Properties

Label 363.2.e.d.202.1
Level $363$
Weight $2$
Character 363.202
Analytic conductor $2.899$
Analytic rank $0$
Dimension $4$
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] = [363,2,Mod(124,363)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(363, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("363.124");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 363.e (of order \(5\), degree \(4\), not 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: \(2.89856959337\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 202.1
Root \(0.809017 - 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 363.202
Dual form 363.2.e.d.124.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.61803 - 1.17557i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.618034 + 1.90211i) q^{4} +(-3.23607 + 2.35114i) q^{5} +(1.61803 - 1.17557i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(-1.61803 - 1.17557i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.618034 + 1.90211i) q^{4} +(-3.23607 + 2.35114i) q^{5} +(1.61803 - 1.17557i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.809017 - 0.587785i) q^{9} +8.00000 q^{10} -2.00000 q^{12} +(-1.61803 - 1.17557i) q^{13} +(-0.618034 + 1.90211i) q^{14} +(-1.23607 - 3.80423i) q^{15} +(3.23607 - 2.35114i) q^{16} +(3.23607 - 2.35114i) q^{17} +(0.618034 + 1.90211i) q^{18} +(0.927051 - 2.85317i) q^{19} +(-6.47214 - 4.70228i) q^{20} +1.00000 q^{21} +2.00000 q^{23} +(3.39919 - 10.4616i) q^{25} +(1.23607 + 3.80423i) q^{26} +(0.809017 - 0.587785i) q^{27} +(1.61803 - 1.17557i) q^{28} +(-1.85410 - 5.70634i) q^{29} +(-2.47214 + 7.60845i) q^{30} +(4.04508 + 2.93893i) q^{31} -8.00000 q^{32} -8.00000 q^{34} +(3.23607 + 2.35114i) q^{35} +(0.618034 - 1.90211i) q^{36} +(0.927051 + 2.85317i) q^{37} +(-4.85410 + 3.52671i) q^{38} +(1.61803 - 1.17557i) q^{39} +(0.618034 - 1.90211i) q^{41} +(-1.61803 - 1.17557i) q^{42} -12.0000 q^{43} +4.00000 q^{45} +(-3.23607 - 2.35114i) q^{46} +(0.618034 - 1.90211i) q^{47} +(1.23607 + 3.80423i) q^{48} +(4.85410 - 3.52671i) q^{49} +(-17.7984 + 12.9313i) q^{50} +(1.23607 + 3.80423i) q^{51} +(1.23607 - 3.80423i) q^{52} +(-4.85410 - 3.52671i) q^{53} -2.00000 q^{54} +(2.42705 + 1.76336i) q^{57} +(-3.70820 + 11.4127i) q^{58} +(-3.09017 - 9.51057i) q^{59} +(6.47214 - 4.70228i) q^{60} +(2.42705 - 1.76336i) q^{61} +(-3.09017 - 9.51057i) q^{62} +(-0.309017 + 0.951057i) q^{63} +(6.47214 + 4.70228i) q^{64} +8.00000 q^{65} -1.00000 q^{67} +(6.47214 + 4.70228i) q^{68} +(-0.618034 + 1.90211i) q^{69} +(-2.47214 - 7.60845i) q^{70} +(3.39919 + 10.4616i) q^{73} +(1.85410 - 5.70634i) q^{74} +(8.89919 + 6.46564i) q^{75} +6.00000 q^{76} -4.00000 q^{78} +(8.89919 + 6.46564i) q^{79} +(-4.94427 + 15.2169i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-3.23607 + 2.35114i) q^{82} +(4.85410 - 3.52671i) q^{83} +(0.618034 + 1.90211i) q^{84} +(-4.94427 + 15.2169i) q^{85} +(19.4164 + 14.1068i) q^{86} +6.00000 q^{87} +12.0000 q^{89} +(-6.47214 - 4.70228i) q^{90} +(-0.618034 + 1.90211i) q^{91} +(1.23607 + 3.80423i) q^{92} +(-4.04508 + 2.93893i) q^{93} +(-3.23607 + 2.35114i) q^{94} +(3.70820 + 11.4127i) q^{95} +(2.47214 - 7.60845i) q^{96} +(-4.04508 - 2.93893i) q^{97} -12.0000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + q^{3} - 2 q^{4} - 4 q^{5} + 2 q^{6} + q^{7} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} + q^{3} - 2 q^{4} - 4 q^{5} + 2 q^{6} + q^{7} - q^{9} + 32 q^{10} - 8 q^{12} - 2 q^{13} + 2 q^{14} + 4 q^{15} + 4 q^{16} + 4 q^{17} - 2 q^{18} - 3 q^{19} - 8 q^{20} + 4 q^{21} + 8 q^{23} - 11 q^{25} - 4 q^{26} + q^{27} + 2 q^{28} + 6 q^{29} + 8 q^{30} + 5 q^{31} - 32 q^{32} - 32 q^{34} + 4 q^{35} - 2 q^{36} - 3 q^{37} - 6 q^{38} + 2 q^{39} - 2 q^{41} - 2 q^{42} - 48 q^{43} + 16 q^{45} - 4 q^{46} - 2 q^{47} - 4 q^{48} + 6 q^{49} - 22 q^{50} - 4 q^{51} - 4 q^{52} - 6 q^{53} - 8 q^{54} + 3 q^{57} + 12 q^{58} + 10 q^{59} + 8 q^{60} + 3 q^{61} + 10 q^{62} + q^{63} + 8 q^{64} + 32 q^{65} - 4 q^{67} + 8 q^{68} + 2 q^{69} + 8 q^{70} - 11 q^{73} - 6 q^{74} + 11 q^{75} + 24 q^{76} - 16 q^{78} + 11 q^{79} + 16 q^{80} - q^{81} - 4 q^{82} + 6 q^{83} - 2 q^{84} + 16 q^{85} + 24 q^{86} + 24 q^{87} + 48 q^{89} - 8 q^{90} + 2 q^{91} - 4 q^{92} - 5 q^{93} - 4 q^{94} - 12 q^{95} - 8 q^{96} - 5 q^{97} - 48 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(244\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.61803 1.17557i −1.14412 0.831254i −0.156434 0.987688i \(-0.550000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(3\) −0.309017 + 0.951057i −0.178411 + 0.549093i
\(4\) 0.618034 + 1.90211i 0.309017 + 0.951057i
\(5\) −3.23607 + 2.35114i −1.44721 + 1.05146i −0.460741 + 0.887535i \(0.652416\pi\)
−0.986472 + 0.163928i \(0.947584\pi\)
\(6\) 1.61803 1.17557i 0.660560 0.479925i
\(7\) −0.309017 0.951057i −0.116797 0.359466i 0.875520 0.483181i \(-0.160519\pi\)
−0.992318 + 0.123716i \(0.960519\pi\)
\(8\) 0 0
\(9\) −0.809017 0.587785i −0.269672 0.195928i
\(10\) 8.00000 2.52982
\(11\) 0 0
\(12\) −2.00000 −0.577350
\(13\) −1.61803 1.17557i −0.448762 0.326045i 0.340345 0.940301i \(-0.389456\pi\)
−0.789107 + 0.614256i \(0.789456\pi\)
\(14\) −0.618034 + 1.90211i −0.165177 + 0.508361i
\(15\) −1.23607 3.80423i −0.319151 0.982247i
\(16\) 3.23607 2.35114i 0.809017 0.587785i
\(17\) 3.23607 2.35114i 0.784862 0.570235i −0.121572 0.992583i \(-0.538794\pi\)
0.906434 + 0.422347i \(0.138794\pi\)
\(18\) 0.618034 + 1.90211i 0.145672 + 0.448332i
