Properties

Label 92.2.e.a.81.2
Level $92$
Weight $2$
Character 92.81
Analytic conductor $0.735$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [92,2,Mod(9,92)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(92, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("92.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 92 = 2^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 92.e (of order \(11\), degree \(10\), 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: \(0.734623698596\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(2\) over \(\Q(\zeta_{11})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 9 x^{19} + 51 x^{18} - 200 x^{17} + 633 x^{16} - 1688 x^{15} + 3957 x^{14} - 8161 x^{13} + 14788 x^{12} - 23925 x^{11} + 35080 x^{10} - 43945 x^{9} + 57269 x^{8} + \cdots + 529 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 81.2
Root \(-0.967148 - 1.11615i\) of defining polynomial
Character \(\chi\) \(=\) 92.81
Dual form 92.2.e.a.25.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.210181 - 1.46184i) q^{3} +(0.926812 - 0.272136i) q^{5} +(-1.14874 - 1.32572i) q^{7} +(0.785668 + 0.230693i) q^{9} +O(q^{10})\) \(q+(0.210181 - 1.46184i) q^{3} +(0.926812 - 0.272136i) q^{5} +(-1.14874 - 1.32572i) q^{7} +(0.785668 + 0.230693i) q^{9} +(0.436414 + 0.280466i) q^{11} +(-2.04423 + 2.35917i) q^{13} +(-0.203022 - 1.41205i) q^{15} +(1.39464 + 3.05384i) q^{17} +(-2.90720 + 6.36588i) q^{19} +(-2.17943 + 1.40064i) q^{21} +(-1.35369 - 4.60082i) q^{23} +(-3.42135 + 2.19877i) q^{25} +(2.34292 - 5.13028i) q^{27} +(1.01343 + 2.21909i) q^{29} +(-0.253078 - 1.76020i) q^{31} +(0.501724 - 0.579020i) q^{33} +(-1.42544 - 0.916075i) q^{35} +(-4.58723 - 1.34693i) q^{37} +(3.01908 + 3.48420i) q^{39} +(12.0596 - 3.54102i) q^{41} +(-0.236292 + 1.64344i) q^{43} +0.790946 q^{45} +5.46023 q^{47} +(0.558283 - 3.88295i) q^{49} +(4.75737 - 1.39689i) q^{51} +(-8.08238 - 9.32757i) q^{53} +(0.480798 + 0.141175i) q^{55} +(8.69489 + 5.58786i) q^{57} +(-0.434046 + 0.500915i) q^{59} +(-0.685355 - 4.76675i) q^{61} +(-0.596695 - 1.30658i) q^{63} +(-1.25260 + 2.74282i) q^{65} +(-9.51795 + 6.11682i) q^{67} +(-7.01020 + 1.01188i) q^{69} +(-4.30334 + 2.76559i) q^{71} +(5.40478 - 11.8348i) q^{73} +(2.49515 + 5.46361i) q^{75} +(-0.129507 - 0.900743i) q^{77} +(-9.56521 + 11.0388i) q^{79} +(-4.94068 - 3.17518i) q^{81} +(2.91071 + 0.854661i) q^{83} +(2.12363 + 2.45080i) q^{85} +(3.45697 - 1.01506i) q^{87} +(-1.78337 + 12.4036i) q^{89} +5.47588 q^{91} -2.62633 q^{93} +(-0.962039 + 6.69113i) q^{95} +(-0.645676 + 0.189588i) q^{97} +(0.278175 + 0.321031i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9} - 2 q^{11} + 6 q^{13} - 17 q^{15} - 9 q^{17} - 11 q^{19} - 47 q^{21} - 22 q^{23} - 16 q^{25} - 19 q^{27} - q^{29} - 13 q^{31} - 5 q^{33} + 14 q^{35} + 34 q^{37} + 30 q^{39} + 28 q^{41} + 44 q^{43} + 78 q^{45} + 26 q^{47} + 60 q^{49} + 62 q^{51} + 14 q^{53} + 26 q^{55} + 3 q^{57} - 10 q^{59} - 56 q^{61} - 27 q^{63} - 87 q^{65} - 44 q^{67} - 51 q^{69} - 37 q^{71} - 12 q^{73} - 53 q^{75} - 47 q^{77} - 6 q^{79} - 10 q^{81} - 25 q^{83} + 8 q^{85} + 48 q^{87} + 10 q^{89} + 26 q^{91} - 14 q^{93} + 29 q^{95} - q^{97} - q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/92\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(47\)
\(\chi(n)\) \(e\left(\frac{10}{11}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.210181 1.46184i 0.121348 0.843996i −0.834683 0.550731i \(-0.814349\pi\)
0.956031 0.293265i \(-0.0947418\pi\)
\(4\) 0 0
\(5\) 0.926812 0.272136i 0.414483 0.121703i −0.0678410 0.997696i \(-0.521611\pi\)
0.482324 + 0.875993i \(0.339793\pi\)
\(6\) 0 0
\(7\) −1.14874 1.32572i −0.434183 0.501074i 0.495922 0.868367i \(-0.334830\pi\)
−0.930105 + 0.367293i \(0.880285\pi\)
\(8\) 0 0
\(9\) 0.785668 + 0.230693i 0.261889 + 0.0768977i
\(10\) 0 0
\(11\) 0.436414 + 0.280466i 0.131584 + 0.0845637i 0.604777 0.796395i \(-0.293262\pi\)
−0.473193 + 0.880959i \(0.656899\pi\)
\(12\) 0 0
\(13\) −2.04423 + 2.35917i −0.566968 + 0.654316i −0.964751 0.263163i \(-0.915234\pi\)
0.397783 + 0.917479i \(0.369780\pi\)
\(14\) 0 0
\(15\) −0.203022 1.41205i −0.0524202 0.364590i
\(16\) 0 0
\(17\) 1.39464 + 3.05384i 0.338251 + 0.740666i 0.999959 0.00909607i \(-0.00289541\pi\)
−0.661708 + 0.749762i \(0.730168\pi\)
\(18\) 0 0
\(19\) −2.90720 + 6.36588i −0.666958 + 1.46043i 0.208936 + 0.977929i \(0.433000\pi\)
−0.875894 + 0.482504i \(0.839727\pi\)
\(20\) 0 0
\(21\) −2.17943 + 1.40064i −0.475591 + 0.305644i
\(22\) 0 0
\(23\) −1.35369 4.60082i −0.282264 0.959337i
\(24\) 0 0
\(25\) −3.42135 + 2.19877i −0.684269 + 0.439753i
\(26\) 0 0
\(27\) 2.34292 5.13028i 0.450895 0.987322i
\(28\) 0 0
\(29\) 1.01343 + 2.21909i 0.188188 + 0.412075i 0.980085 0.198581i \(-0.0636332\pi\)
−0.791896 + 0.610656i \(0.790906\pi\)
\(30\) 0 0
\(31\) −0.253078 1.76020i −0.0454542 0.316141i −0.999845 0.0175820i \(-0.994403\pi\)
0.954391 0.298559i \(-0.0965059\pi\)
\(32\) 0 0
\(33\) 0.501724 0.579020i 0.0873389 0.100794i
\(34\) 0 0
\(35\) −1.42544 0.916075i −0.240943 0.154845i
\(36\) 0 0
\(37\) −4.58723 1.34693i −0.754135 0.221434i −0.118002 0.993013i \(-0.537649\pi\)
−0.636133 + 0.771579i \(0.719467\pi\)
\(38\) 0 0
\(39\) 3.01908 + 3.48420i 0.483439 + 0.557919i
\(40\) 0 0
\(41\) 12.0596 3.54102i 1.88339 0.553014i 0.887687 0.460447i \(-0.152311\pi\)
0.995706 0.0925673i \(-0.0295073\pi\)
\(42\) 0 0
\(43\) −0.236292 + 1.64344i −0.0360341 + 0.250623i −0.999874 0.0158584i \(-0.994952\pi\)
0.963840 + 0.266481i \(0.0858610\pi\)
\(44\) 0 0
\(45\) 0.790946 0.117907
\(46\) 0 0
\(47\) 5.46023 0.796456 0.398228 0.917286i \(-0.369625\pi\)
0.398228 + 0.917286i \(0.369625\pi\)
\(48\) 0 0
\(49\) 0.558283 3.88295i 0.0797547 0.554706i
\(50\) 0 0
