Properties

Label 585.2.bs.a.334.3
Level $585$
Weight $2$
Character 585.334
Analytic conductor $4.671$
Analytic rank $0$
Dimension $12$
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] = [585,2,Mod(289,585)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(585, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("585.289");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 585.bs (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.67124851824\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 8x^{10} + 54x^{8} - 78x^{6} + 92x^{4} - 10x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 334.3
Root \(-0.286513 + 0.165418i\) of defining polynomial
Character \(\chi\) \(=\) 585.334
Dual form 585.2.bs.a.289.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.286513 - 0.165418i) q^{2} +(-0.945274 - 1.63726i) q^{4} +(2.12291 + 0.702335i) q^{5} +(-2.90420 + 1.67674i) q^{7} +1.28714i q^{8} +O(q^{10})\) \(q+(-0.286513 - 0.165418i) q^{2} +(-0.945274 - 1.63726i) q^{4} +(2.12291 + 0.702335i) q^{5} +(-2.90420 + 1.67674i) q^{7} +1.28714i q^{8} +(-0.492061 - 0.552395i) q^{10} +(-1.62291 + 2.81095i) q^{11} +(1.21648 + 3.39414i) q^{13} +1.10945 q^{14} +(-1.67763 + 2.90574i) q^{16} +(-1.68772 + 0.974404i) q^{17} +(-0.622905 - 1.07890i) q^{19} +(-0.856821 - 4.13965i) q^{20} +(0.929966 - 0.536916i) q^{22} +(2.33117 + 1.34590i) q^{23} +(4.01345 + 2.98198i) q^{25} +(0.212916 - 1.17369i) q^{26} +(5.49052 + 3.16995i) q^{28} +(-1.50000 + 2.59808i) q^{29} +3.78109 q^{31} +(3.19071 - 1.84216i) q^{32} +0.644737 q^{34} +(-7.34297 + 1.51984i) q^{35} +(1.68772 + 0.974404i) q^{37} +0.412160i q^{38} +(-0.904000 + 2.73247i) q^{40} +(1.39055 - 2.40850i) q^{41} +(-7.56654 + 4.36854i) q^{43} +6.13636 q^{44} +(-0.445274 - 0.771236i) q^{46} -6.86960i q^{47} +(2.12291 - 3.67698i) q^{49} +(-0.656632 - 1.51827i) q^{50} +(4.40719 - 5.20008i) q^{52} +12.8336i q^{53} +(-5.41950 + 4.82757i) q^{55} +(-2.15819 - 3.73809i) q^{56} +(0.859539 - 0.496255i) q^{58} +(1.26764 + 2.19562i) q^{59} +(3.74581 + 6.48793i) q^{61} +(-1.08333 - 0.625462i) q^{62} +5.49162 q^{64} +(0.198649 + 8.05981i) q^{65} +(-3.47722 - 2.00758i) q^{67} +(3.19071 + 1.84216i) q^{68} +(2.35526 + 0.779207i) q^{70} +(2.62291 + 4.54300i) q^{71} -5.46493i q^{73} +(-0.322368 - 0.558359i) q^{74} +(-1.17763 + 2.03972i) q^{76} -10.8848i q^{77} -13.7811 q^{79} +(-5.60226 + 4.99036i) q^{80} +(-0.796819 + 0.460044i) q^{82} -8.61955i q^{83} +(-4.26722 + 0.883225i) q^{85} +2.89055 q^{86} +(-3.61808 - 2.08890i) q^{88} +(-5.15819 + 8.93425i) q^{89} +(-9.22398 - 7.81753i) q^{91} -5.08898i q^{92} +(-1.13636 + 1.96823i) q^{94} +(-0.564617 - 2.72790i) q^{95} +(4.56055 - 2.63304i) q^{97} +(-1.21648 + 0.702335i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{4} + 6 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 4 q^{4} + 6 q^{5} + 7 q^{10} + 44 q^{14} - 16 q^{16} + 12 q^{19} + q^{20} - 2 q^{25} - 24 q^{26} - 18 q^{29} - 16 q^{31} + 16 q^{34} - 10 q^{35} + 70 q^{40} - 14 q^{41} + 4 q^{44} + 10 q^{46} + 6 q^{49} + 31 q^{50} - 26 q^{55} + 16 q^{56} + 4 q^{59} + 6 q^{61} - 12 q^{64} - 23 q^{65} + 20 q^{70} + 12 q^{71} - 8 q^{74} - 10 q^{76} - 104 q^{79} - 33 q^{80} + 21 q^{85} + 4 q^{86} - 20 q^{89} - 44 q^{91} + 56 q^{94} - 20 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\) \(496\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.286513 0.165418i −0.202595 0.116968i 0.395270 0.918565i \(-0.370651\pi\)
−0.597865 + 0.801597i \(0.703984\pi\)
\(3\) 0 0
\(4\) −0.945274 1.63726i −0.472637 0.818631i
\(5\) 2.12291 + 0.702335i 0.949392 + 0.314094i
\(6\) 0 0
\(7\) −2.90420 + 1.67674i −1.09768 + 0.633748i −0.935611 0.353031i \(-0.885151\pi\)
−0.162072 + 0.986779i \(0.551818\pi\)
\(8\) 1.28714i 0.455071i
\(9\) 0 0
\(10\) −0.492061 0.552395i −0.155603 0.174683i
\(11\) −1.62291 + 2.81095i −0.489324 + 0.847535i −0.999925 0.0122837i \(-0.996090\pi\)
0.510600 + 0.859818i \(0.329423\pi\)
\(12\) 0 0
\(13\) 1.21648 + 3.39414i 0.337391 + 0.941365i
\(14\) 1.10945 0.296514
\(15\) 0 0
\(16\) −1.67763 + 2.90574i −0.419408 + 0.726436i
\(17\) −1.68772 + 0.974404i −0.409332 + 0.236328i −0.690503 0.723330i \(-0.742611\pi\)
0.281171 + 0.959658i \(0.409277\pi\)
\(18\) 0 0
\(19\) −0.622905 1.07890i −0.142904 0.247517i 0.785685 0.618627i \(-0.212311\pi\)
−0.928589 + 0.371110i \(0.878977\pi\)
\(20\) −0.856821 4.13965i −0.191591 0.925654i
\(21\) 0 0
\(22\) 0.929966 0.536916i 0.198269 0.114471i
\(23\) 2.33117 + 1.34590i 0.486083 + 0.280640i 0.722948 0.690903i \(-0.242787\pi\)
−0.236865 + 0.971543i \(0.576120\pi\)
\(24\) 0 0
\(25\) 4.01345 + 2.98198i 0.802690 + 0.596396i
\(26\) 0.212916 1.17369i 0.0417562 0.230180i
\(27\) 0 0
\(28\) 5.49052 + 3.16995i 1.03761 + 0.599065i
\(29\) −1.50000 + 2.59808i −0.278543 + 0.482451i −0.971023 0.238987i \(-0.923185\pi\)
0.692480 + 0.721437i \(0.256518\pi\)
\(30\) 0 0
\(31\) 3.78109 0.679105 0.339552 0.940587i \(-0.389724\pi\)
0.339552 + 0.940587i \(0.389724\pi\)
\(32\) 3.19071 1.84216i 0.564043 0.325650i
\(33\) 0 0
\(34\) 0.644737 0.110571
\(35\) −7.34297 + 1.51984i −1.24119 + 0.256900i
\(36\) 0 0
\(37\) 1.68772 + 0.974404i 0.277459 + 0.160191i 0.632273 0.774746i \(-0.282122\pi\)
−0.354813 + 0.934937i \(0.615456\pi\)
\(38\) 0.412160i 0.0668611i
\(39\) 0 0
\(40\) −0.904000 + 2.73247i −0.142935 + 0.432041i
\(41\) 1.39055 2.40850i 0.217167 0.376144i −0.736774 0.676139i \(-0.763652\pi\)
0.953941 + 0.299995i \(0.0969851\pi\)
\(42\) 0 0
\(43\) −7.56654 + 4.36854i −1.15389 + 0.666197i −0.949831 0.312763i \(-0.898745\pi\)
−0.204055 + 0.978959i \(0.565412\pi\)
\(44\) 6.13636 0.925091
\(45\) 0 0
\(46\) −0.445274 0.771236i −0.0656520 0.113713i
\(47\) 6.86960i 1.00203i −0.865437 0.501017i \(-0.832959\pi\)
0.865437 0.501017i \(-0.167041\pi\)
\(48\) 0 0
\(49\) 2.12291 3.67698i 0.303272 0.525283i
\(50\) −0.656632 1.51827i −0.0928618 0.214716i
\(51\) 0 0
\(52\) 4.40719 5.20008i 0.611167 0.721122i
\(53\) 12.8336i 1.76282i 0.472347 + 0.881412i \(0.343407\pi\)
−0.472347 + 0.881412i \(0.656593\pi\)
\(54\) 0 0
\(55\) −5.41950 + 4.82757i −0.730766 + 0.650949i
\(56\) −2.15819 3.73809i −0.288400 0.499524i
\(57\) 0 0
\(58\) 0.859539 0.496255i 0.112863 0.0651614i
\(59\) 1.26764 + 2.19562i 0.165033 + 0.285845i 0.936667 0.350221i \(-0.113894\pi\)
−0.771634 + 0.636067i \(0.780560\pi\)
\(60\) 0 0
\(61\) 3.74581 + 6.48793i 0.479602 + 0.830695i 0.999726 0.0233957i \(-0.00744777\pi\)
