Properties

Label 675.2.l.f.151.3
Level $675$
Weight $2$
Character 675.151
Analytic conductor $5.390$
Analytic rank $0$
Dimension $66$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [675,2,Mod(76,675)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(675, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([14, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("675.76");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.l (of order \(9\), degree \(6\), 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: \(5.38990213644\)
Analytic rank: \(0\)
Dimension: \(66\)
Relative dimension: \(11\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 151.3
Character \(\chi\) \(=\) 675.151
Dual form 675.2.l.f.76.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.23677 - 1.03778i) q^{2} +(1.21085 + 1.23848i) q^{3} +(0.105334 + 0.597379i) q^{4} +(-0.212279 - 2.78832i) q^{6} +(0.302296 - 1.71440i) q^{7} +(-1.12482 + 1.94825i) q^{8} +(-0.0676836 + 2.99924i) q^{9} +O(q^{10})\) \(q+(-1.23677 - 1.03778i) q^{2} +(1.21085 + 1.23848i) q^{3} +(0.105334 + 0.597379i) q^{4} +(-0.212279 - 2.78832i) q^{6} +(0.302296 - 1.71440i) q^{7} +(-1.12482 + 1.94825i) q^{8} +(-0.0676836 + 2.99924i) q^{9} +(2.93339 - 1.06767i) q^{11} +(-0.612300 + 0.853791i) q^{12} +(-1.44992 + 1.21663i) q^{13} +(-2.15304 + 1.80662i) q^{14} +(4.55303 - 1.65717i) q^{16} +(3.21175 + 5.56291i) q^{17} +(3.19625 - 3.63914i) q^{18} +(2.43505 - 4.21762i) q^{19} +(2.48930 - 1.70150i) q^{21} +(-4.73595 - 1.72374i) q^{22} +(-0.481999 - 2.73355i) q^{23} +(-3.77487 + 0.965965i) q^{24} +3.05582 q^{26} +(-3.79646 + 3.54780i) q^{27} +1.05599 q^{28} +(5.94510 + 4.98853i) q^{29} +(-0.687222 - 3.89743i) q^{31} +(-3.12289 - 1.13664i) q^{32} +(4.87419 + 2.34017i) q^{33} +(1.80085 - 10.2132i) q^{34} +(-1.79881 + 0.275489i) q^{36} +(0.406524 + 0.704120i) q^{37} +(-7.38856 + 2.68922i) q^{38} +(-3.26242 - 0.322550i) q^{39} +(5.80103 - 4.86764i) q^{41} +(-4.84447 - 0.478965i) q^{42} +(2.47752 - 0.901745i) q^{43} +(0.946788 + 1.63988i) q^{44} +(-2.24069 + 3.88100i) q^{46} +(-1.24015 + 7.03326i) q^{47} +(7.56541 + 3.63227i) q^{48} +(3.73005 + 1.35763i) q^{49} +(-3.00063 + 10.7136i) q^{51} +(-0.879516 - 0.738001i) q^{52} +1.86813 q^{53} +(8.37719 - 0.447951i) q^{54} +(3.00006 + 2.51735i) q^{56} +(8.17194 - 2.09115i) q^{57} +(-2.17576 - 12.3394i) q^{58} +(0.971077 + 0.353443i) q^{59} +(-1.78476 + 10.1219i) q^{61} +(-3.19472 + 5.53342i) q^{62} +(5.12144 + 1.02269i) q^{63} +(-2.16250 - 3.74556i) q^{64} +(-3.59969 - 7.95259i) q^{66} +(10.4447 - 8.76411i) q^{67} +(-2.98486 + 2.50460i) q^{68} +(2.80183 - 3.90687i) q^{69} +(4.06389 + 7.03886i) q^{71} +(-5.76713 - 3.50548i) q^{72} +(4.92790 - 8.53538i) q^{73} +(0.227941 - 1.29272i) q^{74} +(2.77601 + 1.01039i) q^{76} +(-0.943662 - 5.35177i) q^{77} +(3.70014 + 3.78459i) q^{78} +(-11.3969 - 9.56310i) q^{79} +(-8.99084 - 0.405998i) q^{81} -12.2261 q^{82} +(-7.06632 - 5.92935i) q^{83} +(1.27865 + 1.30783i) q^{84} +(-3.99995 - 1.45586i) q^{86} +(1.02041 + 13.4033i) q^{87} +(-1.21946 + 6.91592i) q^{88} +(-6.28136 + 10.8796i) q^{89} +(1.64749 + 2.85354i) q^{91} +(1.58220 - 0.575872i) q^{92} +(3.99478 - 5.57031i) q^{93} +(8.83274 - 7.41155i) q^{94} +(-2.37364 - 5.24395i) q^{96} +(14.8157 - 5.39248i) q^{97} +(-3.20432 - 5.55004i) q^{98} +(3.00365 + 8.87020i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9} + 15 q^{11} - 18 q^{12} + 15 q^{14} + 18 q^{16} - 30 q^{17} + 12 q^{18} + 12 q^{19} + 12 q^{21} + 45 q^{22} - 36 q^{23} - 39 q^{24} + 6 q^{26} - 51 q^{27} + 36 q^{28} - 15 q^{29} + 3 q^{31} - 27 q^{32} + 3 q^{33} + 30 q^{36} - 6 q^{37} + 12 q^{38} - 15 q^{39} + 39 q^{41} - 48 q^{42} - 12 q^{43} + 51 q^{44} + 9 q^{46} - 30 q^{47} + 132 q^{48} - 6 q^{49} - 9 q^{52} + 24 q^{53} + 75 q^{54} + 144 q^{56} - 33 q^{57} - 27 q^{58} + 45 q^{59} - 54 q^{61} - 66 q^{62} + 120 q^{63} - 24 q^{64} + 48 q^{66} - 9 q^{67} + 69 q^{68} + 51 q^{69} - 15 q^{71} - 9 q^{72} + 15 q^{73} + 96 q^{74} - 48 q^{76} + 36 q^{77} + 18 q^{78} + 48 q^{79} - 54 q^{81} + 36 q^{82} - 30 q^{83} + 57 q^{84} - 111 q^{86} + 33 q^{87} - 36 q^{88} - 12 q^{89} + 9 q^{91} + 219 q^{92} - 63 q^{93} + 36 q^{94} - 249 q^{96} - 57 q^{97} - 75 q^{98} - 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{2}{9}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.23677 1.03778i −0.874532 0.733819i 0.0905154 0.995895i \(-0.471149\pi\)
−0.965047 + 0.262076i \(0.915593\pi\)
\(3\) 1.21085 + 1.23848i 0.699085 + 0.715039i
\(4\) 0.105334 + 0.597379i 0.0526670 + 0.298689i
\(5\) 0 0
\(6\) −0.212279 2.78832i −0.0866625 1.13833i
\(7\) 0.302296 1.71440i 0.114257 0.647984i −0.872858 0.487974i \(-0.837736\pi\)
0.987115 0.160010i \(-0.0511527\pi\)
\(8\) −1.12482 + 1.94825i −0.397685 + 0.688811i
\(9\) −0.0676836 + 2.99924i −0.0225612 + 0.999745i
\(10\) 0 0
\(11\) 2.93339 1.06767i 0.884451 0.321914i 0.140447 0.990088i \(-0.455146\pi\)
0.744005 + 0.668174i \(0.232924\pi\)
\(12\) −0.612300 + 0.853791i −0.176756 + 0.246468i
\(13\) −1.44992 + 1.21663i −0.402137 + 0.337433i −0.821319 0.570469i \(-0.806761\pi\)
0.419182 + 0.907902i \(0.362317\pi\)
\(14\) −2.15304 + 1.80662i −0.575424 + 0.482838i
\(15\) 0 0
\(16\) 4.55303 1.65717i 1.13826 0.414292i
\(17\) 3.21175 + 5.56291i 0.778964 + 1.34921i 0.932539 + 0.361068i \(0.117588\pi\)
−0.153576 + 0.988137i \(0.549079\pi\)
\(18\) 3.19625 3.63914i 0.753363 0.857754i
\(19\) 2.43505 4.21762i 0.558638 0.967590i −0.438972 0.898501i \(-0.644657\pi\)
0.997611 0.0690890i \(-0.0220092\pi\)
\(20\) 0 0
\(21\) 2.48930 1.70150i 0.543209 0.371297i
\(22\) −4.73595 1.72374i −1.00971 0.367504i
