Properties

Label 460.2.x.a.17.11
Level $460$
Weight $2$
Character 460.17
Analytic conductor $3.673$
Analytic rank $0$
Dimension $240$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [460,2,Mod(17,460)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(460, base_ring=CyclotomicField(44))
 
chi = DirichletCharacter(H, H._module([0, 11, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("460.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 460.x (of order \(44\), degree \(20\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.67311849298\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(12\) over \(\Q(\zeta_{44})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label 17.11
Character \(\chi\) \(=\) 460.17
Dual form 460.2.x.a.433.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.20798 - 1.20565i) q^{3} +(1.99649 + 1.00699i) q^{5} +(-0.375619 - 0.501768i) q^{7} +(1.79966 - 2.80032i) q^{9} +O(q^{10})\) \(q+(2.20798 - 1.20565i) q^{3} +(1.99649 + 1.00699i) q^{5} +(-0.375619 - 0.501768i) q^{7} +(1.79966 - 2.80032i) q^{9} +(-0.0603661 + 0.0275683i) q^{11} +(0.355624 + 0.266217i) q^{13} +(5.62228 - 0.183642i) q^{15} +(0.0449704 + 0.628768i) q^{17} +(-0.607236 - 0.700788i) q^{19} +(-1.43431 - 0.655028i) q^{21} +(-3.74968 - 2.98996i) q^{23} +(2.97193 + 4.02090i) q^{25} +(0.0590001 - 0.824930i) q^{27} +(2.43256 + 2.10783i) q^{29} +(-4.49518 + 1.31991i) q^{31} +(-0.100049 + 0.133650i) q^{33} +(-0.244642 - 1.38002i) q^{35} +(-6.71439 + 1.46063i) q^{37} +(1.10617 + 0.159044i) q^{39} +(2.16351 - 1.39041i) q^{41} +(-5.43629 - 9.95581i) q^{43} +(6.41290 - 3.77857i) q^{45} +(2.75870 + 2.75870i) q^{47} +(1.86145 - 6.33950i) q^{49} +(0.857366 + 1.33409i) q^{51} +(-2.18926 + 1.63886i) q^{53} +(-0.148281 - 0.00574849i) q^{55} +(-2.18567 - 0.815211i) q^{57} +(-0.540372 + 0.0776937i) q^{59} +(1.64111 + 5.58909i) q^{61} +(-2.08110 + 0.148843i) q^{63} +(0.441921 + 0.889611i) q^{65} +(2.01402 + 5.39980i) q^{67} +(-11.8841 - 2.08098i) q^{69} +(-2.22873 + 4.88024i) q^{71} +(6.01580 + 0.430258i) q^{73} +(11.4097 + 5.29496i) q^{75} +(0.0365075 + 0.0199346i) q^{77} +(1.20741 + 8.39774i) q^{79} +(3.28414 + 7.19125i) q^{81} +(-3.42936 - 15.7645i) q^{83} +(-0.543382 + 1.30061i) q^{85} +(7.91234 + 1.72122i) q^{87} +(-6.87021 - 2.01727i) q^{89} -0.278437i q^{91} +(-8.33393 + 8.33393i) q^{93} +(-0.506651 - 2.01060i) q^{95} +(-2.64185 + 12.1444i) q^{97} +(-0.0314383 + 0.218658i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q + 4 q^{3}+O(q^{10}) \) Copy content Toggle raw display \( 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(277\) \(281\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{7}{22}\right)\)

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
\(3\) 2.20798 1.20565i 1.27478 0.696081i 0.307923 0.951411i \(-0.400366\pi\)
0.966854 + 0.255331i \(0.0821844\pi\)
\(4\) 0 0
\(5\) 1.99649 + 1.00699i 0.892857 + 0.450341i
\(6\) 0 0
\(7\) −0.375619 0.501768i −0.141970 0.189650i 0.723920 0.689884i \(-0.242338\pi\)
−0.865891 + 0.500233i \(0.833248\pi\)
\(8\) 0 0
\(9\) 1.79966 2.80032i 0.599886 0.933441i
\(10\) 0 0
\(11\) −0.0603661 + 0.0275683i −0.0182010 + 0.00831214i −0.424495 0.905430i \(-0.639548\pi\)
0.406294 + 0.913743i \(0.366821\pi\)
\(12\) 0 0
\(13\) 0.355624 + 0.266217i 0.0986325 + 0.0738353i 0.647456 0.762103i \(-0.275833\pi\)
−0.548823 + 0.835938i \(0.684924\pi\)
\(14\) 0 0
\(15\) 5.62228 0.183642i 1.45167 0.0474162i
\(16\) 0 0
\(17\) 0.0449704 + 0.628768i 0.0109069 + 0.152499i 0.999987 + 0.00511887i \(0.00162939\pi\)
−0.989080 + 0.147380i \(0.952916\pi\)
\(18\) 0 0
\(19\) −0.607236 0.700788i −0.139309 0.160772i 0.681808 0.731532i \(-0.261194\pi\)
−0.821117 + 0.570760i \(0.806649\pi\)
\(20\) 0 0
\(21\) −1.43431 0.655028i −0.312993 0.142939i
\(22\) 0 0
\(23\) −3.74968 2.98996i −0.781863 0.623450i
\(24\) 0 0
\(25\) 2.97193 + 4.02090i 0.594386 + 0.804180i
\(26\) 0 0
\(27\) 0.0590001 0.824930i 0.0113546 0.158758i
\(28\) 0 0
\(29\) 2.43256 + 2.10783i 0.451715 + 0.391414i 0.850791 0.525505i \(-0.176123\pi\)
−0.399075 + 0.916918i \(0.630669\pi\)
\(30\) 0 0
\(31\) −4.49518 + 1.31991i −0.807359 + 0.237062i −0.659264 0.751911i \(-0.729132\pi\)
−0.148095 + 0.988973i \(0.547314\pi\)
\(32\) 0 0
\(33\) −0.100049 + 0.133650i −0.0174163 + 0.0232655i
\(34\) 0 0
\(35\) −0.244642 1.38002i −0.0413520 0.233266i
\(36\) 0 0
\(37\) −6.71439 + 1.46063i −1.10384 + 0.240126i −0.727330 0.686287i \(-0.759239\pi\)
−0.376509 + 0.926413i \(0.622876\pi\)
\(38\) 0 0
\(39\) 1.10617 + 0.159044i 0.177130 + 0.0254674i
\(40\) 0 0
\(41\) 2.16351 1.39041i 0.337884 0.217145i −0.360685 0.932688i \(-0.617457\pi\)
0.698569 + 0.715543i \(0.253821\pi\)
\(42\) 0 0
\(43\) −5.43629 9.95581i −0.829026 1.51825i −0.855026 0.518586i \(-0.826459\pi\)
0.0259998 0.999662i \(-0.491723\pi\)
\(44\) 0 0
\(45\) 6.41290 3.77857i 0.955979 0.563276i
\(46\) 0 0
\(47\) 2.75870 + 2.75870i 0.402398 + 0.402398i 0.879077 0.476679i \(-0.158160\pi\)
−0.476679 + 0.879077i \(0.658160\pi\)
\(48\) 0 0
\(49\) 1.86145 6.33950i 0.265921 0.905643i
\(50\) 0 0
\(51\) 0.857366 + 1.33409i 0.120055 + 0.186810i
\(52\) 0 0
\(53\) −2.18926 + 1.63886i −0.300718 + 0.225114i −0.738971 0.673737i \(-0.764688\pi\)
0.438254 + 0.898851i \(0.355597\pi\)
\(54\) 0 0
\(55\) −0.148281 0.00574849i −0.0199942 0.000775127i
\(56\) 0 0
\(57\) −2.18567 0.815211i −0.289499 0.107977i
\(58\) 0 0
\(59\) −0.540372 + 0.0776937i −0.0703504 + 0.0101149i −0.177400 0.984139i \(-0.556769\pi\)
0.107050 + 0.994254i \(0.465860\pi\)
\(60\) 0 0
\(61\) 1.64111 + 5.58909i 0.210122 + 0.715610i 0.995343 + 0.0963944i \(0.0307310\pi\)
−0.785221 + 0.619215i \(0.787451\pi\)
\(62\) 0 0
\(63\) −2.08110 + 0.148843i −0.262194 + 0.0187525i