\(19\) 0.927051 2.85317i 0.212680 0.654562i −0.786630 0.617425i \(-0.788176\pi\)
0.999310 0.0371374i \(-0.0118239\pi\)
\(20\) −6.47214 4.70228i −1.44721 1.05146i
\(21\) 1.00000 0.218218
\(22\) 0 0
\(23\) 2.00000 0.417029 0.208514 0.978019i \(-0.433137\pi\)
0.208514 + 0.978019i \(0.433137\pi\)
\(24\) 0 0
\(25\) 3.39919 10.4616i 0.679837 2.09232i
\(26\) 1.23607 + 3.80423i 0.242413 + 0.746070i
\(27\) 0.809017 0.587785i 0.155695 0.113119i
\(28\) 1.61803 1.17557i 0.305780 0.222162i
\(29\) −1.85410 5.70634i −0.344298 1.05964i −0.961958 0.273196i \(-0.911919\pi\)
0.617660 0.786445i \(-0.288081\pi\)
\(30\) −2.47214 + 7.60845i −0.451348 + 1.38911i
\(31\) 4.04508 + 2.93893i 0.726519 + 0.527847i 0.888460 0.458954i \(-0.151776\pi\)
−0.161942 + 0.986800i \(0.551776\pi\)
\(32\) −8.00000 −1.41421
\(33\) 0 0
\(34\) −8.00000 −1.37199
\(35\) 3.23607 + 2.35114i 0.546995 + 0.397415i
\(36\) 0.618034 1.90211i 0.103006 0.317019i
\(37\) 0.927051 + 2.85317i 0.152406 + 0.469058i 0.997889 0.0649448i \(-0.0206871\pi\)
−0.845483 + 0.534003i \(0.820687\pi\)
\(38\) −4.85410 + 3.52671i −0.787439 + 0.572108i
\(39\) 1.61803 1.17557i 0.259093 0.188242i
\(40\) 0 0
\(41\) 0.618034 1.90211i 0.0965207 0.297060i −0.891126 0.453755i \(-0.850084\pi\)
0.987647 + 0.156695i \(0.0500840\pi\)
\(42\) −1.61803 1.17557i −0.249668 0.181394i
\(43\) −12.0000 −1.82998 −0.914991 0.403473i \(-0.867803\pi\)
−0.914991 + 0.403473i \(0.867803\pi\)
\(44\) 0 0
\(45\) 4.00000 0.596285
\(46\) −3.23607 2.35114i −0.477132 0.346657i
\(47\) 0.618034 1.90211i 0.0901495 0.277452i −0.895810 0.444438i \(-0.853403\pi\)
0.985959 + 0.166986i \(0.0534035\pi\)
\(48\) 1.23607 + 3.80423i 0.178411 + 0.549093i
\(49\) 4.85410 3.52671i 0.693443 0.503816i
\(50\) −17.7984 + 12.9313i −2.51707 + 1.82876i
\(51\) 1.23607 + 3.80423i 0.173084 + 0.532698i
\(52\) 1.23607 3.80423i 0.171412 0.527551i
\(53\) −4.85410 3.52671i −0.666762 0.484431i 0.202178 0.979349i \(-0.435198\pi\)
−0.868940 + 0.494918i \(0.835198\pi\)
\(54\) −2.00000 −0.272166
\(55\) 0 0
\(56\) 0 0
\(57\) 2.42705 + 1.76336i 0.321471 + 0.233562i
\(58\) −3.70820 + 11.4127i −0.486911 + 1.49856i
\(59\) −3.09017 9.51057i −0.402306 1.23817i −0.923124 0.384502i \(-0.874373\pi\)
0.520818 0.853668i \(-0.325627\pi\)
\(60\) 6.47214 4.70228i 0.835549 0.607062i
\(61\) 2.42705 1.76336i 0.310752 0.225775i −0.421467 0.906844i \(-0.638485\pi\)
0.732219 + 0.681069i \(0.238485\pi\)
\(62\) −3.09017 9.51057i −0.392452 1.20784i
\(63\) −0.309017 + 0.951057i −0.0389325 + 0.119822i
\(64\) 6.47214 + 4.70228i 0.809017 + 0.587785i
\(65\) 8.00000 0.992278
\(66\) 0 0
\(67\) −1.00000 −0.122169 −0.0610847 0.998133i \(-0.519456\pi\)
−0.0610847 + 0.998133i \(0.519456\pi\)
\(68\) 6.47214 + 4.70228i 0.784862 + 0.570235i
\(69\) −0.618034 + 1.90211i −0.0744025 + 0.228988i
\(70\) −2.47214 7.60845i −0.295477 0.909384i
\(71\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(72\) 0 0
\(73\) 3.39919 + 10.4616i 0.397845 + 1.22444i 0.926724 + 0.375743i \(0.122612\pi\)
−0.528879 + 0.848697i \(0.677388\pi\)
\(74\) 1.85410 5.70634i 0.215535 0.663348i
\(75\) 8.89919 + 6.46564i 1.02759 + 0.746588i
\(76\) 6.00000 0.688247
\(77\) 0 0
\(78\) −4.00000 −0.452911
\(79\) 8.89919 + 6.46564i 1.00124 + 0.727441i 0.962353 0.271803i \(-0.0876198\pi\)
0.0388837 + 0.999244i \(0.487620\pi\)
\(80\) −4.94427 + 15.2169i −0.552786 + 1.70130i
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) −3.23607 + 2.35114i −0.357364 + 0.259640i
\(83\) 4.85410 3.52671i 0.532807 0.387107i −0.288600 0.957450i \(-0.593190\pi\)
0.821407 + 0.570343i \(0.193190\pi\)
\(84\) 0.618034 + 1.90211i 0.0674330 + 0.207538i
\(85\) −4.94427 + 15.2169i −0.536282 + 1.65051i
\(86\) 19.4164 + 14.1068i 2.09373 + 1.52118i
\(87\) 6.00000 0.643268
\(88\) 0 0
\(89\) 12.0000 1.27200 0.635999 0.771690i \(-0.280588\pi\)
0.635999 + 0.771690i \(0.280588\pi\)
\(90\) −6.47214 4.70228i −0.682223 0.495664i
\(91\) −0.618034 + 1.90211i −0.0647876 + 0.199396i
\(92\) 1.23607 + 3.80423i 0.128869 + 0.396618i
\(93\) −4.04508 + 2.93893i −0.419456 + 0.304752i
\(94\) −3.23607 + 2.35114i −0.333775 + 0.242502i
\(95\) 3.70820 + 11.4127i 0.380454 + 1.17092i
\(96\) 2.47214 7.60845i 0.252311 0.776534i
\(97\) −4.04508 2.93893i −0.410716 0.298403i 0.363176 0.931721i \(-0.381693\pi\)
−0.773892 + 0.633318i \(0.781693\pi\)
\(98\) −12.0000 −1.21218
\(99\) 0 0
\(100\) 22.0000 2.20000
\(101\) −8.09017 5.87785i −0.805002 0.584868i 0.107375 0.994219i \(-0.465755\pi\)
−0.912377 + 0.409350i \(0.865755\pi\)
\(102\) 2.47214 7.60845i 0.244778 0.753349i
\(103\) −2.16312 6.65740i −0.213138 0.655973i −0.999281 0.0379269i \(-0.987925\pi\)
0.786142 0.618046i \(-0.212075\pi\)
\(104\) 0 0
\(105\) −3.23607 + 2.35114i −0.315808 + 0.229448i
\(106\) 3.70820 + 11.4127i 0.360173 + 1.10850i
\(107\) 5.56231 17.1190i 0.537728 1.65496i −0.199950 0.979806i \(-0.564078\pi\)
0.737679 0.675152i \(-0.235922\pi\)
\(108\) 1.61803 + 1.17557i 0.155695 + 0.113119i
\(109\) −1.00000 −0.0957826 −0.0478913 0.998853i \(-0.515250\pi\)
−0.0478913 + 0.998853i \(0.515250\pi\)
\(110\) 0 0
\(111\) −3.00000 −0.284747
\(112\) −3.23607 2.35114i −0.305780 0.222162i
\(113\) 1.85410 5.70634i 0.174419 0.536807i −0.825187 0.564859i \(-0.808930\pi\)
0.999606 + 0.0280521i \(0.00893043\pi\)
\(114\) −1.85410 5.70634i −0.173653 0.534448i
\(115\) −6.47214 + 4.70228i −0.603530 + 0.438490i
\(116\) 9.70820 7.05342i 0.901384 0.654894i
\(117\) 0.618034 + 1.90211i 0.0571373 + 0.175850i
\(118\) −6.18034 + 19.0211i −0.568946 + 1.75104i
\(119\) −3.23607 2.35114i −0.296650 0.215529i
