Properties

Label 735.2.b.d.146.6
Level $735$
Weight $2$
Character 735.146
Analytic conductor $5.869$
Analytic rank $0$
Dimension $8$
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] = [735,2,Mod(146,735)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(735, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("735.146");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 735.b (of order \(2\), degree \(1\), 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: \(5.86900454856\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.856615824.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 146.6
Root \(-1.07834i\) of defining polynomial
Character \(\chi\) \(=\) 735.146
Dual form 735.2.b.d.146.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.07834i q^{2} +(0.812371 + 1.52972i) q^{3} +0.837188 q^{4} -1.00000 q^{5} +(-1.64956 + 0.876010i) q^{6} +3.05945i q^{8} +(-1.68011 + 2.48541i) q^{9} +O(q^{10})\) \(q+1.07834i q^{2} +(0.812371 + 1.52972i) q^{3} +0.837188 q^{4} -1.00000 q^{5} +(-1.64956 + 0.876010i) q^{6} +3.05945i q^{8} +(-1.68011 + 2.48541i) q^{9} -1.07834i q^{10} +4.43975i q^{11} +(0.680107 + 1.28067i) q^{12} -0.955682i q^{13} +(-0.812371 - 1.52972i) q^{15} -1.62474 q^{16} +0.507522 q^{17} +(-2.68011 - 1.81172i) q^{18} -5.09347i q^{19} -0.837188 q^{20} -4.78755 q^{22} -4.29713i q^{23} +(-4.68011 + 2.48541i) q^{24} +1.00000 q^{25} +1.03055 q^{26} +(-5.16685 - 0.551027i) q^{27} +6.89526i q^{29} +(1.64956 - 0.876010i) q^{30} +5.89355i q^{31} +4.36687i q^{32} +(-6.79159 + 3.60673i) q^{33} +0.547280i q^{34} +(-1.40656 + 2.08075i) q^{36} +7.52707 q^{37} +5.49248 q^{38} +(1.46193 - 0.776369i) q^{39} -3.05945i q^{40} -4.65529 q^{41} -0.492478 q^{43} +3.71691i q^{44} +(1.68011 - 2.48541i) q^{45} +4.63376 q^{46} -6.65933 q^{47} +(-1.31989 - 2.48541i) q^{48} +1.07834i q^{50} +(0.412296 + 0.776369i) q^{51} -0.800085i q^{52} -9.13231i q^{53} +(0.594194 - 5.57161i) q^{54} -4.43975i q^{55} +(7.79159 - 4.13778i) q^{57} -7.43542 q^{58} +11.6288 q^{59} +(-0.680107 - 1.28067i) q^{60} -0.461313i q^{61} -6.35524 q^{62} -7.95845 q^{64} +0.955682i q^{65} +(-3.88927 - 7.32363i) q^{66} -3.70492 q^{67} +0.424891 q^{68} +(6.57342 - 3.49086i) q^{69} +7.90386i q^{71} +(-7.60397 - 5.14020i) q^{72} -6.31443i q^{73} +8.11672i q^{74} +(0.812371 + 1.52972i) q^{75} -4.26419i q^{76} +(0.837188 + 1.57645i) q^{78} +14.7610 q^{79} +1.62474 q^{80} +(-3.35448 - 8.35149i) q^{81} -5.01998i q^{82} +10.7916 q^{83} -0.507522 q^{85} -0.531057i q^{86} +(-10.5478 + 5.60151i) q^{87} -13.5832 q^{88} +7.15426 q^{89} +(2.68011 + 1.81172i) q^{90} -3.59750i q^{92} +(-9.01550 + 4.78775i) q^{93} -7.18101i q^{94} +5.09347i q^{95} +(-6.68011 + 3.54752i) q^{96} -6.91148i q^{97} +(-11.0346 - 7.45926i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + q^{3} - 6 q^{4} - 8 q^{5} + 5 q^{6} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + q^{3} - 6 q^{4} - 8 q^{5} + 5 q^{6} + q^{9} - 9 q^{12} - q^{15} - 2 q^{16} + 24 q^{17} - 7 q^{18} + 6 q^{20} - 40 q^{22} - 23 q^{24} + 8 q^{25} + 12 q^{26} + 4 q^{27} - 5 q^{30} + 2 q^{33} + 9 q^{36} - 14 q^{37} + 24 q^{38} - 12 q^{39} - 30 q^{41} + 16 q^{43} - q^{45} + 14 q^{46} + 12 q^{47} - 25 q^{48} - 6 q^{51} - 10 q^{54} + 6 q^{57} + 26 q^{58} + 24 q^{59} + 9 q^{60} + 24 q^{62} + 38 q^{64} - 38 q^{66} - 8 q^{67} - 13 q^{69} + q^{72} + q^{75} - 6 q^{78} + 58 q^{79} + 2 q^{80} + 13 q^{81} + 30 q^{83} - 24 q^{85} - 61 q^{87} + 4 q^{88} + 6 q^{89} + 7 q^{90} - 36 q^{93} - 39 q^{96} - 34 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

\(n\) \(346\) \(442\) \(491\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.07834i 0.762500i 0.924472 + 0.381250i \(0.124506\pi\)
−0.924472 + 0.381250i \(0.875494\pi\)
\(3\) 0.812371 + 1.52972i 0.469023 + 0.883186i
\(4\) 0.837188 0.418594
\(5\) −1.00000 −0.447214
\(6\) −1.64956 + 0.876010i −0.673429 + 0.357630i
\(7\) 0 0
\(8\) 3.05945i 1.08168i
\(9\) −1.68011 + 2.48541i −0.560036 + 0.828469i
\(10\) 1.07834i 0.341000i
\(11\) 4.43975i 1.33864i 0.742976 + 0.669318i \(0.233414\pi\)
−0.742976 + 0.669318i \(0.766586\pi\)
\(12\) 0.680107 + 1.28067i 0.196330 + 0.369696i
\(13\) 0.955682i 0.265059i −0.991179 0.132529i \(-0.957690\pi\)
0.991179 0.132529i \(-0.0423099\pi\)
\(14\) 0 0
\(15\) −0.812371 1.52972i −0.209753 0.394973i
\(16\) −1.62474 −0.406185
\(17\) 0.507522 0.123092 0.0615461 0.998104i \(-0.480397\pi\)
0.0615461 + 0.998104i \(0.480397\pi\)
\(18\) −2.68011 1.81172i −0.631707 0.427027i
\(19\) 5.09347i 1.16852i −0.811566 0.584261i \(-0.801385\pi\)
0.811566 0.584261i \(-0.198615\pi\)
\(20\) −0.837188 −0.187201
\(21\) 0 0
\(22\) −4.78755 −1.02071
\(23\) 4.29713i 0.896013i −0.894030 0.448007i \(-0.852134\pi\)
0.894030 0.448007i \(-0.147866\pi\)
\(24\) −4.68011 + 2.48541i −0.955323 + 0.507331i
\(25\) 1.00000 0.200000
\(26\) 1.03055 0.202107
\(27\) −5.16685 0.551027i −0.994361 0.106045i
\(28\) 0 0
\(29\) 6.89526i 1.28042i 0.768201 + 0.640209i \(0.221152\pi\)
−0.768201 + 0.640209i \(0.778848\pi\)
\(30\) 1.64956 0.876010i 0.301167 0.159937i
\(31\) 5.89355i 1.05851i 0.848462 + 0.529257i \(0.177529\pi\)
−0.848462 + 0.529257i \(0.822471\pi\)
\(32\) 4.36687i 0.771961i
\(33\) −6.79159 + 3.60673i −1.18226 + 0.627851i
\(34\) 0.547280i 0.0938578i
\(35\) 0 0
\(36\) −1.40656 + 2.08075i −0.234427 + 0.346792i
\(37\) 7.52707 1.23744 0.618721 0.785611i \(-0.287651\pi\)
0.618721 + 0.785611i \(0.287651\pi\)
\(38\) 5.49248 0.890998
\(39\) 1.46193 0.776369i 0.234096 0.124318i
\(40\) 3.05945i 0.483741i
\(41\) −4.65529 −0.727034 −0.363517 0.931588i \(-0.618424\pi\)
−0.363517 + 0.931588i \(0.618424\pi\)
\(42\) 0 0
\(43\) −0.492478 −0.0751022 −0.0375511 0.999295i \(-0.511956\pi\)
−0.0375511 + 0.999295i \(0.511956\pi\)
\(44\) 3.71691i 0.560345i
\(45\) 1.68011 2.48541i 0.250456 0.370502i
\(46\) 4.63376 0.683210
\(47\) −6.65933 −0.971363 −0.485682 0.874136i \(-0.661429\pi\)
−0.485682 + 0.874136i \(0.661429\pi\)
\(48\) −1.31989 2.48541i −0.190510 0.358737i
\(49\) 0 0
\(50\) 1.07834i 0.152500i
\(51\) 0.412296 + 0.776369i 0.0577330 + 0.108713i
