Properties

Label 896.2.bh.a.81.17
Level $896$
Weight $2$
Character 896.81
Analytic conductor $7.155$
Analytic rank $0$
Dimension $240$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [896,2,Mod(81,896)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(896, base_ring=CyclotomicField(24))
 
chi = DirichletCharacter(H, H._module([0, 9, 16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("896.81");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 896 = 2^{7} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 896.bh (of order \(24\), degree \(8\), 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: \(7.15459602111\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(30\) over \(\Q(\zeta_{24})\)
Twist minimal: no (minimal twist has level 224)
Sato-Tate group: $\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label 81.17
Character \(\chi\) \(=\) 896.81
Dual form 896.2.bh.a.177.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.360007 - 0.276243i) q^{3} +(0.0970846 - 0.126523i) q^{5} +(-2.18584 - 1.49067i) q^{7} +(-0.723162 + 2.69888i) q^{9} +O(q^{10})\) \(q+(0.360007 - 0.276243i) q^{3} +(0.0970846 - 0.126523i) q^{5} +(-2.18584 - 1.49067i) q^{7} +(-0.723162 + 2.69888i) q^{9} +(-0.0199338 + 0.151412i) q^{11} +(-2.07041 + 4.99842i) q^{13} -0.0723681i q^{15} +(1.65868 + 0.957641i) q^{17} +(1.10766 - 0.145826i) q^{19} +(-1.19870 + 0.0671739i) q^{21} +(-1.51595 + 5.65760i) q^{23} +(1.28751 + 4.80506i) q^{25} +(1.00616 + 2.42909i) q^{27} +(1.98245 + 0.821158i) q^{29} +(1.46735 - 2.54152i) q^{31} +(0.0346503 + 0.0600160i) q^{33} +(-0.400816 + 0.131839i) q^{35} +(1.11464 - 1.45263i) q^{37} +(0.635415 + 2.37140i) q^{39} +(3.80184 + 3.80184i) q^{41} +(0.423050 - 0.175233i) q^{43} +(0.271263 + 0.353516i) q^{45} +(-7.58989 + 4.38203i) q^{47} +(2.55583 + 6.51673i) q^{49} +(0.861678 - 0.113442i) q^{51} +(1.30273 - 9.89522i) q^{53} +(0.0172219 + 0.0172219i) q^{55} +(0.358480 - 0.358480i) q^{57} +(10.7606 + 1.41667i) q^{59} +(-1.31206 - 9.96606i) q^{61} +(5.60385 - 4.82133i) q^{63} +(0.431410 + 0.747225i) q^{65} +(-7.98075 + 6.12384i) q^{67} +(1.01712 + 2.45554i) q^{69} +(-9.25562 + 9.25562i) q^{71} +(-13.3187 + 3.56873i) q^{73} +(1.79088 + 1.37419i) q^{75} +(0.269277 - 0.301249i) q^{77} +(-7.28306 + 4.20487i) q^{79} +(-6.22600 - 3.59458i) q^{81} +(1.14890 - 2.77370i) q^{83} +(0.282196 - 0.116889i) q^{85} +(0.940534 - 0.252015i) q^{87} +(0.998840 + 0.267638i) q^{89} +(11.9766 - 7.83947i) q^{91} +(-0.173822 - 1.32031i) q^{93} +(0.0890859 - 0.154301i) q^{95} +12.3695 q^{97} +(-0.394228 - 0.163295i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{11} - 16 q^{13} + 4 q^{19} - 8 q^{21} + 12 q^{23} - 4 q^{25} + 16 q^{27} - 16 q^{29} + 56 q^{31} - 8 q^{33} + 32 q^{35} - 4 q^{37} + 4 q^{39} - 16 q^{41} + 8 q^{45} + 28 q^{51} - 20 q^{53} + 16 q^{55} - 16 q^{57} + 36 q^{59} - 4 q^{61} + 16 q^{63} - 8 q^{65} - 36 q^{67} - 16 q^{69} - 48 q^{71} - 4 q^{73} - 16 q^{75} - 8 q^{77} + 96 q^{83} - 56 q^{85} + 4 q^{87} - 4 q^{89} + 56 q^{91} + 20 q^{93} + 8 q^{95} - 32 q^{97} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/896\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(645\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{8}\right)\)

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
\(3\) 0.360007 0.276243i 0.207850 0.159489i −0.499591 0.866262i \(-0.666516\pi\)
0.707441 + 0.706773i \(0.249850\pi\)
\(4\) 0 0
\(5\) 0.0970846 0.126523i 0.0434175 0.0565829i −0.771140 0.636666i \(-0.780313\pi\)
0.814558 + 0.580083i \(0.196980\pi\)
\(6\) 0 0
\(7\) −2.18584 1.49067i −0.826171 0.563419i
\(8\) 0 0
\(9\) −0.723162 + 2.69888i −0.241054 + 0.899626i
\(10\) 0 0
\(11\) −0.0199338 + 0.151412i −0.00601027 + 0.0456525i −0.994187 0.107665i \(-0.965663\pi\)
0.988177 + 0.153318i \(0.0489958\pi\)
\(12\) 0 0
\(13\) −2.07041 + 4.99842i −0.574229 + 1.38631i 0.323695 + 0.946162i \(0.395075\pi\)
−0.897924 + 0.440151i \(0.854925\pi\)
\(14\) 0 0
\(15\) 0.0723681i 0.0186854i
\(16\) 0 0
\(17\) 1.65868 + 0.957641i 0.402290 + 0.232262i 0.687471 0.726211i \(-0.258721\pi\)
−0.285182 + 0.958473i \(0.592054\pi\)
\(18\) 0 0
\(19\) 1.10766 0.145826i 0.254113 0.0334547i −0.00239318 0.999997i \(-0.500762\pi\)
0.256507 + 0.966542i \(0.417428\pi\)
\(20\) 0 0
\(21\) −1.19870 + 0.0671739i −0.261579 + 0.0146585i
\(22\) 0 0
\(23\) −1.51595 + 5.65760i −0.316097 + 1.17969i 0.606867 + 0.794804i \(0.292426\pi\)
−0.922964 + 0.384887i \(0.874240\pi\)
\(24\) 0 0
\(25\) 1.28751 + 4.80506i 0.257503 + 0.961012i
\(26\) 0 0
\(27\) 1.00616 + 2.42909i 0.193636 + 0.467479i
\(28\) 0 0
\(29\) 1.98245 + 0.821158i 0.368132 + 0.152485i 0.559077 0.829115i \(-0.311155\pi\)
−0.190946 + 0.981601i \(0.561155\pi\)
\(30\) 0 0
\(31\) 1.46735 2.54152i 0.263544 0.456471i −0.703637 0.710559i \(-0.748442\pi\)
0.967181 + 0.254088i \(0.0817754\pi\)
\(32\) 0 0
\(33\) 0.0346503 + 0.0600160i 0.00603184 + 0.0104474i
\(34\) 0 0
\(35\) −0.400816 + 0.131839i −0.0677502 + 0.0222849i
\(36\) 0 0
\(37\) 1.11464 1.45263i 0.183246 0.238811i −0.692693 0.721232i \(-0.743576\pi\)
0.875939 + 0.482422i \(0.160243\pi\)
\(38\) 0 0
\(39\) 0.635415 + 2.37140i 0.101748 + 0.379728i
\(40\) 0 0
\(41\) 3.80184 + 3.80184i 0.593748 + 0.593748i 0.938642 0.344894i \(-0.112085\pi\)
−0.344894 + 0.938642i \(0.612085\pi\)
\(42\) 0 0
\(43\) 0.423050 0.175233i 0.0645145 0.0267228i −0.350193 0.936678i \(-0.613884\pi\)
0.414707 + 0.909955i \(0.363884\pi\)
\(44\) 0 0
\(45\) 0.271263 + 0.353516i 0.0404374 + 0.0526991i
\(46\) 0 0
\(47\) −7.58989 + 4.38203i −1.10710 + 0.639184i −0.938077 0.346428i \(-0.887395\pi\)
−0.169023 + 0.985612i \(0.554061\pi\)
\(48\) 0 0
\(49\) 2.55583 + 6.51673i 0.365118 + 0.930961i
\(50\) 0 0
\(51\) 0.861678 0.113442i 0.120659 0.0158851i
\(52\) 0 0
