Properties

Label 297.2.n.b.235.4
Level $297$
Weight $2$
Character 297.235
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 235.4
Character \(\chi\) \(=\) 297.235
Dual form 297.2.n.b.91.4

$q$-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 \(\left(\mathbb{Z}/297\mathbb{Z}\right)^\times\).

\(n\) \(56\) \(244\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{5}\right)\)

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 −0.584785 0.811188i \(-0.698821\pi\)
0.211533 + 0.977371i \(0.432154\pi\)
\(3\) 0 0
\(4\) −1.11486 + 1.23818i −0.557430 + 0.619089i
\(5\) −2.74468 1.22201i −1.22746 0.546500i −0.312450 0.949934i \(-0.601150\pi\)
−0.915009 + 0.403434i \(0.867816\pi\)
\(6\) 0 0
\(7\) 1.13888 + 0.242076i 0.430455 + 0.0914960i 0.418044 0.908427i \(-0.362716\pi\)
0.0124114 + 0.999923i \(0.496049\pi\)
\(8\) 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 −0.775192 0.631726i \(-0.782347\pi\)
0.889595 0.456750i \(-0.150986\pi\)
\(14\) −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 −0.618183 0.786034i \(-0.712131\pi\)
0.556534 + 0.830825i \(0.312131\pi\)
\(18\) 0 0
\(19\) 1.96794 6.05670i 0.451477 1.38950i −0.423746 0.905781i \(-0.639285\pi\)
0.875222 0.483721i \(-0.160715\pi\)
\(20\) 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 0.861534 0.507700i \(-0.169504\pi\)
−0.870448 + 0.492260i \(0.836171\pi\)
\(24\) 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 −0.553913 0.832575i \(-0.686866\pi\)
−0.844663 + 0.535298i \(0.820199\pi\)
\(30\) 0 0
\(31\) −0.682449 + 6.49307i −0.122571 + 1.16619i 0.744366 + 0.667772i \(0.232752\pi\)
−0.866937 + 0.498418i \(0.833915\pi\)
\(32\) 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 −0.974855 0.222838i \(-0.928468\pi\)
0.657694 0.753286i \(-0.271532\pi\)
\(38\) 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 0.258409 0.966036i \(-0.416802\pi\)
0.628990 + 0.777413i \(0.283468\pi\)
\(42\) 0 0
\(43\) 3.39229 5.87562i 0.517320 0.896024i −0.482478 0.875908i \(-0.660263\pi\)
0.999798 0.0201157i \(-0.00640347\pi\)
\(44\) −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 0.758926 0.651176i \(-0.225724\pi\)
−0.726939 + 0.686703i \(0.759058\pi\)
\(48\) 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 0.444978 0.895541i \(-0.353211\pi\)
−0.714205 + 0.699937i \(0.753211\pi\)
\(54\) 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 −0.634790 0.772685i \(-0.718913\pi\)
0.834805 + 0.550545i \(0.185580\pi\)
\(60\) 0 0
\(61\) 1.43070 + 13.6122i 0.183183 + 1.74287i 0.570839 + 0.821062i \(0.306618\pi\)
−0.387656 + 0.921804i \(0.626715\pi\)
\(62\) −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 −0.963552 0.267521i \(-0.913795\pi\)
0.250096 0.968221i \(-0.419538\pi\)
\(68\) 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 −0.0845279 0.996421i \(-0.526938\pi\)
0.921532 + 0.388302i \(0.126938\pi\)
\(72\) 0 0
\(73\) 0.910538 + 2.80235i 0.106570 + 0.327990i 0.990096 0.140393i \(-0.0448367\pi\)
−0.883525 + 0.468383i \(0.844837\pi\)
\(74\) 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 −0.808979 0.587838i \(-0.799979\pi\)
−0.104464 + 0.994529i \(0.533313\pi\)
\(80\) −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 0.985441 + 0.170018i \(0.0543827\pi\)
−0.928558 + 0.371188i \(0.878951\pi\)
\(84\) 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 −0.410853 0.911702i \(-0.634769\pi\)