−0.520124 + 0.854090i \(0.674114\pi\)
\(62\) −1.08333 0.625462i −0.137583 0.0794338i
\(63\) 0 0
\(64\) 5.49162 0.686453
\(65\) 0.198649 + 8.05981i 0.0246394 + 0.999696i
\(66\) 0 0
\(67\) −3.47722 2.00758i −0.424810 0.245264i 0.272323 0.962206i \(-0.412208\pi\)
−0.697133 + 0.716942i \(0.745541\pi\)
\(68\) 3.19071 + 1.84216i 0.386930 + 0.223394i
\(69\) 0 0
\(70\) 2.35526 + 0.779207i 0.281508 + 0.0931331i
\(71\) 2.62291 + 4.54300i 0.311282 + 0.539155i 0.978640 0.205581i \(-0.0659084\pi\)
−0.667359 + 0.744737i \(0.732575\pi\)
\(72\) 0 0
\(73\) 5.46493i 0.639622i −0.947481 0.319811i \(-0.896381\pi\)
0.947481 0.319811i \(-0.103619\pi\)
\(74\) −0.322368 0.558359i −0.0374746 0.0649079i
\(75\) 0 0
\(76\) −1.17763 + 2.03972i −0.135084 + 0.233972i
\(77\) 10.8848i 1.24043i
\(78\) 0 0
\(79\) −13.7811 −1.55049 −0.775247 0.631658i \(-0.782375\pi\)
−0.775247 + 0.631658i \(0.782375\pi\)
\(80\) −5.60226 + 4.99036i −0.626351 + 0.557939i
\(81\) 0 0
\(82\) −0.796819 + 0.460044i −0.0879940 + 0.0508033i
\(83\) 8.61955i 0.946119i −0.881031 0.473059i \(-0.843150\pi\)
0.881031 0.473059i \(-0.156850\pi\)
\(84\) 0 0
\(85\) −4.26722 + 0.883225i −0.462845 + 0.0957992i
\(86\) 2.89055 0.311696
\(87\) 0 0
\(88\) −3.61808 2.08890i −0.385688 0.222677i
\(89\) −5.15819 + 8.93425i −0.546767 + 0.947028i 0.451726 + 0.892156i \(0.350808\pi\)
−0.998493 + 0.0548717i \(0.982525\pi\)
\(90\) 0 0
\(91\) −9.22398 7.81753i −0.966936 0.819500i
\(92\) 5.08898i 0.530563i
\(93\) 0 0
\(94\) −1.13636 + 1.96823i −0.117206 + 0.203007i
\(95\) −0.564617 2.72790i −0.0579285 0.279876i
\(96\) 0 0
\(97\) 4.56055 2.63304i 0.463054 0.267344i −0.250273 0.968175i \(-0.580521\pi\)
0.713328 + 0.700831i \(0.247187\pi\)
\(98\) −1.21648 + 0.702335i −0.122883 + 0.0709465i
\(99\) 0 0
\(100\) 1.08847 9.38986i 0.108847 0.938986i
\(101\) 2.85526 4.94546i 0.284109 0.492092i −0.688283 0.725442i \(-0.741635\pi\)
0.972393 + 0.233350i \(0.0749688\pi\)
\(102\) 0 0
\(103\) 7.36863i 0.726052i −0.931779 0.363026i \(-0.881744\pi\)
0.931779 0.363026i \(-0.118256\pi\)
\(104\) −4.36872 + 1.56577i −0.428388 + 0.153537i
\(105\) 0 0
\(106\) 2.12291 3.67698i 0.206195 0.357140i
\(107\) −7.42568 4.28722i −0.717868 0.414461i 0.0960996 0.995372i \(-0.469363\pi\)
−0.813967 + 0.580911i \(0.802697\pi\)
\(108\) 0 0
\(109\) 8.49162 0.813350 0.406675 0.913573i \(-0.366688\pi\)
0.406675 + 0.913573i \(0.366688\pi\)
\(110\) 2.35133 0.486675i 0.224190 0.0464026i
\(111\) 0 0
\(112\) 11.2518i 1.06320i
\(113\) 6.35006 3.66621i 0.597363 0.344888i −0.170640 0.985333i \(-0.554584\pi\)
0.768004 + 0.640446i \(0.221250\pi\)
\(114\) 0 0
\(115\) 4.00358 + 4.49448i 0.373336 + 0.419113i
\(116\) 5.67164 0.526599
\(117\) 0 0
\(118\) 0.838765i 0.0772145i
\(119\) 3.26764 5.65972i 0.299544 0.518826i
\(120\) 0 0
\(121\) 0.232358 + 0.402456i 0.0211234 + 0.0365869i
\(122\) 2.47850i 0.224393i
\(123\) 0 0
\(124\) −3.57417 6.19064i −0.320970 0.555936i
\(125\) 6.42583 + 9.14925i 0.574744 + 0.818333i
\(126\) 0 0
\(127\) −7.93599 4.58185i −0.704205 0.406573i 0.104707 0.994503i \(-0.466610\pi\)
−0.808912 + 0.587930i \(0.799943\pi\)
\(128\) −7.95484 4.59273i −0.703115 0.405944i
\(129\) 0 0
\(130\) 1.27632 2.34210i 0.111941 0.205416i
\(131\) −10.0000 −0.873704 −0.436852 0.899533i \(-0.643907\pi\)
−0.436852 + 0.899533i \(0.643907\pi\)
\(132\) 0 0
\(133\) 3.61808 + 2.08890i 0.313727 + 0.181130i
\(134\) 0.664179 + 1.15039i 0.0573763 + 0.0993787i
\(135\) 0 0
\(136\) −1.25419 2.17232i −0.107546 0.186275i
\(137\) 14.5914 8.42435i 1.24663 0.719741i 0.276193 0.961102i \(-0.410927\pi\)
0.970435 + 0.241361i \(0.0775938\pi\)
\(138\) 0 0
\(139\) −0.513452 0.889325i −0.0435505 0.0754316i 0.843429 0.537241i \(-0.180534\pi\)
−0.886979 + 0.461810i \(0.847200\pi\)
\(140\) 9.42949 + 10.5857i 0.796937 + 0.894654i
\(141\) 0 0
\(142\) 1.73551i 0.145640i
\(143\) −11.5150 2.08890i −0.962933 0.174682i
\(144\) 0 0
\(145\) −5.00908 + 4.46197i −0.415981 + 0.370546i
\(146\) −0.904000 + 1.56577i −0.0748155 + 0.129584i
\(147\) 0 0
\(148\) 3.68431i 0.302849i
\(149\) −7.92583 13.7279i −0.649309 1.12464i −0.983288 0.182056i \(-0.941725\pi\)
0.333979 0.942581i \(-0.391609\pi\)
\(150\) 0 0
\(151\) 14.5454 1.18369 0.591845 0.806052i \(-0.298400\pi\)
0.591845 + 0.806052i \(0.298400\pi\)
\(152\) 1.38869 0.801763i 0.112638 0.0650316i
\(153\) 0 0
\(154\) −1.80054 + 3.11862i −0.145091 + 0.251306i
\(155\) 8.02690 + 2.65559i 0.644736 + 0.213302i
\(156\) 0 0
\(157\) 10.9210i 0.871588i −0.900047 0.435794i \(-0.856468\pi\)
0.900047 0.435794i \(-0.143532\pi\)
\(158\) 3.94846 + 2.27964i 0.314123 + 0.181359i
\(159\) 0 0
\(160\) 8.06738 1.66978i 0.637783 0.132008i
\(161\) −9.02690 −0.711420
\(162\) 0 0
\(163\) −3.61808 + 2.08890i −0.283390 + 0.163615i −0.634957 0.772547i \(-0.718982\pi\)
0.351567 + 0.936163i \(0.385649\pi\)
\(164\) −5.25779 −0.410564
\(165\) 0 0
\(166\) −1.42583 + 2.46961i −0.110666 + 0.191679i
\(167\) 2.90420 + 1.67674i 0.224733 + 0.129750i 0.608140 0.793830i \(-0.291916\pi\)
−0.383407 + 0.923580i \(0.625249\pi\)
\(168\) 0 0
\(169\) −10.0404 + 8.25780i −0.772335 + 0.635215i
\(170\) 1.36872 + 0.452821i 0.104976 + 0.0347298i
\(171\) 0 0
\(172\) 14.3049 + 8.25894i 1.09074 + 0.629738i
\(173\) −7.56654 + 4.36854i −0.575273 + 0.332134i −0.759253 0.650796i \(-0.774435\pi\)
0.183979 + 0.982930i \(0.441102\pi\)
\(174\) 0 0
\(175\) −16.6559 1.93074i −1.25906 0.145950i
\(176\) −5.44527 9.43149i −0.410453 0.710925i
\(177\) 0 0
\(178\) 2.95577 1.70652i 0.221545 0.127909i
\(179\) 9.00507 15.5972i 0.673071 1.16579i −0.303958 0.952685i \(-0.598308\pi\)
0.977029 0.213107i \(-0.0683584\pi\)
\(180\) 0 0
\(181\) 1.04366 0.0775749 0.0387875 0.999247i \(-0.487650\pi\)
0.0387875 + 0.999247i \(0.487650\pi\)
\(182\) 1.34963 + 3.76564i 0.100041 + 0.279128i
\(183\) 0 0
\(184\) −1.73236 + 3.00053i −0.127711 + 0.221202i
\(185\) 2.89851 + 3.25391i 0.213102 + 0.239232i
\(186\) 0 0
\(187\) 6.32546i 0.462564i
\(188\) −11.2473 + 6.49365i −0.820296 + 0.473598i
\(189\) 0 0
\(190\) −0.289474 + 0.874976i −0.0210006 + 0.0634774i
\(191\) 12.7593 + 22.0997i 0.923228 + 1.59908i 0.794387 + 0.607412i \(0.207792\pi\)
0.128841 + 0.991665i \(0.458874\pi\)
\(192\) 0 0
\(193\) 17.1652 + 9.91035i 1.23558 + 0.713362i 0.968188 0.250225i \(-0.0805047\pi\)
0.267392 + 0.963588i \(0.413838\pi\)
\(194\) −1.74221 −0.125083
\(195\) 0 0
\(196\) −8.02690 −0.573350
\(197\) −18.7512 10.8260i −1.33596 0.771319i −0.349758 0.936840i \(-0.613736\pi\)
