Properties

Label 729.2.c.d.487.5
Level $729$
Weight $2$
Character 729.487
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
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] = [729,2,Mod(244,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.244");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 487.5
Root \(-1.13697i\) of defining polynomial
Character \(\chi\) \(=\) 729.487
Dual form 729.2.c.d.244.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.06251 - 1.84033i) q^{2} +(-1.25787 - 2.17870i) q^{4} +(1.03547 + 1.79349i) q^{5} +(-2.42434 + 4.19907i) q^{7} -1.09598 q^{8} +O(q^{10})\) \(q+(1.06251 - 1.84033i) q^{2} +(-1.25787 - 2.17870i) q^{4} +(1.03547 + 1.79349i) q^{5} +(-2.42434 + 4.19907i) q^{7} -1.09598 q^{8} +4.40081 q^{10} +(-2.07474 + 3.59356i) q^{11} +(0.608008 + 1.05310i) q^{13} +(5.15178 + 8.92315i) q^{14} +(1.35126 - 2.34044i) q^{16} +2.36364 q^{17} -1.83801 q^{19} +(2.60498 - 4.51196i) q^{20} +(4.40889 + 7.63642i) q^{22} +(2.15178 + 3.72700i) q^{23} +(0.355603 - 0.615922i) q^{25} +2.58407 q^{26} +12.1980 q^{28} +(-1.49091 + 2.58233i) q^{29} +(-0.736793 - 1.27616i) q^{31} +(-3.96743 - 6.87180i) q^{32} +(2.51140 - 4.34987i) q^{34} -10.0413 q^{35} +8.97108 q^{37} +(-1.95291 + 3.38254i) q^{38} +(-1.13485 - 1.96562i) q^{40} +(-1.13026 - 1.95767i) q^{41} +(2.74243 - 4.75003i) q^{43} +10.4391 q^{44} +9.14521 q^{46} +(-3.59157 + 6.22077i) q^{47} +(-8.25481 - 14.2978i) q^{49} +(-0.755667 - 1.30885i) q^{50} +(1.52959 - 2.64933i) q^{52} -6.32803 q^{53} -8.59334 q^{55} +(2.65702 - 4.60209i) q^{56} +(3.16823 + 5.48753i) q^{58} +(-0.131128 - 0.227121i) q^{59} +(2.22780 - 3.85867i) q^{61} -3.13141 q^{62} -11.4568 q^{64} +(-1.25915 + 2.18091i) q^{65} +(-2.06555 - 3.57764i) q^{67} +(-2.97316 - 5.14966i) q^{68} +(-10.6690 + 18.4793i) q^{70} +3.08551 q^{71} +12.7601 q^{73} +(9.53190 - 16.5097i) q^{74} +(2.31198 + 4.00447i) q^{76} +(-10.0598 - 17.4240i) q^{77} +(-2.27620 + 3.94250i) q^{79} +5.59674 q^{80} -4.80368 q^{82} +(4.22653 - 7.32056i) q^{83} +(2.44748 + 4.23915i) q^{85} +(-5.82774 - 10.0939i) q^{86} +(2.27387 - 3.93846i) q^{88} +16.9632 q^{89} -5.89606 q^{91} +(5.41335 - 9.37619i) q^{92} +(7.63218 + 13.2193i) q^{94} +(-1.90320 - 3.29644i) q^{95} +(2.55489 - 4.42519i) q^{97} -35.0834 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} - 9 q^{4} - 3 q^{5} - 6 q^{7} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{2} - 9 q^{4} - 3 q^{5} - 6 q^{7} - 12 q^{8} + 12 q^{10} - 6 q^{11} - 6 q^{13} + 24 q^{14} - 15 q^{16} + 18 q^{17} + 24 q^{19} - 21 q^{20} - 3 q^{22} - 12 q^{23} - 9 q^{25} - 48 q^{26} + 6 q^{28} + 21 q^{29} - 15 q^{31} - 60 q^{35} + 6 q^{37} + 15 q^{38} - 3 q^{40} - 12 q^{41} - 6 q^{43} + 66 q^{44} - 6 q^{46} - 15 q^{47} - 12 q^{49} - 24 q^{50} - 3 q^{52} + 18 q^{53} + 30 q^{55} + 12 q^{56} + 15 q^{58} + 6 q^{59} - 24 q^{61} + 60 q^{62} + 12 q^{64} - 15 q^{65} - 15 q^{67} + 36 q^{68} + 15 q^{70} + 24 q^{73} + 24 q^{74} - 9 q^{76} + 15 q^{77} - 24 q^{79} + 42 q^{80} - 42 q^{82} - 6 q^{83} + 18 q^{85} - 30 q^{86} + 21 q^{88} + 18 q^{89} + 36 q^{91} + 6 q^{92} + 6 q^{94} - 33 q^{95} + 21 q^{97} - 36 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.06251 1.84033i 0.751311 1.30131i −0.195876 0.980629i \(-0.562755\pi\)
0.947187 0.320680i \(-0.103912\pi\)
\(3\) 0 0
\(4\) −1.25787 2.17870i −0.628937 1.08935i
\(5\) 1.03547 + 1.79349i 0.463076 + 0.802072i 0.999112 0.0421233i \(-0.0134122\pi\)
−0.536036 + 0.844195i \(0.680079\pi\)
\(6\) 0 0
\(7\) −2.42434 + 4.19907i −0.916313 + 1.58710i −0.111346 + 0.993782i \(0.535516\pi\)
−0.804967 + 0.593319i \(0.797817\pi\)
\(8\) −1.09598 −0.387487
\(9\) 0 0
\(10\) 4.40081 1.39166
\(11\) −2.07474 + 3.59356i −0.625559 + 1.08350i 0.362874 + 0.931838i \(0.381796\pi\)
−0.988432 + 0.151662i \(0.951538\pi\)
\(12\) 0 0
\(13\) 0.608008 + 1.05310i 0.168631 + 0.292077i 0.937939 0.346801i \(-0.112732\pi\)
−0.769308 + 0.638878i \(0.779399\pi\)
\(14\) 5.15178 + 8.92315i 1.37687 + 2.38481i
\(15\) 0 0
\(16\) 1.35126 2.34044i 0.337814 0.585111i
\(17\) 2.36364 0.573266 0.286633 0.958040i \(-0.407464\pi\)
0.286633 + 0.958040i \(0.407464\pi\)
\(18\) 0 0
\(19\) −1.83801 −0.421668 −0.210834 0.977522i \(-0.567618\pi\)
−0.210834 + 0.977522i \(0.567618\pi\)
\(20\) 2.60498 4.51196i 0.582491 1.00890i
\(21\) 0 0
\(22\) 4.40889 + 7.63642i 0.939979 + 1.62809i
\(23\) 2.15178 + 3.72700i 0.448678 + 0.777133i 0.998300 0.0582801i \(-0.0185617\pi\)
−0.549622 + 0.835413i \(0.685228\pi\)
\(24\) 0 0
\(25\) 0.355603 0.615922i 0.0711206 0.123184i
\(26\) 2.58407 0.506777
\(27\) 0 0
\(28\) 12.1980 2.30521
\(29\) −1.49091 + 2.58233i −0.276855 + 0.479527i −0.970601 0.240692i \(-0.922626\pi\)
0.693746 + 0.720219i \(0.255959\pi\)
\(30\) 0 0
\(31\) −0.736793 1.27616i −0.132332 0.229206i 0.792243 0.610206i \(-0.208913\pi\)
−0.924575 + 0.381000i \(0.875580\pi\)
\(32\) −3.96743 6.87180i −0.701350 1.21477i
\(33\) 0 0
\(34\) 2.51140 4.34987i 0.430701 0.745997i
\(35\) −10.0413 −1.69729
\(36\) 0 0
\(37\) 8.97108 1.47484 0.737418 0.675436i \(-0.236045\pi\)
0.737418 + 0.675436i \(0.236045\pi\)
\(38\) −1.95291 + 3.38254i −0.316804 + 0.548720i
\(39\) 0 0
\(40\) −1.13485 1.96562i −0.179436 0.310792i
\(41\) −1.13026 1.95767i −0.176517 0.305737i 0.764168 0.645017i \(-0.223150\pi\)
−0.940685 + 0.339280i \(0.889816\pi\)
\(42\) 0 0
\(43\) 2.74243 4.75003i 0.418216 0.724372i −0.577544 0.816360i \(-0.695989\pi\)
0.995760 + 0.0919876i \(0.0293220\pi\)
\(44\) 10.4391 1.57375
\(45\) 0 0
\(46\) 9.14521 1.34839
\(47\) −3.59157 + 6.22077i −0.523884 + 0.907393i 0.475730 + 0.879591i \(0.342184\pi\)
−0.999613 + 0.0278017i \(0.991149\pi\)
\(48\) 0 0
\(49\) −8.25481 14.2978i −1.17926 2.04254i
\(50\) −0.755667 1.30885i −0.106867 0.185100i
\(51\) 0 0
\(52\) 1.52959 2.64933i 0.212116 0.367396i
\(53\) −6.32803 −0.869222 −0.434611 0.900618i \(-0.643114\pi\)
−0.434611 + 0.900618i \(0.643114\pi\)
\(54\) 0 0
\(55\) −8.59334 −1.15873
\(56\) 2.65702 4.60209i 0.355059 0.614980i
\(57\) 0 0
