Properties

Label 810.2.s.a.773.11
Level $810$
Weight $2$
Character 810.773
Analytic conductor $6.468$
Analytic rank $0$
Dimension $216$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [810,2,Mod(17,810)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(810, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([22, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("810.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 810.s (of order \(36\), degree \(12\), 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: \(6.46788256372\)
Analytic rank: \(0\)
Dimension: \(216\)
Relative dimension: \(18\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 270)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 773.11
Character \(\chi\) \(=\) 810.773
Dual form 810.2.s.a.197.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-2.20857 - 0.349587i) q^{5} +(-1.10212 - 0.771712i) q^{7} +(0.965926 + 0.258819i) q^{8} +O(q^{10})\) \(q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-2.20857 - 0.349587i) q^{5} +(-1.10212 - 0.771712i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-2.16970 - 0.540747i) q^{10} +(1.46618 - 4.02828i) q^{11} +(-0.298865 - 3.41605i) q^{13} +(-1.03067 - 0.864832i) q^{14} +(0.939693 + 0.342020i) q^{16} +(-7.43061 + 1.99103i) q^{17} +(6.12582 - 3.53674i) q^{19} +(-2.11431 - 0.727791i) q^{20} +(1.81168 - 3.88517i) q^{22} +(-2.78440 - 3.97654i) q^{23} +(4.75558 + 1.54418i) q^{25} -3.42910i q^{26} +(-0.951369 - 0.951369i) q^{28} +(-0.00478023 + 0.00401109i) q^{29} +(0.582373 - 3.30280i) q^{31} +(0.906308 + 0.422618i) q^{32} +(-7.57586 + 1.33583i) q^{34} +(2.16433 + 2.08967i) q^{35} +(-1.24815 - 4.65816i) q^{37} +(6.41076 - 2.98938i) q^{38} +(-2.04284 - 0.909296i) q^{40} +(-0.705833 + 0.841179i) q^{41} +(3.14516 + 6.74482i) q^{43} +(2.14340 - 3.71249i) q^{44} +(-2.42723 - 4.20409i) q^{46} +(2.04873 - 2.92589i) q^{47} +(-1.77501 - 4.87681i) q^{49} +(4.60290 + 1.95278i) q^{50} +(0.298865 - 3.41605i) q^{52} +(8.13905 - 8.13905i) q^{53} +(-4.64639 + 8.38420i) q^{55} +(-0.864832 - 1.03067i) q^{56} +(-0.00511163 + 0.00357920i) q^{58} +(-8.71384 + 3.17158i) q^{59} +(1.24279 + 7.04819i) q^{61} +(0.868015 - 3.23947i) q^{62} +(0.866025 + 0.500000i) q^{64} +(-0.534140 + 7.64906i) q^{65} +(-5.54705 + 0.485304i) q^{67} +(-7.66346 + 0.670466i) q^{68} +(1.97397 + 2.27035i) q^{70} +(2.37880 + 1.37340i) q^{71} +(-2.76825 + 10.3313i) q^{73} +(-0.837415 - 4.74922i) q^{74} +(6.64690 - 2.41927i) q^{76} +(-4.72458 + 3.30818i) q^{77} +(-3.61314 - 4.30597i) q^{79} +(-1.95581 - 1.08388i) q^{80} +(-0.776460 + 0.776460i) q^{82} +(-1.20379 + 13.7594i) q^{83} +(17.1071 - 1.79968i) q^{85} +(2.54534 + 6.99327i) q^{86} +(2.45881 - 3.51155i) q^{88} +(0.692740 + 1.19986i) q^{89} +(-2.30682 + 3.99553i) q^{91} +(-2.05158 - 4.39964i) q^{92} +(2.29594 - 2.73620i) q^{94} +(-14.7657 + 5.66964i) q^{95} +(-4.62517 + 2.15675i) q^{97} +(-1.34322 - 5.01296i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216 q+O(q^{10}) \) Copy content Toggle raw display \( 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86} + 48 q^{92} + 60 q^{95} - 72 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).

\(n\) \(487\) \(731\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.996195 + 0.0871557i 0.704416 + 0.0616284i
\(3\) 0 0
\(4\) 0.984808 + 0.173648i 0.492404 + 0.0868241i
\(5\) −2.20857 0.349587i −0.987703 0.156340i
\(6\) 0 0
\(7\) −1.10212 0.771712i −0.416562 0.291680i 0.346445 0.938070i \(-0.387389\pi\)
−0.763007 + 0.646391i \(0.776278\pi\)
\(8\) 0.965926 + 0.258819i 0.341506 + 0.0915064i
\(9\) 0 0
\(10\) −2.16970 0.540747i −0.686119 0.170999i
\(11\) 1.46618 4.02828i 0.442068 1.21457i −0.496061 0.868288i \(-0.665221\pi\)
0.938129 0.346285i \(-0.112557\pi\)
\(12\) 0 0
\(13\) −0.298865 3.41605i −0.0828903 0.947441i −0.917797 0.397050i \(-0.870034\pi\)
0.834907 0.550391i \(-0.185521\pi\)
\(14\) −1.03067 0.864832i −0.275457 0.231136i
\(15\) 0 0
\(16\) 0.939693 + 0.342020i 0.234923 + 0.0855050i
\(17\) −7.43061 + 1.99103i −1.80219 + 0.482895i −0.994317 0.106464i \(-0.966047\pi\)
−0.807871 + 0.589359i \(0.799380\pi\)
\(18\) 0 0
\(19\) 6.12582 3.53674i 1.40536 0.811384i 0.410423 0.911895i \(-0.365381\pi\)
0.994936 + 0.100511i \(0.0320477\pi\)
\(20\) −2.11431 0.727791i −0.472775 0.162739i
\(21\) 0 0
\(22\) 1.81168 3.88517i 0.386252 0.828321i
\(23\) −2.78440 3.97654i −0.580588 0.829166i 0.416198 0.909274i \(-0.363362\pi\)
−0.996786 + 0.0801079i \(0.974474\pi\)
\(24\) 0 0
\(25\) 4.75558 + 1.54418i 0.951116 + 0.308835i
\(26\) 3.42910i 0.672501i
\(27\) 0 0
\(28\) −0.951369 0.951369i −0.179792 0.179792i
\(29\) −0.00478023 + 0.00401109i −0.000887667 + 0.000744841i −0.643231 0.765672i \(-0.722407\pi\)
0.642344 + 0.766417i \(0.277962\pi\)
\(30\) 0 0
\(31\) 0.582373 3.30280i 0.104597 0.593200i −0.886783 0.462186i \(-0.847065\pi\)
0.991380 0.131015i \(-0.0418235\pi\)
\(32\) 0.906308 + 0.422618i 0.160214 + 0.0747091i
\(33\) 0 0
\(34\) −7.57586 + 1.33583i −1.29925 + 0.229093i
\(35\) 2.16433 + 2.08967i 0.365838 + 0.353218i
\(36\) 0 0
\(37\) −1.24815 4.65816i −0.205195 0.765797i −0.989390 0.145283i \(-0.953591\pi\)
0.784196 0.620514i \(-0.213076\pi\)
\(38\) 6.41076 2.98938i 1.03996 0.484942i
\(39\) 0 0
\(40\) −2.04284 0.909296i −0.323001 0.143772i
\(41\) −0.705833 + 0.841179i −0.110233 + 0.131370i −0.818339 0.574735i \(-0.805105\pi\)
0.708107 + 0.706105i \(0.249549\pi\)
\(42\) 0 0
\(43\) 3.14516 + 6.74482i 0.479632 + 1.02857i 0.986075 + 0.166301i \(0.0531824\pi\)
−0.506443 + 0.862274i \(0.669040\pi\)
\(44\) 2.14340 3.71249i 0.323130 0.559678i
\(45\) 0 0
\(46\) −2.42723 4.20409i −0.357876 0.619859i
\(47\) 2.04873 2.92589i 0.298838 0.426785i −0.641450 0.767165i \(-0.721667\pi\)
0.940288 + 0.340380i \(0.110556\pi\)
\(48\) 0 0
\(49\) −1.77501 4.87681i −0.253573 0.696687i
\(50\) 4.60290 + 1.95278i 0.650948 + 0.276164i
\(51\) 0 0
\(52\) 0.298865 3.41605i 0.0414452 0.473720i
\(53\) 8.13905 8.13905i 1.11798 1.11798i 0.125947 0.992037i \(-0.459803\pi\)
0.992037 0.125947i \(-0.0401971\pi\)
\(54\) 0 0
\(55\) −4.64639 + 8.38420i −0.626519 + 1.13052i
\(56\) −0.864832 1.03067i −0.115568 0.137729i
\(57\) 0 0
\(58\) −0.00511163 + 0.00357920i −0.000671190 + 0.000469972i
\(59\) −8.71384 + 3.17158i −1.13444 + 0.412904i −0.839904 0.542735i \(-0.817389\pi\)
−0.294541 + 0.955639i \(0.595167\pi\)
\(60\) 0 0
\(61\) 1.24279 + 7.04819i 0.159122 + 0.902428i 0.954920 + 0.296865i \(0.0959411\pi\)
−0.795797 + 0.605563i \(0.792948\pi\)