0.402612 + 0.915371i \(0.368102\pi\)
\(98\) 3.26138 0.329449
\(99\) 0 0
\(100\) −6.70883 −0.670883
\(101\) 1.87869 0.836447i 0.186937 0.0832296i −0.311134 0.950366i \(-0.600709\pi\)
0.498071 + 0.867137i \(0.334042\pi\)
\(102\) 0 0
\(103\) −2.01858 + 2.24186i −0.198896 + 0.220897i −0.834340 0.551251i \(-0.814151\pi\)
0.635443 + 0.772148i \(0.280817\pi\)
\(104\) −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 0.595815 + 0.803121i \(0.296829\pi\)
−0.954088 + 0.299527i \(0.903171\pi\)
\(108\) 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 0.795907 0.605419i \(-0.206995\pi\)
0.973343 + 0.229354i \(0.0736612\pi\)
\(114\) 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 −0.00356461 0.999994i \(-0.501135\pi\)
0.949949 + 0.312405i \(0.101135\pi\)
\(128\) −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 −0.928939 0.370233i \(-0.879278\pi\)
0.143839 0.989601i \(-0.454055\pi\)
\(132\) 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 −0.782836 0.622228i \(-0.786228\pi\)
0.636361 0.771391i \(-0.280439\pi\)
\(138\) 0 0
\(139\) −7.96373 + 8.84461i −0.675475 + 0.750190i −0.979273 0.202546i \(-0.935078\pi\)
0.303798 + 0.952736i \(0.401745\pi\)
\(140\) 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 0.569246 0.822167i \(-0.307235\pi\)
−0.230090 + 0.973169i \(0.573902\pi\)
\(150\) 0 0
\(151\) −1.96113 2.17806i −0.159595 0.177248i 0.658044 0.752979i \(-0.271384\pi\)
−0.817639 + 0.575732i \(0.804717\pi\)
\(152\) −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 0.560481 0.828167i \(-0.310616\pi\)
0.848871 + 0.528600i \(0.177283\pi\)
\(158\) 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 0.756803 0.653643i \(-0.226760\pi\)
−0.387786 + 0.921749i \(0.626760\pi\)
\(164\) −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 0.955260 + 0.295769i \(0.0955757\pi\)
−0.995879 + 0.0906956i \(0.971091\pi\)
\(168\) 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 0.995132 0.0985486i \(-0.0314200\pi\)
−0.202028 + 0.979380i \(0.564753\pi\)
\(174\) 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 −0.998868 0.0475668i \(-0.984853\pi\)
0.836060 + 0.548638i \(0.184853\pi\)
\(180\) 0 0
\(181\) −2.02068 + 1.46811i −0.150196 + 0.109124i −0.660345 0.750962i \(-0.729590\pi\)
0.510149 + 0.860086i \(0.329590\pi\)
\(182\) 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 −0.230461 0.973081i \(-0.574024\pi\)
−0.606325 + 0.795217i \(0.707357\pi\)
\(192\) 0 0
\(193\) 6.16338 + 2.74411i 0.443650 + 0.197526i 0.616389 0.787442i \(-0.288595\pi\)
−0.172739 + 0.984968i \(0.555262\pi\)
\(194\) 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 −0.922584 0.385797i \(-0.873926\pi\)
0.982635 0.185551i \(-0.0594068\pi\)
\(212\) 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 0.734488 0.678622i \(-0.237422\pi\)
−0.751679 + 0.659529i \(0.770756\pi\)
\(224\) 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 0.751422 0.659822i \(-0.229368\pi\)
0.418084 + 0.908408i \(0.362702\pi\)
\(228\) 0 0
\(229\) −1.40359 + 13.3543i −0.0927521 + 0.882478i 0.844905 + 0.534916i \(0.179657\pi\)
−0.937657 + 0.347561i \(0.887010\pi\)
\(230\) −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 0.494897 0.868952i \(-0.335206\pi\)
−0.673490 + 0.739196i \(0.735206\pi\)