\(53\) 1.30273 9.89522i 0.178944 1.35921i −0.632399 0.774643i \(-0.717930\pi\)
0.811343 0.584571i \(-0.198737\pi\)
\(54\) 0 0
\(55\) 0.0172219 + 0.0172219i 0.00232220 + 0.00232220i
\(56\) 0 0
\(57\) 0.358480 0.358480i 0.0474818 0.0474818i
\(58\) 0 0
\(59\) 10.7606 + 1.41667i 1.40092 + 0.184434i 0.792833 0.609439i \(-0.208605\pi\)
0.608083 + 0.793873i \(0.291939\pi\)
\(60\) 0 0
\(61\) −1.31206 9.96606i −0.167992 1.27602i −0.842880 0.538102i \(-0.819141\pi\)
0.674888 0.737920i \(-0.264192\pi\)
\(62\) 0 0
\(63\) 5.60385 4.82133i 0.706019 0.607431i
\(64\) 0 0
\(65\) 0.431410 + 0.747225i 0.0535099 + 0.0926818i
\(66\) 0 0
\(67\) −7.98075 + 6.12384i −0.975004 + 0.748147i −0.967772 0.251827i \(-0.918969\pi\)
−0.00723138 + 0.999974i \(0.502302\pi\)
\(68\) 0 0
\(69\) 1.01712 + 2.45554i 0.122447 + 0.295613i
\(70\) 0 0
\(71\) −9.25562 + 9.25562i −1.09844 + 1.09844i −0.103847 + 0.994593i \(0.533115\pi\)
−0.994593 + 0.103847i \(0.966885\pi\)
\(72\) 0 0
\(73\) −13.3187 + 3.56873i −1.55883 + 0.417688i −0.932294 0.361701i \(-0.882196\pi\)
−0.626540 + 0.779389i \(0.715529\pi\)
\(74\) 0 0
\(75\) 1.79088 + 1.37419i 0.206793 + 0.158678i
\(76\) 0 0
\(77\) 0.269277 0.301249i 0.0306870 0.0343305i
\(78\) 0 0
\(79\) −7.28306 + 4.20487i −0.819408 + 0.473085i −0.850212 0.526440i \(-0.823526\pi\)
0.0308045 + 0.999525i \(0.490193\pi\)
\(80\) 0 0
\(81\) −6.22600 3.59458i −0.691778 0.399398i
\(82\) 0 0
\(83\) 1.14890 2.77370i 0.126108 0.304453i −0.848198 0.529679i \(-0.822312\pi\)
0.974306 + 0.225227i \(0.0723123\pi\)
\(84\) 0 0
\(85\) 0.282196 0.116889i 0.0306085 0.0126784i
\(86\) 0 0
\(87\) 0.940534 0.252015i 0.100836 0.0270189i
\(88\) 0 0
\(89\) 0.998840 + 0.267638i 0.105877 + 0.0283696i 0.311368 0.950289i \(-0.399213\pi\)
−0.205492 + 0.978659i \(0.565879\pi\)
\(90\) 0 0
\(91\) 11.9766 7.83947i 1.25549 0.821800i
\(92\) 0 0
\(93\) −0.173822 1.32031i −0.0180245 0.136910i
\(94\) 0 0
\(95\) 0.0890859 0.154301i 0.00914002 0.0158310i
\(96\) 0 0
\(97\) 12.3695 1.25593 0.627965 0.778242i \(-0.283888\pi\)
0.627965 + 0.778242i \(0.283888\pi\)
\(98\) 0 0
\(99\) −0.394228 0.163295i −0.0396214 0.0164117i
\(100\) 0 0
\(101\) −15.8675 2.08899i −1.57887 0.207862i −0.710471 0.703726i \(-0.751518\pi\)
−0.868400 + 0.495864i \(0.834851\pi\)
\(102\) 0 0
\(103\) 12.6282 + 3.38372i 1.24429 + 0.333408i 0.820130 0.572177i \(-0.193901\pi\)
0.424165 + 0.905585i \(0.360568\pi\)
\(104\) 0 0
\(105\) −0.107877 + 0.158185i −0.0105277 + 0.0154373i
\(106\) 0 0
\(107\) 3.21518 + 2.46710i 0.310824 + 0.238503i 0.752379 0.658731i \(-0.228906\pi\)
−0.441555 + 0.897234i \(0.645573\pi\)
\(108\) 0 0
\(109\) 7.73265 + 10.0774i 0.740654 + 0.965239i 1.00000 0.000545510i \(-0.000173641\pi\)
−0.259346 + 0.965784i \(0.583507\pi\)
\(110\) 0 0
\(111\) 0.830868i 0.0788625i
\(112\) 0 0
\(113\) 3.79905i 0.357385i −0.983905 0.178692i \(-0.942813\pi\)
0.983905 0.178692i \(-0.0571867\pi\)
\(114\) 0 0
\(115\) 0.568642 + 0.741068i 0.0530261 + 0.0691050i
\(116\) 0 0
\(117\) −11.9929 9.20246i −1.10874 0.850768i
\(118\) 0 0
\(119\) −2.19810 4.56580i −0.201499 0.418546i
\(120\) 0 0
\(121\) 10.6027 + 2.84097i 0.963878 + 0.258270i
\(122\) 0 0
\(123\) 2.41892 + 0.318457i 0.218107 + 0.0287143i
\(124\) 0 0
\(125\) 1.46965 + 0.608747i 0.131449 + 0.0544480i
\(126\) 0 0
\(127\) 0.560714 0.0497553 0.0248777 0.999691i \(-0.492080\pi\)
0.0248777 + 0.999691i \(0.492080\pi\)
\(128\) 0 0
\(129\) 0.103894 0.179950i 0.00914735 0.0158437i
\(130\) 0 0
\(131\) −2.16060 16.4114i −0.188773 1.43387i −0.779197 0.626779i \(-0.784373\pi\)
0.590424 0.807093i \(-0.298961\pi\)
\(132\) 0 0
\(133\) −2.63854 1.33239i −0.228790 0.115533i
\(134\) 0 0
\(135\) 0.405019 + 0.108525i 0.0348585 + 0.00934031i
\(136\) 0 0
\(137\) −10.0392 + 2.69000i −0.857709 + 0.229823i −0.660766 0.750592i \(-0.729768\pi\)
−0.196944 + 0.980415i \(0.563102\pi\)
\(138\) 0 0
\(139\) 3.82964 1.58629i 0.324826 0.134547i −0.214311 0.976766i \(-0.568751\pi\)
0.539137 + 0.842218i \(0.318751\pi\)
\(140\) 0 0
\(141\) −1.52191 + 3.67421i −0.128168 + 0.309425i
\(142\) 0 0
\(143\) −0.715551 0.413123i −0.0598374 0.0345471i
\(144\) 0 0
\(145\) 0.296361 0.171104i 0.0246114 0.0142094i
\(146\) 0 0
\(147\) 2.72032 + 1.64004i 0.224368 + 0.135268i
\(148\) 0 0
\(149\) −1.93679 1.48615i −0.158668 0.121750i 0.526376 0.850252i \(-0.323550\pi\)
−0.685044 + 0.728502i \(0.740217\pi\)
\(150\) 0 0
\(151\) −11.7305 + 3.14318i −0.954614 + 0.255788i −0.702319 0.711862i \(-0.747852\pi\)
−0.252295 + 0.967650i \(0.581185\pi\)
\(152\) 0 0
\(153\) −3.78405 + 3.78405i −0.305923 + 0.305923i
\(154\) 0 0
\(155\) −0.179104 0.432396i −0.0143860 0.0347309i
\(156\) 0 0
\(157\) −0.145265 + 0.111466i −0.0115934 + 0.00889592i −0.614542 0.788884i \(-0.710659\pi\)
0.602948 + 0.797780i \(0.293992\pi\)
\(158\) 0 0
\(159\) −2.26449 3.92222i −0.179586 0.311052i
\(160\) 0 0
\(161\) 11.7472 10.1069i 0.925811 0.796532i
\(162\) 0 0
\(163\) 1.27833 + 9.70988i 0.100127 + 0.760536i 0.965683 + 0.259725i \(0.0836318\pi\)
−0.865556 + 0.500812i \(0.833035\pi\)
\(164\) 0 0
\(165\) 0.0109574 + 0.00144257i 0.000853034 + 0.000112304i
\(166\) 0 0
\(167\) −5.34878 + 5.34878i −0.413901 + 0.413901i −0.883095 0.469194i \(-0.844545\pi\)
0.469194 + 0.883095i \(0.344545\pi\)
\(168\) 0 0
\(169\) −11.5052 11.5052i −0.885015 0.885015i
\(170\) 0 0
\(171\) −0.407449 + 3.09488i −0.0311584 + 0.236672i
\(172\) 0 0
\(173\) 11.1584 1.46903i 0.848354 0.111688i 0.306200 0.951967i \(-0.400942\pi\)
0.542154 + 0.840279i \(0.317609\pi\)
\(174\) 0 0
\(175\) 4.34844 12.4224i 0.328711 0.939043i
\(176\) 0 0
\(177\) 4.26525 2.46254i 0.320596 0.185096i
\(178\) 0 0
\(179\) −9.58636 12.4932i −0.716518 0.933785i 0.283162 0.959072i \(-0.408617\pi\)
−0.999680 + 0.0252874i \(0.991950\pi\)
\(180\) 0 0
\(181\) 18.5983 7.70368i 1.38240 0.572610i 0.437280 0.899326i \(-0.355942\pi\)
