Properties

Label 864.2.bn.a.35.5
Level $864$
Weight $2$
Character 864.35
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(35,864)]
 
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([12, 9, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("864.35");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.bn (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 35.5
Character \(\chi\) \(=\) 864.35
Dual form 864.2.bn.a.395.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.33268 + 0.473259i) q^{2} +(1.55205 - 1.26140i) q^{4} +(2.25126 + 1.72746i) q^{5} +(-0.665173 + 0.178233i) q^{7} +(-1.47141 + 2.41556i) q^{8} +O(q^{10})\) \(q+(-1.33268 + 0.473259i) q^{2} +(1.55205 - 1.26140i) q^{4} +(2.25126 + 1.72746i) q^{5} +(-0.665173 + 0.178233i) q^{7} +(-1.47141 + 2.41556i) q^{8} +(-3.81774 - 1.23671i) q^{10} +(-0.358825 + 2.72555i) q^{11} +(-5.62707 + 0.740818i) q^{13} +(0.802110 - 0.552325i) q^{14} +(0.817733 - 3.91552i) q^{16} -6.90574 q^{17} +(-2.38448 - 0.987682i) q^{19} +(5.67309 - 0.158646i) q^{20} +(-0.811692 - 3.80209i) q^{22} +(-1.70613 + 6.36737i) q^{23} +(0.789991 + 2.94829i) q^{25} +(7.14846 - 3.65033i) q^{26} +(-0.807560 + 1.11568i) q^{28} +(-5.76873 - 7.51796i) q^{29} +(3.44542 - 1.98921i) q^{31} +(0.763282 + 5.60512i) q^{32} +(9.20312 - 3.26820i) q^{34} +(-1.80537 - 0.747808i) q^{35} +(0.725444 + 1.75138i) q^{37} +(3.64516 + 0.187787i) q^{38} +(-7.48532 + 2.89627i) q^{40} +(-4.20094 - 1.12564i) q^{41} +(10.4679 + 1.37812i) q^{43} +(2.88110 + 4.68282i) q^{44} +(-0.739692 - 9.29308i) q^{46} +(6.13150 + 3.54002i) q^{47} +(-5.65149 + 3.26289i) q^{49} +(-2.44810 - 3.55524i) q^{50} +(-7.79904 + 8.24778i) q^{52} +(0.365072 + 0.881362i) q^{53} +(-5.51608 + 5.51608i) q^{55} +(0.548213 - 1.86902i) q^{56} +(11.2458 + 7.28890i) q^{58} +(0.148994 - 0.194173i) q^{59} +(4.69833 - 3.60515i) q^{61} +(-3.65021 + 4.28155i) q^{62} +(-3.66988 - 7.10858i) q^{64} +(-13.9477 - 8.05274i) q^{65} +(-3.54169 + 0.466272i) q^{67} +(-10.7181 + 8.71092i) q^{68} +(2.75988 + 0.142180i) q^{70} +(1.97464 - 1.97464i) q^{71} +(0.741298 + 0.741298i) q^{73} +(-1.79564 - 1.99070i) q^{74} +(-4.94669 + 1.47485i) q^{76} +(-0.247101 - 1.87692i) q^{77} +(-4.86357 + 8.42396i) q^{79} +(8.60482 - 7.40228i) q^{80} +(6.13122 - 0.488020i) q^{82} +(-0.212004 - 0.276289i) q^{83} +(-15.5467 - 11.9294i) q^{85} +(-14.6025 + 3.11742i) q^{86} +(-6.05575 - 4.87718i) q^{88} +(-2.50973 - 2.50973i) q^{89} +(3.61094 - 1.49570i) q^{91} +(5.38380 + 12.0346i) q^{92} +(-9.84665 - 1.81592i) q^{94} +(-3.66191 - 6.34261i) q^{95} +(-2.87742 + 4.98384i) q^{97} +(5.98742 - 7.02299i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34} - 16 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 24 q^{47} + 168 q^{50} - 4 q^{52} - 16 q^{55} + 12 q^{56} + 32 q^{58} + 12 q^{59} - 4 q^{61} - 16 q^{64} + 24 q^{65} - 4 q^{67} + 60 q^{68} - 4 q^{70} - 16 q^{73} + 12 q^{74} - 28 q^{76} + 12 q^{77} - 8 q^{79} - 16 q^{82} + 132 q^{83} - 24 q^{85} + 12 q^{86} - 4 q^{88} - 16 q^{91} - 216 q^{92} - 20 q^{94} - 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.33268 + 0.473259i −0.942344 + 0.334644i
\(3\) 0 0
\(4\) 1.55205 1.26140i 0.776026 0.630701i
\(5\) 2.25126 + 1.72746i 1.00680 + 0.772542i 0.973914 0.226918i \(-0.0728648\pi\)
0.0328818 + 0.999459i \(0.489532\pi\)
\(6\) 0 0
\(7\) −0.665173 + 0.178233i −0.251412 + 0.0673656i −0.382324 0.924028i \(-0.624876\pi\)
0.130912 + 0.991394i \(0.458209\pi\)
\(8\) −1.47141 + 2.41556i −0.520223 + 0.854030i
\(9\) 0 0
\(10\) −3.81774 1.23671i −1.20728 0.391082i
\(11\) −0.358825 + 2.72555i −0.108190 + 0.821784i 0.848197 + 0.529681i \(0.177688\pi\)
−0.956387 + 0.292103i \(0.905645\pi\)
\(12\) 0 0
\(13\) −5.62707 + 0.740818i −1.56067 + 0.205466i −0.860851 0.508856i \(-0.830068\pi\)
−0.699817 + 0.714322i \(0.746735\pi\)
\(14\) 0.802110 0.552325i 0.214373 0.147615i
\(15\) 0 0
\(16\) 0.817733 3.91552i 0.204433 0.978881i
\(17\) −6.90574 −1.67489 −0.837444 0.546522i \(-0.815951\pi\)
−0.837444 + 0.546522i \(0.815951\pi\)
\(18\) 0 0
\(19\) −2.38448 0.987682i −0.547036 0.226590i 0.0920101 0.995758i \(-0.470671\pi\)
−0.639046 + 0.769168i \(0.720671\pi\)
\(20\) 5.67309 0.158646i 1.26854 0.0354743i
\(21\) 0 0
\(22\) −0.811692 3.80209i −0.173053 0.810609i
\(23\) −1.70613 + 6.36737i −0.355753 + 1.32769i 0.523782 + 0.851853i \(0.324521\pi\)
−0.879535 + 0.475835i \(0.842146\pi\)
\(24\) 0 0
\(25\) 0.789991 + 2.94829i 0.157998 + 0.589657i
\(26\) 7.14846 3.65033i 1.40193 0.715889i
\(27\) 0 0
\(28\) −0.807560 + 1.11568i −0.152615 + 0.210843i
\(29\) −5.76873 7.51796i −1.07123 1.39605i −0.912669 0.408700i \(-0.865982\pi\)
−0.158558 0.987350i \(-0.550684\pi\)
\(30\) 0 0
\(31\) 3.44542 1.98921i 0.618815 0.357273i −0.157592 0.987504i \(-0.550373\pi\)
0.776408 + 0.630231i \(0.217040\pi\)
\(32\) 0.763282 + 5.60512i 0.134930 + 0.990855i
\(33\) 0 0
\(34\) 9.20312 3.26820i 1.57832 0.560492i
\(35\) −1.80537 0.747808i −0.305163 0.126403i
\(36\) 0 0
\(37\) 0.725444 + 1.75138i 0.119262 + 0.287925i 0.972225 0.234047i \(-0.0751968\pi\)
−0.852963 + 0.521971i \(0.825197\pi\)
\(38\) 3.64516 + 0.187787i 0.591324 + 0.0304630i
\(39\) 0 0
\(40\) −7.48532 + 2.89627i −1.18353 + 0.457940i
\(41\) −4.20094 1.12564i −0.656077 0.175795i −0.0846021 0.996415i \(-0.526962\pi\)
−0.571475 + 0.820620i \(0.693629\pi\)
\(42\) 0 0
\(43\) 10.4679 + 1.37812i 1.59633 + 0.210161i 0.875595 0.483046i \(-0.160470\pi\)
0.720739 + 0.693207i \(0.243803\pi\)
\(44\) 2.88110 + 4.68282i 0.434342 + 0.705962i
\(45\) 0 0
\(46\) −0.739692 9.29308i −0.109062 1.37019i
\(47\) 6.13150 + 3.54002i 0.894371 + 0.516365i 0.875370 0.483454i \(-0.160618\pi\)
0.0190010 + 0.999819i \(0.493951\pi\)
\(48\) 0 0
\(49\) −5.65149 + 3.26289i −0.807356 + 0.466127i
\(50\) −2.44810 3.55524i −0.346214 0.502787i
\(51\) 0 0
\(52\) −7.79904 + 8.24778i −1.08153 + 1.14376i
\(53\) 0.365072 + 0.881362i 0.0501465 + 0.121064i 0.946968 0.321329i \(-0.104130\pi\)
−0.896821 + 0.442393i \(0.854130\pi\)
\(54\) 0 0
\(55\) −5.51608 + 5.51608i −0.743788 + 0.743788i
\(56\) 0.548213 1.86902i 0.0732581 0.249758i
\(57\) 0 0
\(58\) 11.2458 + 7.28890i 1.47664 + 0.957080i
\(59\) 0.148994 0.194173i 0.0193974 0.0252792i −0.783554 0.621324i \(-0.786595\pi\)
0.802951 + 0.596045i \(0.203262\pi\)
\(60\) 0 0
\(61\) 4.69833 3.60515i 0.601559 0.461593i −0.262535 0.964922i \(-0.584559\pi\)
0.864094 + 0.503330i \(0.167892\pi\)
\(62\) −3.65021 + 4.28155i −0.463577 + 0.543757i
\(63\) 0 0
