Properties

Label 441.2.g.e.79.3
Level $441$
Weight $2$
Character 441.79
Analytic conductor $3.521$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(67,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.3
Root \(0.500000 - 2.05195i\) of defining polynomial
Character \(\chi\) \(=\) 441.79
Dual form 441.2.g.e.67.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.23025 + 2.13086i) q^{2} +(0.933463 + 1.45899i) q^{3} +(-2.02704 + 3.51094i) q^{4} -2.59358 q^{5} +(-1.96050 + 3.78400i) q^{6} -5.05408 q^{8} +(-1.25729 + 2.72382i) q^{9} +O(q^{10})\) \(q+(1.23025 + 2.13086i) q^{2} +(0.933463 + 1.45899i) q^{3} +(-2.02704 + 3.51094i) q^{4} -2.59358 q^{5} +(-1.96050 + 3.78400i) q^{6} -5.05408 q^{8} +(-1.25729 + 2.72382i) q^{9} +(-3.19076 - 5.52655i) q^{10} +4.51459 q^{11} +(-7.01459 + 0.319901i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-2.42101 - 3.78400i) q^{15} +(-2.16372 - 3.74766i) q^{16} +(0.472958 + 0.819187i) q^{17} +(-7.35087 + 0.671871i) q^{18} +(2.02704 - 3.51094i) q^{19} +(5.25729 - 9.10590i) q^{20} +(5.55408 + 9.61996i) q^{22} -0.273346 q^{23} +(-4.71780 - 7.37385i) q^{24} +1.72665 q^{25} +(1.23025 - 2.13086i) q^{26} +(-5.14766 + 0.708209i) q^{27} +(-1.23025 + 2.13086i) q^{29} +(5.08472 - 9.81411i) q^{30} +(-1.16372 + 2.01561i) q^{31} +(0.269748 - 0.467216i) q^{32} +(4.21420 + 6.58673i) q^{33} +(-1.16372 + 2.01561i) q^{34} +(-7.01459 - 9.93559i) q^{36} +(-0.890369 + 1.54216i) q^{37} +9.97509 q^{38} +(0.796790 - 1.53790i) q^{39} +13.1082 q^{40} +(3.20321 + 5.54812i) q^{41} +(5.21780 - 9.03749i) q^{43} +(-9.15126 + 15.8505i) q^{44} +(3.26089 - 7.06445i) q^{45} +(-0.336285 - 0.582462i) q^{46} +(6.08113 + 10.5328i) q^{47} +(3.44805 - 6.65514i) q^{48} +(2.12422 + 3.67926i) q^{50} +(-0.753696 + 1.45472i) q^{51} +4.05408 q^{52} +(3.13667 + 5.43288i) q^{53} +(-7.84202 - 10.0977i) q^{54} -11.7089 q^{55} +(7.01459 - 0.319901i) q^{57} -6.05408 q^{58} +(1.36333 - 2.36135i) q^{59} +(18.1929 - 0.829688i) q^{60} +(1.13667 + 1.96878i) q^{61} -5.72665 q^{62} -7.32743 q^{64} +(1.29679 + 2.24611i) q^{65} +(-8.85087 + 17.0832i) q^{66} +(7.90856 - 13.6980i) q^{67} -3.83482 q^{68} +(-0.255158 - 0.398809i) q^{69} +3.27335 q^{71} +(6.35447 - 13.7664i) q^{72} +(0.753696 + 1.30544i) q^{73} -4.38151 q^{74} +(1.61177 + 2.51917i) q^{75} +(8.21780 + 14.2336i) q^{76} +(4.25729 - 0.194154i) q^{78} +(-7.35447 - 12.7383i) q^{79} +(5.61177 + 9.71987i) q^{80} +(-5.83842 - 6.84929i) q^{81} +(-7.88151 + 13.6512i) q^{82} +(0.472958 - 0.819187i) q^{83} +(-1.22665 - 2.12463i) q^{85} +25.6768 q^{86} +(-4.25729 + 0.194154i) q^{87} -22.8171 q^{88} +(7.17830 - 12.4332i) q^{89} +(19.0651 - 1.74255i) q^{90} +(0.554084 - 0.959702i) q^{92} +(-4.02704 + 0.183653i) q^{93} +(-14.9626 + 25.9161i) q^{94} +(-5.25729 + 9.10590i) q^{95} +(0.933463 - 0.0425706i) q^{96} +(5.74484 - 9.95036i) q^{97} +(-5.67617 + 12.2969i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + q^{2} + 2 q^{3} - 3 q^{4} - 10 q^{5} + q^{6} - 12 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + q^{2} + 2 q^{3} - 3 q^{4} - 10 q^{5} + q^{6} - 12 q^{8} + 8 q^{9} - 4 q^{11} - 11 q^{12} - 3 q^{13} + 11 q^{15} - 3 q^{16} + 12 q^{17} - 23 q^{18} + 3 q^{19} + 16 q^{20} + 15 q^{22} + 12 q^{25} + q^{26} - 7 q^{27} - q^{29} - 5 q^{30} + 3 q^{31} + 8 q^{32} + 5 q^{33} + 3 q^{34} - 11 q^{36} + 3 q^{37} + 16 q^{38} + 2 q^{39} + 42 q^{40} + 22 q^{41} + 3 q^{43} - 23 q^{44} - 4 q^{45} - 12 q^{46} + 9 q^{47} - 14 q^{48} - 10 q^{50} + 3 q^{51} + 6 q^{52} + 18 q^{53} + 4 q^{54} - 12 q^{55} + 11 q^{57} - 18 q^{58} + 9 q^{59} + 37 q^{60} + 6 q^{61} - 36 q^{62} - 24 q^{64} + 5 q^{65} - 32 q^{66} + 12 q^{68} - 39 q^{69} + 18 q^{71} + 9 q^{72} - 3 q^{73} + 12 q^{74} - 35 q^{75} + 21 q^{76} + 10 q^{78} - 15 q^{79} - 11 q^{80} + 8 q^{81} - 9 q^{82} + 12 q^{83} - 9 q^{85} + 68 q^{86} - 10 q^{87} - 42 q^{88} + 2 q^{89} + 73 q^{90} - 15 q^{92} - 15 q^{93} - 24 q^{94} - 16 q^{95} + 2 q^{96} - 3 q^{97} - 46 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.23025 + 2.13086i 0.869920 + 1.50675i 0.862078 + 0.506776i \(0.169163\pi\)
0.00784213 + 0.999969i \(0.497504\pi\)
\(3\) 0.933463 + 1.45899i 0.538935 + 0.842347i
\(4\) −2.02704 + 3.51094i −1.01352 + 1.75547i
\(5\) −2.59358 −1.15988 −0.579942 0.814658i \(-0.696925\pi\)
−0.579942 + 0.814658i \(0.696925\pi\)
\(6\) −1.96050 + 3.78400i −0.800373 + 1.54481i
\(7\) 0 0
\(8\) −5.05408 −1.78689
\(9\) −1.25729 + 2.72382i −0.419098 + 0.907941i
\(10\) −3.19076 5.52655i −1.00901 1.74765i
\(11\) 4.51459 1.36120 0.680600 0.732655i \(-0.261719\pi\)
0.680600 + 0.732655i \(0.261719\pi\)
\(12\) −7.01459 + 0.319901i −2.02494 + 0.0923474i
\(13\) −0.500000 0.866025i −0.138675 0.240192i 0.788320 0.615265i \(-0.210951\pi\)
−0.926995 + 0.375073i \(0.877618\pi\)
\(14\) 0 0
\(15\) −2.42101 3.78400i −0.625102 0.977025i
\(16\) −2.16372 3.74766i −0.540929 0.936916i
\(17\) 0.472958 + 0.819187i 0.114709 + 0.198682i 0.917663 0.397359i \(-0.130073\pi\)
−0.802954 + 0.596041i \(0.796740\pi\)
\(18\) −7.35087 + 0.671871i −1.73262 + 0.158362i
\(19\) 2.02704 3.51094i 0.465035 0.805465i −0.534168 0.845378i \(-0.679375\pi\)
0.999203 + 0.0399136i \(0.0127083\pi\)
\(20\) 5.25729 9.10590i 1.17557 2.03614i
\(21\) 0 0
\(22\) 5.55408 + 9.61996i 1.18413 + 2.05098i
\(23\) −0.273346 −0.0569966 −0.0284983 0.999594i \(-0.509073\pi\)
−0.0284983 + 0.999594i \(0.509073\pi\)
\(24\) −4.71780 7.37385i −0.963017 1.50518i
\(25\) 1.72665 0.345331
\(26\) 1.23025 2.13086i 0.241272 0.417896i
