Properties

Label 403.2.be.c.57.18
Level $403$
Weight $2$
Character 403.57
Analytic conductor $3.218$
Analytic rank $0$
Dimension $136$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [403,2,Mod(57,403)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(403, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([9, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("403.57");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.be (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(136\)
Relative dimension: \(34\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 57.18
Character \(\chi\) \(=\) 403.57
Dual form 403.2.be.c.99.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0740210 - 0.0740210i) q^{2} +(-1.19559 - 0.690275i) q^{3} +1.98904i q^{4} +(2.69078 + 0.720992i) q^{5} +(-0.139594 + 0.0374041i) q^{6} +(-0.0708884 + 0.0189945i) q^{7} +(0.295273 + 0.295273i) q^{8} +(-0.547040 - 0.947500i) q^{9} +O(q^{10})\) \(q+(0.0740210 - 0.0740210i) q^{2} +(-1.19559 - 0.690275i) q^{3} +1.98904i q^{4} +(2.69078 + 0.720992i) q^{5} +(-0.139594 + 0.0374041i) q^{6} +(-0.0708884 + 0.0189945i) q^{7} +(0.295273 + 0.295273i) q^{8} +(-0.547040 - 0.947500i) q^{9} +(0.252543 - 0.145806i) q^{10} +(2.17289 + 0.582225i) q^{11} +(1.37299 - 2.37808i) q^{12} +(-0.881260 + 3.49620i) q^{13} +(-0.00384124 + 0.00665322i) q^{14} +(-2.71939 - 2.71939i) q^{15} -3.93437 q^{16} +(-0.781680 + 1.35391i) q^{17} +(-0.110627 - 0.0296425i) q^{18} +(1.41688 + 5.28786i) q^{19} +(-1.43408 + 5.35207i) q^{20} +(0.0978650 + 0.0262228i) q^{21} +(0.203937 - 0.117743i) q^{22} +7.81062 q^{23} +(-0.149206 - 0.556846i) q^{24} +(2.39034 + 1.38006i) q^{25} +(0.193560 + 0.324024i) q^{26} +5.65208i q^{27} +(-0.0377808 - 0.141000i) q^{28} -5.86541i q^{29} -0.402584 q^{30} +(4.87932 + 2.68183i) q^{31} +(-0.881772 + 0.881772i) q^{32} +(-2.19600 - 2.19600i) q^{33} +(0.0423570 + 0.158078i) q^{34} -0.204440 q^{35} +(1.88462 - 1.08808i) q^{36} +(-0.0140476 - 0.0524265i) q^{37} +(0.496292 + 0.286534i) q^{38} +(3.46697 - 3.57171i) q^{39} +(0.581625 + 1.00740i) q^{40} +(-6.76629 - 1.81302i) q^{41} +(0.00918511 - 0.00530302i) q^{42} +(4.14205 - 7.17424i) q^{43} +(-1.15807 + 4.32197i) q^{44} +(-0.788822 - 2.94393i) q^{45} +(0.578150 - 0.578150i) q^{46} +(8.95916 + 8.95916i) q^{47} +(4.70390 + 2.71580i) q^{48} +(-6.05751 + 3.49731i) q^{49} +(0.279089 - 0.0747816i) q^{50} +(1.86914 - 1.07915i) q^{51} +(-6.95408 - 1.75286i) q^{52} +(-1.63355 + 0.943131i) q^{53} +(0.418373 + 0.418373i) q^{54} +(5.42699 + 3.13328i) q^{55} +(-0.0265400 - 0.0153229i) q^{56} +(1.95607 - 7.30016i) q^{57} +(-0.434163 - 0.434163i) q^{58} +(-1.74192 + 0.466747i) q^{59} +(5.40898 - 5.40898i) q^{60} -9.87311i q^{61} +(0.559684 - 0.162660i) q^{62} +(0.0567760 + 0.0567760i) q^{63} -7.73820i q^{64} +(-4.89201 + 8.77211i) q^{65} -0.325100 q^{66} +(-10.2075 - 2.73509i) q^{67} +(-2.69298 - 1.55479i) q^{68} +(-9.33832 - 5.39148i) q^{69} +(-0.0151328 + 0.0151328i) q^{70} +(-6.07642 - 1.62817i) q^{71} +(0.118245 - 0.441297i) q^{72} +(-0.858544 - 0.230046i) q^{73} +(-0.00492048 - 0.00284084i) q^{74} +(-1.90525 - 3.29998i) q^{75} +(-10.5178 + 2.81823i) q^{76} -0.165092 q^{77} +(-0.00775345 - 0.521010i) q^{78} +(-5.20913 - 3.00749i) q^{79} +(-10.5865 - 2.83665i) q^{80} +(2.26038 - 3.91509i) q^{81} +(-0.635050 + 0.366646i) q^{82} +(3.62924 - 13.5445i) q^{83} +(-0.0521583 + 0.194658i) q^{84} +(-3.07949 + 3.07949i) q^{85} +(-0.224446 - 0.837643i) q^{86} +(-4.04875 + 7.01264i) q^{87} +(0.469681 + 0.813511i) q^{88} +(1.09355 - 1.09355i) q^{89} +(-0.276302 - 0.159523i) q^{90} +(-0.00393735 - 0.264579i) q^{91} +15.5356i q^{92} +(-3.98247 - 6.57445i) q^{93} +1.32633 q^{94} +15.2500i q^{95} +(1.66291 - 0.445574i) q^{96} +(8.85333 - 8.85333i) q^{97} +(-0.189509 + 0.707258i) q^{98} +(-0.637000 - 2.37732i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 136 q - 4 q^{2} - 24 q^{3} + 2 q^{5} - 36 q^{6} - 2 q^{7} - 8 q^{8} + 60 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 136 q - 4 q^{2} - 24 q^{3} + 2 q^{5} - 36 q^{6} - 2 q^{7} - 8 q^{8} + 60 q^{9} - 18 q^{11} - 6 q^{13} + 4 q^{14} - 168 q^{16} - 50 q^{18} - 22 q^{19} + 22 q^{20} - 54 q^{21} + 84 q^{22} + 36 q^{24} + 12 q^{26} + 20 q^{28} + 12 q^{31} + 20 q^{32} - 12 q^{33} + 24 q^{34} - 16 q^{35} + 30 q^{37} - 16 q^{39} + 16 q^{40} + 2 q^{41} - 84 q^{42} - 90 q^{44} - 4 q^{45} - 40 q^{47} + 12 q^{48} + 4 q^{50} + 96 q^{52} + 84 q^{53} - 132 q^{57} + 34 q^{59} - 20 q^{63} + 66 q^{65} - 152 q^{66} + 24 q^{67} - 128 q^{70} - 52 q^{71} + 60 q^{72} + 48 q^{74} + 70 q^{76} + 124 q^{78} + 168 q^{79} + 54 q^{80} - 28 q^{81} - 90 q^{83} - 66 q^{84} - 126 q^{86} + 108 q^{87} - 184 q^{93} + 56 q^{94} + 240 q^{96} + 52 q^{97} - 12 q^{98} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0740210 0.0740210i 0.0523408 0.0523408i −0.680452 0.732793i \(-0.738216\pi\)
0.732793 + 0.680452i \(0.238216\pi\)
\(3\) −1.19559 0.690275i −0.690275 0.398531i 0.113440 0.993545i \(-0.463813\pi\)
−0.803715 + 0.595014i \(0.797146\pi\)
\(4\) 1.98904i 0.994521i
\(5\) 2.69078 + 0.720992i 1.20335 + 0.322438i 0.804151 0.594425i \(-0.202620\pi\)
0.399202 + 0.916863i \(0.369287\pi\)
\(6\) −0.139594 + 0.0374041i −0.0569890 + 0.0152701i
\(7\) −0.0708884 + 0.0189945i −0.0267933 + 0.00717924i −0.272191 0.962243i \(-0.587748\pi\)
0.245398 + 0.969423i \(0.421082\pi\)
\(8\) 0.295273 + 0.295273i 0.104395 + 0.104395i
\(9\) −0.547040 0.947500i −0.182347 0.315833i
\(10\) 0.252543 0.145806i 0.0798611 0.0461078i
\(11\) 2.17289 + 0.582225i 0.655151 + 0.175547i 0.571057 0.820910i \(-0.306534\pi\)
0.0840946 + 0.996458i \(0.473200\pi\)
\(12\) 1.37299 2.37808i 0.396347 0.686493i
\(13\) −0.881260 + 3.49620i −0.244417 + 0.969670i
\(14\) −0.00384124 + 0.00665322i −0.00102661 + 0.00177815i
\(15\) −2.71939 2.71939i −0.702144 0.702144i
\(16\) −3.93437 −0.983593
\(17\) −0.781680 + 1.35391i −0.189585 + 0.328371i −0.945112 0.326747i \(-0.894048\pi\)
0.755527 + 0.655118i \(0.227381\pi\)
\(18\) −0.110627 0.0296425i −0.0260751 0.00698681i
\(19\) 1.41688 + 5.28786i 0.325054 + 1.21312i 0.914257 + 0.405134i \(0.132775\pi\)
−0.589203 + 0.807985i \(0.700558\pi\)
\(20\) −1.43408 + 5.35207i −0.320671 + 1.19676i
\(21\) 0.0978650 + 0.0262228i 0.0213559 + 0.00572229i
\(22\) 0.203937 0.117743i 0.0434794 0.0251029i
\(23\) 7.81062 1.62863 0.814313 0.580425i \(-0.197114\pi\)
0.814313 + 0.580425i \(0.197114\pi\)
\(24\) −0.149206 0.556846i −0.0304566 0.113666i
\(25\) 2.39034 + 1.38006i 0.478067 + 0.276012i
\(26\) 0.193560 + 0.324024i 0.0379603 + 0.0635463i
\(27\) 5.65208i 1.08774i
\(28\) −0.0377808 0.141000i −0.00713990 0.0266465i
\(29\) 5.86541i 1.08918i −0.838703 0.544589i \(-0.816686\pi\)
0.838703 0.544589i \(-0.183314\pi\)
\(30\) −0.402584 −0.0735015
\(31\) 4.87932 + 2.68183i 0.876352 + 0.481672i
\(32\) −0.881772 + 0.881772i −0.155877 + 0.155877i
\(33\) −2.19600 2.19600i −0.382274 0.382274i
\(34\) 0.0423570 + 0.158078i 0.00726416 + 0.0271102i
\(35\) −0.204440 −0.0345566
\(36\) 1.88462 1.08808i 0.314103 0.181347i
\(37\) −0.0140476 0.0524265i −0.00230942 0.00861886i 0.964762 0.263126i \(-0.0847535\pi\)
−0.967071 + 0.254507i \(0.918087\pi\)
\(38\) 0.496292 + 0.286534i 0.0805092 + 0.0464820i
\(39\) 3.46697 3.57171i 0.555159 0.571932i
\(40\) 0.581625 + 1.00740i 0.0919630 + 0.159285i
\(41\) −6.76629 1.81302i −1.05672 0.283147i −0.311692 0.950183i \(-0.600896\pi\)
−0.745025 + 0.667036i \(0.767563\pi\)
\(42\) 0.00918511 0.00530302i 0.00141729 0.000818274i
\(43\) 4.14205 7.17424i 0.631657 1.09406i −0.355556 0.934655i \(-0.615709\pi\)
0.987213 0.159407i \(-0.0509581\pi\)
\(44\) −1.15807 + 4.32197i −0.174585 + 0.651562i
\(45\) −0.788822 2.94393i −0.117591 0.438855i
\(46\) 0.578150 0.578150i 0.0852436 0.0852436i
\(47\) 8.95916 + 8.95916i 1.30683 + 1.30683i 0.923692 + 0.383137i \(0.125156\pi\)
0.383137 + 0.923692i \(0.374844\pi\)
\(48\) 4.70390 + 2.71580i 0.678950 + 0.391992i
\(49\) −6.05751 + 3.49731i −0.865359 + 0.499615i
\(50\) 0.279089 0.0747816i 0.0394691 0.0105757i