\(64\) −3.66988 7.10858i −0.458735 0.888573i
\(65\) −13.9477 8.05274i −1.73001 0.998819i
\(66\) 0 0
\(67\) −3.54169 + 0.466272i −0.432686 + 0.0569642i −0.343724 0.939071i \(-0.611688\pi\)
−0.0889622 + 0.996035i \(0.528355\pi\)
\(68\) −10.7181 + 8.71092i −1.29976 + 1.05635i
\(69\) 0 0
\(70\) 2.75988 + 0.142180i 0.329869 + 0.0169937i
\(71\) 1.97464 1.97464i 0.234346 0.234346i −0.580158 0.814504i \(-0.697009\pi\)
0.814504 + 0.580158i \(0.197009\pi\)
\(72\) 0 0
\(73\) 0.741298 + 0.741298i 0.0867624 + 0.0867624i 0.749156 0.662394i \(-0.230459\pi\)
−0.662394 + 0.749156i \(0.730459\pi\)
\(74\) −1.79564 1.99070i −0.208739 0.231414i
\(75\) 0 0
\(76\) −4.94669 + 1.47485i −0.567425 + 0.169176i
\(77\) −0.247101 1.87692i −0.0281597 0.213894i
\(78\) 0 0
\(79\) −4.86357 + 8.42396i −0.547195 + 0.947769i 0.451270 + 0.892387i \(0.350971\pi\)
−0.998465 + 0.0553821i \(0.982362\pi\)
\(80\) 8.60482 7.40228i 0.962048 0.827600i
\(81\) 0 0
\(82\) 6.13122 0.488020i 0.677079 0.0538928i
\(83\) −0.212004 0.276289i −0.0232705 0.0303267i 0.781573 0.623814i \(-0.214418\pi\)
−0.804844 + 0.593487i \(0.797751\pi\)
\(84\) 0 0
\(85\) −15.5467 11.9294i −1.68627 1.29392i
\(86\) −14.6025 + 3.11742i −1.57463 + 0.336160i
\(87\) 0 0
\(88\) −6.05575 4.87718i −0.645546 0.519909i
\(89\) −2.50973 2.50973i −0.266031 0.266031i 0.561468 0.827499i \(-0.310237\pi\)
−0.827499 + 0.561468i \(0.810237\pi\)
\(90\) 0 0
\(91\) 3.61094 1.49570i 0.378529 0.156792i
\(92\) 5.38380 + 12.0346i 0.561300 + 1.25469i
\(93\) 0 0
\(94\) −9.84665 1.81592i −1.01560 0.187298i
\(95\) −3.66191 6.34261i −0.375704 0.650738i
\(96\) 0 0
\(97\) −2.87742 + 4.98384i −0.292158 + 0.506033i −0.974320 0.225169i \(-0.927707\pi\)
0.682162 + 0.731201i \(0.261040\pi\)
\(98\) 5.98742 7.02299i 0.604820 0.709429i
\(99\) 0 0
\(100\) 4.94508 + 3.57940i 0.494508 + 0.357940i
\(101\) −0.864700 + 6.56805i −0.0860409 + 0.653545i 0.893026 + 0.450006i \(0.148578\pi\)
−0.979067 + 0.203540i \(0.934755\pi\)
\(102\) 0 0
\(103\) 0.105943 0.395385i 0.0104389 0.0389585i −0.960510 0.278246i \(-0.910247\pi\)
0.970949 + 0.239287i \(0.0769137\pi\)
\(104\) 6.49026 14.6826i 0.636422 1.43975i
\(105\) 0 0
\(106\) −0.903635 1.00180i −0.0877688 0.0973031i
\(107\) −15.0654 + 6.24030i −1.45643 + 0.603272i −0.963718 0.266921i \(-0.913994\pi\)
−0.492710 + 0.870194i \(0.663994\pi\)
\(108\) 0 0
\(109\) −2.99282 + 7.22530i −0.286660 + 0.692058i −0.999961 0.00879943i \(-0.997199\pi\)
0.713302 + 0.700857i \(0.247199\pi\)
\(110\) 4.74061 9.96168i 0.452000 0.949809i
\(111\) 0 0
\(112\) 0.153940 + 2.75025i 0.0145459 + 0.259874i
\(113\) 8.07055 + 13.9786i 0.759213 + 1.31500i 0.943252 + 0.332077i \(0.107749\pi\)
−0.184039 + 0.982919i \(0.558917\pi\)
\(114\) 0 0
\(115\) −14.8403 + 11.3874i −1.38386 + 1.06188i
\(116\) −18.4365 4.39158i −1.71179 0.407748i
\(117\) 0 0
\(118\) −0.106667 + 0.329282i −0.00981948 + 0.0303129i
\(119\) 4.59351 1.23083i 0.421087 0.112830i
\(120\) 0 0
\(121\) 3.32532 + 0.891016i 0.302302 + 0.0810015i
\(122\) −4.55518 + 7.02803i −0.412407 + 0.636288i
\(123\) 0 0
\(124\) 2.83827 7.43341i 0.254884 0.667540i
\(125\) 2.11506 5.10622i 0.189177 0.456714i
\(126\) 0 0
\(127\) 6.33134i 0.561815i −0.959735 0.280908i \(-0.909365\pi\)
0.959735 0.280908i \(-0.0906355\pi\)
\(128\) 8.25496 + 7.73664i 0.729643 + 0.683829i
\(129\) 0 0
\(130\) 22.3989 + 4.13080i 1.96451 + 0.362295i
\(131\) −1.59079 12.0833i −0.138988 1.05572i −0.908736 0.417372i \(-0.862951\pi\)
0.769747 0.638349i \(-0.220382\pi\)
\(132\) 0 0
\(133\) 1.76213 + 0.231988i 0.152796 + 0.0201159i
\(134\) 4.49926 2.29752i 0.388676 0.198476i
\(135\) 0 0
\(136\) 10.1612 16.6813i 0.871317 1.43041i
\(137\) 2.09601 + 7.82241i 0.179074 + 0.668314i 0.995822 + 0.0913185i \(0.0291081\pi\)
−0.816748 + 0.576995i \(0.804225\pi\)
\(138\) 0 0
\(139\) −0.983954 + 1.28231i −0.0834579 + 0.108764i −0.833216 0.552947i \(-0.813503\pi\)
0.749758 + 0.661712i \(0.230170\pi\)
\(140\) −3.74531 + 1.11666i −0.316537 + 0.0943747i
\(141\) 0 0
\(142\) −1.69704 + 3.56607i −0.142412 + 0.299258i
\(143\) 15.6027i 1.30476i
\(144\) 0 0
\(145\) 26.8901i 2.23310i
\(146\) −1.33874 0.637085i −0.110795 0.0527255i
\(147\) 0 0
\(148\) 3.33512 + 1.80315i 0.274145 + 0.148218i
\(149\) 1.27617 1.66314i 0.104548 0.136249i −0.738149 0.674638i \(-0.764300\pi\)
0.842697 + 0.538388i \(0.180967\pi\)
\(150\) 0 0
\(151\) 3.27641 + 12.2277i 0.266630 + 0.995077i 0.961245 + 0.275696i \(0.0889082\pi\)
−0.694615 + 0.719382i \(0.744425\pi\)
\(152\) 5.89436 4.30656i 0.478096 0.349308i
\(153\) 0 0
\(154\) 1.21757 + 2.38438i 0.0981148 + 0.192139i
\(155\) 11.1928 + 1.47356i 0.899029 + 0.118359i
\(156\) 0 0
\(157\) 0.658648 + 5.00293i 0.0525658 + 0.399277i 0.997420 + 0.0717858i \(0.0228698\pi\)
−0.944854 + 0.327491i \(0.893797\pi\)
\(158\) 2.49486 13.5281i 0.198480 1.07624i
\(159\) 0 0
\(160\) −7.96425 + 13.9371i −0.629629 + 1.10183i
\(161\) 4.53949i 0.357762i
\(162\) 0 0
\(163\) −2.58256 + 6.23486i −0.202282 + 0.488352i −0.992169 0.124900i \(-0.960139\pi\)
0.789887 + 0.613252i \(0.210139\pi\)
\(164\) −7.93997 + 3.55202i −0.620007 + 0.277366i
\(165\) 0 0
\(166\) 0.413289 + 0.267871i 0.0320775 + 0.0207908i
\(167\) 21.1569 + 5.66896i 1.63717 + 0.438678i 0.955980 0.293432i \(-0.0947974\pi\)
0.681187 + 0.732109i \(0.261464\pi\)
\(168\) 0 0
\(169\) 18.5581 4.97262i 1.42754 0.382509i
\(170\) 26.3643 + 8.54039i 2.02205 + 0.655018i
\(171\) 0 0
\(172\) 17.9850 11.0653i 1.37135 0.843718i
\(173\) 7.68421 5.89630i 0.584219 0.448287i −0.273885 0.961762i \(-0.588309\pi\)
0.858105 + 0.513475i \(0.171642\pi\)
\(174\) 0 0
\(175\) −1.05096 1.82032i −0.0794452 0.137603i
\(176\) 10.3785 + 3.63376i 0.782311 + 0.273905i
\(177\) 0 0
\(178\) 4.53241 + 2.15691i 0.339719 + 0.161667i
\(179\) −7.98790 + 19.2845i −0.597043 + 1.44139i 0.279537 + 0.960135i \(0.409819\pi\)
−0.876580 + 0.481256i \(0.840181\pi\)
\(180\) 0 0
\(181\) 0.663688 0.274908i 0.0493315 0.0204338i −0.357881 0.933767i \(-0.616501\pi\)
0.407213 + 0.913333i \(0.366501\pi\)
\(182\) −4.10436 + 3.70219i −0.304235 + 0.274425i
\(183\) 0 0
\(184\) −12.8703 13.4903i −0.948814 0.994518i
\(185\) −1.39226 + 5.19598i −0.102361 + 0.382016i
\(186\) 0 0
\(187\) 2.47796 18.8219i 0.181206 1.37640i
\(188\) 13.9818 2.23998i 1.01973 0.163367i
\(189\) 0 0
\(190\) 7.88183 + 6.71961i 0.571808 + 0.487492i
\(191\) −2.72351 + 4.71725i −0.197066 + 0.341328i −0.947576 0.319531i \(-0.896475\pi\)
0.750510 + 0.660859i \(0.229808\pi\)
\(192\) 0 0
\(193\) 2.75978 + 4.78007i 0.198653 + 0.344077i 0.948092 0.317996i \(-0.103010\pi\)
