Properties

Label 350.2.g.b.293.4
Level $350$
Weight $2$
Character 350.293
Analytic conductor $2.795$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [350,2,Mod(293,350)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(350, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("350.293");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 350.g (of order \(4\), degree \(2\), 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: \(2.79476407074\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4 x^{15} + 22 x^{14} - 52 x^{13} + 72 x^{12} - 32 x^{11} + 148 x^{10} + 268 x^{9} - 461 x^{8} - 1548 x^{7} - 840 x^{6} + 1800 x^{5} + 2772 x^{4} + 1296 x^{3} + 54 x^{2} + \cdots + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 293.4
Root \(-0.269499 - 2.04705i\) of defining polynomial
Character \(\chi\) \(=\) 350.293
Dual form 350.2.g.b.307.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(2.28737 - 2.28737i) q^{3} -1.00000i q^{4} +3.23483i q^{6} +(2.51027 - 0.835798i) q^{7} +(0.707107 + 0.707107i) q^{8} -7.46410i q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(2.28737 - 2.28737i) q^{3} -1.00000i q^{4} +3.23483i q^{6} +(2.51027 - 0.835798i) q^{7} +(0.707107 + 0.707107i) q^{8} -7.46410i q^{9} -1.73205 q^{11} +(-2.28737 - 2.28737i) q^{12} +(-1.67447 + 1.67447i) q^{13} +(-1.18403 + 2.36603i) q^{14} -1.00000 q^{16} +(3.96184 + 3.96184i) q^{17} +(5.27792 + 5.27792i) q^{18} -5.60288 q^{19} +(3.83013 - 7.65368i) q^{21} +(1.22474 - 1.22474i) q^{22} +(1.55291 + 1.55291i) q^{23} +3.23483 q^{24} -2.36806i q^{26} +(-10.2110 - 10.2110i) q^{27} +(-0.835798 - 2.51027i) q^{28} +1.26795i q^{29} -4.10160i q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.96184 + 3.96184i) q^{33} -5.60288 q^{34} -7.46410 q^{36} +(5.79555 - 5.79555i) q^{37} +(3.96184 - 3.96184i) q^{38} +7.66025i q^{39} +9.70448i q^{41} +(2.70366 + 8.12028i) q^{42} +(-2.44949 - 2.44949i) q^{43} +1.73205i q^{44} -2.19615 q^{46} +(2.90027 + 2.90027i) q^{47} +(-2.28737 + 2.28737i) q^{48} +(5.60288 - 4.19615i) q^{49} +18.1244 q^{51} +(1.67447 + 1.67447i) q^{52} +(2.68973 + 2.68973i) q^{53} +14.4406 q^{54} +(2.36603 + 1.18403i) q^{56} +(-12.8159 + 12.8159i) q^{57} +(-0.896575 - 0.896575i) q^{58} +11.2058i q^{61} +(2.90027 + 2.90027i) q^{62} +(-6.23848 - 18.7369i) q^{63} +1.00000i q^{64} -5.60288i q^{66} +(2.77766 - 2.77766i) q^{67} +(3.96184 - 3.96184i) q^{68} +7.10417 q^{69} -2.19615 q^{71} +(5.27792 - 5.27792i) q^{72} +(-5.18763 + 5.18763i) q^{73} +8.19615i q^{74} +5.60288i q^{76} +(-4.34791 + 1.44764i) q^{77} +(-5.41662 - 5.41662i) q^{78} +2.00000i q^{79} -24.3205 q^{81} +(-6.86210 - 6.86210i) q^{82} +(-6.86210 + 6.86210i) q^{83} +(-7.65368 - 3.83013i) q^{84} +3.46410 q^{86} +(2.90027 + 2.90027i) q^{87} +(-1.22474 - 1.22474i) q^{88} -9.70448 q^{89} +(-2.80385 + 5.60288i) q^{91} +(1.55291 - 1.55291i) q^{92} +(-9.38186 - 9.38186i) q^{93} -4.10160 q^{94} -3.23483i q^{96} +(3.34894 + 3.34894i) q^{97} +(-0.994709 + 6.92896i) q^{98} +12.9282i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{16} - 8 q^{21} - 64 q^{36} + 48 q^{46} + 96 q^{51} + 24 q^{56} + 48 q^{71} - 112 q^{81} - 128 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) 2.28737 2.28737i 1.32061 1.32061i 0.407332 0.913280i \(-0.366459\pi\)
0.913280 0.407332i \(-0.133541\pi\)
\(4\) 1.00000i 0.500000i
\(5\) 0 0
\(6\) 3.23483i 1.32061i
\(7\) 2.51027 0.835798i 0.948792 0.315902i
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 7.46410i 2.48803i
\(10\) 0 0
\(11\) −1.73205 −0.522233 −0.261116 0.965307i \(-0.584091\pi\)
−0.261116 + 0.965307i \(0.584091\pi\)
\(12\) −2.28737 2.28737i −0.660306 0.660306i
\(13\) −1.67447 + 1.67447i −0.464414 + 0.464414i −0.900099 0.435685i \(-0.856506\pi\)
0.435685 + 0.900099i \(0.356506\pi\)
\(14\) −1.18403 + 2.36603i −0.316445 + 0.632347i
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 3.96184 + 3.96184i 0.960887 + 0.960887i 0.999263 0.0383767i \(-0.0122187\pi\)
−0.0383767 + 0.999263i \(0.512219\pi\)
\(18\) 5.27792 + 5.27792i 1.24402 + 1.24402i
\(19\) −5.60288 −1.28539 −0.642695 0.766122i \(-0.722184\pi\)
−0.642695 + 0.766122i \(0.722184\pi\)
\(20\) 0 0
\(21\) 3.83013 7.65368i 0.835802 1.67017i
\(22\) 1.22474 1.22474i 0.261116 0.261116i
\(23\) 1.55291 + 1.55291i 0.323805 + 0.323805i 0.850225 0.526420i \(-0.176466\pi\)
−0.526420 + 0.850225i \(0.676466\pi\)
\(24\) 3.23483 0.660306
\(25\) 0 0
\(26\) 2.36806i 0.464414i
\(27\) −10.2110 10.2110i −1.96512 1.96512i
\(28\) −0.835798 2.51027i −0.157951 0.474396i
\(29\) 1.26795i 0.235452i 0.993046 + 0.117726i \(0.0375605\pi\)
−0.993046 + 0.117726i \(0.962440\pi\)
\(30\) 0 0
\(31\) 4.10160i 0.736668i −0.929693 0.368334i \(-0.879928\pi\)
0.929693 0.368334i \(-0.120072\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −3.96184 + 3.96184i −0.689667 + 0.689667i
\(34\) −5.60288 −0.960887
\(35\) 0 0
\(36\) −7.46410 −1.24402
\(37\) 5.79555 5.79555i 0.952783 0.952783i −0.0461511 0.998934i \(-0.514696\pi\)
0.998934 + 0.0461511i \(0.0146956\pi\)
\(38\) 3.96184 3.96184i 0.642695 0.642695i
\(39\) 7.66025i 1.22662i
\(40\) 0 0
\(41\) 9.70448i 1.51559i 0.652496 + 0.757793i \(0.273722\pi\)
−0.652496 + 0.757793i \(0.726278\pi\)
\(42\) 2.70366 + 8.12028i 0.417184 + 1.25299i
\(43\) −2.44949 2.44949i −0.373544 0.373544i 0.495222 0.868766i \(-0.335087\pi\)
−0.868766 + 0.495222i \(0.835087\pi\)
\(44\) 1.73205i 0.261116i
\(45\) 0 0
\(46\) −2.19615 −0.323805
\(47\) 2.90027 + 2.90027i 0.423047 + 0.423047i 0.886252 0.463204i \(-0.153300\pi\)
−0.463204 + 0.886252i \(0.653300\pi\)
\(48\) −2.28737 + 2.28737i −0.330153 + 0.330153i
\(49\) 5.60288 4.19615i 0.800412 0.599450i
\(50\) 0 0
\(51\) 18.1244 2.53792
\(52\) 1.67447 + 1.67447i 0.232207 + 0.232207i
\(53\) 2.68973 + 2.68973i 0.369462 + 0.369462i 0.867281 0.497819i \(-0.165866\pi\)
−0.497819 + 0.867281i \(0.665866\pi\)
\(54\) 14.4406 1.96512
\(55\) 0 0
\(56\) 2.36603 + 1.18403i 0.316173 + 0.158222i
\(57\) −12.8159 + 12.8159i −1.69750 + 1.69750i
\(58\) −0.896575 0.896575i −0.117726 0.117726i
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 11.2058i 1.43475i 0.696686 + 0.717376i \(0.254657\pi\)