\(62\) 0.868015 3.23947i 0.110238 0.411414i
\(63\) 0 0
\(64\) 0.866025 + 0.500000i 0.108253 + 0.0625000i
\(65\) −0.534140 + 7.64906i −0.0662520 + 0.948750i
\(66\) 0 0
\(67\) −5.54705 + 0.485304i −0.677680 + 0.0592893i −0.420799 0.907154i \(-0.638250\pi\)
−0.256881 + 0.966443i \(0.582695\pi\)
\(68\) −7.66346 + 0.670466i −0.929331 + 0.0813059i
\(69\) 0 0
\(70\) 1.97397 + 2.27035i 0.235934 + 0.271359i
\(71\) 2.37880 + 1.37340i 0.282312 + 0.162993i 0.634470 0.772948i \(-0.281219\pi\)
−0.352158 + 0.935941i \(0.614552\pi\)
\(72\) 0 0
\(73\) −2.76825 + 10.3313i −0.323999 + 1.20918i 0.591315 + 0.806441i \(0.298609\pi\)
−0.915314 + 0.402741i \(0.868058\pi\)
\(74\) −0.837415 4.74922i −0.0973475 0.552085i
\(75\) 0 0
\(76\) 6.64690 2.41927i 0.762452 0.277510i
\(77\) −4.72458 + 3.30818i −0.538415 + 0.377002i
\(78\) 0 0
\(79\) −3.61314 4.30597i −0.406510 0.484459i 0.523484 0.852036i \(-0.324632\pi\)
−0.929993 + 0.367576i \(0.880188\pi\)
\(80\) −1.95581 1.08388i −0.218667 0.121182i
\(81\) 0 0
\(82\) −0.776460 + 0.776460i −0.0857457 + 0.0857457i
\(83\) −1.20379 + 13.7594i −0.132133 + 1.51029i 0.583672 + 0.811989i \(0.301615\pi\)
−0.715806 + 0.698300i \(0.753940\pi\)
\(84\) 0 0
\(85\) 17.1071 1.79968i 1.85552 0.195202i
\(86\) 2.54534 + 6.99327i 0.274471 + 0.754104i
\(87\) 0 0
\(88\) 2.45881 3.51155i 0.262110 0.374332i
\(89\) 0.692740 + 1.19986i 0.0734303 + 0.127185i 0.900403 0.435058i \(-0.143272\pi\)
−0.826972 + 0.562243i \(0.809939\pi\)
\(90\) 0 0
\(91\) −2.30682 + 3.99553i −0.241820 + 0.418845i
\(92\) −2.05158 4.39964i −0.213892 0.458694i
\(93\) 0 0
\(94\) 2.29594 2.73620i 0.236808 0.282217i
\(95\) −14.7657 + 5.66964i −1.51493 + 0.581693i
\(96\) 0 0
\(97\) −4.62517 + 2.15675i −0.469615 + 0.218985i −0.642995 0.765870i \(-0.722309\pi\)
0.173381 + 0.984855i \(0.444531\pi\)
\(98\) −1.34322 5.01296i −0.135685 0.506385i
\(99\) 0 0
\(100\) 4.41519 + 2.34651i 0.441519 + 0.234651i
\(101\) 14.0387 2.47539i 1.39690 0.246311i 0.576030 0.817428i \(-0.304601\pi\)
0.820868 + 0.571118i \(0.193490\pi\)
\(102\) 0 0
\(103\) 1.83486 + 0.855607i 0.180794 + 0.0843055i 0.510908 0.859636i \(-0.329309\pi\)
−0.330114 + 0.943941i \(0.607087\pi\)
\(104\) 0.595456 3.37700i 0.0583893 0.331142i
\(105\) 0 0
\(106\) 8.81744 7.39871i 0.856426 0.718626i
\(107\) 6.58564 + 6.58564i 0.636658 + 0.636658i 0.949730 0.313071i \(-0.101358\pi\)
−0.313071 + 0.949730i \(0.601358\pi\)
\(108\) 0 0
\(109\) 0.997902i 0.0955817i −0.998857 0.0477908i \(-0.984782\pi\)
0.998857 0.0477908i \(-0.0152181\pi\)
\(110\) −5.35944 + 7.94733i −0.511002 + 0.757748i
\(111\) 0 0
\(112\) −0.771712 1.10212i −0.0729200 0.104140i
\(113\) 4.69253 10.0632i 0.441436 0.946662i −0.552167 0.833733i \(-0.686199\pi\)
0.993603 0.112929i \(-0.0360231\pi\)
\(114\) 0 0
\(115\) 4.75941 + 9.75587i 0.443817 + 0.909739i
\(116\) −0.00540413 + 0.00312007i −0.000501761 + 0.000289692i
\(117\) 0 0
\(118\) −8.95710 + 2.40005i −0.824568 + 0.220942i
\(119\) 9.72592 + 3.53994i 0.891573 + 0.324506i
\(120\) 0 0
\(121\) −5.65090 4.74167i −0.513719 0.431061i
\(122\) 0.623767 + 7.12968i 0.0564732 + 0.645491i
\(123\) 0 0
\(124\) 1.14705 3.15149i 0.103008 0.283013i
\(125\) −9.96321 5.07291i −0.891137 0.453735i
\(126\) 0 0
\(127\) 10.7439 + 2.87882i 0.953368 + 0.255454i 0.701791 0.712383i \(-0.252384\pi\)
0.251577 + 0.967837i \(0.419051\pi\)
\(128\) 0.819152 + 0.573576i 0.0724035 + 0.0506975i
\(129\) 0 0
\(130\) −1.19877 + 7.57340i −0.105139 + 0.664231i
\(131\) 7.17885 + 1.26582i 0.627219 + 0.110596i 0.478218 0.878241i \(-0.341283\pi\)
0.149001 + 0.988837i \(0.452394\pi\)
\(132\) 0 0
\(133\) −9.48073 0.829456i −0.822084 0.0719230i
\(134\) −5.56824 −0.481023
\(135\) 0 0
\(136\) −7.69273 −0.659646
\(137\) −11.8699 1.03848i −1.01411 0.0887234i −0.432035 0.901857i \(-0.642204\pi\)
−0.582078 + 0.813133i \(0.697760\pi\)
\(138\) 0 0
\(139\) −6.01894 1.06130i −0.510520 0.0900184i −0.0875463 0.996160i \(-0.527903\pi\)
−0.422974 + 0.906142i \(0.639014\pi\)
\(140\) 1.76858 + 2.43375i 0.149472 + 0.205690i
\(141\) 0 0
\(142\) 2.25005 + 1.57550i 0.188820 + 0.132213i
\(143\) −14.1990 3.80461i −1.18738 0.318157i
\(144\) 0 0
\(145\) 0.0119597 0.00718767i 0.000993200 0.000596904i
\(146\) −3.65814 + 10.0507i −0.302750 + 0.831799i
\(147\) 0 0
\(148\) −0.420307 4.80413i −0.0345490 0.394897i
\(149\) 1.65154 + 1.38581i 0.135299 + 0.113530i 0.707926 0.706287i \(-0.249631\pi\)
−0.572627 + 0.819816i \(0.694075\pi\)
\(150\) 0 0
\(151\) 14.2033 + 5.16957i 1.15585 + 0.420693i 0.847612 0.530617i \(-0.178040\pi\)
0.308234 + 0.951311i \(0.400262\pi\)
\(152\) 6.83246 1.83075i 0.554186 0.148494i
\(153\) 0 0
\(154\) −4.99492 + 2.88382i −0.402502 + 0.232385i
\(155\) −2.44083 + 7.09088i −0.196052 + 0.569553i
\(156\) 0 0
\(157\) −0.631683 + 1.35465i −0.0504138 + 0.108113i −0.929901 0.367810i \(-0.880108\pi\)
0.879487 + 0.475922i \(0.157886\pi\)
\(158\) −3.22410 4.60449i −0.256495 0.366314i
\(159\) 0 0
\(160\) −1.85390 1.25022i −0.146564 0.0988383i
\(161\) 6.53138i 0.514745i
\(162\) 0 0
\(163\) −11.5642 11.5642i −0.905779 0.905779i 0.0901493 0.995928i \(-0.471266\pi\)
−0.995928 + 0.0901493i \(0.971266\pi\)
\(164\) −0.841179 + 0.705833i −0.0656850 + 0.0551163i
\(165\) 0 0
\(166\) −2.39842 + 13.6021i −0.186153 + 1.05573i
\(167\) −7.74478 3.61145i −0.599309 0.279462i 0.0991955 0.995068i \(-0.468373\pi\)
−0.698505 + 0.715606i \(0.746151\pi\)
\(168\) 0 0
\(169\) 1.22245 0.215550i 0.0940343 0.0165808i
\(170\) 17.1988 0.301850i 1.31909 0.0231509i
\(171\) 0 0
\(172\) 1.92615 + 7.18850i 0.146868 + 0.548118i
\(173\) 18.7601 8.74798i 1.42630 0.665097i 0.452350 0.891840i \(-0.350586\pi\)
0.973954 + 0.226744i \(0.0728080\pi\)
\(174\) 0 0
\(175\) −4.04955 5.37180i −0.306118 0.406070i
\(176\) 2.75551 3.28389i 0.207704 0.247532i
\(177\) 0 0
\(178\) 0.585529 + 1.25567i 0.0438873 + 0.0941166i
\(179\) 7.96252 13.7915i 0.595147 1.03082i −0.398379 0.917221i \(-0.630427\pi\)
0.993526 0.113604i \(-0.0362394\pi\)
\(180\) 0 0
\(181\) −3.45571 5.98546i −0.256861 0.444896i 0.708538 0.705672i \(-0.249355\pi\)
−0.965399 + 0.260776i \(0.916022\pi\)
\(182\) −2.64628 + 3.77927i −0.196155 + 0.280138i
\(183\) 0 0
\(184\) −1.66032 4.56170i −0.122401 0.336293i
\(185\) 1.12820 + 10.7242i 0.0829467 + 0.788460i
\(186\) 0 0
\(187\) −2.87416 + 32.8518i −0.210179 + 2.40236i
\(188\) 2.52568 2.52568i 0.184204 0.184204i
\(189\) 0 0
\(190\) −15.2037 + 4.36115i −1.10299 + 0.316391i
\(191\) 17.4482 + 20.7940i 1.26251 + 1.50460i 0.775712 + 0.631087i \(0.217391\pi\)
0.486798 + 0.873515i \(0.338165\pi\)