−0.749439 + 0.662074i \(0.769677\pi\)
\(194\) 1.47603 8.00362i 0.105973 0.574626i
\(195\) 0 0
\(196\) −4.65559 + 12.1930i −0.332542 + 0.870927i
\(197\) −12.2289 + 5.06537i −0.871272 + 0.360893i −0.773106 0.634277i \(-0.781298\pi\)
−0.0981665 + 0.995170i \(0.531298\pi\)
\(198\) 0 0
\(199\) 6.95404 + 6.95404i 0.492959 + 0.492959i 0.909237 0.416278i \(-0.136666\pi\)
−0.416278 + 0.909237i \(0.636666\pi\)
\(200\) −8.28417 2.42988i −0.585779 0.171818i
\(201\) 0 0
\(202\) −1.95602 9.16231i −0.137625 0.644658i
\(203\) 5.17715 + 3.97257i 0.363365 + 0.278820i
\(204\) 0 0
\(205\) −7.51294 9.79105i −0.524726 0.683837i
\(206\) 0.0459316 + 0.577059i 0.00320021 + 0.0402056i
\(207\) 0 0
\(208\) −1.70075 + 22.6387i −0.117926 + 1.56971i
\(209\) 3.54759 6.14460i 0.245392 0.425031i
\(210\) 0 0
\(211\) 3.46120 + 26.2905i 0.238279 + 1.80991i 0.524133 + 0.851637i \(0.324390\pi\)
−0.285854 + 0.958273i \(0.592277\pi\)
\(212\) 1.67836 + 0.907417i 0.115270 + 0.0623217i
\(213\) 0 0
\(214\) 17.1240 15.4461i 1.17058 1.05588i
\(215\) 21.1853 + 21.1853i 1.44482 + 1.44482i
\(216\) 0 0
\(217\) −1.93726 + 1.93726i −0.131509 + 0.131509i
\(218\) 0.569020 11.0454i 0.0385389 0.748086i
\(219\) 0 0
\(220\) −1.60325 + 15.5192i −0.108091 + 1.04631i
\(221\) 38.8591 5.11590i 2.61395 0.344133i
\(222\) 0 0
\(223\) −8.56303 4.94387i −0.573423 0.331066i 0.185092 0.982721i \(-0.440742\pi\)
−0.758515 + 0.651655i \(0.774075\pi\)
\(224\) −1.50673 3.59233i −0.100673 0.240023i
\(225\) 0 0
\(226\) −17.3709 14.8095i −1.15550 0.985112i
\(227\) 3.33189 2.55665i 0.221145 0.169691i −0.492247 0.870455i \(-0.663824\pi\)
0.713392 + 0.700765i \(0.247158\pi\)
\(228\) 0 0
\(229\) 6.58129 8.57691i 0.434904 0.566778i −0.523561 0.851988i \(-0.675397\pi\)
0.958465 + 0.285210i \(0.0920634\pi\)
\(230\) 14.3881 22.1990i 0.948726 1.46376i
\(231\) 0 0
\(232\) 26.6483 2.87270i 1.74955 0.188602i
\(233\) −10.6338 + 10.6338i −0.696643 + 0.696643i −0.963685 0.267042i \(-0.913954\pi\)
0.267042 + 0.963685i \(0.413954\pi\)
\(234\) 0 0
\(235\) 7.68839 + 18.5614i 0.501535 + 1.21081i
\(236\) −0.0136833 0.489308i −0.000890708 0.0318512i
\(237\) 0 0
\(238\) −5.53917 + 3.81422i −0.359051 + 0.247239i
\(239\) 18.4321 10.6418i 1.19227 0.688360i 0.233453 0.972368i \(-0.424998\pi\)
0.958822 + 0.284008i \(0.0916643\pi\)
\(240\) 0 0
\(241\) 16.5010 + 9.52685i 1.06292 + 0.613679i 0.926239 0.376936i \(-0.123022\pi\)
0.136683 + 0.990615i \(0.456356\pi\)
\(242\) −4.85325 + 0.386300i −0.311979 + 0.0248323i
\(243\) 0 0
\(244\) 2.74450 11.5219i 0.175699 0.737612i
\(245\) −18.3595 2.41707i −1.17294 0.154421i
\(246\) 0 0
\(247\) 14.1493 + 3.79129i 0.900298 + 0.241234i
\(248\) −0.264569 + 11.2496i −0.0168002 + 0.714349i
\(249\) 0 0
\(250\) −0.402134 + 7.80591i −0.0254332 + 0.493689i
\(251\) −3.99971 9.65617i −0.252460 0.609492i 0.745942 0.666011i \(-0.232000\pi\)
−0.998401 + 0.0565194i \(0.982000\pi\)
\(252\) 0 0
\(253\) −16.7424 6.93492i −1.05258 0.435994i
\(254\) 2.99636 + 8.43762i 0.188008 + 0.529424i
\(255\) 0 0
\(256\) −14.6626 6.40370i −0.916414 0.400231i
\(257\) −15.3667 + 8.87198i −0.958550 + 0.553419i −0.895726 0.444606i \(-0.853344\pi\)
−0.0628236 + 0.998025i \(0.520011\pi\)
\(258\) 0 0
\(259\) −0.794698 1.03567i −0.0493801 0.0643535i
\(260\) −31.8054 + 5.09544i −1.97248 + 0.316006i
\(261\) 0 0
\(262\) 7.83853 + 15.3502i 0.484266 + 0.948341i
\(263\) −4.66995 17.4285i −0.287961 1.07469i −0.946648 0.322269i \(-0.895554\pi\)
0.658687 0.752417i \(-0.271112\pi\)
\(264\) 0 0
\(265\) −0.700640 + 2.61482i −0.0430400 + 0.160627i
\(266\) −2.45813 + 0.524776i −0.150718 + 0.0321761i
\(267\) 0 0
\(268\) −4.90873 + 5.19117i −0.299848 + 0.317101i
\(269\) −17.7192 7.33955i −1.08036 0.447500i −0.229725 0.973256i \(-0.573783\pi\)
−0.850636 + 0.525755i \(0.823783\pi\)
\(270\) 0 0
\(271\) 17.7624 1.07899 0.539496 0.841988i \(-0.318615\pi\)
0.539496 + 0.841988i \(0.318615\pi\)
\(272\) −5.64705 + 27.0396i −0.342403 + 1.63952i
\(273\) 0 0
\(274\) −6.49532 9.43279i −0.392397 0.569855i
\(275\) −8.31917 + 1.09524i −0.501665 + 0.0660454i
\(276\) 0 0
\(277\) 3.89595 29.5927i 0.234085 1.77805i −0.321816 0.946802i \(-0.604293\pi\)
0.555901 0.831249i \(-0.312373\pi\)
\(278\) 0.704426 2.17457i 0.0422486 0.130422i
\(279\) 0 0
\(280\) 4.46282 3.26064i 0.266705 0.194861i
\(281\) −8.44615 + 2.26314i −0.503855 + 0.135008i −0.501789 0.864990i \(-0.667324\pi\)
−0.00206658 + 0.999998i \(0.500658\pi\)
\(282\) 0 0
\(283\) 13.9045 + 10.6693i 0.826534 + 0.634222i 0.932912 0.360104i \(-0.117259\pi\)
−0.106378 + 0.994326i \(0.533925\pi\)
\(284\) 0.573930 5.55555i 0.0340565 0.329661i
\(285\) 0 0
\(286\) 7.38411 + 20.7933i 0.436631 + 1.22954i
\(287\) 2.99498 0.176788
\(288\) 0 0
\(289\) 30.6893 1.80525
\(290\) 12.7260 + 35.8358i 0.747296 + 2.10435i
\(291\) 0 0
\(292\) 2.08561 + 0.215459i 0.122051 + 0.0126088i
\(293\) −19.6836 15.1038i −1.14993 0.882371i −0.155505 0.987835i \(-0.549701\pi\)
−0.994423 + 0.105464i \(0.966367\pi\)
\(294\) 0 0
\(295\) 0.670850 0.179754i 0.0390584 0.0104657i
\(296\) −5.29799 0.824646i −0.307939 0.0479316i
\(297\) 0 0
\(298\) −0.913626 + 2.82038i −0.0529250 + 0.163380i
\(299\) 4.88346 37.0935i 0.282418 2.14517i
\(300\) 0 0
\(301\) −7.20856 + 0.949025i −0.415495 + 0.0547009i
\(302\) −10.1533 14.7450i −0.584255 0.848479i
\(303\) 0 0
\(304\) −5.81715 + 8.52881i −0.333637 + 0.489161i
\(305\) 16.8049 0.962247
\(306\) 0 0
\(307\) −19.8889 8.23823i −1.13512 0.470181i −0.265600 0.964083i \(-0.585570\pi\)
−0.869517 + 0.493903i \(0.835570\pi\)
\(308\) −2.75106 2.60138i −0.156756 0.148227i
\(309\) 0 0
\(310\) −15.6138 + 3.33332i −0.886803 + 0.189320i
\(311\) −2.04169 + 7.61971i −0.115774 + 0.432074i −0.999344 0.0362256i \(-0.988467\pi\)
0.883570 + 0.468300i \(0.155133\pi\)
\(312\) 0 0
\(313\) 4.61577 + 17.2263i 0.260899 + 0.973687i 0.964713 + 0.263303i \(0.0848120\pi\)
−0.703814 + 0.710384i \(0.748521\pi\)
\(314\) −3.24544 6.35557i −0.183151 0.358666i
\(315\) 0 0
\(316\) 3.07747 + 19.2093i 0.173121 + 1.08061i
\(317\) −15.7983 20.5887i −0.887321 1.15638i −0.986897 0.161349i \(-0.948415\pi\)
0.0995765 0.995030i \(-0.468251\pi\)
\(318\) 0 0
\(319\) 22.5605 13.0253i 1.26315 0.729279i
\(320\) 4.01789 22.3429i 0.224607 1.24900i
\(321\) 0 0
\(322\) 2.14835 + 6.04967i 0.119723 + 0.337135i
\(323\) 16.4666 + 6.82068i 0.916225 + 0.379513i
\(324\) 0 0
\(325\) −6.62948 16.0050i −0.367737 0.887796i
\(326\) 0.491019 9.53127i 0.0271950 0.527888i
