Properties

Label 637.2.g.j.263.4
Level $637$
Weight $2$
Character 637.263
Analytic conductor $5.086$
Analytic rank $0$
Dimension $8$
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] = [637,2,Mod(263,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.263");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.g (of order \(3\), 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: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 7x^{6} + 38x^{4} - 16x^{3} + 15x^{2} + 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 263.4
Root \(1.37054 - 2.37385i\) of defining polynomial
Character \(\chi\) \(=\) 637.263
Dual form 637.2.g.j.373.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.37054 - 2.37385i) q^{2} -1.36482 q^{3} +(-2.75677 - 4.77486i) q^{4} +(0.370541 + 0.641796i) q^{5} +(-1.87054 + 3.23987i) q^{6} -9.63087 q^{8} -1.13727 q^{9} +O(q^{10})\) \(q+(1.37054 - 2.37385i) q^{2} -1.36482 q^{3} +(-2.75677 - 4.77486i) q^{4} +(0.370541 + 0.641796i) q^{5} +(-1.87054 + 3.23987i) q^{6} -9.63087 q^{8} -1.13727 q^{9} +2.03137 q^{10} -1.36482 q^{11} +(3.76249 + 6.51682i) q^{12} +(-0.301907 + 3.59289i) q^{13} +(-0.505722 - 0.875935i) q^{15} +(-7.68598 + 13.3125i) q^{16} +(-2.07436 - 3.59289i) q^{17} +(-1.55867 + 2.69970i) q^{18} -7.26606 q^{19} +(2.04299 - 3.53856i) q^{20} +(-1.87054 + 3.23987i) q^{22} +(1.16673 - 2.02083i) q^{23} +13.1444 q^{24} +(2.22540 - 3.85450i) q^{25} +(8.11519 + 5.64088i) q^{26} +5.64662 q^{27} +(0.203815 + 0.353017i) q^{29} -2.77245 q^{30} +(-1.38622 + 2.40101i) q^{31} +(11.4370 + 19.8095i) q^{32} +1.86273 q^{33} -11.3720 q^{34} +(3.13518 + 5.43029i) q^{36} +(3.05295 - 5.28787i) q^{37} +(-9.95843 + 17.2485i) q^{38} +(0.412049 - 4.90364i) q^{39} +(-3.56863 - 6.18106i) q^{40} +(0.627306 + 1.08653i) q^{41} +(0.870541 - 1.50782i) q^{43} +(3.76249 + 6.51682i) q^{44} +(-0.421404 - 0.729894i) q^{45} +(-3.19809 - 5.53926i) q^{46} +(-2.92921 - 5.07355i) q^{47} +(10.4900 - 18.1692i) q^{48} +(-6.10000 - 10.5655i) q^{50} +(2.83112 + 4.90364i) q^{51} +(17.9878 - 8.46319i) q^{52} +(-2.28389 + 3.95582i) q^{53} +(7.73893 - 13.4042i) q^{54} +(-0.505722 - 0.875935i) q^{55} +9.91685 q^{57} +1.11734 q^{58} +(-5.49213 - 9.51264i) q^{59} +(-2.78831 + 4.82950i) q^{60} -6.52497 q^{61} +(3.79975 + 6.58137i) q^{62} +31.9557 q^{64} +(-2.41777 + 1.13755i) q^{65} +(2.55295 - 4.42184i) q^{66} -13.7597 q^{67} +(-11.4370 + 19.8095i) q^{68} +(-1.59237 + 2.75807i) q^{69} +(2.40763 - 4.17014i) q^{71} +10.9529 q^{72} +(3.03494 - 5.25666i) q^{73} +(-8.36839 - 14.4945i) q^{74} +(-3.03727 + 5.26070i) q^{75} +(20.0308 + 34.6944i) q^{76} +(-11.0758 - 7.69879i) q^{78} +(4.56291 + 7.90320i) q^{79} -11.3919 q^{80} -4.29482 q^{81} +3.43900 q^{82} -11.7368 q^{83} +(1.53727 - 2.66263i) q^{85} +(-2.38622 - 4.13306i) q^{86} +(-0.278170 - 0.481805i) q^{87} +13.1444 q^{88} +(-0.880503 + 1.52508i) q^{89} -2.31021 q^{90} -12.8656 q^{92} +(1.89195 - 3.27695i) q^{93} -16.0584 q^{94} +(-2.69237 - 4.66332i) q^{95} +(-15.6095 - 27.0364i) q^{96} +(4.76691 - 8.25652i) q^{97} +1.55217 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + q^{2} - 2 q^{3} - 5 q^{4} - 7 q^{5} - 5 q^{6} - 12 q^{8} + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + q^{2} - 2 q^{3} - 5 q^{4} - 7 q^{5} - 5 q^{6} - 12 q^{8} + 14 q^{9} + 22 q^{10} - 2 q^{11} + 12 q^{12} - 4 q^{13} - 3 q^{15} - 19 q^{16} - 4 q^{17} + 3 q^{18} - 2 q^{19} - 2 q^{20} - 5 q^{22} + 2 q^{23} + 6 q^{24} - 5 q^{25} - 3 q^{26} + 52 q^{27} - q^{29} - 8 q^{30} - 4 q^{31} + 33 q^{32} + 38 q^{33} - 6 q^{34} + 34 q^{36} + 10 q^{37} - 23 q^{38} - 19 q^{39} - 17 q^{40} - 22 q^{41} - 3 q^{43} + 12 q^{44} - 11 q^{45} - 24 q^{46} + 2 q^{47} + 11 q^{48} - 43 q^{50} - 7 q^{51} + 34 q^{52} - 2 q^{53} + 5 q^{54} - 3 q^{55} - 34 q^{57} - 22 q^{58} - 8 q^{59} + 11 q^{60} - 16 q^{61} - 5 q^{62} + 28 q^{64} + 4 q^{65} + 6 q^{66} - 12 q^{67} - 33 q^{68} - 18 q^{69} + 14 q^{71} + 10 q^{72} - 8 q^{73} - 20 q^{74} - 7 q^{75} + 32 q^{76} - q^{78} + 26 q^{79} - 14 q^{80} + 48 q^{81} + 28 q^{82} - 5 q^{85} - 12 q^{86} + 13 q^{87} + 6 q^{88} - q^{89} - 52 q^{90} + 24 q^{92} + 7 q^{93} - 66 q^{94} - 21 q^{95} - 58 q^{96} + 3 q^{97} + 46 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.37054 2.37385i 0.969119 1.67856i 0.271003 0.962579i \(-0.412645\pi\)
0.698116 0.715984i \(-0.254022\pi\)
\(3\) −1.36482 −0.787979 −0.393989 0.919115i \(-0.628905\pi\)
−0.393989 + 0.919115i \(0.628905\pi\)
\(4\) −2.75677 4.77486i −1.37838 2.38743i
\(5\) 0.370541 + 0.641796i 0.165711 + 0.287020i 0.936908 0.349577i \(-0.113675\pi\)
−0.771197 + 0.636597i \(0.780341\pi\)
\(6\) −1.87054 + 3.23987i −0.763645 + 1.32267i
\(7\) 0 0
\(8\) −9.63087 −3.40503
\(9\) −1.13727 −0.379089
\(10\) 2.03137 0.642374
\(11\) −1.36482 −0.411509 −0.205754 0.978604i \(-0.565965\pi\)
−0.205754 + 0.978604i \(0.565965\pi\)
\(12\) 3.76249 + 6.51682i 1.08614 + 1.88124i
\(13\) −0.301907 + 3.59289i −0.0837339 + 0.996488i
\(14\) 0 0
\(15\) −0.505722 0.875935i −0.130577 0.226166i
\(16\) −7.68598 + 13.3125i −1.92149 + 3.32813i
\(17\) −2.07436 3.59289i −0.503105 0.871404i −0.999994 0.00358919i \(-0.998858\pi\)
0.496888 0.867814i \(-0.334476\pi\)
\(18\) −1.55867 + 2.69970i −0.367383 + 0.636325i
\(19\) −7.26606 −1.66695 −0.833474 0.552559i \(-0.813651\pi\)
−0.833474 + 0.552559i \(0.813651\pi\)
\(20\) 2.04299 3.53856i 0.456826 0.791246i
\(21\) 0 0
\(22\) −1.87054 + 3.23987i −0.398801 + 0.690743i
\(23\) 1.16673 2.02083i 0.243279 0.421372i −0.718367 0.695664i \(-0.755110\pi\)
0.961646 + 0.274292i \(0.0884435\pi\)
\(24\) 13.1444 2.68309
\(25\) 2.22540 3.85450i 0.445080 0.770901i
\(26\) 8.11519 + 5.64088i 1.59152 + 1.10627i
\(27\) 5.64662 1.08669
\(28\) 0 0
\(29\) 0.203815 + 0.353017i 0.0378474 + 0.0655536i 0.884329 0.466865i \(-0.154617\pi\)
−0.846481 + 0.532419i \(0.821283\pi\)
\(30\) −2.77245 −0.506178
\(31\) −1.38622 + 2.40101i −0.248973 + 0.431234i −0.963241 0.268638i \(-0.913426\pi\)
0.714268 + 0.699872i \(0.246760\pi\)
\(32\) 11.4370 + 19.8095i 2.02180 + 3.50186i
\(33\) 1.86273 0.324260
\(34\) −11.3720 −1.95027
\(35\) 0 0
\(36\) 3.13518 + 5.43029i 0.522530 + 0.905049i
\(37\) 3.05295 5.28787i 0.501902 0.869320i −0.498096 0.867122i \(-0.665967\pi\)
0.999998 0.00219764i \(-0.000699531\pi\)
\(38\) −9.95843 + 17.2485i −1.61547 + 2.79808i
\(39\) 0.412049 4.90364i 0.0659806 0.785212i
\(40\) −3.56863 6.18106i −0.564251 0.977311i
\(41\) 0.627306 + 1.08653i 0.0979688 + 0.169687i 0.910844 0.412751i \(-0.135432\pi\)
−0.812875 + 0.582438i \(0.802099\pi\)
\(42\) 0 0
\(43\) 0.870541 1.50782i 0.132756 0.229941i −0.791982 0.610545i \(-0.790951\pi\)
0.924738 + 0.380604i \(0.124284\pi\)
\(44\) 3.76249 + 6.51682i 0.567216 + 0.982447i
\(45\) −0.421404 0.729894i −0.0628193 0.108806i
\(46\) −3.19809 5.53926i −0.471533 0.816719i
\(47\) −2.92921 5.07355i −0.427270 0.740053i 0.569360 0.822089i \(-0.307191\pi\)