\(52\) 0.800085i 0.110952i
\(53\) 9.13231i 1.25442i −0.778850 0.627210i \(-0.784197\pi\)
0.778850 0.627210i \(-0.215803\pi\)
\(54\) 0.594194 5.57161i 0.0808595 0.758200i
\(55\) 4.43975i 0.598656i
\(56\) 0 0
\(57\) 7.79159 4.13778i 1.03202 0.548063i
\(58\) −7.43542 −0.976319
\(59\) 11.6288 1.51394 0.756969 0.653450i \(-0.226679\pi\)
0.756969 + 0.653450i \(0.226679\pi\)
\(60\) −0.680107 1.28067i −0.0878014 0.165333i
\(61\) 0.461313i 0.0590651i −0.999564 0.0295326i \(-0.990598\pi\)
0.999564 0.0295326i \(-0.00940187\pi\)
\(62\) −6.35524 −0.807116
\(63\) 0 0
\(64\) −7.95845 −0.994806
\(65\) 0.955682i 0.118538i
\(66\) −3.88927 7.32363i −0.478736 0.901477i
\(67\) −3.70492 −0.452628 −0.226314 0.974054i \(-0.572668\pi\)
−0.226314 + 0.974054i \(0.572668\pi\)
\(68\) 0.424891 0.0515256
\(69\) 6.57342 3.49086i 0.791346 0.420250i
\(70\) 0 0
\(71\) 7.90386i 0.938015i 0.883194 + 0.469008i \(0.155388\pi\)
−0.883194 + 0.469008i \(0.844612\pi\)
\(72\) −7.60397 5.14020i −0.896136 0.605778i
\(73\) 6.31443i 0.739048i −0.929221 0.369524i \(-0.879521\pi\)
0.929221 0.369524i \(-0.120479\pi\)
\(74\) 8.11672i 0.943550i
\(75\) 0.812371 + 1.52972i 0.0938045 + 0.176637i
\(76\) 4.26419i 0.489136i
\(77\) 0 0
\(78\) 0.837188 + 1.57645i 0.0947928 + 0.178498i
\(79\) 14.7610 1.66075 0.830374 0.557207i \(-0.188127\pi\)
0.830374 + 0.557207i \(0.188127\pi\)
\(80\) 1.62474 0.181652
\(81\) −3.35448 8.35149i −0.372720 0.927944i
\(82\) 5.01998i 0.554364i
\(83\) 10.7916 1.18453 0.592266 0.805743i \(-0.298234\pi\)
0.592266 + 0.805743i \(0.298234\pi\)
\(84\) 0 0
\(85\) −0.507522 −0.0550485
\(86\) 0.531057i 0.0572654i
\(87\) −10.5478 + 5.60151i −1.13085 + 0.600545i
\(88\) −13.5832 −1.44797
\(89\) 7.15426 0.758350 0.379175 0.925325i \(-0.376208\pi\)
0.379175 + 0.925325i \(0.376208\pi\)
\(90\) 2.68011 + 1.81172i 0.282508 + 0.190972i
\(91\) 0 0
\(92\) 3.59750i 0.375066i
\(93\) −9.01550 + 4.78775i −0.934864 + 0.496467i
\(94\) 7.18101i 0.740664i
\(95\) 5.09347i 0.522579i
\(96\) −6.68011 + 3.54752i −0.681786 + 0.362067i
\(97\) 6.91148i 0.701755i −0.936421 0.350877i \(-0.885883\pi\)
0.936421 0.350877i \(-0.114117\pi\)
\(98\) 0 0
\(99\) −11.0346 7.45926i −1.10902 0.749684i
\(100\) 0.837188 0.0837188
\(101\) −2.39076 −0.237890 −0.118945 0.992901i \(-0.537951\pi\)
−0.118945 + 0.992901i \(0.537951\pi\)
\(102\) −0.837188 + 0.444595i −0.0828939 + 0.0440214i
\(103\) 14.9622i 1.47427i 0.675745 + 0.737135i \(0.263822\pi\)
−0.675745 + 0.737135i \(0.736178\pi\)
\(104\) 2.92386 0.286708
\(105\) 0 0
\(106\) 9.84772 0.956495
\(107\) 13.5614i 1.31103i −0.755181 0.655517i \(-0.772451\pi\)
0.755181 0.655517i \(-0.227549\pi\)
\(108\) −4.32562 0.461313i −0.416233 0.0443899i
\(109\) 16.1213 1.54414 0.772068 0.635540i \(-0.219222\pi\)
0.772068 + 0.635540i \(0.219222\pi\)
\(110\) 4.78755 0.456475
\(111\) 6.11477 + 11.5143i 0.580388 + 1.09289i
\(112\) 0 0
\(113\) 5.05678i 0.475702i −0.971302 0.237851i \(-0.923557\pi\)
0.971302 0.237851i \(-0.0764429\pi\)
\(114\) 4.46193 + 8.40197i 0.417898 + 0.786917i
\(115\) 4.29713i 0.400709i
\(116\) 5.77263i 0.535975i
\(117\) 2.37526 + 1.60565i 0.219593 + 0.148442i
\(118\) 12.5398i 1.15438i
\(119\) 0 0
\(120\) 4.68011 2.48541i 0.427233 0.226885i
\(121\) −8.71141 −0.791947
\(122\) 0.497451 0.0450371
\(123\) −3.78182 7.12131i −0.340995 0.642107i
\(124\) 4.93401i 0.443087i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 8.05009 0.714330 0.357165 0.934041i \(-0.383743\pi\)
0.357165 + 0.934041i \(0.383743\pi\)
\(128\) 0.151850i 0.0134218i
\(129\) −0.400075 0.753355i −0.0352246 0.0663292i
\(130\) −1.03055 −0.0903851
\(131\) 2.09927 0.183414 0.0917069 0.995786i \(-0.470768\pi\)
0.0917069 + 0.995786i \(0.470768\pi\)
\(132\) −5.68584 + 3.01951i −0.494889 + 0.262814i
\(133\) 0 0
\(134\) 3.99516i 0.345129i
\(135\) 5.16685 + 0.551027i 0.444692 + 0.0474249i
\(136\) 1.55274i 0.133146i
\(137\) 4.94709i 0.422659i −0.977415 0.211329i \(-0.932221\pi\)
0.977415 0.211329i \(-0.0677793\pi\)
\(138\) 3.76433 + 7.08836i 0.320441 + 0.603402i
\(139\) 10.7217i 0.909406i 0.890643 + 0.454703i \(0.150255\pi\)
−0.890643 + 0.454703i \(0.849745\pi\)
\(140\) 0 0
\(141\) −5.40985 10.1869i −0.455591 0.857895i
\(142\) −8.52303 −0.715236
\(143\) 4.24299 0.354817
\(144\) 2.72974 4.03814i 0.227478 0.336512i
\(145\) 6.89526i 0.572620i
\(146\) 6.80909 0.563524
\(147\) 0 0
\(148\) 6.30157 0.517986
\(149\) 5.26356i 0.431207i 0.976481 + 0.215604i \(0.0691719\pi\)
−0.976481 + 0.215604i \(0.930828\pi\)
\(150\) −1.64956 + 0.876010i −0.134686 + 0.0715259i
\(151\) −7.00901 −0.570385 −0.285193 0.958470i \(-0.592058\pi\)
−0.285193 + 0.958470i \(0.592058\pi\)
\(152\) 15.5832 1.26396
\(153\) −0.852692 + 1.26140i −0.0689360 + 0.101978i
\(154\) 0 0
\(155\) 5.89355i 0.473381i
\(156\) 1.22391 0.649966i 0.0979912 0.0520389i
\(157\) 2.90010i 0.231453i 0.993281 + 0.115727i \(0.0369197\pi\)
−0.993281 + 0.115727i \(0.963080\pi\)
\(158\) 15.9174i 1.26632i
\(159\) 13.9699 7.41883i 1.10789 0.588351i
\(160\) 4.36687i 0.345232i
\(161\) 0 0
\(162\) 9.00573 3.61726i 0.707557 0.284199i
\(163\) −12.7586 −0.999330 −0.499665 0.866219i \(-0.666544\pi\)
−0.499665 + 0.866219i \(0.666544\pi\)
\(164\) −3.89735 −0.304332
\(165\) 6.79159 3.60673i 0.528725 0.280783i
\(166\) 11.6370i 0.903205i
\(167\) 15.7766 1.22083 0.610413 0.792083i \(-0.291003\pi\)
0.610413 + 0.792083i \(0.291003\pi\)
\(168\) 0 0
\(169\) 12.0867 0.929744
\(170\) 0.547280i 0.0419745i
\(171\) 12.6593 + 8.55757i 0.968083 + 0.654414i
\(172\) −0.412296 −0.0314373
\(173\) −10.1733 −0.773465 −0.386732 0.922192i \(-0.626396\pi\)
−0.386732 + 0.922192i \(0.626396\pi\)
\(174\) −6.04032 11.3741i −0.457916 0.862271i
\(175\) 0 0
\(176\) 7.21345i 0.543735i
\(177\) 9.44689 + 17.7888i 0.710071 + 1.33709i
\(178\) 7.71471i 0.578242i
\(179\) 5.26215i 0.393312i −0.980473 0.196656i \(-0.936992\pi\)
0.980473 0.196656i \(-0.0630081\pi\)
\(180\) 1.40656 2.08075i 0.104839 0.155090i
\(181\) 9.71314i 0.721972i 0.932571 + 0.360986i \(0.117560\pi\)
−0.932571 + 0.360986i \(0.882440\pi\)
\(182\) 0 0
\(183\) 0.705682 0.374757i 0.0521655 0.0277029i