\(64\) 0 0
\(65\) 0.441921 + 0.889611i 0.0548136 + 0.110343i
\(66\) 0 0
\(67\) 2.01402 + 5.39980i 0.246052 + 0.659691i 0.999996 + 0.00275241i \(0.000876121\pi\)
−0.753944 + 0.656938i \(0.771851\pi\)
\(68\) 0 0
\(69\) −11.8841 2.08098i −1.43067 0.250520i
\(70\) 0 0
\(71\) −2.22873 + 4.88024i −0.264502 + 0.579178i −0.994555 0.104212i \(-0.966768\pi\)
0.730053 + 0.683390i \(0.239495\pi\)
\(72\) 0 0
\(73\) 6.01580 + 0.430258i 0.704096 + 0.0503579i 0.418796 0.908080i \(-0.362452\pi\)
0.285300 + 0.958438i \(0.407907\pi\)
\(74\) 0 0
\(75\) 11.4097 + 5.29496i 1.31748 + 0.611409i
\(76\) 0 0
\(77\) 0.0365075 + 0.0199346i 0.00416041 + 0.00227176i
\(78\) 0 0
\(79\) 1.20741 + 8.39774i 0.135844 + 0.944819i 0.937736 + 0.347349i \(0.112918\pi\)
−0.801891 + 0.597470i \(0.796173\pi\)
\(80\) 0 0
\(81\) 3.28414 + 7.19125i 0.364904 + 0.799028i
\(82\) 0 0
\(83\) −3.42936 15.7645i −0.376422 1.73038i −0.642370 0.766395i \(-0.722049\pi\)
0.265948 0.963987i \(-0.414315\pi\)
\(84\) 0 0
\(85\) −0.543382 + 1.30061i −0.0589381 + 0.141071i
\(86\) 0 0
\(87\) 7.91234 + 1.72122i 0.848292 + 0.184535i
\(88\) 0 0
\(89\) −6.87021 2.01727i −0.728240 0.213831i −0.103463 0.994633i \(-0.532992\pi\)
−0.624778 + 0.780803i \(0.714810\pi\)
\(90\) 0 0
\(91\) 0.278437i 0.0291881i
\(92\) 0 0
\(93\) −8.33393 + 8.33393i −0.864188 + 0.864188i
\(94\) 0 0
\(95\) −0.506651 2.01060i −0.0519813 0.206283i
\(96\) 0 0
\(97\) −2.64185 + 12.1444i −0.268239 + 1.23308i 0.623968 + 0.781450i \(0.285520\pi\)
−0.892207 + 0.451626i \(0.850844\pi\)
\(98\) 0 0
\(99\) −0.0314383 + 0.218658i −0.00315966 + 0.0219759i
\(100\) 0 0
\(101\) −2.30151 1.47909i −0.229009 0.147175i 0.421105 0.907012i \(-0.361642\pi\)
−0.650114 + 0.759837i \(0.725279\pi\)
\(102\) 0 0
\(103\) −0.327369 + 0.877710i −0.0322566 + 0.0864833i −0.952080 0.305850i \(-0.901059\pi\)
0.919823 + 0.392333i \(0.128332\pi\)
\(104\) 0 0
\(105\) −2.20398 2.75210i −0.215086 0.268577i
\(106\) 0 0
\(107\) 8.54004 15.6399i 0.825597 1.51197i −0.0330817 0.999453i \(-0.510532\pi\)
0.858678 0.512515i \(-0.171286\pi\)
\(108\) 0 0
\(109\) −10.8950 + 12.5735i −1.04355 + 1.20432i −0.0650903 + 0.997879i \(0.520734\pi\)
−0.978459 + 0.206441i \(0.933812\pi\)
\(110\) 0 0
\(111\) −13.0642 + 11.3202i −1.24000 + 1.07447i
\(112\) 0 0
\(113\) −12.2744 + 4.57810i −1.15468 + 0.430672i −0.852575 0.522604i \(-0.824961\pi\)
−0.302100 + 0.953276i \(0.597688\pi\)
\(114\) 0 0
\(115\) −4.47533 9.74533i −0.417326 0.908757i
\(116\) 0 0
\(117\) 1.38550 0.516763i 0.128089 0.0477748i
\(118\) 0 0
\(119\) 0.298604 0.258742i 0.0273730 0.0237188i
\(120\) 0 0
\(121\) −7.20058 + 8.30992i −0.654599 + 0.755447i
\(122\) 0 0
\(123\) 3.10065 5.67842i 0.279576 0.512006i
\(124\) 0 0
\(125\) 1.88441 + 11.0204i 0.168547 + 0.985694i
\(126\) 0 0
\(127\) 4.22789 11.3354i 0.375165 1.00586i −0.602948 0.797780i \(-0.706007\pi\)
0.978113 0.208075i \(-0.0667198\pi\)
\(128\) 0 0
\(129\) −24.0064 15.4280i −2.11365 1.35836i
\(130\) 0 0
\(131\) 1.82067 12.6630i 0.159073 1.10637i −0.741274 0.671202i \(-0.765778\pi\)
0.900347 0.435173i \(-0.143313\pi\)
\(132\) 0 0
\(133\) −0.123543 + 0.567920i −0.0107126 + 0.0492449i
\(134\) 0 0
\(135\) 0.948491 1.58755i 0.0816331 0.136635i
\(136\) 0 0
\(137\) 4.36585 4.36585i 0.372999 0.372999i −0.495569 0.868569i \(-0.665040\pi\)
0.868569 + 0.495569i \(0.165040\pi\)
\(138\) 0 0
\(139\) 18.5854i 1.57639i 0.615425 + 0.788196i \(0.288984\pi\)
−0.615425 + 0.788196i \(0.711016\pi\)
\(140\) 0 0
\(141\) 9.41717 + 2.76513i 0.793069 + 0.232866i
\(142\) 0 0
\(143\) −0.0288068 0.00626653i −0.00240894 0.000524034i
\(144\) 0 0
\(145\) 2.73401 + 6.65782i 0.227048 + 0.552902i
\(146\) 0 0
\(147\) −3.53317 16.2417i −0.291411 1.33960i
\(148\) 0 0
\(149\) −1.26806 2.77667i −0.103884 0.227474i 0.850551 0.525892i \(-0.176268\pi\)
−0.954435 + 0.298418i \(0.903541\pi\)
\(150\) 0 0
\(151\) 1.58415 + 11.0180i 0.128916 + 0.896633i 0.946931 + 0.321436i \(0.104165\pi\)
−0.818015 + 0.575197i \(0.804925\pi\)
\(152\) 0 0
\(153\) 1.84168 + 1.00564i 0.148891 + 0.0813008i
\(154\) 0 0
\(155\) −10.3037 1.89144i −0.827614 0.151924i
\(156\) 0 0
\(157\) 3.01861 + 0.215895i 0.240911 + 0.0172303i 0.191273 0.981537i \(-0.438739\pi\)
0.0496386 + 0.998767i \(0.484193\pi\)
\(158\) 0 0
\(159\) −2.85795 + 6.25803i −0.226650 + 0.496294i
\(160\) 0 0
\(161\) −0.0918158 + 3.00456i −0.00723610 + 0.236792i
\(162\) 0 0
\(163\) −3.67174 9.84431i −0.287593 0.771066i −0.997751 0.0670242i \(-0.978650\pi\)
0.710159 0.704042i \(-0.248623\pi\)
\(164\) 0 0
\(165\) −0.334332 + 0.166082i −0.0260277 + 0.0129295i
\(166\) 0 0
\(167\) 17.4831 1.25042i 1.35289 0.0967603i 0.624015 0.781412i \(-0.285500\pi\)
0.728870 + 0.684652i \(0.240046\pi\)
\(168\) 0 0
\(169\) −3.60693 12.2841i −0.277456 0.944928i
\(170\) 0 0
\(171\) −3.05525 + 0.439278i −0.233641 + 0.0335925i
\(172\) 0 0
\(173\) 7.34127 + 2.73815i 0.558147 + 0.208178i 0.612676 0.790334i \(-0.290093\pi\)
−0.0545294 + 0.998512i \(0.517366\pi\)
\(174\) 0 0
\(175\) 0.901245 3.00154i 0.0681277 0.226895i
\(176\) 0 0
\(177\) −1.09946 + 0.823044i −0.0826403 + 0.0618638i
\(178\) 0 0
\(179\) −0.945877 1.47181i −0.0706981 0.110008i 0.804104 0.594488i \(-0.202645\pi\)
−0.874802 + 0.484480i \(0.839009\pi\)
\(180\) 0 0
\(181\) −4.53893 + 15.4582i −0.337376 + 1.14900i 0.599803 + 0.800148i \(0.295246\pi\)
−0.937179 + 0.348849i \(0.886572\pi\)
\(182\) 0 0
\(183\) 10.3620 + 10.3620i 0.765981 + 0.765981i
\(184\) 0 0
\(185\) −14.8760 3.84522i −1.09371 0.282706i
\(186\) 0 0
\(187\) −0.0200487 0.0367165i −0.00146611 0.00268497i
\(188\) 0 0
\(189\) −0.436085 + 0.280255i −0.0317205 + 0.0203855i
\(190\) 0 0
\(191\) −16.9585 2.43827i −1.22708 0.176427i −0.501861 0.864948i \(-0.667351\pi\)
