Properties

Label 289.2.c.d.251.5
Level $289$
Weight $2$
Character 289.251
Analytic conductor $2.308$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [289,2,Mod(38,289)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(289, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("289.38");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 289.c (of order \(4\), 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: \(2.30767661842\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.722204136308736.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 18x^{8} + 69x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 251.5
Root \(1.08335 - 1.08335i\) of defining polynomial
Character \(\chi\) \(=\) 289.251
Dual form 289.2.c.d.38.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.87939i q^{2} +(-1.79046 - 1.79046i) q^{3} -1.53209 q^{4} +(0.0852875 + 0.0852875i) q^{5} +(3.36496 - 3.36496i) q^{6} +(-1.08335 + 1.08335i) q^{7} +0.879385i q^{8} +3.41147i q^{9} +O(q^{10})\) \(q+1.87939i q^{2} +(-1.79046 - 1.79046i) q^{3} -1.53209 q^{4} +(0.0852875 + 0.0852875i) q^{5} +(3.36496 - 3.36496i) q^{6} +(-1.08335 + 1.08335i) q^{7} +0.879385i q^{8} +3.41147i q^{9} +(-0.160288 + 0.160288i) q^{10} +(-1.90536 + 1.90536i) q^{11} +(2.74314 + 2.74314i) q^{12} -4.57398 q^{13} +(-2.03603 - 2.03603i) q^{14} -0.305407i q^{15} -4.71688 q^{16} -6.41147 q^{18} +1.87939i q^{19} +(-0.130668 - 0.130668i) q^{20} +3.87939 q^{21} +(-3.58091 - 3.58091i) q^{22} +(-5.24070 + 5.24070i) q^{23} +(1.57450 - 1.57450i) q^{24} -4.98545i q^{25} -8.59627i q^{26} +(0.736727 - 0.736727i) q^{27} +(1.65979 - 1.65979i) q^{28} +(2.41228 + 2.41228i) q^{29} +0.573978 q^{30} +(-2.71352 - 2.71352i) q^{31} -7.10607i q^{32} +6.82295 q^{33} -0.184793 q^{35} -5.22668i q^{36} +(3.71158 + 3.71158i) q^{37} -3.53209 q^{38} +(8.18951 + 8.18951i) q^{39} +(-0.0750006 + 0.0750006i) q^{40} +(4.41869 - 4.41869i) q^{41} +7.29086i q^{42} +5.49020i q^{43} +(2.91919 - 2.91919i) q^{44} +(-0.290956 + 0.290956i) q^{45} +(-9.84930 - 9.84930i) q^{46} +7.34730 q^{47} +(8.44537 + 8.44537i) q^{48} +4.65270i q^{49} +9.36959 q^{50} +7.00774 q^{52} -0.822948i q^{53} +(1.38459 + 1.38459i) q^{54} -0.325008 q^{55} +(-0.952682 - 0.952682i) q^{56} +(3.36496 - 3.36496i) q^{57} +(-4.53360 + 4.53360i) q^{58} -3.14290i q^{59} +0.467911i q^{60} +(0.867395 - 0.867395i) q^{61} +(5.09975 - 5.09975i) q^{62} +(-3.69582 - 3.69582i) q^{63} +3.92127 q^{64} +(-0.390103 - 0.390103i) q^{65} +12.8229i q^{66} -14.6236 q^{67} +18.7665 q^{69} -0.347296i q^{70} +(0.120381 + 0.120381i) q^{71} -3.00000 q^{72} +(-8.34433 - 8.34433i) q^{73} +(-6.97549 + 6.97549i) q^{74} +(-8.92624 + 8.92624i) q^{75} -2.87939i q^{76} -4.12836i q^{77} +(-15.3912 + 15.3912i) q^{78} +(2.93305 - 2.93305i) q^{79} +(-0.402291 - 0.402291i) q^{80} +7.59627 q^{81} +(8.30442 + 8.30442i) q^{82} +2.43376i q^{83} -5.94356 q^{84} -10.3182 q^{86} -8.63816i q^{87} +(-1.67555 - 1.67555i) q^{88} +15.0915 q^{89} +(-0.546819 - 0.546819i) q^{90} +(4.95522 - 4.95522i) q^{91} +(8.02922 - 8.02922i) q^{92} +9.71688i q^{93} +13.8084i q^{94} +(-0.160288 + 0.160288i) q^{95} +(-12.7231 + 12.7231i) q^{96} +(7.91432 + 7.91432i) q^{97} -8.74422 q^{98} +(-6.50010 - 6.50010i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 24 q^{13} - 24 q^{16} - 36 q^{18} + 24 q^{21} - 24 q^{30} + 12 q^{35} - 24 q^{38} + 84 q^{47} + 84 q^{50} - 12 q^{52} - 24 q^{55} + 12 q^{64} - 36 q^{67} + 84 q^{69} - 36 q^{72} + 36 q^{81} - 12 q^{84} + 24 q^{86} + 60 q^{89} + 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/289\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.87939i 1.32893i 0.747321 + 0.664463i \(0.231340\pi\)
−0.747321 + 0.664463i \(0.768660\pi\)
\(3\) −1.79046 1.79046i −1.03372 1.03372i −0.999411 0.0343097i \(-0.989077\pi\)
−0.0343097 0.999411i \(-0.510923\pi\)
\(4\) −1.53209 −0.766044
\(5\) 0.0852875 + 0.0852875i 0.0381417 + 0.0381417i 0.725920 0.687779i \(-0.241414\pi\)
−0.687779 + 0.725920i \(0.741414\pi\)
\(6\) 3.36496 3.36496i 1.37374 1.37374i
\(7\) −1.08335 + 1.08335i −0.409468 + 0.409468i −0.881553 0.472085i \(-0.843502\pi\)
0.472085 + 0.881553i \(0.343502\pi\)
\(8\) 0.879385i 0.310910i
\(9\) 3.41147i 1.13716i
\(10\) −0.160288 + 0.160288i −0.0506875 + 0.0506875i
\(11\) −1.90536 + 1.90536i −0.574489 + 0.574489i −0.933380 0.358891i \(-0.883155\pi\)
0.358891 + 0.933380i \(0.383155\pi\)
\(12\) 2.74314 + 2.74314i 0.791876 + 0.791876i
\(13\) −4.57398 −1.26859 −0.634297 0.773090i \(-0.718710\pi\)
−0.634297 + 0.773090i \(0.718710\pi\)
\(14\) −2.03603 2.03603i −0.544153 0.544153i
\(15\) 0.305407i 0.0788558i
\(16\) −4.71688 −1.17922
\(17\) 0 0
\(18\) −6.41147 −1.51120
\(19\) 1.87939i 0.431161i 0.976486 + 0.215580i \(0.0691643\pi\)
−0.976486 + 0.215580i \(0.930836\pi\)
\(20\) −0.130668 0.130668i −0.0292183 0.0292183i
\(21\) 3.87939 0.846551
\(22\) −3.58091 3.58091i −0.763454 0.763454i
\(23\) −5.24070 + 5.24070i −1.09276 + 1.09276i −0.0975296 + 0.995233i \(0.531094\pi\)
−0.995233 + 0.0975296i \(0.968906\pi\)
\(24\) 1.57450 1.57450i 0.321394 0.321394i
\(25\) 4.98545i 0.997090i
\(26\) 8.59627i 1.68587i
\(27\) 0.736727 0.736727i 0.141783 0.141783i
\(28\) 1.65979 1.65979i 0.313671 0.313671i
\(29\) 2.41228 + 2.41228i 0.447948 + 0.447948i 0.894672 0.446724i \(-0.147409\pi\)
−0.446724 + 0.894672i \(0.647409\pi\)
\(30\) 0.573978 0.104794
\(31\) −2.71352 2.71352i −0.487363 0.487363i 0.420110 0.907473i \(-0.361991\pi\)
−0.907473 + 0.420110i \(0.861991\pi\)
\(32\) 7.10607i 1.25619i
\(33\) 6.82295 1.18772
\(34\) 0 0
\(35\) −0.184793 −0.0312356
\(36\) 5.22668i 0.871114i
\(37\) 3.71158 + 3.71158i 0.610180 + 0.610180i 0.942993 0.332813i \(-0.107998\pi\)
−0.332813 + 0.942993i \(0.607998\pi\)
\(38\) −3.53209 −0.572980
\(39\) 8.18951 + 8.18951i 1.31137 + 1.31137i
\(40\) −0.0750006 + 0.0750006i −0.0118586 + 0.0118586i
\(41\) 4.41869 4.41869i 0.690083 0.690083i −0.272167 0.962250i \(-0.587740\pi\)
0.962250 + 0.272167i \(0.0877402\pi\)
\(42\) 7.29086i 1.12500i
\(43\) 5.49020i 0.837248i 0.908160 + 0.418624i \(0.137487\pi\)
−0.908160 + 0.418624i \(0.862513\pi\)
\(44\) 2.91919 2.91919i 0.440084 0.440084i
\(45\) −0.290956 + 0.290956i −0.0433732 + 0.0433732i
\(46\) −9.84930 9.84930i −1.45220 1.45220i
\(47\) 7.34730 1.07171 0.535857 0.844309i \(-0.319989\pi\)
0.535857 + 0.844309i \(0.319989\pi\)
\(48\) 8.44537 + 8.44537i 1.21898 + 1.21898i
\(49\) 4.65270i 0.664672i
\(50\) 9.36959 1.32506
\(51\) 0 0
\(52\) 7.00774 0.971799
\(53\) 0.822948i 0.113041i −0.998401 0.0565203i \(-0.981999\pi\)
0.998401 0.0565203i \(-0.0180006\pi\)
\(54\) 1.38459 + 1.38459i 0.188419 + 0.188419i
\(55\) −0.325008 −0.0438240
\(56\) −0.952682 0.952682i −0.127308 0.127308i
\(57\) 3.36496 3.36496i 0.445700 0.445700i