−0.696686 + 0.717376i \(0.745343\pi\)
\(62\) 2.90027 + 2.90027i 0.368334 + 0.368334i
\(63\) −6.23848 18.7369i −0.785975 2.36063i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 5.60288i 0.689667i
\(67\) 2.77766 2.77766i 0.339345 0.339345i −0.516776 0.856121i \(-0.672868\pi\)
0.856121 + 0.516776i \(0.172868\pi\)
\(68\) 3.96184 3.96184i 0.480443 0.480443i
\(69\) 7.10417 0.855242
\(70\) 0 0
\(71\) −2.19615 −0.260635 −0.130318 0.991472i \(-0.541600\pi\)
−0.130318 + 0.991472i \(0.541600\pi\)
\(72\) 5.27792 5.27792i 0.622008 0.622008i
\(73\) −5.18763 + 5.18763i −0.607167 + 0.607167i −0.942205 0.335038i \(-0.891251\pi\)
0.335038 + 0.942205i \(0.391251\pi\)
\(74\) 8.19615i 0.952783i
\(75\) 0 0
\(76\) 5.60288i 0.642695i
\(77\) −4.34791 + 1.44764i −0.495490 + 0.164974i
\(78\) −5.41662 5.41662i −0.613311 0.613311i
\(79\) 2.00000i 0.225018i 0.993651 + 0.112509i \(0.0358886\pi\)
−0.993651 + 0.112509i \(0.964111\pi\)
\(80\) 0 0
\(81\) −24.3205 −2.70228
\(82\) −6.86210 6.86210i −0.757793 0.757793i
\(83\) −6.86210 + 6.86210i −0.753214 + 0.753214i −0.975078 0.221864i \(-0.928786\pi\)
0.221864 + 0.975078i \(0.428786\pi\)
\(84\) −7.65368 3.83013i −0.835085 0.417901i
\(85\) 0 0
\(86\) 3.46410 0.373544
\(87\) 2.90027 + 2.90027i 0.310941 + 0.310941i
\(88\) −1.22474 1.22474i −0.130558 0.130558i
\(89\) −9.70448 −1.02867 −0.514336 0.857589i \(-0.671962\pi\)
−0.514336 + 0.857589i \(0.671962\pi\)
\(90\) 0 0
\(91\) −2.80385 + 5.60288i −0.293923 + 0.587342i
\(92\) 1.55291 1.55291i 0.161903 0.161903i
\(93\) −9.38186 9.38186i −0.972853 0.972853i
\(94\) −4.10160 −0.423047
\(95\) 0 0
\(96\) 3.23483i 0.330153i
\(97\) 3.34894 + 3.34894i 0.340033 + 0.340033i 0.856380 0.516347i \(-0.172708\pi\)
−0.516347 + 0.856380i \(0.672708\pi\)
\(98\) −0.994709 + 6.92896i −0.100481 + 0.699931i
\(99\) 12.9282i 1.29933i
\(100\) 0 0
\(101\) 7.10417i 0.706892i −0.935455 0.353446i \(-0.885010\pi\)
0.935455 0.353446i \(-0.114990\pi\)
\(102\) −12.8159 + 12.8159i −1.26896 + 1.26896i
\(103\) 3.34894 3.34894i 0.329981 0.329981i −0.522598 0.852579i \(-0.675037\pi\)
0.852579 + 0.522598i \(0.175037\pi\)
\(104\) −2.36806 −0.232207
\(105\) 0 0
\(106\) −3.80385 −0.369462
\(107\) −9.46979 + 9.46979i −0.915479 + 0.915479i −0.996696 0.0812173i \(-0.974119\pi\)
0.0812173 + 0.996696i \(0.474119\pi\)
\(108\) −10.2110 + 10.2110i −0.982558 + 0.982558i
\(109\) 2.00000i 0.191565i −0.995402 0.0957826i \(-0.969465\pi\)
0.995402 0.0957826i \(-0.0305354\pi\)
\(110\) 0 0
\(111\) 26.5131i 2.51651i
\(112\) −2.51027 + 0.835798i −0.237198 + 0.0789755i
\(113\) 7.91688 + 7.91688i 0.744757 + 0.744757i 0.973489 0.228732i \(-0.0734581\pi\)
−0.228732 + 0.973489i \(0.573458\pi\)
\(114\) 18.1244i 1.69750i
\(115\) 0 0
\(116\) 1.26795 0.117726
\(117\) 12.4984 + 12.4984i 1.15548 + 1.15548i
\(118\) 0 0
\(119\) 13.2566 + 6.63397i 1.21523 + 0.608135i
\(120\) 0 0
\(121\) −8.00000 −0.727273
\(122\) −7.92367 7.92367i −0.717376 0.717376i
\(123\) 22.1977 + 22.1977i 2.00150 + 2.00150i
\(124\) −4.10160 −0.368334
\(125\) 0 0
\(126\) 17.6603 + 8.83771i 1.57330 + 0.787326i
\(127\) 12.7279 12.7279i 1.12942 1.12942i 0.139149 0.990271i \(-0.455563\pi\)
0.990271 0.139149i \(-0.0444367\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −11.2058 −0.986613
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 3.96184 + 3.96184i 0.344834 + 0.344834i
\(133\) −14.0647 + 4.68288i −1.21957 + 0.406057i
\(134\) 3.92820i 0.339345i
\(135\) 0 0
\(136\) 5.60288i 0.480443i
\(137\) −0.568406 + 0.568406i −0.0485622 + 0.0485622i −0.730971 0.682409i \(-0.760932\pi\)
0.682409 + 0.730971i \(0.260932\pi\)
\(138\) −5.02341 + 5.02341i −0.427621 + 0.427621i
\(139\) 2.60031 0.220555 0.110278 0.993901i \(-0.464826\pi\)
0.110278 + 0.993901i \(0.464826\pi\)
\(140\) 0 0
\(141\) 13.2679 1.11736
\(142\) 1.55291 1.55291i 0.130318 0.130318i
\(143\) 2.90027 2.90027i 0.242532 0.242532i
\(144\) 7.46410i 0.622008i
\(145\) 0 0
\(146\) 7.33642i 0.607167i
\(147\) 3.21771 22.4140i 0.265392 1.84868i
\(148\) −5.79555 5.79555i −0.476392 0.476392i
\(149\) 16.3923i 1.34291i −0.741045 0.671455i \(-0.765670\pi\)
0.741045 0.671455i \(-0.234330\pi\)
\(150\) 0 0
\(151\) −16.5885 −1.34995 −0.674975 0.737841i \(-0.735845\pi\)
−0.674975 + 0.737841i \(0.735845\pi\)
\(152\) −3.96184 3.96184i −0.321347 0.321347i
\(153\) 29.5716 29.5716i 2.39072 2.39072i
\(154\) 2.05080 4.09808i 0.165258 0.330232i
\(155\) 0 0
\(156\) 7.66025 0.613311
\(157\) −15.3987 15.3987i −1.22895 1.22895i −0.964362 0.264586i \(-0.914765\pi\)
−0.264586 0.964362i \(-0.585235\pi\)
\(158\) −1.41421 1.41421i −0.112509 0.112509i
\(159\) 12.3048 0.975833
\(160\) 0 0
\(161\) 5.19615 + 2.60031i 0.409514 + 0.204933i
\(162\) 17.1972 17.1972i 1.35114 1.35114i
\(163\) −2.77766 2.77766i −0.217563 0.217563i 0.589908 0.807471i \(-0.299164\pi\)
−0.807471 + 0.589908i \(0.799164\pi\)
\(164\) 9.70448 0.757793
\(165\) 0 0
\(166\) 9.70448i 0.753214i
\(167\) 15.8473 + 15.8473i 1.22630 + 1.22630i 0.965351 + 0.260953i \(0.0840368\pi\)
0.260953 + 0.965351i \(0.415963\pi\)
\(168\) 8.12028 2.70366i 0.626493 0.208592i
\(169\) 7.39230i 0.568639i
\(170\) 0 0
\(171\) 41.8205i 3.19809i
\(172\) −2.44949 + 2.44949i −0.186772 + 0.186772i
\(173\) 10.8239 10.8239i 0.822929 0.822929i −0.163598 0.986527i \(-0.552310\pi\)
0.986527 + 0.163598i \(0.0523100\pi\)
\(174\) −4.10160 −0.310941
\(175\) 0 0
\(176\) 1.73205 0.130558
\(177\) 0 0
\(178\) 6.86210 6.86210i 0.514336 0.514336i
\(179\) 6.80385i 0.508543i −0.967133 0.254272i \(-0.918164\pi\)
0.967133 0.254272i \(-0.0818358\pi\)
\(180\) 0 0
\(181\) 3.00258i 0.223180i 0.993754 + 0.111590i \(0.0355943\pi\)
−0.993754 + 0.111590i \(0.964406\pi\)
\(182\) −1.97922 5.94446i −0.146709 0.440632i
\(183\) 25.6317 + 25.6317i 1.89475 + 1.89475i
\(184\) 2.19615i 0.161903i
\(185\) 0 0
\(186\) 13.2679 0.972853
\(187\) −6.86210 6.86210i −0.501807 0.501807i
\(188\) 2.90027 2.90027i 0.211524 0.211524i
\(189\) −34.1668 17.0981i −2.48527 1.24370i
\(190\) 0 0
\(191\) 12.9282 0.935452 0.467726 0.883874i \(-0.345073\pi\)
0.467726 + 0.883874i \(0.345073\pi\)
\(192\) 2.28737 + 2.28737i 0.165077 + 0.165077i
