Properties

Label 672.2.bs.b.155.10
Level $672$
Weight $2$
Character 672.155
Analytic conductor $5.366$
Analytic rank $0$
Dimension $192$
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] = [672,2,Mod(155,672)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(672, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([4, 1, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("672.155");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 672.bs (of order \(8\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.36594701583\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(48\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 155.10
Character \(\chi\) \(=\) 672.155
Dual form 672.2.bs.b.659.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.16411 - 0.803019i) q^{2} +(0.712483 - 1.57872i) q^{3} +(0.710322 + 1.86961i) q^{4} +(-0.879803 + 2.12403i) q^{5} +(-2.09716 + 1.26568i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.674435 - 2.74684i) q^{8} +(-1.98474 - 2.24963i) q^{9} +O(q^{10})\) \(q+(-1.16411 - 0.803019i) q^{2} +(0.712483 - 1.57872i) q^{3} +(0.710322 + 1.86961i) q^{4} +(-0.879803 + 2.12403i) q^{5} +(-2.09716 + 1.26568i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.674435 - 2.74684i) q^{8} +(-1.98474 - 2.24963i) q^{9} +(2.72983 - 1.76612i) q^{10} +(-1.89409 + 4.57273i) q^{11} +(3.45769 + 0.210663i) q^{12} +(1.90209 - 0.787870i) q^{13} +(-1.39097 + 0.255333i) q^{14} +(2.72642 + 2.90230i) q^{15} +(-2.99088 + 2.65605i) q^{16} +5.98130 q^{17} +(0.503966 + 4.21260i) q^{18} +(-1.79840 - 4.34172i) q^{19} +(-4.59606 - 0.136141i) q^{20} +(-0.612525 - 1.62013i) q^{21} +(5.87692 - 3.80219i) q^{22} +(6.62402 - 6.62402i) q^{23} +(-3.85598 - 3.02182i) q^{24} +(-0.201929 - 0.201929i) q^{25} +(-2.84692 - 0.610240i) q^{26} +(-4.96563 + 1.53053i) q^{27} +(1.82429 + 0.819740i) q^{28} +(6.03436 - 2.49951i) q^{29} +(-0.843255 - 5.56798i) q^{30} +7.02684i q^{31} +(5.61459 - 0.690212i) q^{32} +(5.86958 + 6.24824i) q^{33} +(-6.96292 - 4.80310i) q^{34} +(0.879803 + 2.12403i) q^{35} +(2.79612 - 5.30864i) q^{36} +(3.95464 + 1.63807i) q^{37} +(-1.39294 + 6.49841i) q^{38} +(0.111375 - 3.56421i) q^{39} +(5.24101 + 3.84920i) q^{40} +(7.37882 + 7.37882i) q^{41} +(-0.587944 + 2.37788i) q^{42} +(4.73975 + 1.96327i) q^{43} +(-9.89464 - 0.293091i) q^{44} +(6.52446 - 2.23642i) q^{45} +(-13.0303 + 2.39190i) q^{46} -7.02461i q^{47} +(2.06222 + 6.61417i) q^{48} -1.00000i q^{49} +(0.0729158 + 0.397222i) q^{50} +(4.26158 - 9.44282i) q^{51} +(2.82410 + 2.99652i) q^{52} +(0.0719647 + 0.0298087i) q^{53} +(7.00960 + 2.20578i) q^{54} +(-8.04621 - 8.04621i) q^{55} +(-1.46541 - 2.41921i) q^{56} +(-8.13571 - 0.254227i) q^{57} +(-9.03184 - 1.93599i) q^{58} +(-1.91661 - 0.793886i) q^{59} +(-3.48954 + 7.15891i) q^{60} +(-2.88990 - 6.97684i) q^{61} +(5.64268 - 8.18004i) q^{62} +(-2.99415 - 0.187307i) q^{63} +(-7.09027 - 3.70513i) q^{64} +4.73326i q^{65} +(-1.81541 - 11.9870i) q^{66} +(-2.97366 + 1.23173i) q^{67} +(4.24865 + 11.1827i) q^{68} +(-5.73799 - 15.1770i) q^{69} +(0.681447 - 3.17912i) q^{70} +(-4.55070 - 4.55070i) q^{71} +(-7.51795 + 3.93453i) q^{72} +(2.91172 - 2.91172i) q^{73} +(-3.28826 - 5.08255i) q^{74} +(-0.462662 + 0.174919i) q^{75} +(6.83988 - 6.44633i) q^{76} +(1.89409 + 4.57273i) q^{77} +(-2.99178 + 4.05971i) q^{78} -0.637536 q^{79} +(-3.01015 - 8.68954i) q^{80} +(-1.12165 + 8.92983i) q^{81} +(-2.66446 - 14.5151i) q^{82} +(-6.69494 + 2.77314i) q^{83} +(2.59392 - 2.29600i) q^{84} +(-5.26237 + 12.7045i) q^{85} +(-3.94106 - 6.09157i) q^{86} +(0.353338 - 11.3075i) q^{87} +(11.2831 + 8.28677i) q^{88} +(0.00115301 - 0.00115301i) q^{89} +(-9.39110 - 2.63582i) q^{90} +(0.787870 - 1.90209i) q^{91} +(17.0895 + 7.67914i) q^{92} +(11.0934 + 5.00650i) q^{93} +(-5.64089 + 8.17744i) q^{94} +10.8042 q^{95} +(2.91065 - 9.35565i) q^{96} +0.867195 q^{97} +(-0.803019 + 1.16411i) q^{98} +(14.0462 - 4.81467i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 16 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 16 q^{4} + 8 q^{10} + 16 q^{16} + 16 q^{22} + 24 q^{27} + 44 q^{30} - 104 q^{36} - 32 q^{37} + 24 q^{39} + 32 q^{46} - 32 q^{48} - 80 q^{52} - 32 q^{55} - 72 q^{58} - 28 q^{60} + 80 q^{61} + 64 q^{64} + 76 q^{66} - 32 q^{67} - 56 q^{69} - 24 q^{70} + 60 q^{72} - 80 q^{75} - 56 q^{76} - 76 q^{78} - 32 q^{79} + 120 q^{82} - 56 q^{87} + 40 q^{88} + 60 q^{90} + 80 q^{93} - 120 q^{94} - 32 q^{96} - 64 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(421\) \(449\) \(577\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.16411 0.803019i −0.823153 0.567820i
\(3\) 0.712483 1.57872i 0.411352 0.911476i
\(4\) 0.710322 + 1.86961i 0.355161 + 0.934805i
\(5\) −0.879803 + 2.12403i −0.393460 + 0.949897i 0.595720 + 0.803192i \(0.296867\pi\)
−0.989180 + 0.146705i \(0.953133\pi\)
\(6\) −2.09716 + 1.26568i −0.856160 + 0.516710i
\(7\) 0.707107 0.707107i 0.267261 0.267261i
\(8\) 0.674435 2.74684i 0.238449 0.971155i
\(9\) −1.98474 2.24963i −0.661579 0.749876i
\(10\) 2.72983 1.76612i 0.863248 0.558496i
\(11\) −1.89409 + 4.57273i −0.571089 + 1.37873i 0.329540 + 0.944142i \(0.393106\pi\)
−0.900629 + 0.434589i \(0.856894\pi\)
\(12\) 3.45769 + 0.210663i 0.998149 + 0.0608131i
\(13\) 1.90209 0.787870i 0.527544 0.218516i −0.102983 0.994683i \(-0.532839\pi\)
0.630527 + 0.776167i \(0.282839\pi\)
\(14\) −1.39097 + 0.255333i −0.371753 + 0.0682406i
\(15\) 2.72642 + 2.90230i 0.703958 + 0.749372i
\(16\) −2.99088 + 2.65605i −0.747721 + 0.664013i
\(17\) 5.98130 1.45068 0.725339 0.688391i \(-0.241683\pi\)
0.725339 + 0.688391i \(0.241683\pi\)
\(18\) 0.503966 + 4.21260i 0.118786 + 0.992920i
\(19\) −1.79840 4.34172i −0.412581 0.996060i −0.984442 0.175709i \(-0.943778\pi\)
0.571861 0.820351i \(-0.306222\pi\)
\(20\) −4.59606 0.136141i −1.02771 0.0304420i
\(21\) −0.612525 1.62013i −0.133664 0.353541i
\(22\) 5.87692 3.80219i 1.25296 0.810631i
\(23\) 6.62402 6.62402i 1.38120 1.38120i 0.538716 0.842487i \(-0.318909\pi\)
0.842487 0.538716i \(-0.181091\pi\)
\(24\) −3.85598 3.02182i −0.787098 0.616827i
\(25\) −0.201929 0.201929i −0.0403859 0.0403859i
\(26\) −2.84692 0.610240i −0.558327 0.119678i
\(27\) −4.96563 + 1.53053i −0.955636 + 0.294550i
\(28\) 1.82429 + 0.819740i 0.344758 + 0.154916i
\(29\) 6.03436 2.49951i 1.12055 0.464148i 0.255993 0.966679i \(-0.417597\pi\)
0.864560 + 0.502530i \(0.167597\pi\)
\(30\) −0.843255 5.56798i −0.153957 1.01657i
\(31\) 7.02684i 1.26206i 0.775760 + 0.631029i \(0.217367\pi\)
−0.775760 + 0.631029i \(0.782633\pi\)
\(32\) 5.61459 0.690212i 0.992528 0.122013i
\(33\) 5.86958 + 6.24824i 1.02176 + 1.08768i
\(34\) −6.96292 4.80310i −1.19413 0.823724i
\(35\) 0.879803 + 2.12403i 0.148714 + 0.359027i
\(36\) 2.79612 5.30864i 0.466021 0.884774i
\(37\) 3.95464 + 1.63807i 0.650139 + 0.269297i 0.683283 0.730154i \(-0.260552\pi\)
−0.0331431 + 0.999451i \(0.510552\pi\)
\(38\) −1.39294 + 6.49841i −0.225965 + 1.05418i
\(39\) 0.111375 3.56421i 0.0178343 0.570730i
\(40\) 5.24101 + 3.84920i 0.828677 + 0.608612i
\(41\) 7.37882 + 7.37882i 1.15238 + 1.15238i 0.986075 + 0.166303i \(0.0531828\pi\)
0.166303 + 0.986075i \(0.446817\pi\)
\(42\) −0.587944 + 2.37788i −0.0907218 + 0.366915i
\(43\) 4.73975 + 1.96327i 0.722804 + 0.299395i 0.713591 0.700562i \(-0.247067\pi\)
0.00921305 + 0.999958i \(0.497067\pi\)
\(44\) −9.89464 0.293091i −1.49167 0.0441852i
\(45\) 6.52446 2.23642i 0.972609 0.333385i
\(46\) −13.0303 + 2.39190i −1.92122 + 0.352667i
\(47\) 7.02461i 1.02464i −0.858793 0.512322i \(-0.828785\pi\)
0.858793 0.512322i \(-0.171215\pi\)
\(48\) 2.06222 + 6.61417i 0.297656 + 0.954673i
\(49\) 1.00000i 0.142857i
\(50\) 0.0729158 + 0.397222i 0.0103119 + 0.0561757i
\(51\) 4.26158 9.44282i 0.596740 1.32226i
\(52\) 2.82410 + 2.99652i 0.391633 + 0.415542i
\(53\) 0.0719647 + 0.0298087i 0.00988511 + 0.00409455i 0.387621 0.921819i \(-0.373297\pi\)
−0.377735 + 0.925914i \(0.623297\pi\)
\(54\) 7.00960 + 2.20578i 0.953886 + 0.300169i
\(55\) −8.04621 8.04621i −1.08495 1.08495i
