Properties

Label 729.2.e.q.82.1
Level $729$
Weight $2$
Character 729.82
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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 82.1
Root \(-0.984808 - 0.173648i\) of defining polynomial
Character \(\chi\) \(=\) 729.82
Dual form 729.2.e.q.649.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.118782 - 0.673648i) q^{2} +(1.43969 - 0.524005i) q^{4} +(-0.802823 - 0.673648i) q^{5} +(0.113341 + 0.0412527i) q^{7} +(-1.20805 - 2.09240i) q^{8} +O(q^{10})\) \(q+(-0.118782 - 0.673648i) q^{2} +(1.43969 - 0.524005i) q^{4} +(-0.802823 - 0.673648i) q^{5} +(0.113341 + 0.0412527i) q^{7} +(-1.20805 - 2.09240i) q^{8} +(-0.358441 + 0.620838i) q^{10} +(4.16247 - 3.49273i) q^{11} +(-0.794263 + 4.50449i) q^{13} +(0.0143269 - 0.0812519i) q^{14} +(1.08125 - 0.907278i) q^{16} +(2.38917 - 4.13816i) q^{17} +(0.294263 + 0.509678i) q^{19} +(-1.50881 - 0.549163i) q^{20} +(-2.84730 - 2.38917i) q^{22} +(-7.32580 + 2.66637i) q^{23} +(-0.677519 - 3.84240i) q^{25} +3.12879 q^{26} +0.184793 q^{28} +(-0.880352 - 4.99273i) q^{29} +(8.23055 - 2.99568i) q^{31} +(-4.44129 - 3.72668i) q^{32} +(-3.07145 - 1.11792i) q^{34} +(-0.0632028 - 0.109470i) q^{35} +(1.09240 - 1.89209i) q^{37} +(0.308391 - 0.258770i) q^{38} +(-0.439693 + 2.49362i) q^{40} +(-1.31250 + 7.44356i) q^{41} +(-1.00000 + 0.839100i) q^{43} +(4.16247 - 7.20961i) q^{44} +(2.66637 + 4.61830i) q^{46} +(2.27038 + 0.826352i) q^{47} +(-5.35117 - 4.49016i) q^{49} +(-2.50795 + 0.912818i) q^{50} +(1.21688 + 6.90128i) q^{52} +3.04628 q^{53} -5.69459 q^{55} +(-0.0506039 - 0.286989i) q^{56} +(-3.25877 + 1.18610i) q^{58} +(0.0336295 + 0.0282185i) q^{59} +(9.59627 + 3.49276i) q^{61} +(-2.99568 - 5.18866i) q^{62} +(-0.571452 + 0.989783i) q^{64} +(3.67209 - 3.08125i) q^{65} +(-0.322948 + 1.83153i) q^{67} +(1.27125 - 7.20961i) q^{68} +(-0.0662372 + 0.0555796i) q^{70} +(-3.25519 + 5.63816i) q^{71} +(-6.11721 - 10.5953i) q^{73} +(-1.40436 - 0.511144i) q^{74} +(0.690722 + 0.579585i) q^{76} +(0.615862 - 0.224155i) q^{77} +(0.121959 + 0.691663i) q^{79} -1.47924 q^{80} +5.17024 q^{82} +(-1.17674 - 6.67365i) q^{83} +(-4.70574 + 1.71275i) q^{85} +(0.684040 + 0.573978i) q^{86} +(-12.3366 - 4.49016i) q^{88} +(3.42782 + 5.93717i) q^{89} +(-0.275845 + 0.477777i) q^{91} +(-9.14971 + 7.67752i) q^{92} +(0.286989 - 1.62760i) q^{94} +(0.107103 - 0.607411i) q^{95} +(-6.91534 + 5.80266i) q^{97} +(-2.38917 + 4.13816i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{4} - 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{4} - 12 q^{7} + 12 q^{10} - 30 q^{13} + 18 q^{16} + 24 q^{19} - 30 q^{22} + 42 q^{25} - 12 q^{28} + 24 q^{31} - 36 q^{34} + 6 q^{37} + 6 q^{40} - 12 q^{43} - 6 q^{46} - 12 q^{49} - 18 q^{52} - 60 q^{55} + 6 q^{58} + 60 q^{61} - 6 q^{64} + 78 q^{67} - 66 q^{70} - 12 q^{73} + 48 q^{76} + 6 q^{79} - 24 q^{82} - 36 q^{85} - 24 q^{88} - 12 q^{94} + 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.118782 0.673648i −0.0839918 0.476341i −0.997570 0.0696772i \(-0.977803\pi\)
0.913578 0.406664i \(-0.133308\pi\)
\(3\) 0 0
\(4\) 1.43969 0.524005i 0.719846 0.262003i
\(5\) −0.802823 0.673648i −0.359033 0.301265i 0.445372 0.895346i \(-0.353071\pi\)
−0.804405 + 0.594081i \(0.797516\pi\)
\(6\) 0 0
\(7\) 0.113341 + 0.0412527i 0.0428388 + 0.0155920i 0.363351 0.931652i \(-0.381633\pi\)
−0.320512 + 0.947244i \(0.603855\pi\)
\(8\) −1.20805 2.09240i −0.427109 0.739774i
\(9\) 0 0
\(10\) −0.358441 + 0.620838i −0.113349 + 0.196326i
\(11\) 4.16247 3.49273i 1.25503 1.05310i 0.258839 0.965921i \(-0.416660\pi\)
0.996193 0.0871759i \(-0.0277842\pi\)
\(12\) 0 0
\(13\) −0.794263 + 4.50449i −0.220289 + 1.24932i 0.651200 + 0.758906i \(0.274266\pi\)
−0.871489 + 0.490415i \(0.836845\pi\)
\(14\) 0.0143269 0.0812519i 0.00382903 0.0217155i
\(15\) 0 0
\(16\) 1.08125 0.907278i 0.270313 0.226820i
\(17\) 2.38917 4.13816i 0.579458 1.00365i −0.416084 0.909326i \(-0.636598\pi\)
0.995542 0.0943239i \(-0.0300689\pi\)
\(18\) 0 0
\(19\) 0.294263 + 0.509678i 0.0675085 + 0.116928i 0.897804 0.440395i \(-0.145162\pi\)
−0.830295 + 0.557323i \(0.811828\pi\)
\(20\) −1.50881 0.549163i −0.337381 0.122797i
\(21\) 0 0
\(22\) −2.84730 2.38917i −0.607046 0.509372i
\(23\) −7.32580 + 2.66637i −1.52754 + 0.555977i −0.963016 0.269443i \(-0.913161\pi\)
−0.564519 + 0.825420i \(0.690938\pi\)
\(24\) 0 0
\(25\) −0.677519 3.84240i −0.135504 0.768480i
\(26\) 3.12879 0.613605
\(27\) 0 0
\(28\) 0.184793 0.0349225
\(29\) −0.880352 4.99273i −0.163477 0.927126i −0.950621 0.310356i \(-0.899552\pi\)
0.787143 0.616770i \(-0.211559\pi\)
\(30\) 0 0
\(31\) 8.23055 2.99568i 1.47825 0.538039i 0.527924 0.849292i \(-0.322971\pi\)
0.950327 + 0.311253i \(0.100749\pi\)
\(32\) −4.44129 3.72668i −0.785116 0.658790i
\(33\) 0 0
\(34\) −3.07145 1.11792i −0.526750 0.191721i
\(35\) −0.0632028 0.109470i −0.0106832 0.0185039i
\(36\) 0 0
\(37\) 1.09240 1.89209i 0.179589 0.311057i −0.762151 0.647399i \(-0.775857\pi\)
0.941740 + 0.336342i \(0.109190\pi\)
\(38\) 0.308391 0.258770i 0.0500276 0.0419781i
\(39\) 0 0
\(40\) −0.439693 + 2.49362i −0.0695215 + 0.394276i
\(41\) −1.31250 + 7.44356i −0.204978 + 1.16249i 0.692496 + 0.721422i \(0.256511\pi\)
−0.897474 + 0.441067i \(0.854600\pi\)
\(42\) 0 0
\(43\) −1.00000 + 0.839100i −0.152499 + 0.127961i −0.715845 0.698259i \(-0.753958\pi\)
0.563346 + 0.826221i \(0.309514\pi\)
\(44\) 4.16247 7.20961i 0.627516 1.08689i
\(45\) 0 0
\(46\) 2.66637 + 4.61830i 0.393135 + 0.680931i
\(47\) 2.27038 + 0.826352i 0.331169 + 0.120536i 0.502253 0.864721i \(-0.332505\pi\)
−0.171084 + 0.985257i \(0.554727\pi\)
\(48\) 0 0
\(49\) −5.35117 4.49016i −0.764452 0.641452i
\(50\) −2.50795 + 0.912818i −0.354677 + 0.129092i
\(51\) 0 0
\(52\) 1.21688 + 6.90128i 0.168751 + 0.957035i
\(53\) 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
\(56\) −0.0506039 0.286989i −0.00676223 0.0383505i
\(57\) 0 0
\(58\) −3.25877 + 1.18610i −0.427898 + 0.155742i
\(59\) 0.0336295 + 0.0282185i 0.00437819 + 0.00367373i 0.644974 0.764204i \(-0.276868\pi\)
−0.640596 + 0.767878i \(0.721313\pi\)
\(60\) 0 0
\(61\) 9.59627 + 3.49276i 1.22868 + 0.447202i 0.873144 0.487463i \(-0.162077\pi\)
0.355532 + 0.934664i \(0.384300\pi\)
\(62\) −2.99568 5.18866i −0.380451 0.658961i
\(63\) 0 0
\(64\) −0.571452 + 0.989783i −0.0714315 + 0.123723i
\(65\) 3.67209 3.08125i 0.455467 0.382182i