\(184\) 13.1468 0.969198
\(185\) −7.52707 −0.553401
\(186\) −5.16281 9.72176i −0.378556 0.712834i
\(187\) 2.25327i 0.164776i
\(188\) −5.57511 −0.406607
\(189\) 0 0
\(190\) −5.49248 −0.398466
\(191\) 9.59049i 0.693943i −0.937876 0.346972i \(-0.887210\pi\)
0.937876 0.346972i \(-0.112790\pi\)
\(192\) −6.46521 12.1742i −0.466586 0.878599i
\(193\) 8.35166 0.601166 0.300583 0.953756i \(-0.402819\pi\)
0.300583 + 0.953756i \(0.402819\pi\)
\(194\) 7.45292 0.535088
\(195\) −1.46193 + 0.776369i −0.104691 + 0.0555969i
\(196\) 0 0
\(197\) 1.77574i 0.126516i 0.997997 + 0.0632580i \(0.0201491\pi\)
−0.997997 + 0.0632580i \(0.979851\pi\)
\(198\) 8.04360 11.8990i 0.571634 0.845626i
\(199\) 3.75858i 0.266438i −0.991087 0.133219i \(-0.957469\pi\)
0.991087 0.133219i \(-0.0425314\pi\)
\(200\) 3.05945i 0.216336i
\(201\) −3.00977 5.66751i −0.212293 0.399755i
\(202\) 2.57805i 0.181391i
\(203\) 0 0
\(204\) 0.345169 + 0.649966i 0.0241667 + 0.0455067i
\(205\) 4.65529 0.325140
\(206\) −16.1343 −1.12413
\(207\) 10.6801 + 7.21963i 0.742319 + 0.501799i
\(208\) 1.55274i 0.107663i
\(209\) 22.6137 1.56422
\(210\) 0 0
\(211\) −9.12126 −0.627933 −0.313967 0.949434i \(-0.601658\pi\)
−0.313967 + 0.949434i \(0.601658\pi\)
\(212\) 7.64546i 0.525092i
\(213\) −12.0907 + 6.42086i −0.828442 + 0.439950i
\(214\) 14.6238 0.999663
\(215\) 0.492478 0.0335867
\(216\) 1.68584 15.8077i 0.114707 1.07558i
\(217\) 0 0
\(218\) 17.3842i 1.17740i
\(219\) 9.65933 5.12966i 0.652717 0.346630i
\(220\) 3.71691i 0.250594i
\(221\) 0.485030i 0.0326266i
\(222\) −12.4163 + 6.59379i −0.833330 + 0.442546i
\(223\) 11.7397i 0.786146i 0.919507 + 0.393073i \(0.128588\pi\)
−0.919507 + 0.393073i \(0.871412\pi\)
\(224\) 0 0
\(225\) −1.68011 + 2.48541i −0.112007 + 0.165694i
\(226\) 5.45292 0.362723
\(227\) 24.2210 1.60760 0.803802 0.594897i \(-0.202807\pi\)
0.803802 + 0.594897i \(0.202807\pi\)
\(228\) 6.52303 3.46410i 0.431998 0.229416i
\(229\) 21.7088i 1.43456i −0.696788 0.717278i \(-0.745388\pi\)
0.696788 0.717278i \(-0.254612\pi\)
\(230\) −4.63376 −0.305541
\(231\) 0 0
\(232\) −21.0957 −1.38500
\(233\) 10.9962i 0.720388i −0.932877 0.360194i \(-0.882711\pi\)
0.932877 0.360194i \(-0.117289\pi\)
\(234\) −1.73143 + 2.56133i −0.113187 + 0.167439i
\(235\) 6.65933 0.434407
\(236\) 9.73547 0.633725
\(237\) 11.9914 + 22.5803i 0.778928 + 1.46675i
\(238\) 0 0
\(239\) 9.02649i 0.583875i −0.956437 0.291938i \(-0.905700\pi\)
0.956437 0.291938i \(-0.0942999\pi\)
\(240\) 1.31989 + 2.48541i 0.0851987 + 0.160432i
\(241\) 5.08099i 0.327295i −0.986519 0.163648i \(-0.947674\pi\)
0.986519 0.163648i \(-0.0523260\pi\)
\(242\) 9.39385i 0.603859i
\(243\) 10.0504 11.9159i 0.644733 0.764408i
\(244\) 0.386206i 0.0247243i
\(245\) 0 0
\(246\) 7.67917 4.07808i 0.489606 0.260009i
\(247\) −4.86774 −0.309727
\(248\) −18.0310 −1.14497
\(249\) 8.76678 + 16.5082i 0.555572 + 1.04616i
\(250\) 1.07834i 0.0682001i
\(251\) −18.6748 −1.17875 −0.589373 0.807861i \(-0.700625\pi\)
−0.589373 + 0.807861i \(0.700625\pi\)
\(252\) 0 0
\(253\) 19.0782 1.19944
\(254\) 8.68072i 0.544677i
\(255\) −0.412296 0.776369i −0.0258190 0.0486181i
\(256\) −16.0806 −1.00504
\(257\) −12.0826 −0.753694 −0.376847 0.926276i \(-0.622992\pi\)
−0.376847 + 0.926276i \(0.622992\pi\)
\(258\) 0.812371 0.431416i 0.0505760 0.0268588i
\(259\) 0 0
\(260\) 0.800085i 0.0496192i
\(261\) −17.1375 11.5848i −1.06079 0.717080i
\(262\) 2.26372i 0.139853i
\(263\) 12.8878i 0.794693i −0.917669 0.397346i \(-0.869931\pi\)
0.917669 0.397346i \(-0.130069\pi\)
\(264\) −11.0346 20.7785i −0.679132 1.27883i
\(265\) 9.13231i 0.560993i
\(266\) 0 0
\(267\) 5.81191 + 10.9440i 0.355683 + 0.669764i
\(268\) −3.10172 −0.189467
\(269\) −0.466444 −0.0284396 −0.0142198 0.999899i \(-0.504526\pi\)
−0.0142198 + 0.999899i \(0.504526\pi\)
\(270\) −0.594194 + 5.57161i −0.0361615 + 0.339078i
\(271\) 23.2907i 1.41481i 0.706809 + 0.707404i \(0.250134\pi\)
−0.706809 + 0.707404i \(0.749866\pi\)
\(272\) −0.824593 −0.0499983
\(273\) 0 0
\(274\) 5.33464 0.322277
\(275\) 4.43975i 0.267727i
\(276\) 5.50318 2.92251i 0.331253 0.175914i
\(277\) −13.8909 −0.834621 −0.417310 0.908764i \(-0.637027\pi\)
−0.417310 + 0.908764i \(0.637027\pi\)
\(278\) −11.5617 −0.693422
\(279\) −14.6479 9.90180i −0.876945 0.592805i
\(280\) 0 0
\(281\) 6.85483i 0.408925i 0.978874 + 0.204462i \(0.0655446\pi\)
−0.978874 + 0.204462i \(0.934455\pi\)
\(282\) 10.9850 5.83364i 0.654145 0.347388i
\(283\) 4.43650i 0.263723i 0.991268 + 0.131861i \(0.0420954\pi\)
−0.991268 + 0.131861i \(0.957905\pi\)
\(284\) 6.61701i 0.392647i
\(285\) −7.79159 + 4.13778i −0.461534 + 0.245101i
\(286\) 4.57538i 0.270548i
\(287\) 0 0
\(288\) −10.8534 7.33681i −0.639546 0.432326i
\(289\) −16.7424 −0.984848
\(290\) 7.43542 0.436623
\(291\) 10.5727 5.61469i 0.619780 0.329139i
\(292\) 5.28636i 0.309361i
\(293\) −30.0822 −1.75742 −0.878709 0.477357i \(-0.841595\pi\)
−0.878709 + 0.477357i \(0.841595\pi\)
\(294\) 0 0
\(295\) −11.6288 −0.677054
\(296\) 23.0287i 1.33851i
\(297\) 2.44643 22.9396i 0.141956 1.33109i
\(298\) −5.67589 −0.328796
\(299\) −4.10669 −0.237496
\(300\) 0.680107 + 1.28067i 0.0392660 + 0.0739392i
\(301\) 0 0
\(302\) 7.55808i 0.434919i
\(303\) −1.94219 3.65720i −0.111576 0.210101i
\(304\) 8.27557i 0.474636i
\(305\) 0.461313i 0.0264147i
\(306\) −1.36021 0.919490i −0.0777582 0.0525637i
\(307\) 32.8300i 1.87371i −0.349722 0.936853i \(-0.613724\pi\)
0.349722 0.936853i \(-0.386276\pi\)
\(308\) 0 0
\(309\) −22.8880 + 12.1549i −1.30206 + 0.691466i
\(310\) 6.35524 0.360953
\(311\) 16.4615 0.933444 0.466722 0.884404i \(-0.345435\pi\)
0.466722 + 0.884404i \(0.345435\pi\)
\(312\) 2.37526 + 4.47270i 0.134473 + 0.253217i
\(313\) 4.60844i 0.260484i 0.991482 + 0.130242i \(0.0415755\pi\)
−0.991482 + 0.130242i \(0.958425\pi\)
\(314\) −3.12729 −0.176483
\(315\) 0 0
\(316\) 12.3578 0.695179
\(317\) 29.4302i 1.65296i 0.562964 + 0.826481i \(0.309661\pi\)
−0.562964 + 0.826481i \(0.690339\pi\)
\(318\) 8.00000 + 15.0643i 0.448618 + 0.844763i
\(319\) −30.6133 −1.71401
\(320\) 7.95845 0.444891
\(321\) 20.7452 11.0169i 1.15789 0.614904i
