Properties

Label 201.3.h.b.172.5
Level $201$
Weight $3$
Character 201.172
Analytic conductor $5.477$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [201,3,Mod(97,201)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(201, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.97");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 201.h (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.47685331364\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 172.5
Character \(\chi\) \(=\) 201.172
Dual form 201.3.h.b.97.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.893138 - 0.515653i) q^{2} -1.73205i q^{3} +(-1.46820 - 2.54300i) q^{4} +8.85241i q^{5} +(-0.893138 + 1.54696i) q^{6} +(7.85559 - 4.53543i) q^{7} +7.15356i q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(-0.893138 - 0.515653i) q^{2} -1.73205i q^{3} +(-1.46820 - 2.54300i) q^{4} +8.85241i q^{5} +(-0.893138 + 1.54696i) q^{6} +(7.85559 - 4.53543i) q^{7} +7.15356i q^{8} -3.00000 q^{9} +(4.56478 - 7.90642i) q^{10} +(3.62479 - 2.09277i) q^{11} +(-4.40461 + 2.54300i) q^{12} +(13.1062 + 7.56688i) q^{13} -9.35483 q^{14} +15.3328 q^{15} +(-2.18406 + 3.78289i) q^{16} +(-0.813277 + 1.40864i) q^{17} +(2.67941 + 1.54696i) q^{18} +(15.2858 - 26.4758i) q^{19} +(22.5117 - 12.9971i) q^{20} +(-7.85559 - 13.6063i) q^{21} -4.31658 q^{22} +(12.8586 - 22.2717i) q^{23} +12.3903 q^{24} -53.3652 q^{25} +(-7.80378 - 13.5165i) q^{26} +5.19615i q^{27} +(-23.0672 - 13.3179i) q^{28} +(11.6799 + 20.2301i) q^{29} +(-13.6943 - 7.90642i) q^{30} +(31.3790 - 18.1167i) q^{31} +(28.6820 - 16.5596i) q^{32} +(-3.62479 - 6.27831i) q^{33} +(1.45274 - 0.838738i) q^{34} +(40.1495 + 69.5409i) q^{35} +(4.40461 + 7.62901i) q^{36} +(-4.84533 + 8.39236i) q^{37} +(-27.3046 + 15.7643i) q^{38} +(13.1062 - 22.7007i) q^{39} -63.3263 q^{40} +(29.7223 - 17.1602i) q^{41} +16.2030i q^{42} +77.4895i q^{43} +(-10.6438 - 6.14523i) q^{44} -26.5572i q^{45} +(-22.9690 + 13.2612i) q^{46} +(-7.25570 - 12.5672i) q^{47} +(6.55217 + 3.78289i) q^{48} +(16.6402 - 28.8217i) q^{49} +(47.6625 + 27.5179i) q^{50} +(2.43983 + 1.40864i) q^{51} -44.4389i q^{52} +65.4446i q^{53} +(2.67941 - 4.64088i) q^{54} +(18.5261 + 32.0881i) q^{55} +(32.4445 + 56.1955i) q^{56} +(-45.8574 - 26.4758i) q^{57} -24.0911i q^{58} -40.1862 q^{59} +(-22.5117 - 38.9914i) q^{60} +(12.1810 + 7.03273i) q^{61} -37.3677 q^{62} +(-23.5668 + 13.6063i) q^{63} -16.6835 q^{64} +(-66.9852 + 116.022i) q^{65} +7.47653i q^{66} +(-18.3984 - 64.4244i) q^{67} +4.77623 q^{68} +(-38.5758 - 22.2717i) q^{69} -82.8128i q^{70} +(-8.72147 - 15.1060i) q^{71} -21.4607i q^{72} +(-35.2921 + 61.1278i) q^{73} +(8.65510 - 4.99702i) q^{74} +92.4313i q^{75} -89.7706 q^{76} +(18.9832 - 32.8799i) q^{77} +(-23.4113 + 13.5165i) q^{78} +(1.93538 - 1.11739i) q^{79} +(-33.4877 - 19.3342i) q^{80} +9.00000 q^{81} -35.3948 q^{82} +(16.3342 - 28.2917i) q^{83} +(-23.0672 + 39.9536i) q^{84} +(-12.4698 - 7.19947i) q^{85} +(39.9577 - 69.2088i) q^{86} +(35.0396 - 20.2301i) q^{87} +(14.9708 + 25.9301i) q^{88} -168.923 q^{89} +(-13.6943 + 23.7193i) q^{90} +137.276 q^{91} -75.5161 q^{92} +(-31.3790 - 54.3500i) q^{93} +14.9657i q^{94} +(234.374 + 135.316i) q^{95} +(-28.6820 - 49.6787i) q^{96} +(162.611 + 93.8833i) q^{97} +(-29.7240 + 17.1612i) q^{98} +(-10.8744 + 6.27831i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 34 q^{4} + 21 q^{7} - 72 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 34 q^{4} + 21 q^{7} - 72 q^{9} + 30 q^{10} + 12 q^{11} + 102 q^{12} + 30 q^{13} + 6 q^{14} - 6 q^{15} - 98 q^{16} + 4 q^{17} + 39 q^{19} + 108 q^{20} - 21 q^{21} - 82 q^{22} - 13 q^{23} - 36 q^{24} - 222 q^{25} + 29 q^{26} + 189 q^{28} - 90 q^{30} - 93 q^{31} - 33 q^{32} - 12 q^{33} + 72 q^{34} - 93 q^{35} - 102 q^{36} - 33 q^{37} - 210 q^{38} + 30 q^{39} + 274 q^{40} - 15 q^{41} - 9 q^{44} - 228 q^{46} - 131 q^{47} + 294 q^{48} + 295 q^{49} - 423 q^{50} - 12 q^{51} - 56 q^{55} + 349 q^{56} - 117 q^{57} - 116 q^{59} - 108 q^{60} + 120 q^{61} + 282 q^{62} - 63 q^{63} - 276 q^{64} + 136 q^{65} - 25 q^{67} + 10 q^{68} + 39 q^{69} + 169 q^{71} + 187 q^{73} + 849 q^{74} + 386 q^{76} - 348 q^{77} + 87 q^{78} + 51 q^{80} + 216 q^{81} - 14 q^{82} + 104 q^{83} + 189 q^{84} - 243 q^{85} + 641 q^{86} - 766 q^{88} + 152 q^{89} - 90 q^{90} + 32 q^{91} - 216 q^{92} + 93 q^{93} + 762 q^{95} + 33 q^{96} - 84 q^{97} - 1086 q^{98} - 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).

\(n\) \(68\) \(136\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.893138 0.515653i −0.446569 0.257827i 0.259811 0.965659i \(-0.416340\pi\)
−0.706380 + 0.707833i \(0.749673\pi\)
\(3\) 1.73205i 0.577350i
\(4\) −1.46820 2.54300i −0.367051 0.635751i
\(5\) 8.85241i 1.77048i 0.465132 + 0.885241i \(0.346007\pi\)
−0.465132 + 0.885241i \(0.653993\pi\)
\(6\) −0.893138 + 1.54696i −0.148856 + 0.257827i
\(7\) 7.85559 4.53543i 1.12223 0.647918i 0.180259 0.983619i \(-0.442307\pi\)
0.941969 + 0.335701i \(0.108973\pi\)
\(8\) 7.15356i 0.894195i
\(9\) −3.00000 −0.333333
\(10\) 4.56478 7.90642i 0.456478 0.790642i
\(11\) 3.62479 2.09277i 0.329526 0.190252i −0.326105 0.945334i \(-0.605736\pi\)
0.655631 + 0.755082i \(0.272403\pi\)
\(12\) −4.40461 + 2.54300i −0.367051 + 0.211917i
\(13\) 13.1062 + 7.56688i 1.00817 + 0.582068i 0.910656 0.413166i \(-0.135577\pi\)
0.0975156 + 0.995234i \(0.468910\pi\)
\(14\) −9.35483 −0.668202
\(15\) 15.3328 1.02219
\(16\) −2.18406 + 3.78289i −0.136503 + 0.236431i
\(17\) −0.813277 + 1.40864i −0.0478398 + 0.0828610i −0.888954 0.457997i \(-0.848567\pi\)
0.841114 + 0.540858i \(0.181900\pi\)
\(18\) 2.67941 + 1.54696i 0.148856 + 0.0859422i
\(19\) 15.2858 26.4758i 0.804515 1.39346i −0.112103 0.993697i \(-0.535759\pi\)
0.916618 0.399765i \(-0.130908\pi\)
\(20\) 22.5117 12.9971i 1.12559 0.649857i
\(21\) −7.85559 13.6063i −0.374076 0.647918i
\(22\) −4.31658 −0.196208
\(23\) 12.8586 22.2717i 0.559069 0.968336i −0.438505 0.898729i \(-0.644492\pi\)
0.997574 0.0696077i \(-0.0221748\pi\)
\(24\) 12.3903 0.516264
\(25\) −53.3652 −2.13461
\(26\) −7.80378 13.5165i −0.300145 0.519867i
\(27\) 5.19615i 0.192450i
\(28\) −23.0672 13.3179i −0.823829 0.475638i
\(29\) 11.6799 + 20.2301i 0.402754 + 0.697591i 0.994057 0.108858i \(-0.0347195\pi\)
−0.591303 + 0.806450i \(0.701386\pi\)
\(30\) −13.6943 7.90642i −0.456478 0.263547i
\(31\) 31.3790 18.1167i 1.01222 0.584408i 0.100383 0.994949i \(-0.467993\pi\)
0.911842 + 0.410541i \(0.134660\pi\)
\(32\) 28.6820 16.5596i 0.896312 0.517486i
\(33\) −3.62479 6.27831i −0.109842 0.190252i
\(34\) 1.45274 0.838738i 0.0427276 0.0246688i
\(35\) 40.1495 + 69.5409i 1.14713 + 1.98688i
\(36\) 4.40461 + 7.62901i 0.122350 + 0.211917i
\(37\) −4.84533 + 8.39236i −0.130955 + 0.226821i −0.924045 0.382284i \(-0.875138\pi\)
0.793090 + 0.609104i \(0.208471\pi\)
\(38\) −27.3046 + 15.7643i −0.718543 + 0.414851i
\(39\) 13.1062 22.7007i 0.336057 0.582068i
\(40\) −63.3263 −1.58316
\(41\) 29.7223 17.1602i 0.724935 0.418541i −0.0916316 0.995793i \(-0.529208\pi\)
0.816566 + 0.577252i \(0.195875\pi\)
\(42\) 16.2030i 0.385787i
\(43\) 77.4895i 1.80208i 0.433735 + 0.901041i \(0.357196\pi\)
−0.433735 + 0.901041i \(0.642804\pi\)
\(44\) −10.6438 6.14523i −0.241906 0.139664i
\(45\) 26.5572i 0.590161i
\(46\) −22.9690 + 13.2612i −0.499326 + 0.288286i