\(66\) 0 0
\(67\) −0.322948 + 1.83153i −0.0394544 + 0.223757i −0.998159 0.0606455i \(-0.980684\pi\)
0.958705 + 0.284403i \(0.0917952\pi\)
\(68\) 1.27125 7.20961i 0.154162 0.874293i
\(69\) 0 0
\(70\) −0.0662372 + 0.0555796i −0.00791686 + 0.00664303i
\(71\) −3.25519 + 5.63816i −0.386320 + 0.669126i −0.991951 0.126619i \(-0.959587\pi\)
0.605631 + 0.795745i \(0.292921\pi\)
\(72\) 0 0
\(73\) −6.11721 10.5953i −0.715965 1.24009i −0.962586 0.270976i \(-0.912653\pi\)
0.246621 0.969112i \(-0.420680\pi\)
\(74\) −1.40436 0.511144i −0.163253 0.0594193i
\(75\) 0 0
\(76\) 0.690722 + 0.579585i 0.0792313 + 0.0664829i
\(77\) 0.615862 0.224155i 0.0701840 0.0255449i
\(78\) 0 0
\(79\) 0.121959 + 0.691663i 0.0137215 + 0.0778182i 0.990900 0.134603i \(-0.0429761\pi\)
−0.977178 + 0.212422i \(0.931865\pi\)
\(80\) −1.47924 −0.165384
\(81\) 0 0
\(82\) 5.17024 0.570958
\(83\) −1.17674 6.67365i −0.129164 0.732528i −0.978747 0.205072i \(-0.934257\pi\)
0.849582 0.527456i \(-0.176854\pi\)
\(84\) 0 0
\(85\) −4.70574 + 1.71275i −0.510409 + 0.185774i
\(86\) 0.684040 + 0.573978i 0.0737620 + 0.0618936i
\(87\) 0 0
\(88\) −12.3366 4.49016i −1.31509 0.478653i
\(89\) 3.42782 + 5.93717i 0.363349 + 0.629338i 0.988510 0.151157i \(-0.0483000\pi\)
−0.625161 + 0.780496i \(0.714967\pi\)
\(90\) 0 0
\(91\) −0.275845 + 0.477777i −0.0289164 + 0.0500846i
\(92\) −9.14971 + 7.67752i −0.953923 + 0.800437i
\(93\) 0 0
\(94\) 0.286989 1.62760i 0.0296007 0.167874i
\(95\) 0.107103 0.607411i 0.0109885 0.0623191i
\(96\) 0 0
\(97\) −6.91534 + 5.80266i −0.702147 + 0.589171i −0.922384 0.386275i \(-0.873761\pi\)
0.220237 + 0.975446i \(0.429317\pi\)
\(98\) −2.38917 + 4.13816i −0.241342 + 0.418017i
\(99\) 0 0
\(100\) −2.98886 5.17685i −0.298886 0.517685i
\(101\) 12.2086 + 4.44356i 1.21480 + 0.442151i 0.868366 0.495923i \(-0.165170\pi\)
0.346434 + 0.938074i \(0.387393\pi\)
\(102\) 0 0
\(103\) 6.94949 + 5.83132i 0.684754 + 0.574577i 0.917391 0.397987i \(-0.130291\pi\)
−0.232637 + 0.972564i \(0.574735\pi\)
\(104\) 10.3847 3.77972i 1.01830 0.370632i
\(105\) 0 0
\(106\) −0.361844 2.05212i −0.0351454 0.199320i
\(107\) −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 \(0.455664\pi\)
\(110\) 0.676417 + 3.83615i 0.0644938 + 0.365763i
\(111\) 0 0
\(112\) 0.159978 0.0582271i 0.0151165 0.00550194i
\(113\) 8.87089 + 7.44356i 0.834503 + 0.700232i 0.956320 0.292321i \(-0.0944276\pi\)
−0.121817 + 0.992553i \(0.538872\pi\)
\(114\) 0 0
\(115\) 7.67752 + 2.79439i 0.715932 + 0.260578i
\(116\) −3.88365 6.72668i −0.360588 0.624557i
\(117\) 0 0
\(118\) 0.0150147 0.0260063i 0.00138222 0.00239407i
\(119\) 0.441500 0.370462i 0.0404722 0.0339602i
\(120\) 0 0
\(121\) 3.21688 18.2438i 0.292444 1.65853i
\(122\) 1.21302 6.87939i 0.109822 0.622830i
\(123\) 0 0
\(124\) 10.2797 8.62571i 0.923146 0.774611i
\(125\) −4.66452 + 8.07919i −0.417208 + 0.722625i
\(126\) 0 0
\(127\) 7.70961 + 13.3534i 0.684117 + 1.18493i 0.973713 + 0.227777i \(0.0731456\pi\)
−0.289596 + 0.957149i \(0.593521\pi\)
\(128\) −10.1614 3.69846i −0.898153 0.326901i
\(129\) 0 0
\(130\) −2.51186 2.10770i −0.220305 0.184858i
\(131\) 12.5506 4.56805i 1.09655 0.399112i 0.270508 0.962718i \(-0.412808\pi\)
0.826044 + 0.563606i \(0.190586\pi\)
\(132\) 0 0
\(133\) 0.0123264 + 0.0699065i 0.00106883 + 0.00606166i
\(134\) 1.27217 0.109899
\(135\) 0 0
\(136\) −11.5449 −0.989965
\(137\) 3.40760 + 19.3255i 0.291131 + 1.65109i 0.682524 + 0.730863i \(0.260882\pi\)
−0.391393 + 0.920224i \(0.628007\pi\)
\(138\) 0 0
\(139\) −15.3229 + 5.57710i −1.29968 + 0.473043i −0.896891 0.442252i \(-0.854180\pi\)
−0.402784 + 0.915295i \(0.631958\pi\)
\(140\) −0.148356 0.124485i −0.0125383 0.0105209i
\(141\) 0 0
\(142\) 4.18479 + 1.52314i 0.351180 + 0.127819i
\(143\) 12.4269 + 21.5239i 1.03919 + 1.79992i
\(144\) 0 0
\(145\) −2.65657 + 4.60132i −0.220616 + 0.382119i
\(146\) −6.41090 + 5.37939i −0.530570 + 0.445201i
\(147\) 0 0
\(148\) 0.581252 3.29644i 0.0477786 0.270966i
\(149\) −1.91841 + 10.8799i −0.157162 + 0.891312i 0.799620 + 0.600507i \(0.205034\pi\)
−0.956782 + 0.290806i \(0.906077\pi\)
\(150\) 0 0
\(151\) −5.20961 + 4.37138i −0.423952 + 0.355738i −0.829664 0.558263i \(-0.811468\pi\)
0.405712 + 0.914001i \(0.367024\pi\)
\(152\) 0.710966 1.23143i 0.0576670 0.0998821i
\(153\) 0 0
\(154\) −0.224155 0.388249i −0.0180630 0.0312860i
\(155\) −8.62571 3.13950i −0.692833 0.252171i
\(156\) 0 0
\(157\) 12.9363 + 10.8548i 1.03243 + 0.866310i 0.991138 0.132837i \(-0.0424087\pi\)
0.0412904 + 0.999147i \(0.486853\pi\)
\(158\) 0.451451 0.164315i 0.0359155 0.0130722i
\(159\) 0 0
\(160\) 1.05509 + 5.98373i 0.0834124 + 0.473055i
\(161\) −0.940307 −0.0741066
\(162\) 0 0
\(163\) 8.41147 0.658838 0.329419 0.944184i \(-0.393147\pi\)
0.329419 + 0.944184i \(0.393147\pi\)
\(164\) 2.01087 + 11.4042i 0.157022 + 0.890518i
\(165\) 0 0
\(166\) −4.35591 + 1.58542i −0.338085 + 0.123053i
\(167\) 2.01087 + 1.68732i 0.155606 + 0.130569i 0.717267 0.696799i \(-0.245393\pi\)
−0.561661 + 0.827368i \(0.689837\pi\)
\(168\) 0 0
\(169\) −7.44356 2.70924i −0.572582 0.208403i
\(170\) 1.71275 + 2.96657i 0.131362 + 0.227525i
\(171\) 0 0
\(172\) −1.00000 + 1.73205i −0.0762493 + 0.132068i
\(173\) −10.0377 + 8.42262i −0.763151 + 0.640360i −0.938945 0.344067i \(-0.888195\pi\)
0.175794 + 0.984427i \(0.443751\pi\)
\(174\) 0 0
\(175\) 0.0817187 0.463450i 0.00617736 0.0350335i
\(176\) 1.33180 7.55303i 0.100388 0.569331i
\(177\) 0 0
\(178\) 3.59240 3.01438i 0.269261 0.225937i
\(179\) −11.0494 + 19.1382i −0.825872 + 1.43045i 0.0753784 + 0.997155i \(0.475984\pi\)
−0.901251 + 0.433298i \(0.857350\pi\)
\(180\) 0 0
\(181\) 1.02956 + 1.78325i 0.0765268 + 0.132548i 0.901749 0.432260i \(-0.142284\pi\)
−0.825222 + 0.564808i \(0.808950\pi\)
\(182\) 0.354619 + 0.129071i 0.0262861 + 0.00956736i
\(183\) 0 0
\(184\) 14.4290 + 12.1074i 1.06372 + 0.892568i
\(185\) −2.15160 + 0.783119i −0.158189 + 0.0575760i
\(186\) 0 0
\(187\) −4.50862 25.5696i −0.329703 1.86984i
\(188\) 3.70167 0.269972
\(189\) 0 0
\(190\) −0.421903 −0.0306081
\(191\) 0.685768 + 3.88919i 0.0496205 + 0.281412i 0.999514 0.0311609i \(-0.00992041\pi\)
−0.949894 + 0.312572i \(0.898809\pi\)
\(192\) 0 0
\(193\) 7.93717 2.88889i 0.571330 0.207947i −0.0401684 0.999193i \(-0.512789\pi\)
0.611498 + 0.791246i \(0.290567\pi\)
\(194\) 4.73037 + 3.96926i 0.339621 + 0.284976i
