Properties

Label 378.2.l.a.341.2
Level $378$
Weight $2$
Character 378.341
Analytic conductor $3.018$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [378,2,Mod(143,378)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(378, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("378.143");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.l (of order \(6\), degree \(2\), 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: \(3.01834519640\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + 2785 x^{8} - 2640 x^{7} - 2601 x^{6} + 10260 x^{5} - 10611 x^{4} - 1944 x^{3} + \cdots + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 341.2
Root \(-1.70672 + 0.295146i\) of defining polynomial
Character \(\chi\) \(=\) 378.341
Dual form 378.2.l.a.143.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000 q^{4} +(-0.483662 - 0.837727i) q^{5} +(-2.16249 + 1.52435i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000 q^{4} +(-0.483662 - 0.837727i) q^{5} +(-2.16249 + 1.52435i) q^{7} +1.00000i q^{8} +(-0.837727 + 0.483662i) q^{10} +(-4.82689 - 2.78681i) q^{11} +(-3.76893 - 2.17600i) q^{13} +(1.52435 + 2.16249i) q^{14} +1.00000 q^{16} +(-1.97267 - 3.41677i) q^{17} +(3.86796 + 2.23317i) q^{19} +(0.483662 + 0.837727i) q^{20} +(-2.78681 + 4.82689i) q^{22} +(-2.29786 + 1.32667i) q^{23} +(2.03214 - 3.51977i) q^{25} +(-2.17600 + 3.76893i) q^{26} +(2.16249 - 1.52435i) q^{28} +(-4.61157 + 2.66249i) q^{29} +6.16655i q^{31} -1.00000i q^{32} +(-3.41677 + 1.97267i) q^{34} +(2.32290 + 1.07431i) q^{35} +(0.243608 - 0.421942i) q^{37} +(2.23317 - 3.86796i) q^{38} +(0.837727 - 0.483662i) q^{40} +(-0.0818856 + 0.141830i) q^{41} +(-4.35045 - 7.53520i) q^{43} +(4.82689 + 2.78681i) q^{44} +(1.32667 + 2.29786i) q^{46} +9.49001 q^{47} +(2.35274 - 6.59277i) q^{49} +(-3.51977 - 2.03214i) q^{50} +(3.76893 + 2.17600i) q^{52} +(1.74520 - 1.00759i) q^{53} +5.39149i q^{55} +(-1.52435 - 2.16249i) q^{56} +(2.66249 + 4.61157i) q^{58} -1.67386 q^{59} -5.17221i q^{61} +6.16655 q^{62} -1.00000 q^{64} +4.20979i q^{65} -5.44252 q^{67} +(1.97267 + 3.41677i) q^{68} +(1.07431 - 2.32290i) q^{70} -3.64006i q^{71} +(-2.15468 + 1.24401i) q^{73} +(-0.421942 - 0.243608i) q^{74} +(-3.86796 - 2.23317i) q^{76} +(14.6862 - 1.33140i) q^{77} +4.60242 q^{79} +(-0.483662 - 0.837727i) q^{80} +(0.141830 + 0.0818856i) q^{82} +(4.20979 + 7.29158i) q^{83} +(-1.90821 + 3.30512i) q^{85} +(-7.53520 + 4.35045i) q^{86} +(2.78681 - 4.82689i) q^{88} +(2.05811 - 3.56475i) q^{89} +(11.4673 - 1.03959i) q^{91} +(2.29786 - 1.32667i) q^{92} -9.49001i q^{94} -4.32040i q^{95} +(10.2669 - 5.92762i) q^{97} +(-6.59277 - 2.35274i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{4} + 2 q^{7} - 12 q^{11} + 6 q^{13} + 6 q^{14} + 16 q^{16} + 18 q^{17} + 6 q^{23} - 8 q^{25} - 12 q^{26} - 2 q^{28} - 6 q^{29} - 30 q^{35} - 2 q^{37} + 6 q^{41} - 2 q^{43} + 12 q^{44} + 6 q^{46} + 36 q^{47} - 8 q^{49} + 12 q^{50} - 6 q^{52} + 36 q^{53} - 6 q^{56} + 6 q^{58} - 60 q^{59} - 36 q^{62} - 16 q^{64} - 28 q^{67} - 18 q^{68} - 18 q^{70} - 18 q^{74} + 42 q^{77} + 32 q^{79} - 12 q^{85} - 24 q^{86} + 24 q^{89} - 12 q^{91} - 6 q^{92} + 6 q^{97} + 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) −0.483662 0.837727i −0.216300 0.374643i 0.737374 0.675485i \(-0.236066\pi\)
−0.953674 + 0.300842i \(0.902732\pi\)
\(6\) 0 0
\(7\) −2.16249 + 1.52435i −0.817345 + 0.576149i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −0.837727 + 0.483662i −0.264913 + 0.152947i
\(11\) −4.82689 2.78681i −1.45536 0.840254i −0.456584 0.889680i \(-0.650927\pi\)
−0.998778 + 0.0494264i \(0.984261\pi\)
\(12\) 0 0
\(13\) −3.76893 2.17600i −1.04531 0.603512i −0.123980 0.992285i \(-0.539566\pi\)
−0.921334 + 0.388772i \(0.872899\pi\)
\(14\) 1.52435 + 2.16249i 0.407399 + 0.577950i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −1.97267 3.41677i −0.478443 0.828688i 0.521251 0.853403i \(-0.325465\pi\)
−0.999695 + 0.0247150i \(0.992132\pi\)
\(18\) 0 0
\(19\) 3.86796 + 2.23317i 0.887371 + 0.512324i 0.873082 0.487574i \(-0.162118\pi\)
0.0142896 + 0.999898i \(0.495451\pi\)
\(20\) 0.483662 + 0.837727i 0.108150 + 0.187322i
\(21\) 0 0
\(22\) −2.78681 + 4.82689i −0.594149 + 1.02910i
\(23\) −2.29786 + 1.32667i −0.479137 + 0.276630i −0.720057 0.693915i \(-0.755884\pi\)
0.240920 + 0.970545i \(0.422551\pi\)
\(24\) 0 0
\(25\) 2.03214 3.51977i 0.406428 0.703955i
\(26\) −2.17600 + 3.76893i −0.426748 + 0.739149i
\(27\) 0 0
\(28\) 2.16249 1.52435i 0.408673 0.288074i
\(29\) −4.61157 + 2.66249i −0.856347 + 0.494412i −0.862787 0.505567i \(-0.831283\pi\)
0.00644015 + 0.999979i \(0.497950\pi\)
\(30\) 0 0
\(31\) 6.16655i 1.10754i 0.832668 + 0.553772i \(0.186812\pi\)
−0.832668 + 0.553772i \(0.813188\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) −3.41677 + 1.97267i −0.585971 + 0.338311i
\(35\) 2.32290 + 1.07431i 0.392642 + 0.181592i
\(36\) 0 0
\(37\) 0.243608 0.421942i 0.0400490 0.0693669i −0.845306 0.534282i \(-0.820582\pi\)
0.885355 + 0.464915i \(0.153915\pi\)
\(38\) 2.23317 3.86796i 0.362268 0.627466i
\(39\) 0 0
\(40\) 0.837727 0.483662i 0.132456 0.0764737i
\(41\) −0.0818856 + 0.141830i −0.0127884 + 0.0221501i −0.872349 0.488884i \(-0.837404\pi\)
0.859560 + 0.511034i \(0.170737\pi\)
\(42\) 0 0
\(43\) −4.35045 7.53520i −0.663437 1.14911i −0.979707 0.200437i \(-0.935764\pi\)
0.316270 0.948669i \(-0.397570\pi\)
\(44\) 4.82689 + 2.78681i 0.727681 + 0.420127i
\(45\) 0 0
\(46\) 1.32667 + 2.29786i 0.195607 + 0.338801i
\(47\) 9.49001 1.38426 0.692130 0.721773i \(-0.256672\pi\)
0.692130 + 0.721773i \(0.256672\pi\)
\(48\) 0 0
\(49\) 2.35274 6.59277i 0.336106 0.941824i
\(50\) −3.51977 2.03214i −0.497771 0.287388i
\(51\) 0 0
\(52\) 3.76893 + 2.17600i 0.522657 + 0.301756i
\(53\) 1.74520 1.00759i 0.239722 0.138403i −0.375327 0.926892i \(-0.622470\pi\)
0.615049 + 0.788489i \(0.289136\pi\)
\(54\) 0 0
\(55\) 5.39149i 0.726988i
\(56\) −1.52435 2.16249i −0.203699 0.288975i
\(57\) 0 0
\(58\) 2.66249 + 4.61157i 0.349602 + 0.605529i
\(59\) −1.67386 −0.217918 −0.108959 0.994046i \(-0.534752\pi\)
−0.108959 + 0.994046i \(0.534752\pi\)
\(60\) 0 0
\(61\) 5.17221i 0.662234i −0.943590 0.331117i \(-0.892574\pi\)
0.943590 0.331117i \(-0.107426\pi\)
\(62\) 6.16655 0.783152