\(23\) −0.481999 2.73355i −0.100504 0.569985i −0.992921 0.118774i \(-0.962103\pi\)
0.892418 0.451211i \(-0.149008\pi\)
\(24\) −3.77487 + 0.965965i −0.770542 + 0.197177i
\(25\) 0 0
\(26\) 3.05582 0.599296
\(27\) −3.79646 + 3.54780i −0.730629 + 0.682775i
\(28\) 1.05599 0.199563
\(29\) 5.94510 + 4.98853i 1.10398 + 0.926346i 0.997686 0.0679886i \(-0.0216582\pi\)
0.106291 + 0.994335i \(0.466103\pi\)
\(30\) 0 0
\(31\) −0.687222 3.89743i −0.123429 0.699999i −0.982229 0.187688i \(-0.939901\pi\)
0.858800 0.512311i \(-0.171210\pi\)
\(32\) −3.12289 1.13664i −0.552054 0.200931i
\(33\) 4.87419 + 2.34017i 0.848487 + 0.407372i
\(34\) 1.80085 10.2132i 0.308844 1.75154i
\(35\) 0 0
\(36\) −1.79881 + 0.275489i −0.299802 + 0.0459148i
\(37\) 0.406524 + 0.704120i 0.0668321 + 0.115757i 0.897505 0.441004i \(-0.145377\pi\)
−0.830673 + 0.556760i \(0.812044\pi\)
\(38\) −7.38856 + 2.68922i −1.19858 + 0.436248i
\(39\) −3.26242 0.322550i −0.522405 0.0516493i
\(40\) 0 0
\(41\) 5.80103 4.86764i 0.905969 0.760198i −0.0653788 0.997861i \(-0.520826\pi\)
0.971348 + 0.237662i \(0.0763811\pi\)
\(42\) −4.84447 0.478965i −0.747519 0.0739059i
\(43\) 2.47752 0.901745i 0.377819 0.137515i −0.146128 0.989266i \(-0.546681\pi\)
0.523947 + 0.851751i \(0.324459\pi\)
\(44\) 0.946788 + 1.63988i 0.142734 + 0.247222i
\(45\) 0 0
\(46\) −2.24069 + 3.88100i −0.330372 + 0.572222i
\(47\) −1.24015 + 7.03326i −0.180895 + 1.02591i 0.750222 + 0.661186i \(0.229946\pi\)
−0.931117 + 0.364720i \(0.881165\pi\)
\(48\) 7.56541 + 3.63227i 1.09197 + 0.524273i
\(49\) 3.73005 + 1.35763i 0.532864 + 0.193947i
\(50\) 0 0
\(51\) −3.00063 + 10.7136i −0.420172 + 1.50020i
\(52\) −0.879516 0.738001i −0.121967 0.102342i
\(53\) 1.86813 0.256608 0.128304 0.991735i \(-0.459047\pi\)
0.128304 + 0.991735i \(0.459047\pi\)
\(54\) 8.37719 0.447951i 1.13999 0.0609584i
\(55\) 0 0
\(56\) 3.00006 + 2.51735i 0.400900 + 0.336395i
\(57\) 8.17194 2.09115i 1.08240 0.276979i
\(58\) −2.17576 12.3394i −0.285692 1.62024i
\(59\) 0.971077 + 0.353443i 0.126423 + 0.0460144i 0.404457 0.914557i \(-0.367460\pi\)
−0.278034 + 0.960571i \(0.589683\pi\)
\(60\) 0 0
\(61\) −1.78476 + 10.1219i −0.228515 + 1.29597i 0.627335 + 0.778749i \(0.284146\pi\)
−0.855850 + 0.517224i \(0.826966\pi\)
\(62\) −3.19472 + 5.53342i −0.405730 + 0.702746i
\(63\) 5.12144 + 1.02269i 0.645241 + 0.128847i
\(64\) −2.16250 3.74556i −0.270312 0.468195i
\(65\) 0 0
\(66\) −3.59969 7.95259i −0.443092 0.978896i
\(67\) 10.4447 8.76411i 1.27602 1.07071i 0.282239 0.959344i \(-0.408923\pi\)
0.993780 0.111363i \(-0.0355215\pi\)
\(68\) −2.98486 + 2.50460i −0.361967 + 0.303727i
\(69\) 2.80183 3.90687i 0.337301 0.470332i
\(70\) 0 0
\(71\) 4.06389 + 7.03886i 0.482294 + 0.835359i 0.999793 0.0203253i \(-0.00647020\pi\)
−0.517499 + 0.855684i \(0.673137\pi\)
\(72\) −5.76713 3.50548i −0.679663 0.413124i
\(73\) 4.92790 8.53538i 0.576768 0.998991i −0.419080 0.907950i \(-0.637647\pi\)
0.995847 0.0910412i \(-0.0290195\pi\)
\(74\) 0.227941 1.29272i 0.0264976 0.150276i
\(75\) 0 0
\(76\) 2.77601 + 1.01039i 0.318430 + 0.115899i
\(77\) −0.943662 5.35177i −0.107540 0.609891i
\(78\) 3.70014 + 3.78459i 0.418959 + 0.428520i
\(79\) −11.3969 9.56310i −1.28225 1.07593i −0.992930 0.118700i \(-0.962127\pi\)
−0.289317 0.957233i \(-0.593428\pi\)
\(80\) 0 0
\(81\) −8.99084 0.405998i −0.998982 0.0451109i
\(82\) −12.2261 −1.35015
\(83\) −7.06632 5.92935i −0.775630 0.650830i 0.166514 0.986039i \(-0.446749\pi\)
−0.942144 + 0.335209i \(0.891193\pi\)
\(84\) 1.27865 + 1.30783i 0.139512 + 0.142696i
\(85\) 0 0
\(86\) −3.99995 1.45586i −0.431326 0.156990i
\(87\) 1.02041 + 13.4033i 0.109399 + 1.43698i
\(88\) −1.21946 + 6.91592i −0.129995 + 0.737240i
\(89\) −6.28136 + 10.8796i −0.665823 + 1.15324i 0.313238 + 0.949675i \(0.398586\pi\)
−0.979061 + 0.203565i \(0.934747\pi\)
\(90\) 0 0
\(91\) 1.64749 + 2.85354i 0.172704 + 0.299132i
\(92\) 1.58220 0.575872i 0.164955 0.0600388i
\(93\) 3.99478 5.57031i 0.414239 0.577615i
\(94\) 8.83274 7.41155i 0.911028 0.764443i
\(95\) 0 0
\(96\) −2.37364 5.24395i −0.242259 0.535208i
\(97\) 14.8157 5.39248i 1.50431 0.547523i 0.547136 0.837044i \(-0.315718\pi\)
0.957172 + 0.289521i \(0.0934959\pi\)
\(98\) −3.20432 5.55004i −0.323685 0.560639i
\(99\) 3.00365 + 8.87020i 0.301878 + 0.891489i
\(100\) 0 0
\(101\) 1.11330 6.31385i 0.110778 0.628251i −0.877977 0.478703i \(-0.841107\pi\)
0.988754 0.149548i \(-0.0477818\pi\)
\(102\) 14.8294 10.1363i 1.46833 1.00364i
\(103\) −6.79875 2.47454i −0.669901 0.243824i −0.0153956 0.999881i \(-0.504901\pi\)
−0.654505 + 0.756058i \(0.727123\pi\)
\(104\) −0.739394 4.19331i −0.0725035 0.411188i
\(105\) 0 0
\(106\) −2.31046 1.93871i −0.224412 0.188304i
\(107\) 4.53705 0.438613 0.219307 0.975656i \(-0.429620\pi\)
0.219307 + 0.975656i \(0.429620\pi\)
\(108\) −2.51928 1.89422i −0.242418 0.182271i
\(109\) −7.64924 −0.732665 −0.366332 0.930484i \(-0.619387\pi\)
−0.366332 + 0.930484i \(0.619387\pi\)
\(110\) 0 0
\(111\) −0.379802 + 1.35606i −0.0360492 + 0.128711i
\(112\) −1.46469 8.30668i −0.138400 0.784908i
\(113\) −3.16293 1.15121i −0.297544 0.108297i 0.188935 0.981990i \(-0.439497\pi\)
−0.486478 + 0.873693i \(0.661719\pi\)
\(114\) −12.2770 5.89437i −1.14985 0.552059i
\(115\) 0 0
\(116\) −2.35382 + 4.07694i −0.218547 + 0.378534i
\(117\) −3.55083 4.43101i −0.328274 0.409647i
\(118\) −0.834208 1.44489i −0.0767951 0.133013i
\(119\) 10.5080 3.82459i 0.963265 0.350600i
\(120\) 0 0
\(121\) −0.961609 + 0.806886i −0.0874190 + 0.0733532i
\(122\) 12.7116 10.6663i 1.15085 0.965681i
\(123\) 13.0527 + 1.29050i 1.17692 + 0.116360i
\(124\) 2.25585 0.821063i 0.202582 0.0737336i
\(125\) 0 0
