Properties

Label 804.2.y.b.361.6
Level $804$
Weight $2$
Character 804.361
Analytic conductor $6.420$
Analytic rank $0$
Dimension $120$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [804,2,Mod(49,804)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(804, base_ring=CyclotomicField(66))
 
chi = DirichletCharacter(H, H._module([0, 0, 46]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("804.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 804.y (of order \(33\), 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: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(6\) over \(\Q(\zeta_{33})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label 361.6
Character \(\chi\) \(=\) 804.361
Dual form 804.2.y.b.49.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.841254 + 0.540641i) q^{3} +(0.567849 - 3.94948i) q^{5} +(-4.15279 + 0.396544i) q^{7} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\) \(q+(-0.841254 + 0.540641i) q^{3} +(0.567849 - 3.94948i) q^{5} +(-4.15279 + 0.396544i) q^{7} +(0.415415 - 0.909632i) q^{9} +(0.739053 - 0.295872i) q^{11} +(-3.13532 + 2.98952i) q^{13} +(1.65754 + 3.62951i) q^{15} +(0.359898 + 1.03986i) q^{17} +(-2.27810 - 0.217532i) q^{19} +(3.27916 - 2.57876i) q^{21} +(0.343734 + 7.21586i) q^{23} +(-10.4785 - 3.07675i) q^{25} +(0.142315 + 0.989821i) q^{27} +(1.98209 + 3.43309i) q^{29} +(7.92820 + 7.55953i) q^{31} +(-0.461771 + 0.648466i) q^{33} +(-0.792020 + 16.6265i) q^{35} +(0.839814 - 1.45460i) q^{37} +(1.02134 - 4.21003i) q^{39} +(1.67972 + 0.323740i) q^{41} +(-3.09358 + 3.57018i) q^{43} +(-3.35668 - 2.15721i) q^{45} +(-9.37215 - 4.83168i) q^{47} +(10.2149 - 1.96877i) q^{49} +(-0.864954 - 0.680208i) q^{51} +(-7.49129 - 8.64541i) q^{53} +(-0.748870 - 3.08688i) q^{55} +(2.03406 - 1.04863i) q^{57} +(-6.92945 + 2.03467i) q^{59} +(-3.49611 - 1.39963i) q^{61} +(-1.36442 + 3.94224i) q^{63} +(10.0267 + 14.0805i) q^{65} +(1.12947 - 8.10705i) q^{67} +(-4.19035 - 5.88453i) q^{69} +(-4.69313 + 13.5599i) q^{71} +(-12.9299 - 5.17635i) q^{73} +(10.4785 - 3.07675i) q^{75} +(-2.95181 + 1.52176i) q^{77} +(0.919920 + 3.79196i) q^{79} +(-0.654861 - 0.755750i) q^{81} +(-7.16855 - 5.63741i) q^{83} +(4.31126 - 0.830927i) q^{85} +(-3.52351 - 1.81650i) q^{87} +(6.83282 + 4.39119i) q^{89} +(11.8349 - 13.6582i) q^{91} +(-10.7566 - 2.07317i) q^{93} +(-2.15275 + 8.87377i) q^{95} +(1.05601 - 1.82906i) q^{97} +(0.0378789 - 0.795176i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{10}{33}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.841254 + 0.540641i −0.485698 + 0.312139i
\(4\) 0 0
\(5\) 0.567849 3.94948i 0.253950 1.76626i −0.320046 0.947402i \(-0.603698\pi\)
0.573996 0.818858i \(-0.305392\pi\)
\(6\) 0 0
\(7\) −4.15279 + 0.396544i −1.56961 + 0.149879i −0.843282 0.537471i \(-0.819380\pi\)
−0.726326 + 0.687351i \(0.758774\pi\)
\(8\) 0 0
\(9\) 0.415415 0.909632i 0.138472 0.303211i
\(10\) 0 0
\(11\) 0.739053 0.295872i 0.222833 0.0892089i −0.257560 0.966262i \(-0.582918\pi\)
0.480393 + 0.877054i \(0.340494\pi\)
\(12\) 0 0
\(13\) −3.13532 + 2.98952i −0.869582 + 0.829145i −0.986460 0.164002i \(-0.947560\pi\)
0.116878 + 0.993146i \(0.462711\pi\)
\(14\) 0 0
\(15\) 1.65754 + 3.62951i 0.427976 + 0.937137i
\(16\) 0 0
\(17\) 0.359898 + 1.03986i 0.0872881 + 0.252202i 0.980194 0.198042i \(-0.0634582\pi\)
−0.892906 + 0.450244i \(0.851337\pi\)
\(18\) 0 0
\(19\) −2.27810 0.217532i −0.522631 0.0499052i −0.169593 0.985514i \(-0.554245\pi\)
−0.353038 + 0.935609i \(0.614851\pi\)
\(20\) 0 0
\(21\) 3.27916 2.57876i 0.715572 0.562732i
\(22\) 0 0
\(23\) 0.343734 + 7.21586i 0.0716734 + 1.50461i 0.692931 + 0.721004i \(0.256319\pi\)
−0.621258 + 0.783606i \(0.713378\pi\)
\(24\) 0 0
\(25\) −10.4785 3.07675i −2.09569 0.615350i
\(26\) 0 0
\(27\) 0.142315 + 0.989821i 0.0273885 + 0.190491i
\(28\) 0 0
\(29\) 1.98209 + 3.43309i 0.368066 + 0.637508i 0.989263 0.146146i \(-0.0466868\pi\)
−0.621197 + 0.783654i \(0.713353\pi\)
\(30\) 0 0
\(31\) 7.92820 + 7.55953i 1.42395 + 1.35773i 0.835871 + 0.548926i \(0.184963\pi\)
0.588077 + 0.808805i \(0.299885\pi\)
\(32\) 0 0
\(33\) −0.461771 + 0.648466i −0.0803839 + 0.112883i
\(34\) 0 0
\(35\) −0.792020 + 16.6265i −0.133876 + 2.81040i
\(36\) 0 0
\(37\) 0.839814 1.45460i 0.138065 0.239135i −0.788699 0.614779i \(-0.789245\pi\)
0.926764 + 0.375644i \(0.122579\pi\)
\(38\) 0 0
\(39\) 1.02134 4.21003i 0.163546 0.674144i
\(40\) 0 0
\(41\) 1.67972 + 0.323740i 0.262329 + 0.0505597i 0.318720 0.947849i \(-0.396747\pi\)
−0.0563909 + 0.998409i \(0.517959\pi\)
\(42\) 0 0
\(43\) −3.09358 + 3.57018i −0.471766 + 0.544447i −0.940902 0.338679i \(-0.890020\pi\)
0.469136 + 0.883126i \(0.344565\pi\)
\(44\) 0 0
\(45\) −3.35668 2.15721i −0.500384 0.321577i
\(46\) 0 0
\(47\) −9.37215 4.83168i −1.36707 0.704773i −0.390625 0.920550i \(-0.627741\pi\)
−0.976443 + 0.215777i \(0.930772\pi\)
\(48\) 0 0
\(49\) 10.2149 1.96877i 1.45928 0.281253i
\(50\) 0 0
\(51\) −0.864954 0.680208i −0.121118 0.0952481i
\(52\) 0 0
\(53\) −7.49129 8.64541i −1.02901 1.18754i −0.982046 0.188642i \(-0.939591\pi\)
−0.0469626 0.998897i \(-0.514954\pi\)
\(54\) 0 0
\(55\) −0.748870 3.08688i −0.100978 0.416235i
\(56\) 0 0
\(57\) 2.03406 1.04863i 0.269418 0.138895i
\(58\) 0 0
\(59\) −6.92945 + 2.03467i −0.902137 + 0.264891i −0.699728 0.714410i \(-0.746695\pi\)
−0.202409 + 0.979301i \(0.564877\pi\)
\(60\) 0 0
\(61\) −3.49611 1.39963i −0.447631 0.179204i 0.136884 0.990587i \(-0.456291\pi\)
−0.584515 + 0.811383i \(0.698715\pi\)
\(62\) 0 0
\(63\) −1.36442 + 3.94224i −0.171901 + 0.496676i
\(64\) 0 0
\(65\) 10.0267 + 14.0805i 1.24365 + 1.74647i
\(66\) 0 0
