Properties

Label 363.2.e.g.202.1
Level $363$
Weight $2$
Character 363.202
Analytic conductor $2.899$
Analytic rank $0$
Dimension $4$
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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 33)
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.g.124.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.809017 + 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.61803 - 1.17557i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(-1.23607 - 3.80423i) q^{7} +(0.927051 - 2.85317i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(0.809017 + 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.61803 - 1.17557i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(-1.23607 - 3.80423i) q^{7} +(0.927051 - 2.85317i) q^{8} +(-0.809017 - 0.587785i) q^{9} +2.00000 q^{10} +1.00000 q^{12} +(-1.61803 - 1.17557i) q^{13} +(1.23607 - 3.80423i) q^{14} +(0.618034 + 1.90211i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-1.61803 + 1.17557i) q^{17} +(-0.309017 - 0.951057i) q^{18} +(-1.61803 - 1.17557i) q^{20} +4.00000 q^{21} +8.00000 q^{23} +(2.42705 + 1.76336i) q^{24} +(-0.309017 + 0.951057i) q^{25} +(-0.618034 - 1.90211i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-3.23607 + 2.35114i) q^{28} +(1.85410 + 5.70634i) q^{29} +(-0.618034 + 1.90211i) q^{30} +(6.47214 + 4.70228i) q^{31} -5.00000 q^{32} -2.00000 q^{34} +(-6.47214 - 4.70228i) q^{35} +(-0.309017 + 0.951057i) q^{36} +(1.85410 + 5.70634i) q^{37} +(1.61803 - 1.17557i) q^{39} +(-1.85410 - 5.70634i) q^{40} +(0.618034 - 1.90211i) q^{41} +(3.23607 + 2.35114i) q^{42} -2.00000 q^{45} +(6.47214 + 4.70228i) q^{46} +(2.47214 - 7.60845i) q^{47} +(0.309017 + 0.951057i) q^{48} +(-7.28115 + 5.29007i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(-0.618034 - 1.90211i) q^{51} +(-0.618034 + 1.90211i) q^{52} +(-4.85410 - 3.52671i) q^{53} +1.00000 q^{54} -12.0000 q^{56} +(-1.85410 + 5.70634i) q^{58} +(-1.23607 - 3.80423i) q^{59} +(1.61803 - 1.17557i) q^{60} +(4.85410 - 3.52671i) q^{61} +(2.47214 + 7.60845i) q^{62} +(-1.23607 + 3.80423i) q^{63} +(-5.66312 - 4.11450i) q^{64} -4.00000 q^{65} -4.00000 q^{67} +(1.61803 + 1.17557i) q^{68} +(-2.47214 + 7.60845i) q^{69} +(-2.47214 - 7.60845i) q^{70} +(-2.42705 + 1.76336i) q^{72} +(4.32624 + 13.3148i) q^{73} +(-1.85410 + 5.70634i) q^{74} +(-0.809017 - 0.587785i) q^{75} +2.00000 q^{78} +(-3.23607 - 2.35114i) q^{79} +(0.618034 - 1.90211i) q^{80} +(0.309017 + 0.951057i) q^{81} +(1.61803 - 1.17557i) q^{82} +(9.70820 - 7.05342i) q^{83} +(-1.23607 - 3.80423i) q^{84} +(-1.23607 + 3.80423i) q^{85} -6.00000 q^{87} -6.00000 q^{89} +(-1.61803 - 1.17557i) q^{90} +(-2.47214 + 7.60845i) q^{91} +(-2.47214 - 7.60845i) q^{92} +(-6.47214 + 4.70228i) q^{93} +(6.47214 - 4.70228i) q^{94} +(1.54508 - 4.75528i) q^{96} +(-1.61803 - 1.17557i) q^{97} -9.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{2} + q^{3} + q^{4} + 2 q^{5} - q^{6} + 4 q^{7} - 3 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{2} + q^{3} + q^{4} + 2 q^{5} - q^{6} + 4 q^{7} - 3 q^{8} - q^{9} + 8 q^{10} + 4 q^{12} - 2 q^{13} - 4 q^{14} - 2 q^{15} + q^{16} - 2 q^{17} + q^{18} - 2 q^{20} + 16 q^{21} + 32 q^{23} + 3 q^{24} + q^{25} + 2 q^{26} + q^{27} - 4 q^{28} - 6 q^{29} + 2 q^{30} + 8 q^{31} - 20 q^{32} - 8 q^{34} - 8 q^{35} + q^{36} - 6 q^{37} + 2 q^{39} + 6 q^{40} - 2 q^{41} + 4 q^{42} - 8 q^{45} + 8 q^{46} - 8 q^{47} - q^{48} - 9 q^{49} - q^{50} + 2 q^{51} + 2 q^{52} - 6 q^{53} + 4 q^{54} - 48 q^{56} + 6 q^{58} + 4 q^{59} + 2 q^{60} + 6 q^{61} - 8 q^{62} + 4 q^{63} - 7 q^{64} - 16 q^{65} - 16 q^{67} + 2 q^{68} + 8 q^{69} + 8 q^{70} - 3 q^{72} - 14 q^{73} + 6 q^{74} - q^{75} + 8 q^{78} - 4 q^{79} - 2 q^{80} - q^{81} + 2 q^{82} + 12 q^{83} + 4 q^{84} + 4 q^{85} - 24 q^{87} - 24 q^{89} - 2 q^{90} + 8 q^{91} + 8 q^{92} - 8 q^{93} + 8 q^{94} - 5 q^{96} - 2 q^{97} - 36 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.809017 + 0.587785i 0.572061 + 0.415627i 0.835853 0.548953i \(-0.184973\pi\)
−0.263792 + 0.964580i \(0.584973\pi\)
\(3\) −0.309017 + 0.951057i −0.178411 + 0.549093i
\(4\) −0.309017 0.951057i −0.154508 0.475528i
\(5\) 1.61803 1.17557i 0.723607 0.525731i −0.163928 0.986472i \(-0.552416\pi\)
0.887535 + 0.460741i \(0.152416\pi\)
\(6\) −0.809017 + 0.587785i −0.330280 + 0.239962i
\(7\) −1.23607 3.80423i −0.467190 1.43786i −0.856208 0.516632i \(-0.827186\pi\)
0.389018 0.921230i \(-0.372814\pi\)
\(8\) 0.927051 2.85317i 0.327762 1.00875i
\(9\) −0.809017 0.587785i −0.269672 0.195928i
\(10\) 2.00000 0.632456
\(11\) 0 0
\(12\) 1.00000 0.288675
\(13\) −1.61803 1.17557i −0.448762 0.326045i 0.340345 0.940301i \(-0.389456\pi\)
−0.789107 + 0.614256i \(0.789456\pi\)
\(14\) 1.23607 3.80423i 0.330353 1.01672i
\(15\) 0.618034 + 1.90211i 0.159576 + 0.491123i
\(16\) 0.809017 0.587785i 0.202254 0.146946i
\(17\) −1.61803 + 1.17557i −0.392431 + 0.285118i −0.766451 0.642303i \(-0.777979\pi\)
0.374020 + 0.927421i \(0.377979\pi\)
\(18\) −0.309017 0.951057i −0.0728360 0.224166i
\(19\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(20\) −1.61803 1.17557i −0.361803 0.262866i
\(21\) 4.00000 0.872872
\(22\) 0 0
\(23\) 8.00000 1.66812 0.834058 0.551677i \(-0.186012\pi\)
0.834058 + 0.551677i \(0.186012\pi\)
\(24\) 2.42705 + 1.76336i 0.495420 + 0.359943i
