Properties

Label 380.2.u.a.81.2
Level $380$
Weight $2$
Character 380.81
Analytic conductor $3.034$
Analytic rank $0$
Dimension $18$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [380,2,Mod(61,380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(380, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("380.61");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.u (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: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(3\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - 3 x^{17} + 3 x^{15} + 36 x^{14} + 72 x^{13} - 134 x^{12} - 741 x^{11} + 486 x^{10} + 5700 x^{9} + \cdots + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 81.2
Root \(-0.344606 + 0.289159i\) of defining polynomial
Character \(\chi\) \(=\) 380.81
Dual form 380.2.u.a.61.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0781159 + 0.443017i) q^{3} +(-0.766044 - 0.642788i) q^{5} +(-1.06981 - 1.85297i) q^{7} +(2.62892 + 0.956847i) q^{9} +O(q^{10})\) \(q+(-0.0781159 + 0.443017i) q^{3} +(-0.766044 - 0.642788i) q^{5} +(-1.06981 - 1.85297i) q^{7} +(2.62892 + 0.956847i) q^{9} +(2.25634 - 3.90810i) q^{11} +(-0.155380 - 0.881206i) q^{13} +(0.344606 - 0.289159i) q^{15} +(-0.00854515 + 0.00311018i) q^{17} +(4.31164 - 0.640134i) q^{19} +(0.904468 - 0.329199i) q^{21} +(4.94633 - 4.15046i) q^{23} +(0.173648 + 0.984808i) q^{25} +(-1.30404 + 2.25866i) q^{27} +(-0.381463 - 0.138841i) q^{29} +(-0.920071 - 1.59361i) q^{31} +(1.55510 + 1.30488i) q^{33} +(-0.371542 + 2.10712i) q^{35} -6.75663 q^{37} +0.402527 q^{39} +(-1.24280 + 7.04829i) q^{41} +(1.04904 + 0.880252i) q^{43} +(-1.39882 - 2.42282i) q^{45} +(1.13486 + 0.413057i) q^{47} +(1.21100 - 2.09751i) q^{49} +(-0.000710351 - 0.00402860i) q^{51} +(1.90313 - 1.59691i) q^{53} +(-4.24054 + 1.54343i) q^{55} +(-0.0532169 + 1.96013i) q^{57} +(8.35638 - 3.04147i) q^{59} +(-4.44422 + 3.72914i) q^{61} +(-1.03944 - 5.89495i) q^{63} +(-0.447400 + 0.774919i) q^{65} +(-14.6860 - 5.34527i) q^{67} +(1.45234 + 2.51552i) q^{69} +(-5.71938 - 4.79913i) q^{71} +(-1.93685 + 10.9844i) q^{73} -0.449851 q^{75} -9.65546 q^{77} +(-1.27942 + 7.25594i) q^{79} +(5.53058 + 4.64071i) q^{81} +(-0.0758467 - 0.131370i) q^{83} +(0.00854515 + 0.00311018i) q^{85} +(0.0913074 - 0.158149i) q^{87} +(1.98885 + 11.2793i) q^{89} +(-1.46662 + 1.23064i) q^{91} +(0.777868 - 0.283121i) q^{93} +(-3.71438 - 2.28110i) q^{95} +(-7.85592 + 2.85932i) q^{97} +(9.67119 - 8.11509i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 3 q^{3} - 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 3 q^{3} - 9 q^{9} + 9 q^{13} - 3 q^{15} + 12 q^{17} + 18 q^{19} + 15 q^{21} - 9 q^{23} - 33 q^{29} - 18 q^{31} + 9 q^{33} + 12 q^{35} + 60 q^{37} - 84 q^{39} - 18 q^{41} + 18 q^{43} + 6 q^{45} - 15 q^{47} - 15 q^{49} - 9 q^{51} + 24 q^{53} + 3 q^{55} + 66 q^{57} + 48 q^{59} - 18 q^{61} - 54 q^{63} + 3 q^{65} - 36 q^{67} - 9 q^{69} + 18 q^{73} - 6 q^{75} + 9 q^{79} - 9 q^{81} - 30 q^{83} - 12 q^{85} - 9 q^{87} + 6 q^{89} + 30 q^{91} + 21 q^{95} + 21 q^{97} - 21 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.0781159 + 0.443017i −0.0451002 + 0.255776i −0.999019 0.0442897i \(-0.985898\pi\)
0.953919 + 0.300066i \(0.0970086\pi\)
\(4\) 0 0
\(5\) −0.766044 0.642788i −0.342585 0.287463i
\(6\) 0 0
\(7\) −1.06981 1.85297i −0.404352 0.700357i 0.589894 0.807481i \(-0.299169\pi\)
−0.994246 + 0.107123i \(0.965836\pi\)
\(8\) 0 0
\(9\) 2.62892 + 0.956847i 0.876305 + 0.318949i
\(10\) 0 0
\(11\) 2.25634 3.90810i 0.680313 1.17834i −0.294573 0.955629i \(-0.595177\pi\)
0.974885 0.222707i \(-0.0714894\pi\)
\(12\) 0 0
\(13\) −0.155380 0.881206i −0.0430947 0.244402i 0.955649 0.294507i \(-0.0951555\pi\)
−0.998744 + 0.0501049i \(0.984044\pi\)
\(14\) 0 0
\(15\) 0.344606 0.289159i 0.0889769 0.0746605i
\(16\) 0 0
\(17\) −0.00854515 + 0.00311018i −0.00207250 + 0.000754330i −0.343056 0.939315i \(-0.611462\pi\)
0.340984 + 0.940069i \(0.389240\pi\)
\(18\) 0 0
\(19\) 4.31164 0.640134i 0.989158 0.146857i
\(20\) 0 0
\(21\) 0.904468 0.329199i 0.197371 0.0718372i
\(22\) 0 0
\(23\) 4.94633 4.15046i 1.03138 0.865431i 0.0403658 0.999185i \(-0.487148\pi\)
0.991015 + 0.133754i \(0.0427032\pi\)
\(24\) 0 0
\(25\) 0.173648 + 0.984808i 0.0347296 + 0.196962i
\(26\) 0 0
\(27\) −1.30404 + 2.25866i −0.250962 + 0.434679i
\(28\) 0 0
\(29\) −0.381463 0.138841i −0.0708359 0.0257822i 0.306359 0.951916i \(-0.400889\pi\)
−0.377195 + 0.926134i \(0.623111\pi\)
\(30\) 0 0
\(31\) −0.920071 1.59361i −0.165250 0.286221i 0.771494 0.636236i \(-0.219510\pi\)
