Properties

Label 201.3.h.b.97.4
Level $201$
Weight $3$
Character 201.97
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 97.4
Character \(\chi\) \(=\) 201.97
Dual form 201.3.h.b.172.4

$q$-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 \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).

\(n\) \(68\) \(136\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

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 −0.875614 0.483012i \(-0.839543\pi\)
−0.0195059 + 0.999810i \(0.506209\pi\)
\(3\) 1.73205i 0.577350i
\(4\) 0.136637 0.236663i 0.0341593 0.0591656i
\(5\) 0.118573i 0.0237146i 0.999930 + 0.0118573i \(0.00377438\pi\)
−0.999930 + 0.0118573i \(0.996226\pi\)
\(6\) −1.79024 3.10078i −0.298373 0.516797i
\(7\) −4.18772 2.41778i −0.598245 0.345397i 0.170106 0.985426i \(-0.445589\pi\)
−0.768351 + 0.640029i \(0.778922\pi\)
\(8\) 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 0.103827 0.994595i \(-0.466891\pi\)
−0.809431 + 0.587214i \(0.800225\pi\)
\(12\) 0.409912 + 0.236663i 0.0341593 + 0.0197219i
\(13\) 3.99056 2.30395i 0.306966 0.177227i −0.338602 0.940930i \(-0.609954\pi\)
0.645568 + 0.763703i \(0.276621\pi\)
\(14\) 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 0.749358 0.662165i \(-0.230362\pi\)
−0.948131 + 0.317881i \(0.897029\pi\)
\(18\) 5.37072 3.10078i 0.298373 0.172266i
\(19\) 2.77232 + 4.80179i 0.145911 + 0.252726i 0.929713 0.368286i \(-0.120055\pi\)
−0.783801 + 0.621012i \(0.786722\pi\)
\(20\) 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 −0.929090 0.369854i \(-0.879408\pi\)
0.144242 0.989542i \(-0.453926\pi\)
\(24\) 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 −0.485154 0.874428i \(-0.661237\pi\)
0.999854 0.0170582i \(-0.00543006\pi\)
\(30\) 0.367669 0.212274i 0.0122556 0.00707579i
\(31\) −0.770869 0.445062i −0.0248668 0.0143568i 0.487515 0.873115i \(-0.337903\pi\)
−0.512382 + 0.858758i \(0.671237\pi\)
\(32\) −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 0.910913 0.412598i \(-0.135379\pi\)
−0.812777 + 0.582575i \(0.802045\pi\)
\(38\) −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 −0.432769 0.901505i \(-0.642464\pi\)
−0.997111 + 0.0759630i \(0.975797\pi\)
\(42\) 17.3136i 0.412229i
\(43\) 4.32723i 0.100633i −0.998733 0.0503166i \(-0.983977\pi\)
0.998733 0.0503166i \(-0.0160230\pi\)
\(44\) −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 −0.543899 0.839150i \(-0.683053\pi\)
0.998675 + 0.0514555i \(0.0163860\pi\)
\(48\) −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 \(0.196546\pi\)
−0.815348 + 0.578972i \(0.803454\pi\)
\(54\) 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 −0.843421 0.537253i \(-0.819462\pi\)
0.0435647 + 0.999051i \(0.486129\pi\)
\(62\) 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 0.452565 + 0.891731i \(0.350509\pi\)
−0.998545 + 0.0539331i \(0.982824\pi\)
\(72\) 23.1115i 0.320994i
\(73\) 17.3628 + 30.0733i 0.237847 + 0.411962i 0.960096 0.279670i \(-0.0902251\pi\)
−0.722250 + 0.691633i \(0.756892\pi\)
\(74\) −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 −0.113811 0.993502i \(-0.536306\pi\)
−0.917304 + 0.398188i \(0.869639\pi\)
\(80\) −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 −0.980481 0.196614i \(-0.937005\pi\)
0.319968 0.947428i \(-0.396328\pi\)
\(84\) −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 −0.171307 0.985218i \(-0.554799\pi\)
0.767570 + 0.640965i \(0.221466\pi\)
\(98\) 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 0.570070 0.821596i \(-0.306916\pi\)
−0.426489 + 0.904493i \(0.640250\pi\)
\(102\) −12.0989 + 20.9559i −0.118617 + 0.205450i
\(103\) 19.5587 33.8767i 0.189891 0.328900i −0.755323 0.655353i \(-0.772520\pi\)
0.945214 + 0.326453i \(0.105853\pi\)
\(104\) −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 \(-0.906056\pi\)
0.956764 0.290867i \(-0.0939436\pi\)
\(110\) 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 0.504824 0.863223i \(-0.331558\pi\)