\(126\) −5.27274 6.57976i −0.469733 0.586171i
\(127\) −8.92679 + 15.4617i −0.792125 + 1.37200i 0.132524 + 0.991180i \(0.457692\pi\)
−0.924649 + 0.380820i \(0.875642\pi\)
\(128\) −2.36670 + 13.4222i −0.209189 + 1.18637i
\(129\) 4.11671 + 1.97649i 0.362456 + 0.174021i
\(130\) 0 0
\(131\) −2.37367 13.4617i −0.207388 1.17616i −0.893637 0.448790i \(-0.851855\pi\)
0.686249 0.727367i \(-0.259256\pi\)
\(132\) −0.884552 + 3.15824i −0.0769904 + 0.274889i
\(133\) −6.49461 5.44962i −0.563154 0.472542i
\(134\) −22.0129 −1.90162
\(135\) 0 0
\(136\) −14.4506 −1.23913
\(137\) −10.6720 8.95490i −0.911773 0.765069i 0.0606822 0.998157i \(-0.480672\pi\)
−0.972456 + 0.233089i \(0.925117\pi\)
\(138\) −7.51970 + 1.92424i −0.640119 + 0.163802i
\(139\) 3.10046 + 17.5836i 0.262977 + 1.49142i 0.774734 + 0.632288i \(0.217884\pi\)
−0.511756 + 0.859131i \(0.671005\pi\)
\(140\) 0 0
\(141\) −10.2122 + 6.98031i −0.860023 + 0.587848i
\(142\) 2.27865 12.9229i 0.191220 1.08446i
\(143\) −2.95424 + 5.11689i −0.247046 + 0.427896i
\(144\) 4.66207 + 13.7678i 0.388506 + 1.14731i
\(145\) 0 0
\(146\) −14.9525 + 5.44228i −1.23748 + 0.450406i
\(147\) 2.83513 + 6.26349i 0.233838 + 0.516604i
\(148\) −0.377806 + 0.317017i −0.0310554 + 0.0260586i
\(149\) −13.7598 + 11.5458i −1.12725 + 0.945872i −0.998948 0.0458641i \(-0.985396\pi\)
−0.128298 + 0.991736i \(0.540951\pi\)
\(150\) 0 0
\(151\) 18.3678 6.68534i 1.49475 0.544045i 0.540057 0.841629i \(-0.318403\pi\)
0.954696 + 0.297583i \(0.0961806\pi\)
\(152\) 5.47800 + 9.48817i 0.444324 + 0.769592i
\(153\) −16.9019 + 9.25628i −1.36644 + 0.748326i
\(154\) −4.38685 + 7.59825i −0.353502 + 0.612284i
\(155\) 0 0
\(156\) −0.150959 1.98287i −0.0120864 0.158757i
\(157\) 7.55982 + 2.75155i 0.603339 + 0.219598i 0.625586 0.780155i \(-0.284860\pi\)
−0.0222470 + 0.999753i \(0.507082\pi\)
\(158\) 4.17098 + 23.6548i 0.331825 + 1.88188i
\(159\) 2.26203 + 2.31365i 0.179391 + 0.183485i
\(160\) 0 0
\(161\) −4.83212 −0.380824
\(162\) 10.6983 + 9.83262i 0.840538 + 0.772523i
\(163\) −5.27505 −0.413174 −0.206587 0.978428i \(-0.566236\pi\)
−0.206587 + 0.978428i \(0.566236\pi\)
\(164\) 3.51887 + 2.95269i 0.274778 + 0.230566i
\(165\) 0 0
\(166\) 2.58611 + 14.6665i 0.200721 + 1.13834i
\(167\) −15.5499 5.65972i −1.20329 0.437962i −0.338919 0.940816i \(-0.610061\pi\)
−0.864372 + 0.502854i \(0.832284\pi\)
\(168\) 0.514927 + 6.76366i 0.0397275 + 0.521828i
\(169\) −1.63534 + 9.27446i −0.125795 + 0.713420i
\(170\) 0 0
\(171\) 12.4848 + 7.58875i 0.954740 + 0.580326i
\(172\) 0.799651 + 1.38504i 0.0609728 + 0.105608i
\(173\) −18.3819 + 6.69046i −1.39755 + 0.508666i −0.927450 0.373948i \(-0.878004\pi\)
−0.470099 + 0.882614i \(0.655782\pi\)
\(174\) 12.6476 17.6358i 0.958811 1.33697i
\(175\) 0 0
\(176\) 11.5865 9.72224i 0.873367 0.732842i
\(177\) 0.738095 + 1.63063i 0.0554786 + 0.122566i
\(178\) 19.0593 6.93701i 1.42855 0.519951i
\(179\) −0.604142 1.04640i −0.0451557 0.0782119i 0.842564 0.538596i \(-0.181045\pi\)
−0.887720 + 0.460384i \(0.847712\pi\)
\(180\) 0 0
\(181\) −10.2446 + 17.7442i −0.761474 + 1.31891i 0.180616 + 0.983554i \(0.442191\pi\)
−0.942090 + 0.335359i \(0.891142\pi\)
\(182\) 0.923761 5.23891i 0.0684738 0.388334i
\(183\) −14.6969 + 10.0457i −1.08642 + 0.742598i
\(184\) 5.86781 + 2.13571i 0.432581 + 0.157447i
\(185\) 0 0
\(186\) −10.7214 + 2.74353i −0.786130 + 0.201166i
\(187\) 15.3607 + 12.8891i 1.12328 + 0.942547i
\(188\) −4.33215 −0.315954
\(189\) 4.93471 + 7.58115i 0.358947 + 0.551447i
\(190\) 0 0
\(191\) −1.41048 1.18353i −0.102059 0.0856373i 0.590331 0.807162i \(-0.298997\pi\)
−0.692389 + 0.721524i \(0.743442\pi\)
\(192\) 2.02035 7.21353i 0.145806 0.520592i
\(193\) −2.29931 13.0401i −0.165508 0.938643i −0.948539 0.316660i \(-0.897438\pi\)
0.783031 0.621983i \(-0.213673\pi\)
\(194\) −23.9199 8.70613i −1.71735 0.625064i
\(195\) 0 0
\(196\) −0.418117 + 2.37126i −0.0298655 + 0.169376i
\(197\) −9.36409 + 16.2191i −0.667164 + 1.15556i 0.311530 + 0.950236i \(0.399159\pi\)
−0.978694 + 0.205325i \(0.934175\pi\)
\(198\) 5.49046 14.0876i 0.390190 1.00116i
\(199\) −3.20552 5.55213i −0.227233 0.393580i 0.729754 0.683710i \(-0.239635\pi\)
−0.956987 + 0.290130i \(0.906301\pi\)
\(200\) 0 0
\(201\) 23.5011 + 2.32352i 1.65764 + 0.163888i
\(202\) −7.92927 + 6.65345i −0.557901 + 0.468135i
\(203\) 10.3495 8.68429i 0.726394 0.609517i
\(204\) −6.71612 0.664011i −0.470222 0.0464901i
\(205\) 0 0
\(206\) 5.84050 + 10.1160i 0.406927 + 0.704818i
\(207\) 8.23119 1.26061i 0.572107 0.0876186i
\(208\) −4.58539 + 7.94212i −0.317939 + 0.550687i
\(209\) 2.63993 14.9718i 0.182608 1.03562i
\(210\) 0 0
\(211\) −15.3119 5.57306i −1.05411 0.383665i −0.243899 0.969801i \(-0.578426\pi\)
−0.810213 + 0.586135i \(0.800649\pi\)
\(212\) 0.196778 + 1.11598i 0.0135148 + 0.0766461i
\(213\) −3.79675 + 13.5561i −0.260149 + 0.928846i
\(214\) −5.61131 4.70845i −0.383581 0.321863i
\(215\) 0 0
\(216\) −2.64166 11.3871i −0.179742 0.774794i
\(217\) −6.88951 −0.467690
\(218\) 9.46039 + 7.93821i 0.640739 + 0.537643i
\(219\) 16.5379 4.23194i 1.11753 0.285968i
\(220\) 0 0
\(221\) −11.4248 4.15829i −0.768516 0.279717i
\(222\) 1.87701 1.28299i 0.125977 0.0861085i
\(223\) −3.25026 + 18.4332i −0.217654 + 1.23438i 0.658588 + 0.752504i \(0.271154\pi\)
−0.876242 + 0.481872i \(0.839957\pi\)
\(224\) −2.89269 + 5.01029i −0.193276 + 0.334764i
\(225\) 0 0
\(226\) 2.71713 + 4.70621i 0.180741 + 0.313053i
\(227\) −16.5040 + 6.00696i −1.09541 + 0.398696i −0.825622 0.564224i \(-0.809175\pi\)
−0.269787 + 0.962920i \(0.586953\pi\)
\(228\) 2.10999 + 4.66147i 0.139737 + 0.308714i
\(229\) −5.79494 + 4.86253i −0.382940 + 0.321325i −0.813855 0.581067i \(-0.802635\pi\)
