Properties

Label 512.2.k.a.49.5
Level $512$
Weight $2$
Character 512.49
Analytic conductor $4.088$
Analytic rank $0$
Dimension $240$
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] = [512,2,Mod(17,512)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(512, base_ring=CyclotomicField(32))
 
chi = DirichletCharacter(H, H._module([0, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("512.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 512 = 2^{9} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 512.k (of order \(32\), degree \(16\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.08834058349\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(15\) over \(\Q(\zeta_{32})\)
Twist minimal: no (minimal twist has level 128)
Sato-Tate group: $\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label 49.5
Character \(\chi\) \(=\) 512.49
Dual form 512.2.k.a.209.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.166477 - 1.69027i) q^{3} +(2.32067 + 1.24042i) q^{5} +(0.239955 - 1.20633i) q^{7} +(0.113053 - 0.0224877i) q^{9} +O(q^{10})\) \(q+(-0.166477 - 1.69027i) q^{3} +(2.32067 + 1.24042i) q^{5} +(0.239955 - 1.20633i) q^{7} +(0.113053 - 0.0224877i) q^{9} +(2.84394 + 3.46535i) q^{11} +(-2.35954 - 4.41439i) q^{13} +(1.71032 - 4.12907i) q^{15} +(2.17351 + 5.24732i) q^{17} +(0.528494 - 1.74221i) q^{19} +(-2.07898 - 0.204761i) q^{21} +(3.92750 + 2.62427i) q^{23} +(1.06901 + 1.59989i) q^{25} +(-1.53593 - 5.06329i) q^{27} +(-4.46356 - 3.66315i) q^{29} +(-0.404410 - 0.404410i) q^{31} +(5.38394 - 5.38394i) q^{33} +(2.05322 - 2.50186i) q^{35} +(-2.42968 + 0.737036i) q^{37} +(-7.06871 + 4.72316i) q^{39} +(2.45626 - 3.67605i) q^{41} +(0.899839 - 9.13621i) q^{43} +(0.290253 + 0.0880474i) q^{45} +(-5.00050 + 2.07128i) q^{47} +(5.06950 + 2.09985i) q^{49} +(8.50756 - 4.54739i) q^{51} +(7.22450 - 5.92899i) q^{53} +(2.30135 + 11.5696i) q^{55} +(-3.03279 - 0.603260i) q^{57} +(-6.16502 + 11.5339i) q^{59} +(-10.4783 + 1.03202i) q^{61} -0.141776i q^{63} -13.1712i q^{65} +(-0.123903 + 0.0122034i) q^{67} +(3.78189 - 7.07543i) q^{69} +(-9.55491 - 1.90059i) q^{71} +(2.35394 + 11.8340i) q^{73} +(2.52628 - 2.07327i) q^{75} +(4.86279 - 2.59921i) q^{77} +(2.76306 + 1.14450i) q^{79} +(-7.98316 + 3.30673i) q^{81} +(2.85237 + 0.865258i) q^{83} +(-1.46490 + 14.8734i) q^{85} +(-5.44863 + 8.15445i) q^{87} +(-8.92598 + 5.96415i) q^{89} +(-5.89141 + 1.78714i) q^{91} +(-0.616238 + 0.750889i) q^{93} +(3.38754 - 3.38754i) q^{95} +(6.34408 + 6.34408i) q^{97} +(0.399444 + 0.327815i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35} - 16 q^{37} + 16 q^{39} - 16 q^{41} + 16 q^{43} - 16 q^{45} + 16 q^{47} - 16 q^{49} + 16 q^{51} - 16 q^{53} + 16 q^{55} - 16 q^{57} + 16 q^{59} - 16 q^{61} + 16 q^{67} - 16 q^{69} + 16 q^{71} - 16 q^{73} + 16 q^{75} - 16 q^{77} + 16 q^{79} - 16 q^{81} + 16 q^{83} - 16 q^{85} + 16 q^{87} - 16 q^{89} + 16 q^{91} - 16 q^{93} + 16 q^{95} - 16 q^{97} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/512\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(511\)
\(\chi(n)\) \(e\left(\frac{5}{32}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.166477 1.69027i −0.0961157 0.975879i −0.915415 0.402512i \(-0.868137\pi\)
0.819299 0.573367i \(-0.194363\pi\)
\(4\) 0 0
\(5\) 2.32067 + 1.24042i 1.03784 + 0.554735i 0.900077 0.435731i \(-0.143510\pi\)
0.137759 + 0.990466i \(0.456010\pi\)
\(6\) 0 0
\(7\) 0.239955 1.20633i 0.0906943 0.455951i −0.908575 0.417722i \(-0.862828\pi\)
0.999269 0.0382286i \(-0.0121715\pi\)
\(8\) 0 0
\(9\) 0.113053 0.0224877i 0.0376844 0.00749589i
\(10\) 0 0
\(11\) 2.84394 + 3.46535i 0.857481 + 1.04484i 0.998495 + 0.0548358i \(0.0174635\pi\)
−0.141015 + 0.990008i \(0.545036\pi\)
\(12\) 0 0
\(13\) −2.35954 4.41439i −0.654419 1.22433i −0.962062 0.272830i \(-0.912040\pi\)
0.307643 0.951502i \(-0.400460\pi\)
\(14\) 0 0
\(15\) 1.71032 4.12907i 0.441602 1.06612i
\(16\) 0 0
\(17\) 2.17351 + 5.24732i 0.527154 + 1.27266i 0.933380 + 0.358890i \(0.116845\pi\)
−0.406225 + 0.913773i \(0.633155\pi\)
\(18\) 0 0
\(19\) 0.528494 1.74221i 0.121245 0.399691i −0.875218 0.483729i \(-0.839282\pi\)
0.996462 + 0.0840387i \(0.0267819\pi\)
\(20\) 0 0
\(21\) −2.07898 0.204761i −0.453670 0.0446826i
\(22\) 0 0
\(23\) 3.92750 + 2.62427i 0.818941 + 0.547199i 0.893001 0.450055i \(-0.148596\pi\)
−0.0740600 + 0.997254i \(0.523596\pi\)
\(24\) 0 0
\(25\) 1.06901 + 1.59989i 0.213802 + 0.319978i
\(26\) 0 0
\(27\) −1.53593 5.06329i −0.295590 0.974431i
\(28\) 0 0
\(29\) −4.46356 3.66315i −0.828862 0.680229i 0.121085 0.992642i \(-0.461363\pi\)
−0.949946 + 0.312413i \(0.898863\pi\)
\(30\) 0 0
\(31\) −0.404410 0.404410i −0.0726343 0.0726343i 0.669856 0.742491i \(-0.266356\pi\)
−0.742491 + 0.669856i \(0.766356\pi\)
\(32\) 0 0
\(33\) 5.38394 5.38394i 0.937223 0.937223i
\(34\) 0 0
\(35\) 2.05322 2.50186i 0.347058 0.422891i
\(36\) 0 0
\(37\) −2.42968 + 0.737036i −0.399437 + 0.121168i −0.483611 0.875283i \(-0.660675\pi\)
0.0841736 + 0.996451i \(0.473175\pi\)
\(38\) 0 0
\(39\) −7.06871 + 4.72316i −1.13190 + 0.756311i
\(40\) 0 0
\(41\) 2.45626 3.67605i 0.383603 0.574103i −0.588547 0.808463i \(-0.700300\pi\)
0.972150 + 0.234361i \(0.0752996\pi\)
\(42\) 0 0
\(43\) 0.899839 9.13621i 0.137224 1.39326i −0.642091 0.766628i \(-0.721933\pi\)
0.779316 0.626632i \(-0.215567\pi\)
\(44\) 0 0
\(45\) 0.290253 + 0.0880474i 0.0432684 + 0.0131253i
\(46\) 0 0
\(47\) −5.00050 + 2.07128i −0.729398 + 0.302127i −0.716305 0.697788i \(-0.754168\pi\)
−0.0130936 + 0.999914i \(0.504168\pi\)
\(48\) 0 0
\(49\) 5.06950 + 2.09985i 0.724214 + 0.299979i
\(50\) 0 0
\(51\) 8.50756 4.54739i 1.19130 0.636762i
\(52\) 0 0
\(53\) 7.22450 5.92899i 0.992362 0.814410i 0.00972534 0.999953i \(-0.496904\pi\)