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 4.20979i 0.522160i
\(66\) 0 0
\(67\) −5.44252 −0.664909 −0.332455 0.943119i \(-0.607877\pi\)
−0.332455 + 0.943119i \(0.607877\pi\)
\(68\) 1.97267 + 3.41677i 0.239222 + 0.414344i
\(69\) 0 0
\(70\) 1.07431 2.32290i 0.128405 0.277640i
\(71\) 3.64006i 0.431996i −0.976394 0.215998i \(-0.930700\pi\)
0.976394 0.215998i \(-0.0693005\pi\)
\(72\) 0 0
\(73\) −2.15468 + 1.24401i −0.252186 + 0.145600i −0.620765 0.783997i \(-0.713178\pi\)
0.368579 + 0.929597i \(0.379845\pi\)
\(74\) −0.421942 0.243608i −0.0490498 0.0283189i
\(75\) 0 0
\(76\) −3.86796 2.23317i −0.443686 0.256162i
\(77\) 14.6862 1.33140i 1.67364 0.151728i
\(78\) 0 0
\(79\) 4.60242 0.517812 0.258906 0.965902i \(-0.416638\pi\)
0.258906 + 0.965902i \(0.416638\pi\)
\(80\) −0.483662 0.837727i −0.0540751 0.0936608i
\(81\) 0 0
\(82\) 0.141830 + 0.0818856i 0.0156625 + 0.00904275i
\(83\) 4.20979 + 7.29158i 0.462085 + 0.800355i 0.999065 0.0432405i \(-0.0137682\pi\)
−0.536980 + 0.843595i \(0.680435\pi\)
\(84\) 0 0
\(85\) −1.90821 + 3.30512i −0.206975 + 0.358491i
\(86\) −7.53520 + 4.35045i −0.812541 + 0.469121i
\(87\) 0 0
\(88\) 2.78681 4.82689i 0.297075 0.514548i
\(89\) 2.05811 3.56475i 0.218159 0.377863i −0.736086 0.676888i \(-0.763328\pi\)
0.954245 + 0.299025i \(0.0966615\pi\)
\(90\) 0 0
\(91\) 11.4673 1.03959i 1.20210 0.108978i
\(92\) 2.29786 1.32667i 0.239569 0.138315i
\(93\) 0 0
\(94\) 9.49001i 0.978820i
\(95\) 4.32040i 0.443263i
\(96\) 0 0
\(97\) 10.2669 5.92762i 1.04245 0.601859i 0.121924 0.992539i \(-0.461094\pi\)
0.920526 + 0.390681i \(0.127760\pi\)
\(98\) −6.59277 2.35274i −0.665970 0.237663i
\(99\) 0 0
\(100\) −2.03214 + 3.51977i −0.203214 + 0.351977i
\(101\) −2.65813 + 4.60402i −0.264494 + 0.458117i −0.967431 0.253135i \(-0.918538\pi\)
0.702937 + 0.711252i \(0.251872\pi\)
\(102\) 0 0
\(103\) 7.74616 4.47225i 0.763252 0.440664i −0.0672102 0.997739i \(-0.521410\pi\)
0.830462 + 0.557075i \(0.188076\pi\)
\(104\) 2.17600 3.76893i 0.213374 0.369574i
\(105\) 0 0
\(106\) −1.00759 1.74520i −0.0978659 0.169509i
\(107\) −16.5898 9.57813i −1.60380 0.925953i −0.990718 0.135931i \(-0.956597\pi\)
−0.613079 0.790022i \(-0.710069\pi\)
\(108\) 0 0
\(109\) −9.62168 16.6652i −0.921590 1.59624i −0.796955 0.604038i \(-0.793557\pi\)
−0.124635 0.992203i \(-0.539776\pi\)
\(110\) 5.39149 0.514058
\(111\) 0 0
\(112\) −2.16249 + 1.52435i −0.204336 + 0.144037i
\(113\) −7.31199 4.22158i −0.687854 0.397133i 0.114953 0.993371i \(-0.463328\pi\)
−0.802808 + 0.596238i \(0.796661\pi\)
\(114\) 0 0
\(115\) 2.22278 + 1.28332i 0.207275 + 0.119670i
\(116\) 4.61157 2.66249i 0.428174 0.247206i
\(117\) 0 0
\(118\) 1.67386i 0.154091i
\(119\) 9.47423 + 4.38170i 0.868501 + 0.401670i
\(120\) 0 0
\(121\) 10.0326 + 17.3769i 0.912053 + 1.57972i
\(122\) −5.17221 −0.468270
\(123\) 0 0
\(124\) 6.16655i 0.553772i
\(125\) −8.76810 −0.784243
\(126\) 0 0
\(127\) 3.31883 0.294498 0.147249 0.989099i \(-0.452958\pi\)
0.147249 + 0.989099i \(0.452958\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) 4.20979 0.369223
\(131\) 9.37335 + 16.2351i 0.818954 + 1.41847i 0.906454 + 0.422305i \(0.138779\pi\)
−0.0875000 + 0.996165i \(0.527888\pi\)
\(132\) 0 0
\(133\) −11.7686 + 1.06690i −1.02046 + 0.0925121i
\(134\) 5.44252i 0.470162i
\(135\) 0 0
\(136\) 3.41677 1.97267i 0.292986 0.169155i
\(137\) −14.6656 8.46717i −1.25296 0.723399i −0.281267 0.959630i \(-0.590755\pi\)
−0.971697 + 0.236230i \(0.924088\pi\)
\(138\) 0 0
\(139\) −10.5033 6.06406i −0.890875 0.514347i −0.0166466 0.999861i \(-0.505299\pi\)
−0.874229 + 0.485514i \(0.838632\pi\)
\(140\) −2.32290 1.07431i −0.196321 0.0907958i
\(141\) 0 0
\(142\) −3.64006 −0.305467
\(143\) 12.1282 + 21.0066i 1.01421 + 1.75666i
\(144\) 0 0
\(145\) 4.46088 + 2.57549i 0.370456 + 0.213883i
\(146\) 1.24401 + 2.15468i 0.102955 + 0.178323i
\(147\) 0 0
\(148\) −0.243608 + 0.421942i −0.0200245 + 0.0346834i
\(149\) 7.56951 4.37026i 0.620118 0.358025i −0.156797 0.987631i \(-0.550117\pi\)
0.776915 + 0.629606i \(0.216783\pi\)
\(150\) 0 0
\(151\) −11.0471 + 19.1341i −0.898997 + 1.55711i −0.0702195 + 0.997532i \(0.522370\pi\)
−0.828778 + 0.559578i \(0.810963\pi\)
\(152\) −2.23317 + 3.86796i −0.181134 + 0.313733i
\(153\) 0 0
\(154\) −1.33140 14.6862i −0.107288 1.18345i
\(155\) 5.16588 2.98252i 0.414934 0.239562i
\(156\) 0 0
\(157\) 1.42457i 0.113693i −0.998383 0.0568467i \(-0.981895\pi\)
0.998383 0.0568467i \(-0.0181046\pi\)
\(158\) 4.60242i 0.366149i
\(159\) 0 0
\(160\) −0.837727 + 0.483662i −0.0662282 + 0.0382368i
\(161\) 2.94680 6.37165i 0.232241 0.502157i
\(162\) 0 0
\(163\) −3.72148 + 6.44579i −0.291489 + 0.504873i −0.974162 0.225851i \(-0.927484\pi\)
0.682673 + 0.730724i \(0.260817\pi\)
\(164\) 0.0818856 0.141830i 0.00639419 0.0110751i
\(165\) 0 0
\(166\) 7.29158 4.20979i 0.565936 0.326743i
\(167\) 3.24855 5.62665i 0.251380 0.435404i −0.712526 0.701646i \(-0.752449\pi\)
0.963906 + 0.266242i \(0.0857822\pi\)
\(168\) 0 0
\(169\) 2.96991 + 5.14404i 0.228455 + 0.395695i
\(170\) 3.30512 + 1.90821i 0.253491 + 0.146353i
\(171\) 0 0
\(172\) 4.35045 + 7.53520i 0.331718 + 0.574553i
\(173\) −11.8188 −0.898564 −0.449282 0.893390i \(-0.648320\pi\)
−0.449282 + 0.893390i \(0.648320\pi\)
\(174\) 0 0
\(175\) 0.970861 + 10.7092i 0.0733902 + 0.809537i
\(176\) −4.82689 2.78681i −0.363841 0.210063i
\(177\) 0 0
\(178\) −3.56475 2.05811i −0.267189 0.154262i
\(179\) 2.10764 1.21685i 0.157533 0.0909515i −0.419161 0.907912i \(-0.637676\pi\)
0.576694 + 0.816960i \(0.304343\pi\)
\(180\) 0 0
\(181\) 11.5342i 0.857327i 0.903464 + 0.428663i \(0.141015\pi\)
−0.903464 + 0.428663i \(0.858985\pi\)
\(182\) −1.03959 11.4673i −0.0770593 0.850010i
\(183\) 0 0
\(184\) −1.32667 2.29786i −0.0978035 0.169401i
\(185\) −0.471297 −0.0346504
\(186\) 0 0
\(187\) 21.9898i 1.60806i
\(188\) −9.49001 −0.692130
\(189\) 0 0
\(190\) −4.32040 −0.313435
\(191\) 22.0689i 1.59685i 0.602094 + 0.798425i \(0.294333\pi\)
−0.602094 + 0.798425i \(0.705667\pi\)
\(192\) 0 0
\(193\) −19.9396 −1.43528 −0.717641 0.696413i \(-0.754778\pi\)
−0.717641 + 0.696413i \(0.754778\pi\)
\(194\) −5.92762 10.2669i −0.425578 0.737123i
\(195\) 0 0
\(196\) −2.35274 + 6.59277i −0.168053 + 0.470912i
\(197\) 4.62560i 0.329560i 0.986330 + 0.164780i \(0.0526914\pi\)
−0.986330 + 0.164780i \(0.947309\pi\)