\(58\) 3.16823 + 5.48753i 0.416009 + 0.720548i
\(59\) −0.131128 0.227121i −0.0170715 0.0295686i 0.857363 0.514711i \(-0.172101\pi\)
−0.874435 + 0.485143i \(0.838768\pi\)
\(60\) 0 0
\(61\) 2.22780 3.85867i 0.285241 0.494052i −0.687427 0.726254i \(-0.741260\pi\)
0.972668 + 0.232202i \(0.0745931\pi\)
\(62\) −3.13141 −0.397690
\(63\) 0 0
\(64\) −11.4568 −1.43210
\(65\) −1.25915 + 2.18091i −0.156178 + 0.270508i
\(66\) 0 0
\(67\) −2.06555 3.57764i −0.252347 0.437078i 0.711824 0.702358i \(-0.247869\pi\)
−0.964172 + 0.265279i \(0.914536\pi\)
\(68\) −2.97316 5.14966i −0.360548 0.624488i
\(69\) 0 0
\(70\) −10.6690 + 18.4793i −1.27519 + 2.20870i
\(71\) 3.08551 0.366183 0.183091 0.983096i \(-0.441390\pi\)
0.183091 + 0.983096i \(0.441390\pi\)
\(72\) 0 0
\(73\) 12.7601 1.49345 0.746726 0.665132i \(-0.231625\pi\)
0.746726 + 0.665132i \(0.231625\pi\)
\(74\) 9.53190 16.5097i 1.10806 1.91922i
\(75\) 0 0
\(76\) 2.31198 + 4.00447i 0.265202 + 0.459344i
\(77\) −10.0598 17.4240i −1.14642 1.98565i
\(78\) 0 0
\(79\) −2.27620 + 3.94250i −0.256093 + 0.443566i −0.965192 0.261543i \(-0.915769\pi\)
0.709099 + 0.705109i \(0.249102\pi\)
\(80\) 5.59674 0.625734
\(81\) 0 0
\(82\) −4.80368 −0.530478
\(83\) 4.22653 7.32056i 0.463922 0.803536i −0.535230 0.844706i \(-0.679775\pi\)
0.999152 + 0.0411700i \(0.0131085\pi\)
\(84\) 0 0
\(85\) 2.44748 + 4.23915i 0.265466 + 0.459801i
\(86\) −5.82774 10.0939i −0.628421 1.08846i
\(87\) 0 0
\(88\) 2.27387 3.93846i 0.242396 0.419842i
\(89\) 16.9632 1.79809 0.899046 0.437854i \(-0.144261\pi\)
0.899046 + 0.437854i \(0.144261\pi\)
\(90\) 0 0
\(91\) −5.89606 −0.618075
\(92\) 5.41335 9.37619i 0.564380 0.977535i
\(93\) 0 0
\(94\) 7.63218 + 13.2193i 0.787199 + 1.36347i
\(95\) −1.90320 3.29644i −0.195264 0.338208i
\(96\) 0 0
\(97\) 2.55489 4.42519i 0.259409 0.449310i −0.706674 0.707539i \(-0.749805\pi\)
0.966084 + 0.258229i \(0.0831388\pi\)
\(98\) −35.0834 −3.54396
\(99\) 0 0
\(100\) −1.78921 −0.178921
\(101\) −9.28994 + 16.0906i −0.924384 + 1.60108i −0.131834 + 0.991272i \(0.542087\pi\)
−0.792550 + 0.609808i \(0.791247\pi\)
\(102\) 0 0
\(103\) −4.50288 7.79923i −0.443682 0.768481i 0.554277 0.832332i \(-0.312995\pi\)
−0.997959 + 0.0638518i \(0.979662\pi\)
\(104\) −0.666363 1.15417i −0.0653422 0.113176i
\(105\) 0 0
\(106\) −6.72362 + 11.6457i −0.653056 + 1.13113i
\(107\) 7.42680 0.717976 0.358988 0.933342i \(-0.383122\pi\)
0.358988 + 0.933342i \(0.383122\pi\)
\(108\) 0 0
\(109\) −5.62396 −0.538678 −0.269339 0.963045i \(-0.586805\pi\)
−0.269339 + 0.963045i \(0.586805\pi\)
\(110\) −9.13055 + 15.8146i −0.870564 + 1.50786i
\(111\) 0 0
\(112\) 6.55179 + 11.3480i 0.619086 + 1.07229i
\(113\) 1.20133 + 2.08077i 0.113012 + 0.195743i 0.916983 0.398926i \(-0.130617\pi\)
−0.803971 + 0.594668i \(0.797283\pi\)
\(114\) 0 0
\(115\) −4.45622 + 7.71839i −0.415544 + 0.719744i
\(116\) 7.50150 0.696497
\(117\) 0 0
\(118\) −0.557303 −0.0513039
\(119\) −5.73025 + 9.92509i −0.525292 + 0.909832i
\(120\) 0 0
\(121\) −3.10913 5.38517i −0.282648 0.489561i
\(122\) −4.73415 8.19978i −0.428609 0.742373i
\(123\) 0 0
\(124\) −1.85359 + 3.21050i −0.166457 + 0.288312i
\(125\) 11.8276 1.05789
\(126\) 0 0
\(127\) −9.23469 −0.819447 −0.409723 0.912210i \(-0.634375\pi\)
−0.409723 + 0.912210i \(0.634375\pi\)
\(128\) −4.23815 + 7.34069i −0.374603 + 0.648831i
\(129\) 0 0
\(130\) 2.67572 + 4.63449i 0.234677 + 0.406472i
\(131\) 7.66950 + 13.2840i 0.670088 + 1.16063i 0.977879 + 0.209172i \(0.0670768\pi\)
−0.307791 + 0.951454i \(0.599590\pi\)
\(132\) 0 0
\(133\) 4.45595 7.71792i 0.386380 0.669229i
\(134\) −8.77871 −0.758365
\(135\) 0 0
\(136\) −2.59049 −0.222133
\(137\) 1.82198 3.15577i 0.155663 0.269616i −0.777637 0.628713i \(-0.783582\pi\)
0.933300 + 0.359097i \(0.116915\pi\)
\(138\) 0 0
\(139\) −6.63777 11.4970i −0.563008 0.975159i −0.997232 0.0743538i \(-0.976311\pi\)
0.434224 0.900805i \(-0.357023\pi\)
\(140\) 12.6307 + 21.8770i 1.06749 + 1.84895i
\(141\) 0 0
\(142\) 3.27840 5.67835i 0.275117 0.476517i
\(143\) −5.04584 −0.421954
\(144\) 0 0
\(145\) −6.17517 −0.512820
\(146\) 13.5577 23.4827i 1.12205 1.94344i
\(147\) 0 0
\(148\) −11.2845 19.5453i −0.927579 1.60661i
\(149\) −4.45549 7.71714i −0.365008 0.632213i 0.623769 0.781608i \(-0.285600\pi\)
−0.988777 + 0.149396i \(0.952267\pi\)
\(150\) 0 0
\(151\) 0.356202 0.616960i 0.0289873 0.0502075i −0.851168 0.524894i \(-0.824105\pi\)
0.880155 + 0.474686i \(0.157438\pi\)
\(152\) 2.01441 0.163391
\(153\) 0 0
\(154\) −42.7545 −3.44526
\(155\) 1.52585 2.64286i 0.122560 0.212279i
\(156\) 0 0
\(157\) 6.90903 + 11.9668i 0.551400 + 0.955054i 0.998174 + 0.0604064i \(0.0192397\pi\)
−0.446773 + 0.894647i \(0.647427\pi\)
\(158\) 4.83700 + 8.37793i 0.384811 + 0.666512i
\(159\) 0 0
\(160\) 8.21632 14.2311i 0.649557 1.12507i
\(161\) −20.8666 −1.64452
\(162\) 0 0
\(163\) −1.19321 −0.0934597 −0.0467298 0.998908i \(-0.514880\pi\)
−0.0467298 + 0.998908i \(0.514880\pi\)
\(164\) −2.84345 + 4.92501i −0.222036 + 0.384578i
\(165\) 0 0
\(166\) −8.98150 15.5564i −0.697099 1.20741i
\(167\) 11.9682 + 20.7295i 0.926124 + 1.60409i 0.789743 + 0.613437i \(0.210214\pi\)
0.136381 + 0.990657i \(0.456453\pi\)
\(168\) 0 0
\(169\) 5.76065 9.97774i 0.443127 0.767519i
\(170\) 10.4019 0.797791
\(171\) 0 0
\(172\) −13.7985 −1.05213
\(173\) 4.57000 7.91547i 0.347451 0.601802i −0.638345 0.769750i \(-0.720381\pi\)
0.985796 + 0.167948i \(0.0537140\pi\)
\(174\) 0 0
\(175\) 1.72420 + 2.98641i 0.130337 + 0.225751i
\(176\) 5.60702 + 9.71164i 0.422645 + 0.732043i
\(177\) 0 0
\(178\) 18.0236 31.2178i 1.35093 2.33987i
\(179\) 10.6008 0.792337 0.396169 0.918178i \(-0.370340\pi\)
0.396169 + 0.918178i \(0.370340\pi\)
\(180\) 0 0
\(181\) −1.46292 −0.108738 −0.0543690 0.998521i \(-0.517315\pi\)
−0.0543690 + 0.998521i \(0.517315\pi\)
\(182\) −6.26465 + 10.8507i −0.464367 + 0.804307i
\(183\) 0 0
\(184\) −2.35831 4.08471i −0.173857 0.301129i
\(185\) 9.28929 + 16.0895i 0.682962 + 1.18292i
\(186\) 0 0
\(187\) −4.90395 + 8.49388i −0.358612 + 0.621134i
\(188\) 18.0709 1.31796
