Properties

Label 729.2.e.r.649.1
Level $729$
Weight $2$
Character 729.649
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(82,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.e (of order \(9\), degree \(6\), 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: \(2\) over \(\Q(\zeta_{9})\)
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: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 649.1
Root \(0.642788 - 0.766044i\) of defining polynomial
Character \(\chi\) \(=\) 729.649
Dual form 729.2.e.r.82.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.223238 + 1.26604i) q^{2} +(0.326352 + 0.118782i) q^{4} +(-0.342020 + 0.286989i) q^{5} +(3.31908 - 1.20805i) q^{7} +(-1.50881 + 2.61334i) q^{8} +O(q^{10})\) \(q+(-0.223238 + 1.26604i) q^{2} +(0.326352 + 0.118782i) q^{4} +(-0.342020 + 0.286989i) q^{5} +(3.31908 - 1.20805i) q^{7} +(-1.50881 + 2.61334i) q^{8} +(-0.286989 - 0.497079i) q^{10} +(2.12965 + 1.78699i) q^{11} +(0.571452 + 3.24086i) q^{13} +(0.788496 + 4.47178i) q^{14} +(-2.43969 - 2.04715i) q^{16} +(-3.51968 - 6.09627i) q^{17} +(2.59240 - 4.49016i) q^{19} +(-0.145708 + 0.0530334i) q^{20} +(-2.73783 + 2.29731i) q^{22} +(6.83807 + 2.48886i) q^{23} +(-0.833626 + 4.72773i) q^{25} -4.23065 q^{26} +1.22668 q^{28} +(-0.628461 + 3.56418i) q^{29} +(1.81908 + 0.662090i) q^{31} +(-1.48686 + 1.24763i) q^{32} +(8.50387 - 3.09516i) q^{34} +(-0.788496 + 1.36571i) q^{35} +(1.61334 + 2.79439i) q^{37} +(5.10602 + 4.28446i) q^{38} +(-0.233956 - 1.32683i) q^{40} +(0.844075 + 4.78699i) q^{41} +(-4.41147 - 3.70167i) q^{43} +(0.482753 + 0.836152i) q^{44} +(-4.67752 + 8.10170i) q^{46} +(2.83564 - 1.03209i) q^{47} +(4.19459 - 3.51968i) q^{49} +(-5.79942 - 2.11081i) q^{50} +(-0.198463 + 1.12554i) q^{52} -8.77141 q^{53} -1.24123 q^{55} +(-1.85083 + 10.4966i) q^{56} +(-4.37211 - 1.59132i) q^{58} +(-2.27038 + 1.90508i) q^{59} +(-7.41147 + 2.69756i) q^{61} +(-1.24432 + 2.15523i) q^{62} +(-4.43242 - 7.67717i) q^{64} +(-1.12554 - 0.944440i) q^{65} +(-1.63903 - 9.29542i) q^{67} +(-0.424525 - 2.40760i) q^{68} +(-1.55303 - 1.30315i) q^{70} +(2.65366 + 4.59627i) q^{71} +(0.777189 - 1.34613i) q^{73} +(-3.89798 + 1.41875i) q^{74} +(1.37939 - 1.15744i) q^{76} +(9.22724 + 3.35844i) q^{77} +(-2.06670 + 11.7209i) q^{79} +1.42193 q^{80} -6.24897 q^{82} +(2.82304 - 16.0103i) q^{83} +(2.95336 + 1.07494i) q^{85} +(5.67128 - 4.75877i) q^{86} +(-7.88326 + 2.86927i) q^{88} +(9.21291 - 15.9572i) q^{89} +(5.81180 + 10.0663i) q^{91} +(1.93599 + 1.62449i) q^{92} +(0.673648 + 3.82045i) q^{94} +(0.401975 + 2.27972i) q^{95} +(7.74763 + 6.50103i) q^{97} +(3.51968 + 6.09627i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{4} + 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{4} + 6 q^{7} + 12 q^{10} + 6 q^{13} - 18 q^{16} + 24 q^{19} + 6 q^{22} - 48 q^{25} - 12 q^{28} - 12 q^{31} + 54 q^{34} + 6 q^{37} - 12 q^{40} - 12 q^{43} - 6 q^{46} + 42 q^{49} + 54 q^{52} - 60 q^{55} + 6 q^{58} - 48 q^{61} - 6 q^{64} - 66 q^{67} + 6 q^{70} - 12 q^{73} - 6 q^{76} + 42 q^{79} - 24 q^{82} - 18 q^{85} - 24 q^{88} + 6 q^{94} + 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.223238 + 1.26604i −0.157853 + 0.895229i 0.798278 + 0.602289i \(0.205745\pi\)
−0.956131 + 0.292939i \(0.905367\pi\)
\(3\) 0 0
\(4\) 0.326352 + 0.118782i 0.163176 + 0.0593912i
\(5\) −0.342020 + 0.286989i −0.152956 + 0.128345i −0.716054 0.698045i \(-0.754054\pi\)
0.563098 + 0.826390i \(0.309609\pi\)
\(6\) 0 0
\(7\) 3.31908 1.20805i 1.25449 0.456598i 0.372576 0.928002i \(-0.378475\pi\)
0.881918 + 0.471403i \(0.156252\pi\)
\(8\) −1.50881 + 2.61334i −0.533446 + 0.923956i
\(9\) 0 0
\(10\) −0.286989 0.497079i −0.0907539 0.157190i
\(11\) 2.12965 + 1.78699i 0.642114 + 0.538797i 0.904667 0.426120i \(-0.140120\pi\)
−0.262553 + 0.964918i \(0.584564\pi\)
\(12\) 0 0
\(13\) 0.571452 + 3.24086i 0.158492 + 0.898854i 0.955523 + 0.294916i \(0.0952915\pi\)
−0.797031 + 0.603938i \(0.793597\pi\)
\(14\) 0.788496 + 4.47178i 0.210734 + 1.19513i
\(15\) 0 0
\(16\) −2.43969 2.04715i −0.609923 0.511786i
\(17\) −3.51968 6.09627i −0.853648 1.47856i −0.877894 0.478856i \(-0.841052\pi\)
0.0242455 0.999706i \(-0.492282\pi\)
\(18\) 0 0
\(19\) 2.59240 4.49016i 0.594736 1.03011i −0.398848 0.917017i \(-0.630590\pi\)
0.993584 0.113097i \(-0.0360769\pi\)
\(20\) −0.145708 + 0.0530334i −0.0325813 + 0.0118586i
\(21\) 0 0
\(22\) −2.73783 + 2.29731i −0.583706 + 0.489788i
\(23\) 6.83807 + 2.48886i 1.42584 + 0.518962i 0.935735 0.352703i \(-0.114737\pi\)
0.490102 + 0.871665i \(0.336960\pi\)
\(24\) 0 0
\(25\) −0.833626 + 4.72773i −0.166725 + 0.945545i
\(26\) −4.23065 −0.829698
\(27\) 0 0
\(28\) 1.22668 0.231821
\(29\) −0.628461 + 3.56418i −0.116702 + 0.661851i 0.869191 + 0.494476i \(0.164640\pi\)
−0.985893 + 0.167375i \(0.946471\pi\)
\(30\) 0 0
\(31\) 1.81908 + 0.662090i 0.326716 + 0.118915i 0.500170 0.865927i \(-0.333271\pi\)
−0.173454 + 0.984842i \(0.555493\pi\)
\(32\) −1.48686 + 1.24763i −0.262843 + 0.220551i
\(33\) 0 0
\(34\) 8.50387 3.09516i 1.45840 0.530815i
\(35\) −0.788496 + 1.36571i −0.133280 + 0.230848i
\(36\) 0 0
\(37\) 1.61334 + 2.79439i 0.265232 + 0.459395i 0.967624 0.252395i \(-0.0812183\pi\)
−0.702393 + 0.711790i \(0.747885\pi\)
\(38\) 5.10602 + 4.28446i 0.828306 + 0.695032i
\(39\) 0 0
\(40\) −0.233956 1.32683i −0.0369916 0.209790i
\(41\) 0.844075 + 4.78699i 0.131822 + 0.747602i 0.977020 + 0.213148i \(0.0683716\pi\)
−0.845198 + 0.534454i \(0.820517\pi\)
\(42\) 0 0
\(43\) −4.41147 3.70167i −0.672743 0.564499i 0.241133 0.970492i \(-0.422481\pi\)
−0.913876 + 0.405993i \(0.866926\pi\)
\(44\) 0.482753 + 0.836152i 0.0727777 + 0.126055i
\(45\) 0 0
\(46\) −4.67752 + 8.10170i −0.689662 + 1.19453i
\(47\) 2.83564 1.03209i 0.413621 0.150546i −0.126824 0.991925i \(-0.540478\pi\)
0.540445 + 0.841380i \(0.318256\pi\)
\(48\) 0 0
\(49\) 4.19459 3.51968i 0.599228 0.502812i
\(50\) −5.79942 2.11081i −0.820161 0.298514i
\(51\) 0 0
\(52\) −0.198463 + 1.12554i −0.0275219 + 0.156084i
\(53\) −8.77141 −1.20485 −0.602423 0.798177i \(-0.705798\pi\)
−0.602423 + 0.798177i \(0.705798\pi\)
\(54\) 0 0
\(55\) −1.24123 −0.167367
\(56\) −1.85083 + 10.4966i −0.247328 + 1.40267i
\(57\) 0 0
\(58\) −4.37211 1.59132i −0.574086 0.208950i
\(59\) −2.27038 + 1.90508i −0.295579 + 0.248020i −0.778501 0.627643i \(-0.784020\pi\)
0.482923 + 0.875663i \(0.339575\pi\)
\(60\) 0 0
\(61\) −7.41147 + 2.69756i −0.948942 + 0.345387i −0.769691 0.638417i \(-0.779590\pi\)