0.945123 + 0.326716i \(0.105942\pi\)
\(182\) 0 0
\(183\) −3.22540 3.22540i −0.238429 0.238429i
\(184\) 0 0
\(185\) −0.0755766 0.282056i −0.00555650 0.0207371i
\(186\) 0 0
\(187\) −0.178062 + 0.232055i −0.0130212 + 0.0169696i
\(188\) 0 0
\(189\) 1.42165 6.80947i 0.103410 0.495316i
\(190\) 0 0
\(191\) −4.41793 7.65208i −0.319670 0.553685i 0.660749 0.750607i \(-0.270239\pi\)
−0.980419 + 0.196922i \(0.936906\pi\)
\(192\) 0 0
\(193\) 0.0958006 0.165931i 0.00689588 0.0119440i −0.862557 0.505960i \(-0.831138\pi\)
0.869453 + 0.494016i \(0.164472\pi\)
\(194\) 0 0
\(195\) 0.361726 + 0.149832i 0.0259037 + 0.0107297i
\(196\) 0 0
\(197\) −5.04265 12.1740i −0.359274 0.867364i −0.995402 0.0957810i \(-0.969465\pi\)
0.636128 0.771583i \(-0.280535\pi\)
\(198\) 0 0
\(199\) −1.76239 6.57734i −0.124933 0.466255i 0.874905 0.484295i \(-0.160924\pi\)
−0.999837 + 0.0180402i \(0.994257\pi\)
\(200\) 0 0
\(201\) −1.18146 + 4.40925i −0.0833334 + 0.311005i
\(202\) 0 0
\(203\) −3.10925 4.75009i −0.218227 0.333391i
\(204\) 0 0
\(205\) 0.850121 0.111921i 0.0593750 0.00781687i
\(206\) 0 0
\(207\) −14.1729 8.18272i −0.985084 0.568739i
\(208\) 0 0
\(209\) 0.170619i 0.0118020i
\(210\) 0 0
\(211\) 8.79848 21.2414i 0.605712 1.46232i −0.261909 0.965093i \(-0.584352\pi\)
0.867621 0.497226i \(-0.165648\pi\)
\(212\) 0 0
\(213\) −0.775287 + 5.88889i −0.0531218 + 0.403500i
\(214\) 0 0
\(215\) 0.0189006 0.0705380i 0.00128901 0.00481065i
\(216\) 0 0
\(217\) −6.99596 + 3.36804i −0.474917 + 0.228638i
\(218\) 0 0
\(219\) −3.80898 + 4.96396i −0.257387 + 0.335433i
\(220\) 0 0
\(221\) −8.22085 + 6.30808i −0.552994 + 0.424327i
\(222\) 0 0
\(223\) 22.4565 1.50380 0.751900 0.659277i \(-0.229138\pi\)
0.751900 + 0.659277i \(0.229138\pi\)
\(224\) 0 0
\(225\) −13.8994 −0.926624
\(226\) 0 0
\(227\) −19.9669 + 15.3211i −1.32525 + 1.01690i −0.327857 + 0.944727i \(0.606326\pi\)
−0.997392 + 0.0721720i \(0.977007\pi\)
\(228\) 0 0
\(229\) 13.5273 17.6291i 0.893907 1.16496i −0.0916796 0.995789i \(-0.529224\pi\)
0.985586 0.169173i \(-0.0541098\pi\)
\(230\) 0 0
\(231\) 0.0137238 0.182838i 0.000902959 0.0120298i
\(232\) 0 0
\(233\) 2.46679 9.20620i 0.161605 0.603118i −0.836844 0.547442i \(-0.815602\pi\)
0.998449 0.0556765i \(-0.0177315\pi\)
\(234\) 0 0
\(235\) −0.182434 + 1.38572i −0.0119007 + 0.0903947i
\(236\) 0 0
\(237\) −1.46038 + 3.52568i −0.0948620 + 0.229017i
\(238\) 0 0
\(239\) 4.53077i 0.293071i −0.989205 0.146536i \(-0.953188\pi\)
0.989205 0.146536i \(-0.0468123\pi\)
\(240\) 0 0
\(241\) 18.2231 + 10.5211i 1.17385 + 0.677725i 0.954585 0.297939i \(-0.0962992\pi\)
0.219270 + 0.975664i \(0.429633\pi\)
\(242\) 0 0
\(243\) −11.0546 + 1.45537i −0.709153 + 0.0933617i
\(244\) 0 0
\(245\) 1.07265 + 0.309303i 0.0685290 + 0.0197606i
\(246\) 0 0
\(247\) −1.56441 + 5.83844i −0.0995408 + 0.371491i
\(248\) 0 0
\(249\) −0.352601 1.31593i −0.0223452 0.0833934i
\(250\) 0 0
\(251\) −2.89265 6.98346i −0.182582 0.440792i 0.805915 0.592031i \(-0.201674\pi\)
−0.988497 + 0.151239i \(0.951674\pi\)
\(252\) 0 0
\(253\) −0.826411 0.342311i −0.0519560 0.0215209i
\(254\) 0 0
\(255\) 0.0693026 0.120036i 0.00433990 0.00751693i
\(256\) 0 0
\(257\) −1.15637 2.00290i −0.0721325 0.124937i 0.827703 0.561166i \(-0.189647\pi\)
−0.899836 + 0.436229i \(0.856314\pi\)
\(258\) 0 0
\(259\) −4.60181 + 1.51366i −0.285943 + 0.0940543i
\(260\) 0 0
\(261\) −3.64984 + 4.75656i −0.225919 + 0.294424i
\(262\) 0 0
\(263\) 5.14514 + 19.2019i 0.317263 + 1.18404i 0.921864 + 0.387513i \(0.126666\pi\)
−0.604601 + 0.796528i \(0.706668\pi\)
\(264\) 0 0
\(265\) −1.12550 1.12550i −0.0691389 0.0691389i
\(266\) 0 0
\(267\) 0.433523 0.179571i 0.0265311 0.0109896i
\(268\) 0 0
\(269\) −1.27198 1.65768i −0.0775540 0.101070i 0.752965 0.658060i \(-0.228623\pi\)
−0.830519 + 0.556990i \(0.811956\pi\)
\(270\) 0 0
\(271\) 28.0616 16.2014i 1.70462 0.984164i 0.763680 0.645595i \(-0.223391\pi\)
0.940942 0.338569i \(-0.109943\pi\)
\(272\) 0 0
\(273\) 2.14605 6.13071i 0.129885 0.371047i
\(274\) 0 0
\(275\) −0.753210 + 0.0991620i −0.0454203 + 0.00597970i
\(276\) 0 0
\(277\) −1.78623 + 13.5678i −0.107324 + 0.815208i 0.850120 + 0.526589i \(0.176529\pi\)
−0.957444 + 0.288619i \(0.906804\pi\)
\(278\) 0 0
\(279\) 5.79813 + 5.79813i 0.347125 + 0.347125i
\(280\) 0 0
\(281\) 1.35616 1.35616i 0.0809019 0.0809019i −0.665498 0.746400i \(-0.731781\pi\)
0.746400 + 0.665498i \(0.231781\pi\)
\(282\) 0 0
\(283\) 17.4293 + 2.29461i 1.03606 + 0.136400i 0.629324 0.777143i \(-0.283332\pi\)
0.406741 + 0.913544i \(0.366665\pi\)
\(284\) 0 0
\(285\) −0.0105531 0.0801589i −0.000625113 0.00474820i
\(286\) 0 0
\(287\) −2.64296 13.9775i −0.156009 0.825066i
\(288\) 0 0
\(289\) −6.66585 11.5456i −0.392109 0.679152i
\(290\) 0 0
\(291\) 4.45310 3.41698i 0.261045 0.200307i
\(292\) 0 0
\(293\) 9.33024 + 22.5252i 0.545078 + 1.31594i 0.921101 + 0.389325i \(0.127292\pi\)
−0.376022 + 0.926611i \(0.622708\pi\)
\(294\) 0 0
\(295\) 1.22393 1.22393i 0.0712602 0.0712602i
\(296\) 0 0
\(297\) −0.387851 + 0.103924i −0.0225054 + 0.00603031i
\(298\) 0 0
\(299\) −25.1404 19.2909i −1.45391 1.11562i
\(300\) 0 0
\(301\) −1.18593 0.247594i −0.0683561 0.0142711i
\(302\) 0 0
\(303\) −6.28946 + 3.63122i −0.361320 + 0.208608i
\(304\) 0 0
\(305\) −1.38832 0.801545i −0.0794948 0.0458963i
\(306\) 0 0
\(307\) 0.0775174 0.187144i 0.00442415 0.0106809i −0.921652 0.388017i \(-0.873160\pi\)
0.926076 + 0.377337i \(0.123160\pi\)
\(308\) 0 0
\(309\) 5.48097 2.27029i 0.311801 0.129152i
\(310\) 0 0
\(311\) 5.74405 1.53911i 0.325715 0.0872751i −0.0922563 0.995735i \(-0.529408\pi\)
0.417971 + 0.908460i \(0.362741\pi\)
\(312\) 0 0
\(313\) 7.22894 + 1.93699i 0.408604 + 0.109485i 0.457265 0.889330i \(-0.348829\pi\)
−0.0486618 + 0.998815i \(0.515496\pi\)
\(314\) 0 0
\(315\) −0.0659628 1.17709i −0.00371658 0.0663217i
