1.88894 2.52333i −0.126493 0.168975i 0.732824 0.680418i \(-0.238202\pi\)
−0.859317 + 0.511443i \(0.829111\pi\)
\(224\) 0 0
\(225\) −12.6765 7.93671i −0.845102 0.529114i
\(226\) 0 0
\(227\) 0.531065 0.289984i 0.0352480 0.0192469i −0.461528 0.887125i \(-0.652699\pi\)
0.496776 + 0.867879i \(0.334517\pi\)
\(228\) 0 0
\(229\) −4.05820 −0.268174 −0.134087 0.990970i \(-0.542810\pi\)
−0.134087 + 0.990970i \(0.542810\pi\)
\(230\) 0 0
\(231\) 1.80410 0.118701
\(232\) 0 0
\(233\) 4.35266 2.37673i 0.285152 0.155705i −0.330307 0.943873i \(-0.607152\pi\)
0.615459 + 0.788169i \(0.288971\pi\)
\(234\) 0 0
\(235\) −0.119483 20.2301i −0.00779419 1.31967i
\(236\) 0 0
\(237\) −0.105445 0.140859i −0.00684941 0.00914974i
\(238\) 0 0
\(239\) 8.48775 13.2072i 0.549027 0.854302i −0.450228 0.892914i \(-0.648657\pi\)
0.999254 + 0.0386117i \(0.0122935\pi\)
\(240\) 0 0
\(241\) −1.35109 + 0.617023i −0.0870315 + 0.0397460i −0.458455 0.888718i \(-0.651597\pi\)
0.371424 + 0.928464i \(0.378870\pi\)
\(242\) 0 0
\(243\) 2.01678 + 1.50975i 0.129377 + 0.0968502i
\(244\) 0 0
\(245\) 39.4229 21.8298i 2.51864 1.39465i
\(246\) 0 0
\(247\) 0.489522 + 6.84441i 0.0311475 + 0.435499i
\(248\) 0 0
\(249\) 0.884092 + 1.02030i 0.0560270 + 0.0646587i
\(250\) 0 0
\(251\) 19.3359 + 8.83043i 1.22047 + 0.557372i 0.918302 0.395882i \(-0.129561\pi\)
0.302172 + 0.953253i \(0.402288\pi\)
\(252\) 0 0
\(253\) 15.3308 8.89813i 0.963837 0.559421i
\(254\) 0 0
\(255\) 0.268532 1.27050i 0.0168161 0.0795619i
\(256\) 0 0
\(257\) −1.08572 + 15.1803i −0.0677251 + 0.946921i 0.844059 + 0.536251i \(0.180160\pi\)
−0.911784 + 0.410670i \(0.865295\pi\)
\(258\) 0 0
\(259\) −32.9032 28.5108i −2.04450 1.77157i
\(260\) 0 0
\(261\) 6.68056 1.96159i 0.413516 0.121419i
\(262\) 0 0
\(263\) 7.20082 9.61917i 0.444022 0.593144i −0.521569 0.853209i \(-0.674653\pi\)
0.965591 + 0.260065i \(0.0837441\pi\)
\(264\) 0 0
\(265\) 22.7019 + 3.12730i 1.39457 + 0.192109i
\(266\) 0 0
\(267\) −1.14296 + 0.248636i −0.0699481 + 0.0152163i
\(268\) 0 0
\(269\) 7.23305 + 1.03996i 0.441007 + 0.0634073i 0.359242 0.933244i \(-0.383035\pi\)
0.0817650 + 0.996652i \(0.473944\pi\)
\(270\) 0 0
\(271\) −5.54876 + 3.56597i −0.337063 + 0.216617i −0.698212 0.715891i \(-0.746021\pi\)
0.361149 + 0.932508i \(0.382385\pi\)
\(272\) 0 0
\(273\) 0.511353 + 0.936474i 0.0309485 + 0.0566780i
\(274\) 0 0
\(275\) −7.87514 16.7187i −0.474889 1.00817i
\(276\) 0 0
\(277\) −9.26408 9.26408i −0.556625 0.556625i 0.371720 0.928345i \(-0.378768\pi\)
−0.928345 + 0.371720i \(0.878768\pi\)
\(278\) 0 0
\(279\) 0.609360 2.07529i 0.0364814 0.124244i
\(280\) 0 0
\(281\) 3.20148 + 4.98161i 0.190985 + 0.297178i 0.923519 0.383552i \(-0.125299\pi\)
−0.732535 + 0.680730i \(0.761663\pi\)
\(282\) 0 0
\(283\) 20.5383 15.3748i 1.22087 0.913934i 0.222732 0.974880i \(-0.428502\pi\)
0.998141 + 0.0609454i \(0.0194116\pi\)
\(284\) 0 0
\(285\) −0.276661 0.596456i −0.0163880 0.0353310i
\(286\) 0 0
\(287\) −25.2084 9.40227i −1.48801 0.554998i
\(288\) 0 0
\(289\) −21.2185 + 3.05076i −1.24815 + 0.179456i
\(290\) 0 0
\(291\) −0.282060 0.960608i −0.0165347 0.0563119i
\(292\) 0 0
\(293\) −14.3219 + 1.02432i −0.836696 + 0.0598417i −0.483109 0.875560i \(-0.660493\pi\)
−0.353587 + 0.935402i \(0.615038\pi\)
\(294\) 0 0
\(295\) 2.02647 + 1.49840i 0.117985 + 0.0872402i
\(296\) 0 0
\(297\) 0.724889 + 1.94350i 0.0420623 + 0.112773i
\(298\) 0 0
\(299\) 8.96417 + 5.43581i 0.518411 + 0.314361i
\(300\) 0 0
\(301\) −1.79218 + 3.92432i −0.103299 + 0.226194i
\(302\) 0 0
\(303\) 0.184993 + 0.0132310i 0.0106276 + 0.000760098i
\(304\) 0 0
\(305\) 5.33105 9.90168i 0.305255 0.566968i
\(306\) 0 0
\(307\) 9.03920 + 4.93578i 0.515895 + 0.281700i 0.716031 0.698068i \(-0.245957\pi\)
−0.200137 + 0.979768i \(0.564139\pi\)
\(308\) 0 0
\(309\) 0.102050 + 0.709775i 0.00580544 + 0.0403777i
\(310\) 0 0
\(311\) −2.93295 6.42227i −0.166313 0.364174i 0.808065 0.589094i \(-0.200515\pi\)
−0.974377 + 0.224920i \(0.927788\pi\)
\(312\) 0 0
\(313\) −6.05696 27.8434i −0.342360 1.57380i −0.750492 0.660880i \(-0.770183\pi\)
0.408132 0.912923i \(-0.366180\pi\)
\(314\) 0 0