\(189\) 0 0
\(190\) −8.08871 −0.586817
\(191\) −6.21114 + 10.7580i −0.449422 + 0.778422i −0.998348 0.0574488i \(-0.981703\pi\)
0.548926 + 0.835871i \(0.315037\pi\)
\(192\) 0 0
\(193\) −10.3867 17.9902i −0.747647 1.29496i −0.948948 0.315434i \(-0.897850\pi\)
0.201300 0.979530i \(-0.435483\pi\)
\(194\) −5.42921 9.40366i −0.389794 0.675143i
\(195\) 0 0
\(196\) −20.7670 + 35.9695i −1.48336 + 2.56925i
\(197\) −14.1887 −1.01090 −0.505450 0.862856i \(-0.668674\pi\)
−0.505450 + 0.862856i \(0.668674\pi\)
\(198\) 0 0
\(199\) 20.3286 1.44106 0.720529 0.693424i \(-0.243899\pi\)
0.720529 + 0.693424i \(0.243899\pi\)
\(200\) −0.389733 + 0.675037i −0.0275583 + 0.0477323i
\(201\) 0 0
\(202\) 19.7414 + 34.1931i 1.38900 + 2.40582i
\(203\) −7.22893 12.5209i −0.507372 0.878794i
\(204\) 0 0
\(205\) 2.34071 4.05422i 0.163482 0.283159i
\(206\) −19.1375 −1.33337
\(207\) 0 0
\(208\) 3.28629 0.227864
\(209\) 3.81339 6.60499i 0.263778 0.456877i
\(210\) 0 0
\(211\) 4.93166 + 8.54189i 0.339509 + 0.588048i 0.984341 0.176278i \(-0.0564056\pi\)
−0.644831 + 0.764325i \(0.723072\pi\)
\(212\) 7.95986 + 13.7869i 0.546685 + 0.946887i
\(213\) 0 0
\(214\) 7.89109 13.6678i 0.539424 0.934309i
\(215\) 11.3588 0.774665
\(216\) 0 0
\(217\) 7.14494 0.485030
\(218\) −5.97554 + 10.3499i −0.404715 + 0.700986i
\(219\) 0 0
\(220\) 10.8093 + 18.7223i 0.728766 + 1.26226i
\(221\) 1.43711 + 2.48915i 0.0966705 + 0.167438i
\(222\) 0 0
\(223\) −7.53569 + 13.0522i −0.504627 + 0.874040i 0.495358 + 0.868689i \(0.335037\pi\)
−0.999986 + 0.00535136i \(0.998297\pi\)
\(224\) 38.4736 2.57062
\(225\) 0 0
\(226\) 5.10574 0.339629
\(227\) 11.3463 19.6523i 0.753079 1.30437i −0.193245 0.981151i \(-0.561901\pi\)
0.946324 0.323221i \(-0.104766\pi\)
\(228\) 0 0
\(229\) −4.35835 7.54888i −0.288008 0.498844i 0.685326 0.728236i \(-0.259660\pi\)
−0.973334 + 0.229392i \(0.926326\pi\)
\(230\) 9.46959 + 16.4018i 0.624406 + 1.08150i
\(231\) 0 0
\(232\) 1.63400 2.83018i 0.107278 0.185810i
\(233\) −23.5890 −1.54536 −0.772682 0.634793i \(-0.781085\pi\)
−0.772682 + 0.634793i \(0.781085\pi\)
\(234\) 0 0
\(235\) −14.8758 −0.970393
\(236\) −0.329886 + 0.571379i −0.0214737 + 0.0371936i
\(237\) 0 0
\(238\) 12.1770 + 21.0911i 0.789315 + 1.36713i
\(239\) −4.97726 8.62086i −0.321952 0.557637i 0.658939 0.752197i \(-0.271006\pi\)
−0.980891 + 0.194559i \(0.937672\pi\)
\(240\) 0 0
\(241\) −2.85672 + 4.94799i −0.184018 + 0.318728i −0.943245 0.332097i \(-0.892244\pi\)
0.759227 + 0.650826i \(0.225577\pi\)
\(242\) −13.2140 −0.849427
\(243\) 0 0
\(244\) −11.2092 −0.717594
\(245\) 17.0952 29.6098i 1.09217 1.89170i
\(246\) 0 0
\(247\) −1.11752 1.93560i −0.0711062 0.123160i
\(248\) 0.807509 + 1.39865i 0.0512769 + 0.0888141i
\(249\) 0 0
\(250\) 12.5670 21.7666i 0.794804 1.37664i
\(251\) −7.28966 −0.460120 −0.230060 0.973176i \(-0.573892\pi\)
−0.230060 + 0.973176i \(0.573892\pi\)
\(252\) 0 0
\(253\) −17.8576 −1.12270
\(254\) −9.81199 + 16.9949i −0.615659 + 1.06635i
\(255\) 0 0
\(256\) −2.45062 4.24459i −0.153163 0.265287i
\(257\) 11.6215 + 20.1291i 0.724932 + 1.25562i 0.959002 + 0.283399i \(0.0914620\pi\)
−0.234071 + 0.972220i \(0.575205\pi\)
\(258\) 0 0
\(259\) −21.7489 + 37.6702i −1.35141 + 2.34071i
\(260\) 6.33539 0.392904
\(261\) 0 0
\(262\) 32.5958 2.01378
\(263\) 13.6998 23.7288i 0.844766 1.46318i −0.0410581 0.999157i \(-0.513073\pi\)
0.885824 0.464021i \(-0.153594\pi\)
\(264\) 0 0
\(265\) −6.55249 11.3492i −0.402516 0.697178i
\(266\) −9.46901 16.4008i −0.580582 1.00560i
\(267\) 0 0
\(268\) −5.19641 + 9.00044i −0.317421 + 0.549789i
\(269\) 9.41973 0.574331 0.287166 0.957881i \(-0.407287\pi\)
0.287166 + 0.957881i \(0.407287\pi\)
\(270\) 0 0
\(271\) 26.2797 1.59638 0.798189 0.602408i \(-0.205792\pi\)
0.798189 + 0.602408i \(0.205792\pi\)
\(272\) 3.19388 5.53196i 0.193657 0.335424i
\(273\) 0 0
\(274\) −3.87177 6.70610i −0.233902 0.405131i
\(275\) 1.47557 + 2.55576i 0.0889803 + 0.154118i
\(276\) 0 0
\(277\) −0.187406 + 0.324597i −0.0112601 + 0.0195031i −0.871601 0.490217i \(-0.836918\pi\)
0.860340 + 0.509720i \(0.170251\pi\)
\(278\) −28.2109 −1.69198
\(279\) 0 0
\(280\) 11.0051 0.657678
\(281\) −6.99079 + 12.1084i −0.417036 + 0.722327i −0.995640 0.0932815i \(-0.970264\pi\)
0.578604 + 0.815609i \(0.303598\pi\)
\(282\) 0 0
\(283\) −7.78094 13.4770i −0.462529 0.801124i 0.536557 0.843864i \(-0.319725\pi\)
−0.999086 + 0.0427401i \(0.986391\pi\)
\(284\) −3.88118 6.72240i −0.230306 0.398901i
\(285\) 0 0
\(286\) −5.36128 + 9.28601i −0.317019 + 0.549093i
\(287\) 10.9605 0.646980
\(288\) 0 0
\(289\) −11.4132 −0.671366
\(290\) −6.56121 + 11.3643i −0.385287 + 0.667337i
\(291\) 0 0
\(292\) −16.0505 27.8004i −0.939287 1.62689i
\(293\) −12.3121 21.3252i −0.719281 1.24583i −0.961285 0.275556i \(-0.911138\pi\)
0.242004 0.970275i \(-0.422195\pi\)
\(294\) 0 0
\(295\) 0.271559 0.470354i 0.0158108 0.0273851i
\(296\) −9.83210 −0.571479
\(297\) 0 0
\(298\) −18.9361 −1.09694
\(299\) −2.61660 + 4.53209i −0.151322 + 0.262097i
\(300\) 0 0
\(301\) 13.2971 + 23.0313i 0.766434 + 1.32750i
\(302\) −0.756939 1.31106i −0.0435570 0.0754429i
\(303\) 0 0
\(304\) −2.48362 + 4.30175i −0.142445 + 0.246722i
\(305\) 9.22729 0.528353
\(306\) 0 0
\(307\) −20.3912 −1.16379 −0.581893 0.813265i \(-0.697688\pi\)
−0.581893 + 0.813265i \(0.697688\pi\)
\(308\) −25.3078 + 43.8344i −1.44205 + 2.49770i
\(309\) 0 0
\(310\) −3.24249 5.61615i −0.184161 0.318976i
\(311\) −11.0895 19.2076i −0.628828 1.08916i −0.987787 0.155809i \(-0.950201\pi\)
0.358959 0.933353i \(-0.383132\pi\)
\(312\) 0 0
\(313\) 5.58602 9.67527i 0.315740 0.546879i −0.663854 0.747862i \(-0.731080\pi\)
0.979595 + 0.200984i \(0.0644138\pi\)
\(314\) 29.3638 1.65709
\(315\) 0 0
\(316\) 11.4527 0.644265
\(317\) −12.6083 + 21.8383i −0.708154 + 1.22656i 0.257387 + 0.966309i \(0.417139\pi\)
−0.965541 + 0.260251i \(0.916195\pi\)
\(318\) 0 0
\(319\) −6.18651 10.7154i −0.346378 0.599945i
\(320\) −11.8632 20.5476i −0.663172 1.14865i
\(321\) 0 0
\(322\) −22.1711 + 38.4014i −1.23554 + 2.14003i
