Properties

Label 600.2.m.c.299.9
Level $600$
Weight $2$
Character 600.299
Analytic conductor $4.791$
Analytic rank $0$
Dimension $16$
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] = [600,2,Mod(299,600)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(600, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("600.299");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 600.m (of order \(2\), degree \(1\), 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: \(4.79102412128\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + x^{14} + 4x^{12} + 12x^{10} + 16x^{8} + 48x^{6} + 64x^{4} + 64x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{11} \)
Twist minimal: no (minimal twist has level 120)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 299.9
Root \(0.199044 - 1.40014i\) of defining polynomial
Character \(\chi\) \(=\) 600.299
Dual form 600.2.m.c.299.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.199044 - 1.40014i) q^{2} +(-1.65195 + 0.520627i) q^{3} +(-1.92076 - 0.557378i) q^{4} +(0.400136 + 2.41659i) q^{6} +1.92736 q^{7} +(-1.16272 + 2.57839i) q^{8} +(2.45790 - 1.72010i) q^{9} +O(q^{10})\) \(q+(0.199044 - 1.40014i) q^{2} +(-1.65195 + 0.520627i) q^{3} +(-1.92076 - 0.557378i) q^{4} +(0.400136 + 2.41659i) q^{6} +1.92736 q^{7} +(-1.16272 + 2.57839i) q^{8} +(2.45790 - 1.72010i) q^{9} -4.02057i q^{11} +(3.46320 - 0.0792373i) q^{12} -4.81675 q^{13} +(0.383629 - 2.69856i) q^{14} +(3.37866 + 2.14118i) q^{16} -5.23126 q^{17} +(-1.91915 - 3.78377i) q^{18} +0.684753 q^{19} +(-3.18390 + 1.00343i) q^{21} +(-5.62935 - 0.800272i) q^{22} -1.72601i q^{23} +(0.578386 - 4.86472i) q^{24} +(-0.958747 + 6.74411i) q^{26} +(-3.16480 + 4.12117i) q^{27} +(-3.70199 - 1.07427i) q^{28} -6.99830 q^{29} +4.23638i q^{31} +(3.67045 - 4.30439i) q^{32} +(2.09322 + 6.64180i) q^{33} +(-1.04125 + 7.32448i) q^{34} +(-5.67978 + 1.93393i) q^{36} -9.83221 q^{37} +(0.136296 - 0.958747i) q^{38} +(7.95705 - 2.50773i) q^{39} -3.44020i q^{41} +(0.771205 + 4.65762i) q^{42} -1.04125i q^{43} +(-2.24098 + 7.72257i) q^{44} +(-2.41664 - 0.343552i) q^{46} +7.55759i q^{47} +(-6.69614 - 1.77811i) q^{48} -3.28530 q^{49} +(8.64180 - 2.72353i) q^{51} +(9.25184 + 2.68475i) q^{52} +4.08251i q^{53} +(5.14027 + 5.25144i) q^{54} +(-2.24098 + 4.96947i) q^{56} +(-1.13118 + 0.356500i) q^{57} +(-1.39297 + 9.79857i) q^{58} -0.994883i q^{59} -3.16761i q^{61} +(5.93151 + 0.843227i) q^{62} +(4.73724 - 3.31525i) q^{63} +(-5.29615 - 5.99590i) q^{64} +(9.71606 - 1.60878i) q^{66} -14.8728i q^{67} +(10.0480 + 2.91579i) q^{68} +(0.898604 + 2.85128i) q^{69} -9.28360 q^{71} +(1.57723 + 8.33741i) q^{72} -11.2836i q^{73} +(-1.95705 + 13.7664i) q^{74} +(-1.31525 - 0.381666i) q^{76} -7.74908i q^{77} +(-1.92736 - 11.6401i) q^{78} -9.25184i q^{79} +(3.08251 - 8.45566i) q^{81} +(-4.81675 - 0.684753i) q^{82} +7.15862 q^{83} +(6.67481 - 0.152718i) q^{84} +(-1.45790 - 0.207256i) q^{86} +(11.5609 - 3.64350i) q^{87} +(10.3666 + 4.67481i) q^{88} +0.829022i q^{89} -9.28360 q^{91} +(-0.962038 + 3.31525i) q^{92} +(-2.20557 - 6.99830i) q^{93} +(10.5817 + 1.50430i) q^{94} +(-3.82243 + 9.02159i) q^{96} -1.45201i q^{97} +(-0.653920 + 4.59986i) q^{98} +(-6.91579 - 9.88215i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{4} - 14 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 2 q^{4} - 14 q^{6} - 12 q^{14} - 14 q^{16} + 8 q^{19} + 8 q^{21} - 18 q^{24} - 32 q^{26} - 38 q^{36} + 32 q^{39} - 60 q^{44} - 16 q^{46} + 32 q^{49} + 40 q^{51} + 30 q^{54} - 60 q^{56} - 50 q^{64} + 36 q^{66} + 40 q^{69} + 48 q^{71} + 64 q^{74} - 24 q^{76} + 16 q^{81} + 4 q^{84} + 16 q^{86} + 48 q^{91} + 80 q^{94} + 34 q^{96} - 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).

\(n\) \(151\) \(301\) \(401\) \(577\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.199044 1.40014i 0.140746 0.990046i
\(3\) −1.65195 + 0.520627i −0.953755 + 0.300584i
\(4\) −1.92076 0.557378i −0.960381 0.278689i
\(5\) 0 0
\(6\) 0.400136 + 2.41659i 0.163355 + 0.986567i
\(7\) 1.92736 0.728472 0.364236 0.931307i \(-0.381330\pi\)
0.364236 + 0.931307i \(0.381330\pi\)
\(8\) −1.16272 + 2.57839i −0.411084 + 0.911597i
\(9\) 2.45790 1.72010i 0.819299 0.573367i
\(10\) 0 0
\(11\) 4.02057i 1.21225i −0.795370 0.606124i \(-0.792723\pi\)
0.795370 0.606124i \(-0.207277\pi\)
\(12\) 3.46320 0.0792373i 0.999738 0.0228738i
\(13\) −4.81675 −1.33593 −0.667963 0.744194i \(-0.732834\pi\)
−0.667963 + 0.744194i \(0.732834\pi\)
\(14\) 0.383629 2.69856i 0.102529 0.721221i
\(15\) 0 0
\(16\) 3.37866 + 2.14118i 0.844665 + 0.535296i
\(17\) −5.23126 −1.26877 −0.634384 0.773018i \(-0.718746\pi\)
−0.634384 + 0.773018i \(0.718746\pi\)
\(18\) −1.91915 3.78377i −0.452347 0.891842i
\(19\) 0.684753 0.157093 0.0785465 0.996910i \(-0.474972\pi\)
0.0785465 + 0.996910i \(0.474972\pi\)
\(20\) 0 0
\(21\) −3.18390 + 1.00343i −0.694784 + 0.218967i
\(22\) −5.62935 0.800272i −1.20018 0.170619i
\(23\) 1.72601i 0.359897i −0.983676 0.179949i \(-0.942407\pi\)
0.983676 0.179949i \(-0.0575931\pi\)
\(24\) 0.578386 4.86472i 0.118063 0.993006i
\(25\) 0 0
\(26\) −0.958747 + 6.74411i −0.188026 + 1.32263i
\(27\) −3.16480 + 4.12117i −0.609066 + 0.793120i
\(28\) −3.70199 1.07427i −0.699611 0.203017i
\(29\) −6.99830 −1.29955 −0.649776 0.760126i \(-0.725137\pi\)
−0.649776 + 0.760126i \(0.725137\pi\)
\(30\) 0 0
\(31\) 4.23638i 0.760876i 0.924806 + 0.380438i \(0.124227\pi\)
−0.924806 + 0.380438i \(0.875773\pi\)
\(32\) 3.67045 4.30439i 0.648850 0.760916i
\(33\) 2.09322 + 6.64180i 0.364382 + 1.15619i
\(34\) −1.04125 + 7.32448i −0.178573 + 1.25614i
\(35\) 0 0
\(36\) −5.67978 + 1.93393i −0.946630 + 0.322321i
\(37\) −9.83221 −1.61640 −0.808202 0.588905i \(-0.799559\pi\)
−0.808202 + 0.588905i \(0.799559\pi\)
\(38\) 0.136296 0.958747i 0.0221102 0.155529i
\(39\) 7.95705 2.50773i 1.27415 0.401558i
\(40\) 0 0
\(41\) 3.44020i 0.537269i −0.963242 0.268635i \(-0.913428\pi\)
0.963242 0.268635i \(-0.0865724\pi\)
\(42\) 0.771205 + 4.65762i 0.119000 + 0.718687i
\(43\) 1.04125i 0.158790i −0.996843 0.0793948i \(-0.974701\pi\)
0.996843 0.0793948i \(-0.0252988\pi\)
\(44\) −2.24098 + 7.72257i −0.337841 + 1.16422i
\(45\) 0 0
\(46\) −2.41664 0.343552i −0.356315 0.0506539i
\(47\) 7.55759i 1.10239i 0.834377 + 0.551194i \(0.185828\pi\)
−0.834377 + 0.551194i \(0.814172\pi\)
\(48\) −6.69614 1.77811i −0.966505 0.256649i
\(49\) −3.28530 −0.469328
\(50\) 0 0
\(51\) 8.64180 2.72353i 1.21009 0.381371i
\(52\) 9.25184 + 2.68475i 1.28300 + 0.372308i
\(53\) 4.08251i 0.560775i 0.959887 + 0.280388i \(0.0904630\pi\)
−0.959887 + 0.280388i \(0.909537\pi\)
\(54\) 5.14027 + 5.25144i 0.699502 + 0.714631i
\(55\) 0 0
\(56\) −2.24098 + 4.96947i −0.299464 + 0.664073i