−0.725216 + 0.688521i \(0.758260\pi\)
\(192\) 0 0
\(193\) 2.45234 0.533474i 0.176523 0.0384003i −0.123435 0.992353i \(-0.539391\pi\)
0.299958 + 0.953952i \(0.403027\pi\)
\(194\) 0 0
\(195\) 2.04831 + 1.43144i 0.146682 + 0.102508i
\(196\) 0 0
\(197\) 13.5755 18.1348i 0.967216 1.29205i 0.0108308 0.999941i \(-0.496552\pi\)
0.956385 0.292108i \(-0.0943567\pi\)
\(198\) 0 0
\(199\) 13.2813 3.89976i 0.941490 0.276446i 0.225250 0.974301i \(-0.427680\pi\)
0.716239 + 0.697855i \(0.245862\pi\)
\(200\) 0 0
\(201\) 10.9572 + 9.49444i 0.772859 + 0.669686i
\(202\) 0 0
\(203\) 0.143924 2.01232i 0.0101015 0.141237i
\(204\) 0 0
\(205\) 5.71956 0.597286i 0.399471 0.0417163i
\(206\) 0 0
\(207\) −15.1210 + 5.11941i −1.05098 + 0.355824i
\(208\) 0 0
\(209\) 0.0559759 + 0.0255633i 0.00387194 + 0.00176825i
\(210\) 0 0
\(211\) 10.5737 + 12.2027i 0.727921 + 0.840065i 0.992236 0.124371i \(-0.0396913\pi\)
−0.264315 + 0.964436i \(0.585146\pi\)
\(212\) 0 0
\(213\) 0.962859 + 13.4625i 0.0659740 + 0.922437i
\(214\) 0 0
\(215\) −0.828047 25.3510i −0.0564723 1.72892i
\(216\) 0 0
\(217\) 2.35076 + 1.75976i 0.159580 + 0.119460i
\(218\) 0 0
\(219\) 13.8015 6.30293i 0.932618 0.425912i
\(220\) 0 0
\(221\) −0.151396 + 0.235577i −0.0101840 + 0.0158466i
\(222\) 0 0
\(223\) −4.07424 5.44255i −0.272832 0.364460i 0.643109 0.765775i \(-0.277644\pi\)
−0.915940 + 0.401315i \(0.868553\pi\)
\(224\) 0 0
\(225\) 16.6083 1.08612i 1.10722 0.0724081i
\(226\) 0 0
\(227\) −2.18768 + 1.19456i −0.145201 + 0.0792860i −0.550207 0.835028i \(-0.685451\pi\)
0.405006 + 0.914314i \(0.367269\pi\)
\(228\) 0 0
\(229\) 20.4130 1.34893 0.674466 0.738306i \(-0.264374\pi\)
0.674466 + 0.738306i \(0.264374\pi\)
\(230\) 0 0
\(231\) 0.104642 0.00688492
\(232\) 0 0
\(233\) 21.9341 11.9769i 1.43695 0.784634i 0.443217 0.896415i \(-0.353837\pi\)
0.993733 + 0.111781i \(0.0356554\pi\)
\(234\) 0 0
\(235\) 2.72972 + 8.28571i 0.178067 + 0.540500i
\(236\) 0 0
\(237\) 12.7906 + 17.0863i 0.830842 + 1.10987i
\(238\) 0 0
\(239\) 5.54892 8.63428i 0.358930 0.558505i −0.614088 0.789238i \(-0.710476\pi\)
0.973017 + 0.230732i \(0.0741122\pi\)
\(240\) 0 0
\(241\) 10.2180 4.66642i 0.658201 0.300590i −0.0581732 0.998307i \(-0.518528\pi\)
0.716374 + 0.697716i \(0.245800\pi\)
\(242\) 0 0
\(243\) 17.9076 + 13.4055i 1.14878 + 0.859963i
\(244\) 0 0
\(245\) 10.1002 10.7823i 0.645278 0.688855i
\(246\) 0 0
\(247\) −0.0293863 0.410874i −0.00186980 0.0261433i
\(248\) 0 0
\(249\) −26.5784 30.6731i −1.68434 1.94383i
\(250\) 0 0
\(251\) 16.9727 + 7.75119i 1.07131 + 0.489251i 0.871405 0.490565i \(-0.163210\pi\)
0.199905 + 0.979815i \(0.435937\pi\)
\(252\) 0 0
\(253\) 0.308782 + 0.0771200i 0.0194129 + 0.00484849i
\(254\) 0 0
\(255\) 0.368304 + 3.52685i 0.0230641 + 0.220860i
\(256\) 0 0
\(257\) 0.484145 6.76923i 0.0302001 0.422253i −0.959752 0.280849i \(-0.909384\pi\)
0.989952 0.141404i \(-0.0451616\pi\)
\(258\) 0 0
\(259\) 3.25495 + 2.82043i 0.202253 + 0.175253i
\(260\) 0 0
\(261\) 10.2804 3.01859i 0.636339 0.186846i
\(262\) 0 0
\(263\) 8.44180 11.2769i 0.520544 0.695365i −0.460827 0.887490i \(-0.652447\pi\)
0.981370 + 0.192125i \(0.0615380\pi\)
\(264\) 0 0
\(265\) −6.02115 + 1.06739i −0.369876 + 0.0655695i
\(266\) 0 0
\(267\) −17.6014 + 3.82895i −1.07719 + 0.234328i
\(268\) 0 0
\(269\) 24.8992 + 3.57996i 1.51813 + 0.218274i 0.850403 0.526132i \(-0.176358\pi\)
0.667727 + 0.744407i \(0.267267\pi\)
\(270\) 0 0
\(271\) −2.52309 + 1.62149i −0.153267 + 0.0984986i −0.615026 0.788507i \(-0.710855\pi\)
0.461760 + 0.887005i \(0.347218\pi\)
\(272\) 0 0
\(273\) −0.335697 0.614783i −0.0203173 0.0372083i
\(274\) 0 0
\(275\) −0.290253 0.160795i −0.0175029 0.00969629i
\(276\) 0 0
\(277\) −14.8274 14.8274i −0.890894 0.890894i 0.103714 0.994607i \(-0.466927\pi\)
−0.994607 + 0.103714i \(0.966927\pi\)
\(278\) 0 0
\(279\) −4.39363 + 14.9633i −0.263040 + 0.895832i
\(280\) 0 0
\(281\) −13.0016 20.2309i −0.775611 1.20687i −0.973955 0.226741i \(-0.927193\pi\)
0.198344 0.980132i \(-0.436444\pi\)
\(282\) 0 0
\(283\) 9.91550 7.42265i 0.589415 0.441231i −0.262484 0.964936i \(-0.584542\pi\)
0.851899 + 0.523706i \(0.175451\pi\)
\(284\) 0 0
\(285\) −3.54274 3.82851i −0.209854 0.226781i
\(286\) 0 0
\(287\) −1.51032 0.563319i −0.0891512 0.0332517i
\(288\) 0 0
\(289\) 16.4336 2.36280i 0.966685 0.138988i
\(290\) 0 0
\(291\) 8.80870 + 29.9997i 0.516375 + 1.75861i
\(292\) 0 0
\(293\) −22.9457 + 1.64111i −1.34050 + 0.0958748i −0.723085 0.690759i \(-0.757276\pi\)
−0.617420 + 0.786634i \(0.711822\pi\)
\(294\) 0 0
\(295\) −1.15708 0.389036i −0.0673680 0.0226505i
\(296\) 0 0
\(297\) 0.0191803 + 0.0514243i 0.00111295 + 0.00298394i
\(298\) 0 0
\(299\) −0.537500 2.06153i −0.0310844 0.119222i
\(300\) 0 0
\(301\) −2.95354 + 6.46734i −0.170239 + 0.372771i
\(302\) 0 0
\(303\) −6.86495 0.490991i −0.394381 0.0282067i
\(304\) 0 0
\(305\) −2.35173 + 12.8111i −0.134660 + 0.733563i
\(306\) 0 0
\(307\) −5.34440 2.91826i −0.305021 0.166554i 0.319448 0.947604i \(-0.396503\pi\)
−0.624469 + 0.781050i \(0.714684\pi\)
\(308\) 0 0
\(309\) 0.335385 + 2.33265i 0.0190794 + 0.132700i
\(310\) 0 0
\(311\) −13.1657 28.8289i −0.746558 1.63473i −0.772455 0.635070i \(-0.780971\pi\)
0.0258965 0.999665i \(-0.491756\pi\)
\(312\) 0 0
\(313\) −1.97651 9.08588i −0.111719 0.513564i −0.998663 0.0516878i \(-0.983540\pi\)
0.886944 0.461877i \(-0.152824\pi\)
\(314\) 0 0
\(315\) −4.30477 1.79849i −0.242546 0.101333i
\(316\) 0 0
\(317\) 13.8144 + 3.00514i 0.775895 + 0.168786i 0.583042 0.812442i \(-0.301862\pi\)
0.192853 + 0.981228i \(0.438226\pi\)
\(318\) 0 0
\(319\) −0.204953 0.0601797i −0.0114752 0.00336942i
\(320\) 0 0
\(321\) 44.8289i 2.50210i
\(322\) 0 0
\(323\) 0.413325 0.413325i 0.0229980 0.0229980i