\(327\) 0 0
\(328\) 8.90038 8.49136i 0.491441 0.468857i
\(329\) −4.70945 1.26189i −0.259640 0.0695705i
\(330\) 0 0
\(331\) −13.2365 1.74262i −0.727545 0.0957831i −0.242350 0.970189i \(-0.577918\pi\)
−0.485195 + 0.874406i \(0.661251\pi\)
\(332\) −0.677553 0.161393i −0.0371856 0.00885759i
\(333\) 0 0
\(334\) −30.8781 + 2.45778i −1.68958 + 0.134483i
\(335\) −8.77874 5.06841i −0.479634 0.276917i
\(336\) 0 0
\(337\) −25.0098 + 14.4394i −1.36237 + 0.786566i −0.989939 0.141493i \(-0.954810\pi\)
−0.372433 + 0.928059i \(0.621476\pi\)
\(338\) −22.3786 + 15.4097i −1.21723 + 0.838175i
\(339\) 0 0
\(340\) −39.1769 + 1.09557i −2.12467 + 0.0594156i
\(341\) 4.18539 + 10.1044i 0.226652 + 0.547186i
\(342\) 0 0
\(343\) 6.58625 6.58625i 0.355624 0.355624i
\(344\) −18.7315 + 23.2580i −1.00993 + 1.25399i
\(345\) 0 0
\(346\) −7.45009 + 11.4945i −0.400519 + 0.617947i
\(347\) −4.02705 + 5.24815i −0.216183 + 0.281736i −0.888839 0.458220i \(-0.848487\pi\)
0.672655 + 0.739956i \(0.265154\pi\)
\(348\) 0 0
\(349\) 11.3771 8.72997i 0.609003 0.467304i −0.257635 0.966242i \(-0.582943\pi\)
0.866638 + 0.498938i \(0.166276\pi\)
\(350\) 2.26207 + 1.92852i 0.120913 + 0.103084i
\(351\) 0 0
\(352\) −15.5509 + 0.0691018i −0.828867 + 0.00368314i
\(353\) 32.2434 + 18.6157i 1.71614 + 0.990816i 0.925681 + 0.378305i \(0.123493\pi\)
0.790462 + 0.612511i \(0.209840\pi\)
\(354\) 0 0
\(355\) 7.85653 1.03433i 0.416981 0.0548966i
\(356\) −7.06101 0.729456i −0.374233 0.0386611i
\(357\) 0 0
\(358\) 1.51873 29.4803i 0.0802673 1.55808i
\(359\) 10.7189 10.7189i 0.565724 0.565724i −0.365204 0.930928i \(-0.619001\pi\)
0.930928 + 0.365204i \(0.119001\pi\)
\(360\) 0 0
\(361\) −8.72482 8.72482i −0.459201 0.459201i
\(362\) −0.754378 + 0.680460i −0.0396492 + 0.0357642i
\(363\) 0 0
\(364\) 3.71769 6.87624i 0.194860 0.360413i
\(365\) 0.388298 + 2.94942i 0.0203244 + 0.154380i
\(366\) 0 0
\(367\) 10.1421 17.5667i 0.529414 0.916972i −0.469997 0.882668i \(-0.655745\pi\)
0.999411 0.0343043i \(-0.0109215\pi\)
\(368\) 23.5364 + 11.8872i 1.22692 + 0.619663i
\(369\) 0 0
\(370\) −0.603613 7.58346i −0.0313804 0.394246i
\(371\) −0.399923 0.521190i −0.0207630 0.0270589i
\(372\) 0 0
\(373\) −0.800414 0.614179i −0.0414439 0.0318010i 0.587832 0.808983i \(-0.299982\pi\)
−0.629276 + 0.777182i \(0.716648\pi\)
\(374\) 5.60534 + 26.2563i 0.289845 + 1.35768i
\(375\) 0 0
\(376\) −17.5731 + 9.60217i −0.906264 + 0.495194i
\(377\) 38.0305 + 38.0305i 1.95867 + 1.95867i
\(378\) 0 0
\(379\) −18.0664 + 7.48335i −0.928009 + 0.384394i −0.794923 0.606711i \(-0.792489\pi\)
−0.133086 + 0.991104i \(0.542489\pi\)
\(380\) −13.6840 5.22493i −0.701977 0.268033i
\(381\) 0 0
\(382\) 1.39707 7.57550i 0.0714804 0.387596i
\(383\) −6.74390 11.6808i −0.344597 0.596860i 0.640683 0.767805i \(-0.278651\pi\)
−0.985280 + 0.170945i \(0.945318\pi\)
\(384\) 0 0
\(385\) 2.68600 4.65229i 0.136891 0.237103i
\(386\) −5.94010 5.06420i −0.302343 0.257761i
\(387\) 0 0
\(388\) 1.82072 + 11.3648i 0.0924328 + 0.576959i
\(389\) −0.811153 + 6.16132i −0.0411271 + 0.312391i 0.958500 + 0.285092i \(0.0920241\pi\)
−0.999627 + 0.0272994i \(0.991309\pi\)
\(390\) 0 0
\(391\) 11.7821 43.9714i 0.595846 2.22373i
\(392\) 0.433971 18.4526i 0.0219188 0.931996i
\(393\) 0 0
\(394\) 13.8999 12.5379i 0.700268 0.631652i
\(395\) −25.5012 + 10.5629i −1.28310 + 0.531479i
\(396\) 0 0
\(397\) 4.30849 10.4016i 0.216237 0.522042i −0.778122 0.628113i \(-0.783827\pi\)
0.994358 + 0.106072i \(0.0338274\pi\)
\(398\) −12.5585 5.97643i −0.629503 0.299571i
\(399\) 0 0
\(400\) 12.1901 0.682316i 0.609504 0.0341158i
\(401\) −5.13657 8.89679i −0.256508 0.444285i 0.708796 0.705413i \(-0.249239\pi\)
−0.965304 + 0.261129i \(0.915905\pi\)
\(402\) 0 0
\(403\) −17.9140 + 13.7459i −0.892358 + 0.684730i
\(404\) 6.94289 + 11.2847i 0.345422 + 0.561434i
\(405\) 0 0
\(406\) −8.77952 2.84401i −0.435720 0.141146i
\(407\) −5.03377 + 1.34880i −0.249515 + 0.0668573i
\(408\) 0 0
\(409\) 11.4231 + 3.06082i 0.564838 + 0.151348i 0.529928 0.848042i \(-0.322219\pi\)
0.0349101 + 0.999390i \(0.488886\pi\)
\(410\) 14.6460 + 9.49274i 0.723315 + 0.468813i
\(411\) 0 0
\(412\) −0.334310 0.747295i −0.0164703 0.0368166i
\(413\) −0.0644989 + 0.155714i −0.00317378 + 0.00766219i
\(414\) 0 0
\(415\) 0.988227i 0.0485102i
\(416\) −8.44741 30.9750i −0.414169 1.51867i
\(417\) 0 0
\(418\) −1.81980 + 9.86769i −0.0890093 + 0.482645i
\(419\) 2.25237 + 17.1084i 0.110035 + 0.835802i 0.954085 + 0.299537i \(0.0968321\pi\)
−0.844049 + 0.536266i \(0.819835\pi\)
\(420\) 0 0
\(421\) −36.2572 4.77334i −1.76707 0.232639i −0.824314 0.566133i \(-0.808439\pi\)
−0.942752 + 0.333495i \(0.891772\pi\)
\(422\) −17.0549 33.3986i −0.830217 1.62582i
\(423\) 0 0
\(424\) −2.66616 0.414994i −0.129480 0.0201539i
\(425\) −5.45548 20.3601i −0.264629 0.987610i
\(426\) 0 0
\(427\) −2.48264 + 3.23545i −0.120144 + 0.156574i
\(428\) −15.5108 + 28.6888i −0.749742 + 1.38673i
\(429\) 0 0
\(430\) −38.2592 18.2070i −1.84502 0.878019i
\(431\) 12.9990i 0.626138i 0.949730 + 0.313069i \(0.101357\pi\)
−0.949730 + 0.313069i \(0.898643\pi\)
\(432\) 0 0
\(433\) 5.96852i 0.286829i −0.989663 0.143414i \(-0.954192\pi\)
0.989663 0.143414i \(-0.0458081\pi\)
\(434\) 1.66491 3.49856i 0.0799183 0.167936i
\(435\) 0 0
\(436\) 4.46899 + 14.9892i 0.214026 + 0.717851i
\(437\) 10.3572 13.4977i 0.495450 0.645683i
\(438\) 0 0
\(439\) −3.10344 11.5822i −0.148119 0.552789i −0.999597 0.0283974i \(-0.990960\pi\)
0.851477 0.524391i \(-0.175707\pi\)
\(440\) −5.20799 21.4409i −0.248281 1.02215i
\(441\) 0 0
\(442\) −49.3655 + 25.2082i −2.34808 + 1.19903i
\(443\) 4.71979 + 0.621372i 0.224244 + 0.0295223i 0.241811 0.970323i \(-0.422259\pi\)
−0.0175669 + 0.999846i \(0.505592\pi\)
\(444\) 0 0
\(445\) −1.31462 9.98552i −0.0623189 0.473359i
\(446\) 13.7515 + 2.53605i 0.651151 + 0.120085i
\(447\) 0 0
\(448\) 3.70809 + 4.07435i 0.175191 + 0.192495i
\(449\) 40.2152i 1.89787i −0.315464 0.948937i \(-0.602160\pi\)
0.315464 0.948937i \(-0.397840\pi\)
\(450\) 0 0
\(451\) 4.57539 11.0460i 0.215447 0.520134i
\(452\) 30.1585 + 11.5153i 1.41854 + 0.541635i
\(453\) 0 0
\(454\) −3.23037 + 4.98403i −0.151609 + 0.233912i
\(455\) 10.7129 + 2.87052i 0.502230 + 0.134572i
\(456\) 0 0
\(457\) −36.0382 + 9.65641i −1.68580 + 0.451708i −0.969300 0.245883i \(-0.920922\pi\)
−0.716497 + 0.697590i \(0.754256\pi\)
\(458\) −4.71164 + 14.5449i −0.220160 + 0.679638i
\(459\) 0 0
\(460\) −8.66888 + 36.3933i −0.404189 + 1.69685i