\(57\) −1.13118 + 0.356500i −0.149828 + 0.0472196i
\(58\) −1.39297 + 9.79857i −0.182906 + 1.28662i
\(59\) 0.994883i 0.129523i −0.997901 0.0647614i \(-0.979371\pi\)
0.997901 0.0647614i \(-0.0206286\pi\)
\(60\) 0 0
\(61\) 3.16761i 0.405571i −0.979223 0.202785i \(-0.935001\pi\)
0.979223 0.202785i \(-0.0649994\pi\)
\(62\) 5.93151 + 0.843227i 0.753302 + 0.107090i
\(63\) 4.73724 3.31525i 0.596836 0.417682i
\(64\) −5.29615 5.99590i −0.662019 0.749487i
\(65\) 0 0
\(66\) 9.71606 1.60878i 1.19596 0.198027i
\(67\) 14.8728i 1.81701i −0.417878 0.908503i \(-0.637226\pi\)
0.417878 0.908503i \(-0.362774\pi\)
\(68\) 10.0480 + 2.91579i 1.21850 + 0.353592i
\(69\) 0.898604 + 2.85128i 0.108179 + 0.343254i
\(70\) 0 0
\(71\) −9.28360 −1.10176 −0.550880 0.834584i \(-0.685708\pi\)
−0.550880 + 0.834584i \(0.685708\pi\)
\(72\) 1.57723 + 8.33741i 0.185879 + 0.982573i
\(73\) 11.2836i 1.32064i −0.750982 0.660322i \(-0.770420\pi\)
0.750982 0.660322i \(-0.229580\pi\)
\(74\) −1.95705 + 13.7664i −0.227502 + 1.60031i
\(75\) 0 0
\(76\) −1.31525 0.381666i −0.150869 0.0437801i
\(77\) 7.74908i 0.883089i
\(78\) −1.92736 11.6401i −0.218230 1.31798i
\(79\) 9.25184i 1.04091i −0.853888 0.520456i \(-0.825762\pi\)
0.853888 0.520456i \(-0.174238\pi\)
\(80\) 0 0
\(81\) 3.08251 8.45566i 0.342501 0.939518i
\(82\) −4.81675 0.684753i −0.531921 0.0756183i
\(83\) 7.15862 0.785760 0.392880 0.919590i \(-0.371479\pi\)
0.392880 + 0.919590i \(0.371479\pi\)
\(84\) 6.67481 0.152718i 0.728282 0.0166630i
\(85\) 0 0
\(86\) −1.45790 0.207256i −0.157209 0.0223489i
\(87\) 11.5609 3.64350i 1.23945 0.390624i
\(88\) 10.3666 + 4.67481i 1.10508 + 0.498337i
\(89\) 0.829022i 0.0878762i 0.999034 + 0.0439381i \(0.0139904\pi\)
−0.999034 + 0.0439381i \(0.986010\pi\)
\(90\) 0 0
\(91\) −9.28360 −0.973185
\(92\) −0.962038 + 3.31525i −0.100299 + 0.345638i
\(93\) −2.20557 6.99830i −0.228707 0.725690i
\(94\) 10.5817 + 1.50430i 1.09141 + 0.155156i
\(95\) 0 0
\(96\) −3.82243 + 9.02159i −0.390125 + 0.920762i
\(97\) 1.45201i 0.147429i −0.997279 0.0737147i \(-0.976515\pi\)
0.997279 0.0737147i \(-0.0234854\pi\)
\(98\) −0.653920 + 4.59986i −0.0660559 + 0.464656i
\(99\) −6.91579 9.88215i −0.695063 0.993194i
\(100\) 0 0
\(101\) 4.20279 0.418193 0.209097 0.977895i \(-0.432948\pi\)
0.209097 + 0.977895i \(0.432948\pi\)
\(102\) −2.09322 12.6418i −0.207259 1.25172i
\(103\) 7.10183 0.699764 0.349882 0.936794i \(-0.386222\pi\)
0.349882 + 0.936794i \(0.386222\pi\)
\(104\) 5.60054 12.4194i 0.549179 1.21783i
\(105\) 0 0
\(106\) 5.71606 + 0.812600i 0.555193 + 0.0789267i
\(107\) −7.76293 −0.750471 −0.375235 0.926930i \(-0.622438\pi\)
−0.375235 + 0.926930i \(0.622438\pi\)
\(108\) 8.37588 6.15180i 0.805969 0.591957i
\(109\) 20.5105i 1.96455i 0.187437 + 0.982277i \(0.439982\pi\)
−0.187437 + 0.982277i \(0.560018\pi\)
\(110\) 0 0
\(111\) 16.2423 5.11891i 1.54165 0.485865i
\(112\) 6.51188 + 4.12682i 0.615315 + 0.389948i
\(113\) 0.215805 0.0203013 0.0101506 0.999948i \(-0.496769\pi\)
0.0101506 + 0.999948i \(0.496769\pi\)
\(114\) 0.273994 + 1.65476i 0.0256619 + 0.154983i
\(115\) 0 0
\(116\) 13.4421 + 3.90070i 1.24806 + 0.362171i
\(117\) −11.8391 + 8.28530i −1.09452 + 0.765976i
\(118\) −1.39297 0.198026i −0.128233 0.0182298i
\(119\) −10.0825 −0.924262
\(120\) 0 0
\(121\) −5.16501 −0.469547
\(122\) −4.43508 0.630495i −0.401534 0.0570823i
\(123\) 1.79106 + 5.68305i 0.161494 + 0.512423i
\(124\) 2.36127 8.13708i 0.212048 0.730731i
\(125\) 0 0
\(126\) −3.69888 7.29266i −0.329522 0.649682i
\(127\) 16.5763 1.47091 0.735455 0.677574i \(-0.236968\pi\)
0.735455 + 0.677574i \(0.236968\pi\)
\(128\) −9.44924 + 6.22189i −0.835203 + 0.549942i
\(129\) 0.542104 + 1.72010i 0.0477296 + 0.151446i
\(130\) 0 0
\(131\) 5.61293i 0.490404i 0.969472 + 0.245202i \(0.0788543\pi\)
−0.969472 + 0.245202i \(0.921146\pi\)
\(132\) −0.318579 13.9240i −0.0277288 1.21193i
\(133\) 1.31976 0.114438
\(134\) −20.8240 2.96035i −1.79892 0.255736i
\(135\) 0 0
\(136\) 6.08251 13.4882i 0.521571 1.15660i
\(137\) 9.41770 0.804608 0.402304 0.915506i \(-0.368209\pi\)
0.402304 + 0.915506i \(0.368209\pi\)
\(138\) 4.17104 0.690637i 0.355063 0.0587910i
\(139\) 6.51634 0.552708 0.276354 0.961056i \(-0.410874\pi\)
0.276354 + 0.961056i \(0.410874\pi\)
\(140\) 0 0
\(141\) −3.93468 12.4848i −0.331360 1.05141i
\(142\) −1.84785 + 12.9983i −0.155068 + 1.09079i
\(143\) 19.3661i 1.61947i
\(144\) 11.9874 0.548828i 0.998954 0.0457357i
\(145\) 0 0
\(146\) −15.7986 2.24594i −1.30750 0.185875i
\(147\) 5.42716 1.71041i 0.447624 0.141072i
\(148\) 18.8853 + 5.48026i 1.55237 + 0.450475i
\(149\) 7.53452 0.617252 0.308626 0.951184i \(-0.400131\pi\)
0.308626 + 0.951184i \(0.400131\pi\)
\(150\) 0 0
\(151\) 9.41085i 0.765844i −0.923781 0.382922i \(-0.874918\pi\)
0.923781 0.382922i \(-0.125082\pi\)
\(152\) −0.796177 + 1.76556i −0.0645785 + 0.143206i
\(153\) −12.8579 + 8.99830i −1.03950 + 0.727469i
\(154\) −10.8498 1.54241i −0.874299 0.124291i
\(155\) 0 0
\(156\) −16.6813 + 0.381666i −1.33558 + 0.0305578i
\(157\) −3.49699 −0.279090 −0.139545 0.990216i \(-0.544564\pi\)
−0.139545 + 0.990216i \(0.544564\pi\)
\(158\) −12.9538 1.84153i −1.03055 0.146504i
\(159\) −2.12546 6.74411i −0.168560 0.534842i
\(160\) 0 0
\(161\) 3.32663i 0.262175i
\(162\) −11.2255 5.99898i −0.881960 0.471324i
\(163\) 16.9553i 1.32804i −0.747713 0.664022i \(-0.768848\pi\)
0.747713 0.664022i \(-0.231152\pi\)
\(164\) −1.91749 + 6.60781i −0.149731 + 0.515983i
\(165\) 0 0
\(166\) 1.42488 10.0230i 0.110592 0.777939i
\(167\) 11.3926i 0.881584i 0.897609 + 0.440792i \(0.145302\pi\)
−0.897609 + 0.440792i \(0.854698\pi\)
\(168\) 1.11476 9.37604i 0.0860053 0.723377i
\(169\) 10.2011 0.784699
\(170\) 0 0
\(171\) 1.68305 1.17784i 0.128706 0.0900720i
\(172\) −0.580372 + 2.00000i −0.0442529 + 0.152499i
\(173\) 2.16501i 0.164603i −0.996607 0.0823014i \(-0.973773\pi\)
0.996607 0.0823014i \(-0.0262270\pi\)
\(174\) −2.80027 16.9120i −0.212288 1.28209i
\(175\) 0 0
\(176\) 8.60878 13.5841i 0.648912 1.02394i
\(177\) 0.517962 + 1.64350i 0.0389324 + 0.123533i
\(178\) 1.16074 + 0.165012i 0.0870014 + 0.0123682i
\(179\) 5.34034i 0.399155i 0.979882 + 0.199578i \(0.0639570\pi\)
−0.979882 + 0.199578i \(0.936043\pi\)
\(180\) 0 0
\(181\) 10.7942i 0.802330i 0.916006 + 0.401165i \(0.131395\pi\)
−0.916006 + 0.401165i \(0.868605\pi\)
\(182\) −1.84785 + 12.9983i −0.136972 + 0.963498i
\(183\) 1.64914 + 5.23274i 0.121908 + 0.386815i
\(184\) 4.45031 + 2.00687i 0.328081 + 0.147948i
\(185\) 0 0
\(186\) −10.2376 + 1.69513i −0.750656 + 0.124293i
\(187\) 21.0327i 1.53806i
\(188\) 4.21244 14.5163i 0.307224 1.05871i
\(189\) −6.09969 + 7.94297i −0.443687 + 0.577766i
\(190\) 0 0
\(191\) −19.7491 −1.42899 −0.714497 0.699639i \(-0.753344\pi\)