0.982636 + 0.185543i \(0.0594043\pi\)
\(54\) 0 0
\(55\) 2.30135 + 11.5696i 0.310313 + 1.56005i
\(56\) 0 0
\(57\) −3.03279 0.603260i −0.401703 0.0799037i
\(58\) 0 0
\(59\) −6.16502 + 11.5339i −0.802618 + 1.50159i 0.0613905 + 0.998114i \(0.480446\pi\)
−0.864008 + 0.503478i \(0.832054\pi\)
\(60\) 0 0
\(61\) −10.4783 + 1.03202i −1.34161 + 0.132137i −0.743208 0.669060i \(-0.766697\pi\)
−0.598400 + 0.801197i \(0.704197\pi\)
\(62\) 0 0
\(63\) 0.141776i 0.0178621i
\(64\) 0 0
\(65\) 13.1712i 1.63368i
\(66\) 0 0
\(67\) −0.123903 + 0.0122034i −0.0151371 + 0.00149088i −0.105583 0.994411i \(-0.533671\pi\)
0.0904457 + 0.995901i \(0.471171\pi\)
\(68\) 0 0
\(69\) 3.78189 7.07543i 0.455287 0.851781i
\(70\) 0 0
\(71\) −9.55491 1.90059i −1.13396 0.225559i −0.407791 0.913075i \(-0.633701\pi\)
−0.726169 + 0.687517i \(0.758701\pi\)
\(72\) 0 0
\(73\) 2.35394 + 11.8340i 0.275507 + 1.38507i 0.832258 + 0.554389i \(0.187048\pi\)
−0.556751 + 0.830680i \(0.687952\pi\)
\(74\) 0 0
\(75\) 2.52628 2.07327i 0.291710 0.239400i
\(76\) 0 0
\(77\) 4.86279 2.59921i 0.554166 0.296208i
\(78\) 0 0
\(79\) 2.76306 + 1.14450i 0.310868 + 0.128766i 0.532663 0.846328i \(-0.321191\pi\)
−0.221795 + 0.975093i \(0.571191\pi\)
\(80\) 0 0
\(81\) −7.98316 + 3.30673i −0.887018 + 0.367415i
\(82\) 0 0
\(83\) 2.85237 + 0.865258i 0.313089 + 0.0949744i 0.442919 0.896562i \(-0.353943\pi\)
−0.129830 + 0.991536i \(0.541443\pi\)
\(84\) 0 0
\(85\) −1.46490 + 14.8734i −0.158891 + 1.61325i
\(86\) 0 0
\(87\) −5.44863 + 8.15445i −0.584155 + 0.874249i
\(88\) 0 0
\(89\) −8.92598 + 5.96415i −0.946152 + 0.632198i −0.929956 0.367670i \(-0.880155\pi\)
−0.0161957 + 0.999869i \(0.505155\pi\)
\(90\) 0 0
\(91\) −5.89141 + 1.78714i −0.617587 + 0.187343i
\(92\) 0 0
\(93\) −0.616238 + 0.750889i −0.0639009 + 0.0778635i
\(94\) 0 0
\(95\) 3.38754 3.38754i 0.347554 0.347554i
\(96\) 0 0
\(97\) 6.34408 + 6.34408i 0.644144 + 0.644144i 0.951572 0.307427i \(-0.0994682\pi\)
−0.307427 + 0.951572i \(0.599468\pi\)
\(98\) 0 0
\(99\) 0.399444 + 0.327815i 0.0401457 + 0.0329467i
\(100\) 0 0
\(101\) 3.85716 + 12.7153i 0.383802 + 1.26522i 0.909910 + 0.414807i \(0.136151\pi\)
−0.526108 + 0.850418i \(0.676349\pi\)
\(102\) 0 0
\(103\) 3.58796 + 5.36976i 0.353532 + 0.529099i 0.965027 0.262150i \(-0.0844315\pi\)
−0.611495 + 0.791248i \(0.709431\pi\)
\(104\) 0 0
\(105\) −4.57063 3.05400i −0.446048 0.298040i
\(106\) 0 0
\(107\) −3.08074 0.303427i −0.297827 0.0293334i −0.0519997 0.998647i \(-0.516559\pi\)
−0.245827 + 0.969314i \(0.579059\pi\)
\(108\) 0 0
\(109\) −2.69072 + 8.87010i −0.257724 + 0.849602i 0.728622 + 0.684916i \(0.240161\pi\)
−0.986346 + 0.164686i \(0.947339\pi\)
\(110\) 0 0
\(111\) 1.65028 + 3.98412i 0.156637 + 0.378156i
\(112\) 0 0
\(113\) −0.445076 + 1.07451i −0.0418692 + 0.101081i −0.943431 0.331570i \(-0.892422\pi\)
0.901561 + 0.432651i \(0.142422\pi\)
\(114\) 0 0
\(115\) 5.85923 + 10.9618i 0.546376 + 1.02220i
\(116\) 0 0
\(117\) −0.366023 0.446000i −0.0338388 0.0412327i
\(118\) 0 0
\(119\) 6.85157 1.36286i 0.628082 0.124933i
\(120\) 0 0
\(121\) −1.77467 + 8.92189i −0.161334 + 0.811081i
\(122\) 0 0
\(123\) −6.62243 3.53977i −0.597125 0.319170i
\(124\) 0 0
\(125\) −0.793320 8.05471i −0.0709567 0.720435i
\(126\) 0 0
\(127\) −13.9234 −1.23550 −0.617751 0.786373i \(-0.711956\pi\)
−0.617751 + 0.786373i \(0.711956\pi\)
\(128\) 0 0
\(129\) −15.5925 −1.37284
\(130\) 0 0
\(131\) 1.61772 + 16.4250i 0.141341 + 1.43506i 0.760267 + 0.649610i \(0.225068\pi\)
−0.618926 + 0.785449i \(0.712432\pi\)
\(132\) 0 0
\(133\) −1.97487 1.05559i −0.171243 0.0915313i
\(134\) 0 0
\(135\) 2.71624 13.6554i 0.233777 1.17527i
\(136\) 0 0
\(137\) 7.85651 1.56276i 0.671227 0.133515i 0.152300 0.988334i \(-0.451332\pi\)
0.518926 + 0.854819i \(0.326332\pi\)
\(138\) 0 0
\(139\) −8.72035 10.6258i −0.739650 0.901267i 0.258247 0.966079i \(-0.416855\pi\)
−0.997897 + 0.0648123i \(0.979355\pi\)
\(140\) 0 0
\(141\) 4.33349 + 8.10739i 0.364946 + 0.682765i
\(142\) 0 0
\(143\) 8.58703 20.7309i 0.718083 1.73361i
\(144\) 0 0
\(145\) −5.81459 14.0377i −0.482876 1.16576i
\(146\) 0 0
\(147\) 2.70537 8.91840i 0.223135 0.735577i
\(148\) 0 0
\(149\) −21.3609 2.10387i −1.74996 0.172356i −0.828280 0.560315i \(-0.810680\pi\)
−0.921676 + 0.387959i \(0.873180\pi\)
\(150\) 0 0
\(151\) −5.78610 3.86615i −0.470866 0.314623i 0.297400 0.954753i \(-0.403880\pi\)
−0.768267 + 0.640130i \(0.778880\pi\)
\(152\) 0 0
\(153\) 0.363722 + 0.544349i 0.0294052 + 0.0440080i
\(154\) 0 0
\(155\) −0.436863 1.44014i −0.0350897 0.115675i
\(156\) 0 0
\(157\) −7.94907 6.52363i −0.634405 0.520643i 0.261319 0.965252i \(-0.415842\pi\)
−0.895724 + 0.444610i \(0.853342\pi\)
\(158\) 0 0
\(159\) −11.2243 11.2243i −0.890147 0.890147i
\(160\) 0 0
\(161\) 4.10817 4.10817i 0.323769 0.323769i
\(162\) 0 0
\(163\) 3.21342 3.91557i 0.251695 0.306691i −0.631800 0.775131i \(-0.717684\pi\)
0.883495 + 0.468440i \(0.155184\pi\)
\(164\) 0 0
\(165\) 19.1727 5.81598i 1.49259 0.452773i
\(166\) 0 0
\(167\) 11.4411 7.64473i 0.885342 0.591567i −0.0276167 0.999619i \(-0.508792\pi\)
0.912959 + 0.408052i \(0.133792\pi\)
\(168\) 0 0
\(169\) −6.69700 + 10.0228i −0.515154 + 0.770982i
\(170\) 0 0
\(171\) 0.0205696 0.208847i 0.00157300 0.0159709i
\(172\) 0 0
\(173\) 7.51099 + 2.27843i 0.571050 + 0.173226i 0.562587 0.826738i \(-0.309806\pi\)
0.00846288 + 0.999964i \(0.497306\pi\)
\(174\) 0 0
\(175\) 2.18651 0.905684i 0.165285 0.0684632i
\(176\) 0 0
\(177\) 20.5218 + 8.50042i 1.54252 + 0.638931i
\(178\) 0 0
\(179\) −7.21589 + 3.85697i −0.539341 + 0.288284i −0.718489 0.695538i \(-0.755166\pi\)
0.179148 + 0.983822i \(0.442666\pi\)
\(180\) 0 0