\(56\) −1.46541 2.41921i −0.195824 0.323280i
\(57\) −8.13571 0.254227i −1.07760 0.0336732i
\(58\) −9.03184 1.93599i −1.18594 0.254207i
\(59\) −1.91661 0.793886i −0.249521 0.103355i 0.254417 0.967095i \(-0.418116\pi\)
−0.503939 + 0.863739i \(0.668116\pi\)
\(60\) −3.48954 + 7.15891i −0.450498 + 0.924211i
\(61\) −2.88990 6.97684i −0.370014 0.893293i −0.993747 0.111656i \(-0.964385\pi\)
0.623733 0.781638i \(-0.285615\pi\)
\(62\) 5.64268 8.18004i 0.716621 1.03887i
\(63\) −2.99415 0.187307i −0.377227 0.0235984i
\(64\) −7.09027 3.70513i −0.886284 0.463142i
\(65\) 4.73326i 0.587089i
\(66\) −1.81541 11.9870i −0.223461 1.47550i
\(67\) −2.97366 + 1.23173i −0.363290 + 0.150480i −0.556859 0.830607i \(-0.687994\pi\)
0.193569 + 0.981087i \(0.437994\pi\)
\(68\) 4.24865 + 11.1827i 0.515225 + 1.35610i
\(69\) −5.73799 15.1770i −0.690773 1.82710i
\(70\) 0.681447 3.17912i 0.0814485 0.379977i
\(71\) −4.55070 4.55070i −0.540068 0.540068i 0.383481 0.923549i \(-0.374725\pi\)
−0.923549 + 0.383481i \(0.874725\pi\)
\(72\) −7.51795 + 3.93453i −0.885998 + 0.463688i
\(73\) 2.91172 2.91172i 0.340791 0.340791i −0.515874 0.856665i \(-0.672533\pi\)
0.856665 + 0.515874i \(0.172533\pi\)
\(74\) −3.28826 5.08255i −0.382252 0.590834i
\(75\) −0.462662 + 0.174919i −0.0534236 + 0.0201980i
\(76\) 6.83988 6.44633i 0.784589 0.739445i
\(77\) 1.89409 + 4.57273i 0.215851 + 0.521111i
\(78\) −2.99178 + 4.05971i −0.338752 + 0.459672i
\(79\) −0.637536 −0.0717284 −0.0358642 0.999357i \(-0.511418\pi\)
−0.0358642 + 0.999357i \(0.511418\pi\)
\(80\) −3.01015 8.68954i −0.336545 0.971520i
\(81\) −1.12165 + 8.92983i −0.124628 + 0.992204i
\(82\) −2.66446 14.5151i −0.294240 1.60293i
\(83\) −6.69494 + 2.77314i −0.734865 + 0.304391i −0.718550 0.695476i \(-0.755194\pi\)
−0.0163157 + 0.999867i \(0.505194\pi\)
\(84\) 2.59392 2.29600i 0.283020 0.250514i
\(85\) −5.26237 + 12.7045i −0.570784 + 1.37799i
\(86\) −3.94106 6.09157i −0.424976 0.656871i
\(87\) 0.353338 11.3075i 0.0378818 1.21229i
\(88\) 11.2831 + 8.28677i 1.20279 + 0.883373i
\(89\) 0.00115301 0.00115301i 0.000122219 0.000122219i −0.707046 0.707168i \(-0.749972\pi\)
0.707168 + 0.707046i \(0.249972\pi\)
\(90\) −9.39110 2.63582i −0.989909 0.277840i
\(91\) 0.787870 1.90209i 0.0825912 0.199393i
\(92\) 17.0895 + 7.67914i 1.78171 + 0.800606i
\(93\) 11.0934 + 5.00650i 1.15034 + 0.519150i
\(94\) −5.64089 + 8.17744i −0.581813 + 0.843439i
\(95\) 10.8042 1.10849
\(96\) 2.91065 9.35565i 0.297067 0.954857i
\(97\) 0.867195 0.0880503 0.0440252 0.999030i \(-0.485982\pi\)
0.0440252 + 0.999030i \(0.485982\pi\)
\(98\) −0.803019 + 1.16411i −0.0811171 + 0.117593i
\(99\) 14.0462 4.81467i 1.41170 0.483893i
\(100\) 0.234094 0.520964i 0.0234094 0.0520964i
\(101\) −2.07890 + 5.01890i −0.206858 + 0.499399i −0.992925 0.118742i \(-0.962114\pi\)
0.786067 + 0.618141i \(0.212114\pi\)
\(102\) −12.5437 + 7.57040i −1.24201 + 0.749581i
\(103\) 11.0561 11.0561i 1.08939 1.08939i 0.0937947 0.995592i \(-0.470100\pi\)
0.995592 0.0937947i \(-0.0298997\pi\)
\(104\) −0.881319 5.75609i −0.0864205 0.564431i
\(105\) 3.98011 + 0.124371i 0.388419 + 0.0121374i
\(106\) −0.0598381 0.0924897i −0.00581199 0.00898340i
\(107\) −3.16233 + 7.63453i −0.305714 + 0.738058i 0.694121 + 0.719859i \(0.255793\pi\)
−0.999834 + 0.0181993i \(0.994207\pi\)
\(108\) −6.38869 8.19662i −0.614752 0.788721i
\(109\) −13.0222 + 5.39395i −1.24730 + 0.516647i −0.905987 0.423305i \(-0.860870\pi\)
−0.341308 + 0.939951i \(0.610870\pi\)
\(110\) 2.90545 + 15.8280i 0.277024 + 1.50914i
\(111\) 5.40367 5.07619i 0.512894 0.481811i
\(112\) −0.236762 + 3.99299i −0.0223719 + 0.377302i
\(113\) −19.8040 −1.86301 −0.931503 0.363733i \(-0.881502\pi\)
−0.931503 + 0.363733i \(0.881502\pi\)
\(114\) 9.26674 + 6.82907i 0.867910 + 0.639601i
\(115\) 8.24180 + 19.8975i 0.768552 + 1.85545i
\(116\) 8.95946 + 9.50644i 0.831865 + 0.882651i
\(117\) −5.54755 2.71527i −0.512871 0.251027i
\(118\) 1.59365 + 2.46325i 0.146707 + 0.226760i
\(119\) 4.22942 4.22942i 0.387710 0.387710i
\(120\) 9.81096 5.53162i 0.895614 0.504965i
\(121\) −9.54415 9.54415i −0.867650 0.867650i
\(122\) −2.23836 + 10.4425i −0.202651 + 0.945418i
\(123\) 16.9064 6.39183i 1.52440 0.576332i
\(124\) −13.1374 + 4.99132i −1.17978 + 0.448234i
\(125\) −10.0136 + 4.14777i −0.895644 + 0.370988i
\(126\) 3.33512 + 2.62240i 0.297116 + 0.233622i
\(127\) 11.3112i 1.00371i −0.864953 0.501853i \(-0.832652\pi\)
0.864953 0.501853i \(-0.167348\pi\)
\(128\) 5.27860 + 10.0068i 0.466566 + 0.884486i
\(129\) 6.47644 6.08395i 0.570219 0.535662i
\(130\) 3.80090 5.51006i 0.333361 0.483264i
\(131\) 2.91768 + 7.04391i 0.254919 + 0.615430i 0.998588 0.0531185i \(-0.0169161\pi\)
−0.743669 + 0.668548i \(0.766916\pi\)
\(132\) −7.51247 + 15.4121i −0.653877 + 1.34145i
\(133\) −4.34172 1.79840i −0.376475 0.155941i
\(134\) 4.45077 + 0.954028i 0.384488 + 0.0824155i
\(135\) 1.11789 11.8937i 0.0962124 1.02365i
\(136\) 4.03400 16.4297i 0.345913 1.40883i
\(137\) 14.5423 + 14.5423i 1.24243 + 1.24243i 0.958989 + 0.283443i \(0.0914767\pi\)
0.283443 + 0.958989i \(0.408523\pi\)
\(138\) −5.50773 + 22.2755i −0.468849 + 1.89621i
\(139\) 13.3402 + 5.52568i 1.13150 + 0.468682i 0.868290 0.496057i \(-0.165219\pi\)
0.263208 + 0.964739i \(0.415219\pi\)
\(140\) −3.34617 + 3.15364i −0.282803 + 0.266531i
\(141\) −11.0899 5.00491i −0.933939 0.421490i
\(142\) 1.64324 + 8.95182i 0.137897 + 0.751220i
\(143\) 10.1900i 0.852133i
\(144\) 11.9112 + 1.45681i 0.992604 + 0.121401i
\(145\) 15.0163i 1.24703i
\(146\) −5.72774 + 1.05141i −0.474031 + 0.0870152i
\(147\) −1.57872 0.712483i −0.130211 0.0587646i
\(148\) −0.253474 + 8.55720i −0.0208355 + 0.703397i
\(149\) 18.0041 + 7.45756i 1.47496 + 0.610947i 0.967983 0.251014i \(-0.0807642\pi\)
0.506974 + 0.861962i \(0.330764\pi\)
\(150\) 0.679055 + 0.167900i 0.0554446 + 0.0137090i
\(151\) 11.1218 + 11.1218i 0.905076 + 0.905076i 0.995870 0.0907934i \(-0.0289403\pi\)
−0.0907934 + 0.995870i \(0.528940\pi\)
\(152\) −13.1389 + 2.01171i −1.06571 + 0.163171i
\(153\) −11.8713 13.4557i −0.959738 1.08783i
\(154\) 1.46706 6.84417i 0.118219 0.551519i
\(155\) −14.9252 6.18223i −1.19882 0.496569i
\(156\) 6.74280 2.32351i 0.539856 0.186030i
\(157\) −0.328287 0.792554i −0.0262001 0.0632527i 0.910238 0.414086i \(-0.135899\pi\)
−0.936438 + 0.350833i \(0.885899\pi\)
\(158\) 0.742165 + 0.511953i 0.0590435 + 0.0407288i
\(159\) 0.0983334 0.0923741i 0.00779834 0.00732574i
\(160\) −3.47370 + 12.5328i −0.274620 + 0.990807i
\(161\) 9.36778i 0.738284i
\(162\) 8.47655 9.49464i 0.665980 0.745969i
\(163\) −8.94041 + 3.70324i −0.700267 + 0.290060i −0.704270 0.709932i \(-0.748726\pi\)
0.00400345 + 0.999992i \(0.498726\pi\)
\(164\) −8.55417 + 19.0368i −0.667968 + 1.48653i
\(165\) −18.4355 + 6.96995i −1.43520 + 0.542610i
\(166\) 10.0206 + 2.14792i 0.777746 + 0.166711i
\(167\) −16.9093 16.9093i −1.30848 1.30848i −0.922511 0.385971i \(-0.873866\pi\)
−0.385971 0.922511i \(-0.626134\pi\)
\(168\) −4.86334 + 0.589836i −0.375215 + 0.0455069i
\(169\) −6.19520 + 6.19520i −0.476554 + 0.476554i
\(170\) 16.3279 10.5637i 1.25230 0.810198i
\(171\) −6.19791 + 12.6629i −0.473966 + 0.968356i
\(172\) −0.303796 + 10.2560i −0.0231642 + 0.782015i
\(173\) −1.71392 4.13777i −0.130307 0.314589i 0.845238 0.534391i \(-0.179459\pi\)
−0.975545 + 0.219802i \(0.929459\pi\)
\(174\) −9.49142 + 12.8794i −0.719543 + 0.976387i
\(175\) −0.285571 −0.0215872
\(176\) −6.48042 18.7073i −0.488480 1.41012i
\(177\) −2.61888 + 2.46017i −0.196847 + 0.184918i
\(178\) −0.00226812 0.000416346i −0.000170003 3.12064e-5i
\(179\) −0.0126700 + 0.00524810i −0.000947003 + 0.000392262i −0.383157 0.923683i \(-0.625163\pi\)
0.382210 + 0.924076i \(0.375163\pi\)
\(180\) 8.81570 + 10.6096i 0.657083 + 0.790795i
\(181\) 2.96509 7.15837i 0.220394 0.532077i −0.774550 0.632513i \(-0.782024\pi\)
0.994944 + 0.100435i \(0.0320236\pi\)
\(182\) −2.44458 + 1.58157i −0.181204 + 0.117234i
\(183\) −13.0735 0.408525i −0.966422 0.0301990i
\(184\) −13.7277 22.6626i −1.01202 1.67071i