\(322\) 0 0
\(323\) 2.58505i 0.143836i
\(324\) −2.80833 6.99177i −0.156018 0.388431i
\(325\) 0.955682i 0.0530117i
\(326\) 13.7581i 0.761989i
\(327\) 13.0964 + 24.6611i 0.724235 + 1.36376i
\(328\) 14.2426i 0.786417i
\(329\) 0 0
\(330\) 3.88927 + 7.32363i 0.214097 + 0.403153i
\(331\) 2.65575 0.145973 0.0729866 0.997333i \(-0.476747\pi\)
0.0729866 + 0.997333i \(0.476747\pi\)
\(332\) 9.03459 0.495837
\(333\) −12.6463 + 18.7078i −0.693012 + 1.02518i
\(334\) 17.0125i 0.930880i
\(335\) 3.70492 0.202422
\(336\) 0 0
\(337\) −21.4599 −1.16900 −0.584499 0.811395i \(-0.698709\pi\)
−0.584499 + 0.811395i \(0.698709\pi\)
\(338\) 13.0335i 0.708930i
\(339\) 7.73547 4.10798i 0.420133 0.223115i
\(340\) −0.424891 −0.0230430
\(341\) −26.1659 −1.41696
\(342\) −9.22795 + 13.6510i −0.498990 + 0.738163i
\(343\) 0 0
\(344\) 1.50671i 0.0812363i
\(345\) −6.57342 + 3.49086i −0.353901 + 0.187942i
\(346\) 10.9703i 0.589767i
\(347\) 18.1637i 0.975077i −0.873102 0.487538i \(-0.837895\pi\)
0.873102 0.487538i \(-0.162105\pi\)
\(348\) −8.83052 + 4.68951i −0.473366 + 0.251384i
\(349\) 13.1543i 0.704135i −0.935975 0.352067i \(-0.885479\pi\)
0.935975 0.352067i \(-0.114521\pi\)
\(350\) 0 0
\(351\) −0.526607 + 4.93787i −0.0281082 + 0.263564i
\(352\) −19.3878 −1.03338
\(353\) −10.2941 −0.547902 −0.273951 0.961744i \(-0.588331\pi\)
−0.273951 + 0.961744i \(0.588331\pi\)
\(354\) −19.1824 + 10.1869i −1.01953 + 0.541429i
\(355\) 7.90386i 0.419493i
\(356\) 5.98946 0.317441
\(357\) 0 0
\(358\) 5.67438 0.299900
\(359\) 11.8002i 0.622790i −0.950281 0.311395i \(-0.899204\pi\)
0.950281 0.311395i \(-0.100796\pi\)
\(360\) 7.60397 + 5.14020i 0.400764 + 0.270912i
\(361\) −6.94340 −0.365442
\(362\) −10.4741 −0.550504
\(363\) −7.07690 13.3261i −0.371441 0.699436i
\(364\) 0 0
\(365\) 6.31443i 0.330512i
\(366\) 0.404115 + 0.760963i 0.0211234 + 0.0397762i
\(367\) 15.9739i 0.833833i 0.908945 + 0.416916i \(0.136889\pi\)
−0.908945 + 0.416916i \(0.863111\pi\)
\(368\) 6.98172i 0.363948i
\(369\) 7.82139 11.5703i 0.407165 0.602325i
\(370\) 8.11672i 0.421968i
\(371\) 0 0
\(372\) −7.54767 + 4.00825i −0.391328 + 0.207818i
\(373\) 5.31669 0.275288 0.137644 0.990482i \(-0.456047\pi\)
0.137644 + 0.990482i \(0.456047\pi\)
\(374\) −2.42979 −0.125641
\(375\) −0.812371 1.52972i −0.0419507 0.0789946i
\(376\) 20.3739i 1.05070i
\(377\) 6.58968 0.339386
\(378\) 0 0
\(379\) 24.0427 1.23499 0.617494 0.786575i \(-0.288148\pi\)
0.617494 + 0.786575i \(0.288148\pi\)
\(380\) 4.26419i 0.218748i
\(381\) 6.53966 + 12.3144i 0.335037 + 0.630887i
\(382\) 10.3418 0.529132
\(383\) 18.8011 0.960690 0.480345 0.877080i \(-0.340512\pi\)
0.480345 + 0.877080i \(0.340512\pi\)
\(384\) −0.232289 + 0.123359i −0.0118539 + 0.00629512i
\(385\) 0 0
\(386\) 9.00591i 0.458389i
\(387\) 0.827415 1.22401i 0.0420599 0.0622198i
\(388\) 5.78621i 0.293750i
\(389\) 12.2172i 0.619437i −0.950828 0.309718i \(-0.899765\pi\)
0.950828 0.309718i \(-0.100235\pi\)
\(390\) −0.837188 1.57645i −0.0423926 0.0798268i
\(391\) 2.18089i 0.110292i
\(392\) 0 0
\(393\) 1.70538 + 3.21130i 0.0860252 + 0.161988i
\(394\) −1.91484 −0.0964685
\(395\) −14.7610 −0.742709
\(396\) −9.23802 6.24480i −0.464228 0.313813i
\(397\) 18.7651i 0.941792i −0.882189 0.470896i \(-0.843931\pi\)
0.882189 0.470896i \(-0.156069\pi\)
\(398\) 4.05302 0.203159
\(399\) 0 0
\(400\) −1.62474 −0.0812371
\(401\) 23.9973i 1.19837i −0.800611 0.599184i \(-0.795492\pi\)
0.800611 0.599184i \(-0.204508\pi\)
\(402\) 6.11149 3.24555i 0.304813 0.161873i
\(403\) 5.63236 0.280568
\(404\) −2.00152 −0.0995792
\(405\) 3.35448 + 8.35149i 0.166686 + 0.414989i
\(406\) 0 0
\(407\) 33.4183i 1.65648i
\(408\) −2.37526 + 1.26140i −0.117593 + 0.0624485i
\(409\) 17.0828i 0.844690i −0.906435 0.422345i \(-0.861207\pi\)
0.906435 0.422345i \(-0.138793\pi\)
\(410\) 5.01998i 0.247919i
\(411\) 7.56769 4.01888i 0.373286 0.198237i
\(412\) 12.5262i 0.617120i
\(413\) 0 0
\(414\) −7.78521 + 11.5168i −0.382622 + 0.566018i
\(415\) −10.7916 −0.529739
\(416\) 4.17334 0.204615
\(417\) −16.4013 + 8.71003i −0.803175 + 0.426532i
\(418\) 24.3852i 1.19272i
\(419\) −39.6524 −1.93714 −0.968572 0.248732i \(-0.919986\pi\)
−0.968572 + 0.248732i \(0.919986\pi\)
\(420\) 0 0
\(421\) −34.1423 −1.66399 −0.831997 0.554779i \(-0.812803\pi\)
−0.831997 + 0.554779i \(0.812803\pi\)
\(422\) 9.83580i 0.478799i
\(423\) 11.1884 16.5511i 0.543998 0.804744i
\(424\) 27.9398 1.35688
\(425\) 0.507522 0.0246184
\(426\) −6.92386 13.0379i −0.335462 0.631687i
\(427\) 0 0
\(428\) 11.3535i 0.548790i
\(429\) 3.44689 + 6.49061i 0.166417 + 0.313369i
\(430\) 0.531057i 0.0256099i
\(431\) 25.7708i 1.24134i 0.784073 + 0.620668i \(0.213139\pi\)
−0.784073 + 0.620668i \(0.786861\pi\)
\(432\) 8.39480 + 0.895277i 0.403895 + 0.0430740i
\(433\) 11.9120i 0.572454i 0.958162 + 0.286227i \(0.0924011\pi\)
−0.958162 + 0.286227i \(0.907599\pi\)
\(434\) 0 0
\(435\) 10.5478 5.60151i 0.505730 0.268572i
\(436\) 13.4965 0.646366
\(437\) −21.8873 −1.04701
\(438\) 5.53151 + 10.4160i 0.264306 + 0.497697i
\(439\) 16.7732i 0.800542i 0.916397 + 0.400271i \(0.131084\pi\)
−0.916397 + 0.400271i \(0.868916\pi\)
\(440\) 13.5832 0.647553
\(441\) 0 0
\(442\) 0.523026 0.0248778
\(443\) 2.39590i 0.113833i −0.998379 0.0569163i \(-0.981873\pi\)
0.998379 0.0569163i \(-0.0181268\pi\)
\(444\) 5.11921 + 9.63965i 0.242947 + 0.457478i
\(445\) −7.15426 −0.339144
\(446\) −12.6593 −0.599437
\(447\) −8.05178 + 4.27596i −0.380836 + 0.202246i
\(448\) 0 0
\(449\) 25.4692i 1.20196i −0.799262 0.600982i \(-0.794776\pi\)
0.799262 0.600982i \(-0.205224\pi\)
\(450\) −2.68011 1.81172i −0.126341 0.0854054i
\(451\) 20.6683i 0.973234i
\(452\) 4.23347i 0.199126i
\(453\) −5.69392 10.7219i −0.267524 0.503757i
\(454\) 26.1184i 1.22580i
\(455\) 0 0
\(456\) 12.6593 + 23.8380i 0.592827 + 1.11632i
\(457\) −3.44191 −0.161006 −0.0805029 0.996754i \(-0.525653\pi\)
−0.0805029 + 0.996754i \(0.525653\pi\)
\(458\) 23.4094 1.09385
\(459\) −2.62229 0.279659i −0.122398 0.0130533i
\(460\) 3.59750i 0.167734i
\(461\) −13.5376 −0.630509 −0.315254 0.949007i \(-0.602090\pi\)
