Properties

Label 729.2.c.c.244.4
Level $729$
Weight $2$
Character 729.244
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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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: \(\Q(\zeta_{36})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{6} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 244.4
Root \(-0.342020 - 0.939693i\) of defining polynomial
Character \(\chi\) \(=\) 729.244
Dual form 729.2.c.c.487.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.342020 + 0.592396i) q^{2} +(0.766044 - 1.32683i) q^{4} +(0.524005 - 0.907604i) q^{5} +(0.0603074 + 0.104455i) q^{7} +2.41609 q^{8} +O(q^{10})\) \(q+(0.342020 + 0.592396i) q^{2} +(0.766044 - 1.32683i) q^{4} +(0.524005 - 0.907604i) q^{5} +(0.0603074 + 0.104455i) q^{7} +2.41609 q^{8} +0.716881 q^{10} +(-2.71686 - 4.70574i) q^{11} +(2.28699 - 3.96118i) q^{13} +(-0.0412527 + 0.0714517i) q^{14} +(-0.705737 - 1.22237i) q^{16} -4.77833 q^{17} -0.588526 q^{19} +(-0.802823 - 1.39053i) q^{20} +(1.85844 - 3.21891i) q^{22} +(-3.89798 + 6.75150i) q^{23} +(1.95084 + 3.37895i) q^{25} +3.12879 q^{26} +0.184793 q^{28} +(2.53487 + 4.39053i) q^{29} +(4.37939 - 7.58532i) q^{31} +(2.89884 - 5.02094i) q^{32} +(-1.63429 - 2.83067i) q^{34} +0.126406 q^{35} -2.18479 q^{37} +(-0.201288 - 0.348641i) q^{38} +(1.26604 - 2.19285i) q^{40} +(3.77920 - 6.54576i) q^{41} +(0.652704 + 1.13052i) q^{43} -8.32494 q^{44} -5.33275 q^{46} +(1.20805 + 2.09240i) q^{47} +(3.49273 - 6.04958i) q^{49} +(-1.33445 + 2.31134i) q^{50} +(-3.50387 - 6.06888i) q^{52} +3.04628 q^{53} -5.69459 q^{55} +(0.145708 + 0.252374i) q^{56} +(-1.73396 + 3.00330i) q^{58} +(-0.0219501 + 0.0380187i) q^{59} +(5.10607 + 8.84397i) q^{61} +5.99135 q^{62} +1.14290 q^{64} +(-2.39679 - 4.15136i) q^{65} +(0.929892 - 1.61062i) q^{67} +(-3.66041 + 6.34002i) q^{68} +(0.0432332 + 0.0748822i) q^{70} +6.51038 q^{71} +12.2344 q^{73} +(-0.747243 - 1.29426i) q^{74} +(-0.450837 + 0.780873i) q^{76} +(0.327693 - 0.567581i) q^{77} +(-0.351167 - 0.608239i) q^{79} -1.47924 q^{80} +5.17024 q^{82} +(3.38830 + 5.86871i) q^{83} +(-2.50387 + 4.33683i) q^{85} +(-0.446476 + 0.773318i) q^{86} +(-6.56418 - 11.3695i) q^{88} -6.85565 q^{89} +0.551689 q^{91} +(5.97205 + 10.3439i) q^{92} +(-0.826352 + 1.43128i) q^{94} +(-0.308391 + 0.534148i) q^{95} +(4.51367 + 7.81791i) q^{97} +4.77833 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 12 q^{7} - 24 q^{10} + 12 q^{13} + 12 q^{16} - 48 q^{19} + 6 q^{22} - 12 q^{28} + 30 q^{31} - 12 q^{37} + 6 q^{40} + 12 q^{43} + 12 q^{46} + 6 q^{49} + 6 q^{52} - 60 q^{55} - 30 q^{58} + 12 q^{61} + 12 q^{64} - 6 q^{67} - 30 q^{70} + 24 q^{73} + 18 q^{76} + 48 q^{79} - 24 q^{82} + 18 q^{85} - 42 q^{88} - 12 q^{94} + 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.342020 + 0.592396i 0.241845 + 0.418887i 0.961240 0.275714i \(-0.0889142\pi\)
−0.719395 + 0.694601i \(0.755581\pi\)
\(3\) 0 0
\(4\) 0.766044 1.32683i 0.383022 0.663414i
\(5\) 0.524005 0.907604i 0.234342 0.405893i −0.724739 0.689023i \(-0.758040\pi\)
0.959081 + 0.283131i \(0.0913730\pi\)
\(6\) 0 0
\(7\) 0.0603074 + 0.104455i 0.0227940 + 0.0394804i 0.877197 0.480130i \(-0.159410\pi\)
−0.854403 + 0.519610i \(0.826077\pi\)
\(8\) 2.41609 0.854217
\(9\) 0 0
\(10\) 0.716881 0.226698
\(11\) −2.71686 4.70574i −0.819164 1.41883i −0.906299 0.422637i \(-0.861105\pi\)
0.0871355 0.996196i \(-0.472229\pi\)
\(12\) 0 0
\(13\) 2.28699 3.96118i 0.634297 1.09863i −0.352367 0.935862i \(-0.614623\pi\)
0.986664 0.162772i \(-0.0520435\pi\)
\(14\) −0.0412527 + 0.0714517i −0.0110252 + 0.0190963i
\(15\) 0 0
\(16\) −0.705737 1.22237i −0.176434 0.305593i
\(17\) −4.77833 −1.15892 −0.579458 0.815002i \(-0.696736\pi\)
−0.579458 + 0.815002i \(0.696736\pi\)
\(18\) 0 0
\(19\) −0.588526 −0.135017 −0.0675085 0.997719i \(-0.521505\pi\)
−0.0675085 + 0.997719i \(0.521505\pi\)
\(20\) −0.802823 1.39053i −0.179517 0.310932i
\(21\) 0 0
\(22\) 1.85844 3.21891i 0.396221 0.686275i
\(23\) −3.89798 + 6.75150i −0.812785 + 1.40778i 0.0981231 + 0.995174i \(0.468716\pi\)
−0.910908 + 0.412610i \(0.864617\pi\)
\(24\) 0 0
\(25\) 1.95084 + 3.37895i 0.390167 + 0.675790i
\(26\) 3.12879 0.613605
\(27\) 0 0
\(28\) 0.184793 0.0349225
\(29\) 2.53487 + 4.39053i 0.470714 + 0.815301i 0.999439 0.0334924i \(-0.0106630\pi\)
−0.528725 + 0.848793i \(0.677330\pi\)
\(30\) 0 0
\(31\) 4.37939 7.58532i 0.786561 1.36236i −0.141501 0.989938i \(-0.545193\pi\)
0.928062 0.372425i \(-0.121474\pi\)
\(32\) 2.89884 5.02094i 0.512448 0.887586i
\(33\) 0 0
\(34\) −1.63429 2.83067i −0.280278 0.485455i
\(35\) 0.126406 0.0213664
\(36\) 0 0
\(37\) −2.18479 −0.359178 −0.179589 0.983742i \(-0.557477\pi\)
−0.179589 + 0.983742i \(0.557477\pi\)
\(38\) −0.201288 0.348641i −0.0326532 0.0565570i
\(39\) 0 0
\(40\) 1.26604 2.19285i 0.200179 0.346721i
\(41\) 3.77920 6.54576i 0.590211 1.02228i −0.403992 0.914762i \(-0.632378\pi\)
0.994204 0.107514i \(-0.0342889\pi\)
\(42\) 0 0
\(43\) 0.652704 + 1.13052i 0.0995364 + 0.172402i 0.911493 0.411316i \(-0.134931\pi\)
−0.811956 + 0.583718i \(0.801597\pi\)
\(44\) −8.32494 −1.25503
\(45\) 0 0
\(46\) −5.33275 −0.786271
\(47\) 1.20805 + 2.09240i 0.176212 + 0.305207i 0.940580 0.339572i \(-0.110282\pi\)
−0.764368 + 0.644780i \(0.776949\pi\)
\(48\) 0 0
\(49\) 3.49273 6.04958i 0.498961 0.864226i
\(50\) −1.33445 + 2.31134i −0.188720 + 0.326872i
\(51\) 0 0
\(52\) −3.50387 6.06888i −0.485899 0.841602i
\(53\) 3.04628 0.418439 0.209219 0.977869i \(-0.432908\pi\)
0.209219 + 0.977869i \(0.432908\pi\)
\(54\) 0 0
\(55\) −5.69459 −0.767859
\(56\) 0.145708 + 0.252374i 0.0194711 + 0.0337249i
\(57\) 0 0
\(58\) −1.73396 + 3.00330i −0.227680 + 0.394352i
\(59\) −0.0219501 + 0.0380187i −0.00285766 + 0.00494961i −0.867451 0.497523i \(-0.834243\pi\)
0.864593 + 0.502473i \(0.167576\pi\)
\(60\) 0 0
\(61\) 5.10607 + 8.84397i 0.653765 + 1.13235i 0.982202 + 0.187828i \(0.0601448\pi\)
−0.328437 + 0.944526i \(0.606522\pi\)
\(62\) 5.99135 0.760902
\(63\) 0 0
\(64\) 1.14290 0.142863