\(120\) 0 0
\(121\) 0 0
\(122\) −6.00000 −0.543214
\(123\) 1.61803 + 1.17557i 0.145893 + 0.105998i
\(124\) −3.09017 + 9.51057i −0.277505 + 0.854074i
\(125\) 7.41641 + 22.8254i 0.663344 + 2.04156i
\(126\) 1.61803 1.17557i 0.144146 0.104728i
\(127\) −10.5172 + 7.64121i −0.933252 + 0.678048i −0.946787 0.321861i \(-0.895692\pi\)
0.0135346 + 0.999908i \(0.495692\pi\)
\(128\) 0 0
\(129\) 3.70820 11.4127i 0.326489 1.00483i
\(130\) −12.9443 9.40456i −1.13529 0.824835i
\(131\) 6.00000 0.524222 0.262111 0.965038i \(-0.415581\pi\)
0.262111 + 0.965038i \(0.415581\pi\)
\(132\) 0 0
\(133\) −3.00000 −0.260133
\(134\) 1.61803 + 1.17557i 0.139777 + 0.101554i
\(135\) −1.23607 + 3.80423i −0.106384 + 0.327416i
\(136\) 0 0
\(137\) −6.47214 + 4.70228i −0.552952 + 0.401743i −0.828873 0.559437i \(-0.811017\pi\)
0.275921 + 0.961180i \(0.411017\pi\)
\(138\) 3.23607 2.35114i 0.275472 0.200142i
\(139\) −4.94427 15.2169i −0.419368 1.29068i −0.908285 0.418351i \(-0.862608\pi\)
0.488918 0.872330i \(-0.337392\pi\)
\(140\) −2.47214 + 7.60845i −0.208934 + 0.643032i
\(141\) 1.61803 + 1.17557i 0.136263 + 0.0990009i
\(142\) 0 0
\(143\) 0 0
\(144\) −4.00000 −0.333333
\(145\) 19.4164 + 14.1068i 1.61244 + 1.17151i
\(146\) 6.79837 20.9232i 0.562637 1.73162i
\(147\) 1.85410 + 5.70634i 0.152924 + 0.470651i
\(148\) −4.85410 + 3.52671i −0.399005 + 0.289894i
\(149\) −12.9443 + 9.40456i −1.06044 + 0.770452i −0.974169 0.225820i \(-0.927494\pi\)
−0.0862671 + 0.996272i \(0.527494\pi\)
\(150\) −6.79837 20.9232i −0.555085 1.70838i
\(151\) 4.94427 15.2169i 0.402359 1.23833i −0.520721 0.853727i \(-0.674337\pi\)
0.923080 0.384607i \(-0.125663\pi\)
\(152\) 0 0
\(153\) −4.00000 −0.323381
\(154\) 0 0
\(155\) −20.0000 −1.60644
\(156\) 3.23607 + 2.35114i 0.259093 + 0.188242i
\(157\) −0.309017 + 0.951057i −0.0246622 + 0.0759026i −0.962630 0.270820i \(-0.912705\pi\)
0.937968 + 0.346722i \(0.112705\pi\)
\(158\) −6.79837 20.9232i −0.540850 1.66456i
\(159\) 4.85410 3.52671i 0.384955 0.279686i
\(160\) 25.8885 18.8091i 2.04667 1.48699i
\(161\) −0.618034 1.90211i −0.0487079 0.149908i
\(162\) 0.618034 1.90211i 0.0485573 0.149444i
\(163\) −20.2254 14.6946i −1.58418 1.15097i −0.911701 0.410854i \(-0.865231\pi\)
−0.672476 0.740119i \(-0.734769\pi\)
\(164\) 4.00000 0.312348
\(165\) 0 0
\(166\) −12.0000 −0.931381
\(167\) −14.5623 10.5801i −1.12687 0.818715i −0.141630 0.989920i \(-0.545234\pi\)
−0.985236 + 0.171204i \(0.945234\pi\)
\(168\) 0 0
\(169\) −2.78115 8.55951i −0.213935 0.658424i
\(170\) 25.8885 18.8091i 1.98556 1.44259i
\(171\) −2.42705 + 1.76336i −0.185601 + 0.134847i
\(172\) −7.41641 22.8254i −0.565496 1.74042i
\(173\) −7.41641 + 22.8254i −0.563859 + 1.73538i 0.107458 + 0.994210i \(0.465729\pi\)
−0.671317 + 0.741170i \(0.734271\pi\)
\(174\) −9.70820 7.05342i −0.735977 0.534719i
\(175\) −11.0000 −0.831522
\(176\) 0 0
\(177\) 10.0000 0.751646
\(178\) −19.4164 14.1068i −1.45532 1.05735i
\(179\) 1.85410 5.70634i 0.138582 0.426512i −0.857548 0.514404i \(-0.828013\pi\)
0.996130 + 0.0878923i \(0.0280131\pi\)
\(180\) 2.47214 + 7.60845i 0.184262 + 0.567101i
\(181\) 18.6074 13.5191i 1.38308 1.00486i 0.386491 0.922293i \(-0.373687\pi\)
0.996585 0.0825708i \(-0.0263131\pi\)
\(182\) 3.23607 2.35114i 0.239873 0.174278i
\(183\) 0.927051 + 2.85317i 0.0685296 + 0.210912i
\(184\) 0 0
\(185\) −9.70820 7.05342i −0.713761 0.518578i
\(186\) 10.0000 0.733236
\(187\) 0 0
\(188\) 4.00000 0.291730
\(189\) −0.809017 0.587785i −0.0588473 0.0427551i
\(190\) 7.41641 22.8254i 0.538043 1.65593i
\(191\) 2.47214 + 7.60845i 0.178877 + 0.550528i 0.999789 0.0205267i \(-0.00653431\pi\)
−0.820912 + 0.571055i \(0.806534\pi\)
\(192\) −6.47214 + 4.70228i −0.467086 + 0.339358i
\(193\) −4.04508 + 2.93893i −0.291172 + 0.211549i −0.723775 0.690036i \(-0.757595\pi\)
0.432604 + 0.901584i \(0.357595\pi\)
\(194\) 3.09017 + 9.51057i 0.221861 + 0.682819i
\(195\) −2.47214 + 7.60845i −0.177033 + 0.544853i
\(196\) 9.70820 + 7.05342i 0.693443 + 0.503816i
\(197\) 8.00000 0.569976 0.284988 0.958531i \(-0.408010\pi\)
0.284988 + 0.958531i \(0.408010\pi\)
\(198\) 0 0
\(199\) −21.0000 −1.48865 −0.744325 0.667817i \(-0.767229\pi\)
−0.744325 + 0.667817i \(0.767229\pi\)
\(200\) 0 0
\(201\) 0.309017 0.951057i 0.0217964 0.0670824i
\(202\) 6.18034 + 19.0211i 0.434847 + 1.33832i
\(203\) −4.85410 + 3.52671i −0.340691 + 0.247527i
\(204\) −6.47214 + 4.70228i −0.453140 + 0.329226i
\(205\) 2.47214 + 7.60845i 0.172661 + 0.531397i
\(206\) −4.32624 + 13.3148i −0.301423 + 0.927685i
\(207\) −1.61803 1.17557i −0.112461 0.0817078i
\(208\) −8.00000 −0.554700
\(209\) 0 0
\(210\) 8.00000 0.552052
\(211\) −16.9894 12.3435i −1.16960 0.849761i −0.178635 0.983915i \(-0.557168\pi\)
−0.990960 + 0.134154i \(0.957168\pi\)
\(212\) 3.70820 11.4127i 0.254680 0.783826i
\(213\) 0 0
\(214\) −29.1246 + 21.1603i −1.99092 + 1.44649i
\(215\) 38.8328 28.2137i 2.64838 1.92416i
\(216\) 0 0
\(217\) 1.54508 4.75528i 0.104887 0.322810i
\(218\) 1.61803 + 1.17557i 0.109587 + 0.0796197i
\(219\) −11.0000 −0.743311
\(220\) 0 0
\(221\) −8.00000 −0.538138
\(222\) 4.85410 + 3.52671i 0.325786 + 0.236697i
\(223\) −5.25329 + 16.1680i −0.351786 + 1.08269i 0.606063 + 0.795416i \(0.292748\pi\)
−0.957850 + 0.287270i \(0.907252\pi\)
\(224\) 2.47214 + 7.60845i 0.165177 + 0.508361i
\(225\) −8.89919 + 6.46564i −0.593279 + 0.431043i
\(226\) −9.70820 + 7.05342i −0.645780 + 0.469187i
\(227\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(228\) −1.85410 + 5.70634i −0.122791 + 0.377912i