\(58\) −4.53360 + 4.53360i −0.595290 + 0.595290i
\(59\) 3.14290i 0.409171i −0.978849 0.204586i \(-0.934415\pi\)
0.978849 0.204586i \(-0.0655847\pi\)
\(60\) 0.467911i 0.0604071i
\(61\) 0.867395 0.867395i 0.111059 0.111059i −0.649394 0.760452i \(-0.724977\pi\)
0.760452 + 0.649394i \(0.224977\pi\)
\(62\) 5.09975 5.09975i 0.647669 0.647669i
\(63\) −3.69582 3.69582i −0.465630 0.465630i
\(64\) 3.92127 0.490159
\(65\) −0.390103 0.390103i −0.0483863 0.0483863i
\(66\) 12.8229i 1.57840i
\(67\) −14.6236 −1.78656 −0.893279 0.449503i \(-0.851601\pi\)
−0.893279 + 0.449503i \(0.851601\pi\)
\(68\) 0 0
\(69\) 18.7665 2.25922
\(70\) 0.347296i 0.0415099i
\(71\) 0.120381 + 0.120381i 0.0142866 + 0.0142866i 0.714214 0.699927i \(-0.246784\pi\)
−0.699927 + 0.714214i \(0.746784\pi\)
\(72\) −3.00000 −0.353553
\(73\) −8.34433 8.34433i −0.976630 0.976630i 0.0231035 0.999733i \(-0.492645\pi\)
−0.999733 + 0.0231035i \(0.992645\pi\)
\(74\) −6.97549 + 6.97549i −0.810885 + 0.810885i
\(75\) −8.92624 + 8.92624i −1.03071 + 1.03071i
\(76\) 2.87939i 0.330288i
\(77\) 4.12836i 0.470470i
\(78\) −15.3912 + 15.3912i −1.74272 + 1.74272i
\(79\) 2.93305 2.93305i 0.329994 0.329994i −0.522590 0.852584i \(-0.675034\pi\)
0.852584 + 0.522590i \(0.175034\pi\)
\(80\) −0.402291 0.402291i −0.0449775 0.0449775i
\(81\) 7.59627 0.844030
\(82\) 8.30442 + 8.30442i 0.917070 + 0.917070i
\(83\) 2.43376i 0.267140i 0.991039 + 0.133570i \(0.0426441\pi\)
−0.991039 + 0.133570i \(0.957356\pi\)
\(84\) −5.94356 −0.648496
\(85\) 0 0
\(86\) −10.3182 −1.11264
\(87\) 8.63816i 0.926108i
\(88\) −1.67555 1.67555i −0.178614 0.178614i
\(89\) 15.0915 1.59970 0.799849 0.600201i \(-0.204913\pi\)
0.799849 + 0.600201i \(0.204913\pi\)
\(90\) −0.546819 0.546819i −0.0576398 0.0576398i
\(91\) 4.95522 4.95522i 0.519448 0.519448i
\(92\) 8.02922 8.02922i 0.837104 0.837104i
\(93\) 9.71688i 1.00759i
\(94\) 13.8084i 1.42423i
\(95\) −0.160288 + 0.160288i −0.0164452 + 0.0164452i
\(96\) −12.7231 + 12.7231i −1.29855 + 1.29855i
\(97\) 7.91432 + 7.91432i 0.803577 + 0.803577i 0.983653 0.180076i \(-0.0576343\pi\)
−0.180076 + 0.983653i \(0.557634\pi\)
\(98\) −8.74422 −0.883300
\(99\) −6.50010 6.50010i −0.653285 0.653285i
\(100\) 7.63816i 0.763816i
\(101\) 7.78106 0.774244 0.387122 0.922028i \(-0.373469\pi\)
0.387122 + 0.922028i \(0.373469\pi\)
\(102\) 0 0
\(103\) −10.8598 −1.07005 −0.535023 0.844837i \(-0.679697\pi\)
−0.535023 + 0.844837i \(0.679697\pi\)
\(104\) 4.02229i 0.394418i
\(105\) 0.330863 + 0.330863i 0.0322889 + 0.0322889i
\(106\) 1.54664 0.150223
\(107\) 8.51490 + 8.51490i 0.823167 + 0.823167i 0.986561 0.163394i \(-0.0522443\pi\)
−0.163394 + 0.986561i \(0.552244\pi\)
\(108\) −1.12873 + 1.12873i −0.108612 + 0.108612i
\(109\) −4.67455 + 4.67455i −0.447741 + 0.447741i −0.894603 0.446862i \(-0.852541\pi\)
0.446862 + 0.894603i \(0.352541\pi\)
\(110\) 0.610815i 0.0582389i
\(111\) 13.2909i 1.26151i
\(112\) 5.11004 5.11004i 0.482853 0.482853i
\(113\) 3.59667 3.59667i 0.338347 0.338347i −0.517398 0.855745i \(-0.673099\pi\)
0.855745 + 0.517398i \(0.173099\pi\)
\(114\) 6.32405 + 6.32405i 0.592302 + 0.592302i
\(115\) −0.893933 −0.0833597
\(116\) −3.69582 3.69582i −0.343148 0.343148i
\(117\) 15.6040i 1.44259i
\(118\) 5.90673 0.543758
\(119\) 0 0
\(120\) 0.268571 0.0245170
\(121\) 3.73917i 0.339925i
\(122\) 1.63017 + 1.63017i 0.147589 + 0.147589i
\(123\) −15.8229 −1.42671
\(124\) 4.15735 + 4.15735i 0.373341 + 0.373341i
\(125\) 0.851634 0.851634i 0.0761725 0.0761725i
\(126\) 6.94587 6.94587i 0.618788 0.618788i
\(127\) 2.20439i 0.195608i −0.995206 0.0978041i \(-0.968818\pi\)
0.995206 0.0978041i \(-0.0311819\pi\)
\(128\) 6.84255i 0.604802i
\(129\) 9.82997 9.82997i 0.865480 0.865480i
\(130\) 0.733154 0.733154i 0.0643019 0.0643019i
\(131\) −1.40940 1.40940i −0.123140 0.123140i 0.642851 0.765991i \(-0.277751\pi\)
−0.765991 + 0.642851i \(0.777751\pi\)
\(132\) −10.4534 −0.909848
\(133\) −2.03603 2.03603i −0.176546 0.176546i
\(134\) 27.4834i 2.37420i
\(135\) 0.125667 0.0108157
\(136\) 0 0
\(137\) −12.6236 −1.07851 −0.539254 0.842143i \(-0.681294\pi\)
−0.539254 + 0.842143i \(0.681294\pi\)
\(138\) 35.2695i 3.00234i
\(139\) −3.70130 3.70130i −0.313940 0.313940i 0.532494 0.846434i \(-0.321255\pi\)
−0.846434 + 0.532494i \(0.821255\pi\)
\(140\) 0.283119 0.0239279
\(141\) −13.1550 13.1550i −1.10785 1.10785i
\(142\) −0.226242 + 0.226242i −0.0189858 + 0.0189858i
\(143\) 8.71510 8.71510i 0.728793 0.728793i
\(144\) 16.0915i 1.34096i
\(145\) 0.411474i 0.0341711i
\(146\) 15.6822 15.6822i 1.29787 1.29787i
\(147\) 8.33047 8.33047i 0.687085 0.687085i
\(148\) −5.68647 5.68647i −0.467425 0.467425i
\(149\) −9.65270 −0.790780 −0.395390 0.918513i \(-0.629391\pi\)
−0.395390 + 0.918513i \(0.629391\pi\)
\(150\) −16.7758 16.7758i −1.36974 1.36974i
\(151\) 1.20708i 0.0982309i −0.998793 0.0491154i \(-0.984360\pi\)
0.998793 0.0491154i \(-0.0156402\pi\)
\(152\) −1.65270 −0.134052
\(153\) 0 0
\(154\) 7.75877 0.625220
\(155\) 0.462859i 0.0371777i
\(156\) −12.5471 12.5471i −1.00457 1.00457i
\(157\) −15.0942 −1.20465 −0.602324 0.798251i \(-0.705759\pi\)
−0.602324 + 0.798251i \(0.705759\pi\)
\(158\) 5.51233 + 5.51233i 0.438537 + 0.438537i
\(159\) −1.47345 + 1.47345i −0.116852 + 0.116852i
\(160\) 0.606059 0.606059i 0.0479132 0.0479132i
\(161\) 11.3550i 0.894902i
\(162\) 14.2763i 1.12165i
\(163\) −4.63464 + 4.63464i −0.363013 + 0.363013i −0.864921 0.501908i \(-0.832632\pi\)
0.501908 + 0.864921i \(0.332632\pi\)
\(164\) −6.76982 + 6.76982i −0.528634 + 0.528634i
\(165\) 0.581912 + 0.581912i 0.0453018 + 0.0453018i
\(166\) −4.57398 −0.355010
\(167\) 2.78852 + 2.78852i 0.215782 + 0.215782i 0.806718 0.590936i \(-0.201241\pi\)
−0.590936 + 0.806718i \(0.701241\pi\)
\(168\) 3.41147i 0.263201i
\(169\) 7.92127 0.609329
\(170\) 0 0
\(171\) −6.41147 −0.490298
\(172\) 8.41147i 0.641369i
\(173\) 13.3884 + 13.3884i 1.01790 + 1.01790i 0.999837 + 0.0180650i \(0.00575057\pi\)
0.0180650 + 0.999837i \(0.494249\pi\)
\(174\) 16.2344 1.23073
\(175\) 5.40099 + 5.40099i 0.408277 + 0.408277i
\(176\) 8.98738 8.98738i 0.677449 0.677449i
\(177\) −5.62723 + 5.62723i −0.422969 + 0.422969i
\(178\) 28.3628i 2.12588i
\(179\) 7.25402i 0.542191i 0.962552 + 0.271096i \(0.0873859\pi\)
−0.962552 + 0.271096i \(0.912614\pi\)
\(180\) 0.445771 0.445771i 0.0332258 0.0332258i
\(181\) −17.7479 + 17.7479i −1.31919 + 1.31919i −0.404769 + 0.914419i \(0.632648\pi\)
−0.914419 + 0.404769i \(0.867352\pi\)
\(182\) 9.31277 + 9.31277i 0.690308 + 0.690308i
\(183\) −3.10607 −0.229607
\(184\) −4.60860 4.60860i −0.339750 0.339750i
\(185\) 0.633103i 0.0465467i
\(186\) −18.2618 −1.33902
\(187\) 0 0
\(188\) −11.2567 −0.820980
\(189\) 1.59627i 0.116111i
\(190\) −0.301243 0.301243i −0.0218545 0.0218545i