\(461\) −1.29260 + 0.991849i −0.0602025 + 0.0461950i −0.638424 0.769685i \(-0.720413\pi\)
0.578222 + 0.815880i \(0.303747\pi\)
\(462\) 0 0
\(463\) 4.71907 + 8.17367i 0.219314 + 0.379863i 0.954598 0.297896i \(-0.0962848\pi\)
−0.735285 + 0.677758i \(0.762951\pi\)
\(464\) −34.1540 + 16.4399i −1.58556 + 0.763204i
\(465\) 0 0
\(466\) 9.13887 19.2039i 0.423350 0.889605i
\(467\) −1.35853 + 3.27978i −0.0628653 + 0.151770i −0.952190 0.305505i \(-0.901175\pi\)
0.889325 + 0.457275i \(0.151175\pi\)
\(468\) 0 0
\(469\) 2.27273 0.941395i 0.104945 0.0434696i
\(470\) −19.0305 21.0978i −0.877810 0.973167i
\(471\) 0 0
\(472\) 0.249805 + 0.645613i 0.0114982 + 0.0297168i
\(473\) −7.51227 + 28.0362i −0.345414 + 1.28910i
\(474\) 0 0
\(475\) 1.02826 7.81038i 0.0471796 0.358365i
\(476\) 5.57681 7.70458i 0.255612 0.353139i
\(477\) 0 0
\(478\) −19.5277 + 22.9052i −0.893177 + 1.04766i
\(479\) −14.3663 + 24.8831i −0.656413 + 1.13694i 0.325125 + 0.945671i \(0.394594\pi\)
−0.981538 + 0.191269i \(0.938740\pi\)
\(480\) 0 0
\(481\) −5.37958 9.31770i −0.245288 0.424851i
\(482\) −26.4991 4.88697i −1.20700 0.222595i
\(483\) 0 0
\(484\) 6.28500 2.81166i 0.285682 0.127803i
\(485\) −15.0872 + 6.24933i −0.685075 + 0.283767i
\(486\) 0 0
\(487\) 6.97840 + 6.97840i 0.316222 + 0.316222i 0.847314 0.531092i \(-0.178218\pi\)
−0.531092 + 0.847314i \(0.678218\pi\)
\(488\) 1.79529 + 16.6538i 0.0812688 + 0.753881i
\(489\) 0 0
\(490\) 25.6112 5.46761i 1.15699 0.247002i
\(491\) 15.7323 + 12.0718i 0.709989 + 0.544794i 0.899412 0.437102i \(-0.143995\pi\)
−0.189423 + 0.981896i \(0.560662\pi\)
\(492\) 0 0
\(493\) 39.8374 + 51.9171i 1.79419 + 2.33823i
\(494\) −20.6507 + 1.64371i −0.929119 + 0.0739541i
\(495\) 0 0
\(496\) −4.97137 15.1172i −0.223221 0.678784i
\(497\) −0.961531 + 1.66542i −0.0431306 + 0.0747043i
\(498\) 0 0
\(499\) −2.16974 16.4808i −0.0971310 0.737783i −0.968827 0.247737i \(-0.920313\pi\)
0.871696 0.490046i \(-0.163020\pi\)
\(500\) −3.15830 10.5931i −0.141243 0.473736i
\(501\) 0 0
\(502\) 9.90019 + 10.9756i 0.441867 + 0.489867i
\(503\) 22.3214 + 22.3214i 0.995261 + 0.995261i 0.999989 0.00472801i \(-0.00150498\pi\)
−0.00472801 + 0.999989i \(0.501505\pi\)
\(504\) 0 0
\(505\) −13.2927 + 13.2927i −0.591517 + 0.591517i
\(506\) 25.5942 + 1.31853i 1.13780 + 0.0586156i
\(507\) 0 0
\(508\) −7.98636 9.82657i −0.354337 0.435983i
\(509\) 14.9175 1.96392i 0.661206 0.0870494i 0.207547 0.978225i \(-0.433452\pi\)
0.453659 + 0.891176i \(0.350119\pi\)
\(510\) 0 0
\(511\) −0.625215 0.360968i −0.0276579 0.0159683i
\(512\) 22.5711 + 1.59485i 0.997513 + 0.0704829i
\(513\) 0 0
\(514\) 16.2801 19.0959i 0.718086 0.842285i
\(515\) 0.921516 0.707104i 0.0406069 0.0311587i
\(516\) 0 0
\(517\) −11.8486 + 15.4414i −0.521103 + 0.679114i
\(518\) 1.54922 + 1.00412i 0.0680686 + 0.0441183i
\(519\) 0 0
\(520\) 39.9748 21.8427i 1.75301 0.957868i
\(521\) 1.96702 1.96702i 0.0861766 0.0861766i −0.662704 0.748881i \(-0.730591\pi\)
0.748881 + 0.662704i \(0.230591\pi\)
\(522\) 0 0
\(523\) 11.8341 + 28.5699i 0.517467 + 1.24928i 0.939454 + 0.342674i \(0.111333\pi\)
−0.421987 + 0.906602i \(0.638667\pi\)
\(524\) −17.7109 16.7472i −0.773702 0.731607i
\(525\) 0 0
\(526\) 14.4717 + 21.0164i 0.630997 + 0.916360i
\(527\) −23.7932 + 13.7370i −1.03645 + 0.598393i
\(528\) 0 0
\(529\) −17.7139 10.2271i −0.770169 0.444657i
\(530\) −0.303762 3.81630i −0.0131946 0.165769i
\(531\) 0 0
\(532\) 3.02754 1.86269i 0.131261 0.0807578i
\(533\) 24.4729 + 3.22192i 1.06004 + 0.139557i
\(534\) 0 0
\(535\) −44.6961 11.9763i −1.93238 0.517779i
\(536\) 4.08498 9.24124i 0.176444 0.399161i
\(537\) 0 0
\(538\) 27.0875 + 1.39546i 1.16783 + 0.0601625i
\(539\) −6.86527 16.5742i −0.295708 0.713902i
\(540\) 0 0
\(541\) 33.8580 + 14.0244i 1.45567 + 0.602958i 0.963540 0.267564i \(-0.0862187\pi\)
0.492129 + 0.870522i \(0.336219\pi\)
\(542\) −23.6716 + 8.40623i −1.01678 + 0.361079i
\(543\) 0 0
\(544\) −5.27103 38.7075i −0.225993 1.65957i
\(545\) −19.2190 + 11.0961i −0.823251 + 0.475304i
\(546\) 0 0
\(547\) −18.2443 23.7765i −0.780071 1.01661i −0.999163 0.0409041i \(-0.986976\pi\)
0.219092 0.975704i \(-0.429690\pi\)
\(548\) 13.1203 + 9.49688i 0.560472 + 0.405687i
\(549\) 0 0
\(550\) 10.5684 5.39672i 0.450639 0.230117i
\(551\) 6.33005 + 23.6241i 0.269669 + 1.00642i
\(552\) 0 0
\(553\) 1.73369 6.47024i 0.0737242 0.275142i
\(554\) 8.81295 + 41.2812i 0.374426 + 1.75387i
\(555\) 0 0
\(556\) 0.0903643 + 3.23138i 0.00383230 + 0.137041i
\(557\) 16.4791 + 6.82585i 0.698240 + 0.289220i 0.703428 0.710766i \(-0.251652\pi\)
−0.00518860 + 0.999987i \(0.501652\pi\)
\(558\) 0 0
\(559\) −59.9243 −2.53453
\(560\) −4.40437 + 6.45745i −0.186119 + 0.272877i
\(561\) 0 0
\(562\) 10.1849 7.01325i 0.429626 0.295836i
\(563\) −5.67086 + 0.746583i −0.238998 + 0.0314647i −0.249074 0.968485i \(-0.580126\pi\)
0.0100754 + 0.999949i \(0.496793\pi\)
\(564\) 0 0
\(565\) −5.97847 + 45.4110i −0.251516 + 1.91046i
\(566\) −23.5795 7.63827i −0.991119 0.321060i
\(567\) 0 0
\(568\) 1.86435 + 7.67537i 0.0782264 + 0.322051i
\(569\) 40.7951 10.9310i 1.71022 0.458252i 0.734742 0.678347i \(-0.237303\pi\)
0.975479 + 0.220095i \(0.0706366\pi\)
\(570\) 0 0
\(571\) 0.180316 + 0.138361i 0.00754599 + 0.00579024i 0.612528 0.790449i \(-0.290153\pi\)
−0.604982 + 0.796239i \(0.706820\pi\)
\(572\) −19.6812 24.2162i −0.822914 1.01253i
\(573\) 0 0
\(574\) −3.99134 + 1.41740i −0.166595 + 0.0591611i
\(575\) −20.1206 −0.839089
\(576\) 0 0
\(577\) 9.78981 0.407555 0.203778 0.979017i \(-0.434678\pi\)
0.203778 + 0.979017i \(0.434678\pi\)
\(578\) −40.8989 + 14.5240i −1.70117 + 0.604118i
\(579\) 0 0
\(580\) −33.9193 41.7349i −1.40842 1.73295i
\(581\) 0.190263 + 0.145994i 0.00789344 + 0.00605685i
\(582\) 0 0
\(583\) −2.53319 + 0.678767i −0.104914 + 0.0281117i
\(584\) −2.88141 + 0.699895i −0.119234 + 0.0289619i
\(585\) 0 0
\(586\) 33.3799 + 10.8130i 1.37891 + 0.446680i
\(587\) 2.99213 22.7275i 0.123499 0.938064i −0.811733 0.584028i \(-0.801476\pi\)
0.935232 0.354036i \(-0.115191\pi\)
\(588\) 0 0
\(589\) −10.1802 + 1.34025i −0.419469 + 0.0552241i
\(590\) −0.808956 + 0.557039i −0.0333042 + 0.0229329i
\(591\) 0 0
\(592\) 7.45078 1.40833i 0.306225 0.0578822i
\(593\) −18.4963 −0.759552 −0.379776 0.925078i \(-0.623999\pi\)
−0.379776 + 0.925078i \(0.623999\pi\)
\(594\) 0 0
\(595\) 12.4674 + 5.16417i 0.511114 + 0.211710i
\(596\) −0.117201 4.19103i −0.00480073 0.171671i
\(597\) 0 0
\(598\) 11.0468 + 51.7448i 0.451736 + 2.11600i
\(599\) 6.65490 24.8364i 0.271912 1.01479i −0.685971 0.727629i \(-0.740622\pi\)
