Properties

Label 201.3.h.b.172.4
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 172.4
Character \(\chi\) \(=\) 201.172
Dual form 201.3.h.b.97.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.79024 - 1.03359i) q^{2} -1.73205i q^{3} +(0.136637 + 0.236663i) q^{4} -0.118573i q^{5} +(-1.79024 + 3.10078i) q^{6} +(-4.18772 + 2.41778i) q^{7} +7.70385i q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(-1.79024 - 1.03359i) q^{2} -1.73205i q^{3} +(0.136637 + 0.236663i) q^{4} -0.118573i q^{5} +(-1.79024 + 3.10078i) q^{6} +(-4.18772 + 2.41778i) q^{7} +7.70385i q^{8} -3.00000 q^{9} +(-0.122556 + 0.212274i) q^{10} +(-7.76165 + 4.48119i) q^{11} +(0.409912 - 0.236663i) q^{12} +(3.99056 + 2.30395i) q^{13} +9.99602 q^{14} -0.205374 q^{15} +(8.50921 - 14.7384i) q^{16} +(-3.37913 + 5.85283i) q^{17} +(5.37072 + 3.10078i) q^{18} +(2.77232 - 4.80179i) q^{19} +(0.0280617 - 0.0162014i) q^{20} +(4.18772 + 7.25334i) q^{21} +18.5269 q^{22} +(-18.0515 + 31.2661i) q^{23} +13.3435 q^{24} +24.9859 q^{25} +(-4.76270 - 8.24924i) q^{26} +5.19615i q^{27} +(-1.14440 - 0.660717i) q^{28} +(14.9263 + 25.8531i) q^{29} +(0.367669 + 0.212274i) q^{30} +(-0.770869 + 0.445062i) q^{31} +(-3.78012 + 2.18245i) q^{32} +(7.76165 + 13.4436i) q^{33} +(12.0989 - 6.98531i) q^{34} +(0.286683 + 0.496549i) q^{35} +(-0.409912 - 0.709988i) q^{36} +(3.63103 - 6.28913i) q^{37} +(-9.92621 + 5.73090i) q^{38} +(3.99056 - 6.91185i) q^{39} +0.913467 q^{40} +(-58.6251 + 33.8472i) q^{41} -17.3136i q^{42} +4.32723i q^{43} +(-2.12106 - 1.22459i) q^{44} +0.355718i q^{45} +(64.6330 - 37.3159i) q^{46} +(21.3745 + 37.0217i) q^{47} +(-25.5276 - 14.7384i) q^{48} +(-12.8087 + 22.1853i) q^{49} +(-44.7308 - 25.8253i) q^{50} +(10.1374 + 5.85283i) q^{51} +1.25922i q^{52} -61.3710i q^{53} +(5.37072 - 9.30235i) q^{54} +(0.531347 + 0.920320i) q^{55} +(-18.6262 - 32.2615i) q^{56} +(-8.31695 - 4.80179i) q^{57} -61.7110i q^{58} -45.4130 q^{59} +(-0.0280617 - 0.0486043i) q^{60} +(-48.7912 - 28.1696i) q^{61} +1.84005 q^{62} +(12.5631 - 7.25334i) q^{63} -59.0506 q^{64} +(0.273186 - 0.473171i) q^{65} -32.0896i q^{66} +(-63.0665 + 22.6188i) q^{67} -1.84686 q^{68} +(54.1545 + 31.2661i) q^{69} -1.18526i q^{70} +(-38.7646 - 67.1422i) q^{71} -23.1115i q^{72} +(17.3628 - 30.0733i) q^{73} +(-13.0008 + 7.50604i) q^{74} -43.2769i q^{75} +1.51521 q^{76} +(21.6691 - 37.5319i) q^{77} +(-14.2881 + 8.24924i) q^{78} +(-81.4581 + 47.0299i) q^{79} +(-1.74757 - 1.00896i) q^{80} +9.00000 q^{81} +139.937 q^{82} +(-54.8226 + 94.9555i) q^{83} +(-1.14440 + 1.98215i) q^{84} +(0.693986 + 0.400673i) q^{85} +(4.47260 - 7.74678i) q^{86} +(44.7789 - 25.8531i) q^{87} +(-34.5224 - 59.7946i) q^{88} +5.63854 q^{89} +(0.367669 - 0.636821i) q^{90} -22.2818 q^{91} -9.86603 q^{92} +(0.770869 + 1.33519i) q^{93} -88.3702i q^{94} +(-0.569362 - 0.328721i) q^{95} +(3.78012 + 6.54736i) q^{96} +(57.8376 + 33.3925i) q^{97} +(45.8612 - 26.4780i) q^{98} +(23.2850 - 13.4436i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.79024 1.03359i −0.895120 0.516797i −0.0195059 0.999810i \(-0.506209\pi\)
−0.875614 + 0.483012i \(0.839543\pi\)
\(3\) 1.73205i 0.577350i
\(4\) 0.136637 + 0.236663i 0.0341593 + 0.0591656i
\(5\) 0.118573i 0.0237146i −0.999930 0.0118573i \(-0.996226\pi\)
0.999930 0.0118573i \(-0.00377438\pi\)
\(6\) −1.79024 + 3.10078i −0.298373 + 0.516797i
\(7\) −4.18772 + 2.41778i −0.598245 + 0.345397i −0.768351 0.640029i \(-0.778922\pi\)
0.170106 + 0.985426i \(0.445589\pi\)
\(8\) 7.70385i 0.962981i
\(9\) −3.00000 −0.333333
\(10\) −0.122556 + 0.212274i −0.0122556 + 0.0212274i
\(11\) −7.76165 + 4.48119i −0.705605 + 0.407381i −0.809431 0.587214i \(-0.800225\pi\)
0.103827 + 0.994595i \(0.466891\pi\)
\(12\) 0.409912 0.236663i 0.0341593 0.0197219i
\(13\) 3.99056 + 2.30395i 0.306966 + 0.177227i 0.645568 0.763703i \(-0.276621\pi\)
−0.338602 + 0.940930i \(0.609954\pi\)
\(14\) 9.99602 0.714001
\(15\) −0.205374 −0.0136916
\(16\) 8.50921 14.7384i 0.531826 0.921149i
\(17\) −3.37913 + 5.85283i −0.198772 + 0.344284i −0.948131 0.317881i \(-0.897029\pi\)
0.749358 + 0.662165i \(0.230362\pi\)
\(18\) 5.37072 + 3.10078i 0.298373 + 0.172266i
\(19\) 2.77232 4.80179i 0.145911 0.252726i −0.783801 0.621012i \(-0.786722\pi\)
0.929713 + 0.368286i \(0.120055\pi\)
\(20\) 0.0280617 0.0162014i 0.00140309 0.000810072i
\(21\) 4.18772 + 7.25334i 0.199415 + 0.345397i
\(22\) 18.5269 0.842134
\(23\) −18.0515 + 31.2661i −0.784848 + 1.35940i 0.144242 + 0.989542i \(0.453926\pi\)
−0.929090 + 0.369854i \(0.879408\pi\)
\(24\) 13.3435 0.555977
\(25\) 24.9859 0.999438
\(26\) −4.76270 8.24924i −0.183181 0.317278i
\(27\) 5.19615i 0.192450i
\(28\) −1.14440 0.660717i −0.0408713 0.0235970i
\(29\) 14.9263 + 25.8531i 0.514700 + 0.891487i 0.999854 + 0.0170582i \(0.00543006\pi\)
−0.485154 + 0.874428i \(0.661237\pi\)
\(30\) 0.367669 + 0.212274i 0.0122556 + 0.00707579i
\(31\) −0.770869 + 0.445062i −0.0248668 + 0.0143568i −0.512382 0.858758i \(-0.671237\pi\)
0.487515 + 0.873115i \(0.337903\pi\)
\(32\) −3.78012 + 2.18245i −0.118129 + 0.0682016i
\(33\) 7.76165 + 13.4436i 0.235202 + 0.407381i
\(34\) 12.0989 6.98531i 0.355850 0.205450i
\(35\) 0.286683 + 0.496549i 0.00819094 + 0.0141871i
\(36\) −0.409912 0.709988i −0.0113864 0.0197219i
\(37\) 3.63103 6.28913i 0.0981360 0.169977i −0.812777 0.582575i \(-0.802045\pi\)
0.910913 + 0.412598i \(0.135379\pi\)
\(38\) −9.92621 + 5.73090i −0.261216 + 0.150813i
\(39\) 3.99056 6.91185i 0.102322 0.177227i
\(40\) 0.913467 0.0228367
\(41\) −58.6251 + 33.8472i −1.42988 + 0.825542i −0.997111 0.0759630i \(-0.975797\pi\)
−0.432769 + 0.901505i \(0.642464\pi\)
\(42\) 17.3136i 0.412229i
\(43\) 4.32723i 0.100633i 0.998733 + 0.0503166i \(0.0160230\pi\)
−0.998733 + 0.0503166i \(0.983977\pi\)
\(44\) −2.12106 1.22459i −0.0482059 0.0278317i
\(45\) 0.355718i 0.00790485i
\(46\) 64.6330 37.3159i 1.40507 0.811215i
\(47\) 21.3745 + 37.0217i 0.454776 + 0.787695i 0.998675 0.0514555i \(-0.0163860\pi\)
−0.543899 + 0.839150i \(0.683053\pi\)
\(48\) −25.5276 14.7384i −0.531826 0.307050i
\(49\) −12.8087 + 22.1853i −0.261402 + 0.452761i
\(50\) −44.7308 25.8253i −0.894616 0.516507i
\(51\) 10.1374 + 5.85283i 0.198772 + 0.114761i
\(52\) 1.25922i 0.0242158i
\(53\) 61.3710i 1.15794i −0.815348 0.578972i \(-0.803454\pi\)
0.815348 0.578972i \(-0.196546\pi\)
\(54\) 5.37072 9.30235i 0.0994577 0.172266i
\(55\) 0.531347 + 0.920320i 0.00966086 + 0.0167331i
\(56\) −18.6262 32.2615i −0.332611 0.576099i
\(57\) −8.31695 4.80179i −0.145911 0.0842419i
\(58\) 61.7110i 1.06398i
\(59\) −45.4130 −0.769712 −0.384856 0.922977i \(-0.625749\pi\)
−0.384856 + 0.922977i \(0.625749\pi\)
\(60\) −0.0280617 0.0486043i −0.000467696 0.000810072i
\(61\) −48.7912 28.1696i −0.799856 0.461797i 0.0435647 0.999051i \(-0.486129\pi\)
−0.843421 + 0.537253i \(0.819462\pi\)
\(62\) 1.84005 0.0296783
\(63\) 12.5631 7.25334i 0.199415 0.115132i
\(64\) −59.0506 −0.922665
\(65\) 0.273186 0.473171i 0.00420286 0.00727956i
\(66\) 32.0896i 0.486206i
\(67\) −63.0665 + 22.6188i −0.941292 + 0.337594i
\(68\) −1.84686 −0.0271597
\(69\) 54.1545 + 31.2661i 0.784848 + 0.453132i
\(70\) 1.18526i 0.0169322i
\(71\) −38.7646 67.1422i −0.545980 0.945665i −0.998545 0.0539331i \(-0.982824\pi\)