−0.986206 + 0.165521i \(0.947070\pi\)
\(198\) 0 0
\(199\) 9.11453 + 15.7868i 0.646112 + 1.11910i 0.984044 + 0.177928i \(0.0569393\pi\)
−0.337932 + 0.941171i \(0.609727\pi\)
\(200\) −3.83821 + 5.16586i −0.271402 + 0.365281i
\(201\) 0 0
\(202\) −1.63614 + 0.944625i −0.115118 + 0.0664636i
\(203\) 10.0604i 0.706104i
\(204\) 0 0
\(205\) 4.64357 4.13638i 0.324321 0.288898i
\(206\) −1.21891 + 2.11121i −0.0849252 + 0.147095i
\(207\) 0 0
\(208\) −11.9033 2.15934i −0.825345 0.149723i
\(209\) 4.04366 0.279706
\(210\) 0 0
\(211\) −9.64981 + 16.7140i −0.664320 + 1.15064i 0.315149 + 0.949042i \(0.397946\pi\)
−0.979469 + 0.201594i \(0.935388\pi\)
\(212\) 21.0119 12.1312i 1.44310 0.833176i
\(213\) 0 0
\(214\) 1.41837 + 2.45669i 0.0969577 + 0.167936i
\(215\) −19.1312 + 3.95976i −1.30474 + 0.270053i
\(216\) 0 0
\(217\) −10.9810 + 6.33991i −0.745442 + 0.430381i
\(218\) −2.43296 1.40467i −0.164781 0.0951362i
\(219\) 0 0
\(220\) 13.0269 + 4.30978i 0.878274 + 0.290565i
\(221\) −5.36034 4.54300i −0.360575 0.305596i
\(222\) 0 0
\(223\) −10.7134 6.18537i −0.717421 0.414203i 0.0963818 0.995344i \(-0.469273\pi\)
−0.813803 + 0.581141i \(0.802606\pi\)
\(224\) −6.17763 + 10.7000i −0.412760 + 0.714922i
\(225\) 0 0
\(226\) −2.42583 −0.161364
\(227\) −5.33715 + 3.08141i −0.354239 + 0.204520i −0.666551 0.745460i \(-0.732230\pi\)
0.312311 + 0.949980i \(0.398897\pi\)
\(228\) 0 0
\(229\) 26.9832 1.78310 0.891551 0.452920i \(-0.149618\pi\)
0.891551 + 0.452920i \(0.149618\pi\)
\(230\) −0.403608 1.94999i −0.0266131 0.128579i
\(231\) 0 0
\(232\) −3.34408 1.93070i −0.219549 0.126757i
\(233\) 0.824319i 0.0540029i −0.999635 0.0270015i \(-0.991404\pi\)
0.999635 0.0270015i \(-0.00859588\pi\)
\(234\) 0 0
\(235\) 4.82476 14.5835i 0.314733 0.951323i
\(236\) 2.39654 4.15092i 0.156001 0.270202i
\(237\) 0 0
\(238\) −1.87244 + 1.08106i −0.121372 + 0.0700744i
\(239\) 4.00000 0.258738 0.129369 0.991596i \(-0.458705\pi\)
0.129369 + 0.991596i \(0.458705\pi\)
\(240\) 0 0
\(241\) −11.3469 19.6534i −0.730917 1.26599i −0.956492 0.291760i \(-0.905759\pi\)
0.225575 0.974226i \(-0.427574\pi\)
\(242\) 0.153745i 0.00988310i
\(243\) 0 0
\(244\) 7.08163 12.2657i 0.453355 0.785234i
\(245\) 7.08920 6.31489i 0.452912 0.403443i
\(246\) 0 0
\(247\) 2.90420 3.42669i 0.184790 0.218035i
\(248\) 4.86678i 0.309041i
\(249\) 0 0
\(250\) −0.327631 3.68433i −0.0207212 0.233017i
\(251\) 9.51345 + 16.4778i 0.600484 + 1.04007i 0.992748 + 0.120216i \(0.0383586\pi\)
−0.392264 + 0.919853i \(0.628308\pi\)
\(252\) 0 0
\(253\) −7.56654 + 4.36854i −0.475704 + 0.274648i
\(254\) 1.51584 + 2.62552i 0.0951124 + 0.164739i
\(255\) 0 0
\(256\) −3.97218 6.88001i −0.248261 0.430001i
\(257\) 1.82857 + 1.05573i 0.114063 + 0.0658544i 0.555946 0.831218i \(-0.312356\pi\)
−0.441883 + 0.897073i \(0.645689\pi\)
\(258\) 0 0
\(259\) −6.53528 −0.406083
\(260\) 13.0082 7.94397i 0.806737 0.492664i
\(261\) 0 0
\(262\) 2.86513 + 1.65418i 0.177008 + 0.102196i
\(263\) 25.9092 + 14.9587i 1.59763 + 0.922391i 0.991943 + 0.126687i \(0.0404343\pi\)
0.605685 + 0.795704i \(0.292899\pi\)
\(264\) 0 0
\(265\) −9.01345 + 27.2444i −0.553692 + 1.67361i
\(266\) −0.691084 1.19699i −0.0423731 0.0733923i
\(267\) 0 0
\(268\) 7.59083i 0.463684i
\(269\) −9.29455 16.0986i −0.566699 0.981551i −0.996889 0.0788127i \(-0.974887\pi\)
0.430191 0.902738i \(-0.358446\pi\)
\(270\) 0 0
\(271\) −2.91238 + 5.04439i −0.176914 + 0.306425i −0.940822 0.338901i \(-0.889945\pi\)
0.763908 + 0.645326i \(0.223278\pi\)
\(272\) 6.53876i 0.396471i
\(273\) 0 0
\(274\) −5.57417 −0.336748
\(275\) −14.8957 + 6.44216i −0.898242 + 0.388477i
\(276\) 0 0
\(277\) 11.7263 6.77017i 0.704564 0.406780i −0.104481 0.994527i \(-0.533318\pi\)
0.809045 + 0.587747i \(0.199985\pi\)
\(278\) 0.339738i 0.0203761i
\(279\) 0 0
\(280\) −1.95624 9.45139i −0.116908 0.564829i
\(281\) 0.464716 0.0277226 0.0138613 0.999904i \(-0.495588\pi\)
0.0138613 + 0.999904i \(0.495588\pi\)
\(282\) 0 0
\(283\) 8.71259 + 5.03022i 0.517910 + 0.299015i 0.736079 0.676896i \(-0.236675\pi\)
−0.218169 + 0.975911i \(0.570009\pi\)
\(284\) 4.95873 8.58877i 0.294246 0.509649i
\(285\) 0 0
\(286\) 2.95365 + 2.50329i 0.174653 + 0.148022i
\(287\) 9.32634i 0.550516i
\(288\) 0 0
\(289\) −6.60107 + 11.4334i −0.388298 + 0.672553i
\(290\) 2.17326 0.449818i 0.127618 0.0264142i
\(291\) 0 0
\(292\) −8.94752 + 5.16586i −0.523614 + 0.302309i
\(293\) 11.6481 6.72506i 0.680492 0.392882i −0.119548 0.992828i \(-0.538145\pi\)
0.800040 + 0.599946i \(0.204811\pi\)
\(294\) 0 0
\(295\) 1.14902 + 5.55140i 0.0668987 + 0.323215i
\(296\) −1.25419 + 2.17232i −0.0728983 + 0.126264i
\(297\) 0 0
\(298\) 5.24431i 0.303795i
\(299\) −1.73236 + 9.54958i −0.100185 + 0.552266i
\(300\) 0 0
\(301\) 14.6498 25.3742i 0.844401 1.46255i
\(302\) −4.16745 2.40608i −0.239810 0.138454i
\(303\) 0 0
\(304\) 4.18002 0.239741
\(305\) 3.39530 + 16.4041i 0.194414 + 0.939295i
\(306\) 0 0
\(307\) 24.6077i 1.40444i 0.711961 + 0.702219i \(0.247807\pi\)
−0.711961 + 0.702219i \(0.752193\pi\)
\(308\) −17.8212 + 10.2891i −1.01546 + 0.586274i
\(309\) 0 0
\(310\) −1.86053 2.08866i −0.105671 0.118628i
\(311\) −2.43781 −0.138236 −0.0691178 0.997609i \(-0.522018\pi\)
−0.0691178 + 0.997609i \(0.522018\pi\)
\(312\) 0 0
\(313\) 19.2965i 1.09071i 0.838207 + 0.545353i \(0.183604\pi\)
−0.838207 + 0.545353i \(0.816396\pi\)
\(314\) −1.80653 + 3.12900i −0.101948 + 0.176579i
\(315\) 0 0
\(316\) 13.0269 + 22.5633i 0.732821 + 1.26928i
\(317\) 28.8217i 1.61879i 0.587265 + 0.809395i \(0.300205\pi\)
−0.587265 + 0.809395i \(0.699795\pi\)
\(318\) 0 0
\(319\) −4.86872 8.43286i −0.272596 0.472150i
\(320\) 11.6582 + 3.85695i 0.651713 + 0.215610i
\(321\) 0 0
\(322\) 2.58632 + 1.49321i 0.144130 + 0.0832136i
\(323\) 2.10258 + 1.21392i 0.116990 + 0.0675445i
\(324\) 0 0
\(325\) −5.23897 + 17.2497i −0.290606 + 0.956843i
\(326\) 1.38217 0.0765512
\(327\) 0 0
\(328\) 3.10006 + 1.78982i 0.171172 + 0.0988264i
\(329\) 11.5185 + 19.9507i 0.635037 + 1.09992i
\(330\) 0 0
\(331\) 1.48655 + 2.57478i 0.0817081 + 0.141522i 0.903984 0.427567i \(-0.140629\pi\)
−0.822276 + 0.569089i \(0.807296\pi\)
\(332\) −14.1125 + 8.14783i −0.774522 + 0.447171i
\(333\) 0 0
\(334\) −0.554726 0.960814i −0.0303533 0.0525734i
\(335\) −5.97182 6.70407i −0.326276 0.366282i
\(336\) 0 0
\(337\) 1.90370i 0.103701i 0.998655 + 0.0518505i \(0.0165119\pi\)
−0.998655 + 0.0518505i \(0.983488\pi\)