\(193\) −4.33057 4.33057i −0.311721 0.311721i 0.533855 0.845576i \(-0.320743\pi\)
−0.845576 + 0.533855i \(0.820743\pi\)
\(194\) −4.73611 −0.340033
\(195\) 0 0
\(196\) −4.19615 5.60288i −0.299725 0.400206i
\(197\) −15.8338 + 15.8338i −1.12811 + 1.12811i −0.137623 + 0.990485i \(0.543946\pi\)
−0.990485 + 0.137623i \(0.956054\pi\)
\(198\) −9.14162 9.14162i −0.649667 0.649667i
\(199\) 15.3074 1.08511 0.542555 0.840020i \(-0.317457\pi\)
0.542555 + 0.840020i \(0.317457\pi\)
\(200\) 0 0
\(201\) 12.7071i 0.896287i
\(202\) 5.02341 + 5.02341i 0.353446 + 0.353446i
\(203\) 1.05975 + 3.18289i 0.0743798 + 0.223395i
\(204\) 18.1244i 1.26896i
\(205\) 0 0
\(206\) 4.73611i 0.329981i
\(207\) 11.5911 11.5911i 0.805638 0.805638i
\(208\) 1.67447 1.67447i 0.116104 0.116104i
\(209\) 9.70448 0.671273
\(210\) 0 0
\(211\) 9.19615 0.633089 0.316545 0.948578i \(-0.397477\pi\)
0.316545 + 0.948578i \(0.397477\pi\)
\(212\) 2.68973 2.68973i 0.184731 0.184731i
\(213\) −5.02341 + 5.02341i −0.344198 + 0.344198i
\(214\) 13.3923i 0.915479i
\(215\) 0 0
\(216\) 14.4406i 0.982558i
\(217\) −3.42811 10.2961i −0.232715 0.698945i
\(218\) 1.41421 + 1.41421i 0.0957826 + 0.0957826i
\(219\) 23.7321i 1.60366i
\(220\) 0 0
\(221\) −13.2679 −0.892499
\(222\) 18.7476 + 18.7476i 1.25826 + 1.25826i
\(223\) −12.0497 + 12.0497i −0.806910 + 0.806910i −0.984165 0.177255i \(-0.943278\pi\)
0.177255 + 0.984165i \(0.443278\pi\)
\(224\) 1.18403 2.36603i 0.0791112 0.158087i
\(225\) 0 0
\(226\) −11.1962 −0.744757
\(227\) −7.92367 7.92367i −0.525913 0.525913i 0.393438 0.919351i \(-0.371285\pi\)
−0.919351 + 0.393438i \(0.871285\pi\)
\(228\) 12.8159 + 12.8159i 0.848751 + 0.848751i
\(229\) −4.10160 −0.271041 −0.135521 0.990775i \(-0.543271\pi\)
−0.135521 + 0.990775i \(0.543271\pi\)
\(230\) 0 0
\(231\) −6.63397 + 13.2566i −0.436483 + 0.872218i
\(232\) −0.896575 + 0.896575i −0.0588631 + 0.0588631i
\(233\) 7.34847 + 7.34847i 0.481414 + 0.481414i 0.905583 0.424169i \(-0.139434\pi\)
−0.424169 + 0.905583i \(0.639434\pi\)
\(234\) −17.6754 −1.15548
\(235\) 0 0
\(236\) 0 0
\(237\) 4.57474 + 4.57474i 0.297161 + 0.297161i
\(238\) −14.0647 + 4.68288i −0.911681 + 0.303546i
\(239\) 25.8564i 1.67251i −0.548339 0.836256i \(-0.684740\pi\)
0.548339 0.836256i \(-0.315260\pi\)
\(240\) 0 0
\(241\) 1.50129i 0.0967065i −0.998830 0.0483532i \(-0.984603\pi\)
0.998830 0.0483532i \(-0.0153973\pi\)
\(242\) 5.65685 5.65685i 0.363636 0.363636i
\(243\) −24.9968 + 24.9968i −1.60355 + 1.60355i
\(244\) 11.2058 0.717376
\(245\) 0 0
\(246\) −31.3923 −2.00150
\(247\) 9.38186 9.38186i 0.596953 0.596953i
\(248\) 2.90027 2.90027i 0.184167 0.184167i
\(249\) 31.3923i 1.98941i
\(250\) 0 0
\(251\) 16.8087i 1.06095i −0.847700 0.530476i \(-0.822013\pi\)
0.847700 0.530476i \(-0.177987\pi\)
\(252\) −18.7369 + 6.23848i −1.18031 + 0.392987i
\(253\) −2.68973 2.68973i −0.169102 0.169102i
\(254\) 18.0000i 1.12942i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −13.7242 13.7242i −0.856092 0.856092i 0.134783 0.990875i \(-0.456966\pi\)
−0.990875 + 0.134783i \(0.956966\pi\)
\(258\) 7.92367 7.92367i 0.493306 0.493306i
\(259\) 9.70448 19.3923i 0.603007 1.20498i
\(260\) 0 0
\(261\) 9.46410 0.585813
\(262\) 0 0
\(263\) −15.8338 15.8338i −0.976351 0.976351i 0.0233759 0.999727i \(-0.492559\pi\)
−0.999727 + 0.0233759i \(0.992559\pi\)
\(264\) −5.60288 −0.344834
\(265\) 0 0
\(266\) 6.63397 13.2566i 0.406755 0.812812i
\(267\) −22.1977 + 22.1977i −1.35848 + 1.35848i
\(268\) −2.77766 2.77766i −0.169673 0.169673i
\(269\) −12.3048 −0.750236 −0.375118 0.926977i \(-0.622398\pi\)
−0.375118 + 0.926977i \(0.622398\pi\)
\(270\) 0 0
\(271\) 19.4090i 1.17901i −0.807765 0.589505i \(-0.799323\pi\)
0.807765 0.589505i \(-0.200677\pi\)
\(272\) −3.96184 3.96184i −0.240222 0.240222i
\(273\) 6.40242 + 19.2293i 0.387492 + 1.16381i
\(274\) 0.803848i 0.0485622i
\(275\) 0 0
\(276\) 7.10417i 0.427621i
\(277\) −14.9372 + 14.9372i −0.897488 + 0.897488i −0.995213 0.0977255i \(-0.968843\pi\)
0.0977255 + 0.995213i \(0.468843\pi\)
\(278\) −1.83869 + 1.83869i −0.110278 + 0.110278i
\(279\) −30.6147 −1.83286
\(280\) 0 0
\(281\) −13.8564 −0.826604 −0.413302 0.910594i \(-0.635625\pi\)
−0.413302 + 0.910594i \(0.635625\pi\)
\(282\) −9.38186 + 9.38186i −0.558681 + 0.558681i
\(283\) 10.2110 10.2110i 0.606983 0.606983i −0.335173 0.942157i \(-0.608795\pi\)
0.942157 + 0.335173i \(0.108795\pi\)
\(284\) 2.19615i 0.130318i
\(285\) 0 0
\(286\) 4.10160i 0.242532i
\(287\) 8.11098 + 24.3608i 0.478776 + 1.43797i
\(288\) −5.27792 5.27792i −0.311004 0.311004i
\(289\) 14.3923i 0.846606i
\(290\) 0 0
\(291\) 15.3205 0.898104
\(292\) 5.18763 + 5.18763i 0.303583 + 0.303583i
\(293\) −2.12314 + 2.12314i −0.124035 + 0.124035i −0.766400 0.642364i \(-0.777954\pi\)
0.642364 + 0.766400i \(0.277954\pi\)
\(294\) 13.5738 + 18.1244i 0.791642 + 1.05703i
\(295\) 0 0
\(296\) 8.19615 0.476392
\(297\) 17.6860 + 17.6860i 1.02625 + 1.02625i
\(298\) 11.5911 + 11.5911i 0.671455 + 0.671455i
\(299\) −5.20061 −0.300759
\(300\) 0 0
\(301\) −8.19615 4.10160i −0.472418 0.236412i
\(302\) 11.7298 11.7298i 0.674975 0.674975i
\(303\) −16.2499 16.2499i −0.933530 0.933530i
\(304\) 5.60288 0.321347
\(305\) 0 0
\(306\) 41.8205i 2.39072i
\(307\) 3.51316 + 3.51316i 0.200507 + 0.200507i 0.800217 0.599710i \(-0.204718\pi\)
−0.599710 + 0.800217i \(0.704718\pi\)
\(308\) 1.44764 + 4.34791i 0.0824872 + 0.247745i
\(309\) 15.3205i 0.871553i
\(310\) 0 0
\(311\) 19.4090i 1.10058i −0.834973 0.550291i \(-0.814517\pi\)
0.834973 0.550291i \(-0.185483\pi\)
\(312\) −5.41662 + 5.41662i −0.306656 + 0.306656i
\(313\) 20.4221 20.4221i 1.15432 1.15432i 0.168648 0.985676i \(-0.446060\pi\)
0.985676 0.168648i \(-0.0539401\pi\)
\(314\) 21.7770 1.22895
\(315\) 0 0
\(316\) 2.00000 0.112509
\(317\) −11.5911 + 11.5911i −0.651022 + 0.651022i −0.953239 0.302217i \(-0.902273\pi\)
0.302217 + 0.953239i \(0.402273\pi\)
\(318\) −8.70080 + 8.70080i −0.487917 + 0.487917i
\(319\) 2.19615i 0.122961i
\(320\) 0 0
\(321\) 43.3218i 2.41799i
\(322\) −5.51293 + 1.83554i −0.307224 + 0.102291i
\(323\) −22.1977 22.1977i −1.23511 1.23511i
\(324\) 24.3205i 1.35114i
\(325\) 0 0
\(326\) 3.92820 0.217563