\(25\) −0.309017 + 0.951057i −0.0618034 + 0.190211i
\(26\) −0.618034 1.90211i −0.121206 0.373035i
\(27\) 0.809017 0.587785i 0.155695 0.113119i
\(28\) −3.23607 + 2.35114i −0.611559 + 0.444324i
\(29\) 1.85410 + 5.70634i 0.344298 + 1.05964i 0.961958 + 0.273196i \(0.0880806\pi\)
−0.617660 + 0.786445i \(0.711919\pi\)
\(30\) −0.618034 + 1.90211i −0.112837 + 0.347277i
\(31\) 6.47214 + 4.70228i 1.16243 + 0.844555i 0.990083 0.140482i \(-0.0448651\pi\)
0.172347 + 0.985036i \(0.444865\pi\)
\(32\) −5.00000 −0.883883
\(33\) 0 0
\(34\) −2.00000 −0.342997
\(35\) −6.47214 4.70228i −1.09399 0.794831i
\(36\) −0.309017 + 0.951057i −0.0515028 + 0.158509i
\(37\) 1.85410 + 5.70634i 0.304812 + 0.938116i 0.979747 + 0.200239i \(0.0641718\pi\)
−0.674935 + 0.737878i \(0.735828\pi\)
\(38\) 0 0
\(39\) 1.61803 1.17557i 0.259093 0.188242i
\(40\) −1.85410 5.70634i −0.293159 0.902251i
\(41\) 0.618034 1.90211i 0.0965207 0.297060i −0.891126 0.453755i \(-0.850084\pi\)
0.987647 + 0.156695i \(0.0500840\pi\)
\(42\) 3.23607 + 2.35114i 0.499336 + 0.362789i
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) −2.00000 −0.298142
\(46\) 6.47214 + 4.70228i 0.954264 + 0.693314i
\(47\) 2.47214 7.60845i 0.360598 1.10981i −0.592094 0.805869i \(-0.701699\pi\)
0.952692 0.303938i \(-0.0983015\pi\)
\(48\) 0.309017 + 0.951057i 0.0446028 + 0.137273i
\(49\) −7.28115 + 5.29007i −1.04016 + 0.755724i
\(50\) −0.809017 + 0.587785i −0.114412 + 0.0831254i
\(51\) −0.618034 1.90211i −0.0865421 0.266349i
\(52\) −0.618034 + 1.90211i −0.0857059 + 0.263776i
\(53\) −4.85410 3.52671i −0.666762 0.484431i 0.202178 0.979349i \(-0.435198\pi\)
−0.868940 + 0.494918i \(0.835198\pi\)
\(54\) 1.00000 0.136083
\(55\) 0 0
\(56\) −12.0000 −1.60357
\(57\) 0 0
\(58\) −1.85410 + 5.70634i −0.243456 + 0.749279i
\(59\) −1.23607 3.80423i −0.160922 0.495268i 0.837790 0.545992i \(-0.183847\pi\)
−0.998713 + 0.0507240i \(0.983847\pi\)
\(60\) 1.61803 1.17557i 0.208887 0.151765i
\(61\) 4.85410 3.52671i 0.621504 0.451549i −0.231942 0.972730i \(-0.574508\pi\)
0.853447 + 0.521180i \(0.174508\pi\)
\(62\) 2.47214 + 7.60845i 0.313962 + 0.966274i
\(63\) −1.23607 + 3.80423i −0.155730 + 0.479287i
\(64\) −5.66312 4.11450i −0.707890 0.514312i
\(65\) −4.00000 −0.496139
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 1.61803 + 1.17557i 0.196215 + 0.142559i
\(69\) −2.47214 + 7.60845i −0.297610 + 0.915950i
\(70\) −2.47214 7.60845i −0.295477 0.909384i
\(71\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(72\) −2.42705 + 1.76336i −0.286031 + 0.207813i
\(73\) 4.32624 + 13.3148i 0.506348 + 1.55838i 0.798493 + 0.602004i \(0.205631\pi\)
−0.292145 + 0.956374i \(0.594369\pi\)
\(74\) −1.85410 + 5.70634i −0.215535 + 0.663348i
\(75\) −0.809017 0.587785i −0.0934172 0.0678716i
\(76\) 0 0
\(77\) 0 0
\(78\) 2.00000 0.226455
\(79\) −3.23607 2.35114i −0.364086 0.264524i 0.390668 0.920532i \(-0.372244\pi\)
−0.754754 + 0.656007i \(0.772244\pi\)
\(80\) 0.618034 1.90211i 0.0690983 0.212663i
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) 1.61803 1.17557i 0.178682 0.129820i
\(83\) 9.70820 7.05342i 1.06561 0.774214i 0.0904951 0.995897i \(-0.471155\pi\)
0.975119 + 0.221683i \(0.0711551\pi\)
\(84\) −1.23607 3.80423i −0.134866 0.415075i
\(85\) −1.23607 + 3.80423i −0.134070 + 0.412626i
\(86\) 0 0
\(87\) −6.00000 −0.643268
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) −1.61803 1.17557i −0.170556 0.123916i
\(91\) −2.47214 + 7.60845i −0.259150 + 0.797582i
\(92\) −2.47214 7.60845i −0.257738 0.793236i
\(93\) −6.47214 + 4.70228i −0.671129 + 0.487604i
\(94\) 6.47214 4.70228i 0.667550 0.485003i
\(95\) 0 0
\(96\) 1.54508 4.75528i 0.157695 0.485334i
\(97\) −1.61803 1.17557i −0.164286 0.119361i 0.502604 0.864517i \(-0.332375\pi\)
−0.666891 + 0.745155i \(0.732375\pi\)
\(98\) −9.00000 −0.909137
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) 1.61803 + 1.17557i 0.161000 + 0.116974i 0.665368 0.746515i \(-0.268274\pi\)
−0.504368 + 0.863489i \(0.668274\pi\)
\(102\) 0.618034 1.90211i 0.0611945 0.188337i
\(103\) 2.47214 + 7.60845i 0.243587 + 0.749683i 0.995866 + 0.0908382i \(0.0289546\pi\)
−0.752279 + 0.658845i \(0.771045\pi\)
\(104\) −4.85410 + 3.52671i −0.475984 + 0.345823i
\(105\) 6.47214 4.70228i 0.631616 0.458896i
\(106\) −1.85410 5.70634i −0.180086 0.554249i
\(107\) 3.70820 11.4127i 0.358486 1.10331i −0.595475 0.803374i \(-0.703036\pi\)
0.953961 0.299932i \(-0.0969638\pi\)
\(108\) −0.809017 0.587785i −0.0778477 0.0565597i
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 0 0
\(111\) −6.00000 −0.569495
\(112\) −3.23607 2.35114i −0.305780 0.222162i
\(113\) −1.85410 + 5.70634i −0.174419 + 0.536807i −0.999606 0.0280521i \(-0.991070\pi\)
0.825187 + 0.564859i \(0.191070\pi\)
\(114\) 0 0
\(115\) 12.9443 9.40456i 1.20706 0.876980i
\(116\) 4.85410 3.52671i 0.450692 0.327447i
\(117\) 0.618034 + 1.90211i 0.0571373 + 0.175850i
\(118\) 1.23607 3.80423i 0.113789 0.350207i
\(119\) 6.47214 + 4.70228i 0.593300 + 0.431057i
\(120\) 6.00000 0.547723
\(121\) 0 0
\(122\) 6.00000 0.543214
\(123\) 1.61803 + 1.17557i 0.145893 + 0.105998i
\(124\) 2.47214 7.60845i 0.222004 0.683259i
\(125\) 3.70820 + 11.4127i 0.331672 + 1.02078i
\(126\) −3.23607 + 2.35114i −0.288292 + 0.209456i
\(127\) −3.23607 + 2.35114i −0.287155 + 0.208630i −0.722032 0.691860i \(-0.756792\pi\)
0.434877 + 0.900490i \(0.356792\pi\)