\(323\) −4.34438 −0.241728
\(324\) 0 0
\(325\) 0.864837 0.0479725
\(326\) −1.26781 + 2.19591i −0.0702173 + 0.121620i
\(327\) 0 0
\(328\) 1.23874 + 2.14556i 0.0683981 + 0.118469i
\(329\) −17.4143 30.1625i −0.960083 1.66291i
\(330\) 0 0
\(331\) 13.0828 22.6602i 0.719098 1.24551i −0.242259 0.970212i \(-0.577888\pi\)
0.961357 0.275303i \(-0.0887782\pi\)
\(332\) −21.2658 −1.16711
\(333\) 0 0
\(334\) 50.8654 2.78323
\(335\) 4.27763 7.40908i 0.233712 0.404801i
\(336\) 0 0
\(337\) −5.47302 9.47956i −0.298135 0.516384i 0.677575 0.735454i \(-0.263031\pi\)
−0.975709 + 0.219070i \(0.929698\pi\)
\(338\) −12.2416 21.2030i −0.665853 1.15329i
\(339\) 0 0
\(340\) 6.15723 10.6646i 0.333923 0.578371i
\(341\) 6.11463 0.331126
\(342\) 0 0
\(343\) 46.1091 2.48966
\(344\) −3.00564 + 5.20592i −0.162053 + 0.280684i
\(345\) 0 0
\(346\) −9.71138 16.8206i −0.522087 0.904282i
\(347\) −1.75669 3.04268i −0.0943040 0.163339i 0.815014 0.579441i \(-0.196729\pi\)
−0.909318 + 0.416102i \(0.863396\pi\)
\(348\) 0 0
\(349\) 14.5984 25.2852i 0.781436 1.35349i −0.149670 0.988736i \(-0.547821\pi\)
0.931105 0.364750i \(-0.118846\pi\)
\(350\) 7.32796 0.391696
\(351\) 0 0
\(352\) 32.9256 1.75494
\(353\) 12.5384 21.7172i 0.667352 1.15589i −0.311290 0.950315i \(-0.600761\pi\)
0.978642 0.205573i \(-0.0659056\pi\)
\(354\) 0 0
\(355\) 3.19495 + 5.53382i 0.169571 + 0.293705i
\(356\) −21.3375 36.9577i −1.13089 1.95875i
\(357\) 0 0
\(358\) 11.2635 19.5089i 0.595292 1.03108i
\(359\) 4.20724 0.222050 0.111025 0.993818i \(-0.464587\pi\)
0.111025 + 0.993818i \(0.464587\pi\)
\(360\) 0 0
\(361\) −15.6217 −0.822196
\(362\) −1.55437 + 2.69225i −0.0816961 + 0.141502i
\(363\) 0 0
\(364\) 7.41650 + 12.8458i 0.388730 + 0.673300i
\(365\) 13.2127 + 22.8850i 0.691582 + 1.19786i
\(366\) 0 0
\(367\) −8.74832 + 15.1525i −0.456658 + 0.790956i −0.998782 0.0493433i \(-0.984287\pi\)
0.542123 + 0.840299i \(0.317620\pi\)
\(368\) 11.6304 0.606279
\(369\) 0 0
\(370\) 39.4800 2.05247
\(371\) 15.3413 26.5719i 0.796479 1.37954i
\(372\) 0 0
\(373\) 14.8273 + 25.6816i 0.767728 + 1.32974i 0.938792 + 0.344483i \(0.111946\pi\)
−0.171065 + 0.985260i \(0.554721\pi\)
\(374\) 10.4210 + 18.0497i 0.538858 + 0.933330i
\(375\) 0 0
\(376\) 3.93627 6.81783i 0.202998 0.351603i
\(377\) −3.62594 −0.186745
\(378\) 0 0
\(379\) 20.9523 1.07625 0.538124 0.842865i \(-0.319133\pi\)
0.538124 + 0.842865i \(0.319133\pi\)
\(380\) −4.78797 + 8.29301i −0.245618 + 0.425422i
\(381\) 0 0
\(382\) 13.1988 + 22.8611i 0.675312 + 1.16967i
\(383\) −4.94839 8.57086i −0.252851 0.437950i 0.711459 0.702728i \(-0.248035\pi\)
−0.964310 + 0.264777i \(0.914702\pi\)
\(384\) 0 0
\(385\) 20.8332 36.0841i 1.06176 1.83902i
\(386\) −44.1439 −2.24686
\(387\) 0 0
\(388\) −12.8549 −0.652608
\(389\) 10.5574 18.2859i 0.535281 0.927133i −0.463869 0.885904i \(-0.653539\pi\)
0.999150 0.0412294i \(-0.0131274\pi\)
\(390\) 0 0
\(391\) 5.08604 + 8.80928i 0.257212 + 0.445504i
\(392\) 9.04709 + 15.6700i 0.456947 + 0.791455i
\(393\) 0 0
\(394\) −15.0757 + 26.1118i −0.759501 + 1.31549i
\(395\) −9.42776 −0.474362
\(396\) 0 0
\(397\) −9.77909 −0.490799 −0.245399 0.969422i \(-0.578919\pi\)
−0.245399 + 0.969422i \(0.578919\pi\)
\(398\) 21.5995 37.4114i 1.08268 1.87526i
\(399\) 0 0
\(400\) −0.961021 1.66454i −0.0480510 0.0832268i
\(401\) 9.56967 + 16.5752i 0.477886 + 0.827724i 0.999679 0.0253491i \(-0.00806972\pi\)
−0.521792 + 0.853073i \(0.674736\pi\)
\(402\) 0 0
\(403\) 0.895952 1.55183i 0.0446305 0.0773024i
\(404\) 46.7423 2.32552
\(405\) 0 0
\(406\) −30.7234 −1.52478
\(407\) −18.6127 + 32.2381i −0.922597 + 1.59799i
\(408\) 0 0
\(409\) −7.49778 12.9865i −0.370741 0.642143i 0.618938 0.785439i \(-0.287563\pi\)
−0.989680 + 0.143297i \(0.954230\pi\)
\(410\) −4.97407 8.61534i −0.245652 0.425481i
\(411\) 0 0
\(412\) −11.3281 + 19.6209i −0.558096 + 0.966651i
\(413\) 1.27160 0.0625712
\(414\) 0 0
\(415\) 17.5058 0.859325
\(416\) 4.82446 8.35621i 0.236539 0.409697i
\(417\) 0 0
\(418\) −8.10357 14.0358i −0.396359 0.686513i
\(419\) −2.90590 5.03317i −0.141963 0.245886i 0.786273 0.617879i \(-0.212008\pi\)
−0.928236 + 0.371993i \(0.878675\pi\)
\(420\) 0 0
\(421\) 6.65676 11.5298i 0.324431 0.561930i −0.656966 0.753920i \(-0.728161\pi\)
0.981397 + 0.191990i \(0.0614940\pi\)
\(422\) 20.9598 1.02031
\(423\) 0 0
\(424\) 6.93538 0.336812
\(425\) 0.840517 1.45582i 0.0407711 0.0706175i
\(426\) 0 0
\(427\) 10.8019 + 18.7094i 0.522740 + 0.905412i
\(428\) −9.34198 16.1808i −0.451562 0.782128i
\(429\) 0 0
\(430\) 12.0689 20.9040i 0.582014 1.00808i
\(431\) −36.4166 −1.75413 −0.877064 0.480374i \(-0.840501\pi\)
−0.877064 + 0.480374i \(0.840501\pi\)
\(432\) 0 0
\(433\) −10.8761 −0.522674 −0.261337 0.965248i \(-0.584163\pi\)
−0.261337 + 0.965248i \(0.584163\pi\)
\(434\) 7.59160 13.1490i 0.364408 0.631174i
\(435\) 0 0
\(436\) 7.07423 + 12.2529i 0.338794 + 0.586809i
\(437\) −3.95499 6.85025i −0.189193 0.327692i
\(438\) 0 0
\(439\) −4.72663 + 8.18677i −0.225590 + 0.390733i −0.956496 0.291745i \(-0.905764\pi\)
0.730906 + 0.682478i \(0.239098\pi\)
\(440\) 9.41811 0.448991
\(441\) 0 0
\(442\) 6.10780 0.290518
\(443\) −8.26196 + 14.3101i −0.392537 + 0.679895i −0.992783 0.119921i \(-0.961736\pi\)
0.600246 + 0.799815i \(0.295069\pi\)
\(444\) 0 0
\(445\) 17.5649 + 30.4232i 0.832654 + 1.44220i
\(446\) 16.0136 + 27.7363i 0.758264 + 1.31335i
\(447\) 0 0
\(448\) 27.7751 48.1080i 1.31225 2.27289i
\(449\) −4.74362 −0.223865 −0.111933 0.993716i \(-0.535704\pi\)
−0.111933 + 0.993716i \(0.535704\pi\)
\(450\) 0 0
\(451\) 9.38002 0.441688
\(452\) 3.02225 5.23470i 0.142155 0.246219i
\(453\) 0 0
\(454\) −24.1112 41.7618i −1.13159 1.95998i
\(455\) −6.10519 10.5745i −0.286216 0.495741i
\(456\) 0 0
\(457\) 11.2043 19.4064i 0.524114 0.907792i −0.475492 0.879720i \(-0.657730\pi\)
0.999606 0.0280718i \(-0.00893670\pi\)
\(458\) −18.5232 −0.865534
\(459\) 0 0
\(460\) 22.4214 1.04540
\(461\) 7.46113 12.9231i 0.347499 0.601887i −0.638305 0.769783i \(-0.720364\pi\)
