Properties

Label 432.2.v.a.251.4
Level $432$
Weight $2$
Character 432.251
Analytic conductor $3.450$
Analytic rank $0$
Dimension $88$
Inner twists $4$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [432,2,Mod(35,432)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("432.35"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(432, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 2])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.v (of order \(12\), degree \(4\), not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(88\)
Relative dimension: \(22\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 251.4
Character \(\chi\) \(=\) 432.251
Dual form 432.2.v.a.179.4

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.25087 - 0.659799i) q^{2} +(1.12933 + 1.65064i) q^{4} +(-2.03779 - 0.546024i) q^{5} +(-0.0638076 + 0.110518i) q^{7} +(-0.323550 - 2.80986i) q^{8} +(2.18873 + 2.02753i) q^{10} +(0.678695 - 0.181856i) q^{11} +(-1.84311 - 0.493860i) q^{13} +(0.152734 - 0.0961430i) q^{14} +(-1.44923 + 3.72824i) q^{16} +4.32243i q^{17} +(-3.97707 - 3.97707i) q^{19} +(-1.40005 - 3.98030i) q^{20} +(-0.968944 - 0.220325i) q^{22} +(-6.81589 + 3.93516i) q^{23} +(-0.475689 - 0.274639i) q^{25} +(1.97963 + 1.83383i) q^{26} +(-0.254485 + 0.0194880i) q^{28} +(0.926957 - 0.248377i) q^{29} +(-4.91353 + 2.83683i) q^{31} +(4.27267 - 3.70733i) q^{32} +(2.85194 - 5.40679i) q^{34} +(0.190372 - 0.190372i) q^{35} +(-6.64358 - 6.64358i) q^{37} +(2.35071 + 7.59884i) q^{38} +(-0.874924 + 5.90257i) q^{40} +(-4.61325 - 7.99038i) q^{41} +(2.91294 + 10.8712i) q^{43} +(1.06665 + 0.914906i) q^{44} +(11.1222 - 0.425234i) q^{46} +(-5.92267 + 10.2584i) q^{47} +(3.49186 + 6.04807i) q^{49} +(0.413816 + 0.657395i) q^{50} +(-1.26629 - 3.60004i) q^{52} +(-0.00259022 + 0.00259022i) q^{53} -1.48233 q^{55} +(0.331185 + 0.143532i) q^{56} +(-1.32338 - 0.300919i) q^{58} +(1.09748 - 4.09587i) q^{59} +(-1.19213 - 4.44908i) q^{61} +(8.01790 - 0.306548i) q^{62} +(-7.79063 + 1.81826i) q^{64} +(3.48621 + 2.01276i) q^{65} +(-0.538862 + 2.01106i) q^{67} +(-7.13478 + 4.88146i) q^{68} +(-0.363737 + 0.112522i) q^{70} -3.80683i q^{71} -1.87674i q^{73} +(3.92680 + 12.6937i) q^{74} +(2.07328 - 11.0561i) q^{76} +(-0.0232076 + 0.0866118i) q^{77} +(3.00919 + 1.73736i) q^{79} +(4.98892 - 6.80604i) q^{80} +(0.498509 + 13.0387i) q^{82} +(0.394284 + 1.47149i) q^{83} +(2.36015 - 8.80821i) q^{85} +(3.52914 - 15.5204i) q^{86} +(-0.730581 - 1.84820i) q^{88} +10.5967 q^{89} +(0.172185 - 0.172185i) q^{91} +(-14.1929 - 6.80649i) q^{92} +(14.1769 - 8.92407i) q^{94} +(5.93284 + 10.2760i) q^{95} +(3.31795 - 5.74685i) q^{97} +(-0.377331 - 9.86925i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38}+ \cdots - 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.25087 0.659799i −0.884496 0.466548i
\(3\) 0 0
\(4\) 1.12933 + 1.65064i 0.564665 + 0.825320i
\(5\) −2.03779 0.546024i −0.911327 0.244189i −0.227452 0.973789i \(-0.573040\pi\)
−0.683874 + 0.729600i \(0.739706\pi\)
\(6\) 0 0
\(7\) −0.0638076 + 0.110518i −0.0241170 + 0.0417719i −0.877832 0.478969i \(-0.841011\pi\)
0.853715 + 0.520741i \(0.174344\pi\)
\(8\) −0.323550 2.80986i −0.114392 0.993436i
\(9\) 0 0
\(10\) 2.18873 + 2.02753i 0.692138 + 0.641162i
\(11\) 0.678695 0.181856i 0.204634 0.0548316i −0.155046 0.987907i \(-0.549553\pi\)
0.359680 + 0.933076i \(0.382886\pi\)
\(12\) 0 0
\(13\) −1.84311 0.493860i −0.511187 0.136972i −0.00599967 0.999982i \(-0.501910\pi\)
−0.505187 + 0.863010i \(0.668576\pi\)
\(14\) 0.152734 0.0961430i 0.0408200 0.0256953i
\(15\) 0 0
\(16\) −1.44923 + 3.72824i −0.362306 + 0.932059i
\(17\) 4.32243i 1.04834i 0.851612 + 0.524172i \(0.175625\pi\)
−0.851612 + 0.524172i \(0.824375\pi\)
\(18\) 0 0
\(19\) −3.97707 3.97707i −0.912401 0.912401i 0.0840594 0.996461i \(-0.473211\pi\)
−0.996461 + 0.0840594i \(0.973211\pi\)
\(20\) −1.40005 3.98030i −0.313060 0.890021i
\(21\) 0 0
\(22\) −0.968944 0.220325i −0.206580 0.0469735i
\(23\) −6.81589 + 3.93516i −1.42121 + 0.820537i −0.996403 0.0847463i \(-0.972992\pi\)
−0.424809 + 0.905283i \(0.639659\pi\)
\(24\) 0 0
\(25\) −0.475689 0.274639i −0.0951377 0.0549278i
\(26\) 1.97963 + 1.83383i 0.388238 + 0.359644i
\(27\) 0 0
\(28\) −0.254485 + 0.0194880i −0.0480932 + 0.00368288i
\(29\) 0.926957 0.248377i 0.172132 0.0461225i −0.171724 0.985145i \(-0.554934\pi\)
0.343855 + 0.939023i \(0.388267\pi\)
\(30\) 0 0
\(31\) −4.91353 + 2.83683i −0.882496 + 0.509509i −0.871480 0.490430i \(-0.836840\pi\)
−0.0110152 + 0.999939i \(0.503506\pi\)
\(32\) 4.27267 3.70733i 0.755309 0.655369i
\(33\) 0 0
\(34\) 2.85194 5.40679i 0.489103 0.927256i
\(35\) 0.190372 0.190372i 0.0321787 0.0321787i
\(36\) 0 0
\(37\) −6.64358 6.64358i −1.09220 1.09220i −0.995294 0.0969037i \(-0.969106\pi\)
−0.0969037 0.995294i \(-0.530894\pi\)
\(38\) 2.35071 + 7.59884i 0.381336 + 1.23269i
\(39\) 0 0
\(40\) −0.874924 + 5.90257i −0.138338 + 0.933278i
\(41\) −4.61325 7.99038i −0.720469 1.24789i −0.960812 0.277200i \(-0.910593\pi\)
0.240344 0.970688i \(-0.422740\pi\)
\(42\) 0 0
\(43\) 2.91294 + 10.8712i 0.444219 + 1.65785i 0.717991 + 0.696053i \(0.245062\pi\)
−0.273772 + 0.961795i \(0.588271\pi\)
\(44\) 1.06665 + 0.914906i 0.160803 + 0.137927i
\(45\) 0 0
\(46\) 11.1222 0.425234i 1.63988 0.0626973i
\(47\) −5.92267 + 10.2584i −0.863910 + 1.49634i 0.00421475 + 0.999991i \(0.498658\pi\)
−0.868125 + 0.496345i \(0.834675\pi\)
\(48\) 0 0
\(49\) 3.49186 + 6.04807i 0.498837 + 0.864011i
\(50\) 0.413816 + 0.657395i 0.0585224 + 0.0929698i
\(51\) 0 0
\(52\) −1.26629 3.60004i −0.175603 0.499236i
\(53\) −0.00259022 + 0.00259022i −0.000355794 + 0.000355794i −0.707285 0.706929i \(-0.750080\pi\)
0.706929 + 0.707285i \(0.250080\pi\)
\(54\) 0 0
\(55\) −1.48233 −0.199878
\(56\) 0.331185 + 0.143532i 0.0442565 + 0.0191803i
\(57\) 0 0
\(58\) −1.32338 0.300919i −0.173768 0.0395125i
\(59\) 1.09748 4.09587i 0.142880 0.533237i −0.856960 0.515382i \(-0.827650\pi\)
0.999841 0.0178541i \(-0.00568344\pi\)
\(60\) 0 0
\(61\) −1.19213 4.44908i −0.152636 0.569646i −0.999296 0.0375117i \(-0.988057\pi\)
0.846660 0.532134i \(-0.178610\pi\)
\(62\) 8.01790 0.306548i 1.01827 0.0389317i
\(63\) 0 0
\(64\) −7.79063 + 1.81826i −0.973829 + 0.227282i
\(65\) 3.48621 + 2.01276i 0.432411 + 0.249652i
\(66\) 0 0
\(67\) −0.538862 + 2.01106i −0.0658325 + 0.245690i −0.990999 0.133872i \(-0.957259\pi\)
0.925166 + 0.379563i \(0.123925\pi\)
\(68\) −7.13478 + 4.88146i −0.865220 + 0.591964i
\(69\) 0 0
