Properties

Label 600.2.m.e.299.16
Level $600$
Weight $2$
Character 600.299
Analytic conductor $4.791$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $8$

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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: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 299.16
Character \(\chi\) \(=\) 600.299
Dual form 600.2.m.e.299.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.244153 + 1.39298i) q^{2} +(1.12950 + 1.31310i) q^{3} +(-1.88078 + 0.680200i) q^{4} +(-1.55335 + 1.89397i) q^{6} -4.34495 q^{7} +(-1.40670 - 2.45381i) q^{8} +(-0.448458 + 2.96629i) q^{9} +O(q^{10})\) \(q+(0.244153 + 1.39298i) q^{2} +(1.12950 + 1.31310i) q^{3} +(-1.88078 + 0.680200i) q^{4} +(-1.55335 + 1.89397i) q^{6} -4.34495 q^{7} +(-1.40670 - 2.45381i) q^{8} +(-0.448458 + 2.96629i) q^{9} +1.83679i q^{11} +(-3.01751 - 1.70136i) q^{12} -0.588129 q^{13} +(-1.06083 - 6.05242i) q^{14} +(3.07466 - 2.55861i) q^{16} -5.37818 q^{17} +(-4.24147 + 0.0995365i) q^{18} +5.38776 q^{19} +(-4.90762 - 5.70535i) q^{21} +(-2.55861 + 0.448458i) q^{22} -2.40885i q^{23} +(1.63323 - 4.61872i) q^{24} +(-0.143593 - 0.819251i) q^{26} +(-4.40157 + 2.76156i) q^{27} +(8.17189 - 2.95543i) q^{28} -7.98077 q^{29} +7.06575i q^{31} +(4.31478 + 3.65824i) q^{32} +(-2.41189 + 2.07466i) q^{33} +(-1.31310 - 7.49169i) q^{34} +(-1.17422 - 5.88398i) q^{36} +2.72080 q^{37} +(1.31544 + 7.50503i) q^{38} +(-0.664291 - 0.772271i) q^{39} -3.42496i q^{41} +(6.74922 - 8.22919i) q^{42} +2.96772i q^{43} +(-1.24939 - 3.45460i) q^{44} +(3.35548 - 0.588129i) q^{46} +9.81525i q^{47} +(6.83253 + 1.14738i) q^{48} +11.8786 q^{49} +(-6.07466 - 7.06208i) q^{51} +(1.10614 - 0.400045i) q^{52} +6.65218i q^{53} +(-4.92145 - 5.45705i) q^{54} +(6.11205 + 10.6617i) q^{56} +(6.08547 + 7.07466i) q^{57} +(-1.94853 - 11.1170i) q^{58} +10.7564i q^{59} -9.27803i q^{61} +(-9.84244 + 1.72512i) q^{62} +(1.94853 - 12.8884i) q^{63} +(-4.04238 + 6.90356i) q^{64} +(-3.47882 - 2.85318i) q^{66} -4.13536i q^{67} +(10.1152 - 3.65824i) q^{68} +(3.16306 - 2.72080i) q^{69} +12.2241 q^{71} +(7.90957 - 3.07226i) q^{72} +4.42003i q^{73} +(0.664291 + 3.79002i) q^{74} +(-10.1332 + 3.66475i) q^{76} -7.98077i q^{77} +(0.913568 - 1.11390i) q^{78} +12.5870i q^{79} +(-8.59777 - 2.66052i) q^{81} +(4.77089 - 0.836213i) q^{82} -11.5594 q^{83} +(13.1109 + 7.39234i) q^{84} +(-4.13398 + 0.724579i) q^{86} +(-9.01428 - 10.4795i) q^{87} +(4.50714 - 2.58382i) q^{88} -4.21222i q^{89} +2.55539 q^{91} +(1.63850 + 4.53052i) q^{92} +(-9.27803 + 7.98077i) q^{93} +(-13.6724 + 2.39642i) q^{94} +(0.0699132 + 9.79771i) q^{96} -2.16763i q^{97} +(2.90019 + 16.5466i) q^{98} +(-5.44846 - 0.823724i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 20 q^{4} + 14 q^{6} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 20 q^{4} + 14 q^{6} + 4 q^{9} - 12 q^{16} + 8 q^{19} - 10 q^{24} + 4 q^{34} + 38 q^{36} - 32 q^{46} + 72 q^{49} - 60 q^{51} + 60 q^{54} - 20 q^{64} + 14 q^{66} - 76 q^{76} - 20 q^{81} + 68 q^{84} - 48 q^{91} - 56 q^{94} - 62 q^{96} - 116 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.244153 + 1.39298i 0.172642 + 0.984985i
\(3\) 1.12950 + 1.31310i 0.652117 + 0.758118i
\(4\) −1.88078 + 0.680200i −0.940389 + 0.340100i
\(5\) 0 0
\(6\) −1.55335 + 1.89397i −0.634152 + 0.773209i
\(7\) −4.34495 −1.64224 −0.821118 0.570758i \(-0.806650\pi\)
−0.821118 + 0.570758i \(0.806650\pi\)
\(8\) −1.40670 2.45381i −0.497344 0.867553i
\(9\) −0.448458 + 2.96629i −0.149486 + 0.988764i
\(10\) 0 0
\(11\) 1.83679i 0.553813i 0.960897 + 0.276907i \(0.0893093\pi\)
−0.960897 + 0.276907i \(0.910691\pi\)
\(12\) −3.01751 1.70136i −0.871080 0.491141i
\(13\) −0.588129 −0.163118 −0.0815588 0.996669i \(-0.525990\pi\)
−0.0815588 + 0.996669i \(0.525990\pi\)
\(14\) −1.06083 6.05242i −0.283520 1.61758i
\(15\) 0 0
\(16\) 3.07466 2.55861i 0.768664 0.639653i
\(17\) −5.37818 −1.30440 −0.652200 0.758047i \(-0.726154\pi\)
−0.652200 + 0.758047i \(0.726154\pi\)
\(18\) −4.24147 + 0.0995365i −0.999725 + 0.0234610i
\(19\) 5.38776 1.23604 0.618018 0.786164i \(-0.287936\pi\)
0.618018 + 0.786164i \(0.287936\pi\)
\(20\) 0 0
\(21\) −4.90762 5.70535i −1.07093 1.24501i
\(22\) −2.55861 + 0.448458i −0.545498 + 0.0956116i
\(23\) 2.40885i 0.502280i −0.967951 0.251140i \(-0.919194\pi\)
0.967951 0.251140i \(-0.0808055\pi\)
\(24\) 1.63323 4.61872i 0.333381 0.942792i
\(25\) 0 0
\(26\) −0.143593 0.819251i −0.0281610 0.160668i
\(27\) −4.40157 + 2.76156i −0.847082 + 0.531462i
\(28\) 8.17189 2.95543i 1.54434 0.558525i
\(29\) −7.98077 −1.48199 −0.740996 0.671510i \(-0.765646\pi\)
−0.740996 + 0.671510i \(0.765646\pi\)
\(30\) 0 0
\(31\) 7.06575i 1.26905i 0.772904 + 0.634523i \(0.218803\pi\)
−0.772904 + 0.634523i \(0.781197\pi\)
\(32\) 4.31478 + 3.65824i 0.762752 + 0.646691i
\(33\) −2.41189 + 2.07466i −0.419856 + 0.361151i
\(34\) −1.31310 7.49169i −0.225195 1.28481i
\(35\) 0 0
\(36\) −1.17422 5.88398i −0.195703 0.980663i
\(37\) 2.72080 0.447297 0.223648 0.974670i \(-0.428203\pi\)
0.223648 + 0.974670i \(0.428203\pi\)
\(38\) 1.31544 + 7.50503i 0.213392 + 1.21748i
\(39\) −0.664291 0.772271i −0.106372 0.123662i
\(40\) 0 0
\(41\) 3.42496i 0.534888i −0.963573 0.267444i \(-0.913821\pi\)
0.963573 0.267444i \(-0.0861791\pi\)
\(42\) 6.74922 8.22919i 1.04143 1.26979i
\(43\) 2.96772i 0.452574i 0.974061 + 0.226287i \(0.0726587\pi\)
−0.974061 + 0.226287i \(0.927341\pi\)
\(44\) −1.24939 3.45460i −0.188352 0.520800i
\(45\) 0 0
\(46\) 3.35548 0.588129i 0.494739 0.0867148i
\(47\) 9.81525i 1.43170i 0.698254 + 0.715850i \(0.253961\pi\)
−0.698254 + 0.715850i \(0.746039\pi\)
\(48\) 6.83253 + 1.14738i 0.986191 + 0.165610i
\(49\) 11.8786 1.69694
\(50\) 0 0
\(51\) −6.07466 7.06208i −0.850622 0.988889i
\(52\) 1.10614 0.400045i 0.153394 0.0554763i
\(53\) 6.65218i 0.913748i 0.889531 + 0.456874i \(0.151031\pi\)
−0.889531 + 0.456874i \(0.848969\pi\)
\(54\) −4.92145 5.45705i −0.669724 0.742610i
\(55\) 0 0
\(56\) 6.11205 + 10.6617i 0.816757 + 1.42473i
\(57\) 6.08547 + 7.07466i 0.806040 + 0.937061i
\(58\) −1.94853 11.1170i −0.255854 1.45974i
\(59\) 10.7564i 1.40036i 0.713967 + 0.700179i \(0.246897\pi\)
−0.713967 + 0.700179i \(0.753103\pi\)
\(60\) 0 0
\(61\) 9.27803i 1.18793i −0.804491 0.593965i \(-0.797562\pi\)
0.804491 0.593965i \(-0.202438\pi\)
\(62\) −9.84244 + 1.72512i −1.24999 + 0.219091i
\(63\) 1.94853 12.8884i 0.245492 1.62378i
\(64\) −4.04238 + 6.90356i −0.505298 + 0.862945i
\(65\) 0 0
\(66\) −3.47882 2.85318i −0.428213 0.351202i
\(67\) 4.13536i 0.505215i −0.967569 0.252607i \(-0.918712\pi\)
0.967569 0.252607i \(-0.0812881\pi\)