\(181\) −7.45160 + 6.11537i −0.553873 + 0.454552i −0.869221 0.494424i \(-0.835379\pi\)
0.315348 + 0.948976i \(0.397879\pi\)
\(182\) 0 0
\(183\) 3.48880 + 17.5394i 0.257899 + 1.29655i
\(184\) 0 0
\(185\) −6.55273 1.30342i −0.481766 0.0958293i
\(186\) 0 0
\(187\) −12.0025 + 22.4551i −0.877709 + 1.64208i
\(188\) 0 0
\(189\) −6.47657 + 0.637887i −0.471101 + 0.0463994i
\(190\) 0 0
\(191\) 13.9561i 1.00983i 0.863170 + 0.504914i \(0.168476\pi\)
−0.863170 + 0.504914i \(0.831524\pi\)
\(192\) 0 0
\(193\) 16.0823i 1.15763i −0.815458 0.578816i \(-0.803515\pi\)
0.815458 0.578816i \(-0.196485\pi\)
\(194\) 0 0
\(195\) −22.2629 + 2.19270i −1.59428 + 0.157023i
\(196\) 0 0
\(197\) 3.35541 6.27754i 0.239063 0.447256i −0.733566 0.679618i \(-0.762145\pi\)
0.972629 + 0.232362i \(0.0746455\pi\)
\(198\) 0 0
\(199\) 14.4188 + 2.86808i 1.02212 + 0.203313i 0.677573 0.735456i \(-0.263032\pi\)
0.344549 + 0.938768i \(0.388032\pi\)
\(200\) 0 0
\(201\) 0.0412540 + 0.207398i 0.00290983 + 0.0146287i
\(202\) 0 0
\(203\) −5.49003 + 4.50555i −0.385324 + 0.316227i
\(204\) 0 0
\(205\) 10.2600 5.48410i 0.716592 0.383026i
\(206\) 0 0
\(207\) 0.503030 + 0.208362i 0.0349630 + 0.0144822i
\(208\) 0 0
\(209\) 7.54038 3.12333i 0.521579 0.216045i
\(210\) 0 0
\(211\) 25.0418 + 7.59635i 1.72395 + 0.522954i 0.988050 0.154135i \(-0.0492592\pi\)
0.735900 + 0.677090i \(0.236759\pi\)
\(212\) 0 0
\(213\) −1.62184 + 16.4668i −0.111127 + 1.12829i
\(214\) 0 0
\(215\) 13.4210 20.0860i 0.915306 1.36985i
\(216\) 0 0
\(217\) −0.584894 + 0.390814i −0.0397052 + 0.0265302i
\(218\) 0 0
\(219\) 19.6108 5.94889i 1.32518 0.401988i
\(220\) 0 0
\(221\) 18.0353 21.9760i 1.21318 1.47827i
\(222\) 0 0
\(223\) −11.2314 + 11.2314i −0.752109 + 0.752109i −0.974873 0.222763i \(-0.928492\pi\)
0.222763 + 0.974873i \(0.428492\pi\)
\(224\) 0 0
\(225\) 0.156833 + 0.156833i 0.0104555 + 0.0104555i
\(226\) 0 0
\(227\) −18.5633 15.2345i −1.23209 1.01115i −0.999253 0.0386372i \(-0.987698\pi\)
−0.232839 0.972515i \(-0.574802\pi\)
\(228\) 0 0
\(229\) −3.61076 11.9031i −0.238606 0.786578i −0.991690 0.128653i \(-0.958935\pi\)
0.753084 0.657924i \(-0.228565\pi\)
\(230\) 0 0
\(231\) −5.20292 7.78672i −0.342327 0.512329i
\(232\) 0 0
\(233\) −15.3098 10.2297i −1.00298 0.670169i −0.0583452 0.998296i \(-0.518582\pi\)
−0.944633 + 0.328128i \(0.893582\pi\)
\(234\) 0 0
\(235\) −14.1738 1.39600i −0.924596 0.0910647i
\(236\) 0 0
\(237\) 1.47452 4.86085i 0.0957805 0.315746i
\(238\) 0 0
\(239\) 4.60829 + 11.1254i 0.298085 + 0.719642i 0.999973 + 0.00735403i \(0.00234088\pi\)
−0.701888 + 0.712288i \(0.747659\pi\)
\(240\) 0 0
\(241\) −0.00151407 + 0.00365530i −9.75300e−5 + 0.000235458i −0.923928 0.382566i \(-0.875041\pi\)
0.923831 + 0.382801i \(0.125041\pi\)
\(242\) 0 0
\(243\) −0.564369 1.05586i −0.0362043 0.0677335i
\(244\) 0 0
\(245\) 9.15992 + 11.1614i 0.585206 + 0.713076i
\(246\) 0 0
\(247\) −8.93780 + 1.77784i −0.568699 + 0.113121i
\(248\) 0 0
\(249\) 0.987666 4.96533i 0.0625908 0.314665i
\(250\) 0 0
\(251\) 21.9077 + 11.7099i 1.38280 + 0.739123i 0.984043 0.177933i \(-0.0569410\pi\)
0.398759 + 0.917056i \(0.369441\pi\)
\(252\) 0 0
\(253\) 2.07555 + 21.0735i 0.130489 + 1.32488i
\(254\) 0 0
\(255\) 25.3840 1.58960
\(256\) 0 0
\(257\) 0.135446 0.00844889 0.00422444 0.999991i \(-0.498655\pi\)
0.00422444 + 0.999991i \(0.498655\pi\)
\(258\) 0 0
\(259\) 0.306098 + 3.10786i 0.0190200 + 0.193113i
\(260\) 0 0
\(261\) −0.586995 0.313755i −0.0363341 0.0194210i
\(262\) 0 0
\(263\) 4.13027 20.7643i 0.254683 1.28038i −0.615690 0.787988i \(-0.711123\pi\)
0.870374 0.492392i \(-0.163877\pi\)
\(264\) 0 0
\(265\) 24.1202 4.79780i 1.48169 0.294726i
\(266\) 0 0
\(267\) 11.5670 + 14.0944i 0.707889 + 0.862565i
\(268\) 0 0
\(269\) 7.66285 + 14.3362i 0.467212 + 0.874093i 0.999619 + 0.0276040i \(0.00878774\pi\)
−0.532407 + 0.846489i \(0.678712\pi\)
\(270\) 0 0
\(271\) 4.27846 10.3291i 0.259898 0.627449i −0.739033 0.673669i \(-0.764717\pi\)
0.998931 + 0.0462196i \(0.0147174\pi\)
\(272\) 0 0
\(273\) 4.00154 + 9.66056i 0.242184 + 0.584684i
\(274\) 0 0
\(275\) −2.50397 + 8.25450i −0.150995 + 0.497765i
\(276\) 0 0
\(277\) 24.0197 + 2.36573i 1.44320 + 0.142143i 0.789101 0.614263i \(-0.210547\pi\)
0.654102 + 0.756407i \(0.273047\pi\)
\(278\) 0 0
\(279\) −0.0548141 0.0366256i −0.00328163 0.00219272i
\(280\) 0 0
\(281\) −17.6077 26.3518i −1.05039 1.57202i −0.796362 0.604821i \(-0.793245\pi\)
−0.254027 0.967197i \(-0.581755\pi\)
\(282\) 0 0
\(283\) 3.30912 + 10.9087i 0.196707 + 0.648455i 0.998693 + 0.0511122i \(0.0162766\pi\)
−0.801986 + 0.597342i \(0.796223\pi\)
\(284\) 0 0
\(285\) −6.28981 5.16192i −0.372576 0.305766i
\(286\) 0 0
\(287\) −3.84515 3.84515i −0.226972 0.226972i
\(288\) 0 0
\(289\) −10.7894 + 10.7894i −0.634673 + 0.634673i
\(290\) 0 0
\(291\) 9.66708 11.7794i 0.566694 0.690519i
\(292\) 0 0
\(293\) 4.15920 1.26168i 0.242983 0.0737080i −0.166444 0.986051i \(-0.553229\pi\)
0.409427 + 0.912343i \(0.365729\pi\)
\(294\) 0 0
\(295\) −28.6140 + 19.1193i −1.66597 + 1.11317i
\(296\) 0 0
\(297\) 13.1780 19.7223i 0.764665 1.14440i
\(298\) 0 0
\(299\) 2.31746 23.5296i 0.134022 1.36075i
\(300\) 0 0
\(301\) −10.8054 3.27778i −0.622813 0.188928i
\(302\) 0 0
\(303\) 20.8503 8.63646i 1.19782 0.496152i
\(304\) 0 0
\(305\) −25.5968 10.6026i −1.46567 0.607101i
\(306\) 0 0
\(307\) −12.3235 + 6.58702i −0.703337 + 0.375941i −0.783967 0.620803i \(-0.786807\pi\)
0.0806300 + 0.996744i \(0.474307\pi\)
\(308\) 0 0
\(309\) 8.47905 6.95857i 0.482356 0.395859i
\(310\) 0 0
\(311\) −0.457287 2.29894i −0.0259304 0.130361i 0.965652 0.259839i \(-0.0836697\pi\)
−0.991582 + 0.129479i \(0.958670\pi\)
\(312\) 0 0
\(313\) −16.5689 3.29576i −0.936529 0.186287i −0.296846 0.954925i \(-0.595935\pi\)