\(128\) 0.927051 + 2.85317i 0.0819405 + 0.252187i
\(129\) 0 0
\(130\) −3.23607 2.35114i −0.283822 0.206209i
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −3.23607 2.35114i −0.279554 0.203108i
\(135\) 0.618034 1.90211i 0.0531919 0.163708i
\(136\) 1.85410 + 5.70634i 0.158988 + 0.489315i
\(137\) −1.61803 + 1.17557i −0.138238 + 0.100436i −0.654755 0.755841i \(-0.727228\pi\)
0.516517 + 0.856277i \(0.327228\pi\)
\(138\) −6.47214 + 4.70228i −0.550945 + 0.400285i
\(139\) 2.47214 + 7.60845i 0.209684 + 0.645340i 0.999488 + 0.0319820i \(0.0101819\pi\)
−0.789805 + 0.613359i \(0.789818\pi\)
\(140\) −2.47214 + 7.60845i −0.208934 + 0.643032i
\(141\) 6.47214 + 4.70228i 0.545052 + 0.396004i
\(142\) 0 0
\(143\) 0 0
\(144\) −1.00000 −0.0833333
\(145\) 9.70820 + 7.05342i 0.806222 + 0.585755i
\(146\) −4.32624 + 13.3148i −0.358042 + 1.10194i
\(147\) −2.78115 8.55951i −0.229386 0.705976i
\(148\) 4.85410 3.52671i 0.399005 0.289894i
\(149\) −17.7984 + 12.9313i −1.45810 + 1.05937i −0.474247 + 0.880392i \(0.657280\pi\)
−0.983853 + 0.178979i \(0.942720\pi\)
\(150\) −0.309017 0.951057i −0.0252311 0.0776534i
\(151\) −6.18034 + 19.0211i −0.502949 + 1.54792i 0.301243 + 0.953548i \(0.402599\pi\)
−0.804192 + 0.594370i \(0.797401\pi\)
\(152\) 0 0
\(153\) 2.00000 0.161690
\(154\) 0 0
\(155\) 16.0000 1.28515
\(156\) −1.61803 1.17557i −0.129546 0.0941210i
\(157\) 4.32624 13.3148i 0.345271 1.06264i −0.616167 0.787616i \(-0.711315\pi\)
0.961438 0.275020i \(-0.0886846\pi\)
\(158\) −1.23607 3.80423i −0.0983363 0.302648i
\(159\) 4.85410 3.52671i 0.384955 0.279686i
\(160\) −8.09017 + 5.87785i −0.639584 + 0.464685i
\(161\) −9.88854 30.4338i −0.779326 2.39852i
\(162\) −0.309017 + 0.951057i −0.0242787 + 0.0747221i
\(163\) −3.23607 2.35114i −0.253468 0.184156i 0.453794 0.891107i \(-0.350070\pi\)
−0.707263 + 0.706951i \(0.750070\pi\)
\(164\) −2.00000 −0.156174
\(165\) 0 0
\(166\) 12.0000 0.931381
\(167\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(168\) 3.70820 11.4127i 0.286094 0.880507i
\(169\) −2.78115 8.55951i −0.213935 0.658424i
\(170\) −3.23607 + 2.35114i −0.248195 + 0.180324i
\(171\) 0 0
\(172\) 0 0
\(173\) 1.85410 5.70634i 0.140965 0.433845i −0.855505 0.517794i \(-0.826753\pi\)
0.996470 + 0.0839492i \(0.0267533\pi\)
\(174\) −4.85410 3.52671i −0.367989 0.267359i
\(175\) 4.00000 0.302372
\(176\) 0 0
\(177\) 4.00000 0.300658
\(178\) −4.85410 3.52671i −0.363830 0.264338i
\(179\) 3.70820 11.4127i 0.277164 0.853024i −0.711474 0.702712i \(-0.751972\pi\)
0.988639 0.150312i \(-0.0480277\pi\)
\(180\) 0.618034 + 1.90211i 0.0460655 + 0.141775i
\(181\) −17.7984 + 12.9313i −1.32294 + 0.961174i −0.323052 + 0.946381i \(0.604709\pi\)
−0.999891 + 0.0147930i \(0.995291\pi\)
\(182\) −6.47214 + 4.70228i −0.479747 + 0.348556i
\(183\) 1.85410 + 5.70634i 0.137059 + 0.421825i
\(184\) 7.41641 22.8254i 0.546745 1.68271i
\(185\) 9.70820 + 7.05342i 0.713761 + 0.518578i
\(186\) −8.00000 −0.586588
\(187\) 0 0
\(188\) −8.00000 −0.583460
\(189\) −3.23607 2.35114i −0.235389 0.171020i
\(190\) 0 0
\(191\) 2.47214 + 7.60845i 0.178877 + 0.550528i 0.999789 0.0205267i \(-0.00653431\pi\)
−0.820912 + 0.571055i \(0.806534\pi\)
\(192\) 5.66312 4.11450i 0.408700 0.296938i
\(193\) −11.3262 + 8.22899i −0.815280 + 0.592336i −0.915357 0.402644i \(-0.868091\pi\)
0.100076 + 0.994980i \(0.468091\pi\)
\(194\) −0.618034 1.90211i −0.0443723 0.136564i
\(195\) 1.23607 3.80423i 0.0885167 0.272426i
\(196\) 7.28115 + 5.29007i 0.520082 + 0.377862i
\(197\) 14.0000 0.997459 0.498729 0.866758i \(-0.333800\pi\)
0.498729 + 0.866758i \(0.333800\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 2.42705 + 1.76336i 0.171618 + 0.124688i
\(201\) 1.23607 3.80423i 0.0871855 0.268329i
\(202\) 0.618034 + 1.90211i 0.0434847 + 0.133832i
\(203\) 19.4164 14.1068i 1.36276 0.990106i
\(204\) −1.61803 + 1.17557i −0.113285 + 0.0823064i
\(205\) −1.23607 3.80423i −0.0863307 0.265699i
\(206\) −2.47214 + 7.60845i −0.172242 + 0.530106i
\(207\) −6.47214 4.70228i −0.449845 0.326831i
\(208\) −2.00000 −0.138675
\(209\) 0 0
\(210\) 8.00000 0.552052
\(211\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(212\) −1.85410 + 5.70634i −0.127340 + 0.391913i
\(213\) 0 0
\(214\) 9.70820 7.05342i 0.663639 0.482162i
\(215\) 0 0
\(216\) −0.927051 2.85317i −0.0630778 0.194134i
\(217\) 9.88854 30.4338i 0.671278 2.06598i
\(218\) 1.61803 + 1.17557i 0.109587 + 0.0796197i
\(219\) −14.0000 −0.946032
\(220\) 0 0
\(221\) 4.00000 0.269069
\(222\) −4.85410 3.52671i −0.325786 0.236697i
\(223\) 4.94427 15.2169i 0.331093 1.01900i −0.637522 0.770432i \(-0.720040\pi\)
0.968615 0.248567i \(-0.0799596\pi\)
\(224\) 6.18034 + 19.0211i 0.412941 + 1.27090i
\(225\) 0.809017 0.587785i 0.0539345 0.0391857i
\(226\) −4.85410 + 3.52671i −0.322890 + 0.234593i
\(227\) −3.70820 11.4127i −0.246122 0.757486i −0.995450 0.0952867i \(-0.969623\pi\)
0.749328 0.662199i \(-0.230377\pi\)
\(228\) 0 0
\(229\) −4.85410 3.52671i −0.320768 0.233052i 0.415735 0.909486i \(-0.363524\pi\)
−0.736503 + 0.676434i \(0.763524\pi\)
\(230\) 16.0000 1.05501
\(231\) 0 0
\(232\) 18.0000 1.18176
\(233\) 24.2705 + 17.6336i 1.59001 + 1.15521i 0.903921 + 0.427698i \(0.140675\pi\)
0.686092 + 0.727514i \(0.259325\pi\)
\(234\) −0.618034 + 1.90211i −0.0404021 + 0.124345i
\(235\) −4.94427 15.2169i −0.322529 0.992641i
