Properties

Label 297.2.n.b.91.4
Level $297$
Weight $2$
Character 297.91
Analytic conductor $2.372$
Analytic rank $0$
Dimension $72$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [297,2,Mod(37,297)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(297, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([10, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("297.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 297 = 3^{3} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 297.n (of order \(15\), degree \(8\), 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: \(2.37155694003\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(9\) over \(\Q(\zeta_{15})\)
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 91.4
Character \(\chi\) \(=\) 297.91
Dual form 297.2.n.b.235.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.527858 - 0.235017i) q^{2} +(-1.11486 - 1.23818i) q^{4} +(-2.74468 + 1.22201i) q^{5} +(1.13888 - 0.242076i) q^{7} +(0.654602 + 2.01466i) q^{8} +1.73599 q^{10} +(2.54741 + 2.12385i) q^{11} +(0.412487 + 3.92455i) q^{13} +(-0.658057 - 0.139874i) q^{14} +(-0.220374 + 2.09672i) q^{16} +(-0.254185 - 0.184677i) q^{17} +(1.96794 + 6.05670i) q^{19} +(4.57300 + 2.03603i) q^{20} +(-0.845527 - 1.71977i) q^{22} +(-0.0427501 + 0.0740453i) q^{23} +(2.69431 - 2.99234i) q^{25} +(0.704604 - 2.16855i) q^{26} +(-1.56942 - 1.14025i) q^{28} +(-7.53156 + 1.60088i) q^{29} +(-0.682449 - 6.49307i) q^{31} +(2.72743 - 4.72404i) q^{32} +(0.0907715 + 0.157221i) q^{34} +(-2.83004 + 2.05614i) q^{35} +(-1.92922 + 5.93753i) q^{37} +(0.384637 - 3.65957i) q^{38} +(-4.25861 - 4.72966i) q^{40} +(5.68213 + 1.20777i) q^{41} +(3.39229 + 5.87562i) q^{43} +(-0.210303 - 5.52194i) q^{44} +(0.0399679 - 0.0290384i) q^{46} +(0.219298 - 0.243555i) q^{47} +(-5.15638 + 2.29577i) q^{49} +(-2.12546 + 0.946318i) q^{50} +(4.39943 - 4.88606i) q^{52} +(-1.96000 + 1.42402i) q^{53} +(-9.58718 - 2.71632i) q^{55} +(1.23321 + 2.13598i) q^{56} +(4.35183 + 0.925009i) q^{58} +(1.53634 + 1.70628i) q^{59} +(1.43070 - 13.6122i) q^{61} +(-1.16575 + 3.58780i) q^{62} +(0.861321 - 0.625787i) q^{64} +(-5.92799 - 10.2676i) q^{65} +(-5.83989 + 10.1150i) q^{67} +(0.0547189 + 0.520616i) q^{68} +(1.97708 - 0.420242i) q^{70} +(7.05272 + 5.12410i) q^{71} +(0.910538 - 2.80235i) q^{73} +(2.41378 - 2.68077i) q^{74} +(5.30529 - 9.18904i) q^{76} +(3.41531 + 1.80213i) q^{77} +(-8.11886 - 3.61475i) q^{79} +(-1.95735 - 6.02412i) q^{80} +(-2.71551 - 1.97293i) q^{82} +(0.518229 - 4.93062i) q^{83} +(0.923335 + 0.196261i) q^{85} +(-0.409774 - 3.89874i) q^{86} +(-2.61129 + 6.52242i) q^{88} -2.12862 q^{89} +(1.41981 + 4.36973i) q^{91} +(0.139342 - 0.0296180i) q^{92} +(-0.172998 + 0.0770236i) q^{94} +(-12.8027 - 14.2189i) q^{95} +(-0.0811587 - 0.0361342i) q^{97} +3.26138 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/297\mathbb{Z}\right)^\times\).

\(n\) \(56\) \(244\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.527858 0.235017i −0.373252 0.166182i 0.211533 0.977371i \(-0.432154\pi\)
−0.584785 + 0.811188i \(0.698821\pi\)
\(3\) 0 0
\(4\) −1.11486 1.23818i −0.557430 0.619089i
\(5\) −2.74468 + 1.22201i −1.22746 + 0.546500i −0.915009 0.403434i \(-0.867816\pi\)
−0.312450 + 0.949934i \(0.601150\pi\)
\(6\) 0 0
\(7\) 1.13888 0.242076i 0.430455 0.0914960i 0.0124114 0.999923i \(-0.496049\pi\)
0.418044 + 0.908427i \(0.362716\pi\)
\(8\) 0.654602 + 2.01466i 0.231437 + 0.712289i
\(9\) 0 0
\(10\) 1.73599 0.548970
\(11\) 2.54741 + 2.12385i 0.768072 + 0.640364i
\(12\) 0 0
\(13\) 0.412487 + 3.92455i 0.114403 + 1.08848i 0.889595 + 0.456750i \(0.150986\pi\)
−0.775192 + 0.631726i \(0.782347\pi\)
\(14\) −0.658057 0.139874i −0.175873 0.0373830i
\(15\) 0 0
\(16\) −0.220374 + 2.09672i −0.0550935 + 0.524179i
\(17\) −0.254185 0.184677i −0.0616490 0.0447906i 0.556534 0.830825i \(-0.312131\pi\)
−0.618183 + 0.786034i \(0.712131\pi\)
\(18\) 0 0
\(19\) 1.96794 + 6.05670i 0.451477 + 1.38950i 0.875222 + 0.483721i \(0.160715\pi\)
−0.423746 + 0.905781i \(0.639285\pi\)
\(20\) 4.57300 + 2.03603i 1.02255 + 0.455271i
\(21\) 0 0
\(22\) −0.845527 1.71977i −0.180267 0.366657i
\(23\) −0.0427501 + 0.0740453i −0.00891401 + 0.0154395i −0.870448 0.492260i \(-0.836171\pi\)
0.861534 + 0.507700i \(0.169504\pi\)
\(24\) 0 0
\(25\) 2.69431 2.99234i 0.538862 0.598467i
\(26\) 0.704604 2.16855i 0.138184 0.425287i
\(27\) 0 0
\(28\) −1.56942 1.14025i −0.296593 0.215487i
\(29\) −7.53156 + 1.60088i −1.39858 + 0.297276i −0.844663 0.535298i \(-0.820199\pi\)
−0.553913 + 0.832575i \(0.686866\pi\)
\(30\) 0 0
\(31\) −0.682449 6.49307i −0.122571 1.16619i −0.866937 0.498418i \(-0.833915\pi\)
0.744366 0.667772i \(-0.232752\pi\)
\(32\) 2.72743 4.72404i 0.482146 0.835101i
\(33\) 0 0
\(34\) 0.0907715 + 0.157221i 0.0155672 + 0.0269632i
\(35\) −2.83004 + 2.05614i −0.478363 + 0.347551i
\(36\) 0 0
\(37\) −1.92922 + 5.93753i −0.317162 + 0.976124i 0.657694 + 0.753286i \(0.271532\pi\)
−0.974855 + 0.222838i \(0.928468\pi\)
\(38\) 0.384637 3.65957i 0.0623963 0.593661i
\(39\) 0 0
\(40\) −4.25861 4.72966i −0.673345 0.747825i
\(41\) 5.68213 + 1.20777i 0.887399 + 0.188623i 0.628990 0.777413i \(-0.283468\pi\)
0.258409 + 0.966036i \(0.416802\pi\)
\(42\) 0 0
\(43\) 3.39229 + 5.87562i 0.517320 + 0.896024i 0.999798 + 0.0201157i \(0.00640347\pi\)
−0.482478 + 0.875908i \(0.660263\pi\)
\(44\) −0.210303 5.52194i −0.0317043 0.832463i
\(45\) 0 0
\(46\) 0.0399679 0.0290384i 0.00589294 0.00428147i
\(47\) 0.219298 0.243555i 0.0319879 0.0355262i −0.726939 0.686703i \(-0.759058\pi\)
0.758926 + 0.651176i \(0.225724\pi\)
\(48\) 0 0
\(49\) −5.15638 + 2.29577i −0.736625 + 0.327967i
\(50\) −2.12546 + 0.946318i −0.300586 + 0.133830i
\(51\) 0 0
\(52\) 4.39943 4.88606i 0.610091 0.677575i
\(53\) −1.96000 + 1.42402i −0.269227 + 0.195605i −0.714205 0.699937i \(-0.753211\pi\)
0.444978 + 0.895541i \(0.353211\pi\)
\(54\) 0 0
\(55\) −9.58718 2.71632i −1.29274 0.366269i
\(56\) 1.23321 + 2.13598i 0.164795 + 0.285433i
\(57\) 0 0
\(58\) 4.35183 + 0.925009i 0.571423 + 0.121460i
\(59\) 1.53634 + 1.70628i 0.200015 + 0.222139i 0.834805 0.550545i \(-0.185580\pi\)
−0.634790 + 0.772685i \(0.718913\pi\)
\(60\) 0 0
\(61\) 1.43070 13.6122i 0.183183 1.74287i −0.387656 0.921804i \(-0.626715\pi\)
0.570839 0.821062i \(-0.306618\pi\)
\(62\) −1.16575 + 3.58780i −0.148050 + 0.455652i
\(63\) 0 0
\(64\) 0.861321 0.625787i 0.107665 0.0782233i
\(65\) −5.92799 10.2676i −0.735277 1.27354i
\(66\) 0 0
\(67\) −5.83989 + 10.1150i −0.713456 + 1.23574i 0.250096 + 0.968221i \(0.419538\pi\)
−0.963552 + 0.267521i \(0.913795\pi\)