\(185\) −6.95862 + 6.95862i −0.511608 + 0.511608i
\(186\) −8.89370 14.7364i −0.652118 1.08052i
\(187\) −11.3291 + 27.3509i −0.828467 + 2.00010i
\(188\) 13.1333 4.98974i 0.957843 0.363914i
\(189\) −2.42898 + 4.59348i −0.176683 + 0.334126i
\(190\) −12.5773 8.67598i −0.912455 0.629421i
\(191\) −0.00348236 −0.000251975 −0.000125987 1.00000i \(-0.500040\pi\)
−0.000125987 1.00000i \(0.500040\pi\)
\(192\) −10.9011 + 8.55374i −0.786718 + 0.617313i
\(193\) 4.41223 0.317599 0.158800 0.987311i \(-0.449238\pi\)
0.158800 + 0.987311i \(0.449238\pi\)
\(194\) −1.00951 0.696374i −0.0724789 0.0499967i
\(195\) 7.47251 + 3.37237i 0.535118 + 0.241500i
\(196\) 1.86961 0.710322i 0.133544 0.0507373i
\(197\) −3.99544 + 9.64585i −0.284663 + 0.687238i −0.999933 0.0116109i \(-0.996304\pi\)
0.715269 + 0.698849i \(0.246304\pi\)
\(198\) −20.2177 5.67454i −1.43681 0.403272i
\(199\) 2.84739 2.84739i 0.201846 0.201846i −0.598945 0.800791i \(-0.704413\pi\)
0.800791 + 0.598945i \(0.204413\pi\)
\(200\) −0.690857 + 0.418480i −0.0488509 + 0.0295910i
\(201\) −0.174120 + 5.57217i −0.0122815 + 0.393030i
\(202\) 6.45035 4.17318i 0.453845 0.293624i
\(203\) 2.49951 6.03436i 0.175432 0.423529i
\(204\) 20.6815 + 1.26004i 1.44799 + 0.0882203i
\(205\) −22.1648 + 9.18094i −1.54805 + 0.641225i
\(206\) −21.7487 + 3.99229i −1.51531 + 0.278156i
\(207\) −28.0485 1.75465i −1.94951 0.121956i
\(208\) −3.59629 + 7.40846i −0.249358 + 0.513685i
\(209\) 23.2599 1.60892
\(210\) −4.53342 3.34088i −0.312836 0.230543i
\(211\) 0.643382 + 1.55326i 0.0442922 + 0.106931i 0.944477 0.328577i \(-0.106569\pi\)
−0.900185 + 0.435508i \(0.856569\pi\)
\(212\) −0.00461260 + 0.155720i −0.000316795 + 0.0106949i
\(213\) −10.4266 + 3.94200i −0.714418 + 0.270101i
\(214\) 9.81198 6.34806i 0.670733 0.433944i
\(215\) −8.34009 + 8.34009i −0.568789 + 0.568789i
\(216\) 0.855120 + 14.6720i 0.0581836 + 0.998306i
\(217\) 4.96872 + 4.96872i 0.337299 + 0.337299i
\(218\) 19.4907 + 4.17785i 1.32008 + 0.282960i
\(219\) −2.52225 6.67135i −0.170438 0.450808i
\(220\) 9.32787 20.7587i 0.628885 1.39955i
\(221\) 11.3769 4.71249i 0.765296 0.316996i
\(222\) −10.3668 + 1.57002i −0.695772 + 0.105373i
\(223\) 3.52106i 0.235787i −0.993026 0.117894i \(-0.962386\pi\)
0.993026 0.117894i \(-0.0376142\pi\)
\(224\) 3.48206 4.45817i 0.232655 0.297874i
\(225\) −0.0534894 + 0.855043i −0.00356596 + 0.0570028i
\(226\) 23.0542 + 15.9030i 1.53354 + 1.05785i
\(227\) −7.74766 18.7045i −0.514230 1.24146i −0.941401 0.337291i \(-0.890490\pi\)
0.427170 0.904171i \(-0.359510\pi\)
\(228\) −5.30367 15.3912i −0.351244 1.01931i
\(229\) 5.13024 + 2.12501i 0.339016 + 0.140425i 0.545695 0.837984i \(-0.316266\pi\)
−0.206679 + 0.978409i \(0.566266\pi\)
\(230\) 6.38364 29.7812i 0.420925 1.96372i
\(231\) 8.56859 + 0.267753i 0.563772 + 0.0176169i
\(232\) −2.79598 18.2612i −0.183565 1.19891i
\(233\) 6.82222 + 6.82222i 0.446939 + 0.446939i 0.894336 0.447397i \(-0.147649\pi\)
−0.447397 + 0.894336i \(0.647649\pi\)
\(234\) 4.27757 + 7.61567i 0.279633 + 0.497852i
\(235\) 14.9205 + 6.18027i 0.973306 + 0.403157i
\(236\) 0.122846 4.14723i 0.00799659 0.269962i
\(237\) −0.454234 + 1.00649i −0.0295057 + 0.0653788i
\(238\) −8.31983 + 1.52722i −0.539294 + 0.0989952i
\(239\) 0.806483i 0.0521671i 0.999660 + 0.0260835i \(0.00830359\pi\)
−0.999660 + 0.0260835i \(0.991696\pi\)
\(240\) −15.8631 1.43895i −1.02396 0.0928839i
\(241\) 26.0896i 1.68058i −0.542140 0.840288i \(-0.682386\pi\)
0.542140 0.840288i \(-0.317614\pi\)
\(242\) 3.44635 + 18.7746i 0.221540 + 1.20688i
\(243\) 13.2986 + 8.13313i 0.853104 + 0.521740i
\(244\) 10.9912 10.3588i 0.703640 0.663154i
\(245\) 2.12403 + 0.879803i 0.135700 + 0.0562086i
\(246\) −24.8137 6.13533i −1.58207 0.391174i
\(247\) −6.84142 6.84142i −0.435309 0.435309i
\(248\) 19.3016 + 4.73915i 1.22565 + 0.300936i
\(249\) −0.392018 + 12.5453i −0.0248431 + 0.795024i
\(250\) 14.9877 + 3.21263i 0.947906 + 0.203185i
\(251\) −16.5941 6.87349i −1.04741 0.433851i −0.208442 0.978035i \(-0.566839\pi\)
−0.838966 + 0.544184i \(0.816839\pi\)
\(252\) −1.77662 5.73094i −0.111917 0.361015i
\(253\) 17.7434 + 42.8364i 1.11552 + 2.69310i
\(254\) −9.08310 + 13.1675i −0.569925 + 0.826204i
\(255\) 16.3075 + 17.3596i 1.02122 + 1.08710i
\(256\) 1.89077 15.8879i 0.118173 0.992993i
\(257\) 4.48917i 0.280027i 0.990150 + 0.140013i \(0.0447145\pi\)
−0.990150 + 0.140013i \(0.955285\pi\)
\(258\) −12.4248 + 1.88171i −0.773537 + 0.117150i
\(259\) 3.95464 1.63807i 0.245730 0.101785i
\(260\) −8.84936 + 3.36214i −0.548814 + 0.208511i
\(261\) −17.5996 8.61419i −1.08939 0.533205i
\(262\) 2.25988 10.5429i 0.139616 0.651341i
\(263\) 11.9971 + 11.9971i 0.739774 + 0.739774i 0.972534 0.232761i \(-0.0747758\pi\)
−0.232761 + 0.972534i \(0.574776\pi\)
\(264\) 21.1216 11.9088i 1.29994 0.732934i
\(265\) −0.126630 + 0.126630i −0.00777879 + 0.00777879i
\(266\) 3.61011 + 5.58003i 0.221350 + 0.342133i
\(267\) −0.000998782 0.00264178i −6.11245e−5 0.000161674i
\(268\) −4.41511 4.68465i −0.269696 0.286161i
\(269\) −0.596251 1.43948i −0.0363541 0.0877665i 0.904660 0.426135i \(-0.140125\pi\)
−0.941014 + 0.338368i \(0.890125\pi\)
\(270\) −10.8522 + 12.9480i −0.660446 + 0.787988i
\(271\) −23.8446 −1.44845 −0.724227 0.689562i \(-0.757803\pi\)
−0.724227 + 0.689562i \(0.757803\pi\)
\(272\) −17.8894 + 15.8867i −1.08470 + 0.963270i
\(273\) −2.44152 2.59903i −0.147768 0.157301i
\(274\) −5.25116 28.6066i −0.317234 1.72819i
\(275\) 1.30584 0.540897i 0.0787452 0.0326173i
\(276\) 24.2992 21.5084i 1.46264 1.29465i
\(277\) −2.88494 + 6.96487i −0.173339 + 0.418479i −0.986543 0.163501i \(-0.947721\pi\)
0.813204 + 0.581979i \(0.197721\pi\)
\(278\) −11.0922 17.1449i −0.665269 1.02828i
\(279\) 15.8078 13.9464i 0.946386 0.834950i
\(280\) 6.42775 0.984157i 0.384132 0.0588146i
\(281\) −11.9419 + 11.9419i −0.712392 + 0.712392i −0.967035 0.254643i \(-0.918042\pi\)
0.254643 + 0.967035i \(0.418042\pi\)
\(282\) 8.89088 + 14.7317i 0.529444 + 0.877260i
\(283\) 6.91845 16.7026i 0.411259 0.992867i −0.573541 0.819177i \(-0.694431\pi\)
0.984800 0.173691i \(-0.0555693\pi\)
\(284\) 5.27556 11.7405i 0.313047 0.696670i
\(285\) 7.69781 17.0568i 0.455979 1.01036i
\(286\) 8.18278 11.8623i 0.483858 0.701435i
\(287\) 10.4352 0.615972
\(288\) −12.6962 11.2608i −0.748130 0.663552i
\(289\) 18.7760 1.10447
\(290\) 12.0583 17.4806i 0.708090 1.02650i
\(291\) 0.617862 1.36906i 0.0362197 0.0802558i
\(292\) 7.51204 + 3.37552i 0.439609 + 0.197537i
\(293\) 0.648643 1.56596i 0.0378941 0.0914845i −0.903799 0.427956i \(-0.859234\pi\)
0.941694 + 0.336472i \(0.109234\pi\)
\(294\) 1.26568 + 2.09716i 0.0738158 + 0.122309i
\(295\) 3.37248 3.37248i 0.196353 0.196353i
\(296\) 7.16666 9.75801i 0.416554 0.567173i
\(297\) 2.40665 25.6055i 0.139648 1.48578i
\(298\) −14.9703 23.1391i −0.867207 1.34041i
\(299\) 7.38059 17.8183i 0.426830 1.03046i
\(300\) −0.655670 0.740748i −0.0378552 0.0427671i
\(301\) 4.73975 1.96327i 0.273194 0.113161i
\(302\) −4.01602 21.8780i −0.231096 1.25894i
\(303\) 6.44228 + 6.85789i 0.370099 + 0.393975i
\(304\) 16.9106 + 8.20894i 0.969892 + 0.470815i
\(305\) 17.3616 0.994122
\(306\) 3.01437 + 25.1968i 0.172320 + 1.44041i
\(307\) −2.99594 7.23284i −0.170987 0.412800i 0.815035 0.579411i \(-0.196717\pi\)
−0.986023 + 0.166611i \(0.946717\pi\)
\(308\) −7.20382 + 6.78932i −0.410475 + 0.386858i
\(309\) −9.57721 25.3317i −0.544828 1.44107i
\(310\) 12.4102 + 19.1821i 0.704853 + 1.08947i
\(311\) 0.967541 0.967541i 0.0548642 0.0548642i −0.679142 0.734007i \(-0.737648\pi\)
0.734007 + 0.679142i \(0.237648\pi\)
\(312\) −9.71521 2.70976i −0.550015 0.153410i
\(313\) −17.9855 17.9855i −1.01660 1.01660i −0.999860 0.0167396i \(-0.994671\pi\)
−0.0167396 0.999860i \(-0.505329\pi\)
\(314\) −0.254273 + 1.18624i −0.0143494 + 0.0669436i
\(315\) 3.03211 6.19487i 0.170840 0.349042i
\(316\) −0.452856 1.19194i −0.0254752 0.0670521i
\(317\) −1.11955 + 0.463733i −0.0628803 + 0.0260459i −0.413902 0.910321i \(-0.635834\pi\)
0.351022 + 0.936367i \(0.385834\pi\)
