Properties

Label 864.2.bk.a.37.9
Level $864$
Weight $2$
Character 864.37
Analytic conductor $6.899$
Analytic rank $0$
Dimension $368$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [864,2,Mod(37,864)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(864, base_ring=CyclotomicField(24))
 
chi = DirichletCharacter(H, H._module([0, 3, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("864.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.bk (of order \(24\), 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: \(6.89907473464\)
Analytic rank: \(0\)
Dimension: \(368\)
Relative dimension: \(46\) over \(\Q(\zeta_{24})\)
Twist minimal: no (minimal twist has level 288)
Sato-Tate group: $\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label 37.9
Character \(\chi\) \(=\) 864.37
Dual form 864.2.bk.a.397.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.15525 + 0.815721i) q^{2} +(0.669198 - 1.88472i) q^{4} +(-1.28782 + 0.988180i) q^{5} +(-0.0841003 + 0.313867i) q^{7} +(0.764318 + 2.72320i) q^{8} +O(q^{10})\) \(q+(-1.15525 + 0.815721i) q^{2} +(0.669198 - 1.88472i) q^{4} +(-1.28782 + 0.988180i) q^{5} +(-0.0841003 + 0.313867i) q^{7} +(0.764318 + 2.72320i) q^{8} +(0.681674 - 2.19210i) q^{10} +(-0.0367145 + 0.00483355i) q^{11} +(0.667924 - 5.07339i) q^{13} +(-0.158871 - 0.431196i) q^{14} +(-3.10435 - 2.52250i) q^{16} -0.259265i q^{17} +(2.17237 - 0.899824i) q^{19} +(1.00064 + 3.08847i) q^{20} +(0.0384715 - 0.0355327i) q^{22} +(-0.774456 - 2.89031i) q^{23} +(-0.612111 + 2.28443i) q^{25} +(3.36685 + 6.40586i) q^{26} +(0.535271 + 0.368544i) q^{28} +(-0.174689 + 0.227659i) q^{29} +(-0.655344 + 1.13509i) q^{31} +(5.64395 + 0.381833i) q^{32} +(0.211488 + 0.299515i) q^{34} +(-0.201851 - 0.487310i) q^{35} +(1.83125 + 0.758528i) q^{37} +(-1.77562 + 2.81157i) q^{38} +(-3.67532 - 2.75171i) q^{40} +(-1.86423 - 6.95740i) q^{41} +(8.20511 - 1.08022i) q^{43} +(-0.0154593 + 0.0724312i) q^{44} +(3.25238 + 2.70728i) q^{46} +(6.61072 - 3.81670i) q^{47} +(5.97074 + 3.44721i) q^{49} +(-1.15632 - 3.13839i) q^{50} +(-9.11495 - 4.65395i) q^{52} +(2.72780 - 6.58549i) q^{53} +(0.0425053 - 0.0425053i) q^{55} +(-0.919001 + 0.0108719i) q^{56} +(0.0161028 - 0.405499i) q^{58} +(10.5427 - 8.08970i) q^{59} +(4.51806 - 5.88805i) q^{61} +(-0.168831 - 1.84589i) q^{62} +(-6.83164 + 4.16278i) q^{64} +(4.15326 + 7.19365i) q^{65} +(-0.949915 - 0.125059i) q^{67} +(-0.488642 - 0.173499i) q^{68} +(0.630697 + 0.398311i) q^{70} +(-5.16049 - 5.16049i) q^{71} +(-9.80103 + 9.80103i) q^{73} +(-2.73429 + 0.617500i) q^{74} +(-0.242174 - 4.69647i) q^{76} +(0.00157061 - 0.0119299i) q^{77} +(13.1750 - 7.60662i) q^{79} +(6.49054 + 0.180876i) q^{80} +(7.82895 + 6.51684i) q^{82} +(11.4321 + 8.77216i) q^{83} +(0.256200 + 0.333887i) q^{85} +(-8.59778 + 7.94101i) q^{86} +(-0.0412243 - 0.0962865i) q^{88} +(-4.05181 - 4.05181i) q^{89} +(1.53619 + 0.636312i) q^{91} +(-5.96569 - 0.474554i) q^{92} +(-4.52366 + 9.80174i) q^{94} +(-1.90843 + 3.30550i) q^{95} +(-5.22067 - 9.04247i) q^{97} +(-9.70965 + 0.888077i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8} - 16 q^{10} + 4 q^{11} - 4 q^{13} + 4 q^{14} - 4 q^{16} - 16 q^{19} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{25} + 16 q^{26} - 16 q^{28} + 4 q^{29} - 8 q^{31} + 4 q^{32} + 4 q^{34} + 16 q^{35} - 16 q^{37} + 60 q^{38} - 4 q^{40} + 4 q^{41} - 4 q^{43} + 104 q^{44} - 16 q^{46} - 48 q^{50} - 4 q^{52} + 16 q^{53} - 16 q^{55} + 84 q^{56} - 40 q^{58} + 4 q^{59} - 4 q^{61} + 24 q^{62} - 16 q^{64} + 8 q^{65} - 4 q^{67} - 12 q^{68} - 4 q^{70} + 16 q^{71} - 16 q^{73} + 4 q^{74} + 20 q^{76} + 4 q^{77} - 48 q^{80} - 16 q^{82} - 36 q^{83} + 16 q^{85} - 100 q^{86} - 4 q^{88} + 16 q^{89} - 16 q^{91} + 80 q^{92} - 20 q^{94} + 136 q^{95} - 8 q^{97} - 104 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.15525 + 0.815721i −0.816884 + 0.576802i
\(3\) 0 0
\(4\) 0.669198 1.88472i 0.334599 0.942361i
\(5\) −1.28782 + 0.988180i −0.575931 + 0.441928i −0.855209 0.518283i \(-0.826572\pi\)
0.279278 + 0.960210i \(0.409905\pi\)
\(6\) 0 0
\(7\) −0.0841003 + 0.313867i −0.0317869 + 0.118630i −0.979996 0.199015i \(-0.936226\pi\)
0.948209 + 0.317646i \(0.102892\pi\)
\(8\) 0.764318 + 2.72320i 0.270227 + 0.962797i
\(9\) 0 0
\(10\) 0.681674 2.19210i 0.215564 0.693202i
\(11\) −0.0367145 + 0.00483355i −0.0110698 + 0.00145737i −0.136059 0.990701i \(-0.543444\pi\)
0.124989 + 0.992158i \(0.460110\pi\)
\(12\) 0 0
\(13\) 0.667924 5.07339i 0.185249 1.40710i −0.605929 0.795519i \(-0.707199\pi\)
0.791178 0.611586i \(-0.209468\pi\)
\(14\) −0.158871 0.431196i −0.0424600 0.115242i
\(15\) 0 0
\(16\) −3.10435 2.52250i −0.776087 0.630626i
\(17\) 0.259265i 0.0628809i −0.999506 0.0314405i \(-0.989991\pi\)
0.999506 0.0314405i \(-0.0100095\pi\)
\(18\) 0 0
\(19\) 2.17237 0.899824i 0.498375 0.206434i −0.119313 0.992857i \(-0.538069\pi\)
0.617688 + 0.786423i \(0.288069\pi\)
\(20\) 1.00064 + 3.08847i 0.223749 + 0.690604i
\(21\) 0 0
\(22\) 0.0384715 0.0355327i 0.00820215 0.00757560i
\(23\) −0.774456 2.89031i −0.161485 0.602671i −0.998462 0.0554333i \(-0.982346\pi\)
0.836977 0.547238i \(-0.184321\pi\)
\(24\) 0 0
\(25\) −0.612111 + 2.28443i −0.122422 + 0.456886i
\(26\) 3.36685 + 6.40586i 0.660294 + 1.25629i
\(27\) 0 0
\(28\) 0.535271 + 0.368544i 0.101157 + 0.0696483i
\(29\) −0.174689 + 0.227659i −0.0324389 + 0.0422751i −0.809291 0.587408i \(-0.800149\pi\)
0.776852 + 0.629683i \(0.216815\pi\)
\(30\) 0 0
\(31\) −0.655344 + 1.13509i −0.117703 + 0.203868i −0.918857 0.394590i \(-0.870886\pi\)
0.801154 + 0.598458i \(0.204220\pi\)
\(32\) 5.64395 + 0.381833i 0.997719 + 0.0674992i
\(33\) 0 0
\(34\) 0.211488 + 0.299515i 0.0362698 + 0.0513664i
\(35\) −0.201851 0.487310i −0.0341190 0.0823705i
\(36\) 0 0
\(37\) 1.83125 + 0.758528i 0.301055 + 0.124701i 0.528097 0.849184i \(-0.322906\pi\)
−0.227042 + 0.973885i \(0.572906\pi\)
\(38\) −1.77562 + 2.81157i −0.288043 + 0.456096i
\(39\) 0 0
\(40\) −3.67532 2.75171i −0.581119 0.435084i
\(41\) −1.86423 6.95740i −0.291144 1.08656i −0.944232 0.329282i \(-0.893193\pi\)
0.653088 0.757282i \(-0.273473\pi\)
\(42\) 0 0
\(43\) 8.20511 1.08022i 1.25127 0.164733i 0.524378 0.851486i \(-0.324298\pi\)
0.726891 + 0.686753i \(0.240965\pi\)
\(44\) −0.0154593 + 0.0724312i −0.00233058 + 0.0109194i
\(45\) 0 0
\(46\) 3.25238 + 2.70728i 0.479537 + 0.399167i
\(47\) 6.61072 3.81670i 0.964272 0.556723i 0.0667869 0.997767i \(-0.478725\pi\)
0.897485 + 0.441045i \(0.145392\pi\)
\(48\) 0 0
\(49\) 5.97074 + 3.44721i 0.852963 + 0.492458i
\(50\) −1.15632 3.13839i −0.163528 0.443836i
\(51\) 0 0
\(52\) −9.11495 4.65395i −1.26402 0.645387i
\(53\) 2.72780 6.58549i 0.374692 0.904586i −0.618250 0.785982i \(-0.712158\pi\)