\(192\) 0 0
\(193\) 14.5121 10.1615i 1.04461 0.731441i 0.0804452 0.996759i \(-0.474366\pi\)
0.964161 + 0.265318i \(0.0854769\pi\)
\(194\) −4.79554 + 1.74543i −0.344300 + 0.125315i
\(195\) 0 0
\(196\) −0.901198 5.11095i −0.0643713 0.365068i
\(197\) −2.27387 + 8.48620i −0.162006 + 0.604616i 0.836397 + 0.548125i \(0.184658\pi\)
−0.998403 + 0.0564917i \(0.982009\pi\)
\(198\) 0 0
\(199\) −10.6250 6.13434i −0.753186 0.434852i 0.0736580 0.997284i \(-0.476533\pi\)
−0.826844 + 0.562431i \(0.809866\pi\)
\(200\) 4.19387 + 2.72239i 0.296552 + 0.192502i
\(201\) 0 0
\(202\) 14.2010 1.24242i 0.999177 0.0874167i
\(203\) 0.00836379 0.000731737i 0.000587023 5.13579e-5i
\(204\) 0 0
\(205\) 1.85295 1.61105i 0.129415 0.112521i
\(206\) 1.75330 + 1.01227i 0.122158 + 0.0705282i
\(207\) 0 0
\(208\) 0.887515 3.31225i 0.0615381 0.229663i
\(209\) −5.26548 29.8620i −0.364221 2.06560i
\(210\) 0 0
\(211\) −6.43443 + 2.34194i −0.442965 + 0.161226i −0.553867 0.832605i \(-0.686848\pi\)
0.110902 + 0.993831i \(0.464626\pi\)
\(212\) 9.42873 6.60207i 0.647568 0.453432i
\(213\) 0 0
\(214\) 5.98661 + 7.13456i 0.409236 + 0.487708i
\(215\) −4.58841 15.9959i −0.312927 1.09091i
\(216\) 0 0
\(217\) −3.19066 + 3.19066i −0.216596 + 0.216596i
\(218\) 0.0869729 0.994105i 0.00589055 0.0673293i
\(219\) 0 0
\(220\) −6.03170 + 7.44998i −0.406657 + 0.502278i
\(221\) 9.02219 + 24.7883i 0.606898 + 1.66744i
\(222\) 0 0
\(223\) 0.0323543 0.0462067i 0.00216660 0.00309423i −0.818067 0.575123i \(-0.804954\pi\)
0.820234 + 0.572028i \(0.193843\pi\)
\(224\) −0.672720 1.16518i −0.0449480 0.0778522i
\(225\) 0 0
\(226\) 5.55173 9.61588i 0.369296 0.639639i
\(227\) 3.14003 + 6.73382i 0.208411 + 0.446939i 0.982531 0.186100i \(-0.0595849\pi\)
−0.774120 + 0.633039i \(0.781807\pi\)
\(228\) 0 0
\(229\) −7.90847 + 9.42495i −0.522606 + 0.622818i −0.961195 0.275870i \(-0.911034\pi\)
0.438589 + 0.898688i \(0.355479\pi\)
\(230\) 3.89102 + 10.1336i 0.256566 + 0.668187i
\(231\) 0 0
\(232\) −0.00565550 + 0.00263720i −0.000371301 + 0.000173141i
\(233\) 3.38830 + 12.6453i 0.221975 + 0.828421i 0.983594 + 0.180396i \(0.0577380\pi\)
−0.761619 + 0.648025i \(0.775595\pi\)
\(234\) 0 0
\(235\) −5.54762 + 5.74582i −0.361887 + 0.374816i
\(236\) −9.13219 + 1.61025i −0.594455 + 0.104818i
\(237\) 0 0
\(238\) 9.38038 + 4.37414i 0.608040 + 0.283534i
\(239\) −0.00469859 + 0.0266470i −0.000303927 + 0.00172365i −0.984959 0.172786i \(-0.944723\pi\)
0.984655 + 0.174510i \(0.0558341\pi\)
\(240\) 0 0
\(241\) 5.56632 4.67069i 0.358558 0.300866i −0.445658 0.895203i \(-0.647030\pi\)
0.804216 + 0.594338i \(0.202586\pi\)
\(242\) −5.21614 5.21614i −0.335306 0.335306i
\(243\) 0 0
\(244\) 7.15692i 0.458175i
\(245\) 2.21538 + 11.3913i 0.141535 + 0.727764i
\(246\) 0 0
\(247\) −13.9125 19.8691i −0.885230 1.26424i
\(248\) 1.41736 3.03953i 0.0900022 0.193010i
\(249\) 0 0
\(250\) −9.48316 5.92196i −0.599768 0.374538i
\(251\) −9.23875 + 5.33400i −0.583145 + 0.336679i −0.762382 0.647127i \(-0.775970\pi\)
0.179237 + 0.983806i \(0.442637\pi\)
\(252\) 0 0
\(253\) −20.1011 + 5.38606i −1.26374 + 0.338619i
\(254\) 10.4521 + 3.80426i 0.655824 + 0.238701i
\(255\) 0 0
\(256\) 0.766044 + 0.642788i 0.0478778 + 0.0401742i
\(257\) −0.545692 6.23728i −0.0340393 0.389071i −0.994035 0.109058i \(-0.965217\pi\)
0.959996 0.280013i \(-0.0903389\pi\)
\(258\) 0 0
\(259\) −2.21915 + 6.09706i −0.137891 + 0.378853i
\(260\) −1.85427 + 7.44010i −0.114997 + 0.461416i
\(261\) 0 0
\(262\) 7.04121 + 1.88669i 0.435007 + 0.116560i
\(263\) −1.84417 1.29130i −0.113716 0.0796249i 0.515335 0.856989i \(-0.327668\pi\)
−0.629051 + 0.777364i \(0.716556\pi\)
\(264\) 0 0
\(265\) −20.8210 + 15.1304i −1.27902 + 0.929451i
\(266\) −9.37236 1.65260i −0.574656 0.101327i
\(267\) 0 0
\(268\) −5.54705 0.485304i −0.338840 0.0296447i
\(269\) 20.0830 1.22448 0.612240 0.790672i \(-0.290269\pi\)
0.612240 + 0.790672i \(0.290269\pi\)
\(270\) 0 0
\(271\) 22.3527 1.35783 0.678914 0.734218i \(-0.262451\pi\)
0.678914 + 0.734218i \(0.262451\pi\)
\(272\) −7.66346 0.670466i −0.464666 0.0406530i
\(273\) 0 0
\(274\) −11.7342 2.06906i −0.708890 0.124996i
\(275\) 13.1929 16.8928i 0.795561 1.01867i
\(276\) 0 0
\(277\) −4.15972 2.91267i −0.249933 0.175005i 0.441896 0.897066i \(-0.354306\pi\)
−0.691829 + 0.722061i \(0.743195\pi\)
\(278\) −5.90354 1.58185i −0.354071 0.0948729i
\(279\) 0 0
\(280\) 1.54974 + 2.57863i 0.0926144 + 0.154103i
\(281\) 5.51412 15.1499i 0.328945 0.903769i −0.659435 0.751762i \(-0.729204\pi\)
0.988379 0.152007i \(-0.0485736\pi\)
\(282\) 0 0
\(283\) 1.35460 + 15.4831i 0.0805226 + 0.920377i 0.923794 + 0.382890i \(0.125071\pi\)
−0.843272 + 0.537488i \(0.819373\pi\)
\(284\) 2.10417 + 1.76561i 0.124860 + 0.104770i
\(285\) 0 0
\(286\) −13.8134 5.02765i −0.816801 0.297291i
\(287\) 1.42706 0.382380i 0.0842367 0.0225712i
\(288\) 0 0
\(289\) 36.5273 21.0891i 2.14867 1.24053i
\(290\) 0.0125406 0.00611796i 0.000736412 0.000359259i
\(291\) 0 0
\(292\) −4.52020 + 9.69360i −0.264525 + 0.567275i
\(293\) −18.4183 26.3041i −1.07601 1.53670i −0.821991 0.569500i \(-0.807137\pi\)
−0.254017 0.967200i \(-0.581752\pi\)
\(294\) 0 0
\(295\) 20.3539 3.95841i 1.18505 0.230468i
\(296\) 4.82248i 0.280301i
\(297\) 0 0
\(298\) 1.52447 + 1.52447i 0.0883104 + 0.0883104i
\(299\) −12.7519 + 10.7001i −0.737461 + 0.618803i
\(300\) 0 0
\(301\) 1.73872 9.86075i 0.100218 0.568364i
\(302\) 13.6987 + 6.38779i 0.788269 + 0.367576i
\(303\) 0 0
\(304\) 6.96602 1.22830i 0.399529 0.0704477i
\(305\) −0.280826 16.0009i −0.0160800 0.916209i
\(306\) 0 0
\(307\) −0.658671 2.45819i −0.0375923 0.140296i 0.944579 0.328284i \(-0.106470\pi\)
−0.982171 + 0.187987i \(0.939804\pi\)
\(308\) −5.22726 + 2.43751i −0.297851 + 0.138890i
\(309\) 0 0
\(310\) −3.04955 + 6.85117i −0.173203 + 0.389120i
\(311\) 10.8671 12.9510i 0.616219 0.734382i −0.364196 0.931322i \(-0.618656\pi\)
0.980415 + 0.196941i \(0.0631006\pi\)
\(312\) 0 0
\(313\) −10.5221 22.5647i −0.594743 1.27543i −0.941354 0.337422i \(-0.890445\pi\)
0.346610 0.938009i \(-0.387333\pi\)
\(314\) −0.747344 + 1.29444i −0.0421751 + 0.0730494i
\(315\) 0 0
\(316\) −2.81052 4.86797i −0.158104 0.273845i
\(317\) 14.7708 21.0949i 0.829611 1.18481i −0.150940 0.988543i \(-0.548230\pi\)
0.980551 0.196264i \(-0.0628811\pi\)
\(318\) 0 0
\(319\) 0.00914915 + 0.0251371i 0.000512254 + 0.00140741i
\(320\) −1.73789 1.40704i −0.0971508 0.0786558i
\(321\) 0 0
\(322\) −0.569248 + 6.50653i −0.0317229 + 0.362595i
\(323\) −38.4768 + 38.4768i −2.14091 + 2.14091i
\(324\) 0 0