\(67\) 1.12947 8.10705i 0.137987 0.990434i
\(68\) 0 0
\(69\) −4.19035 5.88453i −0.504459 0.708414i
\(70\) 0 0
\(71\) −4.69313 + 13.5599i −0.556972 + 1.60927i 0.217086 + 0.976152i \(0.430345\pi\)
−0.774059 + 0.633114i \(0.781777\pi\)
\(72\) 0 0
\(73\) −12.9299 5.17635i −1.51333 0.605846i −0.541327 0.840812i \(-0.682078\pi\)
−0.972004 + 0.234966i \(0.924502\pi\)
\(74\) 0 0
\(75\) 10.4785 3.07675i 1.20995 0.355273i
\(76\) 0 0
\(77\) −2.95181 + 1.52176i −0.336390 + 0.173421i
\(78\) 0 0
\(79\) 0.919920 + 3.79196i 0.103499 + 0.426629i 0.999861 0.0166946i \(-0.00531431\pi\)
−0.896361 + 0.443324i \(0.853799\pi\)
\(80\) 0 0
\(81\) −0.654861 0.755750i −0.0727623 0.0839722i
\(82\) 0 0
\(83\) −7.16855 5.63741i −0.786850 0.618786i 0.141735 0.989905i \(-0.454732\pi\)
−0.928585 + 0.371119i \(0.878974\pi\)
\(84\) 0 0
\(85\) 4.31126 0.830927i 0.467622 0.0901267i
\(86\) 0 0
\(87\) −3.52351 1.81650i −0.377760 0.194749i
\(88\) 0 0
\(89\) 6.83282 + 4.39119i 0.724277 + 0.465465i 0.850122 0.526585i \(-0.176528\pi\)
−0.125845 + 0.992050i \(0.540164\pi\)
\(90\) 0 0
\(91\) 11.8349 13.6582i 1.24063 1.43176i
\(92\) 0 0
\(93\) −10.7566 2.07317i −1.11541 0.214978i
\(94\) 0 0
\(95\) −2.15275 + 8.87377i −0.220868 + 0.910429i
\(96\) 0 0
\(97\) 1.05601 1.82906i 0.107221 0.185713i −0.807422 0.589974i \(-0.799138\pi\)
0.914644 + 0.404261i \(0.132471\pi\)
\(98\) 0 0
\(99\) 0.0378789 0.795176i 0.00380697 0.0799182i
\(100\) 0 0
\(101\) −1.01562 + 1.42624i −0.101058 + 0.141916i −0.862008 0.506894i \(-0.830794\pi\)
0.760951 + 0.648810i \(0.224733\pi\)
\(102\) 0 0
\(103\) 4.97032 + 4.73919i 0.489741 + 0.466967i 0.894250 0.447567i \(-0.147709\pi\)
−0.404510 + 0.914534i \(0.632558\pi\)
\(104\) 0 0
\(105\) −8.32270 14.4153i −0.812212 1.40679i
\(106\) 0 0
\(107\) −0.807747 5.61800i −0.0780879 0.543113i −0.990886 0.134702i \(-0.956992\pi\)
0.912798 0.408411i \(-0.133917\pi\)
\(108\) 0 0
\(109\) −9.42574 2.76765i −0.902822 0.265093i −0.202806 0.979219i \(-0.565006\pi\)
−0.700017 + 0.714127i \(0.746824\pi\)
\(110\) 0 0
\(111\) 0.0799199 + 1.67773i 0.00758567 + 0.159243i
\(112\) 0 0
\(113\) −1.38274 + 1.08740i −0.130077 + 0.102294i −0.681078 0.732211i \(-0.738488\pi\)
0.551001 + 0.834505i \(0.314246\pi\)
\(114\) 0 0
\(115\) 28.6940 + 2.73995i 2.67573 + 0.255502i
\(116\) 0 0
\(117\) 1.41691 + 4.09388i 0.130993 + 0.378480i
\(118\) 0 0
\(119\) −1.90693 4.17559i −0.174808 0.382776i
\(120\) 0 0
\(121\) −7.50242 + 7.15354i −0.682038 + 0.650322i
\(122\) 0 0
\(123\) −1.58810 + 0.635779i −0.143194 + 0.0573263i
\(124\) 0 0
\(125\) −9.81403 + 21.4897i −0.877793 + 1.92210i
\(126\) 0 0
\(127\) −10.1197 + 0.966319i −0.897982 + 0.0857469i −0.533829 0.845592i \(-0.679248\pi\)
−0.364153 + 0.931339i \(0.618641\pi\)
\(128\) 0 0
\(129\) 0.672298 4.67594i 0.0591926 0.411693i
\(130\) 0 0
\(131\) 5.88426 3.78158i 0.514110 0.330398i −0.257728 0.966217i \(-0.582974\pi\)
0.771838 + 0.635819i \(0.219338\pi\)
\(132\) 0 0
\(133\) 9.54672 0.827806
\(134\) 0 0
\(135\) 3.99009 0.343412
\(136\) 0 0
\(137\) 10.0866 6.48225i 0.861754 0.553816i −0.0334661 0.999440i \(-0.510655\pi\)
0.895220 + 0.445624i \(0.147018\pi\)
\(138\) 0 0
\(139\) 2.68219 18.6551i 0.227501 1.58230i −0.481084 0.876675i \(-0.659757\pi\)
0.708584 0.705626i \(-0.249334\pi\)
\(140\) 0 0
\(141\) 10.4966 1.00230i 0.883969 0.0844088i
\(142\) 0 0
\(143\) −1.43265 + 3.13707i −0.119804 + 0.262335i
\(144\) 0 0
\(145\) 14.6844 5.87876i 1.21948 0.488205i
\(146\) 0 0
\(147\) −7.52896 + 7.17884i −0.620978 + 0.592101i
\(148\) 0 0
\(149\) 6.84988 + 14.9992i 0.561164 + 1.22878i 0.951370 + 0.308051i \(0.0996766\pi\)
−0.390206 + 0.920728i \(0.627596\pi\)
\(150\) 0 0
\(151\) −5.74385 16.5958i −0.467428 1.35054i −0.894800 0.446468i \(-0.852682\pi\)
0.427372 0.904076i \(-0.359440\pi\)
\(152\) 0 0
\(153\) 1.09539 + 0.104597i 0.0885573 + 0.00845620i
\(154\) 0 0
\(155\) 34.3582 27.0196i 2.75972 2.17027i
\(156\) 0 0
\(157\) 0.703087 + 14.7596i 0.0561124 + 1.17794i 0.834807 + 0.550542i \(0.185579\pi\)
−0.778695 + 0.627403i \(0.784118\pi\)
\(158\) 0 0
\(159\) 10.9761 + 3.22289i 0.870465 + 0.255591i
\(160\) 0 0
\(161\) −4.28886 29.8296i −0.338009 2.35091i
\(162\) 0 0
\(163\) 3.41948 + 5.92270i 0.267834 + 0.463902i 0.968302 0.249782i \(-0.0803588\pi\)
−0.700468 + 0.713684i \(0.747025\pi\)
\(164\) 0 0
\(165\) 2.29889 + 2.19198i 0.178968 + 0.170646i
\(166\) 0 0
\(167\) −4.97340 + 6.98416i −0.384853 + 0.540450i −0.960874 0.276984i \(-0.910665\pi\)
0.576021 + 0.817435i \(0.304604\pi\)
\(168\) 0 0
\(169\) 0.274429 5.76096i 0.0211099 0.443151i
\(170\) 0 0
\(171\) −1.14423 + 1.98186i −0.0875014 + 0.151557i
\(172\) 0 0
\(173\) 1.22138 5.03458i 0.0928595 0.382772i −0.906350 0.422528i \(-0.861143\pi\)
0.999209 + 0.0397559i \(0.0126580\pi\)
\(174\) 0 0
\(175\) 44.7349 + 8.62195i 3.38164 + 0.651758i
\(176\) 0 0
\(177\) 4.72940 5.45801i 0.355483 0.410249i
\(178\) 0 0
\(179\) 11.4700 + 7.37133i 0.857309 + 0.550959i 0.893846 0.448373i \(-0.147996\pi\)
−0.0365375 + 0.999332i \(0.511633\pi\)
\(180\) 0 0
\(181\) 13.0200 + 6.71228i 0.967770 + 0.498920i 0.868256 0.496116i \(-0.165241\pi\)
0.0995137 + 0.995036i \(0.468271\pi\)
\(182\) 0 0
\(183\) 3.69781 0.712695i 0.273350 0.0526839i
\(184\) 0 0
\(185\) −5.26803 4.14282i −0.387313 0.304586i
\(186\) 0 0
\(187\) 0.573648 + 0.662026i 0.0419493 + 0.0484121i
\(188\) 0 0
\(189\) −0.983511 4.05409i −0.0715399 0.294892i
\(190\) 0 0
\(191\) −5.55560 + 2.86411i −0.401989 + 0.207240i −0.647351 0.762192i \(-0.724123\pi\)
0.245362 + 0.969431i \(0.421093\pi\)
\(192\) 0 0
\(193\) −8.01543 + 2.35354i −0.576963 + 0.169412i −0.557179 0.830393i \(-0.688116\pi\)