0.992942 0.118605i \(-0.0378421\pi\)
\(54\) 0 0
\(55\) 0.0425053 0.0425053i 0.00573141 0.00573141i
\(56\) −0.919001 + 0.0108719i −0.122807 + 0.00145281i
\(57\) 0 0
\(58\) 0.0161028 0.405499i 0.00211439 0.0532447i
\(59\) 10.5427 8.08970i 1.37254 1.05319i 0.380839 0.924641i \(-0.375635\pi\)
0.991703 0.128548i \(-0.0410315\pi\)
\(60\) 0 0
\(61\) 4.51806 5.88805i 0.578478 0.753887i −0.408846 0.912603i \(-0.634069\pi\)
0.987324 + 0.158716i \(0.0507355\pi\)
\(62\) −0.168831 1.84589i −0.0214416 0.234428i
\(63\) 0 0
\(64\) −6.83164 + 4.16278i −0.853955 + 0.520348i
\(65\) 4.15326 + 7.19365i 0.515148 + 0.892262i
\(66\) 0 0
\(67\) −0.949915 0.125059i −0.116051 0.0152783i 0.0722772 0.997385i \(-0.476973\pi\)
−0.188328 + 0.982106i \(0.560307\pi\)
\(68\) −0.488642 0.173499i −0.0592565 0.0210399i
\(69\) 0 0
\(70\) 0.630697 + 0.398311i 0.0753827 + 0.0476072i
\(71\) −5.16049 5.16049i −0.612437 0.612437i 0.331143 0.943580i \(-0.392566\pi\)
−0.943580 + 0.331143i \(0.892566\pi\)
\(72\) 0 0
\(73\) −9.80103 + 9.80103i −1.14712 + 1.14712i −0.160009 + 0.987116i \(0.551152\pi\)
−0.987116 + 0.160009i \(0.948848\pi\)
\(74\) −2.73429 + 0.617500i −0.317855 + 0.0717829i
\(75\) 0 0
\(76\) −0.242174 4.69647i −0.0277793 0.538722i
\(77\) 0.00157061 0.0119299i 0.000178987 0.00135954i
\(78\) 0 0
\(79\) 13.1750 7.60662i 1.48231 0.855811i 0.482510 0.875890i \(-0.339725\pi\)
0.999798 + 0.0200789i \(0.00639175\pi\)
\(80\) 6.49054 + 0.180876i 0.725664 + 0.0202226i
\(81\) 0 0
\(82\) 7.82895 + 6.51684i 0.864563 + 0.719664i
\(83\) 11.4321 + 8.77216i 1.25484 + 0.962870i 0.999992 0.00411184i \(-0.00130884\pi\)
0.254845 + 0.966982i \(0.417976\pi\)
\(84\) 0 0
\(85\) 0.256200 + 0.333887i 0.0277888 + 0.0362151i
\(86\) −8.59778 + 7.94101i −0.927123 + 0.856301i
\(87\) 0 0
\(88\) −0.0412243 0.0962865i −0.00439452 0.0102642i
\(89\) −4.05181 4.05181i −0.429491 0.429491i 0.458964 0.888455i \(-0.348221\pi\)
−0.888455 + 0.458964i \(0.848221\pi\)
\(90\) 0 0
\(91\) 1.53619 + 0.636312i 0.161037 + 0.0667037i
\(92\) −5.96569 0.474554i −0.621966 0.0494757i
\(93\) 0 0
\(94\) −4.52366 + 9.80174i −0.466580 + 1.01097i
\(95\) −1.90843 + 3.30550i −0.195801 + 0.339138i
\(96\) 0 0
\(97\) −5.22067 9.04247i −0.530079 0.918123i −0.999384 0.0350875i \(-0.988829\pi\)
0.469305 0.883036i \(-0.344504\pi\)
\(98\) −9.70965 + 0.888077i −0.980822 + 0.0897094i
\(99\) 0 0
\(100\) 3.89589 + 2.68239i 0.389589 + 0.268239i
\(101\) 1.24813 + 9.48049i 0.124194 + 0.943344i 0.934157 + 0.356863i \(0.116154\pi\)
−0.809963 + 0.586481i \(0.800513\pi\)
\(102\) 0 0
\(103\) 8.11028 2.17314i 0.799130 0.214126i 0.163928 0.986472i \(-0.447584\pi\)
0.635202 + 0.772346i \(0.280917\pi\)
\(104\) 14.3264 2.05879i 1.40481 0.201881i
\(105\) 0 0
\(106\) 2.22064 + 9.83300i 0.215687 + 0.955065i
\(107\) −5.77649 + 13.9457i −0.558435 + 1.34818i 0.352571 + 0.935785i \(0.385308\pi\)
−0.911005 + 0.412395i \(0.864692\pi\)
\(108\) 0 0
\(109\) 17.3516 7.18725i 1.66198 0.688414i 0.663751 0.747953i \(-0.268963\pi\)
0.998226 + 0.0595396i \(0.0189633\pi\)
\(110\) −0.0144317 + 0.0837766i −0.00137601 + 0.00798779i
\(111\) 0 0
\(112\) 1.05281 0.762208i 0.0994808 0.0720219i
\(113\) −4.17527 2.41059i −0.392776 0.226769i 0.290586 0.956849i \(-0.406150\pi\)
−0.683362 + 0.730079i \(0.739483\pi\)
\(114\) 0 0
\(115\) 3.85351 + 2.95690i 0.359341 + 0.275732i
\(116\) 0.312172 + 0.481588i 0.0289844 + 0.0447143i
\(117\) 0 0
\(118\) −5.58050 + 17.9455i −0.513726 + 1.65202i
\(119\) 0.0813745 + 0.0218042i 0.00745959 + 0.00199879i
\(120\) 0 0
\(121\) −10.6239 + 2.84665i −0.965805 + 0.258787i
\(122\) −0.416473 + 10.4876i −0.0377057 + 0.949506i
\(123\) 0 0
\(124\) 1.70077 + 1.99474i 0.152734 + 0.179133i
\(125\) −4.57512 11.0453i −0.409211 0.987923i
\(126\) 0 0
\(127\) −18.5137 −1.64283 −0.821413 0.570334i \(-0.806814\pi\)
−0.821413 + 0.570334i \(0.806814\pi\)
\(128\) 4.49657 10.3818i 0.397444 0.917626i
\(129\) 0 0
\(130\) −10.6661 4.92255i −0.935475 0.431736i
\(131\) 19.4768 + 2.56417i 1.70170 + 0.224032i 0.917851 0.396925i \(-0.129923\pi\)
0.783844 + 0.620958i \(0.213256\pi\)
\(132\) 0 0
\(133\) 0.0997279 + 0.757509i 0.00864751 + 0.0656844i
\(134\) 1.19940 0.630392i 0.103612 0.0544576i
\(135\) 0 0
\(136\) 0.706029 0.198161i 0.0605415 0.0169921i
\(137\) 5.47381 + 1.46670i 0.467660 + 0.125309i 0.484951 0.874542i \(-0.338838\pi\)
−0.0172912 + 0.999850i \(0.505504\pi\)
\(138\) 0 0
\(139\) −0.287146 0.374216i −0.0243554 0.0317406i 0.781017 0.624510i \(-0.214701\pi\)
−0.805372 + 0.592769i \(0.798035\pi\)
\(140\) −1.05352 + 0.0543251i −0.0890389 + 0.00459131i
\(141\) 0 0
\(142\) 10.1712 + 1.75213i 0.853545 + 0.147035i
\(143\) 0.189495i 0.0158464i
\(144\) 0 0
\(145\) 0.465808i 0.0386832i
\(146\) 3.32772 19.3175i 0.275404 1.59873i
\(147\) 0 0
\(148\) 2.65508 2.94379i 0.218246 0.241978i
\(149\) −9.47835 12.3524i −0.776497 1.01195i −0.999312 0.0370899i \(-0.988191\pi\)
0.222815 0.974861i \(-0.428475\pi\)
\(150\) 0 0
\(151\) 17.7034 + 4.74362i 1.44068 + 0.386030i 0.892773 0.450506i \(-0.148756\pi\)
0.547911 + 0.836536i \(0.315423\pi\)
\(152\) 4.11078 + 5.22804i 0.333428 + 0.424050i
\(153\) 0 0
\(154\) 0.00791707 + 0.0150632i 0.000637976 + 0.00121383i
\(155\) −0.277706 2.10939i −0.0223059 0.169430i
\(156\) 0 0
\(157\) −21.7162 2.85900i −1.73314 0.228173i −0.803158 0.595766i \(-0.796849\pi\)
−0.929987 + 0.367593i \(0.880182\pi\)
\(158\) −9.01557 + 19.5347i −0.717241 + 1.55410i
\(159\) 0 0
\(160\) −7.64573 + 5.08551i −0.604448 + 0.402045i
\(161\) 0.972303 0.0766282
\(162\) 0 0
\(163\) 1.33166 + 3.21491i 0.104304 + 0.251811i 0.967412 0.253208i \(-0.0814856\pi\)
−0.863108 + 0.505019i \(0.831486\pi\)
\(164\) −14.3603 1.14232i −1.12135 0.0892004i
\(165\) 0 0
\(166\) −20.3626 0.808616i −1.58044 0.0627608i
\(167\) −14.2590 + 3.82068i −1.10339 + 0.295653i −0.764145 0.645045i \(-0.776839\pi\)
−0.339247 + 0.940697i \(0.610172\pi\)
\(168\) 0 0
\(169\) −12.7361 3.41263i −0.979700 0.262510i
\(170\) −0.568333 0.176734i −0.0435892 0.0135549i
\(171\) 0 0
\(172\) 3.45492 16.1872i 0.263435 1.23427i
\(173\) −16.4868 12.6508i −1.25347 0.961822i −0.253487 0.967339i \(-0.581577\pi\)
−0.999985 + 0.00551656i \(0.998244\pi\)
\(174\) 0 0
\(175\) −0.665527 0.384242i −0.0503091 0.0290460i
\(176\) 0.126167 + 0.0776073i 0.00951021 + 0.00584987i
\(177\) 0 0
\(178\) 7.98600 + 1.37570i 0.598576 + 0.103113i
\(179\) 3.24981 1.34611i 0.242902 0.100613i −0.257911 0.966169i \(-0.583034\pi\)
0.500813 + 0.865555i \(0.333034\pi\)
\(180\) 0 0
\(181\) −1.00409 + 2.42408i −0.0746333 + 0.180181i −0.956793 0.290769i \(-0.906089\pi\)
0.882160 + 0.470950i \(0.156089\pi\)