\(234\) 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 −0.871308 0.490736i \(-0.836728\pi\)
−0.596379 + 0.802703i \(0.703394\pi\)
\(240\) 0 0
\(241\) −7.58206 + 13.1325i −0.488404 + 0.845940i −0.999911 0.0133389i \(-0.995754\pi\)
0.511507 + 0.859279i \(0.329087\pi\)
\(242\) 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 0.572818 0.819682i \(-0.305850\pi\)
−0.602554 + 0.798078i \(0.705850\pi\)
\(252\) 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 −0.469313 0.883032i \(-0.655498\pi\)
0.927251 + 0.374440i \(0.122165\pi\)
\(258\) 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 −0.997970 0.0636896i \(-0.979713\pi\)
0.554142 + 0.832422i \(0.313047\pi\)
\(264\) 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 −0.575660 0.817689i \(-0.695255\pi\)
0.599780 + 0.800165i \(0.295255\pi\)
\(270\) 0 0
\(271\) 6.77950 + 20.8652i 0.411825 + 1.26747i 0.915060 + 0.403318i \(0.132143\pi\)
−0.503234 + 0.864150i \(0.667857\pi\)
\(272\) 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 −0.326469 0.945208i \(-0.605859\pi\)
0.483976 + 0.875081i \(0.339192\pi\)
\(278\) 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 0.892318 + 0.451406i \(0.149078\pi\)
−0.778967 + 0.627066i \(0.784256\pi\)
\(282\) 0 0
\(283\) 20.0883 4.26991i 1.19413 0.253820i 0.432378 0.901692i \(-0.357674\pi\)
0.761749 + 0.647873i \(0.224341\pi\)
\(284\) −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 −0.759721 0.650250i \(-0.774664\pi\)
0.726100 + 0.687589i \(0.241331\pi\)
\(294\) 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 0.102932 0.994688i \(-0.467178\pi\)
0.498610 + 0.866827i \(0.333844\pi\)
\(312\) 0 0
\(313\) 2.95618 + 28.1261i 0.167093 + 1.58978i 0.681226 + 0.732073i \(0.261447\pi\)
−0.514133 + 0.857710i \(0.671886\pi\)
\(314\) −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 −0.377996 0.925807i \(-0.623387\pi\)
0.435080 + 0.900392i \(0.356720\pi\)
\(318\) 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 −0.644281 0.764789i \(-0.722843\pi\)
0.984467 + 0.175569i \(0.0561764\pi\)
\(332\) −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 −0.445740 0.895163i \(-0.647059\pi\)
0.936851 + 0.349728i \(0.113726\pi\)
\(338\) 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 0.153781 0.988105i \(-0.450855\pi\)
−0.631406 + 0.775453i \(0.717522\pi\)
\(348\) 0 0
\(349\) −2.97107 3.29971i −0.159038 0.176629i 0.658360 0.752703i \(-0.271251\pi\)
−0.817397 + 0.576074i \(0.804584\pi\)
\(350\) −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 −0.000996749 1.00000i \(-0.500317\pi\)
0.866523 0.499137i \(-0.166349\pi\)
\(354\) 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 0.873571 + 0.486697i \(0.161799\pi\)
−0.420660 + 0.907218i \(0.638201\pi\)
\(360\) 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 0.177889 0.984051i \(-0.443073\pi\)
−0.237740 + 0.971329i \(0.576407\pi\)
\(368\) −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 −0.997186 0.0749719i \(-0.976113\pi\)
0.433665 0.901074i \(-0.357220\pi\)
\(374\) −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 −0.196588 0.980486i \(-0.562986\pi\)
0.871749 + 0.489953i \(0.162986\pi\)
\(380\) −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 −0.965453 0.260577i \(-0.916087\pi\)
0.998533 0.0541542i \(-0.0172463\pi\)
\(384\) 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 0.189943 0.981795i \(-0.439170\pi\)