\(51\) 4.75737 1.39689i 0.666165 0.195604i
\(52\) 0 0
\(53\) −8.08238 9.32757i −1.11020 1.28124i −0.956054 0.293192i \(-0.905282\pi\)
−0.154147 0.988048i \(-0.549263\pi\)
\(54\) 0 0
\(55\) 0.480798 + 0.141175i 0.0648308 + 0.0190361i
\(56\) 0 0
\(57\) 8.69489 + 5.58786i 1.15167 + 0.740131i
\(58\) 0 0
\(59\) −0.434046 + 0.500915i −0.0565079 + 0.0652136i −0.783300 0.621644i \(-0.786465\pi\)
0.726792 + 0.686858i \(0.241010\pi\)
\(60\) 0 0
\(61\) −0.685355 4.76675i −0.0877507 0.610320i −0.985482 0.169777i \(-0.945695\pi\)
0.897732 0.440542i \(-0.145214\pi\)
\(62\) 0 0
\(63\) −0.596695 1.30658i −0.0751765 0.164613i
\(64\) 0 0
\(65\) −1.25260 + 2.74282i −0.155366 + 0.340205i
\(66\) 0 0
\(67\) −9.51795 + 6.11682i −1.16280 + 0.747288i −0.972148 0.234369i \(-0.924698\pi\)
−0.190655 + 0.981657i \(0.561061\pi\)
\(68\) 0 0
\(69\) −7.01020 + 1.01188i −0.843928 + 0.121816i
\(70\) 0 0
\(71\) −4.30334 + 2.76559i −0.510713 + 0.328215i −0.770489 0.637454i \(-0.779988\pi\)
0.259776 + 0.965669i \(0.416351\pi\)
\(72\) 0 0
\(73\) 5.40478 11.8348i 0.632582 1.38516i −0.273424 0.961894i \(-0.588156\pi\)
0.906005 0.423267i \(-0.139117\pi\)
\(74\) 0 0
\(75\) 2.49515 + 5.46361i 0.288115 + 0.630884i
\(76\) 0 0
\(77\) −0.129507 0.900743i −0.0147587 0.102649i
\(78\) 0 0
\(79\) −9.56521 + 11.0388i −1.07617 + 1.24197i −0.107344 + 0.994222i \(0.534235\pi\)
−0.968825 + 0.247744i \(0.920311\pi\)
\(80\) 0 0
\(81\) −4.94068 3.17518i −0.548964 0.352798i
\(82\) 0 0
\(83\) 2.91071 + 0.854661i 0.319492 + 0.0938113i 0.437546 0.899196i \(-0.355848\pi\)
−0.118055 + 0.993007i \(0.537666\pi\)
\(84\) 0 0
\(85\) 2.12363 + 2.45080i 0.230340 + 0.265827i
\(86\) 0 0
\(87\) 3.45697 1.01506i 0.370626 0.108826i
\(88\) 0 0
\(89\) −1.78337 + 12.4036i −0.189036 + 1.31478i 0.645473 + 0.763783i \(0.276660\pi\)
−0.834509 + 0.550994i \(0.814249\pi\)
\(90\) 0 0
\(91\) 5.47588 0.574028
\(92\) 0 0
\(93\) −2.62633 −0.272337
\(94\) 0 0
\(95\) −0.962039 + 6.69113i −0.0987032 + 0.686495i
\(96\) 0 0
\(97\) −0.645676 + 0.189588i −0.0655585 + 0.0192497i −0.314347 0.949308i \(-0.601786\pi\)
0.248789 + 0.968558i \(0.419967\pi\)
\(98\) 0 0
\(99\) 0.278175 + 0.321031i 0.0279576 + 0.0322648i
\(100\) 0 0
\(101\) −14.2284 4.17782i −1.41578 0.415709i −0.517704 0.855560i \(-0.673213\pi\)
−0.898071 + 0.439851i \(0.855031\pi\)
\(102\) 0 0
\(103\) 9.56379 + 6.14627i 0.942348 + 0.605610i 0.919060 0.394119i \(-0.128950\pi\)
0.0232883 + 0.999729i \(0.492586\pi\)
\(104\) 0 0
\(105\) −1.63876 + 1.89123i −0.159927 + 0.184565i
\(106\) 0 0
\(107\) −1.97206 13.7160i −0.190646 1.32597i −0.830303 0.557313i \(-0.811832\pi\)
0.639656 0.768661i \(-0.279077\pi\)
\(108\) 0 0
\(109\) 1.58189 + 3.46385i 0.151517 + 0.331777i 0.970136 0.242560i \(-0.0779872\pi\)
−0.818619 + 0.574337i \(0.805260\pi\)
\(110\) 0 0
\(111\) −2.93315 + 6.42271i −0.278402 + 0.609616i
\(112\) 0 0
\(113\) 9.78498 6.28843i 0.920494 0.591565i 0.00769277 0.999970i \(-0.497551\pi\)
0.912801 + 0.408405i \(0.133915\pi\)
\(114\) 0 0
\(115\) −2.50667 3.89570i −0.233748 0.363276i
\(116\) 0 0
\(117\) −2.15033 + 1.38193i −0.198798 + 0.127760i
\(118\) 0 0
\(119\) 2.44645 5.35697i 0.224265 0.491073i
\(120\) 0 0
\(121\) −4.45777 9.76115i −0.405252 0.887378i
\(122\) 0 0
\(123\) −2.64171 18.3735i −0.238195 1.65668i
\(124\) 0 0
\(125\) −5.73536 + 6.61895i −0.512986 + 0.592017i
\(126\) 0 0
\(127\) 3.16060 + 2.03119i 0.280458 + 0.180239i 0.673306 0.739364i \(-0.264874\pi\)
−0.392848 + 0.919603i \(0.628510\pi\)
\(128\) 0 0
\(129\) 2.35279 + 0.690843i 0.207152 + 0.0608253i
\(130\) 0 0
\(131\) 8.75057 + 10.0987i 0.764541 + 0.882328i 0.995893 0.0905426i \(-0.0288601\pi\)
−0.231351 + 0.972870i \(0.574315\pi\)
\(132\) 0 0
\(133\) 11.7790 3.45862i 1.02137 0.299900i
\(134\) 0 0
\(135\) 0.775309 5.39240i 0.0667280 0.464103i
\(136\) 0 0
\(137\) 0.928329 0.0793125 0.0396563 0.999213i \(-0.487374\pi\)
0.0396563 + 0.999213i \(0.487374\pi\)
\(138\) 0 0
\(139\) 11.2717 0.956053 0.478027 0.878345i \(-0.341352\pi\)
0.478027 + 0.878345i \(0.341352\pi\)
\(140\) 0 0
\(141\) 1.14764 7.98200i 0.0966486 0.672206i
\(142\) 0 0
\(143\) −1.55380 + 0.456236i −0.129935 + 0.0381524i
\(144\) 0 0
\(145\) 1.54315 + 1.78089i 0.128152 + 0.147895i
\(146\) 0 0
\(147\) −5.55892 1.63225i −0.458492 0.134625i
\(148\) 0 0
\(149\) 13.4172 + 8.62268i 1.09918 + 0.706398i 0.958908 0.283716i \(-0.0915672\pi\)
0.140268 + 0.990114i \(0.455204\pi\)
\(150\) 0 0
\(151\) 11.6433 13.4370i 0.947515 1.09349i −0.0479968 0.998847i \(-0.515284\pi\)
0.995511 0.0946426i \(-0.0301708\pi\)
\(152\) 0 0
\(153\) 0.391227 + 2.72104i 0.0316288 + 0.219983i
\(154\) 0 0
\(155\) −0.713570 1.56250i −0.0573153 0.125503i
\(156\) 0 0
\(157\) 2.41260 5.28287i 0.192547 0.421619i −0.788594 0.614915i \(-0.789190\pi\)
0.981140 + 0.193296i \(0.0619178\pi\)
\(158\) 0 0
\(159\) −15.3342 + 9.85470i −1.21608 + 0.781529i
\(160\) 0 0
\(161\) −4.54434 + 7.07975i −0.358144 + 0.557963i
\(162\) 0 0
\(163\) −3.22681 + 2.07375i −0.252744 + 0.162428i −0.660878 0.750493i \(-0.729816\pi\)
0.408134 + 0.912922i \(0.366180\pi\)
\(164\) 0 0
\(165\) 0.307431 0.673180i 0.0239335 0.0524070i
\(166\) 0 0
\(167\) −6.00365 13.1462i −0.464577 1.01728i −0.986420 0.164240i \(-0.947483\pi\)
0.521844 0.853041i \(-0.325244\pi\)
\(168\) 0 0
\(169\) 0.463296 + 3.22229i 0.0356382 + 0.247869i
\(170\) 0 0
\(171\) −3.75266 + 4.33080i −0.286973 + 0.331185i
\(172\) 0 0
\(173\) 12.0019 + 7.71317i 0.912490 + 0.586422i 0.910470 0.413576i \(-0.135720\pi\)
0.00202060 + 0.999998i \(0.499357\pi\)
\(174\) 0 0
\(175\) 6.84517 + 2.00992i 0.517447 + 0.151936i
\(176\) 0 0
\(177\) 0.641032 + 0.739790i 0.0481829 + 0.0556060i
\(178\) 0 0
\(179\) −15.0136 + 4.40840i −1.12217 + 0.329499i −0.789626 0.613589i \(-0.789725\pi\)