−0.996629 + 0.0820357i \(0.973858\pi\)
\(48\) 10.4900 18.1692i 1.51410 2.62249i
\(49\) 0 0
\(50\) −6.10000 10.5655i −0.862670 1.49419i
\(51\) 2.83112 + 4.90364i 0.396436 + 0.686648i
\(52\) 17.9878 8.46319i 2.49446 1.17363i
\(53\) −2.28389 + 3.95582i −0.313717 + 0.543373i −0.979164 0.203072i \(-0.934908\pi\)
0.665447 + 0.746445i \(0.268241\pi\)
\(54\) 7.73893 13.4042i 1.05313 1.82408i
\(55\) −0.505722 0.875935i −0.0681915 0.118111i
\(56\) 0 0
\(57\) 9.91685 1.31352
\(58\) 1.11734 0.146715
\(59\) −5.49213 9.51264i −0.715014 1.23844i −0.962954 0.269665i \(-0.913087\pi\)
0.247940 0.968775i \(-0.420246\pi\)
\(60\) −2.78831 + 4.82950i −0.359969 + 0.623485i
\(61\) −6.52497 −0.835437 −0.417719 0.908576i \(-0.637170\pi\)
−0.417719 + 0.908576i \(0.637170\pi\)
\(62\) 3.79975 + 6.58137i 0.482569 + 0.835834i
\(63\) 0 0
\(64\) 31.9557 3.99446
\(65\) −2.41777 + 1.13755i −0.299887 + 0.141096i
\(66\) 2.55295 4.42184i 0.314247 0.544291i
\(67\) −13.7597 −1.68101 −0.840505 0.541804i \(-0.817742\pi\)
−0.840505 + 0.541804i \(0.817742\pi\)
\(68\) −11.4370 + 19.8095i −1.38694 + 2.40226i
\(69\) −1.59237 + 2.75807i −0.191699 + 0.332032i
\(70\) 0 0
\(71\) 2.40763 4.17014i 0.285733 0.494904i −0.687054 0.726607i \(-0.741096\pi\)
0.972787 + 0.231703i \(0.0744296\pi\)
\(72\) 10.9529 1.29081
\(73\) 3.03494 5.25666i 0.355212 0.615246i −0.631942 0.775016i \(-0.717742\pi\)
0.987154 + 0.159770i \(0.0510752\pi\)
\(74\) −8.36839 14.4945i −0.972805 1.68495i
\(75\) −3.03727 + 5.26070i −0.350713 + 0.607453i
\(76\) 20.0308 + 34.6944i 2.29769 + 3.97972i
\(77\) 0 0
\(78\) −11.0758 7.69879i −1.25408 0.871716i
\(79\) 4.56291 + 7.90320i 0.513368 + 0.889179i 0.999880 + 0.0155052i \(0.00493564\pi\)
−0.486512 + 0.873674i \(0.661731\pi\)
\(80\) −11.3919 −1.27365
\(81\) −4.29482 −0.477202
\(82\) 3.43900 0.379774
\(83\) −11.7368 −1.28828 −0.644139 0.764908i \(-0.722784\pi\)
−0.644139 + 0.764908i \(0.722784\pi\)
\(84\) 0 0
\(85\) 1.53727 2.66263i 0.166740 0.288802i
\(86\) −2.38622 4.13306i −0.257313 0.445679i
\(87\) −0.278170 0.481805i −0.0298230 0.0516549i
\(88\) 13.1444 1.40120
\(89\) −0.880503 + 1.52508i −0.0933331 + 0.161658i −0.908912 0.416989i \(-0.863085\pi\)
0.815579 + 0.578646i \(0.196419\pi\)
\(90\) −2.31021 −0.243517
\(91\) 0 0
\(92\) −12.8656 −1.34133
\(93\) 1.89195 3.27695i 0.196186 0.339803i
\(94\) −16.0584 −1.65630
\(95\) −2.69237 4.66332i −0.276231 0.478447i
\(96\) −15.6095 27.0364i −1.59313 2.75939i
\(97\) 4.76691 8.25652i 0.484006 0.838323i −0.515825 0.856694i \(-0.672515\pi\)
0.999831 + 0.0183708i \(0.00584795\pi\)
\(98\) 0 0
\(99\) 1.55217 0.155998
\(100\) −24.5396 −2.45396
\(101\) 7.49361 0.745642 0.372821 0.927903i \(-0.378391\pi\)
0.372821 + 0.927903i \(0.378391\pi\)
\(102\) 15.5207 1.53678
\(103\) 1.40424 + 2.43221i 0.138364 + 0.239653i 0.926877 0.375364i \(-0.122482\pi\)
−0.788514 + 0.615017i \(0.789149\pi\)
\(104\) 2.90763 34.6027i 0.285116 3.39307i
\(105\) 0 0
\(106\) 6.26033 + 10.8432i 0.608057 + 1.05319i
\(107\) −0.743235 + 1.28732i −0.0718512 + 0.124450i −0.899713 0.436483i \(-0.856224\pi\)
0.827861 + 0.560933i \(0.189557\pi\)
\(108\) −15.5664 26.9618i −1.49788 2.59440i
\(109\) −1.43561 + 2.48654i −0.137506 + 0.238168i −0.926552 0.376167i \(-0.877242\pi\)
0.789046 + 0.614334i \(0.210575\pi\)
\(110\) −2.77245 −0.264343
\(111\) −4.16673 + 7.21698i −0.395488 + 0.685006i
\(112\) 0 0
\(113\) 6.20972 10.7555i 0.584161 1.01180i −0.410819 0.911717i \(-0.634757\pi\)
0.994979 0.100079i \(-0.0319096\pi\)
\(114\) 13.5915 23.5411i 1.27296 2.20483i
\(115\) 1.72928 0.161256
\(116\) 1.12374 1.94637i 0.104336 0.180716i
\(117\) 0.343349 4.08608i 0.0317426 0.377758i
\(118\) −30.1087 −2.77173
\(119\) 0 0
\(120\) 4.87054 + 8.43602i 0.444618 + 0.770100i
\(121\) −9.13727 −0.830661
\(122\) −8.94274 + 15.4893i −0.809638 + 1.40233i
\(123\) −0.856160 1.48291i −0.0771973 0.133710i
\(124\) 15.2860 1.37272
\(125\) 7.00382 0.626440
\(126\) 0 0
\(127\) −2.71526 4.70296i −0.240940 0.417321i 0.720042 0.693930i \(-0.244122\pi\)
−0.960982 + 0.276610i \(0.910789\pi\)
\(128\) 20.9226 36.2390i 1.84931 3.20310i
\(129\) −1.18813 + 2.05790i −0.104609 + 0.181188i
\(130\) −0.613284 + 7.29847i −0.0537886 + 0.640119i
\(131\) −5.66100 9.80515i −0.494604 0.856680i 0.505376 0.862899i \(-0.331354\pi\)
−0.999981 + 0.00621925i \(0.998020\pi\)
\(132\) −5.13512 8.89428i −0.446954 0.774148i
\(133\) 0 0
\(134\) −18.8582 + 32.6633i −1.62910 + 2.82168i
\(135\) 2.09231 + 3.62398i 0.180077 + 0.311902i
\(136\) 19.9779 + 34.6027i 1.71309 + 2.96715i
\(137\) 6.98771 + 12.1031i 0.597000 + 1.03403i 0.993261 + 0.115897i \(0.0369741\pi\)
−0.396261 + 0.918138i \(0.629693\pi\)
\(138\) 4.36482 + 7.56009i 0.371558 + 0.643558i
\(139\) 5.21544 9.03340i 0.442368 0.766203i −0.555497 0.831518i \(-0.687472\pi\)
0.997865 + 0.0653153i \(0.0208053\pi\)
\(140\) 0 0
\(141\) 3.99785 + 6.92447i 0.336679 + 0.583146i
\(142\) −6.59951 11.4307i −0.553818 0.959242i
\(143\) 0.412049 4.90364i 0.0344572 0.410063i
\(144\) 8.74102 15.1399i 0.728418 1.26166i
\(145\) −0.151043 + 0.261615i −0.0125435 + 0.0217259i
\(146\) −8.31901 14.4089i −0.688486 1.19249i
\(147\) 0 0
\(148\) −33.6651 −2.76725
\(149\) 8.16433 0.668848 0.334424 0.942423i \(-0.391458\pi\)
0.334424 + 0.942423i \(0.391458\pi\)
\(150\) 8.32540 + 14.4200i 0.679766 + 1.17739i
\(151\) 1.23094 2.13205i 0.100173 0.173504i −0.811583 0.584237i \(-0.801394\pi\)
0.911756 + 0.410733i \(0.134727\pi\)
\(152\) 69.9785 5.67600
\(153\) 2.35910 + 4.08608i 0.190722 + 0.330340i
\(154\) 0 0
\(155\) −2.05461 −0.165030
\(156\) −24.5501 + 11.5507i −1.96558 + 0.924798i
\(157\) −6.45991 + 11.1889i −0.515557 + 0.892971i 0.484280 + 0.874913i \(0.339082\pi\)
−0.999837 + 0.0180576i \(0.994252\pi\)
\(158\) 25.0146 1.99006
\(159\) 3.11710 5.39897i 0.247202 0.428167i
\(160\) −8.47577 + 14.6805i −0.670069 + 1.16059i
\(161\) 0 0
\(162\) −5.88622 + 10.1952i −0.462465 + 0.801014i
\(163\) −6.02742 −0.472104 −0.236052 0.971740i \(-0.575854\pi\)
−0.236052 + 0.971740i \(0.575854\pi\)
\(164\) 3.45867 5.99060i 0.270077 0.467787i
\(165\) 0.690219 + 1.19549i 0.0537334 + 0.0930691i
\(166\) −16.0857 + 27.8613i −1.24850 + 2.16246i
\(167\) 3.82558 + 6.62610i 0.296032 + 0.512743i 0.975224 0.221218i \(-0.0710031\pi\)
−0.679192 + 0.733960i \(0.737670\pi\)
\(168\) 0 0
\(169\) −12.8177 2.16944i −0.985977 0.166880i
\(170\) −4.21378 7.29847i −0.323182 0.559767i
\(171\) 8.26345 0.631922
\(172\) −9.59951 −0.731956
\(173\) 0.164460 0.0125036 0.00625182 0.999980i \(-0.498010\pi\)
0.00625182 + 0.999980i \(0.498010\pi\)
\(174\) −1.52497 −0.115608
\(175\) 0 0
\(176\) 10.4900 18.1692i 0.790711 1.36955i
\(177\) 7.49576 + 12.9830i 0.563416 + 0.975865i
\(178\) 2.41353 + 4.18036i 0.180902 + 0.313331i
\(179\) 0.768633 0.0574503 0.0287252 0.999587i \(-0.490855\pi\)
0.0287252 + 0.999587i \(0.490855\pi\)
\(180\) −2.32343 + 4.02429i −0.173178 + 0.299953i