−0.495161 + 0.868801i \(0.664891\pi\)
\(114\) 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 −0.508781 0.860896i \(-0.669904\pi\)
0.999948 + 0.0101688i \(0.00323689\pi\)
\(128\) 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 \(0.0955132\pi\)
−0.955318 + 0.295581i \(0.904487\pi\)
\(138\) −64.6330 + 111.948i −0.468355 + 0.811215i
\(139\) 14.3806i 0.103457i −0.998661 0.0517286i \(-0.983527\pi\)
0.998661 0.0517286i \(-0.0164731\pi\)
\(140\) −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 0.862577 0.505925i \(-0.168849\pi\)
−0.869433 + 0.494051i \(0.835515\pi\)
\(152\) 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 0.783188 0.621785i \(-0.213592\pi\)
−0.930076 + 0.367368i \(0.880259\pi\)
\(158\) 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 0.471365 + 0.881938i \(0.343762\pi\)
−0.999463 + 0.0327552i \(0.989572\pi\)
\(164\) −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 −0.298209 0.954501i \(-0.596389\pi\)
0.975726 0.218994i \(-0.0702774\pi\)
\(168\) −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 0.990749 + 0.135706i \(0.0433302\pi\)
−0.377850 + 0.925867i \(0.623336\pi\)
\(174\) −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 \(0.0528503\pi\)
−0.986248 + 0.165272i \(0.947150\pi\)
\(180\) −0.0841852 0.0486043i −0.000467696 0.000270024i
\(181\) 4.59559 7.95980i 0.0253900 0.0439768i −0.853051 0.521827i \(-0.825251\pi\)
0.878441 + 0.477850i \(0.158584\pi\)
\(182\) 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 −0.638289 + 0.769797i \(0.720357\pi\)
−0.985808 + 0.167876i \(0.946309\pi\)
\(192\) 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 0.766049 0.642782i \(-0.222220\pi\)
−0.173641 + 0.984809i \(0.555553\pi\)
\(198\) −55.5808 −0.280711
\(199\) 156.917 + 271.788i 0.788526 + 1.36577i 0.926870 + 0.375383i \(0.122489\pi\)
−0.138344 + 0.990384i \(0.544178\pi\)
\(200\) 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 0.958782 0.284142i \(-0.0917086\pi\)
−0.725465 + 0.688259i \(0.758375\pi\)
\(212\) 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 −0.795095 0.606485i \(-0.792579\pi\)
0.922779 + 0.385330i \(0.125912\pi\)
\(228\) 2.62441i 0.0115106i
\(229\) 217.881 125.794i 0.951447 0.549318i 0.0579168 0.998321i \(-0.481554\pi\)
0.893530 + 0.449003i \(0.148221\pi\)
\(230\) −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 0.866941 0.498412i \(-0.166083\pi\)
0.00183311 + 0.999998i \(0.499417\pi\)
\(234\) 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 −0.109153 0.994025i \(-0.534814\pi\)
−0.915427 + 0.402484i \(0.868147\pi\)
\(240\) −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 −0.791820 0.610755i \(-0.790866\pi\)
0.133019 + 0.991113i \(0.457533\pi\)
\(252\) 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 −0.445489 0.895287i \(-0.646970\pi\)
0.998086 0.0618389i \(-0.0196965\pi\)
\(258\) −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 \(0.0952457\pi\)
−0.955566 + 0.294778i \(0.904754\pi\)
\(272\) 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 −0.597990 0.801503i \(-0.704034\pi\)
0.395127 + 0.918626i \(0.370701\pi\)
\(282\) −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 −0.920953 0.389674i \(-0.872588\pi\)
0.123009 0.992406i \(-0.460746\pi\)
\(308\) 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 \(0.0364769\pi\)
−0.993441 + 0.114345i \(0.963523\pi\)
\(312\) 53.2478 30.7426i 0.170666 0.0985341i
\(313\) 210.567i 0.672737i −0.941730 0.336369i \(-0.890801\pi\)
0.941730 0.336369i \(-0.109199\pi\)
\(314\) 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 0.917101 0.398656i \(-0.130523\pi\)
−0.803796 + 0.594904i \(0.797190\pi\)
\(318\) 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 −0.0709576 0.997479i \(-0.522606\pi\)
−0.899321 + 0.437289i \(0.855939\pi\)
\(332\) −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 0.301543 0.953452i \(-0.402498\pi\)
0.976486 + 0.215582i \(0.0691648\pi\)