\(324\) 0 0
\(325\) −0.0135409 + 2.22111i −0.000751116 + 0.123205i
\(326\) 0 0
\(327\) −8.89669 + 40.8974i −0.491988 + 2.26163i
\(328\) 0 0
\(329\) 0.348008 2.42045i 0.0191863 0.133444i
\(330\) 0 0
\(331\) −25.3702 16.3045i −1.39447 0.896174i −0.394730 0.918797i \(-0.629162\pi\)
−0.999744 + 0.0226235i \(0.992798\pi\)
\(332\) 0 0
\(333\) −7.99339 + 21.4311i −0.438035 + 1.17442i
\(334\) 0 0
\(335\) −1.41659 + 12.8087i −0.0773966 + 0.699817i
\(336\) 0 0
\(337\) 9.29950 17.0308i 0.506576 0.927725i −0.491797 0.870710i \(-0.663660\pi\)
0.998373 0.0570153i \(-0.0181584\pi\)
\(338\) 0 0
\(339\) −21.5820 + 24.9069i −1.17217 + 1.35276i
\(340\) 0 0
\(341\) 0.234969 0.203602i 0.0127243 0.0110257i
\(342\) 0 0
\(343\) −7.99102 + 2.98050i −0.431474 + 0.160932i
\(344\) 0 0
\(345\) −21.6309 16.1218i −1.16457 0.867969i
\(346\) 0 0
\(347\) −10.9819 + 4.09604i −0.589539 + 0.219887i −0.626489 0.779430i \(-0.715509\pi\)
0.0369497 + 0.999317i \(0.488236\pi\)
\(348\) 0 0
\(349\) −3.14419 + 2.72446i −0.168305 + 0.145837i −0.734941 0.678131i \(-0.762790\pi\)
0.566636 + 0.823968i \(0.308245\pi\)
\(350\) 0 0
\(351\) 0.240592 0.277658i 0.0128419 0.0148203i
\(352\) 0 0
\(353\) −12.5382 + 22.9620i −0.667340 + 1.22214i 0.296340 + 0.955082i \(0.404234\pi\)
−0.963680 + 0.267059i \(0.913948\pi\)
\(354\) 0 0
\(355\) −9.36400 + 7.49903i −0.496990 + 0.398007i
\(356\) 0 0
\(357\) 0.347359 0.931306i 0.0183842 0.0492900i
\(358\) 0 0
\(359\) 6.36390 + 4.08983i 0.335874 + 0.215853i 0.697696 0.716394i \(-0.254209\pi\)
−0.361822 + 0.932247i \(0.617845\pi\)
\(360\) 0 0
\(361\) 2.58161 17.9555i 0.135874 0.945027i
\(362\) 0 0
\(363\) −5.87990 + 27.0295i −0.308615 + 1.41868i
\(364\) 0 0
\(365\) 11.5772 + 6.91687i 0.605978 + 0.362045i
\(366\) 0 0
\(367\) −18.7614 + 18.7614i −0.979339 + 0.979339i −0.999791 0.0204514i \(-0.993490\pi\)
0.0204514 + 0.999791i \(0.493490\pi\)
\(368\) 0 0
\(369\) 8.56079i 0.445657i
\(370\) 0 0
\(371\) 1.64465 + 0.482913i 0.0853861 + 0.0250716i
\(372\) 0 0
\(373\) 11.7344 + 2.55265i 0.607582 + 0.132171i 0.505823 0.862638i \(-0.331189\pi\)
0.101760 + 0.994809i \(0.467553\pi\)
\(374\) 0 0
\(375\) 17.4474 + 22.0608i 0.900982 + 1.13922i
\(376\) 0 0
\(377\) 0.303939 + 1.39718i 0.0156536 + 0.0719586i
\(378\) 0 0
\(379\) 8.74596 + 19.1510i 0.449250 + 0.983720i 0.989807 + 0.142413i \(0.0454860\pi\)
−0.540558 + 0.841307i \(0.681787\pi\)
\(380\) 0 0
\(381\) −4.33142 30.1257i −0.221905 1.54339i
\(382\) 0 0
\(383\) −14.7924 8.07728i −0.755858 0.412730i 0.0546135 0.998508i \(-0.482607\pi\)
−0.810472 + 0.585778i \(0.800789\pi\)
\(384\) 0 0
\(385\) 0.0528127 + 0.0765619i 0.00269159 + 0.00390196i
\(386\) 0 0
\(387\) −37.6630 2.69371i −1.91452 0.136929i
\(388\) 0 0
\(389\) −1.66613 + 3.64832i −0.0844762 + 0.184977i −0.947156 0.320774i \(-0.896057\pi\)
0.862680 + 0.505751i \(0.168784\pi\)
\(390\) 0 0
\(391\) 1.71137 2.49214i 0.0865476 0.126033i
\(392\) 0 0
\(393\) −11.2472 30.1548i −0.567344 1.52111i
\(394\) 0 0
\(395\) −6.04588 + 17.9818i −0.304201 + 0.904764i
\(396\) 0 0
\(397\) −5.79219 + 0.414266i −0.290702 + 0.0207914i −0.215929 0.976409i \(-0.569278\pi\)
−0.0747732 + 0.997201i \(0.523823\pi\)
\(398\) 0 0
\(399\) 0.411930 + 1.40291i 0.0206223 + 0.0702331i
\(400\) 0 0
\(401\) 25.1757 3.61972i 1.25722 0.180760i 0.518676 0.854971i \(-0.326425\pi\)
0.738539 + 0.674210i \(0.235516\pi\)
\(402\) 0 0
\(403\) −1.94998 0.727304i −0.0971353 0.0362296i
\(404\) 0 0
\(405\) −0.684803 + 17.6644i −0.0340281 + 0.877749i
\(406\) 0 0
\(407\) 0.365054 0.273276i 0.0180951 0.0135458i
\(408\) 0 0
\(409\) 7.07719 + 11.0123i 0.349944 + 0.544524i 0.970950 0.239282i \(-0.0769120\pi\)
−0.621006 + 0.783806i \(0.713276\pi\)
\(410\) 0 0
\(411\) 4.37602 14.9034i 0.215853 0.735129i
\(412\) 0 0
\(413\) 0.241958 + 0.241958i 0.0119060 + 0.0119060i
\(414\) 0 0
\(415\) 9.02809 34.9271i 0.443171 1.71450i
\(416\) 0 0
\(417\) 22.4074 + 41.0361i 1.09730 + 2.00955i
\(418\) 0 0
\(419\) −7.82261 + 5.02729i −0.382160 + 0.245599i −0.717590 0.696466i \(-0.754755\pi\)
0.335430 + 0.942065i \(0.391118\pi\)
\(420\) 0 0
\(421\) −18.1246 2.60592i −0.883338 0.127005i −0.314308 0.949321i \(-0.601772\pi\)
−0.569031 + 0.822316i \(0.692681\pi\)
\(422\) 0 0
\(423\) 12.6900 2.76054i 0.617008 0.134222i
\(424\) 0 0
\(425\) −2.39456 + 2.04948i −0.116153 + 0.0994142i
\(426\) 0 0
\(427\) 2.18800 2.92282i 0.105885 0.141445i
\(428\) 0 0
\(429\) −0.0711600 + 0.0208945i −0.00343564 + 0.00100879i
\(430\) 0 0
\(431\) 8.96570 + 7.76882i 0.431862 + 0.374211i 0.843493 0.537140i \(-0.180495\pi\)
−0.411631 + 0.911351i \(0.635041\pi\)
\(432\) 0 0
\(433\) 1.73635 24.2774i 0.0834438 1.16670i −0.767361 0.641215i \(-0.778431\pi\)
0.850805 0.525482i \(-0.176115\pi\)
\(434\) 0 0
\(435\) 14.0636 + 11.4041i 0.674299 + 0.546783i
\(436\) 0 0
\(437\) 0.181614 + 4.44334i 0.00868776 + 0.212554i
\(438\) 0 0
\(439\) 0.292086 + 0.133391i 0.0139405 + 0.00636641i 0.422373 0.906422i \(-0.361197\pi\)
−0.408433 + 0.912788i \(0.633924\pi\)
\(440\) 0 0
\(441\) −14.4027 16.6216i −0.685842 0.791504i
\(442\) 0 0
\(443\) −0.618405 8.64643i −0.0293813 0.410804i −0.990765 0.135592i \(-0.956706\pi\)
0.961383 0.275212i \(-0.0887481\pi\)
\(444\) 0 0
\(445\) −11.6849 10.9457i −0.553918 0.518877i
\(446\) 0 0
\(447\) −6.14755 4.60200i −0.290769 0.217667i
\(448\) 0 0
\(449\) 23.3864 10.6802i 1.10367 0.504031i 0.221598 0.975138i \(-0.428873\pi\)
0.882076 + 0.471107i \(0.156145\pi\)
\(450\) 0 0
\(451\) −0.0922717 + 0.143578i −0.00434490 + 0.00676080i
\(452\) 0 0
\(453\) 16.7816 + 22.4176i 0.788468 + 1.05327i
\(454\) 0 0
\(455\) 0.280384 0.555896i 0.0131446 0.0260608i
\(456\) 0 0
\(457\) −11.0496 + 6.03353i −0.516878 + 0.282237i −0.716440 0.697648i \(-0.754230\pi\)