−0.179251 + 0.983803i \(0.557367\pi\)
\(62\) −1.24432 + 2.15523i −0.158029 + 0.273714i
\(63\) 0 0
\(64\) −4.43242 7.67717i −0.554052 0.959647i
\(65\) −1.12554 0.944440i −0.139606 0.117143i
\(66\) 0 0
\(67\) −1.63903 9.29542i −0.200240 1.13562i −0.904757 0.425929i \(-0.859947\pi\)
0.704517 0.709687i \(-0.251164\pi\)
\(68\) −0.424525 2.40760i −0.0514813 0.291965i
\(69\) 0 0
\(70\) −1.55303 1.30315i −0.185623 0.155756i
\(71\) 2.65366 + 4.59627i 0.314931 + 0.545476i 0.979423 0.201819i \(-0.0646853\pi\)
−0.664492 + 0.747296i \(0.731352\pi\)
\(72\) 0 0
\(73\) 0.777189 1.34613i 0.0909631 0.157553i −0.816954 0.576703i \(-0.804339\pi\)
0.907917 + 0.419151i \(0.137672\pi\)
\(74\) −3.89798 + 1.41875i −0.453131 + 0.164926i
\(75\) 0 0
\(76\) 1.37939 1.15744i 0.158226 0.132768i
\(77\) 9.22724 + 3.35844i 1.05154 + 0.382730i
\(78\) 0 0
\(79\) −2.06670 + 11.7209i −0.232522 + 1.31870i 0.615247 + 0.788335i \(0.289056\pi\)
−0.847769 + 0.530365i \(0.822055\pi\)
\(80\) 1.42193 0.158977
\(81\) 0 0
\(82\) −6.24897 −0.690083
\(83\) 2.82304 16.0103i 0.309869 1.75736i −0.289781 0.957093i \(-0.593583\pi\)
0.599650 0.800262i \(-0.295306\pi\)
\(84\) 0 0
\(85\) 2.95336 + 1.07494i 0.320337 + 0.116593i
\(86\) 5.67128 4.75877i 0.611550 0.513151i
\(87\) 0 0
\(88\) −7.88326 + 2.86927i −0.840358 + 0.305865i
\(89\) 9.21291 15.9572i 0.976567 1.69146i 0.301902 0.953339i \(-0.402378\pi\)
0.674665 0.738125i \(-0.264288\pi\)
\(90\) 0 0
\(91\) 5.81180 + 10.0663i 0.609243 + 1.05524i
\(92\) 1.93599 + 1.62449i 0.201840 + 0.169364i
\(93\) 0 0
\(94\) 0.673648 + 3.82045i 0.0694815 + 0.394049i
\(95\) 0.401975 + 2.27972i 0.0412418 + 0.233894i
\(96\) 0 0
\(97\) 7.74763 + 6.50103i 0.786652 + 0.660080i 0.944914 0.327318i \(-0.106145\pi\)
−0.158262 + 0.987397i \(0.550589\pi\)
\(98\) 3.51968 + 6.09627i 0.355541 + 0.615816i
\(99\) 0 0
\(100\) −0.833626 + 1.44388i −0.0833626 + 0.144388i
\(101\) −1.95529 + 0.711667i −0.194558 + 0.0708135i −0.437462 0.899237i \(-0.644122\pi\)
0.242903 + 0.970051i \(0.421900\pi\)
\(102\) 0 0
\(103\) −1.10947 + 0.930956i −0.109319 + 0.0917298i −0.695809 0.718227i \(-0.744954\pi\)
0.586490 + 0.809957i \(0.300510\pi\)
\(104\) −9.33170 3.39646i −0.915048 0.333050i
\(105\) 0 0
\(106\) 1.95811 11.1050i 0.190189 1.07861i
\(107\) 2.23583 0.216146 0.108073 0.994143i \(-0.465532\pi\)
0.108073 + 0.994143i \(0.465532\pi\)
\(108\) 0 0
\(109\) −11.5030 −1.10179 −0.550893 0.834576i \(-0.685713\pi\)
−0.550893 + 0.834576i \(0.685713\pi\)
\(110\) 0.277089 1.57145i 0.0264194 0.149832i
\(111\) 0 0
\(112\) −10.5706 3.84737i −0.998825 0.363543i
\(113\) −1.29320 + 1.08512i −0.121654 + 0.102080i −0.701585 0.712586i \(-0.747524\pi\)
0.579931 + 0.814666i \(0.303079\pi\)
\(114\) 0 0
\(115\) −3.05303 + 1.11121i −0.284697 + 0.103621i
\(116\) −0.628461 + 1.08853i −0.0583511 + 0.101067i
\(117\) 0 0
\(118\) −1.90508 3.29969i −0.175377 0.303761i
\(119\) −19.0467 15.9820i −1.74600 1.46507i
\(120\) 0 0
\(121\) −0.568048 3.22156i −0.0516407 0.292869i
\(122\) −1.76070 9.98545i −0.159407 0.904040i
\(123\) 0 0
\(124\) 0.515015 + 0.432149i 0.0462497 + 0.0388081i
\(125\) −2.18788 3.78952i −0.195690 0.338945i
\(126\) 0 0
\(127\) 1.33615 2.31428i 0.118564 0.205359i −0.800635 0.599153i \(-0.795504\pi\)
0.919199 + 0.393793i \(0.128837\pi\)
\(128\) 7.06131 2.57011i 0.624138 0.227168i
\(129\) 0 0
\(130\) 1.44697 1.21415i 0.126907 0.106488i
\(131\) −2.74378 0.998656i −0.239726 0.0872530i 0.219364 0.975643i \(-0.429602\pi\)
−0.459089 + 0.888390i \(0.651824\pi\)
\(132\) 0 0
\(133\) 3.18004 18.0349i 0.275745 1.56383i
\(134\) 12.1343 1.04824
\(135\) 0 0
\(136\) 21.2422 1.82150
\(137\) 0.808718 4.58647i 0.0690934 0.391848i −0.930575 0.366101i \(-0.880692\pi\)
0.999668 0.0257471i \(-0.00819647\pi\)
\(138\) 0 0
\(139\) 7.52007 + 2.73708i 0.637844 + 0.232156i 0.640642 0.767840i \(-0.278668\pi\)
−0.00279796 + 0.999996i \(0.500891\pi\)
\(140\) −0.419550 + 0.352044i −0.0354584 + 0.0297532i
\(141\) 0 0
\(142\) −6.41147 + 2.33359i −0.538039 + 0.195830i
\(143\) −4.57440 + 7.92309i −0.382530 + 0.662562i
\(144\) 0 0
\(145\) −0.807934 1.39938i −0.0670952 0.116212i
\(146\) 1.53076 + 1.28446i 0.126687 + 0.106303i
\(147\) 0 0
\(148\) 0.194593 + 1.10359i 0.0159954 + 0.0907145i
\(149\) −3.50973 19.9047i −0.287528 1.63065i −0.696112 0.717933i \(-0.745088\pi\)
0.408584 0.912721i \(-0.366023\pi\)
\(150\) 0 0
\(151\) 5.13429 + 4.30818i 0.417822 + 0.350594i 0.827334 0.561710i \(-0.189856\pi\)
−0.409512 + 0.912305i \(0.634301\pi\)
\(152\) 7.82288 + 13.5496i 0.634520 + 1.09902i
\(153\) 0 0
\(154\) −6.31180 + 10.9324i −0.508620 + 0.880955i
\(155\) −0.812174 + 0.295607i −0.0652354 + 0.0237437i
\(156\) 0 0
\(157\) 4.07919 3.42285i 0.325555 0.273173i −0.465331 0.885137i \(-0.654065\pi\)
0.790886 + 0.611964i \(0.209620\pi\)
\(158\) −14.3778 5.23308i −1.14383 0.416321i
\(159\) 0 0
\(160\) 0.150482 0.853427i 0.0118967 0.0674693i
\(161\) 25.7028 2.02566
\(162\) 0 0
\(163\) 3.81521 0.298830 0.149415 0.988775i \(-0.452261\pi\)
0.149415 + 0.988775i \(0.452261\pi\)
\(164\) −0.293144 + 1.66250i −0.0228907 + 0.129820i
\(165\) 0 0
\(166\) 19.6395 + 7.14819i 1.52432 + 0.554807i
\(167\) 6.99811 5.87211i 0.541530 0.454398i −0.330531 0.943795i \(-0.607228\pi\)
0.872061 + 0.489398i \(0.162783\pi\)
\(168\) 0 0
\(169\) 2.03936 0.742267i 0.156874 0.0570975i
\(170\) −2.02022 + 3.49912i −0.154944 + 0.268370i
\(171\) 0 0
\(172\) −1.00000 1.73205i −0.0762493 0.132068i
\(173\) 4.65284 + 3.90420i 0.353749 + 0.296831i 0.802293 0.596930i \(-0.203613\pi\)
−0.448544 + 0.893761i \(0.648057\pi\)
\(174\) 0 0
\(175\) 2.94444 + 16.6988i 0.222579 + 1.26231i
\(176\) −1.53747 8.71941i −0.115891 0.657250i
\(177\) 0 0
\(178\) 18.1459 + 15.2262i 1.36009 + 1.14125i
\(179\) −5.14057 8.90373i −0.384224 0.665496i 0.607437 0.794368i \(-0.292198\pi\)
−0.991661 + 0.128872i \(0.958864\pi\)
\(180\) 0 0
\(181\) 11.5706 20.0408i 0.860034 1.48962i −0.0118609 0.999930i \(-0.503776\pi\)
0.871895 0.489693i \(-0.162891\pi\)
\(182\) −14.0418 + 5.11081i −1.04085 + 0.378839i
\(183\) 0 0
\(184\) −16.8216 + 14.1150i −1.24011 + 1.04057i
\(185\) −1.35375 0.492726i −0.0995299 0.0362259i
\(186\) 0 0
\(187\) 3.39827 19.2725i 0.248506 1.40935i
\(188\) 1.04801 0.0764340
\(189\) 0 0
\(190\) −2.97596 −0.215899
\(191\) 2.54747 14.4474i 0.184329 1.04538i −0.742486 0.669861i \(-0.766354\pi\)
0.926815 0.375518i \(-0.122535\pi\)
\(192\) 0 0
\(193\) −22.0278 8.01747i −1.58560 0.577110i −0.609185 0.793028i \(-0.708503\pi\)