\(327\) −4.57474 4.57474i −0.252983 0.252983i
\(328\) −6.86210 + 6.86210i −0.378896 + 0.378896i
\(329\) 9.70448 + 4.85641i 0.535025 + 0.267742i
\(330\) 0 0
\(331\) −23.5885 −1.29654 −0.648269 0.761411i \(-0.724507\pi\)
−0.648269 + 0.761411i \(0.724507\pi\)
\(332\) 6.86210 + 6.86210i 0.376607 + 0.376607i
\(333\) −43.2586 43.2586i −2.37056 2.37056i
\(334\) −22.4115 −1.22630
\(335\) 0 0
\(336\) −3.83013 + 7.65368i −0.208951 + 0.417543i
\(337\) 18.1953 18.1953i 0.991162 0.991162i −0.00879972 0.999961i \(-0.502801\pi\)
0.999961 + 0.00879972i \(0.00280107\pi\)
\(338\) −5.22715 5.22715i −0.284319 0.284319i
\(339\) 36.2176 1.96707
\(340\) 0 0
\(341\) 7.10417i 0.384712i
\(342\) −29.5716 29.5716i −1.59905 1.59905i
\(343\) 10.5576 15.2163i 0.570057 0.821605i
\(344\) 3.46410i 0.186772i
\(345\) 0 0
\(346\) 15.3074i 0.822929i
\(347\) 21.0609 21.0609i 1.13061 1.13061i 0.140532 0.990076i \(-0.455119\pi\)
0.990076 0.140532i \(-0.0448814\pi\)
\(348\) 2.90027 2.90027i 0.155471 0.155471i
\(349\) 7.10417 0.380278 0.190139 0.981757i \(-0.439106\pi\)
0.190139 + 0.981757i \(0.439106\pi\)
\(350\) 0 0
\(351\) 34.1962 1.82526
\(352\) −1.22474 + 1.22474i −0.0652791 + 0.0652791i
\(353\) −19.5247 + 19.5247i −1.03920 + 1.03920i −0.0399971 + 0.999200i \(0.512735\pi\)
−0.999200 + 0.0399971i \(0.987265\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 9.70448i 0.514336i
\(357\) 45.4970 15.1483i 2.40796 0.801733i
\(358\) 4.81105 + 4.81105i 0.254272 + 0.254272i
\(359\) 10.3923i 0.548485i −0.961661 0.274242i \(-0.911573\pi\)
0.961661 0.274242i \(-0.0884271\pi\)
\(360\) 0 0
\(361\) 12.3923 0.652227
\(362\) −2.12314 2.12314i −0.111590 0.111590i
\(363\) −18.2989 + 18.2989i −0.960445 + 0.960445i
\(364\) 5.60288 + 2.80385i 0.293671 + 0.146962i
\(365\) 0 0
\(366\) −36.2487 −1.89475
\(367\) 3.34894 + 3.34894i 0.174813 + 0.174813i 0.789090 0.614277i \(-0.210552\pi\)
−0.614277 + 0.789090i \(0.710552\pi\)
\(368\) −1.55291 1.55291i −0.0809513 0.0809513i
\(369\) 72.4352 3.77083
\(370\) 0 0
\(371\) 9.00000 + 4.50386i 0.467257 + 0.233829i
\(372\) −9.38186 + 9.38186i −0.486427 + 0.486427i
\(373\) 9.38186 + 9.38186i 0.485774 + 0.485774i 0.906970 0.421196i \(-0.138389\pi\)
−0.421196 + 0.906970i \(0.638389\pi\)
\(374\) 9.70448 0.501807
\(375\) 0 0
\(376\) 4.10160i 0.211524i
\(377\) −2.12314 2.12314i −0.109347 0.109347i
\(378\) 36.2497 12.0694i 1.86449 0.620784i
\(379\) 33.9808i 1.74547i 0.488190 + 0.872737i \(0.337657\pi\)
−0.488190 + 0.872737i \(0.662343\pi\)
\(380\) 0 0
\(381\) 58.2269i 2.98305i
\(382\) −9.14162 + 9.14162i −0.467726 + 0.467726i
\(383\) 13.7242 13.7242i 0.701274 0.701274i −0.263410 0.964684i \(-0.584847\pi\)
0.964684 + 0.263410i \(0.0848472\pi\)
\(384\) −3.23483 −0.165077
\(385\) 0 0
\(386\) 6.12436 0.311721
\(387\) −18.2832 + 18.2832i −0.929389 + 0.929389i
\(388\) 3.34894 3.34894i 0.170017 0.170017i
\(389\) 0.339746i 0.0172258i 0.999963 + 0.00861290i \(0.00274161\pi\)
−0.999963 + 0.00861290i \(0.997258\pi\)
\(390\) 0 0
\(391\) 12.3048i 0.622280i
\(392\) 6.92896 + 0.994709i 0.349966 + 0.0502404i
\(393\) 0 0
\(394\) 22.3923i 1.12811i
\(395\) 0 0
\(396\) 12.9282 0.649667
\(397\) −8.37235 8.37235i −0.420196 0.420196i 0.465075 0.885271i \(-0.346027\pi\)
−0.885271 + 0.465075i \(0.846027\pi\)
\(398\) −10.8239 + 10.8239i −0.542555 + 0.542555i
\(399\) −21.4598 + 42.8827i −1.07433 + 2.14682i
\(400\) 0 0
\(401\) 14.0718 0.702712 0.351356 0.936242i \(-0.385721\pi\)
0.351356 + 0.936242i \(0.385721\pi\)
\(402\) 8.98525 + 8.98525i 0.448143 + 0.448143i
\(403\) 6.86800 + 6.86800i 0.342119 + 0.342119i
\(404\) −7.10417 −0.353446
\(405\) 0 0
\(406\) −3.00000 1.50129i −0.148888 0.0745077i
\(407\) −10.0382 + 10.0382i −0.497575 + 0.497575i
\(408\) 12.8159 + 12.8159i 0.634479 + 0.634479i
\(409\) −35.1186 −1.73650 −0.868251 0.496125i \(-0.834756\pi\)
−0.868251 + 0.496125i \(0.834756\pi\)
\(410\) 0 0
\(411\) 2.60031i 0.128264i
\(412\) −3.34894 3.34894i −0.164990 0.164990i
\(413\) 0 0
\(414\) 16.3923i 0.805638i
\(415\) 0 0
\(416\) 2.36806i 0.116104i
\(417\) 5.94786 5.94786i 0.291268 0.291268i
\(418\) −6.86210 + 6.86210i −0.335636 + 0.335636i
\(419\) −36.2176 −1.76935 −0.884673 0.466212i \(-0.845618\pi\)
−0.884673 + 0.466212i \(0.845618\pi\)
\(420\) 0 0
\(421\) 29.1769 1.42200 0.710998 0.703194i \(-0.248244\pi\)
0.710998 + 0.703194i \(0.248244\pi\)
\(422\) −6.50266 + 6.50266i −0.316545 + 0.316545i
\(423\) 21.6479 21.6479i 1.05256 1.05256i
\(424\) 3.80385i 0.184731i
\(425\) 0 0
\(426\) 7.10417i 0.344198i
\(427\) 9.36576 + 28.1295i 0.453241 + 1.36128i
\(428\) 9.46979 + 9.46979i 0.457740 + 0.457740i
\(429\) 13.2679i 0.640583i
\(430\) 0 0
\(431\) 7.51666 0.362065 0.181032 0.983477i \(-0.442056\pi\)
0.181032 + 0.983477i \(0.442056\pi\)
\(432\) 10.2110 + 10.2110i 0.491279 + 0.491279i
\(433\) −15.2344 + 15.2344i −0.732121 + 0.732121i −0.971040 0.238919i \(-0.923207\pi\)
0.238919 + 0.971040i \(0.423207\pi\)
\(434\) 9.70448 + 4.85641i 0.465830 + 0.233115i
\(435\) 0 0
\(436\) −2.00000 −0.0957826
\(437\) −8.70080 8.70080i −0.416216 0.416216i
\(438\) −16.7811 16.7811i −0.801832 0.801832i
\(439\) −8.20319 −0.391517 −0.195758 0.980652i \(-0.562717\pi\)
−0.195758 + 0.980652i \(0.562717\pi\)
\(440\) 0 0
\(441\) −31.3205 41.8205i −1.49145 1.99145i
\(442\) 9.38186 9.38186i 0.446249 0.446249i
\(443\) −10.6066 10.6066i −0.503935 0.503935i 0.408723 0.912658i \(-0.365974\pi\)
−0.912658 + 0.408723i \(0.865974\pi\)
\(444\) −26.5131 −1.25826
\(445\) 0 0
\(446\) 17.0409i 0.806910i
\(447\) −37.4952 37.4952i −1.77346 1.77346i
\(448\) 0.835798 + 2.51027i 0.0394877 + 0.118599i
\(449\) 1.14359i 0.0539695i 0.999636 + 0.0269848i \(0.00859056\pi\)
−0.999636 + 0.0269848i \(0.991409\pi\)
\(450\) 0 0
\(451\) 16.8087i 0.791488i
\(452\) 7.91688 7.91688i 0.372378 0.372378i
\(453\) −37.9439 + 37.9439i −1.78276 + 1.78276i
\(454\) 11.2058 0.525913
\(455\) 0 0
\(456\) −18.1244 −0.848751
\(457\) −9.05369 + 9.05369i −0.423514 + 0.423514i −0.886412 0.462898i \(-0.846810\pi\)
0.462898 + 0.886412i \(0.346810\pi\)
\(458\) 2.90027 2.90027i 0.135521 0.135521i
\(459\) 80.9090i 3.77651i
\(460\) 0 0