−0.639684 + 0.768638i \(0.720935\pi\)
\(314\) 0 0
\(315\) 0.175862 0.329015i 0.00990871 0.0185379i
\(316\) 0 0
\(317\) 15.5842 1.53491i 0.875296 0.0862092i 0.349618 0.936892i \(-0.386311\pi\)
0.525679 + 0.850683i \(0.323811\pi\)
\(318\) 0 0
\(319\) 25.8856i 1.44931i
\(320\) 0 0
\(321\) 5.25780i 0.293462i
\(322\) 0 0
\(323\) 10.2906 1.01354i 0.572586 0.0563948i
\(324\) 0 0
\(325\) 4.54016 8.49404i 0.251843 0.471165i
\(326\) 0 0
\(327\) 15.4408 + 3.07137i 0.853880 + 0.169847i
\(328\) 0 0
\(329\) 1.29876 + 6.52928i 0.0716027 + 0.359971i
\(330\) 0 0
\(331\) 7.46294 6.12468i 0.410200 0.336643i −0.406556 0.913626i \(-0.633270\pi\)
0.816756 + 0.576983i \(0.195770\pi\)
\(332\) 0 0
\(333\) −0.258109 + 0.137962i −0.0141443 + 0.00756028i
\(334\) 0 0
\(335\) −0.302675 0.125372i −0.0165369 0.00684981i
\(336\) 0 0
\(337\) −27.4666 + 11.3770i −1.49620 + 0.619747i −0.972656 0.232251i \(-0.925391\pi\)
−0.523545 + 0.851998i \(0.675391\pi\)
\(338\) 0 0
\(339\) 1.89031 + 0.573418i 0.102667 + 0.0311438i
\(340\) 0 0
\(341\) 0.251305 2.55155i 0.0136089 0.138174i
\(342\) 0 0
\(343\) 8.53290 12.7704i 0.460733 0.689536i
\(344\) 0 0
\(345\) 17.5531 11.7286i 0.945025 0.631446i
\(346\) 0 0
\(347\) 0.420104 0.127437i 0.0225524 0.00684118i −0.278988 0.960294i \(-0.589999\pi\)
0.301541 + 0.953453i \(0.402499\pi\)
\(348\) 0 0
\(349\) 6.62883 8.07725i 0.354833 0.432365i −0.564749 0.825262i \(-0.691027\pi\)
0.919582 + 0.392897i \(0.128527\pi\)
\(350\) 0 0
\(351\) −18.7273 + 18.7273i −0.999587 + 0.999587i
\(352\) 0 0
\(353\) −4.92601 4.92601i −0.262185 0.262185i 0.563756 0.825941i \(-0.309356\pi\)
−0.825941 + 0.563756i \(0.809356\pi\)
\(354\) 0 0
\(355\) −19.8163 16.2628i −1.05174 0.863140i
\(356\) 0 0
\(357\) −3.44423 11.3541i −0.182288 0.600924i
\(358\) 0 0
\(359\) −9.29622 13.9128i −0.490636 0.734288i 0.500703 0.865619i \(-0.333075\pi\)
−0.991339 + 0.131331i \(0.958075\pi\)
\(360\) 0 0
\(361\) 13.0419 + 8.71434i 0.686417 + 0.458649i
\(362\) 0 0
\(363\) 15.3759 + 1.51439i 0.807023 + 0.0794849i
\(364\) 0 0
\(365\) −9.21652 + 30.3828i −0.482414 + 1.59031i
\(366\) 0 0
\(367\) 2.90211 + 7.00630i 0.151489 + 0.365726i 0.981346 0.192249i \(-0.0615783\pi\)
−0.829857 + 0.557976i \(0.811578\pi\)
\(368\) 0 0
\(369\) 0.195022 0.470824i 0.0101524 0.0245101i
\(370\) 0 0
\(371\) −5.41879 10.1378i −0.281330 0.526331i
\(372\) 0 0
\(373\) −6.57935 8.01696i −0.340666 0.415103i 0.574293 0.818650i \(-0.305277\pi\)
−0.914959 + 0.403547i \(0.867777\pi\)
\(374\) 0 0
\(375\) −13.4826 + 2.68185i −0.696237 + 0.138490i
\(376\) 0 0
\(377\) −5.63862 + 28.3472i −0.290403 + 1.45996i
\(378\) 0 0
\(379\) −20.2626 10.8306i −1.04082 0.556329i −0.139832 0.990175i \(-0.544656\pi\)
−0.900987 + 0.433846i \(0.857156\pi\)
\(380\) 0 0
\(381\) 2.31793 + 23.5343i 0.118751 + 1.20570i
\(382\) 0 0
\(383\) 2.22072 0.113473 0.0567366 0.998389i \(-0.481930\pi\)
0.0567366 + 0.998389i \(0.481930\pi\)
\(384\) 0 0
\(385\) 14.5091 0.739450
\(386\) 0 0
\(387\) −0.103723 1.05311i −0.00527251 0.0535327i
\(388\) 0 0
\(389\) −20.3349 10.8692i −1.03102 0.551092i −0.133033 0.991112i \(-0.542472\pi\)
−0.897988 + 0.440019i \(0.854972\pi\)
\(390\) 0 0
\(391\) −5.23394 + 26.3128i −0.264692 + 1.33069i
\(392\) 0 0
\(393\) 27.4934 5.46878i 1.38686 0.275863i
\(394\) 0 0
\(395\) 4.99249 + 6.08336i 0.251199 + 0.306087i
\(396\) 0 0
\(397\) 6.76073 + 12.6484i 0.339311 + 0.634806i 0.992480 0.122406i \(-0.0390609\pi\)
−0.653169 + 0.757212i \(0.726561\pi\)
\(398\) 0 0
\(399\) −1.45546 + 3.51380i −0.0728643 + 0.175910i
\(400\) 0 0
\(401\) 5.55475 + 13.4103i 0.277391 + 0.669680i 0.999762 0.0218252i \(-0.00694771\pi\)
−0.722371 + 0.691506i \(0.756948\pi\)
\(402\) 0 0
\(403\) −0.831003 + 2.73945i −0.0413952 + 0.136462i
\(404\) 0 0
\(405\) −22.6280 2.22867i −1.12440 0.110743i
\(406\) 0 0
\(407\) −9.46397 6.32362i −0.469111 0.313450i
\(408\) 0 0
\(409\) −6.30735 9.43961i −0.311878 0.466759i 0.642106 0.766616i \(-0.278061\pi\)
−0.953984 + 0.299857i \(0.903061\pi\)
\(410\) 0 0
\(411\) −3.94941 13.0195i −0.194810 0.642203i
\(412\) 0 0
\(413\) 12.4345 + 10.2047i 0.611859 + 0.502140i
\(414\) 0 0
\(415\) 5.54614 + 5.54614i 0.272249 + 0.272249i
\(416\) 0 0
\(417\) −16.5087 + 16.5087i −0.808435 + 0.808435i
\(418\) 0 0
\(419\) −10.5649 + 12.8733i −0.516127 + 0.628903i −0.964226 0.265081i \(-0.914601\pi\)
0.448099 + 0.893984i \(0.352101\pi\)
\(420\) 0 0
\(421\) −10.7929 + 3.27399i −0.526013 + 0.159564i −0.542112 0.840306i \(-0.682375\pi\)
0.0160991 + 0.999870i \(0.494875\pi\)
\(422\) 0 0
\(423\) −0.518744 + 0.346614i −0.0252222 + 0.0168529i
\(424\) 0 0
\(425\) −6.07163 + 9.08683i −0.294517 + 0.440776i
\(426\) 0 0
\(427\) −1.26935 + 12.8880i −0.0614283 + 0.623692i
\(428\) 0 0
\(429\) −36.4704 11.0632i −1.76081 0.534135i
\(430\) 0 0
\(431\) −6.77521 + 2.80638i −0.326350 + 0.135179i −0.539842 0.841766i \(-0.681516\pi\)
0.213492 + 0.976945i \(0.431516\pi\)
\(432\) 0 0
\(433\) 18.9855 + 7.86406i 0.912385 + 0.377922i 0.788969 0.614433i \(-0.210615\pi\)
0.123416 + 0.992355i \(0.460615\pi\)
\(434\) 0 0
\(435\) −22.7595 + 12.1652i −1.09123 + 0.583276i
\(436\) 0 0
\(437\) 6.64770 5.45562i 0.318003 0.260978i
\(438\) 0 0
\(439\) 0.118473 + 0.595603i 0.00565439 + 0.0284266i 0.983509 0.180857i \(-0.0578870\pi\)
−0.977855 + 0.209283i \(0.932887\pi\)
\(440\) 0 0
\(441\) 0.620343 + 0.123394i 0.0295401 + 0.00587590i
\(442\) 0 0
\(443\) 13.4576 25.1774i 0.639390 1.19622i −0.328419 0.944532i \(-0.606516\pi\)
0.967810 0.251683i \(-0.0809841\pi\)
\(444\) 0 0
\(445\) −28.1123 + 2.76882i −1.33265 + 0.131255i
\(446\) 0 0
\(447\) 36.4560i 1.72431i
\(448\) 0 0
\(449\) 5.68438i 0.268263i 0.990964 + 0.134131i \(0.0428244\pi\)
−0.990964 + 0.134131i \(0.957176\pi\)