0.199562 + 0.979885i \(0.436048\pi\)
\(458\) 0 0
\(459\) 0.521343 0.0243342
\(460\) 0 0
\(461\) 26.5054 1.23448 0.617241 0.786774i \(-0.288251\pi\)
0.617241 + 0.786774i \(0.288251\pi\)
\(462\) 0 0
\(463\) −14.1938 + 7.75038i −0.659640 + 0.360191i −0.773943 0.633255i \(-0.781718\pi\)
0.114303 + 0.993446i \(0.463537\pi\)
\(464\) 0 0
\(465\) −25.0308 + 8.24638i −1.16078 + 0.382417i
\(466\) 0 0
\(467\) 0.655124 + 0.875143i 0.0303155 + 0.0404968i 0.815443 0.578838i \(-0.196493\pi\)
−0.785127 + 0.619334i \(0.787403\pi\)
\(468\) 0 0
\(469\) 1.95294 3.03884i 0.0901785 0.140320i
\(470\) 0 0
\(471\) 6.92532 3.16269i 0.319102 0.145729i
\(472\) 0 0
\(473\) 0.602632 + 0.451124i 0.0277090 + 0.0207427i
\(474\) 0 0
\(475\) 1.01313 4.52433i 0.0464857 0.207590i
\(476\) 0 0
\(477\) 0.649415 + 9.08001i 0.0297347 + 0.415745i
\(478\) 0 0
\(479\) −14.6334 16.8878i −0.668616 0.771624i 0.315543 0.948911i \(-0.397813\pi\)
−0.984159 + 0.177287i \(0.943268\pi\)
\(480\) 0 0
\(481\) −2.77665 1.26805i −0.126604 0.0578182i
\(482\) 0 0
\(483\) 3.41971 + 6.74469i 0.155602 + 0.306894i
\(484\) 0 0
\(485\) −17.5037 + 21.5858i −0.794804 + 0.980161i
\(486\) 0 0
\(487\) −2.46915 + 34.5233i −0.111888 + 1.56440i 0.562986 + 0.826467i \(0.309653\pi\)
−0.674874 + 0.737933i \(0.735802\pi\)
\(488\) 0 0
\(489\) −19.9759 17.3092i −0.903340 0.782749i
\(490\) 0 0
\(491\) −12.5216 + 3.67666i −0.565090 + 0.165925i −0.551785 0.833986i \(-0.686053\pi\)
−0.0133046 + 0.999911i \(0.504235\pi\)
\(492\) 0 0
\(493\) −1.21594 + 1.62431i −0.0547632 + 0.0731551i
\(494\) 0 0
\(495\) −0.282953 + 0.404890i −0.0127178 + 0.0181984i
\(496\) 0 0
\(497\) 3.28590 0.714804i 0.147393 0.0320633i
\(498\) 0 0
\(499\) 40.5651 + 5.83238i 1.81594 + 0.261093i 0.964638 0.263579i \(-0.0849030\pi\)
0.851304 + 0.524672i \(0.175812\pi\)
\(500\) 0 0
\(501\) 37.0948 23.8394i 1.65727 1.06507i
\(502\) 0 0
\(503\) −9.70407 17.7717i −0.432683 0.792400i 0.566822 0.823840i \(-0.308173\pi\)
−0.999506 + 0.0314399i \(0.989991\pi\)
\(504\) 0 0
\(505\) −3.10551 5.27060i −0.138193 0.234538i
\(506\) 0 0
\(507\) −22.7743 22.7743i −1.01144 1.01144i
\(508\) 0 0
\(509\) −12.4509 + 42.4037i −0.551874 + 1.87951i −0.0823239 + 0.996606i \(0.526234\pi\)
−0.469550 + 0.882906i \(0.655584\pi\)
\(510\) 0 0
\(511\) −2.04376 3.18015i −0.0904104 0.140681i
\(512\) 0 0
\(513\) −0.613927 + 0.459580i −0.0271056 + 0.0202910i
\(514\) 0 0
\(515\) −1.53744 + 1.42268i −0.0677475 + 0.0626907i
\(516\) 0 0
\(517\) −0.242585 0.0904793i −0.0106689 0.00397928i
\(518\) 0 0
\(519\) 19.5106 2.80520i 0.856421 0.123135i
\(520\) 0 0
\(521\) −3.21246 10.9406i −0.140740 0.479317i 0.858710 0.512461i \(-0.171266\pi\)
−0.999451 + 0.0331439i \(0.989448\pi\)
\(522\) 0 0
\(523\) 14.9697 1.07066i 0.654581 0.0468165i 0.259901 0.965635i \(-0.416310\pi\)
0.394680 + 0.918819i \(0.370856\pi\)
\(524\) 0 0
\(525\) −1.62887 7.71392i −0.0710899 0.336663i
\(526\) 0 0
\(527\) −1.03206 2.76707i −0.0449574 0.120535i
\(528\) 0 0
\(529\) 5.12025 + 22.4228i 0.222620 + 0.974905i
\(530\) 0 0
\(531\) −0.754917 + 1.65304i −0.0327606 + 0.0717357i
\(532\) 0 0
\(533\) 1.13955 + 0.0815021i 0.0493593 + 0.00353025i
\(534\) 0 0
\(535\) 32.7994 22.6251i 1.41804 0.978170i
\(536\) 0 0
\(537\) −3.86296 2.10934i −0.166699 0.0910246i
\(538\) 0 0
\(539\) 0.0624009 + 0.434008i 0.00268780 + 0.0186940i
\(540\) 0 0
\(541\) 2.75542 + 6.03353i 0.118465 + 0.259402i 0.959570 0.281470i \(-0.0908218\pi\)
−0.841105 + 0.540871i \(0.818095\pi\)
\(542\) 0 0
\(543\) 8.61525 + 39.6037i 0.369716 + 1.69956i
\(544\) 0 0
\(545\) −34.4131 + 14.1316i −1.47409 + 0.605332i
\(546\) 0 0
\(547\) 2.89385 + 0.629519i 0.123732 + 0.0269163i 0.274005 0.961728i \(-0.411652\pi\)
−0.150273 + 0.988645i \(0.548015\pi\)
\(548\) 0 0
\(549\) 18.6047 + 5.46283i 0.794029 + 0.233148i
\(550\) 0 0
\(551\) 2.98466i 0.127151i
\(552\) 0 0
\(553\) 3.76019 3.76019i 0.159899 0.159899i
\(554\) 0 0
\(555\) −37.4820 + 9.44510i −1.59102 + 0.400922i
\(556\) 0 0
\(557\) −5.88830 + 27.0681i −0.249495 + 1.14691i 0.666432 + 0.745566i \(0.267821\pi\)
−0.915927 + 0.401345i \(0.868543\pi\)
\(558\) 0 0
\(559\) 0.717132 4.98776i 0.0303315 0.210960i
\(560\) 0 0
\(561\) −0.0885342 0.0568975i −0.00373792 0.00240221i
\(562\) 0 0
\(563\) −5.69270 + 15.2627i −0.239919 + 0.643247i −0.999978 0.00660664i \(-0.997897\pi\)
0.760060 + 0.649853i \(0.225170\pi\)
\(564\) 0 0
\(565\) −29.1158 3.22007i −1.22491 0.135470i
\(566\) 0 0
\(567\) 2.37476 4.34904i 0.0997304 0.182643i
\(568\) 0 0
\(569\) 20.3645 23.5018i 0.853722 0.985248i −0.146270 0.989245i \(-0.546727\pi\)
0.999992 + 0.00399652i \(0.00127213\pi\)
\(570\) 0 0
\(571\) −24.2033 + 20.9723i −1.01288 + 0.877663i −0.992514 0.122130i \(-0.961027\pi\)
−0.0203625 + 0.999793i \(0.506482\pi\)
\(572\) 0 0
\(573\) −40.3838 + 15.0624i −1.68706 + 0.629240i
\(574\) 0 0
\(575\) 0.878538 23.9631i 0.0366376 0.999329i
\(576\) 0 0
\(577\) −7.44290 + 2.77606i −0.309852 + 0.115569i −0.499580 0.866268i \(-0.666512\pi\)
0.189728 + 0.981837i \(0.439239\pi\)
\(578\) 0 0
\(579\) 4.77153 4.13455i 0.198298 0.171826i
\(580\) 0 0
\(581\) −6.62200 + 7.64220i −0.274727 + 0.317052i
\(582\) 0 0
\(583\) 0.0869764 0.159285i 0.00360219 0.00659693i
\(584\) 0 0
\(585\) 3.28650 + 0.363473i 0.135880 + 0.0150278i
\(586\) 0 0
\(587\) 2.85130 7.64463i 0.117686 0.315528i −0.864729 0.502238i \(-0.832510\pi\)
0.982415 + 0.186711i \(0.0597827\pi\)
\(588\) 0 0
\(589\) 3.65461 + 2.34868i 0.150586 + 0.0967755i
\(590\) 0 0
\(591\) 8.11031 56.4085i 0.333614 2.32033i
\(592\) 0 0
\(593\) −2.23157 + 10.2584i −0.0916398 + 0.421261i 0.908356 + 0.418199i \(0.137338\pi\)
−0.999995 + 0.00306243i \(0.999025\pi\)
\(594\) 0 0
\(595\) 0.856710 0.215883i 0.0351217 0.00885033i