\(65\) −2.39679 4.15136i −0.297285 0.514913i
\(66\) 0 0
\(67\) 0.929892 1.61062i 0.113604 0.196769i −0.803617 0.595147i \(-0.797094\pi\)
0.917221 + 0.398379i \(0.130427\pi\)
\(68\) −3.66041 + 6.34002i −0.443890 + 0.768841i
\(69\) 0 0
\(70\) 0.0432332 + 0.0748822i 0.00516736 + 0.00895013i
\(71\) 6.51038 0.772640 0.386320 0.922365i \(-0.373746\pi\)
0.386320 + 0.922365i \(0.373746\pi\)
\(72\) 0 0
\(73\) 12.2344 1.43193 0.715965 0.698136i \(-0.245987\pi\)
0.715965 + 0.698136i \(0.245987\pi\)
\(74\) −0.747243 1.29426i −0.0868652 0.150455i
\(75\) 0 0
\(76\) −0.450837 + 0.780873i −0.0517145 + 0.0895722i
\(77\) 0.327693 0.567581i 0.0373441 0.0646819i
\(78\) 0 0
\(79\) −0.351167 0.608239i −0.0395093 0.0684322i 0.845595 0.533826i \(-0.179246\pi\)
−0.885104 + 0.465394i \(0.845913\pi\)
\(80\) −1.47924 −0.165384
\(81\) 0 0
\(82\) 5.17024 0.570958
\(83\) 3.38830 + 5.86871i 0.371914 + 0.644174i 0.989860 0.142046i \(-0.0453682\pi\)
−0.617946 + 0.786221i \(0.712035\pi\)
\(84\) 0 0
\(85\) −2.50387 + 4.33683i −0.271583 + 0.470395i
\(86\) −0.446476 + 0.773318i −0.0481447 + 0.0833891i
\(87\) 0 0
\(88\) −6.56418 11.3695i −0.699744 1.21199i
\(89\) −6.85565 −0.726697 −0.363349 0.931653i \(-0.618367\pi\)
−0.363349 + 0.931653i \(0.618367\pi\)
\(90\) 0 0
\(91\) 0.551689 0.0578327
\(92\) 5.97205 + 10.3439i 0.622629 + 1.07843i
\(93\) 0 0
\(94\) −0.826352 + 1.43128i −0.0852317 + 0.147626i
\(95\) −0.308391 + 0.534148i −0.0316402 + 0.0548025i
\(96\) 0 0
\(97\) 4.51367 + 7.81791i 0.458294 + 0.793788i 0.998871 0.0475063i \(-0.0151274\pi\)
−0.540577 + 0.841294i \(0.681794\pi\)
\(98\) 4.77833 0.482684
\(99\) 0 0
\(100\) 5.97771 0.597771
\(101\) 6.49605 + 11.2515i 0.646382 + 1.11957i 0.983981 + 0.178276i \(0.0570519\pi\)
−0.337599 + 0.941290i \(0.609615\pi\)
\(102\) 0 0
\(103\) −4.53596 + 7.85651i −0.446941 + 0.774125i −0.998185 0.0602191i \(-0.980820\pi\)
0.551244 + 0.834344i \(0.314153\pi\)
\(104\) 5.52557 9.57057i 0.541827 0.938472i
\(105\) 0 0
\(106\) 1.04189 + 1.80460i 0.101197 + 0.175279i
\(107\) −11.3865 −1.10077 −0.550386 0.834911i \(-0.685519\pi\)
−0.550386 + 0.834911i \(0.685519\pi\)
\(108\) 0 0
\(109\) 2.89899 0.277672 0.138836 0.990315i \(-0.455664\pi\)
0.138836 + 0.990315i \(0.455664\pi\)
\(110\) −1.94767 3.37346i −0.185703 0.321646i
\(111\) 0 0
\(112\) 0.0851223 0.147436i 0.00804330 0.0139314i
\(113\) −5.79006 + 10.0287i −0.544683 + 0.943419i 0.453943 + 0.891031i \(0.350017\pi\)
−0.998627 + 0.0523888i \(0.983316\pi\)
\(114\) 0 0
\(115\) 4.08512 + 7.07564i 0.380940 + 0.659807i
\(116\) 7.76730 0.721176
\(117\) 0 0
\(118\) −0.0300295 −0.00276444
\(119\) −0.288169 0.499123i −0.0264164 0.0457545i
\(120\) 0 0
\(121\) −9.26264 + 16.0434i −0.842058 + 1.45849i
\(122\) −3.49276 + 6.04963i −0.316219 + 0.547708i
\(123\) 0 0
\(124\) −6.70961 11.6214i −0.602541 1.04363i
\(125\) 9.32905 0.834415
\(126\) 0 0
\(127\) −15.4192 −1.36823 −0.684117 0.729372i \(-0.739812\pi\)
−0.684117 + 0.729372i \(0.739812\pi\)
\(128\) −5.40679 9.36484i −0.477897 0.827742i
\(129\) 0 0
\(130\) 1.63950 2.83970i 0.143794 0.249058i
\(131\) 6.67804 11.5667i 0.583463 1.01059i −0.411602 0.911364i \(-0.635031\pi\)
0.995065 0.0992240i \(-0.0316360\pi\)
\(132\) 0 0
\(133\) −0.0354925 0.0614747i −0.00307759 0.00533054i
\(134\) 1.27217 0.109899
\(135\) 0 0
\(136\) −11.5449 −0.989965
\(137\) −9.81180 16.9945i −0.838279 1.45194i −0.891333 0.453350i \(-0.850229\pi\)
0.0530541 0.998592i \(-0.483104\pi\)
\(138\) 0 0
\(139\) −8.15317 + 14.1217i −0.691543 + 1.19779i 0.279789 + 0.960061i \(0.409735\pi\)
−0.971332 + 0.237726i \(0.923598\pi\)
\(140\) 0.0968323 0.167718i 0.00818382 0.0141748i
\(141\) 0 0
\(142\) 2.22668 + 3.85673i 0.186859 + 0.323649i
\(143\) −24.8537 −2.07837
\(144\) 0 0
\(145\) 5.31315 0.441233
\(146\) 4.18442 + 7.24763i 0.346305 + 0.599818i
\(147\) 0 0
\(148\) −1.67365 + 2.89884i −0.137573 + 0.238283i
\(149\) 5.52385 9.56758i 0.452531 0.783807i −0.546011 0.837778i \(-0.683854\pi\)
0.998543 + 0.0539709i \(0.0171878\pi\)
\(150\) 0 0
\(151\) 3.40033 + 5.88954i 0.276715 + 0.479284i 0.970566 0.240834i \(-0.0774209\pi\)
−0.693851 + 0.720118i \(0.744088\pi\)
\(152\) −1.42193 −0.115334
\(153\) 0 0
\(154\) 0.448311 0.0361259
\(155\) −4.58964 7.94949i −0.368649 0.638519i
\(156\) 0 0
\(157\) −8.44356 + 14.6247i −0.673870 + 1.16718i 0.302928 + 0.953013i \(0.402036\pi\)
−0.976798 + 0.214163i \(0.931298\pi\)
\(158\) 0.240212 0.416060i 0.0191103 0.0330999i
\(159\) 0 0
\(160\) −3.03802 5.26200i −0.240176 0.415998i
\(161\) −0.940307 −0.0741066
\(162\) 0 0
\(163\) 8.41147 0.658838 0.329419 0.944184i \(-0.393147\pi\)
0.329419 + 0.944184i \(0.393147\pi\)
\(164\) −5.79006 10.0287i −0.452128 0.783109i
\(165\) 0 0
\(166\) −2.31773 + 4.01443i −0.179891 + 0.311580i
\(167\) −1.31250 + 2.27332i −0.101564 + 0.175915i −0.912329 0.409457i \(-0.865718\pi\)
0.810765 + 0.585372i \(0.199051\pi\)
\(168\) 0 0
\(169\) −3.96064 6.86002i −0.304664 0.527694i
\(170\) −3.42550 −0.262724
\(171\) 0 0
\(172\) 2.00000 0.152499
\(173\) 6.55163 + 11.3478i 0.498112 + 0.862754i 0.999998 0.00217926i \(-0.000693680\pi\)
−0.501886 + 0.864934i \(0.667360\pi\)
\(174\) 0 0
\(175\) −0.235300 + 0.407551i −0.0177870 + 0.0308080i
\(176\) −3.83478 + 6.64203i −0.289057 + 0.500662i
\(177\) 0 0
\(178\) −2.34477 4.06126i −0.175748 0.304404i
\(179\) 22.0988 1.65174 0.825872 0.563857i \(-0.190683\pi\)
0.825872 + 0.563857i \(0.190683\pi\)
\(180\) 0 0
\(181\) −2.05913 −0.153054 −0.0765268 0.997068i \(-0.524383\pi\)
−0.0765268 + 0.997068i \(0.524383\pi\)
\(182\) 0.188689 + 0.326819i 0.0139865 + 0.0242254i
\(183\) 0 0
\(184\) −9.41787 + 16.3122i −0.694295 + 1.20255i
\(185\) −1.14484 + 1.98293i −0.0841705 + 0.145788i
\(186\) 0 0
\(187\) 12.9820 + 22.4856i 0.949341 + 1.64431i
\(188\) 3.70167 0.269972
\(189\) 0 0
\(190\) −0.421903 −0.0306081
\(191\) −1.97459 3.42009i −0.142876 0.247469i 0.785702 0.618605i \(-0.212302\pi\)
−0.928579 + 0.371136i \(0.878968\pi\)
\(192\) 0 0
\(193\) 4.22328 7.31493i 0.303998 0.526540i −0.673040 0.739606i \(-0.735012\pi\)