\(315\) 26.4746 + 22.6680i 1.49168 + 1.27720i
\(316\) 0 0
\(317\) 22.4721 + 4.88851i 1.26216 + 0.274566i 0.793368 0.608742i \(-0.208326\pi\)
0.468793 + 0.883308i \(0.344689\pi\)
\(318\) 0 0
\(319\) 8.25485 + 2.42384i 0.462183 + 0.135709i
\(320\) 0 0
\(321\) 1.60785i 0.0897416i
\(322\) 0 0
\(323\) −13.7613 + 13.7613i −0.765697 + 0.765697i
\(324\) 0 0
\(325\) 6.44620 8.82654i 0.357571 0.489609i
\(326\) 0 0
\(327\) −0.328145 + 1.50846i −0.0181464 + 0.0834178i
\(328\) 0 0
\(329\) −6.70934 + 46.6645i −0.369898 + 2.57270i
\(330\) 0 0
\(331\) 16.4282 + 10.5577i 0.902973 + 0.580306i 0.907671 0.419683i \(-0.137859\pi\)
−0.00469731 + 0.999989i \(0.501495\pi\)
\(332\) 0 0
\(333\) 8.73380 23.4162i 0.478609 1.28320i
\(334\) 0 0
\(335\) 3.39955 7.56185i 0.185737 0.413148i
\(336\) 0 0
\(337\) 9.73706 17.8321i 0.530412 0.971376i −0.465840 0.884869i \(-0.654248\pi\)
0.996251 0.0865071i \(-0.0275705\pi\)
\(338\) 0 0
\(339\) −0.218188 + 0.251802i −0.0118503 + 0.0136760i
\(340\) 0 0
\(341\) 2.01981 1.75018i 0.109379 0.0947775i
\(342\) 0 0
\(343\) −64.2167 + 23.9516i −3.46738 + 1.29327i
\(344\) 0 0
\(345\) −0.987888 0.182013i −0.0531861 0.00979927i
\(346\) 0 0
\(347\) −16.7555 + 6.24949i −0.899484 + 0.335490i −0.756315 0.654208i \(-0.773002\pi\)
−0.143170 + 0.989698i \(0.545729\pi\)
\(348\) 0 0
\(349\) −3.02435 + 2.62061i −0.161890 + 0.140278i −0.732039 0.681263i \(-0.761431\pi\)
0.570149 + 0.821541i \(0.306886\pi\)
\(350\) 0 0
\(351\) −0.803371 + 0.927139i −0.0428807 + 0.0494870i
\(352\) 0 0
\(353\) −3.87521 + 7.09691i −0.206257 + 0.377731i −0.960246 0.279156i \(-0.909945\pi\)
0.753989 + 0.656887i \(0.228127\pi\)
\(354\) 0 0
\(355\) −26.5653 + 10.0875i −1.40994 + 0.535387i
\(356\) 0 0
\(357\) −1.05753 + 2.83534i −0.0559703 + 0.150062i
\(358\) 0 0
\(359\) 5.37915 + 3.45697i 0.283901 + 0.182452i 0.674839 0.737965i \(-0.264213\pi\)
−0.390938 + 0.920417i \(0.627849\pi\)
\(360\) 0 0
\(361\) 1.30165 9.05318i 0.0685079 0.476483i
\(362\) 0 0
\(363\) −0.0529894 + 0.243589i −0.00278122 + 0.0127851i
\(364\) 0 0
\(365\) −1.85639 2.11700i −0.0971679 0.110809i
\(366\) 0 0
\(367\) −9.22004 + 9.22004i −0.481282 + 0.481282i −0.905541 0.424259i \(-0.860535\pi\)
0.424259 + 0.905541i \(0.360535\pi\)
\(368\) 0 0
\(369\) 15.4444i 0.804002i
\(370\) 0 0
\(371\) −51.2401 15.0454i −2.66025 0.781120i
\(372\) 0 0
\(373\) −15.7177 3.41918i −0.813832 0.177038i −0.213659 0.976908i \(-0.568538\pi\)
−0.600173 + 0.799870i \(0.704902\pi\)
\(374\) 0 0
\(375\) −0.277203 + 1.00993i −0.0143147 + 0.0521524i
\(376\) 0 0
\(377\) 1.08158 + 4.97193i 0.0557041 + 0.256068i
\(378\) 0 0
\(379\) 2.89732 + 6.34424i 0.148825 + 0.325882i 0.969332 0.245755i \(-0.0790359\pi\)
−0.820507 + 0.571637i \(0.806309\pi\)
\(380\) 0 0
\(381\) 0.0413017 + 0.287260i 0.00211595 + 0.0147168i
\(382\) 0 0
\(383\) 6.49950 + 3.54900i 0.332109 + 0.181345i 0.636648 0.771155i \(-0.280321\pi\)
−0.304539 + 0.952500i \(0.598502\pi\)
\(384\) 0 0
\(385\) 12.3771 + 41.2496i 0.630794 + 2.10227i
\(386\) 0 0
\(387\) −2.47020 0.176672i −0.125567 0.00898074i
\(388\) 0 0
\(389\) 5.34994 11.7147i 0.271253 0.593960i −0.724160 0.689632i \(-0.757773\pi\)
0.995413 + 0.0956713i \(0.0304998\pi\)
\(390\) 0 0
\(391\) 4.99779 + 29.3098i 0.252749 + 1.48226i
\(392\) 0 0
\(393\) 0.0430383 + 0.115390i 0.00217099 + 0.00582066i
\(394\) 0 0
\(395\) 2.49722 3.37729i 0.125649 0.169930i
\(396\) 0 0
\(397\) −24.3832 + 1.74392i −1.22376 + 0.0875249i −0.668218 0.743965i \(-0.732943\pi\)
−0.555540 + 0.831490i \(0.687488\pi\)
\(398\) 0 0
\(399\) 0.431672 + 1.47014i 0.0216106 + 0.0735990i
\(400\) 0 0
\(401\) 11.6429 1.67400i 0.581420 0.0835956i 0.154672 0.987966i \(-0.450568\pi\)
0.426749 + 0.904370i \(0.359659\pi\)
\(402\) 0 0
\(403\) 1.48097 + 0.552375i 0.0737726 + 0.0275158i
\(404\) 0 0
\(405\) −6.86067 + 18.7313i −0.340910 + 0.930766i
\(406\) 0 0
\(407\) 24.7218 18.5065i 1.22542 0.917335i
\(408\) 0 0
\(409\) 12.2604 + 19.0776i 0.606238 + 0.943325i 0.999712 + 0.0239890i \(0.00763665\pi\)
−0.393474 + 0.919336i \(0.628727\pi\)
\(410\) 0 0
\(411\) 0.509469 1.73509i 0.0251302 0.0855857i
\(412\) 0 0
\(413\) −4.15294 4.15294i −0.204353 0.204353i