−0.332544 + 0.943088i \(0.607907\pi\)
\(180\) 0 0
\(181\) 0.601363 4.18257i 0.0446990 0.310888i −0.955190 0.295993i \(-0.904349\pi\)
0.999889 0.0148951i \(-0.00474144\pi\)
\(182\) 0 0
\(183\) −7.11229 −0.525756
\(184\) 0 0
\(185\) −4.61804 −0.339525
\(186\) 0 0
\(187\) −0.247858 + 1.72389i −0.0181252 + 0.126063i
\(188\) 0 0
\(189\) −9.49270 + 2.78731i −0.690492 + 0.202747i
\(190\) 0 0
\(191\) −9.42330 10.8751i −0.681846 0.786892i 0.304335 0.952565i \(-0.401566\pi\)
−0.986181 + 0.165673i \(0.947020\pi\)
\(192\) 0 0
\(193\) −8.89288 2.61118i −0.640123 0.187957i −0.0544655 0.998516i \(-0.517346\pi\)
−0.585658 + 0.810559i \(0.699164\pi\)
\(194\) 0 0
\(195\) 3.74630 + 2.40760i 0.268278 + 0.172412i
\(196\) 0 0
\(197\) −13.9825 + 16.1367i −0.996215 + 1.14969i −0.00748628 + 0.999972i \(0.502383\pi\)
−0.988728 + 0.149721i \(0.952162\pi\)
\(198\) 0 0
\(199\) 0.0166440 + 0.115762i 0.00117986 + 0.00820612i 0.990403 0.138211i \(-0.0441351\pi\)
−0.989223 + 0.146417i \(0.953226\pi\)
\(200\) 0 0
\(201\) 6.94133 + 15.1994i 0.489604 + 1.07208i
\(202\) 0 0
\(203\) 1.77772 3.89267i 0.124772 0.273212i
\(204\) 0 0
\(205\) 10.2133 6.56372i 0.713331 0.458430i
\(206\) 0 0
\(207\) −0.00217724 3.92700i −0.000151329 0.272946i
\(208\) 0 0
\(209\) −3.05416 + 1.96279i −0.211260 + 0.135769i
\(210\) 0 0
\(211\) −2.51034 + 5.49689i −0.172819 + 0.378421i −0.976145 0.217118i \(-0.930334\pi\)
0.803326 + 0.595539i \(0.203062\pi\)
\(212\) 0 0
\(213\) 3.13838 + 6.87209i 0.215038 + 0.470868i
\(214\) 0 0
\(215\) 0.228243 + 1.58747i 0.0155661 + 0.108264i
\(216\) 0 0
\(217\) −2.04280 + 2.35752i −0.138674 + 0.160039i
\(218\) 0 0
\(219\) −16.1647 10.3884i −1.09231 0.701983i
\(220\) 0 0
\(221\) −10.0555 2.95256i −0.676407 0.198611i
\(222\) 0 0
\(223\) 7.73402 + 8.92553i 0.517908 + 0.597698i 0.953106 0.302637i \(-0.0978670\pi\)
−0.435198 + 0.900335i \(0.643322\pi\)
\(224\) 0 0
\(225\) −3.19528 + 0.938220i −0.213019 + 0.0625480i
\(226\) 0 0
\(227\) −1.25236 + 8.71033i −0.0831219 + 0.578125i 0.905112 + 0.425174i \(0.139787\pi\)
−0.988234 + 0.152952i \(0.951122\pi\)
\(228\) 0 0
\(229\) 22.9248 1.51492 0.757458 0.652884i \(-0.226441\pi\)
0.757458 + 0.652884i \(0.226441\pi\)
\(230\) 0 0
\(231\) −1.34397 −0.0884265
\(232\) 0 0
\(233\) −0.909316 + 6.32443i −0.0595713 + 0.414327i 0.938114 + 0.346327i \(0.112571\pi\)
−0.997685 + 0.0680007i \(0.978338\pi\)
\(234\) 0 0
\(235\) 5.06060 1.48593i 0.330117 0.0969312i
\(236\) 0 0
\(237\) 14.1266 + 16.3030i 0.917623 + 1.05899i
\(238\) 0 0
\(239\) 11.3585 + 3.33516i 0.734720 + 0.215733i 0.627625 0.778516i \(-0.284027\pi\)
0.107095 + 0.994249i \(0.465845\pi\)
\(240\) 0 0
\(241\) −13.6815 8.79254i −0.881300 0.566377i 0.0198895 0.999802i \(-0.493669\pi\)
−0.901190 + 0.433425i \(0.857305\pi\)
\(242\) 0 0
\(243\) 5.40009 6.23203i 0.346416 0.399785i
\(244\) 0 0
\(245\) −0.539268 3.75069i −0.0344525 0.239623i
\(246\) 0 0
\(247\) −9.07521 19.8719i −0.577442 1.26442i
\(248\) 0 0
\(249\) 1.86116 4.07537i 0.117946 0.258266i
\(250\) 0 0
\(251\) 2.38953 1.53565i 0.150826 0.0969297i −0.463051 0.886331i \(-0.653245\pi\)
0.613877 + 0.789402i \(0.289609\pi\)
\(252\) 0 0
\(253\) 0.699603 2.38752i 0.0439837 0.150102i
\(254\) 0 0
\(255\) 4.02904 2.58931i 0.252308 0.162149i
\(256\) 0 0
\(257\) 3.00213 6.57375i 0.187268 0.410060i −0.792590 0.609755i \(-0.791268\pi\)
0.979858 + 0.199695i \(0.0639952\pi\)
\(258\) 0 0
\(259\) 3.48388 + 7.62863i 0.216478 + 0.474020i
\(260\) 0 0
\(261\) 0.284287 + 1.97726i 0.0175969 + 0.122389i
\(262\) 0 0
\(263\) 16.4597 18.9955i 1.01495 1.17131i 0.0298105 0.999556i \(-0.490510\pi\)
0.985139 0.171759i \(-0.0549449\pi\)
\(264\) 0 0
\(265\) −10.0292 6.44539i −0.616090 0.395937i
\(266\) 0 0
\(267\) 17.7573 + 5.21400i 1.08673 + 0.319092i
\(268\) 0 0
\(269\) −14.8108 17.0926i −0.903031 1.04215i −0.998906 0.0467599i \(-0.985110\pi\)
0.0958752 0.995393i \(-0.469435\pi\)
\(270\) 0 0
\(271\) −0.834682 + 0.245085i −0.0507033 + 0.0148878i −0.306986 0.951714i \(-0.599320\pi\)
0.256283 + 0.966602i \(0.417502\pi\)
\(272\) 0 0
\(273\) 1.15093 8.00488i 0.0696573 0.484477i
\(274\) 0 0
\(275\) −2.10980 −0.127226
\(276\) 0 0
\(277\) 2.07085 0.124426 0.0622128 0.998063i \(-0.480184\pi\)
0.0622128 + 0.998063i \(0.480184\pi\)
\(278\) 0 0
\(279\) 0.207230 1.44131i 0.0124065 0.0862893i
\(280\) 0 0
\(281\) 1.62178 0.476198i 0.0967474 0.0284076i −0.233001 0.972477i \(-0.574854\pi\)
0.329748 + 0.944069i \(0.393036\pi\)
\(282\) 0 0
\(283\) −1.55734 1.79727i −0.0925743 0.106836i 0.707572 0.706641i \(-0.249790\pi\)
−0.800147 + 0.599805i \(0.795245\pi\)
\(284\) 0 0
\(285\) 9.57918 + 2.81270i 0.567422 + 0.166610i
\(286\) 0 0
\(287\) −18.5477 11.9199i −1.09484 0.703610i
\(288\) 0 0
\(289\) 3.75171 4.32970i 0.220689 0.254688i
\(290\) 0 0
\(291\) 0.141438 + 0.983726i 0.00829127 + 0.0576670i
\(292\) 0 0
\(293\) 3.58917 + 7.85918i 0.209681 + 0.459138i 0.985027 0.172399i \(-0.0551518\pi\)
−0.775346 + 0.631537i \(0.782424\pi\)
\(294\) 0 0
\(295\) −0.265961 + 0.582374i −0.0154849 + 0.0339071i
\(296\) 0 0
\(297\) 2.46135 1.58181i 0.142822 0.0917862i
\(298\) 0 0
\(299\) 13.6214 + 6.21155i 0.787744 + 0.359223i
\(300\) 0 0
\(301\) 2.45018 1.57463i 0.141226 0.0907603i
\(302\) 0 0
\(303\) −9.09786 + 19.9215i −0.522659 + 1.14446i
\(304\) 0 0
\(305\) −1.93240 4.23137i −0.110649 0.242287i
\(306\) 0 0
\(307\) 2.60364 + 18.1087i 0.148598 + 1.03352i 0.918518 + 0.395380i \(0.129387\pi\)
−0.769920 + 0.638141i \(0.779704\pi\)
\(308\) 0 0
\(309\) 10.9950 12.6889i 0.625485 0.721848i
\(310\) 0 0
\(311\) 25.2335 + 16.2166i 1.43086 + 0.919559i 0.999852 + 0.0172116i \(0.00547889\pi\)
0.431010 + 0.902347i \(0.358157\pi\)
\(312\) 0 0
\(313\) −18.5863 5.45743i −1.05056 0.308472i −0.289516 0.957173i \(-0.593494\pi\)