0.430915 + 0.902392i \(0.358191\pi\)
\(230\) 0 0
\(231\) 5.48545 7.64890i 0.360916 0.503261i
\(232\) −16.4061 + 5.97133i −1.07711 + 0.392037i
\(233\) 3.47331 + 6.01595i 0.227544 + 0.394118i 0.957080 0.289825i \(-0.0935971\pi\)
−0.729536 + 0.683943i \(0.760264\pi\)
\(234\) −0.206829 + 9.16513i −0.0135208 + 0.599143i
\(235\) 0 0
\(236\) −0.108852 + 0.617330i −0.00708566 + 0.0401848i
\(237\) −1.95615 25.6943i −0.127065 1.66902i
\(238\) −16.9651 6.17478i −1.09968 0.400252i
\(239\) −3.56006 20.1901i −0.230281 1.30599i −0.852327 0.523009i \(-0.824809\pi\)
0.622046 0.782981i \(-0.286302\pi\)
\(240\) 0 0
\(241\) −17.8973 15.0176i −1.15287 0.967369i −0.153083 0.988213i \(-0.548920\pi\)
−0.999783 + 0.0208438i \(0.993365\pi\)
\(242\) 2.02666 0.130279
\(243\) −10.3837 11.6266i −0.666117 0.745847i
\(244\) −6.23459 −0.399129
\(245\) 0 0
\(246\) −14.8040 15.1418i −0.943867 0.965408i
\(247\) 1.60066 + 9.07779i 0.101847 + 0.577606i
\(248\) 8.36617 + 3.04504i 0.531252 + 0.193360i
\(249\) −1.21286 15.9311i −0.0768616 1.00959i
\(250\) 0 0
\(251\) 4.60669 7.97903i 0.290772 0.503632i −0.683221 0.730212i \(-0.739421\pi\)
0.973992 + 0.226580i \(0.0727546\pi\)
\(252\) −0.0714732 + 3.16716i −0.00450239 + 0.199513i
\(253\) −4.33242 7.50397i −0.272377 0.471770i
\(254\) 27.0862 9.85857i 1.69954 0.618581i
\(255\) 0 0
\(256\) 10.2301 8.58408i 0.639381 0.536505i
\(257\) 19.7561 16.5773i 1.23235 1.03406i 0.234266 0.972172i \(-0.424731\pi\)
0.998083 0.0618912i \(-0.0197132\pi\)
\(258\) −3.04028 6.71670i −0.189279 0.418164i
\(259\) 1.33004 0.484094i 0.0826445 0.0300801i
\(260\) 0 0
\(261\) −15.3642 + 17.4931i −0.951018 + 1.08280i
\(262\) −11.0346 + 19.1125i −0.681719 + 1.18077i
\(263\) 3.97396 22.5375i 0.245045 1.38972i −0.575343 0.817912i \(-0.695131\pi\)
0.820388 0.571807i \(-0.193758\pi\)
\(264\) −10.0418 + 6.86386i −0.618033 + 0.422441i
\(265\) 0 0
\(266\) 2.37687 + 13.4799i 0.145735 + 0.826507i
\(267\) −21.0801 + 5.39425i −1.29008 + 0.330123i
\(268\) 6.33567 + 5.31626i 0.387013 + 0.324742i
\(269\) 18.4780 1.12662 0.563311 0.826245i \(-0.309527\pi\)
0.563311 + 0.826245i \(0.309527\pi\)
\(270\) 0 0
\(271\) 4.64576 0.282210 0.141105 0.989995i \(-0.454935\pi\)
0.141105 + 0.989995i \(0.454935\pi\)
\(272\) 23.8419 + 20.0057i 1.44563 + 1.21302i
\(273\) −1.53920 + 5.49560i −0.0931563 + 0.332609i
\(274\) 3.90571 + 22.1504i 0.235953 + 1.33815i
\(275\) 0 0
\(276\) 2.62901 + 1.26223i 0.158248 + 0.0759772i
\(277\) 4.49325 25.4825i 0.269973 1.53109i −0.484517 0.874782i \(-0.661005\pi\)
0.754490 0.656311i \(-0.227884\pi\)
\(278\) 14.4133 24.9645i 0.864450 1.49727i
\(279\) 11.7358 1.79735i 0.702605 0.107604i
\(280\) 0 0
\(281\) 10.1177 3.68254i 0.603572 0.219682i −0.0221165 0.999755i \(-0.507040\pi\)
0.625688 + 0.780073i \(0.284818\pi\)
\(282\) 19.8742 + 1.96493i 1.18349 + 0.117010i
\(283\) 12.1469 10.1924i 0.722056 0.605877i −0.205897 0.978574i \(-0.566011\pi\)
0.927953 + 0.372697i \(0.121567\pi\)
\(284\) −3.77680 + 3.16911i −0.224112 + 0.188052i
\(285\) 0 0
\(286\) 8.96393 3.26260i 0.530048 0.192922i
\(287\) −6.59148 11.4168i −0.389083 0.673911i
\(288\) 3.62042 9.28935i 0.213335 0.547380i
\(289\) −12.1307 + 21.0110i −0.713569 + 1.23594i
\(290\) 0 0
\(291\) 24.6181 + 11.8195i 1.44314 + 0.692873i
\(292\) 5.61793 + 2.04476i 0.328765 + 0.119661i
\(293\) 0.577683 + 3.27620i 0.0337486 + 0.191398i 0.997021 0.0771274i \(-0.0245748\pi\)
−0.963273 + 0.268525i \(0.913464\pi\)
\(294\) 2.99369 10.6888i 0.174595 0.623382i
\(295\) 0 0
\(296\) −1.82907 −0.106313
\(297\) −7.34864 + 14.4605i −0.426411 + 0.839081i
\(298\) 28.9998 1.67991
\(299\) 4.02459 + 3.37703i 0.232748 + 0.195299i
\(300\) 0 0
\(301\) −0.797010 4.52007i −0.0459389 0.260532i
\(302\) −29.6548 10.7935i −1.70644 0.621093i
\(303\) 9.16764 6.26632i 0.526667 0.359990i
\(304\) 4.09753 23.2382i 0.235009 1.33280i
\(305\) 0 0
\(306\) 30.5098 + 6.09245i 1.74413 + 0.348282i
\(307\) −2.19929 3.80928i −0.125520 0.217407i 0.796416 0.604749i \(-0.206727\pi\)
−0.921936 + 0.387342i \(0.873393\pi\)
\(308\) 3.09763 1.12745i 0.176504 0.0642422i
\(309\) −5.16759 11.4164i −0.293974 0.649459i
\(310\) 0 0
\(311\) −11.8600 + 9.95173i −0.672519 + 0.564311i −0.913810 0.406142i \(-0.866874\pi\)
0.241290 + 0.970453i \(0.422429\pi\)
\(312\) 4.29805 5.99320i 0.243329 0.339298i
\(313\) −10.1811 + 3.70561i −0.575469 + 0.209454i −0.613327 0.789829i \(-0.710169\pi\)
0.0378572 + 0.999283i \(0.487947\pi\)
\(314\) −6.49430 11.2485i −0.366495 0.634787i
\(315\) 0 0
\(316\) 4.51232 7.81556i 0.253838 0.439660i
\(317\) 1.83589 10.4118i 0.103114 0.584787i −0.888843 0.458212i \(-0.848490\pi\)
0.991957 0.126576i \(-0.0403987\pi\)
\(318\) −0.396565 5.20895i −0.0222383 0.292104i
\(319\) 22.7654 + 8.28593i 1.27462 + 0.463923i
\(320\) 0 0
\(321\) 5.49369 + 5.61906i 0.306628 + 0.313626i
\(322\) 5.97624 + 5.01466i 0.333043 + 0.279456i
\(323\) 31.2831 1.74064
\(324\) −0.704506 5.41370i −0.0391392 0.300761i
\(325\) 0 0
\(326\) 6.52405 + 5.47433i 0.361334 + 0.303195i
\(327\) −9.26209 9.47346i −0.512195 0.523884i
\(328\) 2.95826 + 16.7771i 0.163342 + 0.926361i
\(329\) 11.6829 + 4.25225i 0.644102 + 0.234434i
\(330\) 0 0
\(331\) −1.83100 + 10.3841i −0.100641 + 0.570762i 0.892231 + 0.451578i \(0.149139\pi\)
−0.992872 + 0.119184i \(0.961972\pi\)
\(332\) 2.79774 4.84583i 0.153546 0.265950i
\(333\) −2.13934 + 1.17160i −0.117235 + 0.0642035i
\(334\) 13.3583 + 23.1372i 0.730931 + 1.26601i
\(335\) 0 0
\(336\) 8.51417 11.8721i 0.464486 0.647679i
\(337\) −0.933557 + 0.783347i −0.0508541 + 0.0426717i −0.667860 0.744287i \(-0.732790\pi\)
0.617006 + 0.786958i \(0.288345\pi\)