\(414\) 0 0
\(415\) −17.2630 + 27.2139i −0.847410 + 1.33588i
\(416\) 0 0
\(417\) −0.633296 1.15980i −0.0310126 0.0567954i
\(418\) 0 0
\(419\) −6.67893 + 4.29228i −0.326287 + 0.209692i −0.693520 0.720437i \(-0.743941\pi\)
0.367234 + 0.930129i \(0.380305\pi\)
\(420\) 0 0
\(421\) −30.5073 4.38629i −1.48684 0.213775i −0.649457 0.760398i \(-0.725004\pi\)
−0.837378 + 0.546624i \(0.815913\pi\)
\(422\) 0 0
\(423\) −26.4442 + 5.75258i −1.28576 + 0.279700i
\(424\) 0 0
\(425\) 30.8914 2.57649i 1.49845 0.124978i
\(426\) 0 0
\(427\) −15.7049 + 20.9792i −0.760011 + 1.01526i
\(428\) 0 0
\(429\) −0.726171 + 0.213223i −0.0350598 + 0.0102945i
\(430\) 0 0
\(431\) 19.7726 + 17.1330i 0.952411 + 0.825269i 0.984709 0.174209i \(-0.0557369\pi\)
−0.0322974 + 0.999478i \(0.510282\pi\)
\(432\) 0 0
\(433\) 0.531798 7.43551i 0.0255566 0.357328i −0.968542 0.248849i \(-0.919948\pi\)
0.994099 0.108478i \(-0.0345979\pi\)
\(434\) 0 0
\(435\) −0.266004 0.408585i −0.0127539 0.0195901i
\(436\) 0 0
\(437\) 10.9192 + 10.3637i 0.522335 + 0.495765i
\(438\) 0 0
\(439\) 18.9660 + 8.66148i 0.905198 + 0.413390i 0.812942 0.582345i \(-0.197865\pi\)
0.0922564 + 0.995735i \(0.470592\pi\)
\(440\) 0 0
\(441\) −39.4763 45.5581i −1.87983 2.16943i
\(442\) 0 0
\(443\) 2.14618 + 30.0075i 0.101968 + 1.42570i 0.748664 + 0.662949i \(0.230696\pi\)
−0.646696 + 0.762748i \(0.723850\pi\)
\(444\) 0 0
\(445\) −13.5262 24.4272i −0.641202 1.15796i
\(446\) 0 0
\(447\) 0.739350 + 0.553470i 0.0349701 + 0.0261783i
\(448\) 0 0
\(449\) −23.6470 + 10.7992i −1.11597 + 0.509647i −0.886063 0.463566i \(-0.846570\pi\)
−0.229908 + 0.973212i \(0.573843\pi\)
\(450\) 0 0
\(451\) 10.3175 16.0544i 0.485833 0.755972i
\(452\) 0 0
\(453\) 0.318443 + 0.425390i 0.0149618 + 0.0199866i
\(454\) 0 0
\(455\) −17.9037 + 18.1164i −0.839337 + 0.849310i
\(456\) 0 0
\(457\) −15.5427 + 8.48697i −0.727058 + 0.397004i −0.799736 0.600352i \(-0.795027\pi\)
0.0726783 + 0.997355i \(0.476845\pi\)
\(458\) 0 0
\(459\) −3.47933 −0.162401
\(460\) 0 0
\(461\) −4.59398 −0.213963 −0.106981 0.994261i \(-0.534119\pi\)
−0.106981 + 0.994261i \(0.534119\pi\)
\(462\) 0 0
\(463\) 21.7956 11.9013i 1.01293 0.553101i 0.115057 0.993359i \(-0.463295\pi\)
0.897871 + 0.440258i \(0.145113\pi\)
\(464\) 0 0
\(465\) −0.151451 0.000894497i −0.00702338 4.14813e-5i
\(466\) 0 0
\(467\) −18.3930 24.5702i −0.851127 1.13697i −0.989203 0.146550i \(-0.953183\pi\)
0.138077 0.990422i \(-0.455908\pi\)
\(468\) 0 0
\(469\) −10.4456 + 16.2536i −0.482332 + 0.750523i
\(470\) 0 0
\(471\) −1.19477 + 0.545632i −0.0550519 + 0.0251414i
\(472\) 0 0
\(473\) −2.44974 1.83385i −0.112639 0.0843205i
\(474\) 0 0
\(475\) 11.7395 10.4176i 0.538645 0.477994i
\(476\) 0 0
\(477\) −2.18694 30.5774i −0.100133 1.40004i
\(478\) 0 0
\(479\) −22.7676 26.2752i −1.04028 1.20054i −0.979302 0.202404i \(-0.935125\pi\)
−0.0609748 0.998139i \(-0.519421\pi\)
\(480\) 0 0
\(481\) 16.6135 + 7.58713i 0.757510 + 0.345943i
\(482\) 0 0
\(483\) 2.21389 + 0.760557i 0.100735 + 0.0346065i
\(484\) 0 0
\(485\) 20.0286 13.0394i 0.909450 0.592087i
\(486\) 0 0
\(487\) −2.63312 + 36.8159i −0.119318 + 1.66829i 0.487256 + 0.873259i \(0.337998\pi\)
−0.606574 + 0.795027i \(0.707457\pi\)
\(488\) 0 0
\(489\) −1.45629 1.26188i −0.0658558 0.0570644i
\(490\) 0 0
\(491\) −11.2432 + 3.30129i −0.507397 + 0.148985i −0.525404 0.850853i \(-0.676086\pi\)
0.0180074 + 0.999838i \(0.494268\pi\)
\(492\) 0 0
\(493\) −8.64814 + 11.5526i −0.389493 + 0.520301i
\(494\) 0 0
\(495\) −19.7030 + 14.9318i −0.885582 + 0.671136i
\(496\) 0 0
\(497\) 64.7064 14.0760i 2.90248 0.631395i
\(498\) 0 0
\(499\) 29.6737 + 4.26643i 1.32838 + 0.190992i 0.769706 0.638399i \(-0.220403\pi\)
0.558670 + 0.829390i \(0.311312\pi\)
\(500\) 0 0
\(501\) 1.60943 1.03432i 0.0719040 0.0462099i
\(502\) 0 0
\(503\) −16.1298 29.5396i −0.719194 1.31711i −0.939794 0.341741i \(-0.888983\pi\)
0.220600 0.975364i \(-0.429198\pi\)
\(504\) 0 0
\(505\) 0.966628 + 4.32050i 0.0430144 + 0.192260i
\(506\) 0 0
\(507\) 0.544560 + 0.544560i 0.0241848 + 0.0241848i
\(508\) 0 0
\(509\) −5.85578 + 19.9430i −0.259553 + 0.883956i 0.721858 + 0.692041i \(0.243288\pi\)