−0.761044 + 0.648701i \(0.775313\pi\)
\(314\) 0 0
\(315\) −0.908591 1.04857i −0.0511933 0.0590802i
\(316\) 0 0
\(317\) 14.7242 4.32340i 0.826991 0.242826i 0.159267 0.987236i \(-0.449087\pi\)
0.667724 + 0.744409i \(0.267269\pi\)
\(318\) 0 0
\(319\) −0.180107 + 1.25267i −0.0100841 + 0.0701363i
\(320\) 0 0
\(321\) −20.4651 −1.14225
\(322\) 0 0
\(323\) −23.4949 −1.30729
\(324\) 0 0
\(325\) 1.80676 12.5663i 0.100221 0.697054i
\(326\) 0 0
\(327\) 5.39609 1.58443i 0.298404 0.0876195i
\(328\) 0 0
\(329\) −6.27238 7.23871i −0.345808 0.399083i
\(330\) 0 0
\(331\) 26.9815 + 7.92249i 1.48304 + 0.435460i 0.920313 0.391183i \(-0.127934\pi\)
0.562727 + 0.826643i \(0.309752\pi\)
\(332\) 0 0
\(333\) −3.29331 2.11648i −0.180472 0.115982i
\(334\) 0 0
\(335\) −7.15674 + 8.25932i −0.391015 + 0.451255i
\(336\) 0 0
\(337\) 4.16083 + 28.9392i 0.226655 + 1.57642i 0.712052 + 0.702126i \(0.247766\pi\)
−0.485397 + 0.874294i \(0.661325\pi\)
\(338\) 0 0
\(339\) −7.13607 15.6258i −0.387578 0.848678i
\(340\) 0 0
\(341\) 0.383229 0.839154i 0.0207530 0.0454428i
\(342\) 0 0
\(343\) −16.1189 + 10.3590i −0.870341 + 0.559334i
\(344\) 0 0
\(345\) −6.22176 + 2.84555i −0.334968 + 0.153199i
\(346\) 0 0
\(347\) 10.3618 6.65914i 0.556252 0.357481i −0.232113 0.972689i \(-0.574564\pi\)
0.788365 + 0.615207i \(0.210928\pi\)
\(348\) 0 0
\(349\) −5.11275 + 11.1954i −0.273679 + 0.599274i −0.995704 0.0925935i \(-0.970484\pi\)
0.722025 + 0.691867i \(0.243212\pi\)
\(350\) 0 0
\(351\) 7.31373 + 16.0148i 0.390378 + 0.854808i
\(352\) 0 0
\(353\) 2.88626 + 20.0744i 0.153620 + 1.06845i 0.910086 + 0.414419i \(0.136015\pi\)
−0.756466 + 0.654033i \(0.773076\pi\)
\(354\) 0 0
\(355\) −3.23577 + 3.73428i −0.171737 + 0.198195i
\(356\) 0 0
\(357\) −7.31686 4.70226i −0.387249 0.248870i
\(358\) 0 0
\(359\) −7.86829 2.31034i −0.415273 0.121935i 0.0674204 0.997725i \(-0.478523\pi\)
−0.482693 + 0.875790i \(0.660341\pi\)
\(360\) 0 0
\(361\) −19.6303 22.6546i −1.03317 1.19235i
\(362\) 0 0
\(363\) −15.2062 + 4.46495i −0.798120 + 0.234349i
\(364\) 0 0
\(365\) 1.78853 12.4395i 0.0936158 0.651112i
\(366\) 0 0
\(367\) −26.6065 −1.38885 −0.694425 0.719565i \(-0.744341\pi\)
−0.694425 + 0.719565i \(0.744341\pi\)
\(368\) 0 0
\(369\) 10.2917 0.535766
\(370\) 0 0
\(371\) −3.08115 + 21.4299i −0.159966 + 1.11258i
\(372\) 0 0
\(373\) −19.3035 + 5.66802i −0.999498 + 0.293479i −0.740250 0.672332i \(-0.765293\pi\)
−0.259248 + 0.965811i \(0.583475\pi\)
\(374\) 0 0
\(375\) 8.47041 + 9.77538i 0.437410 + 0.504798i
\(376\) 0 0
\(377\) −7.30689 2.14550i −0.376324 0.110499i
\(378\) 0 0
\(379\) −28.4289 18.2701i −1.46029 0.938474i −0.998678 0.0513937i \(-0.983634\pi\)
−0.461615 0.887080i \(-0.652730\pi\)
\(380\) 0 0
\(381\) 3.63358 4.19338i 0.186154 0.214833i
\(382\) 0 0
\(383\) 3.60713 + 25.0882i 0.184316 + 1.28195i 0.846413 + 0.532527i \(0.178758\pi\)
−0.662097 + 0.749418i \(0.730333\pi\)
\(384\) 0 0
\(385\) −0.365154 0.799576i −0.0186100 0.0407501i
\(386\) 0 0
\(387\) −0.564778 + 1.23669i −0.0287093 + 0.0628645i
\(388\) 0 0
\(389\) 29.2499 18.7977i 1.48303 0.953083i 0.486170 0.873865i \(-0.338394\pi\)
0.996857 0.0792189i \(-0.0252426\pi\)
\(390\) 0 0
\(391\) 12.1623 10.5505i 0.615071 0.533560i
\(392\) 0 0
\(393\) 16.6019 10.6694i 0.837457 0.538201i
\(394\) 0 0
\(395\) −5.86108 + 12.8340i −0.294903 + 0.645747i
\(396\) 0 0
\(397\) 8.60673 + 18.8461i 0.431960 + 0.945860i 0.993005 + 0.118074i \(0.0376721\pi\)
−0.561045 + 0.827785i \(0.689601\pi\)
\(398\) 0 0
\(399\) −2.58024 17.9460i −0.129173 0.898421i
\(400\) 0 0
\(401\) 10.3045 11.8921i 0.514584 0.593862i −0.437682 0.899130i \(-0.644201\pi\)
0.952266 + 0.305268i \(0.0987460\pi\)
\(402\) 0 0
\(403\) 4.66996 + 3.00120i 0.232627 + 0.149500i
\(404\) 0 0
\(405\) −5.44316 1.59826i −0.270473 0.0794180i
\(406\) 0 0
\(407\) −1.62416 1.87438i −0.0805066 0.0929096i
\(408\) 0 0
\(409\) −33.6390 + 9.87730i −1.66334 + 0.488401i −0.972167 0.234288i \(-0.924724\pi\)
−0.691173 + 0.722689i \(0.742906\pi\)
\(410\) 0 0
\(411\) 0.195117 1.35707i 0.00962444 0.0669394i
\(412\) 0 0
\(413\) 1.16268 0.0572116
\(414\) 0 0
\(415\) 2.93026 0.143841
\(416\) 0 0
\(417\) 2.36910 16.4775i 0.116015 0.806905i
\(418\) 0 0
\(419\) 37.4554 10.9979i 1.82982 0.537282i 0.830025 0.557727i \(-0.188326\pi\)
0.999791 + 0.0204444i \(0.00650811\pi\)
\(420\) 0 0
\(421\) 22.9972 + 26.5402i 1.12082 + 1.29349i 0.951404 + 0.307944i \(0.0996410\pi\)
0.169411 + 0.985546i \(0.445814\pi\)
\(422\) 0 0
\(423\) 4.28993 + 1.25964i 0.208583 + 0.0612456i
\(424\) 0 0
\(425\) −11.4862 7.38176i −0.557164 0.358068i
\(426\) 0 0
\(427\) −5.53206 + 6.38434i −0.267715 + 0.308960i
\(428\) 0 0
\(429\) 0.340367 + 2.36730i 0.0164331 + 0.114294i
\(430\) 0 0
\(431\) 4.54066 + 9.94266i 0.218716 + 0.478921i 0.986905 0.161302i \(-0.0515693\pi\)
−0.768189 + 0.640223i \(0.778842\pi\)
\(432\) 0 0
\(433\) −4.11321 + 9.00667i −0.197668 + 0.432833i −0.982347 0.187070i \(-0.940101\pi\)
0.784678 + 0.619903i \(0.212828\pi\)
\(434\) 0 0
\(435\) 2.92772 1.88153i 0.140374 0.0902127i
\(436\) 0 0
\(437\) 33.2237 + 4.75805i 1.58931 + 0.227608i
\(438\) 0 0
\(439\) 12.1438 7.80436i 0.579593 0.372482i −0.217753 0.976004i \(-0.569873\pi\)
0.797346 + 0.603522i \(0.206236\pi\)
\(440\) 0 0
\(441\) 1.33439 2.92191i 0.0635425 0.139139i
\(442\) 0 0
\(443\) −10.0060 21.9102i −0.475401 1.04098i −0.983702 0.179804i \(-0.942454\pi\)
0.508301 0.861179i \(-0.330274\pi\)
\(444\) 0 0
\(445\) 1.72262 + 11.9811i 0.0816601 + 0.567959i
\(446\) 0 0
\(447\) 15.4251 17.8015i 0.729580 0.841980i
\(448\) 0 0
\(449\) −4.17750 2.68471i −0.197148 0.126700i 0.438342 0.898808i \(-0.355566\pi\)
−0.635491 + 0.772109i \(0.719202\pi\)
\(450\) 0 0
\(451\) 6.25611 + 1.83696i 0.294589 + 0.0864991i
\(452\) 0 0
