Properties

Label 675.2.l.f.76.3
Level $675$
Weight $2$
Character 675.76
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 76.3
Character \(\chi\) \(=\) 675.76
Dual form 675.2.l.f.151.3

$q$-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 \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\) \(1\)

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 −0.965047 0.262076i \(-0.915593\pi\)
0.0905154 + 0.995895i \(0.471149\pi\)
\(3\) 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 0.987115 + 0.160010i \(0.0511527\pi\)
−0.872858 + 0.487974i \(0.837736\pi\)
\(8\) −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 0.744005 0.668174i \(-0.232924\pi\)
0.140447 + 0.990088i \(0.455146\pi\)
\(12\) −0.612300 0.853791i −0.176756 0.246468i
\(13\) −1.44992 1.21663i −0.402137 0.337433i 0.419182 0.907902i \(-0.362317\pi\)
−0.821319 + 0.570469i \(0.806761\pi\)
\(14\) −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 −0.153576 0.988137i \(-0.549079\pi\)
0.932539 0.361068i \(-0.117588\pi\)
\(18\) 3.19625 + 3.63914i 0.753363 + 0.857754i
\(19\) 2.43505 + 4.21762i 0.558638 + 0.967590i 0.997611 + 0.0690890i \(0.0220092\pi\)
−0.438972 + 0.898501i \(0.644657\pi\)
\(20\) 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 0.892418 + 0.451211i \(0.149008\pi\)
−0.992921 + 0.118774i \(0.962103\pi\)
\(24\) −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 0.106291 0.994335i \(-0.466103\pi\)
0.997686 + 0.0679886i \(0.0216582\pi\)
\(30\) 0 0
\(31\) −0.687222 + 3.89743i −0.123429 + 0.699999i 0.858800 + 0.512311i \(0.171210\pi\)
−0.982229 + 0.187688i \(0.939901\pi\)
\(32\) −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 −0.830673 0.556760i \(-0.812044\pi\)
0.897505 + 0.441004i \(0.145377\pi\)
\(38\) −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 0.971348 0.237662i \(-0.0763811\pi\)
−0.0653788 + 0.997861i \(0.520826\pi\)
\(42\) −4.84447 + 0.478965i −0.747519 + 0.0739059i
\(43\) 2.47752 + 0.901745i 0.377819 + 0.137515i 0.523947 0.851751i \(-0.324459\pi\)
−0.146128 + 0.989266i \(0.546681\pi\)
\(44\) 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 −0.931117 0.364720i \(-0.881165\pi\)
0.750222 0.661186i \(-0.229946\pi\)
\(48\) 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 −0.278034 0.960571i \(-0.589683\pi\)
0.404457 + 0.914557i \(0.367460\pi\)
\(60\) 0 0
\(61\) −1.78476 10.1219i −0.228515 1.29597i −0.855850 0.517224i \(-0.826966\pi\)
0.627335 0.778749i \(-0.284146\pi\)
\(62\) −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 0.993780 + 0.111363i \(0.0355215\pi\)
0.282239 + 0.959344i \(0.408923\pi\)
\(68\) −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 −0.517499 0.855684i \(-0.673137\pi\)
0.999793 + 0.0203253i \(0.00647020\pi\)
\(72\) −5.76713 + 3.50548i −0.679663 + 0.413124i
\(73\) 4.92790 + 8.53538i 0.576768 + 0.998991i 0.995847 + 0.0910412i \(0.0290195\pi\)
−0.419080 + 0.907950i \(0.637647\pi\)
\(74\) 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 −0.289317 + 0.957233i \(0.593428\pi\)
−0.992930 + 0.118700i \(0.962127\pi\)
\(80\) 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 −0.942144 0.335209i \(-0.891193\pi\)
0.166514 + 0.986039i \(0.446749\pi\)
\(84\) 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 −0.979061 0.203565i \(-0.934747\pi\)
0.313238 0.949675i \(-0.398586\pi\)
\(90\) 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 0.957172 0.289521i \(-0.0934959\pi\)
0.547136 + 0.837044i \(0.315718\pi\)
