Properties

Label 555.2.bb.a.454.18
Level $555$
Weight $2$
Character 555.454
Analytic conductor $4.432$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [555,2,Mod(454,555)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(555, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("555.454");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 555 = 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 555.bb (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: \(4.43169731218\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(36\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 454.18
Character \(\chi\) \(=\) 555.454
Dual form 555.2.bb.a.544.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.113794 - 0.0656990i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.991367 - 1.71710i) q^{4} +(0.217380 - 2.22548i) q^{5} +0.131398 q^{6} +(-1.67003 + 0.964193i) q^{7} +0.523323i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.113794 - 0.0656990i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.991367 - 1.71710i) q^{4} +(0.217380 - 2.22548i) q^{5} +0.131398 q^{6} +(-1.67003 + 0.964193i) q^{7} +0.523323i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.170948 + 0.238964i) q^{10} -4.70575 q^{11} +(1.71710 + 0.991367i) q^{12} +(0.630070 - 0.363771i) q^{13} +0.253386 q^{14} +(0.924481 + 2.03601i) q^{15} +(-1.94835 + 3.37465i) q^{16} +(2.98832 + 1.72531i) q^{17} +(-0.113794 + 0.0656990i) q^{18} +(1.88651 + 3.26753i) q^{19} +(-4.03687 + 1.83300i) q^{20} +(0.964193 - 1.67003i) q^{21} +(0.535486 + 0.309163i) q^{22} +4.47345i q^{23} +(-0.261662 - 0.453211i) q^{24} +(-4.90549 - 0.967550i) q^{25} -0.0955976 q^{26} +1.00000i q^{27} +(3.31123 + 1.91174i) q^{28} +0.0315057 q^{29} +(0.0285633 - 0.292423i) q^{30} -5.76147 q^{31} +(1.34984 - 0.779333i) q^{32} +(4.07530 - 2.35287i) q^{33} +(-0.226702 - 0.392660i) q^{34} +(1.78276 + 3.92621i) q^{35} -1.98273 q^{36} +(-2.34626 + 5.61205i) q^{37} -0.495768i q^{38} +(-0.363771 + 0.630070i) q^{39} +(1.16464 + 0.113760i) q^{40} +(-4.60419 - 7.97469i) q^{41} +(-0.219439 + 0.126693i) q^{42} +7.05252i q^{43} +(4.66513 + 8.08024i) q^{44} +(-1.81863 - 1.30100i) q^{45} +(0.293901 - 0.509051i) q^{46} -0.393644i q^{47} -3.89671i q^{48} +(-1.64066 + 2.84171i) q^{49} +(0.494648 + 0.432387i) q^{50} -3.45062 q^{51} +(-1.24926 - 0.721262i) q^{52} +(-6.17510 - 3.56520i) q^{53} +(0.0656990 - 0.113794i) q^{54} +(-1.02294 + 10.4725i) q^{55} +(-0.504585 - 0.873967i) q^{56} +(-3.26753 - 1.88651i) q^{57} +(-0.00358515 - 0.00206989i) q^{58} +(3.77054 - 6.53076i) q^{59} +(2.57953 - 3.60586i) q^{60} +(-2.80510 - 4.85857i) q^{61} +(0.655620 + 0.378523i) q^{62} +1.92839i q^{63} +7.58861 q^{64} +(-0.672599 - 1.48128i) q^{65} -0.618326 q^{66} +(-10.5416 + 6.08619i) q^{67} -6.84166i q^{68} +(-2.23672 - 3.87412i) q^{69} +(0.0550812 - 0.563905i) q^{70} +(-4.60707 - 7.97969i) q^{71} +(0.453211 + 0.261662i) q^{72} -2.63048i q^{73} +(0.635696 - 0.484470i) q^{74} +(4.73206 - 1.61482i) q^{75} +(3.74045 - 6.47865i) q^{76} +(7.85875 - 4.53725i) q^{77} +(0.0827899 - 0.0477988i) q^{78} +(3.61265 + 6.25729i) q^{79} +(7.08666 + 5.06960i) q^{80} +(-0.500000 - 0.866025i) q^{81} +1.20996i q^{82} +(-10.7476 - 6.20513i) q^{83} -3.82348 q^{84} +(4.48924 - 6.27540i) q^{85} +(0.463344 - 0.802535i) q^{86} +(-0.0272847 + 0.0157528i) q^{87} -2.46263i q^{88} +(-1.10616 + 1.91592i) q^{89} +(0.121475 + 0.267527i) q^{90} +(-0.701492 + 1.21502i) q^{91} +(7.68135 - 4.43483i) q^{92} +(4.98958 - 2.88073i) q^{93} +(-0.0258620 + 0.0447943i) q^{94} +(7.68191 - 3.48809i) q^{95} +(-0.779333 + 1.34984i) q^{96} +10.7793i q^{97} +(0.373395 - 0.215580i) q^{98} +(-2.35287 + 4.07530i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9} - 8 q^{11} - 16 q^{14} - 24 q^{16} + 4 q^{19} + 4 q^{20} + 12 q^{21} + 10 q^{25} + 24 q^{26} + 16 q^{29} + 12 q^{30} + 24 q^{31} - 44 q^{34} - 2 q^{35} + 64 q^{36} - 8 q^{39} + 46 q^{40} - 48 q^{41} - 8 q^{44} - 4 q^{45} - 64 q^{46} + 32 q^{49} - 46 q^{50} - 8 q^{51} - 12 q^{55} - 72 q^{56} + 32 q^{59} - 68 q^{60} - 8 q^{61} - 136 q^{64} - 42 q^{65} - 32 q^{66} - 4 q^{69} + 4 q^{70} + 12 q^{71} - 96 q^{74} - 8 q^{75} + 8 q^{76} - 8 q^{79} - 44 q^{80} - 36 q^{81} + 136 q^{84} + 4 q^{85} + 8 q^{86} + 8 q^{91} - 28 q^{94} + 18 q^{95} - 20 q^{96} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/555\mathbb{Z}\right)^\times\).

\(n\) \(76\) \(112\) \(371\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.113794 0.0656990i −0.0804645 0.0464562i 0.459228 0.888318i \(-0.348126\pi\)
−0.539692 + 0.841862i \(0.681459\pi\)
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) −0.991367 1.71710i −0.495684 0.858549i
\(5\) 0.217380 2.22548i 0.0972155 0.995263i
\(6\) 0.131398 0.0536430
\(7\) −1.67003 + 0.964193i −0.631213 + 0.364431i −0.781222 0.624254i \(-0.785403\pi\)
0.150009 + 0.988685i \(0.452070\pi\)
\(8\) 0.523323i 0.185023i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) −0.170948 + 0.238964i −0.0540585 + 0.0755671i
\(11\) −4.70575 −1.41884 −0.709418 0.704788i \(-0.751042\pi\)
−0.709418 + 0.704788i \(0.751042\pi\)
\(12\) 1.71710 + 0.991367i 0.495684 + 0.286183i
\(13\) 0.630070 0.363771i 0.174750 0.100892i −0.410074 0.912052i \(-0.634497\pi\)
0.584824 + 0.811160i \(0.301164\pi\)
\(14\) 0.253386 0.0677203
\(15\) 0.924481 + 2.03601i 0.238700 + 0.525695i
\(16\) −1.94835 + 3.37465i −0.487088 + 0.843661i
\(17\) 2.98832 + 1.72531i 0.724775 + 0.418449i 0.816508 0.577335i \(-0.195907\pi\)
−0.0917325 + 0.995784i \(0.529240\pi\)
\(18\) −0.113794 + 0.0656990i −0.0268215 + 0.0154854i
\(19\) 1.88651 + 3.26753i 0.432796 + 0.749624i 0.997113 0.0759341i \(-0.0241939\pi\)
−0.564317 + 0.825558i \(0.690861\pi\)
\(20\) −4.03687 + 1.83300i −0.902671 + 0.409872i
\(21\) 0.964193 1.67003i 0.210404 0.364431i
\(22\) 0.535486 + 0.309163i 0.114166 + 0.0659138i
\(23\) 4.47345i 0.932778i 0.884580 + 0.466389i \(0.154445\pi\)
−0.884580 + 0.466389i \(0.845555\pi\)
\(24\) −0.261662 0.453211i −0.0534115 0.0925113i
\(25\) −4.90549 0.967550i −0.981098 0.193510i
\(26\) −0.0955976 −0.0187482
\(27\) 1.00000i 0.192450i
\(28\) 3.31123 + 1.91174i 0.625764 + 0.361285i
\(29\) 0.0315057 0.00585045 0.00292523 0.999996i \(-0.499069\pi\)
0.00292523 + 0.999996i \(0.499069\pi\)
\(30\) 0.0285633 0.292423i 0.00521493 0.0533889i
\(31\) −5.76147 −1.03479 −0.517395 0.855747i \(-0.673098\pi\)
−0.517395 + 0.855747i \(0.673098\pi\)
\(32\) 1.34984 0.779333i 0.238621 0.137768i
\(33\) 4.07530 2.35287i 0.709418 0.409583i
\(34\) −0.226702 0.392660i −0.0388791 0.0673406i
\(35\) 1.78276 + 3.92621i 0.301341 + 0.663651i
\(36\) −1.98273 −0.330456
\(37\) −2.34626 + 5.61205i −0.385723 + 0.922615i
\(38\) 0.495768i 0.0804241i
\(39\) −0.363771 + 0.630070i −0.0582500 + 0.100892i
\(40\) 1.16464 + 0.113760i 0.184146 + 0.0179871i
\(41\) −4.60419 7.97469i −0.719054 1.24544i −0.961375 0.275242i \(-0.911242\pi\)
0.242321 0.970196i \(-0.422091\pi\)
\(42\) −0.219439 + 0.126693i −0.0338601 + 0.0195492i
\(43\) 7.05252i 1.07550i 0.843104 + 0.537750i \(0.180726\pi\)
−0.843104 + 0.537750i \(0.819274\pi\)
\(44\) 4.66513 + 8.08024i 0.703294 + 1.21814i
\(45\) −1.81863 1.30100i −0.271105 0.193941i
\(46\) 0.293901 0.509051i 0.0433333 0.0750555i
\(47\) 0.393644i 0.0574189i −0.999588 0.0287095i \(-0.990860\pi\)
0.999588 0.0287095i \(-0.00913976\pi\)
\(48\) 3.89671i 0.562441i
\(49\) −1.64066 + 2.84171i −0.234380 + 0.405959i
\(50\) 0.494648 + 0.432387i 0.0699538 + 0.0611488i
\(51\) −3.45062 −0.483183
\(52\) −1.24926 0.721262i −0.173241 0.100021i
\(53\) −6.17510 3.56520i −0.848216 0.489718i 0.0118327 0.999930i \(-0.496233\pi\)