\(461\) 26.5131i 1.23484i 0.786634 + 0.617420i \(0.211822\pi\)
−0.786634 + 0.617420i \(0.788178\pi\)
\(462\) −4.68288 14.0647i −0.217867 0.654351i
\(463\) 26.2880 + 26.2880i 1.22171 + 1.22171i 0.967024 + 0.254685i \(0.0819718\pi\)
0.254685 + 0.967024i \(0.418028\pi\)
\(464\) 1.26795i 0.0588631i
\(465\) 0 0
\(466\) −10.3923 −0.481414
\(467\) −5.80053 5.80053i −0.268417 0.268417i 0.560045 0.828462i \(-0.310784\pi\)
−0.828462 + 0.560045i \(0.810784\pi\)
\(468\) 12.4984 12.4984i 0.577739 0.577739i
\(469\) 4.65111 9.29423i 0.214768 0.429168i
\(470\) 0 0
\(471\) −70.4449 −3.24593
\(472\) 0 0
\(473\) 4.24264 + 4.24264i 0.195077 + 0.195077i
\(474\) −6.46965 −0.297161
\(475\) 0 0
\(476\) 6.63397 13.2566i 0.304068 0.607614i
\(477\) 20.0764 20.0764i 0.919235 0.919235i
\(478\) 18.2832 + 18.2832i 0.836256 + 0.836256i
\(479\) −19.4090 −0.886818 −0.443409 0.896319i \(-0.646231\pi\)
−0.443409 + 0.896319i \(0.646231\pi\)
\(480\) 0 0
\(481\) 19.4090i 0.884972i
\(482\) 1.06157 + 1.06157i 0.0483532 + 0.0483532i
\(483\) 17.8334 5.93765i 0.811446 0.270173i
\(484\) 8.00000i 0.363636i
\(485\) 0 0
\(486\) 35.3508i 1.60355i
\(487\) −14.5211 + 14.5211i −0.658013 + 0.658013i −0.954910 0.296897i \(-0.904048\pi\)
0.296897 + 0.954910i \(0.404048\pi\)
\(488\) −7.92367 + 7.92367i −0.358688 + 0.358688i
\(489\) −12.7071 −0.574633
\(490\) 0 0
\(491\) −18.9282 −0.854218 −0.427109 0.904200i \(-0.640468\pi\)
−0.427109 + 0.904200i \(0.640468\pi\)
\(492\) 22.1977 22.1977i 1.00075 1.00075i
\(493\) −5.02341 + 5.02341i −0.226243 + 0.226243i
\(494\) 13.2679i 0.596953i
\(495\) 0 0
\(496\) 4.10160i 0.184167i
\(497\) −5.51293 + 1.83554i −0.247289 + 0.0823352i
\(498\) −22.1977 22.1977i −0.994703 0.994703i
\(499\) 24.7846i 1.10951i 0.832013 + 0.554756i \(0.187188\pi\)
−0.832013 + 0.554756i \(0.812812\pi\)
\(500\) 0 0
\(501\) 72.4974 3.23895
\(502\) 11.8855 + 11.8855i 0.530476 + 0.530476i
\(503\) −12.9471 + 12.9471i −0.577282 + 0.577282i −0.934153 0.356872i \(-0.883843\pi\)
0.356872 + 0.934153i \(0.383843\pi\)
\(504\) 8.83771 17.6603i 0.393663 0.786650i
\(505\) 0 0
\(506\) 3.80385 0.169102
\(507\) 16.9089 + 16.9089i 0.750951 + 0.750951i
\(508\) −12.7279 12.7279i −0.564710 0.564710i
\(509\) −33.6173 −1.49006 −0.745030 0.667031i \(-0.767565\pi\)
−0.745030 + 0.667031i \(0.767565\pi\)
\(510\) 0 0
\(511\) −8.68653 + 17.3582i −0.384270 + 0.767880i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 57.2113 + 57.2113i 2.52594 + 2.52594i
\(514\) 19.4090 0.856092
\(515\) 0 0
\(516\) 11.2058i 0.493306i
\(517\) −5.02341 5.02341i −0.220929 0.220929i
\(518\) 6.85033 + 20.5745i 0.300986 + 0.903993i
\(519\) 49.5167i 2.17354i
\(520\) 0 0
\(521\) 29.1134i 1.27548i 0.770251 + 0.637741i \(0.220131\pi\)
−0.770251 + 0.637741i \(0.779869\pi\)
\(522\) −6.69213 + 6.69213i −0.292907 + 0.292907i
\(523\) 23.9352 23.9352i 1.04662 1.04662i 0.0477563 0.998859i \(-0.484793\pi\)
0.998859 0.0477563i \(-0.0152071\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 22.3923 0.976351
\(527\) 16.2499 16.2499i 0.707855 0.707855i
\(528\) 3.96184 3.96184i 0.172417 0.172417i
\(529\) 18.1769i 0.790301i
\(530\) 0 0
\(531\) 0 0
\(532\) 4.68288 + 14.0647i 0.203029 + 0.609784i
\(533\) −16.2499 16.2499i −0.703859 0.703859i
\(534\) 31.3923i 1.35848i
\(535\) 0 0
\(536\) 3.92820 0.169673
\(537\) −15.5629 15.5629i −0.671589 0.671589i
\(538\) 8.70080 8.70080i 0.375118 0.375118i
\(539\) −9.70448 + 7.26795i −0.418002 + 0.313053i
\(540\) 0 0
\(541\) 44.5885 1.91701 0.958504 0.285080i \(-0.0920201\pi\)
0.958504 + 0.285080i \(0.0920201\pi\)
\(542\) 13.7242 + 13.7242i 0.589505 + 0.589505i
\(543\) 6.86800 + 6.86800i 0.294734 + 0.294734i
\(544\) 5.60288 0.240222
\(545\) 0 0
\(546\) −18.1244 9.06996i −0.775651 0.388158i
\(547\) −5.22715 + 5.22715i −0.223497 + 0.223497i −0.809969 0.586472i \(-0.800516\pi\)
0.586472 + 0.809969i \(0.300516\pi\)
\(548\) 0.568406 + 0.568406i 0.0242811 + 0.0242811i
\(549\) 83.6410 3.56971
\(550\) 0 0
\(551\) 7.10417i 0.302648i
\(552\) 5.02341 + 5.02341i 0.213810 + 0.213810i
\(553\) 1.67160 + 5.02053i 0.0710835 + 0.213495i
\(554\) 21.1244i 0.897488i
\(555\) 0 0
\(556\) 2.60031i 0.110278i
\(557\) 23.1822 23.1822i 0.982262 0.982262i −0.0175832 0.999845i \(-0.505597\pi\)
0.999845 + 0.0175832i \(0.00559720\pi\)
\(558\) 21.6479 21.6479i 0.916428 0.916428i
\(559\) 8.20319 0.346958
\(560\) 0 0
\(561\) −31.3923 −1.32538
\(562\) 9.79796 9.79796i 0.413302 0.413302i
\(563\) 13.7242 13.7242i 0.578406 0.578406i −0.356058 0.934464i \(-0.615879\pi\)
0.934464 + 0.356058i \(0.115879\pi\)
\(564\) 13.2679i 0.558681i
\(565\) 0 0
\(566\) 14.4406i 0.606983i
\(567\) −61.0510 + 20.3270i −2.56390 + 0.853655i
\(568\) −1.55291 1.55291i −0.0651588 0.0651588i
\(569\) 16.1769i 0.678172i 0.940755 + 0.339086i \(0.110118\pi\)
−0.940755 + 0.339086i \(0.889882\pi\)
\(570\) 0 0
\(571\) 9.60770 0.402070 0.201035 0.979584i \(-0.435570\pi\)
0.201035 + 0.979584i \(0.435570\pi\)
\(572\) −2.90027 2.90027i −0.121266 0.121266i
\(573\) 29.5716 29.5716i 1.23537 1.23537i
\(574\) −22.9610 11.4904i −0.958375 0.479599i
\(575\) 0 0
\(576\) 7.46410 0.311004
\(577\) 12.2140 + 12.2140i 0.508474 + 0.508474i 0.914058 0.405584i \(-0.132932\pi\)
−0.405584 + 0.914058i \(0.632932\pi\)
\(578\) −10.1769 10.1769i −0.423303 0.423303i
\(579\) −19.8112 −0.823327
\(580\) 0 0
\(581\) −11.4904 + 22.9610i −0.476701 + 0.952585i
\(582\) −10.8332 + 10.8332i −0.449052 + 0.449052i
\(583\) −4.65874 4.65874i −0.192945 0.192945i
\(584\) −7.33642 −0.303583
\(585\) 0 0
\(586\) 3.00258i 0.124035i
\(587\) 3.18471 + 3.18471i 0.131447 + 0.131447i 0.769769 0.638322i \(-0.220371\pi\)
−0.638322 + 0.769769i \(0.720371\pi\)
\(588\) −22.4140 3.21771i −0.924338 0.132696i
\(589\) 22.9808i 0.946906i
\(590\) 0 0
\(591\) 72.4352i 2.97959i
\(592\) −5.79555 + 5.79555i −0.238196 + 0.238196i
\(593\) 14.0087 14.0087i 0.575266 0.575266i −0.358329 0.933595i \(-0.616653\pi\)
0.933595 + 0.358329i \(0.116653\pi\)
\(594\) −25.0118 −1.02625
\(595\) 0 0
\(596\) −16.3923 −0.671455
\(597\) 35.0136 35.0136i 1.43301 1.43301i
\(598\) 3.67739 3.67739i 0.150380 0.150380i
\(599\) 22.7321i 0.928806i −0.885624 0.464403i \(-0.846269\pi\)