−0.0197845 + 0.999804i \(0.506298\pi\)
\(194\) 0 0
\(195\) −16.0475 6.42443i −1.14918 0.460063i
\(196\) 0 0
\(197\) 0.736663 2.12845i 0.0524850 0.151646i −0.915712 0.401836i \(-0.868372\pi\)
0.968197 + 0.250191i \(0.0804933\pi\)
\(198\) 0 0
\(199\) −11.9046 16.7177i −0.843896 1.18509i −0.980900 0.194515i \(-0.937687\pi\)
0.137004 0.990571i \(-0.456253\pi\)
\(200\) 0 0
\(201\) 3.43283 + 7.43072i 0.242133 + 0.524123i
\(202\) 0 0
\(203\) −9.59260 13.4709i −0.673268 0.945473i
\(204\) 0 0
\(205\) 2.23243 6.45019i 0.155920 0.450501i
\(206\) 0 0
\(207\) 6.70657 + 2.68490i 0.466139 + 0.186614i
\(208\) 0 0
\(209\) −1.74800 + 0.513258i −0.120911 + 0.0355028i
\(210\) 0 0
\(211\) −18.9585 + 9.77380i −1.30516 + 0.672856i −0.963687 0.267036i \(-0.913956\pi\)
−0.341472 + 0.939892i \(0.610925\pi\)
\(212\) 0 0
\(213\) −3.38293 13.9446i −0.231795 0.955470i
\(214\) 0 0
\(215\) 12.3436 + 14.2453i 0.841830 + 0.971523i
\(216\) 0 0
\(217\) −35.9219 28.2493i −2.43854 1.91769i
\(218\) 0 0
\(219\) 13.6759 2.63581i 0.924130 0.178111i
\(220\) 0 0
\(221\) −4.23707 2.18436i −0.285016 0.146936i
\(222\) 0 0
\(223\) −14.6881 9.43946i −0.983587 0.632113i −0.0531585 0.998586i \(-0.516929\pi\)
−0.930429 + 0.366473i \(0.880565\pi\)
\(224\) 0 0
\(225\) −7.15162 + 8.25341i −0.476775 + 0.550227i
\(226\) 0 0
\(227\) 2.65846 + 0.512375i 0.176448 + 0.0340075i 0.276710 0.960954i \(-0.410756\pi\)
−0.100262 + 0.994961i \(0.531968\pi\)
\(228\) 0 0
\(229\) 3.98529 16.4276i 0.263356 1.08557i −0.674426 0.738342i \(-0.735609\pi\)
0.937782 0.347225i \(-0.112876\pi\)
\(230\) 0 0
\(231\) 1.66049 2.87606i 0.109252 0.189231i
\(232\) 0 0
\(233\) −1.33179 + 27.9576i −0.0872482 + 1.83157i 0.355222 + 0.934782i \(0.384405\pi\)
−0.442470 + 0.896783i \(0.645898\pi\)
\(234\) 0 0
\(235\) −24.4046 + 34.2714i −1.59198 + 2.23562i
\(236\) 0 0
\(237\) −2.82398 2.69266i −0.183437 0.174907i
\(238\) 0 0
\(239\) 3.36704 + 5.83189i 0.217796 + 0.377234i 0.954134 0.299380i \(-0.0967800\pi\)
−0.736338 + 0.676614i \(0.763447\pi\)
\(240\) 0 0
\(241\) −3.83205 26.6525i −0.246844 1.71684i −0.616233 0.787564i \(-0.711342\pi\)
0.369389 0.929275i \(-0.379567\pi\)
\(242\) 0 0
\(243\) 0.959493 + 0.281733i 0.0615515 + 0.0180732i
\(244\) 0 0
\(245\) −1.97506 41.4616i −0.126182 2.64889i
\(246\) 0 0
\(247\) 7.79288 6.12839i 0.495849 0.389940i
\(248\) 0 0
\(249\) 9.07838 + 0.866880i 0.575319 + 0.0549363i
\(250\) 0 0
\(251\) 2.73956 + 7.91543i 0.172919 + 0.499618i 0.997844 0.0656244i \(-0.0209039\pi\)
−0.824925 + 0.565242i \(0.808783\pi\)
\(252\) 0 0
\(253\) 2.38901 + 5.23120i 0.150196 + 0.328883i
\(254\) 0 0
\(255\) −3.17763 + 3.02986i −0.198991 + 0.189737i
\(256\) 0 0
\(257\) 10.7480 4.30286i 0.670443 0.268405i −0.0113656 0.999935i \(-0.503618\pi\)
0.681809 + 0.731530i \(0.261194\pi\)
\(258\) 0 0
\(259\) −2.91076 + 6.37368i −0.180866 + 0.396041i
\(260\) 0 0
\(261\) 3.94624 0.376820i 0.244266 0.0233246i
\(262\) 0 0
\(263\) −3.19366 + 22.2124i −0.196930 + 1.36968i 0.616199 + 0.787591i \(0.288672\pi\)
−0.813128 + 0.582084i \(0.802237\pi\)
\(264\) 0 0
\(265\) −38.3988 + 24.6774i −2.35882 + 1.51592i
\(266\) 0 0
\(267\) −8.12219 −0.497070
\(268\) 0 0
\(269\) −22.2330 −1.35557 −0.677784 0.735261i \(-0.737060\pi\)
−0.677784 + 0.735261i \(0.737060\pi\)
\(270\) 0 0
\(271\) −14.1129 + 9.06983i −0.857299 + 0.550953i −0.893843 0.448379i \(-0.852001\pi\)
0.0365442 + 0.999332i \(0.488365\pi\)
\(272\) 0 0
\(273\) −2.57196 + 17.8884i −0.155662 + 1.08265i
\(274\) 0 0
\(275\) −8.65446 + 0.826401i −0.521884 + 0.0498338i
\(276\) 0 0
\(277\) −9.75679 + 21.3644i −0.586229 + 1.28366i 0.351465 + 0.936201i \(0.385683\pi\)
−0.937694 + 0.347461i \(0.887044\pi\)
\(278\) 0 0
\(279\) 10.1699 4.07141i 0.608855 0.243749i
\(280\) 0 0
\(281\) 12.1180 11.5545i 0.722901 0.689285i −0.236405 0.971655i \(-0.575969\pi\)
0.959306 + 0.282370i \(0.0911206\pi\)
\(282\) 0 0
\(283\) 1.11485 + 2.44117i 0.0662707 + 0.145113i 0.939869 0.341535i \(-0.110947\pi\)
−0.873598 + 0.486648i \(0.838220\pi\)
\(284\) 0 0
\(285\) −2.98651 8.62895i −0.176906 0.511135i
\(286\) 0 0
\(287\) −7.10392 0.678342i −0.419331 0.0400413i
\(288\) 0 0
\(289\) 12.4111 9.76022i 0.730066 0.574130i
\(290\) 0 0
\(291\) 0.100494 + 2.10962i 0.00589105 + 0.123668i
\(292\) 0 0
\(293\) 12.7944 + 3.75678i 0.747458 + 0.219474i 0.633211 0.773979i \(-0.281736\pi\)
0.114247 + 0.993452i \(0.463555\pi\)
\(294\) 0 0
\(295\) 4.10100 + 28.5231i 0.238769 + 1.66068i
\(296\) 0 0
\(297\) 0.398039 + 0.689424i 0.0230966 + 0.0400044i
\(298\) 0 0
\(299\) −22.6497 21.5964i −1.30987 1.24895i
\(300\) 0 0
\(301\) 11.4312 16.0529i 0.658886 0.925276i
\(302\) 0 0
\(303\) 0.0833109 1.74891i 0.00478609 0.100472i
\(304\) 0 0
\(305\) −7.51307 + 13.0130i −0.430197 + 0.745124i
\(306\) 0 0
\(307\) 1.53177 6.31405i 0.0874229 0.360362i −0.911251 0.411852i \(-0.864882\pi\)
0.998673 + 0.0514903i \(0.0163971\pi\)
\(308\) 0 0
\(309\) −6.74350 1.29970i −0.383625 0.0739376i
\(310\) 0 0
\(311\) 15.9088 18.3597i 0.902105 1.04108i −0.0968461 0.995299i \(-0.530875\pi\)
0.998951 0.0457855i \(-0.0145791\pi\)
\(312\) 0 0
\(313\) −17.4194 11.1948i −0.984604 0.632767i −0.0539026 0.998546i \(-0.517166\pi\)
−0.930702 + 0.365780i \(0.880802\pi\)
\(314\) 0 0
\(315\) 14.7950 + 7.62736i 0.833605 + 0.429753i
\(316\) 0 0
\(317\) 31.2130 6.01582i 1.75310 0.337882i 0.791256 0.611485i \(-0.209428\pi\)
0.961843 + 0.273603i \(0.0882156\pi\)
\(318\) 0 0
\(319\) 2.48063 + 1.95079i 0.138889 + 0.109223i
\(320\) 0 0
\(321\) 3.71684 + 4.28946i 0.207454 + 0.239415i
\(322\) 0 0
\(323\) −0.593680 2.44718i −0.0330332 0.136165i
\(324\) 0 0
\(325\) 42.0514 21.6790i 2.33259 1.20253i