0.452565 0.891731i \(-0.350509\pi\)
\(72\) 23.1115i 0.320994i
\(73\) 17.3628 30.0733i 0.237847 0.411962i −0.722250 0.691633i \(-0.756892\pi\)
0.960096 + 0.279670i \(0.0902251\pi\)
\(74\) −13.0008 + 7.50604i −0.175687 + 0.101433i
\(75\) 43.2769i 0.577026i
\(76\) 1.51521 0.0199369
\(77\) 21.6691 37.5319i 0.281416 0.487428i
\(78\) −14.2881 + 8.24924i −0.183181 + 0.105759i
\(79\) −81.4581 + 47.0299i −1.03112 + 0.595315i −0.917304 0.398188i \(-0.869639\pi\)
−0.113811 + 0.993502i \(0.536306\pi\)
\(80\) −1.74757 1.00896i −0.0218446 0.0126120i
\(81\) 9.00000 0.111111
\(82\) 139.937 1.70655
\(83\) −54.8226 + 94.9555i −0.660513 + 1.14404i 0.319968 + 0.947428i \(0.396328\pi\)
−0.980481 + 0.196614i \(0.937005\pi\)
\(84\) −1.14440 + 1.98215i −0.0136238 + 0.0235970i
\(85\) 0.693986 + 0.400673i 0.00816454 + 0.00471380i
\(86\) 4.47260 7.74678i 0.0520070 0.0900788i
\(87\) 44.7789 25.8531i 0.514700 0.297162i
\(88\) −34.5224 59.7946i −0.392300 0.679484i
\(89\) 5.63854 0.0633544 0.0316772 0.999498i \(-0.489915\pi\)
0.0316772 + 0.999498i \(0.489915\pi\)
\(90\) 0.367669 0.636821i 0.00408521 0.00707579i
\(91\) −22.2818 −0.244855
\(92\) −9.86603 −0.107239
\(93\) 0.770869 + 1.33519i 0.00828892 + 0.0143568i
\(94\) 88.3702i 0.940108i
\(95\) −0.569362 0.328721i −0.00599328 0.00346022i
\(96\) 3.78012 + 6.54736i 0.0393762 + 0.0682016i
\(97\) 57.8376 + 33.3925i 0.596264 + 0.344253i 0.767570 0.640965i \(-0.221466\pi\)
−0.171307 + 0.985218i \(0.554799\pi\)
\(98\) 45.8612 26.4780i 0.467972 0.270184i
\(99\) 23.2850 13.4436i 0.235202 0.135794i
\(100\) 3.41401 + 5.91324i 0.0341401 + 0.0591324i
\(101\) 14.5017 8.37255i 0.143581 0.0828966i −0.426489 0.904493i \(-0.640250\pi\)
0.570070 + 0.821596i \(0.306916\pi\)
\(102\) −12.0989 20.9559i −0.118617 0.205450i
\(103\) 19.5587 + 33.8767i 0.189891 + 0.328900i 0.945214 0.326453i \(-0.105853\pi\)
−0.755323 + 0.655353i \(0.772520\pi\)
\(104\) −17.7493 + 30.7426i −0.170666 + 0.295602i
\(105\) 0.860048 0.496549i 0.00819094 0.00472904i
\(106\) −63.4328 + 109.869i −0.598422 + 1.03650i
\(107\) 26.5806 0.248417 0.124209 0.992256i \(-0.460361\pi\)
0.124209 + 0.992256i \(0.460361\pi\)
\(108\) −1.22973 + 0.709988i −0.0113864 + 0.00657396i
\(109\) 63.4089i 0.581733i 0.956764 + 0.290867i \(0.0939436\pi\)
−0.956764 + 0.290867i \(0.906056\pi\)
\(110\) 2.19679i 0.0199708i
\(111\) −10.8931 6.28913i −0.0981360 0.0566589i
\(112\) 82.2936i 0.734764i
\(113\) 1.09189 0.630402i 0.00966273 0.00557878i −0.495161 0.868801i \(-0.664891\pi\)
0.504824 + 0.863223i \(0.331558\pi\)
\(114\) 9.92621 + 17.1927i 0.0870721 + 0.150813i
\(115\) 3.70731 + 2.14042i 0.0322375 + 0.0186123i
\(116\) −4.07898 + 7.06499i −0.0351636 + 0.0609051i
\(117\) −11.9717 6.91185i −0.102322 0.0590756i
\(118\) 81.3001 + 46.9387i 0.688984 + 0.397785i
\(119\) 32.6800i 0.274622i
\(120\) 1.58217i 0.0131848i
\(121\) −20.3378 + 35.2262i −0.168081 + 0.291126i
\(122\) 58.2320 + 100.861i 0.477311 + 0.826727i
\(123\) 58.6251 + 101.542i 0.476627 + 0.825542i
\(124\) −0.210659 0.121624i −0.00169886 0.000980838i
\(125\) 5.92697i 0.0474158i
\(126\) −29.9881 −0.238000
\(127\) 62.3783 + 108.042i 0.491168 + 0.850727i 0.999948 0.0101688i \(-0.00323689\pi\)
−0.508781 + 0.860896i \(0.669904\pi\)
\(128\) 120.835 + 69.7642i 0.944025 + 0.545033i
\(129\) 7.49498 0.0581006
\(130\) −0.978135 + 0.564727i −0.00752412 + 0.00434405i
\(131\) −11.6604 −0.0890105 −0.0445053 0.999009i \(-0.514171\pi\)
−0.0445053 + 0.999009i \(0.514171\pi\)
\(132\) −2.12106 + 3.67378i −0.0160686 + 0.0278317i
\(133\) 26.8114i 0.201589i
\(134\) 136.283 + 24.6922i 1.01704 + 0.184270i
\(135\) 0.616122 0.00456387
\(136\) −45.0893 26.0323i −0.331539 0.191414i
\(137\) 80.9892i 0.591162i −0.955318 0.295581i \(-0.904487\pi\)
0.955318 0.295581i \(-0.0955132\pi\)
\(138\) −64.6330 111.948i −0.468355 0.811215i
\(139\) 14.3806i 0.103457i 0.998661 + 0.0517286i \(0.0164731\pi\)
−0.998661 + 0.0517286i \(0.983527\pi\)
\(140\) −0.0783431 + 0.135694i −0.000559593 + 0.000969244i
\(141\) 64.1234 37.0217i 0.454776 0.262565i
\(142\) 160.267i 1.12864i
\(143\) −41.2977 −0.288795
\(144\) −25.5276 + 44.2151i −0.177275 + 0.307050i
\(145\) 3.06548 1.76985i 0.0211412 0.0122059i
\(146\) −62.1671 + 35.8922i −0.425802 + 0.245837i
\(147\) 38.4261 + 22.1853i 0.261402 + 0.150920i
\(148\) 1.98454 0.0134090
\(149\) 46.2165 0.310178 0.155089 0.987901i \(-0.450434\pi\)
0.155089 + 0.987901i \(0.450434\pi\)
\(150\) −44.7308 + 77.4760i −0.298205 + 0.516507i
\(151\) −1.03515 + 1.79293i −0.00685528 + 0.0118737i −0.869433 0.494051i \(-0.835515\pi\)
0.862577 + 0.505925i \(0.168849\pi\)
\(152\) 36.9923 + 21.3575i 0.243370 + 0.140510i
\(153\) 10.1374 17.5585i 0.0662575 0.114761i
\(154\) −77.5856 + 44.7941i −0.503803 + 0.290871i
\(155\) 0.0527722 + 0.0914041i 0.000340466 + 0.000589704i
\(156\) 2.18103 0.0139810
\(157\) −23.0614 + 39.9435i −0.146888 + 0.254417i −0.930076 0.367368i \(-0.880259\pi\)
0.783188 + 0.621785i \(0.213592\pi\)
\(158\) 194.439 1.23063
\(159\) −106.298 −0.668539
\(160\) 0.258779 + 0.448219i 0.00161737 + 0.00280137i
\(161\) 174.578i 1.08434i
\(162\) −16.1122 9.30235i −0.0994577 0.0574219i
\(163\) −86.0801 149.095i −0.528099 0.914694i −0.999463 0.0327552i \(-0.989572\pi\)
0.471365 0.881938i \(-0.343762\pi\)
\(164\) −16.0207 9.24957i −0.0976874 0.0563998i
\(165\) 1.59404 0.920320i 0.00966086 0.00557770i
\(166\) 196.291 113.329i 1.18248 0.682703i
\(167\) 113.145 + 195.974i 0.677517 + 1.17349i 0.975726 + 0.218994i \(0.0702774\pi\)
−0.298209 + 0.954501i \(0.596389\pi\)
\(168\) −55.8786 + 32.2615i −0.332611 + 0.192033i
\(169\) −73.8836 127.970i −0.437181 0.757220i
\(170\) −0.828267 1.43460i −0.00487216 0.00843883i
\(171\) −8.31695 + 14.4054i −0.0486371 + 0.0842419i
\(172\) −1.02409 + 0.591261i −0.00595403 + 0.00343756i
\(173\) 106.032 183.652i 0.612899 1.06157i −0.377850 0.925867i \(-0.623336\pi\)
0.990749 0.135706i \(-0.0433302\pi\)
\(174\) −106.887 −0.614291
\(175\) −104.634 + 60.4105i −0.597909 + 0.345203i
\(176\) 152.526i 0.866623i
\(177\) 78.6576i 0.444393i
\(178\) −10.0943 5.82797i −0.0567097 0.0327414i
\(179\) 59.1674i 0.330544i −0.986248 0.165272i \(-0.947150\pi\)
0.986248 0.165272i \(-0.0528503\pi\)
\(180\) −0.0841852 + 0.0486043i −0.000467696 + 0.000270024i
\(181\) 4.59559 + 7.95980i 0.0253900 + 0.0439768i 0.878441 0.477850i \(-0.158584\pi\)
−0.853051 + 0.521827i \(0.825251\pi\)
\(182\) 39.8897 + 23.0303i 0.219174 + 0.126540i
\(183\) −48.7912 + 84.5089i −0.266619 + 0.461797i
\(184\) −240.870 139.066i −1.30907 0.755794i
\(185\) −0.745720 0.430542i −0.00403092 0.00232725i
\(186\) 3.18707i 0.0171348i
\(187\) 60.5701i 0.323904i
\(188\) −5.84109 + 10.1171i −0.0310696 + 0.0538142i
\(189\) −12.5631 21.7600i −0.0664717 0.115132i
\(190\) 0.679529 + 1.17698i 0.00357647 + 0.00619462i
\(191\) −310.202 179.095i −1.62410 0.937673i −0.985808 0.167876i \(-0.946309\pi\)
−0.638289 0.769797i \(-0.720357\pi\)
\(192\) 102.279i 0.532701i
\(193\) 215.516 1.11666 0.558332 0.829617i \(-0.311441\pi\)
0.558332 + 0.829617i \(0.311441\pi\)
\(194\) −69.0287 119.561i −0.355818 0.616295i
\(195\) −0.819557 0.473171i −0.00420286 0.00242652i
\(196\) −7.00057 −0.0357172
\(197\) 116.704 67.3794i 0.592409 0.342027i −0.173641 0.984809i \(-0.555553\pi\)