\(229\) 14.5623 + 10.5801i 0.962304 + 0.699155i 0.953685 0.300808i \(-0.0972563\pi\)
0.00861950 + 0.999963i \(0.497256\pi\)
\(230\) 16.0000 1.05501
\(231\) 0 0
\(232\) 0 0
\(233\) 14.5623 + 10.5801i 0.954008 + 0.693128i 0.951752 0.306870i \(-0.0992816\pi\)
0.00225687 + 0.999997i \(0.499282\pi\)
\(234\) 1.23607 3.80423i 0.0808043 0.248690i
\(235\) 2.47214 + 7.60845i 0.161264 + 0.496321i
\(236\) 16.1803 11.7557i 1.05325 0.765231i
\(237\) −8.89919 + 6.46564i −0.578064 + 0.419988i
\(238\) 2.47214 + 7.60845i 0.160245 + 0.493183i
\(239\) −1.85410 + 5.70634i −0.119932 + 0.369112i −0.992944 0.118587i \(-0.962164\pi\)
0.873012 + 0.487699i \(0.162164\pi\)
\(240\) −12.9443 9.40456i −0.835549 0.607062i
\(241\) 14.0000 0.901819 0.450910 0.892570i \(-0.351100\pi\)
0.450910 + 0.892570i \(0.351100\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 4.85410 + 3.52671i 0.310752 + 0.225775i
\(245\) −7.41641 + 22.8254i −0.473817 + 1.45826i
\(246\) −1.23607 3.80423i −0.0788088 0.242549i
\(247\) −4.85410 + 3.52671i −0.308859 + 0.224399i
\(248\) 0 0
\(249\) 1.85410 + 5.70634i 0.117499 + 0.361625i
\(250\) 14.8328 45.6507i 0.938110 2.88720i
\(251\) 1.61803 + 1.17557i 0.102129 + 0.0742014i 0.637678 0.770303i \(-0.279895\pi\)
−0.535548 + 0.844504i \(0.679895\pi\)
\(252\) −2.00000 −0.125988
\(253\) 0 0
\(254\) 26.0000 1.63139
\(255\) −12.9443 9.40456i −0.810602 0.588937i
\(256\) 4.94427 15.2169i 0.309017 0.951057i
\(257\) −4.32624 13.3148i −0.269863 0.830554i −0.990533 0.137275i \(-0.956166\pi\)
0.720670 0.693279i \(-0.243834\pi\)
\(258\) −19.4164 + 14.1068i −1.20881 + 0.878254i
\(259\) 2.42705 1.76336i 0.150810 0.109570i
\(260\) 4.94427 + 15.2169i 0.306631 + 0.943712i
\(261\) −1.85410 + 5.70634i −0.114766 + 0.353214i
\(262\) −9.70820 7.05342i −0.599775 0.435762i
\(263\) 10.0000 0.616626 0.308313 0.951285i \(-0.400236\pi\)
0.308313 + 0.951285i \(0.400236\pi\)
\(264\) 0 0
\(265\) 24.0000 1.47431
\(266\) 4.85410 + 3.52671i 0.297624 + 0.216237i
\(267\) −3.70820 + 11.4127i −0.226938 + 0.698445i
\(268\) −0.618034 1.90211i −0.0377524 0.116190i
\(269\) 11.3262 8.22899i 0.690573 0.501731i −0.186275 0.982498i \(-0.559642\pi\)
0.876848 + 0.480767i \(0.159642\pi\)
\(270\) 6.47214 4.70228i 0.393882 0.286172i
\(271\) −2.47214 7.60845i −0.150172 0.462181i 0.847468 0.530846i \(-0.178126\pi\)
−0.997640 + 0.0686657i \(0.978126\pi\)
\(272\) 4.94427 15.2169i 0.299791 0.922660i
\(273\) −1.61803 1.17557i −0.0979279 0.0711488i
\(274\) 16.0000 0.966595
\(275\) 0 0
\(276\) −4.00000 −0.240772
\(277\) −8.89919 6.46564i −0.534700 0.388483i 0.287413 0.957807i \(-0.407205\pi\)
−0.822113 + 0.569324i \(0.807205\pi\)
\(278\) −9.88854 + 30.4338i −0.593075 + 1.82530i
\(279\) −1.54508 4.75528i −0.0925018 0.284691i
\(280\) 0 0
\(281\) −9.70820 + 7.05342i −0.579143 + 0.420772i −0.838415 0.545032i \(-0.816517\pi\)
0.259272 + 0.965804i \(0.416517\pi\)
\(282\) −1.23607 3.80423i −0.0736068 0.226538i
\(283\) 3.39919 10.4616i 0.202061 0.621879i −0.797761 0.602974i \(-0.793982\pi\)
0.999821 0.0189045i \(-0.00601786\pi\)
\(284\) 0 0
\(285\) −12.0000 −0.710819
\(286\) 0 0
\(287\) −2.00000 −0.118056
\(288\) 6.47214 + 4.70228i 0.381374 + 0.277085i
\(289\) −0.309017 + 0.951057i −0.0181775 + 0.0559445i
\(290\) −14.8328 45.6507i −0.871013 2.68070i
\(291\) 4.04508 2.93893i 0.237127 0.172283i
\(292\) −17.7984 + 12.9313i −1.04157 + 0.756746i
\(293\) −3.70820 11.4127i −0.216636 0.666736i −0.999033 0.0439568i \(-0.986004\pi\)
0.782398 0.622779i \(-0.213996\pi\)
\(294\) 3.70820 11.4127i 0.216267 0.665601i
\(295\) 32.3607 + 23.5114i 1.88411 + 1.36889i
\(296\) 0 0
\(297\) 0 0
\(298\) 32.0000 1.85371
\(299\) −3.23607 2.35114i −0.187147 0.135970i
\(300\) −6.79837 + 20.9232i −0.392504 + 1.20800i
\(301\) 3.70820 + 11.4127i 0.213737 + 0.657816i
\(302\) −25.8885 + 18.8091i −1.48972 + 1.08234i
\(303\) 8.09017 5.87785i 0.464768 0.337674i
\(304\) −3.70820 11.4127i −0.212680 0.654562i
\(305\) −3.70820 + 11.4127i −0.212331 + 0.653488i
\(306\) 6.47214 + 4.70228i 0.369987 + 0.268812i
\(307\) 19.0000 1.08439 0.542194 0.840254i \(-0.317594\pi\)
0.542194 + 0.840254i \(0.317594\pi\)
\(308\) 0 0
\(309\) 7.00000 0.398216
\(310\) 32.3607 + 23.5114i 1.83796 + 1.33536i
\(311\) 7.41641 22.8254i 0.420546 1.29431i −0.486649 0.873597i \(-0.661781\pi\)
0.907195 0.420710i \(-0.138219\pi\)
\(312\) 0 0
\(313\) 8.09017 5.87785i 0.457283 0.332236i −0.335181 0.942154i \(-0.608798\pi\)
0.792465 + 0.609918i \(0.208798\pi\)
\(314\) 1.61803 1.17557i 0.0913109 0.0663413i
\(315\) −1.23607 3.80423i −0.0696445 0.214344i
\(316\) −6.79837 + 20.9232i −0.382438 + 1.17702i
\(317\) 16.1803 + 11.7557i 0.908778 + 0.660266i 0.940706 0.339224i \(-0.110164\pi\)
−0.0319272 + 0.999490i \(0.510164\pi\)
\(318\) −12.0000 −0.672927
\(319\) 0 0
\(320\) −32.0000 −1.78885
\(321\) 14.5623 + 10.5801i 0.812789 + 0.590526i
\(322\) −1.23607 + 3.80423i −0.0688834 + 0.212001i
\(323\) −3.70820 11.4127i −0.206330 0.635018i
\(324\) −1.61803 + 1.17557i −0.0898908 + 0.0653095i
\(325\) −17.7984 + 12.9313i −0.987276 + 0.717298i
\(326\) 15.4508 + 47.5528i 0.855743 + 2.63371i
\(327\) 0.309017 0.951057i 0.0170887 0.0525935i
\(328\) 0 0
\(329\) −2.00000 −0.110264
\(330\) 0 0
\(331\) −11.0000 −0.604615 −0.302307 0.953211i \(-0.597757\pi\)
−0.302307 + 0.953211i \(0.597757\pi\)
\(332\) 9.70820 + 7.05342i 0.532807 + 0.387107i
\(333\) 0.927051 2.85317i 0.0508021 0.156353i
\(334\) 11.1246 + 34.2380i 0.608712 + 1.87342i
\(335\) 3.23607 2.35114i 0.176805 0.128457i
\(336\) 3.23607 2.35114i 0.176542 0.128265i