\(47\) −7.25570 12.5672i −0.154376 0.267388i 0.778455 0.627700i \(-0.216004\pi\)
−0.932832 + 0.360312i \(0.882670\pi\)
\(48\) 6.55217 + 3.78289i 0.136503 + 0.0788103i
\(49\) 16.6402 28.8217i 0.339596 0.588198i
\(50\) 47.6625 + 27.5179i 0.953250 + 0.550359i
\(51\) 2.43983 + 1.40864i 0.0478398 + 0.0276203i
\(52\) 44.4389i 0.854594i
\(53\) 65.4446i 1.23480i 0.786648 + 0.617402i \(0.211815\pi\)
−0.786648 + 0.617402i \(0.788185\pi\)
\(54\) 2.67941 4.64088i 0.0496188 0.0859422i
\(55\) 18.5261 + 32.0881i 0.336838 + 0.583420i
\(56\) 32.4445 + 56.1955i 0.579365 + 1.00349i
\(57\) −45.8574 26.4758i −0.804515 0.464487i
\(58\) 24.0911i 0.415363i
\(59\) −40.1862 −0.681121 −0.340561 0.940223i \(-0.610617\pi\)
−0.340561 + 0.940223i \(0.610617\pi\)
\(60\) −22.5117 38.9914i −0.375195 0.649857i
\(61\) 12.1810 + 7.03273i 0.199689 + 0.115291i 0.596511 0.802605i \(-0.296553\pi\)
−0.396821 + 0.917896i \(0.629887\pi\)
\(62\) −37.3677 −0.602704
\(63\) −23.5668 + 13.6063i −0.374076 + 0.215973i
\(64\) −16.6835 −0.260680
\(65\) −66.9852 + 116.022i −1.03054 + 1.78495i
\(66\) 7.47653i 0.113281i
\(67\) −18.3984 64.4244i −0.274603 0.961558i
\(68\) 4.77623 0.0702386
\(69\) −38.5758 22.2717i −0.559069 0.322779i
\(70\) 82.8128i 1.18304i
\(71\) −8.72147 15.1060i −0.122838 0.212761i 0.798048 0.602594i \(-0.205866\pi\)
−0.920886 + 0.389833i \(0.872533\pi\)
\(72\) 21.4607i 0.298065i
\(73\) −35.2921 + 61.1278i −0.483454 + 0.837367i −0.999819 0.0190016i \(-0.993951\pi\)
0.516366 + 0.856368i \(0.327285\pi\)
\(74\) 8.65510 4.99702i 0.116961 0.0675273i
\(75\) 92.4313i 1.23242i
\(76\) −89.7706 −1.18119
\(77\) 18.9832 32.8799i 0.246535 0.427012i
\(78\) −23.4113 + 13.5165i −0.300145 + 0.173289i
\(79\) 1.93538 1.11739i 0.0244985 0.0141442i −0.487701 0.873011i \(-0.662164\pi\)
0.512199 + 0.858867i \(0.328831\pi\)
\(80\) −33.4877 19.3342i −0.418597 0.241677i
\(81\) 9.00000 0.111111
\(82\) −35.3948 −0.431644
\(83\) 16.3342 28.2917i 0.196798 0.340863i −0.750691 0.660654i \(-0.770279\pi\)
0.947488 + 0.319790i \(0.103612\pi\)
\(84\) −23.0672 + 39.9536i −0.274610 + 0.475638i
\(85\) −12.4698 7.19947i −0.146704 0.0846996i
\(86\) 39.9577 69.2088i 0.464625 0.804753i
\(87\) 35.0396 20.2301i 0.402754 0.232530i
\(88\) 14.9708 + 25.9301i 0.170122 + 0.294661i
\(89\) −168.923 −1.89801 −0.949004 0.315263i \(-0.897907\pi\)
−0.949004 + 0.315263i \(0.897907\pi\)
\(90\) −13.6943 + 23.7193i −0.152159 + 0.263547i
\(91\) 137.276 1.50853
\(92\) −75.5161 −0.820827
\(93\) −31.3790 54.3500i −0.337408 0.584408i
\(94\) 14.9657i 0.159210i
\(95\) 234.374 + 135.316i 2.46710 + 1.42438i
\(96\) −28.6820 49.6787i −0.298771 0.517486i
\(97\) 162.611 + 93.8833i 1.67640 + 0.967869i 0.963926 + 0.266169i \(0.0857580\pi\)
0.712473 + 0.701700i \(0.247575\pi\)
\(98\) −29.7240 + 17.1612i −0.303306 + 0.175114i
\(99\) −10.8744 + 6.27831i −0.109842 + 0.0634173i
\(100\) 78.3510 + 135.708i 0.783510 + 1.35708i
\(101\) −6.70212 + 3.86947i −0.0663576 + 0.0383116i −0.532812 0.846234i \(-0.678865\pi\)
0.466454 + 0.884545i \(0.345531\pi\)
\(102\) −1.45274 2.51621i −0.0142425 0.0246688i
\(103\) −70.3871 121.914i −0.683370 1.18363i −0.973946 0.226779i \(-0.927180\pi\)
0.290576 0.956852i \(-0.406153\pi\)
\(104\) −54.1302 + 93.7562i −0.520482 + 0.901502i
\(105\) 120.448 69.5409i 1.14713 0.662295i
\(106\) 33.7467 58.4511i 0.318365 0.551425i
\(107\) −4.59014 −0.0428985 −0.0214493 0.999770i \(-0.506828\pi\)
−0.0214493 + 0.999770i \(0.506828\pi\)
\(108\) 13.2138 7.62901i 0.122350 0.0706390i
\(109\) 23.7429i 0.217824i −0.994051 0.108912i \(-0.965263\pi\)
0.994051 0.108912i \(-0.0347367\pi\)
\(110\) 38.2121i 0.347383i
\(111\) 14.5360 + 8.39236i 0.130955 + 0.0756069i
\(112\) 39.6225i 0.353772i
\(113\) 69.4795 40.1140i 0.614862 0.354991i −0.160004 0.987116i \(-0.551151\pi\)
0.774866 + 0.632125i \(0.217817\pi\)
\(114\) 27.3046 + 47.2930i 0.239514 + 0.414851i
\(115\) 197.159 + 113.830i 1.71442 + 0.989822i
\(116\) 34.2969 59.4039i 0.295663 0.512103i
\(117\) −39.3187 22.7007i −0.336057 0.194023i
\(118\) 35.8918 + 20.7221i 0.304168 + 0.175611i
\(119\) 14.7542i 0.123985i
\(120\) 109.684i 0.914036i
\(121\) −51.7406 + 89.6174i −0.427608 + 0.740640i
\(122\) −7.25290 12.5624i −0.0594500 0.102970i
\(123\) −29.7223 51.4806i −0.241645 0.418541i
\(124\) −92.1414 53.1979i −0.743076 0.429015i
\(125\) 251.101i 2.00880i
\(126\) 28.0645 0.222734
\(127\) −118.302 204.905i −0.931512 1.61343i −0.780739 0.624857i \(-0.785157\pi\)
−0.150773 0.988568i \(-0.548176\pi\)
\(128\) −99.8273 57.6353i −0.779901 0.450276i
\(129\) 134.216 1.04043
\(130\) 119.654 69.0823i 0.920415 0.531402i
\(131\) −230.163 −1.75697 −0.878486 0.477767i \(-0.841446\pi\)
−0.878486 + 0.477767i \(0.841446\pi\)
\(132\) −10.6438 + 18.4357i −0.0806352 + 0.139664i
\(133\) 277.310i 2.08504i
\(134\) −16.7884 + 67.0270i −0.125286 + 0.500202i
\(135\) −45.9985 −0.340730
\(136\) −10.0768 5.81783i −0.0740939 0.0427782i
\(137\) 146.341i 1.06819i −0.845426 0.534093i \(-0.820653\pi\)
0.845426 0.534093i \(-0.179347\pi\)
\(138\) 22.9690 + 39.7835i 0.166442 + 0.288286i
\(139\) 118.950i 0.855755i 0.903837 + 0.427878i \(0.140739\pi\)
−0.903837 + 0.427878i \(0.859261\pi\)
\(140\) 117.895 204.200i 0.842108 1.45857i
\(141\) −21.7671 + 12.5672i −0.154376 + 0.0891293i
\(142\) 17.9890i 0.126683i
\(143\) 63.3430 0.442958
\(144\) 6.55217 11.3487i 0.0455012 0.0788103i
\(145\) −179.086 + 103.395i −1.23507 + 0.713070i
\(146\) 63.0415 36.3970i 0.431791 0.249295i
\(147\) −49.9206 28.8217i −0.339596 0.196066i
\(148\) 28.4557 0.192268
\(149\) 238.194 1.59862 0.799309 0.600920i \(-0.205199\pi\)
0.799309 + 0.600920i \(0.205199\pi\)
\(150\) 47.6625 82.5538i 0.317750 0.550359i
\(151\) −46.2665 + 80.1359i −0.306401 + 0.530701i −0.977572 0.210601i \(-0.932458\pi\)
0.671172 + 0.741302i \(0.265791\pi\)
\(152\) 189.396 + 109.348i 1.24603 + 0.719394i
\(153\) 2.43983 4.22591i 0.0159466 0.0276203i
\(154\) −33.9093 + 19.5775i −0.220190 + 0.127127i
\(155\) 160.376 + 277.780i 1.03468 + 1.79213i
\(156\) −76.9704 −0.493400
\(157\) 86.5926 149.983i 0.551546 0.955305i −0.446618 0.894725i \(-0.647372\pi\)
0.998163 0.0605800i \(-0.0192950\pi\)
\(158\) −2.30475 −0.0145870
\(159\) 113.353 0.712915
\(160\) 146.592 + 253.905i 0.916200 + 1.58691i
\(161\) 233.277i 1.44892i
\(162\) −8.03824 4.64088i −0.0496188 0.0286474i
\(163\) −48.0514 83.2274i −0.294794 0.510598i 0.680143 0.733079i \(-0.261918\pi\)
−0.974937 + 0.222482i \(0.928584\pi\)
\(164\) −87.2768 50.3893i −0.532176 0.307252i
\(165\) 55.5782 32.0881i 0.336838 0.194473i
\(166\) −29.1774 + 16.8456i −0.175767 + 0.101479i
\(167\) 30.7370 + 53.2380i 0.184054 + 0.318790i 0.943257 0.332063i \(-0.107745\pi\)
−0.759204 + 0.650853i \(0.774411\pi\)
\(168\) 97.3334 56.1955i 0.579365 0.334497i
\(169\) 30.0155 + 51.9883i 0.177606 + 0.307623i
\(170\) 7.42486 + 12.8602i 0.0436756 + 0.0756484i
\(171\) −45.8574 + 79.4273i −0.268172 + 0.464487i
\(172\) 197.056 113.770i 1.14567 0.661455i
\(173\) −162.839 + 282.045i −0.941263 + 1.63032i −0.178198 + 0.983995i \(0.557027\pi\)
−0.763066 + 0.646321i \(0.776307\pi\)
\(174\) −41.7270 −0.239810
\(175\) −419.215 + 242.034i −2.39552 + 1.38305i
\(176\) 18.2829i 0.103880i
\(177\) 69.6045i 0.393246i
\(178\) 150.871 + 87.1056i 0.847592 + 0.489357i