0.766049 + 0.642782i \(0.222220\pi\)
\(198\) −55.5808 −0.280711
\(199\) 156.917 271.788i 0.788526 1.36577i −0.138344 0.990384i \(-0.544178\pi\)
0.926870 0.375383i \(-0.122489\pi\)
\(200\) 192.488i 0.962440i
\(201\) 39.1769 + 109.234i 0.194910 + 0.543455i
\(202\) −34.6153 −0.171363
\(203\) −125.014 72.1770i −0.615834 0.355552i
\(204\) 3.19885i 0.0156807i
\(205\) 4.01336 + 6.95134i 0.0195774 + 0.0339090i
\(206\) 80.8632i 0.392540i
\(207\) 54.1545 93.7984i 0.261616 0.453132i
\(208\) 67.9130 39.2096i 0.326505 0.188508i
\(209\) 49.6931i 0.237766i
\(210\) −2.05292 −0.00977582
\(211\) 49.2300 85.2688i 0.233317 0.404117i −0.725465 0.688259i \(-0.758375\pi\)
0.958782 + 0.284142i \(0.0917086\pi\)
\(212\) 14.5242 8.38556i 0.0685105 0.0395545i
\(213\) −116.294 + 67.1422i −0.545980 + 0.315222i
\(214\) −47.5857 27.4736i −0.222363 0.128381i
\(215\) 0.513092 0.00238647
\(216\) −40.0304 −0.185326
\(217\) 2.15212 3.72758i 0.00991761 0.0171778i
\(218\) 65.5391 113.517i 0.300638 0.520721i
\(219\) −52.0884 30.0733i −0.237847 0.137321i
\(220\) −0.145204 + 0.251500i −0.000660016 + 0.00114318i
\(221\) −26.9692 + 15.5707i −0.122033 + 0.0704556i
\(222\) 13.0008 + 22.5181i 0.0585623 + 0.101433i
\(223\) −326.631 −1.46471 −0.732357 0.680921i \(-0.761580\pi\)
−0.732357 + 0.680921i \(0.761580\pi\)
\(224\) 10.5534 18.2790i 0.0471133 0.0816026i
\(225\) −74.9578 −0.333146
\(226\) −2.60632 −0.0115324
\(227\) 28.9842 + 50.2021i 0.127684 + 0.221155i 0.922779 0.385330i \(-0.125912\pi\)
−0.795095 + 0.606485i \(0.792579\pi\)
\(228\) 2.62441i 0.0115106i
\(229\) 217.881 + 125.794i 0.951447 + 0.549318i 0.893530 0.449003i \(-0.148221\pi\)
0.0579168 + 0.998321i \(0.481554\pi\)
\(230\) −4.42465 7.66372i −0.0192376 0.0333205i
\(231\) −65.0072 37.5319i −0.281416 0.162476i
\(232\) −199.169 + 114.990i −0.858485 + 0.495647i
\(233\) 202.424 116.870i 0.868774 0.501587i 0.00183311 0.999998i \(-0.499417\pi\)
0.866941 + 0.498412i \(0.166083\pi\)
\(234\) 14.2881 + 24.7477i 0.0610603 + 0.105759i
\(235\) 4.38976 2.53443i 0.0186798 0.0107848i
\(236\) −6.20511 10.7476i −0.0262928 0.0455405i
\(237\) 81.4581 + 141.090i 0.343705 + 0.595315i
\(238\) −33.7779 + 58.5050i −0.141924 + 0.245819i
\(239\) −244.875 + 141.378i −1.02458 + 0.591541i −0.915427 0.402484i \(-0.868147\pi\)
−0.109153 + 0.994025i \(0.534814\pi\)
\(240\) −1.74757 + 3.02688i −0.00728155 + 0.0126120i
\(241\) −228.298 −0.947296 −0.473648 0.880714i \(-0.657063\pi\)
−0.473648 + 0.880714i \(0.657063\pi\)
\(242\) 72.8192 42.0422i 0.300906 0.173728i
\(243\) 15.5885i 0.0641500i
\(244\) 15.3961i 0.0630987i
\(245\) 2.63057 + 1.51876i 0.0107370 + 0.00619903i
\(246\) 242.378i 0.985278i
\(247\) 22.1262 12.7745i 0.0895796 0.0517188i
\(248\) −3.42869 5.93866i −0.0138254 0.0239462i
\(249\) 164.468 + 94.9555i 0.660513 + 0.381348i
\(250\) −6.12609 + 10.6107i −0.0245044 + 0.0424428i
\(251\) −165.359 95.4700i −0.658800 0.380359i 0.133019 0.991113i \(-0.457533\pi\)
−0.791820 + 0.610755i \(0.790866\pi\)
\(252\) 3.43319 + 1.98215i 0.0136238 + 0.00786568i
\(253\) 323.569i 1.27893i
\(254\) 257.896i 1.01534i
\(255\) 0.693986 1.20202i 0.00272151 0.00471380i
\(256\) −26.1147 45.2320i −0.102010 0.176687i
\(257\) 142.017 + 245.981i 0.552597 + 0.957126i 0.998086 + 0.0618389i \(0.0196965\pi\)
−0.445489 + 0.895287i \(0.646970\pi\)
\(258\) −13.4178 7.74678i −0.0520070 0.0300263i
\(259\) 35.1161i 0.135584i
\(260\) 0.149309 0.000574266
\(261\) −44.7789 77.5593i −0.171567 0.297162i
\(262\) 20.8749 + 12.0521i 0.0796751 + 0.0460004i
\(263\) 391.805 1.48975 0.744876 0.667203i \(-0.232509\pi\)
0.744876 + 0.667203i \(0.232509\pi\)
\(264\) −103.567 + 59.7946i −0.392300 + 0.226495i
\(265\) −7.27693 −0.0274601
\(266\) 27.7121 47.9988i 0.104181 0.180447i
\(267\) 9.76624i 0.0365777i
\(268\) −13.9703 11.8349i −0.0521278 0.0441601i
\(269\) 328.017 1.21939 0.609697 0.792635i \(-0.291291\pi\)
0.609697 + 0.792635i \(0.291291\pi\)
\(270\) −1.10301 0.636821i −0.00408521 0.00235860i
\(271\) 159.770i 0.589556i −0.955566 0.294778i \(-0.904754\pi\)
0.955566 0.294778i \(-0.0952457\pi\)
\(272\) 57.5075 + 99.6059i 0.211425 + 0.366198i
\(273\) 38.5931i 0.141367i
\(274\) −83.7100 + 144.990i −0.305511 + 0.529161i
\(275\) −193.932 + 111.967i −0.705208 + 0.407152i
\(276\) 17.0885i 0.0619147i
\(277\) 396.390 1.43101 0.715506 0.698607i \(-0.246196\pi\)
0.715506 + 0.698607i \(0.246196\pi\)
\(278\) 14.8637 25.7446i 0.0534664 0.0926066i
\(279\) 2.31261 1.33519i 0.00828892 0.00478561i
\(280\) −3.82534 + 2.20856i −0.0136619 + 0.00788772i
\(281\) −57.0045 32.9116i −0.202863 0.117123i 0.395127 0.918626i \(-0.370701\pi\)
−0.597990 + 0.801503i \(0.704034\pi\)
\(282\) −153.062 −0.542772
\(283\) 521.842 1.84396 0.921982 0.387233i \(-0.126569\pi\)
0.921982 + 0.387233i \(0.126569\pi\)
\(284\) 10.5934 18.3482i 0.0373006 0.0646065i
\(285\) −0.569362 + 0.986163i −0.00199776 + 0.00346022i
\(286\) 73.9328 + 42.6851i 0.258506 + 0.149249i
\(287\) 163.670 283.485i 0.570279 0.987753i
\(288\) 11.3404 6.54736i 0.0393762 0.0227339i
\(289\) 121.663 + 210.726i 0.420979 + 0.729157i
\(290\) −7.31724 −0.0252319
\(291\) 57.8376 100.178i 0.198755 0.344253i
\(292\) 9.48962 0.0324987
\(293\) −430.557 −1.46948 −0.734738 0.678351i \(-0.762695\pi\)
−0.734738 + 0.678351i \(0.762695\pi\)
\(294\) −45.8612 79.4340i −0.155991 0.270184i
\(295\) 5.38475i 0.0182534i
\(296\) 48.4505 + 27.9729i 0.163684 + 0.0945032i
\(297\) −23.2850 40.3307i −0.0784005 0.135794i
\(298\) −82.7386 47.7692i −0.277646 0.160299i
\(299\) −144.071 + 83.1795i −0.481843 + 0.278192i
\(300\) 10.2420 5.91324i 0.0341401 0.0197108i
\(301\) −10.4623 18.1212i −0.0347584 0.0602034i
\(302\) 3.70632 2.13985i 0.0122726 0.00708558i
\(303\) −14.5017 25.1177i −0.0478604 0.0828966i
\(304\) −47.1804 81.7189i −0.155199 0.268812i
\(305\) −3.34015 + 5.78531i −0.0109513 + 0.0189682i
\(306\) −36.2967 + 20.9559i −0.118617 + 0.0684834i
\(307\) −244.969 + 424.298i −0.797944 + 1.38208i 0.123009 + 0.992406i \(0.460746\pi\)
−0.920953 + 0.389674i \(0.872588\pi\)
\(308\) 11.8432 0.0384519
\(309\) 58.6762 33.8767i 0.189891 0.109633i
\(310\) 0.218180i 0.000703807i
\(311\) 71.1225i 0.228690i −0.993441 0.114345i \(-0.963523\pi\)
0.993441 0.114345i \(-0.0364769\pi\)
\(312\) 53.2478 + 30.7426i 0.170666 + 0.0985341i
\(313\) 210.567i 0.672737i 0.941730 + 0.336369i \(0.109199\pi\)
−0.941730 + 0.336369i \(0.890801\pi\)
\(314\) 82.5708 47.6722i 0.262964 0.151822i
\(315\) −0.860048 1.48965i −0.00273031 0.00472904i
\(316\) −22.2604 12.8521i −0.0704443 0.0406711i
\(317\) 35.9174 62.2108i 0.113304 0.196249i −0.803796 0.594904i \(-0.797190\pi\)
0.917101 + 0.398656i \(0.130523\pi\)
\(318\) 190.298 + 109.869i 0.598422 + 0.345499i
\(319\) −231.706 133.775i −0.726350 0.419358i
\(320\) 7.00179i 0.0218806i
\(321\) 46.0390i 0.143424i
\(322\) −180.443 + 312.537i −0.560383 + 0.970611i
\(323\) 18.7360 + 32.4518i 0.0580063 + 0.100470i
\(324\) 1.22973 + 2.12996i 0.00379548 + 0.00657396i
\(325\) 99.7078 + 57.5663i 0.306793 + 0.177127i
\(326\) 355.888i 1.09168i
\(327\) 109.827 0.335864
\(328\) −260.754 451.639i −0.794981 1.37695i
\(329\) −179.020 103.357i −0.544135 0.314156i
\(330\) −3.80495 −0.0115302
\(331\) −321.162 + 185.423i −0.970279 + 0.560191i −0.899321 0.437289i \(-0.855939\pi\)