\(236\) −3.23607 + 2.35114i −0.210650 + 0.153046i
\(237\) 3.23607 2.35114i 0.210205 0.152723i
\(238\) 2.47214 + 7.60845i 0.160245 + 0.493183i
\(239\) −7.41641 + 22.8254i −0.479728 + 1.47645i 0.359747 + 0.933050i \(0.382863\pi\)
−0.839474 + 0.543400i \(0.817137\pi\)
\(240\) 1.61803 + 1.17557i 0.104444 + 0.0758827i
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) −4.85410 3.52671i −0.310752 0.225775i
\(245\) −5.56231 + 17.1190i −0.355363 + 1.09369i
\(246\) 0.618034 + 1.90211i 0.0394044 + 0.121274i
\(247\) 0 0
\(248\) 19.4164 14.1068i 1.23294 0.895786i
\(249\) 3.70820 + 11.4127i 0.234998 + 0.723249i
\(250\) −3.70820 + 11.4127i −0.234527 + 0.721801i
\(251\) −3.23607 2.35114i −0.204259 0.148403i 0.480953 0.876746i \(-0.340291\pi\)
−0.685212 + 0.728343i \(0.740291\pi\)
\(252\) 4.00000 0.251976
\(253\) 0 0
\(254\) −4.00000 −0.250982
\(255\) −3.23607 2.35114i −0.202650 0.147234i
\(256\) −5.25329 + 16.1680i −0.328331 + 1.01050i
\(257\) −4.32624 13.3148i −0.269863 0.830554i −0.990533 0.137275i \(-0.956166\pi\)
0.720670 0.693279i \(-0.243834\pi\)
\(258\) 0 0
\(259\) 19.4164 14.1068i 1.20648 0.876557i
\(260\) 1.23607 + 3.80423i 0.0766577 + 0.235928i
\(261\) 1.85410 5.70634i 0.114766 0.353214i
\(262\) 9.70820 + 7.05342i 0.599775 + 0.435762i
\(263\) 16.0000 0.986602 0.493301 0.869859i \(-0.335790\pi\)
0.493301 + 0.869859i \(0.335790\pi\)
\(264\) 0 0
\(265\) −12.0000 −0.737154
\(266\) 0 0
\(267\) 1.85410 5.70634i 0.113469 0.349222i
\(268\) 1.23607 + 3.80423i 0.0755049 + 0.232380i
\(269\) 1.61803 1.17557i 0.0986533 0.0716758i −0.537365 0.843350i \(-0.680580\pi\)
0.636018 + 0.771674i \(0.280580\pi\)
\(270\) 1.61803 1.17557i 0.0984704 0.0715429i
\(271\) −6.18034 19.0211i −0.375429 1.15545i −0.943189 0.332257i \(-0.892190\pi\)
0.567760 0.823194i \(-0.307810\pi\)
\(272\) −0.618034 + 1.90211i −0.0374738 + 0.115333i
\(273\) −6.47214 4.70228i −0.391711 0.284595i
\(274\) −2.00000 −0.120824
\(275\) 0 0
\(276\) 8.00000 0.481543
\(277\) −21.0344 15.2824i −1.26384 0.918231i −0.264898 0.964277i \(-0.585338\pi\)
−0.998939 + 0.0460451i \(0.985338\pi\)
\(278\) −2.47214 + 7.60845i −0.148269 + 0.456325i
\(279\) −2.47214 7.60845i −0.148003 0.455506i
\(280\) −19.4164 + 14.1068i −1.16035 + 0.843045i
\(281\) −14.5623 + 10.5801i −0.868714 + 0.631158i −0.930242 0.366947i \(-0.880403\pi\)
0.0615273 + 0.998105i \(0.480403\pi\)
\(282\) 2.47214 + 7.60845i 0.147214 + 0.453077i
\(283\) −4.94427 + 15.2169i −0.293906 + 0.904551i 0.689680 + 0.724114i \(0.257751\pi\)
−0.983587 + 0.180437i \(0.942249\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −8.00000 −0.472225
\(288\) 4.04508 + 2.93893i 0.238359 + 0.173178i
\(289\) −4.01722 + 12.3637i −0.236307 + 0.727279i
\(290\) 3.70820 + 11.4127i 0.217753 + 0.670176i
\(291\) 1.61803 1.17557i 0.0948508 0.0689132i
\(292\) 11.3262 8.22899i 0.662818 0.481565i
\(293\) 1.85410 + 5.70634i 0.108318 + 0.333368i 0.990495 0.137550i \(-0.0439228\pi\)
−0.882177 + 0.470918i \(0.843923\pi\)
\(294\) 2.78115 8.55951i 0.162200 0.499201i
\(295\) −6.47214 4.70228i −0.376822 0.273777i
\(296\) 18.0000 1.04623
\(297\) 0 0
\(298\) −22.0000 −1.27443
\(299\) −12.9443 9.40456i −0.748587 0.543880i
\(300\) −0.309017 + 0.951057i −0.0178411 + 0.0549093i
\(301\) 0 0
\(302\) −16.1803 + 11.7557i −0.931074 + 0.676465i
\(303\) −1.61803 + 1.17557i −0.0929536 + 0.0675348i
\(304\) 0 0
\(305\) 3.70820 11.4127i 0.212331 0.653488i
\(306\) 1.61803 + 1.17557i 0.0924968 + 0.0672029i
\(307\) −32.0000 −1.82634 −0.913168 0.407583i \(-0.866372\pi\)
−0.913168 + 0.407583i \(0.866372\pi\)
\(308\) 0 0
\(309\) −8.00000 −0.455104
\(310\) 12.9443 + 9.40456i 0.735185 + 0.534143i
\(311\) −7.41641 + 22.8254i −0.420546 + 1.29431i 0.486649 + 0.873597i \(0.338219\pi\)
−0.907195 + 0.420710i \(0.861781\pi\)
\(312\) −1.85410 5.70634i −0.104968 0.323058i
\(313\) 17.7984 12.9313i 1.00602 0.730919i 0.0426523 0.999090i \(-0.486419\pi\)
0.963371 + 0.268171i \(0.0864192\pi\)
\(314\) 11.3262 8.22899i 0.639177 0.464389i
\(315\) 2.47214 + 7.60845i 0.139289 + 0.428688i
\(316\) −1.23607 + 3.80423i −0.0695343 + 0.214004i
\(317\) −17.7984 12.9313i −0.999656 0.726293i −0.0376418 0.999291i \(-0.511985\pi\)
−0.962014 + 0.272999i \(0.911985\pi\)
\(318\) 6.00000 0.336463
\(319\) 0 0
\(320\) −14.0000 −0.782624
\(321\) 9.70820 + 7.05342i 0.541859 + 0.393684i
\(322\) 9.88854 30.4338i 0.551067 1.69601i
\(323\) 0 0
\(324\) 0.809017 0.587785i 0.0449454 0.0326547i
\(325\) 1.61803 1.17557i 0.0897524 0.0652089i
\(326\) −1.23607 3.80423i −0.0684595 0.210697i
\(327\) −0.618034 + 1.90211i −0.0341774 + 0.105187i
\(328\) −4.85410 3.52671i −0.268023 0.194730i
\(329\) −32.0000 −1.76422
\(330\) 0 0
\(331\) −20.0000 −1.09930 −0.549650 0.835395i \(-0.685239\pi\)
−0.549650 + 0.835395i \(0.685239\pi\)
\(332\) −9.70820 7.05342i −0.532807 0.387107i
\(333\) 1.85410 5.70634i 0.101604 0.312705i
\(334\) 0 0
\(335\) −6.47214 + 4.70228i −0.353611 + 0.256913i
\(336\) 3.23607 2.35114i 0.176542 0.128265i
\(337\) 6.79837 + 20.9232i 0.370331 + 1.13976i 0.946575 + 0.322484i \(0.104518\pi\)
−0.576244 + 0.817278i \(0.695482\pi\)
\(338\) 2.78115 8.55951i 0.151275 0.465576i
\(339\) −4.85410 3.52671i −0.263639 0.191545i
\(340\) 4.00000 0.216930
\(341\) 0 0
\(342\) 0 0
\(343\) 6.47214 + 4.70228i 0.349462 + 0.253899i
\(344\) 0 0
\(345\) 4.94427 + 15.2169i 0.266191 + 0.819251i