0.957883 0.287160i \(-0.0927111\pi\)
\(600\) 0 0
\(601\) 4.64278 + 17.3271i 0.189383 + 0.706787i 0.993650 + 0.112519i \(0.0358918\pi\)
−0.804267 + 0.594269i \(0.797442\pi\)
\(602\) 9.15755 4.67626i 0.373234 0.190590i
\(603\) 0 0
\(604\) 20.5092 + 14.8452i 0.834508 + 0.604042i
\(605\) 5.94698 + 7.75025i 0.241779 + 0.315093i
\(606\) 0 0
\(607\) 31.3908 18.1235i 1.27411 0.735609i 0.298353 0.954456i \(-0.403563\pi\)
0.975759 + 0.218847i \(0.0702295\pi\)
\(608\) 3.71605 14.1192i 0.150706 0.572607i
\(609\) 0 0
\(610\) −22.3955 + 7.95307i −0.906768 + 0.322010i
\(611\) −37.1249 15.3776i −1.50191 0.622112i
\(612\) 0 0
\(613\) −9.80226 23.6648i −0.395910 0.955811i −0.988625 0.150399i \(-0.951944\pi\)
0.592716 0.805412i \(-0.298056\pi\)
\(614\) 30.4042 + 1.56632i 1.22701 + 0.0632117i
\(615\) 0 0
\(616\) 4.89740 + 2.16483i 0.197322 + 0.0872237i
\(617\) −11.7940 3.16019i −0.474807 0.127224i 0.0134763 0.999909i \(-0.495710\pi\)
−0.488284 + 0.872685i \(0.662377\pi\)
\(618\) 0 0
\(619\) −40.2814 5.30315i −1.61905 0.213152i −0.734167 0.678969i \(-0.762427\pi\)
−0.884881 + 0.465817i \(0.845760\pi\)
\(620\) 19.2306 11.8316i 0.772319 0.475168i
\(621\) 0 0
\(622\) −0.885175 11.1209i −0.0354923 0.445906i
\(623\) 2.11672 + 1.22209i 0.0848046 + 0.0489620i
\(624\) 0 0
\(625\) 26.7991 15.4725i 1.07197 0.618900i
\(626\) −14.3038 20.7726i −0.571696 0.830240i
\(627\) 0 0
\(628\) 7.33295 + 6.93398i 0.292617 + 0.276696i
\(629\) −5.00973 12.0946i −0.199751 0.482242i
\(630\) 0 0
\(631\) −7.40747 + 7.40747i −0.294887 + 0.294887i −0.839007 0.544120i \(-0.816863\pi\)
0.544120 + 0.839007i \(0.316863\pi\)
\(632\) −13.1923 24.1434i −0.524760 0.960373i
\(633\) 0 0
\(634\) 30.7978 + 19.9614i 1.22314 + 0.792770i
\(635\) 10.9371 14.2535i 0.434026 0.565633i
\(636\) 0 0
\(637\) 29.3841 22.5472i 1.16424 0.893354i
\(638\) −23.9015 + 28.0355i −0.946271 + 1.10994i
\(639\) 0 0
\(640\) 5.21940 + 31.6773i 0.206315 + 1.25216i
\(641\) 15.8499 + 9.15095i 0.626034 + 0.361441i 0.779215 0.626757i \(-0.215618\pi\)
−0.153180 + 0.988198i \(0.548952\pi\)
\(642\) 0 0
\(643\) −39.7687 + 5.23565i −1.56832 + 0.206474i −0.864032 0.503437i \(-0.832069\pi\)
−0.704292 + 0.709911i \(0.748735\pi\)
\(644\) −5.72612 7.04552i −0.225641 0.277632i
\(645\) 0 0
\(646\) −25.1726 1.29681i −0.990401 0.0510222i
\(647\) −4.46265 + 4.46265i −0.175445 + 0.175445i −0.789367 0.613922i \(-0.789591\pi\)
0.613922 + 0.789367i \(0.289591\pi\)
\(648\) 0 0
\(649\) 0.475765 + 0.475765i 0.0186754 + 0.0186754i
\(650\) 16.4094 + 18.1920i 0.643631 + 0.713549i
\(651\) 0 0
\(652\) 3.85639 + 12.9345i 0.151028 + 0.506553i
\(653\) 2.16541 + 16.4479i 0.0847389 + 0.643656i 0.980127 + 0.198370i \(0.0635647\pi\)
−0.895388 + 0.445286i \(0.853102\pi\)
\(654\) 0 0
\(655\) 17.2920 29.9507i 0.675655 1.17027i
\(656\) −7.84271 + 15.5284i −0.306207 + 0.606283i
\(657\) 0 0
\(658\) 6.87338 0.547093i 0.267952 0.0213279i
\(659\) 11.2120 + 14.6117i 0.436756 + 0.569191i 0.958928 0.283649i \(-0.0915449\pi\)
−0.522172 + 0.852840i \(0.674878\pi\)
\(660\) 0 0
\(661\) 7.36568 + 5.65188i 0.286492 + 0.219833i 0.742002 0.670398i \(-0.233877\pi\)
−0.455510 + 0.890231i \(0.650543\pi\)
\(662\) 18.4647 3.94195i 0.717651 0.153208i
\(663\) 0 0
\(664\) 0.979339 0.105573i 0.0380057 0.00409704i
\(665\) 3.56626 + 3.56626i 0.138294 + 0.138294i
\(666\) 0 0
\(667\) 57.7118 23.9050i 2.23461 0.925606i
\(668\) 39.9874 17.8888i 1.54716 0.692137i
\(669\) 0 0
\(670\) 14.0979 + 2.59993i 0.544649 + 0.100444i
\(671\) 8.14014 + 14.0991i 0.314247 + 0.544291i
\(672\) 0 0
\(673\) 15.0839 26.1260i 0.581440 1.00708i −0.413869 0.910336i \(-0.635823\pi\)
0.995309 0.0967468i \(-0.0308437\pi\)
\(674\) 26.4964 31.0792i 1.02060 1.19713i
\(675\) 0 0
\(676\) 22.5306 31.1269i 0.866562 1.19719i
\(677\) −0.0555242 + 0.421748i −0.00213397 + 0.0162091i −0.992479 0.122417i \(-0.960935\pi\)
0.990345 + 0.138626i \(0.0442687\pi\)
\(678\) 0 0
\(679\) 1.02570 3.82797i 0.0393628 0.146904i
\(680\) 51.6917 20.0009i 1.98229 0.766998i
\(681\) 0 0
\(682\) −10.3598 11.4852i −0.396697 0.439790i
\(683\) 30.9070 12.8021i 1.18262 0.489858i 0.297276 0.954791i \(-0.403922\pi\)
0.885346 + 0.464933i \(0.153922\pi\)
\(684\) 0 0
\(685\) −8.79420 + 21.2311i −0.336009 + 0.811197i
\(686\) −5.66034 + 11.8943i −0.216113 + 0.454128i
\(687\) 0 0
\(688\) 13.9560 39.8602i 0.532066 1.51966i
\(689\) −2.70721 4.68903i −0.103137 0.178638i
\(690\) 0 0
\(691\) 29.0147 22.2637i 1.10377 0.846953i 0.114555 0.993417i \(-0.463456\pi\)
0.989216 + 0.146464i \(0.0467893\pi\)
\(692\) 4.48869 18.8442i 0.170634 0.716350i
\(693\) 0 0
\(694\) 2.88302 8.89993i 0.109438 0.337837i
\(695\) −4.43028 + 1.18709i −0.168050 + 0.0450289i
\(696\) 0 0
\(697\) 29.0106 + 7.77338i 1.09886 + 0.294438i
\(698\) −11.0305 + 17.0185i −0.417510 + 0.644161i
\(699\) 0 0
\(700\) −3.92730 1.49955i −0.148438 0.0566775i
\(701\) 10.6564 25.7268i 0.402487 0.971689i −0.584574 0.811340i \(-0.698738\pi\)
0.987061 0.160348i \(-0.0512617\pi\)
\(702\) 0 0
\(703\) 4.89262i 0.184529i
\(704\) 20.6916 7.45170i 0.779846 0.280847i
\(705\) 0 0
\(706\) −51.7801 9.54928i −1.94877 0.359392i
\(707\) −0.595465 4.52301i −0.0223948 0.170105i
\(708\) 0 0
\(709\) 1.65908 + 0.218421i 0.0623079 + 0.00820299i 0.161616 0.986854i \(-0.448330\pi\)
−0.0993078 + 0.995057i \(0.531663\pi\)
\(710\) −9.98071 + 5.09660i −0.374569 + 0.191272i
\(711\) 0 0
\(712\) 9.75527 2.36956i 0.365594 0.0888029i
\(713\) 6.78771 + 25.3321i 0.254202 + 0.948694i
\(714\) 0 0
\(715\) 26.9529 35.1258i 1.00798 1.31363i
\(716\) 11.9278 + 40.0065i 0.445765 + 1.49511i
\(717\) 0 0
\(718\) −9.21204 + 19.3577i −0.343790 + 0.722423i
\(719\) 36.1234i 1.34718i −0.739107 0.673588i \(-0.764752\pi\)
0.739107 0.673588i \(-0.235248\pi\)
\(720\) 0 0
\(721\) 0.281882i 0.0104978i
\(722\) 15.7565 + 7.49827i 0.586395 + 0.279057i
\(723\) 0 0
\(724\) 0.683308 1.26385i 0.0253949 0.0469706i
\(725\) 17.6078 22.9470i 0.653939 0.852230i
\(726\) 0 0
\(727\) 9.21373 + 34.3861i 0.341718 + 1.27531i 0.896399 + 0.443247i \(0.146174\pi\)
−0.554681 + 0.832063i \(0.687160\pi\)
\(728\) −1.70023 + 10.9232i −0.0630147 + 0.404842i
\(729\) 0 0
\(730\) −1.91331 3.74685i −0.0708149 0.138677i
\(731\) −72.2884 9.51694i −2.67368 0.351997i
\(732\) 0 0
\(733\) 5.26871 + 40.0199i 0.194604 + 1.47817i 0.758149 + 0.652081i \(0.226104\pi\)
−0.563545 + 0.826086i \(0.690563\pi\)
\(734\) −5.20258 + 28.2105i −0.192031 + 1.04127i
\(735\) 0 0
\(736\) −36.9921 4.70298i −1.36355 0.173354i