\(198\) 0 0
\(199\) −18.1024 + 10.4514i −1.28324 + 0.740882i −0.977440 0.211212i \(-0.932259\pi\)
−0.305805 + 0.952094i \(0.598925\pi\)
\(200\) 3.51977 + 2.03214i 0.248886 + 0.143694i
\(201\) 0 0
\(202\) 4.60402 + 2.65813i 0.323938 + 0.187025i
\(203\) 5.91393 12.7872i 0.415076 0.897489i
\(204\) 0 0
\(205\) 0.158420 0.0110645
\(206\) −4.47225 7.74616i −0.311596 0.539701i
\(207\) 0 0
\(208\) −3.76893 2.17600i −0.261329 0.150878i
\(209\) −12.4468 21.5585i −0.860965 1.49123i
\(210\) 0 0
\(211\) −3.34310 + 5.79042i −0.230148 + 0.398629i −0.957852 0.287263i \(-0.907254\pi\)
0.727703 + 0.685892i \(0.240588\pi\)
\(212\) −1.74520 + 1.00759i −0.119861 + 0.0692017i
\(213\) 0 0
\(214\) −9.57813 + 16.5898i −0.654747 + 1.13406i
\(215\) −4.20829 + 7.28898i −0.287003 + 0.497104i
\(216\) 0 0
\(217\) −9.39995 13.3351i −0.638110 0.905246i
\(218\) −16.6652 + 9.62168i −1.12871 + 0.651663i
\(219\) 0 0
\(220\) 5.39149i 0.363494i
\(221\) 17.1701i 1.15499i
\(222\) 0 0
\(223\) 7.08622 4.09123i 0.474528 0.273969i −0.243605 0.969875i \(-0.578330\pi\)
0.718133 + 0.695905i \(0.244997\pi\)
\(224\) 1.52435 + 2.16249i 0.101850 + 0.144488i
\(225\) 0 0
\(226\) −4.22158 + 7.31199i −0.280815 + 0.486386i
\(227\) 5.34688 9.26106i 0.354885 0.614678i −0.632214 0.774794i \(-0.717853\pi\)
0.987098 + 0.160116i \(0.0511868\pi\)
\(228\) 0 0
\(229\) 25.2942 14.6036i 1.67149 0.965034i 0.704682 0.709524i \(-0.251090\pi\)
0.966806 0.255510i \(-0.0822435\pi\)
\(230\) 1.28332 2.22278i 0.0846197 0.146566i
\(231\) 0 0
\(232\) −2.66249 4.61157i −0.174801 0.302764i
\(233\) −5.57664 3.21967i −0.365338 0.210928i 0.306082 0.952005i \(-0.400982\pi\)
−0.671420 + 0.741077i \(0.734315\pi\)
\(234\) 0 0
\(235\) −4.58996 7.95004i −0.299416 0.518603i
\(236\) 1.67386 0.108959
\(237\) 0 0
\(238\) 4.38170 9.47423i 0.284023 0.614123i
\(239\) 4.01452 + 2.31778i 0.259678 + 0.149925i 0.624187 0.781275i \(-0.285430\pi\)
−0.364510 + 0.931200i \(0.618763\pi\)
\(240\) 0 0
\(241\) 9.08846 + 5.24722i 0.585439 + 0.338003i 0.763292 0.646054i \(-0.223582\pi\)
−0.177853 + 0.984057i \(0.556915\pi\)
\(242\) 17.3769 10.0326i 1.11703 0.644919i
\(243\) 0 0
\(244\) 5.17221i 0.331117i
\(245\) −6.66087 + 1.21772i −0.425548 + 0.0777971i
\(246\) 0 0
\(247\) −9.71873 16.8333i −0.618388 1.07108i
\(248\) −6.16655 −0.391576
\(249\) 0 0
\(250\) 8.76810i 0.554543i
\(251\) −7.85271 −0.495659 −0.247829 0.968804i \(-0.579717\pi\)
−0.247829 + 0.968804i \(0.579717\pi\)
\(252\) 0 0
\(253\) 14.7887 0.929758
\(254\) 3.31883i 0.208242i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 1.71568 + 2.97164i 0.107021 + 0.185366i 0.914562 0.404445i \(-0.132535\pi\)
−0.807541 + 0.589811i \(0.799202\pi\)
\(258\) 0 0
\(259\) 0.116385 + 1.28379i 0.00723178 + 0.0797708i
\(260\) 4.20979i 0.261080i
\(261\) 0 0
\(262\) 16.2351 9.37335i 1.00301 0.579088i
\(263\) 3.17080 + 1.83066i 0.195520 + 0.112883i 0.594564 0.804048i \(-0.297325\pi\)
−0.399044 + 0.916932i \(0.630658\pi\)
\(264\) 0 0
\(265\) −1.68817 0.974668i −0.103704 0.0598734i
\(266\) 1.06690 + 11.7686i 0.0654160 + 0.721577i
\(267\) 0 0
\(268\) 5.44252 0.332455
\(269\) 6.34303 + 10.9865i 0.386741 + 0.669856i 0.992009 0.126166i \(-0.0402673\pi\)
−0.605268 + 0.796022i \(0.706934\pi\)
\(270\) 0 0
\(271\) −17.2136 9.93828i −1.04565 0.603708i −0.124223 0.992254i \(-0.539644\pi\)
−0.921429 + 0.388547i \(0.872977\pi\)
\(272\) −1.97267 3.41677i −0.119611 0.207172i
\(273\) 0 0
\(274\) −8.46717 + 14.6656i −0.511520 + 0.885979i
\(275\) −19.6179 + 11.3264i −1.18300 + 0.683006i
\(276\) 0 0
\(277\) 3.73302 6.46579i 0.224296 0.388491i −0.731812 0.681506i \(-0.761325\pi\)
0.956108 + 0.293015i \(0.0946585\pi\)
\(278\) −6.06406 + 10.5033i −0.363698 + 0.629944i
\(279\) 0 0
\(280\) −1.07431 + 2.32290i −0.0642023 + 0.138820i
\(281\) 19.2746 11.1282i 1.14983 0.663854i 0.200983 0.979595i \(-0.435586\pi\)
0.948845 + 0.315741i \(0.102253\pi\)
\(282\) 0 0
\(283\) 16.1802i 0.961815i −0.876771 0.480908i \(-0.840307\pi\)
0.876771 0.480908i \(-0.159693\pi\)
\(284\) 3.64006i 0.215998i
\(285\) 0 0
\(286\) 21.0066 12.1282i 1.24215 0.717153i
\(287\) −0.0391210 0.431528i −0.00230924 0.0254723i
\(288\) 0 0
\(289\) 0.717124 1.24210i 0.0421838 0.0730644i
\(290\) 2.57549 4.46088i 0.151238 0.261952i
\(291\) 0 0
\(292\) 2.15468 1.24401i 0.126093 0.0727999i
\(293\) 4.43406 7.68002i 0.259041 0.448672i −0.706944 0.707269i \(-0.749927\pi\)
0.965985 + 0.258597i \(0.0832603\pi\)
\(294\) 0 0
\(295\) 0.809584 + 1.40224i 0.0471358 + 0.0816416i
\(296\) 0.421942 + 0.243608i 0.0245249 + 0.0141595i
\(297\) 0 0
\(298\) −4.37026 7.56951i −0.253162 0.438490i
\(299\) 11.5473 0.667799
\(300\) 0 0
\(301\) 20.8940 + 9.66321i 1.20431 + 0.556978i
\(302\) 19.1341 + 11.0471i 1.10104 + 0.635687i
\(303\) 0 0
\(304\) 3.86796 + 2.23317i 0.221843 + 0.128081i
\(305\) −4.33290 + 2.50160i −0.248101 + 0.143241i
\(306\) 0 0
\(307\) 27.1427i 1.54912i −0.632501 0.774559i \(-0.717972\pi\)
0.632501 0.774559i \(-0.282028\pi\)
\(308\) −14.6862 + 1.33140i −0.836822 + 0.0758638i
\(309\) 0 0
\(310\) −2.98252 5.16588i −0.169396 0.293402i
\(311\) −16.8955 −0.958055 −0.479028 0.877800i \(-0.659011\pi\)
−0.479028 + 0.877800i \(0.659011\pi\)
\(312\) 0 0
\(313\) 4.27739i 0.241772i 0.992666 + 0.120886i \(0.0385736\pi\)
−0.992666 + 0.120886i \(0.961426\pi\)
\(314\) −1.42457 −0.0803934
\(315\) 0 0
\(316\) −4.60242 −0.258906
\(317\) 6.62940i 0.372344i −0.982517 0.186172i \(-0.940392\pi\)
0.982517 0.186172i \(-0.0596082\pi\)
\(318\) 0 0
\(319\) 29.6794 1.66173
\(320\) 0.483662 + 0.837727i 0.0270375 + 0.0468304i
\(321\) 0 0
\(322\) −6.37165 2.94680i −0.355078 0.164219i
\(323\) 17.6212i 0.980472i
\(324\) 0 0
\(325\) −15.3180 + 8.84386i −0.849691 + 0.490569i
\(326\) 6.44579 + 3.72148i 0.356999 + 0.206114i
\(327\) 0 0
\(328\) −0.141830 0.0818856i −0.00783125 0.00452137i
\(329\) −20.5221 + 14.4661i −1.13142 + 0.797539i
\(330\) 0 0
\(331\) −0.757792 −0.0416520 −0.0208260 0.999783i \(-0.506630\pi\)
−0.0208260 + 0.999783i \(0.506630\pi\)
\(332\) −4.20979 7.29158i −0.231042 0.400177i
\(333\) 0 0
\(334\) −5.62665 3.24855i −0.307877 0.177753i
\(335\) 2.63234 + 4.55935i 0.143820 + 0.249104i
\(336\) 0 0
\(337\) 1.01088 1.75089i 0.0550660 0.0953772i −0.837178 0.546930i \(-0.815796\pi\)
0.892244 + 0.451553i \(0.149130\pi\)