0.985805 + 0.167897i \(0.0536975\pi\)
\(462\) 0 0
\(463\) 7.42359 + 12.8580i 0.345003 + 0.597563i 0.985354 0.170519i \(-0.0545444\pi\)
−0.640351 + 0.768082i \(0.721211\pi\)
\(464\) 4.02920 + 6.97878i 0.187051 + 0.323982i
\(465\) 0 0
\(466\) −25.0636 + 43.4114i −1.16105 + 2.01100i
\(467\) −15.3514 −0.710379 −0.355190 0.934794i \(-0.615584\pi\)
−0.355190 + 0.934794i \(0.615584\pi\)
\(468\) 0 0
\(469\) 20.0304 0.924917
\(470\) −15.8058 + 27.3764i −0.729067 + 1.26278i
\(471\) 0 0
\(472\) 0.143714 + 0.248920i 0.00661496 + 0.0114574i
\(473\) 11.3797 + 19.7102i 0.523238 + 0.906275i
\(474\) 0 0
\(475\) −0.653601 + 1.13207i −0.0299893 + 0.0519429i
\(476\) 28.8317 1.32150
\(477\) 0 0
\(478\) −21.1536 −0.967545
\(479\) −5.22430 + 9.04876i −0.238705 + 0.413448i −0.960343 0.278822i \(-0.910056\pi\)
0.721638 + 0.692270i \(0.243389\pi\)
\(480\) 0 0
\(481\) 5.45449 + 9.44745i 0.248703 + 0.430766i
\(482\) 6.07062 + 10.5146i 0.276509 + 0.478928i
\(483\) 0 0
\(484\) −7.82178 + 13.5477i −0.355536 + 0.615806i
\(485\) 10.5820 0.480505
\(486\) 0 0
\(487\) −16.1649 −0.732500 −0.366250 0.930516i \(-0.619359\pi\)
−0.366250 + 0.930516i \(0.619359\pi\)
\(488\) −2.44162 + 4.22901i −0.110527 + 0.191438i
\(489\) 0 0
\(490\) −36.3278 62.9217i −1.64112 2.84251i
\(491\) 5.38867 + 9.33345i 0.243187 + 0.421213i 0.961620 0.274383i \(-0.0884737\pi\)
−0.718433 + 0.695596i \(0.755140\pi\)
\(492\) 0 0
\(493\) −3.52397 + 6.10370i −0.158712 + 0.274897i
\(494\) −4.74953 −0.213692
\(495\) 0 0
\(496\) −3.98238 −0.178814
\(497\) −7.48032 + 12.9563i −0.335538 + 0.581169i
\(498\) 0 0
\(499\) 9.59359 + 16.6166i 0.429468 + 0.743861i 0.996826 0.0796106i \(-0.0253677\pi\)
−0.567358 + 0.823471i \(0.692034\pi\)
\(500\) −14.8776 25.7687i −0.665346 1.15241i
\(501\) 0 0
\(502\) −7.74537 + 13.4154i −0.345693 + 0.598758i
\(503\) −12.0251 −0.536171 −0.268086 0.963395i \(-0.586391\pi\)
−0.268086 + 0.963395i \(0.586391\pi\)
\(504\) 0 0
\(505\) −38.4778 −1.71224
\(506\) −18.9740 + 32.8639i −0.843496 + 1.46098i
\(507\) 0 0
\(508\) 11.6161 + 20.1196i 0.515380 + 0.892664i
\(509\) 7.47651 + 12.9497i 0.331391 + 0.573985i 0.982785 0.184754i \(-0.0591489\pi\)
−0.651394 + 0.758739i \(0.725816\pi\)
\(510\) 0 0
\(511\) −30.9347 + 53.5804i −1.36847 + 2.37026i
\(512\) −27.3678 −1.20950
\(513\) 0 0
\(514\) 49.3922 2.17860
\(515\) 9.32521 16.1517i 0.410918 0.711730i
\(516\) 0 0
\(517\) −14.9032 25.8130i −0.655440 1.13526i
\(518\) 46.2171 + 80.0503i 2.03066 + 3.51721i
\(519\) 0 0
\(520\) 1.38000 2.39023i 0.0605169 0.104818i
\(521\) 37.4188 1.63935 0.819673 0.572832i \(-0.194155\pi\)
0.819673 + 0.572832i \(0.194155\pi\)
\(522\) 0 0
\(523\) −8.44979 −0.369483 −0.184742 0.982787i \(-0.559145\pi\)
−0.184742 + 0.982787i \(0.559145\pi\)
\(524\) 19.2945 33.4191i 0.842885 1.45992i
\(525\) 0 0
\(526\) −29.1125 50.4243i −1.26936 2.19860i
\(527\) −1.74151 3.01639i −0.0758615 0.131396i
\(528\) 0 0
\(529\) 2.23965 3.87918i 0.0973760 0.168660i
\(530\) −27.8484 −1.20966
\(531\) 0 0
\(532\) −22.4201 −0.972033
\(533\) 1.37442 2.38056i 0.0595326 0.103113i
\(534\) 0 0
\(535\) 7.69023 + 13.3199i 0.332478 + 0.575868i
\(536\) 2.26380 + 3.92101i 0.0977812 + 0.169362i
\(537\) 0 0
\(538\) 10.0086 17.3354i 0.431501 0.747382i
\(539\) 68.5065 2.95078
\(540\) 0 0
\(541\) 12.6259 0.542828 0.271414 0.962463i \(-0.412509\pi\)
0.271414 + 0.962463i \(0.412509\pi\)
\(542\) 27.9225 48.3633i 1.19938 2.07738i
\(543\) 0 0
\(544\) −9.37758 16.2424i −0.402060 0.696389i
\(545\) −5.82345 10.0865i −0.249449 0.432058i
\(546\) 0 0
\(547\) −15.6975 + 27.1889i −0.671178 + 1.16251i 0.306393 + 0.951905i \(0.400878\pi\)
−0.977570 + 0.210609i \(0.932455\pi\)
\(548\) −9.16731 −0.391608
\(549\) 0 0
\(550\) 6.27126 0.267407
\(551\) 2.74030 4.74634i 0.116741 0.202201i
\(552\) 0 0
\(553\) −11.0366 19.1159i −0.469322 0.812890i
\(554\) 0.398243 + 0.689777i 0.0169197 + 0.0293058i
\(555\) 0 0
\(556\) −16.6989 + 28.9234i −0.708193 + 1.22663i
\(557\) −15.9303 −0.674988 −0.337494 0.941328i \(-0.609579\pi\)
−0.337494 + 0.941328i \(0.609579\pi\)
\(558\) 0 0
\(559\) 6.66967 0.282097
\(560\) −13.5684 + 23.5011i −0.573369 + 0.993103i
\(561\) 0 0
\(562\) 14.8556 + 25.7307i 0.626647 + 1.08538i
\(563\) 12.4304 + 21.5301i 0.523880 + 0.907387i 0.999614 + 0.0277973i \(0.00884931\pi\)
−0.475734 + 0.879589i \(0.657817\pi\)
\(564\) 0 0
\(565\) −2.48789 + 4.30915i −0.104666 + 0.181287i
\(566\) −33.0695 −1.39001
\(567\) 0 0
\(568\) −3.38165 −0.141891
\(569\) −9.59500 + 16.6190i −0.402243 + 0.696706i −0.993996 0.109413i \(-0.965103\pi\)
0.591753 + 0.806119i \(0.298436\pi\)
\(570\) 0 0
\(571\) 10.1896 + 17.6489i 0.426422 + 0.738585i 0.996552 0.0829696i \(-0.0264404\pi\)
−0.570130 + 0.821555i \(0.693107\pi\)
\(572\) 6.34703 + 10.9934i 0.265383 + 0.459656i
\(573\) 0 0
\(574\) 11.6457 20.1710i 0.486084 0.841921i
\(575\) 3.06072 0.127641
\(576\) 0 0
\(577\) 23.2991 0.969953 0.484976 0.874527i \(-0.338828\pi\)
0.484976 + 0.874527i \(0.338828\pi\)
\(578\) −12.1267 + 21.0041i −0.504404 + 0.873654i
\(579\) 0 0
\(580\) 7.76758 + 13.4539i 0.322531 + 0.558641i
\(581\) 20.4931 + 35.4950i 0.850195 + 1.47258i
\(582\) 0 0
\(583\) 13.1290 22.7402i 0.543749 0.941802i
\(584\) −13.9847 −0.578693
\(585\) 0 0
\(586\) −52.3272 −2.16162
\(587\) 18.4546 31.9644i 0.761704 1.31931i −0.180267 0.983618i \(-0.557696\pi\)
0.941971 0.335693i \(-0.108970\pi\)
\(588\) 0 0
\(589\) 1.35423 + 2.34560i 0.0558001 + 0.0966486i
\(590\) −0.577071 0.999516i −0.0237576 0.0411494i
\(591\) 0 0
\(592\) 12.1222 20.9963i 0.498220 0.862943i
\(593\) 4.36830 0.179385 0.0896923 0.995970i \(-0.471412\pi\)
0.0896923 + 0.995970i \(0.471412\pi\)
\(594\) 0 0
\(595\) −23.7340 −0.973000
\(596\) −11.2089 + 19.4144i −0.459134 + 0.795244i
\(597\) 0 0
\(598\) 5.56036 + 9.63082i 0.227380 + 0.393833i
\(599\) 15.6028 + 27.0249i 0.637513 + 1.10421i 0.985977 + 0.166883i \(0.0533702\pi\)
−0.348463 + 0.937322i \(0.613296\pi\)
\(600\) 0 0
\(601\) −21.9686 + 38.0507i −0.896116 + 1.55212i −0.0636987 + 0.997969i \(0.520290\pi\)