\(68\) 10.1152 3.65824i 1.22664 0.443626i
\(69\) 3.16306 2.72080i 0.380788 0.327546i
\(70\) 0 0
\(71\) 12.2241 1.45073 0.725367 0.688363i \(-0.241670\pi\)
0.725367 + 0.688363i \(0.241670\pi\)
\(72\) 7.90957 3.07226i 0.932151 0.362069i
\(73\) 4.42003i 0.517325i 0.965968 + 0.258663i \(0.0832818\pi\)
−0.965968 + 0.258663i \(0.916718\pi\)
\(74\) 0.664291 + 3.79002i 0.0772223 + 0.440580i
\(75\) 0 0
\(76\) −10.1332 + 3.66475i −1.16235 + 0.420376i
\(77\) 7.98077i 0.909493i
\(78\) 0.913568 1.11390i 0.103441 0.126124i
\(79\) 12.5870i 1.41614i 0.706141 + 0.708072i \(0.250435\pi\)
−0.706141 + 0.708072i \(0.749565\pi\)
\(80\) 0 0
\(81\) −8.59777 2.66052i −0.955308 0.295613i
\(82\) 4.77089 0.836213i 0.526857 0.0923443i
\(83\) −11.5594 −1.26881 −0.634404 0.773002i \(-0.718754\pi\)
−0.634404 + 0.773002i \(0.718754\pi\)
\(84\) 13.1109 + 7.39234i 1.43052 + 0.806570i
\(85\) 0 0
\(86\) −4.13398 + 0.724579i −0.445778 + 0.0781334i
\(87\) −9.01428 10.4795i −0.966432 1.12352i
\(88\) 4.50714 2.58382i 0.480463 0.275436i
\(89\) 4.21222i 0.446495i −0.974762 0.223247i \(-0.928334\pi\)
0.974762 0.223247i \(-0.0716658\pi\)
\(90\) 0 0
\(91\) 2.55539 0.267878
\(92\) 1.63850 + 4.53052i 0.170826 + 0.472339i
\(93\) −9.27803 + 7.98077i −0.962087 + 0.827567i
\(94\) −13.6724 + 2.39642i −1.41020 + 0.247172i
\(95\) 0 0
\(96\) 0.0699132 + 9.79771i 0.00713549 + 0.999975i
\(97\) 2.16763i 0.220090i −0.993927 0.110045i \(-0.964901\pi\)
0.993927 0.110045i \(-0.0350995\pi\)
\(98\) 2.90019 + 16.5466i 0.292964 + 1.67146i
\(99\) −5.44846 0.823724i −0.547591 0.0827874i
\(100\) 0 0
\(101\) 3.16306 0.314736 0.157368 0.987540i \(-0.449699\pi\)
0.157368 + 0.987540i \(0.449699\pi\)
\(102\) 8.35418 10.1861i 0.827188 1.00857i
\(103\) 12.5870 1.24023 0.620115 0.784511i \(-0.287086\pi\)
0.620115 + 0.784511i \(0.287086\pi\)
\(104\) 0.827322 + 1.44316i 0.0811256 + 0.141513i
\(105\) 0 0
\(106\) −9.26635 + 1.62415i −0.900027 + 0.157751i
\(107\) −3.79002 −0.366395 −0.183197 0.983076i \(-0.558645\pi\)
−0.183197 + 0.983076i \(0.558645\pi\)
\(108\) 6.39996 8.18782i 0.615837 0.787874i
\(109\) 0.588129i 0.0563325i −0.999603 0.0281663i \(-0.991033\pi\)
0.999603 0.0281663i \(-0.00896678\pi\)
\(110\) 0 0
\(111\) 3.07314 + 3.57268i 0.291690 + 0.339104i
\(112\) −13.3592 + 11.1170i −1.26233 + 1.05046i
\(113\) −11.0621 −1.04064 −0.520319 0.853972i \(-0.674187\pi\)
−0.520319 + 0.853972i \(0.674187\pi\)
\(114\) −8.36906 + 10.2042i −0.783834 + 0.955714i
\(115\) 0 0
\(116\) 15.0101 5.42852i 1.39365 0.504025i
\(117\) 0.263751 1.74456i 0.0243838 0.161285i
\(118\) −14.9834 + 2.62620i −1.37933 + 0.241761i
\(119\) 23.3679 2.14213
\(120\) 0 0
\(121\) 7.62620 0.693291
\(122\) 12.9241 2.26526i 1.17009 0.205087i
\(123\) 4.49731 3.86849i 0.405508 0.348810i
\(124\) −4.80612 13.2891i −0.431603 1.19340i
\(125\) 0 0
\(126\) 18.4290 0.432481i 1.64178 0.0385285i
\(127\) 12.9552 1.14959 0.574796 0.818297i \(-0.305081\pi\)
0.574796 + 0.818297i \(0.305081\pi\)
\(128\) −10.6035 3.94542i −0.937223 0.348730i
\(129\) −3.89692 + 3.35205i −0.343104 + 0.295131i
\(130\) 0 0
\(131\) 2.98699i 0.260974i 0.991450 + 0.130487i \(0.0416541\pi\)
−0.991450 + 0.130487i \(0.958346\pi\)
\(132\) 3.12505 5.54254i 0.272000 0.482416i
\(133\) −23.4095 −2.02986
\(134\) 5.76047 1.00966i 0.497629 0.0872214i
\(135\) 0 0
\(136\) 7.56550 + 13.1970i 0.648736 + 1.13164i
\(137\) 5.66820 0.484267 0.242133 0.970243i \(-0.422153\pi\)
0.242133 + 0.970243i \(0.422153\pi\)
\(138\) 4.56229 + 3.74179i 0.388368 + 0.318522i
\(139\) 2.69075 0.228226 0.114113 0.993468i \(-0.463597\pi\)
0.114113 + 0.993468i \(0.463597\pi\)
\(140\) 0 0
\(141\) −12.8884 + 11.0863i −1.08540 + 0.933637i
\(142\) 2.98455 + 17.0279i 0.250458 + 1.42895i
\(143\) 1.08027i 0.0903367i
\(144\) 6.21073 + 10.2678i 0.517561 + 0.855646i
\(145\) 0 0
\(146\) −6.15701 + 1.07916i −0.509558 + 0.0893122i
\(147\) 13.4169 + 15.5978i 1.10661 + 1.28648i
\(148\) −5.11722 + 1.85069i −0.420633 + 0.152126i
\(149\) −20.9591 −1.71703 −0.858517 0.512785i \(-0.828614\pi\)
−0.858517 + 0.512785i \(0.828614\pi\)
\(150\) 0 0
\(151\) 3.16869i 0.257865i −0.991653 0.128932i \(-0.958845\pi\)
0.991653 0.128932i \(-0.0411550\pi\)
\(152\) −7.57896 13.2205i −0.614735 1.07233i
\(153\) 2.41189 15.9533i 0.194990 1.28974i
\(154\) 11.1170 1.94853i 0.895836 0.157017i
\(155\) 0 0
\(156\) 1.77468 + 1.00062i 0.142088 + 0.0801137i
\(157\) 11.9988 0.957611 0.478805 0.877921i \(-0.341070\pi\)
0.478805 + 0.877921i \(0.341070\pi\)
\(158\) −17.5334 + 3.07314i −1.39488 + 0.244486i
\(159\) −8.73498 + 7.51364i −0.692729 + 0.595871i
\(160\) 0 0
\(161\) 10.4663i 0.824864i
\(162\) 1.60687 12.6261i 0.126248 0.991999i
\(163\) 13.1816i 1.03246i 0.856449 + 0.516231i \(0.172665\pi\)
−0.856449 + 0.516231i \(0.827335\pi\)
\(164\) 2.32965 + 6.44158i 0.181915 + 0.503003i
\(165\) 0 0
\(166\) −2.82226 16.1020i −0.219050 1.24976i
\(167\) 3.73744i 0.289211i 0.989489 + 0.144606i \(0.0461914\pi\)
−0.989489 + 0.144606i \(0.953809\pi\)
\(168\) −7.09629 + 20.0681i −0.547491 + 1.54829i
\(169\) −12.6541 −0.973393
\(170\) 0 0
\(171\) −2.41618 + 15.9817i −0.184770 + 1.22215i
\(172\) −2.01865 5.58163i −0.153920 0.425596i
\(173\) 6.65218i 0.505756i 0.967498 + 0.252878i \(0.0813772\pi\)
−0.967498 + 0.252878i \(0.918623\pi\)
\(174\) 12.3969 15.1153i 0.939807 1.14589i
\(175\) 0 0
\(176\) 4.69963 + 5.64750i 0.354248 + 0.425696i
\(177\) −14.1242 + 12.1493i −1.06164 + 0.913198i
\(178\) 5.86754 1.02843i 0.439791 0.0770839i
\(179\) 18.4093i 1.37598i −0.725722 0.687988i \(-0.758494\pi\)
0.725722 0.687988i \(-0.241506\pi\)
\(180\) 0 0
\(181\) 19.5125i 1.45035i 0.688564 + 0.725175i \(0.258241\pi\)
−0.688564 + 0.725175i \(0.741759\pi\)
\(182\) 0.623906 + 3.55960i 0.0462470 + 0.263855i
\(183\) 12.1830 10.4795i 0.900591 0.774670i
\(184\) −5.91087 + 3.38854i −0.435755 + 0.249806i
\(185\) 0 0
\(186\) −13.3823 10.9756i −0.981238 0.804768i
\(187\) 9.87859i 0.722394i
\(188\) −6.67633 18.4603i −0.486921 1.34636i
\(189\) 19.1246 11.9988i 1.39111 0.872786i
\(190\) 0 0
\(191\) −8.73498 −0.632041 −0.316020 0.948752i \(-0.602347\pi\)
−0.316020 + 0.948752i \(0.602347\pi\)
\(192\) −13.6309 + 2.48953i −0.983728 + 0.179666i
\(193\) 1.47689i 0.106309i −0.998586 0.0531543i \(-0.983072\pi\)
0.998586 0.0531543i \(-0.0169275\pi\)
\(194\) 3.01947 0.529235i 0.216785 0.0379968i
\(195\) 0 0
\(196\) −22.3410 + 8.07982i −1.59579 + 0.577130i
\(197\) 11.1438i 0.793965i −0.917826 0.396982i \(-0.870057\pi\)
0.917826 0.396982i \(-0.129943\pi\)
\(198\) −0.182828 7.79070i −0.0129930 0.553661i
\(199\) 2.80041i 0.198516i −0.995062 0.0992578i \(-0.968353\pi\)