−0.976411 + 0.215918i \(0.930725\pi\)
\(194\) −9.96016 + 8.35756i −0.715098 + 0.600038i
\(195\) 0 0
\(196\) 1.78699 0.650411i 0.127642 0.0464579i
\(197\) 4.51384 7.81820i 0.321598 0.557024i −0.659220 0.751950i \(-0.729113\pi\)
0.980818 + 0.194926i \(0.0624468\pi\)
\(198\) 0 0
\(199\) −1.30200 2.25514i −0.0922966 0.159862i 0.816181 0.577797i \(-0.196087\pi\)
−0.908477 + 0.417935i \(0.862754\pi\)
\(200\) −11.0974 9.31180i −0.784703 0.658444i
\(201\) 0 0
\(202\) −0.464508 2.63435i −0.0326826 0.185352i
\(203\) 2.21978 + 12.5890i 0.155798 + 0.883574i
\(204\) 0 0
\(205\) −1.66250 1.39501i −0.116114 0.0974315i
\(206\) −0.930956 1.61246i −0.0648628 0.112346i
\(207\) 0 0
\(208\) 5.24035 9.07656i 0.363353 0.629346i
\(209\) 13.5448 4.92989i 0.936911 0.341008i
\(210\) 0 0
\(211\) −12.5287 + 10.5128i −0.862510 + 0.723732i −0.962507 0.271256i \(-0.912561\pi\)
0.0999971 + 0.994988i \(0.468117\pi\)
\(212\) −2.86257 1.04189i −0.196602 0.0715572i
\(213\) 0 0
\(214\) −0.499123 + 2.83067i −0.0341193 + 0.193500i
\(215\) 2.57115 0.175351
\(216\) 0 0
\(217\) 6.83750 0.464159
\(218\) 2.56790 14.5633i 0.173920 0.986351i
\(219\) 0 0
\(220\) −0.405078 0.147436i −0.0273103 0.00994014i
\(221\) 17.7458 14.8905i 1.19371 1.00165i
\(222\) 0 0
\(223\) −3.47906 + 1.26627i −0.232975 + 0.0847959i −0.455869 0.890047i \(-0.650672\pi\)
0.222895 + 0.974843i \(0.428449\pi\)
\(224\) −3.42782 + 5.93717i −0.229031 + 0.396694i
\(225\) 0 0
\(226\) −1.08512 1.87949i −0.0721813 0.125022i
\(227\) −8.09002 6.78833i −0.536954 0.450557i 0.333541 0.942736i \(-0.391756\pi\)
−0.870495 + 0.492178i \(0.836201\pi\)
\(228\) 0 0
\(229\) 2.34864 + 13.3198i 0.155203 + 0.880197i 0.958600 + 0.284755i \(0.0919122\pi\)
−0.803398 + 0.595443i \(0.796977\pi\)
\(230\) −0.725293 4.11334i −0.0478244 0.271226i
\(231\) 0 0
\(232\) −8.36618 7.02006i −0.549267 0.460890i
\(233\) −6.35035 10.9991i −0.416025 0.720576i 0.579510 0.814965i \(-0.303244\pi\)
−0.995535 + 0.0943883i \(0.969910\pi\)
\(234\) 0 0
\(235\) −0.673648 + 1.16679i −0.0439440 + 0.0761132i
\(236\) −0.967233 + 0.352044i −0.0629615 + 0.0229161i
\(237\) 0 0
\(238\) 24.4859 20.5461i 1.58719 1.33181i
\(239\) 5.49865 + 2.00134i 0.355678 + 0.129456i 0.513678 0.857983i \(-0.328282\pi\)
−0.158000 + 0.987439i \(0.550505\pi\)
\(240\) 0 0
\(241\) −1.48293 + 8.41009i −0.0955237 + 0.541742i 0.899062 + 0.437821i \(0.144250\pi\)
−0.994586 + 0.103920i \(0.966861\pi\)
\(242\) 4.20545 0.270337
\(243\) 0 0
\(244\) −2.73917 −0.175357
\(245\) −0.424525 + 2.40760i −0.0271219 + 0.153816i
\(246\) 0 0
\(247\) 16.0334 + 5.83569i 1.02018 + 0.371316i
\(248\) −4.47492 + 3.75490i −0.284157 + 0.238436i
\(249\) 0 0
\(250\) 5.28611 1.92399i 0.334323 0.121684i
\(251\) 3.37895 5.85251i 0.213277 0.369407i −0.739461 0.673199i \(-0.764920\pi\)
0.952738 + 0.303792i \(0.0982529\pi\)
\(252\) 0 0
\(253\) 10.1152 + 17.5200i 0.635934 + 1.10147i
\(254\) 2.63171 + 2.20826i 0.165128 + 0.138559i
\(255\) 0 0
\(256\) −1.40121 7.94664i −0.0875754 0.496665i
\(257\) 0.639540 + 3.62701i 0.0398934 + 0.226247i 0.998236 0.0593754i \(-0.0189109\pi\)
−0.958342 + 0.285622i \(0.907800\pi\)
\(258\) 0 0
\(259\) 8.73055 + 7.32580i 0.542490 + 0.455203i
\(260\) −0.255139 0.441914i −0.0158231 0.0274064i
\(261\) 0 0
\(262\) 1.87686 3.25082i 0.115953 0.200836i
\(263\) −3.41847 + 1.24422i −0.210792 + 0.0767220i −0.445258 0.895402i \(-0.646888\pi\)
0.234466 + 0.972124i \(0.424666\pi\)
\(264\) 0 0
\(265\) 3.00000 2.51730i 0.184289 0.154636i
\(266\) 22.1231 + 8.05216i 1.35646 + 0.493709i
\(267\) 0 0
\(268\) 0.569230 3.22826i 0.0347713 0.197198i
\(269\) −7.08672 −0.432085 −0.216042 0.976384i \(-0.569315\pi\)
−0.216042 + 0.976384i \(0.569315\pi\)
\(270\) 0 0
\(271\) −19.0000 −1.15417 −0.577084 0.816685i \(-0.695809\pi\)
−0.577084 + 0.816685i \(0.695809\pi\)
\(272\) −3.89300 + 22.0783i −0.236048 + 1.33869i
\(273\) 0 0
\(274\) 5.62613 + 2.04775i 0.339887 + 0.123709i
\(275\) −10.2237 + 8.57873i −0.616514 + 0.517317i
\(276\) 0 0
\(277\) 13.0544 4.75140i 0.784362 0.285484i 0.0813714 0.996684i \(-0.474070\pi\)
0.702990 + 0.711200i \(0.251848\pi\)
\(278\) −5.14403 + 8.90972i −0.308518 + 0.534369i
\(279\) 0 0
\(280\) −2.37939 4.12122i −0.142195 0.246290i
\(281\) 16.9506 + 14.2233i 1.01119 + 0.848490i 0.988495 0.151253i \(-0.0483307\pi\)
0.0226955 + 0.999742i \(0.492775\pi\)
\(282\) 0 0
\(283\) −4.12108 23.3718i −0.244973 1.38931i −0.820556 0.571567i \(-0.806336\pi\)
0.575583 0.817744i \(-0.304775\pi\)
\(284\) 0.320070 + 1.81521i 0.0189927 + 0.107713i
\(285\) 0 0
\(286\) −9.00980 7.56012i −0.532761 0.447039i
\(287\) 8.58445 + 14.8687i 0.506724 + 0.877672i
\(288\) 0 0
\(289\) −16.2763 + 28.1914i −0.957430 + 1.65832i
\(290\) 1.95204 0.710485i 0.114628 0.0417211i
\(291\) 0 0
\(292\) 0.413534 0.346996i 0.0242002 0.0203064i
\(293\) −17.4840 6.36366i −1.02143 0.371769i −0.223616 0.974677i \(-0.571786\pi\)
−0.797810 + 0.602909i \(0.794008\pi\)
\(294\) 0 0
\(295\) 0.229780 1.30315i 0.0133783 0.0758723i
\(296\) −9.73692 −0.565947
\(297\) 0 0
\(298\) 25.9837 1.50520
\(299\) −4.15841 + 23.5835i −0.240487 + 1.36387i
\(300\) 0 0
\(301\) −19.1138 6.95686i −1.10170 0.400987i
\(302\) −6.60051 + 5.53849i −0.379817 + 0.318704i
\(303\) 0 0
\(304\) −15.5167 + 5.64760i −0.889942 + 0.323912i
\(305\) 1.76070 3.04963i 0.100818 0.174621i
\(306\) 0 0
\(307\) −10.3735 17.9674i −0.592044 1.02545i −0.993957 0.109773i \(-0.964988\pi\)
0.401912 0.915678i \(-0.368346\pi\)
\(308\) 2.61240 + 2.19207i 0.148855 + 0.124905i
\(309\) 0 0
\(310\) −0.192944 1.09424i −0.0109585 0.0621486i
\(311\) 3.53990 + 20.0758i 0.200729 + 1.13839i 0.904020 + 0.427491i \(0.140602\pi\)
−0.703290 + 0.710903i \(0.748287\pi\)
\(312\) 0 0
\(313\) −22.8594 19.1813i −1.29209 1.08419i −0.991455 0.130451i \(-0.958357\pi\)
−0.300633 0.953740i \(-0.597198\pi\)
\(314\) 3.42285 + 5.92855i 0.193163 + 0.334567i
\(315\) 0 0
\(316\) −2.06670 + 3.57964i −0.116261 + 0.201370i
\(317\) −4.05629 + 1.47637i −0.227824 + 0.0829210i −0.453410 0.891302i \(-0.649793\pi\)
0.225586 + 0.974223i \(0.427570\pi\)
\(318\) 0 0
\(319\) −7.70755 + 6.46740i −0.431540 + 0.362105i
\(320\) 3.71924 + 1.35369i 0.207912 + 0.0756737i
\(321\) 0 0
\(322\) −5.73783 + 32.5408i −0.319757 + 1.81343i
\(323\) −36.4976 −2.03078
\(324\) 0 0
\(325\) −15.7983 −0.876332
\(326\) −0.851698 + 4.83022i −0.0471712 + 0.267521i
\(327\) 0 0
\(328\) −13.7836 5.01681i −0.761071 0.277007i