\(346\) 4.85410 3.52671i 0.260958 0.189597i
\(347\) 3.23607 2.35114i 0.173721 0.126216i −0.497527 0.867448i \(-0.665758\pi\)
0.671248 + 0.741233i \(0.265758\pi\)
\(348\) 1.85410 + 5.70634i 0.0993903 + 0.305892i
\(349\) −1.85410 + 5.70634i −0.0992478 + 0.305453i −0.988337 0.152280i \(-0.951338\pi\)
0.889090 + 0.457733i \(0.151338\pi\)
\(350\) 3.23607 + 2.35114i 0.172975 + 0.125674i
\(351\) −2.00000 −0.106752
\(352\) 0 0
\(353\) 18.0000 0.958043 0.479022 0.877803i \(-0.340992\pi\)
0.479022 + 0.877803i \(0.340992\pi\)
\(354\) 3.23607 + 2.35114i 0.171995 + 0.124962i
\(355\) 0 0
\(356\) 1.85410 + 5.70634i 0.0982672 + 0.302435i
\(357\) −6.47214 + 4.70228i −0.342542 + 0.248871i
\(358\) 9.70820 7.05342i 0.513095 0.372785i
\(359\) 2.47214 + 7.60845i 0.130474 + 0.401559i 0.994859 0.101273i \(-0.0322915\pi\)
−0.864384 + 0.502832i \(0.832292\pi\)
\(360\) −1.85410 + 5.70634i −0.0977198 + 0.300750i
\(361\) 15.3713 + 11.1679i 0.809017 + 0.587785i
\(362\) −22.0000 −1.15629
\(363\) 0 0
\(364\) 8.00000 0.419314
\(365\) 22.6525 + 16.4580i 1.18568 + 0.861450i
\(366\) −1.85410 + 5.70634i −0.0969155 + 0.298275i
\(367\) −9.88854 30.4338i −0.516178 1.58863i −0.781129 0.624370i \(-0.785356\pi\)
0.264951 0.964262i \(-0.414644\pi\)
\(368\) 6.47214 4.70228i 0.337383 0.245123i
\(369\) −1.61803 + 1.17557i −0.0842315 + 0.0611978i
\(370\) 3.70820 + 11.4127i 0.192780 + 0.593317i
\(371\) −7.41641 + 22.8254i −0.385041 + 1.18503i
\(372\) 6.47214 + 4.70228i 0.335565 + 0.243802i
\(373\) 2.00000 0.103556 0.0517780 0.998659i \(-0.483511\pi\)
0.0517780 + 0.998659i \(0.483511\pi\)
\(374\) 0 0
\(375\) −12.0000 −0.619677
\(376\) −19.4164 14.1068i −1.00132 0.727505i
\(377\) 3.70820 11.4127i 0.190982 0.587783i
\(378\) −1.23607 3.80423i −0.0635765 0.195668i
\(379\) −22.6525 + 16.4580i −1.16358 + 0.845390i −0.990226 0.139470i \(-0.955460\pi\)
−0.173353 + 0.984860i \(0.555460\pi\)
\(380\) 0 0
\(381\) −1.23607 3.80423i −0.0633257 0.194896i
\(382\) −2.47214 + 7.60845i −0.126485 + 0.389282i
\(383\) 12.9443 + 9.40456i 0.661421 + 0.480551i 0.867143 0.498060i \(-0.165954\pi\)
−0.205721 + 0.978611i \(0.565954\pi\)
\(384\) −3.00000 −0.153093
\(385\) 0 0
\(386\) −14.0000 −0.712581
\(387\) 0 0
\(388\) −0.618034 + 1.90211i −0.0313759 + 0.0965652i
\(389\) −5.56231 17.1190i −0.282020 0.867969i −0.987276 0.159016i \(-0.949168\pi\)
0.705256 0.708953i \(-0.250832\pi\)
\(390\) 3.23607 2.35114i 0.163865 0.119055i
\(391\) −12.9443 + 9.40456i −0.654620 + 0.475609i
\(392\) 8.34346 + 25.6785i 0.421408 + 1.29696i
\(393\) −3.70820 + 11.4127i −0.187054 + 0.575693i
\(394\) 11.3262 + 8.22899i 0.570608 + 0.414571i
\(395\) −8.00000 −0.402524
\(396\) 0 0
\(397\) −2.00000 −0.100377 −0.0501886 0.998740i \(-0.515982\pi\)
−0.0501886 + 0.998740i \(0.515982\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.309017 + 0.951057i 0.0154508 + 0.0475528i
\(401\) −21.0344 + 15.2824i −1.05041 + 0.763167i −0.972290 0.233777i \(-0.924892\pi\)
−0.0781195 + 0.996944i \(0.524892\pi\)
\(402\) 3.23607 2.35114i 0.161400 0.117264i
\(403\) −4.94427 15.2169i −0.246292 0.758008i
\(404\) 0.618034 1.90211i 0.0307483 0.0946337i
\(405\) 1.61803 + 1.17557i 0.0804008 + 0.0584146i
\(406\) 24.0000 1.19110
\(407\) 0 0
\(408\) −6.00000 −0.297044
\(409\) 14.5623 + 10.5801i 0.720060 + 0.523154i 0.886403 0.462914i \(-0.153196\pi\)
−0.166344 + 0.986068i \(0.553196\pi\)
\(410\) 1.23607 3.80423i 0.0610450 0.187877i
\(411\) −0.618034 1.90211i −0.0304854 0.0938243i
\(412\) 6.47214 4.70228i 0.318859 0.231665i
\(413\) −12.9443 + 9.40456i −0.636946 + 0.462768i
\(414\) −2.47214 7.60845i −0.121499 0.373935i
\(415\) 7.41641 22.8254i 0.364057 1.12045i
\(416\) 8.09017 + 5.87785i 0.396653 + 0.288185i
\(417\) −8.00000 −0.391762
\(418\) 0 0
\(419\) −4.00000 −0.195413 −0.0977064 0.995215i \(-0.531151\pi\)
−0.0977064 + 0.995215i \(0.531151\pi\)
\(420\) −6.47214 4.70228i −0.315808 0.229448i
\(421\) −8.03444 + 24.7275i −0.391575 + 1.20514i 0.540022 + 0.841651i \(0.318416\pi\)
−0.931597 + 0.363492i \(0.881584\pi\)
\(422\) 0 0
\(423\) −6.47214 + 4.70228i −0.314686 + 0.228633i
\(424\) −14.5623 + 10.5801i −0.707208 + 0.513817i
\(425\) −0.618034 1.90211i −0.0299791 0.0922660i
\(426\) 0 0
\(427\) −19.4164 14.1068i −0.939626 0.682678i
\(428\) −12.0000 −0.580042
\(429\) 0 0
\(430\) 0 0
\(431\) −19.4164 14.1068i −0.935255 0.679503i 0.0120185 0.999928i \(-0.496174\pi\)
−0.947274 + 0.320425i \(0.896174\pi\)
\(432\) 0.309017 0.951057i 0.0148676 0.0457577i
\(433\) 10.5066 + 32.3359i 0.504914 + 1.55397i 0.800915 + 0.598778i \(0.204347\pi\)
−0.296001 + 0.955188i \(0.595653\pi\)
\(434\) 25.8885 18.8091i 1.24269 0.902867i
\(435\) −9.70820 + 7.05342i −0.465473 + 0.338186i
\(436\) −0.618034 1.90211i −0.0295985 0.0910947i
\(437\) 0 0
\(438\) −11.3262 8.22899i −0.541189 0.393197i
\(439\) 20.0000 0.954548 0.477274 0.878755i \(-0.341625\pi\)
0.477274 + 0.878755i \(0.341625\pi\)
\(440\) 0 0
\(441\) 9.00000 0.428571
\(442\) 3.23607 + 2.35114i 0.153924 + 0.111832i
\(443\) 8.65248 26.6296i 0.411092 1.26521i −0.504609 0.863348i \(-0.668363\pi\)
0.915700 0.401862i \(-0.131637\pi\)
\(444\) 1.85410 + 5.70634i 0.0879918 + 0.270811i
\(445\) −9.70820 + 7.05342i −0.460213 + 0.334364i
\(446\) 12.9443 9.40456i 0.612929 0.445319i
\(447\) −6.79837 20.9232i −0.321552 0.989635i
\(448\) −8.65248 + 26.6296i −0.408791 + 1.25813i