\(195\) 0 0
\(196\) −10.0569 3.66041i −0.718350 0.261458i
\(197\) −1.14749 1.98751i −0.0817553 0.141604i 0.822249 0.569128i \(-0.192719\pi\)
−0.904004 + 0.427524i \(0.859386\pi\)
\(198\) 0 0
\(199\) 11.7515 20.3542i 0.833042 1.44287i −0.0625736 0.998040i \(-0.519931\pi\)
0.895615 0.444830i \(-0.146736\pi\)
\(200\) −7.22135 + 6.05943i −0.510626 + 0.428466i
\(201\) 0 0
\(202\) 1.54323 8.75211i 0.108582 0.615796i
\(203\) 0.106183 0.602196i 0.00745262 0.0422659i
\(204\) 0 0
\(205\) 6.06805 5.09170i 0.423811 0.355620i
\(206\) 3.10278 5.37417i 0.216181 0.374436i
\(207\) 0 0
\(208\) 3.22803 + 5.59110i 0.223823 + 0.387673i
\(209\) 3.00503 + 1.09374i 0.207862 + 0.0756556i
\(210\) 0 0
\(211\) −1.27719 1.07169i −0.0879253 0.0737781i 0.597766 0.801671i \(-0.296055\pi\)
−0.685691 + 0.727893i \(0.740500\pi\)
\(212\) 4.38571 1.59627i 0.301212 0.109632i
\(213\) 0 0
\(214\) 1.35251 + 7.67047i 0.0924557 + 0.524343i
\(215\) 1.36808 0.0933023
\(216\) 0 0
\(217\) 1.05644 0.0717156
\(218\) −0.344348 1.95290i −0.0233222 0.132267i
\(219\) 0 0
\(220\) −8.19846 + 2.98400i −0.552740 + 0.201181i
\(221\) 16.7427 + 14.0488i 1.12623 + 0.945021i
\(222\) 0 0
\(223\) 9.20961 + 3.35202i 0.616721 + 0.224468i 0.631441 0.775424i \(-0.282464\pi\)
−0.0147205 + 0.999892i \(0.504686\pi\)
\(224\) −0.349643 0.605600i −0.0233615 0.0404634i
\(225\) 0 0
\(226\) 3.96064 6.86002i 0.263458 0.456322i
\(227\) 11.8589 9.95084i 0.787106 0.660460i −0.157921 0.987452i \(-0.550479\pi\)
0.945027 + 0.326991i \(0.106035\pi\)
\(228\) 0 0
\(229\) −1.95424 + 11.0830i −0.129140 + 0.732388i 0.849623 + 0.527391i \(0.176830\pi\)
−0.978763 + 0.204997i \(0.934281\pi\)
\(230\) 0.970481 5.50387i 0.0639916 0.362914i
\(231\) 0 0
\(232\) −9.38326 + 7.87349i −0.616041 + 0.516920i
\(233\) −2.61738 + 4.53343i −0.171470 + 0.296995i −0.938934 0.344097i \(-0.888185\pi\)
0.767464 + 0.641092i \(0.221518\pi\)
\(234\) 0 0
\(235\) −1.26604 2.19285i −0.0825876 0.143046i
\(236\) 0.0632028 + 0.0230039i 0.00411415 + 0.00149743i
\(237\) 0 0
\(238\) −0.302004 0.253411i −0.0195760 0.0164262i
\(239\) 9.68804 3.52616i 0.626667 0.228088i −0.00911276 0.999958i \(-0.502901\pi\)
0.635780 + 0.771870i \(0.280679\pi\)
\(240\) 0 0
\(241\) 1.86571 + 10.5810i 0.120181 + 0.681582i 0.984054 + 0.177871i \(0.0569211\pi\)
−0.863873 + 0.503710i \(0.831968\pi\)
\(242\) −12.6720 −0.814590
\(243\) 0 0
\(244\) 15.6459 1.00163
\(245\) 1.27125 + 7.20961i 0.0812171 + 0.460605i
\(246\) 0 0
\(247\) −2.52956 + 0.920686i −0.160952 + 0.0585818i
\(248\) −16.2110 13.6027i −1.02940 0.863770i
\(249\) 0 0
\(250\) 5.99660 + 2.18258i 0.379258 + 0.138039i
\(251\) −7.53644 13.0535i −0.475696 0.823930i 0.523916 0.851770i \(-0.324470\pi\)
−0.999612 + 0.0278401i \(0.991137\pi\)
\(252\) 0 0
\(253\) −21.1805 + 36.6857i −1.33161 + 2.30641i
\(254\) 8.07975 6.77972i 0.506969 0.425397i
\(255\) 0 0
\(256\) −1.68139 + 9.53563i −0.105087 + 0.595977i
\(257\) −0.576937 + 3.27197i −0.0359884 + 0.204100i −0.997500 0.0706633i \(-0.977488\pi\)
0.961512 + 0.274763i \(0.0885995\pi\)
\(258\) 0 0
\(259\) 0.201867 0.169386i 0.0125434 0.0105251i
\(260\) 3.67209 6.36025i 0.227734 0.394446i
\(261\) 0 0
\(262\) −4.56805 7.91209i −0.282215 0.488811i
\(263\) −8.30564 3.02300i −0.512147 0.186406i 0.0730022 0.997332i \(-0.476742\pi\)
−0.585150 + 0.810925i \(0.698964\pi\)
\(264\) 0 0
\(265\) −2.44562 2.05212i −0.150233 0.126061i
\(266\) 0.0456282 0.0166073i 0.00279765 0.00101826i
\(267\) 0 0
\(268\) 0.494785 + 2.80607i 0.0302238 + 0.171408i
\(269\) 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 \(0.695809\pi\)
\(272\) −1.17117 6.64203i −0.0710125 0.402732i
\(273\) 0 0
\(274\) 12.6138 4.59105i 0.762028 0.277356i
\(275\) −16.2406 13.6275i −0.979345 0.821768i
\(276\) 0 0
\(277\) 3.97431 + 1.44653i 0.238793 + 0.0869135i 0.458645 0.888620i \(-0.348335\pi\)
−0.219852 + 0.975533i \(0.570557\pi\)
\(278\) 5.57710 + 9.65982i 0.334492 + 0.579357i
\(279\) 0 0
\(280\) −0.152704 + 0.264490i −0.00912579 + 0.0158063i
\(281\) 5.59375 4.69372i 0.333695 0.280004i −0.460508 0.887655i \(-0.652333\pi\)
0.794204 + 0.607652i \(0.207888\pi\)
\(282\) 0 0
\(283\) 2.78194 15.7771i 0.165369 0.937854i −0.783314 0.621626i \(-0.786472\pi\)
0.948683 0.316228i \(-0.102416\pi\)
\(284\) −1.73205 + 9.82295i −0.102778 + 0.582885i
\(285\) 0 0
\(286\) 13.0235 10.9280i 0.770094 0.646186i
\(287\) −0.455827 + 0.789515i −0.0269066 + 0.0466036i
\(288\) 0 0
\(289\) −2.91622 5.05104i −0.171542 0.297120i
\(290\) 3.41523 + 1.24304i 0.200549 + 0.0729939i
\(291\) 0 0
\(292\) −14.3589 12.0486i −0.840292 0.705088i
\(293\) −16.9187 + 6.15792i −0.988403 + 0.359749i −0.785102 0.619367i \(-0.787389\pi\)
−0.203302 + 0.979116i \(0.565167\pi\)
\(294\) 0 0
\(295\) −0.00798918 0.0453089i −0.000465148 0.00263799i
\(296\) −5.27866 −0.306816
\(297\) 0 0
\(298\) 7.55707 0.437769
\(299\) −6.19204 35.1168i −0.358095 2.03086i
\(300\) 0 0
\(301\) −0.147956 + 0.0538515i −0.00852804 + 0.00310395i
\(302\) 3.56358 + 2.99020i 0.205061 + 0.172067i
\(303\) 0 0
\(304\) 0.780592 + 0.284112i 0.0447700 + 0.0162950i
\(305\) −5.35121 9.26857i −0.306409 0.530717i
\(306\) 0 0
\(307\) 6.75537 11.7006i 0.385549 0.667791i −0.606296 0.795239i \(-0.707345\pi\)
0.991845 + 0.127448i \(0.0406787\pi\)
\(308\) 0.769193 0.645430i 0.0438288 0.0367768i
\(309\) 0 0
\(310\) −1.09034 + 6.18361i −0.0619270 + 0.351205i
\(311\) 2.85170 16.1728i 0.161705 0.917074i −0.790692 0.612214i \(-0.790279\pi\)
0.952397 0.304860i \(-0.0986097\pi\)
\(312\) 0 0
\(313\) −14.9875 + 12.5760i −0.847144 + 0.710838i −0.959159 0.282868i \(-0.908714\pi\)
0.112015 + 0.993707i \(0.464270\pi\)
\(314\) 5.77574 10.0039i 0.325944 0.564551i
\(315\) 0 0
\(316\) 0.538019 + 0.931876i 0.0302659 + 0.0524221i
\(317\) 22.9084 + 8.33796i 1.28666 + 0.468307i 0.892630 0.450790i \(-0.148858\pi\)
0.394032 + 0.919097i \(0.371080\pi\)
\(318\) 0 0
\(319\) −21.1027 17.7072i −1.18152 0.991415i
\(320\) 1.12554 0.409663i 0.0629196 0.0229009i
\(321\) 0 0
\(322\) 0.111692 + 0.633436i 0.00622435 + 0.0353000i
\(323\) 2.81217 0.156473
\(324\) 0 0
\(325\) 17.8462 0.989927
\(326\) −0.999135 5.66637i −0.0553370 0.313831i
\(327\) 0 0
\(328\) 17.1604 6.24589i 0.947527 0.344872i
\(329\) 0.223238 + 0.187319i 0.0123075 + 0.0103272i
\(330\) 0 0
\(331\) −26.7802 9.74719i −1.47197 0.535754i −0.523337 0.852126i \(-0.675313\pi\)