0.977038 + 0.213066i \(0.0683450\pi\)
\(194\) −3.08753 + 5.34776i −0.221672 + 0.383947i
\(195\) 0 0
\(196\) −5.35117 9.26849i −0.382226 0.662035i
\(197\) 2.29498 0.163511 0.0817553 0.996652i \(-0.473947\pi\)
0.0817553 + 0.996652i \(0.473947\pi\)
\(198\) 0 0
\(199\) −23.5030 −1.66608 −0.833042 0.553210i \(-0.813403\pi\)
−0.833042 + 0.553210i \(0.813403\pi\)
\(200\) 4.71340 + 8.16385i 0.333288 + 0.577271i
\(201\) 0 0
\(202\) −4.44356 + 7.69648i −0.312648 + 0.541522i
\(203\) −0.305743 + 0.529563i −0.0214590 + 0.0371680i
\(204\) 0 0
\(205\) −3.96064 6.86002i −0.276623 0.479125i
\(206\) −6.20556 −0.432362
\(207\) 0 0
\(208\) −6.45605 −0.447647
\(209\) 1.59894 + 2.76945i 0.110601 + 0.191567i
\(210\) 0 0
\(211\) 0.833626 1.44388i 0.0573892 0.0994010i −0.835904 0.548876i \(-0.815056\pi\)
0.893293 + 0.449475i \(0.148389\pi\)
\(212\) 2.33359 4.04189i 0.160271 0.277598i
\(213\) 0 0
\(214\) −3.89440 6.74530i −0.266216 0.461099i
\(215\) 1.36808 0.0933023
\(216\) 0 0
\(217\) 1.05644 0.0717156
\(218\) 0.991511 + 1.71735i 0.0671536 + 0.116313i
\(219\) 0 0
\(220\) −4.36231 + 7.55574i −0.294107 + 0.509408i
\(221\) −10.9280 + 18.9278i −0.735096 + 1.27322i
\(222\) 0 0
\(223\) 4.90033 + 8.48762i 0.328150 + 0.568373i 0.982145 0.188126i \(-0.0602414\pi\)
−0.653995 + 0.756499i \(0.726908\pi\)
\(224\) 0.699287 0.0467231
\(225\) 0 0
\(226\) −7.92127 −0.526915
\(227\) −7.74038 13.4067i −0.513747 0.889836i −0.999873 0.0159469i \(-0.994924\pi\)
0.486126 0.873889i \(-0.338410\pi\)
\(228\) 0 0
\(229\) 5.62701 9.74627i 0.371843 0.644052i −0.618006 0.786174i \(-0.712059\pi\)
0.989849 + 0.142122i \(0.0453925\pi\)
\(230\) −2.79439 + 4.84002i −0.184257 + 0.319142i
\(231\) 0 0
\(232\) 6.12449 + 10.6079i 0.402092 + 0.696444i
\(233\) 5.23476 0.342940 0.171470 0.985189i \(-0.445148\pi\)
0.171470 + 0.985189i \(0.445148\pi\)
\(234\) 0 0
\(235\) 2.53209 0.165175
\(236\) 0.0336295 + 0.0582480i 0.00218909 + 0.00379162i
\(237\) 0 0
\(238\) 0.197119 0.341420i 0.0127773 0.0221310i
\(239\) 5.15490 8.92855i 0.333443 0.577540i −0.649742 0.760155i \(-0.725123\pi\)
0.983184 + 0.182615i \(0.0584563\pi\)
\(240\) 0 0
\(241\) −5.37211 9.30477i −0.346048 0.599373i 0.639496 0.768795i \(-0.279143\pi\)
−0.985544 + 0.169422i \(0.945810\pi\)
\(242\) −12.6720 −0.814590
\(243\) 0 0
\(244\) 15.6459 1.00163
\(245\) −3.66041 6.34002i −0.233855 0.405049i
\(246\) 0 0
\(247\) −1.34595 + 2.33126i −0.0856409 + 0.148334i
\(248\) 10.5810 18.3268i 0.671894 1.16375i
\(249\) 0 0
\(250\) 3.19072 + 5.52649i 0.201799 + 0.349526i
\(251\) 15.0729 0.951392 0.475696 0.879610i \(-0.342196\pi\)
0.475696 + 0.879610i \(0.342196\pi\)
\(252\) 0 0
\(253\) 42.3610 2.66321
\(254\) −5.27368 9.13429i −0.330900 0.573136i
\(255\) 0 0
\(256\) 4.84137 8.38549i 0.302585 0.524093i
\(257\) 1.66122 2.87733i 0.103624 0.179483i −0.809551 0.587050i \(-0.800289\pi\)
0.913175 + 0.407567i \(0.133623\pi\)
\(258\) 0 0
\(259\) −0.131759 0.228213i −0.00818711 0.0141805i
\(260\) −7.34419 −0.455467
\(261\) 0 0
\(262\) 9.13610 0.564430
\(263\) −4.41934 7.65451i −0.272508 0.471998i 0.696995 0.717076i \(-0.254520\pi\)
−0.969503 + 0.245078i \(0.921186\pi\)
\(264\) 0 0
\(265\) 1.59627 2.76481i 0.0980579 0.169841i
\(266\) 0.0242783 0.0420512i 0.00148860 0.00257832i
\(267\) 0 0
\(268\) −1.42468 2.46761i −0.0870261 0.150734i
\(269\) 8.09267 0.493419 0.246709 0.969090i \(-0.420651\pi\)
0.246709 + 0.969090i \(0.420651\pi\)
\(270\) 0 0
\(271\) −19.0000 −1.15417 −0.577084 0.816685i \(-0.695809\pi\)
−0.577084 + 0.816685i \(0.695809\pi\)
\(272\) 3.37225 + 5.84090i 0.204472 + 0.354157i
\(273\) 0 0
\(274\) 6.71167 11.6249i 0.405467 0.702289i
\(275\) 10.6003 18.3603i 0.639222 1.10716i
\(276\) 0 0
\(277\) 2.11468 + 3.66274i 0.127059 + 0.220073i 0.922536 0.385911i \(-0.126113\pi\)
−0.795477 + 0.605984i \(0.792780\pi\)
\(278\) −11.1542 −0.668984
\(279\) 0 0
\(280\) 0.305407 0.0182516
\(281\) −3.65106 6.32383i −0.217804 0.377248i 0.736332 0.676620i \(-0.236556\pi\)
−0.954136 + 0.299372i \(0.903223\pi\)
\(282\) 0 0
\(283\) −8.01027 + 13.8742i −0.476161 + 0.824735i −0.999627 0.0273116i \(-0.991305\pi\)
0.523466 + 0.852047i \(0.324639\pi\)
\(284\) 4.98724 8.63816i 0.295938 0.512580i
\(285\) 0 0
\(286\) −8.50047 14.7232i −0.502643 0.870603i
\(287\) 0.911654 0.0538132
\(288\) 0 0
\(289\) 5.83244 0.343085
\(290\) 1.81720 + 3.14749i 0.106710 + 0.184827i
\(291\) 0 0
\(292\) 9.37211 16.2330i 0.548461 0.949963i
\(293\) −9.00227 + 15.5924i −0.525918 + 0.910918i 0.473626 + 0.880726i \(0.342945\pi\)
−0.999544 + 0.0301913i \(0.990388\pi\)
\(294\) 0 0
\(295\) 0.0230039 + 0.0398440i 0.00133934 + 0.00231981i
\(296\) −5.27866 −0.306816
\(297\) 0 0
\(298\) 7.55707 0.437769
\(299\) 17.8293 + 30.8812i 1.03109 + 1.78591i
\(300\) 0 0
\(301\) −0.0787257 + 0.136357i −0.00453767 + 0.00785948i
\(302\) −2.32596 + 4.02869i −0.133844 + 0.231825i
\(303\) 0 0
\(304\) 0.415345 + 0.719398i 0.0238216 + 0.0412603i
\(305\) 10.7024 0.612819
\(306\) 0 0
\(307\) −13.5107 −0.771098 −0.385549 0.922687i \(-0.625988\pi\)
−0.385549 + 0.922687i \(0.625988\pi\)
\(308\) −0.502055 0.869585i −0.0286072 0.0495492i
\(309\) 0 0
\(310\) 3.13950 5.43777i 0.178312 0.308845i
\(311\) −8.21113 + 14.2221i −0.465611 + 0.806461i −0.999229 0.0392643i \(-0.987499\pi\)
0.533618 + 0.845725i \(0.320832\pi\)
\(312\) 0 0
\(313\) 9.78240 + 16.9436i 0.552934 + 0.957710i 0.998061 + 0.0622425i \(0.0198252\pi\)
−0.445127 + 0.895467i \(0.646841\pi\)
\(314\) −11.5515 −0.651887
\(315\) 0 0
\(316\) −1.07604 −0.0605318
\(317\) 12.1893 + 21.1125i 0.684619 + 1.18579i 0.973557 + 0.228446i \(0.0733645\pi\)
−0.288938 + 0.957348i \(0.593302\pi\)
\(318\) 0 0
\(319\) 13.7738 23.8569i 0.771184 1.33573i
\(320\) 0.598887 1.03730i 0.0334788 0.0579870i
\(321\) 0 0
\(322\) −0.321604 0.557035i −0.0179223 0.0310423i
\(323\) 2.81217 0.156473
\(324\) 0 0
\(325\) 17.8462 0.989927
\(326\) 2.87689 + 4.98293i 0.159336 + 0.275979i
\(327\) 0 0
\(328\) 9.13088 15.8152i 0.504169 0.873246i
\(329\) −0.145708 + 0.252374i −0.00803315 + 0.0139138i
\(330\) 0 0