\(318\) −0.188649 + 0.0285705i −0.0105789 + 0.00160215i
\(319\) 32.3278i 1.81001i
\(320\) 14.1079 11.8002i 0.788654 0.659651i
\(321\) 9.79971 + 10.4319i 0.546966 + 0.582253i
\(322\) −7.52250 + 10.9052i −0.419213 + 0.607721i
\(323\) −10.7568 25.9692i −0.598523 1.44496i
\(324\) −17.4920 + 4.24602i −0.971780 + 0.235890i
\(325\) −0.543181 0.224993i −0.0301303 0.0124804i
\(326\) 13.3814 + 2.86832i 0.741128 + 0.158862i
\(327\) −0.762504 + 24.4015i −0.0421666 + 1.34940i
\(328\) 25.2450 15.2919i 1.39392 0.844354i
\(329\) −4.96715 4.96715i −0.273848 0.273848i
\(330\) 27.0581 + 6.69025i 1.48950 + 0.368286i
\(331\) −7.01066 2.90391i −0.385341 0.159613i 0.181599 0.983373i \(-0.441873\pi\)
−0.566940 + 0.823759i \(0.691873\pi\)
\(332\) −9.94025 10.5471i −0.545542 0.578848i
\(333\) −4.16388 12.1476i −0.228179 0.665685i
\(334\) 6.10588 + 33.2629i 0.334099 + 1.82006i
\(335\) 7.39982i 0.404295i
\(336\) 6.13513 + 3.21872i 0.334699 + 0.175595i
\(337\) 27.6238i 1.50476i 0.658727 + 0.752382i \(0.271095\pi\)
−0.658727 + 0.752382i \(0.728905\pi\)
\(338\) 12.1868 2.23706i 0.662873 0.121680i
\(339\) −14.1100 + 31.2651i −0.766352 + 1.69809i
\(340\) −27.4904 0.814299i −1.49088 0.0441616i
\(341\) −32.1318 13.3094i −1.74004 0.720747i
\(342\) 17.3836 9.76403i 0.939998 0.527978i
\(343\) −0.707107 0.707107i −0.0381802 0.0381802i
\(344\) 8.58943 11.6952i 0.463111 0.630565i
\(345\) 37.2848 + 1.16508i 2.00734 + 0.0627260i
\(346\) −1.32751 + 6.19315i −0.0713673 + 0.332946i
\(347\) −30.8079 12.7610i −1.65385 0.685048i −0.656270 0.754527i \(-0.727867\pi\)
−0.997583 + 0.0694782i \(0.977867\pi\)
\(348\) 21.3915 7.37133i 1.14671 0.395145i
\(349\) 9.56086 + 23.0820i 0.511781 + 1.23555i 0.942846 + 0.333228i \(0.108138\pi\)
−0.431065 + 0.902321i \(0.641862\pi\)
\(350\) 0.332438 + 0.229319i 0.0177695 + 0.0122576i
\(351\) −8.23920 + 6.82346i −0.439776 + 0.364210i
\(352\) −7.47837 + 26.9813i −0.398598 + 1.43811i
\(353\) 9.41412i 0.501063i −0.968108 0.250532i \(-0.919395\pi\)
0.968108 0.250532i \(-0.0806054\pi\)
\(354\) 5.02424 0.760907i 0.267035 0.0404418i
\(355\) 13.6695 5.66211i 0.725504 0.300514i
\(356\) 0.00297468 + 0.00133667i 0.000157658 + 7.08433e-5i
\(357\) −3.66369 9.69047i −0.193903 0.512874i
\(358\) 0.0189637 + 0.00406489i 0.00100226 + 0.000214836i
\(359\) −17.1400 17.1400i −0.904612 0.904612i 0.0912189 0.995831i \(-0.470924\pi\)
−0.995831 + 0.0912189i \(0.970924\pi\)
\(360\) −1.74275 19.4300i −0.0918510 1.02405i
\(361\) −2.18128 + 2.18128i −0.114804 + 0.114804i
\(362\) −9.20001 + 5.95213i −0.483542 + 0.312837i
\(363\) −21.8676 + 8.26753i −1.14775 + 0.433933i
\(364\) 4.11580 + 0.121915i 0.215727 + 0.00639008i
\(365\) 3.62285 + 8.74633i 0.189629 + 0.457804i
\(366\) 14.8910 + 10.9738i 0.778365 + 0.573612i
\(367\) −16.5217 −0.862425 −0.431212 0.902250i \(-0.641914\pi\)
−0.431212 + 0.902250i \(0.641914\pi\)
\(368\) −2.21793 + 37.4054i −0.115618 + 1.94989i
\(369\) 1.95459 31.2446i 0.101752 1.62653i
\(370\) 13.6885 2.51272i 0.711632 0.130630i
\(371\) 0.0719647 0.0298087i 0.00373622 0.00154759i
\(372\) −1.48029 + 24.2966i −0.0767496 + 1.25972i
\(373\) −1.14564 + 2.76583i −0.0593192 + 0.143209i −0.950760 0.309928i \(-0.899695\pi\)
0.891441 + 0.453137i \(0.149695\pi\)
\(374\) 35.1517 22.7421i 1.81765 1.17596i
\(375\) −0.586340 + 18.7639i −0.0302785 + 0.968965i
\(376\) −19.2955 4.73764i −0.995088 0.244325i
\(377\) 9.50858 9.50858i 0.489717 0.489717i
\(378\) 6.51626 3.39681i 0.335160 0.174713i
\(379\) −9.82421 + 23.7177i −0.504636 + 1.21830i 0.442298 + 0.896868i \(0.354163\pi\)
−0.946933 + 0.321430i \(0.895837\pi\)
\(380\) 7.67447 + 20.1996i 0.393692 + 1.03622i
\(381\) −17.8573 8.05904i −0.914855 0.412877i
\(382\) 0.00405387 + 0.00279640i 0.000207414 + 0.000143076i
\(383\) 6.74364 0.344584 0.172292 0.985046i \(-0.444883\pi\)
0.172292 + 0.985046i \(0.444883\pi\)
\(384\) 19.5589 1.20375i 0.998111 0.0614289i
\(385\) −11.3791 −0.579931
\(386\) −5.13634 3.54310i −0.261433 0.180339i
\(387\) −4.99052 14.5592i −0.253683 0.740087i
\(388\) 0.615988 + 1.62132i 0.0312721 + 0.0823099i
\(389\) 4.98763 12.0412i 0.252883 0.610513i −0.745552 0.666448i \(-0.767814\pi\)
0.998434 + 0.0559349i \(0.0178139\pi\)
\(390\) −5.99078 9.92639i −0.303355 0.502642i
\(391\) 39.6203 39.6203i 2.00368 2.00368i
\(392\) −2.74684 0.674435i −0.138736 0.0340641i
\(393\) 13.1992 + 0.412452i 0.665811 + 0.0208054i
\(394\) 12.3969 8.02045i 0.624549 0.404065i
\(395\) 0.560906 1.35415i 0.0282223 0.0681346i
\(396\) 18.9789 + 22.8410i 0.953726 + 1.14780i
\(397\) −4.58259 + 1.89817i −0.229994 + 0.0952665i −0.494704 0.869061i \(-0.664724\pi\)
0.264711 + 0.964328i \(0.414724\pi\)
\(398\) −5.60119 + 1.02818i −0.280762 + 0.0515379i
\(399\) −5.93258 + 5.57305i −0.297001 + 0.279001i
\(400\) 1.14028 + 0.0676124i 0.0570141 + 0.00338062i
\(401\) 11.0425 0.551436 0.275718 0.961239i \(-0.411084\pi\)
0.275718 + 0.961239i \(0.411084\pi\)
\(402\) 4.67725 6.34681i 0.233280 0.316550i
\(403\) 5.53623 + 13.3656i 0.275779 + 0.665790i
\(404\) −10.8601 0.321689i −0.540309 0.0160046i
\(405\) −17.9804 10.2389i −0.893455 0.508776i
\(406\) −7.75543 + 5.01753i −0.384895 + 0.249016i
\(407\) −14.9809 + 14.9809i −0.742575 + 0.742575i
\(408\) −23.0638 18.0744i −1.14183 0.894819i
\(409\) −0.579216 0.579216i −0.0286404 0.0286404i 0.692642 0.721282i \(-0.256447\pi\)
−0.721282 + 0.692642i \(0.756447\pi\)
\(410\) 33.1748 + 7.11105i 1.63839 + 0.351190i
\(411\) 33.3194 12.5971i 1.64352 0.621370i
\(412\) 28.5239 + 12.8172i 1.40527 + 0.631456i
\(413\) −1.91661 + 0.793886i −0.0943103 + 0.0390646i
\(414\) 31.2426 + 24.5661i 1.53549 + 1.20736i
\(415\) 16.6601i 0.817812i
\(416\) 10.1356 5.73641i 0.496940 0.281250i
\(417\) 18.2282 17.1235i 0.892637 0.838540i
\(418\) −27.0771 18.6781i −1.32439 0.913576i
\(419\) 6.05747 + 14.6240i 0.295927 + 0.714431i 0.999991 + 0.00429410i \(0.00136686\pi\)
−0.704064 + 0.710137i \(0.748633\pi\)
\(420\) 2.59463 + 7.52959i 0.126605 + 0.367406i
\(421\) −11.3524 4.70231i −0.553281 0.229176i 0.0884846 0.996078i \(-0.471798\pi\)
−0.641765 + 0.766901i \(0.721798\pi\)
\(422\) 0.498328 2.32482i 0.0242582 0.113170i
\(423\) −15.8027 + 13.9420i −0.768356 + 0.677883i
\(424\) 0.130415 0.177571i 0.00633353 0.00862363i
\(425\) −1.20780 1.20780i −0.0585870 0.0585870i
\(426\) 15.3032 + 3.78381i 0.741444 + 0.183326i
\(427\) −6.97684 2.88990i −0.337633 0.139852i
\(428\) −16.5199 0.489338i −0.798518 0.0236531i
\(429\) 16.0872 + 7.26022i 0.776699 + 0.350527i
\(430\) 16.4061 3.01157i 0.791170 0.145231i
\(431\) 34.3277i 1.65351i −0.562565 0.826753i \(-0.690185\pi\)
0.562565 0.826753i \(-0.309815\pi\)
\(432\) 10.7865 17.7666i 0.518964 0.854796i
\(433\) 3.64194i 0.175021i 0.996164 + 0.0875103i \(0.0278911\pi\)
−0.996164 + 0.0875103i \(0.972109\pi\)
\(434\) −1.79418 9.77414i −0.0861235 0.469174i
\(435\) 23.7065 + 10.6988i 1.13664 + 0.512970i
\(436\) −19.3345 20.5149i −0.925955 0.982486i
\(437\) −40.6723 16.8470i −1.94562 0.805902i
\(438\) −2.42103 + 9.79163i −0.115681 + 0.467862i
\(439\) −16.4562 16.4562i −0.785412 0.785412i 0.195326 0.980738i \(-0.437423\pi\)
−0.980738 + 0.195326i \(0.937423\pi\)
\(440\) −27.5283 + 16.6750i −1.31236 + 0.794950i
\(441\) −2.24963 + 1.98474i −0.107125 + 0.0945112i
\(442\) −17.0283 3.65003i −0.809953 0.173614i
\(443\) 1.58849 + 0.657974i 0.0754714 + 0.0312613i 0.420100 0.907478i \(-0.361995\pi\)
−0.344628 + 0.938739i \(0.611995\pi\)
\(444\) 13.3289 + 6.49702i 0.632559 + 0.308335i
\(445\) 0.00143461 + 0.00346345i 6.80069e−5 + 0.000164183i
\(446\) −2.82747 + 4.09891i −0.133885 + 0.194089i
\(447\) 24.6011 23.1102i 1.16359 1.09307i
\(448\) −7.63351 + 2.39366i −0.360649 + 0.113090i
\(449\) 25.2872i 1.19337i −0.802474 0.596687i \(-0.796483\pi\)
0.802474 0.596687i \(-0.203517\pi\)
\(450\) 0.748883 0.952414i 0.0353027 0.0448972i
\(451\) −47.7175 + 19.7652i −2.24693 + 0.930708i
\(452\) −14.0672 37.0258i −0.661668 1.74155i
\(453\) 25.4823 9.63412i 1.19726 0.452651i
\(454\) −6.00091 + 27.9957i −0.281637 + 1.31390i