−0.948635 + 0.316372i \(0.897535\pi\)
\(332\) −5.19118 8.99138i −0.284903 0.493466i
\(333\) 0 0
\(334\) 0.897804 1.55504i 0.0491256 0.0850881i
\(335\) 1.49308 1.25284i 0.0815755 0.0684500i
\(336\) 0 0
\(337\) −3.02956 + 17.1815i −0.165031 + 0.935936i 0.784002 + 0.620758i \(0.213175\pi\)
−0.949033 + 0.315178i \(0.897936\pi\)
\(338\) −0.940908 + 5.33615i −0.0511786 + 0.290248i
\(339\) 0 0
\(340\) −5.87733 + 4.93166i −0.318743 + 0.267457i
\(341\) 23.7963 41.2165i 1.28864 2.23200i
\(342\) 0 0
\(343\) −0.843426 1.46086i −0.0455407 0.0788788i
\(344\) 2.96377 + 1.07873i 0.159796 + 0.0581610i
\(345\) 0 0
\(346\) 6.86618 + 5.76141i 0.369128 + 0.309735i
\(347\) −23.6699 + 8.61515i −1.27067 + 0.462486i −0.887335 0.461125i \(-0.847446\pi\)
−0.383333 + 0.923610i \(0.625224\pi\)
\(348\) 0 0
\(349\) −2.05809 11.6720i −0.110167 0.624787i −0.989030 0.147713i \(-0.952809\pi\)
0.878863 0.477074i \(-0.158302\pi\)
\(350\) −0.321909 −0.0172068
\(351\) 0 0
\(352\) −31.5030 −1.67912
\(353\) −1.45821 8.26991i −0.0776126 0.440163i −0.998708 0.0508251i \(-0.983815\pi\)
0.921095 0.389338i \(-0.127296\pi\)
\(354\) 0 0
\(355\) 6.41147 2.33359i 0.340286 0.123854i
\(356\) 8.04612 + 6.75150i 0.426444 + 0.357829i
\(357\) 0 0
\(358\) 14.2049 + 5.17015i 0.750750 + 0.273251i
\(359\) −1.32012 2.28652i −0.0696735 0.120678i 0.829084 0.559124i \(-0.188862\pi\)
−0.898758 + 0.438446i \(0.855529\pi\)
\(360\) 0 0
\(361\) 9.32682 16.1545i 0.490885 0.850238i
\(362\) 1.07899 0.905382i 0.0567106 0.0475858i
\(363\) 0 0
\(364\) −0.146774 + 0.832396i −0.00769304 + 0.0436294i
\(365\) −2.22648 + 12.6270i −0.116539 + 0.660928i
\(366\) 0 0
\(367\) 7.04576 5.91209i 0.367786 0.308609i −0.440099 0.897949i \(-0.645057\pi\)
0.807885 + 0.589340i \(0.200612\pi\)
\(368\) −5.50190 + 9.52956i −0.286806 + 0.496763i
\(369\) 0 0
\(370\) 0.783119 + 1.35640i 0.0407124 + 0.0705159i
\(371\) 0.345268 + 0.125667i 0.0179254 + 0.00652432i
\(372\) 0 0
\(373\) −20.5232 17.2210i −1.06265 0.891671i −0.0682855 0.997666i \(-0.521753\pi\)
−0.994367 + 0.105995i \(0.966197\pi\)
\(374\) −16.6894 + 6.07444i −0.862988 + 0.314102i
\(375\) 0 0
\(376\) −1.01367 5.74881i −0.0522761 0.296472i
\(377\) 23.1889 1.19429
\(378\) 0 0
\(379\) −27.1242 −1.39328 −0.696639 0.717422i \(-0.745322\pi\)
−0.696639 + 0.717422i \(0.745322\pi\)
\(380\) −0.164091 0.930608i −0.00841770 0.0477392i
\(381\) 0 0
\(382\) 2.53849 0.923933i 0.129880 0.0472725i
\(383\) −26.3725 22.1291i −1.34757 1.13075i −0.979611 0.200904i \(-0.935612\pi\)
−0.367959 0.929842i \(-0.619943\pi\)
\(384\) 0 0
\(385\) −0.645430 0.234917i −0.0328941 0.0119725i
\(386\) −2.88889 5.00371i −0.147041 0.254682i
\(387\) 0 0
\(388\) −6.91534 + 11.9777i −0.351073 + 0.608077i
\(389\) −0.579585 + 0.486329i −0.0293861 + 0.0246579i −0.657362 0.753575i \(-0.728328\pi\)
0.627976 + 0.778232i \(0.283883\pi\)
\(390\) 0 0
\(391\) −6.46868 + 36.6857i −0.327135 + 1.85528i
\(392\) −2.93075 + 16.6211i −0.148025 + 0.839491i
\(393\) 0 0
\(394\) −1.20258 + 1.00909i −0.0605852 + 0.0508370i
\(395\) 0.368026 0.637441i 0.0185174 0.0320731i
\(396\) 0 0
\(397\) −3.50387 6.06888i −0.175854 0.304588i 0.764602 0.644502i \(-0.222935\pi\)
−0.940457 + 0.339914i \(0.889602\pi\)
\(398\) −15.1074 5.49866i −0.757267 0.275623i
\(399\) 0 0
\(400\) −4.21869 3.53990i −0.210935 0.176995i
\(401\) −8.88084 + 3.23236i −0.443488 + 0.161417i −0.554105 0.832447i \(-0.686940\pi\)
0.110617 + 0.993863i \(0.464717\pi\)
\(402\) 0 0
\(403\) 6.95677 + 39.4538i 0.346541 + 1.96533i
\(404\) 19.9051 0.990314
\(405\) 0 0
\(406\) −0.418281 −0.0207590
\(407\) −2.06147 11.6912i −0.102183 0.579511i
\(408\) 0 0
\(409\) −5.18479 + 1.88711i −0.256371 + 0.0933116i −0.467009 0.884253i \(-0.654668\pi\)
0.210637 + 0.977564i \(0.432446\pi\)
\(410\) −4.15079 3.48293i −0.204993 0.172009i
\(411\) 0 0
\(412\) 13.0608 + 4.75373i 0.643458 + 0.234200i
\(413\) 0.00264750 + 0.00458561i 0.000130275 + 0.000225643i
\(414\) 0 0
\(415\) −3.55097 + 6.15047i −0.174310 + 0.301915i
\(416\) 20.3143 17.0458i 0.995993 0.835737i
\(417\) 0 0
\(418\) 0.379852 2.15425i 0.0185792 0.105368i
\(419\) 0.0809857 0.459293i 0.00395641 0.0224379i −0.982766 0.184856i \(-0.940818\pi\)
0.986722 + 0.162418i \(0.0519293\pi\)
\(420\) 0 0
\(421\) −1.84936 + 1.55179i −0.0901321 + 0.0756298i −0.686740 0.726903i \(-0.740959\pi\)
0.596608 + 0.802533i \(0.296515\pi\)
\(422\) −0.570234 + 0.987674i −0.0277585 + 0.0480792i
\(423\) 0 0
\(424\) −3.68004 6.37402i −0.178719 0.309550i
\(425\) −17.5191 6.37645i −0.849804 0.309303i
\(426\) 0 0
\(427\) 0.943563 + 0.791743i 0.0456622 + 0.0383151i
\(428\) −16.3930 + 5.96657i −0.792386 + 0.288405i
\(429\) 0 0
\(430\) −0.162504 0.921605i −0.00783663 0.0444437i
\(431\) −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 \(0.204104\pi\)
\(434\) −0.125486 0.711667i −0.00602352 0.0341611i
\(435\) 0 0
\(436\) 4.17365 1.51908i 0.199881 0.0727509i
\(437\) −3.51471 2.94919i −0.168131 0.141079i
\(438\) 0 0
\(439\) 8.49912 + 3.09343i 0.405641 + 0.147641i 0.536779 0.843723i \(-0.319641\pi\)
−0.131138 + 0.991364i \(0.541863\pi\)
\(440\) 6.87933 + 11.9153i 0.327959 + 0.568042i
\(441\) 0 0
\(442\) 7.47519 12.9474i 0.355558 0.615845i
\(443\) −3.58288 + 3.00640i −0.170228 + 0.142838i −0.723922 0.689882i \(-0.757662\pi\)
0.553694 + 0.832720i \(0.313218\pi\)
\(444\) 0 0
\(445\) 1.24763 7.07564i 0.0591432 0.335417i
\(446\) 1.16415 6.60220i 0.0551239 0.312623i
\(447\) 0 0
\(448\) −0.105600 + 0.0886089i −0.00498913 + 0.00418638i
\(449\) 13.3534 23.1288i 0.630187 1.09152i −0.357326 0.933980i \(-0.616311\pi\)
0.987513 0.157537i \(-0.0503553\pi\)
\(450\) 0 0
\(451\) 20.5351 + 35.5678i 0.966959 + 1.67482i
\(452\) 16.6718 + 6.06805i 0.784177 + 0.285417i
\(453\) 0 0
\(454\) −8.11200 6.80677i −0.380715 0.319458i
\(455\) 0.543308 0.197748i 0.0254707 0.00927056i
\(456\) 0 0
\(457\) −0.114218 0.647763i −0.00534290 0.0303011i 0.982020 0.188778i \(-0.0604527\pi\)
−0.987363 + 0.158477i \(0.949342\pi\)
\(458\) 7.69820 0.359713
\(459\) 0 0
\(460\) 12.5175 0.583633
\(461\) 3.59516 + 20.3892i 0.167443 + 0.949619i 0.946509 + 0.322677i \(0.104583\pi\)
−0.779066 + 0.626942i \(0.784306\pi\)
\(462\) 0 0
\(463\) 23.3268 8.49027i 1.08409 0.394576i 0.262661 0.964888i \(-0.415400\pi\)
0.821428 + 0.570312i \(0.193178\pi\)
\(464\) −5.48167 4.59967i −0.254480 0.213534i