\(325\) 3.85370 16.7068i 0.213765 0.926725i
\(326\) −10.5123 12.5281i −0.582223 0.693867i
\(327\) 0 0
\(328\) −0.899495 + 0.629833i −0.0496663 + 0.0347767i
\(329\) −4.51589 + 1.64365i −0.248969 + 0.0906173i
\(330\) 0 0
\(331\) 0.572221 + 3.24523i 0.0314521 + 0.178374i 0.996487 0.0837477i \(-0.0266890\pi\)
−0.965035 + 0.262121i \(0.915578\pi\)
\(332\) −3.57479 + 13.3413i −0.196192 + 0.732200i
\(333\) 0 0
\(334\) −7.40055 4.27271i −0.404940 0.233792i
\(335\) 12.4207 + 0.867349i 0.678616 + 0.0473883i
\(336\) 0 0
\(337\) 23.2238 2.03182i 1.26508 0.110680i 0.565208 0.824949i \(-0.308796\pi\)
0.699872 + 0.714269i \(0.253241\pi\)
\(338\) 1.23658 0.108187i 0.0672611 0.00588459i
\(339\) 0 0
\(340\) 17.1597 + 1.19827i 0.930615 + 0.0649856i
\(341\) −12.4508 7.18844i −0.674246 0.389276i
\(342\) 0 0
\(343\) −4.24479 + 15.8418i −0.229197 + 0.855376i
\(344\) 1.29230 + 7.32902i 0.0696764 + 0.395154i
\(345\) 0 0
\(346\) 19.4512 7.07964i 1.04570 0.380604i
\(347\) −4.06509 + 2.84641i −0.218226 + 0.152803i −0.677578 0.735451i \(-0.736970\pi\)
0.459352 + 0.888254i \(0.348082\pi\)
\(348\) 0 0
\(349\) −18.4096 21.9397i −0.985443 1.17440i −0.984674 0.174405i \(-0.944200\pi\)
−0.000768814 1.00000i \(-0.500245\pi\)
\(350\) −3.56596 5.70430i −0.190609 0.304908i
\(351\) 0 0
\(352\) 3.03123 3.03123i 0.161565 0.161565i
\(353\) −1.14797 + 13.1214i −0.0611003 + 0.698380i 0.902440 + 0.430816i \(0.141774\pi\)
−0.963540 + 0.267564i \(0.913781\pi\)
\(354\) 0 0
\(355\) −4.77363 3.86485i −0.253358 0.205125i
\(356\) 0.473862 + 1.30193i 0.0251146 + 0.0690019i
\(357\) 0 0
\(358\) 9.13423 13.0450i 0.482759 0.689451i
\(359\) −2.89200 5.00910i −0.152634 0.264370i 0.779561 0.626326i \(-0.215442\pi\)
−0.932195 + 0.361956i \(0.882109\pi\)
\(360\) 0 0
\(361\) 15.5171 26.8764i 0.816690 1.41455i
\(362\) −2.92089 6.26387i −0.153519 0.329222i
\(363\) 0 0
\(364\) −2.96559 + 3.53425i −0.155439 + 0.185245i
\(365\) 9.72555 21.8496i 0.509059 1.14366i
\(366\) 0 0
\(367\) −9.77555 + 4.55841i −0.510280 + 0.237947i −0.660666 0.750680i \(-0.729726\pi\)
0.150386 + 0.988627i \(0.451948\pi\)
\(368\) −1.25643 4.68905i −0.0654958 0.244434i
\(369\) 0 0
\(370\) 0.189226 + 10.7817i 0.00983740 + 0.560516i
\(371\) −15.2512 + 2.68920i −0.791803 + 0.139616i
\(372\) 0 0
\(373\) 3.38202 + 1.57706i 0.175114 + 0.0816572i 0.508199 0.861240i \(-0.330312\pi\)
−0.333084 + 0.942897i \(0.608089\pi\)
\(374\) −5.72644 + 32.4763i −0.296107 + 1.67931i
\(375\) 0 0
\(376\) 2.73620 2.29594i 0.141109 0.118404i
\(377\) 0.0151307 + 0.0151307i 0.000779272 + 0.000779272i
\(378\) 0 0
\(379\) 20.3733i 1.04651i 0.852177 + 0.523253i \(0.175282\pi\)
−0.852177 + 0.523253i \(0.824718\pi\)
\(380\) −15.5259 + 3.01947i −0.796462 + 0.154896i
\(381\) 0 0
\(382\) 15.5695 + 22.2356i 0.796606 + 1.13767i
\(383\) 5.74785 12.3263i 0.293701 0.629845i −0.702983 0.711206i \(-0.748149\pi\)
0.996685 + 0.0813617i \(0.0259269\pi\)
\(384\) 0 0
\(385\) 11.5911 5.65471i 0.590735 0.288191i
\(386\) 15.3425 8.85802i 0.780915 0.450861i
\(387\) 0 0
\(388\) −4.92942 + 1.32083i −0.250253 + 0.0670551i
\(389\) 6.23872 + 2.27071i 0.316316 + 0.115129i 0.495299 0.868723i \(-0.335059\pi\)
−0.178983 + 0.983852i \(0.557281\pi\)
\(390\) 0 0
\(391\) 28.6072 + 24.0043i 1.44673 + 1.21395i
\(392\) −0.452320 5.17004i −0.0228456 0.261127i
\(393\) 0 0
\(394\) −3.00484 + 8.25572i −0.151382 + 0.415917i
\(395\) 6.47456 + 10.7731i 0.325771 + 0.542056i
\(396\) 0 0
\(397\) −28.2089 7.55855i −1.41576 0.379353i −0.531785 0.846879i \(-0.678479\pi\)
−0.883979 + 0.467527i \(0.845145\pi\)
\(398\) −10.0499 7.03703i −0.503757 0.352734i
\(399\) 0 0
\(400\) 3.94064 + 3.07755i 0.197032 + 0.153878i
\(401\) 13.2541 + 2.33705i 0.661876 + 0.116707i 0.494488 0.869184i \(-0.335356\pi\)
0.167388 + 0.985891i \(0.446467\pi\)
\(402\) 0 0
\(403\) −11.4566 1.00232i −0.570692 0.0499291i
\(404\) 14.2552 0.709224
\(405\) 0 0
\(406\) 0.00839574 0.000416674
\(407\) −20.5944 1.80178i −1.02083 0.0893107i
\(408\) 0 0
\(409\) −8.85097 1.56066i −0.437652 0.0771699i −0.0495190 0.998773i \(-0.515769\pi\)
−0.388133 + 0.921603i \(0.626880\pi\)
\(410\) 1.98631 1.44343i 0.0980968 0.0712858i
\(411\) 0 0
\(412\) 1.65841 + 1.16123i 0.0817038 + 0.0572096i
\(413\) 12.0512 + 3.22912i 0.593002 + 0.158894i
\(414\) 0 0
\(415\) 7.46876 29.9678i 0.366627 1.47106i
\(416\) 1.17282 3.22230i 0.0575022 0.157986i
\(417\) 0 0
\(418\) −2.64280 30.2073i −0.129263 1.47749i
\(419\) 9.47636 + 7.95161i 0.462950 + 0.388461i 0.844215 0.536004i \(-0.180067\pi\)
−0.381265 + 0.924466i \(0.624511\pi\)
\(420\) 0 0
\(421\) −18.9688 6.90407i −0.924481 0.336484i −0.164461 0.986384i \(-0.552589\pi\)
−0.760020 + 0.649900i \(0.774811\pi\)
\(422\) −6.61406 + 1.77223i −0.321967 + 0.0862709i
\(423\) 0 0
\(424\) 9.96826 5.75518i 0.484101 0.279496i
\(425\) −38.4113 2.00569i −1.86322 0.0972904i
\(426\) 0 0
\(427\) 4.06948 8.72702i 0.196936 0.422330i
\(428\) 5.34201 + 7.62918i 0.258216 + 0.368770i
\(429\) 0 0
\(430\) −3.17681 16.3350i −0.153200 0.787741i
\(431\) 8.26858i 0.398283i −0.979971 0.199142i \(-0.936185\pi\)
0.979971 0.199142i \(-0.0638154\pi\)
\(432\) 0 0
\(433\) 24.6631 + 24.6631i 1.18523 + 1.18523i 0.978369 + 0.206865i \(0.0663262\pi\)
0.206865 + 0.978369i \(0.433674\pi\)
\(434\) −3.45660 + 2.90043i −0.165922 + 0.139225i
\(435\) 0 0
\(436\) 0.173284 0.982742i 0.00829879 0.0470648i
\(437\) −31.1208 14.5118i −1.48871 0.694196i
\(438\) 0 0
\(439\) 2.32992 0.410828i 0.111201 0.0196077i −0.117771 0.993041i \(-0.537575\pi\)
0.228972 + 0.973433i \(0.426464\pi\)
\(440\) −6.65806 + 6.89594i −0.317410 + 0.328751i
\(441\) 0 0
\(442\) 6.82742 + 25.4803i 0.324747 + 1.21197i
\(443\) −3.14927 + 1.46853i −0.149626 + 0.0697719i −0.495989 0.868329i \(-0.665194\pi\)
0.346363 + 0.938101i \(0.387417\pi\)
\(444\) 0 0
\(445\) −1.11051 2.89215i −0.0526432 0.137101i
\(446\) 0.0362583 0.0432110i 0.00171688 0.00204610i
\(447\) 0 0
\(448\) −0.568607 1.21938i −0.0268642 0.0576104i
\(449\) 2.75309 4.76849i 0.129926 0.225039i −0.793721 0.608281i \(-0.791859\pi\)
0.923648 + 0.383242i \(0.125193\pi\)
\(450\) 0 0
\(451\) 2.35363 + 4.07661i 0.110828 + 0.191960i
\(452\) 6.36868 9.09542i 0.299558 0.427813i
\(453\) 0 0
\(454\) 2.54119 + 6.98187i 0.119264 + 0.327675i
\(455\) 6.49156 8.01798i 0.304329 0.375889i
\(456\) 0 0
\(457\) 0.879530 10.0531i 0.0411427 0.470263i −0.947477 0.319825i \(-0.896376\pi\)
0.988619 0.150438i \(-0.0480685\pi\)
\(458\) −8.69981 + 8.69981i −0.406516 + 0.406516i
\(459\) 0 0
\(460\) 2.99301 + 10.4341i 0.139550 + 0.486493i