0.995062 0.0992578i \(-0.0316469\pi\)
\(200\) 0 0
\(201\) 5.43014 4.67089i 0.383012 0.329459i
\(202\) 0.772271 + 4.40608i 0.0543368 + 0.310011i
\(203\) 34.6760 2.43378
\(204\) 16.2287 + 9.15023i 1.13624 + 0.640645i
\(205\) 0 0
\(206\) 3.07314 + 17.5334i 0.214116 + 1.22161i
\(207\) 7.14536 + 1.08027i 0.496637 + 0.0750839i
\(208\) −1.80829 + 1.50479i −0.125383 + 0.104339i
\(209\) 9.89618i 0.684533i
\(210\) 0 0
\(211\) 9.86464 0.679110 0.339555 0.940586i \(-0.389724\pi\)
0.339555 + 0.940586i \(0.389724\pi\)
\(212\) −4.52481 12.5113i −0.310766 0.859279i
\(213\) 13.8071 + 16.0515i 0.946048 + 1.09983i
\(214\) −0.925344 5.27941i −0.0632552 0.360893i
\(215\) 0 0
\(216\) 12.9680 + 6.91593i 0.882363 + 0.470569i
\(217\) 30.7003i 2.08407i
\(218\) 0.819251 0.143593i 0.0554867 0.00972537i
\(219\) −5.80394 + 4.99243i −0.392194 + 0.337357i
\(220\) 0 0
\(221\) 3.16306 0.212771
\(222\) −4.22635 + 5.15310i −0.283654 + 0.345854i
\(223\) 1.62415 0.108761 0.0543806 0.998520i \(-0.482682\pi\)
0.0543806 + 0.998520i \(0.482682\pi\)
\(224\) −18.7475 15.8949i −1.25262 1.06202i
\(225\) 0 0
\(226\) −2.70085 15.4093i −0.179658 1.02501i
\(227\) −4.94021 −0.327893 −0.163947 0.986469i \(-0.552422\pi\)
−0.163947 + 0.986469i \(0.552422\pi\)
\(228\) −16.2576 9.16653i −1.07669 0.607068i
\(229\) 15.2471i 1.00756i −0.863832 0.503779i \(-0.831942\pi\)
0.863832 0.503779i \(-0.168058\pi\)
\(230\) 0 0
\(231\) 10.4795 9.01428i 0.689503 0.593096i
\(232\) 11.2266 + 19.5833i 0.737060 + 1.28571i
\(233\) 22.3000 1.46092 0.730460 0.682955i \(-0.239306\pi\)
0.730460 + 0.682955i \(0.239306\pi\)
\(234\) 2.49453 0.0585403i 0.163073 0.00382690i
\(235\) 0 0
\(236\) −7.31648 20.2303i −0.476262 1.31688i
\(237\) −16.5279 + 14.2170i −1.07360 + 0.923492i
\(238\) 5.70535 + 32.5510i 0.369823 + 2.10997i
\(239\) 14.8813 0.962589 0.481294 0.876559i \(-0.340167\pi\)
0.481294 + 0.876559i \(0.340167\pi\)
\(240\) 0 0
\(241\) −0.523114 −0.0336968 −0.0168484 0.999858i \(-0.505363\pi\)
−0.0168484 + 0.999858i \(0.505363\pi\)
\(242\) 1.86196 + 10.6231i 0.119691 + 0.682881i
\(243\) −6.21766 14.2948i −0.398863 0.917010i
\(244\) 6.31091 + 17.4499i 0.404015 + 1.11712i
\(245\) 0 0
\(246\) 6.48675 + 5.32015i 0.413580 + 0.339200i
\(247\) −3.16869 −0.201619
\(248\) 17.3380 9.93940i 1.10097 0.631153i
\(249\) −13.0563 15.1786i −0.827412 0.961906i
\(250\) 0 0
\(251\) 4.82378i 0.304474i −0.988344 0.152237i \(-0.951352\pi\)
0.988344 0.152237i \(-0.0486477\pi\)
\(252\) 5.10193 + 25.5656i 0.321391 + 1.61048i
\(253\) 4.42456 0.278170
\(254\) 3.16306 + 18.0464i 0.198468 + 1.13233i
\(255\) 0 0
\(256\) 2.90702 15.7337i 0.181689 0.983356i
\(257\) 22.8859 1.42758 0.713792 0.700358i \(-0.246976\pi\)
0.713792 + 0.700358i \(0.246976\pi\)
\(258\) −5.62077 4.60991i −0.349934 0.287000i
\(259\) −11.8217 −0.734567
\(260\) 0 0
\(261\) 3.57904 23.6733i 0.221537 1.46534i
\(262\) −4.16081 + 0.729282i −0.257056 + 0.0450552i
\(263\) 13.5527i 0.835694i 0.908517 + 0.417847i \(0.137215\pi\)
−0.908517 + 0.417847i \(0.862785\pi\)
\(264\) 8.48362 + 2.99990i 0.522131 + 0.184631i
\(265\) 0 0
\(266\) −5.71551 32.6090i −0.350440 1.99938i
\(267\) 5.53107 4.75771i 0.338496 0.291167i
\(268\) 2.81287 + 7.77769i 0.171823 + 0.475098i
\(269\) −12.9783 −0.791301 −0.395651 0.918401i \(-0.629481\pi\)
−0.395651 + 0.918401i \(0.629481\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) −16.5361 + 13.7607i −1.00265 + 0.834363i
\(273\) 2.88631 + 3.35548i 0.174688 + 0.203083i
\(274\) 1.38391 + 7.89568i 0.0836049 + 0.476995i
\(275\) 0 0
\(276\) −4.09833 + 7.26874i −0.246691 + 0.437526i
\(277\) −16.7917 −1.00891 −0.504457 0.863437i \(-0.668307\pi\)
−0.504457 + 0.863437i \(0.668307\pi\)
\(278\) 0.656955 + 3.74816i 0.0394015 + 0.224799i
\(279\) −20.9591 3.16869i −1.25479 0.189705i
\(280\) 0 0
\(281\) 11.0464i 0.658972i 0.944161 + 0.329486i \(0.106875\pi\)
−0.944161 + 0.329486i \(0.893125\pi\)
\(282\) −18.5897 15.2465i −1.10700 0.907915i
\(283\) 18.7047i 1.11188i −0.831223 0.555940i \(-0.812359\pi\)
0.831223 0.555940i \(-0.187641\pi\)
\(284\) −22.9908 + 8.31483i −1.36425 + 0.493394i
\(285\) 0 0
\(286\) 1.50479 0.263751i 0.0889802 0.0155959i
\(287\) 14.8813i 0.878413i
\(288\) −12.7864 + 11.1583i −0.753446 + 0.657510i
\(289\) 11.9248 0.701460
\(290\) 0 0
\(291\) 2.84632 2.44834i 0.166854 0.143524i
\(292\) −3.00650 8.31310i −0.175942 0.486487i
\(293\) 29.4457i 1.72024i −0.510093 0.860119i \(-0.670389\pi\)
0.510093 0.860119i \(-0.329611\pi\)
\(294\) −18.4516 + 22.4977i −1.07612 + 1.31209i
\(295\) 0 0
\(296\) −3.82735 6.67633i −0.222460 0.388054i
\(297\) −5.07240 8.08476i −0.294331 0.469125i
\(298\) −5.11722 29.1955i −0.296433 1.69125i
\(299\) 1.41672i 0.0819308i
\(300\) 0 0
\(301\) 12.8946i 0.743233i
\(302\) 4.41392 0.773646i 0.253993 0.0445183i
\(303\) 3.57268 + 4.15341i 0.205245 + 0.238607i
\(304\) 16.5655 13.7852i 0.950096 0.790634i
\(305\) 0 0
\(306\) 22.8114 0.535325i 1.30404 0.0306025i
\(307\) 33.2095i 1.89537i −0.319213 0.947683i \(-0.603419\pi\)
0.319213 0.947683i \(-0.396581\pi\)
\(308\) 5.42852 + 15.0101i 0.309318 + 0.855277i
\(309\) 14.2170 + 16.5279i 0.808775 + 0.940241i
\(310\) 0 0
\(311\) −25.7768 −1.46167 −0.730834 0.682556i \(-0.760868\pi\)
−0.730834 + 0.682556i \(0.760868\pi\)
\(312\) −0.960548 + 2.71640i −0.0543803 + 0.153786i
\(313\) 9.65410i 0.545682i −0.962059 0.272841i \(-0.912037\pi\)
0.962059 0.272841i \(-0.0879633\pi\)
\(314\) 2.92955 + 16.7141i 0.165324 + 0.943232i
\(315\) 0 0
\(316\) −8.56165 23.6733i −0.481630 1.33173i
\(317\) 4.81770i 0.270589i 0.990805 + 0.135295i \(0.0431981\pi\)
−0.990805 + 0.135295i \(0.956802\pi\)
\(318\) −12.5990 10.3332i −0.706518 0.579455i
\(319\) 14.6590i 0.820747i
\(320\) 0 0
\(321\) −4.28082 4.97667i −0.238932 0.277770i
\(322\) −14.5794 + 2.55539i −0.812478 + 0.142406i
\(323\) −28.9763 −1.61229
\(324\) 17.9802 0.844363i 0.998899 0.0469090i
\(325\) 0 0
\(326\) −18.3617 + 3.21832i −1.01696 + 0.178247i
\(327\) 0.772271 0.664291i 0.0427067 0.0367354i
\(328\) −8.40420 + 4.81789i −0.464044 + 0.266024i
\(329\) 42.6468i 2.35119i
\(330\) 0 0
\(331\) −1.37380 −0.0755110 −0.0377555 0.999287i \(-0.512021\pi\)
−0.0377555 + 0.999287i \(0.512021\pi\)
\(332\) 21.7407 7.86270i 1.19317 0.431521i
\(333\) −1.22016 + 8.07068i −0.0668646 + 0.442271i
\(334\) −5.20617 + 0.912506i −0.284869 + 0.0499301i
\(335\) 0 0
\(336\) −29.6870 4.98529i −1.61956 0.271970i
\(337\) 13.0925i 0.713192i 0.934259 + 0.356596i \(0.116063\pi\)
−0.934259 + 0.356596i \(0.883937\pi\)
\(338\) −3.08954 17.6269i −0.168049 0.958777i
\(339\) −12.4947 14.5257i −0.678618 0.788927i
\(340\) 0 0
\(341\) −12.9783 −0.702815