\(453\) −17.1956 19.8448i −0.807922 0.932392i
\(454\) 0 0
\(455\) 5.07511 1.49019i 0.237925 0.0698610i
\(456\) 0 0
\(457\) 2.49898 17.3808i 0.116897 0.813040i −0.844041 0.536278i \(-0.819830\pi\)
0.960939 0.276761i \(-0.0892612\pi\)
\(458\) 0 0
\(459\) 18.9346 0.883791
\(460\) 0 0
\(461\) −26.5086 −1.23463 −0.617313 0.786717i \(-0.711779\pi\)
−0.617313 + 0.786717i \(0.711779\pi\)
\(462\) 0 0
\(463\) −3.32533 + 23.1282i −0.154541 + 1.07486i 0.753944 + 0.656939i \(0.228149\pi\)
−0.908485 + 0.417918i \(0.862760\pi\)
\(464\) 0 0
\(465\) −2.43411 + 0.714719i −0.112879 + 0.0331443i
\(466\) 0 0
\(467\) −12.8583 14.8393i −0.595013 0.686682i 0.375750 0.926721i \(-0.377385\pi\)
−0.970763 + 0.240039i \(0.922840\pi\)
\(468\) 0 0
\(469\) 19.0428 + 5.59147i 0.879315 + 0.258190i
\(470\) 0 0
\(471\) −7.21564 4.63721i −0.332479 0.213671i
\(472\) 0 0
\(473\) −0.564051 + 0.650950i −0.0259351 + 0.0299307i
\(474\) 0 0
\(475\) −4.05054 28.1721i −0.185852 1.29263i
\(476\) 0 0
\(477\) −4.19827 9.19292i −0.192225 0.420915i
\(478\) 0 0
\(479\) 9.42917 20.6470i 0.430830 0.943386i −0.562362 0.826891i \(-0.690107\pi\)
0.993191 0.116494i \(-0.0371656\pi\)
\(480\) 0 0
\(481\) 12.5550 8.06861i 0.572459 0.367897i
\(482\) 0 0
\(483\) 9.39436 + 8.13114i 0.427458 + 0.369980i
\(484\) 0 0
\(485\) −0.546827 + 0.351424i −0.0248301 + 0.0159573i
\(486\) 0 0
\(487\) −5.54926 + 12.1512i −0.251461 + 0.550623i −0.992699 0.120620i \(-0.961512\pi\)
0.741238 + 0.671243i \(0.234239\pi\)
\(488\) 0 0
\(489\) 2.35328 + 5.15296i 0.106419 + 0.233025i
\(490\) 0 0
\(491\) 0.207720 + 1.44472i 0.00937426 + 0.0651994i 0.993972 0.109638i \(-0.0349691\pi\)
−0.984597 + 0.174837i \(0.944060\pi\)
\(492\) 0 0
\(493\) −5.36339 + 6.18968i −0.241555 + 0.278769i
\(494\) 0 0
\(495\) 0.345180 + 0.221834i 0.0155147 + 0.00997068i
\(496\) 0 0
\(497\) 8.60980 + 2.52807i 0.386202 + 0.113399i
\(498\) 0 0
\(499\) −12.7402 14.7029i −0.570328 0.658194i 0.395169 0.918609i \(-0.370686\pi\)
−0.965497 + 0.260415i \(0.916141\pi\)
\(500\) 0 0
\(501\) −20.4795 + 6.01332i −0.914957 + 0.268656i
\(502\) 0 0
\(503\) −0.875808 + 6.09138i −0.0390503 + 0.271601i −0.999987 0.00516853i \(-0.998355\pi\)
0.960936 + 0.276770i \(0.0892639\pi\)
\(504\) 0 0
\(505\) −14.3240 −0.637408
\(506\) 0 0
\(507\) 4.80787 0.213525
\(508\) 0 0
\(509\) 2.75237 19.1431i 0.121996 0.848504i −0.833293 0.552832i \(-0.813547\pi\)
0.955289 0.295672i \(-0.0955437\pi\)
\(510\) 0 0
\(511\) −21.8983 + 6.42992i −0.968723 + 0.284443i
\(512\) 0 0
\(513\) 25.8474 + 29.8295i 1.14119 + 1.31700i
\(514\) 0 0
\(515\) 10.5365 + 3.09378i 0.464292 + 0.136328i
\(516\) 0 0
\(517\) 2.38292 + 1.53141i 0.104801 + 0.0673513i
\(518\) 0 0
\(519\) 13.7980 15.9238i 0.605667 0.698977i
\(520\) 0 0
\(521\) 3.00225 + 20.8811i 0.131531 + 0.914817i 0.943560 + 0.331201i \(0.107454\pi\)
−0.812030 + 0.583616i \(0.801637\pi\)
\(522\) 0 0
\(523\) −2.84292 6.22513i −0.124312 0.272206i 0.837236 0.546842i \(-0.184170\pi\)
−0.961548 + 0.274636i \(0.911443\pi\)
\(524\) 0 0
\(525\) 4.37692 9.58413i 0.191025 0.418286i
\(526\) 0 0
\(527\) 5.02241 3.22771i 0.218780 0.140601i
\(528\) 0 0
\(529\) −19.3350 + 12.4562i −0.840654 + 0.541573i
\(530\) 0 0
\(531\) −0.456573 + 0.293422i −0.0198136 + 0.0127334i
\(532\) 0 0
\(533\) −16.2988 + 35.6893i −0.705978 + 1.54588i
\(534\) 0 0
\(535\) −5.56035 12.1755i −0.240395 0.526391i
\(536\) 0 0
\(537\) 3.28880 + 22.8741i 0.141922 + 0.987091i
\(538\) 0 0
\(539\) 1.33268 1.53799i 0.0574025 0.0662460i
\(540\) 0 0
\(541\) 12.5393 + 8.05852i 0.539107 + 0.346463i 0.781689 0.623668i \(-0.214358\pi\)
−0.242583 + 0.970131i \(0.577995\pi\)
\(542\) 0 0
\(543\) −5.98787 1.75820i −0.256964 0.0754515i
\(544\) 0 0
\(545\) 2.40875 + 2.77985i 0.103180 + 0.119076i
\(546\) 0 0
\(547\) −35.8353 + 10.5222i −1.53221 + 0.449897i −0.935725 0.352729i \(-0.885254\pi\)
−0.596483 + 0.802626i \(0.703436\pi\)
\(548\) 0 0
\(549\) 0.561194 3.90319i 0.0239512 0.166584i
\(550\) 0 0
\(551\) −17.0727 −0.727322
\(552\) 0 0
\(553\) 25.6223 1.08957
\(554\) 0 0
\(555\) −0.970627 + 6.75086i −0.0412008 + 0.286558i
\(556\) 0 0
\(557\) −18.8763 + 5.54258i −0.799815 + 0.234847i −0.656003 0.754758i \(-0.727754\pi\)
−0.143812 + 0.989605i \(0.545936\pi\)
\(558\) 0 0
\(559\) −3.39413 3.91703i −0.143556 0.165673i
\(560\) 0 0
\(561\) 2.46796 + 0.724659i 0.104197 + 0.0305951i
\(562\) 0 0
\(563\) −16.1788 10.3975i −0.681857 0.438203i 0.153325 0.988176i \(-0.451002\pi\)
−0.835183 + 0.549973i \(0.814638\pi\)
\(564\) 0 0
\(565\) 7.35752 8.49104i 0.309533 0.357221i
\(566\) 0 0
\(567\) 1.46616 + 10.1974i 0.0615731 + 0.428250i
\(568\) 0 0
\(569\) 7.42264 + 16.2533i 0.311173 + 0.681374i 0.999010 0.0444912i \(-0.0141667\pi\)
−0.687837 + 0.725866i \(0.741439\pi\)
\(570\) 0 0
\(571\) 6.13161 13.4264i 0.256600 0.561876i −0.736861 0.676044i \(-0.763693\pi\)
0.993461 + 0.114168i \(0.0364203\pi\)
\(572\) 0 0
\(573\) −17.8782 + 11.4897i −0.746874 + 0.479987i
\(574\) 0 0
\(575\) 14.7476 + 12.7645i 0.615016 + 0.532318i
\(576\) 0 0
\(577\) −15.5628 + 10.0016i −0.647888 + 0.416372i −0.822894 0.568195i \(-0.807642\pi\)
0.175006 + 0.984567i \(0.444005\pi\)
\(578\) 0 0
\(579\) −5.68626 + 12.4512i −0.236313 + 0.517453i
\(580\) 0 0
\(581\) −2.21061 4.84056i −0.0917115 0.200820i
\(582\) 0 0
\(583\) −0.911197 6.33751i −0.0377379 0.262473i
\(584\) 0 0
\(585\) −1.61688 + 1.86598i −0.0668497 + 0.0771486i
\(586\) 0 0
\(587\) −4.18945 2.69240i −0.172917 0.111127i 0.451319 0.892362i \(-0.350954\pi\)
−0.624237 + 0.781235i \(0.714590\pi\)
\(588\) 0 0
\(589\) 11.9410 + 3.50618i 0.492019 + 0.144470i
\(590\) 0 0
\(591\) 20.6505 + 23.8319i 0.849447 + 0.980314i
\(592\) 0 0
\(593\) 20.9865 6.16220i 0.861813 0.253051i 0.179183 0.983816i \(-0.442654\pi\)