\(182\) −2.29374 + 0.518007i −0.170023 + 0.0383973i
\(183\) 0 0
\(184\) 7.27896 4.31811i 0.536612 0.318335i
\(185\) −3.10788 + 0.832755i −0.228496 + 0.0612253i
\(186\) 0 0
\(187\) 0.00125317 + 0.00951876i 9.16408e−5 + 0.000696081i
\(188\) −2.76954 15.0135i −0.201989 1.09497i
\(189\) 0 0
\(190\) −0.491655 5.37543i −0.0356684 0.389974i
\(191\) 1.31948 + 2.28541i 0.0954744 + 0.165367i 0.909807 0.415033i \(-0.136230\pi\)
−0.814332 + 0.580399i \(0.802897\pi\)
\(192\) 0 0
\(193\) −7.29475 + 12.6349i −0.525088 + 0.909479i 0.474485 + 0.880263i \(0.342634\pi\)
−0.999573 + 0.0292154i \(0.990699\pi\)
\(194\) 13.4073 + 6.18768i 0.962588 + 0.444250i
\(195\) 0 0
\(196\) 10.4926 8.94631i 0.749474 0.639022i
\(197\) −1.64691 0.682173i −0.117338 0.0486028i 0.323242 0.946316i \(-0.395227\pi\)
−0.440580 + 0.897713i \(0.645227\pi\)
\(198\) 0 0
\(199\) −1.50902 1.50902i −0.106971 0.106971i 0.651595 0.758567i \(-0.274100\pi\)
−0.758567 + 0.651595i \(0.774100\pi\)
\(200\) −6.68880 + 0.0791292i −0.472970 + 0.00559528i
\(201\) 0 0
\(202\) −9.17534 9.93420i −0.645575 0.698968i
\(203\) −0.0567631 0.0739751i −0.00398399 0.00519203i
\(204\) 0 0
\(205\) 9.27597 + 7.11770i 0.647862 + 0.497122i
\(206\) −7.59671 + 9.12625i −0.529288 + 0.635856i
\(207\) 0 0
\(208\) −14.8711 + 14.0647i −1.03113 + 0.975213i
\(209\) −0.0754080 + 0.0435368i −0.00521608 + 0.00301150i
\(210\) 0 0
\(211\) −0.0958431 + 0.728001i −0.00659811 + 0.0501176i −0.994427 0.105426i \(-0.966379\pi\)
0.987829 + 0.155543i \(0.0497128\pi\)
\(212\) −10.5864 9.54813i −0.727075 0.655768i
\(213\) 0 0
\(214\) −4.70251 20.8227i −0.321457 1.42341i
\(215\) −9.49927 + 9.49927i −0.647845 + 0.647845i
\(216\) 0 0
\(217\) −0.301152 0.301152i −0.0204435 0.0204435i
\(218\) −14.1826 + 22.4571i −0.960564 + 1.52099i
\(219\) 0 0
\(220\) −0.0516662 0.108555i −0.00348333 0.00731878i
\(221\) −1.31535 0.173169i −0.0884800 0.0116486i
\(222\) 0 0
\(223\) −8.52921 14.7730i −0.571158 0.989275i −0.996447 0.0842175i \(-0.973161\pi\)
0.425289 0.905057i \(-0.360172\pi\)
\(224\) −0.594503 + 1.73934i −0.0397219 + 0.116214i
\(225\) 0 0
\(226\) 6.78984 0.621022i 0.451654 0.0413098i
\(227\) 9.81627 12.7928i 0.651529 0.849089i −0.344438 0.938809i \(-0.611931\pi\)
0.995967 + 0.0897201i \(0.0285973\pi\)
\(228\) 0 0
\(229\) −0.846213 + 0.649322i −0.0559194 + 0.0429084i −0.636343 0.771406i \(-0.719554\pi\)
0.580424 + 0.814315i \(0.302887\pi\)
\(230\) −6.86377 0.272566i −0.452583 0.0179725i
\(231\) 0 0
\(232\) −0.753478 0.301709i −0.0494682 0.0198081i
\(233\) −11.9471 + 11.9471i −0.782679 + 0.782679i −0.980282 0.197603i \(-0.936684\pi\)
0.197603 + 0.980282i \(0.436684\pi\)
\(234\) 0 0
\(235\) −4.74184 + 11.4478i −0.309323 + 0.746773i
\(236\) −8.19168 25.2837i −0.533233 1.64583i
\(237\) 0 0
\(238\) −0.111794 + 0.0411896i −0.00724652 + 0.00266993i
\(239\) −5.55246 3.20572i −0.359159 0.207361i 0.309553 0.950882i \(-0.399821\pi\)
−0.668712 + 0.743522i \(0.733154\pi\)
\(240\) 0 0
\(241\) −11.8239 + 6.82651i −0.761642 + 0.439734i −0.829885 0.557935i \(-0.811594\pi\)
0.0682430 + 0.997669i \(0.478261\pi\)
\(242\) 9.95112 11.9547i 0.639682 0.768477i
\(243\) 0 0
\(244\) −8.07385 12.4555i −0.516876 0.797385i
\(245\) −11.0957 + 1.46078i −0.708879 + 0.0933257i
\(246\) 0 0
\(247\) −3.11418 11.6223i −0.198150 0.739508i
\(248\) −3.59196 0.917064i −0.228090 0.0582336i
\(249\) 0 0
\(250\) 14.2953 + 9.02806i 0.904114 + 0.570985i
\(251\) −6.46764 2.67898i −0.408234 0.169096i 0.169110 0.985597i \(-0.445911\pi\)
−0.577344 + 0.816501i \(0.695911\pi\)
\(252\) 0 0
\(253\) 0.0424042 + 0.102373i 0.00266593 + 0.00643612i
\(254\) 21.3879 15.1020i 1.34200 0.947586i
\(255\) 0 0
\(256\) 3.27397 + 15.6615i 0.204623 + 0.978841i
\(257\) −1.65386 + 2.86456i −0.103165 + 0.178686i −0.912987 0.407989i \(-0.866230\pi\)
0.809822 + 0.586675i \(0.199564\pi\)
\(258\) 0 0
\(259\) −0.392085 + 0.510975i −0.0243630 + 0.0317504i
\(260\) 16.3374 3.01376i 1.01320 0.186905i
\(261\) 0 0
\(262\) −24.5922 + 12.9254i −1.51931 + 0.798533i
\(263\) −5.19980 + 19.4059i −0.320634 + 1.19662i 0.597996 + 0.801499i \(0.295964\pi\)
−0.918629 + 0.395121i \(0.870703\pi\)
\(264\) 0 0
\(265\) 2.99473 + 11.1765i 0.183965 + 0.686566i
\(266\) −0.733127 0.793761i −0.0449509 0.0486686i
\(267\) 0 0
\(268\) −0.871381 + 1.70664i −0.0532281 + 0.104249i
\(269\) 0.922988 0.382314i 0.0562756 0.0233101i −0.354368 0.935106i \(-0.615304\pi\)
0.410644 + 0.911796i \(0.365304\pi\)
\(270\) 0 0
\(271\) 15.2219i 0.924665i −0.886707 0.462332i \(-0.847013\pi\)
0.886707 0.462332i \(-0.152987\pi\)
\(272\) −0.653996 + 0.804848i −0.0396543 + 0.0488011i
\(273\) 0 0
\(274\) −7.52004 + 2.77070i −0.454302 + 0.167384i
\(275\) 0.0114314 0.0868303i 0.000689341 0.00523606i
\(276\) 0 0
\(277\) −31.1275 + 4.09802i −1.87027 + 0.246226i −0.978498 0.206255i \(-0.933872\pi\)
−0.891774 + 0.452481i \(0.850539\pi\)
\(278\) 0.636982 + 0.198082i 0.0382036 + 0.0118801i
\(279\) 0 0
\(280\) 1.17277 0.922140i 0.0700862 0.0551084i
\(281\) 7.00393 26.1390i 0.417820 1.55932i −0.361300 0.932449i \(-0.617667\pi\)
0.779120 0.626875i \(-0.215666\pi\)
\(282\) 0 0
\(283\) 10.3917 7.97381i 0.617721 0.473994i −0.251874 0.967760i \(-0.581047\pi\)
0.869595 + 0.493766i \(0.164380\pi\)
\(284\) −13.1795 + 6.27269i −0.782057 + 0.372216i
\(285\) 0 0
\(286\) −0.154575 0.218914i −0.00914023 0.0129447i
\(287\) 2.34048 0.138154
\(288\) 0 0
\(289\) 16.9328 0.996046
\(290\) 0.379969 + 0.538124i 0.0223126 + 0.0315997i
\(291\) 0 0
\(292\) 11.9134 + 25.0310i 0.697178 + 1.46483i
\(293\) 12.2162 9.37385i 0.713680 0.547626i −0.186867 0.982385i \(-0.559833\pi\)
0.900547 + 0.434759i \(0.143167\pi\)
\(294\) 0 0
\(295\) −5.58304 + 20.8362i −0.325057 + 1.21313i
\(296\) −0.665967 + 5.56661i −0.0387086 + 0.323553i
\(297\) 0 0
\(298\) 21.0260 + 6.53843i 1.21800 + 0.378761i
\(299\) −15.1809 + 1.99861i −0.877936 + 0.115582i
\(300\) 0 0
\(301\) −0.351006 + 2.66616i −0.0202317 + 0.153675i
\(302\) −24.3213 + 8.96100i −1.39954 + 0.515648i
\(303\) 0 0
\(304\) −9.01359 2.68643i −0.516965 0.154078i
\(305\) 12.0474i 0.689833i
\(306\) 0 0
\(307\) 9.36797 3.88034i 0.534658 0.221463i −0.0989838 0.995089i \(-0.531559\pi\)
0.633642 + 0.773626i \(0.281559\pi\)
\(308\) −0.0214336 0.0109437i −0.00122129 0.000623572i
\(309\) 0 0
\(310\) 2.04149 + 2.21034i 0.115949 + 0.125539i
\(311\) 4.41050 + 16.4602i 0.250096 + 0.933372i 0.970753 + 0.240080i \(0.0771737\pi\)
−0.720657 + 0.693292i \(0.756160\pi\)
\(312\) 0 0
\(313\) −3.22504 + 12.0360i −0.182290 + 0.680315i 0.812905 + 0.582397i \(0.197885\pi\)
−0.995194 + 0.0979183i \(0.968782\pi\)
\(314\) 27.4198 14.4115i 1.54739 0.813291i
\(315\) 0 0
\(316\) −5.51964 29.9216i −0.310504 1.68322i