\(27\) −5.14766 + 0.708209i −0.990668 + 0.136295i
\(28\) 0 0
\(29\) −1.23025 + 2.13086i −0.228452 + 0.395691i −0.957350 0.288932i \(-0.906700\pi\)
0.728897 + 0.684623i \(0.240033\pi\)
\(30\) 5.08472 9.81411i 0.928340 1.79180i
\(31\) −1.16372 + 2.01561i −0.209009 + 0.362015i −0.951403 0.307949i \(-0.900357\pi\)
0.742393 + 0.669964i \(0.233691\pi\)
\(32\) 0.269748 0.467216i 0.0476851 0.0825930i
\(33\) 4.21420 + 6.58673i 0.733598 + 1.14660i
\(34\) −1.16372 + 2.01561i −0.199576 + 0.345675i
\(35\) 0 0
\(36\) −7.01459 9.93559i −1.16910 1.65593i
\(37\) −0.890369 + 1.54216i −0.146376 + 0.253530i −0.929885 0.367849i \(-0.880094\pi\)
0.783510 + 0.621380i \(0.213428\pi\)
\(38\) 9.97509 1.61817
\(39\) 0.796790 1.53790i 0.127588 0.246261i
\(40\) 13.1082 2.07258
\(41\) 3.20321 + 5.54812i 0.500257 + 0.866471i 1.00000 0.000297253i \(9.46187e-5\pi\)
−0.499743 + 0.866174i \(0.666572\pi\)
\(42\) 0 0
\(43\) 5.21780 9.03749i 0.795707 1.37820i −0.126682 0.991943i \(-0.540433\pi\)
0.922389 0.386262i \(-0.126234\pi\)
\(44\) −9.15126 + 15.8505i −1.37960 + 2.38955i
\(45\) 3.26089 7.06445i 0.486105 1.05311i
\(46\) −0.336285 0.582462i −0.0495825 0.0858794i
\(47\) 6.08113 + 10.5328i 0.887023 + 1.53637i 0.843377 + 0.537323i \(0.180564\pi\)
0.0436467 + 0.999047i \(0.486102\pi\)
\(48\) 3.44805 6.65514i 0.497683 0.960587i
\(49\) 0 0
\(50\) 2.12422 + 3.67926i 0.300410 + 0.520326i
\(51\) −0.753696 + 1.45472i −0.105539 + 0.203702i
\(52\) 4.05408 0.562200
\(53\) 3.13667 + 5.43288i 0.430855 + 0.746263i 0.996947 0.0780790i \(-0.0248786\pi\)
−0.566092 + 0.824342i \(0.691545\pi\)
\(54\) −7.84202 10.0977i −1.06716 1.37412i
\(55\) −11.7089 −1.57883
\(56\) 0 0
\(57\) 7.01459 0.319901i 0.929105 0.0423719i
\(58\) −6.05408 −0.794940
\(59\) 1.36333 2.36135i 0.177490 0.307422i −0.763530 0.645772i \(-0.776536\pi\)
0.941020 + 0.338350i \(0.109869\pi\)
\(60\) 18.1929 0.829688i 2.34869 0.107112i
\(61\) 1.13667 + 1.96878i 0.145536 + 0.252076i 0.929573 0.368639i \(-0.120176\pi\)
−0.784037 + 0.620714i \(0.786843\pi\)
\(62\) −5.72665 −0.727286
\(63\) 0 0
\(64\) −7.32743 −0.915929
\(65\) 1.29679 + 2.24611i 0.160847 + 0.278595i
\(66\) −8.85087 + 17.0832i −1.08947 + 2.10280i
\(67\) 7.90856 13.6980i 0.966184 1.67348i 0.259784 0.965667i \(-0.416349\pi\)
0.706400 0.707813i \(-0.250318\pi\)
\(68\) −3.83482 −0.465041
\(69\) −0.255158 0.398809i −0.0307175 0.0480110i
\(70\) 0 0
\(71\) 3.27335 0.388475 0.194237 0.980955i \(-0.437777\pi\)
0.194237 + 0.980955i \(0.437777\pi\)
\(72\) 6.35447 13.7664i 0.748882 1.62239i
\(73\) 0.753696 + 1.30544i 0.0882134 + 0.152790i 0.906756 0.421656i \(-0.138551\pi\)
−0.818543 + 0.574446i \(0.805218\pi\)
\(74\) −4.38151 −0.509341
\(75\) 1.61177 + 2.51917i 0.186111 + 0.290888i
\(76\) 8.21780 + 14.2336i 0.942646 + 1.63271i
\(77\) 0 0
\(78\) 4.25729 0.194154i 0.482044 0.0219836i
\(79\) −7.35447 12.7383i −0.827443 1.43317i −0.900038 0.435811i \(-0.856461\pi\)
0.0725952 0.997361i \(-0.476872\pi\)
\(80\) 5.61177 + 9.71987i 0.627415 + 1.08671i
\(81\) −5.83842 6.84929i −0.648713 0.761033i
\(82\) −7.88151 + 13.6512i −0.870368 + 1.50752i
\(83\) 0.472958 0.819187i 0.0519139 0.0899175i −0.838901 0.544285i \(-0.816801\pi\)
0.890815 + 0.454367i \(0.150135\pi\)
\(84\) 0 0
\(85\) −1.22665 2.12463i −0.133049 0.230448i
\(86\) 25.6768 2.76881
\(87\) −4.25729 + 0.194154i −0.456430 + 0.0208155i
\(88\) −22.8171 −2.43231
\(89\) 7.17830 12.4332i 0.760899 1.31792i −0.181489 0.983393i \(-0.558092\pi\)
0.942388 0.334522i \(-0.108575\pi\)
\(90\) 19.0651 1.74255i 2.00964 0.183681i
\(91\) 0 0
\(92\) 0.554084 0.959702i 0.0577673 0.100056i
\(93\) −4.02704 + 0.183653i −0.417585 + 0.0190440i
\(94\) −14.9626 + 25.9161i −1.54328 + 2.67304i
\(95\) −5.25729 + 9.10590i −0.539387 + 0.934246i
\(96\) 0.933463 0.0425706i 0.0952711 0.00434485i
\(97\) 5.74484 9.95036i 0.583300 1.01031i −0.411785 0.911281i \(-0.635094\pi\)
0.995085 0.0990246i \(-0.0315722\pi\)
\(98\) 0 0
\(99\) −5.67617 + 12.2969i −0.570476 + 1.23589i
\(100\) −3.50000 + 6.06218i −0.350000 + 0.606218i
\(101\) −3.67977 −0.366150 −0.183075 0.983099i \(-0.558605\pi\)
−0.183075 + 0.983099i \(0.558605\pi\)
\(102\) −4.02704 + 0.183653i −0.398737 + 0.0181844i
\(103\) −9.72665 −0.958396 −0.479198 0.877707i \(-0.659072\pi\)
−0.479198 + 0.877707i \(0.659072\pi\)
\(104\) 2.52704 + 4.37697i 0.247797 + 0.429197i
\(105\) 0 0
\(106\) −7.71780 + 13.3676i −0.749619 + 1.29838i
\(107\) 0.687159 1.19019i 0.0664301 0.115060i −0.830897 0.556426i \(-0.812172\pi\)
0.897327 + 0.441365i \(0.145506\pi\)
\(108\) 7.94805 19.5087i 0.764802 1.87723i
\(109\) 1.69961 + 2.94381i 0.162793 + 0.281966i 0.935869 0.352347i \(-0.114616\pi\)
−0.773076 + 0.634313i \(0.781283\pi\)
\(110\) −14.4050 24.9501i −1.37346 2.37890i
\(111\) −3.08113 + 0.140515i −0.292448 + 0.0133371i
\(112\) 0 0
\(113\) −5.19436 8.99689i −0.488644 0.846356i 0.511271 0.859420i \(-0.329175\pi\)
−0.999915 + 0.0130636i \(0.995842\pi\)
\(114\) 9.31138 + 14.5535i 0.872091 + 1.36306i
\(115\) 0.708945 0.0661095
\(116\) −4.98755 8.63868i −0.463082 0.802082i
\(117\) 2.98755 0.273062i 0.276199 0.0252446i
\(118\) 6.70895 0.617608
\(119\) 0 0
\(120\) 12.2360 + 19.1247i 1.11699 + 1.74584i
\(121\) 9.38151 0.852865
\(122\) −2.79679 + 4.84418i −0.253209 + 0.438572i
\(123\) −5.10457 + 9.85241i −0.460264 + 0.888362i
\(124\) −4.71780 8.17147i −0.423671 0.733820i
\(125\) 8.48968 0.759340
\(126\) 0 0
\(127\) 0.672570 0.0596809 0.0298405 0.999555i \(-0.490500\pi\)
0.0298405 + 0.999555i \(0.490500\pi\)