\(596\) 0 0
\(597\) 24.6232 24.6232i 1.00776 1.00776i
\(598\) 0 0
\(599\) 11.0925i 0.453227i −0.973985 0.226614i \(-0.927235\pi\)
0.973985 0.226614i \(-0.0727654\pi\)
\(600\) 0 0
\(601\) −6.06702 1.78144i −0.247479 0.0726664i 0.155640 0.987814i \(-0.450256\pi\)
−0.403119 + 0.915147i \(0.632074\pi\)
\(602\) 0 0
\(603\) 18.7457 + 4.07789i 0.763386 + 0.166064i
\(604\) 0 0
\(605\) −22.7439 + 9.33971i −0.924671 + 0.379713i
\(606\) 0 0
\(607\) −6.87335 31.5963i −0.278981 1.28245i −0.876813 0.480832i \(-0.840335\pi\)
0.597832 0.801621i \(-0.296029\pi\)
\(608\) 0 0
\(609\) −2.10837 4.61668i −0.0854353 0.187077i
\(610\) 0 0
\(611\) 0.246648 + 1.71548i 0.00997832 + 0.0694007i
\(612\) 0 0
\(613\) −33.4827 18.2829i −1.35235 0.738440i −0.370633 0.928779i \(-0.620859\pi\)
−0.981718 + 0.190339i \(0.939041\pi\)
\(614\) 0 0
\(615\) 11.9085 8.21456i 0.480199 0.331243i
\(616\) 0 0
\(617\) −15.0077 1.07337i −0.604188 0.0432124i −0.234105 0.972211i \(-0.575216\pi\)
−0.370083 + 0.928999i \(0.620671\pi\)
\(618\) 0 0
\(619\) −0.577910 + 1.26545i −0.0232282 + 0.0508626i −0.920891 0.389821i \(-0.872537\pi\)
0.897662 + 0.440684i \(0.145264\pi\)
\(620\) 0 0
\(621\) −2.68774 + 2.91682i −0.107855 + 0.117048i
\(622\) 0 0
\(623\) 1.56837 + 4.20497i 0.0628356 + 0.168469i
\(624\) 0 0
\(625\) −7.33526 + 23.8997i −0.293410 + 0.955987i
\(626\) 0 0
\(627\) 0.154414 0.0110439i 0.00616670 0.000441051i
\(628\) 0 0
\(629\) −1.22034 4.15611i −0.0486583 0.165715i
\(630\) 0 0
\(631\) −40.4216 + 5.81176i −1.60916 + 0.231362i −0.887474 0.460858i \(-0.847542\pi\)
−0.721686 + 0.692220i \(0.756633\pi\)
\(632\) 0 0
\(633\) 38.0585 + 14.1951i 1.51269 + 0.564204i
\(634\) 0 0
\(635\) 19.8556 18.3736i 0.787946 0.729133i
\(636\) 0 0
\(637\) 2.34966 1.75893i 0.0930969 0.0696915i
\(638\) 0 0
\(639\) 9.65529 + 15.0239i 0.381958 + 0.594338i
\(640\) 0 0
\(641\) −9.59468 + 32.6765i −0.378967 + 1.29064i 0.520577 + 0.853815i \(0.325717\pi\)
−0.899544 + 0.436829i \(0.856101\pi\)
\(642\) 0 0
\(643\) 23.4585 + 23.4585i 0.925112 + 0.925112i 0.997385 0.0722733i \(-0.0230254\pi\)
−0.0722733 + 0.997385i \(0.523025\pi\)
\(644\) 0 0
\(645\) −32.3926 54.9760i −1.27546 2.16468i
\(646\) 0 0
\(647\) 6.45768 + 11.8264i 0.253878 + 0.464942i 0.973271 0.229661i \(-0.0737618\pi\)
−0.719393 + 0.694603i \(0.755580\pi\)
\(648\) 0 0
\(649\) 0.0304782 0.0195872i 0.00119638 0.000768864i
\(650\) 0 0
\(651\) 7.31207 + 1.05132i 0.286583 + 0.0412044i
\(652\) 0 0
\(653\) 37.1674 8.08527i 1.45447 0.316401i 0.585262 0.810844i \(-0.300992\pi\)
0.869210 + 0.494443i \(0.164628\pi\)
\(654\) 0 0
\(655\) 16.3865 23.4482i 0.640275 0.916197i
\(656\) 0 0
\(657\) 12.0312 16.0719i 0.469383 0.627023i
\(658\) 0 0
\(659\) −27.8366 + 8.17355i −1.08436 + 0.318396i −0.774621 0.632426i \(-0.782059\pi\)
−0.309738 + 0.950822i \(0.600241\pi\)
\(660\) 0 0
\(661\) 13.6495 + 11.8273i 0.530902 + 0.460030i 0.878587 0.477582i \(-0.158487\pi\)
−0.347685 + 0.937611i \(0.613032\pi\)
\(662\) 0 0
\(663\) −0.0502566 + 0.702679i −0.00195181 + 0.0272898i
\(664\) 0 0
\(665\) −0.818545 + 1.00944i −0.0317418 + 0.0391444i
\(666\) 0 0
\(667\) −2.81901 15.1769i −0.109153 0.587654i
\(668\) 0 0
\(669\) −15.5576 7.10493i −0.601493 0.274693i
\(670\) 0 0
\(671\) −0.253149 0.292149i −0.00977269 0.0112783i
\(672\) 0 0
\(673\) −3.21307 44.9246i −0.123855 1.73171i −0.557106 0.830442i \(-0.688088\pi\)
0.433251 0.901273i \(-0.357366\pi\)
\(674\) 0 0
\(675\) 3.49230 2.21440i 0.134419 0.0852323i
\(676\) 0 0
\(677\) 23.2096 + 17.3745i 0.892018 + 0.667756i 0.943663 0.330909i \(-0.107355\pi\)
−0.0516449 + 0.998666i \(0.516446\pi\)
\(678\) 0 0
\(679\) 7.08599 3.23606i 0.271935 0.124189i
\(680\) 0 0
\(681\) −3.39013 + 5.27514i −0.129910 + 0.202144i
\(682\) 0 0
\(683\) 26.6171 + 35.5563i 1.01848 + 1.36053i 0.931268 + 0.364336i \(0.118704\pi\)
0.0872093 + 0.996190i \(0.472205\pi\)
\(684\) 0 0
\(685\) 13.1127 4.31999i 0.501012 0.165058i
\(686\) 0 0
\(687\) 45.0715 24.6109i 1.71959 0.938965i
\(688\) 0 0
\(689\) −1.21485 −0.0462819
\(690\) 0 0
\(691\) 49.5944 1.88666 0.943330 0.331856i \(-0.107675\pi\)
0.943330 + 0.331856i \(0.107675\pi\)
\(692\) 0 0
\(693\) 0.121524 0.0663573i 0.00461632 0.00252070i
\(694\) 0 0
\(695\) −18.7153 + 37.1055i −0.709913 + 1.40749i
\(696\) 0 0
\(697\) 0.971536 + 1.29782i 0.0367996 + 0.0491585i
\(698\) 0 0
\(699\) 33.9900 52.8895i 1.28562 2.00047i
\(700\) 0 0
\(701\) 35.3225 16.1312i 1.33411 0.609268i 0.384624 0.923073i \(-0.374331\pi\)
0.949487 + 0.313805i \(0.101604\pi\)
\(702\) 0 0
\(703\) 5.10081 + 3.81842i 0.192381 + 0.144014i
\(704\) 0 0
\(705\) 16.0168 + 15.0036i 0.603228 + 0.565067i
\(706\) 0 0
\(707\) 0.122330 + 1.71040i 0.00460070 + 0.0643262i
\(708\) 0 0
\(709\) −9.20810 10.6267i −0.345817 0.399094i 0.556021 0.831168i \(-0.312327\pi\)
−0.901838 + 0.432074i \(0.857782\pi\)
\(710\) 0 0
\(711\) 25.6893 + 11.7319i 0.963424 + 0.439981i
\(712\) 0 0
\(713\) 20.8020 + 8.49120i 0.779040 + 0.317998i
\(714\) 0 0
\(715\) −0.0512021 0.0415193i −0.00191485 0.00155273i
\(716\) 0 0
\(717\) 1.84199 25.7543i 0.0687903 0.961813i
\(718\) 0 0
\(719\) −32.6514 28.2926i −1.21769 1.05514i −0.996808 0.0798375i \(-0.974560\pi\)
−0.220885 0.975300i \(-0.570895\pi\)
\(720\) 0 0
\(721\) 0.563372 0.165421i 0.0209811 0.00616060i
\(722\) 0 0
\(723\) 16.9351 22.6227i 0.629824 0.841347i
\(724\) 0 0
\(725\) −1.24595 + 16.0454i −0.0462735 + 0.595911i
\(726\) 0 0
\(727\) −5.04338 + 1.09712i −0.187049 + 0.0406900i −0.305114 0.952316i \(-0.598695\pi\)
0.118065 + 0.993006i \(0.462331\pi\)
\(728\) 0 0
\(729\) 32.2264 + 4.63345i 1.19357 + 0.171609i
\(730\) 0 0
\(731\) 6.01542 3.86588i 0.222489 0.142985i
\(732\) 0 0
\(733\) 10.7627 + 19.7104i 0.397529 + 0.728019i 0.997399 0.0720780i \(-0.0229631\pi\)