\(326\) 0 0
\(327\) 9.42574 2.76765i 0.521245 0.153051i
\(328\) 0 0
\(329\) 40.8365 + 16.3485i 2.25139 + 0.901321i
\(330\) 0 0
\(331\) 5.18267 14.9743i 0.284865 0.823064i −0.708254 0.705958i \(-0.750517\pi\)
0.993119 0.117107i \(-0.0373620\pi\)
\(332\) 0 0
\(333\) −0.974280 1.36819i −0.0533902 0.0749761i
\(334\) 0 0
\(335\) −31.3773 9.06439i −1.71432 0.495241i
\(336\) 0 0
\(337\) 16.4174 + 23.0550i 0.894312 + 1.25589i 0.966022 + 0.258460i \(0.0832150\pi\)
−0.0717099 + 0.997426i \(0.522846\pi\)
\(338\) 0 0
\(339\) 0.575342 1.66234i 0.0312483 0.0902859i
\(340\) 0 0
\(341\) 8.09602 + 3.24116i 0.438424 + 0.175519i
\(342\) 0 0
\(343\) −13.6209 + 3.99946i −0.735460 + 0.215951i
\(344\) 0 0
\(345\) −25.6203 + 13.2082i −1.37935 + 0.711105i
\(346\) 0 0
\(347\) −3.03740 12.5203i −0.163056 0.672127i −0.993383 0.114850i \(-0.963361\pi\)
0.830327 0.557277i \(-0.188154\pi\)
\(348\) 0 0
\(349\) 1.42380 + 1.64315i 0.0762140 + 0.0879557i 0.792576 0.609773i \(-0.208739\pi\)
−0.716362 + 0.697729i \(0.754194\pi\)
\(350\) 0 0
\(351\) −3.40530 2.67796i −0.181761 0.142939i
\(352\) 0 0
\(353\) −1.87805 + 0.361965i −0.0999587 + 0.0192655i −0.238985 0.971023i \(-0.576815\pi\)
0.139027 + 0.990289i \(0.455603\pi\)
\(354\) 0 0
\(355\) 50.8896 + 26.2354i 2.70094 + 1.39243i
\(356\) 0 0
\(357\) 3.86171 + 2.48177i 0.204383 + 0.131349i
\(358\) 0 0
\(359\) −20.5008 + 23.6592i −1.08199 + 1.24869i −0.115141 + 0.993349i \(0.536732\pi\)
−0.966852 + 0.255338i \(0.917813\pi\)
\(360\) 0 0
\(361\) −13.5142 2.60466i −0.711276 0.137087i
\(362\) 0 0
\(363\) 2.44394 10.0741i 0.128273 0.528751i
\(364\) 0 0
\(365\) −27.7861 + 48.1270i −1.45439 + 2.51908i
\(366\) 0 0
\(367\) 0.508970 10.6846i 0.0265680 0.557732i −0.945867 0.324556i \(-0.894785\pi\)
0.972435 0.233176i \(-0.0749118\pi\)
\(368\) 0 0
\(369\) 0.992266 1.39344i 0.0516553 0.0725398i
\(370\) 0 0
\(371\) 34.5381 + 32.9320i 1.79313 + 1.70974i
\(372\) 0 0
\(373\) 7.19678 + 12.4652i 0.372635 + 0.645423i 0.989970 0.141277i \(-0.0451210\pi\)
−0.617335 + 0.786701i \(0.711788\pi\)
\(374\) 0 0
\(375\) −3.36214 23.3842i −0.173620 1.20755i
\(376\) 0 0
\(377\) −16.4778 4.83832i −0.848650 0.249186i
\(378\) 0 0
\(379\) −0.904935 18.9969i −0.0464834 0.975807i −0.894842 0.446384i \(-0.852712\pi\)
0.848358 0.529423i \(-0.177591\pi\)
\(380\) 0 0
\(381\) 7.99084 6.28407i 0.409383 0.321943i
\(382\) 0 0
\(383\) −17.0233 1.62552i −0.869848 0.0830604i −0.349420 0.936966i \(-0.613621\pi\)
−0.520428 + 0.853906i \(0.674228\pi\)
\(384\) 0 0
\(385\) 4.33399 + 12.5222i 0.220880 + 0.638192i
\(386\) 0 0
\(387\) 1.96243 + 4.29712i 0.0997559 + 0.218435i
\(388\) 0 0
\(389\) −22.3772 + 21.3366i −1.13457 + 1.08181i −0.138762 + 0.990326i \(0.544312\pi\)
−0.995807 + 0.0914835i \(0.970839\pi\)
\(390\) 0 0
\(391\) −7.37975 + 2.95441i −0.373210 + 0.149411i
\(392\) 0 0
\(393\) −2.90567 + 6.36254i −0.146572 + 0.320948i
\(394\) 0 0
\(395\) 15.4987 1.47994i 0.779822 0.0744640i
\(396\) 0 0
\(397\) −2.34044 + 16.2782i −0.117464 + 0.816977i 0.842869 + 0.538119i \(0.180865\pi\)
−0.960332 + 0.278858i \(0.910044\pi\)
\(398\) 0 0
\(399\) −8.03121 + 5.16135i −0.402064 + 0.258391i
\(400\) 0 0
\(401\) 14.1520 0.706718 0.353359 0.935488i \(-0.385039\pi\)
0.353359 + 0.935488i \(0.385039\pi\)
\(402\) 0 0
\(403\) −47.4569 −2.36399
\(404\) 0 0
\(405\) −3.35668 + 2.15721i −0.166795 + 0.107192i
\(406\) 0 0
\(407\) 0.190291 1.32351i 0.00943239 0.0656037i
\(408\) 0 0
\(409\) 2.04232 0.195018i 0.100986 0.00964300i −0.0444406 0.999012i \(-0.514151\pi\)
0.145427 + 0.989369i \(0.453544\pi\)
\(410\) 0 0
\(411\) −4.98080 + 10.9064i −0.245685 + 0.537974i
\(412\) 0 0
\(413\) 27.9697 11.1974i 1.37630 0.550987i
\(414\) 0 0
\(415\) −26.3355 + 25.1108i −1.29276 + 1.23264i
\(416\) 0 0
\(417\) 7.82928 + 17.1437i 0.383401 + 0.839532i
\(418\) 0 0
\(419\) −8.95004 25.8595i −0.437238 1.26332i −0.921495 0.388391i \(-0.873031\pi\)
0.484256 0.874926i \(-0.339090\pi\)
\(420\) 0 0
\(421\) 14.8404 + 1.41709i 0.723278 + 0.0690647i 0.450201 0.892927i \(-0.351352\pi\)
0.273077 + 0.961992i \(0.411958\pi\)
\(422\) 0 0
\(423\) −8.28838 + 6.51805i −0.402995 + 0.316919i
\(424\) 0 0
\(425\) −0.571793 12.0034i −0.0277360 0.582251i
\(426\) 0 0
\(427\) 15.0736 + 4.42602i 0.729464 + 0.214190i
\(428\) 0 0
\(429\) −0.490805 3.41362i −0.0236963 0.164811i
\(430\) 0 0
\(431\) −8.62573 14.9402i −0.415487 0.719644i 0.579993 0.814622i \(-0.303055\pi\)
−0.995479 + 0.0949775i \(0.969722\pi\)
\(432\) 0 0
\(433\) −4.06882 3.87961i −0.195535 0.186442i 0.585986 0.810321i \(-0.300707\pi\)
−0.781521 + 0.623879i \(0.785556\pi\)
\(434\) 0 0
\(435\) −9.17503 + 12.8845i −0.439909 + 0.617766i
\(436\) 0 0
\(437\) 0.786620 16.5132i 0.0376291 0.789933i
\(438\) 0 0
\(439\) −10.3430 + 17.9145i −0.493643 + 0.855014i −0.999973 0.00732524i \(-0.997668\pi\)
0.506330 + 0.862340i \(0.331002\pi\)
\(440\) 0 0
\(441\) 2.45258 10.1097i 0.116790 0.481414i
\(442\) 0 0
\(443\) 16.1897 + 3.12031i 0.769195 + 0.148250i 0.558728 0.829351i \(-0.311289\pi\)
0.210467 + 0.977601i \(0.432502\pi\)
\(444\) 0 0
\(445\) 21.2229 24.4925i 1.00606 1.16106i
\(446\) 0 0
\(447\) −13.8716 8.91476i −0.656106 0.421654i
\(448\) 0 0
\(449\) −25.7486 13.2743i −1.21515 0.626455i −0.273122 0.961980i \(-0.588056\pi\)
−0.942031 + 0.335525i \(0.891086\pi\)
\(450\) 0 0
\(451\) 1.33719 0.257722i 0.0629658 0.0121357i
\(452\) 0 0
\(453\) 13.8044 + 10.8559i 0.648586 + 0.510054i
\(454\) 0 0
\(455\) −47.2222 54.4973i −2.21381 2.55487i
\(456\) 0 0
\(457\) −0.764064 3.14952i −0.0357414 0.147328i 0.951145 0.308745i \(-0.0999089\pi\)
−0.986886 + 0.161417i \(0.948394\pi\)