\(455\) 3.34692 + 3.34692i 0.156906 + 0.156906i
\(456\) −6.18533 + 22.1760i −0.289655 + 1.03849i
\(457\) −15.3855 + 15.3855i −0.719702 + 0.719702i −0.968544 0.248842i \(-0.919950\pi\)
0.248842 + 0.968544i \(0.419950\pi\)
\(458\) −4.26576 6.59344i −0.199326 0.308091i
\(459\) −29.7009 + 9.15455i −1.38632 + 0.427298i
\(460\) −31.3462 + 29.5426i −1.46152 + 1.37743i
\(461\) −4.66284 11.2571i −0.217170 0.524295i 0.777322 0.629102i \(-0.216577\pi\)
−0.994493 + 0.104807i \(0.966577\pi\)
\(462\) −9.75980 7.19243i −0.454067 0.334622i
\(463\) 6.17854 0.287141 0.143570 0.989640i \(-0.454142\pi\)
0.143570 + 0.989640i \(0.454142\pi\)
\(464\) −11.4092 + 23.5033i −0.529661 + 1.09112i
\(465\) −20.3940 + 19.1581i −0.945750 + 0.888435i
\(466\) −2.46347 13.4202i −0.114118 0.621680i
\(467\) 21.4387 8.88019i 0.992064 0.410926i 0.173183 0.984890i \(-0.444595\pi\)
0.818881 + 0.573963i \(0.194595\pi\)
\(468\) 1.13595 12.3005i 0.0525092 0.568590i
\(469\) −1.23173 + 2.97366i −0.0568759 + 0.137311i
\(470\) −12.4063 19.1760i −0.572259 0.884522i
\(471\) −1.48512 0.0464075i −0.0684309 0.00213835i
\(472\) −3.47331 + 4.72920i −0.159872 + 0.217679i
\(473\) −17.9550 + 17.9550i −0.825571 + 0.825571i
\(474\) 1.33701 0.806915i 0.0614110 0.0370628i
\(475\) −0.513572 + 1.23987i −0.0235643 + 0.0568892i
\(476\) 10.9116 + 4.90311i 0.500133 + 0.224734i
\(477\) −0.0757723 0.221056i −0.00346938 0.0101215i
\(478\) 0.647621 0.938839i 0.0296215 0.0429415i
\(479\) 9.27063 0.423586 0.211793 0.977315i \(-0.432070\pi\)
0.211793 + 0.977315i \(0.432070\pi\)
\(480\) 17.3109 + 14.4134i 0.790131 + 0.657880i
\(481\) 8.81265 0.401822
\(482\) −20.9504 + 30.3712i −0.954264 + 1.38337i
\(483\) −14.7891 6.67438i −0.672929 0.303695i
\(484\) 11.0644 24.6233i 0.502928 1.11924i
\(485\) −0.762961 + 1.84195i −0.0346443 + 0.0836387i
\(486\) −8.95001 20.1469i −0.405981 0.913882i
\(487\) 2.83609 2.83609i 0.128515 0.128515i −0.639923 0.768439i \(-0.721034\pi\)
0.768439 + 0.639923i \(0.221034\pi\)
\(488\) −21.1133 + 3.23268i −0.955756 + 0.146336i
\(489\) −0.523500 + 16.7529i −0.0236735 + 0.757594i
\(490\) −1.76612 2.72983i −0.0797851 0.123321i
\(491\) −13.4188 + 32.3959i −0.605583 + 1.46201i 0.262175 + 0.965020i \(0.415560\pi\)
−0.867758 + 0.496987i \(0.834440\pi\)
\(492\) 23.9592 + 27.0681i 1.08016 + 1.22032i
\(493\) 36.0933 14.9504i 1.62556 0.673330i
\(494\) 2.47041 + 13.4580i 0.111149 + 0.605503i
\(495\) −2.13137 + 34.0706i −0.0957982 + 1.53136i
\(496\) −18.6636 21.0165i −0.838022 0.943667i
\(497\) −6.43565 −0.288679
\(498\) 10.5304 14.2893i 0.471880 0.640320i
\(499\) 5.10493 + 12.3244i 0.228528 + 0.551715i 0.995999 0.0893687i \(-0.0284849\pi\)
−0.767471 + 0.641084i \(0.778485\pi\)
\(500\) −14.8676 15.7753i −0.664899 0.705492i
\(501\) −38.7427 + 14.6475i −1.73090 + 0.654403i
\(502\) 13.7978 + 21.3269i 0.615828 + 0.951865i
\(503\) 5.40651 5.40651i 0.241064 0.241064i −0.576226 0.817290i \(-0.695475\pi\)
0.817290 + 0.576226i \(0.195475\pi\)
\(504\) −2.53386 + 8.09812i −0.112867 + 0.360719i
\(505\) −8.83130 8.83130i −0.392987 0.392987i
\(506\) 13.7430 64.1147i 0.610953 2.85024i
\(507\) 5.36653 + 14.1945i 0.238336 + 0.630399i
\(508\) 21.1475 8.03460i 0.938270 0.356478i
\(509\) 14.4726 5.99475i 0.641487 0.265713i −0.0381379 0.999272i \(-0.512143\pi\)
0.679625 + 0.733560i \(0.262143\pi\)
\(510\) −5.04376 33.3037i −0.223342 1.47471i
\(511\) 4.11779i 0.182160i
\(512\) −14.9593 + 16.9770i −0.661116 + 0.750284i
\(513\) 15.5753 + 18.8069i 0.687667 + 0.830344i
\(514\) 3.60488 5.22590i 0.159005 0.230505i
\(515\) 13.7563 + 33.2106i 0.606174 + 1.46343i
\(516\) 15.9750 + 7.78686i 0.703259 + 0.342797i
\(517\) 32.1217 + 13.3052i 1.41271 + 0.585163i
\(518\) −5.91905 1.26876i −0.260068 0.0557459i
\(519\) −7.75354 0.242285i −0.340343 0.0106351i
\(520\) 13.0015 + 3.19228i 0.570154 + 0.139991i
\(521\) 11.4828 + 11.4828i 0.503071 + 0.503071i 0.912391 0.409320i \(-0.134234\pi\)
−0.409320 + 0.912391i \(0.634234\pi\)
\(522\) 13.5706 + 24.1607i 0.593968 + 1.05749i
\(523\) −17.1008 7.08338i −0.747766 0.309735i −0.0239362 0.999713i \(-0.507620\pi\)
−0.723830 + 0.689979i \(0.757620\pi\)
\(524\) −11.0969 + 10.4584i −0.484769 + 0.456877i
\(525\) −0.203465 + 0.450838i −0.00887993 + 0.0196762i
\(526\) −4.33210 23.5999i −0.188889 1.02900i
\(527\) 42.0296i 1.83084i
\(528\) −34.1509 3.09785i −1.48623 0.134817i
\(529\) 64.7553i 2.81545i
\(530\) 0.249097 0.0457253i 0.0108201 0.00198618i
\(531\) 2.01802 + 5.88732i 0.0875745 + 0.255488i
\(532\) 0.278284 9.39477i 0.0120652 0.407315i
\(533\) 19.8487 + 8.22159i 0.859742 + 0.356117i
\(534\) −0.000958702 0.00387737i −4.14871e−5 0.000167790i
\(535\) −13.4338 13.4338i −0.580793 0.580793i
\(536\) 1.37782 + 8.99888i 0.0595129 + 0.388692i
\(537\) −0.000741886 0.0237417i −3.20148e−5 0.00102453i
\(538\) −0.461823 + 2.15452i −0.0199106 + 0.0928878i
\(539\) 4.57273 + 1.89409i 0.196962 + 0.0815842i
\(540\) 23.0307 6.35837i 0.991083 0.273621i
\(541\) −0.631442 1.52444i −0.0271478 0.0655406i 0.909724 0.415213i \(-0.136293\pi\)
−0.936872 + 0.349672i \(0.886293\pi\)
\(542\) 27.7578 + 19.1476i 1.19230 + 0.822461i
\(543\) −9.18851 9.78128i −0.394317 0.419755i
\(544\) 33.5826 4.12837i 1.43984 0.177002i
\(545\) 32.4051i 1.38808i
\(546\) 0.755140 + 4.98616i 0.0323170 + 0.213388i
\(547\) 2.48998 1.03138i 0.106464 0.0440988i −0.328816 0.944394i \(-0.606650\pi\)
0.435280 + 0.900295i \(0.356650\pi\)
\(548\) −16.8587 + 37.5181i −0.720168 + 1.60270i
\(549\) −9.95961 + 20.3484i −0.425066 + 0.868448i
\(550\) −1.95450 0.418949i −0.0833401 0.0178640i
\(551\) −21.7044 21.7044i −0.924639 0.924639i
\(552\) −45.5587 + 5.52546i −1.93911 + 0.235179i
\(553\) −0.450806 + 0.450806i −0.0191702 + 0.0191702i
\(554\) 8.95132 5.79124i 0.380305 0.246046i
\(555\) 6.02784 + 15.9436i 0.255867 + 0.676769i
\(556\) −0.855043 + 28.8659i −0.0362619 + 1.22419i
\(557\) −7.14547 17.2507i −0.302763 0.730935i −0.999902 0.0139987i \(-0.995544\pi\)
0.697139 0.716936i \(-0.254456\pi\)
\(558\) −29.6013 + 3.54129i −1.25312 + 0.149915i
\(559\) 10.5622 0.446733
\(560\) −8.27293 4.01593i −0.349595 0.169704i
\(561\) 35.1077 + 37.3726i 1.48225 + 1.57787i
\(562\) 23.4912 4.31215i 0.990918 0.181897i
\(563\) −9.20923 + 3.81459i −0.388123 + 0.160766i −0.568207 0.822885i \(-0.692363\pi\)
0.180085 + 0.983651i \(0.442363\pi\)
\(564\) 1.47982 24.2889i 0.0623118 1.02275i
\(565\) 17.4237 42.0644i 0.733019 1.76966i
\(566\) −21.4664 + 13.8881i −0.902299 + 0.583760i
\(567\) 5.52122 + 7.10747i 0.231869 + 0.298486i
\(568\) −15.5692 + 9.43089i −0.653269 + 0.395711i
\(569\) −10.5774 + 10.5774i −0.443430 + 0.443430i −0.893163 0.449733i \(-0.851519\pi\)
0.449733 + 0.893163i \(0.351519\pi\)
\(570\) −22.6581 + 13.6746i −0.949043 + 0.572767i
\(571\) −3.81459 + 9.20923i −0.159636 + 0.385394i −0.983378 0.181570i \(-0.941882\pi\)
0.823742 + 0.566964i \(0.191882\pi\)
\(572\) −19.0514 + 7.23820i −0.796578 + 0.302644i
\(573\) −0.00248112 + 0.00549769i −0.000103650 + 0.000229669i
\(574\) −12.1478 8.37968i −0.507039 0.349761i
\(575\) −2.67517 −0.111562
\(576\) 5.73715 + 23.3042i 0.239048 + 0.971008i
\(577\) 18.6182 0.775085 0.387543 0.921852i \(-0.373324\pi\)
0.387543 + 0.921852i \(0.373324\pi\)
\(578\) −21.8574 15.0775i −0.909147 0.627140i
\(579\) 3.14364 6.96569i 0.130645 0.289484i
\(580\) −28.0746 + 10.6664i −1.16573 + 0.442898i
\(581\) −2.77314 + 6.69494i −0.115049 + 0.277753i
\(582\) −1.81864 + 1.09759i −0.0753852 + 0.0454965i
\(583\) −0.272615 + 0.272615i −0.0112906 + 0.0112906i
\(584\) −6.03427 9.96180i −0.249700 0.412222i
\(585\) 10.6481 9.39428i 0.440244 0.388406i
\(586\) −2.01259 + 1.30209i −0.0831394 + 0.0537887i
\(587\) −7.63366 + 18.4293i −0.315075 + 0.760658i 0.684427 + 0.729082i \(0.260053\pi\)
−0.999501 + 0.0315759i \(0.989947\pi\)
\(588\) 0.210663 3.45769i 0.00868758 0.142593i
\(589\) 30.5086 12.6371i 1.25708 0.520701i
\(590\) −6.63412 + 1.21779i −0.273122 + 0.0501355i
\(591\) 12.3814 + 13.1802i 0.509304 + 0.542161i
\(592\) −16.1787 + 5.60447i −0.664939 + 0.230342i