\(338\) 5.14404 2.96991i 0.279799 0.161542i
\(339\) 0 0
\(340\) 1.90821 3.30512i 0.103487 0.179245i
\(341\) 17.1850 29.7652i 0.930618 1.61188i
\(342\) 0 0
\(343\) 4.96188 + 17.8432i 0.267916 + 0.963442i
\(344\) 7.53520 4.35045i 0.406271 0.234560i
\(345\) 0 0
\(346\) 11.8188i 0.635381i
\(347\) 20.9661i 1.12552i −0.826620 0.562761i \(-0.809739\pi\)
0.826620 0.562761i \(-0.190261\pi\)
\(348\) 0 0
\(349\) −5.36406 + 3.09694i −0.287132 + 0.165776i −0.636648 0.771155i \(-0.719679\pi\)
0.349516 + 0.936930i \(0.386346\pi\)
\(350\) 10.7092 0.970861i 0.572429 0.0518947i
\(351\) 0 0
\(352\) −2.78681 + 4.82689i −0.148537 + 0.257274i
\(353\) −9.41889 + 16.3140i −0.501317 + 0.868306i 0.498682 + 0.866785i \(0.333818\pi\)
−0.999999 + 0.00152110i \(0.999516\pi\)
\(354\) 0 0
\(355\) −3.04938 + 1.76056i −0.161844 + 0.0934409i
\(356\) −2.05811 + 3.56475i −0.109080 + 0.188931i
\(357\) 0 0
\(358\) −1.21685 2.10764i −0.0643124 0.111392i
\(359\) 24.0735 + 13.8988i 1.27055 + 0.733553i 0.975092 0.221803i \(-0.0711942\pi\)
0.295459 + 0.955355i \(0.404527\pi\)
\(360\) 0 0
\(361\) 0.474089 + 0.821146i 0.0249520 + 0.0432182i
\(362\) 11.5342 0.606222
\(363\) 0 0
\(364\) −11.4673 + 1.03959i −0.601048 + 0.0544892i
\(365\) 2.08428 + 1.20336i 0.109096 + 0.0629866i
\(366\) 0 0
\(367\) −18.8390 10.8767i −0.983388 0.567759i −0.0800968 0.996787i \(-0.525523\pi\)
−0.903291 + 0.429028i \(0.858856\pi\)
\(368\) −2.29786 + 1.32667i −0.119784 + 0.0691575i
\(369\) 0 0
\(370\) 0.471297i 0.0245016i
\(371\) −2.23806 + 4.83920i −0.116194 + 0.251239i
\(372\) 0 0
\(373\) −5.86560 10.1595i −0.303709 0.526040i 0.673264 0.739402i \(-0.264892\pi\)
−0.976973 + 0.213362i \(0.931558\pi\)
\(374\) 21.9898 1.13707
\(375\) 0 0
\(376\) 9.49001i 0.489410i
\(377\) 23.1743 1.19354
\(378\) 0 0
\(379\) 34.8881 1.79208 0.896041 0.443971i \(-0.146431\pi\)
0.896041 + 0.443971i \(0.146431\pi\)
\(380\) 4.32040i 0.221632i
\(381\) 0 0
\(382\) 22.0689 1.12914
\(383\) −5.92412 10.2609i −0.302708 0.524306i 0.674040 0.738695i \(-0.264557\pi\)
−0.976748 + 0.214389i \(0.931224\pi\)
\(384\) 0 0
\(385\) −8.21849 11.6591i −0.418853 0.594200i
\(386\) 19.9396i 1.01490i
\(387\) 0 0
\(388\) −10.2669 + 5.92762i −0.521225 + 0.300929i
\(389\) 5.50224 + 3.17672i 0.278975 + 0.161066i 0.632959 0.774185i \(-0.281840\pi\)
−0.353984 + 0.935251i \(0.615173\pi\)
\(390\) 0 0
\(391\) 9.06586 + 5.23418i 0.458480 + 0.264704i
\(392\) 6.59277 + 2.35274i 0.332985 + 0.118831i
\(393\) 0 0
\(394\) 4.62560 0.233034
\(395\) −2.22601 3.85557i −0.112003 0.193995i
\(396\) 0 0
\(397\) −7.42647 4.28768i −0.372724 0.215192i 0.301924 0.953332i \(-0.402371\pi\)
−0.674648 + 0.738140i \(0.735704\pi\)
\(398\) 10.4514 + 18.1024i 0.523883 + 0.907391i
\(399\) 0 0
\(400\) 2.03214 3.51977i 0.101607 0.175989i
\(401\) 20.0216 11.5595i 0.999833 0.577254i 0.0916343 0.995793i \(-0.470791\pi\)
0.908199 + 0.418539i \(0.137458\pi\)
\(402\) 0 0
\(403\) 13.4184 23.2413i 0.668417 1.15773i
\(404\) 2.65813 4.60402i 0.132247 0.229058i
\(405\) 0 0
\(406\) −12.7872 5.91393i −0.634620 0.293503i
\(407\) −2.35174 + 1.35778i −0.116572 + 0.0673026i
\(408\) 0 0
\(409\) 1.55989i 0.0771318i 0.999256 + 0.0385659i \(0.0122790\pi\)
−0.999256 + 0.0385659i \(0.987721\pi\)
\(410\) 0.158420i 0.00782380i
\(411\) 0 0
\(412\) −7.74616 + 4.47225i −0.381626 + 0.220332i
\(413\) 3.61971 2.55154i 0.178114 0.125553i
\(414\) 0 0
\(415\) 4.07224 7.05332i 0.199898 0.346234i
\(416\) −2.17600 + 3.76893i −0.106687 + 0.184787i
\(417\) 0 0
\(418\) −21.5585 + 12.4468i −1.05446 + 0.608794i
\(419\) −3.40822 + 5.90321i −0.166502 + 0.288391i −0.937188 0.348825i \(-0.886581\pi\)
0.770685 + 0.637216i \(0.219914\pi\)
\(420\) 0 0
\(421\) −6.75727 11.7039i −0.329329 0.570415i 0.653050 0.757315i \(-0.273489\pi\)
−0.982379 + 0.186900i \(0.940156\pi\)
\(422\) 5.79042 + 3.34310i 0.281873 + 0.162740i
\(423\) 0 0
\(424\) 1.00759 + 1.74520i 0.0489330 + 0.0847544i
\(425\) −16.0350 −0.777812
\(426\) 0 0
\(427\) 7.88424 + 11.1849i 0.381545 + 0.541274i
\(428\) 16.5898 + 9.57813i 0.801899 + 0.462976i
\(429\) 0 0
\(430\) 7.28898 + 4.20829i 0.351506 + 0.202942i
\(431\) −12.2628 + 7.07990i −0.590676 + 0.341027i −0.765365 0.643597i \(-0.777441\pi\)
0.174689 + 0.984624i \(0.444108\pi\)
\(432\) 0 0
\(433\) 23.4830i 1.12852i 0.825597 + 0.564260i \(0.190839\pi\)
−0.825597 + 0.564260i \(0.809161\pi\)
\(434\) −13.3351 + 9.39995i −0.640105 + 0.451212i
\(435\) 0 0
\(436\) 9.62168 + 16.6652i 0.460795 + 0.798121i
\(437\) −11.8507 −0.566897
\(438\) 0 0
\(439\) 4.23080i 0.201925i 0.994890 + 0.100963i \(0.0321922\pi\)
−0.994890 + 0.100963i \(0.967808\pi\)
\(440\) −5.39149 −0.257029
\(441\) 0 0
\(442\) 17.1701 0.816699
\(443\) 29.8098i 1.41631i −0.706058 0.708154i \(-0.749528\pi\)
0.706058 0.708154i \(-0.250472\pi\)
\(444\) 0 0
\(445\) −3.98172 −0.188751
\(446\) −4.09123 7.08622i −0.193725 0.335542i
\(447\) 0 0
\(448\) 2.16249 1.52435i 0.102168 0.0720186i
\(449\) 8.41716i 0.397230i −0.980078 0.198615i \(-0.936356\pi\)
0.980078 0.198615i \(-0.0636444\pi\)
\(450\) 0 0
\(451\) 0.790505 0.456399i 0.0372234 0.0214910i
\(452\) 7.31199 + 4.22158i 0.343927 + 0.198566i
\(453\) 0 0
\(454\) −9.26106 5.34688i −0.434643 0.250941i
\(455\) −6.41717 9.10363i −0.300841 0.426785i
\(456\) 0 0
\(457\) −3.88219 −0.181601 −0.0908006 0.995869i \(-0.528943\pi\)
−0.0908006 + 0.995869i \(0.528943\pi\)
\(458\) −14.6036 25.2942i −0.682382 1.18192i
\(459\) 0 0
\(460\) −2.22278 1.28332i −0.103638 0.0598352i
\(461\) 17.0423 + 29.5181i 0.793739 + 1.37480i 0.923637 + 0.383269i \(0.125202\pi\)
−0.129898 + 0.991527i \(0.541465\pi\)
\(462\) 0 0
\(463\) −6.10962 + 10.5822i −0.283938 + 0.491796i −0.972351 0.233523i \(-0.924974\pi\)
0.688413 + 0.725319i \(0.258308\pi\)
\(464\) −4.61157 + 2.66249i −0.214087 + 0.123603i
\(465\) 0 0
\(466\) −3.21967 + 5.57664i −0.149148 + 0.258333i
\(467\) −15.4057 + 26.6835i −0.712893 + 1.23477i 0.250874 + 0.968020i \(0.419282\pi\)
−0.963767 + 0.266747i \(0.914051\pi\)
\(468\) 0 0
\(469\) 11.7694 8.29628i 0.543460 0.383087i
\(470\) −7.95004 + 4.58996i −0.366708 + 0.211719i
\(471\) 0 0
\(472\) 1.67386i 0.0770457i
\(473\) 48.4954i 2.22982i
\(474\) 0 0
\(475\) 15.7205 9.07623i 0.721306 0.416446i
\(476\) −9.47423 4.38170i −0.434250 0.200835i
\(477\) 0 0