\(68\) 0.0547189 + 0.520616i 0.00663564 + 0.0631339i
\(69\) 0 0
\(70\) 1.97708 0.420242i 0.236307 0.0502286i
\(71\) 7.05272 + 5.12410i 0.837004 + 0.608119i 0.921532 0.388302i \(-0.126938\pi\)
−0.0845279 + 0.996421i \(0.526938\pi\)
\(72\) 0 0
\(73\) 0.910538 2.80235i 0.106570 0.327990i −0.883525 0.468383i \(-0.844837\pi\)
0.990096 + 0.140393i \(0.0448367\pi\)
\(74\) 2.41378 2.68077i 0.280596 0.311633i
\(75\) 0 0
\(76\) 5.30529 9.18904i 0.608559 1.05405i
\(77\) 3.41531 + 1.80213i 0.389211 + 0.205372i
\(78\) 0 0
\(79\) −8.11886 3.61475i −0.913443 0.406691i −0.104464 0.994529i \(-0.533313\pi\)
−0.808979 + 0.587838i \(0.799979\pi\)
\(80\) −1.95735 6.02412i −0.218839 0.673517i
\(81\) 0 0
\(82\) −2.71551 1.97293i −0.299878 0.217874i
\(83\) 0.518229 4.93062i 0.0568831 0.541206i −0.928558 0.371188i \(-0.878951\pi\)
0.985441 0.170018i \(-0.0543827\pi\)
\(84\) 0 0
\(85\) 0.923335 + 0.196261i 0.100150 + 0.0212875i
\(86\) −0.409774 3.89874i −0.0441871 0.420412i
\(87\) 0 0
\(88\) −2.61129 + 6.52242i −0.278364 + 0.695293i
\(89\) −2.12862 −0.225634 −0.112817 0.993616i \(-0.535987\pi\)
−0.112817 + 0.993616i \(0.535987\pi\)
\(90\) 0 0
\(91\) 1.41981 + 4.36973i 0.148837 + 0.458072i
\(92\) 0.139342 0.0296180i 0.0145274 0.00308789i
\(93\) 0 0
\(94\) −0.172998 + 0.0770236i −0.0178434 + 0.00794437i
\(95\) −12.8027 14.2189i −1.31353 1.45882i
\(96\) 0 0
\(97\) −0.0811587 0.0361342i −0.00824041 0.00366887i 0.402612 0.915371i \(-0.368102\pi\)
−0.410853 + 0.911702i \(0.634769\pi\)
\(98\) 3.26138 0.329449
\(99\) 0 0
\(100\) −6.70883 −0.670883
\(101\) 1.87869 + 0.836447i 0.186937 + 0.0832296i 0.498071 0.867137i \(-0.334042\pi\)
−0.311134 + 0.950366i \(0.600709\pi\)
\(102\) 0 0
\(103\) −2.01858 2.24186i −0.198896 0.220897i 0.635443 0.772148i \(-0.280817\pi\)
−0.834340 + 0.551251i \(0.814151\pi\)
\(104\) −7.63662 + 3.40004i −0.748832 + 0.333401i
\(105\) 0 0
\(106\) 1.36927 0.291048i 0.132995 0.0282690i
\(107\) −3.70600 11.4059i −0.358272 1.10265i −0.954088 0.299527i \(-0.903171\pi\)
0.595815 0.803121i \(-0.296829\pi\)
\(108\) 0 0
\(109\) 5.20013 0.498082 0.249041 0.968493i \(-0.419885\pi\)
0.249041 + 0.968493i \(0.419885\pi\)
\(110\) 4.42228 + 3.68699i 0.421648 + 0.351540i
\(111\) 0 0
\(112\) 0.256586 + 2.44125i 0.0242451 + 0.230676i
\(113\) 18.8074 + 3.99763i 1.76925 + 0.376066i 0.973343 0.229354i \(-0.0736612\pi\)
0.795907 + 0.605419i \(0.206995\pi\)
\(114\) 0 0
\(115\) 0.0268512 0.255472i 0.00250389 0.0238229i
\(116\) 10.3788 + 7.54065i 0.963649 + 0.700132i
\(117\) 0 0
\(118\) −0.409965 1.26174i −0.0377403 0.116153i
\(119\) −0.334192 0.148792i −0.0306353 0.0136397i
\(120\) 0 0
\(121\) 1.97856 + 10.8206i 0.179869 + 0.983691i
\(122\) −3.95432 + 6.84907i −0.358007 + 0.620086i
\(123\) 0 0
\(124\) −7.27874 + 8.08386i −0.653650 + 0.725952i
\(125\) 0.903736 2.78141i 0.0808326 0.248777i
\(126\) 0 0
\(127\) 10.6652 + 7.74873i 0.946384 + 0.687588i 0.949949 0.312405i \(-0.101135\pi\)
−0.00356461 + 0.999994i \(0.501135\pi\)
\(128\) −11.2730 + 2.39616i −0.996405 + 0.211792i
\(129\) 0 0
\(130\) 0.716076 + 6.81300i 0.0628040 + 0.597540i
\(131\) −8.98588 + 15.5640i −0.785100 + 1.35983i 0.143839 + 0.989601i \(0.454055\pi\)
−0.928939 + 0.370233i \(0.879278\pi\)
\(132\) 0 0
\(133\) 3.70742 + 6.42144i 0.321474 + 0.556810i
\(134\) 5.45983 3.96680i 0.471657 0.342679i
\(135\) 0 0
\(136\) 0.205670 0.632986i 0.0176360 0.0542781i
\(137\) −1.71445 + 16.3119i −0.146475 + 1.39362i 0.636361 + 0.771391i \(0.280439\pi\)
−0.782836 + 0.622228i \(0.786228\pi\)
\(138\) 0 0
\(139\) −7.96373 8.84461i −0.675475 0.750190i 0.303798 0.952736i \(-0.401745\pi\)
−0.979273 + 0.202546i \(0.935078\pi\)
\(140\) 5.70096 + 1.21178i 0.481819 + 0.102414i
\(141\) 0 0
\(142\) −2.51858 4.36231i −0.211355 0.366077i
\(143\) −7.28438 + 10.8735i −0.609150 + 0.909287i
\(144\) 0 0
\(145\) 18.7154 13.5976i 1.55423 1.12922i
\(146\) −1.13923 + 1.26525i −0.0942837 + 0.104713i
\(147\) 0 0
\(148\) 9.50253 4.23080i 0.781103 0.347770i
\(149\) 4.13993 1.84321i 0.339156 0.151002i −0.230090 0.973169i \(-0.573902\pi\)
0.569246 + 0.822167i \(0.307235\pi\)
\(150\) 0 0
\(151\) −1.96113 + 2.17806i −0.159595 + 0.177248i −0.817639 0.575732i \(-0.804717\pi\)
0.658044 + 0.752979i \(0.271384\pi\)
\(152\) −10.9140 + 7.92945i −0.885239 + 0.643164i
\(153\) 0 0
\(154\) −1.37927 1.75393i −0.111144 0.141336i
\(155\) 9.80771 + 16.9874i 0.787774 + 1.36446i
\(156\) 0 0
\(157\) 17.6591 + 3.75356i 1.40935 + 0.299567i 0.848871 0.528600i \(-0.177283\pi\)
0.560481 + 0.828167i \(0.310616\pi\)
\(158\) 3.43607 + 3.81614i 0.273359 + 0.303596i
\(159\) 0 0
\(160\) −1.71309 + 16.2989i −0.135431 + 1.28854i
\(161\) −0.0307625 + 0.0946773i −0.00242443 + 0.00746161i
\(162\) 0 0
\(163\) 4.71129 3.42295i 0.369017 0.268106i −0.387786 0.921749i \(-0.626760\pi\)
0.756803 + 0.653643i \(0.226760\pi\)
\(164\) −4.83934 8.38199i −0.377889 0.654523i
\(165\) 0 0
\(166\) −1.43233 + 2.48087i −0.111171 + 0.192553i
\(167\) −0.524913 4.99422i −0.0406190 0.386464i −0.995879 0.0906956i \(-0.971091\pi\)
0.955260 0.295769i \(-0.0955757\pi\)
\(168\) 0 0
\(169\) −2.51606 + 0.534805i −0.193543 + 0.0411388i
\(170\) −0.441265 0.320598i −0.0338435 0.0245887i
\(171\) 0 0
\(172\) 3.49313 10.7508i 0.266349 0.819738i
\(173\) 10.4317 11.5855i 0.793104 0.880831i −0.202028 0.979380i \(-0.564753\pi\)
0.995132 + 0.0985486i \(0.0314200\pi\)
\(174\) 0 0
\(175\) 2.34412 4.06013i 0.177199 0.306917i
\(176\) −5.01449 + 4.87315i −0.377981 + 0.367327i
\(177\) 0 0
\(178\) 1.12361 + 0.500263i 0.0842181 + 0.0374963i
\(179\) −2.17822 6.70387i −0.162808 0.501071i 0.836060 0.548638i \(-0.184853\pi\)
−0.998868 + 0.0475668i \(0.984853\pi\)
\(180\) 0 0
\(181\) −2.02068 1.46811i −0.150196 0.109124i 0.510149 0.860086i \(-0.329590\pi\)
−0.660345 + 0.750962i \(0.729590\pi\)
\(182\) 0.277504 2.64028i 0.0205700 0.195710i
\(183\) 0 0
\(184\) −0.177160 0.0376566i −0.0130604 0.00277608i
\(185\) −1.96063 18.6542i −0.144148 1.37148i
\(186\) 0 0
\(187\) −0.255289 1.01030i −0.0186686 0.0738802i
\(188\) −0.546051 −0.0398249
\(189\) 0 0
\(190\) 3.41633 + 10.5144i 0.247847 + 0.762795i
\(191\) −11.5646 + 2.45814i −0.836786 + 0.177864i −0.606325 0.795217i \(-0.707357\pi\)
−0.230461 + 0.973081i \(0.574024\pi\)
\(192\) 0 0
\(193\) 6.16338 2.74411i 0.443650 0.197526i −0.172739 0.984968i \(-0.555262\pi\)
0.616389 + 0.787442i \(0.288595\pi\)
\(194\) 0.0343481 + 0.0381474i 0.00246605 + 0.00273882i
\(195\) 0 0
\(196\) 8.59121 + 3.82505i 0.613658 + 0.273218i
\(197\) 20.6474 1.47107 0.735534 0.677488i \(-0.236931\pi\)