\(337\) −1.54508 4.75528i −0.0841661 0.259037i 0.900113 0.435656i \(-0.143484\pi\)
−0.984279 + 0.176620i \(0.943484\pi\)
\(338\) −5.56231 + 17.1190i −0.302550 + 0.931152i
\(339\) 4.85410 + 3.52671i 0.263639 + 0.191545i
\(340\) −32.0000 −1.73544
\(341\) 0 0
\(342\) 6.00000 0.324443
\(343\) −10.5172 7.64121i −0.567877 0.412586i
\(344\) 0 0
\(345\) −2.47214 7.60845i −0.133095 0.409625i
\(346\) 38.8328 28.2137i 2.08767 1.51678i
\(347\) −1.61803 + 1.17557i −0.0868606 + 0.0631079i −0.630368 0.776296i \(-0.717096\pi\)
0.543507 + 0.839404i \(0.317096\pi\)
\(348\) 3.70820 + 11.4127i 0.198781 + 0.611784i
\(349\) −4.63525 + 14.2658i −0.248120 + 0.763633i 0.746988 + 0.664837i \(0.231499\pi\)
−0.995108 + 0.0987960i \(0.968501\pi\)
\(350\) 17.7984 + 12.9313i 0.951363 + 0.691206i
\(351\) −2.00000 −0.106752
\(352\) 0 0
\(353\) −12.0000 −0.638696 −0.319348 0.947638i \(-0.603464\pi\)
−0.319348 + 0.947638i \(0.603464\pi\)
\(354\) −16.1803 11.7557i −0.859975 0.624809i
\(355\) 0 0
\(356\) 7.41641 + 22.8254i 0.393069 + 1.20974i
\(357\) 3.23607 2.35114i 0.171271 0.124436i
\(358\) −9.70820 + 7.05342i −0.513095 + 0.372785i
\(359\) −1.23607 3.80423i −0.0652372 0.200779i 0.913125 0.407680i \(-0.133662\pi\)
−0.978362 + 0.206901i \(0.933662\pi\)
\(360\) 0 0
\(361\) 8.09017 + 5.87785i 0.425798 + 0.309361i
\(362\) −46.0000 −2.41771
\(363\) 0 0
\(364\) −4.00000 −0.209657
\(365\) −35.5967 25.8626i −1.86322 1.35371i
\(366\) 1.85410 5.70634i 0.0969155 0.298275i
\(367\) −2.47214 7.60845i −0.129044 0.397158i 0.865572 0.500785i \(-0.166955\pi\)
−0.994616 + 0.103627i \(0.966955\pi\)
\(368\) 6.47214 4.70228i 0.337383 0.245123i
\(369\) −1.61803 + 1.17557i −0.0842315 + 0.0611978i
\(370\) 7.41641 + 22.8254i 0.385561 + 1.18663i
\(371\) −1.85410 + 5.70634i −0.0962602 + 0.296258i
\(372\) −8.09017 5.87785i −0.419456 0.304752i
\(373\) −7.00000 −0.362446 −0.181223 0.983442i \(-0.558006\pi\)
−0.181223 + 0.983442i \(0.558006\pi\)
\(374\) 0 0
\(375\) −24.0000 −1.23935
\(376\) 0 0
\(377\) −3.70820 + 11.4127i −0.190982 + 0.587783i
\(378\) 0.618034 + 1.90211i 0.0317882 + 0.0978341i
\(379\) −12.9443 + 9.40456i −0.664903 + 0.483080i −0.868315 0.496013i \(-0.834797\pi\)
0.203412 + 0.979093i \(0.434797\pi\)
\(380\) −19.4164 + 14.1068i −0.996041 + 0.723666i
\(381\) −4.01722 12.3637i −0.205808 0.633413i
\(382\) 4.94427 15.2169i 0.252971 0.778565i
\(383\) −21.0344 15.2824i −1.07481 0.780895i −0.0980391 0.995183i \(-0.531257\pi\)
−0.976771 + 0.214288i \(0.931257\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 10.0000 0.508987
\(387\) 9.70820 + 7.05342i 0.493496 + 0.358546i
\(388\) 3.09017 9.51057i 0.156880 0.482826i
\(389\) 5.56231 + 17.1190i 0.282020 + 0.867969i 0.987276 + 0.159016i \(0.0508321\pi\)
−0.705256 + 0.708953i \(0.749168\pi\)
\(390\) 12.9443 9.40456i 0.655459 0.476219i
\(391\) 6.47214 4.70228i 0.327310 0.237805i
\(392\) 0 0
\(393\) −1.85410 + 5.70634i −0.0935271 + 0.287847i
\(394\) −12.9443 9.40456i −0.652123 0.473795i
\(395\) −44.0000 −2.21388
\(396\) 0 0
\(397\) 31.0000 1.55585 0.777923 0.628360i \(-0.216273\pi\)
0.777923 + 0.628360i \(0.216273\pi\)
\(398\) 33.9787 + 24.6870i 1.70320 + 1.23745i
\(399\) 0.927051 2.85317i 0.0464106 0.142837i
\(400\) −13.5967 41.8465i −0.679837 2.09232i
\(401\) 22.6525 16.4580i 1.13121 0.821873i 0.145340 0.989382i \(-0.453572\pi\)
0.985871 + 0.167509i \(0.0535724\pi\)
\(402\) −1.61803 + 1.17557i −0.0807002 + 0.0586321i
\(403\) −3.09017 9.51057i −0.153932 0.473755i
\(404\) 6.18034 19.0211i 0.307483 0.946337i
\(405\) −3.23607 2.35114i −0.160802 0.116829i
\(406\) 12.0000 0.595550
\(407\) 0 0
\(408\) 0 0
\(409\) 16.9894 + 12.3435i 0.840070 + 0.610346i 0.922390 0.386260i \(-0.126233\pi\)
−0.0823205 + 0.996606i \(0.526233\pi\)
\(410\) 4.94427 15.2169i 0.244180 0.751509i
\(411\) −2.47214 7.60845i −0.121941 0.375297i
\(412\) 11.3262 8.22899i 0.558004 0.405413i
\(413\) −8.09017 + 5.87785i −0.398091 + 0.289230i
\(414\) 1.23607 + 3.80423i 0.0607494 + 0.186968i
\(415\) −7.41641 + 22.8254i −0.364057 + 1.12045i
\(416\) 12.9443 + 9.40456i 0.634645 + 0.461097i
\(417\) 16.0000 0.783523
\(418\) 0 0
\(419\) 26.0000 1.27018 0.635092 0.772437i \(-0.280962\pi\)
0.635092 + 0.772437i \(0.280962\pi\)
\(420\) −6.47214 4.70228i −0.315808 0.229448i
\(421\) −0.618034 + 1.90211i −0.0301211 + 0.0927033i −0.964987 0.262298i \(-0.915520\pi\)
0.934866 + 0.355001i \(0.115520\pi\)
\(422\) 12.9787 + 39.9444i 0.631794 + 1.94446i
\(423\) −1.61803 + 1.17557i −0.0786715 + 0.0571582i
\(424\) 0 0
\(425\) −13.5967 41.8465i −0.659539 2.02985i
\(426\) 0 0
\(427\) −2.42705 1.76336i −0.117453 0.0853348i
\(428\) 36.0000 1.74013
\(429\) 0 0
\(430\) −96.0000 −4.62953
\(431\) 14.5623 + 10.5801i 0.701442 + 0.509627i 0.880401 0.474229i \(-0.157273\pi\)
−0.178960 + 0.983856i \(0.557273\pi\)
\(432\) 1.23607 3.80423i 0.0594703 0.183031i
\(433\) −5.25329 16.1680i −0.252457 0.776983i −0.994320 0.106431i \(-0.966058\pi\)
0.741863 0.670551i \(-0.233942\pi\)
\(434\) −8.09017 + 5.87785i −0.388341 + 0.282146i
\(435\) −19.4164 + 14.1068i −0.930946 + 0.676371i
\(436\) −0.618034 1.90211i −0.0295985 0.0910947i
\(437\) 1.85410 5.70634i 0.0886937 0.272971i
\(438\) 17.7984 + 12.9313i 0.850439 + 0.617880i
\(439\) −37.0000 −1.76591 −0.882957 0.469454i \(-0.844451\pi\)
−0.882957 + 0.469454i \(0.844451\pi\)
\(440\) 0 0
\(441\) −6.00000 −0.285714
\(442\) 12.9443 + 9.40456i 0.615696 + 0.447329i
\(443\) 1.23607 3.80423i 0.0587274 0.180744i −0.917389 0.397991i \(-0.869708\pi\)