−0.936744 + 0.350016i \(0.886176\pi\)
\(32\) 0 0
\(33\) 1.55510 + 1.30488i 0.270708 + 0.227151i
\(34\) 0 0
\(35\) −0.371542 + 2.10712i −0.0628021 + 0.356169i
\(36\) 0 0
\(37\) −6.75663 −1.11078 −0.555392 0.831589i \(-0.687432\pi\)
−0.555392 + 0.831589i \(0.687432\pi\)
\(38\) 0 0
\(39\) 0.402527 0.0644559
\(40\) 0 0
\(41\) −1.24280 + 7.04829i −0.194093 + 1.10076i 0.719611 + 0.694378i \(0.244320\pi\)
−0.913704 + 0.406380i \(0.866791\pi\)
\(42\) 0 0
\(43\) 1.04904 + 0.880252i 0.159978 + 0.134237i 0.719263 0.694738i \(-0.244480\pi\)
−0.559285 + 0.828975i \(0.688924\pi\)
\(44\) 0 0
\(45\) −1.39882 2.42282i −0.208523 0.361173i
\(46\) 0 0
\(47\) 1.13486 + 0.413057i 0.165537 + 0.0602505i 0.423459 0.905915i \(-0.360816\pi\)
−0.257922 + 0.966166i \(0.583038\pi\)
\(48\) 0 0
\(49\) 1.21100 2.09751i 0.173000 0.299644i
\(50\) 0 0
\(51\) −0.000710351 0.00402860i −9.94691e−5 0.000564117i
\(52\) 0 0
\(53\) 1.90313 1.59691i 0.261415 0.219353i −0.502654 0.864487i \(-0.667643\pi\)
0.764069 + 0.645135i \(0.223199\pi\)
\(54\) 0 0
\(55\) −4.24054 + 1.54343i −0.571794 + 0.208116i
\(56\) 0 0
\(57\) −0.0532169 + 1.96013i −0.00704875 + 0.259626i
\(58\) 0 0
\(59\) 8.35638 3.04147i 1.08791 0.395966i 0.265062 0.964231i \(-0.414607\pi\)
0.822845 + 0.568265i \(0.192385\pi\)
\(60\) 0 0
\(61\) −4.44422 + 3.72914i −0.569024 + 0.477468i −0.881322 0.472517i \(-0.843346\pi\)
0.312298 + 0.949984i \(0.398901\pi\)
\(62\) 0 0
\(63\) −1.03944 5.89495i −0.130957 0.742694i
\(64\) 0 0
\(65\) −0.447400 + 0.774919i −0.0554931 + 0.0961169i
\(66\) 0 0
\(67\) −14.6860 5.34527i −1.79418 0.653029i −0.998905 0.0467817i \(-0.985103\pi\)
−0.795276 0.606247i \(-0.792674\pi\)
\(68\) 0 0
\(69\) 1.45234 + 2.51552i 0.174841 + 0.302834i
\(70\) 0 0
\(71\) −5.71938 4.79913i −0.678766 0.569552i 0.236879 0.971539i \(-0.423875\pi\)
−0.915646 + 0.401987i \(0.868320\pi\)
\(72\) 0 0
\(73\) −1.93685 + 10.9844i −0.226691 + 1.28563i 0.632735 + 0.774369i \(0.281932\pi\)
−0.859426 + 0.511260i \(0.829179\pi\)
\(74\) 0 0
\(75\) −0.449851 −0.0519444
\(76\) 0 0
\(77\) −9.65546 −1.10034
\(78\) 0 0
\(79\) −1.27942 + 7.25594i −0.143946 + 0.816357i 0.824262 + 0.566209i \(0.191590\pi\)
−0.968208 + 0.250148i \(0.919521\pi\)
\(80\) 0 0
\(81\) 5.53058 + 4.64071i 0.614509 + 0.515634i
\(82\) 0 0
\(83\) −0.0758467 0.131370i −0.00832526 0.0144198i 0.861833 0.507193i \(-0.169317\pi\)
−0.870158 + 0.492773i \(0.835983\pi\)
\(84\) 0 0
\(85\) 0.00854515 + 0.00311018i 0.000926852 + 0.000337346i
\(86\) 0 0
\(87\) 0.0913074 0.158149i 0.00978918 0.0169554i
\(88\) 0 0
\(89\) 1.98885 + 11.2793i 0.210817 + 1.19560i 0.888019 + 0.459807i \(0.152081\pi\)
−0.677202 + 0.735797i \(0.736808\pi\)
\(90\) 0 0
\(91\) −1.46662 + 1.23064i −0.153744 + 0.129006i
\(92\) 0 0
\(93\) 0.777868 0.283121i 0.0806612 0.0293583i
\(94\) 0 0
\(95\) −3.71438 2.28110i −0.381087 0.234036i
\(96\) 0 0
\(97\) −7.85592 + 2.85932i −0.797648 + 0.290320i −0.708511 0.705699i \(-0.750633\pi\)
−0.0891365 + 0.996019i \(0.528411\pi\)
\(98\) 0 0
\(99\) 9.67119 8.11509i 0.971991 0.815597i
\(100\) 0 0
\(101\) 1.53748 + 8.71948i 0.152985 + 0.867621i 0.960605 + 0.277918i \(0.0896442\pi\)
−0.807620 + 0.589703i \(0.799245\pi\)
\(102\) 0 0
\(103\) −8.48725 + 14.7003i −0.836273 + 1.44847i 0.0567161 + 0.998390i \(0.481937\pi\)
−0.892989 + 0.450078i \(0.851396\pi\)
\(104\) 0 0
\(105\) −0.904468 0.329199i −0.0882670 0.0321266i
\(106\) 0 0
\(107\) −3.73769 6.47387i −0.361336 0.625853i 0.626845 0.779144i \(-0.284346\pi\)
−0.988181 + 0.153291i \(0.951013\pi\)
\(108\) 0 0
\(109\) −0.821088 0.688975i −0.0786460 0.0659918i 0.602617 0.798030i \(-0.294125\pi\)
−0.681263 + 0.732039i \(0.738569\pi\)
\(110\) 0 0
\(111\) 0.527800 2.99330i 0.0500966 0.284112i
\(112\) 0 0
\(113\) 18.3614 1.72729 0.863647 0.504097i \(-0.168175\pi\)
0.863647 + 0.504097i \(0.168175\pi\)
\(114\) 0 0
\(115\) −6.45697 −0.602116
\(116\) 0 0
\(117\) 0.434697 2.46529i 0.0401878 0.227916i
\(118\) 0 0
\(119\) 0.0149048 + 0.0125066i 0.00136632 + 0.00114648i
\(120\) 0 0
\(121\) −4.68216 8.10974i −0.425651 0.737249i
\(122\) 0 0
\(123\) −3.02543 1.10117i −0.272794 0.0992889i
\(124\) 0 0
\(125\) 0.500000 0.866025i 0.0447214 0.0774597i
\(126\) 0 0
\(127\) 1.45854 + 8.27177i 0.129424 + 0.734001i 0.978581 + 0.205861i \(0.0659994\pi\)
−0.849157 + 0.528140i \(0.822889\pi\)
\(128\) 0 0
\(129\) −0.471913 + 0.395982i −0.0415497 + 0.0348643i
\(130\) 0 0
\(131\) 17.0821 6.21737i 1.49247 0.543214i 0.538370 0.842709i \(-0.319040\pi\)
0.954098 + 0.299495i \(0.0968181\pi\)
\(132\) 0 0