\(51\) 1.86914 1.07915i 0.261732 0.151111i
\(52\) −6.95408 1.75286i −0.964357 0.243078i
\(53\) −1.63355 + 0.943131i −0.224385 + 0.129549i −0.607979 0.793953i \(-0.708020\pi\)
0.383594 + 0.923502i \(0.374686\pi\)
\(54\) 0.418373 + 0.418373i 0.0569334 + 0.0569334i
\(55\) 5.42699 + 3.13328i 0.731776 + 0.422491i
\(56\) −0.0265400 0.0153229i −0.00354655 0.00204760i
\(57\) 1.95607 7.30016i 0.259088 0.966930i
\(58\) −0.434163 0.434163i −0.0570085 0.0570085i
\(59\) −1.74192 + 0.466747i −0.226779 + 0.0607653i −0.370419 0.928865i \(-0.620786\pi\)
0.143640 + 0.989630i \(0.454119\pi\)
\(60\) 5.40898 5.40898i 0.698297 0.698297i
\(61\) 9.87311i 1.26412i −0.774919 0.632061i \(-0.782209\pi\)
0.774919 0.632061i \(-0.217791\pi\)
\(62\) 0.559684 0.162660i 0.0710800 0.0206579i
\(63\) 0.0567760 + 0.0567760i 0.00715310 + 0.00715310i
\(64\) 7.73820i 0.967275i
\(65\) −4.89201 + 8.77211i −0.606779 + 1.08805i
\(66\) −0.325100 −0.0400170
\(67\) −10.2075 2.73509i −1.24704 0.334144i −0.425850 0.904794i \(-0.640025\pi\)
−0.821194 + 0.570649i \(0.806692\pi\)
\(68\) −2.69298 1.55479i −0.326572 0.188546i
\(69\) −9.33832 5.39148i −1.12420 0.649058i
\(70\) −0.0151328 + 0.0151328i −0.00180872 + 0.00180872i
\(71\) −6.07642 1.62817i −0.721138 0.193228i −0.120459 0.992718i \(-0.538437\pi\)
−0.600679 + 0.799490i \(0.705103\pi\)
\(72\) 0.118245 0.441297i 0.0139353 0.0520074i
\(73\) −0.858544 0.230046i −0.100485 0.0269249i 0.208226 0.978081i \(-0.433231\pi\)
−0.308711 + 0.951156i \(0.599898\pi\)
\(74\) −0.00492048 0.00284084i −0.000571994 0.000330241i
\(75\) −1.90525 3.29998i −0.219999 0.381049i
\(76\) −10.5178 + 2.81823i −1.20647 + 0.323273i
\(77\) −0.165092 −0.0188140
\(78\) −0.00775345 0.521010i −0.000877905 0.0589928i
\(79\) −5.20913 3.00749i −0.586073 0.338370i 0.177470 0.984126i \(-0.443209\pi\)
−0.763543 + 0.645757i \(0.776542\pi\)
\(80\) −10.5865 2.83665i −1.18361 0.317147i
\(81\) 2.26038 3.91509i 0.251153 0.435010i
\(82\) −0.635050 + 0.366646i −0.0701295 + 0.0404893i
\(83\) 3.62924 13.5445i 0.398361 1.48670i −0.417619 0.908622i \(-0.637135\pi\)
0.815980 0.578080i \(-0.196198\pi\)
\(84\) −0.0521583 + 0.194658i −0.00569094 + 0.0212389i
\(85\) −3.07949 + 3.07949i −0.334017 + 0.334017i
\(86\) −0.224446 0.837643i −0.0242026 0.0903254i
\(87\) −4.04875 + 7.01264i −0.434071 + 0.751833i
\(88\) 0.469681 + 0.813511i 0.0500682 + 0.0867206i
\(89\) 1.09355 1.09355i 0.115916 0.115916i −0.646769 0.762686i \(-0.723880\pi\)
0.762686 + 0.646769i \(0.223880\pi\)
\(90\) −0.276302 0.159523i −0.0291248 0.0168152i
\(91\) −0.00393735 0.264579i −0.000412746 0.0277354i
\(92\) 15.5356i 1.61970i
\(93\) −3.98247 6.57445i −0.412963 0.681739i
\(94\) 1.32633 0.136801
\(95\) 15.2500i 1.56462i
\(96\) 1.66291 0.445574i 0.169720 0.0454762i
\(97\) 8.85333 8.85333i 0.898920 0.898920i −0.0964208 0.995341i \(-0.530739\pi\)
0.995341 + 0.0964208i \(0.0307395\pi\)
\(98\) −0.189509 + 0.707258i −0.0191433 + 0.0714438i
\(99\) −0.637000 2.37732i −0.0640209 0.238929i
\(100\) −2.74500 + 4.75448i −0.274500 + 0.475448i
\(101\) 13.0681i 1.30033i −0.759795 0.650163i \(-0.774701\pi\)
0.759795 0.650163i \(-0.225299\pi\)
\(102\) 0.0584760 0.218235i 0.00578999 0.0216085i
\(103\) 15.3195 8.84469i 1.50947 0.871494i 0.509532 0.860452i \(-0.329818\pi\)
0.999939 0.0110421i \(-0.00351490\pi\)
\(104\) −1.29254 + 0.772120i −0.126744 + 0.0757126i
\(105\) 0.244427 + 0.141120i 0.0238536 + 0.0137719i
\(106\) −0.0511056 + 0.190729i −0.00496381 + 0.0185252i
\(107\) −5.95544 + 10.3151i −0.575734 + 0.997201i 0.420227 + 0.907419i \(0.361950\pi\)
−0.995961 + 0.0897821i \(0.971383\pi\)
\(108\) −11.2422 −1.08178
\(109\) −2.01278 + 2.01278i −0.192789 + 0.192789i −0.796900 0.604111i \(-0.793528\pi\)
0.604111 + 0.796900i \(0.293528\pi\)
\(110\) 0.633640 0.169783i 0.0604152 0.0161882i
\(111\) −0.0193935 + 0.0723774i −0.00184075 + 0.00686976i
\(112\) 0.278901 0.0747313i 0.0263537 0.00706145i
\(113\) 0.343884 + 0.595625i 0.0323499 + 0.0560316i 0.881747 0.471722i \(-0.156368\pi\)
−0.849397 + 0.527754i \(0.823034\pi\)
\(114\) −0.395575 0.685156i −0.0370490 0.0641708i
\(115\) 21.0167 + 5.63140i 1.95981 + 0.525130i
\(116\) 11.6665 1.08321
\(117\) 3.79473 1.07756i 0.350823 0.0996208i
\(118\) −0.0943899 + 0.163488i −0.00868930 + 0.0150503i
\(119\) 0.0296952 0.110824i 0.00272215 0.0101592i
\(120\) 1.60593i 0.146600i
\(121\) −5.14381 2.96978i −0.467619 0.269980i
\(122\) −0.730818 0.730818i −0.0661651 0.0661651i
\(123\) 6.83824 + 6.83824i 0.616584 + 0.616584i
\(124\) −5.33428 + 9.70517i −0.479032 + 0.871550i
\(125\) −4.41208 4.41208i −0.394628 0.394628i
\(126\) 0.00840524 0.000748798
\(127\) −0.315251 + 0.546031i −0.0279740 + 0.0484524i −0.879673 0.475578i \(-0.842239\pi\)
0.851699 + 0.524031i \(0.175572\pi\)
\(128\) −2.33633 2.33633i −0.206505 0.206505i
\(129\) −9.90441 + 5.71831i −0.872034 + 0.503469i
\(130\) 0.287209 + 1.01143i 0.0251899 + 0.0887084i
\(131\) −1.50149 + 2.60066i −0.131186 + 0.227221i −0.924134 0.382069i \(-0.875212\pi\)
0.792948 + 0.609289i \(0.208545\pi\)
\(132\) 4.36793 4.36793i 0.380179 0.380179i
\(133\) −0.200880 0.347935i −0.0174185 0.0301698i
\(134\) −0.958023 + 0.553115i −0.0827606 + 0.0477819i
\(135\) −4.07511 + 15.2085i −0.350730 + 1.30894i
\(136\) −0.630582 + 0.168964i −0.0540719 + 0.0144885i
\(137\) 15.7505 + 4.22034i 1.34566 + 0.360568i 0.858531 0.512762i \(-0.171378\pi\)
0.487128 + 0.873330i \(0.338044\pi\)
\(138\) −1.09031 + 0.292149i −0.0928137 + 0.0248694i
\(139\) 19.3415i 1.64053i −0.571986 0.820263i \(-0.693827\pi\)
0.571986 0.820263i \(-0.306173\pi\)
\(140\) 0.406639i 0.0343673i
\(141\) −4.52722 16.8958i −0.381260 1.42288i
\(142\) −0.570302 + 0.329264i −0.0478587 + 0.0276312i
\(143\) −3.95045 + 7.08376i −0.330353 + 0.592374i
\(144\) 2.15226 + 3.72782i 0.179355 + 0.310651i
\(145\) 4.22891 15.7825i 0.351192 1.31067i
\(146\) −0.0805786 + 0.0465221i −0.00666873 + 0.00385019i
\(147\) 9.65642 0.796448
\(148\) 0.104278 0.0279413i 0.00857163 0.00229676i
\(149\) 1.60877 + 6.00401i 0.131795 + 0.491867i 0.999991 0.00435572i \(-0.00138647\pi\)
−0.868195 + 0.496223i \(0.834720\pi\)
\(150\) −0.385296 0.103240i −0.0314593 0.00842950i
\(151\) 10.0841 10.0841i 0.820635 0.820635i −0.165564 0.986199i \(-0.552944\pi\)
0.986199 + 0.165564i \(0.0529443\pi\)
\(152\) −1.14300 + 1.97973i −0.0927093 + 0.160577i
\(153\) 1.71044 0.138281
\(154\) −0.0122203 + 0.0122203i −0.000984737 + 0.000984737i
\(155\) 11.1956 + 10.7342i 0.899252 + 0.862190i
\(156\) 7.10428 + 6.89594i 0.568798 + 0.552117i
\(157\) 10.8613 0.866825 0.433412 0.901196i \(-0.357309\pi\)
0.433412 + 0.901196i \(0.357309\pi\)
\(158\) −0.608203 + 0.162968i −0.0483861 + 0.0129650i
\(159\) 2.60408 0.206517
\(160\) −3.00840 + 1.73690i −0.237835 + 0.137314i
\(161\) −0.553682 + 0.148359i −0.0436363 + 0.0116923i
\(162\) −0.122483 0.457114i −0.00962320 0.0359143i
\(163\) −9.55496 9.55496i −0.748403 0.748403i 0.225777 0.974179i \(-0.427508\pi\)
−0.974179 + 0.225777i \(0.927508\pi\)
\(164\) 3.60618 13.4584i 0.281595 1.05093i
\(165\) −4.32565 7.49224i −0.336751 0.583270i
\(166\) −0.733938 1.27122i −0.0569646 0.0986656i
\(167\) 1.54657 + 5.77187i 0.119677 + 0.446640i 0.999594 0.0284866i \(-0.00906880\pi\)
−0.879917 + 0.475127i \(0.842402\pi\)
\(168\) 0.0211540 + 0.0366398i 0.00163207 + 0.00282682i
\(169\) −11.4468 6.16211i −0.880520 0.474009i
\(170\) 0.455893i 0.0349654i
\(171\) 4.23516 4.23516i 0.323871 0.323871i
\(172\) 14.2699 + 8.23871i 1.08807 + 0.628196i
\(173\) −10.9624 + 6.32912i −0.833452 + 0.481194i −0.855033 0.518573i \(-0.826463\pi\)
0.0215810 + 0.999767i \(0.493130\pi\)
\(174\) 0.219390 + 0.818775i 0.0166319 + 0.0620712i
\(175\) −0.195661 0.0524271i −0.0147906 0.00396312i
\(176\) −8.54896 2.29069i −0.644402 0.172667i
\(177\) 2.40482 + 0.644368i 0.180757 + 0.0484337i
\(178\) 0.161892i 0.0121343i
\(179\) −9.00517 + 15.5974i −0.673078 + 1.16580i 0.303949 + 0.952688i \(0.401695\pi\)
−0.977027 + 0.213117i \(0.931639\pi\)
\(180\) 5.85559 1.56900i 0.436450 0.116946i