\(316\) 0 0
\(317\) 3.83886 + 29.1590i 0.215612 + 1.63773i 0.666751 + 0.745281i \(0.267685\pi\)
−0.451139 + 0.892454i \(0.648982\pi\)
\(318\) 0 0
\(319\) −0.163851 + 0.283798i −0.00917390 + 0.0158897i
\(320\) 0 0
\(321\) 1.83901 0.102643
\(322\) 0 0
\(323\) 1.97690 + 0.818857i 0.109997 + 0.0455624i
\(324\) 0 0
\(325\) −26.6834 3.51294i −1.48013 0.194863i
\(326\) 0 0
\(327\) 5.56762 + 1.49184i 0.307890 + 0.0824988i
\(328\) 0 0
\(329\) 23.1225 + 1.73557i 1.27478 + 0.0956852i
\(330\) 0 0
\(331\) 6.03896 + 4.63386i 0.331931 + 0.254700i 0.761258 0.648450i \(-0.224582\pi\)
−0.429326 + 0.903149i \(0.641249\pi\)
\(332\) 0 0
\(333\) 3.11440 + 4.05877i 0.170668 + 0.222419i
\(334\) 0 0
\(335\) 1.60428i 0.0876512i
\(336\) 0 0
\(337\) 7.70471i 0.419703i −0.977733 0.209851i \(-0.932702\pi\)
0.977733 0.209851i \(-0.0672980\pi\)
\(338\) 0 0
\(339\) −1.04946 1.36769i −0.0569989 0.0742825i
\(340\) 0 0
\(341\) 0.355568 + 0.272837i 0.0192551 + 0.0147749i
\(342\) 0 0
\(343\) 4.12763 18.0544i 0.222871 0.974848i
\(344\) 0 0
\(345\) 0.409430 + 0.109706i 0.0220430 + 0.00590639i
\(346\) 0 0
\(347\) −25.0665 3.30007i −1.34564 0.177157i −0.576951 0.816779i \(-0.695758\pi\)
−0.768690 + 0.639621i \(0.779091\pi\)
\(348\) 0 0
\(349\) 12.5757 + 5.20902i 0.673162 + 0.278833i 0.692965 0.720971i \(-0.256304\pi\)
−0.0198034 + 0.999804i \(0.506304\pi\)
\(350\) 0 0
\(351\) −14.2248 −0.759264
\(352\) 0 0
\(353\) 15.8665 27.4816i 0.844489 1.46270i −0.0415755 0.999135i \(-0.513238\pi\)
0.886064 0.463562i \(-0.153429\pi\)
\(354\) 0 0
\(355\) 0.272472 + 2.06963i 0.0144613 + 0.109844i
\(356\) 0 0
\(357\) −2.05260 1.03651i −0.108635 0.0548578i
\(358\) 0 0
\(359\) 18.9545 + 5.07883i 1.00038 + 0.268051i 0.721604 0.692306i \(-0.243405\pi\)
0.278774 + 0.960357i \(0.410072\pi\)
\(360\) 0 0
\(361\) −17.1470 + 4.59451i −0.902471 + 0.241816i
\(362\) 0 0
\(363\) 4.60183 1.90614i 0.241533 0.100046i
\(364\) 0 0
\(365\) −0.841512 + 2.03159i −0.0440468 + 0.106338i
\(366\) 0 0
\(367\) 3.78068 + 2.18278i 0.197350 + 0.113940i 0.595419 0.803416i \(-0.296986\pi\)
−0.398069 + 0.917356i \(0.630320\pi\)
\(368\) 0 0
\(369\) −13.0101 + 7.51136i −0.677277 + 0.391026i
\(370\) 0 0
\(371\) −17.5980 + 19.6875i −0.913645 + 1.02212i
\(372\) 0 0
\(373\) 0.234375 + 0.179843i 0.0121355 + 0.00931189i 0.614811 0.788674i \(-0.289232\pi\)
−0.602676 + 0.797986i \(0.705899\pi\)
\(374\) 0 0
\(375\) 0.697244 0.186826i 0.0360055 0.00964766i
\(376\) 0 0
\(377\) −8.20898 + 8.20898i −0.422784 + 0.422784i
\(378\) 0 0
\(379\) 12.3097 + 29.7181i 0.632304 + 1.52652i 0.836719 + 0.547633i \(0.184471\pi\)
−0.204414 + 0.978884i \(0.565529\pi\)
\(380\) 0 0
\(381\) 0.201861 0.154893i 0.0103416 0.00793543i
\(382\) 0 0
\(383\) 4.98813 + 8.63970i 0.254882 + 0.441468i 0.964863 0.262752i \(-0.0846301\pi\)
−0.709982 + 0.704220i \(0.751297\pi\)
\(384\) 0 0
\(385\) −0.0119723 0.0633164i −0.000610163 0.00322690i
\(386\) 0 0
\(387\) 0.166999 + 1.26848i 0.00848903 + 0.0644806i
\(388\) 0 0
\(389\) −17.5831 2.31486i −0.891497 0.117368i −0.329158 0.944275i \(-0.606765\pi\)
−0.562339 + 0.826907i \(0.690098\pi\)
\(390\) 0 0
\(391\) −7.93242 + 7.93242i −0.401160 + 0.401160i
\(392\) 0 0
\(393\) −5.31137 5.31137i −0.267923 0.267923i
\(394\) 0 0
\(395\) −0.175059 + 1.32970i −0.00880816 + 0.0669046i
\(396\) 0 0
\(397\) 10.8133 1.42360i 0.542705 0.0714485i 0.145810 0.989313i \(-0.453421\pi\)
0.396895 + 0.917864i \(0.370088\pi\)
\(398\) 0 0
\(399\) −1.31796 + 0.249207i −0.0659803 + 0.0124760i
\(400\) 0 0
\(401\) −23.0182 + 13.2896i −1.14947 + 0.663649i −0.948759 0.316001i \(-0.897660\pi\)
−0.200715 + 0.979650i \(0.564326\pi\)
\(402\) 0 0
\(403\) 9.66558 + 12.5964i 0.481477 + 0.627473i
\(404\) 0 0
\(405\) −1.05925 + 0.438754i −0.0526344 + 0.0218019i
\(406\) 0 0
\(407\) 0.197727 + 0.197727i 0.00980095 + 0.00980095i
\(408\) 0 0
\(409\) −5.83984 21.7946i −0.288761 1.07767i −0.946047 0.324030i \(-0.894962\pi\)
0.657285 0.753642i \(-0.271705\pi\)
\(410\) 0 0
\(411\) −2.87110 + 3.74169i −0.141621 + 0.184564i
\(412\) 0 0
\(413\) −21.4093 19.1371i −1.05348 0.941677i
\(414\) 0 0
\(415\) −0.239396 0.414646i −0.0117515 0.0203542i
\(416\) 0 0
\(417\) 0.940496 1.62899i 0.0460563 0.0797718i
\(418\) 0 0
\(419\) 37.1232 + 15.3769i 1.81358 + 0.751211i 0.980052 + 0.198741i \(0.0636853\pi\)
0.833533 + 0.552470i \(0.186315\pi\)
\(420\) 0 0
\(421\) 13.3295 + 32.1802i 0.649640 + 1.56837i 0.813295 + 0.581851i \(0.197671\pi\)
−0.163656 + 0.986518i \(0.552329\pi\)
\(422\) 0 0
\(423\) −6.33784 23.6531i −0.308156 1.15005i
\(424\) 0 0
\(425\) −2.46595 + 9.20305i −0.119616 + 0.446413i
\(426\) 0 0
\(427\) −11.9881 + 23.7401i −0.580145 + 1.14886i
\(428\) 0 0
\(429\) −0.371726 + 0.0489386i −0.0179471 + 0.00236278i
\(430\) 0 0
\(431\) 18.9058 + 10.9153i 0.910661 + 0.525770i 0.880644 0.473779i \(-0.157110\pi\)
0.0300172 + 0.999549i \(0.490444\pi\)
\(432\) 0 0
\(433\) 5.08162i 0.244207i 0.992517 + 0.122104i \(0.0389640\pi\)
−0.992517 + 0.122104i \(0.961036\pi\)
\(434\) 0 0
\(435\) 0.0594256 0.143466i 0.00284924 0.00687867i
\(436\) 0 0
\(437\) −0.854126 + 6.48773i −0.0408584 + 0.310350i
\(438\) 0 0
\(439\) 4.88370 18.2262i 0.233087 0.869891i −0.745916 0.666041i \(-0.767988\pi\)
0.979002 0.203850i \(-0.0653456\pi\)
\(440\) 0 0
\(441\) −19.4361 + 2.18522i −0.925530 + 0.104058i
\(442\) 0 0
\(443\) −9.47340 + 12.3460i −0.450095 + 0.586575i −0.962199 0.272348i \(-0.912200\pi\)
0.512104 + 0.858924i \(0.328866\pi\)
\(444\) 0 0
\(445\) 0.130834 0.100393i 0.00620215 0.00475908i
\(446\) 0 0
\(447\) −1.10780 −0.0523969
\(448\) 0 0
\(449\) −19.6746 −0.928500 −0.464250 0.885704i \(-0.653676\pi\)
−0.464250 + 0.885704i \(0.653676\pi\)
\(450\) 0 0
\(451\) −0.651431 + 0.499860i −0.0306747 + 0.0235375i
\(452\) 0 0
\(453\) −3.35478 + 4.37203i −0.157621 + 0.205416i