−0.315254 + 0.949007i \(0.602090\pi\)
\(462\) 0 0
\(463\) −5.13770 −0.238769 −0.119385 0.992848i \(-0.538092\pi\)
−0.119385 + 0.992848i \(0.538092\pi\)
\(464\) 11.2030i 0.520087i
\(465\) 9.01550 4.78775i 0.418084 0.222027i
\(466\) 11.8577 0.549296
\(467\) −9.21788 −0.426553 −0.213276 0.976992i \(-0.568413\pi\)
−0.213276 + 0.976992i \(0.568413\pi\)
\(468\) 1.98854 + 1.34423i 0.0919201 + 0.0621370i
\(469\) 0 0
\(470\) 7.18101i 0.331235i
\(471\) −4.43635 + 2.35596i −0.204416 + 0.108557i
\(472\) 35.5776i 1.63759i
\(473\) 2.18648i 0.100534i
\(474\) −24.3492 + 12.9308i −1.11840 + 0.593933i
\(475\) 5.09347i 0.233704i
\(476\) 0 0
\(477\) 22.6975 + 15.3433i 1.03925 + 0.702520i
\(478\) 9.73361 0.445205
\(479\) −20.6373 −0.942943 −0.471472 0.881881i \(-0.656277\pi\)
−0.471472 + 0.881881i \(0.656277\pi\)
\(480\) 6.68011 3.54752i 0.304904 0.161921i
\(481\) 7.19348i 0.327995i
\(482\) 5.47902 0.249563
\(483\) 0 0
\(484\) −7.29309 −0.331504
\(485\) 6.91148i 0.313834i
\(486\) 12.8494 + 10.8377i 0.582861 + 0.491609i
\(487\) 2.47498 0.112152 0.0560761 0.998426i \(-0.482141\pi\)
0.0560761 + 0.998426i \(0.482141\pi\)
\(488\) 1.41136 0.0638894
\(489\) −10.3647 19.5171i −0.468709 0.882595i
\(490\) 0 0
\(491\) 21.2827i 0.960476i −0.877138 0.480238i \(-0.840550\pi\)
0.877138 0.480238i \(-0.159450\pi\)
\(492\) −3.16609 5.96187i −0.142739 0.268782i
\(493\) 3.49950i 0.157609i
\(494\) 5.24906i 0.236167i
\(495\) 11.0346 + 7.45926i 0.495968 + 0.335269i
\(496\) 9.57550i 0.429953i
\(497\) 0 0
\(498\) −17.8014 + 9.45355i −0.797698 + 0.423624i
\(499\) 32.7379 1.46555 0.732775 0.680471i \(-0.238225\pi\)
0.732775 + 0.680471i \(0.238225\pi\)
\(500\) −0.837188 −0.0374402
\(501\) 12.8164 + 24.1338i 0.572595 + 1.07822i
\(502\) 20.1378i 0.898793i
\(503\) 0.675693 0.0301277 0.0150638 0.999887i \(-0.495205\pi\)
0.0150638 + 0.999887i \(0.495205\pi\)
\(504\) 0 0
\(505\) 2.39076 0.106388
\(506\) 20.5727i 0.914570i
\(507\) 9.81886 + 18.4893i 0.436071 + 0.821137i
\(508\) 6.73944 0.299014
\(509\) −33.1038 −1.46730 −0.733649 0.679528i \(-0.762184\pi\)
−0.733649 + 0.679528i \(0.762184\pi\)
\(510\) 0.837188 0.444595i 0.0370713 0.0196870i
\(511\) 0 0
\(512\) 17.0367i 0.752921i
\(513\) −2.80664 + 26.3172i −0.123916 + 1.16193i
\(514\) 13.0292i 0.574692i
\(515\) 14.9622i 0.659314i
\(516\) −0.334938 0.630699i −0.0147448 0.0277650i
\(517\) 29.5658i 1.30030i
\(518\) 0 0
\(519\) −8.26453 15.5624i −0.362773 0.683114i
\(520\) −2.92386 −0.128220
\(521\) −42.9449 −1.88145 −0.940726 0.339169i \(-0.889854\pi\)
−0.940726 + 0.339169i \(0.889854\pi\)
\(522\) 12.4923 18.4800i 0.546773 0.808849i
\(523\) 38.1919i 1.67001i −0.550239 0.835007i \(-0.685463\pi\)
0.550239 0.835007i \(-0.314537\pi\)
\(524\) 1.75748 0.0767759
\(525\) 0 0
\(526\) 13.8974 0.605953
\(527\) 2.99111i 0.130295i
\(528\) 11.0346 5.86000i 0.480219 0.255024i
\(529\) 4.53469 0.197160
\(530\) −9.84772 −0.427758
\(531\) −19.5376 + 28.9022i −0.847859 + 1.25425i
\(532\) 0 0
\(533\) 4.44898i 0.192707i
\(534\) −11.8014 + 6.26720i −0.510695 + 0.271208i
\(535\) 13.5614i 0.586312i
\(536\) 11.3350i 0.489598i
\(537\) 8.04963 4.27482i 0.347367 0.184472i
\(538\) 0.502984i 0.0216852i
\(539\) 0 0
\(540\) 4.32562 + 0.461313i 0.186145 + 0.0198518i
\(541\) −0.409847 −0.0176207 −0.00881035 0.999961i \(-0.502804\pi\)
−0.00881035 + 0.999961i \(0.502804\pi\)
\(542\) −25.1152 −1.07879
\(543\) −14.8584 + 7.89068i −0.637636 + 0.338621i
\(544\) 2.21628i 0.0950224i
\(545\) −16.1213 −0.690559
\(546\) 0 0
\(547\) −10.9605 −0.468638 −0.234319 0.972160i \(-0.575286\pi\)
−0.234319 + 0.972160i \(0.575286\pi\)
\(548\) 4.14165i 0.176922i
\(549\) 1.14655 + 0.775055i 0.0489336 + 0.0330786i
\(550\) −4.78755 −0.204142
\(551\) 35.1208 1.49620
\(552\) 10.6801 + 20.1110i 0.454576 + 0.855982i
\(553\) 0 0
\(554\) 14.9790i 0.636398i
\(555\) −6.11477 11.5143i −0.259558 0.488756i
\(556\) 8.97611i 0.380672i
\(557\) 6.01934i 0.255048i 0.991835 + 0.127524i \(0.0407030\pi\)
−0.991835 + 0.127524i \(0.959297\pi\)
\(558\) 10.6775 15.7953i 0.452014 0.668670i
\(559\) 0.470652i 0.0199065i
\(560\) 0 0
\(561\) −3.44689 + 1.83049i −0.145528 + 0.0772835i
\(562\) −7.39182 −0.311805
\(563\) −14.8693 −0.626667 −0.313334 0.949643i \(-0.601446\pi\)
−0.313334 + 0.949643i \(0.601446\pi\)
\(564\) −4.52906 8.52837i −0.190708 0.359109i
\(565\) 5.05678i 0.212740i
\(566\) −4.78405 −0.201089
\(567\) 0 0
\(568\) −24.1814 −1.01463
\(569\) 5.26405i 0.220681i −0.993894 0.110340i \(-0.964806\pi\)
0.993894 0.110340i \(-0.0351941\pi\)
\(570\) −4.46193 8.40197i −0.186890 0.351920i
\(571\) 45.7550 1.91479 0.957394 0.288786i \(-0.0932517\pi\)
0.957394 + 0.288786i \(0.0932517\pi\)
\(572\) 3.55218 0.148524
\(573\) 14.6708 7.79103i 0.612881 0.325475i
\(574\) 0 0
\(575\) 4.29713i 0.179203i
\(576\) 13.3710 19.7800i 0.557127 0.824165i
\(577\) 5.03122i 0.209452i −0.994501 0.104726i \(-0.966603\pi\)
0.994501 0.104726i \(-0.0333966\pi\)
\(578\) 18.0540i 0.750947i
\(579\) 6.78465 + 12.7757i 0.281960 + 0.530941i
\(580\) 5.77263i 0.239695i
\(581\) 0 0
\(582\) 6.05453 + 11.4009i 0.250968 + 0.472582i
\(583\) 40.5452 1.67921
\(584\) 19.3187 0.799412
\(585\) −2.37526 1.60565i −0.0982048 0.0663854i
\(586\) 32.4387i 1.34003i
\(587\) 18.5075 0.763887 0.381944 0.924186i \(-0.375255\pi\)
0.381944 + 0.924186i \(0.375255\pi\)
\(588\) 0 0
\(589\) 30.0186 1.23690
\(590\) 12.5398i 0.516254i
\(591\) −2.71639 + 1.44256i −0.111737 + 0.0593389i
\(592\) −12.2295 −0.502631
\(593\) −18.5385 −0.761286 −0.380643 0.924722i \(-0.624297\pi\)
−0.380643 + 0.924722i \(0.624297\pi\)
\(594\) 24.7366 + 2.63807i 1.01495 + 0.108241i
\(595\) 0 0
\(596\) 4.40658i 0.180501i
\(597\) 5.74958 3.05336i 0.235315 0.124966i
\(598\) 4.42840i 0.181091i
\(599\) 0.578987i 0.0236568i −0.999930 0.0118284i \(-0.996235\pi\)
0.999930 0.0118284i \(-0.00376518\pi\)
\(600\) −4.68011 + 2.48541i −0.191065 + 0.101466i
\(601\) 29.8618i 1.21809i 0.793137 + 0.609044i \(0.208447\pi\)
−0.793137 + 0.609044i \(0.791553\pi\)
\(602\) 0 0
\(603\) 6.22467 9.20824i 0.253488 0.374988i
\(604\) −5.86786 −0.238760
\(605\) 8.71141 0.354169