\(338\) 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 0.358352 0.933587i \(-0.383339\pi\)
−0.629334 + 0.777135i \(0.716672\pi\)
\(348\) 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 −0.938076 0.346431i \(-0.887394\pi\)
−0.169020 + 0.985613i \(0.554060\pi\)
\(354\) 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 0.231609 0.972809i \(-0.425601\pi\)
−0.726673 + 0.686984i \(0.758934\pi\)
\(368\) 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 0.433827 0.900996i \(-0.357163\pi\)
−0.563372 + 0.826203i \(0.690496\pi\)
\(374\) −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 0.478120 0.878294i \(-0.341318\pi\)
0.999685 + 0.0250828i \(0.00798493\pi\)
\(380\) 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 −0.578130 0.815944i \(-0.696218\pi\)
0.417563 + 0.908648i \(0.362884\pi\)
\(384\) 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 0.991634 + 0.129080i \(0.0412025\pi\)
−0.384030 + 0.923321i \(0.625464\pi\)
\(390\) 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 \(-0.934318\pi\)
0.978786 0.204886i \(-0.0656825\pi\)
\(402\) 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 0.369392 0.929274i \(-0.379566\pi\)
−0.620078 + 0.784540i \(0.712899\pi\)
\(410\) 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 0.922112 0.386922i \(-0.126462\pi\)
−0.796141 + 0.605112i \(0.793129\pi\)
\(420\) 0.235029 0.135694i 0.000559593 0.000323081i
\(421\) −30.2089 52.3234i −0.0717552 0.124284i 0.827915 0.560853i \(-0.189527\pi\)
−0.899671 + 0.436569i \(0.856193\pi\)
\(422\) −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 −0.992776 0.119983i \(-0.961716\pi\)
0.600296 + 0.799778i \(0.295049\pi\)
\(432\) 76.5829 44.2151i 0.177275 0.102350i
\(433\) −479.598 276.896i −1.10762 0.639483i −0.169405 0.985546i \(-0.554185\pi\)
−0.938211 + 0.346064i \(0.887518\pi\)
\(434\) −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 0.963048 0.269331i \(-0.0868025\pi\)
−0.714771 + 0.699358i \(0.753469\pi\)
\(440\) −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 −0.986516 0.163664i \(-0.947669\pi\)
−0.634996 0.772516i \(-0.718998\pi\)
\(444\) 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 −0.953195 0.302355i \(-0.902227\pi\)
0.738445 + 0.674314i \(0.235560\pi\)
\(450\) 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 −0.636071 0.771630i \(-0.719441\pi\)
0.986287 + 0.165038i \(0.0527748\pi\)
\(458\) −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 −0.865389 0.501100i \(-0.832929\pi\)
0.00127068 + 0.999999i \(0.499596\pi\)
\(464\) 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 0.877302 0.479939i \(-0.159341\pi\)
−0.854291 + 0.519796i \(0.826008\pi\)
\(468\) 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 0.886829 0.462098i \(-0.152903\pi\)
−0.843603 + 0.536967i \(0.819570\pi\)
\(480\) 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 −0.967656 0.252274i \(-0.918822\pi\)
−0.265352 + 0.964152i \(0.585488\pi\)
\(488\) 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 −0.252103 0.967700i \(-0.581122\pi\)
0.712002 + 0.702178i \(0.247789\pi\)
\(500\) 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 −0.147839 0.989011i \(-0.547232\pi\)
−0.930429 + 0.366473i \(0.880565\pi\)
\(504\) 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 \(0.134992\pi\)
−0.911413 + 0.411492i \(0.865008\pi\)
\(522\) 185.133i 0.354661i
\(523\) 407.049 + 705.030i 0.778297 + 1.34805i 0.932922 + 0.360077i \(0.117250\pi\)
−0.154625 + 0.987973i \(0.549417\pi\)
\(524\) −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 \(0.119708\pi\)
−0.930114 + 0.367271i \(0.880292\pi\)
\(542\) −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 0.0506337 0.998717i \(-0.483876\pi\)
−0.839598 + 0.543209i \(0.817209\pi\)
\(548\) 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 −0.178613 0.983919i \(-0.557161\pi\)
0.941406 0.337276i \(-0.109506\pi\)
\(558\) −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 \(-0.898977\pi\)