\(458\) 0 0
\(459\) −0.978054 + 0.504222i −0.0456516 + 0.0235351i
\(460\) 0 0
\(461\) −32.5734 + 9.56442i −1.51710 + 0.445459i −0.931072 0.364835i \(-0.881125\pi\)
−0.586023 + 0.810294i \(0.699307\pi\)
\(462\) 0 0
\(463\) −10.9332 4.37701i −0.508111 0.203417i 0.103420 0.994638i \(-0.467022\pi\)
−0.611530 + 0.791221i \(0.709446\pi\)
\(464\) 0 0
\(465\) −14.2961 + 41.3058i −0.662964 + 1.91551i
\(466\) 0 0
\(467\) 1.31181 + 1.84219i 0.0607035 + 0.0852462i 0.843812 0.536639i \(-0.180306\pi\)
−0.783108 + 0.621885i \(0.786367\pi\)
\(468\) 0 0
\(469\) −1.47565 + 34.1148i −0.0681392 + 1.57527i
\(470\) 0 0
\(471\) −8.57112 12.0365i −0.394936 0.554611i
\(472\) 0 0
\(473\) −1.23000 + 3.55385i −0.0565555 + 0.163406i
\(474\) 0 0
\(475\) 23.2016 + 9.28854i 1.06456 + 0.426187i
\(476\) 0 0
\(477\) −10.9761 + 3.22289i −0.502563 + 0.147566i
\(478\) 0 0
\(479\) −19.4396 + 10.0218i −0.888218 + 0.457908i −0.841037 0.540978i \(-0.818054\pi\)
−0.0471815 + 0.998886i \(0.515024\pi\)
\(480\) 0 0
\(481\) 1.71548 + 7.07129i 0.0782190 + 0.322423i
\(482\) 0 0
\(483\) 19.7351 + 22.7756i 0.897980 + 1.03632i
\(484\) 0 0
\(485\) −6.62418 5.20931i −0.300789 0.236543i
\(486\) 0 0
\(487\) 5.42062 1.04474i 0.245632 0.0473416i −0.0649493 0.997889i \(-0.520689\pi\)
0.310581 + 0.950547i \(0.399476\pi\)
\(488\) 0 0
\(489\) −6.07870 3.13379i −0.274888 0.141715i
\(490\) 0 0
\(491\) −11.2543 7.23272i −0.507901 0.326408i 0.261469 0.965212i \(-0.415793\pi\)
−0.769370 + 0.638804i \(0.779430\pi\)
\(492\) 0 0
\(493\) −2.85657 + 3.29666i −0.128653 + 0.148474i
\(494\) 0 0
\(495\) −3.11902 0.601142i −0.140190 0.0270193i
\(496\) 0 0
\(497\) 14.1125 58.1726i 0.633033 2.60940i
\(498\) 0 0
\(499\) −10.6081 + 18.3738i −0.474885 + 0.822526i −0.999586 0.0287609i \(-0.990844\pi\)
0.524701 + 0.851287i \(0.324177\pi\)
\(500\) 0 0
\(501\) 0.407966 8.56427i 0.0182266 0.382623i
\(502\) 0 0
\(503\) −1.45754 + 2.04682i −0.0649883 + 0.0912633i −0.845791 0.533514i \(-0.820871\pi\)
0.780803 + 0.624778i \(0.214810\pi\)
\(504\) 0 0
\(505\) 5.05617 + 4.82105i 0.224997 + 0.214534i
\(506\) 0 0
\(507\) 2.88375 + 4.99480i 0.128072 + 0.221827i
\(508\) 0 0
\(509\) 1.58281 + 11.0087i 0.0701569 + 0.487952i 0.994361 + 0.106052i \(0.0338210\pi\)
−0.924204 + 0.381900i \(0.875270\pi\)
\(510\) 0 0
\(511\) 55.7479 + 16.3691i 2.46614 + 0.724124i
\(512\) 0 0
\(513\) −0.108889 2.28587i −0.00480758 0.100923i
\(514\) 0 0
\(515\) 21.5397 16.9390i 0.949154 0.746423i
\(516\) 0 0
\(517\) −8.35607 0.797908i −0.367500 0.0350920i
\(518\) 0 0
\(519\) 1.69441 + 4.89568i 0.0743764 + 0.214897i
\(520\) 0 0
\(521\) −5.53380 12.1173i −0.242440 0.530870i 0.748823 0.662770i \(-0.230619\pi\)
−0.991263 + 0.131901i \(0.957892\pi\)
\(522\) 0 0
\(523\) −11.9597 + 11.4036i −0.522962 + 0.498643i −0.904947 0.425525i \(-0.860089\pi\)
0.381984 + 0.924169i \(0.375241\pi\)
\(524\) 0 0
\(525\) −42.2948 + 16.9323i −1.84590 + 0.738985i
\(526\) 0 0
\(527\) −5.00748 + 10.9649i −0.218129 + 0.477637i
\(528\) 0 0
\(529\) −29.0546 + 2.77438i −1.26324 + 0.120625i
\(530\) 0 0
\(531\) −1.02780 + 7.14848i −0.0446026 + 0.310218i
\(532\) 0 0
\(533\) −6.23430 + 4.00654i −0.270038 + 0.173543i
\(534\) 0 0
\(535\) −22.6469 −0.979109
\(536\) 0 0
\(537\) −13.6344 −0.588369
\(538\) 0 0
\(539\) 6.96688 4.47734i 0.300085 0.192853i
\(540\) 0 0
\(541\) 1.24913 8.68787i 0.0537042 0.373521i −0.945191 0.326519i \(-0.894124\pi\)
0.998895 0.0470017i \(-0.0149666\pi\)
\(542\) 0 0
\(543\) −14.5821 + 1.39242i −0.625776 + 0.0597544i
\(544\) 0 0
\(545\) −16.2832 + 35.6551i −0.697494 + 1.52730i
\(546\) 0 0
\(547\) 34.8916 13.9685i 1.49186 0.597249i 0.524668 0.851307i \(-0.324190\pi\)
0.967189 + 0.254058i \(0.0817653\pi\)
\(548\) 0 0
\(549\) −2.72549 + 2.59875i −0.116321 + 0.110912i
\(550\) 0 0
\(551\) −3.76860 8.25207i −0.160548 0.351550i
\(552\) 0 0
\(553\) −5.32392 15.3825i −0.226396 0.654128i
\(554\) 0 0
\(555\) 6.67152 + 0.637053i 0.283190 + 0.0270414i
\(556\) 0 0
\(557\) 25.1241 19.7578i 1.06454 0.837164i 0.0773970 0.997000i \(-0.475339\pi\)
0.987144 + 0.159836i \(0.0510967\pi\)
\(558\) 0 0
\(559\) −0.973771 20.4420i −0.0411861 0.864603i
\(560\) 0 0
\(561\) −0.840502 0.246794i −0.0354860 0.0104196i
\(562\) 0 0
\(563\) −2.54760 17.7190i −0.107369 0.746765i −0.970381 0.241581i \(-0.922334\pi\)
0.863012 0.505184i \(-0.168575\pi\)
\(564\) 0 0
\(565\) 3.50946 + 6.07857i 0.147644 + 0.255727i
\(566\) 0 0
\(567\) 3.01919 + 2.87879i 0.126794 + 0.120898i
\(568\) 0 0
\(569\) −6.38681 + 8.96903i −0.267749 + 0.376001i −0.926459 0.376396i \(-0.877163\pi\)
0.658710 + 0.752397i \(0.271103\pi\)
\(570\) 0 0
\(571\) −0.553774 + 11.6251i −0.0231747 + 0.486497i 0.957209 + 0.289398i \(0.0934551\pi\)
−0.980384 + 0.197099i \(0.936848\pi\)
\(572\) 0 0
\(573\) 3.12521 5.41303i 0.130558 0.226132i
\(574\) 0 0
\(575\) 18.5996 76.6686i 0.775657 3.19730i
\(576\) 0 0
\(577\) −25.9820 5.00763i −1.08165 0.208470i −0.382864 0.923805i \(-0.625062\pi\)
−0.698782 + 0.715335i \(0.746274\pi\)
\(578\) 0 0
\(579\) 5.47059 6.31340i 0.227350 0.262376i
\(580\) 0 0
\(581\) 32.0050 + 20.5683i 1.32779 + 0.853318i
\(582\) 0 0
\(583\) −8.09440 4.17296i −0.335236 0.172826i
\(584\) 0 0
\(585\) 16.9733 3.27133i 0.701759 0.135253i
\(586\) 0 0
\(587\) 23.2001 + 18.2447i 0.957569 + 0.753041i 0.969043 0.246894i \(-0.0794098\pi\)
−0.0114736 + 0.999934i \(0.503652\pi\)
\(588\) 0 0
\(589\) −16.4168 18.9460i −0.676441 0.780655i
\(590\) 0 0
\(591\) 0.531005 + 2.18883i 0.0218426 + 0.0900366i
\(592\) 0 0
\(593\) 27.1678 14.0060i 1.11565 0.575157i 0.201075 0.979576i \(-0.435556\pi\)
0.914574 + 0.404419i \(0.132526\pi\)
\(594\) 0 0