\(191\) −14.1557 −1.02427 −0.512135 0.858905i \(-0.671145\pi\)
−0.512135 + 0.858905i \(0.671145\pi\)
\(192\) −7.02087 7.02087i −0.506688 0.506688i
\(193\) 11.6185 11.6185i 0.836320 0.836320i −0.152053 0.988372i \(-0.548588\pi\)
0.988372 + 0.152053i \(0.0485884\pi\)
\(194\) −14.8740 + 14.8740i −1.06789 + 1.06789i
\(195\) 1.39693i 0.100036i
\(196\) 7.12836i 0.509168i
\(197\) −14.3115 + 14.3115i −1.01965 + 1.01965i −0.0198470 + 0.999803i \(0.506318\pi\)
−0.999803 + 0.0198470i \(0.993682\pi\)
\(198\) 12.2162 12.2162i 0.868167 0.868167i
\(199\) 15.6803 + 15.6803i 1.11155 + 1.11155i 0.992941 + 0.118606i \(0.0378425\pi\)
0.118606 + 0.992941i \(0.462158\pi\)
\(200\) 4.38413 0.310005
\(201\) 26.1829 + 26.1829i 1.84680 + 1.84680i
\(202\) 14.6236i 1.02891i
\(203\) −5.22668 −0.366841
\(204\) 0 0
\(205\) 0.753718 0.0526420
\(206\) 20.4097i 1.42201i
\(207\) −17.8785 17.8785i −1.24264 1.24264i
\(208\) 21.5749 1.49595
\(209\) −3.58091 3.58091i −0.247697 0.247697i
\(210\) −0.621819 + 0.621819i −0.0429096 + 0.0429096i
\(211\) 5.08232 5.08232i 0.349881 0.349881i −0.510184 0.860065i \(-0.670423\pi\)
0.860065 + 0.510184i \(0.170423\pi\)
\(212\) 1.26083i 0.0865942i
\(213\) 0.431074i 0.0295367i
\(214\) −16.0028 + 16.0028i −1.09393 + 1.09393i
\(215\) −0.468245 + 0.468245i −0.0319341 + 0.0319341i
\(216\) 0.647867 + 0.647867i 0.0440817 + 0.0440817i
\(217\) 5.87939 0.399119
\(218\) −8.78528 8.78528i −0.595014 0.595014i
\(219\) 29.8803i 2.01912i
\(220\) 0.497941 0.0335711
\(221\) 0 0
\(222\) 24.9786 1.67646
\(223\) 6.01960i 0.403102i 0.979478 + 0.201551i \(0.0645982\pi\)
−0.979478 + 0.201551i \(0.935402\pi\)
\(224\) 7.69836 + 7.69836i 0.514368 + 0.514368i
\(225\) 17.0077 1.13385
\(226\) 6.75954 + 6.75954i 0.449638 + 0.449638i
\(227\) −15.5812 + 15.5812i −1.03416 + 1.03416i −0.0347620 + 0.999396i \(0.511067\pi\)
−0.999396 + 0.0347620i \(0.988933\pi\)
\(228\) −5.15542 + 5.15542i −0.341426 + 0.341426i
\(229\) 3.69965i 0.244479i 0.992501 + 0.122240i \(0.0390077\pi\)
−0.992501 + 0.122240i \(0.960992\pi\)
\(230\) 1.68004i 0.110779i
\(231\) −7.39164 + 7.39164i −0.486334 + 0.486334i
\(232\) −2.12132 + 2.12132i −0.139272 + 0.139272i
\(233\) −20.6126 20.6126i −1.35038 1.35038i −0.885237 0.465141i \(-0.846004\pi\)
−0.465141 0.885237i \(-0.653996\pi\)
\(234\) 29.3259 1.91710
\(235\) 0.626633 + 0.626633i 0.0408770 + 0.0408770i
\(236\) 4.81521i 0.313443i
\(237\) −10.5030 −0.682243
\(238\) 0 0
\(239\) 12.4834 0.807484 0.403742 0.914873i \(-0.367709\pi\)
0.403742 + 0.914873i \(0.367709\pi\)
\(240\) 1.44057i 0.0929884i
\(241\) −11.4673 11.4673i −0.738673 0.738673i 0.233649 0.972321i \(-0.424933\pi\)
−0.972321 + 0.233649i \(0.924933\pi\)
\(242\) −7.02734 −0.451735
\(243\) −15.8110 15.8110i −1.01427 1.01427i
\(244\) −1.32893 + 1.32893i −0.0850758 + 0.0850758i
\(245\) −0.396818 + 0.396818i −0.0253517 + 0.0253517i
\(246\) 29.7374i 1.89599i
\(247\) 8.59627i 0.546967i
\(248\) 2.38623 2.38623i 0.151526 0.151526i
\(249\) 4.35755 4.35755i 0.276148 0.276148i
\(250\) 1.60055 + 1.60055i 0.101228 + 0.101228i
\(251\) −15.9959 −1.00965 −0.504826 0.863221i \(-0.668443\pi\)
−0.504826 + 0.863221i \(0.668443\pi\)
\(252\) 5.66233 + 5.66233i 0.356693 + 0.356693i
\(253\) 19.9709i 1.25556i
\(254\) 4.14290 0.259949
\(255\) 0 0
\(256\) 20.7023 1.29390
\(257\) 9.66044i 0.602602i 0.953529 + 0.301301i \(0.0974209\pi\)
−0.953529 + 0.301301i \(0.902579\pi\)
\(258\) 18.4743 + 18.4743i 1.15016 + 1.15016i
\(259\) −8.04189 −0.499699
\(260\) 0.597673 + 0.597673i 0.0370661 + 0.0370661i
\(261\) −8.22942 + 8.22942i −0.509388 + 0.509388i
\(262\) 2.64881 2.64881i 0.163644 0.163644i
\(263\) 27.9813i 1.72540i 0.505714 + 0.862701i \(0.331229\pi\)
−0.505714 + 0.862701i \(0.668771\pi\)
\(264\) 6.00000i 0.369274i
\(265\) 0.0701872 0.0701872i 0.00431157 0.00431157i
\(266\) 3.82649 3.82649i 0.234617 0.234617i
\(267\) −27.0207 27.0207i −1.65364 1.65364i
\(268\) 22.4047 1.36858
\(269\) 4.69936 + 4.69936i 0.286525 + 0.286525i 0.835704 0.549179i \(-0.185060\pi\)
−0.549179 + 0.835704i \(0.685060\pi\)
\(270\) 0.236177i 0.0143733i
\(271\) 17.0000 1.03268 0.516338 0.856385i \(-0.327295\pi\)
0.516338 + 0.856385i \(0.327295\pi\)
\(272\) 0 0
\(273\) −17.7442 −1.07393
\(274\) 23.7246i 1.43326i
\(275\) 9.49910 + 9.49910i 0.572818 + 0.572818i
\(276\) −28.7520 −1.73066
\(277\) 14.2474 + 14.2474i 0.856044 + 0.856044i 0.990869 0.134825i \(-0.0430473\pi\)
−0.134825 + 0.990869i \(0.543047\pi\)
\(278\) 6.95616 6.95616i 0.417203 0.417203i
\(279\) 9.25710 9.25710i 0.554208 0.554208i
\(280\) 0.162504i 0.00971146i
\(281\) 16.4730i 0.982695i 0.870964 + 0.491347i \(0.163495\pi\)
−0.870964 + 0.491347i \(0.836505\pi\)
\(282\) 24.7234 24.7234i 1.47225 1.47225i
\(283\) 13.0430 13.0430i 0.775327 0.775327i −0.203705 0.979032i \(-0.565298\pi\)
0.979032 + 0.203705i \(0.0652983\pi\)
\(284\) −0.184435 0.184435i −0.0109442 0.0109442i
\(285\) 0.573978 0.0339995
\(286\) 16.3790 + 16.3790i 0.968512 + 0.968512i
\(287\) 9.57398i 0.565134i
\(288\) 24.2422 1.42848
\(289\) 0 0
\(290\) −0.773318 −0.0454108
\(291\) 28.3405i 1.66135i
\(292\) 12.7842 + 12.7842i 0.748142 + 0.748142i
\(293\) 10.9513 0.639782 0.319891 0.947454i \(-0.396354\pi\)
0.319891 + 0.947454i \(0.396354\pi\)
\(294\) 15.6562 + 15.6562i 0.913086 + 0.913086i
\(295\) 0.268050 0.268050i 0.0156065 0.0156065i
\(296\) −3.26391 + 3.26391i −0.189711 + 0.189711i
\(297\) 2.80747i 0.162906i
\(298\) 18.1411i 1.05089i
\(299\) 23.9709 23.9709i 1.38627 1.38627i
\(300\) 13.6758 13.6758i 0.789572 0.789572i
\(301\) −5.94781 5.94781i −0.342826 0.342826i
\(302\) 2.26857 0.130542
\(303\) −13.9317 13.9317i −0.800353 0.800353i
\(304\) 8.86484i 0.508433i
\(305\) 0.147956 0.00847193
\(306\) 0 0
\(307\) −5.78106 −0.329942 −0.164971 0.986298i \(-0.552753\pi\)
−0.164971 + 0.986298i \(0.552753\pi\)
\(308\) 6.32501i 0.360401i
\(309\) 19.4440 + 19.4440i 1.10613 + 1.10613i
\(310\) 0.869890 0.0494064
\(311\) 0.0852875 + 0.0852875i 0.00483621 + 0.00483621i 0.709521 0.704685i \(-0.248911\pi\)
−0.704685 + 0.709521i \(0.748911\pi\)
\(312\) −7.20174 + 7.20174i −0.407718 + 0.407718i
\(313\) 7.34626 7.34626i 0.415235 0.415235i −0.468322 0.883558i \(-0.655141\pi\)
0.883558 + 0.468322i \(0.155141\pi\)
\(314\) 28.3678i 1.60089i
\(315\) 0.630415i 0.0355199i
\(316\) −4.49369 + 4.49369i −0.252790 + 0.252790i
\(317\) −19.6587 + 19.6587i −1.10414 + 1.10414i −0.110237 + 0.993905i \(0.535161\pi\)
−0.993905 + 0.110237i \(0.964839\pi\)
\(318\) −2.76919 2.76919i −0.155288 0.155288i
\(319\) −9.19253 −0.514683
\(320\) 0.334436 + 0.334436i 0.0186955 + 0.0186955i
\(321\) 30.4911i 1.70185i
\(322\) 21.3405 1.18926
\(323\) 0 0
\(324\) −11.6382 −0.646564
\(325\) 22.8033i 1.26490i