0.735534 + 0.677488i \(0.236931\pi\)
\(198\) 0 0
\(199\) −13.2862 −0.941832 −0.470916 0.882178i \(-0.656077\pi\)
−0.470916 + 0.882178i \(0.656077\pi\)
\(200\) 7.79224 + 3.46933i 0.550994 + 0.245318i
\(201\) 0 0
\(202\) −0.795102 0.883050i −0.0559432 0.0621312i
\(203\) −8.18999 + 3.64642i −0.574824 + 0.255928i
\(204\) 0 0
\(205\) −17.0715 + 3.62867i −1.19233 + 0.253437i
\(206\) 0.538646 + 1.65778i 0.0375292 + 0.115503i
\(207\) 0 0
\(208\) −8.31958 −0.576859
\(209\) −7.85035 + 19.6085i −0.543020 + 1.35635i
\(210\) 0 0
\(211\) 0.872292 + 8.29930i 0.0600510 + 0.571348i 0.982635 + 0.185551i \(0.0594068\pi\)
−0.922584 + 0.385797i \(0.873926\pi\)
\(212\) 3.94832 + 0.839242i 0.271172 + 0.0576394i
\(213\) 0 0
\(214\) −0.724343 + 6.89166i −0.0495150 + 0.471104i
\(215\) −16.4908 11.9813i −1.12467 0.817117i
\(216\) 0 0
\(217\) −2.34904 7.22960i −0.159463 0.490778i
\(218\) −2.74493 1.22212i −0.185910 0.0827724i
\(219\) 0 0
\(220\) 7.32508 + 14.8990i 0.493857 + 1.00449i
\(221\) 0.619925 1.07374i 0.0417007 0.0722277i
\(222\) 0 0
\(223\) −0.256716 + 0.285112i −0.0171910 + 0.0190925i −0.751679 0.659529i \(-0.770756\pi\)
0.734488 + 0.678622i \(0.237422\pi\)
\(224\) 1.96263 6.04035i 0.131134 0.403588i
\(225\) 0 0
\(226\) −8.98811 6.53024i −0.597880 0.434385i
\(227\) 17.6204 3.74533i 1.16951 0.248586i 0.418084 0.908408i \(-0.362702\pi\)
0.751422 + 0.659822i \(0.229368\pi\)
\(228\) 0 0
\(229\) −1.40359 13.3543i −0.0927521 0.882478i −0.937657 0.347561i \(-0.887010\pi\)
0.844905 0.534916i \(-0.179657\pi\)
\(230\) −0.0742139 + 0.128542i −0.00489352 + 0.00847583i
\(231\) 0 0
\(232\) −8.15540 14.1256i −0.535428 0.927389i
\(233\) −2.72611 + 1.98063i −0.178593 + 0.129756i −0.673490 0.739196i \(-0.735206\pi\)
0.494897 + 0.868952i \(0.335206\pi\)
\(234\) 0 0
\(235\) −0.304276 + 0.936466i −0.0198488 + 0.0610883i
\(236\) 0.399873 3.80454i 0.0260295 0.247654i
\(237\) 0 0
\(238\) 0.141437 + 0.157082i 0.00916800 + 0.0101821i
\(239\) −22.6899 4.82289i −1.46769 0.311967i −0.596379 0.802703i \(-0.703394\pi\)
−0.871308 + 0.490736i \(0.836728\pi\)
\(240\) 0 0
\(241\) −7.58206 13.1325i −0.488404 0.845940i 0.511507 0.859279i \(-0.329087\pi\)
−0.999911 + 0.0133389i \(0.995754\pi\)
\(242\) 1.49863 6.17673i 0.0963358 0.397055i
\(243\) 0 0
\(244\) −18.4494 + 13.4043i −1.18110 + 0.858120i
\(245\) 11.3472 12.6023i 0.724944 0.805131i
\(246\) 0 0
\(247\) −22.9581 + 10.2216i −1.46079 + 0.650385i
\(248\) 12.6346 5.62528i 0.802297 0.357205i
\(249\) 0 0
\(250\) −1.13072 + 1.25580i −0.0715133 + 0.0794235i
\(251\) −0.471095 + 0.342271i −0.0297353 + 0.0216039i −0.602554 0.798078i \(-0.705850\pi\)
0.572818 + 0.819682i \(0.305850\pi\)
\(252\) 0 0
\(253\) −0.266163 + 0.0978289i −0.0167335 + 0.00615045i
\(254\) −3.80863 6.59673i −0.238974 0.413916i
\(255\) 0 0
\(256\) 4.43092 + 0.941821i 0.276933 + 0.0588638i
\(257\) 7.34131 + 8.15335i 0.457939 + 0.508592i 0.927251 0.374440i \(-0.122165\pi\)
−0.469313 + 0.883032i \(0.655498\pi\)
\(258\) 0 0
\(259\) −0.759813 + 7.22913i −0.0472125 + 0.449197i
\(260\) −6.10421 + 18.7868i −0.378567 + 1.16511i
\(261\) 0 0
\(262\) 8.40108 6.10374i 0.519020 0.377090i
\(263\) −7.19768 12.4668i −0.443828 0.768733i 0.554142 0.832422i \(-0.313047\pi\)
−0.997970 + 0.0636896i \(0.979713\pi\)
\(264\) 0 0
\(265\) 3.63940 6.30363i 0.223567 0.387229i
\(266\) −0.447840 4.26092i −0.0274589 0.261254i
\(267\) 0 0
\(268\) 19.0348 4.04598i 1.16274 0.247147i
\(269\) 0.395590 + 0.287413i 0.0241195 + 0.0175239i 0.599780 0.800165i \(-0.295255\pi\)
−0.575660 + 0.817689i \(0.695255\pi\)
\(270\) 0 0
\(271\) 6.77950 20.8652i 0.411825 1.26747i −0.503234 0.864150i \(-0.667857\pi\)
0.915060 0.403318i \(-0.132143\pi\)
\(272\) 0.443230 0.492257i 0.0268748 0.0298475i
\(273\) 0 0
\(274\) 4.73856 8.20743i 0.286267 0.495829i
\(275\) 13.2188 1.90039i 0.797122 0.114598i
\(276\) 0 0
\(277\) 2.62144 + 1.16714i 0.157507 + 0.0701267i 0.483976 0.875081i \(-0.339192\pi\)
−0.326469 + 0.945208i \(0.605859\pi\)
\(278\) 2.12508 + 6.54031i 0.127454 + 0.392262i
\(279\) 0 0
\(280\) −5.99497 4.35560i −0.358268 0.260297i
\(281\) 1.90013 18.0785i 0.113352 1.07847i −0.778967 0.627066i \(-0.784256\pi\)
0.892318 0.451406i \(-0.149078\pi\)
\(282\) 0 0
\(283\) 20.0883 + 4.26991i 1.19413 + 0.253820i 0.761749 0.647873i \(-0.224341\pi\)
0.432378 + 0.901692i \(0.357674\pi\)
\(284\) −1.51825 14.4452i −0.0900916 0.857164i
\(285\) 0 0
\(286\) 6.40057 4.02770i 0.378474 0.238163i
\(287\) 6.76362 0.399244
\(288\) 0 0
\(289\) −5.22278 16.0741i −0.307223 0.945534i
\(290\) −13.0747 + 2.77912i −0.767776 + 0.163196i
\(291\) 0 0
\(292\) −4.48493 + 1.99682i −0.262461 + 0.116855i
\(293\) −0.575497 0.639154i −0.0336209 0.0373398i 0.726100 0.687589i \(-0.241331\pi\)
−0.759721 + 0.650250i \(0.774664\pi\)
\(294\) 0 0
\(295\) −6.30187 2.80578i −0.366909 0.163359i
\(296\) −13.2250 −0.768685
\(297\) 0 0
\(298\) −2.61848 −0.151684
\(299\) −0.308229 0.137232i −0.0178253 0.00793635i
\(300\) 0 0
\(301\) 5.28575 + 5.87042i 0.304665 + 0.338365i
\(302\) 1.54708 0.688804i 0.0890244 0.0396362i
\(303\) 0 0
\(304\) −13.1329 + 2.79148i −0.753221 + 0.160102i
\(305\) 12.7075 + 39.1095i 0.727627 + 2.23941i
\(306\) 0 0
\(307\) 3.48920 0.199139 0.0995696 0.995031i \(-0.468253\pi\)
0.0995696 + 0.995031i \(0.468253\pi\)
\(308\) −1.57624 6.23790i −0.0898144 0.355437i
\(309\) 0 0
\(310\) −1.18473 11.2719i −0.0672880 0.640203i
\(311\) 10.6083 + 2.25486i 0.601542 + 0.127862i 0.498610 0.866827i \(-0.333844\pi\)
0.102932 + 0.994688i \(0.467178\pi\)
\(312\) 0 0
\(313\) 2.95618 28.1261i 0.167093 1.58978i −0.514133 0.857710i \(-0.671886\pi\)
0.681226 0.732073i \(-0.261447\pi\)
\(314\) −8.43935 6.13155i −0.476260 0.346023i
\(315\) 0 0
\(316\) 4.57569 + 14.0825i 0.257403 + 0.792204i
\(317\) 1.01634 + 0.452505i 0.0570836 + 0.0254152i 0.435080 0.900392i \(-0.356720\pi\)
−0.377996 + 0.925807i \(0.623387\pi\)
\(318\) 0 0
\(319\) −22.5860 11.9178i −1.26457 0.667267i
\(320\) −1.59933 + 2.77013i −0.0894055 + 0.154855i
\(321\) 0 0
\(322\) 0.0384890 0.0427464i 0.00214491 0.00238216i
\(323\) 0.618308 1.90296i 0.0344036 0.105883i
\(324\) 0 0
\(325\) 12.8550 + 9.33967i 0.713065 + 0.518072i
\(326\) −3.29134 + 0.699597i −0.182291 + 0.0387471i
\(327\) 0 0
\(328\) 1.28628 + 12.2382i 0.0710230 + 0.675739i
\(329\) 0.190795 0.330466i 0.0105188 0.0182192i
\(330\) 0 0
\(331\) 6.18915 + 10.7199i 0.340187 + 0.589221i 0.984467 0.175569i \(-0.0561764\pi\)
−0.644281 + 0.764789i \(0.722843\pi\)
\(332\) −6.68275 + 4.85530i −0.366763 + 0.266469i
\(333\) 0 0
\(334\) −0.896648 + 2.75960i −0.0490624 + 0.150999i