\(70\) −0.363737 + 0.112522i −0.0434749 + 0.0134490i
\(71\) 3.80683i 0.451788i −0.974152 0.225894i \(-0.927470\pi\)
0.974152 0.225894i \(-0.0725303\pi\)
\(72\) 0 0
\(73\) 1.87674i 0.219656i −0.993951 0.109828i \(-0.964970\pi\)
0.993951 0.109828i \(-0.0350300\pi\)
\(74\) 3.92680 + 12.6937i 0.456481 + 1.47561i
\(75\) 0 0
\(76\) 2.07328 11.0561i 0.237822 1.26822i
\(77\) −0.0232076 + 0.0866118i −0.00264475 + 0.00987033i
\(78\) 0 0
\(79\) 3.00919 + 1.73736i 0.338560 + 0.195468i 0.659635 0.751586i \(-0.270711\pi\)
−0.321075 + 0.947054i \(0.604044\pi\)
\(80\) 4.98892 6.80604i 0.557778 0.760939i
\(81\) 0 0
\(82\) 0.498509 + 13.0387i 0.0550511 + 1.43989i
\(83\) 0.394284 + 1.47149i 0.0432783 + 0.161517i 0.984183 0.177155i \(-0.0566892\pi\)
−0.940905 + 0.338671i \(0.890023\pi\)
\(84\) 0 0
\(85\) 2.36015 8.80821i 0.255994 0.955384i
\(86\) 3.52914 15.5204i 0.380556 1.67361i
\(87\) 0 0
\(88\) −0.730581 1.84820i −0.0778802 0.197019i
\(89\) 10.5967 1.12325 0.561624 0.827392i \(-0.310177\pi\)
0.561624 + 0.827392i \(0.310177\pi\)
\(90\) 0 0
\(91\) 0.172185 0.172185i 0.0180499 0.0180499i
\(92\) −14.1929 6.80649i −1.47971 0.709626i
\(93\) 0 0
\(94\) 14.1769 8.92407i 1.46224 0.920447i
\(95\) 5.93284 + 10.2760i 0.608697 + 1.05429i
\(96\) 0 0
\(97\) 3.31795 5.74685i 0.336886 0.583504i −0.646959 0.762525i \(-0.723960\pi\)
0.983845 + 0.179021i \(0.0572928\pi\)
\(98\) −0.377331 9.86925i −0.0381162 0.996945i
\(99\) 0 0
\(100\) −0.0838795 1.09535i −0.00838795 0.109535i
\(101\) −3.24008 12.0922i −0.322400 1.20321i −0.916899 0.399118i \(-0.869316\pi\)
0.594499 0.804096i \(-0.297350\pi\)
\(102\) 0 0
\(103\) −4.21850 7.30665i −0.415661 0.719946i 0.579837 0.814733i \(-0.303116\pi\)
−0.995498 + 0.0947868i \(0.969783\pi\)
\(104\) −0.791339 + 5.33867i −0.0775972 + 0.523499i
\(105\) 0 0
\(106\) 0.00494904 0.00153099i 0.000480693 0.000148703i
\(107\) −7.25071 7.25071i −0.700953 0.700953i 0.263662 0.964615i \(-0.415070\pi\)
−0.964615 + 0.263662i \(0.915070\pi\)
\(108\) 0 0
\(109\) 10.2850 10.2850i 0.985128 0.985128i −0.0147630 0.999891i \(-0.504699\pi\)
0.999891 + 0.0147630i \(0.00469937\pi\)
\(110\) 1.85420 + 0.978042i 0.176791 + 0.0932527i
\(111\) 0 0
\(112\) −0.319566 0.398055i −0.0301961 0.0376127i
\(113\) 18.2964 10.5634i 1.72118 0.993722i 0.804652 0.593747i \(-0.202352\pi\)
0.916526 0.399976i \(-0.130981\pi\)
\(114\) 0 0
\(115\) 16.0380 4.29738i 1.49555 0.400732i
\(116\) 1.45682 + 1.24957i 0.135263 + 0.116020i
\(117\) 0 0
\(118\) −4.07526 + 4.39926i −0.375158 + 0.404985i
\(119\) −0.477707 0.275804i −0.0437913 0.0252829i
\(120\) 0 0
\(121\) −9.09872 + 5.25315i −0.827157 + 0.477559i
\(122\) −1.44431 + 6.35176i −0.130761 + 0.575061i
\(123\) 0 0
\(124\) −10.2316 4.90675i −0.918823 0.440639i
\(125\) 8.27822 + 8.27822i 0.740426 + 0.740426i
\(126\) 0 0
\(127\) 13.1109i 1.16340i 0.813403 + 0.581700i \(0.197612\pi\)
−0.813403 + 0.581700i \(0.802388\pi\)
\(128\) 10.9447 + 2.86585i 0.967386 + 0.253308i
\(129\) 0 0
\(130\) −3.03276 4.81789i −0.265990 0.422557i
\(131\) −4.74891 1.27247i −0.414914 0.111176i 0.0453222 0.998972i \(-0.485569\pi\)
−0.460236 + 0.887797i \(0.652235\pi\)
\(132\) 0 0
\(133\) 0.693305 0.185770i 0.0601171 0.0161083i
\(134\) 2.00094 2.16003i 0.172855 0.186598i
\(135\) 0 0
\(136\) 12.1454 1.39852i 1.04146 0.119922i
\(137\) −3.41217 + 5.91005i −0.291521 + 0.504930i −0.974170 0.225817i \(-0.927495\pi\)
0.682648 + 0.730747i \(0.260828\pi\)
\(138\) 0 0
\(139\) 10.3427 + 2.77132i 0.877258 + 0.235061i 0.669224 0.743061i \(-0.266627\pi\)
0.208035 + 0.978121i \(0.433293\pi\)
\(140\) 0.529228 + 0.0992427i 0.0447279 + 0.00838754i
\(141\) 0 0
\(142\) −2.51174 + 4.76184i −0.210781 + 0.399604i
\(143\) −1.34072 −0.112117
\(144\) 0 0
\(145\) −2.02456 −0.168131
\(146\) −1.23827 + 2.34755i −0.102480 + 0.194285i
\(147\) 0 0
\(148\) 3.46336 18.4690i 0.284687 1.51814i
\(149\) 0.204036 + 0.0546714i 0.0167153 + 0.00447885i 0.267167 0.963650i \(-0.413912\pi\)
−0.250452 + 0.968129i \(0.580579\pi\)
\(150\) 0 0
\(151\) 1.14798 1.98835i 0.0934210 0.161810i −0.815528 0.578718i \(-0.803553\pi\)
0.908949 + 0.416908i \(0.136886\pi\)
\(152\) −9.88822 + 12.4618i −0.802040 + 1.01078i
\(153\) 0 0
\(154\) 0.0861759 0.0930274i 0.00694425 0.00749636i
\(155\) 11.5617 3.09795i 0.928658 0.248833i
\(156\) 0 0
\(157\) −16.2150 4.34480i −1.29410 0.346753i −0.454883 0.890551i \(-0.650319\pi\)
−0.839216 + 0.543799i \(0.816985\pi\)
\(158\) −2.61779 4.15866i −0.208260 0.330845i
\(159\) 0 0
\(160\) −10.7311 + 5.22176i −0.848367 + 0.412817i
\(161\) 1.00437i 0.0791556i
\(162\) 0 0
\(163\) 0.490399 + 0.490399i 0.0384110 + 0.0384110i 0.726051 0.687640i \(-0.241353\pi\)
−0.687640 + 0.726051i \(0.741353\pi\)
\(164\) 7.97936 16.6386i 0.623084 1.29926i
\(165\) 0 0
\(166\) 0.477690 2.10078i 0.0370759 0.163052i
\(167\) −9.34175 + 5.39346i −0.722887 + 0.417359i −0.815814 0.578314i \(-0.803711\pi\)
0.0929276 + 0.995673i \(0.470378\pi\)
\(168\) 0 0
\(169\) −8.10518 4.67953i −0.623475 0.359963i
\(170\) −8.76388 + 9.46066i −0.672159 + 0.725599i
\(171\) 0 0
\(172\) −14.6548 + 17.0854i −1.11742 + 1.30275i
\(173\) −4.61598 + 1.23685i −0.350946 + 0.0940358i −0.429986 0.902836i \(-0.641481\pi\)
0.0790394 + 0.996871i \(0.474815\pi\)
\(174\) 0 0
\(175\) 0.0607051 0.0350481i 0.00458888 0.00264939i
\(176\) −0.305581 + 2.79388i −0.0230340 + 0.210597i
\(177\) 0 0
\(178\) −13.2551 6.99170i −0.993509 0.524050i
\(179\) −3.52882 + 3.52882i −0.263756 + 0.263756i −0.826578 0.562822i \(-0.809716\pi\)
0.562822 + 0.826578i \(0.309716\pi\)
\(180\) 0 0
\(181\) 7.34860 + 7.34860i 0.546217 + 0.546217i 0.925344 0.379127i \(-0.123776\pi\)
−0.379127 + 0.925344i \(0.623776\pi\)
\(182\) −0.328987 + 0.101773i −0.0243862 + 0.00754390i
\(183\) 0 0
\(184\) 13.2625 + 17.8785i 0.977726 + 1.31802i
\(185\) 9.91065 + 17.1658i 0.728646 + 1.26205i
\(186\) 0 0
\(187\) 0.786059 + 2.93361i 0.0574824 + 0.214527i
\(188\) −23.6215 + 1.80889i −1.72278 + 0.131927i
\(189\) 0 0
\(190\) −0.641105 16.7684i −0.0465106 1.21651i
\(191\) 2.58888 4.48407i 0.187325 0.324456i −0.757033 0.653377i \(-0.773352\pi\)
0.944357 + 0.328921i \(0.106685\pi\)
\(192\) 0 0
\(193\) 13.2173 + 22.8930i 0.951401 + 1.64787i 0.742398 + 0.669960i \(0.233689\pi\)
0.209003 + 0.977915i \(0.432978\pi\)
\(194\) −7.94207 + 4.99936i −0.570208 + 0.358933i
\(195\) 0 0
\(196\) −6.03973 + 12.5941i −0.431410 + 0.899577i
\(197\) −5.14652 + 5.14652i −0.366674 + 0.366674i −0.866263 0.499588i \(-0.833485\pi\)
0.499588 + 0.866263i \(0.333485\pi\)