\(181\) 7.72943 + 13.3878i 0.574524 + 0.995105i 0.996093 + 0.0883084i \(0.0281461\pi\)
−0.421569 + 0.906796i \(0.638521\pi\)
\(182\) −0.0198758 0.0192929i −0.00147329 0.00143009i
\(183\) −6.81516 + 11.8042i −0.503791 + 0.872592i
\(184\) 2.30626 + 2.30626i 0.170020 + 0.170020i
\(185\) 0.151196i 0.0111162i
\(186\) −0.781435 0.191861i −0.0572976 0.0140679i
\(187\) −2.48678 + 2.48678i −0.181852 + 0.181852i
\(188\) −17.8202 + 17.8202i −1.29967 + 1.29967i
\(189\) −0.107358 0.400667i −0.00780917 0.0291442i
\(190\) 1.12882 + 1.12882i 0.0818934 + 0.0818934i
\(191\) −11.0220 19.0907i −0.797527 1.38136i −0.921222 0.389037i \(-0.872808\pi\)
0.123695 0.992320i \(-0.460525\pi\)
\(192\) −5.34149 + 9.25173i −0.385489 + 0.667686i
\(193\) 2.67921 0.717893i 0.192854 0.0516750i −0.161099 0.986938i \(-0.551504\pi\)
0.353953 + 0.935263i \(0.384837\pi\)
\(194\) 1.31067i 0.0941003i
\(195\) 11.9040 7.11103i 0.852464 0.509232i
\(196\) −6.95629 12.0486i −0.496878 0.860618i
\(197\) −1.36377 + 5.08966i −0.0971647 + 0.362624i −0.997339 0.0729067i \(-0.976772\pi\)
0.900174 + 0.435530i \(0.143439\pi\)
\(198\) −0.223123 0.128820i −0.0158566 0.00915483i
\(199\) −0.227452 0.393959i −0.0161237 0.0279270i 0.857851 0.513898i \(-0.171799\pi\)
−0.873975 + 0.485972i \(0.838466\pi\)
\(200\) 0.298307 + 1.11330i 0.0210935 + 0.0787220i
\(201\) 10.3160 + 10.3160i 0.727637 + 0.727637i
\(202\) −0.967315 0.967315i −0.0680600 0.0680600i
\(203\) 0.111410 + 0.415789i 0.00781947 + 0.0291827i
\(204\) 2.14647 + 3.71780i 0.150283 + 0.260298i
\(205\) −16.8994 9.75689i −1.18031 0.681451i
\(206\) 0.479269 1.78866i 0.0333922 0.124622i
\(207\) −4.27272 7.40056i −0.296974 0.514375i
\(208\) 3.46720 13.7553i 0.240407 0.953760i
\(209\) 12.3149i 0.851839i
\(210\) 0.0285385 0.00764688i 0.00196935 0.000527685i
\(211\) −10.2458 + 17.7462i −0.705348 + 1.22170i 0.261217 + 0.965280i \(0.415876\pi\)
−0.966566 + 0.256419i \(0.917457\pi\)
\(212\) −1.87593 3.24920i −0.128839 0.223156i
\(213\) 6.14103 + 6.14103i 0.420777 + 0.420777i
\(214\) 0.322708 + 1.20436i 0.0220599 + 0.0823286i
\(215\) 16.3179 16.3179i 1.11287 1.11287i
\(216\) −1.66891 + 1.66891i −0.113555 + 0.113555i
\(217\) −0.396827 0.0974307i −0.0269384 0.00661402i
\(218\) 0.297976i 0.0201815i
\(219\) 0.867674 + 0.867674i 0.0586319 + 0.0586319i
\(220\) −6.23222 + 10.7945i −0.420176 + 0.727766i
\(221\) −4.04467 3.92605i −0.272074 0.264095i
\(222\) 0.00392193 + 0.00679297i 0.000263222 + 0.000455915i
\(223\) 0.997688 0.267330i 0.0668102 0.0179017i −0.225259 0.974299i \(-0.572323\pi\)
0.292069 + 0.956397i \(0.405656\pi\)
\(224\) 0.0457586 0.0792562i 0.00305737 0.00529553i
\(225\) 3.01979i 0.201320i
\(226\) 0.0695434 + 0.0186341i 0.00462596 + 0.00123952i
\(227\) 17.1999 + 4.60869i 1.14160 + 0.305890i 0.779592 0.626287i \(-0.215426\pi\)
0.362003 + 0.932177i \(0.382093\pi\)
\(228\) 14.5203 + 3.89071i 0.961632 + 0.257669i
\(229\) −2.07203 7.73291i −0.136923 0.511005i −0.999983 0.00590222i \(-0.998121\pi\)
0.863059 0.505103i \(-0.168545\pi\)
\(230\) 1.97252 1.13883i 0.130064 0.0750924i
\(231\) 0.197382 + 0.113959i 0.0129868 + 0.00749794i
\(232\) 1.73190 1.73190i 0.113705 0.113705i
\(233\) 13.7114i 0.898266i 0.893465 + 0.449133i \(0.148267\pi\)
−0.893465 + 0.449133i \(0.851733\pi\)
\(234\) 0.201127 0.360652i 0.0131481 0.0235766i
\(235\) 17.6476 + 30.5666i 1.15121 + 1.99395i
\(236\) −0.928380 3.46476i −0.0604324 0.225537i
\(237\) 4.15200 + 7.19147i 0.269701 + 0.467136i
\(238\) −0.00600523 0.0104014i −0.000389262 0.000674221i
\(239\) −0.783614 + 2.92449i −0.0506878 + 0.189169i −0.986628 0.162991i \(-0.947886\pi\)
0.935940 + 0.352160i \(0.114553\pi\)
\(240\) 10.6991 + 10.6991i 0.690624 + 0.690624i
\(241\) 0.485418 + 1.81160i 0.0312685 + 0.116696i 0.979796 0.199999i \(-0.0640937\pi\)
−0.948528 + 0.316694i \(0.897427\pi\)
\(242\) −0.600576 + 0.160924i −0.0386065 + 0.0103446i
\(243\) 9.27957 5.35756i 0.595285 0.343688i
\(244\) 19.6380 1.25720
\(245\) −18.8210 + 5.04306i −1.20243 + 0.322189i
\(246\) 1.01235 0.0645449
\(247\) −19.7360 + 0.293703i −1.25577 + 0.0186879i
\(248\) 0.648858 + 2.23260i 0.0412025 + 0.141771i
\(249\) −13.6885 + 13.6885i −0.867475 + 0.867475i
\(250\) −0.653173 −0.0413103
\(251\) 2.81566 4.87687i 0.177723 0.307825i −0.763377 0.645953i \(-0.776460\pi\)
0.941100 + 0.338128i \(0.109794\pi\)
\(252\) −0.112930 + 0.112930i −0.00711391 + 0.00711391i
\(253\) 16.9716 + 4.54753i 1.06700 + 0.285901i
\(254\) 0.0170826 + 0.0637530i 0.00107185 + 0.00400022i
\(255\) 5.80750 1.55612i 0.363680 0.0974477i
\(256\) 15.1305 0.945658
\(257\) −22.2461 + 12.8438i −1.38768 + 0.801175i −0.993053 0.117668i \(-0.962458\pi\)
−0.394623 + 0.918843i \(0.629125\pi\)
\(258\) −0.309859 + 1.15641i −0.0192910 + 0.0719949i
\(259\) 0.00199163 + 0.00344960i 0.000123754 + 0.000214348i
\(260\) −17.4481 9.73040i −1.08208 0.603454i
\(261\) −5.55748 + 3.20861i −0.343999 + 0.198608i
\(262\) 0.0813615 + 0.303645i 0.00502653 + 0.0187593i
\(263\) 0.515053i 0.0317595i 0.999874 + 0.0158798i \(0.00505490\pi\)
−0.999874 + 0.0158798i \(0.994945\pi\)
\(264\) 1.29684i 0.0798148i
\(265\) −5.07551 + 1.35998i −0.311786 + 0.0835429i
\(266\) −0.0406239 0.0108851i −0.00249081 0.000667410i
\(267\) −2.06229 + 0.552590i −0.126210 + 0.0338179i
\(268\) 5.44021 20.3031i 0.332314 1.24021i
\(269\) −18.6727 + 10.7807i −1.13849 + 0.657309i −0.946057 0.324000i \(-0.894972\pi\)
−0.192436 + 0.981309i \(0.561639\pi\)
\(270\) 0.824106 + 1.42739i 0.0501535 + 0.0868684i
\(271\) 15.6750 15.6750i 0.952191 0.952191i −0.0467172 0.998908i \(-0.514876\pi\)
0.998908 + 0.0467172i \(0.0148759\pi\)
\(272\) 3.07542 5.32678i 0.186475 0.322983i
\(273\) −0.177925 + 0.319046i −0.0107685 + 0.0193095i
\(274\) 1.47826 0.853476i 0.0893052 0.0515604i
\(275\) 4.39044 + 4.39044i 0.264753 + 0.264753i
\(276\) 10.7239 18.5743i 0.645502 1.11804i
\(277\) 30.3293 1.82231 0.911154 0.412065i \(-0.135192\pi\)
0.911154 + 0.412065i \(0.135192\pi\)
\(278\) −1.43168 1.43168i −0.0858664 0.0858664i
\(279\) −0.128143 6.09023i −0.00767170 0.364612i
\(280\) −0.0603655 0.0603655i −0.00360753 0.00360753i
\(281\) 2.93330 + 2.93330i 0.174986 + 0.174986i 0.789166 0.614180i \(-0.210513\pi\)
−0.614180 + 0.789166i \(0.710513\pi\)
\(282\) −1.58575 0.915535i −0.0944302 0.0545193i
\(283\) 9.38211i 0.557708i 0.960333 + 0.278854i \(0.0899546\pi\)
−0.960333 + 0.278854i \(0.910045\pi\)
\(284\) 3.23850 12.0863i 0.192170 0.717187i
\(285\) 10.5267 18.2328i 0.623549 1.08002i
\(286\) 0.231931 + 0.816764i 0.0137144 + 0.0482963i
\(287\) 0.514089 0.0303457
\(288\) 1.31784 + 0.353115i 0.0776547 + 0.0208075i
\(289\) 7.27795 + 12.6058i 0.428115 + 0.741517i
\(290\) −0.855210 1.48127i −0.0502196 0.0869830i
\(291\) −16.6962 + 4.47374i −0.978749 + 0.262255i
\(292\) 0.457572 1.70768i 0.0267774 0.0999344i
\(293\) 28.2983 7.58251i 1.65320 0.442975i 0.692697 0.721229i \(-0.256422\pi\)
0.960507 + 0.278254i \(0.0897558\pi\)
\(294\) 0.714778 0.714778i 0.0416867 0.0416867i
\(295\) −5.02365 −0.292488
\(296\) 0.0113322 0.0196280i 0.000658673 0.00114085i
\(297\) −3.29078 + 12.2814i −0.190951 + 0.712637i
\(298\) 0.563505 + 0.325340i 0.0326430 + 0.0188464i
\(299\) −6.88319 + 27.3075i −0.398065 + 1.57923i
\(300\) 6.56380 3.78961i 0.378961 0.218793i
\(301\) −0.157352 + 0.587246i −0.00906963 + 0.0338483i
\(302\) 1.49288i 0.0859054i
\(303\) −9.02060 + 15.6241i −0.518220 + 0.897583i
\(304\) −5.57453 20.8044i −0.319721 1.19321i
\(305\) 7.11843 26.5664i 0.407600 1.52119i
\(306\) 0.126608 0.126608i 0.00723772 0.00723772i
\(307\) −15.0537 + 4.03361i −0.859157 + 0.230211i −0.661393 0.750039i \(-0.730035\pi\)
−0.197764 + 0.980250i \(0.563368\pi\)
\(308\) 0.328374i 0.0187109i
\(309\) −24.4211 −1.38927
\(310\) 1.62326 0.0341546i 0.0921952 0.00193985i
\(311\) 9.70458i 0.550296i 0.961402 + 0.275148i \(0.0887269\pi\)
−0.961402 + 0.275148i \(0.911273\pi\)
\(312\) 2.07833 0.0309288i 0.117662 0.00175100i
\(313\) −22.0060 12.7052i −1.24385 0.718139i −0.273977 0.961736i \(-0.588339\pi\)
−0.969876 + 0.243597i \(0.921672\pi\)
