Properties

Label 600.2.m.d.299.7
Level $600$
Weight $2$
Character 600.299
Analytic conductor $4.791$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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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 299.7
Root \(-0.199044 - 1.40014i\) of defining polynomial
Character \(\chi\) \(=\) 600.299
Dual form 600.2.m.d.299.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.199044 - 1.40014i) q^{2} +(1.65195 - 0.520627i) q^{3} +(-1.92076 + 0.557378i) q^{4} +(-1.05776 - 2.20933i) q^{6} +1.92736 q^{7} +(1.16272 + 2.57839i) q^{8} +(2.45790 - 1.72010i) q^{9} +O(q^{10})\) \(q+(-0.199044 - 1.40014i) q^{2} +(1.65195 - 0.520627i) q^{3} +(-1.92076 + 0.557378i) q^{4} +(-1.05776 - 2.20933i) q^{6} +1.92736 q^{7} +(1.16272 + 2.57839i) q^{8} +(2.45790 - 1.72010i) q^{9} -4.02057i q^{11} +(-2.88282 + 1.92076i) q^{12} -4.81675 q^{13} +(-0.383629 - 2.69856i) q^{14} +(3.37866 - 2.14118i) q^{16} +5.23126 q^{17} +(-2.89761 - 3.09901i) q^{18} +0.684753 q^{19} +(3.18390 - 1.00343i) q^{21} +(-5.62935 + 0.800272i) q^{22} -1.72601i q^{23} +(3.26314 + 3.65403i) 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} +(-3.76229 + 4.67388i) q^{36} -9.83221 q^{37} +(-0.136296 - 0.958747i) q^{38} +(-7.95705 + 2.50773i) q^{39} -3.44020i q^{41} +(-2.03868 - 4.25817i) q^{42} +1.04125i q^{43} +(2.24098 + 7.72257i) q^{44} +(-2.41664 + 0.343552i) q^{46} +7.55759i q^{47} +(4.46663 - 5.29615i) q^{48} -3.28530 q^{49} +(8.64180 - 2.72353i) q^{51} +(9.25184 - 2.68475i) q^{52} +4.08251i q^{53} +(-6.40014 - 3.61085i) 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} +(-8.88278 + 4.25280i) q^{66} +14.8728i q^{67} +(-10.0480 + 2.91579i) q^{68} +(-0.898604 - 2.85128i) q^{69} +9.28360 q^{71} +(7.29294 + 4.33741i) q^{72} +11.2836i q^{73} +(1.95705 + 13.7664i) q^{74} +(-1.31525 + 0.381666i) q^{76} -7.74908i q^{77} +(5.09497 + 10.6418i) q^{78} +9.25184i q^{79} +(3.08251 - 8.45566i) q^{81} +(-4.81675 + 0.684753i) q^{82} -7.15862 q^{83} +(-5.55623 + 3.70199i) 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} +(-8.30439 - 5.19972i) q^{96} +1.45201i q^{97} +(0.653920 + 4.59986i) q^{98} +(-6.91579 - 9.88215i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{4} + 2 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 2 q^{4} + 2 q^{6} + 12 q^{14} - 14 q^{16} + 8 q^{19} - 8 q^{21} + 22 q^{24} + 32 q^{26} + 26 q^{36} - 32 q^{39} + 60 q^{44} - 16 q^{46} + 32 q^{49} + 40 q^{51} - 82 q^{54} + 60 q^{56} - 50 q^{64} - 68 q^{66} - 40 q^{69} - 48 q^{71} - 64 q^{74} - 24 q^{76} + 16 q^{81} - 116 q^{84} - 16 q^{86} + 48 q^{91} + 80 q^{94} - 86 q^{96} - 32 q^{99}+O(q^{100}) \) 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
\(6\) −1.05776 2.20933i −0.431829 0.901956i
\(7\) 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 \(-0.207277\pi\)
\(12\) −2.88282 + 1.92076i −0.832199 + 0.554476i
\(13\) −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 \(-0.281254\pi\)
0.634384 + 0.773018i \(0.281254\pi\)
\(18\) −2.89761 3.09901i −0.682972 0.730444i
\(19\) 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 \(-0.0575931\pi\)
\(24\) 3.26314 + 3.65403i 0.666085 + 0.745875i
\(25\) 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 \(-0.274863\pi\)
0.649776 + 0.760126i \(0.274863\pi\)
\(30\) 0 0
\(31\) 4.23638i 0.760876i −0.924806 0.380438i \(-0.875773\pi\)
0.924806 0.380438i \(-0.124227\pi\)
\(32\) −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