−0.0709576 + 0.997479i \(0.522606\pi\)
\(332\) −29.9632 −0.0902507
\(333\) −10.8931 + 18.8674i −0.0327120 + 0.0566589i
\(334\) 467.786i 1.40056i
\(335\) 2.68197 + 7.47798i 0.00800589 + 0.0223223i
\(336\) 142.537 0.424216
\(337\) 430.696 + 248.662i 1.27803 + 0.737870i 0.976486 0.215582i \(-0.0691648\pi\)
0.301543 + 0.953452i \(0.402498\pi\)
\(338\) 305.463i 0.903737i
\(339\) −1.09189 1.89121i −0.00322091 0.00557878i
\(340\) 0.218987i 0.000644080i
\(341\) 3.98881 6.90883i 0.0116974 0.0202605i
\(342\) 29.7786 17.1927i 0.0870721 0.0502711i
\(343\) 360.817i 1.05194i
\(344\) −33.3363 −0.0969080
\(345\) 3.70731 6.42125i 0.0107458 0.0186123i
\(346\) −379.644 + 219.187i −1.09724 + 0.633490i
\(347\) −94.0307 + 54.2887i −0.270982 + 0.156451i −0.629334 0.777135i \(-0.716672\pi\)
0.358352 + 0.933587i \(0.383339\pi\)
\(348\) 12.2369 + 7.06499i 0.0351636 + 0.0203017i
\(349\) −72.0314 −0.206394 −0.103197 0.994661i \(-0.532907\pi\)
−0.103197 + 0.994661i \(0.532907\pi\)
\(350\) 249.760 0.713600
\(351\) −11.9717 + 20.7355i −0.0341073 + 0.0590756i
\(352\) 19.5600 33.8789i 0.0555681 0.0962468i
\(353\) −390.805 225.631i −1.10710 0.639182i −0.169020 0.985613i \(-0.554060\pi\)
−0.938076 + 0.346431i \(0.887394\pi\)
\(354\) 81.3001 140.816i 0.229661 0.397785i
\(355\) −7.96123 + 4.59642i −0.0224260 + 0.0129477i
\(356\) 0.770434 + 1.33443i 0.00216414 + 0.00374840i
\(357\) −56.6034 −0.158553
\(358\) −61.1552 + 105.924i −0.170825 + 0.295877i
\(359\) −271.625 −0.756617 −0.378308 0.925680i \(-0.623494\pi\)
−0.378308 + 0.925680i \(0.623494\pi\)
\(360\) −2.74040 −0.00761222
\(361\) 165.129 + 286.011i 0.457420 + 0.792274i
\(362\) 18.9999i 0.0524860i
\(363\) 61.0135 + 35.2262i 0.168081 + 0.0970418i
\(364\) −3.04452 5.27326i −0.00836406 0.0144870i
\(365\) −3.56587 2.05876i −0.00976951 0.00564043i
\(366\) 174.696 100.861i 0.477311 0.275576i
\(367\) −181.688 + 104.898i −0.495063 + 0.285825i −0.726673 0.686984i \(-0.758934\pi\)
0.231609 + 0.972809i \(0.425601\pi\)
\(368\) 307.208 + 532.100i 0.834805 + 1.44592i
\(369\) 175.875 101.542i 0.476627 0.275181i
\(370\) 0.890011 + 1.54155i 0.00240544 + 0.00416634i
\(371\) 148.382 + 257.004i 0.399950 + 0.692734i
\(372\) −0.210659 + 0.364872i −0.000566287 + 0.000980838i
\(373\) −48.3202 + 27.8977i −0.129545 + 0.0747926i −0.563372 0.826203i \(-0.690496\pi\)
0.433827 + 0.900996i \(0.357163\pi\)
\(374\) −62.6050 + 108.435i −0.167393 + 0.289933i
\(375\) −10.2658 −0.0273755
\(376\) −285.209 + 164.666i −0.758535 + 0.437941i
\(377\) 137.558i 0.364875i
\(378\) 51.9408i 0.137410i
\(379\) 560.088 + 323.367i 1.47781 + 0.853212i 0.999685 0.0250828i \(-0.00798493\pi\)
0.478120 + 0.878294i \(0.341318\pi\)
\(380\) 0.179662i 0.000472795i
\(381\) 187.135 108.042i 0.491168 0.283576i
\(382\) 370.224 + 641.247i 0.969174 + 1.67866i
\(383\) −61.4972 35.5054i −0.160567 0.0927034i 0.417563 0.908648i \(-0.362884\pi\)
−0.578130 + 0.815944i \(0.696218\pi\)
\(384\) 120.835 209.293i 0.314675 0.545033i
\(385\) −4.45026 2.56936i −0.0115591 0.00667366i
\(386\) −385.826 222.756i −0.999548 0.577089i
\(387\) 12.9817i 0.0335444i
\(388\) 18.2506i 0.0470377i
\(389\) 236.358 409.384i 0.607604 1.05240i −0.384030 0.923321i \(-0.625464\pi\)
0.991634 0.129080i \(-0.0412025\pi\)
\(390\) 0.978135 + 1.69418i 0.00250804 + 0.00434405i
\(391\) −121.997 211.305i −0.312012 0.540421i
\(392\) −170.912 98.6762i −0.436000 0.251725i
\(393\) 20.1964i 0.0513903i
\(394\) −278.572 −0.707035
\(395\) 5.57646 + 9.65871i 0.0141176 + 0.0244524i
\(396\) 6.36318 + 3.67378i 0.0160686 + 0.00927723i
\(397\) 746.333 1.87993 0.939965 0.341270i \(-0.110857\pi\)
0.939965 + 0.341270i \(0.110857\pi\)
\(398\) −561.837 + 324.377i −1.41165 + 0.815016i
\(399\) 46.4387 0.116388
\(400\) 212.611 368.252i 0.531526 0.920631i
\(401\) 164.319i 0.409773i 0.978786 + 0.204886i \(0.0656825\pi\)
−0.978786 + 0.204886i \(0.934318\pi\)
\(402\) 42.7681 236.049i 0.106388 0.587186i
\(403\) −4.10160 −0.0101777
\(404\) 3.96294 + 2.28800i 0.00980926 + 0.00566338i
\(405\) 1.06715i 0.00263495i
\(406\) 149.204 + 258.428i 0.367497 + 0.636523i
\(407\) 65.0854i 0.159915i
\(408\) −45.0893 + 78.0970i −0.110513 + 0.191414i
\(409\) −102.531 + 59.1961i −0.250686 + 0.144734i −0.620078 0.784540i \(-0.712899\pi\)
0.369392 + 0.929274i \(0.379566\pi\)
\(410\) 16.5927i 0.0404701i
\(411\) −140.277 −0.341307
\(412\) −5.34490 + 9.25764i −0.0129731 + 0.0224700i
\(413\) 190.177 109.799i 0.460477 0.265856i
\(414\) −193.899 + 111.948i −0.468355 + 0.270405i
\(415\) 11.2591 + 6.50047i 0.0271305 + 0.0156638i
\(416\) −20.1130 −0.0483486
\(417\) 24.9079 0.0597311
\(418\) 51.3625 88.9625i 0.122877 0.212829i
\(419\) 52.7821 91.4213i 0.125972 0.218189i −0.796141 0.605112i \(-0.793129\pi\)
0.922112 + 0.386922i \(0.126462\pi\)
\(420\) 0.235029 + 0.135694i 0.000559593 + 0.000323081i
\(421\) −30.2089 + 52.3234i −0.0717552 + 0.124284i −0.899671 0.436569i \(-0.856193\pi\)
0.827915 + 0.560853i \(0.189527\pi\)
\(422\) −176.267 + 101.768i −0.417694 + 0.241156i
\(423\) −64.1234 111.065i −0.151592 0.262565i
\(424\) 472.793 1.11508
\(425\) −84.4308 + 146.238i −0.198661 + 0.344090i
\(426\) 277.591 0.651623
\(427\) 272.432 0.638013
\(428\) 3.63190 + 6.29064i 0.00848576 + 0.0146978i
\(429\) 71.5298i 0.166736i
\(430\) −0.918557 0.530329i −0.00213618 0.00123332i
\(431\) −169.159 292.992i −0.392480 0.679795i 0.600296 0.799778i \(-0.295049\pi\)
−0.992776 + 0.119983i \(0.961716\pi\)
\(432\) 76.5829 + 44.2151i 0.177275 + 0.102350i
\(433\) −479.598 + 276.896i −1.10762 + 0.639483i −0.938211 0.346064i \(-0.887518\pi\)
−0.169405 + 0.985546i \(0.554185\pi\)
\(434\) −7.70563 + 4.44884i −0.0177549 + 0.0102508i
\(435\) −3.06548 5.30956i −0.00704707 0.0122059i
\(436\) −15.0065 + 8.66402i −0.0344186 + 0.0198716i
\(437\) 100.089 + 173.359i 0.229036 + 0.396703i
\(438\) 62.1671 + 107.677i 0.141934 + 0.245837i
\(439\) 108.993 188.782i 0.248277 0.430028i −0.714771 0.699358i \(-0.753469\pi\)
0.963048 + 0.269331i \(0.0868025\pi\)
\(440\) −7.09001 + 4.09342i −0.0161137 + 0.00930323i
\(441\) 38.4261 66.5559i 0.0871339 0.150920i
\(442\) 64.3752 0.145645
\(443\) −718.330 + 414.728i −1.62151 + 0.936180i −0.634996 + 0.772516i \(0.718998\pi\)
−0.986516 + 0.163664i \(0.947669\pi\)
\(444\) 3.43732i 0.00774171i
\(445\) 0.668577i 0.00150242i
\(446\) 584.748 + 337.604i 1.31109 + 0.756961i
\(447\) 80.0493i 0.179081i
\(448\) 247.287 142.771i 0.551980 0.318686i
\(449\) −96.4228 167.009i −0.214750 0.371958i 0.738445 0.674314i \(-0.235560\pi\)
−0.953195 + 0.302355i \(0.902227\pi\)
\(450\) 134.192 + 77.4760i 0.298205 + 0.172169i
\(451\) 303.352 525.420i 0.672620 1.16501i
\(452\) 0.298385 + 0.172273i 0.000660144 + 0.000381134i
\(453\) 3.10544 + 1.79293i 0.00685528 + 0.00395790i
\(454\) 119.832i 0.263947i
\(455\) 2.64201i 0.00580662i
\(456\) 36.9923 64.0725i 0.0811234 0.140510i
\(457\) 160.049 + 277.213i 0.350216 + 0.606592i 0.986287 0.165038i \(-0.0527748\pi\)
−0.636071 + 0.771630i \(0.719441\pi\)
\(458\) −260.040 450.402i −0.567772 0.983411i
\(459\) −30.4122 17.5585i −0.0662575 0.0382538i
\(460\) 1.16984i 0.00254313i
\(461\) 292.926 0.635415 0.317707 0.948189i \(-0.397087\pi\)
0.317707 + 0.948189i \(0.397087\pi\)