−0.225810 + 0.974171i \(0.572503\pi\)
\(390\) 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 0.531466 0.847079i \(-0.321641\pi\)
−0.273882 + 0.961763i \(0.588308\pi\)
\(402\) 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 0.942586 + 0.333962i \(0.108386\pi\)
−0.991423 + 0.130690i \(0.958281\pi\)
\(410\) 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 0.867871 0.496790i \(-0.165488\pi\)
−0.864168 + 0.503203i \(0.832155\pi\)
\(420\) 0 0
\(421\) 11.3595 + 12.6160i 0.553630 + 0.614868i 0.953386 0.301753i \(-0.0975719\pi\)
−0.399756 + 0.916622i \(0.630905\pi\)
\(422\) 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 −0.0289998 0.999579i \(-0.509232\pi\)
−0.959618 + 0.281307i \(0.909232\pi\)
\(432\) 0 0
\(433\) 5.10950 + 15.7254i 0.245547 + 0.755716i 0.995546 + 0.0942769i \(0.0300539\pi\)
−0.749999 + 0.661439i \(0.769946\pi\)
\(434\) −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 0.164403 0.986393i \(-0.447430\pi\)
0.772040 0.635574i \(-0.219237\pi\)
\(440\) −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 −0.990561 0.137075i \(-0.956230\pi\)
−0.0327827 0.999463i \(-0.510437\pi\)
\(444\) 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 −0.0275281 0.999621i \(-0.508764\pi\)
−0.959203 + 0.282719i \(0.908764\pi\)
\(450\) 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 0.980605 + 0.195994i \(0.0627932\pi\)
−0.918427 + 0.395590i \(0.870540\pi\)
\(458\) −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 −0.997908 0.0646502i \(-0.979407\pi\)
0.554943 + 0.831889i \(0.312740\pi\)
\(462\) 0 0
\(463\) 11.4334 + 19.8032i 0.531353 + 0.920331i 0.999330 + 0.0365903i \(0.0116497\pi\)
−0.467977 + 0.883741i \(0.655017\pi\)
\(464\) −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 −0.248392 0.968660i \(-0.579902\pi\)
0.844493 + 0.535567i \(0.179902\pi\)
\(468\) 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 −0.961312 0.275463i \(-0.911169\pi\)
0.883033 0.469311i \(-0.155498\pi\)
\(480\) 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 −0.654966 0.755658i \(-0.727317\pi\)
0.974044 0.226361i \(-0.0726828\pi\)
\(488\) 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 0.529836 0.848100i \(-0.322253\pi\)
0.788071 0.615584i \(-0.211080\pi\)
\(492\) 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 −0.964752 0.263161i \(-0.915235\pi\)
0.362563 + 0.931959i \(0.381902\pi\)
\(500\) −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 −0.850994 0.525176i \(-0.824000\pi\)
0.997159 + 0.0753254i \(0.0239995\pi\)
\(504\) 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 −0.928715 + 0.370794i \(0.879086\pi\)
−0.999239 + 0.0390051i \(0.987581\pi\)
\(510\) 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 −0.997805 0.0662243i \(-0.978905\pi\)
0.768315 0.640071i \(-0.221095\pi\)
\(522\) 0 0
\(523\) −24.4438 + 17.7595i −1.06885 + 0.776567i −0.975706 0.219085i \(-0.929693\pi\)
−0.0931472 + 0.995652i \(0.529693\pi\)
\(524\) 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 0.362699 0.931906i \(-0.381855\pi\)
−0.774216 + 0.632922i \(0.781855\pi\)
\(542\) −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 0.778461 0.627693i \(-0.216001\pi\)
−0.705626 + 0.708585i \(0.749334\pi\)
\(548\) 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 0.867519 0.497404i \(-0.165713\pi\)