\(36\) −3.76229 + 4.67388i −0.627048 + 0.778981i
\(37\) −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 \(-0.0865724\pi\)
\(42\) −2.03868 4.25817i −0.314575 0.657050i
\(43\) 1.04125i 0.158790i 0.996843 + 0.0793948i \(0.0252988\pi\)
−0.996843 + 0.0793948i \(0.974701\pi\)
\(44\) 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 \(0.814172\pi\)
\(48\) 4.46663 5.29615i 0.644702 0.764434i
\(49\) −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 \(0.909537\pi\)
\(54\) −6.40014 3.61085i −0.870948 0.491375i
\(55\) 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 \(0.0649994\pi\)
−0.979223 + 0.202785i \(0.935001\pi\)
\(62\) −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
\(66\) −8.88278 + 4.25280i −1.09339 + 0.523484i
\(67\) 14.8728i 1.81701i 0.417878 + 0.908503i \(0.362774\pi\)
−0.417878 + 0.908503i \(0.637226\pi\)
\(68\) −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 \(-0.314292\pi\)
0.550880 + 0.834584i \(0.314292\pi\)
\(72\) 7.29294 + 4.33741i 0.859481 + 0.511168i
\(73\) 11.2836i 1.32064i 0.750982 + 0.660322i \(0.229580\pi\)
−0.750982 + 0.660322i \(0.770420\pi\)
\(74\) 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
\(78\) 5.09497 + 10.6418i 0.576891 + 1.20495i
\(79\) 9.25184i 1.04091i 0.853888 + 0.520456i \(0.174238\pi\)
−0.853888 + 0.520456i \(0.825762\pi\)
\(80\) 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 \(-0.628521\pi\)
−0.392880 + 0.919590i \(0.628521\pi\)
\(84\) −5.55623 + 3.70199i −0.606234 + 0.403921i
\(85\) 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
\(96\) −8.30439 5.19972i −0.847563 0.530694i
\(97\) 1.45201i 0.147429i 0.997279 + 0.0737147i \(0.0234854\pi\)
−0.997279 + 0.0737147i \(0.976515\pi\)
\(98\) 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 \(-0.567052\pi\)
−0.209097 + 0.977895i \(0.567052\pi\)
\(102\) −5.53342 11.5576i −0.547890 1.14437i
\(103\) 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 \(-0.377562\pi\)
0.375235 + 0.926930i \(0.377562\pi\)
\(108\) −3.78177 + 9.67978i −0.363901 + 0.931437i
\(109\) 20.5105i 1.96455i −0.187437 0.982277i \(-0.560018\pi\)
0.187437 0.982277i \(-0.439982\pi\)
\(110\) 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 \(-0.503231\pi\)
−0.0101506 + 0.999948i \(0.503231\pi\)
\(114\) −0.724304 1.51285i −0.0678373 0.141691i
\(115\) 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
\(126\) −5.58472 5.97290i −0.497526 0.532108i
\(127\) 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 \(0.921146\pi\)
\(132\) 7.72257 + 11.5906i 0.672163 + 1.00883i
\(133\) 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 \(-0.631791\pi\)
−0.402304 + 0.915506i \(0.631791\pi\)
\(138\) −3.81332 + 1.82570i −0.324611 + 0.155414i
\(139\) 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
\(144\) 4.62134 11.0744i 0.385112 0.922870i
\(145\) 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 \(-0.599869\pi\)
−0.308626 + 0.951184i \(0.599869\pi\)
\(150\) 0 0
\(151\) 9.41085i 0.765844i 0.923781 + 0.382922i \(0.125082\pi\)
−0.923781 + 0.382922i \(0.874918\pi\)
\(152\) 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
\(156\) 13.8858 9.25184i 1.11176 0.740740i
\(157\) −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
\(162\) −12.4526 2.63288i −0.978371 0.206858i
\(163\) 16.9553i 1.32804i 0.747713 + 0.664022i \(0.231152\pi\)
−0.747713 + 0.664022i \(0.768848\pi\)