−0.860048 + 0.510212i \(0.829567\pi\)
\(54\) 0.0656990 0.113794i 0.00894050 0.0154854i
\(55\) −1.02294 + 10.4725i −0.137933 + 1.41212i
\(56\) −0.504585 0.873967i −0.0674280 0.116789i
\(57\) −3.26753 1.88651i −0.432796 0.249875i
\(58\) −0.00358515 0.00206989i −0.000470754 0.000271790i
\(59\) 3.77054 6.53076i 0.490882 0.850233i −0.509063 0.860729i \(-0.670008\pi\)
0.999945 + 0.0104965i \(0.00334119\pi\)
\(60\) 2.57953 3.60586i 0.333016 0.465514i
\(61\) −2.80510 4.85857i −0.359156 0.622076i 0.628664 0.777677i \(-0.283602\pi\)
−0.987820 + 0.155601i \(0.950269\pi\)
\(62\) 0.655620 + 0.378523i 0.0832639 + 0.0480724i
\(63\) 1.92839i 0.242954i
\(64\) 7.58861 0.948576
\(65\) −0.672599 1.48128i −0.0834257 0.183731i
\(66\) −0.618326 −0.0761107
\(67\) −10.5416 + 6.08619i −1.28786 + 0.743547i −0.978272 0.207324i \(-0.933525\pi\)
−0.309588 + 0.950871i \(0.600191\pi\)
\(68\) 6.84166i 0.829674i
\(69\) −2.23672 3.87412i −0.269270 0.466389i
\(70\) 0.0550812 0.563905i 0.00658346 0.0673995i
\(71\) −4.60707 7.97969i −0.546759 0.947014i −0.998494 0.0548623i \(-0.982528\pi\)
0.451735 0.892152i \(-0.350805\pi\)
\(72\) 0.453211 + 0.261662i 0.0534115 + 0.0308371i
\(73\) 2.63048i 0.307875i −0.988081 0.153937i \(-0.950805\pi\)
0.988081 0.153937i \(-0.0491954\pi\)
\(74\) 0.635696 0.484470i 0.0738982 0.0563185i
\(75\) 4.73206 1.61482i 0.546411 0.186464i
\(76\) 3.74045 6.47865i 0.429059 0.743153i
\(77\) 7.85875 4.53725i 0.895588 0.517068i
\(78\) 0.0827899 0.0477988i 0.00937412 0.00541215i
\(79\) 3.61265 + 6.25729i 0.406454 + 0.704000i 0.994490 0.104836i \(-0.0334316\pi\)
−0.588035 + 0.808835i \(0.700098\pi\)
\(80\) 7.08666 + 5.06960i 0.792313 + 0.566798i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 1.20996i 0.133618i
\(83\) −10.7476 6.20513i −1.17970 0.681101i −0.223757 0.974645i \(-0.571832\pi\)
−0.955946 + 0.293544i \(0.905165\pi\)
\(84\) −3.82348 −0.417176
\(85\) 4.48924 6.27540i 0.486926 0.680662i
\(86\) 0.463344 0.802535i 0.0499636 0.0865395i
\(87\) −0.0272847 + 0.0157528i −0.00292523 + 0.00168888i
\(88\) 2.46263i 0.262517i
\(89\) −1.10616 + 1.91592i −0.117252 + 0.203087i −0.918678 0.395007i \(-0.870742\pi\)
0.801425 + 0.598095i \(0.204075\pi\)
\(90\) 0.121475 + 0.267527i 0.0128046 + 0.0281999i
\(91\) −0.701492 + 1.21502i −0.0735363 + 0.127369i
\(92\) 7.68135 4.43483i 0.800836 0.462363i
\(93\) 4.98958 2.88073i 0.517395 0.298718i
\(94\) −0.0258620 + 0.0447943i −0.00266746 + 0.00462018i
\(95\) 7.68191 3.48809i 0.788148 0.357871i
\(96\) −0.779333 + 1.34984i −0.0795403 + 0.137768i
\(97\) 10.7793i 1.09447i 0.836978 + 0.547237i \(0.184320\pi\)
−0.836978 + 0.547237i \(0.815680\pi\)
\(98\) 0.373395 0.215580i 0.0377186 0.0217768i
\(99\) −2.35287 + 4.07530i −0.236473 + 0.409583i
\(100\) 3.20177 + 9.38241i 0.320177 + 0.938241i
\(101\) 7.32587 0.728951 0.364476 0.931213i \(-0.381248\pi\)
0.364476 + 0.931213i \(0.381248\pi\)
\(102\) 0.392660 + 0.226702i 0.0388791 + 0.0224469i
\(103\) 4.94014i 0.486766i 0.969930 + 0.243383i \(0.0782572\pi\)
−0.969930 + 0.243383i \(0.921743\pi\)
\(104\) 0.190370 + 0.329730i 0.0186673 + 0.0323327i
\(105\) −3.50702 2.50882i −0.342250 0.244836i
\(106\) 0.468460 + 0.811396i 0.0455008 + 0.0788098i
\(107\) 11.7114 6.76157i 1.13218 0.653665i 0.187699 0.982227i \(-0.439897\pi\)
0.944483 + 0.328561i \(0.106564\pi\)
\(108\) 1.71710 0.991367i 0.165228 0.0953944i
\(109\) 3.63311 6.29273i 0.347989 0.602734i −0.637903 0.770117i \(-0.720198\pi\)
0.985892 + 0.167382i \(0.0535314\pi\)
\(110\) 0.804439 1.12451i 0.0767003 0.107217i
\(111\) −0.774103 6.03330i −0.0734746 0.572656i
\(112\) 7.51436i 0.710040i
\(113\) 4.19749 + 2.42342i 0.394866 + 0.227976i 0.684266 0.729232i \(-0.260123\pi\)
−0.289400 + 0.957208i \(0.593456\pi\)
\(114\) 0.247884 + 0.429347i 0.0232164 + 0.0402121i
\(115\) 9.95555 + 0.972439i 0.928360 + 0.0906804i
\(116\) −0.0312337 0.0540983i −0.00289997 0.00502290i
\(117\) 0.727542i 0.0672613i
\(118\) −0.858129 + 0.495441i −0.0789972 + 0.0456090i
\(119\) −6.65413 −0.609983
\(120\) −1.06549 + 0.483803i −0.0972656 + 0.0441649i
\(121\) 11.1441 1.01310
\(122\) 0.737168i 0.0667401i
\(123\) 7.97469 + 4.60419i 0.719054 + 0.415146i
\(124\) 5.71173 + 9.89301i 0.512929 + 0.888418i
\(125\) −3.21962 + 10.7067i −0.287971 + 0.957639i
\(126\) 0.126693 0.219439i 0.0112867 0.0195492i
\(127\) −0.938941 0.542098i −0.0833176 0.0481034i 0.457762 0.889075i \(-0.348651\pi\)
−0.541080 + 0.840971i \(0.681984\pi\)
\(128\) −3.56323 2.05723i −0.314948 0.181835i
\(129\) −3.52626 6.10766i −0.310470 0.537750i
\(130\) −0.0207810 + 0.212750i −0.00182262 + 0.0186594i
\(131\) −5.54027 + 9.59603i −0.484056 + 0.838409i −0.999832 0.0183140i \(-0.994170\pi\)
0.515777 + 0.856723i \(0.327503\pi\)
\(132\) −8.08024 4.66513i −0.703294 0.406047i
\(133\) −6.30107 3.63793i −0.546372 0.315448i
\(134\) 1.59943 0.138169
\(135\) 2.22548 + 0.217380i 0.191539 + 0.0187091i
\(136\) −0.902895 + 1.56386i −0.0774226 + 0.134100i
\(137\) 14.1232i 1.20662i −0.797506 0.603311i \(-0.793848\pi\)
0.797506 0.603311i \(-0.206152\pi\)
\(138\) 0.587802i 0.0500370i
\(139\) 8.68951 15.0507i 0.737035 1.27658i −0.216790 0.976218i \(-0.569559\pi\)
0.953825 0.300363i \(-0.0971079\pi\)
\(140\) 4.97433 6.95349i 0.420407 0.587677i
\(141\) 0.196822 + 0.340906i 0.0165754 + 0.0287095i
\(142\) 1.21072i 0.101601i
\(143\) −2.96495 + 1.71182i −0.247942 + 0.143149i
\(144\) 1.94835 + 3.37465i 0.162363 + 0.281220i
\(145\) 0.00684871 0.0701151i 0.000568755 0.00582274i
\(146\) −0.172820 + 0.299333i −0.0143027 + 0.0247730i
\(147\) 3.28132i 0.270639i
\(148\) 11.9624 1.53484i 0.983307 0.126163i
\(149\) 4.50166 0.368790 0.184395 0.982852i \(-0.440967\pi\)
0.184395 + 0.982852i \(0.440967\pi\)
\(150\) −0.644572 0.127134i −0.0526290 0.0103805i
\(151\) −0.499345 0.864891i −0.0406361 0.0703838i 0.844992 0.534779i \(-0.179605\pi\)
−0.885628 + 0.464395i \(0.846272\pi\)
\(152\) −1.70998 + 0.987255i −0.138697 + 0.0800770i
\(153\) 2.98832 1.72531i 0.241592 0.139483i
\(154\) −1.19237 −0.0960840
\(155\) −1.25243 + 12.8220i −0.100598 + 1.02989i
\(156\) 1.44252 0.115494
\(157\) −6.86341 3.96259i −0.547760 0.316249i 0.200458 0.979702i \(-0.435757\pi\)
−0.748218 + 0.663453i \(0.769090\pi\)
\(158\) 0.949389i 0.0755293i
\(159\) 7.13040 0.565477
\(160\) −1.44096 3.17346i −0.113918 0.250884i
\(161\) −4.31327 7.47080i −0.339933 0.588781i
\(162\) 0.131398i 0.0103236i
\(163\) −13.4995 7.79392i −1.05736 0.610467i −0.132659 0.991162i \(-0.542351\pi\)
−0.924701 + 0.380695i \(0.875685\pi\)
\(164\) −9.12889 + 15.8117i −0.712847 + 1.23469i
\(165\) −4.35038 9.58095i −0.338676 0.745876i
\(166\) 0.815341 + 1.41221i 0.0632828 + 0.109609i
\(167\) −17.8657 + 10.3148i −1.38249 + 0.798180i −0.992454 0.122620i \(-0.960870\pi\)
−0.390035 + 0.920800i \(0.627537\pi\)
\(168\) 0.873967 + 0.504585i 0.0674280 + 0.0389296i
\(169\) −6.23534 + 10.7999i −0.479642 + 0.830764i
\(170\) −0.923136 + 0.419164i −0.0708013 + 0.0321484i
\(171\) 3.77302 0.288530
\(172\) 12.1099 6.99164i 0.923369 0.533108i
\(173\) −8.06540 4.65656i −0.613201 0.354032i 0.161016 0.986952i \(-0.448523\pi\)
−0.774217 + 0.632920i \(0.781856\pi\)
\(174\) 0.00413978 0.000313836
\(175\) 9.12523 3.11400i 0.689803 0.235397i
\(176\) 9.16846 15.8802i 0.691099 1.19702i
\(177\) 7.54108i 0.566822i
\(178\) 0.251748 0.145347i 0.0188693 0.0108942i
\(179\) −2.75912 −0.206226 −0.103113 0.994670i \(-0.532880\pi\)
−0.103113 + 0.994670i \(0.532880\pi\)
\(180\) −0.431008 + 4.41253i −0.0321254 + 0.328891i
\(181\) −10.1108 17.5124i −0.751528 1.30168i −0.947082 0.320992i \(-0.895984\pi\)
0.195554 0.980693i \(-0.437350\pi\)