\(338\) 4.24268 0.705107i 0.230771 0.0383528i
\(339\) 0 0
\(340\) 5.47976 + 6.15167i 0.297182 + 0.333621i
\(341\) −6.13636 + 10.6285i −0.332302 + 0.575565i
\(342\) 0 0
\(343\) 9.23611i 0.498703i
\(344\) −5.62291 9.73916i −0.303167 0.525100i
\(345\) 0 0
\(346\) 2.89055 0.155397
\(347\) 10.9420 6.31735i 0.587396 0.339133i −0.176671 0.984270i \(-0.556533\pi\)
0.764067 + 0.645137i \(0.223200\pi\)
\(348\) 0 0
\(349\) 4.48655 7.77093i 0.240159 0.415968i −0.720600 0.693351i \(-0.756134\pi\)
0.960760 + 0.277383i \(0.0894670\pi\)
\(350\) 4.45274 + 3.30837i 0.238009 + 0.176840i
\(351\) 0 0
\(352\) 11.9586i 0.637395i
\(353\) 29.6618 + 17.1252i 1.57874 + 0.911484i 0.995036 + 0.0995150i \(0.0317291\pi\)
0.583701 + 0.811969i \(0.301604\pi\)
\(354\) 0 0
\(355\) 2.37747 + 11.4865i 0.126183 + 0.609641i
\(356\) 19.5036 1.03369
\(357\) 0 0
\(358\) −5.16014 + 2.97921i −0.272722 + 0.157456i
\(359\) 22.4043 1.18245 0.591227 0.806505i \(-0.298644\pi\)
0.591227 + 0.806505i \(0.298644\pi\)
\(360\) 0 0
\(361\) 8.72398 15.1104i 0.459157 0.795283i
\(362\) −0.299023 0.172641i −0.0157163 0.00907381i
\(363\) 0 0
\(364\) −4.08016 + 22.4918i −0.213858 + 1.17889i
\(365\) 3.83821 11.6015i 0.200901 0.607252i
\(366\) 0 0
\(367\) 11.4273 + 6.59753i 0.596498 + 0.344388i 0.767663 0.640854i \(-0.221420\pi\)
−0.171165 + 0.985242i \(0.554753\pi\)
\(368\) −7.82169 + 4.51586i −0.407734 + 0.235405i
\(369\) 0 0
\(370\) −0.292203 1.41175i −0.0151909 0.0733935i
\(371\) −21.5185 37.2712i −1.11719 1.93502i
\(372\) 0 0
\(373\) 13.2168 7.63070i 0.684338 0.395103i −0.117149 0.993114i \(-0.537376\pi\)
0.801488 + 0.598012i \(0.204042\pi\)
\(374\) −1.04635 + 1.81233i −0.0541053 + 0.0937131i
\(375\) 0 0
\(376\) 8.84210 0.455997
\(377\) −10.6430 1.93070i −0.548140 0.0994362i
\(378\) 0 0
\(379\) 9.11453 15.7868i 0.468182 0.810915i −0.531157 0.847273i \(-0.678243\pi\)
0.999339 + 0.0363588i \(0.0115759\pi\)
\(380\) −3.93256 + 3.50304i −0.201736 + 0.179702i
\(381\) 0 0
\(382\) 8.44246i 0.431954i
\(383\) 1.24784 0.720440i 0.0637616 0.0368128i −0.467780 0.883845i \(-0.654946\pi\)
0.531542 + 0.847032i \(0.321613\pi\)
\(384\) 0 0
\(385\) 7.64474 23.1073i 0.389612 1.17766i
\(386\) −3.27870 5.67888i −0.166882 0.289048i
\(387\) 0 0
\(388\) −8.62194 4.97788i −0.437713 0.252714i
\(389\) −18.7912 −0.952754 −0.476377 0.879241i \(-0.658050\pi\)
−0.476377 + 0.879241i \(0.658050\pi\)
\(390\) 0 0
\(391\) −5.24581 −0.265292
\(392\) 4.73277 + 2.73247i 0.239041 + 0.138010i
\(393\) 0 0
\(394\) 3.58163 + 6.20357i 0.180440 + 0.312531i
\(395\) −29.2560 9.67894i −1.47203 0.487000i
\(396\) 0 0
\(397\) −14.8027 + 8.54634i −0.742926 + 0.428928i −0.823132 0.567850i \(-0.807775\pi\)
0.0802063 + 0.996778i \(0.474442\pi\)
\(398\) 6.03084i 0.302298i
\(399\) 0 0
\(400\) −15.3980 + 6.65940i −0.769898 + 0.332970i
\(401\) 11.1011 19.2276i 0.554361 0.960182i −0.443592 0.896229i \(-0.646296\pi\)
0.997953 0.0639527i \(-0.0203707\pi\)
\(402\) 0 0
\(403\) 4.59962 + 12.8336i 0.229124 + 0.639285i
\(404\) −10.7960 −0.537122
\(405\) 0 0
\(406\) −1.66418 + 2.88244i −0.0825918 + 0.143053i
\(407\) −5.47801 + 3.16273i −0.271535 + 0.156771i
\(408\) 0 0
\(409\) −4.81638 8.34221i −0.238155 0.412496i 0.722030 0.691862i \(-0.243209\pi\)
−0.960185 + 0.279366i \(0.909876\pi\)
\(410\) −2.01468 + 0.416996i −0.0994978 + 0.0205939i
\(411\) 0 0
\(412\) −12.0644 + 6.96537i −0.594369 + 0.343159i
\(413\) −7.36296 4.25101i −0.362308 0.209178i
\(414\) 0 0
\(415\) 6.05381 18.2985i 0.297170 0.898238i
\(416\) 10.1340 + 8.58877i 0.496859 + 0.421099i
\(417\) 0 0
\(418\) −1.15856 0.668896i −0.0566671 0.0327168i
\(419\) 0.978168 1.69424i 0.0477866 0.0827689i −0.841143 0.540813i \(-0.818117\pi\)
0.888929 + 0.458044i \(0.151450\pi\)
\(420\) 0 0
\(421\) −12.0807 −0.588778 −0.294389 0.955686i \(-0.595116\pi\)
−0.294389 + 0.955686i \(0.595116\pi\)
\(422\) 5.52959 3.19251i 0.269176 0.155409i
\(423\) 0 0
\(424\) −16.5185 −0.802210
\(425\) −9.67923 1.12201i −0.469511 0.0544257i
\(426\) 0 0
\(427\) −21.7571 12.5615i −1.05290 0.607893i
\(428\) 16.2104i 0.783558i
\(429\) 0 0
\(430\) 6.13636 + 2.03013i 0.295921 + 0.0979016i
\(431\) 12.2945 21.2948i 0.592207 1.02573i −0.401727 0.915759i \(-0.631590\pi\)
0.993934 0.109974i \(-0.0350767\pi\)
\(432\) 0 0
\(433\) 31.2400 18.0364i 1.50130 0.866775i 0.501299 0.865274i \(-0.332856\pi\)
0.999999 0.00150085i \(-0.000477735\pi\)
\(434\) 4.19495 0.201364
\(435\) 0 0
\(436\) −8.02690 13.9030i −0.384419 0.665833i
\(437\) 3.35348i 0.160419i
\(438\) 0 0
\(439\) 1.26764 2.19562i 0.0605013 0.104791i −0.834188 0.551480i \(-0.814063\pi\)
0.894690 + 0.446688i \(0.147397\pi\)
\(440\) −6.21373 6.97563i −0.296228 0.332550i
\(441\) 0 0
\(442\) 0.784309 + 2.18833i 0.0373058 + 0.104088i
\(443\) 19.3579i 0.919721i −0.887991 0.459860i \(-0.847899\pi\)
0.887991 0.459860i \(-0.152101\pi\)
\(444\) 0 0
\(445\) −17.2252 + 15.3438i −0.816552 + 0.727365i
\(446\) 2.04635 + 3.54438i 0.0968973 + 0.167831i
\(447\) 0 0
\(448\) −15.9487 + 9.20801i −0.753507 + 0.435038i
\(449\) 12.4040 + 21.4844i 0.585381 + 1.01391i 0.994828 + 0.101576i \(0.0323884\pi\)
−0.409447 + 0.912334i \(0.634278\pi\)
\(450\) 0 0
\(451\) 4.51345 + 7.81753i 0.212530 + 0.368113i
\(452\) −12.0051 6.93114i −0.564672 0.326013i
\(453\) 0 0
\(454\) 2.03888 0.0956896
\(455\) −14.0911 23.0742i −0.660601 1.08173i
\(456\) 0 0
\(457\) −6.55363 3.78374i −0.306566 0.176996i 0.338823 0.940850i \(-0.389971\pi\)
−0.645389 + 0.763854i \(0.723305\pi\)
\(458\) −7.73105 4.46352i −0.361248 0.208567i
\(459\) 0 0
\(460\) 3.57417 10.8034i 0.166646 0.503712i
\(461\) −6.17164 10.6896i −0.287442 0.497864i 0.685756 0.727831i \(-0.259472\pi\)
−0.973198 + 0.229967i \(0.926138\pi\)
\(462\) 0 0
\(463\) 22.8578i 1.06229i −0.847281 0.531146i \(-0.821762\pi\)
0.847281 0.531146i \(-0.178238\pi\)
\(464\) −5.03289 8.71723i −0.233646 0.404687i
\(465\) 0 0
\(466\) −0.136357 + 0.236178i −0.00631664 + 0.0109407i
\(467\) 15.2976i 0.707889i 0.935266 + 0.353945i \(0.115160\pi\)
−0.935266 + 0.353945i \(0.884840\pi\)
\(468\) 0 0
\(469\) 13.4647 0.621743
\(470\) −3.79473 + 3.38026i −0.175038 + 0.155920i
\(471\) 0 0
\(472\) −2.82606 + 1.63163i −0.130080 + 0.0751017i
\(473\) 28.3589i 1.30394i
\(474\) 0 0
\(475\) 0.717267 6.18762i 0.0329105 0.283907i
\(476\) −12.3553 −0.566303
\(477\) 0 0
\(478\) −1.14605 0.661673i −0.0524192 0.0302642i
\(479\) −12.1414 + 21.0296i −0.554756 + 0.960866i 0.443166 + 0.896439i \(0.353855\pi\)