\(198\) 0 0
\(199\) −1.37436 −0.0974261 −0.0487130 0.998813i \(-0.515512\pi\)
−0.0487130 + 0.998813i \(0.515512\pi\)
\(200\) −0.617788 + 1.42548i −0.0436842 + 0.100797i
\(201\) 0 0
\(202\) −3.92549 + 17.2635i −0.276196 + 1.21465i
\(203\) −0.0316967 + 0.118294i −0.00222468 + 0.00830260i
\(204\) 0 0
\(205\) 5.03789 + 18.8017i 0.351861 + 1.31316i
\(206\) 0.455852 + 11.9230i 0.0317607 + 0.830715i
\(207\) 0 0
\(208\) 4.51231 6.15583i 0.312872 0.426830i
\(209\) −3.42246 1.97596i −0.236737 0.136680i
\(210\) 0 0
\(211\) −2.98444 + 11.1381i −0.205457 + 0.766776i 0.783853 + 0.620947i \(0.213252\pi\)
−0.989310 + 0.145829i \(0.953415\pi\)
\(212\) −0.00720073 0.00135031i −0.000494548 9.27394e-5i
\(213\) 0 0
\(214\) 4.28566 + 13.8537i 0.292961 + 0.947018i
\(215\) 23.7438i 1.61931i
\(216\) 0 0
\(217\) 0.724045i 0.0491514i
\(218\) −19.6513 + 6.07914i −1.33095 + 0.411732i
\(219\) 0 0
\(220\) −1.67404 2.44680i −0.112864 0.164963i
\(221\) 2.13468 7.96672i 0.143594 0.535900i
\(222\) 0 0
\(223\) −17.9819 10.3819i −1.20416 0.695220i −0.242680 0.970106i \(-0.578026\pi\)
−0.961477 + 0.274886i \(0.911360\pi\)
\(224\) 0.137097 + 0.708763i 0.00916019 + 0.0473562i
\(225\) 0 0
\(226\) −29.8560 + 1.14149i −1.98599 + 0.0759305i
\(227\) −2.05090 7.65406i −0.136123 0.508018i −0.999991 0.00429906i \(-0.998632\pi\)
0.863868 0.503718i \(-0.168035\pi\)
\(228\) 0 0
\(229\) −0.120227 + 0.448692i −0.00794481 + 0.0296504i −0.969784 0.243963i \(-0.921552\pi\)
0.961840 + 0.273614i \(0.0882190\pi\)
\(230\) −22.8968 5.20643i −1.50977 0.343302i
\(231\) 0 0
\(232\) −0.997823 2.52426i −0.0655103 0.165726i
\(233\) −9.13737 −0.598609 −0.299305 0.954158i \(-0.596755\pi\)
−0.299305 + 0.954158i \(0.596755\pi\)
\(234\) 0 0
\(235\) 17.6705 17.6705i 1.15269 1.15269i
\(236\) 8.00023 2.81404i 0.520770 0.183178i
\(237\) 0 0
\(238\) 0.415572 + 0.660185i 0.0269375 + 0.0427934i
\(239\) 3.65824 + 6.33626i 0.236632 + 0.409859i 0.959746 0.280870i \(-0.0906231\pi\)
−0.723114 + 0.690729i \(0.757290\pi\)
\(240\) 0 0
\(241\) −1.24858 + 2.16261i −0.0804282 + 0.139306i −0.903434 0.428727i \(-0.858962\pi\)
0.823006 + 0.568033i \(0.192295\pi\)
\(242\) 14.8473 0.567657i 0.954421 0.0364904i
\(243\) 0 0
\(244\) 5.99752 6.99225i 0.383952 0.447633i
\(245\) −3.81327 14.2313i −0.243621 0.909206i
\(246\) 0 0
\(247\) 5.36605 + 9.29428i 0.341434 + 0.591381i
\(248\) 9.56086 + 12.8885i 0.607115 + 0.818419i
\(249\) 0 0
\(250\) −4.89298 15.8169i −0.309459 1.00035i
\(251\) 2.77626 + 2.77626i 0.175236 + 0.175236i 0.789275 0.614039i \(-0.210456\pi\)
−0.614039 + 0.789275i \(0.710456\pi\)
\(252\) 0 0
\(253\) −3.91028 + 3.91028i −0.245837 + 0.245837i
\(254\) 8.65053 16.3999i 0.542783 1.02902i
\(255\) 0 0
\(256\) −11.7995 10.8061i −0.737468 0.675382i
\(257\) 9.61957 5.55386i 0.600052 0.346440i −0.169010 0.985614i \(-0.554057\pi\)
0.769062 + 0.639174i \(0.220724\pi\)
\(258\) 0 0
\(259\) 1.15815 0.310324i 0.0719637 0.0192826i
\(260\) 0.614733 + 8.02755i 0.0381241 + 0.497847i
\(261\) 0 0
\(262\) 5.10067 + 4.72501i 0.315121 + 0.291912i
\(263\) 16.6320 + 9.60247i 1.02557 + 0.592114i 0.915713 0.401834i \(-0.131627\pi\)
0.109858 + 0.993947i \(0.464960\pi\)
\(264\) 0 0
\(265\) 0.00669264 0.00386400i 0.000411125 0.000237363i
\(266\) −0.989802 0.225068i −0.0606887 0.0137998i
\(267\) 0 0
\(268\) −3.92809 + 1.38169i −0.239947 + 0.0843999i
\(269\) −7.66476 7.66476i −0.467329 0.467329i 0.433719 0.901048i \(-0.357201\pi\)
−0.901048 + 0.433719i \(0.857201\pi\)
\(270\) 0 0
\(271\) 12.9801i 0.788486i 0.919006 + 0.394243i \(0.128993\pi\)
−0.919006 + 0.394243i \(0.871007\pi\)
\(272\) −16.1151 6.26418i −0.977119 0.379822i
\(273\) 0 0
\(274\) 8.16761 5.14133i 0.493423 0.310599i
\(275\) −0.372792 0.0998893i −0.0224802 0.00602355i
\(276\) 0 0
\(277\) 23.9833 6.42631i 1.44102 0.386119i 0.548127 0.836395i \(-0.315341\pi\)
0.892890 + 0.450276i \(0.148674\pi\)
\(278\) −11.1088 10.2907i −0.666264 0.617194i
\(279\) 0 0
\(280\) −0.596513 0.473324i −0.0356485 0.0282865i
\(281\) −3.69120 + 6.39334i −0.220198 + 0.381395i −0.954868 0.297030i \(-0.904004\pi\)
0.734670 + 0.678425i \(0.237337\pi\)
\(282\) 0 0
\(283\) −5.99708 1.60691i −0.356490 0.0955211i 0.0761294 0.997098i \(-0.475744\pi\)
−0.432619 + 0.901577i \(0.642410\pi\)
\(284\) 6.28371 4.29917i 0.372870 0.255109i
\(285\) 0 0
\(286\) 1.67706 + 0.884606i 0.0991667 + 0.0523078i
\(287\) 1.17744 0.0695022
\(288\) 0 0
\(289\) −1.68344 −0.0990261
\(290\) 2.53246 + 1.33580i 0.148711 + 0.0784411i
\(291\) 0 0
\(292\) 3.09783 2.11946i 0.181287 0.124032i
\(293\) −24.0140 6.43453i −1.40291 0.375909i −0.523522 0.852012i \(-0.675382\pi\)
−0.879390 + 0.476103i \(0.842049\pi\)
\(294\) 0 0
\(295\) −4.47288 + 7.74726i −0.260421 + 0.451063i
\(296\) −16.5180 + 20.8171i −0.960089 + 1.20997i
\(297\) 0 0
\(298\) −0.219150 0.203009i −0.0126950 0.0117600i
\(299\) 14.5058 3.88683i 0.838895 0.224781i
\(300\) 0 0
\(301\) −1.38734 0.371735i −0.0799647 0.0214265i
\(302\) −2.74788 + 1.72973i −0.158123 + 0.0995347i
\(303\) 0 0
\(304\) 20.5911 9.06377i 1.18098 0.519843i
\(305\) 9.71720i 0.556406i
\(306\) 0 0
\(307\) −17.3773 17.3773i −0.991773 0.991773i 0.00819381 0.999966i \(-0.497392\pi\)
−0.999966 + 0.00819381i \(0.997392\pi\)
\(308\) −0.169174 + 0.0595060i −0.00963958 + 0.00339067i
\(309\) 0 0
\(310\) −16.5062 3.75328i −0.937487 0.213172i
\(311\) 11.9437 6.89568i 0.677264 0.391018i −0.121560 0.992584i \(-0.538790\pi\)
0.798823 + 0.601566i \(0.205456\pi\)
\(312\) 0 0
\(313\) 17.6368 + 10.1826i 0.996890 + 0.575555i 0.907327 0.420426i \(-0.138119\pi\)
0.0895635 + 0.995981i \(0.471453\pi\)
\(314\) 17.4161 + 16.1334i 0.982848 + 0.910461i
\(315\) 0 0
\(316\) 0.530619 + 6.92914i 0.0298497 + 0.389795i
\(317\) −20.3136 + 5.44301i −1.14092 + 0.305710i −0.779322 0.626623i \(-0.784437\pi\)
−0.361601 + 0.932333i \(0.617770\pi\)
\(318\) 0 0
\(319\) 0.583952 0.337145i 0.0326950 0.0188765i
\(320\) 16.8685 + 0.548641i 0.942976 + 0.0306700i
\(321\) 0 0
\(322\) −0.662684 + 1.25633i −0.0369299 + 0.0700128i
\(323\) 17.1906 17.1906i 0.956511 0.956511i
\(324\) 0 0
\(325\) 0.741113 + 0.741113i 0.0411096 + 0.0411096i
\(326\) −0.289859 0.936989i −0.0160538 0.0518950i
\(327\) 0 0
\(328\) −20.9592 + 15.5479i −1.15728 + 0.858488i
\(329\) −0.755823 1.30912i −0.0416699 0.0721743i
\(330\) 0 0
\(331\) −4.57199 17.0629i −0.251299 0.937862i −0.970112 0.242658i \(-0.921981\pi\)
0.718813 0.695204i \(-0.244686\pi\)
\(332\) −1.98362 + 2.31262i −0.108865 + 0.126921i
\(333\) 0 0