0.682630 + 0.730765i \(0.260836\pi\)
\(594\) 0 0
\(595\) 0.809568 5.63067i 0.0331891 0.230835i
\(596\) 0 0
\(597\) 0.172724 0.00706911
\(598\) 0 0
\(599\) −44.8557 −1.83275 −0.916377 0.400316i \(-0.868900\pi\)
−0.916377 + 0.400316i \(0.868900\pi\)
\(600\) 0 0
\(601\) −0.0139146 + 0.0967780i −0.000567587 + 0.00394766i −0.990103 0.140341i \(-0.955180\pi\)
0.989536 + 0.144288i \(0.0460893\pi\)
\(602\) 0 0
\(603\) −8.88906 + 2.61006i −0.361990 + 0.106290i
\(604\) 0 0
\(605\) −6.78788 7.83363i −0.275966 0.318482i
\(606\) 0 0
\(607\) −34.6159 10.1642i −1.40502 0.412550i −0.510614 0.859810i \(-0.670582\pi\)
−0.894404 + 0.447260i \(0.852400\pi\)
\(608\) 0 0
\(609\) −5.31683 3.41692i −0.215449 0.138461i
\(610\) 0 0
\(611\) −11.1620 + 12.8816i −0.451565 + 0.521134i
\(612\) 0 0
\(613\) 4.27965 + 29.7656i 0.172853 + 1.20222i 0.872818 + 0.488045i \(0.162290\pi\)
−0.699965 + 0.714177i \(0.746801\pi\)
\(614\) 0 0
\(615\) −7.44847 16.3099i −0.300351 0.657678i
\(616\) 0 0
\(617\) 20.1029 44.0193i 0.809314 1.77215i 0.198984 0.980003i \(-0.436236\pi\)
0.610330 0.792147i \(-0.291037\pi\)
\(618\) 0 0
\(619\) 20.1459 12.9470i 0.809733 0.520384i −0.0690459 0.997613i \(-0.521995\pi\)
0.878778 + 0.477230i \(0.158359\pi\)
\(620\) 0 0
\(621\) −26.7751 3.83452i −1.07445 0.153874i
\(622\) 0 0
\(623\) 18.4922 11.8842i 0.740876 0.476132i
\(624\) 0 0
\(625\) 4.93305 10.8019i 0.197322 0.432075i
\(626\) 0 0
\(627\) 2.22736 + 4.87724i 0.0889523 + 0.194778i
\(628\) 0 0
\(629\) −2.28423 15.8872i −0.0910781 0.633462i
\(630\) 0 0
\(631\) 20.2589 23.3800i 0.806495 0.930745i −0.192224 0.981351i \(-0.561570\pi\)
0.998719 + 0.0506061i \(0.0161153\pi\)
\(632\) 0 0
\(633\) 7.50796 + 4.82507i 0.298415 + 0.191779i
\(634\) 0 0
\(635\) 3.48204 + 1.02242i 0.138180 + 0.0405735i
\(636\) 0 0
\(637\) 8.01927 + 9.25473i 0.317735 + 0.366686i
\(638\) 0 0
\(639\) −4.01900 + 1.18008i −0.158989 + 0.0466834i
\(640\) 0 0
\(641\) −1.56606 + 10.8922i −0.0618558 + 0.430217i 0.935237 + 0.354022i \(0.115186\pi\)
−0.997093 + 0.0761947i \(0.975723\pi\)
\(642\) 0 0
\(643\) 28.9985 1.14359 0.571794 0.820397i \(-0.306248\pi\)
0.571794 + 0.820397i \(0.306248\pi\)
\(644\) 0 0
\(645\) 2.36860 0.0932635
\(646\) 0 0
\(647\) −5.55195 + 38.6146i −0.218270 + 1.51810i 0.526154 + 0.850390i \(0.323634\pi\)
−0.744423 + 0.667708i \(0.767275\pi\)
\(648\) 0 0
\(649\) −0.329913 + 0.0968713i −0.0129502 + 0.00380253i
\(650\) 0 0
\(651\) 3.01697 + 3.48176i 0.118244 + 0.136461i
\(652\) 0 0
\(653\) −20.2959 5.95942i −0.794240 0.233210i −0.140651 0.990059i \(-0.544920\pi\)
−0.653589 + 0.756849i \(0.726738\pi\)
\(654\) 0 0
\(655\) 10.8584 + 6.97824i 0.424271 + 0.272663i
\(656\) 0 0
\(657\) 6.97657 8.05139i 0.272182 0.314115i
\(658\) 0 0
\(659\) −3.70420 25.7633i −0.144295 1.00360i −0.925345 0.379127i \(-0.876225\pi\)
0.781050 0.624469i \(-0.214685\pi\)
\(660\) 0 0
\(661\) −14.9423 32.7190i −0.581187 1.27262i −0.940623 0.339452i \(-0.889758\pi\)
0.359437 0.933169i \(-0.382969\pi\)
\(662\) 0 0
\(663\) −6.42967 + 14.0790i −0.249708 + 0.546783i
\(664\) 0 0
\(665\) 9.97567 6.41097i 0.386840 0.248607i
\(666\) 0 0
\(667\) 8.83777 7.66655i 0.342200 0.296850i
\(668\) 0 0
\(669\) 14.6733 9.42995i 0.567302 0.364583i
\(670\) 0 0
\(671\) 1.03781 2.27249i 0.0400643 0.0877286i
\(672\) 0 0
\(673\) −4.84641 10.6122i −0.186815 0.409068i 0.792931 0.609311i \(-0.208554\pi\)
−0.979746 + 0.200243i \(0.935827\pi\)
\(674\) 0 0
\(675\) 3.26434 + 22.7040i 0.125645 + 0.873877i
\(676\) 0 0
\(677\) −5.15162 + 5.94529i −0.197993 + 0.228496i −0.846061 0.533087i \(-0.821032\pi\)
0.648068 + 0.761583i \(0.275577\pi\)
\(678\) 0 0
\(679\) 0.993053 + 0.638197i 0.0381099 + 0.0244917i
\(680\) 0 0
\(681\) 12.4699 + 3.66150i 0.477849 + 0.140309i
\(682\) 0 0
\(683\) 13.7880 + 15.9122i 0.527583 + 0.608863i 0.955513 0.294949i \(-0.0953026\pi\)
−0.427930 + 0.903812i \(0.640757\pi\)
\(684\) 0 0
\(685\) 0.860386 0.252632i 0.0328737 0.00965258i
\(686\) 0 0
\(687\) 4.81838 33.5125i 0.183833 1.27858i
\(688\) 0 0
\(689\) 38.5276 1.46778
\(690\) 0 0
\(691\) −5.33705 −0.203031 −0.101516 0.994834i \(-0.532369\pi\)
−0.101516 + 0.994834i \(0.532369\pi\)
\(692\) 0 0
\(693\) 0.106045 0.737562i 0.00402833 0.0280176i
\(694\) 0 0
\(695\) 10.4467 3.06744i 0.396268 0.116355i
\(696\) 0 0
\(697\) 27.6326 + 31.8897i 1.04666 + 1.20791i
\(698\) 0 0
\(699\) 9.05421 + 2.65856i 0.342462 + 0.100556i
\(700\) 0 0
\(701\) 4.41204 + 2.83545i 0.166640 + 0.107093i 0.621303 0.783571i \(-0.286604\pi\)
−0.454662 + 0.890664i \(0.650240\pi\)
\(702\) 0 0
\(703\) 21.9104 25.2859i 0.826366 0.953677i
\(704\) 0 0
\(705\) −1.10855 7.71013i −0.0417504 0.290380i
\(706\) 0 0
\(707\) 10.8061 + 23.6620i 0.406404 + 0.889901i
\(708\) 0 0
\(709\) −0.665926 + 1.45817i −0.0250094 + 0.0547629i −0.921724 0.387845i \(-0.873219\pi\)
0.896715 + 0.442608i \(0.145947\pi\)
\(710\) 0 0
\(711\) −10.0617 + 6.46624i −0.377342 + 0.242503i
\(712\) 0 0
\(713\) −7.75576 + 3.54713i −0.290455 + 0.132841i
\(714\) 0 0
\(715\) −1.31592 + 0.845690i −0.0492126 + 0.0316270i
\(716\) 0 0
\(717\) 7.26282 15.9034i 0.271235 0.593922i
\(718\) 0 0
\(719\) −16.8993 37.0043i −0.630238 1.38003i −0.907833 0.419331i \(-0.862265\pi\)
0.277595 0.960698i \(-0.410463\pi\)
\(720\) 0 0
\(721\) −2.83809 19.7393i −0.105696 0.735131i
\(722\) 0 0
\(723\) −15.7289 + 18.1521i −0.584964 + 0.675085i
\(724\) 0 0
\(725\) −8.34654 5.36400i −0.309983 0.199214i
\(726\) 0 0
\(727\) 28.8374 + 8.46742i 1.06952 + 0.314039i 0.768679 0.639635i \(-0.220914\pi\)
0.300841 + 0.953674i \(0.402733\pi\)
\(728\) 0 0
\(729\) −19.5132 22.5195i −0.722713 0.834055i
\(730\) 0 0
\(731\) −5.34836 + 1.57042i −0.197816 + 0.0580841i
\(732\) 0 0
\(733\) 1.15854 8.05783i 0.0427917 0.297623i −0.957175 0.289509i \(-0.906508\pi\)