−0.832417 + 0.554149i \(0.813044\pi\)
\(602\) 56.5136 2.30332
\(603\) 0 0
\(604\) −1.79223 −0.0729247
\(605\) 6.43882 11.1524i 0.261775 0.453408i
\(606\) 0 0
\(607\) −8.67933 15.0330i −0.352283 0.610172i 0.634366 0.773033i \(-0.281261\pi\)
−0.986649 + 0.162861i \(0.947928\pi\)
\(608\) 7.29217 + 12.6304i 0.295736 + 0.512231i
\(609\) 0 0
\(610\) 9.80413 16.9813i 0.396958 0.687551i
\(611\) −8.73480 −0.353372
\(612\) 0 0
\(613\) −1.19805 −0.0483887 −0.0241944 0.999707i \(-0.507702\pi\)
−0.0241944 + 0.999707i \(0.507702\pi\)
\(614\) −21.6659 + 37.5265i −0.874365 + 1.51444i
\(615\) 0 0
\(616\) 11.0253 + 19.0963i 0.444221 + 0.769413i
\(617\) −13.0069 22.5285i −0.523636 0.906965i −0.999621 0.0275115i \(-0.991242\pi\)
0.475985 0.879453i \(-0.342092\pi\)
\(618\) 0 0
\(619\) −4.81567 + 8.34099i −0.193558 + 0.335253i −0.946427 0.322918i \(-0.895336\pi\)
0.752869 + 0.658171i \(0.228670\pi\)
\(620\) −7.67733 −0.308329
\(621\) 0 0
\(622\) −47.1311 −1.88978
\(623\) −41.1244 + 71.2296i −1.64762 + 2.85375i
\(624\) 0 0
\(625\) 10.4691 + 18.1330i 0.418763 + 0.725319i
\(626\) −11.8705 20.5602i −0.474439 0.821752i
\(627\) 0 0
\(628\) 17.3814 30.1054i 0.693592 1.20134i
\(629\) 21.2044 0.845474
\(630\) 0 0
\(631\) −14.1673 −0.563992 −0.281996 0.959416i \(-0.590997\pi\)
−0.281996 + 0.959416i \(0.590997\pi\)
\(632\) 2.49467 4.32089i 0.0992325 0.171876i
\(633\) 0 0
\(634\) 26.7931 + 46.4069i 1.06409 + 1.84306i
\(635\) −9.56225 16.5623i −0.379466 0.657255i
\(636\) 0 0
\(637\) 10.0380 17.3863i 0.397719 0.688870i
\(638\) −26.2930 −1.04095
\(639\) 0 0
\(640\) −17.5539 −0.693879
\(641\) −11.1005 + 19.2266i −0.438442 + 0.759403i −0.997570 0.0696782i \(-0.977803\pi\)
0.559128 + 0.829081i \(0.311136\pi\)
\(642\) 0 0
\(643\) −10.7684 18.6514i −0.424664 0.735540i 0.571725 0.820445i \(-0.306274\pi\)
−0.996389 + 0.0849056i \(0.972941\pi\)
\(644\) 26.2475 + 45.4621i 1.03430 + 1.79146i
\(645\) 0 0
\(646\) −4.61597 + 7.99509i −0.181613 + 0.314563i
\(647\) 13.4037 0.526952 0.263476 0.964666i \(-0.415131\pi\)
0.263476 + 0.964666i \(0.415131\pi\)
\(648\) 0 0
\(649\) 1.08823 0.0427168
\(650\) 0.918902 1.59159i 0.0360423 0.0624271i
\(651\) 0 0
\(652\) 1.50091 + 2.59966i 0.0587802 + 0.101810i
\(653\) 9.45543 + 16.3773i 0.370020 + 0.640893i 0.989568 0.144066i \(-0.0460176\pi\)
−0.619548 + 0.784958i \(0.712684\pi\)
\(654\) 0 0
\(655\) −15.8831 + 27.5103i −0.620603 + 1.07492i
\(656\) −6.10909 −0.238520
\(657\) 0 0
\(658\) −74.0119 −2.88528
\(659\) 0.0140907 0.0244058i 0.000548897 0.000950717i −0.865751 0.500475i \(-0.833159\pi\)
0.866300 + 0.499525i \(0.166492\pi\)
\(660\) 0 0
\(661\) 22.5209 + 39.0073i 0.875960 + 1.51721i 0.855736 + 0.517412i \(0.173105\pi\)
0.0202238 + 0.999795i \(0.493562\pi\)
\(662\) −27.8014 48.1535i −1.08053 1.87154i
\(663\) 0 0
\(664\) −4.63218 + 8.02317i −0.179763 + 0.311359i
\(665\) 18.4560 0.715693
\(666\) 0 0
\(667\) −12.8325 −0.496875
\(668\) 30.1089 52.1501i 1.16495 2.01775i
\(669\) 0 0
\(670\) −9.09010 15.7445i −0.351181 0.608263i
\(671\) 9.24424 + 16.0115i 0.356870 + 0.618117i
\(672\) 0 0
\(673\) 4.87984 8.45214i 0.188104 0.325806i −0.756514 0.653978i \(-0.773099\pi\)
0.944618 + 0.328172i \(0.106432\pi\)
\(674\) −23.2607 −0.895968
\(675\) 0 0
\(676\) −28.9847 −1.11480
\(677\) −20.4404 + 35.4038i −0.785588 + 1.36068i 0.143060 + 0.989714i \(0.454306\pi\)
−0.928647 + 0.370964i \(0.879027\pi\)
\(678\) 0 0
\(679\) 12.3878 + 21.4563i 0.475400 + 0.823417i
\(680\) −2.68238 4.64602i −0.102865 0.178167i
\(681\) 0 0
\(682\) 6.49688 11.2529i 0.248779 0.430897i
\(683\) −44.0251 −1.68457 −0.842287 0.539029i \(-0.818791\pi\)
−0.842287 + 0.539029i \(0.818791\pi\)
\(684\) 0 0
\(685\) 7.54644 0.288335
\(686\) 48.9916 84.8559i 1.87051 3.23981i
\(687\) 0 0
\(688\) −7.41144 12.8370i −0.282559 0.489406i
\(689\) −3.84749 6.66405i −0.146578 0.253880i
\(690\) 0 0
\(691\) −10.7758 + 18.6642i −0.409931 + 0.710021i −0.994882 0.101048i \(-0.967781\pi\)
0.584951 + 0.811069i \(0.301114\pi\)
\(692\) −22.9939 −0.874098
\(693\) 0 0
\(694\) −7.46603 −0.283407
\(695\) 13.7464 23.8095i 0.521432 0.903146i
\(696\) 0 0
\(697\) −2.67153 4.62723i −0.101191 0.175269i
\(698\) −31.0221 53.7318i −1.17420 2.03378i
\(699\) 0 0
\(700\) 4.33766 7.51304i 0.163948 0.283966i
\(701\) −12.8521 −0.485419 −0.242709 0.970099i \(-0.578036\pi\)
−0.242709 + 0.970099i \(0.578036\pi\)
\(702\) 0 0
\(703\) −16.4889 −0.621891
\(704\) 23.7699 41.1707i 0.895863 1.55168i
\(705\) 0 0
\(706\) −26.6445 46.1496i −1.00278 1.73686i
\(707\) −45.0439 78.0183i −1.69405 2.93418i
\(708\) 0 0
\(709\) 24.8559 43.0516i 0.933481 1.61684i 0.156161 0.987732i \(-0.450088\pi\)
0.777320 0.629105i \(-0.216578\pi\)
\(710\) 13.5787 0.509601
\(711\) 0 0
\(712\) −18.5912 −0.696737
\(713\) 3.17084 5.49206i 0.118749 0.205679i
\(714\) 0 0
\(715\) −5.22482 9.04965i −0.195397 0.338438i
\(716\) −13.3344 23.0959i −0.498330 0.863133i
\(717\) 0 0
\(718\) 4.47026 7.74271i 0.166828 0.288955i
\(719\) −5.63745 −0.210242 −0.105121 0.994459i \(-0.533523\pi\)
−0.105121 + 0.994459i \(0.533523\pi\)
\(720\) 0 0
\(721\) 43.6660 1.62621
\(722\) −16.5983 + 28.7491i −0.617725 + 1.06993i
\(723\) 0 0
\(724\) 1.84017 + 3.18727i 0.0683893 + 0.118454i
\(725\) 1.06034 + 1.83657i 0.0393802 + 0.0682085i
\(726\) 0 0
\(727\) 22.7071 39.3299i 0.842161 1.45867i −0.0459026 0.998946i \(-0.514616\pi\)
0.888064 0.459720i \(-0.152050\pi\)
\(728\) 6.46195 0.239496
\(729\) 0 0
\(730\) 56.1546 2.07837
\(731\) 6.48211 11.2273i 0.239749 0.415258i
\(732\) 0 0
\(733\) 12.8334 + 22.2281i 0.474013 + 0.821015i 0.999557 0.0297511i \(-0.00947148\pi\)
−0.525544 + 0.850766i \(0.676138\pi\)
\(734\) 18.5904 + 32.1996i 0.686185 + 1.18851i
\(735\) 0 0
\(736\) 17.0741 29.5733i 0.629361 1.09008i
\(737\) 17.1420 0.631433
\(738\) 0 0
\(739\) −14.4553 −0.531745 −0.265873 0.964008i \(-0.585660\pi\)
−0.265873 + 0.964008i \(0.585660\pi\)
\(740\) 23.3695 40.4772i 0.859080 1.48797i
\(741\) 0 0
\(742\) −32.6006 56.4660i −1.19681 2.07293i