0.885624 0.464403i \(-0.153731\pi\)
\(600\) 0 0
\(601\) 12.7071i 0.518332i −0.965833 0.259166i \(-0.916552\pi\)
0.965833 0.259166i \(-0.0834476\pi\)
\(602\) 8.69582 2.89529i 0.354415 0.118003i
\(603\) −20.7327 20.7327i −0.844302 0.844302i
\(604\) 16.5885i 0.674975i
\(605\) 0 0
\(606\) 22.9808 0.933530
\(607\) −3.34894 3.34894i −0.135929 0.135929i 0.635868 0.771798i \(-0.280642\pi\)
−0.771798 + 0.635868i \(0.780642\pi\)
\(608\) −3.96184 + 3.96184i −0.160674 + 0.160674i
\(609\) 9.70448 + 4.85641i 0.393245 + 0.196792i
\(610\) 0 0
\(611\) −9.71281 −0.392938
\(612\) −29.5716 29.5716i −1.19536 1.19536i
\(613\) −4.24264 4.24264i −0.171359 0.171359i 0.616217 0.787576i \(-0.288664\pi\)
−0.787576 + 0.616217i \(0.788664\pi\)
\(614\) −4.96836 −0.200507
\(615\) 0 0
\(616\) −4.09808 2.05080i −0.165116 0.0826290i
\(617\) −8.48528 + 8.48528i −0.341605 + 0.341605i −0.856970 0.515366i \(-0.827656\pi\)
0.515366 + 0.856970i \(0.327656\pi\)
\(618\) 10.8332 + 10.8332i 0.435777 + 0.435777i
\(619\) −47.0211 −1.88994 −0.944969 0.327160i \(-0.893908\pi\)
−0.944969 + 0.327160i \(0.893908\pi\)
\(620\) 0 0
\(621\) 31.7137i 1.27263i
\(622\) 13.7242 + 13.7242i 0.550291 + 0.550291i
\(623\) −24.3608 + 8.11098i −0.975996 + 0.324960i
\(624\) 7.66025i 0.306656i
\(625\) 0 0
\(626\) 28.8812i 1.15432i
\(627\) 22.1977 22.1977i 0.886491 0.886491i
\(628\) −15.3987 + 15.3987i −0.614474 + 0.614474i
\(629\) 45.9221 1.83103
\(630\) 0 0
\(631\) 36.9808 1.47218 0.736090 0.676883i \(-0.236670\pi\)
0.736090 + 0.676883i \(0.236670\pi\)
\(632\) −1.41421 + 1.41421i −0.0562544 + 0.0562544i
\(633\) 21.0350 21.0350i 0.836065 0.836065i
\(634\) 16.3923i 0.651022i
\(635\) 0 0
\(636\) 12.3048i 0.487917i
\(637\) −2.35553 + 16.4082i −0.0933294 + 0.650116i
\(638\) 1.55291 + 1.55291i 0.0614805 + 0.0614805i
\(639\) 16.3923i 0.648470i
\(640\) 0 0
\(641\) −36.0000 −1.42191 −0.710957 0.703235i \(-0.751738\pi\)
−0.710957 + 0.703235i \(0.751738\pi\)
\(642\) −30.6331 30.6331i −1.20899 1.20899i
\(643\) 20.4221 20.4221i 0.805368 0.805368i −0.178561 0.983929i \(-0.557144\pi\)
0.983929 + 0.178561i \(0.0571440\pi\)
\(644\) 2.60031 5.19615i 0.102466 0.204757i
\(645\) 0 0
\(646\) 31.3923 1.23511
\(647\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(648\) −17.1972 17.1972i −0.675570 0.675570i
\(649\) 0 0
\(650\) 0 0
\(651\) −31.3923 15.7096i −1.23036 0.615709i
\(652\) −2.77766 + 2.77766i −0.108782 + 0.108782i
\(653\) 35.1894 + 35.1894i 1.37707 + 1.37707i 0.849532 + 0.527537i \(0.176884\pi\)
0.527537 + 0.849532i \(0.323116\pi\)
\(654\) 6.46965 0.252983
\(655\) 0 0
\(656\) 9.70448i 0.378896i
\(657\) 38.7210 + 38.7210i 1.51065 + 1.51065i
\(658\) −10.2961 + 3.42811i −0.401384 + 0.133641i
\(659\) 11.8756i 0.462609i 0.972881 + 0.231305i \(0.0742994\pi\)
−0.972881 + 0.231305i \(0.925701\pi\)
\(660\) 0 0
\(661\) 26.5131i 1.03124i −0.856817 0.515621i \(-0.827561\pi\)
0.856817 0.515621i \(-0.172439\pi\)
\(662\) 16.6796 16.6796i 0.648269 0.648269i
\(663\) −30.3487 + 30.3487i −1.17864 + 1.17864i
\(664\) −9.70448 −0.376607
\(665\) 0 0
\(666\) 61.1769 2.37056
\(667\) −1.96902 + 1.96902i −0.0762406 + 0.0762406i
\(668\) 15.8473 15.8473i 0.613152 0.613152i
\(669\) 55.1244i 2.13123i
\(670\) 0 0
\(671\) 19.4090i 0.749275i
\(672\) −2.70366 8.12028i −0.104296 0.313247i
\(673\) 1.13681 + 1.13681i 0.0438209 + 0.0438209i 0.728678 0.684857i \(-0.240135\pi\)
−0.684857 + 0.728678i \(0.740135\pi\)
\(674\) 25.7321i 0.991162i
\(675\) 0 0
\(676\) 7.39230 0.284319
\(677\) 33.2489 + 33.2489i 1.27786 + 1.27786i 0.941863 + 0.335998i \(0.109074\pi\)
0.335998 + 0.941863i \(0.390926\pi\)
\(678\) −25.6097 + 25.6097i −0.983535 + 0.983535i
\(679\) 11.2058 + 5.60770i 0.430038 + 0.215204i
\(680\) 0 0
\(681\) −36.2487 −1.38905
\(682\) −5.02341 5.02341i −0.192356 0.192356i
\(683\) −0.152304 0.152304i −0.00582775 0.00582775i 0.704187 0.710015i \(-0.251312\pi\)
−0.710015 + 0.704187i \(0.751312\pi\)
\(684\) 41.8205 1.59905
\(685\) 0 0
\(686\) 3.29423 + 18.2249i 0.125774 + 0.695831i
\(687\) −9.38186 + 9.38186i −0.357940 + 0.357940i
\(688\) 2.44949 + 2.44949i 0.0933859 + 0.0933859i
\(689\) −9.00773 −0.343167
\(690\) 0 0
\(691\) 16.8087i 0.639431i −0.947514 0.319716i \(-0.896413\pi\)
0.947514 0.319716i \(-0.103587\pi\)
\(692\) −10.8239 10.8239i −0.411464 0.411464i
\(693\) 10.8054 + 32.4532i 0.410462 + 1.23280i
\(694\) 29.7846i 1.13061i
\(695\) 0 0
\(696\) 4.10160i 0.155471i
\(697\) −38.4476 + 38.4476i −1.45631 + 1.45631i
\(698\) −5.02341 + 5.02341i −0.190139 + 0.190139i
\(699\) 33.6173 1.27152
\(700\) 0 0
\(701\) −18.9282 −0.714908 −0.357454 0.933931i \(-0.616355\pi\)
−0.357454 + 0.933931i \(0.616355\pi\)
\(702\) −24.1803 + 24.1803i −0.912628 + 0.912628i
\(703\) −32.4718 + 32.4718i −1.22470 + 1.22470i
\(704\) 1.73205i 0.0652791i
\(705\) 0 0
\(706\) 27.6121i 1.03920i
\(707\) −5.93765 17.8334i −0.223308 0.670693i
\(708\) 0 0
\(709\) 0.392305i 0.0147333i 0.999973 + 0.00736666i \(0.00234490\pi\)
−0.999973 + 0.00736666i \(0.997655\pi\)
\(710\) 0 0
\(711\) 14.9282 0.559851
\(712\) −6.86210 6.86210i −0.257168 0.257168i
\(713\) 6.36943 6.36943i 0.238537 0.238537i
\(714\) −21.4598 + 42.8827i −0.803111 + 1.60484i
\(715\) 0 0
\(716\) −6.80385 −0.254272
\(717\) −59.1431 59.1431i −2.20874 2.20874i
\(718\) 7.34847 + 7.34847i 0.274242 + 0.274242i
\(719\) 26.5131 0.988773 0.494386 0.869242i \(-0.335393\pi\)
0.494386 + 0.869242i \(0.335393\pi\)
\(720\) 0 0
\(721\) 5.60770 11.2058i 0.208841 0.417325i
\(722\) −8.76268 + 8.76268i −0.326113 + 0.326113i
\(723\) −3.43400 3.43400i −0.127712 0.127712i
\(724\) 3.00258 0.111590
\(725\) 0 0
\(726\) 25.8786i 0.960445i
\(727\) 25.4455 + 25.4455i 0.943721 + 0.943721i 0.998499 0.0547775i \(-0.0174450\pi\)
−0.0547775 + 0.998499i \(0.517445\pi\)
\(728\) −5.94446 + 1.97922i −0.220316 + 0.0733547i
\(729\) 41.3923i 1.53305i
\(730\) 0 0
\(731\) 19.4090i 0.717866i
\(732\) 25.6317 25.6317i 0.947375 0.947375i
\(733\) −3.34894 + 3.34894i −0.123696 + 0.123696i −0.766245 0.642549i \(-0.777877\pi\)
0.642549 + 0.766245i \(0.277877\pi\)
\(734\) −4.73611 −0.174813
\(735\) 0 0
\(736\) 2.19615 0.0809513