\(450\) 0 0
\(451\) 19.7243 1.94267i 0.928780 0.0914768i
\(452\) 0 0
\(453\) −5.57159 + 10.4237i −0.261776 + 0.489749i
\(454\) 0 0
\(455\) −15.8888 3.16049i −0.744880 0.148166i
\(456\) 0 0
\(457\) −1.50389 7.56059i −0.0703492 0.353669i 0.929537 0.368728i \(-0.120207\pi\)
−0.999887 + 0.0150585i \(0.995207\pi\)
\(458\) 0 0
\(459\) 23.2304 19.0647i 1.08430 0.889863i
\(460\) 0 0
\(461\) 14.9822 8.00813i 0.697789 0.372976i −0.0840457 0.996462i \(-0.526784\pi\)
0.781834 + 0.623486i \(0.214284\pi\)
\(462\) 0 0
\(463\) 0.476273 + 0.197279i 0.0221343 + 0.00916832i 0.393723 0.919229i \(-0.371187\pi\)
−0.371589 + 0.928397i \(0.621187\pi\)
\(464\) 0 0
\(465\) −2.36151 + 0.978169i −0.109512 + 0.0453615i
\(466\) 0 0
\(467\) −0.640297 0.194232i −0.0296294 0.00898798i 0.275435 0.961320i \(-0.411178\pi\)
−0.305065 + 0.952332i \(0.598678\pi\)
\(468\) 0 0
\(469\) −0.0150097 + 0.152396i −0.000693085 + 0.00703701i
\(470\) 0 0
\(471\) −9.70337 + 14.5221i −0.447108 + 0.669144i
\(472\) 0 0
\(473\) 34.2193 22.8646i 1.57341 1.05132i
\(474\) 0 0
\(475\) 3.35231 1.01691i 0.153815 0.0466591i
\(476\) 0 0
\(477\) 0.683423 0.832753i 0.0312918 0.0381292i
\(478\) 0 0
\(479\) −19.3257 + 19.3257i −0.883013 + 0.883013i −0.993840 0.110826i \(-0.964650\pi\)
0.110826 + 0.993840i \(0.464650\pi\)
\(480\) 0 0
\(481\) 8.98650 + 8.98650i 0.409749 + 0.409749i
\(482\) 0 0
\(483\) −7.62784 6.26000i −0.347079 0.284840i
\(484\) 0 0
\(485\) 6.85318 + 22.5919i 0.311187 + 1.02584i
\(486\) 0 0
\(487\) −5.99682 8.97488i −0.271742 0.406690i 0.670350 0.742045i \(-0.266144\pi\)
−0.942092 + 0.335354i \(0.891144\pi\)
\(488\) 0 0
\(489\) −7.15334 4.77971i −0.323485 0.216146i
\(490\) 0 0
\(491\) −14.5775 1.43576i −0.657875 0.0647950i −0.236429 0.971649i \(-0.575977\pi\)
−0.421446 + 0.906854i \(0.638477\pi\)
\(492\) 0 0
\(493\) 9.52012 31.3836i 0.428765 1.41345i
\(494\) 0 0
\(495\) 0.520348 + 1.25623i 0.0233879 + 0.0564634i
\(496\) 0 0
\(497\) −4.58549 + 11.0704i −0.205687 + 0.496573i
\(498\) 0 0
\(499\) −8.21471 15.3686i −0.367741 0.687995i 0.628195 0.778056i \(-0.283794\pi\)
−0.995936 + 0.0900606i \(0.971294\pi\)
\(500\) 0 0
\(501\) −14.8263 18.0660i −0.662392 0.807128i
\(502\) 0 0
\(503\) 38.7570 7.70925i 1.72809 0.343739i 0.771735 0.635944i \(-0.219389\pi\)
0.956355 + 0.292206i \(0.0943893\pi\)
\(504\) 0 0
\(505\) −6.82124 + 34.2927i −0.303541 + 1.52600i
\(506\) 0 0
\(507\) 18.0561 + 9.65119i 0.801900 + 0.428624i
\(508\) 0 0
\(509\) 1.16391 + 11.8173i 0.0515893 + 0.523795i 0.985900 + 0.167335i \(0.0535162\pi\)
−0.934311 + 0.356459i \(0.883984\pi\)
\(510\) 0 0
\(511\) 14.8406 0.656510
\(512\) 0 0
\(513\) −9.63305 −0.425310
\(514\) 0 0
\(515\) 1.66569 + 16.9121i 0.0733992 + 0.745234i
\(516\) 0 0
\(517\) −21.3988 11.4379i −0.941120 0.503039i
\(518\) 0 0
\(519\) 2.60076 13.0749i 0.114161 0.573925i
\(520\) 0 0
\(521\) 0.0812832 0.0161682i 0.00356108 0.000708343i −0.193309 0.981138i \(-0.561922\pi\)
0.196871 + 0.980429i \(0.436922\pi\)
\(522\) 0 0
\(523\) 16.0428 + 19.5483i 0.701504 + 0.854785i 0.994864 0.101217i \(-0.0322735\pi\)
−0.293360 + 0.956002i \(0.594774\pi\)
\(524\) 0 0
\(525\) −1.89486 3.54503i −0.0826983 0.154718i
\(526\) 0 0
\(527\) 1.24308 3.00106i 0.0541495 0.130728i
\(528\) 0 0
\(529\) −0.263255 0.635553i −0.0114458 0.0276327i
\(530\) 0 0
\(531\) −0.437603 + 1.44259i −0.0189904 + 0.0626029i
\(532\) 0 0
\(533\) −22.0232 2.16909i −0.953929 0.0939538i
\(534\) 0 0
\(535\) −6.77301 4.52558i −0.292823 0.195658i
\(536\) 0 0
\(537\) 7.72061 + 11.5547i 0.333169 + 0.498623i
\(538\) 0 0
\(539\) 7.14062 + 23.5395i 0.307568 + 1.01392i
\(540\) 0 0
\(541\) −16.3412 13.4108i −0.702562 0.576577i 0.213825 0.976872i \(-0.431408\pi\)
−0.916387 + 0.400295i \(0.868908\pi\)
\(542\) 0 0
\(543\) 11.5772 + 11.5772i 0.496823 + 0.496823i
\(544\) 0 0
\(545\) −17.2470 + 17.2470i −0.738779 + 0.738779i
\(546\) 0 0
\(547\) 10.0002 12.1852i 0.427576 0.521003i −0.514006 0.857787i \(-0.671839\pi\)
0.941582 + 0.336784i \(0.109339\pi\)
\(548\) 0 0
\(549\) −1.16140 + 0.352306i −0.0495672 + 0.0150360i
\(550\) 0 0
\(551\) −8.74094 + 5.84051i −0.372376 + 0.248814i
\(552\) 0 0
\(553\) 2.04365 3.05854i 0.0869049 0.130062i
\(554\) 0 0
\(555\) −1.11225 + 11.2929i −0.0472125 + 0.479356i
\(556\) 0 0
\(557\) −5.53316 1.67847i −0.234448 0.0711189i 0.170875 0.985293i \(-0.445341\pi\)
−0.405322 + 0.914174i \(0.632841\pi\)
\(558\) 0 0
\(559\) −42.4540 + 17.5850i −1.79561 + 0.743768i
\(560\) 0 0
\(561\) 39.9533 + 16.5492i 1.68683 + 0.698708i
\(562\) 0 0
\(563\) −22.9888 + 12.2878i −0.968863 + 0.517868i −0.878345 0.478027i \(-0.841352\pi\)
−0.0905175 + 0.995895i \(0.528852\pi\)
\(564\) 0 0
\(565\) −2.36572 + 1.94150i −0.0995267 + 0.0816794i
\(566\) 0 0
\(567\) 2.07343 + 10.4238i 0.0870757 + 0.437759i
\(568\) 0 0
\(569\) 19.6192 + 3.90249i 0.822478 + 0.163601i 0.588352 0.808605i \(-0.299777\pi\)
0.234126 + 0.972206i \(0.424777\pi\)
\(570\) 0 0
\(571\) 3.74397 7.00448i 0.156680 0.293128i −0.791317 0.611406i \(-0.790604\pi\)
0.947998 + 0.318278i \(0.103104\pi\)
\(572\) 0 0
\(573\) 23.5896 2.32337i 0.985469 0.0970602i
\(574\) 0 0
\(575\) 9.08895i 0.379035i
\(576\) 0 0
\(577\) 31.9709i 1.33097i −0.746413 0.665483i \(-0.768226\pi\)
0.746413 0.665483i \(-0.231774\pi\)
\(578\) 0 0
\(579\) −27.1835 + 2.67734i −1.12971 + 0.111267i
\(580\) 0 0
\(581\) 1.72823 3.23329i 0.0716990 0.134139i
\(582\) 0 0
\(583\) 41.0921 + 8.17373i 1.70186 + 0.338521i
\(584\) 0 0
\(585\) −0.296189 1.48904i −0.0122459 0.0615644i
\(586\) 0 0
\(587\) −20.8006 + 17.0706i −0.858532 + 0.704579i −0.956852 0.290576i \(-0.906153\pi\)
0.0983198 + 0.995155i \(0.468653\pi\)
\(588\) 0 0
\(589\) −0.918297 + 0.490840i −0.0378378 + 0.0202247i