\(462\) 77.5856 + 134.382i 0.167934 + 0.290871i
\(463\) −400.087 230.990i −0.864119 0.498899i 0.00127068 0.999999i \(-0.499596\pi\)
−0.865389 + 0.501100i \(0.832929\pi\)
\(464\) 508.044 1.09492
\(465\) 0.158317 0.0914041i 0.000340466 0.000196568i
\(466\) −483.184 −1.03687
\(467\) 10.7462 18.6129i 0.0230111 0.0398563i −0.854291 0.519796i \(-0.826008\pi\)
0.877302 + 0.479939i \(0.159341\pi\)
\(468\) 3.77766i 0.00807193i
\(469\) 209.418 247.202i 0.446519 0.527083i
\(470\) −10.4783 −0.0222942
\(471\) 69.1841 + 39.9435i 0.146888 + 0.0848057i
\(472\) 349.855i 0.741218i
\(473\) −19.3911 33.5865i −0.0409961 0.0710073i
\(474\) 336.779i 0.710504i
\(475\) 69.2689 119.977i 0.145829 0.252584i
\(476\) 7.73412 4.46530i 0.0162482 0.00938088i
\(477\) 184.113i 0.385981i
\(478\) 584.512 1.22283
\(479\) 20.7049 35.8620i 0.0432253 0.0748684i −0.843603 0.536967i \(-0.819570\pi\)
0.886829 + 0.462098i \(0.152903\pi\)
\(480\) 0.776338 0.448219i 0.00161737 0.000933790i
\(481\) 28.9797 16.7314i 0.0602488 0.0347847i
\(482\) 408.708 + 235.968i 0.847943 + 0.489560i
\(483\) −302.378 −0.626042
\(484\) −11.1156 −0.0229662
\(485\) 3.95945 6.85796i 0.00816380 0.0141401i
\(486\) −16.1122 + 27.9071i −0.0331526 + 0.0574219i
\(487\) −600.475 346.684i −1.23301 0.711878i −0.265352 0.964152i \(-0.585488\pi\)
−0.967656 + 0.252274i \(0.918822\pi\)
\(488\) 217.015 375.880i 0.444702 0.770246i
\(489\) −258.240 + 149.095i −0.528099 + 0.304898i
\(490\) −3.13957 5.43789i −0.00640728 0.0110977i
\(491\) −288.019 −0.586596 −0.293298 0.956021i \(-0.594753\pi\)
−0.293298 + 0.956021i \(0.594753\pi\)
\(492\) −16.0207 + 27.7487i −0.0325625 + 0.0563998i
\(493\) −201.752 −0.409233
\(494\) −52.8148 −0.106913
\(495\) −1.59404 2.76096i −0.00322029 0.00557770i
\(496\) 15.1485i 0.0305413i
\(497\) 324.670 + 187.448i 0.653259 + 0.377160i
\(498\) −196.291 339.986i −0.394159 0.682703i
\(499\) 229.489 + 132.496i 0.459899 + 0.265523i 0.712002 0.702178i \(-0.247789\pi\)
−0.252103 + 0.967700i \(0.581122\pi\)
\(500\) 1.40269 0.809845i 0.00280538 0.00161969i
\(501\) 339.436 195.974i 0.677517 0.391165i
\(502\) 197.355 + 341.828i 0.393137 + 0.680933i
\(503\) −542.369 + 313.137i −1.07827 + 0.622538i −0.930429 0.366473i \(-0.880565\pi\)
−0.147839 + 0.989011i \(0.547232\pi\)
\(504\) 55.8786 + 96.7846i 0.110870 + 0.192033i
\(505\) −0.992757 1.71951i −0.00196586 0.00340496i
\(506\) −334.439 + 579.266i −0.660947 + 1.14479i
\(507\) −221.651 + 127.970i −0.437181 + 0.252407i
\(508\) −17.0464 + 29.5252i −0.0335559 + 0.0581205i
\(509\) −926.021 −1.81929 −0.909647 0.415382i \(-0.863648\pi\)
−0.909647 + 0.415382i \(0.863648\pi\)
\(510\) −2.48480 + 1.43460i −0.00487216 + 0.00281294i
\(511\) 167.918i 0.328606i
\(512\) 450.146i 0.879191i
\(513\) 24.9508 + 14.4054i 0.0486371 + 0.0280806i
\(514\) 587.154i 1.14232i
\(515\) 4.01686 2.31913i 0.00779972 0.00450317i
\(516\) 1.02409 + 1.77378i 0.00198468 + 0.00343756i
\(517\) −331.802 191.566i −0.641784 0.370534i
\(518\) 36.2959 62.8663i 0.0700693 0.121364i
\(519\) −318.095 183.652i −0.612899 0.353858i
\(520\) 3.64524 + 2.10458i 0.00701008 + 0.00404727i
\(521\) 428.775i 0.822984i −0.911413 0.411492i \(-0.865008\pi\)
0.911413 0.411492i \(-0.134992\pi\)
\(522\) 185.133i 0.354661i
\(523\) 407.049 705.030i 0.778297 1.34805i −0.154625 0.987973i \(-0.549417\pi\)
0.932922 0.360077i \(-0.117250\pi\)
\(524\) −1.59324 2.75957i −0.00304054 0.00526636i
\(525\) 104.634 + 181.231i 0.199303 + 0.345203i
\(526\) −701.424 404.967i −1.33351 0.769900i
\(527\) 6.01569i 0.0114150i
\(528\) 264.182 0.500345
\(529\) −387.214 670.674i −0.731973 1.26781i
\(530\) 13.0274 + 7.52140i 0.0245801 + 0.0141913i
\(531\) 136.239 0.256571
\(532\) −6.34525 + 3.66343i −0.0119272 + 0.00688615i
\(533\) −311.929 −0.585233
\(534\) −10.0943 + 17.4839i −0.0189032 + 0.0327414i
\(535\) 3.15174i 0.00589110i
\(536\) −174.252 485.855i −0.325097 0.906446i
\(537\) −102.481 −0.190840
\(538\) −587.229 339.037i −1.09150 0.630180i
\(539\) 229.593i 0.425960i
\(540\) 0.0841852 + 0.145813i 0.000155899 + 0.000270024i
\(541\) 397.388i 0.734543i −0.930114 0.367271i \(-0.880292\pi\)
0.930114 0.367271i \(-0.119708\pi\)
\(542\) −165.137 + 286.026i −0.304681 + 0.527723i
\(543\) 13.7868 7.95980i 0.0253900 0.0146589i
\(544\) 29.4992i 0.0542264i
\(545\) 7.51857 0.0137955
\(546\) 39.8897 69.0909i 0.0730580 0.126540i
\(547\) −431.563 + 249.163i −0.788964 + 0.455509i −0.839598 0.543209i \(-0.817209\pi\)
0.0506337 + 0.998717i \(0.483876\pi\)
\(548\) 19.1671 11.0661i 0.0349765 0.0201937i
\(549\) 146.374 + 84.5089i 0.266619 + 0.153932i
\(550\) 462.913 0.841660
\(551\) 165.522 0.300402
\(552\) −240.870 + 417.198i −0.436358 + 0.755794i
\(553\) 227.416 393.895i 0.411240 0.712288i
\(554\) −709.633 409.707i −1.28093 0.739543i
\(555\) −0.745720 + 1.29163i −0.00134364 + 0.00232725i
\(556\) −3.40334 + 1.96492i −0.00612111 + 0.00353403i
\(557\) 424.875 + 735.906i 0.762792 + 1.32120i 0.941406 + 0.337276i \(0.109506\pi\)
−0.178613 + 0.983919i \(0.557161\pi\)
\(558\) −5.52016 −0.00989276
\(559\) −9.96972 + 17.2681i −0.0178349 + 0.0308910i
\(560\) 9.75778 0.0174246
\(561\) −104.911 −0.187006
\(562\) 68.0345 + 117.839i 0.121058 + 0.209678i
\(563\) 351.391i 0.624141i 0.950059 + 0.312071i \(0.101023\pi\)
−0.950059 + 0.312071i \(0.898977\pi\)
\(564\) 17.5233 + 10.1171i 0.0310696 + 0.0179381i
\(565\) −0.0747485 0.129468i −0.000132298 0.000229147i
\(566\) −934.221 539.373i −1.65057 0.952956i
\(567\) −37.6894 + 21.7600i −0.0664717 + 0.0383774i
\(568\) 517.253 298.636i 0.910657 0.525768i
\(569\) 142.495 + 246.808i 0.250430 + 0.433758i 0.963644 0.267189i \(-0.0860946\pi\)
−0.713214 + 0.700946i \(0.752761\pi\)
\(570\) 2.03859 1.17698i 0.00357647 0.00206487i
\(571\) 83.3463 + 144.360i 0.145965 + 0.252820i 0.929733 0.368235i \(-0.120038\pi\)
−0.783767 + 0.621055i \(0.786704\pi\)
\(572\) −5.64281 9.77363i −0.00986505 0.0170868i
\(573\) −310.202 + 537.286i −0.541366 + 0.937673i
\(574\) −586.017 + 338.337i −1.02094 + 0.589438i
\(575\) −451.034 + 781.214i −0.784407 + 1.35863i
\(576\) 177.152 0.307555
\(577\) −573.576 + 331.154i −0.994066 + 0.573924i −0.906487 0.422233i \(-0.861246\pi\)
−0.0875787 + 0.996158i \(0.527913\pi\)
\(578\) 503.001i 0.870244i
\(579\) 373.285i 0.644706i
\(580\) 0.837716 + 0.483655i 0.00144434 + 0.000833889i
\(581\) 530.196i 0.912557i
\(582\) −207.086 + 119.561i −0.355818 + 0.205432i
\(583\) 275.015 + 476.340i 0.471724 + 0.817050i
\(584\) 231.680 + 133.760i 0.396712 + 0.229042i
\(585\) −0.819557 + 1.41951i −0.00140095 + 0.00242652i
\(586\) 770.799 + 445.021i 1.31536 + 0.759422i
\(587\) 643.066 + 371.274i 1.09551 + 0.632494i 0.935039 0.354546i \(-0.115364\pi\)
0.160474 + 0.987040i \(0.448698\pi\)
\(588\) 12.1253i 0.0206213i
\(589\) 4.93541i 0.00837930i
\(590\) 5.56565 9.63998i 0.00943330 0.0163390i
\(591\) −116.704 202.138i −0.197470 0.342027i
\(592\) −61.7944 107.031i −0.104383 0.180796i
\(593\) −435.635 251.514i −0.734628 0.424138i 0.0854847 0.996339i \(-0.472756\pi\)
−0.820113 + 0.572202i \(0.806089\pi\)
\(594\) 96.2688i 0.162069i
\(595\) −3.87495 −0.00651253
\(596\) 6.31489 + 10.9377i 0.0105955 + 0.0183519i
\(597\) −470.750 271.788i −0.788526 0.455256i
\(598\) 343.896 0.575076