\(331\) −14.2494 24.6807i −0.783220 1.35658i −0.930057 0.367416i \(-0.880243\pi\)
0.146837 0.989161i \(-0.453091\pi\)
\(332\) 10.3824 0.569806
\(333\) 0 0
\(334\) −1.79561 −0.0982512
\(335\) −0.974537 1.68795i −0.0532446 0.0922224i
\(336\) 0 0
\(337\) 8.72328 15.1092i 0.475187 0.823048i −0.524409 0.851467i \(-0.675714\pi\)
0.999596 + 0.0284181i \(0.00904699\pi\)
\(338\) 2.70924 4.69253i 0.147363 0.255240i
\(339\) 0 0
\(340\) 3.83615 + 6.64441i 0.208045 + 0.360344i
\(341\) −47.5927 −2.57729
\(342\) 0 0
\(343\) 1.68685 0.0910814
\(344\) 1.57699 + 2.73143i 0.0850257 + 0.147269i
\(345\) 0 0
\(346\) −4.48158 + 7.76233i −0.240931 + 0.417305i
\(347\) −12.5945 + 21.8143i −0.676109 + 1.17105i 0.300035 + 0.953928i \(0.403002\pi\)
−0.976144 + 0.217126i \(0.930332\pi\)
\(348\) 0 0
\(349\) 5.92602 + 10.2642i 0.317213 + 0.549428i 0.979905 0.199463i \(-0.0639198\pi\)
−0.662693 + 0.748891i \(0.730586\pi\)
\(350\) −0.321909 −0.0172068
\(351\) 0 0
\(352\) −31.5030 −1.67912
\(353\) 4.19875 + 7.27244i 0.223477 + 0.387073i 0.955861 0.293818i \(-0.0949260\pi\)
−0.732385 + 0.680891i \(0.761593\pi\)
\(354\) 0 0
\(355\) 3.41147 5.90885i 0.181062 0.313609i
\(356\) −5.25173 + 9.09627i −0.278341 + 0.482101i
\(357\) 0 0
\(358\) 7.55825 + 13.0913i 0.399466 + 0.691895i
\(359\) 2.64025 0.139347 0.0696735 0.997570i \(-0.477804\pi\)
0.0696735 + 0.997570i \(0.477804\pi\)
\(360\) 0 0
\(361\) −18.6536 −0.981770
\(362\) −0.704262 1.21982i −0.0370152 0.0641122i
\(363\) 0 0
\(364\) 0.422618 0.731997i 0.0221512 0.0383671i
\(365\) 6.41090 11.1040i 0.335562 0.581210i
\(366\) 0 0
\(367\) −4.59879 7.96534i −0.240055 0.415788i 0.720675 0.693273i \(-0.243832\pi\)
−0.960730 + 0.277486i \(0.910499\pi\)
\(368\) 11.0038 0.573612
\(369\) 0 0
\(370\) −1.56624 −0.0814248
\(371\) 0.183713 + 0.318201i 0.00953791 + 0.0165201i
\(372\) 0 0
\(373\) 13.3956 23.2018i 0.693597 1.20135i −0.277054 0.960854i \(-0.589358\pi\)
0.970651 0.240491i \(-0.0773084\pi\)
\(374\) −8.88024 + 15.3810i −0.459186 + 0.795334i
\(375\) 0 0
\(376\) 2.91875 + 5.05542i 0.150523 + 0.260713i
\(377\) 23.1889 1.19429
\(378\) 0 0
\(379\) −27.1242 −1.39328 −0.696639 0.717422i \(-0.745322\pi\)
−0.696639 + 0.717422i \(0.745322\pi\)
\(380\) 0.472482 + 0.818363i 0.0242378 + 0.0419811i
\(381\) 0 0
\(382\) 1.35070 2.33948i 0.0691078 0.119698i
\(383\) 17.2134 29.8145i 0.879564 1.52345i 0.0277437 0.999615i \(-0.491168\pi\)
0.851820 0.523834i \(-0.175499\pi\)
\(384\) 0 0
\(385\) −0.343426 0.594831i −0.0175026 0.0303154i
\(386\) 5.77778 0.294081
\(387\) 0 0
\(388\) 13.8307 0.702147
\(389\) 0.378297 + 0.655230i 0.0191804 + 0.0332215i 0.875456 0.483297i \(-0.160561\pi\)
−0.856276 + 0.516519i \(0.827228\pi\)
\(390\) 0 0
\(391\) 18.6258 32.2609i 0.941949 1.63150i
\(392\) 8.43874 14.6163i 0.426221 0.738236i
\(393\) 0 0
\(394\) 0.784930 + 1.35954i 0.0395442 + 0.0684925i
\(395\) −0.736053 −0.0370348
\(396\) 0 0
\(397\) 7.00774 0.351708 0.175854 0.984416i \(-0.443731\pi\)
0.175854 + 0.984416i \(0.443731\pi\)
\(398\) −8.03850 13.9231i −0.402933 0.697901i
\(399\) 0 0
\(400\) 2.75356 4.76930i 0.137678 0.238465i
\(401\) −4.72540 + 8.18463i −0.235975 + 0.408721i −0.959556 0.281519i \(-0.909162\pi\)
0.723580 + 0.690240i \(0.242495\pi\)
\(402\) 0 0
\(403\) −20.0312 34.6951i −0.997826 1.72828i
\(404\) 19.9051 0.990314
\(405\) 0 0
\(406\) −0.418281 −0.0207590
\(407\) 5.93577 + 10.2811i 0.294225 + 0.509613i
\(408\) 0 0
\(409\) −2.75877 + 4.77833i −0.136412 + 0.236273i −0.926136 0.377189i \(-0.876891\pi\)
0.789724 + 0.613463i \(0.210224\pi\)
\(410\) 2.70924 4.69253i 0.133800 0.231748i
\(411\) 0 0
\(412\) 6.94949 + 12.0369i 0.342377 + 0.593014i
\(413\) −0.00529501 −0.000260550
\(414\) 0 0
\(415\) 7.10195 0.348621
\(416\) −13.2592 22.9657i −0.650088 1.12599i
\(417\) 0 0
\(418\) −1.09374 + 1.89441i −0.0534966 + 0.0926588i
\(419\) −0.233189 + 0.403895i −0.0113920 + 0.0197316i −0.871665 0.490102i \(-0.836960\pi\)
0.860273 + 0.509833i \(0.170293\pi\)
\(420\) 0 0
\(421\) 1.20708 + 2.09073i 0.0588295 + 0.101896i 0.893940 0.448186i \(-0.147930\pi\)
−0.835111 + 0.550082i \(0.814596\pi\)
\(422\) 1.14047 0.0555171
\(423\) 0 0
\(424\) 7.36009 0.357438
\(425\) −9.32174 16.1457i −0.452171 0.783183i
\(426\) 0 0
\(427\) −0.615867 + 1.06671i −0.0298039 + 0.0516219i
\(428\) −8.72254 + 15.1079i −0.421620 + 0.730267i
\(429\) 0 0
\(430\) 0.467911 + 0.810446i 0.0225647 + 0.0390832i
\(431\) −12.0992 −0.582796 −0.291398 0.956602i \(-0.594120\pi\)
−0.291398 + 0.956602i \(0.594120\pi\)
\(432\) 0 0
\(433\) 33.3509 1.60274 0.801371 0.598167i \(-0.204104\pi\)
0.801371 + 0.598167i \(0.204104\pi\)
\(434\) 0.361323 + 0.625829i 0.0173440 + 0.0300408i
\(435\) 0 0
\(436\) 2.22075 3.84645i 0.106355 0.184212i
\(437\) 2.29406 3.97343i 0.109740 0.190075i
\(438\) 0 0
\(439\) 4.52229 + 7.83283i 0.215837 + 0.373841i 0.953531 0.301294i \(-0.0974187\pi\)
−0.737694 + 0.675135i \(0.764085\pi\)
\(440\) −13.7587 −0.655918
\(441\) 0 0
\(442\) −14.9504 −0.711117
\(443\) 2.33856 + 4.05051i 0.111108 + 0.192445i 0.916217 0.400681i \(-0.131227\pi\)
−0.805109 + 0.593127i \(0.797893\pi\)
\(444\) 0 0
\(445\) −3.59240 + 6.22221i −0.170296 + 0.294961i
\(446\) −3.35202 + 5.80587i −0.158723 + 0.274916i
\(447\) 0 0
\(448\) 0.0689255 + 0.119382i 0.00325642 + 0.00564029i
\(449\) −26.7069 −1.26037 −0.630187 0.776443i \(-0.717022\pi\)
−0.630187 + 0.776443i \(0.717022\pi\)
\(450\) 0 0
\(451\) −41.0702 −1.93392
\(452\) 8.87089 + 15.3648i 0.417252 + 0.722701i
\(453\) 0 0
\(454\) 5.29473 9.17074i 0.248494 0.430404i
\(455\) 0.289088 0.500715i 0.0135527 0.0234739i
\(456\) 0 0
\(457\) 0.328878 + 0.569633i 0.0153843 + 0.0266463i 0.873615 0.486618i \(-0.161770\pi\)
−0.858231 + 0.513264i \(0.828436\pi\)
\(458\) 7.69820 0.359713
\(459\) 0 0
\(460\) 12.5175 0.583633
\(461\) −10.3519 17.9299i −0.482134 0.835081i 0.517655 0.855589i \(-0.326805\pi\)
−0.999790 + 0.0205082i \(0.993472\pi\)
\(462\) 0 0
\(463\) 12.4119 21.4981i 0.576832 0.999102i −0.419008 0.907982i \(-0.637622\pi\)
0.995840 0.0911195i \(-0.0290445\pi\)