\(593\) 12.9659 0.532447 0.266224 0.963911i \(-0.414224\pi\)
0.266224 + 0.963911i \(0.414224\pi\)
\(594\) −23.3633 + 27.8751i −0.958607 + 1.14373i
\(595\) 5.26237 + 12.7045i 0.215736 + 0.520833i
\(596\) −1.15398 + 38.9580i −0.0472690 + 1.59578i
\(597\) −2.46652 6.52395i −0.100948 0.267008i
\(598\) −22.9003 + 14.8158i −0.936462 + 0.605863i
\(599\) 5.57399 5.57399i 0.227747 0.227747i −0.584004 0.811751i \(-0.698515\pi\)
0.811751 + 0.584004i \(0.198515\pi\)
\(600\) 0.168440 + 1.38883i 0.00687655 + 0.0566988i
\(601\) −1.18178 1.18178i −0.0482057 0.0482057i 0.682593 0.730799i \(-0.260852\pi\)
−0.730799 + 0.682593i \(0.760852\pi\)
\(602\) −7.09414 1.52064i −0.289136 0.0619765i
\(603\) 8.67285 + 4.24496i 0.353186 + 0.172868i
\(604\) −12.8933 + 28.6934i −0.524622 + 1.16752i
\(605\) 28.6691 11.8751i 1.16556 0.482792i
\(606\) −1.99254 13.1566i −0.0809413 0.534452i
\(607\) 39.8739i 1.61843i 0.587511 + 0.809216i \(0.300108\pi\)
−0.587511 + 0.809216i \(0.699892\pi\)
\(608\) −13.0940 23.1357i −0.531031 0.938277i
\(609\) −7.74573 8.24542i −0.313873 0.334121i
\(610\) −20.2109 13.9417i −0.818314 0.564482i
\(611\) −5.53447 13.3614i −0.223901 0.540544i
\(612\) 16.7245 31.7526i 0.676046 1.28352i
\(613\) −24.7703 10.2602i −1.00046 0.414405i −0.178495 0.983941i \(-0.557123\pi\)
−0.821966 + 0.569536i \(0.807123\pi\)
\(614\) −2.32049 + 10.8256i −0.0936472 + 0.436887i
\(615\) −1.29784 + 41.5333i −0.0523341 + 1.67478i
\(616\) 13.8380 2.11875i 0.557549 0.0853667i
\(617\) −3.34041 3.34041i −0.134480 0.134480i 0.636663 0.771142i \(-0.280314\pi\)
−0.771142 + 0.636663i \(0.780314\pi\)
\(618\) −9.19288 + 37.1797i −0.369792 + 1.49559i
\(619\) −44.5632 18.4587i −1.79114 0.741916i −0.989576 0.144014i \(-0.953999\pi\)
−0.801569 0.597902i \(-0.796001\pi\)
\(620\) 0.956639 32.2957i 0.0384195 1.29703i
\(621\) −22.7542 + 43.0307i −0.913094 + 1.72676i
\(622\) −1.90328 + 0.349375i −0.0763146 + 0.0140086i
\(623\) 0.00163060i 6.53286e-5i
\(624\) 9.13362 + 10.9560i 0.365637 + 0.438589i
\(625\) 26.3463i 1.05385i
\(626\) 6.49447 + 35.3798i 0.259571 + 1.41406i
\(627\) 16.5723 36.7209i 0.661832 1.46649i
\(628\) 1.24858 1.17674i 0.0498237 0.0469569i
\(629\) 23.6539 + 9.79777i 0.943144 + 0.390663i
\(630\) −8.50432 + 4.77670i −0.338820 + 0.190308i
\(631\) 30.2416 + 30.2416i 1.20390 + 1.20390i 0.972971 + 0.230927i \(0.0741759\pi\)
0.230927 + 0.972971i \(0.425824\pi\)
\(632\) −0.429977 + 1.75121i −0.0171036 + 0.0696594i
\(633\) 2.91057 + 0.0909502i 0.115685 + 0.00361495i
\(634\) 1.67567 + 0.359182i 0.0665494 + 0.0142649i
\(635\) 24.0254 + 9.95163i 0.953418 + 0.394918i
\(636\) 0.242552 + 0.118230i 0.00961781 + 0.00468811i
\(637\) −0.787870 1.90209i −0.0312165 0.0753634i
\(638\) 25.9598 37.6333i 1.02776 1.48992i
\(639\) −1.20544 + 19.2693i −0.0476865 + 0.762282i
\(640\) −25.8989 + 2.40788i −1.02375 + 0.0951798i
\(641\) 19.0486i 0.752375i 0.926544 + 0.376187i \(0.122765\pi\)
−0.926544 + 0.376187i \(0.877235\pi\)
\(642\) −3.03096 20.0133i −0.119622 0.789861i
\(643\) −7.22415 + 2.99234i −0.284893 + 0.118006i −0.520554 0.853829i \(-0.674274\pi\)
0.235661 + 0.971835i \(0.424274\pi\)
\(644\) 17.5141 6.65414i 0.690152 0.262210i
\(645\) 7.22452 + 19.1089i 0.284465 + 0.752411i
\(646\) −8.33160 + 38.8690i −0.327802 + 1.52928i
\(647\) 4.11050 + 4.11050i 0.161601 + 0.161601i 0.783275 0.621675i \(-0.213547\pi\)
−0.621675 + 0.783275i \(0.713547\pi\)
\(648\) 23.7724 + 9.10358i 0.933866 + 0.357622i
\(649\) 7.26046 7.26046i 0.284998 0.284998i
\(650\) 0.451651 + 0.698102i 0.0177152 + 0.0273818i
\(651\) 11.3844 4.30411i 0.446189 0.168691i
\(652\) −13.2742 14.0846i −0.519857 0.551595i
\(653\) 8.93828 + 21.5789i 0.349782 + 0.844448i 0.996645 + 0.0818424i \(0.0260804\pi\)
−0.646863 + 0.762606i \(0.723920\pi\)
\(654\) 20.4825 27.7938i 0.800928 1.08682i
\(655\) −17.5285 −0.684895
\(656\) −41.6677 2.47066i −1.62685 0.0964632i
\(657\) −12.3293 0.771290i −0.481011 0.0300909i
\(658\) 1.79361 + 9.77104i 0.0699224 + 0.380915i
\(659\) 24.7223 10.2403i 0.963044 0.398906i 0.154925 0.987926i \(-0.450486\pi\)
0.808118 + 0.589020i \(0.200486\pi\)
\(660\) −26.1263 29.5163i −1.01696 1.14892i
\(661\) 4.30518 10.3936i 0.167452 0.404265i −0.817770 0.575545i \(-0.804790\pi\)
0.985222 + 0.171279i \(0.0547901\pi\)
\(662\) 5.82931 + 9.01017i 0.226563 + 0.350190i
\(663\) 0.666170 21.3186i 0.0258719 0.827947i
\(664\) 3.10206 + 20.2602i 0.120383 + 0.786250i
\(665\) 7.63973 7.63973i 0.296256 0.296256i
\(666\) −4.90752 + 17.4849i −0.190162 + 0.677525i
\(667\) 23.4149 56.5286i 0.906629 2.18880i
\(668\) 19.6028 43.6249i 0.758453 1.68790i
\(669\) −5.55878 2.50869i −0.214915 0.0969917i
\(670\) −5.94219 + 8.61424i −0.229567 + 0.332797i
\(671\) 37.3770 1.44292
\(672\) −4.55730 8.67358i −0.175802 0.334591i
\(673\) −5.06231 −0.195138 −0.0975688 0.995229i \(-0.531107\pi\)
−0.0975688 + 0.995229i \(0.531107\pi\)
\(674\) 22.1824 32.1572i 0.854435 1.23865i
\(675\) 1.31177 + 0.693648i 0.0504899 + 0.0266985i
\(676\) −15.9832 7.18202i −0.614738 0.276231i
\(677\) 10.6377 25.6816i 0.408839 0.987025i −0.576605 0.817023i \(-0.695623\pi\)
0.985444 0.170001i \(-0.0543772\pi\)
\(678\) 41.5321 25.0655i 1.59503 0.962635i
\(679\) 0.613200 0.613200i 0.0235324 0.0235324i
\(680\) 31.3481 + 23.0232i 1.20214 + 0.882901i
\(681\) −35.0493 1.09523i −1.34309 0.0419693i
\(682\) 26.7174 + 41.2962i 1.02306 + 1.58131i
\(683\) −6.75951 + 16.3189i −0.258645 + 0.624425i −0.998849 0.0479570i \(-0.984729\pi\)
0.740204 + 0.672382i \(0.234729\pi\)
\(684\) −28.0772 2.59293i −1.07356 0.0991431i
\(685\) −43.6827 + 18.0940i −1.66903 + 0.691335i
\(686\) 0.255333 + 1.39097i 0.00974866 + 0.0531076i
\(687\) 7.01002 6.58519i 0.267449 0.251241i
\(688\) −19.3906 + 6.71711i −0.739258 + 0.256087i
\(689\) 0.160368 0.00610955
\(690\) −42.4681 31.2966i −1.61673 1.19144i
\(691\) −8.94198 21.5879i −0.340169 0.821241i −0.997698 0.0678116i \(-0.978398\pi\)
0.657529 0.753429i \(-0.271602\pi\)
\(692\) 6.51858 6.14352i 0.247799 0.233541i
\(693\) 6.52768 13.3367i 0.247966 0.506618i
\(694\) 25.6165 + 39.5946i 0.972390 + 1.50299i
\(695\) −23.4734 + 23.4734i −0.890398 + 0.890398i
\(696\) −30.8215 8.59671i −1.16828 0.325857i
\(697\) 44.1349 + 44.1349i 1.67173 + 1.67173i
\(698\) 7.40531 34.5476i 0.280295 1.30764i
\(699\) 15.6311 5.90969i 0.591223 0.223525i
\(700\) −0.202848 0.533907i −0.00766692 0.0201798i
\(701\) −27.8994 + 11.5563i −1.05375 + 0.436476i −0.841228 0.540681i \(-0.818167\pi\)
−0.212518 + 0.977157i \(0.568167\pi\)
\(702\) 15.0707 1.32706i 0.568808 0.0500867i
\(703\) 20.1159i 0.758684i
\(704\) 30.3722 25.4041i 1.14470 0.957452i
\(705\) 20.3875 19.1520i 0.767839 0.721306i
\(706\) −7.55971 + 10.9591i −0.284514 + 0.412451i
\(707\) 2.07890 + 5.01890i 0.0781850 + 0.188755i
\(708\) −6.45980 3.14877i −0.242774 0.118338i
\(709\) 15.3125 + 6.34264i 0.575072 + 0.238203i 0.651214 0.758894i \(-0.274260\pi\)
−0.0761417 + 0.997097i \(0.524260\pi\)
\(710\) −20.4597 4.38556i −0.767838 0.164587i
\(711\) 1.26534 + 1.43422i 0.0474540 + 0.0537874i
\(712\) −0.00238950 0.00394476i −8.95503e−5 0.000147836i
\(713\) 46.5459 + 46.5459i 1.74316 + 1.74316i
\(714\) −3.51667 + 14.2228i −0.131608 + 0.532276i
\(715\) −21.6439 8.96522i −0.809438 0.335280i
\(716\) −0.0188117 0.0199602i −0.000703027 0.000745947i
\(717\) 1.27321 + 0.574606i 0.0475491 + 0.0214590i
\(718\) 6.18916 + 33.7166i 0.230977 + 1.25829i
\(719\) 12.1850i 0.454423i 0.973845 + 0.227211i \(0.0729608\pi\)
−0.973845 + 0.227211i \(0.927039\pi\)
\(720\) −13.5739 + 24.0182i −0.505868 + 0.895104i
\(721\) 15.6356i 0.582301i
\(722\) 4.29088 0.787652i 0.159690 0.0293134i
\(723\) −41.1882 18.5884i −1.53181 0.691309i
\(724\) 15.4895 + 0.458818i 0.575664 + 0.0170519i
\(725\) −1.72324 0.713790i −0.0639996 0.0265095i
\(726\) 32.0954 + 7.93575i 1.19117 + 0.294523i
\(727\) −23.0203 23.0203i −0.853777 0.853777i 0.136819 0.990596i \(-0.456312\pi\)
−0.990596 + 0.136819i \(0.956312\pi\)
\(728\) −4.69336 3.44699i −0.173947 0.127754i