\(317\) 3.22942 4.20866i 0.181382 0.236382i −0.693809 0.720159i \(-0.744069\pi\)
0.875191 + 0.483777i \(0.160735\pi\)
\(318\) 0 0
\(319\) 0.00531320 0.00920273i 0.000297482 0.000515254i
\(320\) 4.68435 12.1118i 0.261863 0.677071i
\(321\) 0 0
\(322\) −1.12325 + 0.793128i −0.0625964 + 0.0441993i
\(323\) −0.233292 0.563218i −0.0129807 0.0313383i
\(324\) 0 0
\(325\) 11.1809 + 4.63130i 0.620207 + 0.256898i
\(326\) −4.16087 2.62776i −0.230449 0.145538i
\(327\) 0 0
\(328\) 17.5215 10.3943i 0.967465 0.573931i
\(329\) 0.641971 + 2.39587i 0.0353930 + 0.132088i
\(330\) 0 0
\(331\) −3.00898 + 0.396139i −0.165388 + 0.0217738i −0.212765 0.977103i \(-0.568247\pi\)
0.0473773 + 0.998877i \(0.484914\pi\)
\(332\) 24.1834 15.6760i 1.32724 0.860334i
\(333\) 0 0
\(334\) 13.3560 16.0452i 0.730810 0.877952i
\(335\) 1.34690 0.777634i 0.0735891 0.0424867i
\(336\) 0 0
\(337\) −8.77985 5.06905i −0.478269 0.276129i 0.241426 0.970419i \(-0.422385\pi\)
−0.719695 + 0.694291i \(0.755718\pi\)
\(338\) 17.4971 6.44668i 0.951718 0.350653i
\(339\) 0 0
\(340\) 0.800732 0.259430i 0.0434258 0.0140696i
\(341\) 0.0185741 0.0448418i 0.00100584 0.00242832i
\(342\) 0 0
\(343\) −3.19247 + 3.19247i −0.172377 + 0.172377i
\(344\) 9.21298 + 21.5185i 0.496731 + 1.16020i
\(345\) 0 0
\(346\) 29.3659 + 1.16615i 1.57872 + 0.0626925i
\(347\) 9.69972 7.44286i 0.520708 0.399554i −0.314693 0.949193i \(-0.601902\pi\)
0.835402 + 0.549640i \(0.185235\pi\)
\(348\) 0 0
\(349\) 3.98704 5.19601i 0.213421 0.278136i −0.674359 0.738404i \(-0.735580\pi\)
0.887780 + 0.460268i \(0.152247\pi\)
\(350\) 1.08228 0.0989894i 0.0578505 0.00529120i
\(351\) 0 0
\(352\) −0.209060 + 0.0132615i −0.0111430 + 0.000706842i
\(353\) 14.1478 + 24.5047i 0.753010 + 1.30425i 0.946358 + 0.323121i \(0.104732\pi\)
−0.193348 + 0.981130i \(0.561934\pi\)
\(354\) 0 0
\(355\) 11.7453 + 1.54630i 0.623375 + 0.0820688i
\(356\) −10.3480 + 4.92508i −0.548443 + 0.261029i
\(357\) 0 0
\(358\) −2.65628 + 4.20603i −0.140389 + 0.222296i
\(359\) 2.97235 + 2.97235i 0.156875 + 0.156875i 0.781180 0.624305i \(-0.214618\pi\)
−0.624305 + 0.781180i \(0.714618\pi\)
\(360\) 0 0
\(361\) −9.52553 + 9.52553i −0.501344 + 0.501344i
\(362\) −0.817405 3.61948i −0.0429619 0.190235i
\(363\) 0 0
\(364\) 2.22729 2.46948i 0.116742 0.129436i
\(365\) 2.93680 22.3072i 0.153719 1.16761i
\(366\) 0 0
\(367\) 3.67285 2.12052i 0.191721 0.110690i −0.401067 0.916049i \(-0.631361\pi\)
0.592788 + 0.805358i \(0.298027\pi\)
\(368\) −4.88663 + 10.9261i −0.254733 + 0.569562i
\(369\) 0 0
\(370\) 2.91108 3.49720i 0.151340 0.181811i
\(371\) 1.83756 + 1.41001i 0.0954011 + 0.0732039i
\(372\) 0 0
\(373\) 5.25913 + 6.85383i 0.272307 + 0.354878i 0.909410 0.415901i \(-0.136534\pi\)
−0.637102 + 0.770779i \(0.719867\pi\)
\(374\) −0.00921238 0.00997430i −0.000476361 0.000515759i
\(375\) 0 0
\(376\) 15.4463 + 15.0851i 0.796583 + 0.777956i
\(377\) 1.03832 + 1.03832i 0.0534763 + 0.0534763i
\(378\) 0 0
\(379\) 6.69444 + 2.77293i 0.343870 + 0.142436i 0.547933 0.836522i \(-0.315415\pi\)
−0.204063 + 0.978958i \(0.565415\pi\)
\(380\) 4.95283 + 5.80890i 0.254075 + 0.297990i
\(381\) 0 0
\(382\) −3.38859 1.56389i −0.173375 0.0800154i
\(383\) −4.73268 + 8.19724i −0.241829 + 0.418859i −0.961235 0.275730i \(-0.911080\pi\)
0.719407 + 0.694589i \(0.244414\pi\)
\(384\) 0 0
\(385\) 0.00976628 + 0.0169157i 0.000497736 + 0.000862103i
\(386\) −1.87929 20.5469i −0.0956534 1.04581i
\(387\) 0 0
\(388\) −20.5362 + 3.78831i −1.04257 + 0.192322i
\(389\) 2.49720 + 18.9681i 0.126613 + 0.961720i 0.930334 + 0.366714i \(0.119517\pi\)
−0.803721 + 0.595007i \(0.797149\pi\)
\(390\) 0 0
\(391\) −0.749355 + 0.200789i −0.0378965 + 0.0101543i
\(392\) −4.82389 + 18.8943i −0.243643 + 0.954305i
\(393\) 0 0
\(394\) 2.45905 0.555341i 0.123885 0.0279777i
\(395\) −9.45040 + 22.8153i −0.475501 + 1.14796i
\(396\) 0 0
\(397\) 5.82577 2.41311i 0.292387 0.121111i −0.231668 0.972795i \(-0.574418\pi\)
0.524056 + 0.851684i \(0.324418\pi\)
\(398\) 2.97422 + 0.512352i 0.149084 + 0.0256819i
\(399\) 0 0
\(400\) 7.66268 5.54761i 0.383134 0.277381i
\(401\) 27.0472 + 15.6157i 1.35067 + 0.779812i 0.988344 0.152239i \(-0.0486482\pi\)
0.362329 + 0.932050i \(0.381982\pi\)
\(402\) 0 0
\(403\) 5.32102 + 4.08297i 0.265059 + 0.203387i
\(404\) 18.7033 + 3.99194i 0.930526 + 0.198607i
\(405\) 0 0
\(406\) 0.125918 + 0.0391567i 0.00624923 + 0.00194332i
\(407\) −0.0708997 0.0189975i −0.00351437 0.000941672i
\(408\) 0 0
\(409\) 22.9935 6.16110i 1.13696 0.304647i 0.359230 0.933249i \(-0.383039\pi\)
0.777727 + 0.628602i \(0.216373\pi\)
\(410\) −16.5221 0.656108i −0.815969 0.0324029i
\(411\) 0 0
\(412\) 1.33161 16.7399i 0.0656038 0.824715i
\(413\) 1.65244 + 3.98935i 0.0813113 + 0.196303i
\(414\) 0 0
\(415\) −23.3910 −1.14822
\(416\) 5.70692 28.3789i 0.279805 1.39139i
\(417\) 0 0
\(418\) 0.0516010 0.111808i 0.00252389 0.00546869i
\(419\) 13.9495 + 1.83648i 0.681477 + 0.0897181i 0.463314 0.886194i \(-0.346660\pi\)
0.218163 + 0.975912i \(0.429994\pi\)
\(420\) 0 0
\(421\) −0.559488 4.24973i −0.0272678 0.207119i 0.972388 0.233372i \(-0.0749759\pi\)
−0.999655 + 0.0262526i \(0.991643\pi\)
\(422\) −0.483123 0.919203i −0.0235181 0.0447461i
\(423\) 0 0
\(424\) 20.0185 + 2.39494i 0.972185 + 0.116308i
\(425\) 0.592271 + 0.158699i 0.0287294 + 0.00769802i
\(426\) 0 0
\(427\) 1.46809 + 1.91325i 0.0710459 + 0.0925888i
\(428\) 22.4181 + 20.2195i 1.08362 + 0.977346i
\(429\) 0 0
\(430\) 3.22526 18.7228i 0.155536 0.902892i
\(431\) 3.33540i 0.160661i 0.996768 + 0.0803304i \(0.0255975\pi\)
−0.996768 + 0.0803304i \(0.974402\pi\)
\(432\) 0 0
\(433\) 2.24064i 0.107678i −0.998550 0.0538392i \(-0.982854\pi\)
0.998550 0.0538392i \(-0.0171458\pi\)
\(434\) 0.593561 + 0.102249i 0.0284918 + 0.00490812i
\(435\) 0 0
\(436\) −1.93434 37.5125i −0.0926382 1.79652i
\(437\) −4.28317 5.58194i −0.204892 0.267020i
\(438\) 0 0
\(439\) −5.46271 1.46373i −0.260721 0.0698599i 0.126091 0.992019i \(-0.459757\pi\)
−0.386812 + 0.922159i \(0.626424\pi\)
\(440\) 0.148238 + 0.0832628i 0.00706697 + 0.00396940i
\(441\) 0 0
\(442\) 1.66081 0.872906i 0.0789968 0.0415199i
\(443\) 1.79988 + 13.6714i 0.0855149 + 0.649550i 0.979499 + 0.201451i \(0.0645656\pi\)
−0.893984 + 0.448099i \(0.852101\pi\)
\(444\) 0 0
\(445\) 9.22194 + 1.21409i 0.437162 + 0.0575534i
\(446\) 21.9040 + 10.1091i 1.03719 + 0.478678i
\(447\) 0 0
\(448\) −0.732015 2.49431i −0.0345845 0.117845i
\(449\) −11.3295 −0.534672 −0.267336 0.963603i \(-0.586143\pi\)
−0.267336 + 0.963603i \(0.586143\pi\)
\(450\) 0 0
\(451\) 0.102073 + 0.246427i 0.00480644 + 0.0116038i
\(452\) −7.33737 + 6.25605i −0.345121 + 0.294260i
\(453\) 0 0
\(454\) −0.904861 + 22.7862i −0.0424672 + 1.06941i