\(182\) 0.159651 0.0921746i 0.0118341 0.00683243i
\(183\) 4.85857 + 2.80510i 0.359156 + 0.207359i
\(184\) −2.34106 −0.172585
\(185\) 11.9794 + 6.44150i 0.880746 + 0.473588i
\(186\) −0.757045 −0.0555092
\(187\) −14.0623 8.11888i −1.02834 0.593711i
\(188\) −0.675926 + 0.390246i −0.0492970 + 0.0284616i
\(189\) −0.964193 1.67003i −0.0701348 0.121477i
\(190\) −1.10332 0.107770i −0.0800432 0.00781847i
\(191\) −12.1924 −0.882212 −0.441106 0.897455i \(-0.645414\pi\)
−0.441106 + 0.897455i \(0.645414\pi\)
\(192\) −6.57193 + 3.79430i −0.474288 + 0.273830i
\(193\) 17.2710i 1.24319i 0.783338 + 0.621596i \(0.213516\pi\)
−0.783338 + 0.621596i \(0.786484\pi\)
\(194\) 0.708190 1.22662i 0.0508451 0.0880663i
\(195\) 1.32313 + 0.946529i 0.0947513 + 0.0677824i
\(196\) 6.50599 0.464714
\(197\) −8.51791 4.91781i −0.606876 0.350380i 0.164866 0.986316i \(-0.447281\pi\)
−0.771742 + 0.635936i \(0.780614\pi\)
\(198\) 0.535486 0.309163i 0.0380553 0.0219713i
\(199\) −13.4990 −0.956918 −0.478459 0.878110i \(-0.658805\pi\)
−0.478459 + 0.878110i \(0.658805\pi\)
\(200\) 0.506341 2.56716i 0.0358037 0.181525i
\(201\) 6.08619 10.5416i 0.429287 0.743547i
\(202\) −0.833640 0.481302i −0.0586547 0.0338643i
\(203\) −0.0526155 + 0.0303775i −0.00369288 + 0.00213209i
\(204\) 3.42083 + 5.92505i 0.239506 + 0.414837i
\(205\) −18.7484 + 8.51298i −1.30944 + 0.594572i
\(206\) 0.324562 0.562158i 0.0226133 0.0391674i
\(207\) 3.87412 + 2.23672i 0.269270 + 0.155463i
\(208\) 2.83502i 0.196573i
\(209\) −8.87745 15.3762i −0.614066 1.06359i
\(210\) 0.234251 + 0.515896i 0.0161648 + 0.0356002i
\(211\) −21.8381 −1.50339 −0.751697 0.659509i \(-0.770764\pi\)
−0.751697 + 0.659509i \(0.770764\pi\)
\(212\) 14.1377i 0.970980i
\(213\) 7.97969 + 4.60707i 0.546759 + 0.315671i
\(214\) −1.77691 −0.121467
\(215\) 15.6952 + 1.53308i 1.07041 + 0.104555i
\(216\) −0.523323 −0.0356076
\(217\) 9.62184 5.55517i 0.653173 0.377110i
\(218\) −0.826852 + 0.477383i −0.0560015 + 0.0323325i
\(219\) 1.31524 + 2.27807i 0.0888758 + 0.153937i
\(220\) 18.9965 8.62564i 1.28074 0.581541i
\(221\) 2.51047 0.168873
\(222\) −0.308294 + 0.737411i −0.0206913 + 0.0494918i
\(223\) 4.02134i 0.269289i 0.990894 + 0.134644i \(0.0429892\pi\)
−0.990894 + 0.134644i \(0.957011\pi\)
\(224\) −1.50286 + 2.60302i −0.100414 + 0.173922i
\(225\) −3.29067 + 3.76451i −0.219378 + 0.250967i
\(226\) −0.318432 0.551541i −0.0211818 0.0366880i
\(227\) 21.8135 12.5941i 1.44782 0.835897i 0.449465 0.893298i \(-0.351615\pi\)
0.998351 + 0.0574013i \(0.0182815\pi\)
\(228\) 7.48091i 0.495435i
\(229\) 7.22513 + 12.5143i 0.477450 + 0.826968i 0.999666 0.0258457i \(-0.00822787\pi\)
−0.522216 + 0.852813i \(0.674895\pi\)
\(230\) −1.06899 0.764727i −0.0704873 0.0504246i
\(231\) −4.53725 + 7.85875i −0.298529 + 0.517068i
\(232\) 0.0164876i 0.00108247i
\(233\) 16.4445i 1.07731i 0.842525 + 0.538657i \(0.181068\pi\)
−0.842525 + 0.538657i \(0.818932\pi\)
\(234\) −0.0477988 + 0.0827899i −0.00312471 + 0.00541215i
\(235\) −0.876046 0.0855705i −0.0571469 0.00558201i
\(236\) −14.9520 −0.973289
\(237\) −6.25729 3.61265i −0.406454 0.234667i
\(238\) 0.757200 + 0.437170i 0.0490820 + 0.0283375i
\(239\) 8.61112 14.9149i 0.557007 0.964765i −0.440737 0.897636i \(-0.645283\pi\)
0.997744 0.0671284i \(-0.0213837\pi\)
\(240\) −8.67203 0.847067i −0.559777 0.0546780i
\(241\) −0.986408 1.70851i −0.0635401 0.110055i 0.832505 0.554017i \(-0.186906\pi\)
−0.896045 + 0.443962i \(0.853572\pi\)
\(242\) −1.26813 0.732155i −0.0815184 0.0470647i
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) −5.56176 + 9.63326i −0.356055 + 0.616706i
\(245\) 5.96751 + 4.26899i 0.381250 + 0.272736i
\(246\) −0.604981 1.04786i −0.0385722 0.0668090i
\(247\) 2.37727 + 1.37252i 0.151262 + 0.0873312i
\(248\) 3.01511i 0.191460i
\(249\) 12.4103 0.786468
\(250\) 1.06979 1.00684i 0.0676597 0.0636779i
\(251\) 14.2516 0.899551 0.449775 0.893142i \(-0.351504\pi\)
0.449775 + 0.893142i \(0.351504\pi\)
\(252\) 3.31123 1.91174i 0.208588 0.120428i
\(253\) 21.0509i 1.32346i
\(254\) 0.0712306 + 0.123375i 0.00446940 + 0.00774123i
\(255\) −0.750097 + 7.67927i −0.0469729 + 0.480895i
\(256\) −7.31829 12.6756i −0.457393 0.792228i
\(257\) 16.0273 + 9.25337i 0.999756 + 0.577209i 0.908176 0.418588i \(-0.137475\pi\)
0.0915798 + 0.995798i \(0.470808\pi\)
\(258\) 0.926687i 0.0576930i
\(259\) −1.49277 11.6345i −0.0927562 0.722936i
\(260\) −1.87672 + 2.62342i −0.116389 + 0.162697i
\(261\) 0.0157528 0.0272847i 0.000975076 0.00168888i
\(262\) 1.26090 0.727980i 0.0778986 0.0449748i
\(263\) −8.83757 + 5.10237i −0.544948 + 0.314626i −0.747082 0.664732i \(-0.768546\pi\)
0.202134 + 0.979358i \(0.435212\pi\)
\(264\) 1.23131 + 2.13270i 0.0757821 + 0.131259i
\(265\) −9.27661 + 12.9675i −0.569858 + 0.796590i
\(266\) 0.478016 + 0.827948i 0.0293090 + 0.0507647i
\(267\) 2.21231i 0.135391i
\(268\) 20.9012 + 12.0673i 1.27674 + 0.737128i
\(269\) 6.13164 0.373852 0.186926 0.982374i \(-0.440147\pi\)
0.186926 + 0.982374i \(0.440147\pi\)
\(270\) −0.238964 0.170948i −0.0145429 0.0104036i
\(271\) −15.0976 + 26.1498i −0.917113 + 1.58849i −0.113334 + 0.993557i \(0.536153\pi\)
−0.803778 + 0.594929i \(0.797180\pi\)
\(272\) −11.6446 + 6.72303i −0.706059 + 0.407643i
\(273\) 1.40298i 0.0849124i
\(274\) −0.927877 + 1.60713i −0.0560551 + 0.0970903i
\(275\) 23.0840 + 4.55305i 1.39202 + 0.274559i
\(276\) −4.43483 + 7.68135i −0.266945 + 0.462363i
\(277\) 12.1146 6.99434i 0.727893 0.420249i −0.0897577 0.995964i \(-0.528609\pi\)
0.817651 + 0.575714i \(0.195276\pi\)
\(278\) −1.97763 + 1.14178i −0.118610 + 0.0684796i
\(279\) −2.88073 + 4.98958i −0.172465 + 0.298718i
\(280\) −2.05468 + 0.932958i −0.122791 + 0.0557549i
\(281\) −6.68503 + 11.5788i −0.398796 + 0.690734i −0.993578 0.113153i \(-0.963905\pi\)
0.594782 + 0.803887i \(0.297238\pi\)
\(282\) 0.0517240i 0.00308012i
\(283\) 16.5340 9.54594i 0.982847 0.567447i 0.0797186 0.996817i \(-0.474598\pi\)
0.903128 + 0.429370i \(0.141265\pi\)
\(284\) −9.13460 + 15.8216i −0.542039 + 0.938839i
\(285\) −4.90869 + 6.86173i −0.290765 + 0.406454i
\(286\) 0.449858 0.0266007
\(287\) 15.3783 + 8.87866i 0.907752 + 0.524091i
\(288\) 1.55867i 0.0918452i
\(289\) −2.54661 4.41086i −0.149801 0.259462i
\(290\) −0.00538583 + 0.00752872i −0.000316267 + 0.000442102i
\(291\) −5.38966 9.33516i −0.315947 0.547237i
\(292\) −4.51680 + 2.60778i −0.264326 + 0.152609i
\(293\) −20.6245 + 11.9076i −1.20490 + 0.695648i −0.961640 0.274314i \(-0.911549\pi\)
−0.243257 + 0.969962i \(0.578216\pi\)
\(294\) −0.215580 + 0.373395i −0.0125729 + 0.0217768i
\(295\) −13.7144 9.81090i −0.798484 0.571213i
\(296\) −2.93691 1.22785i −0.170705 0.0713675i
\(297\) 4.70575i 0.273055i
\(298\) −0.512261 0.295754i −0.0296745 0.0171326i
\(299\) 1.62731 + 2.81859i 0.0941098 + 0.163003i
\(300\) −7.46401 6.52452i −0.430935 0.376693i
\(301\) −6.80000 11.7779i −0.391945 0.678869i
\(302\) 0.131226i 0.00755120i
\(303\) −6.34439 + 3.66294i −0.364476 + 0.210430i
\(304\) −14.7024 −0.843238
\(305\) −11.4224 + 5.18652i −0.654045 + 0.296979i
\(306\) −0.453404 −0.0259194
\(307\) 0.184371i 0.0105226i 0.999986 + 0.00526130i \(0.00167473\pi\)
−0.999986 + 0.00526130i \(0.998325\pi\)
\(308\) −15.5818 8.99617i −0.887857 0.512604i
\(309\) −2.47007 4.27828i −0.140517 0.243383i
\(310\) 0.984912 1.37678i 0.0559392 0.0781961i
\(311\) −13.5188 + 23.4152i −0.766580 + 1.32775i 0.172828 + 0.984952i \(0.444710\pi\)
−0.939407 + 0.342803i \(0.888624\pi\)
\(312\) −0.329730 0.190370i −0.0186673 0.0107776i
\(313\) 22.2068 + 12.8211i 1.25520 + 0.724692i 0.972138 0.234409i \(-0.0753154\pi\)
0.283065 + 0.959101i \(0.408649\pi\)