\(729\) 22.3150 15.2001i 0.826480 0.562966i
\(730\) 2.80606 13.0909i 0.103857 0.484517i
\(731\) 28.3499 + 11.7429i 1.04856 + 0.434327i
\(732\) −8.52263 24.7326i −0.315005 0.914142i
\(733\) −7.35218 17.7497i −0.271559 0.655601i 0.727991 0.685586i \(-0.240454\pi\)
−0.999550 + 0.0299850i \(0.990454\pi\)
\(734\) 19.2331 + 13.2672i 0.709907 + 0.489702i
\(735\) 2.90230 2.72642i 0.107053 0.100565i
\(736\) 32.6192 41.7631i 1.20236 1.53941i
\(737\) 15.9307i 0.586816i
\(738\) −27.3653 + 34.8027i −1.00733 + 1.28110i
\(739\) 31.8376 13.1876i 1.17117 0.485113i 0.289588 0.957151i \(-0.406482\pi\)
0.881578 + 0.472039i \(0.156482\pi\)
\(740\) −17.9528 8.06704i −0.659957 0.296550i
\(741\) −15.6751 + 5.92632i −0.575840 + 0.217709i
\(742\) −0.107712 0.0230882i −0.00395423 0.000847594i
\(743\) 23.2004 + 23.2004i 0.851140 + 0.851140i 0.990274 0.139134i \(-0.0444318\pi\)
−0.139134 + 0.990274i \(0.544432\pi\)
\(744\) 21.2339 27.0953i 0.778471 0.993363i
\(745\) −31.6802 + 31.6802i −1.16067 + 1.16067i
\(746\) 3.55467 2.29977i 0.130146 0.0842004i
\(747\) 19.5262 + 9.55718i 0.714427 + 0.349679i
\(748\) −59.1828 1.75307i −2.16394 0.0640985i
\(749\) 3.16233 + 7.63453i 0.115549 + 0.278960i
\(750\) 15.7503 21.3725i 0.575121 0.780414i
\(751\) −29.1882 −1.06509 −0.532547 0.846400i \(-0.678765\pi\)
−0.532547 + 0.846400i \(0.678765\pi\)
\(752\) 18.6577 + 21.0098i 0.680377 + 0.766148i
\(753\) −22.6743 + 21.3002i −0.826298 + 0.776222i
\(754\) −18.7046 + 3.43350i −0.681183 + 0.125041i
\(755\) −33.4080 + 13.8380i −1.21584 + 0.503618i
\(756\) −10.3134 1.27840i −0.375094 0.0464951i
\(757\) 12.2421 29.5549i 0.444945 1.07419i −0.529246 0.848468i \(-0.677525\pi\)
0.974191 0.225724i \(-0.0724748\pi\)
\(758\) 30.4823 19.7211i 1.10717 0.716303i
\(759\) 80.2686 + 2.50826i 2.91357 + 0.0910439i
\(760\) 7.28674 29.6774i 0.264318 1.07651i
\(761\) −34.3705 + 34.3705i −1.24593 + 1.24593i −0.288430 + 0.957501i \(0.593133\pi\)
−0.957501 + 0.288430i \(0.906867\pi\)
\(762\) 14.3163 + 23.7213i 0.518626 + 0.859334i
\(763\) −5.39395 + 13.0222i −0.195274 + 0.471434i
\(764\) −0.00247360 0.00651066i −8.94917e−5 0.000235547i
\(765\) 39.0248 13.3767i 1.41094 0.483635i
\(766\) −7.85037 5.41527i −0.283645 0.195662i
\(767\) −4.27104 −0.154218
\(768\) −23.7354 14.3049i −0.856479 0.516182i
\(769\) −46.4281 −1.67424 −0.837120 0.547019i \(-0.815763\pi\)
−0.837120 + 0.547019i \(0.815763\pi\)
\(770\) 13.2465 + 9.13760i 0.477372 + 0.329296i
\(771\) 7.08715 + 3.19846i 0.255238 + 0.115190i
\(772\) 3.13411 + 8.24915i 0.112799 + 0.296893i
\(773\) −7.45607 + 18.0005i −0.268176 + 0.647435i −0.999398 0.0347056i \(-0.988951\pi\)
0.731221 + 0.682140i \(0.238951\pi\)
\(774\) −5.88179 + 20.9561i −0.211417 + 0.753251i
\(775\) 1.41893 1.41893i 0.0509693 0.0509693i
\(776\) 0.584867 2.38205i 0.0209955 0.0855105i
\(777\) 0.231562 7.41038i 0.00830723 0.265846i
\(778\) −15.4755 + 10.0122i −0.554823 + 0.358954i
\(779\) 18.7667 45.3068i 0.672387 1.62329i
\(780\) −0.997122 + 16.3662i −0.0357027 + 0.586002i
\(781\) 29.4285 12.1897i 1.05304 0.436182i
\(782\) −77.9383 + 14.3067i −2.78707 + 0.511606i
\(783\) −26.1388 + 21.6474i −0.934126 + 0.773616i
\(784\) 2.65605 + 2.99088i 0.0948590 + 0.106817i
\(785\) 1.97224 0.0703923
\(786\) −15.0342 11.0793i −0.536251 0.395187i
\(787\) 13.3868 + 32.3186i 0.477188 + 1.15203i 0.960922 + 0.276818i \(0.0892800\pi\)
−0.483735 + 0.875215i \(0.660720\pi\)
\(788\) −20.8720 0.618254i −0.743535 0.0220244i
\(789\) 27.4879 10.3924i 0.978594 0.369979i
\(790\) −1.74037 + 1.12596i −0.0619194 + 0.0400600i
\(791\) −14.0036 + 14.0036i −0.497909 + 0.497909i
\(792\) −3.75189 41.8299i −0.133318 1.48636i
\(793\) −10.9937 10.9937i −0.390397 0.390397i
\(794\) 6.85893 + 1.47022i 0.243414 + 0.0521761i
\(795\) 0.109692 + 0.290134i 0.00389036 + 0.0102900i
\(796\) 7.34607 + 3.30094i 0.260374 + 0.116999i
\(797\) 6.47238 2.68095i 0.229263 0.0949640i −0.265095 0.964222i \(-0.585403\pi\)
0.494358 + 0.869258i \(0.335403\pi\)
\(798\) 11.3815 1.72369i 0.402899 0.0610181i
\(799\) 42.0163i 1.48643i
\(800\) −1.27312 0.994377i −0.0450118 0.0351565i
\(801\) −0.00488226 0.000305422i −0.000172506 1.07916e-5i
\(802\) −12.8547 8.86733i −0.453916 0.313116i
\(803\) 7.79946 + 18.8296i 0.275237 + 0.664481i
\(804\) −10.5415 + 3.63250i −0.371769 + 0.128108i
\(805\) 19.8975 + 8.24180i 0.701294 + 0.290485i
\(806\) 4.28806 20.0048i 0.151040 0.704640i
\(807\) −2.69736 0.0842877i −0.0949514 0.00296707i
\(808\) 12.3840 + 9.09533i 0.435669 + 0.319972i
\(809\) −30.9437 30.9437i −1.08792 1.08792i −0.995742 0.0921810i \(-0.970616\pi\)
−0.0921810 0.995742i \(-0.529384\pi\)
\(810\) 12.7092 + 26.3579i 0.446557 + 0.926122i
\(811\) −1.50385 0.622915i −0.0528073 0.0218735i 0.356123 0.934439i \(-0.384098\pi\)
−0.408931 + 0.912565i \(0.634098\pi\)
\(812\) 13.0574 + 0.386775i 0.458224 + 0.0135731i
\(813\) −16.9888 + 37.6440i −0.595825 + 1.32023i
\(814\) 29.4694 5.40953i 1.03290 0.189604i
\(815\) 22.2478i 0.779308i
\(816\) 12.3347 + 39.5614i 0.431803 + 1.38492i
\(817\) 24.1094i 0.843481i
\(818\) 0.209152 + 1.13939i 0.00731283 + 0.0398380i
\(819\) −5.84270 + 2.00272i −0.204160 + 0.0699808i
\(820\) −32.9089 34.9180i −1.14923 1.21939i
\(821\) 11.6681 + 4.83310i 0.407221 + 0.168676i 0.576885 0.816826i \(-0.304268\pi\)
−0.169664 + 0.985502i \(0.554268\pi\)
\(822\) −48.9033 12.0916i −1.70570 0.421743i
\(823\) 17.0025 + 17.0025i 0.592669 + 0.592669i 0.938352 0.345682i \(-0.112353\pi\)
−0.345682 + 0.938352i \(0.612353\pi\)
\(824\) −22.9127 37.8258i −0.798200 1.31773i
\(825\) 0.0764627 2.44694i 0.00266209 0.0851916i
\(826\) 2.86866 + 0.614900i 0.0998134 + 0.0213951i
\(827\) −47.2545 19.5735i −1.64320 0.680636i −0.646584 0.762842i \(-0.723803\pi\)
−0.996615 + 0.0822069i \(0.973803\pi\)
\(828\) −16.6430 53.6861i −0.578383 1.86572i
\(829\) 2.30566 + 5.56636i 0.0800789 + 0.193328i 0.958848 0.283919i \(-0.0916348\pi\)
−0.878769 + 0.477247i \(0.841635\pi\)
\(830\) −13.3784 + 19.3942i −0.464370 + 0.673184i
\(831\) 8.94013 + 9.51688i 0.310130 + 0.330137i
\(832\) −16.4055 1.46127i −0.568757 0.0506604i
\(833\) 5.98130i 0.207240i
\(834\) −34.9701 + 5.29613i −1.21092 + 0.183390i
\(835\) 50.7928 21.0391i 1.75776 0.728087i
\(836\) 16.5220 + 43.4869i 0.571426 + 1.50403i
\(837\) −10.7548 34.8927i −0.371739 1.20607i
\(838\) 4.69178 21.8883i 0.162075 0.756119i
\(839\) −20.3833 20.3833i −0.703709 0.703709i 0.261496 0.965205i \(-0.415784\pi\)
−0.965205 + 0.261496i \(0.915784\pi\)
\(840\) 3.02595 10.8488i 0.104405 0.374321i
\(841\) 9.65986 9.65986i 0.333099 0.333099i
\(842\) 9.43941 + 14.5902i 0.325304 + 0.502811i
\(843\) 10.3445 + 27.3613i 0.356284 + 0.942372i
\(844\) −2.44698 + 2.30619i −0.0842287 + 0.0793823i
\(845\) −7.70825 18.6094i −0.265172 0.640182i
\(846\) 29.5919 3.54016i 1.01739 0.121713i
\(847\) −13.4975 −0.463778
\(848\) −0.294412 + 0.101987i −0.0101101 + 0.00350226i
\(849\) −21.4395 22.8226i −0.735803 0.783271i
\(850\) 0.436131 + 2.37590i 0.0149592 + 0.0814929i
\(851\) 37.0462 15.3450i 1.26993 0.526022i
\(852\) −14.7762 16.6936i −0.506225 0.571912i
\(853\) 17.5965 42.4816i 0.602491 1.45454i −0.268518 0.963275i \(-0.586534\pi\)
0.871009 0.491267i \(-0.163466\pi\)
\(854\) 5.80120 + 8.96671i 0.198513 + 0.306835i
\(855\) −21.4435 24.3054i −0.733352 0.831228i
\(856\) 18.8381 + 13.8354i 0.643872 + 0.472884i
\(857\) 4.54509 4.54509i 0.155257 0.155257i −0.625204 0.780461i \(-0.714984\pi\)
0.780461 + 0.625204i \(0.214984\pi\)
\(858\) −12.8973 21.3701i −0.440306 0.729562i
\(859\) −16.1076 + 38.8871i −0.549583 + 1.32681i 0.368207 + 0.929744i \(0.379972\pi\)
−0.917790 + 0.397066i \(0.870028\pi\)
\(860\) −21.5169 9.66856i −0.733719 0.329695i
\(861\) 7.43492 16.4743i 0.253381 0.561444i
\(862\) −27.5658 + 39.9613i −0.938894 + 1.36109i
\(863\) −23.6963 −0.806632 −0.403316 0.915061i \(-0.632142\pi\)
−0.403316 + 0.915061i \(0.632142\pi\)
\(864\) −26.8236 + 12.0206i −0.912557 + 0.408950i
\(865\) 10.2967 0.350098
\(866\) 2.92455 4.23963i 0.0993801 0.144069i
\(867\) 13.3776 29.6421i 0.454326 1.00670i