\(338\) 11.6474 9.77330i 0.633533 0.531597i
\(339\) −2.40408 5.31119i −0.130572 0.288464i
\(340\) 0 0
\(341\) −6.17705 10.6990i −0.334506 0.579381i
\(342\) −7.56551 22.3421i −0.409096 1.20812i
\(343\) 9.54808 16.5378i 0.515548 0.892955i
\(344\) −1.02995 + 5.84114i −0.0555312 + 0.314933i
\(345\) 0 0
\(346\) 29.6775 + 10.8017i 1.59547 + 0.580703i
\(347\) 0.177046 + 1.00408i 0.00950431 + 0.0539016i 0.989191 0.146632i \(-0.0468434\pi\)
−0.979687 + 0.200534i \(0.935732\pi\)
\(348\) −7.89934 + 2.02139i −0.423449 + 0.108358i
\(349\) −19.3802 16.2620i −1.03740 0.870483i −0.0456879 0.998956i \(-0.514548\pi\)
−0.991713 + 0.128473i \(0.958992\pi\)
\(350\) 0 0
\(351\) 1.18821 9.76293i 0.0634222 0.521107i
\(352\) −10.3742 −0.552947
\(353\) −11.2458 9.43633i −0.598552 0.502245i 0.292428 0.956288i \(-0.405537\pi\)
−0.890980 + 0.454043i \(0.849981\pi\)
\(354\) 0.779373 2.78270i 0.0414232 0.147899i
\(355\) 0 0
\(356\) −7.16091 2.60636i −0.379527 0.138137i
\(357\) 17.4603 + 8.38295i 0.924096 + 0.443673i
\(358\) −0.338747 + 1.92113i −0.0179033 + 0.101535i
\(359\) −11.7675 + 20.3820i −0.621067 + 1.07572i 0.368221 + 0.929738i \(0.379967\pi\)
−0.989287 + 0.145981i \(0.953366\pi\)
\(360\) 0 0
\(361\) −2.35891 4.08575i −0.124153 0.215039i
\(362\) 31.0847 11.3139i 1.63378 0.594646i
\(363\) −2.16368 0.213919i −0.113564 0.0112278i
\(364\) −1.53111 + 1.28475i −0.0802517 + 0.0673392i
\(365\) 0 0
\(366\) 28.6019 + 2.82782i 1.49504 + 0.147812i
\(367\) −23.4316 + 8.52841i −1.22312 + 0.445180i −0.871236 0.490864i \(-0.836681\pi\)
−0.351884 + 0.936043i \(0.614459\pi\)
\(368\) −6.72451 11.6472i −0.350539 0.607152i
\(369\) 14.2066 + 17.7281i 0.739565 + 0.922890i
\(370\) 0 0
\(371\) 0.564729 3.20274i 0.0293193 0.166278i
\(372\) 3.74837 + 1.79965i 0.194344 + 0.0933076i
\(373\) 12.0820 + 4.39750i 0.625584 + 0.227694i 0.635308 0.772259i \(-0.280873\pi\)
−0.00972404 + 0.999953i \(0.503095\pi\)
\(374\) −5.62164 31.8819i −0.290688 1.64857i
\(375\) 0 0
\(376\) −12.3076 10.3273i −0.634716 0.532590i
\(377\) −14.6891 −0.756529
\(378\) 1.76442 14.4973i 0.0907520 0.745661i
\(379\) 3.07162 0.157779 0.0788894 0.996883i \(-0.474863\pi\)
0.0788894 + 0.996883i \(0.474863\pi\)
\(380\) 0 0
\(381\) −29.9580 + 7.66606i −1.53480 + 0.392744i
\(382\) 0.516201 + 2.92752i 0.0264112 + 0.149785i
\(383\) 6.80599 + 2.47718i 0.347770 + 0.126578i 0.509998 0.860175i \(-0.329646\pi\)
−0.162229 + 0.986753i \(0.551868\pi\)
\(384\) −19.4890 + 13.3212i −0.994542 + 0.679795i
\(385\) 0 0
\(386\) −10.6889 + 18.5138i −0.544053 + 0.942327i
\(387\) 2.53686 + 7.49171i 0.128956 + 0.380825i
\(388\) 4.78195 + 8.28258i 0.242767 + 0.420484i
\(389\) −6.63847 + 2.41621i −0.336584 + 0.122507i −0.504782 0.863247i \(-0.668427\pi\)
0.168198 + 0.985753i \(0.446205\pi\)
\(390\) 0 0
\(391\) 13.6585 11.4608i 0.690738 0.579598i
\(392\) −6.84065 + 5.73999i −0.345505 + 0.289913i
\(393\) 13.7980 19.2399i 0.696016 0.970524i
\(394\) 28.4131 10.3415i 1.43143 0.520998i
\(395\) 0 0
\(396\) −4.98248 + 2.72865i −0.250379 + 0.137120i
\(397\) 12.9728 22.4696i 0.651088 1.12772i −0.331771 0.943360i \(-0.607646\pi\)
0.982859 0.184358i \(-0.0590206\pi\)
\(398\) −1.79736 + 10.1933i −0.0900936 + 0.510946i
\(399\) −1.11473 14.6421i −0.0558062 0.733024i
\(400\) 0 0
\(401\) 2.29238 + 13.0007i 0.114476 + 0.649226i 0.987008 + 0.160670i \(0.0513654\pi\)
−0.872532 + 0.488557i \(0.837524\pi\)
\(402\) −26.6543 27.2626i −1.32940 1.35974i
\(403\) 5.73815 + 4.81488i 0.285838 + 0.239846i
\(404\) 3.88903 0.193486
\(405\) 0 0
\(406\) −21.8124 −1.08253
\(407\) 1.94426 + 1.63143i 0.0963734 + 0.0808669i
\(408\) −17.4975 17.8968i −0.866256 0.886026i
\(409\) −2.60351 14.7653i −0.128735 0.730095i −0.979019 0.203770i \(-0.934681\pi\)
0.850283 0.526325i \(-0.176430\pi\)
\(410\) 0 0
\(411\) −1.83174 24.0602i −0.0903529 1.18680i
\(412\) 0.762100 4.32208i 0.0375460 0.212934i
\(413\) 0.899496 1.55797i 0.0442613 0.0766628i
\(414\) −11.4884 6.98305i −0.564623 0.343198i
\(415\) 0 0
\(416\) 5.91082 2.15136i 0.289802 0.105479i
\(417\) −18.0228 + 25.1309i −0.882579 + 1.23067i
\(418\) −18.8024 + 15.7771i −0.919654 + 0.771681i
\(419\) 21.5326 18.0680i 1.05194 0.882681i 0.0586424 0.998279i \(-0.481323\pi\)
0.993296 + 0.115598i \(0.0368784\pi\)
\(420\) 0 0
\(421\) 26.6729 9.70814i 1.29996 0.473146i 0.402974 0.915211i \(-0.367976\pi\)
0.896983 + 0.442066i \(0.145754\pi\)
\(422\) 13.1537 + 22.7829i 0.640313 + 1.10906i
\(423\) −21.0105 4.19555i −1.02156 0.203995i
\(424\) −2.10132 + 3.63959i −0.102049 + 0.176754i
\(425\) 0 0
\(426\) 18.7639 12.8256i 0.909114 0.621403i
\(427\) 16.8135 + 6.11960i 0.813660 + 0.296148i
\(428\) 0.477906 + 2.71034i 0.0231004 + 0.131009i
\(429\) −9.91433 + 2.53701i −0.478668 + 0.122488i
\(430\) 0 0
\(431\) 8.66843 0.417543 0.208772 0.977964i \(-0.433053\pi\)
0.208772 + 0.977964i \(0.433053\pi\)
\(432\) −11.4061 + 22.4446i −0.548776 + 1.07987i
\(433\) 8.61185 0.413859 0.206929 0.978356i \(-0.433653\pi\)
0.206929 + 0.978356i \(0.433653\pi\)
\(434\) 8.52077 + 7.14978i 0.409010 + 0.343200i
\(435\) 0 0
\(436\) −0.805725 4.56949i −0.0385872 0.218839i
\(437\) −12.7028 4.62344i −0.607657 0.221169i
\(438\) −24.8455 11.9287i −1.18716 0.569975i
\(439\) −2.79044 + 15.8254i −0.133181 + 0.755305i 0.842929 + 0.538025i \(0.180829\pi\)
−0.976109 + 0.217280i \(0.930282\pi\)
\(440\) 0 0
\(441\) −4.32431 + 11.0954i −0.205919 + 0.528353i
\(442\) 9.81454 + 16.9993i 0.466830 + 0.808573i
\(443\) 8.68429 3.16082i 0.412603 0.150175i −0.127374 0.991855i \(-0.540655\pi\)
0.539977 + 0.841679i \(0.318433\pi\)
\(444\) −0.850086 0.0840465i −0.0403433 0.00398867i
\(445\) 0 0
\(446\) 23.1494 19.4246i 1.09615 0.919782i