\(314\) 0.520676 + 0.901838i 0.0293835 + 0.0508936i
\(315\) 4.29158 + 0.419193i 0.241803 + 0.0236189i
\(316\) 7.16292 12.4065i 0.402946 0.697922i
\(317\) −27.2695 15.7441i −1.53161 0.884275i −0.999288 0.0377320i \(-0.987987\pi\)
−0.532321 0.846543i \(-0.678680\pi\)
\(318\) −0.811396 0.468460i −0.0455008 0.0262699i
\(319\) −0.148258 −0.00830084
\(320\) 1.64961 16.8883i 0.0922162 0.944083i
\(321\) −6.76157 + 11.7114i −0.377394 + 0.653665i
\(322\) 1.13351i 0.0631680i
\(323\) 13.0193i 0.724412i
\(324\) −0.991367 + 1.71710i −0.0550760 + 0.0953944i
\(325\) −3.44277 + 1.17485i −0.190971 + 0.0651691i
\(326\) 1.02410 + 1.77380i 0.0567199 + 0.0982418i
\(327\) 7.26622i 0.401823i
\(328\) 4.17334 2.40948i 0.230434 0.133041i
\(329\) 0.379549 + 0.657399i 0.0209252 + 0.0362436i
\(330\) −0.134412 + 1.37607i −0.00739913 + 0.0757501i
\(331\) 1.73146 2.99897i 0.0951694 0.164838i −0.814510 0.580150i \(-0.802994\pi\)
0.909679 + 0.415311i \(0.136327\pi\)
\(332\) 24.6063i 1.35044i
\(333\) 3.68704 + 4.83794i 0.202049 + 0.265118i
\(334\) 2.71068 0.148322
\(335\) 11.2531 + 24.7831i 0.614825 + 1.35404i
\(336\) 3.75718 + 6.50762i 0.204971 + 0.355020i
\(337\) −15.2132 + 8.78334i −0.828715 + 0.478459i −0.853413 0.521236i \(-0.825471\pi\)
0.0246972 + 0.999695i \(0.492138\pi\)
\(338\) 1.41909 0.819311i 0.0771882 0.0445646i
\(339\) −4.84684 −0.263244
\(340\) −15.2260 1.48724i −0.825744 0.0806571i
\(341\) 27.1120 1.46820
\(342\) −0.429347 0.247884i −0.0232164 0.0134040i
\(343\) 19.8264i 1.07052i
\(344\) −3.69075 −0.198992
\(345\) −9.10798 + 4.13562i −0.490357 + 0.222654i
\(346\) 0.611863 + 1.05978i 0.0328940 + 0.0569740i
\(347\) 25.2741i 1.35678i 0.734701 + 0.678391i \(0.237323\pi\)
−0.734701 + 0.678391i \(0.762677\pi\)
\(348\) 0.0540983 + 0.0312337i 0.00289997 + 0.00167430i
\(349\) 14.5392 25.1827i 0.778267 1.34800i −0.154673 0.987966i \(-0.549432\pi\)
0.932940 0.360033i \(-0.117234\pi\)
\(350\) −1.24298 0.245164i −0.0664403 0.0131046i
\(351\) 0.363771 + 0.630070i 0.0194167 + 0.0336307i
\(352\) −6.35203 + 3.66734i −0.338564 + 0.195470i
\(353\) −27.2188 15.7148i −1.44871 0.836412i −0.450304 0.892875i \(-0.648684\pi\)
−0.998405 + 0.0564629i \(0.982018\pi\)
\(354\) 0.495441 0.858129i 0.0263324 0.0456090i
\(355\) −18.7601 + 8.51831i −0.995682 + 0.452105i
\(356\) 4.38643 0.232480
\(357\) 5.76265 3.32707i 0.304992 0.176087i
\(358\) 0.313971 + 0.181271i 0.0165939 + 0.00958047i
\(359\) 34.5378 1.82283 0.911417 0.411483i \(-0.134989\pi\)
0.911417 + 0.411483i \(0.134989\pi\)
\(360\) 0.680841 0.951731i 0.0358835 0.0501606i
\(361\) 2.38215 4.12600i 0.125376 0.217158i
\(362\) 2.65707i 0.139653i
\(363\) −9.65106 + 5.57204i −0.506549 + 0.292456i
\(364\) 2.78174 0.145803
\(365\) −5.85408 0.571816i −0.306417 0.0299302i
\(366\) −0.368584 0.638406i −0.0192662 0.0333700i
\(367\) 28.5194 16.4657i 1.48870 0.859500i 0.488782 0.872406i \(-0.337441\pi\)
0.999917 + 0.0129056i \(0.00410811\pi\)
\(368\) −15.0963 8.71585i −0.786949 0.454345i
\(369\) −9.20838 −0.479369
\(370\) −0.939989 1.52004i −0.0488677 0.0790232i
\(371\) 13.7502 0.713873
\(372\) −9.89301 5.71173i −0.512929 0.296139i
\(373\) −2.49061 + 1.43795i −0.128959 + 0.0744544i −0.563092 0.826394i \(-0.690388\pi\)
0.434133 + 0.900849i \(0.357055\pi\)
\(374\) 1.06680 + 1.84776i 0.0551631 + 0.0955453i
\(375\) −2.56509 10.8821i −0.132461 0.561950i
\(376\) 0.206003 0.0106238
\(377\) 0.0198508 0.0114609i 0.00102237 0.000590264i
\(378\) 0.253386i 0.0130328i
\(379\) −5.77117 + 9.99596i −0.296445 + 0.513458i −0.975320 0.220796i \(-0.929135\pi\)
0.678875 + 0.734254i \(0.262468\pi\)
\(380\) −13.6050 9.73262i −0.697921 0.499273i
\(381\) 1.08420 0.0555450
\(382\) 1.38742 + 0.801029i 0.0709868 + 0.0409842i
\(383\) 20.0001 11.5471i 1.02196 0.590028i 0.107288 0.994228i \(-0.465783\pi\)
0.914671 + 0.404200i \(0.132450\pi\)
\(384\) 4.11446 0.209965
\(385\) −8.38921 18.4758i −0.427554 0.941613i
\(386\) 1.13469 1.96533i 0.0577540 0.100033i
\(387\) 6.10766 + 3.52626i 0.310470 + 0.179250i
\(388\) 18.5091 10.6863i 0.939659 0.542513i
\(389\) −2.74022 4.74619i −0.138934 0.240642i 0.788159 0.615472i \(-0.211034\pi\)
−0.927094 + 0.374830i \(0.877701\pi\)
\(390\) −0.0883782 0.194638i −0.00447520 0.00985586i
\(391\) −7.71808 + 13.3681i −0.390320 + 0.676054i
\(392\) −1.48713 0.858596i −0.0751115 0.0433657i
\(393\) 11.0805i 0.558939i
\(394\) 0.646191 + 1.11924i 0.0325546 + 0.0563863i
\(395\) 14.7108 6.67965i 0.740179 0.336090i
\(396\) 9.33025 0.468863
\(397\) 10.3805i 0.520981i −0.965476 0.260490i \(-0.916116\pi\)
0.965476 0.260490i \(-0.0838843\pi\)
\(398\) 1.53610 + 0.886870i 0.0769979 + 0.0444548i
\(399\) 7.27585 0.364248
\(400\) 12.8228 14.6692i 0.641138 0.733458i
\(401\) −8.40952 −0.419951 −0.209976 0.977707i \(-0.567338\pi\)
−0.209976 + 0.977707i \(0.567338\pi\)
\(402\) −1.38514 + 0.799713i −0.0690847 + 0.0398861i
\(403\) −3.63013 + 2.09586i −0.180830 + 0.104402i
\(404\) −7.26263 12.5792i −0.361329 0.625841i
\(405\) −2.03601 + 0.924481i −0.101170 + 0.0459378i
\(406\) 0.00798310 0.000396194
\(407\) 11.0409 26.4089i 0.547278 1.30904i
\(408\) 1.80579i 0.0893999i
\(409\) 7.53047 13.0432i 0.372358 0.644943i −0.617570 0.786516i \(-0.711883\pi\)
0.989928 + 0.141573i \(0.0452161\pi\)
\(410\) 2.69274 + 0.263022i 0.132985 + 0.0129897i
\(411\) 7.06158 + 12.2310i 0.348322 + 0.603311i
\(412\) 8.48270 4.89749i 0.417913 0.241282i
\(413\) 14.5421i 0.715571i
\(414\) −0.293901 0.509051i −0.0144444 0.0250185i
\(415\) −16.1457 + 22.5697i −0.792561 + 1.10790i
\(416\) 0.566998 0.982069i 0.0277993 0.0481499i
\(417\) 17.3790i 0.851054i
\(418\) 2.33296i 0.114109i
\(419\) −3.93907 + 6.82267i −0.192436 + 0.333309i −0.946057 0.324000i \(-0.894972\pi\)
0.753621 + 0.657309i \(0.228305\pi\)
\(420\) −0.831149 + 8.50906i −0.0405559 + 0.415200i
\(421\) 39.1270 1.90693 0.953466 0.301500i \(-0.0974873\pi\)
0.953466 + 0.301500i \(0.0974873\pi\)
\(422\) 2.48504 + 1.43474i 0.120970 + 0.0698420i
\(423\) −0.340906 0.196822i −0.0165754 0.00956982i
\(424\) 1.86575 3.23158i 0.0906089 0.156939i
\(425\) −12.9899 11.3548i −0.630102 0.550791i
\(426\) −0.605360 1.04851i −0.0293298 0.0508007i
\(427\) 9.36920 + 5.40931i 0.453408 + 0.261775i
\(428\) −23.2205 13.4064i −1.12241 0.648022i
\(429\) 1.71182 2.96495i 0.0826473 0.143149i
\(430\) −1.68530 1.20562i −0.0812724 0.0581399i
\(431\) −7.96516 13.7961i −0.383668 0.664533i 0.607915 0.794002i \(-0.292006\pi\)
−0.991583 + 0.129469i \(0.958673\pi\)
\(432\) −3.37465 1.94835i −0.162363 0.0937402i
\(433\) 33.5864i 1.61406i 0.590511 + 0.807029i \(0.298926\pi\)
−0.590511 + 0.807029i \(0.701074\pi\)
\(434\) −1.45988 −0.0700763
\(435\) 0.0291264 + 0.0641458i 0.00139650 + 0.00307556i
\(436\) −14.4070 −0.689970
\(437\) −14.6171 + 8.43921i −0.699233 + 0.403702i
\(438\) 0.345640i 0.0165153i
\(439\) 2.10728 + 3.64991i 0.100575 + 0.174201i 0.911922 0.410364i \(-0.134598\pi\)
−0.811347 + 0.584565i \(0.801265\pi\)
\(440\) −5.48052 0.535327i −0.261274 0.0255207i
\(441\) 1.64066 + 2.84171i 0.0781268 + 0.135320i
\(442\) −0.285677 0.164935i −0.0135883 0.00784518i
\(443\) 24.7062i 1.17383i −0.809649 0.586914i \(-0.800343\pi\)
0.809649 0.586914i \(-0.199657\pi\)
\(444\) −9.59236 + 7.31043i −0.455233 + 0.346938i
\(445\) 4.02338 + 2.87821i 0.190726 + 0.136440i
\(446\) 0.264198 0.457604i 0.0125101 0.0216682i
\(447\) −3.89855 + 2.25083i −0.184395 + 0.106461i
\(448\) −12.6732 + 7.31688i −0.598753 + 0.345690i
\(449\) −14.8316 25.6891i −0.699947 1.21234i −0.968484 0.249075i \(-0.919874\pi\)
0.268537 0.963269i \(-0.413460\pi\)
\(450\) 0.621782 0.212184i 0.0293111 0.0100025i
\(451\) 21.6662 + 37.5269i 1.02022 + 1.76707i