\(454\) 0 0
\(455\) 0.170867 2.27641i 0.00801037 0.106720i
\(456\) 0 0
\(457\) 6.03318 22.5161i 0.282220 1.05326i −0.668626 0.743599i \(-0.733117\pi\)
0.950847 0.309662i \(-0.100216\pi\)
\(458\) 0 0
\(459\) −0.657293 + 4.99264i −0.0306798 + 0.233036i
\(460\) 0 0
\(461\) −0.196404 + 0.474162i −0.00914747 + 0.0220839i −0.928387 0.371614i \(-0.878804\pi\)
0.919240 + 0.393698i \(0.128804\pi\)
\(462\) 0 0
\(463\) 35.0056i 1.62685i 0.581670 + 0.813425i \(0.302400\pi\)
−0.581670 + 0.813425i \(0.697600\pi\)
\(464\) 0 0
\(465\) −0.183925 0.106189i −0.00852933 0.00492441i
\(466\) 0 0
\(467\) −33.0969 + 4.35729i −1.53154 + 0.201631i −0.848676 0.528913i \(-0.822600\pi\)
−0.682865 + 0.730544i \(0.739266\pi\)
\(468\) 0 0
\(469\) 26.5733 1.48913i 1.22704 0.0687618i
\(470\) 0 0
\(471\) −0.0215047 + 0.0802567i −0.000990885 + 0.00369803i
\(472\) 0 0
\(473\) 0.0180994 + 0.0675480i 0.000832212 + 0.00310586i
\(474\) 0 0
\(475\) 2.12682 + 5.13460i 0.0975852 + 0.235592i
\(476\) 0 0
\(477\) 25.7639 + 10.6718i 1.17965 + 0.488627i
\(478\) 0 0
\(479\) −17.5477 + 30.3935i −0.801775 + 1.38872i 0.116671 + 0.993171i \(0.462778\pi\)
−0.918447 + 0.395545i \(0.870556\pi\)
\(480\) 0 0
\(481\) 4.95308 + 8.57898i 0.225841 + 0.391168i
\(482\) 0 0
\(483\) 1.43713 6.88362i 0.0653918 0.313216i
\(484\) 0 0
\(485\) 1.20089 1.56502i 0.0545294 0.0710641i
\(486\) 0 0
\(487\) 4.35966 + 16.2705i 0.197555 + 0.737286i 0.991591 + 0.129414i \(0.0413097\pi\)
−0.794036 + 0.607871i \(0.792024\pi\)
\(488\) 0 0
\(489\) 3.14249 + 3.14249i 0.142108 + 0.142108i
\(490\) 0 0
\(491\) 28.8429 11.9471i 1.30166 0.539167i 0.379223 0.925305i \(-0.376191\pi\)
0.922441 + 0.386139i \(0.126191\pi\)
\(492\) 0 0
\(493\) 2.50188 + 3.26051i 0.112679 + 0.146846i
\(494\) 0 0
\(495\) −0.0589340 + 0.0340256i −0.00264889 + 0.00152934i
\(496\) 0 0
\(497\) 34.0284 6.43430i 1.52638 0.288618i
\(498\) 0 0
\(499\) 16.4292 2.16294i 0.735472 0.0968267i 0.246520 0.969138i \(-0.420713\pi\)
0.488951 + 0.872311i \(0.337380\pi\)
\(500\) 0 0
\(501\) −0.448035 + 3.40316i −0.0200167 + 0.152042i
\(502\) 0 0
\(503\) 9.63469 + 9.63469i 0.429590 + 0.429590i 0.888488 0.458899i \(-0.151756\pi\)
−0.458899 + 0.888488i \(0.651756\pi\)
\(504\) 0 0
\(505\) −1.80479 + 1.80479i −0.0803122 + 0.0803122i
\(506\) 0 0
\(507\) −7.32018 0.963720i −0.325101 0.0428003i
\(508\) 0 0
\(509\) −0.0166976 0.126831i −0.000740108 0.00562168i 0.991071 0.133337i \(-0.0425691\pi\)
−0.991811 + 0.127715i \(0.959236\pi\)
\(510\) 0 0
\(511\) 34.4324 + 12.0530i 1.52320 + 0.533195i
\(512\) 0 0
\(513\) 1.46871 + 2.54387i 0.0648450 + 0.112315i
\(514\) 0 0
\(515\) 1.65412 1.26925i 0.0728894 0.0559300i
\(516\) 0 0
\(517\) −0.512197 1.23655i −0.0225264 0.0543836i
\(518\) 0 0
\(519\) 3.61128 3.61128i 0.158517 0.158517i
\(520\) 0 0
\(521\) 34.0651 9.12771i 1.49242 0.399892i 0.581865 0.813285i \(-0.302323\pi\)
0.910553 + 0.413393i \(0.135656\pi\)
\(522\) 0 0
\(523\) −17.3331 13.3002i −0.757925 0.581576i 0.155858 0.987780i \(-0.450186\pi\)
−0.913783 + 0.406203i \(0.866853\pi\)
\(524\) 0 0
\(525\) −1.86612 5.67336i −0.0814442 0.247606i
\(526\) 0 0
\(527\) 4.86773 2.81039i 0.212042 0.122422i
\(528\) 0 0
\(529\) −9.79173 5.65326i −0.425727 0.245794i
\(530\) 0 0
\(531\) −11.6051 + 28.0172i −0.503618 + 1.21584i
\(532\) 0 0
\(533\) −26.8746 + 11.1318i −1.16407 + 0.482173i
\(534\) 0 0
\(535\) 0.624290 0.167278i 0.0269904 0.00723205i
\(536\) 0 0
\(537\) −6.90231 1.84947i −0.297857 0.0798104i
\(538\) 0 0
\(539\) −1.03766 + 0.257080i −0.0446952 + 0.0110732i
\(540\) 0 0
\(541\) 3.64022 + 27.6502i 0.156505 + 1.18878i 0.871768 + 0.489920i \(0.162974\pi\)
−0.715262 + 0.698856i \(0.753693\pi\)
\(542\) 0 0
\(543\) 4.56744 7.91103i 0.196007 0.339495i
\(544\) 0 0
\(545\) 2.02574 0.0867734
\(546\) 0 0
\(547\) −23.2728 9.63989i −0.995071 0.412172i −0.175084 0.984554i \(-0.556020\pi\)
−0.819987 + 0.572382i \(0.806020\pi\)
\(548\) 0 0
\(549\) 27.8460 + 3.66600i 1.18844 + 0.156461i
\(550\) 0 0
\(551\) 2.31562 + 0.620467i 0.0986486 + 0.0264328i
\(552\) 0 0
\(553\) 22.1877 + 1.66541i 0.943516 + 0.0708203i
\(554\) 0 0
\(555\) −0.105124 0.0806644i −0.00446226 0.00342401i
\(556\) 0 0
\(557\) −19.1103 24.9050i −0.809729 1.05526i −0.997331 0.0730137i \(-0.976738\pi\)
0.187602 0.982245i \(-0.439928\pi\)
\(558\) 0 0
\(559\) 2.47738i 0.104782i
\(560\) 0 0
\(561\) 0.132730i 0.00560387i
\(562\) 0 0
\(563\) −5.55027 7.23325i −0.233916 0.304845i 0.661616 0.749843i \(-0.269871\pi\)
−0.895532 + 0.444998i \(0.853204\pi\)
\(564\) 0 0
\(565\) −0.480668 0.368830i −0.0202219 0.0155168i
\(566\) 0 0
\(567\) 8.25074 + 17.1381i 0.346499 + 0.719732i
\(568\) 0 0
\(569\) −6.26840 1.67961i −0.262785 0.0704130i 0.125021 0.992154i \(-0.460100\pi\)
−0.387806 + 0.921741i \(0.626767\pi\)
\(570\) 0 0
\(571\) −22.1724 2.91905i −0.927885 0.122158i −0.348589 0.937276i \(-0.613339\pi\)
−0.579296 + 0.815117i \(0.696672\pi\)
\(572\) 0 0
\(573\) −3.70432 1.53438i −0.154750 0.0640996i
\(574\) 0 0
\(575\) −29.1369 −1.21509
\(576\) 0 0
\(577\) −21.7606 + 37.6904i −0.905905 + 1.56907i −0.0862065 + 0.996277i \(0.527474\pi\)
−0.819698 + 0.572796i \(0.805859\pi\)
\(578\) 0 0
\(579\) −0.0113485 0.0862007i −0.000471629 0.00358238i
\(580\) 0 0
\(581\) −6.64598 + 4.35024i −0.275722 + 0.180478i
\(582\) 0 0
\(583\) 1.47229 + 0.394499i 0.0609760 + 0.0163385i
\(584\) 0 0
\(585\) −2.32865 + 0.623959i −0.0962778 + 0.0257975i
\(586\) 0 0
\(587\) 18.5686 7.69135i 0.766406 0.317456i 0.0349905 0.999388i \(-0.488860\pi\)
0.731416 + 0.681932i \(0.238860\pi\)
\(588\) 0 0
\(589\) 1.25470 3.02911i 0.0516989 0.124812i
\(590\) 0 0
\(591\) −5.17838 2.98974i −0.213010 0.122981i
\(592\) 0 0
\(593\) −13.3007 + 7.67919i −0.546196 + 0.315346i −0.747586 0.664165i \(-0.768787\pi\)
0.201390 + 0.979511i \(0.435454\pi\)
\(594\) 0 0