\(133\) −5.79880 7.30452i −0.502820 0.633382i
\(134\) 0 0
\(135\) 2.45079 0.892014i 0.210930 0.0767723i
\(136\) 0 0
\(137\) −12.1065 + 10.1585i −1.03432 + 0.867901i −0.991359 0.131175i \(-0.958125\pi\)
−0.0429651 + 0.999077i \(0.513680\pi\)
\(138\) 0 0
\(139\) −1.06326 6.03005i −0.0901845 0.511462i −0.996117 0.0880396i \(-0.971940\pi\)
0.905932 0.423422i \(-0.139171\pi\)
\(140\) 0 0
\(141\) −0.271642 + 0.470498i −0.0228764 + 0.0396231i
\(142\) 0 0
\(143\) −3.79443 1.38106i −0.317306 0.115490i
\(144\) 0 0
\(145\) 0.202972 + 0.351558i 0.0168559 + 0.0291953i
\(146\) 0 0
\(147\) 0.834634 + 0.700341i 0.0688395 + 0.0577632i
\(148\) 0 0
\(149\) 1.54257 8.74835i 0.126372 0.716693i −0.854111 0.520091i \(-0.825898\pi\)
0.980483 0.196602i \(-0.0629908\pi\)
\(150\) 0 0
\(151\) 14.4216 1.17362 0.586808 0.809726i \(-0.300384\pi\)
0.586808 + 0.809726i \(0.300384\pi\)
\(152\) 0 0
\(153\) −0.0254405 −0.00205674
\(154\) 0 0
\(155\) −0.319537 + 1.81219i −0.0256658 + 0.145558i
\(156\) 0 0
\(157\) 9.18908 + 7.71055i 0.733368 + 0.615369i 0.931048 0.364898i \(-0.118896\pi\)
−0.197679 + 0.980267i \(0.563340\pi\)
\(158\) 0 0
\(159\) 0.558796 + 0.967862i 0.0443154 + 0.0767565i
\(160\) 0 0
\(161\) −12.9823 4.72518i −1.02315 0.372397i
\(162\) 0 0
\(163\) −3.03640 + 5.25920i −0.237829 + 0.411932i −0.960091 0.279687i \(-0.909769\pi\)
0.722262 + 0.691620i \(0.243102\pi\)
\(164\) 0 0
\(165\) −0.352512 1.99920i −0.0274430 0.155637i
\(166\) 0 0
\(167\) 6.34194 5.32152i 0.490754 0.411792i −0.363542 0.931578i \(-0.618433\pi\)
0.854296 + 0.519786i \(0.173988\pi\)
\(168\) 0 0
\(169\) 11.4636 4.17242i 0.881817 0.320955i
\(170\) 0 0
\(171\) 11.9474 + 2.44272i 0.913644 + 0.186799i
\(172\) 0 0
\(173\) 19.7600 7.19207i 1.50233 0.546803i 0.545666 0.838003i \(-0.316277\pi\)
0.956662 + 0.291200i \(0.0940545\pi\)
\(174\) 0 0
\(175\) 1.63905 1.37533i 0.123901 0.103965i
\(176\) 0 0
\(177\) 0.694659 + 3.93961i 0.0522138 + 0.296119i
\(178\) 0 0
\(179\) −5.30897 + 9.19540i −0.396811 + 0.687296i −0.993330 0.115302i \(-0.963216\pi\)
0.596520 + 0.802598i \(0.296550\pi\)
\(180\) 0 0
\(181\) −11.7436 4.27432i −0.872895 0.317708i −0.133556 0.991041i \(-0.542640\pi\)
−0.739339 + 0.673333i \(0.764862\pi\)
\(182\) 0 0
\(183\) −1.30491 2.26017i −0.0964617 0.167077i
\(184\) 0 0
\(185\) 5.17588 + 4.34308i 0.380538 + 0.319310i
\(186\) 0 0
\(187\) −0.00712589 + 0.0404129i −0.000521097 + 0.00295529i
\(188\) 0 0
\(189\) 5.58031 0.405908
\(190\) 0 0
\(191\) −5.16539 −0.373755 −0.186877 0.982383i \(-0.559837\pi\)
−0.186877 + 0.982383i \(0.559837\pi\)
\(192\) 0 0
\(193\) 3.30453 18.7409i 0.237866 1.34900i −0.598629 0.801027i \(-0.704287\pi\)
0.836494 0.547976i \(-0.184601\pi\)
\(194\) 0 0
\(195\) −0.308353 0.258739i −0.0220817 0.0185287i
\(196\) 0 0
\(197\) −11.2779 19.5339i −0.803516 1.39173i −0.917288 0.398223i \(-0.869627\pi\)
0.113773 0.993507i \(-0.463706\pi\)
\(198\) 0 0
\(199\) −3.01263 1.09651i −0.213559 0.0777293i 0.233025 0.972471i \(-0.425138\pi\)
−0.446585 + 0.894741i \(0.647360\pi\)
\(200\) 0 0
\(201\) 3.51526 6.08860i 0.247947 0.429457i
\(202\) 0 0
\(203\) 0.150826 + 0.855375i 0.0105859 + 0.0600355i
\(204\) 0 0
\(205\) 5.48260 4.60044i 0.382921 0.321309i
\(206\) 0 0
\(207\) 16.9748 6.17833i 1.17983 0.429424i
\(208\) 0 0
\(209\) 7.22682 18.2947i 0.499890 1.26547i
\(210\) 0 0
\(211\) −12.1660 + 4.42808i −0.837545 + 0.304841i −0.724952 0.688800i \(-0.758138\pi\)
−0.112593 + 0.993641i \(0.535916\pi\)
\(212\) 0 0
\(213\) 2.57287 2.15890i 0.176290 0.147925i
\(214\) 0 0
\(215\) −0.237799 1.34862i −0.0162177 0.0919754i
\(216\) 0 0
\(217\) −1.96861 + 3.40973i −0.133638 + 0.231468i
\(218\) 0 0
\(219\) −4.71499 1.71611i −0.318609 0.115964i
\(220\) 0 0
\(221\) 0.00406846 + 0.00704677i 0.000273674 + 0.000474017i
\(222\) 0 0
\(223\) 6.59373 + 5.53280i 0.441549 + 0.370504i 0.836289 0.548289i \(-0.184721\pi\)
−0.394740 + 0.918793i \(0.629165\pi\)
\(224\) 0 0
\(225\) −0.485804 + 2.75513i −0.0323869 + 0.183675i
\(226\) 0 0
\(227\) 7.99196 0.530445 0.265223 0.964187i \(-0.414555\pi\)
0.265223 + 0.964187i \(0.414555\pi\)
\(228\) 0 0
\(229\) −11.9777 −0.791510 −0.395755 0.918356i \(-0.629517\pi\)
−0.395755 + 0.918356i \(0.629517\pi\)
\(230\) 0 0
\(231\) 0.754245 4.27754i 0.0496257 0.281441i
\(232\) 0 0
\(233\) 18.4257 + 15.4610i 1.20711 + 1.01288i 0.999398 + 0.0346928i \(0.0110453\pi\)
0.207709 + 0.978191i \(0.433399\pi\)
\(234\) 0 0
\(235\) −0.603849 1.04590i −0.0393907 0.0682268i
\(236\) 0 0
\(237\) −3.11456 1.13361i −0.202313 0.0736357i
\(238\) 0 0