\(326\) −8.71028 8.71028i −0.482418 0.482418i
\(327\) 16.7392 0.925678
\(328\) 3.88573 + 3.88573i 0.214554 + 0.214554i
\(329\) −7.95970 + 7.95970i −0.438832 + 0.438832i
\(330\) −1.09364 + 1.09364i −0.0602028 + 0.0602028i
\(331\) 8.77837i 0.482503i 0.970463 + 0.241251i \(0.0775579\pi\)
−0.970463 + 0.241251i \(0.922442\pi\)
\(332\) 3.72874i 0.204641i
\(333\) −12.6620 + 12.6620i −0.693872 + 0.693872i
\(334\) −5.24070 + 5.24070i −0.286759 + 0.286759i
\(335\) −1.24721 1.24721i −0.0681424 0.0681424i
\(336\) −18.2986 −0.998270
\(337\) −1.03316 1.03316i −0.0562796 0.0562796i 0.678407 0.734686i \(-0.262671\pi\)
−0.734686 + 0.678407i \(0.762671\pi\)
\(338\) 14.8871i 0.809753i
\(339\) −12.8794 −0.699512
\(340\) 0 0
\(341\) 10.3405 0.559969
\(342\) 12.0496i 0.651569i
\(343\) −12.6240 12.6240i −0.681630 0.681630i
\(344\) −4.82800 −0.260308
\(345\) 1.60055 + 1.60055i 0.0861707 + 0.0861707i
\(346\) −25.1620 + 25.1620i −1.35272 + 1.35272i
\(347\) 22.1720 22.1720i 1.19026 1.19026i 0.213261 0.976995i \(-0.431591\pi\)
0.976995 0.213261i \(-0.0684085\pi\)
\(348\) 13.2344i 0.709440i
\(349\) 29.7743i 1.59378i −0.604125 0.796890i \(-0.706477\pi\)
0.604125 0.796890i \(-0.293523\pi\)
\(350\) −10.1505 + 10.1505i −0.542569 + 0.542569i
\(351\) −3.36977 + 3.36977i −0.179865 + 0.179865i
\(352\) 13.5396 + 13.5396i 0.721666 + 0.721666i
\(353\) 28.3141 1.50701 0.753503 0.657444i \(-0.228362\pi\)
0.753503 + 0.657444i \(0.228362\pi\)
\(354\) −10.5757 10.5757i −0.562094 0.562094i
\(355\) 0.0205340i 0.00108983i
\(356\) −23.1215 −1.22544
\(357\) 0 0
\(358\) −13.6331 −0.720532
\(359\) 2.81790i 0.148723i 0.997231 + 0.0743614i \(0.0236918\pi\)
−0.997231 + 0.0743614i \(0.976308\pi\)
\(360\) −0.255863 0.255863i −0.0134851 0.0134851i
\(361\) 15.4679 0.814101
\(362\) −33.3551 33.3551i −1.75310 1.75310i
\(363\) 6.69482 6.69482i 0.351387 0.351387i
\(364\) −7.59184 + 7.59184i −0.397920 + 0.397920i
\(365\) 1.42333i 0.0745007i
\(366\) 5.83750i 0.305131i
\(367\) −5.88186 + 5.88186i −0.307030 + 0.307030i −0.843757 0.536726i \(-0.819661\pi\)
0.536726 + 0.843757i \(0.319661\pi\)
\(368\) 24.7198 24.7198i 1.28861 1.28861i
\(369\) 15.0742 + 15.0742i 0.784734 + 0.784734i
\(370\) −1.18984 −0.0618571
\(371\) 0.891541 + 0.891541i 0.0462865 + 0.0462865i
\(372\) 14.8871i 0.771862i
\(373\) −9.21894 −0.477339 −0.238669 0.971101i \(-0.576711\pi\)
−0.238669 + 0.971101i \(0.576711\pi\)
\(374\) 0 0
\(375\) −3.04963 −0.157482
\(376\) 6.46110i 0.333206i
\(377\) −11.0337 11.0337i −0.568264 0.568264i
\(378\) −3.00000 −0.154303
\(379\) −7.32759 7.32759i −0.376393 0.376393i 0.493406 0.869799i \(-0.335752\pi\)
−0.869799 + 0.493406i \(0.835752\pi\)
\(380\) 0.245576 0.245576i 0.0125978 0.0125978i
\(381\) −3.94687 + 3.94687i −0.202204 + 0.202204i
\(382\) 26.6040i 1.36118i
\(383\) 13.2713i 0.678130i 0.940763 + 0.339065i \(0.110111\pi\)
−0.940763 + 0.339065i \(0.889889\pi\)
\(384\) −12.2513 + 12.2513i −0.625196 + 0.625196i
\(385\) 0.352097 0.352097i 0.0179445 0.0179445i
\(386\) 21.8357 + 21.8357i 1.11141 + 1.11141i
\(387\) −18.7297 −0.952083
\(388\) −12.1254 12.1254i −0.615576 0.615576i
\(389\) 26.2763i 1.33226i 0.745835 + 0.666131i \(0.232051\pi\)
−0.745835 + 0.666131i \(0.767949\pi\)
\(390\) −2.62536 −0.132940
\(391\) 0 0
\(392\) −4.09152 −0.206653
\(393\) 5.04694i 0.254585i
\(394\) −26.8968 26.8968i −1.35504 1.35504i
\(395\) 0.500305 0.0251731
\(396\) 9.95874 + 9.95874i 0.500445 + 0.500445i
\(397\) 18.0147 18.0147i 0.904130 0.904130i −0.0916602 0.995790i \(-0.529217\pi\)
0.995790 + 0.0916602i \(0.0292173\pi\)
\(398\) −29.4693 + 29.4693i −1.47716 + 1.47716i
\(399\) 7.29086i 0.365000i
\(400\) 23.5158i 1.17579i
\(401\) 0.636920 0.636920i 0.0318062 0.0318062i −0.691025 0.722831i \(-0.742840\pi\)
0.722831 + 0.691025i \(0.242840\pi\)
\(402\) −49.2078 + 49.2078i −2.45426 + 2.45426i
\(403\) 12.4116 + 12.4116i 0.618265 + 0.618265i
\(404\) −11.9213 −0.593106
\(405\) 0.647867 + 0.647867i 0.0321928 + 0.0321928i
\(406\) 9.82295i 0.487505i
\(407\) −14.1438 −0.701084
\(408\) 0 0
\(409\) −15.3259 −0.757819 −0.378910 0.925434i \(-0.623701\pi\)
−0.378910 + 0.925434i \(0.623701\pi\)
\(410\) 1.41653i 0.0699573i
\(411\) 22.6020 + 22.6020i 1.11488 + 1.11488i
\(412\) 16.6382 0.819703
\(413\) 3.40487 + 3.40487i 0.167542 + 0.167542i
\(414\) 33.6006 33.6006i 1.65138 1.65138i
\(415\) −0.207570 + 0.207570i −0.0101892 + 0.0101892i
\(416\) 32.5030i 1.59359i
\(417\) 13.2540i 0.649052i
\(418\) 6.72992 6.72992i 0.329171 0.329171i
\(419\) 1.68584 1.68584i 0.0823585 0.0823585i −0.664727 0.747086i \(-0.731452\pi\)
0.747086 + 0.664727i \(0.231452\pi\)
\(420\) −0.506912 0.506912i −0.0247348 0.0247348i
\(421\) 8.28581 0.403826 0.201913 0.979404i \(-0.435284\pi\)
0.201913 + 0.979404i \(0.435284\pi\)
\(422\) 9.55163 + 9.55163i 0.464966 + 0.464966i
\(423\) 25.0651i 1.21871i
\(424\) 0.723689 0.0351454
\(425\) 0 0
\(426\) 0.810155 0.0392521
\(427\) 1.87939i 0.0909498i
\(428\) −13.0456 13.0456i −0.630582 0.630582i
\(429\) −31.2080 −1.50674
\(430\) −0.880014 0.880014i −0.0424380 0.0424380i
\(431\) 22.8531 22.8531i 1.10079 1.10079i 0.106479 0.994315i \(-0.466042\pi\)
0.994315 0.106479i \(-0.0339577\pi\)
\(432\) −3.47505 + 3.47505i −0.167194 + 0.167194i
\(433\) 15.0642i 0.723938i −0.932190 0.361969i \(-0.882105\pi\)
0.932190 0.361969i \(-0.117895\pi\)
\(434\) 11.0496i 0.530399i
\(435\) 0.736727 0.736727i 0.0353233 0.0353233i
\(436\) 7.16183 7.16183i 0.342989 0.342989i
\(437\) −9.84930 9.84930i −0.471156 0.471156i
\(438\) −56.1566 −2.68327
\(439\) −1.81942 1.81942i −0.0868360 0.0868360i 0.662355 0.749191i \(-0.269557\pi\)
−0.749191 + 0.662355i \(0.769557\pi\)
\(440\) 0.285807i 0.0136253i
\(441\) −15.8726 −0.755837
\(442\) 0 0
\(443\) 23.4662 1.11491 0.557455 0.830207i \(-0.311778\pi\)
0.557455 + 0.830207i \(0.311778\pi\)
\(444\) 20.3628i 0.966375i
\(445\) 1.28712 + 1.28712i 0.0610153 + 0.0610153i
\(446\) −11.3131 −0.535693
\(447\) 17.2828 + 17.2828i 0.817446 + 0.817446i
\(448\) −4.24811 + 4.24811i −0.200705 + 0.200705i
\(449\) −13.3346 + 13.3346i −0.629301 + 0.629301i −0.947892 0.318591i \(-0.896790\pi\)
0.318591 + 0.947892i \(0.396790\pi\)
\(450\) 31.9641i 1.50680i
\(451\) 16.8384i 0.792891i
\(452\) −5.51043 + 5.51043i −0.259189 + 0.259189i
\(453\) −2.16123 + 2.16123i −0.101543 + 0.101543i
\(454\) −29.2830 29.2830i −1.37432 1.37432i
\(455\) 0.845237 0.0396253
\(456\) 2.95910 + 2.95910i 0.138572 + 0.138572i
\(457\) 2.10782i 0.0985997i 0.998784 + 0.0492999i \(0.0156990\pi\)
−0.998784 + 0.0492999i \(0.984301\pi\)
\(458\) −6.95306 −0.324895
\(459\) 0 0
\(460\) 1.36959 0.0638572
\(461\) 21.9077i 1.02034i 0.860073 + 0.510171i \(0.170418\pi\)
−0.860073 + 0.510171i \(0.829582\pi\)
\(462\) −13.8917 13.8917i −0.646303 0.646303i