\(449\) −1.61803 1.17557i −0.0763597 0.0554786i 0.548950 0.835855i \(-0.315028\pi\)
−0.625310 + 0.780376i \(0.715028\pi\)
\(450\) 1.00000 0.0471405
\(451\) 0 0
\(452\) 6.00000 0.282216
\(453\) −16.1803 11.7557i −0.760219 0.552331i
\(454\) 3.70820 11.4127i 0.174035 0.535624i
\(455\) 4.94427 + 15.2169i 0.231791 + 0.713379i
\(456\) 0 0
\(457\) 14.5623 10.5801i 0.681196 0.494918i −0.192558 0.981286i \(-0.561678\pi\)
0.873754 + 0.486368i \(0.161678\pi\)
\(458\) −1.85410 5.70634i −0.0866365 0.266640i
\(459\) −0.618034 + 1.90211i −0.0288474 + 0.0887830i
\(460\) −12.9443 9.40456i −0.603530 0.438490i
\(461\) 30.0000 1.39724 0.698620 0.715493i \(-0.253798\pi\)
0.698620 + 0.715493i \(0.253798\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 4.85410 + 3.52671i 0.225346 + 0.163723i
\(465\) −4.94427 + 15.2169i −0.229285 + 0.705667i
\(466\) 9.27051 + 28.5317i 0.429448 + 1.32171i
\(467\) 9.70820 7.05342i 0.449242 0.326393i −0.340054 0.940406i \(-0.610445\pi\)
0.789296 + 0.614012i \(0.210445\pi\)
\(468\) 1.61803 1.17557i 0.0747936 0.0543408i
\(469\) 4.94427 + 15.2169i 0.228305 + 0.702651i
\(470\) 4.94427 15.2169i 0.228062 0.701903i
\(471\) 11.3262 + 8.22899i 0.521885 + 0.379172i
\(472\) −12.0000 −0.552345
\(473\) 0 0
\(474\) 4.00000 0.183726
\(475\) 0 0
\(476\) 2.47214 7.60845i 0.113310 0.348733i
\(477\) 1.85410 + 5.70634i 0.0848935 + 0.261275i
\(478\) −19.4164 + 14.1068i −0.888086 + 0.645232i
\(479\) 6.47214 4.70228i 0.295719 0.214853i −0.430025 0.902817i \(-0.641495\pi\)
0.725745 + 0.687964i \(0.241495\pi\)
\(480\) −3.09017 9.51057i −0.141046 0.434096i
\(481\) 3.70820 11.4127i 0.169080 0.520373i
\(482\) −8.09017 5.87785i −0.368497 0.267729i
\(483\) 32.0000 1.45605
\(484\) 0 0
\(485\) −4.00000 −0.181631
\(486\) −0.809017 0.587785i −0.0366978 0.0266625i
\(487\) −4.94427 + 15.2169i −0.224046 + 0.689544i 0.774341 + 0.632769i \(0.218082\pi\)
−0.998387 + 0.0567748i \(0.981918\pi\)
\(488\) −5.56231 17.1190i −0.251794 0.774942i
\(489\) 3.23607 2.35114i 0.146340 0.106322i
\(490\) −14.5623 + 10.5801i −0.657858 + 0.477962i
\(491\) −1.23607 3.80423i −0.0557830 0.171682i 0.919283 0.393597i \(-0.128769\pi\)
−0.975066 + 0.221915i \(0.928769\pi\)
\(492\) 0.618034 1.90211i 0.0278631 0.0857539i
\(493\) −9.70820 7.05342i −0.437236 0.317670i
\(494\) 0 0
\(495\) 0 0
\(496\) 8.00000 0.359211
\(497\) 0 0
\(498\) −3.70820 + 11.4127i −0.166169 + 0.511414i
\(499\) −1.23607 3.80423i −0.0553340 0.170301i 0.919570 0.392926i \(-0.128537\pi\)
−0.974904 + 0.222626i \(0.928537\pi\)
\(500\) 9.70820 7.05342i 0.434164 0.315439i
\(501\) 0 0
\(502\) −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 \(-0.152848\pi\)
\(504\) 9.70820 + 7.05342i 0.432438 + 0.314184i
\(505\) 4.00000 0.177998
\(506\) 0 0
\(507\) 9.00000 0.399704
\(508\) 3.23607 + 2.35114i 0.143577 + 0.104315i
\(509\) 9.27051 28.5317i 0.410908 1.26465i −0.504952 0.863147i \(-0.668490\pi\)
0.915860 0.401498i \(-0.131510\pi\)
\(510\) −1.23607 3.80423i −0.0547340 0.168454i
\(511\) 45.3050 32.9160i 2.00417 1.45612i
\(512\) −8.89919 + 6.46564i −0.393292 + 0.285744i
\(513\) 0 0
\(514\) 4.32624 13.3148i 0.190822 0.587290i
\(515\) 12.9443 + 9.40456i 0.570393 + 0.414415i
\(516\) 0 0
\(517\) 0 0
\(518\) 24.0000 1.05450
\(519\) 4.85410 + 3.52671i 0.213071 + 0.154805i
\(520\) −3.70820 + 11.4127i −0.162615 + 0.500479i
\(521\) −9.27051 28.5317i −0.406148 1.25000i −0.919933 0.392077i \(-0.871757\pi\)
0.513784 0.857920i \(-0.328243\pi\)
\(522\) 4.85410 3.52671i 0.212458 0.154360i
\(523\) −12.9443 + 9.40456i −0.566013 + 0.411233i −0.833655 0.552286i \(-0.813756\pi\)
0.267641 + 0.963519i \(0.413756\pi\)
\(524\) −3.70820 11.4127i −0.161994 0.498565i
\(525\) −1.23607 + 3.80423i −0.0539464 + 0.166030i
\(526\) 12.9443 + 9.40456i 0.564397 + 0.410058i
\(527\) −16.0000 −0.696971
\(528\) 0 0
\(529\) 41.0000 1.78261
\(530\) −9.70820 7.05342i −0.421697 0.306381i
\(531\) −1.23607 + 3.80423i −0.0536408 + 0.165089i
\(532\) 0 0
\(533\) −3.23607 + 2.35114i −0.140170 + 0.101839i
\(534\) 4.85410 3.52671i 0.210058 0.152616i
\(535\) −7.41641 22.8254i −0.320639 0.986826i
\(536\) −3.70820 + 11.4127i −0.160170 + 0.492953i
\(537\) 9.70820 + 7.05342i 0.418940 + 0.304378i
\(538\) 2.00000 0.0862261
\(539\) 0 0
\(540\) −2.00000 −0.0860663
\(541\) 37.2148 + 27.0381i 1.59999 + 1.16246i 0.887535 + 0.460740i \(0.152416\pi\)
0.712453 + 0.701719i \(0.247584\pi\)
\(542\) 6.18034 19.0211i 0.265468 0.817028i
\(543\) −6.79837 20.9232i −0.291746 0.897902i
\(544\) 8.09017 5.87785i 0.346863 0.252011i
\(545\) 3.23607 2.35114i 0.138618 0.100712i
\(546\) −2.47214 7.60845i −0.105798 0.325612i
\(547\) −2.47214 + 7.60845i −0.105701 + 0.325314i −0.989894 0.141807i \(-0.954709\pi\)
0.884193 + 0.467121i \(0.154709\pi\)
\(548\) 1.61803 + 1.17557i 0.0691190 + 0.0502179i
\(549\) −6.00000 −0.256074
\(550\) 0 0
\(551\) 0 0
\(552\) 19.4164 + 14.1068i 0.826417 + 0.600427i
\(553\) −4.94427 + 15.2169i −0.210252 + 0.647089i
\(554\) −8.03444 24.7275i −0.341351 1.05057i
\(555\) −9.70820 + 7.05342i −0.412090 + 0.299401i
\(556\) 6.47214 4.70228i 0.274480 0.199421i
\(557\) 4.32624 + 13.3148i 0.183309 + 0.564166i 0.999915 0.0130289i \(-0.00414735\pi\)
−0.816607 + 0.577195i \(0.804147\pi\)
\(558\) 2.47214 7.60845i 0.104654 0.322091i
\(559\) 0 0
\(560\) −8.00000 −0.338062
\(561\) 0 0
\(562\) −18.0000 −0.759284