\(447\) −30.9604 3.06100i −1.46438 0.144780i
\(448\) −7.07511 + 2.57513i −0.334268 + 0.121663i
\(449\) 18.5220 + 32.0810i 0.874106 + 1.51400i 0.857713 + 0.514130i \(0.171885\pi\)
0.0163930 + 0.999866i \(0.494782\pi\)
\(450\) 0 0
\(451\) 11.8197 20.4723i 0.556567 0.964002i
\(452\) 0.354546 2.01073i 0.0166764 0.0945768i
\(453\) 30.5204 + 14.6533i 1.43397 + 0.688472i
\(454\) 26.6456 + 9.69821i 1.25054 + 0.455160i
\(455\) 0 0
\(456\) −5.11791 + 18.2732i −0.239668 + 0.855719i
\(457\) −1.04395 0.875976i −0.0488338 0.0409764i 0.618044 0.786143i \(-0.287925\pi\)
−0.666878 + 0.745167i \(0.732370\pi\)
\(458\) 12.2133 0.570688
\(459\) −31.9294 9.72473i −1.49034 0.453912i
\(460\) 0 0
\(461\) −6.41944 5.38655i −0.298983 0.250876i 0.480938 0.876755i \(-0.340296\pi\)
−0.779921 + 0.625878i \(0.784741\pi\)
\(462\) −14.7221 + 3.76730i −0.684935 + 0.175271i
\(463\) 4.96946 + 28.1832i 0.230950 + 1.30978i 0.850977 + 0.525203i \(0.176011\pi\)
−0.620027 + 0.784581i \(0.712878\pi\)
\(464\) 35.3350 + 12.8609i 1.64039 + 0.597052i
\(465\) 0 0
\(466\) 1.94751 11.0449i 0.0902168 0.511645i
\(467\) −1.15409 + 1.99894i −0.0534049 + 0.0925000i −0.891492 0.453036i \(-0.850341\pi\)
0.838087 + 0.545536i \(0.183674\pi\)
\(468\) 2.27297 2.58792i 0.105068 0.119627i
\(469\) −11.8679 20.5557i −0.548006 0.949175i
\(470\) 0 0
\(471\) 5.74606 + 12.6944i 0.264765 + 0.584928i
\(472\) −1.78089 + 1.49434i −0.0819719 + 0.0687826i
\(473\) 6.30479 5.29034i 0.289894 0.243250i
\(474\) −24.2457 + 33.8081i −1.11364 + 1.55286i
\(475\) 0 0
\(476\) 3.39158 + 5.87438i 0.155453 + 0.269252i
\(477\) −0.126442 + 5.60298i −0.00578938 + 0.256543i
\(478\) −16.5498 + 28.6652i −0.756972 + 1.31111i
\(479\) −0.150408 + 0.853009i −0.00687234 + 0.0389750i −0.988051 0.154127i \(-0.950744\pi\)
0.981179 + 0.193102i \(0.0618547\pi\)
\(480\) 0 0
\(481\) −1.44608 0.526331i −0.0659357 0.0239986i
\(482\) 6.54999 + 37.1468i 0.298344 + 1.69199i
\(483\) −5.85097 5.98450i −0.266228 0.272304i
\(484\) −0.583306 0.489452i −0.0265139 0.0222478i
\(485\) 0 0
\(486\) 0.776512 + 25.1555i 0.0352233 + 1.14108i
\(487\) 20.4700 0.927584 0.463792 0.885944i \(-0.346488\pi\)
0.463792 + 0.885944i \(0.346488\pi\)
\(488\) −17.7124 14.8625i −0.801803 0.672793i
\(489\) −6.38730 6.53307i −0.288844 0.295435i
\(490\) 0 0
\(491\) −40.3022 14.6688i −1.81881 0.661993i −0.995539 0.0943459i \(-0.969924\pi\)
−0.823272 0.567647i \(-0.807854\pi\)
\(492\) 0.603976 + 7.93333i 0.0272293 + 0.357662i
\(493\) −8.65659 + 49.0940i −0.389873 + 2.21108i
\(494\) 7.44107 12.8883i 0.334790 0.579872i
\(495\) 0 0
\(496\) −9.58763 16.6063i −0.430497 0.745643i
\(497\) 13.2959 4.83932i 0.596404 0.217073i
\(498\) −15.0329 + 20.9618i −0.673639 + 0.939322i
\(499\) 4.70186 3.94533i 0.210484 0.176617i −0.531451 0.847089i \(-0.678353\pi\)
0.741935 + 0.670472i \(0.233908\pi\)
\(500\) 0 0
\(501\) −11.8192 26.1114i −0.528042 1.16657i
\(502\) −13.9779 + 5.08754i −0.623864 + 0.227068i
\(503\) −3.43713 5.95329i −0.153254 0.265444i 0.779168 0.626815i \(-0.215642\pi\)
−0.932422 + 0.361371i \(0.882309\pi\)
\(504\) −7.75318 + 8.82751i −0.345354 + 0.393208i
\(505\) 0 0
\(506\) −2.42922 + 13.7768i −0.107992 + 0.612454i
\(507\) −13.4664 + 9.20464i −0.598064 + 0.408792i
\(508\) −10.1768 3.70404i −0.451521 0.164340i
\(509\) −2.31722 13.1416i −0.102709 0.582493i −0.992111 0.125366i \(-0.959990\pi\)
0.889401 0.457127i \(-0.151122\pi\)
\(510\) 0 0
\(511\) −13.1434 11.0286i −0.581430 0.487878i
\(512\) 5.69791 0.251815
\(513\) 5.71874 + 24.6511i 0.252488 + 1.08837i
\(514\) −41.6373 −1.83654
\(515\) 0 0
\(516\) −0.747087 + 2.66743i −0.0328887 + 0.117427i
\(517\) 3.87133 + 21.9554i 0.170261 + 0.965596i
\(518\) −2.14734 0.781567i −0.0943486 0.0343401i
\(519\) −30.5437 14.6645i −1.34072 0.643701i
\(520\) 0 0
\(521\) −12.2664 + 21.2461i −0.537401 + 0.930807i 0.461642 + 0.887067i \(0.347261\pi\)
−0.999043 + 0.0437400i \(0.986073\pi\)
\(522\) 37.1560 5.69046i 1.62627 0.249065i
\(523\) 19.7850 + 34.2687i 0.865140 + 1.49847i 0.866908 + 0.498468i \(0.166104\pi\)
−0.00176851 + 0.999998i \(0.500563\pi\)
\(524\) 7.79172 2.83595i 0.340383 0.123889i
\(525\) 0 0
\(526\) −28.3038 + 23.7497i −1.23410 + 1.03554i
\(527\) 19.4739 16.3405i 0.848295 0.711804i
\(528\) 26.0704 + 2.57753i 1.13457 + 0.112173i
\(529\) 14.3729 5.23132i 0.624911 0.227449i
\(530\) 0 0
\(531\) −1.12578 + 2.88857i −0.0488549 + 0.125353i
\(532\) 2.57139 4.45377i 0.111484 0.193095i
\(533\) −2.48893 + 14.1154i −0.107808 + 0.611407i
\(534\) 31.6693 + 15.2049i 1.37047 + 0.657982i
\(535\) 0 0
\(536\) 5.32629 + 30.2069i 0.230061 + 1.30474i
\(537\) 0.564429 2.01526i 0.0243569 0.0869648i
\(538\) −22.8531 19.1760i −0.985267 0.826737i
\(539\) 12.3912 0.533727
\(540\) 0 0
\(541\) 32.1065 1.38036 0.690182 0.723635i \(-0.257530\pi\)
0.690182 + 0.723635i \(0.257530\pi\)
\(542\) −5.74576 4.82126i −0.246801 0.207091i
\(543\) −34.3805 + 8.79775i −1.47541 + 0.377548i
\(544\) −3.70692 21.0230i −0.158933 0.901352i
\(545\) 0 0
\(546\) 7.60684 5.19947i 0.325543 0.222517i
\(547\) 3.82427 21.6885i 0.163514 0.927333i −0.787070 0.616864i \(-0.788403\pi\)
0.950583 0.310469i \(-0.100486\pi\)
\(548\) 4.22534 7.31850i 0.180497 0.312631i
\(549\) −30.2371 6.03800i −1.29049 0.257696i
\(550\) 0 0
\(551\) 35.5163 12.9269i 1.51305 0.550704i
\(552\) 4.46000 + 9.85321i 0.189830 + 0.419380i
\(553\) −19.8402 + 16.6479i −0.843693 + 0.707942i
\(554\) −32.0023 + 26.8531i −1.35965 + 1.14088i
\(555\) 0 0
\(556\) −10.1775 + 3.70429i −0.431621 + 0.157097i
\(557\) −11.1210 19.2621i −0.471212 0.816163i 0.528246 0.849092i \(-0.322850\pi\)
−0.999458 + 0.0329284i \(0.989517\pi\)