\(179\) 95.8352i 0.535392i 0.963503 + 0.267696i \(0.0862623\pi\)
−0.963503 + 0.267696i \(0.913738\pi\)
\(180\) −67.5351 + 38.9914i −0.375195 + 0.216619i
\(181\) −17.3203 29.9996i −0.0956923 0.165744i 0.814205 0.580577i \(-0.197173\pi\)
−0.909897 + 0.414834i \(0.863840\pi\)
\(182\) −122.607 70.7869i −0.673662 0.388939i
\(183\) 12.1810 21.0982i 0.0665631 0.115291i
\(184\) 159.322 + 91.9847i 0.865882 + 0.499917i
\(185\) −74.2926 42.8929i −0.401582 0.231853i
\(186\) 64.7227i 0.347971i
\(187\) 6.80801i 0.0364065i
\(188\) −21.3057 + 36.9025i −0.113328 + 0.196290i
\(189\) 23.5668 + 40.8188i 0.124692 + 0.215973i
\(190\) −139.552 241.712i −0.734486 1.27217i
\(191\) −247.333 142.798i −1.29494 0.747633i −0.315413 0.948954i \(-0.602143\pi\)
−0.979525 + 0.201321i \(0.935476\pi\)
\(192\) 28.8967i 0.150504i
\(193\) −128.395 −0.665260 −0.332630 0.943057i \(-0.607936\pi\)
−0.332630 + 0.943057i \(0.607936\pi\)
\(194\) −96.8225 167.701i −0.499085 0.864441i
\(195\) 200.956 + 116.022i 1.03054 + 0.594983i
\(196\) −97.7248 −0.498596
\(197\) 26.6529 15.3881i 0.135294 0.0781120i −0.430825 0.902435i \(-0.641777\pi\)
0.566119 + 0.824323i \(0.308444\pi\)
\(198\) 12.9497 0.0654027
\(199\) −48.2515 + 83.5740i −0.242470 + 0.419970i −0.961417 0.275094i \(-0.911291\pi\)
0.718947 + 0.695064i \(0.244624\pi\)
\(200\) 381.751i 1.90876i
\(201\) −111.586 + 31.8669i −0.555156 + 0.158542i
\(202\) 7.98122 0.0395110
\(203\) 183.505 + 105.946i 0.903964 + 0.521904i
\(204\) 8.27267i 0.0405523i
\(205\) 151.909 + 263.114i 0.741020 + 1.28348i
\(206\) 145.181i 0.704764i
\(207\) −38.5758 + 66.8152i −0.186356 + 0.322779i
\(208\) −57.2494 + 33.0530i −0.275238 + 0.158909i
\(209\) 127.959i 0.612242i
\(210\) −143.436 −0.683029
\(211\) −13.3867 + 23.1864i −0.0634439 + 0.109888i −0.896003 0.444049i \(-0.853542\pi\)
0.832559 + 0.553937i \(0.186875\pi\)
\(212\) 166.426 96.0860i 0.785028 0.453236i
\(213\) −26.1644 + 15.1060i −0.122838 + 0.0709203i
\(214\) 4.09963 + 2.36692i 0.0191571 + 0.0110604i
\(215\) −685.969 −3.19055
\(216\) −37.1710 −0.172088
\(217\) 164.334 284.634i 0.757298 1.31168i
\(218\) −12.2431 + 21.2056i −0.0561609 + 0.0972736i
\(219\) 105.876 + 61.1278i 0.483454 + 0.279122i
\(220\) 54.4001 94.2237i 0.247273 0.428290i
\(221\) −21.3180 + 12.3079i −0.0964615 + 0.0556921i
\(222\) −8.65510 14.9911i −0.0389869 0.0675273i
\(223\) 10.9612 0.0491535 0.0245768 0.999698i \(-0.492176\pi\)
0.0245768 + 0.999698i \(0.492176\pi\)
\(224\) 150.209 260.170i 0.670577 1.16147i
\(225\) 160.096 0.711536
\(226\) −82.7396 −0.366105
\(227\) 85.5638 + 148.201i 0.376933 + 0.652867i 0.990614 0.136687i \(-0.0436454\pi\)
−0.613681 + 0.789554i \(0.710312\pi\)
\(228\) 155.487i 0.681962i
\(229\) −67.2387 38.8203i −0.293619 0.169521i 0.345954 0.938251i \(-0.387555\pi\)
−0.639573 + 0.768731i \(0.720889\pi\)
\(230\) −117.393 203.331i −0.510405 0.884048i
\(231\) −56.9497 32.8799i −0.246535 0.142337i
\(232\) −144.718 + 83.5527i −0.623783 + 0.360141i
\(233\) −67.3067 + 38.8596i −0.288870 + 0.166779i −0.637432 0.770506i \(-0.720003\pi\)
0.348562 + 0.937286i \(0.386670\pi\)
\(234\) 23.4113 + 40.5496i 0.100048 + 0.173289i
\(235\) 111.250 64.2304i 0.473406 0.273321i
\(236\) 59.0015 + 102.194i 0.250006 + 0.433023i
\(237\) −1.93538 3.35218i −0.00816616 0.0141442i
\(238\) 7.60807 13.1776i 0.0319667 0.0553679i
\(239\) −288.452 + 166.538i −1.20691 + 0.696812i −0.962084 0.272754i \(-0.912065\pi\)
−0.244830 + 0.969566i \(0.578732\pi\)
\(240\) −33.4877 + 58.0025i −0.139532 + 0.241677i
\(241\) 146.823 0.609224 0.304612 0.952476i \(-0.401473\pi\)
0.304612 + 0.952476i \(0.401473\pi\)
\(242\) 92.4230 53.3604i 0.381913 0.220498i
\(243\) 15.5885i 0.0641500i
\(244\) 41.3019i 0.169270i
\(245\) 255.141 + 147.306i 1.04139 + 0.601249i
\(246\) 61.3056i 0.249210i
\(247\) 400.678 231.332i 1.62218 0.936565i
\(248\) 129.599 + 224.471i 0.522575 + 0.905127i
\(249\) −49.0026 28.2917i −0.196798 0.113621i
\(250\) −129.481 + 224.267i −0.517923 + 0.897070i
\(251\) −267.648 154.527i −1.06633 0.615644i −0.139151 0.990271i \(-0.544437\pi\)
−0.927176 + 0.374627i \(0.877771\pi\)
\(252\) 69.2016 + 39.9536i 0.274610 + 0.158546i
\(253\) 107.640i 0.425456i
\(254\) 244.011i 0.960674i
\(255\) −12.4698 + 21.5984i −0.0489013 + 0.0846996i
\(256\) 92.8067 + 160.746i 0.362526 + 0.627914i
\(257\) −166.839 288.974i −0.649180 1.12441i −0.983319 0.181889i \(-0.941779\pi\)
0.334139 0.942524i \(-0.391554\pi\)
\(258\) −119.873 69.2088i −0.464625 0.268251i
\(259\) 87.9026i 0.339392i
\(260\) 393.391 1.51304
\(261\) −35.0396 60.6904i −0.134251 0.232530i
\(262\) 205.568 + 118.685i 0.784609 + 0.452994i
\(263\) −262.341 −0.997496 −0.498748 0.866747i \(-0.666207\pi\)
−0.498748 + 0.866747i \(0.666207\pi\)
\(264\) 44.9123 25.9301i 0.170122 0.0982202i
\(265\) −579.343 −2.18620
\(266\) −142.996 + 247.676i −0.537579 + 0.931114i
\(267\) 292.583i 1.09582i
\(268\) −136.819 + 141.375i −0.510518 + 0.527519i
\(269\) −319.062 −1.18611 −0.593053 0.805164i \(-0.702077\pi\)
−0.593053 + 0.805164i \(0.702077\pi\)
\(270\) 41.0830 + 23.7193i 0.152159 + 0.0878492i
\(271\) 303.898i 1.12140i −0.828020 0.560698i \(-0.810533\pi\)
0.828020 0.560698i \(-0.189467\pi\)
\(272\) −3.55249 6.15308i −0.0130606 0.0226216i
\(273\) 237.769i 0.870950i
\(274\) −75.4614 + 130.703i −0.275407 + 0.477018i
\(275\) −193.437 + 111.681i −0.703409 + 0.406113i
\(276\) 130.798i 0.473905i
\(277\) 374.292 1.35123 0.675617 0.737253i \(-0.263877\pi\)
0.675617 + 0.737253i \(0.263877\pi\)
\(278\) 61.3369 106.239i 0.220636 0.382154i
\(279\) −94.1369 + 54.3500i −0.337408 + 0.194803i
\(280\) −497.465 + 287.212i −1.77666 + 1.02576i
\(281\) 132.843 + 76.6970i 0.472751 + 0.272943i 0.717391 0.696671i \(-0.245336\pi\)
−0.244639 + 0.969614i \(0.578670\pi\)
\(282\) 25.9213 0.0919197
\(283\) −296.462 −1.04757 −0.523784 0.851851i \(-0.675480\pi\)
−0.523784 + 0.851851i \(0.675480\pi\)
\(284\) −25.6098 + 44.3574i −0.0901752 + 0.156188i
\(285\) 234.374 405.948i 0.822366 1.42438i
\(286\) −56.5740 32.6630i −0.197811 0.114206i
\(287\) 155.658 269.607i 0.542361 0.939397i
\(288\) −86.0460 + 49.6787i −0.298771 + 0.172495i
\(289\) 143.177 + 247.990i 0.495423 + 0.858097i
\(290\) 213.264 0.735393
\(291\) 162.611 281.650i 0.558800 0.967869i
\(292\) 207.264 0.709809
\(293\) 4.07829 0.0139191 0.00695954 0.999976i \(-0.497785\pi\)
0.00695954 + 0.999976i \(0.497785\pi\)
\(294\) 29.7240 + 51.4835i 0.101102 + 0.175114i
\(295\) 355.744i 1.20591i
\(296\) −60.0353 34.6614i −0.202822 0.117099i
\(297\) 10.8744 + 18.8349i 0.0366140 + 0.0634173i
\(298\) −212.740 122.826i −0.713893 0.412166i
\(299\) 337.055 194.599i 1.12728 0.650833i
\(300\) 235.053 135.708i 0.783510 0.452360i
\(301\) 351.448 + 608.726i 1.16760 + 2.02234i
\(302\) 82.6447 47.7149i 0.273658 0.157996i
\(303\) 6.70212 + 11.6084i 0.0221192 + 0.0383116i
\(304\) 66.7700 + 115.649i 0.219638 + 0.380425i
\(305\) −62.2566 + 107.832i −0.204120 + 0.353546i
\(306\) −4.35821 + 2.51621i −0.0142425 + 0.00822292i
\(307\) 184.507 319.576i 0.601001 1.04096i −0.391668 0.920106i \(-0.628102\pi\)
0.992670 0.120858i \(-0.0385647\pi\)
\(308\) −111.485 −0.361964
\(309\) −211.161 + 121.914i −0.683370 + 0.394544i
\(310\) 330.794i 1.06708i
\(311\) 451.365i 1.45134i 0.688046 + 0.725668i \(0.258469\pi\)
−0.688046 + 0.725668i \(0.741531\pi\)