\(463\) −14.1557 −0.657871 −0.328936 0.944352i \(-0.606690\pi\)
−0.328936 + 0.944352i \(0.606690\pi\)
\(464\) −11.3784 11.3784i −0.528230 0.528230i
\(465\) −0.828729 + 0.828729i −0.0384314 + 0.0384314i
\(466\) 38.7391 38.7391i 1.79455 1.79455i
\(467\) 29.6878i 1.37379i −0.726758 0.686893i \(-0.758974\pi\)
0.726758 0.686893i \(-0.241026\pi\)
\(468\) 23.9067i 1.10509i
\(469\) 15.8425 15.8425i 0.731538 0.731538i
\(470\) −1.17768 + 1.17768i −0.0543225 + 0.0543225i
\(471\) 27.0255 + 27.0255i 1.24527 + 1.24527i
\(472\) 2.76382 0.127215
\(473\) −10.4608 10.4608i −0.480990 0.480990i
\(474\) 19.7392i 0.906650i
\(475\) 9.36959 0.429906
\(476\) 0 0
\(477\) 2.80747 0.128545
\(478\) 23.4611i 1.07309i
\(479\) −27.0793 27.0793i −1.23728 1.23728i −0.961106 0.276178i \(-0.910932\pi\)
−0.276178 0.961106i \(-0.589068\pi\)
\(480\) −2.17024 −0.0990577
\(481\) −16.9767 16.9767i −0.774071 0.774071i
\(482\) 21.5514 21.5514i 0.981641 0.981641i
\(483\) −20.3307 + 20.3307i −0.925079 + 0.925079i
\(484\) 5.72874i 0.260397i
\(485\) 1.34998i 0.0612996i
\(486\) 29.7149 29.7149i 1.34790 1.34790i
\(487\) 16.5116 16.5116i 0.748212 0.748212i −0.225932 0.974143i \(-0.572543\pi\)
0.974143 + 0.225932i \(0.0725426\pi\)
\(488\) 0.762774 + 0.762774i 0.0345292 + 0.0345292i
\(489\) 16.5963 0.750509
\(490\) −0.745773 0.745773i −0.0336906 0.0336906i
\(491\) 31.3928i 1.41674i −0.705843 0.708369i \(-0.749431\pi\)
0.705843 0.708369i \(-0.250569\pi\)
\(492\) 24.2422 1.09292
\(493\) 0 0
\(494\) 16.1557 0.726879
\(495\) 1.10876i 0.0498348i
\(496\) 12.7994 + 12.7994i 0.574708 + 0.574708i
\(497\) −0.260830 −0.0116998
\(498\) 8.18951 + 8.18951i 0.366981 + 0.366981i
\(499\) −11.4064 + 11.4064i −0.510619 + 0.510619i −0.914716 0.404097i \(-0.867586\pi\)
0.404097 + 0.914716i \(0.367586\pi\)
\(500\) −1.30478 + 1.30478i −0.0583515 + 0.0583515i
\(501\) 9.98545i 0.446117i
\(502\) 30.0624i 1.34175i
\(503\) −24.2988 + 24.2988i −1.08343 + 1.08343i −0.0872435 + 0.996187i \(0.527806\pi\)
−0.996187 + 0.0872435i \(0.972194\pi\)
\(504\) 3.25005 3.25005i 0.144769 0.144769i
\(505\) 0.663627 + 0.663627i 0.0295310 + 0.0295310i
\(506\) 37.5330 1.66855
\(507\) −14.1827 14.1827i −0.629876 0.629876i
\(508\) 3.37733i 0.149845i
\(509\) 20.0283 0.887738 0.443869 0.896092i \(-0.353606\pi\)
0.443869 + 0.896092i \(0.353606\pi\)
\(510\) 0 0
\(511\) 18.0797 0.799797
\(512\) 25.2226i 1.11469i
\(513\) 1.38459 + 1.38459i 0.0611313 + 0.0611313i
\(514\) −18.1557 −0.800813
\(515\) −0.926204 0.926204i −0.0408134 0.0408134i
\(516\) −15.0604 + 15.0604i −0.662996 + 0.662996i
\(517\) −13.9993 + 13.9993i −0.615688 + 0.615688i
\(518\) 15.1138i 0.664063i
\(519\) 47.9427i 2.10445i
\(520\) 0.343051 0.343051i 0.0150438 0.0150438i
\(521\) 3.94978 3.94978i 0.173043 0.173043i −0.615272 0.788315i \(-0.710954\pi\)
0.788315 + 0.615272i \(0.210954\pi\)
\(522\) −15.4662 15.4662i −0.676939 0.676939i
\(523\) −5.51249 −0.241044 −0.120522 0.992711i \(-0.538457\pi\)
−0.120522 + 0.992711i \(0.538457\pi\)
\(524\) 2.15933 + 2.15933i 0.0943306 + 0.0943306i
\(525\) 19.3405i 0.844088i
\(526\) −52.5877 −2.29293
\(527\) 0 0
\(528\) −32.1830 −1.40059
\(529\) 31.9299i 1.38826i
\(530\) 0.131909 + 0.131909i 0.00572975 + 0.00572975i
\(531\) 10.7219 0.465292
\(532\) 3.11938 + 3.11938i 0.135242 + 0.135242i
\(533\) −20.2110 + 20.2110i −0.875435 + 0.875435i
\(534\) 50.7823 50.7823i 2.19757 2.19757i
\(535\) 1.45243i 0.0627940i
\(536\) 12.8598i 0.555458i
\(537\) 12.9880 12.9880i 0.560474 0.560474i
\(538\) −8.83190 + 8.83190i −0.380770 + 0.380770i
\(539\) −8.86510 8.86510i −0.381847 0.381847i
\(540\) −0.192533 −0.00828531
\(541\) −9.89592 9.89592i −0.425459 0.425459i 0.461619 0.887078i \(-0.347269\pi\)
−0.887078 + 0.461619i \(0.847269\pi\)
\(542\) 31.9495i 1.37235i
\(543\) 63.5536 2.72734
\(544\) 0 0
\(545\) −0.797362 −0.0341552
\(546\) 33.3482i 1.42717i
\(547\) 20.8013 + 20.8013i 0.889399 + 0.889399i 0.994465 0.105066i \(-0.0335055\pi\)
−0.105066 + 0.994465i \(0.533506\pi\)
\(548\) 19.3405 0.826185
\(549\) 2.95910 + 2.95910i 0.126291 + 0.126291i
\(550\) −17.8525 + 17.8525i −0.761232 + 0.761232i
\(551\) −4.53360 + 4.53360i −0.193138 + 0.193138i
\(552\) 16.5030i 0.702414i
\(553\) 6.35504i 0.270244i
\(554\) −26.7764 + 26.7764i −1.13762 + 1.13762i
\(555\) 1.13354 1.13354i 0.0481163 0.0481163i
\(556\) 5.67071 + 5.67071i 0.240492 + 0.240492i
\(557\) −32.0574 −1.35831 −0.679157 0.733993i \(-0.737655\pi\)
−0.679157 + 0.733993i \(0.737655\pi\)
\(558\) 17.3977 + 17.3977i 0.736502 + 0.736502i
\(559\) 25.1121i 1.06213i
\(560\) 0.871644 0.0368337
\(561\) 0 0
\(562\) −30.9590 −1.30593
\(563\) 18.6483i 0.785930i −0.919553 0.392965i \(-0.871449\pi\)
0.919553 0.392965i \(-0.128551\pi\)
\(564\) 20.1547 + 20.1547i 0.848664 + 0.848664i
\(565\) 0.613503 0.0258103
\(566\) 24.5129 + 24.5129i 1.03035 + 1.03035i
\(567\) −8.22942 + 8.22942i −0.345603 + 0.345603i
\(568\) −0.105861 + 0.105861i −0.00444184 + 0.00444184i
\(569\) 27.6554i 1.15937i 0.814839 + 0.579687i \(0.196825\pi\)
−0.814839 + 0.579687i \(0.803175\pi\)
\(570\) 1.07873i 0.0451828i
\(571\) 23.4591 23.4591i 0.981734 0.981734i −0.0181018 0.999836i \(-0.505762\pi\)
0.999836 + 0.0181018i \(0.00576229\pi\)
\(572\) −13.3523 + 13.3523i −0.558288 + 0.558288i
\(573\) 25.3452 + 25.3452i 1.05881 + 1.05881i
\(574\) −17.9932 −0.751021
\(575\) 26.1273 + 26.1273i 1.08958 + 1.08958i
\(576\) 13.3773i 0.557389i
\(577\) 2.70233 0.112500 0.0562498 0.998417i \(-0.482086\pi\)
0.0562498 + 0.998417i \(0.482086\pi\)
\(578\) 0 0
\(579\) −41.6049 −1.72904
\(580\) 0.630415i 0.0261766i
\(581\) −2.63662 2.63662i −0.109385 0.109385i
\(582\) 53.2627 2.20781
\(583\) 1.56802 + 1.56802i 0.0649406 + 0.0649406i
\(584\) 7.33788 7.33788i 0.303644 0.303644i
\(585\) 1.33083 1.33083i 0.0550229 0.0550229i
\(586\) 20.5817i 0.850223i
\(587\) 6.31551i 0.260669i 0.991470 + 0.130335i \(0.0416051\pi\)
−0.991470 + 0.130335i \(0.958395\pi\)
\(588\) −12.7630 + 12.7630i −0.526338 + 0.526338i
\(589\) 5.09975 5.09975i 0.210131 0.210131i
\(590\) 0.503770 + 0.503770i 0.0207399 + 0.0207399i
\(591\) 51.2481 2.10807
\(592\) −17.5071 17.5071i −0.719537 0.719537i
\(593\) 10.2148i 0.419472i 0.977758 + 0.209736i \(0.0672605\pi\)
−0.977758 + 0.209736i \(0.932739\pi\)
\(594\) −5.27631 −0.216490
\(595\) 0 0
\(596\) 14.7888 0.605773
\(597\) 56.1498i 2.29806i
\(598\) 45.0505 + 45.0505i 1.84225 + 1.84225i
\(599\) 21.4347 0.875798 0.437899 0.899024i \(-0.355723\pi\)
0.437899 + 0.899024i \(0.355723\pi\)
\(600\) −7.84960 7.84960i −0.320459 0.320459i
\(601\) −12.3431 + 12.3431i −0.503484 + 0.503484i −0.912519 0.409035i \(-0.865865\pi\)
0.409035 + 0.912519i \(0.365865\pi\)
\(602\) 11.1782 11.1782i 0.455591 0.455591i
\(603\) 49.8881i 2.03160i
\(604\) 1.84936i 0.0752492i