\(590\) 0 0
\(591\) −11.1693 4.62649i −0.459445 0.190309i
\(592\) 0 0
\(593\) −23.9376 + 9.91530i −0.983001 + 0.407172i −0.815536 0.578706i \(-0.803558\pi\)
−0.167465 + 0.985878i \(0.553558\pi\)
\(594\) 0 0
\(595\) 17.5908 + 5.33610i 0.721151 + 0.218759i
\(596\) 0 0
\(597\) 2.44743 24.8491i 0.100167 1.01701i
\(598\) 0 0
\(599\) −6.56909 + 9.83133i −0.268406 + 0.401697i −0.941049 0.338269i \(-0.890159\pi\)
0.672644 + 0.739966i \(0.265159\pi\)
\(600\) 0 0
\(601\) 5.51163 3.68275i 0.224824 0.150223i −0.438057 0.898947i \(-0.644333\pi\)
0.662881 + 0.748724i \(0.269333\pi\)
\(602\) 0 0
\(603\) −0.0137332 + 0.00416591i −0.000559258 + 0.000169649i
\(604\) 0 0
\(605\) −15.1854 + 18.5034i −0.617373 + 0.752271i
\(606\) 0 0
\(607\) 20.8059 20.8059i 0.844487 0.844487i −0.144952 0.989439i \(-0.546303\pi\)
0.989439 + 0.144952i \(0.0463028\pi\)
\(608\) 0 0
\(609\) 8.52956 + 8.52956i 0.345635 + 0.345635i
\(610\) 0 0
\(611\) 20.9423 + 17.1869i 0.847235 + 0.695308i
\(612\) 0 0
\(613\) 7.55366 + 24.9011i 0.305089 + 1.00574i 0.966703 + 0.255900i \(0.0823718\pi\)
−0.661614 + 0.749845i \(0.730128\pi\)
\(614\) 0 0
\(615\) −10.9777 16.4293i −0.442663 0.662492i
\(616\) 0 0
\(617\) 17.2556 + 11.5298i 0.694684 + 0.464173i 0.852113 0.523357i \(-0.175321\pi\)
−0.157429 + 0.987530i \(0.550321\pi\)
\(618\) 0 0
\(619\) −12.2321 1.20475i −0.491648 0.0484231i −0.150844 0.988558i \(-0.548199\pi\)
−0.340804 + 0.940134i \(0.610699\pi\)
\(620\) 0 0
\(621\) 7.25508 23.9168i 0.291136 0.959748i
\(622\) 0 0
\(623\) 5.05292 + 12.1988i 0.202441 + 0.488736i
\(624\) 0 0
\(625\) 11.8320 28.5649i 0.473279 1.14260i
\(626\) 0 0
\(627\) −6.53457 12.2253i −0.260966 0.488233i
\(628\) 0 0
\(629\) −9.14841 11.1474i −0.364771 0.444475i
\(630\) 0 0
\(631\) 1.69710 0.337574i 0.0675604 0.0134386i −0.161194 0.986923i \(-0.551535\pi\)
0.228755 + 0.973484i \(0.426535\pi\)
\(632\) 0 0
\(633\) 8.67101 43.5921i 0.344642 1.73263i
\(634\) 0 0
\(635\) −32.3117 17.2709i −1.28225 0.685376i
\(636\) 0 0
\(637\) −2.69211 27.3334i −0.106665 1.08299i
\(638\) 0 0
\(639\) −1.12295 −0.0444233
\(640\) 0 0
\(641\) 18.6498 0.736623 0.368312 0.929702i \(-0.379936\pi\)
0.368312 + 0.929702i \(0.379936\pi\)
\(642\) 0 0
\(643\) −0.304767 3.09435i −0.0120188 0.122029i 0.987303 0.158847i \(-0.0507778\pi\)
−0.999322 + 0.0368181i \(0.988278\pi\)
\(644\) 0 0
\(645\) −36.1850 19.3413i −1.42478 0.761563i
\(646\) 0 0
\(647\) −0.0407744 + 0.204987i −0.00160301 + 0.00805886i −0.981579 0.191059i \(-0.938808\pi\)
0.979975 + 0.199118i \(0.0638077\pi\)
\(648\) 0 0
\(649\) −57.5022 + 11.4379i −2.25716 + 0.448977i
\(650\) 0 0
\(651\) 0.757952 + 0.923568i 0.0297065 + 0.0361975i
\(652\) 0 0
\(653\) 17.7105 + 33.1340i 0.693064 + 1.29663i 0.944421 + 0.328737i \(0.106623\pi\)
−0.251357 + 0.967894i \(0.580877\pi\)
\(654\) 0 0
\(655\) −16.6198 + 40.1237i −0.649389 + 1.56776i
\(656\) 0 0
\(657\) 0.532239 + 1.28494i 0.0207646 + 0.0501303i
\(658\) 0 0
\(659\) 9.14628 30.1512i 0.356288 1.17453i −0.577407 0.816457i \(-0.695935\pi\)
0.933695 0.358069i \(-0.116565\pi\)
\(660\) 0 0
\(661\) 32.8774 + 3.23814i 1.27878 + 0.125949i 0.714502 0.699633i \(-0.246653\pi\)
0.564281 + 0.825582i \(0.309153\pi\)
\(662\) 0 0
\(663\) −40.1479 26.8260i −1.55921 1.04183i
\(664\) 0 0
\(665\) −3.27365 4.89936i −0.126947 0.189989i
\(666\) 0 0
\(667\) −7.91753 26.1006i −0.306568 1.01062i
\(668\) 0 0
\(669\) 20.8539 + 17.1143i 0.806257 + 0.661678i
\(670\) 0 0
\(671\) −33.3760 33.3760i −1.28847 1.28847i
\(672\) 0 0
\(673\) 23.6949 23.6949i 0.913370 0.913370i −0.0831659 0.996536i \(-0.526503\pi\)
0.996536 + 0.0831659i \(0.0265031\pi\)
\(674\) 0 0
\(675\) 6.45878 7.87004i 0.248598 0.302918i
\(676\) 0 0
\(677\) 4.78697 1.45211i 0.183978 0.0558092i −0.196951 0.980413i \(-0.563104\pi\)
0.380929 + 0.924604i \(0.375604\pi\)
\(678\) 0 0
\(679\) 9.17537 6.13078i 0.352118 0.235278i
\(680\) 0 0
\(681\) −22.6601 + 33.9133i −0.868339 + 1.29956i
\(682\) 0 0
\(683\) 1.30338 13.2334i 0.0498725 0.506364i −0.937504 0.347974i \(-0.886870\pi\)
0.987377 0.158390i \(-0.0506302\pi\)
\(684\) 0 0
\(685\) 20.1709 + 6.11876i 0.770689 + 0.233786i
\(686\) 0 0
\(687\) −19.5183 + 8.08475i −0.744670 + 0.308453i
\(688\) 0 0
\(689\) −43.2194 17.9021i −1.64653 0.682014i
\(690\) 0 0
\(691\) 17.9144 9.57545i 0.681496 0.364267i −0.0940417 0.995568i \(-0.529979\pi\)
0.775538 + 0.631301i \(0.217479\pi\)
\(692\) 0 0
\(693\) 0.491303 0.403202i 0.0186631 0.0153164i
\(694\) 0 0
\(695\) −7.05659 35.4759i −0.267672 1.34568i
\(696\) 0 0
\(697\) 24.6281 + 4.89884i 0.932857 + 0.185557i
\(698\) 0 0
\(699\) −14.7422 + 27.5807i −0.557602 + 1.04320i
\(700\) 0 0
\(701\) 32.3427 3.18548i 1.22157 0.120314i 0.533398 0.845865i \(-0.320915\pi\)
0.688169 + 0.725551i \(0.258415\pi\)
\(702\) 0 0
\(703\) 4.62254i 0.174342i
\(704\) 0 0
\(705\) 24.1899i 0.911046i
\(706\) 0 0
\(707\) 16.2645 1.60191i 0.611689 0.0602461i
\(708\) 0 0
\(709\) −10.4682 + 19.5846i −0.393141 + 0.735515i −0.998156 0.0606989i \(-0.980667\pi\)
0.605015 + 0.796214i \(0.293167\pi\)
\(710\) 0 0
\(711\) 0.338109 + 0.0672541i 0.0126801 + 0.00252223i
\(712\) 0 0
\(713\) −0.527040 2.64961i −0.0197378 0.0992286i
\(714\) 0 0
\(715\) 45.6428 37.4581i 1.70694 1.40085i
\(716\) 0 0
\(717\) 18.0378 9.64138i 0.673632 0.360064i
\(718\) 0 0
\(719\) 2.41192 + 0.999049i 0.0899493 + 0.0372582i 0.427204 0.904155i \(-0.359498\pi\)
−0.337255 + 0.941413i \(0.609498\pi\)
\(720\) 0 0
\(721\) 7.33867 3.03978i 0.273306 0.113207i
\(722\) 0 0
\(723\) 0.00643050 + 0.00195067i 0.000239153 + 7.25463e-5i
\(724\) 0 0
\(725\) 1.08903 11.0571i 0.0404457 0.410652i
\(726\) 0 0
\(727\) 1.51724 2.27071i 0.0562713 0.0842160i −0.802267 0.596965i \(-0.796373\pi\)