\(595\) −0.791080 0.165158i −0.0324311 0.00677083i
\(596\) 0 0
\(597\) −2.45142 1.88104i −0.100330 0.0769858i
\(598\) 0 0
\(599\) 5.42629 1.45397i 0.221712 0.0594076i −0.146253 0.989247i \(-0.546721\pi\)
0.367965 + 0.929840i \(0.380055\pi\)
\(600\) 0 0
\(601\) 9.59925 9.59925i 0.391562 0.391562i −0.483682 0.875244i \(-0.660701\pi\)
0.875244 + 0.483682i \(0.160701\pi\)
\(602\) 0 0
\(603\) −10.7561 25.9676i −0.438024 1.05748i
\(604\) 0 0
\(605\) 1.38880 1.06567i 0.0564629 0.0433255i
\(606\) 0 0
\(607\) 10.4318 + 18.0684i 0.423413 + 0.733373i 0.996271 0.0862819i \(-0.0274986\pi\)
−0.572858 + 0.819655i \(0.694165\pi\)
\(608\) 0 0
\(609\) −2.43153 0.851157i −0.0985306 0.0344906i
\(610\) 0 0
\(611\) −6.18899 47.0101i −0.250380 1.90182i
\(612\) 0 0
\(613\) 43.6071 + 5.74098i 1.76127 + 0.231876i 0.940598 0.339521i \(-0.110265\pi\)
0.820674 + 0.571397i \(0.193598\pi\)
\(614\) 0 0
\(615\) 0.275132 0.275132i 0.0110944 0.0110944i
\(616\) 0 0
\(617\) 3.01401 + 3.01401i 0.121339 + 0.121339i 0.765169 0.643830i \(-0.222655\pi\)
−0.643830 + 0.765169i \(0.722655\pi\)
\(618\) 0 0
\(619\) −3.30864 + 25.1316i −0.132985 + 1.01012i 0.786663 + 0.617382i \(0.211807\pi\)
−0.919649 + 0.392742i \(0.871527\pi\)
\(620\) 0 0
\(621\) −15.2681 + 2.01009i −0.612689 + 0.0806620i
\(622\) 0 0
\(623\) −1.78435 2.07395i −0.0714884 0.0830912i
\(624\) 0 0
\(625\) −21.3208 + 12.3096i −0.852832 + 0.492383i
\(626\) 0 0
\(627\) 0.0471324 + 0.0614241i 0.00188229 + 0.00245304i
\(628\) 0 0
\(629\) 3.23993 1.34202i 0.129184 0.0535100i
\(630\) 0 0
\(631\) −5.06316 5.06316i −0.201561 0.201561i 0.599107 0.800669i \(-0.295522\pi\)
−0.800669 + 0.599107i \(0.795522\pi\)
\(632\) 0 0
\(633\) −2.70028 10.0776i −0.107326 0.400547i
\(634\) 0 0
\(635\) 0.0544367 0.0709433i 0.00216025 0.00281530i
\(636\) 0 0
\(637\) −37.8650 0.717222i −1.50026 0.0284174i
\(638\) 0 0
\(639\) −18.2865 31.6731i −0.723402 1.25297i
\(640\) 0 0
\(641\) −16.4584 + 28.5069i −0.650070 + 1.12595i 0.333036 + 0.942914i \(0.391927\pi\)
−0.983106 + 0.183039i \(0.941406\pi\)
\(642\) 0 0
\(643\) 9.11504 + 3.77557i 0.359462 + 0.148894i 0.555103 0.831782i \(-0.312679\pi\)
−0.195641 + 0.980676i \(0.562679\pi\)
\(644\) 0 0
\(645\) −0.0126813 0.0306153i −0.000499325 0.00120548i
\(646\) 0 0
\(647\) −10.0339 37.4471i −0.394474 1.47220i −0.822674 0.568514i \(-0.807519\pi\)
0.428200 0.903684i \(-0.359148\pi\)
\(648\) 0 0
\(649\) −0.429001 + 1.60105i −0.0168398 + 0.0628468i
\(650\) 0 0
\(651\) −1.58819 + 3.14510i −0.0622462 + 0.123266i
\(652\) 0 0
\(653\) −13.7785 + 1.81397i −0.539193 + 0.0709861i −0.395204 0.918593i \(-0.629326\pi\)
−0.143989 + 0.989579i \(0.545993\pi\)
\(654\) 0 0
\(655\) −2.28619 1.31993i −0.0893287 0.0515739i
\(656\) 0 0
\(657\) 38.5263i 1.50305i
\(658\) 0 0
\(659\) 7.04625 17.0112i 0.274483 0.662660i −0.725182 0.688558i \(-0.758244\pi\)
0.999665 + 0.0258972i \(0.00824425\pi\)
\(660\) 0 0
\(661\) −4.06536 + 30.8795i −0.158124 + 1.20107i 0.709810 + 0.704393i \(0.248781\pi\)
−0.867934 + 0.496679i \(0.834553\pi\)
\(662\) 0 0
\(663\) −1.21700 + 4.54190i −0.0472643 + 0.176393i
\(664\) 0 0
\(665\) −0.424740 + 0.204481i −0.0164707 + 0.00792944i
\(666\) 0 0
\(667\) −7.65107 + 9.97107i −0.296251 + 0.386081i
\(668\) 0 0
\(669\) 8.08450 6.20346i 0.312565 0.239839i
\(670\) 0 0
\(671\) 1.53514 0.0592633
\(672\) 0 0
\(673\) 5.52017 0.212787 0.106393 0.994324i \(-0.466070\pi\)
0.106393 + 0.994324i \(0.466070\pi\)
\(674\) 0 0
\(675\) −10.3765 + 7.96217i −0.399392 + 0.306464i
\(676\) 0 0
\(677\) 20.2563 26.3985i 0.778513 1.01458i −0.220716 0.975338i \(-0.570840\pi\)
0.999230 0.0392404i \(-0.0124938\pi\)
\(678\) 0 0
\(679\) −27.0377 18.4388i −1.03761 0.707615i
\(680\) 0 0
\(681\) −2.95586 + 11.0314i −0.113269 + 0.422725i
\(682\) 0 0
\(683\) 4.35066 33.0465i 0.166473 1.26449i −0.680457 0.732788i \(-0.738219\pi\)
0.846931 0.531703i \(-0.178448\pi\)
\(684\) 0 0
\(685\) −0.634307 + 1.53135i −0.0242356 + 0.0585100i
\(686\) 0 0
\(687\) 10.0834i 0.384706i
\(688\) 0 0
\(689\) 46.7633 + 26.9988i 1.78154 + 1.02857i
\(690\) 0 0
\(691\) 44.6446 5.87757i 1.69836 0.223593i 0.781811 0.623515i \(-0.214296\pi\)
0.916549 + 0.399922i \(0.130963\pi\)
\(692\) 0 0
\(693\) 0.618303 + 0.944599i 0.0234874 + 0.0358823i
\(694\) 0 0
\(695\) 0.171097 0.638543i 0.00649008 0.0242213i
\(696\) 0 0
\(697\) 2.66525 + 9.94685i 0.100954 + 0.376764i
\(698\) 0 0
\(699\) −1.65508 3.99573i −0.0626011 0.151132i
\(700\) 0 0
\(701\) 31.6386 + 13.1051i 1.19497 + 0.494974i 0.889371 0.457186i \(-0.151143\pi\)
0.305601 + 0.952160i \(0.401143\pi\)
\(702\) 0 0
\(703\) 1.02281 1.77155i 0.0385759 0.0668154i
\(704\) 0 0
\(705\) 0.317119 + 0.549266i 0.0119434 + 0.0206866i
\(706\) 0 0
\(707\) 31.5698 + 28.2193i 1.18730 + 1.06130i
\(708\) 0 0
\(709\) 9.86479 12.8560i 0.370480 0.482819i −0.570492 0.821303i \(-0.693248\pi\)
0.940972 + 0.338484i \(0.109914\pi\)
\(710\) 0 0
\(711\) −6.08161 22.6969i −0.228078 0.851200i
\(712\) 0 0
\(713\) 12.1545 + 12.1545i 0.455189 + 0.455189i
\(714\) 0 0
\(715\) −0.121739 + 0.0504258i −0.00455277 + 0.00188582i
\(716\) 0 0
\(717\) −1.25159 1.63111i −0.0467417 0.0609149i
\(718\) 0 0
\(719\) 21.8413 12.6101i 0.814544 0.470277i −0.0339873 0.999422i \(-0.510821\pi\)
0.848531 + 0.529145i \(0.177487\pi\)
\(720\) 0 0
\(721\) −22.5593 26.2207i −0.840152 0.976511i
\(722\) 0 0
\(723\) 9.46684 1.24633i 0.352075 0.0463516i
\(724\) 0 0
\(725\) −1.39328 + 10.5830i −0.0517453 + 0.393044i
\(726\) 0 0
\(727\) −19.2070 19.2070i −0.712349 0.712349i 0.254677 0.967026i \(-0.418031\pi\)
−0.967026 + 0.254677i \(0.918031\pi\)
\(728\) 0 0
\(729\) 11.6728 11.6728i 0.432327 0.432327i
\(730\) 0 0
\(731\) 0.869515 + 0.114474i 0.0321602 + 0.00423397i
\(732\) 0 0
\(733\) −5.54280 42.1017i −0.204728 1.55506i −0.717512 0.696546i \(-0.754719\pi\)