\(329\) 8.16490 6.85117i 0.450146 0.377717i
\(330\) 0 0
\(331\) 2.74288 0.998326i 0.150762 0.0548730i −0.265537 0.964101i \(-0.585549\pi\)
0.416299 + 0.909228i \(0.363327\pi\)
\(332\) 2.82304 4.88965i 0.154935 0.268355i
\(333\) 0 0
\(334\) 5.87211 + 10.1708i 0.321308 + 0.556521i
\(335\) 3.22826 + 2.70884i 0.176379 + 0.148000i
\(336\) 0 0
\(337\) 2.50774 + 14.2221i 0.136605 + 0.774727i 0.973728 + 0.227713i \(0.0731247\pi\)
−0.837123 + 0.547015i \(0.815764\pi\)
\(338\) 0.484481 + 2.74763i 0.0263523 + 0.149451i
\(339\) 0 0
\(340\) 0.836152 + 0.701615i 0.0453467 + 0.0380504i
\(341\) 2.69085 + 4.66069i 0.145718 + 0.252391i
\(342\) 0 0
\(343\) −2.69207 + 4.66280i −0.145358 + 0.251767i
\(344\) 16.3298 5.94356i 0.880444 0.320455i
\(345\) 0 0
\(346\) −5.98158 + 5.01914i −0.321572 + 0.269831i
\(347\) 1.36635 + 0.497312i 0.0733496 + 0.0266971i 0.378434 0.925628i \(-0.376463\pi\)
−0.305085 + 0.952325i \(0.598685\pi\)
\(348\) 0 0
\(349\) −4.78952 + 27.1627i −0.256377 + 1.45399i 0.536137 + 0.844131i \(0.319883\pi\)
−0.792514 + 0.609854i \(0.791228\pi\)
\(350\) −21.7987 −1.16519
\(351\) 0 0
\(352\) −5.39599 −0.287607
\(353\) 1.82888 10.3721i 0.0973416 0.552052i −0.896663 0.442714i \(-0.854016\pi\)
0.994005 0.109338i \(-0.0348731\pi\)
\(354\) 0 0
\(355\) −2.22668 0.810446i −0.118180 0.0430140i
\(356\) 4.90209 4.11334i 0.259810 0.218007i
\(357\) 0 0
\(358\) 12.4201 4.52054i 0.656422 0.238918i
\(359\) −7.35273 + 12.7353i −0.388062 + 0.672143i −0.992189 0.124745i \(-0.960189\pi\)
0.604127 + 0.796888i \(0.293522\pi\)
\(360\) 0 0
\(361\) −3.94104 6.82608i −0.207423 0.359267i
\(362\) 22.7896 + 19.1227i 1.19779 + 1.00507i
\(363\) 0 0
\(364\) 0.700989 + 3.97551i 0.0367418 + 0.208373i
\(365\) 0.120510 + 0.683448i 0.00630780 + 0.0357733i
\(366\) 0 0
\(367\) −16.3648 13.7317i −0.854238 0.716790i 0.106481 0.994315i \(-0.466042\pi\)
−0.960719 + 0.277524i \(0.910486\pi\)
\(368\) −11.5878 20.0706i −0.604053 1.04625i
\(369\) 0 0
\(370\) 0.926022 1.60392i 0.0481416 0.0833837i
\(371\) −29.1130 + 10.5963i −1.51147 + 0.550131i
\(372\) 0 0
\(373\) 17.3314 14.5428i 0.897386 0.752996i −0.0722916 0.997384i \(-0.523031\pi\)
0.969678 + 0.244387i \(0.0785868\pi\)
\(374\) 23.6413 + 8.60472i 1.22246 + 0.444940i
\(375\) 0 0
\(376\) −1.58125 + 8.96773i −0.0815468 + 0.462475i
\(377\) −11.9101 −0.613404
\(378\) 0 0
\(379\) −17.0743 −0.877047 −0.438523 0.898720i \(-0.644498\pi\)
−0.438523 + 0.898720i \(0.644498\pi\)
\(380\) −0.139605 + 0.791737i −0.00716156 + 0.0406152i
\(381\) 0 0
\(382\) 17.7224 + 6.45043i 0.906757 + 0.330033i
\(383\) −29.8693 + 25.0633i −1.52625 + 1.28067i −0.707054 + 0.707160i \(0.749976\pi\)
−0.819195 + 0.573515i \(0.805579\pi\)
\(384\) 0 0
\(385\) −4.11974 + 1.49946i −0.209961 + 0.0764196i
\(386\) 15.0679 26.0984i 0.766936 1.32837i
\(387\) 0 0
\(388\) 1.75624 + 3.04190i 0.0891598 + 0.154429i
\(389\) 7.82288 + 6.56418i 0.396636 + 0.332817i 0.819192 0.573520i \(-0.194422\pi\)
−0.422556 + 0.906337i \(0.638867\pi\)
\(390\) 0 0
\(391\) −8.89512 50.4467i −0.449845 2.55120i
\(392\) 2.86927 + 16.2724i 0.144920 + 0.821882i
\(393\) 0 0
\(394\) 8.89053 + 7.46004i 0.447898 + 0.375831i
\(395\) −2.65690 4.60189i −0.133683 0.231546i
\(396\) 0 0
\(397\) 0.571452 0.989783i 0.0286803 0.0496758i −0.851329 0.524632i \(-0.824203\pi\)
0.880009 + 0.474956i \(0.157536\pi\)
\(398\) 3.14576 1.14496i 0.157683 0.0573918i
\(399\) 0 0
\(400\) 11.7121 9.82765i 0.585607 0.491382i
\(401\) 19.3144 + 7.02987i 0.964515 + 0.351055i 0.775801 0.630977i \(-0.217346\pi\)
0.188714 + 0.982032i \(0.439568\pi\)
\(402\) 0 0
\(403\) −1.10623 + 6.27374i −0.0551052 + 0.312517i
\(404\) −0.722645 −0.0359530
\(405\) 0 0
\(406\) −16.4338 −0.815594
\(407\) −1.55769 + 8.83409i −0.0772118 + 0.437890i
\(408\) 0 0
\(409\) 7.63816 + 2.78006i 0.377682 + 0.137465i 0.523884 0.851790i \(-0.324483\pi\)
−0.146201 + 0.989255i \(0.546705\pi\)
\(410\) 2.13727 1.79339i 0.105552 0.0885690i
\(411\) 0 0
\(412\) −0.472659 + 0.172034i −0.0232862 + 0.00847549i
\(413\) −5.23416 + 9.06583i −0.257556 + 0.446100i
\(414\) 0 0
\(415\) 3.62923 + 6.28602i 0.178152 + 0.308568i
\(416\) −4.89306 4.10576i −0.239902 0.201302i
\(417\) 0 0
\(418\) 3.21776 + 18.2488i 0.157386 + 0.892579i
\(419\) 6.21286 + 35.2349i 0.303518 + 1.72134i 0.630399 + 0.776271i \(0.282891\pi\)
−0.326881 + 0.945066i \(0.605998\pi\)
\(420\) 0 0
\(421\) −10.0496 8.43264i −0.489789 0.410982i 0.364162 0.931336i \(-0.381356\pi\)
−0.853951 + 0.520354i \(0.825800\pi\)
\(422\) −10.5128 18.2087i −0.511756 0.886387i
\(423\) 0 0
\(424\) 13.2344 22.9227i 0.642720 1.11322i
\(425\) 31.7556 11.5581i 1.54037 0.560650i
\(426\) 0 0
\(427\) −21.3405 + 17.9068i −1.03274 + 0.866571i
\(428\) 0.729669 + 0.265578i 0.0352699 + 0.0128372i
\(429\) 0 0
\(430\) −0.573978 + 3.25519i −0.0276797 + 0.156979i
\(431\) 9.48411 0.456833 0.228417 0.973563i \(-0.426645\pi\)
0.228417 + 0.973563i \(0.426645\pi\)
\(432\) 0 0
\(433\) 17.6628 0.848820 0.424410 0.905470i \(-0.360481\pi\)
0.424410 + 0.905470i \(0.360481\pi\)
\(434\) −1.52639 + 8.65657i −0.0732689 + 0.415529i
\(435\) 0 0
\(436\) −3.75402 1.36635i −0.179785 0.0654364i
\(437\) 28.9024 24.2520i 1.38259 1.16013i
\(438\) 0 0
\(439\) 16.6001 6.04196i 0.792281 0.288367i 0.0859973 0.996295i \(-0.472592\pi\)
0.706284 + 0.707929i \(0.250370\pi\)
\(440\) 1.87278 3.24376i 0.0892814 0.154640i
\(441\) 0 0
\(442\) 14.8905 + 25.7912i 0.708270 + 1.22676i
\(443\) −9.95253 8.35117i −0.472859 0.396776i 0.374977 0.927034i \(-0.377651\pi\)
−0.847836 + 0.530258i \(0.822095\pi\)
\(444\) 0 0
\(445\) 1.42855 + 8.10170i 0.0677197 + 0.384057i
\(446\) −0.826501 4.68732i −0.0391359 0.221951i
\(447\) 0 0
\(448\) −23.9859 20.1266i −1.13323 0.950891i
\(449\) 2.31428 + 4.00846i 0.109218 + 0.189171i 0.915454 0.402424i \(-0.131832\pi\)
−0.806236 + 0.591594i \(0.798499\pi\)
\(450\) 0 0
\(451\) −6.75671 + 11.7030i −0.318161 + 0.551071i
\(452\) −0.550931 + 0.200522i −0.0259136 + 0.00943178i
\(453\) 0 0
\(454\) 10.4003 8.72691i 0.488112 0.409574i
\(455\) −4.87668 1.77497i −0.228622 0.0832117i
\(456\) 0 0
\(457\) 3.57145 20.2547i 0.167065 0.947475i −0.779844 0.625974i \(-0.784702\pi\)
0.946909 0.321501i \(-0.104187\pi\)
\(458\) −17.3878 −0.812477
\(459\) 0 0
\(460\) −1.12836 −0.0526098
\(461\) −5.82980 + 33.0624i −0.271521 + 1.53987i 0.478280 + 0.878207i \(0.341260\pi\)
−0.749801 + 0.661663i \(0.769851\pi\)
\(462\) 0 0
\(463\) −12.3391 4.49108i −0.573449 0.208718i 0.0389856 0.999240i \(-0.487587\pi\)