−0.994204 + 0.107507i \(0.965713\pi\)
\(558\) 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 0.805281 + 0.592893i \(0.202014\pi\)
−0.910953 + 0.412510i \(0.864652\pi\)
\(564\) 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 0.984659 + 0.174492i \(0.0558283\pi\)
0.0706111 + 0.997504i \(0.477505\pi\)
\(570\) 0 0
\(571\) 7.37740 + 12.7780i 0.308735 + 0.534744i 0.978086 0.208202i \(-0.0667612\pi\)
−0.669351 + 0.742946i \(0.733428\pi\)
\(572\) 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 −0.144937 0.989441i \(-0.546298\pi\)
0.896226 + 0.443598i \(0.146298\pi\)
\(578\) −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 0.157166 0.987572i \(-0.449764\pi\)
−0.258104 + 0.966117i \(0.583098\pi\)
\(588\) 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 0.955353 0.295466i \(-0.0954749\pi\)
0.419682 + 0.907671i \(0.362142\pi\)
\(600\) 0 0
\(601\) 15.1166 + 3.21313i 0.616618 + 0.131066i 0.505623 0.862755i \(-0.331263\pi\)
0.110995 + 0.993821i \(0.464596\pi\)
\(602\) −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 −0.797228 0.603678i \(-0.793701\pi\)
0.905319 0.424733i \(-0.139632\pi\)
\(608\) 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 0.379211 + 0.925310i \(0.376195\pi\)
−0.850672 + 0.525697i \(0.823805\pi\)
\(614\) −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 0.887115 + 0.461549i \(0.152706\pi\)
−0.0438437 + 0.999038i \(0.513960\pi\)
\(618\) 0 0
\(619\) −4.00783 4.45115i −0.161088 0.178907i 0.657197 0.753719i \(-0.271742\pi\)
−0.818286 + 0.574812i \(0.805075\pi\)
\(620\) 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 −0.991813 0.127702i \(-0.959240\pi\)
0.727332 0.686286i \(-0.240760\pi\)
\(632\) 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 0.549232 0.835670i \(-0.314920\pi\)
−0.888502 + 0.458872i \(0.848254\pi\)
\(642\) 0 0
\(643\) 25.9041 + 11.5332i 1.02156 + 0.454827i 0.848000 0.529997i \(-0.177807\pi\)
0.173558 + 0.984824i \(0.444473\pi\)
\(644\) 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 0.273717 0.961810i \(-0.411747\pi\)
−0.830153 + 0.557536i \(0.811747\pi\)
\(648\) 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 −0.225230 0.974306i \(-0.572313\pi\)
0.992511 + 0.122153i \(0.0389799\pi\)
\(654\) 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 −0.461728 0.887021i \(-0.652771\pi\)
0.999047 0.0436422i \(-0.0138961\pi\)
\(660\) 0 0
\(661\) −14.8776 25.7688i −0.578672 1.00229i −0.995632 0.0933649i \(-0.970238\pi\)
0.416960 0.908925i \(-0.363096\pi\)
\(662\) −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 −0.229659 0.973271i \(-0.573761\pi\)
0.569609 + 0.821916i \(0.307094\pi\)
\(674\) −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 0.994323 0.106403i \(-0.0339335\pi\)
−0.994717 + 0.102653i \(0.967267\pi\)
\(678\) 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 0.252116 0.967697i \(-0.418873\pi\)
0.887838 + 0.460157i \(0.152207\pi\)
\(692\) −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 −0.886927 0.461909i \(-0.847165\pi\)
0.989043 + 0.147630i \(0.0471646\pi\)
\(702\) 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 −0.912227 0.409685i \(-0.865639\pi\)
0.807114 0.590395i \(-0.201028\pi\)
\(710\) 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 0.999532 0.0305782i \(-0.00973486\pi\)
−0.826612 + 0.562772i \(0.809735\pi\)