\(181\) 9.92152 0.737461 0.368730 0.929536i \(-0.379793\pi\)
0.368730 + 0.929536i \(0.379793\pi\)
\(182\) 0 0
\(183\) 8.90541 0.658307
\(184\) −11.2366 + 19.4624i −0.828373 + 1.43478i
\(185\) 4.52497 0.332683
\(186\) −5.18598 8.98238i −0.380254 0.658620i
\(187\) 2.83112 + 4.90364i 0.207032 + 0.358590i
\(188\) −16.1503 + 27.9732i −1.17788 + 2.04015i
\(189\) 0 0
\(190\) −14.7600 −1.07080
\(191\) 9.89693 0.716117 0.358058 0.933699i \(-0.383439\pi\)
0.358058 + 0.933699i \(0.383439\pi\)
\(192\) −43.6138 −3.14755
\(193\) 8.70075 0.626293 0.313147 0.949705i \(-0.398617\pi\)
0.313147 + 0.949705i \(0.398617\pi\)
\(194\) −13.0665 22.6318i −0.938119 1.62487i
\(195\) 3.29982 1.55255i 0.236305 0.111180i
\(196\) 0 0
\(197\) 13.0093 + 22.5328i 0.926874 + 1.60539i 0.788520 + 0.615009i \(0.210848\pi\)
0.138354 + 0.990383i \(0.455819\pi\)
\(198\) 2.12731 3.68460i 0.151181 0.261853i
\(199\) 5.06648 + 8.77540i 0.359153 + 0.622072i 0.987820 0.155603i \(-0.0497322\pi\)
−0.628666 + 0.777675i \(0.716399\pi\)
\(200\) −21.4325 + 37.1222i −1.51551 + 2.62494i
\(201\) 18.7795 1.32460
\(202\) 10.2703 17.7887i 0.722615 1.25161i
\(203\) 0 0
\(204\) 15.6095 27.0364i 1.09288 1.89293i
\(205\) −0.464885 + 0.805205i −0.0324690 + 0.0562380i
\(206\) 7.69827 0.536364
\(207\) −1.32688 + 2.29822i −0.0922246 + 0.159738i
\(208\) −45.5099 31.6340i −3.15554 2.19342i
\(209\) 9.91685 0.685963
\(210\) 0 0
\(211\) −8.33911 14.4438i −0.574088 0.994349i −0.996140 0.0877779i \(-0.972023\pi\)
0.422052 0.906572i \(-0.361310\pi\)
\(212\) 25.1846 1.72969
\(213\) −3.28598 + 5.69148i −0.225152 + 0.389974i
\(214\) 2.03727 + 3.52865i 0.139265 + 0.241214i
\(215\) 1.29028 0.0879967
\(216\) −54.3819 −3.70022
\(217\) 0 0
\(218\) 3.93511 + 6.81582i 0.266520 + 0.461625i
\(219\) −4.14214 + 7.17439i −0.279900 + 0.484801i
\(220\) −2.78831 + 4.82950i −0.187988 + 0.325605i
\(221\) 13.5351 6.36821i 0.910470 0.428372i
\(222\) 11.4213 + 19.7823i 0.766550 + 1.32770i
\(223\) 0.535180 + 0.926959i 0.0358383 + 0.0620738i 0.883388 0.468642i \(-0.155257\pi\)
−0.847550 + 0.530716i \(0.821923\pi\)
\(224\) 0 0
\(225\) −2.53087 + 4.38360i −0.168725 + 0.292240i
\(226\) −17.0213 29.4818i −1.13224 1.96110i
\(227\) −12.2332 21.1885i −0.811947 1.40633i −0.911500 0.411300i \(-0.865075\pi\)
0.0995534 0.995032i \(-0.468259\pi\)
\(228\) −27.3384 47.3516i −1.81053 3.13593i
\(229\) 2.36482 + 4.09599i 0.156272 + 0.270670i 0.933521 0.358522i \(-0.116719\pi\)
−0.777250 + 0.629192i \(0.783386\pi\)
\(230\) 2.37005 4.10505i 0.156276 0.270679i
\(231\) 0 0
\(232\) −1.96291 3.39986i −0.128871 0.223212i
\(233\) −10.2753 17.7974i −0.673160 1.16595i −0.977003 0.213226i \(-0.931603\pi\)
0.303843 0.952722i \(-0.401730\pi\)
\(234\) −9.22915 6.41519i −0.603328 0.419374i
\(235\) 2.17079 3.75991i 0.141607 0.245270i
\(236\) −30.2810 + 52.4482i −1.97113 + 3.41409i
\(237\) −6.22755 10.7864i −0.404523 0.700654i
\(238\) 0 0
\(239\) 6.25461 0.404577 0.202289 0.979326i \(-0.435162\pi\)
0.202289 + 0.979326i \(0.435162\pi\)
\(240\) 15.5479 1.00361
\(241\) −6.07220 10.5174i −0.391145 0.677483i 0.601456 0.798906i \(-0.294588\pi\)
−0.992601 + 0.121423i \(0.961254\pi\)
\(242\) −12.5230 + 21.6905i −0.805009 + 1.39432i
\(243\) −11.0782 −0.710668
\(244\) 17.9878 + 31.1558i 1.15155 + 1.99455i
\(245\) 0 0
\(246\) −4.69361 −0.299254
\(247\) 2.19367 26.1061i 0.139580 1.66109i
\(248\) 13.3506 23.1238i 0.847761 1.46836i
\(249\) 16.0186 1.01514
\(250\) 9.59902 16.6260i 0.607095 1.05152i
\(251\) −3.15719 + 5.46842i −0.199280 + 0.345163i −0.948295 0.317390i \(-0.897194\pi\)
0.749015 + 0.662553i \(0.230527\pi\)
\(252\) 0 0
\(253\) −1.59237 + 2.75807i −0.100112 + 0.173398i
\(254\) −14.8855 −0.933999
\(255\) −2.09809 + 3.63400i −0.131388 + 0.227570i
\(256\) −25.3948 43.9850i −1.58717 2.74907i
\(257\) 12.1781 21.0931i 0.759649 1.31575i −0.183380 0.983042i \(-0.558704\pi\)
0.943030 0.332709i \(-0.107963\pi\)
\(258\) 3.25677 + 5.64088i 0.202757 + 0.351186i
\(259\) 0 0
\(260\) 12.0969 + 8.40855i 0.750216 + 0.521476i
\(261\) −0.231792 0.401475i −0.0143475 0.0248507i
\(262\) −31.0346 −1.91732
\(263\) −9.57910 −0.590672 −0.295336 0.955393i \(-0.595432\pi\)
−0.295336 + 0.955393i \(0.595432\pi\)
\(264\) −17.9397 −1.10411
\(265\) −3.38510 −0.207945
\(266\) 0 0
\(267\) 1.20173 2.08145i 0.0735445 0.127383i
\(268\) 37.9322 + 65.7004i 2.31708 + 4.01329i
\(269\) 14.6995 + 25.4603i 0.896245 + 1.55234i 0.832256 + 0.554391i \(0.187049\pi\)
0.0639886 + 0.997951i \(0.479618\pi\)
\(270\) 11.4704 0.698064
\(271\) −0.150192 + 0.260141i −0.00912354 + 0.0158024i −0.870551 0.492078i \(-0.836237\pi\)
0.861428 + 0.507880i \(0.169571\pi\)
\(272\) 63.7738 3.86686
\(273\) 0 0
\(274\) 38.3078 2.31426
\(275\) −3.03727 + 5.26070i −0.183154 + 0.317232i
\(276\) 17.5592 1.05694
\(277\) 16.3855 + 28.3805i 0.984509 + 1.70522i 0.644100 + 0.764941i \(0.277232\pi\)
0.340408 + 0.940278i \(0.389435\pi\)
\(278\) −14.2959 24.7613i −0.857414 1.48508i
\(279\) 1.57651 2.73059i 0.0943831 0.163476i
\(280\) 0 0
\(281\) 4.29482 0.256207 0.128104 0.991761i \(-0.459111\pi\)
0.128104 + 0.991761i \(0.459111\pi\)
\(282\) 21.9169 1.30513
\(283\) 21.1003 1.25428 0.627140 0.778907i \(-0.284225\pi\)
0.627140 + 0.778907i \(0.284225\pi\)
\(284\) −26.5491 −1.57540
\(285\) 3.67460 + 6.36460i 0.217665 + 0.377006i
\(286\) −11.0758 7.69879i −0.654924 0.455239i
\(287\) 0 0
\(288\) −13.0070 22.5287i −0.766442 1.32752i
\(289\) −0.105901 + 0.183427i −0.00622950 + 0.0107898i
\(290\) 0.414022 + 0.717107i 0.0243122 + 0.0421100i
\(291\) −6.50597 + 11.2687i −0.381387 + 0.660581i
\(292\) −33.4664 −1.95847
\(293\) 8.88192 15.3839i 0.518887 0.898739i −0.480872 0.876791i \(-0.659680\pi\)
0.999759 0.0219482i \(-0.00698688\pi\)
\(294\) 0 0
\(295\) 4.07012 7.04965i 0.236971 0.410446i
\(296\) −29.4026 + 50.9268i −1.70899 + 2.96006i
\(297\) −7.70662 −0.447184
\(298\) 11.1895 19.3809i 0.648193 1.12270i
\(299\) 6.90837 + 4.80202i 0.399522 + 0.277708i
\(300\) 33.4921 1.93367
\(301\) 0 0
\(302\) −3.37411 5.84413i −0.194158 0.336292i
\(303\) −10.2274 −0.587550
\(304\) 55.8467 96.7294i 3.20303 5.54781i
\(305\) −2.41777 4.18770i −0.138441 0.239787i
\(306\) 12.9330 0.739328
\(307\) −18.0156 −1.02821 −0.514103 0.857729i \(-0.671875\pi\)
−0.514103 + 0.857729i \(0.671875\pi\)
\(308\) 0 0
\(309\) −1.91653 3.31953i −0.109028 0.188842i
\(310\) −2.81593 + 4.87733i −0.159934 + 0.277014i
\(311\) 8.62724 14.9428i 0.489206 0.847330i −0.510717 0.859749i \(-0.670620\pi\)
0.999923 + 0.0124194i \(0.00395331\pi\)
\(312\) −3.96839 + 47.2264i −0.224666 + 2.67367i
\(313\) 3.40763 + 5.90219i 0.192611 + 0.333611i 0.946115 0.323832i \(-0.104971\pi\)
−0.753504 + 0.657443i \(0.771638\pi\)
\(314\) 17.7071 + 30.6697i 0.999272 + 1.73079i
\(315\) 0 0
\(316\) 25.1578 43.5745i 1.41523 2.45126i
\(317\) 12.5385 + 21.7173i 0.704233 + 1.21977i 0.966968 + 0.254899i \(0.0820421\pi\)
−0.262735 + 0.964868i \(0.584625\pi\)