\(558\) −16.3798 9.95625i −0.693413 0.421482i
\(559\) −2.49513 + 4.32169i −0.105533 + 0.182788i
\(560\) 0 0
\(561\) 2.63649 + 34.6307i 0.111313 + 1.46211i
\(562\) −16.3350 5.94545i −0.689050 0.250794i
\(563\) −2.45892 13.9452i −0.103631 0.587721i −0.991758 0.128123i \(-0.959105\pi\)
0.888127 0.459598i \(-0.152006\pi\)
\(564\) −5.24558 5.36529i −0.220879 0.225920i
\(565\) 0 0
\(566\) −25.6004 −1.07607
\(567\) −3.41394 + 15.2912i −0.143372 + 0.642170i
\(568\) −18.2846 −0.767205
\(569\) −4.81198 4.03773i −0.201729 0.169270i 0.536327 0.844010i \(-0.319811\pi\)
−0.738056 + 0.674740i \(0.764256\pi\)
\(570\) 0 0
\(571\) −5.42129 30.7457i −0.226874 1.28667i −0.859070 0.511858i \(-0.828957\pi\)
0.632196 0.774809i \(-0.282154\pi\)
\(572\) −3.36790 1.22582i −0.140819 0.0512540i
\(573\) −0.242093 3.17993i −0.0101136 0.132844i
\(574\) −3.69590 + 20.9605i −0.154264 + 0.874873i
\(575\) 0 0
\(576\) 11.3802 6.23233i 0.474174 0.259680i
\(577\) −9.13906 15.8293i −0.380464 0.658983i 0.610664 0.791889i \(-0.290902\pi\)
−0.991129 + 0.132906i \(0.957569\pi\)
\(578\) 36.8076 13.3969i 1.53100 0.557237i
\(579\) 13.3658 18.6372i 0.555462 0.774536i
\(580\) 0 0
\(581\) −12.3014 + 10.3221i −0.510349 + 0.428233i
\(582\) −18.1810 40.1662i −0.753627 1.66494i
\(583\) 5.47997 1.99455i 0.226957 0.0826057i
\(584\) 11.0860 + 19.2016i 0.458744 + 0.794568i
\(585\) 0 0
\(586\) 2.68551 4.65143i 0.110937 0.192149i
\(587\) 1.42984 8.10900i 0.0590156 0.334694i −0.940977 0.338470i \(-0.890091\pi\)
0.999993 + 0.00377558i \(0.00120181\pi\)
\(588\) −3.44304 + 2.35341i −0.141989 + 0.0970529i
\(589\) −18.1113 6.59198i −0.746263 0.271618i
\(590\) 0 0
\(591\) −31.4256 + 8.04160i −1.29268 + 0.330787i
\(592\) 3.01776 + 2.53220i 0.124029 + 0.104073i
\(593\) −38.8812 −1.59666 −0.798329 0.602222i \(-0.794282\pi\)
−0.798329 + 0.602222i \(0.794282\pi\)
\(594\) 24.0953 10.2581i 0.988644 0.420894i
\(595\) 0 0
\(596\) −8.34661 7.00364i −0.341890 0.286880i
\(597\) 2.99481 10.6928i 0.122569 0.437626i
\(598\) −1.47290 8.35325i −0.0602315 0.341590i
\(599\) 0.729650 + 0.265571i 0.0298127 + 0.0108509i 0.356883 0.934149i \(-0.383839\pi\)
−0.327071 + 0.945000i \(0.606062\pi\)
\(600\) 0 0
\(601\) −4.46708 + 25.3341i −0.182216 + 1.03340i 0.747265 + 0.664527i \(0.231367\pi\)
−0.929481 + 0.368871i \(0.879744\pi\)
\(602\) −3.70510 + 6.41743i −0.151009 + 0.261555i
\(603\) 25.5787 + 31.9192i 1.04165 + 1.29985i
\(604\) 5.92844 + 10.2684i 0.241225 + 0.417813i
\(605\) 0 0
\(606\) −17.8413 1.76394i −0.724755 0.0716553i
\(607\) 5.10054 4.27987i 0.207025 0.173714i −0.533380 0.845876i \(-0.679078\pi\)
0.740405 + 0.672161i \(0.234634\pi\)
\(608\) −12.3983 + 10.4034i −0.502817 + 0.421914i
\(609\) 23.2871 + 2.30235i 0.943640 + 0.0932961i
\(610\) 0 0
\(611\) −6.75875 11.7065i −0.273430 0.473594i
\(612\) −7.30985 9.12182i −0.295483 0.368728i
\(613\) 16.4901 28.5617i 0.666030 1.15360i −0.312975 0.949761i \(-0.601326\pi\)
0.979005 0.203837i \(-0.0653412\pi\)
\(614\) −1.23316 + 6.99359i −0.0497662 + 0.282238i
\(615\) 0 0
\(616\) 11.4880 + 4.18131i 0.462867 + 0.168470i
\(617\) 6.36077 + 36.0737i 0.256075 + 1.45227i 0.793298 + 0.608834i \(0.208362\pi\)
−0.537223 + 0.843440i \(0.680527\pi\)
\(618\) −5.45658 + 19.4824i −0.219496 + 0.783696i
\(619\) 10.7534 + 9.02320i 0.432217 + 0.362673i 0.832787 0.553593i \(-0.186744\pi\)
−0.400571 + 0.916266i \(0.631188\pi\)
\(620\) 0 0
\(621\) 11.5280 + 8.66779i 0.462602 + 0.347826i
\(622\) 24.9958 1.00224
\(623\) 16.7533 + 14.0577i 0.671206 + 0.563208i
\(624\) −15.3884 + 3.93779i −0.616029 + 0.157638i
\(625\) 0 0
\(626\) 16.4373 + 5.98270i 0.656967 + 0.239117i
\(627\) 21.7389 14.8591i 0.868166 0.593414i
\(628\) −0.847411 + 4.80591i −0.0338154 + 0.191777i
\(629\) −2.61131 + 4.52292i −0.104120 + 0.180340i
\(630\) 0 0
\(631\) 1.61405 + 2.79562i 0.0642543 + 0.111292i 0.896363 0.443321i \(-0.146200\pi\)
−0.832109 + 0.554613i \(0.812866\pi\)
\(632\) 31.4508 11.4471i 1.25104 0.455343i
\(633\) −11.6382 25.7116i −0.462578 1.02195i
\(634\) −13.0758 + 10.9719i −0.519305 + 0.435748i
\(635\) 0 0
\(636\) −1.14386 + 1.59500i −0.0453569 + 0.0632457i
\(637\) −7.06002 + 2.56964i −0.279728 + 0.101813i
\(638\) −19.5567 33.8732i −0.774258 1.34105i
\(639\) −21.3863 + 11.7121i −0.846027 + 0.463325i
\(640\) 0 0
\(641\) −1.01704 + 5.76795i −0.0401709 + 0.227820i −0.998283 0.0585725i \(-0.981345\pi\)
0.958112 + 0.286393i \(0.0924562\pi\)
\(642\) −0.963120 12.6507i −0.0380113 0.499285i
\(643\) 15.6152 + 5.68345i 0.615802 + 0.224134i 0.631040 0.775750i \(-0.282628\pi\)
−0.0152381 + 0.999884i \(0.504851\pi\)
\(644\) −0.508986 2.88660i −0.0200569 0.113748i
\(645\) 0 0
\(646\) −38.6901 32.4648i −1.52224 1.27731i
\(647\) 5.31018 0.208765 0.104382 0.994537i \(-0.466713\pi\)
0.104382 + 0.994537i \(0.466713\pi\)
\(648\) 10.9041 17.0597i 0.428353 0.670170i
\(649\) 3.22591 0.126628
\(650\) 0 0
\(651\) −8.34216 8.53254i −0.326955 0.334417i
\(652\) −0.555642 3.15120i −0.0217606 0.123411i
\(653\) −23.6382 8.60359i −0.925034 0.336685i −0.164794 0.986328i \(-0.552696\pi\)
−0.760239 + 0.649643i \(0.774918\pi\)
\(654\) 1.62377 + 21.3285i 0.0634945 + 0.834011i
\(655\) 0 0
\(656\) 18.3458 31.7758i 0.716282 1.24064i
\(657\) 25.2661 + 15.3577i 0.985724 + 0.599159i
\(658\) −10.0363 17.3834i −0.391255 0.677674i
\(659\) 0.253053 0.0921038i 0.00985755 0.00358786i −0.337087 0.941474i \(-0.609442\pi\)
0.346944 + 0.937886i \(0.387219\pi\)
\(660\) 0 0
\(661\) −17.1827 + 14.4180i −0.668329 + 0.560795i −0.912570 0.408920i \(-0.865906\pi\)
0.244241 + 0.969714i \(0.421461\pi\)
\(662\) 13.0409 10.9426i 0.506850 0.425298i
\(663\) −8.68376 19.1845i −0.337249 0.745064i