\(452\) 9.60999i 0.452016i
\(453\) 0.864891 + 0.499345i 0.0406361 + 0.0234613i
\(454\) −3.30967 −0.155330
\(455\) 2.55151 + 1.82527i 0.119616 + 0.0855702i
\(456\) 0.987255 1.70998i 0.0462325 0.0800770i
\(457\) −17.7792 + 10.2648i −0.831674 + 0.480167i −0.854425 0.519574i \(-0.826091\pi\)
0.0227515 + 0.999741i \(0.492757\pi\)
\(458\) 1.89873i 0.0887220i
\(459\) −1.72531 + 2.98832i −0.0805306 + 0.139483i
\(460\) −8.19983 18.0587i −0.382319 0.841991i
\(461\) −10.8248 + 18.7491i −0.504162 + 0.873235i 0.495826 + 0.868422i \(0.334865\pi\)
−0.999988 + 0.00481284i \(0.998468\pi\)
\(462\) 1.03262 0.596186i 0.0480420 0.0277371i
\(463\) 22.6762 13.0921i 1.05385 0.608443i 0.130129 0.991497i \(-0.458461\pi\)
0.923726 + 0.383054i \(0.125128\pi\)
\(464\) −0.0613841 + 0.106320i −0.00284969 + 0.00493580i
\(465\) −5.32637 11.7304i −0.247004 0.543984i
\(466\) 1.08039 1.87128i 0.0500479 0.0866855i
\(467\) 36.9707i 1.71080i 0.517969 + 0.855400i \(0.326688\pi\)
−0.517969 + 0.855400i \(0.673312\pi\)
\(468\) −1.24926 + 0.721262i −0.0577472 + 0.0333403i
\(469\) 11.7365 20.3283i 0.541943 0.938672i
\(470\) 0.0940669 + 0.0672927i 0.00433898 + 0.00310398i
\(471\) 7.92518 0.365173
\(472\) 3.41770 + 1.97321i 0.157312 + 0.0908244i
\(473\) 33.1874i 1.52596i
\(474\) 0.474694 + 0.822195i 0.0218034 + 0.0377647i
\(475\) −6.09277 17.8542i −0.279555 0.819205i
\(476\) 6.59669 + 11.4258i 0.302359 + 0.523701i
\(477\) −6.17510 + 3.56520i −0.282739 + 0.163239i
\(478\) −1.95979 + 1.13148i −0.0896386 + 0.0517529i
\(479\) −14.9311 + 25.8614i −0.682217 + 1.18164i 0.292085 + 0.956392i \(0.405651\pi\)
−0.974303 + 0.225243i \(0.927682\pi\)
\(480\) 2.83463 + 2.02782i 0.129383 + 0.0925567i
\(481\) 0.563192 + 4.38949i 0.0256794 + 0.200143i
\(482\) 0.259224i 0.0118073i
\(483\) 7.47080 + 4.31327i 0.339933 + 0.196260i
\(484\) −11.0479 19.1355i −0.502176 0.869795i
\(485\) 23.9891 + 2.34321i 1.08929 + 0.106400i
\(486\) −0.0656990 0.113794i −0.00298017 0.00516180i
\(487\) 27.2480i 1.23472i −0.786679 0.617362i \(-0.788201\pi\)
0.786679 0.617362i \(-0.211799\pi\)
\(488\) 2.54260 1.46797i 0.115098 0.0664520i
\(489\) 15.5878 0.704906
\(490\) −0.398599 0.877844i −0.0180069 0.0396570i
\(491\) 23.3549 1.05399 0.526996 0.849868i \(-0.323318\pi\)
0.526996 + 0.849868i \(0.323318\pi\)
\(492\) 18.2578i 0.823124i
\(493\) 0.0941491 + 0.0543570i 0.00424026 + 0.00244812i
\(494\) −0.180346 0.312368i −0.00811415 0.0140541i
\(495\) 8.55801 + 6.12216i 0.384654 + 0.275171i
\(496\) 11.2254 19.4429i 0.504034 0.873013i
\(497\) 15.3879 + 8.88422i 0.690243 + 0.398512i
\(498\) −1.41221 0.815341i −0.0632828 0.0365363i
\(499\) 10.2603 + 17.7714i 0.459314 + 0.795556i 0.998925 0.0463591i \(-0.0147618\pi\)
−0.539611 + 0.841915i \(0.681429\pi\)
\(500\) 21.5763 5.08590i 0.964923 0.227448i
\(501\) 10.3148 17.8657i 0.460830 0.798180i
\(502\) −1.62174 0.936313i −0.0723819 0.0417897i
\(503\) −15.2193 8.78687i −0.678596 0.391787i 0.120730 0.992685i \(-0.461476\pi\)
−0.799326 + 0.600898i \(0.794810\pi\)
\(504\) −1.00917 −0.0449520
\(505\) 1.59250 16.3036i 0.0708654 0.725499i
\(506\) −1.38302 + 2.39547i −0.0614829 + 0.106492i
\(507\) 12.4707i 0.553842i
\(508\) 2.14967i 0.0953763i
\(509\) 2.55351 4.42280i 0.113182 0.196037i −0.803869 0.594806i \(-0.797229\pi\)
0.917052 + 0.398769i \(0.130562\pi\)
\(510\) 0.589877 0.824574i 0.0261202 0.0365128i
\(511\) 2.53630 + 4.39299i 0.112199 + 0.194335i
\(512\) 10.1521i 0.448665i
\(513\) −3.26753 + 1.88651i −0.144265 + 0.0832915i
\(514\) −1.21587 2.10596i −0.0536299 0.0928897i
\(515\) 10.9942 + 1.07389i 0.484461 + 0.0473212i
\(516\) −6.99164 + 12.1099i −0.307790 + 0.533108i
\(517\) 1.85239i 0.0814681i
\(518\) −0.594510 + 1.42201i −0.0261213 + 0.0624797i
\(519\) 9.31313 0.408801
\(520\) 0.775190 0.351987i 0.0339943 0.0154356i
\(521\) 12.7661 + 22.1115i 0.559291 + 0.968721i 0.997556 + 0.0698751i \(0.0222601\pi\)
−0.438264 + 0.898846i \(0.644407\pi\)
\(522\) −0.00358515 + 0.00206989i −0.000156918 + 9.05966e-5i
\(523\) 28.1108 16.2298i 1.22920 0.709679i 0.262337 0.964976i \(-0.415507\pi\)
0.966862 + 0.255298i \(0.0821735\pi\)
\(524\) 21.9698 0.959754
\(525\) −6.34568 + 7.25942i −0.276948 + 0.316827i
\(526\) 1.34088 0.0584653
\(527\) −17.2171 9.94032i −0.749990 0.433007i
\(528\) 18.3369i 0.798012i
\(529\) 2.98828 0.129925
\(530\) 1.90758 0.866165i 0.0828598 0.0376238i
\(531\) −3.77054 6.53076i −0.163627 0.283411i
\(532\) 14.4261i 0.625450i
\(533\) −5.80193 3.34974i −0.251309 0.145094i
\(534\) −0.145347 + 0.251748i −0.00628977 + 0.0108942i
\(535\) −12.5019 27.5332i −0.540504 1.19037i
\(536\) −3.18505 5.51666i −0.137573 0.238283i
\(537\) 2.38946 1.37956i 0.103113 0.0595323i
\(538\) −0.697743 0.402842i −0.0300818 0.0173678i
\(539\) 7.72054 13.3724i 0.332547 0.575989i
\(540\) −1.83300 4.03687i −0.0788798 0.173719i
\(541\) 21.8256 0.938355 0.469177 0.883104i \(-0.344551\pi\)
0.469177 + 0.883104i \(0.344551\pi\)
\(542\) 3.43603 1.98379i 0.147590 0.0852111i
\(543\) 17.5124 + 10.1108i 0.751528 + 0.433895i
\(544\) 5.37836 0.230595
\(545\) −13.2146 9.45332i −0.566050 0.404936i
\(546\) −0.0921746 + 0.159651i −0.00394471 + 0.00683243i
\(547\) 7.15186i 0.305791i −0.988242 0.152896i \(-0.951140\pi\)
0.988242 0.152896i \(-0.0488598\pi\)
\(548\) −24.2509 + 14.0012i −1.03595 + 0.598103i
\(549\) −5.61019 −0.239437
\(550\) −2.32769 2.03471i −0.0992531 0.0867601i
\(551\) 0.0594358 + 0.102946i 0.00253205 + 0.00438564i
\(552\) 2.02742 1.17053i 0.0862926 0.0498210i
\(553\) −12.0665 6.96658i −0.513119 0.296249i
\(554\) −1.83808 −0.0780927
\(555\) −13.5953 + 0.411225i −0.577086 + 0.0174555i
\(556\) −34.4580 −1.46134
\(557\) −7.70945 4.45105i −0.326660 0.188597i 0.327697 0.944783i \(-0.393727\pi\)
−0.654357 + 0.756186i \(0.727061\pi\)
\(558\) 0.655620 0.378523i 0.0277546 0.0160241i
\(559\) 2.56550 + 4.44358i 0.108509 + 0.187944i
\(560\) −16.7230 1.63347i −0.706677 0.0690269i
\(561\) 16.2378 0.685559
\(562\) 1.52143 0.878400i 0.0641778 0.0370531i
\(563\) 15.2521i 0.642799i 0.946944 + 0.321399i \(0.104153\pi\)
−0.946944 + 0.321399i \(0.895847\pi\)
\(564\) 0.390246 0.675926i 0.0164323 0.0284616i
\(565\) 6.30571 8.81460i 0.265283 0.370833i
\(566\) −2.50863 −0.105446
\(567\) 1.67003 + 0.964193i 0.0701348 + 0.0404923i
\(568\) 4.17595 2.41099i 0.175219 0.101163i
\(569\) 15.7504 0.660292 0.330146 0.943930i \(-0.392902\pi\)
0.330146 + 0.943930i \(0.392902\pi\)
\(570\) 1.00939 0.458328i 0.0422786 0.0191972i
\(571\) −12.4399 + 21.5465i −0.520593 + 0.901694i 0.479120 + 0.877750i \(0.340956\pi\)
−0.999713 + 0.0239449i \(0.992377\pi\)
\(572\) 5.87871 + 3.39408i 0.245801 + 0.141914i
\(573\) 10.5589 6.09621i 0.441106 0.254673i
\(574\) −1.16664 2.02068i −0.0486945 0.0843414i
\(575\) 4.32828 21.9445i 0.180502 0.915147i
\(576\) 3.79430 6.57193i 0.158096 0.273830i
\(577\) 31.7849 + 18.3510i 1.32322 + 0.763962i 0.984241 0.176832i \(-0.0565849\pi\)
0.338980 + 0.940794i \(0.389918\pi\)
\(578\) 0.669239i 0.0278367i
\(579\) −8.63549 14.9571i −0.358879 0.621596i
\(580\) −0.127184 + 0.0577499i −0.00528103 + 0.00239793i
\(581\) 23.9318 0.992858
\(582\) 1.41638i 0.0587108i
\(583\) 29.0585 + 16.7769i 1.20348 + 0.694829i
\(584\) 1.37659 0.0569638
\(585\) −1.61913 0.158153i −0.0669427 0.00653884i
\(586\) 3.12926 0.129269
\(587\) 10.1890 5.88263i 0.420545 0.242802i −0.274765 0.961511i \(-0.588600\pi\)
0.695311 + 0.718709i \(0.255267\pi\)
\(588\) −5.63436 + 3.25300i −0.232357 + 0.134151i
\(589\) −10.8691 18.8258i −0.447853 0.775703i
\(590\) 0.916052 + 2.01745i 0.0377133 + 0.0830569i
\(591\) 9.83563 0.404584
\(592\) −14.3673 18.8520i −0.590494 0.774814i