\(318\) −8.54423 14.7990i −0.479136 0.829889i
\(319\) −0.278170 0.481805i −0.0155745 0.0269759i
\(320\) 11.8409 + 20.5090i 0.661927 + 1.14649i
\(321\) 1.01438 1.75696i 0.0566172 0.0980639i
\(322\) 0 0
\(323\) 15.0724 + 26.1061i 0.838650 + 1.45258i
\(324\) 11.8398 + 20.5071i 0.657767 + 1.13929i
\(325\) 13.1769 + 9.15931i 0.730925 + 0.508067i
\(326\) −8.26083 + 14.3082i −0.457525 + 0.792456i
\(327\) 1.95934 3.39368i 0.108352 0.187671i
\(328\) −6.04151 10.4642i −0.333586 0.577789i
\(329\) 0 0
\(330\) 3.78389 0.208296
\(331\) −2.99534 −0.164639 −0.0823193 0.996606i \(-0.526233\pi\)
−0.0823193 + 0.996606i \(0.526233\pi\)
\(332\) 32.3555 + 56.0414i 1.77574 + 3.07567i
\(333\) −3.47202 + 6.01372i −0.190266 + 0.329550i
\(334\) 20.9724 1.14756
\(335\) −5.09852 8.83089i −0.278562 0.482483i
\(336\) 0 0
\(337\) −29.4888 −1.60636 −0.803179 0.595738i \(-0.796860\pi\)
−0.803179 + 0.595738i \(0.796860\pi\)
\(338\) −22.7171 + 27.4540i −1.23565 + 1.49330i
\(339\) −8.47514 + 14.6794i −0.460306 + 0.797274i
\(340\) −16.9515 −0.919326
\(341\) 1.89195 3.27695i 0.102455 0.177457i
\(342\) 11.3254 19.6162i 0.612407 1.06072i
\(343\) 0 0
\(344\) −8.38407 + 14.5216i −0.452039 + 0.782954i
\(345\) −2.36015 −0.127066
\(346\) 0.225399 0.390402i 0.0121175 0.0209881i
\(347\) 2.99343 + 5.18477i 0.160696 + 0.278333i 0.935118 0.354336i \(-0.115293\pi\)
−0.774423 + 0.632668i \(0.781960\pi\)
\(348\) −1.53370 + 2.65644i −0.0822149 + 0.142400i
\(349\) −15.1681 26.2719i −0.811929 1.40630i −0.911513 0.411272i \(-0.865085\pi\)
0.0995840 0.995029i \(-0.468249\pi\)
\(350\) 0 0
\(351\) −1.70476 + 20.2877i −0.0909931 + 1.08288i
\(352\) −15.6095 27.0364i −0.831988 1.44104i
\(353\) 28.6063 1.52256 0.761280 0.648424i \(-0.224572\pi\)
0.761280 + 0.648424i \(0.224572\pi\)
\(354\) 41.0930 2.18407
\(355\) 3.56850 0.189396
\(356\) 9.70936 0.514595
\(357\) 0 0
\(358\) 1.05344 1.82462i 0.0556762 0.0964340i
\(359\) −11.7309 20.3185i −0.619132 1.07237i −0.989644 0.143540i \(-0.954151\pi\)
0.370513 0.928827i \(-0.379182\pi\)
\(360\) 4.05849 + 7.02952i 0.213901 + 0.370488i
\(361\) 33.7956 1.77871
\(362\) 13.5978 23.5522i 0.714687 1.23787i
\(363\) 12.4707 0.654543
\(364\) 0 0
\(365\) 4.49827 0.235450
\(366\) 12.2052 21.1401i 0.637978 1.10501i
\(367\) −36.5197 −1.90631 −0.953156 0.302479i \(-0.902186\pi\)
−0.953156 + 0.302479i \(0.902186\pi\)
\(368\) 17.9349 + 31.0641i 0.934920 + 1.61933i
\(369\) −0.713415 1.23567i −0.0371389 0.0643265i
\(370\) 6.20166 10.7416i 0.322409 0.558429i
\(371\) 0 0
\(372\) −20.8626 −1.08168
\(373\) −13.0498 −0.675694 −0.337847 0.941201i \(-0.609699\pi\)
−0.337847 + 0.941201i \(0.609699\pi\)
\(374\) 15.5207 0.802555
\(375\) −9.55894 −0.493622
\(376\) 28.2109 + 48.8627i 1.45487 + 2.51990i
\(377\) −1.32988 + 0.625705i −0.0684925 + 0.0322254i
\(378\) 0 0
\(379\) −15.3018 26.5036i −0.786003 1.36140i −0.928398 0.371587i \(-0.878814\pi\)
0.142395 0.989810i \(-0.454520\pi\)
\(380\) −14.8445 + 25.7114i −0.761505 + 1.31897i
\(381\) 3.70584 + 6.41870i 0.189856 + 0.328840i
\(382\) 13.5641 23.4938i 0.694002 1.20205i
\(383\) 4.88598 0.249662 0.124831 0.992178i \(-0.460161\pi\)
0.124831 + 0.992178i \(0.460161\pi\)
\(384\) −28.5555 + 49.4596i −1.45722 + 2.52398i
\(385\) 0 0
\(386\) 11.9247 20.6542i 0.606953 1.05127i
\(387\) −0.990038 + 1.71480i −0.0503265 + 0.0871680i
\(388\) −52.5650 −2.66858
\(389\) 0.927126 1.60583i 0.0470072 0.0814188i −0.841564 0.540157i \(-0.818365\pi\)
0.888572 + 0.458738i \(0.151698\pi\)
\(390\) 0.837022 9.96110i 0.0423842 0.504400i
\(391\) −9.68082 −0.489580
\(392\) 0 0
\(393\) 7.72625 + 13.3823i 0.389738 + 0.675046i
\(394\) 71.3191 3.59300
\(395\) −3.38149 + 5.85692i −0.170141 + 0.294693i
\(396\) −4.27896 7.41137i −0.215026 0.372435i
\(397\) −21.5134 −1.07973 −0.539863 0.841753i \(-0.681524\pi\)
−0.539863 + 0.841753i \(0.681524\pi\)
\(398\) 27.7753 1.39225
\(399\) 0 0
\(400\) 34.2087 + 59.2513i 1.71044 + 2.96256i
\(401\) 7.28266 12.6139i 0.363678 0.629910i −0.624885 0.780717i \(-0.714854\pi\)
0.988563 + 0.150808i \(0.0481874\pi\)
\(402\) 25.7380 44.5795i 1.28370 2.22343i
\(403\) −8.20805 5.70543i −0.408872 0.284208i
\(404\) −20.6581 35.7809i −1.02778 1.78017i
\(405\) −1.59141 2.75640i −0.0790776 0.136966i
\(406\) 0 0
\(407\) −4.16673 + 7.21698i −0.206537 + 0.357733i
\(408\) −27.2662 47.2264i −1.34988 2.33805i
\(409\) −11.0645 19.1643i −0.547105 0.947613i −0.998471 0.0552745i \(-0.982397\pi\)
0.451366 0.892339i \(-0.350937\pi\)
\(410\) 1.27429 + 2.20713i 0.0629326 + 0.109003i
\(411\) −9.53696 16.5185i −0.470423 0.814797i
\(412\) 7.74232 13.4101i 0.381437 0.660668i
\(413\) 0 0
\(414\) 3.63709 + 6.29962i 0.178753 + 0.309610i
\(415\) −4.34896 7.53261i −0.213482 0.369761i
\(416\) −74.6263 + 35.1113i −3.65885 + 1.72147i
\(417\) −7.11813 + 12.3290i −0.348576 + 0.603752i
\(418\) 13.5915 23.5411i 0.664780 1.15143i
\(419\) 1.68795 + 2.92362i 0.0824618 + 0.142828i 0.904307 0.426883i \(-0.140388\pi\)
−0.821845 + 0.569711i \(0.807055\pi\)
\(420\) 0 0
\(421\) −25.1101 −1.22379 −0.611895 0.790939i \(-0.709593\pi\)
−0.611895 + 0.790939i \(0.709593\pi\)
\(422\) −45.7164 −2.22544
\(423\) 3.33130 + 5.76998i 0.161973 + 0.280546i
\(424\) 21.9959 38.0980i 1.06821 1.85020i
\(425\) −18.4651 −0.895688
\(426\) 9.00714 + 15.6008i 0.436397 + 0.755862i
\(427\) 0 0
\(428\) 8.19570 0.396154
\(429\) −0.562372 + 6.69259i −0.0271516 + 0.323121i
\(430\) 1.76839 3.06294i 0.0852792 0.147708i
\(431\) 10.7948 0.519969 0.259985 0.965613i \(-0.416282\pi\)
0.259985 + 0.965613i \(0.416282\pi\)
\(432\) −43.3998 + 75.1707i −2.08808 + 3.61665i
\(433\) −7.25910 + 12.5731i −0.348850 + 0.604226i −0.986045 0.166476i \(-0.946761\pi\)
0.637195 + 0.770702i \(0.280094\pi\)
\(434\) 0 0
\(435\) 0.206147 0.357057i 0.00988398 0.0171196i
\(436\) 15.8305 0.758144
\(437\) −8.47750 + 14.6835i −0.405534 + 0.702405i
\(438\) 11.3539 + 19.6656i 0.542512 + 0.939659i
\(439\) −7.21544 + 12.4975i −0.344374 + 0.596473i −0.985240 0.171180i \(-0.945242\pi\)
0.640866 + 0.767653i \(0.278575\pi\)
\(440\) 4.87054 + 8.43602i 0.232194 + 0.402172i
\(441\) 0 0
\(442\) 3.43327 40.8582i 0.163304 1.94343i
\(443\) 15.1215 + 26.1912i 0.718445 + 1.24438i 0.961616 + 0.274400i \(0.0884792\pi\)
−0.243171 + 0.969984i \(0.578187\pi\)
\(444\) 45.9467 2.18054
\(445\) −1.30505 −0.0618653
\(446\) 2.93395 0.138926
\(447\) −11.1428 −0.527038
\(448\) 0 0
\(449\) −15.6380 + 27.0858i −0.738003 + 1.27826i 0.215390 + 0.976528i \(0.430898\pi\)
−0.953393 + 0.301731i \(0.902435\pi\)
\(450\) 6.93733 + 12.0158i 0.327029 + 0.566431i
\(451\) −0.856160 1.48291i −0.0403150 0.0698276i
\(452\) −68.4749 −3.22079
\(453\) −1.68001 + 2.90987i −0.0789338 + 0.136717i
\(454\) −67.0645 −3.14749
\(455\) 0 0
\(456\) −95.5080 −4.47257
\(457\) −10.3233 + 17.8805i −0.482904 + 0.836415i −0.999807 0.0196293i \(-0.993751\pi\)
0.516903 + 0.856044i \(0.327085\pi\)
\(458\) 12.9643 0.605783