0.976117 + 0.217247i \(0.0697076\pi\)
\(444\) −1.85410 5.70634i −0.0879918 0.270811i
\(445\) −38.8328 + 28.2137i −1.84085 + 1.33746i
\(446\) 27.5066 19.9847i 1.30247 0.946303i
\(447\) −4.94427 15.2169i −0.233856 0.719735i
\(448\) 2.47214 7.60845i 0.116797 0.359466i
\(449\) −16.1803 11.7557i −0.763597 0.554786i 0.136414 0.990652i \(-0.456442\pi\)
−0.900012 + 0.435866i \(0.856442\pi\)
\(450\) 22.0000 1.03709
\(451\) 0 0
\(452\) 12.0000 0.564433
\(453\) 12.9443 + 9.40456i 0.608175 + 0.441865i
\(454\) 0 0
\(455\) −2.47214 7.60845i −0.115896 0.356690i
\(456\) 0 0
\(457\) 14.5623 10.5801i 0.681196 0.494918i −0.192558 0.981286i \(-0.561678\pi\)
0.873754 + 0.486368i \(0.161678\pi\)
\(458\) −11.1246 34.2380i −0.519819 1.59984i
\(459\) 1.23607 3.80423i 0.0576947 0.177566i
\(460\) −12.9443 9.40456i −0.603530 0.438490i
\(461\) 6.00000 0.279448 0.139724 0.990190i \(-0.455378\pi\)
0.139724 + 0.990190i \(0.455378\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) −19.4164 14.1068i −0.901384 0.654894i
\(465\) 6.18034 19.0211i 0.286606 0.882084i
\(466\) −11.1246 34.2380i −0.515338 1.58605i
\(467\) −19.4164 + 14.1068i −0.898484 + 0.652787i −0.938076 0.346429i \(-0.887394\pi\)
0.0395920 + 0.999216i \(0.487394\pi\)
\(468\) −3.23607 + 2.35114i −0.149587 + 0.108682i
\(469\) 0.309017 + 0.951057i 0.0142691 + 0.0439157i
\(470\) 4.94427 15.2169i 0.228062 0.701903i
\(471\) −0.809017 0.587785i −0.0372775 0.0270837i
\(472\) 0 0
\(473\) 0 0
\(474\) 22.0000 1.01049
\(475\) −26.6976 19.3969i −1.22497 0.889991i
\(476\) 2.47214 7.60845i 0.113310 0.348733i
\(477\) 1.85410 + 5.70634i 0.0848935 + 0.261275i
\(478\) 9.70820 7.05342i 0.444043 0.322616i
\(479\) −17.7984 + 12.9313i −0.813228 + 0.590845i −0.914765 0.403987i \(-0.867624\pi\)
0.101536 + 0.994832i \(0.467624\pi\)
\(480\) 9.88854 + 30.4338i 0.451348 + 1.38911i
\(481\) 1.85410 5.70634i 0.0845398 0.260187i
\(482\) −22.6525 16.4580i −1.03179 0.749641i
\(483\) 2.00000 0.0910032
\(484\) 0 0
\(485\) 20.0000 0.908153
\(486\) 1.61803 + 1.17557i 0.0733955 + 0.0533250i
\(487\) −12.3607 + 38.0423i −0.560116 + 1.72386i 0.121919 + 0.992540i \(0.461095\pi\)
−0.682035 + 0.731319i \(0.738905\pi\)
\(488\) 0 0
\(489\) 20.2254 14.6946i 0.914625 0.664514i
\(490\) 38.8328 28.2137i 1.75429 1.27456i
\(491\) 4.32624 + 13.3148i 0.195240 + 0.600888i 0.999974 + 0.00725163i \(0.00230829\pi\)
−0.804733 + 0.593636i \(0.797692\pi\)
\(492\) −1.23607 + 3.80423i −0.0557262 + 0.171508i
\(493\) −19.4164 14.1068i −0.874471 0.635340i
\(494\) 12.0000 0.539906
\(495\) 0 0
\(496\) 20.0000 0.898027
\(497\) 0 0
\(498\) 3.70820 11.4127i 0.166169 0.511414i
\(499\) 7.10739 + 21.8743i 0.318171 + 0.979228i 0.974430 + 0.224693i \(0.0721378\pi\)
−0.656259 + 0.754536i \(0.727862\pi\)
\(500\) −38.8328 + 28.2137i −1.73666 + 1.26175i
\(501\) 14.5623 10.5801i 0.650596 0.472686i
\(502\) −1.23607 3.80423i −0.0551684 0.169791i
\(503\) 9.88854 30.4338i 0.440908 1.35698i −0.446001 0.895033i \(-0.647152\pi\)
0.886909 0.461944i \(-0.152848\pi\)
\(504\) 0 0
\(505\) 40.0000 1.77998
\(506\) 0 0
\(507\) 9.00000 0.399704
\(508\) −21.0344 15.2824i −0.933252 0.678048i
\(509\) 1.85410 5.70634i 0.0821816 0.252929i −0.901520 0.432737i \(-0.857548\pi\)
0.983702 + 0.179808i \(0.0575477\pi\)
\(510\) 9.88854 + 30.4338i 0.437872 + 1.34763i
\(511\) 8.89919 6.46564i 0.393677 0.286023i
\(512\) −25.8885 + 18.8091i −1.14412 + 0.831254i
\(513\) −0.927051 2.85317i −0.0409303 0.125971i
\(514\) −8.65248 + 26.6296i −0.381644 + 1.17458i
\(515\) 22.6525 + 16.4580i 0.998187 + 0.725226i
\(516\) 24.0000 1.05654
\(517\) 0 0
\(518\) −6.00000 −0.263625
\(519\) −19.4164 14.1068i −0.852286 0.619222i
\(520\) 0 0
\(521\) −1.85410 5.70634i −0.0812297 0.249999i 0.902191 0.431336i \(-0.141958\pi\)
−0.983421 + 0.181337i \(0.941958\pi\)
\(522\) 9.70820 7.05342i 0.424917 0.308720i
\(523\) 23.4615 17.0458i 1.02590 0.745360i 0.0584156 0.998292i \(-0.481395\pi\)
0.967484 + 0.252933i \(0.0813951\pi\)
\(524\) 3.70820 + 11.4127i 0.161994 + 0.498565i
\(525\) 3.39919 10.4616i 0.148353 0.456583i
\(526\) −16.1803 11.7557i −0.705496 0.512573i
\(527\) 20.0000 0.871214
\(528\) 0 0
\(529\) −19.0000 −0.826087
\(530\) −38.8328 28.2137i −1.68679 1.22552i
\(531\) −3.09017 + 9.51057i −0.134102 + 0.412723i
\(532\) −1.85410 5.70634i −0.0803855 0.247401i
\(533\) −3.23607 + 2.35114i −0.140170 + 0.101839i
\(534\) 19.4164 14.1068i 0.840230 0.610463i
\(535\) 22.2492 + 68.4761i 0.961918 + 2.96048i
\(536\) 0 0
\(537\) 4.85410 + 3.52671i 0.209470 + 0.152189i
\(538\) −28.0000 −1.20717
\(539\) 0 0
\(540\) −8.00000 −0.344265
\(541\) −1.61803 1.17557i −0.0695647 0.0505417i 0.552459 0.833540i \(-0.313689\pi\)
−0.622024 + 0.782998i \(0.713689\pi\)
\(542\) −4.94427 + 15.2169i −0.212375 + 0.653622i
\(543\) 7.10739 + 21.8743i 0.305007 + 0.938716i
\(544\) −25.8885 + 18.8091i −1.10996 + 0.806435i
\(545\) 3.23607 2.35114i 0.138618 0.100712i
\(546\) 1.23607 + 3.80423i 0.0528988 + 0.162806i
\(547\) −6.18034 + 19.0211i −0.264252 + 0.813285i 0.727612 + 0.685988i \(0.240630\pi\)
−0.991865 + 0.127296i \(0.959370\pi\)
\(548\) −12.9443 9.40456i −0.552952 0.401743i
\(549\) −3.00000 −0.128037
\(550\) 0 0
\(551\) −18.0000 −0.766826
\(552\) 0 0
\(553\) 3.39919 10.4616i 0.144548 0.444873i
\(554\) 6.79837 + 20.9232i 0.288835 + 0.888943i
\(555\) 9.70820 7.05342i 0.412090 0.299401i
\(556\) 25.8885 18.8091i 1.09792 0.797685i
\(557\) 2.47214 + 7.60845i 0.104748 + 0.322380i 0.989671 0.143356i \(-0.0457894\pi\)
−0.884923 + 0.465737i \(0.845789\pi\)