\(312\) 162.391 + 93.7562i 0.520482 + 0.300501i
\(313\) 302.563i 0.966654i −0.875440 0.483327i \(-0.839428\pi\)
0.875440 0.483327i \(-0.160572\pi\)
\(314\) −154.678 + 89.3036i −0.492606 + 0.284406i
\(315\) −120.448 208.623i −0.382376 0.662295i
\(316\) −5.68306 3.28112i −0.0179844 0.0103833i
\(317\) 217.373 376.500i 0.685718 1.18770i −0.287493 0.957783i \(-0.592822\pi\)
0.973211 0.229915i \(-0.0738449\pi\)
\(318\) −101.240 58.4511i −0.318365 0.183808i
\(319\) 84.6741 + 48.8866i 0.265436 + 0.153250i
\(320\) 147.689i 0.461529i
\(321\) 7.95036i 0.0247675i
\(322\) −120.290 + 208.348i −0.373571 + 0.647045i
\(323\) 24.8632 + 43.0643i 0.0769758 + 0.133326i
\(324\) −13.2138 22.8870i −0.0407834 0.0706390i
\(325\) −699.417 403.808i −2.15205 1.24249i
\(326\) 99.1114i 0.304023i
\(327\) −41.1238 −0.125761
\(328\) 122.756 + 212.620i 0.374258 + 0.648233i
\(329\) −113.996 65.8154i −0.346491 0.200047i
\(330\) −66.1853 −0.200562
\(331\) −428.471 + 247.378i −1.29447 + 0.747365i −0.979444 0.201716i \(-0.935348\pi\)
−0.315030 + 0.949082i \(0.602015\pi\)
\(332\) −95.9277 −0.288939
\(333\) 14.5360 25.1771i 0.0436516 0.0756069i
\(334\) 63.3985i 0.189816i
\(335\) 570.311 162.870i 1.70242 0.486179i
\(336\) 68.6282 0.204251
\(337\) 504.751 + 291.418i 1.49778 + 0.864741i 0.999997 0.00256219i \(-0.000815570\pi\)
0.497779 + 0.867304i \(0.334149\pi\)
\(338\) 61.9103i 0.183167i
\(339\) −69.4795 120.342i −0.204954 0.354991i
\(340\) 42.2811i 0.124356i
\(341\) 75.8280 131.338i 0.222370 0.385155i
\(342\) 81.9139 47.2930i 0.239514 0.138284i
\(343\) 142.590i 0.415715i
\(344\) −554.326 −1.61141
\(345\) 197.159 341.489i 0.571474 0.989822i
\(346\) 290.874 167.936i 0.840678 0.485365i
\(347\) −150.759 + 87.0408i −0.434464 + 0.250838i −0.701247 0.712919i \(-0.747373\pi\)
0.266782 + 0.963757i \(0.414040\pi\)
\(348\) −102.891 59.4039i −0.295663 0.170701i
\(349\) 241.316 0.691451 0.345725 0.938336i \(-0.387633\pi\)
0.345725 + 0.938336i \(0.387633\pi\)
\(350\) 499.223 1.42635
\(351\) −39.3187 + 68.1020i −0.112019 + 0.194023i
\(352\) 69.3107 120.050i 0.196905 0.341050i
\(353\) 88.4568 + 51.0706i 0.250586 + 0.144676i 0.620033 0.784576i \(-0.287119\pi\)
−0.369447 + 0.929252i \(0.620453\pi\)
\(354\) 35.8918 62.1664i 0.101389 0.175611i
\(355\) 133.725 77.2060i 0.376689 0.217482i
\(356\) 248.013 + 429.571i 0.696666 + 1.20666i
\(357\) 25.5551 0.0715829
\(358\) 49.4177 85.5940i 0.138038 0.239090i
\(359\) 434.606 1.21060 0.605301 0.795996i \(-0.293053\pi\)
0.605301 + 0.795996i \(0.293053\pi\)
\(360\) 189.979 0.527719
\(361\) −286.811 496.771i −0.794490 1.37610i
\(362\) 35.7251i 0.0986881i
\(363\) 155.222 + 89.6174i 0.427608 + 0.246880i
\(364\) −201.549 349.094i −0.553707 0.959049i
\(365\) −541.128 312.421i −1.48254 0.855947i
\(366\) −21.7587 + 12.5624i −0.0594500 + 0.0343235i
\(367\) −354.050 + 204.411i −0.964713 + 0.556978i −0.897620 0.440769i \(-0.854706\pi\)
−0.0670929 + 0.997747i \(0.521372\pi\)
\(368\) 56.1678 + 97.2854i 0.152630 + 0.264363i
\(369\) −89.1670 + 51.4806i −0.241645 + 0.139514i
\(370\) 44.2357 + 76.6185i 0.119556 + 0.207077i
\(371\) 296.819 + 514.106i 0.800052 + 1.38573i
\(372\) −92.1414 + 159.594i −0.247692 + 0.429015i
\(373\) −86.8670 + 50.1527i −0.232887 + 0.134458i −0.611903 0.790933i \(-0.709596\pi\)
0.379016 + 0.925390i \(0.376263\pi\)
\(374\) 3.51057 6.08049i 0.00938656 0.0162580i
\(375\) −434.919 −1.15978
\(376\) 89.9005 51.9041i 0.239097 0.138043i
\(377\) 353.521i 0.937722i
\(378\) 48.6091i 0.128596i
\(379\) 359.205 + 207.387i 0.947772 + 0.547196i 0.892388 0.451269i \(-0.149028\pi\)
0.0553837 + 0.998465i \(0.482362\pi\)
\(380\) 794.686i 2.09128i
\(381\) −354.906 + 204.905i −0.931512 + 0.537809i
\(382\) 147.268 + 255.076i 0.385519 + 0.667739i
\(383\) 535.422 + 309.126i 1.39797 + 0.807118i 0.994180 0.107733i \(-0.0343593\pi\)
0.403790 + 0.914852i \(0.367693\pi\)
\(384\) −99.8273 + 172.906i −0.259967 + 0.450276i
\(385\) 291.066 + 168.047i 0.756017 + 0.436486i
\(386\) 114.675 + 66.2074i 0.297084 + 0.171522i
\(387\) 232.468i 0.600694i
\(388\) 551.359i 1.42103i
\(389\) −25.6639 + 44.4512i −0.0659740 + 0.114270i −0.897126 0.441775i \(-0.854349\pi\)
0.831152 + 0.556046i \(0.187682\pi\)
\(390\) −119.654 207.247i −0.306805 0.531402i
\(391\) 20.9152 + 36.2262i 0.0534916 + 0.0926501i
\(392\) 206.178 + 119.037i 0.525963 + 0.303665i
\(393\) 398.655i 1.01439i
\(394\) −31.7396 −0.0805575
\(395\) 9.89161 + 17.1328i 0.0250421 + 0.0433741i
\(396\) 31.9315 + 18.4357i 0.0806352 + 0.0465547i
\(397\) 386.868 0.974479 0.487239 0.873268i \(-0.338004\pi\)
0.487239 + 0.873268i \(0.338004\pi\)
\(398\) 86.1905 49.7621i 0.216559 0.125030i
\(399\) −480.316 −1.20380
\(400\) 116.553 201.875i 0.291381 0.504687i
\(401\) 542.650i 1.35324i 0.736332 + 0.676620i \(0.236556\pi\)
−0.736332 + 0.676620i \(0.763444\pi\)
\(402\) 116.094 + 29.0783i 0.288792 + 0.0723341i
\(403\) 548.347 1.36066
\(404\) 19.6801 + 11.3623i 0.0487132 + 0.0281246i
\(405\) 79.6717i 0.196720i
\(406\) −109.263 189.250i −0.269121 0.466132i
\(407\) 40.5607i 0.0996577i
\(408\) −10.0768 + 17.4535i −0.0246980 + 0.0427782i
\(409\) 70.8960 40.9318i 0.173340 0.100078i −0.410820 0.911717i \(-0.634757\pi\)
0.584160 + 0.811639i \(0.301424\pi\)
\(410\) 313.330i 0.764219i
\(411\) −253.471 −0.616717
\(412\) −206.685 + 357.989i −0.501663 + 0.868905i
\(413\) −315.686 + 182.261i −0.764373 + 0.441311i
\(414\) 68.9070 39.7835i 0.166442 0.0960953i
\(415\) 250.449 + 144.597i 0.603493 + 0.348427i
\(416\) 501.217 1.20485
\(417\) 206.027 0.494070
\(418\) −65.9823 + 114.285i −0.157852 + 0.273408i
\(419\) −86.7252 + 150.213i −0.206981 + 0.358502i −0.950762 0.309921i \(-0.899697\pi\)
0.743781 + 0.668424i \(0.233031\pi\)
\(420\) −353.686 204.200i −0.842108 0.486192i
\(421\) 190.924 330.691i 0.453502 0.785488i −0.545099 0.838372i \(-0.683508\pi\)
0.998601 + 0.0528834i \(0.0168412\pi\)
\(422\) 23.9123 13.8058i 0.0566642 0.0327151i
\(423\) 21.7671 + 37.7017i 0.0514588 + 0.0891293i
\(424\) −468.162 −1.10416
\(425\) 43.4007 75.1722i 0.102119 0.176876i
\(426\) 31.1579 0.0731406
\(427\) 127.586 0.298796
\(428\) 6.73926 + 11.6727i 0.0157459 + 0.0272728i
\(429\) 109.713i 0.255742i
\(430\) 612.665 + 353.722i 1.42480 + 0.822610i
\(431\) −167.188 289.578i −0.387907 0.671874i 0.604261 0.796786i \(-0.293468\pi\)
−0.992168 + 0.124912i \(0.960135\pi\)
\(432\) −19.6565 11.3487i −0.0455012 0.0262701i
\(433\) −286.583 + 165.459i −0.661854 + 0.382121i −0.792983 0.609244i \(-0.791473\pi\)
0.131129 + 0.991365i \(0.458140\pi\)
\(434\) −293.545 + 169.478i −0.676371 + 0.390503i
\(435\) 179.086 + 310.185i 0.411691 + 0.713070i
\(436\) −60.3781 + 34.8593i −0.138482 + 0.0799526i
\(437\) −393.108 680.882i −0.899560 1.55808i
\(438\) −63.0415 109.191i −0.143930 0.249295i
\(439\) −100.383 + 173.868i −0.228663 + 0.396055i −0.957412 0.288725i \(-0.906769\pi\)
0.728749 + 0.684780i \(0.240102\pi\)
\(440\) −229.544 + 132.527i −0.521691 + 0.301199i
\(441\) −49.9206 + 86.4650i −0.113199 + 0.196066i
\(442\) 25.3865 0.0574356
\(443\) 566.736 327.205i 1.27931 0.738612i 0.302591 0.953121i \(-0.402148\pi\)
0.976722 + 0.214509i \(0.0688151\pi\)
\(444\) 49.2868i 0.111006i
\(445\) 1495.37i 3.36039i
\(446\) −9.78989 5.65220i −0.0219504 0.0126731i
\(447\) 412.564i 0.922963i