−0.612434 + 0.790522i \(0.709810\pi\)
\(464\) 8.82964 7.40895i 0.409906 0.343952i
\(465\) 0 0
\(466\) 15.3430 5.58440i 0.710751 0.258692i
\(467\) −11.8154 + 20.4648i −0.546750 + 0.946999i 0.451745 + 0.892147i \(0.350802\pi\)
−0.998495 + 0.0548513i \(0.982532\pi\)
\(468\) 0 0
\(469\) −16.6694 28.8722i −0.769720 1.33319i
\(470\) −1.32683 1.11334i −0.0612020 0.0513546i
\(471\) 0 0
\(472\) −1.55303 8.80769i −0.0714842 0.405407i
\(473\) −2.78006 15.7665i −0.127827 0.724945i
\(474\) 0 0
\(475\) 19.0672 + 15.9993i 0.874862 + 0.734096i
\(476\) −4.31753 7.47818i −0.197894 0.342762i
\(477\) 0 0
\(478\) −3.76130 + 6.51476i −0.172038 + 0.297978i
\(479\) 5.52557 2.01114i 0.252470 0.0918915i −0.212685 0.977121i \(-0.568221\pi\)
0.465155 + 0.885229i \(0.345999\pi\)
\(480\) 0 0
\(481\) −8.13429 + 6.82548i −0.370891 + 0.311215i
\(482\) −10.3165 3.75490i −0.469904 0.171031i
\(483\) 0 0
\(484\) 0.197281 1.11884i 0.00896732 0.0508562i
\(485\) −4.51557 −0.205041
\(486\) 0 0
\(487\) 38.7965 1.75804 0.879020 0.476786i \(-0.158198\pi\)
0.879020 + 0.476786i \(0.158198\pi\)
\(488\) 4.13290 23.4388i 0.187087 1.06103i
\(489\) 0 0
\(490\) −2.95336 1.07494i −0.133419 0.0485607i
\(491\) −28.7912 + 24.1587i −1.29933 + 1.09027i −0.309068 + 0.951040i \(0.600017\pi\)
−0.990261 + 0.139227i \(0.955538\pi\)
\(492\) 0 0
\(493\) 23.9402 8.71351i 1.07821 0.392437i
\(494\) −10.9675 + 18.9963i −0.493452 + 0.854684i
\(495\) 0 0
\(496\) −3.08260 5.33921i −0.138413 0.239738i
\(497\) 14.3602 + 12.0496i 0.644143 + 0.540500i
\(498\) 0 0
\(499\) 5.86097 + 33.2392i 0.262373 + 1.48799i 0.776413 + 0.630225i \(0.217037\pi\)
−0.514040 + 0.857766i \(0.671852\pi\)
\(500\) −0.263890 1.49660i −0.0118015 0.0669298i
\(501\) 0 0
\(502\) 6.65523 + 5.58440i 0.297037 + 0.249244i
\(503\) 9.35597 + 16.2050i 0.417162 + 0.722546i 0.995653 0.0931429i \(-0.0296913\pi\)
−0.578491 + 0.815689i \(0.696358\pi\)
\(504\) 0 0
\(505\) 0.464508 0.804551i 0.0206703 0.0358020i
\(506\) −24.4391 + 8.89512i −1.08645 + 0.395436i
\(507\) 0 0
\(508\) 0.710952 0.596559i 0.0315434 0.0264680i
\(509\) −20.4554 7.44516i −0.906670 0.330001i −0.153747 0.988110i \(-0.549134\pi\)
−0.752922 + 0.658109i \(0.771356\pi\)
\(510\) 0 0
\(511\) 0.953363 5.40679i 0.0421743 0.239182i
\(512\) 25.4026 1.12265
\(513\) 0 0
\(514\) −4.73473 −0.208840
\(515\) 0.112287 0.636812i 0.00494796 0.0280613i
\(516\) 0 0
\(517\) 7.88326 + 2.86927i 0.346705 + 0.126190i
\(518\) −11.2238 + 9.41787i −0.493145 + 0.413797i
\(519\) 0 0
\(520\) 4.16637 1.51644i 0.182708 0.0665001i
\(521\) 3.23822 5.60876i 0.141869 0.245724i −0.786332 0.617805i \(-0.788022\pi\)
0.928200 + 0.372081i \(0.121356\pi\)
\(522\) 0 0
\(523\) 5.43629 + 9.41593i 0.237712 + 0.411730i 0.960057 0.279803i \(-0.0902691\pi\)
−0.722345 + 0.691533i \(0.756936\pi\)
\(524\) −0.776816 0.651826i −0.0339354 0.0284752i
\(525\) 0 0
\(526\) −0.812109 4.60570i −0.0354096 0.200818i
\(527\) −2.36630 13.4199i −0.103077 0.584581i
\(528\) 0 0
\(529\) 22.9458 + 19.2538i 0.997645 + 0.837124i
\(530\) 2.51730 + 4.36009i 0.109344 + 0.189390i
\(531\) 0 0
\(532\) 3.18004 5.50800i 0.137872 0.238802i
\(533\) −15.0316 + 5.47107i −0.651092 + 0.236978i
\(534\) 0 0
\(535\) −0.764700 + 0.641660i −0.0330609 + 0.0277414i
\(536\) 26.7651 + 9.74170i 1.15608 + 0.420777i
\(537\) 0 0
\(538\) 1.58202 8.97210i 0.0682059 0.386815i
\(539\) 15.2226 0.655686
\(540\) 0 0
\(541\) 24.6459 1.05961 0.529805 0.848120i \(-0.322265\pi\)
0.529805 + 0.848120i \(0.322265\pi\)
\(542\) 4.24152 24.0548i 0.182189 1.03324i
\(543\) 0 0
\(544\) 12.8391 + 4.67307i 0.550474 + 0.200356i
\(545\) 3.93426 3.30123i 0.168525 0.141409i
\(546\) 0 0
\(547\) −29.0621 + 10.5777i −1.24261 + 0.452272i −0.877897 0.478850i \(-0.841054\pi\)
−0.364709 + 0.931121i \(0.618832\pi\)
\(548\) 0.808718 1.40074i 0.0345467 0.0598367i
\(549\) 0 0
\(550\) −8.57873 14.8588i −0.365798 0.633581i
\(551\) 14.3745 + 12.0617i 0.612375 + 0.513844i
\(552\) 0 0
\(553\) 7.29978 + 41.3991i 0.310418 + 1.76047i
\(554\) 3.10126 + 17.5881i 0.131760 + 0.747247i
\(555\) 0 0
\(556\) 2.12907 + 1.78650i 0.0902927 + 0.0757646i
\(557\) −11.6813 20.2327i −0.494954 0.857286i 0.505029 0.863102i \(-0.331482\pi\)
−0.999983 + 0.00581674i \(0.998148\pi\)
\(558\) 0 0
\(559\) 9.47565 16.4123i 0.400777 0.694167i
\(560\) 4.71950 1.71776i 0.199435 0.0725886i
\(561\) 0 0
\(562\) −21.7913 + 18.2851i −0.919212 + 0.771310i
\(563\) −31.6561 11.5219i −1.33415 0.485589i −0.426182 0.904638i \(-0.640142\pi\)
−0.907964 + 0.419048i \(0.862364\pi\)
\(564\) 0 0
\(565\) 0.130882 0.742267i 0.00550624 0.0312274i
\(566\) 30.5097 1.28242
\(567\) 0 0
\(568\) −16.0155 −0.671995
\(569\) −5.34764 + 30.3280i −0.224185 + 1.27142i 0.640052 + 0.768331i \(0.278913\pi\)
−0.864237 + 0.503085i \(0.832198\pi\)
\(570\) 0 0
\(571\) 28.0736 + 10.2179i 1.17484 + 0.427608i 0.854378 0.519653i \(-0.173939\pi\)
0.320465 + 0.947260i \(0.396161\pi\)
\(572\) −2.43398 + 2.04236i −0.101770 + 0.0853952i
\(573\) 0 0
\(574\) −20.7408 + 7.54904i −0.865705 + 0.315091i
\(575\) −17.4670 + 30.2538i −0.728425 + 1.26167i
\(576\) 0 0
\(577\) −2.40373 4.16339i −0.100069 0.173324i 0.811644 0.584152i \(-0.198573\pi\)
−0.911713 + 0.410828i \(0.865240\pi\)
\(578\) −32.0581 26.8999i −1.33344 1.11889i
\(579\) 0 0
\(580\) −0.0974487 0.552659i −0.00404634 0.0229479i
\(581\) −9.97124 56.5497i −0.413677 2.34608i
\(582\) 0 0
\(583\) −18.6800 15.6744i −0.773648 0.649168i
\(584\) 2.34527 + 4.06212i 0.0970478 + 0.168092i
\(585\) 0 0
\(586\) 11.9598 20.7149i 0.494053 0.855725i
\(587\) −7.45891 + 2.71482i −0.307862 + 0.112053i −0.491331 0.870973i \(-0.663490\pi\)
0.183469 + 0.983026i \(0.441267\pi\)
\(588\) 0 0
\(589\) 7.68866 6.45155i 0.316806 0.265832i
\(590\) 1.59855 + 0.581825i 0.0658113 + 0.0239533i
\(591\) 0 0
\(592\) 1.78446 10.1202i 0.0733410 0.415937i
\(593\) 36.2753 1.48965 0.744824 0.667261i \(-0.232533\pi\)
0.744824 + 0.667261i \(0.232533\pi\)
\(594\) 0 0
\(595\) 11.1010 0.455097
\(596\) 1.21892 6.91282i 0.0499288 0.283160i
\(597\) 0 0
\(598\) −28.9295 10.5295i −1.18301 0.430582i
\(599\) 25.7736 21.6266i 1.05308 0.883639i 0.0596658 0.998218i \(-0.480996\pi\)
0.993414 + 0.114579i \(0.0365521\pi\)
\(600\) 0 0
\(601\) 2.79813 1.01844i 0.114138 0.0415429i −0.284320 0.958730i \(-0.591768\pi\)
0.398458 + 0.917187i \(0.369545\pi\)
\(602\) 13.0746 22.6459i 0.532882 0.922978i
\(603\) 0 0
\(604\) 1.16385 + 2.01584i 0.0473563 + 0.0820235i