\(164\) 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 \(0.854698\pi\)
\(168\) 6.28923 + 7.04261i 0.485225 + 0.543350i
\(169\) 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 \(-0.0262270\pi\)
\(174\) −7.40252 15.4616i −0.561184 1.17214i
\(175\) 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 \(-0.868605\pi\)
0.916006 0.401165i \(-0.131395\pi\)
\(182\) 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
\(186\) −9.35956 + 4.48107i −0.686277 + 0.328568i
\(187\) 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 \(-0.246656\pi\)
0.714497 + 0.699639i \(0.246656\pi\)
\(192\) −5.62737 + 12.6623i −0.406121 + 0.913819i
\(193\) 5.45201i 0.392444i 0.980559 + 0.196222i \(0.0628674\pi\)
−0.980559 + 0.196222i \(0.937133\pi\)
\(194\) 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 \(-0.298836\pi\)
\(198\) −12.4598 + 11.6500i −0.885480 + 0.827932i
\(199\) 18.8853i 1.33875i 0.742926 + 0.669373i \(0.233437\pi\)
−0.742926 + 0.669373i \(0.766563\pi\)
\(200\) 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
\(204\) −15.0808 + 10.0480i −1.05587 + 0.703502i
\(205\) 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
\(216\) 14.3058 + 3.36829i 0.973383 + 0.229183i
\(217\) 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
\(222\) 10.4001 + 21.7226i 0.698010 + 1.45793i
\(223\) −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 \(-0.768545\pi\)
−0.747080 + 0.664735i \(0.768545\pi\)
\(228\) −1.97402 + 1.31525i −0.130733 + 0.0871044i
\(229\) 12.8839i 0.851392i 0.904866 + 0.425696i \(0.139971\pi\)
−0.904866 + 0.425696i \(0.860029\pi\)
\(230\) 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 \(-0.615668\pi\)
−0.355437 + 0.934700i \(0.615668\pi\)
\(234\) 13.9570 + 14.9272i 0.912401 + 0.975820i
\(235\) 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 \(-0.568794\pi\)
−0.214446 + 0.976736i \(0.568794\pi\)
\(240\) 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
\(246\) −7.60054 + 3.63891i −0.484593 + 0.232008i
\(247\) −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 \(0.840211\pi\)
\(252\) −7.25127 + 9.00824i −0.456787 + 0.567466i
\(253\) −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 \(-0.331573\pi\)
0.504782 + 0.863247i \(0.331573\pi\)
\(258\) 2.30047 1.10140i 0.143221 0.0685699i
\(259\) −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 \(-0.230337\pi\)
\(264\) 14.6913 13.1197i 0.904186 0.807461i
\(265\) 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 \(-0.747782\pi\)
−0.702163 + 0.712016i \(0.747782\pi\)
\(270\) 0 0
\(271\) 16.1914i 0.983556i −0.870721 0.491778i \(-0.836347\pi\)
0.870721 0.491778i \(-0.163653\pi\)
\(272\) 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
\(276\) 3.31525 + 4.97577i 0.199554 + 0.299506i
\(277\) −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 \(0.686276\pi\)
\(282\) 16.6972 7.99412i 0.994305 0.476043i
\(283\) 5.58924i 0.332246i −0.986105 0.166123i \(-0.946875\pi\)
0.986105 0.166123i \(-0.0531249\pi\)
\(284\) −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
\(288\) −16.4256 4.26620i −0.967886 0.251388i
\(289\) 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 \(-0.0560772\pi\)
\(294\) 3.47506 + 7.25831i 0.202669 + 0.423313i
\(295\) 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
\(306\) −15.1581 16.2117i −0.866533 0.926764i
\(307\) 4.79033i 0.273399i 0.990613 + 0.136699i \(0.0436494\pi\)
−0.990613 + 0.136699i \(0.956351\pi\)