\(459\) −11.7131 20.2877i −0.546721 0.946948i
\(460\) −4.76722 8.25707i −0.222273 0.384988i
\(461\) 13.6480 23.6391i 0.635653 1.10098i −0.350724 0.936479i \(-0.614064\pi\)
0.986376 0.164504i \(-0.0526022\pi\)
\(462\) 0 0
\(463\) 5.65977 0.263032 0.131516 0.991314i \(-0.458016\pi\)
0.131516 + 0.991314i \(0.458016\pi\)
\(464\) −6.26606 −0.290894
\(465\) 2.80417 0.130040
\(466\) −56.3311 −2.60949
\(467\) 21.1073 + 36.5588i 0.976727 + 1.69174i 0.674114 + 0.738628i \(0.264526\pi\)
0.302614 + 0.953113i \(0.402141\pi\)
\(468\) −20.4570 + 9.62491i −0.945624 + 0.444912i
\(469\) 0 0
\(470\) −5.95031 10.3062i −0.274467 0.475391i
\(471\) 8.81661 15.2708i 0.406248 0.703642i
\(472\) 52.8940 + 91.6151i 2.43464 + 4.21692i
\(473\) −1.18813 + 2.05790i −0.0546303 + 0.0946225i
\(474\) −34.1405 −1.56812
\(475\) −16.1699 + 28.0070i −0.741925 + 1.28505i
\(476\) 0 0
\(477\) 2.59740 4.49882i 0.118927 0.205987i
\(478\) 8.57220 14.8475i 0.392083 0.679108i
\(479\) −32.5316 −1.48641 −0.743204 0.669065i \(-0.766695\pi\)
−0.743204 + 0.669065i \(0.766695\pi\)
\(480\) 11.5679 20.0362i 0.528000 0.914523i
\(481\) 18.0770 + 12.5654i 0.824241 + 0.572931i
\(482\) −33.2888 −1.51626
\(483\) 0 0
\(484\) 25.1893 + 43.6292i 1.14497 + 1.98314i
\(485\) 7.06534 0.320820
\(486\) −15.1832 + 26.2980i −0.688722 + 1.19290i
\(487\) −13.4291 23.2600i −0.608533 1.05401i −0.991482 0.130240i \(-0.958425\pi\)
0.382950 0.923769i \(-0.374908\pi\)
\(488\) 62.8412 2.84469
\(489\) 8.22634 0.372008
\(490\) 0 0
\(491\) −21.8439 37.8348i −0.985802 1.70746i −0.638317 0.769774i \(-0.720369\pi\)
−0.347485 0.937685i \(-0.612964\pi\)
\(492\) −4.72046 + 8.17608i −0.212815 + 0.368606i
\(493\) 0.845567 1.46457i 0.0380824 0.0659607i
\(494\) −58.9654 40.9870i −2.65298 1.84409i
\(495\) 0.575141 + 0.996173i 0.0258507 + 0.0447747i
\(496\) −21.3090 36.9082i −0.956801 1.65723i
\(497\) 0 0
\(498\) 21.9541 38.0257i 0.983788 1.70397i
\(499\) 9.05098 + 15.6768i 0.405177 + 0.701788i 0.994342 0.106225i \(-0.0338764\pi\)
−0.589165 + 0.808013i \(0.700543\pi\)
\(500\) −19.3079 33.4422i −0.863474 1.49558i
\(501\) −5.22122 9.04343i −0.233267 0.404030i
\(502\) 8.65412 + 14.9894i 0.386252 + 0.669009i
\(503\) −14.2077 + 24.6085i −0.633492 + 1.09724i 0.353341 + 0.935495i \(0.385046\pi\)
−0.986833 + 0.161745i \(0.948288\pi\)
\(504\) 0 0
\(505\) 2.77669 + 4.80937i 0.123561 + 0.214014i
\(506\) 4.36482 + 7.56009i 0.194040 + 0.336087i
\(507\) 17.4939 + 2.96089i 0.776929 + 0.131498i
\(508\) −14.9707 + 25.9299i −0.664215 + 1.15045i
\(509\) 8.73956 15.1374i 0.387374 0.670952i −0.604721 0.796437i \(-0.706715\pi\)
0.992095 + 0.125485i \(0.0400488\pi\)
\(510\) 5.75104 + 9.96110i 0.254660 + 0.441085i
\(511\) 0 0
\(512\) −55.5280 −2.45402
\(513\) −41.0287 −1.81146
\(514\) −33.3812 57.8179i −1.47238 2.55024i
\(515\) −1.04066 + 1.80247i −0.0458568 + 0.0794263i
\(516\) 13.1016 0.576766
\(517\) 3.99785 + 6.92447i 0.175825 + 0.304538i
\(518\) 0 0
\(519\) −0.224458 −0.00985260
\(520\) 23.2852 10.9556i 1.02113 0.480435i
\(521\) 9.65437 16.7219i 0.422966 0.732598i −0.573263 0.819372i \(-0.694322\pi\)
0.996228 + 0.0867740i \(0.0276558\pi\)
\(522\) −1.27072 −0.0556179
\(523\) −5.01144 + 8.68007i −0.219135 + 0.379553i −0.954544 0.298071i \(-0.903657\pi\)
0.735409 + 0.677624i \(0.236990\pi\)
\(524\) −31.2121 + 54.0610i −1.36351 + 2.36167i
\(525\) 0 0
\(526\) −13.1285 + 22.7393i −0.572432 + 0.991481i
\(527\) 11.5021 0.501039
\(528\) −14.3169 + 24.7976i −0.623064 + 1.07918i
\(529\) 8.77750 + 15.2031i 0.381630 + 0.661003i
\(530\) −4.63942 + 8.03571i −0.201524 + 0.349049i
\(531\) 6.24602 + 10.8184i 0.271054 + 0.469479i
\(532\) 0 0
\(533\) −4.09316 + 1.92581i −0.177294 + 0.0834162i
\(534\) −3.29403 5.70543i −0.142547 0.246898i
\(535\) −1.10160 −0.0476261
\(536\) 132.518 5.72389
\(537\) −1.04904 −0.0452696
\(538\) 80.5851 3.47427
\(539\) 0 0
\(540\) 11.5360 19.9809i 0.496430 0.859842i
\(541\) −8.80763 15.2553i −0.378670 0.655875i 0.612199 0.790703i \(-0.290285\pi\)
−0.990869 + 0.134829i \(0.956952\pi\)
\(542\) 0.411690 + 0.713067i 0.0176836 + 0.0306289i
\(543\) −13.5411 −0.581103
\(544\) 47.4489 82.1839i 2.03435 3.52361i
\(545\) −2.12780 −0.0911451
\(546\) 0 0
\(547\) 2.98425 0.127597 0.0637987 0.997963i \(-0.479678\pi\)
0.0637987 + 0.997963i \(0.479678\pi\)
\(548\) 38.5269 66.7306i 1.64579 2.85059i
\(549\) 7.42064 0.316705
\(550\) 8.32540 + 14.4200i 0.354996 + 0.614871i
\(551\) −1.48093 2.56504i −0.0630896 0.109274i
\(552\) 15.3359 26.5626i 0.652740 1.13058i
\(553\) 0 0
\(554\) 89.8279 3.81642
\(555\) −6.17577 −0.262147
\(556\) −57.5109 −2.43901
\(557\) 7.25596 0.307445 0.153722 0.988114i \(-0.450874\pi\)
0.153722 + 0.988114i \(0.450874\pi\)
\(558\) −4.32134 7.48478i −0.182937 0.316856i
\(559\) 5.15461 + 3.58298i 0.218017 + 0.151544i
\(560\) 0 0
\(561\) −3.86397 6.69259i −0.163137 0.282561i
\(562\) 5.88622 10.1952i 0.248295 0.430060i
\(563\) 2.13967 + 3.70601i 0.0901762 + 0.156190i 0.907585 0.419868i \(-0.137924\pi\)
−0.817409 + 0.576058i \(0.804590\pi\)
\(564\) 22.0423 38.1783i 0.928146 1.60760i
\(565\) 9.20382 0.387207
\(566\) 28.9188 50.0888i 1.21555 2.10539i
\(567\) 0 0
\(568\) −23.1876 + 40.1621i −0.972929 + 1.68516i
\(569\) 9.88131 17.1149i 0.414246 0.717495i −0.581103 0.813830i \(-0.697379\pi\)
0.995349 + 0.0963347i \(0.0307119\pi\)
\(570\) 20.1448 0.843771
\(571\) 9.96182 17.2544i 0.416889 0.722073i −0.578736 0.815515i \(-0.696454\pi\)
0.995625 + 0.0934422i \(0.0297870\pi\)
\(572\) −24.5501 + 11.5507i −1.02649 + 0.482960i
\(573\) −13.5075 −0.564285
\(574\) 0 0
\(575\) −5.19286 8.99430i −0.216557 0.375088i
\(576\) −36.3422 −1.51426
\(577\) −14.3650 + 24.8809i −0.598023 + 1.03581i 0.395090 + 0.918642i \(0.370713\pi\)
−0.993113 + 0.117163i \(0.962620\pi\)
\(578\) 0.290284 + 0.502787i 0.0120742 + 0.0209132i
\(579\) −11.8749 −0.493506
\(580\) 1.66556 0.0691587
\(581\) 0 0
\(582\) 17.8334 + 30.8883i 0.739218 + 1.28036i
\(583\) 3.11710 5.39897i 0.129097 0.223603i
\(584\) −29.2291 + 50.6263i −1.20951 + 2.09493i
\(585\) 2.74965 1.29370i 0.113684 0.0534879i
\(586\) −24.3461 42.1686i −1.00573 1.74197i
\(587\) 15.7694 + 27.3134i 0.650872 + 1.12734i 0.982912 + 0.184078i \(0.0589299\pi\)
−0.332040 + 0.943265i \(0.607737\pi\)
\(588\) 0 0
\(589\) 10.0724 17.4459i 0.415025 0.718845i
\(590\) −11.1565 19.3237i −0.459307 0.795542i
\(591\) −17.7553 30.7531i −0.730357 1.26502i
\(592\) 46.9298 + 81.2848i 1.92880 + 3.34079i
\(593\) −5.55903 9.62852i −0.228282 0.395396i 0.729017 0.684496i \(-0.239977\pi\)
−0.957299 + 0.289099i \(0.906644\pi\)
\(594\) −10.5622 + 18.2943i −0.433374 + 0.750626i
\(595\) 0 0
\(596\) −22.5071 38.9835i −0.921928 1.59683i
\(597\) −6.91483 11.9768i −0.283005 0.490179i
\(598\) 20.8675 9.81805i 0.853334 0.401490i
\(599\) 3.64786 6.31828i 0.149048 0.258158i −0.781828 0.623494i \(-0.785713\pi\)
0.930876 + 0.365336i \(0.119046\pi\)
\(600\) 29.2515 50.6652i 1.19419 2.06840i