\(239\) 4.44437 7.69788i 0.287483 0.497935i −0.685726 0.727860i \(-0.740515\pi\)
0.973208 + 0.229926i \(0.0738483\pi\)
\(240\) 0 0
\(241\) 4.14103 + 23.4850i 0.266747 + 1.51280i 0.764013 + 0.645201i \(0.223226\pi\)
−0.497266 + 0.867598i \(0.665663\pi\)
\(242\) 0 0
\(243\) −8.48164 + 7.11694i −0.544097 + 0.456552i
\(244\) 0 0
\(245\) −2.27593 + 0.828371i −0.145404 + 0.0529227i
\(246\) 0 0
\(247\) −1.23403 3.69998i −0.0785197 0.235424i
\(248\) 0 0
\(249\) 0.0641241 0.0233393i 0.00406370 0.00147907i
\(250\) 0 0
\(251\) 2.90062 2.43391i 0.183086 0.153627i −0.546639 0.837369i \(-0.684093\pi\)
0.729724 + 0.683741i \(0.239648\pi\)
\(252\) 0 0
\(253\) −5.05981 28.6956i −0.318107 1.80408i
\(254\) 0 0
\(255\) −0.00204538 + 0.00354269i −0.000128086 + 0.000221852i
\(256\) 0 0
\(257\) 6.30524 + 2.29492i 0.393310 + 0.143153i 0.531102 0.847308i \(-0.321778\pi\)
−0.137792 + 0.990461i \(0.544000\pi\)
\(258\) 0 0
\(259\) 7.22834 + 12.5198i 0.449147 + 0.777946i
\(260\) 0 0
\(261\) −0.869985 0.730004i −0.0538507 0.0451861i
\(262\) 0 0
\(263\) −3.90776 + 22.1620i −0.240963 + 1.36657i 0.588721 + 0.808336i \(0.299632\pi\)
−0.829684 + 0.558233i \(0.811479\pi\)
\(264\) 0 0
\(265\) −2.48436 −0.152613
\(266\) 0 0
\(267\) −5.15229 −0.315315
\(268\) 0 0
\(269\) −4.97959 + 28.2406i −0.303611 + 1.72186i 0.326362 + 0.945245i \(0.394177\pi\)
−0.629973 + 0.776617i \(0.716934\pi\)
\(270\) 0 0
\(271\) 9.15115 + 7.67872i 0.555892 + 0.466449i 0.876931 0.480617i \(-0.159587\pi\)
−0.321038 + 0.947066i \(0.604032\pi\)
\(272\) 0 0
\(273\) −0.430629 0.745871i −0.0260628 0.0451422i
\(274\) 0 0
\(275\) 4.24054 + 1.54343i 0.255714 + 0.0930723i
\(276\) 0 0
\(277\) 13.6617 23.6628i 0.820852 1.42176i −0.0841968 0.996449i \(-0.526832\pi\)
0.905049 0.425308i \(-0.139834\pi\)
\(278\) 0 0
\(279\) −0.893948 5.06983i −0.0535193 0.303523i
\(280\) 0 0
\(281\) −2.31699 + 1.94419i −0.138220 + 0.115980i −0.709276 0.704930i \(-0.750978\pi\)
0.571056 + 0.820911i \(0.306534\pi\)
\(282\) 0 0
\(283\) −13.3558 + 4.86113i −0.793923 + 0.288964i −0.706966 0.707248i \(-0.749936\pi\)
−0.0869569 + 0.996212i \(0.527714\pi\)
\(284\) 0 0
\(285\) 1.30072 1.46734i 0.0770478 0.0869179i
\(286\) 0 0
\(287\) 14.3898 5.23748i 0.849406 0.309158i
\(288\) 0 0
\(289\) −13.0227 + 10.9273i −0.766041 + 0.642784i
\(290\) 0 0
\(291\) −0.653056 3.70367i −0.0382828 0.217113i
\(292\) 0 0
\(293\) −0.0582602 + 0.100910i −0.00340360 + 0.00589520i −0.867722 0.497050i \(-0.834417\pi\)
0.864319 + 0.502945i \(0.167750\pi\)
\(294\) 0 0
\(295\) −8.35638 3.04147i −0.486527 0.177081i
\(296\) 0 0
\(297\) 5.88471 + 10.1926i 0.341465 + 0.591435i
\(298\) 0 0
\(299\) −4.42597 3.71383i −0.255961 0.214776i
\(300\) 0 0
\(301\) 0.508801 2.88555i 0.0293268 0.166320i
\(302\) 0 0
\(303\) −3.98298 −0.228816
\(304\) 0 0
\(305\) 5.80151 0.332194
\(306\) 0 0
\(307\) −0.0503112 + 0.285329i −0.00287141 + 0.0162846i −0.986210 0.165500i \(-0.947076\pi\)
0.983338 + 0.181785i \(0.0581873\pi\)
\(308\) 0 0
\(309\) −5.84952 4.90833i −0.332767 0.279225i
\(310\) 0 0
\(311\) −10.4600 18.1173i −0.593133 1.02734i −0.993807 0.111116i \(-0.964557\pi\)
0.400674 0.916221i \(-0.368776\pi\)
\(312\) 0 0
\(313\) −31.0335 11.2953i −1.75412 0.638446i −0.754280 0.656553i \(-0.772014\pi\)
−0.999836 + 0.0181073i \(0.994236\pi\)
\(314\) 0 0
\(315\) −2.99295 + 5.18394i −0.168633 + 0.292082i
\(316\) 0 0
\(317\) 0.452529 + 2.56642i 0.0254165 + 0.144144i 0.994875 0.101110i \(-0.0322395\pi\)
−0.969459 + 0.245255i \(0.921128\pi\)
\(318\) 0 0
\(319\) −1.40332 + 1.17752i −0.0785706 + 0.0659286i
\(320\) 0 0
\(321\) 3.16001 1.15015i 0.176375 0.0641951i
\(322\) 0 0
\(323\) −0.0348527 + 0.0188800i −0.00193925 + 0.00105051i
\(324\) 0 0
\(325\) 0.840837 0.306040i 0.0466412 0.0169760i
\(326\) 0 0
\(327\) 0.369368 0.309936i 0.0204261 0.0171395i
\(328\) 0 0
\(329\) −0.448711 2.54477i −0.0247382 0.140297i
\(330\) 0 0
\(331\) −9.50939 + 16.4708i −0.522684 + 0.905314i 0.476968 + 0.878921i \(0.341736\pi\)
−0.999652 + 0.0263938i \(0.991598\pi\)
\(332\) 0 0
\(333\) −17.7626 6.46506i −0.973385 0.354283i
\(334\) 0 0
\(335\) 7.81426 + 13.5347i 0.426939 + 0.739480i
\(336\) 0 0
\(337\) 16.5519 + 13.8887i 0.901642 + 0.756568i 0.970511 0.241058i \(-0.0774945\pi\)
−0.0688686 + 0.997626i \(0.521939\pi\)
\(338\) 0 0
\(339\) −1.43432 + 8.13441i −0.0779014 + 0.441801i
\(340\) 0 0
\(341\) −8.30398 −0.449686
\(342\) 0 0
\(343\) −20.1596 −1.08851
\(344\) 0 0
\(345\) 0.504392 2.86055i 0.0271555 0.154007i
\(346\) 0 0
\(347\) 10.7429 + 9.01436i 0.576709 + 0.483916i 0.883865 0.467743i \(-0.154933\pi\)