\(737\) −4.81105 + 4.81105i −0.177217 + 0.177217i
\(738\) −51.2194 + 51.2194i −1.88541 + 1.88541i
\(739\) 16.7846i 0.617432i −0.951154 0.308716i \(-0.900101\pi\)
0.951154 0.308716i \(-0.0998992\pi\)
\(740\) 0 0
\(741\) 42.9195i 1.57669i
\(742\) −9.54867 + 3.17925i −0.350543 + 0.116714i
\(743\) −4.65874 4.65874i −0.170913 0.170913i 0.616468 0.787380i \(-0.288563\pi\)
−0.787380 + 0.616468i \(0.788563\pi\)
\(744\) 13.2679i 0.486427i
\(745\) 0 0
\(746\) −13.2679 −0.485774
\(747\) 51.2194 + 51.2194i 1.87402 + 1.87402i
\(748\) −6.86210 + 6.86210i −0.250903 + 0.250903i
\(749\) −15.8569 + 31.6865i −0.579398 + 1.15780i
\(750\) 0 0
\(751\) −13.8038 −0.503710 −0.251855 0.967765i \(-0.581041\pi\)
−0.251855 + 0.967765i \(0.581041\pi\)
\(752\) −2.90027 2.90027i −0.105762 0.105762i
\(753\) −38.4476 38.4476i −1.40111 1.40111i
\(754\) 3.00258 0.109347
\(755\) 0 0
\(756\) −17.0981 + 34.1668i −0.621851 + 1.24263i
\(757\) 28.8019 28.8019i 1.04682 1.04682i 0.0479746 0.998849i \(-0.484723\pi\)
0.998849 0.0479746i \(-0.0152767\pi\)
\(758\) −24.0280 24.0280i −0.872737 0.872737i
\(759\) −12.3048 −0.446635
\(760\) 0 0
\(761\) 29.1134i 1.05536i 0.849443 + 0.527681i \(0.176938\pi\)
−0.849443 + 0.527681i \(0.823062\pi\)
\(762\) 41.1726 + 41.1726i 1.49153 + 1.49153i
\(763\) −1.67160 5.02053i −0.0605158 0.181756i
\(764\) 12.9282i 0.467726i
\(765\) 0 0
\(766\) 19.4090i 0.701274i
\(767\) 0 0
\(768\) 2.28737 2.28737i 0.0825383 0.0825383i
\(769\) 1.50129 0.0541378 0.0270689 0.999634i \(-0.491383\pi\)
0.0270689 + 0.999634i \(0.491383\pi\)
\(770\) 0 0
\(771\) −62.7846 −2.26113
\(772\) −4.33057 + 4.33057i −0.155861 + 0.155861i
\(773\) −11.6011 + 11.6011i −0.417261 + 0.417261i −0.884259 0.466997i \(-0.845336\pi\)
0.466997 + 0.884259i \(0.345336\pi\)
\(774\) 25.8564i 0.929389i
\(775\) 0 0
\(776\) 4.73611i 0.170017i
\(777\) −22.1596 66.5550i −0.794972 2.38765i
\(778\) −0.240237 0.240237i −0.00861290 0.00861290i
\(779\) 54.3731i 1.94812i
\(780\) 0 0
\(781\) 3.80385 0.136112
\(782\) −8.70080 8.70080i −0.311140 0.311140i
\(783\) 12.9471 12.9471i 0.462691 0.462691i
\(784\) −5.60288 + 4.19615i −0.200103 + 0.149863i
\(785\) 0 0
\(786\) 0 0
\(787\) 10.3753 + 10.3753i 0.369838 + 0.369838i 0.867418 0.497580i \(-0.165778\pi\)
−0.497580 + 0.867418i \(0.665778\pi\)
\(788\) 15.8338 + 15.8338i 0.564054 + 0.564054i
\(789\) −72.4352 −2.57876
\(790\) 0 0
\(791\) 26.4904 + 13.2566i 0.941890 + 0.471349i
\(792\) −9.14162 + 9.14162i −0.324833 + 0.324833i
\(793\) −18.7637 18.7637i −0.666319 0.666319i
\(794\) 11.8403 0.420196
\(795\) 0 0
\(796\) 15.3074i 0.542555i
\(797\) −25.3253 25.3253i −0.897067 0.897067i 0.0981086 0.995176i \(-0.468721\pi\)
−0.995176 + 0.0981086i \(0.968721\pi\)
\(798\) −15.1483 45.4970i −0.536244 1.61058i
\(799\) 22.9808i 0.813001i
\(800\) 0 0
\(801\) 72.4352i 2.55937i
\(802\) −9.95026 + 9.95026i −0.351356 + 0.351356i
\(803\) 8.98525 8.98525i 0.317082 0.317082i
\(804\) −12.7071 −0.448143
\(805\) 0 0
\(806\) −9.71281 −0.342119
\(807\) −28.1456 + 28.1456i −0.990771 + 0.990771i
\(808\) 5.02341 5.02341i 0.176723 0.176723i
\(809\) 51.0333i 1.79424i 0.441791 + 0.897118i \(0.354343\pi\)
−0.441791 + 0.897118i \(0.645657\pi\)
\(810\) 0 0
\(811\) 41.8205i 1.46852i −0.678870 0.734258i \(-0.737530\pi\)
0.678870 0.734258i \(-0.262470\pi\)
\(812\) 3.18289 1.05975i 0.111698 0.0371899i
\(813\) −44.3954 44.3954i −1.55702 1.55702i
\(814\) 14.1962i 0.497575i
\(815\) 0 0
\(816\) −18.1244 −0.634479
\(817\) 13.7242 + 13.7242i 0.480149 + 0.480149i
\(818\) 24.8326 24.8326i 0.868251 0.868251i
\(819\) 41.8205 + 20.9282i 1.46133 + 0.731291i
\(820\) 0 0
\(821\) −33.1244 −1.15605 −0.578024 0.816020i \(-0.696176\pi\)
−0.578024 + 0.816020i \(0.696176\pi\)
\(822\) −1.83869 1.83869i −0.0641319 0.0641319i
\(823\) 0.896575 + 0.896575i 0.0312527 + 0.0312527i 0.722560 0.691308i \(-0.242965\pi\)
−0.691308 + 0.722560i \(0.742965\pi\)
\(824\) 4.73611 0.164990
\(825\) 0 0
\(826\) 0 0
\(827\) 19.9241 19.9241i 0.692828 0.692828i −0.270025 0.962853i \(-0.587032\pi\)
0.962853 + 0.270025i \(0.0870319\pi\)
\(828\) −11.5911 11.5911i −0.402819 0.402819i
\(829\) 14.2083 0.493476 0.246738 0.969082i \(-0.420641\pi\)
0.246738 + 0.969082i \(0.420641\pi\)
\(830\) 0 0
\(831\) 68.3336i 2.37047i
\(832\) −1.67447 1.67447i −0.0580518 0.0580518i
\(833\) 38.8222 + 5.57324i 1.34511 + 0.193101i
\(834\) 8.41154i 0.291268i
\(835\) 0 0
\(836\) 9.70448i 0.335636i
\(837\) −41.8816 + 41.8816i −1.44764 + 1.44764i
\(838\) 25.6097 25.6097i 0.884673 0.884673i
\(839\) 21.3125 0.735790 0.367895 0.929867i \(-0.380079\pi\)
0.367895 + 0.929867i \(0.380079\pi\)
\(840\) 0 0
\(841\) 27.3923 0.944562
\(842\) −20.6312 + 20.6312i −0.710998 + 0.710998i
\(843\) −31.6947 + 31.6947i −1.09162 + 1.09162i
\(844\) 9.19615i 0.316545i
\(845\) 0 0
\(846\) 30.6147i 1.05256i
\(847\) −20.0821 + 6.68638i −0.690030 + 0.229747i
\(848\) −2.68973 2.68973i −0.0923656 0.0923656i
\(849\) 46.7128i 1.60318i
\(850\) 0 0
\(851\) 18.0000 0.617032
\(852\) 5.02341 + 5.02341i 0.172099 + 0.172099i
\(853\) 7.02633 7.02633i 0.240577 0.240577i −0.576512 0.817089i \(-0.695587\pi\)
0.817089 + 0.576512i \(0.195587\pi\)
\(854\) −26.5131 13.2679i −0.907261 0.454020i
\(855\) 0 0
\(856\) −13.3923 −0.457740
\(857\) 15.5629 + 15.5629i 0.531619 + 0.531619i 0.921054 0.389435i \(-0.127330\pi\)
−0.389435 + 0.921054i \(0.627330\pi\)
\(858\) 9.38186 + 9.38186i 0.320291 + 0.320291i
\(859\) 36.2176 1.23573 0.617864 0.786285i \(-0.287998\pi\)
0.617864 + 0.786285i \(0.287998\pi\)
\(860\) 0 0
\(861\) 74.2750 + 37.1694i 2.53128 + 1.26673i
\(862\) −5.31508 + 5.31508i −0.181032 + 0.181032i
\(863\) 22.3500 + 22.3500i 0.760803 + 0.760803i 0.976468 0.215664i \(-0.0691917\pi\)
−0.215664 + 0.976468i \(0.569192\pi\)
\(864\) −14.4406 −0.491279
\(865\) 0 0
\(866\) 21.5448i 0.732121i
\(867\) 32.9205 + 32.9205i 1.11804 + 1.11804i
\(868\) −10.2961 + 3.42811i −0.349472 + 0.116357i
\(869\) 3.46410i 0.117512i
\(870\) 0 0
\(871\) 9.30221i 0.315193i
\(872\) 1.41421 1.41421i 0.0478913 0.0478913i
\(873\) 24.9968 24.9968i 0.846014 0.846014i
\(874\) 12.3048 0.416216
\(875\) 0 0
\(876\) 23.7321 0.801832