−0.714497 + 0.699639i \(0.753344\pi\)
\(192\) 11.8706 + 7.14762i 0.856688 + 0.515835i
\(193\) 5.45201i 0.392444i −0.980559 0.196222i \(-0.937133\pi\)
0.980559 0.196222i \(-0.0628674\pi\)
\(194\) −2.03301 0.289015i −0.145962 0.0207500i
\(195\) 0 0
\(196\) 6.31028 + 1.83115i 0.450734 + 0.130797i
\(197\) 22.6497i 1.61372i −0.590740 0.806862i \(-0.701164\pi\)
0.590740 0.806862i \(-0.298836\pi\)
\(198\) −15.2129 + 7.71606i −1.08113 + 0.548357i
\(199\) 18.8853i 1.33875i −0.742926 0.669373i \(-0.766563\pi\)
0.742926 0.669373i \(-0.233437\pi\)
\(200\) 0 0
\(201\) 7.74319 + 24.5692i 0.546163 + 1.73298i
\(202\) 0.836542 5.88448i 0.0588589 0.414031i
\(203\) −13.4882 −0.946687
\(204\) −18.1169 + 0.414511i −1.26844 + 0.0290216i
\(205\) 0 0
\(206\) 1.41358 9.94353i 0.0984887 0.692799i
\(207\) −2.96890 4.24234i −0.206353 0.294863i
\(208\) −16.2742 10.3135i −1.12841 0.715116i
\(209\) 2.75310i 0.190436i
\(210\) 0 0
\(211\) −10.7673 −0.741249 −0.370624 0.928783i \(-0.620856\pi\)
−0.370624 + 0.928783i \(0.620856\pi\)
\(212\) 2.27550 7.84153i 0.156282 0.538558i
\(213\) 15.3361 4.83329i 1.05081 0.331171i
\(214\) −1.54517 + 10.8692i −0.105625 + 0.743001i
\(215\) 0 0
\(216\) −6.94619 12.9519i −0.472628 0.881262i
\(217\) 8.16501i 0.554277i
\(218\) 28.7175 + 4.08251i 1.94500 + 0.276502i
\(219\) 5.87454 + 18.6400i 0.396965 + 1.25957i
\(220\) 0 0
\(221\) 25.1977 1.69498
\(222\) −3.93422 23.7604i −0.264048 1.59469i
\(223\) −6.54540 −0.438313 −0.219156 0.975690i \(-0.570330\pi\)
−0.219156 + 0.975690i \(0.570330\pi\)
\(224\) 7.07427 8.29610i 0.472669 0.554306i
\(225\) 0 0
\(226\) 0.0429548 0.302157i 0.00285731 0.0200992i
\(227\) 22.5118 1.49416 0.747080 0.664735i \(-0.231455\pi\)
0.747080 + 0.664735i \(0.231455\pi\)
\(228\) 2.37143 0.0542579i 0.157052 0.00359332i
\(229\) 12.8839i 0.851392i −0.904866 0.425696i \(-0.860029\pi\)
0.904866 0.425696i \(-0.139971\pi\)
\(230\) 0 0
\(231\) 4.03438 + 12.8011i 0.265442 + 0.842251i
\(232\) 8.13708 18.0443i 0.534225 1.18467i
\(233\) 10.8510 0.710875 0.355437 0.934700i \(-0.384332\pi\)
0.355437 + 0.934700i \(0.384332\pi\)
\(234\) 9.24404 + 18.2255i 0.604302 + 1.19144i
\(235\) 0 0
\(236\) −0.554526 + 1.91093i −0.0360966 + 0.124391i
\(237\) 4.81675 + 15.2836i 0.312882 + 0.992776i
\(238\) −2.00687 + 14.1169i −0.130086 + 0.915062i
\(239\) 6.63049 0.428891 0.214446 0.976736i \(-0.431206\pi\)
0.214446 + 0.976736i \(0.431206\pi\)
\(240\) 0 0
\(241\) −15.9519 −1.02755 −0.513775 0.857925i \(-0.671753\pi\)
−0.513775 + 0.857925i \(0.671753\pi\)
\(242\) −1.02807 + 7.23172i −0.0660866 + 0.464873i
\(243\) −0.689915 + 15.5732i −0.0442580 + 0.999020i
\(244\) −1.76556 + 6.08423i −0.113028 + 0.389503i
\(245\) 0 0
\(246\) 8.31355 1.37655i 0.530052 0.0877656i
\(247\) −3.29828 −0.209865
\(248\) −10.9230 4.92573i −0.693613 0.312784i
\(249\) −11.8257 + 3.72697i −0.749423 + 0.236187i
\(250\) 0 0
\(251\) 15.2464i 0.962346i 0.876626 + 0.481173i \(0.159789\pi\)
−0.876626 + 0.481173i \(0.840211\pi\)
\(252\) −10.9470 + 3.72737i −0.689594 + 0.234802i
\(253\) −6.93953 −0.436285
\(254\) 3.29942 23.2091i 0.207024 1.45627i
\(255\) 0 0
\(256\) 6.83067 + 14.4687i 0.426917 + 0.904291i
\(257\) −16.1845 −1.00956 −0.504782 0.863247i \(-0.668427\pi\)
−0.504782 + 0.863247i \(0.668427\pi\)
\(258\) 2.51628 0.416643i 0.156657 0.0259391i
\(259\) −18.9502 −1.17751
\(260\) 0 0
\(261\) −17.2011 + 12.0378i −1.06472 + 0.745120i
\(262\) 7.85886 + 1.11722i 0.485522 + 0.0690222i
\(263\) 21.4751i 1.32421i −0.749411 0.662105i \(-0.769663\pi\)
0.749411 0.662105i \(-0.230337\pi\)
\(264\) −19.5590 2.32545i −1.20377 0.143121i
\(265\) 0 0
\(266\) 0.262691 1.84785i 0.0161066 0.113299i
\(267\) −0.431611 1.36951i −0.0264142 0.0838124i
\(268\) −8.28980 + 28.5672i −0.506380 + 1.74502i
\(269\) 23.0327 1.40433 0.702163 0.712016i \(-0.252218\pi\)
0.702163 + 0.712016i \(0.252218\pi\)
\(270\) 0 0
\(271\) 16.1914i 0.983556i 0.870721 + 0.491778i \(0.163653\pi\)
−0.870721 + 0.491778i \(0.836347\pi\)
\(272\) −17.6746 11.2011i −1.07168 0.679166i
\(273\) 15.3361 4.83329i 0.928181 0.292524i
\(274\) 1.87454 13.1861i 0.113245 0.796599i
\(275\) 0 0
\(276\) −0.136764 5.97749i −0.00823223 0.359803i
\(277\) −3.81503 −0.229223 −0.114611 0.993410i \(-0.536562\pi\)
−0.114611 + 0.993410i \(0.536562\pi\)
\(278\) 1.29704 9.12376i 0.0777913 0.547207i
\(279\) 7.28700 + 10.4126i 0.436261 + 0.623385i
\(280\) 0 0
\(281\) 27.9474i 1.66720i 0.552368 + 0.833600i \(0.313724\pi\)
−0.552368 + 0.833600i \(0.686276\pi\)
\(282\) −18.2636 + 3.02407i −1.08758 + 0.180080i
\(283\) 5.58924i 0.332246i 0.986105 + 0.166123i \(0.0531249\pi\)
−0.986105 + 0.166123i \(0.946875\pi\)
\(284\) 17.8316 + 5.17448i 1.05811 + 0.307049i
\(285\) 0 0
\(286\) 27.1152 + 3.85471i 1.60335 + 0.227934i
\(287\) 6.63049i 0.391386i
\(288\) 1.61760 16.8933i 0.0953179 0.995447i
\(289\) 10.3661 0.609771
\(290\) 0 0
\(291\) 0.755956 + 2.39865i 0.0443149 + 0.140612i
\(292\) −6.28923 + 21.6731i −0.368049 + 1.26832i
\(293\) 6.00000i 0.350524i −0.984522 0.175262i \(-0.943923\pi\)
0.984522 0.175262i \(-0.0560772\pi\)
\(294\) −1.31457 7.93921i −0.0766671 0.463024i
\(295\) 0 0
\(296\) 11.4321 25.3512i 0.664479 1.47351i
\(297\) 16.5695 + 12.7243i 0.961458 + 0.738339i
\(298\) 1.49970 10.5494i 0.0868755 0.611107i
\(299\) 8.31374i 0.480796i
\(300\) 0 0
\(301\) 2.00687i 0.115674i
\(302\) −13.1765 1.87318i −0.758221 0.107789i
\(303\) −6.94281 + 2.18808i −0.398854 + 0.125702i
\(304\) 2.31355 + 1.46618i 0.132691 + 0.0840912i
\(305\) 0 0
\(306\) 10.0396 + 19.7939i 0.573923 + 1.13154i
\(307\) 4.79033i 0.273399i −0.990613 0.136699i \(-0.956351\pi\)
0.990613 0.136699i \(-0.0436494\pi\)
\(308\) −4.31917 + 14.8841i −0.246107 + 0.848103i
\(309\) −11.7319 + 3.69740i −0.667404 + 0.210338i
\(310\) 0 0
\(311\) 12.8780 0.730245 0.365123 0.930959i \(-0.381027\pi\)
0.365123 + 0.930959i \(0.381027\pi\)
\(312\) −2.78594 + 23.4321i −0.157723 + 1.32658i
\(313\) 20.4022i 1.15320i 0.817027 + 0.576600i \(0.195621\pi\)
−0.817027 + 0.576600i \(0.804379\pi\)
\(314\) −0.696056 + 4.89626i −0.0392807 + 0.276312i
\(315\) 0 0
\(316\) −5.15677 + 17.7706i −0.290091 + 0.999673i
\(317\) 5.34350i 0.300121i 0.988677 + 0.150060i \(0.0479468\pi\)
−0.988677 + 0.150060i \(0.952053\pi\)
\(318\) −9.86573 + 1.63356i −0.553243 + 0.0916054i
\(319\) 28.1372i 1.57538i
\(320\) 0 0
\(321\) 12.8240 4.04159i 0.715766 0.225579i
\(322\) −4.65773 0.662146i −0.259565 0.0369000i
\(323\) −3.58212 −0.199315
\(324\) −10.6338 + 14.5232i −0.590765 + 0.806844i
\(325\) 0 0
\(326\) −23.7398 3.37486i −1.31483 0.186916i
\(327\) −10.6783 33.8824i −0.590513 1.87370i
\(328\) 8.87017 + 4.00000i 0.489773 + 0.220863i
\(329\) 14.5662i 0.803059i
\(330\) 0 0