\(465\) 0 0
\(466\) 3.36484 + 1.22470i 0.155873 + 0.0567332i
\(467\) −13.3365 23.0994i −0.617138 1.06891i −0.990005 0.141029i \(-0.954959\pi\)
0.372868 0.927884i \(-0.378375\pi\)
\(468\) 0 0
\(469\) −0.112159 + 0.194265i −0.00517901 + 0.00897031i
\(470\) −1.32683 + 1.11334i −0.0612020 + 0.0513546i
\(471\) 0 0
\(472\) 0.0184183 0.104455i 0.000847772 0.00480795i
\(473\) −1.23172 + 6.98545i −0.0566347 + 0.321191i
\(474\) 0 0
\(475\) 1.75902 1.47599i 0.0807093 0.0677232i
\(476\) 0.441500 0.764700i 0.0202361 0.0350500i
\(477\) 0 0
\(478\) −3.52616 6.10749i −0.161283 0.279350i
\(479\) 3.03195 + 1.10354i 0.138533 + 0.0504221i 0.410356 0.911925i \(-0.365404\pi\)
−0.271823 + 0.962347i \(0.587627\pi\)
\(480\) 0 0
\(481\) 7.65523 + 6.42350i 0.349048 + 0.292886i
\(482\) 6.90625 2.51367i 0.314571 0.114495i
\(483\) 0 0
\(484\) −4.92855 27.9512i −0.224025 1.27051i
\(485\) 9.46075 0.429590
\(486\) 0 0
\(487\) −7.77930 −0.352514 −0.176257 0.984344i \(-0.556399\pi\)
−0.176257 + 0.984344i \(0.556399\pi\)
\(488\) −4.28450 24.2986i −0.193950 1.09995i
\(489\) 0 0
\(490\) 4.70574 1.71275i 0.212584 0.0773741i
\(491\) 13.0580 + 10.9569i 0.589297 + 0.494479i 0.887985 0.459872i \(-0.152105\pi\)
−0.298688 + 0.954351i \(0.596549\pi\)
\(492\) 0 0
\(493\) −22.7640 8.28541i −1.02524 0.373156i
\(494\) 0.920686 + 1.59467i 0.0414236 + 0.0717478i
\(495\) 0 0
\(496\) 6.18139 10.7065i 0.277553 0.480735i
\(497\) −0.601535 + 0.504748i −0.0269825 + 0.0226410i
\(498\) 0 0
\(499\) 1.37716 7.81028i 0.0616503 0.349636i −0.938342 0.345708i \(-0.887639\pi\)
0.999992 0.00392784i \(-0.00125027\pi\)
\(500\) −2.48194 + 14.0758i −0.110996 + 0.629488i
\(501\) 0 0
\(502\) −7.89827 + 6.62744i −0.352517 + 0.295797i
\(503\) −12.4748 + 21.6070i −0.556224 + 0.963409i 0.441583 + 0.897220i \(0.354417\pi\)
−0.997807 + 0.0661881i \(0.978916\pi\)
\(504\) 0 0
\(505\) −6.80793 11.7917i −0.302949 0.524723i
\(506\) 27.2291 + 9.91060i 1.21048 + 0.440580i
\(507\) 0 0
\(508\) 18.0967 + 15.1850i 0.802913 + 0.673724i
\(509\) 38.0284 13.8412i 1.68558 0.613501i 0.691521 0.722356i \(-0.256941\pi\)
0.994058 + 0.108855i \(0.0347185\pi\)
\(510\) 0 0
\(511\) −0.256244 1.45323i −0.0113356 0.0642873i
\(512\) −15.0038 −0.663080
\(513\) 0 0
\(514\) 2.27269 0.100244
\(515\) −1.65095 9.36303i −0.0727497 0.412584i
\(516\) 0 0
\(517\) 12.3366 4.49016i 0.542564 0.197477i
\(518\) −0.138085 0.115867i −0.00606710 0.00509090i
\(519\) 0 0
\(520\) −10.8833 3.96118i −0.477262 0.173709i
\(521\) −12.6837 21.9688i −0.555684 0.962473i −0.997850 0.0655394i \(-0.979123\pi\)
0.442166 0.896933i \(-0.354210\pi\)
\(522\) 0 0
\(523\) −6.36097 + 11.0175i −0.278146 + 0.481762i −0.970924 0.239388i \(-0.923053\pi\)
0.692778 + 0.721151i \(0.256386\pi\)
\(524\) 15.6753 13.1532i 0.684780 0.574599i
\(525\) 0 0
\(526\) −1.04988 + 5.95416i −0.0457769 + 0.259614i
\(527\) 7.26758 41.2165i 0.316581 1.79542i
\(528\) 0 0
\(529\) 28.9388 24.2825i 1.25821 1.05576i
\(530\) −1.09191 + 1.89124i −0.0474296 + 0.0821504i
\(531\) 0 0
\(532\) 0.0543776 + 0.0941848i 0.00235757 + 0.00408343i
\(533\) −32.4870 11.8243i −1.40717 0.512167i
\(534\) 0 0
\(535\) 9.14131 + 7.67047i 0.395213 + 0.331623i
\(536\) 4.22242 1.53684i 0.182381 0.0663812i
\(537\) 0 0
\(538\) −0.961266 5.45161i −0.0414431 0.235036i
\(539\) −37.9570 −1.63492
\(540\) 0 0
\(541\) 2.09327 0.0899969 0.0449984 0.998987i \(-0.485672\pi\)
0.0449984 + 0.998987i \(0.485672\pi\)
\(542\) 2.25686 + 12.7993i 0.0969406 + 0.549778i
\(543\) 0 0
\(544\) −26.0326 + 9.47508i −1.11614 + 0.406241i
\(545\) −2.32737 1.95290i −0.0996936 0.0836529i
\(546\) 0 0
\(547\) −3.24288 1.18031i −0.138655 0.0504665i 0.271760 0.962365i \(-0.412394\pi\)
−0.410416 + 0.911899i \(0.634616\pi\)
\(548\) 15.0326 + 26.0371i 0.642159 + 1.11225i
\(549\) 0 0
\(550\) −7.25103 + 12.5592i −0.309185 + 0.535524i
\(551\) 2.28563 1.91787i 0.0973711 0.0817040i
\(552\) 0 0
\(553\) −0.0147100 + 0.0834248i −0.000625535 + 0.00354758i
\(554\) 0.502374 2.84911i 0.0213438 0.121047i
\(555\) 0 0
\(556\) −19.1379 + 16.0586i −0.811628 + 0.681037i
\(557\) 5.55017 9.61318i 0.235168 0.407323i −0.724153 0.689639i \(-0.757769\pi\)
0.959322 + 0.282316i \(0.0911025\pi\)
\(558\) 0 0
\(559\) −2.98545 5.17095i −0.126271 0.218708i
\(560\) −0.167658 0.0610226i −0.00708485 0.00257868i
\(561\) 0 0
\(562\) −3.82635 3.21069i −0.161405 0.135435i
\(563\) −22.8446 + 8.31474i −0.962784 + 0.350425i −0.775124 0.631810i \(-0.782312\pi\)
−0.187660 + 0.982234i \(0.560090\pi\)
\(564\) 0 0
\(565\) −2.10741 11.9517i −0.0886594 0.502813i
\(566\) −10.9587 −0.460628
\(567\) 0 0
\(568\) 15.7297 0.660002
\(569\) 7.42588 + 42.1143i 0.311309 + 1.76552i 0.592208 + 0.805785i \(0.298256\pi\)
−0.280899 + 0.959737i \(0.590633\pi\)
\(570\) 0 0
\(571\) −16.9410 + 6.16603i −0.708960 + 0.258040i −0.671232 0.741248i \(-0.734234\pi\)
−0.0377286 + 0.999288i \(0.512012\pi\)
\(572\) 29.1695 + 24.4761i 1.21964 + 1.02340i
\(573\) 0 0
\(574\) 0.586000 + 0.213286i 0.0244592 + 0.00890240i
\(575\) 15.2086 + 26.3421i 0.634244 + 1.09854i
\(576\) 0 0
\(577\) −12.6382 + 21.8899i −0.526133 + 0.911290i 0.473403 + 0.880846i \(0.343025\pi\)
−0.999536 + 0.0304438i \(0.990308\pi\)
\(578\) −3.05623 + 2.56448i −0.127122 + 0.106668i
\(579\) 0 0
\(580\) −1.41353 + 8.01655i −0.0586938 + 0.332869i
\(581\) 0.141933 0.804940i 0.00588836 0.0333946i
\(582\) 0 0
\(583\) 12.6800 10.6398i 0.525154 0.440656i
\(584\) −14.7797 + 25.5993i −0.611590 + 1.05930i
\(585\) 0 0
\(586\) 6.15792 + 10.6658i 0.254381 + 0.440601i
\(587\) −26.8426 9.76991i −1.10791 0.403248i −0.277686 0.960672i \(-0.589567\pi\)
−0.830228 + 0.557424i \(0.811790\pi\)
\(588\) 0 0
\(589\) 3.94878 + 3.31342i 0.162707 + 0.136527i
\(590\) −0.0295733 + 0.0107638i −0.00121751 + 0.000443138i
\(591\) 0 0
\(592\) −0.535492 3.03693i −0.0220086 0.124817i
\(593\) 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
\(596\) 2.93918 + 16.6689i 0.120393 + 0.682785i
\(597\) 0 0
\(598\) −22.9209 + 8.34251i −0.937304 + 0.341151i
\(599\) −11.0883 9.30423i −0.453057 0.380160i 0.387512 0.921865i \(-0.373335\pi\)
−0.840569 + 0.541705i \(0.817779\pi\)
\(600\) 0 0
\(601\) 12.5496 + 4.56769i 0.511910 + 0.186320i 0.585043 0.811002i \(-0.301078\pi\)
−0.0731331 + 0.997322i \(0.523300\pi\)
\(602\) 0.0538515 + 0.0932736i 0.00219483 + 0.00380155i
\(603\) 0 0