\(461\) −7.75567 9.24285i −0.361218 0.430482i 0.554575 0.832134i \(-0.312881\pi\)
−0.915793 + 0.401651i \(0.868436\pi\)
\(462\) 0 0
\(463\) −8.32374 + 5.82835i −0.386837 + 0.270866i −0.750776 0.660556i \(-0.770320\pi\)
0.363939 + 0.931423i \(0.381432\pi\)
\(464\) −0.00586382 + 0.00213426i −0.000272221 + 9.90804e-5i
\(465\) 0 0
\(466\) 2.27329 + 12.8925i 0.105308 + 0.597233i
\(467\) −5.28342 + 19.7180i −0.244487 + 0.912440i 0.729153 + 0.684351i \(0.239914\pi\)
−0.973640 + 0.228089i \(0.926752\pi\)
\(468\) 0 0
\(469\) 6.48803 + 3.74587i 0.299589 + 0.172968i
\(470\) −6.02729 + 5.24045i −0.278018 + 0.241724i
\(471\) 0 0
\(472\) −9.23778 + 0.808201i −0.425203 + 0.0372005i
\(473\) 31.7814 2.78051i 1.46131 0.127848i
\(474\) 0 0
\(475\) 34.5932 7.35991i 1.58724 0.337696i
\(476\) 8.96345 + 5.17505i 0.410839 + 0.237198i
\(477\) 0 0
\(478\) −0.00700316 + 0.0261361i −0.000320317 + 0.00119544i
\(479\) −7.22274 40.9622i −0.330015 1.87161i −0.471789 0.881711i \(-0.656392\pi\)
0.141774 0.989899i \(-0.454719\pi\)
\(480\) 0 0
\(481\) −15.5395 + 5.65590i −0.708538 + 0.257887i
\(482\) 5.95221 4.16778i 0.271116 0.189837i
\(483\) 0 0
\(484\) −4.74167 5.65090i −0.215531 0.256859i
\(485\) 10.9690 3.14644i 0.498076 0.142872i
\(486\) 0 0
\(487\) 21.5643 21.5643i 0.977171 0.977171i −0.0225745 0.999745i \(-0.507186\pi\)
0.999745 + 0.0225745i \(0.00718628\pi\)
\(488\) −0.623767 + 7.12968i −0.0282366 + 0.322746i
\(489\) 0 0
\(490\) 1.21413 + 11.5410i 0.0548487 + 0.521371i
\(491\) −2.06551 5.67493i −0.0932150 0.256106i 0.884319 0.466883i \(-0.154623\pi\)
−0.977534 + 0.210777i \(0.932401\pi\)
\(492\) 0 0
\(493\) 0.0275339 0.0393224i 0.00124006 0.00177099i
\(494\) −12.1278 21.0060i −0.545657 0.945105i
\(495\) 0 0
\(496\) 1.67688 2.90443i 0.0752939 0.130413i
\(497\) −1.56185 3.34940i −0.0700586 0.150241i
\(498\) 0 0
\(499\) −9.82974 + 11.7146i −0.440040 + 0.524419i −0.939791 0.341750i \(-0.888980\pi\)
0.499751 + 0.866169i \(0.333425\pi\)
\(500\) −8.93094 6.72594i −0.399404 0.300793i
\(501\) 0 0
\(502\) −9.66849 + 4.50849i −0.431526 + 0.201224i
\(503\) 4.09733 + 15.2915i 0.182691 + 0.681813i 0.995113 + 0.0987425i \(0.0314820\pi\)
−0.812422 + 0.583070i \(0.801851\pi\)
\(504\) 0 0
\(505\) −31.8707 + 0.559351i −1.41823 + 0.0248908i
\(506\) −20.4940 + 3.61364i −0.911069 + 0.160646i
\(507\) 0 0
\(508\) 10.0808 + 4.70075i 0.447263 + 0.208562i
\(509\) −5.47407 + 31.0450i −0.242634 + 1.37604i 0.583291 + 0.812264i \(0.301765\pi\)
−0.825924 + 0.563781i \(0.809346\pi\)
\(510\) 0 0
\(511\) 11.0237 9.24998i 0.487660 0.409195i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 0 0
\(514\) 6.26111i 0.276166i
\(515\) −3.75330 2.53111i −0.165390 0.111534i
\(516\) 0 0
\(517\) −8.78251 12.5427i −0.386254 0.551628i
\(518\) −2.74210 + 5.88045i −0.120481 + 0.258372i
\(519\) 0 0
\(520\) −2.49566 + 7.25018i −0.109442 + 0.317942i
\(521\) 18.5639 10.7179i 0.813300 0.469559i −0.0348007 0.999394i \(-0.511080\pi\)
0.848100 + 0.529835i \(0.177746\pi\)
\(522\) 0 0
\(523\) 33.9851 9.10628i 1.48606 0.398190i 0.577658 0.816279i \(-0.303967\pi\)
0.908406 + 0.418089i \(0.137300\pi\)
\(524\) 6.84998 + 2.49319i 0.299243 + 0.108915i
\(525\) 0 0
\(526\) −1.72460 1.44711i −0.0751963 0.0630972i
\(527\) 2.24858 + 25.7013i 0.0979495 + 1.11957i
\(528\) 0 0
\(529\) −0.193512 + 0.531670i −0.00841357 + 0.0231161i
\(530\) −22.0604 + 13.2581i −0.958245 + 0.575896i
\(531\) 0 0
\(532\) −9.19266 2.46317i −0.398553 0.106792i
\(533\) 3.08445 + 2.15976i 0.133603 + 0.0935495i
\(534\) 0 0
\(535\) −12.2426 16.8471i −0.529294 0.728364i
\(536\) −5.48365 0.966915i −0.236857 0.0417644i
\(537\) 0 0
\(538\) 20.0065 + 1.75035i 0.862543 + 0.0754628i
\(539\) −22.2477 −0.958274
\(540\) 0 0
\(541\) −1.73780 −0.0747137 −0.0373569 0.999302i \(-0.511894\pi\)
−0.0373569 + 0.999302i \(0.511894\pi\)
\(542\) 22.2676 + 1.94816i 0.956476 + 0.0836808i
\(543\) 0 0
\(544\) −7.57586 1.33583i −0.324812 0.0572732i
\(545\) −0.348854 + 2.20394i −0.0149432 + 0.0944063i
\(546\) 0 0
\(547\) −24.3181 17.0277i −1.03977 0.728052i −0.0766277 0.997060i \(-0.524415\pi\)
−0.963138 + 0.269008i \(0.913304\pi\)
\(548\) −11.5092 3.08389i −0.491650 0.131737i
\(549\) 0 0
\(550\) 14.6150 15.6787i 0.623185 0.668540i
\(551\) −0.0150966 + 0.0414777i −0.000643138 + 0.00176701i
\(552\) 0 0
\(553\) 0.659139 + 7.53399i 0.0280294 + 0.320378i
\(554\) −3.89003 3.26413i −0.165272 0.138679i
\(555\) 0 0
\(556\) −5.74321 2.09036i −0.243566 0.0886508i
\(557\) 30.6627 8.21606i 1.29922 0.348125i 0.458066 0.888918i \(-0.348542\pi\)
0.841156 + 0.540793i \(0.181876\pi\)
\(558\) 0 0
\(559\) 22.1006 12.7598i 0.934757 0.539682i
\(560\) 1.31910 + 2.70389i 0.0557419 + 0.114260i
\(561\) 0 0
\(562\) 6.81354 14.6117i 0.287412 0.616357i
\(563\) −12.2805 17.5384i −0.517561 0.739154i 0.472262 0.881458i \(-0.343438\pi\)
−0.989823 + 0.142305i \(0.954549\pi\)
\(564\) 0 0
\(565\) −13.8817 + 20.5848i −0.584009 + 0.866007i
\(566\) 15.5423i 0.653291i
\(567\) 0 0
\(568\) 1.94228 + 1.94228i 0.0814964 + 0.0814964i
\(569\) 26.5911 22.3126i 1.11476 0.935393i 0.116430 0.993199i \(-0.462855\pi\)
0.998328 + 0.0578062i \(0.0184105\pi\)
\(570\) 0 0
\(571\) −3.94694 + 22.3842i −0.165174 + 0.936750i 0.783710 + 0.621127i \(0.213325\pi\)
−0.948885 + 0.315623i \(0.897786\pi\)
\(572\) −13.3226 6.21244i −0.557046 0.259755i
\(573\) 0 0
\(574\) 1.45496 0.256548i 0.0607287 0.0107081i
\(575\) −7.10097 23.2104i −0.296131 0.967939i
\(576\) 0 0
\(577\) 5.75013 + 21.4598i 0.239381 + 0.893383i 0.976125 + 0.217210i \(0.0696958\pi\)
−0.736744 + 0.676172i \(0.763638\pi\)
\(578\) 38.2264 17.8253i 1.59001 0.741433i
\(579\) 0 0
\(580\) 0.0130261 0.00500169i 0.000540881 0.000207684i
\(581\) 11.9450 14.2355i 0.495562 0.590588i
\(582\) 0 0
\(583\) −20.8531 44.7197i −0.863648 1.85210i
\(584\) −5.34785 + 9.26275i −0.221296 + 0.383295i
\(585\) 0 0
\(586\) −16.0557 27.8092i −0.663253 1.14879i
\(587\) −4.24785 + 6.06656i −0.175327 + 0.250394i −0.897192 0.441641i \(-0.854397\pi\)
0.721864 + 0.692034i \(0.243285\pi\)
\(588\) 0 0
\(589\) −8.11364 22.2921i −0.334317 0.918528i
\(590\) 20.6214 2.16939i 0.848970 0.0893124i
\(591\) 0 0
\(592\) 0.420307 4.80413i 0.0172745 0.197449i
\(593\) 10.8659 10.8659i 0.446208 0.446208i −0.447884 0.894092i \(-0.647822\pi\)
0.894092 + 0.447884i \(0.147822\pi\)
\(594\) 0 0
\(595\) −20.2429 11.2183i −0.829877 0.459905i
\(596\) 1.38581 + 1.65154i 0.0567648 + 0.0676497i
\(597\) 0 0
\(598\) −13.6359 + 9.54799i −0.557615 + 0.390446i
\(599\) 37.1726 13.5297i 1.51883 0.552809i 0.557974 0.829858i \(-0.311579\pi\)