\(331\) 25.1694 1.38344 0.691719 0.722167i \(-0.256854\pi\)
0.691719 + 0.722167i \(0.256854\pi\)
\(332\) −13.7500 3.99006i −0.754630 0.218983i
\(333\) −24.1665 + 16.9124i −1.32432 + 0.926793i
\(334\) 15.9512 + 2.26763i 0.872809 + 0.124079i
\(335\) 0 0
\(336\) −12.9059 3.42706i −0.704072 0.186961i
\(337\) 20.1616i 1.09827i −0.835733 0.549136i \(-0.814957\pi\)
0.835733 0.549136i \(-0.185043\pi\)
\(338\) 2.03047 14.2829i 0.110443 0.776888i
\(339\) −0.356500 + 0.112354i −0.0193624 + 0.00610223i
\(340\) 0 0
\(341\) 17.0327 0.922371
\(342\) −1.31414 2.59094i −0.0710605 0.140102i
\(343\) −19.8234 −1.07036
\(344\) 2.68475 + 1.21069i 0.144752 + 0.0652759i
\(345\) 0 0
\(346\) −3.03131 0.430933i −0.162964 0.0231671i
\(347\) 9.41442 0.505392 0.252696 0.967546i \(-0.418683\pi\)
0.252696 + 0.967546i \(0.418683\pi\)
\(348\) −24.2365 + 0.554526i −1.29921 + 0.0297257i
\(349\) 10.3968i 0.556530i −0.960504 0.278265i \(-0.910241\pi\)
0.960504 0.278265i \(-0.0897593\pi\)
\(350\) 0 0
\(351\) 15.2440 19.8507i 0.813667 1.05955i
\(352\) −17.3061 14.7573i −0.922420 0.786568i
\(353\) −20.4254 −1.08713 −0.543567 0.839366i \(-0.682927\pi\)
−0.543567 + 0.839366i \(0.682927\pi\)
\(354\) 2.40422 0.398089i 0.127783 0.0211582i
\(355\) 0 0
\(356\) 0.462079 1.59235i 0.0244901 0.0843946i
\(357\) 16.6558 5.24922i 0.881520 0.277818i
\(358\) 7.47720 + 1.06296i 0.395182 + 0.0561794i
\(359\) −6.87107 −0.362641 −0.181320 0.983424i \(-0.558037\pi\)
−0.181320 + 0.983424i \(0.558037\pi\)
\(360\) 0 0
\(361\) −18.5311 −0.975322
\(362\) 15.1134 + 2.14853i 0.794343 + 0.112924i
\(363\) 8.53236 2.68904i 0.447833 0.141138i
\(364\) 17.8316 + 5.17448i 0.934629 + 0.271216i
\(365\) 0 0
\(366\) 7.65480 1.26748i 0.400123 0.0662520i
\(367\) −15.8130 −0.825431 −0.412715 0.910860i \(-0.635420\pi\)
−0.412715 + 0.910860i \(0.635420\pi\)
\(368\) 3.69569 5.83158i 0.192651 0.303992i
\(369\) −5.91749 8.45566i −0.308052 0.440184i
\(370\) 0 0
\(371\) 7.86844i 0.408509i
\(372\) 0.335679 + 14.6714i 0.0174042 + 0.760677i
\(373\) −7.51072 −0.388890 −0.194445 0.980913i \(-0.562291\pi\)
−0.194445 + 0.980913i \(0.562291\pi\)
\(374\) 29.4486 + 4.18643i 1.52275 + 0.216475i
\(375\) 0 0
\(376\) −19.4864 8.78738i −1.00493 0.453175i
\(377\) 33.7091 1.73610
\(378\) 9.90712 + 10.1214i 0.509567 + 0.520589i
\(379\) 13.1468 0.675307 0.337654 0.941270i \(-0.390367\pi\)
0.337654 + 0.941270i \(0.390367\pi\)
\(380\) 0 0
\(381\) −27.3833 + 8.63007i −1.40289 + 0.442132i
\(382\) −3.93094 + 27.6514i −0.201124 + 1.41477i
\(383\) 23.0887i 1.17978i −0.807484 0.589889i \(-0.799172\pi\)
0.807484 0.589889i \(-0.200828\pi\)
\(384\) 12.3704 15.1978i 0.631275 0.775559i
\(385\) 0 0
\(386\) −7.63356 1.08519i −0.388538 0.0552348i
\(387\) −1.79106 2.55929i −0.0910447 0.130096i
\(388\) −0.809320 + 2.78897i −0.0410870 + 0.141588i
\(389\) −12.9040 −0.654260 −0.327130 0.944979i \(-0.606081\pi\)
−0.327130 + 0.944979i \(0.606081\pi\)
\(390\) 0 0
\(391\) 9.02919i 0.456626i
\(392\) 3.81989 8.47077i 0.192934 0.427838i
\(393\) −2.92224 9.27229i −0.147407 0.467725i
\(394\) −31.7127 4.50829i −1.59766 0.227125i
\(395\) 0 0
\(396\) 7.77550 + 22.8360i 0.390733 + 1.14755i
\(397\) 18.1459 0.910719 0.455359 0.890308i \(-0.349511\pi\)
0.455359 + 0.890308i \(0.349511\pi\)
\(398\) −26.4420 3.75902i −1.32542 0.188423i
\(399\) −2.18019 + 0.687103i −0.109146 + 0.0343982i
\(400\) 0 0
\(401\) 33.7433i 1.68506i −0.538651 0.842529i \(-0.681066\pi\)
0.538651 0.842529i \(-0.318934\pi\)
\(402\) 35.9415 5.95116i 1.79260 0.296817i
\(403\) 20.4056i 1.01647i
\(404\) −8.07256 2.34254i −0.401625 0.116546i
\(405\) 0 0
\(406\) −2.68475 + 18.8853i −0.133242 + 0.937264i
\(407\) 39.5311i 1.95948i
\(408\) −3.02569 + 25.4486i −0.149794 + 1.25989i
\(409\) −31.6480 −1.56489 −0.782446 0.622718i \(-0.786028\pi\)
−0.782446 + 0.622718i \(0.786028\pi\)
\(410\) 0 0
\(411\) −15.5576 + 4.90310i −0.767399 + 0.241852i
\(412\) −13.6409 3.95841i −0.672041 0.195017i
\(413\) 1.91749i 0.0943537i
\(414\) −6.53080 + 3.31246i −0.320971 + 0.162798i
\(415\) 0 0
\(416\) −17.6796 + 20.7332i −0.866816 + 1.01653i
\(417\) −10.7647 + 3.39258i −0.527149 + 0.166135i
\(418\) −3.85471 0.547989i −0.188540 0.0268030i
\(419\) 29.8954i 1.46049i −0.683188 0.730243i \(-0.739407\pi\)
0.683188 0.730243i \(-0.260593\pi\)
\(420\) 0 0
\(421\) 6.86330i 0.334497i −0.985915 0.167248i \(-0.946512\pi\)
0.985915 0.167248i \(-0.0534882\pi\)
\(422\) −2.14316 + 15.0756i −0.104327 + 0.733870i
\(423\) 12.9998 + 18.5758i 0.632073 + 0.903185i
\(424\) −10.5263 4.74682i −0.511201 0.230526i
\(425\) 0 0
\(426\) −3.71470 22.4346i −0.179978 1.08696i
\(427\) 6.10511i 0.295447i
\(428\) 14.9108 + 4.32689i 0.720738 + 0.209148i
\(429\) −10.0825 31.9919i −0.486788 1.54458i
\(430\) 0 0
\(431\) −20.0226 −0.964455 −0.482228 0.876046i \(-0.660172\pi\)
−0.482228 + 0.876046i \(0.660172\pi\)
\(432\) −19.5170 + 7.14762i −0.939010 + 0.343890i
\(433\) 10.2112i 0.490717i −0.969432 0.245358i \(-0.921094\pi\)
0.969432 0.245358i \(-0.0789057\pi\)
\(434\) 11.4321 + 1.62520i 0.548760 + 0.0780121i
\(435\) 0 0
\(436\) 11.4321 39.3959i 0.547500 1.88672i
\(437\) 1.18189i 0.0565373i
\(438\) 27.2678 4.51497i 1.30291 0.215734i
\(439\) 33.6933i 1.60809i 0.594566 + 0.804047i \(0.297324\pi\)
−0.594566 + 0.804047i \(0.702676\pi\)
\(440\) 0 0
\(441\) −8.07492 + 5.65104i −0.384520 + 0.269097i
\(442\) 5.01546 35.2802i 0.238561 1.67811i
\(443\) 4.46465 0.212122 0.106061 0.994360i \(-0.466176\pi\)
0.106061 + 0.994360i \(0.466176\pi\)
\(444\) −34.0509 + 0.779077i −1.61598 + 0.0369734i
\(445\) 0 0
\(446\) −1.30283 + 9.16445i −0.0616906 + 0.433949i
\(447\) −12.4467 + 3.92267i −0.588707 + 0.185536i
\(448\) −10.2076 11.5562i −0.482263 0.545980i
\(449\) 27.5500i 1.30016i −0.759865 0.650081i \(-0.774735\pi\)
0.759865 0.650081i \(-0.225265\pi\)
\(450\) 0 0
\(451\) −13.8316 −0.651304
\(452\) −0.414511 0.120285i −0.0194970 0.00565774i
\(453\) 4.89954 + 15.5463i 0.230200 + 0.730428i
\(454\) 4.48084 31.5196i 0.210296 1.47929i
\(455\) 0 0
\(456\) 0.396052 3.33113i 0.0185468 0.155994i
\(457\) 11.5016i 0.538020i −0.963137 0.269010i \(-0.913303\pi\)
0.963137 0.269010i \(-0.0866965\pi\)
\(458\) −18.0392 2.56447i −0.842917 0.119830i
\(459\) 16.5559 21.5589i 0.772763 1.00628i
\(460\) 0 0
\(461\) −8.25929 −0.384673 −0.192337 0.981329i \(-0.561607\pi\)
−0.192337 + 0.981329i \(0.561607\pi\)
\(462\) 18.7263 3.10069i 0.871227 0.144257i
\(463\) 11.7199 0.544669 0.272334 0.962203i \(-0.412204\pi\)
0.272334 + 0.962203i \(0.412204\pi\)
\(464\) −23.6449 14.9846i −1.09769 0.695644i
\(465\) 0 0
\(466\) 2.15984 15.1929i 0.100052 0.703799i
\(467\) −17.1895 −0.795437 −0.397718 0.917508i \(-0.630198\pi\)
−0.397718 + 0.917508i \(0.630198\pi\)