−0.981411 + 0.191916i \(0.938530\pi\)
\(510\) 0 0
\(511\) 3.54740 + 5.51986i 0.156928 + 0.244184i
\(512\) 0 0
\(513\) −1.41029 + 1.05573i −0.0622657 + 0.0466115i
\(514\) 0 0
\(515\) −15.5284 + 7.20272i −0.684263 + 0.317390i
\(516\) 0 0
\(517\) −31.3316 11.6861i −1.37796 0.513954i
\(518\) 0 0
\(519\) −0.399448 + 0.0574320i −0.0175338 + 0.00252098i
\(520\) 0 0
\(521\) −6.36709 21.6843i −0.278947 0.950007i −0.973139 0.230217i \(-0.926056\pi\)
0.694192 0.719790i \(-0.255762\pi\)
\(522\) 0 0
\(523\) −25.5022 + 1.82395i −1.11513 + 0.0797558i −0.616718 0.787184i \(-0.711538\pi\)
−0.498413 + 0.866940i \(0.666084\pi\)
\(524\) 0 0
\(525\) 0.987544 2.23182i 0.0431000 0.0974044i
\(526\) 0 0
\(527\) 1.56662 + 4.20027i 0.0682430 + 0.182966i
\(528\) 0 0
\(529\) 22.5642 4.45625i 0.981051 0.193750i
\(530\) 0 0
\(531\) 1.40053 3.06674i 0.0607780 0.133085i
\(532\) 0 0
\(533\) 11.2579 + 0.805180i 0.487633 + 0.0348762i
\(534\) 0 0
\(535\) 36.7624 11.0307i 1.58938 0.476898i
\(536\) 0 0
\(537\) −1.32896 0.725666i −0.0573488 0.0313148i
\(538\) 0 0
\(539\) −10.6007 73.7295i −0.456604 3.17575i
\(540\) 0 0
\(541\) 15.5497 + 34.0491i 0.668534 + 1.46389i 0.874350 + 0.485295i \(0.161288\pi\)
−0.205816 + 0.978591i \(0.565985\pi\)
\(542\) 0 0
\(543\) 0.200117 + 0.919922i 0.00858784 + 0.0394777i
\(544\) 0 0
\(545\) −36.7410 + 2.84597i −1.57381 + 0.121908i
\(546\) 0 0
\(547\) 24.9800 + 5.43406i 1.06807 + 0.232344i 0.712045 0.702134i \(-0.247769\pi\)
0.356022 + 0.934478i \(0.384133\pi\)
\(548\) 0 0
\(549\) −14.4341 4.23822i −0.616030 0.180883i
\(550\) 0 0
\(551\) 7.30671i 0.311276i
\(552\) 0 0
\(553\) −6.92126 + 6.92126i −0.294322 + 0.294322i
\(554\) 0 0
\(555\) −1.74627 0.114534i −0.0741251 0.00486169i
\(556\) 0 0
\(557\) 2.91394 13.3952i 0.123468 0.567572i −0.873296 0.487189i \(-0.838022\pi\)
0.996764 0.0803824i \(-0.0256141\pi\)
\(558\) 0 0
\(559\) 0.257563 1.79139i 0.0108938 0.0757678i
\(560\) 0 0
\(561\) −1.80573 1.16047i −0.0762380 0.0489952i
\(562\) 0 0
\(563\) −7.20354 + 19.3134i −0.303593 + 0.813964i 0.692147 + 0.721757i \(0.256665\pi\)
−0.995740 + 0.0922075i \(0.970608\pi\)
\(564\) 0 0
\(565\) −7.25416 3.26122i −0.305185 0.137201i
\(566\) 0 0
\(567\) 22.2786 40.8003i 0.935615 1.71345i
\(568\) 0 0
\(569\) 5.30428 6.12147i 0.222367 0.256625i −0.633594 0.773666i \(-0.718421\pi\)
0.855961 + 0.517041i \(0.172966\pi\)
\(570\) 0 0
\(571\) −16.5118 + 14.3075i −0.690996 + 0.598752i −0.927921 0.372776i \(-0.878406\pi\)
0.236925 + 0.971528i \(0.423860\pi\)
\(572\) 0 0
\(573\) −1.20157 + 0.448163i −0.0501963 + 0.0187223i
\(574\) 0 0
\(575\) −2.61580 23.8361i −0.109086 0.994032i
\(576\) 0 0
\(577\) −6.94505 + 2.59037i −0.289126 + 0.107838i −0.489843 0.871811i \(-0.662946\pi\)
0.200716 + 0.979649i \(0.435673\pi\)
\(578\) 0 0
\(579\) 1.73739 1.50546i 0.0722034 0.0625646i
\(580\) 0 0
\(581\) 49.1811 56.7580i 2.04038 2.35472i
\(582\) 0 0
\(583\) 18.1537 33.2461i 0.751851 1.37691i
\(584\) 0 0
\(585\) −13.3354 5.99514i −0.551351 0.247868i
\(586\) 0 0
\(587\) −8.34600 + 22.3765i −0.344476 + 0.923577i 0.643008 + 0.765859i \(0.277686\pi\)
−0.987484 + 0.157717i \(0.949587\pi\)
\(588\) 0 0
\(589\) 1.90948 + 1.22715i 0.0786787 + 0.0505637i
\(590\) 0 0
\(591\) 0.140994 0.980633i 0.00579971 0.0403378i
\(592\) 0 0
\(593\) −9.86386 + 45.3434i −0.405060 + 1.86203i 0.0941617 + 0.995557i \(0.469983\pi\)
−0.499222 + 0.866474i \(0.666381\pi\)
\(594\) 0 0
\(595\) −72.0832 4.72776i −2.95512 0.193819i
\(596\) 0 0
\(597\) 0.308958 0.308958i 0.0126448 0.0126448i
\(598\) 0 0
\(599\) 21.0837i 0.861457i −0.902482 0.430729i \(-0.858257\pi\)
0.902482 0.430729i \(-0.141743\pi\)
\(600\) 0 0
\(601\) 3.89733 + 1.14436i 0.158976 + 0.0466794i 0.360252 0.932855i \(-0.382691\pi\)
−0.201276 + 0.979534i \(0.564509\pi\)
\(602\) 0 0
\(603\) −10.8374 2.35753i −0.441332 0.0960059i
\(604\) 0 0
\(605\) −5.93302 + 0.459573i −0.241211 + 0.0186843i
\(606\) 0 0
\(607\) 8.53964 + 39.2561i 0.346613 + 1.59336i 0.739098 + 0.673598i \(0.235252\pi\)
−0.392485 + 0.919759i \(0.628384\pi\)
\(608\) 0 0
\(609\) 0.471976 + 1.03348i 0.0191254 + 0.0418789i
\(610\) 0 0