\(128\) −9.55408 16.5482i −0.844470 1.46266i
\(129\) 18.0562 0.823455i 1.58976 0.0725012i
\(130\) −3.19076 + 5.52655i −0.279848 + 0.484711i
\(131\) 7.91381 0.691433 0.345717 0.938339i \(-0.387636\pi\)
0.345717 + 0.938339i \(0.387636\pi\)
\(132\) −31.6680 + 1.44422i −2.75634 + 0.125703i
\(133\) 0 0
\(134\) 38.9181 3.36201
\(135\) 13.3509 1.83680i 1.14906 0.158086i
\(136\) −2.39037 4.14024i −0.204972 0.355023i
\(137\) −3.67257 −0.313769 −0.156884 0.987617i \(-0.550145\pi\)
−0.156884 + 0.987617i \(0.550145\pi\)
\(138\) 0.535897 1.03434i 0.0456185 0.0880491i
\(139\) 1.02704 + 1.77889i 0.0871126 + 0.150883i 0.906289 0.422658i \(-0.138903\pi\)
−0.819177 + 0.573541i \(0.805569\pi\)
\(140\) 0 0
\(141\) −9.69076 + 18.7043i −0.816109 + 1.57519i
\(142\) 4.02704 + 6.97504i 0.337942 + 0.585332i
\(143\) −2.25729 3.90975i −0.188764 0.326950i
\(144\) 12.9284 1.18166i 1.07737 0.0984715i
\(145\) 3.19076 5.52655i 0.264978 0.458955i
\(146\) −1.85447 + 3.21204i −0.153477 + 0.265830i
\(147\) 0 0
\(148\) −3.60963 6.25206i −0.296710 0.513917i
\(149\) −13.5438 −1.10955 −0.554774 0.832001i \(-0.687195\pi\)
−0.554774 + 0.832001i \(0.687195\pi\)
\(150\) −3.38511 + 6.53366i −0.276393 + 0.533471i
\(151\) 9.92821 0.807946 0.403973 0.914771i \(-0.367629\pi\)
0.403973 + 0.914771i \(0.367629\pi\)
\(152\) −10.2448 + 17.7446i −0.830966 + 1.43928i
\(153\) −2.82597 + 0.258294i −0.228466 + 0.0208818i
\(154\) 0 0
\(155\) 3.01819 5.22765i 0.242427 0.419895i
\(156\) 3.78434 + 5.91486i 0.302989 + 0.473568i
\(157\) −3.02704 + 5.24299i −0.241584 + 0.418436i −0.961166 0.275972i \(-0.911000\pi\)
0.719581 + 0.694408i \(0.244334\pi\)
\(158\) 18.0957 31.3427i 1.43962 2.49349i
\(159\) −4.99854 + 9.64776i −0.396410 + 0.765117i
\(160\) −0.699612 + 1.21176i −0.0553092 + 0.0957983i
\(161\) 0 0
\(162\) 7.41216 20.8672i 0.582354 1.63948i
\(163\) −8.90856 + 15.4301i −0.697772 + 1.20858i 0.271465 + 0.962448i \(0.412492\pi\)
−0.969237 + 0.246128i \(0.920842\pi\)
\(164\) −25.9722 −2.02809
\(165\) −10.9299 17.0832i −0.850889 1.32993i
\(166\) 2.32743 0.180644
\(167\) 4.23385 + 7.33325i 0.327625 + 0.567464i 0.982040 0.188672i \(-0.0604183\pi\)
−0.654415 + 0.756136i \(0.727085\pi\)
\(168\) 0 0
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) 3.01819 5.22765i 0.231484 0.400943i
\(171\) 7.01459 + 9.93559i 0.536419 + 0.759793i
\(172\) 21.1534 + 36.6388i 1.61293 + 2.79368i
\(173\) −8.67830 15.0313i −0.659799 1.14281i −0.980667 0.195682i \(-0.937308\pi\)
0.320868 0.947124i \(-0.396025\pi\)
\(174\) −5.65126 8.83284i −0.428421 0.669616i
\(175\) 0 0
\(176\) −9.76829 16.9192i −0.736312 1.27533i
\(177\) 4.71780 0.215155i 0.354612 0.0161721i
\(178\) 35.3245 2.64768
\(179\) 5.67471 + 9.82888i 0.424147 + 0.734645i 0.996340 0.0854741i \(-0.0272405\pi\)
−0.572193 + 0.820119i \(0.693907\pi\)
\(180\) 18.1929 + 25.7687i 1.35602 + 1.92069i
\(181\) 21.8889 1.62699 0.813495 0.581572i \(-0.197562\pi\)
0.813495 + 0.581572i \(0.197562\pi\)
\(182\) 0 0
\(183\) −1.81138 + 3.49617i −0.133901 + 0.258444i
\(184\) 1.38151 0.101847
\(185\) 2.30924 3.99973i 0.169779 0.294066i
\(186\) −5.34562 8.35512i −0.391960 0.612627i
\(187\) 2.13521 + 3.69829i 0.156142 + 0.270446i
\(188\) −49.3068 −3.59607
\(189\) 0 0
\(190\) −25.8712 −1.87689
\(191\) 0.350874 + 0.607731i 0.0253883 + 0.0439739i 0.878440 0.477852i \(-0.158584\pi\)
−0.853052 + 0.521826i \(0.825251\pi\)
\(192\) −6.83988 10.6906i −0.493626 0.771530i
\(193\) −6.07227 + 10.5175i −0.437092 + 0.757065i −0.997464 0.0711760i \(-0.977325\pi\)
0.560372 + 0.828241i \(0.310658\pi\)
\(194\) 28.2704 2.02970
\(195\) −2.06654 + 3.98866i −0.147988 + 0.285634i
\(196\) 0 0
\(197\) −16.4107 −1.16921 −0.584607 0.811317i \(-0.698751\pi\)
−0.584607 + 0.811317i \(0.698751\pi\)
\(198\) −33.1862 + 3.03322i −2.35844 + 0.215562i
\(199\) −11.3530 19.6640i −0.804794 1.39394i −0.916430 0.400194i \(-0.868943\pi\)
0.111637 0.993749i \(-0.464391\pi\)
\(200\) −8.72665 −0.617068
\(201\) 27.3676 1.24810i 1.93036 0.0880342i
\(202\) −4.52704 7.84107i −0.318522 0.551696i
\(203\) 0 0
\(204\) −3.57966 5.59496i −0.250627 0.391726i
\(205\) −8.30778 14.3895i −0.580241 1.00501i
\(206\) −11.9662 20.7261i −0.833727 1.44406i
\(207\) 0.343677 0.744547i 0.0238872 0.0517496i
\(208\) −2.16372 + 3.74766i −0.150027 + 0.259854i
\(209\) 9.15126 15.8505i 0.633006 1.09640i
\(210\) 0 0
\(211\) −2.28074 3.95035i −0.157012 0.271954i 0.776778 0.629775i \(-0.216853\pi\)
−0.933790 + 0.357822i \(0.883520\pi\)
\(212\) −25.4327 −1.74672
\(213\) 3.05555 + 4.77577i 0.209363 + 0.327231i
\(214\) 3.38151 0.231156
\(215\) −13.5328 + 23.4395i −0.922928 + 1.59856i
\(216\) 26.0167 3.57935i 1.77021 0.243544i
\(217\) 0 0
\(218\) −4.18190 + 7.24327i −0.283234 + 0.490576i
\(219\) −1.20107 + 2.31821i −0.0811611 + 0.156650i
\(220\) 23.7345 41.1094i 1.60018 2.77160i
\(221\) 0.472958 0.819187i 0.0318146 0.0551045i
\(222\) −4.08998 6.39258i −0.274502 0.429042i
\(223\) −6.66225 + 11.5394i −0.446137 + 0.772733i −0.998131 0.0611159i \(-0.980534\pi\)
0.551993 + 0.833849i \(0.313867\pi\)
\(224\) 0 0
\(225\) −2.17091 + 4.70310i −0.144727 + 0.313540i
\(226\) 12.7807 22.1369i 0.850162 1.47252i
\(227\) 1.38151 0.0916943 0.0458472 0.998948i \(-0.485401\pi\)
0.0458472 + 0.998948i \(0.485401\pi\)
\(228\) −13.0957 + 25.2763i −0.867285 + 1.67396i
\(229\) −17.9794 −1.18811 −0.594055 0.804424i \(-0.702474\pi\)
−0.594055 + 0.804424i \(0.702474\pi\)
\(230\) 0.872181 + 1.51066i 0.0575099 + 0.0996101i
\(231\) 0 0