\(314\) 0.803963 0.803963i 0.0453703 0.0453703i
\(315\) 0.111837 + 0.193707i 0.00630128 + 0.0109141i
\(316\) 5.98203 10.3612i 0.336516 0.582862i
\(317\) −0.661669 2.46938i −0.0371631 0.138694i 0.944852 0.327498i \(-0.106206\pi\)
−0.982015 + 0.188804i \(0.939539\pi\)
\(318\) 0.192757 0.192757i 0.0108093 0.0108093i
\(319\) 3.41498 12.7449i 0.191202 0.713577i
\(320\) 5.57918 20.8218i 0.311886 1.16397i
\(321\) 14.2406 8.22179i 0.794831 0.458896i
\(322\) −0.0300024 + 0.0519658i −0.00167197 + 0.00289594i
\(323\) −8.26683 2.21509i −0.459979 0.123251i
\(324\) 7.78727 + 4.49598i 0.432626 + 0.249777i
\(325\) −6.93147 + 7.14089i −0.384489 + 0.396105i
\(326\) −1.41454 −0.0783439
\(327\) 3.79583 1.01709i 0.209910 0.0562453i
\(328\) −1.46257 2.53324i −0.0807567 0.139875i
\(329\) −0.805275 0.464926i −0.0443963 0.0256322i
\(330\) −0.874772 0.234394i −0.0481546 0.0129030i
\(331\) −3.70770 + 13.8373i −0.203793 + 0.760568i 0.786020 + 0.618200i \(0.212138\pi\)
−0.989814 + 0.142367i \(0.954529\pi\)
\(332\) 26.9406 + 7.21871i 1.47856 + 0.396178i
\(333\) −0.0419895 + 0.0419895i −0.00230101 + 0.00230101i
\(334\) 0.541718 + 0.312761i 0.0296415 + 0.0171135i
\(335\) −25.4941 14.7190i −1.39289 0.804187i
\(336\) −0.385037 0.103170i −0.0210055 0.00562841i
\(337\) −16.3476 −0.890512 −0.445256 0.895403i \(-0.646887\pi\)
−0.445256 + 0.895403i \(0.646887\pi\)
\(338\) −1.30343 + 0.391175i −0.0708971 + 0.0212771i
\(339\) 0.949499i 0.0515697i
\(340\) −6.12522 6.12522i −0.332187 0.332187i
\(341\) 9.04080 + 8.66819i 0.489587 + 0.469409i
\(342\) 0.626982i 0.0339033i
\(343\) 0.726235 0.726235i 0.0392130 0.0392130i
\(344\) 3.34139 0.895324i 0.180156 0.0482726i
\(345\) −21.2401 21.2401i −1.14353 1.14353i
\(346\) −0.342957 + 1.27993i −0.0184375 + 0.0688096i
\(347\) −4.62600 2.67082i −0.248337 0.143377i 0.370666 0.928766i \(-0.379130\pi\)
−0.619002 + 0.785389i \(0.712463\pi\)
\(348\) −13.9484 8.05313i −0.747714 0.431693i
\(349\) −10.6617 10.6617i −0.570707 0.570707i 0.361619 0.932326i \(-0.382224\pi\)
−0.932326 + 0.361619i \(0.882224\pi\)
\(350\) −0.0183637 + 0.0106023i −0.000981581 + 0.000566716i
\(351\) −19.7608 4.98095i −1.05475 0.265864i
\(352\) −2.42938 + 1.40261i −0.129487 + 0.0747591i
\(353\) 32.0152 8.57845i 1.70400 0.456585i 0.730057 0.683386i \(-0.239493\pi\)
0.973941 + 0.226801i \(0.0728268\pi\)
\(354\) 0.225704 0.130310i 0.0119960 0.00692590i
\(355\) −15.1764 8.76210i −0.805480 0.465044i
\(356\) 2.17512 + 2.17512i 0.115281 + 0.115281i
\(357\) −0.112002 + 0.112002i −0.00592780 + 0.00592780i
\(358\) 0.487964 + 1.82111i 0.0257897 + 0.0962485i
\(359\) −2.39109 + 8.92367i −0.126197 + 0.470973i −0.999880 0.0155230i \(-0.995059\pi\)
0.873683 + 0.486496i \(0.161725\pi\)
\(360\) 0.636344 1.10218i 0.0335383 0.0580900i
\(361\) −9.49947 + 5.48452i −0.499972 + 0.288659i
\(362\) 1.56312 + 0.418836i 0.0821556 + 0.0220135i
\(363\) 4.09993 + 7.10129i 0.215191 + 0.372721i
\(364\) 0.526258 0.00783155i 0.0275834 0.000410485i
\(365\) −2.14429 1.23801i −0.112237 0.0648003i
\(366\) 0.369294 + 1.37823i 0.0193033 + 0.0720410i
\(367\) −14.3380 + 8.27805i −0.748438 + 0.432111i −0.825129 0.564944i \(-0.808898\pi\)
0.0766915 + 0.997055i \(0.475564\pi\)
\(368\) −30.7299 −1.60191
\(369\) 1.98359 + 7.40286i 0.103262 + 0.385378i
\(370\) −0.0111917 0.0111917i −0.000581829 0.000581829i
\(371\) 0.0978854 0.0978854i 0.00508196 0.00508196i
\(372\) 13.0769 7.92131i 0.678004 0.410701i
\(373\) 14.3797 0.744555 0.372277 0.928122i \(-0.378577\pi\)
0.372277 + 0.928122i \(0.378577\pi\)
\(374\) 0.368149i 0.0190365i
\(375\) 2.22950 + 8.32060i 0.115131 + 0.429674i
\(376\) 5.29080i 0.272852i
\(377\) 20.5066 + 5.16895i 1.05614 + 0.266214i
\(378\) −0.0376046 0.0217110i −0.00193417 0.00111669i
\(379\) 1.50350 + 5.61113i 0.0772295 + 0.288224i 0.993730 0.111810i \(-0.0356648\pi\)
−0.916500 + 0.400034i \(0.868998\pi\)
\(380\) −30.3330 −1.55605
\(381\) 0.753823 0.435220i 0.0386195 0.0222970i
\(382\) −2.22898 0.597253i −0.114044 0.0305581i
\(383\) 2.84790 10.6285i 0.145521 0.543091i −0.854211 0.519927i \(-0.825959\pi\)
0.999732 0.0231643i \(-0.00737407\pi\)
\(384\) 1.18059 + 4.40602i 0.0602467 + 0.224844i
\(385\) −0.444226 0.119030i −0.0226398 0.00606632i
\(386\) 0.145179 0.251457i 0.00738941 0.0127988i
\(387\) −9.06346 −0.460722
\(388\) 17.6097 + 17.6097i 0.893995 + 0.893995i
\(389\) 3.22126 5.57939i 0.163325 0.282887i −0.772734 0.634729i \(-0.781112\pi\)
0.936059 + 0.351843i \(0.114445\pi\)
\(390\) 0.354781 1.40751i 0.0179651 0.0712722i
\(391\) −6.10540 + 10.5749i −0.308763 + 0.534794i
\(392\) −2.82128 0.755960i −0.142496 0.0381817i
\(393\) 3.59034 2.07289i 0.181109 0.104563i
\(394\) 0.275794 + 0.477690i 0.0138943 + 0.0240657i
\(395\) −11.8482 11.8482i −0.596150 0.596150i
\(396\) 4.72858 1.26702i 0.237620 0.0636701i
\(397\) −29.2245 + 7.83067i −1.46673 + 0.393010i −0.901810 0.432133i \(-0.857761\pi\)
−0.564924 + 0.825143i \(0.691094\pi\)
\(398\) −0.0459975 0.0123250i −0.00230564 0.000617795i
\(399\) 0.554651i 0.0277673i
\(400\) −9.40447 5.42967i −0.470224 0.271484i
\(401\) 7.14528 7.14528i 0.356818 0.356818i −0.505820 0.862639i \(-0.668810\pi\)
0.862639 + 0.505820i \(0.168810\pi\)
\(402\) 1.52721 0.0761702
\(403\) −13.6762 + 14.6957i −0.681258 + 0.732043i
\(404\) 25.9930 1.29320
\(405\) 8.90492 8.90492i 0.442489 0.442489i
\(406\) 0.0390238 + 0.0225304i 0.00193672 + 0.00111817i
\(407\) 0.122096i 0.00605207i
\(408\) 0.870550 + 0.233263i 0.0430986 + 0.0115482i
\(409\) 7.60189 2.03692i 0.375889 0.100719i −0.0659278 0.997824i \(-0.521001\pi\)
0.441817 + 0.897105i \(0.354334\pi\)
\(410\) −1.97313 + 0.528698i −0.0974458 + 0.0261105i
\(411\) −15.9180 15.9180i −0.785178 0.785178i
\(412\) 17.5925 + 30.4710i 0.866719 + 1.50120i
\(413\) 0.114617 0.0661739i 0.00563991 0.00325620i
\(414\) −0.864068 0.231526i −0.0424666 0.0113789i
\(415\) 19.5310 33.8286i 0.958737 1.66058i
\(416\) −2.30578 3.85992i −0.113050 0.189248i
\(417\) −13.3510 + 23.1246i −0.653800 + 1.13241i
\(418\) 0.911561 + 0.911561i 0.0445859 + 0.0445859i
\(419\) 2.54743 0.124450 0.0622252 0.998062i \(-0.480180\pi\)
0.0622252 + 0.998062i \(0.480180\pi\)
\(420\) −0.280693 + 0.486175i −0.0136964 + 0.0237229i
\(421\) −25.3642 6.79631i −1.23617 0.331232i −0.419194 0.907897i \(-0.637687\pi\)
−0.816981 + 0.576665i \(0.804354\pi\)
\(422\) 0.555189 + 2.07199i 0.0270262 + 0.100863i
\(423\) 3.58779 13.3898i 0.174445 0.651036i
\(424\) −0.760824 0.203862i −0.0369489 0.00990043i
\(425\) −3.73696 + 2.15753i −0.181269 + 0.104656i
\(426\) 0.909131 0.0440475
\(427\) 0.187535 + 0.699888i 0.00907543 + 0.0338700i
\(428\) −20.5172 11.8456i −0.991737 0.572580i
\(429\) 9.61288 5.74239i 0.464114 0.277245i
\(430\) 2.41574i 0.116497i
\(431\) −7.71347 28.7871i −0.371545 1.38662i −0.858328 0.513102i \(-0.828496\pi\)
0.486783 0.873523i \(-0.338170\pi\)
\(432\) 22.2374i 1.06990i
\(433\) 0.397520 0.0191036 0.00955180 0.999954i \(-0.496960\pi\)
0.00955180 + 0.999954i \(0.496960\pi\)
\(434\) −0.0365855 + 0.0221616i −0.00175616 + 0.00106379i
\(435\) −15.9503 + 15.9503i −0.764760 + 0.764760i
\(436\) −4.00350 4.00350i −0.191733 0.191733i
\(437\) 11.0667 + 41.3015i 0.529392 + 1.97572i
\(438\) 0.128452 0.00613768
\(439\) 30.7626 17.7608i 1.46822 0.847678i 0.468854 0.883276i \(-0.344667\pi\)
0.999366 + 0.0355980i \(0.0113336\pi\)
\(440\) 0.677273 + 2.52762i 0.0322877 + 0.120499i
\(441\) 6.62740 + 3.82633i 0.315590 + 0.182206i
\(442\) −0.590001 + 0.00878014i −0.0280635 + 0.000417629i
\(443\) −1.68511 2.91870i −0.0800620 0.138671i 0.823214 0.567731i \(-0.192178\pi\)
−0.903276 + 0.429059i \(0.858845\pi\)
\(444\) −0.143962 0.0385744i −0.00683212 0.00183066i
\(445\) 3.73095 2.15406i 0.176864 0.102112i
\(446\) 0.0540619 0.0936379i 0.00255990 0.00443389i
\(447\) 2.22099 8.28884i 0.105049 0.392049i
\(448\) 0.146983 + 0.548548i 0.00694430 + 0.0259165i
\(449\) 16.4205 16.4205i 0.774930 0.774930i −0.204034 0.978964i \(-0.565405\pi\)
0.978964 + 0.204034i \(0.0654053\pi\)
\(450\) −0.223528 0.223528i −0.0105372 0.0105372i