\(455\) −2.60714 + 0.698580i −0.122224 + 0.0327499i
\(456\) 0 0
\(457\) −30.1863 8.08840i −1.41206 0.378359i −0.529398 0.848374i \(-0.677582\pi\)
−0.882659 + 0.470014i \(0.844249\pi\)
\(458\) 0.447921 1.44040i 0.0209300 0.0673056i
\(459\) 0 0
\(460\) 8.15169 5.28404i 0.380075 0.246370i
\(461\) 15.5771 + 11.9527i 0.725498 + 0.556694i 0.904149 0.427218i \(-0.140506\pi\)
−0.178650 + 0.983913i \(0.557173\pi\)
\(462\) 0 0
\(463\) −13.2606 7.65604i −0.616274 0.355806i 0.159143 0.987256i \(-0.449127\pi\)
−0.775417 + 0.631449i \(0.782460\pi\)
\(464\) 1.11656 0.266079i 0.0518352 0.0123524i
\(465\) 0 0
\(466\) 4.05636 23.5473i 0.187907 1.09081i
\(467\) 15.4177 6.38624i 0.713448 0.295520i 0.00371732 0.999993i \(-0.498817\pi\)
0.709730 + 0.704473i \(0.248817\pi\)
\(468\) 0 0
\(469\) 0.119140 0.287629i 0.00550137 0.0132815i
\(470\) −3.86022 17.0931i −0.178059 0.788445i
\(471\) 0 0
\(472\) 30.0878 + 22.5268i 1.38490 + 1.03688i
\(473\) −0.296025 + 0.0793197i −0.0136112 + 0.00364712i
\(474\) 0 0
\(475\) 0.725854 + 5.51341i 0.0333045 + 0.252973i
\(476\) 0.0955505 0.138777i 0.00437955 0.00636083i
\(477\) 0 0
\(478\) 9.02944 0.825864i 0.412997 0.0377741i
\(479\) −11.9576 20.7111i −0.546356 0.946316i −0.998520 0.0543816i \(-0.982681\pi\)
0.452164 0.891935i \(-0.350652\pi\)
\(480\) 0 0
\(481\) 5.07144 8.78399i 0.231238 0.400515i
\(482\) 8.09097 17.5313i 0.368534 0.798528i
\(483\) 0 0
\(484\) −1.74431 + 21.9280i −0.0792869 + 0.996727i
\(485\) 15.6589 + 6.48612i 0.711033 + 0.294520i
\(486\) 0 0
\(487\) 5.04460 + 5.04460i 0.228593 + 0.228593i 0.812105 0.583512i \(-0.198322\pi\)
−0.583512 + 0.812105i \(0.698322\pi\)
\(488\) 19.4876 + 7.80323i 0.882160 + 0.353236i
\(489\) 0 0
\(490\) 11.6267 10.7386i 0.525241 0.485119i
\(491\) −15.5178 20.2232i −0.700309 0.912661i 0.298823 0.954308i \(-0.403406\pi\)
−0.999132 + 0.0416479i \(0.986739\pi\)
\(492\) 0 0
\(493\) 0.0590238 + 0.0452906i 0.00265830 + 0.00203978i
\(494\) 13.0782 + 10.8863i 0.588415 + 0.489798i
\(495\) 0 0
\(496\) 4.89768 1.87061i 0.219912 0.0839926i
\(497\) 2.05370 1.18571i 0.0921212 0.0531862i
\(498\) 0 0
\(499\) 4.33075 32.8953i 0.193871 1.47260i −0.567012 0.823709i \(-0.691901\pi\)
0.760884 0.648888i \(-0.224766\pi\)
\(500\) −23.8790 + 1.23133i −1.06790 + 0.0550666i
\(501\) 0 0
\(502\) 9.65703 2.18090i 0.431014 0.0973382i
\(503\) 13.8468 13.8468i 0.617399 0.617399i −0.327465 0.944863i \(-0.606194\pi\)
0.944863 + 0.327465i \(0.106194\pi\)
\(504\) 0 0
\(505\) −10.9758 10.9758i −0.488417 0.488417i
\(506\) −0.132495 0.0836760i −0.00589012 0.00371985i
\(507\) 0 0
\(508\) −12.3893 + 34.8932i −0.549688 + 1.54813i
\(509\) 14.6823 + 1.93296i 0.650781 + 0.0856770i 0.448687 0.893689i \(-0.351892\pi\)
0.202094 + 0.979366i \(0.435225\pi\)
\(510\) 0 0
\(511\) −2.25195 3.90049i −0.0996203 0.172547i
\(512\) −16.5576 15.4222i −0.731751 0.681573i
\(513\) 0 0
\(514\) −0.426070 4.65837i −0.0187931 0.205472i
\(515\) −8.29714 + 10.8130i −0.365616 + 0.476479i
\(516\) 0 0
\(517\) −0.224261 + 0.172081i −0.00986298 + 0.00756813i
\(518\) 0.0361423 0.910135i 0.00158800 0.0399890i
\(519\) 0 0
\(520\) −16.4153 + 16.8084i −0.719860 + 0.737096i
\(521\) −27.2589 + 27.2589i −1.19423 + 1.19423i −0.218367 + 0.975867i \(0.570073\pi\)
−0.975867 + 0.218367i \(0.929927\pi\)
\(522\) 0 0
\(523\) −16.0324 + 38.7056i −0.701046 + 1.69248i 0.0201988 + 0.999796i \(0.493570\pi\)
−0.721245 + 0.692680i \(0.756430\pi\)
\(524\) 17.8666 34.9924i 0.780504 1.52865i
\(525\) 0 0
\(526\) −9.82276 26.6603i −0.428293 1.16244i
\(527\) 0.294288 + 0.169907i 0.0128194 + 0.00740128i
\(528\) 0 0
\(529\) 12.1645 7.02317i 0.528890 0.305355i
\(530\) −12.5766 10.4688i −0.546291 0.454734i
\(531\) 0 0
\(532\) 1.49443 + 0.318964i 0.0647918 + 0.0138288i
\(533\) −36.5428 + 4.81095i −1.58284 + 0.208385i
\(534\) 0 0
\(535\) −6.34176 23.6678i −0.274178 1.02325i
\(536\) −0.385477 2.68239i −0.0166501 0.115862i
\(537\) 0 0
\(538\) −0.754419 + 1.19457i −0.0325253 + 0.0515015i
\(539\) −0.235875 0.0977025i −0.0101598 0.00420835i
\(540\) 0 0
\(541\) −16.2506 39.2325i −0.698669 1.68674i −0.726540 0.687124i \(-0.758873\pi\)
0.0278709 0.999612i \(-0.491127\pi\)
\(542\) 12.4168 + 17.5851i 0.533348 + 0.755344i
\(543\) 0 0
\(544\) 0.0989958 1.46328i 0.00424441 0.0627375i
\(545\) −15.2434 + 26.4024i −0.652956 + 1.13095i
\(546\) 0 0
\(547\) −27.4373 + 35.7571i −1.17314 + 1.52886i −0.374305 + 0.927305i \(0.622119\pi\)
−0.798831 + 0.601556i \(0.794548\pi\)
\(548\) 6.42739 9.33510i 0.274565 0.398776i
\(549\) 0 0
\(550\) 0.0576232 + 0.109635i 0.00245706 + 0.00467487i
\(551\) −0.174635 + 0.651747i −0.00743971 + 0.0277654i
\(552\) 0 0
\(553\) 1.27944 + 4.77493i 0.0544072 + 0.203051i
\(554\) 32.6172 30.1256i 1.38577 1.27991i
\(555\) 0 0
\(556\) −0.897451 + 0.290766i −0.0380604 + 0.0123312i
\(557\) 29.7260 12.3129i 1.25953 0.521716i 0.349767 0.936837i \(-0.386261\pi\)
0.909766 + 0.415121i \(0.136261\pi\)
\(558\) 0 0
\(559\) 42.3492i 1.79118i
\(560\) −0.602627 + 2.02195i −0.0254656 + 0.0854430i
\(561\) 0 0
\(562\) 13.2309 + 35.9103i 0.558111 + 1.51479i
\(563\) −0.209242 + 1.58935i −0.00881851 + 0.0669833i −0.995288 0.0969601i \(-0.969088\pi\)
0.986470 + 0.163943i \(0.0524214\pi\)
\(564\) 0 0
\(565\) 7.75910 1.02150i 0.326428 0.0429750i
\(566\) −5.50056 + 17.6884i −0.231206 + 0.743501i
\(567\) 0 0
\(568\) 10.1088 17.9973i 0.424155 0.755150i
\(569\) −1.05096 + 3.92222i −0.0440584 + 0.164428i −0.984450 0.175666i \(-0.943792\pi\)
0.940391 + 0.340094i \(0.110459\pi\)
\(570\) 0 0
\(571\) −9.27875 + 7.11984i −0.388304 + 0.297956i −0.784403 0.620252i \(-0.787030\pi\)
0.396099 + 0.918208i \(0.370364\pi\)
\(572\) 0.357146 + 0.126810i 0.0149330 + 0.00530218i
\(573\) 0 0
\(574\) −2.70383 + 1.90918i −0.112856 + 0.0796876i
\(575\) 7.07676 0.295121
\(576\) 0 0
\(577\) 31.1072 1.29501 0.647505 0.762061i \(-0.275812\pi\)
0.647505 + 0.762061i \(0.275812\pi\)
\(578\) −19.5616 + 13.8124i −0.813654 + 0.574521i
\(579\) 0 0
\(580\) −0.877918 0.311717i −0.0364535 0.0129434i
\(581\) −3.71473 + 2.85041i −0.154113 + 0.118255i
\(582\) 0 0
\(583\) −0.0683184 + 0.254968i −0.00282946 + 0.0105597i
\(584\) −34.1813 19.1991i −1.41443 0.794463i
\(585\) 0 0
\(586\) −6.46634 + 20.7942i −0.267122 + 0.858999i
\(587\) −7.79166 + 1.02579i −0.321596 + 0.0423390i −0.289596 0.957149i \(-0.593521\pi\)
−0.0320001 + 0.999488i \(0.510188\pi\)
\(588\) 0 0
\(589\) −0.402267 + 3.05552i −0.0165751 + 0.125901i
\(590\) −10.5467 28.6252i −0.434202 1.17848i
\(591\) 0 0
\(592\) −3.77144 6.97406i −0.155005 0.286632i
\(593\) 30.5081i 1.25282i 0.779495 + 0.626408i \(0.215476\pi\)
−0.779495 + 0.626408i \(0.784524\pi\)
\(594\) 0 0