\(468\) 27.3581 9.31525i 1.26463 0.430597i
\(469\) 28.6653i 1.32364i
\(470\) 0 0
\(471\) 5.77686 1.82062i 0.266184 0.0838900i
\(472\) 2.56519 + 1.15677i 0.118073 + 0.0532448i
\(473\) −4.18643 −0.192492
\(474\) 22.3579 3.70199i 1.02693 0.170038i
\(475\) 0 0
\(476\) 19.3661 + 5.61977i 0.887644 + 0.257582i
\(477\) 7.02232 + 10.0344i 0.321530 + 0.459442i
\(478\) 1.31976 9.28360i 0.0603645 0.424622i
\(479\) 11.5379 0.527181 0.263591 0.964635i \(-0.415093\pi\)
0.263591 + 0.964635i \(0.415093\pi\)
\(480\) 0 0
\(481\) 47.3593 2.15940
\(482\) −3.17513 + 22.3348i −0.144623 + 1.01732i
\(483\) 1.73193 + 5.49543i 0.0788056 + 0.250051i
\(484\) 9.92076 + 2.87887i 0.450944 + 0.130858i
\(485\) 0 0
\(486\) 21.6673 + 4.06573i 0.982847 + 0.184425i
\(487\) −33.1015 −1.49997 −0.749985 0.661455i \(-0.769939\pi\)
−0.749985 + 0.661455i \(0.769939\pi\)
\(488\) 8.16732 + 3.68305i 0.369717 + 0.166724i
\(489\) 8.82740 + 28.0094i 0.399189 + 1.26663i
\(490\) 0 0
\(491\) 21.3635i 0.964121i −0.876138 0.482061i \(-0.839888\pi\)
0.876138 0.482061i \(-0.160112\pi\)
\(492\) −0.272592 11.9141i −0.0122894 0.537129i
\(493\) 36.6099 1.64883
\(494\) −0.656505 + 4.61805i −0.0295375 + 0.207776i
\(495\) 0 0
\(496\) −9.07086 + 14.3133i −0.407294 + 0.642685i
\(497\) −17.8928 −0.802602
\(498\) 2.86442 + 17.2994i 0.128358 + 0.775206i
\(499\) −14.8464 −0.664614 −0.332307 0.943171i \(-0.607827\pi\)
−0.332307 + 0.943171i \(0.607827\pi\)
\(500\) 0 0
\(501\) −5.93128 18.8200i −0.264990 0.840816i
\(502\) 21.3471 + 3.03472i 0.952767 + 0.135446i
\(503\) 1.86841i 0.0833084i −0.999132 0.0416542i \(-0.986737\pi\)
0.999132 0.0416542i \(-0.0132628\pi\)
\(504\) 3.03989 + 16.0692i 0.135408 + 0.715777i
\(505\) 0 0
\(506\) −1.38127 + 9.71629i −0.0614051 + 0.431942i
\(507\) −16.8517 + 5.31096i −0.748411 + 0.235868i
\(508\) −31.8392 9.23928i −1.41263 0.409927i
\(509\) 1.62879 0.0721950 0.0360975 0.999348i \(-0.488507\pi\)
0.0360975 + 0.999348i \(0.488507\pi\)
\(510\) 0 0
\(511\) 21.7475i 0.962053i
\(512\) 21.6177 6.68396i 0.955376 0.295392i
\(513\) −2.16710 + 2.82198i −0.0956800 + 0.124594i
\(514\) −3.22144 + 22.6605i −0.142092 + 0.999514i
\(515\) 0 0
\(516\) −0.0825061 3.60606i −0.00363213 0.158748i
\(517\) 30.3858 1.33637
\(518\) −3.77192 + 26.5328i −0.165729 + 1.16578i
\(519\) 1.12716 + 3.57650i 0.0494770 + 0.156991i
\(520\) 0 0
\(521\) 7.82768i 0.342937i 0.985190 + 0.171469i \(0.0548512\pi\)
−0.985190 + 0.171469i \(0.945149\pi\)
\(522\) 13.4308 + 26.4799i 0.587848 + 1.15899i
\(523\) 32.2423i 1.40986i 0.709277 + 0.704930i \(0.249021\pi\)
−0.709277 + 0.704930i \(0.750979\pi\)
\(524\) 3.12852 10.7811i 0.136670 0.470975i
\(525\) 0 0
\(526\) −30.0680 4.27449i −1.31103 0.186377i
\(527\) 22.1616i 0.965375i
\(528\) −7.14904 + 26.9223i −0.311122 + 1.17164i
\(529\) 20.0209 0.870474
\(530\) 0 0
\(531\) −1.71130 2.44532i −0.0742640 0.106118i
\(532\) −2.53495 0.735607i −0.109904 0.0318926i
\(533\) 16.5706i 0.717752i
\(534\) −2.00340 + 0.331722i −0.0866958 + 0.0143550i
\(535\) 0 0
\(536\) 38.3479 + 17.2930i 1.65638 + 0.746943i
\(537\) −2.78032 8.82198i −0.119980 0.380697i
\(538\) 4.58452 32.2489i 0.197653 1.39035i
\(539\) 13.2088i 0.568942i
\(540\) 0 0
\(541\) 3.25040i 0.139746i 0.997556 + 0.0698728i \(0.0222593\pi\)
−0.997556 + 0.0698728i \(0.977741\pi\)
\(542\) 22.6701 + 3.22280i 0.973765 + 0.138431i
\(543\) −5.61977 17.8316i −0.241167 0.765227i
\(544\) −19.2011 + 22.5174i −0.823240 + 0.965426i
\(545\) 0 0
\(546\) −3.71470 22.4346i −0.158975 0.960113i
\(547\) 10.3248i 0.441459i 0.975335 + 0.220729i \(0.0708437\pi\)
−0.975335 + 0.220729i \(0.929156\pi\)
\(548\) −18.0892 5.24922i −0.772731 0.224236i
\(549\) −5.44861 7.78565i −0.232541 0.332284i
\(550\) 0 0
\(551\) −4.79210 −0.204150
\(552\) −8.39653 0.998298i −0.357380 0.0424904i
\(553\) 17.8316i 0.758276i
\(554\) −0.759359 + 5.34156i −0.0322621 + 0.226941i
\(555\) 0 0
\(556\) −12.5163 3.63207i −0.530811 0.154034i
\(557\) 8.33343i 0.353099i −0.984292 0.176549i \(-0.943506\pi\)
0.984292 0.176549i \(-0.0564935\pi\)
\(558\) 16.0295 8.13023i 0.678581 0.344180i
\(559\) 5.01546i 0.212131i
\(560\) 0 0
\(561\) −10.9502 34.7450i −0.462316 1.46693i
\(562\) 39.1301 + 5.56277i 1.65060 + 0.234651i
\(563\) 14.0982 0.594166 0.297083 0.954852i \(-0.403986\pi\)
0.297083 + 0.954852i \(0.403986\pi\)
\(564\) 0.598843 + 26.1734i 0.0252158 + 1.10210i
\(565\) 0 0
\(566\) 7.82570 + 1.11251i 0.328939 + 0.0467622i
\(567\) 5.94109 16.2971i 0.249502 0.684412i
\(568\) 10.7942 23.9367i 0.452916 1.00436i
\(569\) 9.37801i 0.393147i 0.980489 + 0.196573i \(0.0629814\pi\)
−0.980489 + 0.196573i \(0.937019\pi\)
\(570\) 0 0
\(571\) 10.1967 0.426717 0.213359 0.976974i \(-0.431560\pi\)
0.213359 + 0.976974i \(0.431560\pi\)
\(572\) 10.7942 37.1977i 0.451330 1.55531i
\(573\) 32.6245 10.2819i 1.36291 0.429532i
\(574\) −9.28360 1.31976i −0.387490 0.0550858i
\(575\) 0 0
\(576\) −23.3309 5.62737i −0.972122 0.234474i
\(577\) 14.9762i 0.623466i 0.950170 + 0.311733i \(0.100910\pi\)
−0.950170 + 0.311733i \(0.899090\pi\)
\(578\) 2.06331 14.5140i 0.0858225 0.603701i
\(579\) 2.83846 + 9.00647i 0.117962 + 0.374296i
\(580\) 0 0
\(581\) 13.7972 0.572405
\(582\) 3.50891 0.581002i 0.145449 0.0240833i
\(583\) 16.4140 0.679799
\(584\) 29.0935 + 13.1197i 1.20390 + 0.542897i
\(585\) 0 0
\(586\) −8.40082 1.19427i −0.347035 0.0493347i
\(587\) −35.1368 −1.45025 −0.725125 0.688617i \(-0.758218\pi\)
−0.725125 + 0.688617i \(0.758218\pi\)
\(588\) −11.3776 + 0.260318i −0.469205 + 0.0107353i
\(589\) 2.90087i 0.119528i
\(590\) 0 0
\(591\) 11.7920 + 37.4162i 0.485059 + 1.53910i
\(592\) −33.2197 21.0526i −1.36532 0.865255i
\(593\) 11.6209 0.477214 0.238607 0.971116i \(-0.423309\pi\)
0.238607 + 0.971116i \(0.423309\pi\)
\(594\) 21.1138 20.6668i 0.866310 0.847970i
\(595\) 0 0
\(596\) −14.4720 4.19958i −0.592797 0.172021i
\(597\) 9.83221 + 31.1977i 0.402405 + 1.27684i
\(598\) 11.6404 + 1.65480i 0.476010 + 0.0676699i
\(599\) −9.69953 −0.396312 −0.198156 0.980170i \(-0.563495\pi\)
−0.198156 + 0.980170i \(0.563495\pi\)
\(600\) 0 0
\(601\) 0.585768 0.0238940 0.0119470 0.999929i \(-0.496197\pi\)
0.0119470 + 0.999929i \(0.496197\pi\)
\(602\) −2.80989 0.399455i −0.114522 0.0162806i
\(603\) −25.5828 36.5559i −1.04181 1.48867i
\(604\) −5.24541 + 18.0760i −0.213433 + 0.735503i
\(605\) 0 0
\(606\) 1.68169 + 10.1564i 0.0683139 + 0.412576i
\(607\) −22.9594 −0.931894 −0.465947 0.884813i \(-0.654286\pi\)
−0.465947 + 0.884813i \(0.654286\pi\)
\(608\) 2.51335 2.94744i 0.101930 0.119535i
\(609\) 22.2819 7.02232i 0.902908 0.284559i
\(610\) 0 0
\(611\) 36.4030i 1.47271i
\(612\) 29.7124 10.1169i 1.20105 0.408951i
\(613\) 4.10130 0.165650 0.0828250 0.996564i \(-0.473606\pi\)