\(593\) 3.11542i 0.127935i −0.997952 0.0639675i \(-0.979625\pi\)
0.997952 0.0639675i \(-0.0203754\pi\)
\(594\) −0.309163 + 0.535486i −0.0126851 + 0.0219713i
\(595\) −1.44648 + 14.8086i −0.0592998 + 0.607094i
\(596\) −4.46280 7.72979i −0.182803 0.316625i
\(597\) 11.6905 6.74950i 0.478459 0.276239i
\(598\) 0.427651i 0.0174879i
\(599\) 8.80233 + 15.2461i 0.359653 + 0.622938i 0.987903 0.155074i \(-0.0495616\pi\)
−0.628249 + 0.778012i \(0.716228\pi\)
\(600\) 0.845074 + 2.47639i 0.0345000 + 0.101098i
\(601\) −3.56489 + 6.17458i −0.145415 + 0.251866i −0.929528 0.368752i \(-0.879785\pi\)
0.784113 + 0.620619i \(0.213118\pi\)
\(602\) 1.78701i 0.0728331i
\(603\) 12.1724i 0.495698i
\(604\) −0.990069 + 1.71485i −0.0402853 + 0.0697762i
\(605\) 2.42250 24.8009i 0.0984888 1.00830i
\(606\) 0.962605 0.0391031
\(607\) −35.5966 20.5517i −1.44482 0.834167i −0.446654 0.894707i \(-0.647385\pi\)
−0.998166 + 0.0605396i \(0.980718\pi\)
\(608\) 5.09299 + 2.94044i 0.206548 + 0.119251i
\(609\) 0.0303775 0.0526155i 0.00123096 0.00213209i
\(610\) 1.64055 + 0.160246i 0.0664239 + 0.00648817i
\(611\) −0.143196 0.248024i −0.00579311 0.0100340i
\(612\) −5.92505 3.42083i −0.239506 0.138279i
\(613\) −22.6416 13.0721i −0.914487 0.527979i −0.0326146 0.999468i \(-0.510383\pi\)
−0.881872 + 0.471489i \(0.843717\pi\)
\(614\) 0.0121130 0.0209803i 0.000488840 0.000846695i
\(615\) 11.9801 16.7466i 0.483083 0.675289i
\(616\) 2.37445 + 4.11267i 0.0956693 + 0.165704i
\(617\) 2.29295 + 1.32384i 0.0923108 + 0.0532957i 0.545445 0.838147i \(-0.316361\pi\)
−0.453134 + 0.891442i \(0.649694\pi\)
\(618\) 0.649124i 0.0261116i
\(619\) −39.5201 −1.58845 −0.794223 0.607626i \(-0.792122\pi\)
−0.794223 + 0.607626i \(0.792122\pi\)
\(620\) 23.2583 10.5608i 0.934075 0.424131i
\(621\) −4.47345 −0.179513
\(622\) 3.07671 1.77634i 0.123365 0.0712247i
\(623\) 4.26620i 0.170922i
\(624\) −1.41751 2.45520i −0.0567458 0.0982866i
\(625\) 23.1277 + 9.49261i 0.925108 + 0.379705i
\(626\) −1.68467 2.91793i −0.0673329 0.116624i
\(627\) 15.3762 + 8.87745i 0.614066 + 0.354531i
\(628\) 15.7135i 0.627038i
\(629\) −16.6939 + 12.7226i −0.665630 + 0.507283i
\(630\) −0.460815 0.329654i −0.0183593 0.0131337i
\(631\) 3.35439 5.80997i 0.133536 0.231291i −0.791501 0.611168i \(-0.790700\pi\)
0.925037 + 0.379876i \(0.124033\pi\)
\(632\) −3.27458 + 1.89058i −0.130256 + 0.0752033i
\(633\) 18.9123 10.9190i 0.751697 0.433993i
\(634\) 2.06874 + 3.58316i 0.0821601 + 0.142305i
\(635\) −1.41053 + 1.97175i −0.0559753 + 0.0782465i
\(636\) −7.06884 12.2436i −0.280298 0.485490i
\(637\) 2.38730i 0.0945884i
\(638\) 0.0168708 + 0.00974038i 0.000667923 + 0.000385625i
\(639\) −9.21415 −0.364506
\(640\) −5.35289 + 7.48267i −0.211592 + 0.295779i
\(641\) 14.5975 25.2837i 0.576568 0.998646i −0.419301 0.907847i \(-0.637725\pi\)
0.995869 0.0907984i \(-0.0289419\pi\)
\(642\) 1.53885 0.888456i 0.0607336 0.0350646i
\(643\) 32.3849i 1.27713i −0.769566 0.638567i \(-0.779527\pi\)
0.769566 0.638567i \(-0.220473\pi\)
\(644\) −8.55206 + 14.8126i −0.336999 + 0.583699i
\(645\) −14.3590 + 6.51993i −0.565385 + 0.256722i
\(646\) 0.855353 1.48151i 0.0336534 0.0582894i
\(647\) −29.1274 + 16.8167i −1.14511 + 0.661132i −0.947692 0.319186i \(-0.896591\pi\)
−0.197423 + 0.980318i \(0.563257\pi\)
\(648\) 0.453211 0.261662i 0.0178038 0.0102790i
\(649\) −17.7432 + 30.7321i −0.696482 + 1.20634i
\(650\) 0.468953 + 0.0924954i 0.0183939 + 0.00362797i
\(651\) −5.55517 + 9.62184i −0.217724 + 0.377110i
\(652\) 30.9065i 1.21039i
\(653\) −2.52052 + 1.45522i −0.0986356 + 0.0569473i −0.548506 0.836146i \(-0.684803\pi\)
0.449871 + 0.893094i \(0.351470\pi\)
\(654\) 0.477383 0.826852i 0.0186672 0.0323325i
\(655\) 20.1514 + 14.4157i 0.787380 + 0.563269i
\(656\) 35.8824 1.40097
\(657\) −2.27807 1.31524i −0.0888758 0.0513125i
\(658\) 0.0997440i 0.00388843i
\(659\) −6.40101 11.0869i −0.249348 0.431884i 0.713997 0.700149i \(-0.246883\pi\)
−0.963345 + 0.268265i \(0.913550\pi\)
\(660\) −12.1386 + 16.9683i −0.472495 + 0.660489i
\(661\) 25.5237 + 44.2084i 0.992758 + 1.71951i 0.600414 + 0.799689i \(0.295002\pi\)
0.392344 + 0.919818i \(0.371664\pi\)
\(662\) −0.394058 + 0.227510i −0.0153155 + 0.00884242i
\(663\) −2.17413 + 1.25524i −0.0844363 + 0.0487493i
\(664\) 3.24729 5.62447i 0.126019 0.218272i
\(665\) −9.46585 + 13.2321i −0.367070 + 0.513118i
\(666\) −0.101715 0.792764i −0.00394140 0.0307190i
\(667\) 0.140939i 0.00545717i
\(668\) 35.4229 + 20.4514i 1.37055 + 0.791290i
\(669\) −2.01067 3.48258i −0.0777369 0.134644i
\(670\) 0.347684 3.55949i 0.0134322 0.137515i
\(671\) 13.2001 + 22.8632i 0.509584 + 0.882625i
\(672\) 3.00571i 0.115948i
\(673\) −23.2784 + 13.4398i −0.897316 + 0.518066i −0.876328 0.481714i \(-0.840014\pi\)
−0.0209874 + 0.999780i \(0.506681\pi\)
\(674\) 2.30823 0.0889095
\(675\) 0.967550 4.90549i 0.0372410 0.188812i
\(676\) 24.7261 0.951002
\(677\) 21.9115i 0.842126i −0.907031 0.421063i \(-0.861657\pi\)
0.907031 0.421063i \(-0.138343\pi\)
\(678\) 0.551541 + 0.318432i 0.0211818 + 0.0122293i
\(679\) −10.3933 18.0018i −0.398860 0.690846i
\(680\) 3.28406 + 2.34932i 0.125938 + 0.0900924i
\(681\) −12.5941 + 21.8135i −0.482605 + 0.835897i
\(682\) −3.08519 1.78123i −0.118138 0.0682069i
\(683\) 21.5260 + 12.4280i 0.823668 + 0.475545i 0.851680 0.524063i \(-0.175584\pi\)
−0.0280118 + 0.999608i \(0.508918\pi\)
\(684\) −3.74045 6.47865i −0.143020 0.247718i
\(685\) −31.4308 3.07010i −1.20091 0.117302i
\(686\) −1.30257 + 2.25612i −0.0497324 + 0.0861391i
\(687\) −12.5143 7.22513i −0.477450 0.275656i
\(688\) −23.7998 13.7408i −0.907358 0.523863i
\(689\) −5.18767 −0.197634
\(690\) 1.30814 + 0.127777i 0.0498000 + 0.00486437i
\(691\) 20.7722 35.9785i 0.790213 1.36869i −0.135623 0.990761i \(-0.543303\pi\)
0.925835 0.377928i \(-0.123363\pi\)
\(692\) 18.4655i 0.701951i
\(693\) 9.07451i 0.344712i
\(694\) 1.66048 2.87604i 0.0630310 0.109173i
\(695\) −31.6060 22.6100i −1.19888 0.857647i
\(696\) −0.00824382 0.0142787i −0.000312481 0.000541233i
\(697\) 31.7746i 1.20355i
\(698\) −3.30895 + 1.91043i −0.125246 + 0.0723107i
\(699\) −8.22224 14.2413i −0.310994 0.538657i
\(700\) −14.3935 12.5818i −0.544024 0.475547i
\(701\) 12.6739 21.9518i 0.478687 0.829109i −0.521015 0.853548i \(-0.674446\pi\)
0.999701 + 0.0244382i \(0.00777970\pi\)
\(702\) 0.0955976i 0.00360810i
\(703\) −22.7638 + 2.92071i −0.858553 + 0.110157i
\(704\) −35.7101 −1.34587
\(705\) 0.801463 0.363917i 0.0301849 0.0137059i
\(706\) 2.06489 + 3.57649i 0.0777131 + 0.134603i
\(707\) −12.2344 + 7.06356i −0.460123 + 0.265652i
\(708\) 12.9488 7.47598i 0.486645 0.280964i
\(709\) 28.4972 1.07024 0.535118 0.844778i \(-0.320267\pi\)
0.535118 + 0.844778i \(0.320267\pi\)
\(710\) 2.69443 + 0.263187i 0.101120 + 0.00987722i
\(711\) 7.22529 0.270970
\(712\) −1.00265 0.578878i −0.0375757 0.0216944i
\(713\) 25.7736i 0.965230i
\(714\) −0.874339 −0.0327213
\(715\) 3.16508 + 6.97055i 0.118367 + 0.260684i
\(716\) 2.73530 + 4.73767i 0.102223 + 0.177055i
\(717\) 17.2222i 0.643176i
\(718\) −3.93019 2.26910i −0.146673 0.0846820i
\(719\) 7.87395 13.6381i 0.293649 0.508614i −0.681021 0.732264i \(-0.738464\pi\)
0.974670 + 0.223649i \(0.0717971\pi\)
\(720\) 7.93373 3.60243i 0.295673 0.134255i
\(721\) −4.76325 8.25019i −0.177393 0.307253i
\(722\) −0.542147 + 0.313009i −0.0201766 + 0.0116490i
\(723\) 1.70851 + 0.986408i 0.0635401 + 0.0366849i
\(724\) −20.0470 + 34.7224i −0.745040 + 1.29045i
\(725\) −0.154551 0.0304833i −0.00573987 0.00113212i
\(726\) 1.46431 0.0543456
\(727\) 5.32240 3.07289i 0.197397 0.113967i −0.398044 0.917366i \(-0.630311\pi\)
0.595441 + 0.803399i \(0.296977\pi\)