\(451\) −13.6468 7.87900i −0.642604 0.371008i
\(452\) −1.18472 + 0.684000i −0.0557246 + 0.0321726i
\(453\) −19.0173 + 5.09568i −0.893513 + 0.239416i
\(454\) 1.61429 0.932012i 0.0757625 0.0437415i
\(455\) 0.180165 0.714761i 0.00844624 0.0335085i
\(456\) 2.73312 1.57797i 0.127990 0.0738950i
\(457\) −25.6173 25.6173i −1.19833 1.19833i −0.974668 0.223658i \(-0.928200\pi\)
−0.223658 0.974668i \(-0.571800\pi\)
\(458\) −0.725771 0.419024i −0.0339131 0.0195797i
\(459\) −7.65241 4.41812i −0.357184 0.206220i
\(460\) −11.2011 + 41.8030i −0.522253 + 1.94908i
\(461\) −25.0801 25.0801i −1.16809 1.16809i −0.982656 0.185439i \(-0.940629\pi\)
−0.185439 0.982656i \(-0.559371\pi\)
\(462\) 0.0230458 0.00617510i 0.00107219 0.000287292i
\(463\) −5.50498 + 5.50498i −0.255838 + 0.255838i −0.823359 0.567521i \(-0.807903\pi\)
0.567521 + 0.823359i \(0.307903\pi\)
\(464\) 23.0767i 1.07131i
\(465\) −5.97583 20.5617i −0.277122 0.953528i
\(466\) 1.01493 + 1.01493i 0.0470159 + 0.0470159i
\(467\) 16.8310i 0.778847i 0.921059 + 0.389424i \(0.127326\pi\)
−0.921059 + 0.389424i \(0.872674\pi\)
\(468\) 2.14332 + 7.54788i 0.0990749 + 0.348901i
\(469\) 0.775544 0.0358113
\(470\) 3.56887 + 0.956276i 0.164620 + 0.0441097i
\(471\) −12.9857 7.49728i −0.598348 0.345456i
\(472\) −0.652161 0.376525i −0.0300181 0.0173310i
\(473\) 13.1772 13.1772i 0.605890 0.605890i
\(474\) 0.839656 + 0.224985i 0.0385667 + 0.0103339i
\(475\) −3.91076 + 14.5952i −0.179438 + 0.669672i
\(476\) 0.220433 + 0.0590650i 0.0101036 + 0.00270724i
\(477\) 1.78723 + 1.03186i 0.0818318 + 0.0472456i
\(478\) 0.158470 + 0.274477i 0.00724823 + 0.0125543i
\(479\) 30.4161 8.14996i 1.38975 0.372381i 0.515094 0.857134i \(-0.327757\pi\)
0.874651 + 0.484753i \(0.161090\pi\)
\(480\) 4.79577 0.218896
\(481\) 0.195673 0.00291192i 0.00892191 0.000132772i
\(482\) 0.170028 + 0.0981657i 0.00774456 + 0.00447132i
\(483\) 0.764386 + 0.204817i 0.0347808 + 0.00931948i
\(484\) 5.90701 10.2312i 0.268501 0.465057i
\(485\) 30.2056 17.4392i 1.37156 0.791873i
\(486\) 0.290311 1.08346i 0.0131688 0.0491465i
\(487\) −8.06270 + 30.0904i −0.365356 + 1.36353i 0.501582 + 0.865110i \(0.332751\pi\)
−0.866938 + 0.498416i \(0.833915\pi\)
\(488\) 2.91526 2.91526i 0.131968 0.131968i
\(489\) 4.82828 + 18.0194i 0.218343 + 0.814865i
\(490\) −1.01985 + 1.76644i −0.0460723 + 0.0797996i
\(491\) 9.04024 + 15.6582i 0.407980 + 0.706643i 0.994663 0.103174i \(-0.0328999\pi\)
−0.586683 + 0.809817i \(0.699567\pi\)
\(492\) −13.6015 + 13.6015i −0.613205 + 0.613205i
\(493\) 7.94123 + 4.58487i 0.357655 + 0.206492i
\(494\) −1.43914 + 1.48262i −0.0647500 + 0.0667063i
\(495\) 6.85610i 0.308159i
\(496\) −19.1971 10.5513i −0.861973 0.473769i
\(497\) 0.461674 0.0207089
\(498\) 2.02648i 0.0908086i
\(499\) 25.2773 6.77303i 1.13157 0.303203i 0.356012 0.934481i \(-0.384136\pi\)
0.775556 + 0.631279i \(0.217470\pi\)
\(500\) 8.77581 8.77581i 0.392466 0.392466i
\(501\) 2.13511 7.96835i 0.0953899 0.356000i
\(502\) −0.152573 0.569409i −0.00680965 0.0254140i
\(503\) −10.0306 + 17.3735i −0.447242 + 0.774647i −0.998205 0.0598831i \(-0.980927\pi\)
0.550963 + 0.834530i \(0.314261\pi\)
\(504\) 0.0335288i 0.00149349i
\(505\) 9.42201 35.1634i 0.419274 1.56475i
\(506\) 1.59287 0.919644i 0.0708117 0.0408832i
\(507\) 9.43210 + 15.2688i 0.418894 + 0.678111i
\(508\) −1.08608 0.627048i −0.0481869 0.0278207i
\(509\) −8.61339 + 32.1456i −0.381782 + 1.42483i 0.461396 + 0.887194i \(0.347349\pi\)
−0.843178 + 0.537635i \(0.819318\pi\)
\(510\) 0.314692 0.545062i 0.0139348 0.0241358i
\(511\) 0.0652304 0.00288562
\(512\) 5.79264 5.79264i 0.256001 0.256001i
\(513\) −29.8875 + 8.00832i −1.31956 + 0.353576i
\(514\) −0.695970 + 2.59739i −0.0306979 + 0.114566i
\(515\) 47.5982 12.7539i 2.09743 0.562004i
\(516\) −11.3740 19.7003i −0.500711 0.867256i
\(517\) 14.2510 + 24.6835i 0.626760 + 1.08558i
\(518\) 0.000402765 0 0.000107921i 1.76965e−5 0 4.74176e-6i
\(519\) 17.4753 0.767082
\(520\) −4.03464 + 1.14569i −0.176931 + 0.0502418i
\(521\) 10.7797 18.6710i 0.472267 0.817991i −0.527229 0.849723i \(-0.676769\pi\)
0.999496 + 0.0317324i \(0.0101024\pi\)
\(522\) −0.173865 + 0.648875i −0.00760988 + 0.0284005i
\(523\) 4.36762i 0.190982i 0.995430 + 0.0954912i \(0.0304422\pi\)
−0.995430 + 0.0954912i \(0.969558\pi\)
\(524\) −5.17282 2.98653i −0.225976 0.130467i
\(525\) 0.197741 + 0.197741i 0.00863013 + 0.00863013i
\(526\) 0.0381248 + 0.0381248i 0.00166232 + 0.00166232i
\(527\) −7.44502 + 4.50982i −0.324310 + 0.196451i
\(528\) 8.63987 + 8.63987i 0.376002 + 0.376002i
\(529\) 38.0058 1.65243
\(530\) −0.275028 + 0.476362i −0.0119464 + 0.0206918i
\(531\) 1.39514 + 1.39514i 0.0605441 + 0.0605441i
\(532\) 0.692057 0.399559i 0.0300045 0.0173231i
\(533\) 12.3015 22.0585i 0.532839 0.955461i
\(534\) −0.111750 + 0.193556i −0.00483589 + 0.00837600i
\(535\) −23.4619 + 23.4619i −1.01435 + 1.01435i
\(536\) −2.20640 3.82159i −0.0953019 0.165068i
\(537\) 21.5330 12.4321i 0.929218 0.536484i
\(538\) −0.584174 + 2.18017i −0.0251855 + 0.0939937i
\(539\) −15.1985 + 4.07244i −0.654647 + 0.175412i
\(540\) −30.2504 8.10556i −1.30177 0.348808i
\(541\) −2.78903 + 0.747317i −0.119910 + 0.0321297i −0.318275 0.947998i \(-0.603103\pi\)
0.198365 + 0.980128i \(0.436437\pi\)
\(542\) 2.32057i 0.0996768i
\(543\) 21.3417i 0.915862i
\(544\) −0.504576 1.88310i −0.0216335 0.0807373i
\(545\) −6.86714 + 3.96475i −0.294156 + 0.169831i
\(546\) 0.0104459 + 0.0367863i 0.000447045 + 0.00157431i
\(547\) 4.44012 + 7.69051i 0.189846 + 0.328822i 0.945199 0.326496i \(-0.105868\pi\)
−0.755353 + 0.655318i \(0.772535\pi\)
\(548\) −8.39444 + 31.3285i −0.358593 + 1.33829i
\(549\) −9.35477 + 5.40098i −0.399252 + 0.230508i
\(550\) 0.649969 0.0277148
\(551\) 31.0155 8.31057i 1.32130 0.354042i
\(552\) −1.16539 4.34931i −0.0496025 0.185119i
\(553\) 0.426393 + 0.114252i 0.0181321 + 0.00485847i
\(554\) 2.24500 2.24500i 0.0953810 0.0953810i
\(555\) −0.104367 + 0.180769i −0.00443014 + 0.00767322i
\(556\) 38.4711 1.63154
\(557\) −13.4959 + 13.4959i −0.571839 + 0.571839i −0.932642 0.360803i \(-0.882503\pi\)
0.360803 + 0.932642i \(0.382503\pi\)
\(558\) −0.460290 0.441320i −0.0194856 0.0186825i
\(559\) 21.4323 + 20.8038i 0.906491 + 0.879906i
\(560\) 0.804342 0.0339896
\(561\) 4.68975 1.25661i 0.198001 0.0530543i
\(562\) 0.434251 0.0183178
\(563\) 11.3522 6.55420i 0.478439 0.276227i −0.241327 0.970444i \(-0.577583\pi\)
0.719766 + 0.694217i \(0.244249\pi\)
\(564\) 33.6065 9.00482i 1.41509 0.379171i
\(565\) 0.495875 + 1.85063i 0.0208616 + 0.0778567i
\(566\) 0.694473 + 0.694473i 0.0291909 + 0.0291909i
\(567\) −0.0858693 + 0.320469i −0.00360617 + 0.0134584i
\(568\) −1.31345 2.27496i −0.0551110 0.0954551i
\(569\) 4.27750 + 7.40885i 0.179322 + 0.310595i 0.941649 0.336598i \(-0.109276\pi\)
−0.762326 + 0.647193i \(0.775943\pi\)
\(570\) −0.570413 2.12881i −0.0238920 0.0891661i
\(571\) −10.7297 18.5843i −0.449023 0.777730i 0.549300 0.835625i \(-0.314894\pi\)
−0.998323 + 0.0578953i \(0.981561\pi\)
\(572\) −14.0899 7.85762i −0.589128 0.328543i
\(573\) 30.4330i 1.27136i
\(574\) 0.0380534 0.0380534i 0.00158832 0.00158832i
\(575\) 18.6700 + 10.7791i 0.778593 + 0.449521i
\(576\) −7.33195 + 4.23310i −0.305498 + 0.176379i
\(577\) 1.25849 + 4.69676i 0.0523917 + 0.195529i 0.987161 0.159726i \(-0.0510609\pi\)
−0.934770 + 0.355254i \(0.884394\pi\)
\(578\) 1.47181 + 0.394372i 0.0612194 + 0.0164037i
\(579\) −3.69879 0.991087i −0.153716 0.0411882i
\(580\) 31.3921 + 8.41148i 1.30349 + 0.349268i
\(581\) 1.02908i 0.0426936i
\(582\) −0.904720 + 1.56702i −0.0375019 + 0.0649551i
\(583\) −4.09864 + 1.09823i −0.169748 + 0.0454840i
\(584\) −0.185578 0.321431i −0.00767929 0.0133009i
\(585\) 10.9877 0.163514i 0.454285 0.00676048i
\(586\) 1.53340 2.65593i 0.0633443 0.109716i
\(587\) 8.77043 + 8.77043i 0.361994 + 0.361994i 0.864547 0.502552i \(-0.167606\pi\)
−0.502552 + 0.864547i \(0.667606\pi\)
\(588\) 19.2070i 0.792084i
\(589\) −7.26777 + 29.6010i −0.299463 + 1.21969i
\(590\) −0.371856 + 0.371856i −0.0153091 + 0.0153091i
\(591\) 5.14379 5.14379i 0.211587 0.211587i