0.999967 0.00811406i \(-0.00258281\pi\)
\(734\) 0 0
\(735\) −5.59626 −0.206421
\(736\) 0 0
\(737\) −5.86932 −0.216199
\(738\) 0 0
\(739\) 3.06022 21.2843i 0.112572 0.782956i −0.852830 0.522189i \(-0.825116\pi\)
0.965402 0.260767i \(-0.0839754\pi\)
\(740\) 0 0
\(741\) −30.9571 + 9.08982i −1.13724 + 0.333923i
\(742\) 0 0
\(743\) −0.0641545 0.0740382i −0.00235360 0.00271620i 0.754572 0.656218i \(-0.227845\pi\)
−0.756925 + 0.653502i \(0.773299\pi\)
\(744\) 0 0
\(745\) 14.7817 + 4.34031i 0.541561 + 0.159017i
\(746\) 0 0
\(747\) 2.08969 + 1.34296i 0.0764576 + 0.0491363i
\(748\) 0 0
\(749\) −15.9181 + 18.3705i −0.581635 + 0.671243i
\(750\) 0 0
\(751\) 1.64953 + 11.4727i 0.0601922 + 0.418646i 0.997531 + 0.0702269i \(0.0223723\pi\)
−0.937339 + 0.348419i \(0.886719\pi\)
\(752\) 0 0
\(753\) −1.74265 3.81588i −0.0635058 0.139058i
\(754\) 0 0
\(755\) 7.13440 15.6222i 0.259647 0.568548i
\(756\) 0 0
\(757\) −15.4162 + 9.90738i −0.560311 + 0.360090i −0.789936 0.613189i \(-0.789886\pi\)
0.229625 + 0.973279i \(0.426250\pi\)
\(758\) 0 0
\(759\) −3.34314 1.52452i −0.121348 0.0553367i
\(760\) 0 0
\(761\) −11.8034 + 7.58561i −0.427874 + 0.274978i −0.736803 0.676107i \(-0.763666\pi\)
0.308929 + 0.951085i \(0.400029\pi\)
\(762\) 0 0
\(763\) 2.77490 6.07619i 0.100458 0.219973i
\(764\) 0 0
\(765\) 1.10309 + 2.41543i 0.0398822 + 0.0873299i
\(766\) 0 0
\(767\) −0.294454 2.04797i −0.0106321 0.0739481i
\(768\) 0 0
\(769\) −11.2852 + 13.0238i −0.406955 + 0.469651i −0.921819 0.387621i \(-0.873297\pi\)
0.514864 + 0.857272i \(0.327842\pi\)
\(770\) 0 0
\(771\) −8.97881 5.77033i −0.323364 0.207813i
\(772\) 0 0
\(773\) −32.9396 9.67193i −1.18475 0.347875i −0.370749 0.928733i \(-0.620899\pi\)
−0.814005 + 0.580858i \(0.802717\pi\)
\(774\) 0 0
\(775\) 4.73613 + 5.46579i 0.170127 + 0.196337i
\(776\) 0 0
\(777\) 11.8841 3.48949i 0.426340 0.125185i
\(778\) 0 0
\(779\) −12.5180 + 87.0645i −0.448503 + 3.11941i
\(780\) 0 0
\(781\) −2.65369 −0.0949565
\(782\) 0 0
\(783\) 13.7589 0.491704
\(784\) 0 0
\(785\) 0.798369 5.55278i 0.0284950 0.198187i
\(786\) 0 0
\(787\) 10.0733 2.95779i 0.359075 0.105434i −0.0972189 0.995263i \(-0.530995\pi\)
0.456294 + 0.889829i \(0.349177\pi\)
\(788\) 0 0
\(789\) −24.3090 28.0540i −0.865422 0.998750i
\(790\) 0 0
\(791\) −19.5771 5.74834i −0.696080 0.204388i
\(792\) 0 0
\(793\) 12.6466 + 8.12747i 0.449094 + 0.288615i
\(794\) 0 0
\(795\) −11.5301 + 13.3065i −0.408931 + 0.471931i
\(796\) 0 0
\(797\) −5.70906 39.7074i −0.202225 1.40651i −0.797662 0.603105i \(-0.793930\pi\)
0.595437 0.803402i \(-0.296979\pi\)
\(798\) 0 0
\(799\) 7.61507 + 16.6747i 0.269402 + 0.589908i
\(800\) 0 0
\(801\) −4.26255 + 9.33369i −0.150610 + 0.329790i
\(802\) 0 0
\(803\) 5.67798 3.64902i 0.200372 0.128771i
\(804\) 0 0
\(805\) −2.28509 + 7.79828i −0.0805387 + 0.274853i
\(806\) 0 0
\(807\) −28.0996 + 18.0585i −0.989154 + 0.635691i
\(808\) 0 0
\(809\) −6.95070 + 15.2199i −0.244374 + 0.535103i −0.991581 0.129487i \(-0.958667\pi\)
0.747208 + 0.664591i \(0.231394\pi\)
\(810\) 0 0
\(811\) 14.1617 + 31.0099i 0.497286 + 1.08890i 0.977342 + 0.211667i \(0.0678892\pi\)
−0.480056 + 0.877238i \(0.659384\pi\)
\(812\) 0 0
\(813\) 0.182841 + 1.27169i 0.00641251 + 0.0446000i
\(814\) 0 0
\(815\) −2.42631 + 2.80011i −0.0849898 + 0.0980834i
\(816\) 0 0
\(817\) −9.77502 6.28203i −0.341985 0.219780i
\(818\) 0 0
\(819\) 4.30222 + 1.26325i 0.150332 + 0.0441414i
\(820\) 0 0
\(821\) 14.7312 + 17.0008i 0.514124 + 0.593331i 0.952150 0.305632i \(-0.0988676\pi\)
−0.438026 + 0.898962i \(0.644322\pi\)
\(822\) 0 0
\(823\) 20.7227 6.08474i 0.722349 0.212101i 0.100164 0.994971i \(-0.468063\pi\)
0.622185 + 0.782870i \(0.286245\pi\)
\(824\) 0 0
\(825\) −0.443441 + 3.08420i −0.0154386 + 0.107378i
\(826\) 0 0
\(827\) −45.6318 −1.58677 −0.793387 0.608718i \(-0.791684\pi\)
−0.793387 + 0.608718i \(0.791684\pi\)
\(828\) 0 0
\(829\) 13.3668 0.464249 0.232125 0.972686i \(-0.425432\pi\)
0.232125 + 0.972686i \(0.425432\pi\)
\(830\) 0 0
\(831\) 0.435255 3.02727i 0.0150988 0.105015i
\(832\) 0 0
\(833\) 12.6365 3.71041i 0.437829 0.128558i
\(834\) 0 0
\(835\) −9.14181 10.5502i −0.316365 0.365105i
\(836\) 0 0
\(837\) −9.62325 2.82564i −0.332628 0.0976684i
\(838\) 0 0
\(839\) 31.2442 + 20.0794i 1.07867 + 0.693220i 0.954250 0.299010i \(-0.0966564\pi\)
0.124421 + 0.992230i \(0.460293\pi\)
\(840\) 0 0
\(841\) 15.0936 17.4190i 0.520470 0.600654i
\(842\) 0 0
\(843\) −0.355259 2.47088i −0.0122358 0.0851016i
\(844\) 0 0
\(845\) 1.30629 + 2.86038i 0.0449378 + 0.0984001i
\(846\) 0 0
\(847\) −7.81970 + 17.1228i −0.268688 + 0.588345i
\(848\) 0 0
\(849\) −2.95465 + 1.89884i −0.101403 + 0.0651679i
\(850\) 0 0
\(851\) 0.0127121 + 22.9283i 0.000435765 + 0.785973i
\(852\) 0 0
\(853\) −7.25367 + 4.66165i −0.248361 + 0.159612i −0.658899 0.752232i \(-0.728977\pi\)
0.410538 + 0.911844i \(0.365341\pi\)
\(854\) 0 0
\(855\) −2.29944 + 5.03507i −0.0786392 + 0.172196i
\(856\) 0 0
\(857\) −0.310055 0.678927i −0.0105913 0.0231917i 0.904262 0.426977i \(-0.140422\pi\)
−0.914854 + 0.403785i \(0.867694\pi\)
\(858\) 0 0
\(859\) −4.37273 30.4130i −0.149196 1.03768i −0.917541 0.397642i \(-0.869829\pi\)
0.768345 0.640036i \(-0.221080\pi\)
\(860\) 0 0
\(861\) −21.3234 + 24.6085i −0.726700 + 0.838657i
\(862\) 0 0
\(863\) 30.6078 + 19.6705i 1.04190 + 0.669590i 0.945457 0.325748i \(-0.105616\pi\)
0.0964463 + 0.995338i \(0.469252\pi\)
\(864\) 0 0
\(865\) 13.2226 + 3.88250i 0.449581 + 0.132009i
\(866\) 0 0
\(867\) −5.54081 6.39443i −0.188176 0.217166i
\(868\) 0 0
\(869\) −7.27041 + 2.13478i −0.246632 + 0.0724176i
\(870\) 0 0
\(871\) 5.02630 34.9587i 0.170310 1.18453i
\(872\) 0 0
\(873\) −0.551024 −0.0186493
\(874\) 0 0
\(875\) 15.3633 0.519374
\(876\) 0 0