\(595\) −0.126342 + 0.0523327i −0.00517953 + 0.00214543i
\(596\) −29.6238 + 9.59784i −1.21344 + 0.393143i
\(597\) 0 0
\(598\) 15.9074 14.6923i 0.650504 0.600813i
\(599\) −4.85719 18.1273i −0.198459 0.740660i −0.991344 0.131289i \(-0.958088\pi\)
0.792885 0.609371i \(-0.208578\pi\)
\(600\) 0 0
\(601\) 6.98707 26.0761i 0.285008 1.06367i −0.663825 0.747888i \(-0.731068\pi\)
0.948833 0.315778i \(-0.102265\pi\)
\(602\) −1.76934 3.36640i −0.0721130 0.137204i
\(603\) 0 0
\(604\) 20.7875 30.1916i 0.845831 1.22848i
\(605\) 10.8686 14.1643i 0.441873 0.575860i
\(606\) 0 0
\(607\) −13.4843 + 23.3554i −0.547309 + 0.947967i 0.451148 + 0.892449i \(0.351015\pi\)
−0.998458 + 0.0555185i \(0.982319\pi\)
\(608\) 12.6043 4.24908i 0.511173 0.172323i
\(609\) 0 0
\(610\) −9.82733 13.9178i −0.397897 0.563513i
\(611\) −14.9481 36.0880i −0.604737 1.45996i
\(612\) 0 0
\(613\) 22.0470 + 9.13217i 0.890470 + 0.368845i 0.780548 0.625095i \(-0.214940\pi\)
0.109922 + 0.993940i \(0.464940\pi\)
\(614\) −7.65706 + 12.1244i −0.309014 + 0.489301i
\(615\) 0 0
\(616\) 0.0336881 0.00484119i 0.00135733 0.000195057i
\(617\) −4.78222 17.8475i −0.192525 0.718513i −0.992894 0.119005i \(-0.962030\pi\)
0.800369 0.599508i \(-0.204637\pi\)
\(618\) 0 0
\(619\) −18.5503 + 2.44220i −0.745601 + 0.0981602i −0.493748 0.869605i \(-0.664373\pi\)
−0.251853 + 0.967765i \(0.581040\pi\)
\(620\) −4.16145 0.888199i −0.167128 0.0356709i
\(621\) 0 0
\(622\) −18.5222 15.4179i −0.742671 0.618201i
\(623\) 1.61249 0.930970i 0.0646030 0.0372985i
\(624\) 0 0
\(625\) 6.56589 + 3.79082i 0.262636 + 0.151633i
\(626\) −6.09231 16.5353i −0.243498 0.660884i
\(627\) 0 0
\(628\) −19.9209 + 39.0158i −0.794929 + 1.55690i
\(629\) 0.196659 0.474778i 0.00784132 0.0189306i
\(630\) 0 0
\(631\) −29.2372 + 29.2372i −1.16391 + 1.16391i −0.180304 + 0.983611i \(0.557708\pi\)
−0.983611 + 0.180304i \(0.942292\pi\)
\(632\) 30.7843 + 30.0644i 1.22453 + 1.19590i
\(633\) 0 0
\(634\) −0.297687 + 7.49636i −0.0118227 + 0.297718i
\(635\) 23.8424 18.2949i 0.946155 0.726010i
\(636\) 0 0
\(637\) 21.4770 27.9894i 0.850951 1.10898i
\(638\) 0.00136880 + 0.0149655i 5.41913e−5 + 0.000592491i
\(639\) 0 0
\(640\) 4.46827 + 17.8133i 0.176624 + 0.704131i
\(641\) 15.6462 + 27.1001i 0.617989 + 1.07039i 0.989852 + 0.142100i \(0.0453856\pi\)
−0.371864 + 0.928287i \(0.621281\pi\)
\(642\) 0 0
\(643\) 15.3439 + 2.02006i 0.605104 + 0.0796634i 0.426852 0.904321i \(-0.359623\pi\)
0.178252 + 0.983985i \(0.442956\pi\)
\(644\) 0.650663 1.83252i 0.0256397 0.0722114i
\(645\) 0 0
\(646\) 0.728940 + 0.460355i 0.0286797 + 0.0181124i
\(647\) 20.0214 + 20.0214i 0.787122 + 0.787122i 0.981021 0.193899i \(-0.0621134\pi\)
−0.193899 + 0.981021i \(0.562113\pi\)
\(648\) 0 0
\(649\) −0.347968 + 0.347968i −0.0136589 + 0.0136589i
\(650\) −16.6946 + 3.77023i −0.654817 + 0.147881i
\(651\) 0 0
\(652\) 6.95035 0.358396i 0.272197 0.0140359i
\(653\) −4.94198 + 37.5381i −0.193395 + 1.46898i 0.569251 + 0.822164i \(0.307233\pi\)
−0.762646 + 0.646816i \(0.776100\pi\)
\(654\) 0 0
\(655\) −27.6165 + 15.9444i −1.07907 + 0.622999i
\(656\) −11.7628 + 26.3007i −0.459262 + 1.02687i
\(657\) 0 0
\(658\) −2.69600 2.24415i −0.105101 0.0874862i
\(659\) 16.1814 + 12.4164i 0.630337 + 0.483674i 0.873832 0.486228i \(-0.161627\pi\)
−0.243495 + 0.969902i \(0.578294\pi\)
\(660\) 0 0
\(661\) 17.4638 + 22.7592i 0.679261 + 0.885231i 0.998039 0.0625990i \(-0.0199389\pi\)
−0.318777 + 0.947830i \(0.603272\pi\)
\(662\) 3.15297 2.91212i 0.122544 0.113183i
\(663\) 0 0
\(664\) −15.1506 + 37.8366i −0.587957 + 1.46835i
\(665\) −0.876987 0.876987i −0.0340081 0.0340081i
\(666\) 0 0
\(667\) 0.793292 + 0.328592i 0.0307164 + 0.0127232i
\(668\) −2.34115 + 29.4310i −0.0905819 + 1.13872i
\(669\) 0 0
\(670\) −0.921673 + 1.99706i −0.0356073 + 0.0771530i
\(671\) −0.137418 + 0.238015i −0.00530496 + 0.00918846i
\(672\) 0 0
\(673\) −7.10196 12.3009i −0.273760 0.474167i 0.696061 0.717982i \(-0.254934\pi\)
−0.969822 + 0.243816i \(0.921601\pi\)
\(674\) 14.2778 1.30590i 0.549962 0.0503014i
\(675\) 0 0
\(676\) −14.9548 + 21.7203i −0.575186 + 0.835396i
\(677\) −0.895883 6.80491i −0.0344316 0.261534i −0.999999 0.00138105i \(-0.999560\pi\)
0.965567 0.260153i \(-0.0837729\pi\)
\(678\) 0 0
\(679\) 3.27719 0.878120i 0.125767 0.0336991i
\(680\) −0.713422 + 0.952880i −0.0273585 + 0.0365413i
\(681\) 0 0
\(682\) 0.0151207 + 0.0669547i 0.000579003 + 0.00256383i
\(683\) 8.76398 21.1581i 0.335344 0.809593i −0.662806 0.748791i \(-0.730634\pi\)
0.998150 0.0608011i \(-0.0193656\pi\)
\(684\) 0 0
\(685\) −8.49867 + 3.52026i −0.324717 + 0.134502i
\(686\) 1.08393 6.29226i 0.0413846 0.240240i
\(687\) 0 0
\(688\) −28.1964 17.3440i −1.07498 0.661235i
\(689\) −31.5888 18.2378i −1.20344 0.694804i
\(690\) 0 0
\(691\) 36.1977 + 27.7755i 1.37703 + 1.05663i 0.990960 + 0.134157i \(0.0428326\pi\)
0.386065 + 0.922472i \(0.373834\pi\)
\(692\) −34.8762 + 22.6072i −1.32579 + 0.859397i
\(693\) 0 0
\(694\) −5.13429 + 16.5106i −0.194895 + 0.626735i
\(695\) 0.739587 + 0.198172i 0.0280541 + 0.00751708i
\(696\) 0 0
\(697\) −1.80381 + 0.483329i −0.0683241 + 0.0183074i
\(698\) −0.367524 + 9.25499i −0.0139110 + 0.350306i
\(699\) 0 0
\(700\) −1.16956 + 0.997199i −0.0442052 + 0.0376906i
\(701\) −10.5425 25.4518i −0.398183 0.961299i −0.988097 0.153833i \(-0.950838\pi\)
0.589914 0.807466i \(-0.299162\pi\)
\(702\) 0 0
\(703\) 4.66068 0.175781
\(704\) 0.230699 0.185855i 0.00869479 0.00700469i
\(705\) 0 0
\(706\) −36.3332 16.7683i −1.36742 0.631085i
\(707\) −3.08058 0.405566i −0.115857 0.0152529i
\(708\) 0 0
\(709\) 0.482385 + 3.66408i 0.0181164 + 0.137607i 0.998113 0.0614078i \(-0.0195590\pi\)
−0.979996 + 0.199015i \(0.936226\pi\)
\(710\) −14.8301 + 7.79452i −0.556562 + 0.292523i
\(711\) 0 0
\(712\) 7.93703 14.1308i 0.297453 0.529573i
\(713\) 3.78829 + 1.01507i 0.141873 + 0.0380147i
\(714\) 0 0
\(715\) −0.187255 0.244036i −0.00700296 0.00912643i
\(716\) −0.362287 7.02580i −0.0135393 0.262566i
\(717\) 0 0
\(718\) −5.85842 1.00919i −0.218634 0.0376628i
\(719\) 2.19382i 0.0818157i −0.999163 0.0409078i \(-0.986975\pi\)
0.999163 0.0409078i \(-0.0130250\pi\)
\(720\) 0 0
\(721\) 2.72831i 0.101607i
\(722\) 3.23418 18.7745i 0.120364 0.698716i
\(723\) 0 0
\(724\) 3.89679 + 3.51462i 0.144823 + 0.130620i
\(725\) −0.413141 0.538416i −0.0153437 0.0199963i
\(726\) 0 0
\(727\) 35.1358 + 9.41461i 1.30311 + 0.349168i 0.842627 0.538498i \(-0.181008\pi\)
0.460487 + 0.887666i \(0.347675\pi\)
\(728\) −0.558666 + 4.66971i −0.0207055 + 0.173071i
\(729\) 0 0
\(730\) 14.8037 + 28.1659i 0.547910 + 1.04247i
\(731\) −0.280064 2.12730i −0.0103585 0.0786809i
\(732\) 0 0
\(733\) −7.60399 1.00108i −0.280860 0.0369759i −0.0112196 0.999937i \(-0.503571\pi\)