\(611\) −2.81459 19.5759i −0.113866 0.791956i
\(612\) 0 0
\(613\) 31.9886 + 17.4671i 1.29201 + 0.705489i 0.970427 0.241393i \(-0.0776043\pi\)
0.321580 + 0.946882i \(0.395786\pi\)
\(614\) 0 0
\(615\) −1.03584 + 0.310808i −0.0417693 + 0.0125330i
\(616\) 0 0
\(617\) −36.9027 2.63934i −1.48565 0.106256i −0.695214 0.718803i \(-0.744690\pi\)
−0.790434 + 0.612547i \(0.790145\pi\)
\(618\) 0 0
\(619\) −9.25412 + 20.2637i −0.371954 + 0.814466i 0.627406 + 0.778693i \(0.284117\pi\)
−0.999360 + 0.0357737i \(0.988610\pi\)
\(620\) 0 0
\(621\) 0.0702169 + 2.69054i 0.00281771 + 0.107968i
\(622\) 0 0
\(623\) 22.7392 + 60.9662i 0.911027 + 2.44256i
\(624\) 0 0
\(625\) −24.9930 + 0.590556i −0.999721 + 0.0236222i
\(626\) 0 0
\(627\) −1.08404 + 0.0775321i −0.0432924 + 0.00309633i
\(628\) 0 0
\(629\) 14.5936 + 49.7011i 0.581884 + 1.98171i
\(630\) 0 0
\(631\) −16.2403 + 2.33500i −0.646515 + 0.0929548i −0.457769 0.889071i \(-0.651351\pi\)
−0.188746 + 0.982026i \(0.560442\pi\)
\(632\) 0 0
\(633\) −0.0971701 0.0362426i −0.00386216 0.00144051i
\(634\) 0 0
\(635\) −6.28464 + 2.91508i −0.249398 + 0.115681i
\(636\) 0 0
\(637\) 35.2668 26.4004i 1.39732 1.04602i
\(638\) 0 0
\(639\) 20.5512 + 31.9783i 0.812992 + 1.26504i
\(640\) 0 0
\(641\) −13.0786 + 44.5416i −0.516573 + 1.75929i 0.124930 + 0.992166i \(0.460129\pi\)
−0.641503 + 0.767121i \(0.721689\pi\)
\(642\) 0 0
\(643\) 2.82024 + 2.82024i 0.111220 + 0.111220i 0.760526 0.649307i \(-0.224941\pi\)
−0.649307 + 0.760526i \(0.724941\pi\)
\(644\) 0 0
\(645\) 0.0378618 + 0.169230i 0.00149081 + 0.00666341i
\(646\) 0 0
\(647\) 4.11924 + 7.54383i 0.161944 + 0.296578i 0.946033 0.324070i \(-0.105051\pi\)
−0.784089 + 0.620648i \(0.786869\pi\)
\(648\) 0 0
\(649\) 3.50457 2.25225i 0.137566 0.0884085i
\(650\) 0 0
\(651\) 0.349350 + 0.0502289i 0.0136921 + 0.00196863i
\(652\) 0 0
\(653\) 4.86422 1.05815i 0.190352 0.0414085i −0.116379 0.993205i \(-0.537129\pi\)
0.306730 + 0.951796i \(0.400765\pi\)
\(654\) 0 0
\(655\) −2.34305 + 1.77567i −0.0915505 + 0.0693813i
\(656\) 0 0
\(657\) −2.25720 + 3.01527i −0.0880618 + 0.117637i
\(658\) 0 0
\(659\) 16.1318 4.73672i 0.628405 0.184516i 0.0480038 0.998847i \(-0.484714\pi\)
0.580401 + 0.814331i \(0.302896\pi\)
\(660\) 0 0
\(661\) 8.96638 + 7.76941i 0.348752 + 0.302195i 0.811567 0.584260i \(-0.198615\pi\)
−0.462815 + 0.886455i \(0.653161\pi\)
\(662\) 0 0
\(663\) 0.0905633 1.26624i 0.00351719 0.0491767i
\(664\) 0 0
\(665\) −30.6522 + 19.9558i −1.18864 + 0.773851i
\(666\) 0 0
\(667\) 9.10803 + 6.45439i 0.352664 + 0.249915i
\(668\) 0 0
\(669\) 0.268574 + 0.122654i 0.0103837 + 0.00474207i
\(670\) 0 0
\(671\) −12.1728 14.0482i −0.469927 0.542325i
\(672\) 0 0
\(673\) 0.813003 + 11.3673i 0.0313390 + 0.438176i 0.988763 + 0.149491i \(0.0477635\pi\)
−0.957424 + 0.288685i \(0.906782\pi\)
\(674\) 0 0
\(675\) 2.80106 + 0.167106i 0.107813 + 0.00643192i
\(676\) 0 0
\(677\) −36.4239 27.2666i −1.39988 1.04794i −0.990784 0.135452i \(-0.956752\pi\)
−0.409101 0.912489i \(-0.634158\pi\)
\(678\) 0 0
\(679\) −50.6607 + 23.1360i −1.94418 + 0.887877i
\(680\) 0 0
\(681\) −0.0306428 + 0.0476811i −0.00117424 + 0.00182715i
\(682\) 0 0
\(683\) −18.5080 24.7237i −0.708188 0.946028i 0.291758 0.956492i \(-0.405760\pi\)
−0.999945 + 0.0104644i \(0.996669\pi\)
\(684\) 0 0
\(685\) 43.1668 0.254951i 1.64932 0.00974117i
\(686\) 0 0
\(687\) 0.333639 0.182181i 0.0127291 0.00695063i
\(688\) 0 0
\(689\) 22.4028 0.853480
\(690\) 0 0
\(691\) −2.37208 −0.0902382 −0.0451191 0.998982i \(-0.514367\pi\)
−0.0451191 + 0.998982i \(0.514367\pi\)
\(692\) 0 0
\(693\) 50.5637 27.6099i 1.92076 1.04881i
\(694\) 0 0
\(695\) 22.1732 22.4366i 0.841076 0.851070i
\(696\) 0 0
\(697\) 19.1833 + 25.6258i 0.726617 + 0.970647i
\(698\) 0 0
\(699\) −0.251151 + 0.390799i −0.00949941 + 0.0147814i
\(700\) 0 0
\(701\) −46.3864 + 21.1839i −1.75199 + 0.800106i −0.764070 + 0.645133i \(0.776802\pi\)
−0.987919 + 0.154973i \(0.950471\pi\)
\(702\) 0 0
\(703\) 20.9960 + 15.7174i 0.791877 + 0.592792i
\(704\) 0 0
\(705\) 0.917994 + 1.65783i 0.0345737 + 0.0624374i
\(706\) 0 0
\(707\) −0.736024 10.2910i −0.0276810 0.387032i
\(708\) 0 0