\(601\) −0.586291 1.01548i −0.0239153 0.0414225i 0.853820 0.520568i \(-0.174280\pi\)
−0.877735 + 0.479146i \(0.840947\pi\)
\(602\) 0 0
\(603\) 15.6484 0.637253
\(604\) −13.5737 −0.552304
\(605\) −3.38573 5.86426i −0.137650 0.238416i
\(606\) −14.0171 + 24.2783i −0.569406 + 0.986240i
\(607\) −0.633838 −0.0257267 −0.0128633 0.999917i \(-0.504095\pi\)
−0.0128633 + 0.999917i \(0.504095\pi\)
\(608\) −83.1020 143.937i −3.37023 5.83741i
\(609\) 0 0
\(610\) −13.2546 −0.536664
\(611\) 19.1130 8.99260i 0.773231 0.363802i
\(612\) 13.0070 22.5287i 0.525775 0.910669i
\(613\) −30.8550 −1.24622 −0.623110 0.782134i \(-0.714131\pi\)
−0.623110 + 0.782134i \(0.714131\pi\)
\(614\) −24.6911 + 42.7663i −0.996453 + 1.72591i
\(615\) 0.634485 1.09896i 0.0255849 0.0443143i
\(616\) 0 0
\(617\) −16.9105 + 29.2898i −0.680790 + 1.17916i 0.293951 + 0.955821i \(0.405030\pi\)
−0.974740 + 0.223341i \(0.928304\pi\)
\(618\) −10.5068 −0.422644
\(619\) −0.202399 + 0.350565i −0.00813509 + 0.0140904i −0.870064 0.492938i \(-0.835923\pi\)
0.861929 + 0.507029i \(0.169256\pi\)
\(620\) 5.66408 + 9.81048i 0.227475 + 0.393998i
\(621\) 6.58807 11.4109i 0.264370 0.457902i
\(622\) −23.6480 40.9595i −0.948197 1.64233i
\(623\) 0 0
\(624\) 62.1128 + 43.1747i 2.48650 + 1.72837i
\(625\) −8.53179 14.7775i −0.341272 0.591100i
\(626\) 18.6812 0.746650
\(627\) −13.5347 −0.540524
\(628\) 71.2338 2.84254
\(629\) −25.3316 −1.01004
\(630\) 0 0
\(631\) −15.2254 + 26.3712i −0.606114 + 1.04982i 0.385761 + 0.922599i \(0.373939\pi\)
−0.991874 + 0.127221i \(0.959394\pi\)
\(632\) −43.9448 76.1147i −1.74803 3.02768i
\(633\) 11.3814 + 19.7131i 0.452369 + 0.783526i
\(634\) 68.7381 2.72994
\(635\) 2.01223 3.48528i 0.0798529 0.138309i
\(636\) −34.3724 −1.36296
\(637\) 0 0
\(638\) −1.52497 −0.0603743
\(639\) −2.73812 + 4.74256i −0.108318 + 0.187613i
\(640\) 31.0107 1.22581
\(641\) −4.82282 8.35337i −0.190490 0.329938i 0.754923 0.655814i \(-0.227674\pi\)
−0.945413 + 0.325875i \(0.894341\pi\)
\(642\) −2.78050 4.81597i −0.109738 0.190071i
\(643\) 4.06648 7.04335i 0.160366 0.277763i −0.774634 0.632410i \(-0.782066\pi\)
0.935000 + 0.354647i \(0.115399\pi\)
\(644\) 0 0
\(645\) −1.76101 −0.0693395
\(646\) 82.6293 3.25101
\(647\) 11.5227 0.453005 0.226503 0.974011i \(-0.427271\pi\)
0.226503 + 0.974011i \(0.427271\pi\)
\(648\) 41.3629 1.62489
\(649\) 7.49576 + 12.9830i 0.294234 + 0.509629i
\(650\) 39.8023 18.7268i 1.56118 0.734526i
\(651\) 0 0
\(652\) 16.6162 + 28.7801i 0.650740 + 1.12711i
\(653\) −21.2020 + 36.7229i −0.829697 + 1.43708i 0.0685797 + 0.997646i \(0.478153\pi\)
−0.898276 + 0.439431i \(0.855180\pi\)
\(654\) −5.37072 9.30236i −0.210012 0.363751i
\(655\) 4.19527 7.26642i 0.163923 0.283922i
\(656\) −19.2858 −0.752986
\(657\) −3.45153 + 5.97823i −0.134657 + 0.233233i
\(658\) 0 0
\(659\) 1.25044 2.16582i 0.0487101 0.0843684i −0.840642 0.541591i \(-0.817822\pi\)
0.889352 + 0.457222i \(0.151156\pi\)
\(660\) 3.80554 6.59139i 0.148130 0.256570i
\(661\) −14.8394 −0.577184 −0.288592 0.957452i \(-0.593187\pi\)
−0.288592 + 0.957452i \(0.593187\pi\)
\(662\) −4.10523 + 7.11047i −0.159554 + 0.276356i
\(663\) −18.4730 + 8.69146i −0.717431 + 0.337548i
\(664\) 113.035 4.38663
\(665\) 0 0
\(666\) 9.51710 + 16.4841i 0.368780 + 0.638746i
\(667\) 0.951183 0.0368300
\(668\) 21.0924 36.5332i 0.816091 1.41351i
\(669\) −0.730424 1.26513i −0.0282398 0.0489128i
\(670\) −27.9509 −1.07984
\(671\) 8.90541 0.343790
\(672\) 0 0
\(673\) −19.8046 34.3025i −0.763410 1.32226i −0.941083 0.338175i \(-0.890190\pi\)
0.177674 0.984089i \(-0.443143\pi\)
\(674\) −40.4156 + 70.0019i −1.55675 + 2.69637i
\(675\) 12.5660 21.7649i 0.483665 0.837733i
\(676\) 24.9766 + 67.1833i 0.960640 + 2.58397i
\(677\) 8.51604 + 14.7502i 0.327298 + 0.566897i 0.981975 0.189012i \(-0.0605285\pi\)
−0.654677 + 0.755909i \(0.727195\pi\)
\(678\) 23.2311 + 40.2374i 0.892183 + 1.54531i
\(679\) 0 0
\(680\) −14.8052 + 25.6434i −0.567755 + 0.983380i
\(681\) 16.6961 + 28.9185i 0.639797 + 1.10816i
\(682\) −5.18598 8.98238i −0.198581 0.343953i
\(683\) −16.4456 28.4846i −0.629272 1.08993i −0.987698 0.156374i \(-0.950020\pi\)
0.358426 0.933558i \(-0.383314\pi\)
\(684\) −22.7804 39.4568i −0.871030 1.50867i
\(685\) −5.17846 + 8.96936i −0.197859 + 0.342702i
\(686\) 0 0
\(687\) −3.22755 5.59028i −0.123139 0.213283i
\(688\) 13.3819 + 23.1782i 0.510181 + 0.883659i
\(689\) −13.5233 9.40006i −0.515196 0.358114i
\(690\) −3.23469 + 5.60265i −0.123143 + 0.213289i
\(691\) −11.8961 + 20.6047i −0.452550 + 0.783839i −0.998544 0.0539500i \(-0.982819\pi\)
0.545994 + 0.837789i \(0.316152\pi\)
\(692\) −0.453377 0.785272i −0.0172348 0.0298515i
\(693\) 0 0
\(694\) 16.4105 0.622933
\(695\) 7.73013 0.293221
\(696\) 2.67902 + 4.64020i 0.101548 + 0.175886i
\(697\) 2.60251 4.50768i 0.0985772 0.170741i
\(698\) −83.1539 −3.14742
\(699\) 14.0240 + 24.2903i 0.530436 + 0.918742i
\(700\) 0 0
\(701\) 29.7796 1.12476 0.562380 0.826879i \(-0.309886\pi\)
0.562380 + 0.826879i \(0.309886\pi\)
\(702\) 45.8234 + 31.8519i 1.72949 + 1.20217i
\(703\) −22.1829 + 38.4219i −0.836644 + 1.44911i
\(704\) −43.6138 −1.64376
\(705\) −2.96273 + 5.13160i −0.111583 + 0.193267i
\(706\) 39.2061 67.9069i 1.47554 2.55571i
\(707\) 0 0
\(708\) 41.3281 71.5824i 1.55321 2.69023i
\(709\) 11.9304 0.448054 0.224027 0.974583i \(-0.428080\pi\)
0.224027 + 0.974583i \(0.428080\pi\)
\(710\) 4.89078 8.47107i 0.183548 0.317914i
\(711\) −5.18925 8.98805i −0.194612 0.337078i
\(712\) 8.48001 14.6878i 0.317802 0.550449i
\(713\) 3.23469 + 5.60265i 0.121140 + 0.209821i
\(714\) 0 0
\(715\) 3.29982 1.55255i 0.123406 0.0580621i
\(716\) −2.11894 3.67011i −0.0791885 0.137159i
\(717\) −8.53642 −0.318798
\(718\) −64.3106 −2.40005
\(719\) −32.3638 −1.20697 −0.603484 0.797375i \(-0.706221\pi\)
−0.603484 + 0.797375i \(0.706221\pi\)
\(720\) 12.9556 0.482827
\(721\) 0 0
\(722\) 46.3182 80.2255i 1.72379 2.98568i
\(723\) 8.28746 + 14.3543i 0.308214 + 0.533842i
\(724\) −27.3513 47.3738i −1.01650 1.76063i
\(725\) 1.81427 0.0673805
\(726\) 17.0916 29.6036i 0.634330 1.09869i
\(727\) 31.4897 1.16789 0.583943 0.811794i \(-0.301509\pi\)
0.583943 + 0.811794i \(0.301509\pi\)
\(728\) 0 0
\(729\) 28.0042 1.03719
\(730\) 6.16507 10.6782i 0.228179 0.395218i
\(731\) −7.22325 −0.267161
\(732\) −24.5501 42.5221i −0.907399 1.57166i
\(733\) 1.33112 + 2.30557i 0.0491661 + 0.0851581i 0.889561 0.456816i \(-0.151010\pi\)
−0.840395 + 0.541974i \(0.817677\pi\)
\(734\) −50.0517 + 86.6921i −1.84744 + 3.19986i
\(735\) 0 0
\(736\) 53.3755 1.96745
\(737\) 18.7795 0.691750
\(738\) −3.91106 −0.143968
\(739\) −35.5828 −1.30893 −0.654467 0.756091i \(-0.727107\pi\)
−0.654467 + 0.756091i \(0.727107\pi\)
\(740\) −12.4743 21.6061i −0.458564 0.794256i
\(741\) −2.99397 + 35.6302i −0.109986 + 1.30891i
\(742\) 0 0
\(743\) −12.1203 20.9929i −0.444650 0.770156i 0.553378 0.832930i \(-0.313339\pi\)