−0.599870 + 0.800097i \(0.704781\pi\)
\(734\) 0 0
\(735\) 9.30137 35.9843i 0.343086 1.32730i
\(736\) 0 0
\(737\) −0.270442 0.270442i −0.00996185 0.00996185i
\(738\) 0 0
\(739\) −12.2377 + 41.6776i −0.450170 + 1.53314i 0.351977 + 0.936009i \(0.385510\pi\)
−0.802146 + 0.597128i \(0.796308\pi\)
\(740\) 0 0
\(741\) −0.560253 0.871771i −0.0205814 0.0320253i
\(742\) 0 0
\(743\) 12.4131 9.29232i 0.455392 0.340902i −0.346830 0.937928i \(-0.612742\pi\)
0.802222 + 0.597026i \(0.203651\pi\)
\(744\) 0 0
\(745\) 0.264415 6.82053i 0.00968742 0.249885i
\(746\) 0 0
\(747\) −50.3175 18.7674i −1.84102 0.686665i
\(748\) 0 0
\(749\) −11.0554 + 1.58953i −0.403956 + 0.0580800i
\(750\) 0 0
\(751\) 7.01304 + 23.8842i 0.255909 + 0.871547i 0.982781 + 0.184774i \(0.0591553\pi\)
−0.726872 + 0.686773i \(0.759026\pi\)
\(752\) 0 0
\(753\) 46.8206 3.34868i 1.70624 0.122033i
\(754\) 0 0
\(755\) −7.93232 + 23.5925i −0.288687 + 0.858621i
\(756\) 0 0
\(757\) −6.46470 17.3325i −0.234964 0.629962i 0.764936 0.644106i \(-0.222770\pi\)
−0.999900 + 0.0141442i \(0.995498\pi\)
\(758\) 0 0
\(759\) 0.774762 0.202002i 0.0281221 0.00733222i
\(760\) 0 0
\(761\) −18.8886 + 41.3602i −0.684710 + 1.49930i 0.172865 + 0.984945i \(0.444697\pi\)
−0.857575 + 0.514359i \(0.828030\pi\)
\(762\) 0 0
\(763\) 10.4013 + 0.743917i 0.376553 + 0.0269316i
\(764\) 0 0
\(765\) 2.66423 + 3.86230i 0.0963256 + 0.139642i
\(766\) 0 0
\(767\) −0.212853 0.116226i −0.00768567 0.00419669i
\(768\) 0 0
\(769\) 3.29776 + 22.9364i 0.118920 + 0.827109i 0.958748 + 0.284256i \(0.0917467\pi\)
−0.839828 + 0.542853i \(0.817344\pi\)
\(770\) 0 0
\(771\) −7.09232 15.5300i −0.255424 0.559300i
\(772\) 0 0
\(773\) 6.57341 + 30.2175i 0.236429 + 1.08685i 0.930315 + 0.366762i \(0.119534\pi\)
−0.693885 + 0.720085i \(0.744103\pi\)
\(774\) 0 0
\(775\) −18.6666 14.1520i −0.670523 0.508355i
\(776\) 0 0
\(777\) 10.5873 + 2.30312i 0.379817 + 0.0826241i
\(778\) 0 0
\(779\) −2.28814 0.671859i −0.0819812 0.0240719i
\(780\) 0 0
\(781\) 0.356043i 0.0127402i
\(782\) 0 0
\(783\) 1.88233 1.88233i 0.0672690 0.0672690i
\(784\) 0 0
\(785\) 5.80922 + 3.47075i 0.207340 + 0.123876i
\(786\) 0 0
\(787\) 0.601648 2.76573i 0.0214464 0.0985877i −0.965179 0.261589i \(-0.915754\pi\)
0.986626 + 0.163001i \(0.0521173\pi\)
\(788\) 0 0
\(789\) 5.04332 35.0770i 0.179547 1.24878i
\(790\) 0 0
\(791\) 6.90763 + 4.43926i 0.245607 + 0.157842i
\(792\) 0 0
\(793\) −0.904295 + 2.42451i −0.0321124 + 0.0860968i
\(794\) 0 0
\(795\) −12.0077 + 9.61616i −0.425868 + 0.341050i
\(796\) 0 0
\(797\) 20.6727 37.8593i 0.732265 1.34104i −0.200190 0.979757i \(-0.564156\pi\)
0.932455 0.361286i \(-0.117662\pi\)
\(798\) 0 0
\(799\) −1.61052 + 1.85864i −0.0569762 + 0.0657541i
\(800\) 0 0
\(801\) −18.0130 + 15.6084i −0.636460 + 0.551495i
\(802\) 0 0
\(803\) −0.375011 + 0.139872i −0.0132339 + 0.00493598i
\(804\) 0 0
\(805\) −3.20888 + 5.90610i −0.113098 + 0.208163i
\(806\) 0 0
\(807\) 59.2930 22.1151i 2.08721 0.778490i
\(808\) 0 0
\(809\) −26.6523 + 23.0943i −0.937043 + 0.811953i −0.982356 0.187020i \(-0.940117\pi\)
0.0453128 + 0.998973i \(0.485572\pi\)
\(810\) 0 0
\(811\) 5.30963 6.12764i 0.186446 0.215170i −0.654830 0.755777i \(-0.727260\pi\)
0.841276 + 0.540606i \(0.181805\pi\)
\(812\) 0 0
\(813\) −3.61598 + 6.62218i −0.126818 + 0.232250i
\(814\) 0 0
\(815\) 2.58257 23.3515i 0.0904634 0.817966i
\(816\) 0 0
\(817\) −3.67580 + 9.85521i −0.128600 + 0.344790i
\(818\) 0 0
\(819\) −0.779713 0.501091i −0.0272454 0.0175095i
\(820\) 0 0
\(821\) −2.05382 + 14.2846i −0.0716788 + 0.498537i 0.922081 + 0.386997i \(0.126487\pi\)
−0.993760 + 0.111540i \(0.964422\pi\)
\(822\) 0 0
\(823\) −7.69710 + 35.3830i −0.268304 + 1.23337i 0.623815 + 0.781572i \(0.285582\pi\)
−0.892119 + 0.451801i \(0.850782\pi\)
\(824\) 0 0
\(825\) −0.834734 0.00508894i −0.0290617 0.000177174i
\(826\) 0 0
\(827\) −25.2641 + 25.2641i −0.878519 + 0.878519i −0.993381 0.114862i \(-0.963357\pi\)
0.114862 + 0.993381i \(0.463357\pi\)
\(828\) 0 0
\(829\) 5.69858i 0.197920i −0.995091 0.0989600i \(-0.968448\pi\)
0.995091 0.0989600i \(-0.0315516\pi\)
\(830\) 0 0
\(831\) −50.6153 14.8620i −1.75582 0.515556i
\(832\) 0 0
\(833\) 4.06979 + 0.885328i 0.141010 + 0.0306748i
\(834\) 0 0
\(835\) 36.1640 + 15.1089i 1.25151 + 0.522867i
\(836\) 0 0
\(837\) 0.823612 + 3.78608i 0.0284682 + 0.130866i
\(838\) 0 0
\(839\) −3.85614 8.44376i −0.133129 0.291511i 0.831314 0.555803i \(-0.187589\pi\)
−0.964443 + 0.264292i \(0.914862\pi\)
\(840\) 0 0
\(841\) −2.65271 18.4500i −0.0914727 0.636206i
\(842\) 0 0
\(843\) −53.0986 28.9940i −1.82881 0.998607i
\(844\) 0 0
\(845\) 5.16878 28.1571i 0.177811 0.968635i
\(846\) 0 0
\(847\) 6.87432 + 0.491661i 0.236204 + 0.0168937i
\(848\) 0 0
\(849\) 12.9441 28.3436i 0.444240 0.972751i
\(850\) 0 0
\(851\) 29.5441 + 14.5989i 1.01276 + 0.500444i
\(852\) 0 0
\(853\) −17.8462 47.8474i −0.611041 1.63826i −0.760380 0.649478i \(-0.774987\pi\)
0.149339 0.988786i \(-0.452285\pi\)
\(854\) 0 0
\(855\) −6.54212 2.19960i −0.223736 0.0752247i
\(856\) 0 0
\(857\) −4.57022 + 0.326869i −0.156116 + 0.0111656i −0.149178 0.988810i \(-0.547663\pi\)
−0.00693755 + 0.999976i \(0.502208\pi\)
\(858\) 0 0
\(859\) 12.7831 + 43.5352i 0.436153 + 1.48540i 0.825549 + 0.564331i \(0.190866\pi\)
−0.389396 + 0.921071i \(0.627316\pi\)
\(860\) 0 0
\(861\) −4.01391 + 0.577113i −0.136794 + 0.0196680i
\(862\) 0 0
\(863\) −32.2387 12.0244i −1.09742 0.409316i −0.265442 0.964127i \(-0.585518\pi\)
−0.831977 + 0.554811i \(0.812791\pi\)
\(864\) 0 0
\(865\) 11.8995 + 12.8593i 0.404594 + 0.437229i
\(866\) 0 0
\(867\) 33.4364 25.0302i 1.13556 0.850069i
\(868\) 0 0
\(869\) −0.304398 0.473652i −0.0103260 0.0160675i
\(870\) 0 0