\(592\) 0.0552686 + 0.206265i 0.00227152 + 0.00847744i
\(593\) −27.1573 27.1573i −1.11522 1.11522i −0.992433 0.122785i \(-0.960817\pi\)
−0.122785 0.992433i \(-0.539183\pi\)
\(594\) 0.665492 + 1.15267i 0.0273055 + 0.0472945i
\(595\) 0.159806 0.276793i 0.00655142 0.0113474i
\(596\) −11.9422 + 3.19991i −0.489172 + 0.131073i
\(597\) 0.628018i 0.0257031i
\(598\) 1.51183 + 2.53083i 0.0618231 + 0.103493i
\(599\) 21.2662 + 36.8342i 0.868915 + 1.50500i 0.863107 + 0.505021i \(0.168515\pi\)
0.00580785 + 0.999983i \(0.498151\pi\)
\(600\) 0.411828 1.53696i 0.0168128 0.0627462i
\(601\) −30.9867 17.8902i −1.26397 0.729756i −0.290133 0.956986i \(-0.593699\pi\)
−0.973841 + 0.227231i \(0.927033\pi\)
\(602\) 0.0318212 + 0.0551159i 0.00129694 + 0.00224636i
\(603\) 2.99240 + 11.1678i 0.121860 + 0.454788i
\(604\) 20.0578 + 20.0578i 0.816139 + 0.816139i
\(605\) −11.6997 11.6997i −0.475659 0.475659i
\(606\) 0.488800 + 1.82423i 0.0198562 + 0.0741042i
\(607\) −2.13933 3.70543i −0.0868327 0.150399i 0.819338 0.573311i \(-0.194341\pi\)
−0.906171 + 0.422912i \(0.861008\pi\)
\(608\) −5.91205 3.41333i −0.239765 0.138429i
\(609\) 0.153808 0.574018i 0.00623260 0.0232604i
\(610\) −1.43956 2.49338i −0.0582859 0.100954i
\(611\) −39.2183 + 23.4276i −1.58660 + 0.947781i
\(612\) 3.40213i 0.137523i
\(613\) −5.93378 + 1.58995i −0.239663 + 0.0642175i −0.376651 0.926355i \(-0.622924\pi\)
0.136988 + 0.990573i \(0.456258\pi\)
\(614\) −0.815714 + 1.41286i −0.0329196 + 0.0570183i
\(615\) 13.4699 + 23.3305i 0.543158 + 0.940777i
\(616\) −0.0487471 0.0487471i −0.00196408 0.00196408i
\(617\) 2.67037 + 9.96597i 0.107505 + 0.401215i 0.998617 0.0525684i \(-0.0167408\pi\)
−0.891112 + 0.453783i \(0.850074\pi\)
\(618\) −1.80768 + 1.80768i −0.0727154 + 0.0727154i
\(619\) −31.1553 + 31.1553i −1.25224 + 1.25224i −0.297520 + 0.954715i \(0.596160\pi\)
−0.954715 + 0.297520i \(0.903840\pi\)
\(620\) −21.3507 + 22.2685i −0.857466 + 0.894325i
\(621\) 44.1463i 1.77153i
\(622\) 0.718343 + 0.718343i 0.0288029 + 0.0288029i
\(623\) −0.0567486 + 0.0982915i −0.00227359 + 0.00393797i
\(624\) −13.6403 + 14.0524i −0.546050 + 0.562548i
\(625\) −15.5912 27.0047i −0.623647 1.08019i
\(626\) −2.56936 + 0.688457i −0.102692 + 0.0275163i
\(627\) 8.50067 14.7236i 0.339484 0.588004i
\(628\) 21.6035i 0.862075i
\(629\) 0.0819614 + 0.0219615i 0.00326801 + 0.000875662i
\(630\) 0.0226166 + 0.00606011i 0.000901068 + 0.000241441i
\(631\) 24.4391 + 6.54844i 0.972905 + 0.260689i 0.710054 0.704147i \(-0.248670\pi\)
0.262851 + 0.964836i \(0.415337\pi\)
\(632\) −0.650084 2.42615i −0.0258590 0.0965070i
\(633\) 24.4995 14.1448i 0.973769 0.562206i
\(634\) −0.231764 0.133809i −0.00920451 0.00531423i
\(635\) −1.24196 + 1.24196i −0.0492855 + 0.0492855i
\(636\) 5.17962i 0.205385i
\(637\) −6.88903 24.2603i −0.272953 0.961228i
\(638\) −0.690610 1.19617i −0.0273415 0.0473569i
\(639\) 1.78135 + 6.64808i 0.0704691 + 0.262994i
\(640\) −4.60208 7.97104i −0.181913 0.315083i
\(641\) 7.72876 + 13.3866i 0.305268 + 0.528739i 0.977321 0.211764i \(-0.0679207\pi\)
−0.672053 + 0.740503i \(0.734587\pi\)
\(642\) 0.445515 1.66269i 0.0175831 0.0656210i
\(643\) −27.7763 27.7763i −1.09539 1.09539i −0.994942 0.100446i \(-0.967973\pi\)
−0.100446 0.994942i \(-0.532027\pi\)
\(644\) −0.295092 1.10130i −0.0116282 0.0433972i
\(645\) −30.7734 + 8.24571i −1.21170 + 0.324675i
\(646\) −0.775882 + 0.447956i −0.0305267 + 0.0176246i
\(647\) 26.3638 1.03647 0.518233 0.855239i \(-0.326590\pi\)
0.518233 + 0.855239i \(0.326590\pi\)
\(648\) 1.82345 0.488591i 0.0716318 0.0191937i
\(649\) −4.05676 −0.159242
\(650\) 0.0155014 + 1.04165i 0.000608015 + 0.0408569i
\(651\) 0.407189 + 0.390407i 0.0159590 + 0.0153013i
\(652\) 19.0052 19.0052i 0.744302 0.744302i
\(653\) 1.04052 0.0407187 0.0203593 0.999793i \(-0.493519\pi\)
0.0203593 + 0.999793i \(0.493519\pi\)
\(654\) 0.205685 0.356258i 0.00804294 0.0139308i
\(655\) −5.91524 + 5.91524i −0.231127 + 0.231127i
\(656\) 26.6211 + 7.13310i 1.03938 + 0.278501i
\(657\) 0.251689 + 0.939315i 0.00981932 + 0.0366462i
\(658\) −0.0940216 + 0.0251930i −0.00366534 + 0.000982126i
\(659\) 6.41205 0.249778 0.124889 0.992171i \(-0.460142\pi\)
0.124889 + 0.992171i \(0.460142\pi\)
\(660\) 14.9024 8.60389i 0.580074 0.334906i
\(661\) 3.95603 14.7641i 0.153872 0.574258i −0.845327 0.534249i \(-0.820595\pi\)
0.999199 0.0400090i \(-0.0127387\pi\)
\(662\) 0.749805 + 1.29870i 0.0291420 + 0.0504754i
\(663\) 2.12572 + 7.48589i 0.0825560 + 0.290728i
\(664\) 5.07094 2.92771i 0.196791 0.113617i
\(665\) −0.289666 1.08105i −0.0112328 0.0419213i
\(666\) 0.00621621i 0.000240873i
\(667\) 45.8125i 1.77387i
\(668\) −11.4805 + 3.07619i −0.444193 + 0.119021i
\(669\) −1.37736 0.369062i −0.0532518 0.0142688i
\(670\) −2.97662 + 0.797583i −0.114997 + 0.0308133i
\(671\) 5.74837 21.4532i 0.221913 0.828191i
\(672\) −0.109417 + 0.0631720i −0.00422086 + 0.00243691i
\(673\) 4.75908 + 8.24296i 0.183449 + 0.317743i 0.943053 0.332643i \(-0.107940\pi\)
−0.759604 + 0.650386i \(0.774607\pi\)
\(674\) −1.21007 + 1.21007i −0.0466101 + 0.0466101i
\(675\) −7.80023 + 13.5104i −0.300231 + 0.520015i
\(676\) 12.2567 22.7681i 0.471412 0.875696i
\(677\) −8.99547 + 5.19354i −0.345724 + 0.199604i −0.662800 0.748796i \(-0.730632\pi\)
0.317076 + 0.948400i \(0.397299\pi\)
\(678\) −0.0702829 0.0702829i −0.00269920 0.00269920i
\(679\) −0.459434 + 0.795763i −0.0176315 + 0.0305386i
\(680\) −1.81858 −0.0697393
\(681\) −17.3828 17.3828i −0.666109 0.666109i
\(682\) 1.31084 0.0275810i 0.0501946 0.00105613i
\(683\) 8.76225 + 8.76225i 0.335278 + 0.335278i 0.854587 0.519309i \(-0.173810\pi\)
−0.519309 + 0.854587i \(0.673810\pi\)
\(684\) 8.42392 + 8.42392i 0.322097 + 0.322097i
\(685\) 39.3384 + 22.7120i 1.50304 + 0.867782i
\(686\) 0.107513i 0.00410488i
\(687\) −2.86054 + 10.6757i −0.109136 + 0.407302i
\(688\) −16.2964 + 28.2261i −0.621293 + 1.07611i
\(689\) −1.85779 6.54236i −0.0707761 0.249244i
\(690\) −3.14443 −0.119707
\(691\) 16.6079 + 4.45008i 0.631795 + 0.169289i 0.560484 0.828165i \(-0.310615\pi\)
0.0713107 + 0.997454i \(0.477282\pi\)
\(692\) −12.5889 21.8046i −0.478557 0.828886i
\(693\) 0.0903117 + 0.156424i 0.00343066 + 0.00594208i
\(694\) −0.540118 + 0.144724i −0.0205026 + 0.00549365i
\(695\) 13.9451 52.0438i 0.528967 1.97413i
\(696\) −3.26613 + 0.875156i −0.123802 + 0.0331727i
\(697\) 7.74374 7.74374i 0.293315 0.293315i
\(698\) −1.57838 −0.0597425
\(699\) 9.46467 16.3933i 0.357987 0.620051i
\(700\) 0.104280 0.389177i 0.00394140 0.0147095i
\(701\) −19.0812 11.0166i −0.720688 0.416090i 0.0943176 0.995542i \(-0.469933\pi\)
−0.815006 + 0.579452i \(0.803266\pi\)
\(702\) −1.83141 + 1.09402i −0.0691221 + 0.0412911i
\(703\) 0.257320 0.148564i 0.00970501 0.00560319i
\(704\) 4.50537 16.8143i 0.169803 0.633712i
\(705\) 48.7270i 1.83516i
\(706\) 1.73481 3.00478i 0.0652906 0.113087i
\(707\) 0.248222 + 0.926377i 0.00933535 + 0.0348400i
\(708\) −1.28168 + 4.78328i −0.0481683 + 0.179767i
\(709\) −16.2336 + 16.2336i −0.609667 + 0.609667i −0.942859 0.333192i \(-0.891874\pi\)
0.333192 + 0.942859i \(0.391874\pi\)
\(710\) −1.77195 + 0.474793i −0.0665002 + 0.0178187i
\(711\) 6.58087i 0.246802i
\(712\) 0.645792 0.0242021
\(713\) 38.1105 + 20.9468i 1.42725 + 0.784463i
\(714\) 0.0165811i 0.000620531i
\(715\) −15.7371 + 16.2126i −0.588535 + 0.606317i
\(716\) −31.0239 17.9117i −1.15942 0.669390i
\(717\) 2.95558 2.95558i 0.110378 0.110378i
\(718\) 0.483548 + 0.837530i 0.0180459 + 0.0312564i
\(719\) −10.2716 + 17.7910i −0.383068 + 0.663493i −0.991499 0.130114i \(-0.958466\pi\)
0.608431 + 0.793607i \(0.291799\pi\)
\(720\) 3.10352 + 11.5825i 0.115661 + 0.431654i
\(721\) −0.917971 + 0.917971i −0.0341870 + 0.0341870i
\(722\) −0.297191 + 1.10913i −0.0110603 + 0.0412776i
\(723\) 0.670144 2.50101i 0.0249229 0.0930136i
\(724\) −26.6288 + 15.3742i −0.989652 + 0.571376i
\(725\) 8.09462 14.0203i 0.300627 0.520701i
\(726\) 0.829126 + 0.222164i 0.0307717 + 0.00824526i
\(727\) −6.93691 4.00503i −0.257276 0.148538i 0.365815 0.930687i \(-0.380790\pi\)