\(334\) 15.2439 0.582819i 0.834108 0.0318904i
\(335\) 2.19618 3.80389i 0.119990 0.207829i
\(336\) 0 0
\(337\) −4.82538 8.35780i −0.262855 0.455279i 0.704144 0.710057i \(-0.251331\pi\)
−0.966999 + 0.254778i \(0.917997\pi\)
\(338\) 7.05094 + 11.2012i 0.383521 + 0.609267i
\(339\) 0 0
\(340\) 17.2046 6.05161i 0.933049 0.328195i
\(341\) −2.81889 + 2.81889i −0.152652 + 0.152652i
\(342\) 0 0
\(343\) −1.78454 −0.0963558
\(344\) 29.6042 11.7023i 1.59615 0.630948i
\(345\) 0 0
\(346\) 6.59004 + 1.49849i 0.354283 + 0.0805592i
\(347\) −4.93125 + 18.4037i −0.264723 + 0.987960i 0.697696 + 0.716393i \(0.254208\pi\)
−0.962420 + 0.271567i \(0.912458\pi\)
\(348\) 0 0
\(349\) 4.68226 + 17.4744i 0.250636 + 0.935385i 0.970467 + 0.241236i \(0.0775527\pi\)
−0.719831 + 0.694150i \(0.755781\pi\)
\(350\) −0.0990587 + 0.00378731i −0.00529491 + 0.000202440i
\(351\) 0 0
\(352\) 2.22564 3.29315i 0.118627 0.175526i
\(353\) −5.65589 3.26543i −0.301033 0.173801i 0.341874 0.939746i \(-0.388938\pi\)
−0.642907 + 0.765944i \(0.722272\pi\)
\(354\) 0 0
\(355\) −2.07862 + 7.75752i −0.110322 + 0.411726i
\(356\) 11.9672 + 17.4914i 0.634259 + 0.927040i
\(357\) 0 0
\(358\) 6.74239 2.08577i 0.356346 0.110236i
\(359\) 22.8075i 1.20373i 0.798597 + 0.601866i \(0.205576\pi\)
−0.798597 + 0.601866i \(0.794424\pi\)
\(360\) 0 0
\(361\) 12.6341i 0.664952i
\(362\) −4.34351 14.0407i −0.228290 0.737963i
\(363\) 0 0
\(364\) 0.478669 + 0.0897616i 0.0250891 + 0.00470479i
\(365\) −1.02475 + 3.82440i −0.0536377 + 0.200178i
\(366\) 0 0
\(367\) −20.7702 11.9917i −1.08419 0.625959i −0.152169 0.988355i \(-0.548626\pi\)
−0.932025 + 0.362395i \(0.881959\pi\)
\(368\) −4.79343 31.1142i −0.249875 1.62194i
\(369\) 0 0
\(370\) −1.07095 28.0111i −0.0556759 1.45623i
\(371\) −0.000120990 0 0.000451542i −6.28150e−6 0 2.34429e-5i
\(372\) 0 0
\(373\) 6.20866 23.1710i 0.321472 1.19975i −0.596338 0.802733i \(-0.703378\pi\)
0.917811 0.397018i \(-0.129955\pi\)
\(374\) 0.952341 4.18820i 0.0492444 0.216567i
\(375\) 0 0
\(376\) 30.7409 + 13.3228i 1.58534 + 0.687070i
\(377\) −1.83115 −0.0943089
\(378\) 0 0
\(379\) 9.96634 9.96634i 0.511936 0.511936i −0.403183 0.915119i \(-0.632096\pi\)
0.915119 + 0.403183i \(0.132096\pi\)
\(380\) −10.2618 + 21.3980i −0.526420 + 1.09769i
\(381\) 0 0
\(382\) −6.19692 + 3.90083i −0.317062 + 0.199584i
\(383\) −2.30770 3.99705i −0.117918 0.204240i 0.801024 0.598632i \(-0.204289\pi\)
−0.918942 + 0.394392i \(0.870955\pi\)
\(384\) 0 0
\(385\) 0.0945842 0.163825i 0.00482046 0.00834927i
\(386\) −1.42826 37.3568i −0.0726967 1.90141i
\(387\) 0 0
\(388\) 13.2330 1.01336i 0.671806 0.0514455i
\(389\) 3.31091 + 12.3565i 0.167870 + 0.626498i 0.997657 + 0.0684178i \(0.0217951\pi\)
−0.829787 + 0.558080i \(0.811538\pi\)
\(390\) 0 0
\(391\) −17.0095 29.4612i −0.860205 1.48992i
\(392\) 15.8645 11.7685i 0.801276 0.594398i
\(393\) 0 0
\(394\) 9.83328 3.04194i 0.495393 0.153251i
\(395\) −5.18345 5.18345i −0.260808 0.260808i
\(396\) 0 0
\(397\) −3.70313 + 3.70313i −0.185855 + 0.185855i −0.793901 0.608047i \(-0.791953\pi\)
0.608047 + 0.793901i \(0.291953\pi\)
\(398\) 1.71915 + 0.906804i 0.0861730 + 0.0454540i
\(399\) 0 0
\(400\) 1.71330 1.37547i 0.0856650 0.0687733i
\(401\) −11.5871 + 6.68983i −0.578633 + 0.334074i −0.760590 0.649232i \(-0.775090\pi\)
0.181957 + 0.983307i \(0.441757\pi\)
\(402\) 0 0
\(403\) 10.4572 2.80199i 0.520908 0.139577i
\(404\) 16.3007 19.0043i 0.810989 0.945497i
\(405\) 0 0
\(406\) 0.117699 0.127056i 0.00584128 0.00630570i
\(407\) −5.71713 3.30079i −0.283388 0.163614i
\(408\) 0 0
\(409\) 24.1053 13.9172i 1.19193 0.688161i 0.233185 0.972432i \(-0.425085\pi\)
0.958744 + 0.284272i \(0.0917518\pi\)
\(410\) 6.10359 26.8423i 0.301435 1.32565i
\(411\) 0 0
\(412\) 7.29658 15.2148i 0.359477 0.749582i
\(413\) 0.382639 + 0.382639i 0.0188285 + 0.0188285i
\(414\) 0 0
\(415\) 3.21387i 0.157763i
\(416\) −9.70590 + 4.72290i −0.475871 + 0.231559i
\(417\) 0 0
\(418\) 2.97731 + 4.72980i 0.145625 + 0.231342i
\(419\) −9.97902 2.67387i −0.487507 0.130627i 0.00668892 0.999978i \(-0.497871\pi\)
−0.494196 + 0.869350i \(0.664538\pi\)
\(420\) 0 0
\(421\) −29.8528 + 7.99904i −1.45494 + 0.389849i −0.897738 0.440529i \(-0.854791\pi\)
−0.557199 + 0.830379i \(0.688124\pi\)
\(422\) 11.0820 11.9631i 0.539464 0.582354i
\(423\) 0 0
\(424\) 0.00811622 + 0.00644009i 0.000394158 + 0.000312758i
\(425\) 1.18711 2.05613i 0.0575833 0.0997371i
\(426\) 0 0
\(427\) 0.567770 + 0.152134i 0.0274763 + 0.00736226i
\(428\) 3.77987 20.1568i 0.182707 0.974314i
\(429\) 0 0
\(430\) −15.6661 + 29.7003i −0.755488 + 1.43228i
\(431\) −14.8449 −0.715053 −0.357526 0.933903i \(-0.616380\pi\)
−0.357526 + 0.933903i \(0.616380\pi\)
\(432\) 0 0
\(433\) −32.1617 −1.54559 −0.772796 0.634654i \(-0.781143\pi\)
−0.772796 + 0.634654i \(0.781143\pi\)
\(434\) −0.477724 + 0.905683i −0.0229315 + 0.0434742i
\(435\) 0 0
\(436\) 28.5921 + 5.36169i 1.36931 + 0.256778i
\(437\) 42.7576 + 11.4569i 2.04537 + 0.548056i
\(438\) 0 0
\(439\) −0.140035 + 0.242548i −0.00668352 + 0.0115762i −0.869348 0.494201i \(-0.835461\pi\)
0.862664 + 0.505777i \(0.168794\pi\)
\(440\) 0.479609 + 4.16515i 0.0228644 + 0.198566i
\(441\) 0 0
\(442\) −7.92663 + 8.55684i −0.377031 + 0.407007i
\(443\) 24.2588 6.50011i 1.15257 0.308830i 0.368574 0.929598i \(-0.379846\pi\)
0.783994 + 0.620768i \(0.213179\pi\)
\(444\) 0 0
\(445\) −21.5938 5.78605i −1.02365 0.274285i
\(446\) 15.6430 + 24.8507i 0.740717 + 1.17672i
\(447\) 0 0
\(448\) 0.296151 0.977024i 0.0139918 0.0461601i
\(449\) 14.2885i 0.674318i 0.941448 + 0.337159i \(0.109466\pi\)
−0.941448 + 0.337159i \(0.890534\pi\)
\(450\) 0 0
\(451\) −4.58408 4.58408i −0.215856 0.215856i
\(452\) 38.0990 + 18.2711i 1.79203 + 0.859402i
\(453\) 0 0
\(454\) −2.48474 + 10.9274i −0.116615 + 0.512847i
\(455\) −0.444893 + 0.256859i −0.0208569 + 0.0120417i
\(456\) 0 0
\(457\) −24.1097 13.9198i −1.12781 0.651139i −0.184424 0.982847i \(-0.559042\pi\)
−0.943382 + 0.331708i \(0.892375\pi\)
\(458\) 0.446434 0.481928i 0.0208605 0.0225190i
\(459\) 0 0
\(460\) 25.2057 + 21.6199i 1.17522 + 1.00803i
\(461\) −16.1887 + 4.33776i −0.753985 + 0.202030i −0.615285 0.788305i \(-0.710959\pi\)
−0.138700 + 0.990334i \(0.544292\pi\)
\(462\) 0 0
\(463\) 26.1951 15.1238i 1.21739 0.702861i 0.253032 0.967458i \(-0.418572\pi\)
0.964359 + 0.264597i \(0.0852389\pi\)
\(464\) −0.417361 + 3.81587i −0.0193755 + 0.177147i
\(465\) 0 0
\(466\) 11.4296 + 6.02883i 0.529467 + 0.279280i
\(467\) −15.9369 + 15.9369i −0.737469 + 0.737469i −0.972088 0.234618i \(-0.924616\pi\)