−0.997922 + 0.0644264i \(0.979478\pi\)
\(480\) 0 0
\(481\) −1.25419 + 6.91369i −0.0571861 + 0.315237i
\(482\) 7.50793i 0.341977i
\(483\) 0 0
\(484\) 0.439284 0.760862i 0.0199674 0.0345846i
\(485\) 11.5309 2.38665i 0.523591 0.108372i
\(486\) 0 0
\(487\) 31.9462 18.4441i 1.44762 0.835783i 0.449280 0.893391i \(-0.351681\pi\)
0.998339 + 0.0576081i \(0.0183474\pi\)
\(488\) −8.35085 + 4.82136i −0.378025 + 0.218253i
\(489\) 0 0
\(490\) −3.07574 + 0.636614i −0.138948 + 0.0287593i
\(491\) −17.6767 + 30.6170i −0.797739 + 1.38172i 0.123346 + 0.992364i \(0.460637\pi\)
−0.921085 + 0.389361i \(0.872696\pi\)
\(492\) 0 0
\(493\) 5.84642i 0.263310i
\(494\) −1.39893 + 0.501383i −0.0629407 + 0.0225583i
\(495\) 0 0
\(496\) −6.34328 + 10.9869i −0.284822 + 0.493326i
\(497\) −15.2349 8.79585i −0.683377 0.394548i
\(498\) 0 0
\(499\) −16.2189 −0.726058 −0.363029 0.931778i \(-0.618257\pi\)
−0.363029 + 0.931778i \(0.618257\pi\)
\(500\) 8.90554 19.1693i 0.398268 0.857278i
\(501\) 0 0
\(502\) 6.29480i 0.280950i
\(503\) 17.5270 10.1192i 0.781489 0.451193i −0.0554688 0.998460i \(-0.517665\pi\)
0.836958 + 0.547268i \(0.184332\pi\)
\(504\) 0 0
\(505\) 9.53482 8.49339i 0.424294 0.377951i
\(506\) 2.89055 0.128500
\(507\) 0 0
\(508\) 17.3244i 0.768646i
\(509\) 10.0185 17.3526i 0.444063 0.769140i −0.553923 0.832568i \(-0.686870\pi\)
0.997986 + 0.0634276i \(0.0202032\pi\)
\(510\) 0 0
\(511\) 9.16326 + 15.8712i 0.405359 + 0.702102i
\(512\) 20.9992i 0.928042i
\(513\) 0 0
\(514\) −0.349273 0.604959i −0.0154058 0.0266836i
\(515\) 5.17524 15.6429i 0.228048 0.689308i
\(516\) 0 0
\(517\) 19.3101 + 11.1487i 0.849259 + 0.490320i
\(518\) 1.87244 + 1.08106i 0.0822704 + 0.0474988i
\(519\) 0 0
\(520\) −10.3741 + 0.255688i −0.454933 + 0.0112127i
\(521\) −16.0269 −0.702151 −0.351076 0.936347i \(-0.614184\pi\)
−0.351076 + 0.936347i \(0.614184\pi\)
\(522\) 0 0
\(523\) −10.1654 5.86898i −0.444501 0.256633i 0.261004 0.965338i \(-0.415946\pi\)
−0.705505 + 0.708705i \(0.749280\pi\)
\(524\) 9.45274 + 16.3726i 0.412945 + 0.715241i
\(525\) 0 0
\(526\) −4.94887 8.57170i −0.215781 0.373744i
\(527\) −6.38142 + 3.68431i −0.277979 + 0.160491i
\(528\) 0 0
\(529\) −7.87709 13.6435i −0.342482 0.593197i
\(530\) 7.08920 6.31489i 0.307935 0.274301i
\(531\) 0 0
\(532\) 7.89832i 0.342436i
\(533\) 9.86635 + 1.78982i 0.427359 + 0.0775258i
\(534\) 0 0
\(535\) −12.7530 14.3167i −0.551358 0.618964i
\(536\) 2.58402 4.47565i 0.111613 0.193319i
\(537\) 0 0
\(538\) 6.14995i 0.265143i
\(539\) 6.89055 + 11.9348i 0.296797 + 0.514067i
\(540\) 0 0
\(541\) −21.8080 −0.937599 −0.468800 0.883305i \(-0.655313\pi\)
−0.468800 + 0.883305i \(0.655313\pi\)
\(542\) 1.66887 0.963521i 0.0716840 0.0413868i
\(543\) 0 0
\(544\) −3.59001 + 6.21808i −0.153920 + 0.266598i
\(545\) 18.0269 + 5.96396i 0.772188 + 0.255468i
\(546\) 0 0
\(547\) 6.30924i 0.269764i −0.990862 0.134882i \(-0.956935\pi\)
0.990862 0.134882i \(-0.0430655\pi\)
\(548\) −27.5858 15.9266i −1.17840 0.680352i
\(549\) 0 0
\(550\) 5.33345 + 0.618252i 0.227419 + 0.0263624i
\(551\) 3.73743 0.159220
\(552\) 0 0
\(553\) 40.0230 23.1073i 1.70195 0.982622i
\(554\) −4.47964 −0.190322
\(555\) 0 0
\(556\) −0.970706 + 1.68131i −0.0411671 + 0.0713035i
\(557\) 31.0364 + 17.9189i 1.31506 + 0.759247i 0.982929 0.183987i \(-0.0589006\pi\)
0.332126 + 0.943235i \(0.392234\pi\)
\(558\) 0 0
\(559\) −24.0320 20.3676i −1.01644 0.861459i
\(560\) 7.90253 23.8865i 0.333943 1.00939i
\(561\) 0 0
\(562\) −0.133147 0.0768725i −0.00561647 0.00324267i
\(563\) 4.33196 2.50106i 0.182570 0.105407i −0.405929 0.913904i \(-0.633052\pi\)
0.588500 + 0.808497i \(0.299719\pi\)
\(564\) 0 0
\(565\) 16.0555 3.32315i 0.675459 0.139806i
\(566\) −1.66418 2.88244i −0.0699507 0.121158i
\(567\) 0 0
\(568\) −5.84746 + 3.37603i −0.245354 + 0.141655i
\(569\) 6.58402 11.4039i 0.276017 0.478075i −0.694375 0.719614i \(-0.744319\pi\)
0.970391 + 0.241539i \(0.0776522\pi\)
\(570\) 0 0
\(571\) 19.8349 0.830065 0.415032 0.909807i \(-0.363770\pi\)
0.415032 + 0.909807i \(0.363770\pi\)
\(572\) 7.46475 + 20.8276i 0.312117 + 0.870848i
\(573\) 0 0
\(574\) 1.54275 2.67212i 0.0643930 0.111532i
\(575\) 5.34259 + 12.3532i 0.222801 + 0.515165i
\(576\) 0 0
\(577\) 10.9210i 0.454646i 0.973819 + 0.227323i \(0.0729972\pi\)
−0.973819 + 0.227323i \(0.927003\pi\)
\(578\) 3.78258 2.18388i 0.157335 0.0908373i
\(579\) 0 0
\(580\) 12.0404 + 3.98339i 0.499949 + 0.165401i
\(581\) 14.4527 + 25.0329i 0.599601 + 1.03854i
\(582\) 0 0
\(583\) −36.0745 20.8276i −1.49406 0.862593i
\(584\) 7.03411 0.291073
\(585\) 0 0
\(586\) −4.44979 −0.183819
\(587\) 35.0303 + 20.2247i 1.44585 + 0.834764i 0.998231 0.0594576i \(-0.0189371\pi\)
0.447624 + 0.894222i \(0.352270\pi\)
\(588\) 0 0
\(589\) −2.35526 4.07944i −0.0970469 0.168090i
\(590\) 0.589093 1.78062i 0.0242526 0.0733069i
\(591\) 0 0
\(592\) −5.66274 + 3.26938i −0.232737 + 0.134371i
\(593\) 1.47709i 0.0606569i 0.999540 + 0.0303284i \(0.00965532\pi\)
−0.999540 + 0.0303284i \(0.990345\pi\)
\(594\) 0 0
\(595\) 10.9119 9.72008i 0.447345 0.398484i
\(596\) −14.9842 + 25.9533i −0.613775 + 1.06309i
\(597\) 0 0
\(598\) 2.07602 2.44951i 0.0848947 0.100168i
\(599\) 2.27271 0.0928606 0.0464303 0.998922i \(-0.485215\pi\)
0.0464303 + 0.998922i \(0.485215\pi\)
\(600\) 0 0
\(601\) −3.70215 + 6.41231i −0.151014 + 0.261563i −0.931600 0.363484i \(-0.881587\pi\)
0.780587 + 0.625048i \(0.214920\pi\)
\(602\) −8.39472 + 4.84669i −0.342143 + 0.197536i
\(603\) 0 0
\(604\) −13.7494 23.8147i −0.559456 0.969005i
\(605\) 0.210615 + 1.01757i 0.00856273 + 0.0413700i
\(606\) 0 0
\(607\) −9.26059 + 5.34661i −0.375876 + 0.217012i −0.676022 0.736881i \(-0.736298\pi\)
0.300146 + 0.953893i \(0.402964\pi\)
\(608\) −3.97502 2.29498i −0.161208 0.0930736i
\(609\) 0 0
\(610\) 1.74074 5.26162i 0.0704804 0.213037i
\(611\) 23.3164 8.35673i 0.943280 0.338077i
\(612\) 0 0
\(613\) 5.26673 + 3.04075i 0.212721 + 0.122815i 0.602575 0.798062i \(-0.294141\pi\)
−0.389854 + 0.920877i \(0.627475\pi\)
\(614\) 4.07057 7.05043i 0.164275 0.284532i
\(615\) 0 0
\(616\) 14.0101 0.564485
\(617\) −27.5732 + 15.9194i −1.11006 + 0.640892i −0.938844 0.344342i \(-0.888102\pi\)
−0.171213 + 0.985234i \(0.554769\pi\)
\(618\) 0 0
\(619\) 26.4043 1.06128 0.530639 0.847598i \(-0.321952\pi\)
0.530639 + 0.847598i \(0.321952\pi\)
\(620\) −3.23972 15.6524i −0.130110 0.628616i
\(621\) 0 0
\(622\) 0.698464 + 0.403259i 0.0280059 + 0.0161692i