\(595\) −17.5743 + 5.16027i −0.720474 + 0.211550i
\(596\) 0 0
\(597\) 19.0531 + 7.62770i 0.779790 + 0.312181i
\(598\) 0 0
\(599\) 10.6763 30.8471i 0.436221 1.26038i −0.486083 0.873912i \(-0.661575\pi\)
0.922304 0.386465i \(-0.126304\pi\)
\(600\) 0 0
\(601\) 13.1166 + 18.4196i 0.535036 + 0.751353i 0.990291 0.139008i \(-0.0443913\pi\)
−0.455255 + 0.890361i \(0.650452\pi\)
\(602\) 0 0
\(603\) −6.90524 4.39519i −0.281203 0.178986i
\(604\) 0 0
\(605\) 23.9925 + 33.6927i 0.975434 + 1.36981i
\(606\) 0 0
\(607\) −6.47303 + 18.7026i −0.262732 + 0.759115i 0.734060 + 0.679084i \(0.237623\pi\)
−0.996792 + 0.0800303i \(0.974498\pi\)
\(608\) 0 0
\(609\) 15.3527 + 6.14631i 0.622124 + 0.249061i
\(610\) 0 0
\(611\) 43.8291 12.8694i 1.77314 0.520640i
\(612\) 0 0
\(613\) 14.1284 7.28370i 0.570641 0.294186i −0.148655 0.988889i \(-0.547495\pi\)
0.719297 + 0.694703i \(0.244464\pi\)
\(614\) 0 0
\(615\) 1.60919 + 6.63319i 0.0648890 + 0.267476i
\(616\) 0 0
\(617\) 7.86306 + 9.07446i 0.316555 + 0.365324i 0.891621 0.452783i \(-0.149569\pi\)
−0.575066 + 0.818107i \(0.695023\pi\)
\(618\) 0 0
\(619\) 23.7793 + 18.7002i 0.955770 + 0.751626i 0.968686 0.248291i \(-0.0798689\pi\)
−0.0129158 + 0.999917i \(0.504111\pi\)
\(620\) 0 0
\(621\) −7.09349 + 1.36716i −0.284652 + 0.0548622i
\(622\) 0 0
\(623\) −30.1166 15.5262i −1.20660 0.622043i
\(624\) 0 0
\(625\) 33.3644 + 21.4420i 1.33457 + 0.857679i
\(626\) 0 0
\(627\) 1.19302 1.37682i 0.0476446 0.0549848i
\(628\) 0 0
\(629\) 1.81482 + 0.349779i 0.0723618 + 0.0139466i
\(630\) 0 0
\(631\) −1.82979 + 7.54250i −0.0728428 + 0.300262i −0.996566 0.0827976i \(-0.973614\pi\)
0.923724 + 0.383060i \(0.125130\pi\)
\(632\) 0 0
\(633\) 10.6648 18.4720i 0.423888 0.734196i
\(634\) 0 0
\(635\) −1.93004 + 40.5164i −0.0765911 + 1.60785i
\(636\) 0 0
\(637\) −26.1414 + 36.7105i −1.03576 + 1.45452i
\(638\) 0 0
\(639\) 10.3849 + 9.90202i 0.410822 + 0.391718i
\(640\) 0 0
\(641\) 20.3932 + 35.3221i 0.805484 + 1.39514i 0.915964 + 0.401261i \(0.131428\pi\)
−0.110480 + 0.993878i \(0.535239\pi\)
\(642\) 0 0
\(643\) −3.47067 24.1390i −0.136870 0.951951i −0.936302 0.351195i \(-0.885776\pi\)
0.799433 0.600756i \(-0.205134\pi\)
\(644\) 0 0
\(645\) −18.0857 5.31045i −0.712125 0.209099i
\(646\) 0 0
\(647\) −0.662080 13.8988i −0.0260290 0.546417i −0.973792 0.227441i \(-0.926964\pi\)
0.947763 0.318976i \(-0.103339\pi\)
\(648\) 0 0
\(649\) −4.51923 + 3.55396i −0.177395 + 0.139505i
\(650\) 0 0
\(651\) 45.4921 + 4.34397i 1.78298 + 0.170254i
\(652\) 0 0
\(653\) −6.71981 19.4156i −0.262966 0.759792i −0.996761 0.0804202i \(-0.974374\pi\)
0.733795 0.679371i \(-0.237747\pi\)
\(654\) 0 0
\(655\) −11.5939 25.3871i −0.453011 0.991956i
\(656\) 0 0
\(657\) −10.0799 + 9.61112i −0.393253 + 0.374966i
\(658\) 0 0
\(659\) −33.8939 + 13.5691i −1.32032 + 0.528576i −0.921473 0.388442i \(-0.873013\pi\)
−0.398845 + 0.917018i \(0.630589\pi\)
\(660\) 0 0
\(661\) 16.6171 36.3863i 0.646329 1.41526i −0.248401 0.968657i \(-0.579905\pi\)
0.894730 0.446607i \(-0.147368\pi\)
\(662\) 0 0
\(663\) 4.74541 0.453131i 0.184296 0.0175982i
\(664\) 0 0
\(665\) 5.42110 37.7046i 0.210221 1.46212i
\(666\) 0 0
\(667\) −24.0914 + 15.4826i −0.932821 + 0.599488i
\(668\) 0 0
\(669\) 17.4598 0.675034
\(670\) 0 0
\(671\) −2.99792 −0.115734
\(672\) 0 0
\(673\) −33.2704 + 21.3816i −1.28248 + 0.824199i −0.991191 0.132437i \(-0.957720\pi\)
−0.291287 + 0.956636i \(0.594083\pi\)
\(674\) 0 0
\(675\) 1.55420 10.8097i 0.0598210 0.416064i
\(676\) 0 0
\(677\) 16.5338 1.57879i 0.635445 0.0606776i 0.227638 0.973746i \(-0.426900\pi\)
0.407807 + 0.913068i \(0.366294\pi\)
\(678\) 0 0
\(679\) −3.66008 + 8.01446i −0.140461 + 0.307567i
\(680\) 0 0
\(681\) −2.51345 + 1.00623i −0.0963155 + 0.0385589i
\(682\) 0 0
\(683\) 2.26401 2.15873i 0.0866298 0.0826013i −0.645527 0.763737i \(-0.723362\pi\)
0.732157 + 0.681136i \(0.238514\pi\)
\(684\) 0 0
\(685\) −19.8738 43.5176i −0.759340 1.66272i
\(686\) 0 0
\(687\) 5.52879 + 15.9744i 0.210937 + 0.609461i
\(688\) 0 0
\(689\) 49.3333 + 4.71076i 1.87945 + 0.179466i
\(690\) 0 0
\(691\) 39.0192 30.6850i 1.48436 1.16731i 0.538551 0.842593i \(-0.318972\pi\)
0.945810 0.324721i \(-0.105270\pi\)
\(692\) 0 0
\(693\) 0.158019 + 3.31722i 0.00600264 + 0.126011i
\(694\) 0 0
\(695\) −72.1546 21.1865i −2.73698 0.803650i
\(696\) 0 0
\(697\) 0.267885 + 1.86318i 0.0101469 + 0.0705731i
\(698\) 0 0
\(699\) −13.9947 24.2395i −0.529327 0.916821i
\(700\) 0 0
\(701\) −9.69625 9.24536i −0.366222 0.349192i 0.484515 0.874783i \(-0.338996\pi\)
−0.850738 + 0.525590i \(0.823844\pi\)
\(702\) 0 0
\(703\) −2.22960 + 3.13104i −0.0840910 + 0.118089i
\(704\) 0 0
\(705\) 2.00190 42.0251i 0.0753959 1.58276i
\(706\) 0 0
\(707\) 3.65209 6.32560i 0.137351 0.237899i
\(708\) 0 0
\(709\) −3.62762 + 14.9532i −0.136238 + 0.561581i 0.862243 + 0.506494i \(0.169059\pi\)
−0.998482 + 0.0550870i \(0.982456\pi\)
\(710\) 0 0
\(711\) 3.83144 + 0.738450i 0.143690 + 0.0276940i
\(712\) 0 0
\(713\) −51.8233 + 59.8072i −1.94080 + 2.23980i
\(714\) 0 0
\(715\) 11.5763 + 7.43961i 0.432928 + 0.278226i
\(716\) 0 0
\(717\) −5.98549 3.08574i −0.223532 0.115239i
\(718\) 0 0
\(719\) 14.5522 2.80471i 0.542707 0.104598i 0.0894720 0.995989i \(-0.471482\pi\)
0.453235 + 0.891391i \(0.350270\pi\)
\(720\) 0 0
\(721\) −22.5200 17.7099i −0.838689 0.659553i
\(722\) 0 0
\(723\) 17.6332 + 20.3498i 0.655784 + 0.756815i
\(724\) 0 0
\(725\) −10.2065 42.0719i −0.379061 1.56251i
\(726\) 0 0
\(727\) 4.01009 2.06735i 0.148726 0.0766736i −0.382257 0.924056i \(-0.624853\pi\)
0.530983 + 0.847382i \(0.321823\pi\)
\(728\) 0 0
\(729\) −0.959493 + 0.281733i −0.0355368 + 0.0104345i