\(709\) −18.0763 20.8612i −0.678871 0.783459i 0.306866 0.951753i \(-0.400720\pi\)
−0.985737 + 0.168294i \(0.946174\pi\)
\(710\) 0 0
\(711\) −5.11101 2.33412i −0.191678 0.0875363i
\(712\) 0 0
\(713\) 3.21641 1.29622i 0.120456 0.0485438i
\(714\) 0 0
\(715\) −9.85709 15.1406i −0.368634 0.566225i
\(716\) 0 0
\(717\) −0.104911 + 1.46684i −0.00391796 + 0.0547802i
\(718\) 0 0
\(719\) −4.52564 3.92149i −0.168778 0.146247i 0.566376 0.824147i \(-0.308345\pi\)
−0.735154 + 0.677900i \(0.762890\pi\)
\(720\) 0 0
\(721\) 38.2743 11.2383i 1.42541 0.418538i
\(722\) 0 0
\(723\) 0.0833787 0.111381i 0.00310089 0.00414230i
\(724\) 0 0
\(725\) 7.51708 8.88510i 0.279177 0.329984i
\(726\) 0 0
\(727\) 13.7349 2.98785i 0.509401 0.110813i 0.0494831 0.998775i \(-0.484243\pi\)
0.459917 + 0.887962i \(0.347879\pi\)
\(728\) 0 0
\(729\) 26.2573 + 3.77523i 0.972494 + 0.139823i
\(730\) 0 0
\(731\) 4.31807 2.77506i 0.159710 0.102639i
\(732\) 0 0
\(733\) 3.72159 + 6.81559i 0.137460 + 0.251740i 0.937337 0.348425i \(-0.113283\pi\)
−0.799876 + 0.600165i \(0.795102\pi\)
\(734\) 0 0
\(735\) −2.26112 + 3.56448i −0.0834025 + 0.131478i
\(736\) 0 0
\(737\) −9.69049 9.69049i −0.356954 0.356954i
\(738\) 0 0
\(739\) 0.354436 1.20710i 0.0130381 0.0444038i −0.952717 0.303859i \(-0.901725\pi\)
0.965755 + 0.259455i \(0.0835430\pi\)
\(740\) 0 0
\(741\) −0.347504 0.540728i −0.0127659 0.0198641i
\(742\) 0 0
\(743\) −3.81643 + 2.85694i −0.140011 + 0.104811i −0.666987 0.745069i \(-0.732417\pi\)
0.526976 + 0.849880i \(0.323326\pi\)
\(744\) 0 0
\(745\) −7.58240 + 20.7018i −0.277798 + 0.758455i
\(746\) 0 0
\(747\) 40.3930 + 15.0658i 1.47790 + 0.551229i
\(748\) 0 0
\(749\) −88.5328 + 12.7291i −3.23492 + 0.465111i
\(750\) 0 0
\(751\) −5.37467 18.3044i −0.196124 0.667938i −0.997557 0.0698536i \(-0.977747\pi\)
0.801433 0.598085i \(-0.204071\pi\)
\(752\) 0 0
\(753\) −1.98609 + 0.142048i −0.0723772 + 0.00517652i
\(754\) 0 0
\(755\) −7.54157 + 10.1994i −0.274466 + 0.371193i
\(756\) 0 0
\(757\) −2.94391 7.89292i −0.106998 0.286873i 0.872406 0.488781i \(-0.162558\pi\)
−0.979404 + 0.201908i \(0.935286\pi\)
\(758\) 0 0
\(759\) −0.860942 + 1.41978i −0.0312502 + 0.0515346i
\(760\) 0 0
\(761\) 2.69497 5.90117i 0.0976927 0.213917i −0.854475 0.519492i \(-0.826121\pi\)
0.952168 + 0.305575i \(0.0988486\pi\)
\(762\) 0 0
\(763\) 85.6576 + 6.12635i 3.10101 + 0.221789i
\(764\) 0 0
\(765\) −11.9175 39.7180i −0.430878 1.43601i
\(766\) 0 0
\(767\) 2.16243 + 1.18077i 0.0780807 + 0.0426353i
\(768\) 0 0
\(769\) −5.20768 36.2202i −0.187794 1.30613i −0.837704 0.546124i \(-0.816103\pi\)
0.649910 0.760011i \(-0.274806\pi\)
\(770\) 0 0
\(771\) −0.592213 1.29677i −0.0213280 0.0467019i
\(772\) 0 0
\(773\) −8.21535 37.7653i −0.295486 1.35833i −0.850277 0.526336i \(-0.823566\pi\)
0.554791 0.831989i \(-0.312798\pi\)
\(774\) 0 0
\(775\) −1.05948 3.45669i −0.0380578 0.124168i
\(776\) 0 0
\(777\) 3.98499 + 0.866882i 0.142961 + 0.0310992i
\(778\) 0 0
\(779\) 15.5512 + 4.56624i 0.557179 + 0.163602i
\(780\) 0 0
\(781\) 46.9704i 1.68073i
\(782\) 0 0
\(783\) −0.923698 + 0.923698i −0.0330103 + 0.0330103i
\(784\) 0 0
\(785\) −20.6722 23.5742i −0.737822 0.841399i
\(786\) 0 0
\(787\) 8.65982 39.8085i 0.308689 1.41902i −0.517527 0.855667i \(-0.673147\pi\)
0.826216 0.563354i \(-0.190489\pi\)
\(788\) 0 0
\(789\) −0.160181 + 1.11409i −0.00570261 + 0.0396625i
\(790\) 0 0
\(791\) 15.5923 + 10.0205i 0.554398 + 0.356290i
\(792\) 0 0
\(793\) 3.84188 10.3005i 0.136429 0.365781i
\(794\) 0 0
\(795\) −2.00679 + 0.762027i −0.0711737 + 0.0270263i
\(796\) 0 0
\(797\) 0.907934 1.66276i 0.0321607 0.0588979i −0.861104 0.508428i \(-0.830227\pi\)
0.893265 + 0.449530i \(0.148409\pi\)
\(798\) 0 0
\(799\) 36.7319 42.3908i 1.29948 1.49968i
\(800\) 0 0
\(801\) −28.2287 + 24.4603i −0.997413 + 0.864263i
\(802\) 0 0
\(803\) −4.36069 + 1.62645i −0.153885 + 0.0573962i
\(804\) 0 0
\(805\) −2.20122 + 55.8368i −0.0775827 + 1.96799i
\(806\) 0 0
\(807\) −0.641341 + 0.239208i −0.0225763 + 0.00842051i
\(808\) 0 0
\(809\) 14.3327 12.4194i 0.503912 0.436643i −0.365440 0.930835i \(-0.619082\pi\)
0.869353 + 0.494192i \(0.164536\pi\)