−0.998028 + 0.0627740i \(0.980005\pi\)
\(744\) −18.2211 + 31.5599i −0.668018 + 1.15704i
\(745\) 3.02522 + 5.23983i 0.110835 + 0.191973i
\(746\) −17.8853 + 30.9783i −0.654828 + 1.13419i
\(747\) 13.3479 0.488373
\(748\) 15.6095 27.0364i 0.570739 0.988549i
\(749\) 0 0
\(750\) −13.1009 + 22.6915i −0.478378 + 0.828575i
\(751\) 14.5705 25.2368i 0.531684 0.920904i −0.467632 0.883923i \(-0.654893\pi\)
0.999316 0.0369807i \(-0.0117740\pi\)
\(752\) 90.0555 3.28399
\(753\) 4.30900 7.46340i 0.157029 0.271981i
\(754\) −0.337334 + 4.01449i −0.0122850 + 0.146199i
\(755\) 1.82446 0.0663988
\(756\) 0 0
\(757\) 2.49495 + 4.32138i 0.0906805 + 0.157063i 0.907798 0.419408i \(-0.137762\pi\)
−0.817117 + 0.576472i \(0.804429\pi\)
\(758\) −83.8872 −3.04692
\(759\) 2.17330 3.76426i 0.0788858 0.136634i
\(760\) 25.9299 + 44.9119i 0.940576 + 1.62913i
\(761\) 11.8372 0.429097 0.214548 0.976713i \(-0.431172\pi\)
0.214548 + 0.976713i \(0.431172\pi\)
\(762\) 20.3160 0.735971
\(763\) 0 0
\(764\) −27.2835 47.2564i −0.987083 1.70968i
\(765\) −1.74828 + 3.02812i −0.0632094 + 0.109482i
\(766\) 6.69643 11.5986i 0.241952 0.419073i
\(767\) 35.8360 16.8607i 1.29396 0.608803i
\(768\) 34.6593 + 60.0316i 1.25066 + 2.16621i
\(769\) −17.9092 31.0196i −0.645821 1.11859i −0.984111 0.177553i \(-0.943182\pi\)
0.338291 0.941042i \(-0.390151\pi\)
\(770\) 0 0
\(771\) −16.6209 + 28.7883i −0.598588 + 1.03678i
\(772\) −23.9859 41.5448i −0.863272 1.49523i
\(773\) −9.97669 17.2801i −0.358837 0.621523i 0.628930 0.777462i \(-0.283493\pi\)
−0.987767 + 0.155939i \(0.950160\pi\)
\(774\) 2.71378 + 4.70040i 0.0975447 + 0.168952i
\(775\) 6.16980 + 10.6864i 0.221626 + 0.383867i
\(776\) −45.9095 + 79.5176i −1.64805 + 2.85451i
\(777\) 0 0
\(778\) −2.54133 4.40171i −0.0911110 0.157809i
\(779\) −4.55804 7.89476i −0.163309 0.282859i
\(780\) −16.5100 11.4762i −0.591154 0.410912i
\(781\) −3.28598 + 5.69148i −0.117582 + 0.203657i
\(782\) −13.2680 + 22.9808i −0.474461 + 0.821791i
\(783\) 1.15086 + 1.99335i 0.0411285 + 0.0712367i
\(784\) 0 0
\(785\) −9.57464 −0.341734
\(786\) 42.3566 1.51081
\(787\) 1.39809 + 2.42157i 0.0498367 + 0.0863196i 0.889868 0.456219i \(-0.150797\pi\)
−0.840031 + 0.542539i \(0.817463\pi\)
\(788\) 71.7271 124.235i 2.55517 4.42569i
\(789\) 13.0737 0.465437
\(790\) 9.26895 + 16.0543i 0.329774 + 0.571186i
\(791\) 0 0
\(792\) −14.9487 −0.531179
\(793\) 1.96994 23.4435i 0.0699545 0.832503i
\(794\) −29.4850 + 51.0695i −1.04638 + 1.81239i
\(795\) 4.62005 0.163856
\(796\) 27.9342 48.3835i 0.990101 1.71491i
\(797\) 0.842809 1.45979i 0.0298538 0.0517083i −0.850712 0.525631i \(-0.823829\pi\)
0.880566 + 0.473923i \(0.157162\pi\)
\(798\) 0 0
\(799\) −12.1525 + 21.0487i −0.429923 + 0.744649i
\(800\) 101.808 3.59945
\(801\) 1.00137 1.73442i 0.0353816 0.0612827i
\(802\) −19.9624 34.5758i −0.704895 1.22091i
\(803\) −4.14214 + 7.17439i −0.146173 + 0.253179i
\(804\) −51.7705 89.6692i −1.82581 3.16239i
\(805\) 0 0
\(806\) −24.7933 + 11.6651i −0.873307 + 0.410887i
\(807\) −20.0622 34.7487i −0.706222 1.22321i
\(808\) −72.1700 −2.53893
\(809\) −43.4372 −1.52717 −0.763585 0.645708i \(-0.776562\pi\)
−0.763585 + 0.645708i \(0.776562\pi\)
\(810\) −8.72435 −0.306542
\(811\) −5.60812 −0.196928 −0.0984639 0.995141i \(-0.531393\pi\)
−0.0984639 + 0.995141i \(0.531393\pi\)
\(812\) 0 0
\(813\) 0.204986 0.355045i 0.00718916 0.0124520i
\(814\) 11.4213 + 19.7823i 0.400318 + 0.693371i
\(815\) −2.23341 3.86837i −0.0782328 0.135503i
\(816\) −87.0397 −3.04700
\(817\) −6.32540 + 10.9559i −0.221298 + 0.383299i
\(818\) −60.6574 −2.12084
\(819\) 0 0
\(820\) 5.12632 0.179019
\(821\) 11.9724 20.7368i 0.417839 0.723718i −0.577883 0.816120i \(-0.696121\pi\)
0.995722 + 0.0924014i \(0.0294543\pi\)
\(822\) −52.2832 −1.82358
\(823\) −17.7058 30.6674i −0.617187 1.06900i −0.989997 0.141091i \(-0.954939\pi\)
0.372810 0.927908i \(-0.378394\pi\)
\(824\) −13.5241 23.4244i −0.471133 0.816026i
\(825\) 4.14532 7.17991i 0.144322 0.249972i
\(826\) 0 0
\(827\) −16.1563 −0.561811 −0.280905 0.959735i \(-0.590635\pi\)
−0.280905 + 0.959735i \(0.590635\pi\)
\(828\) 14.6316 0.508483
\(829\) 52.7010 1.83038 0.915190 0.403022i \(-0.132040\pi\)
0.915190 + 0.403022i \(0.132040\pi\)
\(830\) −23.8417 −0.827557
\(831\) −22.3632 38.7343i −0.775772 1.34368i
\(832\) −9.64766 + 114.813i −0.334472 + 3.98044i
\(833\) 0 0
\(834\) 19.5114 + 33.7947i 0.675624 + 1.17021i
\(835\) −2.83507 + 4.91048i −0.0981116 + 0.169934i
\(836\) −27.3384 47.3516i −0.945520 1.63769i
\(837\) −7.82749 + 13.5576i −0.270558 + 0.468619i
\(838\) 9.25363 0.319661
\(839\) −11.2169 + 19.4283i −0.387251 + 0.670738i −0.992079 0.125618i \(-0.959909\pi\)
0.604828 + 0.796356i \(0.293242\pi\)
\(840\) 0 0
\(841\) 14.4169 24.9708i 0.497135 0.861063i
\(842\) −34.4144 + 59.6075i −1.18600 + 2.05421i
\(843\) −5.86165 −0.201886
\(844\) −45.9779 + 79.6361i −1.58263 + 2.74119i
\(845\) −3.35715 9.03021i −0.115489 0.310649i
\(846\) 18.2627 0.627886
\(847\) 0 0
\(848\) −35.1079 60.8086i −1.20561 2.08818i
\(849\) −28.7980 −0.988346
\(850\) −25.3071 + 43.8333i −0.868028 + 1.50347i
\(851\) −7.12392 12.3390i −0.244205 0.422975i
\(852\) 36.2347 1.24138
\(853\) −30.8521 −1.05635 −0.528177 0.849134i \(-0.677124\pi\)
−0.528177 + 0.849134i \(0.677124\pi\)
\(854\) 0 0
\(855\) 3.06195 + 5.30345i 0.104716 + 0.181374i
\(856\) 7.15800 12.3980i 0.244655 0.423756i
\(857\) 13.3700 23.1575i 0.456710 0.791045i −0.542075 0.840330i \(-0.682361\pi\)
0.998785 + 0.0492854i \(0.0156944\pi\)
\(858\) 15.1164 + 10.5075i 0.516066 + 0.358719i
\(859\) −2.57902 4.46699i −0.0879950 0.152412i 0.818669 0.574266i \(-0.194713\pi\)
−0.906664 + 0.421855i \(0.861379\pi\)
\(860\) −3.55701 6.16092i −0.121293 0.210086i
\(861\) 0 0
\(862\) 14.7948 25.6253i 0.503912 0.872801i
\(863\) −4.08407 7.07382i −0.139023 0.240796i 0.788104 0.615542i \(-0.211063\pi\)
−0.927127 + 0.374747i \(0.877730\pi\)
\(864\) 64.5806 + 111.857i 2.19708 + 3.80545i
\(865\) 0.0609391 + 0.105550i 0.00207199 + 0.00358879i
\(866\) 19.8978 + 34.4640i 0.676154 + 1.17113i
\(867\) 0.144536 0.250344i 0.00490871 0.00850214i
\(868\) 0 0
\(869\) −6.22755 10.7864i −0.211255 0.365905i
\(870\) −0.565065 0.978722i −0.0191575 0.0331818i
\(871\) 4.15414 49.4369i 0.140758 1.67511i
\(872\) 13.8261 23.9476i 0.468212 0.810968i
\(873\) −5.42125 + 9.38988i −0.183481 + 0.317799i
\(874\) 23.2375 + 40.2486i 0.786021 + 1.36143i
\(875\) 0 0
\(876\) 45.6756 1.54324
\(877\) 15.6184 0.527398 0.263699 0.964605i \(-0.415058\pi\)
0.263699 + 0.964605i \(0.415058\pi\)
\(878\) 19.7781 + 34.2567i 0.667479 + 1.15611i
\(879\) −12.1222 + 20.9963i −0.408872 + 0.708187i
\(880\) 15.5479 0.524118
\(881\) −23.2188 40.2161i −0.782260 1.35491i −0.930622 0.365981i \(-0.880734\pi\)
0.148362 0.988933i \(-0.452600\pi\)
\(882\) 0 0
\(883\) 15.6588 0.526960 0.263480 0.964665i \(-0.415130\pi\)
0.263480 + 0.964665i \(0.415130\pi\)
\(884\) −67.7204 47.0726i −2.27768 1.58322i