\(730\) 0 0
\(731\) −4.82584 1.93198i −0.178490 0.0714567i
\(732\) 0 0
\(733\) −7.48676 + 21.6316i −0.276530 + 0.798980i 0.718143 + 0.695896i \(0.244992\pi\)
−0.994673 + 0.103084i \(0.967129\pi\)
\(734\) 0 0
\(735\) 24.0774 + 33.8119i 0.888107 + 1.24717i
\(736\) 0 0
\(737\) −1.56391 6.32572i −0.0576075 0.233011i
\(738\) 0 0
\(739\) 5.16284 + 7.25019i 0.189918 + 0.266703i 0.898546 0.438880i \(-0.144625\pi\)
−0.708628 + 0.705583i \(0.750685\pi\)
\(740\) 0 0
\(741\) −3.24253 + 9.36868i −0.119117 + 0.344167i
\(742\) 0 0
\(743\) 26.2717 + 10.5176i 0.963816 + 0.385854i 0.799575 0.600566i \(-0.205058\pi\)
0.164241 + 0.986420i \(0.447482\pi\)
\(744\) 0 0
\(745\) 63.1285 18.5362i 2.31285 0.679114i
\(746\) 0 0
\(747\) −8.10589 + 4.17887i −0.296579 + 0.152897i
\(748\) 0 0
\(749\) 5.58219 + 23.0101i 0.203969 + 0.840771i
\(750\) 0 0
\(751\) 4.52676 + 5.22416i 0.165184 + 0.190632i 0.832307 0.554315i \(-0.187020\pi\)
−0.667123 + 0.744948i \(0.732474\pi\)
\(752\) 0 0
\(753\) −6.58407 5.17777i −0.239937 0.188688i
\(754\) 0 0
\(755\) −68.8062 + 13.2613i −2.50412 + 0.482629i
\(756\) 0 0
\(757\) 6.13858 + 3.16466i 0.223110 + 0.115021i 0.566158 0.824296i \(-0.308429\pi\)
−0.343048 + 0.939318i \(0.611459\pi\)
\(758\) 0 0
\(759\) −4.83796 3.10917i −0.175607 0.112856i
\(760\) 0 0
\(761\) 31.5078 36.3619i 1.14216 1.31812i 0.201216 0.979547i \(-0.435511\pi\)
0.940941 0.338572i \(-0.109944\pi\)
\(762\) 0 0
\(763\) 40.2406 + 7.75575i 1.45681 + 0.280777i
\(764\) 0 0
\(765\) 1.03512 4.26684i 0.0374250 0.154268i
\(766\) 0 0
\(767\) 15.6434 27.0951i 0.564849 0.978347i
\(768\) 0 0
\(769\) −0.875196 + 18.3726i −0.0315604 + 0.662534i 0.926556 + 0.376156i \(0.122754\pi\)
−0.958117 + 0.286378i \(0.907549\pi\)
\(770\) 0 0
\(771\) −6.71551 + 9.43061i −0.241853 + 0.339635i
\(772\) 0 0
\(773\) 37.4587 + 35.7168i 1.34729 + 1.28464i 0.925902 + 0.377764i \(0.123307\pi\)
0.421393 + 0.906878i \(0.361541\pi\)
\(774\) 0 0
\(775\) −59.8165 103.605i −2.14867 3.72161i
\(776\) 0 0
\(777\) −0.997183 6.93556i −0.0357737 0.248812i
\(778\) 0 0
\(779\) −3.75615 1.10290i −0.134578 0.0395156i
\(780\) 0 0
\(781\) 0.543529 + 11.4101i 0.0194490 + 0.408284i
\(782\) 0 0
\(783\) −3.11606 + 2.45050i −0.111359 + 0.0875737i
\(784\) 0 0
\(785\) 58.6920 + 5.60441i 2.09481 + 0.200030i
\(786\) 0 0
\(787\) −12.8630 37.1653i −0.458518 1.32480i −0.903242 0.429132i \(-0.858819\pi\)
0.444724 0.895668i \(-0.353302\pi\)
\(788\) 0 0
\(789\) −9.32225 20.4129i −0.331881 0.726718i
\(790\) 0 0
\(791\) 5.31102 5.06405i 0.188838 0.180057i
\(792\) 0 0
\(793\) 15.1457 6.06341i 0.537838 0.215318i
\(794\) 0 0
\(795\) 18.9615 41.5199i 0.672495 1.47256i
\(796\) 0 0
\(797\) −2.00108 + 0.191080i −0.0708819 + 0.00676840i −0.130437 0.991457i \(-0.541638\pi\)
0.0595548 + 0.998225i \(0.481032\pi\)
\(798\) 0 0
\(799\) 1.65124 11.4846i 0.0584165 0.406296i
\(800\) 0 0
\(801\) 6.83282 4.39119i 0.241426 0.155155i
\(802\) 0 0
\(803\) −11.0874 −0.391267
\(804\) 0 0
\(805\) −120.247 −4.23815
\(806\) 0 0
\(807\) 18.7036 12.0201i 0.658397 0.423126i
\(808\) 0 0
\(809\) −5.64434 + 39.2573i −0.198445 + 1.38021i 0.610355 + 0.792128i \(0.291027\pi\)
−0.808800 + 0.588084i \(0.799882\pi\)
\(810\) 0 0
\(811\) 11.0279 1.05304i 0.387242 0.0369771i 0.100380 0.994949i \(-0.467994\pi\)
0.286861 + 0.957972i \(0.407388\pi\)
\(812\) 0 0
\(813\) 6.96903 15.2600i 0.244415 0.535193i
\(814\) 0 0
\(815\) 25.3333 10.1419i 0.887388 0.355257i
\(816\) 0 0
\(817\) 7.82409 7.46026i 0.273730 0.261001i
\(818\) 0 0
\(819\) −7.50752 16.4392i −0.262334 0.574431i
\(820\) 0 0
\(821\) −15.8032 45.6603i −0.551535 1.59355i −0.783874 0.620920i \(-0.786759\pi\)
0.232340 0.972635i \(-0.425362\pi\)
\(822\) 0 0
\(823\) 14.5200 + 1.38650i 0.506137 + 0.0483302i 0.345001 0.938602i \(-0.387878\pi\)
0.161135 + 0.986932i \(0.448484\pi\)
\(824\) 0 0
\(825\) 6.83381 5.37417i 0.237923 0.187105i
\(826\) 0 0
\(827\) 0.795543 + 16.7005i 0.0276638 + 0.580734i 0.969564 + 0.244840i \(0.0787353\pi\)
−0.941900 + 0.335894i \(0.890962\pi\)
\(828\) 0 0
\(829\) −12.0902 3.55001i −0.419911 0.123297i 0.0649495 0.997889i \(-0.479311\pi\)
−0.484860 + 0.874592i \(0.661130\pi\)
\(830\) 0 0
\(831\) −3.34253 23.2478i −0.115951 0.806457i
\(832\) 0 0
\(833\) 5.72357 + 9.91352i 0.198310 + 0.343483i
\(834\) 0 0
\(835\) 24.7596 + 23.6083i 0.856843 + 0.816998i
\(836\) 0 0
\(837\) −6.35428 + 8.92334i −0.219636 + 0.308436i
\(838\) 0 0
\(839\) −1.60684 + 33.7318i −0.0554744 + 1.16455i 0.783861 + 0.620936i \(0.213247\pi\)
−0.839335 + 0.543614i \(0.817056\pi\)
\(840\) 0 0
\(841\) 6.64260 11.5053i 0.229055 0.396735i
\(842\) 0 0
\(843\) −3.94749 + 16.2718i −0.135959 + 0.560430i
\(844\) 0 0
\(845\) −22.5970 4.35521i −0.777359 0.149824i
\(846\) 0 0
\(847\) 28.3193 32.6822i 0.973062 1.12297i
\(848\) 0 0
\(849\) −2.25767 1.45091i −0.0774829 0.0497952i
\(850\) 0 0
\(851\) 10.7849 + 5.55998i 0.369700 + 0.190594i
\(852\) 0 0
\(853\) 9.09741 1.75338i 0.311490 0.0600347i −0.0311108 0.999516i \(-0.509904\pi\)
0.342600 + 0.939481i \(0.388692\pi\)
\(854\) 0 0
\(855\) 7.17758 + 5.64451i 0.245468 + 0.193038i
\(856\) 0 0
\(857\) 8.33254 + 9.61627i 0.284634 + 0.328485i 0.880004 0.474966i \(-0.157540\pi\)
−0.595370 + 0.803452i \(0.702994\pi\)
\(858\) 0 0
\(859\) −7.97939 32.8915i −0.272253 1.12224i −0.929575 0.368633i \(-0.879826\pi\)
0.657322 0.753610i \(-0.271689\pi\)
\(860\) 0 0
\(861\) 6.34293 3.27001i 0.216167 0.111442i
\(862\) 0 0
\(863\) −0.621236 + 0.182411i −0.0211471 + 0.00620936i −0.292289 0.956330i \(-0.594417\pi\)
0.271142 + 0.962539i \(0.412599\pi\)
\(864\) 0 0
\(865\) −19.1904 7.68268i −0.652493 0.261219i
\(866\) 0 0