\(606\) 3.94370 2.09433i 0.160202 0.0850764i
\(607\) 25.1099i 1.01918i −0.860417 0.509591i \(-0.829797\pi\)
0.860417 0.509591i \(-0.170203\pi\)
\(608\) 22.2425 0.902053
\(609\) 0 0
\(610\) −0.497451 −0.0201412
\(611\) 6.36420i 0.257468i
\(612\) −0.713863 + 1.05603i −0.0288562 + 0.0426874i
\(613\) −1.45986 −0.0589634 −0.0294817 0.999565i \(-0.509386\pi\)
−0.0294817 + 0.999565i \(0.509386\pi\)
\(614\) 35.4018 1.42870
\(615\) 3.78182 + 7.12131i 0.152498 + 0.287159i
\(616\) 0 0
\(617\) 6.56208i 0.264179i −0.991238 0.132090i \(-0.957831\pi\)
0.991238 0.132090i \(-0.0421687\pi\)
\(618\) −13.1070 24.6810i −0.527243 0.992817i
\(619\) 21.0639i 0.846629i 0.905983 + 0.423315i \(0.139133\pi\)
−0.905983 + 0.423315i \(0.860867\pi\)
\(620\) 4.93401i 0.198155i
\(621\) −2.36784 + 22.2026i −0.0950179 + 0.890961i
\(622\) 17.7510i 0.711751i
\(623\) 0 0
\(624\) −2.37526 + 1.26140i −0.0950864 + 0.0504964i
\(625\) 1.00000 0.0400000
\(626\) −4.96945 −0.198619
\(627\) 18.3707 + 34.5928i 0.733657 + 1.38150i
\(628\) 2.42793i 0.0968850i
\(629\) 3.82015 0.152319
\(630\) 0 0
\(631\) 17.5069 0.696937 0.348468 0.937321i \(-0.386702\pi\)
0.348468 + 0.937321i \(0.386702\pi\)
\(632\) 45.1606i 1.79639i
\(633\) −7.40985 13.9530i −0.294515 0.554582i
\(634\) −31.7357 −1.26038
\(635\) −8.05009 −0.319458
\(636\) 11.6954 6.21095i 0.463754 0.246280i
\(637\) 0 0
\(638\) 33.0114i 1.30694i
\(639\) −19.6443 13.2793i −0.777116 0.525322i
\(640\) 0.151850i 0.00600240i
\(641\) 11.5348i 0.455597i 0.973708 + 0.227798i \(0.0731527\pi\)
−0.973708 + 0.227798i \(0.926847\pi\)
\(642\) 11.8800 + 22.3704i 0.468865 + 0.882889i
\(643\) 17.3489i 0.684173i −0.939668 0.342087i \(-0.888866\pi\)
0.939668 0.342087i \(-0.111134\pi\)
\(644\) 0 0
\(645\) 0.400075 + 0.753355i 0.0157529 + 0.0296633i
\(646\) 2.78755 0.109675
\(647\) −7.86774 −0.309313 −0.154656 0.987968i \(-0.549427\pi\)
−0.154656 + 0.987968i \(0.549427\pi\)
\(648\) 25.5509 10.2629i 1.00374 0.403163i
\(649\) 51.6289i 2.02661i
\(650\) 1.03055 0.0404214
\(651\) 0 0
\(652\) −10.6813 −0.418314
\(653\) 2.00359i 0.0784065i 0.999231 + 0.0392033i \(0.0124820\pi\)
−0.999231 + 0.0392033i \(0.987518\pi\)
\(654\) −26.5930 + 14.1224i −1.03987 + 0.552229i
\(655\) −2.09927 −0.0820251
\(656\) 7.56365 0.295311
\(657\) 15.6939 + 10.6089i 0.612278 + 0.413893i
\(658\) 0 0
\(659\) 44.8494i 1.74709i 0.486747 + 0.873543i \(0.338183\pi\)
−0.486747 + 0.873543i \(0.661817\pi\)
\(660\) 5.68584 3.01951i 0.221321 0.117534i
\(661\) 12.0555i 0.468905i 0.972128 + 0.234453i \(0.0753298\pi\)
−0.972128 + 0.234453i \(0.924670\pi\)
\(662\) 2.86380i 0.111305i
\(663\) 0.741962 0.394024i 0.0288154 0.0153026i
\(664\) 33.0163i 1.28128i
\(665\) 0 0
\(666\) −20.1733 13.6370i −0.781701 0.528421i
\(667\) 29.6298 1.14727
\(668\) 13.2079 0.511030
\(669\) −17.9584 + 9.53697i −0.694314 + 0.368720i
\(670\) 3.99516i 0.154346i
\(671\) 2.04812 0.0790667
\(672\) 0 0
\(673\) 11.5641 0.445763 0.222882 0.974845i \(-0.428454\pi\)
0.222882 + 0.974845i \(0.428454\pi\)
\(674\) 23.1411i 0.891361i
\(675\) −5.16685 0.551027i −0.198872 0.0212091i
\(676\) 10.1188 0.389185
\(677\) 21.4934 0.826058 0.413029 0.910718i \(-0.364471\pi\)
0.413029 + 0.910718i \(0.364471\pi\)
\(678\) 4.42979 + 8.34145i 0.170125 + 0.320352i
\(679\) 0 0
\(680\) 1.55274i 0.0595447i
\(681\) 19.6764 + 37.0514i 0.754002 + 1.41981i
\(682\) 28.2157i 1.08044i
\(683\) 17.3367i 0.663372i −0.943390 0.331686i \(-0.892383\pi\)
0.943390 0.331686i \(-0.107617\pi\)
\(684\) 10.5982 + 7.16429i 0.405234 + 0.273933i
\(685\) 4.94709i 0.189019i
\(686\) 0 0
\(687\) 33.2084 17.6356i 1.26698 0.672839i
\(688\) 0.800149 0.0305054
\(689\) −8.72759 −0.332495
\(690\) −3.76433 7.08836i −0.143306 0.269849i
\(691\) 13.5390i 0.515048i 0.966272 + 0.257524i \(0.0829067\pi\)
−0.966272 + 0.257524i \(0.917093\pi\)
\(692\) −8.51700 −0.323768
\(693\) 0 0
\(694\) 19.5866 0.743496
\(695\) 10.7217i 0.406699i
\(696\) −17.1375 32.2706i −0.649596 1.22321i
\(697\) −2.36266 −0.0894922
\(698\) 14.1848 0.536903
\(699\) 16.8212 8.93303i 0.636237 0.337878i
\(700\) 0 0
\(701\) 41.8503i 1.58066i −0.612679 0.790332i \(-0.709908\pi\)
0.612679 0.790332i \(-0.290092\pi\)
\(702\) −5.32469 0.567860i −0.200968 0.0214325i
\(703\) 38.3389i 1.44598i
\(704\) 35.3335i 1.33168i
\(705\) 5.40985 + 10.1869i 0.203747 + 0.383662i
\(706\) 11.1006i 0.417775i
\(707\) 0 0
\(708\) 7.90881 + 14.8926i 0.297231 + 0.559697i
\(709\) −45.4794 −1.70802 −0.854008 0.520261i \(-0.825835\pi\)
−0.854008 + 0.520261i \(0.825835\pi\)
\(710\) 8.52303 0.319863
\(711\) −24.8001 + 36.6872i −0.930078 + 1.37588i
\(712\) 21.8881i 0.820290i
\(713\) 25.3253 0.948442
\(714\) 0 0
\(715\) −4.24299 −0.158679
\(716\) 4.40541i 0.164638i
\(717\) 13.8080 7.33286i 0.515670 0.273851i
\(718\) 12.7246 0.474878
\(719\) 0.228621 0.00852614 0.00426307 0.999991i \(-0.498643\pi\)
0.00426307 + 0.999991i \(0.498643\pi\)
\(720\) −2.72974 + 4.03814i −0.101731 + 0.150493i
\(721\) 0 0
\(722\) 7.48733i 0.278650i
\(723\) 7.77251 4.12765i 0.289063 0.153509i
\(724\) 8.13172i 0.302213i
\(725\) 6.89526i 0.256084i
\(726\) 14.3700 7.63129i 0.533320 0.283224i
\(727\) 19.2284i 0.713140i −0.934269 0.356570i \(-0.883946\pi\)
0.934269 0.356570i \(-0.116054\pi\)
\(728\) 0 0
\(729\) 26.3927 + 5.69415i 0.977509 + 0.210895i
\(730\) −6.80909 −0.252016
\(731\) −0.249943 −0.00924449
\(732\) 0.590788 0.313742i 0.0218361 0.0115962i
\(733\) 8.25651i 0.304961i 0.988306 + 0.152481i \(0.0487261\pi\)
−0.988306 + 0.152481i \(0.951274\pi\)
\(734\) −17.2253 −0.635797
\(735\) 0 0
\(736\) 18.7650 0.691688
\(737\) 16.4489i 0.605905i
\(738\) 12.4767 + 8.43410i 0.459273 + 0.310463i
\(739\) −10.3433 −0.380485 −0.190243 0.981737i \(-0.560927\pi\)
−0.190243 + 0.981737i \(0.560927\pi\)
\(740\) −6.30157 −0.231650
\(741\) −3.95441 7.44629i −0.145269 0.273546i
\(742\) 0 0
\(743\) 37.7580i 1.38521i −0.721318 0.692604i \(-0.756463\pi\)
0.721318 0.692604i \(-0.243537\pi\)
\(744\) −14.6479 27.5825i −0.537017 1.01122i
\(745\) 5.26356i 0.192842i
\(746\) 5.73318i 0.209907i
\(747\) −18.1310 + 26.8215i −0.663380 + 0.981347i