\(342\) −22.8520 + 0.536278i −1.23570 + 0.0289986i
\(343\) −21.1972 −1.14454
\(344\) 7.28224 4.17470i 0.392632 0.225085i
\(345\) 0 0
\(346\) −9.26635 + 1.62415i −0.498162 + 0.0873149i
\(347\) −3.97936 −0.213623 −0.106812 0.994279i \(-0.534064\pi\)
−0.106812 + 0.994279i \(0.534064\pi\)
\(348\) 24.0820 + 13.5782i 1.29093 + 0.727867i
\(349\) 12.5870i 0.673764i 0.941547 + 0.336882i \(0.109372\pi\)
−0.941547 + 0.336882i \(0.890628\pi\)
\(350\) 0 0
\(351\) 2.58869 1.62415i 0.138174 0.0866908i
\(352\) −6.71942 + 7.92534i −0.358146 + 0.422422i
\(353\) −0.787269 −0.0419021 −0.0209510 0.999781i \(-0.506669\pi\)
−0.0209510 + 0.999781i \(0.506669\pi\)
\(354\) −20.3722 16.7084i −1.08277 0.888040i
\(355\) 0 0
\(356\) 2.86515 + 7.92226i 0.151853 + 0.419879i
\(357\) 26.3941 + 30.6844i 1.39692 + 1.62399i
\(358\) 25.6438 4.49469i 1.35531 0.237552i
\(359\) −1.08027 −0.0570144 −0.0285072 0.999594i \(-0.509075\pi\)
−0.0285072 + 0.999594i \(0.509075\pi\)
\(360\) 0 0
\(361\) 10.0279 0.527785
\(362\) −27.1805 + 4.76403i −1.42857 + 0.250392i
\(363\) 8.61379 + 10.0140i 0.452107 + 0.525596i
\(364\) −4.80612 + 1.73818i −0.251909 + 0.0911052i
\(365\) 0 0
\(366\) 17.5723 + 14.4120i 0.918518 + 0.753328i
\(367\) −14.5794 −0.761038 −0.380519 0.924773i \(-0.624255\pi\)
−0.380519 + 0.924773i \(0.624255\pi\)
\(368\) −6.16332 7.40639i −0.321285 0.386085i
\(369\) 10.1594 + 1.53595i 0.528878 + 0.0799583i
\(370\) 0 0
\(371\) 28.9034i 1.50059i
\(372\) 12.0214 21.3210i 0.623281 1.10544i
\(373\) 31.5719 1.63473 0.817366 0.576118i \(-0.195433\pi\)
0.817366 + 0.576118i \(0.195433\pi\)
\(374\) 13.7607 2.41189i 0.711547 0.124716i
\(375\) 0 0
\(376\) 24.0848 13.8071i 1.24208 0.712048i
\(377\) 4.69372 0.241739
\(378\) 21.3834 + 23.7106i 1.09985 + 1.21954i
\(379\) −4.61224 −0.236915 −0.118458 0.992959i \(-0.537795\pi\)
−0.118458 + 0.992959i \(0.537795\pi\)
\(380\) 0 0
\(381\) 14.6330 + 17.0115i 0.749669 + 0.871526i
\(382\) −2.13267 12.1676i −0.109117 0.622550i
\(383\) 14.6330i 0.747709i 0.927487 + 0.373854i \(0.121964\pi\)
−0.927487 + 0.373854i \(0.878036\pi\)
\(384\) −6.79589 18.3798i −0.346801 0.937939i
\(385\) 0 0
\(386\) 2.05727 0.360586i 0.104712 0.0183533i
\(387\) −8.80314 1.33090i −0.447489 0.0676535i
\(388\) 1.47442 + 4.07684i 0.0748526 + 0.206970i
\(389\) 15.1388 0.767570 0.383785 0.923422i \(-0.374620\pi\)
0.383785 + 0.923422i \(0.374620\pi\)
\(390\) 0 0
\(391\) 12.9552i 0.655175i
\(392\) −16.7096 29.1478i −0.843964 1.47219i
\(393\) −3.92221 + 3.37380i −0.197849 + 0.170186i
\(394\) 15.5231 2.72080i 0.782043 0.137072i
\(395\) 0 0
\(396\) 10.8076 2.15680i 0.543104 0.108383i
\(397\) 18.3362 0.920268 0.460134 0.887849i \(-0.347801\pi\)
0.460134 + 0.887849i \(0.347801\pi\)
\(398\) 3.90091 0.683728i 0.195535 0.0342722i
\(399\) −26.4411 30.7390i −1.32371 1.53888i
\(400\) 0 0
\(401\) 34.2381i 1.70977i −0.518820 0.854884i \(-0.673628\pi\)
0.518820 0.854884i \(-0.326372\pi\)
\(402\) 7.83223 + 6.42365i 0.390636 + 0.320383i
\(403\) 4.15557i 0.207004i
\(404\) −5.94902 + 2.15151i −0.295975 + 0.107042i
\(405\) 0 0
\(406\) 8.46626 + 48.3030i 0.420173 + 2.39724i
\(407\) 4.99754i 0.247719i
\(408\) −8.78379 + 24.8403i −0.434862 + 1.22978i
\(409\) −18.6926 −0.924291 −0.462146 0.886804i \(-0.652920\pi\)
−0.462146 + 0.886804i \(0.652920\pi\)
\(410\) 0 0
\(411\) 6.40223 + 7.44290i 0.315799 + 0.367131i
\(412\) −23.6733 + 8.56165i −1.16630 + 0.421802i
\(413\) 46.7359i 2.29972i
\(414\) 0.239769 + 10.2171i 0.0117840 + 0.502142i
\(415\) 0 0
\(416\) −2.53764 2.15151i −0.124418 0.105487i
\(417\) 3.03920 + 3.53322i 0.148830 + 0.173023i
\(418\) −13.7852 + 2.41618i −0.674255 + 0.118179i
\(419\) 5.24599i 0.256283i 0.991756 + 0.128142i \(0.0409012\pi\)
−0.991756 + 0.128142i \(0.959099\pi\)
\(420\) 0 0
\(421\) 4.42456i 0.215640i 0.994170 + 0.107820i \(0.0343870\pi\)
−0.994170 + 0.107820i \(0.965613\pi\)
\(422\) 2.40848 + 13.7412i 0.117243 + 0.668913i
\(423\) −29.1149 4.40173i −1.41561 0.214019i
\(424\) 16.3232 9.35764i 0.792725 0.454447i
\(425\) 0 0
\(426\) −18.9883 + 23.1520i −0.919985 + 1.12172i
\(427\) 40.3126i 1.95086i
\(428\) 7.12818 2.57797i 0.344554 0.124611i
\(429\) 1.41850 1.22016i 0.0684859 0.0589101i
\(430\) 0 0
\(431\) −5.89797 −0.284095 −0.142048 0.989860i \(-0.545369\pi\)
−0.142048 + 0.989860i \(0.545369\pi\)
\(432\) −6.46756 + 19.7527i −0.311171 + 0.950354i
\(433\) 32.2158i 1.54819i 0.633069 + 0.774095i \(0.281795\pi\)
−0.633069 + 0.774095i \(0.718205\pi\)
\(434\) 42.7649 7.49558i 2.05278 0.359799i
\(435\) 0 0
\(436\) 0.400045 + 1.10614i 0.0191587 + 0.0529745i
\(437\) 12.9783i 0.620837i
\(438\) −8.37139 6.86585i −0.400001 0.328063i
\(439\) 2.27291i 0.108480i −0.998528 0.0542399i \(-0.982726\pi\)
0.998528 0.0542399i \(-0.0172736\pi\)
\(440\) 0 0
\(441\) −5.32705 + 35.2354i −0.253669 + 1.67787i
\(442\) 0.772271 + 4.40608i 0.0367332 + 0.209576i
\(443\) −4.59091 −0.218121 −0.109060 0.994035i \(-0.534784\pi\)
−0.109060 + 0.994035i \(0.534784\pi\)
\(444\) −8.21004 4.62907i −0.389631 0.219686i
\(445\) 0 0
\(446\) 0.396541 + 2.26241i 0.0187768 + 0.107128i
\(447\) −23.6733 27.5213i −1.11971 1.30171i
\(448\) 17.5639 29.9956i 0.829818 1.41716i
\(449\) 39.0461i 1.84270i 0.388736 + 0.921349i \(0.372912\pi\)
−0.388736 + 0.921349i \(0.627088\pi\)
\(450\) 0 0
\(451\) 6.29093 0.296228
\(452\) 20.8054 7.52446i 0.978605 0.353921i
\(453\) 4.16081 3.57904i 0.195492 0.168158i
\(454\) −1.20617 6.88161i −0.0566082 0.322970i
\(455\) 0 0
\(456\) 8.79943 24.8845i 0.412071 1.16532i
\(457\) 4.96147i 0.232088i 0.993244 + 0.116044i \(0.0370213\pi\)
−0.993244 + 0.116044i \(0.962979\pi\)
\(458\) 21.2389 3.72263i 0.992430 0.173947i
\(459\) 23.6724 14.8522i 1.10493 0.693239i
\(460\) 0 0
\(461\) 14.1271 0.657963 0.328981 0.944336i \(-0.393295\pi\)
0.328981 + 0.944336i \(0.393295\pi\)
\(462\) 15.1153 + 12.3969i 0.703228 + 0.576756i
\(463\) −14.2907 −0.664146 −0.332073 0.943254i \(-0.607748\pi\)
−0.332073 + 0.943254i \(0.607748\pi\)
\(464\) −24.5381 + 20.4197i −1.13915 + 0.947960i
\(465\) 0 0
\(466\) 5.44461 + 31.0634i 0.252217 + 1.43898i
\(467\) 31.8469 1.47370 0.736849 0.676058i \(-0.236313\pi\)
0.736849 + 0.676058i \(0.236313\pi\)
\(468\) 0.690593 + 3.46054i 0.0319227 + 0.159963i
\(469\) 17.9679i 0.829682i
\(470\) 0 0
\(471\) 13.5527 + 15.7557i 0.624475 + 0.725982i
\(472\) 26.3941 15.1310i 1.21489 0.696460i
\(473\) −5.45109 −0.250641
\(474\) −23.8393 19.5519i −1.09497 0.898050i
\(475\) 0 0
\(476\) −43.9499 + 15.8949i −2.01444 + 0.728540i
\(477\) −19.7323 2.98323i −0.903481 0.136593i
\(478\) 3.63331 + 20.7293i 0.166184 + 0.948135i
\(479\) 25.9566 1.18599 0.592994 0.805207i \(-0.297946\pi\)