\(335\) 3.66801 34.8988i 0.200405 1.90673i
\(336\) 0 0
\(337\) 9.01561 + 10.0128i 0.491112 + 0.545435i 0.936851 0.349728i \(-0.113726\pi\)
−0.445740 + 0.895163i \(0.647059\pi\)
\(338\) 1.45381 + 0.309017i 0.0790768 + 0.0168083i
\(339\) 0 0
\(340\) −0.786384 1.36206i −0.0426477 0.0738679i
\(341\) 12.0518 17.9899i 0.652642 0.974208i
\(342\) 0 0
\(343\) −11.9104 + 8.65342i −0.643102 + 0.467241i
\(344\) −9.61676 + 10.6805i −0.518501 + 0.575854i
\(345\) 0 0
\(346\) −8.22923 + 3.66389i −0.442406 + 0.196972i
\(347\) −8.89717 + 3.96128i −0.477625 + 0.212652i −0.631406 0.775453i \(-0.717522\pi\)
0.153781 + 0.988105i \(0.450855\pi\)
\(348\) 0 0
\(349\) −2.97107 + 3.29971i −0.159038 + 0.176629i −0.817397 0.576074i \(-0.804584\pi\)
0.658360 + 0.752703i \(0.271251\pi\)
\(350\) −2.19156 + 1.59226i −0.117144 + 0.0851100i
\(351\) 0 0
\(352\) 16.9810 6.24142i 0.905090 0.332669i
\(353\) 16.2618 + 28.1662i 0.865527 + 1.49914i 0.866523 + 0.499137i \(0.166349\pi\)
−0.000996749 1.00000i \(0.500317\pi\)
\(354\) 0 0
\(355\) −25.6192 5.44553i −1.35973 0.289019i
\(356\) 2.37312 + 2.63561i 0.125775 + 0.139687i
\(357\) 0 0
\(358\) −0.425736 + 4.05061i −0.0225008 + 0.214081i
\(359\) 8.58143 26.4109i 0.452911 1.39392i −0.420660 0.907218i \(-0.638201\pi\)
0.873571 0.486697i \(-0.161799\pi\)
\(360\) 0 0
\(361\) −17.4395 + 12.6705i −0.917868 + 0.666870i
\(362\) 0.721600 + 1.24985i 0.0379264 + 0.0656905i
\(363\) 0 0
\(364\) 3.82761 6.62962i 0.200621 0.347487i
\(365\) 0.925362 + 8.80424i 0.0484357 + 0.460835i
\(366\) 0 0
\(367\) −1.14658 + 0.243713i −0.0598511 + 0.0127217i −0.237740 0.971329i \(-0.576407\pi\)
0.177889 + 0.984051i \(0.443073\pi\)
\(368\) −0.145831 0.105952i −0.00760197 0.00552315i
\(369\) 0 0
\(370\) −3.34912 + 10.3075i −0.174112 + 0.535862i
\(371\) −1.88748 + 2.09626i −0.0979929 + 0.108832i
\(372\) 0 0
\(373\) −10.8834 + 18.8506i −0.563520 + 0.976046i 0.433665 + 0.901074i \(0.357220\pi\)
−0.997186 + 0.0749719i \(0.976113\pi\)
\(374\) −0.102681 + 0.593290i −0.00530951 + 0.0306783i
\(375\) 0 0
\(376\) 0.634233 + 0.282379i 0.0327081 + 0.0145626i
\(377\) −9.38942 28.8977i −0.483580 1.48831i
\(378\) 0 0
\(379\) 13.1440 + 9.54967i 0.675161 + 0.490533i 0.871749 0.489953i \(-0.162986\pi\)
−0.196588 + 0.980486i \(0.562986\pi\)
\(380\) −3.33224 + 31.7041i −0.170940 + 1.62639i
\(381\) 0 0
\(382\) 6.68218 + 1.42034i 0.341890 + 0.0726709i
\(383\) 0.647381 + 6.15942i 0.0330796 + 0.314732i 0.998533 + 0.0541542i \(0.0172463\pi\)
−0.965453 + 0.260577i \(0.916087\pi\)
\(384\) 0 0
\(385\) −11.5762 0.772734i −0.589977 0.0393821i
\(386\) −3.89830 −0.198418
\(387\) 0 0
\(388\) 0.0457401 + 0.140773i 0.00232210 + 0.00714669i
\(389\) −0.707409 + 0.150365i −0.0358671 + 0.00762378i −0.225810 0.974171i \(-0.572503\pi\)
0.189943 + 0.981795i \(0.439170\pi\)
\(390\) 0 0
\(391\) 0.0245409 0.0109263i 0.00124109 0.000552567i
\(392\) −8.00056 8.88552i −0.404089 0.448787i
\(393\) 0 0
\(394\) −10.8989 4.85250i −0.549079 0.244466i
\(395\) 26.7009 1.34347
\(396\) 0 0
\(397\) 4.08994 0.205268 0.102634 0.994719i \(-0.467273\pi\)
0.102634 + 0.994719i \(0.467273\pi\)
\(398\) 7.01321 + 3.12248i 0.351540 + 0.156516i
\(399\) 0 0
\(400\) 5.68033 + 6.30864i 0.284016 + 0.315432i
\(401\) 5.15812 2.29654i 0.257584 0.114684i −0.273882 0.961763i \(-0.588308\pi\)
0.531466 + 0.847079i \(0.321641\pi\)
\(402\) 0 0
\(403\) 25.2009 5.35662i 1.25535 0.266832i
\(404\) −1.05881 3.25868i −0.0526777 0.162125i
\(405\) 0 0
\(406\) 5.18012 0.257085
\(407\) −17.5249 + 11.0279i −0.868677 + 0.546634i
\(408\) 0 0
\(409\) −0.987666 9.39701i −0.0488369 0.464652i −0.991423 0.130690i \(-0.958281\pi\)
0.942586 0.333962i \(-0.108386\pi\)
\(410\) 9.86414 + 2.09669i 0.487155 + 0.103548i
\(411\) 0 0
\(412\) −0.525386 + 4.99871i −0.0258839 + 0.246269i
\(413\) 2.16276 + 1.57134i 0.106422 + 0.0773204i
\(414\) 0 0
\(415\) 4.60290 + 14.1663i 0.225948 + 0.695395i
\(416\) 19.6648 + 8.75533i 0.964145 + 0.429265i
\(417\) 0 0
\(418\) 8.75220 8.50551i 0.428084 0.416018i
\(419\) 0.0757820 0.131258i 0.00370219 0.00641238i −0.864168 0.503203i \(-0.832155\pi\)
0.867871 + 0.496790i \(0.165488\pi\)
\(420\) 0 0
\(421\) 11.3595 12.6160i 0.553630 0.614868i −0.399756 0.916622i \(-0.630905\pi\)
0.953386 + 0.301753i \(0.0975719\pi\)
\(422\) 1.49003 4.58585i 0.0725337 0.223236i
\(423\) 0 0
\(424\) −4.15194 3.01656i −0.201636 0.146497i
\(425\) −1.23747 + 0.263032i −0.0600261 + 0.0127589i
\(426\) 0 0
\(427\) −1.66580 15.8490i −0.0806135 0.766986i
\(428\) −9.99085 + 17.3047i −0.482926 + 0.836453i
\(429\) 0 0
\(430\) 5.88900 + 10.2000i 0.283993 + 0.491890i
\(431\) −20.5242 + 14.9117i −0.988618 + 0.718273i −0.959618 0.281307i \(-0.909232\pi\)
−0.0289998 + 0.999579i \(0.509232\pi\)
\(432\) 0 0
\(433\) 5.10950 15.7254i 0.245547 0.755716i −0.749999 0.661439i \(-0.769946\pi\)
0.995546 0.0942769i \(-0.0300539\pi\)
\(434\) −0.459123 + 4.36827i −0.0220386 + 0.209684i
\(435\) 0 0
\(436\) −5.79742 6.43868i −0.277646 0.308357i
\(437\) −0.532600 0.113208i −0.0254777 0.00541545i
\(438\) 0 0
\(439\) 19.6207 + 33.9840i 0.936443 + 1.62197i 0.772040 + 0.635574i \(0.219237\pi\)
0.164403 + 0.986393i \(0.447430\pi\)
\(440\) −0.803326 21.0930i −0.0382971 1.00557i
\(441\) 0 0
\(442\) −0.579580 + 0.421089i −0.0275678 + 0.0200292i
\(443\) −21.5389 + 23.9214i −1.02334 + 1.13654i −0.0327827 + 0.999463i \(0.510437\pi\)
−0.990561 + 0.137075i \(0.956230\pi\)
\(444\) 0 0
\(445\) 5.84239 2.60120i 0.276956 0.123309i
\(446\) 0.202515 0.0901657i 0.00958939 0.00426947i
\(447\) 0 0
\(448\) 0.829451 0.921199i 0.0391879 0.0435226i
\(449\) −20.9085 + 15.1909i −0.986731 + 0.716902i −0.959203 0.282719i \(-0.908764\pi\)
−0.0275281 + 0.999621i \(0.508764\pi\)
\(450\) 0 0
\(451\) 11.9096 + 15.1447i 0.560799 + 0.713134i
\(452\) −16.0178 27.7437i −0.753415 1.30495i
\(453\) 0 0
\(454\) −10.1813 2.16410i −0.477831 0.101566i
\(455\) −9.23679 10.2585i −0.433027 0.480926i
\(456\) 0 0
\(457\) 1.32921 12.6466i 0.0621780 0.591584i −0.918427 0.395590i \(-0.870540\pi\)
0.980605 0.195994i \(-0.0627932\pi\)
\(458\) −2.39760 + 7.37904i −0.112032 + 0.344800i
\(459\) 0 0
\(460\) −0.346255 + 0.251569i −0.0161442 + 0.0117295i
\(461\) −9.51087 16.4733i −0.442965 0.767238i 0.554943 0.831889i \(-0.312740\pi\)
−0.997908 + 0.0646502i \(0.979407\pi\)
\(462\) 0 0
\(463\) 11.4334 19.8032i 0.531353 0.920331i −0.467977 0.883741i \(-0.655017\pi\)
0.999330 0.0365903i \(-0.0116497\pi\)
\(464\) −1.69684 16.1443i −0.0787738 0.749482i
\(465\) 0 0
\(466\) 1.90448 0.404810i 0.0882233 0.0187524i
\(467\) 12.8819 + 9.35921i 0.596101 + 0.433093i 0.844493 0.535567i \(-0.179902\pi\)