\(98\) −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 0.988754 + 0.149548i \(0.0477818\pi\)
−0.877977 + 0.478703i \(0.841107\pi\)
\(102\) 14.8294 + 10.1363i 1.46833 + 1.00364i
\(103\) −6.79875 + 2.47454i −0.669901 + 0.243824i −0.654505 0.756058i \(-0.727123\pi\)
−0.0153956 + 0.999881i \(0.504901\pi\)
\(104\) −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 −0.486478 0.873693i \(-0.661719\pi\)
0.188935 + 0.981990i \(0.439497\pi\)
\(114\) −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 −0.924649 0.380820i \(-0.875642\pi\)
0.132524 0.991180i \(-0.457692\pi\)
\(128\) −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 0.686249 + 0.727367i \(0.259256\pi\)
−0.893637 + 0.448790i \(0.851855\pi\)
\(132\) −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 −0.972456 0.233089i \(-0.925117\pi\)
0.0606822 + 0.998157i \(0.480672\pi\)
\(138\) −7.51970 1.92424i −0.640119 0.163802i
\(139\) 3.10046 17.5836i 0.262977 1.49142i −0.511756 0.859131i \(-0.671005\pi\)
0.774734 0.632288i \(-0.217884\pi\)
\(140\) 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 −0.128298 0.991736i \(-0.540951\pi\)
−0.998948 + 0.0458641i \(0.985396\pi\)
\(150\) 0 0
\(151\) 18.3678 + 6.68534i 1.49475 + 0.544045i 0.954696 0.297583i \(-0.0961806\pi\)
0.540057 + 0.841629i \(0.318403\pi\)
\(152\) 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 −0.0222470 0.999753i \(-0.507082\pi\)
0.625586 + 0.780155i \(0.284860\pi\)
\(158\) 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 −0.864372 0.502854i \(-0.832284\pi\)
−0.338919 + 0.940816i \(0.610061\pi\)
\(168\) 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 −0.470099 0.882614i \(-0.655782\pi\)
−0.927450 + 0.373948i \(0.878004\pi\)
\(174\) 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 −0.887720 0.460384i \(-0.847712\pi\)
0.842564 + 0.538596i \(0.181045\pi\)
\(180\) 0 0
\(181\) −10.2446 17.7442i −0.761474 1.31891i −0.942090 0.335359i \(-0.891142\pi\)
0.180616 0.983554i \(-0.442191\pi\)
\(182\) 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 −0.692389 0.721524i \(-0.743442\pi\)
0.590331 + 0.807162i \(0.298997\pi\)
\(192\) 2.02035 + 7.21353i 0.145806 + 0.520592i
\(193\) −2.29931 + 13.0401i −0.165508 + 0.938643i 0.783031 + 0.621983i \(0.213673\pi\)
−0.948539 + 0.316660i \(0.897438\pi\)
\(194\) −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 −0.978694 0.205325i \(-0.934175\pi\)
0.311530 0.950236i \(-0.399159\pi\)
\(198\) 5.49046 + 14.0876i 0.390190 + 1.00116i
\(199\) −3.20552 + 5.55213i −0.227233 + 0.393580i −0.956987 0.290130i \(-0.906301\pi\)
0.729754 + 0.683710i \(0.239635\pi\)
\(200\) 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 −0.810213 0.586135i \(-0.800649\pi\)
−0.243899 + 0.969801i \(0.578426\pi\)
\(212\) 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 −0.876242 0.481872i \(-0.839957\pi\)
0.658588 0.752504i \(-0.271154\pi\)
\(224\) −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 −0.269787 0.962920i \(-0.586953\pi\)
−0.825622 + 0.564224i \(0.809175\pi\)
\(228\) 2.10999 4.66147i 0.139737 0.308714i
\(229\) −5.79494 4.86253i −0.382940 0.321325i 0.430915 0.902392i \(-0.358191\pi\)
−0.813855 + 0.581067i \(0.802635\pi\)
\(230\) 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 −0.729536 0.683943i \(-0.760264\pi\)
0.957080 + 0.289825i \(0.0935971\pi\)
\(234\) −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 0.622046 + 0.782981i \(0.286302\pi\)
−0.852327 + 0.523009i \(0.824809\pi\)
\(240\) 0 0
\(241\) −17.8973 + 15.0176i −1.15287 + 0.967369i −0.999783 0.0208438i \(-0.993365\pi\)