−0.307155 + 0.951659i \(0.599377\pi\)
\(348\) 0 0
\(349\) −10.0053 17.3296i −0.535570 0.927634i −0.999136 0.0415713i \(-0.986764\pi\)
0.463566 0.886062i \(-0.346570\pi\)
\(350\) 0 0
\(351\) 2.19296 + 0.798174i 0.117052 + 0.0426034i
\(352\) 0 0
\(353\) 6.53402 11.3173i 0.347771 0.602357i −0.638082 0.769968i \(-0.720272\pi\)
0.985853 + 0.167611i \(0.0536053\pi\)
\(354\) 0 0
\(355\) 1.29648 + 7.35270i 0.0688100 + 0.390241i
\(356\) 0 0
\(357\) −0.00670494 + 0.00562612i −0.000354863 + 0.000297766i
\(358\) 0 0
\(359\) −19.9748 + 7.27025i −1.05423 + 0.383709i −0.810258 0.586073i \(-0.800673\pi\)
−0.243973 + 0.969782i \(0.578451\pi\)
\(360\) 0 0
\(361\) 18.1805 5.52006i 0.956866 0.290529i
\(362\) 0 0
\(363\) 3.95851 1.44078i 0.207768 0.0756212i
\(364\) 0 0
\(365\) 8.54436 7.16957i 0.447232 0.375272i
\(366\) 0 0
\(367\) 3.75221 + 21.2799i 0.195864 + 1.11080i 0.911183 + 0.412002i \(0.135170\pi\)
−0.715319 + 0.698798i \(0.753719\pi\)
\(368\) 0 0
\(369\) −10.0114 + 17.3402i −0.521171 + 0.902694i
\(370\) 0 0
\(371\) −4.99503 1.81804i −0.259329 0.0943880i
\(372\) 0 0
\(373\) 9.22242 + 15.9737i 0.477519 + 0.827086i 0.999668 0.0257676i \(-0.00820299\pi\)
−0.522149 + 0.852854i \(0.674870\pi\)
\(374\) 0 0
\(375\) 0.344606 + 0.289159i 0.0177954 + 0.0149321i
\(376\) 0 0
\(377\) −0.0630758 + 0.357721i −0.00324857 + 0.0184235i
\(378\) 0 0
\(379\) −28.0324 −1.43993 −0.719964 0.694012i \(-0.755842\pi\)
−0.719964 + 0.694012i \(0.755842\pi\)
\(380\) 0 0
\(381\) −3.77847 −0.193577
\(382\) 0 0
\(383\) −4.29445 + 24.3550i −0.219436 + 1.24448i 0.653604 + 0.756836i \(0.273256\pi\)
−0.873040 + 0.487648i \(0.837855\pi\)
\(384\) 0 0
\(385\) 7.39651 + 6.20641i 0.376961 + 0.316308i
\(386\) 0 0
\(387\) 1.91558 + 3.31788i 0.0973744 + 0.168657i
\(388\) 0 0
\(389\) −12.0959 4.40256i −0.613289 0.223219i 0.0166528 0.999861i \(-0.494699\pi\)
−0.629942 + 0.776642i \(0.716921\pi\)
\(390\) 0 0
\(391\) −0.0293584 + 0.0508503i −0.00148472 + 0.00257161i
\(392\) 0 0
\(393\) 1.42002 + 8.05333i 0.0716305 + 0.406237i
\(394\) 0 0
\(395\) 5.64412 4.73598i 0.283986 0.238293i
\(396\) 0 0
\(397\) −4.54281 + 1.65345i −0.227997 + 0.0829842i −0.453493 0.891260i \(-0.649822\pi\)
0.225495 + 0.974244i \(0.427600\pi\)
\(398\) 0 0
\(399\) 3.68901 1.99837i 0.184681 0.100044i
\(400\) 0 0
\(401\) −24.8719 + 9.05262i −1.24204 + 0.452066i −0.877705 0.479201i \(-0.840926\pi\)
−0.364336 + 0.931267i \(0.618704\pi\)
\(402\) 0 0
\(403\) −1.26134 + 1.05839i −0.0628316 + 0.0527220i
\(404\) 0 0
\(405\) −1.25368 7.10997i −0.0622959 0.353297i
\(406\) 0 0
\(407\) −15.2453 + 26.4056i −0.755680 + 1.30888i
\(408\) 0 0
\(409\) −9.15328 3.33152i −0.452601 0.164733i 0.105654 0.994403i \(-0.466306\pi\)
−0.558254 + 0.829670i \(0.688529\pi\)
\(410\) 0 0
\(411\) −3.55469 6.15691i −0.175340 0.303698i
\(412\) 0 0
\(413\) −14.5755 12.2303i −0.717215 0.601815i
\(414\) 0 0
\(415\) −0.0263413 + 0.149389i −0.00129304 + 0.00733321i
\(416\) 0 0
\(417\) 2.75447 0.134887
\(418\) 0 0
\(419\) −12.5930 −0.615211 −0.307605 0.951514i \(-0.599528\pi\)
−0.307605 + 0.951514i \(0.599528\pi\)
\(420\) 0 0
\(421\) −0.389772 + 2.21051i −0.0189963 + 0.107734i −0.992832 0.119521i \(-0.961864\pi\)
0.973835 + 0.227255i \(0.0729751\pi\)
\(422\) 0 0
\(423\) 2.58823 + 2.17178i 0.125844 + 0.105596i
\(424\) 0 0
\(425\) −0.00454678 0.00787525i −0.000220551 0.000382006i
\(426\) 0 0
\(427\) 11.6645 + 4.24552i 0.564484 + 0.205455i
\(428\) 0 0
\(429\) 0.908238 1.57312i 0.0438502 0.0759507i
\(430\) 0 0
\(431\) −1.94744 11.0445i −0.0938051 0.531995i −0.995107 0.0988036i \(-0.968498\pi\)
0.901302 0.433192i \(-0.142613\pi\)
\(432\) 0 0
\(433\) 20.4565 17.1651i 0.983078 0.824900i −0.00147297 0.999999i \(-0.500469\pi\)
0.984551 + 0.175099i \(0.0560244\pi\)
\(434\) 0 0
\(435\) −0.171602 + 0.0624579i −0.00822767 + 0.00299463i
\(436\) 0 0
\(437\) 18.6699 21.0616i 0.893103 1.00751i
\(438\) 0 0
\(439\) 2.65088 0.964842i 0.126520 0.0460494i −0.277984 0.960586i \(-0.589666\pi\)
0.404504 + 0.914536i \(0.367444\pi\)
\(440\) 0 0
\(441\) 5.19061 4.35544i 0.247172 0.207402i
\(442\) 0 0
\(443\) 0.321970 + 1.82598i 0.0152973 + 0.0867551i 0.991501 0.130102i \(-0.0415305\pi\)
−0.976203 + 0.216857i \(0.930419\pi\)
\(444\) 0 0
\(445\) 5.72665 9.91886i 0.271469 0.470199i
\(446\) 0 0
\(447\) 3.75517 + 1.36677i 0.177614 + 0.0646460i
\(448\) 0 0
\(449\) −9.89875 17.1451i −0.467151 0.809129i 0.532145 0.846653i \(-0.321386\pi\)
−0.999296 + 0.0375242i \(0.988053\pi\)
\(450\) 0 0
\(451\) 24.7412 + 20.7604i 1.16502 + 0.977567i