0.950059 0.312071i \(-0.101023\pi\)
\(564\) 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 −0.713214 0.700946i \(-0.752761\pi\)
0.963644 + 0.267189i \(0.0860946\pi\)
\(570\) 2.03859 + 1.17698i 0.00357647 + 0.00206487i
\(571\) 83.3463 144.360i 0.145965 0.252820i −0.783767 0.621055i \(-0.786704\pi\)
0.929733 + 0.368235i \(0.120038\pi\)
\(572\) −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 −0.0875787 0.996158i \(-0.527913\pi\)
−0.906487 + 0.422233i \(0.861246\pi\)
\(578\) 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 0.160474 0.987040i \(-0.448698\pi\)
0.935039 + 0.354546i \(0.115364\pi\)
\(588\) 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 −0.820113 0.572202i \(-0.806089\pi\)
0.0854847 + 0.996339i \(0.472756\pi\)
\(594\) 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 0.994190 0.107636i \(-0.0343282\pi\)
0.403879 + 0.914812i \(0.367662\pi\)
\(600\) 333.399 0.555665
\(601\) 149.764 + 259.399i 0.249192 + 0.431613i 0.963302 0.268421i \(-0.0865017\pi\)
−0.714110 + 0.700033i \(0.753168\pi\)
\(602\) 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 −0.736397 0.676549i \(-0.763475\pi\)
0.954108 + 0.299464i \(0.0968079\pi\)
\(608\) 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 0.855176 0.518338i \(-0.173449\pi\)
−0.876482 + 0.481435i \(0.840116\pi\)
\(614\) 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 −0.998736 0.0502597i \(-0.983995\pi\)
0.455842 0.890061i \(-0.349338\pi\)
\(620\) −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 −0.525144 0.851013i \(-0.675989\pi\)
0.474427 + 0.880295i \(0.342655\pi\)
\(632\) −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 0.806173 0.591680i \(-0.201535\pi\)
−0.109324 + 0.994006i \(0.534868\pi\)
\(642\) −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 0.476979 0.878915i \(-0.341732\pi\)
0.999652 + 0.0263812i \(0.00839837\pi\)
\(648\) 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 −0.552095 0.833781i \(-0.686171\pi\)
0.446028 + 0.895019i \(0.352838\pi\)
\(654\) −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 −0.0433956 0.999058i \(-0.513818\pi\)
0.886907 0.461947i \(-0.152849\pi\)
\(660\) 0.435611 0.251500i 0.000660016 0.000381061i
\(661\) 836.224i 1.26509i −0.774524 0.632544i \(-0.782011\pi\)
0.774524 0.632544i \(-0.217989\pi\)
\(662\) 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 \(-0.902855\pi\)
0.953790 0.300475i \(-0.0971451\pi\)
\(674\) −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 0.997536 0.0701605i \(-0.0223511\pi\)
0.438007 + 0.898972i \(0.355684\pi\)
\(678\) 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 0.255829 0.966722i \(-0.417652\pi\)
0.965120 + 0.261807i \(0.0843182\pi\)
\(684\) −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 −0.0493370 0.998782i \(-0.515711\pi\)
0.889639 0.456664i \(-0.150956\pi\)
\(692\) 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 0.313173 0.949696i \(-0.398608\pi\)
−0.665874 + 0.746064i \(0.731941\pi\)
\(702\) 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 −0.765423 0.643528i \(-0.777470\pi\)
−0.174600 0.984639i \(-0.555863\pi\)
\(710\) 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 0.752039 0.659118i \(-0.229070\pi\)
−0.946833 + 0.321726i \(0.895737\pi\)
\(720\) 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 −0.975307 0.220852i \(-0.929116\pi\)
−0.296391 + 0.955067i \(0.595783\pi\)
\(728\) 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 −0.0506174 0.998718i \(-0.516119\pi\)
−0.890224 + 0.455523i \(0.849452\pi\)
\(734\) 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 −0.0417595 0.999128i \(-0.513296\pi\)
0.844390 + 0.535729i \(0.179963\pi\)
\(740\) 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 0.982075 0.188491i \(-0.0603597\pi\)
−0.654276 + 0.756256i \(0.727026\pi\)
\(744\) −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 0.0753346 0.997158i \(-0.475998\pi\)
−0.825897 + 0.563821i \(0.809331\pi\)