\(877\) 1.31268 1.31268i 0.0443260 0.0443260i −0.684596 0.728922i \(-0.740022\pi\)
0.728922 + 0.684596i \(0.240022\pi\)
\(878\) 5.80053 5.80053i 0.195758 0.195758i
\(879\) 9.71281i 0.327605i
\(880\) 0 0
\(881\) 53.0263i 1.78650i −0.449560 0.893250i \(-0.648419\pi\)
0.449560 0.893250i \(-0.351581\pi\)
\(882\) 51.7185 + 7.42461i 1.74145 + 0.250000i
\(883\) 12.3998 + 12.3998i 0.417285 + 0.417285i 0.884267 0.466982i \(-0.154659\pi\)
−0.466982 + 0.884267i \(0.654659\pi\)
\(884\) 13.2679i 0.446249i
\(885\) 0 0
\(886\) 15.0000 0.503935
\(887\) −8.70080 8.70080i −0.292144 0.292144i 0.545783 0.837927i \(-0.316232\pi\)
−0.837927 + 0.545783i \(0.816232\pi\)
\(888\) 18.7476 18.7476i 0.629129 0.629129i
\(889\) 21.3125 42.5885i 0.714799 1.42837i
\(890\) 0 0
\(891\) 42.1244 1.41122
\(892\) 12.0497 + 12.0497i 0.403455 + 0.403455i
\(893\) −16.2499 16.2499i −0.543781 0.543781i
\(894\) 53.0263 1.77346
\(895\) 0 0
\(896\) −2.36603 1.18403i −0.0790434 0.0395556i
\(897\) −11.8957 + 11.8957i −0.397186 + 0.397186i
\(898\) −0.808643 0.808643i −0.0269848 0.0269848i
\(899\) 5.20061 0.173450
\(900\) 0 0
\(901\) 21.3125i 0.710023i
\(902\) 11.8855 + 11.8855i 0.395744 + 0.395744i
\(903\) −28.1295 + 9.36576i −0.936090 + 0.311673i
\(904\) 11.1962i 0.372378i
\(905\) 0 0
\(906\) 53.6608i 1.78276i
\(907\) −31.6675 + 31.6675i −1.05150 + 1.05150i −0.0529024 + 0.998600i \(0.516847\pi\)
−0.998600 + 0.0529024i \(0.983153\pi\)
\(908\) −7.92367 + 7.92367i −0.262956 + 0.262956i
\(909\) −53.0263 −1.75877
\(910\) 0 0
\(911\) −24.0000 −0.795155 −0.397578 0.917568i \(-0.630149\pi\)
−0.397578 + 0.917568i \(0.630149\pi\)
\(912\) 12.8159 12.8159i 0.424375 0.424375i
\(913\) 11.8855 11.8855i 0.393353 0.393353i
\(914\) 12.8038i 0.423514i
\(915\) 0 0
\(916\) 4.10160i 0.135521i
\(917\) 0 0
\(918\) 57.2113 + 57.2113i 1.88825 + 1.88825i
\(919\) 9.60770i 0.316929i 0.987365 + 0.158464i \(0.0506543\pi\)
−0.987365 + 0.158464i \(0.949346\pi\)
\(920\) 0 0
\(921\) 16.0718 0.529584
\(922\) −18.7476 18.7476i −0.617420 0.617420i
\(923\) 3.67739 3.67739i 0.121043 0.121043i
\(924\) 13.2566 + 6.63397i 0.436109 + 0.218242i
\(925\) 0 0
\(926\) −37.1769 −1.22171
\(927\) −24.9968 24.9968i −0.821003 0.821003i
\(928\) 0.896575 + 0.896575i 0.0294315 + 0.0294315i
\(929\) 38.8179 1.27357 0.636787 0.771040i \(-0.280263\pi\)
0.636787 + 0.771040i \(0.280263\pi\)
\(930\) 0 0
\(931\) −31.3923 + 23.5106i −1.02884 + 0.770527i
\(932\) 7.34847 7.34847i 0.240707 0.240707i
\(933\) −44.3954 44.3954i −1.45344 1.45344i
\(934\) 8.20319 0.268417
\(935\) 0 0
\(936\) 17.6754i 0.577739i
\(937\) −35.9850 35.9850i −1.17558 1.17558i −0.980859 0.194719i \(-0.937620\pi\)
−0.194719 0.980859i \(-0.562380\pi\)
\(938\) 3.28318 + 9.86084i 0.107200 + 0.321968i
\(939\) 93.4256i 3.04883i
\(940\) 0 0
\(941\) 14.2083i 0.463179i −0.972814 0.231589i \(-0.925607\pi\)
0.972814 0.231589i \(-0.0743926\pi\)
\(942\) 49.8120 49.8120i 1.62296 1.62296i
\(943\) −15.0702 + 15.0702i −0.490754 + 0.490754i
\(944\) 0 0
\(945\) 0 0
\(946\) −6.00000 −0.195077
\(947\) −5.07484 + 5.07484i −0.164910 + 0.164910i −0.784738 0.619828i \(-0.787202\pi\)
0.619828 + 0.784738i \(0.287202\pi\)
\(948\) 4.57474 4.57474i 0.148580 0.148580i
\(949\) 17.3731i 0.563954i
\(950\) 0 0
\(951\) 53.0263i 1.71949i
\(952\) 4.68288 + 14.0647i 0.151773 + 0.455841i
\(953\) 3.67423 + 3.67423i 0.119020 + 0.119020i 0.764108 0.645088i \(-0.223179\pi\)
−0.645088 + 0.764108i \(0.723179\pi\)
\(954\) 28.3923i 0.919235i
\(955\) 0 0
\(956\) −25.8564 −0.836256
\(957\) −5.02341 5.02341i −0.162384 0.162384i
\(958\) 13.7242 13.7242i 0.443409 0.443409i
\(959\) −0.951779 + 1.90192i −0.0307345 + 0.0614163i
\(960\) 0 0
\(961\) 14.1769 0.457320
\(962\) −13.7242 13.7242i −0.442486 0.442486i
\(963\) 70.6835 + 70.6835i 2.27774 + 2.27774i
\(964\) −1.50129 −0.0483532
\(965\) 0 0
\(966\) −8.41154 + 16.8087i −0.270637 + 0.540809i
\(967\) 14.2808 14.2808i 0.459241 0.459241i −0.439165 0.898406i \(-0.644726\pi\)
0.898406 + 0.439165i \(0.144726\pi\)
\(968\) −5.65685 5.65685i −0.181818 0.181818i
\(969\) −101.549 −3.26221
\(970\) 0 0
\(971\) 11.6080i 0.372520i 0.982501 + 0.186260i \(0.0596366\pi\)
−0.982501 + 0.186260i \(0.940363\pi\)
\(972\) 24.9968 + 24.9968i 0.801773 + 0.801773i
\(973\) 6.52747 2.17333i 0.209261 0.0696738i
\(974\) 20.5359i 0.658013i
\(975\) 0 0
\(976\) 11.2058i 0.358688i
\(977\) 36.4785 36.4785i 1.16705 1.16705i 0.184155 0.982897i \(-0.441045\pi\)
0.982897 0.184155i \(-0.0589548\pi\)
\(978\) 8.98525 8.98525i 0.287316 0.287316i
\(979\) 16.8087 0.537207
\(980\) 0 0
\(981\) −14.9282 −0.476621
\(982\) 13.3843 13.3843i 0.427109 0.427109i
\(983\) −26.6713 + 26.6713i −0.850682 + 0.850682i −0.990217 0.139535i \(-0.955439\pi\)
0.139535 + 0.990217i \(0.455439\pi\)
\(984\) 31.3923i 1.00075i
\(985\) 0 0
\(986\) 7.10417i 0.226243i
\(987\) 33.3061 11.0893i 1.06014 0.352977i
\(988\) −9.38186 9.38186i −0.298477 0.298477i
\(989\) 7.60770i 0.241911i
\(990\) 0 0
\(991\) −4.19615 −0.133295 −0.0666476 0.997777i \(-0.521230\pi\)
−0.0666476 + 0.997777i \(0.521230\pi\)
\(992\) −2.90027 2.90027i −0.0920835 0.0920835i
\(993\) −53.9555 + 53.9555i −1.71223 + 1.71223i
\(994\) 2.60031 5.19615i 0.0824767 0.164812i
\(995\) 0 0
\(996\) 31.3923 0.994703
\(997\) 8.37235 + 8.37235i 0.265155 + 0.265155i 0.827144 0.561989i \(-0.189964\pi\)
−0.561989 + 0.827144i \(0.689964\pi\)
\(998\) −17.5254 17.5254i −0.554756 0.554756i
\(999\) −118.357 −3.74466
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 350.2.g.b.293.4 yes 16
5.2 odd 4 inner 350.2.g.b.307.1 yes 16
5.3 odd 4 inner 350.2.g.b.307.8 yes 16
5.4 even 2 inner 350.2.g.b.293.5 yes 16
7.6 odd 2 inner 350.2.g.b.293.1 16
35.13 even 4 inner 350.2.g.b.307.5 yes 16
35.27 even 4 inner 350.2.g.b.307.4 yes 16
35.34 odd 2 inner 350.2.g.b.293.8 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
350.2.g.b.293.1 16 7.6 odd 2 inner
350.2.g.b.293.4 yes 16 1.1 even 1 trivial
350.2.g.b.293.5 yes 16 5.4 even 2 inner
350.2.g.b.293.8 yes 16 35.34 odd 2 inner
350.2.g.b.307.1 yes 16 5.2 odd 4 inner
350.2.g.b.307.4 yes 16 35.27 even 4 inner
350.2.g.b.307.5 yes 16 35.13 even 4 inner
350.2.g.b.307.8 yes 16 5.3 odd 4 inner