\(885\) −5.55497 + 9.62149i −0.186728 + 0.323423i
\(886\) 82.8986 2.78503
\(887\) 15.7554 27.2891i 0.529013 0.916278i −0.470414 0.882446i \(-0.655896\pi\)
0.999428 0.0338320i \(-0.0107711\pi\)
\(888\) 40.1292 69.5059i 1.34665 2.33246i
\(889\) 0 0
\(890\) −1.78862 + 3.09799i −0.0599548 + 0.103845i
\(891\) 5.86165 0.196373
\(892\) 2.95073 5.11082i 0.0987978 0.171123i
\(893\) 21.2838 + 36.8647i 0.712236 + 1.23363i
\(894\) −15.2717 + 26.4514i −0.510762 + 0.884666i
\(895\) 0.284810 + 0.493305i 0.00952015 + 0.0164894i
\(896\) 0 0
\(897\) −9.42868 6.55389i −0.314815 0.218828i
\(898\) 42.8651 + 74.2445i 1.43043 + 2.47757i
\(899\) −1.13013 −0.0376920
\(900\) 27.9081 0.930270
\(901\) 18.9504 0.631330
\(902\) −4.69361 −0.156280
\(903\) 0 0
\(904\) −59.8050 + 103.585i −1.98908 + 3.44520i
\(905\) 3.67633 + 6.36759i 0.122205 + 0.211666i
\(906\) 4.60505 + 7.97618i 0.152993 + 0.264991i
\(907\) −0.747991 −0.0248366 −0.0124183 0.999923i \(-0.503953\pi\)
−0.0124183 + 0.999923i \(0.503953\pi\)
\(908\) −67.4482 + 116.824i −2.23835 + 3.87693i
\(909\) −8.52224 −0.282665
\(910\) 0 0
\(911\) 24.9000 0.824973 0.412486 0.910964i \(-0.364660\pi\)
0.412486 + 0.910964i \(0.364660\pi\)
\(912\) −76.2207 + 132.018i −2.52392 + 4.37156i
\(913\) 16.0186 0.530138
\(914\) 28.2970 + 49.0119i 0.935983 + 1.62117i
\(915\) 3.29982 + 5.71546i 0.109089 + 0.188947i
\(916\) 13.0385 22.5834i 0.430804 0.746175i
\(917\) 0 0
\(918\) −64.2132 −2.11935
\(919\) 0.586495 0.0193467 0.00967334 0.999953i \(-0.496921\pi\)
0.00967334 + 0.999953i \(0.496921\pi\)
\(920\) −16.6545 −0.549082
\(921\) 24.5881 0.810204
\(922\) −37.4104 64.7967i −1.23205 2.13397i
\(923\) 14.2560 + 9.90934i 0.469240 + 0.326170i
\(924\) 0 0
\(925\) −13.5881 23.5352i −0.446773 0.773833i
\(926\) 7.75694 13.4354i 0.254909 0.441515i
\(927\) −1.59700 2.76608i −0.0524523 0.0908500i
\(928\) −4.66206 + 8.07493i −0.153040 + 0.265073i
\(929\) 50.1949 1.64684 0.823421 0.567431i \(-0.192062\pi\)
0.823421 + 0.567431i \(0.192062\pi\)
\(930\) 3.84324 6.65668i 0.126025 0.218281i
\(931\) 0 0
\(932\) −56.6534 + 98.1266i −1.85574 + 3.21424i
\(933\) −11.7746 + 20.3943i −0.385484 + 0.667678i
\(934\) 115.713 3.78626
\(935\) −2.09809 + 3.63400i −0.0686150 + 0.118845i
\(936\) −3.30675 + 39.3525i −0.108085 + 1.28628i
\(937\) −22.7130 −0.742003 −0.371001 0.928632i \(-0.620985\pi\)
−0.371001 + 0.928632i \(0.620985\pi\)
\(938\) 0 0
\(939\) −4.65080 8.05542i −0.151773 0.262879i
\(940\) −23.9374 −0.780752
\(941\) −24.9367 + 43.1916i −0.812914 + 1.40801i 0.0979030 + 0.995196i \(0.468787\pi\)
−0.910816 + 0.412812i \(0.864547\pi\)
\(942\) −24.1670 41.8586i −0.787405 1.36383i
\(943\) 2.92758 0.0953351
\(944\) 168.849 5.49558
\(945\) 0 0
\(946\) 3.25677 + 5.64088i 0.105887 + 0.183401i
\(947\) −0.133207 + 0.230722i −0.00432865 + 0.00749745i −0.868182 0.496247i \(-0.834711\pi\)
0.863853 + 0.503744i \(0.168045\pi\)
\(948\) −34.3358 + 59.4713i −1.11517 + 1.93154i
\(949\) 17.9703 + 12.4912i 0.583342 + 0.405482i
\(950\) 44.3229 + 76.7696i 1.43803 + 2.49073i
\(951\) −17.1128 29.6402i −0.554920 0.961150i
\(952\) 0 0
\(953\) −3.91014 + 6.77257i −0.126662 + 0.219385i −0.922381 0.386281i \(-0.873760\pi\)
0.795719 + 0.605665i \(0.207093\pi\)
\(954\) −7.11968 12.3316i −0.230508 0.399252i
\(955\) 3.66722 + 6.35181i 0.118668 + 0.205540i
\(956\) −17.2425 29.8649i −0.557662 0.965899i
\(957\) 0.379652 + 0.657576i 0.0122724 + 0.0212564i
\(958\) −44.5859 + 77.2251i −1.44051 + 2.49503i
\(959\) 0 0
\(960\) −16.1607 27.9911i −0.521584 0.903410i
\(961\) 11.6568 + 20.1901i 0.376025 + 0.651294i
\(962\) 54.6035 25.6907i 1.76049 0.828302i
\(963\) 0.845257 1.46403i 0.0272380 0.0471776i
\(964\) −33.4793 + 57.9878i −1.07829 + 1.86766i
\(965\) 3.22398 + 5.58410i 0.103784 + 0.179759i
\(966\) 0 0
\(967\) 39.8224 1.28060 0.640301 0.768124i \(-0.278810\pi\)
0.640301 + 0.768124i \(0.278810\pi\)
\(968\) 87.9999 2.82842
\(969\) −20.5711 35.6302i −0.660838 1.14461i
\(970\) 9.68333 16.7720i 0.310913 0.538517i
\(971\) 45.9295 1.47395 0.736974 0.675921i \(-0.236254\pi\)
0.736974 + 0.675921i \(0.236254\pi\)
\(972\) 30.5401 + 52.8969i 0.979573 + 1.69667i
\(973\) 0 0
\(974\) −73.6208 −2.35896
\(975\) −17.9841 12.5008i −0.575954 0.400346i
\(976\) 50.1508 86.8637i 1.60529 2.78044i
\(977\) −28.6627 −0.917002 −0.458501 0.888694i \(-0.651613\pi\)
−0.458501 + 0.888694i \(0.651613\pi\)
\(978\) 11.2745 19.5281i 0.360520 0.624439i
\(979\) 1.20173 2.08145i 0.0384074 0.0665235i
\(980\) 0 0
\(981\) 1.63267 2.82787i 0.0521271 0.0902868i
\(982\) −119.752 −3.82144
\(983\) −23.0600 + 39.9411i −0.735500 + 1.27392i 0.219003 + 0.975724i \(0.429720\pi\)
−0.954503 + 0.298200i \(0.903614\pi\)
\(984\) 8.24557 + 14.2817i 0.262859 + 0.455285i
\(985\) −9.64095 + 16.6986i −0.307186 + 0.532062i
\(986\) −2.31777 4.01449i −0.0738128 0.127848i
\(987\) 0 0
\(988\) −130.700 + 61.4940i −4.15814 + 1.95638i
\(989\) −2.03137 3.51843i −0.0645937 0.111880i
\(990\) 3.15302 0.100209
\(991\) 37.8249 1.20155 0.600773 0.799419i \(-0.294859\pi\)
0.600773 + 0.799419i \(0.294859\pi\)
\(992\) −63.4171 −2.01350
\(993\) 4.08809 0.129732
\(994\) 0 0
\(995\) −3.75468 + 6.50329i −0.119031 + 0.206168i
\(996\) −44.1595 76.4864i −1.39925 2.42357i
\(997\) 19.1874 + 33.2335i 0.607671 + 1.05252i 0.991623 + 0.129164i \(0.0412293\pi\)
−0.383952 + 0.923353i \(0.625437\pi\)
\(998\) 49.6189 1.57066
\(999\) 17.2389 29.8586i 0.545414 0.944684i
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 637.2.g.j.263.4 8
7.2 even 3 637.2.h.i.471.1 8
7.3 odd 6 91.2.f.c.29.4 yes 8
7.4 even 3 637.2.f.i.393.4 8
7.5 odd 6 637.2.h.h.471.1 8
7.6 odd 2 637.2.g.k.263.4 8
13.9 even 3 637.2.h.i.165.1 8
21.17 even 6 819.2.o.h.757.1 8
28.3 even 6 1456.2.s.q.1121.3 8
91.3 odd 6 1183.2.a.k.1.1 4
91.9 even 3 inner 637.2.g.j.373.4 8
91.10 odd 6 1183.2.a.l.1.4 4
91.24 even 12 1183.2.c.g.337.1 8
91.48 odd 6 637.2.h.h.165.1 8
91.61 odd 6 637.2.g.k.373.4 8
91.74 even 3 637.2.f.i.295.4 8
91.80 even 12 1183.2.c.g.337.8 8
91.81 even 3 8281.2.a.bp.1.1 4
91.87 odd 6 91.2.f.c.22.4 8
91.88 even 6 8281.2.a.bt.1.4 4
273.269 even 6 819.2.o.h.568.1 8
364.87 even 6 1456.2.s.q.113.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.f.c.22.4 8 91.87 odd 6
91.2.f.c.29.4 yes 8 7.3 odd 6
637.2.f.i.295.4 8 91.74 even 3
637.2.f.i.393.4 8 7.4 even 3
637.2.g.j.263.4 8 1.1 even 1 trivial
637.2.g.j.373.4 8 91.9 even 3 inner
637.2.g.k.263.4 8 7.6 odd 2
637.2.g.k.373.4 8 91.61 odd 6
637.2.h.h.165.1 8 91.48 odd 6
637.2.h.h.471.1 8 7.5 odd 6
637.2.h.i.165.1 8 13.9 even 3
637.2.h.i.471.1 8 7.2 even 3
819.2.o.h.568.1 8 273.269 even 6
819.2.o.h.757.1 8 21.17 even 6
1183.2.a.k.1.1 4 91.3 odd 6
1183.2.a.l.1.4 4 91.10 odd 6
1183.2.c.g.337.1 8 91.24 even 12
1183.2.c.g.337.8 8 91.80 even 12
1456.2.s.q.113.3 8 364.87 even 6
1456.2.s.q.1121.3 8 28.3 even 6
8281.2.a.bp.1.1 4 91.81 even 3
8281.2.a.bt.1.4 4 91.88 even 6