\(232\) 6.21780 10.7695i 0.408219 0.707055i
\(233\) 9.49115 16.4391i 0.621786 1.07696i −0.367367 0.930076i \(-0.619741\pi\)
0.989153 0.146888i \(-0.0469258\pi\)
\(234\) 4.25729 + 6.03011i 0.278308 + 0.394200i
\(235\) −15.7719 27.3177i −1.02884 1.78201i
\(236\) 5.52704 + 9.57312i 0.359780 + 0.623157i
\(237\) 11.7199 22.6208i 0.761292 1.46938i
\(238\) 0 0
\(239\) −2.44592 4.23645i −0.158213 0.274033i 0.776011 0.630719i \(-0.217240\pi\)
−0.934224 + 0.356686i \(0.883907\pi\)
\(240\) −8.94280 + 17.2606i −0.577255 + 1.11417i
\(241\) −26.1593 −1.68507 −0.842535 0.538641i \(-0.818938\pi\)
−0.842535 + 0.538641i \(0.818938\pi\)
\(242\) 11.5416 + 19.9907i 0.741924 + 1.28505i
\(243\) 4.54309 14.9118i 0.291440 0.956589i
\(244\) −9.21634 −0.590016
\(245\) 0 0
\(246\) −27.2740 + 1.24383i −1.73893 + 0.0793039i
\(247\) −4.05408 −0.257955
\(248\) 5.88151 10.1871i 0.373477 0.646880i
\(249\) 1.63667 0.0746406i 0.103720 0.00473015i
\(250\) 10.4445 + 18.0903i 0.660565 + 1.14413i
\(251\) 18.4576 1.16503 0.582516 0.812819i \(-0.302068\pi\)
0.582516 + 0.812819i \(0.302068\pi\)
\(252\) 0 0
\(253\) −1.23405 −0.0775838
\(254\) 0.827430 + 1.43315i 0.0519176 + 0.0899239i
\(255\) 1.95477 3.77293i 0.122412 0.236270i
\(256\) 16.1804 28.0253i 1.01128 1.75158i
\(257\) −11.7339 −0.731938 −0.365969 0.930627i \(-0.619262\pi\)
−0.365969 + 0.930627i \(0.619262\pi\)
\(258\) 23.9684 + 37.4622i 1.49221 + 2.33230i
\(259\) 0 0
\(260\) −10.5146 −0.652087
\(261\) −4.25729 6.03011i −0.263520 0.373254i
\(262\) 9.73599 + 16.8632i 0.601491 + 1.04181i
\(263\) −7.52179 −0.463813 −0.231907 0.972738i \(-0.574496\pi\)
−0.231907 + 0.972738i \(0.574496\pi\)
\(264\) −21.2989 33.2899i −1.31086 2.04885i
\(265\) −8.13521 14.0906i −0.499742 0.865579i
\(266\) 0 0
\(267\) 24.8406 1.13285i 1.52022 0.0693296i
\(268\) 32.0620 + 55.5329i 1.95850 + 3.39221i
\(269\) 9.41741 + 16.3114i 0.574190 + 0.994526i 0.996129 + 0.0879017i \(0.0280161\pi\)
−0.421939 + 0.906624i \(0.638651\pi\)
\(270\) 20.3389 + 26.1891i 1.23779 + 1.59382i
\(271\) 11.9911 20.7693i 0.728410 1.26164i −0.229145 0.973392i \(-0.573593\pi\)
0.957555 0.288251i \(-0.0930738\pi\)
\(272\) 2.04669 3.54498i 0.124099 0.214946i
\(273\) 0 0
\(274\) −4.51819 7.82573i −0.272954 0.472770i
\(275\) 7.79513 0.470064
\(276\) 1.91741 0.0874436i 0.115415 0.00526349i
\(277\) 7.16225 0.430338 0.215169 0.976577i \(-0.430970\pi\)
0.215169 + 0.976577i \(0.430970\pi\)
\(278\) −2.52704 + 4.37697i −0.151562 + 0.262513i
\(279\) −4.02704 5.70397i −0.241093 0.341488i
\(280\) 0 0
\(281\) −7.44085 + 12.8879i −0.443884 + 0.768830i −0.997974 0.0636271i \(-0.979733\pi\)
0.554090 + 0.832457i \(0.313067\pi\)
\(282\) −51.7783 + 2.36135i −3.08335 + 0.140616i
\(283\) −9.99854 + 17.3180i −0.594351 + 1.02945i 0.399287 + 0.916826i \(0.369258\pi\)
−0.993638 + 0.112621i \(0.964076\pi\)
\(284\) −6.63521 + 11.4925i −0.393727 + 0.681956i
\(285\) −18.1929 + 0.829688i −1.07765 + 0.0491465i
\(286\) 5.55408 9.61996i 0.328420 0.568840i
\(287\) 0 0
\(288\) 0.933463 + 1.32217i 0.0550048 + 0.0779098i
\(289\) 8.05262 13.9475i 0.473684 0.820444i
\(290\) 15.7017 0.922038
\(291\) 19.8801 0.906631i 1.16539 0.0531476i
\(292\) −6.11109 −0.357625
\(293\) −7.53278 13.0472i −0.440070 0.762223i 0.557625 0.830093i \(-0.311713\pi\)
−0.997694 + 0.0678705i \(0.978380\pi\)
\(294\) 0 0
\(295\) −3.53590 + 6.12435i −0.205868 + 0.356574i
\(296\) 4.50000 7.79423i 0.261557 0.453030i
\(297\) −23.2396 + 3.19727i −1.34850 + 0.185525i
\(298\) −16.6623 28.8599i −0.965218 1.67181i
\(299\) 0.136673 + 0.236725i 0.00790401 + 0.0136901i
\(300\) −12.1118 + 0.552358i −0.699273 + 0.0318904i
\(301\) 0 0
\(302\) 12.2142 + 21.1556i 0.702848 + 1.21737i
\(303\) −3.43493 5.36874i −0.197331 0.308426i
\(304\) −17.5438 −1.00620
\(305\) −2.94805 5.10618i −0.168805 0.292379i
\(306\) −4.02704 5.70397i −0.230211 0.326075i
\(307\) −27.2704 −1.55641 −0.778203 0.628013i \(-0.783868\pi\)
−0.778203 + 0.628013i \(0.783868\pi\)
\(308\) 0 0
\(309\) −9.07947 14.1911i −0.516513 0.807302i
\(310\) 14.8525 0.843567
\(311\) 7.99115 13.8411i 0.453136 0.784855i −0.545443 0.838148i \(-0.683638\pi\)
0.998579 + 0.0532931i \(0.0169718\pi\)
\(312\) −4.02704 + 7.77266i −0.227986 + 0.440040i
\(313\) −5.79893 10.0440i −0.327775 0.567722i 0.654295 0.756239i \(-0.272965\pi\)
−0.982070 + 0.188517i \(0.939632\pi\)
\(314\) −14.8961 −0.840636
\(315\) 0 0
\(316\) 59.6313 3.35452
\(317\) 1.00885 + 1.74739i 0.0566629 + 0.0981430i 0.892965 0.450125i \(-0.148621\pi\)
−0.836303 + 0.548268i \(0.815287\pi\)
\(318\) −26.7075 + 1.21800i −1.49768 + 0.0683018i
\(319\) −5.55408 + 9.61996i −0.310969 + 0.538614i
\(320\) 19.0043 1.06237
\(321\) 2.37792 0.108445i 0.132722 0.00605281i
\(322\) 0 0
\(323\) 3.83482 0.213375
\(324\) 35.8822 6.61454i 1.99345 0.367474i
\(325\) −0.863327 1.49533i −0.0478888 0.0829458i
\(326\) −43.8391 −2.42802
\(327\) −2.70847 + 5.22765i −0.149779 + 0.289090i
\(328\) −16.1893 28.0407i −0.893904 1.54829i
\(329\) 0 0
\(330\) 22.9554 44.3067i 1.26366 2.43900i
\(331\) 9.85447 + 17.0684i 0.541651 + 0.938167i 0.998809 + 0.0487815i \(0.0155338\pi\)
−0.457159 + 0.889385i \(0.651133\pi\)
\(332\) 1.91741 + 3.32105i 0.105232 + 0.182266i
\(333\) −3.08113 4.36416i −0.168845 0.239155i
\(334\) −10.4174 + 18.0435i −0.570015 + 0.987296i
\(335\) −20.5115 + 35.5269i −1.12066 + 1.94104i
\(336\) 0 0
\(337\) 14.5256 + 25.1590i 0.791259 + 1.37050i 0.925188 + 0.379509i \(0.123907\pi\)
−0.133929 + 0.990991i \(0.542759\pi\)
\(338\) 29.5261 1.60601