\(599\) 837.444 483.498i 1.39807 0.807176i 0.403879 0.914812i \(-0.367662\pi\)
0.994190 + 0.107636i \(0.0343282\pi\)
\(600\) 333.399 0.555665
\(601\) 149.764 259.399i 0.249192 0.431613i −0.714110 0.700033i \(-0.753168\pi\)
0.963302 + 0.268421i \(0.0865017\pi\)
\(602\) 43.2551i 0.0718523i
\(603\) 189.200 67.8564i 0.313764 0.112531i
\(604\) −0.565759 −0.000936686
\(605\) 4.17687 + 2.41152i 0.00690391 + 0.00398598i
\(606\) 59.9555i 0.0989364i
\(607\) 132.150 + 228.891i 0.217710 + 0.377085i 0.954108 0.299464i \(-0.0968079\pi\)
−0.736397 + 0.676549i \(0.763475\pi\)
\(608\) 24.2018i 0.0398056i
\(609\) −125.014 + 216.531i −0.205278 + 0.355552i
\(610\) 11.9593 6.90473i 0.0196055 0.0113192i
\(611\) 196.983i 0.322394i
\(612\) 5.54058 0.00905323
\(613\) −13.0608 + 22.6221i −0.0213064 + 0.0369038i −0.876482 0.481435i \(-0.840116\pi\)
0.855176 + 0.518338i \(0.173449\pi\)
\(614\) 877.105 506.397i 1.42851 0.824751i
\(615\) 12.0401 6.95134i 0.0195774 0.0113030i
\(616\) 289.140 + 166.935i 0.469384 + 0.270999i
\(617\) −315.081 −0.510666 −0.255333 0.966853i \(-0.582185\pi\)
−0.255333 + 0.966853i \(0.582185\pi\)
\(618\) −140.059 −0.226633
\(619\) −336.052 + 582.058i −0.542894 + 0.940320i 0.455842 + 0.890061i \(0.349338\pi\)
−0.998736 + 0.0502597i \(0.983995\pi\)
\(620\) −0.0144213 + 0.0249784i −2.32601e−5 + 4.02877e-5i
\(621\) −162.464 93.7984i −0.261616 0.151044i
\(622\) −73.5119 + 127.326i −0.118186 + 0.204705i
\(623\) −23.6126 + 13.6327i −0.0379015 + 0.0218824i
\(624\) −67.9130 117.629i −0.108835 0.188508i
\(625\) 623.946 0.998313
\(626\) 217.641 376.965i 0.347669 0.602180i
\(627\) 86.0710 0.137274
\(628\) −12.6042 −0.0200703
\(629\) 24.5395 + 42.5036i 0.0390135 + 0.0675733i
\(630\) 3.55577i 0.00564407i
\(631\) −32.0022 18.4765i −0.0507167 0.0292813i 0.474427 0.880295i \(-0.342655\pi\)
−0.525144 + 0.851013i \(0.675989\pi\)
\(632\) −362.311 627.541i −0.573277 0.992945i
\(633\) −147.690 85.2688i −0.233317 0.134706i
\(634\) −128.602 + 74.2481i −0.202841 + 0.117111i
\(635\) 12.8109 7.39637i 0.0201746 0.0116478i
\(636\) −14.5242 25.1567i −0.0228368 0.0395545i
\(637\) −102.228 + 59.0211i −0.160483 + 0.0926548i
\(638\) 276.539 + 478.979i 0.433446 + 0.750751i
\(639\) 116.294 + 201.427i 0.181993 + 0.315222i
\(640\) 8.27213 14.3278i 0.0129252 0.0223871i
\(641\) 446.680 257.891i 0.696849 0.402326i −0.109324 0.994006i \(-0.534868\pi\)
0.806173 + 0.591680i \(0.201535\pi\)
\(642\) −47.5857 + 82.4209i −0.0741210 + 0.128381i
\(643\) 367.612 0.571714 0.285857 0.958272i \(-0.407722\pi\)
0.285857 + 0.958272i \(0.407722\pi\)
\(644\) 41.3161 23.8539i 0.0641555 0.0370402i
\(645\) 0.888701i 0.00137783i
\(646\) 77.4619i 0.119910i
\(647\) 955.380 + 551.589i 1.47663 + 0.852533i 0.999652 0.0263812i \(-0.00839837\pi\)
0.476979 + 0.878915i \(0.341732\pi\)
\(648\) 69.3346i 0.106998i
\(649\) 352.480 203.504i 0.543112 0.313566i
\(650\) −119.001 206.115i −0.183078 0.317100i
\(651\) −6.45637 3.72758i −0.00991761 0.00572594i
\(652\) 23.5235 40.7439i 0.0360789 0.0624906i
\(653\) −69.2618 39.9883i −0.106067 0.0612379i 0.446028 0.895019i \(-0.352838\pi\)
−0.552095 + 0.833781i \(0.686171\pi\)
\(654\) −196.617 113.517i −0.300638 0.173574i
\(655\) 1.38260i 0.00211084i
\(656\) 1152.05i 1.75618i
\(657\) −52.0884 + 90.2198i −0.0792822 + 0.137321i
\(658\) 213.660 + 370.069i 0.324711 + 0.562415i
\(659\) 555.874 + 962.802i 0.843512 + 1.46101i 0.886907 + 0.461947i \(0.152849\pi\)
−0.0433956 + 0.999058i \(0.513818\pi\)
\(660\) 0.435611 + 0.251500i 0.000660016 + 0.000381061i
\(661\) 836.224i 1.26509i 0.774524 + 0.632544i \(0.217989\pi\)
−0.774524 + 0.632544i \(0.782011\pi\)
\(662\) 766.610 1.15802
\(663\) 26.9692 + 46.7121i 0.0406776 + 0.0704556i
\(664\) −731.523 422.345i −1.10169 0.636062i
\(665\) 3.17910 0.00478060
\(666\) 39.0025 22.5181i 0.0585623 0.0338110i
\(667\) −1077.77 −1.61585
\(668\) −30.9197 + 53.5545i −0.0462870 + 0.0801715i
\(669\) 565.742i 0.845653i
\(670\) 2.92782 16.1594i 0.00436988 0.0241186i
\(671\) 504.934 0.752510
\(672\) −31.6601 18.2790i −0.0471133 0.0272009i
\(673\) 404.439i 0.600950i 0.953790 + 0.300475i \(0.0971451\pi\)
−0.953790 + 0.300475i \(0.902855\pi\)
\(674\) −514.032 890.330i −0.762659 1.32096i
\(675\) 129.831i 0.192342i
\(676\) 20.1905 34.9710i 0.0298676 0.0517322i
\(677\) 971.862 561.105i 1.43554 0.828811i 0.438007 0.898972i \(-0.355684\pi\)
0.997536 + 0.0701605i \(0.0223511\pi\)
\(678\) 4.51428i 0.00665823i
\(679\) −322.943 −0.475616
\(680\) −3.08672 + 5.34636i −0.00453930 + 0.00786230i
\(681\) 86.9526 50.2021i 0.127684 0.0737182i
\(682\) −14.2819 + 8.24563i −0.0209411 + 0.0120904i
\(683\) 833.908 + 481.457i 1.22095 + 0.704915i 0.965120 0.261807i \(-0.0843182\pi\)
0.255829 + 0.966722i \(0.417652\pi\)
\(684\) −4.54562 −0.00664564
\(685\) −9.60311 −0.0140191
\(686\) −372.938 + 645.948i −0.543642 + 0.941615i
\(687\) 217.881 377.382i 0.317149 0.549318i
\(688\) 63.7764 + 36.8213i 0.0926982 + 0.0535194i
\(689\) 141.396 244.904i 0.205219 0.355449i
\(690\) −13.2739 + 7.66372i −0.0192376 + 0.0111068i
\(691\) 580.649 + 1005.71i 0.840302 + 1.45545i 0.889639 + 0.456664i \(0.150956\pi\)
−0.0493370 + 0.998782i \(0.515711\pi\)
\(692\) 57.9514 0.0837448
\(693\) −65.0072 + 112.596i −0.0938055 + 0.162476i
\(694\) 224.450 0.323415
\(695\) 1.70514 0.00245344
\(696\) 199.169 + 344.970i 0.286162 + 0.495647i
\(697\) 457.497i 0.656380i
\(698\) 128.953 + 74.4513i 0.184747 + 0.106664i
\(699\) −202.424 350.609i −0.289591 0.501587i
\(700\) −28.5938 16.5086i −0.0408483 0.0235838i
\(701\) −247.243 + 142.746i −0.352701 + 0.203632i −0.665874 0.746064i \(-0.731941\pi\)
0.313173 + 0.949696i \(0.398608\pi\)
\(702\) 42.8643 24.7477i 0.0610603 0.0352532i
\(703\) −20.1327 34.8709i −0.0286383 0.0496030i
\(704\) 458.330 264.617i 0.651037 0.375876i
\(705\) −4.38976 7.60329i −0.00622661 0.0107848i
\(706\) 466.423 + 807.868i 0.660655 + 1.14429i
\(707\) −40.4860 + 70.1238i −0.0572645 + 0.0991850i
\(708\) −18.6153 + 10.7476i −0.0262928 + 0.0151802i
\(709\) −666.476 + 1154.37i −0.940023 + 1.62817i −0.174600 + 0.984639i \(0.555863\pi\)
−0.765423 + 0.643528i \(0.777470\pi\)
\(710\) 19.0034 0.0267653
\(711\) 244.374 141.090i 0.343705 0.198438i
\(712\) 43.4385i 0.0610091i
\(713\) 32.1361i 0.0450717i
\(714\) 101.334 + 58.5050i 0.141924 + 0.0819397i
\(715\) 4.89679i 0.00684865i
\(716\) 14.0027 8.08447i 0.0195569 0.0112912i
\(717\) 244.875 + 424.135i 0.341527 + 0.591541i
\(718\) 486.274 + 280.751i 0.677262 + 0.391018i
\(719\) −140.056 + 242.585i −0.194793 + 0.337392i −0.946833 0.321726i \(-0.895737\pi\)
0.752039 + 0.659118i \(0.229070\pi\)
\(720\) 5.24271 + 3.02688i 0.00728155 + 0.00420400i
\(721\) −163.813 94.5774i −0.227202 0.131175i
\(722\) 682.704i 0.945574i
\(723\) 395.424i 0.546921i
\(724\) −1.25586 + 2.17521i −0.00173461 + 0.00300443i
\(725\) 372.948 + 645.964i 0.514411 + 0.890985i
\(726\) −72.8192 126.127i −0.100302 0.173728i
\(727\) −924.524 533.774i −1.27170 0.734215i −0.296391 0.955067i \(-0.595783\pi\)
−0.975307 + 0.220852i \(0.929116\pi\)
\(728\) 171.655i 0.235790i
\(729\) −27.0000 −0.0370370
\(730\) 4.25584 + 7.37133i 0.00582992 + 0.0100977i
\(731\) −25.3265 14.6223i −0.0346464 0.0200031i
\(732\) −26.6668 −0.0364300