\(737\) 9.82036i 0.361737i
\(738\) 0 0
\(739\) −15.5905 + 37.6388i −0.573506 + 1.38457i 0.325046 + 0.945698i \(0.394620\pi\)
−0.898552 + 0.438868i \(0.855380\pi\)
\(740\) 4.39336 + 9.82064i 0.161503 + 0.361014i
\(741\) 0 0
\(742\) 0.779626 + 0.505311i 0.0286210 + 0.0185505i
\(743\) −36.6464 9.81938i −1.34443 0.360238i −0.486353 0.873763i \(-0.661673\pi\)
−0.858075 + 0.513524i \(0.828340\pi\)
\(744\) 0 0
\(745\) 5.74598 1.53963i 0.210517 0.0564077i
\(746\) 1.35736 + 0.439699i 0.0496964 + 0.0160985i
\(747\) 0 0
\(748\) −19.8961 32.3383i −0.727474 1.18241i
\(749\) 8.90888 6.83602i 0.325523 0.249783i
\(750\) 0 0
\(751\) 8.29232 + 14.3627i 0.302591 + 0.524103i 0.976722 0.214509i \(-0.0688150\pi\)
−0.674131 + 0.738612i \(0.735482\pi\)
\(752\) 18.8750 21.1132i 0.688299 0.769920i
\(753\) 0 0
\(754\) −68.6806 32.6841i −2.50120 1.19028i
\(755\) −13.7468 + 33.1877i −0.500297 + 1.20782i
\(756\) 0 0
\(757\) −12.3850 + 5.13003i −0.450140 + 0.186454i −0.596224 0.802818i \(-0.703333\pi\)
0.146084 + 0.989272i \(0.453333\pi\)
\(758\) 20.5351 18.5230i 0.745869 0.672784i
\(759\) 0 0
\(760\) 20.7091 + 0.487041i 0.751200 + 0.0176668i
\(761\) −3.50886 + 13.0952i −0.127196 + 0.474702i −0.999908 0.0135326i \(-0.995692\pi\)
0.872712 + 0.488235i \(0.162359\pi\)
\(762\) 0 0
\(763\) 0.702957 5.33949i 0.0254488 0.193302i
\(764\) 1.72332 + 10.7569i 0.0623477 + 0.389170i
\(765\) 0 0
\(766\) 14.5155 + 12.3751i 0.524465 + 0.447130i
\(767\) −0.694553 + 1.20300i −0.0250789 + 0.0434379i
\(768\) 0 0
\(769\) 8.64344 + 14.9709i 0.311690 + 0.539863i 0.978728 0.205160i \(-0.0657715\pi\)
−0.667038 + 0.745024i \(0.732438\pi\)
\(770\) −1.37783 + 7.47117i −0.0496536 + 0.269242i
\(771\) 0 0
\(772\) 10.3129 + 3.93774i 0.371170 + 0.141722i
\(773\) 16.9010 7.00063i 0.607887 0.251795i −0.0574376 0.998349i \(-0.518293\pi\)
0.665325 + 0.746554i \(0.268293\pi\)
\(774\) 0 0
\(775\) 8.58661 + 8.58661i 0.308440 + 0.308440i
\(776\) −7.80490 14.2839i −0.280180 0.512762i
\(777\) 0 0
\(778\) −1.83489 8.59493i −0.0657841 0.308143i
\(779\) 8.90527 + 6.83325i 0.319064 + 0.244827i
\(780\) 0 0
\(781\) 4.67342 + 6.09053i 0.167228 + 0.217936i
\(782\) 5.10812 + 64.1756i 0.182666 + 2.29492i
\(783\) 0 0
\(784\) 8.15451 + 24.7967i 0.291232 + 0.885597i
\(785\) −7.15954 + 12.4007i −0.255535 + 0.442600i
\(786\) 0 0
\(787\) −3.16847 24.0670i −0.112944 0.857894i −0.950322 0.311270i \(-0.899246\pi\)
0.837378 0.546625i \(-0.184088\pi\)
\(788\) −12.5904 + 23.2873i −0.448515 + 0.829574i
\(789\) 0 0
\(790\) 28.9858 26.1457i 1.03127 0.930221i
\(791\) −7.85975 7.85975i −0.279461 0.279461i
\(792\) 0 0
\(793\) −23.7671 + 23.7671i −0.843993 + 0.843993i
\(794\) −0.819167 + 15.9010i −0.0290711 + 0.564305i
\(795\) 0 0
\(796\) 19.5649 + 2.02120i 0.693459 + 0.0716395i
\(797\) −4.98819 + 0.656708i −0.176691 + 0.0232618i −0.218352 0.975870i \(-0.570068\pi\)
0.0416616 + 0.999132i \(0.486735\pi\)
\(798\) 0 0
\(799\) −42.3425 24.4465i −1.49797 0.864854i
\(800\) −15.9225 + 6.67837i −0.562946 + 0.236116i
\(801\) 0 0
\(802\) 11.0559 + 9.42562i 0.390396 + 0.332830i
\(803\) −2.28644 + 1.75445i −0.0806868 + 0.0619131i
\(804\) 0 0
\(805\) 7.84176 10.2196i 0.276386 0.360193i
\(806\) 17.3682 26.7967i 0.611767 0.943874i
\(807\) 0 0
\(808\) −14.5932 11.7531i −0.513387 0.413471i
\(809\) 0.504387 0.504387i 0.0177333 0.0177333i −0.698185 0.715918i \(-0.746008\pi\)
0.715918 + 0.698185i \(0.246008\pi\)
\(810\) 0 0
\(811\) 13.1867 + 31.8355i 0.463047 + 1.11789i 0.967140 + 0.254245i \(0.0818269\pi\)
−0.504093 + 0.863649i \(0.668173\pi\)
\(812\) 13.0462 0.364833i 0.457832 0.0128031i
\(813\) 0 0
\(814\) 6.07006 4.17979i 0.212756 0.146501i
\(815\) −16.5845 + 9.57505i −0.580929 + 0.335399i
\(816\) 0 0
\(817\) −23.5992 13.6250i −0.825632 0.476679i
\(818\) −16.6719 + 1.32702i −0.582920 + 0.0463981i
\(819\) 0 0
\(820\) −24.0109 5.71939i −0.838498 0.199730i
\(821\) −20.2261 2.66282i −0.705897 0.0929332i −0.230974 0.972960i \(-0.574191\pi\)
−0.474924 + 0.880027i \(0.657524\pi\)
\(822\) 0 0
\(823\) 25.8740 + 6.93293i 0.901912 + 0.241667i 0.679837 0.733363i \(-0.262050\pi\)
0.222075 + 0.975030i \(0.428717\pi\)
\(824\) 0.799191 + 0.837688i 0.0278411 + 0.0291822i
\(825\) 0 0
\(826\) 0.0122631 0.238041i 0.000426687 0.00828251i
\(827\) −14.6945 35.4756i −0.510977 1.23361i −0.943316 0.331896i \(-0.892312\pi\)
0.432339 0.901711i \(-0.357688\pi\)
\(828\) 0 0
\(829\) 3.50068 + 1.45003i 0.121584 + 0.0503616i 0.442646 0.896696i \(-0.354040\pi\)
−0.321062 + 0.947058i \(0.604040\pi\)
\(830\) 0.467687 + 1.31699i 0.0162337 + 0.0457133i
\(831\) 0 0
\(832\) 25.9168 + 37.2818i 0.898505 + 1.29251i
\(833\) 39.0277 22.5327i 1.35223 0.780711i
\(834\) 0 0
\(835\) 37.8368 + 49.3099i 1.30940 + 1.70644i
\(836\) −2.24477 14.0117i −0.0776369 0.484604i
\(837\) 0 0
\(838\) −11.0984 21.7341i −0.383388 0.750791i
\(839\) 1.80004 + 6.71785i 0.0621444 + 0.231926i 0.990012 0.140984i \(-0.0450267\pi\)
−0.927867 + 0.372910i \(0.878360\pi\)
\(840\) 0 0
\(841\) −15.7357 + 58.7263i −0.542609 + 2.02505i
\(842\) 50.5781 10.7977i 1.74304 0.372113i
\(843\) 0 0
\(844\) 38.5348 + 36.4382i 1.32642 + 1.25425i
\(845\) 50.3691 + 20.8636i 1.73275 + 0.717728i
\(846\) 0 0
\(847\) −2.37072 −0.0814589
\(848\) 3.74952 0.708729i 0.128759 0.0243379i
\(849\) 0 0
\(850\) 16.9060 + 24.5516i 0.579870 + 0.842112i
\(851\) −12.3894 + 1.63109i −0.424702 + 0.0559131i
\(852\) 0 0
\(853\) −4.16449 + 31.6324i −0.142589 + 1.08307i 0.759188 + 0.650872i \(0.225596\pi\)
−0.901777 + 0.432202i \(0.857737\pi\)
\(854\) 1.77736 5.48673i 0.0608200 0.187752i
\(855\) 0 0
\(856\) 7.09363 45.5735i 0.242455 1.55767i
\(857\) −13.8148 + 3.70167i −0.471905 + 0.126447i −0.486931 0.873441i \(-0.661884\pi\)
0.0150259 + 0.999887i \(0.495217\pi\)
\(858\) 0 0
\(859\) −19.1963 14.7298i −0.654970 0.502576i 0.226992 0.973897i \(-0.427111\pi\)
−0.881962 + 0.471321i \(0.843777\pi\)
\(860\) 59.6038 + 6.15752i 2.03247 + 0.209970i
\(861\) 0 0
\(862\) −6.15188 17.3234i −0.209534 0.590038i
\(863\) −4.17868 −0.142244 −0.0711219 0.997468i \(-0.522658\pi\)
−0.0711219 + 0.997468i \(0.522658\pi\)
\(864\) 0 0
\(865\) 27.4848 0.934510
\(866\) 2.82465 + 7.95410i 0.0959856 + 0.270291i
\(867\) 0 0
\(868\) −0.563065 + 5.45038i −0.0191117 + 0.184998i
\(869\) −21.2147 16.2786i −0.719661 0.552215i
\(870\) 0 0
\(871\) 19.5839 5.24749i 0.663575 0.177804i
\(872\) −13.0495 17.8607i −0.441911 0.604841i
\(873\) 0 0
\(874\) −7.41483 + 22.8897i −0.250810 + 0.774256i
\(875\) −0.496789 + 3.77349i −0.0167945 + 0.127567i