0.234618 + 0.972088i \(0.424616\pi\)
\(468\) 0 0
\(469\) −0.187875 0.187875i −0.00867527 0.00867527i
\(470\) −33.7623 + 10.4444i −1.55734 + 0.481765i
\(471\) 0 0
\(472\) −11.8639 1.75856i −0.546081 0.0809443i
\(473\) 3.95399 + 6.84851i 0.181805 + 0.314895i
\(474\) 0 0
\(475\) 0.799588 + 2.98410i 0.0366876 + 0.136920i
\(476\) −0.0842354 1.10000i −0.00386092 0.0504183i
\(477\) 0 0
\(478\) −0.395311 10.3395i −0.0180811 0.472919i
\(479\) 14.8100 25.6516i 0.676684 1.17205i −0.299289 0.954163i \(-0.596749\pi\)
0.975973 0.217889i \(-0.0699172\pi\)
\(480\) 0 0
\(481\) 8.96385 + 15.5258i 0.408716 + 0.707917i
\(482\) 2.98869 1.88132i 0.136131 0.0856916i
\(483\) 0 0
\(484\) −18.9465 9.08618i −0.861206 0.413008i
\(485\) −9.89919 + 9.89919i −0.449499 + 0.449499i
\(486\) 0 0
\(487\) 25.6320 1.16150 0.580749 0.814083i \(-0.302760\pi\)
0.580749 + 0.814083i \(0.302760\pi\)
\(488\) −12.1156 + 4.78921i −0.548446 + 0.216797i
\(489\) 0 0
\(490\) −4.61993 + 20.3175i −0.208707 + 0.917850i
\(491\) 1.40692 5.25069i 0.0634933 0.236960i −0.926885 0.375345i \(-0.877524\pi\)
0.990379 + 0.138385i \(0.0441910\pi\)
\(492\) 0 0
\(493\) 1.07360 + 4.00671i 0.0483523 + 0.180453i
\(494\) −0.579857 15.1664i −0.0260890 0.682369i
\(495\) 0 0
\(496\) −3.45555 22.4300i −0.155159 1.00714i
\(497\) 0.420724 + 0.242905i 0.0188720 + 0.0108958i
\(498\) 0 0
\(499\) 5.78179 21.5779i 0.258829 0.965961i −0.707092 0.707122i \(-0.749993\pi\)
0.965920 0.258840i \(-0.0833401\pi\)
\(500\) −4.31551 + 23.0132i −0.192996 + 1.02918i
\(501\) 0 0
\(502\) −1.64096 5.30451i −0.0732395 0.236752i
\(503\) 24.7337i 1.10282i 0.834235 + 0.551410i \(0.185910\pi\)
−0.834235 + 0.551410i \(0.814090\pi\)
\(504\) 0 0
\(505\) 26.4104i 1.17525i
\(506\) 7.47123 2.31124i 0.332137 0.102747i
\(507\) 0 0
\(508\) −21.6413 + 14.8065i −0.960178 + 0.656932i
\(509\) 2.31048 8.62284i 0.102410 0.382201i −0.895628 0.444804i \(-0.853274\pi\)
0.998039 + 0.0626029i \(0.0199402\pi\)
\(510\) 0 0
\(511\) 0.207414 + 0.119751i 0.00917545 + 0.00529745i
\(512\) 7.62971 + 21.3023i 0.337189 + 0.941437i
\(513\) 0 0
\(514\) −15.6972 + 0.600152i −0.692375 + 0.0264716i
\(515\) 4.60680 + 17.1928i 0.203000 + 0.757606i
\(516\) 0 0
\(517\) −2.15414 + 8.03937i −0.0947391 + 0.353571i
\(518\) −1.65344 0.375970i −0.0726479 0.0165192i
\(519\) 0 0
\(520\) 4.52762 10.4470i 0.198549 0.458131i
\(521\) −14.1129 −0.618299 −0.309149 0.951013i \(-0.600044\pi\)
−0.309149 + 0.951013i \(0.600044\pi\)
\(522\) 0 0
\(523\) −27.5776 + 27.5776i −1.20588 + 1.20588i −0.233534 + 0.972349i \(0.575029\pi\)
−0.972349 + 0.233534i \(0.924971\pi\)
\(524\) −3.26270 9.27577i −0.142532 0.405214i
\(525\) 0 0
\(526\) −14.4687 22.9852i −0.630863 1.00220i
\(527\) −12.2620 21.2384i −0.534141 0.925159i
\(528\) 0 0
\(529\) 19.4709 33.7246i 0.846561 1.46629i
\(530\) −0.0109211 0.000417544i −0.000474380 1.81370e-5i
\(531\) 0 0
\(532\) 1.08961 + 0.934600i 0.0472406 + 0.0405201i
\(533\) 4.55660 + 17.0054i 0.197368 + 0.736588i
\(534\) 0 0
\(535\) 10.8164 + 18.7345i 0.467632 + 0.809962i
\(536\) 5.82515 + 0.863450i 0.251608 + 0.0372953i
\(537\) 0 0
\(538\) 4.53038 + 14.6448i 0.195319 + 0.631381i
\(539\) 3.46978 + 3.46978i 0.149454 + 0.149454i
\(540\) 0 0
\(541\) 7.82995 7.82995i 0.336636 0.336636i −0.518464 0.855100i \(-0.673496\pi\)
0.855100 + 0.518464i \(0.173496\pi\)
\(542\) 8.56427 16.2364i 0.367867 0.697412i
\(543\) 0 0
\(544\) 16.0247 + 18.4684i 0.687052 + 0.791824i
\(545\) −26.5746 + 15.3429i −1.13833 + 0.657216i
\(546\) 0 0
\(547\) −21.7416 + 5.82566i −0.929606 + 0.249087i −0.691686 0.722198i \(-0.743132\pi\)
−0.237919 + 0.971285i \(0.576465\pi\)
\(548\) −13.6088 + 1.04214i −0.581340 + 0.0445178i
\(549\) 0 0
\(550\) 0.400406 + 0.370916i 0.0170734 + 0.0158159i
\(551\) −4.67438 2.69876i −0.199135 0.114971i
\(552\) 0 0
\(553\) −0.384019 + 0.221713i −0.0163301 + 0.00942821i
\(554\) −34.2400 7.78571i −1.45472 0.330783i
\(555\) 0 0
\(556\) 7.10589 + 20.2019i 0.301357 + 0.856750i
\(557\) 25.5918 + 25.5918i 1.08436 + 1.08436i 0.996097 + 0.0882628i \(0.0281315\pi\)
0.0882628 + 0.996097i \(0.471868\pi\)
\(558\) 0 0
\(559\) 21.4755i 0.908315i
\(560\) 0.433859 + 0.985643i 0.0183339 + 0.0416510i
\(561\) 0 0
\(562\) 8.83552 5.56176i 0.372704 0.234609i
\(563\) −11.3728 3.04735i −0.479308 0.128430i 0.0110721 0.999939i \(-0.496476\pi\)
−0.490381 + 0.871508i \(0.663142\pi\)
\(564\) 0 0
\(565\) −43.0520 + 11.5357i −1.81121 + 0.485313i
\(566\) 6.44131 + 5.96690i 0.270748 + 0.250808i
\(567\) 0 0
\(568\) −10.6967 + 1.23170i −0.448822 + 0.0516810i
\(569\) −0.819418 + 1.41927i −0.0343518 + 0.0594990i −0.882690 0.469955i \(-0.844270\pi\)
0.848338 + 0.529454i \(0.177603\pi\)
\(570\) 0 0
\(571\) −32.7015 8.76233i −1.36851 0.366692i −0.501578 0.865112i \(-0.667247\pi\)
−0.866936 + 0.498420i \(0.833914\pi\)
\(572\) −1.51412 2.21305i −0.0633083 0.0925321i
\(573\) 0 0
\(574\) −1.47282 0.776875i −0.0614744 0.0324261i
\(575\) 4.32299 0.180281
\(576\) 0 0
\(577\) −16.0429 −0.667873 −0.333936 0.942596i \(-0.608377\pi\)
−0.333936 + 0.942596i \(0.608377\pi\)
\(578\) 2.10576 + 1.11073i 0.0875882 + 0.0462005i
\(579\) 0 0
\(580\) −2.28640 3.34182i −0.0949376 0.138762i
\(581\) −0.187784 0.0503166i −0.00779060 0.00208749i
\(582\) 0 0
\(583\) −0.00128692 + 0.00222901i −5.32988e−5 + 9.23163e-5i
\(584\) −5.27339 + 0.607220i −0.218214 + 0.0251269i
\(585\) 0 0
\(586\) 25.7928 + 23.8931i 1.06549 + 0.987016i
\(587\) −36.9837 + 9.90974i −1.52648 + 0.409019i −0.921869 0.387502i \(-0.873338\pi\)
−0.604611 + 0.796521i \(0.706671\pi\)
\(588\) 0 0
\(589\) 30.8237 + 8.25918i 1.27007 + 0.340313i
\(590\) 10.7066 6.73958i 0.440784 0.277464i
\(591\) 0 0
\(592\) 34.3969 15.1408i 1.41370 0.622282i
\(593\) 32.2597i 1.32475i −0.749173 0.662374i \(-0.769549\pi\)
0.749173 0.662374i \(-0.230451\pi\)
\(594\) 0 0
\(595\) 0.822870 + 0.822870i 0.0337344 + 0.0337344i
\(596\) 0.140182 + 0.398533i 0.00574206 + 0.0163245i
\(597\) 0 0
\(598\) −20.7094 4.70904i −0.846870 0.192567i
\(599\) −11.7417 + 6.77905i −0.479751 + 0.276984i −0.720313 0.693649i \(-0.756002\pi\)
0.240562 + 0.970634i \(0.422668\pi\)
\(600\) 0 0
\(601\) −0.496416 0.286606i −0.0202492 0.0116909i 0.489841 0.871812i \(-0.337055\pi\)
−0.510090 + 0.860121i \(0.670388\pi\)
\(602\) 1.49010 + 1.38035i 0.0607319 + 0.0562590i
\(603\) 0 0
\(604\) 4.57850 0.350612i 0.186297 0.0142662i
\(605\) 21.4096 5.73669i 0.870425 0.233230i
\(606\) 0 0
\(607\) 29.1103 16.8068i 1.18155 0.682168i 0.225178 0.974318i \(-0.427704\pi\)