\(720\) 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 0.489363 + 0.872080i \(0.337229\pi\)
−0.999925 + 0.0122391i \(0.996104\pi\)
\(728\) −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 0.239251 0.970958i \(-0.423098\pi\)
0.940630 0.339433i \(-0.110235\pi\)
\(734\) 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 0.565416 0.824806i \(-0.308716\pi\)
−0.609714 + 0.792622i \(0.708716\pi\)
\(740\) −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 0.687823 0.725879i \(-0.258567\pi\)
−0.0791896 + 0.996860i \(0.525233\pi\)
\(744\) 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 −0.128813 0.991669i \(-0.541117\pi\)
0.285672 + 0.958328i \(0.407783\pi\)
\(752\) 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 0.771483 0.636249i \(-0.219515\pi\)
−0.366708 + 0.930336i \(0.619515\pi\)
\(758\) −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 0.762456 + 0.647041i \(0.223994\pi\)
−0.880321 + 0.474378i \(0.842673\pi\)
\(762\) 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 0.597661 0.801749i \(-0.296097\pi\)
−0.993165 + 0.116715i \(0.962764\pi\)
\(770\) 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 −0.855182 0.518327i \(-0.826555\pi\)
0.996522 + 0.0833281i \(0.0265549\pi\)
\(774\) 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 0.105951 0.994371i \(-0.466211\pi\)
−0.668067 + 0.744102i \(0.732878\pi\)
\(788\) −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 −0.251538 0.967847i \(-0.580936\pi\)
−0.887563 + 0.460687i \(0.847603\pi\)
\(798\) 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 −0.825096 0.564992i \(-0.808879\pi\)
0.282371 + 0.959305i \(0.408879\pi\)
\(810\) 0 0
\(811\) −9.59769 + 29.5387i −0.337020 + 1.03724i 0.628698 + 0.777650i \(0.283588\pi\)
−0.965718 + 0.259593i \(0.916412\pi\)
\(812\) 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 0.747826 0.663895i \(-0.231098\pi\)
0.413143 + 0.910666i \(0.364431\pi\)
\(822\) 0 0
\(823\) −1.62605 + 15.4708i −0.0566804 + 0.539278i 0.928931 + 0.370252i \(0.120729\pi\)
−0.985612 + 0.169026i \(0.945938\pi\)
\(824\) 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 0.789949 0.613172i \(-0.210107\pi\)
−0.339054 + 0.940767i \(0.610107\pi\)
\(828\) 0 0
\(829\) 5.90205 + 18.1646i 0.204987 + 0.630884i 0.999714 + 0.0239173i \(0.00761382\pi\)
−0.794727 + 0.606967i \(0.792386\pi\)
\(830\) 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 0.725713 0.687997i \(-0.241510\pi\)
−0.760086 + 0.649823i \(0.774843\pi\)
\(840\) 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 −0.825825 0.563926i \(-0.809290\pi\)
0.690532 0.723302i \(-0.257376\pi\)
\(854\) −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 −0.645539 0.763727i \(-0.723367\pi\)
0.984177 + 0.177189i \(0.0567005\pi\)
\(858\) 0 0
\(859\) 7.85764 + 13.6098i 0.268099 + 0.464362i 0.968371 0.249515i \(-0.0802711\pi\)
−0.700272 + 0.713876i \(0.746938\pi\)
\(860\) 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 −0.470218 0.882550i \(-0.655825\pi\)
0.694050 + 0.719927i \(0.255825\pi\)
\(864\) 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 −0.165881 0.986146i \(-0.553047\pi\)
0.249562 + 0.968359i \(0.419713\pi\)
\(878\) −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 −0.713315 0.700844i \(-0.752807\pi\)
0.989029 0.147719i \(-0.0471930\pi\)