\(743\) −17.3969 30.1323i −0.638229 1.10545i −0.985821 0.167799i \(-0.946334\pi\)
0.347592 0.937646i \(-0.386999\pi\)
\(744\) 0 0
\(745\) 9.22706 15.9817i 0.338053 0.585525i
\(746\) 63.0168 2.30721
\(747\) 0 0
\(748\) 24.6742 0.902177
\(749\) −18.0051 + 31.1857i −0.657891 + 1.13950i
\(750\) 0 0
\(751\) −9.05922 15.6910i −0.330576 0.572574i 0.652049 0.758177i \(-0.273910\pi\)
−0.982625 + 0.185603i \(0.940576\pi\)
\(752\) 9.70624 + 16.8117i 0.353950 + 0.613060i
\(753\) 0 0
\(754\) −3.85261 + 6.67292i −0.140304 + 0.243013i
\(755\) 1.47535 0.0536933
\(756\) 0 0
\(757\) −37.0045 −1.34495 −0.672475 0.740120i \(-0.734769\pi\)
−0.672475 + 0.740120i \(0.734769\pi\)
\(758\) 22.2621 38.5592i 0.808598 1.40053i
\(759\) 0 0
\(760\) 2.08587 + 3.61282i 0.0756623 + 0.131051i
\(761\) 6.22221 + 10.7772i 0.225555 + 0.390673i 0.956486 0.291779i \(-0.0942472\pi\)
−0.730931 + 0.682452i \(0.760914\pi\)
\(762\) 0 0
\(763\) 13.6344 23.6154i 0.493598 0.854936i
\(764\) 31.2513 1.13063
\(765\) 0 0
\(766\) −21.0309 −0.759878
\(767\) 0.159454 0.276183i 0.00575755 0.00997238i
\(768\) 0 0
\(769\) 20.4428 + 35.4079i 0.737186 + 1.27684i 0.953758 + 0.300576i \(0.0971790\pi\)
−0.216572 + 0.976267i \(0.569488\pi\)
\(770\) −44.2711 76.6797i −1.59542 2.76335i
\(771\) 0 0
\(772\) −26.1302 + 45.2588i −0.940446 + 1.62890i
\(773\) −36.4162 −1.30980 −0.654900 0.755716i \(-0.727289\pi\)
−0.654900 + 0.755716i \(0.727289\pi\)
\(774\) 0 0
\(775\) −1.04802 −0.0376461
\(776\) −2.80010 + 4.84991i −0.100518 + 0.174102i
\(777\) 0 0
\(778\) −22.4347 38.8581i −0.804324 1.39313i
\(779\) 2.07743 + 3.59821i 0.0744316 + 0.128919i
\(780\) 0 0
\(781\) −6.40165 + 11.0880i −0.229069 + 0.396759i
\(782\) 21.6160 0.772985
\(783\) 0 0
\(784\) −44.6174 −1.59348
\(785\) −14.3082 + 24.7825i −0.510681 + 0.884525i
\(786\) 0 0
\(787\) −9.17358 15.8891i −0.327003 0.566385i 0.654913 0.755704i \(-0.272705\pi\)
−0.981916 + 0.189319i \(0.939372\pi\)
\(788\) 17.8475 + 30.9128i 0.635792 + 1.10122i
\(789\) 0 0
\(790\) −10.0171 + 17.3502i −0.356394 + 0.617292i
\(791\) −11.6498 −0.414218
\(792\) 0 0
\(793\) 5.41808 0.192402
\(794\) −10.3904 + 17.9967i −0.368742 + 0.638681i
\(795\) 0 0
\(796\) −25.5709 44.2900i −0.906335 1.56982i
\(797\) −1.73246 3.00071i −0.0613670 0.106291i 0.833710 0.552203i \(-0.186213\pi\)
−0.895077 + 0.445912i \(0.852879\pi\)
\(798\) 0 0
\(799\) −8.48916 + 14.7037i −0.300325 + 0.520178i
\(800\) −5.64333 −0.199522
\(801\) 0 0
\(802\) 40.6716 1.43617
\(803\) −26.4739 + 45.8541i −0.934243 + 1.61816i
\(804\) 0 0
\(805\) −21.6067 37.4240i −0.761537 1.31902i
\(806\) −1.90392 3.29769i −0.0670628 0.116156i
\(807\) 0 0
\(808\) 10.1816 17.6350i 0.358186 0.620397i
\(809\) −24.8406 −0.873348 −0.436674 0.899620i \(-0.643844\pi\)
−0.436674 + 0.899620i \(0.643844\pi\)
\(810\) 0 0
\(811\) −40.3286 −1.41613 −0.708063 0.706149i \(-0.750431\pi\)
−0.708063 + 0.706149i \(0.750431\pi\)
\(812\) −18.1862 + 31.4994i −0.638209 + 1.10541i
\(813\) 0 0
\(814\) 39.5525 + 68.5070i 1.38632 + 2.40117i
\(815\) −1.23554 2.14001i −0.0432790 0.0749614i
\(816\) 0 0
\(817\) −5.04060 + 8.73058i −0.176348 + 0.305444i
\(818\) −31.8660 −1.11417
\(819\) 0 0
\(820\) −11.7772 −0.411279
\(821\) −20.0908 + 34.7983i −0.701174 + 1.21447i 0.266880 + 0.963730i \(0.414007\pi\)
−0.968055 + 0.250740i \(0.919326\pi\)
\(822\) 0 0
\(823\) 23.9777 + 41.5306i 0.835810 + 1.44766i 0.893370 + 0.449323i \(0.148335\pi\)
−0.0575599 + 0.998342i \(0.518332\pi\)
\(824\) 4.93506 + 8.54777i 0.171921 + 0.297776i
\(825\) 0 0
\(826\) 1.35109 2.34016i 0.0470104 0.0814245i
\(827\) −5.00048 −0.173884 −0.0869419 0.996213i \(-0.527709\pi\)
−0.0869419 + 0.996213i \(0.527709\pi\)
\(828\) 0 0
\(829\) 29.7037 1.03165 0.515826 0.856693i \(-0.327485\pi\)
0.515826 + 0.856693i \(0.327485\pi\)
\(830\) 18.6001 32.2164i 0.645620 1.11825i
\(831\) 0 0
\(832\) −6.96582 12.0652i −0.241496 0.418284i
\(833\) −19.5114 33.7947i −0.676030 1.17092i
\(834\) 0 0
\(835\) −24.7853 + 42.9295i −0.857732 + 1.48564i
\(836\) −19.1871 −0.663599
\(837\) 0 0
\(838\) −12.3502 −0.426632
\(839\) 12.9523 22.4340i 0.447162 0.774507i −0.551038 0.834480i \(-0.685768\pi\)
0.998200 + 0.0599731i \(0.0191015\pi\)
\(840\) 0 0
\(841\) 10.0544 + 17.4147i 0.346703 + 0.600507i
\(842\) −14.1458 24.5012i −0.487497 0.844369i
\(843\) 0 0
\(844\) 12.4068 21.4892i 0.427060 0.739690i
\(845\) 23.8599 0.820807
\(846\) 0 0
\(847\) 30.1503 1.03598
\(848\) −8.55078 + 14.8104i −0.293635 + 0.508591i
\(849\) 0 0
\(850\) −1.78612 3.09365i −0.0612635 0.106111i
\(851\) 19.3038 + 33.4352i 0.661727 + 1.14614i
\(852\) 0 0
\(853\) 2.49583 4.32290i 0.0854556 0.148013i −0.820130 0.572178i \(-0.806099\pi\)
0.905585 + 0.424164i \(0.139432\pi\)
\(854\) 45.9086 1.57096
\(855\) 0 0
\(856\) −8.13961 −0.278206
\(857\) 7.34151 12.7159i 0.250781 0.434366i −0.712960 0.701205i \(-0.752646\pi\)
0.963741 + 0.266839i \(0.0859792\pi\)
\(858\) 0 0
\(859\) 8.74243 + 15.1423i 0.298288 + 0.516650i 0.975744 0.218913i \(-0.0702511\pi\)
−0.677457 + 0.735563i \(0.736918\pi\)
\(860\) −14.2880 24.7475i −0.487215 0.843881i
\(861\) 0 0
\(862\) −38.6932 + 67.0186i −1.31790 + 2.28266i
\(863\) 6.33263 0.215565 0.107783 0.994174i \(-0.465625\pi\)
0.107783 + 0.994174i \(0.465625\pi\)
\(864\) 0 0
\(865\) 18.9284 0.643585
\(866\) −11.5560 + 20.0157i −0.392691 + 0.680160i
\(867\) 0 0
\(868\) −8.98743 15.5667i −0.305053 0.528368i
\(869\) −9.44508 16.3594i −0.320402 0.554953i
\(870\) 0 0
\(871\) 2.51174 4.35047i 0.0851072 0.147410i
\(872\) 6.16374 0.208730
\(873\) 0 0
\(874\) −16.8090 −0.568571
\(875\) −28.6740 + 49.6648i −0.969358 + 1.67898i
\(876\) 0 0
\(877\) −16.2655 28.1727i −0.549247 0.951323i −0.998326 0.0578315i \(-0.981581\pi\)
0.449080 0.893492i \(-0.351752\pi\)
\(878\) 10.0442 + 17.3971i 0.338976 + 0.587124i
\(879\) 0 0
\(880\) −11.6118 + 20.1122i −0.391434 + 0.677983i
\(881\) −33.3599 −1.12393 −0.561963 0.827163i \(-0.689954\pi\)
−0.561963 + 0.827163i \(0.689954\pi\)
\(882\) 0 0
\(883\) −54.8511 −1.84589 −0.922944 0.384934i \(-0.874224\pi\)