\(308\) 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 \(-0.618973\pi\)
−0.365123 + 0.930959i \(0.618973\pi\)
\(312\) −15.7177 17.6005i −0.889841 0.996435i
\(313\) 20.4022i 1.15320i −0.817027 0.576600i \(-0.804379\pi\)
0.817027 0.576600i \(-0.195621\pi\)
\(314\) 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 \(0.952053\pi\)
\(318\) 9.01961 4.31831i 0.505794 0.242159i
\(319\) 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
\(324\) −1.20776 + 17.9594i −0.0670979 + 0.997746i
\(325\) 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
\(336\) 8.60878 10.2076i 0.469648 0.556869i
\(337\) 20.1616i 1.09827i 0.835733 + 0.549136i \(0.185043\pi\)
−0.835733 + 0.549136i \(0.814957\pi\)
\(338\) −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
\(342\) −1.98414 2.12206i −0.107290 0.114748i
\(343\) −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 \(-0.581317\pi\)
−0.252696 + 0.967546i \(0.581317\pi\)
\(348\) −20.1749 + 13.4421i −1.08149 + 0.720571i
\(349\) 10.3968i 0.556530i 0.960504 + 0.278265i \(0.0897593\pi\)
−0.960504 + 0.278265i \(0.910241\pi\)
\(350\) 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 \(-0.317073\pi\)
0.543567 + 0.839366i \(0.317073\pi\)
\(354\) −2.19803 + 1.05235i −0.116824 + 0.0559316i
\(355\) 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 \(-0.441963\pi\)
0.181320 + 0.983424i \(0.441963\pi\)
\(360\) 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
\(366\) 6.99830 3.35057i 0.365807 0.175137i
\(367\) −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
\(372\) 8.13708 + 12.2127i 0.421888 + 0.633201i
\(373\) −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
\(378\) −12.3353 6.95940i −0.634462 0.357953i
\(379\) 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 \(-0.200828\pi\)
\(384\) 18.8490 + 5.35874i 0.961883 + 0.273462i
\(385\) 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 \(-0.393919\pi\)
0.327130 + 0.944979i \(0.393919\pi\)
\(390\) 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
\(396\) 18.7917 + 15.1266i 0.944318 + 0.760138i
\(397\) 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 \(-0.318934\pi\)
\(402\) 32.8590 15.7319i 1.63886 0.784635i
\(403\) 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
\(408\) 17.0703 + 19.1152i 0.845108 + 0.946342i
\(409\) −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
\(414\) −5.34891 + 5.00128i −0.262885 + 0.245800i
\(415\) 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 \(0.0534882\pi\)
−0.985915 + 0.167248i \(0.946512\pi\)
\(422\) 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
\(426\) −9.81981 20.5105i −0.475772 0.993739i
\(427\) 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 \(-0.339828\pi\)
0.482228 + 0.876046i \(0.339828\pi\)
\(432\) 1.86859 20.7004i 0.0899026 0.995951i
\(433\) 10.2112i 0.490717i 0.969432 + 0.245358i \(0.0789057\pi\)
−0.969432 + 0.245358i \(0.921094\pi\)
\(434\) −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
\(438\) 24.9292 11.9353i 1.19116 0.570292i
\(439\) 33.6933i 1.60809i −0.594566 0.804047i \(-0.702676\pi\)
0.594566 0.804047i \(-0.297324\pi\)
\(440\) 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 \(-0.533824\pi\)
−0.106061 + 0.994360i \(0.533824\pi\)
\(444\) 28.3445 18.8853i 1.34517 0.896258i
\(445\) 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
\(456\) 2.23444 + 2.50211i 0.104637 + 0.117172i
\(457\) 11.5016i 0.538020i 0.963137 + 0.269010i \(0.0866965\pi\)