\(464\) 3.57791 6.19712i 0.166100 0.287694i
\(465\) 0 0
\(466\) 1.79039 + 3.10105i 0.0829383 + 0.143653i
\(467\) 26.6729 1.23428 0.617138 0.786855i \(-0.288292\pi\)
0.617138 + 0.786855i \(0.288292\pi\)
\(468\) 0 0
\(469\) 0.224318 0.0103580
\(470\) 0.866025 + 1.50000i 0.0399468 + 0.0691898i
\(471\) 0 0
\(472\) −0.0530334 + 0.0918566i −0.00244106 + 0.00422804i
\(473\) 3.54661 6.14290i 0.163073 0.282451i
\(474\) 0 0
\(475\) −1.14812 1.98860i −0.0526793 0.0912432i
\(476\) −0.883000 −0.0404722
\(477\) 0 0
\(478\) 7.05232 0.322566
\(479\) 1.61327 + 2.79426i 0.0737121 + 0.127673i 0.900525 0.434803i \(-0.143182\pi\)
−0.826813 + 0.562476i \(0.809849\pi\)
\(480\) 0 0
\(481\) −4.99660 + 8.65436i −0.227825 + 0.394605i
\(482\) 3.67474 6.36484i 0.167380 0.289910i
\(483\) 0 0
\(484\) 14.1912 + 24.5799i 0.645054 + 1.11727i
\(485\) 9.46075 0.429590
\(486\) 0 0
\(487\) −7.77930 −0.352514 −0.176257 0.984344i \(-0.556399\pi\)
−0.176257 + 0.984344i \(0.556399\pi\)
\(488\) 12.3367 + 21.3678i 0.558457 + 0.967276i
\(489\) 0 0
\(490\) 2.50387 4.33683i 0.113113 0.195918i
\(491\) −8.52298 + 14.7622i −0.384637 + 0.666210i −0.991719 0.128429i \(-0.959007\pi\)
0.607082 + 0.794639i \(0.292340\pi\)
\(492\) 0 0
\(493\) −12.1125 20.9794i −0.545518 0.944865i
\(494\) −1.84137 −0.0828472
\(495\) 0 0
\(496\) −12.3628 −0.555105
\(497\) 0.392624 + 0.680045i 0.0176116 + 0.0305042i
\(498\) 0 0
\(499\) −3.96538 + 6.86825i −0.177515 + 0.307465i −0.941029 0.338327i \(-0.890139\pi\)
0.763514 + 0.645792i \(0.223472\pi\)
\(500\) 7.14647 12.3780i 0.319600 0.553563i
\(501\) 0 0
\(502\) 5.15523 + 8.92912i 0.230089 + 0.398526i
\(503\) 24.9496 1.11245 0.556224 0.831032i \(-0.312250\pi\)
0.556224 + 0.831032i \(0.312250\pi\)
\(504\) 0 0
\(505\) 13.6159 0.605898
\(506\) 14.4883 + 25.0945i 0.644085 + 1.11559i
\(507\) 0 0
\(508\) −11.8118 + 20.4586i −0.524064 + 0.907706i
\(509\) 20.2345 35.0472i 0.896878 1.55344i 0.0654147 0.997858i \(-0.479163\pi\)
0.831463 0.555580i \(-0.187504\pi\)
\(510\) 0 0
\(511\) 0.737826 + 1.27795i 0.0326395 + 0.0565333i
\(512\) −15.0038 −0.663080
\(513\) 0 0
\(514\) 2.27269 0.100244
\(515\) 4.75373 + 8.23371i 0.209475 + 0.362820i
\(516\) 0 0
\(517\) 6.56418 11.3695i 0.288692 0.500030i
\(518\) 0.0901285 0.156107i 0.00396002 0.00685896i
\(519\) 0 0
\(520\) −5.79086 10.0301i −0.253946 0.439847i
\(521\) 25.3674 1.11137 0.555684 0.831394i \(-0.312457\pi\)
0.555684 + 0.831394i \(0.312457\pi\)
\(522\) 0 0
\(523\) 12.7219 0.556291 0.278146 0.960539i \(-0.410280\pi\)
0.278146 + 0.960539i \(0.410280\pi\)
\(524\) −10.2314 17.7212i −0.446959 0.774155i
\(525\) 0 0
\(526\) 3.02300 5.23600i 0.131809 0.228300i
\(527\) −20.9262 + 36.2452i −0.911557 + 1.57886i
\(528\) 0 0
\(529\) −18.8885 32.7158i −0.821238 1.42243i
\(530\) 2.18382 0.0948591
\(531\) 0 0
\(532\) −0.108755 −0.00471514
\(533\) −17.2860 29.9402i −0.748738 1.29685i
\(534\) 0 0
\(535\) −5.96657 + 10.3344i −0.257957 + 0.446795i
\(536\) 2.24670 3.89141i 0.0970429 0.168083i
\(537\) 0 0
\(538\) 2.76786 + 4.79407i 0.119331 + 0.206687i
\(539\) −37.9570 −1.63492
\(540\) 0 0
\(541\) 2.09327 0.0899969 0.0449984 0.998987i \(-0.485672\pi\)
0.0449984 + 0.998987i \(0.485672\pi\)
\(542\) −6.49838 11.2555i −0.279129 0.483466i
\(543\) 0 0
\(544\) −13.8516 + 23.9917i −0.593884 + 1.02864i
\(545\) 1.51908 2.63113i 0.0650704 0.112705i
\(546\) 0 0
\(547\) −1.72550 2.98865i −0.0737770 0.127786i 0.826777 0.562530i \(-0.190172\pi\)
−0.900554 + 0.434745i \(0.856839\pi\)
\(548\) −30.0651 −1.28432
\(549\) 0 0
\(550\) 14.5021 0.618370
\(551\) −1.49184 2.58394i −0.0635545 0.110080i
\(552\) 0 0
\(553\) 0.0423559 0.0733626i 0.00180116 0.00311969i
\(554\) −1.44653 + 2.50546i −0.0614572 + 0.106447i
\(555\) 0 0
\(556\) 12.4914 + 21.6357i 0.529753 + 0.917558i
\(557\) −11.1003 −0.470337 −0.235168 0.971955i \(-0.575564\pi\)
−0.235168 + 0.971955i \(0.575564\pi\)
\(558\) 0 0
\(559\) 5.97090 0.252542
\(560\) −0.0892091 0.154515i −0.00376977 0.00652944i
\(561\) 0 0
\(562\) 2.49747 4.32575i 0.105350 0.182471i
\(563\) −12.1553 + 21.0537i −0.512286 + 0.887306i 0.487612 + 0.873060i \(0.337868\pi\)
−0.999899 + 0.0142457i \(0.995465\pi\)
\(564\) 0 0
\(565\) 6.06805 + 10.5102i 0.255285 + 0.442166i
\(566\) −10.9587 −0.460628
\(567\) 0 0
\(568\) 15.7297 0.660002
\(569\) −21.3820 37.0347i −0.896379 1.55257i −0.832088 0.554643i \(-0.812855\pi\)
−0.0642907 0.997931i \(-0.520478\pi\)
\(570\) 0 0
\(571\) −9.01414 + 15.6129i −0.377230 + 0.653381i −0.990658 0.136369i \(-0.956457\pi\)
0.613428 + 0.789751i \(0.289790\pi\)
\(572\) −19.0390 + 32.9766i −0.796062 + 1.37882i
\(573\) 0 0
\(574\) 0.311804 + 0.540060i 0.0130144 + 0.0225417i
\(575\) −30.4173 −1.26849
\(576\) 0 0
\(577\) 25.2763 1.05227 0.526133 0.850402i \(-0.323641\pi\)
0.526133 + 0.850402i \(0.323641\pi\)
\(578\) 1.99481 + 3.45512i 0.0829733 + 0.143714i
\(579\) 0 0
\(580\) 4.07011 7.04963i 0.169002 0.292720i
\(581\) −0.408679 + 0.707853i −0.0169549 + 0.0293667i
\(582\) 0 0
\(583\) −8.27631 14.3350i −0.342770 0.593695i
\(584\) 29.5595 1.22318
\(585\) 0 0
\(586\) −12.3158 −0.508763
\(587\) −14.2827 24.7383i −0.589508 1.02106i −0.994297 0.106648i \(-0.965988\pi\)
0.404788 0.914410i \(-0.367345\pi\)
\(588\) 0 0
\(589\) −2.57738 + 4.46416i −0.106199 + 0.183942i
\(590\) −0.0157356 + 0.0272549i −0.000647825 + 0.00112207i
\(591\) 0 0
\(592\) 1.54189 + 2.67063i 0.0633713 + 0.109762i
\(593\) 20.6009 0.845977 0.422989 0.906135i \(-0.360981\pi\)
0.422989 + 0.906135i \(0.360981\pi\)
\(594\) 0 0
\(595\) −0.604007 −0.0247619
\(596\) −8.46302 14.6584i −0.346659 0.600431i
\(597\) 0 0
\(598\) −12.1959 + 21.1240i −0.498729 + 0.863824i
\(599\) 7.23740 12.5355i 0.295712 0.512189i −0.679438 0.733733i \(-0.737776\pi\)
0.975150 + 0.221544i \(0.0711097\pi\)
\(600\) 0 0
\(601\) 6.67752 + 11.5658i 0.272382 + 0.471779i 0.969471 0.245205i \(-0.0788553\pi\)
−0.697090 + 0.716984i \(0.745522\pi\)
\(602\) −0.107703 −0.00438965
\(603\) 0 0
\(604\) 10.4192 0.423952
\(605\) 9.70735 + 16.8136i 0.394660 + 0.683571i
\(606\) 0 0