−0.153083 + 0.988213i \(0.548920\pi\)
\(242\) 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 0.973992 0.226580i \(-0.0727546\pi\)
−0.683221 + 0.730212i \(0.739421\pi\)
\(252\) −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 0.998083 + 0.0618912i \(0.0197132\pi\)
0.234266 + 0.972172i \(0.424731\pi\)
\(258\) −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 0.820388 + 0.571807i \(0.193758\pi\)
−0.575343 + 0.817912i \(0.695131\pi\)
\(264\) −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 0.754490 + 0.656311i \(0.227884\pi\)
−0.484517 + 0.874782i \(0.661005\pi\)
\(278\) 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 0.625688 0.780073i \(-0.284818\pi\)
−0.0221165 + 0.999755i \(0.507040\pi\)
\(282\) 19.8742 1.96493i 1.18349 0.117010i
\(283\) 12.1469 + 10.1924i 0.722056 + 0.605877i 0.927953 0.372697i \(-0.121567\pi\)
−0.205897 + 0.978574i \(0.566011\pi\)
\(284\) −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 −0.963273 0.268525i \(-0.913464\pi\)
0.997021 + 0.0771274i \(0.0245748\pi\)
\(294\) 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 −0.921936 0.387342i \(-0.873393\pi\)
0.796416 + 0.604749i \(0.206727\pi\)
\(308\) 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 0.241290 0.970453i \(-0.422429\pi\)
−0.913810 + 0.406142i \(0.866874\pi\)
\(312\) 4.29805 + 5.99320i 0.243329 + 0.339298i
\(313\) −10.1811 3.70561i −0.575469 0.209454i 0.0378572 0.999283i \(-0.487947\pi\)
−0.613327 + 0.789829i \(0.710169\pi\)
\(314\) −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 0.991957 + 0.126576i \(0.0403987\pi\)
−0.888843 + 0.458212i \(0.848490\pi\)
\(318\) −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 −0.992872 0.119184i \(-0.961972\pi\)
0.892231 0.451578i \(-0.149139\pi\)
\(332\) 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 0.617006 0.786958i \(-0.288345\pi\)
−0.667860 + 0.744287i \(0.732790\pi\)
\(338\) 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 −0.979687 0.200534i \(-0.935732\pi\)
0.989191 + 0.146632i \(0.0468434\pi\)
\(348\) −7.89934 2.02139i −0.423449 0.108358i
\(349\) −19.3802 + 16.2620i −1.03740 + 0.870483i −0.991713 0.128473i \(-0.958992\pi\)
−0.0456879 + 0.998956i \(0.514548\pi\)
\(350\) 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 −0.890980 0.454043i \(-0.849981\pi\)
0.292428 + 0.956288i \(0.405537\pi\)
\(354\) 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 −0.989287 0.145981i \(-0.953366\pi\)
0.368221 0.929738i \(-0.379967\pi\)
\(360\) 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 −0.351884 0.936043i \(-0.614459\pi\)
−0.871236 + 0.490864i \(0.836681\pi\)
\(368\) −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 −0.00972404 0.999953i \(-0.503095\pi\)
0.635308 + 0.772259i \(0.280873\pi\)
\(374\) −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 −0.162229 0.986753i \(-0.551868\pi\)
0.509998 + 0.860175i \(0.329646\pi\)
\(384\) −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 0.168198 0.985753i \(-0.446205\pi\)
−0.504782 + 0.863247i \(0.668427\pi\)
\(390\) 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 0.982859 + 0.184358i \(0.0590206\pi\)
−0.331771 + 0.943360i \(0.607646\pi\)
\(398\) −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 −0.872532 0.488557i \(-0.837524\pi\)
0.987008 0.160670i \(-0.0513654\pi\)
\(402\) −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 0.850283 + 0.526325i \(0.176430\pi\)
−0.979019 + 0.203770i \(0.934681\pi\)