\(478\) 2.31778 4.01452i 0.106013 0.183620i
\(479\) 20.8747 36.1560i 0.953788 1.65201i 0.216670 0.976245i \(-0.430481\pi\)
0.737118 0.675764i \(-0.236186\pi\)
\(480\) 0 0
\(481\) −1.83629 + 1.06018i −0.0837276 + 0.0483401i
\(482\) 5.24722 9.08846i 0.239004 0.413968i
\(483\) 0 0
\(484\) −10.0326 17.3769i −0.456026 0.789861i
\(485\) −9.93146 5.73393i −0.450964 0.260364i
\(486\) 0 0
\(487\) 10.5832 + 18.3306i 0.479568 + 0.830637i 0.999725 0.0234338i \(-0.00745988\pi\)
−0.520157 + 0.854071i \(0.674127\pi\)
\(488\) 5.17221 0.234135
\(489\) 0 0
\(490\) 1.21772 + 6.66087i 0.0550109 + 0.300908i
\(491\) −32.3428 18.6731i −1.45961 0.842707i −0.460619 0.887598i \(-0.652372\pi\)
−0.998992 + 0.0448915i \(0.985706\pi\)
\(492\) 0 0
\(493\) 18.1942 + 10.5044i 0.819427 + 0.473097i
\(494\) −16.8333 + 9.71873i −0.757368 + 0.437266i
\(495\) 0 0
\(496\) 6.16655i 0.276886i
\(497\) 5.54872 + 7.87161i 0.248894 + 0.353090i
\(498\) 0 0
\(499\) −13.7099 23.7462i −0.613738 1.06303i −0.990605 0.136758i \(-0.956332\pi\)
0.376867 0.926267i \(-0.377001\pi\)
\(500\) 8.76810 0.392121
\(501\) 0 0
\(502\) 7.85271i 0.350484i
\(503\) 11.2791 0.502909 0.251454 0.967869i \(-0.419091\pi\)
0.251454 + 0.967869i \(0.419091\pi\)
\(504\) 0 0
\(505\) 5.14255 0.228840
\(506\) 14.7887i 0.657438i
\(507\) 0 0
\(508\) −3.31883 −0.147249
\(509\) −9.31667 16.1370i −0.412954 0.715258i 0.582257 0.813005i \(-0.302170\pi\)
−0.995211 + 0.0977470i \(0.968836\pi\)
\(510\) 0 0
\(511\) 2.76319 5.97463i 0.122236 0.264302i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 2.97164 1.71568i 0.131074 0.0756753i
\(515\) −7.49305 4.32611i −0.330183 0.190631i
\(516\) 0 0
\(517\) −45.8072 26.4468i −2.01460 1.16313i
\(518\) 1.28379 0.116385i 0.0564065 0.00511364i
\(519\) 0 0
\(520\) −4.20979 −0.184611
\(521\) 7.64255 + 13.2373i 0.334826 + 0.579936i 0.983451 0.181172i \(-0.0579891\pi\)
−0.648625 + 0.761108i \(0.724656\pi\)
\(522\) 0 0
\(523\) −31.5991 18.2437i −1.38173 0.797743i −0.389368 0.921082i \(-0.627306\pi\)
−0.992365 + 0.123339i \(0.960640\pi\)
\(524\) −9.37335 16.2351i −0.409477 0.709235i
\(525\) 0 0
\(526\) 1.83066 3.17080i 0.0798207 0.138253i
\(527\) 21.0697 12.1646i 0.917809 0.529897i
\(528\) 0 0
\(529\) −7.97989 + 13.8216i −0.346952 + 0.600938i
\(530\) −0.974668 + 1.68817i −0.0423369 + 0.0733296i
\(531\) 0 0
\(532\) 11.7686 1.06690i 0.510232 0.0462561i
\(533\) 0.617243 0.356365i 0.0267358 0.0154359i
\(534\) 0 0
\(535\) 18.5303i 0.801135i
\(536\) 5.44252i 0.235081i
\(537\) 0 0
\(538\) 10.9865 6.34303i 0.473660 0.273467i
\(539\) −29.7292 + 25.2659i −1.28053 + 1.08828i
\(540\) 0 0
\(541\) 2.63647 4.56649i 0.113351 0.196329i −0.803769 0.594942i \(-0.797175\pi\)
0.917119 + 0.398613i \(0.130508\pi\)
\(542\) −9.93828 + 17.2136i −0.426886 + 0.739388i
\(543\) 0 0
\(544\) −3.41677 + 1.97267i −0.146493 + 0.0845776i
\(545\) −9.30729 + 16.1207i −0.398680 + 0.690535i
\(546\) 0 0
\(547\) −9.29831 16.1051i −0.397567 0.688606i 0.595858 0.803090i \(-0.296812\pi\)
−0.993425 + 0.114484i \(0.963479\pi\)
\(548\) 14.6656 + 8.46717i 0.626482 + 0.361700i
\(549\) 0 0
\(550\) 11.3264 + 19.6179i 0.482958 + 0.836508i
\(551\) −23.7832 −1.01320
\(552\) 0 0
\(553\) −9.95268 + 7.01567i −0.423231 + 0.298337i
\(554\) −6.46579 3.73302i −0.274705 0.158601i
\(555\) 0 0
\(556\) 10.5033 + 6.06406i 0.445438 + 0.257174i
\(557\) −23.8694 + 13.7810i −1.01138 + 0.583920i −0.911595 0.411089i \(-0.865149\pi\)
−0.0997845 + 0.995009i \(0.531815\pi\)
\(558\) 0 0
\(559\) 37.8662i 1.60157i
\(560\) 2.32290 + 1.07431i 0.0981605 + 0.0453979i
\(561\) 0 0
\(562\) −11.1282 19.2746i −0.469416 0.813052i
\(563\) 18.8515 0.794497 0.397249 0.917711i \(-0.369965\pi\)
0.397249 + 0.917711i \(0.369965\pi\)
\(564\) 0 0
\(565\) 8.16727i 0.343600i
\(566\) −16.1802 −0.680106
\(567\) 0 0
\(568\) 3.64006 0.152734
\(569\) 4.46988i 0.187387i 0.995601 + 0.0936936i \(0.0298674\pi\)
−0.995601 + 0.0936936i \(0.970133\pi\)
\(570\) 0 0
\(571\) 18.6249 0.779428 0.389714 0.920936i \(-0.372574\pi\)
0.389714 + 0.920936i \(0.372574\pi\)
\(572\) −12.1282 21.0066i −0.507104 0.878329i
\(573\) 0 0
\(574\) −0.431528 + 0.0391210i −0.0180116 + 0.00163288i
\(575\) 10.7839i 0.449721i
\(576\) 0 0
\(577\) 31.9418 18.4416i 1.32976 0.767735i 0.344495 0.938788i \(-0.388050\pi\)
0.985262 + 0.171053i \(0.0547170\pi\)
\(578\) −1.24210 0.717124i −0.0516644 0.0298284i
\(579\) 0 0
\(580\) −4.46088 2.57549i −0.185228 0.106941i
\(581\) −20.2185 9.35079i −0.838806 0.387936i
\(582\) 0 0
\(583\) −11.2319 −0.465176
\(584\) −1.24401 2.15468i −0.0514773 0.0891614i
\(585\) 0 0
\(586\) −7.68002 4.43406i −0.317259 0.183170i
\(587\) −13.2295 22.9141i −0.546039 0.945766i −0.998541 0.0540032i \(-0.982802\pi\)
0.452502 0.891763i \(-0.350531\pi\)
\(588\) 0 0
\(589\) −13.7709 + 23.8520i −0.567422 + 0.982803i
\(590\) 1.40224 0.809584i 0.0577293 0.0333300i
\(591\) 0 0
\(592\) 0.243608 0.421942i 0.0100122 0.0173417i
\(593\) 17.3351 30.0254i 0.711869 1.23299i −0.252285 0.967653i \(-0.581182\pi\)
0.964155 0.265341i \(-0.0854845\pi\)
\(594\) 0 0
\(595\) −0.911654 10.0561i −0.0373742 0.412259i
\(596\) −7.56951 + 4.37026i −0.310059 + 0.179013i
\(597\) 0 0
\(598\) 11.5473i 0.472205i
\(599\) 24.4887i 1.00058i −0.865857 0.500291i \(-0.833226\pi\)
0.865857 0.500291i \(-0.166774\pi\)
\(600\) 0 0
\(601\) −19.3812 + 11.1898i −0.790577 + 0.456440i −0.840166 0.542330i \(-0.817542\pi\)
0.0495885 + 0.998770i \(0.484209\pi\)
\(602\) 9.66321 20.8940i 0.393843 0.851578i
\(603\) 0 0
\(604\) 11.0471 19.1341i 0.449499 0.778555i
\(605\) 9.70476 16.8091i 0.394554 0.683388i
\(606\) 0 0
\(607\) −28.2180 + 16.2917i −1.14533 + 0.661259i −0.947746 0.319026i \(-0.896644\pi\)
−0.197589 + 0.980285i \(0.563311\pi\)
\(608\) 2.23317 3.86796i 0.0905670 0.156867i
\(609\) 0 0
\(610\) 2.50160 + 4.33290i 0.101287 + 0.175434i
\(611\) −35.7672 20.6502i −1.44699 0.835418i
\(612\) 0 0
\(613\) 5.86931 + 10.1659i 0.237059 + 0.410598i 0.959869 0.280449i \(-0.0904832\pi\)
−0.722810 + 0.691047i \(0.757150\pi\)
\(614\) −27.1427 −1.09539
\(615\) 0 0
\(616\) 1.33140 + 14.6862i 0.0536438 + 0.591723i
\(617\) 38.1947 + 22.0517i 1.53766 + 0.887770i 0.998975 + 0.0452639i \(0.0144129\pi\)
0.538687 + 0.842506i \(0.318920\pi\)
\(618\) 0 0
\(619\) −4.28374 2.47322i −0.172178 0.0994070i 0.411434 0.911439i \(-0.365028\pi\)