−0.248392 + 0.968660i \(0.579902\pi\)
\(468\) 0 0
\(469\) −4.20232 + 12.9334i −0.194045 + 0.597210i
\(470\) 0.380700 0.422810i 0.0175604 0.0195028i
\(471\) 0 0
\(472\) −2.43188 + 4.21215i −0.111936 + 0.193880i
\(473\) −3.83737 + 22.1723i −0.176443 + 1.01948i
\(474\) 0 0
\(475\) 23.4259 + 10.4299i 1.07486 + 0.478556i
\(476\) 0.188347 + 0.579671i 0.00863285 + 0.0265692i
\(477\) 0 0
\(478\) 10.8436 + 7.87832i 0.495973 + 0.360346i
\(479\) −1.71322 + 16.3002i −0.0782789 + 0.744774i 0.883033 + 0.469311i \(0.155498\pi\)
−0.961312 + 0.275463i \(0.911169\pi\)
\(480\) 0 0
\(481\) −24.0979 5.12217i −1.09877 0.233551i
\(482\) 0.915880 + 8.71402i 0.0417172 + 0.396913i
\(483\) 0 0
\(484\) 11.1920 14.5133i 0.508728 0.659694i
\(485\) 0.266911 0.0121198
\(486\) 0 0
\(487\) 7.04142 + 21.6713i 0.319077 + 0.982019i 0.974044 + 0.226361i \(0.0726828\pi\)
−0.654966 + 0.755658i \(0.727317\pi\)
\(488\) 28.3605 6.02821i 1.28382 0.272884i
\(489\) 0 0
\(490\) −8.95145 + 3.98544i −0.404385 + 0.180044i
\(491\) 29.2029 + 32.4331i 1.31791 + 1.46368i 0.788071 + 0.615584i \(0.211080\pi\)
0.529836 + 0.848100i \(0.322253\pi\)
\(492\) 0 0
\(493\) 2.21006 + 0.983982i 0.0995360 + 0.0443163i
\(494\) 14.5209 0.653324
\(495\) 0 0
\(496\) 13.7645 0.618045
\(497\) 9.27261 + 4.12843i 0.415933 + 0.185185i
\(498\) 0 0
\(499\) −13.4519 14.9398i −0.602189 0.668798i 0.362563 0.931959i \(-0.381902\pi\)
−0.964752 + 0.263161i \(0.915235\pi\)
\(500\) −4.45142 + 1.98190i −0.199074 + 0.0886333i
\(501\) 0 0
\(502\) 0.329111 0.0699546i 0.0146889 0.00312223i
\(503\) 3.27815 + 10.0891i 0.146165 + 0.449850i 0.997159 0.0753254i \(-0.0239995\pi\)
−0.850994 + 0.525176i \(0.824000\pi\)
\(504\) 0 0
\(505\) −6.17856 −0.274942
\(506\) 0.163487 + 0.0109131i 0.00726791 + 0.000485148i
\(507\) 0 0
\(508\) −2.29592 21.8442i −0.101865 0.969179i
\(509\) −43.4966 9.24549i −1.92795 0.409799i −0.999239 0.0390051i \(-0.987581\pi\)
−0.928715 0.370794i \(-0.879086\pi\)
\(510\) 0 0
\(511\) 0.358610 3.41195i 0.0158640 0.150936i
\(512\) 16.5301 + 12.0098i 0.730534 + 0.530764i
\(513\) 0 0
\(514\) −1.95899 6.02915i −0.0864073 0.265934i
\(515\) 8.27992 + 3.68646i 0.364857 + 0.162445i
\(516\) 0 0
\(517\) 1.07591 0.154679i 0.0473187 0.00680275i
\(518\) 2.10004 3.63738i 0.0922707 0.159817i
\(519\) 0 0
\(520\) 16.8052 18.6641i 0.736956 0.818473i
\(521\) −5.23819 + 16.1215i −0.229489 + 0.706296i 0.768315 + 0.640071i \(0.221095\pi\)
−0.997805 + 0.0662243i \(0.978905\pi\)
\(522\) 0 0
\(523\) −24.4438 17.7595i −1.06885 0.776567i −0.0931472 0.995652i \(-0.529693\pi\)
−0.975706 + 0.219085i \(0.929693\pi\)
\(524\) 29.2890 6.22557i 1.27950 0.271965i
\(525\) 0 0
\(526\) 0.869448 + 8.27225i 0.0379098 + 0.360687i
\(527\) −1.02565 + 1.77648i −0.0446780 + 0.0773845i
\(528\) 0 0
\(529\) 11.4963 + 19.9123i 0.499841 + 0.865750i
\(530\) −3.40255 + 2.47210i −0.147797 + 0.107381i
\(531\) 0 0
\(532\) 3.81763 11.7495i 0.165515 0.509404i
\(533\) −2.39617 + 22.7980i −0.103790 + 0.987491i
\(534\) 0 0
\(535\) 24.1099 + 26.7768i 1.04236 + 1.15766i
\(536\) −24.2010 5.14409i −1.04533 0.222191i
\(537\) 0 0
\(538\) −0.141268 0.244683i −0.00609050 0.0105491i
\(539\) −18.0112 5.10310i −0.775799 0.219806i
\(540\) 0 0
\(541\) −9.57164 + 6.95421i −0.411517 + 0.298985i −0.774216 0.632922i \(-0.781855\pi\)
0.362699 + 0.931906i \(0.381855\pi\)
\(542\) −8.48229 + 9.42053i −0.364345 + 0.404647i
\(543\) 0 0
\(544\) −1.56569 + 0.697091i −0.0671285 + 0.0298875i
\(545\) −14.2727 + 6.35461i −0.611375 + 0.272202i
\(546\) 0 0
\(547\) 1.70348 1.89190i 0.0728355 0.0808920i −0.705626 0.708585i \(-0.749334\pi\)
0.778461 + 0.627693i \(0.216001\pi\)
\(548\) 22.1084 16.0627i 0.944424 0.686164i
\(549\) 0 0
\(550\) −7.42425 2.10350i −0.316571 0.0896937i
\(551\) −24.5177 42.4659i −1.04449 1.80911i
\(552\) 0 0
\(553\) −10.1214 2.15137i −0.430407 0.0914857i
\(554\) −1.10945 1.23217i −0.0471360 0.0523498i
\(555\) 0 0
\(556\) −2.07276 + 19.7210i −0.0879048 + 0.836358i
\(557\) −2.98987 + 9.20189i −0.126685 + 0.389896i −0.994204 0.107507i \(-0.965713\pi\)
0.867519 + 0.497404i \(0.165713\pi\)
\(558\) 0 0
\(559\) −21.6599 + 15.7368i −0.916117 + 0.665598i
\(560\) −3.68748 6.38690i −0.155824 0.269896i
\(561\) 0 0
\(562\) −5.25175 + 9.09630i −0.221532 + 0.383704i
\(563\) −2.50735 23.8558i −0.105672 1.00540i −0.910953 0.412510i \(-0.864652\pi\)
0.805281 0.592893i \(-0.202014\pi\)
\(564\) 0 0
\(565\) −56.5054 + 12.0106i −2.37720 + 0.505290i
\(566\) −9.60027 6.97501i −0.403530 0.293181i
\(567\) 0 0
\(568\) −5.70659 + 17.5631i −0.239443 + 0.736930i
\(569\) 25.1721 27.9565i 1.05527 1.17200i 0.0706111 0.997504i \(-0.477505\pi\)
0.984659 0.174492i \(-0.0558283\pi\)
\(570\) 0 0
\(571\) 7.37740 12.7780i 0.308735 0.534744i −0.669351 0.742946i \(-0.733428\pi\)
0.978086 + 0.208202i \(0.0667612\pi\)
\(572\) 21.5844 3.10307i 0.902488 0.129746i
\(573\) 0 0
\(574\) −3.57023 1.58957i −0.149018 0.0663473i
\(575\) 0.106386 + 0.327424i 0.00443662 + 0.0136545i
\(576\) 0 0
\(577\) 18.0466 + 13.1116i 0.751289 + 0.545843i 0.896226 0.443598i \(-0.146298\pi\)
−0.144937 + 0.989441i \(0.546298\pi\)
\(578\) −1.02080 + 9.71227i −0.0424597 + 0.403977i
\(579\) 0 0
\(580\) −37.7013 8.01366i −1.56546 0.332749i
\(581\) −0.603385 5.74083i −0.0250326 0.238170i
\(582\) 0 0
\(583\) −8.01732 0.535173i −0.332044 0.0221646i
\(584\) 6.24181 0.258288
\(585\) 0 0
\(586\) 0.153568 + 0.472634i 0.00634384 + 0.0195243i
\(587\) −2.44553 + 0.519814i −0.100938 + 0.0214550i −0.258104 0.966117i \(-0.583098\pi\)
0.157166 + 0.987572i \(0.449764\pi\)
\(588\) 0 0
\(589\) 37.9836 16.9114i 1.56508 0.696821i
\(590\) 2.66709 + 2.96210i 0.109802 + 0.121948i
\(591\) 0 0
\(592\) −12.0242 5.35351i −0.494190 0.220028i
\(593\) 10.8953 0.447417 0.223708 0.974656i \(-0.428184\pi\)
0.223708 + 0.974656i \(0.428184\pi\)
\(594\) 0 0
\(595\) 1.09907 0.0450577
\(596\) −6.89767 3.07104i −0.282540 0.125795i
\(597\) 0 0
\(598\) 0.130449 + 0.144878i 0.00533445 + 0.00592451i
\(599\) 33.6533 14.9834i 1.37504 0.612205i 0.419682 0.907671i \(-0.362142\pi\)
0.955353 + 0.295466i \(0.0954749\pi\)
\(600\) 0 0
\(601\) 15.1166 3.21313i 0.616618 0.131066i 0.110995 0.993821i \(-0.464596\pi\)
0.505623 + 0.862755i \(0.331263\pi\)
\(602\) −1.41047 4.34099i −0.0574866 0.176925i
\(603\) 0 0
\(604\) 4.88321 0.198695
\(605\) −18.6534 27.2813i −0.758368 1.10914i
\(606\) 0 0
\(607\) 2.66306 + 25.3373i 0.108090 + 1.02841i 0.905319 + 0.424733i \(0.139632\pi\)
−0.797228 + 0.603678i \(0.793701\pi\)
\(608\) 33.9795 + 7.22257i 1.37805 + 0.292914i