\(884\) −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 0.0943729 0.995537i \(-0.469915\pi\)
0.980219 0.197918i \(-0.0634179\pi\)
\(888\) 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 −0.694771 0.719231i \(-0.744494\pi\)
0.530052 0.847965i \(-0.322172\pi\)
\(908\) −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 0.0714850 0.997442i \(-0.477226\pi\)
0.789076 + 0.614295i \(0.210560\pi\)
\(912\) 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 −0.967110 0.254358i \(-0.918136\pi\)
−0.0569449 + 0.998377i \(0.518136\pi\)
\(920\) 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 0.993198 + 0.116438i \(0.0371476\pi\)
−0.947285 + 0.320391i \(0.896186\pi\)
\(930\) 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 0.863961 0.503559i \(-0.167976\pi\)
−0.211934 + 0.977284i \(0.567976\pi\)
\(938\) 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 0.279371 0.960183i \(-0.409874\pi\)
−0.526620 + 0.850101i \(0.676541\pi\)
\(942\) 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 −0.373503 0.927629i \(-0.621844\pi\)
0.990102 0.140351i \(-0.0448231\pi\)
\(948\) 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 0.828778 + 0.559578i \(0.189037\pi\)
−0.341583 + 0.939852i \(0.610963\pi\)
\(954\) 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 0.764170 0.645015i \(-0.223149\pi\)
−0.940684 + 0.339283i \(0.889816\pi\)
\(968\) −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 −0.994702 0.102796i \(-0.967221\pi\)
0.865153 + 0.501508i \(0.167221\pi\)
\(972\) 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 0.960266 + 0.279085i \(0.0900312\pi\)
−0.997307 + 0.0733360i \(0.976635\pi\)
\(978\) 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 −0.223767 0.974643i \(-0.571835\pi\)
−0.600844 + 0.799366i \(0.705169\pi\)
\(984\) 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 −0.147765 0.989022i \(-0.547208\pi\)
−0.537262 + 0.843416i \(0.680541\pi\)
\(998\) 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.235.4 72
3.2 odd 2 99.2.m.b.70.6 yes 72
9.2 odd 6 891.2.f.f.730.4 36
9.4 even 3 inner 297.2.n.b.37.6 72
9.5 odd 6 99.2.m.b.4.4 72
9.7 even 3 891.2.f.e.730.6 36
11.3 even 5 inner 297.2.n.b.289.6 72
33.5 odd 10 1089.2.e.p.727.8 36
33.14 odd 10 99.2.m.b.25.4 yes 72
33.17 even 10 1089.2.e.o.727.11 36
99.5 odd 30 1089.2.e.p.364.8 36
99.14 odd 30 99.2.m.b.58.6 yes 72
99.16 even 15 9801.2.a.cp.1.8 18
99.25 even 15 891.2.f.e.487.6 36
99.38 odd 30 9801.2.a.cm.1.11 18
99.47 odd 30 891.2.f.f.487.4 36
99.50 even 30 1089.2.e.o.364.11 36
99.58 even 15 inner 297.2.n.b.91.4 72
99.61 odd 30 9801.2.a.cn.1.11 18
99.83 even 30 9801.2.a.co.1.8 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.b.4.4 72 9.5 odd 6
99.2.m.b.25.4 yes 72 33.14 odd 10
99.2.m.b.58.6 yes 72 99.14 odd 30
99.2.m.b.70.6 yes 72 3.2 odd 2
297.2.n.b.37.6 72 9.4 even 3 inner
297.2.n.b.91.4 72 99.58 even 15 inner
297.2.n.b.235.4 72 1.1 even 1 trivial
297.2.n.b.289.6 72 11.3 even 5 inner
891.2.f.e.487.6 36 99.25 even 15
891.2.f.e.730.6 36 9.7 even 3
891.2.f.f.487.4 36 99.47 odd 30
891.2.f.f.730.4 36 9.2 odd 6
1089.2.e.o.364.11 36 99.50 even 30
1089.2.e.o.727.11 36 33.17 even 10
1089.2.e.p.364.8 36 99.5 odd 30
1089.2.e.p.727.8 36 33.5 odd 10
9801.2.a.cm.1.11 18 99.38 odd 30
9801.2.a.cn.1.11 18 99.61 odd 30
9801.2.a.co.1.8 18 99.83 even 30
9801.2.a.cp.1.8 18 99.16 even 15