\(563\) −35.5967 25.8626i −1.50022 1.08998i −0.970292 0.241936i \(-0.922217\pi\)
−0.529932 0.848040i \(-0.677783\pi\)
\(564\) 2.47214 7.60845i 0.104096 0.320374i
\(565\) 3.70820 + 11.4127i 0.156005 + 0.480135i
\(566\) −12.9443 + 9.40456i −0.544088 + 0.395303i
\(567\) 3.23607 2.35114i 0.135902 0.0987386i
\(568\) 0 0
\(569\) 12.9787 39.9444i 0.544096 1.67456i −0.179034 0.983843i \(-0.557297\pi\)
0.723130 0.690712i \(-0.242703\pi\)
\(570\) 0 0
\(571\) 16.0000 0.669579 0.334790 0.942293i \(-0.391335\pi\)
0.334790 + 0.942293i \(0.391335\pi\)
\(572\) 0 0
\(573\) −8.00000 −0.334205
\(574\) −6.47214 4.70228i −0.270142 0.196269i
\(575\) −2.47214 + 7.60845i −0.103095 + 0.317294i
\(576\) 2.16312 + 6.65740i 0.0901300 + 0.277391i
\(577\) 24.2705 17.6336i 1.01039 0.734095i 0.0461028 0.998937i \(-0.485320\pi\)
0.964292 + 0.264842i \(0.0853198\pi\)
\(578\) −10.5172 + 7.64121i −0.437459 + 0.317832i
\(579\) −4.32624 13.3148i −0.179792 0.553344i
\(580\) 3.70820 11.4127i 0.153975 0.473886i
\(581\) −38.8328 28.2137i −1.61106 1.17050i
\(582\) 2.00000 0.0829027
\(583\) 0 0
\(584\) 42.0000 1.73797
\(585\) 3.23607 + 2.35114i 0.133795 + 0.0972077i
\(586\) −1.85410 + 5.70634i −0.0765922 + 0.235727i
\(587\) 8.65248 + 26.6296i 0.357126 + 1.09912i 0.954767 + 0.297356i \(0.0961050\pi\)
−0.597641 + 0.801764i \(0.703895\pi\)
\(588\) −7.28115 + 5.29007i −0.300270 + 0.218159i
\(589\) 0 0
\(590\) −2.47214 7.60845i −0.101776 0.313235i
\(591\) −4.32624 + 13.3148i −0.177958 + 0.547697i
\(592\) 4.85410 + 3.52671i 0.199502 + 0.144947i
\(593\) −38.0000 −1.56047 −0.780236 0.625485i \(-0.784901\pi\)
−0.780236 + 0.625485i \(0.784901\pi\)
\(594\) 0 0
\(595\) 16.0000 0.655936
\(596\) 17.7984 + 12.9313i 0.729050 + 0.529686i
\(597\) 0 0
\(598\) −4.94427 15.2169i −0.202186 0.622265i
\(599\) 6.47214 4.70228i 0.264444 0.192130i −0.447660 0.894204i \(-0.647742\pi\)
0.712104 + 0.702074i \(0.247742\pi\)
\(600\) −2.42705 + 1.76336i −0.0990839 + 0.0719887i
\(601\) −8.03444 24.7275i −0.327732 1.00865i −0.970192 0.242336i \(-0.922086\pi\)
0.642461 0.766319i \(-0.277914\pi\)
\(602\) 0 0
\(603\) 3.23607 + 2.35114i 0.131783 + 0.0957459i
\(604\) 20.0000 0.813788
\(605\) 0 0
\(606\) −2.00000 −0.0812444
\(607\) −3.23607 2.35114i −0.131348 0.0954299i 0.520171 0.854062i \(-0.325868\pi\)
−0.651519 + 0.758632i \(0.725868\pi\)
\(608\) 0 0
\(609\) 7.41641 + 22.8254i 0.300528 + 0.924930i
\(610\) 9.70820 7.05342i 0.393074 0.285585i
\(611\) −12.9443 + 9.40456i −0.523669 + 0.380468i
\(612\) −0.618034 1.90211i −0.0249825 0.0768884i
\(613\) −4.32624 + 13.3148i −0.174735 + 0.537779i −0.999621 0.0275195i \(-0.991239\pi\)
0.824886 + 0.565299i \(0.191239\pi\)
\(614\) −25.8885 18.8091i −1.04478 0.759075i
\(615\) 4.00000 0.161296
\(616\) 0 0
\(617\) −30.0000 −1.20775 −0.603877 0.797077i \(-0.706378\pi\)
−0.603877 + 0.797077i \(0.706378\pi\)
\(618\) −6.47214 4.70228i −0.260347 0.189154i
\(619\) 13.5967 41.8465i 0.546499 1.68195i −0.170898 0.985289i \(-0.554667\pi\)
0.717398 0.696664i \(-0.245333\pi\)
\(620\) −4.94427 15.2169i −0.198567 0.611126i
\(621\) 6.47214 4.70228i 0.259718 0.188696i
\(622\) −19.4164 + 14.1068i −0.778527 + 0.565633i
\(623\) 7.41641 + 22.8254i 0.297132 + 0.914479i
\(624\) 0.618034 1.90211i 0.0247412 0.0761455i
\(625\) 15.3713 + 11.1679i 0.614853 + 0.446717i
\(626\) 22.0000 0.879297
\(627\) 0 0
\(628\) −14.0000 −0.558661
\(629\) −9.70820 7.05342i −0.387091 0.281238i
\(630\) −2.47214 + 7.60845i −0.0984923 + 0.303128i
\(631\) 4.94427 + 15.2169i 0.196828 + 0.605775i 0.999950 + 0.00996082i \(0.00317068\pi\)
−0.803122 + 0.595815i \(0.796829\pi\)
\(632\) −9.70820 + 7.05342i −0.386172 + 0.280570i
\(633\) 0 0
\(634\) −6.79837 20.9232i −0.269998 0.830968i
\(635\) −2.47214 + 7.60845i −0.0981037 + 0.301932i
\(636\) −4.85410 3.52671i −0.192478 0.139843i
\(637\) 18.0000 0.713186
\(638\) 0 0
\(639\) 0 0
\(640\) 4.85410 + 3.52671i 0.191875 + 0.139406i
\(641\) 5.56231 17.1190i 0.219698 0.676161i −0.779089 0.626914i \(-0.784318\pi\)
0.998787 0.0492469i \(-0.0156821\pi\)
\(642\) 3.70820 + 11.4127i 0.146351 + 0.450422i
\(643\) −16.1803 + 11.7557i −0.638090 + 0.463600i −0.859194 0.511651i \(-0.829034\pi\)
0.221103 + 0.975250i \(0.429034\pi\)
\(644\) −25.8885 + 18.8091i −1.02015 + 0.741183i
\(645\) 0 0
\(646\) 0 0
\(647\) −6.47214 4.70228i −0.254446 0.184866i 0.453249 0.891384i \(-0.350265\pi\)
−0.707695 + 0.706518i \(0.750265\pi\)
\(648\) 3.00000 0.117851
\(649\) 0 0
\(650\) 2.00000 0.0784465
\(651\) 25.8885 + 18.8091i 1.01465 + 0.737188i
\(652\) −1.23607 + 3.80423i −0.0484082 + 0.148985i
\(653\) −0.618034 1.90211i −0.0241855 0.0744354i 0.938235 0.345998i \(-0.112460\pi\)
−0.962421 + 0.271563i \(0.912460\pi\)
\(654\) −1.61803 + 1.17557i −0.0632701 + 0.0459684i
\(655\) 19.4164 14.1068i 0.758662 0.551200i
\(656\) −0.618034 1.90211i −0.0241302 0.0742650i
\(657\) 4.32624 13.3148i 0.168783 0.519459i
\(658\) −25.8885 18.8091i −1.00924 0.733256i
\(659\) −4.00000 −0.155818 −0.0779089 0.996960i \(-0.524824\pi\)
−0.0779089 + 0.996960i \(0.524824\pi\)
\(660\) 0 0
\(661\) −26.0000 −1.01128 −0.505641 0.862744i \(-0.668744\pi\)
−0.505641 + 0.862744i \(0.668744\pi\)
\(662\) −16.1803 11.7557i −0.628867 0.456898i
\(663\) −1.23607 + 3.80423i −0.0480049 + 0.147744i
\(664\) −11.1246 34.2380i −0.431719 1.32869i
\(665\) 0 0