\(558\) −3.09017 + 9.51057i −0.130817 + 0.402614i
\(559\) 19.4164 + 14.1068i 0.821227 + 0.596656i
\(560\) 16.0000 0.676123
\(561\) 0 0
\(562\) 24.0000 1.01238
\(563\) 22.6525 + 16.4580i 0.954688 + 0.693621i 0.951911 0.306375i \(-0.0991160\pi\)
0.00277703 + 0.999996i \(0.499116\pi\)
\(564\) −1.23607 + 3.80423i −0.0520479 + 0.160187i
\(565\) 7.41641 + 22.8254i 0.312011 + 0.960270i
\(566\) −17.7984 + 12.9313i −0.748121 + 0.543542i
\(567\) 0.809017 0.587785i 0.0339755 0.0246847i
\(568\) 0 0
\(569\) −3.70820 + 11.4127i −0.155456 + 0.478444i −0.998207 0.0598595i \(-0.980935\pi\)
0.842751 + 0.538304i \(0.180935\pi\)
\(570\) 19.4164 + 14.1068i 0.813264 + 0.590871i
\(571\) 25.0000 1.04622 0.523109 0.852266i \(-0.324772\pi\)
0.523109 + 0.852266i \(0.324772\pi\)
\(572\) 0 0
\(573\) −8.00000 −0.334205
\(574\) 3.23607 + 2.35114i 0.135071 + 0.0981347i
\(575\) 6.79837 20.9232i 0.283512 0.872560i
\(576\) −2.47214 7.60845i −0.103006 0.317019i
\(577\) −12.1353 + 8.81678i −0.505197 + 0.367047i −0.810999 0.585048i \(-0.801076\pi\)
0.305801 + 0.952095i \(0.401076\pi\)
\(578\) 1.61803 1.17557i 0.0673013 0.0488973i
\(579\) −1.54508 4.75528i −0.0642115 0.197623i
\(580\) −14.8328 + 45.6507i −0.615899 + 1.89554i
\(581\) −4.85410 3.52671i −0.201382 0.146313i
\(582\) −10.0000 −0.414513
\(583\) 0 0
\(584\) 0 0
\(585\) −6.47214 4.70228i −0.267590 0.194415i
\(586\) −7.41641 + 22.8254i −0.306369 + 0.942907i
\(587\) 1.23607 + 3.80423i 0.0510180 + 0.157017i 0.973320 0.229454i \(-0.0736940\pi\)
−0.922302 + 0.386471i \(0.873694\pi\)
\(588\) −9.70820 + 7.05342i −0.400360 + 0.290878i
\(589\) 12.1353 8.81678i 0.500024 0.363289i
\(590\) −24.7214 76.0845i −1.01776 3.13235i
\(591\) −2.47214 + 7.60845i −0.101690 + 0.312970i
\(592\) 9.70820 + 7.05342i 0.399005 + 0.289894i
\(593\) 46.0000 1.88899 0.944497 0.328521i \(-0.106550\pi\)
0.944497 + 0.328521i \(0.106550\pi\)
\(594\) 0 0
\(595\) 16.0000 0.655936
\(596\) −25.8885 18.8091i −1.06044 0.770452i
\(597\) 6.48936 19.9722i 0.265592 0.817407i
\(598\) 2.47214 + 7.60845i 0.101093 + 0.311133i
\(599\) 6.47214 4.70228i 0.264444 0.192130i −0.447660 0.894204i \(-0.647742\pi\)
0.712104 + 0.702074i \(0.247742\pi\)
\(600\) 0 0
\(601\) 0.309017 + 0.951057i 0.0126051 + 0.0387944i 0.957161 0.289556i \(-0.0935075\pi\)
−0.944556 + 0.328350i \(0.893507\pi\)
\(602\) 7.41641 22.8254i 0.302270 0.930292i
\(603\) 0.809017 + 0.587785i 0.0329457 + 0.0239365i
\(604\) 32.0000 1.30206
\(605\) 0 0
\(606\) −20.0000 −0.812444
\(607\) 6.47214 + 4.70228i 0.262696 + 0.190860i 0.711335 0.702853i \(-0.248091\pi\)
−0.448639 + 0.893713i \(0.648091\pi\)
\(608\) −7.41641 + 22.8254i −0.300775 + 0.925690i
\(609\) −1.85410 5.70634i −0.0751320 0.231233i
\(610\) 19.4164 14.1068i 0.786147 0.571170i
\(611\) −3.23607 + 2.35114i −0.130917 + 0.0951170i
\(612\) −2.47214 7.60845i −0.0999302 0.307553i
\(613\) 4.01722 12.3637i 0.162254 0.499367i −0.836569 0.547861i \(-0.815442\pi\)
0.998823 + 0.0484944i \(0.0154423\pi\)
\(614\) −30.7426 22.3358i −1.24067 0.901401i
\(615\) −8.00000 −0.322591
\(616\) 0 0
\(617\) −24.0000 −0.966204 −0.483102 0.875564i \(-0.660490\pi\)
−0.483102 + 0.875564i \(0.660490\pi\)
\(618\) −11.3262 8.22899i −0.455608 0.331019i
\(619\) −1.23607 + 3.80423i −0.0496818 + 0.152905i −0.972820 0.231565i \(-0.925616\pi\)
0.923138 + 0.384469i \(0.125616\pi\)
\(620\) −12.3607 38.0423i −0.496417 1.52781i
\(621\) 1.61803 1.17557i 0.0649295 0.0471740i
\(622\) −38.8328 + 28.2137i −1.55705 + 1.13127i
\(623\) −3.70820 11.4127i −0.148566 0.457239i
\(624\) 2.47214 7.60845i 0.0989646 0.304582i
\(625\) −33.1697 24.0992i −1.32679 0.963968i
\(626\) −20.0000 −0.799361
\(627\) 0 0
\(628\) −2.00000 −0.0798087
\(629\) 9.70820 + 7.05342i 0.387091 + 0.281238i
\(630\) −2.47214 + 7.60845i −0.0984923 + 0.303128i
\(631\) −9.88854 30.4338i −0.393657 1.21155i −0.930003 0.367553i \(-0.880196\pi\)
0.536346 0.843998i \(-0.319804\pi\)
\(632\) 0 0
\(633\) 16.9894 12.3435i 0.675266 0.490610i
\(634\) −12.3607 38.0423i −0.490905 1.51085i
\(635\) 16.0689 49.4549i 0.637674 1.96256i
\(636\) 9.70820 + 7.05342i 0.384955 + 0.279686i
\(637\) −12.0000 −0.475457
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −7.41641 + 22.8254i −0.292930 + 0.901547i 0.690978 + 0.722876i \(0.257180\pi\)
−0.983909 + 0.178672i \(0.942820\pi\)
\(642\) −11.1246 34.2380i −0.439053 1.35127i
\(643\) 29.9336 21.7481i 1.18047 0.857660i 0.188243 0.982123i \(-0.439721\pi\)
0.992224 + 0.124463i \(0.0397208\pi\)
\(644\) 3.23607 2.35114i 0.127519 0.0926479i
\(645\) 14.8328 + 45.6507i 0.584042 + 1.79750i
\(646\) −7.41641 + 22.8254i −0.291795 + 0.898052i
\(647\) 3.23607 + 2.35114i 0.127223 + 0.0924329i 0.649577 0.760296i \(-0.274946\pi\)
−0.522354 + 0.852729i \(0.674946\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 44.0000 1.72582
\(651\) 4.04508 + 2.93893i 0.158539 + 0.115186i
\(652\) 15.4508 47.5528i 0.605102 1.86231i
\(653\) 3.09017 + 9.51057i 0.120928 + 0.372177i 0.993137 0.116955i \(-0.0373134\pi\)
−0.872209 + 0.489133i \(0.837313\pi\)
\(654\) −1.61803 + 1.17557i −0.0632701 + 0.0459684i
\(655\) −19.4164 + 14.1068i −0.758662 + 0.551200i
\(656\) −2.47214 7.60845i −0.0965207 0.297060i
\(657\) 3.39919 10.4616i 0.132615 0.408147i
\(658\) 3.23607 + 2.35114i 0.126155 + 0.0916570i
\(659\) −46.0000 −1.79191 −0.895953 0.444149i \(-0.853506\pi\)
−0.895953 + 0.444149i \(0.853506\pi\)
\(660\) 0 0
\(661\) −5.00000 −0.194477 −0.0972387 0.995261i \(-0.531001\pi\)
−0.0972387 + 0.995261i \(0.531001\pi\)
\(662\) 17.7984 + 12.9313i 0.691753 + 0.502588i