−0.963137 + 0.269010i \(0.913303\pi\)
\(458\) 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 \(-0.438393\pi\)
0.192337 + 0.981329i \(0.438393\pi\)
\(462\) −17.1203 + 8.19666i −0.796507 + 0.381343i
\(463\) 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 \(-0.369802\pi\)
0.397718 + 0.917508i \(0.369802\pi\)
\(468\) 18.1220 22.5129i 0.837690 1.04066i
\(469\) 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
\(474\) 20.4404 9.78622i 0.938857 0.449496i
\(475\) 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 \(-0.584907\pi\)
−0.263591 + 0.964635i \(0.584907\pi\)
\(480\) 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
\(486\) −21.9419 + 2.13378i −0.995305 + 0.0967902i
\(487\) −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 \(-0.160112\pi\)
\(492\) 6.60781 + 9.91749i 0.297903 + 0.447115i
\(493\) 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
\(498\) 7.57210 + 15.8158i 0.339314 + 0.708721i
\(499\) −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 \(-0.0132628\pi\)
\(504\) 14.0561 + 8.35973i 0.626108 + 0.372372i
\(505\) 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 \(-0.511493\pi\)
−0.0360975 + 0.999348i \(0.511493\pi\)
\(510\) 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
\(516\) −2.00000 3.00175i −0.0880451 0.132145i
\(517\) 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 \(0.945149\pi\)
\(522\) −20.2783 21.6878i −0.887557 0.949250i
\(523\) 32.2423i 1.40986i −0.709277 0.704930i \(-0.750979\pi\)
0.709277 0.704930i \(-0.249021\pi\)
\(524\) −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
\(528\) −21.2936 17.9584i −0.926684 0.781539i
\(529\) 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
\(534\) 1.83158 0.876906i 0.0792604 0.0379474i
\(535\) 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 \(-0.977741\pi\)
0.997556 0.0698728i \(-0.0222593\pi\)
\(542\) −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
\(546\) 9.81981 + 20.5105i 0.420249 + 0.877770i
\(547\) 10.3248i 0.441459i −0.975335 0.220729i \(-0.929156\pi\)
0.975335 0.220729i \(-0.0708437\pi\)
\(548\) 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
\(552\) 6.30687 5.63220i 0.268438 0.239722i
\(553\) 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 \(-0.0564935\pi\)
\(558\) −13.1286 + 12.2754i −0.555778 + 0.519657i
\(559\) 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 \(-0.596014\pi\)
−0.297083 + 0.954852i \(0.596014\pi\)
\(564\) −14.5163 21.7872i −0.611248 0.917406i
\(565\) 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
\(576\) −2.70385 + 23.8472i −0.112660 + 0.993634i
\(577\) 14.9762i 0.623466i −0.950170 0.311733i \(-0.899090\pi\)
0.950170 0.311733i \(-0.100910\pi\)
\(578\) −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
\(582\) 3.20797 1.53588i 0.132975 0.0636642i
\(583\) 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 \(-0.241782\pi\)
0.725125 + 0.688617i \(0.241782\pi\)
\(588\) 9.47093 6.31028i 0.390575 0.260231i
\(589\) 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 \(-0.576691\pi\)
−0.238607 + 0.971116i \(0.576691\pi\)
\(594\) −14.5177 + 25.7322i −0.595668 + 1.05581i
\(595\) 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 \(-0.436505\pi\)
0.198156 + 0.980170i \(0.436505\pi\)
\(600\) 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
\(606\) 4.44554 + 9.28536i 0.180588 + 0.377192i
\(607\) −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