\(452\) 0 0
\(453\) −1.12656 + 6.38903i −0.0529303 + 0.300183i
\(454\) 0 0
\(455\) 1.91454 0.0897549
\(456\) 0 0
\(457\) 27.6117 1.29162 0.645811 0.763497i \(-0.276519\pi\)
0.645811 + 0.763497i \(0.276519\pi\)
\(458\) 0 0
\(459\) 0.00411836 0.0233564i 0.000192228 0.00109018i
\(460\) 0 0
\(461\) −27.3590 22.9569i −1.27424 1.06921i −0.994011 0.109278i \(-0.965146\pi\)
−0.280226 0.959934i \(-0.590409\pi\)
\(462\) 0 0
\(463\) −4.24784 7.35747i −0.197414 0.341931i 0.750275 0.661126i \(-0.229921\pi\)
−0.947689 + 0.319195i \(0.896588\pi\)
\(464\) 0 0
\(465\) −0.777868 0.283121i −0.0360728 0.0131294i
\(466\) 0 0
\(467\) 8.09252 14.0167i 0.374477 0.648613i −0.615772 0.787925i \(-0.711156\pi\)
0.990249 + 0.139311i \(0.0444889\pi\)
\(468\) 0 0
\(469\) 5.80666 + 32.9312i 0.268127 + 1.52062i
\(470\) 0 0
\(471\) −4.13372 + 3.46860i −0.190472 + 0.159825i
\(472\) 0 0
\(473\) 5.80711 2.11362i 0.267011 0.0971841i
\(474\) 0 0
\(475\) 1.37912 + 4.13498i 0.0632783 + 0.189726i
\(476\) 0 0
\(477\) 6.53116 2.37715i 0.299041 0.108842i
\(478\) 0 0
\(479\) 7.14947 5.99912i 0.326668 0.274107i −0.464673 0.885482i \(-0.653828\pi\)
0.791340 + 0.611376i \(0.209384\pi\)
\(480\) 0 0
\(481\) 1.04985 + 5.95398i 0.0478689 + 0.271478i
\(482\) 0 0
\(483\) 3.10746 5.38228i 0.141394 0.244902i
\(484\) 0 0
\(485\) 7.85592 + 2.85932i 0.356719 + 0.129835i
\(486\) 0 0
\(487\) −17.1310 29.6718i −0.776281 1.34456i −0.934071 0.357086i \(-0.883770\pi\)
0.157790 0.987473i \(-0.449563\pi\)
\(488\) 0 0
\(489\) −2.09272 1.75600i −0.0946362 0.0794092i
\(490\) 0 0
\(491\) 3.00626 17.0493i 0.135670 0.769425i −0.838720 0.544563i \(-0.816696\pi\)
0.974391 0.224862i \(-0.0721932\pi\)
\(492\) 0 0
\(493\) 0.00369148 0.000166256
\(494\) 0 0
\(495\) −12.6248 −0.567444
\(496\) 0 0
\(497\) −2.77398 + 15.7320i −0.124430 + 0.705678i
\(498\) 0 0
\(499\) 11.3552 + 9.52812i 0.508327 + 0.426537i 0.860540 0.509383i \(-0.170126\pi\)
−0.352213 + 0.935920i \(0.614571\pi\)
\(500\) 0 0
\(501\) 1.86212 + 3.22528i 0.0831933 + 0.144095i
\(502\) 0 0
\(503\) −0.934331 0.340069i −0.0416598 0.0151629i 0.321106 0.947043i \(-0.395945\pi\)
−0.362766 + 0.931880i \(0.618168\pi\)
\(504\) 0 0
\(505\) 4.42700 7.66778i 0.196999 0.341212i
\(506\) 0 0
\(507\) 0.952962 + 5.40451i 0.0423225 + 0.240023i
\(508\) 0 0
\(509\) 8.66391 7.26988i 0.384021 0.322232i −0.430258 0.902706i \(-0.641577\pi\)
0.814279 + 0.580474i \(0.197133\pi\)
\(510\) 0 0
\(511\) 22.4259 8.16235i 0.992063 0.361081i
\(512\) 0 0
\(513\) −4.17669 + 10.5733i −0.184405 + 0.466822i
\(514\) 0 0
\(515\) 15.9508 5.80562i 0.702877 0.255826i
\(516\) 0 0
\(517\) 4.17491 3.50316i 0.183612 0.154069i
\(518\) 0 0
\(519\) 1.64264 + 9.31585i 0.0721037 + 0.408921i
\(520\) 0 0
\(521\) −20.2138 + 35.0113i −0.885582 + 1.53387i −0.0405365 + 0.999178i \(0.512907\pi\)
−0.845045 + 0.534695i \(0.820427\pi\)
\(522\) 0 0
\(523\) −26.2979 9.57167i −1.14993 0.418540i −0.304439 0.952532i \(-0.598469\pi\)
−0.845490 + 0.533992i \(0.820691\pi\)
\(524\) 0 0
\(525\) 0.481257 + 0.833562i 0.0210038 + 0.0363796i
\(526\) 0 0
\(527\) 0.0128186 + 0.0107560i 0.000558385 + 0.000468541i
\(528\) 0 0
\(529\) 3.24591 18.4085i 0.141127 0.800369i
\(530\) 0 0
\(531\) 24.8784 1.07963
\(532\) 0 0
\(533\) 6.40410 0.277392
\(534\) 0 0
\(535\) −1.29809 + 7.36182i −0.0561212 + 0.318279i
\(536\) 0 0
\(537\) −3.65900 3.07027i −0.157898 0.132492i
\(538\) 0 0
\(539\) −5.46485 9.46540i −0.235388 0.407703i
\(540\) 0 0
\(541\) 10.0543 + 3.65946i 0.432268 + 0.157333i 0.548984 0.835833i \(-0.315015\pi\)
−0.116717 + 0.993165i \(0.537237\pi\)
\(542\) 0 0
\(543\) 2.81096 4.86872i 0.120630 0.208937i
\(544\) 0 0
\(545\) 0.186126 + 1.05557i 0.00797274 + 0.0452157i
\(546\) 0 0
\(547\) 21.6218 18.1429i 0.924483 0.775734i −0.0503355 0.998732i \(-0.516029\pi\)
0.974819 + 0.222999i \(0.0715846\pi\)
\(548\) 0 0
\(549\) −15.2517 + 5.55116i −0.650926 + 0.236918i
\(550\) 0 0
\(551\) −1.73361 0.354445i −0.0738542 0.0150999i
\(552\) 0 0
\(553\) 14.8138 5.39178i 0.629946 0.229282i
\(554\) 0 0
\(555\) −2.32838 + 1.95374i −0.0988341 + 0.0829317i
\(556\) 0 0
\(557\) −4.01173 22.7517i −0.169983 0.964019i −0.943777 0.330582i \(-0.892755\pi\)
0.773795 0.633436i \(-0.218356\pi\)
\(558\) 0 0
\(559\) 0.612682 1.06120i 0.0259137 0.0448838i
\(560\) 0 0
\(561\) −0.0173470 0.00631378i −0.000732390 0.000266568i
\(562\) 0 0
\(563\) 17.5328 + 30.3677i 0.738918 + 1.27984i 0.952983 + 0.303025i \(0.0979965\pi\)
−0.214064 + 0.976820i \(0.568670\pi\)
\(564\) 0 0
\(565\) −14.0656 11.8025i −0.591746 0.496534i