\(448\) −131.059 + 75.6669i −0.292542 + 0.168899i
\(449\) −48.5320 84.0599i −0.108089 0.187216i 0.806907 0.590678i \(-0.201140\pi\)
−0.914996 + 0.403463i \(0.867807\pi\)
\(450\) −142.987 82.5538i −0.317750 0.183453i
\(451\) 71.8247 124.404i 0.159256 0.275840i
\(452\) −204.020 117.791i −0.451372 0.260599i
\(453\) 138.799 + 80.1359i 0.306401 + 0.176900i
\(454\) 176.485i 0.388733i
\(455\) 1215.23i 2.67083i
\(456\) 189.396 328.044i 0.415342 0.719394i
\(457\) −7.57835 13.1261i −0.0165828 0.0287223i 0.857615 0.514292i \(-0.171945\pi\)
−0.874198 + 0.485570i \(0.838612\pi\)
\(458\) 40.0356 + 69.3437i 0.0874140 + 0.151405i
\(459\) −7.31950 4.22591i −0.0159466 0.00920678i
\(460\) 668.500i 1.45326i
\(461\) −199.095 −0.431875 −0.215938 0.976407i \(-0.569281\pi\)
−0.215938 + 0.976407i \(0.569281\pi\)
\(462\) 33.9093 + 58.7326i 0.0733967 + 0.127127i
\(463\) −735.628 424.715i −1.58883 0.917312i −0.993500 0.113830i \(-0.963688\pi\)
−0.595330 0.803481i \(-0.702979\pi\)
\(464\) −102.038 −0.219909
\(465\) 481.128 277.780i 1.03468 0.597375i
\(466\) 80.1523 0.172001
\(467\) 355.436 615.632i 0.761104 1.31827i −0.181178 0.983450i \(-0.557991\pi\)
0.942282 0.334820i \(-0.108676\pi\)
\(468\) 133.317i 0.284865i
\(469\) −436.722 422.647i −0.931177 0.901166i
\(470\) −132.482 −0.281878
\(471\) −259.778 149.983i −0.551546 0.318435i
\(472\) 287.474i 0.609056i
\(473\) 162.168 + 280.883i 0.342849 + 0.593833i
\(474\) 3.99194i 0.00842181i
\(475\) −815.729 + 1412.88i −1.71733 + 2.97449i
\(476\) 37.5201 21.6622i 0.0788237 0.0455089i
\(477\) 196.334i 0.411601i
\(478\) 343.503 0.718627
\(479\) −206.555 + 357.764i −0.431221 + 0.746898i −0.996979 0.0776743i \(-0.975251\pi\)
0.565757 + 0.824572i \(0.308584\pi\)
\(480\) 439.776 253.905i 0.916200 0.528968i
\(481\) −127.008 + 73.3281i −0.264050 + 0.152449i
\(482\) −131.133 75.7098i −0.272061 0.157074i
\(483\) −404.047 −0.836537
\(484\) 303.863 0.627816
\(485\) −831.094 + 1439.50i −1.71360 + 2.96803i
\(486\) −8.03824 + 13.9226i −0.0165396 + 0.0286474i
\(487\) −190.165 109.792i −0.390483 0.225446i 0.291886 0.956453i \(-0.405717\pi\)
−0.682370 + 0.731007i \(0.739050\pi\)
\(488\) −50.3091 + 87.1379i −0.103092 + 0.178561i
\(489\) −144.154 + 83.2274i −0.294794 + 0.170199i
\(490\) −151.918 263.129i −0.310036 0.536998i
\(491\) 403.831 0.822467 0.411233 0.911530i \(-0.365098\pi\)
0.411233 + 0.911530i \(0.365098\pi\)
\(492\) −87.2768 + 151.168i −0.177392 + 0.307252i
\(493\) −37.9959 −0.0770708
\(494\) −477.148 −0.965886
\(495\) −55.5782 96.2643i −0.112279 0.194473i
\(496\) 158.271i 0.319095i
\(497\) −137.025 79.1112i −0.275703 0.159177i
\(498\) 29.1774 + 50.5367i 0.0585891 + 0.101479i
\(499\) −480.448 277.387i −0.962821 0.555885i −0.0657810 0.997834i \(-0.520954\pi\)
−0.897040 + 0.441949i \(0.854287\pi\)
\(500\) −638.549 + 368.667i −1.27710 + 0.737333i
\(501\) 92.2109 53.2380i 0.184054 0.106263i
\(502\) 159.364 + 276.027i 0.317459 + 0.549855i
\(503\) 429.174 247.784i 0.853228 0.492611i −0.00851063 0.999964i \(-0.502709\pi\)
0.861739 + 0.507352i \(0.169376\pi\)
\(504\) −97.3334 168.586i −0.193122 0.334497i
\(505\) −34.2541 59.3299i −0.0678300 0.117485i
\(506\) −55.5051 + 96.1377i −0.109694 + 0.189995i
\(507\) 90.0464 51.9883i 0.177606 0.102541i
\(508\) −347.383 + 601.685i −0.683824 + 1.18442i
\(509\) −334.188 −0.656559 −0.328279 0.944581i \(-0.606469\pi\)
−0.328279 + 0.944581i \(0.606469\pi\)
\(510\) 22.2746 12.8602i 0.0436756 0.0252161i
\(511\) 640.260i 1.25295i
\(512\) 269.658i 0.526676i
\(513\) 137.572 + 79.4273i 0.268172 + 0.154829i
\(514\) 344.125i 0.669503i
\(515\) 1079.23 623.095i 2.09560 1.20989i
\(516\) −197.056 341.311i −0.381891 0.661455i
\(517\) −52.6007 30.3690i −0.101742 0.0587408i
\(518\) 45.3273 78.5091i 0.0875044 0.151562i
\(519\) 488.516 + 282.045i 0.941263 + 0.543439i
\(520\) −829.969 479.183i −1.59609 0.921505i
\(521\) 123.707i 0.237442i 0.992928 + 0.118721i \(0.0378794\pi\)
−0.992928 + 0.118721i \(0.962121\pi\)
\(522\) 72.2732i 0.138454i
\(523\) 27.0155 46.7923i 0.0516549 0.0894690i −0.839042 0.544067i \(-0.816884\pi\)
0.890697 + 0.454598i \(0.150217\pi\)
\(524\) 337.927 + 585.306i 0.644898 + 1.11700i
\(525\) 419.215 + 726.102i 0.798505 + 1.38305i
\(526\) 234.307 + 135.277i 0.445451 + 0.257181i
\(527\) 58.9355i 0.111832i
\(528\) 31.6669 0.0599752
\(529\) −66.1868 114.639i −0.125117 0.216709i
\(530\) 517.433 + 298.740i 0.976289 + 0.563660i
\(531\) 120.558 0.227040
\(532\) −705.201 + 407.148i −1.32557 + 0.765316i
\(533\) 519.397 0.974478
\(534\) 150.871 261.317i 0.282531 0.489357i
\(535\) 40.6338i 0.0759511i
\(536\) 460.864 131.614i 0.859820 0.245548i
\(537\) 165.991 0.309109
\(538\) 284.967 + 164.526i 0.529678 + 0.305810i
\(539\) 139.297i 0.258435i
\(540\) 67.5351 + 116.974i 0.125065 + 0.216619i
\(541\) 531.474i 0.982391i 0.871049 + 0.491196i \(0.163440\pi\)
−0.871049 + 0.491196i \(0.836560\pi\)
\(542\) −156.706 + 271.423i −0.289126 + 0.500781i
\(543\) −51.9609 + 29.9996i −0.0956923 + 0.0552480i
\(544\) 53.8700i 0.0990258i
\(545\) 210.182 0.385654
\(546\) −122.607 + 212.361i −0.224554 + 0.388939i
\(547\) −160.609 + 92.7274i −0.293617 + 0.169520i −0.639572 0.768731i \(-0.720888\pi\)
0.345955 + 0.938251i \(0.387555\pi\)
\(548\) −372.147 + 214.859i −0.679100 + 0.392078i
\(549\) −36.5431 21.0982i −0.0665631 0.0384302i
\(550\) 230.355 0.418827
\(551\) 714.145 1.29609
\(552\) 159.322 275.954i 0.288627 0.499917i
\(553\) 10.1357 17.5555i 0.0183286 0.0317460i
\(554\) −334.294 193.005i −0.603419 0.348384i
\(555\) −74.2926 + 128.679i −0.133861 + 0.231853i
\(556\) 302.490 174.643i 0.544047 0.314106i
\(557\) −418.899 725.555i −0.752063 1.30261i −0.946821 0.321760i \(-0.895726\pi\)
0.194758 0.980851i \(-0.437608\pi\)
\(558\) 112.103 0.200901
\(559\) −586.354 + 1015.59i −1.04893 + 1.81681i
\(560\) −350.755 −0.626348
\(561\) 11.7918 0.0210193
\(562\) −79.0981 137.002i −0.140744 0.243776i
\(563\) 848.338i 1.50682i −0.657553 0.753408i \(-0.728408\pi\)
0.657553 0.753408i \(-0.271592\pi\)
\(564\) 63.9170 + 36.9025i 0.113328 + 0.0654300i
\(565\) 355.106 + 615.061i 0.628505 + 1.08860i
\(566\) 264.781 + 152.872i 0.467811 + 0.270091i
\(567\) 70.7003 40.8188i 0.124692 0.0719909i
\(568\) 108.062 62.3895i 0.190250 0.109841i
\(569\) −125.522 217.411i −0.220602 0.382093i 0.734389 0.678729i \(-0.237469\pi\)
−0.954991 + 0.296635i \(0.904135\pi\)
\(570\) −418.657 + 241.712i −0.734486 + 0.424056i
\(571\) 43.1664 + 74.7664i 0.0755979 + 0.130939i 0.901346 0.433100i \(-0.142580\pi\)
−0.825748 + 0.564039i \(0.809247\pi\)
\(572\) −93.0004 161.081i −0.162588 0.281611i
\(573\) −247.333 + 428.394i −0.431646 + 0.747633i
\(574\) −278.047 + 160.531i −0.484403 + 0.279670i
\(575\) −686.202 + 1188.54i −1.19339 + 2.06702i
\(576\) 50.0505 0.0868933
\(577\) −563.673 + 325.437i −0.976903 + 0.564015i −0.901334 0.433126i \(-0.857411\pi\)
−0.0755690 + 0.997141i \(0.524077\pi\)
\(578\) 295.319i 0.510933i
\(579\) 222.387i 0.384088i
\(580\) 525.868 + 303.610i 0.906669 + 0.523466i
\(581\) 296.330i 0.510035i
\(582\) −290.467 + 167.701i −0.499085 + 0.288147i
\(583\) 136.961 + 237.223i 0.234924 + 0.406900i
\(584\) −437.281 252.464i −0.748769 0.432302i
\(585\) 200.956 348.065i 0.343514 0.594983i
\(586\) −3.64247 2.10298i −0.00621582 0.00358871i
\(587\) 246.745 + 142.459i 0.420350 + 0.242689i 0.695227 0.718790i \(-0.255304\pi\)