\(410\) 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 0.993296 0.115598i \(-0.0368784\pi\)
0.0586424 + 0.998279i \(0.481323\pi\)
\(420\) 0 0
\(421\) 26.6729 + 9.70814i 1.29996 + 0.473146i 0.896983 0.442066i \(-0.145754\pi\)
0.402974 + 0.915211i \(0.367976\pi\)
\(422\) 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 −0.976109 0.217280i \(-0.930282\pi\)
0.842929 0.538025i \(-0.180829\pi\)
\(440\) 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 0.539977 0.841679i \(-0.318433\pi\)
−0.127374 + 0.991855i \(0.540655\pi\)
\(444\) −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 0.0163930 0.999866i \(-0.494782\pi\)
0.857713 0.514130i \(-0.171885\pi\)
\(450\) 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 −0.666878 0.745167i \(-0.732370\pi\)
0.618044 + 0.786143i \(0.287925\pi\)
\(458\) 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 −0.779921 0.625878i \(-0.784741\pi\)
0.480938 + 0.876755i \(0.340296\pi\)
\(462\) −14.7221 3.76730i −0.684935 0.175271i
\(463\) 4.96946 28.1832i 0.230950 1.30978i −0.620027 0.784581i \(-0.712878\pi\)
0.850977 0.525203i \(-0.176011\pi\)
\(464\) 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 0.838087 0.545536i \(-0.183674\pi\)
−0.891492 + 0.453036i \(0.850341\pi\)
\(468\) 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 0.981179 0.193102i \(-0.0618547\pi\)
−0.988051 + 0.154127i \(0.950744\pi\)
\(480\) 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 −0.823272 + 0.567647i \(0.807854\pi\)
−0.995539 + 0.0943459i \(0.969924\pi\)
\(492\) 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 0.741935 0.670472i \(-0.233908\pi\)
−0.531451 + 0.847089i \(0.678353\pi\)
\(500\) 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 −0.932422 0.361371i \(-0.882309\pi\)
0.779168 + 0.626815i \(0.215642\pi\)
\(504\) −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 0.889401 + 0.457127i \(0.151122\pi\)
−0.992111 + 0.125366i \(0.959990\pi\)
\(510\) 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 −0.999043 0.0437400i \(-0.986073\pi\)
0.461642 0.887067i \(-0.347261\pi\)
\(522\) 37.1560 + 5.69046i 1.62627 + 0.249065i
\(523\) 19.7850 34.2687i 0.865140 1.49847i −0.00176851 0.999998i \(-0.500563\pi\)
0.866908 0.498468i \(-0.166104\pi\)
\(524\) 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 0.950583 + 0.310469i \(0.100486\pi\)
−0.787070 + 0.616864i \(0.788403\pi\)
\(548\) 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 −0.999458 0.0329284i \(-0.989517\pi\)
0.528246 + 0.849092i \(0.322850\pi\)
\(558\) −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 0.888127 + 0.459598i \(0.152006\pi\)
−0.991758 + 0.128123i \(0.959105\pi\)
\(564\) −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 −0.738056 0.674740i \(-0.764256\pi\)
0.536327 + 0.844010i \(0.319811\pi\)
\(570\) 0 0
\(571\) −5.42129 + 30.7457i −0.226874 + 1.28667i 0.632196 + 0.774809i \(0.282154\pi\)
−0.859070 + 0.511858i \(0.828957\pi\)
\(572\) −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 −0.991129 0.132906i \(-0.957569\pi\)
0.610664 + 0.791889i \(0.290902\pi\)
\(578\) 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 0.999993 0.00377558i \(-0.00120181\pi\)
−0.940977 + 0.338470i \(0.890091\pi\)
\(588\) −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 −0.327071 0.945000i \(-0.606062\pi\)
0.356883 + 0.934149i \(0.383839\pi\)
\(600\) 0 0
\(601\) −4.46708 25.3341i −0.182216 1.03340i −0.929481 0.368871i \(-0.879744\pi\)
0.747265 0.664527i \(-0.231367\pi\)