\(867\) −5.16413 + 14.9208i −0.175383 + 0.506736i
\(868\) 0 0
\(869\) 1.80181 + 2.53028i 0.0611221 + 0.0858340i
\(870\) 0 0
\(871\) 20.6950 + 28.7948i 0.701223 + 0.975674i
\(872\) 0 0
\(873\) −1.22509 1.72040i −0.0414630 0.0582267i
\(874\) 0 0
\(875\) 32.2340 93.1340i 1.08971 3.14850i
\(876\) 0 0
\(877\) 6.81456 + 2.72814i 0.230111 + 0.0921227i 0.483853 0.875149i \(-0.339237\pi\)
−0.253741 + 0.967272i \(0.581661\pi\)
\(878\) 0 0
\(879\) −12.7944 + 3.75678i −0.431545 + 0.126713i
\(880\) 0 0
\(881\) 13.6705 7.04763i 0.460571 0.237441i −0.212294 0.977206i \(-0.568094\pi\)
0.672865 + 0.739765i \(0.265063\pi\)
\(882\) 0 0
\(883\) 6.82429 + 28.1301i 0.229656 + 0.946654i 0.963580 + 0.267422i \(0.0861718\pi\)
−0.733924 + 0.679232i \(0.762313\pi\)
\(884\) 0 0
\(885\) −18.8707 21.7780i −0.634332 0.732059i
\(886\) 0 0
\(887\) 2.72534 + 2.14323i 0.0915080 + 0.0719627i 0.662865 0.748739i \(-0.269340\pi\)
−0.571357 + 0.820702i \(0.693583\pi\)
\(888\) 0 0
\(889\) 41.6420 8.02584i 1.39663 0.269178i
\(890\) 0 0
\(891\) −0.707582 0.364784i −0.0237049 0.0122207i
\(892\) 0 0
\(893\) 20.2996 + 13.0458i 0.679301 + 0.436560i
\(894\) 0 0
\(895\) 35.6261 41.1147i 1.19085 1.37431i
\(896\) 0 0
\(897\) 30.7300 + 5.92273i 1.02605 + 0.197754i
\(898\) 0 0
\(899\) −10.2381 + 42.2019i −0.341459 + 1.40751i
\(900\) 0 0
\(901\) 6.29389 10.9013i 0.209680 0.363176i
\(902\) 0 0
\(903\) −0.937702 + 19.6848i −0.0312048 + 0.655069i
\(904\) 0 0
\(905\) 33.9034 47.6107i 1.12699 1.58263i
\(906\) 0 0
\(907\) −34.6371 33.0264i −1.15011 1.09662i −0.994055 0.108875i \(-0.965275\pi\)
−0.156051 0.987749i \(-0.549876\pi\)
\(908\) 0 0
\(909\) 0.875448 + 1.51632i 0.0290368 + 0.0502932i
\(910\) 0 0
\(911\) 2.47617 + 17.2222i 0.0820392 + 0.570595i 0.988834 + 0.149023i \(0.0476127\pi\)
−0.906795 + 0.421573i \(0.861478\pi\)
\(912\) 0 0
\(913\) −6.96589 2.04537i −0.230537 0.0676919i
\(914\) 0 0
\(915\) −0.714973 15.0091i −0.0236363 0.496186i
\(916\) 0 0
\(917\) −22.9365 + 18.0375i −0.757431 + 0.595650i
\(918\) 0 0
\(919\) −29.4514 2.81226i −0.971511 0.0927680i −0.402784 0.915295i \(-0.631958\pi\)
−0.568726 + 0.822527i \(0.692564\pi\)
\(920\) 0 0
\(921\) 2.12503 + 6.13986i 0.0700220 + 0.202315i
\(922\) 0 0
\(923\) −25.8232 56.5449i −0.849981 1.86120i
\(924\) 0 0
\(925\) −13.2754 + 12.6581i −0.436493 + 0.416195i
\(926\) 0 0
\(927\) 6.37567 2.55243i 0.209404 0.0838329i
\(928\) 0 0
\(929\) −14.6572 + 32.0948i −0.480887 + 1.05300i 0.501331 + 0.865255i \(0.332844\pi\)
−0.982219 + 0.187741i \(0.939884\pi\)
\(930\) 0 0
\(931\) −23.6989 + 2.26297i −0.776700 + 0.0741658i
\(932\) 0 0
\(933\) −3.45731 + 24.0461i −0.113187 + 0.787235i
\(934\) 0 0
\(935\) 2.94040 1.88968i 0.0961614 0.0617992i
\(936\) 0 0
\(937\) 41.8938 1.36861 0.684305 0.729196i \(-0.260106\pi\)
0.684305 + 0.729196i \(0.260106\pi\)
\(938\) 0 0
\(939\) 20.7065 0.675731
\(940\) 0 0
\(941\) 18.5739 11.9367i 0.605491 0.389125i −0.201673 0.979453i \(-0.564638\pi\)
0.807164 + 0.590328i \(0.201001\pi\)
\(942\) 0 0
\(943\) −1.75868 + 12.2319i −0.0572706 + 0.398326i
\(944\) 0 0
\(945\) −16.5700 + 1.58224i −0.539023 + 0.0514704i
\(946\) 0 0
\(947\) −1.50268 + 3.29042i −0.0488307 + 0.106924i −0.932475 0.361235i \(-0.882355\pi\)
0.883644 + 0.468159i \(0.155083\pi\)
\(948\) 0 0
\(949\) 56.0143 22.4247i 1.81830 0.727937i
\(950\) 0 0
\(951\) −23.0057 + 21.9359i −0.746010 + 0.711319i
\(952\) 0 0
\(953\) 6.47331 + 14.1746i 0.209691 + 0.459159i 0.985029 0.172387i \(-0.0551479\pi\)
−0.775338 + 0.631546i \(0.782421\pi\)
\(954\) 0 0
\(955\) 8.15700 + 23.5681i 0.263954 + 0.762646i
\(956\) 0 0
\(957\) −3.14151 0.299978i −0.101551 0.00969692i
\(958\) 0 0
\(959\) −39.3169 + 30.9192i −1.26961 + 0.998433i
\(960\) 0 0
\(961\) 4.23493 + 88.9021i 0.136611 + 2.86781i
\(962\) 0 0
\(963\) −5.44587 1.59905i −0.175491 0.0515287i
\(964\) 0 0
\(965\) 4.74371 + 32.9932i 0.152705 + 1.06209i
\(966\) 0 0
\(967\) 29.2921 + 50.7354i 0.941970 + 1.63154i 0.761707 + 0.647922i \(0.224362\pi\)
0.180263 + 0.983618i \(0.442305\pi\)
\(968\) 0 0
\(969\) 1.82248 + 1.73773i 0.0585466 + 0.0558240i
\(970\) 0 0
\(971\) 18.1858 25.5384i 0.583611 0.819567i −0.412191 0.911097i \(-0.635236\pi\)
0.995802 + 0.0915304i \(0.0291759\pi\)
\(972\) 0 0
\(973\) −3.74104 + 78.5342i −0.119932 + 2.51769i
\(974\) 0 0
\(975\) −23.6553 + 40.9722i −0.757576 + 1.31216i
\(976\) 0 0
\(977\) 3.80703 15.6928i 0.121798 0.502057i −0.877932 0.478786i \(-0.841077\pi\)
0.999729 0.0232706i \(-0.00740792\pi\)
\(978\) 0 0
\(979\) 6.34905 + 1.22368i 0.202916 + 0.0391089i
\(980\) 0 0
\(981\) −6.43313 + 7.42423i −0.205394 + 0.237038i
\(982\) 0 0
\(983\) −21.8476 14.0406i −0.696832 0.447826i 0.143677 0.989625i \(-0.454107\pi\)
−0.840509 + 0.541798i \(0.817744\pi\)
\(984\) 0 0
\(985\) −7.98794 4.11807i −0.254517 0.131213i
\(986\) 0 0
\(987\) −43.1926 + 8.32468i −1.37483 + 0.264978i
\(988\) 0 0
\(989\) −26.8252 21.0956i −0.852993 0.670801i
\(990\) 0 0
\(991\) −31.7083 36.5934i −1.00725 1.16243i −0.986686 0.162638i \(-0.948000\pi\)
−0.0205629 0.999789i \(-0.506546\pi\)
\(992\) 0 0
\(993\) 3.73580 + 15.3992i 0.118552 + 0.488678i
\(994\) 0 0
\(995\) −72.7862 + 37.5239i −2.30748 + 1.18959i
\(996\) 0 0
\(997\) 44.8205 13.1605i 1.41948 0.416797i 0.520152 0.854074i \(-0.325875\pi\)
0.899327 + 0.437277i \(0.144057\pi\)
\(998\) 0 0
\(999\) 1.55931 + 0.624255i 0.0493345 + 0.0197506i
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 804.2.y.b.361.6 yes 120
67.49 even 33 inner 804.2.y.b.49.6 120
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
804.2.y.b.49.6 120 67.49 even 33 inner
804.2.y.b.361.6 yes 120 1.1 even 1 trivial