0.592994 + 0.805207i \(0.297946\pi\)
\(480\) 0 0
\(481\) −1.60018 −0.0729619
\(482\) −0.127720 0.728687i −0.00581748 0.0331908i
\(483\) −13.7433 + 11.8217i −0.625344 + 0.537908i
\(484\) −14.3432 + 5.18734i −0.651963 + 0.235788i
\(485\) 0 0
\(486\) 18.3943 12.1512i 0.834380 0.551189i
\(487\) 24.4456 1.10773 0.553867 0.832605i \(-0.313152\pi\)
0.553867 + 0.832605i \(0.313152\pi\)
\(488\) −22.7665 + 13.0514i −1.03059 + 0.590810i
\(489\) −17.3087 + 14.8886i −0.782728 + 0.673286i
\(490\) 0 0
\(491\) 37.6630i 1.69971i 0.527018 + 0.849854i \(0.323310\pi\)
−0.527018 + 0.849854i \(0.676690\pi\)
\(492\) −5.82709 + 10.3348i −0.262706 + 0.465930i
\(493\) 42.9220 1.93311
\(494\) −0.773646 4.41392i −0.0348080 0.198592i
\(495\) 0 0
\(496\) 18.0785 + 21.7248i 0.811749 + 0.975470i
\(497\) −53.1131 −2.38245
\(498\) 17.9558 21.8931i 0.804617 0.981053i
\(499\) 36.7249 1.64403 0.822016 0.569464i \(-0.192849\pi\)
0.822016 + 0.569464i \(0.192849\pi\)
\(500\) 0 0
\(501\) −4.90762 + 4.22143i −0.219256 + 0.188600i
\(502\) 6.71942 1.17774i 0.299902 0.0525651i
\(503\) 29.5142i 1.31597i 0.753029 + 0.657987i \(0.228592\pi\)
−0.753029 + 0.657987i \(0.771408\pi\)
\(504\) −34.3667 + 13.3488i −1.53081 + 0.594603i
\(505\) 0 0
\(506\) 1.08027 + 6.16332i 0.0480238 + 0.273993i
\(507\) −14.2928 16.6161i −0.634766 0.737947i
\(508\) −24.3659 + 8.81215i −1.08106 + 0.390976i
\(509\) 2.16054 0.0957642 0.0478821 0.998853i \(-0.484753\pi\)
0.0478821 + 0.998853i \(0.484753\pi\)
\(510\) 0 0
\(511\) 19.2048i 0.849571i
\(512\) 22.6265 + 0.207989i 0.999958 + 0.00919190i
\(513\) −23.7146 + 14.8786i −1.04702 + 0.656906i
\(514\) 5.58767 + 31.8796i 0.246461 + 1.40615i
\(515\) 0 0
\(516\) 5.04918 8.95514i 0.222278 0.394228i
\(517\) −18.0286 −0.792895
\(518\) −2.88631 16.4674i −0.126817 0.723537i
\(519\) −8.73498 + 7.51364i −0.383423 + 0.329812i
\(520\) 0 0
\(521\) 9.39893i 0.411775i 0.978576 + 0.205887i \(0.0660080\pi\)
−0.978576 + 0.205887i \(0.933992\pi\)
\(522\) 33.8502 0.794377i 1.48158 0.0347690i
\(523\) 9.68638i 0.423556i 0.977318 + 0.211778i \(0.0679253\pi\)
−0.977318 + 0.211778i \(0.932075\pi\)
\(524\) −2.03175 5.61786i −0.0887573 0.245417i
\(525\) 0 0
\(526\) −18.8786 + 3.30893i −0.823146 + 0.144276i
\(527\) 38.0009i 1.65534i
\(528\) −2.10749 + 12.5499i −0.0917168 + 0.546166i
\(529\) 17.1974 0.747714
\(530\) 0 0
\(531\) −31.9065 4.82378i −1.38462 0.209334i
\(532\) 44.0281 15.9232i 1.90886 0.690357i
\(533\) 2.01431i 0.0872497i
\(534\) 7.97781 + 6.54305i 0.345234 + 0.283145i
\(535\) 0 0
\(536\) −10.1474 + 5.81722i −0.438301 + 0.251265i
\(537\) 24.1732 20.7933i 1.04315 0.897298i
\(538\) −3.16869 18.0785i −0.136612 0.779420i
\(539\) 21.8185i 0.939789i
\(540\) 0 0
\(541\) 13.1751i 0.566441i −0.959055 0.283221i \(-0.908597\pi\)
0.959055 0.283221i \(-0.0914029\pi\)
\(542\) 0 0
\(543\) −25.6218 + 22.0393i −1.09954 + 0.945799i
\(544\) −23.2056 19.6747i −0.994934 0.843544i
\(545\) 0 0
\(546\) −3.96941 + 4.83982i −0.169875 + 0.207125i
\(547\) 28.4113i 1.21478i 0.794404 + 0.607390i \(0.207783\pi\)
−0.794404 + 0.607390i \(0.792217\pi\)
\(548\) −10.6606 + 3.85551i −0.455399 + 0.164699i
\(549\) 27.5213 + 4.16081i 1.17458 + 0.177579i
\(550\) 0 0
\(551\) −42.9984 −1.83179
\(552\) −11.1258 3.93420i −0.473546 0.167451i
\(553\) 54.6897i 2.32564i
\(554\) −4.09974 23.3904i −0.174181 0.993765i
\(555\) 0 0
\(556\) −5.06070 + 1.83025i −0.214622 + 0.0776198i
\(557\) 32.1029i 1.36024i −0.733099 0.680122i \(-0.761927\pi\)
0.733099 0.680122i \(-0.238073\pi\)
\(558\) −0.703300 29.9692i −0.0297731 1.26870i
\(559\) 1.74540i 0.0738227i
\(560\) 0 0
\(561\) 12.9716 11.1579i 0.547660 0.471086i
\(562\) −15.3874 + 2.69701i −0.649077 + 0.113766i
\(563\) 14.2406 0.600170 0.300085 0.953913i \(-0.402985\pi\)
0.300085 + 0.953913i \(0.402985\pi\)
\(564\) 16.6993 29.6176i 0.703167 1.24713i
\(565\) 0 0
\(566\) 26.0552 4.56681i 1.09518 0.191957i
\(567\) 37.3569 + 11.5598i 1.56884 + 0.485466i
\(568\) −17.1957 29.9956i −0.721514 1.25859i
\(569\) 9.08328i 0.380791i 0.981707 + 0.190396i \(0.0609770\pi\)
−0.981707 + 0.190396i \(0.939023\pi\)
\(570\) 0 0
\(571\) −15.7432 −0.658834 −0.329417 0.944185i \(-0.606852\pi\)
−0.329417 + 0.944185i \(0.606852\pi\)
\(572\) 0.734799 + 2.03175i 0.0307235 + 0.0849516i
\(573\) −9.86616 11.4699i −0.412165 0.479161i
\(574\) −20.7293 + 3.63331i −0.865224 + 0.151651i
\(575\) 0 0
\(576\) −18.6651 15.0868i −0.777714 0.628618i
\(577\) 33.1974i 1.38203i 0.722842 + 0.691014i \(0.242836\pi\)
−0.722842 + 0.691014i \(0.757164\pi\)
\(578\) 2.91148 + 16.6110i 0.121102 + 0.690927i
\(579\) 1.93930 1.66814i 0.0805944 0.0693256i
\(580\) 0 0
\(581\) 50.2250 2.08368
\(582\) 4.10543 + 3.36709i 0.170175 + 0.139570i
\(583\) −12.2187 −0.506046
\(584\) 10.8459 6.21766i 0.448807 0.257289i
\(585\) 0 0
\(586\) 41.0173 7.18927i 1.69441 0.296986i
\(587\) −0.613686 −0.0253295 −0.0126648 0.999920i \(-0.504031\pi\)
−0.0126648 + 0.999920i \(0.504031\pi\)
\(588\) −35.8438 20.2098i −1.47817 0.833438i
\(589\) 38.0685i 1.56859i
\(590\) 0 0
\(591\) 14.6330 12.5870i 0.601919 0.517758i
\(592\) 8.36552 6.96147i 0.343821 0.286115i
\(593\) 15.5545 0.638747 0.319374 0.947629i \(-0.396528\pi\)
0.319374 + 0.947629i \(0.396528\pi\)
\(594\) 10.0235 9.03967i 0.411267 0.370902i
\(595\) 0 0
\(596\) 39.4194 14.2564i 1.61468 0.583963i
\(597\) 3.67721 3.16306i 0.150498 0.129456i
\(598\) −1.97345 + 0.345895i −0.0807005 + 0.0141447i
\(599\) −39.0811 −1.59681 −0.798406 0.602119i \(-0.794323\pi\)
−0.798406 + 0.602119i \(0.794323\pi\)
\(600\) 0 0
\(601\) −20.5231 −0.837155 −0.418578 0.908181i \(-0.637471\pi\)
−0.418578 + 0.908181i \(0.637471\pi\)
\(602\) 17.9619 3.14826i 0.732073 0.128313i
\(603\) 12.2667 + 1.85454i 0.499538 + 0.0755225i
\(604\) 2.15534 + 5.95961i 0.0876997 + 0.242493i
\(605\) 0 0
\(606\) −4.91334 + 5.99073i −0.199591 + 0.243357i
\(607\) −10.8832 −0.441735 −0.220868 0.975304i \(-0.570889\pi\)
−0.220868 + 0.975304i \(0.570889\pi\)
\(608\) 23.2470 + 19.7097i 0.942789 + 0.799333i
\(609\) 39.1666 + 45.5331i 1.58711 + 1.84509i
\(610\) 0 0
\(611\) 5.77263i 0.233535i
\(612\) 6.31517 + 31.6451i 0.255276 + 1.27918i
\(613\) −30.3350 −1.22522 −0.612610 0.790385i \(-0.709881\pi\)
−0.612610 + 0.790385i \(0.709881\pi\)
\(614\) 46.2601 8.10820i 1.86691 0.327220i
\(615\) 0 0
\(616\) −19.5833 + 11.2266i −0.789033 + 0.452331i
\(617\) 8.71447 0.350831 0.175416 0.984494i \(-0.443873\pi\)
0.175416 + 0.984494i \(0.443873\pi\)
\(618\) −19.5519 + 23.8393i −0.786494 + 0.958956i
\(619\) −13.0323 −0.523811 −0.261906 0.965093i \(-0.584351\pi\)
−0.261906 + 0.965093i \(0.584351\pi\)