−0.583612 + 0.812032i \(0.698361\pi\)
\(620\) −5.16588 + 2.98252i −0.207467 + 0.119781i
\(621\) 0 0
\(622\) 16.8955i 0.677447i
\(623\) 0.983266 + 10.8460i 0.0393937 + 0.434536i
\(624\) 0 0
\(625\) −5.91991 10.2536i −0.236797 0.410144i
\(626\) 4.27739 0.170959
\(627\) 0 0
\(628\) 1.42457i 0.0568467i
\(629\) −1.92224 −0.0766447
\(630\) 0 0
\(631\) −9.08478 −0.361659 −0.180830 0.983514i \(-0.557878\pi\)
−0.180830 + 0.983514i \(0.557878\pi\)
\(632\) 4.60242i 0.183074i
\(633\) 0 0
\(634\) −6.62940 −0.263287
\(635\) −1.60519 2.78027i −0.0637001 0.110332i
\(636\) 0 0
\(637\) −23.2132 + 19.7282i −0.919739 + 0.781658i
\(638\) 29.6794i 1.17502i
\(639\) 0 0
\(640\) 0.837727 0.483662i 0.0331141 0.0191184i
\(641\) 12.1954 + 7.04105i 0.481691 + 0.278105i 0.721121 0.692809i \(-0.243627\pi\)
−0.239430 + 0.970914i \(0.576960\pi\)
\(642\) 0 0
\(643\) 7.33157 + 4.23288i 0.289129 + 0.166929i 0.637549 0.770410i \(-0.279948\pi\)
−0.348420 + 0.937339i \(0.613282\pi\)
\(644\) −2.94680 + 6.37165i −0.116120 + 0.251078i
\(645\) 0 0
\(646\) −17.6212 −0.693299
\(647\) 12.1662 + 21.0725i 0.478304 + 0.828446i 0.999691 0.0248742i \(-0.00791854\pi\)
−0.521387 + 0.853320i \(0.674585\pi\)
\(648\) 0 0
\(649\) 8.07955 + 4.66473i 0.317150 + 0.183107i
\(650\) 8.84386 + 15.3180i 0.346885 + 0.600822i
\(651\) 0 0
\(652\) 3.72148 6.44579i 0.145744 0.252437i
\(653\) 36.0653 20.8223i 1.41134 0.814840i 0.415829 0.909443i \(-0.363491\pi\)
0.995515 + 0.0946029i \(0.0301581\pi\)
\(654\) 0 0
\(655\) 9.06707 15.7046i 0.354280 0.613631i
\(656\) −0.0818856 + 0.141830i −0.00319709 + 0.00553753i
\(657\) 0 0
\(658\) 14.4661 + 20.5221i 0.563946 + 0.800033i
\(659\) 9.09866 5.25312i 0.354434 0.204632i −0.312203 0.950016i \(-0.601067\pi\)
0.666636 + 0.745383i \(0.267733\pi\)
\(660\) 0 0
\(661\) 19.5131i 0.758972i 0.925198 + 0.379486i \(0.123899\pi\)
−0.925198 + 0.379486i \(0.876101\pi\)
\(662\) 0.757792i 0.0294524i
\(663\) 0 0
\(664\) −7.29158 + 4.20979i −0.282968 + 0.163372i
\(665\) 6.58578 + 9.34282i 0.255386 + 0.362299i
\(666\) 0 0
\(667\) 7.06450 12.2361i 0.273539 0.473783i
\(668\) −3.24855 + 5.62665i −0.125690 + 0.217702i
\(669\) 0 0
\(670\) 4.55935 2.63234i 0.176143 0.101696i
\(671\) −14.4140 + 24.9657i −0.556445 + 0.963790i
\(672\) 0 0
\(673\) −3.10277 5.37415i −0.119603 0.207158i 0.800007 0.599990i \(-0.204829\pi\)
−0.919610 + 0.392832i \(0.871495\pi\)
\(674\) −1.75089 1.01088i −0.0674419 0.0389376i
\(675\) 0 0
\(676\) −2.96991 5.14404i −0.114227 0.197848i
\(677\) −24.7531 −0.951339 −0.475669 0.879624i \(-0.657794\pi\)
−0.475669 + 0.879624i \(0.657794\pi\)
\(678\) 0 0
\(679\) −13.1664 + 28.4688i −0.505281 + 1.09253i
\(680\) −3.30512 1.90821i −0.126746 0.0731767i
\(681\) 0 0
\(682\) −29.7652 17.1850i −1.13977 0.658046i
\(683\) 18.3119 10.5724i 0.700687 0.404542i −0.106916 0.994268i \(-0.534098\pi\)
0.807603 + 0.589726i \(0.200764\pi\)
\(684\) 0 0
\(685\) 16.3810i 0.625886i
\(686\) 17.8432 4.96188i 0.681257 0.189445i
\(687\) 0 0
\(688\) −4.35045 7.53520i −0.165859 0.287277i
\(689\) −8.77006 −0.334113
\(690\) 0 0
\(691\) 6.44470i 0.245168i 0.992458 + 0.122584i \(0.0391181\pi\)
−0.992458 + 0.122584i \(0.960882\pi\)
\(692\) 11.8188 0.449282
\(693\) 0 0
\(694\) −20.9661 −0.795864
\(695\) 11.7318i 0.445014i
\(696\) 0 0
\(697\) 0.646134 0.0244741
\(698\) 3.09694 + 5.36406i 0.117221 + 0.203033i
\(699\) 0 0
\(700\) −0.970861 10.7092i −0.0366951 0.404768i
\(701\) 24.5717i 0.928061i 0.885819 + 0.464031i \(0.153597\pi\)
−0.885819 + 0.464031i \(0.846403\pi\)
\(702\) 0 0
\(703\) 1.88454 1.08804i 0.0710767 0.0410361i
\(704\) 4.82689 + 2.78681i 0.181920 + 0.105032i
\(705\) 0 0
\(706\) 16.3140 + 9.41889i 0.613985 + 0.354484i
\(707\) −1.26993 14.0081i −0.0477606 0.526827i
\(708\) 0 0
\(709\) 44.2740 1.66275 0.831373 0.555715i \(-0.187555\pi\)
0.831373 + 0.555715i \(0.187555\pi\)
\(710\) 1.76056 + 3.04938i 0.0660727 + 0.114441i
\(711\) 0 0
\(712\) 3.56475 + 2.05811i 0.133595 + 0.0771309i
\(713\) −8.18098 14.1699i −0.306380 0.530666i
\(714\) 0 0
\(715\) 11.7319 20.3202i 0.438747 0.759931i
\(716\) −2.10764 + 1.21685i −0.0787663 + 0.0454757i
\(717\) 0 0
\(718\) 13.8988 24.0735i 0.518700 0.898415i
\(719\) −2.22433 + 3.85266i −0.0829537 + 0.143680i −0.904517 0.426437i \(-0.859769\pi\)
0.821564 + 0.570117i \(0.193102\pi\)
\(720\) 0 0
\(721\) −9.93376 + 21.4790i −0.369952 + 0.799921i
\(722\) 0.821146 0.474089i 0.0305599 0.0176438i
\(723\) 0 0
\(724\) 11.5342i 0.428663i
\(725\) 21.6422i 0.803773i
\(726\) 0 0
\(727\) 30.4270 17.5670i 1.12848 0.651525i 0.184924 0.982753i \(-0.440796\pi\)
0.943551 + 0.331227i \(0.107463\pi\)
\(728\) 1.03959 + 11.4673i 0.0385297 + 0.425005i
\(729\) 0 0
\(730\) 1.20336 2.08428i 0.0445382 0.0771425i
\(731\) −17.1640 + 29.7289i −0.634834 + 1.09956i
\(732\) 0 0
\(733\) −5.03789 + 2.90863i −0.186079 + 0.107433i −0.590145 0.807297i \(-0.700930\pi\)
0.404067 + 0.914729i \(0.367596\pi\)
\(734\) −10.8767 + 18.8390i −0.401467 + 0.695360i
\(735\) 0 0
\(736\) 1.32667 + 2.29786i 0.0489018 + 0.0847003i
\(737\) 26.2704 + 15.1672i 0.967684 + 0.558693i
\(738\) 0 0
\(739\) −5.51675 9.55529i −0.202937 0.351497i 0.746537 0.665344i \(-0.231715\pi\)
−0.949473 + 0.313847i \(0.898382\pi\)
\(740\) 0.471297 0.0173252
\(741\) 0 0
\(742\) 4.83920 + 2.23806i 0.177652 + 0.0821618i
\(743\) 0.543196 + 0.313615i 0.0199279 + 0.0115054i 0.509931 0.860215i \(-0.329671\pi\)
−0.490003 + 0.871721i \(0.663004\pi\)
\(744\) 0 0
\(745\) −7.32216 4.22745i −0.268263 0.154882i
\(746\) −10.1595 + 5.86560i −0.371966 + 0.214755i
\(747\) 0 0
\(748\) 21.9898i 0.804028i
\(749\) 50.4757 4.57598i 1.84434 0.167202i
\(750\) 0 0
\(751\) −2.23529 3.87163i −0.0815668 0.141278i 0.822356 0.568973i \(-0.192659\pi\)
−0.903923 + 0.427695i \(0.859326\pi\)
\(752\) 9.49001 0.346065
\(753\) 0 0
\(754\) 23.1743i 0.843957i
\(755\) 21.3722 0.777813
\(756\) 0 0
\(757\) 5.75624 0.209214 0.104607 0.994514i \(-0.466642\pi\)
0.104607 + 0.994514i \(0.466642\pi\)
\(758\) 34.8881i 1.26719i
\(759\) 0 0
\(760\) 4.32040 0.156717
\(761\) 10.4970 + 18.1813i 0.380516 + 0.659073i 0.991136 0.132851i \(-0.0424131\pi\)
−0.610620 + 0.791924i \(0.709080\pi\)
\(762\) 0 0
\(763\) 46.2104 + 21.3717i 1.67293 + 0.773707i
\(764\) 22.0689i 0.798425i
\(765\) 0 0