−0.269640 + 0.962961i \(0.586905\pi\)
\(734\) −2.51330 + 5.44575i −0.0927676 + 0.201006i
\(735\) 0 0
\(736\) −3.26738 16.6085i −0.120437 0.612197i
\(737\) 0.0354801 0.00130693
\(738\) 0 0
\(739\) −8.41240 20.3093i −0.309455 0.747091i −0.999723 0.0235370i \(-0.992507\pi\)
0.690268 0.723554i \(-0.257493\pi\)
\(740\) −0.510277 + 6.41477i −0.0187582 + 0.235812i
\(741\) 0 0
\(742\) −3.27301 0.129974i −0.120156 0.00477150i
\(743\) −36.6542 + 9.82146i −1.34471 + 0.360314i −0.858180 0.513349i \(-0.828405\pi\)
−0.486531 + 0.873663i \(0.661738\pi\)
\(744\) 0 0
\(745\) 24.4129 + 6.54141i 0.894418 + 0.239659i
\(746\) −11.6664 3.62789i −0.427138 0.132827i
\(747\) 0 0
\(748\) 0.0187788 + 0.00400806i 0.000686622 + 0.000146549i
\(749\) −3.89128 2.98588i −0.142184 0.109102i
\(750\) 0 0
\(751\) 0.408583 + 0.235896i 0.0149094 + 0.00860796i 0.507436 0.861689i \(-0.330593\pi\)
−0.492527 + 0.870297i \(0.663927\pi\)
\(752\) −30.1496 4.82718i −1.09944 0.176029i
\(753\) 0 0
\(754\) −2.04650 0.352538i −0.0745292 0.0128387i
\(755\) −27.4864 + 11.3852i −1.00033 + 0.414351i
\(756\) 0 0
\(757\) 14.1627 34.1918i 0.514752 1.24272i −0.426338 0.904564i \(-0.640197\pi\)
0.941090 0.338157i \(-0.109803\pi\)
\(758\) −9.99568 + 2.25738i −0.363060 + 0.0819917i
\(759\) 0 0
\(760\) −10.4602 2.67059i −0.379431 0.0968725i
\(761\) 20.0598 5.37501i 0.727168 0.194844i 0.123800 0.992307i \(-0.460492\pi\)
0.603368 + 0.797463i \(0.293825\pi\)
\(762\) 0 0
\(763\) 0.796566 + 6.05052i 0.0288376 + 0.219044i
\(764\) 5.19036 0.957465i 0.187781 0.0346399i
\(765\) 0 0
\(766\) −1.21924 13.3304i −0.0440530 0.481647i
\(767\) −34.0004 58.8905i −1.22768 2.12641i
\(768\) 0 0
\(769\) −10.4249 + 18.0564i −0.375931 + 0.651132i −0.990466 0.137758i \(-0.956010\pi\)
0.614535 + 0.788890i \(0.289344\pi\)
\(770\) −0.0250810 0.0115753i −0.000903855 0.000417144i
\(771\) 0 0
\(772\) 18.9316 + 22.2038i 0.681363 + 0.799133i
\(773\) −34.6918 14.3698i −1.24778 0.516846i −0.341641 0.939831i \(-0.610983\pi\)
−0.906137 + 0.422984i \(0.860983\pi\)
\(774\) 0 0
\(775\) −2.19189 2.19189i −0.0787349 0.0787349i
\(776\) 20.6342 21.1282i 0.740724 0.758460i
\(777\) 0 0
\(778\) −18.3576 19.8758i −0.658150 0.712583i
\(779\) −10.3102 13.4366i −0.369402 0.481415i
\(780\) 0 0
\(781\) 0.214408 + 0.164521i 0.00767212 + 0.00588703i
\(782\) 0.701903 0.843226i 0.0251000 0.0301537i
\(783\) 0 0
\(784\) −9.83967 25.7625i −0.351417 0.920091i
\(785\) 30.7919 17.7777i 1.09901 0.634513i
\(786\) 0 0
\(787\) 4.61183 35.0303i 0.164394 1.24870i −0.687967 0.725742i \(-0.741497\pi\)
0.852361 0.522954i \(-0.175170\pi\)
\(788\) −2.38781 + 2.64746i −0.0850624 + 0.0943119i
\(789\) 0 0
\(790\) −7.69336 34.0662i −0.273717 1.21202i
\(791\) 1.10775 1.10775i 0.0393869 0.0393869i
\(792\) 0 0
\(793\) −26.8546 26.8546i −0.953636 0.953636i
\(794\) −4.76179 + 7.53995i −0.168989 + 0.267583i
\(795\) 0 0
\(796\) −3.85390 + 1.83424i −0.136598 + 0.0650130i
\(797\) 51.9963 + 6.84544i 1.84180 + 0.242478i 0.969256 0.246053i \(-0.0791336\pi\)
0.872547 + 0.488531i \(0.162467\pi\)
\(798\) 0 0
\(799\) −0.989535 1.71392i −0.0350072 0.0606343i
\(800\) −4.32699 + 12.6595i −0.152982 + 0.447580i
\(801\) 0 0
\(802\) −43.9843 + 4.02296i −1.55314 + 0.142056i
\(803\) 0.312466 0.407214i 0.0110267 0.0143703i
\(804\) 0 0
\(805\) −1.25215 + 0.960811i −0.0441326 + 0.0338641i
\(806\) −9.47767 0.376367i −0.333837 0.0132570i
\(807\) 0 0
\(808\) −24.8633 + 10.6450i −0.874688 + 0.374490i
\(809\) −0.546406 + 0.546406i −0.0192106 + 0.0192106i −0.716647 0.697436i \(-0.754324\pi\)
0.697436 + 0.716647i \(0.254324\pi\)
\(810\) 0 0
\(811\) −12.1836 + 29.4138i −0.427824 + 1.03286i 0.552152 + 0.833743i \(0.313807\pi\)
−0.979976 + 0.199115i \(0.936193\pi\)
\(812\) −0.177408 + 0.0574786i −0.00622580 + 0.00201710i
\(813\) 0 0
\(814\) 0.0974034 0.0358875i 0.00341399 0.00125786i
\(815\) −4.89185 2.82431i −0.171354 0.0989313i
\(816\) 0 0
\(817\) 16.8525 9.72980i 0.589595 0.340403i
\(818\) −21.5375 + 25.8739i −0.753041 + 0.904660i
\(819\) 0 0
\(820\) 19.6223 12.7195i 0.685242 0.444183i
\(821\) −14.3182 + 1.88503i −0.499709 + 0.0657879i −0.376168 0.926552i \(-0.622758\pi\)
−0.123541 + 0.992339i \(0.539425\pi\)
\(822\) 0 0
\(823\) 0.00325332 + 0.0121416i 0.000113404 + 0.000423228i 0.965983 0.258607i \(-0.0832636\pi\)
−0.965869 + 0.259031i \(0.916597\pi\)
\(824\) 12.1167 + 20.4249i 0.422106 + 0.711537i
\(825\) 0 0
\(826\) −5.16317 3.26075i −0.179650 0.113456i
\(827\) −41.3829 17.1413i −1.43902 0.596063i −0.479462 0.877563i \(-0.659168\pi\)
−0.959561 + 0.281500i \(0.909168\pi\)
\(828\) 0 0
\(829\) −1.57622 3.80533i −0.0547444 0.132165i 0.894141 0.447786i \(-0.147787\pi\)
−0.948885 + 0.315621i \(0.897787\pi\)
\(830\) 27.0224 19.0805i 0.937962 0.662295i
\(831\) 0 0
\(832\) 16.5564 + 37.4400i 0.573989 + 1.29800i
\(833\) 0.893739 1.54800i 0.0309662 0.0536351i
\(834\) 0 0
\(835\) 14.5875 19.0108i 0.504821 0.657895i
\(836\) 0.0315919 + 0.171258i 0.00109263 + 0.00592307i
\(837\) 0 0
\(838\) −17.6132 + 9.25729i −0.608437 + 0.319788i
\(839\) −5.19361 + 19.3828i −0.179303 + 0.669170i 0.816475 + 0.577381i \(0.195925\pi\)
−0.995778 + 0.0917889i \(0.970742\pi\)
\(840\) 0 0
\(841\) 7.48444 + 27.9323i 0.258084 + 0.963183i
\(842\) 4.11294 + 4.45311i 0.141741 + 0.153464i
\(843\) 0 0
\(844\) 1.30794 + 0.667814i 0.0450212 + 0.0229871i
\(845\) 19.7741 8.19071i 0.680251 0.281769i
\(846\) 0 0
\(847\) 3.57388i 0.122800i
\(848\) −25.0799 + 13.5628i −0.861249 + 0.465748i
\(849\) 0 0
\(850\) −0.813674 + 0.299792i −0.0279088 + 0.0102828i
\(851\) 0.774158 5.88032i 0.0265378 0.201575i
\(852\) 0 0
\(853\) −18.1160 + 2.38502i −0.620280 + 0.0816614i −0.434115 0.900857i \(-0.642939\pi\)
−0.186164 + 0.982519i \(0.559606\pi\)
\(854\) −3.25669 1.01273i −0.111442 0.0346549i
\(855\) 0 0
\(856\) −42.3920 5.07161i −1.44893 0.173344i
\(857\) 10.1654 37.9379i 0.347244 1.29593i −0.542724 0.839911i \(-0.682607\pi\)
0.889969 0.456022i \(-0.150726\pi\)
\(858\) 0 0
\(859\) −30.4283 + 23.3485i −1.03820 + 0.796640i −0.979461 0.201634i \(-0.935375\pi\)
−0.0587400 + 0.998273i \(0.518708\pi\)
\(860\) 11.5466 + 24.2604i 0.393735 + 0.827271i
\(861\) 0 0
\(862\) −2.72076 3.85322i −0.0926695 0.131241i
\(863\) −8.87721 −0.302184 −0.151092 0.988520i \(-0.548279\pi\)
−0.151092 + 0.988520i \(0.548279\pi\)
\(864\) 0 0
\(865\) 33.7334 1.14697
\(866\) 1.82774 + 2.58850i 0.0621091 + 0.0879607i
\(867\) 0 0
\(868\) −0.769117 + 0.366057i −0.0261055 + 0.0124248i
\(869\) −0.446948 + 0.342955i −0.0151617 + 0.0116340i
\(870\) 0 0
\(871\) −1.26894 + 4.73576i −0.0429965 + 0.160465i
\(872\) 32.8344 + 41.7584i 1.11191 + 1.41412i
\(873\) 0 0