−0.623091 + 0.782149i \(0.714123\pi\)
\(728\) 0.0769603 0.0792855i 0.00285234 0.00293852i
\(729\) −28.3550 −1.05019
\(730\) −0.250361 + 0.0670841i −0.00926629 + 0.00248289i
\(731\) 6.47551 + 11.2159i 0.239505 + 0.414836i
\(732\) −23.4791 13.5556i −0.867811 0.501031i
\(733\) −32.3064 8.65648i −1.19327 0.319735i −0.393090 0.919500i \(-0.628594\pi\)
−0.800176 + 0.599766i \(0.795261\pi\)
\(734\) −0.448564 + 1.67406i −0.0165568 + 0.0617908i
\(735\) 25.9833 + 6.96220i 0.958408 + 0.256805i
\(736\) −6.88719 + 6.88719i −0.253865 + 0.253865i
\(737\) −20.5873 11.8861i −0.758344 0.437830i
\(738\) 0.694795 + 0.401140i 0.0255757 + 0.0147662i
\(739\) −8.15266 2.18450i −0.299900 0.0803581i 0.105731 0.994395i \(-0.466282\pi\)
−0.405632 + 0.914037i \(0.632948\pi\)
\(740\) 0.300736 0.0110553
\(741\) 23.7990 + 13.2722i 0.874278 + 0.487565i
\(742\) 0.0144912i 0.000531987i
\(743\) −17.6525 17.6525i −0.647608 0.647608i 0.304806 0.952414i \(-0.401408\pi\)
−0.952414 + 0.304806i \(0.901408\pi\)
\(744\) 0.765342 3.11718i 0.0280588 0.114281i
\(745\) 17.3154i 0.634386i
\(746\) 1.06440 1.06440i 0.0389706 0.0389706i
\(747\) −14.8188 + 3.97067i −0.542190 + 0.145279i
\(748\) −4.94632 4.94632i −0.180855 0.180855i
\(749\) 0.226241 0.844343i 0.00826667 0.0308516i
\(750\) 0.780929 + 0.450870i 0.0285155 + 0.0164634i
\(751\) −0.856850 0.494703i −0.0312669 0.0180520i 0.484285 0.874910i \(-0.339080\pi\)
−0.515552 + 0.856858i \(0.672413\pi\)
\(752\) −35.2487 35.2487i −1.28539 1.28539i
\(753\) −6.73277 + 3.88717i −0.245356 + 0.141656i
\(754\) 1.90053 1.13531i 0.0692133 0.0413455i
\(755\) 34.4048 19.8636i 1.25212 0.722911i
\(756\) 0.796943 0.213540i 0.0289845 0.00776639i
\(757\) −8.49539 + 4.90482i −0.308770 + 0.178269i −0.646376 0.763019i \(-0.723716\pi\)
0.337606 + 0.941288i \(0.390383\pi\)
\(758\) 0.526632 + 0.304051i 0.0191281 + 0.0110436i
\(759\) −17.1521 17.1521i −0.622582 0.622582i
\(760\) −4.50292 + 4.50292i −0.163338 + 0.163338i
\(761\) 11.3085 + 42.2037i 0.409931 + 1.52988i 0.794776 + 0.606903i \(0.207588\pi\)
−0.384845 + 0.922981i \(0.625745\pi\)
\(762\) 0.0235833 0.0880142i 0.000854334 0.00318842i
\(763\) 0.104451 0.180914i 0.00378138 0.00654954i
\(764\) 37.9723 21.9233i 1.37379 0.793157i
\(765\) 4.60241 + 1.23321i 0.166401 + 0.0445869i
\(766\) −0.575928 0.997537i −0.0208091 0.0360425i
\(767\) −0.0967516 6.50143i −0.00349350 0.234753i
\(768\) −18.0899 10.4442i −0.652765 0.376874i
\(769\) 0.328810 + 1.22713i 0.0118572 + 0.0442516i 0.971601 0.236625i \(-0.0760414\pi\)
−0.959744 + 0.280877i \(0.909375\pi\)
\(770\) −0.0416927 + 0.0240713i −0.00150250 + 0.000867470i
\(771\) 35.4631 1.27717
\(772\) 1.42792 + 5.32906i 0.0513919 + 0.191797i
\(773\) 4.60675 + 4.60675i 0.165693 + 0.165693i 0.785083 0.619390i \(-0.212620\pi\)
−0.619390 + 0.785083i \(0.712620\pi\)
\(774\) −0.670887 + 0.670887i −0.0241145 + 0.0241145i
\(775\) 7.96212 + 13.1443i 0.286008 + 0.472155i
\(776\) 5.22830 0.187685
\(777\) 0.00549908i 0.000197279i
\(778\) −0.174551 0.651434i −0.00625796 0.0233550i
\(779\) 38.3481i 1.37396i
\(780\) 14.1441 + 23.6776i 0.506442 + 0.847793i
\(781\) −12.2554 7.07568i −0.438534 0.253188i
\(782\) 0.330834 + 1.23469i 0.0118306 + 0.0441524i
\(783\) 33.1518 1.18475
\(784\) 23.8325 13.7597i 0.851161 0.491418i
\(785\) 29.2253 + 7.83090i 1.04310 + 0.279497i
\(786\) 0.112324 0.419198i 0.00400646 0.0149523i
\(787\) 2.51165 + 9.37360i 0.0895306 + 0.334133i 0.996134 0.0878520i \(-0.0280002\pi\)
−0.906603 + 0.421985i \(0.861334\pi\)
\(788\) −10.1236 2.71260i −0.360637 0.0966323i
\(789\) 0.355528 0.615793i 0.0126571 0.0219228i
\(790\) −1.75404 −0.0624059
\(791\) −0.0356909 0.0356909i −0.00126902 0.00126902i
\(792\) 0.513868 0.890046i 0.0182595 0.0316264i
\(793\) 34.5183 + 8.70077i 1.22578 + 0.308974i
\(794\) −1.58359 + 2.74286i −0.0561995 + 0.0973404i
\(795\) 7.00701 + 1.87752i 0.248513 + 0.0665888i
\(796\) 0.783600 0.452412i 0.0277740 0.0160353i
\(797\) −12.1691 21.0775i −0.431051 0.746602i 0.565913 0.824465i \(-0.308524\pi\)
−0.996964 + 0.0778631i \(0.975190\pi\)
\(798\) 0.0410559 + 0.0410559i 0.00145336 + 0.00145336i
\(799\) −19.1331 + 5.12670i −0.676880 + 0.181369i
\(800\) −3.32463 + 0.890833i −0.117544 + 0.0314957i
\(801\) −1.63436 0.437924i −0.0577471 0.0154733i
\(802\) 1.05780i 0.0373523i
\(803\) −1.73159 0.999731i −0.0611063 0.0352797i
\(804\) −20.5190 + 20.5190i −0.723650 + 0.723650i
\(805\) −1.59680 −0.0562799
\(806\) 0.0754644 + 2.10011i 0.00265812 + 0.0739733i
\(807\) 29.7665 1.04783
\(808\) 3.85866 3.85866i 0.135747 0.135747i
\(809\) 6.97672 + 4.02801i 0.245289 + 0.141617i 0.617605 0.786488i \(-0.288103\pi\)
−0.372316 + 0.928106i \(0.621436\pi\)
\(810\) 1.31830i 0.0463204i
\(811\) 32.3110 + 8.65770i 1.13459 + 0.304013i 0.776774 0.629779i \(-0.216855\pi\)
0.357817 + 0.933792i \(0.383521\pi\)
\(812\) −0.827022 + 0.221600i −0.0290228 + 0.00777663i
\(813\) −29.5611 + 7.92086i −1.03675 + 0.277797i
\(814\) −0.00903766 0.00903766i −0.000316770 0.000316770i
\(815\) −18.8212 32.5994i −0.659280 1.14191i
\(816\) −7.35389 + 4.24577i −0.257438 + 0.148632i
\(817\) 43.8052 + 11.7376i 1.53255 + 0.410645i
\(818\) 0.411925 0.713474i 0.0144026 0.0249461i
\(819\) −0.248534 + 0.148466i −0.00868450 + 0.00518781i
\(820\) 19.4069 33.6137i 0.677717 1.17384i
\(821\) −8.61692 8.61692i −0.300733 0.300733i 0.540568 0.841300i \(-0.318209\pi\)
−0.841300 + 0.540568i \(0.818209\pi\)
\(822\) −2.35654 −0.0821936
\(823\) −4.14424 + 7.17804i −0.144459 + 0.250211i −0.929171 0.369650i \(-0.879478\pi\)
0.784712 + 0.619861i \(0.212811\pi\)
\(824\) 7.13502 + 1.91182i 0.248560 + 0.0666015i
\(825\) −2.21856 8.27978i −0.0772404 0.288265i
\(826\) 0.00358577 0.0133823i 0.000124765 0.000465629i
\(827\) −21.0142 5.63075i −0.730736 0.195800i −0.125779 0.992058i \(-0.540143\pi\)
−0.604957 + 0.796258i \(0.706810\pi\)
\(828\) 14.7200 8.49861i 0.511556 0.295347i
\(829\) −20.5305 −0.713054 −0.356527 0.934285i \(-0.616039\pi\)
−0.356527 + 0.934285i \(0.616039\pi\)
\(830\) −1.05833 3.94973i −0.0367351 0.137097i
\(831\) −36.2614 20.9355i −1.25789 0.726246i
\(832\) 27.0543 + 6.81937i 0.937938 + 0.236419i
\(833\) 10.9351i 0.378879i
\(834\) 0.723451 + 2.69996i 0.0250511 + 0.0934919i
\(835\) 16.6459i 0.576054i
\(836\) −24.4948 −0.847172
\(837\) −15.1580 + 27.5783i −0.523935 + 0.953247i
\(838\) 0.188564 0.188564i 0.00651382 0.00651382i
\(839\) 28.4393 + 28.4393i 0.981833 + 0.981833i 0.999838 0.0180046i \(-0.00573135\pi\)
−0.0180046 + 0.999838i \(0.505731\pi\)
\(840\) 0.0305037 + 0.113841i 0.00105248 + 0.00392790i
\(841\) −5.40300 −0.186310
\(842\) −2.38055 + 1.37441i −0.0820393 + 0.0473654i
\(843\) −1.48224 5.53181i −0.0510512 0.190526i
\(844\) −35.2979 20.3793i −1.21501 0.701484i
\(845\) −26.3579 24.8339i −0.906739 0.854313i
\(846\) −0.725557 1.25670i −0.0249452 0.0432063i
\(847\) 0.421045 + 0.112819i 0.0144673 + 0.00387650i
\(848\) 6.42699 3.71063i 0.220704 0.127423i
\(849\) 6.47624 11.2172i 0.222264 0.384972i
\(850\) −0.116911 + 0.436316i −0.00401000 + 0.0149655i
\(851\) −0.109721 0.409483i −0.00376118 0.0140369i
\(852\) −12.2148 + 12.2148i −0.418471 + 0.418471i
\(853\) 32.6412 + 32.6412i 1.11761 + 1.11761i 0.992091 + 0.125522i \(0.0400606\pi\)
0.125522 + 0.992091i \(0.459939\pi\)
\(854\) 0.0656880 + 0.0379250i 0.00224780 + 0.00129777i
\(855\) 14.4494 8.34237i 0.494159 0.285303i
\(856\) −4.80426 + 1.28730i −0.164206 + 0.0439989i
\(857\) 17.1825 9.92032i 0.586943 0.338872i −0.176945 0.984221i \(-0.556621\pi\)
0.763888 + 0.645349i \(0.223288\pi\)
\(858\) 0.286497 1.13661i 0.00978086 0.0388033i
\(859\) −8.29682 + 4.79017i −0.283084 + 0.163438i −0.634819 0.772661i \(-0.718925\pi\)
0.351735 + 0.936100i \(0.385592\pi\)
\(860\) 32.4570 + 32.4570i 1.10677 + 1.10677i
\(861\) −0.614641 0.354863i −0.0209469 0.0120937i
\(862\) −2.70181 1.55989i −0.0920240 0.0531301i
\(863\) 1.70248 6.35373i 0.0579530 0.216284i −0.930877 0.365334i \(-0.880955\pi\)
0.988830 + 0.149050i \(0.0476216\pi\)
\(864\) −4.98385 4.98385i −0.169554 0.169554i