\(609\) 0 0
\(610\) 2.48369 23.6307i 0.100562 0.956781i
\(611\) 1.04630 + 0.760183i 0.0423289 + 0.0307537i
\(612\) 0 0
\(613\) −11.6728 35.9252i −0.471461 1.45101i −0.850672 0.525697i \(-0.823805\pi\)
0.379211 0.925310i \(-0.376195\pi\)
\(614\) −1.84180 0.820023i −0.0743290 0.0330934i
\(615\) 0 0
\(616\) −1.39501 + 8.06037i −0.0562066 + 0.324761i
\(617\) 20.9464 36.2802i 0.843271 1.46059i −0.0438437 0.999038i \(-0.513960\pi\)
0.887115 0.461549i \(-0.152706\pi\)
\(618\) 0 0
\(619\) −4.00783 + 4.45115i −0.161088 + 0.178907i −0.818286 0.574812i \(-0.805075\pi\)
0.657197 + 0.753719i \(0.271742\pi\)
\(620\) 10.0993 31.0823i 0.405596 1.24830i
\(621\) 0 0
\(622\) −5.06974 3.68338i −0.203278 0.147690i
\(623\) −2.42424 + 0.515288i −0.0971251 + 0.0206446i
\(624\) 0 0
\(625\) 3.02291 + 28.7611i 0.120917 + 1.15044i
\(626\) −8.17057 + 14.1518i −0.326562 + 0.565621i
\(627\) 0 0
\(628\) −15.0399 26.0498i −0.600157 1.03950i
\(629\) 1.58690 1.15295i 0.0632739 0.0459712i
\(630\) 0 0
\(631\) −6.64368 + 20.4471i −0.264481 + 0.813988i 0.727332 + 0.686286i \(0.240760\pi\)
−0.991813 + 0.127702i \(0.959240\pi\)
\(632\) 1.96786 18.7229i 0.0782772 0.744758i
\(633\) 0 0
\(634\) −0.430138 0.477717i −0.0170830 0.0189726i
\(635\) −38.7416 8.23479i −1.53741 0.326788i
\(636\) 0 0
\(637\) −11.1368 19.2895i −0.441256 0.764278i
\(638\) 9.12129 + 11.5990i 0.361115 + 0.459208i
\(639\) 0 0
\(640\) 28.0127 20.3525i 1.10730 0.804501i
\(641\) −8.58963 + 9.53975i −0.339270 + 0.376798i −0.888502 0.458872i \(-0.848254\pi\)
0.549232 + 0.835670i \(0.314920\pi\)
\(642\) 0 0
\(643\) 25.9041 11.5332i 1.02156 0.454827i 0.173558 0.984824i \(-0.444473\pi\)
0.848000 + 0.529997i \(0.177807\pi\)
\(644\) 0.151523 0.0674625i 0.00597085 0.00265839i
\(645\) 0 0
\(646\) −0.773607 + 0.859177i −0.0304372 + 0.0338039i
\(647\) −14.1536 + 10.2832i −0.556436 + 0.404274i −0.830153 0.557536i \(-0.811747\pi\)
0.273717 + 0.961810i \(0.411747\pi\)
\(648\) 0 0
\(649\) 0.289810 + 7.60956i 0.0113760 + 0.298701i
\(650\) −4.59060 7.95116i −0.180058 0.311870i
\(651\) 0 0
\(652\) −9.49066 2.01730i −0.371683 0.0790036i
\(653\) 19.6070 + 21.7758i 0.767282 + 0.852152i 0.992511 0.122153i \(-0.0389799\pi\)
−0.225230 + 0.974306i \(0.572313\pi\)
\(654\) 0 0
\(655\) 5.64400 53.6991i 0.220529 2.09820i
\(656\) −3.78455 + 11.6477i −0.147762 + 0.454764i
\(657\) 0 0
\(658\) −0.178378 + 0.129599i −0.00695388 + 0.00505229i
\(659\) 13.7935 + 23.8911i 0.537319 + 0.930664i 0.999047 + 0.0436422i \(0.0138961\pi\)
−0.461728 + 0.887021i \(0.652771\pi\)
\(660\) 0 0
\(661\) −14.8776 + 25.7688i −0.578672 + 1.00229i 0.416960 + 0.908925i \(0.363096\pi\)
−0.995632 + 0.0933649i \(0.970238\pi\)
\(662\) −0.747623 7.11315i −0.0290572 0.276461i
\(663\) 0 0
\(664\) 10.2728 2.18354i 0.398660 0.0847378i
\(665\) −18.0228 13.0943i −0.698893 0.507775i
\(666\) 0 0
\(667\) 0.203437 0.626115i 0.00787711 0.0242433i
\(668\) −5.59853 + 6.21779i −0.216613 + 0.240574i
\(669\) 0 0
\(670\) −10.1380 + 17.5596i −0.391666 + 0.678385i
\(671\) 32.5548 31.6373i 1.25677 1.22134i
\(672\) 0 0
\(673\) 8.81907 + 3.92650i 0.339950 + 0.151356i 0.569609 0.821916i \(-0.307094\pi\)
−0.229659 + 0.973271i \(0.573761\pi\)
\(674\) −2.40577 7.40418i −0.0926666 0.285198i
\(675\) 0 0
\(676\) 3.46724 + 2.51910i 0.133355 + 0.0968883i
\(677\) −0.0102558 + 0.0975777i −0.000394163 + 0.00375021i −0.994717 0.102653i \(-0.967267\pi\)
0.994323 + 0.106403i \(0.0339335\pi\)
\(678\) 0 0
\(679\) −0.101177 0.0215058i −0.00388281 0.000825318i
\(680\) 0.209018 + 1.98868i 0.00801549 + 0.0762623i
\(681\) 0 0
\(682\) −10.5896 + 6.66372i −0.405496 + 0.255167i
\(683\) −30.5246 −1.16799 −0.583996 0.811756i \(-0.698512\pi\)
−0.583996 + 0.811756i \(0.698512\pi\)
\(684\) 0 0
\(685\) −15.2277 46.8660i −0.581820 1.79066i
\(686\) 8.32071 1.76862i 0.317686 0.0675263i
\(687\) 0 0
\(688\) −13.0671 + 5.81784i −0.498178 + 0.221803i
\(689\) −6.39713 7.10473i −0.243711 0.270669i
\(690\) 0 0
\(691\) 29.9658 + 13.3416i 1.13995 + 0.507540i 0.887838 0.460157i \(-0.152207\pi\)
0.252116 + 0.967697i \(0.418873\pi\)
\(692\) −25.9748 −0.987413
\(693\) 0 0
\(694\) 5.62741 0.213614
\(695\) 32.6661 + 14.5439i 1.23910 + 0.551681i
\(696\) 0 0
\(697\) −1.22127 1.35635i −0.0462588 0.0513756i
\(698\) 2.34379 1.04352i 0.0887138 0.0394979i
\(699\) 0 0
\(700\) −7.64053 + 1.62405i −0.288785 + 0.0613831i
\(701\) 2.70365 + 8.32098i 0.102115 + 0.314279i 0.989043 0.147630i \(-0.0471646\pi\)
−0.886927 + 0.461909i \(0.847165\pi\)
\(702\) 0 0
\(703\) −39.7584 −1.49952
\(704\) 3.52321 + 0.235181i 0.132786 + 0.00886373i
\(705\) 0 0
\(706\) −1.96435 18.6895i −0.0739293 0.703390i
\(707\) 2.34208 + 0.497825i 0.0880831 + 0.0187226i
\(708\) 0 0
\(709\) −2.79884 + 26.6292i −0.105113 + 1.00008i 0.807114 + 0.590395i \(0.201028\pi\)
−0.912227 + 0.409685i \(0.865639\pi\)
\(710\) 12.2435 + 8.89542i 0.459490 + 0.333839i
\(711\) 0 0
\(712\) −1.39340 4.28845i −0.0522199 0.160716i
\(713\) 0.509956 + 0.227047i 0.0190980 + 0.00850298i
\(714\) 0 0
\(715\) 6.70577 38.7459i 0.250781 1.44901i
\(716\) −5.87217 + 10.1709i −0.219453 + 0.380105i
\(717\) 0 0
\(718\) −10.7368 + 11.9244i −0.400694 + 0.445016i
\(719\) 4.63672 14.2703i 0.172920 0.532194i −0.826612 0.562772i \(-0.809735\pi\)
0.999532 + 0.0305782i \(0.00973486\pi\)
\(720\) 0 0
\(721\) −2.84161 2.06455i −0.105827 0.0768879i
\(722\) 12.1834 2.58965i 0.453418 0.0963769i
\(723\) 0 0
\(724\) 0.434995 + 4.13870i 0.0161665 + 0.153814i
\(725\) −15.5020 + 26.8502i −0.575730 + 0.997193i
\(726\) 0 0
\(727\) −13.7663 23.8438i −0.510562 0.884319i −0.999925 0.0122391i \(-0.996104\pi\)
0.489363 0.872080i \(-0.337229\pi\)
\(728\) −7.87410 + 5.72087i −0.291834 + 0.212029i
\(729\) 0 0
\(730\) 1.58069 4.86486i 0.0585039 0.180057i
\(731\) 0.222818 2.11997i 0.00824123 0.0784101i
\(732\) 0 0
\(733\) 31.9441 + 35.4775i 1.17988 + 1.31039i 0.940630 + 0.339433i \(0.110235\pi\)
0.239251 + 0.970958i \(0.423098\pi\)
\(734\) 0.662509 + 0.140821i 0.0244536 + 0.00519778i
\(735\) 0 0
\(736\) 0.233195 + 0.403906i 0.00859570 + 0.0148882i
\(737\) −36.3593 + 13.3640i −1.33931 + 0.492267i
\(738\) 0 0
\(739\) −1.20421 + 0.874910i −0.0442976 + 0.0321841i −0.609714 0.792622i \(-0.708716\pi\)
0.565416 + 0.824806i \(0.308716\pi\)
\(740\) −20.9113 + 23.2244i −0.768716 + 0.853746i
\(741\) 0 0
\(742\) 1.48898 0.662935i 0.0546620 0.0243371i
\(743\) 16.5901 7.38641i 0.608633 0.270981i −0.0791896 0.996860i \(-0.525233\pi\)
0.687823 + 0.725879i \(0.258567\pi\)
\(744\) 0 0
\(745\) −9.11035 + 10.1181i −0.333778 + 0.370698i
\(746\) 10.1751 7.39264i 0.372537 0.270664i