\(605\) 1.11884 + 0.938815i 0.0454872 + 0.0381683i
\(606\) 0 0
\(607\) −2.71735 15.4108i −0.110294 0.625507i −0.988973 0.148095i \(-0.952686\pi\)
0.878679 0.477412i \(-0.158425\pi\)
\(608\) 1.74751 + 9.91060i 0.0708707 + 0.401928i
\(609\) 0 0
\(610\) 3.46791 + 2.90992i 0.140412 + 0.117819i
\(611\) 4.96529 + 8.60014i 0.200874 + 0.347924i
\(612\) 0 0
\(613\) 0.533433 0.923933i 0.0215452 0.0373173i −0.855052 0.518543i \(-0.826475\pi\)
0.876597 + 0.481225i \(0.159808\pi\)
\(614\) 25.0632 9.12226i 1.01147 0.368145i
\(615\) 0 0
\(616\) −22.6989 + 19.0467i −0.914566 + 0.767412i
\(617\) 12.2817 + 4.47019i 0.494444 + 0.179963i 0.577194 0.816607i \(-0.304148\pi\)
−0.0827492 + 0.996570i \(0.526370\pi\)
\(618\) 0 0
\(619\) 3.56283 20.2058i 0.143202 0.812141i −0.825591 0.564270i \(-0.809158\pi\)
0.968793 0.247871i \(-0.0797310\pi\)
\(620\) −0.300167 −0.0120550
\(621\) 0 0
\(622\) −26.2071 −1.05081
\(623\) 11.3013 64.0929i 0.452777 2.56783i
\(624\) 0 0
\(625\) −20.7199 7.54142i −0.828795 0.301657i
\(626\) 29.3874 24.6590i 1.17456 0.985572i
\(627\) 0 0
\(628\) 1.73783 0.632517i 0.0693468 0.0252402i
\(629\) 11.3569 19.6707i 0.452829 0.784323i
\(630\) 0 0
\(631\) 5.15611 + 8.93064i 0.205261 + 0.355523i 0.950216 0.311592i \(-0.100862\pi\)
−0.744955 + 0.667115i \(0.767529\pi\)
\(632\) −27.5123 23.0856i −1.09438 0.918295i
\(633\) 0 0
\(634\) −0.963630 5.46502i −0.0382706 0.217044i
\(635\) 0.207183 + 1.17499i 0.00822180 + 0.0466281i
\(636\) 0 0
\(637\) 13.8038 + 11.5828i 0.546927 + 0.458926i
\(638\) −6.46740 11.2019i −0.256047 0.443486i
\(639\) 0 0
\(640\) −1.67752 + 2.90555i −0.0663097 + 0.114852i
\(641\) −3.29472 + 1.19918i −0.130133 + 0.0473647i −0.406266 0.913755i \(-0.633169\pi\)
0.276133 + 0.961120i \(0.410947\pi\)
\(642\) 0 0
\(643\) 24.1700 20.2810i 0.953172 0.799806i −0.0266572 0.999645i \(-0.508486\pi\)
0.979829 + 0.199839i \(0.0640418\pi\)
\(644\) 8.38814 + 3.05303i 0.330539 + 0.120306i
\(645\) 0 0
\(646\) 8.14765 46.2076i 0.320565 1.81801i
\(647\) −3.04628 −0.119762 −0.0598808 0.998206i \(-0.519072\pi\)
−0.0598808 + 0.998206i \(0.519072\pi\)
\(648\) 0 0
\(649\) −8.23947 −0.323428
\(650\) 3.52678 20.0013i 0.138332 0.784517i
\(651\) 0 0
\(652\) 1.24510 + 0.453179i 0.0487619 + 0.0177479i
\(653\) −23.5462 + 19.7576i −0.921433 + 0.773174i −0.974259 0.225430i \(-0.927621\pi\)
0.0528264 + 0.998604i \(0.483177\pi\)
\(654\) 0 0
\(655\) 1.22503 0.445875i 0.0478660 0.0174218i
\(656\) 7.74038 13.4067i 0.302211 0.523445i
\(657\) 0 0
\(658\) 6.85117 + 11.8666i 0.267086 + 0.462607i
\(659\) −25.4204 21.3302i −0.990237 0.830907i −0.00463496 0.999989i \(-0.501475\pi\)
−0.985602 + 0.169082i \(0.945920\pi\)
\(660\) 0 0
\(661\) −2.58869 14.6812i −0.100688 0.571032i −0.992855 0.119326i \(-0.961927\pi\)
0.892167 0.451706i \(-0.149184\pi\)
\(662\) 0.651611 + 3.69547i 0.0253256 + 0.143629i
\(663\) 0 0
\(664\) 37.5808 + 31.5341i 1.45842 + 1.22376i
\(665\) 4.08819 + 7.08095i 0.158533 + 0.274587i
\(666\) 0 0
\(667\) −13.1682 + 22.8080i −0.509874 + 0.883128i
\(668\) 2.98135 1.08512i 0.115352 0.0419846i
\(669\) 0 0
\(670\) −4.15018 + 3.48241i −0.160335 + 0.134537i
\(671\) −20.6044 7.49937i −0.795422 0.289510i
\(672\) 0 0
\(673\) 1.19624 6.78422i 0.0461117 0.261513i −0.953033 0.302867i \(-0.902056\pi\)
0.999145 + 0.0413545i \(0.0131673\pi\)
\(674\) −18.5656 −0.715122
\(675\) 0 0
\(676\) 0.753718 0.0289892
\(677\) −2.29029 + 12.9889i −0.0880228 + 0.499202i 0.908640 + 0.417579i \(0.137121\pi\)
−0.996663 + 0.0816229i \(0.973990\pi\)
\(678\) 0 0
\(679\) 33.5685 + 12.2179i 1.28824 + 0.468882i
\(680\) −7.26525 + 6.09627i −0.278610 + 0.233781i
\(681\) 0 0
\(682\) −6.50134 + 2.36630i −0.248949 + 0.0906101i
\(683\) 1.68907 2.92556i 0.0646305 0.111943i −0.831900 0.554926i \(-0.812746\pi\)
0.896530 + 0.442983i \(0.146080\pi\)
\(684\) 0 0
\(685\) 1.03967 + 1.80076i 0.0397237 + 0.0688034i
\(686\) −5.30234 4.44919i −0.202444 0.169871i
\(687\) 0 0
\(688\) 3.18479 + 18.0619i 0.121419 + 0.688602i
\(689\) −5.01244 28.4270i −0.190959 1.08298i
\(690\) 0 0
\(691\) 17.9370 + 15.0509i 0.682356 + 0.572565i 0.916694 0.399591i \(-0.130848\pi\)
−0.234338 + 0.972155i \(0.575292\pi\)
\(692\) 1.05471 + 1.82682i 0.0400942 + 0.0694452i
\(693\) 0 0
\(694\) −0.934640 + 1.61884i −0.0354785 + 0.0614505i
\(695\) −3.35753 + 1.22204i −0.127358 + 0.0463546i
\(696\) 0 0
\(697\) 26.2119 21.9944i 0.992846 0.833097i
\(698\) −33.3200 12.1275i −1.26118 0.459032i
\(699\) 0 0
\(700\) −1.02259 + 5.79942i −0.0386504 + 0.219197i
\(701\) 45.5001 1.71852 0.859258 0.511543i \(-0.170926\pi\)
0.859258 + 0.511543i \(0.170926\pi\)
\(702\) 0 0
\(703\) 16.7297 0.630972
\(704\) 4.27952 24.2704i 0.161291 0.914724i
\(705\) 0 0
\(706\) 12.7233 + 4.63089i 0.478847 + 0.174286i
\(707\) −5.63003 + 4.72416i −0.211739 + 0.177670i
\(708\) 0 0
\(709\) −36.2879 + 13.2077i −1.36282 + 0.496026i −0.916926 0.399058i \(-0.869337\pi\)
−0.445896 + 0.895085i \(0.647115\pi\)
\(710\) 1.52314 2.63816i 0.0571624 0.0990082i
\(711\) 0 0
\(712\) 27.8011 + 48.1530i 1.04189 + 1.80461i
\(713\) 10.7911 + 9.05484i 0.404131 + 0.339107i
\(714\) 0 0
\(715\) −0.709303 4.02266i −0.0265264 0.150439i
\(716\) −0.620029 3.51636i −0.0231716 0.131413i
\(717\) 0 0
\(718\) −14.4820 12.1519i −0.540465 0.453504i
\(719\) 24.6591 + 42.7108i 0.919630 + 1.59285i 0.799978 + 0.600030i \(0.204845\pi\)
0.119652 + 0.992816i \(0.461822\pi\)
\(720\) 0 0
\(721\) −2.55778 + 4.43021i −0.0952567 + 0.164990i
\(722\) 9.52190 3.46569i 0.354369 0.128980i
\(723\) 0 0
\(724\) 6.15657 5.16598i 0.228807 0.191992i
\(725\) −16.3266 5.94238i −0.606353 0.220694i
\(726\) 0 0
\(727\) −5.60788 + 31.8039i −0.207985 + 1.17954i 0.684689 + 0.728836i \(0.259938\pi\)
−0.892673 + 0.450704i \(0.851173\pi\)
\(728\) −35.0757 −1.29999
\(729\) 0 0
\(730\) −0.892178 −0.0330210
\(731\) −7.03936 + 39.9222i −0.260360 + 1.47658i
\(732\) 0 0
\(733\) −37.0861 13.4982i −1.36980 0.498568i −0.450733 0.892659i \(-0.648837\pi\)
−0.919072 + 0.394091i \(0.871060\pi\)
\(734\) 21.0382 17.6532i 0.776535 0.651590i
\(735\) 0 0
\(736\) −13.2724 + 4.83077i −0.489229 + 0.178065i
\(737\) 13.1202 22.7249i 0.483290 0.837083i
\(738\) 0 0
\(739\) −17.6545 30.5785i −0.649432 1.12485i −0.983259 0.182215i \(-0.941673\pi\)
0.333827 0.942634i \(-0.391660\pi\)
\(740\) −0.383273 0.321604i −0.0140894 0.0118224i
\(741\) 0 0
\(742\) −6.91622 39.2238i −0.253902 1.43995i
\(743\) −8.23276 46.6903i −0.302031 1.71290i −0.637162 0.770730i \(-0.719892\pi\)