\(766\) −10.2609 + 5.92412i −0.370740 + 0.214047i
\(767\) 6.30868 + 3.64232i 0.227793 + 0.131516i
\(768\) 0 0
\(769\) 34.1729 + 19.7298i 1.23231 + 0.711473i 0.967511 0.252831i \(-0.0813616\pi\)
0.264797 + 0.964304i \(0.414695\pi\)
\(770\) −11.6591 + 8.21849i −0.420163 + 0.296174i
\(771\) 0 0
\(772\) 19.9396 0.717641
\(773\) −17.3164 29.9929i −0.622829 1.07877i −0.988956 0.148206i \(-0.952650\pi\)
0.366128 0.930565i \(-0.380683\pi\)
\(774\) 0 0
\(775\) 21.7048 + 12.5313i 0.779661 + 0.450137i
\(776\) 5.92762 + 10.2669i 0.212789 + 0.368562i
\(777\) 0 0
\(778\) 3.17672 5.50224i 0.113891 0.197265i
\(779\) −0.633461 + 0.365729i −0.0226961 + 0.0131036i
\(780\) 0 0
\(781\) −10.1442 + 17.5702i −0.362986 + 0.628711i
\(782\) 5.23418 9.06586i 0.187174 0.324195i
\(783\) 0 0
\(784\) 2.35274 6.59277i 0.0840264 0.235456i
\(785\) −1.19340 + 0.689012i −0.0425944 + 0.0245919i
\(786\) 0 0
\(787\) 35.3099i 1.25866i −0.777137 0.629332i \(-0.783329\pi\)
0.777137 0.629332i \(-0.216671\pi\)
\(788\) 4.62560i 0.164780i
\(789\) 0 0
\(790\) −3.85557 + 2.22601i −0.137175 + 0.0791980i
\(791\) 22.2473 2.01687i 0.791022 0.0717116i
\(792\) 0 0
\(793\) −11.2547 + 19.4937i −0.399667 + 0.692243i
\(794\) −4.28768 + 7.42647i −0.152164 + 0.263556i
\(795\) 0 0
\(796\) 18.1024 10.4514i 0.641622 0.370441i
\(797\) −9.60992 + 16.6449i −0.340401 + 0.589591i −0.984507 0.175344i \(-0.943896\pi\)
0.644106 + 0.764936i \(0.277229\pi\)
\(798\) 0 0
\(799\) −18.7207 32.4252i −0.662290 1.14712i
\(800\) −3.51977 2.03214i −0.124443 0.0718471i
\(801\) 0 0
\(802\) −11.5595 20.0216i −0.408180 0.706989i
\(803\) 13.8672 0.489363
\(804\) 0 0
\(805\) −6.76296 + 0.613110i −0.238363 + 0.0216093i
\(806\) −23.2413 13.4184i −0.818640 0.472642i
\(807\) 0 0
\(808\) −4.60402 2.65813i −0.161969 0.0935127i
\(809\) 34.0157 19.6390i 1.19593 0.690469i 0.236283 0.971684i \(-0.424071\pi\)
0.959645 + 0.281215i \(0.0907374\pi\)
\(810\) 0 0
\(811\) 9.68436i 0.340064i −0.985439 0.170032i \(-0.945613\pi\)
0.985439 0.170032i \(-0.0543871\pi\)
\(812\) −5.91393 + 12.7872i −0.207538 + 0.448744i
\(813\) 0 0
\(814\) 1.35778 + 2.35174i 0.0475901 + 0.0824285i
\(815\) 7.19975 0.252196
\(816\) 0 0
\(817\) 38.8611i 1.35958i
\(818\) 1.55989 0.0545404
\(819\) 0 0
\(820\) −0.158420 −0.00553226
\(821\) 12.6924i 0.442968i 0.975164 + 0.221484i \(0.0710900\pi\)
−0.975164 + 0.221484i \(0.928910\pi\)
\(822\) 0 0
\(823\) 17.4767 0.609201 0.304600 0.952480i \(-0.401477\pi\)
0.304600 + 0.952480i \(0.401477\pi\)
\(824\) 4.47225 + 7.74616i 0.155798 + 0.269850i
\(825\) 0 0
\(826\) −2.55154 3.61971i −0.0887796 0.125946i
\(827\) 46.9482i 1.63255i 0.577665 + 0.816274i \(0.303964\pi\)
−0.577665 + 0.816274i \(0.696036\pi\)
\(828\) 0 0
\(829\) −1.99797 + 1.15353i −0.0693924 + 0.0400637i −0.534295 0.845298i \(-0.679423\pi\)
0.464902 + 0.885362i \(0.346089\pi\)
\(830\) −7.05332 4.07224i −0.244824 0.141349i
\(831\) 0 0
\(832\) 3.76893 + 2.17600i 0.130664 + 0.0754391i
\(833\) −27.1672 + 4.96661i −0.941286 + 0.172083i
\(834\) 0 0
\(835\) −6.28480 −0.217495
\(836\) 12.4468 + 21.5585i 0.430482 + 0.745617i
\(837\) 0 0
\(838\) 5.90321 + 3.40822i 0.203923 + 0.117735i
\(839\) −8.51664 14.7513i −0.294027 0.509270i 0.680731 0.732533i \(-0.261662\pi\)
−0.974758 + 0.223264i \(0.928329\pi\)
\(840\) 0 0
\(841\) −0.322276 + 0.558199i −0.0111130 + 0.0192482i
\(842\) −11.7039 + 6.75727i −0.403344 + 0.232871i
\(843\) 0 0
\(844\) 3.34310 5.79042i 0.115074 0.199314i
\(845\) 2.87287 4.97595i 0.0988296 0.171178i
\(846\) 0 0
\(847\) −48.1838 22.2844i −1.65562 0.765700i
\(848\) 1.74520 1.00759i 0.0599304 0.0346008i
\(849\) 0 0
\(850\) 16.0350i 0.549996i
\(851\) 1.29275i 0.0443150i
\(852\) 0 0
\(853\) 2.87158 1.65791i 0.0983209 0.0567656i −0.450033 0.893012i \(-0.648588\pi\)
0.548354 + 0.836246i \(0.315255\pi\)
\(854\) 11.1849 7.88424i 0.382738 0.269793i
\(855\) 0 0
\(856\) 9.57813 16.5898i 0.327374 0.567028i
\(857\) 4.74512 8.21879i 0.162090 0.280748i −0.773528 0.633762i \(-0.781510\pi\)
0.935618 + 0.353014i \(0.114843\pi\)
\(858\) 0 0
\(859\) −25.5104 + 14.7284i −0.870404 + 0.502528i −0.867482 0.497468i \(-0.834263\pi\)
−0.00292142 + 0.999996i \(0.500930\pi\)
\(860\) 4.20829 7.28898i 0.143502 0.248552i
\(861\) 0 0
\(862\) 7.07990 + 12.2628i 0.241143 + 0.417671i
\(863\) −13.4610 7.77172i −0.458218 0.264553i 0.253076 0.967446i \(-0.418558\pi\)
−0.711295 + 0.702894i \(0.751891\pi\)
\(864\) 0 0
\(865\) 5.71629 + 9.90090i 0.194360 + 0.336641i
\(866\) 23.4830 0.797985
\(867\) 0 0
\(868\) 9.39995 + 13.3351i 0.319055 + 0.452623i
\(869\) −22.2154 12.8260i −0.753604 0.435094i
\(870\) 0 0
\(871\) 20.5125 + 11.8429i 0.695039 + 0.401281i
\(872\) 16.6652 9.62168i 0.564356 0.325831i
\(873\) 0 0
\(874\) 11.8507i 0.400857i
\(875\) 18.9609 13.3656i 0.640997 0.451840i
\(876\) 0 0
\(877\) 22.7249 + 39.3606i 0.767364 + 1.32911i 0.938988 + 0.343950i \(0.111765\pi\)
−0.171624 + 0.985163i \(0.554901\pi\)
\(878\) 4.23080 0.142783
\(879\) 0 0
\(880\) 5.39149i 0.181747i
\(881\) −15.6912 −0.528651 −0.264326 0.964433i \(-0.585149\pi\)
−0.264326 + 0.964433i \(0.585149\pi\)
\(882\) 0 0
\(883\) −10.5344 −0.354510 −0.177255 0.984165i \(-0.556722\pi\)
−0.177255 + 0.984165i \(0.556722\pi\)
\(884\) 17.1701i 0.577493i
\(885\) 0 0
\(886\) −29.8098 −1.00148
\(887\) −0.0302741 0.0524362i −0.00101650 0.00176064i 0.865517 0.500880i \(-0.166990\pi\)
−0.866533 + 0.499119i \(0.833657\pi\)
\(888\) 0 0
\(889\) −7.17694 + 5.05904i −0.240707 + 0.169675i
\(890\) 3.98172i 0.133467i
\(891\) 0 0
\(892\) −7.08622 + 4.09123i −0.237264 + 0.136985i
\(893\) 36.7070 + 21.1928i 1.22835 + 0.709190i
\(894\) 0 0
\(895\) −2.03877 1.17709i −0.0681487 0.0393456i
\(896\) −1.52435 2.16249i −0.0509248 0.0722438i
\(897\) 0 0
\(898\) −8.41716 −0.280884
\(899\) −16.4184 28.4375i −0.547583 0.948442i
\(900\) 0 0
\(901\) −6.88542 3.97530i −0.229386 0.132436i
\(902\) −0.456399 0.790505i −0.0151964 0.0263210i
\(903\) 0 0
\(904\) 4.22158 7.31199i 0.140408 0.243193i
\(905\) 9.66247 5.57863i 0.321192 0.185440i
\(906\) 0 0
\(907\) −12.0490 + 20.8695i −0.400081 + 0.692961i −0.993735 0.111760i \(-0.964351\pi\)
0.593654 + 0.804720i \(0.297685\pi\)
\(908\) −5.34688 + 9.26106i −0.177442 + 0.307339i
\(909\) 0 0
\(910\) −9.10363 + 6.41717i −0.301782 + 0.212727i