0.0828250 + 0.996564i \(0.473606\pi\)
\(614\) −6.70712 0.953488i −0.270677 0.0384797i
\(615\) 0 0
\(616\) 19.9801 + 9.01003i 0.805022 + 0.363024i
\(617\) −14.1493 −0.569630 −0.284815 0.958583i \(-0.591932\pi\)
−0.284815 + 0.958583i \(0.591932\pi\)
\(618\) 2.84170 + 17.1622i 0.114310 + 0.690365i
\(619\) 10.1108 0.406386 0.203193 0.979139i \(-0.434868\pi\)
0.203193 + 0.979139i \(0.434868\pi\)
\(620\) 0 0
\(621\) 7.11317 + 5.46246i 0.285441 + 0.219201i
\(622\) 2.56330 18.0310i 0.102779 0.722976i
\(623\) 1.59782i 0.0640153i
\(624\) 32.2536 + 8.56473i 1.29118 + 0.342864i
\(625\) 0 0
\(626\) 28.5658 + 4.06094i 1.14172 + 0.162308i
\(627\) 1.43334 + 4.54799i 0.0572419 + 0.181629i
\(628\) 6.71689 + 1.94915i 0.268033 + 0.0777794i
\(629\) 51.4349 2.05084
\(630\) 0 0
\(631\) 28.7572i 1.14481i −0.819972 0.572404i \(-0.806011\pi\)
0.819972 0.572404i \(-0.193989\pi\)
\(632\) 23.8548 + 10.7573i 0.948893 + 0.427903i
\(633\) 17.7870 5.60572i 0.706970 0.222807i
\(634\) 7.48162 + 1.06359i 0.297133 + 0.0422407i
\(635\) 0 0
\(636\) 0.323487 + 14.1385i 0.0128271 + 0.560629i
\(637\) 15.8245 0.626988
\(638\) 39.3959 + 5.60054i 1.55970 + 0.221728i
\(639\) −22.8181 + 15.9687i −0.902671 + 0.631713i
\(640\) 0 0
\(641\) 35.7751i 1.41303i −0.707698 0.706515i \(-0.750266\pi\)
0.707698 0.706515i \(-0.249734\pi\)
\(642\) −3.10623 18.7598i −0.122593 0.740390i
\(643\) 4.64793i 0.183296i 0.995791 + 0.0916481i \(0.0292135\pi\)
−0.995791 + 0.0916481i \(0.970786\pi\)
\(644\) −1.85419 + 6.38966i −0.0730653 + 0.251788i
\(645\) 0 0
\(646\) −0.713001 + 5.01546i −0.0280526 + 0.197330i
\(647\) 6.90109i 0.271310i −0.990756 0.135655i \(-0.956686\pi\)
0.990756 0.135655i \(-0.0433138\pi\)
\(648\) 18.2179 + 17.7795i 0.715665 + 0.698444i
\(649\) −4.00000 −0.157014
\(650\) 0 0
\(651\) −4.25092 13.4882i −0.166607 0.528645i
\(652\) −9.45054 + 32.5672i −0.370112 + 1.27543i
\(653\) 16.8181i 0.658144i 0.944305 + 0.329072i \(0.106736\pi\)
−0.944305 + 0.329072i \(0.893264\pi\)
\(654\) −49.5655 + 8.20701i −1.93816 + 0.320919i
\(655\) 0 0
\(656\) 7.36610 11.6233i 0.287598 0.453812i
\(657\) −19.4089 27.7339i −0.757214 1.08200i
\(658\) 20.3946 + 2.89931i 0.795065 + 0.113027i
\(659\) 15.3712i 0.598779i 0.954131 + 0.299389i \(0.0967830\pi\)
−0.954131 + 0.299389i \(0.903217\pi\)
\(660\) 0 0
\(661\) 14.7252i 0.572743i −0.958119 0.286372i \(-0.907551\pi\)
0.958119 0.286372i \(-0.0924492\pi\)
\(662\) 5.00983 35.2406i 0.194713 1.36967i
\(663\) −41.6254 + 13.1186i −1.61660 + 0.509484i
\(664\) −8.32349 + 18.4577i −0.323014 + 0.716297i
\(665\) 0 0
\(666\) 18.8694 + 37.2028i 0.731176 + 1.44158i
\(667\) 12.0791i 0.467705i
\(668\) 6.34998 21.8824i 0.245688 0.846657i
\(669\) 10.8127 3.40771i 0.418043 0.131750i
\(670\) 0 0
\(671\) −12.7356 −0.491653
\(672\) −7.36719 + 17.3878i −0.284195 + 0.670749i
\(673\) 44.9434i 1.73244i 0.499663 + 0.866220i \(0.333457\pi\)
−0.499663 + 0.866220i \(0.666543\pi\)
\(674\) −28.2290 4.01305i −1.08734 0.154577i
\(675\) 0 0
\(676\) −19.5939 5.68587i −0.753610 0.218687i
\(677\) 31.3401i 1.20450i 0.798308 + 0.602249i \(0.205728\pi\)
−0.798308 + 0.602249i \(0.794272\pi\)
\(678\) 0.0863516 + 0.521513i 0.00331631 + 0.0200286i
\(679\) 2.79854i 0.107398i
\(680\) 0 0
\(681\) −37.1884 + 11.7202i −1.42506 + 0.449120i
\(682\) 3.39026 23.8481i 0.129820 0.913190i
\(683\) 6.76121 0.258710 0.129355 0.991598i \(-0.458709\pi\)
0.129355 + 0.991598i \(0.458709\pi\)
\(684\) −3.88925 + 1.32426i −0.148709 + 0.0506344i
\(685\) 0 0
\(686\) −3.94574 + 27.7555i −0.150649 + 1.05971i
\(687\) 6.70770 + 21.2836i 0.255915 + 0.812020i
\(688\) 2.22951 3.51804i 0.0849994 0.134124i
\(689\) 19.6644i 0.749155i
\(690\) 0 0
\(691\) 14.4304 0.548959 0.274480 0.961593i \(-0.411494\pi\)
0.274480 + 0.961593i \(0.411494\pi\)
\(692\) −1.20673 + 4.15847i −0.0458730 + 0.158081i
\(693\) −13.3292 19.0464i −0.506334 0.723514i
\(694\) 1.87389 13.1815i 0.0711317 0.500362i
\(695\) 0 0
\(696\) −4.04772 + 34.0447i −0.153428 + 1.29046i
\(697\) 17.9966i 0.681670i
\(698\) −14.5570 2.06943i −0.550990 0.0783291i
\(699\) −17.9254 + 5.64934i −0.678001 + 0.213677i
\(700\) 0 0
\(701\) 9.83499 0.371462 0.185731 0.982601i \(-0.440535\pi\)
0.185731 + 0.982601i \(0.440535\pi\)
\(702\) −24.7594 25.2949i −0.934483 0.954694i
\(703\) −6.73263 −0.253926
\(704\) −24.1069 + 21.2936i −0.908565 + 0.802532i
\(705\) 0 0
\(706\) −4.06556 + 28.5983i −0.153009 + 1.07631i
\(707\) 8.10028 0.304642
\(708\) −0.0788318 3.44547i −0.00296268 0.129489i
\(709\) 20.4277i 0.767180i 0.923503 + 0.383590i \(0.125312\pi\)
−0.923503 + 0.383590i \(0.874688\pi\)
\(710\) 0 0
\(711\) −15.9141 22.7401i −0.596825 0.852819i
\(712\) −2.13754 0.963923i −0.0801077 0.0361245i
\(713\) 7.31201 0.273837
\(714\) −4.03438 24.3652i −0.150983 0.911847i
\(715\) 0 0
\(716\) 2.97659 10.2575i 0.111240 0.383341i
\(717\) −10.9533 + 3.45201i −0.409057 + 0.128918i
\(718\) −1.36765 + 9.62043i −0.0510401 + 0.359031i
\(719\) −28.2338 −1.05294 −0.526471 0.850193i \(-0.676485\pi\)
−0.526471 + 0.850193i \(0.676485\pi\)
\(720\) 0 0
\(721\) 13.6878 0.509759
\(722\) −3.68851 + 25.9461i −0.137272 + 0.965613i
\(723\) 26.3517 8.30497i 0.980032 0.308865i
\(724\) 6.01648 20.7332i 0.223601 0.770543i
\(725\) 0 0
\(726\) −2.06671 12.4817i −0.0767027 0.463239i
\(727\) 28.1339 1.04343 0.521714 0.853120i \(-0.325293\pi\)
0.521714 + 0.853120i \(0.325293\pi\)
\(728\) 10.7942 23.9367i 0.400061 0.887153i
\(729\) −6.96811 26.0854i −0.258078 0.966124i
\(730\) 0 0
\(731\) 5.44707i 0.201467i
\(732\) −0.250993 10.9701i −0.00927696 0.405465i
\(733\) 10.2296 0.377840 0.188920 0.981993i \(-0.439501\pi\)
0.188920 + 0.981993i \(0.439501\pi\)
\(734\) −3.14748 + 22.1403i −0.116176 + 0.817214i
\(735\) 0 0
\(736\) −7.42941 6.33522i −0.273852 0.233519i
\(737\) −59.7973 −2.20266
\(738\) −13.0169 + 6.60225i −0.479159 + 0.243032i
\(739\) 48.0440 1.76733 0.883664 0.468121i \(-0.155069\pi\)
0.883664 + 0.468121i \(0.155069\pi\)
\(740\) 0 0
\(741\) 5.44861 1.71717i 0.200160 0.0630819i
\(742\) 11.0169 + 1.56617i 0.404443 + 0.0574959i
\(743\) 35.9667i 1.31949i 0.751489 + 0.659745i \(0.229336\pi\)
−0.751489 + 0.659745i \(0.770664\pi\)
\(744\) 20.6088 + 2.45026i 0.755555 + 0.0898310i
\(745\) 0 0
\(746\) −1.49497 + 10.5160i −0.0547346 + 0.385019i
\(747\) 17.5951 12.3135i 0.643772 0.450529i
\(748\) 11.7232 40.3988i 0.428641 1.47713i
\(749\) −14.9619 −0.546697
\(750\) 0 0
\(751\) 26.4357i 0.964654i −0.875991 0.482327i \(-0.839792\pi\)
0.875991 0.482327i \(-0.160208\pi\)
\(752\) −16.1822 + 25.5345i −0.590104 + 0.931148i
\(753\) −7.93770 25.1864i −0.289266 0.917843i
\(754\) 6.70960 47.1973i 0.244349 1.71882i
\(755\) 0 0
\(756\) 16.1433 11.8567i 0.587126 0.431225i