\(810\) 0 0
\(811\) −25.9379 + 29.9339i −0.910802 + 1.05112i 0.0876859 + 0.996148i \(0.472053\pi\)
−0.998488 + 0.0549733i \(0.982493\pi\)
\(812\) 0 0
\(813\) 0.296100 0.542266i 0.0103847 0.0190181i
\(814\) 0 0
\(815\) 18.8612 41.9542i 0.660679 1.46959i
\(816\) 0 0
\(817\) 0.908224 2.43504i 0.0317747 0.0851914i
\(818\) 0 0
\(819\) 28.6634 + 18.4209i 1.00158 + 0.643677i
\(820\) 0 0
\(821\) 1.55883 10.8419i 0.0544035 0.378385i −0.944371 0.328883i \(-0.893328\pi\)
0.998774 0.0495014i \(-0.0157632\pi\)
\(822\) 0 0
\(823\) 1.01471 4.66453i 0.0353704 0.162595i −0.956074 0.293126i \(-0.905304\pi\)
0.991444 + 0.130531i \(0.0416681\pi\)
\(824\) 0 0
\(825\) 1.39798 + 1.02097i 0.0486713 + 0.0355456i
\(826\) 0 0
\(827\) 30.5587 30.5587i 1.06263 1.06263i 0.0647275 0.997903i \(-0.479382\pi\)
0.997903 0.0647275i \(-0.0206178\pi\)
\(828\) 0 0
\(829\) 9.00927i 0.312905i 0.987686 + 0.156452i \(0.0500058\pi\)
−0.987686 + 0.156452i \(0.949994\pi\)
\(830\) 0 0
\(831\) 1.17752 + 0.345750i 0.0408476 + 0.0119939i
\(832\) 0 0
\(833\) 122.088 + 26.5585i 4.23008 + 0.920198i
\(834\) 0 0
\(835\) 34.6904 + 29.7025i 1.20051 + 1.02790i
\(836\) 0 0
\(837\) 0.0862588 + 0.396525i 0.00298154 + 0.0137059i
\(838\) 0 0
\(839\) −5.77968 12.6557i −0.199537 0.436924i 0.783240 0.621719i \(-0.213565\pi\)
−0.982777 + 0.184794i \(0.940838\pi\)
\(840\) 0 0
\(841\) −3.35606 23.3419i −0.115726 0.804894i
\(842\) 0 0
\(843\) −0.486840 0.265835i −0.0167676 0.00915583i
\(844\) 0 0
\(845\) −8.71503 + 16.1869i −0.299806 + 0.556848i
\(846\) 0 0
\(847\) 13.8322 + 0.989296i 0.475279 + 0.0339926i
\(848\) 0 0
\(849\) −0.998320 + 2.18602i −0.0342623 + 0.0750239i
\(850\) 0 0
\(851\) 38.1389 12.2881i 1.30739 0.421231i
\(852\) 0 0
\(853\) −14.5223 38.9357i −0.497232 1.33313i −0.907073 0.420974i \(-0.861688\pi\)
0.409840 0.912157i \(-0.365584\pi\)
\(854\) 0 0
\(855\) −16.8821 12.4829i −0.577356 0.426906i
\(856\) 0 0
\(857\) −50.0636 + 3.58062i −1.71014 + 0.122312i −0.891801 0.452427i \(-0.850558\pi\)
−0.818337 + 0.574738i \(0.805104\pi\)
\(858\) 0 0
\(859\) −6.21934 21.1811i −0.212201 0.722690i −0.994952 0.100355i \(-0.968002\pi\)
0.782751 0.622335i \(-0.213816\pi\)
\(860\) 0 0
\(861\) 2.49456 0.358664i 0.0850144 0.0122232i
\(862\) 0 0
\(863\) 4.80760 + 1.79314i 0.163653 + 0.0610393i 0.429955 0.902850i \(-0.358529\pi\)
−0.266303 + 0.963889i \(0.585802\pi\)
\(864\) 0 0
\(865\) −4.05356 8.73909i −0.137825 0.297138i
\(866\) 0 0
\(867\) 1.60749 1.20335i 0.0545933 0.0408680i
\(868\) 0 0
\(869\) −3.75359 5.84069i −0.127332 0.198132i
\(870\) 0 0
\(871\) 2.28347 7.77679i 0.0773725 0.263507i
\(872\) 0 0
\(873\) −22.6064 22.6064i −0.765110 0.765110i
\(874\) 0 0
\(875\) 57.8039 + 7.26814i 1.95413 + 0.245708i
\(876\) 0 0
\(877\) −18.0652 33.0839i −0.610017 1.11716i −0.981992 0.188920i \(-0.939501\pi\)
0.371976 0.928243i \(-0.378680\pi\)
\(878\) 0 0
\(879\) 1.13147 0.727153i 0.0381636 0.0245263i
\(880\) 0 0
\(881\) −3.51891 0.505942i −0.118555 0.0170456i 0.0827819 0.996568i \(-0.473620\pi\)
−0.201337 + 0.979522i \(0.564529\pi\)
\(882\) 0 0
\(883\) −19.1818 + 4.17274i −0.645519 + 0.140424i −0.523394 0.852091i \(-0.675334\pi\)
−0.122125 + 0.992515i \(0.538971\pi\)
\(884\) 0 0
\(885\) −0.233869 0.0322167i −0.00786142 0.00108295i
\(886\) 0 0
\(887\) −9.99376 + 13.3501i −0.335558 + 0.448252i −0.936306 0.351186i \(-0.885779\pi\)
0.600748 + 0.799438i \(0.294869\pi\)
\(888\) 0 0
\(889\) 15.4903 4.54837i 0.519529 0.152547i
\(890\) 0 0
\(891\) 24.9197 + 21.5930i 0.834840 + 0.723393i
\(892\) 0 0
\(893\) 2.02605 28.3279i 0.0677991 0.947956i
\(894\) 0 0
\(895\) 7.47452 35.3641i 0.249846 1.18209i
\(896\) 0 0
\(897\) −0.981001 0.0444777i −0.0327547 0.00148507i
\(898\) 0 0
\(899\) 1.53100 + 0.699184i 0.0510617 + 0.0233191i
\(900\) 0 0
\(901\) 41.6084 + 48.0187i 1.38618 + 1.59973i
\(902\) 0 0
\(903\) −0.0288293 0.403087i −0.000959380 0.0134139i
\(904\) 0 0
\(905\) −19.6605 + 10.8867i −0.653536 + 0.361885i
\(906\) 0 0
\(907\) −20.2185 15.1354i −0.671343 0.502561i 0.208380 0.978048i \(-0.433181\pi\)
−0.879723 + 0.475487i \(0.842272\pi\)
\(908\) 0 0
\(909\) 5.38729 2.46029i 0.178685 0.0816028i