\(911\) −22.0494 + 12.7302i −0.730528 + 0.421771i −0.818615 0.574342i \(-0.805258\pi\)
0.0880873 + 0.996113i \(0.471925\pi\)
\(912\) 0 0
\(913\) 46.9275i 1.55307i
\(914\) 3.88219i 0.128411i
\(915\) 0 0
\(916\) −25.2942 + 14.6036i −0.835744 + 0.482517i
\(917\) −45.0177 20.8201i −1.48662 0.687540i
\(918\) 0 0
\(919\) 11.4534 19.8378i 0.377812 0.654389i −0.612932 0.790136i \(-0.710010\pi\)
0.990744 + 0.135747i \(0.0433433\pi\)
\(920\) −1.28332 + 2.22278i −0.0423098 + 0.0732828i
\(921\) 0 0
\(922\) 29.5181 17.0423i 0.972128 0.561258i
\(923\) −7.92076 + 13.7192i −0.260715 + 0.451572i
\(924\) 0 0
\(925\) −0.990094 1.71489i −0.0325541 0.0563853i
\(926\) 10.5822 + 6.10962i 0.347752 + 0.200775i
\(927\) 0 0
\(928\) 2.66249 + 4.61157i 0.0874006 + 0.151382i
\(929\) −28.7973 −0.944809 −0.472404 0.881382i \(-0.656614\pi\)
−0.472404 + 0.881382i \(0.656614\pi\)
\(930\) 0 0
\(931\) 23.8231 20.2465i 0.780770 0.663553i
\(932\) 5.57664 + 3.21967i 0.182669 + 0.105464i
\(933\) 0 0
\(934\) 26.6835 + 15.4057i 0.873112 + 0.504091i
\(935\) 18.4215 10.6356i 0.602447 0.347823i
\(936\) 0 0
\(937\) 53.6825i 1.75373i −0.480736 0.876865i \(-0.659631\pi\)
0.480736 0.876865i \(-0.340369\pi\)
\(938\) −8.29628 11.7694i −0.270883 0.384284i
\(939\) 0 0
\(940\) 4.58996 + 7.95004i 0.149708 + 0.259302i
\(941\) 45.9021 1.49637 0.748184 0.663492i \(-0.230926\pi\)
0.748184 + 0.663492i \(0.230926\pi\)
\(942\) 0 0
\(943\) 0.434541i 0.0141506i
\(944\) −1.67386 −0.0544796
\(945\) 0 0
\(946\) 48.4954 1.57672
\(947\) 28.9183i 0.939718i −0.882741 0.469859i \(-0.844305\pi\)
0.882741 0.469859i \(-0.155695\pi\)
\(948\) 0 0
\(949\) 10.8278 0.351485
\(950\) −9.07623 15.7205i −0.294472 0.510040i
\(951\) 0 0
\(952\) −4.38170 + 9.47423i −0.142012 + 0.307061i
\(953\) 12.8715i 0.416949i 0.978028 + 0.208475i \(0.0668498\pi\)
−0.978028 + 0.208475i \(0.933150\pi\)
\(954\) 0 0
\(955\) 18.4877 10.6739i 0.598249 0.345399i
\(956\) −4.01452 2.31778i −0.129839 0.0749624i
\(957\) 0 0
\(958\) −36.1560 20.8747i −1.16815 0.674430i
\(959\) 44.6211 4.04521i 1.44089 0.130627i
\(960\) 0 0
\(961\) −7.02628 −0.226654
\(962\) 1.06018 + 1.83629i 0.0341816 + 0.0592043i
\(963\) 0 0
\(964\) −9.08846 5.24722i −0.292719 0.169002i
\(965\) 9.64402 + 16.7039i 0.310452 + 0.537719i
\(966\) 0 0
\(967\) 3.11725 5.39923i 0.100244 0.173627i −0.811541 0.584295i \(-0.801371\pi\)
0.911785 + 0.410668i \(0.134704\pi\)
\(968\) −17.3769 + 10.0326i −0.558516 + 0.322459i
\(969\) 0 0
\(970\) −5.73393 + 9.93146i −0.184105 + 0.318880i
\(971\) 19.6863 34.0977i 0.631764 1.09425i −0.355426 0.934704i \(-0.615664\pi\)
0.987191 0.159544i \(-0.0510023\pi\)
\(972\) 0 0
\(973\) 31.9570 2.89712i 1.02449 0.0928774i
\(974\) 18.3306 10.5832i 0.587349 0.339106i
\(975\) 0 0
\(976\) 5.17221i 0.165559i
\(977\) 26.8438i 0.858809i −0.903112 0.429405i \(-0.858723\pi\)
0.903112 0.429405i \(-0.141277\pi\)
\(978\) 0 0
\(979\) −19.8685 + 11.4711i −0.635001 + 0.366618i
\(980\) 6.66087 1.21772i 0.212774 0.0388986i
\(981\) 0 0
\(982\) −18.6731 + 32.3428i −0.595884 + 1.03210i
\(983\) −5.98457 + 10.3656i −0.190878 + 0.330611i −0.945541 0.325502i \(-0.894467\pi\)
0.754663 + 0.656112i \(0.227800\pi\)
\(984\) 0 0
\(985\) 3.87499 2.23723i 0.123467 0.0712839i
\(986\) 10.5044 18.1942i 0.334530 0.579423i
\(987\) 0 0
\(988\) 9.71873 + 16.8333i 0.309194 + 0.535540i
\(989\) 19.9935 + 11.5432i 0.635755 + 0.367053i
\(990\) 0 0
\(991\) −5.40420 9.36036i −0.171670 0.297342i 0.767334 0.641248i \(-0.221583\pi\)
−0.939004 + 0.343906i \(0.888250\pi\)
\(992\) 6.16655 0.195788
\(993\) 0 0
\(994\) 7.87161 5.54872i 0.249672 0.175995i
\(995\) 17.5109 + 10.1099i 0.555132 + 0.320506i
\(996\) 0 0
\(997\) −11.6653 6.73498i −0.369445 0.213299i 0.303771 0.952745i \(-0.401754\pi\)
−0.673216 + 0.739446i \(0.735088\pi\)
\(998\) −23.7462 + 13.7099i −0.751672 + 0.433978i
\(999\) 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 378.2.l.a.341.2 16
3.2 odd 2 126.2.l.a.5.7 16
4.3 odd 2 3024.2.ca.c.2609.4 16
7.2 even 3 2646.2.m.b.881.2 16
7.3 odd 6 378.2.t.a.17.6 16
7.4 even 3 2646.2.t.b.2285.7 16
7.5 odd 6 2646.2.m.a.881.3 16
7.6 odd 2 2646.2.l.a.1097.3 16
9.2 odd 6 378.2.t.a.89.6 16
9.4 even 3 1134.2.k.b.971.6 16
9.5 odd 6 1134.2.k.a.971.3 16
9.7 even 3 126.2.t.a.47.1 yes 16
12.11 even 2 1008.2.ca.c.257.5 16
21.2 odd 6 882.2.m.b.293.6 16
21.5 even 6 882.2.m.a.293.7 16
21.11 odd 6 882.2.t.a.815.4 16
21.17 even 6 126.2.t.a.59.1 yes 16
21.20 even 2 882.2.l.b.509.6 16
28.3 even 6 3024.2.df.c.17.4 16
36.7 odd 6 1008.2.df.c.929.7 16
36.11 even 6 3024.2.df.c.1601.4 16
63.2 odd 6 2646.2.m.a.1763.3 16
63.11 odd 6 2646.2.l.a.521.7 16
63.16 even 3 882.2.m.a.587.7 16
63.20 even 6 2646.2.t.b.1979.7 16
63.25 even 3 882.2.l.b.227.2 16
63.31 odd 6 1134.2.k.a.647.3 16
63.34 odd 6 882.2.t.a.803.4 16
63.38 even 6 inner 378.2.l.a.143.6 16
63.47 even 6 2646.2.m.b.1763.2 16
63.52 odd 6 126.2.l.a.101.3 yes 16
63.59 even 6 1134.2.k.b.647.6 16
63.61 odd 6 882.2.m.b.587.6 16
84.59 odd 6 1008.2.df.c.689.7 16
252.115 even 6 1008.2.ca.c.353.5 16
252.227 odd 6 3024.2.ca.c.2033.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.l.a.5.7 16 3.2 odd 2
126.2.l.a.101.3 yes 16 63.52 odd 6
126.2.t.a.47.1 yes 16 9.7 even 3
126.2.t.a.59.1 yes 16 21.17 even 6
378.2.l.a.143.6 16 63.38 even 6 inner
378.2.l.a.341.2 16 1.1 even 1 trivial
378.2.t.a.17.6 16 7.3 odd 6
378.2.t.a.89.6 16 9.2 odd 6
882.2.l.b.227.2 16 63.25 even 3
882.2.l.b.509.6 16 21.20 even 2
882.2.m.a.293.7 16 21.5 even 6
882.2.m.a.587.7 16 63.16 even 3
882.2.m.b.293.6 16 21.2 odd 6
882.2.m.b.587.6 16 63.61 odd 6
882.2.t.a.803.4 16 63.34 odd 6
882.2.t.a.815.4 16 21.11 odd 6
1008.2.ca.c.257.5 16 12.11 even 2
1008.2.ca.c.353.5 16 252.115 even 6
1008.2.df.c.689.7 16 84.59 odd 6
1008.2.df.c.929.7 16 36.7 odd 6
1134.2.k.a.647.3 16 63.31 odd 6
1134.2.k.a.971.3 16 9.5 odd 6
1134.2.k.b.647.6 16 63.59 even 6
1134.2.k.b.971.6 16 9.4 even 3
2646.2.l.a.521.7 16 63.11 odd 6
2646.2.l.a.1097.3 16 7.6 odd 2
2646.2.m.a.881.3 16 7.5 odd 6
2646.2.m.a.1763.3 16 63.2 odd 6
2646.2.m.b.881.2 16 7.2 even 3
2646.2.m.b.1763.2 16 63.47 even 6
2646.2.t.b.1979.7 16 63.20 even 6
2646.2.t.b.2285.7 16 7.4 even 3
3024.2.ca.c.2033.4 16 252.227 odd 6
3024.2.ca.c.2609.4 16 4.3 odd 2
3024.2.df.c.17.4 16 28.3 even 6
3024.2.df.c.1601.4 16 36.11 even 6