\(748\) 1.88641i 0.0689741i
\(749\) 0 0
\(750\) 1.64956 0.876010i 0.0602334 0.0319874i
\(751\) −42.8883 −1.56502 −0.782509 0.622640i \(-0.786060\pi\)
−0.782509 + 0.622640i \(0.786060\pi\)
\(752\) 10.8197 0.394554
\(753\) −15.1709 28.5673i −0.552858 1.04105i
\(754\) 7.10590i 0.258782i
\(755\) 7.00901 0.255084
\(756\) 0 0
\(757\) −30.1051 −1.09419 −0.547094 0.837071i \(-0.684266\pi\)
−0.547094 + 0.837071i \(0.684266\pi\)
\(758\) 25.9261i 0.941679i
\(759\) 15.4986 + 29.1844i 0.562562 + 1.05932i
\(760\) −15.5832 −0.565262
\(761\) 37.7720 1.36924 0.684618 0.728902i \(-0.259969\pi\)
0.684618 + 0.728902i \(0.259969\pi\)
\(762\) −13.2791 + 7.05196i −0.481051 + 0.255466i
\(763\) 0 0
\(764\) 8.02904i 0.290480i
\(765\) 0.852692 1.26140i 0.0308291 0.0456060i
\(766\) 20.2739i 0.732526i
\(767\) 11.1134i 0.401282i
\(768\) −13.0634 24.5989i −0.471386 0.887637i
\(769\) 33.3656i 1.20319i 0.798800 + 0.601597i \(0.205469\pi\)
−0.798800 + 0.601597i \(0.794531\pi\)
\(770\) 0 0
\(771\) −9.81558 18.4831i −0.353499 0.665652i
\(772\) 6.99191 0.251644
\(773\) 1.14671 0.0412443 0.0206222 0.999787i \(-0.493435\pi\)
0.0206222 + 0.999787i \(0.493435\pi\)
\(774\) 1.31989 + 0.892233i 0.0474426 + 0.0320707i
\(775\) 5.89355i 0.211703i
\(776\) 21.1453 0.759073
\(777\) 0 0
\(778\) 13.1743 0.472321
\(779\) 23.7116i 0.849555i
\(780\) −1.22391 + 0.649966i −0.0438230 + 0.0232725i
\(781\) −35.0912 −1.25566
\(782\) 2.35173 0.0840978
\(783\) 3.79948 35.6268i 0.135782 1.27320i
\(784\) 0 0
\(785\) 2.90010i 0.103509i
\(786\) −3.46286 + 1.83898i −0.123516 + 0.0655942i
\(787\) 41.4786i 1.47855i −0.673403 0.739276i \(-0.735168\pi\)
0.673403 0.739276i \(-0.264832\pi\)
\(788\) 1.48663i 0.0529588i
\(789\) 19.7147 10.4696i 0.701862 0.372729i
\(790\) 15.9174i 0.566315i
\(791\) 0 0
\(792\) 22.8212 33.7597i 0.810916 1.19960i
\(793\) −0.440869 −0.0156557
\(794\) 20.2351 0.718117
\(795\) −13.9699 + 7.41883i −0.495462 + 0.263119i
\(796\) 3.14663i 0.111529i
\(797\) −49.5086 −1.75369 −0.876843 0.480777i \(-0.840355\pi\)
−0.876843 + 0.480777i \(0.840355\pi\)
\(798\) 0 0
\(799\) −3.37976 −0.119567
\(800\) 4.36687i 0.154392i
\(801\) −12.0199 + 17.7812i −0.424703 + 0.628269i
\(802\) 25.8772 0.913756
\(803\) 28.0345 0.989317
\(804\) −2.51974 4.74477i −0.0888645 0.167335i
\(805\) 0 0
\(806\) 6.07359i 0.213933i
\(807\) −0.378925 0.713530i −0.0133388 0.0251174i
\(808\) 7.31441i 0.257320i
\(809\) 25.1255i 0.883367i 0.897171 + 0.441683i \(0.145619\pi\)
−0.897171 + 0.441683i \(0.854381\pi\)
\(810\) −9.00573 + 3.61726i −0.316429 + 0.127098i
\(811\) 4.97517i 0.174702i −0.996178 0.0873509i \(-0.972160\pi\)
0.996178 0.0873509i \(-0.0278401\pi\)
\(812\) 0 0
\(813\) −35.6283 + 18.9207i −1.24954 + 0.663577i
\(814\) −36.0362 −1.26307
\(815\) 12.7586 0.446914
\(816\) −0.669875 1.26140i −0.0234503 0.0441578i
\(817\) 2.50842i 0.0877585i
\(818\) 18.4210 0.644076
\(819\) 0 0
\(820\) 3.89735 0.136101
\(821\) 13.8573i 0.483624i 0.970323 + 0.241812i \(0.0777417\pi\)
−0.970323 + 0.241812i \(0.922258\pi\)
\(822\) 4.33371 + 8.16052i 0.151155 + 0.284631i
\(823\) 46.1558 1.60889 0.804446 0.594026i \(-0.202462\pi\)
0.804446 + 0.594026i \(0.202462\pi\)
\(824\) −45.7761 −1.59469
\(825\) −6.79159 + 3.60673i −0.236453 + 0.125570i
\(826\) 0 0
\(827\) 18.6880i 0.649844i −0.945741 0.324922i \(-0.894662\pi\)
0.945741 0.324922i \(-0.105338\pi\)
\(828\) 8.94125 + 6.04419i 0.310730 + 0.210050i
\(829\) 17.2579i 0.599391i −0.954035 0.299695i \(-0.903115\pi\)
0.954035 0.299695i \(-0.0968851\pi\)
\(830\) 11.6370i 0.403926i
\(831\) −11.2845 21.2492i −0.391456 0.737126i
\(832\) 7.60575i 0.263682i
\(833\) 0 0
\(834\) −9.39235 17.6861i −0.325231 0.612421i
\(835\) −15.7766 −0.545970
\(836\) 18.9319 0.654775
\(837\) 3.24751 30.4511i 0.112250 1.05254i
\(838\) 42.7586i 1.47707i
\(839\) 49.1689 1.69750 0.848750 0.528795i \(-0.177356\pi\)
0.848750 + 0.528795i \(0.177356\pi\)
\(840\) 0 0
\(841\) −18.5446 −0.639470
\(842\) 36.8170i 1.26880i
\(843\) −10.4860 + 5.56866i −0.361157 + 0.191795i
\(844\) −7.63621 −0.262849
\(845\) −12.0867 −0.415794
\(846\) 17.8477 + 12.0649i 0.613617 + 0.414798i
\(847\) 0 0
\(848\) 14.8377i 0.509527i
\(849\) −6.78662 + 3.60409i −0.232916 + 0.123692i
\(850\) 0.547280i 0.0187716i
\(851\) 32.3448i 1.10876i
\(852\) −10.1222 + 5.37547i −0.346781 + 0.184160i
\(853\) 8.86218i 0.303435i 0.988424 + 0.151718i \(0.0484804\pi\)
−0.988424 + 0.151718i \(0.951520\pi\)
\(854\) 0 0
\(855\) −12.6593 8.55757i −0.432940 0.292663i
\(856\) 41.4905 1.41812
\(857\) −0.983563 −0.0335979 −0.0167989 0.999859i \(-0.505348\pi\)
−0.0167989 + 0.999859i \(0.505348\pi\)
\(858\) −6.99907 + 3.71691i −0.238944 + 0.126893i
\(859\) 27.2791i 0.930750i 0.885114 + 0.465375i \(0.154081\pi\)
−0.885114 + 0.465375i \(0.845919\pi\)
\(860\) 0.412296 0.0140592
\(861\) 0 0
\(862\) −27.7897 −0.946519
\(863\) 4.55257i 0.154971i 0.996993 + 0.0774857i \(0.0246892\pi\)
−0.996993 + 0.0774857i \(0.975311\pi\)
\(864\) 2.40627 22.5630i 0.0818628 0.767608i
\(865\) 10.1733 0.345904
\(866\) −12.8451 −0.436496
\(867\) −13.6011 25.6113i −0.461916 0.869804i
\(868\) 0 0
\(869\) 65.5354i 2.22314i
\(870\) 6.04032 + 11.3741i 0.204786 + 0.385619i
\(871\) 3.54073i 0.119973i
\(872\) 49.3221i 1.67026i
\(873\) 17.1778 + 11.6120i 0.581382 + 0.393008i
\(874\) 23.6019i 0.798346i
\(875\) 0 0
\(876\) 8.08667 4.29449i 0.273223 0.145097i
\(877\) 21.3568 0.721169 0.360584 0.932727i \(-0.382577\pi\)
0.360584 + 0.932727i \(0.382577\pi\)
\(878\) −18.0872 −0.610414
\(879\) −24.4379 46.0174i −0.824269 1.55213i
\(880\) 7.21345i 0.243165i
\(881\) 33.2551 1.12039 0.560196 0.828360i \(-0.310726\pi\)
0.560196 + 0.828360i \(0.310726\pi\)
\(882\) 0 0
\(883\) 12.0561 0.405721 0.202860 0.979208i \(-0.434976\pi\)
0.202860 + 0.979208i \(0.434976\pi\)
\(884\) 0.406061i 0.0136573i
\(885\) −9.44689 17.7888i −0.317554 0.597965i
\(886\) 2.58359 0.0867974
\(887\) 23.4128 0.786123 0.393062 0.919512i \(-0.371416\pi\)
0.393062 + 0.919512i \(0.371416\pi\)
\(888\) −35.2275 + 18.7078i −1.18216 + 0.627793i
\(889\) 0 0
\(890\) 7.71471i 0.258598i