0.960856 + 0.277049i \(0.0893566\pi\)
\(600\) 0 0
\(601\) −1.53626 8.71259i −0.0626655 0.355394i −0.999976 0.00689897i \(-0.997804\pi\)
0.937311 0.348495i \(-0.113307\pi\)
\(602\) 2.59152 9.67169i 0.105623 0.394189i
\(603\) 0 0
\(604\) 13.0898 + 7.55740i 0.532616 + 0.307506i
\(605\) 10.8228 + 12.4478i 0.440009 + 0.506075i
\(606\) 0 0
\(607\) −19.5481 + 1.71024i −0.793433 + 0.0694164i −0.476663 0.879086i \(-0.658154\pi\)
−0.316770 + 0.948502i \(0.602598\pi\)
\(608\) 7.04657 0.616495i 0.285776 0.0250022i
\(609\) 0 0
\(610\) 1.11481 15.9645i 0.0451374 0.646383i
\(611\) −10.6073 6.12411i −0.429124 0.247755i
\(612\) 0 0
\(613\) −10.4403 + 38.9638i −0.421680 + 1.57373i 0.349387 + 0.936979i \(0.386390\pi\)
−0.771067 + 0.636754i \(0.780277\pi\)
\(614\) −0.441919 2.50625i −0.0178344 0.101144i
\(615\) 0 0
\(616\) −5.41981 + 1.97265i −0.218370 + 0.0794803i
\(617\) −3.15147 + 2.20668i −0.126873 + 0.0888377i −0.635291 0.772273i \(-0.719120\pi\)
0.508417 + 0.861111i \(0.330231\pi\)
\(618\) 0 0
\(619\) 31.5228 + 37.5674i 1.26701 + 1.50996i 0.763223 + 0.646135i \(0.223616\pi\)
0.503786 + 0.863828i \(0.331940\pi\)
\(620\) −3.63506 + 6.55931i −0.145988 + 0.263428i
\(621\) 0 0
\(622\) 11.9545 11.9545i 0.479334 0.479334i
\(623\) 0.162465 1.85699i 0.00650903 0.0743986i
\(624\) 0 0
\(625\) 20.2310 + 14.6869i 0.809242 + 0.587476i
\(626\) −8.51540 23.3959i −0.340344 0.935087i
\(627\) 0 0
\(628\) −0.857318 + 1.22438i −0.0342107 + 0.0488580i
\(629\) 18.5490 + 32.1279i 0.739598 + 1.28102i
\(630\) 0 0
\(631\) −21.7434 + 37.6606i −0.865590 + 1.49925i 0.000870334 1.00000i \(0.499723\pi\)
−0.866460 + 0.499246i \(0.833610\pi\)
\(632\) −2.37556 5.09440i −0.0944945 0.202644i
\(633\) 0 0
\(634\) 16.5531 19.7273i 0.657409 0.783470i
\(635\) −22.7223 10.1140i −0.901707 0.401363i
\(636\) 0 0
\(637\) −16.1289 + 7.52104i −0.639051 + 0.297994i
\(638\) 0.00692349 + 0.0258388i 0.000274104 + 0.00102297i
\(639\) 0 0
\(640\) −1.60864 1.55315i −0.0635871 0.0613936i
\(641\) −31.6672 + 5.58379i −1.25078 + 0.220546i −0.759530 0.650472i \(-0.774571\pi\)
−0.491250 + 0.871018i \(0.663460\pi\)
\(642\) 0 0
\(643\) −15.3924 7.17758i −0.607016 0.283056i 0.0947082 0.995505i \(-0.469808\pi\)
−0.701724 + 0.712449i \(0.747586\pi\)
\(644\) −1.13416 + 6.43216i −0.0446923 + 0.253462i
\(645\) 0 0
\(646\) −41.6839 + 34.9769i −1.64003 + 1.37615i
\(647\) 21.6407 + 21.6407i 0.850784 + 0.850784i 0.990230 0.139446i \(-0.0445320\pi\)
−0.139446 + 0.990230i \(0.544532\pi\)
\(648\) 0 0
\(649\) 39.7519i 1.56040i
\(650\) 5.29513 16.3073i 0.207692 0.639626i
\(651\) 0 0
\(652\) −9.38042 13.3966i −0.367366 0.524652i
\(653\) −8.25358 + 17.6999i −0.322988 + 0.692649i −0.999022 0.0442212i \(-0.985919\pi\)
0.676034 + 0.736870i \(0.263697\pi\)
\(654\) 0 0
\(655\) −15.4125 5.30530i −0.602216 0.207295i
\(656\) −0.950966 + 0.549040i −0.0371290 + 0.0214364i
\(657\) 0 0
\(658\) −4.64196 + 1.24381i −0.180962 + 0.0484887i
\(659\) −3.03288 1.10388i −0.118144 0.0430009i 0.282272 0.959335i \(-0.408912\pi\)
−0.400416 + 0.916334i \(0.631134\pi\)
\(660\) 0 0
\(661\) −13.9565 11.7109i −0.542844 0.455500i 0.329665 0.944098i \(-0.393064\pi\)
−0.872509 + 0.488598i \(0.837509\pi\)
\(662\) 0.287203 + 3.28275i 0.0111625 + 0.127588i
\(663\) 0 0
\(664\) −4.72396 + 12.9790i −0.183325 + 0.503682i
\(665\) 20.6489 + 5.14626i 0.800730 + 0.199563i
\(666\) 0 0
\(667\) 0.0292604 + 0.00784029i 0.00113297 + 0.000303577i
\(668\) −7.00000 4.90145i −0.270838 0.189643i
\(669\) 0 0
\(670\) 12.2979 + 1.94659i 0.475108 + 0.0752032i
\(671\) 30.2142 + 5.32759i 1.16641 + 0.205669i
\(672\) 0 0
\(673\) −47.1598 4.12595i −1.81788 0.159044i −0.873268 0.487239i \(-0.838004\pi\)
−0.944610 + 0.328196i \(0.893559\pi\)
\(674\) 23.3125 0.897963
\(675\) 0 0
\(676\) 1.24130 0.0477425
\(677\) 9.89706 + 0.865881i 0.380375 + 0.0332785i 0.275740 0.961232i \(-0.411077\pi\)
0.104635 + 0.994511i \(0.466633\pi\)
\(678\) 0 0
\(679\) 6.76188 + 1.19230i 0.259497 + 0.0457563i
\(680\) 16.9900 + 2.68928i 0.651535 + 0.103129i
\(681\) 0 0
\(682\) −11.7769 8.24624i −0.450959 0.315765i
\(683\) 17.7729 + 4.76224i 0.680062 + 0.182222i 0.582283 0.812986i \(-0.302160\pi\)
0.0977790 + 0.995208i \(0.468826\pi\)
\(684\) 0 0
\(685\) 25.8525 + 6.44312i 0.987772 + 0.246179i
\(686\) −5.60934 + 15.4115i −0.214166 + 0.588416i
\(687\) 0 0
\(688\) 0.648620 + 7.41376i 0.0247284 + 0.282647i
\(689\) −30.2359 25.3709i −1.15189 0.966554i
\(690\) 0 0
\(691\) 7.98078 + 2.90477i 0.303603 + 0.110503i 0.489329 0.872099i \(-0.337242\pi\)
−0.185726 + 0.982602i \(0.559464\pi\)
\(692\) 19.9942 5.35742i 0.760064 0.203659i
\(693\) 0 0
\(694\) −4.29770 + 2.48128i −0.163139 + 0.0941881i
\(695\) 12.9222 + 4.44810i 0.490169 + 0.168726i
\(696\) 0 0
\(697\) 3.56996 7.65580i 0.135222 0.289984i
\(698\) −16.4274 23.4607i −0.621785 0.888001i
\(699\) 0 0
\(700\) −3.05523 5.99339i −0.115477 0.226529i
\(701\) 21.8864i 0.826637i 0.910586 + 0.413319i \(0.135630\pi\)
−0.910586 + 0.413319i \(0.864370\pi\)
\(702\) 0 0
\(703\) −24.1207 24.1207i −0.909728 0.909728i
\(704\) 3.28389 2.75551i 0.123766 0.103852i
\(705\) 0 0
\(706\) −2.28721 + 12.9714i −0.0860801 + 0.488185i
\(707\) −17.3826 8.10562i −0.653739 0.304843i
\(708\) 0 0
\(709\) −2.29997 + 0.405546i −0.0863770 + 0.0152306i −0.216670 0.976245i \(-0.569519\pi\)
0.130293 + 0.991476i \(0.458408\pi\)
\(710\) −4.41862 4.26620i −0.165828 0.160107i
\(711\) 0 0
\(712\) 0.358589 + 1.33827i 0.0134387 + 0.0501538i
\(713\) −14.7553 + 6.88050i −0.552590 + 0.257677i
\(714\) 0 0
\(715\) 30.0294 + 13.3665i 1.12304 + 0.499880i
\(716\) 10.2364 12.1993i 0.382553 0.455909i
\(717\) 0 0
\(718\) −2.44443 5.24209i −0.0912252 0.195633i
\(719\) −20.7200 + 35.8882i −0.772727 + 1.33840i 0.163336 + 0.986570i \(0.447774\pi\)
−0.936063 + 0.351832i \(0.885559\pi\)
\(720\) 0 0
\(721\) −1.36195 2.35896i −0.0507216 0.0878524i
\(722\) 17.8005 25.4217i 0.662466 0.946099i
\(723\) 0 0
\(724\) −2.36384 6.49461i −0.0878516 0.241370i
\(725\) −0.0289266 + 0.0116935i −0.00107431 + 0.000434287i
\(726\) 0 0
\(727\) 0.853202 9.75214i 0.0316435 0.361687i −0.963821 0.266551i \(-0.914116\pi\)
0.995464 0.0951358i \(-0.0303285\pi\)
\(728\) −3.26234 + 3.26234i −0.120910 + 0.120910i
\(729\) 0 0
\(730\) 11.5929 20.9188i 0.429071 0.774239i
\(731\) −36.7996 43.8560i −1.36108 1.62207i
\(732\) 0 0
\(733\) 29.1774 20.4302i 1.07769 0.754608i 0.106837 0.994277i \(-0.465928\pi\)
0.970855 + 0.239669i \(0.0770389\pi\)
\(734\) −10.1356 + 3.68907i −0.374114 + 0.136166i
\(735\) 0 0