0.335131 0.942171i \(-0.391219\pi\)
\(744\) 0 0
\(745\) 6.91282 + 5.80054i 0.253266 + 0.212515i
\(746\) 14.5428 + 25.1888i 0.532449 + 0.922228i
\(747\) 0 0
\(748\) 3.39827 5.88598i 0.124253 0.215213i
\(749\) 7.42091 2.70099i 0.271154 0.0986920i
\(750\) 0 0
\(751\) −6.83931 + 5.73886i −0.249570 + 0.209414i −0.758987 0.651106i \(-0.774305\pi\)
0.509417 + 0.860520i \(0.329861\pi\)
\(752\) −9.03093 3.28699i −0.329324 0.119864i
\(753\) 0 0
\(754\) 2.65880 15.0788i 0.0968276 0.549137i
\(755\) −2.99243 −0.108906
\(756\) 0 0
\(757\) −3.63816 −0.132231 −0.0661155 0.997812i \(-0.521061\pi\)
−0.0661155 + 0.997812i \(0.521061\pi\)
\(758\) 3.81163 21.6168i 0.138444 0.785158i
\(759\) 0 0
\(760\) −6.56418 2.38917i −0.238108 0.0866641i
\(761\) −5.12392 + 4.29948i −0.185742 + 0.155856i −0.730917 0.682466i \(-0.760907\pi\)
0.545175 + 0.838322i \(0.316463\pi\)
\(762\) 0 0
\(763\) −38.1793 + 13.8961i −1.38218 + 0.503074i
\(764\) 2.54747 4.41235i 0.0921643 0.159633i
\(765\) 0 0
\(766\) −25.0633 43.4109i −0.905574 1.56850i
\(767\) −7.47151 6.26934i −0.269781 0.226373i
\(768\) 0 0
\(769\) −3.72844 21.1450i −0.134451 0.762509i −0.975241 0.221147i \(-0.929020\pi\)
0.840790 0.541362i \(-0.182091\pi\)
\(770\) −0.978704 5.55051i −0.0352701 0.200026i
\(771\) 0 0
\(772\) −6.23648 5.23303i −0.224456 0.188341i
\(773\) 5.12208 + 8.87170i 0.184228 + 0.319093i 0.943316 0.331895i \(-0.107688\pi\)
−0.759088 + 0.650988i \(0.774355\pi\)
\(774\) 0 0
\(775\) −4.64661 + 8.04817i −0.166911 + 0.289099i
\(776\) −28.6791 + 10.4383i −1.02952 + 0.374715i
\(777\) 0 0
\(778\) −10.0569 + 8.43874i −0.360557 + 0.302544i
\(779\) 23.6825 + 8.61974i 0.848515 + 0.308834i
\(780\) 0 0
\(781\) −2.56212 + 14.5305i −0.0916798 + 0.519942i
\(782\) 65.8535 2.35492
\(783\) 0 0
\(784\) −17.4388 −0.622815
\(785\) −0.412846 + 2.34137i −0.0147351 + 0.0835670i
\(786\) 0 0
\(787\) −0.890530 0.324126i −0.0317440 0.0115539i 0.326099 0.945335i \(-0.394266\pi\)
−0.357843 + 0.933782i \(0.616488\pi\)
\(788\) 2.40176 2.01532i 0.0855593 0.0717928i
\(789\) 0 0
\(790\) 6.41932 2.33644i 0.228389 0.0831269i
\(791\) −2.98135 + 5.16385i −0.106005 + 0.183605i
\(792\) 0 0
\(793\) −12.9777 22.4781i −0.460852 0.798219i
\(794\) 1.12554 + 0.944440i 0.0399439 + 0.0335169i
\(795\) 0 0
\(796\) −0.157041 0.890623i −0.00556617 0.0315673i
\(797\) 1.21740 + 6.90420i 0.0431224 + 0.244559i 0.998748 0.0500247i \(-0.0159300\pi\)
−0.955626 + 0.294584i \(0.904819\pi\)
\(798\) 0 0
\(799\) −16.2724 13.6542i −0.575678 0.483051i
\(800\) −4.65895 8.06953i −0.164719 0.285301i
\(801\) 0 0
\(802\) −13.2118 + 22.8836i −0.466526 + 0.808047i
\(803\) 4.06066 1.47796i 0.143298 0.0521561i
\(804\) 0 0
\(805\) −8.79086 + 7.37641i −0.309837 + 0.259984i
\(806\) −7.69588 2.80107i −0.271076 0.0986635i
\(807\) 0 0
\(808\) 1.09034 6.18361i 0.0383579 0.217539i
\(809\) −45.1028 −1.58573 −0.792866 0.609396i \(-0.791412\pi\)
−0.792866 + 0.609396i \(0.791412\pi\)
\(810\) 0 0
\(811\) 8.07285 0.283476 0.141738 0.989904i \(-0.454731\pi\)
0.141738 + 0.989904i \(0.454731\pi\)
\(812\) −0.770921 + 4.37211i −0.0270540 + 0.153431i
\(813\) 0 0
\(814\) −10.8366 3.94421i −0.379823 0.138244i
\(815\) −1.30488 + 1.09492i −0.0457079 + 0.0383535i
\(816\) 0 0
\(817\) −28.0574 + 10.2120i −0.981603 + 0.357274i
\(818\) −5.22481 + 9.04963i −0.182681 + 0.316413i
\(819\) 0 0
\(820\) −0.376859 0.652739i −0.0131605 0.0227946i
\(821\) 4.80261 + 4.02987i 0.167612 + 0.140643i 0.722735 0.691125i \(-0.242884\pi\)
−0.555123 + 0.831768i \(0.687329\pi\)
\(822\) 0 0
\(823\) −3.43700 19.4922i −0.119806 0.679456i −0.984258 0.176739i \(-0.943445\pi\)
0.864451 0.502717i \(-0.167666\pi\)
\(824\) −0.758922 4.30406i −0.0264383 0.149939i
\(825\) 0 0
\(826\) −10.3093 8.65051i −0.358706 0.300990i
\(827\) 20.9001 + 36.2001i 0.726769 + 1.25880i 0.958242 + 0.285960i \(0.0923124\pi\)
−0.231472 + 0.972841i \(0.574354\pi\)
\(828\) 0 0
\(829\) −16.8640 + 29.2092i −0.585710 + 1.01448i 0.409077 + 0.912500i \(0.365851\pi\)
−0.994787 + 0.101979i \(0.967483\pi\)
\(830\) −8.76856 + 3.19149i −0.304361 + 0.110778i
\(831\) 0 0
\(832\) 22.3478 18.7520i 0.774769 0.650109i
\(833\) −36.2205 13.1832i −1.25497 0.456771i
\(834\) 0 0
\(835\) −0.708263 + 4.01676i −0.0245105 + 0.139006i
\(836\) 5.00594 0.173134
\(837\) 0 0
\(838\) −45.9959 −1.58890
\(839\) 5.08559 28.8418i 0.175574 0.995731i −0.761905 0.647689i \(-0.775736\pi\)
0.937479 0.348042i \(-0.113153\pi\)
\(840\) 0 0
\(841\) 14.9427 + 5.43869i 0.515265 + 0.187541i
\(842\) 12.9196 10.8408i 0.445237 0.373598i
\(843\) 0 0
\(844\) −5.33750 + 1.94269i −0.183724 + 0.0668701i
\(845\) −0.484481 + 0.839145i −0.0166666 + 0.0288675i
\(846\) 0 0
\(847\) −5.77719 10.0064i −0.198507 0.343823i
\(848\) 21.3996 + 17.9564i 0.734864 + 0.616624i
\(849\) 0 0
\(850\) 7.54400 + 42.7842i 0.258757 + 1.46749i
\(851\) 4.07732 + 23.1236i 0.139769 + 0.792667i
\(852\) 0 0
\(853\) 28.8018 + 24.1676i 0.986156 + 0.827483i 0.985007 0.172516i \(-0.0551896\pi\)
0.00114955 + 0.999999i \(0.499634\pi\)
\(854\) −17.9068 31.0155i −0.612758 1.06133i
\(855\) 0 0
\(856\) −3.37346 + 5.84300i −0.115302 + 0.199710i
\(857\) −27.2604 + 9.92199i −0.931199 + 0.338929i −0.762685 0.646771i \(-0.776119\pi\)
−0.168514 + 0.985699i \(0.553897\pi\)
\(858\) 0 0
\(859\) −19.0496 + 15.9845i −0.649965 + 0.545385i −0.907060 0.421001i \(-0.861679\pi\)
0.257095 + 0.966386i \(0.417235\pi\)
\(860\) 0.839100 + 0.305407i 0.0286131 + 0.0104143i
\(861\) 0 0
\(862\) −2.11721 + 12.0073i −0.0721125 + 0.408970i
\(863\) −42.4018 −1.44337 −0.721687 0.692219i \(-0.756633\pi\)
−0.721687 + 0.692219i \(0.756633\pi\)
\(864\) 0 0
\(865\) −2.71183 −0.0922050
\(866\) −3.94301 + 22.3619i −0.133989 + 0.759888i
\(867\) 0 0
\(868\) 2.23143 + 0.812174i 0.0757396 + 0.0275670i
\(869\) −25.3464 + 21.2682i −0.859818 + 0.721473i
\(870\) 0 0
\(871\) 29.1886 10.6238i 0.989017 0.359973i
\(872\) 17.3559 30.0612i 0.587744 1.01800i
\(873\) 0 0
\(874\) 24.2520 + 42.0056i 0.820335 + 1.42086i
\(875\) −11.8396 9.93464i −0.400253 0.335852i
\(876\) 0 0
\(877\) 2.09327 + 11.8715i 0.0706848 + 0.400874i 0.999537 + 0.0304232i \(0.00968552\pi\)
−0.928852 + 0.370450i \(0.879203\pi\)
\(878\) 3.94361 + 22.3653i 0.133090 + 0.754792i
\(879\) 0 0
\(880\) 3.02822 + 2.54098i 0.102081 + 0.0856563i
\(881\) −7.39133 12.8022i −0.249020 0.431316i 0.714234 0.699907i \(-0.246775\pi\)
−0.963254 + 0.268591i \(0.913442\pi\)
\(882\) 0 0
\(883\) 12.9231 22.3834i 0.434896 0.753263i −0.562391 0.826872i \(-0.690118\pi\)