\(666\) 4.85410 3.52671i 0.188093 0.136657i
\(667\) 14.8328 + 45.6507i 0.574329 + 1.76760i
\(668\) 0 0
\(669\) 12.9443 + 9.40456i 0.500454 + 0.363601i
\(670\) −8.00000 −0.309067
\(671\) 0 0
\(672\) −20.0000 −0.771517
\(673\) −37.2148 27.0381i −1.43452 1.04224i −0.989152 0.146898i \(-0.953071\pi\)
−0.445373 0.895345i \(-0.646929\pi\)
\(674\) −6.79837 + 20.9232i −0.261864 + 0.805933i
\(675\) 0.309017 + 0.951057i 0.0118941 + 0.0366062i
\(676\) −7.28115 + 5.29007i −0.280044 + 0.203464i
\(677\) 14.5623 10.5801i 0.559675 0.406628i −0.271665 0.962392i \(-0.587574\pi\)
0.831340 + 0.555764i \(0.187574\pi\)
\(678\) −1.85410 5.70634i −0.0712064 0.219151i
\(679\) −2.47214 + 7.60845i −0.0948719 + 0.291986i
\(680\) 9.70820 + 7.05342i 0.372293 + 0.270486i
\(681\) 12.0000 0.459841
\(682\) 0 0
\(683\) 20.0000 0.765279 0.382639 0.923898i \(-0.375015\pi\)
0.382639 + 0.923898i \(0.375015\pi\)
\(684\) 0 0
\(685\) −1.23607 + 3.80423i −0.0472277 + 0.145352i
\(686\) 2.47214 + 7.60845i 0.0943866 + 0.290492i
\(687\) 4.85410 3.52671i 0.185196 0.134552i
\(688\) 0 0
\(689\) 3.70820 + 11.4127i 0.141271 + 0.434788i
\(690\) −4.94427 + 15.2169i −0.188225 + 0.579298i
\(691\) 22.6525 + 16.4580i 0.861741 + 0.626091i 0.928358 0.371687i \(-0.121221\pi\)
−0.0666172 + 0.997779i \(0.521221\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) 4.00000 0.151838
\(695\) 12.9443 + 9.40456i 0.491004 + 0.356735i
\(696\) −5.56231 + 17.1190i −0.210839 + 0.648895i
\(697\) 1.23607 + 3.80423i 0.0468194 + 0.144095i
\(698\) −4.85410 + 3.52671i −0.183730 + 0.133488i
\(699\) −24.2705 + 17.6336i −0.917995 + 0.666962i
\(700\) −1.23607 3.80423i −0.0467190 0.143786i
\(701\) −15.4508 + 47.5528i −0.583571 + 1.79605i 0.0213660 + 0.999772i \(0.493198\pi\)
−0.604936 + 0.796274i \(0.706802\pi\)
\(702\) −1.61803 1.17557i −0.0610688 0.0443690i
\(703\) 0 0
\(704\) 0 0
\(705\) 16.0000 0.602595
\(706\) 14.5623 + 10.5801i 0.548060 + 0.398189i
\(707\) 2.47214 7.60845i 0.0929742 0.286145i
\(708\) −1.23607 3.80423i −0.0464543 0.142972i
\(709\) −30.7426 + 22.3358i −1.15456 + 0.838840i −0.989081 0.147373i \(-0.952918\pi\)
−0.165483 + 0.986213i \(0.552918\pi\)
\(710\) 0 0
\(711\) 1.23607 + 3.80423i 0.0463562 + 0.142670i
\(712\) −5.56231 + 17.1190i −0.208456 + 0.641562i
\(713\) 51.7771 + 37.6183i 1.93907 + 1.40881i
\(714\) −8.00000 −0.299392
\(715\) 0 0
\(716\) −12.0000 −0.448461
\(717\) −19.4164 14.1068i −0.725119 0.526830i
\(718\) −2.47214 + 7.60845i −0.0922593 + 0.283945i
\(719\) 7.41641 + 22.8254i 0.276585 + 0.851242i 0.988796 + 0.149276i \(0.0476943\pi\)
−0.712210 + 0.701966i \(0.752306\pi\)
\(720\) −1.61803 + 1.17557i −0.0603006 + 0.0438109i
\(721\) 25.8885 18.8091i 0.964140 0.700489i
\(722\) 5.87132 + 18.0701i 0.218508 + 0.672499i
\(723\) 3.09017 9.51057i 0.114925 0.353702i
\(724\) 17.7984 + 12.9313i 0.661471 + 0.480587i
\(725\) −6.00000 −0.222834
\(726\) 0 0
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 19.4164 + 14.1068i 0.719620 + 0.522834i
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) 8.65248 + 26.6296i 0.320242 + 0.985605i
\(731\) 0 0
\(732\) 4.85410 3.52671i 0.179413 0.130351i
\(733\) −9.27051 28.5317i −0.342414 1.05384i −0.962954 0.269667i \(-0.913086\pi\)
0.620540 0.784175i \(-0.286914\pi\)
\(734\) 9.88854 30.4338i 0.364993 1.12333i
\(735\) −14.5623 10.5801i −0.537139 0.390254i
\(736\) −40.0000 −1.47442
\(737\) 0 0
\(738\) −2.00000 −0.0736210
\(739\) 6.47214 + 4.70228i 0.238081 + 0.172976i 0.700428 0.713723i \(-0.252992\pi\)
−0.462347 + 0.886699i \(0.652992\pi\)
\(740\) 3.70820 11.4127i 0.136316 0.419538i
\(741\) 0 0
\(742\) −19.4164 + 14.1068i −0.712799 + 0.517879i
\(743\) 32.3607 23.5114i 1.18720 0.862550i 0.194233 0.980955i \(-0.437778\pi\)
0.992965 + 0.118405i \(0.0377783\pi\)
\(744\) 7.41641 + 22.8254i 0.271899 + 0.836818i
\(745\) −13.5967 + 41.8465i −0.498146 + 1.53314i
\(746\) 1.61803 + 1.17557i 0.0592404 + 0.0430407i
\(747\) −12.0000 −0.439057
\(748\) 0 0
\(749\) −48.0000 −1.75388
\(750\) −9.70820 7.05342i −0.354493 0.257555i
\(751\) −2.47214 + 7.60845i −0.0902095 + 0.277636i −0.985976 0.166889i \(-0.946628\pi\)
0.895766 + 0.444526i \(0.146628\pi\)
\(752\) −2.47214 7.60845i −0.0901495 0.277452i
\(753\) 3.23607 2.35114i 0.117929 0.0856803i
\(754\) 9.70820 7.05342i 0.353552 0.256871i
\(755\) 12.3607 + 38.0423i 0.449851 + 1.38450i
\(756\) −1.23607 + 3.80423i −0.0449554 + 0.138358i
\(757\) 8.09017 + 5.87785i 0.294042 + 0.213634i 0.725019 0.688729i \(-0.241831\pi\)
−0.430977 + 0.902363i \(0.641831\pi\)
\(758\) −28.0000 −1.01701
\(759\) 0 0
\(760\) 0 0
\(761\) 4.85410 + 3.52671i 0.175961 + 0.127843i 0.672280 0.740297i \(-0.265315\pi\)
−0.496319 + 0.868140i \(0.665315\pi\)
\(762\) 1.23607 3.80423i 0.0447780 0.137813i
\(763\) −2.47214 7.60845i −0.0894973 0.275444i
\(764\) 6.47214 4.70228i 0.234154 0.170123i
\(765\) 3.23607 2.35114i 0.117000 0.0850057i
\(766\) 4.94427 + 15.2169i 0.178644 + 0.549809i
\(767\) −2.47214 + 7.60845i −0.0892637 + 0.274725i
\(768\) −13.7533 9.99235i −0.496279 0.360568i
\(769\) −2.00000 −0.0721218 −0.0360609 0.999350i \(-0.511481\pi\)
−0.0360609 + 0.999350i \(0.511481\pi\)
\(770\) 0 0
\(771\) 14.0000 0.504198
\(772\) 11.3262 + 8.22899i 0.407640 + 0.296168i
\(773\) 1.85410 5.70634i 0.0666874 0.205243i −0.912160 0.409834i \(-0.865587\pi\)
0.978847 + 0.204591i \(0.0655866\pi\)
\(774\) 0 0