\(620\) 0 0
\(621\) 6.65218 + 10.6027i 0.266943 + 0.425473i
\(622\) −6.29348 35.9065i −0.252346 1.43972i
\(623\) 18.3019i 0.733250i
\(624\) −4.01841 0.674805i −0.160865 0.0270138i
\(625\) 0 0
\(626\) 13.4480 2.35708i 0.537489 0.0942078i
\(627\) −12.9947 + 11.1777i −0.518957 + 0.446396i
\(628\) −22.5671 + 8.16160i −0.900527 + 0.325683i
\(629\) −14.6330 −0.583454
\(630\) 0 0
\(631\) 14.8599i 0.591562i −0.955256 0.295781i \(-0.904420\pi\)
0.955256 0.295781i \(-0.0955798\pi\)
\(632\) 30.8860 17.7061i 1.22858 0.704311i
\(633\) 11.1421 + 12.9533i 0.442859 + 0.514845i
\(634\) −6.71096 + 1.17626i −0.266526 + 0.0467151i
\(635\) 0 0
\(636\) 11.3178 20.0730i 0.448779 0.795947i
\(637\) −6.98614 −0.276801
\(638\) 20.4197 3.57904i 0.808423 0.141696i
\(639\) −5.48200 + 36.2602i −0.216864 + 1.43443i
\(640\) 0 0
\(641\) 5.97397i 0.235958i −0.993016 0.117979i \(-0.962358\pi\)
0.993016 0.117979i \(-0.0376415\pi\)
\(642\) 5.88721 7.17816i 0.232350 0.283300i
\(643\) 15.7938i 0.622848i −0.950271 0.311424i \(-0.899194\pi\)
0.950271 0.311424i \(-0.100806\pi\)
\(644\) −7.11921 19.6849i −0.280536 0.775693i
\(645\) 0 0
\(646\) −7.07466 40.3634i −0.278349 1.58808i
\(647\) 14.8128i 0.582351i 0.956670 + 0.291175i \(0.0940463\pi\)
−0.956670 + 0.291175i \(0.905954\pi\)
\(648\) 5.56610 + 24.8399i 0.218657 + 0.975802i
\(649\) −19.7572 −0.775537
\(650\) 0 0
\(651\) 40.3126 34.6760i 1.57997 1.35906i
\(652\) −8.96611 24.7916i −0.351140 0.970916i
\(653\) 3.48912i 0.136540i −0.997667 0.0682699i \(-0.978252\pi\)
0.997667 0.0682699i \(-0.0217479\pi\)
\(654\) 1.11390 + 0.913568i 0.0435568 + 0.0357234i
\(655\) 0 0
\(656\) −8.76313 10.5306i −0.342143 0.411149i
\(657\) −13.1111 1.98220i −0.511513 0.0773329i
\(658\) 59.4060 10.4123i 2.31589 0.405915i
\(659\) 36.5563i 1.42403i 0.702163 + 0.712017i \(0.252218\pi\)
−0.702163 + 0.712017i \(0.747782\pi\)
\(660\) 0 0
\(661\) 42.9220i 1.66947i 0.550650 + 0.834736i \(0.314380\pi\)
−0.550650 + 0.834736i \(0.685620\pi\)
\(662\) −0.335418 1.91368i −0.0130364 0.0743772i
\(663\) 3.57268 + 4.15341i 0.138751 + 0.161305i
\(664\) 16.2606 + 28.3646i 0.631034 + 1.10076i
\(665\) 0 0
\(666\) −11.5402 + 0.270819i −0.447174 + 0.0104940i
\(667\) 19.2245i 0.744375i
\(668\) −2.54220 7.02929i −0.0983608 0.271971i
\(669\) 1.83448 + 2.13267i 0.0709251 + 0.0824538i
\(670\) 0 0
\(671\) 17.0418 0.657892
\(672\) −0.303769 42.5706i −0.0117182 1.64220i
\(673\) 46.2899i 1.78434i 0.451696 + 0.892172i \(0.350819\pi\)
−0.451696 + 0.892172i \(0.649181\pi\)
\(674\) −18.2375 + 3.19656i −0.702483 + 0.123127i
\(675\) 0 0
\(676\) 23.7996 8.60732i 0.915368 0.331051i
\(677\) 27.7911i 1.06810i 0.845453 + 0.534049i \(0.179330\pi\)
−0.845453 + 0.534049i \(0.820670\pi\)
\(678\) 17.1833 20.9513i 0.659922 0.804631i
\(679\) 9.41826i 0.361440i
\(680\) 0 0
\(681\) −5.57997 6.48699i −0.213825 0.248582i
\(682\) −3.16869 18.0785i −0.121336 0.692262i
\(683\) −33.6521 −1.28766 −0.643832 0.765167i \(-0.722656\pi\)
−0.643832 + 0.765167i \(0.722656\pi\)
\(684\) −6.32641 31.7014i −0.241896 1.21213i
\(685\) 0 0
\(686\) −5.17537 29.5273i −0.197597 1.12736i
\(687\) 20.0210 17.2216i 0.763849 0.657047i
\(688\) 7.59325 + 9.12473i 0.289490 + 0.347877i
\(689\) 3.91234i 0.149048i
\(690\) 0 0
\(691\) −22.6820 −0.862864 −0.431432 0.902145i \(-0.641992\pi\)
−0.431432 + 0.902145i \(0.641992\pi\)
\(692\) −4.52481 12.5113i −0.172008 0.475608i
\(693\) 23.6733 + 3.57904i 0.899274 + 0.135956i
\(694\) −0.971573 5.54316i −0.0368804 0.210416i
\(695\) 0 0
\(696\) −13.0344 + 36.8609i −0.494068 + 1.39721i
\(697\) 18.4200i 0.697708i
\(698\) −17.5334 + 3.07314i −0.663648 + 0.116320i
\(699\) 25.1878 + 29.2821i 0.952692 + 1.10755i
\(700\) 0 0
\(701\) −10.6379 −0.401789 −0.200895 0.979613i \(-0.564385\pi\)
−0.200895 + 0.979613i \(0.564385\pi\)
\(702\) 2.89444 + 3.20945i 0.109244 + 0.121133i
\(703\) 14.6590 0.552875
\(704\) −12.6804 7.42501i −0.477911 0.279841i
\(705\) 0 0
\(706\) −0.192214 1.09665i −0.00723407 0.0412729i
\(707\) −13.7433 −0.516872
\(708\) 18.3005 32.4574i 0.687774 1.21982i
\(709\) 20.5295i 0.771002i −0.922707 0.385501i \(-0.874029\pi\)
0.922707 0.385501i \(-0.125971\pi\)
\(710\) 0 0
\(711\) −37.3366 5.64472i −1.40023 0.211694i
\(712\) −10.3360 + 5.92534i −0.387358 + 0.222062i
\(713\) 17.0203 0.637417
\(714\) −36.2985 + 44.2581i −1.35844 + 1.65632i
\(715\) 0 0
\(716\) 12.5220 + 34.6238i 0.467969 + 1.29395i
\(717\) 16.8084 + 19.5406i 0.627721 + 0.729756i
\(718\) −0.263751 1.50479i −0.00984310 0.0561583i
\(719\) −14.8813 −0.554977 −0.277489 0.960729i \(-0.589502\pi\)
−0.277489 + 0.960729i \(0.589502\pi\)
\(720\) 0 0
\(721\) −54.6897 −2.03675
\(722\) 2.44834 + 13.9687i 0.0911179 + 0.519860i
\(723\) −0.590858 0.686901i −0.0219742 0.0255461i
\(724\) −13.2724 36.6986i −0.493264 1.36389i
\(725\) 0 0
\(726\) −11.8461 + 14.4438i −0.439651 + 0.536058i
\(727\) 16.1239 0.598004 0.299002 0.954253i \(-0.403346\pi\)
0.299002 + 0.954253i \(0.403346\pi\)
\(728\) −3.59467 6.27044i −0.133227 0.232398i
\(729\) 11.7476 24.3104i 0.435096 0.900384i
\(730\) 0 0
\(731\) 15.9610i 0.590337i
\(732\) −15.7853 + 27.9965i −0.583441 + 1.03478i
\(733\) −16.7310 −0.617975 −0.308988 0.951066i \(-0.599990\pi\)
−0.308988 + 0.951066i \(0.599990\pi\)
\(734\) −3.55960 20.3088i −0.131387 0.749611i
\(735\) 0 0
\(736\) 8.81215 10.3937i 0.324820 0.383115i
\(737\) 7.59579 0.279795
\(738\) 0.340908 + 14.5269i 0.0125490 + 0.534741i
\(739\) −12.5693 −0.462371 −0.231185 0.972910i \(-0.574260\pi\)
−0.231185 + 0.972910i \(0.574260\pi\)
\(740\) 0 0
\(741\) −3.57904 4.16081i −0.131479 0.152851i
\(742\) 40.2618 7.05685i 1.47806 0.259065i
\(743\) 22.2877i 0.817655i −0.912612 0.408827i \(-0.865938\pi\)
0.912612 0.408827i \(-0.134062\pi\)
\(744\) 32.6347 + 11.5400i 1.19645 + 0.423076i
\(745\) 0 0
\(746\) 7.70838 + 43.9790i 0.282224 + 1.61019i
\(747\) 5.18390 34.2885i 0.189669 1.25455i
\(748\) 6.71942 + 18.5794i 0.245686 + 0.679332i
\(749\) 16.4674 0.601707
\(750\) 0 0
\(751\) 35.1279i 1.28183i −0.767610 0.640917i \(-0.778554\pi\)
0.767610 0.640917i \(-0.221446\pi\)
\(752\) 25.1134 + 30.1785i 0.915791 + 1.10050i
\(753\) 6.33410 5.44846i 0.230827 0.198553i
\(754\) 1.14599 + 6.53825i 0.0417343 + 0.238109i
\(755\) 0 0
\(756\) −27.8075 + 35.5757i −1.01135 + 1.29388i
\(757\) −20.6887 −0.751945 −0.375972 0.926631i \(-0.622691\pi\)
−0.375972 + 0.926631i \(0.622691\pi\)
\(758\) −1.12609 6.42476i −0.0409016 0.233358i
\(759\) 4.99754 + 5.80988i 0.181399 + 0.210885i
\(760\) 0 0
\(761\) 22.8130i 0.826971i 0.910511 + 0.413485i \(0.135689\pi\)
−0.910511 + 0.413485i \(0.864311\pi\)
\(762\) −20.1240 + 24.5368i −0.729016 + 0.888874i