\(612\) −19.6815 + 24.4503i −0.795578 + 0.988345i
\(613\) 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 \(-0.408068\pi\)
0.284815 + 0.958583i \(0.408068\pi\)
\(618\) −7.51203 15.6903i −0.302178 0.631156i
\(619\) 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
\(624\) −21.5146 + 25.5102i −0.861275 + 1.02123i
\(625\) 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 \(0.193989\pi\)
−0.819972 + 0.572404i \(0.806011\pi\)
\(632\) −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
\(636\) −7.84153 11.7691i −0.310937 0.466677i
\(637\) 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 \(-0.249734\pi\)
\(642\) −8.21132 17.1509i −0.324075 0.676892i
\(643\) 4.64793i 0.183296i −0.995791 0.0916481i \(-0.970786\pi\)
0.995791 0.0916481i \(-0.0292135\pi\)
\(644\) 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 \(-0.0433138\pi\)
\(648\) 25.3861 1.88369i 0.997258 0.0739984i
\(649\) −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 \(0.893264\pi\)
\(654\) −45.3146 + 21.6952i −1.77194 + 0.848350i
\(655\) 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 \(0.0924492\pi\)
−0.958119 + 0.286372i \(0.907551\pi\)
\(662\) −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
\(666\) 28.4899 + 30.4701i 1.10396 + 1.18069i
\(667\) 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
\(672\) −16.0055 10.0217i −0.617426 0.386596i
\(673\) 44.9434i 1.73244i −0.499663 0.866220i \(-0.666543\pi\)
0.499663 0.866220i \(-0.333457\pi\)
\(674\) 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 \(0.794272\pi\)
\(678\) 0.228270 + 0.476786i 0.00876667 + 0.0183108i
\(679\) 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 \(-0.541291\pi\)
−0.129355 + 0.991598i \(0.541291\pi\)
\(684\) −2.57624 + 3.20045i −0.0985049 + 0.122372i
\(685\) 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
\(696\) 22.8364 + 25.5720i 0.865612 + 0.969303i
\(697\) 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 \(-0.559465\pi\)
−0.185731 + 0.982601i \(0.559465\pi\)
\(702\) 30.8279 + 17.3926i 1.16352 + 0.656441i
\(703\) −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
\(708\) 1.91093 + 2.86807i 0.0718173 + 0.107789i
\(709\) 20.4277i 0.767180i −0.923503 0.383590i \(-0.874688\pi\)
0.923503 0.383590i \(-0.125312\pi\)
\(710\) 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
\(714\) −10.6649 22.2756i −0.399123 0.833643i
\(715\) 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 \(-0.323515\pi\)
0.526471 + 0.850193i \(0.323515\pi\)
\(720\) 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
\(726\) 5.46334 + 11.4112i 0.202764 + 0.423510i
\(727\) 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
\(732\) −6.08423 9.13166i −0.224879 0.337516i
\(733\) 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
\(738\) −10.6612 + 9.96835i −0.392445 + 0.366940i
\(739\) 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 \(0.770664\pi\)
\(744\) 15.4798 13.8239i 0.567519 0.506809i
\(745\) 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 \(0.160208\pi\)
−0.875991 + 0.482327i \(0.839792\pi\)
\(752\) 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
\(756\) −7.28883 + 18.6564i −0.265092 + 0.678526i
\(757\) 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 \(0.680606\pi\)
\(762\) −17.5338 36.6226i −0.635181 1.32670i
\(763\) 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
\(768\) 3.75118 27.4578i 0.135359 0.990797i