\(728\) −0.635848 0.367107i −0.0235661 0.0136059i
\(729\) −1.00000 −0.0370370
\(730\) 0.628591 + 0.449676i 0.0232652 + 0.0166433i
\(731\) −12.1678 + 21.0752i −0.450042 + 0.779495i
\(732\) 11.1235i 0.411137i
\(733\) −23.0501 + 13.3080i −0.851375 + 0.491542i −0.861115 0.508411i \(-0.830233\pi\)
0.00973930 + 0.999953i \(0.496900\pi\)
\(734\) −4.32711 −0.159716
\(735\) −7.30251 0.713295i −0.269357 0.0263103i
\(736\) 3.48630 + 6.03845i 0.128507 + 0.222580i
\(737\) 49.6061 28.6401i 1.82726 1.05497i
\(738\) 1.04786 + 0.604981i 0.0385722 + 0.0222697i
\(739\) −43.7638 −1.60988 −0.804938 0.593359i \(-0.797802\pi\)
−0.804938 + 0.593359i \(0.797802\pi\)
\(740\) −0.815350 26.9558i −0.0299729 0.990914i
\(741\) −2.74504 −0.100841
\(742\) −1.56469 0.903372i −0.0574414 0.0331638i
\(743\) −17.8071 + 10.2809i −0.653280 + 0.377171i −0.789712 0.613478i \(-0.789770\pi\)
0.136432 + 0.990649i \(0.456436\pi\)
\(744\) 1.50755 + 2.61116i 0.0552696 + 0.0957298i
\(745\) 0.978572 10.0183i 0.0358521 0.367043i
\(746\) 0.377888 0.0138355
\(747\) −10.7476 + 6.20513i −0.393234 + 0.227034i
\(748\) 32.1952i 1.17717i
\(749\) −13.0389 + 22.5841i −0.476432 + 0.825204i
\(750\) −0.423051 + 1.40684i −0.0154476 + 0.0513706i
\(751\) 1.02130 0.0372678 0.0186339 0.999826i \(-0.494068\pi\)
0.0186339 + 0.999826i \(0.494068\pi\)
\(752\) 1.32841 + 0.766958i 0.0484421 + 0.0279681i
\(753\) −12.3422 + 7.12578i −0.449775 + 0.259678i
\(754\) −0.00301187 −0.000109686
\(755\) −2.03334 + 0.923271i −0.0740009 + 0.0336013i
\(756\) −1.91174 + 3.31123i −0.0695293 + 0.120428i
\(757\) −5.10352 2.94652i −0.185491 0.107093i 0.404379 0.914591i \(-0.367488\pi\)
−0.589870 + 0.807498i \(0.700821\pi\)
\(758\) 1.31345 0.758320i 0.0477066 0.0275434i
\(759\) 10.5255 + 18.2306i 0.382050 + 0.661730i
\(760\) 1.82540 + 4.02012i 0.0662142 + 0.145825i
\(761\) −19.3400 + 33.4978i −0.701073 + 1.21429i 0.267017 + 0.963692i \(0.413962\pi\)
−0.968090 + 0.250603i \(0.919371\pi\)
\(762\) −0.123375 0.0712306i −0.00446940 0.00258041i
\(763\) 14.0121i 0.507272i
\(764\) 12.0872 + 20.9356i 0.437298 + 0.757423i
\(765\) −3.19003 7.02549i −0.115336 0.254007i
\(766\) −3.03452 −0.109642
\(767\) 5.48645i 0.198104i
\(768\) 12.6756 + 7.31829i 0.457393 + 0.264076i
\(769\) −18.0409 −0.650573 −0.325287 0.945615i \(-0.605461\pi\)
−0.325287 + 0.945615i \(0.605461\pi\)
\(770\) −0.259198 + 2.65359i −0.00934085 + 0.0956289i
\(771\) −18.5067 −0.666504
\(772\) 29.6560 17.1219i 1.06734 0.616230i
\(773\) 20.0181 11.5574i 0.720000 0.415692i −0.0947528 0.995501i \(-0.530206\pi\)
0.814753 + 0.579809i \(0.196873\pi\)
\(774\) −0.463344 0.802535i −0.0166545 0.0288465i
\(775\) 28.2628 + 5.57451i 1.01523 + 0.200242i
\(776\) −5.64107 −0.202502
\(777\) 7.11005 + 9.32943i 0.255072 + 0.334691i
\(778\) 0.720117i 0.0258175i
\(779\) 17.3717 30.0887i 0.622407 1.07804i
\(780\) 0.313576 3.21030i 0.0112278 0.114947i
\(781\) 21.6797 + 37.5504i 0.775762 + 1.34366i
\(782\) 1.75654 1.01414i 0.0628138 0.0362656i
\(783\) 0.0315057i 0.00112592i
\(784\) −6.39318 11.0733i −0.228328 0.395475i
\(785\) −10.3106 + 14.4130i −0.368002 + 0.514421i
\(786\) −0.727980 + 1.26090i −0.0259662 + 0.0449748i
\(787\) 44.3883i 1.58227i 0.611641 + 0.791135i \(0.290510\pi\)
−0.611641 + 0.791135i \(0.709490\pi\)
\(788\) 19.5014i 0.694710i
\(789\) 5.10237 8.83757i 0.181649 0.314626i
\(790\) −2.11284 0.206378i −0.0751716 0.00734262i
\(791\) −9.34658 −0.332326
\(792\) −2.13270 1.23131i −0.0757821 0.0437528i
\(793\) −3.53482 2.04083i −0.125525 0.0724719i
\(794\) −0.681986 + 1.18124i −0.0242028 + 0.0419205i
\(795\) 1.55001 15.8685i 0.0549731 0.562799i
\(796\) 13.3825 + 23.1791i 0.474329 + 0.821561i
\(797\) −9.09440 5.25066i −0.322140 0.185988i 0.330206 0.943909i \(-0.392882\pi\)
−0.652346 + 0.757921i \(0.726215\pi\)
\(798\) −0.827948 0.478016i −0.0293090 0.0169216i
\(799\) 0.679158 1.17634i 0.0240269 0.0416158i
\(800\) −7.37569 + 2.51697i −0.260770 + 0.0889883i
\(801\) 1.10616 + 1.91592i 0.0390841 + 0.0676957i
\(802\) 0.956952 + 0.552497i 0.0337912 + 0.0195093i
\(803\) 12.3784i 0.436824i
\(804\) −24.1346 −0.851162
\(805\) −17.5637 + 7.97507i −0.619039 + 0.281084i
\(806\) 0.550783 0.0194005
\(807\) −5.31015 + 3.06582i −0.186926 + 0.107922i
\(808\) 3.83380i 0.134873i
\(809\) −15.9119 27.5603i −0.559433 0.968967i −0.997544 0.0700457i \(-0.977685\pi\)
0.438110 0.898921i \(-0.355648\pi\)
\(810\) 0.292423 + 0.0285633i 0.0102747 + 0.00100361i
\(811\) 2.66697 + 4.61934i 0.0936501 + 0.162207i 0.909044 0.416699i \(-0.136813\pi\)
−0.815394 + 0.578906i \(0.803480\pi\)
\(812\) 0.104322 + 0.0602306i 0.00366100 + 0.00211368i
\(813\) 30.1952i 1.05899i
\(814\) −2.99143 + 2.27980i −0.104849 + 0.0799068i
\(815\) −20.2797 + 28.3485i −0.710367 + 0.993004i
\(816\) 6.72303 11.6446i 0.235353 0.407643i
\(817\) −23.0444 + 13.3047i −0.806220 + 0.465471i
\(818\) −1.71384 + 0.989488i −0.0599232 + 0.0345966i
\(819\) 0.701492 + 1.21502i 0.0245121 + 0.0424562i
\(820\) 33.2041 + 23.7533i 1.15954 + 0.829501i
\(821\) −16.5642 28.6900i −0.578094 1.00129i −0.995698 0.0926596i \(-0.970463\pi\)
0.417603 0.908629i \(-0.362870\pi\)
\(822\) 1.85575i 0.0647269i
\(823\) −32.1686 18.5726i −1.12133 0.647399i −0.179588 0.983742i \(-0.557477\pi\)
−0.941740 + 0.336343i \(0.890810\pi\)
\(824\) −2.58529 −0.0900628
\(825\) −22.2679 + 7.59895i −0.775268 + 0.264562i
\(826\) 0.955402 1.65480i 0.0332427 0.0575780i
\(827\) 20.2648 11.6999i 0.704677 0.406846i −0.104410 0.994534i \(-0.533295\pi\)
0.809087 + 0.587689i \(0.199962\pi\)
\(828\) 8.86966i 0.308242i
\(829\) 7.90893 13.6987i 0.274689 0.475775i −0.695368 0.718654i \(-0.744759\pi\)
0.970057 + 0.242879i \(0.0780919\pi\)
\(830\) 3.32009 1.50754i 0.115242 0.0523273i
\(831\) −6.99434 + 12.1146i −0.242631 + 0.420249i
\(832\) 4.78135 2.76052i 0.165764 0.0957037i
\(833\) −9.80566 + 5.66130i −0.339746 + 0.196152i
\(834\) 1.14178 1.97763i 0.0395367 0.0684796i
\(835\) 19.0716 + 42.0019i 0.660000 + 1.45354i
\(836\) −17.6016 + 30.4869i −0.608765 + 1.05441i
\(837\) 5.76147i 0.199145i
\(838\) 0.896485 0.517586i 0.0309685 0.0178797i
\(839\) 4.74656 8.22129i 0.163870 0.283830i −0.772384 0.635156i \(-0.780936\pi\)
0.936253 + 0.351326i \(0.114269\pi\)
\(840\) 1.31292 1.83531i 0.0453002 0.0633240i
\(841\) −28.9990 −0.999966
\(842\) −4.45241 2.57060i −0.153440 0.0885888i
\(843\) 13.3701i 0.460490i
\(844\) 21.6495 + 37.4981i 0.745208 + 1.29074i
\(845\) 22.6795 + 16.2243i 0.780200 + 0.558133i
\(846\) 0.0258620 + 0.0447943i 0.000889155 + 0.00154006i
\(847\) −18.6110 + 10.7450i −0.639480 + 0.369204i
\(848\) 24.0626 13.8925i 0.826312 0.477071i
\(849\) −9.54594 + 16.5340i −0.327616 + 0.567447i
\(850\) 0.732168 + 2.14553i 0.0251132 + 0.0735912i
\(851\) −25.1052 10.4959i −0.860595 0.359794i
\(852\) 18.2692i 0.625893i
\(853\) 27.9396 + 16.1309i 0.956634 + 0.552313i 0.895135 0.445794i \(-0.147079\pi\)
0.0614986 + 0.998107i \(0.480412\pi\)
\(854\) −0.710773 1.23109i −0.0243221 0.0421272i
\(855\) 0.820181 8.39678i 0.0280496 0.287164i
\(856\) 3.53848 + 6.12883i 0.120943 + 0.209479i
\(857\) 10.6197i 0.362761i 0.983413 + 0.181380i \(0.0580565\pi\)
−0.983413 + 0.181380i \(0.941944\pi\)
\(858\) −0.389589 + 0.224929i −0.0133003 + 0.00767896i
\(859\) −1.98651 −0.0677790 −0.0338895 0.999426i \(-0.510789\pi\)
−0.0338895 + 0.999426i \(0.510789\pi\)
\(860\) −12.9273 28.4701i −0.440817 0.970822i
\(861\) −17.7573 −0.605168
\(862\) 2.09321i 0.0712951i
\(863\) 35.6325 + 20.5725i 1.21295 + 0.700295i 0.963400 0.268068i \(-0.0863853\pi\)
0.249546 + 0.968363i \(0.419719\pi\)
\(864\) 0.779333 + 1.34984i 0.0265134 + 0.0459226i