\(607\) −15.6065 + 27.0313i −0.633450 + 1.09717i 0.353392 + 0.935475i \(0.385028\pi\)
−0.986841 + 0.161692i \(0.948305\pi\)
\(608\) −1.70604 + 2.95496i −0.0691892 + 0.119839i
\(609\) 0 0
\(610\) 3.66044 + 6.34008i 0.148207 + 0.256702i
\(611\) 11.0511 0.447082
\(612\) 0 0
\(613\) 30.0651 1.21432 0.607159 0.794580i \(-0.292309\pi\)
0.607159 + 0.794580i \(0.292309\pi\)
\(614\) −4.62094 8.00371i −0.186486 0.323003i
\(615\) 0 0
\(616\) 0.791737 1.37133i 0.0319000 0.0552524i
\(617\) 21.0768 36.5061i 0.848521 1.46968i −0.0340062 0.999422i \(-0.510827\pi\)
0.882528 0.470261i \(-0.155840\pi\)
\(618\) 0 0
\(619\) −5.80541 10.0553i −0.233339 0.404155i 0.725450 0.688275i \(-0.241632\pi\)
−0.958789 + 0.284120i \(0.908299\pi\)
\(620\) −14.0635 −0.564803
\(621\) 0 0
\(622\) −11.2335 −0.450422
\(623\) −0.413446 0.716110i −0.0165644 0.0286903i
\(624\) 0 0
\(625\) −4.86571 + 8.42767i −0.194629 + 0.337107i
\(626\) −6.69156 + 11.5901i −0.267448 + 0.463234i
\(627\) 0 0
\(628\) 12.9363 + 22.4063i 0.516214 + 0.894109i
\(629\) 10.4397 0.416257
\(630\) 0 0
\(631\) −29.3105 −1.16683 −0.583415 0.812174i \(-0.698284\pi\)
−0.583415 + 0.812174i \(0.698284\pi\)
\(632\) −0.848451 1.46956i −0.0337496 0.0584560i
\(633\) 0 0
\(634\) −8.33796 + 14.4418i −0.331143 + 0.573556i
\(635\) −8.07975 + 13.9945i −0.320635 + 0.555356i
\(636\) 0 0
\(637\) −15.9757 27.6706i −0.632978 1.09635i
\(638\) 18.8436 0.746027
\(639\) 0 0
\(640\) −11.3327 −0.447966
\(641\) 15.5489 + 26.9315i 0.614146 + 1.06373i 0.990534 + 0.137270i \(0.0438327\pi\)
−0.376388 + 0.926462i \(0.622834\pi\)
\(642\) 0 0
\(643\) −21.0360 + 36.4354i −0.829577 + 1.43687i 0.0687930 + 0.997631i \(0.478085\pi\)
−0.898370 + 0.439239i \(0.855248\pi\)
\(644\) −0.720317 + 1.24763i −0.0283845 + 0.0491634i
\(645\) 0 0
\(646\) 0.961819 + 1.66592i 0.0378423 + 0.0655447i
\(647\) 4.66717 0.183485 0.0917427 0.995783i \(-0.470756\pi\)
0.0917427 + 0.995783i \(0.470756\pi\)
\(648\) 0 0
\(649\) 0.238541 0.00936356
\(650\) 6.10375 + 10.5720i 0.239409 + 0.414668i
\(651\) 0 0
\(652\) 6.44356 11.1606i 0.252349 0.437082i
\(653\) −1.56206 + 2.70557i −0.0611283 + 0.105877i −0.894970 0.446126i \(-0.852803\pi\)
0.833842 + 0.552004i \(0.186137\pi\)
\(654\) 0 0
\(655\) −6.99866 12.1220i −0.273460 0.473647i
\(656\) −10.6685 −0.416534
\(657\) 0 0
\(658\) −0.199340 −0.00777110
\(659\) 18.7146 + 32.4146i 0.729017 + 1.26269i 0.957299 + 0.289100i \(0.0933559\pi\)
−0.228282 + 0.973595i \(0.573311\pi\)
\(660\) 0 0
\(661\) −13.2502 + 22.9499i −0.515371 + 0.892649i 0.484470 + 0.874808i \(0.339013\pi\)
−0.999841 + 0.0178410i \(0.994321\pi\)
\(662\) 9.74719 16.8826i 0.378835 0.656162i
\(663\) 0 0
\(664\) 8.18644 + 14.1793i 0.317696 + 0.550265i
\(665\) −0.0743929 −0.00288483
\(666\) 0 0
\(667\) −39.5235 −1.53036
\(668\) 2.01087 + 3.48293i 0.0778028 + 0.134758i
\(669\) 0 0
\(670\) 0.666623 1.15462i 0.0257539 0.0446070i
\(671\) 27.7449 48.0556i 1.07108 1.85517i
\(672\) 0 0
\(673\) −0.860500 1.49043i −0.0331698 0.0574519i 0.848964 0.528451i \(-0.177227\pi\)
−0.882134 + 0.470999i \(0.843894\pi\)
\(674\) 11.9341 0.459686
\(675\) 0 0
\(676\) −12.1361 −0.466773
\(677\) −14.1396 24.4905i −0.543429 0.941247i −0.998704 0.0508957i \(-0.983792\pi\)
0.455275 0.890351i \(-0.349541\pi\)
\(678\) 0 0
\(679\) −0.544415 + 0.942955i −0.0208927 + 0.0361873i
\(680\) −6.04958 + 10.4782i −0.231991 + 0.401820i
\(681\) 0 0
\(682\) −16.2777 28.1937i −0.623304 1.07959i
\(683\) −24.7139 −0.945651 −0.472825 0.881156i \(-0.656766\pi\)
−0.472825 + 0.881156i \(0.656766\pi\)
\(684\) 0 0
\(685\) −20.5657 −0.785777
\(686\) 0.576937 + 0.999285i 0.0220276 + 0.0381529i
\(687\) 0 0
\(688\) 0.921274 1.59569i 0.0351233 0.0608353i
\(689\) 6.96681 12.0669i 0.265414 0.459711i
\(690\) 0 0
\(691\) 21.8862 + 37.9081i 0.832592 + 1.44209i 0.895976 + 0.444103i \(0.146477\pi\)
−0.0633838 + 0.997989i \(0.520189\pi\)
\(692\) 20.0754 0.763151
\(693\) 0 0
\(694\) −17.2303 −0.654053
\(695\) 8.54461 + 14.7997i 0.324115 + 0.561384i
\(696\) 0 0
\(697\) −18.0582 + 31.2778i −0.684005 + 1.18473i
\(698\) −4.05364 + 7.02111i −0.153432 + 0.265753i
\(699\) 0 0
\(700\) 0.360500 + 0.624404i 0.0136256 + 0.0236003i
\(701\) −14.6504 −0.553338 −0.276669 0.960965i \(-0.589231\pi\)
−0.276669 + 0.960965i \(0.589231\pi\)
\(702\) 0 0
\(703\) 1.28581 0.0484951
\(704\) −3.10511 5.37820i −0.117028 0.202699i
\(705\) 0 0
\(706\) −2.87211 + 4.97464i −0.108093 + 0.187223i
\(707\) −0.783520 + 1.35710i −0.0294673 + 0.0510389i
\(708\) 0 0
\(709\) −2.53684 4.39393i −0.0952729 0.165018i 0.814450 0.580234i \(-0.197039\pi\)
−0.909722 + 0.415217i \(0.863706\pi\)
\(710\) 4.66717 0.175156
\(711\) 0 0
\(712\) −16.5639 −0.620757
\(713\) 34.1415 + 59.1348i 1.27861 + 2.21462i
\(714\) 0 0
\(715\) −13.0235 + 22.5573i −0.487050 + 0.843596i
\(716\) 16.9287 29.3214i 0.632655 1.09579i
\(717\) 0 0
\(718\) 0.903018 + 1.56407i 0.0337003 + 0.0583707i
\(719\) −5.33717 −0.199043 −0.0995213 0.995035i \(-0.531731\pi\)
−0.0995213 + 0.995035i \(0.531731\pi\)
\(720\) 0 0
\(721\) −1.09421 −0.0407504
\(722\) −6.37992 11.0503i −0.237436 0.411251i
\(723\) 0 0
\(724\) −1.57738 + 2.73210i −0.0586229 + 0.101538i
\(725\) −9.89025 + 17.1304i −0.367315 + 0.636208i
\(726\) 0 0
\(727\) −18.5599 32.1467i −0.688348 1.19225i −0.972372 0.233437i \(-0.925003\pi\)
0.284023 0.958817i \(-0.408331\pi\)
\(728\) 1.33293 0.0494017
\(729\) 0 0
\(730\) 8.77063 0.324616
\(731\) −3.11883 5.40198i −0.115354 0.199799i
\(732\) 0 0
\(733\) −14.9731 + 25.9342i −0.553045 + 0.957902i 0.445008 + 0.895527i \(0.353201\pi\)
−0.998053 + 0.0623753i \(0.980132\pi\)
\(734\) 3.14576 5.44862i 0.116112 0.201112i
\(735\) 0 0
\(736\) 22.5993 + 39.1431i 0.833020 + 1.44283i
\(737\) −10.1055 −0.372243
\(738\) 0 0
\(739\) −28.6100 −1.05244 −0.526218 0.850350i \(-0.676390\pi\)
−0.526218 + 0.850350i \(0.676390\pi\)
\(740\) 1.75400 + 3.03802i 0.0644784 + 0.111680i
\(741\) 0 0
\(742\) −0.125667 + 0.217662i −0.00461339 + 0.00799062i
\(743\) −24.8218 + 42.9926i −0.910624 + 1.57725i −0.0974381 + 0.995242i \(0.531065\pi\)