\(865\) −34.0605 + 9.12649i −1.15809 + 0.310310i
\(866\) 0.0294249 0.0294249i 0.000999897 0.000999897i
\(867\) 20.0952i 0.682468i
\(868\) 0.193794 0.789305i 0.00657778 0.0267908i
\(869\) −9.56785 9.56785i −0.324567 0.324567i
\(870\) 2.36132i 0.0800563i
\(871\) 18.5579 33.2771i 0.628809 1.12755i
\(872\) −1.18864 −0.0402524
\(873\) −13.2317 3.54541i −0.447824 0.119994i
\(874\) 3.87635 + 2.23801i 0.131119 + 0.0757018i
\(875\) 0.396570 + 0.228960i 0.0134065 + 0.00774026i
\(876\) −1.72584 + 1.72584i −0.0583107 + 0.0583107i
\(877\) 5.81689 + 1.55863i 0.196422 + 0.0526312i 0.355689 0.934604i \(-0.384246\pi\)
−0.159267 + 0.987236i \(0.550913\pi\)
\(878\) 0.962408 3.59176i 0.0324797 0.121216i
\(879\) −39.0672 10.4680i −1.31771 0.353078i
\(880\) −21.3518 12.3275i −0.719769 0.415559i
\(881\) −12.0436 20.8601i −0.405759 0.702796i 0.588650 0.808388i \(-0.299659\pi\)
−0.994410 + 0.105592i \(0.966326\pi\)
\(882\) 0.773796 0.207338i 0.0260551 0.00698143i
\(883\) 39.0313 1.31351 0.656753 0.754106i \(-0.271929\pi\)
0.656753 + 0.754106i \(0.271929\pi\)
\(884\) 7.80908 8.04501i 0.262648 0.270583i
\(885\) 6.00624 + 3.46771i 0.201898 + 0.116566i
\(886\) −0.340778 0.0913113i −0.0114487 0.00306766i
\(887\) −15.3578 + 26.6005i −0.515664 + 0.893157i 0.484170 + 0.874974i \(0.339121\pi\)
−0.999835 + 0.0181829i \(0.994212\pi\)
\(888\) −0.0270975 + 0.0156447i −0.000909331 + 0.000525003i
\(889\) 0.0119761 0.0446953i 0.000401664 0.00149903i
\(890\) 0.116723 0.435615i 0.00391255 0.0146018i
\(891\) 7.19101 7.19101i 0.240908 0.240908i
\(892\) 0.531730 + 1.98444i 0.0178036 + 0.0664441i
\(893\) −34.6808 + 60.0689i −1.16055 + 2.01013i
\(894\) −0.449148 0.777948i −0.0150218 0.0260185i
\(895\) −35.4765 + 35.4765i −1.18585 + 1.18585i
\(896\) 0.209996 + 0.121241i 0.00701548 + 0.00405039i
\(897\) 27.0791 27.8973i 0.904146 0.931463i
\(898\) 2.43092i 0.0811209i
\(899\) 15.7300 28.6192i 0.524626 0.954504i
\(900\) 6.00650 0.200217
\(901\) 2.94890i 0.0982423i
\(902\) −1.59336 + 0.426941i −0.0530532 + 0.0142156i
\(903\) 0.593491 0.593491i 0.0197501 0.0197501i
\(904\) −0.0743322 + 0.277411i −0.00247225 + 0.00922657i
\(905\) 11.1457 + 41.5964i 0.370496 + 1.38271i
\(906\) −1.03050 + 1.78487i −0.0342359 + 0.0592984i
\(907\) 19.3187i 0.641465i 0.947170 + 0.320733i \(0.103929\pi\)
−0.947170 + 0.320733i \(0.896071\pi\)
\(908\) −9.16688 + 34.2113i −0.304214 + 1.13534i
\(909\) −12.3820 + 7.14877i −0.410686 + 0.237110i
\(910\) −0.0395714 0.0662433i −0.00131178 0.00219595i
\(911\) −20.9064 12.0703i −0.692658 0.399907i 0.111949 0.993714i \(-0.464291\pi\)
−0.804607 + 0.593807i \(0.797624\pi\)
\(912\) −7.69592 + 28.7216i −0.254837 + 0.951066i
\(913\) 15.7719 27.3177i 0.521973 0.904084i
\(914\) −3.79243 −0.125443
\(915\) −26.8488 + 26.8488i −0.887596 + 0.887596i
\(916\) 15.3811 4.12135i 0.508205 0.136173i
\(917\) 0.0570401 0.212877i 0.00188363 0.00702980i
\(918\) −0.893473 + 0.239405i −0.0294890 + 0.00790155i
\(919\) −24.3271 42.1358i −0.802477 1.38993i −0.917981 0.396624i \(-0.870182\pi\)
0.115504 0.993307i \(-0.463152\pi\)
\(920\) 4.54285 + 7.86845i 0.149773 + 0.259415i
\(921\) 20.7823 + 5.56861i 0.684801 + 0.183492i
\(922\) −3.71290 −0.122278
\(923\) 11.0473 19.8095i 0.363627 0.652038i
\(924\) −0.226669 + 0.392602i −0.00745686 + 0.0129157i
\(925\) 0.0387732 0.144704i 0.00127485 0.00475782i
\(926\) 0.814968i 0.0267815i
\(927\) −16.7607 9.67680i −0.550494 0.317828i
\(928\) 5.17195 + 5.17195i 0.169778 + 0.169778i
\(929\) −18.6609 18.6609i −0.612243 0.612243i 0.331287 0.943530i \(-0.392517\pi\)
−0.943530 + 0.331287i \(0.892517\pi\)
\(930\) −1.96434 1.07966i −0.0644132 0.0354036i
\(931\) −27.0760 27.0760i −0.887381 0.887381i
\(932\) −27.2726 −0.893344
\(933\) 6.69884 11.6027i 0.219310 0.379856i
\(934\) 1.24585 + 1.24585i 0.0407655 + 0.0407655i
\(935\) −8.48434 + 4.89844i −0.277468 + 0.160196i
\(936\) 1.43866 + 0.802306i 0.0470240 + 0.0262242i
\(937\) 27.2457 47.1909i 0.890078 1.54166i 0.0502966 0.998734i \(-0.483983\pi\)
0.839781 0.542925i \(-0.182683\pi\)
\(938\) 0.0574066 0.0574066i 0.00187439 0.00187439i
\(939\) 17.5401 + 30.3804i 0.572401 + 0.991427i
\(940\) −60.7983 + 35.1019i −1.98302 + 1.14490i
\(941\) 11.4103 42.5837i 0.371964 1.38819i −0.485767 0.874089i \(-0.661459\pi\)
0.857730 0.514100i \(-0.171874\pi\)
\(942\) −1.51617 + 0.406256i −0.0493994 + 0.0132365i
\(943\) −52.8489 14.1608i −1.72100 0.461140i
\(944\) 6.85338 1.83636i 0.223058 0.0597683i
\(945\) 1.15551i 0.0375888i
\(946\) 1.95079i 0.0634255i
\(947\) −8.48105 31.6517i −0.275597 1.02854i −0.955440 0.295185i \(-0.904619\pi\)
0.679843 0.733358i \(-0.262048\pi\)
\(948\) −14.3041 + 8.25850i −0.464577 + 0.268224i
\(949\) 1.56089 2.79891i 0.0506685 0.0908564i
\(950\) 0.790870 + 1.36983i 0.0256592 + 0.0444431i
\(951\) −0.913468 + 3.40911i −0.0296212 + 0.110548i
\(952\) 0.0414915 0.0239551i 0.00134475 0.000776390i
\(953\) 18.6271 0.603390 0.301695 0.953405i \(-0.402448\pi\)
0.301695 + 0.953405i \(0.402448\pi\)
\(954\) 0.208672 0.0559135i 0.00675601 0.00181027i
\(955\) −15.8936 59.3158i −0.514305 1.91941i
\(956\) −5.81693 1.55864i −0.188133 0.0504100i
\(957\) −12.8804 + 12.8804i −0.416365 + 0.416365i
\(958\) 1.64816 2.85470i 0.0532496 0.0922310i
\(959\) −1.19669 −0.0386432
\(960\) −21.0432 + 21.0432i −0.679166 + 0.679166i
\(961\) 16.6155 + 26.1711i 0.535985 + 0.844228i
\(962\) 0.0142684 0.0146994i 0.000460030 0.000473929i
\(963\) 13.0314 0.419933
\(964\) −3.60336 + 0.965517i −0.116056 + 0.0310972i
\(965\) 7.72676 0.248733
\(966\) 0.0717414 0.0414199i 0.00230824 0.00133266i
\(967\) −30.0412 + 8.04951i −0.966060 + 0.258855i −0.707163 0.707050i \(-0.750025\pi\)
−0.258896 + 0.965905i \(0.583359\pi\)
\(968\) −0.641932 2.39572i −0.0206325 0.0770014i
\(969\) 8.35473 + 8.35473i 0.268393 + 0.268393i
\(970\) 0.944980 3.52671i 0.0303415 0.113236i
\(971\) 10.9304 + 18.9319i 0.350772 + 0.607555i 0.986385 0.164453i \(-0.0525859\pi\)
−0.635613 + 0.772008i \(0.719253\pi\)
\(972\) 10.6564 + 18.4575i 0.341805 + 0.592023i
\(973\) 0.367382 + 1.37109i 0.0117777 + 0.0439551i
\(974\) 1.63051 + 2.82413i 0.0522450 + 0.0904910i
\(975\) 13.2164 3.75297i 0.423263 0.120191i
\(976\) 38.8445i 1.24338i
\(977\) −1.36791 + 1.36791i −0.0437632 + 0.0437632i −0.728650 0.684887i \(-0.759852\pi\)
0.684887 + 0.728650i \(0.259852\pi\)
\(978\) 1.69121 + 0.976420i 0.0540789 + 0.0312225i
\(979\) 3.01286 1.73948i 0.0962915 0.0555939i
\(980\) −10.0309 37.4357i −0.320424 1.19584i
\(981\) 3.00818 + 0.806039i 0.0960437 + 0.0257348i
\(982\) 1.82820 + 0.489865i 0.0583402 + 0.0156322i
\(983\) −8.59347 2.30261i −0.274089 0.0734420i 0.119156 0.992876i \(-0.461981\pi\)
−0.393245 + 0.919434i \(0.628648\pi\)
\(984\) 4.03830i 0.128736i
\(985\) −7.33922 + 12.7119i −0.233847 + 0.405035i
\(986\) 0.927194 0.248441i 0.0295279 0.00791197i
\(987\) 0.641854 + 1.11172i 0.0204304 + 0.0353865i
\(988\) −0.584188 39.2558i −0.0185855 1.24889i
\(989\) 32.3520 56.0353i 1.02873 1.78182i
\(990\) −0.507496 0.507496i −0.0161293 0.0161293i
\(991\) 0.395315i 0.0125576i 0.999980 + 0.00627880i \(0.00199862\pi\)
−0.999980 + 0.00627880i \(0.998001\pi\)
\(992\) −6.66721 + 1.93768i −0.211684 + 0.0615215i
\(993\) 13.9845 13.9845i 0.443783 0.443783i
\(994\) 0.0341736 0.0341736i 0.00108392 0.00108392i
\(995\) −0.327982 1.22405i −0.0103977 0.0388049i
\(996\) −27.2271 27.2271i −0.862722 0.862722i
\(997\) −9.49803 16.4511i −0.300806 0.521011i 0.675513 0.737348i \(-0.263922\pi\)
−0.976319 + 0.216337i \(0.930589\pi\)
\(998\) 1.36971 2.37240i 0.0433573 0.0750970i
\(999\) 0.296319 0.0793984i 0.00937511 0.00251205i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 403.2.be.c.57.18 136
13.8 odd 4 inner 403.2.be.c.398.18 yes 136
31.6 odd 6 inner 403.2.be.c.161.18 yes 136
403.99 even 12 inner 403.2.be.c.99.18 yes 136
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
403.2.be.c.57.18 136 1.1 even 1 trivial
403.2.be.c.99.18 yes 136 403.99 even 12 inner
403.2.be.c.161.18 yes 136 31.6 odd 6 inner
403.2.be.c.398.18 yes 136 13.8 odd 4 inner