\(865\) −12.1163 + 16.9371i −0.411968 + 0.575879i
\(866\) 2.20659 3.82193i 0.0749830 0.129874i
\(867\) 4.41086 + 2.54661i 0.149801 + 0.0864874i
\(868\) −19.0775 11.0144i −0.647534 0.373854i
\(869\) −17.0002 29.4452i −0.576693 0.998861i
\(870\) 0.000899907 0.00921298i 3.05097e−5 0.000312349i
\(871\) −4.42796 + 7.66946i −0.150036 + 0.259870i
\(872\) 3.29313 + 1.90129i 0.111520 + 0.0643858i
\(873\) 9.33516 + 5.38966i 0.315947 + 0.182412i
\(874\) 2.21779 0.0750179
\(875\) −4.94650 20.9849i −0.167222 0.709420i
\(876\) 2.60778 4.51680i 0.0881086 0.152609i
\(877\) 57.2662i 1.93374i 0.255267 + 0.966871i \(0.417837\pi\)
−0.255267 + 0.966871i \(0.582163\pi\)
\(878\) 0.553784i 0.0186893i
\(879\) 11.9076 20.6245i 0.401632 0.695648i
\(880\) −33.3481 23.8562i −1.12416 0.804194i
\(881\) 9.57031 + 16.5763i 0.322432 + 0.558469i 0.980989 0.194062i \(-0.0621663\pi\)
−0.658557 + 0.752531i \(0.728833\pi\)
\(882\) 0.431159i 0.0145179i
\(883\) −11.1806 + 6.45510i −0.376256 + 0.217231i −0.676188 0.736729i \(-0.736369\pi\)
0.299932 + 0.953961i \(0.403036\pi\)
\(884\) −2.48880 4.31073i −0.0837074 0.144986i
\(885\) 16.7825 + 1.63928i 0.564137 + 0.0551039i
\(886\) −1.62317 + 2.81142i −0.0545316 + 0.0944515i
\(887\) 24.7920i 0.832433i −0.909266 0.416216i \(-0.863356\pi\)
0.909266 0.416216i \(-0.136644\pi\)
\(888\) 3.15737 0.405106i 0.105954 0.0135945i
\(889\) 2.09075 0.0701215
\(890\) −0.268741 0.591855i −0.00900821 0.0198390i
\(891\) 2.35287 + 4.07530i 0.0788243 + 0.136528i
\(892\) 6.90503 3.98662i 0.231198 0.133482i
\(893\) 1.28625 0.742615i 0.0430426 0.0248506i
\(894\) 0.591509 0.0197830
\(895\) −0.599778 + 6.14035i −0.0200484 + 0.205249i
\(896\) 7.93427 0.265065
\(897\) −2.81859 1.62731i −0.0941098 0.0543343i
\(898\) 3.89769i 0.130068i
\(899\) −0.181519 −0.00605399
\(900\) 9.72629 + 1.91839i 0.324210 + 0.0639465i
\(901\) −12.3021 21.3079i −0.409844 0.709870i
\(902\) 5.69378i 0.189582i
\(903\) 11.7779 + 6.80000i 0.391945 + 0.226290i
\(904\) −1.26823 + 2.19664i −0.0421808 + 0.0730592i
\(905\) −41.1713 + 18.6944i −1.36858 + 0.621425i
\(906\) −0.0656129 0.113645i −0.00217984 0.00377560i
\(907\) −47.0385 + 27.1577i −1.56189 + 0.901756i −0.564821 + 0.825214i \(0.691055\pi\)
−0.997066 + 0.0765424i \(0.975612\pi\)
\(908\) −43.2505 24.9707i −1.43532 0.828681i
\(909\) 3.66294 6.34439i 0.121492 0.210430i
\(910\) −0.170427 0.375337i −0.00564961 0.0124423i
\(911\) −1.28498 −0.0425732 −0.0212866 0.999773i \(-0.506776\pi\)
−0.0212866 + 0.999773i \(0.506776\pi\)
\(912\) 12.7326 7.35118i 0.421619 0.243422i
\(913\) 50.5755 + 29.1998i 1.67381 + 0.966372i
\(914\) 2.69755 0.0892270
\(915\) 7.29884 10.2029i 0.241292 0.337296i
\(916\) 14.3255 24.8125i 0.473328 0.819829i
\(917\) 21.3676i 0.705619i
\(918\) 0.392660 0.226702i 0.0129597 0.00748229i
\(919\) 54.4437 1.79593 0.897966 0.440064i \(-0.145044\pi\)
0.897966 + 0.440064i \(0.145044\pi\)
\(920\) −0.508900 + 5.20997i −0.0167779 + 0.171768i
\(921\) −0.0921854 0.159670i −0.00303761 0.00526130i
\(922\) 2.46360 1.42236i 0.0811343 0.0468429i
\(923\) −5.80556 3.35184i −0.191092 0.110327i
\(924\) 17.9923 0.591904
\(925\) 16.9395 25.2597i 0.556967 0.830535i
\(926\) −3.44056 −0.113064
\(927\) 4.27828 + 2.47007i 0.140517 + 0.0811277i
\(928\) 0.0425277 0.0245534i 0.00139604 0.000806005i
\(929\) 4.43388 + 7.67971i 0.145471 + 0.251963i 0.929549 0.368700i \(-0.120197\pi\)
−0.784078 + 0.620663i \(0.786864\pi\)
\(930\) −0.164567 + 1.68479i −0.00539636 + 0.0552463i
\(931\) −12.3805 −0.405755
\(932\) 28.2368 16.3025i 0.924926 0.534007i
\(933\) 27.0376i 0.885170i
\(934\) 2.42894 4.20704i 0.0794772 0.137659i
\(935\) −21.1252 + 29.5305i −0.690869 + 0.965749i
\(936\) 0.380740 0.0124449
\(937\) 23.2218 + 13.4071i 0.758623 + 0.437991i 0.828801 0.559543i \(-0.189023\pi\)
−0.0701779 + 0.997534i \(0.522357\pi\)
\(938\) −2.67109 + 1.54216i −0.0872143 + 0.0503532i
\(939\) −25.6422 −0.836802
\(940\) 0.721550 + 1.58909i 0.0235344 + 0.0518304i
\(941\) 1.53591 2.66028i 0.0500693 0.0867226i −0.839905 0.542734i \(-0.817389\pi\)
0.889974 + 0.456012i \(0.150722\pi\)
\(942\) −0.901838 0.520676i −0.0293835 0.0169645i
\(943\) 35.6744 20.5966i 1.16172 0.670718i
\(944\) 14.6927 + 25.4485i 0.478206 + 0.828277i
\(945\) −3.92621 + 1.78276i −0.127720 + 0.0579931i
\(946\) −2.18038 + 3.77653i −0.0708902 + 0.122785i
\(947\) 13.3413 + 7.70260i 0.433534 + 0.250301i 0.700851 0.713308i \(-0.252804\pi\)
−0.267317 + 0.963609i \(0.586137\pi\)
\(948\) 14.3258i 0.465282i
\(949\) −0.956895 1.65739i −0.0310621 0.0538012i
\(950\) −0.479680 + 2.43198i −0.0155629 + 0.0789040i
\(951\) 31.4881 1.02107
\(952\) 3.48226i 0.112861i
\(953\) 24.0471 + 13.8836i 0.778963 + 0.449735i 0.836063 0.548634i \(-0.184852\pi\)
−0.0570996 + 0.998368i \(0.518185\pi\)
\(954\) 0.936919 0.0303339
\(955\) −2.65039 + 27.1339i −0.0857647 + 0.878034i
\(956\) −34.1471 −1.10440
\(957\) 0.128395 0.0741289i 0.00415042 0.00239625i
\(958\) 3.39813 1.96191i 0.109789 0.0633865i
\(959\) 13.6175 + 23.5861i 0.439731 + 0.761636i
\(960\) 7.01552 + 15.4505i 0.226425 + 0.498662i
\(961\) 2.19452 0.0707908
\(962\) 0.224297 0.536498i 0.00723162 0.0172974i
\(963\) 13.5231i 0.435777i
\(964\) −1.95579 + 3.38752i −0.0629916 + 0.109105i
\(965\) 38.4362 + 3.75437i 1.23730 + 0.120858i
\(966\) −0.566755 0.981648i −0.0182350 0.0315840i
\(967\) −12.6278 + 7.29068i −0.406083 + 0.234452i −0.689106 0.724661i \(-0.741996\pi\)
0.283022 + 0.959113i \(0.408663\pi\)
\(968\) 5.83196i 0.187446i
\(969\) −6.50964 11.2750i −0.209120 0.362206i
\(970\) −2.57587 1.84270i −0.0827062 0.0591656i
\(971\) −16.2950 + 28.2238i −0.522932 + 0.905744i 0.476712 + 0.879059i \(0.341828\pi\)
−0.999644 + 0.0266848i \(0.991505\pi\)
\(972\) 1.98273i 0.0635962i
\(973\) 33.5135i 1.07439i
\(974\) −1.79017 + 3.10066i −0.0573606 + 0.0993515i
\(975\) 2.39410 2.73884i 0.0766726 0.0877130i
\(976\) 21.8613 0.699762
\(977\) 3.25389 + 1.87863i 0.104101 + 0.0601028i 0.551147 0.834408i \(-0.314190\pi\)
−0.447046 + 0.894511i \(0.647524\pi\)
\(978\) −1.77380 1.02410i −0.0567199 0.0327473i
\(979\) 5.20530 9.01584i 0.166362 0.288148i
\(980\) 1.41428 14.4789i 0.0451774 0.462513i
\(981\) −3.63311 6.29273i −0.115996 0.200911i
\(982\) −2.65765 1.53439i −0.0848089 0.0489645i
\(983\) −10.6986 6.17682i −0.341231 0.197010i 0.319585 0.947558i \(-0.396457\pi\)
−0.660816 + 0.750548i \(0.729790\pi\)
\(984\) −2.40948 + 4.17334i −0.0768114 + 0.133041i
\(985\) −12.7961 + 17.8874i −0.407718 + 0.569939i
\(986\) −0.00714240 0.0123710i −0.000227460 0.000393973i
\(987\) −0.657399 0.379549i −0.0209252 0.0120812i
\(988\) 5.44268i 0.173155i
\(989\) −31.5491 −1.00320
\(990\) −0.571631 1.25892i −0.0181676 0.0400110i
\(991\) −51.5517 −1.63759 −0.818797 0.574083i \(-0.805359\pi\)
−0.818797 + 0.574083i \(0.805359\pi\)
\(992\) −7.77708 + 4.49010i −0.246923 + 0.142561i
\(993\) 3.46291i 0.109892i
\(994\) −1.16737 2.02194i −0.0370267 0.0641321i
\(995\) −2.93442 + 30.0417i −0.0930272 + 0.952386i
\(996\) −12.3031 21.3096i −0.389839 0.675222i
\(997\) −20.2958 11.7178i −0.642773 0.371105i 0.142909 0.989736i \(-0.454354\pi\)
−0.785682 + 0.618631i \(0.787688\pi\)
\(998\) 2.69637i 0.0853520i
\(999\) −5.61205 2.34626i −0.177557 0.0742324i
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 555.2.bb.a.454.18 72
5.4 even 2 inner 555.2.bb.a.454.19 yes 72
37.26 even 3 inner 555.2.bb.a.544.19 yes 72
185.174 even 6 inner 555.2.bb.a.544.18 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
555.2.bb.a.454.18 72 1.1 even 1 trivial
555.2.bb.a.454.19 yes 72 5.4 even 2 inner
555.2.bb.a.544.18 yes 72 185.174 even 6 inner
555.2.bb.a.544.19 yes 72 37.26 even 3 inner