−0.813185 + 0.582005i \(0.802269\pi\)
\(744\) 0 0
\(745\) −5.78905 10.0269i −0.212094 0.367358i
\(746\) 18.3262 0.670971
\(747\) 0 0
\(748\) 39.7793 1.45448
\(749\) −0.686688 1.18938i −0.0250910 0.0434589i
\(750\) 0 0
\(751\) 15.8118 27.3868i 0.576981 0.999360i −0.418842 0.908059i \(-0.637564\pi\)
0.995823 0.0913013i \(-0.0291026\pi\)
\(752\) 1.70513 2.95336i 0.0621795 0.107698i
\(753\) 0 0
\(754\) 7.93107 + 13.7370i 0.288833 + 0.500273i
\(755\) 7.12716 0.259384
\(756\) 0 0
\(757\) 3.04189 0.110559 0.0552797 0.998471i \(-0.482395\pi\)
0.0552797 + 0.998471i \(0.482395\pi\)
\(758\) −9.27704 16.0683i −0.336957 0.583627i
\(759\) 0 0
\(760\) −0.745100 + 1.29055i −0.0270276 + 0.0468132i
\(761\) −18.9642 + 32.8469i −0.687450 + 1.19070i 0.285210 + 0.958465i \(0.407937\pi\)
−0.972660 + 0.232234i \(0.925397\pi\)
\(762\) 0 0
\(763\) 0.174830 + 0.302815i 0.00632928 + 0.0109626i
\(764\) −6.05050 −0.218899
\(765\) 0 0
\(766\) 23.5493 0.850872
\(767\) 0.100399 + 0.173897i 0.00362521 + 0.00627904i
\(768\) 0 0
\(769\) 10.1939 17.6563i 0.367601 0.636703i −0.621589 0.783343i \(-0.713513\pi\)
0.989190 + 0.146640i \(0.0468460\pi\)
\(770\) 0.234917 0.406889i 0.00846583 0.0146632i
\(771\) 0 0
\(772\) −6.47044 11.2071i −0.232876 0.403353i
\(773\) 24.4664 0.879994 0.439997 0.897999i \(-0.354979\pi\)
0.439997 + 0.897999i \(0.354979\pi\)
\(774\) 0 0
\(775\) 34.1739 1.22756
\(776\) 10.9054 + 18.8888i 0.391482 + 0.678068i
\(777\) 0 0
\(778\) −0.258770 + 0.448204i −0.00927737 + 0.0160689i
\(779\) −2.22415 + 3.85235i −0.0796886 + 0.138025i
\(780\) 0 0
\(781\) −17.6878 30.6361i −0.632919 1.09625i
\(782\) 25.4816 0.911221
\(783\) 0 0
\(784\) −9.85978 −0.352135
\(785\) 8.84894 + 15.3268i 0.315832 + 0.547038i
\(786\) 0 0
\(787\) −18.7875 + 32.5408i −0.669700 + 1.15996i 0.308287 + 0.951293i \(0.400244\pi\)
−0.977988 + 0.208662i \(0.933089\pi\)
\(788\) 1.75806 3.04504i 0.0626282 0.108475i
\(789\) 0 0
\(790\) −0.251745 0.436035i −0.00895668 0.0155134i
\(791\) −1.39673 −0.0496622
\(792\) 0 0
\(793\) 46.7101 1.65872
\(794\) 2.39679 + 4.15136i 0.0850588 + 0.147326i
\(795\) 0 0
\(796\) −18.0043 + 31.1844i −0.638147 + 1.10530i
\(797\) −1.15247 + 1.99613i −0.0408224 + 0.0707065i −0.885715 0.464230i \(-0.846331\pi\)
0.844892 + 0.534936i \(0.179664\pi\)
\(798\) 0 0
\(799\) −5.77244 9.99816i −0.204214 0.353710i
\(800\) 22.6207 0.799762
\(801\) 0 0
\(802\) −6.46473 −0.228277
\(803\) −33.2392 57.5720i −1.17299 2.03167i
\(804\) 0 0
\(805\) −0.492726 + 0.853427i −0.0173663 + 0.0300793i
\(806\) 13.7022 23.7328i 0.482638 0.835953i
\(807\) 0 0
\(808\) 15.6951 + 27.1846i 0.552150 + 0.956352i
\(809\) −28.8614 −1.01471 −0.507356 0.861736i \(-0.669377\pi\)
−0.507356 + 0.861736i \(0.669377\pi\)
\(810\) 0 0
\(811\) −51.8631 −1.82116 −0.910580 0.413334i \(-0.864364\pi\)
−0.910580 + 0.413334i \(0.864364\pi\)
\(812\) 0.468426 + 0.811337i 0.0164385 + 0.0284723i
\(813\) 0 0
\(814\) −4.06031 + 7.03266i −0.142314 + 0.246495i
\(815\) 4.40766 7.63429i 0.154393 0.267417i
\(816\) 0 0
\(817\) −0.384133 0.665338i −0.0134391 0.0232772i
\(818\) −3.77422 −0.131963
\(819\) 0 0
\(820\) −12.1361 −0.423811
\(821\) −9.22054 15.9704i −0.321799 0.557372i 0.659060 0.752090i \(-0.270954\pi\)
−0.980859 + 0.194718i \(0.937621\pi\)
\(822\) 0 0
\(823\) 17.3833 30.1087i 0.605942 1.04952i −0.385960 0.922516i \(-0.626130\pi\)
0.991902 0.127007i \(-0.0405371\pi\)
\(824\) −10.9593 + 18.9820i −0.381785 + 0.661271i
\(825\) 0 0
\(826\) −0.00181100 0.00313674i −6.30127e−5 0.000109141i
\(827\) −32.7773 −1.13978 −0.569889 0.821722i \(-0.693014\pi\)
−0.569889 + 0.821722i \(0.693014\pi\)
\(828\) 0 0
\(829\) 5.35267 0.185906 0.0929530 0.995670i \(-0.470369\pi\)
0.0929530 + 0.995670i \(0.470369\pi\)
\(830\) 2.42901 + 4.20717i 0.0843121 + 0.146033i
\(831\) 0 0
\(832\) 2.61381 4.52725i 0.0906175 0.156954i
\(833\) −16.6894 + 28.9069i −0.578253 + 1.00156i
\(834\) 0 0
\(835\) 1.37551 + 2.38246i 0.0476017 + 0.0824485i
\(836\) 4.89944 0.169451
\(837\) 0 0
\(838\) −0.319022 −0.0110204
\(839\) −2.71919 4.70977i −0.0938768 0.162599i 0.815263 0.579092i \(-0.196593\pi\)
−0.909139 + 0.416492i \(0.863259\pi\)
\(840\) 0 0
\(841\) 1.64883 2.85586i 0.0568563 0.0984780i
\(842\) −0.825692 + 1.43014i −0.0284552 + 0.0492859i
\(843\) 0 0
\(844\) −1.27719 2.21216i −0.0439627 0.0761455i
\(845\) −8.30158 −0.285583
\(846\) 0 0
\(847\) −2.23442 −0.0767757
\(848\) −2.14987 3.72369i −0.0738269 0.127872i
\(849\) 0 0
\(850\) 6.37645 11.0443i 0.218710 0.378817i
\(851\) 8.51627 14.7506i 0.291934 0.505645i
\(852\) 0 0
\(853\) 23.5586 + 40.8046i 0.806629 + 1.39712i 0.915185 + 0.403033i \(0.132044\pi\)
−0.108556 + 0.994090i \(0.534623\pi\)
\(854\) −0.842556 −0.0288317
\(855\) 0 0
\(856\) −27.5107 −0.940298
\(857\) 23.4780 + 40.6651i 0.801993 + 1.38909i 0.918302 + 0.395880i \(0.129560\pi\)
−0.116309 + 0.993213i \(0.537106\pi\)
\(858\) 0 0
\(859\) −3.58172 + 6.20372i −0.122207 + 0.211668i −0.920638 0.390418i \(-0.872330\pi\)
0.798431 + 0.602086i \(0.205664\pi\)
\(860\) 1.04801 1.81521i 0.0357369 0.0618981i
\(861\) 0 0
\(862\) −4.13816 7.16750i −0.140946 0.244126i
\(863\) −35.4309 −1.20608 −0.603041 0.797710i \(-0.706045\pi\)
−0.603041 + 0.797710i \(0.706045\pi\)
\(864\) 0 0
\(865\) 13.7324 0.466914
\(866\) 11.4067 + 19.7570i 0.387615 + 0.671369i
\(867\) 0 0
\(868\) 0.809278 1.40171i 0.0274687 0.0475771i
\(869\) −1.90814 + 3.30500i −0.0647292 + 0.112114i
\(870\) 0 0
\(871\) −4.25331 7.36694i −0.144118 0.249619i
\(872\) 7.00421 0.237193
\(873\) 0 0
\(874\) 3.13846 0.106160
\(875\) 0.562610 + 0.974470i 0.0190197 + 0.0329431i
\(876\) 0 0
\(877\) −4.08647 + 7.07797i −0.137990 + 0.239006i −0.926736 0.375714i \(-0.877398\pi\)
0.788746 + 0.614720i \(0.210731\pi\)
\(878\) −3.09343 + 5.35797i −0.104398 + 0.180823i
\(879\) 0 0
\(880\) 4.01889 + 6.96091i 0.135477 + 0.234652i
\(881\) −33.2307 −1.11957 −0.559785 0.828638i \(-0.689116\pi\)
−0.559785 + 0.828638i \(0.689116\pi\)
\(882\) 0 0
\(883\) 33.0479 1.11215 0.556075 0.831132i \(-0.312307\pi\)
0.556075 + 0.831132i \(0.312307\pi\)