−0.274877 + 0.961479i \(0.588637\pi\)
\(588\) 169.264i 0.287865i
\(589\) 1107.71i 1.88066i
\(590\) −183.441 + 317.729i −0.310917 + 0.538523i
\(591\) −26.6529 46.1642i −0.0450980 0.0781120i
\(592\) −21.1649 36.6588i −0.0357516 0.0619236i
\(593\) −190.443 109.952i −0.321152 0.185417i 0.330754 0.943717i \(-0.392697\pi\)
−0.651906 + 0.758300i \(0.726030\pi\)
\(594\) 22.4296i 0.0377603i
\(595\) −130.611 −0.219514
\(596\) −349.717 605.728i −0.586774 1.01632i
\(597\) 144.754 + 83.5740i 0.242470 + 0.139990i
\(598\) −401.382 −0.671208
\(599\) −69.0141 + 39.8453i −0.115215 + 0.0665197i −0.556500 0.830847i \(-0.687856\pi\)
0.441285 + 0.897367i \(0.354523\pi\)
\(600\) −661.213 −1.10202
\(601\) 553.344 958.421i 0.920706 1.59471i 0.122381 0.992483i \(-0.460947\pi\)
0.798325 0.602227i \(-0.205720\pi\)
\(602\) 724.901i 1.20416i
\(603\) 55.1951 + 193.273i 0.0915342 + 0.320519i
\(604\) 271.714 0.449858
\(605\) −793.330 458.029i −1.31129 0.757073i
\(606\) 13.8239i 0.0228117i
\(607\) 100.021 + 173.241i 0.164779 + 0.285405i 0.936577 0.350463i \(-0.113976\pi\)
−0.771798 + 0.635868i \(0.780642\pi\)
\(608\) 1012.50i 1.66530i
\(609\) 183.505 317.839i 0.301321 0.521904i
\(610\) 111.208 64.2057i 0.182307 0.105255i
\(611\) 219.612i 0.359430i
\(612\) −14.3287 −0.0234129
\(613\) −41.8422 + 72.4728i −0.0682581 + 0.118226i −0.898135 0.439721i \(-0.855077\pi\)
0.829877 + 0.557947i \(0.188411\pi\)
\(614\) −329.581 + 190.284i −0.536777 + 0.309908i
\(615\) 455.727 263.114i 0.741020 0.427828i
\(616\) 235.208 + 135.798i 0.381832 + 0.220451i
\(617\) 641.259 1.03932 0.519659 0.854374i \(-0.326059\pi\)
0.519659 + 0.854374i \(0.326059\pi\)
\(618\) 251.461 0.406896
\(619\) 342.851 593.836i 0.553879 0.959347i −0.444110 0.895972i \(-0.646480\pi\)
0.997990 0.0633753i \(-0.0201865\pi\)
\(620\) 470.930 815.674i 0.759564 1.31560i
\(621\) 115.727 + 66.8152i 0.186356 + 0.107593i
\(622\) 232.748 403.131i 0.374193 0.648121i
\(623\) −1326.99 + 766.137i −2.13000 + 1.22975i
\(624\) 57.2494 + 99.1590i 0.0917459 + 0.158909i
\(625\) 888.716 1.42194
\(626\) −156.017 + 270.230i −0.249229 + 0.431677i
\(627\) −221.631 −0.353478
\(628\) −508.542 −0.809781
\(629\) −7.88120 13.6506i −0.0125297 0.0217021i
\(630\) 248.439i 0.394347i
\(631\) −488.710 282.157i −0.774501 0.447158i 0.0599769 0.998200i \(-0.480897\pi\)
−0.834478 + 0.551041i \(0.814231\pi\)
\(632\) 7.99333 + 13.8449i 0.0126477 + 0.0219064i
\(633\) 40.1600 + 23.1864i 0.0634439 + 0.0366294i
\(634\) −388.287 + 224.178i −0.612440 + 0.353593i
\(635\) 1813.90 1047.26i 2.85654 1.64923i
\(636\) −166.426 288.258i −0.261676 0.453236i
\(637\) 436.181 251.829i 0.684742 0.395336i
\(638\) −50.4171 87.3250i −0.0790236 0.136873i
\(639\) 26.1644 + 45.3181i 0.0409458 + 0.0709203i
\(640\) 510.212 883.712i 0.797206 1.38080i
\(641\) −815.332 + 470.732i −1.27197 + 0.734372i −0.975358 0.220627i \(-0.929190\pi\)
−0.296611 + 0.954998i \(0.595856\pi\)
\(642\) 4.09963 7.10077i 0.00638572 0.0110604i
\(643\) 3.01700 0.00469207 0.00234603 0.999997i \(-0.499253\pi\)
0.00234603 + 0.999997i \(0.499253\pi\)
\(644\) −593.224 + 342.498i −0.921155 + 0.531829i
\(645\) 1188.13i 1.84207i
\(646\) 51.2831i 0.0793856i
\(647\) 575.495 + 332.262i 0.889482 + 0.513543i 0.873773 0.486334i \(-0.161666\pi\)
0.0157090 + 0.999877i \(0.494999\pi\)
\(648\) 64.3821i 0.0993550i
\(649\) −145.666 + 84.1004i −0.224447 + 0.129585i
\(650\) 416.450 + 721.313i 0.640693 + 1.10971i
\(651\) −493.001 284.634i −0.757298 0.437226i
\(652\) −141.098 + 244.390i −0.216409 + 0.374831i
\(653\) 136.579 + 78.8537i 0.209156 + 0.120756i 0.600919 0.799310i \(-0.294801\pi\)
−0.391763 + 0.920066i \(0.628135\pi\)
\(654\) 36.7292 + 21.2056i 0.0561609 + 0.0324245i
\(655\) 2037.50i 3.11069i
\(656\) 149.915i 0.228529i
\(657\) 105.876 183.383i 0.161151 0.279122i
\(658\) 67.8758 + 117.564i 0.103155 + 0.178669i
\(659\) −73.9670 128.115i −0.112241 0.194408i 0.804432 0.594044i \(-0.202470\pi\)
−0.916674 + 0.399637i \(0.869136\pi\)
\(660\) −163.200 94.2237i −0.247273 0.142763i
\(661\) 784.817i 1.18732i 0.804717 + 0.593659i \(0.202317\pi\)
−0.804717 + 0.593659i \(0.797683\pi\)
\(662\) 510.245 0.770763
\(663\) 21.3180 + 36.9238i 0.0321538 + 0.0556921i
\(664\) 202.386 + 116.848i 0.304798 + 0.175975i
\(665\) 2454.87 3.69153
\(666\) −25.9653 + 14.9911i −0.0389869 + 0.0225091i
\(667\) 600.747 0.900670
\(668\) 90.2562 156.328i 0.135114 0.234024i
\(669\) 18.9854i 0.0283788i
\(670\) −593.351 148.618i −0.885598 0.221817i
\(671\) 58.8716 0.0877371
\(672\) −450.628 260.170i −0.670577 0.387158i
\(673\) 970.736i 1.44240i 0.692727 + 0.721200i \(0.256409\pi\)
−0.692727 + 0.721200i \(0.743591\pi\)
\(674\) −300.541 520.553i −0.445907 0.772333i
\(675\) 277.294i 0.410806i
\(676\) 88.1376 152.659i 0.130381 0.225827i
\(677\) −252.486 + 145.773i −0.372948 + 0.215321i −0.674745 0.738051i \(-0.735747\pi\)
0.301798 + 0.953372i \(0.402413\pi\)
\(678\) 143.309i 0.211371i
\(679\) 1703.20 2.50840
\(680\) 51.5018 89.2038i 0.0757380 0.131182i
\(681\) 256.691 148.201i 0.376933 0.217622i
\(682\) −135.450 + 78.2019i −0.198607 + 0.114666i
\(683\) −928.624 536.141i −1.35962 0.784980i −0.370051 0.929011i \(-0.620660\pi\)
−0.989573 + 0.144032i \(0.953993\pi\)
\(684\) 269.312 0.393731
\(685\) 1295.47 1.89120
\(686\) 73.5271 127.353i 0.107182 0.185645i
\(687\) −67.2387 + 116.461i −0.0978729 + 0.169521i
\(688\) −293.135 169.241i −0.426068 0.245990i
\(689\) −495.212 + 857.732i −0.718740 + 1.24489i
\(690\) −352.180 + 203.331i −0.510405 + 0.294683i
\(691\) 179.868 + 311.541i 0.260302 + 0.450855i 0.966322 0.257336i \(-0.0828447\pi\)
−0.706020 + 0.708191i \(0.749511\pi\)
\(692\) 956.320 1.38197
\(693\) −56.9497 + 98.6397i −0.0821784 + 0.142337i
\(694\) 179.532 0.258691
\(695\) −1052.99 −1.51510
\(696\) 144.718 + 250.658i 0.207928 + 0.360141i
\(697\) 55.8240i 0.0800918i
\(698\) −215.529 124.436i −0.308780 0.178274i
\(699\) 67.3067 + 116.579i 0.0962900 + 0.166779i
\(700\) 1230.99 + 710.710i 1.75855 + 1.01530i
\(701\) 277.821 160.400i 0.396320 0.228816i −0.288575 0.957457i \(-0.593181\pi\)
0.684895 + 0.728642i \(0.259848\pi\)
\(702\) 70.2340 40.5496i 0.100048 0.0577630i
\(703\) 148.129 + 256.568i 0.210710 + 0.364961i
\(704\) −60.4742 + 34.9148i −0.0859008 + 0.0495948i
\(705\) −111.250 192.691i −0.157802 0.273321i
\(706\) −52.6694 91.2261i −0.0746026 0.129215i
\(707\) −35.0994 + 60.7939i −0.0496455 + 0.0859886i
\(708\) 177.004 102.194i 0.250006 0.144341i
\(709\) −85.4216 + 147.955i −0.120482 + 0.208681i −0.919958 0.392017i \(-0.871777\pi\)
0.799476 + 0.600698i \(0.205111\pi\)
\(710\) −159.246 −0.224290
\(711\) −5.80614 + 3.35218i −0.00816616 + 0.00471473i
\(712\) 1208.40i 1.69719i
\(713\) 931.819i 1.30690i
\(714\) −22.8242 13.1776i −0.0319667 0.0184560i
\(715\) 560.738i 0.784250i
\(716\) 243.709 140.706i 0.340376 0.196516i
\(717\) 288.452 + 499.614i 0.402304 + 0.696812i
\(718\) −388.163 224.106i −0.540618 0.312126i
\(719\) 519.539 899.868i 0.722585 1.25155i −0.237375 0.971418i \(-0.576287\pi\)
0.959960 0.280136i \(-0.0903796\pi\)
\(720\) 100.463 + 58.0025i 0.139532 + 0.0805590i
\(721\) −1105.86 638.471i −1.53379 0.885535i
\(722\) 591.580i 0.819362i
\(723\) 254.305i 0.351736i
\(724\) −50.8594 + 88.0911i −0.0702479 + 0.121673i