\(769\) −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 \(-0.268646\pi\)
\(774\) 3.22686 3.01714i 0.115987 0.108449i
\(775\) 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
\(786\) 12.4008 5.93713i 0.442322 0.211770i
\(787\) 48.4300i 1.72634i 0.504912 + 0.863171i \(0.331525\pi\)
−0.504912 + 0.863171i \(0.668475\pi\)
\(788\) 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
\(792\) 17.4389 29.3218i 0.619663 1.04190i
\(793\) 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 \(-0.192317\pi\)
\(798\) −1.39599 2.91579i −0.0494176 0.103218i
\(799\) 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
\(804\) −28.5672 42.8758i −1.00749 1.51211i
\(805\) 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
\(816\) 23.3661 27.7056i 0.817977 0.969889i
\(817\) 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 \(-0.193569\pi\)
0.820726 + 0.571322i \(0.193569\pi\)
\(822\) 9.96166 + 20.8068i 0.347453 + 0.725721i
\(823\) −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 \(-0.682660\pi\)
−0.542864 + 0.839821i \(0.682660\pi\)
\(828\) 8.06715 + 6.49373i 0.280353 + 0.225673i
\(829\) 42.0990i 1.46216i 0.682292 + 0.731080i \(0.260983\pi\)
−0.682292 + 0.731080i \(0.739017\pi\)
\(830\) 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
\(834\) −6.89272 14.3967i −0.238675 0.498519i
\(835\) 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 \(-0.421967\pi\)
0.242701 + 0.970101i \(0.421967\pi\)
\(840\) 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
\(846\) 23.4211 21.8989i 0.805233 0.752900i
\(847\) −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
\(852\) −26.7630 + 17.8316i −0.916884 + 0.610900i
\(853\) −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 \(-0.794297\pi\)
−0.798357 + 0.602185i \(0.794297\pi\)
\(858\) 42.7861 20.4847i 1.46069 0.699336i
\(859\) −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 \(0.766142\pi\)
\(864\) −29.3554 + 1.50402i −0.998690 + 0.0511679i
\(865\) 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
\(876\) −21.6731 32.5286i −0.732267 1.09904i
\(877\) −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 \(-0.268114\pi\)
\(882\) 9.51950 + 10.1812i 0.320538 + 0.342818i
\(883\) 25.7701i 0.867231i −0.901098 0.433616i \(-0.857238\pi\)
0.901098 0.433616i \(-0.142762\pi\)
\(884\) 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 \(-0.117405\pi\)
\(888\) −32.0839 35.9272i −1.07666 1.20564i
\(889\) 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
\(894\) 7.96971 + 16.6462i 0.266547 + 0.556734i
\(895\) 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
\(906\) 20.7917 9.95442i 0.690758 0.330714i
\(907\) 34.5984i 1.14882i −0.818568 0.574410i \(-0.805231\pi\)
0.818568 0.574410i \(-0.194769\pi\)
\(908\) 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 \(-0.390788\pi\)
0.336407 + 0.941717i \(0.390788\pi\)
\(912\) 3.05854 3.62655i 0.101278 0.120087i
\(913\) 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
\(918\) −33.4808 18.8893i −1.10503 0.623440i
\(919\) 11.1280i 0.367080i −0.983012 0.183540i \(-0.941244\pi\)
0.983012 0.183540i \(-0.0587556\pi\)
\(920\) 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
\(924\) 14.8841 + 22.3392i 0.489652 + 0.734907i
\(925\) 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
\(936\) −35.1283 20.8922i −1.14820 0.682883i
\(937\) 35.4418i 1.15783i −0.815387 0.578917i \(-0.803476\pi\)
0.815387 0.578917i \(-0.196524\pi\)