\(623\) 34.5957i 1.38605i
\(624\) 0 0
\(625\) 7.21560 + 23.9361i 0.288624 + 0.957443i
\(626\) 3.19200 5.52871i 0.127578 0.220972i
\(627\) 0 0
\(628\) −17.8805 + 10.3233i −0.713509 + 0.411944i
\(629\) −3.79785 −0.151430
\(630\) 0 0
\(631\) −17.5840 30.4564i −0.700009 1.21245i −0.968463 0.249158i \(-0.919846\pi\)
0.268454 0.963293i \(-0.413487\pi\)
\(632\) 17.7381i 0.705585i
\(633\) 0 0
\(634\) 4.76764 8.25780i 0.189347 0.327959i
\(635\) −13.6294 15.3005i −0.540865 0.607184i
\(636\) 0 0
\(637\) 15.0626 + 2.73247i 0.596804 + 0.108264i
\(638\) 3.22150i 0.127540i
\(639\) 0 0
\(640\) −13.6617 15.3369i −0.540028 0.606244i
\(641\) 2.76257 + 4.78491i 0.109115 + 0.188993i 0.915412 0.402518i \(-0.131865\pi\)
−0.806297 + 0.591511i \(0.798532\pi\)
\(642\) 0 0
\(643\) 27.8472 16.0776i 1.09819 0.634039i 0.162444 0.986718i \(-0.448062\pi\)
0.935744 + 0.352679i \(0.114729\pi\)
\(644\) 8.53289 + 14.7794i 0.336243 + 0.582390i
\(645\) 0 0
\(646\) −0.401610 0.695609i −0.0158011 0.0273684i
\(647\) −11.9376 6.89216i −0.469314 0.270959i 0.246638 0.969108i \(-0.420674\pi\)
−0.715953 + 0.698149i \(0.754007\pi\)
\(648\) 0 0
\(649\) −8.22905 −0.323019
\(650\) 4.35445 4.07565i 0.170796 0.159860i
\(651\) 0 0
\(652\) 6.84015 + 3.94916i 0.267881 + 0.154661i
\(653\) −7.36296 4.25101i −0.288135 0.166355i 0.348965 0.937136i \(-0.386533\pi\)
−0.637100 + 0.770781i \(0.719866\pi\)
\(654\) 0 0
\(655\) −21.2291 7.02335i −0.829488 0.274425i
\(656\) 4.66565 + 8.08115i 0.182163 + 0.315516i
\(657\) 0 0
\(658\) 7.62150i 0.297117i
\(659\) −2.02183 3.50192i −0.0787594 0.136415i 0.823956 0.566654i \(-0.191763\pi\)
−0.902715 + 0.430239i \(0.858429\pi\)
\(660\) 0 0
\(661\) −15.6364 + 27.0830i −0.608184 + 1.05341i 0.383356 + 0.923601i \(0.374768\pi\)
−0.991540 + 0.129805i \(0.958565\pi\)
\(662\) 0.983609i 0.0382290i
\(663\) 0 0
\(664\) 11.0945 0.430551
\(665\) 6.21373 + 6.97563i 0.240958 + 0.270503i
\(666\) 0 0
\(667\) −6.99351 + 4.03771i −0.270790 + 0.156341i
\(668\) 6.33991i 0.245298i
\(669\) 0 0
\(670\) 0.602029 + 2.90865i 0.0232584 + 0.112371i
\(671\) −24.3164 −0.938723
\(672\) 0 0
\(673\) −27.7768 16.0370i −1.07072 0.618179i −0.142340 0.989818i \(-0.545463\pi\)
−0.928377 + 0.371639i \(0.878796\pi\)
\(674\) 0.314906 0.545433i 0.0121297 0.0210093i
\(675\) 0 0
\(676\) 23.0111 + 8.63282i 0.885041 + 0.332031i
\(677\) 14.2382i 0.547220i −0.961841 0.273610i \(-0.911782\pi\)
0.961841 0.273610i \(-0.0882177\pi\)
\(678\) 0 0
\(679\) −8.82983 + 15.2937i −0.338858 + 0.586919i
\(680\) −1.13683 5.49249i −0.0435954 0.210627i
\(681\) 0 0
\(682\) 3.51629 2.03013i 0.134646 0.0777377i
\(683\) −22.3302 + 12.8923i −0.854440 + 0.493311i −0.862146 0.506659i \(-0.830880\pi\)
0.00770647 + 0.999970i \(0.497547\pi\)
\(684\) 0 0
\(685\) 36.8929 7.63605i 1.40961 0.291759i
\(686\) −1.52782 + 2.64626i −0.0583325 + 0.101035i
\(687\) 0 0
\(688\) 29.3152i 1.11763i
\(689\) −43.5589 + 15.6118i −1.65946 + 0.594761i
\(690\) 0 0
\(691\) 0.0218318 0.0378138i 0.000830522 0.00143851i −0.865610 0.500719i \(-0.833069\pi\)
0.866440 + 0.499281i \(0.166402\pi\)
\(692\) 14.3049 + 8.25894i 0.543791 + 0.313958i
\(693\) 0 0
\(694\) −4.18002 −0.158671
\(695\) −0.465407 2.24857i −0.0176539 0.0852931i
\(696\) 0 0
\(697\) 5.41982i 0.205290i
\(698\) −2.57091 + 1.48431i −0.0973103 + 0.0561821i
\(699\) 0 0
\(700\) 12.5832 + 29.0951i 0.475601 + 1.09969i
\(701\) 14.5454 0.549373 0.274687 0.961534i \(-0.411426\pi\)
0.274687 + 0.961534i \(0.411426\pi\)
\(702\) 0 0
\(703\) 2.42785i 0.0915679i
\(704\) −8.91238 + 15.4367i −0.335898 + 0.581792i
\(705\) 0 0
\(706\) −5.66565 9.81320i −0.213230 0.369325i
\(707\) 19.1501i 0.720214i
\(708\) 0 0
\(709\) 9.81638 + 17.0025i 0.368662 + 0.638541i 0.989357 0.145511i \(-0.0464827\pi\)
−0.620695 + 0.784052i \(0.713149\pi\)
\(710\) 1.21891 3.68431i 0.0457447 0.138270i
\(711\) 0 0
\(712\) −11.4996 6.63929i −0.430965 0.248818i
\(713\) 8.81438 + 5.08898i 0.330101 + 0.190584i
\(714\) 0 0
\(715\) −22.9781 12.5219i −0.859334 0.468293i
\(716\) −34.0490 −1.27247
\(717\) 0 0
\(718\) −6.41912 3.70608i −0.239559 0.138310i
\(719\) −23.7156 41.0766i −0.884443 1.53190i −0.846351 0.532625i \(-0.821206\pi\)
−0.0380914 0.999274i \(-0.512128\pi\)
\(720\) 0 0
\(721\) 12.3553 + 21.3999i 0.460134 + 0.796976i
\(722\) −4.99906 + 2.88621i −0.186046 + 0.107414i
\(723\) 0 0
\(724\) −0.986548 1.70875i −0.0366648 0.0635052i
\(725\) −13.7676 + 5.95429i −0.511315 + 0.221137i
\(726\) 0 0
\(727\) 34.0951i 1.26452i 0.774757 + 0.632259i \(0.217872\pi\)
−0.774757 + 0.632259i \(0.782128\pi\)
\(728\) 10.0622 11.8725i 0.372931 0.440024i
\(729\) 0 0
\(730\) −3.01880 + 2.68908i −0.111731 + 0.0995272i
\(731\) 8.51345 14.7457i 0.314881 0.545391i
\(732\) 0 0
\(733\) 14.3920i 0.531580i 0.964031 + 0.265790i \(0.0856327\pi\)
−0.964031 + 0.265790i \(0.914367\pi\)
\(734\) −2.18270 3.78055i −0.0805651 0.139543i
\(735\) 0 0
\(736\) 9.91745 0.365562
\(737\) 11.2864 6.51621i 0.415740 0.240028i
\(738\) 0 0
\(739\) −17.2240 + 29.8328i −0.633594 + 1.09742i 0.353217 + 0.935541i \(0.385088\pi\)
−0.986811 + 0.161876i \(0.948246\pi\)
\(740\) 2.58762 7.82145i 0.0951228 0.287522i
\(741\) 0 0
\(742\) 14.2382i 0.522702i
\(743\) −35.2589 20.3567i −1.29352 0.746816i −0.314246 0.949342i \(-0.601752\pi\)
−0.979277 + 0.202526i \(0.935085\pi\)
\(744\) 0 0
\(745\) −7.18418 34.7097i −0.263208 1.27167i
\(746\) −5.04903 −0.184858
\(747\) 0 0
\(748\) −10.3564 + 5.97929i −0.378669 + 0.218625i
\(749\) 28.7542 1.05066
\(750\) 0 0
\(751\) −16.2509 + 28.1474i −0.593003 + 1.02711i 0.400822 + 0.916156i \(0.368725\pi\)
−0.993825 + 0.110956i \(0.964609\pi\)
\(752\) 19.9613 + 11.5247i 0.727914 + 0.420261i
\(753\) 0 0
\(754\) 2.72997 + 2.31371i 0.0994196 + 0.0842603i
\(755\) 30.8786 + 10.2158i 1.12379 + 0.371790i
\(756\) 0 0
\(757\) 11.2864 + 6.51621i 0.410211 + 0.236836i 0.690881 0.722969i \(-0.257223\pi\)
−0.280669 + 0.959805i \(0.590556\pi\)
\(758\) −5.22286 + 3.01542i −0.189703 + 0.109525i
\(759\) 0 0
\(760\) 3.51117 0.726739i 0.127364 0.0263616i
\(761\) −1.99493 3.45532i −0.0723161 0.125255i 0.827600 0.561318i \(-0.189706\pi\)
−0.899916 + 0.436063i \(0.856372\pi\)
\(762\) 0 0
\(763\) −24.6613 + 14.2382i −0.892800 + 0.515458i
\(764\) 24.1220 41.7805i 0.872703 1.51157i
\(765\) 0 0
\(766\) −0.476696 −0.0172237
\(767\) −5.91018 + 6.97348i −0.213404 + 0.251798i
\(768\) 0 0
\(769\) 3.33343 5.77367i 0.120207 0.208204i −0.799642 0.600476i \(-0.794978\pi\)