\(747\) 0 0
\(748\) −0.966316 + 1.44243i −0.0353320 + 0.0527406i
\(749\) −6.98177 12.0928i −0.255108 0.441860i
\(750\) 0 0
\(751\) 4.29862 + 0.913700i 0.156859 + 0.0333414i 0.285672 0.958328i \(-0.407783\pi\)
−0.128813 + 0.991669i \(0.541117\pi\)
\(752\) 0.462338 + 0.513479i 0.0168597 + 0.0187246i
\(753\) 0 0
\(754\) −1.83518 + 17.4605i −0.0668332 + 0.635875i
\(755\) 2.72107 8.37459i 0.0990299 0.304783i
\(756\) 0 0
\(757\) 11.1369 8.09140i 0.404776 0.294087i −0.366708 0.930336i \(-0.619515\pi\)
0.771483 + 0.636249i \(0.219515\pi\)
\(758\) −4.69382 8.12993i −0.170487 0.295292i
\(759\) 0 0
\(760\) 20.2655 35.1008i 0.735105 1.27324i
\(761\) −3.25147 30.9357i −0.117866 1.12142i −0.880321 0.474378i \(-0.842673\pi\)
0.762456 0.647041i \(-0.223994\pi\)
\(762\) 0 0
\(763\) 5.92230 1.25882i 0.214402 0.0455725i
\(764\) 15.9365 + 11.5786i 0.576564 + 0.418898i
\(765\) 0 0
\(766\) 1.10585 3.40344i 0.0399558 0.122971i
\(767\) −6.06268 + 6.73329i −0.218911 + 0.243125i
\(768\) 0 0
\(769\) −10.9677 + 18.9966i −0.395504 + 0.685034i −0.993165 0.116715i \(-0.962764\pi\)
0.597661 + 0.801749i \(0.296097\pi\)
\(770\) 5.92897 + 3.12850i 0.213665 + 0.112743i
\(771\) 0 0
\(772\) −10.2690 4.57206i −0.369590 0.164552i
\(773\) 3.92965 + 12.0942i 0.141340 + 0.434999i 0.996522 0.0833281i \(-0.0265549\pi\)
−0.855182 + 0.518327i \(0.826555\pi\)
\(774\) 0 0
\(775\) −21.2682 15.4522i −0.763976 0.555061i
\(776\) 0.0196714 0.187160i 0.000706160 0.00671867i
\(777\) 0 0
\(778\) 0.408750 + 0.0868824i 0.0146544 + 0.00311489i
\(779\) 3.86697 + 36.7918i 0.138549 + 1.31820i
\(780\) 0 0
\(781\) 7.08334 + 28.0321i 0.253462 + 1.00307i
\(782\) −0.0155220 −0.000555064
\(783\) 0 0
\(784\) −3.67724 11.3174i −0.131330 0.404193i
\(785\) −53.0556 + 11.2773i −1.89363 + 0.402504i
\(786\) 0 0
\(787\) −15.7693 + 7.02095i −0.562115 + 0.250270i −0.668067 0.744102i \(-0.732878\pi\)
0.105951 + 0.994371i \(0.466211\pi\)
\(788\) −23.0190 25.5652i −0.820018 0.910722i
\(789\) 0 0
\(790\) −14.0943 6.27518i −0.501452 0.223261i
\(791\) 22.3870 0.795991
\(792\) 0 0
\(793\) 54.0120 1.91802
\(794\) −2.15890 0.961206i −0.0766166 0.0341119i
\(795\) 0 0
\(796\) 14.8122 + 16.4507i 0.525006 + 0.583078i
\(797\) −32.1582 + 14.3177i −1.13910 + 0.507161i −0.887563 0.460687i \(-0.847603\pi\)
−0.251538 + 0.967847i \(0.580936\pi\)
\(798\) 0 0
\(799\) −0.100721 + 0.0214090i −0.00356326 + 0.000757395i
\(800\) −6.78739 20.8894i −0.239970 0.738553i
\(801\) 0 0
\(802\) −3.26248 −0.115202
\(803\) 8.27126 5.20487i 0.291887 0.183676i
\(804\) 0 0
\(805\) −0.0312634 0.297451i −0.00110189 0.0104838i
\(806\) −14.5614 3.09512i −0.512903 0.109021i
\(807\) 0 0
\(808\) −0.455360 + 4.33246i −0.0160195 + 0.152415i
\(809\) −15.4367 11.2154i −0.542725 0.394313i 0.282371 0.959305i \(-0.408879\pi\)
−0.825096 + 0.564992i \(0.808879\pi\)
\(810\) 0 0
\(811\) −9.59769 29.5387i −0.337020 1.03724i −0.965718 0.259593i \(-0.916412\pi\)
0.628698 0.777650i \(-0.283588\pi\)
\(812\) 13.6456 + 6.07542i 0.478867 + 0.213205i
\(813\) 0 0
\(814\) 11.8424 1.70252i 0.415076 0.0596733i
\(815\) −8.74810 + 15.1522i −0.306433 + 0.530757i
\(816\) 0 0
\(817\) −28.9110 + 32.1090i −1.01147 + 1.12335i
\(818\) −1.68711 + 5.19240i −0.0589885 + 0.181548i
\(819\) 0 0
\(820\) 23.5253 + 17.0922i 0.821540 + 0.596884i
\(821\) 33.2653 7.07077i 1.16097 0.246771i 0.413143 0.910666i \(-0.364431\pi\)
0.747826 + 0.663895i \(0.231098\pi\)
\(822\) 0 0
\(823\) −1.62605 15.4708i −0.0566804 0.539278i −0.985612 0.169026i \(-0.945938\pi\)
0.928931 0.370252i \(-0.120729\pi\)
\(824\) 3.19521 5.53426i 0.111310 0.192795i
\(825\) 0 0
\(826\) −0.772337 1.33773i −0.0268730 0.0465455i
\(827\) 12.9667 9.42084i 0.450895 0.327595i −0.339054 0.940767i \(-0.610107\pi\)
0.789949 + 0.613172i \(0.210107\pi\)
\(828\) 0 0
\(829\) 5.90205 18.1646i 0.204987 0.630884i −0.794727 0.606967i \(-0.792386\pi\)
0.999714 0.0239173i \(-0.00761382\pi\)
\(830\) 0.899644 8.55954i 0.0312271 0.297106i
\(831\) 0 0
\(832\) 2.81122 + 3.12217i 0.0974614 + 0.108242i
\(833\) 1.73465 + 0.368711i 0.0601021 + 0.0127751i
\(834\) 0 0
\(835\) 7.54371 + 13.0661i 0.261061 + 0.452171i
\(836\) 33.0308 12.1406i 1.14240 0.419891i
\(837\) 0 0
\(838\) −0.0708501 + 0.0514756i −0.00244747 + 0.00177819i
\(839\) −0.995613 + 1.10574i −0.0343724 + 0.0381744i −0.760086 0.649823i \(-0.774843\pi\)
0.725713 + 0.687997i \(0.241510\pi\)
\(840\) 0 0
\(841\) 27.6687 12.3189i 0.954095 0.424790i
\(842\) −8.96121 + 3.98979i −0.308824 + 0.137497i
\(843\) 0 0
\(844\) 9.30353 10.3326i 0.320241 0.355663i
\(845\) 6.25224 4.54252i 0.215084 0.156267i
\(846\) 0 0
\(847\) 4.87274 + 11.8444i 0.167429 + 0.406977i
\(848\) −2.55384 4.42338i −0.0876993 0.151900i
\(849\) 0 0
\(850\) 0.715025 + 0.151983i 0.0245252 + 0.00521298i
\(851\) −0.357172 0.396680i −0.0122437 0.0135980i
\(852\) 0 0
\(853\) −3.95139 + 37.5950i −0.135293 + 1.28723i 0.690532 + 0.723302i \(0.257376\pi\)
−0.825825 + 0.563926i \(0.809290\pi\)
\(854\) −2.84548 + 8.75750i −0.0973704 + 0.299675i
\(855\) 0 0
\(856\) 20.5530 14.9326i 0.702487 0.510387i
\(857\) 9.91348 + 17.1706i 0.338638 + 0.586538i 0.984177 0.177189i \(-0.0567005\pi\)
−0.645539 + 0.763727i \(0.723367\pi\)
\(858\) 0 0
\(859\) 7.85764 13.6098i 0.268099 0.464362i −0.700272 0.713876i \(-0.746938\pi\)
0.968371 + 0.249515i \(0.0802711\pi\)
\(860\) 3.55001 + 33.7761i 0.121054 + 1.15175i
\(861\) 0 0
\(862\) 14.3384 3.04772i 0.488368 0.103806i
\(863\) 6.57548 + 4.77736i 0.223832 + 0.162623i 0.694050 0.719927i \(-0.255825\pi\)
−0.470218 + 0.882550i \(0.655825\pi\)
\(864\) 0 0
\(865\) −14.4739 + 44.5462i −0.492128 + 1.51462i
\(866\) −6.39284 + 7.09997i −0.217237 + 0.241267i
\(867\) 0 0
\(868\) −6.33269 + 10.9685i −0.214945 + 0.372296i
\(869\) −13.0049 26.4514i −0.441159 0.897303i
\(870\) 0 0
\(871\) −42.1057 18.7467i −1.42670 0.635206i
\(872\) 3.40401 + 10.4765i 0.115274 + 0.354778i
\(873\) 0 0
\(874\) 0.254531 + 0.184928i 0.00860964 + 0.00625527i
\(875\) 0.355931 3.38646i 0.0120327 0.114483i
\(876\) 0 0
\(877\) 2.47817 + 0.526750i 0.0836817 + 0.0177871i 0.249562 0.968359i \(-0.419713\pi\)
−0.165881 + 0.986146i \(0.553047\pi\)
\(878\) −2.37009 22.5499i −0.0799867 0.761022i
\(879\) 0 0
\(880\) 7.80812 19.5030i 0.263212 0.657446i
\(881\) 47.4109 1.59731 0.798657 0.601786i \(-0.205544\pi\)
0.798657 + 0.601786i \(0.205544\pi\)
\(882\) 0 0
\(883\) 8.19295 + 25.2153i 0.275715 + 0.848563i 0.989029 + 0.147719i \(0.0471930\pi\)
−0.713315 + 0.700844i \(0.752807\pi\)
\(884\) −2.02061 + 0.429495i −0.0679606 + 0.0144455i
\(885\) 0 0