\(938\) 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 \(-0.429698\pi\)
0.219070 + 0.975709i \(0.429698\pi\)
\(942\) 3.69897 + 7.72601i 0.120519 + 0.251727i
\(943\) −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 \(-0.525690\pi\)
−0.0806208 + 0.996745i \(0.525690\pi\)
\(948\) −17.7706 26.6714i −0.577162 0.866247i
\(949\) 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 \(-0.186761\pi\)
0.832757 + 0.553639i \(0.186761\pi\)
\(954\) 12.6517 11.8295i 0.409615 0.382994i
\(955\) 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
\(966\) −7.34962 + 3.51877i −0.236470 + 0.113215i
\(967\) 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 \(0.866139\pi\)
\(972\) 7.35499 + 30.2969i 0.235911 + 0.971775i
\(973\) 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 \(-0.640182\pi\)
−0.426296 + 0.904584i \(0.640182\pi\)
\(978\) 37.4600 17.9347i 1.19784 0.573488i
\(979\) 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 \(-0.270403\pi\)
\(984\) 12.5706 11.2259i 0.400736 0.357867i
\(985\) 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 \(-0.862339\pi\)
0.907931 0.419119i \(-0.137661\pi\)
\(992\) −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
\(996\) 20.6370 13.7500i 0.653909 0.435686i
\(997\) −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.d.299.7 16
3.2 odd 2 600.2.m.c.299.10 16
4.3 odd 2 2400.2.m.c.1199.2 16
5.2 odd 4 120.2.b.b.11.7 yes 8
5.3 odd 4 600.2.b.e.251.2 8
5.4 even 2 inner 600.2.m.d.299.10 16
8.3 odd 2 600.2.m.c.299.8 16
8.5 even 2 2400.2.m.d.1199.2 16
12.11 even 2 2400.2.m.d.1199.16 16
15.2 even 4 120.2.b.a.11.2 yes 8
15.8 even 4 600.2.b.f.251.7 8
15.14 odd 2 600.2.m.c.299.7 16
20.3 even 4 2400.2.b.e.2351.3 8
20.7 even 4 480.2.b.a.431.6 8
20.19 odd 2 2400.2.m.c.1199.15 16
24.5 odd 2 2400.2.m.c.1199.16 16
24.11 even 2 inner 600.2.m.d.299.9 16
40.3 even 4 600.2.b.f.251.8 8
40.13 odd 4 2400.2.b.f.2351.3 8
40.19 odd 2 600.2.m.c.299.9 16
40.27 even 4 120.2.b.a.11.1 8
40.29 even 2 2400.2.m.d.1199.15 16
40.37 odd 4 480.2.b.b.431.6 8
60.23 odd 4 2400.2.b.f.2351.4 8
60.47 odd 4 480.2.b.b.431.5 8
60.59 even 2 2400.2.m.d.1199.1 16
120.29 odd 2 2400.2.m.c.1199.1 16
120.53 even 4 2400.2.b.e.2351.4 8
120.59 even 2 inner 600.2.m.d.299.8 16
120.77 even 4 480.2.b.a.431.5 8
120.83 odd 4 600.2.b.e.251.1 8
120.107 odd 4 120.2.b.b.11.8 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
120.2.b.a.11.1 8 40.27 even 4
120.2.b.a.11.2 yes 8 15.2 even 4
120.2.b.b.11.7 yes 8 5.2 odd 4
120.2.b.b.11.8 yes 8 120.107 odd 4
480.2.b.a.431.5 8 120.77 even 4
480.2.b.a.431.6 8 20.7 even 4
480.2.b.b.431.5 8 60.47 odd 4
480.2.b.b.431.6 8 40.37 odd 4
600.2.b.e.251.1 8 120.83 odd 4
600.2.b.e.251.2 8 5.3 odd 4
600.2.b.f.251.7 8 15.8 even 4
600.2.b.f.251.8 8 40.3 even 4
600.2.m.c.299.7 16 15.14 odd 2
600.2.m.c.299.8 16 8.3 odd 2
600.2.m.c.299.9 16 40.19 odd 2
600.2.m.c.299.10 16 3.2 odd 2
600.2.m.d.299.7 16 1.1 even 1 trivial
600.2.m.d.299.8 16 120.59 even 2 inner
600.2.m.d.299.9 16 24.11 even 2 inner
600.2.m.d.299.10 16 5.4 even 2 inner
2400.2.b.e.2351.3 8 20.3 even 4
2400.2.b.e.2351.4 8 120.53 even 4
2400.2.b.f.2351.3 8 40.13 odd 4
2400.2.b.f.2351.4 8 60.23 odd 4
2400.2.m.c.1199.1 16 120.29 odd 2
2400.2.m.c.1199.2 16 4.3 odd 2
2400.2.m.c.1199.15 16 20.19 odd 2
2400.2.m.c.1199.16 16 24.5 odd 2
2400.2.m.d.1199.1 16 60.59 even 2
2400.2.m.d.1199.2 16 8.5 even 2
2400.2.m.d.1199.15 16 40.29 even 2
2400.2.m.d.1199.16 16 12.11 even 2