\(604\) −5.20961 + 9.02330i −0.211976 + 0.367153i
\(605\) −14.8725 + 12.4795i −0.604654 + 0.507365i
\(606\) 0 0
\(607\) 5.42009 30.7389i 0.219995 1.24765i −0.652031 0.758192i \(-0.726083\pi\)
0.872026 0.489460i \(-0.162806\pi\)
\(608\) 0.592503 3.36025i 0.0240292 0.136276i
\(609\) 0 0
\(610\) −5.60813 + 4.70578i −0.227066 + 0.190531i
\(611\) −5.52557 + 9.57057i −0.223541 + 0.387184i
\(612\) 0 0
\(613\) −15.0326 26.0372i −0.607159 1.05163i −0.991706 0.128525i \(-0.958976\pi\)
0.384547 0.923105i \(-0.374358\pi\)
\(614\) −8.68453 3.16091i −0.350479 0.127564i
\(615\) 0 0
\(616\) −1.21301 1.01784i −0.0488736 0.0410098i
\(617\) 39.6115 14.4174i 1.59470 0.580423i 0.616366 0.787460i \(-0.288604\pi\)
0.978333 + 0.207037i \(0.0663822\pi\)
\(618\) 0 0
\(619\) 2.01620 + 11.4344i 0.0810378 + 0.459588i 0.998141 + 0.0609394i \(0.0194096\pi\)
−0.917104 + 0.398649i \(0.869479\pi\)
\(620\) −14.0635 −0.564803
\(621\) 0 0
\(622\) −11.2335 −0.450422
\(623\) 0.143588 + 0.814330i 0.00575275 + 0.0326254i
\(624\) 0 0
\(625\) −9.14455 + 3.32834i −0.365782 + 0.133134i
\(626\) 10.2521 + 8.60250i 0.409755 + 0.343825i
\(627\) 0 0
\(628\) 24.3123 + 8.84894i 0.970165 + 0.353111i
\(629\) −5.21983 9.04101i −0.208128 0.360489i
\(630\) 0 0
\(631\) 14.6552 25.3836i 0.583415 1.01051i −0.411655 0.911340i \(-0.635049\pi\)
0.995071 0.0991657i \(-0.0316174\pi\)
\(632\) 1.29990 1.09075i 0.0517073 0.0433876i
\(633\) 0 0
\(634\) 2.89574 16.4226i 0.115005 0.652224i
\(635\) 2.80607 15.9140i 0.111355 0.631528i
\(636\) 0 0
\(637\) 24.4761 20.5379i 0.969779 0.813741i
\(638\) −9.42182 + 16.3191i −0.373014 + 0.646078i
\(639\) 0 0
\(640\) 5.66637 + 9.81445i 0.223983 + 0.387950i
\(641\) 29.2224 + 10.6361i 1.15422 + 0.420101i 0.847028 0.531548i \(-0.178390\pi\)
0.307189 + 0.951649i \(0.400612\pi\)
\(642\) 0 0
\(643\) 32.2290 + 27.0433i 1.27099 + 1.06648i 0.994420 + 0.105489i \(0.0336408\pi\)
0.276566 + 0.960995i \(0.410804\pi\)
\(644\) −1.35375 + 0.492726i −0.0533454 + 0.0194161i
\(645\) 0 0
\(646\) −0.334036 1.89441i −0.0131425 0.0745347i
\(647\) 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
\(650\) −2.11981 12.0220i −0.0831458 0.471543i
\(651\) 0 0
\(652\) 12.1099 4.40766i 0.474262 0.172617i
\(653\) 2.39322 + 2.00815i 0.0936540 + 0.0785850i 0.688413 0.725319i \(-0.258308\pi\)
−0.594759 + 0.803904i \(0.702752\pi\)
\(654\) 0 0
\(655\) −13.1532 4.78736i −0.513937 0.187058i
\(656\) 5.33424 + 9.23917i 0.208267 + 0.360729i
\(657\) 0 0
\(658\) 0.0996702 0.172634i 0.00388555 0.00672997i
\(659\) −28.6724 + 24.0590i −1.11692 + 0.937206i −0.998445 0.0557508i \(-0.982245\pi\)
−0.118474 + 0.992957i \(0.537800\pi\)
\(660\) 0 0
\(661\) 4.60173 26.0977i 0.178987 1.01508i −0.754455 0.656352i \(-0.772099\pi\)
0.933441 0.358731i \(-0.116790\pi\)
\(662\) −3.38516 + 19.1982i −0.131568 + 0.746160i
\(663\) 0 0
\(664\) −12.5424 + 10.5243i −0.486738 + 0.408422i
\(665\) 0.0371965 0.0644262i 0.00144242 0.00249834i
\(666\) 0 0
\(667\) 19.7618 + 34.2284i 0.765179 + 1.32533i
\(668\) 3.77920 + 1.37551i 0.146221 + 0.0532203i
\(669\) 0 0
\(670\) −1.02133 0.856994i −0.0394572 0.0331085i
\(671\) 52.1434 18.9786i 2.01297 0.732662i
\(672\) 0 0
\(673\) 0.298849 + 1.69485i 0.0115198 + 0.0653318i 0.990026 0.140887i \(-0.0449953\pi\)
−0.978506 + 0.206219i \(0.933884\pi\)
\(674\) 11.9341 0.459686
\(675\) 0 0
\(676\) −12.1361 −0.466773
\(677\) 4.91063 + 27.8496i 0.188731 + 1.07035i 0.921067 + 0.389403i \(0.127319\pi\)
−0.732337 + 0.680943i \(0.761570\pi\)
\(678\) 0 0
\(679\) −1.02317 + 0.372402i −0.0392655 + 0.0142915i
\(680\) 9.26849 + 7.77719i 0.355430 + 0.298242i
\(681\) 0 0
\(682\) −30.5920 11.1346i −1.17143 0.426365i
\(683\) 12.3569 + 21.4029i 0.472825 + 0.818958i 0.999516 0.0310993i \(-0.00990082\pi\)
−0.526691 + 0.850057i \(0.676567\pi\)
\(684\) 0 0
\(685\) 10.2829 17.8105i 0.392888 0.680502i
\(686\) −0.883919 + 0.741696i −0.0337482 + 0.0283181i
\(687\) 0 0
\(688\) −0.319955 + 1.81456i −0.0121982 + 0.0691793i
\(689\) −2.41955 + 13.7219i −0.0921774 + 0.522764i
\(690\) 0 0
\(691\) −33.5317 + 28.1364i −1.27561 + 1.07036i −0.281771 + 0.959482i \(0.590922\pi\)
−0.993834 + 0.110878i \(0.964634\pi\)
\(692\) −10.0377 + 17.3858i −0.381576 + 0.660908i
\(693\) 0 0
\(694\) 8.61515 + 14.9219i 0.327027 + 0.566427i
\(695\) 16.0586 + 5.84486i 0.609138 + 0.221708i
\(696\) 0 0
\(697\) 27.6668 + 23.2152i 1.04796 + 0.879340i
\(698\) −7.61835 + 2.77285i −0.288359 + 0.104954i
\(699\) 0 0
\(700\) −0.125200 0.710047i −0.00473213 0.0268372i
\(701\) −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
\(704\) 1.07839 + 6.11587i 0.0406434 + 0.230500i
\(705\) 0 0
\(706\) −5.39780 + 1.96464i −0.203149 + 0.0739402i
\(707\) 1.20042 + 1.00727i 0.0451465 + 0.0378824i
\(708\) 0 0
\(709\) −4.76769 1.73530i −0.179054 0.0651705i 0.250937 0.968003i \(-0.419261\pi\)
−0.429992 + 0.902833i \(0.641483\pi\)
\(710\) −2.33359 4.04189i −0.0875779 0.151689i
\(711\) 0 0
\(712\) 8.28194 14.3447i 0.310379 0.537592i
\(713\) −52.3078 + 43.8915i −1.95894 + 1.64375i
\(714\) 0 0
\(715\) 4.52300 25.6512i 0.169151 0.959302i
\(716\) −5.87927 + 33.3430i −0.219719 + 1.24609i
\(717\) 0 0
\(718\) −1.38350 + 1.16090i −0.0516319 + 0.0433243i
\(719\) 2.66858 4.62212i 0.0995213 0.172376i −0.811965 0.583706i \(-0.801602\pi\)
0.911487 + 0.411330i \(0.134936\pi\)
\(720\) 0 0
\(721\) 0.547104 + 0.947611i 0.0203752 + 0.0352909i
\(722\) −11.9903 4.36412i −0.446234 0.162416i
\(723\) 0 0
\(724\) 2.41669 + 2.02784i 0.0898155 + 0.0753642i
\(725\) −18.5876 + 6.76533i −0.690326 + 0.251258i
\(726\) 0 0
\(727\) 6.44578 + 36.5559i 0.239061 + 1.35578i 0.833890 + 0.551930i \(0.186108\pi\)
−0.594830 + 0.803852i \(0.702780\pi\)
\(728\) 1.33293 0.0494017
\(729\) 0 0
\(730\) 8.77063 0.324616
\(731\) 1.08316 + 6.14290i 0.0400621 + 0.227203i
\(732\) 0 0
\(733\) −28.1403 + 10.2422i −1.03938 + 0.378305i −0.804647 0.593754i \(-0.797645\pi\)
−0.234738 + 0.972059i \(0.575423\pi\)
\(734\) −4.81958 4.04411i −0.177894 0.149271i
\(735\) 0 0
\(736\) 42.4727 + 15.4588i 1.56557 + 0.569819i
\(737\) 5.05277 + 8.75166i 0.186121 + 0.322371i
\(738\) 0 0
\(739\) 14.3050 24.7770i 0.526218 0.911436i −0.473316 0.880893i \(-0.656943\pi\)
0.999533 0.0305431i \(-0.00972368\pi\)
\(740\) −2.68729 + 2.25490i −0.0987866 + 0.0828918i
\(741\) 0 0
\(742\) 0.0436438 0.247516i 0.00160221 0.00908660i