0.858538 + 0.512749i \(0.171373\pi\)
\(728\) 0 0
\(729\) −23.2447 + 15.5316i −0.860915 + 0.575245i
\(730\) 0 0
\(731\) 49.8965 15.1359i 1.84549 0.559823i
\(732\) 0 0
\(733\) −18.0423 + 21.9846i −0.666408 + 0.812021i −0.991004 0.133832i \(-0.957272\pi\)
0.324596 + 0.945853i \(0.394772\pi\)
\(734\) 0 0
\(735\) 17.3409 17.3409i 0.639628 0.639628i
\(736\) 0 0
\(737\) −0.394662 0.394662i −0.0145375 0.0145375i
\(738\) 0 0
\(739\) 23.3875 + 19.1936i 0.860323 + 0.706049i 0.957256 0.289242i \(-0.0934033\pi\)
−0.0969331 + 0.995291i \(0.530903\pi\)
\(740\) 0 0
\(741\) 4.49297 + 14.8113i 0.165053 + 0.544108i
\(742\) 0 0
\(743\) 28.5843 + 42.7795i 1.04866 + 1.56943i 0.799223 + 0.601035i \(0.205245\pi\)
0.249434 + 0.968392i \(0.419755\pi\)
\(744\) 0 0
\(745\) −46.9620 31.3790i −1.72056 1.14964i
\(746\) 0 0
\(747\) 0.341927 + 0.0336769i 0.0125105 + 0.00123217i
\(748\) 0 0
\(749\) −1.10527 + 3.64359i −0.0403858 + 0.133134i
\(750\) 0 0
\(751\) −1.76767 4.26752i −0.0645030 0.155724i 0.888341 0.459184i \(-0.151858\pi\)
−0.952844 + 0.303460i \(0.901858\pi\)
\(752\) 0 0
\(753\) 16.1458 38.9794i 0.588385 1.42049i
\(754\) 0 0
\(755\) −8.63198 16.1493i −0.314150 0.587733i
\(756\) 0 0
\(757\) 9.60667 + 11.7058i 0.349160 + 0.425453i 0.917744 0.397172i \(-0.130008\pi\)
−0.568584 + 0.822625i \(0.692508\pi\)
\(758\) 0 0
\(759\) 35.2743 7.01650i 1.28038 0.254683i
\(760\) 0 0
\(761\) 0.714883 3.59396i 0.0259145 0.130281i −0.965662 0.259800i \(-0.916343\pi\)
0.991577 + 0.129519i \(0.0413434\pi\)
\(762\) 0 0
\(763\) 10.0546 + 5.37432i 0.364003 + 0.194563i
\(764\) 0 0
\(765\) 0.168856 + 1.71443i 0.00610501 + 0.0619852i
\(766\) 0 0
\(767\) 65.4620 2.36369
\(768\) 0 0
\(769\) 10.6192 0.382937 0.191468 0.981499i \(-0.438675\pi\)
0.191468 + 0.981499i \(0.438675\pi\)
\(770\) 0 0
\(771\) −0.0225487 0.228940i −0.000812070 0.00824509i
\(772\) 0 0
\(773\) 22.0656 + 11.7943i 0.793645 + 0.424212i 0.817804 0.575496i \(-0.195191\pi\)
−0.0241597 + 0.999708i \(0.507691\pi\)
\(774\) 0 0
\(775\) 0.214692 1.07933i 0.00771198 0.0387707i
\(776\) 0 0
\(777\) 5.20217 1.03478i 0.186627 0.0371224i
\(778\) 0 0
\(779\) −5.10634 6.22209i −0.182954 0.222930i
\(780\) 0 0
\(781\) −20.5874 38.5163i −0.736675 1.37822i
\(782\) 0 0
\(783\) −11.6919 + 28.2266i −0.417833 + 1.00874i
\(784\) 0 0
\(785\) −10.3551 24.9994i −0.369590 0.892268i
\(786\) 0 0
\(787\) 8.74150 28.8169i 0.311601 1.02721i −0.651630 0.758537i \(-0.725915\pi\)
0.963231 0.268674i \(-0.0865854\pi\)
\(788\) 0 0
\(789\) −35.7849 3.52450i −1.27397 0.125476i
\(790\) 0 0
\(791\) 1.18942 + 0.794743i 0.0422908 + 0.0282578i
\(792\) 0 0
\(793\) 29.2797 + 43.8202i 1.03975 + 1.55610i
\(794\) 0 0
\(795\) −12.1250 39.9709i −0.430031 1.41762i
\(796\) 0 0
\(797\) −20.2702 16.6353i −0.718007 0.589253i 0.202824 0.979215i \(-0.434988\pi\)
−0.920831 + 0.389962i \(0.872488\pi\)
\(798\) 0 0
\(799\) −21.7373 21.7373i −0.769011 0.769011i
\(800\) 0 0
\(801\) −0.874990 + 0.874990i −0.0309162 + 0.0309162i
\(802\) 0 0
\(803\) −34.3146 + 41.8125i −1.21094 + 1.47553i
\(804\) 0 0
\(805\) 14.6296 4.43784i 0.515625 0.156413i
\(806\) 0 0
\(807\) 22.9564 15.3389i 0.808102 0.539956i
\(808\) 0 0
\(809\) 17.8427 26.7034i 0.627315 0.938843i −0.372626 0.927982i \(-0.621543\pi\)
0.999941 0.0108614i \(-0.00345735\pi\)
\(810\) 0 0
\(811\) 0.900862 9.14660i 0.0316335 0.321181i −0.966325 0.257323i \(-0.917160\pi\)
0.997959 0.0638578i \(-0.0203404\pi\)
\(812\) 0 0
\(813\) −18.1713 5.51220i −0.637295 0.193321i
\(814\) 0 0
\(815\) 12.3143 5.10074i 0.431350 0.178671i
\(816\) 0 0
\(817\) −15.4417 6.39614i −0.540235 0.223773i
\(818\) 0 0
\(819\) −0.625853 + 0.334526i −0.0218691 + 0.0116893i
\(820\) 0 0
\(821\) 7.20043 5.90924i 0.251297 0.206234i −0.500308 0.865847i \(-0.666780\pi\)
0.751605 + 0.659614i \(0.229280\pi\)
\(822\) 0 0
\(823\) 6.63857 + 33.3743i 0.231406 + 1.16336i 0.905380 + 0.424601i \(0.139586\pi\)
−0.673974 + 0.738755i \(0.735414\pi\)
\(824\) 0 0
\(825\) 14.3692 + 2.85821i 0.500271 + 0.0995101i
\(826\) 0 0
\(827\) 12.5341 23.4497i 0.435855 0.815427i −0.564092 0.825712i \(-0.690774\pi\)
0.999947 + 0.0102847i \(0.00327378\pi\)
\(828\) 0 0
\(829\) 30.1919 2.97364i 1.04861 0.103279i 0.440993 0.897511i \(-0.354626\pi\)
0.607615 + 0.794232i \(0.292126\pi\)
\(830\) 0 0
\(831\) 40.9936i 1.42205i
\(832\) 0 0
\(833\) 31.1654i 1.07982i
\(834\) 0 0
\(835\) 36.0338 3.54902i 1.24700 0.122819i
\(836\) 0 0
\(837\) −1.42650 + 2.66880i −0.0493071 + 0.0922471i
\(838\) 0 0
\(839\) −7.84784 1.56103i −0.270938 0.0538929i 0.0577516 0.998331i \(-0.481607\pi\)
−0.328689 + 0.944438i \(0.606607\pi\)
\(840\) 0 0
\(841\) 0.847081 + 4.25856i 0.0292097 + 0.146847i
\(842\) 0 0
\(843\) −41.6104 + 34.1488i −1.43314 + 1.17615i
\(844\) 0 0
\(845\) −27.9740 + 14.9524i −0.962336 + 0.514379i
\(846\) 0 0
\(847\) 10.3369 + 4.28170i 0.355181 + 0.147121i
\(848\) 0 0
\(849\) 17.8878 7.40935i 0.613906 0.254288i
\(850\) 0 0
\(851\) −11.4768 3.48144i −0.393418 0.119342i
\(852\) 0 0
\(853\) 0.964497 9.79271i 0.0330238 0.335296i −0.964450 0.264264i \(-0.914871\pi\)
0.997474 0.0710316i \(-0.0226291\pi\)
\(854\) 0 0
\(855\) 0.306794 0.459150i 0.0104921 0.0157026i
\(856\) 0 0
\(857\) 29.7750 19.8950i 1.01709 0.679600i 0.0690078 0.997616i \(-0.478017\pi\)
0.948085 + 0.318016i \(0.103017\pi\)
\(858\) 0 0
\(859\) −32.6428 + 9.90208i −1.11376 + 0.337855i −0.792948 0.609289i \(-0.791455\pi\)
−0.320809 + 0.947144i \(0.603955\pi\)
\(860\) 0 0
\(861\) −5.85922 + 7.13948i −0.199682 + 0.243313i
\(862\) 0 0
\(863\) 24.9118 24.9118i 0.848007 0.848007i −0.141877 0.989884i \(-0.545314\pi\)
0.989884 + 0.141877i \(0.0453139\pi\)
\(864\) 0 0
\(865\) 14.6043 + 14.6043i 0.496561 + 0.496561i
\(866\) 0 0