0.956373 + 0.292149i \(0.0943705\pi\)
\(608\) −31.7370 2.24843i −1.28710 0.0911858i
\(609\) 0 0
\(610\) 6.41140 12.1549i 0.259590 0.492138i
\(611\) 15.9823 15.9823i 0.646576 0.646576i
\(612\) 0 0
\(613\) 26.5621 + 26.5621i 1.07283 + 1.07283i 0.997130 + 0.0757042i \(0.0241205\pi\)
0.0757042 + 0.997130i \(0.475880\pi\)
\(614\) 10.2711 + 33.2021i 0.414509 + 1.33993i
\(615\) 0 0
\(616\) 0.250876 + 0.0371868i 0.0101081 + 0.00149830i
\(617\) −11.8730 20.5647i −0.477991 0.827904i 0.521691 0.853134i \(-0.325301\pi\)
−0.999682 + 0.0252305i \(0.991968\pi\)
\(618\) 0 0
\(619\) 4.60330 + 17.1798i 0.185022 + 0.690513i 0.994626 + 0.103535i \(0.0330155\pi\)
−0.809603 + 0.586977i \(0.800318\pi\)
\(620\) 18.1706 + 15.5856i 0.729748 + 0.625933i
\(621\) 0 0
\(622\) −19.4897 + 0.745149i −0.781466 + 0.0298778i
\(623\) −0.676151 + 1.17113i −0.0270894 + 0.0469202i
\(624\) 0 0
\(625\) −10.9760 19.0109i −0.439038 0.760436i
\(626\) −15.3428 24.3738i −0.613221 0.974173i
\(627\) 0 0
\(628\) −11.1404 31.6719i −0.444550 1.26384i
\(629\) 28.7164 28.7164i 1.14500 1.14500i
\(630\) 0 0
\(631\) 16.0572 0.639228 0.319614 0.947548i \(-0.396447\pi\)
0.319614 + 0.947548i \(0.396447\pi\)
\(632\) 3.90811 9.01753i 0.155456 0.358698i
\(633\) 0 0
\(634\) 29.0008 + 6.59441i 1.15177 + 0.261897i
\(635\) 7.15884 26.7172i 0.284090 1.06024i
\(636\) 0 0
\(637\) −3.44897 12.8717i −0.136653 0.509997i
\(638\) −0.952893 + 0.0364320i −0.0377254 + 0.00144235i
\(639\) 0 0
\(640\) −20.7382 11.8161i −0.819749 0.467071i
\(641\) −35.3930 20.4342i −1.39794 0.807102i −0.403764 0.914863i \(-0.632298\pi\)
−0.994177 + 0.107761i \(0.965632\pi\)
\(642\) 0 0
\(643\) −8.91467 + 33.2700i −0.351560 + 1.31204i 0.533198 + 0.845991i \(0.320990\pi\)
−0.884758 + 0.466050i \(0.845677\pi\)
\(644\) 1.65786 1.13427i 0.0653287 0.0446964i
\(645\) 0 0
\(646\) −32.8455 + 10.1608i −1.29229 + 0.399771i
\(647\) 28.1696i 1.10746i −0.832696 0.553730i \(-0.813204\pi\)
0.832696 0.553730i \(-0.186796\pi\)
\(648\) 0 0
\(649\) 2.97943i 0.116953i
\(650\) −0.438047 1.41602i −0.0171816 0.0555408i
\(651\) 0 0
\(652\) −0.255650 + 1.36330i −0.0100120 + 0.0533908i
\(653\) −2.17456 + 8.11558i −0.0850972 + 0.317587i −0.995333 0.0965042i \(-0.969234\pi\)
0.910235 + 0.414091i \(0.135901\pi\)
\(654\) 0 0
\(655\) 8.98247 + 5.18603i 0.350974 + 0.202635i
\(656\) 36.4757 5.61941i 1.42414 0.219401i
\(657\) 0 0
\(658\) 0.0816744 + 2.13623i 0.00318400 + 0.0832789i
\(659\) 6.62788 + 24.7356i 0.258186 + 0.963562i 0.966290 + 0.257455i \(0.0828838\pi\)
−0.708105 + 0.706107i \(0.750450\pi\)
\(660\) 0 0
\(661\) −5.44473 + 20.3200i −0.211775 + 0.790357i 0.775501 + 0.631346i \(0.217497\pi\)
−0.987277 + 0.159011i \(0.949170\pi\)
\(662\) −5.53914 + 24.3600i −0.215285 + 0.946778i
\(663\) 0 0
\(664\) 4.00710 1.58398i 0.155506 0.0614704i
\(665\) −1.51424 −0.0587198
\(666\) 0 0
\(667\) −5.34063 + 5.34063i −0.206790 + 0.206790i
\(668\) −19.4526 9.32887i −0.752644 0.360945i
\(669\) 0 0
\(670\) −5.25692 + 3.30912i −0.203093 + 0.127842i
\(671\) −1.61818 2.80277i −0.0624691 0.108200i
\(672\) 0 0
\(673\) −12.5221 + 21.6890i −0.482693 + 0.836048i −0.999803 0.0198709i \(-0.993674\pi\)
0.517110 + 0.855919i \(0.327008\pi\)
\(674\) 0.521432 + 13.6383i 0.0200848 + 0.525327i
\(675\) 0 0
\(676\) −1.42921 18.6635i −0.0549696 0.717825i
\(677\) 4.91241 + 18.3334i 0.188799 + 0.704608i 0.993785 + 0.111314i \(0.0355060\pi\)
−0.804986 + 0.593294i \(0.797827\pi\)
\(678\) 0 0
\(679\) 0.423420 + 0.733386i 0.0162494 + 0.0281448i
\(680\) −25.5135 3.78180i −0.978396 0.145026i
\(681\) 0 0
\(682\) 5.38596 1.66615i 0.206239 0.0638003i
\(683\) −3.70253 3.70253i −0.141673 0.141673i 0.632713 0.774386i \(-0.281941\pi\)
−0.774386 + 0.632713i \(0.781941\pi\)
\(684\) 0 0
\(685\) 10.1803 10.1803i 0.388969 0.388969i
\(686\) 2.23221 + 1.17743i 0.0852263 + 0.0449547i
\(687\) 0 0
\(688\) −44.7520 4.89475i −1.70616 0.186611i
\(689\) 0.00605326 0.00349485i 0.000230611 0.000133143i
\(690\) 0 0
\(691\) 8.18783 2.19392i 0.311480 0.0834607i −0.0996929 0.995018i \(-0.531786\pi\)
0.411173 + 0.911558i \(0.365119\pi\)
\(692\) −7.25455 6.22251i −0.275777 0.236544i
\(693\) 0 0
\(694\) 18.3110 19.7669i 0.695078 0.750340i
\(695\) −19.5631 11.2947i −0.742070 0.428434i
\(696\) 0 0
\(697\) 34.5379 19.9405i 1.30822 0.755299i
\(698\) 5.67274 24.9475i 0.214716 0.944278i
\(699\) 0 0
\(700\) 0.126408 + 0.0606214i 0.00477777 + 0.00229127i
\(701\) −16.2977 16.2977i −0.615557 0.615557i 0.328831 0.944389i \(-0.393345\pi\)
−0.944389 + 0.328831i \(0.893345\pi\)
\(702\) 0 0
\(703\) 52.8439i 1.99304i
\(704\) −4.95680 + 2.65081i −0.186816 + 0.0999063i
\(705\) 0 0
\(706\) 4.92023 + 7.81637i 0.185175 + 0.294173i
\(707\) 1.54314 + 0.413484i 0.0580359 + 0.0155507i
\(708\) 0 0
\(709\) −18.6437 + 4.99557i −0.700180 + 0.187613i −0.591311 0.806443i \(-0.701390\pi\)
−0.108869 + 0.994056i \(0.534723\pi\)
\(710\) 7.71848 8.33214i 0.289669 0.312700i
\(711\) 0 0
\(712\) −3.42856 29.7753i −0.128491 1.11588i
\(713\) 22.3267 38.6710i 0.836142 1.44824i
\(714\) 0 0
\(715\) 2.73210 + 0.732065i 0.102175 + 0.0273777i
\(716\) −9.81001 1.83961i −0.366617 0.0687493i
\(717\) 0 0
\(718\) 15.0483 28.5291i 0.561599 1.06470i
\(719\) 24.2401 0.904003 0.452002 0.892017i \(-0.350710\pi\)
0.452002 + 0.892017i \(0.350710\pi\)
\(720\) 0 0
\(721\) 1.07669 0.0400980
\(722\) 8.33596 15.8036i 0.310232 0.588148i
\(723\) 0 0
\(724\) −3.83090 + 20.4289i −0.142374 + 0.759234i
\(725\) −0.509157 0.136428i −0.0189096 0.00506682i
\(726\) 0 0
\(727\) −8.10074 + 14.0309i −0.300440 + 0.520377i −0.976236 0.216712i \(-0.930467\pi\)
0.675796 + 0.737089i \(0.263800\pi\)
\(728\) −0.539526 0.428105i −0.0199962 0.0158666i
\(729\) 0 0
\(730\) 3.80516 4.10769i 0.140835 0.152032i
\(731\) −46.9902 + 12.5910i −1.73800 + 0.465694i
\(732\) 0 0
\(733\) 8.04180 + 2.15479i 0.297031 + 0.0795891i 0.404257 0.914646i \(-0.367530\pi\)
−0.107226 + 0.994235i \(0.534197\pi\)
\(734\) 18.0686 + 28.7041i 0.666924 + 1.05949i
\(735\) 0 0
\(736\) −14.5332 + 42.0824i −0.535700 + 1.55118i
\(737\) 1.46289i 0.0538863i
\(738\) 0 0
\(739\) 22.8405 + 22.8405i 0.840203 + 0.840203i 0.988885 0.148682i \(-0.0475030\pi\)
−0.148682 + 0.988885i \(0.547503\pi\)
\(740\) −17.1421 + 35.7447i −0.630155 + 1.31400i
\(741\) 0 0
\(742\) −0.000146584 0 0.000644647i −5.38128e−6 0 2.36657e-5i
\(743\) 7.19608 4.15466i 0.263999 0.152420i −0.362159 0.932116i \(-0.617960\pi\)
0.626157 + 0.779697i \(0.284627\pi\)
\(744\) 0 0