\(743\) 8.62052 48.8894i 0.316256 1.79358i −0.248831 0.968547i \(-0.580046\pi\)
0.565087 0.825031i \(-0.308843\pi\)
\(744\) 0 0
\(745\) 8.86934 7.44226i 0.324947 0.272663i
\(746\) −9.16312 + 15.8710i −0.335486 + 0.581078i
\(747\) 0 0
\(748\) −19.8897 34.4499i −0.727238 1.25961i
\(749\) −1.29055 0.469722i −0.0471557 0.0171633i
\(750\) 0 0
\(751\) −24.2251 20.3273i −0.883986 0.741752i 0.0830087 0.996549i \(-0.473547\pi\)
−0.966995 + 0.254796i \(0.917992\pi\)
\(752\) 3.20459 1.16637i 0.116859 0.0425333i
\(753\) 0 0
\(754\) −2.75443 15.6212i −0.100311 0.568889i
\(755\) 7.12716 0.259384
\(756\) 0 0
\(757\) 3.04189 0.110559 0.0552797 0.998471i \(-0.482395\pi\)
0.0552797 + 0.998471i \(0.482395\pi\)
\(758\) 3.22188 + 18.2722i 0.117024 + 0.663676i
\(759\) 0 0
\(760\) −1.40033 + 0.509678i −0.0507953 + 0.0184880i
\(761\) 29.0548 + 24.3799i 1.05323 + 0.883769i 0.993430 0.114441i \(-0.0365077\pi\)
0.0598048 + 0.998210i \(0.480952\pi\)
\(762\) 0 0
\(763\) 0.328573 + 0.119591i 0.0118952 + 0.00432948i
\(764\) 3.02525 + 5.23989i 0.109450 + 0.189572i
\(765\) 0 0
\(766\) −11.7747 + 20.3943i −0.425436 + 0.736877i
\(767\) −0.153821 + 0.129071i −0.00555414 + 0.00466048i
\(768\) 0 0
\(769\) −3.54030 + 20.0780i −0.127666 + 0.724032i 0.852022 + 0.523506i \(0.175376\pi\)
−0.979688 + 0.200526i \(0.935735\pi\)
\(770\) −0.0815859 + 0.462697i −0.00294015 + 0.0166744i
\(771\) 0 0
\(772\) 9.91329 8.31823i 0.356787 0.299380i
\(773\) −12.2332 + 21.1885i −0.439997 + 0.762097i −0.997689 0.0679509i \(-0.978354\pi\)
0.557692 + 0.830048i \(0.311687\pi\)
\(774\) 0 0
\(775\) −17.0869 29.5954i −0.613781 1.06310i
\(776\) 20.4955 + 7.45976i 0.735746 + 0.267790i
\(777\) 0 0
\(778\) 0.396459 + 0.332669i 0.0142138 + 0.0119268i
\(779\) −4.18004 + 1.52141i −0.149766 + 0.0545102i
\(780\) 0 0
\(781\) 6.14290 + 34.8381i 0.219810 + 1.24661i
\(782\) 25.4816 0.911221
\(783\) 0 0
\(784\) −9.85978 −0.352135
\(785\) −3.07321 17.4290i −0.109687 0.622068i
\(786\) 0 0
\(787\) −35.3089 + 12.8514i −1.25863 + 0.458102i −0.883307 0.468794i \(-0.844689\pi\)
−0.375318 + 0.926896i \(0.622466\pi\)
\(788\) −2.69350 2.26011i −0.0959520 0.0805133i
\(789\) 0 0
\(790\) −0.473126 0.172204i −0.0168331 0.00612673i
\(791\) 0.698367 + 1.20961i 0.0248311 + 0.0430087i
\(792\) 0 0
\(793\) −23.3550 + 40.4521i −0.829362 + 1.43650i
\(794\) −3.67209 + 3.08125i −0.130318 + 0.109350i
\(795\) 0 0
\(796\) 6.25284 35.4616i 0.221626 1.25690i
\(797\) 0.400247 2.26991i 0.0141775 0.0804045i −0.976898 0.213706i \(-0.931447\pi\)
0.991076 + 0.133301i \(0.0425578\pi\)
\(798\) 0 0
\(799\) 8.84389 7.42091i 0.312874 0.262533i
\(800\) −11.3103 + 19.5901i −0.399881 + 0.692614i
\(801\) 0 0
\(802\) 3.23236 + 5.59862i 0.114139 + 0.197694i
\(803\) −62.4693 22.7369i −2.20449 0.802369i
\(804\) 0 0
\(805\) 0.754900 + 0.633436i 0.0266067 + 0.0223257i
\(806\) 25.7516 9.37283i 0.907062 0.330144i
\(807\) 0 0
\(808\) −5.45084 30.9132i −0.191760 1.08752i
\(809\) −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 \(0.864364\pi\)
\(812\) −0.162683 0.922618i −0.00570904 0.0323776i
\(813\) 0 0
\(814\) −7.63088 + 2.77741i −0.267462 + 0.0973483i
\(815\) −6.75292 5.66637i −0.236545 0.198484i
\(816\) 0 0
\(817\) −0.721934 0.262762i −0.0252573 0.00919289i
\(818\) 1.88711 + 3.26857i 0.0659813 + 0.114283i
\(819\) 0 0
\(820\) 6.06805 10.5102i 0.211905 0.367031i
\(821\) 14.1267 11.8537i 0.493025 0.413697i −0.362084 0.932145i \(-0.617935\pi\)
0.855109 + 0.518449i \(0.173490\pi\)
\(822\) 0 0
\(823\) −6.03714 + 34.2383i −0.210442 + 1.19347i 0.678202 + 0.734875i \(0.262759\pi\)
−0.888644 + 0.458598i \(0.848352\pi\)
\(824\) 3.80612 21.5856i 0.132593 0.751970i
\(825\) 0 0
\(826\) 0.00277461 0.00232818i 9.65411e−5 8.10076e-5i
\(827\) 16.3886 28.3859i 0.569889 0.987076i −0.426688 0.904399i \(-0.640320\pi\)
0.996576 0.0826770i \(-0.0263470\pi\)
\(828\) 0 0
\(829\) −2.67634 4.63555i −0.0929530 0.160999i 0.815799 0.578335i \(-0.196297\pi\)
−0.908752 + 0.417336i \(0.862964\pi\)
\(830\) 4.56504 + 1.66154i 0.158455 + 0.0576729i
\(831\) 0 0
\(832\) −4.00459 3.36025i −0.138834 0.116496i
\(833\) −31.3658 + 11.4162i −1.08676 + 0.395549i
\(834\) 0 0
\(835\) −0.477711 2.70924i −0.0165319 0.0937570i
\(836\) 4.89944 0.169451
\(837\) 0 0
\(838\) −0.319022 −0.0110204
\(839\) 0.944364 + 5.35575i 0.0326031 + 0.184901i 0.996760 0.0804308i \(-0.0256296\pi\)
−0.964157 + 0.265332i \(0.914518\pi\)
\(840\) 0 0
\(841\) 3.09879 1.12787i 0.106855 0.0388920i
\(842\) 1.26503 + 1.06149i 0.0435959 + 0.0365813i
\(843\) 0 0
\(844\) −2.40033 0.873649i −0.0826228 0.0300722i
\(845\) 4.15079 + 7.18938i 0.142791 + 0.247322i
\(846\) 0 0
\(847\) 1.11721 1.93507i 0.0383878 0.0664897i
\(848\) 3.29380 2.76382i 0.113109 0.0949101i
\(849\) 0 0
\(850\) −2.21452 + 12.5592i −0.0759573 + 0.430775i
\(851\) −2.95767 + 16.7738i −0.101388 + 0.574998i
\(852\) 0 0
\(853\) −36.0938 + 30.2863i −1.23583 + 1.03698i −0.237990 + 0.971268i \(0.576488\pi\)
−0.997838 + 0.0657152i \(0.979067\pi\)
\(854\) 0.421278 0.729675i 0.0144158 0.0249690i
\(855\) 0 0
\(856\) 13.7554 + 23.8250i 0.470149 + 0.814322i
\(857\) 44.1242 + 16.0599i 1.50725 + 0.548596i 0.957927 0.287012i \(-0.0926619\pi\)
0.549327 + 0.835607i \(0.314884\pi\)
\(858\) 0 0
\(859\) 5.48751 + 4.60457i 0.187231 + 0.157106i 0.731585 0.681750i \(-0.238781\pi\)
−0.544354 + 0.838856i \(0.683225\pi\)
\(860\) 1.96962 0.716881i 0.0671633 0.0244455i
\(861\) 0 0
\(862\) 1.43717 + 8.15058i 0.0489501 + 0.277610i
\(863\) −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
\(866\) −3.96150 22.4668i −0.134617 0.763452i
\(867\) 0 0
\(868\) 1.52094 0.553579i 0.0516242 0.0187897i
\(869\) 2.92344 + 2.45306i 0.0991710 + 0.0832143i
\(870\) 0 0
\(871\) −7.99360 2.90943i −0.270853 0.0985824i
\(872\) −3.50211 6.06583i −0.118596 0.205415i
\(873\) 0 0
\(874\) −1.56923 + 2.71799i −0.0530800 + 0.0919373i
\(875\) −0.861969 + 0.723278i −0.0291399 + 0.0244513i
\(876\) 0 0
\(877\) 1.41921 8.04877i 0.0479235 0.271788i −0.951425 0.307881i \(-0.900380\pi\)
0.999348 + 0.0360932i \(0.0114913\pi\)
\(878\) 1.07434 6.09286i 0.0362571 0.205624i
\(879\) 0 0
\(880\) −6.15729 + 5.16658i −0.207562 + 0.174165i
\(881\) 16.6153 28.7786i 0.559785 0.969575i −0.437729 0.899107i \(-0.644217\pi\)
0.997514 0.0704686i \(-0.0224494\pi\)
\(882\) 0 0
\(883\) −16.5239 28.6203i −0.556075 0.963150i −0.997819 0.0660087i \(-0.978973\pi\)