\(871\) −0.721284 + 2.45647i −0.0244398 + 0.0832343i
\(872\) 0 0
\(873\) 29.2538 + 29.2538i 0.990091 + 0.990091i
\(874\) 0 0
\(875\) 4.82186 5.08500i 0.163009 0.171904i
\(876\) 0 0
\(877\) 22.0748 + 40.4271i 0.745414 + 1.36512i 0.924458 + 0.381283i \(0.124518\pi\)
−0.179044 + 0.983841i \(0.557300\pi\)
\(878\) 0 0
\(879\) −48.6851 + 31.2880i −1.64211 + 1.05532i
\(880\) 0 0
\(881\) −37.4715 5.38759i −1.26245 0.181512i −0.521602 0.853189i \(-0.674665\pi\)
−0.740844 + 0.671677i \(0.765574\pi\)
\(882\) 0 0
\(883\) −28.3370 + 6.16433i −0.953615 + 0.207446i −0.662349 0.749196i \(-0.730440\pi\)
−0.291266 + 0.956642i \(0.594077\pi\)
\(884\) 0 0
\(885\) −3.02385 + 0.536051i −0.101646 + 0.0180192i
\(886\) 0 0
\(887\) −31.9121 + 42.6295i −1.07150 + 1.43136i −0.177046 + 0.984203i \(0.556654\pi\)
−0.894456 + 0.447157i \(0.852437\pi\)
\(888\) 0 0
\(889\) −7.27582 + 2.13637i −0.244023 + 0.0716517i
\(890\) 0 0
\(891\) −0.396501 0.343570i −0.0132833 0.0115100i
\(892\) 0 0
\(893\) 0.258081 3.60845i 0.00863636 0.120752i
\(894\) 0 0
\(895\) −0.406327 3.89095i −0.0135820 0.130060i
\(896\) 0 0
\(897\) −3.67227 3.90379i −0.122614 0.130344i
\(898\) 0 0
\(899\) −13.7169 6.26432i −0.457486 0.208927i
\(900\) 0 0
\(901\) −1.12891 1.30283i −0.0376095 0.0434037i
\(902\) 0 0
\(903\) 1.27599 + 17.8407i 0.0424623 + 0.593700i
\(904\) 0 0
\(905\) −24.6282 + 26.2914i −0.818669 + 0.873956i
\(906\) 0 0
\(907\) −1.48982 1.11527i −0.0494688 0.0370319i 0.574257 0.818675i \(-0.305291\pi\)
−0.623726 + 0.781643i \(0.714382\pi\)
\(908\) 0 0
\(909\) −8.28387 + 3.78312i −0.274759 + 0.125478i
\(910\) 0 0
\(911\) −13.8084 + 21.4863i −0.457492 + 0.711871i −0.990991 0.133929i \(-0.957240\pi\)
0.533499 + 0.845801i \(0.320877\pi\)
\(912\) 0 0
\(913\) 0.641618 + 0.857101i 0.0212345 + 0.0283659i
\(914\) 0 0
\(915\) 10.2531 + 31.1221i 0.338959 + 1.02886i
\(916\) 0 0
\(917\) −7.03778 + 3.84292i −0.232408 + 0.126904i
\(918\) 0 0
\(919\) 11.6605 0.384644 0.192322 0.981332i \(-0.438398\pi\)
0.192322 + 0.981332i \(0.438398\pi\)
\(920\) 0 0
\(921\) −15.3187 −0.504769
\(922\) 0 0
\(923\) −2.09179 + 1.14221i −0.0688523 + 0.0375962i
\(924\) 0 0
\(925\) −25.8277 22.6570i −0.849211 0.744958i
\(926\) 0 0
\(927\) 1.86872 + 2.49632i 0.0613768 + 0.0819898i
\(928\) 0 0
\(929\) 5.14718 8.00916i 0.168873 0.262772i −0.746494 0.665393i \(-0.768264\pi\)
0.915367 + 0.402620i \(0.131901\pi\)
\(930\) 0 0
\(931\) −5.57298 + 2.54510i −0.182647 + 0.0834122i
\(932\) 0 0
\(933\) −63.8270 47.7803i −2.08960 1.56426i
\(934\) 0 0
\(935\) −0.00305379 0.0934929i −9.98696e−5 0.00305755i
\(936\) 0 0
\(937\) −1.18848 16.6172i −0.0388260 0.542859i −0.979224 0.202782i \(-0.935002\pi\)
0.940398 0.340076i \(-0.110453\pi\)
\(938\) 0 0
\(939\) −15.3185 17.6785i −0.499899 0.576914i
\(940\) 0 0
\(941\) 37.4588 + 17.1069i 1.22112 + 0.557668i 0.918492 0.395439i \(-0.129408\pi\)
0.302631 + 0.953108i \(0.402135\pi\)
\(942\) 0 0
\(943\) −12.2698 1.25524i −0.399558 0.0408763i
\(944\) 0 0
\(945\) −1.15285 + 0.120391i −0.0375023 + 0.00391631i
\(946\) 0 0
\(947\) −1.80278 + 25.2061i −0.0585824 + 0.819090i 0.880205 + 0.474593i \(0.157405\pi\)
−0.938788 + 0.344496i \(0.888050\pi\)
\(948\) 0 0
\(949\) 2.02482 + 1.75452i 0.0657285 + 0.0569541i
\(950\) 0 0
\(951\) 34.1251 10.0200i 1.10658 0.324922i
\(952\) 0 0
\(953\) −0.508094 + 0.678733i −0.0164588 + 0.0219863i −0.808695 0.588228i \(-0.799826\pi\)
0.792236 + 0.610214i \(0.208917\pi\)
\(954\) 0 0
\(955\) −31.4022 21.9451i −1.01615 0.710127i
\(956\) 0 0
\(957\) −0.525088 + 0.114226i −0.0169737 + 0.00369240i
\(958\) 0 0
\(959\) −3.83053 0.550748i −0.123694 0.0177846i
\(960\) 0 0
\(961\) −7.61433 + 4.89343i −0.245624 + 0.157853i
\(962\) 0 0
\(963\) −28.4277 52.0614i −0.916068 1.67765i
\(964\) 0 0
\(965\) 5.43327 + 1.40441i 0.174903 + 0.0452097i
\(966\) 0 0
\(967\) −5.19326 5.19326i −0.167004 0.167004i 0.618657 0.785661i \(-0.287677\pi\)
−0.785661 + 0.618657i \(0.787677\pi\)
\(968\) 0 0
\(969\) 0.414288 1.41094i 0.0133089 0.0453258i
\(970\) 0 0
\(971\) −24.5163 38.1481i −0.786765 1.22423i −0.970464 0.241247i \(-0.922444\pi\)
0.183699 0.982983i \(-0.441193\pi\)
\(972\) 0 0
\(973\) 9.32554 6.98101i 0.298963 0.223801i
\(974\) 0 0
\(975\) 2.64798 + 4.92048i 0.0848031 + 0.157582i
\(976\) 0 0
\(977\) 23.9432 + 8.93037i 0.766012 + 0.285708i 0.701939 0.712237i \(-0.252318\pi\)
0.0640736 + 0.997945i \(0.479591\pi\)
\(978\) 0 0
\(979\) 0.470340 0.0676247i 0.0150321 0.00216129i
\(980\) 0 0
\(981\) 15.6025 + 53.1374i 0.498151 + 1.69655i
\(982\) 0 0
\(983\) −7.65470 + 0.547475i −0.244147 + 0.0174617i −0.192876 0.981223i \(-0.561782\pi\)
−0.0512706 + 0.998685i \(0.516327\pi\)
\(984\) 0 0
\(985\) 45.3650 22.5354i 1.44545 0.718038i
\(986\) 0 0
\(987\) −2.14981 5.76387i −0.0684293 0.183466i
\(988\) 0 0
\(989\) −9.38316 + 53.5854i −0.298367 + 1.70392i
\(990\) 0 0
\(991\) −11.2360 + 24.6034i −0.356923 + 0.781551i 0.642955 + 0.765904i \(0.277708\pi\)
−0.999878 + 0.0156474i \(0.995019\pi\)
\(992\) 0 0
\(993\) −75.6743 5.41233i −2.40145 0.171755i
\(994\) 0 0
\(995\) 30.4431 + 5.58841i 0.965111 + 0.177164i
\(996\) 0 0
\(997\) −45.4417 24.8131i −1.43915 0.785837i −0.445178 0.895442i \(-0.646860\pi\)
−0.993975 + 0.109605i \(0.965042\pi\)
\(998\) 0 0
\(999\) 0.808764 + 5.62508i 0.0255882 + 0.177970i
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 460.2.x.a.17.11 240
5.3 odd 4 inner 460.2.x.a.293.11 yes 240
23.19 odd 22 inner 460.2.x.a.157.11 yes 240
115.88 even 44 inner 460.2.x.a.433.11 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
460.2.x.a.17.11 240 1.1 even 1 trivial
460.2.x.a.157.11 yes 240 23.19 odd 22 inner
460.2.x.a.293.11 yes 240 5.3 odd 4 inner
460.2.x.a.433.11 yes 240 115.88 even 44 inner