\(663\) 2.47214 7.60845i 0.0960098 0.295488i
\(664\) 0 0
\(665\) 9.70820 7.05342i 0.376468 0.273520i
\(666\) −4.85410 + 3.52671i −0.188093 + 0.136657i
\(667\) −3.70820 11.4127i −0.143582 0.441901i
\(668\) 11.1246 34.2380i 0.430424 1.32471i
\(669\) −13.7533 9.99235i −0.531733 0.386327i
\(670\) −8.00000 −0.309067
\(671\) 0 0
\(672\) −8.00000 −0.308607
\(673\) −10.5172 7.64121i −0.405409 0.294547i 0.366332 0.930484i \(-0.380614\pi\)
−0.771741 + 0.635937i \(0.780614\pi\)
\(674\) −3.09017 + 9.51057i −0.119029 + 0.366333i
\(675\) −3.39919 10.4616i −0.130835 0.402668i
\(676\) 14.5623 10.5801i 0.560089 0.406928i
\(677\) 9.70820 7.05342i 0.373117 0.271085i −0.385386 0.922756i \(-0.625932\pi\)
0.758502 + 0.651671i \(0.225932\pi\)
\(678\) −3.70820 11.4127i −0.142413 0.438301i
\(679\) −1.54508 + 4.75528i −0.0592949 + 0.182491i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −34.0000 −1.30097 −0.650487 0.759517i \(-0.725435\pi\)
−0.650487 + 0.759517i \(0.725435\pi\)
\(684\) −4.85410 3.52671i −0.185601 0.134847i
\(685\) 9.88854 30.4338i 0.377822 1.16282i
\(686\) 8.03444 + 24.7275i 0.306756 + 0.944099i
\(687\) −14.5623 + 10.5801i −0.555587 + 0.403657i
\(688\) −38.8328 + 28.2137i −1.48049 + 1.07564i
\(689\) 3.70820 + 11.4127i 0.141271 + 0.434788i
\(690\) −4.94427 + 15.2169i −0.188225 + 0.579298i
\(691\) −8.89919 6.46564i −0.338541 0.245964i 0.405505 0.914093i \(-0.367096\pi\)
−0.744046 + 0.668128i \(0.767096\pi\)
\(692\) −48.0000 −1.82469
\(693\) 0 0
\(694\) 4.00000 0.151838
\(695\) 51.7771 + 37.6183i 1.96402 + 1.42694i
\(696\) 0 0
\(697\) −2.47214 7.60845i −0.0936388 0.288191i
\(698\) 24.2705 17.6336i 0.918652 0.667440i
\(699\) −14.5623 + 10.5801i −0.550797 + 0.400177i
\(700\) −6.79837 20.9232i −0.256954 0.790824i
\(701\) −15.4508 + 47.5528i −0.583571 + 1.79605i 0.0213660 + 0.999772i \(0.493198\pi\)
−0.604936 + 0.796274i \(0.706802\pi\)
\(702\) 3.23607 + 2.35114i 0.122138 + 0.0887381i
\(703\) 9.00000 0.339441
\(704\) 0 0
\(705\) −8.00000 −0.301297
\(706\) 19.4164 + 14.1068i 0.730746 + 0.530918i
\(707\) −3.09017 + 9.51057i −0.116218 + 0.357682i
\(708\) 6.18034 + 19.0211i 0.232271 + 0.714858i
\(709\) −21.0344 + 15.2824i −0.789965 + 0.573943i −0.907953 0.419072i \(-0.862356\pi\)
0.117988 + 0.993015i \(0.462356\pi\)
\(710\) 0 0
\(711\) −3.39919 10.4616i −0.127479 0.392341i
\(712\) 0 0
\(713\) 8.09017 + 5.87785i 0.302979 + 0.220127i
\(714\) −8.00000 −0.299392
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) −4.85410 3.52671i −0.181280 0.131707i
\(718\) −2.47214 + 7.60845i −0.0922593 + 0.283945i
\(719\) −1.85410 5.70634i −0.0691463 0.212811i 0.910512 0.413482i \(-0.135688\pi\)
−0.979659 + 0.200672i \(0.935688\pi\)
\(720\) 12.9443 9.40456i 0.482405 0.350487i
\(721\) −5.66312 + 4.11450i −0.210906 + 0.153232i
\(722\) −6.18034 19.0211i −0.230008 0.707893i
\(723\) −4.32624 + 13.3148i −0.160895 + 0.495182i
\(724\) 37.2148 + 27.0381i 1.38308 + 1.00486i
\(725\) −66.0000 −2.45118
\(726\) 0 0
\(727\) −12.0000 −0.445055 −0.222528 0.974926i \(-0.571431\pi\)
−0.222528 + 0.974926i \(0.571431\pi\)
\(728\) 0 0
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) 27.1935 + 83.6930i 1.00648 + 3.09762i
\(731\) −38.8328 + 28.2137i −1.43628 + 1.04352i
\(732\) −4.85410 + 3.52671i −0.179413 + 0.130351i
\(733\) 9.27051 + 28.5317i 0.342414 + 1.05384i 0.962954 + 0.269667i \(0.0869136\pi\)
−0.620540 + 0.784175i \(0.713086\pi\)
\(734\) −4.94427 + 15.2169i −0.182496 + 0.561666i
\(735\) −19.4164 14.1068i −0.716185 0.520339i
\(736\) −16.0000 −0.589768
\(737\) 0 0
\(738\) 4.00000 0.147242
\(739\) 33.1697 + 24.0992i 1.22017 + 0.886503i 0.996114 0.0880737i \(-0.0280711\pi\)
0.224053 + 0.974577i \(0.428071\pi\)
\(740\) 7.41641 22.8254i 0.272633 0.839077i
\(741\) −1.85410 5.70634i −0.0681121 0.209628i
\(742\) 9.70820 7.05342i 0.356399 0.258939i
\(743\) −16.1803 + 11.7557i −0.593599 + 0.431275i −0.843601 0.536970i \(-0.819569\pi\)
0.250002 + 0.968245i \(0.419569\pi\)
\(744\) 0 0
\(745\) 19.7771 60.8676i 0.724576 2.23002i
\(746\) 11.3262 + 8.22899i 0.414683 + 0.301285i
\(747\) −6.00000 −0.219529
\(748\) 0 0
\(749\) −18.0000 −0.657706
\(750\) 38.8328 + 28.2137i 1.41797 + 1.03022i
\(751\) 5.87132 18.0701i 0.214248 0.659386i −0.784959 0.619548i \(-0.787316\pi\)
0.999206 0.0398381i \(-0.0126842\pi\)
\(752\) −2.47214 7.60845i −0.0901495 0.277452i
\(753\) −1.61803 + 1.17557i −0.0589644 + 0.0428402i
\(754\) 19.4164 14.1068i 0.707104 0.513741i
\(755\) 19.7771 + 60.8676i 0.719762 + 2.21520i
\(756\) 0.618034 1.90211i 0.0224777 0.0691792i
\(757\) −4.04508 2.93893i −0.147021 0.106817i 0.511843 0.859079i \(-0.328963\pi\)
−0.658864 + 0.752262i \(0.728963\pi\)
\(758\) 32.0000 1.16229
\(759\) 0 0
\(760\) 0 0
\(761\) −19.4164 14.1068i −0.703844 0.511373i 0.177338 0.984150i \(-0.443252\pi\)
−0.881182 + 0.472777i \(0.843252\pi\)
\(762\) −8.03444 + 24.7275i −0.291057 + 0.895782i
\(763\) 0.309017 + 0.951057i 0.0111872 + 0.0344306i
\(764\) −12.9443 + 9.40456i −0.468307 + 0.340245i
\(765\) 12.9443 9.40456i 0.468001 0.340023i
\(766\) 16.0689 + 49.4549i 0.580592 + 1.78688i
\(767\) −6.18034 + 19.0211i −0.223159 + 0.686813i
\(768\) 12.9443 + 9.40456i 0.467086 + 0.339358i
\(769\) −11.0000 −0.396670 −0.198335 0.980134i \(-0.563553\pi\)
−0.198335 + 0.980134i \(0.563553\pi\)
\(770\) 0 0
\(771\) 14.0000 0.504198
\(772\) −8.09017 5.87785i −0.291172 0.211549i
\(773\) 11.1246 34.2380i 0.400124 1.23146i −0.524774 0.851242i \(-0.675850\pi\)
0.924898 0.380215i \(-0.124150\pi\)
\(774\)