0.512784 0.858517i \(-0.328614\pi\)
\(734\) 0 0
\(735\) 0.471603 0.184960i 0.0173953 0.00682237i
\(736\) 0 0
\(737\) −0.768138 1.33045i −0.0282947 0.0490079i
\(738\) 0 0
\(739\) 31.4859 24.1600i 1.15823 0.888739i 0.163029 0.986621i \(-0.447874\pi\)
0.995198 + 0.0978823i \(0.0312069\pi\)
\(740\) 0 0
\(741\) 1.04963 + 2.53404i 0.0385592 + 0.0930901i
\(742\) 0 0
\(743\) 7.24090 7.24090i 0.265643 0.265643i −0.561699 0.827342i \(-0.689852\pi\)
0.827342 + 0.561699i \(0.189852\pi\)
\(744\) 0 0
\(745\) −0.376065 + 0.100766i −0.0137779 + 0.00369179i
\(746\) 0 0
\(747\) 6.65503 + 5.10658i 0.243495 + 0.186840i
\(748\) 0 0
\(749\) −3.35027 10.1855i −0.122416 0.372168i
\(750\) 0 0
\(751\) −8.65821 + 4.99882i −0.315942 + 0.182409i −0.649583 0.760291i \(-0.725056\pi\)
0.333640 + 0.942701i \(0.391723\pi\)
\(752\) 0 0
\(753\) −2.97050 1.71502i −0.108251 0.0624989i
\(754\) 0 0
\(755\) −0.741165 + 1.78933i −0.0269738 + 0.0651204i
\(756\) 0 0
\(757\) 11.9833 4.96365i 0.435541 0.180407i −0.154130 0.988051i \(-0.549258\pi\)
0.589671 + 0.807644i \(0.299258\pi\)
\(758\) 0 0
\(759\) −0.392075 + 0.105056i −0.0142314 + 0.00381329i
\(760\) 0 0
\(761\) −7.51962 2.01488i −0.272586 0.0730392i 0.119937 0.992782i \(-0.461731\pi\)
−0.392523 + 0.919742i \(0.628398\pi\)
\(762\) 0 0
\(763\) −1.88035 33.5544i −0.0680731 1.21475i
\(764\) 0 0
\(765\) 0.111397 + 0.846143i 0.00402756 + 0.0305924i
\(766\) 0 0
\(767\) −29.3601 + 50.8531i −1.06013 + 1.83620i
\(768\) 0 0
\(769\) −12.2525 −0.441838 −0.220919 0.975292i \(-0.570906\pi\)
−0.220919 + 0.975292i \(0.570906\pi\)
\(770\) 0 0
\(771\) −0.969588 0.401616i −0.0349188 0.0144639i
\(772\) 0 0
\(773\) −34.9820 4.60546i −1.25821 0.165647i −0.528224 0.849105i \(-0.677142\pi\)
−0.729990 + 0.683458i \(0.760475\pi\)
\(774\) 0 0
\(775\) 14.1014 + 3.77846i 0.506537 + 0.135726i
\(776\) 0 0
\(777\) −1.23855 + 1.81615i −0.0444326 + 0.0651539i
\(778\) 0 0
\(779\) 4.76554 + 3.65672i 0.170743 + 0.131016i
\(780\) 0 0
\(781\) −1.21692 1.58591i −0.0435446 0.0567485i
\(782\) 0 0
\(783\) 5.64177i 0.201621i
\(784\) 0 0
\(785\) 0.0292009i 0.00104223i
\(786\) 0 0
\(787\) 4.86740 + 6.34332i 0.173504 + 0.226115i 0.872008 0.489491i \(-0.162817\pi\)
−0.698504 + 0.715606i \(0.746151\pi\)
\(788\) 0 0
\(789\) 7.15668 + 5.49151i 0.254785 + 0.195503i
\(790\) 0 0
\(791\) −5.66312 + 8.30414i −0.201357 + 0.295261i
\(792\) 0 0
\(793\) 52.5310 + 14.0756i 1.86543 + 0.499841i
\(794\) 0 0
\(795\) −0.716099 0.0942762i −0.0253974 0.00334363i
\(796\) 0 0
\(797\) −47.4115 19.6385i −1.67940 0.695631i −0.680104 0.733116i \(-0.738065\pi\)
−0.999297 + 0.0374853i \(0.988065\pi\)
\(798\) 0 0
\(799\) −16.7856 −0.593833
\(800\) 0 0
\(801\) −1.44465 + 2.50220i −0.0510441 + 0.0884110i
\(802\) 0 0
\(803\) −0.274858 2.08775i −0.00969951 0.0736751i
\(804\) 0 0
\(805\) −0.138276 2.46751i −0.00487360 0.0869685i
\(806\) 0 0
\(807\) −0.915844 0.245400i −0.0322392 0.00863847i
\(808\) 0 0
\(809\) 25.9173 6.94451i 0.911202 0.244156i 0.227381 0.973806i \(-0.426984\pi\)
0.683821 + 0.729650i \(0.260317\pi\)
\(810\) 0 0
\(811\) −34.4290 + 14.2610i −1.20897 + 0.500770i −0.893886 0.448294i \(-0.852032\pi\)
−0.315081 + 0.949065i \(0.602032\pi\)
\(812\) 0 0
\(813\) 5.62685 13.5844i 0.197342 0.476427i
\(814\) 0 0
\(815\) 1.35263 + 0.780941i 0.0473806 + 0.0273552i
\(816\) 0 0
\(817\) 0.443040 0.255789i 0.0155000 0.00894893i
\(818\) 0 0
\(819\) 12.4968 + 37.9925i 0.436672 + 1.32757i
\(820\) 0 0
\(821\) −22.1747 17.0152i −0.773901 0.593835i 0.144491 0.989506i \(-0.453845\pi\)
−0.918392 + 0.395671i \(0.870512\pi\)
\(822\) 0 0
\(823\) −7.16061 + 1.91868i −0.249603 + 0.0668809i −0.381451 0.924389i \(-0.624576\pi\)
0.131848 + 0.991270i \(0.457909\pi\)
\(824\) 0 0
\(825\) −0.243768 + 0.243768i −0.00848691 + 0.00848691i
\(826\) 0 0
\(827\) −8.58472 20.7253i −0.298520 0.720691i −0.999968 0.00797060i \(-0.997463\pi\)
0.701448 0.712720i \(-0.252537\pi\)
\(828\) 0 0
\(829\) 26.1235 20.0453i 0.907308 0.696202i −0.0457621 0.998952i \(-0.514572\pi\)
0.953070 + 0.302751i \(0.0979050\pi\)
\(830\) 0 0
\(831\) 3.10494 + 5.37792i 0.107709 + 0.186558i
\(832\) 0 0
\(833\) −2.00138 + 13.2567i −0.0693437 + 0.459319i
\(834\) 0 0
\(835\) 0.157460 + 1.19603i 0.00544913 + 0.0413903i
\(836\) 0 0
\(837\) 7.64999 + 1.00714i 0.264422 + 0.0348119i
\(838\) 0 0
\(839\) 0.657491 0.657491i 0.0226991 0.0226991i −0.695666 0.718365i \(-0.744891\pi\)
0.718365 + 0.695666i \(0.244891\pi\)
\(840\) 0 0
\(841\) −17.2503 17.2503i −0.594838 0.594838i
\(842\) 0 0
\(843\) 0.113597 0.862858i 0.00391250 0.0297184i
\(844\) 0 0
\(845\) −2.57265 + 0.338696i −0.0885019 + 0.0116515i
\(846\) 0 0
\(847\) −18.9408 22.0149i −0.650814 0.756443i
\(848\) 0 0
\(849\) 6.90854 3.98865i 0.237100 0.136890i
\(850\) 0 0
\(851\) 6.52865 + 8.50830i 0.223799 + 0.291661i
\(852\) 0 0
\(853\) 5.37097 2.22473i 0.183898 0.0761732i −0.288834 0.957379i \(-0.593268\pi\)
0.472733 + 0.881206i \(0.343268\pi\)
\(854\) 0 0
\(855\) 0.352017 + 0.352017i 0.0120387 + 0.0120387i
\(856\) 0 0
\(857\) −1.12130 4.18475i −0.0383029 0.142948i 0.944126 0.329584i \(-0.106908\pi\)
−0.982429 + 0.186635i \(0.940242\pi\)
\(858\) 0 0
\(859\) −12.2400 + 15.9515i −0.417624 + 0.544258i −0.954034 0.299699i \(-0.903114\pi\)
0.536410 + 0.843958i \(0.319780\pi\)
\(860\) 0 0
\(861\) −4.81267 4.30190i −0.164015 0.146608i
\(862\) 0 0
\(863\) −8.99800 15.5850i −0.306295 0.530519i 0.671254 0.741228i \(-0.265756\pi\)
−0.977549 + 0.210709i \(0.932423\pi\)
\(864\) 0 0
\(865\) 0.897439 1.55441i 0.0305138 0.0528515i
\(866\) 0 0
\(867\) −5.58914 2.31510i −0.189817 0.0786248i
\(868\) 0 0
\(869\) −0.491490 1.18656i −0.0166727 0.0402514i
\(870\) 0 0
\(871\) −14.0861 52.5700i −0.477289 1.78127i
\(872\) 0 0
\(873\) −8.94514 + 33.3837i −0.302747 + 1.12987i
\(874\) 0 0
\(875\) −2.30498 3.52138i −0.0779224 0.119044i