\(605\) −0.318905 + 0.318905i −0.0129653 + 0.0129653i
\(606\) 26.1829 26.1829i 1.06361 1.06361i
\(607\) −6.01734 6.01734i −0.244236 0.244236i 0.574364 0.818600i \(-0.305249\pi\)
−0.818600 + 0.574364i \(0.805249\pi\)
\(608\) 13.3550 0.541618
\(609\) 9.35815 + 9.35815i 0.379211 + 0.379211i
\(610\) 0.278066i 0.0112586i
\(611\) −33.6064 −1.35957
\(612\) 0 0
\(613\) 9.78106 0.395053 0.197527 0.980298i \(-0.436709\pi\)
0.197527 + 0.980298i \(0.436709\pi\)
\(614\) 10.8648i 0.438469i
\(615\) −1.34950 1.34950i −0.0544171 0.0544171i
\(616\) 3.63041 0.146274
\(617\) 16.1583 + 16.1583i 0.650507 + 0.650507i 0.953115 0.302608i \(-0.0978574\pi\)
−0.302608 + 0.953115i \(0.597857\pi\)
\(618\) −36.5427 + 36.5427i −1.46996 + 1.46996i
\(619\) −29.1771 + 29.1771i −1.17273 + 1.17273i −0.191171 + 0.981557i \(0.561229\pi\)
−0.981557 + 0.191171i \(0.938771\pi\)
\(620\) 0.709141i 0.0284798i
\(621\) 7.72193i 0.309871i
\(622\) −0.160288 + 0.160288i −0.00642697 + 0.00642697i
\(623\) −16.3494 + 16.3494i −0.655025 + 0.655025i
\(624\) −38.6290 38.6290i −1.54640 1.54640i
\(625\) −24.7820 −0.991280
\(626\) 13.8065 + 13.8065i 0.551817 + 0.551817i
\(627\) 12.8229i 0.512099i
\(628\) 23.1257 0.922815
\(629\) 0 0
\(630\) 1.18479 0.0472033
\(631\) 9.54252i 0.379882i −0.981796 0.189941i \(-0.939170\pi\)
0.981796 0.189941i \(-0.0608296\pi\)
\(632\) 2.57928 + 2.57928i 0.102598 + 0.102598i
\(633\) −18.1993 −0.723359
\(634\) −36.9463 36.9463i −1.46732 1.46732i
\(635\) 0.188007 0.188007i 0.00746084 0.00746084i
\(636\) 2.25746 2.25746i 0.0895142 0.0895142i
\(637\) 21.2814i 0.843198i
\(638\) 17.2763i 0.683976i
\(639\) −0.410677 + 0.410677i −0.0162461 + 0.0162461i
\(640\) 0.583584 0.583584i 0.0230682 0.0230682i
\(641\) 6.66711 + 6.66711i 0.263335 + 0.263335i 0.826407 0.563073i \(-0.190381\pi\)
−0.563073 + 0.826407i \(0.690381\pi\)
\(642\) 57.3046 2.26163
\(643\) −7.78241 7.78241i −0.306908 0.306908i 0.536801 0.843709i \(-0.319633\pi\)
−0.843709 + 0.536801i \(0.819633\pi\)
\(644\) 17.3969i 0.685535i
\(645\) 1.67675 0.0660219
\(646\) 0 0
\(647\) 28.9840 1.13948 0.569740 0.821825i \(-0.307044\pi\)
0.569740 + 0.821825i \(0.307044\pi\)
\(648\) 6.68004i 0.262417i
\(649\) 5.98838 + 5.98838i 0.235064 + 0.235064i
\(650\) −42.8563 −1.68096
\(651\) −10.5268 10.5268i −0.412577 0.412577i
\(652\) 7.10069 7.10069i 0.278084 0.278084i
\(653\) −10.4071 + 10.4071i −0.407260 + 0.407260i −0.880782 0.473522i \(-0.842982\pi\)
0.473522 + 0.880782i \(0.342982\pi\)
\(654\) 31.4593i 1.23016i
\(655\) 0.240408i 0.00939354i
\(656\) −20.8424 + 20.8424i −0.813760 + 0.813760i
\(657\) 28.4665 28.4665i 1.11058 1.11058i
\(658\) −14.9593 14.9593i −0.583176 0.583176i
\(659\) −2.19759 −0.0856058 −0.0428029 0.999084i \(-0.513629\pi\)
−0.0428029 + 0.999084i \(0.513629\pi\)
\(660\) −0.891541 0.891541i −0.0347032 0.0347032i
\(661\) 26.6023i 1.03471i 0.855772 + 0.517354i \(0.173083\pi\)
−0.855772 + 0.517354i \(0.826917\pi\)
\(662\) −16.4979 −0.641211
\(663\) 0 0
\(664\) −2.14022 −0.0830565
\(665\) 0.347296i 0.0134676i
\(666\) −23.7967 23.7967i −0.922104 0.922104i
\(667\) −25.2841 −0.979002
\(668\) −4.27226 4.27226i −0.165299 0.165299i
\(669\) 10.7778 10.7778i 0.416695 0.416695i
\(670\) 2.34399 2.34399i 0.0905562 0.0905562i
\(671\) 3.30541i 0.127604i
\(672\) 27.5672i 1.06343i
\(673\) 5.12222 5.12222i 0.197447 0.197447i −0.601458 0.798905i \(-0.705413\pi\)
0.798905 + 0.601458i \(0.205413\pi\)
\(674\) 1.94170 1.94170i 0.0747915 0.0747915i
\(675\) −3.67292 3.67292i −0.141371 0.141371i
\(676\) −12.1361 −0.466773
\(677\) −16.2120 16.2120i −0.623079 0.623079i 0.323239 0.946317i \(-0.395228\pi\)
−0.946317 + 0.323239i \(0.895228\pi\)
\(678\) 24.2053i 0.929600i
\(679\) −17.1480 −0.658078
\(680\) 0 0
\(681\) 55.7948 2.13806
\(682\) 19.4338i 0.744157i
\(683\) −3.03767 3.03767i −0.116233 0.116233i 0.646598 0.762831i \(-0.276191\pi\)
−0.762831 + 0.646598i \(0.776191\pi\)
\(684\) 9.82295 0.375590
\(685\) −1.07664 1.07664i −0.0411362 0.0411362i
\(686\) 23.7253 23.7253i 0.905836 0.905836i
\(687\) 6.62406 6.62406i 0.252724 0.252724i
\(688\) 25.8966i 0.987299i
\(689\) 3.76415i 0.143403i
\(690\) −3.00805 + 3.00805i −0.114514 + 0.114514i
\(691\) −14.5898 + 14.5898i −0.555022 + 0.555022i −0.927886 0.372864i \(-0.878376\pi\)
0.372864 + 0.927886i \(0.378376\pi\)
\(692\) −20.5122 20.5122i −0.779758 0.779758i
\(693\) 14.0838 0.534998
\(694\) 41.6698 + 41.6698i 1.58176 + 1.58176i
\(695\) 0.631349i 0.0239484i
\(696\) 7.59627 0.287936
\(697\) 0 0
\(698\) 55.9573 2.11801
\(699\) 73.8120i 2.79183i
\(700\) −8.27480 8.27480i −0.312758 0.312758i
\(701\) 28.2772 1.06802 0.534008 0.845479i \(-0.320685\pi\)
0.534008 + 0.845479i \(0.320685\pi\)
\(702\) −6.33310 6.33310i −0.239027 0.239027i
\(703\) −6.97549 + 6.97549i −0.263086 + 0.263086i
\(704\) −7.47146 + 7.47146i −0.281591 + 0.281591i
\(705\) 2.24392i 0.0845108i
\(706\) 53.2131i 2.00270i
\(707\) −8.42961 + 8.42961i −0.317028 + 0.317028i
\(708\) 8.62142 8.62142i 0.324013 0.324013i
\(709\) −19.1627 19.1627i −0.719671 0.719671i 0.248866 0.968538i \(-0.419942\pi\)
−0.968538 + 0.248866i \(0.919942\pi\)
\(710\) −0.0385913 −0.00144831
\(711\) 10.0060 + 10.0060i 0.375255 + 0.375255i
\(712\) 13.2713i 0.497361i
\(713\) 28.4415 1.06514
\(714\) 0 0
\(715\) 1.48658 0.0555949
\(716\) 11.1138i 0.415342i
\(717\) −22.3510 22.3510i −0.834713 0.834713i
\(718\) −5.29591 −0.197642
\(719\) 18.2718 + 18.2718i 0.681422 + 0.681422i 0.960321 0.278899i \(-0.0899693\pi\)
−0.278899 + 0.960321i \(0.589969\pi\)
\(720\) 1.37241 1.37241i 0.0511465 0.0511465i
\(721\) 11.7650 11.7650i 0.438150 0.438150i
\(722\) 29.0702i 1.08188i
\(723\) 41.0634i 1.52716i
\(724\) 27.1913 27.1913i 1.01056 1.01056i
\(725\) 12.0263 12.0263i 0.446645 0.446645i
\(726\) 12.5822 + 12.5822i 0.466968 + 0.466968i
\(727\) 31.6290 1.17305 0.586527 0.809930i \(-0.300495\pi\)
0.586527 + 0.809930i \(0.300495\pi\)
\(728\) 4.35755 + 4.35755i 0.161501 + 0.161501i
\(729\) 33.8289i 1.25292i
\(730\) 2.67499 0.0990059
\(731\) 0 0
\(732\) 4.75877 0.175889
\(733\) 25.6040i 0.945706i −0.881141 0.472853i \(-0.843224\pi\)
0.881141 0.472853i \(-0.156776\pi\)
\(734\) −11.0543 11.0543i −0.408021 0.408021i
\(735\) 1.42097 0.0524133
\(736\) 37.2408 + 37.2408i 1.37271 + 1.37271i
\(737\) 27.8633 27.8633i 1.02636 1.02636i
\(738\) −28.3303 + 28.3303i −1.04285 + 1.04285i
\(739\) 21.6382i 0.795972i 0.917391 + 0.397986i \(0.130291\pi\)
−0.917391 + 0.397986i \(0.869709\pi\)
\(740\) 0.969971i 0.0356568i
\(741\) −15.3912 + 15.3912i −0.565412 + 0.565412i
\(742\) −1.67555 + 1.67555i −0.0615114 + 0.0615114i
\(743\) 18.9184 + 18.9184i 0.694049 + 0.694049i 0.963120 0.269072i \(-0.0867168\pi\)
−0.269072 + 0.963120i \(0.586717\pi\)
\(744\) −8.54488 −0.313271