\(733\) −689.637 + 398.162i −0.940841 + 0.543195i −0.890224 0.455523i \(-0.849452\pi\)
−0.0506174 + 0.998718i \(0.516119\pi\)
\(734\) 433.687 0.590855
\(735\) 2.63057 4.55628i 0.00357901 0.00619903i
\(736\) 157.586i 0.214112i
\(737\) 388.141 458.173i 0.526650 0.621672i
\(738\) −419.812 −0.568850
\(739\) 593.144 + 342.452i 0.802631 + 0.463399i 0.844390 0.535729i \(-0.179963\pi\)
−0.0417595 + 0.999128i \(0.513296\pi\)
\(740\) 0.235312i 0.000317989i
\(741\) −22.1262 38.3236i −0.0298599 0.0517188i
\(742\) 613.466i 0.826773i
\(743\) 243.555 421.849i 0.327799 0.567765i −0.654276 0.756256i \(-0.727026\pi\)
0.982075 + 0.188491i \(0.0603597\pi\)
\(744\) −10.2861 + 5.93866i −0.0138254 + 0.00798207i
\(745\) 5.48002i 0.00735573i
\(746\) 115.339 0.154611
\(747\) 164.468 284.867i 0.220171 0.381348i
\(748\) 14.3347 8.27613i 0.0191640 0.0110643i
\(749\) −111.312 + 64.2661i −0.148614 + 0.0858026i
\(750\) 18.3783 + 10.6107i 0.0245044 + 0.0141476i
\(751\) −605.727 −0.806560 −0.403280 0.915077i \(-0.632130\pi\)
−0.403280 + 0.915077i \(0.632130\pi\)
\(752\) 727.519 0.967446
\(753\) −165.359 + 286.410i −0.219600 + 0.380359i
\(754\) 142.179 246.261i 0.188566 0.326606i
\(755\) 0.212592 + 0.122740i 0.000281579 + 0.000162570i
\(756\) 3.43319 5.94645i 0.00454125 0.00786568i
\(757\) −568.176 + 328.036i −0.750563 + 0.433338i −0.825897 0.563821i \(-0.809331\pi\)
0.0753346 + 0.997158i \(0.475998\pi\)
\(758\) −668.461 1157.81i −0.881875 1.52745i
\(759\) −560.438 −0.738390
\(760\) 2.53242 4.38628i 0.00333213 0.00577142i
\(761\) 38.1467 0.0501270 0.0250635 0.999686i \(-0.492021\pi\)
0.0250635 + 0.999686i \(0.492021\pi\)
\(762\) −446.688 −0.586205
\(763\) −153.309 265.539i −0.200929 0.348019i
\(764\) 97.8844i 0.128121i
\(765\) −2.08196 1.20202i −0.00272151 0.00157127i
\(766\) 73.3964 + 127.126i 0.0958178 + 0.165961i
\(767\) −181.223 104.629i −0.236275 0.136414i
\(768\) −78.3440 + 45.2320i −0.102010 + 0.0588958i
\(769\) −732.905 + 423.143i −0.953062 + 0.550251i −0.894031 0.448006i \(-0.852134\pi\)
−0.0590312 + 0.998256i \(0.518801\pi\)
\(770\) 5.31136 + 9.19954i 0.00689787 + 0.0119475i
\(771\) 426.052 245.981i 0.552597 0.319042i
\(772\) 29.4475 + 51.0046i 0.0381445 + 0.0660682i
\(773\) 425.430 + 736.867i 0.550363 + 0.953256i 0.998248 + 0.0591652i \(0.0188439\pi\)
−0.447886 + 0.894091i \(0.647823\pi\)
\(774\) −13.4178 + 23.2403i −0.0173357 + 0.0300263i
\(775\) −19.2609 + 11.1203i −0.0248528 + 0.0143488i
\(776\) −257.251 + 445.572i −0.331509 + 0.574191i
\(777\) 60.8230 0.0782792
\(778\) −846.274 + 488.597i −1.08776 + 0.628016i
\(779\) 375.341i 0.481824i
\(780\) 0.258611i 0.000331553i
\(781\) 601.754 + 347.423i 0.770492 + 0.444844i
\(782\) 504.381i 0.644989i
\(783\) −134.337 + 77.5593i −0.171567 + 0.0990541i
\(784\) 217.984 + 377.559i 0.278040 + 0.481580i
\(785\) 4.73621 + 2.73445i 0.00603339 + 0.00348338i
\(786\) 20.8749 36.1563i 0.0265584 0.0460004i
\(787\) −340.308 196.477i −0.432411 0.249653i 0.267962 0.963429i \(-0.413650\pi\)
−0.700373 + 0.713777i \(0.746983\pi\)
\(788\) 31.8923 + 18.4131i 0.0404725 + 0.0233668i
\(789\) 678.625i 0.860108i
\(790\) 23.0552i 0.0291838i
\(791\) −3.04835 + 5.27989i −0.00385379 + 0.00667496i
\(792\) 103.567 + 179.384i 0.130767 + 0.226495i
\(793\) −129.803 224.825i −0.163686 0.283512i
\(794\) −1336.11 771.406i −1.68276 0.971544i
\(795\) 12.6040i 0.0158541i
\(796\) 85.7626 0.107742
\(797\) −634.880 1099.64i −0.796587 1.37973i −0.921826 0.387603i \(-0.873303\pi\)
0.125239 0.992127i \(-0.460030\pi\)
\(798\) −83.1363 47.9988i −0.104181 0.0601489i
\(799\) −288.908 −0.361588
\(800\) −94.4498 + 54.5306i −0.118062 + 0.0681633i
\(801\) −16.9156 −0.0211181
\(802\) 169.839 294.170i 0.211769 0.366795i
\(803\) 311.224i 0.387577i
\(804\) −20.4987 + 24.1972i −0.0254959 + 0.0300960i
\(805\) −20.7002 −0.0257146
\(806\) 7.34284 + 4.23939i 0.00911022 + 0.00525979i
\(807\) 568.142i 0.704018i
\(808\) 64.5009 + 111.719i 0.0798278 + 0.138266i
\(809\) 1098.14i 1.35741i −0.734412 0.678704i \(-0.762542\pi\)
0.734412 0.678704i \(-0.237458\pi\)
\(810\) −1.10301 + 1.91046i −0.00136174 + 0.00235860i
\(811\) −190.084 + 109.745i −0.234382 + 0.135321i −0.612592 0.790399i \(-0.709873\pi\)
0.378210 + 0.925720i \(0.376540\pi\)
\(812\) 39.4483i 0.0485816i
\(813\) −276.729 −0.340380
\(814\) 67.2720 116.518i 0.0826437 0.143143i
\(815\) −17.6786 + 10.2068i −0.0216915 + 0.0125236i
\(816\) 172.522 99.6059i 0.211425 0.122066i
\(817\) 20.7785 + 11.9964i 0.0254326 + 0.0146835i
\(818\) 244.739 0.299192
\(819\) 66.8453 0.0816182
\(820\) −1.09675 + 1.89962i −0.00133750 + 0.00231661i
\(821\) 665.793 1153.19i 0.810954 1.40461i −0.101243 0.994862i \(-0.532282\pi\)
0.912197 0.409752i \(-0.134385\pi\)
\(822\) 251.130 + 144.990i 0.305511 + 0.176387i
\(823\) 743.262 1287.37i 0.903113 1.56424i 0.0796827 0.996820i \(-0.474609\pi\)
0.823430 0.567417i \(-0.192057\pi\)
\(824\) −260.981 + 150.678i −0.316725 + 0.182861i
\(825\) 193.932 + 335.900i 0.235069 + 0.407152i
\(826\) −453.949 −0.549575
\(827\) −168.953 + 292.634i −0.204296 + 0.353851i −0.949908 0.312529i \(-0.898824\pi\)
0.745612 + 0.666380i \(0.232157\pi\)
\(828\) 29.5981 0.0357465
\(829\) −1048.33 −1.26457 −0.632287 0.774734i \(-0.717884\pi\)
−0.632287 + 0.774734i \(0.717884\pi\)
\(830\) −13.4377 23.2748i −0.0161900 0.0280419i
\(831\) 686.568i 0.826195i
\(832\) −235.645 136.050i −0.283227 0.163521i
\(833\) −86.5645 149.934i −0.103919 0.179993i
\(834\) −44.5910 25.7446i −0.0534664 0.0308689i
\(835\) 23.2371 13.4160i 0.0278289 0.0160670i
\(836\) −11.7605 + 6.78993i −0.0140676 + 0.00812192i
\(837\) −2.31261 4.00556i −0.00276297 0.00478561i
\(838\) −188.985 + 109.111i −0.225519 + 0.130204i
\(839\) −134.005 232.103i −0.159720 0.276643i 0.775048 0.631903i \(-0.217726\pi\)
−0.934768 + 0.355260i \(0.884392\pi\)
\(840\) 3.82534 + 6.62568i 0.00455398 + 0.00788772i
\(841\) −25.0890 + 43.4554i −0.0298324 + 0.0516712i
\(842\) 108.162 62.4476i 0.128459 0.0741658i
\(843\) −57.0045 + 98.7348i −0.0676211 + 0.117123i
\(844\) 26.9066 0.0318798
\(845\) −15.1738 + 8.76059i −0.0179571 + 0.0103676i
\(846\) 265.110i 0.313369i
\(847\) 196.690i 0.232219i
\(848\) −904.509 522.219i −1.06664 0.615824i
\(849\) 903.856i 1.06461i
\(850\) 302.303 174.534i 0.355650 0.205335i
\(851\) 131.091 + 227.057i 0.154044 + 0.266812i
\(852\) −31.7801 18.3482i −0.0373006 0.0215355i
\(853\) 705.717 1222.34i 0.827335 1.43299i −0.0727869 0.997348i \(-0.523189\pi\)
0.900122 0.435638i \(-0.143477\pi\)
\(854\) −487.718 281.584i −0.571098 0.329724i
\(855\) 1.70808 + 0.986163i 0.00199776 + 0.00115341i
\(856\) 204.773i 0.239221i
\(857\) 838.727i 0.978678i −0.872094 0.489339i \(-0.837238\pi\)
0.872094 0.489339i \(-0.162762\pi\)
\(858\) 73.9328 128.055i 0.0861688 0.149249i
\(859\) 239.724 + 415.213i 0.279073 + 0.483368i 0.971155 0.238451i \(-0.0766396\pi\)
−0.692082 + 0.721819i \(0.743306\pi\)
\(860\) 0.0701074 + 0.121430i 8.15202e−5 + 0.000141197i
\(861\) −491.010 283.485i −0.570279 0.329251i
\(862\) 699.367i 0.811330i
\(863\) 490.391 0.568239 0.284120 0.958789i \(-0.408299\pi\)
0.284120 + 0.958789i \(0.408299\pi\)
\(864\) −11.3404 19.6421i −0.0131254 0.0227339i
\(865\) −21.7761 12.5725i −0.0251747 0.0145346i
\(866\) 1144.79 1.32193