\(725\) −623.299 1079.59i −0.859723 1.48908i
\(726\) −92.4230 160.081i −0.127304 0.220498i
\(727\) 150.280 + 86.7644i 0.206713 + 0.119346i 0.599783 0.800163i \(-0.295254\pi\)
−0.393070 + 0.919509i \(0.628587\pi\)
\(728\) 982.014i 1.34892i
\(729\) −27.0000 −0.0370370
\(730\) 322.201 + 558.069i 0.441372 + 0.764478i
\(731\) −109.155 63.0205i −0.149322 0.0862113i
\(732\) −71.5370 −0.0977282
\(733\) 1095.90 632.715i 1.49508 0.863186i 0.495098 0.868837i \(-0.335132\pi\)
0.999984 + 0.00565120i \(0.00179884\pi\)
\(734\) 421.620 0.574415
\(735\) 255.141 441.918i 0.347131 0.601249i
\(736\) 851.730i 1.15724i
\(737\) −201.516 195.021i −0.273427 0.264615i
\(738\) 106.184 0.143881
\(739\) 149.227 + 86.1564i 0.201931 + 0.116585i 0.597556 0.801827i \(-0.296139\pi\)
−0.395625 + 0.918412i \(0.629472\pi\)
\(740\) 251.902i 0.340408i
\(741\) −400.678 693.995i −0.540726 0.936565i
\(742\) 612.223i 0.825099i
\(743\) 247.519 428.715i 0.333135 0.577006i −0.649990 0.759943i \(-0.725227\pi\)
0.983125 + 0.182937i \(0.0585603\pi\)
\(744\) 388.796 224.471i 0.522575 0.301709i
\(745\) 2108.59i 2.83033i
\(746\) 103.446 0.138667
\(747\) −49.0026 + 84.8750i −0.0655992 + 0.113621i
\(748\) 17.3128 9.99555i 0.0231454 0.0133630i
\(749\) −36.0583 + 20.8183i −0.0481419 + 0.0277947i
\(750\) 388.443 + 224.267i 0.517923 + 0.299023i
\(751\) 39.4467 0.0525255 0.0262628 0.999655i \(-0.491639\pi\)
0.0262628 + 0.999655i \(0.491639\pi\)
\(752\) 63.3874 0.0842917
\(753\) −267.648 + 463.580i −0.355442 + 0.615644i
\(754\) 182.294 315.743i 0.241770 0.418757i
\(755\) −709.396 409.570i −0.939597 0.542477i
\(756\) 69.2016 119.861i 0.0915365 0.158546i
\(757\) −843.319 + 486.891i −1.11403 + 0.643185i −0.939870 0.341533i \(-0.889054\pi\)
−0.174159 + 0.984718i \(0.555721\pi\)
\(758\) −213.880 370.451i −0.282164 0.488722i
\(759\) −186.439 −0.245637
\(760\) −967.992 + 1676.61i −1.27367 + 2.20607i
\(761\) −628.450 −0.825821 −0.412911 0.910772i \(-0.635488\pi\)
−0.412911 + 0.910772i \(0.635488\pi\)
\(762\) 422.640 0.554646
\(763\) −107.684 186.514i −0.141132 0.244448i
\(764\) 838.626i 1.09768i
\(765\) 37.4095 + 21.5984i 0.0489013 + 0.0282332i
\(766\) −318.804 552.185i −0.416193 0.720868i
\(767\) −526.689 304.084i −0.686687 0.396459i
\(768\) 278.420 160.746i 0.362526 0.209305i
\(769\) −970.422 + 560.274i −1.26193 + 0.728574i −0.973447 0.228912i \(-0.926483\pi\)
−0.288480 + 0.957486i \(0.593150\pi\)
\(770\) −173.308 300.179i −0.225076 0.389843i
\(771\) −500.518 + 288.974i −0.649180 + 0.374804i
\(772\) 188.510 + 326.509i 0.244184 + 0.422939i
\(773\) 306.667 + 531.163i 0.396723 + 0.687145i 0.993319 0.115397i \(-0.0368140\pi\)
−0.596596 + 0.802541i \(0.703481\pi\)
\(774\) −119.873 + 207.626i −0.154875 + 0.268251i
\(775\) −1674.55 + 966.799i −2.16070 + 1.24748i
\(776\) −671.600 + 1163.25i −0.865464 + 1.49903i
\(777\) 152.252 0.195948
\(778\) 45.8428 26.4673i 0.0589239 0.0340197i
\(779\) 1049.23i 1.34689i
\(780\) 681.374i 0.873556i
\(781\) −63.2269 36.5041i −0.0809563 0.0467401i
\(782\) 43.1400i 0.0551662i
\(783\) −105.119 + 60.6904i −0.134251 + 0.0775101i
\(784\) 72.6863 + 125.896i 0.0927121 + 0.160582i
\(785\) 1327.71 + 766.554i 1.69135 + 0.976502i
\(786\) 205.568 356.054i 0.261536 0.452994i
\(787\) −906.846 523.568i −1.15228 0.665270i −0.202840 0.979212i \(-0.565017\pi\)
−0.949442 + 0.313942i \(0.898350\pi\)
\(788\) −78.2638 45.1856i −0.0993196 0.0573422i
\(789\) 454.389i 0.575905i
\(790\) 20.4026i 0.0258260i
\(791\) 363.868 630.238i 0.460010 0.796761i
\(792\) −44.9123 77.7904i −0.0567074 0.0982202i
\(793\) 106.432 + 184.345i 0.134214 + 0.232465i
\(794\) −345.526 199.490i −0.435172 0.251247i
\(795\) 1003.45i 1.26220i
\(796\) 283.372 0.355995
\(797\) −480.523 832.290i −0.602915 1.04428i −0.992377 0.123236i \(-0.960673\pi\)
0.389463 0.921042i \(-0.372661\pi\)
\(798\) 428.988 + 247.676i 0.537579 + 0.310371i
\(799\) 23.6036 0.0295414
\(800\) −1530.62 + 883.704i −1.91328 + 1.10463i
\(801\) 506.768 0.632670
\(802\) 279.819 484.661i 0.348902 0.604315i
\(803\) 295.433i 0.367912i
\(804\) 244.869 + 236.977i 0.304563 + 0.294748i
\(805\) 2065.06 2.56530
\(806\) −489.749 282.757i −0.607629 0.350815i
\(807\) 552.632i 0.684798i
\(808\) −27.6805 47.9440i −0.0342580 0.0593367i
\(809\) 1326.28i 1.63940i −0.572791 0.819702i \(-0.694139\pi\)
0.572791 0.819702i \(-0.305861\pi\)
\(810\) 41.0830 71.1578i 0.0507197 0.0878492i
\(811\) −200.890 + 115.984i −0.247706 + 0.143013i −0.618714 0.785617i \(-0.712346\pi\)
0.371007 + 0.928630i \(0.379012\pi\)
\(812\) 622.204i 0.766261i
\(813\) −526.368 −0.647439
\(814\) 20.9152 36.2263i 0.0256944 0.0445040i
\(815\) 736.764 425.371i 0.904005 0.521927i
\(816\) −10.6575 + 6.15308i −0.0130606 + 0.00754055i
\(817\) 2051.59 + 1184.49i 2.51113 + 1.44980i
\(818\) −84.4266 −0.103211
\(819\) −411.829 −0.502843
\(820\) 446.067 772.610i 0.543984 0.942208i
\(821\) −344.443 + 596.593i −0.419541 + 0.726667i −0.995893 0.0905348i \(-0.971142\pi\)
0.576352 + 0.817201i \(0.304476\pi\)
\(822\) 226.384 + 130.703i 0.275407 + 0.159006i
\(823\) −584.062 + 1011.62i −0.709674 + 1.22919i 0.255304 + 0.966861i \(0.417824\pi\)
−0.964978 + 0.262331i \(0.915509\pi\)
\(824\) 872.119 503.518i 1.05840 0.611066i
\(825\) 193.437 + 335.043i 0.234470 + 0.406113i
\(826\) 375.935 0.455127
\(827\) 473.436 820.015i 0.572474 0.991554i −0.423837 0.905739i \(-0.639317\pi\)
0.996311 0.0858157i \(-0.0273496\pi\)
\(828\) 226.548 0.273609
\(829\) −38.6720 −0.0466490 −0.0233245 0.999728i \(-0.507425\pi\)
−0.0233245 + 0.999728i \(0.507425\pi\)
\(830\) −149.124 258.290i −0.179667 0.311193i
\(831\) 648.293i 0.780136i
\(832\) −218.658 126.242i −0.262810 0.151733i
\(833\) 27.0662 + 46.8800i 0.0324924 + 0.0562786i
\(834\) −184.011 106.239i −0.220636 0.127385i
\(835\) −471.284 + 272.096i −0.564413 + 0.325864i
\(836\) −325.399 + 187.869i −0.389233 + 0.224724i
\(837\) 94.1369 + 163.050i 0.112469 + 0.194803i
\(838\) 154.915 89.4403i 0.184863 0.106731i
\(839\) −10.8901 18.8623i −0.0129799 0.0224818i 0.859463 0.511199i \(-0.170798\pi\)
−0.872442 + 0.488717i \(0.837465\pi\)
\(840\) 497.465 + 861.635i 0.592221 + 1.02576i
\(841\) 147.661 255.756i 0.175578 0.304110i
\(842\) −341.043 + 196.902i −0.405040 + 0.233850i
\(843\) 132.843 230.091i 0.157584 0.272943i
\(844\) 78.6174 0.0931486
\(845\) −460.222 + 265.709i −0.544641 + 0.314449i
\(846\) 44.8971i 0.0530698i
\(847\) 938.663i 1.10822i
\(848\) −247.570 142.935i −0.291946 0.168555i
\(849\) 513.487i 0.604814i
\(850\) −77.5256 + 44.7594i −0.0912066 + 0.0526582i
\(851\) 124.608 + 215.828i 0.146426 + 0.253617i
\(852\) 76.8293 + 44.3574i 0.0901752 + 0.0520627i
\(853\) −680.590 + 1178.82i −0.797878 + 1.38196i 0.123118 + 0.992392i \(0.460711\pi\)
−0.920996 + 0.389573i \(0.872623\pi\)
\(854\) −113.952 65.7900i −0.133433 0.0770375i
\(855\) −703.123 405.948i −0.822366 0.474793i
\(856\) 32.8359i 0.0383597i
\(857\) 222.964i 0.260169i −0.991503 0.130084i \(-0.958475\pi\)
0.991503 0.130084i \(-0.0415248\pi\)
\(858\) −56.5740 + 97.9891i −0.0659371 + 0.114206i
\(859\) 543.104 + 940.685i 0.632252 + 1.09509i 0.987090 + 0.160165i \(0.0512026\pi\)
−0.354838 + 0.934928i \(0.615464\pi\)
\(860\) 1007.14 + 1744.42i 1.17110 + 2.02840i
\(861\) −466.973 269.607i −0.542361 0.313132i
\(862\) 344.844i 0.400051i