\(757\) 24.6881 0.897303 0.448652 0.893707i \(-0.351904\pi\)
0.448652 + 0.893707i \(0.351904\pi\)
\(758\) 2.61680 18.4074i 0.0950465 0.668585i
\(759\) 11.4638 3.61290i 0.416109 0.131140i
\(760\) 0 0
\(761\) 46.5273i 1.68661i 0.537434 + 0.843306i \(0.319394\pi\)
−0.537434 + 0.843306i \(0.680606\pi\)
\(762\) 6.63278 + 40.0581i 0.240280 + 1.45115i
\(763\) 39.5311i 1.43112i
\(764\) 37.9333 + 11.0077i 1.37238 + 0.398245i
\(765\) 0 0
\(766\) −32.3273 4.59568i −1.16803 0.166049i
\(767\) 4.79210i 0.173033i
\(768\) −18.8167 20.3453i −0.678990 0.734148i
\(769\) −36.8643 −1.32936 −0.664680 0.747129i \(-0.731432\pi\)
−0.664680 + 0.747129i \(0.731432\pi\)
\(770\) 0 0
\(771\) 26.7361 8.42609i 0.962876 0.303458i
\(772\) −3.03883 + 10.4720i −0.109370 + 0.376896i
\(773\) 41.5537i 1.49458i −0.664496 0.747292i \(-0.731354\pi\)
0.664496 0.747292i \(-0.268646\pi\)
\(774\) −3.93986 + 1.99832i −0.141615 + 0.0718280i
\(775\) 0 0
\(776\) 3.74385 + 1.68829i 0.134396 + 0.0606059i
\(777\) 31.3048 9.86596i 1.12305 0.353939i
\(778\) −2.56847 + 18.0674i −0.0920842 + 0.647747i
\(779\) 2.35569i 0.0844013i
\(780\) 0 0
\(781\) 37.3254i 1.33561i
\(782\) 12.6421 + 1.79721i 0.452080 + 0.0642681i
\(783\) 22.1482 28.8412i 0.791512 1.03070i
\(784\) −11.0999 7.03442i −0.396425 0.251229i
\(785\) 0 0
\(786\) −13.5641 + 2.24594i −0.483816 + 0.0801099i
\(787\) 48.4300i 1.72634i −0.504912 0.863171i \(-0.668475\pi\)
0.504912 0.863171i \(-0.331525\pi\)
\(788\) −12.6245 + 43.5047i −0.449727 + 1.54979i
\(789\) 11.1805 + 35.4758i 0.398036 + 1.26297i
\(790\) 0 0
\(791\) 0.415934 0.0147889
\(792\) 33.5212 6.34138i 1.19112 0.225331i
\(793\) 15.2576i 0.541813i
\(794\) 3.61185 25.4068i 0.128180 0.901653i
\(795\) 0 0
\(796\) −10.5263 + 36.2743i −0.373094 + 1.28571i
\(797\) 32.0757i 1.13618i −0.822967 0.568090i \(-0.807683\pi\)
0.822967 0.568090i \(-0.192317\pi\)
\(798\) 0.528085 + 3.18932i 0.0186940 + 0.112901i
\(799\) 39.5357i 1.39867i
\(800\) 0 0
\(801\) 1.42600 + 2.03765i 0.0503853 + 0.0719968i
\(802\) −47.2452 6.71640i −1.66828 0.237164i
\(803\) −45.3665 −1.60095
\(804\) −1.17848 51.5075i −0.0415619 1.81653i
\(805\) 0 0
\(806\) −28.5706 4.06162i −1.00636 0.143064i
\(807\) −38.0489 + 11.9914i −1.33938 + 0.422118i
\(808\) −4.88668 + 10.8364i −0.171913 + 0.381224i
\(809\) 1.09505i 0.0385001i −0.999815 0.0192500i \(-0.993872\pi\)
0.999815 0.0192500i \(-0.00612785\pi\)
\(810\) 0 0
\(811\) 3.56617 0.125225 0.0626126 0.998038i \(-0.480057\pi\)
0.0626126 + 0.998038i \(0.480057\pi\)
\(812\) 25.9077 + 7.51804i 0.909181 + 0.263831i
\(813\) −8.42966 26.7474i −0.295641 0.938071i
\(814\) 55.3489 + 7.86844i 1.93998 + 0.275789i
\(815\) 0 0
\(816\) 35.0293 + 9.30178i 1.22627 + 0.325627i
\(817\) 0.713001i 0.0249447i
\(818\) −6.29935 + 44.3115i −0.220252 + 1.54932i
\(819\) −22.8181 + 15.9687i −0.797329 + 0.557992i
\(820\) 0 0
\(821\) −47.0327 −1.64145 −0.820726 0.571322i \(-0.806431\pi\)
−0.820726 + 0.571322i \(0.806431\pi\)
\(822\) 3.76836 + 22.7587i 0.131437 + 0.793800i
\(823\) −30.2235 −1.05353 −0.526763 0.850012i \(-0.676595\pi\)
−0.526763 + 0.850012i \(0.676595\pi\)
\(824\) −8.25746 + 18.3113i −0.287662 + 0.637903i
\(825\) 0 0
\(826\) −2.68475 0.381666i −0.0934145 0.0132799i
\(827\) 31.2229 1.08573 0.542864 0.839821i \(-0.317340\pi\)
0.542864 + 0.839821i \(0.317340\pi\)
\(828\) 3.33797 + 9.80334i 0.116002 + 0.340689i
\(829\) 42.0990i 1.46216i −0.682292 0.731080i \(-0.739017\pi\)
0.682292 0.731080i \(-0.260983\pi\)
\(830\) 0 0
\(831\) 6.30224 1.98620i 0.218622 0.0689006i
\(832\) 25.5102 + 28.8807i 0.884409 + 1.00126i
\(833\) 17.1863 0.595468
\(834\) 2.60742 + 15.7473i 0.0902876 + 0.545284i
\(835\) 0 0
\(836\) −1.53452 + 5.28805i −0.0530724 + 0.182891i
\(837\) −17.4588 13.4073i −0.603466 0.463424i
\(838\) −41.8576 5.95051i −1.44595 0.205557i
\(839\) −14.0599 −0.485402 −0.242701 0.970101i \(-0.578033\pi\)
−0.242701 + 0.970101i \(0.578033\pi\)
\(840\) 0 0
\(841\) 19.9762 0.688834
\(842\) −9.60956 1.36610i −0.331167 0.0470790i
\(843\) −14.5501 46.1677i −0.501134 1.59010i
\(844\) 20.6813 + 6.00144i 0.711881 + 0.206578i
\(845\) 0 0
\(846\) 28.5961 14.5041i 0.983156 0.498662i
\(847\) −9.95482 −0.342052
\(848\) −8.74139 + 13.7934i −0.300181 + 0.473667i
\(849\) −2.90991 9.23316i −0.0998678 0.316881i
\(850\) 0 0
\(851\) 16.9704i 0.581739i
\(852\) −32.1509 + 0.735607i −1.10147 + 0.0252015i
\(853\) −25.1966 −0.862716 −0.431358 0.902181i \(-0.641965\pi\)
−0.431358 + 0.902181i \(0.641965\pi\)
\(854\) −8.54799 1.21519i −0.292506 0.0415829i
\(855\) 0 0
\(856\) 9.02614 20.0158i 0.308507 0.684127i
\(857\) 46.7431 1.59671 0.798357 0.602185i \(-0.205703\pi\)
0.798357 + 0.602185i \(0.205703\pi\)
\(858\) −46.7999 + 7.74908i −1.59772 + 0.264549i
\(859\) −40.8430 −1.39354 −0.696772 0.717293i \(-0.745381\pi\)
−0.696772 + 0.717293i \(0.745381\pi\)
\(860\) 0 0
\(861\) 3.45201 + 10.9533i 0.117644 + 0.373286i
\(862\) −3.98539 + 28.0344i −0.135743 + 0.954855i
\(863\) 39.3858i 1.34071i 0.742042 + 0.670354i \(0.233858\pi\)
−0.742042 + 0.670354i \(0.766142\pi\)
\(864\) 6.12290 + 28.7491i 0.208305 + 0.978064i
\(865\) 0 0
\(866\) −14.2970 2.03247i −0.485832 0.0690662i
\(867\) −17.1243 + 5.39687i −0.581572 + 0.183287i
\(868\) 4.55100 15.6831i 0.154471 0.532317i
\(869\) −37.1977 −1.26185
\(870\) 0 0
\(871\) 71.6388i 2.42739i
\(872\) −52.8841 23.8481i −1.79088 0.807597i
\(873\) −2.49761 3.56889i −0.0845312 0.120789i
\(874\) −1.65480 0.235248i −0.0559745 0.00795738i
\(875\) 0 0
\(876\) −0.894082 39.0773i −0.0302082 1.32030i
\(877\) −57.4498 −1.93994 −0.969972 0.243218i \(-0.921797\pi\)
−0.969972 + 0.243218i \(0.921797\pi\)
\(878\) 47.1752 + 6.70646i 1.59209 + 0.226332i
\(879\) 3.12376 + 9.91172i 0.105362 + 0.334314i
\(880\) 0 0
\(881\) 44.2957i 1.49236i −0.665744 0.746180i \(-0.731886\pi\)
0.665744 0.746180i \(-0.268114\pi\)
\(882\) 6.30496 + 12.4308i 0.212299 + 0.418567i
\(883\) 25.7701i 0.867231i 0.901098 + 0.433616i \(0.142762\pi\)
−0.901098 + 0.433616i \(0.857238\pi\)
\(884\) −48.3988 14.0446i −1.62783 0.472373i
\(885\) 0 0
\(886\) 0.888663 6.25112i 0.0298552 0.210010i
\(887\) 21.4751i 0.721063i −0.932747 0.360531i \(-0.882595\pi\)
0.932747 0.360531i \(-0.117405\pi\)
\(888\) −5.68681 + 47.8309i −0.190837 + 1.60510i
\(889\) 31.9485 1.07152
\(890\) 0 0
\(891\) −33.9966 12.3934i −1.13893 0.415196i
\(892\) 12.5722 + 3.64827i 0.420947 + 0.122153i
\(893\) 5.17508i 0.173177i
\(894\) 3.01483 + 18.2078i 0.100831 + 0.608960i
\(895\) 0 0
\(896\) −18.2121 + 11.9918i −0.608422 + 0.400618i
\(897\) −4.32835 13.7339i −0.144520 0.458562i
\(898\) −38.5737 5.48366i −1.28722 0.182992i
\(899\) 29.6474i 0.988798i
\(900\) 0 0
\(901\) 21.3567i 0.711493i
\(902\) −2.75310 + 19.3661i −0.0916682 + 0.644821i