\(867\) 364.989 210.726i 0.420979 0.243052i
\(868\) 1.17624 0.00135511
\(869\) 421.500 730.059i 0.485040 0.840113i
\(870\) 12.6738i 0.0145676i
\(871\) −303.783 55.0405i −0.348775 0.0631923i
\(872\) −488.493 −0.560198
\(873\) −173.513 100.178i −0.198755 0.114751i
\(874\) 413.806i 0.473462i
\(875\) 14.3301 + 24.8205i 0.0163773 + 0.0283663i
\(876\) 16.4365i 0.0187631i
\(877\) −580.708 + 1005.82i −0.662152 + 1.14688i 0.317897 + 0.948125i \(0.397023\pi\)
−0.980049 + 0.198756i \(0.936310\pi\)
\(878\) −390.248 + 225.310i −0.444474 + 0.256617i
\(879\) 745.746i 0.848403i
\(880\) 18.0854 0.0205516
\(881\) −746.188 + 1292.44i −0.846978 + 1.46701i 0.0369135 + 0.999318i \(0.488247\pi\)
−0.883892 + 0.467691i \(0.845086\pi\)
\(882\) −137.584 + 79.4340i −0.155991 + 0.0900612i
\(883\) 56.3661 32.5430i 0.0638348 0.0368550i −0.467743 0.883865i \(-0.654933\pi\)
0.531578 + 0.847010i \(0.321599\pi\)
\(884\) −7.37000 4.25507i −0.00833710 0.00481343i
\(885\) 9.32665 0.0105386
\(886\) 1714.64 1.93526
\(887\) 284.127 492.122i 0.320323 0.554816i −0.660232 0.751062i \(-0.729542\pi\)
0.980555 + 0.196246i \(0.0628752\pi\)
\(888\) 48.4505 83.9188i 0.0545614 0.0945032i
\(889\) −522.445 301.634i −0.587677 0.339296i
\(890\) −0.691038 + 1.19691i −0.000776447 + 0.00134485i
\(891\) −69.8549 + 40.3307i −0.0784005 + 0.0452646i
\(892\) −44.6300 77.3014i −0.0500336 0.0866607i
\(893\) 237.027 0.265428
\(894\) −82.7386 + 143.307i −0.0925488 + 0.160299i
\(895\) −7.01565 −0.00783871
\(896\) −674.698 −0.753011
\(897\) 144.071 + 249.538i 0.160614 + 0.278192i
\(898\) 398.649i 0.443929i
\(899\) −23.0125 13.2863i −0.0255978 0.0147789i
\(900\) −10.2420 17.7397i −0.0113800 0.0197108i
\(901\) 359.194 + 207.381i 0.398661 + 0.230167i
\(902\) −1086.14 + 627.085i −1.20415 + 0.695217i
\(903\) −31.3869 + 18.1212i −0.0347584 + 0.0200678i
\(904\) 4.85652 + 8.41174i 0.00537226 + 0.00930503i
\(905\) 0.943816 0.544912i 0.00104289 0.000602113i
\(906\) −3.70632 6.41954i −0.00409086 0.00708558i
\(907\) −238.893 413.775i −0.263388 0.456202i 0.703752 0.710446i \(-0.251507\pi\)
−0.967140 + 0.254244i \(0.918173\pi\)
\(908\) −7.92064 + 13.7190i −0.00872317 + 0.0151090i
\(909\) −43.5051 + 25.1177i −0.0478604 + 0.0276322i
\(910\) 2.73077 4.72983i 0.00300084 0.00519761i
\(911\) −431.123 −0.473241 −0.236621 0.971602i \(-0.576040\pi\)
−0.236621 + 0.971602i \(0.576040\pi\)
\(912\) −141.541 + 81.7189i −0.155199 + 0.0896040i
\(913\) 982.682i 1.07632i
\(914\) 661.702i 0.723963i
\(915\) 10.0205 + 5.78531i 0.0109513 + 0.00632274i
\(916\) 68.7525i 0.0750573i
\(917\) 48.8304 28.1922i 0.0532501 0.0307440i
\(918\) 36.2967 + 62.8678i 0.0395389 + 0.0684834i
\(919\) 1020.62 + 589.257i 1.11058 + 0.641193i 0.938979 0.343973i \(-0.111773\pi\)
0.171600 + 0.985167i \(0.445106\pi\)
\(920\) −16.4895 + 28.5606i −0.0179233 + 0.0310441i
\(921\) 734.906 + 424.298i 0.797944 + 0.460693i
\(922\) −524.408 302.767i −0.568772 0.328381i
\(923\) 357.246i 0.387049i
\(924\) 20.5130i 0.0222002i
\(925\) 90.7248 157.140i 0.0980808 0.169881i
\(926\) 477.501 + 827.056i 0.515660 + 0.893149i
\(927\) −58.6762 101.630i −0.0632969 0.109633i
\(928\) −112.846 65.1519i −0.121602 0.0702068i
\(929\) 814.595i 0.876851i 0.898767 + 0.438426i \(0.144464\pi\)
−0.898767 + 0.438426i \(0.855536\pi\)
\(930\) −0.377899 −0.000406343
\(931\) 71.0194 + 123.009i 0.0762830 + 0.132126i
\(932\) 55.3174 + 31.9375i 0.0593534 + 0.0342677i
\(933\) −123.188 −0.132034
\(934\) −38.4764 + 22.2144i −0.0411953 + 0.0237841i
\(935\) −7.18197 −0.00768125
\(936\) 53.2478 92.2279i 0.0568887 0.0985341i
\(937\) 1794.75i 1.91542i −0.287733 0.957711i \(-0.592902\pi\)
0.287733 0.957711i \(-0.407098\pi\)
\(938\) −630.414 + 226.098i −0.672084 + 0.241043i
\(939\) 364.712 0.388405
\(940\) 1.19961 + 0.692595i 0.00127618 + 0.000736803i
\(941\) 881.908i 0.937203i −0.883410 0.468601i \(-0.844758\pi\)
0.883410 0.468601i \(-0.155242\pi\)
\(942\) −82.5708 143.017i −0.0876547 0.151822i
\(943\) 2443.97i 2.59170i
\(944\) −386.429 + 669.314i −0.409353 + 0.709019i
\(945\) −2.58015 + 1.48965i −0.00273031 + 0.00157635i
\(946\) 80.1704i 0.0847467i
\(947\) 1091.61 1.15270 0.576350 0.817203i \(-0.304476\pi\)
0.576350 + 0.817203i \(0.304476\pi\)
\(948\) −22.2604 + 38.5562i −0.0234814 + 0.0406711i
\(949\) 138.575 80.0060i 0.146022 0.0843056i
\(950\) −248.016 + 143.192i −0.261069 + 0.150728i
\(951\) −107.752 62.2108i −0.113304 0.0654162i
\(952\) 251.762 0.264455
\(953\) 369.818 0.388057 0.194029 0.980996i \(-0.437845\pi\)
0.194029 + 0.980996i \(0.437845\pi\)
\(954\) 190.298 329.606i 0.199474 0.345499i
\(955\) −21.2358 + 36.7816i −0.0222365 + 0.0385147i
\(956\) −66.9179 38.6351i −0.0699978 0.0404133i
\(957\) −231.706 + 401.326i −0.242117 + 0.419358i
\(958\) −74.1335 + 42.8010i −0.0773836 + 0.0446774i
\(959\) 195.814 + 339.160i 0.204186 + 0.353660i
\(960\) 12.1275 0.0126328
\(961\) −480.104 + 831.564i −0.499588 + 0.865311i
\(962\) −69.1741 −0.0719065
\(963\) −79.7419 −0.0828058
\(964\) −31.1940 54.0296i −0.0323589 0.0560473i
\(965\) 25.5544i 0.0264812i
\(966\) 541.330 + 312.537i 0.560383 + 0.323537i
\(967\) 528.820 + 915.944i 0.546867 + 0.947201i 0.998487 + 0.0549909i \(0.0175130\pi\)
−0.451620 + 0.892210i \(0.649154\pi\)
\(968\) −271.377 156.680i −0.280348 0.161859i
\(969\) 56.2081 32.4518i 0.0580063 0.0334900i
\(970\) −14.1767 + 8.18493i −0.0146152 + 0.00843807i
\(971\) 725.593 + 1256.76i 0.747264 + 1.29430i 0.949130 + 0.314886i \(0.101966\pi\)
−0.201866 + 0.979413i \(0.564700\pi\)
\(972\) 3.68920 2.12996i 0.00379548 0.00219132i
\(973\) −34.7690 60.2217i −0.0357338 0.0618928i
\(974\) 716.663 + 1241.30i 0.735793 + 1.27443i
\(975\) 99.7078 172.699i 0.102264 0.177127i
\(976\) −830.349 + 479.402i −0.850768 + 0.491191i
\(977\) 91.7030 158.834i 0.0938618 0.162573i −0.815271 0.579079i \(-0.803412\pi\)
0.909133 + 0.416506i \(0.136745\pi\)
\(978\) 616.416 0.630282
\(979\) −43.7644 + 25.2674i −0.0447031 + 0.0258094i
\(980\) 0.830077i 0.000847017i
\(981\) 190.227i 0.193911i
\(982\) 515.623 + 297.695i 0.525074 + 0.303152i
\(983\) 794.947i 0.808695i 0.914606 + 0.404347i \(0.132501\pi\)
−0.914606 + 0.404347i \(0.867499\pi\)
\(984\) −782.261 + 451.639i −0.794981 + 0.458983i
\(985\) −7.98936 13.8380i −0.00811102 0.0140487i
\(986\) 361.184 + 208.530i 0.366312 + 0.211490i
\(987\) −179.020 + 310.072i −0.181378 + 0.314156i
\(988\) 6.04651 + 3.49096i 0.00611995 + 0.00353336i
\(989\) −135.296 78.1130i −0.136801 0.0789818i
\(990\) 6.59037i 0.00665694i
\(991\) 1735.88i 1.75164i −0.482635 0.875821i \(-0.660320\pi\)
0.482635 0.875821i \(-0.339680\pi\)
\(992\) 1.94265 3.36477i 0.00195832 0.00339191i
\(993\) 321.162 + 556.269i 0.323426 + 0.560191i
\(994\) −387.491 671.154i −0.389830 0.675206i
\(995\) −32.2266 18.6060i −0.0323886 0.0186995i
\(996\) 51.8978i 0.0521062i
\(997\) −902.846 −0.905562 −0.452781 0.891622i \(-0.649568\pi\)
−0.452781 + 0.891622i \(0.649568\pi\)
\(998\) −273.894 474.398i −0.274443 0.475349i
\(999\) 32.6793 + 18.8674i 0.0327120 + 0.0188863i
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.172.4 yes 24
67.30 odd 6 inner 201.3.h.b.97.4 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.3.h.b.97.4 24 67.30 odd 6 inner
201.3.h.b.172.4 yes 24 1.1 even 1 trivial