\(339\) 8.27762 15.9768i 0.449579 0.867739i
\(340\) 9.94592 0.539393
\(341\) −5.25370 + 9.09967i −0.284504 + 0.492775i
\(342\) −12.5416 + 27.1704i −0.678174 + 1.46921i
\(343\) 0 0
\(344\) −26.3712 + 45.6763i −1.42184 + 2.46270i
\(345\) 0.661774 + 1.03434i 0.0356287 + 0.0556871i
\(346\) 21.3530 36.9845i 1.14794 1.98830i
\(347\) −14.5416 + 25.1868i −0.780636 + 1.35210i 0.150936 + 0.988544i \(0.451771\pi\)
−0.931572 + 0.363557i \(0.881562\pi\)
\(348\) 7.94805 15.3407i 0.426060 0.822346i
\(349\) −12.3815 + 21.4454i −0.662767 + 1.14795i 0.317118 + 0.948386i \(0.397285\pi\)
−0.979885 + 0.199561i \(0.936049\pi\)
\(350\) 0 0
\(351\) 3.18716 + 4.10390i 0.170118 + 0.219050i
\(352\) 1.21780 2.10929i 0.0649089 0.112426i
\(353\) −33.3025 −1.77251 −0.886257 0.463193i \(-0.846704\pi\)
−0.886257 + 0.463193i \(0.846704\pi\)
\(354\) 6.26255 + 9.78827i 0.332851 + 0.520241i
\(355\) −8.48968 −0.450586
\(356\) 29.1015 + 50.4052i 1.54237 + 2.67147i
\(357\) 0 0
\(358\) −13.9626 + 24.1840i −0.737949 + 1.27816i
\(359\) −12.7683 + 22.1153i −0.673884 + 1.16720i 0.302909 + 0.953019i \(0.402042\pi\)
−0.976794 + 0.214182i \(0.931291\pi\)
\(360\) −16.4808 + 35.7043i −0.868616 + 1.88178i
\(361\) 1.28220 + 2.22084i 0.0674842 + 0.116886i
\(362\) 26.9289 + 46.6422i 1.41535 + 2.45146i
\(363\) 8.75729 + 13.6875i 0.459639 + 0.718409i
\(364\) 0 0
\(365\) −1.95477 3.38576i −0.102317 0.177219i
\(366\) −9.67830 + 0.441380i −0.505893 + 0.0230713i
\(367\) 27.4504 1.43290 0.716449 0.697639i \(-0.245766\pi\)
0.716449 + 0.697639i \(0.245766\pi\)
\(368\) 0.591443 + 1.02441i 0.0308311 + 0.0534011i
\(369\) −19.1395 + 1.74935i −0.996362 + 0.0910676i
\(370\) 11.3638 0.590776
\(371\) 0 0
\(372\) 7.51819 14.5110i 0.389800 0.752359i
\(373\) 16.3274 0.845402 0.422701 0.906269i \(-0.361082\pi\)
0.422701 + 0.906269i \(0.361082\pi\)
\(374\) −5.25370 + 9.09967i −0.271662 + 0.470533i
\(375\) 7.92480 + 12.3863i 0.409235 + 0.639628i
\(376\) −30.7345 53.2338i −1.58501 2.74532i
\(377\) 2.46050 0.126722
\(378\) 0 0
\(379\) 12.0364 0.618267 0.309134 0.951019i \(-0.399961\pi\)
0.309134 + 0.951019i \(0.399961\pi\)
\(380\) −21.3135 36.9161i −1.09336 1.89376i
\(381\) 0.627819 + 0.981271i 0.0321641 + 0.0502721i
\(382\) −0.863327 + 1.49533i −0.0441716 + 0.0765075i
\(383\) −12.4356 −0.635429 −0.317715 0.948186i \(-0.602915\pi\)
−0.317715 + 0.948186i \(0.602915\pi\)
\(384\) 15.2252 29.3864i 0.776957 1.49962i
\(385\) 0 0
\(386\) −29.8817 −1.52094
\(387\) 18.0562 + 25.5752i 0.917849 + 1.30006i
\(388\) 23.2901 + 40.3396i 1.18237 + 2.04793i
\(389\) 20.6008 1.04450 0.522250 0.852792i \(-0.325093\pi\)
0.522250 + 0.852792i \(0.325093\pi\)
\(390\) −11.0416 + 0.503554i −0.559115 + 0.0254985i
\(391\) −0.129281 0.223922i −0.00653803 0.0113242i
\(392\) 0 0
\(393\) 7.38725 + 11.5462i 0.372637 + 0.582427i
\(394\) −20.1893 34.9689i −1.01712 1.76171i
\(395\) 19.0744 + 33.0378i 0.959738 + 1.66231i
\(396\) −31.6680 44.8551i −1.59138 2.25405i
\(397\) 11.8186 20.4704i 0.593157 1.02738i −0.400647 0.916233i \(-0.631215\pi\)
0.993804 0.111146i \(-0.0354521\pi\)
\(398\) 27.9341 48.3833i 1.40021 2.42524i
\(399\) 0 0
\(400\) −3.73599 6.47092i −0.186799 0.323546i
\(401\) −2.56440 −0.128060 −0.0640300 0.997948i \(-0.520395\pi\)
−0.0640300 + 0.997948i \(0.520395\pi\)
\(402\) 36.3286 + 56.7810i 1.81191 + 2.83198i
\(403\) 2.32743 0.115938
\(404\) 7.45904 12.9194i 0.371101 0.642766i
\(405\) 15.1424 + 17.7642i 0.752432 + 0.882710i
\(406\) 0 0
\(407\) −4.01965 + 6.96224i −0.199247 + 0.345105i
\(408\) 3.80924 7.35228i 0.188586 0.363992i
\(409\) 17.1623 29.7259i 0.848619 1.46985i −0.0338223 0.999428i \(-0.510768\pi\)
0.882441 0.470423i \(-0.155899\pi\)
\(410\) 20.4413 35.4054i 1.00953 1.74855i
\(411\) −3.42821 5.35824i −0.169101 0.264302i
\(412\) 19.7163 34.1497i 0.971354 1.68243i
\(413\) 0 0
\(414\) 2.00933 0.183653i 0.0987533 0.00902607i
\(415\) −1.22665 + 2.12463i −0.0602141 + 0.104294i
\(416\) −0.539495 −0.0264509
\(417\) −1.63667 + 3.15897i −0.0801482 + 0.154695i
\(418\) 45.0335 2.20266
\(419\) −2.02850 3.51347i −0.0990989 0.171644i 0.812213 0.583361i \(-0.198263\pi\)
−0.911312 + 0.411717i \(0.864929\pi\)
\(420\) 0 0
\(421\) 10.5344 18.2462i 0.513417 0.889264i −0.486462 0.873702i \(-0.661713\pi\)
0.999879 0.0155624i \(-0.00495387\pi\)
\(422\) 5.61177 9.71987i 0.273177 0.473156i
\(423\) −36.3353 + 3.32105i −1.76668 + 0.161475i
\(424\) −15.8530 27.4582i −0.769890 1.33349i
\(425\) 0.816635 + 1.41445i 0.0396126 + 0.0686110i
\(426\) −6.41741 + 12.3863i −0.310925 + 0.600121i
\(427\) 0 0
\(428\) 2.78580 + 4.82515i 0.134657 + 0.233232i
\(429\) 3.59718 6.94297i 0.173673 0.335210i
\(430\) −66.5949 −3.21149
\(431\) −11.3092 19.5882i −0.544747 0.943530i −0.998623 0.0524646i \(-0.983292\pi\)
0.453876 0.891065i \(-0.350041\pi\)
\(432\) 13.7922 + 17.7594i 0.663578 + 0.854447i
\(433\) 2.41789 0.116196 0.0580982 0.998311i \(-0.481496\pi\)
0.0580982 + 0.998311i \(0.481496\pi\)
\(434\) 0 0
\(435\) 11.0416 0.503554i 0.529406 0.0241436i
\(436\) −13.7807 −0.659978
\(437\) −0.554084 + 0.959702i −0.0265054 + 0.0459088i
\(438\) −6.41741 + 0.292666i −0.306636 + 0.0139841i
\(439\) 11.7448 + 20.3427i 0.560551 + 0.970902i 0.997448 + 0.0713911i \(0.0227438\pi\)
−0.436898 + 0.899511i \(0.643923\pi\)
\(440\) 59.1780 2.82120
\(441\) 0 0
\(442\) 2.32743 0.110705
\(443\) 6.70895 + 11.6202i 0.318752 + 0.552094i 0.980228 0.197872i \(-0.0634031\pi\)
−0.661476 + 0.749966i \(0.730070\pi\)
\(444\) 5.75223 11.1025i 0.272989 0.526900i