\(736\) −0.842968 4.78071i −0.0310722 0.176219i
\(737\) −6.17801 + 23.0566i −0.227570 + 0.849302i
\(738\) 0 0
\(739\) 43.5295 + 25.1318i 1.60126 + 0.924487i 0.991236 + 0.132104i \(0.0421732\pi\)
0.610023 + 0.792384i \(0.291160\pi\)
\(740\) −0.751184 + 10.7572i −0.0276141 + 0.395443i
\(741\) 0 0
\(742\) −15.4276 + 1.34974i −0.566363 + 0.0495504i
\(743\) −13.4718 + 1.17863i −0.494232 + 0.0432397i −0.331548 0.943439i \(-0.607571\pi\)
−0.162684 + 0.986678i \(0.552015\pi\)
\(744\) 0 0
\(745\) −3.16308 3.63801i −0.115886 0.133286i
\(746\) 3.23170 + 1.86582i 0.118321 + 0.0683127i
\(747\) 0 0
\(748\) −8.53515 + 31.8536i −0.312076 + 1.16468i
\(749\) −2.17594 12.3404i −0.0795072 0.450908i
\(750\) 0 0
\(751\) −40.9996 + 14.9226i −1.49610 + 0.544535i −0.955047 0.296455i \(-0.904195\pi\)
−0.541051 + 0.840990i \(0.681973\pi\)
\(752\) 2.92589 2.04873i 0.106696 0.0747095i
\(753\) 0 0
\(754\) 0.0137544 + 0.0163919i 0.000500906 + 0.000596957i
\(755\) −29.5617 16.3826i −1.07586 0.596225i
\(756\) 0 0
\(757\) 17.7448 17.7448i 0.644944 0.644944i −0.306823 0.951767i \(-0.599266\pi\)
0.951767 + 0.306823i \(0.0992658\pi\)
\(758\) −1.77565 + 20.2958i −0.0644945 + 0.737176i
\(759\) 0 0
\(760\) −15.7300 + 1.65481i −0.570587 + 0.0600262i
\(761\) 12.4805 + 34.2900i 0.452419 + 1.24301i 0.931016 + 0.364977i \(0.118923\pi\)
−0.478597 + 0.878035i \(0.658854\pi\)
\(762\) 0 0
\(763\) −0.770093 + 1.09981i −0.0278792 + 0.0398157i
\(764\) 13.5723 + 23.5079i 0.491029 + 0.850488i
\(765\) 0 0
\(766\) 6.80029 11.7784i 0.245704 0.425572i
\(767\) 13.4385 + 28.8190i 0.485237 + 1.04059i
\(768\) 0 0
\(769\) −11.5933 + 13.8163i −0.418063 + 0.498228i −0.933439 0.358736i \(-0.883208\pi\)
0.515376 + 0.856964i \(0.327652\pi\)
\(770\) 12.0398 4.62296i 0.433884 0.166600i
\(771\) 0 0
\(772\) 16.0562 7.48712i 0.577875 0.269467i
\(773\) 7.27975 + 27.1684i 0.261834 + 0.977179i 0.964160 + 0.265323i \(0.0854785\pi\)
−0.702325 + 0.711856i \(0.747855\pi\)
\(774\) 0 0
\(775\) 7.86962 14.8074i 0.282685 0.531899i
\(776\) −5.02578 + 0.886180i −0.180415 + 0.0318120i
\(777\) 0 0
\(778\) 6.01707 + 2.80581i 0.215723 + 0.100593i
\(779\) −1.34877 + 7.64926i −0.0483247 + 0.274063i
\(780\) 0 0
\(781\) 9.02019 7.56884i 0.322768 0.270834i
\(782\) 26.4062 + 26.4062i 0.944286 + 0.944286i
\(783\) 0 0
\(784\) 5.18979i 0.185350i
\(785\) 1.86868 2.77101i 0.0666962 0.0989015i
\(786\) 0 0
\(787\) 21.8945 + 31.2685i 0.780453 + 1.11460i 0.990581 + 0.136929i \(0.0437232\pi\)
−0.210127 + 0.977674i \(0.567388\pi\)
\(788\) −3.71294 + 7.96242i −0.132268 + 0.283649i
\(789\) 0 0
\(790\) 5.51098 + 11.2964i 0.196072 + 0.401910i
\(791\) −12.9376 + 7.46952i −0.460007 + 0.265585i
\(792\) 0 0
\(793\) 23.7055 6.35187i 0.841808 0.225562i
\(794\) −27.4428 9.98836i −0.973908 0.354473i
\(795\) 0 0
\(796\) −9.39836 7.88616i −0.333116 0.279518i
\(797\) 2.84657 + 32.5365i 0.100831 + 1.15250i 0.863028 + 0.505156i \(0.168565\pi\)
−0.762197 + 0.647345i \(0.775879\pi\)
\(798\) 0 0
\(799\) −9.39779 + 25.8202i −0.332470 + 0.913453i
\(800\) 3.65742 + 3.40929i 0.129309 + 0.120537i
\(801\) 0 0
\(802\) 12.9999 + 3.48332i 0.459044 + 0.123000i
\(803\) 37.5585 + 26.2987i 1.32541 + 0.928062i
\(804\) 0 0
\(805\) 2.28329 14.4250i 0.0804753 0.508415i
\(806\) −11.3256 1.99701i −0.398928 0.0703417i
\(807\) 0 0
\(808\) 14.2010 + 1.24242i 0.499589 + 0.0437083i
\(809\) −18.8465 −0.662608 −0.331304 0.943524i \(-0.607488\pi\)
−0.331304 + 0.943524i \(0.607488\pi\)
\(810\) 0 0
\(811\) 23.8763 0.838409 0.419205 0.907892i \(-0.362309\pi\)
0.419205 + 0.907892i \(0.362309\pi\)
\(812\) 0.00836379 0.000731737i 0.000293512 2.56789e-5i
\(813\) 0 0
\(814\) −20.3590 3.58984i −0.713582 0.125824i
\(815\) 21.4977 + 29.5831i 0.753031 + 1.03625i
\(816\) 0 0
\(817\) 43.1214 + 30.1939i 1.50863 + 1.05635i
\(818\) −8.68127 2.32614i −0.303533 0.0813315i
\(819\) 0 0
\(820\) 2.10455 1.26482i 0.0734942 0.0441693i
\(821\) −7.71011 + 21.1833i −0.269085 + 0.739304i 0.729390 + 0.684098i \(0.239804\pi\)
−0.998475 + 0.0552062i \(0.982418\pi\)
\(822\) 0 0
\(823\) 4.54252 + 51.9212i 0.158342 + 1.80986i 0.495712 + 0.868487i \(0.334907\pi\)
−0.337370 + 0.941372i \(0.609537\pi\)
\(824\) 1.55089 + 1.30135i 0.0540277 + 0.0453346i
\(825\) 0 0
\(826\) 11.7239 + 4.26716i 0.407928 + 0.148474i
\(827\) −19.7756 + 5.29886i −0.687665 + 0.184259i −0.585699 0.810529i \(-0.699180\pi\)
−0.101966 + 0.994788i \(0.532513\pi\)
\(828\) 0 0
\(829\) 8.17054 4.71726i 0.283775 0.163837i −0.351356 0.936242i \(-0.614279\pi\)
0.635131 + 0.772404i \(0.280946\pi\)
\(830\) 10.0522 29.2028i 0.348917 1.01364i
\(831\) 0 0
\(832\) 1.44920 3.10782i 0.0502419 0.107744i
\(833\) 22.8993 + 32.7036i 0.793413 + 1.13311i
\(834\) 0 0
\(835\) 15.8424 + 10.6836i 0.548248 + 0.369722i
\(836\) 30.3227i 1.04873i
\(837\) 0 0
\(838\) 8.74727 + 8.74727i 0.302169 + 0.302169i
\(839\) −34.6389 + 29.0655i −1.19587 + 1.00345i −0.196129 + 0.980578i \(0.562837\pi\)
−0.999738 + 0.0228742i \(0.992718\pi\)
\(840\) 0 0
\(841\) −5.03579 + 28.5594i −0.173648 + 0.984806i
\(842\) −18.2949 8.53103i −0.630482 0.293999i
\(843\) 0 0
\(844\) −6.74335 + 1.18903i −0.232116 + 0.0409283i
\(845\) −2.77521 + 0.0487068i −0.0954703 + 0.00167556i
\(846\) 0 0
\(847\) 2.56876 + 9.58676i 0.0882638 + 0.329405i
\(848\) 10.4319 4.86449i 0.358234 0.167047i
\(849\) 0 0
\(850\) −38.0904 5.34583i −1.30649 0.183360i
\(851\) −15.0480 + 17.9335i −0.515839 + 0.614753i
\(852\) 0 0
\(853\) 18.5338 + 39.7458i 0.634584 + 1.36087i 0.915959 + 0.401272i \(0.131432\pi\)
−0.281375 + 0.959598i \(0.590791\pi\)
\(854\) 4.81460 8.33913i 0.164752 0.285359i
\(855\) 0 0
\(856\) 4.65675 + 8.06573i 0.159165 + 0.275681i
\(857\) −1.31729 + 1.88128i −0.0449977 + 0.0642633i −0.841020 0.541003i \(-0.818045\pi\)
0.796023 + 0.605267i \(0.206934\pi\)
\(858\) 0 0
\(859\) −1.23367 3.38949i −0.0420924 0.115648i 0.916866 0.399196i \(-0.130711\pi\)
−0.958958 + 0.283548i \(0.908488\pi\)
\(860\) −1.74104 16.5497i −0.0593689 0.564339i
\(861\) 0 0
\(862\) 0.720654 8.23711i 0.0245456 0.280557i
\(863\) −11.9419 + 11.9419i −0.406507 + 0.406507i −0.880518 0.474012i \(-0.842805\pi\)
0.474012 + 0.880518i \(0.342805\pi\)
\(864\) 0 0
\(865\) −44.4912 + 12.7623i −1.51275 + 0.433930i
\(866\) 22.4198 + 26.7188i 0.761854 + 0.907942i
\(867\) 0 0
\(868\) −3.69623 + 2.58813i −0.125458 + 0.0878469i
\(869\) −22.6432 + 8.24143i −0.768116 + 0.279571i
\(870\) 0 0
\(871\) 3.31564 + 18.8039i 0.112346 + 0.637148i
\(872\) 0.258276 0.963899i 0.00874633 0.0326417i
\(873\) 0 0
\(874\) −29.7375 17.1690i −1.00589 0.580749i