\(664\) 19.5002 7.09750i 0.756755 0.275436i
\(665\) 0 0
\(666\) 3.86174 + 0.771146i 0.149640 + 0.0298813i
\(667\) 10.7709 18.6557i 0.417050 0.722352i
\(668\) 1.74306 9.88537i 0.0674409 0.382476i
\(669\) −26.7647 + 18.2944i −1.03478 + 0.707302i
\(670\) 0 0
\(671\) 5.57140 + 31.5970i 0.215081 + 1.21979i
\(672\) −9.70778 + 2.48416i −0.374486 + 0.0958285i
\(673\) −12.7839 10.7270i −0.492784 0.413494i 0.362239 0.932085i \(-0.382012\pi\)
−0.855023 + 0.518591i \(0.826457\pi\)
\(674\) 1.96754 0.0757868
\(675\) 0 0
\(676\) −5.71262 −0.219716
\(677\) 22.7606 + 19.0984i 0.874762 + 0.734012i 0.965095 0.261899i \(-0.0843489\pi\)
−0.0903336 + 0.995912i \(0.528793\pi\)
\(678\) −2.53853 + 9.06364i −0.0974915 + 0.348087i
\(679\) −4.76616 27.0302i −0.182908 1.03733i
\(680\) 0 0
\(681\) −27.4234 13.1664i −1.05087 0.504537i
\(682\) −3.46352 + 19.6426i −0.132625 + 0.752154i
\(683\) 6.26849 10.8573i 0.239857 0.415445i −0.720816 0.693126i \(-0.756233\pi\)
0.960673 + 0.277682i \(0.0895661\pi\)
\(684\) −3.21828 + 8.25753i −0.123054 + 0.315735i
\(685\) 0 0
\(686\) −28.9713 + 10.5447i −1.10613 + 0.402599i
\(687\) −13.0390 1.28914i −0.497467 0.0491838i
\(688\) 9.78590 8.21134i 0.373084 0.313054i
\(689\) −2.70865 + 2.27283i −0.103191 + 0.0865879i
\(690\) 0 0
\(691\) −6.85438 + 2.49479i −0.260753 + 0.0949064i −0.469089 0.883151i \(-0.655418\pi\)
0.208336 + 0.978057i \(0.433195\pi\)
\(692\) −5.93297 10.2762i −0.225538 0.390643i
\(693\) 16.1151 2.46804i 0.612162 0.0937530i
\(694\) 0.823042 1.42555i 0.0312422 0.0541131i
\(695\) 0 0
\(696\) −27.2607 13.0883i −1.03331 0.496110i
\(697\) 45.7098 + 16.6370i 1.73138 + 0.630171i
\(698\) 7.09271 + 40.2248i 0.268463 + 1.52253i
\(699\) −3.24500 + 11.5860i −0.122737 + 0.438225i
\(700\) 0 0
\(701\) −10.1934 −0.384998 −0.192499 0.981297i \(-0.561659\pi\)
−0.192499 + 0.981297i \(0.561659\pi\)
\(702\) −11.6013 + 10.8414i −0.437863 + 0.409184i
\(703\) 3.95962 0.149340
\(704\) −10.3425 8.67836i −0.389796 0.327078i
\(705\) 0 0
\(706\) 4.11569 + 23.3412i 0.154896 + 0.878459i
\(707\) −10.4879 3.81730i −0.394439 0.143564i
\(708\) −0.896357 + 0.612683i −0.0336871 + 0.0230260i
\(709\) 3.06522 17.3837i 0.115117 0.652860i −0.871575 0.490261i \(-0.836901\pi\)
0.986692 0.162599i \(-0.0519876\pi\)
\(710\) 0 0
\(711\) 29.4534 33.5346i 1.10459 1.25765i
\(712\) −14.1309 24.4754i −0.529576 0.917253i
\(713\) −10.3226 + 3.75711i −0.386584 + 0.140705i
\(714\) −12.8948 28.4877i −0.482576 1.06613i
\(715\) 0 0
\(716\) 0.561463 0.471123i 0.0209828 0.0176067i
\(717\) 20.6944 28.8563i 0.772847 1.07766i
\(718\) 35.7057 12.9958i 1.33253 0.485000i
\(719\) 1.57416 + 2.72652i 0.0587062 + 0.101682i 0.893885 0.448297i \(-0.147969\pi\)
−0.835179 + 0.549979i \(0.814636\pi\)
\(720\) 0 0
\(721\) −6.29760 + 10.9078i −0.234535 + 0.406226i
\(722\) −1.32266 + 7.50117i −0.0492242 + 0.279165i
\(723\) −3.07187 40.3496i −0.114244 1.50062i
\(724\) −11.6791 4.25084i −0.434050 0.157981i
\(725\) 0 0
\(726\) 2.45398 + 2.50999i 0.0910759 + 0.0931544i
\(727\) −25.1799 21.1284i −0.933869 0.783609i 0.0426388 0.999091i \(-0.486424\pi\)
−0.976508 + 0.215481i \(0.930868\pi\)
\(728\) −7.41254 −0.274727
\(729\) 1.82622 26.9382i 0.0676377 0.997710i
\(730\) 0 0
\(731\) 12.9735 + 10.8861i 0.479843 + 0.402636i
\(732\) −7.54915 7.72143i −0.279025 0.285392i
\(733\) −1.20830 6.85262i −0.0446297 0.253107i 0.954328 0.298762i \(-0.0965737\pi\)
−0.998957 + 0.0456547i \(0.985463\pi\)
\(734\) 37.8302 + 13.7691i 1.39634 + 0.508226i
\(735\) 0 0
\(736\) −1.60183 + 9.08444i −0.0590443 + 0.334857i
\(737\) 21.2811 36.8600i 0.783901 1.35776i
\(738\) 0.827507 36.6690i 0.0304609 1.34980i
\(739\) 3.80631 + 6.59273i 0.140017 + 0.242517i 0.927503 0.373816i \(-0.121951\pi\)
−0.787485 + 0.616333i \(0.788617\pi\)
\(740\) 0 0
\(741\) −9.30453 + 12.9742i −0.341811 + 0.476620i
\(742\) −4.02217 + 3.37500i −0.147658 + 0.123900i
\(743\) 2.40844 2.02092i 0.0883571 0.0741404i −0.597539 0.801840i \(-0.703855\pi\)
0.685896 + 0.727699i \(0.259410\pi\)
\(744\) 6.35895 + 14.0485i 0.233130 + 0.515041i
\(745\) 0 0
\(746\) −10.3791 17.9772i −0.380007 0.658191i
\(747\) 18.2618 20.7922i 0.668164 0.760749i
\(748\) −6.08169 + 10.5338i −0.222369 + 0.385154i
\(749\) 1.37153 7.77834i 0.0501146 0.284214i
\(750\) 0 0
\(751\) 4.55689 + 1.65857i 0.166283 + 0.0605222i 0.423821 0.905746i \(-0.360689\pi\)
−0.257537 + 0.966268i \(0.582911\pi\)
\(752\) 6.00883 + 34.0778i 0.219119 + 1.24269i
\(753\) 15.4599 3.95609i 0.563390 0.144168i
\(754\) 18.1672 + 15.2441i 0.661609 + 0.555156i
\(755\) 0 0
\(756\) −4.00902 + 3.74644i −0.145807 + 0.136257i
\(757\) −16.2063 −0.589028 −0.294514 0.955647i \(-0.595158\pi\)
−0.294514 + 0.955647i \(0.595158\pi\)
\(758\) −3.79891 3.18766i −0.137983 0.115781i
\(759\) 4.04763 14.4518i 0.146920 0.524567i
\(760\) 0 0
\(761\) −37.9046 13.7961i −1.37404 0.500110i −0.453674 0.891168i \(-0.649887\pi\)
−0.920366 + 0.391058i \(0.872109\pi\)
\(762\) 45.0070 + 21.6086i 1.63043 + 0.782795i
\(763\) −2.31233 + 13.1139i −0.0837121 + 0.474755i
\(764\) 0.558445 0.967255i 0.0202038 0.0349941i
\(765\) 0 0
\(766\) −5.84672 10.1268i −0.211250 0.365896i
\(767\) −1.83800 + 0.668976i −0.0663662 + 0.0241553i
\(768\) 23.0184 + 2.27579i 0.830604 + 0.0821204i
\(769\) 8.23144 6.90700i 0.296833 0.249073i −0.482191 0.876066i \(-0.660159\pi\)
0.779025 + 0.626993i \(0.215715\pi\)
\(770\) 0 0
\(771\) 44.4523 + 4.39493i 1.60091 + 0.158279i
\(772\) 7.54765 2.74712i 0.271646 0.0988711i
\(773\) 27.2618 + 47.2189i 0.980540 + 1.69835i 0.660286 + 0.751014i \(0.270435\pi\)
0.320254 + 0.947332i \(0.396232\pi\)
\(774\) 4.63721 11.8983i 0.166681 0.427674i
\(775\) 0 0