\(445\) −18.6175 + 32.2465i −0.882554 + 1.52863i
\(446\) −32.7850 −1.55242
\(447\) −12.6426 19.7602i −0.597975 0.934625i
\(448\) 0 0
\(449\) −9.16225 −0.432393 −0.216197 0.976350i \(-0.569365\pi\)
−0.216197 + 0.976350i \(0.569365\pi\)
\(450\) −12.6924 + 1.16009i −0.598326 + 0.0546871i
\(451\) 14.4612 + 25.0475i 0.680950 + 1.17944i
\(452\) 42.1167 1.98100
\(453\) 9.26761 + 14.4851i 0.435430 + 0.680571i
\(454\) 1.69961 + 2.94381i 0.0797667 + 0.138160i
\(455\) 0 0
\(456\) −35.4523 + 1.61680i −1.66021 + 0.0757138i
\(457\) −4.40856 7.63584i −0.206224 0.357190i 0.744298 0.667847i \(-0.232784\pi\)
−0.950522 + 0.310658i \(0.899451\pi\)
\(458\) −22.1192 38.3115i −1.03356 1.79018i
\(459\) −3.01478 3.88195i −0.140718 0.181194i
\(460\) −1.43706 + 2.48906i −0.0670033 + 0.116053i
\(461\) 2.82957 4.90095i 0.131786 0.228260i −0.792579 0.609769i \(-0.791262\pi\)
0.924365 + 0.381509i \(0.124595\pi\)
\(462\) 0 0
\(463\) −7.86333 13.6197i −0.365440 0.632960i 0.623407 0.781898i \(-0.285748\pi\)
−0.988847 + 0.148937i \(0.952415\pi\)
\(464\) 10.6477 0.494305
\(465\) 10.4445 0.476320i 0.484350 0.0220888i
\(466\) 46.7060 2.16361
\(467\) 10.9985 19.0500i 0.508952 0.881530i −0.490995 0.871163i \(-0.663367\pi\)
0.999946 0.0103675i \(-0.00330013\pi\)
\(468\) −5.09718 + 11.0426i −0.235617 + 0.510445i
\(469\) 0 0
\(470\) 38.8068 67.2153i 1.79002 3.10041i
\(471\) −10.4751 + 0.477717i −0.482667 + 0.0220120i
\(472\) −6.89037 + 11.9345i −0.317155 + 0.549328i
\(473\) 23.5562 40.8006i 1.08312 1.87601i
\(474\) 62.6203 2.85580i 2.87625 0.131171i
\(475\) 3.50000 6.06218i 0.160591 0.278152i
\(476\) 0 0
\(477\) −18.7419 + 1.71301i −0.858133 + 0.0784336i
\(478\) 6.01819 10.4238i 0.275265 0.476774i
\(479\) 24.9751 1.14114 0.570571 0.821249i \(-0.306722\pi\)
0.570571 + 0.821249i \(0.306722\pi\)
\(480\) −2.42101 + 0.110410i −0.110503 + 0.00503952i
\(481\) 1.78074 0.0811947
\(482\) −32.1826 55.7419i −1.46588 2.53897i
\(483\) 0 0
\(484\) −19.0167 + 32.9379i −0.864397 + 1.49718i
\(485\) −14.8997 + 25.8070i −0.676561 + 1.17184i
\(486\) 37.3640 8.66452i 1.69487 0.393031i
\(487\) 8.79893 + 15.2402i 0.398717 + 0.690599i 0.993568 0.113238i \(-0.0361221\pi\)
−0.594851 + 0.803836i \(0.702789\pi\)
\(488\) −5.74484 9.95036i −0.260057 0.450432i
\(489\) −30.8281 + 1.40592i −1.39410 + 0.0635778i
\(490\) 0 0
\(491\) −6.89757 11.9469i −0.311283 0.539158i 0.667358 0.744737i \(-0.267425\pi\)
−0.978640 + 0.205580i \(0.934092\pi\)
\(492\) −24.2441 37.8931i −1.09301 1.70835i
\(493\) −2.32743 −0.104822
\(494\) −4.98755 8.63868i −0.224400 0.388673i
\(495\) 14.7216 31.8931i 0.661686 1.43349i
\(496\) 10.0718 0.452237
\(497\) 0 0
\(498\) 2.17257 + 3.39569i 0.0973552 + 0.152165i
\(499\) 13.0875 0.585879 0.292939 0.956131i \(-0.405367\pi\)
0.292939 + 0.956131i \(0.405367\pi\)
\(500\) −17.2089 + 29.8068i −0.769607 + 1.33300i
\(501\) −6.74698 + 13.0225i −0.301433 + 0.581800i
\(502\) 22.7075 + 39.3305i 1.01348 + 1.75541i
\(503\) −22.3068 −0.994611 −0.497305 0.867576i \(-0.665677\pi\)
−0.497305 + 0.867576i \(0.665677\pi\)
\(504\) 0 0
\(505\) 9.54377 0.424692
\(506\) −1.51819 2.62958i −0.0674917 0.116899i
\(507\) 20.7630 0.946899i 0.922119 0.0420533i
\(508\) −1.36333 + 2.36135i −0.0604879 + 0.104768i
\(509\) −15.8932 −0.704453 −0.352226 0.935915i \(-0.614575\pi\)
−0.352226 + 0.935915i \(0.614575\pi\)
\(510\) 10.4445 0.476320i 0.462488 0.0210918i
\(511\) 0 0
\(512\) 41.4078 1.82998
\(513\) −7.94805 + 19.5087i −0.350915 + 0.861330i
\(514\) −14.4356 25.0032i −0.636727 1.10284i
\(515\) 25.2268 1.11163
\(516\) −33.7096 + 65.0635i −1.48398 + 2.86426i
\(517\) 27.4538 + 47.5514i 1.20742 + 2.09131i
\(518\) 0 0
\(519\) 13.8296 26.6927i 0.607051 1.17168i
\(520\) −6.55408 11.3520i −0.287416 0.497818i
\(521\) −2.20895 3.82600i −0.0967756 0.167620i 0.813573 0.581463i \(-0.197520\pi\)
−0.910348 + 0.413843i \(0.864186\pi\)
\(522\) 7.61177 16.4903i 0.333158 0.721759i
\(523\) −12.6367 + 21.8874i −0.552563 + 0.957067i 0.445526 + 0.895269i \(0.353017\pi\)
−0.998089 + 0.0617982i \(0.980316\pi\)
\(524\) −16.0416 + 27.7849i −0.700782 + 1.21379i
\(525\) 0 0
\(526\) −9.25370 16.0279i −0.403480 0.698848i
\(527\) −2.20155 −0.0959012
\(528\) 15.5665 30.0452i 0.677447 1.30755i
\(529\) −22.9253 −0.996751
\(530\) 20.0167 34.6700i 0.869471 1.50597i
\(531\) 4.71780 + 6.68238i 0.204735 + 0.289990i
\(532\) 0 0
\(533\) 3.20321 5.54812i 0.138746 0.240316i
\(534\) 32.9741 + 51.5380i 1.42693 + 2.23027i
\(535\) −1.78220 + 3.08686i −0.0770513 + 0.133457i
\(536\) −39.9705 + 69.2310i −1.72646 + 2.99032i
\(537\) −9.04309 + 17.4542i −0.390238 + 0.753205i
\(538\) −23.1716 + 40.1344i −0.998998 + 1.73032i
\(539\) 0 0
\(540\) −20.6139 + 50.5974i −0.887081 + 2.17736i
\(541\) 1.71926 2.97785i 0.0739168 0.128028i −0.826698 0.562646i \(-0.809783\pi\)
0.900615 + 0.434618i \(0.143117\pi\)
\(542\) 59.0085 2.53463
\(543\) 20.4325 + 31.9357i 0.876842 + 1.37049i
\(544\) 0.510317 0.0218797
\(545\) −4.40808 7.63501i −0.188821 0.327048i
\(546\) 0 0
\(547\) 3.46410 6.00000i 0.148114 0.256542i −0.782416 0.622756i \(-0.786013\pi\)
0.930531 + 0.366214i \(0.119346\pi\)
\(548\) 7.44445 12.8942i 0.318011 0.550812i
\(549\) −6.79173 + 0.620765i −0.289864 + 0.0264936i
\(550\) 9.58998 + 16.6103i 0.408918 + 0.708267i
\(551\) 4.98755 + 8.63868i 0.212477 + 0.368020i
\(552\) 1.28959 + 2.01561i 0.0548887 + 0.0857902i
\(553\) 0 0
\(554\) 8.81138 + 15.2618i 0.374360 + 0.648410i
\(555\) 7.99115 0.364437i 0.339205 0.0154695i
\(556\) −8.32743 −0.353162