\(874\) 9.50143 + 2.95465i 0.321391 + 0.0999426i
\(875\) 3.85152 0.507063i 0.130205 0.0171418i
\(876\) 0 0
\(877\) −0.661443 + 5.02416i −0.0223353 + 0.169654i −0.998977 0.0452207i \(-0.985601\pi\)
0.976642 + 0.214874i \(0.0689342\pi\)
\(878\) 7.50478 2.76508i 0.253274 0.0933168i
\(879\) 0 0
\(880\) −0.239171 + 0.0247316i −0.00806245 + 0.000833701i
\(881\) 39.0897i 1.31697i −0.752595 0.658483i \(-0.771198\pi\)
0.752595 0.658483i \(-0.228802\pi\)
\(882\) 0 0
\(883\) 23.3116 9.65597i 0.784497 0.324949i 0.0457683 0.998952i \(-0.485426\pi\)
0.738729 + 0.674003i \(0.235426\pi\)
\(884\) −1.20660 + 2.36318i −0.0405825 + 0.0794825i
\(885\) 0 0
\(886\) −13.2314 14.3257i −0.444517 0.481282i
\(887\) 2.62983 + 9.81464i 0.0883009 + 0.329543i 0.995919 0.0902538i \(-0.0287678\pi\)
−0.907618 + 0.419797i \(0.862101\pi\)
\(888\) 0 0
\(889\) 1.55701 5.81084i 0.0522204 0.194889i
\(890\) −11.6440 + 6.11995i −0.390307 + 0.205141i
\(891\) 0 0
\(892\) −33.5508 + 6.18911i −1.12336 + 0.207227i
\(893\) 10.9265 14.2398i 0.365643 0.476515i
\(894\) 0 0
\(895\) −2.85497 + 4.94495i −0.0954311 + 0.165291i
\(896\) 2.88032 + 2.28443i 0.0962249 + 0.0763175i
\(897\) 0 0
\(898\) 13.0884 9.24170i 0.436765 0.308400i
\(899\) −0.143932 0.347482i −0.00480039 0.0115892i
\(900\) 0 0
\(901\) −1.70738 0.707221i −0.0568812 0.0235610i
\(902\) −0.318935 0.201421i −0.0106194 0.00670657i
\(903\) 0 0
\(904\) 3.37329 13.2125i 0.112194 0.439443i
\(905\) −1.10235 4.11401i −0.0366432 0.136754i
\(906\) 0 0
\(907\) −14.9550 + 1.96887i −0.496573 + 0.0653751i −0.374654 0.927165i \(-0.622238\pi\)
−0.121920 + 0.992540i \(0.538905\pi\)
\(908\) −17.5419 27.0619i −0.582147 0.898079i
\(909\) 0 0
\(910\) 2.44204 2.93373i 0.0809529 0.0972522i
\(911\) 46.1844 26.6646i 1.53016 0.883437i 0.530803 0.847495i \(-0.321890\pi\)
0.999354 0.0359415i \(-0.0114430\pi\)
\(912\) 0 0
\(913\) −0.462124 0.266808i −0.0152941 0.00883005i
\(914\) 41.4706 15.2795i 1.37172 0.505401i
\(915\) 0 0
\(916\) 0.657508 + 2.02940i 0.0217247 + 0.0670533i
\(917\) −2.44281 + 5.89747i −0.0806687 + 0.194751i
\(918\) 0 0
\(919\) −4.12257 + 4.12257i −0.135991 + 0.135991i −0.771826 0.635834i \(-0.780656\pi\)
0.635834 + 0.771826i \(0.280656\pi\)
\(920\) −5.10693 + 12.7539i −0.168370 + 0.420483i
\(921\) 0 0
\(922\) −27.7455 1.10180i −0.913750 0.0362859i
\(923\) −29.6280 + 22.7343i −0.975216 + 0.748310i
\(924\) 0 0
\(925\) −2.85373 + 3.71905i −0.0938300 + 0.122282i
\(926\) 21.5645 1.97237i 0.708654 0.0648160i
\(927\) 0 0
\(928\) −1.07286 + 1.21819i −0.0352184 + 0.0399891i
\(929\) −9.84686 17.0553i −0.323065 0.559565i 0.658054 0.752971i \(-0.271380\pi\)
−0.981119 + 0.193406i \(0.938047\pi\)
\(930\) 0 0
\(931\) 16.0725 + 2.11599i 0.526755 + 0.0693487i
\(932\) 14.5220 + 30.5119i 0.475683 + 0.999450i
\(933\) 0 0
\(934\) −12.6019 + 19.9543i −0.412348 + 0.652923i
\(935\) −0.0110201 0.0110201i −0.000360396 0.000360396i
\(936\) 0 0
\(937\) 1.70773 1.70773i 0.0557891 0.0557891i −0.678662 0.734451i \(-0.737440\pi\)
0.734451 + 0.678662i \(0.237440\pi\)
\(938\) 0.0969890 + 0.429468i 0.00316680 + 0.0140226i
\(939\) 0 0
\(940\) 18.4027 + 16.5979i 0.600230 + 0.541363i
\(941\) −7.82656 + 59.4487i −0.255139 + 1.93797i 0.0822644 + 0.996611i \(0.473785\pi\)
−0.337403 + 0.941360i \(0.609549\pi\)
\(942\) 0 0
\(943\) −18.6653 + 10.7764i −0.607825 + 0.350928i
\(944\) −53.1345 1.48074i −1.72938 0.0481939i
\(945\) 0 0
\(946\) 0.277280 0.333108i 0.00901514 0.0108303i
\(947\) 9.21368 + 7.06990i 0.299404 + 0.229741i 0.747528 0.664231i \(-0.231241\pi\)
−0.448123 + 0.893972i \(0.647907\pi\)
\(948\) 0 0
\(949\) 43.1781 + 56.2708i 1.40162 + 1.82663i
\(950\) −5.33595 5.77726i −0.173121 0.187439i
\(951\) 0 0
\(952\) 0.00281869 + 0.238264i 9.13542e−5 + 0.00772219i
\(953\) 26.7046 + 26.7046i 0.865046 + 0.865046i 0.991919 0.126873i \(-0.0404939\pi\)
−0.126873 + 0.991919i \(0.540494\pi\)
\(954\) 0 0
\(955\) −3.95766 1.63932i −0.128067 0.0530470i
\(956\) −9.75758 + 8.31959i −0.315583 + 0.269075i
\(957\) 0 0
\(958\) 30.7085 + 14.1725i 0.992147 + 0.457891i
\(959\) −0.920699 + 1.59470i −0.0297309 + 0.0514955i
\(960\) 0 0
\(961\) 14.6410 + 25.3590i 0.472292 + 0.818034i
\(962\) 1.30652 + 14.2846i 0.0421238 + 0.460553i
\(963\) 0 0
\(964\) 4.95357 + 26.8530i 0.159544 + 0.864876i
\(965\) −3.09120 23.4800i −0.0995093 0.755848i
\(966\) 0 0
\(967\) 21.6129 5.79116i 0.695025 0.186231i 0.106024 0.994364i \(-0.466188\pi\)
0.589001 + 0.808132i \(0.299521\pi\)
\(968\) −15.8720 26.7551i −0.510146 0.859943i
\(969\) 0 0
\(970\) −23.3808 + 5.28020i −0.750711 + 0.169537i
\(971\) 20.0398 48.3803i 0.643106 1.55260i −0.179361 0.983783i \(-0.557403\pi\)
0.822467 0.568813i \(-0.192597\pi\)
\(972\) 0 0
\(973\) 0.141603 0.0586539i 0.00453959 0.00188036i
\(974\) −9.94276 1.71278i −0.318586 0.0548810i
\(975\) 0 0
\(976\) −28.8782 + 6.88174i −0.924370 + 0.220279i
\(977\) −7.10520 4.10219i −0.227316 0.131241i 0.382017 0.924155i \(-0.375229\pi\)
−0.609333 + 0.792914i \(0.708563\pi\)
\(978\) 0 0
\(979\) 0.168345 + 0.129176i 0.00538033 + 0.00412847i
\(980\) −4.67206 + 21.8899i −0.149244 + 0.699246i
\(981\) 0 0
\(982\) 34.4234 + 10.7046i 1.09850 + 0.341598i
\(983\) −12.1698 3.26089i −0.388157 0.104006i 0.0594624 0.998231i \(-0.481061\pi\)
−0.447619 + 0.894224i \(0.647728\pi\)
\(984\) 0 0
\(985\) 2.79504 0.748928i 0.0890573 0.0238628i
\(986\) −0.105132 0.00417487i −0.00334807 0.000132955i
\(987\) 0 0
\(988\) −23.9888 1.90824i −0.763184 0.0607092i
\(989\) −9.47668 22.8787i −0.301341 0.727501i
\(990\) 0 0
\(991\) 33.1493 1.05302 0.526511 0.850168i \(-0.323500\pi\)
0.526511 + 0.850168i \(0.323500\pi\)
\(992\) −4.13214 + 6.15615i −0.131196 + 0.195458i
\(993\) 0 0
\(994\) −1.40533 + 3.04503i −0.0445744 + 0.0965826i
\(995\) 3.43452 + 0.452163i 0.108882 + 0.0143345i
\(996\) 0 0
\(997\) 0.688470 + 5.22945i 0.0218041 + 0.165618i 0.998883 0.0472610i \(-0.0150492\pi\)
−0.977079 + 0.212879i \(0.931716\pi\)
\(998\) 21.8303 + 41.5350i 0.691027 + 1.31477i
\(999\) 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 864.2.bk.a.37.9 368
3.2 odd 2 288.2.bc.a.229.38 yes 368
9.2 odd 6 288.2.bc.a.133.7 yes 368
9.7 even 3 inner 864.2.bk.a.613.40 368
32.13 even 8 inner 864.2.bk.a.685.40 368
96.77 odd 8 288.2.bc.a.13.7 368
288.173 odd 24 288.2.bc.a.205.38 yes 368
288.205 even 24 inner 864.2.bk.a.397.9 368
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
288.2.bc.a.13.7 368 96.77 odd 8
288.2.bc.a.133.7 yes 368 9.2 odd 6
288.2.bc.a.205.38 yes 368 288.173 odd 24
288.2.bc.a.229.38 yes 368 3.2 odd 2
864.2.bk.a.37.9 368 1.1 even 1 trivial
864.2.bk.a.397.9 368 288.205 even 24 inner
864.2.bk.a.613.40 368 9.7 even 3 inner
864.2.bk.a.685.40 368 32.13 even 8 inner