\(566\) 0 0
\(567\) 2.68241 15.2127i 0.112651 0.638873i
\(568\) 0 0
\(569\) 19.9610 0.836811 0.418405 0.908260i \(-0.362589\pi\)
0.418405 + 0.908260i \(0.362589\pi\)
\(570\) 0 0
\(571\) −13.1675 −0.551044 −0.275522 0.961295i \(-0.588851\pi\)
−0.275522 + 0.961295i \(0.588851\pi\)
\(572\) 0 0
\(573\) 0.403499 2.28836i 0.0168564 0.0955975i
\(574\) 0 0
\(575\) 4.94633 + 4.15046i 0.206276 + 0.173086i
\(576\) 0 0
\(577\) 9.96695 + 17.2633i 0.414930 + 0.718679i 0.995421 0.0955871i \(-0.0304729\pi\)
−0.580491 + 0.814266i \(0.697140\pi\)
\(578\) 0 0
\(579\) 8.04442 + 2.92793i 0.334315 + 0.121681i
\(580\) 0 0
\(581\) −0.162284 + 0.281084i −0.00673266 + 0.0116613i
\(582\) 0 0
\(583\) −1.94679 11.0408i −0.0806278 0.457263i
\(584\) 0 0
\(585\) −1.91766 + 1.60910i −0.0792853 + 0.0665283i
\(586\) 0 0
\(587\) 17.0954 6.22220i 0.705601 0.256818i 0.0358006 0.999359i \(-0.488602\pi\)
0.669800 + 0.742541i \(0.266380\pi\)
\(588\) 0 0
\(589\) −4.98714 6.28210i −0.205491 0.258849i
\(590\) 0 0
\(591\) 9.53482 3.47039i 0.392210 0.142753i
\(592\) 0 0
\(593\) −3.42900 + 2.87727i −0.140812 + 0.118155i −0.710473 0.703724i \(-0.751519\pi\)
0.569661 + 0.821880i \(0.307075\pi\)
\(594\) 0 0
\(595\) −0.00337864 0.0191612i −0.000138511 0.000785534i
\(596\) 0 0
\(597\) 0.721105 1.24899i 0.0295129 0.0511178i
\(598\) 0 0
\(599\) −13.0414 4.74670i −0.532859 0.193945i 0.0615555 0.998104i \(-0.480394\pi\)
−0.594414 + 0.804159i \(0.702616\pi\)
\(600\) 0 0
\(601\) −11.7807 20.4048i −0.480545 0.832328i 0.519206 0.854649i \(-0.326228\pi\)
−0.999751 + 0.0223210i \(0.992894\pi\)
\(602\) 0 0
\(603\) −33.4937 28.1045i −1.36397 1.14450i
\(604\) 0 0
\(605\) −1.62610 + 9.22206i −0.0661103 + 0.374930i
\(606\) 0 0
\(607\) 39.7548 1.61360 0.806799 0.590826i \(-0.201198\pi\)
0.806799 + 0.590826i \(0.201198\pi\)
\(608\) 0 0
\(609\) −0.390727 −0.0158331
\(610\) 0 0
\(611\) 0.187652 1.06423i 0.00759160 0.0430541i
\(612\) 0 0
\(613\) 30.8058 + 25.8492i 1.24424 + 1.04404i 0.997181 + 0.0750365i \(0.0239073\pi\)
0.247055 + 0.969001i \(0.420537\pi\)
\(614\) 0 0
\(615\) 1.60980 + 2.78825i 0.0649133 + 0.112433i
\(616\) 0 0
\(617\) −1.58432 0.576645i −0.0637823 0.0232149i 0.309932 0.950759i \(-0.399694\pi\)
−0.373714 + 0.927544i \(0.621916\pi\)
\(618\) 0 0
\(619\) 4.54040 7.86421i 0.182494 0.316089i −0.760235 0.649648i \(-0.774916\pi\)
0.942729 + 0.333559i \(0.108250\pi\)
\(620\) 0 0
\(621\) 2.92428 + 16.5844i 0.117347 + 0.665510i
\(622\) 0 0
\(623\) 18.7725 15.7520i 0.752106 0.631092i
\(624\) 0 0
\(625\) −0.939693 + 0.342020i −0.0375877 + 0.0136808i
\(626\) 0 0
\(627\) 7.54033 + 4.63071i 0.301132 + 0.184933i
\(628\) 0 0
\(629\) 0.0577364 0.0210143i 0.00230210 0.000837897i
\(630\) 0 0
\(631\) 5.65759 4.74728i 0.225225 0.188986i −0.523192 0.852215i \(-0.675259\pi\)
0.748417 + 0.663229i \(0.230814\pi\)
\(632\) 0 0
\(633\) −1.01135 5.73567i −0.0401977 0.227972i
\(634\) 0 0
\(635\) 4.19969 7.27407i 0.166660 0.288663i
\(636\) 0 0
\(637\) −2.03650 0.741226i −0.0806891 0.0293684i
\(638\) 0 0
\(639\) −10.4437 18.0891i −0.413148 0.715594i
\(640\) 0 0
\(641\) −1.25431 1.05249i −0.0495424 0.0415710i 0.617680 0.786429i \(-0.288073\pi\)
−0.667223 + 0.744858i \(0.732517\pi\)
\(642\) 0 0
\(643\) −1.84236 + 10.4486i −0.0726557 + 0.412051i 0.926688 + 0.375831i \(0.122643\pi\)
−0.999344 + 0.0362197i \(0.988468\pi\)
\(644\) 0 0
\(645\) 0.616039 0.0242565
\(646\) 0 0
\(647\) −31.6557 −1.24451 −0.622257 0.782813i \(-0.713784\pi\)
−0.622257 + 0.782813i \(0.713784\pi\)
\(648\) 0 0
\(649\) 6.96847 39.5202i 0.273536 1.55130i
\(650\) 0 0
\(651\) −1.35679 1.13848i −0.0531768 0.0446206i
\(652\) 0 0
\(653\) 21.3857 + 37.0410i 0.836885 + 1.44953i 0.892486 + 0.451075i \(0.148959\pi\)
−0.0556007 + 0.998453i \(0.517707\pi\)
\(654\) 0 0
\(655\) −17.0821 6.21737i −0.667452 0.242933i
\(656\) 0 0
\(657\) −15.6022 + 27.0238i −0.608701 + 1.05430i
\(658\) 0 0
\(659\) −4.87136 27.6269i −0.189761 1.07619i −0.919684 0.392660i \(-0.871555\pi\)
0.729922 0.683530i \(-0.239556\pi\)
\(660\) 0 0
\(661\) 28.0335 23.5229i 1.09038 0.914935i 0.0936364 0.995606i \(-0.470151\pi\)
0.996741 + 0.0806714i \(0.0257064\pi\)
\(662\) 0 0
\(663\) −0.00343965 + 0.00125193i −0.000133585 + 4.86210e-5i
\(664\) 0 0
\(665\) −0.253115 + 9.32298i −0.00981539 + 0.361530i
\(666\) 0 0
\(667\) −2.46310 + 0.896494i −0.0953715 + 0.0347124i
\(668\) 0 0
\(669\) −2.96620 + 2.48894i −0.114680 + 0.0962279i
\(670\) 0 0
\(671\) 4.54618 + 25.7827i 0.175503 + 0.995329i
\(672\) 0 0
\(673\) 18.4796 32.0075i 0.712335 1.23380i −0.251644 0.967820i \(-0.580971\pi\)