\(557\) −16.7917 29.0841i −0.711488 1.23233i −0.964298 0.264818i \(-0.914688\pi\)
0.252810 0.967516i \(-0.418645\pi\)
\(558\) 7.20009 15.5984i 0.304804 0.660333i
\(559\) −10.4356 −0.441379
\(560\) 0 0
\(561\) −3.40263 + 6.56747i −0.143659 + 0.277279i
\(562\) −36.6165 −1.54457
\(563\) −21.2396 + 36.7880i −0.895142 + 1.55043i −0.0615128 + 0.998106i \(0.519593\pi\)
−0.833629 + 0.552325i \(0.813741\pi\)
\(564\) −46.0261 71.9380i −1.93805 3.02914i
\(565\) 13.4720 + 23.3341i 0.566770 + 0.981675i
\(566\) −49.2029 −2.06815
\(567\) 0 0
\(568\) −16.5438 −0.694161
\(569\) −5.20175 9.00969i −0.218069 0.377706i 0.736149 0.676820i \(-0.236642\pi\)
−0.954217 + 0.299114i \(0.903309\pi\)
\(570\) −24.1498 37.7458i −1.01152 1.58100i
\(571\) −8.92480 + 15.4582i −0.373491 + 0.646906i −0.990100 0.140364i \(-0.955173\pi\)
0.616609 + 0.787270i \(0.288506\pi\)
\(572\) 18.3025 0.765267
\(573\) −0.559145 + 1.07922i −0.0233586 + 0.0450849i
\(574\) 0 0
\(575\) −0.471974 −0.0196827
\(576\) 9.21274 19.9586i 0.383864 0.831609i
\(577\) −5.97150 10.3429i −0.248597 0.430582i 0.714540 0.699595i \(-0.246636\pi\)
−0.963137 + 0.269013i \(0.913303\pi\)
\(578\) 39.6270 1.64827
\(579\) −21.0131 + 0.958305i −0.873276 + 0.0398258i
\(580\) 12.9356 + 22.4051i 0.537122 + 0.930322i
\(581\) 0 0
\(582\) 26.3894 + 41.2462i 1.09388 + 1.70971i
\(583\) 14.1608 + 24.5272i 0.586480 + 1.01581i
\(584\) −3.80924 6.59780i −0.157628 0.273019i
\(585\) −7.74844 + 0.708209i −0.320359 + 0.0292808i
\(586\) 18.5344 32.1026i 0.765650 1.32615i
\(587\) −11.9299 + 20.6631i −0.492398 + 0.852859i −0.999962 0.00875568i \(-0.997213\pi\)
0.507563 + 0.861614i \(0.330546\pi\)
\(588\) 0 0
\(589\) 4.71780 + 8.17147i 0.194394 + 0.336699i
\(590\) −17.4002 −0.716354
\(591\) −15.3188 23.9430i −0.630130 0.984884i
\(592\) 7.70602 0.316715
\(593\) −9.79007 + 16.9569i −0.402030 + 0.696336i −0.993971 0.109645i \(-0.965029\pi\)
0.591941 + 0.805981i \(0.298362\pi\)
\(594\) −35.4035 45.5868i −1.45262 1.87045i
\(595\) 0 0
\(596\) 27.4538 47.5514i 1.12455 1.94778i
\(597\) 18.0919 34.9195i 0.740453 1.42916i
\(598\) −0.336285 + 0.582462i −0.0137517 + 0.0238187i
\(599\) −9.27335 + 16.0619i −0.378899 + 0.656272i −0.990902 0.134583i \(-0.957030\pi\)
0.612004 + 0.790855i \(0.290364\pi\)
\(600\) −8.14601 12.7321i −0.332559 0.519785i
\(601\) 9.09931 15.7605i 0.371169 0.642883i −0.618577 0.785724i \(-0.712290\pi\)
0.989746 + 0.142841i \(0.0456238\pi\)
\(602\) 0 0
\(603\) 27.3676 + 38.7640i 1.11449 + 1.57859i
\(604\) −20.1249 + 34.8573i −0.818870 + 1.41832i
\(605\) −24.3317 −0.989224
\(606\) 7.21420 13.9242i 0.293057 0.565634i
\(607\) −22.3097 −0.905524 −0.452762 0.891631i \(-0.649561\pi\)
−0.452762 + 0.891631i \(0.649561\pi\)
\(608\) −1.09358 1.89413i −0.0443505 0.0768173i
\(609\) 0 0
\(610\) 7.25370 12.5638i 0.293694 0.508692i
\(611\) 6.08113 10.5328i 0.246016 0.426112i
\(612\) 4.82150 10.4454i 0.194898 0.422229i
\(613\) −5.11849 8.86548i −0.206734 0.358073i 0.743950 0.668235i \(-0.232950\pi\)
−0.950684 + 0.310162i \(0.899617\pi\)
\(614\) −33.5495 58.1094i −1.35395 2.34511i
\(615\) 13.2391 25.5530i 0.533852 1.03040i
\(616\) 0 0
\(617\) 5.66372 + 9.80984i 0.228013 + 0.394929i 0.957219 0.289364i \(-0.0934439\pi\)
−0.729206 + 0.684294i \(0.760111\pi\)
\(618\) 19.0692 36.8057i 0.767074 1.48054i
\(619\) 8.63327 0.347000 0.173500 0.984834i \(-0.444492\pi\)
0.173500 + 0.984834i \(0.444492\pi\)
\(620\) 12.2360 + 21.1934i 0.491409 + 0.851145i
\(621\) 1.40709 0.193586i 0.0564647 0.00776835i
\(622\) 39.3245 1.57677
\(623\) 0 0
\(624\) −7.48755 + 0.341470i −0.299742 + 0.0136697i
\(625\) −30.6519 −1.22608
\(626\) 14.2683 24.7134i 0.570275 0.987746i
\(627\) 31.6680 1.44422i 1.26470 0.0576766i
\(628\) −12.2719 21.2555i −0.489701 0.848188i
\(629\) −1.68443 −0.0671626
\(630\) 0 0
\(631\) −14.8535 −0.591308 −0.295654 0.955295i \(-0.595538\pi\)
−0.295654 + 0.955295i \(0.595538\pi\)
\(632\) 37.1701 + 64.3805i 1.47855 + 2.56092i
\(633\) 3.63454 7.01508i 0.144460 0.278824i
\(634\) −2.48229 + 4.29945i −0.0985844 + 0.170753i
\(635\) −1.74436 −0.0692229
\(636\) −23.7405 37.1060i −0.941370 1.47135i
\(637\) 0 0
\(638\) −27.3317 −1.08207
\(639\) −4.11556 + 8.91601i −0.162809 + 0.352712i
\(640\) 24.7793 + 42.9190i 0.979487 + 1.69652i
\(641\) −34.1593 −1.34921 −0.674606 0.738178i \(-0.735687\pi\)
−0.674606 + 0.738178i \(0.735687\pi\)
\(642\) 3.15652 + 4.93359i 0.124578 + 0.194713i
\(643\) 5.41741 + 9.38323i 0.213642 + 0.370039i 0.952852 0.303437i \(-0.0981341\pi\)
−0.739210 + 0.673475i \(0.764801\pi\)
\(644\) 0 0
\(645\) −46.8302 + 2.13570i −1.84394 + 0.0840929i
\(646\) 4.71780 + 8.17147i 0.185619 + 0.321502i
\(647\) −16.4846 28.5522i −0.648077 1.12250i −0.983582 0.180464i \(-0.942240\pi\)
0.335504 0.942039i \(-0.391093\pi\)
\(648\) 29.5079 + 34.6169i 1.15918 + 1.35988i
\(649\) 6.15486 10.6605i 0.241599 0.418462i
\(650\) 2.12422 3.67926i 0.0833188 0.144312i
\(651\) 0 0
\(652\) −36.1160 62.5548i −1.41441 2.44984i
\(653\) −3.93113 −0.153837 −0.0769185 0.997037i \(-0.524508\pi\)
−0.0769185 + 0.997037i \(0.524508\pi\)
\(654\) −14.4715 + 0.659973i −0.565880 + 0.0258070i
\(655\) −20.5251 −0.801982
\(656\) 13.8617 24.0091i 0.541207 0.937399i
\(657\) −4.50340 + 0.411612i −0.175695 + 0.0160585i
\(658\) 0 0
\(659\) −8.40856 + 14.5640i −0.327551 + 0.567335i −0.982025 0.188749i \(-0.939557\pi\)
0.654474 + 0.756084i \(0.272890\pi\)
\(660\) 82.1334 3.74570i 3.19704 0.145801i
\(661\) 8.51080 14.7411i 0.331032 0.573364i −0.651683 0.758492i \(-0.725937\pi\)