0.919849 + 0.392272i \(0.128311\pi\)
\(770\) −6.01268 + 5.35596i −0.216682 + 0.193015i
\(771\) 0 0
\(772\) 37.4720i 1.34865i
\(773\) 41.8593 24.1675i 1.50557 0.869244i 0.505595 0.862771i \(-0.331273\pi\)
0.999979 0.00647254i \(-0.00206029\pi\)
\(774\) 0 0
\(775\) 15.1752 + 11.2751i 0.545111 + 0.405015i
\(776\) 3.38907 + 5.87005i 0.121661 + 0.210723i
\(777\) 0 0
\(778\) 5.38393 + 3.10841i 0.193023 + 0.111442i
\(779\) −3.46472 −0.124136
\(780\) 0 0
\(781\) −17.0269 −0.609271
\(782\) 1.50299 + 0.867753i 0.0537469 + 0.0310308i
\(783\) 0 0
\(784\) 7.12291 + 12.3372i 0.254389 + 0.440615i
\(785\) 7.67017 23.1842i 0.273760 0.827478i
\(786\) 0 0
\(787\) −24.2151 + 13.9806i −0.863176 + 0.498355i −0.865074 0.501643i \(-0.832729\pi\)
0.00189876 + 0.999998i \(0.499396\pi\)
\(788\) 40.9341i 1.45822i
\(789\) 0 0
\(790\) 6.78113 + 7.61261i 0.241262 + 0.270845i
\(791\) −12.2945 + 21.2948i −0.437144 + 0.757155i
\(792\) 0 0
\(793\) −17.4642 + 20.6062i −0.620174 + 0.731749i
\(794\) 5.65488 0.200684
\(795\) 0 0
\(796\) 17.2314 29.8457i 0.610752 1.05785i
\(797\) −32.2529 + 18.6212i −1.14246 + 0.659597i −0.947038 0.321123i \(-0.895940\pi\)
−0.195418 + 0.980720i \(0.562607\pi\)
\(798\) 0 0
\(799\) 6.69377 + 11.5939i 0.236808 + 0.410164i
\(800\) 18.2990 + 2.12122i 0.646969 + 0.0749965i
\(801\) 0 0
\(802\) −6.36120 + 3.67264i −0.224622 + 0.129685i
\(803\) 15.3617 + 8.86907i 0.542102 + 0.312983i
\(804\) 0 0
\(805\) −19.1633 6.33991i −0.675416 0.223452i
\(806\) 0.805054 4.43784i 0.0283568 0.156316i
\(807\) 0 0
\(808\) 6.36548 + 3.67511i 0.223937 + 0.129290i
\(809\) −7.26434 + 12.5822i −0.255400 + 0.442367i −0.965004 0.262234i \(-0.915541\pi\)
0.709604 + 0.704601i \(0.248874\pi\)
\(810\) 0 0
\(811\) 44.0538 1.54694 0.773469 0.633834i \(-0.218520\pi\)
0.773469 + 0.633834i \(0.218520\pi\)
\(812\) −16.4716 + 9.50986i −0.578039 + 0.333731i
\(813\) 0 0
\(814\) 2.09269 0.0733489
\(815\) −9.14794 + 1.89343i −0.320438 + 0.0663240i
\(816\) 0 0
\(817\) 9.42647 + 5.44238i 0.329790 + 0.190405i
\(818\) 3.18687i 0.111426i
\(819\) 0 0
\(820\) −11.1618 3.69273i −0.389787 0.128956i
\(821\) 13.5135 23.4060i 0.471623 0.816875i −0.527850 0.849337i \(-0.677002\pi\)
0.999473 + 0.0324629i \(0.0103351\pi\)
\(822\) 0 0
\(823\) 34.2914 19.7981i 1.19532 0.690120i 0.235814 0.971798i \(-0.424225\pi\)
0.959509 + 0.281679i \(0.0908912\pi\)
\(824\) 9.48442 0.330405
\(825\) 0 0
\(826\) 1.40639 + 2.43594i 0.0489345 + 0.0847571i
\(827\) 26.5639i 0.923716i 0.886954 + 0.461858i \(0.152817\pi\)
−0.886954 + 0.461858i \(0.847183\pi\)
\(828\) 0 0
\(829\) 6.99162 12.1098i 0.242829 0.420592i −0.718690 0.695331i \(-0.755258\pi\)
0.961519 + 0.274738i \(0.0885913\pi\)
\(830\) −4.76140 + 4.24134i −0.165271 + 0.147219i
\(831\) 0 0
\(832\) 6.68044 + 18.6393i 0.231603 + 0.646202i
\(833\) 8.27427i 0.286686i
\(834\) 0 0
\(835\) 4.98770 + 5.59927i 0.172607 + 0.193771i
\(836\) −3.82237 6.62054i −0.132199 0.228976i
\(837\) 0 0
\(838\) −0.560515 + 0.323614i −0.0193627 + 0.0111791i
\(839\) −7.19707 12.4657i −0.248471 0.430364i 0.714631 0.699502i \(-0.246595\pi\)
−0.963102 + 0.269138i \(0.913261\pi\)
\(840\) 0 0
\(841\) 10.0000 + 17.3205i 0.344828 + 0.597259i
\(842\) 3.46128 + 1.99837i 0.119284 + 0.0688684i
\(843\) 0 0
\(844\) 36.4868 1.25593
\(845\) −27.1145 + 10.4788i −0.932766 + 0.360483i
\(846\) 0 0
\(847\) −1.34963 0.779207i −0.0463737 0.0267739i
\(848\) −37.2910 21.5300i −1.28058 0.739343i
\(849\) 0 0
\(850\) 2.58762 + 1.92259i 0.0887547 + 0.0659444i
\(851\) 2.62291 + 4.54300i 0.0899120 + 0.155732i
\(852\) 0 0
\(853\) 27.2633i 0.933478i 0.884395 + 0.466739i \(0.154571\pi\)
−0.884395 + 0.466739i \(0.845429\pi\)
\(854\) 4.15580 + 7.19806i 0.142209 + 0.246312i
\(855\) 0 0
\(856\) 5.51823 9.55786i 0.188609 0.326681i
\(857\) 50.6201i 1.72915i 0.502503 + 0.864575i \(0.332413\pi\)
−0.502503 + 0.864575i \(0.667587\pi\)
\(858\) 0 0
\(859\) −1.27992 −0.0436702 −0.0218351 0.999762i \(-0.506951\pi\)
−0.0218351 + 0.999762i \(0.506951\pi\)
\(860\) 24.5674 + 27.5798i 0.837742 + 0.940462i
\(861\) 0 0
\(862\) −7.04509 + 4.06749i −0.239957 + 0.138539i
\(863\) 8.38448i 0.285411i 0.989765 + 0.142706i \(0.0455802\pi\)
−0.989765 + 0.142706i \(0.954420\pi\)
\(864\) 0 0
\(865\) −19.1312 + 3.95976i −0.650481 + 0.134636i
\(866\) −11.9342 −0.405541
\(867\) 0 0
\(868\) 20.7602 + 11.9859i 0.704646 + 0.406828i
\(869\) 22.3654 38.7380i 0.758695 1.31410i
\(870\) 0 0
\(871\) 2.58402 14.2443i 0.0875562 0.482651i
\(872\) 10.9299i 0.370132i
\(873\) 0 0
\(874\) −0.554726 + 0.960814i −0.0187639 + 0.0325000i
\(875\) −34.0028 15.7968i −1.14950 0.534028i
\(876\) 0 0
\(877\) −48.3989 + 27.9431i −1.63431 + 0.943572i −0.651573 + 0.758586i \(0.725890\pi\)
−0.982741 + 0.184985i \(0.940776\pi\)
\(878\) −0.726391 + 0.419382i −0.0245145 + 0.0141535i
\(879\) 0 0
\(880\) −4.93574 23.8466i −0.166384 0.803867i
\(881\) 12.5975 21.8195i 0.424420 0.735116i −0.571946 0.820291i \(-0.693811\pi\)
0.996366 + 0.0851746i \(0.0271448\pi\)
\(882\) 0 0
\(883\) 30.7868i 1.03606i 0.855363 + 0.518029i \(0.173334\pi\)
−0.855363 + 0.518029i \(0.826666\pi\)
\(884\) −2.37110 + 13.0707i −0.0797489 + 0.439614i
\(885\) 0 0
\(886\) −3.20215 + 5.54628i −0.107578 + 0.186331i
\(887\) −10.8011 6.23603i −0.362666 0.209385i 0.307584 0.951521i \(-0.400480\pi\)
−0.670250 + 0.742136i \(0.733813\pi\)
\(888\) 0 0
\(889\) 30.7302 1.03066
\(890\) 7.47338 1.54683i 0.250508 0.0518499i
\(891\) 0 0
\(892\) 23.3875i 0.783071i
\(893\) −7.41163 + 4.27911i −0.248021 + 0.143195i
\(894\) 0 0
\(895\) 30.0714 26.7869i 1.00518 0.895387i
\(896\) 30.8032 1.02906
\(897\) 0 0
\(898\) 8.20739i 0.273884i
\(899\) −5.67164 + 9.82357i −0.189160 + 0.327634i
\(900\) 0 0
\(901\) −12.5051 21.6594i −0.416604 0.721580i
\(902\) 2.98643i 0.0994372i
\(903\) 0 0
\(904\) 4.71891 + 8.17338i 0.156948 + 0.271843i
\(905\) 2.21560 + 0.733001i 0.0736490 + 0.0243658i
\(906\) 0 0
\(907\) 33.6807 + 19.4455i 1.11835 + 0.645678i 0.940979 0.338466i \(-0.109908\pi\)
0.177369 + 0.984144i \(0.443241\pi\)
\(908\) 10.0901 + 5.82555i 0.334853 + 0.193328i
\(909\) 0 0
\(910\) 0.220391 + 8.94198i 0.00730591 + 0.296424i
\(911\) −0.165096 −0.00546989 −0.00273494 0.999996i \(-0.500871\pi\)
−0.00273494 + 0.999996i \(0.500871\pi\)
\(912\) 0 0
\(913\) 24.2292 + 13.9887i 0.801868 + 0.462959i
\(914\) 1.25180 + 2.16818i 0.0414059 + 0.0717171i
\(915\) 0 0
\(916\) −25.5065 44.1786i −0.842760 1.45970i
\(917\) 29.0420 16.7674i 0.959050 0.553708i