\(903\) 1.04483 + 3.31525i 0.0347697 + 0.110325i
\(904\) −0.250922 + 0.556430i −0.00834554 + 0.0185066i
\(905\) 0 0
\(906\) 22.7421 3.76562i 0.755557 0.125104i
\(907\) 34.5984i 1.14882i 0.818568 + 0.574410i \(0.194769\pi\)
−0.818568 + 0.574410i \(0.805231\pi\)
\(908\) −43.2398 12.5476i −1.43496 0.416406i
\(909\) 10.3300 7.22923i 0.342625 0.239778i
\(910\) 0 0
\(911\) −20.3074 −0.672815 −0.336407 0.941717i \(-0.609212\pi\)
−0.336407 + 0.941717i \(0.609212\pi\)
\(912\) −4.58520 1.21757i −0.151831 0.0403177i
\(913\) 28.7818i 0.952537i
\(914\) −16.1038 2.28932i −0.532665 0.0757240i
\(915\) 0 0
\(916\) −7.18121 + 24.7469i −0.237274 + 0.817661i
\(917\) 10.8181i 0.357246i
\(918\) −26.8901 27.4717i −0.887505 0.906701i
\(919\) 11.1280i 0.367080i 0.983012 + 0.183540i \(0.0587556\pi\)
−0.983012 + 0.183540i \(0.941244\pi\)
\(920\) 0 0
\(921\) 2.49397 + 7.91340i 0.0821792 + 0.260755i
\(922\) −1.64396 + 11.5641i −0.0541411 + 0.380844i
\(923\) 44.7168 1.47187
\(924\) −0.614016 26.8366i −0.0201996 0.882858i
\(925\) 0 0
\(926\) 2.33278 16.4094i 0.0766597 0.539247i
\(927\) 17.4556 12.2159i 0.573316 0.401222i
\(928\) −25.6869 + 30.1234i −0.843214 + 0.988850i
\(929\) 20.3857i 0.668834i 0.942425 + 0.334417i \(0.108539\pi\)
−0.942425 + 0.334417i \(0.891461\pi\)
\(930\) 0 0
\(931\) −2.24962 −0.0737282
\(932\) −20.8423 6.04813i −0.682711 0.198113i
\(933\) −21.2739 + 6.70464i −0.696475 + 0.219500i
\(934\) −3.42148 + 24.0677i −0.111954 + 0.787519i
\(935\) 0 0
\(936\) −7.59714 40.1592i −0.248320 1.31264i
\(937\) 35.4418i 1.15783i 0.815387 + 0.578917i \(0.196524\pi\)
−0.815387 + 0.578917i \(0.803476\pi\)
\(938\) −40.1353 5.70566i −1.31046 0.186296i
\(939\) −10.6219 33.7034i −0.346633 1.09987i
\(940\) 0 0
\(941\) −13.4402 −0.438139 −0.219070 0.975709i \(-0.570302\pi\)
−0.219070 + 0.975709i \(0.570302\pi\)
\(942\) −1.39927 8.45078i −0.0455907 0.275341i
\(943\) −5.93781 −0.193362
\(944\) 2.13023 3.36137i 0.0693330 0.109403i
\(945\) 0 0
\(946\) −0.833286 + 5.86158i −0.0270925 + 0.190576i
\(947\) 4.96195 0.161242 0.0806208 0.996745i \(-0.474310\pi\)
0.0806208 + 0.996745i \(0.474310\pi\)
\(948\) −0.733090 32.0409i −0.0238097 1.04064i
\(949\) 54.3503i 1.76428i
\(950\) 0 0
\(951\) −2.78197 8.82720i −0.0902114 0.286242i
\(952\) 11.7232 25.9966i 0.379950 0.842555i
\(953\) −51.4156 −1.66551 −0.832757 0.553639i \(-0.813239\pi\)
−0.832757 + 0.553639i \(0.813239\pi\)
\(954\) 15.4472 7.83492i 0.500123 0.253665i
\(955\) 0 0
\(956\) −12.7356 3.69569i −0.411899 0.119527i
\(957\) −14.6490 46.4813i −0.473534 1.50253i
\(958\) 2.29656 16.1547i 0.0741984 0.521933i
\(959\) 18.1513 0.586135
\(960\) 0 0
\(961\) 13.0531 0.421068
\(962\) 9.42660 66.3095i 0.303926 2.13790i
\(963\) −19.0805 + 13.3530i −0.614860 + 0.430295i
\(964\) 30.6398 + 8.89123i 0.986840 + 0.286367i
\(965\) 0 0
\(966\) 8.03908 1.33110i 0.258653 0.0428276i
\(967\) 20.9875 0.674911 0.337456 0.941341i \(-0.390434\pi\)
0.337456 + 0.941341i \(0.390434\pi\)
\(968\) 6.00548 13.3174i 0.193023 0.428037i
\(969\) 5.91749 1.86495i 0.190097 0.0599107i
\(970\) 0 0
\(971\) 25.4429i 0.816502i 0.912870 + 0.408251i \(0.133861\pi\)
−0.912870 + 0.408251i \(0.866139\pi\)
\(972\) 10.0053 29.5278i 0.320921 0.947106i
\(973\) 12.5593 0.402633
\(974\) −6.58866 + 46.3466i −0.211114 + 1.48504i
\(975\) 0 0
\(976\) 6.78243 10.7023i 0.217100 0.342571i
\(977\) 26.6495 0.852593 0.426296 0.904584i \(-0.359818\pi\)
0.426296 + 0.904584i \(0.359818\pi\)
\(978\) 40.9741 6.78445i 1.31021 0.216943i
\(979\) 3.33314 0.106528
\(980\) 0 0
\(981\) 35.2802 + 50.4128i 1.12641 + 1.60956i
\(982\) −29.9118 4.25228i −0.954524 0.135696i
\(983\) 47.0887i 1.50190i −0.660361 0.750948i \(-0.729597\pi\)
0.660361 0.750948i \(-0.270403\pi\)
\(984\) −16.7356 1.98977i −0.533512 0.0634314i
\(985\) 0 0
\(986\) 7.28700 51.2589i 0.232065 1.63242i
\(987\) −7.58353 24.0626i −0.241387 0.765922i
\(988\) 6.33522 + 1.83839i 0.201550 + 0.0584870i
\(989\) −1.79721 −0.0571479
\(990\) 0 0
\(991\) 26.3879i 0.838238i 0.907931 + 0.419119i \(0.137661\pi\)
−0.907931 + 0.419119i \(0.862339\pi\)
\(992\) 18.2350 + 15.5494i 0.578963 + 0.493695i
\(993\) −41.5787 + 13.1039i −1.31946 + 0.415839i
\(994\) −3.56146 + 25.0524i −0.112963 + 0.794612i
\(995\) 0 0
\(996\) 24.7917 0.567230i 0.785555 0.0179734i
\(997\) −10.2047 −0.323186 −0.161593 0.986858i \(-0.551663\pi\)
−0.161593 + 0.986858i \(0.551663\pi\)
\(998\) −2.95508 + 20.7869i −0.0935416 + 0.657999i
\(999\) 31.1170 40.5202i 0.984497 1.28200i
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 600.2.m.c.299.9 16
3.2 odd 2 600.2.m.d.299.8 16
4.3 odd 2 2400.2.m.d.1199.15 16
5.2 odd 4 600.2.b.f.251.8 8
5.3 odd 4 120.2.b.a.11.1 8
5.4 even 2 inner 600.2.m.c.299.8 16
8.3 odd 2 600.2.m.d.299.10 16
8.5 even 2 2400.2.m.c.1199.15 16
12.11 even 2 2400.2.m.c.1199.1 16
15.2 even 4 600.2.b.e.251.1 8
15.8 even 4 120.2.b.b.11.8 yes 8
15.14 odd 2 600.2.m.d.299.9 16
20.3 even 4 480.2.b.b.431.6 8
20.7 even 4 2400.2.b.f.2351.3 8
20.19 odd 2 2400.2.m.d.1199.2 16
24.5 odd 2 2400.2.m.d.1199.1 16
24.11 even 2 inner 600.2.m.c.299.7 16
40.3 even 4 120.2.b.b.11.7 yes 8
40.13 odd 4 480.2.b.a.431.6 8
40.19 odd 2 600.2.m.d.299.7 16
40.27 even 4 600.2.b.e.251.2 8
40.29 even 2 2400.2.m.c.1199.2 16
40.37 odd 4 2400.2.b.e.2351.3 8
60.23 odd 4 480.2.b.a.431.5 8
60.47 odd 4 2400.2.b.e.2351.4 8
60.59 even 2 2400.2.m.c.1199.16 16
120.29 odd 2 2400.2.m.d.1199.16 16
120.53 even 4 480.2.b.b.431.5 8
120.59 even 2 inner 600.2.m.c.299.10 16
120.77 even 4 2400.2.b.f.2351.4 8
120.83 odd 4 120.2.b.a.11.2 yes 8
120.107 odd 4 600.2.b.f.251.7 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
120.2.b.a.11.1 8 5.3 odd 4
120.2.b.a.11.2 yes 8 120.83 odd 4
120.2.b.b.11.7 yes 8 40.3 even 4
120.2.b.b.11.8 yes 8 15.8 even 4
480.2.b.a.431.5 8 60.23 odd 4
480.2.b.a.431.6 8 40.13 odd 4
480.2.b.b.431.5 8 120.53 even 4
480.2.b.b.431.6 8 20.3 even 4
600.2.b.e.251.1 8 15.2 even 4
600.2.b.e.251.2 8 40.27 even 4
600.2.b.f.251.7 8 120.107 odd 4
600.2.b.f.251.8 8 5.2 odd 4
600.2.m.c.299.7 16 24.11 even 2 inner
600.2.m.c.299.8 16 5.4 even 2 inner
600.2.m.c.299.9 16 1.1 even 1 trivial
600.2.m.c.299.10 16 120.59 even 2 inner
600.2.m.d.299.7 16 40.19 odd 2
600.2.m.d.299.8 16 3.2 odd 2
600.2.m.d.299.9 16 15.14 odd 2
600.2.m.d.299.10 16 8.3 odd 2
2400.2.b.e.2351.3 8 40.37 odd 4
2400.2.b.e.2351.4 8 60.47 odd 4
2400.2.b.f.2351.3 8 20.7 even 4
2400.2.b.f.2351.4 8 120.77 even 4
2400.2.m.c.1199.1 16 12.11 even 2
2400.2.m.c.1199.2 16 40.29 even 2
2400.2.m.c.1199.15 16 8.5 even 2
2400.2.m.c.1199.16 16 60.59 even 2
2400.2.m.d.1199.1 16 24.5 odd 2
2400.2.m.d.1199.2 16 20.19 odd 2
2400.2.m.d.1199.15 16 4.3 odd 2
2400.2.m.d.1199.16 16 120.29 odd 2