\(602\) −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 0.740405 0.672161i \(-0.234634\pi\)
−0.533380 + 0.845876i \(0.679078\pi\)
\(608\) −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 0.979005 + 0.203837i \(0.0653412\pi\)
−0.312975 + 0.949761i \(0.601326\pi\)
\(614\) −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 −0.537223 0.843440i \(-0.680527\pi\)
0.793298 0.608834i \(-0.208362\pi\)
\(618\) −5.45658 19.4824i −0.219496 0.783696i
\(619\) 10.7534 9.02320i 0.432217 0.362673i −0.400571 0.916266i \(-0.631188\pi\)
0.832787 + 0.553593i \(0.186744\pi\)
\(620\) 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 −0.832109 0.554613i \(-0.812866\pi\)
0.896363 + 0.443321i \(0.146200\pi\)
\(632\) 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 0.958112 0.286393i \(-0.0924562\pi\)
−0.998283 + 0.0585725i \(0.981345\pi\)
\(642\) −0.963120 + 12.6507i −0.0380113 + 0.499285i
\(643\) 15.6152 5.68345i 0.615802 0.224134i −0.0152381 0.999884i \(-0.504851\pi\)
0.631040 + 0.775750i \(0.282628\pi\)
\(644\) −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 −0.760239 0.649643i \(-0.774918\pi\)
−0.164794 + 0.986328i \(0.552696\pi\)
\(654\) 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 0.346944 0.937886i \(-0.387219\pi\)
−0.337087 + 0.941474i \(0.609442\pi\)
\(660\) 0 0
\(661\) −17.1827 14.4180i −0.668329 0.560795i 0.244241 0.969714i \(-0.421461\pi\)
−0.912570 + 0.408920i \(0.865906\pi\)
\(662\) 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 −0.855023 0.518591i \(-0.826457\pi\)
0.362239 + 0.932085i \(0.382012\pi\)
\(674\) 1.96754 0.0757868
\(675\) 0 0
\(676\) −5.71262 −0.219716
\(677\) 22.7606 19.0984i 0.874762 0.734012i −0.0903336 0.995912i \(-0.528793\pi\)
0.965095 + 0.261899i \(0.0843489\pi\)
\(678\) −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 0.960673 0.277682i \(-0.0895661\pi\)
−0.720816 + 0.693126i \(0.756233\pi\)
\(684\) −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 0.208336 0.978057i \(-0.433195\pi\)
−0.469089 + 0.883151i \(0.655418\pi\)
\(692\) −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 0.986692 + 0.162599i \(0.0519876\pi\)
−0.871575 + 0.490261i \(0.836901\pi\)
\(710\) 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 −0.835179 0.549979i \(-0.814636\pi\)
0.893885 + 0.448297i \(0.147969\pi\)
\(720\) 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 −0.976508 0.215481i \(-0.930868\pi\)
0.0426388 + 0.999091i \(0.486424\pi\)
\(728\) −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 −0.998957 0.0456547i \(-0.985463\pi\)
0.954328 + 0.298762i \(0.0965737\pi\)
\(734\) 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 −0.787485 0.616333i \(-0.788617\pi\)
0.927503 + 0.373816i \(0.121951\pi\)
\(740\) 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 0.685896 0.727699i \(-0.259410\pi\)
−0.597539 + 0.801840i \(0.703855\pi\)
\(744\) 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 −0.257537 0.966268i \(-0.582911\pi\)
0.423821 + 0.905746i \(0.360689\pi\)
\(752\) 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 −0.920366 0.391058i \(-0.872109\pi\)
−0.453674 + 0.891168i \(0.649887\pi\)
\(762\) 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 0.779025 0.626993i \(-0.215715\pi\)
−0.482191 + 0.876066i \(0.660159\pi\)
\(770\) 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 0.320254 0.947332i \(-0.396232\pi\)
0.660286 0.751014i \(-0.270435\pi\)
\(774\) 4.63721 + 11.8983i 0.166681 + 0.427674i
\(775\) 0 0
\(776\) −6.15916