\(886\) 16.9914 7.56506i 0.570837 0.254153i
\(887\) 32.0041 + 35.5441i 1.07459 + 1.19345i 0.980219 + 0.197918i \(0.0634179\pi\)
0.0943729 + 0.995537i \(0.469915\pi\)
\(888\) 0 0
\(889\) 14.0221 + 6.24306i 0.470288 + 0.209386i
\(890\) −3.69528 −0.123866
\(891\) 0 0
\(892\) 0.639221 0.0214027
\(893\) 1.90671 + 0.848920i 0.0638055 + 0.0284080i
\(894\) 0 0
\(895\) 14.1707 + 15.7382i 0.473675 + 0.526069i
\(896\) −12.2585 + 5.45786i −0.409529 + 0.182334i
\(897\) 0 0
\(898\) 14.6068 3.10477i 0.487435 0.103608i
\(899\) 15.5345 + 47.8104i 0.518106 + 1.59457i
\(900\) 0 0
\(901\) 0.761187 0.0253588
\(902\) −2.72730 10.7932i −0.0908090 0.359373i
\(903\) 0 0
\(904\) 4.25749 + 40.5073i 0.141602 + 1.34725i
\(905\) 7.34017 + 1.56020i 0.243995 + 0.0518628i
\(906\) 0 0
\(907\) −4.96075 + 47.1984i −0.164719 + 1.56720i 0.530052 + 0.847965i \(0.322172\pi\)
−0.694771 + 0.719231i \(0.744494\pi\)
\(908\) −24.2817 17.6417i −0.805815 0.585459i
\(909\) 0 0
\(910\) 2.46479 + 7.58583i 0.0817068 + 0.251468i
\(911\) 25.9741 + 11.5644i 0.860561 + 0.383147i 0.789076 0.614295i \(-0.210560\pi\)
0.0714850 + 0.997442i \(0.477226\pi\)
\(912\) 0 0
\(913\) 11.7920 11.4597i 0.390259 0.379259i
\(914\) −3.67381 + 6.36322i −0.121519 + 0.210477i
\(915\) 0 0
\(916\) −14.9702 + 16.6261i −0.494629 + 0.549342i
\(917\) −6.46615 + 19.9008i −0.213531 + 0.657181i
\(918\) 0 0
\(919\) −31.0442 22.5550i −1.02406 0.744020i −0.0569449 0.998377i \(-0.518136\pi\)
−0.967110 + 0.254358i \(0.918136\pi\)
\(920\) 0.532265 0.113136i 0.0175483 0.00373000i
\(921\) 0 0
\(922\) 1.14887 + 10.9308i 0.0378361 + 0.359986i
\(923\) −17.2007 + 29.7924i −0.566167 + 0.980629i
\(924\) 0 0
\(925\) 12.5692 + 21.7704i 0.413272 + 0.715808i
\(926\) −10.6893 + 7.76621i −0.351271 + 0.255214i
\(927\) 0 0
\(928\) −12.9791 + 39.9457i −0.426061 + 1.31128i
\(929\) 1.39939 13.3143i 0.0459126 0.436829i −0.947285 0.320391i \(-0.896186\pi\)
0.993198 0.116438i \(-0.0371476\pi\)
\(930\) 0 0
\(931\) −24.0522 26.7127i −0.788280 0.875473i
\(932\) 5.49160 + 1.16728i 0.179883 + 0.0382354i
\(933\) 0 0
\(934\) −4.60021 7.96779i −0.150523 0.260714i
\(935\) 1.93528 + 2.46098i 0.0632905 + 0.0804826i
\(936\) 0 0
\(937\) 19.9588 14.5010i 0.652027 0.473725i −0.211934 0.977284i \(-0.567976\pi\)
0.863961 + 0.503559i \(0.167976\pi\)
\(938\) 5.25781 5.83939i 0.171674 0.190663i
\(939\) 0 0
\(940\) 1.49874 0.667281i 0.0488834 0.0217643i
\(941\) −7.58453 + 3.37685i −0.247249 + 0.110082i −0.526620 0.850101i \(-0.676541\pi\)
0.279371 + 0.960183i \(0.409874\pi\)
\(942\) 0 0
\(943\) −0.332341 + 0.369103i −0.0108225 + 0.0120196i
\(944\) −3.91616 + 2.84526i −0.127460 + 0.0926053i
\(945\) 0 0
\(946\) 7.23646 10.8020i 0.235278 0.351202i
\(947\) 18.9748 + 32.8653i 0.616598 + 1.06798i 0.990102 + 0.140351i \(0.0448231\pi\)
−0.373503 + 0.927629i \(0.621844\pi\)
\(948\) 0 0
\(949\) 11.3735 + 2.41752i 0.369201 + 0.0784761i
\(950\) −9.91435 11.0110i −0.321664 0.357244i
\(951\) 0 0
\(952\) 0.0810019 0.770681i 0.00262529 0.0249779i
\(953\) 15.0400 46.2884i 0.487194 1.49943i −0.341583 0.939852i \(-0.610963\pi\)
0.828778 0.559578i \(-0.189037\pi\)
\(954\) 0 0
\(955\) 28.7373 20.8789i 0.929918 0.675625i
\(956\) 19.3245 + 33.4710i 0.624998 + 1.08253i
\(957\) 0 0
\(958\) 4.73516 8.20154i 0.152986 0.264980i
\(959\) 1.99617 + 18.9923i 0.0644596 + 0.613292i
\(960\) 0 0
\(961\) −11.3716 + 2.41712i −0.366827 + 0.0779716i
\(962\) 11.5165 + 8.36721i 0.371306 + 0.269770i
\(963\) 0 0
\(964\) −7.80746 + 24.0289i −0.251461 + 0.773918i
\(965\) −13.5632 + 15.0634i −0.436614 + 0.484909i
\(966\) 0 0
\(967\) −5.48901 + 9.50724i −0.176515 + 0.305732i −0.940684 0.339283i \(-0.889816\pi\)
0.764170 + 0.645015i \(0.223149\pi\)
\(968\) −20.5046 + 11.0693i −0.659044 + 0.355781i
\(969\) 0 0
\(970\) −0.140891 0.0627287i −0.00452374 0.00201410i
\(971\) −4.03687 12.4242i −0.129549 0.398712i 0.865153 0.501508i \(-0.167221\pi\)
−0.994702 + 0.102796i \(0.967221\pi\)
\(972\) 0 0
\(973\) −11.2108 8.14510i −0.359401 0.261120i
\(974\) 1.37626 13.0942i 0.0440981 0.419565i
\(975\) 0 0
\(976\) 28.2257 + 5.99955i 0.903482 + 0.192041i
\(977\) −1.15779 11.0156i −0.0370410 0.352421i −0.997307 0.0733360i \(-0.976635\pi\)
0.960266 0.279085i \(-0.0900312\pi\)
\(978\) 0 0
\(979\) −5.42247 4.52087i −0.173303 0.144488i
\(980\) −28.2544 −0.902554
\(981\) 0 0
\(982\) −7.79262 23.9832i −0.248673 0.765336i
\(983\) −25.8539 + 5.49541i −0.824611 + 0.175277i −0.600844 0.799366i \(-0.705169\pi\)
−0.223767 + 0.974643i \(0.571835\pi\)
\(984\) 0 0
\(985\) −56.6706 + 25.2314i −1.80568 + 0.803938i
\(986\) −0.935344 1.03880i −0.0297874 0.0330823i
\(987\) 0 0
\(988\) 38.2512 + 17.0305i 1.21693 + 0.541814i
\(989\) −0.580083 −0.0184456
\(990\) 0 0
\(991\) −18.9911 −0.603272 −0.301636 0.953423i \(-0.597533\pi\)
−0.301636 + 0.953423i \(0.597533\pi\)
\(992\) −32.5349 14.4855i −1.03298 0.459914i
\(993\) 0 0
\(994\) −3.92436 4.35845i −0.124473 0.138242i
\(995\) 36.4663 16.2359i 1.15606 0.514711i
\(996\) 0 0
\(997\) −21.6299 + 4.59758i −0.685027 + 0.145607i −0.537262 0.843416i \(-0.680541\pi\)
−0.147765 + 0.989022i \(0.547208\pi\)
\(998\) 3.58956 + 11.0475i 0.113625 + 0.349703i
\(999\) 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 297.2.n.b.91.4 72
3.2 odd 2 99.2.m.b.58.6 yes 72
9.2 odd 6 99.2.m.b.25.4 yes 72
9.4 even 3 891.2.f.e.487.6 36
9.5 odd 6 891.2.f.f.487.4 36
9.7 even 3 inner 297.2.n.b.289.6 72
11.4 even 5 inner 297.2.n.b.37.6 72
33.2 even 10 1089.2.e.o.364.11 36
33.20 odd 10 1089.2.e.p.364.8 36
33.26 odd 10 99.2.m.b.4.4 72
99.2 even 30 1089.2.e.o.727.11 36
99.4 even 15 891.2.f.e.730.6 36
99.13 odd 30 9801.2.a.cn.1.11 18
99.20 odd 30 1089.2.e.p.727.8 36
99.31 even 15 9801.2.a.cp.1.8 18
99.59 odd 30 891.2.f.f.730.4 36
99.68 even 30 9801.2.a.co.1.8 18
99.70 even 15 inner 297.2.n.b.235.4 72
99.86 odd 30 9801.2.a.cm.1.11 18
99.92 odd 30 99.2.m.b.70.6 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.b.4.4 72 33.26 odd 10
99.2.m.b.25.4 yes 72 9.2 odd 6
99.2.m.b.58.6 yes 72 3.2 odd 2
99.2.m.b.70.6 yes 72 99.92 odd 30
297.2.n.b.37.6 72 11.4 even 5 inner
297.2.n.b.91.4 72 1.1 even 1 trivial
297.2.n.b.235.4 72 99.70 even 15 inner
297.2.n.b.289.6 72 9.7 even 3 inner
891.2.f.e.487.6 36 9.4 even 3
891.2.f.e.730.6 36 99.4 even 15
891.2.f.f.487.4 36 9.5 odd 6
891.2.f.f.730.4 36 99.59 odd 30
1089.2.e.o.364.11 36 33.2 even 10
1089.2.e.o.727.11 36 99.2 even 30
1089.2.e.p.364.8 36 33.20 odd 10
1089.2.e.p.727.8 36 99.20 odd 30
9801.2.a.cm.1.11 18 99.86 odd 30
9801.2.a.cn.1.11 18 99.13 odd 30
9801.2.a.co.1.8 18 99.68 even 30
9801.2.a.cp.1.8 18 99.31 even 15