\(875\) 7.06582 + 13.2797i 0.238868 + 0.448935i
\(876\) 0 0
\(877\) 44.3005 3.87579i 1.49592 0.130876i 0.690394 0.723434i \(-0.257437\pi\)
0.805528 + 0.592558i \(0.201882\pi\)
\(878\) 2.35686 0.206198i 0.0795401 0.00695886i
\(879\) 0 0
\(880\) −7.23374 + 6.28941i −0.243849 + 0.212016i
\(881\) −20.0596 11.5814i −0.675825 0.390188i 0.122455 0.992474i \(-0.460923\pi\)
−0.798280 + 0.602286i \(0.794257\pi\)
\(882\) 0 0
\(883\) 5.68779 21.2271i 0.191409 0.714350i −0.801758 0.597649i \(-0.796102\pi\)
0.993167 0.116701i \(-0.0372318\pi\)
\(884\) 4.58069 + 25.9784i 0.154065 + 0.873747i
\(885\) 0 0
\(886\) −3.26528 + 1.18846i −0.109699 + 0.0399272i
\(887\) 29.4217 20.6013i 0.987883 0.691723i 0.0363722 0.999338i \(-0.488420\pi\)
0.951511 + 0.307615i \(0.0995309\pi\)
\(888\) 0 0
\(889\) −9.61945 11.4640i −0.322626 0.384491i
\(890\) −0.854217 2.97793i −0.0286334 0.0998206i
\(891\) 0 0
\(892\) 0.0398865 0.0398865i 0.00133550 0.00133550i
\(893\) 2.20203 25.1693i 0.0736880 0.842258i
\(894\) 0 0
\(895\) −22.4071 + 27.6759i −0.748988 + 0.925103i
\(896\) −0.460167 1.26430i −0.0153731 0.0422373i
\(897\) 0 0
\(898\) 3.15822 4.51040i 0.105391 0.150514i
\(899\) 0.0104640 + 0.0181241i 0.000348992 + 0.000604472i
\(900\) 0 0
\(901\) −44.2730 + 76.6832i −1.47495 + 2.55469i
\(902\) 1.98938 + 4.26623i 0.0662390 + 0.142050i
\(903\) 0 0
\(904\) 7.13717 8.50575i 0.237379 0.282897i
\(905\) 5.53974 + 14.4274i 0.184147 + 0.479583i
\(906\) 0 0
\(907\) −23.5226 + 10.9688i −0.781055 + 0.364212i −0.771898 0.635746i \(-0.780693\pi\)
−0.00915710 + 0.999958i \(0.502915\pi\)
\(908\) 1.92301 + 7.17678i 0.0638174 + 0.238170i
\(909\) 0 0
\(910\) 7.16567 7.42169i 0.237540 0.246027i
\(911\) 13.9071 2.45220i 0.460763 0.0812449i 0.0615515 0.998104i \(-0.480395\pi\)
0.399211 + 0.916859i \(0.369284\pi\)
\(912\) 0 0
\(913\) 53.6617 + 25.0229i 1.77594 + 0.828136i
\(914\) 1.75237 9.93817i 0.0579631 0.328725i
\(915\) 0 0
\(916\) −9.42495 + 7.90847i −0.311409 + 0.261303i
\(917\) −6.93510 6.93510i −0.229017 0.229017i
\(918\) 0 0
\(919\) 27.7976i 0.916959i −0.888705 0.458479i \(-0.848394\pi\)
0.888705 0.458479i \(-0.151606\pi\)
\(920\) 2.07223 + 10.6553i 0.0683194 + 0.351294i
\(921\) 0 0
\(922\) −6.92059 9.88363i −0.227917 0.325500i
\(923\) 3.98066 8.53656i 0.131025 0.280984i
\(924\) 0 0
\(925\) 1.25735 24.0796i 0.0413413 0.791733i
\(926\) −8.80004 + 5.08071i −0.289187 + 0.166962i
\(927\) 0 0
\(928\) −0.00602752 + 0.00161507i −0.000197863 + 5.30172e-5i
\(929\) −30.6608 11.1596i −1.00595 0.366135i −0.214072 0.976818i \(-0.568673\pi\)
−0.791875 + 0.610683i \(0.790895\pi\)
\(930\) 0 0
\(931\) −28.1214 23.5967i −0.921643 0.773350i
\(932\) 1.14099 + 13.0416i 0.0373743 + 0.427190i
\(933\) 0 0
\(934\) −6.98185 + 19.1825i −0.228453 + 0.627670i
\(935\) 17.8323 71.5508i 0.583180 2.33996i
\(936\) 0 0
\(937\) −40.8389 10.9427i −1.33415 0.357484i −0.479888 0.877330i \(-0.659323\pi\)
−0.854260 + 0.519846i \(0.825989\pi\)
\(938\) 6.13687 + 4.29708i 0.200376 + 0.140305i
\(939\) 0 0
\(940\) −6.46109 + 4.69520i −0.210737 + 0.153140i
\(941\) −55.9278 9.86158i −1.82319 0.321478i −0.845896 0.533348i \(-0.820934\pi\)
−0.977298 + 0.211869i \(0.932045\pi\)
\(942\) 0 0
\(943\) 5.31031 + 0.464592i 0.172927 + 0.0151292i
\(944\) −9.27307 −0.301813
\(945\) 0 0
\(946\) 31.9028 1.03725
\(947\) 44.2394 + 3.87045i 1.43759 + 0.125773i 0.779138 0.626852i \(-0.215657\pi\)
0.658450 + 0.752625i \(0.271212\pi\)
\(948\) 0 0
\(949\) 36.1194 + 6.36882i 1.17248 + 0.206741i
\(950\) 35.1030 4.31691i 1.13889 0.140059i
\(951\) 0 0
\(952\) 8.47831 + 5.93658i 0.274784 + 0.192406i
\(953\) 9.05327 + 2.42582i 0.293264 + 0.0785799i 0.402452 0.915441i \(-0.368158\pi\)
−0.109187 + 0.994021i \(0.534825\pi\)
\(954\) 0 0
\(955\) −31.2664 52.0247i −1.01176 1.68348i
\(956\) −0.00925442 + 0.0254263i −0.000299309 + 0.000822346i
\(957\) 0 0
\(958\) −3.62516 41.4358i −0.117124 1.33873i
\(959\) 12.2806 + 10.3047i 0.396562 + 0.332755i
\(960\) 0 0
\(961\) 18.5611 + 6.75570i 0.598747 + 0.217926i
\(962\) −15.9733 + 4.28003i −0.514999 + 0.137994i
\(963\) 0 0
\(964\) 6.29281 3.63315i 0.202678 0.117016i
\(965\) −35.6034 + 17.3692i −1.14611 + 0.559133i
\(966\) 0 0
\(967\) 10.2031 21.8807i 0.328111 0.703636i −0.671180 0.741295i \(-0.734212\pi\)
0.999291 + 0.0376584i \(0.0119899\pi\)
\(968\) −4.23112 6.04266i −0.135993 0.194219i
\(969\) 0 0
\(970\) 11.2015 2.17846i 0.359658 0.0699460i
\(971\) 42.1000i 1.35105i −0.737336 0.675526i \(-0.763917\pi\)
0.737336 0.675526i \(-0.236083\pi\)
\(972\) 0 0
\(973\) 5.81457 + 5.81457i 0.186407 + 0.186407i
\(974\) 23.3617 19.6028i 0.748556 0.628113i
\(975\) 0 0
\(976\) −1.24279 + 7.04819i −0.0397806 + 0.225607i
\(977\) −14.8310 6.91579i −0.474484 0.221256i 0.170640 0.985333i \(-0.445417\pi\)
−0.645124 + 0.764078i \(0.723194\pi\)
\(978\) 0 0
\(979\) 5.84906 1.03135i 0.186937 0.0329620i
\(980\) 0.203639 + 11.6029i 0.00650501 + 0.370642i
\(981\) 0 0
\(982\) −1.56304 5.83336i −0.0498787 0.186150i
\(983\) −5.97463 + 2.78601i −0.190561 + 0.0888601i −0.515557 0.856855i \(-0.672415\pi\)
0.324996 + 0.945715i \(0.394637\pi\)
\(984\) 0 0
\(985\) 7.98867 17.9475i 0.254540 0.571854i
\(986\) 0.0308562 0.0367730i 0.000982663 0.00117109i
\(987\) 0 0
\(988\) −10.2509 21.9831i −0.326124 0.699375i
\(989\) 18.0636 31.2872i 0.574391 0.994874i
\(990\) 0 0
\(991\) −27.5644 47.7429i −0.875612 1.51660i −0.856110 0.516794i \(-0.827125\pi\)
−0.0195020 0.999810i \(-0.506208\pi\)
\(992\) 1.92363 2.74723i 0.0610754 0.0872247i
\(993\) 0 0
\(994\) −1.26399 3.47278i −0.0400913 0.110150i
\(995\) 21.3216 + 17.2625i 0.675939 + 0.547258i
\(996\) 0 0
\(997\) 2.30128 26.3037i 0.0728822 0.833047i −0.868497 0.495695i \(-0.834913\pi\)
0.941379 0.337352i \(-0.109531\pi\)
\(998\) −10.8133 + 10.8133i −0.342290 + 0.342290i
\(999\) 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 810.2.s.a.773.11 216
3.2 odd 2 270.2.r.a.113.1 216
5.2 odd 4 inner 810.2.s.a.287.7 216
15.2 even 4 270.2.r.a.167.14 yes 216
27.11 odd 18 inner 810.2.s.a.683.7 216
27.16 even 9 270.2.r.a.173.14 yes 216
135.92 even 36 inner 810.2.s.a.197.11 216
135.97 odd 36 270.2.r.a.227.1 yes 216
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
270.2.r.a.113.1 216 3.2 odd 2
270.2.r.a.167.14 yes 216 15.2 even 4
270.2.r.a.173.14 yes 216 27.16 even 9
270.2.r.a.227.1 yes 216 135.97 odd 36
810.2.s.a.197.11 216 135.92 even 36 inner
810.2.s.a.287.7 216 5.2 odd 4 inner
810.2.s.a.683.7 216 27.11 odd 18 inner
810.2.s.a.773.11 216 1.1 even 1 trivial