\(745\) −0.823255 0.823255i −0.0301617 0.0301617i
\(746\) 17.3259i 0.634348i
\(747\) −8.30272 −0.303781
\(748\) 0 0
\(749\) −18.4492 −0.674121
\(750\) 5.73143i 0.209282i
\(751\) 29.6641 + 29.6641i 1.08246 + 1.08246i 0.996280 + 0.0861767i \(0.0274650\pi\)
0.0861767 + 0.996280i \(0.472535\pi\)
\(752\) −34.6563 −1.26379
\(753\) 28.6399 + 28.6399i 1.04370 + 1.04370i
\(754\) 20.7366 20.7366i 0.755181 0.755181i
\(755\) 0.102949 0.102949i 0.00374670 0.00374670i
\(756\) 2.44562i 0.0889464i
\(757\) 4.99319i 0.181481i −0.995875 0.0907403i \(-0.971077\pi\)
0.995875 0.0907403i \(-0.0289233\pi\)
\(758\) 13.7714 13.7714i 0.500199 0.500199i
\(759\) −35.7570 + 35.7570i −1.29790 + 1.29790i
\(760\) −0.140955 0.140955i −0.00511297 0.00511297i
\(761\) −13.2935 −0.481891 −0.240945 0.970539i \(-0.577457\pi\)
−0.240945 + 0.970539i \(0.577457\pi\)
\(762\) −7.41769 7.41769i −0.268715 0.268715i
\(763\) 10.1284i 0.366671i
\(764\) 21.6878 0.784637
\(765\) 0 0
\(766\) −24.9418 −0.901184
\(767\) 14.3756i 0.519072i
\(768\) −37.0666 37.0666i −1.33753 1.33753i
\(769\) −8.25166 −0.297562 −0.148781 0.988870i \(-0.547535\pi\)
−0.148781 + 0.988870i \(0.547535\pi\)
\(770\) 0.661726 + 0.661726i 0.0238470 + 0.0238470i
\(771\) 17.2966 17.2966i 0.622922 0.622922i
\(772\) −17.8006 + 17.8006i −0.640658 + 0.640658i
\(773\) 26.1043i 0.938907i 0.882957 + 0.469453i \(0.155549\pi\)
−0.882957 + 0.469453i \(0.844451\pi\)
\(774\) 35.2003i 1.26525i
\(775\) −13.5281 + 13.5281i −0.485944 + 0.485944i
\(776\) −6.95973 + 6.95973i −0.249840 + 0.249840i
\(777\) 14.3987 + 14.3987i 0.516549 + 0.516549i
\(778\) −49.3833 −1.77048
\(779\) 8.30442 + 8.30442i 0.297537 + 0.297537i
\(780\) 2.14022i 0.0766320i
\(781\) −0.458740 −0.0164150
\(782\) 0 0
\(783\) 3.55438 0.127023
\(784\) 21.9463i 0.783795i
\(785\) −1.28735 1.28735i −0.0459474 0.0459474i
\(786\) −9.48515 −0.338324
\(787\) −18.9953 18.9953i −0.677109 0.677109i 0.282236 0.959345i \(-0.408924\pi\)
−0.959345 + 0.282236i \(0.908924\pi\)
\(788\) 21.9264 21.9264i 0.781097 0.781097i
\(789\) 50.0994 50.0994i 1.78359 1.78359i
\(790\) 0.940265i 0.0334531i
\(791\) 7.79292i 0.277084i
\(792\) 5.71609 5.71609i 0.203113 0.203113i
\(793\) −3.96745 + 3.96745i −0.140888 + 0.140888i
\(794\) 33.8565 + 33.8565i 1.20152 + 1.20152i
\(795\) −0.251334 −0.00891391
\(796\) −24.0236 24.0236i −0.851495 0.851495i
\(797\) 18.8212i 0.666681i 0.942807 + 0.333340i \(0.108176\pi\)
−0.942807 + 0.333340i \(0.891824\pi\)
\(798\) −13.7023 −0.485057
\(799\) 0 0
\(800\) −35.4270 −1.25253
\(801\) 51.4843i 1.81911i
\(802\) 1.19702 + 1.19702i 0.0422681 + 0.0422681i
\(803\) 31.7980 1.12213
\(804\) −40.1146 40.1146i −1.41473 1.41473i
\(805\) 0.968443 0.968443i 0.0341331 0.0341331i
\(806\) −23.3261 + 23.3261i −0.821628 + 0.821628i
\(807\) 16.8280i 0.592374i
\(808\) 6.84255i 0.240720i
\(809\) −18.2132 + 18.2132i −0.640342 + 0.640342i −0.950639 0.310298i \(-0.899571\pi\)
0.310298 + 0.950639i \(0.399571\pi\)
\(810\) −1.21759 + 1.21759i −0.0427818 + 0.0427818i
\(811\) −18.7018 18.7018i −0.656708 0.656708i 0.297891 0.954600i \(-0.403717\pi\)
−0.954600 + 0.297891i \(0.903717\pi\)
\(812\) 8.00774 0.281017
\(813\) −30.4378 30.4378i −1.06750 1.06750i
\(814\) 26.5817i 0.931689i
\(815\) −0.790555 −0.0276919
\(816\) 0 0
\(817\) −10.3182 −0.360988
\(818\) 28.8033i 1.00709i
\(819\) 16.9046 + 16.9046i 0.590695 + 0.590695i
\(820\) −1.15476 −0.0403261
\(821\) −22.2760 22.2760i −0.777437 0.777437i 0.201957 0.979394i \(-0.435270\pi\)
−0.979394 + 0.201957i \(0.935270\pi\)
\(822\) −42.4779 + 42.4779i −1.48159 + 1.48159i
\(823\) −8.26575 + 8.26575i −0.288126 + 0.288126i −0.836339 0.548213i \(-0.815308\pi\)
0.548213 + 0.836339i \(0.315308\pi\)
\(824\) 9.54993i 0.332688i
\(825\) 34.0155i 1.18427i
\(826\) −6.39905 + 6.39905i −0.222652 + 0.222652i
\(827\) 2.34946 2.34946i 0.0816989 0.0816989i −0.665076 0.746775i \(-0.731601\pi\)
0.746775 + 0.665076i \(0.231601\pi\)
\(828\) 27.3915 + 27.3915i 0.951920 + 0.951920i
\(829\) −6.01186 −0.208801 −0.104400 0.994535i \(-0.533292\pi\)
−0.104400 + 0.994535i \(0.533292\pi\)
\(830\) −0.390103 0.390103i −0.0135407 0.0135407i
\(831\) 51.0188i 1.76982i
\(832\) −17.9358 −0.621813
\(833\) 0 0
\(834\) −24.9094 −0.862542
\(835\) 0.475652i 0.0164606i
\(836\) 5.48628 + 5.48628i 0.189747 + 0.189747i
\(837\) −3.99825 −0.138200
\(838\) 3.16834 + 3.16834i 0.109448 + 0.109448i
\(839\) −29.2823 + 29.2823i −1.01094 + 1.01094i −0.0109989 + 0.999940i \(0.503501\pi\)
−0.999940 + 0.0109989i \(0.996499\pi\)
\(840\) −0.290956 + 0.290956i −0.0100389 + 0.0100389i
\(841\) 17.3618i 0.598684i
\(842\) 15.5722i 0.536654i
\(843\) 29.4941 29.4941i 1.01583 1.01583i
\(844\) −7.78656 + 7.78656i −0.268024 + 0.268024i
\(845\) 0.675586 + 0.675586i 0.0232409 + 0.0232409i
\(846\) −47.1070 −1.61957
\(847\) −4.05083 4.05083i −0.139188 0.139188i
\(848\) 3.88175i 0.133300i
\(849\) −46.7060 −1.60294
\(850\) 0 0
\(851\) −38.9026 −1.33356
\(852\) 0.660444i 0.0226265i
\(853\) −16.9693 16.9693i −0.581019 0.581019i 0.354165 0.935183i \(-0.384765\pi\)
−0.935183 + 0.354165i \(0.884765\pi\)
\(854\) −3.53209 −0.120866
\(855\) −0.546819 0.546819i −0.0187008 0.0187008i
\(856\) −7.48788 + 7.48788i −0.255930 + 0.255930i
\(857\) 22.5251 22.5251i 0.769444 0.769444i −0.208565 0.978009i \(-0.566879\pi\)
0.978009 + 0.208565i \(0.0668792\pi\)
\(858\) 58.6519i 2.00234i
\(859\) 24.0806i 0.821619i 0.911721 + 0.410810i \(0.134754\pi\)
−0.911721 + 0.410810i \(0.865246\pi\)
\(860\) 0.717394 0.717394i 0.0244629 0.0244629i
\(861\) 17.1418 17.1418i 0.584191 0.584191i
\(862\) 42.9497 + 42.9497i 1.46287 + 1.46287i
\(863\) 20.8590 0.710047 0.355024 0.934857i \(-0.384473\pi\)
0.355024 + 0.934857i \(0.384473\pi\)
\(864\) −5.23523 5.23523i −0.178106 0.178106i
\(865\) 2.28373i 0.0776491i
\(866\) 28.3114 0.962060
\(867\) 0 0
\(868\) −9.00774 −0.305743
\(869\) 11.1771i 0.379156i
\(870\) 1.38459 + 1.38459i 0.0469421 + 0.0469421i
\(871\) 66.8881 2.26642
\(872\) −4.11073 4.11073i −0.139207 0.139207i
\(873\) −26.9995 + 26.9995i −0.913794 + 0.913794i
\(874\) 18.5106 18.5106i 0.626131 0.626131i
\(875\) 1.84524i 0.0623804i
\(876\) 45.7793i 1.54674i
\(877\) 15.8158 15.8158i 0.534061 0.534061i −0.387717 0.921778i \(-0.626736\pi\)
0.921778 + 0.387717i \(0.126736\pi\)
\(878\) 3.41939 3.41939i 0.115399 0.115399i
\(879\) −19.6078 19.6078i −0.661356 0.661356i
\(880\) 1.53302 0.0516782
\(881\) −39.9005 39.9005i −1.34428 1.34428i −0.891745 0.452539i \(-0.850518\pi\)
−0.452539 0.891745i \(-0.649482\pi\)
\(882\) 29.8307i 1.00445i
\(883\) −45.4219 −1.52857 −0.764284 0.644879i \(-0.776908\pi\)
−0.764284 + 0.644879i \(0.776908\pi\)
\(884\) 0 0
\(885\) −0.959866 −0.0322655
\(886\) 44.1019i 1.48163i