\(863\) 204.645 0.237132 0.118566 0.992946i \(-0.462170\pi\)
0.118566 + 0.992946i \(0.462170\pi\)
\(864\) 86.0460 + 149.036i 0.0995902 + 0.172495i
\(865\) −2496.78 1441.51i −2.88645 1.66649i
\(866\) 341.277 0.394084
\(867\) 429.531 247.990i 0.495423 0.286032i
\(868\) −965.100 −1.11187
\(869\) 4.67689 8.10061i 0.00538192 0.00932176i
\(870\) 369.384i 0.424580i
\(871\) 246.359 983.579i 0.282846 1.12925i
\(872\) 169.846 0.194778
\(873\) −487.832 281.650i −0.558800 0.322623i
\(874\) 810.829i 0.927722i
\(875\) −1138.85 1972.54i −1.30154 2.25434i
\(876\) 358.992i 0.409808i
\(877\) 608.470 1053.90i 0.693808 1.20171i −0.276772 0.960936i \(-0.589265\pi\)
0.970581 0.240776i \(-0.0774019\pi\)
\(878\) 179.311 103.526i 0.204227 0.117911i
\(879\) 7.06380i 0.00803618i
\(880\) −161.848 −0.183918
\(881\) −502.933 + 871.106i −0.570866 + 0.988769i 0.425611 + 0.904906i \(0.360059\pi\)
−0.996477 + 0.0838631i \(0.973274\pi\)
\(882\) 89.1720 51.4835i 0.101102 0.0583713i
\(883\) 241.155 139.231i 0.273108 0.157679i −0.357191 0.934031i \(-0.616265\pi\)
0.630299 + 0.776352i \(0.282932\pi\)
\(884\) 62.5983 + 36.1411i 0.0708126 + 0.0408836i
\(885\) −616.168 −0.696234
\(886\) −674.897 −0.761735
\(887\) −603.963 + 1046.09i −0.680905 + 1.17936i 0.293800 + 0.955867i \(0.405080\pi\)
−0.974705 + 0.223496i \(0.928253\pi\)
\(888\) −60.0353 + 103.984i −0.0676073 + 0.117099i
\(889\) −1858.66 1073.10i −2.09074 1.20709i
\(890\) −771.095 + 1335.57i −0.866398 + 1.50065i
\(891\) 32.6231 18.8349i 0.0366140 0.0211391i
\(892\) −16.0933 27.8744i −0.0180418 0.0312494i
\(893\) −443.636 −0.496793
\(894\) −212.740 + 368.477i −0.237964 + 0.412166i
\(895\) −848.373 −0.947903
\(896\) −1045.60 −1.16697
\(897\) −337.055 583.797i −0.375758 0.650833i
\(898\) 100.103i 0.111473i
\(899\) 733.005 + 423.201i 0.815356 + 0.470746i
\(900\) −235.053 407.124i −0.261170 0.452360i
\(901\) −92.1878 53.2246i −0.102317 0.0590728i
\(902\) −128.299 + 74.0733i −0.142238 + 0.0821211i
\(903\) 1054.34 608.726i 1.16760 0.674115i
\(904\) 286.958 + 497.026i 0.317431 + 0.549807i
\(905\) 265.569 153.326i 0.293447 0.169421i
\(906\) −82.6447 143.145i −0.0912193 0.157996i
\(907\) 814.057 + 1409.99i 0.897527 + 1.55456i 0.830646 + 0.556801i \(0.187971\pi\)
0.0668806 + 0.997761i \(0.478695\pi\)
\(908\) 251.250 435.178i 0.276707 0.479271i
\(909\) 20.1064 11.6084i 0.0221192 0.0127705i
\(910\) 626.635 1085.36i 0.688610 1.19271i
\(911\) 1227.72 1.34766 0.673830 0.738887i \(-0.264648\pi\)
0.673830 + 0.738887i \(0.264648\pi\)
\(912\) 200.310 115.649i 0.219638 0.126808i
\(913\) 136.735i 0.149764i
\(914\) 15.6312i 0.0171020i
\(915\) 186.770 + 107.832i 0.204120 + 0.117849i
\(916\) 227.984i 0.248891i
\(917\) −1808.07 + 1043.89i −1.97172 + 1.13837i
\(918\) 4.35821 + 7.54864i 0.00474751 + 0.00822292i
\(919\) 784.538 + 452.953i 0.853687 + 0.492876i 0.861893 0.507090i \(-0.169279\pi\)
−0.00820645 + 0.999966i \(0.502612\pi\)
\(920\) −814.287 + 1410.39i −0.885095 + 1.53303i
\(921\) −553.522 319.576i −0.601001 0.346988i
\(922\) 177.819 + 102.664i 0.192862 + 0.111349i
\(923\) 263.977i 0.285999i
\(924\) 193.098i 0.208980i
\(925\) 258.572 447.860i 0.279537 0.484173i
\(926\) 438.012 + 758.658i 0.473015 + 0.819286i
\(927\) 211.161 + 365.742i 0.227790 + 0.394544i
\(928\) 670.004 + 386.827i 0.721987 + 0.416840i
\(929\) 330.672i 0.355944i 0.984036 + 0.177972i \(0.0569537\pi\)
−0.984036 + 0.177972i \(0.943046\pi\)
\(930\) −572.952 −0.616077
\(931\) −508.717 881.124i −0.546420 0.946428i
\(932\) 197.640 + 114.107i 0.212060 + 0.122433i
\(933\) 781.787 0.837929
\(934\) −634.906 + 366.563i −0.679771 + 0.392466i
\(935\) −60.2673 −0.0644570
\(936\) 162.391 281.269i 0.173494 0.300501i
\(937\) 720.759i 0.769219i −0.923079 0.384610i \(-0.874336\pi\)
0.923079 0.384610i \(-0.125664\pi\)
\(938\) 172.114 + 602.679i 0.183490 + 0.642515i
\(939\) −524.054 −0.558098
\(940\) −326.676 188.607i −0.347528 0.200645i
\(941\) 1076.92i 1.14445i 0.820098 + 0.572223i \(0.193919\pi\)
−0.820098 + 0.572223i \(0.806081\pi\)
\(942\) 154.678 + 267.911i 0.164202 + 0.284406i
\(943\) 882.624i 0.935974i
\(944\) 87.7688 152.020i 0.0929754 0.161038i
\(945\) −361.345 + 208.623i −0.382376 + 0.220765i
\(946\) 334.489i 0.353583i
\(947\) −575.790 −0.608015 −0.304007 0.952670i \(-0.598325\pi\)
−0.304007 + 0.952670i \(0.598325\pi\)
\(948\) −5.68306 + 9.84335i −0.00599479 + 0.0103833i
\(949\) −925.093 + 534.103i −0.974809 + 0.562806i
\(950\) 1457.12 841.267i 1.53381 0.885544i
\(951\) −652.118 376.500i −0.685718 0.395899i
\(952\) −105.545 −0.110867
\(953\) 954.587 1.00166 0.500832 0.865544i \(-0.333027\pi\)
0.500832 + 0.865544i \(0.333027\pi\)
\(954\) −101.240 + 175.353i −0.106122 + 0.183808i
\(955\) 1264.11 2189.50i 1.32367 2.29267i
\(956\) 847.013 + 489.023i 0.885997 + 0.511531i
\(957\) 84.6741 146.660i 0.0884787 0.153250i
\(958\) 368.964 213.022i 0.385140 0.222361i
\(959\) −663.721 1149.60i −0.692097 1.19875i
\(960\) −255.805 −0.266464
\(961\) 175.926 304.714i 0.183066 0.317080i
\(962\) 151.248 0.157222
\(963\) 13.7704 0.0142995
\(964\) −215.566 373.371i −0.223616 0.387315i
\(965\) 1136.61i 1.17783i
\(966\) 360.870 + 208.348i 0.373571 + 0.215682i
\(967\) 72.9115 + 126.286i 0.0753997 + 0.130596i 0.901260 0.433279i \(-0.142643\pi\)
−0.825860 + 0.563875i \(0.809310\pi\)
\(968\) −641.084 370.130i −0.662276 0.382365i
\(969\) 74.5895 43.0643i 0.0769758 0.0444420i
\(970\) 1484.56 857.113i 1.53048 0.883621i
\(971\) −144.025 249.458i −0.148326 0.256908i 0.782283 0.622923i \(-0.214055\pi\)
−0.930609 + 0.366015i \(0.880722\pi\)
\(972\) −39.6415 + 22.8870i −0.0407834 + 0.0235463i
\(973\) 539.489 + 934.422i 0.554459 + 0.960352i
\(974\) 113.229 + 196.119i 0.116252 + 0.201354i
\(975\) −699.417 + 1211.43i −0.717350 + 1.24249i
\(976\) −53.2082 + 30.7197i −0.0545166 + 0.0314751i
\(977\) 59.4668 103.000i 0.0608668 0.105424i −0.833986 0.551785i \(-0.813947\pi\)
0.894853 + 0.446361i \(0.147280\pi\)
\(978\) 171.666 0.175528
\(979\) −612.309 + 353.517i −0.625443 + 0.361100i
\(980\) 865.100i 0.882756i
\(981\) 71.2286i 0.0726081i
\(982\) −360.677 208.237i −0.367288 0.212054i
\(983\) 1619.12i 1.64712i 0.567232 + 0.823558i \(0.308014\pi\)
−0.567232 + 0.823558i \(0.691986\pi\)
\(984\) 368.269 212.620i 0.374258 0.216078i
\(985\) 136.222 + 235.943i 0.138296 + 0.239536i
\(986\) 33.9356 + 19.5927i 0.0344174 + 0.0198709i
\(987\) −113.996 + 197.446i −0.115497 + 0.200047i
\(988\) −1176.55 679.284i −1.19084 0.687534i
\(989\) 1725.83 + 996.406i 1.74502 + 1.00749i
\(990\) 114.636i 0.115794i
\(991\) 931.161i 0.939618i −0.882768 0.469809i \(-0.844323\pi\)
0.882768 0.469809i \(-0.155677\pi\)
\(992\) 600.008 1039.24i 0.604846 1.04762i
\(993\) 428.471 + 742.134i 0.431491 + 0.747365i
\(994\) 81.5879 + 141.314i 0.0820803 + 0.142167i
\(995\) −739.832 427.142i −0.743550 0.429289i
\(996\) 166.152i 0.166819i
\(997\) −641.815 −0.643747 −0.321873 0.946783i \(-0.604313\pi\)
−0.321873 + 0.946783i \(0.604313\pi\)
\(998\) 286.071 + 495.489i 0.286644 + 0.496482i
\(999\) −43.6080 25.1771i −0.0436516 0.0252023i
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 201.3.h.b.172.5 yes 24
67.30 odd 6 inner 201.3.h.b.97.5 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.3.h.b.97.5 24 67.30 odd 6 inner
201.3.h.b.172.5 yes 24 1.1 even 1 trivial