\(891\) 37.0786 14.8931i 1.24218 0.498937i
\(892\) 9.82831i 0.329076i
\(893\) 33.9191i 1.13506i
\(894\) −4.61093 8.68254i −0.154213 0.290388i
\(895\) 5.26215i 0.175894i
\(896\) 0 0
\(897\) −3.33616 6.28210i −0.111391 0.209753i
\(898\) 27.4644 0.916498
\(899\) −40.6376 −1.35534
\(900\) −1.40656 + 2.08075i −0.0468855 + 0.0693584i
\(901\) 4.63485i 0.154409i
\(902\) 22.2875 0.742091
\(903\) 0 0
\(904\) 15.4709 0.514556
\(905\) 9.71314i 0.322876i
\(906\) 11.5618 6.13997i 0.384114 0.203987i
\(907\) −41.5017 −1.37804 −0.689020 0.724742i \(-0.741959\pi\)
−0.689020 + 0.724742i \(0.741959\pi\)
\(908\) 20.2775 0.672933
\(909\) 4.01674 5.94201i 0.133227 0.197084i
\(910\) 0 0
\(911\) 57.6428i 1.90979i 0.296941 + 0.954896i \(0.404034\pi\)
−0.296941 + 0.954896i \(0.595966\pi\)
\(912\) −12.6593 + 6.72283i −0.419192 + 0.222615i
\(913\) 47.9120i 1.58566i
\(914\) 3.71154i 0.122767i
\(915\) −0.705682 + 0.374757i −0.0233291 + 0.0123891i
\(916\) 18.1743i 0.600496i
\(917\) 0 0
\(918\) 0.301566 2.82772i 0.00995318 0.0933286i
\(919\) −10.9154 −0.360065 −0.180033 0.983661i \(-0.557620\pi\)
−0.180033 + 0.983661i \(0.557620\pi\)
\(920\) −13.1468 −0.433438
\(921\) 50.2208 26.6701i 1.65483 0.878811i
\(922\) 14.5981i 0.480763i
\(923\) 7.55357 0.248629
\(924\) 0 0
\(925\) 7.52707 0.247488
\(926\) 5.54017i 0.182061i
\(927\) −37.1872 25.1381i −1.22139 0.825644i
\(928\) −30.1107 −0.988433
\(929\) −40.4127 −1.32590 −0.662950 0.748664i \(-0.730696\pi\)
−0.662950 + 0.748664i \(0.730696\pi\)
\(930\) 5.16281 + 9.72176i 0.169295 + 0.318789i
\(931\) 0 0
\(932\) 9.20592i 0.301550i
\(933\) 13.3728 + 25.1815i 0.437806 + 0.824404i
\(934\) 9.93999i 0.325246i
\(935\) 2.25327i 0.0736899i
\(936\) −4.91240 + 7.26698i −0.160567 + 0.237529i
\(937\) 5.67805i 0.185494i −0.995690 0.0927468i \(-0.970435\pi\)
0.995690 0.0927468i \(-0.0295647\pi\)
\(938\) 0 0
\(939\) −7.04963 + 3.74376i −0.230056 + 0.122173i
\(940\) 5.57511 0.181840
\(941\) 12.5927 0.410510 0.205255 0.978709i \(-0.434198\pi\)
0.205255 + 0.978709i \(0.434198\pi\)
\(942\) −2.54052 4.78389i −0.0827746 0.155868i
\(943\) 20.0044i 0.651432i
\(944\) −18.8938 −0.614940
\(945\) 0 0
\(946\) 2.35776 0.0766575
\(947\) 31.3417i 1.01847i −0.860628 0.509234i \(-0.829929\pi\)
0.860628 0.509234i \(-0.170071\pi\)
\(948\) 10.0391 + 18.9040i 0.326054 + 0.613972i
\(949\) −6.03459 −0.195891
\(950\) 5.49248 0.178200
\(951\) −45.0200 + 23.9082i −1.45987 + 0.775277i
\(952\) 0 0
\(953\) 43.7751i 1.41802i 0.705200 + 0.709008i \(0.250857\pi\)
−0.705200 + 0.709008i \(0.749143\pi\)
\(954\) −16.5452 + 24.4756i −0.535671 + 0.792426i
\(955\) 9.59049i 0.310341i
\(956\) 7.55686i 0.244406i
\(957\) −24.8693 46.8298i −0.803911 1.51379i
\(958\) 22.2540i 0.718994i
\(959\) 0 0
\(960\) 6.46521 + 12.1742i 0.208664 + 0.392921i
\(961\) −3.73396 −0.120450
\(962\) 7.75701 0.250096
\(963\) 33.7057 + 22.7847i 1.08615 + 0.734225i
\(964\) 4.25374i 0.137004i
\(965\) −8.35166 −0.268849
\(966\) 0 0
\(967\) 36.3052 1.16750 0.583748 0.811935i \(-0.301585\pi\)
0.583748 + 0.811935i \(0.301585\pi\)
\(968\) 26.6521i 0.856631i
\(969\) 3.95441 2.10002i 0.127034 0.0674623i
\(970\) −7.45292 −0.239299
\(971\) −49.8257 −1.59898 −0.799492 0.600677i \(-0.794898\pi\)
−0.799492 + 0.600677i \(0.794898\pi\)
\(972\) 8.41406 9.97588i 0.269881 0.319976i
\(973\) 0 0
\(974\) 2.66887i 0.0855161i
\(975\) 1.46193 0.776369i 0.0468192 0.0248637i
\(976\) 0.749515i 0.0239914i
\(977\) 27.7554i 0.887974i 0.896033 + 0.443987i \(0.146436\pi\)
−0.896033 + 0.443987i \(0.853564\pi\)
\(978\) 21.0461 11.1767i 0.672979 0.357390i
\(979\) 31.7631i 1.01515i
\(980\) 0 0
\(981\) −27.0854 + 40.0679i −0.864772 + 1.27927i
\(982\) 22.9500 0.732363
\(983\) 42.0792 1.34212 0.671060 0.741403i \(-0.265839\pi\)
0.671060 + 0.741403i \(0.265839\pi\)
\(984\) 21.7873 11.5703i 0.694552 0.368847i
\(985\) 1.77574i 0.0565797i
\(986\) −3.77364 −0.120177
\(987\) 0 0
\(988\) −4.07521 −0.129650
\(989\) 2.11624i 0.0672925i
\(990\) −8.04360 + 11.8990i −0.255642 + 0.378176i
\(991\) 5.72308 0.181799 0.0908997 0.995860i \(-0.471026\pi\)
0.0908997 + 0.995860i \(0.471026\pi\)
\(992\) −25.7364 −0.817131
\(993\) 2.15745 + 4.06256i 0.0684647 + 0.128922i
\(994\) 0 0
\(995\) 3.75858i 0.119155i
\(996\) 7.33944 + 13.8204i 0.232559 + 0.437917i
\(997\) 11.1344i 0.352629i 0.984334 + 0.176315i \(0.0564176\pi\)
−0.984334 + 0.176315i \(0.943582\pi\)
\(998\) 35.3025i 1.11748i
\(999\) −38.8912 4.14762i −1.23046 0.131225i
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 735.2.b.d.146.6 8
3.2 odd 2 735.2.b.c.146.3 8
7.2 even 3 735.2.s.l.521.3 8
7.3 odd 6 735.2.s.k.656.2 8
7.4 even 3 105.2.s.c.26.2 8
7.5 odd 6 105.2.s.d.101.3 yes 8
7.6 odd 2 735.2.b.c.146.6 8
21.2 odd 6 735.2.s.k.521.2 8
21.5 even 6 105.2.s.c.101.2 yes 8
21.11 odd 6 105.2.s.d.26.3 yes 8
21.17 even 6 735.2.s.l.656.3 8
21.20 even 2 inner 735.2.b.d.146.3 8
35.4 even 6 525.2.t.g.26.3 8
35.12 even 12 525.2.q.e.374.6 16
35.18 odd 12 525.2.q.f.299.3 16
35.19 odd 6 525.2.t.f.101.2 8
35.32 odd 12 525.2.q.f.299.6 16
35.33 even 12 525.2.q.e.374.3 16
105.32 even 12 525.2.q.e.299.3 16
105.47 odd 12 525.2.q.f.374.3 16
105.53 even 12 525.2.q.e.299.6 16
105.68 odd 12 525.2.q.f.374.6 16
105.74 odd 6 525.2.t.f.26.2 8
105.89 even 6 525.2.t.g.101.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.s.c.26.2 8 7.4 even 3
105.2.s.c.101.2 yes 8 21.5 even 6
105.2.s.d.26.3 yes 8 21.11 odd 6
105.2.s.d.101.3 yes 8 7.5 odd 6
525.2.q.e.299.3 16 105.32 even 12
525.2.q.e.299.6 16 105.53 even 12
525.2.q.e.374.3 16 35.33 even 12
525.2.q.e.374.6 16 35.12 even 12
525.2.q.f.299.3 16 35.18 odd 12
525.2.q.f.299.6 16 35.32 odd 12
525.2.q.f.374.3 16 105.47 odd 12
525.2.q.f.374.6 16 105.68 odd 12
525.2.t.f.26.2 8 105.74 odd 6
525.2.t.f.101.2 8 35.19 odd 6
525.2.t.g.26.3 8 35.4 even 6
525.2.t.g.101.3 8 105.89 even 6
735.2.b.c.146.3 8 3.2 odd 2
735.2.b.c.146.6 8 7.6 odd 2
735.2.b.d.146.3 8 21.20 even 2 inner
735.2.b.d.146.6 8 1.1 even 1 trivial
735.2.s.k.521.2 8 21.2 odd 6
735.2.s.k.656.2 8 7.3 odd 6
735.2.s.l.521.3 8 7.2 even 3
735.2.s.l.656.3 8 21.17 even 6