−0.922944 + 0.384934i \(0.874224\pi\)
\(884\) 3.61541 6.26207i 0.121599 0.210616i
\(885\) 0 0
\(886\) 17.5569 + 30.4094i 0.589835 + 1.02162i
\(887\) −10.5239 18.2279i −0.353357 0.612032i 0.633478 0.773760i \(-0.281627\pi\)
−0.986835 + 0.161728i \(0.948293\pi\)
\(888\) 0 0
\(889\) 22.3880 38.7772i 0.750870 1.30054i
\(890\) 74.6516 2.50233
\(891\) 0 0
\(892\) 37.9158 1.26951
\(893\) 6.60132 11.4338i 0.220905 0.382618i
\(894\) 0 0
\(895\) 10.9768 + 19.0123i 0.366913 + 0.635512i
\(896\) −20.5494 35.5926i −0.686507 1.18906i
\(897\) 0 0
\(898\) −5.04016 + 8.72982i −0.168192 + 0.291318i
\(899\) 4.39397 0.146547
\(900\) 0 0
\(901\) −14.9572 −0.498296
\(902\) 9.96641 17.2623i 0.331845 0.574772i
\(903\) 0 0
\(904\) −1.31664 2.28048i −0.0437906 0.0758476i
\(905\) −1.51481 2.62373i −0.0503540 0.0872157i
\(906\) 0 0
\(907\) −7.41902 + 12.8501i −0.246344 + 0.426681i −0.962509 0.271251i \(-0.912563\pi\)
0.716164 + 0.697932i \(0.245896\pi\)
\(908\) −57.0887 −1.89456
\(909\) 0 0
\(910\) −25.9474 −0.860149
\(911\) −9.01477 + 15.6140i −0.298673 + 0.517316i −0.975833 0.218520i \(-0.929877\pi\)
0.677160 + 0.735836i \(0.263211\pi\)
\(912\) 0 0
\(913\) 17.5379 + 30.3766i 0.580421 + 1.00532i
\(914\) −23.8094 41.2391i −0.787545 1.36407i
\(915\) 0 0
\(916\) −10.9645 + 18.9911i −0.362278 + 0.627483i
\(917\) −74.3738 −2.45604
\(918\) 0 0
\(919\) 13.4881 0.444932 0.222466 0.974940i \(-0.428589\pi\)
0.222466 + 0.974940i \(0.428589\pi\)
\(920\) 4.88391 8.45919i 0.161018 0.278891i
\(921\) 0 0
\(922\) −15.8551 27.4619i −0.522160 0.904408i
\(923\) 1.87601 + 3.24935i 0.0617497 + 0.106954i
\(924\) 0 0
\(925\) 3.19014 5.52549i 0.104891 0.181677i
\(926\) 31.5507 1.03682
\(927\) 0 0
\(928\) 23.6603 0.776689
\(929\) 18.8106 32.5809i 0.617155 1.06894i −0.372847 0.927893i \(-0.621619\pi\)
0.990002 0.141051i \(-0.0450481\pi\)
\(930\) 0 0
\(931\) 15.1724 + 26.2794i 0.497255 + 0.861272i
\(932\) 29.6719 + 51.3933i 0.971936 + 1.68344i
\(933\) 0 0
\(934\) −16.3111 + 28.2517i −0.533716 + 0.924423i
\(935\) −20.3116 −0.664259
\(936\) 0 0
\(937\) 4.14458 0.135398 0.0676988 0.997706i \(-0.478434\pi\)
0.0676988 + 0.997706i \(0.478434\pi\)
\(938\) 21.2826 36.8625i 0.694900 1.20360i
\(939\) 0 0
\(940\) 18.7119 + 32.4100i 0.610316 + 1.05710i
\(941\) 1.76516 + 3.05735i 0.0575427 + 0.0996668i 0.893362 0.449338i \(-0.148340\pi\)
−0.835819 + 0.549005i \(0.815007\pi\)
\(942\) 0 0
\(943\) 4.86416 8.42497i 0.158399 0.274355i
\(944\) −0.708752 −0.0230679
\(945\) 0 0
\(946\) 48.3643 1.57246
\(947\) 7.12754 12.3453i 0.231614 0.401167i −0.726669 0.686987i \(-0.758933\pi\)
0.958283 + 0.285820i \(0.0922661\pi\)
\(948\) 0 0
\(949\) 7.75822 + 13.4376i 0.251842 + 0.436204i
\(950\) 1.38892 + 2.40568i 0.0450625 + 0.0780506i
\(951\) 0 0
\(952\) 6.28023 10.8777i 0.203543 0.352547i
\(953\) 11.6426 0.377141 0.188570 0.982060i \(-0.439615\pi\)
0.188570 + 0.982060i \(0.439615\pi\)
\(954\) 0 0
\(955\) −25.7258 −0.832467
\(956\) −12.5215 + 21.6879i −0.404975 + 0.701437i
\(957\) 0 0
\(958\) 11.1018 + 19.2289i 0.358683 + 0.621257i
\(959\) 8.83421 + 15.3013i 0.285271 + 0.494105i
\(960\) 0 0
\(961\) 14.4143 24.9663i 0.464976 0.805363i
\(962\) 23.1819 0.747414
\(963\) 0 0
\(964\) 14.3736 0.462942
\(965\) 21.5101 37.2566i 0.692436 1.19933i
\(966\) 0 0
\(967\) −14.5341 25.1737i −0.467384 0.809533i 0.531922 0.846794i \(-0.321470\pi\)
−0.999306 + 0.0372608i \(0.988137\pi\)
\(968\) 3.40754 + 5.90202i 0.109522 + 0.189698i
\(969\) 0 0
\(970\) 11.2436 19.4744i 0.361009 0.625286i
\(971\) 47.5792 1.52689 0.763444 0.645874i \(-0.223507\pi\)
0.763444 + 0.645874i \(0.223507\pi\)
\(972\) 0 0
\(973\) 64.3687 2.06357
\(974\) −17.1754 + 29.7487i −0.550336 + 0.953209i
\(975\) 0 0
\(976\) −6.02066 10.4281i −0.192717 0.333795i
\(977\) −3.05815 5.29687i −0.0978389 0.169462i 0.812951 0.582332i \(-0.197860\pi\)
−0.910790 + 0.412870i \(0.864526\pi\)
\(978\) 0 0
\(979\) −35.1942 + 60.9582i −1.12481 + 1.94823i
\(980\) −86.0145 −2.74763
\(981\) 0 0
\(982\) 22.9022 0.730837
\(983\) −5.32591 + 9.22474i −0.169870 + 0.294224i −0.938374 0.345621i \(-0.887668\pi\)
0.768504 + 0.639845i \(0.221001\pi\)
\(984\) 0 0
\(985\) −14.6919 25.4472i −0.468124 0.810814i
\(986\) 7.48854 + 12.9705i 0.238484 + 0.413066i
\(987\) 0 0
\(988\) −2.81140 + 4.86949i −0.0894426 + 0.154919i
\(989\) 23.6045 0.750578
\(990\) 0 0
\(991\) 23.9856 0.761928 0.380964 0.924590i \(-0.375592\pi\)
0.380964 + 0.924590i \(0.375592\pi\)
\(992\) −5.84636 + 10.1262i −0.185622 + 0.321507i
\(993\) 0 0
\(994\) 15.8959 + 27.5325i 0.504187 + 0.873277i
\(995\) 21.0497 + 36.4591i 0.667320 + 1.15583i
\(996\) 0 0
\(997\) −2.15709 + 3.73619i −0.0683157 + 0.118326i −0.898160 0.439669i \(-0.855096\pi\)
0.829844 + 0.557995i \(0.188429\pi\)
\(998\) 40.7733 1.29066
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 729.2.c.d.487.5 12
3.2 odd 2 729.2.c.a.487.2 12
9.2 odd 6 729.2.a.e.1.5 yes 6
9.4 even 3 inner 729.2.c.d.244.5 12
9.5 odd 6 729.2.c.a.244.2 12
9.7 even 3 729.2.a.b.1.2 6
27.2 odd 18 729.2.e.k.325.2 12
27.4 even 9 729.2.e.s.163.2 12
27.5 odd 18 729.2.e.k.406.2 12
27.7 even 9 729.2.e.j.82.1 12
27.11 odd 18 729.2.e.l.568.1 12
27.13 even 9 729.2.e.j.649.1 12
27.14 odd 18 729.2.e.u.649.2 12
27.16 even 9 729.2.e.s.568.2 12
27.20 odd 18 729.2.e.u.82.2 12
27.22 even 9 729.2.e.t.406.1 12
27.23 odd 18 729.2.e.l.163.1 12
27.25 even 9 729.2.e.t.325.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
729.2.a.b.1.2 6 9.7 even 3
729.2.a.e.1.5 yes 6 9.2 odd 6
729.2.c.a.244.2 12 9.5 odd 6
729.2.c.a.487.2 12 3.2 odd 2
729.2.c.d.244.5 12 9.4 even 3 inner
729.2.c.d.487.5 12 1.1 even 1 trivial
729.2.e.j.82.1 12 27.7 even 9
729.2.e.j.649.1 12 27.13 even 9
729.2.e.k.325.2 12 27.2 odd 18
729.2.e.k.406.2 12 27.5 odd 18
729.2.e.l.163.1 12 27.23 odd 18
729.2.e.l.568.1 12 27.11 odd 18
729.2.e.s.163.2 12 27.4 even 9
729.2.e.s.568.2 12 27.16 even 9
729.2.e.t.325.1 12 27.25 even 9
729.2.e.t.406.1 12 27.22 even 9
729.2.e.u.82.2 12 27.20 odd 18
729.2.e.u.649.2 12 27.14 odd 18