\(877\) 1.92171 13.3658i 0.0648916 0.451331i −0.931308 0.364233i \(-0.881331\pi\)
0.996200 0.0870988i \(-0.0277596\pi\)
\(878\) 0 0
\(879\) 12.2433 3.59495i 0.412955 0.121255i
\(880\) 0 0
\(881\) −19.3669 22.3506i −0.652488 0.753011i 0.329043 0.944315i \(-0.393274\pi\)
−0.981531 + 0.191304i \(0.938728\pi\)
\(882\) 0 0
\(883\) 11.0148 + 3.23425i 0.370679 + 0.108841i 0.461766 0.887002i \(-0.347216\pi\)
−0.0910870 + 0.995843i \(0.529034\pi\)
\(884\) 0 0
\(885\) 0.795439 + 0.511198i 0.0267384 + 0.0171837i
\(886\) 0 0
\(887\) −27.5712 + 31.8189i −0.925751 + 1.06837i 0.0717284 + 0.997424i \(0.477149\pi\)
−0.997480 + 0.0709499i \(0.977397\pi\)
\(888\) 0 0
\(889\) −0.937918 6.52336i −0.0314568 0.218787i
\(890\) 0 0
\(891\) −1.26565 2.77139i −0.0424008 0.0928449i
\(892\) 0 0
\(893\) −15.8740 + 34.7592i −0.531203 + 1.16317i
\(894\) 0 0
\(895\) −12.7151 + 8.17150i −0.425019 + 0.273143i
\(896\) 0 0
\(897\) 11.9433 18.6068i 0.398774 0.621262i
\(898\) 0 0
\(899\) 3.64957 2.34543i 0.121720 0.0782246i
\(900\) 0 0
\(901\) 17.2129 37.6910i 0.573444 1.25567i
\(902\) 0 0
\(903\) −1.78689 3.91273i −0.0594638 0.130208i
\(904\) 0 0
\(905\) −0.580880 4.04011i −0.0193091 0.134298i
\(906\) 0 0
\(907\) −16.6320 + 19.1943i −0.552255 + 0.637336i −0.961407 0.275130i \(-0.911279\pi\)
0.409152 + 0.912466i \(0.365825\pi\)
\(908\) 0 0
\(909\) −10.2150 6.56477i −0.338809 0.217740i
\(910\) 0 0
\(911\) −42.7734 12.5594i −1.41715 0.416112i −0.518611 0.855010i \(-0.673551\pi\)
−0.898537 + 0.438898i \(0.855369\pi\)
\(912\) 0 0
\(913\) 1.03057 + 1.18934i 0.0341069 + 0.0393614i
\(914\) 0 0
\(915\) −6.59175 + 1.93551i −0.217917 + 0.0639861i
\(916\) 0 0
\(917\) 3.33588 23.2016i 0.110160 0.766183i
\(918\) 0 0
\(919\) 15.9451 0.525981 0.262991 0.964798i \(-0.415291\pi\)
0.262991 + 0.964798i \(0.415291\pi\)
\(920\) 0 0
\(921\) 27.0194 0.890319
\(922\) 0 0
\(923\) 2.27253 15.8058i 0.0748014 0.520255i
\(924\) 0 0
\(925\) 18.6561 5.47792i 0.613408 0.180113i
\(926\) 0 0
\(927\) 6.09606 + 7.03523i 0.200221 + 0.231067i
\(928\) 0 0
\(929\) 0.0663141 + 0.0194716i 0.00217569 + 0.000638841i 0.282820 0.959173i \(-0.408730\pi\)
−0.280645 + 0.959812i \(0.590548\pi\)
\(930\) 0 0
\(931\) 23.0953 + 14.8425i 0.756919 + 0.486442i
\(932\) 0 0
\(933\) 29.0097 33.4790i 0.949736 1.09605i
\(934\) 0 0
\(935\) 0.239416 + 1.66517i 0.00782972 + 0.0544569i
\(936\) 0 0
\(937\) 1.97100 + 4.31588i 0.0643897 + 0.140994i 0.939091 0.343669i \(-0.111670\pi\)
−0.874701 + 0.484662i \(0.838942\pi\)
\(938\) 0 0
\(939\) −11.8844 + 26.0232i −0.387833 + 0.849236i
\(940\) 0 0
\(941\) 11.1562 7.16965i 0.363681 0.233724i −0.346019 0.938228i \(-0.612467\pi\)
0.709700 + 0.704504i \(0.248830\pi\)
\(942\) 0 0
\(943\) −32.6166 50.6906i −1.06214 1.65071i
\(944\) 0 0
\(945\) −8.03941 + 5.16662i −0.261522 + 0.168070i
\(946\) 0 0
\(947\) 24.0061 52.5661i 0.780095 1.70817i 0.0770457 0.997028i \(-0.475451\pi\)
0.703049 0.711141i \(-0.251821\pi\)
\(948\) 0 0
\(949\) 16.8717 + 36.9439i 0.547679 + 1.19925i
\(950\) 0 0
\(951\) −3.22540 22.4331i −0.104591 0.727444i
\(952\) 0 0
\(953\) 33.3901 38.5342i 1.08161 1.24825i 0.114627 0.993409i \(-0.463433\pi\)
0.966984 0.254837i \(-0.0820218\pi\)
\(954\) 0 0
\(955\) −11.6931 7.51471i −0.378381 0.243170i
\(956\) 0 0
\(957\) 1.79336 + 0.526577i 0.0579710 + 0.0170218i
\(958\) 0 0
\(959\) −1.06641 1.23070i −0.0344361 0.0397414i
\(960\) 0 0
\(961\) 26.7100 7.84277i 0.861614 0.252993i
\(962\) 0 0
\(963\) 1.61480 11.2311i 0.0520360 0.361919i
\(964\) 0 0
\(965\) −8.95262 −0.288195
\(966\) 0 0
\(967\) 1.97410 0.0634829 0.0317414 0.999496i \(-0.489895\pi\)
0.0317414 + 0.999496i \(0.489895\pi\)
\(968\) 0 0
\(969\) −4.93819 + 34.3459i −0.158638 + 1.10335i
\(970\) 0 0
\(971\) 31.1698 9.15228i 1.00029 0.293711i 0.259713 0.965686i \(-0.416372\pi\)
0.740573 + 0.671975i \(0.234554\pi\)
\(972\) 0 0
\(973\) −12.9482 14.9431i −0.415102 0.479053i
\(974\) 0 0
\(975\) −17.9903 5.28242i −0.576149 0.169173i
\(976\) 0 0
\(977\) 9.46633 + 6.08364i 0.302855 + 0.194633i 0.683237 0.730196i \(-0.260571\pi\)
−0.380383 + 0.924829i \(0.624208\pi\)
\(978\) 0 0
\(979\) −4.25707 + 4.91292i −0.136056 + 0.157018i
\(980\) 0 0
\(981\) 0.443752 + 3.08637i 0.0141679 + 0.0985401i
\(982\) 0 0
\(983\) 10.8560 + 23.7713i 0.346253 + 0.758188i 0.999999 + 0.00147372i \(0.000469099\pi\)
−0.653746 + 0.756714i \(0.726804\pi\)
\(984\) 0 0
\(985\) −8.56779 + 18.7608i −0.272993 + 0.597770i
\(986\) 0 0
\(987\) −11.9002 + 7.64780i −0.378788 + 0.243432i
\(988\) 0 0
\(989\) 7.88105 1.13758i 0.250603 0.0361731i
\(990\) 0 0
\(991\) 15.9462 10.2480i 0.506549 0.325539i −0.262282 0.964991i \(-0.584475\pi\)
0.768831 + 0.639452i \(0.220839\pi\)
\(992\) 0 0
\(993\) 17.2525 37.7776i 0.547490 1.19884i
\(994\) 0 0
\(995\) 0.0469288 + 0.102760i 0.00148774 + 0.00325770i
\(996\) 0 0
\(997\) 5.70019 + 39.6457i 0.180527 + 1.25559i 0.855521 + 0.517769i \(0.173237\pi\)
−0.674994 + 0.737824i \(0.735854\pi\)
\(998\) 0 0
\(999\) −17.6576 + 20.3780i −0.558663 + 0.644731i
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 92.2.e.a.81.2 yes 20
3.2 odd 2 828.2.q.a.541.1 20
4.3 odd 2 368.2.m.d.81.1 20
23.2 even 11 inner 92.2.e.a.25.2 20
23.5 odd 22 2116.2.a.i.1.4 10
23.18 even 11 2116.2.a.j.1.4 10
69.2 odd 22 828.2.q.a.577.1 20
92.51 even 22 8464.2.a.cd.1.7 10
92.71 odd 22 368.2.m.d.209.1 20
92.87 odd 22 8464.2.a.ce.1.7 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
92.2.e.a.25.2 20 23.2 even 11 inner
92.2.e.a.81.2 yes 20 1.1 even 1 trivial
368.2.m.d.81.1 20 4.3 odd 2
368.2.m.d.209.1 20 92.71 odd 22
828.2.q.a.541.1 20 3.2 odd 2
828.2.q.a.577.1 20 69.2 odd 22
2116.2.a.i.1.4 10 23.5 odd 22
2116.2.a.j.1.4 10 23.18 even 11
8464.2.a.cd.1.7 10 92.51 even 22
8464.2.a.ce.1.7 10 92.87 odd 22