\(918\) 0 0
\(919\) 0.447663 + 0.775375i 0.0147670 + 0.0255773i 0.873314 0.487157i \(-0.161966\pi\)
−0.858547 + 0.512734i \(0.828633\pi\)
\(920\) −5.78501 + 5.15315i −0.190726 + 0.169894i
\(921\) 0 0
\(922\) 4.08361i 0.134486i
\(923\) −12.2289 + 14.4290i −0.402518 + 0.474935i
\(924\) 0 0
\(925\) 3.86792 + 8.94346i 0.127176 + 0.294059i
\(926\) −3.78109 + 6.54905i −0.124254 + 0.215215i
\(927\) 0 0
\(928\) 11.0529i 0.362831i
\(929\) 6.14474 + 10.6430i 0.201602 + 0.349185i 0.949045 0.315141i \(-0.102052\pi\)
−0.747443 + 0.664326i \(0.768718\pi\)
\(930\) 0 0
\(931\) −5.28947 −0.173356
\(932\) −1.34963 + 0.779207i −0.0442085 + 0.0255238i
\(933\) 0 0
\(934\) 2.53051 4.38296i 0.0828007 0.143415i
\(935\) 4.44259 13.4284i 0.145288 0.439154i
\(936\) 0 0
\(937\) 5.77242i 0.188577i −0.995545 0.0942884i \(-0.969942\pi\)
0.995545 0.0942884i \(-0.0300576\pi\)
\(938\) −3.85781 2.22731i −0.125962 0.0727242i
\(939\) 0 0
\(940\) −28.4377 + 5.88601i −0.927537 + 0.191981i
\(941\) 55.8887 1.82192 0.910960 0.412495i \(-0.135342\pi\)
0.910960 + 0.412495i \(0.135342\pi\)
\(942\) 0 0
\(943\) 6.48321 3.74308i 0.211122 0.121891i
\(944\) −8.50655 −0.276864
\(945\) 0 0
\(946\) −4.69108 + 8.12520i −0.152520 + 0.264173i
\(947\) −1.64231 0.948188i −0.0533679 0.0308120i 0.473079 0.881020i \(-0.343143\pi\)
−0.526447 + 0.850208i \(0.676476\pi\)
\(948\) 0 0
\(949\) 18.5487 6.64798i 0.602117 0.215802i
\(950\) −1.22905 + 1.65418i −0.0398757 + 0.0536688i
\(951\) 0 0
\(952\) 7.28483 + 4.20590i 0.236103 + 0.136314i
\(953\) 29.1438 16.8262i 0.944059 0.545053i 0.0528285 0.998604i \(-0.483176\pi\)
0.891230 + 0.453551i \(0.149843\pi\)
\(954\) 0 0
\(955\) 11.5653 + 55.8768i 0.374245 + 1.80813i
\(956\) −3.78109 6.54905i −0.122289 0.211811i
\(957\) 0 0
\(958\) 6.95735 4.01683i 0.224782 0.129778i
\(959\) −28.2509 + 48.9320i −0.912269 + 1.58010i
\(960\) 0 0
\(961\) −16.7033 −0.538817
\(962\) 1.50299 1.77339i 0.0484584 0.0571765i
\(963\) 0 0
\(964\) −21.4518 + 37.1556i −0.690917 + 1.19670i
\(965\) 29.4798 + 33.0945i 0.948987 + 1.06535i
\(966\) 0 0
\(967\) 23.0493i 0.741216i −0.928789 0.370608i \(-0.879149\pi\)
0.928789 0.370608i \(-0.120851\pi\)
\(968\) −0.518015 + 0.299076i −0.0166496 + 0.00961267i
\(969\) 0 0
\(970\) −3.69855 1.22361i −0.118753 0.0392879i
\(971\) 7.45964 + 12.9205i 0.239391 + 0.414638i 0.960540 0.278143i \(-0.0897188\pi\)
−0.721148 + 0.692781i \(0.756385\pi\)
\(972\) 0 0
\(973\) 2.98233 + 1.72185i 0.0956092 + 0.0552000i
\(974\) −12.2040 −0.391041
\(975\) 0 0
\(976\) −25.1364 −0.804595
\(977\) −20.2339 11.6821i −0.647341 0.373742i 0.140096 0.990138i \(-0.455259\pi\)
−0.787437 + 0.616396i \(0.788592\pi\)
\(978\) 0 0
\(979\) −16.7425 28.9989i −0.535093 0.926808i
\(980\) −17.0404 5.63757i −0.544334 0.180086i
\(981\) 0 0
\(982\) 10.1292 5.84810i 0.323236 0.186620i
\(983\) 5.31119i 0.169401i 0.996406 + 0.0847003i \(0.0269933\pi\)
−0.996406 + 0.0847003i \(0.973007\pi\)
\(984\) 0 0
\(985\) −32.2035 36.1521i −1.02609 1.15190i
\(986\) −0.967105 + 1.67508i −0.0307989 + 0.0533453i
\(987\) 0 0
\(988\) −8.35565 1.51577i −0.265829 0.0482231i
\(989\) −23.5185 −0.747846
\(990\) 0 0
\(991\) 12.0440 20.8607i 0.382589 0.662663i −0.608843 0.793291i \(-0.708366\pi\)
0.991432 + 0.130628i \(0.0416992\pi\)
\(992\) 12.0644 6.96537i 0.383044 0.221151i
\(993\) 0 0
\(994\) 2.90999 + 5.04025i 0.0922993 + 0.159867i
\(995\) 8.26164 + 39.9154i 0.261912 + 1.26540i
\(996\) 0 0
\(997\) 17.6755 10.2050i 0.559790 0.323195i −0.193271 0.981145i \(-0.561910\pi\)
0.753061 + 0.657951i \(0.228576\pi\)
\(998\) 4.64692 + 2.68290i 0.147096 + 0.0849258i
\(999\) 0 0
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 585.2.bs.a.334.3 12
3.2 odd 2 65.2.n.a.9.4 yes 12
5.4 even 2 inner 585.2.bs.a.334.4 12
12.11 even 2 1040.2.dh.a.529.1 12
13.3 even 3 inner 585.2.bs.a.289.4 12
15.2 even 4 325.2.e.e.126.3 12
15.8 even 4 325.2.e.e.126.4 12
15.14 odd 2 65.2.n.a.9.3 12
39.2 even 12 845.2.l.f.699.7 24
39.5 even 4 845.2.l.f.654.8 24
39.8 even 4 845.2.l.f.654.6 24
39.11 even 12 845.2.l.f.699.5 24
39.17 odd 6 845.2.b.e.339.4 6
39.20 even 12 845.2.d.d.844.7 12
39.23 odd 6 845.2.n.e.484.4 12
39.29 odd 6 65.2.n.a.29.3 yes 12
39.32 even 12 845.2.d.d.844.5 12
39.35 odd 6 845.2.b.d.339.3 6
39.38 odd 2 845.2.n.e.529.3 12
60.59 even 2 1040.2.dh.a.529.6 12
65.29 even 6 inner 585.2.bs.a.289.3 12
156.107 even 6 1040.2.dh.a.289.6 12
195.17 even 12 4225.2.a.bq.1.3 6
195.29 odd 6 65.2.n.a.29.4 yes 12
195.44 even 4 845.2.l.f.654.5 24
195.59 even 12 845.2.d.d.844.6 12
195.68 even 12 325.2.e.e.276.4 12
195.74 odd 6 845.2.b.d.339.4 6
195.89 even 12 845.2.l.f.699.8 24
195.107 even 12 325.2.e.e.276.3 12
195.113 even 12 4225.2.a.br.1.3 6
195.119 even 12 845.2.l.f.699.6 24
195.134 odd 6 845.2.b.e.339.3 6
195.149 even 12 845.2.d.d.844.8 12
195.152 even 12 4225.2.a.br.1.4 6
195.164 even 4 845.2.l.f.654.7 24
195.173 even 12 4225.2.a.bq.1.4 6
195.179 odd 6 845.2.n.e.484.3 12
195.194 odd 2 845.2.n.e.529.4 12
780.419 even 6 1040.2.dh.a.289.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.n.a.9.3 12 15.14 odd 2
65.2.n.a.9.4 yes 12 3.2 odd 2
65.2.n.a.29.3 yes 12 39.29 odd 6
65.2.n.a.29.4 yes 12 195.29 odd 6
325.2.e.e.126.3 12 15.2 even 4
325.2.e.e.126.4 12 15.8 even 4
325.2.e.e.276.3 12 195.107 even 12
325.2.e.e.276.4 12 195.68 even 12
585.2.bs.a.289.3 12 65.29 even 6 inner
585.2.bs.a.289.4 12 13.3 even 3 inner
585.2.bs.a.334.3 12 1.1 even 1 trivial
585.2.bs.a.334.4 12 5.4 even 2 inner
845.2.b.d.339.3 6 39.35 odd 6
845.2.b.d.339.4 6 195.74 odd 6
845.2.b.e.339.3 6 195.134 odd 6
845.2.b.e.339.4 6 39.17 odd 6
845.2.d.d.844.5 12 39.32 even 12
845.2.d.d.844.6 12 195.59 even 12
845.2.d.d.844.7 12 39.20 even 12
845.2.d.d.844.8 12 195.149 even 12
845.2.l.f.654.5 24 195.44 even 4
845.2.l.f.654.6 24 39.8 even 4
845.2.l.f.654.7 24 195.164 even 4
845.2.l.f.654.8 24 39.5 even 4
845.2.l.f.699.5 24 39.11 even 12
845.2.l.f.699.6 24 195.119 even 12
845.2.l.f.699.7 24 39.2 even 12
845.2.l.f.699.8 24 195.89 even 12
845.2.n.e.484.3 12 195.179 odd 6
845.2.n.e.484.4 12 39.23 odd 6
845.2.n.e.529.3 12 39.38 odd 2
845.2.n.e.529.4 12 195.194 odd 2
1040.2.dh.a.289.1 12 780.419 even 6
1040.2.dh.a.289.6 12 156.107 even 6
1040.2.dh.a.529.1 12 12.11 even 2
1040.2.dh.a.529.6 12 60.59 even 2
4225.2.a.bq.1.3 6 195.17 even 12
4225.2.a.bq.1.4 6 195.173 even 12
4225.2.a.br.1.3 6 195.113 even 12
4225.2.a.br.1.4 6 195.152 even 12