\(876\) 0 0
\(877\) 12.7862 1.68334i 0.431761 0.0568424i 0.0884860 0.996077i \(-0.471797\pi\)
0.343275 + 0.939235i \(0.388464\pi\)
\(878\) 9.61727 + 13.9666i 0.324567 + 0.471350i
\(879\) 0 0
\(880\) 17.0876 + 26.1090i 0.576024 + 0.880134i
\(881\) −42.3840 −1.42795 −0.713977 0.700169i \(-0.753108\pi\)
−0.713977 + 0.700169i \(0.753108\pi\)
\(882\) 0 0
\(883\) −16.3800 6.78482i −0.551231 0.228327i 0.0896423 0.995974i \(-0.471428\pi\)
−0.640873 + 0.767647i \(0.721428\pi\)
\(884\) 53.8582 56.9571i 1.81145 1.91567i
\(885\) 0 0
\(886\) −6.58402 + 1.40559i −0.221195 + 0.0472218i
\(887\) 5.38743 20.1062i 0.180892 0.675099i −0.814580 0.580051i \(-0.803033\pi\)
0.995473 0.0950485i \(-0.0303006\pi\)
\(888\) 0 0
\(889\) 1.12845 + 4.21143i 0.0378470 + 0.141247i
\(890\) 6.47769 + 12.6853i 0.217133 + 0.425212i
\(891\) 0 0
\(892\) −19.5265 + 3.12828i −0.653795 + 0.104742i
\(893\) −11.1240 14.4971i −0.372250 0.485126i
\(894\) 0 0
\(895\) −51.2960 + 29.6157i −1.71463 + 0.989945i
\(896\) −6.86990 3.67490i −0.229507 0.122770i
\(897\) 0 0
\(898\) 19.0322 + 53.5939i 0.635113 + 1.78845i
\(899\) −34.8305 14.4273i −1.16166 0.481176i
\(900\) 0 0
\(901\) −2.52109 6.08646i −0.0839898 0.202769i
\(902\) −0.869913 + 16.8860i −0.0289649 + 0.562244i
\(903\) 0 0
\(904\) −45.6413 1.07340i −1.51801 0.0357007i
\(905\) 1.96903 + 0.527600i 0.0654527 + 0.0175380i
\(906\) 0 0
\(907\) −35.0384 4.61289i −1.16343 0.153168i −0.476017 0.879436i \(-0.657920\pi\)
−0.687412 + 0.726267i \(0.741253\pi\)
\(908\) 1.94630 8.17089i 0.0645904 0.271161i
\(909\) 0 0
\(910\) −15.6354 + 1.24451i −0.518307 + 0.0412552i
\(911\) 15.2050 + 8.77860i 0.503764 + 0.290848i 0.730266 0.683162i \(-0.239396\pi\)
−0.226503 + 0.974011i \(0.572729\pi\)
\(912\) 0 0
\(913\) 0.829112 0.478688i 0.0274396 0.0158423i
\(914\) 43.4573 29.9243i 1.43744 0.989807i
\(915\) 0 0
\(916\) −0.604413 21.6135i −0.0199704 0.714129i
\(917\) 3.21179 + 7.75394i 0.106063 + 0.256058i
\(918\) 0 0
\(919\) −21.4242 + 21.4242i −0.706718 + 0.706718i −0.965844 0.259126i \(-0.916566\pi\)
0.259126 + 0.965844i \(0.416566\pi\)
\(920\) −5.67065 52.6032i −0.186956 1.73427i
\(921\) 0 0
\(922\) 1.25322 1.93355i 0.0412726 0.0636780i
\(923\) −9.64858 + 12.5743i −0.317587 + 0.413887i
\(924\) 0 0
\(925\) −4.59047 + 3.52239i −0.150934 + 0.115815i
\(926\) −10.1573 8.65951i −0.333788 0.284569i
\(927\) 0 0
\(928\) 37.7359 38.0728i 1.23874 1.24980i
\(929\) 6.13817 + 3.54387i 0.201387 + 0.116271i 0.597302 0.802016i \(-0.296239\pi\)
−0.395915 + 0.918287i \(0.629573\pi\)
\(930\) 0 0
\(931\) 16.6985 2.19840i 0.547272 0.0720498i
\(932\) −3.09072 + 29.9177i −0.101240 + 0.979986i
\(933\) 0 0
\(934\) 0.258295 5.01382i 0.00845169 0.164057i
\(935\) 38.0926 38.0926i 1.24576 1.24576i
\(936\) 0 0
\(937\) −6.65530 6.65530i −0.217419 0.217419i 0.589991 0.807410i \(-0.299131\pi\)
−0.807410 + 0.589991i \(0.799131\pi\)
\(938\) −2.58329 + 2.33016i −0.0843474 + 0.0760826i
\(939\) 0 0
\(940\) 35.3462 + 19.1101i 1.15286 + 0.623304i
\(941\) −3.05083 23.1733i −0.0994541 0.755429i −0.966403 0.257032i \(-0.917256\pi\)
0.866949 0.498397i \(-0.166078\pi\)
\(942\) 0 0
\(943\) 14.3347 24.8285i 0.466803 0.808526i
\(944\) −0.638451 0.742171i −0.0207798 0.0241556i
\(945\) 0 0
\(946\) −3.25694 40.9184i −0.105892 1.33037i
\(947\) −12.6319 16.4622i −0.410481 0.534949i 0.541664 0.840595i \(-0.317794\pi\)
−0.952145 + 0.305646i \(0.901128\pi\)
\(948\) 0 0
\(949\) −4.72050 3.62217i −0.153234 0.117581i
\(950\) 2.32600 + 10.8953i 0.0754653 + 0.353491i
\(951\) 0 0
\(952\) −3.78582 + 12.9070i −0.122699 + 0.418318i
\(953\) −19.2927 19.2927i −0.624952 0.624952i 0.321841 0.946794i \(-0.395698\pi\)
−0.946794 + 0.321841i \(0.895698\pi\)
\(954\) 0 0
\(955\) −14.2802 + 5.91504i −0.462096 + 0.191406i
\(956\) 15.1840 39.7669i 0.491087 1.28615i
\(957\) 0 0
\(958\) 7.36945 39.9602i 0.238096 1.29105i
\(959\) −2.78842 4.82968i −0.0900426 0.155958i
\(960\) 0 0
\(961\) −7.58607 + 13.1395i −0.244712 + 0.423854i
\(962\) 11.5789 + 9.87155i 0.373319 + 0.318271i
\(963\) 0 0
\(964\) 37.6276 6.02820i 1.21190 0.194155i
\(965\) −2.04438 + 15.5286i −0.0658109 + 0.499883i
\(966\) 0 0
\(967\) −12.8166 + 47.8320i −0.412152 + 1.53817i 0.378319 + 0.925675i \(0.376502\pi\)
−0.790472 + 0.612499i \(0.790164\pi\)
\(968\) −7.04523 + 6.72146i −0.226442 + 0.216036i
\(969\) 0 0
\(970\) 17.1488 15.4685i 0.550615 0.496663i
\(971\) 47.4354 19.6484i 1.52228 0.630547i 0.544229 0.838937i \(-0.316822\pi\)
0.978046 + 0.208390i \(0.0668222\pi\)
\(972\) 0 0
\(973\) 0.425949 1.02833i 0.0136553 0.0329668i
\(974\) −12.6025 5.99736i −0.403811 0.192168i
\(975\) 0 0
\(976\) −10.2741 21.3445i −0.328865 0.683219i
\(977\) −3.79556 6.57411i −0.121431 0.210324i 0.798901 0.601462i \(-0.205415\pi\)
−0.920332 + 0.391138i \(0.872082\pi\)
\(978\) 0 0
\(979\) 7.74095 5.93984i 0.247402 0.189838i
\(980\) −31.5438 + 19.4073i −1.00763 + 0.619942i
\(981\) 0 0
\(982\) −26.6792 8.64238i −0.851367 0.275790i
\(983\) −25.7659 + 6.90394i −0.821803 + 0.220201i −0.645135 0.764069i \(-0.723199\pi\)
−0.176668 + 0.984270i \(0.556532\pi\)
\(984\) 0 0
\(985\) −36.2807 9.72137i −1.15600 0.309749i
\(986\) −77.6606 50.3353i −2.47322 1.60300i
\(987\) 0 0
\(988\) 26.7428 11.9637i 0.850802 0.380615i
\(989\) −26.6345 + 64.3014i −0.846929 + 2.04467i
\(990\) 0 0
\(991\) 25.3003i 0.803691i −0.915707 0.401846i \(-0.868369\pi\)
0.915707 0.401846i \(-0.131631\pi\)
\(992\) 13.7796 + 17.7937i 0.437503 + 0.564949i
\(993\) 0 0
\(994\) 0.493235 2.67452i 0.0156445 0.0848306i
\(995\) 3.64258 + 27.6682i 0.115478 + 0.877140i
\(996\) 0 0
\(997\) −4.97372 0.654802i −0.157519 0.0207378i 0.0513541 0.998681i \(-0.483646\pi\)
−0.208873 + 0.977943i \(0.566980\pi\)
\(998\) 10.6913 + 20.9368i 0.338426 + 0.662741i
\(999\) 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.bn.a.35.5 368
3.2 odd 2 288.2.bf.a.227.42 yes 368
9.4 even 3 288.2.bf.a.131.27 yes 368
9.5 odd 6 inner 864.2.bn.a.611.20 368
32.11 odd 8 inner 864.2.bn.a.683.20 368
96.11 even 8 288.2.bf.a.11.27 368
288.139 odd 24 288.2.bf.a.203.42 yes 368
288.203 even 24 inner 864.2.bn.a.395.5 368
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
288.2.bf.a.11.27 368 96.11 even 8
288.2.bf.a.131.27 yes 368 9.4 even 3
288.2.bf.a.203.42 yes 368 288.139 odd 24
288.2.bf.a.227.42 yes 368 3.2 odd 2
864.2.bn.a.35.5 368 1.1 even 1 trivial
864.2.bn.a.395.5 368 288.203 even 24 inner
864.2.bn.a.611.20 368 9.5 odd 6 inner
864.2.bn.a.683.20 368 32.11 odd 8 inner