0.982714 + 0.185128i \(0.0592700\pi\)
\(662\) −24.2470 + 41.9970i −0.942386 + 1.63226i
\(663\) 1.63667 0.0746406i 0.0635631 0.00289880i
\(664\) −2.39037 + 4.14024i −0.0927643 + 0.160672i
\(665\) 0 0
\(666\) 5.50885 11.9345i 0.213464 0.462451i
\(667\) 0.336285 0.582462i 0.0130210 0.0225530i
\(668\) −34.3288 −1.32822
\(669\) −23.0548 + 1.05141i −0.891348 + 0.0406500i
\(670\) −100.937 −3.89954
\(671\) 5.13161 + 8.88821i 0.198104 + 0.343126i
\(672\) 0 0
\(673\) −14.3727 + 24.8942i −0.554025 + 0.959600i 0.443953 + 0.896050i \(0.353576\pi\)
−0.997979 + 0.0635501i \(0.979758\pi\)
\(674\) −35.7403 + 61.9039i −1.37666 + 2.38445i
\(675\) −8.88823 + 1.22283i −0.342108 + 0.0470668i
\(676\) 24.3245 + 42.1313i 0.935558 + 1.62043i
\(677\) 3.01819 + 5.22765i 0.115998 + 0.200915i 0.918178 0.396167i \(-0.129660\pi\)
−0.802180 + 0.597082i \(0.796327\pi\)
\(678\) 44.2278 2.01701i 1.69856 0.0774628i
\(679\) 0 0
\(680\) 6.19961 + 10.7380i 0.237744 + 0.411785i
\(681\) 1.28959 + 2.01561i 0.0494173 + 0.0772385i
\(682\) −25.8535 −0.989981
\(683\) −10.2556 17.7633i −0.392421 0.679693i 0.600347 0.799739i \(-0.295029\pi\)
−0.992768 + 0.120046i \(0.961696\pi\)
\(684\) −49.1021 + 4.48794i −1.87747 + 0.171601i
\(685\) 9.52510 0.363935
\(686\) 0 0
\(687\) −16.7831 26.2317i −0.640314 1.00080i
\(688\) −45.1593 −1.72168
\(689\) 3.13667 5.43288i 0.119498 0.206976i
\(690\) −1.38989 + 2.68265i −0.0529122 + 0.102127i
\(691\) 7.50146 + 12.9929i 0.285369 + 0.494274i 0.972699 0.232072i \(-0.0745505\pi\)
−0.687330 + 0.726346i \(0.741217\pi\)
\(692\) 70.3652 2.67488
\(693\) 0 0
\(694\) −71.5595 −2.71636
\(695\) −2.66372 4.61369i −0.101040 0.175007i
\(696\) 21.5167 0.981271i 0.815589 0.0371950i
\(697\) −3.02997 + 5.24806i −0.114768 + 0.198784i
\(698\) −60.9296 −2.30622
\(699\) 32.8442 1.49786i 1.24228 0.0566542i
\(700\) 0 0
\(701\) 38.5113 1.45455 0.727275 0.686346i \(-0.240786\pi\)
0.727275 + 0.686346i \(0.240786\pi\)
\(702\) −4.82383 + 11.8402i −0.182064 + 0.446880i
\(703\) 3.60963 + 6.25206i 0.136140 + 0.235801i
\(704\) −33.0803 −1.24676
\(705\) 25.1337 48.5111i 0.946592 1.82703i
\(706\) −40.9705 70.9630i −1.54195 2.67073i
\(707\) 0 0
\(708\) −8.80778 + 17.0000i −0.331017 + 0.638901i
\(709\) −3.82004 6.61650i −0.143465 0.248488i 0.785334 0.619072i \(-0.212491\pi\)
−0.928799 + 0.370584i \(0.879158\pi\)
\(710\) −10.4445 18.0903i −0.391973 0.678918i
\(711\) 43.9437 4.01646i 1.64802 0.150629i
\(712\) −36.2798 + 62.8384i −1.35964 + 2.35497i
\(713\) 0.318097 0.550960i 0.0119128 0.0206336i
\(714\) 0 0
\(715\) 5.85447 + 10.1402i 0.218945 + 0.379224i
\(716\) −46.0115 −1.71953
\(717\) 3.89776 7.52313i 0.145565 0.280956i
\(718\) −62.8329 −2.34490
\(719\) 15.0182 26.0123i 0.560084 0.970094i −0.437405 0.899265i \(-0.644102\pi\)
0.997488 0.0708289i \(-0.0225644\pi\)
\(720\) −33.5308 + 3.06472i −1.24962 + 0.114216i
\(721\) 0 0
\(722\) −3.15486 + 5.46438i −0.117412 + 0.203363i
\(723\) −24.4188 38.1662i −0.908143 1.41941i
\(724\) −44.3697 + 76.8506i −1.64899 + 2.85613i
\(725\) −2.12422 + 3.67926i −0.0788916 + 0.136644i
\(726\) −18.3925 + 35.4997i −0.682610 + 1.31752i
\(727\) −1.72812 + 2.99319i −0.0640923 + 0.111011i −0.896291 0.443466i \(-0.853749\pi\)
0.832199 + 0.554478i \(0.187082\pi\)
\(728\) 0 0
\(729\) 25.9969 7.29124i 0.962847 0.270046i
\(730\) 4.80972 8.33068i 0.178016 0.308332i
\(731\) 9.87120 0.365099
\(732\) −8.60311 13.4465i −0.317980 0.496998i
\(733\) 38.5261 1.42299 0.711496 0.702690i \(-0.248018\pi\)
0.711496 + 0.702690i \(0.248018\pi\)
\(734\) 33.7709 + 58.4929i 1.24651 + 2.15901i
\(735\) 0 0
\(736\) −0.0737345 + 0.127712i −0.00271789 + 0.00470752i
\(737\) 35.7039 61.8409i 1.31517 2.27794i
\(738\) −27.2740 38.6314i −1.00397 1.42204i
\(739\) −22.5620 39.0785i −0.829955 1.43752i −0.898073 0.439847i \(-0.855033\pi\)
0.0681179 0.997677i \(-0.478301\pi\)
\(740\) 9.36186 + 16.2152i 0.344149 + 0.596084i
\(741\) −3.78434 5.91486i −0.139021 0.217288i
\(742\) 0 0
\(743\) −4.74338 8.21577i −0.174018 0.301407i 0.765803 0.643075i \(-0.222342\pi\)
−0.939821 + 0.341668i \(0.889008\pi\)
\(744\) 20.3530 0.928200i 0.746178 0.0340295i
\(745\) 35.1268 1.28695
\(746\) 20.0869 + 34.7915i 0.735432 + 1.27381i
\(747\) 1.63667 + 2.31821i 0.0598827 + 0.0848190i
\(748\) −17.3126 −0.633013
\(749\) 0 0
\(750\) −16.6441 + 32.1250i −0.607755 + 1.17304i
\(751\) −9.83190 −0.358771 −0.179386 0.983779i \(-0.557411\pi\)
−0.179386 + 0.983779i \(0.557411\pi\)
\(752\) 26.3157 45.5800i 0.959633 1.66213i
\(753\) 17.2295 + 26.9294i 0.627877 + 0.981362i
\(754\) 3.02704 + 5.24299i 0.110238 + 0.190938i
\(755\) −25.7496 −0.937124
\(756\) 0 0
\(757\) −41.8171 −1.51987 −0.759934 0.650000i \(-0.774769\pi\)
−0.759934 + 0.650000i \(0.774769\pi\)
\(758\) 14.8078 + 25.6478i 0.537843 + 0.931571i
\(759\) −1.15194 1.80046i −0.0418126 0.0653525i
\(760\) 26.5708 46.0220i 0.963825 1.66939i
\(761\) 22.9794 0.833001 0.416501 0.909135i \(-0.363256\pi\)
0.416501 + 0.909135i \(0.363256\pi\)
\(762\) −1.31858 + 2.54500i −0.0477670 + 0.0921958i
\(763\) 0 0
\(764\) −2.84494 −0.102926
\(765\) 7.32937 0.669906i 0.264994 0.0242205i
\(766\) −15.2989 26.4985i −0.552773 0.957430i
\(767\) −2.72665 −0.0984538
\(768\) 55.9925 2.55354i 2.02046 0.0921429i
\(769\) −3.04329 5.27113i −0.109744 0.190082i 0.805923 0.592021i \(-0.201670\pi\)
−0.915666 + 0.401939i \(0.868336\pi\)
\(770\) 0 0
\(771\) −10.9531 17.1196i −0.394467 0.616546i
\(772\) −24.6175 42.6388i −0.886003 1.53460i
\(773\) 20.9107