\(745\) −0.385931 0.222817i −0.0141394 0.00816339i
\(746\) −23.0544 + 24.8874i −0.844083 + 0.911192i
\(747\) 0 0
\(748\) −3.95462 + 4.61052i −0.144595 + 0.168577i
\(749\) 1.26399 0.338684i 0.0461850 0.0123752i
\(750\) 0 0
\(751\) 28.0215 16.1782i 1.02252 0.590352i 0.107687 0.994185i \(-0.465656\pi\)
0.914833 + 0.403833i \(0.132322\pi\)
\(752\) −29.6623 36.9478i −1.08167 1.34735i
\(753\) 0 0
\(754\) 2.29052 + 1.20819i 0.0834158 + 0.0439996i
\(755\) −3.42502 + 3.42502i −0.124649 + 0.124649i
\(756\) 0 0
\(757\) 3.76265 + 3.76265i 0.136756 + 0.136756i 0.772171 0.635415i \(-0.219171\pi\)
−0.635415 + 0.772171i \(0.719171\pi\)
\(758\) −19.0423 + 5.89077i −0.691649 + 0.213962i
\(759\) 0 0
\(760\) 26.9545 19.9953i 0.977743 0.725304i
\(761\) −13.1168 22.7190i −0.475485 0.823564i 0.524121 0.851644i \(-0.324394\pi\)
−0.999606 + 0.0280801i \(0.991061\pi\)
\(762\) 0 0
\(763\) 0.480419 + 1.79295i 0.0173923 + 0.0649090i
\(764\) 10.3253 0.790689i 0.373556 0.0286061i
\(765\) 0 0
\(766\) 0.249371 + 6.52239i 0.00901012 + 0.235664i
\(767\) −4.04557 + 7.00713i −0.146077 + 0.253013i
\(768\) 0 0
\(769\) −9.31591 16.1356i −0.335940 0.581865i 0.647725 0.761874i \(-0.275721\pi\)
−0.983665 + 0.180009i \(0.942387\pi\)
\(770\) −0.226403 + 0.142516i −0.00815901 + 0.00513592i
\(771\) 0 0
\(772\) −22.8614 + 47.6707i −0.822801 + 1.71571i
\(773\) 4.69430 4.69430i 0.168842 0.168842i −0.617628 0.786470i \(-0.711906\pi\)
0.786470 + 0.617628i \(0.211906\pi\)
\(774\) 0 0
\(775\) 3.11641 0.111945
\(776\) −17.2214 7.46357i −0.618211 0.267927i
\(777\) 0 0
\(778\) 4.01129 17.6408i 0.143812 0.632454i
\(779\) −13.4311 + 50.1255i −0.481218 + 1.79593i
\(780\) 0 0
\(781\) −0.692294 2.58368i −0.0247722 0.0924512i
\(782\) 1.83805 + 48.0749i 0.0657284 + 1.71915i
\(783\) 0 0
\(784\) −27.6091 + 4.25344i −0.986041 + 0.151909i
\(785\) 30.6704 + 17.7076i 1.09467 + 0.632010i
\(786\) 0 0
\(787\) −11.7352 + 43.7964i −0.418315 + 1.56117i 0.359786 + 0.933035i \(0.382850\pi\)
−0.778101 + 0.628139i \(0.783817\pi\)
\(788\) −14.3072 2.68293i −0.509672 0.0955755i
\(789\) 0 0
\(790\) 3.06377 + 9.90384i 0.109004 + 0.352363i
\(791\) 2.69611i 0.0958625i
\(792\) 0 0
\(793\) 8.78888i 0.312102i
\(794\) 7.07544 2.18880i 0.251098 0.0776775i
\(795\) 0 0
\(796\) −1.55211 2.26858i −0.0550131 0.0804077i
\(797\) 9.77347 36.4751i 0.346194 1.29201i −0.545017 0.838425i \(-0.683477\pi\)
0.891211 0.453589i \(-0.149857\pi\)
\(798\) 0 0
\(799\) −44.3411 25.6004i −1.56868 0.905676i
\(800\) −3.05064 + 0.590090i −0.107856 + 0.0208628i
\(801\) 0 0
\(802\) 18.9079 0.722905i 0.667660 0.0255266i
\(803\) −0.341296 1.27374i −0.0120441 0.0449492i
\(804\) 0 0
\(805\) −0.548411 + 2.04670i −0.0193289 + 0.0721366i
\(806\) −14.9293 3.39472i −0.525861 0.119574i
\(807\) 0 0
\(808\) −32.9290 + 13.0166i −1.15844 + 0.457922i
\(809\) 24.0071 0.844045 0.422023 0.906585i \(-0.361320\pi\)
0.422023 + 0.906585i \(0.361320\pi\)
\(810\) 0 0
\(811\) −0.243845 + 0.243845i −0.00856256 + 0.00856256i −0.711375 0.702813i \(-0.751927\pi\)
0.702813 + 0.711375i \(0.251927\pi\)
\(812\) −0.231057 + 0.0812729i −0.00810850 + 0.00285212i
\(813\) 0 0
\(814\) 4.97351 + 7.90100i 0.174321 + 0.276930i
\(815\) −0.731560 1.26710i −0.0256254 0.0443846i
\(816\) 0 0
\(817\) 31.6507 54.8205i 1.10732 1.91793i
\(818\) −39.3350 + 1.50389i −1.37532 + 0.0525824i
\(819\) 0 0
\(820\) −25.3453 + 29.5490i −0.885097 + 1.03190i
\(821\) 12.4067 + 46.3025i 0.432998 + 1.61597i 0.745813 + 0.666156i \(0.232061\pi\)
−0.312815 + 0.949814i \(0.601272\pi\)
\(822\) 0 0
\(823\) −0.737958 1.27818i −0.0257236 0.0445546i 0.852877 0.522112i \(-0.174856\pi\)
−0.878601 + 0.477557i \(0.841522\pi\)
\(824\) −19.1658 + 14.2175i −0.667672 + 0.495289i
\(825\) 0 0
\(826\) −0.226165 0.731096i −0.00786930 0.0254381i
\(827\) 11.5464 + 11.5464i 0.401509 + 0.401509i 0.878764 0.477256i \(-0.158368\pi\)
−0.477256 + 0.878764i \(0.658368\pi\)
\(828\) 0 0
\(829\) 34.7961 34.7961i 1.20852 1.20852i 0.237010 0.971507i \(-0.423833\pi\)
0.971507 0.237010i \(-0.0761675\pi\)
\(830\) −2.12051 + 4.02012i −0.0736039 + 0.139540i
\(831\) 0 0
\(832\) 15.2569 + 0.496227i 0.528940 + 0.0172036i
\(833\) −26.1424 + 15.0933i −0.905781 + 0.522953i
\(834\) 0 0
\(835\) 21.9815 5.88992i 0.760700 0.203829i
\(836\) −0.603493 7.88077i −0.0208722 0.272562i
\(837\) 0 0
\(838\) 10.7182 + 9.92880i 0.370254 + 0.342985i
\(839\) 41.3065 + 23.8483i 1.42606 + 0.823335i 0.996807 0.0798497i \(-0.0254440\pi\)
0.429252 + 0.903185i \(0.358777\pi\)
\(840\) 0 0
\(841\) −24.3172 + 14.0395i −0.838523 + 0.484122i
\(842\) 42.6196 + 9.69114i 1.46877 + 0.333979i
\(843\) 0 0
\(844\) −21.7553 + 7.65233i −0.748850 + 0.263404i
\(845\) 13.9615 + 13.9615i 0.480290 + 0.480290i
\(846\) 0 0
\(847\) 1.34076i 0.0460692i
\(848\) −0.00590313 0.0134108i −0.000202714 0.000460527i
\(849\) 0 0
\(850\) −2.84155 + 1.78869i −0.0974643 + 0.0613517i
\(851\) 71.4254 + 19.1384i 2.44843 + 0.656055i
\(852\) 0 0
\(853\) 42.5120 11.3911i 1.45558 0.390023i 0.557622 0.830095i \(-0.311714\pi\)
0.897962 + 0.440072i \(0.145047\pi\)
\(854\) −0.609827 0.564913i −0.0208678 0.0193309i
\(855\) 0 0
\(856\) −18.0275 + 22.7195i −0.616168 + 0.776535i
\(857\) −4.36756 + 7.56483i −0.149193 + 0.258410i −0.930929 0.365199i \(-0.881001\pi\)
0.781736 + 0.623609i \(0.214334\pi\)
\(858\) 0 0
\(859\) −48.4800 12.9902i −1.65411 0.443219i −0.693354 0.720597i \(-0.743868\pi\)
−0.960761 + 0.277378i \(0.910534\pi\)
\(860\) 39.1925 26.8146i 1.33645 0.914370i
\(861\) 0 0
\(862\) 18.5690 + 9.79464i 0.632461 + 0.333607i
\(863\) 3.87853 0.132027 0.0660134 0.997819i \(-0.478972\pi\)
0.0660134 + 0.997819i \(0.478972\pi\)
\(864\) 0 0
\(865\) 10.0817 0.342789
\(866\) 40.2300 + 21.2203i 1.36707 + 0.721094i
\(867\) 0 0
\(868\) 1.19514 0.817686i 0.0405656 0.0277541i
\(869\) 2.35827 + 0.631896i 0.0799988 + 0.0214356i
\(870\) 0 0
\(871\) 1.98636 3.44049i 0.0673054 0.116576i
\(872\) −32.2272 25.5718i −1.09135 0.865970i
\(873\) 0 0
\(874\) −45.9248 42.5424i −1.55343 1.43902i
\(875\) −1.44311 + 0.386679i −0.0487859 + 0.0130721i
\(876\) 0 0
\(877\) −20.2871 5.43592i −0.685047 0.183558i −0.100524 0.994935i \(-0.532052\pi\)
−0.584524 + 0.811377i \(0.698719\pi\)
\(878\) 0.335198 0.211000i 0.0113124 0.00712091i
\(879\) 0 0
\(880\) 2.14824 5.52649i 0.0724170 0.186298i
\(881\) 7.45496i 0.251164i −0.992083 0.125582i \(-0.959920\pi\)
0.992083 0.125582i \(-0.0400798\pi\)
\(882\) 0 0
\(883\) −9.55597 9.55597i −0.321584 0.321584i 0.527791 0.849375i \(-0.323021\pi\)