0.963979 0.265980i \(-0.0856954\pi\)
\(674\) 0 0
\(675\) −2.45079 0.892014i −0.0943309 0.0343336i
\(676\) 0 0
\(677\) 4.75900 + 8.24282i 0.182903 + 0.316797i 0.942868 0.333167i \(-0.108117\pi\)
−0.759965 + 0.649964i \(0.774784\pi\)
\(678\) 0 0
\(679\) 13.7026 + 11.4979i 0.525858 + 0.441247i
\(680\) 0 0
\(681\) −0.624299 + 3.54058i −0.0239232 + 0.135675i
\(682\) 0 0
\(683\) −47.2832 −1.80924 −0.904620 0.426218i \(-0.859846\pi\)
−0.904620 + 0.426218i \(0.859846\pi\)
\(684\) 0 0
\(685\) 15.8039 0.603834
\(686\) 0 0
\(687\) 0.935650 5.30634i 0.0356973 0.202449i
\(688\) 0 0
\(689\) −1.70292 1.42892i −0.0648760 0.0544374i
\(690\) 0 0
\(691\) −22.4880 38.9504i −0.855485 1.48174i −0.876195 0.481958i \(-0.839926\pi\)
0.0207098 0.999786i \(-0.493407\pi\)
\(692\) 0 0
\(693\) −25.3834 9.23880i −0.964236 0.350953i
\(694\) 0 0
\(695\) −3.06153 + 5.30273i −0.116131 + 0.201144i
\(696\) 0 0
\(697\) −0.0113015 0.0640940i −0.000428075 0.00242773i
\(698\) 0 0
\(699\) −8.28882 + 6.95515i −0.313512 + 0.263068i
\(700\) 0 0
\(701\) −37.2174 + 13.5460i −1.40568 + 0.511626i −0.929859 0.367916i \(-0.880071\pi\)
−0.475821 + 0.879542i \(0.657849\pi\)
\(702\) 0 0
\(703\) −29.1322 + 4.32515i −1.09874 + 0.163126i
\(704\) 0 0
\(705\) 0.510520 0.185814i 0.0192273 0.00699817i
\(706\) 0 0
\(707\) 14.5121 12.1771i 0.545785 0.457968i
\(708\) 0 0
\(709\) 2.81747 + 15.9787i 0.105812 + 0.600092i 0.990893 + 0.134654i \(0.0429922\pi\)
−0.885080 + 0.465438i \(0.845897\pi\)
\(710\) 0 0
\(711\) −10.3063 + 17.8510i −0.386516 + 0.669466i
\(712\) 0 0
\(713\) −11.1652 4.06379i −0.418139 0.152190i
\(714\) 0 0
\(715\) 2.01897 + 3.49697i 0.0755054 + 0.130779i
\(716\) 0 0
\(717\) 3.06312 + 2.57026i 0.114394 + 0.0959881i
\(718\) 0 0
\(719\) −3.00667 + 17.0517i −0.112130 + 0.635920i 0.876001 + 0.482309i \(0.160202\pi\)
−0.988131 + 0.153612i \(0.950909\pi\)
\(720\) 0 0
\(721\) 36.3191 1.35259
\(722\) 0 0
\(723\) −10.7277 −0.398968
\(724\) 0 0
\(725\) 0.0704915 0.399777i 0.00261799 0.0148474i
\(726\) 0 0
\(727\) −12.4738 10.4668i −0.462628 0.388191i 0.381469 0.924382i \(-0.375418\pi\)
−0.844097 + 0.536191i \(0.819863\pi\)
\(728\) 0 0
\(729\) 8.33911 + 14.4438i 0.308856 + 0.534954i
\(730\) 0 0
\(731\) −0.0117020 0.00425917i −0.000432813 0.000157531i
\(732\) 0 0
\(733\) −3.13699 + 5.43342i −0.115867 + 0.200688i −0.918126 0.396288i \(-0.870298\pi\)
0.802259 + 0.596976i \(0.203631\pi\)
\(734\) 0 0
\(735\) −0.189196 1.07299i −0.00697861 0.0395777i
\(736\) 0 0
\(737\) −54.0265 + 45.3336i −1.99009 + 1.66989i
\(738\) 0 0
\(739\) 40.7952 14.8482i 1.50068 0.546201i 0.544440 0.838800i \(-0.316742\pi\)
0.956235 + 0.292598i \(0.0945199\pi\)
\(740\) 0 0
\(741\) 1.73555 0.257671i 0.0637570 0.00946579i
\(742\) 0 0
\(743\) 50.4446 18.3603i 1.85063 0.673575i 0.865718 0.500532i \(-0.166862\pi\)
0.984914 0.173043i \(-0.0553599\pi\)
\(744\) 0 0
\(745\) −6.80501 + 5.71008i −0.249316 + 0.209201i
\(746\) 0 0
\(747\) −0.0736932 0.417935i −0.00269629 0.0152914i
\(748\) 0 0
\(749\) −7.99727 + 13.8517i −0.292214 + 0.506129i
\(750\) 0 0
\(751\) 49.2594 + 17.9290i 1.79750 + 0.654237i 0.998607 + 0.0527677i \(0.0168043\pi\)
0.798896 + 0.601470i \(0.205418\pi\)
\(752\) 0 0
\(753\) 0.851680 + 1.47515i 0.0310369 + 0.0537576i
\(754\) 0 0
\(755\) −11.0476 9.27005i −0.402064 0.337372i
\(756\) 0 0
\(757\) 1.15681 6.56062i 0.0420451 0.238450i −0.956542 0.291596i \(-0.905814\pi\)
0.998587 + 0.0531460i \(0.0169249\pi\)
\(758\) 0 0
\(759\) 13.1079 0.475786
\(760\) 0 0
\(761\) 11.7342 0.425364 0.212682 0.977121i \(-0.431780\pi\)
0.212682 + 0.977121i \(0.431780\pi\)
\(762\) 0 0
\(763\) −0.398239 + 2.25853i −0.0144172 + 0.0817642i
\(764\) 0 0
\(765\) 0.0194885 + 0.0163528i 0.000704609 + 0.000591237i
\(766\) 0 0
\(767\) −3.97858 6.89110i −0.143658 0.248823i
\(768\) 0 0
\(769\) 1.95903 + 0.713030i 0.0706446 + 0.0257125i 0.377101 0.926172i \(-0.376921\pi\)
−0.306456 + 0.951885i \(0.599143\pi\)
\(770\) 0 0
\(771\) −1.50923 + 2.61406i −0.0543535 + 0.0941431i
\(772\) 0 0
\(773\) 5.65027 + 32.0443i 0.203226 + 1.15255i 0.900207 + 0.435463i \(0.143415\pi\)
−0.696980 + 0.717090i \(0.745474\pi\)
\(774\) 0 0
\(775\) 1.40963 1.18282i 0.0506354 0.0424882i
\(776\) 0 0
\(777\) −6.11116 + 2.22428i −0.219236 + 0.0797956i
\(778\) 0 0
\(779\) −0.846667 + 31.1852i −0.0303350 + 1.11733i
\(780\) 0 0
\(781\) −31.6604 + 11.5234i −1.13290 + 0.412341i
\(782\) 0 0
\(783\) 0.811037 0.680541i 0.0289841 0.0243205i
\(784\) 0 0
\(785\) −2.08300 11.8133i −0.0743453 0.421633i
\(786\) 0 0
\(787\) −20.4871 +