\(884\) 16.7427 + 28.9991i 0.563116 + 0.975346i
\(885\) 0 0
\(886\) −1.59967 + 2.77071i −0.0537420 + 0.0930838i
\(887\) 24.8736 43.0823i 0.835174 1.44656i −0.0587148 0.998275i \(-0.518700\pi\)
0.893889 0.448289i \(-0.147966\pi\)
\(888\) 0 0
\(889\) −0.929892 1.61062i −0.0311876 0.0540185i
\(890\) −4.91469 −0.164741
\(891\) 0 0
\(892\) 15.0155 0.502756
\(893\) −0.710966 1.23143i −0.0237916 0.0412082i
\(894\) 0 0
\(895\) 11.5799 20.0570i 0.387074 0.670431i
\(896\) 0.652139 1.12954i 0.0217864 0.0377352i
\(897\) 0 0
\(898\) −9.13429 15.8210i −0.304815 0.527955i
\(899\) 44.4047 1.48098
\(900\) 0 0
\(901\) −14.5561 −0.484935
\(902\) −14.0468 24.3298i −0.467708 0.810094i
\(903\) 0 0
\(904\) −13.9893 + 24.2302i −0.465278 + 0.805885i
\(905\) −1.07899 + 1.86887i −0.0358669 + 0.0621233i
\(906\) 0 0
\(907\) −17.2743 29.9199i −0.573582 0.993473i −0.996194 0.0871627i \(-0.972220\pi\)
0.422612 0.906311i \(-0.361113\pi\)
\(908\) −23.7179 −0.787106
\(909\) 0 0
\(910\) 0.395496 0.0131106
\(911\) 6.81845 + 11.8099i 0.225905 + 0.391280i 0.956591 0.291435i \(-0.0941326\pi\)
−0.730685 + 0.682714i \(0.760799\pi\)
\(912\) 0 0
\(913\) 18.4111 31.8889i 0.609317 1.05537i
\(914\) −0.224966 + 0.389652i −0.00744121 + 0.0128886i
\(915\) 0 0
\(916\) −8.62108 14.9322i −0.284849 0.493372i
\(917\) 1.61094 0.0531979
\(918\) 0 0
\(919\) 32.7701 1.08099 0.540493 0.841348i \(-0.318238\pi\)
0.540493 + 0.841348i \(0.318238\pi\)
\(920\) 9.87003 + 17.0954i 0.325405 + 0.563618i
\(921\) 0 0
\(922\) 7.08109 12.2648i 0.233203 0.403920i
\(923\) 14.8892 25.7888i 0.490083 0.848849i
\(924\) 0 0
\(925\) −4.26217 7.38230i −0.140139 0.242729i
\(926\) 16.9805 0.558015
\(927\) 0 0
\(928\) 29.3928 0.964866
\(929\) −2.76573 4.79039i −0.0907408 0.157168i 0.817082 0.576521i \(-0.195590\pi\)
−0.907823 + 0.419353i \(0.862257\pi\)
\(930\) 0 0
\(931\) −2.05556 + 3.56033i −0.0673682 + 0.116685i
\(932\) 4.01006 6.94562i 0.131354 0.227511i
\(933\) 0 0
\(934\) 9.12267 + 15.8009i 0.298503 + 0.517022i
\(935\) 27.2106 0.889883
\(936\) 0 0
\(937\) −0.994014 −0.0324730 −0.0162365 0.999868i \(-0.505168\pi\)
−0.0162365 + 0.999868i \(0.505168\pi\)
\(938\) 0.0767211 + 0.132885i 0.00250503 + 0.00433884i
\(939\) 0 0
\(940\) 1.93969 3.35965i 0.0632658 0.109580i
\(941\) −5.72859 + 9.92221i −0.186747 + 0.323455i −0.944164 0.329477i \(-0.893128\pi\)
0.757417 + 0.652931i \(0.226461\pi\)
\(942\) 0 0
\(943\) 29.4624 + 51.0305i 0.959429 + 1.66178i
\(944\) 0.0619640 0.00201676
\(945\) 0 0
\(946\) 4.85204 0.157754
\(947\) 22.8425 + 39.5644i 0.742282 + 1.28567i 0.951454 + 0.307791i \(0.0995898\pi\)
−0.209172 + 0.977879i \(0.567077\pi\)
\(948\) 0 0
\(949\) 27.9800 48.4628i 0.908269 1.57317i
\(950\) 0.785359 1.36028i 0.0254804 0.0441334i
\(951\) 0 0
\(952\) −0.696242 1.20593i −0.0225653 0.0390843i
\(953\) −14.5053 −0.469873 −0.234936 0.972011i \(-0.575488\pi\)
−0.234936 + 0.972011i \(0.575488\pi\)
\(954\) 0 0
\(955\) −4.13878 −0.133928
\(956\) −7.89776 13.6793i −0.255432 0.442421i
\(957\) 0 0
\(958\) −1.10354 + 1.91139i −0.0356538 + 0.0617542i
\(959\) 1.18345 2.04979i 0.0382155 0.0661912i
\(960\) 0 0
\(961\) −22.8580 39.5913i −0.737356 1.27714i
\(962\) −6.83575 −0.220393
\(963\) 0 0
\(964\) −16.4611 −0.530176
\(965\) −4.42604 7.66613i −0.142479 0.246781i
\(966\) 0 0
\(967\) 12.5184 21.6825i 0.402565 0.697263i −0.591470 0.806327i \(-0.701452\pi\)
0.994035 + 0.109064i \(0.0347853\pi\)
\(968\) −22.3794 + 38.7622i −0.719301 + 1.24587i
\(969\) 0 0
\(970\) 3.23577 + 5.60451i 0.103894 + 0.179950i
\(971\) 27.0907 0.869383 0.434692 0.900579i \(-0.356857\pi\)
0.434692 + 0.900579i \(0.356857\pi\)
\(972\) 0 0
\(973\) −1.96679 −0.0630522
\(974\) −2.66068 4.60843i −0.0852536 0.147664i
\(975\) 0 0
\(976\) 7.20708 12.4830i 0.230693 0.399572i
\(977\) 1.23670 2.14203i 0.0395655 0.0685295i −0.845565 0.533873i \(-0.820736\pi\)
0.885130 + 0.465344i \(0.154069\pi\)
\(978\) 0 0
\(979\) 18.6258 + 32.2609i 0.595284 + 1.03106i
\(980\) −11.2162 −0.358287
\(981\) 0 0
\(982\) −11.6601 −0.372089
\(983\) −9.55401 16.5480i −0.304726 0.527800i 0.672475 0.740120i \(-0.265231\pi\)
−0.977200 + 0.212320i \(0.931898\pi\)
\(984\) 0 0
\(985\) 1.20258 2.08293i 0.0383174 0.0663678i
\(986\) 8.28541 14.3508i 0.263861 0.457021i
\(987\) 0 0
\(988\) 2.06212 + 3.57169i 0.0656047 + 0.113631i
\(989\) −10.1769 −0.323607
\(990\) 0 0
\(991\) −38.3164 −1.21716 −0.608581 0.793492i \(-0.708261\pi\)
−0.608581 + 0.793492i \(0.708261\pi\)
\(992\) −25.3903 43.9773i −0.806143 1.39628i
\(993\) 0 0
\(994\) −0.268571 + 0.465178i −0.00851854 + 0.0147546i
\(995\) −12.3157 + 21.3314i −0.390434 + 0.676251i
\(996\) 0 0
\(997\) −20.6873 35.8315i −0.655174 1.13479i −0.981850 0.189658i \(-0.939262\pi\)
0.326676 0.945136i \(-0.394071\pi\)
\(998\) −5.42497 −0.171724
\(999\) 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.c.244.4 12
3.2 odd 2 inner 729.2.c.c.244.3 12
9.2 odd 6 inner 729.2.c.c.487.3 12
9.4 even 3 729.2.a.c.1.3 6
9.5 odd 6 729.2.a.c.1.4 yes 6
9.7 even 3 inner 729.2.c.c.487.4 12
27.2 odd 18 729.2.e.q.82.2 12
27.4 even 9 729.2.e.q.649.1 12
27.5 odd 18 729.2.e.m.163.1 12
27.7 even 9 729.2.e.m.568.2 12
27.11 odd 18 729.2.e.r.325.2 12
27.13 even 9 729.2.e.r.406.1 12
27.14 odd 18 729.2.e.r.406.2 12
27.16 even 9 729.2.e.r.325.1 12
27.20 odd 18 729.2.e.m.568.1 12
27.22 even 9 729.2.e.m.163.2 12
27.23 odd 18 729.2.e.q.649.2 12
27.25 even 9 729.2.e.q.82.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
729.2.a.c.1.3 6 9.4 even 3
729.2.a.c.1.4 yes 6 9.5 odd 6
729.2.c.c.244.3 12 3.2 odd 2 inner
729.2.c.c.244.4 12 1.1 even 1 trivial
729.2.c.c.487.3 12 9.2 odd 6 inner
729.2.c.c.487.4 12 9.7 even 3 inner
729.2.e.m.163.1 12 27.5 odd 18
729.2.e.m.163.2 12 27.22 even 9
729.2.e.m.568.1 12 27.20 odd 18
729.2.e.m.568.2 12 27.7 even 9
729.2.e.q.82.1 12 27.25 even 9
729.2.e.q.82.2 12 27.2 odd 18
729.2.e.q.649.1 12 27.4 even 9
729.2.e.q.649.2 12 27.23 odd 18
729.2.e.r.325.1 12 27.16 even 9
729.2.e.r.325.2 12 27.11 odd 18
729.2.e.r.406.1 12 27.13 even 9
729.2.e.r.406.2 12 27.14 odd 18