\(763\) 2.55539i 0.0925113i
\(764\) 16.4286 5.94153i 0.594364 0.214957i
\(765\) 0 0
\(766\) −20.3834 + 3.57268i −0.736482 + 0.129086i
\(767\) 6.32612i 0.228423i
\(768\) 23.9434 13.9540i 0.863982 0.503522i
\(769\) 46.3082 1.66992 0.834958 0.550313i \(-0.185492\pi\)
0.834958 + 0.550313i \(0.185492\pi\)
\(770\) 0 0
\(771\) 25.8496 + 30.0515i 0.930952 + 1.08228i
\(772\) 1.00458 + 2.77769i 0.0361555 + 0.0999714i
\(773\) 30.2684i 1.08868i −0.838865 0.544340i \(-0.816780\pi\)
0.838865 0.544340i \(-0.183220\pi\)
\(774\) −0.295397 12.5875i −0.0106178 0.452449i
\(775\) 0 0
\(776\) −5.31897 + 3.04922i −0.190940 + 0.109460i
\(777\) −13.3527 15.5231i −0.479024 0.556889i
\(778\) 3.69620 + 21.0881i 0.132515 + 0.756045i
\(779\) 18.4528i 0.661141i
\(780\) 0 0
\(781\) 22.4531i 0.803436i
\(782\) −18.0464 + 3.16306i −0.645337 + 0.113111i
\(783\) 35.1279 22.0393i 1.25537 0.787622i
\(784\) 36.5226 30.3927i 1.30438 1.08545i
\(785\) 0 0
\(786\) −5.65725 4.63983i −0.201788 0.165497i
\(787\) 19.4080i 0.691819i −0.938268 0.345910i \(-0.887570\pi\)
0.938268 0.345910i \(-0.112430\pi\)
\(788\) 7.58003 + 20.9591i 0.270027 + 0.746636i
\(789\) −17.7960 + 15.3078i −0.633555 + 0.544971i
\(790\) 0 0
\(791\) 48.0644 1.70897
\(792\) 5.64309 + 14.5282i 0.200519 + 0.516238i
\(793\) 5.45667i 0.193772i
\(794\) 4.47684 + 25.5420i 0.158877 + 0.906450i
\(795\) 0 0
\(796\) 1.90484 + 5.26695i 0.0675152 + 0.186682i
\(797\) 30.7743i 1.09008i 0.838409 + 0.545041i \(0.183486\pi\)
−0.838409 + 0.545041i \(0.816514\pi\)
\(798\) 36.3631 44.3369i 1.28724 1.56951i
\(799\) 52.7882i 1.86751i
\(800\) 0 0
\(801\) 12.4947 + 1.88901i 0.441478 + 0.0667448i
\(802\) 47.6929 8.35933i 1.68409 0.295178i
\(803\) −8.11867 −0.286502
\(804\) −7.03575 + 12.4785i −0.248132 + 0.440082i
\(805\) 0 0
\(806\) 5.78862 1.01460i 0.203895 0.0357376i
\(807\) −14.6590 17.0418i −0.516021 0.599900i
\(808\) −4.44948 7.76156i −0.156532 0.273051i
\(809\) 37.5744i 1.32104i −0.750807 0.660522i \(-0.770335\pi\)
0.750807 0.660522i \(-0.229665\pi\)
\(810\) 0 0
\(811\) −30.3492 −1.06571 −0.532853 0.846208i \(-0.678880\pi\)
−0.532853 + 0.846208i \(0.678880\pi\)
\(812\) −65.2179 + 23.5866i −2.28870 + 0.827729i
\(813\) 0 0
\(814\) −6.96147 + 1.22016i −0.243999 + 0.0427668i
\(815\) 0 0
\(816\) −36.7466 6.17080i −1.28639 0.216021i
\(817\) 15.9894i 0.559397i
\(818\) −4.56386 26.0384i −0.159572 0.910413i
\(819\) −1.14599 + 7.58003i −0.0400440 + 0.264868i
\(820\) 0 0
\(821\) −6.97824 −0.243542 −0.121771 0.992558i \(-0.538857\pi\)
−0.121771 + 0.992558i \(0.538857\pi\)
\(822\) −8.80468 + 10.7354i −0.307099 + 0.374439i
\(823\) 0.569147 0.0198392 0.00991960 0.999951i \(-0.496842\pi\)
0.00991960 + 0.999951i \(0.496842\pi\)
\(824\) −17.7061 30.8860i −0.616821 1.07597i
\(825\) 0 0
\(826\) 65.1020 11.4107i 2.26519 0.397029i
\(827\) −23.0851 −0.802748 −0.401374 0.915914i \(-0.631467\pi\)
−0.401374 + 0.915914i \(0.631467\pi\)
\(828\) −14.1736 + 2.82852i −0.492568 + 0.0982980i
\(829\) 48.3636i 1.67974i −0.542790 0.839869i \(-0.682632\pi\)
0.542790 0.839869i \(-0.317368\pi\)
\(830\) 0 0
\(831\) −18.9662 22.0491i −0.657930 0.764876i
\(832\) 2.37744 4.06018i 0.0824229 0.140761i
\(833\) −63.8852 −2.21349
\(834\) −4.17967 + 5.09619i −0.144730 + 0.176467i
\(835\) 0 0
\(836\) −6.73138 18.6125i −0.232810 0.643728i
\(837\) −19.5125 31.1004i −0.674450 1.07499i
\(838\) −7.30755 + 1.28082i −0.252435 + 0.0442453i
\(839\) 22.0393 0.760883 0.380441 0.924805i \(-0.375772\pi\)
0.380441 + 0.924805i \(0.375772\pi\)
\(840\) 0 0
\(841\) 34.6926 1.19630
\(842\) −6.16332 + 1.08027i −0.212402 + 0.0372285i
\(843\) −14.5050 + 12.4769i −0.499578 + 0.429727i
\(844\) −18.5532 + 6.70993i −0.638628 + 0.230965i
\(845\) 0 0
\(846\) −0.976975 41.6311i −0.0335891 1.43131i
\(847\) −33.1355 −1.13855
\(848\) 17.0203 + 20.4532i 0.584481 + 0.702365i
\(849\) 24.5611 21.1270i 0.842936 0.725076i
\(850\) 0 0
\(851\) 6.55400i 0.224668i
\(852\) −36.8863 20.7976i −1.26371 0.712515i
\(853\) −6.39801 −0.219064 −0.109532 0.993983i \(-0.534935\pi\)
−0.109532 + 0.993983i \(0.534935\pi\)
\(854\) −56.1546 + 9.84244i −1.92157 + 0.336801i
\(855\) 0 0
\(856\) 5.33142 + 9.29998i 0.182224 + 0.317867i
\(857\) 27.2124 0.929559 0.464780 0.885426i \(-0.346134\pi\)
0.464780 + 0.885426i \(0.346134\pi\)
\(858\) 2.04599 + 1.67803i 0.0698491 + 0.0572871i
\(859\) −23.4663 −0.800658 −0.400329 0.916371i \(-0.631104\pi\)
−0.400329 + 0.916371i \(0.631104\pi\)
\(860\) 0 0
\(861\) −19.5406 + 16.8084i −0.665941 + 0.572828i
\(862\) −1.44001 8.21575i −0.0490469 0.279830i
\(863\) 12.4724i 0.424566i 0.977208 + 0.212283i \(0.0680898\pi\)
−0.977208 + 0.212283i \(0.931910\pi\)
\(864\) −29.0942 4.18648i −0.989805 0.142427i
\(865\) 0 0
\(866\) −44.8759 + 7.86557i −1.52494 + 0.267283i
\(867\) 13.4691 + 15.6585i 0.457434 + 0.531790i
\(868\) 20.8824 + 57.7405i 0.708794 + 1.95984i
\(869\) −23.1196 −0.784279
\(870\) 0 0
\(871\) 2.43212i 0.0824093i
\(872\) −1.44316 + 0.827322i −0.0488715 + 0.0280166i
\(873\) 6.42984 + 0.972093i 0.217617 + 0.0329004i
\(874\) 18.0785 3.16869i 0.611515 0.107183i
\(875\) 0 0
\(876\) 7.52007 13.3375i 0.254080 0.450632i
\(877\) −48.9517 −1.65298 −0.826491 0.562950i \(-0.809667\pi\)
−0.826491 + 0.562950i \(0.809667\pi\)
\(878\) 3.16611 0.554937i 0.106851 0.0187282i
\(879\) 38.6652 33.2590i 1.30414 1.12180i
\(880\) 0 0
\(881\) 9.76612i 0.329029i −0.986375 0.164514i \(-0.947394\pi\)
0.986375 0.164514i \(-0.0526057\pi\)
\(882\) −50.3827 + 1.18235i −1.69647 + 0.0398119i
\(883\) 37.1170i 1.24909i 0.780990 + 0.624544i \(0.214715\pi\)
−0.780990 + 0.624544i \(0.785285\pi\)
\(884\) −5.94902 + 2.15151i −0.200087 + 0.0723633i
\(885\) 0 0
\(886\) −1.12088 6.39504i −0.0376569 0.214846i
\(887\) 20.7792i 0.697699i 0.937179 + 0.348849i \(0.113427\pi\)
−0.937179 + 0.348849i \(0.886573\pi\)
\(888\) 4.44368 12.5666i 0.149120 0.421708i
\(889\) −56.2899 −1.88790
\(890\) 0 0
\(891\) 4.88681 15.7923i 0.163714 0.529062i
\(892\) −3.05467 + 1.10475i −0.102278 + 0.0369897i
\(893\) 52.8821i 1.76963i
\(894\) 32.5567 39.6958i 1.08886 1.32763i
\(895\) 0 0
\(896\) 46.0716 + 17.1427i 1.53914 + 0.572697i
\(897\) −1.86029 + 1.60018i −0.0621132 + 0.0534285i
\(898\) −54.3904 + 9.53322i −1.81503 + 0.318128i
\(899\) 56.3901i 1.88072i
\(900\) 0 0
\(901\) 35.7766i 1.19189i
\(902\) 1.53595 + 8.76313i 0.0511415 + 0.291780i
\(903\) 16.9319 14.5645i 0.563459 0.484675i
\(904\) 15.5611 + 27.1444i 0.517555 + 0.902809i
\(905\) 0 0
\(906\) 6.00140 + 4.92208i 0.199383 + 0.163525i
\(907\) 25.5231i 0.847481i 0.905784 + 0.423741i \(0.139283\pi\)
−0.905784 + 0.423741i \(0.860717\pi\)