0.997287 + 0.0736089i \(0.0234516\pi\)
\(884\) 7.56012 2.75166i 0.254274 0.0925483i
\(885\) 0 0
\(886\) 12.7947 10.7361i 0.429847 0.360685i
\(887\) 43.0905 + 15.6837i 1.44684 + 0.526606i 0.941706 0.336436i \(-0.109222\pi\)
0.505132 + 0.863042i \(0.331444\pi\)
\(888\) 0 0
\(889\) 1.63903 9.29542i 0.0549714 0.311758i
\(890\) −10.5760 −0.354509
\(891\) 0 0
\(892\) −1.28581 −0.0430520
\(893\) 2.71686 15.4081i 0.0909162 0.515611i
\(894\) 0 0
\(895\) 4.31345 + 1.56997i 0.144183 + 0.0524783i
\(896\) 20.3322 17.0608i 0.679252 0.569960i
\(897\) 0 0
\(898\) −5.59152 + 2.03515i −0.186591 + 0.0679137i
\(899\) −3.50303 + 6.06742i −0.116832 + 0.202360i
\(900\) 0 0
\(901\) 30.8726 + 53.4729i 1.02851 + 1.78144i
\(902\) −13.3081 11.1668i −0.443112 0.371815i
\(903\) 0 0
\(904\) −0.884600 5.01681i −0.0294214 0.166857i
\(905\) 1.79413 + 10.1750i 0.0596388 + 0.338228i
\(906\) 0 0
\(907\) −8.96270 7.52060i −0.297601 0.249717i 0.481744 0.876312i \(-0.340004\pi\)
−0.779345 + 0.626595i \(0.784448\pi\)
\(908\) −1.83386 3.17634i −0.0608587 0.105410i
\(909\) 0 0
\(910\) 3.33585 5.77786i 0.110582 0.191534i
\(911\) 26.9459 9.80752i 0.892759 0.324938i 0.145412 0.989371i \(-0.453549\pi\)
0.747347 + 0.664434i \(0.231327\pi\)
\(912\) 0 0
\(913\) 34.6223 29.0515i 1.14583 0.961465i
\(914\) 24.8461 + 9.04323i 0.821835 + 0.299124i
\(915\) 0 0
\(916\) −0.815674 + 4.62592i −0.0269506 + 0.152845i
\(917\) −10.3133 −0.340574
\(918\) 0 0
\(919\) 4.33511 0.143002 0.0715011 0.997441i \(-0.477221\pi\)
0.0715011 + 0.997441i \(0.477221\pi\)
\(920\) 1.70248 9.65523i 0.0561290 0.318324i
\(921\) 0 0
\(922\) −40.5571 14.7616i −1.33568 0.486146i
\(923\) −13.3794 + 11.2267i −0.440390 + 0.369531i
\(924\) 0 0
\(925\) −14.5560 + 5.29796i −0.478599 + 0.174196i
\(926\) 8.44047 14.6193i 0.277371 0.480421i
\(927\) 0 0
\(928\) −3.51233 6.08353i −0.115298 0.199702i
\(929\) 9.87500 + 8.28611i 0.323988 + 0.271859i 0.790245 0.612791i \(-0.209953\pi\)
−0.466257 + 0.884649i \(0.654398\pi\)
\(930\) 0 0
\(931\) −4.92989 27.9588i −0.161571 0.916313i
\(932\) −0.765945 4.34389i −0.0250894 0.142289i
\(933\) 0 0
\(934\) −23.2717 19.5273i −0.761474 0.638953i
\(935\) 4.36873 + 7.56687i 0.142873 + 0.247463i
\(936\) 0 0
\(937\) 26.6040 46.0795i 0.869115 1.50535i 0.00621270 0.999981i \(-0.498022\pi\)
0.862902 0.505371i \(-0.168644\pi\)
\(938\) 40.2747 14.6588i 1.31502 0.478627i
\(939\) 0 0
\(940\) −0.358441 + 0.300767i −0.0116910 + 0.00980995i
\(941\) 31.3927 + 11.4260i 1.02337 + 0.372478i 0.798554 0.601923i \(-0.205598\pi\)
0.224820 + 0.974400i \(0.427821\pi\)
\(942\) 0 0
\(943\) −6.14227 + 34.8346i −0.200020 + 1.13437i
\(944\) 9.43901 0.307214
\(945\) 0 0
\(946\) 20.5817 0.669169
\(947\) −2.69237 + 15.2692i −0.0874903 + 0.496182i 0.909301 + 0.416139i \(0.136617\pi\)
−0.996791 + 0.0800434i \(0.974494\pi\)
\(948\) 0 0
\(949\) 4.80675 + 1.74951i 0.156034 + 0.0567916i
\(950\) −24.5123 + 20.5682i −0.795283 + 0.667322i
\(951\) 0 0
\(952\) 70.5044 25.6615i 2.28506 0.831694i
\(953\) −11.2524 + 19.4898i −0.364502 + 0.631336i −0.988696 0.149933i \(-0.952094\pi\)
0.624194 + 0.781269i \(0.285427\pi\)
\(954\) 0 0
\(955\) 3.27497 + 5.67241i 0.105975 + 0.183555i
\(956\) 1.55677 + 1.30628i 0.0503495 + 0.0422483i
\(957\) 0 0
\(958\) 1.31268 + 7.44459i 0.0424108 + 0.240524i
\(959\) −2.85646 16.1998i −0.0922400 0.523119i
\(960\) 0 0
\(961\) −20.8767 17.5176i −0.673442 0.565085i
\(962\) −6.82548 11.8221i −0.220062 0.381159i
\(963\) 0 0
\(964\) −1.48293 + 2.56850i −0.0477618 + 0.0827259i
\(965\) 9.83488 3.57960i 0.316596 0.115231i
\(966\) 0 0
\(967\) −32.0271 + 26.8739i −1.02992 + 0.864207i −0.990842 0.135029i \(-0.956887\pi\)
−0.0390802 + 0.999236i \(0.512443\pi\)
\(968\) 9.27612 + 3.37623i 0.298146 + 0.108516i
\(969\) 0 0
\(970\) 1.00805 5.71691i 0.0323664 0.183559i
\(971\) 35.8662 1.15100 0.575501 0.817801i \(-0.304807\pi\)
0.575501 + 0.817801i \(0.304807\pi\)
\(972\) 0 0
\(973\) 28.2662 0.906173
\(974\) −8.66085 + 49.1181i −0.277512 + 1.57385i
\(975\) 0 0
\(976\) 23.6040 + 8.59116i 0.755546 + 0.274996i
\(977\) 10.7630 9.03121i 0.344338 0.288934i −0.454174 0.890913i \(-0.650065\pi\)
0.798512 + 0.601979i \(0.205621\pi\)
\(978\) 0 0
\(979\) 48.1357 17.5200i 1.53842 0.559940i
\(980\) −0.424525 + 0.735300i −0.0135610 + 0.0234883i
\(981\) 0 0
\(982\) −24.1587 41.8441i −0.770935 1.33530i
\(983\) −13.5507 11.3704i −0.432199 0.362658i 0.400582 0.916261i \(-0.368808\pi\)
−0.832781 + 0.553603i \(0.813253\pi\)
\(984\) 0 0
\(985\) 0.699913 + 3.96940i 0.0223011 + 0.126476i
\(986\) 5.68734 + 32.2545i 0.181122 + 1.02719i
\(987\) 0 0
\(988\) 4.53936 + 3.80898i 0.144416 + 0.121180i
\(989\) −20.9531 36.2918i −0.666269 1.15401i
\(990\) 0 0
\(991\) −16.4479 + 28.4886i −0.522485 + 0.904970i 0.477173 + 0.878809i \(0.341662\pi\)
−0.999658 + 0.0261608i \(0.991672\pi\)
\(992\) −3.53076 + 1.28509i −0.112102 + 0.0408017i
\(993\) 0 0
\(994\) −18.4611 + 15.4907i −0.585551 + 0.491335i
\(995\) 1.09251 + 0.397641i 0.0346349 + 0.0126061i
\(996\) 0 0
\(997\) 3.47415 19.7029i 0.110027 0.623996i −0.879065 0.476701i \(-0.841832\pi\)
0.989093 0.147295i \(-0.0470565\pi\)
\(998\) −43.3907 −1.37351
\(999\) 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.e.r.649.1 12
3.2 odd 2 inner 729.2.e.r.649.2 12
9.2 odd 6 729.2.e.q.163.1 12
9.4 even 3 729.2.e.m.406.1 12
9.5 odd 6 729.2.e.m.406.2 12
9.7 even 3 729.2.e.q.163.2 12
27.2 odd 18 729.2.c.c.487.2 12
27.4 even 9 729.2.e.m.325.1 12
27.5 odd 18 729.2.e.q.568.1 12
27.7 even 9 729.2.c.c.244.5 12
27.11 odd 18 729.2.a.c.1.5 yes 6
27.13 even 9 inner 729.2.e.r.82.1 12
27.14 odd 18 inner 729.2.e.r.82.2 12
27.16 even 9 729.2.a.c.1.2 6
27.20 odd 18 729.2.c.c.244.2 12
27.22 even 9 729.2.e.q.568.2 12
27.23 odd 18 729.2.e.m.325.2 12
27.25 even 9 729.2.c.c.487.5 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
729.2.a.c.1.2 6 27.16 even 9
729.2.a.c.1.5 yes 6 27.11 odd 18
729.2.c.c.244.2 12 27.20 odd 18
729.2.c.c.244.5 12 27.7 even 9
729.2.c.c.487.2 12 27.2 odd 18
729.2.c.c.487.5 12 27.25 even 9
729.2.e.m.325.1 12 27.4 even 9
729.2.e.m.325.2 12 27.23 odd 18
729.2.e.m.406.1 12 9.4 even 3
729.2.e.m.406.2 12 9.5 odd 6
729.2.e.q.163.1 12 9.2 odd 6
729.2.e.q.163.2 12 9.7 even 3
729.2.e.q.568.1 12 27.5 odd 18
729.2.e.q.568.2 12 27.22 even 9
729.2.e.r.82.1 12 27.13 even 9 inner
729.2.e.r.82.2 12 27.14 odd 18 inner
729.2.e.r.649.1 12 1.1 even 1 trivial
729.2.e.r.649.2 12 3.2 odd 2 inner