\(887\) −12.3614 12.3614i −0.415055 0.415055i 0.468440 0.883495i \(-0.344816\pi\)
−0.883495 + 0.468440i \(0.844816\pi\)
\(888\) 11.6878 0.392216
\(889\) 2.38813 + 2.38813i 0.0800953 + 0.0800953i
\(890\) −2.41899 + 2.41899i −0.0810848 + 0.0810848i
\(891\) −14.4737 + 14.4737i −0.484886 + 0.484886i
\(892\) 9.22256i 0.308794i
\(893\) 13.8084i 0.462080i
\(894\) −32.4810 + 32.4810i −1.08633 + 1.08633i
\(895\) −0.618678 + 0.618678i −0.0206801 + 0.0206801i
\(896\) 7.41288 + 7.41288i 0.247647 + 0.247647i
\(897\) −85.8376 −2.86603
\(898\) −25.0609 25.0609i −0.836294 0.836294i
\(899\) 13.0915i 0.436627i
\(900\) −26.0574 −0.868579
\(901\) 0 0
\(902\) −31.6459 −1.05369
\(903\) 21.2986i 0.708773i
\(904\) 3.16286 + 3.16286i 0.105195 + 0.105195i
\(905\) −3.02734 −0.100632
\(906\) −4.06178 4.06178i −0.134944 0.134944i
\(907\) 7.36370 7.36370i 0.244508 0.244508i −0.574204 0.818712i \(-0.694689\pi\)
0.818712 + 0.574204i \(0.194689\pi\)
\(908\) 23.8717 23.8717i 0.792211 0.792211i
\(909\) 26.5449i 0.880438i
\(910\) 1.58853i 0.0526591i
\(911\) 31.3052 31.3052i 1.03719 1.03719i 0.0379051 0.999281i \(-0.487932\pi\)
0.999281 0.0379051i \(-0.0120685\pi\)
\(912\) −15.8721 + 15.8721i −0.525578 + 0.525578i
\(913\) −4.63721 4.63721i −0.153469 0.153469i
\(914\) −3.96141 −0.131032
\(915\) −0.264909 0.264909i −0.00875761 0.00875761i
\(916\) 5.66819i 0.187282i
\(917\) 3.05375 0.100844
\(918\) 0 0
\(919\) −31.0615 −1.02462 −0.512312 0.858799i \(-0.671211\pi\)
−0.512312 + 0.858799i \(0.671211\pi\)
\(920\) 0.786112i 0.0259173i
\(921\) 10.3507 + 10.3507i 0.341068 + 0.341068i
\(922\) −41.1729 −1.35596
\(923\) −0.550621 0.550621i −0.0181239 0.0181239i
\(924\) 11.3247 11.3247i 0.372554 0.372554i
\(925\) 18.5039 18.5039i 0.608405 0.608405i
\(926\) 26.6040i 0.874262i
\(927\) 37.0479i 1.21681i
\(928\) 17.1418 17.1418i 0.562707 0.562707i
\(929\) −15.8370 + 15.8370i −0.519596 + 0.519596i −0.917449 0.397853i \(-0.869755\pi\)
0.397853 + 0.917449i \(0.369755\pi\)
\(930\) −1.55750 1.55750i −0.0510725 0.0510725i
\(931\) −8.74422 −0.286580
\(932\) 31.5804 + 31.5804i 1.03445 + 1.03445i
\(933\) 0.305407i 0.00999859i
\(934\) 55.7948 1.82566
\(935\) 0 0
\(936\) 13.7219 0.448515
\(937\) 58.1661i 1.90020i −0.311939 0.950102i \(-0.600978\pi\)
0.311939 0.950102i \(-0.399022\pi\)
\(938\) 29.7741 + 29.7741i 0.972160 + 0.972160i
\(939\) −26.3063 −0.858475
\(940\) −0.960057 0.960057i −0.0313136 0.0313136i
\(941\) −7.38202 + 7.38202i −0.240647 + 0.240647i −0.817118 0.576471i \(-0.804429\pi\)
0.576471 + 0.817118i \(0.304429\pi\)
\(942\) −50.7914 + 50.7914i −1.65487 + 1.65487i
\(943\) 46.3141i 1.50819i
\(944\) 14.8247i 0.482503i
\(945\) −0.136142 + 0.136142i −0.00442869 + 0.00442869i
\(946\) 19.6599 19.6599i 0.639200 0.639200i
\(947\) −2.85929 2.85929i −0.0929144 0.0929144i 0.659122 0.752036i \(-0.270928\pi\)
−0.752036 + 0.659122i \(0.770928\pi\)
\(948\) 16.0915 0.522628
\(949\) 38.1668 + 38.1668i 1.23895 + 1.23895i
\(950\) 17.6091i 0.571313i
\(951\) 70.3961 2.28275
\(952\) 0 0
\(953\) 4.37639 0.141765 0.0708826 0.997485i \(-0.477418\pi\)
0.0708826 + 0.997485i \(0.477418\pi\)
\(954\) 5.27631i 0.170827i
\(955\) −1.20730 1.20730i −0.0390674 0.0390674i
\(956\) −19.1257 −0.618568
\(957\) 16.4588 + 16.4588i 0.532039 + 0.532039i
\(958\) 50.8924 50.8924i 1.64426 1.64426i
\(959\) 13.6758 13.6758i 0.441614 0.441614i
\(960\) 1.19759i 0.0386519i
\(961\) 16.2736i 0.524956i
\(962\) 31.9058 31.9058i 1.02868 1.02868i
\(963\) −29.0484 + 29.0484i −0.936071 + 0.936071i
\(964\) 17.5689 + 17.5689i 0.565856 + 0.565856i
\(965\) 1.98183 0.0637974
\(966\) −38.2092 38.2092i −1.22936 1.22936i
\(967\) 24.4371i 0.785843i −0.919572 0.392921i \(-0.871464\pi\)
0.919572 0.392921i \(-0.128536\pi\)
\(968\) −3.28817 −0.105686
\(969\) 0 0
\(970\) −2.53714 −0.0814627
\(971\) 20.5253i 0.658688i −0.944210 0.329344i \(-0.893172\pi\)
0.944210 0.329344i \(-0.106828\pi\)
\(972\) 24.2238 + 24.2238i 0.776979 + 0.776979i
\(973\) 8.01960 0.257097
\(974\) 31.0316 + 31.0316i 0.994318 + 0.994318i
\(975\) 40.8284 40.8284i 1.30756 1.30756i
\(976\) −4.09140 + 4.09140i −0.130962 + 0.130962i
\(977\) 28.3073i 0.905630i 0.891605 + 0.452815i \(0.149580\pi\)
−0.891605 + 0.452815i \(0.850420\pi\)
\(978\) 31.1908i 0.997371i
\(979\) −28.7548 + 28.7548i −0.919009 + 0.919009i
\(980\) 0.607960 0.607960i 0.0194206 0.0194206i
\(981\) −15.9471 15.9471i −0.509152 0.509152i
\(982\) 58.9992 1.88274
\(983\) 18.8615 + 18.8615i 0.601588 + 0.601588i 0.940734 0.339146i \(-0.110138\pi\)
−0.339146 + 0.940734i \(0.610138\pi\)
\(984\) 13.9145i 0.443577i
\(985\) −2.44118 −0.0777824
\(986\) 0 0
\(987\) 28.5030 0.907260
\(988\) 13.1702i 0.419001i
\(989\) −28.7725 28.7725i −0.914913 0.914913i
\(990\) 2.08378 0.0662268
\(991\) 24.6679 + 24.6679i 0.783602 + 0.783602i 0.980437 0.196835i \(-0.0630662\pi\)
−0.196835 + 0.980437i \(0.563066\pi\)
\(992\) −19.2825 + 19.2825i −0.612218 + 0.612218i
\(993\) 15.7173 15.7173i 0.498773 0.498773i
\(994\) 0.490200i 0.0155482i
\(995\) 2.67467i 0.0847927i
\(996\) −6.67615 + 6.67615i −0.211542 + 0.211542i
\(997\) 32.0436 32.0436i 1.01483 1.01483i 0.0149416 0.999888i \(-0.495244\pi\)
0.999888 0.0149416i \(-0.00475622\pi\)
\(998\) −21.4370 21.4370i −0.678575 0.678575i
\(999\) 5.46884 0.173027
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 289.2.c.d.251.5 12
17.2 even 8 289.2.a.d.1.1 3
17.3 odd 16 289.2.d.f.134.5 24
17.4 even 4 inner 289.2.c.d.38.1 12
17.5 odd 16 289.2.d.f.155.2 24
17.6 odd 16 289.2.d.f.179.1 24
17.7 odd 16 289.2.d.f.110.5 24
17.8 even 8 289.2.b.d.288.6 6
17.9 even 8 289.2.b.d.288.5 6
17.10 odd 16 289.2.d.f.110.6 24
17.11 odd 16 289.2.d.f.179.2 24
17.12 odd 16 289.2.d.f.155.1 24
17.13 even 4 inner 289.2.c.d.38.2 12
17.14 odd 16 289.2.d.f.134.6 24
17.15 even 8 289.2.a.e.1.1 yes 3
17.16 even 2 inner 289.2.c.d.251.6 12
51.2 odd 8 2601.2.a.x.1.3 3
51.32 odd 8 2601.2.a.w.1.3 3
68.15 odd 8 4624.2.a.bd.1.1 3
68.19 odd 8 4624.2.a.bg.1.3 3
85.19 even 8 7225.2.a.t.1.3 3
85.49 even 8 7225.2.a.s.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.2.a.d.1.1 3 17.2 even 8
289.2.a.e.1.1 yes 3 17.15 even 8
289.2.b.d.288.5 6 17.9 even 8
289.2.b.d.288.6 6 17.8 even 8
289.2.c.d.38.1 12 17.4 even 4 inner
289.2.c.d.38.2 12 17.13 even 4 inner
289.2.c.d.251.5 12 1.1 even 1 trivial
289.2.c.d.251.6 12 17.16 even 2 inner
289.2.d.f.110.5 24 17.7 odd 16
289.2.d.f.110.6 24 17.10 odd 16
289.2.d.f.134.5 24 17.3 odd 16
289.2.d.f.134.6 24 17.14 odd 16
289.2.d.f.155.1 24 17.12 odd 16
289.2.d.f.155.2 24 17.5 odd 16
289.2.d.f.179.1 24 17.6 odd 16
289.2.d.f.179.2 24 17.11 odd 16
2601.2.a.w.1.3 3 51.32 odd 8
2601.2.a.x.1.3 3 51.2 odd 8
4624.2.a.bd.1.1 3 68.15 odd 8
4624.2.a.bg.1.3 3 68.19 odd 8
7225.2.a.s.1.3 3 85.49 even 8
7225.2.a.t.1.3 3 85.19 even 8