−0.849375 + 0.527791i \(0.823021\pi\)
\(884\) 15.5609 5.47348i 0.523371 0.184093i
\(885\) 0 0
\(886\) −34.6332 7.87514i −1.16353 0.264570i
\(887\) 41.0581 23.7049i 1.37860 0.795934i 0.386607 0.922245i \(-0.373647\pi\)
0.991991 + 0.126311i \(0.0403138\pi\)
\(888\) 0 0
\(889\) −1.44899 0.836573i −0.0485975 0.0280578i
\(890\) 23.1934 + 21.4852i 0.777444 + 0.720185i
\(891\) 0 0
\(892\) −3.17080 41.4062i −0.106166 1.38638i
\(893\) 64.3530 17.2433i 2.15349 0.577027i
\(894\) 0 0
\(895\) 9.11780 5.26416i 0.304774 0.175962i
\(896\) −1.01508 + 1.02673i −0.0339116 + 0.0343005i
\(897\) 0 0
\(898\) 9.42757 17.8731i 0.314602 0.596431i
\(899\) −3.85003 + 3.85003i −0.128406 + 0.128406i
\(900\) 0 0
\(901\) −0.0111960 0.0111960i −0.000372994 0.000372994i
\(902\) 2.70950 + 8.75865i 0.0902165 + 0.291631i
\(903\) 0 0
\(904\) −35.6015 47.9925i −1.18409 1.59621i
\(905\) −10.9624 18.9874i −0.364402 0.631162i
\(906\) 0 0
\(907\) −3.66301 13.6705i −0.121628 0.453923i 0.878069 0.478534i \(-0.158832\pi\)
−0.999697 + 0.0246114i \(0.992165\pi\)
\(908\) 10.3180 12.0293i 0.342413 0.399205i
\(909\) 0 0
\(910\) 0.725977 0.0277563i 0.0240659 0.000920111i
\(911\) −20.0062 + 34.6517i −0.662834 + 1.14806i 0.317034 + 0.948414i \(0.397313\pi\)
−0.979868 + 0.199648i \(0.936020\pi\)
\(912\) 0 0
\(913\) 0.535197 + 0.926988i 0.0177124 + 0.0306788i
\(914\) 20.9738 + 33.3193i 0.693751 + 1.10211i
\(915\) 0 0
\(916\) −0.876405 + 0.308271i −0.0289572 + 0.0101856i
\(917\) 0.443647 0.443647i 0.0146505 0.0146505i
\(918\) 0 0
\(919\) −18.6876 −0.616446 −0.308223 0.951314i \(-0.599734\pi\)
−0.308223 + 0.951314i \(0.599734\pi\)
\(920\) −17.2641 43.6742i −0.569182 1.43990i
\(921\) 0 0
\(922\) 23.1120 + 5.25536i 0.761153 + 0.173076i
\(923\) −1.88004 + 7.01641i −0.0618823 + 0.230948i
\(924\) 0 0
\(925\) 1.33569 + 4.98486i 0.0439172 + 0.163901i
\(926\) −42.7452 + 1.63428i −1.40470 + 0.0537057i
\(927\) 0 0
\(928\) 3.03977 4.49777i 0.0997853 0.147646i
\(929\) 8.76538 + 5.06070i 0.287583 + 0.166036i 0.636851 0.770987i \(-0.280237\pi\)
−0.349268 + 0.937023i \(0.613570\pi\)
\(930\) 0 0
\(931\) 10.1662 37.9409i 0.333185 1.24346i
\(932\) −10.3191 15.0825i −0.338014 0.494044i
\(933\) 0 0
\(934\) 30.4500 9.41974i 0.996354 0.308223i
\(935\) 6.40729i 0.209541i
\(936\) 0 0
\(937\) 19.1375i 0.625194i −0.949886 0.312597i \(-0.898801\pi\)
0.949886 0.312597i \(-0.101199\pi\)
\(938\) 0.111047 + 0.358966i 0.00362580 + 0.0117207i
\(939\) 0 0
\(940\) 49.1234 + 9.21178i 1.60223 + 0.300455i
\(941\) −11.1081 + 41.4559i −0.362113 + 1.35142i 0.509179 + 0.860660i \(0.329949\pi\)
−0.871292 + 0.490764i \(0.836718\pi\)
\(942\) 0 0
\(943\) 62.8868 + 36.3077i 2.04788 + 1.18234i
\(944\) 13.6799 + 10.0275i 0.445241 + 0.326368i
\(945\) 0 0
\(946\) −0.427269 11.1754i −0.0138917 0.363344i
\(947\) −12.0721 45.0535i −0.392289 1.46404i −0.826349 0.563159i \(-0.809586\pi\)
0.434060 0.900884i \(-0.357081\pi\)
\(948\) 0 0
\(949\) −0.926848 + 3.45904i −0.0300867 + 0.112285i
\(950\) 0.968731 4.26028i 0.0314298 0.138222i
\(951\) 0 0
\(952\) −0.620410 + 1.43153i −0.0201076 + 0.0463960i
\(953\) 20.2249 0.655149 0.327575 0.944825i \(-0.393769\pi\)
0.327575 + 0.944825i \(0.393769\pi\)
\(954\) 0 0
\(955\) −7.72399 + 7.72399i −0.249943 + 0.249943i
\(956\) −6.32752 + 13.1942i −0.204647 + 0.426730i
\(957\) 0 0
\(958\) −35.4502 + 22.3151i −1.14534 + 0.720969i
\(959\) −0.435445 0.754212i −0.0140612 0.0243548i
\(960\) 0 0
\(961\) 0.595170 1.03087i 0.0191990 0.0332537i
\(962\) −0.968635 25.3351i −0.0312301 0.816836i
\(963\) 0 0
\(964\) −4.97974 + 0.381338i −0.160387 + 0.0122821i
\(965\) −14.4339 53.8680i −0.464644 1.73407i
\(966\) 0 0
\(967\) 15.9815 + 27.6807i 0.513930 + 0.890152i 0.999869 + 0.0161601i \(0.00514413\pi\)
−0.485940 + 0.873992i \(0.661523\pi\)
\(968\) 17.7045 + 23.8665i 0.569045 + 0.767098i
\(969\) 0 0
\(970\) 18.9140 5.85108i 0.607293 0.187867i
\(971\) −4.69660 4.69660i −0.150721 0.150721i 0.627719 0.778440i \(-0.283989\pi\)
−0.778440 + 0.627719i \(0.783989\pi\)
\(972\) 0 0
\(973\) −0.966226 + 0.966226i −0.0309758 + 0.0309758i
\(974\) −32.0622 16.9120i −1.02734 0.541895i
\(975\) 0 0
\(976\) 18.3149 + 2.00319i 0.586245 + 0.0641205i
\(977\) 22.7888 13.1571i 0.729079 0.420934i −0.0890064 0.996031i \(-0.528369\pi\)
0.818085 + 0.575097i \(0.195036\pi\)
\(978\) 0 0
\(979\) 7.19193 1.92707i 0.229855 0.0615895i
\(980\) 19.1844 22.3662i 0.612822 0.714463i
\(981\) 0 0
\(982\) −5.22426 + 5.63962i −0.166713 + 0.179968i
\(983\) −19.6448 11.3420i −0.626573 0.361752i 0.152851 0.988249i \(-0.451155\pi\)
−0.779424 + 0.626497i \(0.784488\pi\)
\(984\) 0 0
\(985\) 13.2976 7.67740i 0.423698 0.244622i
\(986\) 1.30070 5.72022i 0.0414228 0.182169i
\(987\) 0 0
\(988\) −9.28146 + 19.3537i −0.295283 + 0.615724i
\(989\) −62.6343 62.6343i −1.99165 1.99165i
\(990\) 0 0
\(991\) 13.0577i 0.414793i −0.978257 0.207396i \(-0.933501\pi\)
0.978257 0.207396i \(-0.0664990\pi\)
\(992\) −10.4769 + 30.3369i −0.332641 + 0.963197i
\(993\) 0 0
\(994\) −0.366000 0.581435i −0.0116088 0.0184420i
\(995\) 2.80066 + 0.750435i 0.0887870 + 0.0237904i
\(996\) 0 0
\(997\) 7.68222 2.05844i 0.243298 0.0651916i −0.135109 0.990831i \(-0.543139\pi\)
0.378407 + 0.925639i \(0.376472\pi\)
\(998\) −21.4694 + 23.1763i −0.679601 + 0.733633i
\(999\) 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 432.2.v.a.251.4 88
3.2 odd 2 144.2.u.a.11.19 88
4.3 odd 2 1728.2.z.a.143.5 88
9.4 even 3 144.2.u.a.59.19 yes 88
9.5 odd 6 inner 432.2.v.a.395.4 88
12.11 even 2 576.2.y.a.335.22 88
16.3 odd 4 inner 432.2.v.a.35.4 88
16.13 even 4 1728.2.z.a.1007.5 88
36.23 even 6 1728.2.z.a.719.5 88
36.31 odd 6 576.2.y.a.527.11 88
48.29 odd 4 576.2.y.a.47.11 88
48.35 even 4 144.2.u.a.83.19 yes 88
144.13 even 12 576.2.y.a.239.22 88
144.67 odd 12 144.2.u.a.131.19 yes 88
144.77 odd 12 1728.2.z.a.1583.5 88
144.131 even 12 inner 432.2.v.a.179.4 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.2.u.a.11.19 88 3.2 odd 2
144.2.u.a.59.19 yes 88 9.4 even 3
144.2.u.a.83.19 yes 88 48.35 even 4
144.2.u.a.131.19 yes 88 144.67 odd 12
432.2.v.a.35.4 88 16.3 odd 4 inner
432.2.v.a.179.4 88 144.131 even 12 inner
432.2.v.a.251.4 88 1.1 even 1 trivial
432.2.v.a.395.4 88 9.5 odd 6 inner
576.2.y.a.47.11 88 48.29 odd 4
576.2.y.a.239.22 88 144.13 even 12
576.2.y.a.335.22 88 12.11 even 2
576.2.y.a.527.11 88 36.31 odd 6
1728.2.z.a.143.5 88 4.3 odd 2
1728.2.z.a.719.5 88 36.23 even 6
1728.2.z.a.1007.5 88 16.13 even 4
1728.2.z.a.1583.5 88 144.77 odd 12