\(910\) 0 0
\(911\) −3.60786 + 5.61394i −0.119534 + 0.185998i −0.895864 0.444328i \(-0.853442\pi\)
0.776330 + 0.630326i \(0.217079\pi\)
\(912\) 0 0
\(913\) 31.9238 + 42.6452i 1.05652 + 1.41135i
\(914\) 0 0
\(915\) 0.00622141 + 1.05337i 0.000205673 + 0.0348235i
\(916\) 0 0
\(917\) 6.01297 3.28333i 0.198566 0.108425i
\(918\) 0 0
\(919\) −9.30621 −0.306984 −0.153492 0.988150i \(-0.549052\pi\)
−0.153492 + 0.988150i \(0.549052\pi\)
\(920\) 0 0
\(921\) −0.964722 −0.0317887
\(922\) 0 0
\(923\) −24.3814 + 13.3132i −0.802523 + 0.438210i
\(924\) 0 0
\(925\) −9.36157 40.7130i −0.307807 1.33864i
\(926\) 0 0
\(927\) 13.7225 + 18.3311i 0.450707 + 0.602073i
\(928\) 0 0
\(929\) −13.9736 + 21.7433i −0.458458 + 0.713374i −0.991122 0.132952i \(-0.957554\pi\)
0.532665 + 0.846326i \(0.321191\pi\)
\(930\) 0 0
\(931\) 57.5446 26.2798i 1.88595 0.861284i
\(932\) 0 0
\(933\) 0.529437 + 0.396332i 0.0173330 + 0.0129753i
\(934\) 0 0
\(935\) 14.1452 49.2482i 0.462597 1.61059i
\(936\) 0 0
\(937\) −0.280166 3.91723i −0.00915262 0.127970i 0.990821 0.135177i \(-0.0431604\pi\)
−0.999974 + 0.00720707i \(0.997706\pi\)
\(938\) 0 0
\(939\) 1.74791 + 2.01720i 0.0570409 + 0.0658287i
\(940\) 0 0
\(941\) 10.6775 + 4.87624i 0.348076 + 0.158961i 0.581778 0.813347i \(-0.302357\pi\)
−0.233703 + 0.972308i \(0.575084\pi\)
\(942\) 0 0
\(943\) 19.4291 15.3514i 0.632698 0.499910i
\(944\) 0 0
\(945\) −6.39774 1.35222i −0.208119 0.0439877i
\(946\) 0 0
\(947\) −0.499312 + 6.98129i −0.0162255 + 0.226861i 0.982869 + 0.184307i \(0.0590041\pi\)
−0.999094 + 0.0425543i \(0.986450\pi\)
\(948\) 0 0
\(949\) −2.08025 1.80254i −0.0675276 0.0585130i
\(950\) 0 0
\(951\) −2.06697 + 0.606917i −0.0670261 + 0.0196806i
\(952\) 0 0
\(953\) 6.37164 8.51151i 0.206398 0.275715i −0.685383 0.728183i \(-0.740365\pi\)
0.891781 + 0.452468i \(0.149456\pi\)
\(954\) 0 0
\(955\) −18.4903 24.3985i −0.598332 0.789515i
\(956\) 0 0
\(957\) −0.787472 + 0.171304i −0.0254553 + 0.00553747i
\(958\) 0 0
\(959\) −99.5722 14.3163i −3.21536 0.462298i
\(960\) 0 0
\(961\) −25.6390 + 16.4772i −0.827065 + 0.531522i
\(962\) 0 0
\(963\) −24.6065 45.0634i −0.792932 1.45215i
\(964\) 0 0
\(965\) 46.3405 + 29.3960i 1.49175 + 0.946290i
\(966\) 0 0
\(967\) −28.4658 28.4658i −0.915397 0.915397i 0.0812932 0.996690i \(-0.474095\pi\)
−0.996690 + 0.0812932i \(0.974095\pi\)
\(968\) 0 0
\(969\) 0.513591 1.74913i 0.0164989 0.0561902i
\(970\) 0 0
\(971\) 31.8548 + 49.5670i 1.02227 + 1.59068i 0.785253 + 0.619175i \(0.212533\pi\)
0.237015 + 0.971506i \(0.423831\pi\)
\(972\) 0 0
\(973\) −58.8478 + 44.0529i −1.88657 + 1.41227i
\(974\) 0 0
\(975\) −0.133724 + 1.01504i −0.00428259 + 0.0325074i
\(976\) 0 0
\(977\) 46.8619 + 17.4786i 1.49925 + 0.559190i 0.959270 0.282491i \(-0.0911608\pi\)
0.539976 + 0.841681i \(0.318433\pi\)
\(978\) 0 0
\(979\) −45.6843 + 6.56840i −1.46008 + 0.209927i
\(980\) 0 0
\(981\) 13.8884 + 47.2995i 0.443422 + 1.51016i
\(982\) 0 0
\(983\) 24.8242 1.77546i 0.791769 0.0566284i 0.330405 0.943839i \(-0.392815\pi\)
0.461364 + 0.887211i \(0.347360\pi\)
\(984\) 0 0
\(985\) 23.3888 3.50391i 0.745228 0.111644i
\(986\) 0 0
\(987\) −1.54326 4.13765i −0.0491226 0.131703i
\(988\) 0 0
\(989\) −2.23307 3.28312i −0.0710075 0.104397i
\(990\) 0 0
\(991\) 19.2444 42.1394i 0.611320 1.33860i −0.310348 0.950623i \(-0.600446\pi\)
0.921668 0.387980i \(-0.126827\pi\)
\(992\) 0 0
\(993\) −1.82457 0.130496i −0.0579011 0.00414117i
\(994\) 0 0
\(995\) 9.18372 + 4.94451i 0.291144 + 0.156751i
\(996\) 0 0
\(997\) 22.0128 + 12.0199i 0.697151 + 0.380673i 0.788407 0.615154i \(-0.210906\pi\)
−0.0912559 + 0.995827i \(0.529088\pi\)
\(998\) 0 0
\(999\) 0.667306 + 4.64121i 0.0211126 + 0.146842i
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 920.2.bv.a.17.17 720
5.3 odd 4 inner 920.2.bv.a.753.17 yes 720
23.19 odd 22 inner 920.2.bv.a.617.17 yes 720
115.88 even 44 inner 920.2.bv.a.433.17 yes 720
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.bv.a.17.17 720 1.1 even 1 trivial
920.2.bv.a.433.17 yes 720 115.88 even 44 inner
920.2.bv.a.617.17 yes 720 23.19 odd 22 inner
920.2.bv.a.753.17 yes 720 5.3 odd 4 inner