0.441744 0.897141i \(-0.354360\pi\)
\(884\) 31.4659 + 11.4526i 1.05831 + 0.385194i
\(885\) 0 0
\(886\) 2.45084 + 2.05650i 0.0823375 + 0.0690893i
\(887\) 46.7471 17.0145i 1.56961 0.571293i 0.596701 0.802464i \(-0.296478\pi\)
0.972913 + 0.231171i \(0.0742558\pi\)
\(888\) 0 0
\(889\) 0.322948 + 1.83153i 0.0108313 + 0.0614276i
\(890\) −4.91469 −0.164741
\(891\) 0 0
\(892\) 15.0155 0.502756
\(893\) 0.246916 + 1.40033i 0.00826273 + 0.0468602i
\(894\) 0 0
\(895\) 21.7631 7.92112i 0.727460 0.264774i
\(896\) −0.999135 0.838374i −0.0333787 0.0280081i
\(897\) 0 0
\(898\) −17.1668 6.24822i −0.572865 0.208506i
\(899\) −22.2024 38.4556i −0.740491 1.28257i
\(900\) 0 0
\(901\) 7.27807 12.6060i 0.242468 0.419966i
\(902\) 21.5210 18.0582i 0.716570 0.601274i
\(903\) 0 0
\(904\) 4.85844 27.5536i 0.161589 0.916419i
\(905\) 0.374730 2.12520i 0.0124565 0.0706441i
\(906\) 0 0
\(907\) 26.4657 22.2074i 0.878779 0.737383i −0.0871488 0.996195i \(-0.527776\pi\)
0.965928 + 0.258812i \(0.0833311\pi\)
\(908\) 11.8589 20.5403i 0.393553 0.681654i
\(909\) 0 0
\(910\) −0.197748 0.342509i −0.00655528 0.0113541i
\(911\) 12.8145 + 4.66410i 0.424563 + 0.154528i 0.545460 0.838137i \(-0.316355\pi\)
−0.120897 + 0.992665i \(0.538577\pi\)
\(912\) 0 0
\(913\) −28.2074 23.6688i −0.933528 0.783323i
\(914\) −0.422797 + 0.153886i −0.0139849 + 0.00509009i
\(915\) 0 0
\(916\) 2.99407 + 16.9802i 0.0989269 + 0.561042i
\(917\) 1.61094 0.0531979
\(918\) 0 0
\(919\) 32.7701 1.08099 0.540493 0.841348i \(-0.318238\pi\)
0.540493 + 0.841348i \(0.318238\pi\)
\(920\) −3.42782 19.4402i −0.113012 0.640923i
\(921\) 0 0
\(922\) 13.3081 4.84375i 0.438279 0.159520i
\(923\) −22.8115 19.1411i −0.750851 0.630039i
\(924\) 0 0
\(925\) −8.01027 2.91550i −0.263376 0.0958610i
\(926\) −8.49027 14.7056i −0.279008 0.483255i
\(927\) 0 0
\(928\) −14.6964 + 25.4549i −0.482433 + 0.835599i
\(929\) 4.23735 3.55556i 0.139023 0.116654i −0.570624 0.821211i \(-0.693299\pi\)
0.709647 + 0.704557i \(0.248854\pi\)
\(930\) 0 0
\(931\) 0.713888 4.04866i 0.0233967 0.132690i
\(932\) −1.39268 + 7.89827i −0.0456187 + 0.258716i
\(933\) 0 0
\(934\) −13.9767 + 11.7279i −0.457333 + 0.383748i
\(935\) −13.6053 + 23.5651i −0.444942 + 0.770662i
\(936\) 0 0
\(937\) 0.497007 + 0.860841i 0.0162365 + 0.0281225i 0.874029 0.485873i \(-0.161498\pi\)
−0.857793 + 0.513995i \(0.828165\pi\)
\(938\) 0.144189 + 0.0524803i 0.00470792 + 0.00171354i
\(939\) 0 0
\(940\) −2.97178 2.49362i −0.0969288 0.0813329i
\(941\) −10.7662 + 3.91859i −0.350969 + 0.127742i −0.511488 0.859291i \(-0.670905\pi\)
0.160519 + 0.987033i \(0.448683\pi\)
\(942\) 0 0
\(943\) −10.2322 58.0297i −0.333206 1.88971i
\(944\) 0.0619640 0.00201676
\(945\) 0 0
\(946\) 4.85204 0.157754
\(947\) −7.93312 44.9910i −0.257792 1.46201i −0.788803 0.614646i \(-0.789299\pi\)
0.531012 0.847365i \(-0.321812\pi\)
\(948\) 0 0
\(949\) 52.5852 19.1394i 1.70699 0.621293i
\(950\) −1.20324 1.00964i −0.0390383 0.0327570i
\(951\) 0 0
\(952\) −1.30851 0.476257i −0.0424089 0.0154356i
\(953\) 7.25265 + 12.5620i 0.234936 + 0.406922i 0.959254 0.282545i \(-0.0911785\pi\)
−0.724318 + 0.689466i \(0.757845\pi\)
\(954\) 0 0
\(955\) 2.06939 3.58429i 0.0669640 0.115985i
\(956\) 12.1001 10.1532i 0.391344 0.328377i
\(957\) 0 0
\(958\) 0.383256 2.17355i 0.0123824 0.0702242i
\(959\) −0.411007 + 2.33094i −0.0132721 + 0.0752699i
\(960\) 0 0
\(961\) 35.0205 29.3857i 1.12969 0.947926i
\(962\) 3.41787 5.91993i 0.110197 0.190866i
\(963\) 0 0
\(964\) 8.23055 + 14.2557i 0.265088 + 0.459146i
\(965\) −8.31823 3.02759i −0.267773 0.0974616i
\(966\) 0 0
\(967\) −19.1793 16.0934i −0.616766 0.517528i 0.280019 0.959994i \(-0.409659\pi\)
−0.896785 + 0.442467i \(0.854104\pi\)
\(968\) −42.0595 + 15.3084i −1.35184 + 0.492031i
\(969\) 0 0
\(970\) −1.12377 6.37322i −0.0360821 0.204632i
\(971\) 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
\(974\) 0.924044 + 5.24051i 0.0296083 + 0.167917i
\(975\) 0 0
\(976\) 13.5449 4.92993i 0.433561 0.157803i
\(977\) −1.89473 1.58987i −0.0606179 0.0508644i 0.611975 0.790877i \(-0.290375\pi\)
−0.672593 + 0.740012i \(0.734820\pi\)
\(978\) 0 0
\(979\) 35.0051 + 12.7408i 1.11877 + 0.407198i
\(980\) 5.60808 + 9.71348i 0.179144 + 0.310286i
\(981\) 0 0
\(982\) 5.83006 10.0980i 0.186045 0.322239i
\(983\) 14.6376 12.2824i 0.466867 0.391748i −0.378783 0.925485i \(-0.623657\pi\)
0.845650 + 0.533738i \(0.179213\pi\)
\(984\) 0 0
\(985\) −0.417652 + 2.36862i −0.0133075 + 0.0754706i
\(986\) −2.87749 + 16.3191i −0.0916381 + 0.519705i
\(987\) 0 0
\(988\) −3.15935 + 2.65101i −0.100512 + 0.0843398i
\(989\) 5.08845 8.81345i 0.161803 0.280251i
\(990\) 0 0
\(991\) 19.1582 + 33.1830i 0.608581 + 1.05409i 0.991475 + 0.130301i \(0.0415943\pi\)
−0.382894 + 0.923792i \(0.625072\pi\)
\(992\) −47.7182 17.3680i −1.51505 0.551434i
\(993\) 0 0
\(994\) 0.411474 + 0.345268i 0.0130512 + 0.0109512i
\(995\) −23.1459 + 8.42443i −0.733775 + 0.267072i
\(996\) 0 0
\(997\) 7.18463 + 40.7461i 0.227540 + 1.29044i 0.857770 + 0.514033i \(0.171849\pi\)
−0.630231 + 0.776408i \(0.717040\pi\)
\(998\) −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.e.q.82.1 12
3.2 odd 2 inner 729.2.e.q.82.2 12
9.2 odd 6 729.2.e.r.325.2 12
9.4 even 3 729.2.e.m.568.2 12
9.5 odd 6 729.2.e.m.568.1 12
9.7 even 3 729.2.e.r.325.1 12
27.2 odd 18 inner 729.2.e.q.649.2 12
27.4 even 9 729.2.c.c.487.4 12
27.5 odd 18 729.2.a.c.1.4 yes 6
27.7 even 9 729.2.e.r.406.1 12
27.11 odd 18 729.2.e.m.163.1 12
27.13 even 9 729.2.c.c.244.4 12
27.14 odd 18 729.2.c.c.244.3 12
27.16 even 9 729.2.e.m.163.2 12
27.20 odd 18 729.2.e.r.406.2 12
27.22 even 9 729.2.a.c.1.3 6
27.23 odd 18 729.2.c.c.487.3 12
27.25 even 9 inner 729.2.e.q.649.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
729.2.a.c.1.3 6 27.22 even 9
729.2.a.c.1.4 yes 6 27.5 odd 18
729.2.c.c.244.3 12 27.14 odd 18
729.2.c.c.244.4 12 27.13 even 9
729.2.c.c.487.3 12 27.23 odd 18
729.2.c.c.487.4 12 27.4 even 9
729.2.e.m.163.1 12 27.11 odd 18
729.2.e.m.163.2 12 27.16 even 9
729.2.e.m.568.1 12 9.5 odd 6
729.2.e.m.568.2 12 9.4 even 3
729.2.e.q.82.1 12 1.1 even 1 trivial
729.2.e.q.82.2 12 3.2 odd 2 inner
729.2.e.q.649.1 12 27.25 even 9 inner
729.2.e.q.649.2 12 27.2 odd 18 inner
729.2.e.r.325.1 12 9.7 even 3
729.2.e.r.325.2 12 9.2 odd 6
729.2.e.r.406.1 12 27.7 even 9
729.2.e.r.406.2 12 27.20 odd 18