\(908\) 9.29144 3.36033i 0.308347 0.111516i
\(909\) −1.41850 + 9.38256i −0.0470487 + 0.311200i
\(910\) 0 0
\(911\) −18.6187 −0.616865 −0.308433 0.951246i \(-0.599804\pi\)
−0.308433 + 0.951246i \(0.599804\pi\)
\(912\) 36.8120 + 6.18178i 1.21897 + 0.204699i
\(913\) 21.2322i 0.702683i
\(914\) −6.91122 + 1.21136i −0.228603 + 0.0400681i
\(915\) 0 0
\(916\) 10.3711 + 28.6765i 0.342671 + 0.947497i
\(917\) 12.9783i 0.428581i
\(918\) 26.4684 + 29.3490i 0.873588 + 0.968661i
\(919\) 27.9743i 0.922788i 0.887195 + 0.461394i \(0.152650\pi\)
−0.887195 + 0.461394i \(0.847350\pi\)
\(920\) 0 0
\(921\) 43.6074 37.5101i 1.43691 1.23600i
\(922\) 3.44916 + 19.6787i 0.113592 + 0.648083i
\(923\) −7.18934 −0.236640
\(924\) −13.5782 + 24.0820i −0.446689 + 0.792241i
\(925\) 0 0
\(926\) −3.48912 19.9067i −0.114660 0.654174i
\(927\) −5.64472 + 37.3366i −0.185397 + 1.22629i
\(928\) −34.4352 29.1955i −1.13039 0.958391i
\(929\) 46.7604i 1.53416i 0.641551 + 0.767080i \(0.278291\pi\)
−0.641551 + 0.767080i \(0.721709\pi\)
\(930\) 0 0
\(931\) 63.9990 2.09748
\(932\) −41.9413 + 15.1685i −1.37383 + 0.496859i
\(933\) −29.1149 33.8475i −0.953178 1.10812i
\(934\) 7.77551 + 44.3620i 0.254422 + 1.45157i
\(935\) 0 0
\(936\) −4.65184 + 1.80688i −0.152050 + 0.0590598i
\(937\) 41.2253i 1.34677i −0.739291 0.673387i \(-0.764839\pi\)
0.739291 0.673387i \(-0.235161\pi\)
\(938\) −25.0289 + 4.38692i −0.817224 + 0.143238i
\(939\) 12.6768 10.9043i 0.413692 0.355849i
\(940\) 0 0
\(941\) 0.179836 0.00586248 0.00293124 0.999996i \(-0.499067\pi\)
0.00293124 + 0.999996i \(0.499067\pi\)
\(942\) −18.6384 + 22.7254i −0.607270 + 0.740433i
\(943\) −8.25021 −0.268664
\(944\) 27.5213 + 33.0721i 0.895743 + 1.07641i
\(945\) 0 0
\(946\) −1.33090 7.59325i −0.0432713 0.246878i
\(947\) −21.3864 −0.694965 −0.347483 0.937686i \(-0.612963\pi\)
−0.347483 + 0.937686i \(0.612963\pi\)
\(948\) 21.4150 37.9813i 0.695526 1.23357i
\(949\) 2.59955i 0.0843849i
\(950\) 0 0
\(951\) −6.32612 + 5.44160i −0.205139 + 0.176456i
\(952\) −32.8717 57.3405i −1.06538 1.85842i
\(953\) 11.0306 0.357317 0.178658 0.983911i \(-0.442824\pi\)
0.178658 + 0.983911i \(0.442824\pi\)
\(954\) −0.662135 28.2151i −0.0214374 0.913496i
\(955\) 0 0
\(956\) −27.9884 + 10.1222i −0.905208 + 0.327376i
\(957\) 19.2487 16.5573i 0.622223 0.535223i
\(958\) 6.33739 + 36.1570i 0.204752 + 1.16818i
\(959\) −24.6280 −0.795281
\(960\) 0 0
\(961\) −18.9248 −0.610478
\(962\) −0.390689 2.22902i −0.0125963 0.0718664i
\(963\) 1.69966 11.2423i 0.0547709 0.362278i
\(964\) 0.983862 0.355822i 0.0316881 0.0114603i
\(965\) 0 0
\(966\) −19.8229 16.2579i −0.637792 0.523089i
\(967\) −10.8832 −0.349980 −0.174990 0.984570i \(-0.555989\pi\)
−0.174990 + 0.984570i \(0.555989\pi\)
\(968\) −10.7278 18.7133i −0.344804 0.601467i
\(969\) −32.7288 38.0488i −1.05140 1.22230i
\(970\) 0 0
\(971\) 2.40482i 0.0771744i −0.999255 0.0385872i \(-0.987714\pi\)
0.999255 0.0385872i \(-0.0122857\pi\)
\(972\) 21.4174 + 22.6561i 0.686962 + 0.726693i
\(973\) −11.6912 −0.374802
\(974\) 5.96846 + 34.0521i 0.191242 + 1.09110i
\(975\) 0 0
\(976\) −23.7389 28.5268i −0.759863 0.913119i
\(977\) −41.7609 −1.33605 −0.668026 0.744138i \(-0.732860\pi\)
−0.668026 + 0.744138i \(0.732860\pi\)
\(978\) −24.9655 20.4756i −0.798308 0.654737i
\(979\) 7.73698 0.247275
\(980\) 0 0
\(981\) 1.74456 + 0.263751i 0.0556995 + 0.00842092i
\(982\) −52.4638 + 9.19554i −1.67419 + 0.293442i
\(983\) 33.2516i 1.06056i −0.847822 0.530281i \(-0.822086\pi\)
0.847822 0.530281i \(-0.177914\pi\)
\(984\) −15.8189 5.59373i −0.504288 0.178322i
\(985\) 0 0
\(986\) 10.4795 + 59.7894i 0.333736 + 1.90408i
\(987\) 55.9994 48.1695i 1.78248 1.53325i
\(988\) 5.95961 2.15534i 0.189600 0.0685707i
\(989\) 7.14881 0.227319
\(990\) 0 0
\(991\) 33.9434i 1.07825i 0.842226 + 0.539124i \(0.181245\pi\)
−0.842226 + 0.539124i \(0.818755\pi\)
\(992\) −25.8482 + 30.4871i −0.820681 + 0.967967i
\(993\) −1.55171 1.80394i −0.0492420 0.0572462i
\(994\) −12.9677 73.9854i −0.411311 2.34667i
\(995\) 0 0
\(996\) 34.8806 + 19.6667i 1.10523 + 0.623164i
\(997\) 45.6428 1.44552 0.722761 0.691098i \(-0.242873\pi\)
0.722761 + 0.691098i \(0.242873\pi\)
\(998\) 8.96650 + 51.1570i 0.283830 + 1.61935i
\(999\) −11.9758 + 7.51364i −0.378897 + 0.237721i
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.e.299.16 24
3.2 odd 2 inner 600.2.m.e.299.10 24
4.3 odd 2 2400.2.m.e.1199.6 24
5.2 odd 4 600.2.b.g.251.2 yes 12
5.3 odd 4 600.2.b.h.251.11 yes 12
5.4 even 2 inner 600.2.m.e.299.9 24
8.3 odd 2 inner 600.2.m.e.299.14 24
8.5 even 2 2400.2.m.e.1199.5 24
12.11 even 2 2400.2.m.e.1199.18 24
15.2 even 4 600.2.b.g.251.11 yes 12
15.8 even 4 600.2.b.h.251.2 yes 12
15.14 odd 2 inner 600.2.m.e.299.15 24
20.3 even 4 2400.2.b.g.2351.9 12
20.7 even 4 2400.2.b.h.2351.4 12
20.19 odd 2 2400.2.m.e.1199.19 24
24.5 odd 2 2400.2.m.e.1199.17 24
24.11 even 2 inner 600.2.m.e.299.12 24
40.3 even 4 600.2.b.h.251.1 yes 12
40.13 odd 4 2400.2.b.g.2351.10 12
40.19 odd 2 inner 600.2.m.e.299.11 24
40.27 even 4 600.2.b.g.251.12 yes 12
40.29 even 2 2400.2.m.e.1199.20 24
40.37 odd 4 2400.2.b.h.2351.3 12
60.23 odd 4 2400.2.b.g.2351.11 12
60.47 odd 4 2400.2.b.h.2351.2 12
60.59 even 2 2400.2.m.e.1199.7 24
120.29 odd 2 2400.2.m.e.1199.8 24
120.53 even 4 2400.2.b.g.2351.12 12
120.59 even 2 inner 600.2.m.e.299.13 24
120.77 even 4 2400.2.b.h.2351.1 12
120.83 odd 4 600.2.b.h.251.12 yes 12
120.107 odd 4 600.2.b.g.251.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
600.2.b.g.251.1 12 120.107 odd 4
600.2.b.g.251.2 yes 12 5.2 odd 4
600.2.b.g.251.11 yes 12 15.2 even 4
600.2.b.g.251.12 yes 12 40.27 even 4
600.2.b.h.251.1 yes 12 40.3 even 4
600.2.b.h.251.2 yes 12 15.8 even 4
600.2.b.h.251.11 yes 12 5.3 odd 4
600.2.b.h.251.12 yes 12 120.83 odd 4
600.2.m.e.299.9 24 5.4 even 2 inner
600.2.m.e.299.10 24 3.2 odd 2 inner
600.2.m.e.299.11 24 40.19 odd 2 inner
600.2.m.e.299.12 24 24.11 even 2 inner
600.2.m.e.299.13 24 120.59 even 2 inner
600.2.m.e.299.14 24 8.3 odd 2 inner
600.2.m.e.299.15 24 15.14 odd 2 inner
600.2.m.e.299.16 24 1.1 even 1 trivial
2400.2.b.g.2351.9 12 20.3 even 4
2400.2.b.g.2351.10 12 40.13 odd 4
2400.2.b.g.2351.11 12 60.23 odd 4
2400.2.b.g.2351.12 12 120.53 even 4
2400.2.b.h.2351.1 12 120.77 even 4
2400.2.b.h.2351.2 12 60.47 odd 4
2400.2.b.h.2351.3 12 40.37 odd 4
2400.2.b.h.2351.4 12 20.7 even 4
2400.2.m.e.1199.5 24 8.5 even 2
2400.2.m.e.1199.6 24 4.3 odd 2
2400.2.m.e.1199.7 24 60.59 even 2
2400.2.m.e.1199.8 24 120.29 odd 2
2400.2.m.e.1199.17 24 24.5 odd 2
2400.2.m.e.1199.18 24 12.11 even 2
2400.2.m.e.1199.19 24 20.19 odd 2
2400.2.m.e.1199.20 24 40.29 even 2