\(876\) 0 0
\(877\) −17.1124 + 2.25289i −0.577844 + 0.0760746i −0.413783 0.910376i \(-0.635793\pi\)
−0.164061 + 0.986450i \(0.552459\pi\)
\(878\) 0 0
\(879\) 9.58137 + 5.53181i 0.323172 + 0.186583i
\(880\) 0 0
\(881\) 30.8266i 1.03857i −0.854600 0.519287i \(-0.826197\pi\)
0.854600 0.519287i \(-0.173803\pi\)
\(882\) 0 0
\(883\) 7.82347 18.8875i 0.263281 0.635616i −0.735857 0.677137i \(-0.763220\pi\)
0.999138 + 0.0415210i \(0.0132204\pi\)
\(884\) 0 0
\(885\) 0.102521 0.778727i 0.00344622 0.0261766i
\(886\) 0 0
\(887\) −9.77597 + 36.4844i −0.328245 + 1.22503i 0.582764 + 0.812641i \(0.301971\pi\)
−0.911009 + 0.412386i \(0.864696\pi\)
\(888\) 0 0
\(889\) −1.22563 0.835838i −0.0411064 0.0280331i
\(890\) 0 0
\(891\) 0.668372 0.871039i 0.0223913 0.0291809i
\(892\) 0 0
\(893\) −7.76797 + 5.96058i −0.259945 + 0.199463i
\(894\) 0 0
\(895\) −2.51136 −0.0839457
\(896\) 0 0
\(897\) −14.3797 −0.480124
\(898\) 0 0
\(899\) 4.99594 3.83352i 0.166624 0.127855i
\(900\) 0 0
\(901\) 11.6369 15.1655i 0.387681 0.505236i
\(902\) 0 0
\(903\) −0.495341 + 0.238470i −0.0164839 + 0.00793580i
\(904\) 0 0
\(905\) 0.830917 3.10103i 0.0276206 0.103082i
\(906\) 0 0
\(907\) −0.990783 + 7.52574i −0.0328984 + 0.249888i −0.999990 0.00454145i \(-0.998554\pi\)
0.967091 + 0.254430i \(0.0818877\pi\)
\(908\) 0 0
\(909\) 17.1127 41.3137i 0.567592 1.37029i
\(910\) 0 0
\(911\) 34.8079i 1.15324i 0.817013 + 0.576619i \(0.195628\pi\)
−0.817013 + 0.576619i \(0.804372\pi\)
\(912\) 0 0
\(913\) 0.397070 + 0.229248i 0.0131411 + 0.00758701i
\(914\) 0 0
\(915\) −0.721225 + 0.0949510i −0.0238429 + 0.00313898i
\(916\) 0 0
\(917\) −19.7412 + 39.0935i −0.651912 + 1.29098i
\(918\) 0 0
\(919\) 4.26821 15.9292i 0.140795 0.525455i −0.859111 0.511789i \(-0.828983\pi\)
0.999907 0.0136665i \(-0.00435030\pi\)
\(920\) 0 0
\(921\) −0.0237903 0.0887866i −0.000783917 0.00292562i
\(922\) 0 0
\(923\) −27.1005 65.4265i −0.892025 2.15354i
\(924\) 0 0
\(925\) 8.41508 + 3.48564i 0.276686 + 0.114607i
\(926\) 0 0
\(927\) −18.2645 + 31.6350i −0.599885 + 1.03903i
\(928\) 0 0
\(929\) 1.04652 + 1.81262i 0.0343351 + 0.0594701i 0.882682 0.469970i \(-0.155735\pi\)
−0.848347 + 0.529440i \(0.822402\pi\)
\(930\) 0 0
\(931\) 3.78128 + 6.84558i 0.123926 + 0.224355i
\(932\) 0 0
\(933\) 1.64273 2.14084i 0.0537805 0.0700881i
\(934\) 0 0
\(935\) 0.0120733 + 0.0450580i 0.000394838 + 0.00147355i
\(936\) 0 0
\(937\) −9.81953 9.81953i −0.320790 0.320790i 0.528280 0.849070i \(-0.322837\pi\)
−0.849070 + 0.528280i \(0.822837\pi\)
\(938\) 0 0
\(939\) 3.13754 1.29961i 0.102390 0.0424113i
\(940\) 0 0
\(941\) −22.6119 29.4684i −0.737127 0.960642i 0.262864 0.964833i \(-0.415333\pi\)
−0.999991 + 0.00419048i \(0.998666\pi\)
\(942\) 0 0
\(943\) −27.2727 + 15.7459i −0.888121 + 0.512757i
\(944\) 0 0
\(945\) −0.723535 0.840967i −0.0235366 0.0273567i
\(946\) 0 0
\(947\) 53.2636 7.01229i 1.73083 0.227869i 0.801730 0.597686i \(-0.203913\pi\)
0.929104 + 0.369818i \(0.120580\pi\)
\(948\) 0 0
\(949\) 9.73717 73.9611i 0.316082 2.40088i
\(950\) 0 0
\(951\) 9.43699 + 9.43699i 0.306015 + 0.306015i
\(952\) 0 0
\(953\) 33.4217 33.4217i 1.08263 1.08263i 0.0863708 0.996263i \(-0.472473\pi\)
0.996263 0.0863708i \(-0.0275270\pi\)
\(954\) 0 0
\(955\) −1.39708 0.183929i −0.0452084 0.00595180i
\(956\) 0 0
\(957\) 0.0194098 + 0.147432i 0.000627430 + 0.00476580i
\(958\) 0 0
\(959\) 25.9541 + 9.08522i 0.838101 + 0.293377i
\(960\) 0 0
\(961\) 11.1938 + 19.3882i 0.361089 + 0.625425i
\(962\) 0 0
\(963\) −8.98350 + 6.89328i −0.289489 + 0.222133i
\(964\) 0 0
\(965\) −0.0116934 0.0282304i −0.000376424 0.000908768i
\(966\) 0 0
\(967\) −5.12909 + 5.12909i −0.164940 + 0.164940i −0.784751 0.619811i \(-0.787209\pi\)
0.619811 + 0.784751i \(0.287209\pi\)
\(968\) 0 0
\(969\) 0.937900 0.251309i 0.0301297 0.00807322i
\(970\) 0 0
\(971\) 22.2531 + 17.0754i 0.714137 + 0.547977i 0.900687 0.434469i \(-0.143064\pi\)
−0.186550 + 0.982446i \(0.559730\pi\)
\(972\) 0 0
\(973\) −10.7356 2.24134i −0.344169 0.0718540i
\(974\) 0 0
\(975\) −10.5766 + 6.10642i −0.338723 + 0.195562i
\(976\) 0 0
\(977\) −49.7040 28.6966i −1.59017 0.918086i −0.993277 0.115766i \(-0.963068\pi\)
−0.596894 0.802320i \(-0.703599\pi\)
\(978\) 0 0
\(979\) −0.0604344 + 0.145902i −0.00193149 + 0.00466304i
\(980\) 0 0
\(981\) −32.7896 + 13.5819i −1.04689 + 0.433637i
\(982\) 0 0
\(983\) 37.1462 9.95329i 1.18478 0.317461i 0.387959 0.921677i \(-0.373180\pi\)
0.796821 + 0.604216i \(0.206514\pi\)
\(984\) 0 0
\(985\) −2.02986 0.543900i −0.0646767 0.0173301i
\(986\) 0 0
\(987\) 8.80368 5.76260i 0.280224 0.183426i
\(988\) 0 0
\(989\) 0.350076 + 2.65909i 0.0111318 + 0.0845541i
\(990\) 0 0
\(991\) 17.8141 30.8549i 0.565882 0.980137i −0.431085 0.902311i \(-0.641869\pi\)
0.996967 0.0778255i \(-0.0247977\pi\)
\(992\) 0 0
\(993\) 3.45414 0.109614
\(994\) 0 0
\(995\) −1.00329 0.415575i −0.0318063 0.0131746i
\(996\) 0 0
\(997\) −7.20202 0.948164i −0.228090 0.0300287i 0.0156146 0.999878i \(-0.495030\pi\)
−0.243705 + 0.969849i \(0.578363\pi\)
\(998\) 0 0
\(999\) 4.65008 + 1.24599i 0.147122 + 0.0394212i
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 896.2.bh.a.81.17 240
4.3 odd 2 224.2.bd.a.221.11 yes 240
7.2 even 3 inner 896.2.bh.a.849.17 240
28.23 odd 6 224.2.bd.a.93.30 yes 240
32.11 odd 8 224.2.bd.a.53.30 240
32.21 even 8 inner 896.2.bh.a.305.17 240
224.107 odd 24 224.2.bd.a.149.11 yes 240
224.149 even 24 inner 896.2.bh.a.177.17 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
224.2.bd.a.53.30 240 32.11 odd 8
224.2.bd.a.93.30 yes 240 28.23 odd 6
224.2.bd.a.149.11 yes 240 224.107 odd 24
224.2.bd.a.221.11 yes 240 4.3 odd 2
896.2.bh.a.81.17 240 1.1 even 1 trivial
896.2.bh.a.177.17 240 224.149 even 24 inner
896.2.bh.a.305.17 240 32.21 even 8 inner
896.2.bh.a.849.17 240 7.2 even 3 inner