\(867\) 20.0333 + 16.4409i 0.680366 + 0.558362i
\(868\) 0 0
\(869\) 3.89189 + 12.8298i 0.132023 + 0.435223i
\(870\) 0 0
\(871\) 0.346224 + 0.518161i 0.0117314 + 0.0175572i
\(872\) 0 0
\(873\) 0.859882 + 0.574555i 0.0291026 + 0.0194457i
\(874\) 0 0
\(875\) −9.90702 0.975756i −0.334918 0.0329866i
\(876\) 0 0
\(877\) −3.79919 + 12.5242i −0.128289 + 0.422913i −0.997430 0.0716522i \(-0.977173\pi\)
0.869140 + 0.494566i \(0.164673\pi\)
\(878\) 0 0
\(879\) −2.82499 6.82013i −0.0952846 0.230037i
\(880\) 0 0
\(881\) 0.186574 0.450428i 0.00628582 0.0151753i −0.920705 0.390258i \(-0.872386\pi\)
0.926991 + 0.375083i \(0.122386\pi\)
\(882\) 0 0
\(883\) −5.72048 10.7023i −0.192509 0.360160i 0.767085 0.641545i \(-0.221706\pi\)
−0.959595 + 0.281385i \(0.909206\pi\)
\(884\) 0 0
\(885\) 37.0803 + 45.1825i 1.24644 + 1.51879i
\(886\) 0 0
\(887\) −37.3800 + 7.43535i −1.25510 + 0.249655i −0.777477 0.628911i \(-0.783501\pi\)
−0.477621 + 0.878566i \(0.658501\pi\)
\(888\) 0 0
\(889\) −3.34099 + 16.7963i −0.112053 + 0.563329i
\(890\) 0 0
\(891\) −34.1626 18.2603i −1.14449 0.611743i
\(892\) 0 0
\(893\) 0.965864 + 9.80659i 0.0323214 + 0.328165i
\(894\) 0 0
\(895\) −21.5300 −0.719668
\(896\) 0 0
\(897\) −40.1572 −1.34081
\(898\) 0 0
\(899\) 0.323694 + 3.28652i 0.0107958 + 0.109612i
\(900\) 0 0
\(901\) 46.8139 + 25.0226i 1.55960 + 0.833622i
\(902\) 0 0
\(903\) −3.74149 + 18.8097i −0.124509 + 0.625949i
\(904\) 0 0
\(905\) −24.8784 + 4.94862i −0.826985 + 0.164498i
\(906\) 0 0
\(907\) 28.6902 + 34.9591i 0.952641 + 1.16080i 0.986892 + 0.161384i \(0.0515956\pi\)
−0.0342504 + 0.999413i \(0.510904\pi\)
\(908\) 0 0
\(909\) 0.722002 + 1.35077i 0.0239473 + 0.0448023i
\(910\) 0 0
\(911\) 16.1999 39.1100i 0.536726 1.29577i −0.390270 0.920700i \(-0.627618\pi\)
0.926996 0.375071i \(-0.122382\pi\)
\(912\) 0 0
\(913\) 5.11356 + 12.3452i 0.169234 + 0.408567i
\(914\) 0 0
\(915\) −13.6599 + 45.0307i −0.451583 + 1.48867i
\(916\) 0 0
\(917\) 20.2022 + 1.98974i 0.667136 + 0.0657071i
\(918\) 0 0
\(919\) 37.9265 + 25.3416i 1.25108 + 0.835944i 0.991542 0.129789i \(-0.0414302\pi\)
0.259537 + 0.965733i \(0.416430\pi\)
\(920\) 0 0
\(921\) 13.1854 + 19.7334i 0.434475 + 0.650238i
\(922\) 0 0
\(923\) 14.1553 + 46.6636i 0.465926 + 1.53595i
\(924\) 0 0
\(925\) −3.77654 3.09932i −0.124172 0.101905i
\(926\) 0 0
\(927\) 0.526384 + 0.526384i 0.0172887 + 0.0172887i
\(928\) 0 0
\(929\) −7.64179 + 7.64179i −0.250719 + 0.250719i −0.821265 0.570546i \(-0.806731\pi\)
0.570546 + 0.821265i \(0.306731\pi\)
\(930\) 0 0
\(931\) 6.33759 7.72237i 0.207706 0.253090i
\(932\) 0 0
\(933\) −3.80970 + 1.15566i −0.124724 + 0.0378346i
\(934\) 0 0
\(935\) −55.7077 + 37.2227i −1.82184 + 1.21731i
\(936\) 0 0
\(937\) 12.7398 19.0665i 0.416193 0.622876i −0.562843 0.826564i \(-0.690293\pi\)
0.979036 + 0.203687i \(0.0652926\pi\)
\(938\) 0 0
\(939\) −2.81238 + 28.5546i −0.0917786 + 0.931844i
\(940\) 0 0
\(941\) 18.6670 + 5.66258i 0.608528 + 0.184595i 0.579484 0.814983i \(-0.303254\pi\)
0.0290432 + 0.999578i \(0.490754\pi\)
\(942\) 0 0
\(943\) 19.2939 7.99180i 0.628297 0.260249i
\(944\) 0 0
\(945\) −15.8212 6.55337i −0.514665 0.213181i
\(946\) 0 0
\(947\) 10.4501 5.58571i 0.339583 0.181511i −0.292786 0.956178i \(-0.594582\pi\)
0.632370 + 0.774667i \(0.282082\pi\)
\(948\) 0 0
\(949\) 46.6858 38.3141i 1.51549 1.24373i
\(950\) 0 0
\(951\) −5.18883 26.0860i −0.168259 0.845897i
\(952\) 0 0
\(953\) −36.6021 7.28060i −1.18566 0.235842i −0.437410 0.899262i \(-0.644104\pi\)
−0.748247 + 0.663420i \(0.769104\pi\)
\(954\) 0 0
\(955\) −17.3115 + 32.3875i −0.560187 + 1.04804i
\(956\) 0 0
\(957\) −43.7537 + 4.30936i −1.41435 + 0.139302i
\(958\) 0 0
\(959\) 9.85256i 0.318156i
\(960\) 0 0
\(961\) 30.6729i 0.989449i
\(962\) 0 0
\(963\) −0.355111 + 0.0349754i −0.0114433 + 0.00112707i
\(964\) 0 0
\(965\) 19.9489 37.3218i 0.642179 1.20143i
\(966\) 0 0
\(967\) −32.8905 6.54233i −1.05769 0.210387i −0.364543 0.931186i \(-0.618775\pi\)
−0.693144 + 0.720799i \(0.743775\pi\)
\(968\) 0 0
\(969\) −3.42631 17.2252i −0.110069 0.553354i
\(970\) 0 0
\(971\) −32.4958 + 26.6686i −1.04284 + 0.855838i −0.989758 0.142752i \(-0.954405\pi\)
−0.0530828 + 0.998590i \(0.516905\pi\)
\(972\) 0 0
\(973\) −14.9107 + 7.96994i −0.478015 + 0.255505i
\(974\) 0 0
\(975\) −15.1131 6.26004i −0.484006 0.200482i
\(976\) 0 0
\(977\) −35.0782 + 14.5299i −1.12225 + 0.464852i −0.865140 0.501530i \(-0.832771\pi\)
−0.257111 + 0.966382i \(0.582771\pi\)
\(978\) 0 0
\(979\) −46.0528 13.9700i −1.47186 0.446482i
\(980\) 0 0
\(981\) −0.104726 + 1.06330i −0.00334364 + 0.0339486i
\(982\) 0 0
\(983\) 11.7766 17.6249i 0.375615 0.562148i −0.594713 0.803938i \(-0.702734\pi\)
0.970329 + 0.241790i \(0.0777345\pi\)
\(984\) 0 0
\(985\) 15.5736 10.4060i 0.496217 0.331562i
\(986\) 0 0
\(987\) 10.8200 3.28223i 0.344406 0.104474i
\(988\) 0 0
\(989\) 27.5100 33.5211i 0.874768 1.06591i
\(990\) 0 0
\(991\) 29.1013 29.1013i 0.924434 0.924434i −0.0729051 0.997339i \(-0.523227\pi\)
0.997339 + 0.0729051i \(0.0232270\pi\)
\(992\) 0 0
\(993\) −11.5948 11.5948i −0.367949 0.367949i
\(994\) 0 0
\(995\) 29.9037 + 24.5413i 0.948010 + 0.778011i
\(996\) 0 0
\(997\) 1.12157 + 3.69733i 0.0355205 + 0.117096i 0.972908 0.231193i \(-0.0742629\pi\)
−0.937387 + 0.348289i \(0.886763\pi\)
\(998\) 0 0
\(999\) 7.46366 + 11.1702i 0.236140 + 0.353408i
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 512.2.k.a.49.5 240
4.3 odd 2 128.2.k.a.53.11 yes 240
128.29 even 32 inner 512.2.k.a.209.5 240
128.99 odd 32 128.2.k.a.29.11 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
128.2.k.a.29.11 240 128.99 odd 32
128.2.k.a.53.11 yes 240 4.3 odd 2
512.2.k.a.49.5 240 1.1 even 1 trivial
512.2.k.a.209.5 240 128.29 even 32 inner