\(758\) −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 −0.0590312 0.998256i \(-0.518801\pi\)
−0.894031 + 0.448006i \(0.852134\pi\)
\(770\) 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 −0.447886 0.894091i \(-0.647823\pi\)
0.998248 0.0591652i \(-0.0188439\pi\)
\(774\) −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 −0.700373 0.713777i \(-0.746983\pi\)
0.267962 + 0.963429i \(0.413650\pi\)
\(788\) 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 0.125239 + 0.992127i \(0.460030\pi\)
−0.921826 + 0.387603i \(0.873303\pi\)
\(798\) −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 \(0.237458\pi\)
−0.734412 + 0.678704i \(0.762542\pi\)
\(810\) −1.10301 1.91046i −0.00136174 0.00235860i
\(811\) −190.084 109.745i −0.234382 0.135321i 0.378210 0.925720i \(-0.376540\pi\)
−0.612592 + 0.790399i \(0.709873\pi\)
\(812\) 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 0.912197 + 0.409752i \(0.134385\pi\)
−0.101243 + 0.994862i \(0.532282\pi\)
\(822\) 251.130 144.990i 0.305511 0.176387i
\(823\) 743.262 + 1287.37i 0.903113 + 1.56424i 0.823430 + 0.567417i \(0.192057\pi\)
0.0796827 + 0.996820i \(0.474609\pi\)
\(824\) −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 0.745612 0.666380i \(-0.232157\pi\)
−0.949908 + 0.312529i \(0.898824\pi\)
\(828\) 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 −0.934768 0.355260i \(-0.884392\pi\)
0.775048 + 0.631903i \(0.217726\pi\)
\(840\) 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 0.900122 + 0.435638i \(0.143477\pi\)
−0.0727869 + 0.997348i \(0.523189\pi\)
\(854\) −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 \(0.162762\pi\)
−0.872094 + 0.489339i \(0.837238\pi\)
\(858\) 73.9328 + 128.055i 0.0861688 + 0.149249i
\(859\) 239.724 415.213i 0.279073 0.483368i −0.692082 0.721819i \(-0.743306\pi\)
0.971155 + 0.238451i \(0.0766396\pi\)
\(860\) 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 −0.980049 0.198756i \(-0.936310\pi\)
0.317897 0.948125i \(-0.397023\pi\)
\(878\) −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 −0.883892 0.467691i \(-0.845086\pi\)
0.0369135 0.999318i \(-0.488247\pi\)
\(882\) −137.584 79.4340i −0.155991 0.0900612i
\(883\) 56.3661 + 32.5430i 0.0638348 + 0.0368550i 0.531578 0.847010i \(-0.321599\pi\)
−0.467743 + 0.883865i \(0.654933\pi\)
\(884\) −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 0.980555 0.196246i \(-0.0628752\pi\)
−0.660232 + 0.751062i \(0.729542\pi\)
\(888\) 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 −0.967140 0.254244i \(-0.918173\pi\)
0.703752 + 0.710446i \(0.251507\pi\)
\(908\) −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 0.171600 0.985167i \(-0.445106\pi\)
0.938979 + 0.343973i \(0.111773\pi\)
\(920\) −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 \(-0.855536\pi\)
0.898767 0.438426i \(-0.144464\pi\)
\(930\) −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 \(0.407098\pi\)
−0.287733 + 0.957711i \(0.592902\pi\)
\(938\) −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 \(0.155242\pi\)
−0.883410 + 0.468601i \(0.844758\pi\)
\(942\) −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 −0.451620 0.892210i \(-0.649154\pi\)
0.998487 0.0549909i \(-0.0175130\pi\)
\(968\) −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 −0.201866 0.979413i \(-0.564700\pi\)
0.949130 0.314886i \(-0.101966\pi\)
\(972\) 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 0.909133 0.416506i \(-0.136745\pi\)
−0.815271 + 0.579079i \(0.803412\pi\)
\(978\) 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 \(-0.867499\pi\)
0.914606 0.404347i \(-0.132501\pi\)
\(984\) −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 \(0.339680\pi\)
−0.482635 + 0.875821i \(0.660320\pi\)
\(992\) 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.97.4 24
67.38 odd 6 inner 201.3.h.b.172.4 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.3.h.b.97.4 24 1.1 even 1 trivial
201.3.h.b.172.4 yes 24 67.38 odd 6 inner