\(868\) −5.76018 + 12.8190i −0.195513 + 0.435104i
\(869\) 1.20755 2.91528i 0.0409633 0.0988942i
\(870\) −19.0057 31.4915i −0.644355 1.06766i
\(871\) −4.68571 + 4.68571i −0.158769 + 0.158769i
\(872\) 6.03373 + 39.4077i 0.204328 + 1.33451i
\(873\) −1.72115 1.95087i −0.0582522 0.0660268i
\(874\) 33.8187 + 52.2725i 1.14394 + 1.76814i
\(875\) −4.14777 + 10.0136i −0.140220 + 0.338522i
\(876\) 10.6812 9.45443i 0.360885 0.319436i
\(877\) 1.87347 0.776018i 0.0632627 0.0262043i −0.350828 0.936440i \(-0.614100\pi\)
0.414090 + 0.910236i \(0.364100\pi\)
\(878\) 5.94226 + 32.3715i 0.200542 + 1.09249i
\(879\) −2.01007 2.13975i −0.0677981 0.0721719i
\(880\) 45.4364 + 2.69413i 1.53166 + 0.0908190i
\(881\) −16.8314 −0.567065 −0.283533 0.958963i \(-0.591506\pi\)
−0.283533 + 0.958963i \(0.591506\pi\)
\(882\) 4.21260 0.503966i 0.141846 0.0169694i
\(883\) 17.8286 + 43.0419i 0.599979 + 1.44848i 0.873603 + 0.486640i \(0.161778\pi\)
−0.273624 + 0.961837i \(0.588222\pi\)
\(884\) 16.8918 + 17.9231i 0.568133 + 0.602818i
\(885\) −2.92138 7.72705i −0.0982011 0.259742i
\(886\) −1.32082 2.04154i −0.0443737 0.0685870i
\(887\) −4.73858 + 4.73858i −0.159106 + 0.159106i −0.782170 0.623064i \(-0.785887\pi\)
0.623064 + 0.782170i \(0.285887\pi\)
\(888\) −10.2991 18.2666i −0.345614 0.612987i
\(889\) −7.99823 7.99823i −0.268252 0.268252i
\(890\) 0.00111117 0.00518386i 3.72464e−5 0.000173764i
\(891\) −38.7092 22.0429i −1.29681 0.738464i
\(892\) 6.58300 2.50109i 0.220415 0.0837426i
\(893\) −30.4989 + 12.6331i −1.02061 + 0.422749i
\(894\) −47.1964 + 7.14776i −1.57848 + 0.239057i
\(895\) 0.0315289i 0.00105389i
\(896\) 10.8084 + 3.34336i 0.361084 + 0.111694i
\(897\) −22.8716 24.3472i −0.763662 0.812928i
\(898\) −20.3061 + 29.4371i −0.677622 + 0.982330i
\(899\) 17.5637 + 42.4025i 0.585782 + 1.41420i
\(900\) −1.63659 + 0.507352i −0.0545530 + 0.0169117i
\(901\) 0.430443 + 0.178295i 0.0143401 + 0.00593987i
\(902\) 71.4204 + 15.3090i 2.37804 + 0.509735i
\(903\) 0.277533 8.88154i 0.00923571 0.295559i
\(904\) −13.3565 + 54.3985i −0.444232 + 1.80927i
\(905\) 12.5959 + 12.5959i 0.418702 + 0.418702i
\(906\) −37.4006 9.24751i −1.24255 0.307228i
\(907\) −43.1386 17.8686i −1.43239 0.593316i −0.474451 0.880282i \(-0.657354\pi\)
−0.957941 + 0.286965i \(0.907354\pi\)
\(908\) 29.4668 27.7713i 0.977890 0.921624i
\(909\) 15.4167 5.28445i 0.511340 0.175274i
\(910\) −1.20856 6.58384i −0.0400633 0.218252i
\(911\) 5.75941i 0.190818i −0.995438 0.0954088i \(-0.969584\pi\)
0.995438 0.0954088i \(-0.0304158\pi\)
\(912\) 25.0082 20.8485i 0.828104 0.690363i
\(913\) 35.8667i 1.18702i
\(914\) 30.2652 5.55562i 1.00109 0.183764i
\(915\) 12.3698 27.4092i 0.408934 0.906119i
\(916\) −0.328825 + 11.1010i −0.0108647 + 0.366787i
\(917\) 7.04391 + 2.91768i 0.232610 + 0.0963504i
\(918\) 41.9265 + 13.1935i 1.38378 + 0.435449i
\(919\) 27.5056 + 27.5056i 0.907326 + 0.907326i 0.996056 0.0887301i \(-0.0282809\pi\)
−0.0887301 + 0.996056i \(0.528281\pi\)
\(920\) 60.2138 9.21937i 1.98519 0.303954i
\(921\) −13.5532 0.423514i −0.446593 0.0139553i
\(922\) −3.61158 + 16.8489i −0.118941 + 0.554889i
\(923\) −12.2412 5.07046i −0.402923 0.166896i
\(924\) 5.58587 + 16.2101i 0.183761 + 0.533273i
\(925\) −0.467785 1.12933i −0.0153807 0.0371322i
\(926\) −7.19252 4.96148i −0.236361 0.163044i
\(927\) −46.8154 2.92866i −1.53762 0.0961898i
\(928\) 32.1553 18.1987i 1.05555 0.597403i
\(929\) 19.1535i 0.628407i −0.949356 0.314204i \(-0.898263\pi\)
0.949356 0.314204i \(-0.101737\pi\)
\(930\) 39.1253 5.92542i 1.28297 0.194302i
\(931\) −4.34172 + 1.79840i −0.142294 + 0.0589402i
\(932\) −7.90892 + 17.6009i −0.259065 + 0.576536i
\(933\) −0.838123 2.21684i −0.0274389 0.0725759i
\(934\) −32.0880 6.87810i −1.04995 0.225058i
\(935\) −48.1268 48.1268i −1.57392 1.57392i
\(936\) −11.1999 + 13.4070i −0.366080 + 0.438220i
\(937\) 1.56265 1.56265i 0.0510494 0.0510494i −0.681121 0.732171i \(-0.738507\pi\)
0.732171 + 0.681121i \(0.238507\pi\)
\(938\) 3.82177 2.47257i 0.124785 0.0807324i
\(939\) −41.2085 + 15.5798i −1.34479 + 0.508426i
\(940\) −0.956335 + 32.2855i −0.0311922 + 1.05304i
\(941\) −8.70894 21.0252i −0.283903 0.685403i 0.716016 0.698084i \(-0.245964\pi\)
−0.999920 + 0.0126803i \(0.995964\pi\)
\(942\) 1.69159 + 1.24661i 0.0551149 + 0.0406166i
\(943\) 97.7548 3.18334
\(944\) 7.84096 2.71620i 0.255202 0.0884047i
\(945\) −7.61967 9.20060i −0.247868 0.299296i
\(946\) 35.3198 6.48346i 1.14835 0.210796i
\(947\) 27.7318 11.4869i 0.901163 0.373274i 0.116496 0.993191i \(-0.462834\pi\)
0.784667 + 0.619917i \(0.212834\pi\)
\(948\) −2.20440 0.134305i −0.0715957 0.00436203i
\(949\) 3.24428 7.83240i 0.105314 0.254250i
\(950\) 1.59350 1.03094i 0.0516998 0.0334483i
\(951\) −0.0655546 + 2.09786i −0.00212575 + 0.0680279i
\(952\) −8.76507 14.4700i −0.284078 0.468976i
\(953\) −33.8056 + 33.8056i −1.09507 + 1.09507i −0.100093 + 0.994978i \(0.531914\pi\)
−0.994978 + 0.100093i \(0.968086\pi\)
\(954\) −0.0893046 + 0.318181i −0.00289134 + 0.0103015i
\(955\) 0.00306379 0.00739665i 9.91421e−5 0.000239350i
\(956\) −1.50781 + 0.572863i −0.0487660 + 0.0185277i
\(957\) 51.0367 + 23.0330i 1.64978 + 0.744552i
\(958\) −10.7921 7.44449i −0.348676 0.240520i
\(959\) 20.5659 0.664108
\(960\) −8.57761 30.6799i −0.276841 0.990188i
\(961\) −18.3764 −0.592788
\(962\) −10.2589 7.07672i −0.330761 0.228163i
\(963\) 23.4512 8.03847i 0.755705 0.259036i
\(964\) 48.7773 18.5320i 1.57101 0.596875i
\(965\) −3.88190 + 9.37173i −0.124963 + 0.301687i
\(966\) 11.8566 + 19.6457i 0.381479 + 0.632090i
\(967\) −1.34092 + 1.34092i −0.0431211 + 0.0431211i −0.728339 0.685217i \(-0.759707\pi\)
0.685217 + 0.728339i \(0.259707\pi\)
\(968\) −32.6532 + 19.7793i −1.04951 + 0.635732i
\(969\) −48.6621 1.52061i −1.56325 0.0488490i
\(970\) 2.36729 1.53157i 0.0760093 0.0491757i
\(971\) 8.55039 20.6425i 0.274395 0.662448i −0.725266 0.688468i \(-0.758283\pi\)
0.999661 + 0.0260200i \(0.00828336\pi\)
\(972\) −5.75949 + 30.6403i −0.184736 + 0.982788i
\(973\) 13.3402 5.52568i 0.427666 0.177145i
\(974\) −5.57896 + 1.02410i −0.178761 + 0.0328142i
\(975\) −0.742209 + 0.697229i −0.0237697 + 0.0223292i
\(976\) 27.1742 + 13.1912i 0.869826 + 0.422240i
\(977\) −14.7904 −0.473187 −0.236593 0.971609i \(-0.576031\pi\)
−0.236593 + 0.971609i \(0.576031\pi\)
\(978\) 14.0623 19.0819i 0.449664 0.610173i
\(979\) 0.00308850 + 0.00745630i 9.87089e−5 + 0.000238304i
\(980\) −0.136141 + 4.59606i −0.00434886 + 0.146816i
\(981\) 37.9799 + 18.5894i 1.21261 + 0.593514i
\(982\) 41.6356 26.9370i 1.32864 0.859593i
\(983\) −11.2141 + 11.2141i −0.357676 + 0.357676i −0.862955 0.505280i \(-0.831389\pi\)
0.505280 + 0.862955i \(0.331389\pi\)
\(984\) −6.15507 50.7500i −0.196217 1.61785i
\(985\) −16.9729 16.9729i −0.540801 0.540801i
\(986\) −54.0222 11.5797i −1.72042 0.368773i
\(987\) −11.3808 + 4.30274i −0.362254 + 0.136958i
\(988\) 7.93118 17.6504i 0.252324 0.561534i
\(989\) 44.4009 18.3914i 1.41187 0.584814i
\(990\) 29.8405 37.9505i 0.948393 1.20615i
\(991\) 9.32409i 0.296189i −0.988973 0.148095i \(-0.952686\pi\)
0.988973 0.148095i \(-0.0473140\pi\)
\(992\) 4.85001 + 39.4528i 0.153988 + 1.25263i
\(993\) −9.57945 + 8.99891i −0.303995 + 0.285572i
\(994\) 7.49184 + 5.16795i 0.237627 + 0.163917i
\(995\) 3.54280 + 8.55309i 0.112314 + 0.271151i
\(996\) −23.7332 + 8.17827i −0.752016 + 0.259138i
\(997\) 9.90478 + 4.10269i 0.313688 + 0.129934i 0.533972 0.845502i \(-0.320699\pi\)
−0.220285 + 0.975436i \(0.570699\pi\)
\(998\) 3.95399 18.4463i 0.125161 0.583909i
\(999\) −22.1444 2.08134i −0.700618 0.0658508i
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 672.2.bs.b.155.10 192
3.2 odd 2 inner 672.2.bs.b.155.39 yes 192
32.19 odd 8 inner 672.2.bs.b.659.39 yes 192
96.83 even 8 inner 672.2.bs.b.659.10 yes 192
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
672.2.bs.b.155.10 192 1.1 even 1 trivial
672.2.bs.b.155.39 yes 192 3.2 odd 2 inner
672.2.bs.b.659.10 yes 192 96.83 even 8 inner
672.2.bs.b.659.39 yes 192 32.19 odd 8 inner